id	sid	tid	token	lemma	pos
ejpam-5827	1	1	european	european	PROPN
ejpam-5827	1	2	journal	journal	PROPN
ejpam-5827	1	3	of	of	ADP
ejpam-5827	1	4	pure	pure	ADJ
ejpam-5827	1	5	and	and	CCONJ
ejpam-5827	1	6	applied	applied	ADJ
ejpam-5827	1	7	mathematics	mathematic	NOUN
ejpam-5827	1	8	2025	2025	NUM
ejpam-5827	1	9	,	,	PUNCT
ejpam-5827	1	10	vol	vol	NOUN
ejpam-5827	1	11	.	.	PROPN
ejpam-5827	1	12	18	18	NUM
ejpam-5827	1	13	,	,	PUNCT
ejpam-5827	1	14	issue	issue	NOUN
ejpam-5827	1	15	1	1	NUM
ejpam-5827	1	16	,	,	PUNCT
ejpam-5827	1	17	article	article	NOUN
ejpam-5827	1	18	number	number	NOUN
ejpam-5827	1	19	5827	5827	NUM
ejpam-5827	1	20	issn	issn	VERB
ejpam-5827	1	21	1307	1307	NUM
ejpam-5827	1	22	-	-	SYM
ejpam-5827	1	23	5543	5543	NUM
ejpam-5827	1	24	–	–	PUNCT
ejpam-5827	1	25	ejpam.com	ejpam.com	X
ejpam-5827	1	26	published	publish	VERB
ejpam-5827	1	27	by	by	ADP
ejpam-5827	1	28	new	new	PROPN
ejpam-5827	1	29	york	york	PROPN
ejpam-5827	1	30	business	business	PROPN
ejpam-5827	1	31	global	global	ADJ
ejpam-5827	1	32	primal	primal	ADJ
ejpam-5827	1	33	approximation	approximation	NOUN
ejpam-5827	1	34	spaces	space	NOUN
ejpam-5827	1	35	by	by	ADP
ejpam-5827	1	36	κ	κ	NOUN
ejpam-5827	1	37	-	-	NOUN
ejpam-5827	1	38	neighborhoods	neighborhood	NOUN
ejpam-5827	1	39	with	with	ADP
ejpam-5827	1	40	applications	application	NOUN
ejpam-5827	1	41	rodyna	rodyna	NOUN
ejpam-5827	1	42	a.	a.	PROPN
ejpam-5827	1	43	hosny1	hosny1	PROPN
ejpam-5827	1	44	,	,	PUNCT
ejpam-5827	2	1	mostafa	mostafa	PROPN
ejpam-5827	2	2	k.	k.	PROPN
ejpam-5827	2	3	el	el	PROPN
ejpam-5827	2	4	-	-	PUNCT
ejpam-5827	2	5	bably2,3,∗	bably2,3,∗	PROPN
ejpam-5827	2	6	,	,	PUNCT
ejpam-5827	2	7	mostafa	mostafa	PROPN
ejpam-5827	2	8	a.	a.	PROPN
ejpam-5827	2	9	el	el	PROPN
ejpam-5827	2	10	-	-	PUNCT
ejpam-5827	2	11	gayar4	gayar4	NOUN
ejpam-5827	2	12	1	1	NUM
ejpam-5827	2	13	department	department	NOUN
ejpam-5827	2	14	of	of	ADP
ejpam-5827	2	15	mathematics	mathematic	NOUN
ejpam-5827	2	16	,	,	PUNCT
ejpam-5827	2	17	faculty	faculty	NOUN
ejpam-5827	2	18	of	of	ADP
ejpam-5827	2	19	science	science	NOUN
ejpam-5827	2	20	,	,	PUNCT
ejpam-5827	2	21	zagazig	zagazig	PROPN
ejpam-5827	2	22	university	university	PROPN
ejpam-5827	2	23	,	,	PUNCT
ejpam-5827	2	24	zagazig	zagazig	PROPN
ejpam-5827	2	25	44519	44519	NUM
ejpam-5827	2	26	,	,	PUNCT
ejpam-5827	2	27	egypt	egypt	PROPN
ejpam-5827	2	28	2	2	NUM
ejpam-5827	2	29	department	department	NOUN
ejpam-5827	2	30	of	of	ADP
ejpam-5827	2	31	mathematics	mathematic	NOUN
ejpam-5827	2	32	,	,	PUNCT
ejpam-5827	2	33	faculty	faculty	NOUN
ejpam-5827	2	34	of	of	ADP
ejpam-5827	2	35	science	science	NOUN
ejpam-5827	2	36	,	,	PUNCT
ejpam-5827	2	37	tanta	tanta	PROPN
ejpam-5827	2	38	university	university	PROPN
ejpam-5827	2	39	,	,	PUNCT
ejpam-5827	2	40	tanta	tanta	PROPN
ejpam-5827	2	41	31527	31527	NUM
ejpam-5827	2	42	,	,	PUNCT
ejpam-5827	2	43	egypt	egypt	PROPN
ejpam-5827	2	44	3	3	NUM
ejpam-5827	2	45	jadara	jadara	PROPN
ejpam-5827	2	46	university	university	PROPN
ejpam-5827	2	47	research	research	NOUN
ejpam-5827	2	48	center	center	NOUN
ejpam-5827	2	49	,	,	PUNCT
ejpam-5827	2	50	jadara	jadara	PROPN
ejpam-5827	2	51	university	university	PROPN
ejpam-5827	2	52	,	,	PUNCT
ejpam-5827	2	53	irbid	irbid	VERB
ejpam-5827	2	54	21110	21110	NUM
ejpam-5827	2	55	,	,	PUNCT
ejpam-5827	2	56	jordan	jordan	PROPN
ejpam-5827	2	57	4	4	NUM
ejpam-5827	2	58	department	department	NOUN
ejpam-5827	2	59	of	of	ADP
ejpam-5827	2	60	mathematics	mathematic	NOUN
ejpam-5827	2	61	,	,	PUNCT
ejpam-5827	2	62	faculty	faculty	NOUN
ejpam-5827	2	63	of	of	ADP
ejpam-5827	2	64	science	science	NOUN
ejpam-5827	2	65	,	,	PUNCT
ejpam-5827	2	66	helwan	helwan	PROPN
ejpam-5827	2	67	university	university	PROPN
ejpam-5827	2	68	,	,	PUNCT
ejpam-5827	2	69	helwan	helwan	PROPN
ejpam-5827	2	70	11795	11795	NUM
ejpam-5827	2	71	,	,	PUNCT
ejpam-5827	2	72	egypt	egypt	PROPN
ejpam-5827	2	73	abstract	abstract	PROPN
ejpam-5827	2	74	.	.	PUNCT
ejpam-5827	3	1	real	real	ADJ
ejpam-5827	3	2	-	-	PUNCT
ejpam-5827	3	3	world	world	NOUN
ejpam-5827	3	4	problems	problem	NOUN
ejpam-5827	3	5	often	often	ADV
ejpam-5827	3	6	involve	involve	VERB
ejpam-5827	3	7	imprecision	imprecision	NOUN
ejpam-5827	3	8	and	and	CCONJ
ejpam-5827	3	9	uncertainty	uncertainty	NOUN
ejpam-5827	3	10	,	,	PUNCT
ejpam-5827	3	11	presenting	present	VERB
ejpam-5827	3	12	challenges	challenge	NOUN
ejpam-5827	3	13	across	across	ADP
ejpam-5827	3	14	various	various	ADJ
ejpam-5827	3	15	domains	domain	NOUN
ejpam-5827	3	16	such	such	ADJ
ejpam-5827	3	17	as	as	ADP
ejpam-5827	3	18	engineering	engineering	NOUN
ejpam-5827	3	19	,	,	PUNCT
ejpam-5827	3	20	artificial	artificial	ADJ
ejpam-5827	3	21	intelligence	intelligence	NOUN
ejpam-5827	3	22	,	,	PUNCT
ejpam-5827	3	23	social	social	ADJ
ejpam-5827	3	24	sciences	science	NOUN
ejpam-5827	3	25	,	,	PUNCT
ejpam-5827	3	26	and	and	CCONJ
ejpam-5827	3	27	medical	medical	ADJ
ejpam-5827	3	28	sciences	science	NOUN
ejpam-5827	3	29	.	.	PUNCT
ejpam-5827	4	1	to	to	PART
ejpam-5827	4	2	bridge	bridge	VERB
ejpam-5827	4	3	this	this	DET
ejpam-5827	4	4	gap	gap	NOUN
ejpam-5827	4	5	,	,	PUNCT
ejpam-5827	4	6	pawlak	pawlak	ADJ
ejpam-5827	4	7	introduced	introduce	VERB
ejpam-5827	4	8	classical	classical	ADJ
ejpam-5827	4	9	rough	rough	ADJ
ejpam-5827	4	10	set	set	NOUN
ejpam-5827	4	11	models	model	NOUN
ejpam-5827	4	12	,	,	PUNCT
ejpam-5827	4	13	focusing	focus	VERB
ejpam-5827	4	14	on	on	ADP
ejpam-5827	4	15	upper	upper	ADJ
ejpam-5827	4	16	and	and	CCONJ
ejpam-5827	4	17	lower	low	ADJ
ejpam-5827	4	18	approximations	approximation	NOUN
ejpam-5827	4	19	based	base	VERB
ejpam-5827	4	20	on	on	ADP
ejpam-5827	4	21	equivalence	equivalence	NOUN
ejpam-5827	4	22	relations	relation	NOUN
ejpam-5827	4	23	.	.	PUNCT
ejpam-5827	5	1	however	however	ADV
ejpam-5827	5	2	,	,	PUNCT
ejpam-5827	5	3	these	these	DET
ejpam-5827	5	4	relations	relation	NOUN
ejpam-5827	5	5	restrict	restrict	VERB
ejpam-5827	5	6	the	the	DET
ejpam-5827	5	7	applicability	applicability	NOUN
ejpam-5827	5	8	of	of	ADP
ejpam-5827	5	9	rough	rough	ADJ
ejpam-5827	5	10	sets	set	NOUN
ejpam-5827	5	11	in	in	ADP
ejpam-5827	5	12	many	many	ADJ
ejpam-5827	5	13	contexts	context	NOUN
ejpam-5827	5	14	.	.	PUNCT
ejpam-5827	6	1	this	this	DET
ejpam-5827	6	2	paper	paper	NOUN
ejpam-5827	6	3	explores	explore	VERB
ejpam-5827	6	4	new	new	ADJ
ejpam-5827	6	5	approaches	approach	NOUN
ejpam-5827	6	6	to	to	ADP
ejpam-5827	6	7	extending	extend	VERB
ejpam-5827	6	8	rough	rough	ADJ
ejpam-5827	6	9	set	set	NOUN
ejpam-5827	6	10	theory	theory	NOUN
ejpam-5827	6	11	by	by	ADP
ejpam-5827	6	12	introducing	introduce	VERB
ejpam-5827	6	13	”	"	PUNCT
ejpam-5827	6	14	primal	primal	ADJ
ejpam-5827	6	15	approximation	approximation	NOUN
ejpam-5827	6	16	spaces	space	NOUN
ejpam-5827	6	17	”	"	PUNCT
ejpam-5827	6	18	.	.	PUNCT
ejpam-5827	7	1	primal	primal	ADJ
ejpam-5827	7	2	is	be	AUX
ejpam-5827	7	3	defined	define	VERB
ejpam-5827	7	4	as	as	ADP
ejpam-5827	7	5	novel	novel	ADJ
ejpam-5827	7	6	structures	structure	NOUN
ejpam-5827	7	7	designed	design	VERB
ejpam-5827	7	8	to	to	PART
ejpam-5827	7	9	generalize	generalize	VERB
ejpam-5827	7	10	rough	rough	ADJ
ejpam-5827	7	11	set	set	VERB
ejpam-5827	7	12	approximations	approximation	NOUN
ejpam-5827	7	13	beyond	beyond	ADP
ejpam-5827	7	14	the	the	DET
ejpam-5827	7	15	traditional	traditional	ADJ
ejpam-5827	7	16	methods	method	NOUN
ejpam-5827	7	17	.	.	PUNCT
ejpam-5827	8	1	this	this	DET
ejpam-5827	8	2	paper	paper	NOUN
ejpam-5827	8	3	proposes	propose	VERB
ejpam-5827	8	4	a	a	DET
ejpam-5827	8	5	new	new	ADJ
ejpam-5827	8	6	technique	technique	NOUN
ejpam-5827	8	7	for	for	ADP
ejpam-5827	8	8	generating	generate	VERB
ejpam-5827	8	9	rough	rough	ADJ
ejpam-5827	8	10	approximations	approximation	NOUN
ejpam-5827	8	11	by	by	ADP
ejpam-5827	8	12	using	use	VERB
ejpam-5827	8	13	κ	κ	NOUN
ejpam-5827	8	14	-	-	PUNCT
ejpam-5827	8	15	neighborhoods	neighborhood	NOUN
ejpam-5827	8	16	and	and	CCONJ
ejpam-5827	8	17	primal	primal	ADJ
ejpam-5827	8	18	which	which	PRON
ejpam-5827	8	19	allows	allow	VERB
ejpam-5827	8	20	for	for	ADP
ejpam-5827	8	21	creating	create	VERB
ejpam-5827	8	22	diverse	diverse	ADJ
ejpam-5827	8	23	supra	supra	NOUN
ejpam-5827	8	24	-	-	PUNCT
ejpam-5827	8	25	topologies	topology	NOUN
ejpam-5827	8	26	and	and	CCONJ
ejpam-5827	8	27	enhancing	enhance	VERB
ejpam-5827	8	28	the	the	DET
ejpam-5827	8	29	flexibility	flexibility	NOUN
ejpam-5827	8	30	of	of	ADP
ejpam-5827	8	31	rough	rough	ADJ
ejpam-5827	8	32	set	set	NOUN
ejpam-5827	8	33	models	model	NOUN
ejpam-5827	8	34	.	.	PUNCT
ejpam-5827	9	1	furthermore	furthermore	ADV
ejpam-5827	9	2	,	,	PUNCT
ejpam-5827	9	3	we	we	PRON
ejpam-5827	9	4	here	here	ADV
ejpam-5827	9	5	introduce	introduce	VERB
ejpam-5827	9	6	bi	bi	ADJ
ejpam-5827	9	7	-	-	ADJ
ejpam-5827	9	8	primal	primal	ADJ
ejpam-5827	9	9	approximation	approximation	NOUN
ejpam-5827	9	10	spaces	space	NOUN
ejpam-5827	9	11	,	,	PUNCT
ejpam-5827	9	12	a	a	DET
ejpam-5827	9	13	new	new	ADJ
ejpam-5827	9	14	form	form	NOUN
ejpam-5827	9	15	of	of	ADP
ejpam-5827	9	16	approximation	approximation	NOUN
ejpam-5827	9	17	that	that	PRON
ejpam-5827	9	18	can	can	AUX
ejpam-5827	9	19	be	be	AUX
ejpam-5827	9	20	examined	examine	VERB
ejpam-5827	9	21	through	through	ADP
ejpam-5827	9	22	two	two	NUM
ejpam-5827	9	23	distinct	distinct	ADJ
ejpam-5827	9	24	methods	method	NOUN
ejpam-5827	9	25	,	,	PUNCT
ejpam-5827	9	26	as	as	ADP
ejpam-5827	9	27	a	a	DET
ejpam-5827	9	28	result	result	NOUN
ejpam-5827	9	29	,	,	PUNCT
ejpam-5827	9	30	revealing	reveal	VERB
ejpam-5827	9	31	their	their	PRON
ejpam-5827	9	32	unique	unique	ADJ
ejpam-5827	9	33	characteristics	characteristic	NOUN
ejpam-5827	9	34	and	and	CCONJ
ejpam-5827	9	35	relationships	relationship	NOUN
ejpam-5827	9	36	.	.	PUNCT
ejpam-5827	10	1	the	the	DET
ejpam-5827	10	2	research	research	NOUN
ejpam-5827	10	3	underlines	underline	VERB
ejpam-5827	10	4	the	the	DET
ejpam-5827	10	5	practical	practical	ADJ
ejpam-5827	10	6	applications	application	NOUN
ejpam-5827	10	7	of	of	ADP
ejpam-5827	10	8	these	these	DET
ejpam-5827	10	9	new	new	ADJ
ejpam-5827	10	10	methods	method	NOUN
ejpam-5827	10	11	by	by	ADP
ejpam-5827	10	12	providing	provide	VERB
ejpam-5827	10	13	a	a	DET
ejpam-5827	10	14	detailed	detailed	ADJ
ejpam-5827	10	15	case	case	NOUN
ejpam-5827	10	16	study	study	NOUN
ejpam-5827	10	17	that	that	PRON
ejpam-5827	10	18	demonstrates	demonstrate	VERB
ejpam-5827	10	19	their	their	PRON
ejpam-5827	10	20	effectiveness	effectiveness	NOUN
ejpam-5827	10	21	in	in	ADP
ejpam-5827	10	22	solving	solve	VERB
ejpam-5827	10	23	decision	decision	NOUN
ejpam-5827	10	24	-	-	PUNCT
ejpam-5827	10	25	making	make	VERB
ejpam-5827	10	26	problems	problem	NOUN
ejpam-5827	10	27	.	.	PUNCT
ejpam-5827	11	1	moreover	moreover	ADV
ejpam-5827	11	2	,	,	PUNCT
ejpam-5827	11	3	this	this	DET
ejpam-5827	11	4	study	study	NOUN
ejpam-5827	11	5	also	also	ADV
ejpam-5827	11	6	compares	compare	VERB
ejpam-5827	11	7	the	the	DET
ejpam-5827	11	8	primal	primal	NOUN
ejpam-5827	11	9	-	-	PUNCT
ejpam-5827	11	10	based	base	VERB
ejpam-5827	11	11	methods	method	NOUN
ejpam-5827	11	12	with	with	ADP
ejpam-5827	11	13	existing	exist	VERB
ejpam-5827	11	14	approaches	approach	NOUN
ejpam-5827	11	15	based	base	VERB
ejpam-5827	11	16	on	on	ADP
ejpam-5827	11	17	ideals	ideal	NOUN
ejpam-5827	11	18	,	,	PUNCT
ejpam-5827	11	19	illustrating	illustrate	VERB
ejpam-5827	11	20	their	their	PRON
ejpam-5827	11	21	distinctive	distinctive	ADJ
ejpam-5827	11	22	advantages	advantage	NOUN
ejpam-5827	11	23	and	and	CCONJ
ejpam-5827	11	24	limitations	limitation	NOUN
ejpam-5827	11	25	.	.	PUNCT
ejpam-5827	12	1	overall	overall	ADV
ejpam-5827	12	2	,	,	PUNCT
ejpam-5827	12	3	this	this	DET
ejpam-5827	12	4	work	work	NOUN
ejpam-5827	12	5	offers	offer	VERB
ejpam-5827	12	6	a	a	DET
ejpam-5827	12	7	remarkable	remarkable	ADJ
ejpam-5827	12	8	advancement	advancement	NOUN
ejpam-5827	12	9	in	in	ADP
ejpam-5827	12	10	rough	rough	ADJ
ejpam-5827	12	11	set	set	NOUN
ejpam-5827	12	12	theory	theory	NOUN
ejpam-5827	12	13	by	by	ADP
ejpam-5827	12	14	expanding	expand	VERB
ejpam-5827	12	15	its	its	PRON
ejpam-5827	12	16	theoretical	theoretical	ADJ
ejpam-5827	12	17	framework	framework	NOUN
ejpam-5827	12	18	and	and	CCONJ
ejpam-5827	12	19	practical	practical	ADJ
ejpam-5827	12	20	applicability	applicability	NOUN
ejpam-5827	12	21	through	through	ADP
ejpam-5827	12	22	the	the	DET
ejpam-5827	12	23	introduction	introduction	NOUN
ejpam-5827	12	24	of	of	ADP
ejpam-5827	12	25	primal	primal	ADJ
ejpam-5827	12	26	and	and	CCONJ
ejpam-5827	12	27	bi	bi	ADJ
ejpam-5827	12	28	-	-	ADJ
ejpam-5827	12	29	primal	primal	ADJ
ejpam-5827	12	30	approximation	approximation	NOUN
ejpam-5827	12	31	spaces	space	NOUN
ejpam-5827	12	32	.	.	PUNCT
ejpam-5827	13	1	2020	2020	NUM
ejpam-5827	13	2	mathematics	mathematic	NOUN
ejpam-5827	13	3	subject	subject	NOUN
ejpam-5827	13	4	classifications	classification	NOUN
ejpam-5827	13	5	:	:	PUNCT
ejpam-5827	13	6	03e99	03e99	NUM
ejpam-5827	13	7	,	,	PUNCT
ejpam-5827	13	8	54a05	54a05	NUM
ejpam-5827	13	9	,	,	PUNCT
ejpam-5827	13	10	54a10	54a10	NUM
ejpam-5827	13	11	,	,	PUNCT
ejpam-5827	13	12	54e99	54e99	DET
ejpam-5827	13	13	key	key	ADJ
ejpam-5827	13	14	words	word	NOUN
ejpam-5827	13	15	and	and	CCONJ
ejpam-5827	13	16	phrases	phrase	NOUN
ejpam-5827	13	17	:	:	PUNCT
ejpam-5827	13	18	supra	supra	ADJ
ejpam-5827	13	19	topology	topology	NOUN
ejpam-5827	13	20	,	,	PUNCT
ejpam-5827	13	21	κ	κ	NOUN
ejpam-5827	13	22	-	-	NOUN
ejpam-5827	13	23	neighborhoods	neighborhood	NOUN
ejpam-5827	13	24	,	,	PUNCT
ejpam-5827	13	25	rough	rough	ADJ
ejpam-5827	13	26	sets	set	NOUN
ejpam-5827	13	27	,	,	PUNCT
ejpam-5827	13	28	approximation	approximation	NOUN
ejpam-5827	13	29	spaces	space	NOUN
ejpam-5827	13	30	1	1	NUM
ejpam-5827	13	31	.	.	PUNCT
ejpam-5827	14	1	introduction	introduction	NOUN
ejpam-5827	14	2	there	there	PRON
ejpam-5827	14	3	are	be	VERB
ejpam-5827	14	4	considerable	considerable	ADJ
ejpam-5827	14	5	real	real	ADJ
ejpam-5827	14	6	-	-	PUNCT
ejpam-5827	14	7	life	life	NOUN
ejpam-5827	14	8	problems	problem	NOUN
ejpam-5827	14	9	involving	involve	VERB
ejpam-5827	14	10	imprecision	imprecision	NOUN
ejpam-5827	14	11	,	,	PUNCT
ejpam-5827	14	12	such	such	ADJ
ejpam-5827	14	13	as	as	ADP
ejpam-5827	14	14	those	those	PRON
ejpam-5827	14	15	in	in	ADP
ejpam-5827	14	16	engineering	engineering	NOUN
ejpam-5827	14	17	,	,	PUNCT
ejpam-5827	14	18	artificial	artificial	ADJ
ejpam-5827	14	19	intelligence	intelligence	NOUN
ejpam-5827	14	20	,	,	PUNCT
ejpam-5827	14	21	social	social	ADJ
ejpam-5827	14	22	science	science	NOUN
ejpam-5827	14	23	,	,	PUNCT
ejpam-5827	14	24	and	and	CCONJ
ejpam-5827	14	25	medical	medical	ADJ
ejpam-5827	14	26	science	science	NOUN
ejpam-5827	14	27	.	.	PUNCT
ejpam-5827	15	1	various	various	ADJ
ejpam-5827	15	2	mathematical	mathematical	ADJ
ejpam-5827	15	3	∗corresponding	∗corresponding	NOUN
ejpam-5827	15	4	author	author	NOUN
ejpam-5827	15	5	.	.	PUNCT
ejpam-5827	16	1	doi	doi	NOUN
ejpam-5827	16	2	:	:	PUNCT
ejpam-5827	16	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5827	https://doi.org/10.29020/nybg.ejpam.v18i1.5827	PROPN
ejpam-5827	16	4	email	email	NOUN
ejpam-5827	16	5	addresses	address	NOUN
ejpam-5827	16	6	:	:	PUNCT
ejpam-5827	17	1	ramahmoud@zu.edu.eg	ramahmoud@zu.edu.eg	NOUN
ejpam-5827	17	2	and	and	CCONJ
ejpam-5827	17	3	hrodyna@yahoo.com	hrodyna@yahoo.com	PROPN
ejpam-5827	17	4	(	(	PUNCT
ejpam-5827	17	5	r.	r.	PROPN
ejpam-5827	17	6	a.	a.	PROPN
ejpam-5827	17	7	hosny	hosny	PROPN
ejpam-5827	17	8	)	)	PUNCT
ejpam-5827	17	9	,	,	PUNCT
ejpam-5827	17	10	mostafa.106163@azhar.moe.edu.eg	mostafa.106163@azhar.moe.edu.eg	PROPN
ejpam-5827	17	11	and	and	CCONJ
ejpam-5827	17	12	mkamel	mkamel	NOUN
ejpam-5827	18	1	bably@yahoo.com	bably@yahoo.com	PROPN
ejpam-5827	19	1	(	(	PUNCT
ejpam-5827	19	2	m.	m.	PROPN
ejpam-5827	19	3	k.	k.	PROPN
ejpam-5827	20	1	el	el	PROPN
ejpam-5827	20	2	-	-	PROPN
ejpam-5827	20	3	bably	bably	ADV
ejpam-5827	20	4	)	)	PUNCT
ejpam-5827	20	5	,	,	PUNCT
ejpam-5827	21	1	m.elgayar@science.helwan.edu.eg	m.elgayar@science.helwan.edu.eg	PROPN
ejpam-5827	21	2	and	and	CCONJ
ejpam-5827	21	3	dr	dr	PROPN
ejpam-5827	21	4	matia75@yahoo.com	matia75@yahoo.com	PROPN
ejpam-5827	21	5	(	(	PUNCT
ejpam-5827	21	6	m.	m.	NOUN
ejpam-5827	21	7	a.	a.	PROPN
ejpam-5827	21	8	el	el	PROPN
ejpam-5827	21	9	-	-	PUNCT
ejpam-5827	21	10	gayar	gayar	NOUN
ejpam-5827	21	11	)	)	PUNCT
ejpam-5827	21	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5827	22	1	1	1	NUM
ejpam-5827	22	2	copyright	copyright	NOUN
ejpam-5827	22	3	:	:	PUNCT
ejpam-5827	22	4	©	©	PROPN
ejpam-5827	22	5	2025	2025	NUM
ejpam-5827	22	6	the	the	DET
ejpam-5827	22	7	author(s	author(s	NOUN
ejpam-5827	22	8	)	)	PUNCT
ejpam-5827	22	9	.	.	PUNCT
ejpam-5827	23	1	(	(	PUNCT
ejpam-5827	23	2	cc	cc	NOUN
ejpam-5827	23	3	by	by	ADP
ejpam-5827	23	4	-	-	PUNCT
ejpam-5827	23	5	nc	nc	PROPN
ejpam-5827	23	6	4.0	4.0	NUM
ejpam-5827	23	7	)	)	PUNCT
ejpam-5827	23	8	r.	r.	PROPN
ejpam-5827	23	9	a.	a.	PROPN
ejpam-5827	23	10	hosny	hosny	PROPN
ejpam-5827	23	11	,	,	PUNCT
ejpam-5827	23	12	m.	m.	PROPN
ejpam-5827	23	13	k.	k.	PROPN
ejpam-5827	24	1	el	el	PROPN
ejpam-5827	24	2	-	-	PROPN
ejpam-5827	24	3	bably	bably	ADV
ejpam-5827	24	4	,	,	PUNCT
ejpam-5827	24	5	m.	m.	NOUN
ejpam-5827	24	6	a.	a.	PROPN
ejpam-5827	24	7	el	el	PROPN
ejpam-5827	24	8	-	-	PROPN
ejpam-5827	24	9	gayar	gayar	PROPN
ejpam-5827	24	10	/	/	SYM
ejpam-5827	24	11	eur	eur	PROPN
ejpam-5827	24	12	.	.	PUNCT
ejpam-5827	25	1	j.	j.	PROPN
ejpam-5827	25	2	pure	pure	PROPN
ejpam-5827	25	3	appl	appl	PROPN
ejpam-5827	25	4	.	.	PROPN
ejpam-5827	25	5	math	math	PROPN
ejpam-5827	25	6	,	,	PUNCT
ejpam-5827	25	7	18	18	NUM
ejpam-5827	25	8	(	(	PUNCT
ejpam-5827	25	9	1	1	NUM
ejpam-5827	25	10	)	)	PUNCT
ejpam-5827	25	11	(	(	PUNCT
ejpam-5827	25	12	2025	2025	NUM
ejpam-5827	25	13	)	)	PUNCT
ejpam-5827	25	14	,	,	PUNCT
ejpam-5827	25	15	5827	5827	NUM
ejpam-5827	25	16	2	2	NUM
ejpam-5827	25	17	of	of	ADP
ejpam-5827	25	18	29	29	NUM
ejpam-5827	25	19	modeling	modeling	NOUN
ejpam-5827	25	20	techniques	technique	NOUN
ejpam-5827	25	21	have	have	AUX
ejpam-5827	25	22	been	be	AUX
ejpam-5827	25	23	presented	present	VERB
ejpam-5827	25	24	to	to	PART
ejpam-5827	25	25	address	address	VERB
ejpam-5827	25	26	these	these	DET
ejpam-5827	25	27	problems	problem	NOUN
ejpam-5827	25	28	,	,	PUNCT
ejpam-5827	25	29	including	include	VERB
ejpam-5827	25	30	the	the	DET
ejpam-5827	25	31	theory	theory	NOUN
ejpam-5827	25	32	of	of	ADP
ejpam-5827	25	33	probability	probability	NOUN
ejpam-5827	25	34	,	,	PUNCT
ejpam-5827	25	35	fuzzy	fuzzy	ADJ
ejpam-5827	25	36	sets	set	NOUN
ejpam-5827	25	37	,	,	PUNCT
ejpam-5827	25	38	rough	rough	ADJ
ejpam-5827	25	39	sets	set	NOUN
ejpam-5827	25	40	,	,	PUNCT
ejpam-5827	25	41	and	and	CCONJ
ejpam-5827	25	42	decision	decision	NOUN
ejpam-5827	25	43	-	-	PUNCT
ejpam-5827	25	44	making	make	VERB
ejpam-5827	25	45	theory	theory	NOUN
ejpam-5827	25	46	.	.	PUNCT
ejpam-5827	26	1	these	these	DET
ejpam-5827	26	2	theories	theory	NOUN
ejpam-5827	26	3	have	have	AUX
ejpam-5827	26	4	reduced	reduce	VERB
ejpam-5827	26	5	the	the	DET
ejpam-5827	26	6	gap	gap	NOUN
ejpam-5827	26	7	between	between	ADP
ejpam-5827	26	8	classical	classical	ADJ
ejpam-5827	26	9	mathematical	mathematical	ADJ
ejpam-5827	26	10	methods	method	NOUN
ejpam-5827	26	11	and	and	CCONJ
ejpam-5827	26	12	the	the	DET
ejpam-5827	26	13	inaccuracies	inaccuracy	NOUN
ejpam-5827	26	14	of	of	ADP
ejpam-5827	26	15	real	real	ADJ
ejpam-5827	26	16	-	-	PUNCT
ejpam-5827	26	17	world	world	NOUN
ejpam-5827	26	18	information	information	NOUN
ejpam-5827	26	19	.	.	PUNCT
ejpam-5827	27	1	however	however	ADV
ejpam-5827	27	2	,	,	PUNCT
ejpam-5827	27	3	each	each	PRON
ejpam-5827	27	4	of	of	ADP
ejpam-5827	27	5	these	these	DET
ejpam-5827	27	6	theories	theory	NOUN
ejpam-5827	27	7	has	have	VERB
ejpam-5827	27	8	inherent	inherent	ADJ
ejpam-5827	27	9	difficulties	difficulty	NOUN
ejpam-5827	27	10	and	and	CCONJ
ejpam-5827	27	11	disadvantages	disadvantage	NOUN
ejpam-5827	27	12	,	,	PUNCT
ejpam-5827	27	13	which	which	PRON
ejpam-5827	27	14	motivated	motivate	VERB
ejpam-5827	27	15	pawlak	pawlak	ADJ
ejpam-5827	27	16	[	[	X
ejpam-5827	27	17	59	59	NUM
ejpam-5827	27	18	]	]	PUNCT
ejpam-5827	27	19	to	to	PART
ejpam-5827	27	20	initiate	initiate	VERB
ejpam-5827	27	21	classical	classical	ADJ
ejpam-5827	27	22	rough	rough	ADJ
ejpam-5827	27	23	set	set	NOUN
ejpam-5827	27	24	models	model	NOUN
ejpam-5827	27	25	as	as	ADP
ejpam-5827	27	26	modern	modern	ADJ
ejpam-5827	27	27	approach	approach	NOUN
ejpam-5827	27	28	to	to	ADP
ejpam-5827	27	29	modeling	model	VERB
ejpam-5827	27	30	the	the	DET
ejpam-5827	27	31	vagueness	vagueness	NOUN
ejpam-5827	27	32	of	of	ADP
ejpam-5827	27	33	data	datum	NOUN
ejpam-5827	27	34	from	from	ADP
ejpam-5827	27	35	real	real	ADJ
ejpam-5827	27	36	-	-	PUNCT
ejpam-5827	27	37	life	life	NOUN
ejpam-5827	27	38	problems	problem	NOUN
ejpam-5827	27	39	.	.	PUNCT
ejpam-5827	28	1	while	while	SCONJ
ejpam-5827	28	2	the	the	DET
ejpam-5827	28	3	core	core	NOUN
ejpam-5827	28	4	concepts	concept	NOUN
ejpam-5827	28	5	include	include	VERB
ejpam-5827	28	6	upper	upper	ADJ
ejpam-5827	28	7	and	and	CCONJ
ejpam-5827	28	8	lower	low	ADJ
ejpam-5827	28	9	approximations	approximation	NOUN
ejpam-5827	28	10	based	base	VERB
ejpam-5827	28	11	on	on	ADP
ejpam-5827	28	12	equivalence	equivalence	NOUN
ejpam-5827	28	13	relations	relation	NOUN
ejpam-5827	28	14	,	,	PUNCT
ejpam-5827	28	15	these	these	PRON
ejpam-5827	28	16	restrict	restrict	VERB
ejpam-5827	28	17	application	application	NOUN
ejpam-5827	28	18	domains	domain	NOUN
ejpam-5827	28	19	.	.	PUNCT
ejpam-5827	29	1	as	as	ADP
ejpam-5827	29	2	a	a	DET
ejpam-5827	29	3	result	result	NOUN
ejpam-5827	29	4	,	,	PUNCT
ejpam-5827	29	5	several	several	ADJ
ejpam-5827	29	6	researchers	researcher	NOUN
ejpam-5827	29	7	have	have	AUX
ejpam-5827	29	8	employed	employ	VERB
ejpam-5827	29	9	topological	topological	ADJ
ejpam-5827	29	10	concepts	concept	NOUN
ejpam-5827	29	11	to	to	PART
ejpam-5827	29	12	generalize	generalize	VERB
ejpam-5827	29	13	these	these	DET
ejpam-5827	29	14	approximations	approximation	NOUN
ejpam-5827	29	15	and	and	CCONJ
ejpam-5827	29	16	replace	replace	VERB
ejpam-5827	29	17	equivalence	equivalence	NOUN
ejpam-5827	29	18	relations	relation	NOUN
ejpam-5827	29	19	with	with	ADP
ejpam-5827	29	20	any	any	DET
ejpam-5827	29	21	binary	binary	ADJ
ejpam-5827	29	22	relation	relation	NOUN
ejpam-5827	29	23	(	(	PUNCT
ejpam-5827	29	24	see	see	VERB
ejpam-5827	29	25	,	,	PUNCT
ejpam-5827	29	26	for	for	ADP
ejpam-5827	29	27	instance	instance	NOUN
ejpam-5827	29	28	,	,	PUNCT
ejpam-5827	29	29	generalized	generalize	VERB
ejpam-5827	29	30	rough	rough	ADJ
ejpam-5827	29	31	sets	set	NOUN
ejpam-5827	29	32	[	[	X
ejpam-5827	29	33	21	21	NUM
ejpam-5827	29	34	,	,	PUNCT
ejpam-5827	29	35	24	24	NUM
ejpam-5827	29	36	,	,	PUNCT
ejpam-5827	29	37	37	37	NUM
ejpam-5827	29	38	,	,	PUNCT
ejpam-5827	29	39	42	42	NUM
ejpam-5827	29	40	,	,	PUNCT
ejpam-5827	29	41	64	64	NUM
ejpam-5827	29	42	]	]	PUNCT
ejpam-5827	29	43	,	,	PUNCT
ejpam-5827	29	44	information	information	NOUN
ejpam-5827	29	45	systems	system	NOUN
ejpam-5827	29	46	[	[	X
ejpam-5827	29	47	65	65	NUM
ejpam-5827	29	48	]	]	PUNCT
ejpam-5827	29	49	,	,	PUNCT
ejpam-5827	29	50	feature	feature	NOUN
ejpam-5827	29	51	selection	selection	NOUN
ejpam-5827	29	52	[	[	X
ejpam-5827	29	53	37	37	NUM
ejpam-5827	29	54	,	,	PUNCT
ejpam-5827	29	55	42	42	NUM
ejpam-5827	29	56	]	]	PUNCT
ejpam-5827	29	57	,	,	PUNCT
ejpam-5827	29	58	topological	topological	ADJ
ejpam-5827	29	59	structures	structure	NOUN
ejpam-5827	29	60	of	of	ADP
ejpam-5827	29	61	rough	rough	ADJ
ejpam-5827	29	62	sets	set	NOUN
ejpam-5827	29	63	[	[	X
ejpam-5827	29	64	26	26	NUM
ejpam-5827	29	65	,	,	PUNCT
ejpam-5827	29	66	28	28	NUM
ejpam-5827	29	67	,	,	PUNCT
ejpam-5827	29	68	50	50	NUM
ejpam-5827	29	69	,	,	PUNCT
ejpam-5827	29	70	53	53	NUM
ejpam-5827	29	71	]	]	PUNCT
ejpam-5827	29	72	,	,	PUNCT
ejpam-5827	29	73	and	and	CCONJ
ejpam-5827	29	74	medical	medical	ADJ
ejpam-5827	29	75	applications	application	NOUN
ejpam-5827	29	76	of	of	ADP
ejpam-5827	29	77	topological	topological	ADJ
ejpam-5827	29	78	rough	rough	ADJ
ejpam-5827	29	79	sets	set	NOUN
ejpam-5827	29	80	[	[	X
ejpam-5827	29	81	5	5	NUM
ejpam-5827	29	82	,	,	PUNCT
ejpam-5827	29	83	22	22	NUM
ejpam-5827	29	84	]	]	PUNCT
ejpam-5827	29	85	)	)	PUNCT
ejpam-5827	29	86	.	.	PUNCT
ejpam-5827	30	1	in	in	ADP
ejpam-5827	30	2	1996	1996	NUM
ejpam-5827	30	3	,	,	PUNCT
ejpam-5827	30	4	yao	yao	PROPN
ejpam-5827	31	1	[	[	X
ejpam-5827	31	2	73	73	NUM
ejpam-5827	31	3	]	]	PUNCT
ejpam-5827	31	4	introduced	introduce	VERB
ejpam-5827	31	5	a	a	DET
ejpam-5827	31	6	method	method	NOUN
ejpam-5827	31	7	that	that	PRON
ejpam-5827	31	8	led	lead	VERB
ejpam-5827	31	9	to	to	ADP
ejpam-5827	31	10	several	several	ADJ
ejpam-5827	31	11	generalizations	generalization	NOUN
ejpam-5827	31	12	incorporating	incorporate	VERB
ejpam-5827	31	13	various	various	ADJ
ejpam-5827	31	14	types	type	NOUN
ejpam-5827	31	15	of	of	ADP
ejpam-5827	31	16	relations	relation	NOUN
ejpam-5827	31	17	,	,	PUNCT
ejpam-5827	31	18	including	include	VERB
ejpam-5827	31	19	tolerance	tolerance	NOUN
ejpam-5827	31	20	relations	relation	NOUN
ejpam-5827	31	21	[	[	X
ejpam-5827	31	22	48	48	NUM
ejpam-5827	31	23	,	,	PUNCT
ejpam-5827	31	24	60	60	NUM
ejpam-5827	31	25	,	,	PUNCT
ejpam-5827	31	26	66	66	NUM
ejpam-5827	31	27	]	]	PUNCT
ejpam-5827	31	28	,	,	PUNCT
ejpam-5827	31	29	similarity	similarity	NOUN
ejpam-5827	31	30	relations	relation	NOUN
ejpam-5827	31	31	[	[	X
ejpam-5827	31	32	67	67	NUM
ejpam-5827	31	33	]	]	PUNCT
ejpam-5827	31	34	,	,	PUNCT
ejpam-5827	31	35	and	and	CCONJ
ejpam-5827	31	36	general	general	ADJ
ejpam-5827	31	37	binary	binary	NOUN
ejpam-5827	31	38	relations	relation	NOUN
ejpam-5827	31	39	[	[	X
ejpam-5827	31	40	7	7	NUM
ejpam-5827	31	41	,	,	PUNCT
ejpam-5827	31	42	12	12	NUM
ejpam-5827	31	43	,	,	PUNCT
ejpam-5827	31	44	13	13	NUM
ejpam-5827	31	45	,	,	PUNCT
ejpam-5827	31	46	49	49	NUM
ejpam-5827	31	47	]	]	PUNCT
ejpam-5827	31	48	.	.	PUNCT
ejpam-5827	32	1	abd	abd	PROPN
ejpam-5827	32	2	el	el	PROPN
ejpam-5827	32	3	-	-	PROPN
ejpam-5827	32	4	monsef	monsef	PROPN
ejpam-5827	32	5	et	et	PROPN
ejpam-5827	32	6	al	al	PROPN
ejpam-5827	32	7	.	.	PUNCT
ejpam-5827	33	1	[	[	X
ejpam-5827	33	2	35	35	NUM
ejpam-5827	33	3	]	]	PUNCT
ejpam-5827	33	4	introduced	introduce	VERB
ejpam-5827	33	5	the	the	DET
ejpam-5827	33	6	notion	notion	NOUN
ejpam-5827	33	7	of	of	ADP
ejpam-5827	33	8	κ	κ	NOUN
ejpam-5827	33	9	-	-	PUNCT
ejpam-5827	33	10	neighborhood	neighborhood	NOUN
ejpam-5827	33	11	spaces	space	NOUN
ejpam-5827	33	12	(	(	PUNCT
ejpam-5827	33	13	briefly	briefly	ADV
ejpam-5827	33	14	,	,	PUNCT
ejpam-5827	33	15	κ	κ	NOUN
ejpam-5827	33	16	-	-	PUNCT
ejpam-5827	33	17	ns	ns	NUM
ejpam-5827	33	18	)	)	PUNCT
ejpam-5827	33	19	to	to	PART
ejpam-5827	33	20	generalize	generalize	VERB
ejpam-5827	33	21	rough	rough	ADJ
ejpam-5827	33	22	set	set	NOUN
ejpam-5827	33	23	theory	theory	NOUN
ejpam-5827	33	24	through	through	ADP
ejpam-5827	33	25	various	various	ADJ
ejpam-5827	33	26	topologies	topology	NOUN
ejpam-5827	33	27	induced	induce	VERB
ejpam-5827	33	28	by	by	ADP
ejpam-5827	33	29	arbitrary	arbitrary	ADJ
ejpam-5827	33	30	relations	relation	NOUN
ejpam-5827	33	31	.	.	PUNCT
ejpam-5827	34	1	these	these	DET
ejpam-5827	34	2	methods	method	NOUN
ejpam-5827	34	3	represent	represent	VERB
ejpam-5827	34	4	an	an	DET
ejpam-5827	34	5	extension	extension	NOUN
ejpam-5827	34	6	of	of	ADP
ejpam-5827	34	7	the	the	DET
ejpam-5827	34	8	work	work	NOUN
ejpam-5827	34	9	[	[	X
ejpam-5827	34	10	21	21	NUM
ejpam-5827	34	11	,	,	PUNCT
ejpam-5827	34	12	49	49	NUM
ejpam-5827	34	13	]	]	PUNCT
ejpam-5827	34	14	,	,	PUNCT
ejpam-5827	34	15	which	which	PRON
ejpam-5827	34	16	opened	open	VERB
ejpam-5827	34	17	the	the	DET
ejpam-5827	34	18	way	way	NOUN
ejpam-5827	34	19	for	for	ADP
ejpam-5827	34	20	more	more	ADJ
ejpam-5827	34	21	topological	topological	ADJ
ejpam-5827	34	22	applications	application	NOUN
ejpam-5827	34	23	in	in	ADP
ejpam-5827	34	24	rough	rough	ADJ
ejpam-5827	34	25	sets	set	NOUN
ejpam-5827	34	26	[	[	X
ejpam-5827	34	27	26	26	NUM
ejpam-5827	34	28	,	,	PUNCT
ejpam-5827	34	29	38	38	NUM
ejpam-5827	34	30	,	,	PUNCT
ejpam-5827	34	31	43	43	NUM
ejpam-5827	34	32	,	,	PUNCT
ejpam-5827	34	33	63	63	NUM
ejpam-5827	34	34	]	]	PUNCT
ejpam-5827	34	35	and	and	CCONJ
ejpam-5827	34	36	their	their	PRON
ejpam-5827	34	37	applications	application	NOUN
ejpam-5827	34	38	in	in	ADP
ejpam-5827	34	39	many	many	ADJ
ejpam-5827	34	40	fields	field	NOUN
ejpam-5827	34	41	[	[	X
ejpam-5827	34	42	18	18	NUM
ejpam-5827	34	43	,	,	PUNCT
ejpam-5827	34	44	32	32	NUM
ejpam-5827	34	45	,	,	PUNCT
ejpam-5827	34	46	71	71	NUM
ejpam-5827	34	47	,	,	PUNCT
ejpam-5827	34	48	72	72	NUM
ejpam-5827	34	49	]	]	PUNCT
ejpam-5827	34	50	.	.	PUNCT
ejpam-5827	35	1	it	it	PRON
ejpam-5827	35	2	is	be	AUX
ejpam-5827	35	3	worth	worth	ADJ
ejpam-5827	35	4	noting	note	VERB
ejpam-5827	35	5	that	that	SCONJ
ejpam-5827	35	6	the	the	DET
ejpam-5827	35	7	concept	concept	NOUN
ejpam-5827	35	8	of	of	ADP
ejpam-5827	35	9	a	a	DET
ejpam-5827	35	10	”	"	PUNCT
ejpam-5827	35	11	basic	basic	ADJ
ejpam-5827	35	12	-	-	PUNCT
ejpam-5827	35	13	neighborhood	neighborhood	NOUN
ejpam-5827	35	14	”	"	PUNCT
ejpam-5827	35	15	(	(	PUNCT
ejpam-5827	35	16	introduced	introduce	VERB
ejpam-5827	35	17	in	in	ADP
ejpam-5827	35	18	[	[	X
ejpam-5827	35	19	7	7	NUM
ejpam-5827	35	20	]	]	PUNCT
ejpam-5827	35	21	)	)	PUNCT
ejpam-5827	35	22	was	be	AUX
ejpam-5827	35	23	studied	study	VERB
ejpam-5827	35	24	by	by	ADP
ejpam-5827	35	25	el	el	PROPN
ejpam-5827	35	26	-	-	PROPN
ejpam-5827	35	27	gayar	gayar	NOUN
ejpam-5827	35	28	et	et	PROPN
ejpam-5827	35	29	al	al	PROPN
ejpam-5827	35	30	.	.	PUNCT
ejpam-5827	36	1	[	[	X
ejpam-5827	36	2	31	31	NUM
ejpam-5827	36	3	]	]	PUNCT
ejpam-5827	36	4	and	and	CCONJ
ejpam-5827	36	5	taher	taher	PROPN
ejpam-5827	36	6	et	et	PROPN
ejpam-5827	36	7	al	al	PROPN
ejpam-5827	36	8	.	.	PUNCT
ejpam-5827	37	1	[	[	X
ejpam-5827	37	2	71	71	NUM
ejpam-5827	37	3	,	,	PUNCT
ejpam-5827	37	4	72	72	NUM
ejpam-5827	37	5	]	]	PUNCT
ejpam-5827	37	6	provided	provide	VERB
ejpam-5827	37	7	a	a	DET
ejpam-5827	37	8	comprehensive	comprehensive	ADJ
ejpam-5827	37	9	analysis	analysis	NOUN
ejpam-5827	37	10	,	,	PUNCT
ejpam-5827	37	11	exploring	explore	VERB
ejpam-5827	37	12	the	the	DET
ejpam-5827	37	13	relationships	relationship	NOUN
ejpam-5827	37	14	between	between	ADP
ejpam-5827	37	15	the	the	DET
ejpam-5827	37	16	generated	generate	VERB
ejpam-5827	37	17	topologies	topology	NOUN
ejpam-5827	37	18	and	and	CCONJ
ejpam-5827	37	19	approximations	approximation	NOUN
ejpam-5827	37	20	.	.	PUNCT
ejpam-5827	38	1	furthermore	furthermore	ADV
ejpam-5827	38	2	,	,	PUNCT
ejpam-5827	38	3	these	these	DET
ejpam-5827	38	4	papers	paper	NOUN
ejpam-5827	38	5	established	establish	VERB
ejpam-5827	38	6	new	new	ADJ
ejpam-5827	38	7	results	result	NOUN
ejpam-5827	38	8	,	,	PUNCT
ejpam-5827	38	9	comparing	compare	VERB
ejpam-5827	38	10	their	their	PRON
ejpam-5827	38	11	methods	method	NOUN
ejpam-5827	38	12	with	with	ADP
ejpam-5827	38	13	previous	previous	ADJ
ejpam-5827	38	14	techniques	technique	NOUN
ejpam-5827	38	15	such	such	ADJ
ejpam-5827	38	16	as	as	ADP
ejpam-5827	38	17	those	those	PRON
ejpam-5827	38	18	in	in	ADP
ejpam-5827	38	19	[	[	X
ejpam-5827	38	20	7	7	NUM
ejpam-5827	38	21	,	,	PUNCT
ejpam-5827	38	22	12	12	NUM
ejpam-5827	38	23	,	,	PUNCT
ejpam-5827	38	24	13	13	NUM
ejpam-5827	38	25	,	,	PUNCT
ejpam-5827	38	26	20	20	NUM
ejpam-5827	38	27	,	,	PUNCT
ejpam-5827	38	28	35	35	NUM
ejpam-5827	38	29	,	,	PUNCT
ejpam-5827	38	30	73	73	NUM
ejpam-5827	38	31	]	]	PUNCT
ejpam-5827	38	32	.	.	PUNCT
ejpam-5827	39	1	additionally	additionally	ADV
ejpam-5827	39	2	,	,	PUNCT
ejpam-5827	39	3	these	these	DET
ejpam-5827	39	4	works	work	NOUN
ejpam-5827	39	5	demonstrated	demonstrate	VERB
ejpam-5827	39	6	impressive	impressive	ADJ
ejpam-5827	39	7	applications	application	NOUN
ejpam-5827	39	8	in	in	ADP
ejpam-5827	39	9	the	the	DET
ejpam-5827	39	10	medical	medical	ADJ
ejpam-5827	39	11	and	and	CCONJ
ejpam-5827	39	12	economic	economic	ADJ
ejpam-5827	39	13	fields	field	NOUN
ejpam-5827	39	14	[	[	X
ejpam-5827	39	15	28	28	NUM
ejpam-5827	39	16	,	,	PUNCT
ejpam-5827	39	17	30	30	NUM
ejpam-5827	39	18	,	,	PUNCT
ejpam-5827	39	19	31	31	NUM
ejpam-5827	39	20	]	]	PUNCT
ejpam-5827	39	21	.	.	PUNCT
ejpam-5827	40	1	mashhour	mashhour	PROPN
ejpam-5827	41	1	[	[	X
ejpam-5827	41	2	56	56	NUM
ejpam-5827	41	3	]	]	PUNCT
ejpam-5827	41	4	expanded	expand	VERB
ejpam-5827	41	5	the	the	DET
ejpam-5827	41	6	notion	notion	NOUN
ejpam-5827	41	7	of	of	ADP
ejpam-5827	41	8	topology	topology	NOUN
ejpam-5827	41	9	to	to	ADP
ejpam-5827	41	10	supra	supra	NOUN
ejpam-5827	41	11	-	-	PUNCT
ejpam-5827	41	12	topology	topology	NOUN
ejpam-5827	41	13	by	by	ADP
ejpam-5827	41	14	ignoring	ignore	VERB
ejpam-5827	41	15	the	the	DET
ejpam-5827	41	16	finite	finite	ADJ
ejpam-5827	41	17	intersection	intersection	NOUN
ejpam-5827	41	18	condition	condition	NOUN
ejpam-5827	41	19	.	.	PUNCT
ejpam-5827	42	1	a	a	DET
ejpam-5827	42	2	supra	supra	NOUN
ejpam-5827	42	3	-	-	PUNCT
ejpam-5827	42	4	topology	topology	NOUN
ejpam-5827	42	5	is	be	AUX
ejpam-5827	42	6	defined	define	VERB
ejpam-5827	42	7	on	on	ADP
ejpam-5827	42	8	a	a	DET
ejpam-5827	42	9	nonempty	nonempty	ADV
ejpam-5827	42	10	set	set	VERB
ejpam-5827	42	11	v	v	NOUN
ejpam-5827	42	12	as	as	ADP
ejpam-5827	42	13	a	a	DET
ejpam-5827	42	14	subclass	subclass	NOUN
ejpam-5827	42	15	s	s	NOUN
ejpam-5827	42	16	of	of	ADP
ejpam-5827	42	17	the	the	DET
ejpam-5827	42	18	power	power	NOUN
ejpam-5827	42	19	set	set	NOUN
ejpam-5827	42	20	of	of	ADP
ejpam-5827	42	21	v	v	NOUN
ejpam-5827	42	22	satisfying	satisfy	VERB
ejpam-5827	42	23	two	two	NUM
ejpam-5827	42	24	axioms	axiom	NOUN
ejpam-5827	42	25	:	:	PUNCT
ejpam-5827	42	26	∅	∅	NOUN
ejpam-5827	42	27	,	,	PUNCT
ejpam-5827	42	28	v	v	NOUN
ejpam-5827	42	29	∈	∈	NOUN
ejpam-5827	42	30	s	s	NOUN
ejpam-5827	42	31	,	,	PUNCT
ejpam-5827	42	32	and	and	CCONJ
ejpam-5827	42	33	s	s	VERB
ejpam-5827	42	34	is	be	AUX
ejpam-5827	42	35	closed	close	VERB
ejpam-5827	42	36	under	under	ADP
ejpam-5827	42	37	arbitrary	arbitrary	ADJ
ejpam-5827	42	38	union	union	NOUN
ejpam-5827	42	39	.	.	PUNCT
ejpam-5827	43	1	this	this	PRON
ejpam-5827	43	2	makes	make	VERB
ejpam-5827	43	3	supra	supra	NOUN
ejpam-5827	43	4	-	-	PUNCT
ejpam-5827	43	5	topology	topology	NOUN
ejpam-5827	43	6	more	more	ADV
ejpam-5827	43	7	elastic	elastic	ADJ
ejpam-5827	43	8	in	in	ADP
ejpam-5827	43	9	characterizing	characterize	VERB
ejpam-5827	43	10	some	some	DET
ejpam-5827	43	11	real	real	ADJ
ejpam-5827	43	12	-	-	PUNCT
ejpam-5827	43	13	life	life	NOUN
ejpam-5827	43	14	problems	problem	NOUN
ejpam-5827	43	15	[	[	X
ejpam-5827	43	16	51	51	NUM
ejpam-5827	43	17	]	]	PUNCT
ejpam-5827	43	18	and	and	CCONJ
ejpam-5827	43	19	establishing	establish	VERB
ejpam-5827	43	20	examples	example	NOUN
ejpam-5827	43	21	that	that	PRON
ejpam-5827	43	22	illustrate	illustrate	VERB
ejpam-5827	43	23	the	the	DET
ejpam-5827	43	24	relationships	relationship	NOUN
ejpam-5827	43	25	between	between	ADP
ejpam-5827	43	26	topological	topological	ADJ
ejpam-5827	43	27	notions	notion	NOUN
ejpam-5827	43	28	.	.	PUNCT
ejpam-5827	44	1	the	the	DET
ejpam-5827	44	2	idea	idea	NOUN
ejpam-5827	44	3	of	of	ADP
ejpam-5827	44	4	minimal	minimal	ADJ
ejpam-5827	44	5	spaces	space	NOUN
ejpam-5827	44	6	as	as	ADP
ejpam-5827	44	7	a	a	DET
ejpam-5827	44	8	generalization	generalization	NOUN
ejpam-5827	44	9	of	of	ADP
ejpam-5827	44	10	topological	topological	ADJ
ejpam-5827	44	11	spaces	space	NOUN
ejpam-5827	44	12	was	be	AUX
ejpam-5827	44	13	introduced	introduce	VERB
ejpam-5827	44	14	in	in	ADP
ejpam-5827	44	15	[	[	X
ejpam-5827	44	16	55	55	NUM
ejpam-5827	44	17	]	]	PUNCT
ejpam-5827	44	18	.	.	PUNCT
ejpam-5827	45	1	these	these	DET
ejpam-5827	45	2	spaces	space	NOUN
ejpam-5827	45	3	have	have	AUX
ejpam-5827	45	4	yielded	yield	VERB
ejpam-5827	45	5	many	many	ADJ
ejpam-5827	45	6	valuable	valuable	ADJ
ejpam-5827	45	7	results	result	NOUN
ejpam-5827	45	8	consistent	consistent	ADJ
ejpam-5827	45	9	with	with	ADP
ejpam-5827	45	10	general	general	ADJ
ejpam-5827	45	11	topology	topology	NOUN
ejpam-5827	45	12	.	.	PUNCT
ejpam-5827	46	1	kuratowski	kuratowski	PROPN
ejpam-5827	47	1	[	[	X
ejpam-5827	47	2	52	52	NUM
ejpam-5827	47	3	]	]	PUNCT
ejpam-5827	47	4	offered	offer	VERB
ejpam-5827	47	5	the	the	DET
ejpam-5827	47	6	concept	concept	NOUN
ejpam-5827	47	7	of	of	ADP
ejpam-5827	47	8	an	an	DET
ejpam-5827	47	9	ideal	ideal	NOUN
ejpam-5827	47	10	from	from	ADP
ejpam-5827	47	11	the	the	DET
ejpam-5827	47	12	filter	filter	NOUN
ejpam-5827	47	13	notion	notion	NOUN
ejpam-5827	47	14	.	.	PUNCT
ejpam-5827	48	1	one	one	PRON
ejpam-5827	48	2	may	may	AUX
ejpam-5827	48	3	consider	consider	VERB
ejpam-5827	48	4	an	an	DET
ejpam-5827	48	5	ideal	ideal	NOUN
ejpam-5827	48	6	as	as	ADP
ejpam-5827	48	7	the	the	DET
ejpam-5827	48	8	dual	dual	ADJ
ejpam-5827	48	9	of	of	ADP
ejpam-5827	48	10	a	a	DET
ejpam-5827	48	11	filter	filter	NOUN
ejpam-5827	48	12	.	.	PUNCT
ejpam-5827	49	1	similarly	similarly	ADV
ejpam-5827	49	2	,	,	PUNCT
ejpam-5827	49	3	one	one	NUM
ejpam-5827	49	4	of	of	ADP
ejpam-5827	49	5	the	the	DET
ejpam-5827	49	6	classical	classical	ADJ
ejpam-5827	49	7	structures	structure	NOUN
ejpam-5827	49	8	of	of	ADP
ejpam-5827	49	9	topology	topology	NOUN
ejpam-5827	49	10	is	be	AUX
ejpam-5827	49	11	the	the	DET
ejpam-5827	49	12	grill	grill	NOUN
ejpam-5827	49	13	,	,	PUNCT
ejpam-5827	49	14	which	which	PRON
ejpam-5827	49	15	was	be	AUX
ejpam-5827	49	16	defined	define	VERB
ejpam-5827	49	17	by	by	ADP
ejpam-5827	49	18	choquet	choquet	NOUN
ejpam-5827	49	19	[	[	X
ejpam-5827	49	20	19	19	NUM
ejpam-5827	49	21	]	]	PUNCT
ejpam-5827	49	22	.	.	PUNCT
ejpam-5827	50	1	acharjee	acharjee	PROPN
ejpam-5827	50	2	et	et	PROPN
ejpam-5827	50	3	al	al	PROPN
ejpam-5827	50	4	.	.	PUNCT
ejpam-5827	51	1	[	[	X
ejpam-5827	51	2	9	9	NUM
ejpam-5827	51	3	]	]	PUNCT
ejpam-5827	51	4	presented	present	VERB
ejpam-5827	51	5	a	a	DET
ejpam-5827	51	6	primal	primal	ADJ
ejpam-5827	51	7	structure	structure	NOUN
ejpam-5827	51	8	,	,	PUNCT
ejpam-5827	51	9	which	which	PRON
ejpam-5827	51	10	is	be	AUX
ejpam-5827	51	11	dual	dual	ADJ
ejpam-5827	51	12	to	to	ADP
ejpam-5827	51	13	the	the	DET
ejpam-5827	51	14	grill	grill	NOUN
ejpam-5827	51	15	and	and	CCONJ
ejpam-5827	51	16	also	also	ADV
ejpam-5827	51	17	generated	generate	VERB
ejpam-5827	51	18	a	a	DET
ejpam-5827	51	19	primal	primal	ADJ
ejpam-5827	51	20	topology	topology	NOUN
ejpam-5827	51	21	.	.	PUNCT
ejpam-5827	52	1	another	another	DET
ejpam-5827	52	2	promising	promising	ADJ
ejpam-5827	52	3	direction	direction	NOUN
ejpam-5827	52	4	for	for	ADP
ejpam-5827	52	5	extending	extend	VERB
ejpam-5827	52	6	rough	rough	ADJ
ejpam-5827	52	7	sets	set	NOUN
ejpam-5827	52	8	involves	involve	VERB
ejpam-5827	52	9	the	the	DET
ejpam-5827	52	10	concept	concept	NOUN
ejpam-5827	52	11	of	of	ADP
ejpam-5827	52	12	ideals	ideal	NOUN
ejpam-5827	52	13	[	[	X
ejpam-5827	52	14	52	52	NUM
ejpam-5827	52	15	]	]	PUNCT
ejpam-5827	52	16	,	,	PUNCT
ejpam-5827	52	17	which	which	PRON
ejpam-5827	52	18	are	be	AUX
ejpam-5827	52	19	foundational	foundational	ADJ
ejpam-5827	52	20	in	in	ADP
ejpam-5827	52	21	both	both	DET
ejpam-5827	52	22	topology	topology	NOUN
ejpam-5827	52	23	and	and	CCONJ
ejpam-5827	52	24	rough	rough	ADJ
ejpam-5827	52	25	set	set	NOUN
ejpam-5827	52	26	theory	theory	NOUN
ejpam-5827	52	27	,	,	PUNCT
ejpam-5827	52	28	albeit	albeit	SCONJ
ejpam-5827	52	29	serving	serve	VERB
ejpam-5827	52	30	different	different	ADJ
ejpam-5827	52	31	purposes	purpose	NOUN
ejpam-5827	52	32	in	in	ADP
ejpam-5827	52	33	each	each	DET
ejpam-5827	52	34	field	field	NOUN
ejpam-5827	52	35	.	.	PUNCT
ejpam-5827	53	1	in	in	ADP
ejpam-5827	53	2	topology	topology	NOUN
ejpam-5827	53	3	,	,	PUNCT
ejpam-5827	53	4	ideals	ideal	NOUN
ejpam-5827	53	5	are	be	AUX
ejpam-5827	53	6	pivotal	pivotal	ADJ
ejpam-5827	53	7	for	for	ADP
ejpam-5827	53	8	defining	define	VERB
ejpam-5827	53	9	closure	closure	NOUN
ejpam-5827	53	10	operations	operation	NOUN
ejpam-5827	53	11	,	,	PUNCT
ejpam-5827	53	12	r.	r.	PROPN
ejpam-5827	53	13	a.	a.	PROPN
ejpam-5827	53	14	hosny	hosny	PROPN
ejpam-5827	53	15	,	,	PUNCT
ejpam-5827	53	16	m.	m.	PROPN
ejpam-5827	53	17	k.	k.	PROPN
ejpam-5827	54	1	el	el	PROPN
ejpam-5827	54	2	-	-	PROPN
ejpam-5827	54	3	bably	bably	ADV
ejpam-5827	54	4	,	,	PUNCT
ejpam-5827	54	5	m.	m.	NOUN
ejpam-5827	54	6	a.	a.	PROPN
ejpam-5827	54	7	el	el	PROPN
ejpam-5827	54	8	-	-	PROPN
ejpam-5827	54	9	gayar	gayar	PROPN
ejpam-5827	54	10	/	/	SYM
ejpam-5827	54	11	eur	eur	PROPN
ejpam-5827	54	12	.	.	PUNCT
ejpam-5827	55	1	j.	j.	PROPN
ejpam-5827	55	2	pure	pure	PROPN
ejpam-5827	55	3	appl	appl	PROPN
ejpam-5827	55	4	.	.	PROPN
ejpam-5827	55	5	math	math	PROPN
ejpam-5827	55	6	,	,	PUNCT
ejpam-5827	55	7	18	18	NUM
ejpam-5827	55	8	(	(	PUNCT
ejpam-5827	55	9	1	1	NUM
ejpam-5827	55	10	)	)	PUNCT
ejpam-5827	55	11	(	(	PUNCT
ejpam-5827	55	12	2025	2025	NUM
ejpam-5827	55	13	)	)	PUNCT
ejpam-5827	55	14	,	,	PUNCT
ejpam-5827	55	15	5827	5827	NUM
ejpam-5827	55	16	3	3	NUM
ejpam-5827	55	17	of	of	ADP
ejpam-5827	55	18	29	29	NUM
ejpam-5827	55	19	characterizing	characterize	VERB
ejpam-5827	55	20	convergence	convergence	NOUN
ejpam-5827	55	21	,	,	PUNCT
ejpam-5827	55	22	and	and	CCONJ
ejpam-5827	55	23	facilitating	facilitate	VERB
ejpam-5827	55	24	compactification	compactification	NOUN
ejpam-5827	55	25	.	.	PUNCT
ejpam-5827	56	1	in	in	ADP
ejpam-5827	56	2	rough	rough	ADJ
ejpam-5827	56	3	set	set	NOUN
ejpam-5827	56	4	theory	theory	NOUN
ejpam-5827	56	5	,	,	PUNCT
ejpam-5827	56	6	they	they	PRON
ejpam-5827	56	7	play	play	VERB
ejpam-5827	56	8	a	a	DET
ejpam-5827	56	9	crucial	crucial	ADJ
ejpam-5827	56	10	role	role	NOUN
ejpam-5827	56	11	in	in	ADP
ejpam-5827	56	12	information	information	NOUN
ejpam-5827	56	13	granulation	granulation	NOUN
ejpam-5827	56	14	,	,	PUNCT
ejpam-5827	56	15	shaping	shape	VERB
ejpam-5827	56	16	lower	low	ADJ
ejpam-5827	56	17	and	and	CCONJ
ejpam-5827	56	18	upper	upper	ADJ
ejpam-5827	56	19	approximations	approximation	NOUN
ejpam-5827	56	20	essential	essential	ADJ
ejpam-5827	56	21	for	for	ADP
ejpam-5827	56	22	managing	manage	VERB
ejpam-5827	56	23	data	datum	NOUN
ejpam-5827	56	24	uncertainty	uncertainty	NOUN
ejpam-5827	56	25	[	[	X
ejpam-5827	56	26	41	41	NUM
ejpam-5827	56	27	,	,	PUNCT
ejpam-5827	56	28	44	44	NUM
ejpam-5827	56	29	,	,	PUNCT
ejpam-5827	56	30	46	46	NUM
ejpam-5827	56	31	,	,	PUNCT
ejpam-5827	56	32	47	47	NUM
ejpam-5827	56	33	]	]	PUNCT
ejpam-5827	56	34	.	.	PUNCT
ejpam-5827	57	1	this	this	DET
ejpam-5827	57	2	framework	framework	NOUN
ejpam-5827	57	3	has	have	AUX
ejpam-5827	57	4	been	be	AUX
ejpam-5827	57	5	applied	apply	VERB
ejpam-5827	57	6	to	to	ADP
ejpam-5827	57	7	various	various	ADJ
ejpam-5827	57	8	domains	domain	NOUN
ejpam-5827	57	9	,	,	PUNCT
ejpam-5827	57	10	as	as	SCONJ
ejpam-5827	57	11	demonstrated	demonstrate	VERB
ejpam-5827	57	12	in	in	ADP
ejpam-5827	57	13	[	[	X
ejpam-5827	57	14	45	45	NUM
ejpam-5827	57	15	,	,	PUNCT
ejpam-5827	57	16	58	58	NUM
ejpam-5827	57	17	]	]	PUNCT
ejpam-5827	57	18	.	.	PUNCT
ejpam-5827	58	1	additionally	additionally	ADV
ejpam-5827	58	2	,	,	PUNCT
ejpam-5827	58	3	numerous	numerous	ADJ
ejpam-5827	58	4	studies	study	NOUN
ejpam-5827	58	5	have	have	VERB
ejpam-5827	58	6	leveraged	leverage	VERB
ejpam-5827	58	7	topological	topological	ADJ
ejpam-5827	58	8	structures	structure	NOUN
ejpam-5827	58	9	to	to	PART
ejpam-5827	58	10	expand	expand	VERB
ejpam-5827	58	11	the	the	DET
ejpam-5827	58	12	applicability	applicability	NOUN
ejpam-5827	58	13	of	of	ADP
ejpam-5827	58	14	rough	rough	ADJ
ejpam-5827	58	15	sets	set	NOUN
ejpam-5827	58	16	[	[	X
ejpam-5827	58	17	3	3	NUM
ejpam-5827	58	18	,	,	PUNCT
ejpam-5827	58	19	6	6	NUM
ejpam-5827	58	20	,	,	PUNCT
ejpam-5827	58	21	23	23	NUM
ejpam-5827	58	22	,	,	PUNCT
ejpam-5827	58	23	27	27	NUM
ejpam-5827	58	24	]	]	PUNCT
ejpam-5827	58	25	.	.	PUNCT
ejpam-5827	59	1	for	for	ADP
ejpam-5827	59	2	a	a	DET
ejpam-5827	59	3	comprehensive	comprehensive	ADJ
ejpam-5827	59	4	overview	overview	NOUN
ejpam-5827	59	5	of	of	ADP
ejpam-5827	59	6	the	the	DET
ejpam-5827	59	7	applications	application	NOUN
ejpam-5827	59	8	of	of	ADP
ejpam-5827	59	9	topological	topological	ADJ
ejpam-5827	59	10	structures	structure	NOUN
ejpam-5827	59	11	and	and	CCONJ
ejpam-5827	59	12	rough	rough	ADJ
ejpam-5827	59	13	sets	set	NOUN
ejpam-5827	59	14	,	,	PUNCT
ejpam-5827	59	15	we	we	PRON
ejpam-5827	59	16	direct	direct	VERB
ejpam-5827	59	17	readers	reader	NOUN
ejpam-5827	59	18	to	to	ADP
ejpam-5827	59	19	the	the	DET
ejpam-5827	59	20	existing	exist	VERB
ejpam-5827	59	21	literature	literature	NOUN
ejpam-5827	59	22	[	[	X
ejpam-5827	59	23	1	1	NUM
ejpam-5827	59	24	,	,	PUNCT
ejpam-5827	59	25	2	2	NUM
ejpam-5827	59	26	,	,	PUNCT
ejpam-5827	59	27	4	4	NUM
ejpam-5827	59	28	,	,	PUNCT
ejpam-5827	59	29	50	50	NUM
ejpam-5827	59	30	,	,	PUNCT
ejpam-5827	59	31	70	70	NUM
ejpam-5827	59	32	,	,	PUNCT
ejpam-5827	59	33	74	74	NUM
ejpam-5827	59	34	]	]	PUNCT
ejpam-5827	59	35	.	.	PUNCT
ejpam-5827	60	1	so	so	ADV
ejpam-5827	60	2	,	,	PUNCT
ejpam-5827	60	3	the	the	DET
ejpam-5827	60	4	current	current	ADJ
ejpam-5827	60	5	manuscript	manuscript	NOUN
ejpam-5827	60	6	emphasizes	emphasize	VERB
ejpam-5827	60	7	the	the	DET
ejpam-5827	60	8	versatility	versatility	NOUN
ejpam-5827	60	9	of	of	ADP
ejpam-5827	60	10	primal	primal	ADJ
ejpam-5827	60	11	as	as	ADP
ejpam-5827	60	12	mathematical	mathematical	ADJ
ejpam-5827	60	13	constructs	construct	NOUN
ejpam-5827	60	14	,	,	PUNCT
ejpam-5827	60	15	demonstrating	demonstrate	VERB
ejpam-5827	60	16	their	their	PRON
ejpam-5827	60	17	impact	impact	NOUN
ejpam-5827	60	18	not	not	PART
ejpam-5827	60	19	only	only	ADV
ejpam-5827	60	20	in	in	ADP
ejpam-5827	60	21	rough	rough	ADJ
ejpam-5827	60	22	set	set	NOUN
ejpam-5827	60	23	theory	theory	NOUN
ejpam-5827	60	24	but	but	CCONJ
ejpam-5827	60	25	also	also	ADV
ejpam-5827	60	26	in	in	ADP
ejpam-5827	60	27	other	other	ADJ
ejpam-5827	60	28	fields	field	NOUN
ejpam-5827	60	29	,	,	PUNCT
ejpam-5827	60	30	especially	especially	ADV
ejpam-5827	60	31	topology	topology	NOUN
ejpam-5827	60	32	.	.	PUNCT
ejpam-5827	61	1	the	the	DET
ejpam-5827	61	2	paper	paper	NOUN
ejpam-5827	61	3	delicacy	delicacy	NOUN
ejpam-5827	61	4	primal	primal	ADJ
ejpam-5827	61	5	as	as	ADP
ejpam-5827	61	6	a	a	DET
ejpam-5827	61	7	class	class	NOUN
ejpam-5827	61	8	of	of	ADP
ejpam-5827	61	9	objects	object	NOUN
ejpam-5827	61	10	within	within	ADP
ejpam-5827	61	11	an	an	DET
ejpam-5827	61	12	information	information	NOUN
ejpam-5827	61	13	system	system	NOUN
ejpam-5827	61	14	,	,	PUNCT
ejpam-5827	61	15	governed	govern	VERB
ejpam-5827	61	16	by	by	ADP
ejpam-5827	61	17	particular	particular	ADJ
ejpam-5827	61	18	conditions	condition	NOUN
ejpam-5827	61	19	.	.	PUNCT
ejpam-5827	62	1	the	the	DET
ejpam-5827	62	2	main	main	ADJ
ejpam-5827	62	3	goal	goal	NOUN
ejpam-5827	62	4	of	of	ADP
ejpam-5827	62	5	the	the	DET
ejpam-5827	62	6	present	present	ADJ
ejpam-5827	62	7	manuscript	manuscript	NOUN
ejpam-5827	62	8	is	be	AUX
ejpam-5827	62	9	to	to	PART
ejpam-5827	62	10	provide	provide	VERB
ejpam-5827	62	11	a	a	DET
ejpam-5827	62	12	new	new	ADJ
ejpam-5827	62	13	framework	framework	NOUN
ejpam-5827	62	14	for	for	ADP
ejpam-5827	62	15	approximate	approximate	ADJ
ejpam-5827	62	16	rough	rough	ADJ
ejpam-5827	62	17	sets	set	NOUN
ejpam-5827	62	18	using	use	VERB
ejpam-5827	62	19	novel	novel	ADJ
ejpam-5827	62	20	structures	structure	NOUN
ejpam-5827	62	21	called	call	VERB
ejpam-5827	62	22	”	"	PUNCT
ejpam-5827	62	23	primal	primal	ADJ
ejpam-5827	62	24	.	.	PUNCT
ejpam-5827	62	25	”	"	PUNCT
ejpam-5827	63	1	the	the	DET
ejpam-5827	63	2	choice	choice	NOUN
ejpam-5827	63	3	of	of	ADP
ejpam-5827	63	4	a	a	DET
ejpam-5827	63	5	primal	primal	NOUN
ejpam-5827	63	6	is	be	AUX
ejpam-5827	63	7	carefully	carefully	ADV
ejpam-5827	63	8	guided	guide	VERB
ejpam-5827	63	9	and	and	CCONJ
ejpam-5827	63	10	prepared	prepare	VERB
ejpam-5827	63	11	by	by	ADP
ejpam-5827	63	12	domain	domain	NOUN
ejpam-5827	63	13	experts	expert	NOUN
ejpam-5827	63	14	,	,	PUNCT
ejpam-5827	63	15	emphasizing	emphasize	VERB
ejpam-5827	63	16	the	the	DET
ejpam-5827	63	17	practical	practical	ADJ
ejpam-5827	63	18	importance	importance	NOUN
ejpam-5827	63	19	of	of	ADP
ejpam-5827	63	20	primal	primal	ADJ
ejpam-5827	63	21	in	in	ADP
ejpam-5827	63	22	customizing	customizing	NOUN
ejpam-5827	63	23	granulation	granulation	NOUN
ejpam-5827	63	24	methods	method	NOUN
ejpam-5827	63	25	for	for	ADP
ejpam-5827	63	26	definite	definite	ADJ
ejpam-5827	63	27	problem	problem	NOUN
ejpam-5827	63	28	domains	domain	NOUN
ejpam-5827	63	29	.	.	PUNCT
ejpam-5827	64	1	two	two	NUM
ejpam-5827	64	2	different	different	ADJ
ejpam-5827	64	3	directions	direction	NOUN
ejpam-5827	64	4	to	to	PART
ejpam-5827	64	5	extend	extend	VERB
ejpam-5827	64	6	pawlak	pawlak	ADJ
ejpam-5827	64	7	’s	’s	PART
ejpam-5827	64	8	philosophy	philosophy	NOUN
ejpam-5827	64	9	are	be	AUX
ejpam-5827	64	10	suggested	suggest	VERB
ejpam-5827	64	11	based	base	VERB
ejpam-5827	64	12	on	on	ADP
ejpam-5827	64	13	primal	primal	ADJ
ejpam-5827	64	14	.	.	PUNCT
ejpam-5827	65	1	in	in	ADP
ejpam-5827	65	2	the	the	DET
ejpam-5827	65	3	first	first	ADJ
ejpam-5827	65	4	direction	direction	NOUN
ejpam-5827	65	5	,	,	PUNCT
ejpam-5827	65	6	we	we	PRON
ejpam-5827	65	7	define	define	VERB
ejpam-5827	65	8	the	the	DET
ejpam-5827	65	9	original	original	ADJ
ejpam-5827	65	10	method	method	NOUN
ejpam-5827	65	11	of	of	ADP
ejpam-5827	65	12	generating	generate	VERB
ejpam-5827	65	13	rough	rough	ADJ
ejpam-5827	65	14	approximations	approximation	NOUN
ejpam-5827	65	15	depending	depend	VERB
ejpam-5827	65	16	on	on	ADP
ejpam-5827	65	17	κ	κ	NOUN
ejpam-5827	65	18	-	-	PUNCT
ejpam-5827	65	19	neighborhoods	neighborhood	NOUN
ejpam-5827	65	20	and	and	CCONJ
ejpam-5827	65	21	primal	primal	ADJ
ejpam-5827	65	22	.	.	PUNCT
ejpam-5827	66	1	the	the	DET
ejpam-5827	66	2	technique	technique	NOUN
ejpam-5827	66	3	represents	represent	VERB
ejpam-5827	66	4	a	a	DET
ejpam-5827	66	5	novel	novel	ADJ
ejpam-5827	66	6	method	method	NOUN
ejpam-5827	66	7	to	to	PART
ejpam-5827	66	8	induce	induce	VERB
ejpam-5827	66	9	different	different	ADJ
ejpam-5827	66	10	supra	supra	NOUN
ejpam-5827	66	11	-	-	PUNCT
ejpam-5827	66	12	topologies	topology	NOUN
ejpam-5827	66	13	via	via	ADP
ejpam-5827	66	14	κ	κ	NOUN
ejpam-5827	66	15	-	-	PUNCT
ejpam-5827	66	16	neighborhoods	neighborhood	NOUN
ejpam-5827	66	17	and	and	CCONJ
ejpam-5827	66	18	primal	primal	ADJ
ejpam-5827	66	19	,	,	PUNCT
ejpam-5827	66	20	which	which	PRON
ejpam-5827	66	21	opens	open	VERB
ejpam-5827	66	22	the	the	DET
ejpam-5827	66	23	way	way	NOUN
ejpam-5827	66	24	for	for	ADP
ejpam-5827	66	25	more	more	ADJ
ejpam-5827	66	26	topological	topological	ADJ
ejpam-5827	66	27	structures	structure	NOUN
ejpam-5827	66	28	in	in	ADP
ejpam-5827	66	29	rough	rough	ADJ
ejpam-5827	66	30	-	-	PUNCT
ejpam-5827	66	31	set	set	VERB
ejpam-5827	66	32	models	model	NOUN
ejpam-5827	66	33	.	.	PUNCT
ejpam-5827	67	1	the	the	DET
ejpam-5827	67	2	current	current	ADJ
ejpam-5827	67	3	paradigm	paradigm	NOUN
ejpam-5827	67	4	loosens	loosen	VERB
ejpam-5827	67	5	the	the	DET
ejpam-5827	67	6	constraints	constraint	NOUN
ejpam-5827	67	7	that	that	PRON
ejpam-5827	67	8	typically	typically	ADV
ejpam-5827	67	9	restrict	restrict	VERB
ejpam-5827	67	10	the	the	DET
ejpam-5827	67	11	modeling	modeling	NOUN
ejpam-5827	67	12	of	of	ADP
ejpam-5827	67	13	a	a	DET
ejpam-5827	67	14	given	give	VERB
ejpam-5827	67	15	problem	problem	NOUN
ejpam-5827	67	16	.	.	PUNCT
ejpam-5827	68	1	by	by	ADP
ejpam-5827	68	2	relaxing	relax	VERB
ejpam-5827	68	3	the	the	DET
ejpam-5827	68	4	primary	primary	ADJ
ejpam-5827	68	5	condition	condition	NOUN
ejpam-5827	68	6	imposed	impose	VERB
ejpam-5827	68	7	on	on	ADP
ejpam-5827	68	8	the	the	DET
ejpam-5827	68	9	model	model	NOUN
ejpam-5827	68	10	,	,	PUNCT
ejpam-5827	68	11	we	we	PRON
ejpam-5827	68	12	achieve	achieve	VERB
ejpam-5827	68	13	greater	great	ADJ
ejpam-5827	68	14	flexibility	flexibility	NOUN
ejpam-5827	68	15	in	in	ADP
ejpam-5827	68	16	describing	describe	VERB
ejpam-5827	68	17	and	and	CCONJ
ejpam-5827	68	18	addressing	address	VERB
ejpam-5827	68	19	practical	practical	ADJ
ejpam-5827	68	20	issues	issue	NOUN
ejpam-5827	68	21	.	.	PUNCT
ejpam-5827	69	1	for	for	ADP
ejpam-5827	69	2	instance	instance	NOUN
ejpam-5827	69	3	,	,	PUNCT
ejpam-5827	69	4	eliminating	eliminate	VERB
ejpam-5827	69	5	the	the	DET
ejpam-5827	69	6	intersection	intersection	NOUN
ejpam-5827	69	7	condition	condition	NOUN
ejpam-5827	69	8	from	from	ADP
ejpam-5827	69	9	topological	topological	ADJ
ejpam-5827	69	10	rough	rough	ADJ
ejpam-5827	69	11	models	model	NOUN
ejpam-5827	69	12	,	,	PUNCT
ejpam-5827	69	13	as	as	SCONJ
ejpam-5827	69	14	proposed	propose	VERB
ejpam-5827	69	15	in	in	ADP
ejpam-5827	69	16	this	this	DET
ejpam-5827	69	17	approach	approach	NOUN
ejpam-5827	69	18	,	,	PUNCT
ejpam-5827	69	19	broadens	broaden	VERB
ejpam-5827	69	20	the	the	DET
ejpam-5827	69	21	scope	scope	NOUN
ejpam-5827	69	22	of	of	ADP
ejpam-5827	69	23	problems	problem	NOUN
ejpam-5827	69	24	that	that	PRON
ejpam-5827	69	25	can	can	AUX
ejpam-5827	69	26	be	be	AUX
ejpam-5827	69	27	addressed	address	VERB
ejpam-5827	69	28	.	.	PUNCT
ejpam-5827	70	1	secondly	secondly	ADV
ejpam-5827	70	2	,	,	PUNCT
ejpam-5827	70	3	a	a	DET
ejpam-5827	70	4	novel	novel	ADJ
ejpam-5827	70	5	type	type	NOUN
ejpam-5827	70	6	of	of	ADP
ejpam-5827	70	7	approximation	approximation	NOUN
ejpam-5827	70	8	space	space	NOUN
ejpam-5827	70	9	,	,	PUNCT
ejpam-5827	70	10	termed	term	VERB
ejpam-5827	70	11	bi	bi	ADJ
ejpam-5827	70	12	-	-	ADJ
ejpam-5827	70	13	primal	primal	ADJ
ejpam-5827	70	14	approximation	approximation	NOUN
ejpam-5827	70	15	spaces	space	NOUN
ejpam-5827	70	16	,	,	PUNCT
ejpam-5827	70	17	was	be	AUX
ejpam-5827	70	18	introduced	introduce	VERB
ejpam-5827	70	19	for	for	ADP
ejpam-5827	70	20	the	the	DET
ejpam-5827	70	21	first	first	ADJ
ejpam-5827	70	22	time	time	NOUN
ejpam-5827	70	23	.	.	PUNCT
ejpam-5827	71	1	this	this	DET
ejpam-5827	71	2	new	new	ADJ
ejpam-5827	71	3	form	form	NOUN
ejpam-5827	71	4	of	of	ADP
ejpam-5827	71	5	approximation	approximation	NOUN
ejpam-5827	71	6	was	be	AUX
ejpam-5827	71	7	examined	examine	VERB
ejpam-5827	71	8	through	through	ADP
ejpam-5827	71	9	two	two	NUM
ejpam-5827	71	10	distinct	distinct	ADJ
ejpam-5827	71	11	methods	method	NOUN
ejpam-5827	71	12	,	,	PUNCT
ejpam-5827	71	13	with	with	SCONJ
ejpam-5827	71	14	their	their	PRON
ejpam-5827	71	15	properties	property	NOUN
ejpam-5827	71	16	thoroughly	thoroughly	ADV
ejpam-5827	71	17	investigated	investigate	VERB
ejpam-5827	71	18	and	and	CCONJ
ejpam-5827	71	19	the	the	DET
ejpam-5827	71	20	relationship	relationship	NOUN
ejpam-5827	71	21	between	between	ADP
ejpam-5827	71	22	these	these	DET
ejpam-5827	71	23	methods	method	NOUN
ejpam-5827	71	24	explored	explore	VERB
ejpam-5827	71	25	.	.	PUNCT
ejpam-5827	72	1	the	the	DET
ejpam-5827	72	2	importance	importance	NOUN
ejpam-5827	72	3	of	of	ADP
ejpam-5827	72	4	these	these	DET
ejpam-5827	72	5	approaches	approach	NOUN
ejpam-5827	72	6	lies	lie	VERB
ejpam-5827	72	7	in	in	ADP
ejpam-5827	72	8	their	their	PRON
ejpam-5827	72	9	foundation	foundation	NOUN
ejpam-5827	72	10	on	on	ADP
ejpam-5827	72	11	the	the	DET
ejpam-5827	72	12	concept	concept	NOUN
ejpam-5827	72	13	of	of	ADP
ejpam-5827	72	14	primal	primal	NOUN
ejpam-5827	72	15	,	,	PUNCT
ejpam-5827	72	16	which	which	PRON
ejpam-5827	72	17	serve	serve	VERB
ejpam-5827	72	18	as	as	ADP
ejpam-5827	72	19	topological	topological	ADJ
ejpam-5827	72	20	tools	tool	NOUN
ejpam-5827	72	21	;	;	PUNCT
ejpam-5827	72	22	here	here	ADV
ejpam-5827	72	23	,	,	PUNCT
ejpam-5827	72	24	the	the	DET
ejpam-5827	72	25	two	two	NUM
ejpam-5827	72	26	primal	primal	NOUN
ejpam-5827	72	27	represent	represent	VERB
ejpam-5827	72	28	two	two	NUM
ejpam-5827	72	29	distinct	distinct	ADJ
ejpam-5827	72	30	perspectives	perspective	NOUN
ejpam-5827	72	31	rather	rather	ADV
ejpam-5827	72	32	than	than	ADP
ejpam-5827	72	33	a	a	DET
ejpam-5827	72	34	single	single	ADJ
ejpam-5827	72	35	one	one	NUM
ejpam-5827	72	36	.	.	PUNCT
ejpam-5827	73	1	it	it	PRON
ejpam-5827	73	2	should	should	AUX
ejpam-5827	73	3	be	be	AUX
ejpam-5827	73	4	noted	note	VERB
ejpam-5827	73	5	that	that	SCONJ
ejpam-5827	73	6	the	the	DET
ejpam-5827	73	7	two	two	NUM
ejpam-5827	73	8	notions	notion	NOUN
ejpam-5827	73	9	,	,	PUNCT
ejpam-5827	73	10	”	"	PUNCT
ejpam-5827	73	11	ideals	ideal	NOUN
ejpam-5827	73	12	”	"	PUNCT
ejpam-5827	73	13	and	and	CCONJ
ejpam-5827	73	14	”	"	PUNCT
ejpam-5827	73	15	primal	primal	ADJ
ejpam-5827	73	16	,	,	PUNCT
ejpam-5827	73	17	”	"	PUNCT
ejpam-5827	73	18	are	be	AUX
ejpam-5827	73	19	not	not	PART
ejpam-5827	73	20	dual	dual	ADJ
ejpam-5827	73	21	;	;	PUNCT
ejpam-5827	73	22	rather	rather	ADV
ejpam-5827	73	23	,	,	PUNCT
ejpam-5827	73	24	they	they	PRON
ejpam-5827	73	25	are	be	AUX
ejpam-5827	73	26	independent	independent	ADJ
ejpam-5827	73	27	,	,	PUNCT
ejpam-5827	73	28	as	as	SCONJ
ejpam-5827	73	29	illustrated	illustrate	VERB
ejpam-5827	73	30	in	in	ADP
ejpam-5827	73	31	the	the	DET
ejpam-5827	73	32	current	current	ADJ
ejpam-5827	73	33	paper	paper	NOUN
ejpam-5827	73	34	.	.	PUNCT
ejpam-5827	74	1	consequently	consequently	ADV
ejpam-5827	74	2	,	,	PUNCT
ejpam-5827	74	3	the	the	DET
ejpam-5827	74	4	methods	method	NOUN
ejpam-5827	74	5	introduced	introduce	VERB
ejpam-5827	74	6	represent	represent	VERB
ejpam-5827	74	7	new	new	ADJ
ejpam-5827	74	8	tools	tool	NOUN
ejpam-5827	74	9	that	that	PRON
ejpam-5827	74	10	are	be	AUX
ejpam-5827	74	11	entirely	entirely	ADV
ejpam-5827	74	12	distinct	distinct	ADJ
ejpam-5827	74	13	from	from	ADP
ejpam-5827	74	14	those	those	PRON
ejpam-5827	74	15	that	that	PRON
ejpam-5827	74	16	use	use	VERB
ejpam-5827	74	17	ideals	ideal	NOUN
ejpam-5827	74	18	in	in	ADP
ejpam-5827	74	19	their	their	PRON
ejpam-5827	74	20	approaches	approach	NOUN
ejpam-5827	74	21	(	(	PUNCT
ejpam-5827	74	22	such	such	ADJ
ejpam-5827	74	23	as	as	ADP
ejpam-5827	74	24	those	those	PRON
ejpam-5827	74	25	proposed	propose	VERB
ejpam-5827	74	26	by	by	ADP
ejpam-5827	74	27	m.	m.	PROPN
ejpam-5827	74	28	hosny	hosny	PROPN
ejpam-5827	74	29	et	et	PROPN
ejpam-5827	74	30	al.[41	al.[41	PROPN
ejpam-5827	74	31	]	]	PUNCT
ejpam-5827	74	32	)	)	PUNCT
ejpam-5827	74	33	.	.	PUNCT
ejpam-5827	75	1	these	these	DET
ejpam-5827	75	2	methods	method	NOUN
ejpam-5827	75	3	offer	offer	VERB
ejpam-5827	75	4	solutions	solution	NOUN
ejpam-5827	75	5	to	to	ADP
ejpam-5827	75	6	problems	problem	NOUN
ejpam-5827	75	7	that	that	PRON
ejpam-5827	75	8	ideals	ideal	NOUN
ejpam-5827	75	9	(	(	PUNCT
ejpam-5827	75	10	or	or	CCONJ
ejpam-5827	75	11	other	other	ADJ
ejpam-5827	75	12	methods	method	NOUN
ejpam-5827	75	13	)	)	PUNCT
ejpam-5827	75	14	maybe	maybe	ADV
ejpam-5827	75	15	unable	unable	ADJ
ejpam-5827	75	16	to	to	PART
ejpam-5827	75	17	address	address	VERB
ejpam-5827	75	18	,	,	PUNCT
ejpam-5827	75	19	as	as	SCONJ
ejpam-5827	75	20	we	we	PRON
ejpam-5827	75	21	will	will	AUX
ejpam-5827	75	22	illustrate	illustrate	VERB
ejpam-5827	75	23	in	in	ADP
ejpam-5827	75	24	the	the	DET
ejpam-5827	75	25	practical	practical	ADJ
ejpam-5827	75	26	application	application	NOUN
ejpam-5827	75	27	presented	present	VERB
ejpam-5827	75	28	at	at	ADP
ejpam-5827	75	29	the	the	DET
ejpam-5827	75	30	end	end	NOUN
ejpam-5827	75	31	of	of	ADP
ejpam-5827	75	32	the	the	DET
ejpam-5827	75	33	paper	paper	NOUN
ejpam-5827	75	34	.	.	PUNCT
ejpam-5827	76	1	thus	thus	ADV
ejpam-5827	76	2	,	,	PUNCT
ejpam-5827	76	3	we	we	PRON
ejpam-5827	76	4	can	can	AUX
ejpam-5827	76	5	conclude	conclude	VERB
ejpam-5827	76	6	that	that	SCONJ
ejpam-5827	76	7	the	the	DET
ejpam-5827	76	8	methods	method	NOUN
ejpam-5827	76	9	based	base	VERB
ejpam-5827	76	10	on	on	ADP
ejpam-5827	76	11	primal	primal	ADJ
ejpam-5827	76	12	provide	provide	VERB
ejpam-5827	76	13	a	a	DET
ejpam-5827	76	14	different	different	ADJ
ejpam-5827	76	15	perspective	perspective	NOUN
ejpam-5827	76	16	and	and	CCONJ
ejpam-5827	76	17	solutions	solution	NOUN
ejpam-5827	76	18	to	to	ADP
ejpam-5827	76	19	decision	decision	NOUN
ejpam-5827	76	20	-	-	PUNCT
ejpam-5827	76	21	making	make	VERB
ejpam-5827	76	22	problems	problem	NOUN
ejpam-5827	76	23	that	that	PRON
ejpam-5827	76	24	ideals	ideal	NOUN
ejpam-5827	76	25	may	may	AUX
ejpam-5827	76	26	not	not	PART
ejpam-5827	76	27	be	be	AUX
ejpam-5827	76	28	able	able	ADJ
ejpam-5827	76	29	to	to	PART
ejpam-5827	76	30	solve	solve	VERB
ejpam-5827	76	31	,	,	PUNCT
ejpam-5827	76	32	while	while	SCONJ
ejpam-5827	76	33	primal	primal	ADJ
ejpam-5827	76	34	may	may	AUX
ejpam-5827	76	35	also	also	ADV
ejpam-5827	76	36	be	be	AUX
ejpam-5827	76	37	limited	limit	VERB
ejpam-5827	76	38	in	in	ADP
ejpam-5827	76	39	solving	solve	VERB
ejpam-5827	76	40	some	some	DET
ejpam-5827	76	41	problems	problem	NOUN
ejpam-5827	76	42	r.	r.	PROPN
ejpam-5827	76	43	a.	a.	PROPN
ejpam-5827	76	44	hosny	hosny	PROPN
ejpam-5827	76	45	,	,	PUNCT
ejpam-5827	76	46	m.	m.	PROPN
ejpam-5827	76	47	k.	k.	PROPN
ejpam-5827	77	1	el	el	PROPN
ejpam-5827	77	2	-	-	PROPN
ejpam-5827	77	3	bably	bably	ADV
ejpam-5827	77	4	,	,	PUNCT
ejpam-5827	77	5	m.	m.	NOUN
ejpam-5827	77	6	a.	a.	PROPN
ejpam-5827	77	7	el	el	PROPN
ejpam-5827	77	8	-	-	PROPN
ejpam-5827	77	9	gayar	gayar	PROPN
ejpam-5827	77	10	/	/	SYM
ejpam-5827	77	11	eur	eur	PROPN
ejpam-5827	77	12	.	.	PUNCT
ejpam-5827	78	1	j.	j.	PROPN
ejpam-5827	78	2	pure	pure	PROPN
ejpam-5827	78	3	appl	appl	PROPN
ejpam-5827	78	4	.	.	PROPN
ejpam-5827	78	5	math	math	PROPN
ejpam-5827	78	6	,	,	PUNCT
ejpam-5827	78	7	18	18	NUM
ejpam-5827	78	8	(	(	PUNCT
ejpam-5827	78	9	1	1	NUM
ejpam-5827	78	10	)	)	PUNCT
ejpam-5827	78	11	(	(	PUNCT
ejpam-5827	78	12	2025	2025	NUM
ejpam-5827	78	13	)	)	PUNCT
ejpam-5827	78	14	,	,	PUNCT
ejpam-5827	78	15	5827	5827	NUM
ejpam-5827	78	16	4	4	NUM
ejpam-5827	78	17	of	of	ADP
ejpam-5827	78	18	29	29	NUM
ejpam-5827	78	19	that	that	PRON
ejpam-5827	78	20	ideals	ideal	NOUN
ejpam-5827	78	21	can	can	AUX
ejpam-5827	78	22	address	address	VERB
ejpam-5827	78	23	.	.	PUNCT
ejpam-5827	79	1	the	the	DET
ejpam-5827	79	2	current	current	ADJ
ejpam-5827	79	3	framework	framework	NOUN
ejpam-5827	79	4	offers	offer	VERB
ejpam-5827	79	5	the	the	DET
ejpam-5827	79	6	flexibility	flexibility	NOUN
ejpam-5827	79	7	to	to	PART
ejpam-5827	79	8	relax	relax	VERB
ejpam-5827	79	9	constraints	constraint	NOUN
ejpam-5827	79	10	that	that	PRON
ejpam-5827	79	11	typically	typically	ADV
ejpam-5827	79	12	limit	limit	VERB
ejpam-5827	79	13	the	the	DET
ejpam-5827	79	14	scope	scope	NOUN
ejpam-5827	79	15	of	of	ADP
ejpam-5827	79	16	modeling	model	VERB
ejpam-5827	79	17	problems	problem	NOUN
ejpam-5827	79	18	.	.	PUNCT
ejpam-5827	80	1	it	it	PRON
ejpam-5827	80	2	is	be	AUX
ejpam-5827	80	3	widely	widely	ADV
ejpam-5827	80	4	recognized	recognize	VERB
ejpam-5827	80	5	that	that	SCONJ
ejpam-5827	80	6	loosening	loosen	VERB
ejpam-5827	80	7	key	key	ADJ
ejpam-5827	80	8	conditions	condition	NOUN
ejpam-5827	80	9	imposed	impose	VERB
ejpam-5827	80	10	on	on	ADP
ejpam-5827	80	11	a	a	DET
ejpam-5827	80	12	model	model	NOUN
ejpam-5827	80	13	allows	allow	VERB
ejpam-5827	80	14	for	for	ADP
ejpam-5827	80	15	greater	great	ADJ
ejpam-5827	80	16	adaptability	adaptability	NOUN
ejpam-5827	80	17	in	in	ADP
ejpam-5827	80	18	tackling	tackle	VERB
ejpam-5827	80	19	real	real	ADJ
ejpam-5827	80	20	-	-	PUNCT
ejpam-5827	80	21	world	world	NOUN
ejpam-5827	80	22	challenges	challenge	NOUN
ejpam-5827	80	23	.	.	PUNCT
ejpam-5827	81	1	for	for	ADP
ejpam-5827	81	2	example	example	NOUN
ejpam-5827	81	3	,	,	PUNCT
ejpam-5827	81	4	in	in	ADP
ejpam-5827	81	5	the	the	DET
ejpam-5827	81	6	proposed	propose	VERB
ejpam-5827	81	7	model	model	NOUN
ejpam-5827	81	8	,	,	PUNCT
ejpam-5827	81	9	removing	remove	VERB
ejpam-5827	81	10	the	the	DET
ejpam-5827	81	11	requirement	requirement	NOUN
ejpam-5827	81	12	for	for	ADP
ejpam-5827	81	13	intersection	intersection	NOUN
ejpam-5827	81	14	in	in	ADP
ejpam-5827	81	15	topological	topological	ADJ
ejpam-5827	81	16	rough	rough	ADJ
ejpam-5827	81	17	models	model	NOUN
ejpam-5827	81	18	broadens	broaden	VERB
ejpam-5827	81	19	the	the	DET
ejpam-5827	81	20	range	range	NOUN
ejpam-5827	81	21	of	of	ADP
ejpam-5827	81	22	problems	problem	NOUN
ejpam-5827	81	23	that	that	PRON
ejpam-5827	81	24	can	can	AUX
ejpam-5827	81	25	be	be	AUX
ejpam-5827	81	26	addressed	address	VERB
ejpam-5827	81	27	.	.	PUNCT
ejpam-5827	82	1	specifically	specifically	ADV
ejpam-5827	82	2	,	,	PUNCT
ejpam-5827	82	3	generating	generate	VERB
ejpam-5827	82	4	a	a	DET
ejpam-5827	82	5	supra	supra	ADJ
ejpam-5827	82	6	-	-	PUNCT
ejpam-5827	82	7	topological	topological	ADJ
ejpam-5827	82	8	space	space	NOUN
ejpam-5827	82	9	leads	lead	VERB
ejpam-5827	82	10	to	to	ADP
ejpam-5827	82	11	unique	unique	ADJ
ejpam-5827	82	12	outcomes	outcome	NOUN
ejpam-5827	82	13	that	that	PRON
ejpam-5827	82	14	are	be	AUX
ejpam-5827	82	15	especially	especially	ADV
ejpam-5827	82	16	useful	useful	ADJ
ejpam-5827	82	17	in	in	ADP
ejpam-5827	82	18	decision	decision	NOUN
ejpam-5827	82	19	-	-	PUNCT
ejpam-5827	82	20	making	make	VERB
ejpam-5827	82	21	processes	process	NOUN
ejpam-5827	82	22	,	,	PUNCT
ejpam-5827	82	23	such	such	ADJ
ejpam-5827	82	24	as	as	ADP
ejpam-5827	82	25	competitive	competitive	ADJ
ejpam-5827	82	26	job	job	NOUN
ejpam-5827	82	27	selection	selection	NOUN
ejpam-5827	82	28	.	.	PUNCT
ejpam-5827	83	1	in	in	ADP
ejpam-5827	83	2	these	these	DET
ejpam-5827	83	3	scenarios	scenario	NOUN
ejpam-5827	83	4	,	,	PUNCT
ejpam-5827	83	5	candidates	candidate	NOUN
ejpam-5827	83	6	are	be	AUX
ejpam-5827	83	7	usually	usually	ADV
ejpam-5827	83	8	required	require	VERB
ejpam-5827	83	9	to	to	PART
ejpam-5827	83	10	meet	meet	VERB
ejpam-5827	83	11	several	several	ADJ
ejpam-5827	83	12	criteria	criterion	NOUN
ejpam-5827	83	13	.	.	PUNCT
ejpam-5827	84	1	however	however	ADV
ejpam-5827	84	2	,	,	PUNCT
ejpam-5827	84	3	applying	apply	VERB
ejpam-5827	84	4	the	the	DET
ejpam-5827	84	5	concept	concept	NOUN
ejpam-5827	84	6	of	of	ADP
ejpam-5827	84	7	supra	supra	NOUN
ejpam-5827	84	8	-	-	PUNCT
ejpam-5827	84	9	topology	topology	NOUN
ejpam-5827	84	10	helps	help	VERB
ejpam-5827	84	11	to	to	PART
ejpam-5827	84	12	systematically	systematically	ADV
ejpam-5827	84	13	eliminate	eliminate	VERB
ejpam-5827	84	14	redundant	redundant	ADJ
ejpam-5827	84	15	or	or	CCONJ
ejpam-5827	84	16	overlapping	overlap	VERB
ejpam-5827	84	17	criteria	criterion	NOUN
ejpam-5827	84	18	,	,	PUNCT
ejpam-5827	84	19	allowing	allow	VERB
ejpam-5827	84	20	for	for	ADP
ejpam-5827	84	21	a	a	DET
ejpam-5827	84	22	more	more	ADV
ejpam-5827	84	23	focused	focused	ADJ
ejpam-5827	84	24	assessment	assessment	NOUN
ejpam-5827	84	25	of	of	ADP
ejpam-5827	84	26	each	each	DET
ejpam-5827	84	27	candidate	candidate	NOUN
ejpam-5827	84	28	’s	’s	PART
ejpam-5827	84	29	distinct	distinct	ADJ
ejpam-5827	84	30	qualifications	qualification	NOUN
ejpam-5827	84	31	.	.	PUNCT
ejpam-5827	85	1	this	this	DET
ejpam-5827	85	2	refined	refined	ADJ
ejpam-5827	85	3	approach	approach	NOUN
ejpam-5827	85	4	reduces	reduce	VERB
ejpam-5827	85	5	the	the	DET
ejpam-5827	85	6	uncertainty	uncertainty	NOUN
ejpam-5827	85	7	involved	involve	VERB
ejpam-5827	85	8	in	in	ADP
ejpam-5827	85	9	making	make	VERB
ejpam-5827	85	10	final	final	ADJ
ejpam-5827	85	11	decisions	decision	NOUN
ejpam-5827	85	12	by	by	ADP
ejpam-5827	85	13	concentrating	concentrate	VERB
ejpam-5827	85	14	on	on	ADP
ejpam-5827	85	15	the	the	DET
ejpam-5827	85	16	most	most	ADV
ejpam-5827	85	17	relevant	relevant	ADJ
ejpam-5827	85	18	attributes	attribute	NOUN
ejpam-5827	85	19	for	for	ADP
ejpam-5827	85	20	the	the	DET
ejpam-5827	85	21	role	role	NOUN
ejpam-5827	85	22	,	,	PUNCT
ejpam-5827	85	23	thereby	thereby	ADV
ejpam-5827	85	24	simplifying	simplify	VERB
ejpam-5827	85	25	the	the	DET
ejpam-5827	85	26	selection	selection	NOUN
ejpam-5827	85	27	process	process	NOUN
ejpam-5827	85	28	.	.	PUNCT
ejpam-5827	86	1	the	the	DET
ejpam-5827	86	2	paper	paper	NOUN
ejpam-5827	86	3	concludes	conclude	VERB
ejpam-5827	86	4	with	with	ADP
ejpam-5827	86	5	a	a	DET
ejpam-5827	86	6	practical	practical	ADJ
ejpam-5827	86	7	example	example	NOUN
ejpam-5827	86	8	that	that	SCONJ
ejpam-5827	86	9	productively	productively	ADV
ejpam-5827	86	10	illustrates	illustrate	VERB
ejpam-5827	86	11	the	the	DET
ejpam-5827	86	12	definitions	definition	NOUN
ejpam-5827	86	13	in	in	ADP
ejpam-5827	86	14	a	a	DET
ejpam-5827	86	15	clear	clear	ADJ
ejpam-5827	86	16	and	and	CCONJ
ejpam-5827	86	17	comprehensive	comprehensive	ADJ
ejpam-5827	86	18	way	way	NOUN
ejpam-5827	86	19	.	.	PUNCT
ejpam-5827	87	1	•	•	NOUN
ejpam-5827	87	2	objectives	objective	NOUN
ejpam-5827	87	3	:	:	PUNCT
ejpam-5827	87	4	the	the	DET
ejpam-5827	87	5	main	main	ADJ
ejpam-5827	87	6	objective	objective	NOUN
ejpam-5827	87	7	of	of	ADP
ejpam-5827	87	8	this	this	DET
ejpam-5827	87	9	research	research	NOUN
ejpam-5827	87	10	is	be	AUX
ejpam-5827	87	11	developing	develop	VERB
ejpam-5827	87	12	a	a	DET
ejpam-5827	87	13	novel	novel	ADJ
ejpam-5827	87	14	framework	framework	NOUN
ejpam-5827	87	15	for	for	ADP
ejpam-5827	87	16	approximate	approximate	ADJ
ejpam-5827	87	17	rough	rough	ADJ
ejpam-5827	87	18	sets	set	NOUN
ejpam-5827	87	19	by	by	ADP
ejpam-5827	87	20	introducing	introduce	VERB
ejpam-5827	87	21	and	and	CCONJ
ejpam-5827	87	22	employing	employ	VERB
ejpam-5827	87	23	the	the	DET
ejpam-5827	87	24	concept	concept	NOUN
ejpam-5827	87	25	of	of	ADP
ejpam-5827	87	26	”	"	PUNCT
ejpam-5827	87	27	primal	primal	ADJ
ejpam-5827	87	28	.	.	PUNCT
ejpam-5827	87	29	”	"	PUNCT
ejpam-5827	88	1	this	this	DET
ejpam-5827	88	2	study	study	NOUN
ejpam-5827	88	3	aims	aim	VERB
ejpam-5827	88	4	to	to	PART
ejpam-5827	88	5	extend	extend	VERB
ejpam-5827	88	6	and	and	CCONJ
ejpam-5827	88	7	refine	refine	VERB
ejpam-5827	88	8	existing	exist	VERB
ejpam-5827	88	9	rough	rough	ADJ
ejpam-5827	88	10	set	set	NOUN
ejpam-5827	88	11	theory	theory	NOUN
ejpam-5827	88	12	by	by	ADP
ejpam-5827	88	13	incorporating	incorporate	VERB
ejpam-5827	88	14	these	these	DET
ejpam-5827	88	15	new	new	ADJ
ejpam-5827	88	16	structures	structure	NOUN
ejpam-5827	88	17	,	,	PUNCT
ejpam-5827	88	18	focusing	focus	VERB
ejpam-5827	88	19	on	on	ADP
ejpam-5827	88	20	enhancing	enhance	VERB
ejpam-5827	88	21	the	the	DET
ejpam-5827	88	22	flexibility	flexibility	NOUN
ejpam-5827	88	23	and	and	CCONJ
ejpam-5827	88	24	applicability	applicability	NOUN
ejpam-5827	88	25	of	of	ADP
ejpam-5827	88	26	rough	rough	ADJ
ejpam-5827	88	27	set	set	NOUN
ejpam-5827	88	28	models	model	NOUN
ejpam-5827	88	29	in	in	ADP
ejpam-5827	88	30	various	various	ADJ
ejpam-5827	88	31	domains	domain	NOUN
ejpam-5827	88	32	.	.	PUNCT
ejpam-5827	89	1	in	in	ADP
ejpam-5827	89	2	short	short	ADJ
ejpam-5827	89	3	,	,	PUNCT
ejpam-5827	89	4	the	the	DET
ejpam-5827	89	5	research	research	NOUN
ejpam-5827	89	6	seeks	seek	VERB
ejpam-5827	89	7	to	to	PART
ejpam-5827	89	8	achieve	achieve	VERB
ejpam-5827	89	9	the	the	DET
ejpam-5827	89	10	following	following	NOUN
ejpam-5827	89	11	:	:	PUNCT
ejpam-5827	89	12	1	1	X
ejpam-5827	89	13	.	.	X
ejpam-5827	89	14	defining	define	VERB
ejpam-5827	89	15	a	a	DET
ejpam-5827	89	16	new	new	ADJ
ejpam-5827	89	17	method	method	NOUN
ejpam-5827	89	18	for	for	ADP
ejpam-5827	89	19	generating	generate	VERB
ejpam-5827	89	20	rough	rough	ADJ
ejpam-5827	89	21	approximations	approximation	NOUN
ejpam-5827	89	22	using	use	VERB
ejpam-5827	89	23	κ	κ	NOUN
ejpam-5827	89	24	-	-	PUNCT
ejpam-5827	89	25	neighborhoods	neighborhood	NOUN
ejpam-5827	89	26	and	and	CCONJ
ejpam-5827	89	27	primals	primal	NOUN
ejpam-5827	89	28	,	,	PUNCT
ejpam-5827	89	29	thereby	thereby	ADV
ejpam-5827	89	30	inducing	induce	VERB
ejpam-5827	89	31	diverse	diverse	ADJ
ejpam-5827	89	32	supra	supra	NOUN
ejpam-5827	89	33	-	-	PUNCT
ejpam-5827	89	34	topologies	topology	NOUN
ejpam-5827	89	35	.	.	PUNCT
ejpam-5827	90	1	2	2	X
ejpam-5827	90	2	.	.	X
ejpam-5827	90	3	introducing	introduce	VERB
ejpam-5827	90	4	and	and	CCONJ
ejpam-5827	90	5	thoroughly	thoroughly	ADV
ejpam-5827	90	6	investigating	investigate	VERB
ejpam-5827	90	7	a	a	DET
ejpam-5827	90	8	new	new	ADJ
ejpam-5827	90	9	type	type	NOUN
ejpam-5827	90	10	of	of	ADP
ejpam-5827	90	11	approximation	approximation	NOUN
ejpam-5827	90	12	space	space	NOUN
ejpam-5827	90	13	called	call	VERB
ejpam-5827	90	14	bi	bi	ADJ
ejpam-5827	90	15	-	-	ADJ
ejpam-5827	90	16	primal	primal	ADJ
ejpam-5827	90	17	approximation	approximation	NOUN
ejpam-5827	90	18	spaces	space	NOUN
ejpam-5827	90	19	,	,	PUNCT
ejpam-5827	90	20	exploring	explore	VERB
ejpam-5827	90	21	the	the	DET
ejpam-5827	90	22	distinct	distinct	ADJ
ejpam-5827	90	23	methods	method	NOUN
ejpam-5827	90	24	and	and	CCONJ
ejpam-5827	90	25	properties	property	NOUN
ejpam-5827	90	26	of	of	ADP
ejpam-5827	90	27	this	this	DET
ejpam-5827	90	28	approach	approach	NOUN
ejpam-5827	90	29	.	.	PUNCT
ejpam-5827	91	1	3	3	X
ejpam-5827	91	2	.	.	X
ejpam-5827	91	3	demonstrating	demonstrate	VERB
ejpam-5827	91	4	the	the	DET
ejpam-5827	91	5	practical	practical	ADJ
ejpam-5827	91	6	applications	application	NOUN
ejpam-5827	91	7	of	of	ADP
ejpam-5827	91	8	these	these	DET
ejpam-5827	91	9	new	new	ADJ
ejpam-5827	91	10	methods	method	NOUN
ejpam-5827	91	11	in	in	ADP
ejpam-5827	91	12	solving	solve	VERB
ejpam-5827	91	13	decisionmaking	decisionmake	VERB
ejpam-5827	91	14	problems	problem	NOUN
ejpam-5827	91	15	that	that	PRON
ejpam-5827	91	16	are	be	AUX
ejpam-5827	91	17	challenging	challenge	VERB
ejpam-5827	91	18	or	or	CCONJ
ejpam-5827	91	19	impossible	impossible	ADJ
ejpam-5827	91	20	to	to	PART
ejpam-5827	91	21	address	address	VERB
ejpam-5827	91	22	by	by	ADP
ejpam-5827	91	23	using	use	VERB
ejpam-5827	91	24	existing	exist	VERB
ejpam-5827	91	25	approaches	approach	NOUN
ejpam-5827	91	26	,	,	PUNCT
ejpam-5827	91	27	such	such	ADJ
ejpam-5827	91	28	as	as	ADP
ejpam-5827	91	29	those	those	PRON
ejpam-5827	91	30	based	base	VERB
ejpam-5827	91	31	on	on	ADP
ejpam-5827	91	32	ideals	ideal	NOUN
ejpam-5827	91	33	.	.	PUNCT
ejpam-5827	92	1	•	•	NUM
ejpam-5827	92	2	motivations	motivation	NOUN
ejpam-5827	92	3	:	:	PUNCT
ejpam-5827	92	4	the	the	DET
ejpam-5827	92	5	motivation	motivation	NOUN
ejpam-5827	92	6	that	that	PRON
ejpam-5827	92	7	drives	drive	VERB
ejpam-5827	92	8	us	we	PRON
ejpam-5827	92	9	to	to	ADP
ejpam-5827	92	10	doing	do	VERB
ejpam-5827	92	11	this	this	DET
ejpam-5827	92	12	research	research	NOUN
ejpam-5827	92	13	arises	arise	VERB
ejpam-5827	92	14	from	from	ADP
ejpam-5827	92	15	the	the	DET
ejpam-5827	92	16	drawbacks	drawback	NOUN
ejpam-5827	92	17	of	of	ADP
ejpam-5827	92	18	the	the	DET
ejpam-5827	92	19	existing	exist	VERB
ejpam-5827	92	20	mathematical	mathematical	ADJ
ejpam-5827	92	21	methods	method	NOUN
ejpam-5827	92	22	in	in	ADP
ejpam-5827	92	23	effectively	effectively	ADV
ejpam-5827	92	24	dealing	deal	VERB
ejpam-5827	92	25	with	with	ADP
ejpam-5827	92	26	the	the	DET
ejpam-5827	92	27	vagueness	vagueness	NOUN
ejpam-5827	92	28	and	and	CCONJ
ejpam-5827	92	29	imprecision	imprecision	NOUN
ejpam-5827	92	30	inherent	inherent	ADJ
ejpam-5827	92	31	in	in	ADP
ejpam-5827	92	32	real	real	ADJ
ejpam-5827	92	33	-	-	PUNCT
ejpam-5827	92	34	world	world	NOUN
ejpam-5827	92	35	problems	problem	NOUN
ejpam-5827	92	36	.	.	PUNCT
ejpam-5827	93	1	while	while	SCONJ
ejpam-5827	93	2	classical	classical	ADJ
ejpam-5827	93	3	rough	rough	ADJ
ejpam-5827	93	4	set	set	NOUN
ejpam-5827	93	5	theory	theory	NOUN
ejpam-5827	93	6	and	and	CCONJ
ejpam-5827	93	7	its	its	PRON
ejpam-5827	93	8	various	various	ADJ
ejpam-5827	93	9	extensions	extension	NOUN
ejpam-5827	93	10	have	have	AUX
ejpam-5827	93	11	made	make	VERB
ejpam-5827	93	12	significant	significant	ADJ
ejpam-5827	93	13	strides	stride	NOUN
ejpam-5827	93	14	,	,	PUNCT
ejpam-5827	93	15	they	they	PRON
ejpam-5827	93	16	still	still	ADV
ejpam-5827	93	17	face	face	VERB
ejpam-5827	93	18	challenges	challenge	NOUN
ejpam-5827	93	19	in	in	ADP
ejpam-5827	93	20	certain	certain	ADJ
ejpam-5827	93	21	applications	application	NOUN
ejpam-5827	93	22	owing	owe	VERB
ejpam-5827	93	23	to	to	ADP
ejpam-5827	93	24	the	the	DET
ejpam-5827	93	25	restrictive	restrictive	ADJ
ejpam-5827	93	26	conditions	condition	NOUN
ejpam-5827	93	27	imposed	impose	VERB
ejpam-5827	93	28	by	by	ADP
ejpam-5827	93	29	traditional	traditional	ADJ
ejpam-5827	93	30	topological	topological	ADJ
ejpam-5827	93	31	and	and	CCONJ
ejpam-5827	93	32	set	set	ADJ
ejpam-5827	93	33	-	-	PUNCT
ejpam-5827	93	34	theoretical	theoretical	ADJ
ejpam-5827	93	35	constructs	construct	NOUN
ejpam-5827	93	36	.	.	PUNCT
ejpam-5827	94	1	the	the	DET
ejpam-5827	94	2	introduction	introduction	NOUN
ejpam-5827	94	3	of	of	ADP
ejpam-5827	94	4	primal	primal	ADJ
ejpam-5827	94	5	and	and	CCONJ
ejpam-5827	94	6	bi	bi	ADJ
ejpam-5827	94	7	-	-	ADJ
ejpam-5827	94	8	primal	primal	ADJ
ejpam-5827	94	9	approximation	approximation	NOUN
ejpam-5827	94	10	spaces	space	NOUN
ejpam-5827	94	11	offers	offer	VERB
ejpam-5827	94	12	a	a	DET
ejpam-5827	94	13	response	response	NOUN
ejpam-5827	94	14	to	to	ADP
ejpam-5827	94	15	these	these	DET
ejpam-5827	94	16	challenges	challenge	NOUN
ejpam-5827	94	17	,	,	PUNCT
ejpam-5827	94	18	offering	offer	VERB
ejpam-5827	94	19	a	a	DET
ejpam-5827	94	20	more	more	ADV
ejpam-5827	94	21	versatile	versatile	ADJ
ejpam-5827	94	22	and	and	CCONJ
ejpam-5827	94	23	adaptable	adaptable	ADJ
ejpam-5827	94	24	framework	framework	NOUN
ejpam-5827	94	25	.	.	PUNCT
ejpam-5827	95	1	this	this	DET
ejpam-5827	95	2	approach	approach	NOUN
ejpam-5827	95	3	is	be	AUX
ejpam-5827	95	4	motivated	motivate	VERB
ejpam-5827	95	5	by	by	ADP
ejpam-5827	95	6	the	the	DET
ejpam-5827	95	7	need	need	NOUN
ejpam-5827	95	8	to	to	PART
ejpam-5827	95	9	:	:	PUNCT
ejpam-5827	95	10	1	1	X
ejpam-5827	95	11	.	.	X
ejpam-5827	95	12	overcome	overcome	VERB
ejpam-5827	95	13	the	the	DET
ejpam-5827	95	14	drawbacks	drawback	NOUN
ejpam-5827	95	15	of	of	ADP
ejpam-5827	95	16	existing	exist	VERB
ejpam-5827	95	17	rough	rough	ADJ
ejpam-5827	95	18	set	set	NOUN
ejpam-5827	95	19	models	model	NOUN
ejpam-5827	95	20	,	,	PUNCT
ejpam-5827	95	21	especially	especially	ADV
ejpam-5827	95	22	those	those	PRON
ejpam-5827	95	23	that	that	PRON
ejpam-5827	95	24	rely	rely	VERB
ejpam-5827	95	25	on	on	ADP
ejpam-5827	95	26	rigid	rigid	ADJ
ejpam-5827	95	27	conditions	condition	NOUN
ejpam-5827	95	28	such	such	ADJ
ejpam-5827	95	29	as	as	ADP
ejpam-5827	95	30	the	the	DET
ejpam-5827	95	31	finite	finite	ADJ
ejpam-5827	95	32	intersection	intersection	NOUN
ejpam-5827	95	33	condition	condition	NOUN
ejpam-5827	95	34	in	in	ADP
ejpam-5827	95	35	topologies	topology	NOUN
ejpam-5827	95	36	.	.	PUNCT
ejpam-5827	96	1	2	2	X
ejpam-5827	96	2	.	.	X
ejpam-5827	96	3	provide	provide	VERB
ejpam-5827	96	4	new	new	ADJ
ejpam-5827	96	5	methods	method	NOUN
ejpam-5827	96	6	which	which	PRON
ejpam-5827	96	7	allow	allow	VERB
ejpam-5827	96	8	for	for	ADP
ejpam-5827	96	9	greater	great	ADJ
ejpam-5827	96	10	flexibility	flexibility	NOUN
ejpam-5827	96	11	in	in	ADP
ejpam-5827	96	12	modeling	modeling	NOUN
ejpam-5827	96	13	and	and	CCONJ
ejpam-5827	96	14	analyzing	analyze	VERB
ejpam-5827	96	15	r.	r.	PROPN
ejpam-5827	96	16	a.	a.	PROPN
ejpam-5827	96	17	hosny	hosny	PROPN
ejpam-5827	96	18	,	,	PUNCT
ejpam-5827	96	19	m.	m.	PROPN
ejpam-5827	96	20	k.	k.	PROPN
ejpam-5827	97	1	el	el	PROPN
ejpam-5827	97	2	-	-	PROPN
ejpam-5827	97	3	bably	bably	ADV
ejpam-5827	97	4	,	,	PUNCT
ejpam-5827	97	5	m.	m.	NOUN
ejpam-5827	97	6	a.	a.	PROPN
ejpam-5827	97	7	el	el	PROPN
ejpam-5827	97	8	-	-	PROPN
ejpam-5827	97	9	gayar	gayar	PROPN
ejpam-5827	97	10	/	/	SYM
ejpam-5827	97	11	eur	eur	PROPN
ejpam-5827	97	12	.	.	PUNCT
ejpam-5827	98	1	j.	j.	PROPN
ejpam-5827	98	2	pure	pure	PROPN
ejpam-5827	98	3	appl	appl	PROPN
ejpam-5827	98	4	.	.	PROPN
ejpam-5827	98	5	math	math	PROPN
ejpam-5827	98	6	,	,	PUNCT
ejpam-5827	98	7	18	18	NUM
ejpam-5827	98	8	(	(	PUNCT
ejpam-5827	98	9	1	1	NUM
ejpam-5827	98	10	)	)	PUNCT
ejpam-5827	98	11	(	(	PUNCT
ejpam-5827	98	12	2025	2025	NUM
ejpam-5827	98	13	)	)	PUNCT
ejpam-5827	98	14	,	,	PUNCT
ejpam-5827	98	15	5827	5827	NUM
ejpam-5827	98	16	5	5	NUM
ejpam-5827	98	17	of	of	ADP
ejpam-5827	98	18	29	29	NUM
ejpam-5827	98	19	complex	complex	ADJ
ejpam-5827	98	20	systems	system	NOUN
ejpam-5827	98	21	,	,	PUNCT
ejpam-5827	98	22	especially	especially	ADV
ejpam-5827	98	23	in	in	ADP
ejpam-5827	98	24	fields	field	NOUN
ejpam-5827	98	25	where	where	SCONJ
ejpam-5827	98	26	traditional	traditional	ADJ
ejpam-5827	98	27	methods	method	NOUN
ejpam-5827	98	28	fall	fall	VERB
ejpam-5827	98	29	short	short	ADJ
ejpam-5827	98	30	.	.	PUNCT
ejpam-5827	99	1	3	3	X
ejpam-5827	99	2	.	.	X
ejpam-5827	99	3	explore	explore	VERB
ejpam-5827	99	4	the	the	DET
ejpam-5827	99	5	potential	potential	NOUN
ejpam-5827	99	6	of	of	ADP
ejpam-5827	99	7	topological	topological	ADJ
ejpam-5827	99	8	structures	structure	NOUN
ejpam-5827	99	9	like	like	ADP
ejpam-5827	99	10	primal	primal	ADJ
ejpam-5827	99	11	in	in	ADP
ejpam-5827	99	12	broadening	broaden	VERB
ejpam-5827	99	13	the	the	DET
ejpam-5827	99	14	scope	scope	NOUN
ejpam-5827	99	15	of	of	ADP
ejpam-5827	99	16	rough	rough	ADJ
ejpam-5827	99	17	set	set	NOUN
ejpam-5827	99	18	theory	theory	NOUN
ejpam-5827	99	19	and	and	CCONJ
ejpam-5827	99	20	its	its	PRON
ejpam-5827	99	21	applications	application	NOUN
ejpam-5827	99	22	across	across	ADP
ejpam-5827	99	23	various	various	ADJ
ejpam-5827	99	24	disciplines	discipline	NOUN
ejpam-5827	99	25	,	,	PUNCT
ejpam-5827	99	26	including	include	VERB
ejpam-5827	99	27	artificial	artificial	ADJ
ejpam-5827	99	28	intelligence	intelligence	NOUN
ejpam-5827	99	29	,	,	PUNCT
ejpam-5827	99	30	engineering	engineering	NOUN
ejpam-5827	99	31	,	,	PUNCT
ejpam-5827	99	32	and	and	CCONJ
ejpam-5827	99	33	medical	medical	ADJ
ejpam-5827	99	34	science	science	NOUN
ejpam-5827	99	35	.	.	PUNCT
ejpam-5827	100	1	•	•	NUM
ejpam-5827	100	2	contributions	contribution	NOUN
ejpam-5827	100	3	:	:	PUNCT
ejpam-5827	100	4	this	this	DET
ejpam-5827	100	5	paper	paper	NOUN
ejpam-5827	100	6	makes	make	VERB
ejpam-5827	100	7	several	several	ADJ
ejpam-5827	100	8	significant	significant	ADJ
ejpam-5827	100	9	contributions	contribution	NOUN
ejpam-5827	100	10	to	to	ADP
ejpam-5827	100	11	the	the	DET
ejpam-5827	100	12	field	field	NOUN
ejpam-5827	100	13	of	of	ADP
ejpam-5827	100	14	rough	rough	ADJ
ejpam-5827	100	15	set	set	NOUN
ejpam-5827	100	16	theory	theory	NOUN
ejpam-5827	100	17	and	and	CCONJ
ejpam-5827	100	18	its	its	PRON
ejpam-5827	100	19	applications	application	NOUN
ejpam-5827	100	20	:	:	PUNCT
ejpam-5827	100	21	1	1	X
ejpam-5827	100	22	.	.	X
ejpam-5827	100	23	introduction	introduction	NOUN
ejpam-5827	100	24	of	of	ADP
ejpam-5827	100	25	primal	primal	ADJ
ejpam-5827	100	26	:	:	PUNCT
ejpam-5827	100	27	the	the	DET
ejpam-5827	100	28	concept	concept	NOUN
ejpam-5827	100	29	of	of	ADP
ejpam-5827	100	30	primal	primal	ADJ
ejpam-5827	100	31	is	be	AUX
ejpam-5827	100	32	introduced	introduce	VERB
ejpam-5827	100	33	as	as	ADP
ejpam-5827	100	34	a	a	DET
ejpam-5827	100	35	novel	novel	ADJ
ejpam-5827	100	36	structure	structure	NOUN
ejpam-5827	100	37	in	in	ADP
ejpam-5827	100	38	rough	rough	ADJ
ejpam-5827	100	39	set	set	NOUN
ejpam-5827	100	40	theory	theory	NOUN
ejpam-5827	100	41	,	,	PUNCT
ejpam-5827	100	42	providing	provide	VERB
ejpam-5827	100	43	a	a	DET
ejpam-5827	100	44	new	new	ADJ
ejpam-5827	100	45	method	method	NOUN
ejpam-5827	100	46	for	for	ADP
ejpam-5827	100	47	generating	generate	VERB
ejpam-5827	100	48	rough	rough	ADJ
ejpam-5827	100	49	approximations	approximation	NOUN
ejpam-5827	100	50	through	through	ADP
ejpam-5827	100	51	κneighborhoods	κneighborhood	NOUN
ejpam-5827	100	52	and	and	CCONJ
ejpam-5827	100	53	primal	primal	ADJ
ejpam-5827	100	54	.	.	PUNCT
ejpam-5827	101	1	this	this	DET
ejpam-5827	101	2	contribution	contribution	NOUN
ejpam-5827	101	3	widens	widen	VERB
ejpam-5827	101	4	the	the	DET
ejpam-5827	101	5	theoretical	theoretical	ADJ
ejpam-5827	101	6	foundations	foundation	NOUN
ejpam-5827	101	7	of	of	ADP
ejpam-5827	101	8	rough	rough	ADJ
ejpam-5827	101	9	set	set	NOUN
ejpam-5827	101	10	models	model	NOUN
ejpam-5827	101	11	and	and	CCONJ
ejpam-5827	101	12	opens	open	VERB
ejpam-5827	101	13	up	up	ADP
ejpam-5827	101	14	further	further	ADJ
ejpam-5827	101	15	avenues	avenue	NOUN
ejpam-5827	101	16	for	for	ADP
ejpam-5827	101	17	topological	topological	ADJ
ejpam-5827	101	18	applications	application	NOUN
ejpam-5827	101	19	.	.	PUNCT
ejpam-5827	102	1	2	2	X
ejpam-5827	102	2	.	.	X
ejpam-5827	102	3	development	development	NOUN
ejpam-5827	102	4	of	of	ADP
ejpam-5827	102	5	bi	bi	ADJ
ejpam-5827	102	6	-	-	ADJ
ejpam-5827	102	7	primal	primal	ADJ
ejpam-5827	102	8	approximation	approximation	NOUN
ejpam-5827	102	9	spaces	space	VERB
ejpam-5827	102	10	:	:	PUNCT
ejpam-5827	102	11	the	the	DET
ejpam-5827	102	12	research	research	NOUN
ejpam-5827	102	13	presents	present	VERB
ejpam-5827	102	14	the	the	DET
ejpam-5827	102	15	first	first	ADJ
ejpam-5827	102	16	-	-	PUNCT
ejpam-5827	102	17	ever	ever	ADV
ejpam-5827	102	18	introduction	introduction	NOUN
ejpam-5827	102	19	of	of	ADP
ejpam-5827	102	20	bi	bi	ADJ
ejpam-5827	102	21	-	-	ADJ
ejpam-5827	102	22	primal	primal	ADJ
ejpam-5827	102	23	approximation	approximation	NOUN
ejpam-5827	102	24	spaces	space	NOUN
ejpam-5827	102	25	,	,	PUNCT
ejpam-5827	102	26	offering	offer	VERB
ejpam-5827	102	27	two	two	NUM
ejpam-5827	102	28	distinct	distinct	ADJ
ejpam-5827	102	29	ways	way	NOUN
ejpam-5827	102	30	for	for	ADP
ejpam-5827	102	31	their	their	PRON
ejpam-5827	102	32	construction	construction	NOUN
ejpam-5827	102	33	and	and	CCONJ
ejpam-5827	102	34	examining	examine	VERB
ejpam-5827	102	35	their	their	PRON
ejpam-5827	102	36	properties	property	NOUN
ejpam-5827	102	37	and	and	CCONJ
ejpam-5827	102	38	relationships	relationship	NOUN
ejpam-5827	102	39	.	.	PUNCT
ejpam-5827	103	1	this	this	DET
ejpam-5827	103	2	contribution	contribution	NOUN
ejpam-5827	103	3	provides	provide	VERB
ejpam-5827	103	4	a	a	DET
ejpam-5827	103	5	new	new	ADJ
ejpam-5827	103	6	perspective	perspective	NOUN
ejpam-5827	103	7	on	on	ADP
ejpam-5827	103	8	approximation	approximation	NOUN
ejpam-5827	103	9	spaces	space	NOUN
ejpam-5827	103	10	and	and	CCONJ
ejpam-5827	103	11	enriches	enrich	VERB
ejpam-5827	103	12	the	the	DET
ejpam-5827	103	13	toolbox	toolbox	NOUN
ejpam-5827	103	14	for	for	ADP
ejpam-5827	103	15	dealing	deal	VERB
ejpam-5827	103	16	with	with	ADP
ejpam-5827	103	17	uncertainty	uncertainty	NOUN
ejpam-5827	103	18	and	and	CCONJ
ejpam-5827	103	19	imprecision	imprecision	NOUN
ejpam-5827	103	20	in	in	ADP
ejpam-5827	103	21	data	datum	NOUN
ejpam-5827	103	22	.	.	PUNCT
ejpam-5827	104	1	3	3	X
ejpam-5827	104	2	.	.	NOUN
ejpam-5827	104	3	practical	practical	ADJ
ejpam-5827	104	4	applications	application	NOUN
ejpam-5827	104	5	and	and	CCONJ
ejpam-5827	104	6	case	case	NOUN
ejpam-5827	104	7	study	study	NOUN
ejpam-5827	104	8	:	:	PUNCT
ejpam-5827	104	9	the	the	DET
ejpam-5827	104	10	paper	paper	NOUN
ejpam-5827	104	11	includes	include	VERB
ejpam-5827	104	12	a	a	DET
ejpam-5827	104	13	practical	practical	ADJ
ejpam-5827	104	14	example	example	NOUN
ejpam-5827	104	15	demonstrating	demonstrate	VERB
ejpam-5827	104	16	the	the	DET
ejpam-5827	104	17	applicability	applicability	NOUN
ejpam-5827	104	18	and	and	CCONJ
ejpam-5827	104	19	effectiveness	effectiveness	NOUN
ejpam-5827	104	20	of	of	ADP
ejpam-5827	104	21	the	the	DET
ejpam-5827	104	22	proposed	propose	VERB
ejpam-5827	104	23	methods	method	NOUN
ejpam-5827	104	24	in	in	ADP
ejpam-5827	104	25	solving	solve	VERB
ejpam-5827	104	26	decision	decision	NOUN
ejpam-5827	104	27	-	-	PUNCT
ejpam-5827	104	28	making	make	VERB
ejpam-5827	104	29	problems	problem	NOUN
ejpam-5827	104	30	.	.	PUNCT
ejpam-5827	105	1	this	this	DET
ejpam-5827	105	2	contribution	contribution	NOUN
ejpam-5827	105	3	highlights	highlight	VERB
ejpam-5827	105	4	the	the	DET
ejpam-5827	105	5	practical	practical	ADJ
ejpam-5827	105	6	value	value	NOUN
ejpam-5827	105	7	of	of	ADP
ejpam-5827	105	8	the	the	DET
ejpam-5827	105	9	research	research	NOUN
ejpam-5827	105	10	and	and	CCONJ
ejpam-5827	105	11	its	its	PRON
ejpam-5827	105	12	potential	potential	ADJ
ejpam-5827	105	13	impact	impact	NOUN
ejpam-5827	105	14	on	on	ADP
ejpam-5827	105	15	various	various	ADJ
ejpam-5827	105	16	real	real	ADJ
ejpam-5827	105	17	-	-	PUNCT
ejpam-5827	105	18	world	world	NOUN
ejpam-5827	105	19	applications	application	NOUN
ejpam-5827	105	20	.	.	PUNCT
ejpam-5827	106	1	4	4	X
ejpam-5827	106	2	.	.	X
ejpam-5827	106	3	comparison	comparison	NOUN
ejpam-5827	106	4	with	with	ADP
ejpam-5827	106	5	existing	exist	VERB
ejpam-5827	106	6	methods	method	NOUN
ejpam-5827	106	7	:	:	PUNCT
ejpam-5827	106	8	the	the	DET
ejpam-5827	106	9	research	research	NOUN
ejpam-5827	106	10	provides	provide	VERB
ejpam-5827	106	11	a	a	DET
ejpam-5827	106	12	detailed	detailed	ADJ
ejpam-5827	106	13	comparison	comparison	NOUN
ejpam-5827	106	14	between	between	ADP
ejpam-5827	106	15	the	the	DET
ejpam-5827	106	16	newly	newly	ADV
ejpam-5827	106	17	introduced	introduce	VERB
ejpam-5827	106	18	methods	method	NOUN
ejpam-5827	106	19	and	and	CCONJ
ejpam-5827	106	20	existing	exist	VERB
ejpam-5827	106	21	approaches	approach	NOUN
ejpam-5827	106	22	based	base	VERB
ejpam-5827	106	23	on	on	ADP
ejpam-5827	106	24	ideals	ideal	NOUN
ejpam-5827	106	25	,	,	PUNCT
ejpam-5827	106	26	illustrating	illustrate	VERB
ejpam-5827	106	27	the	the	DET
ejpam-5827	106	28	unique	unique	ADJ
ejpam-5827	106	29	advantages	advantage	NOUN
ejpam-5827	106	30	and	and	CCONJ
ejpam-5827	106	31	limitations	limitation	NOUN
ejpam-5827	106	32	of	of	ADP
ejpam-5827	106	33	each	each	PRON
ejpam-5827	106	34	.	.	PUNCT
ejpam-5827	107	1	this	this	DET
ejpam-5827	107	2	contribution	contribution	NOUN
ejpam-5827	107	3	helps	help	VERB
ejpam-5827	107	4	to	to	PART
ejpam-5827	107	5	clarify	clarify	VERB
ejpam-5827	107	6	the	the	DET
ejpam-5827	107	7	distinctiveness	distinctiveness	NOUN
ejpam-5827	107	8	and	and	CCONJ
ejpam-5827	107	9	utility	utility	NOUN
ejpam-5827	107	10	of	of	ADP
ejpam-5827	107	11	the	the	DET
ejpam-5827	107	12	primal	primal	NOUN
ejpam-5827	107	13	-	-	PUNCT
ejpam-5827	107	14	based	base	VERB
ejpam-5827	107	15	methods	method	NOUN
ejpam-5827	107	16	in	in	ADP
ejpam-5827	107	17	different	different	ADJ
ejpam-5827	107	18	contexts	contexts	NOUN
ejpam-5827	107	19	.	.	PUNCT
ejpam-5827	108	1	2	2	X
ejpam-5827	108	2	.	.	X
ejpam-5827	108	3	fundamental	fundamental	ADJ
ejpam-5827	108	4	ideas	idea	NOUN
ejpam-5827	108	5	this	this	DET
ejpam-5827	108	6	part	part	NOUN
ejpam-5827	108	7	exhibits	exhibit	VERB
ejpam-5827	108	8	the	the	DET
ejpam-5827	108	9	master	master	NOUN
ejpam-5827	108	10	ideas	idea	NOUN
ejpam-5827	108	11	about	about	ADP
ejpam-5827	108	12	primal	primal	ADJ
ejpam-5827	108	13	,	,	PUNCT
ejpam-5827	108	14	κ	κ	NOUN
ejpam-5827	108	15	-	-	NOUN
ejpam-5827	108	16	neighborhood	neighborhood	NOUN
ejpam-5827	108	17	,	,	PUNCT
ejpam-5827	108	18	and	and	CCONJ
ejpam-5827	108	19	supra	supra	PROPN
ejpam-5827	108	20	topological	topological	ADJ
ejpam-5827	108	21	spaces	space	NOUN
ejpam-5827	108	22	cited	cite	VERB
ejpam-5827	108	23	in	in	ADP
ejpam-5827	108	24	[	[	X
ejpam-5827	108	25	9	9	NUM
ejpam-5827	108	26	,	,	PUNCT
ejpam-5827	108	27	12	12	NUM
ejpam-5827	108	28	,	,	PUNCT
ejpam-5827	108	29	13	13	NUM
ejpam-5827	108	30	,	,	PUNCT
ejpam-5827	108	31	35	35	NUM
ejpam-5827	108	32	,	,	PUNCT
ejpam-5827	108	33	56	56	NUM
ejpam-5827	108	34	,	,	PUNCT
ejpam-5827	108	35	73	73	NUM
ejpam-5827	108	36	]	]	PUNCT
ejpam-5827	108	37	.	.	PUNCT
ejpam-5827	109	1	definition	definition	NOUN
ejpam-5827	109	2	1	1	NUM
ejpam-5827	109	3	.	.	PUNCT
ejpam-5827	110	1	[	[	X
ejpam-5827	110	2	9	9	NUM
ejpam-5827	110	3	]	]	PUNCT
ejpam-5827	110	4	let	let	VERB
ejpam-5827	110	5	v	v	ADP
ejpam-5827	110	6	̸=	̸=	PROPN
ejpam-5827	110	7	∅.	∅.	ADP
ejpam-5827	110	8	a	a	DET
ejpam-5827	110	9	class	class	NOUN
ejpam-5827	110	10	p	p	NOUN
ejpam-5827	110	11	⊆	⊆	NUM
ejpam-5827	110	12	2v	2v	PROPN
ejpam-5827	110	13	is	be	AUX
ejpam-5827	110	14	named	name	VERB
ejpam-5827	110	15	a	a	DET
ejpam-5827	110	16	primal	primal	NOUN
ejpam-5827	110	17	on	on	ADP
ejpam-5827	110	18	v	v	NOUN
ejpam-5827	110	19	,	,	PUNCT
ejpam-5827	110	20	if	if	SCONJ
ejpam-5827	110	21	it	it	PRON
ejpam-5827	110	22	satisfies	satisfy	VERB
ejpam-5827	110	23	the	the	DET
ejpam-5827	110	24	next	next	ADJ
ejpam-5827	110	25	conditions	condition	NOUN
ejpam-5827	110	26	:	:	PUNCT
ejpam-5827	110	27	(	(	PUNCT
ejpam-5827	110	28	i	i	NOUN
ejpam-5827	110	29	)	)	PUNCT
ejpam-5827	110	30	v	v	NOUN
ejpam-5827	110	31	/∈	/∈	PUNCT
ejpam-5827	111	1	p	p	X
ejpam-5827	111	2	,	,	PUNCT
ejpam-5827	111	3	(	(	PUNCT
ejpam-5827	111	4	ii	ii	NOUN
ejpam-5827	111	5	)	)	PUNCT
ejpam-5827	111	6	o	o	NOUN
ejpam-5827	111	7	/∈	/∈	PUNCT
ejpam-5827	112	1	p	p	NOUN
ejpam-5827	112	2	and	and	CCONJ
ejpam-5827	112	3	o	o	NOUN
ejpam-5827	112	4	⊆	⊆	NUM
ejpam-5827	112	5	h	h	NOUN
ejpam-5827	112	6	⇒	⇒	NOUN
ejpam-5827	112	7	h	h	NOUN
ejpam-5827	112	8	/∈	/∈	PUNCT
ejpam-5827	113	1	p	p	X
ejpam-5827	113	2	,	,	PUNCT
ejpam-5827	113	3	(	(	PUNCT
ejpam-5827	113	4	iii	iii	NOUN
ejpam-5827	113	5	)	)	PUNCT
ejpam-5827	113	6	h	h	NOUN
ejpam-5827	113	7	/∈	/∈	PUNCT
ejpam-5827	114	1	p	p	NOUN
ejpam-5827	114	2	and	and	CCONJ
ejpam-5827	114	3	o	o	NOUN
ejpam-5827	114	4	/∈	/∈	PUNCT
ejpam-5827	115	1	p	p	X
ejpam-5827	115	2	⇒	⇒	NOUN
ejpam-5827	116	1	h	h	NOUN
ejpam-5827	116	2	∩o	∩o	NOUN
ejpam-5827	116	3	/∈	/∈	PUNCT
ejpam-5827	117	1	p.	p.	NOUN
ejpam-5827	117	2	lemma	lemma	PROPN
ejpam-5827	118	1	1	1	X
ejpam-5827	118	2	.	.	PUNCT
ejpam-5827	118	3	let	let	VERB
ejpam-5827	118	4	p	p	PRON
ejpam-5827	118	5	be	be	AUX
ejpam-5827	118	6	a	a	DET
ejpam-5827	118	7	primal	primal	NOUN
ejpam-5827	118	8	on	on	ADP
ejpam-5827	118	9	v.	v.	ADP
ejpam-5827	118	10	h	h	NOUN
ejpam-5827	118	11	/∈	/∈	PUNCT
ejpam-5827	119	1	p	p	NOUN
ejpam-5827	119	2	and	and	CCONJ
ejpam-5827	119	3	o	o	INTJ
ejpam-5827	119	4	/∈	/∈	PUNCT
ejpam-5827	120	1	p	p	X
ejpam-5827	120	2	⇔	⇔	PROPN
ejpam-5827	120	3	h	h	PROPN
ejpam-5827	120	4	∩o	∩o	NOUN
ejpam-5827	120	5	/∈	/∈	PUNCT
ejpam-5827	121	1	p.	p.	NOUN
ejpam-5827	121	2	proof	proof	NOUN
ejpam-5827	121	3	.	.	PUNCT
ejpam-5827	122	1	by	by	ADP
ejpam-5827	122	2	definition	definition	NOUN
ejpam-5827	122	3	1	1	NUM
ejpam-5827	122	4	,	,	PUNCT
ejpam-5827	122	5	the	the	DET
ejpam-5827	122	6	proof	proof	NOUN
ejpam-5827	122	7	is	be	AUX
ejpam-5827	122	8	obvious	obvious	ADJ
ejpam-5827	122	9	.	.	PUNCT
ejpam-5827	123	1	r.	r.	PROPN
ejpam-5827	123	2	a.	a.	PROPN
ejpam-5827	123	3	hosny	hosny	PROPN
ejpam-5827	123	4	,	,	PUNCT
ejpam-5827	123	5	m.	m.	PROPN
ejpam-5827	123	6	k.	k.	PROPN
ejpam-5827	124	1	el	el	PROPN
ejpam-5827	124	2	-	-	PROPN
ejpam-5827	124	3	bably	bably	ADV
ejpam-5827	124	4	,	,	PUNCT
ejpam-5827	124	5	m.	m.	NOUN
ejpam-5827	124	6	a.	a.	PROPN
ejpam-5827	124	7	el	el	PROPN
ejpam-5827	124	8	-	-	PROPN
ejpam-5827	124	9	gayar	gayar	PROPN
ejpam-5827	124	10	/	/	SYM
ejpam-5827	124	11	eur	eur	PROPN
ejpam-5827	124	12	.	.	PUNCT
ejpam-5827	125	1	j.	j.	PROPN
ejpam-5827	125	2	pure	pure	PROPN
ejpam-5827	125	3	appl	appl	PROPN
ejpam-5827	125	4	.	.	PROPN
ejpam-5827	125	5	math	math	PROPN
ejpam-5827	125	6	,	,	PUNCT
ejpam-5827	125	7	18	18	NUM
ejpam-5827	125	8	(	(	PUNCT
ejpam-5827	125	9	1	1	NUM
ejpam-5827	125	10	)	)	PUNCT
ejpam-5827	125	11	(	(	PUNCT
ejpam-5827	125	12	2025	2025	NUM
ejpam-5827	125	13	)	)	PUNCT
ejpam-5827	125	14	,	,	PUNCT
ejpam-5827	125	15	5827	5827	NUM
ejpam-5827	125	16	6	6	NUM
ejpam-5827	125	17	of	of	ADP
ejpam-5827	125	18	29	29	NUM
ejpam-5827	125	19	remark	remark	NOUN
ejpam-5827	125	20	1	1	NUM
ejpam-5827	125	21	.	.	PUNCT
ejpam-5827	126	1	the	the	DET
ejpam-5827	126	2	class	class	NOUN
ejpam-5827	126	3	p	p	NOUN
ejpam-5827	126	4	=	=	X
ejpam-5827	126	5	{	{	PUNCT
ejpam-5827	126	6	∅	∅	NOUN
ejpam-5827	126	7	}	}	PUNCT
ejpam-5827	126	8	does	do	AUX
ejpam-5827	126	9	not	not	PART
ejpam-5827	126	10	constitute	constitute	VERB
ejpam-5827	126	11	a	a	DET
ejpam-5827	126	12	primal	primal	NOUN
ejpam-5827	126	13	on	on	ADP
ejpam-5827	126	14	any	any	DET
ejpam-5827	126	15	set	set	NOUN
ejpam-5827	126	16	.	.	PUNCT
ejpam-5827	127	1	for	for	ADP
ejpam-5827	127	2	example	example	NOUN
ejpam-5827	127	3	,	,	PUNCT
ejpam-5827	127	4	consider	consider	VERB
ejpam-5827	127	5	v	v	NOUN
ejpam-5827	127	6	=	=	PUNCT
ejpam-5827	127	7	{	{	PUNCT
ejpam-5827	127	8	a	a	DET
ejpam-5827	127	9	,	,	PUNCT
ejpam-5827	127	10	b	b	NOUN
ejpam-5827	127	11	}	}	PUNCT
ejpam-5827	127	12	.	.	PUNCT
ejpam-5827	128	1	in	in	ADP
ejpam-5827	128	2	this	this	DET
ejpam-5827	128	3	case	case	NOUN
ejpam-5827	128	4	,	,	PUNCT
ejpam-5827	128	5	we	we	PRON
ejpam-5827	128	6	have	have	AUX
ejpam-5827	128	7	{	{	PUNCT
ejpam-5827	128	8	a}∩{b	a}∩{b	NUM
ejpam-5827	128	9	}	}	PUNCT
ejpam-5827	128	10	=	=	NOUN
ejpam-5827	128	11	∅	∅	NOUN
ejpam-5827	128	12	∈	∈	NOUN
ejpam-5827	128	13	p	p	X
ejpam-5827	128	14	,	,	PUNCT
ejpam-5827	128	15	despite	despite	SCONJ
ejpam-5827	128	16	the	the	DET
ejpam-5827	128	17	fact	fact	NOUN
ejpam-5827	128	18	that	that	SCONJ
ejpam-5827	128	19	{	{	PUNCT
ejpam-5827	128	20	a	a	PRON
ejpam-5827	128	21	}	}	PUNCT
ejpam-5827	128	22	̸∈	̸∈	PROPN
ejpam-5827	128	23	p	p	PROPN
ejpam-5827	128	24	and	and	CCONJ
ejpam-5827	128	25	{	{	PUNCT
ejpam-5827	128	26	b	b	PROPN
ejpam-5827	128	27	}	}	PUNCT
ejpam-5827	128	28	̸∈	̸∈	PROPN
ejpam-5827	128	29	p.	p.	PROPN
ejpam-5827	128	30	remark	remark	NOUN
ejpam-5827	128	31	2	2	NUM
ejpam-5827	128	32	.	.	PUNCT
ejpam-5827	129	1	when	when	SCONJ
ejpam-5827	129	2	the	the	DET
ejpam-5827	129	3	universe	universe	NOUN
ejpam-5827	129	4	consists	consist	VERB
ejpam-5827	129	5	of	of	ADP
ejpam-5827	129	6	a	a	DET
ejpam-5827	129	7	single	single	ADJ
ejpam-5827	129	8	element	element	NOUN
ejpam-5827	129	9	,	,	PUNCT
ejpam-5827	129	10	such	such	ADJ
ejpam-5827	129	11	as	as	ADP
ejpam-5827	129	12	v	v	NOUN
ejpam-5827	129	13	=	=	PUNCT
ejpam-5827	129	14	{	{	PUNCT
ejpam-5827	129	15	a	a	NOUN
ejpam-5827	129	16	}	}	PUNCT
ejpam-5827	129	17	,	,	PUNCT
ejpam-5827	129	18	it	it	PRON
ejpam-5827	129	19	is	be	AUX
ejpam-5827	129	20	possible	possible	ADJ
ejpam-5827	129	21	to	to	PART
ejpam-5827	129	22	construct	construct	VERB
ejpam-5827	129	23	an	an	DET
ejpam-5827	129	24	ideal	ideal	NOUN
ejpam-5827	129	25	;	;	PUNCT
ejpam-5827	129	26	however	however	ADV
ejpam-5827	129	27	,	,	PUNCT
ejpam-5827	129	28	constructing	construct	VERB
ejpam-5827	129	29	a	a	DET
ejpam-5827	129	30	primal	primal	NOUN
ejpam-5827	129	31	is	be	AUX
ejpam-5827	129	32	not	not	PART
ejpam-5827	129	33	feasible	feasible	ADJ
ejpam-5827	129	34	.	.	PUNCT
ejpam-5827	130	1	to	to	PART
ejpam-5827	130	2	construct	construct	VERB
ejpam-5827	130	3	a	a	DET
ejpam-5827	130	4	primal	primal	NOUN
ejpam-5827	130	5	,	,	PUNCT
ejpam-5827	130	6	the	the	DET
ejpam-5827	130	7	set	set	NOUN
ejpam-5827	130	8	v	v	NOUN
ejpam-5827	130	9	must	must	AUX
ejpam-5827	130	10	contain	contain	VERB
ejpam-5827	130	11	at	at	ADV
ejpam-5827	130	12	least	least	ADJ
ejpam-5827	130	13	two	two	NUM
ejpam-5827	130	14	distinct	distinct	ADJ
ejpam-5827	130	15	elements	element	NOUN
ejpam-5827	130	16	.	.	PUNCT
ejpam-5827	131	1	remark	remark	NOUN
ejpam-5827	131	2	3	3	NUM
ejpam-5827	131	3	.	.	PUNCT
ejpam-5827	132	1	[	[	X
ejpam-5827	132	2	9	9	NUM
ejpam-5827	132	3	]	]	X
ejpam-5827	132	4	the	the	DET
ejpam-5827	132	5	collection	collection	NOUN
ejpam-5827	132	6	of	of	ADP
ejpam-5827	132	7	sets	set	NOUN
ejpam-5827	132	8	obtained	obtain	VERB
ejpam-5827	132	9	through	through	ADP
ejpam-5827	132	10	the	the	DET
ejpam-5827	132	11	intersection	intersection	NOUN
ejpam-5827	132	12	(	(	PUNCT
ejpam-5827	132	13	or	or	CCONJ
ejpam-5827	132	14	union	union	NOUN
ejpam-5827	132	15	)	)	PUNCT
ejpam-5827	132	16	of	of	ADP
ejpam-5827	132	17	elements	element	NOUN
ejpam-5827	132	18	from	from	ADP
ejpam-5827	132	19	two	two	NUM
ejpam-5827	132	20	primal	primal	NOUN
ejpam-5827	132	21	does	do	AUX
ejpam-5827	132	22	not	not	PART
ejpam-5827	132	23	necessarily	necessarily	ADV
ejpam-5827	132	24	form	form	VERB
ejpam-5827	132	25	a	a	DET
ejpam-5827	132	26	primal	primal	NOUN
ejpam-5827	132	27	on	on	ADP
ejpam-5827	132	28	v	v	NOUN
ejpam-5827	132	29	,	,	PUNCT
ejpam-5827	132	30	as	as	SCONJ
ejpam-5827	132	31	demonstrated	demonstrate	VERB
ejpam-5827	132	32	in	in	ADP
ejpam-5827	132	33	the	the	DET
ejpam-5827	132	34	next	next	ADJ
ejpam-5827	132	35	example	example	NOUN
ejpam-5827	132	36	:	:	PUNCT
ejpam-5827	132	37	example	example	NOUN
ejpam-5827	133	1	1	1	X
ejpam-5827	133	2	.	.	PUNCT
ejpam-5827	134	1	let	let	VERB
ejpam-5827	134	2	p	p	NOUN
ejpam-5827	134	3	=	=	X
ejpam-5827	134	4	{	{	PUNCT
ejpam-5827	134	5	∅	∅	NOUN
ejpam-5827	134	6	,	,	PUNCT
ejpam-5827	134	7	{	{	PUNCT
ejpam-5827	134	8	a	a	X
ejpam-5827	134	9	}	}	PUNCT
ejpam-5827	134	10	,	,	PUNCT
ejpam-5827	134	11	{	{	PUNCT
ejpam-5827	134	12	b	b	NOUN
ejpam-5827	134	13	}	}	PUNCT
ejpam-5827	134	14	,	,	PUNCT
ejpam-5827	134	15	{	{	PUNCT
ejpam-5827	134	16	d	d	X
ejpam-5827	134	17	}	}	PUNCT
ejpam-5827	134	18	,	,	PUNCT
ejpam-5827	134	19	{	{	PUNCT
ejpam-5827	134	20	a	a	DET
ejpam-5827	134	21	,	,	PUNCT
ejpam-5827	134	22	b	b	NOUN
ejpam-5827	134	23	}	}	PUNCT
ejpam-5827	134	24	,	,	PUNCT
ejpam-5827	134	25	{	{	PUNCT
ejpam-5827	134	26	b	b	X
ejpam-5827	134	27	,	,	PUNCT
ejpam-5827	134	28	d	d	NOUN
ejpam-5827	134	29	}	}	PUNCT
ejpam-5827	134	30	,	,	PUNCT
ejpam-5827	134	31	{	{	PUNCT
ejpam-5827	134	32	a	a	DET
ejpam-5827	134	33	,	,	PUNCT
ejpam-5827	134	34	d	d	NOUN
ejpam-5827	134	35	}	}	PUNCT
ejpam-5827	134	36	,	,	PUNCT
ejpam-5827	134	37	{	{	PUNCT
ejpam-5827	134	38	a	a	DET
ejpam-5827	134	39	,	,	PUNCT
ejpam-5827	134	40	b	b	NOUN
ejpam-5827	134	41	,	,	PUNCT
ejpam-5827	134	42	d	d	NOUN
ejpam-5827	134	43	}	}	PUNCT
ejpam-5827	134	44	}	}	PUNCT
ejpam-5827	134	45	,	,	PUNCT
ejpam-5827	134	46	and	and	CCONJ
ejpam-5827	134	47	p̃	p̃	PROPN
ejpam-5827	134	48	=	=	PUNCT
ejpam-5827	134	49	{	{	PUNCT
ejpam-5827	134	50	∅	∅	NOUN
ejpam-5827	134	51	,	,	PUNCT
ejpam-5827	134	52	{	{	PUNCT
ejpam-5827	134	53	a	a	X
ejpam-5827	134	54	}	}	PUNCT
ejpam-5827	134	55	,	,	PUNCT
ejpam-5827	134	56	{	{	PUNCT
ejpam-5827	134	57	b	b	NOUN
ejpam-5827	134	58	}	}	PUNCT
ejpam-5827	134	59	,	,	PUNCT
ejpam-5827	134	60	{	{	PUNCT
ejpam-5827	134	61	c	c	X
ejpam-5827	134	62	}	}	PUNCT
ejpam-5827	134	63	,	,	PUNCT
ejpam-5827	134	64	{	{	PUNCT
ejpam-5827	134	65	a	a	DET
ejpam-5827	134	66	,	,	PUNCT
ejpam-5827	134	67	b	b	NOUN
ejpam-5827	134	68	}	}	PUNCT
ejpam-5827	134	69	,	,	PUNCT
ejpam-5827	134	70	{	{	PUNCT
ejpam-5827	134	71	b	b	X
ejpam-5827	134	72	,	,	PUNCT
ejpam-5827	134	73	c	c	NOUN
ejpam-5827	134	74	}	}	PUNCT
ejpam-5827	134	75	,	,	PUNCT
ejpam-5827	134	76	{	{	PUNCT
ejpam-5827	134	77	a	a	X
ejpam-5827	134	78	,	,	PUNCT
ejpam-5827	134	79	c	c	NOUN
ejpam-5827	134	80	}	}	PUNCT
ejpam-5827	134	81	,	,	PUNCT
ejpam-5827	134	82	{	{	PUNCT
ejpam-5827	134	83	a	a	PRON
ejpam-5827	134	84	,	,	PUNCT
ejpam-5827	134	85	b	b	NOUN
ejpam-5827	134	86	,	,	PUNCT
ejpam-5827	134	87	c	c	NOUN
ejpam-5827	134	88	}	}	PUNCT
ejpam-5827	134	89	}	}	PUNCT
ejpam-5827	134	90	be	be	AUX
ejpam-5827	134	91	two	two	NUM
ejpam-5827	134	92	primals	primal	NOUN
ejpam-5827	134	93	on	on	ADP
ejpam-5827	134	94	v	v	NOUN
ejpam-5827	134	95	=	=	PUNCT
ejpam-5827	134	96	{	{	PUNCT
ejpam-5827	134	97	a	a	PRON
ejpam-5827	134	98	,	,	PUNCT
ejpam-5827	134	99	b	b	NOUN
ejpam-5827	134	100	,	,	PUNCT
ejpam-5827	134	101	c	c	NOUN
ejpam-5827	134	102	,	,	PUNCT
ejpam-5827	134	103	d	d	NOUN
ejpam-5827	134	104	}	}	PUNCT
ejpam-5827	134	105	.	.	PUNCT
ejpam-5827	135	1	then	then	ADV
ejpam-5827	135	2	(	(	PUNCT
ejpam-5827	135	3	i	i	NOUN
ejpam-5827	135	4	)	)	PUNCT
ejpam-5827	135	5	p	p	NOUN
ejpam-5827	135	6	∪	∪	ADP
ejpam-5827	135	7	p̃	p̃	PROPN
ejpam-5827	135	8	=	=	SYM
ejpam-5827	135	9	2v	2v	PROPN
ejpam-5827	135	10	\	\	PROPN
ejpam-5827	135	11	{	{	PUNCT
ejpam-5827	135	12	v	v	NOUN
ejpam-5827	135	13	,	,	PUNCT
ejpam-5827	135	14	{	{	PUNCT
ejpam-5827	135	15	a	a	PRON
ejpam-5827	135	16	,	,	PUNCT
ejpam-5827	135	17	c	c	NOUN
ejpam-5827	135	18	,	,	PUNCT
ejpam-5827	135	19	d	d	NOUN
ejpam-5827	135	20	}	}	PUNCT
ejpam-5827	135	21	,	,	PUNCT
ejpam-5827	135	22	{	{	PUNCT
ejpam-5827	135	23	b	b	X
ejpam-5827	135	24	,	,	PUNCT
ejpam-5827	135	25	c	c	NOUN
ejpam-5827	135	26	,	,	PUNCT
ejpam-5827	135	27	d	d	NOUN
ejpam-5827	135	28	}	}	PUNCT
ejpam-5827	135	29	,	,	PUNCT
ejpam-5827	135	30	{	{	PUNCT
ejpam-5827	135	31	c	c	X
ejpam-5827	135	32	,	,	PUNCT
ejpam-5827	135	33	d	d	NOUN
ejpam-5827	135	34	}	}	PUNCT
ejpam-5827	135	35	}	}	PUNCT
ejpam-5827	135	36	is	be	AUX
ejpam-5827	135	37	a	a	DET
ejpam-5827	135	38	primal	primal	NOUN
ejpam-5827	135	39	.	.	PUNCT
ejpam-5827	136	1	(	(	PUNCT
ejpam-5827	136	2	ii	ii	NOUN
ejpam-5827	136	3	)	)	PUNCT
ejpam-5827	136	4	the	the	DET
ejpam-5827	136	5	family	family	NOUN
ejpam-5827	136	6	∇	∇	X
ejpam-5827	136	7	=	=	PUNCT
ejpam-5827	136	8	{	{	PUNCT
ejpam-5827	136	9	a∩b	a∩b	X
ejpam-5827	136	10	:	:	PUNCT
ejpam-5827	136	11	a	a	DET
ejpam-5827	136	12	∈	∈	PROPN
ejpam-5827	136	13	p	p	X
ejpam-5827	136	14	,	,	PUNCT
ejpam-5827	136	15	b	b	PROPN
ejpam-5827	136	16	∈	∈	PROPN
ejpam-5827	136	17	p̃	p̃	PROPN
ejpam-5827	136	18	}	}	PUNCT
ejpam-5827	136	19	=	=	SYM
ejpam-5827	136	20	{	{	PUNCT
ejpam-5827	136	21	∅	∅	NOUN
ejpam-5827	136	22	,	,	PUNCT
ejpam-5827	136	23	{	{	PUNCT
ejpam-5827	136	24	a	a	X
ejpam-5827	136	25	}	}	PUNCT
ejpam-5827	136	26	,	,	PUNCT
ejpam-5827	136	27	{	{	PUNCT
ejpam-5827	136	28	b	b	NOUN
ejpam-5827	136	29	}	}	PUNCT
ejpam-5827	136	30	,	,	PUNCT
ejpam-5827	136	31	{	{	PUNCT
ejpam-5827	136	32	a	a	DET
ejpam-5827	136	33	,	,	PUNCT
ejpam-5827	136	34	b	b	NOUN
ejpam-5827	136	35	}	}	PUNCT
ejpam-5827	136	36	}	}	PUNCT
ejpam-5827	136	37	is	be	AUX
ejpam-5827	136	38	not	not	PART
ejpam-5827	136	39	a	a	DET
ejpam-5827	136	40	primal	primal	NOUN
ejpam-5827	136	41	on	on	ADP
ejpam-5827	136	42	v	v	NOUN
ejpam-5827	136	43	since	since	SCONJ
ejpam-5827	136	44	{	{	PUNCT
ejpam-5827	136	45	a	a	PRON
ejpam-5827	136	46	,	,	PUNCT
ejpam-5827	136	47	b	b	NOUN
ejpam-5827	136	48	,	,	PUNCT
ejpam-5827	136	49	c	c	NOUN
ejpam-5827	136	50	}	}	PUNCT
ejpam-5827	136	51	∩	∩	NOUN
ejpam-5827	136	52	{	{	PUNCT
ejpam-5827	136	53	a	a	PRON
ejpam-5827	136	54	,	,	PUNCT
ejpam-5827	136	55	b	b	NOUN
ejpam-5827	136	56	,	,	PUNCT
ejpam-5827	136	57	d	d	NOUN
ejpam-5827	136	58	}	}	PUNCT
ejpam-5827	136	59	=	=	SYM
ejpam-5827	136	60	{	{	PUNCT
ejpam-5827	136	61	a	a	PRON
ejpam-5827	136	62	,	,	PUNCT
ejpam-5827	136	63	b	b	NOUN
ejpam-5827	136	64	}	}	PUNCT
ejpam-5827	136	65	∈	∈	NOUN
ejpam-5827	136	66	∇	∇	X
ejpam-5827	136	67	but	but	CCONJ
ejpam-5827	136	68	neither	neither	CCONJ
ejpam-5827	136	69	{	{	PUNCT
ejpam-5827	136	70	a	a	PROPN
ejpam-5827	136	71	,	,	PUNCT
ejpam-5827	136	72	b	b	NOUN
ejpam-5827	136	73	,	,	PUNCT
ejpam-5827	136	74	c	c	NOUN
ejpam-5827	136	75	}	}	PUNCT
ejpam-5827	136	76	∈	∈	NOUN
ejpam-5827	136	77	∇	∇	X
ejpam-5827	136	78	nor	nor	CCONJ
ejpam-5827	136	79	{	{	PUNCT
ejpam-5827	136	80	a	a	PRON
ejpam-5827	136	81	,	,	PUNCT
ejpam-5827	136	82	b	b	NOUN
ejpam-5827	136	83	,	,	PUNCT
ejpam-5827	136	84	d	d	NOUN
ejpam-5827	136	85	}	}	PUNCT
ejpam-5827	136	86	∈	∈	NOUN
ejpam-5827	136	87	∇.	∇.	X
ejpam-5827	136	88	(	(	PUNCT
ejpam-5827	136	89	iii	iii	NOUN
ejpam-5827	136	90	)	)	PUNCT
ejpam-5827	136	91	the	the	DET
ejpam-5827	136	92	family	family	NOUN
ejpam-5827	136	93	△	△	PROPN
ejpam-5827	136	94	=	=	SYM
ejpam-5827	136	95	{	{	PUNCT
ejpam-5827	136	96	a	a	NOUN
ejpam-5827	136	97	∪b	∪b	X
ejpam-5827	136	98	:	:	PUNCT
ejpam-5827	136	99	a	a	DET
ejpam-5827	136	100	∈	∈	PROPN
ejpam-5827	136	101	p	p	X
ejpam-5827	136	102	,	,	PUNCT
ejpam-5827	136	103	b	b	PROPN
ejpam-5827	136	104	∈	∈	PROPN
ejpam-5827	136	105	p̃	p̃	PROPN
ejpam-5827	136	106	}	}	PUNCT
ejpam-5827	136	107	=	=	PUNCT
ejpam-5827	136	108	2v	2v	PROPN
ejpam-5827	136	109	is	be	AUX
ejpam-5827	136	110	not	not	PART
ejpam-5827	136	111	a	a	DET
ejpam-5827	136	112	primal	primal	NOUN
ejpam-5827	136	113	on	on	ADP
ejpam-5827	136	114	v	v	NOUN
ejpam-5827	136	115	,	,	PUNCT
ejpam-5827	136	116	since	since	SCONJ
ejpam-5827	136	117	v	v	NUM
ejpam-5827	136	118	∈	∈	PROPN
ejpam-5827	136	119	△	△	PROPN
ejpam-5827	136	120	.	.	PUNCT
ejpam-5827	136	121	definition	definition	NOUN
ejpam-5827	136	122	2	2	NUM
ejpam-5827	136	123	.	.	PUNCT
ejpam-5827	137	1	[	[	X
ejpam-5827	137	2	56	56	NUM
ejpam-5827	137	3	]	]	PUNCT
ejpam-5827	137	4	let	let	VERB
ejpam-5827	137	5	s	s	PRON
ejpam-5827	137	6	be	be	AUX
ejpam-5827	137	7	a	a	DET
ejpam-5827	137	8	supra	supra	NOUN
ejpam-5827	137	9	-	-	PUNCT
ejpam-5827	137	10	topology	topology	NOUN
ejpam-5827	137	11	on	on	ADP
ejpam-5827	137	12	v.	v.	ADP
ejpam-5827	137	13	a	a	DET
ejpam-5827	137	14	set	set	NOUN
ejpam-5827	137	15	h	h	NOUN
ejpam-5827	137	16	⊆	⊆	NUM
ejpam-5827	137	17	v	v	NOUN
ejpam-5827	137	18	is	be	AUX
ejpam-5827	137	19	called	call	VERB
ejpam-5827	137	20	supra	supra	NOUN
ejpam-5827	137	21	-	-	PUNCT
ejpam-5827	137	22	open	open	ADJ
ejpam-5827	137	23	(	(	PUNCT
ejpam-5827	137	24	resp	resp	NOUN
ejpam-5827	137	25	.	.	PUNCT
ejpam-5827	138	1	supra	supra	NOUN
ejpam-5827	138	2	-	-	PUNCT
ejpam-5827	138	3	closed	closed	ADJ
ejpam-5827	138	4	)	)	PUNCT
ejpam-5827	138	5	if	if	SCONJ
ejpam-5827	138	6	it	it	PRON
ejpam-5827	138	7	is	be	AUX
ejpam-5827	138	8	a	a	DET
ejpam-5827	138	9	member	member	NOUN
ejpam-5827	138	10	of	of	ADP
ejpam-5827	138	11	s	s	PROPN
ejpam-5827	138	12	(	(	PUNCT
ejpam-5827	138	13	resp	resp	NOUN
ejpam-5827	138	14	.	.	PUNCT
ejpam-5827	139	1	its	its	PRON
ejpam-5827	139	2	complement	complement	NOUN
ejpam-5827	139	3	belongs	belong	VERB
ejpam-5827	139	4	to	to	ADP
ejpam-5827	139	5	s	s	NOUN
ejpam-5827	139	6	)	)	PUNCT
ejpam-5827	139	7	.	.	PUNCT
ejpam-5827	140	1	the	the	DET
ejpam-5827	140	2	suprainterior	suprainterior	ADJ
ejpam-5827	140	3	points	point	NOUN
ejpam-5827	140	4	of	of	ADP
ejpam-5827	140	5	a	a	DET
ejpam-5827	140	6	set	set	ADJ
ejpam-5827	140	7	h	h	NOUN
ejpam-5827	140	8	,	,	PUNCT
ejpam-5827	140	9	denoted	denote	VERB
ejpam-5827	140	10	by	by	ADP
ejpam-5827	140	11	sint(h	sint(h	PROPN
ejpam-5827	140	12	)	)	PUNCT
ejpam-5827	140	13	,	,	PUNCT
ejpam-5827	140	14	is	be	AUX
ejpam-5827	140	15	defined	define	VERB
ejpam-5827	140	16	as	as	ADP
ejpam-5827	140	17	a	a	DET
ejpam-5827	140	18	union	union	NOUN
ejpam-5827	140	19	of	of	ADP
ejpam-5827	140	20	all	all	DET
ejpam-5827	140	21	supra	supra	NOUN
ejpam-5827	140	22	-	-	PUNCT
ejpam-5827	140	23	open	open	ADJ
ejpam-5827	140	24	subsets	subset	NOUN
ejpam-5827	140	25	of	of	ADP
ejpam-5827	140	26	this	this	DET
ejpam-5827	140	27	set	set	NOUN
ejpam-5827	140	28	.	.	PUNCT
ejpam-5827	141	1	also	also	ADV
ejpam-5827	141	2	,	,	PUNCT
ejpam-5827	141	3	the	the	DET
ejpam-5827	141	4	supra	supra	NOUN
ejpam-5827	141	5	-	-	PUNCT
ejpam-5827	141	6	closure	closure	NOUN
ejpam-5827	141	7	points	point	NOUN
ejpam-5827	141	8	of	of	ADP
ejpam-5827	141	9	a	a	DET
ejpam-5827	141	10	h	h	NOUN
ejpam-5827	141	11	,	,	PUNCT
ejpam-5827	141	12	denoted	denote	VERB
ejpam-5827	141	13	by	by	ADP
ejpam-5827	141	14	scl(h	scl(h	PROPN
ejpam-5827	141	15	)	)	PUNCT
ejpam-5827	141	16	,	,	PUNCT
ejpam-5827	141	17	is	be	AUX
ejpam-5827	141	18	defined	define	VERB
ejpam-5827	141	19	as	as	ADP
ejpam-5827	141	20	an	an	DET
ejpam-5827	141	21	intersection	intersection	NOUN
ejpam-5827	141	22	of	of	ADP
ejpam-5827	141	23	all	all	DET
ejpam-5827	141	24	supra	supra	NOUN
ejpam-5827	141	25	-	-	PUNCT
ejpam-5827	141	26	closed	close	VERB
ejpam-5827	141	27	supersets	superset	NOUN
ejpam-5827	141	28	of	of	ADP
ejpam-5827	141	29	this	this	DET
ejpam-5827	141	30	set	set	NOUN
ejpam-5827	141	31	.	.	PUNCT
ejpam-5827	142	1	various	various	ADJ
ejpam-5827	142	2	types	type	NOUN
ejpam-5827	142	3	of	of	ADP
ejpam-5827	142	4	neighborhoods	neighborhood	NOUN
ejpam-5827	142	5	in	in	ADP
ejpam-5827	142	6	a	a	DET
ejpam-5827	142	7	set	set	NOUN
ejpam-5827	142	8	v	v	NOUN
ejpam-5827	142	9	based	base	VERB
ejpam-5827	142	10	on	on	ADP
ejpam-5827	142	11	a	a	DET
ejpam-5827	142	12	binary	binary	ADJ
ejpam-5827	142	13	relation	relation	NOUN
ejpam-5827	142	14	r	r	NOUN
ejpam-5827	142	15	were	be	AUX
ejpam-5827	142	16	defined	define	VERB
ejpam-5827	142	17	.	.	PUNCT
ejpam-5827	143	1	these	these	DET
ejpam-5827	143	2	neighborhoods	neighborhood	NOUN
ejpam-5827	143	3	are	be	AUX
ejpam-5827	143	4	determined	determine	VERB
ejpam-5827	143	5	by	by	ADP
ejpam-5827	143	6	different	different	ADJ
ejpam-5827	143	7	ways	way	NOUN
ejpam-5827	143	8	in	in	ADP
ejpam-5827	143	9	which	which	PRON
ejpam-5827	143	10	elements	element	NOUN
ejpam-5827	143	11	of	of	ADP
ejpam-5827	143	12	v	v	NOUN
ejpam-5827	143	13	relate	relate	VERB
ejpam-5827	143	14	to	to	ADP
ejpam-5827	143	15	each	each	DET
ejpam-5827	143	16	other	other	ADJ
ejpam-5827	143	17	according	accord	VERB
ejpam-5827	143	18	to	to	ADP
ejpam-5827	143	19	r.	r.	PROPN
ejpam-5827	143	20	here	here	ADV
ejpam-5827	143	21	’s	’	VERB
ejpam-5827	143	22	an	an	DET
ejpam-5827	143	23	explanation	explanation	NOUN
ejpam-5827	143	24	of	of	ADP
ejpam-5827	143	25	the	the	DET
ejpam-5827	143	26	different	different	ADJ
ejpam-5827	143	27	neighborhoods	neighborhood	NOUN
ejpam-5827	143	28	:	:	PUNCT
ejpam-5827	143	29	definition	definition	NOUN
ejpam-5827	143	30	3	3	NUM
ejpam-5827	143	31	.	.	PUNCT
ejpam-5827	144	1	[	[	X
ejpam-5827	144	2	12	12	NUM
ejpam-5827	144	3	,	,	PUNCT
ejpam-5827	144	4	13	13	NUM
ejpam-5827	144	5	,	,	PUNCT
ejpam-5827	144	6	35	35	NUM
ejpam-5827	144	7	,	,	PUNCT
ejpam-5827	144	8	49	49	NUM
ejpam-5827	144	9	,	,	PUNCT
ejpam-5827	144	10	73	73	NUM
ejpam-5827	144	11	]	]	PUNCT
ejpam-5827	144	12	if	if	SCONJ
ejpam-5827	144	13	r	r	NOUN
ejpam-5827	144	14	is	be	AUX
ejpam-5827	144	15	a	a	DET
ejpam-5827	144	16	binary	binary	ADJ
ejpam-5827	144	17	relation	relation	NOUN
ejpam-5827	144	18	on	on	ADP
ejpam-5827	144	19	v.	v.	CCONJ
ejpam-5827	144	20	then	then	ADV
ejpam-5827	144	21	,	,	PUNCT
ejpam-5827	144	22	κ	κ	NOUN
ejpam-5827	144	23	-	-	PUNCT
ejpam-5827	144	24	neighborhoods	neighborhood	NOUN
ejpam-5827	144	25	of	of	ADP
ejpam-5827	144	26	y∈v	y∈v	NOUN
ejpam-5827	144	27	(	(	PUNCT
ejpam-5827	144	28	briefly	briefly	ADV
ejpam-5827	144	29	,	,	PUNCT
ejpam-5827	144	30	nκ(y	nκ(y	NOUN
ejpam-5827	144	31	)	)	PUNCT
ejpam-5827	144	32	)	)	PUNCT
ejpam-5827	145	1	,	,	PUNCT
ejpam-5827	145	2	for	for	ADP
ejpam-5827	145	3	various	various	ADJ
ejpam-5827	145	4	choices	choice	NOUN
ejpam-5827	145	5	of	of	ADP
ejpam-5827	145	6	κ	κ	NOUN
ejpam-5827	145	7	(	(	PUNCT
ejpam-5827	145	8	κ	κ	PROPN
ejpam-5827	145	9	∈	∈	PROPN
ejpam-5827	145	10	{	{	PUNCT
ejpam-5827	145	11	r	r	NOUN
ejpam-5827	145	12	,	,	PUNCT
ejpam-5827	145	13	l	l	NOUN
ejpam-5827	145	14	,	,	PUNCT
ejpam-5827	145	15	i	i	PRON
ejpam-5827	145	16	,	,	PUNCT
ejpam-5827	145	17	u	u	PROPN
ejpam-5827	145	18	,	,	PUNCT
ejpam-5827	145	19	⟨r⟩	⟨r⟩	PROPN
ejpam-5827	145	20	,	,	PUNCT
ejpam-5827	145	21	⟨l⟩	⟨l⟩	PROPN
ejpam-5827	145	22	,	,	PUNCT
ejpam-5827	145	23	⟨i⟩	⟨i⟩	PROPN
ejpam-5827	145	24	,	,	PUNCT
ejpam-5827	145	25	⟨u⟩	⟨u⟩	PROPN
ejpam-5827	145	26	}	}	PUNCT
ejpam-5827	145	27	)	)	PUNCT
ejpam-5827	145	28	is	be	AUX
ejpam-5827	145	29	defined	define	VERB
ejpam-5827	145	30	as	as	SCONJ
ejpam-5827	145	31	follows	follow	VERB
ejpam-5827	145	32	:	:	PUNCT
ejpam-5827	145	33	(	(	PUNCT
ejpam-5827	145	34	i	i	NOUN
ejpam-5827	145	35	)	)	PUNCT
ejpam-5827	145	36	r	r	NOUN
ejpam-5827	145	37	-	-	PUNCT
ejpam-5827	145	38	neighborhood	neighborhood	NOUN
ejpam-5827	145	39	:	:	PUNCT
ejpam-5827	145	40	nr(y	nr(y	NUM
ejpam-5827	145	41	)	)	PUNCT
ejpam-5827	146	1	=	=	SYM
ejpam-5827	146	2	{	{	PUNCT
ejpam-5827	146	3	z∈v	z∈v	NOUN
ejpam-5827	146	4	:	:	PUNCT
ejpam-5827	146	5	yrz	yrz	NOUN
ejpam-5827	146	6	}	}	PUNCT
ejpam-5827	146	7	.	.	PUNCT
ejpam-5827	147	1	(	(	PUNCT
ejpam-5827	147	2	ii	ii	NOUN
ejpam-5827	147	3	)	)	PUNCT
ejpam-5827	147	4	l	l	NOUN
ejpam-5827	147	5	-	-	NOUN
ejpam-5827	147	6	neighborhood	neighborhood	NOUN
ejpam-5827	147	7	:	:	PUNCT
ejpam-5827	147	8	nl(y	nl(y	X
ejpam-5827	147	9	)	)	PUNCT
ejpam-5827	147	10	=	=	PRON
ejpam-5827	148	1	{	{	PUNCT
ejpam-5827	148	2	z∈v	z∈v	NOUN
ejpam-5827	148	3	:	:	PUNCT
ejpam-5827	148	4	zry	zry	PROPN
ejpam-5827	148	5	}	}	PUNCT
ejpam-5827	148	6	.	.	PUNCT
ejpam-5827	149	1	(	(	PUNCT
ejpam-5827	149	2	iii	iii	X
ejpam-5827	149	3	)	)	PUNCT
ejpam-5827	149	4	i	i	NOUN
ejpam-5827	149	5	-	-	PUNCT
ejpam-5827	149	6	neighborhood	neighborhood	NOUN
ejpam-5827	149	7	:	:	PUNCT
ejpam-5827	149	8	ni(y	ni(y	NOUN
ejpam-5827	149	9	)	)	PUNCT
ejpam-5827	149	10	=	=	SYM
ejpam-5827	149	11	nr(y	nr(y	ADJ
ejpam-5827	149	12	)	)	PUNCT
ejpam-5827	149	13	∩nl(y	∩nl(y	PROPN
ejpam-5827	149	14	)	)	PUNCT
ejpam-5827	149	15	.	.	PUNCT
ejpam-5827	150	1	(	(	PUNCT
ejpam-5827	150	2	iv	iv	X
ejpam-5827	150	3	)	)	PUNCT
ejpam-5827	150	4	u	u	NOUN
ejpam-5827	150	5	-	-	NOUN
ejpam-5827	150	6	neighborhood	neighborhood	NOUN
ejpam-5827	150	7	:	:	PUNCT
ejpam-5827	150	8	nu(y	nu(y	X
ejpam-5827	150	9	)	)	PUNCT
ejpam-5827	151	1	=	=	SYM
ejpam-5827	151	2	nr(y	nr(y	ADJ
ejpam-5827	151	3	)	)	PUNCT
ejpam-5827	151	4	∪nl(y	∪nl(y	NOUN
ejpam-5827	151	5	)	)	PUNCT
ejpam-5827	151	6	.	.	PUNCT
ejpam-5827	152	1	(	(	PUNCT
ejpam-5827	152	2	v	v	NOUN
ejpam-5827	152	3	)	)	PUNCT
ejpam-5827	152	4	⟨r⟩-neighborhood	⟨r⟩-neighborhood	NOUN
ejpam-5827	152	5	:	:	PUNCT
ejpam-5827	152	6	n⟨r⟩(y	n⟨r⟩(y	NOUN
ejpam-5827	152	7	)	)	PUNCT
ejpam-5827	152	8	=	=	SYM
ejpam-5827	152	9	∩{nr(z	∩{nr(z	PROPN
ejpam-5827	152	10	)	)	PUNCT
ejpam-5827	152	11	:	:	PUNCT
ejpam-5827	153	1	y	y	PROPN
ejpam-5827	153	2	∈	∈	PROPN
ejpam-5827	153	3	nr(z	nr(z	NUM
ejpam-5827	153	4	)	)	PUNCT
ejpam-5827	153	5	}	}	PUNCT
ejpam-5827	153	6	provided	provide	VERB
ejpam-5827	153	7	that	that	SCONJ
ejpam-5827	153	8	there	there	PRON
ejpam-5827	153	9	exists	exist	VERB
ejpam-5827	153	10	nr(z	nr(z	NOUN
ejpam-5827	153	11	)	)	PUNCT
ejpam-5827	153	12	containing	contain	VERB
ejpam-5827	153	13	y.	y.	PROPN
ejpam-5827	153	14	otherwise	otherwise	ADV
ejpam-5827	153	15	,	,	PUNCT
ejpam-5827	153	16	n⟨r⟩(y	n⟨r⟩(y	PROPN
ejpam-5827	153	17	)	)	PUNCT
ejpam-5827	153	18	=	=	PUNCT
ejpam-5827	153	19	∅.	∅.	PROPN
ejpam-5827	153	20	r.	r.	PROPN
ejpam-5827	153	21	a.	a.	PROPN
ejpam-5827	153	22	hosny	hosny	PROPN
ejpam-5827	153	23	,	,	PUNCT
ejpam-5827	153	24	m.	m.	PROPN
ejpam-5827	153	25	k.	k.	PROPN
ejpam-5827	153	26	el	el	PROPN
ejpam-5827	153	27	-	-	PROPN
ejpam-5827	153	28	bably	bably	ADV
ejpam-5827	153	29	,	,	PUNCT
ejpam-5827	153	30	m.	m.	NOUN
ejpam-5827	153	31	a.	a.	PROPN
ejpam-5827	153	32	el	el	PROPN
ejpam-5827	153	33	-	-	PROPN
ejpam-5827	153	34	gayar	gayar	PROPN
ejpam-5827	153	35	/	/	SYM
ejpam-5827	153	36	eur	eur	PROPN
ejpam-5827	153	37	.	.	PUNCT
ejpam-5827	154	1	j.	j.	PROPN
ejpam-5827	154	2	pure	pure	PROPN
ejpam-5827	154	3	appl	appl	PROPN
ejpam-5827	154	4	.	.	PROPN
ejpam-5827	154	5	math	math	PROPN
ejpam-5827	154	6	,	,	PUNCT
ejpam-5827	154	7	18	18	NUM
ejpam-5827	154	8	(	(	PUNCT
ejpam-5827	154	9	1	1	NUM
ejpam-5827	154	10	)	)	PUNCT
ejpam-5827	154	11	(	(	PUNCT
ejpam-5827	154	12	2025	2025	NUM
ejpam-5827	154	13	)	)	PUNCT
ejpam-5827	154	14	,	,	PUNCT
ejpam-5827	154	15	5827	5827	NUM
ejpam-5827	154	16	7	7	NUM
ejpam-5827	154	17	of	of	ADP
ejpam-5827	154	18	29	29	NUM
ejpam-5827	154	19	(	(	PUNCT
ejpam-5827	154	20	vi	vi	NOUN
ejpam-5827	154	21	)	)	PUNCT
ejpam-5827	154	22	⟨l⟩-neighborhood	⟨l⟩-neighborhood	NOUN
ejpam-5827	154	23	:	:	PUNCT
ejpam-5827	154	24	n⟨l⟩(y	n⟨l⟩(y	NUM
ejpam-5827	154	25	)	)	PUNCT
ejpam-5827	154	26	=	=	SYM
ejpam-5827	154	27	∩{nl(z	∩{nl(z	NOUN
ejpam-5827	154	28	)	)	PUNCT
ejpam-5827	154	29	:	:	PUNCT
ejpam-5827	154	30	y∈nl(z	y∈nl(z	PROPN
ejpam-5827	154	31	)	)	PUNCT
ejpam-5827	154	32	}	}	PUNCT
ejpam-5827	154	33	provided	provide	VERB
ejpam-5827	154	34	that	that	SCONJ
ejpam-5827	154	35	there	there	PRON
ejpam-5827	154	36	exists	exist	VERB
ejpam-5827	154	37	nl(z	nl(z	NOUN
ejpam-5827	154	38	)	)	PUNCT
ejpam-5827	154	39	containing	contain	VERB
ejpam-5827	154	40	y.	y.	PROPN
ejpam-5827	154	41	otherwise	otherwise	ADV
ejpam-5827	154	42	,	,	PUNCT
ejpam-5827	154	43	n⟨l⟩(y	n⟨l⟩(y	PUNCT
ejpam-5827	154	44	)	)	PUNCT
ejpam-5827	154	45	=	=	PUNCT
ejpam-5827	154	46	∅.	∅.	X
ejpam-5827	154	47	(	(	PUNCT
ejpam-5827	154	48	vii	vii	PROPN
ejpam-5827	154	49	)	)	PUNCT
ejpam-5827	154	50	⟨i⟩-neighborhood	⟨i⟩-neighborhood	NOUN
ejpam-5827	154	51	:	:	PUNCT
ejpam-5827	154	52	n⟨i⟩(y	n⟨i⟩(y	NOUN
ejpam-5827	154	53	)	)	PUNCT
ejpam-5827	154	54	=	=	SYM
ejpam-5827	154	55	n⟨r⟩(y	n⟨r⟩(y	NOUN
ejpam-5827	154	56	)	)	PUNCT
ejpam-5827	154	57	∩n⟨l⟩(y	∩n⟨l⟩(y	NOUN
ejpam-5827	154	58	)	)	PUNCT
ejpam-5827	154	59	.	.	PUNCT
ejpam-5827	155	1	(	(	PUNCT
ejpam-5827	155	2	viii	viii	NOUN
ejpam-5827	155	3	)	)	PUNCT
ejpam-5827	155	4	⟨u⟩-neighborhood	⟨u⟩-neighborhood	NOUN
ejpam-5827	155	5	:	:	PUNCT
ejpam-5827	155	6	n⟨u⟩(y	n⟨u⟩(y	X
ejpam-5827	155	7	)	)	PUNCT
ejpam-5827	155	8	=	=	SYM
ejpam-5827	155	9	n⟨r⟩(y	n⟨r⟩(y	NOUN
ejpam-5827	155	10	)	)	PUNCT
ejpam-5827	155	11	∪n⟨l⟩(y	∪n⟨l⟩(y	NUM
ejpam-5827	155	12	)	)	PUNCT
ejpam-5827	155	13	.	.	PUNCT
ejpam-5827	156	1	henceforward	henceforward	ADJ
ejpam-5827	156	2	,	,	PUNCT
ejpam-5827	156	3	κ	κ	NOUN
ejpam-5827	156	4	,	,	PUNCT
ejpam-5827	156	5	∀	∀	X
ejpam-5827	156	6	κ∈{r	κ∈{r	NOUN
ejpam-5827	156	7	,	,	PUNCT
ejpam-5827	156	8	l	l	PROPN
ejpam-5827	156	9	,	,	PUNCT
ejpam-5827	156	10	i	i	PRON
ejpam-5827	156	11	,	,	PUNCT
ejpam-5827	156	12	u	u	PROPN
ejpam-5827	156	13	,	,	PUNCT
ejpam-5827	156	14	⟨r⟩	⟨r⟩	PROPN
ejpam-5827	156	15	,	,	PUNCT
ejpam-5827	156	16	⟨l⟩	⟨l⟩	PROPN
ejpam-5827	156	17	,	,	PUNCT
ejpam-5827	156	18	⟨i⟩	⟨i⟩	PROPN
ejpam-5827	156	19	,	,	PUNCT
ejpam-5827	156	20	⟨u⟩	⟨u⟩	PROPN
ejpam-5827	156	21	}	}	PUNCT
ejpam-5827	156	22	,	,	PUNCT
ejpam-5827	156	23	will	will	AUX
ejpam-5827	156	24	be	be	AUX
ejpam-5827	156	25	treated	treat	VERB
ejpam-5827	156	26	,	,	PUNCT
ejpam-5827	156	27	unless	unless	SCONJ
ejpam-5827	156	28	otherwise	otherwise	ADV
ejpam-5827	156	29	noted	note	VERB
ejpam-5827	156	30	.	.	PUNCT
ejpam-5827	157	1	definition	definition	NOUN
ejpam-5827	157	2	4	4	NUM
ejpam-5827	157	3	.	.	PUNCT
ejpam-5827	158	1	[	[	X
ejpam-5827	158	2	35	35	NUM
ejpam-5827	158	3	]	]	PUNCT
ejpam-5827	158	4	let	let	VERB
ejpam-5827	158	5	r	r	PRON
ejpam-5827	158	6	be	be	AUX
ejpam-5827	158	7	a	a	DET
ejpam-5827	158	8	binary	binary	ADJ
ejpam-5827	158	9	relation	relation	NOUN
ejpam-5827	158	10	on	on	ADP
ejpam-5827	158	11	v	v	NOUN
ejpam-5827	158	12	,	,	PUNCT
ejpam-5827	158	13	and	and	CCONJ
ejpam-5827	158	14	ζκ	ζκ	NOUN
ejpam-5827	158	15	:	:	PUNCT
ejpam-5827	158	16	v	v	PART
ejpam-5827	158	17	−→	−→	NOUN
ejpam-5827	158	18	2v	2v	PROPN
ejpam-5827	158	19	be	be	VERB
ejpam-5827	158	20	a	a	DET
ejpam-5827	158	21	mapping	mapping	NOUN
ejpam-5827	158	22	which	which	PRON
ejpam-5827	158	23	designates	designate	VERB
ejpam-5827	158	24	for	for	ADP
ejpam-5827	158	25	each	each	DET
ejpam-5827	158	26	y	y	PROPN
ejpam-5827	158	27	in	in	ADP
ejpam-5827	158	28	v	v	NUM
ejpam-5827	158	29	its	its	PRON
ejpam-5827	158	30	κ	κ	NOUN
ejpam-5827	158	31	-	-	PUNCT
ejpam-5827	158	32	neighborhood	neighborhood	NOUN
ejpam-5827	158	33	in	in	ADP
ejpam-5827	158	34	2v	2v	PROPN
ejpam-5827	158	35	.	.	PUNCT
ejpam-5827	159	1	then	then	ADV
ejpam-5827	159	2	(	(	PUNCT
ejpam-5827	159	3	v	v	NOUN
ejpam-5827	159	4	,	,	PUNCT
ejpam-5827	159	5	r	r	NOUN
ejpam-5827	159	6	,	,	PUNCT
ejpam-5827	159	7	ζκ	ζκ	NOUN
ejpam-5827	159	8	)	)	PUNCT
ejpam-5827	159	9	is	be	AUX
ejpam-5827	159	10	named	name	VERB
ejpam-5827	159	11	a	a	DET
ejpam-5827	159	12	κ	κ	NOUN
ejpam-5827	159	13	-	-	PUNCT
ejpam-5827	159	14	neighborhood	neighborhood	NOUN
ejpam-5827	159	15	space	space	NOUN
ejpam-5827	159	16	(	(	PUNCT
ejpam-5827	159	17	κ	κ	NOUN
ejpam-5827	159	18	-	-	PUNCT
ejpam-5827	159	19	ns	ns	NUM
ejpam-5827	159	20	)	)	PUNCT
ejpam-5827	159	21	.	.	PUNCT
ejpam-5827	160	1	proposition	proposition	NOUN
ejpam-5827	160	2	1	1	NUM
ejpam-5827	160	3	.	.	PUNCT
ejpam-5827	161	1	[	[	X
ejpam-5827	161	2	6	6	NUM
ejpam-5827	161	3	,	,	PUNCT
ejpam-5827	161	4	22	22	NUM
ejpam-5827	161	5	,	,	PUNCT
ejpam-5827	161	6	31	31	NUM
ejpam-5827	161	7	,	,	PUNCT
ejpam-5827	161	8	43	43	NUM
ejpam-5827	161	9	,	,	PUNCT
ejpam-5827	161	10	71	71	NUM
ejpam-5827	161	11	,	,	PUNCT
ejpam-5827	161	12	72	72	NUM
ejpam-5827	161	13	]	]	PUNCT
ejpam-5827	161	14	let	let	ADJ
ejpam-5827	161	15	(	(	PUNCT
ejpam-5827	161	16	v	v	NOUN
ejpam-5827	161	17	,	,	PUNCT
ejpam-5827	161	18	r	r	NOUN
ejpam-5827	161	19	,	,	PUNCT
ejpam-5827	161	20	ζκ	ζκ	NOUN
ejpam-5827	161	21	)	)	PUNCT
ejpam-5827	161	22	be	be	AUX
ejpam-5827	161	23	a	a	DET
ejpam-5827	161	24	κ	κ	NOUN
ejpam-5827	161	25	-	-	ADJ
ejpam-5827	161	26	ns	ns	ADJ
ejpam-5827	161	27	and	and	CCONJ
ejpam-5827	161	28	λ	λ	X
ejpam-5827	161	29	∈	∈	PROPN
ejpam-5827	162	1	v.	v.	CCONJ
ejpam-5827	162	2	then	then	ADV
ejpam-5827	162	3	,	,	PUNCT
ejpam-5827	162	4	(	(	PUNCT
ejpam-5827	162	5	i	i	NOUN
ejpam-5827	162	6	)	)	PUNCT
ejpam-5827	162	7	λ	λ	X
ejpam-5827	162	8	∈	∈	PROPN
ejpam-5827	162	9	nκ(λ	nκ(λ	NUM
ejpam-5827	162	10	)	)	PUNCT
ejpam-5827	162	11	,	,	PUNCT
ejpam-5827	162	12	i.	i.	PROPN
ejpam-5827	162	13	e.	e.	PROPN
ejpam-5827	162	14	nκ(λ	nκ(λ	PROPN
ejpam-5827	162	15	)	)	PUNCT
ejpam-5827	163	1	̸=	̸=	PROPN
ejpam-5827	163	2	∅	∅	NOUN
ejpam-5827	163	3	,	,	PUNCT
ejpam-5827	163	4	for	for	ADP
ejpam-5827	163	5	each	each	DET
ejpam-5827	163	6	κ	κ	NOUN
ejpam-5827	163	7	,	,	PUNCT
ejpam-5827	163	8	if	if	SCONJ
ejpam-5827	163	9	r	r	NOUN
ejpam-5827	163	10	is	be	AUX
ejpam-5827	163	11	a	a	DET
ejpam-5827	163	12	reflexive	reflexive	ADJ
ejpam-5827	163	13	relation	relation	NOUN
ejpam-5827	163	14	.	.	PUNCT
ejpam-5827	164	1	(	(	PUNCT
ejpam-5827	164	2	ii	ii	NOUN
ejpam-5827	164	3	)	)	PUNCT
ejpam-5827	164	4	n⟨κ⟩(λ	n⟨κ⟩(λ	PROPN
ejpam-5827	164	5	)	)	PUNCT
ejpam-5827	164	6	⊆	⊆	NUM
ejpam-5827	164	7	nκ(λ	nκ(λ	NUM
ejpam-5827	164	8	)	)	PUNCT
ejpam-5827	164	9	,	,	PUNCT
ejpam-5827	164	10	κ∈{r	κ∈{r	PROPN
ejpam-5827	164	11	,	,	PUNCT
ejpam-5827	164	12	l	l	PROPN
ejpam-5827	164	13	,	,	PUNCT
ejpam-5827	164	14	i	i	PRON
ejpam-5827	164	15	,	,	PUNCT
ejpam-5827	164	16	u	u	NOUN
ejpam-5827	164	17	}	}	PUNCT
ejpam-5827	164	18	,	,	PUNCT
ejpam-5827	164	19	if	if	SCONJ
ejpam-5827	164	20	r	r	NOUN
ejpam-5827	164	21	is	be	AUX
ejpam-5827	164	22	a	a	DET
ejpam-5827	164	23	reflexive	reflexive	ADJ
ejpam-5827	164	24	relation	relation	NOUN
ejpam-5827	164	25	.	.	PUNCT
ejpam-5827	165	1	(	(	PUNCT
ejpam-5827	165	2	iii	iii	NOUN
ejpam-5827	165	3	)	)	PUNCT
ejpam-5827	165	4	nr(λ	nr(λ	NOUN
ejpam-5827	165	5	)	)	PUNCT
ejpam-5827	165	6	=	=	PUNCT
ejpam-5827	165	7	nl(λ	nl(λ	NUM
ejpam-5827	165	8	)	)	PUNCT
ejpam-5827	165	9	=	=	SYM
ejpam-5827	165	10	ni(λ	ni(λ	PRON
ejpam-5827	165	11	)	)	PUNCT
ejpam-5827	165	12	=	=	SYM
ejpam-5827	165	13	nu(λ	nu(λ	NOUN
ejpam-5827	165	14	)	)	PUNCT
ejpam-5827	165	15	and	and	CCONJ
ejpam-5827	165	16	n⟨r⟩(λ	n⟨r⟩(λ	NOUN
ejpam-5827	165	17	)	)	PUNCT
ejpam-5827	165	18	=	=	SYM
ejpam-5827	165	19	n⟨l⟩(λ	n⟨l⟩(λ	ADJ
ejpam-5827	165	20	)	)	PUNCT
ejpam-5827	165	21	=	=	SYM
ejpam-5827	165	22	n⟨i⟩(λ	n⟨i⟩(λ	PROPN
ejpam-5827	165	23	)	)	PUNCT
ejpam-5827	165	24	=	=	SYM
ejpam-5827	165	25	n⟨u⟩(λ	n⟨u⟩(λ	PROPN
ejpam-5827	165	26	)	)	PUNCT
ejpam-5827	165	27	,	,	PUNCT
ejpam-5827	165	28	if	if	SCONJ
ejpam-5827	165	29	r	r	NOUN
ejpam-5827	165	30	is	be	AUX
ejpam-5827	165	31	a	a	DET
ejpam-5827	165	32	symmetric	symmetric	ADJ
ejpam-5827	165	33	relation	relation	NOUN
ejpam-5827	165	34	.	.	PUNCT
ejpam-5827	166	1	(	(	PUNCT
ejpam-5827	166	2	iv	iv	X
ejpam-5827	166	3	)	)	PUNCT
ejpam-5827	166	4	n⟨κ⟩(λ	n⟨κ⟩(λ	PROPN
ejpam-5827	166	5	)	)	PUNCT
ejpam-5827	166	6	=	=	SYM
ejpam-5827	167	1	nκ(λ	nκ(λ	NUM
ejpam-5827	167	2	)	)	PUNCT
ejpam-5827	167	3	,	,	PUNCT
ejpam-5827	167	4	κ∈{r	κ∈{r	PROPN
ejpam-5827	167	5	,	,	PUNCT
ejpam-5827	167	6	l	l	PROPN
ejpam-5827	167	7	,	,	PUNCT
ejpam-5827	167	8	i	i	PRON
ejpam-5827	167	9	,	,	PUNCT
ejpam-5827	167	10	u	u	NOUN
ejpam-5827	167	11	}	}	PUNCT
ejpam-5827	167	12	,	,	PUNCT
ejpam-5827	167	13	if	if	SCONJ
ejpam-5827	167	14	r	r	NOUN
ejpam-5827	167	15	is	be	AUX
ejpam-5827	167	16	a	a	DET
ejpam-5827	167	17	preorder	preorder	NOUN
ejpam-5827	167	18	(	(	PUNCT
ejpam-5827	167	19	reflexive	reflexive	ADJ
ejpam-5827	167	20	and	and	CCONJ
ejpam-5827	167	21	transitive	transitive	ADJ
ejpam-5827	167	22	)	)	PUNCT
ejpam-5827	167	23	relation	relation	NOUN
ejpam-5827	167	24	.	.	PUNCT
ejpam-5827	168	1	theorem	theorem	NOUN
ejpam-5827	168	2	1	1	NUM
ejpam-5827	168	3	.	.	PUNCT
ejpam-5827	169	1	[	[	X
ejpam-5827	169	2	35	35	NUM
ejpam-5827	169	3	]	]	X
ejpam-5827	169	4	let	let	ADJ
ejpam-5827	169	5	(	(	PUNCT
ejpam-5827	169	6	v	v	NOUN
ejpam-5827	169	7	,	,	PUNCT
ejpam-5827	169	8	r	r	NOUN
ejpam-5827	169	9	,	,	PUNCT
ejpam-5827	169	10	ζκ	ζκ	NOUN
ejpam-5827	169	11	)	)	PUNCT
ejpam-5827	169	12	be	be	AUX
ejpam-5827	169	13	a	a	DET
ejpam-5827	169	14	κ	κ	NOUN
ejpam-5827	169	15	-	-	PUNCT
ejpam-5827	169	16	ns	ns	ADJ
ejpam-5827	169	17	,	,	PUNCT
ejpam-5827	169	18	and	and	CCONJ
ejpam-5827	169	19	let	let	VERB
ejpam-5827	169	20	h	h	PRON
ejpam-5827	169	21	⊆	⊆	NUM
ejpam-5827	169	22	v.	v.	ADP
ejpam-5827	169	23	then	then	ADV
ejpam-5827	169	24	,	,	PUNCT
ejpam-5827	169	25	for	for	ADP
ejpam-5827	169	26	each	each	DET
ejpam-5827	169	27	κ	κ	NOUN
ejpam-5827	169	28	,	,	PUNCT
ejpam-5827	169	29	the	the	DET
ejpam-5827	169	30	class	class	NOUN
ejpam-5827	169	31	τκ	τκ	NOUN
ejpam-5827	169	32	=	=	PRON
ejpam-5827	169	33	{	{	PUNCT
ejpam-5827	169	34	h	h	NOUN
ejpam-5827	169	35	⊆	⊆	NUM
ejpam-5827	169	36	v	v	NOUN
ejpam-5827	169	37	:	:	PUNCT
ejpam-5827	169	38	∀y	∀y	NUM
ejpam-5827	169	39	∈	∈	PROPN
ejpam-5827	169	40	h	h	NOUN
ejpam-5827	169	41	,	,	PUNCT
ejpam-5827	169	42	nκ(y	nκ(y	NOUN
ejpam-5827	169	43	)	)	PUNCT
ejpam-5827	169	44	⊆	⊆	NUM
ejpam-5827	169	45	h	h	NOUN
ejpam-5827	169	46	}	}	PUNCT
ejpam-5827	169	47	is	be	AUX
ejpam-5827	169	48	a	a	DET
ejpam-5827	169	49	topology	topology	NOUN
ejpam-5827	169	50	on	on	ADP
ejpam-5827	169	51	v.	v.	ADP
ejpam-5827	169	52	definition	definition	NOUN
ejpam-5827	169	53	5	5	NUM
ejpam-5827	169	54	.	.	PUNCT
ejpam-5827	170	1	[	[	X
ejpam-5827	170	2	35	35	NUM
ejpam-5827	170	3	]	]	X
ejpam-5827	170	4	let	let	ADJ
ejpam-5827	170	5	(	(	PUNCT
ejpam-5827	170	6	v	v	NOUN
ejpam-5827	170	7	,	,	PUNCT
ejpam-5827	170	8	r	r	NOUN
ejpam-5827	170	9	,	,	PUNCT
ejpam-5827	170	10	ζκ	ζκ	NOUN
ejpam-5827	170	11	)	)	PUNCT
ejpam-5827	170	12	be	be	AUX
ejpam-5827	170	13	a	a	DET
ejpam-5827	170	14	κ	κ	NOUN
ejpam-5827	170	15	-	-	PUNCT
ejpam-5827	170	16	ns	ns	ADJ
ejpam-5827	170	17	.	.	PUNCT
ejpam-5827	171	1	a	a	DET
ejpam-5827	171	2	set	set	NOUN
ejpam-5827	171	3	h	h	NOUN
ejpam-5827	171	4	⊆	⊆	NUM
ejpam-5827	171	5	v	v	NOUN
ejpam-5827	171	6	is	be	AUX
ejpam-5827	171	7	called	call	VERB
ejpam-5827	171	8	a	a	DET
ejpam-5827	171	9	τκ	τκ	NOUN
ejpam-5827	171	10	-	-	PUNCT
ejpam-5827	171	11	open	open	NOUN
ejpam-5827	171	12	set	set	NOUN
ejpam-5827	171	13	if	if	SCONJ
ejpam-5827	171	14	h	h	PROPN
ejpam-5827	171	15	∈	∈	PROPN
ejpam-5827	171	16	τκ	τκ	PROPN
ejpam-5827	171	17	,	,	PUNCT
ejpam-5827	171	18	and	and	CCONJ
ejpam-5827	171	19	its	its	PRON
ejpam-5827	171	20	complement	complement	NOUN
ejpam-5827	171	21	is	be	AUX
ejpam-5827	171	22	called	call	VERB
ejpam-5827	171	23	a	a	DET
ejpam-5827	171	24	τκ	τκ	NOUN
ejpam-5827	171	25	-	-	PUNCT
ejpam-5827	171	26	closed	close	VERB
ejpam-5827	171	27	set	set	NOUN
ejpam-5827	171	28	.	.	PUNCT
ejpam-5827	172	1	the	the	DET
ejpam-5827	172	2	family	family	NOUN
ejpam-5827	172	3	υκ	υκ	PROPN
ejpam-5827	172	4	of	of	ADP
ejpam-5827	172	5	all	all	DET
ejpam-5827	172	6	τκ	τκ	NOUN
ejpam-5827	172	7	-	-	PUNCT
ejpam-5827	172	8	closed	close	VERB
ejpam-5827	172	9	sets	set	NOUN
ejpam-5827	172	10	is	be	AUX
ejpam-5827	172	11	defined	define	VERB
ejpam-5827	172	12	as	as	ADP
ejpam-5827	172	13	υκ	υκ	PROPN
ejpam-5827	172	14	=	=	X
ejpam-5827	172	15	{	{	PUNCT
ejpam-5827	172	16	e	e	PROPN
ejpam-5827	172	17	⊆	⊆	NUM
ejpam-5827	172	18	v	v	NOUN
ejpam-5827	172	19	:	:	PUNCT
ejpam-5827	172	20	ec	ec	PROPN
ejpam-5827	172	21	∈	∈	PROPN
ejpam-5827	172	22	τκ	τκ	PROPN
ejpam-5827	172	23	}	}	PUNCT
ejpam-5827	172	24	,	,	PUNCT
ejpam-5827	172	25	where	where	SCONJ
ejpam-5827	172	26	ec	ec	PROPN
ejpam-5827	172	27	is	be	AUX
ejpam-5827	172	28	the	the	DET
ejpam-5827	172	29	complement	complement	NOUN
ejpam-5827	172	30	of	of	ADP
ejpam-5827	172	31	e.	e.	PROPN
ejpam-5827	172	32	definition	definition	PROPN
ejpam-5827	172	33	6	6	NUM
ejpam-5827	172	34	.	.	PUNCT
ejpam-5827	173	1	[	[	X
ejpam-5827	173	2	35	35	NUM
ejpam-5827	173	3	]	]	PUNCT
ejpam-5827	173	4	let	let	VERB
ejpam-5827	173	5	τκ	τκ	PRON
ejpam-5827	173	6	be	be	AUX
ejpam-5827	173	7	a	a	DET
ejpam-5827	173	8	topology	topology	NOUN
ejpam-5827	173	9	on	on	ADP
ejpam-5827	173	10	v	v	NUM
ejpam-5827	173	11	generated	generate	VERB
ejpam-5827	173	12	by	by	ADP
ejpam-5827	173	13	κ	κ	NOUN
ejpam-5827	173	14	-	-	PUNCT
ejpam-5827	173	15	ns	ns	ADJ
ejpam-5827	173	16	.	.	PUNCT
ejpam-5827	174	1	then	then	ADV
ejpam-5827	174	2	the	the	DET
ejpam-5827	174	3	κ	κ	NOUN
ejpam-5827	174	4	-	-	PUNCT
ejpam-5827	174	5	lower	low	ADJ
ejpam-5827	174	6	,	,	PUNCT
ejpam-5827	174	7	κ	κ	NOUN
ejpam-5827	174	8	-	-	ADJ
ejpam-5827	174	9	upper	upper	ADJ
ejpam-5827	174	10	approximations	approximation	NOUN
ejpam-5827	174	11	,	,	PUNCT
ejpam-5827	174	12	κ	κ	NOUN
ejpam-5827	174	13	-	-	NOUN
ejpam-5827	174	14	boundary	boundary	ADJ
ejpam-5827	174	15	and	and	CCONJ
ejpam-5827	174	16	κ	κ	NOUN
ejpam-5827	174	17	-	-	PUNCT
ejpam-5827	174	18	accuracy	accuracy	NOUN
ejpam-5827	174	19	of	of	ADP
ejpam-5827	174	20	a	a	DET
ejpam-5827	174	21	subset	subset	NOUN
ejpam-5827	174	22	h	h	NOUN
ejpam-5827	174	23	⊆	⊆	NUM
ejpam-5827	174	24	v	v	NOUN
ejpam-5827	174	25	are	be	AUX
ejpam-5827	174	26	defined	define	VERB
ejpam-5827	174	27	respectively	respectively	ADV
ejpam-5827	174	28	for	for	ADP
ejpam-5827	174	29	each	each	DET
ejpam-5827	174	30	κ	κ	NOUN
ejpam-5827	174	31	as	as	ADP
ejpam-5827	174	32	:	:	PUNCT
ejpam-5827	174	33	(	(	PUNCT
ejpam-5827	174	34	i	i	NOUN
ejpam-5827	174	35	)	)	PUNCT
ejpam-5827	174	36	τκl(h	τκl(h	PROPN
ejpam-5827	174	37	)	)	PUNCT
ejpam-5827	174	38	=	=	SYM
ejpam-5827	174	39	τκint(h	τκint(h	NOUN
ejpam-5827	174	40	)	)	PUNCT
ejpam-5827	174	41	,	,	PUNCT
ejpam-5827	174	42	where	where	SCONJ
ejpam-5827	174	43	τκint(h	τκint(h	NOUN
ejpam-5827	174	44	)	)	PUNCT
ejpam-5827	174	45	represents	represent	VERB
ejpam-5827	174	46	interior	interior	NOUN
ejpam-5827	174	47	of	of	ADP
ejpam-5827	174	48	h	h	PROPN
ejpam-5827	174	49	w.r.t	w.r.t	PROPN
ejpam-5827	174	50	.	.	PUNCT
ejpam-5827	175	1	τκ	τκ	PROPN
ejpam-5827	175	2	.	.	PUNCT
ejpam-5827	176	1	(	(	PUNCT
ejpam-5827	176	2	ii	ii	NOUN
ejpam-5827	176	3	)	)	PUNCT
ejpam-5827	176	4	τκu(h	τκu(h	PROPN
ejpam-5827	176	5	)	)	PUNCT
ejpam-5827	176	6	=	=	SYM
ejpam-5827	176	7	τκcl(h	τκcl(h	PROPN
ejpam-5827	176	8	)	)	PUNCT
ejpam-5827	176	9	,	,	PUNCT
ejpam-5827	176	10	where	where	SCONJ
ejpam-5827	176	11	τκcl(h	τκcl(h	X
ejpam-5827	176	12	)	)	PUNCT
ejpam-5827	176	13	represents	represent	VERB
ejpam-5827	176	14	closure	closure	NOUN
ejpam-5827	176	15	of	of	ADP
ejpam-5827	176	16	h	h	NOUN
ejpam-5827	176	17	w.r.t	w.r.t	NOUN
ejpam-5827	176	18	.	.	PUNCT
ejpam-5827	177	1	τκ	τκ	PROPN
ejpam-5827	177	2	.	.	PUNCT
ejpam-5827	178	1	(	(	PUNCT
ejpam-5827	178	2	iii	iii	NOUN
ejpam-5827	178	3	)	)	PUNCT
ejpam-5827	178	4	τκb(h	τκb(h	PROPN
ejpam-5827	178	5	)	)	PUNCT
ejpam-5827	178	6	=	=	SYM
ejpam-5827	178	7	τκu(h	τκu(h	PROPN
ejpam-5827	178	8	)	)	PUNCT
ejpam-5827	178	9	−	−	PROPN
ejpam-5827	179	1	τκl(h	τκl(h	NUM
ejpam-5827	179	2	)	)	PUNCT
ejpam-5827	179	3	.	.	PUNCT
ejpam-5827	180	1	(	(	PUNCT
ejpam-5827	180	2	iv	iv	X
ejpam-5827	180	3	)	)	PUNCT
ejpam-5827	180	4	τκσ(h	τκσ(h	PROPN
ejpam-5827	180	5	)	)	PUNCT
ejpam-5827	181	1	=	=	SYM
ejpam-5827	181	2	|τκl(h)|	|τκl(h)|	PROPN
ejpam-5827	181	3	|τκu(h)|	|τκu(h)|	NUM
ejpam-5827	181	4	,	,	PUNCT
ejpam-5827	181	5	where	where	SCONJ
ejpam-5827	181	6	|τκu(h)|≠0	|τκu(h)|≠0	ADJ
ejpam-5827	181	7	.	.	PUNCT
ejpam-5827	182	1	in	in	ADP
ejpam-5827	182	2	[	[	X
ejpam-5827	182	3	41	41	NUM
ejpam-5827	182	4	]	]	PUNCT
ejpam-5827	182	5	(	(	PUNCT
ejpam-5827	182	6	which	which	PRON
ejpam-5827	182	7	were	be	AUX
ejpam-5827	182	8	corrected	correct	VERB
ejpam-5827	182	9	by	by	ADP
ejpam-5827	182	10	r.	r.	PROPN
ejpam-5827	182	11	hosny	hosny	PROPN
ejpam-5827	182	12	et	et	PROPN
ejpam-5827	182	13	al	al	PROPN
ejpam-5827	182	14	.	.	PUNCT
ejpam-5827	183	1	in	in	ADP
ejpam-5827	183	2	[	[	X
ejpam-5827	183	3	44	44	NUM
ejpam-5827	183	4	]	]	SYM
ejpam-5827	183	5	)	)	PUNCT
ejpam-5827	183	6	,	,	PUNCT
ejpam-5827	183	7	hosny	hosny	PROPN
ejpam-5827	183	8	used	use	VERB
ejpam-5827	183	9	the	the	DET
ejpam-5827	183	10	method	method	NOUN
ejpam-5827	183	11	of	of	ADP
ejpam-5827	183	12	[	[	X
ejpam-5827	183	13	35	35	NUM
ejpam-5827	183	14	]	]	PUNCT
ejpam-5827	183	15	to	to	PART
ejpam-5827	183	16	define	define	VERB
ejpam-5827	183	17	a	a	DET
ejpam-5827	183	18	new	new	ADJ
ejpam-5827	183	19	technique	technique	NOUN
ejpam-5827	183	20	for	for	ADP
ejpam-5827	183	21	generating	generate	VERB
ejpam-5827	183	22	different	different	ADJ
ejpam-5827	183	23	topologies	topology	NOUN
ejpam-5827	183	24	via	via	ADP
ejpam-5827	183	25	κ	κ	ADV
ejpam-5827	183	26	-	-	PUNCT
ejpam-5827	183	27	ns	ns	ADJ
ejpam-5827	183	28	and	and	CCONJ
ejpam-5827	183	29	ideals	ideal	NOUN
ejpam-5827	183	30	,	,	PUNCT
ejpam-5827	183	31	as	as	SCONJ
ejpam-5827	183	32	illustrated	illustrate	VERB
ejpam-5827	183	33	in	in	ADP
ejpam-5827	183	34	the	the	DET
ejpam-5827	183	35	following	following	NOUN
ejpam-5827	183	36	theorem	theorem	PROPN
ejpam-5827	183	37	.	.	PUNCT
ejpam-5827	183	38	r.	r.	PROPN
ejpam-5827	183	39	a.	a.	PROPN
ejpam-5827	183	40	hosny	hosny	PROPN
ejpam-5827	183	41	,	,	PUNCT
ejpam-5827	183	42	m.	m.	PROPN
ejpam-5827	183	43	k.	k.	PROPN
ejpam-5827	184	1	el	el	PROPN
ejpam-5827	184	2	-	-	PROPN
ejpam-5827	184	3	bably	bably	ADV
ejpam-5827	184	4	,	,	PUNCT
ejpam-5827	184	5	m.	m.	NOUN
ejpam-5827	184	6	a.	a.	PROPN
ejpam-5827	184	7	el	el	PROPN
ejpam-5827	184	8	-	-	PROPN
ejpam-5827	184	9	gayar	gayar	PROPN
ejpam-5827	184	10	/	/	SYM
ejpam-5827	184	11	eur	eur	PROPN
ejpam-5827	184	12	.	.	PUNCT
ejpam-5827	185	1	j.	j.	PROPN
ejpam-5827	185	2	pure	pure	PROPN
ejpam-5827	185	3	appl	appl	PROPN
ejpam-5827	185	4	.	.	PROPN
ejpam-5827	185	5	math	math	PROPN
ejpam-5827	185	6	,	,	PUNCT
ejpam-5827	185	7	18	18	NUM
ejpam-5827	185	8	(	(	PUNCT
ejpam-5827	185	9	1	1	NUM
ejpam-5827	185	10	)	)	PUNCT
ejpam-5827	185	11	(	(	PUNCT
ejpam-5827	185	12	2025	2025	NUM
ejpam-5827	185	13	)	)	PUNCT
ejpam-5827	185	14	,	,	PUNCT
ejpam-5827	185	15	5827	5827	NUM
ejpam-5827	185	16	8	8	NUM
ejpam-5827	185	17	of	of	ADP
ejpam-5827	185	18	29	29	NUM
ejpam-5827	185	19	theorem	theorem	NOUN
ejpam-5827	185	20	2	2	NUM
ejpam-5827	185	21	.	.	PUNCT
ejpam-5827	186	1	[	[	X
ejpam-5827	186	2	41	41	NUM
ejpam-5827	186	3	,	,	PUNCT
ejpam-5827	186	4	44	44	NUM
ejpam-5827	186	5	]	]	PUNCT
ejpam-5827	186	6	let	let	ADJ
ejpam-5827	186	7	(	(	PUNCT
ejpam-5827	186	8	v	v	NOUN
ejpam-5827	186	9	,	,	PUNCT
ejpam-5827	186	10	r	r	NOUN
ejpam-5827	186	11	,	,	PUNCT
ejpam-5827	186	12	ζκ	ζκ	NOUN
ejpam-5827	186	13	)	)	PUNCT
ejpam-5827	186	14	be	be	AUX
ejpam-5827	186	15	a	a	DET
ejpam-5827	186	16	κ	κ	NOUN
ejpam-5827	186	17	-	-	PUNCT
ejpam-5827	186	18	ns	ns	ADJ
ejpam-5827	186	19	,	,	PUNCT
ejpam-5827	186	20	and	and	CCONJ
ejpam-5827	186	21	let	let	VERB
ejpam-5827	186	22	h	h	PRON
ejpam-5827	186	23	⊆	⊆	NUM
ejpam-5827	186	24	v.	v.	ADP
ejpam-5827	186	25	if	if	SCONJ
ejpam-5827	186	26	i	i	PRON
ejpam-5827	186	27	is	be	AUX
ejpam-5827	186	28	an	an	DET
ejpam-5827	186	29	ideal	ideal	NOUN
ejpam-5827	186	30	on	on	ADP
ejpam-5827	186	31	v	v	NOUN
ejpam-5827	186	32	,	,	PUNCT
ejpam-5827	186	33	then	then	ADV
ejpam-5827	186	34	for	for	ADP
ejpam-5827	186	35	each	each	DET
ejpam-5827	186	36	κ	κ	NOUN
ejpam-5827	186	37	,	,	PUNCT
ejpam-5827	186	38	the	the	DET
ejpam-5827	186	39	class	class	NOUN
ejpam-5827	186	40	τiκ	τiκ	NOUN
ejpam-5827	186	41	=	=	PUNCT
ejpam-5827	186	42	{	{	PUNCT
ejpam-5827	186	43	h	h	NOUN
ejpam-5827	186	44	⊆	⊆	NUM
ejpam-5827	186	45	v	v	NOUN
ejpam-5827	186	46	:	:	PUNCT
ejpam-5827	186	47	∀y	∀y	NUM
ejpam-5827	186	48	∈	∈	PROPN
ejpam-5827	186	49	h	h	NOUN
ejpam-5827	186	50	,	,	PUNCT
ejpam-5827	186	51	nκ(y)−h	nκ(y)−h	PROPN
ejpam-5827	186	52	∈	∈	PROPN
ejpam-5827	187	1	i	i	PRON
ejpam-5827	187	2	}	}	PUNCT
ejpam-5827	187	3	is	be	AUX
ejpam-5827	187	4	a	a	DET
ejpam-5827	187	5	topology	topology	NOUN
ejpam-5827	187	6	on	on	ADP
ejpam-5827	187	7	v.	v.	ADP
ejpam-5827	187	8	definition	definition	NOUN
ejpam-5827	187	9	7	7	NUM
ejpam-5827	187	10	.	.	PUNCT
ejpam-5827	188	1	[	[	X
ejpam-5827	188	2	41	41	NUM
ejpam-5827	188	3	,	,	PUNCT
ejpam-5827	188	4	44	44	NUM
ejpam-5827	188	5	]	]	PUNCT
ejpam-5827	188	6	let	let	VERB
ejpam-5827	188	7	τiκ	τiκ	NOUN
ejpam-5827	188	8	be	be	AUX
ejpam-5827	188	9	a	a	DET
ejpam-5827	188	10	topology	topology	NOUN
ejpam-5827	188	11	on	on	ADP
ejpam-5827	188	12	v	v	NUM
ejpam-5827	188	13	generated	generate	VERB
ejpam-5827	188	14	by	by	ADP
ejpam-5827	188	15	κ	κ	ADV
ejpam-5827	188	16	-	-	PUNCT
ejpam-5827	188	17	ns	ns	ADJ
ejpam-5827	188	18	and	and	CCONJ
ejpam-5827	188	19	ideal	ideal	ADJ
ejpam-5827	188	20	i.	i.	NOUN
ejpam-5827	188	21	then	then	ADV
ejpam-5827	188	22	,	,	PUNCT
ejpam-5827	188	23	for	for	ADP
ejpam-5827	188	24	every	every	DET
ejpam-5827	188	25	κ	κ	NOUN
ejpam-5827	188	26	,	,	PUNCT
ejpam-5827	188	27	the	the	DET
ejpam-5827	188	28	κ	κ	NOUN
ejpam-5827	188	29	-	-	PUNCT
ejpam-5827	188	30	lower	low	ADJ
ejpam-5827	188	31	,	,	PUNCT
ejpam-5827	188	32	κ	κ	NOUN
ejpam-5827	188	33	-	-	ADJ
ejpam-5827	188	34	upper	upper	ADJ
ejpam-5827	188	35	approximations	approximation	NOUN
ejpam-5827	188	36	,	,	PUNCT
ejpam-5827	188	37	and	and	CCONJ
ejpam-5827	188	38	κ	κ	NOUN
ejpam-5827	188	39	-	-	PUNCT
ejpam-5827	188	40	accuracy	accuracy	NOUN
ejpam-5827	188	41	of	of	ADP
ejpam-5827	188	42	a	a	DET
ejpam-5827	188	43	set	set	ADJ
ejpam-5827	188	44	h	h	NOUN
ejpam-5827	188	45	are	be	AUX
ejpam-5827	188	46	respectively	respectively	ADV
ejpam-5827	188	47	given	give	VERB
ejpam-5827	188	48	as	as	ADP
ejpam-5827	188	49	:	:	PUNCT
ejpam-5827	188	50	(	(	PUNCT
ejpam-5827	188	51	i	i	NOUN
ejpam-5827	188	52	)	)	PUNCT
ejpam-5827	188	53	τiκl(h	τiκl(h	PROPN
ejpam-5827	188	54	)	)	PUNCT
ejpam-5827	188	55	=	=	PUNCT
ejpam-5827	188	56	τiκ	τiκ	NOUN
ejpam-5827	188	57	int(h	int(h	X
ejpam-5827	188	58	)	)	PUNCT
ejpam-5827	188	59	,	,	PUNCT
ejpam-5827	188	60	where	where	SCONJ
ejpam-5827	188	61	τiκ	τiκ	NOUN
ejpam-5827	188	62	int(h	int(h	ADV
ejpam-5827	188	63	)	)	PUNCT
ejpam-5827	188	64	represents	represent	VERB
ejpam-5827	188	65	interior	interior	NOUN
ejpam-5827	188	66	of	of	ADP
ejpam-5827	188	67	h	h	PROPN
ejpam-5827	188	68	w.r.t	w.r.t	NOUN
ejpam-5827	188	69	.	.	PUNCT
ejpam-5827	189	1	τiκ	τiκ	INTJ
ejpam-5827	189	2	.	.	PUNCT
ejpam-5827	190	1	(	(	PUNCT
ejpam-5827	190	2	ii	ii	NOUN
ejpam-5827	190	3	)	)	PUNCT
ejpam-5827	190	4	τiκu(h	τiκu(h	PROPN
ejpam-5827	190	5	)	)	PUNCT
ejpam-5827	190	6	=	=	NOUN
ejpam-5827	190	7	τiκ	τiκ	NOUN
ejpam-5827	190	8	cl(h	cl(h	NUM
ejpam-5827	190	9	)	)	PUNCT
ejpam-5827	190	10	,	,	PUNCT
ejpam-5827	190	11	where	where	SCONJ
ejpam-5827	190	12	τiκ	τiκ	NOUN
ejpam-5827	190	13	cl(h	cl(h	CCONJ
ejpam-5827	190	14	)	)	PUNCT
ejpam-5827	190	15	represents	represent	VERB
ejpam-5827	190	16	closure	closure	NOUN
ejpam-5827	190	17	of	of	ADP
ejpam-5827	190	18	h	h	NOUN
ejpam-5827	190	19	w.r.t	w.r.t	NOUN
ejpam-5827	190	20	.	.	PUNCT
ejpam-5827	191	1	τiκ	τiκ	INTJ
ejpam-5827	191	2	.	.	PUNCT
ejpam-5827	192	1	(	(	PUNCT
ejpam-5827	192	2	iii	iii	X
ejpam-5827	192	3	)	)	PUNCT
ejpam-5827	192	4	τiκ	τiκ	NOUN
ejpam-5827	192	5	σ(h	σ(h	PROPN
ejpam-5827	192	6	)	)	PUNCT
ejpam-5827	192	7	=	=	SYM
ejpam-5827	193	1	|τiκl(h)|	|τiκl(h)|	PROPN
ejpam-5827	193	2	|τiκu(h)|	|τiκu(h)|	PROPN
ejpam-5827	193	3	,	,	PUNCT
ejpam-5827	193	4	where	where	SCONJ
ejpam-5827	193	5	|τiκu(h)|̸=0	|τiκu(h)|̸=0	NOUN
ejpam-5827	193	6	.	.	PUNCT
ejpam-5827	194	1	in	in	ADP
ejpam-5827	194	2	what	what	PRON
ejpam-5827	194	3	follows	follow	VERB
ejpam-5827	194	4	,	,	PUNCT
ejpam-5827	194	5	we	we	PRON
ejpam-5827	194	6	explore	explore	VERB
ejpam-5827	194	7	some	some	PRON
ejpam-5827	194	8	of	of	ADP
ejpam-5827	194	9	the	the	DET
ejpam-5827	194	10	previous	previous	ADJ
ejpam-5827	194	11	generations	generation	NOUN
ejpam-5827	194	12	of	of	ADP
ejpam-5827	194	13	rough	rough	ADJ
ejpam-5827	194	14	sets	set	NOUN
ejpam-5827	194	15	.	.	PUNCT
ejpam-5827	195	1	definition	definition	NOUN
ejpam-5827	195	2	8	8	NUM
ejpam-5827	195	3	.	.	PUNCT
ejpam-5827	196	1	yao	yao	NOUN
ejpam-5827	196	2	approach	approach	NOUN
ejpam-5827	196	3	[	[	X
ejpam-5827	196	4	73	73	NUM
ejpam-5827	196	5	]	]	PUNCT
ejpam-5827	196	6	let	let	VERB
ejpam-5827	196	7	r	r	PRON
ejpam-5827	196	8	be	be	AUX
ejpam-5827	196	9	a	a	DET
ejpam-5827	196	10	binary	binary	ADJ
ejpam-5827	196	11	relation	relation	NOUN
ejpam-5827	196	12	on	on	ADP
ejpam-5827	196	13	v.	v.	CCONJ
ejpam-5827	196	14	for	for	ADP
ejpam-5827	196	15	each	each	DET
ejpam-5827	196	16	g⊆w	g⊆w	PROPN
ejpam-5827	196	17	,	,	PUNCT
ejpam-5827	196	18	the	the	DET
ejpam-5827	196	19	y	y	NOUN
ejpam-5827	196	20	-	-	PUNCT
ejpam-5827	196	21	lower	low	ADJ
ejpam-5827	196	22	(	(	PUNCT
ejpam-5827	196	23	resp	resp	NOUN
ejpam-5827	196	24	.	.	PUNCT
ejpam-5827	197	1	y	y	NOUN
ejpam-5827	197	2	-	-	PUNCT
ejpam-5827	197	3	upper	upper	ADJ
ejpam-5827	197	4	)	)	PUNCT
ejpam-5827	197	5	approximation	approximation	NOUN
ejpam-5827	197	6	,	,	PUNCT
ejpam-5827	197	7	y	y	ADJ
ejpam-5827	197	8	-	-	PUNCT
ejpam-5827	197	9	boundary	boundary	NOUN
ejpam-5827	197	10	region	region	NOUN
ejpam-5827	197	11	and	and	CCONJ
ejpam-5827	197	12	y	y	NOUN
ejpam-5827	197	13	-	-	PUNCT
ejpam-5827	197	14	accuracy	accuracy	NOUN
ejpam-5827	197	15	of	of	ADP
ejpam-5827	197	16	the	the	DET
ejpam-5827	197	17	approximations	approximation	NOUN
ejpam-5827	197	18	are	be	AUX
ejpam-5827	197	19	defined	define	VERB
ejpam-5827	197	20	as	as	SCONJ
ejpam-5827	197	21	follows	follow	VERB
ejpam-5827	197	22	:	:	PUNCT
ejpam-5827	197	23	yr(g	yr(g	PUNCT
ejpam-5827	197	24	)	)	PUNCT
ejpam-5827	198	1	=	=	PRON
ejpam-5827	198	2	{	{	PUNCT
ejpam-5827	198	3	λ	λ	X
ejpam-5827	198	4	∈	∈	PROPN
ejpam-5827	198	5	v	v	NOUN
ejpam-5827	198	6	:	:	PUNCT
ejpam-5827	198	7	nr(λ	nr(λ	NUM
ejpam-5827	198	8	)	)	PUNCT
ejpam-5827	198	9	⊆	⊆	NUM
ejpam-5827	198	10	g	g	NOUN
ejpam-5827	198	11	}	}	PUNCT
ejpam-5827	198	12	;	;	PUNCT
ejpam-5827	198	13	yr(g	yr(g	PUNCT
ejpam-5827	198	14	)	)	PUNCT
ejpam-5827	199	1	=	=	PRON
ejpam-5827	199	2	{	{	PUNCT
ejpam-5827	199	3	λ	λ	X
ejpam-5827	199	4	∈	∈	PROPN
ejpam-5827	199	5	v	v	NOUN
ejpam-5827	199	6	:	:	PUNCT
ejpam-5827	199	7	nr(λ	nr(λ	NUM
ejpam-5827	199	8	)	)	PUNCT
ejpam-5827	199	9	∩	∩	NOUN
ejpam-5827	199	10	g	g	PROPN
ejpam-5827	199	11	̸=	̸=	PROPN
ejpam-5827	199	12	∅	∅	NOUN
ejpam-5827	199	13	}	}	PUNCT
ejpam-5827	199	14	;	;	PUNCT
ejpam-5827	199	15	by(g	by(g	X
ejpam-5827	199	16	)	)	PUNCT
ejpam-5827	200	1	=	=	SYM
ejpam-5827	200	2	yr(g)−	yr(g)−	NOUN
ejpam-5827	200	3	yr(g	yr(g	PROPN
ejpam-5827	200	4	)	)	PUNCT
ejpam-5827	200	5	;	;	PUNCT
ejpam-5827	200	6	and	and	CCONJ
ejpam-5827	200	7	σy(g	σy(g	X
ejpam-5827	200	8	)	)	PUNCT
ejpam-5827	200	9	=	=	NOUN
ejpam-5827	200	10	|y	|y	NOUN
ejpam-5827	200	11	r	r	NOUN
ejpam-5827	200	12	(	(	PUNCT
ejpam-5827	200	13	g)|	g)|	CCONJ
ejpam-5827	200	14	|yr(g)|	|yr(g)|	PROPN
ejpam-5827	200	15	,	,	PUNCT
ejpam-5827	200	16	|	|	ADV
ejpam-5827	200	17	yr(g	yr(g	NUM
ejpam-5827	200	18	)	)	PUNCT
ejpam-5827	200	19	|≠	|≠	NOUN
ejpam-5827	200	20	0	0	NUM
ejpam-5827	200	21	.	.	PUNCT
ejpam-5827	201	1	definition	definition	NOUN
ejpam-5827	201	2	9	9	NUM
ejpam-5827	201	3	.	.	PUNCT
ejpam-5827	202	1	allam	allam	PROPN
ejpam-5827	202	2	et	et	PROPN
ejpam-5827	202	3	al	al	PROPN
ejpam-5827	202	4	.	.	PROPN
ejpam-5827	202	5	approach	approach	NOUN
ejpam-5827	202	6	[	[	X
ejpam-5827	202	7	12	12	NUM
ejpam-5827	202	8	,	,	PUNCT
ejpam-5827	202	9	13	13	NUM
ejpam-5827	202	10	]	]	PUNCT
ejpam-5827	202	11	let	let	VERB
ejpam-5827	202	12	r	r	PRON
ejpam-5827	202	13	be	be	AUX
ejpam-5827	202	14	a	a	DET
ejpam-5827	202	15	binary	binary	ADJ
ejpam-5827	202	16	relation	relation	NOUN
ejpam-5827	202	17	on	on	ADP
ejpam-5827	202	18	v.	v.	CCONJ
ejpam-5827	202	19	for	for	ADP
ejpam-5827	202	20	each	each	DET
ejpam-5827	202	21	g⊆v	g⊆v	PROPN
ejpam-5827	202	22	,	,	PUNCT
ejpam-5827	202	23	the	the	DET
ejpam-5827	202	24	a	a	ADV
ejpam-5827	202	25	-	-	PUNCT
ejpam-5827	202	26	lower	low	ADJ
ejpam-5827	202	27	(	(	PUNCT
ejpam-5827	202	28	resp	resp	NOUN
ejpam-5827	202	29	.	.	PUNCT
ejpam-5827	203	1	a	a	DET
ejpam-5827	203	2	-	-	PUNCT
ejpam-5827	203	3	upper	upper	ADJ
ejpam-5827	203	4	)	)	PUNCT
ejpam-5827	203	5	approximation	approximation	NOUN
ejpam-5827	203	6	,	,	PUNCT
ejpam-5827	203	7	a	a	DET
ejpam-5827	203	8	-	-	PUNCT
ejpam-5827	203	9	boundary	boundary	NOUN
ejpam-5827	203	10	region	region	NOUN
ejpam-5827	203	11	and	and	CCONJ
ejpam-5827	203	12	a	a	DET
ejpam-5827	203	13	-	-	PUNCT
ejpam-5827	203	14	accuracy	accuracy	NOUN
ejpam-5827	203	15	of	of	ADP
ejpam-5827	203	16	the	the	DET
ejpam-5827	203	17	approximations	approximation	NOUN
ejpam-5827	203	18	are	be	AUX
ejpam-5827	203	19	defined	define	VERB
ejpam-5827	203	20	as	as	SCONJ
ejpam-5827	203	21	follows	follow	VERB
ejpam-5827	203	22	:	:	PUNCT
ejpam-5827	203	23	a⟨r⟩(g	a⟨r⟩(g	X
ejpam-5827	203	24	)	)	PUNCT
ejpam-5827	203	25	=	=	SYM
ejpam-5827	203	26	{	{	PUNCT
ejpam-5827	203	27	λ	λ	X
ejpam-5827	203	28	∈	∈	PROPN
ejpam-5827	203	29	v	v	NOUN
ejpam-5827	203	30	:	:	PUNCT
ejpam-5827	203	31	n⟨r⟩(λ	n⟨r⟩(λ	NOUN
ejpam-5827	203	32	)	)	PUNCT
ejpam-5827	203	33	⊆	⊆	NUM
ejpam-5827	203	34	g	g	NOUN
ejpam-5827	203	35	}	}	PUNCT
ejpam-5827	203	36	;	;	PUNCT
ejpam-5827	203	37	a⟨r⟩(g	a⟨r⟩(g	X
ejpam-5827	203	38	)	)	PUNCT
ejpam-5827	203	39	=	=	SYM
ejpam-5827	203	40	{	{	PUNCT
ejpam-5827	203	41	λ	λ	X
ejpam-5827	203	42	∈	∈	PROPN
ejpam-5827	203	43	v	v	NOUN
ejpam-5827	203	44	:	:	PUNCT
ejpam-5827	203	45	n⟨r⟩(λ	n⟨r⟩(λ	NOUN
ejpam-5827	203	46	)	)	PUNCT
ejpam-5827	203	47	∩	∩	NOUN
ejpam-5827	203	48	g	g	PROPN
ejpam-5827	203	49	̸=	̸=	PROPN
ejpam-5827	203	50	∅	∅	NOUN
ejpam-5827	203	51	}	}	PUNCT
ejpam-5827	203	52	;	;	PUNCT
ejpam-5827	203	53	ba(g	ba(g	NUM
ejpam-5827	203	54	)	)	PUNCT
ejpam-5827	203	55	=	=	SYM
ejpam-5827	203	56	a⟨r⟩(g)−a⟨r⟩(g	a⟨r⟩(g)−a⟨r⟩(g	NOUN
ejpam-5827	203	57	)	)	PUNCT
ejpam-5827	203	58	;	;	PUNCT
ejpam-5827	203	59	and	and	CCONJ
ejpam-5827	203	60	σa(g	σa(g	ADJ
ejpam-5827	203	61	)	)	PUNCT
ejpam-5827	204	1	=	=	PUNCT
ejpam-5827	204	2	|a⟨r⟩(g)|	|a⟨r⟩(g)|	PROPN
ejpam-5827	204	3	|a⟨r⟩(g)|	|a⟨r⟩(g)|	PROPN
ejpam-5827	204	4	,	,	PUNCT
ejpam-5827	204	5	|	|	ADV
ejpam-5827	204	6	a⟨r⟩(g	a⟨r⟩(g	NOUN
ejpam-5827	204	7	)	)	PUNCT
ejpam-5827	204	8	|≠	|≠	NOUN
ejpam-5827	204	9	0	0	NUM
ejpam-5827	204	10	.	.	PUNCT
ejpam-5827	205	1	definition	definition	NOUN
ejpam-5827	205	2	10	10	NUM
ejpam-5827	205	3	.	.	PUNCT
ejpam-5827	206	1	[	[	X
ejpam-5827	206	2	20	20	NUM
ejpam-5827	206	3	]	]	PUNCT
ejpam-5827	206	4	suppose	suppose	VERB
ejpam-5827	206	5	r	r	NOUN
ejpam-5827	206	6	is	be	AUX
ejpam-5827	206	7	a	a	DET
ejpam-5827	206	8	binary	binary	ADJ
ejpam-5827	206	9	relation	relation	NOUN
ejpam-5827	206	10	on	on	ADP
ejpam-5827	206	11	v.	v.	CCONJ
ejpam-5827	206	12	for	for	ADP
ejpam-5827	206	13	each	each	DET
ejpam-5827	206	14	λ∈v	λ∈v	NOUN
ejpam-5827	206	15	,	,	PUNCT
ejpam-5827	206	16	the	the	DET
ejpam-5827	206	17	maximal	maximal	ADJ
ejpam-5827	206	18	right	right	ADJ
ejpam-5827	206	19	neighborhood	neighborhood	NOUN
ejpam-5827	206	20	(	(	PUNCT
ejpam-5827	206	21	shortened	shorten	VERB
ejpam-5827	206	22	by	by	ADP
ejpam-5827	206	23	nm	nm	NOUN
ejpam-5827	206	24	)	)	PUNCT
ejpam-5827	206	25	is	be	AUX
ejpam-5827	206	26	defined	define	VERB
ejpam-5827	206	27	as	as	SCONJ
ejpam-5827	206	28	follows	follow	VERB
ejpam-5827	206	29	:	:	PUNCT
ejpam-5827	206	30	nm(λ	nm(λ	NOUN
ejpam-5827	206	31	)	)	PUNCT
ejpam-5827	206	32	=	=	SYM
ejpam-5827	206	33	∪λ∈nr(µ)nr(µ	∪λ∈nr(µ)nr(µ	PROPN
ejpam-5827	206	34	)	)	PUNCT
ejpam-5827	206	35	.	.	PUNCT
ejpam-5827	207	1	r.	r.	PROPN
ejpam-5827	207	2	a.	a.	PROPN
ejpam-5827	207	3	hosny	hosny	PROPN
ejpam-5827	207	4	,	,	PUNCT
ejpam-5827	207	5	m.	m.	PROPN
ejpam-5827	207	6	k.	k.	PROPN
ejpam-5827	208	1	el	el	PROPN
ejpam-5827	208	2	-	-	PROPN
ejpam-5827	208	3	bably	bably	ADV
ejpam-5827	208	4	,	,	PUNCT
ejpam-5827	208	5	m.	m.	NOUN
ejpam-5827	208	6	a.	a.	PROPN
ejpam-5827	208	7	el	el	PROPN
ejpam-5827	208	8	-	-	PROPN
ejpam-5827	208	9	gayar	gayar	PROPN
ejpam-5827	208	10	/	/	SYM
ejpam-5827	208	11	eur	eur	PROPN
ejpam-5827	208	12	.	.	PUNCT
ejpam-5827	209	1	j.	j.	PROPN
ejpam-5827	209	2	pure	pure	PROPN
ejpam-5827	209	3	appl	appl	PROPN
ejpam-5827	209	4	.	.	PROPN
ejpam-5827	209	5	math	math	PROPN
ejpam-5827	209	6	,	,	PUNCT
ejpam-5827	209	7	18	18	NUM
ejpam-5827	209	8	(	(	PUNCT
ejpam-5827	209	9	1	1	NUM
ejpam-5827	209	10	)	)	PUNCT
ejpam-5827	209	11	(	(	PUNCT
ejpam-5827	209	12	2025	2025	NUM
ejpam-5827	209	13	)	)	PUNCT
ejpam-5827	209	14	,	,	PUNCT
ejpam-5827	209	15	5827	5827	NUM
ejpam-5827	209	16	9	9	NUM
ejpam-5827	209	17	of	of	ADP
ejpam-5827	209	18	29	29	NUM
ejpam-5827	209	19	definition	definition	NOUN
ejpam-5827	209	20	11	11	NUM
ejpam-5827	209	21	.	.	PUNCT
ejpam-5827	210	1	dai	dai	PROPN
ejpam-5827	210	2	et	et	PROPN
ejpam-5827	210	3	al	al	PROPN
ejpam-5827	210	4	.	.	PROPN
ejpam-5827	210	5	approach	approach	NOUN
ejpam-5827	210	6	[	[	X
ejpam-5827	210	7	20	20	NUM
ejpam-5827	210	8	]	]	PUNCT
ejpam-5827	210	9	let	let	VERB
ejpam-5827	210	10	r	r	PRON
ejpam-5827	210	11	be	be	AUX
ejpam-5827	210	12	a	a	DET
ejpam-5827	210	13	binary	binary	ADJ
ejpam-5827	210	14	relation	relation	NOUN
ejpam-5827	210	15	on	on	ADP
ejpam-5827	210	16	v.	v.	CCONJ
ejpam-5827	210	17	for	for	ADP
ejpam-5827	210	18	any	any	DET
ejpam-5827	210	19	subset	subset	NOUN
ejpam-5827	210	20	g	g	PROPN
ejpam-5827	210	21	⊆	⊆	NUM
ejpam-5827	210	22	v	v	NOUN
ejpam-5827	210	23	,	,	PUNCT
ejpam-5827	210	24	the	the	DET
ejpam-5827	210	25	d	d	NOUN
ejpam-5827	210	26	-	-	PUNCT
ejpam-5827	210	27	lower	low	ADJ
ejpam-5827	210	28	(	(	PUNCT
ejpam-5827	210	29	resp	resp	NOUN
ejpam-5827	210	30	.	.	PUNCT
ejpam-5827	211	1	d	d	X
ejpam-5827	211	2	-	-	ADJ
ejpam-5827	211	3	upper	upper	ADJ
ejpam-5827	211	4	)	)	PUNCT
ejpam-5827	211	5	approximation	approximation	NOUN
ejpam-5827	211	6	,	,	PUNCT
ejpam-5827	211	7	d	d	ADJ
ejpam-5827	211	8	-	-	PUNCT
ejpam-5827	211	9	boundary	boundary	ADJ
ejpam-5827	211	10	region	region	NOUN
ejpam-5827	211	11	,	,	PUNCT
ejpam-5827	211	12	and	and	CCONJ
ejpam-5827	212	1	d	d	X
ejpam-5827	212	2	-	-	PUNCT
ejpam-5827	212	3	accuracy	accuracy	NOUN
ejpam-5827	212	4	of	of	ADP
ejpam-5827	212	5	the	the	DET
ejpam-5827	212	6	approximations	approximation	NOUN
ejpam-5827	212	7	are	be	AUX
ejpam-5827	212	8	defined	define	VERB
ejpam-5827	212	9	as	as	SCONJ
ejpam-5827	212	10	follows	follow	VERB
ejpam-5827	212	11	:	:	PUNCT
ejpam-5827	212	12	dm(g	dm(g	X
ejpam-5827	212	13	)	)	PUNCT
ejpam-5827	213	1	=	=	SYM
ejpam-5827	213	2	{	{	PUNCT
ejpam-5827	213	3	λ	λ	X
ejpam-5827	213	4	∈	∈	NOUN
ejpam-5827	213	5	v	v	NOUN
ejpam-5827	213	6	:	:	PUNCT
ejpam-5827	213	7	nm(λ	nm(λ	NOUN
ejpam-5827	213	8	)	)	PUNCT
ejpam-5827	213	9	⊆	⊆	NUM
ejpam-5827	213	10	g	g	NOUN
ejpam-5827	213	11	}	}	PUNCT
ejpam-5827	213	12	;	;	PUNCT
ejpam-5827	213	13	dm(g	dm(g	X
ejpam-5827	213	14	)	)	PUNCT
ejpam-5827	213	15	=	=	SYM
ejpam-5827	213	16	{	{	PUNCT
ejpam-5827	213	17	λ	λ	X
ejpam-5827	213	18	∈	∈	NOUN
ejpam-5827	213	19	v	v	NOUN
ejpam-5827	213	20	:	:	PUNCT
ejpam-5827	213	21	nm(λ	nm(λ	NOUN
ejpam-5827	213	22	)	)	PUNCT
ejpam-5827	213	23	∩	∩	NOUN
ejpam-5827	213	24	g	g	PROPN
ejpam-5827	213	25	̸=	̸=	PROPN
ejpam-5827	213	26	∅	∅	NOUN
ejpam-5827	213	27	}	}	PUNCT
ejpam-5827	213	28	;	;	PUNCT
ejpam-5827	213	29	bd(g	bd(g	X
ejpam-5827	213	30	)	)	PUNCT
ejpam-5827	213	31	=	=	SYM
ejpam-5827	213	32	dm(g)−dm(g	dm(g)−dm(g	PROPN
ejpam-5827	213	33	)	)	PUNCT
ejpam-5827	213	34	;	;	PUNCT
ejpam-5827	213	35	and	and	CCONJ
ejpam-5827	213	36	σd(g	σd(g	NUM
ejpam-5827	213	37	)	)	PUNCT
ejpam-5827	214	1	=	=	PUNCT
ejpam-5827	214	2	|am(g)|	|am(g)|	ADP
ejpam-5827	214	3	|dm(g)|	|dm(g)|	NOUN
ejpam-5827	214	4	,	,	PUNCT
ejpam-5827	214	5	|	|	ADV
ejpam-5827	214	6	dm(g	dm(g	PUNCT
ejpam-5827	214	7	)	)	PUNCT
ejpam-5827	214	8	|̸=	|̸=	NOUN
ejpam-5827	214	9	0	0	NUM
ejpam-5827	214	10	.	.	NOUN
ejpam-5827	214	11	3	3	NUM
ejpam-5827	214	12	.	.	NUM
ejpam-5827	214	13	approximations	approximation	NOUN
ejpam-5827	214	14	and	and	CCONJ
ejpam-5827	214	15	supra	supra	NOUN
ejpam-5827	214	16	topologies	topology	NOUN
ejpam-5827	214	17	generated	generate	VERB
ejpam-5827	214	18	by	by	ADP
ejpam-5827	214	19	different	different	ADJ
ejpam-5827	214	20	κ	κ	NOUN
ejpam-5827	214	21	-	-	ADJ
ejpam-5827	214	22	ns	ns	ADJ
ejpam-5827	214	23	and	and	CCONJ
ejpam-5827	214	24	primal	primal	ADJ
ejpam-5827	214	25	the	the	DET
ejpam-5827	214	26	aim	aim	NOUN
ejpam-5827	214	27	of	of	ADP
ejpam-5827	214	28	this	this	DET
ejpam-5827	214	29	section	section	NOUN
ejpam-5827	214	30	is	be	AUX
ejpam-5827	214	31	to	to	PART
ejpam-5827	214	32	present	present	VERB
ejpam-5827	214	33	eight	eight	NUM
ejpam-5827	214	34	distinct	distinct	ADJ
ejpam-5827	214	35	supra	supra	NOUN
ejpam-5827	214	36	-	-	PUNCT
ejpam-5827	214	37	topologies	topology	NOUN
ejpam-5827	214	38	generated	generate	VERB
ejpam-5827	214	39	from	from	ADP
ejpam-5827	214	40	primal	primal	ADJ
ejpam-5827	214	41	and	and	CCONJ
ejpam-5827	214	42	κ	κ	NOUN
ejpam-5827	214	43	-	-	NOUN
ejpam-5827	214	44	neighborhoods	neighborhood	NOUN
ejpam-5827	214	45	,	,	PUNCT
ejpam-5827	214	46	where	where	SCONJ
ejpam-5827	214	47	κ	κ	PROPN
ejpam-5827	214	48	∈	∈	PROPN
ejpam-5827	214	49	{	{	PUNCT
ejpam-5827	214	50	r	r	NOUN
ejpam-5827	214	51	,	,	PUNCT
ejpam-5827	214	52	l	l	NOUN
ejpam-5827	214	53	,	,	PUNCT
ejpam-5827	214	54	i	i	PRON
ejpam-5827	214	55	,	,	PUNCT
ejpam-5827	214	56	u	u	PROPN
ejpam-5827	214	57	,	,	PUNCT
ejpam-5827	214	58	⟨r⟩	⟨r⟩	PROPN
ejpam-5827	214	59	,	,	PUNCT
ejpam-5827	214	60	⟨l⟩	⟨l⟩	PROPN
ejpam-5827	214	61	,	,	PUNCT
ejpam-5827	214	62	⟨i⟩	⟨i⟩	PROPN
ejpam-5827	214	63	,	,	PUNCT
ejpam-5827	214	64	⟨u⟩	⟨u⟩	PROPN
ejpam-5827	214	65	}	}	PUNCT
ejpam-5827	214	66	.	.	PUNCT
ejpam-5827	215	1	the	the	DET
ejpam-5827	215	2	relationships	relationship	NOUN
ejpam-5827	215	3	between	between	ADP
ejpam-5827	215	4	these	these	DET
ejpam-5827	215	5	topologies	topology	NOUN
ejpam-5827	215	6	will	will	AUX
ejpam-5827	215	7	be	be	AUX
ejpam-5827	215	8	examined	examine	VERB
ejpam-5827	215	9	,	,	PUNCT
ejpam-5827	215	10	along	along	ADP
ejpam-5827	215	11	with	with	ADP
ejpam-5827	215	12	comparisons	comparison	NOUN
ejpam-5827	215	13	to	to	PART
ejpam-5827	215	14	highlight	highlight	VERB
ejpam-5827	215	15	their	their	PRON
ejpam-5827	215	16	differences	difference	NOUN
ejpam-5827	215	17	.	.	PUNCT
ejpam-5827	216	1	additionally	additionally	ADV
ejpam-5827	216	2	,	,	PUNCT
ejpam-5827	216	3	new	new	ADJ
ejpam-5827	216	4	rough	rough	ADJ
ejpam-5827	216	5	approximations	approximation	NOUN
ejpam-5827	216	6	derived	derive	VERB
ejpam-5827	216	7	from	from	ADP
ejpam-5827	216	8	these	these	DET
ejpam-5827	216	9	topologies	topology	NOUN
ejpam-5827	216	10	will	will	AUX
ejpam-5827	216	11	be	be	AUX
ejpam-5827	216	12	constructed	construct	VERB
ejpam-5827	216	13	,	,	PUNCT
ejpam-5827	216	14	and	and	CCONJ
ejpam-5827	216	15	some	some	PRON
ejpam-5827	216	16	of	of	ADP
ejpam-5827	216	17	their	their	PRON
ejpam-5827	216	18	properties	property	NOUN
ejpam-5827	216	19	will	will	AUX
ejpam-5827	216	20	be	be	AUX
ejpam-5827	216	21	explored	explore	VERB
ejpam-5827	216	22	.	.	PUNCT
ejpam-5827	217	1	it	it	PRON
ejpam-5827	217	2	is	be	AUX
ejpam-5827	217	3	evident	evident	ADJ
ejpam-5827	217	4	that	that	SCONJ
ejpam-5827	217	5	the	the	DET
ejpam-5827	217	6	best	good	ADJ
ejpam-5827	217	7	approximations	approximation	NOUN
ejpam-5827	217	8	and	and	CCONJ
ejpam-5827	217	9	the	the	DET
ejpam-5827	217	10	highest	high	ADJ
ejpam-5827	217	11	accuracy	accuracy	NOUN
ejpam-5827	217	12	measures	measure	NOUN
ejpam-5827	217	13	are	be	AUX
ejpam-5827	217	14	obtained	obtain	VERB
ejpam-5827	217	15	for	for	ADP
ejpam-5827	217	16	κ	κ	PROPN
ejpam-5827	217	17	∈	∈	PROPN
ejpam-5827	217	18	{	{	PUNCT
ejpam-5827	217	19	i	i	PROPN
ejpam-5827	217	20	,	,	PUNCT
ejpam-5827	217	21	⟨i⟩	⟨i⟩	PROPN
ejpam-5827	217	22	}	}	PUNCT
ejpam-5827	217	23	.	.	PUNCT
ejpam-5827	218	1	furthermore	furthermore	ADV
ejpam-5827	218	2	,	,	PUNCT
ejpam-5827	218	3	the	the	DET
ejpam-5827	218	4	proposed	propose	VERB
ejpam-5827	218	5	approximations	approximation	NOUN
ejpam-5827	218	6	will	will	AUX
ejpam-5827	218	7	be	be	AUX
ejpam-5827	218	8	compared	compare	VERB
ejpam-5827	218	9	with	with	ADP
ejpam-5827	218	10	previous	previous	ADJ
ejpam-5827	218	11	ones	one	NOUN
ejpam-5827	218	12	from	from	ADP
ejpam-5827	218	13	the	the	DET
ejpam-5827	218	14	literature	literature	NOUN
ejpam-5827	218	15	[	[	X
ejpam-5827	218	16	12	12	NUM
ejpam-5827	218	17	,	,	PUNCT
ejpam-5827	218	18	20	20	NUM
ejpam-5827	218	19	,	,	PUNCT
ejpam-5827	218	20	35	35	NUM
ejpam-5827	218	21	,	,	PUNCT
ejpam-5827	218	22	73	73	NUM
ejpam-5827	218	23	]	]	PUNCT
ejpam-5827	218	24	.	.	PUNCT
ejpam-5827	219	1	we	we	PRON
ejpam-5827	219	2	will	will	AUX
ejpam-5827	219	3	prove	prove	VERB
ejpam-5827	219	4	that	that	SCONJ
ejpam-5827	219	5	primal	primal	ADJ
ejpam-5827	219	6	play	play	VERB
ejpam-5827	219	7	a	a	DET
ejpam-5827	219	8	key	key	ADJ
ejpam-5827	219	9	role	role	NOUN
ejpam-5827	219	10	in	in	ADP
ejpam-5827	219	11	extending	extend	VERB
ejpam-5827	219	12	these	these	DET
ejpam-5827	219	13	methods	method	NOUN
ejpam-5827	219	14	.	.	PUNCT
ejpam-5827	220	1	the	the	DET
ejpam-5827	220	2	following	follow	VERB
ejpam-5827	220	3	result	result	NOUN
ejpam-5827	220	4	presents	present	VERB
ejpam-5827	220	5	a	a	DET
ejpam-5827	220	6	method	method	NOUN
ejpam-5827	220	7	for	for	ADP
ejpam-5827	220	8	generating	generate	VERB
ejpam-5827	220	9	κ	κ	PROPN
ejpam-5827	220	10	-	-	ADJ
ejpam-5827	220	11	supra	supra	ADJ
ejpam-5827	220	12	topology	topology	NOUN
ejpam-5827	220	13	structures	structure	NOUN
ejpam-5827	220	14	from	from	ADP
ejpam-5827	220	15	nκ	nκ	ADJ
ejpam-5827	220	16	-	-	PUNCT
ejpam-5827	220	17	neighborhood	neighborhood	NOUN
ejpam-5827	220	18	systems	system	NOUN
ejpam-5827	220	19	and	and	CCONJ
ejpam-5827	220	20	primal	primal	ADJ
ejpam-5827	220	21	.	.	PUNCT
ejpam-5827	221	1	theorem	theorem	NOUN
ejpam-5827	221	2	3	3	X
ejpam-5827	221	3	.	.	PUNCT
ejpam-5827	222	1	let	let	AUX
ejpam-5827	222	2	(	(	PUNCT
ejpam-5827	222	3	v	v	NOUN
ejpam-5827	222	4	,	,	PUNCT
ejpam-5827	222	5	r	r	NOUN
ejpam-5827	222	6	,	,	PUNCT
ejpam-5827	222	7	ζκ	ζκ	NOUN
ejpam-5827	222	8	)	)	PUNCT
ejpam-5827	222	9	be	be	AUX
ejpam-5827	222	10	a	a	DET
ejpam-5827	222	11	κ	κ	NOUN
ejpam-5827	222	12	-	-	PUNCT
ejpam-5827	222	13	ns	ns	ADJ
ejpam-5827	222	14	,	,	PUNCT
ejpam-5827	222	15	p	p	NOUN
ejpam-5827	222	16	be	be	AUX
ejpam-5827	222	17	a	a	DET
ejpam-5827	222	18	primal	primal	NOUN
ejpam-5827	222	19	on	on	ADP
ejpam-5827	222	20	v	v	NOUN
ejpam-5827	222	21	,	,	PUNCT
ejpam-5827	222	22	and	and	CCONJ
ejpam-5827	222	23	h	h	NOUN
ejpam-5827	222	24	⊆v	⊆v	NOUN
ejpam-5827	222	25	.	.	PUNCT
ejpam-5827	223	1	then	then	ADV
ejpam-5827	223	2	,	,	PUNCT
ejpam-5827	223	3	for	for	ADP
ejpam-5827	223	4	every	every	DET
ejpam-5827	223	5	κ	κ	NOUN
ejpam-5827	223	6	,	,	PUNCT
ejpam-5827	223	7	the	the	DET
ejpam-5827	223	8	class	class	NOUN
ejpam-5827	223	9	τpκ	τpκ	NOUN
ejpam-5827	223	10	=	=	SYM
ejpam-5827	223	11	{	{	PUNCT
ejpam-5827	223	12	h	h	NOUN
ejpam-5827	223	13	⊆v	⊆v	NOUN
ejpam-5827	223	14	:	:	PUNCT
ejpam-5827	223	15	∀z	∀z	X
ejpam-5827	223	16	∈h	∈h	NOUN
ejpam-5827	223	17	,	,	PUNCT
ejpam-5827	223	18	nκ(z)−h	nκ(z)−h	PROPN
ejpam-5827	223	19	∈p	∈p	PROPN
ejpam-5827	223	20	}	}	PUNCT
ejpam-5827	223	21	is	be	AUX
ejpam-5827	223	22	a	a	DET
ejpam-5827	223	23	supra	supra	ADJ
ejpam-5827	223	24	topology	topology	NOUN
ejpam-5827	223	25	on	on	ADP
ejpam-5827	223	26	v.	v.	ADP
ejpam-5827	223	27	proof	proof	NOUN
ejpam-5827	223	28	.	.	PUNCT
ejpam-5827	224	1	(	(	PUNCT
ejpam-5827	224	2	i	i	NOUN
ejpam-5827	224	3	)	)	PUNCT
ejpam-5827	224	4	clearly	clearly	ADV
ejpam-5827	224	5	v	v	VERB
ejpam-5827	224	6	and	and	CCONJ
ejpam-5827	224	7	∅	∅	NOUN
ejpam-5827	224	8	belong	belong	VERB
ejpam-5827	224	9	to	to	ADP
ejpam-5827	224	10	τpκ	τpκ	NOUN
ejpam-5827	224	11	.	.	PUNCT
ejpam-5827	225	1	(	(	PUNCT
ejpam-5827	225	2	ii	ii	AUX
ejpam-5827	225	3	)	)	PUNCT
ejpam-5827	225	4	let	let	VERB
ejpam-5827	225	5	hα	hα	ADP
ejpam-5827	225	6	∈τpκ	∈τpκ	NOUN
ejpam-5827	225	7	,	,	PUNCT
ejpam-5827	225	8	α	α	PROPN
ejpam-5827	225	9	∈ω	∈ω	NOUN
ejpam-5827	225	10	and	and	CCONJ
ejpam-5827	225	11	z	z	NOUN
ejpam-5827	225	12	∈∪α∈ωhα	∈∪α∈ωhα	NOUN
ejpam-5827	225	13	,	,	PUNCT
ejpam-5827	225	14	then	then	ADV
ejpam-5827	225	15	there	there	PRON
ejpam-5827	225	16	exists	exist	VERB
ejpam-5827	225	17	α0	α0	PROPN
ejpam-5827	225	18	∈ω	∈ω	PRON
ejpam-5827	225	19	s.t	s.t	PROPN
ejpam-5827	225	20	.	.	PROPN
ejpam-5827	225	21	z	z	PROPN
ejpam-5827	225	22	∈hα0	∈hα0	PROPN
ejpam-5827	225	23	.	.	PUNCT
ejpam-5827	226	1	hence	hence	ADV
ejpam-5827	226	2	,	,	PUNCT
ejpam-5827	226	3	nκ(z	nκ(z	NUM
ejpam-5827	226	4	)	)	PUNCT
ejpam-5827	226	5	−	−	PROPN
ejpam-5827	226	6	hα0	hα0	PROPN
ejpam-5827	226	7	∈p	∈p	NOUN
ejpam-5827	226	8	.	.	PUNCT
ejpam-5827	227	1	since	since	SCONJ
ejpam-5827	227	2	−(∪α∈ωhα	−(∪α∈ωhα	PROPN
ejpam-5827	227	3	)	)	PUNCT
ejpam-5827	227	4	⊆	⊆	NUM
ejpam-5827	227	5	−hα0	−hα0	PROPN
ejpam-5827	227	6	,	,	PUNCT
ejpam-5827	227	7	then	then	ADV
ejpam-5827	227	8	nκ(z	nκ(z	NUM
ejpam-5827	227	9	)	)	PUNCT
ejpam-5827	227	10	−	−	PROPN
ejpam-5827	227	11	(	(	PUNCT
ejpam-5827	227	12	∪α∈ωhα	∪α∈ωhα	NOUN
ejpam-5827	227	13	)	)	PUNCT
ejpam-5827	227	14	∈p	∈p	NUM
ejpam-5827	227	15	i.e	i.e	PRON
ejpam-5827	227	16	∪α∈ωhα	∪α∈ωhα	PROPN
ejpam-5827	227	17	∈	∈	PROPN
ejpam-5827	227	18	τpκ	τpκ	NOUN
ejpam-5827	227	19	.	.	PUNCT
ejpam-5827	228	1	so	so	ADV
ejpam-5827	228	2	,	,	PUNCT
ejpam-5827	228	3	τpκ	τpκ	NOUN
ejpam-5827	228	4	is	be	AUX
ejpam-5827	228	5	a	a	DET
ejpam-5827	228	6	supra	supra	ADJ
ejpam-5827	228	7	topology	topology	NOUN
ejpam-5827	228	8	on	on	ADP
ejpam-5827	228	9	v.	v.	ADP
ejpam-5827	228	10	the	the	DET
ejpam-5827	228	11	next	next	ADJ
ejpam-5827	228	12	example	example	NOUN
ejpam-5827	228	13	shows	show	VERB
ejpam-5827	228	14	that	that	SCONJ
ejpam-5827	228	15	τpκ	τpκ	NOUN
ejpam-5827	228	16	need	need	AUX
ejpam-5827	228	17	not	not	PART
ejpam-5827	228	18	be	be	AUX
ejpam-5827	228	19	a	a	DET
ejpam-5827	228	20	topology	topology	NOUN
ejpam-5827	228	21	.	.	PUNCT
ejpam-5827	229	1	example	example	NOUN
ejpam-5827	230	1	2	2	NUM
ejpam-5827	230	2	.	.	PUNCT
ejpam-5827	230	3	let	let	VERB
ejpam-5827	230	4	v	v	VERB
ejpam-5827	230	5	=	=	PUNCT
ejpam-5827	230	6	{	{	PUNCT
ejpam-5827	230	7	a	a	PRON
ejpam-5827	230	8	,	,	PUNCT
ejpam-5827	230	9	b	b	NOUN
ejpam-5827	230	10	,	,	PUNCT
ejpam-5827	230	11	c	c	NOUN
ejpam-5827	230	12	}	}	PUNCT
ejpam-5827	230	13	,	,	PUNCT
ejpam-5827	230	14	and	and	CCONJ
ejpam-5827	230	15	consider	consider	VERB
ejpam-5827	230	16	the	the	DET
ejpam-5827	230	17	collection	collection	NOUN
ejpam-5827	230	18	p	p	X
ejpam-5827	230	19	=	=	NOUN
ejpam-5827	230	20	{	{	PUNCT
ejpam-5827	230	21	∅	∅	NOUN
ejpam-5827	230	22	,	,	PUNCT
ejpam-5827	230	23	{	{	PUNCT
ejpam-5827	230	24	a	a	X
ejpam-5827	230	25	}	}	PUNCT
ejpam-5827	230	26	,	,	PUNCT
ejpam-5827	230	27	{	{	PUNCT
ejpam-5827	230	28	b	b	NOUN
ejpam-5827	230	29	}	}	PUNCT
ejpam-5827	230	30	,	,	PUNCT
ejpam-5827	230	31	{	{	PUNCT
ejpam-5827	230	32	c	c	X
ejpam-5827	230	33	}	}	PUNCT
ejpam-5827	230	34	,	,	PUNCT
ejpam-5827	230	35	{	{	PUNCT
ejpam-5827	230	36	a	a	DET
ejpam-5827	230	37	,	,	PUNCT
ejpam-5827	230	38	b	b	NOUN
ejpam-5827	230	39	}	}	PUNCT
ejpam-5827	230	40	,	,	PUNCT
ejpam-5827	230	41	{	{	PUNCT
ejpam-5827	230	42	a	a	PRON
ejpam-5827	230	43	,	,	PUNCT
ejpam-5827	230	44	c	c	NOUN
ejpam-5827	230	45	}	}	PUNCT
ejpam-5827	230	46	}	}	PUNCT
ejpam-5827	230	47	,	,	PUNCT
ejpam-5827	230	48	which	which	PRON
ejpam-5827	230	49	forms	form	VERB
ejpam-5827	230	50	a	a	DET
ejpam-5827	230	51	primal	primal	NOUN
ejpam-5827	230	52	on	on	ADP
ejpam-5827	230	53	v.	v.	CCONJ
ejpam-5827	230	54	let	let	VERB
ejpam-5827	230	55	r	r	NOUN
ejpam-5827	230	56	=	=	PRON
ejpam-5827	230	57	{	{	PUNCT
ejpam-5827	230	58	(	(	PUNCT
ejpam-5827	230	59	a	a	DET
ejpam-5827	230	60	,	,	PUNCT
ejpam-5827	230	61	b	b	NOUN
ejpam-5827	230	62	)	)	PUNCT
ejpam-5827	230	63	,	,	PUNCT
ejpam-5827	230	64	(	(	PUNCT
ejpam-5827	230	65	a	a	DET
ejpam-5827	230	66	,	,	PUNCT
ejpam-5827	230	67	c	c	NOUN
ejpam-5827	230	68	)	)	PUNCT
ejpam-5827	230	69	,	,	PUNCT
ejpam-5827	230	70	(	(	PUNCT
ejpam-5827	230	71	b	b	X
ejpam-5827	230	72	,	,	PUNCT
ejpam-5827	230	73	b	b	NOUN
ejpam-5827	230	74	)	)	PUNCT
ejpam-5827	230	75	,	,	PUNCT
ejpam-5827	230	76	(	(	PUNCT
ejpam-5827	230	77	b	b	X
ejpam-5827	230	78	,	,	PUNCT
ejpam-5827	230	79	c	c	NOUN
ejpam-5827	230	80	)	)	PUNCT
ejpam-5827	230	81	,	,	PUNCT
ejpam-5827	230	82	(	(	PUNCT
ejpam-5827	230	83	c	c	X
ejpam-5827	230	84	,	,	PUNCT
ejpam-5827	230	85	b	b	NOUN
ejpam-5827	230	86	)	)	PUNCT
ejpam-5827	230	87	}	}	PUNCT
ejpam-5827	230	88	be	be	AUX
ejpam-5827	230	89	an	an	DET
ejpam-5827	230	90	arbitrary	arbitrary	ADJ
ejpam-5827	230	91	relation	relation	NOUN
ejpam-5827	230	92	on	on	ADP
ejpam-5827	230	93	v.	v.	CCONJ
ejpam-5827	230	94	then	then	ADV
ejpam-5827	230	95	,	,	PUNCT
ejpam-5827	230	96	the	the	DET
ejpam-5827	230	97	associated	associated	ADJ
ejpam-5827	230	98	structure	structure	NOUN
ejpam-5827	230	99	is	be	AUX
ejpam-5827	230	100	given	give	VERB
ejpam-5827	230	101	by	by	ADP
ejpam-5827	230	102	:	:	PUNCT
ejpam-5827	230	103	τpr	τpr	NOUN
ejpam-5827	230	104	=	=	SYM
ejpam-5827	230	105	{	{	PUNCT
ejpam-5827	230	106	∅,v	∅,v	X
ejpam-5827	230	107	,	,	PUNCT
ejpam-5827	230	108	{	{	PUNCT
ejpam-5827	230	109	b	b	NOUN
ejpam-5827	230	110	}	}	PUNCT
ejpam-5827	230	111	,	,	PUNCT
ejpam-5827	230	112	{	{	PUNCT
ejpam-5827	230	113	c	c	X
ejpam-5827	230	114	}	}	PUNCT
ejpam-5827	230	115	,	,	PUNCT
ejpam-5827	230	116	{	{	PUNCT
ejpam-5827	230	117	a	a	DET
ejpam-5827	230	118	,	,	PUNCT
ejpam-5827	230	119	b	b	NOUN
ejpam-5827	230	120	}	}	PUNCT
ejpam-5827	230	121	,	,	PUNCT
ejpam-5827	230	122	{	{	PUNCT
ejpam-5827	230	123	a	a	X
ejpam-5827	230	124	,	,	PUNCT
ejpam-5827	230	125	c	c	NOUN
ejpam-5827	230	126	}	}	PUNCT
ejpam-5827	230	127	,	,	PUNCT
ejpam-5827	230	128	{	{	PUNCT
ejpam-5827	230	129	b	b	X
ejpam-5827	230	130	,	,	PUNCT
ejpam-5827	230	131	c	c	NOUN
ejpam-5827	230	132	}	}	PUNCT
ejpam-5827	230	133	}	}	PUNCT
ejpam-5827	230	134	.	.	PUNCT
ejpam-5827	231	1	r.	r.	PROPN
ejpam-5827	231	2	a.	a.	PROPN
ejpam-5827	231	3	hosny	hosny	PROPN
ejpam-5827	231	4	,	,	PUNCT
ejpam-5827	231	5	m.	m.	PROPN
ejpam-5827	231	6	k.	k.	PROPN
ejpam-5827	232	1	el	el	PROPN
ejpam-5827	232	2	-	-	PROPN
ejpam-5827	232	3	bably	bably	ADV
ejpam-5827	232	4	,	,	PUNCT
ejpam-5827	232	5	m.	m.	NOUN
ejpam-5827	232	6	a.	a.	PROPN
ejpam-5827	232	7	el	el	PROPN
ejpam-5827	232	8	-	-	PROPN
ejpam-5827	232	9	gayar	gayar	PROPN
ejpam-5827	232	10	/	/	SYM
ejpam-5827	232	11	eur	eur	PROPN
ejpam-5827	232	12	.	.	PUNCT
ejpam-5827	233	1	j.	j.	PROPN
ejpam-5827	233	2	pure	pure	PROPN
ejpam-5827	233	3	appl	appl	PROPN
ejpam-5827	233	4	.	.	PROPN
ejpam-5827	233	5	math	math	PROPN
ejpam-5827	233	6	,	,	PUNCT
ejpam-5827	233	7	18	18	NUM
ejpam-5827	233	8	(	(	PUNCT
ejpam-5827	233	9	1	1	NUM
ejpam-5827	233	10	)	)	PUNCT
ejpam-5827	233	11	(	(	PUNCT
ejpam-5827	233	12	2025	2025	NUM
ejpam-5827	233	13	)	)	PUNCT
ejpam-5827	233	14	,	,	PUNCT
ejpam-5827	233	15	5827	5827	NUM
ejpam-5827	233	16	10	10	NUM
ejpam-5827	233	17	of	of	ADP
ejpam-5827	233	18	29	29	NUM
ejpam-5827	233	19	notably	notably	ADV
ejpam-5827	233	20	,	,	PUNCT
ejpam-5827	233	21	while	while	SCONJ
ejpam-5827	233	22	{	{	PUNCT
ejpam-5827	233	23	a	a	DET
ejpam-5827	233	24	,	,	PUNCT
ejpam-5827	233	25	b	b	NOUN
ejpam-5827	233	26	}	}	PUNCT
ejpam-5827	233	27	,	,	PUNCT
ejpam-5827	233	28	{	{	PUNCT
ejpam-5827	233	29	a	a	PRON
ejpam-5827	233	30	,	,	PUNCT
ejpam-5827	233	31	c	c	NOUN
ejpam-5827	233	32	}	}	PUNCT
ejpam-5827	233	33	∈	∈	PROPN
ejpam-5827	233	34	τpr	τpr	NOUN
ejpam-5827	233	35	,	,	PUNCT
ejpam-5827	233	36	their	their	PRON
ejpam-5827	233	37	intersection	intersection	NOUN
ejpam-5827	233	38	{	{	PUNCT
ejpam-5827	233	39	a	a	PROPN
ejpam-5827	233	40	,	,	PUNCT
ejpam-5827	233	41	b	b	NOUN
ejpam-5827	233	42	}	}	PUNCT
ejpam-5827	233	43	∩	∩	NOUN
ejpam-5827	233	44	{	{	PUNCT
ejpam-5827	233	45	a	a	PRON
ejpam-5827	233	46	,	,	PUNCT
ejpam-5827	233	47	c	c	NOUN
ejpam-5827	233	48	}	}	PUNCT
ejpam-5827	233	49	=	=	SYM
ejpam-5827	233	50	{	{	PUNCT
ejpam-5827	233	51	a	a	NOUN
ejpam-5827	233	52	}	}	PUNCT
ejpam-5827	233	53	/∈	/∈	PROPN
ejpam-5827	233	54	τpr	τpr	NOUN
ejpam-5827	233	55	,	,	PUNCT
ejpam-5827	233	56	illustrating	illustrate	VERB
ejpam-5827	233	57	that	that	PRON
ejpam-5827	233	58	τpr	τpr	NOUN
ejpam-5827	233	59	is	be	AUX
ejpam-5827	233	60	not	not	PART
ejpam-5827	233	61	necessarily	necessarily	ADV
ejpam-5827	233	62	closed	close	VERB
ejpam-5827	233	63	under	under	ADP
ejpam-5827	233	64	intersections	intersection	NOUN
ejpam-5827	233	65	.	.	PUNCT
ejpam-5827	234	1	τpκ	τpκ	NOUN
ejpam-5827	234	2	is	be	AUX
ejpam-5827	234	3	a	a	DET
ejpam-5827	234	4	collection	collection	NOUN
ejpam-5827	234	5	of	of	ADP
ejpam-5827	234	6	subsets	subset	NOUN
ejpam-5827	234	7	of	of	ADP
ejpam-5827	234	8	v	v	NOUN
ejpam-5827	234	9	that	that	PRON
ejpam-5827	234	10	forms	form	VERB
ejpam-5827	234	11	a	a	DET
ejpam-5827	234	12	supra	supra	ADJ
ejpam-5827	234	13	topology	topology	NOUN
ejpam-5827	234	14	.	.	PUNCT
ejpam-5827	235	1	its	its	PRON
ejpam-5827	235	2	structure	structure	NOUN
ejpam-5827	235	3	is	be	AUX
ejpam-5827	235	4	determined	determine	VERB
ejpam-5827	235	5	by	by	ADP
ejpam-5827	235	6	the	the	DET
ejpam-5827	235	7	properties	property	NOUN
ejpam-5827	235	8	of	of	ADP
ejpam-5827	235	9	the	the	DET
ejpam-5827	235	10	κ	κ	NOUN
ejpam-5827	235	11	-	-	NOUN
ejpam-5827	235	12	neighborhoods	neighborhood	NOUN
ejpam-5827	235	13	and	and	CCONJ
ejpam-5827	235	14	the	the	DET
ejpam-5827	235	15	primal	primal	ADJ
ejpam-5827	235	16	p	p	NOUN
ejpam-5827	235	17	,	,	PUNCT
ejpam-5827	235	18	making	make	VERB
ejpam-5827	235	19	it	it	PRON
ejpam-5827	235	20	a	a	DET
ejpam-5827	235	21	flexible	flexible	ADJ
ejpam-5827	235	22	framework	framework	NOUN
ejpam-5827	235	23	for	for	ADP
ejpam-5827	235	24	studying	study	VERB
ejpam-5827	235	25	generalized	generalize	VERB
ejpam-5827	235	26	topological	topological	ADJ
ejpam-5827	235	27	spaces	space	NOUN
ejpam-5827	235	28	.	.	PUNCT
ejpam-5827	236	1	remark	remark	PROPN
ejpam-5827	236	2	4	4	NUM
ejpam-5827	236	3	.	.	PUNCT
ejpam-5827	237	1	the	the	DET
ejpam-5827	237	2	process	process	NOUN
ejpam-5827	237	3	of	of	ADP
ejpam-5827	237	4	obtaining	obtain	VERB
ejpam-5827	237	5	a	a	DET
ejpam-5827	237	6	supra	supra	ADJ
ejpam-5827	237	7	-	-	PUNCT
ejpam-5827	237	8	topological	topological	ADJ
ejpam-5827	237	9	space	space	NOUN
ejpam-5827	237	10	yields	yield	NOUN
ejpam-5827	237	11	distinctive	distinctive	ADJ
ejpam-5827	237	12	outcomes	outcome	NOUN
ejpam-5827	237	13	.	.	PUNCT
ejpam-5827	238	1	for	for	ADP
ejpam-5827	238	2	instance	instance	NOUN
ejpam-5827	238	3	,	,	PUNCT
ejpam-5827	238	4	when	when	SCONJ
ejpam-5827	238	5	applying	apply	VERB
ejpam-5827	238	6	for	for	ADP
ejpam-5827	238	7	a	a	DET
ejpam-5827	238	8	position	position	NOUN
ejpam-5827	238	9	through	through	ADP
ejpam-5827	238	10	a	a	DET
ejpam-5827	238	11	competitive	competitive	ADJ
ejpam-5827	238	12	process	process	NOUN
ejpam-5827	238	13	,	,	PUNCT
ejpam-5827	238	14	various	various	ADJ
ejpam-5827	238	15	selection	selection	NOUN
ejpam-5827	238	16	criteria	criterion	NOUN
ejpam-5827	238	17	are	be	AUX
ejpam-5827	238	18	typically	typically	ADV
ejpam-5827	238	19	required	require	VERB
ejpam-5827	238	20	.	.	PUNCT
ejpam-5827	239	1	by	by	ADP
ejpam-5827	239	2	employing	employ	VERB
ejpam-5827	239	3	the	the	DET
ejpam-5827	239	4	concept	concept	NOUN
ejpam-5827	239	5	of	of	ADP
ejpam-5827	239	6	supra	supra	NOUN
ejpam-5827	239	7	-	-	PUNCT
ejpam-5827	239	8	topology	topology	NOUN
ejpam-5827	239	9	in	in	ADP
ejpam-5827	239	10	the	the	DET
ejpam-5827	239	11	decisionmaking	decisionmake	VERB
ejpam-5827	239	12	process	process	NOUN
ejpam-5827	239	13	,	,	PUNCT
ejpam-5827	239	14	it	it	PRON
ejpam-5827	239	15	becomes	become	VERB
ejpam-5827	239	16	possible	possible	ADJ
ejpam-5827	239	17	to	to	PART
ejpam-5827	239	18	eliminate	eliminate	VERB
ejpam-5827	239	19	shared	share	VERB
ejpam-5827	239	20	or	or	CCONJ
ejpam-5827	239	21	redundant	redundant	ADJ
ejpam-5827	239	22	conditions	condition	NOUN
ejpam-5827	239	23	.	.	PUNCT
ejpam-5827	240	1	this	this	DET
ejpam-5827	240	2	approach	approach	NOUN
ejpam-5827	240	3	allows	allow	VERB
ejpam-5827	240	4	for	for	ADP
ejpam-5827	240	5	a	a	DET
ejpam-5827	240	6	focus	focus	NOUN
ejpam-5827	240	7	on	on	ADP
ejpam-5827	240	8	the	the	DET
ejpam-5827	240	9	unique	unique	ADJ
ejpam-5827	240	10	qualifications	qualification	NOUN
ejpam-5827	240	11	of	of	ADP
ejpam-5827	240	12	each	each	DET
ejpam-5827	240	13	candidate	candidate	NOUN
ejpam-5827	240	14	,	,	PUNCT
ejpam-5827	240	15	thereby	thereby	ADV
ejpam-5827	240	16	reducing	reduce	VERB
ejpam-5827	240	17	uncertainties	uncertainty	NOUN
ejpam-5827	240	18	associated	associate	VERB
ejpam-5827	240	19	with	with	ADP
ejpam-5827	240	20	the	the	DET
ejpam-5827	240	21	final	final	ADJ
ejpam-5827	240	22	selection	selection	NOUN
ejpam-5827	240	23	.	.	PUNCT
ejpam-5827	241	1	lemma	lemma	PROPN
ejpam-5827	241	2	2	2	X
ejpam-5827	241	3	.	.	PUNCT
ejpam-5827	242	1	let	let	VERB
ejpam-5827	242	2	v	v	NOUN
ejpam-5827	242	3	=	=	VERB
ejpam-5827	242	4	̸	̸	ADV
ejpam-5827	242	5	∅.	∅.	ADV
ejpam-5827	242	6	then	then	ADV
ejpam-5827	242	7	the	the	DET
ejpam-5827	242	8	following	follow	VERB
ejpam-5827	242	9	families	family	NOUN
ejpam-5827	242	10	are	be	AUX
ejpam-5827	242	11	primal	primal	ADJ
ejpam-5827	242	12	on	on	ADP
ejpam-5827	242	13	v	v	PROPN
ejpam-5827	242	14	(	(	PUNCT
ejpam-5827	242	15	i	i	NOUN
ejpam-5827	242	16	)	)	PUNCT
ejpam-5827	243	1	[	[	X
ejpam-5827	243	2	9	9	NUM
ejpam-5827	243	3	]	]	SYM
ejpam-5827	243	4	2v	2v	PROPN
ejpam-5827	243	5	\	\	PROPN
ejpam-5827	243	6	{	{	PUNCT
ejpam-5827	243	7	v	v	NOUN
ejpam-5827	243	8	}	}	PUNCT
ejpam-5827	243	9	(	(	PUNCT
ejpam-5827	243	10	trivial	trivial	ADJ
ejpam-5827	243	11	primal	primal	NOUN
ejpam-5827	243	12	)	)	PUNCT
ejpam-5827	243	13	.	.	PUNCT
ejpam-5827	244	1	(	(	PUNCT
ejpam-5827	244	2	ii	ii	NOUN
ejpam-5827	244	3	)	)	PUNCT
ejpam-5827	244	4	py	py	NOUN
ejpam-5827	244	5	=	=	PUNCT
ejpam-5827	244	6	{	{	PUNCT
ejpam-5827	244	7	m	m	PROPN
ejpam-5827	244	8	⊆	⊆	NUM
ejpam-5827	244	9	v	v	NOUN
ejpam-5827	244	10	:	:	PUNCT
ejpam-5827	244	11	y	y	PROPN
ejpam-5827	244	12	/∈	/∈	PUNCT
ejpam-5827	244	13	m	m	AUX
ejpam-5827	244	14	}	}	PUNCT
ejpam-5827	244	15	(	(	PUNCT
ejpam-5827	244	16	excluded	exclude	VERB
ejpam-5827	244	17	point	point	NOUN
ejpam-5827	244	18	primal	primal	ADJ
ejpam-5827	244	19	)	)	PUNCT
ejpam-5827	244	20	.	.	PUNCT
ejpam-5827	245	1	(	(	PUNCT
ejpam-5827	245	2	iii	iii	X
ejpam-5827	245	3	)	)	PUNCT
ejpam-5827	245	4	po	po	NOUN
ejpam-5827	245	5	=	=	PUNCT
ejpam-5827	245	6	{	{	PUNCT
ejpam-5827	245	7	m	m	PROPN
ejpam-5827	245	8	⊆	⊆	NUM
ejpam-5827	245	9	v	v	NOUN
ejpam-5827	245	10	:	:	PUNCT
ejpam-5827	245	11	m	m	VERB
ejpam-5827	245	12	∪o	∪o	ADV
ejpam-5827	246	1	̸=	̸=	PROPN
ejpam-5827	246	2	v	v	NOUN
ejpam-5827	246	3	}	}	PUNCT
ejpam-5827	246	4	.	.	PUNCT
ejpam-5827	247	1	proof	proof	NOUN
ejpam-5827	247	2	.	.	PUNCT
ejpam-5827	248	1	direct	direct	ADJ
ejpam-5827	248	2	to	to	PART
ejpam-5827	248	3	prove	prove	VERB
ejpam-5827	248	4	.	.	PUNCT
ejpam-5827	249	1	remark	remark	NOUN
ejpam-5827	249	2	5	5	NUM
ejpam-5827	249	3	.	.	PUNCT
ejpam-5827	250	1	(	(	PUNCT
ejpam-5827	250	2	i	i	NOUN
ejpam-5827	250	3	)	)	PUNCT
ejpam-5827	250	4	if	if	SCONJ
ejpam-5827	250	5	p	p	NOUN
ejpam-5827	250	6	=	=	VERB
ejpam-5827	250	7	py	py	PROPN
ejpam-5827	250	8	,	,	PUNCT
ejpam-5827	250	9	then	then	ADV
ejpam-5827	250	10	the	the	DET
ejpam-5827	250	11	supra	supra	PROPN
ejpam-5827	250	12	topology	topology	NOUN
ejpam-5827	250	13	τpκ	τpκ	NOUN
ejpam-5827	250	14	will	will	AUX
ejpam-5827	250	15	consist	consist	VERB
ejpam-5827	250	16	of	of	ADP
ejpam-5827	250	17	all	all	DET
ejpam-5827	250	18	subsets	subset	NOUN
ejpam-5827	250	19	h	h	NOUN
ejpam-5827	250	20	⊆v	⊆v	NOUN
ejpam-5827	250	21	such	such	ADJ
ejpam-5827	250	22	that	that	PRON
ejpam-5827	250	23	for	for	ADP
ejpam-5827	250	24	each	each	DET
ejpam-5827	250	25	z	z	PROPN
ejpam-5827	250	26	∈v	∈v	PROPN
ejpam-5827	250	27	,	,	PUNCT
ejpam-5827	250	28	the	the	DET
ejpam-5827	250	29	difference	difference	NOUN
ejpam-5827	250	30	nκ(z)−h	nκ(z)−h	NOUN
ejpam-5827	250	31	does	do	AUX
ejpam-5827	250	32	not	not	PART
ejpam-5827	250	33	contain	contain	VERB
ejpam-5827	250	34	y.	y.	NOUN
ejpam-5827	250	35	this	this	PRON
ejpam-5827	250	36	implies	imply	VERB
ejpam-5827	250	37	that	that	SCONJ
ejpam-5827	250	38	y	y	PROPN
ejpam-5827	250	39	will	will	AUX
ejpam-5827	250	40	be	be	AUX
ejpam-5827	250	41	excluded	exclude	VERB
ejpam-5827	250	42	from	from	ADP
ejpam-5827	250	43	certain	certain	ADJ
ejpam-5827	250	44	neighborhoods	neighborhood	NOUN
ejpam-5827	250	45	that	that	PRON
ejpam-5827	250	46	are	be	AUX
ejpam-5827	250	47	needed	need	VERB
ejpam-5827	250	48	to	to	PART
ejpam-5827	250	49	define	define	VERB
ejpam-5827	250	50	the	the	DET
ejpam-5827	250	51	supra	supra	PROPN
ejpam-5827	250	52	topology	topology	NOUN
ejpam-5827	250	53	.	.	PUNCT
ejpam-5827	251	1	(	(	PUNCT
ejpam-5827	251	2	ii	ii	X
ejpam-5827	251	3	)	)	PUNCT
ejpam-5827	251	4	the	the	DET
ejpam-5827	251	5	primal	primal	ADJ
ejpam-5827	251	6	po	po	NOUN
ejpam-5827	251	7	is	be	AUX
ejpam-5827	251	8	dependent	dependent	ADJ
ejpam-5827	251	9	on	on	ADP
ejpam-5827	251	10	the	the	DET
ejpam-5827	251	11	set	set	NOUN
ejpam-5827	251	12	o	o	NOUN
ejpam-5827	251	13	,	,	PUNCT
ejpam-5827	251	14	where	where	SCONJ
ejpam-5827	251	15	the	the	DET
ejpam-5827	251	16	choice	choice	NOUN
ejpam-5827	251	17	of	of	ADP
ejpam-5827	251	18	o	o	NOUN
ejpam-5827	251	19	directly	directly	ADV
ejpam-5827	251	20	affects	affect	VERB
ejpam-5827	251	21	for	for	ADP
ejpam-5827	251	22	sets	set	NOUN
ejpam-5827	251	23	belong	belong	VERB
ejpam-5827	251	24	to	to	ADP
ejpam-5827	251	25	τpκ	τpκ	NOUN
ejpam-5827	251	26	.	.	PUNCT
ejpam-5827	252	1	when	when	SCONJ
ejpam-5827	252	2	o	o	NOUN
ejpam-5827	252	3	is	be	AUX
ejpam-5827	252	4	an	an	DET
ejpam-5827	252	5	empty	empty	ADJ
ejpam-5827	252	6	set	set	NOUN
ejpam-5827	252	7	,	,	PUNCT
ejpam-5827	252	8	then	then	ADV
ejpam-5827	252	9	po	po	NOUN
ejpam-5827	252	10	includes	include	VERB
ejpam-5827	252	11	all	all	DET
ejpam-5827	252	12	proper	proper	ADJ
ejpam-5827	252	13	subsets	subset	NOUN
ejpam-5827	252	14	of	of	ADP
ejpam-5827	252	15	v	v	NOUN
ejpam-5827	252	16	,	,	PUNCT
ejpam-5827	252	17	which	which	PRON
ejpam-5827	252	18	making	make	VERB
ejpam-5827	252	19	τpκ	τpκ	NOUN
ejpam-5827	252	20	potentially	potentially	ADV
ejpam-5827	252	21	larger	large	ADJ
ejpam-5827	252	22	.	.	PUNCT
ejpam-5827	253	1	the	the	DET
ejpam-5827	253	2	κ	κ	NOUN
ejpam-5827	253	3	-	-	PUNCT
ejpam-5827	253	4	supra	supra	ADJ
ejpam-5827	253	5	topology	topology	NOUN
ejpam-5827	253	6	τpκ	τpκ	NOUN
ejpam-5827	253	7	is	be	AUX
ejpam-5827	253	8	finer	fine	ADJ
ejpam-5827	253	9	than	than	SCONJ
ejpam-5827	253	10	the	the	DET
ejpam-5827	253	11	κ	κ	NOUN
ejpam-5827	253	12	-	-	NOUN
ejpam-5827	253	13	topology	topology	NOUN
ejpam-5827	253	14	τκ	τκ	NOUN
ejpam-5827	253	15	generated	generate	VERB
ejpam-5827	253	16	bynκ	bynκ	NOUN
ejpam-5827	253	17	-	-	PUNCT
ejpam-5827	253	18	neighbourhood	neighbourhood	NOUN
ejpam-5827	253	19	for	for	ADP
ejpam-5827	253	20	various	various	ADJ
ejpam-5827	253	21	choices	choice	NOUN
ejpam-5827	253	22	of	of	ADP
ejpam-5827	253	23	κ	κ	NOUN
ejpam-5827	253	24	.	.	PUNCT
ejpam-5827	254	1	the	the	DET
ejpam-5827	254	2	present	present	ADJ
ejpam-5827	254	3	sort	sort	NOUN
ejpam-5827	254	4	of	of	ADP
ejpam-5827	254	5	these	these	DET
ejpam-5827	254	6	topologies	topology	NOUN
ejpam-5827	254	7	are	be	AUX
ejpam-5827	254	8	finer	fine	ADJ
ejpam-5827	254	9	than	than	ADP
ejpam-5827	254	10	the	the	DET
ejpam-5827	254	11	previous	previous	ADJ
ejpam-5827	254	12	one	one	NUM
ejpam-5827	254	13	[	[	X
ejpam-5827	254	14	35	35	NUM
ejpam-5827	254	15	]	]	PUNCT
ejpam-5827	254	16	as	as	SCONJ
ejpam-5827	254	17	it	it	PRON
ejpam-5827	254	18	is	be	AUX
ejpam-5827	254	19	exhibited	exhibit	VERB
ejpam-5827	254	20	in	in	ADP
ejpam-5827	254	21	the	the	DET
ejpam-5827	254	22	next	next	ADJ
ejpam-5827	254	23	result	result	NOUN
ejpam-5827	254	24	.	.	PUNCT
ejpam-5827	255	1	theorem	theorem	ADJ
ejpam-5827	255	2	4	4	NUM
ejpam-5827	255	3	.	.	PUNCT
ejpam-5827	256	1	let	let	AUX
ejpam-5827	256	2	(	(	PUNCT
ejpam-5827	256	3	v	v	NOUN
ejpam-5827	256	4	,	,	PUNCT
ejpam-5827	256	5	r	r	NOUN
ejpam-5827	256	6	,	,	PUNCT
ejpam-5827	256	7	ζκ	ζκ	NOUN
ejpam-5827	256	8	)	)	PUNCT
ejpam-5827	256	9	be	be	AUX
ejpam-5827	256	10	a	a	DET
ejpam-5827	256	11	κ	κ	NOUN
ejpam-5827	256	12	-	-	PUNCT
ejpam-5827	256	13	ns	ns	ADJ
ejpam-5827	256	14	,	,	PUNCT
ejpam-5827	256	15	and	and	CCONJ
ejpam-5827	256	16	p	p	NOUN
ejpam-5827	256	17	be	be	AUX
ejpam-5827	256	18	a	a	DET
ejpam-5827	256	19	primal	primal	NOUN
ejpam-5827	256	20	on	on	ADP
ejpam-5827	256	21	v.	v.	CCONJ
ejpam-5827	256	22	then	then	ADV
ejpam-5827	256	23	,	,	PUNCT
ejpam-5827	256	24	for	for	ADP
ejpam-5827	256	25	every	every	DET
ejpam-5827	256	26	κ	κ	NOUN
ejpam-5827	256	27	,	,	PUNCT
ejpam-5827	256	28	τκ	τκ	ADP
ejpam-5827	256	29	⊆	⊆	NUM
ejpam-5827	256	30	τpκ	τpκ	NOUN
ejpam-5827	256	31	.	.	PUNCT
ejpam-5827	257	1	proof	proof	NOUN
ejpam-5827	257	2	.	.	PUNCT
ejpam-5827	258	1	let	let	VERB
ejpam-5827	258	2	h	h	NOUN
ejpam-5827	258	3	∈τκ	∈τκ	PROPN
ejpam-5827	258	4	.	.	PUNCT
ejpam-5827	259	1	then	then	ADV
ejpam-5827	259	2	,	,	PUNCT
ejpam-5827	259	3	nκ(y	nκ(y	PUNCT
ejpam-5827	259	4	)	)	PUNCT
ejpam-5827	259	5	⊆h	⊆h	ADJ
ejpam-5827	259	6	,	,	PUNCT
ejpam-5827	259	7	∀y	∀y	NUM
ejpam-5827	259	8	∈h	∈h	NOUN
ejpam-5827	259	9	and	and	CCONJ
ejpam-5827	259	10	so	so	ADV
ejpam-5827	259	11	nκ(y	nκ(y	PUNCT
ejpam-5827	259	12	)	)	PUNCT
ejpam-5827	259	13	−	−	NOUN
ejpam-5827	259	14	h	h	NOUN
ejpam-5827	259	15	=	=	NOUN
ejpam-5827	259	16	∅	∅	NOUN
ejpam-5827	259	17	∈p	∈p	ADJ
ejpam-5827	259	18	,	,	PUNCT
ejpam-5827	259	19	∀y	∀y	NUM
ejpam-5827	259	20	∈h	∈h	NOUN
ejpam-5827	259	21	.	.	PUNCT
ejpam-5827	260	1	therefore	therefore	ADV
ejpam-5827	260	2	,	,	PUNCT
ejpam-5827	260	3	h	h	NOUN
ejpam-5827	260	4	∈τpκ	∈τpκ	NOUN
ejpam-5827	260	5	.	.	PUNCT
ejpam-5827	261	1	hence	hence	ADV
ejpam-5827	261	2	,	,	PUNCT
ejpam-5827	261	3	τκ	τκ	ADP
ejpam-5827	261	4	⊆	⊆	NUM
ejpam-5827	261	5	τpκ	τpκ	NOUN
ejpam-5827	261	6	.	.	PUNCT
ejpam-5827	262	1	remark	remark	PROPN
ejpam-5827	262	2	6	6	NUM
ejpam-5827	262	3	.	.	PUNCT
ejpam-5827	263	1	according	accord	VERB
ejpam-5827	263	2	to	to	ADP
ejpam-5827	263	3	theorem	theorem	ADJ
ejpam-5827	263	4	4	4	NUM
ejpam-5827	263	5	,	,	PUNCT
ejpam-5827	263	6	the	the	DET
ejpam-5827	263	7	present	present	ADJ
ejpam-5827	263	8	approaches	approach	NOUN
ejpam-5827	263	9	are	be	AUX
ejpam-5827	263	10	consider	consider	VERB
ejpam-5827	263	11	as	as	ADP
ejpam-5827	263	12	extensions	extension	NOUN
ejpam-5827	263	13	to	to	ADP
ejpam-5827	263	14	abd	abd	PROPN
ejpam-5827	263	15	el	el	PROPN
ejpam-5827	263	16	-	-	PROPN
ejpam-5827	263	17	monsef	monsef	PROPN
ejpam-5827	263	18	et	et	PROPN
ejpam-5827	263	19	al	al	PROPN
ejpam-5827	263	20	.	.	PROPN
ejpam-5827	263	21	’s	’s	PART
ejpam-5827	263	22	results	result	NOUN
ejpam-5827	263	23	[	[	X
ejpam-5827	263	24	35	35	NUM
ejpam-5827	263	25	]	]	PUNCT
ejpam-5827	263	26	.	.	PUNCT
ejpam-5827	264	1	the	the	DET
ejpam-5827	264	2	converse	converse	NOUN
ejpam-5827	264	3	of	of	ADP
ejpam-5827	264	4	theorem	theorem	NOUN
ejpam-5827	264	5	4	4	NUM
ejpam-5827	264	6	does	do	AUX
ejpam-5827	264	7	n’t	not	PART
ejpam-5827	264	8	hold	hold	VERB
ejpam-5827	264	9	as	as	SCONJ
ejpam-5827	264	10	the	the	DET
ejpam-5827	264	11	next	next	ADJ
ejpam-5827	264	12	example	example	NOUN
ejpam-5827	264	13	exhibited	exhibit	VERB
ejpam-5827	264	14	.	.	PUNCT
ejpam-5827	265	1	r.	r.	PROPN
ejpam-5827	265	2	a.	a.	PROPN
ejpam-5827	265	3	hosny	hosny	PROPN
ejpam-5827	265	4	,	,	PUNCT
ejpam-5827	265	5	m.	m.	PROPN
ejpam-5827	265	6	k.	k.	PROPN
ejpam-5827	266	1	el	el	PROPN
ejpam-5827	266	2	-	-	PROPN
ejpam-5827	266	3	bably	bably	ADV
ejpam-5827	266	4	,	,	PUNCT
ejpam-5827	266	5	m.	m.	NOUN
ejpam-5827	266	6	a.	a.	PROPN
ejpam-5827	266	7	el	el	PROPN
ejpam-5827	266	8	-	-	PROPN
ejpam-5827	266	9	gayar	gayar	PROPN
ejpam-5827	266	10	/	/	SYM
ejpam-5827	266	11	eur	eur	PROPN
ejpam-5827	266	12	.	.	PUNCT
ejpam-5827	267	1	j.	j.	PROPN
ejpam-5827	267	2	pure	pure	PROPN
ejpam-5827	267	3	appl	appl	PROPN
ejpam-5827	267	4	.	.	PROPN
ejpam-5827	267	5	math	math	PROPN
ejpam-5827	267	6	,	,	PUNCT
ejpam-5827	267	7	18	18	NUM
ejpam-5827	267	8	(	(	PUNCT
ejpam-5827	267	9	1	1	NUM
ejpam-5827	267	10	)	)	PUNCT
ejpam-5827	267	11	(	(	PUNCT
ejpam-5827	267	12	2025	2025	NUM
ejpam-5827	267	13	)	)	PUNCT
ejpam-5827	267	14	,	,	PUNCT
ejpam-5827	267	15	5827	5827	NUM
ejpam-5827	267	16	11	11	NUM
ejpam-5827	267	17	of	of	ADP
ejpam-5827	267	18	29	29	NUM
ejpam-5827	267	19	example	example	NOUN
ejpam-5827	267	20	3	3	NUM
ejpam-5827	267	21	.	.	PUNCT
ejpam-5827	267	22	continuation	continuation	NOUN
ejpam-5827	267	23	of	of	ADP
ejpam-5827	267	24	example	example	NOUN
ejpam-5827	268	1	2	2	NUM
ejpam-5827	268	2	.	.	PUNCT
ejpam-5827	269	1	the	the	DET
ejpam-5827	269	2	following	follow	VERB
ejpam-5827	269	3	structures	structure	NOUN
ejpam-5827	269	4	are	be	AUX
ejpam-5827	269	5	obtained	obtain	VERB
ejpam-5827	269	6	:	:	PUNCT
ejpam-5827	269	7	τr	τr	ADP
ejpam-5827	269	8	=	=	SYM
ejpam-5827	269	9	{	{	PUNCT
ejpam-5827	269	10	∅,v	∅,v	X
ejpam-5827	269	11	,	,	PUNCT
ejpam-5827	269	12	{	{	PUNCT
ejpam-5827	269	13	b	b	NOUN
ejpam-5827	269	14	,	,	PUNCT
ejpam-5827	269	15	c	c	NOUN
ejpam-5827	269	16	}	}	PUNCT
ejpam-5827	269	17	}	}	PUNCT
ejpam-5827	269	18	,	,	PUNCT
ejpam-5827	269	19	τl	τl	ADP
ejpam-5827	269	20	=	=	PUNCT
ejpam-5827	269	21	{	{	PUNCT
ejpam-5827	269	22	∅,v	∅,v	X
ejpam-5827	269	23	,	,	PUNCT
ejpam-5827	269	24	{	{	PUNCT
ejpam-5827	269	25	a	a	X
ejpam-5827	269	26	}	}	PUNCT
ejpam-5827	269	27	}	}	PUNCT
ejpam-5827	269	28	,	,	PUNCT
ejpam-5827	269	29	τi	τi	ADP
ejpam-5827	269	30	=	=	SYM
ejpam-5827	269	31	{	{	PUNCT
ejpam-5827	269	32	∅,v	∅,v	X
ejpam-5827	269	33	,	,	PUNCT
ejpam-5827	269	34	{	{	PUNCT
ejpam-5827	269	35	a	a	X
ejpam-5827	269	36	}	}	PUNCT
ejpam-5827	269	37	,	,	PUNCT
ejpam-5827	269	38	{	{	PUNCT
ejpam-5827	269	39	b	b	X
ejpam-5827	269	40	,	,	PUNCT
ejpam-5827	269	41	c	c	NOUN
ejpam-5827	269	42	}	}	PUNCT
ejpam-5827	269	43	}	}	PUNCT
ejpam-5827	269	44	,	,	PUNCT
ejpam-5827	269	45	τu	τu	ADP
ejpam-5827	269	46	=	=	PUNCT
ejpam-5827	269	47	{	{	PUNCT
ejpam-5827	269	48	∅,v	∅,v	NOUN
ejpam-5827	269	49	}	}	PUNCT
ejpam-5827	269	50	,	,	PUNCT
ejpam-5827	269	51	additionally	additionally	ADV
ejpam-5827	269	52	,	,	PUNCT
ejpam-5827	269	53	we	we	PRON
ejpam-5827	269	54	have	have	VERB
ejpam-5827	269	55	:	:	PUNCT
ejpam-5827	269	56	τ⟨r⟩	τ⟨r⟩	X
ejpam-5827	269	57	=	=	SYM
ejpam-5827	269	58	τ⟨i⟩	τ⟨i⟩	NOUN
ejpam-5827	269	59	=	=	SYM
ejpam-5827	269	60	{	{	PUNCT
ejpam-5827	269	61	∅,v	∅,v	X
ejpam-5827	269	62	,	,	PUNCT
ejpam-5827	269	63	{	{	PUNCT
ejpam-5827	269	64	a	a	X
ejpam-5827	269	65	}	}	PUNCT
ejpam-5827	269	66	,	,	PUNCT
ejpam-5827	269	67	{	{	PUNCT
ejpam-5827	269	68	b	b	NOUN
ejpam-5827	269	69	}	}	PUNCT
ejpam-5827	269	70	,	,	PUNCT
ejpam-5827	269	71	{	{	PUNCT
ejpam-5827	269	72	a	a	DET
ejpam-5827	269	73	,	,	PUNCT
ejpam-5827	269	74	b	b	NOUN
ejpam-5827	269	75	}	}	PUNCT
ejpam-5827	269	76	,	,	PUNCT
ejpam-5827	269	77	{	{	PUNCT
ejpam-5827	269	78	b	b	X
ejpam-5827	269	79	,	,	PUNCT
ejpam-5827	269	80	c	c	NOUN
ejpam-5827	269	81	}	}	PUNCT
ejpam-5827	269	82	}	}	PUNCT
ejpam-5827	269	83	,	,	PUNCT
ejpam-5827	269	84	τ⟨l⟩	τ⟨l⟩	NUM
ejpam-5827	269	85	=	=	SYM
ejpam-5827	269	86	τ⟨u⟩	τ⟨u⟩	NUM
ejpam-5827	269	87	=	=	SYM
ejpam-5827	269	88	{	{	PUNCT
ejpam-5827	269	89	∅,v	∅,v	X
ejpam-5827	269	90	,	,	PUNCT
ejpam-5827	269	91	{	{	PUNCT
ejpam-5827	269	92	a	a	PRON
ejpam-5827	269	93	,	,	PUNCT
ejpam-5827	269	94	b	b	NOUN
ejpam-5827	269	95	}	}	PUNCT
ejpam-5827	269	96	}	}	PUNCT
ejpam-5827	269	97	.	.	PUNCT
ejpam-5827	270	1	for	for	ADP
ejpam-5827	270	2	the	the	DET
ejpam-5827	270	3	primal	primal	ADJ
ejpam-5827	270	4	structures	structure	NOUN
ejpam-5827	270	5	,	,	PUNCT
ejpam-5827	270	6	we	we	PRON
ejpam-5827	270	7	obtain	obtain	VERB
ejpam-5827	270	8	:	:	PUNCT
ejpam-5827	270	9	τpr	τpr	NOUN
ejpam-5827	270	10	=	=	SYM
ejpam-5827	270	11	τpu	τpu	NOUN
ejpam-5827	270	12	=	=	SYM
ejpam-5827	270	13	{	{	PUNCT
ejpam-5827	270	14	∅,v	∅,v	X
ejpam-5827	270	15	,	,	PUNCT
ejpam-5827	270	16	{	{	PUNCT
ejpam-5827	270	17	b	b	NOUN
ejpam-5827	270	18	}	}	PUNCT
ejpam-5827	270	19	,	,	PUNCT
ejpam-5827	270	20	{	{	PUNCT
ejpam-5827	270	21	c	c	X
ejpam-5827	270	22	}	}	PUNCT
ejpam-5827	270	23	,	,	PUNCT
ejpam-5827	270	24	{	{	PUNCT
ejpam-5827	270	25	a	a	DET
ejpam-5827	270	26	,	,	PUNCT
ejpam-5827	270	27	b	b	NOUN
ejpam-5827	270	28	}	}	PUNCT
ejpam-5827	270	29	,	,	PUNCT
ejpam-5827	270	30	{	{	PUNCT
ejpam-5827	270	31	a	a	X
ejpam-5827	270	32	,	,	PUNCT
ejpam-5827	270	33	c	c	NOUN
ejpam-5827	270	34	}	}	PUNCT
ejpam-5827	270	35	,	,	PUNCT
ejpam-5827	270	36	{	{	PUNCT
ejpam-5827	270	37	b	b	X
ejpam-5827	270	38	,	,	PUNCT
ejpam-5827	270	39	c	c	NOUN
ejpam-5827	270	40	}	}	PUNCT
ejpam-5827	270	41	}	}	PUNCT
ejpam-5827	270	42	,	,	PUNCT
ejpam-5827	270	43	τpl	τpl	NOUN
ejpam-5827	271	1	=	=	SYM
ejpam-5827	271	2	τpi	τpi	NOUN
ejpam-5827	271	3	=	=	PUNCT
ejpam-5827	272	1	τp⟨r⟩	τp⟨r⟩	X
ejpam-5827	272	2	=	=	PUNCT
ejpam-5827	272	3	τp⟨l⟩	τp⟨l⟩	PUNCT
ejpam-5827	272	4	=	=	PUNCT
ejpam-5827	272	5	τp⟨i⟩	τp⟨i⟩	PROPN
ejpam-5827	272	6	=	=	PUNCT
ejpam-5827	272	7	τp⟨u⟩	τp⟨u⟩	PROPN
ejpam-5827	272	8	=	=	SYM
ejpam-5827	272	9	2v	2v	PROPN
ejpam-5827	272	10	.	.	PUNCT
ejpam-5827	273	1	these	these	DET
ejpam-5827	273	2	results	result	NOUN
ejpam-5827	273	3	illustrate	illustrate	VERB
ejpam-5827	273	4	the	the	DET
ejpam-5827	273	5	structural	structural	ADJ
ejpam-5827	273	6	differences	difference	NOUN
ejpam-5827	273	7	between	between	ADP
ejpam-5827	273	8	various	various	ADJ
ejpam-5827	273	9	topological	topological	ADJ
ejpam-5827	273	10	and	and	CCONJ
ejpam-5827	273	11	primal	primal	ADJ
ejpam-5827	273	12	frameworks	framework	NOUN
ejpam-5827	273	13	.	.	PUNCT
ejpam-5827	274	1	definition	definition	NOUN
ejpam-5827	274	2	12	12	NUM
ejpam-5827	274	3	.	.	PUNCT
ejpam-5827	275	1	the	the	DET
ejpam-5827	275	2	system	system	NOUN
ejpam-5827	275	3	(	(	PUNCT
ejpam-5827	275	4	v	v	NOUN
ejpam-5827	275	5	,	,	PUNCT
ejpam-5827	275	6	τpκ	τpκ	NOUN
ejpam-5827	275	7	)	)	PUNCT
ejpam-5827	275	8	is	be	AUX
ejpam-5827	275	9	called	call	VERB
ejpam-5827	275	10	a	a	DET
ejpam-5827	275	11	κ	κ	NOUN
ejpam-5827	275	12	-	-	PUNCT
ejpam-5827	275	13	supra	supra	ADJ
ejpam-5827	275	14	topological	topological	ADJ
ejpam-5827	275	15	space	space	NOUN
ejpam-5827	275	16	,	,	PUNCT
ejpam-5827	275	17	where	where	SCONJ
ejpam-5827	275	18	τpκ	τpκ	NOUN
ejpam-5827	275	19	is	be	AUX
ejpam-5827	275	20	a	a	DET
ejpam-5827	275	21	supra	supra	ADJ
ejpam-5827	275	22	topology	topology	NOUN
ejpam-5827	275	23	on	on	ADP
ejpam-5827	275	24	v.	v.	ADP
ejpam-5827	275	25	a	a	DET
ejpam-5827	275	26	set	set	ADJ
ejpam-5827	275	27	h	h	NOUN
ejpam-5827	275	28	of	of	ADP
ejpam-5827	275	29	v	v	NOUN
ejpam-5827	275	30	is	be	AUX
ejpam-5827	275	31	called	call	VERB
ejpam-5827	275	32	a	a	DET
ejpam-5827	275	33	τpκ	τpκ	NOUN
ejpam-5827	275	34	open	open	ADJ
ejpam-5827	275	35	set	set	NOUN
ejpam-5827	275	36	if	if	SCONJ
ejpam-5827	275	37	h	h	NOUN
ejpam-5827	275	38	∈τpκ	∈τpκ	NOUN
ejpam-5827	275	39	,	,	PUNCT
ejpam-5827	275	40	and	and	CCONJ
ejpam-5827	275	41	its	its	PRON
ejpam-5827	275	42	complement	complement	NOUN
ejpam-5827	275	43	is	be	AUX
ejpam-5827	275	44	termed	term	VERB
ejpam-5827	275	45	a	a	DET
ejpam-5827	275	46	τpκ	τpκ	ADV
ejpam-5827	275	47	-closed	-close	VERB
ejpam-5827	275	48	set	set	NOUN
ejpam-5827	275	49	.	.	PUNCT
ejpam-5827	276	1	the	the	DET
ejpam-5827	276	2	family	family	NOUN
ejpam-5827	276	3	υp	υp	PROPN
ejpam-5827	276	4	κ	κ	PROPN
ejpam-5827	276	5	of	of	ADP
ejpam-5827	276	6	all	all	DET
ejpam-5827	276	7	τpκ	τpκ	NOUN
ejpam-5827	276	8	closed	close	VERB
ejpam-5827	276	9	sets	set	NOUN
ejpam-5827	276	10	is	be	AUX
ejpam-5827	276	11	given	give	VERB
ejpam-5827	276	12	by	by	ADP
ejpam-5827	276	13	υp	υp	PROPN
ejpam-5827	276	14	κ	κ	PROPN
ejpam-5827	276	15	=	=	PUNCT
ejpam-5827	276	16	{	{	PUNCT
ejpam-5827	276	17	f	f	PROPN
ejpam-5827	276	18	⊆	⊆	NUM
ejpam-5827	276	19	v	v	NOUN
ejpam-5827	276	20	:	:	PUNCT
ejpam-5827	276	21	f	f	PROPN
ejpam-5827	276	22	c	c	PROPN
ejpam-5827	276	23	∈	∈	PROPN
ejpam-5827	276	24	τpκ	τpκ	NOUN
ejpam-5827	276	25	}	}	PUNCT
ejpam-5827	276	26	,	,	PUNCT
ejpam-5827	276	27	where	where	SCONJ
ejpam-5827	276	28	f	f	PROPN
ejpam-5827	276	29	c	c	PROPN
ejpam-5827	276	30	is	be	AUX
ejpam-5827	276	31	the	the	DET
ejpam-5827	276	32	complement	complement	NOUN
ejpam-5827	276	33	of	of	ADP
ejpam-5827	276	34	f	f	PROPN
ejpam-5827	276	35	.	.	PUNCT
ejpam-5827	277	1	according	accord	VERB
ejpam-5827	277	2	to	to	ADP
ejpam-5827	277	3	proposition	proposition	NOUN
ejpam-5827	277	4	1	1	NUM
ejpam-5827	277	5	,	,	PUNCT
ejpam-5827	277	6	the	the	DET
ejpam-5827	277	7	proof	proof	NOUN
ejpam-5827	277	8	of	of	ADP
ejpam-5827	277	9	the	the	DET
ejpam-5827	277	10	next	next	ADJ
ejpam-5827	277	11	theorem	theorem	NOUN
ejpam-5827	277	12	is	be	AUX
ejpam-5827	277	13	explicit	explicit	ADJ
ejpam-5827	277	14	.	.	PUNCT
ejpam-5827	278	1	theorem	theorem	NOUN
ejpam-5827	278	2	5	5	NUM
ejpam-5827	278	3	.	.	PUNCT
ejpam-5827	279	1	let	let	AUX
ejpam-5827	279	2	(	(	PUNCT
ejpam-5827	279	3	v	v	NOUN
ejpam-5827	279	4	,	,	PUNCT
ejpam-5827	279	5	r	r	NOUN
ejpam-5827	279	6	,	,	PUNCT
ejpam-5827	279	7	ζκ	ζκ	NOUN
ejpam-5827	279	8	)	)	PUNCT
ejpam-5827	279	9	be	be	AUX
ejpam-5827	279	10	a	a	DET
ejpam-5827	279	11	κ	κ	NOUN
ejpam-5827	279	12	-	-	PUNCT
ejpam-5827	279	13	ns	ns	ADJ
ejpam-5827	279	14	,	,	PUNCT
ejpam-5827	279	15	and	and	CCONJ
ejpam-5827	279	16	p	p	NOUN
ejpam-5827	279	17	be	be	AUX
ejpam-5827	279	18	a	a	DET
ejpam-5827	279	19	primal	primal	NOUN
ejpam-5827	279	20	on	on	ADP
ejpam-5827	279	21	v.	v.	CCONJ
ejpam-5827	279	22	then	then	ADV
ejpam-5827	279	23	,	,	PUNCT
ejpam-5827	279	24	(	(	PUNCT
ejpam-5827	279	25	i	i	NOUN
ejpam-5827	279	26	)	)	PUNCT
ejpam-5827	279	27	τpκ	τpκ	NOUN
ejpam-5827	279	28	⊆	⊆	NUM
ejpam-5827	279	29	τp⟨κ⟩	τp⟨κ⟩	PROPN
ejpam-5827	279	30	,	,	PUNCT
ejpam-5827	279	31	κ∈{r	κ∈{r	NOUN
ejpam-5827	279	32	,	,	PUNCT
ejpam-5827	279	33	l	l	PROPN
ejpam-5827	279	34	,	,	PUNCT
ejpam-5827	279	35	i	i	PRON
ejpam-5827	279	36	,	,	PUNCT
ejpam-5827	279	37	u	u	NOUN
ejpam-5827	279	38	}	}	PUNCT
ejpam-5827	279	39	,	,	PUNCT
ejpam-5827	279	40	if	if	SCONJ
ejpam-5827	279	41	r	r	NOUN
ejpam-5827	279	42	is	be	AUX
ejpam-5827	279	43	a	a	DET
ejpam-5827	279	44	reflexive	reflexive	ADJ
ejpam-5827	279	45	relation	relation	NOUN
ejpam-5827	279	46	.	.	PUNCT
ejpam-5827	280	1	(	(	PUNCT
ejpam-5827	280	2	ii	ii	NOUN
ejpam-5827	280	3	)	)	PUNCT
ejpam-5827	280	4	τpr	τpr	NOUN
ejpam-5827	281	1	=	=	SYM
ejpam-5827	281	2	τpl	τpl	PROPN
ejpam-5827	281	3	=	=	SYM
ejpam-5827	281	4	τpi	τpi	NOUN
ejpam-5827	281	5	=	=	NOUN
ejpam-5827	281	6	τpu	τpu	NOUN
ejpam-5827	281	7	and	and	CCONJ
ejpam-5827	281	8	τp⟨r⟩	τp⟨r⟩	PROPN
ejpam-5827	281	9	=	=	PUNCT
ejpam-5827	282	1	τp⟨l⟩	τp⟨l⟩	PUNCT
ejpam-5827	282	2	=	=	PUNCT
ejpam-5827	282	3	τp⟨i⟩	τp⟨i⟩	PROPN
ejpam-5827	282	4	=	=	SYM
ejpam-5827	282	5	τp⟨u⟩	τp⟨u⟩	PROPN
ejpam-5827	282	6	,	,	PUNCT
ejpam-5827	282	7	if	if	SCONJ
ejpam-5827	282	8	r	r	NOUN
ejpam-5827	282	9	is	be	AUX
ejpam-5827	282	10	a	a	DET
ejpam-5827	282	11	symmetric	symmetric	ADJ
ejpam-5827	282	12	relation	relation	NOUN
ejpam-5827	282	13	.	.	PUNCT
ejpam-5827	283	1	(	(	PUNCT
ejpam-5827	283	2	iii	iii	NOUN
ejpam-5827	283	3	)	)	PUNCT
ejpam-5827	283	4	τpκ	τpκ	NOUN
ejpam-5827	283	5	=	=	SYM
ejpam-5827	283	6	τp⟨κ⟩	τp⟨κ⟩	PROPN
ejpam-5827	283	7	,	,	PUNCT
ejpam-5827	283	8	κ∈{r	κ∈{r	NOUN
ejpam-5827	283	9	,	,	PUNCT
ejpam-5827	283	10	l	l	PROPN
ejpam-5827	283	11	,	,	PUNCT
ejpam-5827	283	12	i	i	PRON
ejpam-5827	283	13	,	,	PUNCT
ejpam-5827	283	14	u	u	NOUN
ejpam-5827	283	15	}	}	PUNCT
ejpam-5827	283	16	,	,	PUNCT
ejpam-5827	283	17	if	if	SCONJ
ejpam-5827	283	18	r	r	NOUN
ejpam-5827	283	19	is	be	AUX
ejpam-5827	283	20	a	a	DET
ejpam-5827	283	21	preorder	preorder	NOUN
ejpam-5827	283	22	relation	relation	NOUN
ejpam-5827	283	23	.	.	PUNCT
ejpam-5827	284	1	remark	remark	PROPN
ejpam-5827	284	2	7	7	NUM
ejpam-5827	284	3	.	.	PUNCT
ejpam-5827	285	1	τp⟨κ⟩	τp⟨κ⟩	PROPN
ejpam-5827	285	2	,	,	PUNCT
ejpam-5827	285	3	τ	τ	PROPN
ejpam-5827	285	4	p	p	NOUN
ejpam-5827	285	5	κ	κ	NOUN
ejpam-5827	285	6	are	be	AUX
ejpam-5827	285	7	generally	generally	ADV
ejpam-5827	285	8	incomparable	incomparable	ADJ
ejpam-5827	285	9	for	for	ADP
ejpam-5827	285	10	κ	κ	PROPN
ejpam-5827	285	11	∈	∈	PROPN
ejpam-5827	285	12	{	{	PUNCT
ejpam-5827	285	13	r	r	NOUN
ejpam-5827	285	14	,	,	PUNCT
ejpam-5827	285	15	l	l	NOUN
ejpam-5827	285	16	,	,	PUNCT
ejpam-5827	285	17	i	i	PRON
ejpam-5827	285	18	,	,	PUNCT
ejpam-5827	285	19	u	u	NOUN
ejpam-5827	285	20	}	}	PUNCT
ejpam-5827	285	21	when	when	SCONJ
ejpam-5827	285	22	r	r	NOUN
ejpam-5827	285	23	is	be	AUX
ejpam-5827	285	24	a	a	DET
ejpam-5827	285	25	transitive	transitive	ADJ
ejpam-5827	285	26	relation	relation	NOUN
ejpam-5827	285	27	as	as	SCONJ
ejpam-5827	285	28	illustrated	illustrate	VERB
ejpam-5827	285	29	in	in	ADP
ejpam-5827	285	30	the	the	DET
ejpam-5827	285	31	next	next	ADJ
ejpam-5827	285	32	example	example	NOUN
ejpam-5827	285	33	:	:	PUNCT
ejpam-5827	285	34	example	example	NOUN
ejpam-5827	285	35	4	4	X
ejpam-5827	285	36	.	.	PUNCT
ejpam-5827	286	1	let	let	VERB
ejpam-5827	286	2	r	r	NOUN
ejpam-5827	286	3	=	=	PRON
ejpam-5827	286	4	{	{	PUNCT
ejpam-5827	286	5	(	(	PUNCT
ejpam-5827	286	6	a	a	DET
ejpam-5827	286	7	,	,	PUNCT
ejpam-5827	286	8	b	b	NOUN
ejpam-5827	286	9	)	)	PUNCT
ejpam-5827	286	10	,	,	PUNCT
ejpam-5827	286	11	(	(	PUNCT
ejpam-5827	286	12	a	a	DET
ejpam-5827	286	13	,	,	PUNCT
ejpam-5827	286	14	c	c	NOUN
ejpam-5827	286	15	)	)	PUNCT
ejpam-5827	286	16	,	,	PUNCT
ejpam-5827	286	17	(	(	PUNCT
ejpam-5827	286	18	b	b	X
ejpam-5827	286	19	,	,	PUNCT
ejpam-5827	286	20	b	b	NOUN
ejpam-5827	286	21	)	)	PUNCT
ejpam-5827	286	22	,	,	PUNCT
ejpam-5827	286	23	(	(	PUNCT
ejpam-5827	286	24	b	b	X
ejpam-5827	286	25	,	,	PUNCT
ejpam-5827	286	26	c	c	NOUN
ejpam-5827	286	27	)	)	PUNCT
ejpam-5827	286	28	,	,	PUNCT
ejpam-5827	286	29	(	(	PUNCT
ejpam-5827	286	30	d	d	X
ejpam-5827	286	31	,	,	PUNCT
ejpam-5827	286	32	d	d	NOUN
ejpam-5827	286	33	)	)	PUNCT
ejpam-5827	286	34	}	}	PUNCT
ejpam-5827	286	35	be	be	AUX
ejpam-5827	286	36	a	a	DET
ejpam-5827	286	37	transitive	transitive	ADJ
ejpam-5827	286	38	relation	relation	NOUN
ejpam-5827	286	39	on	on	ADP
ejpam-5827	286	40	v	v	NOUN
ejpam-5827	286	41	=	=	PUNCT
ejpam-5827	286	42	{	{	PUNCT
ejpam-5827	286	43	a	a	PRON
ejpam-5827	286	44	,	,	PUNCT
ejpam-5827	286	45	b	b	NOUN
ejpam-5827	286	46	,	,	PUNCT
ejpam-5827	286	47	c	c	NOUN
ejpam-5827	286	48	,	,	PUNCT
ejpam-5827	286	49	d	d	NOUN
ejpam-5827	286	50	}	}	PUNCT
ejpam-5827	286	51	.	.	PUNCT
ejpam-5827	287	1	if	if	SCONJ
ejpam-5827	287	2	p	p	NOUN
ejpam-5827	287	3	=	=	PUNCT
ejpam-5827	287	4	{	{	PUNCT
ejpam-5827	287	5	∅	∅	NOUN
ejpam-5827	287	6	,	,	PUNCT
ejpam-5827	287	7	{	{	PUNCT
ejpam-5827	287	8	a	a	X
ejpam-5827	287	9	}	}	PUNCT
ejpam-5827	287	10	}	}	PUNCT
ejpam-5827	287	11	,	,	PUNCT
ejpam-5827	287	12	then	then	ADV
ejpam-5827	287	13	τpr	τpr	NOUN
ejpam-5827	287	14	=	=	SYM
ejpam-5827	287	15	{	{	PUNCT
ejpam-5827	287	16	∅,v	∅,v	X
ejpam-5827	287	17	,	,	PUNCT
ejpam-5827	287	18	{	{	PUNCT
ejpam-5827	287	19	c	c	NOUN
ejpam-5827	287	20	}	}	PUNCT
ejpam-5827	287	21	,	,	PUNCT
ejpam-5827	287	22	{	{	PUNCT
ejpam-5827	287	23	d	d	X
ejpam-5827	287	24	}	}	PUNCT
ejpam-5827	287	25	,	,	PUNCT
ejpam-5827	287	26	{	{	PUNCT
ejpam-5827	287	27	b	b	X
ejpam-5827	287	28	,	,	PUNCT
ejpam-5827	287	29	c	c	NOUN
ejpam-5827	287	30	}	}	PUNCT
ejpam-5827	287	31	,	,	PUNCT
ejpam-5827	287	32	{	{	PUNCT
ejpam-5827	287	33	c	c	X
ejpam-5827	287	34	,	,	PUNCT
ejpam-5827	287	35	d	d	NOUN
ejpam-5827	287	36	}	}	PUNCT
ejpam-5827	287	37	,	,	PUNCT
ejpam-5827	287	38	{	{	PUNCT
ejpam-5827	287	39	a	a	DET
ejpam-5827	287	40	,	,	PUNCT
ejpam-5827	287	41	b	b	NOUN
ejpam-5827	287	42	,	,	PUNCT
ejpam-5827	287	43	c	c	NOUN
ejpam-5827	287	44	}	}	PUNCT
ejpam-5827	287	45	,	,	PUNCT
ejpam-5827	287	46	{	{	PUNCT
ejpam-5827	287	47	b	b	X
ejpam-5827	287	48	,	,	PUNCT
ejpam-5827	287	49	c	c	NOUN
ejpam-5827	287	50	,	,	PUNCT
ejpam-5827	287	51	d	d	NOUN
ejpam-5827	287	52	}	}	PUNCT
ejpam-5827	287	53	}	}	PUNCT
ejpam-5827	287	54	,	,	PUNCT
ejpam-5827	287	55	τp⟨r⟩	τp⟨r⟩	PROPN
ejpam-5827	287	56	=	=	PUNCT
ejpam-5827	287	57	{	{	PUNCT
ejpam-5827	287	58	∅,v	∅,v	X
ejpam-5827	287	59	,	,	PUNCT
ejpam-5827	287	60	{	{	PUNCT
ejpam-5827	287	61	a	a	X
ejpam-5827	287	62	}	}	PUNCT
ejpam-5827	287	63	,	,	PUNCT
ejpam-5827	287	64	{	{	PUNCT
ejpam-5827	287	65	d	d	NOUN
ejpam-5827	287	66	}	}	PUNCT
ejpam-5827	287	67	,	,	PUNCT
ejpam-5827	287	68	{	{	PUNCT
ejpam-5827	287	69	a	a	PRON
ejpam-5827	287	70	,	,	PUNCT
ejpam-5827	287	71	d	d	NOUN
ejpam-5827	287	72	}	}	PUNCT
ejpam-5827	287	73	,	,	PUNCT
ejpam-5827	287	74	{	{	PUNCT
ejpam-5827	287	75	b	b	X
ejpam-5827	287	76	,	,	PUNCT
ejpam-5827	287	77	c	c	NOUN
ejpam-5827	287	78	}	}	PUNCT
ejpam-5827	287	79	,	,	PUNCT
ejpam-5827	287	80	{	{	PUNCT
ejpam-5827	287	81	a	a	DET
ejpam-5827	287	82	,	,	PUNCT
ejpam-5827	287	83	b	b	NOUN
ejpam-5827	287	84	,	,	PUNCT
ejpam-5827	287	85	c	c	NOUN
ejpam-5827	287	86	}	}	PUNCT
ejpam-5827	287	87	,	,	PUNCT
ejpam-5827	287	88	{	{	PUNCT
ejpam-5827	287	89	b	b	X
ejpam-5827	287	90	,	,	PUNCT
ejpam-5827	287	91	c	c	NOUN
ejpam-5827	287	92	,	,	PUNCT
ejpam-5827	287	93	d	d	NOUN
ejpam-5827	287	94	}	}	PUNCT
ejpam-5827	287	95	}	}	PUNCT
ejpam-5827	287	96	.	.	PUNCT
ejpam-5827	288	1	example	example	NOUN
ejpam-5827	288	2	5	5	NUM
ejpam-5827	288	3	.	.	PUNCT
ejpam-5827	289	1	let	let	VERB
ejpam-5827	289	2	v	v	VERB
ejpam-5827	289	3	=	=	PUNCT
ejpam-5827	289	4	{	{	PUNCT
ejpam-5827	289	5	a	a	PRON
ejpam-5827	289	6	,	,	PUNCT
ejpam-5827	289	7	b	b	NOUN
ejpam-5827	289	8	,	,	PUNCT
ejpam-5827	289	9	c	c	NOUN
ejpam-5827	289	10	,	,	PUNCT
ejpam-5827	289	11	d	d	NOUN
ejpam-5827	289	12	}	}	PUNCT
ejpam-5827	289	13	and	and	CCONJ
ejpam-5827	289	14	r	r	NOUN
ejpam-5827	289	15	=	=	SYM
ejpam-5827	289	16	{	{	PUNCT
ejpam-5827	289	17	(	(	PUNCT
ejpam-5827	289	18	a	a	PRON
ejpam-5827	289	19	,	,	PUNCT
ejpam-5827	289	20	a	a	NOUN
ejpam-5827	289	21	)	)	PUNCT
ejpam-5827	289	22	,	,	PUNCT
ejpam-5827	289	23	(	(	PUNCT
ejpam-5827	289	24	a	a	DET
ejpam-5827	289	25	,	,	PUNCT
ejpam-5827	289	26	b	b	NOUN
ejpam-5827	289	27	)	)	PUNCT
ejpam-5827	289	28	,	,	PUNCT
ejpam-5827	289	29	(	(	PUNCT
ejpam-5827	289	30	a	a	DET
ejpam-5827	289	31	,	,	PUNCT
ejpam-5827	289	32	c	c	NOUN
ejpam-5827	289	33	)	)	PUNCT
ejpam-5827	289	34	,	,	PUNCT
ejpam-5827	289	35	(	(	PUNCT
ejpam-5827	289	36	b	b	X
ejpam-5827	289	37	,	,	PUNCT
ejpam-5827	289	38	c	c	NOUN
ejpam-5827	289	39	)	)	PUNCT
ejpam-5827	289	40	,	,	PUNCT
ejpam-5827	289	41	(	(	PUNCT
ejpam-5827	289	42	c	c	X
ejpam-5827	289	43	,	,	PUNCT
ejpam-5827	289	44	d	d	NOUN
ejpam-5827	289	45	)	)	PUNCT
ejpam-5827	289	46	}	}	PUNCT
ejpam-5827	289	47	.	.	PUNCT
ejpam-5827	290	1	hence	hence	ADV
ejpam-5827	290	2	,	,	PUNCT
ejpam-5827	290	3	τr	τr	PUNCT
ejpam-5827	290	4	=	=	PRON
ejpam-5827	290	5	{	{	PUNCT
ejpam-5827	290	6	∅,v	∅,v	X
ejpam-5827	290	7	,	,	PUNCT
ejpam-5827	290	8	{	{	PUNCT
ejpam-5827	290	9	d	d	NOUN
ejpam-5827	290	10	}	}	PUNCT
ejpam-5827	290	11	,	,	PUNCT
ejpam-5827	290	12	{	{	PUNCT
ejpam-5827	290	13	c	c	X
ejpam-5827	290	14	,	,	PUNCT
ejpam-5827	290	15	d	d	NOUN
ejpam-5827	290	16	}	}	PUNCT
ejpam-5827	290	17	,	,	PUNCT
ejpam-5827	290	18	{	{	PUNCT
ejpam-5827	290	19	b	b	X
ejpam-5827	290	20	,	,	PUNCT
ejpam-5827	290	21	c	c	NOUN
ejpam-5827	290	22	,	,	PUNCT
ejpam-5827	290	23	d	d	NOUN
ejpam-5827	290	24	}	}	PUNCT
ejpam-5827	290	25	}	}	PUNCT
ejpam-5827	290	26	,	,	PUNCT
ejpam-5827	290	27	τl	τl	ADP
ejpam-5827	290	28	=	=	PUNCT
ejpam-5827	290	29	{	{	PUNCT
ejpam-5827	290	30	∅,v	∅,v	X
ejpam-5827	290	31	,	,	PUNCT
ejpam-5827	290	32	{	{	PUNCT
ejpam-5827	290	33	a	a	X
ejpam-5827	290	34	}	}	PUNCT
ejpam-5827	290	35	,	,	PUNCT
ejpam-5827	290	36	{	{	PUNCT
ejpam-5827	290	37	a	a	DET
ejpam-5827	290	38	,	,	PUNCT
ejpam-5827	290	39	b	b	NOUN
ejpam-5827	290	40	}	}	PUNCT
ejpam-5827	290	41	,	,	PUNCT
ejpam-5827	290	42	{	{	PUNCT
ejpam-5827	290	43	a	a	PRON
ejpam-5827	290	44	,	,	PUNCT
ejpam-5827	290	45	b	b	NOUN
ejpam-5827	290	46	,	,	PUNCT
ejpam-5827	290	47	c	c	NOUN
ejpam-5827	290	48	}	}	PUNCT
ejpam-5827	290	49	}	}	PUNCT
ejpam-5827	290	50	,	,	PUNCT
ejpam-5827	290	51	τi	τi	ADP
ejpam-5827	290	52	=	=	SYM
ejpam-5827	290	53	2v	2v	PROPN
ejpam-5827	290	54	,	,	PUNCT
ejpam-5827	290	55	τu	τu	ADP
ejpam-5827	290	56	=	=	X
ejpam-5827	290	57	{	{	PUNCT
ejpam-5827	290	58	∅,v	∅,v	NOUN
ejpam-5827	290	59	}	}	PUNCT
ejpam-5827	290	60	,	,	PUNCT
ejpam-5827	290	61	τ⟨r⟩	τ⟨r⟩	X
ejpam-5827	290	62	=	=	PUNCT
ejpam-5827	290	63	τ⟨u⟩	τ⟨u⟩	NUM
ejpam-5827	290	64	=	=	SYM
ejpam-5827	290	65	{	{	PUNCT
ejpam-5827	290	66	∅,v	∅,v	X
ejpam-5827	290	67	,	,	PUNCT
ejpam-5827	290	68	{	{	PUNCT
ejpam-5827	290	69	c	c	NOUN
ejpam-5827	290	70	}	}	PUNCT
ejpam-5827	290	71	,	,	PUNCT
ejpam-5827	290	72	{	{	PUNCT
ejpam-5827	290	73	d	d	X
ejpam-5827	290	74	}	}	PUNCT
ejpam-5827	290	75	,	,	PUNCT
ejpam-5827	290	76	{	{	PUNCT
ejpam-5827	290	77	c	c	X
ejpam-5827	290	78	,	,	PUNCT
ejpam-5827	290	79	d	d	NOUN
ejpam-5827	290	80	}	}	PUNCT
ejpam-5827	290	81	,	,	PUNCT
ejpam-5827	290	82	{	{	PUNCT
ejpam-5827	290	83	a	a	DET
ejpam-5827	290	84	,	,	PUNCT
ejpam-5827	290	85	b	b	NOUN
ejpam-5827	290	86	,	,	PUNCT
ejpam-5827	290	87	c	c	NOUN
ejpam-5827	290	88	}	}	PUNCT
ejpam-5827	290	89	}	}	PUNCT
ejpam-5827	290	90	,	,	PUNCT
ejpam-5827	290	91	τ⟨l⟩	τ⟨l⟩	NUM
ejpam-5827	290	92	=	=	SYM
ejpam-5827	290	93	τ⟨i⟩	τ⟨i⟩	NOUN
ejpam-5827	290	94	=	=	SYM
ejpam-5827	290	95	{	{	PUNCT
ejpam-5827	290	96	∅,v	∅,v	X
ejpam-5827	290	97	,	,	PUNCT
ejpam-5827	290	98	{	{	PUNCT
ejpam-5827	290	99	a	a	X
ejpam-5827	290	100	}	}	PUNCT
ejpam-5827	290	101	,	,	PUNCT
ejpam-5827	290	102	{	{	PUNCT
ejpam-5827	290	103	c	c	X
ejpam-5827	290	104	}	}	PUNCT
ejpam-5827	290	105	,	,	PUNCT
ejpam-5827	290	106	{	{	PUNCT
ejpam-5827	290	107	d	d	X
ejpam-5827	290	108	}	}	PUNCT
ejpam-5827	290	109	,	,	PUNCT
ejpam-5827	290	110	{	{	PUNCT
ejpam-5827	290	111	a	a	DET
ejpam-5827	290	112	,	,	PUNCT
ejpam-5827	290	113	b	b	NOUN
ejpam-5827	290	114	}	}	PUNCT
ejpam-5827	290	115	,	,	PUNCT
ejpam-5827	290	116	{	{	PUNCT
ejpam-5827	290	117	a	a	X
ejpam-5827	290	118	,	,	PUNCT
ejpam-5827	290	119	c	c	NOUN
ejpam-5827	290	120	}	}	PUNCT
ejpam-5827	290	121	,	,	PUNCT
ejpam-5827	290	122	{	{	PUNCT
ejpam-5827	290	123	a	a	PRON
ejpam-5827	290	124	,	,	PUNCT
ejpam-5827	290	125	d	d	NOUN
ejpam-5827	290	126	}	}	PUNCT
ejpam-5827	290	127	,	,	PUNCT
ejpam-5827	290	128	{	{	PUNCT
ejpam-5827	290	129	c	c	X
ejpam-5827	290	130	,	,	PUNCT
ejpam-5827	290	131	d	d	NOUN
ejpam-5827	290	132	}	}	PUNCT
ejpam-5827	290	133	,	,	PUNCT
ejpam-5827	290	134	{	{	PUNCT
ejpam-5827	290	135	a	a	DET
ejpam-5827	290	136	,	,	PUNCT
ejpam-5827	290	137	b	b	NOUN
ejpam-5827	290	138	,	,	PUNCT
ejpam-5827	290	139	c	c	NOUN
ejpam-5827	290	140	}	}	PUNCT
ejpam-5827	290	141	,	,	PUNCT
ejpam-5827	290	142	{	{	PUNCT
ejpam-5827	290	143	a	a	DET
ejpam-5827	290	144	,	,	PUNCT
ejpam-5827	290	145	b	b	NOUN
ejpam-5827	290	146	,	,	PUNCT
ejpam-5827	290	147	d	d	NOUN
ejpam-5827	290	148	}	}	PUNCT
ejpam-5827	290	149	,	,	PUNCT
ejpam-5827	290	150	{	{	PUNCT
ejpam-5827	290	151	a	a	PRON
ejpam-5827	290	152	,	,	PUNCT
ejpam-5827	290	153	c	c	NOUN
ejpam-5827	290	154	,	,	PUNCT
ejpam-5827	290	155	d	d	NOUN
ejpam-5827	290	156	}	}	PUNCT
ejpam-5827	290	157	}	}	PUNCT
ejpam-5827	290	158	.	.	PUNCT
ejpam-5827	291	1	if	if	SCONJ
ejpam-5827	291	2	p	p	NOUN
ejpam-5827	291	3	=	=	PUNCT
ejpam-5827	291	4	{	{	PUNCT
ejpam-5827	291	5	∅	∅	NOUN
ejpam-5827	291	6	,	,	PUNCT
ejpam-5827	291	7	{	{	PUNCT
ejpam-5827	291	8	a	a	X
ejpam-5827	291	9	}	}	PUNCT
ejpam-5827	291	10	,	,	PUNCT
ejpam-5827	291	11	{	{	PUNCT
ejpam-5827	291	12	b	b	NOUN
ejpam-5827	291	13	}	}	PUNCT
ejpam-5827	291	14	,	,	PUNCT
ejpam-5827	291	15	{	{	PUNCT
ejpam-5827	291	16	c	c	X
ejpam-5827	291	17	}	}	PUNCT
ejpam-5827	291	18	,	,	PUNCT
ejpam-5827	291	19	{	{	PUNCT
ejpam-5827	291	20	a	a	DET
ejpam-5827	291	21	,	,	PUNCT
ejpam-5827	291	22	b	b	NOUN
ejpam-5827	291	23	}	}	PUNCT
ejpam-5827	291	24	,	,	PUNCT
ejpam-5827	291	25	{	{	PUNCT
ejpam-5827	291	26	b	b	X
ejpam-5827	291	27	,	,	PUNCT
ejpam-5827	291	28	c	c	NOUN
ejpam-5827	291	29	}	}	PUNCT
ejpam-5827	291	30	,	,	PUNCT
ejpam-5827	291	31	{	{	PUNCT
ejpam-5827	291	32	a	a	X
ejpam-5827	291	33	,	,	PUNCT
ejpam-5827	291	34	c	c	NOUN
ejpam-5827	291	35	}	}	PUNCT
ejpam-5827	291	36	,	,	PUNCT
ejpam-5827	291	37	{	{	PUNCT
ejpam-5827	291	38	a	a	DET
ejpam-5827	291	39	,	,	PUNCT
ejpam-5827	291	40	b	b	NOUN
ejpam-5827	291	41	,	,	PUNCT
ejpam-5827	291	42	c	c	NOUN
ejpam-5827	291	43	}	}	PUNCT
ejpam-5827	291	44	}	}	PUNCT
ejpam-5827	291	45	,	,	PUNCT
ejpam-5827	291	46	then	then	ADV
ejpam-5827	291	47	r.	r.	PROPN
ejpam-5827	291	48	a.	a.	PROPN
ejpam-5827	291	49	hosny	hosny	PROPN
ejpam-5827	291	50	,	,	PUNCT
ejpam-5827	291	51	m.	m.	PROPN
ejpam-5827	291	52	k.	k.	PROPN
ejpam-5827	292	1	el	el	PROPN
ejpam-5827	292	2	-	-	PROPN
ejpam-5827	292	3	bably	bably	ADV
ejpam-5827	292	4	,	,	PUNCT
ejpam-5827	292	5	m.	m.	NOUN
ejpam-5827	292	6	a.	a.	PROPN
ejpam-5827	292	7	el	el	PROPN
ejpam-5827	292	8	-	-	PROPN
ejpam-5827	292	9	gayar	gayar	PROPN
ejpam-5827	292	10	/	/	SYM
ejpam-5827	292	11	eur	eur	PROPN
ejpam-5827	292	12	.	.	PUNCT
ejpam-5827	293	1	j.	j.	PROPN
ejpam-5827	293	2	pure	pure	PROPN
ejpam-5827	293	3	appl	appl	PROPN
ejpam-5827	293	4	.	.	PROPN
ejpam-5827	293	5	math	math	PROPN
ejpam-5827	293	6	,	,	PUNCT
ejpam-5827	293	7	18	18	NUM
ejpam-5827	293	8	(	(	PUNCT
ejpam-5827	293	9	1	1	NUM
ejpam-5827	293	10	)	)	PUNCT
ejpam-5827	293	11	(	(	PUNCT
ejpam-5827	293	12	2025	2025	NUM
ejpam-5827	293	13	)	)	PUNCT
ejpam-5827	293	14	,	,	PUNCT
ejpam-5827	293	15	5827	5827	NUM
ejpam-5827	293	16	12	12	NUM
ejpam-5827	293	17	of	of	ADP
ejpam-5827	293	18	29	29	NUM
ejpam-5827	293	19	τpu	τpu	NOUN
ejpam-5827	293	20	=	=	PUNCT
ejpam-5827	293	21	τpr	τpr	NOUN
ejpam-5827	293	22	=	=	X
ejpam-5827	293	23	{	{	PUNCT
ejpam-5827	293	24	∅,v	∅,v	X
ejpam-5827	293	25	,	,	PUNCT
ejpam-5827	293	26	{	{	PUNCT
ejpam-5827	293	27	a	a	X
ejpam-5827	293	28	}	}	PUNCT
ejpam-5827	293	29	,	,	PUNCT
ejpam-5827	293	30	{	{	PUNCT
ejpam-5827	293	31	b	b	NOUN
ejpam-5827	293	32	}	}	PUNCT
ejpam-5827	293	33	,	,	PUNCT
ejpam-5827	293	34	{	{	PUNCT
ejpam-5827	293	35	d	d	X
ejpam-5827	293	36	}	}	PUNCT
ejpam-5827	293	37	,	,	PUNCT
ejpam-5827	293	38	{	{	PUNCT
ejpam-5827	293	39	a	a	DET
ejpam-5827	293	40	,	,	PUNCT
ejpam-5827	293	41	b	b	NOUN
ejpam-5827	293	42	}	}	PUNCT
ejpam-5827	293	43	,	,	PUNCT
ejpam-5827	293	44	{	{	PUNCT
ejpam-5827	293	45	a	a	DET
ejpam-5827	293	46	,	,	PUNCT
ejpam-5827	293	47	d	d	NOUN
ejpam-5827	293	48	}	}	PUNCT
ejpam-5827	293	49	,	,	PUNCT
ejpam-5827	293	50	{	{	PUNCT
ejpam-5827	293	51	b	b	X
ejpam-5827	293	52	,	,	PUNCT
ejpam-5827	293	53	d	d	NOUN
ejpam-5827	293	54	}	}	PUNCT
ejpam-5827	293	55	,	,	PUNCT
ejpam-5827	293	56	{	{	PUNCT
ejpam-5827	293	57	c	c	X
ejpam-5827	293	58	,	,	PUNCT
ejpam-5827	293	59	d	d	NOUN
ejpam-5827	293	60	}	}	PUNCT
ejpam-5827	293	61	,	,	PUNCT
ejpam-5827	293	62	{	{	PUNCT
ejpam-5827	293	63	a	a	DET
ejpam-5827	293	64	,	,	PUNCT
ejpam-5827	293	65	b	b	NOUN
ejpam-5827	293	66	,	,	PUNCT
ejpam-5827	293	67	d	d	NOUN
ejpam-5827	293	68	}	}	PUNCT
ejpam-5827	293	69	,	,	PUNCT
ejpam-5827	293	70	{	{	PUNCT
ejpam-5827	293	71	a	a	PRON
ejpam-5827	293	72	,	,	PUNCT
ejpam-5827	293	73	c	c	NOUN
ejpam-5827	293	74	,	,	PUNCT
ejpam-5827	293	75	d	d	NOUN
ejpam-5827	293	76	}	}	PUNCT
ejpam-5827	293	77	,	,	PUNCT
ejpam-5827	293	78	{	{	PUNCT
ejpam-5827	293	79	b	b	X
ejpam-5827	293	80	,	,	PUNCT
ejpam-5827	293	81	c	c	NOUN
ejpam-5827	293	82	,	,	PUNCT
ejpam-5827	293	83	d	d	NOUN
ejpam-5827	293	84	}	}	PUNCT
ejpam-5827	293	85	}	}	PUNCT
ejpam-5827	293	86	,	,	PUNCT
ejpam-5827	293	87	τpi	τpi	NOUN
ejpam-5827	293	88	=	=	SYM
ejpam-5827	293	89	τpl	τpl	PROPN
ejpam-5827	294	1	=	=	SYM
ejpam-5827	294	2	2v	2v	PROPN
ejpam-5827	294	3	,	,	PUNCT
ejpam-5827	294	4	τp⟨r⟩	τp⟨r⟩	PROPN
ejpam-5827	294	5	=	=	PUNCT
ejpam-5827	294	6	τp⟨l⟩	τp⟨l⟩	PUNCT
ejpam-5827	294	7	=	=	PUNCT
ejpam-5827	294	8	τp⟨i⟩	τp⟨i⟩	PROPN
ejpam-5827	294	9	=	=	PUNCT
ejpam-5827	294	10	τp⟨u⟩	τp⟨u⟩	PROPN
ejpam-5827	294	11	=	=	PUNCT
ejpam-5827	294	12	2v	2v	PROPN
ejpam-5827	294	13	.	.	PUNCT
ejpam-5827	295	1	if	if	SCONJ
ejpam-5827	295	2	p̃	p̃	PROPN
ejpam-5827	295	3	=	=	SYM
ejpam-5827	295	4	2v	2v	PROPN
ejpam-5827	295	5	\	\	PROPN
ejpam-5827	295	6	{	{	PUNCT
ejpam-5827	295	7	v	v	NOUN
ejpam-5827	295	8	,	,	PUNCT
ejpam-5827	295	9	{	{	PUNCT
ejpam-5827	295	10	b	b	NOUN
ejpam-5827	295	11	,	,	PUNCT
ejpam-5827	295	12	d	d	NOUN
ejpam-5827	295	13	}	}	PUNCT
ejpam-5827	295	14	,	,	PUNCT
ejpam-5827	295	15	{	{	PUNCT
ejpam-5827	295	16	a	a	DET
ejpam-5827	295	17	,	,	PUNCT
ejpam-5827	295	18	b	b	NOUN
ejpam-5827	295	19	,	,	PUNCT
ejpam-5827	295	20	d	d	NOUN
ejpam-5827	295	21	}	}	PUNCT
ejpam-5827	295	22	,	,	PUNCT
ejpam-5827	295	23	{	{	PUNCT
ejpam-5827	295	24	b	b	X
ejpam-5827	295	25	,	,	PUNCT
ejpam-5827	295	26	c	c	NOUN
ejpam-5827	295	27	,	,	PUNCT
ejpam-5827	295	28	d	d	NOUN
ejpam-5827	295	29	}	}	PUNCT
ejpam-5827	295	30	}	}	PUNCT
ejpam-5827	295	31	,	,	PUNCT
ejpam-5827	295	32	then	then	ADV
ejpam-5827	295	33	τ	τ	PROPN
ejpam-5827	295	34	p̃i	p̃i	PROPN
ejpam-5827	295	35	=	=	PUNCT
ejpam-5827	295	36	τ	τ	PROPN
ejpam-5827	295	37	p̃l	p̃l	PROPN
ejpam-5827	295	38	=	=	SYM
ejpam-5827	295	39	τ	τ	PROPN
ejpam-5827	295	40	p̃r	p̃r	NOUN
ejpam-5827	295	41	=	=	PUNCT
ejpam-5827	295	42	2v	2v	PROPN
ejpam-5827	295	43	,	,	PUNCT
ejpam-5827	295	44	τ	τ	PROPN
ejpam-5827	295	45	p̃u	p̃u	ADJ
ejpam-5827	295	46	=	=	NOUN
ejpam-5827	295	47	{	{	PUNCT
ejpam-5827	295	48	∅,v	∅,v	X
ejpam-5827	295	49	,	,	PUNCT
ejpam-5827	295	50	{	{	PUNCT
ejpam-5827	295	51	a	a	X
ejpam-5827	295	52	}	}	PUNCT
ejpam-5827	295	53	,	,	PUNCT
ejpam-5827	295	54	{	{	PUNCT
ejpam-5827	295	55	b	b	NOUN
ejpam-5827	295	56	}	}	PUNCT
ejpam-5827	295	57	,	,	PUNCT
ejpam-5827	295	58	{	{	PUNCT
ejpam-5827	295	59	d	d	X
ejpam-5827	295	60	}	}	PUNCT
ejpam-5827	295	61	,	,	PUNCT
ejpam-5827	295	62	{	{	PUNCT
ejpam-5827	295	63	a	a	DET
ejpam-5827	295	64	,	,	PUNCT
ejpam-5827	295	65	b	b	NOUN
ejpam-5827	295	66	}	}	PUNCT
ejpam-5827	295	67	,	,	PUNCT
ejpam-5827	295	68	{	{	PUNCT
ejpam-5827	295	69	a	a	PRON
ejpam-5827	295	70	,	,	PUNCT
ejpam-5827	295	71	d	d	NOUN
ejpam-5827	295	72	}	}	PUNCT
ejpam-5827	295	73	,	,	PUNCT
ejpam-5827	295	74	{	{	PUNCT
ejpam-5827	295	75	b	b	X
ejpam-5827	295	76	,	,	PUNCT
ejpam-5827	295	77	c	c	NOUN
ejpam-5827	295	78	}	}	PUNCT
ejpam-5827	295	79	,	,	PUNCT
ejpam-5827	295	80	{	{	PUNCT
ejpam-5827	295	81	b	b	X
ejpam-5827	295	82	,	,	PUNCT
ejpam-5827	295	83	d	d	NOUN
ejpam-5827	295	84	}	}	PUNCT
ejpam-5827	295	85	,	,	PUNCT
ejpam-5827	295	86	{	{	PUNCT
ejpam-5827	295	87	c	c	X
ejpam-5827	295	88	,	,	PUNCT
ejpam-5827	295	89	d	d	NOUN
ejpam-5827	295	90	}	}	PUNCT
ejpam-5827	295	91	,	,	PUNCT
ejpam-5827	295	92	{	{	PUNCT
ejpam-5827	295	93	a	a	DET
ejpam-5827	295	94	,	,	PUNCT
ejpam-5827	295	95	b	b	NOUN
ejpam-5827	295	96	,	,	PUNCT
ejpam-5827	295	97	c	c	NOUN
ejpam-5827	295	98	}	}	PUNCT
ejpam-5827	295	99	,	,	PUNCT
ejpam-5827	295	100	{	{	PUNCT
ejpam-5827	295	101	a	a	DET
ejpam-5827	295	102	,	,	PUNCT
ejpam-5827	295	103	b	b	NOUN
ejpam-5827	295	104	,	,	PUNCT
ejpam-5827	295	105	d	d	NOUN
ejpam-5827	295	106	}	}	PUNCT
ejpam-5827	295	107	,	,	PUNCT
ejpam-5827	295	108	{	{	PUNCT
ejpam-5827	295	109	a	a	PRON
ejpam-5827	295	110	,	,	PUNCT
ejpam-5827	295	111	c	c	NOUN
ejpam-5827	295	112	,	,	PUNCT
ejpam-5827	295	113	d	d	NOUN
ejpam-5827	295	114	}	}	PUNCT
ejpam-5827	295	115	,	,	PUNCT
ejpam-5827	295	116	{	{	PUNCT
ejpam-5827	295	117	b	b	X
ejpam-5827	295	118	,	,	PUNCT
ejpam-5827	295	119	c	c	NOUN
ejpam-5827	295	120	,	,	PUNCT
ejpam-5827	295	121	d	d	NOUN
ejpam-5827	295	122	}	}	PUNCT
ejpam-5827	295	123	}	}	PUNCT
ejpam-5827	295	124	,	,	PUNCT
ejpam-5827	295	125	τp⟨r⟩	τp⟨r⟩	PROPN
ejpam-5827	295	126	=	=	PUNCT
ejpam-5827	295	127	τ	τ	X
ejpam-5827	295	128	p̃⟨l⟩	p̃⟨l⟩	NOUN
ejpam-5827	295	129	=	=	PROPN
ejpam-5827	295	130	τ	τ	PROPN
ejpam-5827	295	131	p̃⟨i⟩	p̃⟨i⟩	NOUN
ejpam-5827	295	132	=	=	SYM
ejpam-5827	295	133	τ	τ	PROPN
ejpam-5827	295	134	p̃⟨u⟩	p̃⟨u⟩	NOUN
ejpam-5827	295	135	=	=	SYM
ejpam-5827	295	136	2v	2v	PROPN
ejpam-5827	295	137	.	.	PUNCT
ejpam-5827	296	1	remark	remark	PROPN
ejpam-5827	296	2	8	8	NUM
ejpam-5827	296	3	.	.	PUNCT
ejpam-5827	297	1	if	if	SCONJ
ejpam-5827	297	2	nκ(z	nκ(z	NUM
ejpam-5827	297	3	)	)	PUNCT
ejpam-5827	297	4	∈	∈	PROPN
ejpam-5827	297	5	p	p	X
ejpam-5827	297	6	∀z	∀z	PROPN
ejpam-5827	297	7	∈	∈	PROPN
ejpam-5827	297	8	h	h	NOUN
ejpam-5827	297	9	,	,	PUNCT
ejpam-5827	297	10	then	then	ADV
ejpam-5827	297	11	it	it	PRON
ejpam-5827	297	12	follows	follow	VERB
ejpam-5827	297	13	that	that	SCONJ
ejpam-5827	297	14	h	h	NOUN
ejpam-5827	297	15	∈	∈	PROPN
ejpam-5827	297	16	τpκ	τpκ	NOUN
ejpam-5827	297	17	.	.	PUNCT
ejpam-5827	298	1	however	however	ADV
ejpam-5827	298	2	,	,	PUNCT
ejpam-5827	298	3	as	as	SCONJ
ejpam-5827	298	4	illustrated	illustrate	VERB
ejpam-5827	298	5	in	in	ADP
ejpam-5827	298	6	example	example	NOUN
ejpam-5827	298	7	5	5	NUM
ejpam-5827	298	8	,	,	PUNCT
ejpam-5827	298	9	the	the	DET
ejpam-5827	298	10	converse	converse	NOUN
ejpam-5827	298	11	does	do	AUX
ejpam-5827	298	12	not	not	PART
ejpam-5827	298	13	necessarily	necessarily	ADV
ejpam-5827	298	14	hold	hold	VERB
ejpam-5827	298	15	.	.	PUNCT
ejpam-5827	299	1	specifically	specifically	ADV
ejpam-5827	299	2	,	,	PUNCT
ejpam-5827	299	3	we	we	PRON
ejpam-5827	299	4	observe	observe	VERB
ejpam-5827	299	5	that	that	SCONJ
ejpam-5827	299	6	{	{	PUNCT
ejpam-5827	299	7	d	d	X
ejpam-5827	299	8	}	}	PUNCT
ejpam-5827	299	9	∈	∈	PROPN
ejpam-5827	299	10	τp⟨r⟩	τp⟨r⟩	NOUN
ejpam-5827	299	11	,	,	PUNCT
ejpam-5827	299	12	while	while	SCONJ
ejpam-5827	299	13	n⟨r⟩({d	n⟨r⟩({d	ADV
ejpam-5827	299	14	}	}	PUNCT
ejpam-5827	299	15	)	)	PUNCT
ejpam-5827	300	1	=	=	PRON
ejpam-5827	300	2	{	{	PUNCT
ejpam-5827	300	3	d	d	X
ejpam-5827	300	4	}	}	PUNCT
ejpam-5827	300	5	̸∈	̸∈	PROPN
ejpam-5827	300	6	p	p	PROPN
ejpam-5827	300	7	,	,	PUNCT
ejpam-5827	300	8	demonstrating	demonstrate	VERB
ejpam-5827	300	9	a	a	DET
ejpam-5827	300	10	counterexample	counterexample	NOUN
ejpam-5827	300	11	to	to	ADP
ejpam-5827	300	12	the	the	DET
ejpam-5827	300	13	converse	converse	NOUN
ejpam-5827	300	14	implication	implication	NOUN
ejpam-5827	300	15	.	.	PUNCT
ejpam-5827	301	1	proposition	proposition	NOUN
ejpam-5827	301	2	2	2	NUM
ejpam-5827	301	3	.	.	PUNCT
ejpam-5827	302	1	let	let	VERB
ejpam-5827	302	2	(	(	PUNCT
ejpam-5827	302	3	v	v	NOUN
ejpam-5827	302	4	,	,	PUNCT
ejpam-5827	302	5	r	r	NOUN
ejpam-5827	302	6	,	,	PUNCT
ejpam-5827	302	7	ζκ	ζκ	NOUN
ejpam-5827	302	8	)	)	PUNCT
ejpam-5827	302	9	be	be	AUX
ejpam-5827	302	10	a	a	DET
ejpam-5827	302	11	κ	κ	NOUN
ejpam-5827	302	12	-	-	ADJ
ejpam-5827	302	13	ns	ns	ADJ
ejpam-5827	302	14	and	and	CCONJ
ejpam-5827	302	15	p	p	NOUN
ejpam-5827	302	16	be	be	AUX
ejpam-5827	302	17	a	a	DET
ejpam-5827	302	18	primal	primal	NOUN
ejpam-5827	302	19	on	on	ADP
ejpam-5827	303	1	v.	v.	ADP
ejpam-5827	303	2	then	then	ADV
ejpam-5827	303	3	the	the	DET
ejpam-5827	303	4	following	follow	VERB
ejpam-5827	303	5	results	result	NOUN
ejpam-5827	303	6	hold	hold	VERB
ejpam-5827	303	7	.	.	PUNCT
ejpam-5827	304	1	(	(	PUNCT
ejpam-5827	304	2	i	i	NOUN
ejpam-5827	304	3	)	)	PUNCT
ejpam-5827	304	4	τpu	τpu	VERB
ejpam-5827	304	5	⊆	⊆	NUM
ejpam-5827	304	6	τpr	τpr	NOUN
ejpam-5827	304	7	∩	∩	NOUN
ejpam-5827	304	8	τpl	τpl	VERB
ejpam-5827	304	9	⊆	⊆	NUM
ejpam-5827	304	10	τpr	τpr	NOUN
ejpam-5827	304	11	∪	∪	NOUN
ejpam-5827	304	12	τpl	τpl	VERB
ejpam-5827	304	13	⊆τpi	⊆τpi	NOUN
ejpam-5827	304	14	.	.	PUNCT
ejpam-5827	305	1	(	(	PUNCT
ejpam-5827	305	2	ii	ii	NOUN
ejpam-5827	305	3	)	)	PUNCT
ejpam-5827	305	4	τp⟨u⟩	τp⟨u⟩	NOUN
ejpam-5827	305	5	⊆	⊆	NUM
ejpam-5827	305	6	τp⟨r⟩	τp⟨r⟩	PROPN
ejpam-5827	305	7	∩	∩	NOUN
ejpam-5827	305	8	τp⟨l⟩	τp⟨l⟩	PROPN
ejpam-5827	305	9	⊆	⊆	NUM
ejpam-5827	305	10	τp⟨r⟩	τp⟨r⟩	PROPN
ejpam-5827	305	11	∪	∪	ADP
ejpam-5827	305	12	τp⟨l⟩	τp⟨l⟩	PROPN
ejpam-5827	305	13	⊆	⊆	NUM
ejpam-5827	305	14	τp⟨i⟩.	τp⟨i⟩.	NOUN
ejpam-5827	305	15	proof	proof	NOUN
ejpam-5827	305	16	.	.	PUNCT
ejpam-5827	306	1	suppose	suppose	VERB
ejpam-5827	306	2	ε	ε	PROPN
ejpam-5827	306	3	=	=	SYM
ejpam-5827	306	4	r	r	PROPN
ejpam-5827	306	5	or	or	CCONJ
ejpam-5827	306	6	l.	l.	NOUN
ejpam-5827	306	7	since	since	SCONJ
ejpam-5827	306	8	ni(x	ni(x	NUM
ejpam-5827	306	9	)	)	PUNCT
ejpam-5827	306	10	⊆	⊆	NUM
ejpam-5827	306	11	nε(x	nε(x	NOUN
ejpam-5827	306	12	)	)	PUNCT
ejpam-5827	306	13	⊆	⊆	NUM
ejpam-5827	306	14	nu(x	nu(x	NOUN
ejpam-5827	306	15	)	)	PUNCT
ejpam-5827	306	16	and	and	CCONJ
ejpam-5827	306	17	n⟨i⟩(x	n⟨i⟩(x	NUM
ejpam-5827	306	18	)	)	PUNCT
ejpam-5827	306	19	⊆	⊆	NUM
ejpam-5827	306	20	n⟨ε⟩(x	n⟨ε⟩(x	NUM
ejpam-5827	306	21	)	)	PUNCT
ejpam-5827	306	22	⊆	⊆	NUM
ejpam-5827	306	23	n⟨u⟩(x	n⟨u⟩(x	NUM
ejpam-5827	306	24	)	)	PUNCT
ejpam-5827	306	25	,	,	PUNCT
ejpam-5827	306	26	for	for	ADP
ejpam-5827	306	27	each	each	DET
ejpam-5827	306	28	x	x	SYM
ejpam-5827	306	29	∈	∈	PROPN
ejpam-5827	306	30	v	v	ADP
ejpam-5827	306	31	then	then	ADV
ejpam-5827	306	32	the	the	DET
ejpam-5827	306	33	proof	proof	NOUN
ejpam-5827	306	34	is	be	AUX
ejpam-5827	306	35	evident	evident	ADJ
ejpam-5827	306	36	.	.	PUNCT
ejpam-5827	307	1	example	example	NOUN
ejpam-5827	307	2	5	5	NUM
ejpam-5827	307	3	shows	show	VERB
ejpam-5827	307	4	that	that	SCONJ
ejpam-5827	307	5	the	the	DET
ejpam-5827	307	6	converse	converse	NOUN
ejpam-5827	307	7	of	of	ADP
ejpam-5827	307	8	item	item	NOUN
ejpam-5827	307	9	1	1	NUM
ejpam-5827	307	10	of	of	ADP
ejpam-5827	307	11	proposition	proposition	NOUN
ejpam-5827	307	12	2	2	NUM
ejpam-5827	307	13	needs	need	VERB
ejpam-5827	307	14	not	not	PART
ejpam-5827	307	15	to	to	PART
ejpam-5827	307	16	be	be	AUX
ejpam-5827	307	17	true	true	ADJ
ejpam-5827	307	18	.	.	PUNCT
ejpam-5827	308	1	proposition	proposition	NOUN
ejpam-5827	308	2	3	3	X
ejpam-5827	308	3	.	.	PUNCT
ejpam-5827	309	1	let	let	VERB
ejpam-5827	309	2	p	p	NOUN
ejpam-5827	309	3	and	and	CCONJ
ejpam-5827	309	4	p̃	p̃	PROPN
ejpam-5827	309	5	be	be	VERB
ejpam-5827	309	6	two	two	NUM
ejpam-5827	309	7	primals	primal	NOUN
ejpam-5827	309	8	on	on	ADP
ejpam-5827	309	9	κ	κ	NOUN
ejpam-5827	309	10	-	-	ADJ
ejpam-5827	309	11	supra	supra	ADJ
ejpam-5827	309	12	topological	topological	ADJ
ejpam-5827	309	13	spaces	space	NOUN
ejpam-5827	309	14	(	(	PUNCT
ejpam-5827	309	15	v	v	NOUN
ejpam-5827	309	16	,	,	PUNCT
ejpam-5827	309	17	τpκ	τpκ	NOUN
ejpam-5827	309	18	)	)	PUNCT
ejpam-5827	309	19	and	and	CCONJ
ejpam-5827	309	20	(	(	PUNCT
ejpam-5827	309	21	v	v	NOUN
ejpam-5827	309	22	,	,	PUNCT
ejpam-5827	309	23	τ	τ	PROPN
ejpam-5827	309	24	p̃κ	p̃κ	NOUN
ejpam-5827	309	25	)	)	PUNCT
ejpam-5827	309	26	,	,	PUNCT
ejpam-5827	309	27	respectively	respectively	ADV
ejpam-5827	309	28	,	,	PUNCT
ejpam-5827	309	29	where	where	SCONJ
ejpam-5827	309	30	p	p	PROPN
ejpam-5827	309	31	⊆	⊆	NUM
ejpam-5827	309	32	p̃.	p̃.	NOUN
ejpam-5827	309	33	then	then	ADV
ejpam-5827	309	34	,	,	PUNCT
ejpam-5827	309	35	for	for	ADP
ejpam-5827	309	36	any	any	DET
ejpam-5827	309	37	κ	κ	NOUN
ejpam-5827	309	38	,	,	PUNCT
ejpam-5827	309	39	it	it	PRON
ejpam-5827	309	40	follows	follow	VERB
ejpam-5827	309	41	that	that	SCONJ
ejpam-5827	309	42	τpκ	τpκ	NOUN
ejpam-5827	309	43	⊆	⊆	NUM
ejpam-5827	309	44	τ	τ	X
ejpam-5827	309	45	p̃κ	p̃κ	NOUN
ejpam-5827	309	46	.	.	PUNCT
ejpam-5827	310	1	proof	proof	NOUN
ejpam-5827	310	2	.	.	PUNCT
ejpam-5827	311	1	direct	direct	ADJ
ejpam-5827	311	2	to	to	PART
ejpam-5827	311	3	prove	prove	VERB
ejpam-5827	311	4	.	.	PUNCT
ejpam-5827	312	1	remark	remark	NOUN
ejpam-5827	312	2	9	9	NUM
ejpam-5827	312	3	.	.	PUNCT
ejpam-5827	313	1	according	accord	VERB
ejpam-5827	313	2	to	to	ADP
ejpam-5827	313	3	example	example	NOUN
ejpam-5827	313	4	5	5	NUM
ejpam-5827	313	5	,	,	PUNCT
ejpam-5827	313	6	the	the	DET
ejpam-5827	313	7	converse	converse	NOUN
ejpam-5827	313	8	of	of	ADP
ejpam-5827	313	9	proposition	proposition	NOUN
ejpam-5827	313	10	3	3	NUM
ejpam-5827	313	11	does	do	AUX
ejpam-5827	313	12	not	not	PART
ejpam-5827	313	13	necessarily	necessarily	ADV
ejpam-5827	313	14	hold	hold	VERB
ejpam-5827	313	15	.	.	PUNCT
ejpam-5827	314	1	consider	consider	VERB
ejpam-5827	314	2	the	the	DET
ejpam-5827	314	3	primals	primal	NOUN
ejpam-5827	314	4	p	p	NOUN
ejpam-5827	314	5	=	=	SYM
ejpam-5827	314	6	{	{	PUNCT
ejpam-5827	314	7	∅	∅	NOUN
ejpam-5827	314	8	,	,	PUNCT
ejpam-5827	314	9	{	{	PUNCT
ejpam-5827	314	10	a	a	X
ejpam-5827	314	11	}	}	PUNCT
ejpam-5827	314	12	,	,	PUNCT
ejpam-5827	314	13	{	{	PUNCT
ejpam-5827	314	14	b	b	NOUN
ejpam-5827	314	15	}	}	PUNCT
ejpam-5827	314	16	,	,	PUNCT
ejpam-5827	314	17	{	{	PUNCT
ejpam-5827	314	18	c	c	X
ejpam-5827	314	19	}	}	PUNCT
ejpam-5827	314	20	,	,	PUNCT
ejpam-5827	314	21	{	{	PUNCT
ejpam-5827	314	22	a	a	DET
ejpam-5827	314	23	,	,	PUNCT
ejpam-5827	314	24	b	b	NOUN
ejpam-5827	314	25	}	}	PUNCT
ejpam-5827	314	26	,	,	PUNCT
ejpam-5827	314	27	{	{	PUNCT
ejpam-5827	314	28	b	b	X
ejpam-5827	314	29	,	,	PUNCT
ejpam-5827	314	30	c	c	NOUN
ejpam-5827	314	31	}	}	PUNCT
ejpam-5827	314	32	,	,	PUNCT
ejpam-5827	314	33	{	{	PUNCT
ejpam-5827	314	34	a	a	X
ejpam-5827	314	35	,	,	PUNCT
ejpam-5827	314	36	c	c	NOUN
ejpam-5827	314	37	}	}	PUNCT
ejpam-5827	314	38	,	,	PUNCT
ejpam-5827	314	39	{	{	PUNCT
ejpam-5827	314	40	a	a	PRON
ejpam-5827	314	41	,	,	PUNCT
ejpam-5827	314	42	b	b	NOUN
ejpam-5827	314	43	,	,	PUNCT
ejpam-5827	314	44	c	c	NOUN
ejpam-5827	314	45	}	}	PUNCT
ejpam-5827	314	46	}	}	PUNCT
ejpam-5827	314	47	,	,	PUNCT
ejpam-5827	314	48	and	and	CCONJ
ejpam-5827	314	49	p̃	p̃	PROPN
ejpam-5827	314	50	=	=	SYM
ejpam-5827	314	51	2v	2v	PROPN
ejpam-5827	314	52	\	\	PROPN
ejpam-5827	314	53	{	{	PUNCT
ejpam-5827	314	54	v	v	NOUN
ejpam-5827	314	55	,	,	PUNCT
ejpam-5827	314	56	{	{	PUNCT
ejpam-5827	314	57	b	b	NOUN
ejpam-5827	314	58	,	,	PUNCT
ejpam-5827	314	59	d	d	NOUN
ejpam-5827	314	60	}	}	PUNCT
ejpam-5827	314	61	,	,	PUNCT
ejpam-5827	314	62	{	{	PUNCT
ejpam-5827	314	63	a	a	DET
ejpam-5827	314	64	,	,	PUNCT
ejpam-5827	314	65	b	b	NOUN
ejpam-5827	314	66	,	,	PUNCT
ejpam-5827	314	67	d	d	NOUN
ejpam-5827	314	68	}	}	PUNCT
ejpam-5827	314	69	,	,	PUNCT
ejpam-5827	314	70	{	{	PUNCT
ejpam-5827	314	71	b	b	X
ejpam-5827	314	72	,	,	PUNCT
ejpam-5827	314	73	c	c	NOUN
ejpam-5827	314	74	,	,	PUNCT
ejpam-5827	314	75	d	d	NOUN
ejpam-5827	314	76	}	}	PUNCT
ejpam-5827	314	77	}	}	PUNCT
ejpam-5827	314	78	on	on	ADP
ejpam-5827	314	79	v.	v.	AUX
ejpam-5827	314	80	suppose	suppose	VERB
ejpam-5827	314	81	κ	κ	PROPN
ejpam-5827	314	82	=	=	PROPN
ejpam-5827	314	83	r.	r.	PROPN
ejpam-5827	314	84	then	then	ADV
ejpam-5827	314	85	,	,	PUNCT
ejpam-5827	314	86	we	we	PRON
ejpam-5827	314	87	have	have	VERB
ejpam-5827	314	88	τpr	τpr	NOUN
ejpam-5827	314	89	=	=	SYM
ejpam-5827	314	90	{	{	PUNCT
ejpam-5827	314	91	∅,v	∅,v	X
ejpam-5827	314	92	,	,	PUNCT
ejpam-5827	314	93	{	{	PUNCT
ejpam-5827	314	94	a	a	X
ejpam-5827	314	95	}	}	PUNCT
ejpam-5827	314	96	,	,	PUNCT
ejpam-5827	314	97	{	{	PUNCT
ejpam-5827	314	98	b	b	NOUN
ejpam-5827	314	99	}	}	PUNCT
ejpam-5827	314	100	,	,	PUNCT
ejpam-5827	314	101	{	{	PUNCT
ejpam-5827	314	102	d	d	X
ejpam-5827	314	103	}	}	PUNCT
ejpam-5827	314	104	,	,	PUNCT
ejpam-5827	314	105	{	{	PUNCT
ejpam-5827	314	106	a	a	DET
ejpam-5827	314	107	,	,	PUNCT
ejpam-5827	314	108	b	b	NOUN
ejpam-5827	314	109	}	}	PUNCT
ejpam-5827	314	110	,	,	PUNCT
ejpam-5827	314	111	{	{	PUNCT
ejpam-5827	314	112	a	a	DET
ejpam-5827	314	113	,	,	PUNCT
ejpam-5827	314	114	d	d	NOUN
ejpam-5827	314	115	}	}	PUNCT
ejpam-5827	314	116	,	,	PUNCT
ejpam-5827	314	117	{	{	PUNCT
ejpam-5827	314	118	b	b	X
ejpam-5827	314	119	,	,	PUNCT
ejpam-5827	314	120	d	d	NOUN
ejpam-5827	314	121	}	}	PUNCT
ejpam-5827	314	122	,	,	PUNCT
ejpam-5827	314	123	{	{	PUNCT
ejpam-5827	314	124	c	c	X
ejpam-5827	314	125	,	,	PUNCT
ejpam-5827	314	126	d	d	NOUN
ejpam-5827	314	127	}	}	PUNCT
ejpam-5827	314	128	,	,	PUNCT
ejpam-5827	314	129	{	{	PUNCT
ejpam-5827	314	130	a	a	DET
ejpam-5827	314	131	,	,	PUNCT
ejpam-5827	314	132	b	b	NOUN
ejpam-5827	314	133	,	,	PUNCT
ejpam-5827	314	134	d	d	NOUN
ejpam-5827	314	135	}	}	PUNCT
ejpam-5827	314	136	,	,	PUNCT
ejpam-5827	314	137	{	{	PUNCT
ejpam-5827	314	138	a	a	PRON
ejpam-5827	314	139	,	,	PUNCT
ejpam-5827	314	140	c	c	NOUN
ejpam-5827	314	141	,	,	PUNCT
ejpam-5827	314	142	d	d	NOUN
ejpam-5827	314	143	}	}	PUNCT
ejpam-5827	314	144	,	,	PUNCT
ejpam-5827	314	145	{	{	PUNCT
ejpam-5827	314	146	b	b	X
ejpam-5827	314	147	,	,	PUNCT
ejpam-5827	314	148	c	c	NOUN
ejpam-5827	314	149	,	,	PUNCT
ejpam-5827	314	150	d	d	NOUN
ejpam-5827	314	151	}	}	PUNCT
ejpam-5827	314	152	}	}	PUNCT
ejpam-5827	314	153	,	,	PUNCT
ejpam-5827	314	154	while	while	SCONJ
ejpam-5827	314	155	τ	τ	PROPN
ejpam-5827	314	156	p̃r	p̃r	NOUN
ejpam-5827	314	157	=	=	PROPN
ejpam-5827	314	158	2v	2v	PROPN
ejpam-5827	314	159	.	.	PUNCT
ejpam-5827	315	1	thus	thus	ADV
ejpam-5827	315	2	,	,	PUNCT
ejpam-5827	315	3	it	it	PRON
ejpam-5827	315	4	follows	follow	VERB
ejpam-5827	315	5	that	that	SCONJ
ejpam-5827	315	6	τ	τ	PROPN
ejpam-5827	315	7	p̃r	p̃r	NOUN
ejpam-5827	315	8	⊈	⊈	PROPN
ejpam-5827	315	9	τpr	τpr	NOUN
ejpam-5827	315	10	.	.	PUNCT
ejpam-5827	316	1	definition	definition	NOUN
ejpam-5827	316	2	13	13	NUM
ejpam-5827	316	3	.	.	PUNCT
ejpam-5827	317	1	let	let	VERB
ejpam-5827	317	2	τpκ	τpκ	NOUN
ejpam-5827	317	3	be	be	AUX
ejpam-5827	317	4	a	a	DET
ejpam-5827	317	5	κ	κ	NOUN
ejpam-5827	317	6	-	-	PUNCT
ejpam-5827	317	7	supra	supra	ADJ
ejpam-5827	317	8	topology	topology	NOUN
ejpam-5827	317	9	generated	generate	VERB
ejpam-5827	317	10	by	by	ADP
ejpam-5827	317	11	κ	κ	ADV
ejpam-5827	317	12	-	-	PUNCT
ejpam-5827	317	13	ns	ns	ADJ
ejpam-5827	317	14	and	and	CCONJ
ejpam-5827	317	15	primal	primal	ADJ
ejpam-5827	317	16	p.	p.	NOUN
ejpam-5827	317	17	then	then	ADV
ejpam-5827	317	18	τpκ	τpκ	PRON
ejpam-5827	317	19	int(h	int(h	NOUN
ejpam-5827	317	20	)	)	PUNCT
ejpam-5827	317	21	,	,	PUNCT
ejpam-5827	317	22	τpκ	τpκ	NOUN
ejpam-5827	317	23	cl(h	cl(h	NOUN
ejpam-5827	317	24	)	)	PUNCT
ejpam-5827	317	25	of	of	ADP
ejpam-5827	317	26	a	a	DET
ejpam-5827	317	27	set	set	ADJ
ejpam-5827	317	28	h	h	NOUN
ejpam-5827	317	29	are	be	AUX
ejpam-5827	317	30	assigned	assign	VERB
ejpam-5827	317	31	respectively	respectively	ADV
ejpam-5827	317	32	for	for	ADP
ejpam-5827	317	33	each	each	DET
ejpam-5827	317	34	κ	κ	NOUN
ejpam-5827	317	35	as	as	ADP
ejpam-5827	317	36	:	:	PUNCT
ejpam-5827	317	37	τpκ	τpκ	NOUN
ejpam-5827	317	38	int(h	int(h	NOUN
ejpam-5827	317	39	)	)	PUNCT
ejpam-5827	317	40	=	=	SYM
ejpam-5827	318	1	∪{w	∪{w	PROPN
ejpam-5827	318	2	∈τpκ	∈τpκ	NOUN
ejpam-5827	318	3	:	:	PUNCT
ejpam-5827	318	4	w	w	PROPN
ejpam-5827	318	5	⊆	⊆	NUM
ejpam-5827	318	6	h	h	NOUN
ejpam-5827	318	7	}	}	PUNCT
ejpam-5827	318	8	,	,	PUNCT
ejpam-5827	318	9	r.	r.	PROPN
ejpam-5827	318	10	a.	a.	PROPN
ejpam-5827	318	11	hosny	hosny	PROPN
ejpam-5827	318	12	,	,	PUNCT
ejpam-5827	318	13	m.	m.	PROPN
ejpam-5827	318	14	k.	k.	PROPN
ejpam-5827	318	15	el	el	PROPN
ejpam-5827	318	16	-	-	PROPN
ejpam-5827	318	17	bably	bably	ADV
ejpam-5827	318	18	,	,	PUNCT
ejpam-5827	318	19	m.	m.	NOUN
ejpam-5827	318	20	a.	a.	PROPN
ejpam-5827	318	21	el	el	PROPN
ejpam-5827	318	22	-	-	PROPN
ejpam-5827	318	23	gayar	gayar	PROPN
ejpam-5827	318	24	/	/	SYM
ejpam-5827	318	25	eur	eur	PROPN
ejpam-5827	318	26	.	.	PUNCT
ejpam-5827	319	1	j.	j.	PROPN
ejpam-5827	319	2	pure	pure	PROPN
ejpam-5827	319	3	appl	appl	PROPN
ejpam-5827	319	4	.	.	PROPN
ejpam-5827	319	5	math	math	PROPN
ejpam-5827	319	6	,	,	PUNCT
ejpam-5827	319	7	18	18	NUM
ejpam-5827	319	8	(	(	PUNCT
ejpam-5827	319	9	1	1	NUM
ejpam-5827	319	10	)	)	PUNCT
ejpam-5827	319	11	(	(	PUNCT
ejpam-5827	319	12	2025	2025	NUM
ejpam-5827	319	13	)	)	PUNCT
ejpam-5827	319	14	,	,	PUNCT
ejpam-5827	319	15	5827	5827	NUM
ejpam-5827	319	16	13	13	NUM
ejpam-5827	319	17	of	of	ADP
ejpam-5827	319	18	29	29	NUM
ejpam-5827	319	19	τpκ	τpκ	NOUN
ejpam-5827	319	20	cl(h	cl(h	NOUN
ejpam-5827	319	21	)	)	PUNCT
ejpam-5827	319	22	=	=	PUNCT
ejpam-5827	319	23	∩{f	∩{f	PROPN
ejpam-5827	319	24	∈υp	∈υp	NOUN
ejpam-5827	319	25	κ	κ	X
ejpam-5827	319	26	:	:	PUNCT
ejpam-5827	319	27	h	h	PROPN
ejpam-5827	319	28	⊆	⊆	NUM
ejpam-5827	319	29	f	f	X
ejpam-5827	319	30	}	}	PUNCT
ejpam-5827	319	31	.	.	PUNCT
ejpam-5827	320	1	the	the	DET
ejpam-5827	320	2	behavior	behavior	NOUN
ejpam-5827	320	3	of	of	ADP
ejpam-5827	320	4	τpκ	τpκ	X
ejpam-5827	320	5	l	l	NOUN
ejpam-5827	320	6	(	(	PUNCT
ejpam-5827	320	7	.	.	PUNCT
ejpam-5827	320	8	)	)	PUNCT
ejpam-5827	320	9	and	and	CCONJ
ejpam-5827	320	10	τpκ	τpκ	DET
ejpam-5827	320	11	u	u	NOUN
ejpam-5827	320	12	(	(	PUNCT
ejpam-5827	320	13	.	.	PUNCT
ejpam-5827	320	14	)	)	PUNCT
ejpam-5827	320	15	can	can	AUX
ejpam-5827	320	16	vary	vary	VERB
ejpam-5827	320	17	significantly	significantly	ADV
ejpam-5827	320	18	based	base	VERB
ejpam-5827	320	19	on	on	ADP
ejpam-5827	320	20	the	the	DET
ejpam-5827	320	21	choice	choice	NOUN
ejpam-5827	320	22	of	of	ADP
ejpam-5827	320	23	κ	κ	NOUN
ejpam-5827	320	24	and	and	CCONJ
ejpam-5827	320	25	the	the	DET
ejpam-5827	320	26	primal	primal	ADJ
ejpam-5827	320	27	set	set	NOUN
ejpam-5827	320	28	p.	p.	NOUN
ejpam-5827	320	29	different	different	ADJ
ejpam-5827	320	30	selections	selection	NOUN
ejpam-5827	320	31	of	of	ADP
ejpam-5827	320	32	κ	κ	NOUN
ejpam-5827	320	33	-	-	PUNCT
ejpam-5827	320	34	neighborhood	neighborhood	NOUN
ejpam-5827	320	35	systems	system	NOUN
ejpam-5827	320	36	and	and	CCONJ
ejpam-5827	320	37	primal	primal	ADJ
ejpam-5827	320	38	structure	structure	NOUN
ejpam-5827	320	39	can	can	AUX
ejpam-5827	320	40	lead	lead	VERB
ejpam-5827	320	41	to	to	ADP
ejpam-5827	320	42	varying	vary	VERB
ejpam-5827	320	43	levels	level	NOUN
ejpam-5827	320	44	of	of	ADP
ejpam-5827	320	45	granularity	granularity	NOUN
ejpam-5827	320	46	in	in	ADP
ejpam-5827	320	47	the	the	DET
ejpam-5827	320	48	approximations	approximation	NOUN
ejpam-5827	320	49	,	,	PUNCT
ejpam-5827	320	50	thus	thus	ADV
ejpam-5827	320	51	tailoring	tailor	VERB
ejpam-5827	320	52	the	the	DET
ejpam-5827	320	53	approach	approach	NOUN
ejpam-5827	320	54	to	to	ADP
ejpam-5827	320	55	specific	specific	ADJ
ejpam-5827	320	56	contexts	context	NOUN
ejpam-5827	320	57	or	or	CCONJ
ejpam-5827	320	58	applications	application	NOUN
ejpam-5827	320	59	.	.	PUNCT
ejpam-5827	321	1	these	these	DET
ejpam-5827	321	2	properties	property	NOUN
ejpam-5827	321	3	help	help	VERB
ejpam-5827	321	4	describe	describe	VERB
ejpam-5827	321	5	how	how	SCONJ
ejpam-5827	321	6	the	the	DET
ejpam-5827	321	7	lower	low	ADJ
ejpam-5827	321	8	and	and	CCONJ
ejpam-5827	321	9	upper	upper	ADJ
ejpam-5827	321	10	approximations	approximation	NOUN
ejpam-5827	321	11	interact	interact	VERB
ejpam-5827	321	12	within	within	ADP
ejpam-5827	321	13	the	the	DET
ejpam-5827	321	14	κ	κ	NOUN
ejpam-5827	321	15	-	-	PUNCT
ejpam-5827	321	16	supra	supra	ADJ
ejpam-5827	321	17	topology	topology	NOUN
ejpam-5827	321	18	,	,	PUNCT
ejpam-5827	321	19	providing	provide	VERB
ejpam-5827	321	20	a	a	DET
ejpam-5827	321	21	framework	framework	NOUN
ejpam-5827	321	22	for	for	ADP
ejpam-5827	321	23	dealing	deal	VERB
ejpam-5827	321	24	with	with	ADP
ejpam-5827	321	25	uncertainty	uncertainty	NOUN
ejpam-5827	321	26	and	and	CCONJ
ejpam-5827	321	27	approximate	approximate	ADJ
ejpam-5827	321	28	reasoning	reasoning	NOUN
ejpam-5827	321	29	.	.	PUNCT
ejpam-5827	322	1	in	in	ADP
ejpam-5827	322	2	the	the	DET
ejpam-5827	322	3	next	next	ADJ
ejpam-5827	322	4	,	,	PUNCT
ejpam-5827	322	5	different	different	ADJ
ejpam-5827	322	6	kinds	kind	NOUN
ejpam-5827	322	7	of	of	ADP
ejpam-5827	322	8	rough	rough	ADJ
ejpam-5827	322	9	approximations	approximation	NOUN
ejpam-5827	322	10	utilizing	utilize	VERB
ejpam-5827	322	11	the	the	DET
ejpam-5827	322	12	topologies	topology	NOUN
ejpam-5827	322	13	generated	generate	VERB
ejpam-5827	322	14	from	from	ADP
ejpam-5827	322	15	κ	κ	ADV
ejpam-5827	322	16	-	-	ADJ
ejpam-5827	322	17	ns	ns	ADJ
ejpam-5827	322	18	and	and	CCONJ
ejpam-5827	322	19	primal	primal	ADJ
ejpam-5827	322	20	p	p	NOUN
ejpam-5827	322	21	will	will	AUX
ejpam-5827	322	22	be	be	AUX
ejpam-5827	322	23	established	establish	VERB
ejpam-5827	322	24	.	.	PUNCT
ejpam-5827	323	1	in	in	ADP
ejpam-5827	323	2	addition	addition	NOUN
ejpam-5827	323	3	,	,	PUNCT
ejpam-5827	323	4	some	some	PRON
ejpam-5827	323	5	of	of	ADP
ejpam-5827	323	6	their	their	PRON
ejpam-5827	323	7	properties	property	NOUN
ejpam-5827	323	8	will	will	AUX
ejpam-5827	323	9	be	be	AUX
ejpam-5827	323	10	studied	study	VERB
ejpam-5827	323	11	.	.	PUNCT
ejpam-5827	324	1	definition	definition	NOUN
ejpam-5827	324	2	14	14	NUM
ejpam-5827	324	3	.	.	PUNCT
ejpam-5827	325	1	let	let	VERB
ejpam-5827	325	2	τpκ	τpκ	NOUN
ejpam-5827	325	3	be	be	AUX
ejpam-5827	325	4	a	a	DET
ejpam-5827	325	5	κ	κ	NOUN
ejpam-5827	325	6	-	-	PUNCT
ejpam-5827	325	7	supra	supra	ADJ
ejpam-5827	325	8	topology	topology	NOUN
ejpam-5827	325	9	generated	generate	VERB
ejpam-5827	325	10	by	by	ADP
ejpam-5827	325	11	κ	κ	ADV
ejpam-5827	325	12	-	-	PUNCT
ejpam-5827	325	13	ns	ns	ADJ
ejpam-5827	325	14	and	and	CCONJ
ejpam-5827	325	15	primal	primal	ADJ
ejpam-5827	325	16	p.	p.	NOUN
ejpam-5827	325	17	then	then	ADV
ejpam-5827	325	18	,	,	PUNCT
ejpam-5827	325	19	the	the	DET
ejpam-5827	325	20	pκ	pκ	NOUN
ejpam-5827	325	21	-	-	PUNCT
ejpam-5827	325	22	lower	low	ADJ
ejpam-5827	325	23	,	,	PUNCT
ejpam-5827	325	24	pκ	pκ	NOUN
ejpam-5827	325	25	-	-	PUNCT
ejpam-5827	325	26	upper	upper	ADJ
ejpam-5827	325	27	approximations	approximation	NOUN
ejpam-5827	325	28	,	,	PUNCT
ejpam-5827	325	29	pκ	pκ	NOUN
ejpam-5827	325	30	-	-	PUNCT
ejpam-5827	325	31	boundary	boundary	NOUN
ejpam-5827	325	32	and	and	CCONJ
ejpam-5827	325	33	pκ	pκ	NOUN
ejpam-5827	325	34	-	-	PUNCT
ejpam-5827	325	35	accuracy	accuracy	NOUN
ejpam-5827	325	36	of	of	ADP
ejpam-5827	325	37	a	a	DET
ejpam-5827	325	38	subset	subset	NOUN
ejpam-5827	325	39	h	h	NOUN
ejpam-5827	325	40	⊆	⊆	NUM
ejpam-5827	325	41	v	v	NOUN
ejpam-5827	325	42	are	be	AUX
ejpam-5827	325	43	assigned	assign	VERB
ejpam-5827	325	44	respectively	respectively	ADV
ejpam-5827	325	45	for	for	ADP
ejpam-5827	325	46	each	each	DET
ejpam-5827	325	47	κ	κ	NOUN
ejpam-5827	325	48	as	as	ADP
ejpam-5827	325	49	:	:	PUNCT
ejpam-5827	325	50	(	(	PUNCT
ejpam-5827	325	51	i	i	NOUN
ejpam-5827	325	52	)	)	PUNCT
ejpam-5827	325	53	τpκ	τpκ	NOUN
ejpam-5827	325	54	l(h	l(h	PROPN
ejpam-5827	325	55	)	)	PUNCT
ejpam-5827	325	56	=	=	PUNCT
ejpam-5827	325	57	τpκ	τpκ	NOUN
ejpam-5827	325	58	int(h	int(h	NOUN
ejpam-5827	325	59	)	)	PUNCT
ejpam-5827	325	60	.	.	PUNCT
ejpam-5827	326	1	(	(	PUNCT
ejpam-5827	326	2	ii	ii	NOUN
ejpam-5827	326	3	)	)	PUNCT
ejpam-5827	326	4	τpκ	τpκ	NOUN
ejpam-5827	326	5	u(h	u(h	PROPN
ejpam-5827	326	6	)	)	PUNCT
ejpam-5827	326	7	=	=	SYM
ejpam-5827	326	8	τpκ	τpκ	NOUN
ejpam-5827	326	9	cl(h	cl(h	NOUN
ejpam-5827	326	10	)	)	PUNCT
ejpam-5827	326	11	.	.	PUNCT
ejpam-5827	327	1	(	(	PUNCT
ejpam-5827	327	2	iii	iii	X
ejpam-5827	327	3	)	)	PUNCT
ejpam-5827	327	4	τpκ	τpκ	NOUN
ejpam-5827	327	5	b(h	b(h	PROPN
ejpam-5827	327	6	)	)	PUNCT
ejpam-5827	327	7	=	=	SYM
ejpam-5827	327	8	τpκ	τpκ	NOUN
ejpam-5827	327	9	u(h	u(h	PROPN
ejpam-5827	327	10	)	)	PUNCT
ejpam-5827	327	11	−	−	ADP
ejpam-5827	327	12	τpκ	τpκ	NOUN
ejpam-5827	327	13	l(h	l(h	PROPN
ejpam-5827	327	14	)	)	PUNCT
ejpam-5827	327	15	.	.	PUNCT
ejpam-5827	328	1	(	(	PUNCT
ejpam-5827	328	2	iv	iv	X
ejpam-5827	328	3	)	)	PUNCT
ejpam-5827	328	4	τpκ	τpκ	NOUN
ejpam-5827	328	5	σ(h	σ(h	NOUN
ejpam-5827	328	6	)	)	PUNCT
ejpam-5827	328	7	=	=	PUNCT
ejpam-5827	328	8	|τpκ	|τpκ	NOUN
ejpam-5827	328	9	l(h)|	l(h)|	ADP
ejpam-5827	328	10	|τpκ	|τpκ	NOUN
ejpam-5827	328	11	u(h)|	u(h)|	X
ejpam-5827	328	12	,	,	PUNCT
ejpam-5827	328	13	where	where	SCONJ
ejpam-5827	328	14	|τpκ	|τpκ	NOUN
ejpam-5827	328	15	u(h)|̸=0	u(h)|̸=0	ADJ
ejpam-5827	328	16	.	.	PUNCT
ejpam-5827	329	1	it	it	PRON
ejpam-5827	329	2	is	be	AUX
ejpam-5827	329	3	evident	evident	ADJ
ejpam-5827	329	4	that	that	SCONJ
ejpam-5827	329	5	0	0	NUM
ejpam-5827	329	6	≤	≤	NUM
ejpam-5827	329	7	τpκ	τpκ	NOUN
ejpam-5827	329	8	σ(h	σ(h	NOUN
ejpam-5827	329	9	)	)	PUNCT
ejpam-5827	329	10	≤	≤	NOUN
ejpam-5827	329	11	1	1	NUM
ejpam-5827	329	12	.	.	PUNCT
ejpam-5827	330	1	if	if	SCONJ
ejpam-5827	330	2	τpκ	τpκ	PRON
ejpam-5827	330	3	σ	σ	NOUN
ejpam-5827	330	4	is	be	AUX
ejpam-5827	330	5	close	close	ADJ
ejpam-5827	330	6	to	to	ADP
ejpam-5827	330	7	1	1	NUM
ejpam-5827	330	8	,	,	PUNCT
ejpam-5827	330	9	it	it	PRON
ejpam-5827	330	10	implies	imply	VERB
ejpam-5827	330	11	that	that	SCONJ
ejpam-5827	330	12	the	the	DET
ejpam-5827	330	13	lower	low	ADJ
ejpam-5827	330	14	and	and	CCONJ
ejpam-5827	330	15	upper	upper	ADJ
ejpam-5827	330	16	bounds	bound	NOUN
ejpam-5827	330	17	are	be	AUX
ejpam-5827	330	18	of	of	ADP
ejpam-5827	330	19	similar	similar	ADJ
ejpam-5827	330	20	magnitude	magnitude	NOUN
ejpam-5827	330	21	,	,	PUNCT
ejpam-5827	330	22	suggesting	suggest	VERB
ejpam-5827	330	23	that	that	SCONJ
ejpam-5827	330	24	the	the	DET
ejpam-5827	330	25	estimates	estimate	NOUN
ejpam-5827	330	26	are	be	AUX
ejpam-5827	330	27	close	close	ADJ
ejpam-5827	330	28	,	,	PUNCT
ejpam-5827	330	29	leading	lead	VERB
ejpam-5827	330	30	to	to	ADP
ejpam-5827	330	31	higher	high	ADJ
ejpam-5827	330	32	accuracy	accuracy	NOUN
ejpam-5827	330	33	.	.	PUNCT
ejpam-5827	331	1	if	if	SCONJ
ejpam-5827	331	2	τpκ	τpκ	PRON
ejpam-5827	331	3	σ(h	σ(h	NOUN
ejpam-5827	331	4	)	)	PUNCT
ejpam-5827	331	5	=	=	SYM
ejpam-5827	331	6	1	1	NUM
ejpam-5827	331	7	,	,	PUNCT
ejpam-5827	331	8	then	then	ADV
ejpam-5827	331	9	h	h	NOUN
ejpam-5827	331	10	is	be	AUX
ejpam-5827	331	11	referred	refer	VERB
ejpam-5827	331	12	to	to	ADP
ejpam-5827	331	13	as	as	ADP
ejpam-5827	331	14	an	an	DET
ejpam-5827	331	15	τpκ	τpκ	NOUN
ejpam-5827	331	16	σ	σ	NOUN
ejpam-5827	331	17	-	-	PUNCT
ejpam-5827	331	18	exact	exact	ADJ
ejpam-5827	331	19	set	set	NOUN
ejpam-5827	331	20	.	.	PUNCT
ejpam-5827	332	1	elsewise	elsewise	PROPN
ejpam-5827	332	2	,	,	PUNCT
ejpam-5827	332	3	h	h	PROPN
ejpam-5827	332	4	is	be	AUX
ejpam-5827	332	5	termed	term	VERB
ejpam-5827	332	6	an	an	DET
ejpam-5827	332	7	τpκ	τpκ	NOUN
ejpam-5827	332	8	σ	σ	NOUN
ejpam-5827	332	9	-	-	PUNCT
ejpam-5827	332	10	rough	rough	ADJ
ejpam-5827	332	11	set	set	NOUN
ejpam-5827	332	12	.	.	PUNCT
ejpam-5827	333	1	definition	definition	NOUN
ejpam-5827	333	2	15	15	NUM
ejpam-5827	333	3	.	.	PUNCT
ejpam-5827	334	1	a	a	DET
ejpam-5827	334	2	subset	subset	ADJ
ejpam-5827	334	3	h	h	NOUN
ejpam-5827	334	4	of	of	ADP
ejpam-5827	334	5	κ	κ	NOUN
ejpam-5827	334	6	-	-	ADJ
ejpam-5827	334	7	supra	supra	ADJ
ejpam-5827	334	8	topological	topological	ADJ
ejpam-5827	334	9	space	space	NOUN
ejpam-5827	334	10	(	(	PUNCT
ejpam-5827	334	11	v	v	NOUN
ejpam-5827	334	12	,	,	PUNCT
ejpam-5827	334	13	τpκ	τpκ	NOUN
ejpam-5827	334	14	)	)	PUNCT
ejpam-5827	334	15	is	be	AUX
ejpam-5827	334	16	called	call	VERB
ejpam-5827	334	17	:	:	PUNCT
ejpam-5827	334	18	(	(	PUNCT
ejpam-5827	334	19	i	i	NOUN
ejpam-5827	334	20	)	)	PUNCT
ejpam-5827	334	21	totally	totally	ADV
ejpam-5827	334	22	pκ	pκ	VERB
ejpam-5827	334	23	-	-	PUNCT
ejpam-5827	334	24	definable	definable	ADJ
ejpam-5827	334	25	,	,	PUNCT
ejpam-5827	334	26	if	if	SCONJ
ejpam-5827	334	27	τpκ	τpκ	NOUN
ejpam-5827	334	28	l(h	l(h	NOUN
ejpam-5827	334	29	)	)	PUNCT
ejpam-5827	334	30	=	=	SYM
ejpam-5827	334	31	h	h	NOUN
ejpam-5827	334	32	=	=	NOUN
ejpam-5827	334	33	τpκ	τpκ	NOUN
ejpam-5827	334	34	u(h	u(h	PROPN
ejpam-5827	334	35	)	)	PUNCT
ejpam-5827	334	36	.	.	PUNCT
ejpam-5827	335	1	this	this	PRON
ejpam-5827	335	2	means	mean	VERB
ejpam-5827	335	3	that	that	SCONJ
ejpam-5827	335	4	every	every	DET
ejpam-5827	335	5	element	element	NOUN
ejpam-5827	335	6	of	of	ADP
ejpam-5827	335	7	h	h	NOUN
ejpam-5827	335	8	can	can	AUX
ejpam-5827	335	9	be	be	AUX
ejpam-5827	335	10	precisely	precisely	ADV
ejpam-5827	335	11	defined	define	VERB
ejpam-5827	335	12	and	and	CCONJ
ejpam-5827	335	13	no	no	DET
ejpam-5827	335	14	ambiguity	ambiguity	NOUN
ejpam-5827	335	15	exists	exist	VERB
ejpam-5827	335	16	about	about	ADP
ejpam-5827	335	17	whether	whether	SCONJ
ejpam-5827	335	18	an	an	DET
ejpam-5827	335	19	element	element	NOUN
ejpam-5827	335	20	belongs	belong	VERB
ejpam-5827	335	21	to	to	ADP
ejpam-5827	335	22	the	the	DET
ejpam-5827	335	23	set	set	NOUN
ejpam-5827	335	24	h.	h.	PROPN
ejpam-5827	335	25	(	(	PUNCT
ejpam-5827	335	26	ii	ii	NOUN
ejpam-5827	335	27	)	)	PUNCT
ejpam-5827	335	28	internally	internally	ADV
ejpam-5827	335	29	pκ	pκ	VERB
ejpam-5827	335	30	-	-	PUNCT
ejpam-5827	335	31	definable	definable	ADJ
ejpam-5827	335	32	,	,	PUNCT
ejpam-5827	335	33	if	if	SCONJ
ejpam-5827	335	34	τpκ	τpκ	NOUN
ejpam-5827	335	35	l(h	l(h	NOUN
ejpam-5827	335	36	)	)	PUNCT
ejpam-5827	335	37	=	=	SYM
ejpam-5827	335	38	h	h	NOUN
ejpam-5827	335	39	and	and	CCONJ
ejpam-5827	335	40	τpκ	τpκ	NOUN
ejpam-5827	335	41	u(h	u(h	PROPN
ejpam-5827	335	42	)	)	PUNCT
ejpam-5827	335	43	̸=h	̸=h	NUM
ejpam-5827	335	44	.	.	PUNCT
ejpam-5827	336	1	this	this	PRON
ejpam-5827	336	2	means	mean	VERB
ejpam-5827	336	3	that	that	SCONJ
ejpam-5827	336	4	the	the	DET
ejpam-5827	336	5	set	set	NOUN
ejpam-5827	336	6	is	be	AUX
ejpam-5827	336	7	fully	fully	ADV
ejpam-5827	336	8	described	describe	VERB
ejpam-5827	336	9	by	by	ADP
ejpam-5827	336	10	its	its	PRON
ejpam-5827	336	11	”	"	PUNCT
ejpam-5827	336	12	core	core	NOUN
ejpam-5827	336	13	”	"	PUNCT
ejpam-5827	336	14	elements	element	NOUN
ejpam-5827	336	15	.	.	PUNCT
ejpam-5827	337	1	(	(	PUNCT
ejpam-5827	337	2	iii	iii	X
ejpam-5827	337	3	)	)	PUNCT
ejpam-5827	337	4	externally	externally	ADV
ejpam-5827	337	5	pκ	pκ	VERB
ejpam-5827	337	6	-	-	PUNCT
ejpam-5827	337	7	definable	definable	ADJ
ejpam-5827	337	8	,	,	PUNCT
ejpam-5827	337	9	if	if	SCONJ
ejpam-5827	337	10	τpκ	τpκ	PRON
ejpam-5827	337	11	l(h	l(h	PROPN
ejpam-5827	337	12	)	)	PUNCT
ejpam-5827	337	13	̸=h	̸=h	NOUN
ejpam-5827	337	14	and	and	CCONJ
ejpam-5827	337	15	τpκ	τpκ	NOUN
ejpam-5827	337	16	u(h	u(h	ADJ
ejpam-5827	337	17	)	)	PUNCT
ejpam-5827	338	1	=	=	VERB
ejpam-5827	339	1	h.	h.	NOUN
ejpam-5827	339	2	this	this	PRON
ejpam-5827	339	3	means	mean	VERB
ejpam-5827	339	4	that	that	SCONJ
ejpam-5827	339	5	there	there	PRON
ejpam-5827	339	6	is	be	VERB
ejpam-5827	339	7	some	some	DET
ejpam-5827	339	8	uncertainty	uncertainty	NOUN
ejpam-5827	339	9	about	about	ADP
ejpam-5827	339	10	which	which	DET
ejpam-5827	339	11	elements	element	NOUN
ejpam-5827	339	12	are	be	AUX
ejpam-5827	339	13	strictly	strictly	ADV
ejpam-5827	339	14	part	part	NOUN
ejpam-5827	339	15	of	of	ADP
ejpam-5827	339	16	the	the	DET
ejpam-5827	339	17	set	set	NOUN
ejpam-5827	339	18	,	,	PUNCT
ejpam-5827	339	19	but	but	CCONJ
ejpam-5827	339	20	it	it	PRON
ejpam-5827	339	21	is	be	AUX
ejpam-5827	339	22	certain	certain	ADJ
ejpam-5827	339	23	that	that	SCONJ
ejpam-5827	339	24	h	h	NOUN
ejpam-5827	339	25	includes	include	VERB
ejpam-5827	339	26	all	all	DET
ejpam-5827	339	27	elements	element	NOUN
ejpam-5827	339	28	from	from	ADP
ejpam-5827	339	29	the	the	DET
ejpam-5827	339	30	upper	upper	ADJ
ejpam-5827	339	31	approximation	approximation	NOUN
ejpam-5827	339	32	(	(	PUNCT
ejpam-5827	339	33	iv	iv	X
ejpam-5827	339	34	)	)	PUNCT
ejpam-5827	339	35	pκ	pκ	NOUN
ejpam-5827	339	36	-	-	PUNCT
ejpam-5827	339	37	rough	rough	ADJ
ejpam-5827	339	38	set	set	NOUN
ejpam-5827	339	39	,	,	PUNCT
ejpam-5827	339	40	if	if	SCONJ
ejpam-5827	339	41	τpκ	τpκ	NOUN
ejpam-5827	339	42	l(h	l(h	NOUN
ejpam-5827	339	43	)	)	PUNCT
ejpam-5827	339	44	̸=h	̸=h	NOUN
ejpam-5827	339	45	and	and	CCONJ
ejpam-5827	339	46	τpκ	τpκ	NOUN
ejpam-5827	339	47	u(h	u(h	PROPN
ejpam-5827	339	48	)	)	PUNCT
ejpam-5827	339	49	̸=h	̸=h	NUM
ejpam-5827	339	50	.	.	PUNCT
ejpam-5827	340	1	this	this	PRON
ejpam-5827	340	2	means	mean	VERB
ejpam-5827	340	3	that	that	SCONJ
ejpam-5827	340	4	there	there	PRON
ejpam-5827	340	5	are	be	VERB
ejpam-5827	340	6	elements	element	NOUN
ejpam-5827	340	7	that	that	PRON
ejpam-5827	340	8	are	be	AUX
ejpam-5827	340	9	not	not	PART
ejpam-5827	340	10	fully	fully	ADV
ejpam-5827	340	11	classified	classify	VERB
ejpam-5827	340	12	as	as	ADP
ejpam-5827	340	13	either	either	CCONJ
ejpam-5827	340	14	definitely	definitely	ADV
ejpam-5827	340	15	in	in	ADP
ejpam-5827	340	16	or	or	CCONJ
ejpam-5827	340	17	definitely	definitely	ADV
ejpam-5827	340	18	out	out	ADP
ejpam-5827	340	19	of	of	ADP
ejpam-5827	340	20	the	the	DET
ejpam-5827	340	21	set	set	NOUN
ejpam-5827	340	22	.	.	PUNCT
ejpam-5827	341	1	remark	remark	PROPN
ejpam-5827	341	2	10	10	NUM
ejpam-5827	341	3	.	.	PUNCT
ejpam-5827	342	1	according	accord	VERB
ejpam-5827	342	2	to	to	ADP
ejpam-5827	342	3	example	example	NOUN
ejpam-5827	342	4	5	5	NUM
ejpam-5827	342	5	,	,	PUNCT
ejpam-5827	342	6	then	then	ADV
ejpam-5827	342	7	(	(	PUNCT
ejpam-5827	342	8	i	i	NOUN
ejpam-5827	342	9	)	)	PUNCT
ejpam-5827	342	10	totally	totally	ADV
ejpam-5827	342	11	pr	pr	ADJ
ejpam-5827	342	12	-	-	PUNCT
ejpam-5827	342	13	definable	definable	ADJ
ejpam-5827	342	14	sets	set	NOUN
ejpam-5827	342	15	are	be	AUX
ejpam-5827	342	16	{	{	PUNCT
ejpam-5827	342	17	a	a	X
ejpam-5827	342	18	}	}	PUNCT
ejpam-5827	342	19	,	,	PUNCT
ejpam-5827	342	20	{	{	PUNCT
ejpam-5827	342	21	b	b	NOUN
ejpam-5827	342	22	}	}	PUNCT
ejpam-5827	342	23	,	,	PUNCT
ejpam-5827	342	24	{	{	PUNCT
ejpam-5827	342	25	a	a	DET
ejpam-5827	342	26	,	,	PUNCT
ejpam-5827	342	27	b	b	NOUN
ejpam-5827	342	28	}	}	PUNCT
ejpam-5827	342	29	,	,	PUNCT
ejpam-5827	342	30	{	{	PUNCT
ejpam-5827	342	31	c	c	X
ejpam-5827	342	32	,	,	PUNCT
ejpam-5827	342	33	d	d	NOUN
ejpam-5827	342	34	}	}	PUNCT
ejpam-5827	342	35	,	,	PUNCT
ejpam-5827	342	36	{	{	PUNCT
ejpam-5827	342	37	a	a	PRON
ejpam-5827	342	38	,	,	PUNCT
ejpam-5827	342	39	c	c	NOUN
ejpam-5827	342	40	,	,	PUNCT
ejpam-5827	342	41	d	d	NOUN
ejpam-5827	342	42	}	}	PUNCT
ejpam-5827	342	43	,	,	PUNCT
ejpam-5827	342	44	{	{	PUNCT
ejpam-5827	342	45	b	b	X
ejpam-5827	342	46	,	,	PUNCT
ejpam-5827	342	47	c	c	NOUN
ejpam-5827	342	48	,	,	PUNCT
ejpam-5827	342	49	d	d	NOUN
ejpam-5827	342	50	}	}	PUNCT
ejpam-5827	342	51	,	,	PUNCT
ejpam-5827	342	52	∅	∅	NOUN
ejpam-5827	342	53	,	,	PUNCT
ejpam-5827	342	54	and	and	CCONJ
ejpam-5827	342	55	v.	v.	PROPN
ejpam-5827	342	56	r.	r.	PROPN
ejpam-5827	342	57	a.	a.	PROPN
ejpam-5827	342	58	hosny	hosny	PROPN
ejpam-5827	342	59	,	,	PUNCT
ejpam-5827	342	60	m.	m.	PROPN
ejpam-5827	342	61	k.	k.	PROPN
ejpam-5827	342	62	el	el	PROPN
ejpam-5827	342	63	-	-	PROPN
ejpam-5827	342	64	bably	bably	ADV
ejpam-5827	342	65	,	,	PUNCT
ejpam-5827	342	66	m.	m.	NOUN
ejpam-5827	342	67	a.	a.	PROPN
ejpam-5827	342	68	el	el	PROPN
ejpam-5827	342	69	-	-	PROPN
ejpam-5827	342	70	gayar	gayar	PROPN
ejpam-5827	342	71	/	/	SYM
ejpam-5827	342	72	eur	eur	PROPN
ejpam-5827	342	73	.	.	PUNCT
ejpam-5827	343	1	j.	j.	PROPN
ejpam-5827	343	2	pure	pure	PROPN
ejpam-5827	343	3	appl	appl	PROPN
ejpam-5827	343	4	.	.	PROPN
ejpam-5827	343	5	math	math	PROPN
ejpam-5827	343	6	,	,	PUNCT
ejpam-5827	343	7	18	18	NUM
ejpam-5827	343	8	(	(	PUNCT
ejpam-5827	343	9	1	1	NUM
ejpam-5827	343	10	)	)	PUNCT
ejpam-5827	343	11	(	(	PUNCT
ejpam-5827	343	12	2025	2025	NUM
ejpam-5827	343	13	)	)	PUNCT
ejpam-5827	343	14	,	,	PUNCT
ejpam-5827	343	15	5827	5827	NUM
ejpam-5827	343	16	14	14	NUM
ejpam-5827	343	17	of	of	ADP
ejpam-5827	343	18	29	29	NUM
ejpam-5827	343	19	(	(	PUNCT
ejpam-5827	343	20	ii	ii	NOUN
ejpam-5827	343	21	)	)	PUNCT
ejpam-5827	343	22	internally	internally	ADV
ejpam-5827	343	23	pr	pr	ADJ
ejpam-5827	343	24	-	-	PUNCT
ejpam-5827	343	25	definable	definable	ADJ
ejpam-5827	343	26	sets	set	NOUN
ejpam-5827	343	27	are	be	AUX
ejpam-5827	343	28	{	{	PUNCT
ejpam-5827	343	29	d	d	NOUN
ejpam-5827	343	30	}	}	PUNCT
ejpam-5827	343	31	,	,	PUNCT
ejpam-5827	343	32	{	{	PUNCT
ejpam-5827	343	33	a	a	DET
ejpam-5827	343	34	,	,	PUNCT
ejpam-5827	343	35	d	d	NOUN
ejpam-5827	343	36	}	}	PUNCT
ejpam-5827	343	37	,	,	PUNCT
ejpam-5827	343	38	{	{	PUNCT
ejpam-5827	343	39	b	b	X
ejpam-5827	343	40	,	,	PUNCT
ejpam-5827	343	41	d	d	NOUN
ejpam-5827	343	42	}	}	PUNCT
ejpam-5827	343	43	,	,	PUNCT
ejpam-5827	343	44	and	and	CCONJ
ejpam-5827	343	45	{	{	PUNCT
ejpam-5827	343	46	a	a	PRON
ejpam-5827	343	47	,	,	PUNCT
ejpam-5827	343	48	b	b	NOUN
ejpam-5827	343	49	,	,	PUNCT
ejpam-5827	343	50	d	d	NOUN
ejpam-5827	343	51	}	}	PUNCT
ejpam-5827	343	52	.	.	PUNCT
ejpam-5827	344	1	(	(	PUNCT
ejpam-5827	344	2	iii	iii	X
ejpam-5827	344	3	)	)	PUNCT
ejpam-5827	344	4	externally	externally	ADV
ejpam-5827	344	5	pr	pr	ADJ
ejpam-5827	344	6	-	-	PUNCT
ejpam-5827	344	7	definable	definable	ADJ
ejpam-5827	344	8	sets	set	NOUN
ejpam-5827	344	9	are	be	AUX
ejpam-5827	344	10	{	{	PUNCT
ejpam-5827	344	11	c	c	NOUN
ejpam-5827	344	12	}	}	PUNCT
ejpam-5827	344	13	,	,	PUNCT
ejpam-5827	344	14	{	{	PUNCT
ejpam-5827	344	15	a	a	X
ejpam-5827	344	16	,	,	PUNCT
ejpam-5827	344	17	c	c	NOUN
ejpam-5827	344	18	}	}	PUNCT
ejpam-5827	344	19	,	,	PUNCT
ejpam-5827	344	20	{	{	PUNCT
ejpam-5827	344	21	b	b	X
ejpam-5827	344	22	,	,	PUNCT
ejpam-5827	344	23	c	c	NOUN
ejpam-5827	344	24	}	}	PUNCT
ejpam-5827	344	25	,	,	PUNCT
ejpam-5827	344	26	and	and	CCONJ
ejpam-5827	344	27	{	{	PUNCT
ejpam-5827	344	28	a	a	PRON
ejpam-5827	344	29	,	,	PUNCT
ejpam-5827	344	30	b	b	NOUN
ejpam-5827	344	31	,	,	PUNCT
ejpam-5827	344	32	c	c	NOUN
ejpam-5827	344	33	}	}	PUNCT
ejpam-5827	344	34	.	.	PUNCT
ejpam-5827	345	1	(	(	PUNCT
ejpam-5827	345	2	iv	iv	X
ejpam-5827	345	3	)	)	PUNCT
ejpam-5827	345	4	there	there	PRON
ejpam-5827	345	5	is	be	VERB
ejpam-5827	345	6	no	no	DET
ejpam-5827	345	7	any	any	DET
ejpam-5827	345	8	pr	pr	NOUN
ejpam-5827	345	9	-	-	PUNCT
ejpam-5827	345	10	rough	rough	ADJ
ejpam-5827	345	11	set	set	NOUN
ejpam-5827	345	12	.	.	PUNCT
ejpam-5827	346	1	proposition	proposition	NOUN
ejpam-5827	346	2	4	4	NUM
ejpam-5827	346	3	.	.	PUNCT
ejpam-5827	347	1	let	let	VERB
ejpam-5827	347	2	h	h	PRON
ejpam-5827	347	3	be	be	AUX
ejpam-5827	347	4	a	a	DET
ejpam-5827	347	5	subset	subset	NOUN
ejpam-5827	347	6	of	of	ADP
ejpam-5827	347	7	κ	κ	NOUN
ejpam-5827	347	8	-	-	PUNCT
ejpam-5827	347	9	supra	supra	ADJ
ejpam-5827	347	10	topological	topological	ADJ
ejpam-5827	347	11	space	space	NOUN
ejpam-5827	347	12	(	(	PUNCT
ejpam-5827	347	13	v	v	NOUN
ejpam-5827	347	14	,	,	PUNCT
ejpam-5827	347	15	τpκ	τpκ	NOUN
ejpam-5827	347	16	)	)	PUNCT
ejpam-5827	347	17	.	.	PUNCT
ejpam-5827	348	1	for	for	ADP
ejpam-5827	348	2	each	each	DET
ejpam-5827	348	3	κ	κ	NOUN
ejpam-5827	348	4	,	,	PUNCT
ejpam-5827	348	5	the	the	DET
ejpam-5827	348	6	following	follow	VERB
ejpam-5827	348	7	statements	statement	NOUN
ejpam-5827	348	8	hold	hold	VERB
ejpam-5827	348	9	:	:	PUNCT
ejpam-5827	348	10	(	(	PUNCT
ejpam-5827	348	11	i	i	NOUN
ejpam-5827	348	12	)	)	PUNCT
ejpam-5827	348	13	τκl(h	τκl(h	PROPN
ejpam-5827	348	14	)	)	PUNCT
ejpam-5827	348	15	⊆	⊆	NUM
ejpam-5827	348	16	τpκ	τpκ	NOUN
ejpam-5827	348	17	l(h	l(h	PROPN
ejpam-5827	348	18	)	)	PUNCT
ejpam-5827	348	19	.	.	PUNCT
ejpam-5827	349	1	(	(	PUNCT
ejpam-5827	349	2	ii	ii	NOUN
ejpam-5827	349	3	)	)	PUNCT
ejpam-5827	349	4	τpκ	τpκ	NOUN
ejpam-5827	349	5	u(h	u(h	PROPN
ejpam-5827	349	6	)	)	PUNCT
ejpam-5827	349	7	⊆	⊆	NUM
ejpam-5827	349	8	τκu(h	τκu(h	NUM
ejpam-5827	349	9	)	)	PUNCT
ejpam-5827	349	10	.	.	PUNCT
ejpam-5827	350	1	(	(	PUNCT
ejpam-5827	350	2	iii	iii	X
ejpam-5827	350	3	)	)	PUNCT
ejpam-5827	350	4	τκσ(h	τκσ(h	PROPN
ejpam-5827	350	5	)	)	PUNCT
ejpam-5827	350	6	≤	≤	NUM
ejpam-5827	350	7	τpκ	τpκ	PRON
ejpam-5827	350	8	σ(h	σ(h	NOUN
ejpam-5827	350	9	)	)	PUNCT
ejpam-5827	350	10	.	.	PUNCT
ejpam-5827	351	1	proof	proof	NOUN
ejpam-5827	351	2	.	.	PUNCT
ejpam-5827	352	1	in	in	ADP
ejpam-5827	352	2	view	view	NOUN
ejpam-5827	352	3	of	of	ADP
ejpam-5827	352	4	theorem	theorem	NOUN
ejpam-5827	352	5	4	4	NUM
ejpam-5827	352	6	,	,	PUNCT
ejpam-5827	352	7	the	the	DET
ejpam-5827	352	8	proof	proof	NOUN
ejpam-5827	352	9	is	be	AUX
ejpam-5827	352	10	clear	clear	ADJ
ejpam-5827	352	11	.	.	PUNCT
ejpam-5827	353	1	proposition	proposition	NOUN
ejpam-5827	353	2	5	5	NUM
ejpam-5827	353	3	.	.	PUNCT
ejpam-5827	354	1	let	let	VERB
ejpam-5827	354	2	h	h	PRON
ejpam-5827	354	3	be	be	AUX
ejpam-5827	354	4	a	a	DET
ejpam-5827	354	5	subset	subset	NOUN
ejpam-5827	354	6	of	of	ADP
ejpam-5827	354	7	κ	κ	NOUN
ejpam-5827	354	8	-	-	PUNCT
ejpam-5827	354	9	supra	supra	ADJ
ejpam-5827	354	10	topological	topological	ADJ
ejpam-5827	354	11	space	space	NOUN
ejpam-5827	354	12	(	(	PUNCT
ejpam-5827	354	13	v	v	NOUN
ejpam-5827	354	14	,	,	PUNCT
ejpam-5827	354	15	τpκ	τpκ	NOUN
ejpam-5827	354	16	)	)	PUNCT
ejpam-5827	354	17	.	.	PUNCT
ejpam-5827	355	1	for	for	ADP
ejpam-5827	355	2	each	each	DET
ejpam-5827	355	3	κ	κ	NOUN
ejpam-5827	355	4	,	,	PUNCT
ejpam-5827	355	5	the	the	DET
ejpam-5827	355	6	following	follow	VERB
ejpam-5827	355	7	statements	statement	NOUN
ejpam-5827	355	8	hold	hold	VERB
ejpam-5827	355	9	:	:	PUNCT
ejpam-5827	355	10	(	(	PUNCT
ejpam-5827	355	11	i	i	NOUN
ejpam-5827	355	12	)	)	PUNCT
ejpam-5827	355	13	if	if	SCONJ
ejpam-5827	355	14	h	h	NOUN
ejpam-5827	355	15	∈	∈	PROPN
ejpam-5827	355	16	τpκ	τpκ	NOUN
ejpam-5827	355	17	,	,	PUNCT
ejpam-5827	355	18	then	then	ADV
ejpam-5827	355	19	τpκ	τpκ	NOUN
ejpam-5827	355	20	l(h	l(h	PROPN
ejpam-5827	355	21	)	)	PUNCT
ejpam-5827	356	1	=	=	SYM
ejpam-5827	356	2	h.	h.	PROPN
ejpam-5827	356	3	(	(	PUNCT
ejpam-5827	356	4	ii	ii	PROPN
ejpam-5827	356	5	)	)	PUNCT
ejpam-5827	356	6	if	if	SCONJ
ejpam-5827	356	7	h	h	NOUN
ejpam-5827	356	8	∈	∈	PROPN
ejpam-5827	356	9	υp	υp	NOUN
ejpam-5827	356	10	κ	κ	PROPN
ejpam-5827	356	11	,	,	PUNCT
ejpam-5827	356	12	then	then	ADV
ejpam-5827	356	13	τpκ	τpκ	NOUN
ejpam-5827	356	14	u(h	u(h	PROPN
ejpam-5827	356	15	)	)	PUNCT
ejpam-5827	356	16	=	=	VERB
ejpam-5827	357	1	h.	h.	NOUN
ejpam-5827	357	2	the	the	DET
ejpam-5827	357	3	next	next	ADJ
ejpam-5827	357	4	proposition	proposition	NOUN
ejpam-5827	357	5	which	which	PRON
ejpam-5827	357	6	explains	explain	VERB
ejpam-5827	357	7	the	the	DET
ejpam-5827	357	8	main	main	ADJ
ejpam-5827	357	9	properties	property	NOUN
ejpam-5827	357	10	of	of	ADP
ejpam-5827	357	11	τpκ	τpκ	NOUN
ejpam-5827	357	12	l	l	NOUN
ejpam-5827	357	13	(	(	PUNCT
ejpam-5827	357	14	.	.	PUNCT
ejpam-5827	357	15	)	)	PUNCT
ejpam-5827	357	16	,	,	PUNCT
ejpam-5827	357	17	τpκ	τpκ	PRON
ejpam-5827	357	18	u	u	NOUN
ejpam-5827	357	19	(	(	PUNCT
ejpam-5827	357	20	.	.	PUNCT
ejpam-5827	357	21	)	)	PUNCT
ejpam-5827	358	1	operators	operator	NOUN
ejpam-5827	358	2	are	be	AUX
ejpam-5827	358	3	intelligible	intelligible	ADJ
ejpam-5827	358	4	,	,	PUNCT
ejpam-5827	358	5	by	by	ADP
ejpam-5827	358	6	observing	observe	VERB
ejpam-5827	358	7	that	that	DET
ejpam-5827	358	8	τpκ	τpκ	NOUN
ejpam-5827	358	9	int	int	NOUN
ejpam-5827	358	10	(	(	PUNCT
ejpam-5827	358	11	.	.	PUNCT
ejpam-5827	358	12	)	)	PUNCT
ejpam-5827	358	13	,	,	PUNCT
ejpam-5827	358	14	τpκ	τpκ	NOUN
ejpam-5827	358	15	cl(h	cl(h	NOUN
ejpam-5827	358	16	)	)	PUNCT
ejpam-5827	358	17	achieve	achieve	VERB
ejpam-5827	358	18	all	all	DET
ejpam-5827	358	19	characteristics	characteristic	NOUN
ejpam-5827	358	20	of	of	ADP
ejpam-5827	358	21	the	the	DET
ejpam-5827	358	22	interior	interior	ADJ
ejpam-5827	358	23	and	and	CCONJ
ejpam-5827	358	24	closure	closure	NOUN
ejpam-5827	358	25	operators	operator	NOUN
ejpam-5827	358	26	of	of	ADP
ejpam-5827	358	27	the	the	DET
ejpam-5827	358	28	topology	topology	NOUN
ejpam-5827	358	29	,	,	PUNCT
ejpam-5827	358	30	respectively	respectively	ADV
ejpam-5827	358	31	.	.	PUNCT
ejpam-5827	359	1	proposition	proposition	NOUN
ejpam-5827	359	2	6	6	NUM
ejpam-5827	359	3	.	.	PUNCT
ejpam-5827	360	1	let	let	VERB
ejpam-5827	360	2	h	h	NOUN
ejpam-5827	360	3	,	,	PUNCT
ejpam-5827	360	4	h́	h́	INTJ
ejpam-5827	360	5	be	be	AUX
ejpam-5827	360	6	subsets	subset	NOUN
ejpam-5827	360	7	of	of	ADP
ejpam-5827	360	8	κ	κ	NOUN
ejpam-5827	360	9	-	-	ADJ
ejpam-5827	360	10	supra	supra	ADJ
ejpam-5827	360	11	topological	topological	ADJ
ejpam-5827	360	12	space	space	NOUN
ejpam-5827	360	13	(	(	PUNCT
ejpam-5827	360	14	v	v	NOUN
ejpam-5827	360	15	,	,	PUNCT
ejpam-5827	360	16	τpκ	τpκ	NOUN
ejpam-5827	360	17	)	)	PUNCT
ejpam-5827	360	18	.	.	PUNCT
ejpam-5827	361	1	then	then	ADV
ejpam-5827	361	2	,	,	PUNCT
ejpam-5827	361	3	the	the	DET
ejpam-5827	361	4	following	follow	VERB
ejpam-5827	361	5	properties	property	NOUN
ejpam-5827	361	6	hold	hold	VERB
ejpam-5827	361	7	for	for	ADP
ejpam-5827	361	8	each	each	DET
ejpam-5827	361	9	κ	κ	NOUN
ejpam-5827	361	10	.	.	PUNCT
ejpam-5827	362	1	(	(	PUNCT
ejpam-5827	362	2	l1	l1	PROPN
ejpam-5827	362	3	)	)	PUNCT
ejpam-5827	362	4	τpκ	τpκ	NOUN
ejpam-5827	362	5	l(h	l(h	PROPN
ejpam-5827	362	6	)	)	PUNCT
ejpam-5827	362	7	⊆	⊆	NUM
ejpam-5827	362	8	h	h	NOUN
ejpam-5827	362	9	(	(	PUNCT
ejpam-5827	362	10	u1	u1	NOUN
ejpam-5827	362	11	)	)	PUNCT
ejpam-5827	362	12	h	h	NOUN
ejpam-5827	363	1	⊆	⊆	NUM
ejpam-5827	363	2	τpκ	τpκ	NOUN
ejpam-5827	363	3	u(h	u(h	PROPN
ejpam-5827	363	4	)	)	PUNCT
ejpam-5827	363	5	(	(	PUNCT
ejpam-5827	363	6	l2	l2	NOUN
ejpam-5827	363	7	)	)	PUNCT
ejpam-5827	363	8	τpκ	τpκ	NOUN
ejpam-5827	363	9	l(∅	l(∅	NOUN
ejpam-5827	363	10	)	)	PUNCT
ejpam-5827	363	11	=	=	NOUN
ejpam-5827	363	12	∅	∅	NOUN
ejpam-5827	363	13	(	(	PUNCT
ejpam-5827	363	14	u2	u2	NOUN
ejpam-5827	363	15	)	)	PUNCT
ejpam-5827	363	16	τpκ	τpκ	NOUN
ejpam-5827	363	17	u(∅	u(∅	NOUN
ejpam-5827	363	18	)	)	PUNCT
ejpam-5827	363	19	=	=	NOUN
ejpam-5827	363	20	∅	∅	NOUN
ejpam-5827	363	21	(	(	PUNCT
ejpam-5827	363	22	l3	l3	NOUN
ejpam-5827	363	23	)	)	PUNCT
ejpam-5827	363	24	τpκ	τpκ	NOUN
ejpam-5827	363	25	l(v	l(v	NOUN
ejpam-5827	363	26	)	)	PUNCT
ejpam-5827	363	27	=	=	SYM
ejpam-5827	363	28	v	v	X
ejpam-5827	363	29	(	(	PUNCT
ejpam-5827	363	30	u3	u3	NOUN
ejpam-5827	363	31	)	)	PUNCT
ejpam-5827	363	32	τpκ	τpκ	NOUN
ejpam-5827	363	33	u(v	u(v	PROPN
ejpam-5827	363	34	)	)	PUNCT
ejpam-5827	363	35	=	=	SYM
ejpam-5827	363	36	v	v	X
ejpam-5827	363	37	(	(	PUNCT
ejpam-5827	363	38	l4	l4	PROPN
ejpam-5827	363	39	)	)	PUNCT
ejpam-5827	363	40	if	if	SCONJ
ejpam-5827	363	41	h	h	PROPN
ejpam-5827	363	42	⊆	⊆	NUM
ejpam-5827	363	43	h́	h́	NOUN
ejpam-5827	363	44	,	,	PUNCT
ejpam-5827	363	45	then	then	ADV
ejpam-5827	363	46	τpκ	τpκ	NOUN
ejpam-5827	363	47	l(h	l(h	PROPN
ejpam-5827	363	48	)	)	PUNCT
ejpam-5827	363	49	⊆	⊆	NUM
ejpam-5827	363	50	τpκ	τpκ	PRON
ejpam-5827	363	51	l(h́	l(h́	NOUN
ejpam-5827	363	52	)	)	PUNCT
ejpam-5827	363	53	(	(	PUNCT
ejpam-5827	363	54	u4	u4	PROPN
ejpam-5827	363	55	)	)	PUNCT
ejpam-5827	363	56	if	if	SCONJ
ejpam-5827	363	57	h	h	PROPN
ejpam-5827	363	58	⊆	⊆	NUM
ejpam-5827	363	59	h́	h́	NOUN
ejpam-5827	363	60	,	,	PUNCT
ejpam-5827	363	61	then	then	ADV
ejpam-5827	363	62	τpκ	τpκ	NOUN
ejpam-5827	363	63	u(h	u(h	PROPN
ejpam-5827	363	64	)	)	PUNCT
ejpam-5827	363	65	⊆	⊆	NUM
ejpam-5827	363	66	τpκ	τpκ	PRON
ejpam-5827	363	67	u(h́	u(h́	NOUN
ejpam-5827	363	68	)	)	PUNCT
ejpam-5827	363	69	(	(	PUNCT
ejpam-5827	363	70	l5	l5	PROPN
ejpam-5827	363	71	)	)	PUNCT
ejpam-5827	363	72	τpκ	τpκ	NOUN
ejpam-5827	363	73	l(h	l(h	PROPN
ejpam-5827	363	74	∩	∩	ADJ
ejpam-5827	363	75	h́	h́	NOUN
ejpam-5827	363	76	)	)	PUNCT
ejpam-5827	363	77	=	=	SYM
ejpam-5827	363	78	τpκ	τpκ	NOUN
ejpam-5827	363	79	l(h	l(h	NOUN
ejpam-5827	363	80	)	)	PUNCT
ejpam-5827	363	81	∩	∩	NOUN
ejpam-5827	363	82	τpκ	τpκ	X
ejpam-5827	363	83	l(h́	l(h́	NOUN
ejpam-5827	363	84	)	)	PUNCT
ejpam-5827	363	85	(	(	PUNCT
ejpam-5827	363	86	u5	u5	PROPN
ejpam-5827	363	87	)	)	PUNCT
ejpam-5827	363	88	τpκ	τpκ	NOUN
ejpam-5827	363	89	u(h	u(h	PROPN
ejpam-5827	363	90	∩	∩	ADJ
ejpam-5827	363	91	h́	h́	NOUN
ejpam-5827	363	92	)	)	PUNCT
ejpam-5827	363	93	⊆	⊆	NUM
ejpam-5827	363	94	τpκ	τpκ	NOUN
ejpam-5827	363	95	u(h	u(h	ADJ
ejpam-5827	363	96	)	)	PUNCT
ejpam-5827	363	97	∩	∩	NOUN
ejpam-5827	363	98	τpκ	τpκ	NOUN
ejpam-5827	363	99	u(h́	u(h́	NOUN
ejpam-5827	363	100	)	)	PUNCT
ejpam-5827	363	101	(	(	PUNCT
ejpam-5827	363	102	l6	l6	PROPN
ejpam-5827	363	103	)	)	PUNCT
ejpam-5827	363	104	τpκ	τpκ	NOUN
ejpam-5827	363	105	l(h	l(h	PROPN
ejpam-5827	363	106	∪	∪	PROPN
ejpam-5827	363	107	h́	h́	PROPN
ejpam-5827	363	108	)	)	PUNCT
ejpam-5827	363	109	⊇	⊇	PROPN
ejpam-5827	363	110	τpκ	τpκ	NOUN
ejpam-5827	363	111	l(h	l(h	PROPN
ejpam-5827	363	112	)	)	PUNCT
ejpam-5827	363	113	∪	∪	ADP
ejpam-5827	363	114	τpκ	τpκ	X
ejpam-5827	363	115	l(h́	l(h́	NOUN
ejpam-5827	363	116	)	)	PUNCT
ejpam-5827	363	117	(	(	PUNCT
ejpam-5827	363	118	u6	u6	NOUN
ejpam-5827	363	119	)	)	PUNCT
ejpam-5827	363	120	τpκ	τpκ	NOUN
ejpam-5827	363	121	u(h	u(h	PROPN
ejpam-5827	363	122	∪	∪	PROPN
ejpam-5827	363	123	h́	h́	PROPN
ejpam-5827	363	124	)	)	PUNCT
ejpam-5827	363	125	=	=	SYM
ejpam-5827	363	126	τpκ	τpκ	NOUN
ejpam-5827	363	127	u(h	u(h	PROPN
ejpam-5827	363	128	)	)	PUNCT
ejpam-5827	363	129	∪	∪	ADP
ejpam-5827	363	130	τpκ	τpκ	X
ejpam-5827	363	131	u(h́	u(h́	NOUN
ejpam-5827	363	132	)	)	PUNCT
ejpam-5827	363	133	(	(	PUNCT
ejpam-5827	363	134	l7	l7	PROPN
ejpam-5827	363	135	)	)	PUNCT
ejpam-5827	363	136	τpκ	τpκ	NOUN
ejpam-5827	363	137	l(h	l(h	PROPN
ejpam-5827	363	138	)	)	PUNCT
ejpam-5827	363	139	=	=	PUNCT
ejpam-5827	364	1	[	[	X
ejpam-5827	364	2	τpκ	τpκ	X
ejpam-5827	364	3	u(hc)]c	u(hc)]c	PROPN
ejpam-5827	364	4	(	(	PUNCT
ejpam-5827	364	5	u7	u7	PROPN
ejpam-5827	364	6	)	)	PUNCT
ejpam-5827	364	7	τpκ	τpκ	NOUN
ejpam-5827	364	8	u(h	u(h	PROPN
ejpam-5827	364	9	)	)	PUNCT
ejpam-5827	364	10	=	=	PUNCT
ejpam-5827	365	1	[	[	X
ejpam-5827	365	2	τpκ	τpκ	X
ejpam-5827	365	3	l(hc)]c	l(hc)]c	PROPN
ejpam-5827	365	4	(	(	PUNCT
ejpam-5827	365	5	l8	l8	PROPN
ejpam-5827	365	6	)	)	PUNCT
ejpam-5827	365	7	τpκ	τpκ	NOUN
ejpam-5827	365	8	l(τpκ	l(τpκ	NOUN
ejpam-5827	365	9	l(h	l(h	PROPN
ejpam-5827	365	10	)	)	PUNCT
ejpam-5827	365	11	)	)	PUNCT
ejpam-5827	366	1	=	=	SYM
ejpam-5827	366	2	τpκ	τpκ	NOUN
ejpam-5827	366	3	l(h	l(h	PROPN
ejpam-5827	366	4	)	)	PUNCT
ejpam-5827	366	5	(	(	PUNCT
ejpam-5827	366	6	u8	u8	PROPN
ejpam-5827	366	7	)	)	PUNCT
ejpam-5827	366	8	τpκ	τpκ	NOUN
ejpam-5827	366	9	u(τpκ	u(τpκ	NOUN
ejpam-5827	366	10	u(h	u(h	PROPN
ejpam-5827	366	11	)	)	PUNCT
ejpam-5827	366	12	)	)	PUNCT
ejpam-5827	367	1	=	=	SYM
ejpam-5827	367	2	τpκ	τpκ	NOUN
ejpam-5827	367	3	u(h	u(h	PROPN
ejpam-5827	367	4	)	)	PUNCT
ejpam-5827	367	5	.	.	PUNCT
ejpam-5827	368	1	remark	remark	PROPN
ejpam-5827	368	2	11	11	NUM
ejpam-5827	368	3	.	.	PUNCT
ejpam-5827	368	4	example	example	NOUN
ejpam-5827	369	1	5	5	NUM
ejpam-5827	369	2	demonstrates	demonstrate	VERB
ejpam-5827	369	3	that	that	SCONJ
ejpam-5827	369	4	the	the	DET
ejpam-5827	369	5	converse	converse	NOUN
ejpam-5827	369	6	of	of	ADP
ejpam-5827	369	7	(	(	PUNCT
ejpam-5827	369	8	l1	l1	PROPN
ejpam-5827	369	9	)	)	PUNCT
ejpam-5827	369	10	,	,	PUNCT
ejpam-5827	369	11	(	(	PUNCT
ejpam-5827	369	12	l4	l4	PROPN
ejpam-5827	369	13	)	)	PUNCT
ejpam-5827	369	14	,	,	PUNCT
ejpam-5827	369	15	(	(	PUNCT
ejpam-5827	369	16	l6	l6	PROPN
ejpam-5827	369	17	)	)	PUNCT
ejpam-5827	369	18	(	(	PUNCT
ejpam-5827	369	19	resp	resp	NOUN
ejpam-5827	369	20	.	.	PUNCT
ejpam-5827	370	1	(	(	PUNCT
ejpam-5827	370	2	u1	u1	NOUN
ejpam-5827	370	3	)	)	PUNCT
ejpam-5827	370	4	,	,	PUNCT
ejpam-5827	370	5	(	(	PUNCT
ejpam-5827	370	6	u4	u4	PROPN
ejpam-5827	370	7	)	)	PUNCT
ejpam-5827	370	8	,	,	PUNCT
ejpam-5827	370	9	(	(	PUNCT
ejpam-5827	370	10	u5	u5	NOUN
ejpam-5827	370	11	)	)	PUNCT
ejpam-5827	370	12	)	)	PUNCT
ejpam-5827	371	1	for	for	ADP
ejpam-5827	371	2	proposition	proposition	NOUN
ejpam-5827	371	3	6	6	NUM
ejpam-5827	371	4	fails	fail	VERB
ejpam-5827	371	5	in	in	ADP
ejpam-5827	371	6	general	general	ADJ
ejpam-5827	371	7	.	.	PUNCT
ejpam-5827	372	1	(	(	PUNCT
ejpam-5827	372	2	l1	l1	PROPN
ejpam-5827	372	3	)	)	PUNCT
ejpam-5827	372	4	suppose	suppose	VERB
ejpam-5827	372	5	that	that	SCONJ
ejpam-5827	372	6	κ	κ	PROPN
ejpam-5827	372	7	=	=	X
ejpam-5827	372	8	r.	r.	PROPN
ejpam-5827	372	9	let	let	VERB
ejpam-5827	372	10	h	h	NOUN
ejpam-5827	372	11	=	=	PRON
ejpam-5827	372	12	{	{	PUNCT
ejpam-5827	372	13	c	c	NOUN
ejpam-5827	372	14	}	}	PUNCT
ejpam-5827	372	15	,	,	PUNCT
ejpam-5827	372	16	then	then	ADV
ejpam-5827	372	17	τpκ	τpκ	NOUN
ejpam-5827	372	18	l(h	l(h	PROPN
ejpam-5827	372	19	)	)	PUNCT
ejpam-5827	372	20	=	=	NOUN
ejpam-5827	372	21	∅	∅	NOUN
ejpam-5827	372	22	and	and	CCONJ
ejpam-5827	372	23	so	so	ADV
ejpam-5827	372	24	h	h	NOUN
ejpam-5827	372	25	⊈	⊈	PROPN
ejpam-5827	372	26	τpκ	τpκ	NOUN
ejpam-5827	372	27	l(h	l(h	PROPN
ejpam-5827	372	28	)	)	PUNCT
ejpam-5827	372	29	,	,	PUNCT
ejpam-5827	373	1	r.	r.	PROPN
ejpam-5827	373	2	a.	a.	PROPN
ejpam-5827	373	3	hosny	hosny	PROPN
ejpam-5827	373	4	,	,	PUNCT
ejpam-5827	373	5	m.	m.	PROPN
ejpam-5827	373	6	k.	k.	PROPN
ejpam-5827	374	1	el	el	PROPN
ejpam-5827	374	2	-	-	PROPN
ejpam-5827	374	3	bably	bably	ADV
ejpam-5827	374	4	,	,	PUNCT
ejpam-5827	374	5	m.	m.	NOUN
ejpam-5827	374	6	a.	a.	PROPN
ejpam-5827	374	7	el	el	PROPN
ejpam-5827	374	8	-	-	PROPN
ejpam-5827	374	9	gayar	gayar	PROPN
ejpam-5827	374	10	/	/	SYM
ejpam-5827	374	11	eur	eur	PROPN
ejpam-5827	374	12	.	.	PUNCT
ejpam-5827	375	1	j.	j.	PROPN
ejpam-5827	375	2	pure	pure	PROPN
ejpam-5827	375	3	appl	appl	PROPN
ejpam-5827	375	4	.	.	PROPN
ejpam-5827	375	5	math	math	PROPN
ejpam-5827	375	6	,	,	PUNCT
ejpam-5827	375	7	18	18	NUM
ejpam-5827	375	8	(	(	PUNCT
ejpam-5827	375	9	1	1	NUM
ejpam-5827	375	10	)	)	PUNCT
ejpam-5827	375	11	(	(	PUNCT
ejpam-5827	375	12	2025	2025	NUM
ejpam-5827	375	13	)	)	PUNCT
ejpam-5827	375	14	,	,	PUNCT
ejpam-5827	375	15	5827	5827	NUM
ejpam-5827	375	16	15	15	NUM
ejpam-5827	375	17	of	of	ADP
ejpam-5827	375	18	29	29	NUM
ejpam-5827	375	19	(	(	PUNCT
ejpam-5827	375	20	l4	l4	PROPN
ejpam-5827	375	21	)	)	PUNCT
ejpam-5827	375	22	suppose	suppose	VERB
ejpam-5827	375	23	that	that	SCONJ
ejpam-5827	375	24	κ	κ	PROPN
ejpam-5827	375	25	=	=	X
ejpam-5827	375	26	r.	r.	PROPN
ejpam-5827	375	27	let	let	VERB
ejpam-5827	375	28	h	h	NOUN
ejpam-5827	375	29	=	=	PUNCT
ejpam-5827	375	30	{	{	PUNCT
ejpam-5827	375	31	b	b	NOUN
ejpam-5827	375	32	,	,	PUNCT
ejpam-5827	375	33	c	c	NOUN
ejpam-5827	375	34	}	}	PUNCT
ejpam-5827	375	35	,	,	PUNCT
ejpam-5827	375	36	h́	h́	NOUN
ejpam-5827	375	37	=	=	PUNCT
ejpam-5827	375	38	{	{	PUNCT
ejpam-5827	375	39	a	a	DET
ejpam-5827	375	40	,	,	PUNCT
ejpam-5827	375	41	b	b	NOUN
ejpam-5827	375	42	}	}	PUNCT
ejpam-5827	375	43	,	,	PUNCT
ejpam-5827	375	44	then	then	ADV
ejpam-5827	375	45	τpκ	τpκ	NOUN
ejpam-5827	375	46	l(h	l(h	PROPN
ejpam-5827	375	47	)	)	PUNCT
ejpam-5827	375	48	=	=	PRON
ejpam-5827	375	49	{	{	PUNCT
ejpam-5827	375	50	b	b	NOUN
ejpam-5827	375	51	}	}	PUNCT
ejpam-5827	375	52	,	,	PUNCT
ejpam-5827	375	53	and	and	CCONJ
ejpam-5827	375	54	τpκ	τpκ	DET
ejpam-5827	375	55	l(h́	l(h́	NOUN
ejpam-5827	375	56	)	)	PUNCT
ejpam-5827	375	57	=	=	PRON
ejpam-5827	375	58	{	{	PUNCT
ejpam-5827	375	59	a	a	PRON
ejpam-5827	375	60	,	,	PUNCT
ejpam-5827	375	61	b	b	NOUN
ejpam-5827	375	62	}	}	PUNCT
ejpam-5827	375	63	.	.	PUNCT
ejpam-5827	376	1	then	then	ADV
ejpam-5827	376	2	τpκ	τpκ	X
ejpam-5827	376	3	l(h	l(h	PROPN
ejpam-5827	376	4	)	)	PUNCT
ejpam-5827	376	5	⊆	⊆	NUM
ejpam-5827	376	6	τpκ	τpκ	DET
ejpam-5827	376	7	l(h́	l(h́	NOUN
ejpam-5827	376	8	)	)	PUNCT
ejpam-5827	376	9	,	,	PUNCT
ejpam-5827	376	10	and	and	CCONJ
ejpam-5827	376	11	h	h	NOUN
ejpam-5827	376	12	⊈	⊈	PROPN
ejpam-5827	376	13	h́	h́	NOUN
ejpam-5827	376	14	,	,	PUNCT
ejpam-5827	376	15	(	(	PUNCT
ejpam-5827	376	16	l6	l6	PROPN
ejpam-5827	376	17	)	)	PUNCT
ejpam-5827	376	18	suppose	suppose	VERB
ejpam-5827	376	19	that	that	SCONJ
ejpam-5827	376	20	κ	κ	PROPN
ejpam-5827	376	21	=	=	X
ejpam-5827	376	22	r.	r.	PROPN
ejpam-5827	376	23	let	let	VERB
ejpam-5827	376	24	h	h	NOUN
ejpam-5827	376	25	=	=	PUNCT
ejpam-5827	376	26	{	{	PUNCT
ejpam-5827	376	27	a	a	X
ejpam-5827	376	28	,	,	PUNCT
ejpam-5827	376	29	c	c	NOUN
ejpam-5827	376	30	}	}	PUNCT
ejpam-5827	376	31	,	,	PUNCT
ejpam-5827	376	32	h́	h́	NOUN
ejpam-5827	376	33	=	=	PUNCT
ejpam-5827	376	34	{	{	PUNCT
ejpam-5827	376	35	a	a	X
ejpam-5827	376	36	,	,	PUNCT
ejpam-5827	376	37	d	d	NOUN
ejpam-5827	376	38	}	}	PUNCT
ejpam-5827	376	39	,	,	PUNCT
ejpam-5827	376	40	then	then	ADV
ejpam-5827	376	41	τpκ	τpκ	NOUN
ejpam-5827	376	42	l(h	l(h	PROPN
ejpam-5827	376	43	)	)	PUNCT
ejpam-5827	376	44	=	=	PRON
ejpam-5827	376	45	{	{	PUNCT
ejpam-5827	376	46	a	a	NOUN
ejpam-5827	376	47	}	}	PUNCT
ejpam-5827	376	48	,	,	PUNCT
ejpam-5827	376	49	and	and	CCONJ
ejpam-5827	376	50	τpκ	τpκ	DET
ejpam-5827	376	51	l(h́	l(h́	NOUN
ejpam-5827	376	52	)	)	PUNCT
ejpam-5827	376	53	=	=	PRON
ejpam-5827	376	54	{	{	PUNCT
ejpam-5827	376	55	a	a	X
ejpam-5827	376	56	,	,	PUNCT
ejpam-5827	376	57	d	d	NOUN
ejpam-5827	376	58	}	}	PUNCT
ejpam-5827	376	59	.	.	PUNCT
ejpam-5827	377	1	so	so	ADV
ejpam-5827	377	2	,	,	PUNCT
ejpam-5827	377	3	τpκ	τpκ	NOUN
ejpam-5827	377	4	l(h	l(h	PROPN
ejpam-5827	377	5	∪	∪	PROPN
ejpam-5827	377	6	h́	h́	PROPN
ejpam-5827	377	7	)	)	PUNCT
ejpam-5827	377	8	=	=	PRON
ejpam-5827	377	9	{	{	PUNCT
ejpam-5827	377	10	a	a	X
ejpam-5827	377	11	,	,	PUNCT
ejpam-5827	377	12	c	c	NOUN
ejpam-5827	377	13	,	,	PUNCT
ejpam-5827	377	14	d	d	NOUN
ejpam-5827	377	15	}	}	PUNCT
ejpam-5827	377	16	,	,	PUNCT
ejpam-5827	377	17	τpκ	τpκ	NOUN
ejpam-5827	377	18	l(h	l(h	NOUN
ejpam-5827	377	19	)	)	PUNCT
ejpam-5827	377	20	∪	∪	ADP
ejpam-5827	377	21	τpκ	τpκ	X
ejpam-5827	377	22	l(h́	l(h́	NOUN
ejpam-5827	377	23	)	)	PUNCT
ejpam-5827	377	24	=	=	PRON
ejpam-5827	377	25	{	{	PUNCT
ejpam-5827	377	26	a	a	X
ejpam-5827	377	27	,	,	PUNCT
ejpam-5827	377	28	d	d	NOUN
ejpam-5827	377	29	}	}	PUNCT
ejpam-5827	377	30	.	.	PUNCT
ejpam-5827	378	1	then	then	ADV
ejpam-5827	378	2	τpκ	τpκ	X
ejpam-5827	378	3	l(h	l(h	PROPN
ejpam-5827	378	4	∪	∪	PROPN
ejpam-5827	378	5	h́	h́	PROPN
ejpam-5827	378	6	)	)	PUNCT
ejpam-5827	378	7	⊈	⊈	PROPN
ejpam-5827	378	8	τpκ	τpκ	NOUN
ejpam-5827	378	9	l(h	l(h	NOUN
ejpam-5827	378	10	)	)	PUNCT
ejpam-5827	378	11	∪	∪	ADP
ejpam-5827	378	12	τpκ	τpκ	NOUN
ejpam-5827	378	13	l(h́	l(h́	NOUN
ejpam-5827	378	14	)	)	PUNCT
ejpam-5827	378	15	.	.	PUNCT
ejpam-5827	379	1	their	their	PRON
ejpam-5827	379	2	specific	specific	ADJ
ejpam-5827	379	3	characteristics	characteristic	NOUN
ejpam-5827	379	4	and	and	CCONJ
ejpam-5827	379	5	relationships	relationship	NOUN
ejpam-5827	379	6	may	may	AUX
ejpam-5827	379	7	be	be	AUX
ejpam-5827	379	8	influenced	influence	VERB
ejpam-5827	379	9	by	by	ADP
ejpam-5827	379	10	the	the	DET
ejpam-5827	379	11	nature	nature	NOUN
ejpam-5827	379	12	of	of	ADP
ejpam-5827	379	13	the	the	DET
ejpam-5827	379	14	primal	primal	ADJ
ejpam-5827	379	15	p	p	NOUN
ejpam-5827	379	16	and	and	CCONJ
ejpam-5827	379	17	the	the	DET
ejpam-5827	379	18	κ	κ	NOUN
ejpam-5827	379	19	-	-	NOUN
ejpam-5827	379	20	neighborhoods	neighborhood	NOUN
ejpam-5827	379	21	,	,	PUNCT
ejpam-5827	379	22	giving	give	VERB
ejpam-5827	379	23	rise	rise	NOUN
ejpam-5827	379	24	to	to	ADP
ejpam-5827	379	25	unique	unique	ADJ
ejpam-5827	379	26	topological	topological	ADJ
ejpam-5827	379	27	structures	structure	NOUN
ejpam-5827	379	28	.	.	PUNCT
ejpam-5827	380	1	proposition	proposition	NOUN
ejpam-5827	380	2	7	7	NUM
ejpam-5827	380	3	.	.	PUNCT
ejpam-5827	381	1	let	let	VERB
ejpam-5827	381	2	(	(	PUNCT
ejpam-5827	381	3	v	v	NOUN
ejpam-5827	381	4	,	,	PUNCT
ejpam-5827	381	5	r	r	NOUN
ejpam-5827	381	6	,	,	PUNCT
ejpam-5827	381	7	p	p	NOUN
ejpam-5827	381	8	)	)	PUNCT
ejpam-5827	381	9	be	be	AUX
ejpam-5827	381	10	a	a	DET
ejpam-5827	381	11	primal	primal	ADJ
ejpam-5827	381	12	approximation	approximation	NOUN
ejpam-5827	381	13	space	space	NOUN
ejpam-5827	381	14	.	.	PUNCT
ejpam-5827	382	1	if	if	SCONJ
ejpam-5827	382	2	r	r	NOUN
ejpam-5827	382	3	is	be	AUX
ejpam-5827	382	4	a	a	DET
ejpam-5827	382	5	preorder	preorder	NOUN
ejpam-5827	382	6	relation	relation	NOUN
ejpam-5827	382	7	,	,	PUNCT
ejpam-5827	382	8	then	then	ADV
ejpam-5827	382	9	for	for	ADP
ejpam-5827	382	10	any	any	DET
ejpam-5827	382	11	w	w	PROPN
ejpam-5827	382	12	∈	∈	PROPN
ejpam-5827	382	13	v	v	NOUN
ejpam-5827	382	14	:	:	PUNCT
ejpam-5827	382	15	τpκ	τpκ	NOUN
ejpam-5827	382	16	l(nκ(w	l(nκ(w	NOUN
ejpam-5827	382	17	)	)	PUNCT
ejpam-5827	382	18	)	)	PUNCT
ejpam-5827	383	1	=	=	SYM
ejpam-5827	383	2	nκ(w	nκ(w	NOUN
ejpam-5827	383	3	)	)	PUNCT
ejpam-5827	383	4	,	,	PUNCT
ejpam-5827	383	5	for	for	ADP
ejpam-5827	383	6	each	each	DET
ejpam-5827	383	7	κ	κ	PROPN
ejpam-5827	383	8	∈	∈	PROPN
ejpam-5827	383	9	{	{	PUNCT
ejpam-5827	383	10	r	r	NOUN
ejpam-5827	383	11	,	,	PUNCT
ejpam-5827	383	12	l	l	NOUN
ejpam-5827	383	13	,	,	PUNCT
ejpam-5827	383	14	i	i	PRON
ejpam-5827	383	15	,	,	PUNCT
ejpam-5827	383	16	⟨r⟩	⟨r⟩	PROPN
ejpam-5827	383	17	,	,	PUNCT
ejpam-5827	383	18	⟨l⟩	⟨l⟩	PROPN
ejpam-5827	383	19	,	,	PUNCT
ejpam-5827	383	20	⟨i⟩	⟨i⟩	PROPN
ejpam-5827	383	21	,	,	PUNCT
ejpam-5827	383	22	u	u	NOUN
ejpam-5827	383	23	,	,	PUNCT
ejpam-5827	383	24	⟨u⟩	⟨u⟩	PROPN
ejpam-5827	383	25	}	}	PUNCT
ejpam-5827	383	26	.	.	PUNCT
ejpam-5827	384	1	proof	proof	NOUN
ejpam-5827	384	2	.	.	PUNCT
ejpam-5827	385	1	according	accord	VERB
ejpam-5827	385	2	to	to	ADP
ejpam-5827	385	3	[	[	X
ejpam-5827	385	4	6	6	NUM
ejpam-5827	385	5	]	]	PUNCT
ejpam-5827	385	6	,	,	PUNCT
ejpam-5827	385	7	since	since	SCONJ
ejpam-5827	385	8	r	r	NOUN
ejpam-5827	385	9	is	be	AUX
ejpam-5827	385	10	preorder	preorder	NOUN
ejpam-5827	385	11	,	,	PUNCT
ejpam-5827	385	12	it	it	PRON
ejpam-5827	385	13	follows	follow	VERB
ejpam-5827	385	14	that	that	SCONJ
ejpam-5827	385	15	nκ(w	nκ(w	NOUN
ejpam-5827	385	16	)	)	PUNCT
ejpam-5827	385	17	∈	∈	PROPN
ejpam-5827	385	18	τκ	τκ	PROPN
ejpam-5827	385	19	.	.	PUNCT
ejpam-5827	386	1	therefore	therefore	ADV
ejpam-5827	386	2	,	,	PUNCT
ejpam-5827	386	3	nκ(w	nκ(w	NOUN
ejpam-5827	386	4	)	)	PUNCT
ejpam-5827	386	5	∈	∈	NOUN
ejpam-5827	386	6	τpκ	τpκ	NOUN
ejpam-5827	386	7	,	,	PUNCT
ejpam-5827	386	8	which	which	PRON
ejpam-5827	386	9	implies	imply	VERB
ejpam-5827	386	10	that	that	SCONJ
ejpam-5827	386	11	τpκ	τpκ	PRON
ejpam-5827	386	12	l(nκ(w	l(nκ(w	NOUN
ejpam-5827	386	13	)	)	PUNCT
ejpam-5827	386	14	)	)	PUNCT
ejpam-5827	387	1	=	=	SYM
ejpam-5827	387	2	nκ(w	nκ(w	NOUN
ejpam-5827	387	3	)	)	PUNCT
ejpam-5827	387	4	for	for	ADP
ejpam-5827	387	5	each	each	DET
ejpam-5827	387	6	κ	κ	PROPN
ejpam-5827	387	7	∈	∈	PROPN
ejpam-5827	387	8	{	{	PUNCT
ejpam-5827	387	9	r	r	NOUN
ejpam-5827	387	10	,	,	PUNCT
ejpam-5827	387	11	l	l	NOUN
ejpam-5827	387	12	,	,	PUNCT
ejpam-5827	387	13	i	i	PRON
ejpam-5827	387	14	,	,	PUNCT
ejpam-5827	387	15	⟨r⟩	⟨r⟩	PROPN
ejpam-5827	387	16	,	,	PUNCT
ejpam-5827	387	17	⟨l⟩	⟨l⟩	PROPN
ejpam-5827	387	18	,	,	PUNCT
ejpam-5827	387	19	⟨i⟩	⟨i⟩	PROPN
ejpam-5827	387	20	,	,	PUNCT
ejpam-5827	387	21	u	u	NOUN
ejpam-5827	387	22	,	,	PUNCT
ejpam-5827	387	23	⟨u⟩	⟨u⟩	PROPN
ejpam-5827	387	24	}	}	PUNCT
ejpam-5827	387	25	.	.	PUNCT
ejpam-5827	388	1	remark	remark	PROPN
ejpam-5827	388	2	12	12	NUM
ejpam-5827	388	3	.	.	PUNCT
ejpam-5827	389	1	according	accord	VERB
ejpam-5827	389	2	to	to	ADP
ejpam-5827	389	3	example	example	NOUN
ejpam-5827	389	4	5	5	NUM
ejpam-5827	389	5	,	,	PUNCT
ejpam-5827	389	6	it	it	PRON
ejpam-5827	389	7	is	be	AUX
ejpam-5827	389	8	observed	observe	VERB
ejpam-5827	389	9	that	that	SCONJ
ejpam-5827	389	10	the	the	DET
ejpam-5827	389	11	preorder	preorder	NOUN
ejpam-5827	389	12	conditions	condition	NOUN
ejpam-5827	389	13	in	in	ADP
ejpam-5827	389	14	proposition	proposition	NOUN
ejpam-5827	389	15	7	7	NUM
ejpam-5827	389	16	are	be	AUX
ejpam-5827	389	17	indeed	indeed	ADV
ejpam-5827	389	18	strict	strict	ADJ
ejpam-5827	389	19	.	.	PUNCT
ejpam-5827	390	1	let	let	VERB
ejpam-5827	390	2	w	w	NOUN
ejpam-5827	390	3	=	=	VERB
ejpam-5827	390	4	a	a	PROPN
ejpam-5827	390	5	and	and	CCONJ
ejpam-5827	390	6	κ	κ	X
ejpam-5827	390	7	=	=	SYM
ejpam-5827	390	8	r.	r.	PROPN
ejpam-5827	390	9	then	then	ADV
ejpam-5827	390	10	nr(a	nr(a	PUNCT
ejpam-5827	390	11	)	)	PUNCT
ejpam-5827	391	1	=	=	PRON
ejpam-5827	391	2	{	{	PUNCT
ejpam-5827	391	3	a	a	DET
ejpam-5827	391	4	,	,	PUNCT
ejpam-5827	391	5	b	b	NOUN
ejpam-5827	391	6	,	,	PUNCT
ejpam-5827	391	7	c	c	NOUN
ejpam-5827	391	8	}	}	PUNCT
ejpam-5827	391	9	,	,	PUNCT
ejpam-5827	391	10	which	which	PRON
ejpam-5827	391	11	implies	imply	VERB
ejpam-5827	391	12	that	that	SCONJ
ejpam-5827	391	13	τpr	τpr	PROPN
ejpam-5827	391	14	l(nr(a	l(nr(a	PROPN
ejpam-5827	391	15	)	)	PUNCT
ejpam-5827	391	16	)	)	PUNCT
ejpam-5827	392	1	=	=	PRON
ejpam-5827	392	2	{	{	PUNCT
ejpam-5827	392	3	a	a	PRON
ejpam-5827	392	4	,	,	PUNCT
ejpam-5827	392	5	b	b	NOUN
ejpam-5827	392	6	}	}	PUNCT
ejpam-5827	392	7	.	.	PUNCT
ejpam-5827	393	1	therefore	therefore	ADV
ejpam-5827	393	2	,	,	PUNCT
ejpam-5827	393	3	τpr	τpr	PROPN
ejpam-5827	393	4	l(nr(a	l(nr(a	NUM
ejpam-5827	393	5	)	)	PUNCT
ejpam-5827	393	6	)	)	PUNCT
ejpam-5827	393	7	̸=	̸=	PROPN
ejpam-5827	393	8	nr(a	nr(a	NUM
ejpam-5827	393	9	)	)	PUNCT
ejpam-5827	393	10	.	.	PUNCT
ejpam-5827	394	1	the	the	DET
ejpam-5827	394	2	next	next	ADJ
ejpam-5827	394	3	propositions	proposition	NOUN
ejpam-5827	394	4	are	be	AUX
ejpam-5827	394	5	straightforward	straightforward	ADJ
ejpam-5827	394	6	,	,	PUNCT
ejpam-5827	394	7	and	and	CCONJ
ejpam-5827	394	8	their	their	PRON
ejpam-5827	394	9	proofs	proof	NOUN
ejpam-5827	394	10	are	be	AUX
ejpam-5827	394	11	omitted	omit	VERB
ejpam-5827	394	12	for	for	ADP
ejpam-5827	394	13	brevity	brevity	NOUN
ejpam-5827	394	14	.	.	PUNCT
ejpam-5827	395	1	proposition	proposition	NOUN
ejpam-5827	395	2	8	8	NUM
ejpam-5827	395	3	.	.	PUNCT
ejpam-5827	396	1	consider	consider	VERB
ejpam-5827	396	2	τpκ	τpκ	NOUN
ejpam-5827	396	3	is	be	AUX
ejpam-5827	396	4	a	a	DET
ejpam-5827	396	5	κ	κ	NOUN
ejpam-5827	396	6	-	-	PUNCT
ejpam-5827	396	7	supra	supra	ADJ
ejpam-5827	396	8	topology	topology	NOUN
ejpam-5827	396	9	generated	generate	VERB
ejpam-5827	396	10	by	by	ADP
ejpam-5827	396	11	κ	κ	ADV
ejpam-5827	396	12	-	-	PUNCT
ejpam-5827	396	13	ns	ns	ADJ
ejpam-5827	396	14	and	and	CCONJ
ejpam-5827	396	15	primal	primal	ADJ
ejpam-5827	396	16	p.	p.	NOUN
ejpam-5827	396	17	if	if	SCONJ
ejpam-5827	396	18	h	h	PROPN
ejpam-5827	396	19	⊆	⊆	NUM
ejpam-5827	396	20	v	v	NOUN
ejpam-5827	397	1	and	and	CCONJ
ejpam-5827	397	2	z	z	NOUN
ejpam-5827	397	3	∈	∈	PROPN
ejpam-5827	397	4	v	v	NOUN
ejpam-5827	397	5	,	,	PUNCT
ejpam-5827	397	6	then	then	ADV
ejpam-5827	397	7	the	the	DET
ejpam-5827	397	8	subsequent	subsequent	ADJ
ejpam-5827	397	9	items	item	NOUN
ejpam-5827	397	10	hold	hold	VERB
ejpam-5827	397	11	:	:	PUNCT
ejpam-5827	397	12	(	(	PUNCT
ejpam-5827	397	13	i	i	NOUN
ejpam-5827	397	14	)	)	PUNCT
ejpam-5827	397	15	τpu	τpu	NOUN
ejpam-5827	397	16	l(h	l(h	PROPN
ejpam-5827	397	17	)	)	PUNCT
ejpam-5827	398	1	⊆	⊆	NUM
ejpam-5827	398	2	τpr	τpr	NOUN
ejpam-5827	398	3	l(h	l(h	PROPN
ejpam-5827	398	4	)	)	PUNCT
ejpam-5827	398	5	⊆	⊆	PROPN
ejpam-5827	398	6	τpi	τpi	NOUN
ejpam-5827	398	7	l(h	l(h	PROPN
ejpam-5827	398	8	)	)	PUNCT
ejpam-5827	398	9	and	and	CCONJ
ejpam-5827	398	10	τpu	τpu	VERB
ejpam-5827	398	11	l(h	l(h	PROPN
ejpam-5827	398	12	)	)	PUNCT
ejpam-5827	399	1	⊆	⊆	NUM
ejpam-5827	399	2	τpl	τpl	NOUN
ejpam-5827	399	3	l(h	l(h	PROPN
ejpam-5827	399	4	)	)	PUNCT
ejpam-5827	399	5	⊆	⊆	NUM
ejpam-5827	399	6	τpi	τpi	NOUN
ejpam-5827	399	7	l(h	l(h	PROPN
ejpam-5827	399	8	)	)	PUNCT
ejpam-5827	399	9	.	.	PUNCT
ejpam-5827	400	1	(	(	PUNCT
ejpam-5827	400	2	ii	ii	NOUN
ejpam-5827	400	3	)	)	PUNCT
ejpam-5827	400	4	τpi	τpi	NOUN
ejpam-5827	400	5	u(h	u(h	PROPN
ejpam-5827	400	6	)	)	PUNCT
ejpam-5827	401	1	⊆	⊆	NUM
ejpam-5827	401	2	τpr	τpr	NOUN
ejpam-5827	401	3	u(h	u(h	PROPN
ejpam-5827	401	4	)	)	PUNCT
ejpam-5827	401	5	⊆	⊆	NUM
ejpam-5827	401	6	τpu	τpu	NOUN
ejpam-5827	401	7	u(h	u(h	ADJ
ejpam-5827	401	8	)	)	PUNCT
ejpam-5827	401	9	and	and	CCONJ
ejpam-5827	401	10	τpi	τpi	NOUN
ejpam-5827	401	11	u(h	u(h	PROPN
ejpam-5827	401	12	)	)	PUNCT
ejpam-5827	401	13	⊆	⊆	NUM
ejpam-5827	401	14	τpl	τpl	NOUN
ejpam-5827	401	15	u(h	u(h	PROPN
ejpam-5827	401	16	)	)	PUNCT
ejpam-5827	401	17	⊆	⊆	NUM
ejpam-5827	401	18	τpu	τpu	NOUN
ejpam-5827	401	19	u(h	u(h	PROPN
ejpam-5827	401	20	)	)	PUNCT
ejpam-5827	401	21	.	.	PUNCT
ejpam-5827	402	1	(	(	PUNCT
ejpam-5827	402	2	iii	iii	X
ejpam-5827	402	3	)	)	PUNCT
ejpam-5827	402	4	τpu	τpu	NOUN
ejpam-5827	402	5	σ(h	σ(h	PROPN
ejpam-5827	402	6	)	)	PUNCT
ejpam-5827	402	7	≤	≤	NUM
ejpam-5827	402	8	τpr	τpr	NOUN
ejpam-5827	402	9	σ(h	σ(h	PROPN
ejpam-5827	402	10	)	)	PUNCT
ejpam-5827	402	11	≤	≤	PROPN
ejpam-5827	402	12	τpi	τpi	PROPN
ejpam-5827	402	13	σ(h	σ(h	PROPN
ejpam-5827	402	14	)	)	PUNCT
ejpam-5827	402	15	and	and	CCONJ
ejpam-5827	402	16	τpu	τpu	PROPN
ejpam-5827	402	17	σ(h	σ(h	PROPN
ejpam-5827	402	18	)	)	PUNCT
ejpam-5827	402	19	≤	≤	NUM
ejpam-5827	402	20	τpl	τpl	VERB
ejpam-5827	402	21	σ(h	σ(h	PROPN
ejpam-5827	402	22	)	)	PUNCT
ejpam-5827	402	23	≤	≤	PROPN
ejpam-5827	402	24	τpi	τpi	PROPN
ejpam-5827	402	25	σ(h	σ(h	PROPN
ejpam-5827	402	26	)	)	PUNCT
ejpam-5827	402	27	.	.	PUNCT
ejpam-5827	403	1	(	(	PUNCT
ejpam-5827	403	2	iv	iv	X
ejpam-5827	403	3	)	)	PUNCT
ejpam-5827	403	4	τp⟨u⟩l(h	τp⟨u⟩l(h	NUM
ejpam-5827	403	5	)	)	PUNCT
ejpam-5827	403	6	⊆	⊆	NUM
ejpam-5827	403	7	τp⟨r⟩l(h	τp⟨r⟩l(h	NUM
ejpam-5827	403	8	)	)	PUNCT
ejpam-5827	403	9	⊆	⊆	NUM
ejpam-5827	403	10	τp⟨i⟩l(h	τp⟨i⟩l(h	NUM
ejpam-5827	403	11	)	)	PUNCT
ejpam-5827	403	12	and	and	CCONJ
ejpam-5827	403	13	τp⟨u⟩l(h	τp⟨u⟩l(h	NUM
ejpam-5827	403	14	)	)	PUNCT
ejpam-5827	403	15	⊆	⊆	NUM
ejpam-5827	403	16	τp⟨l⟩l(h	τp⟨l⟩l(h	NUM
ejpam-5827	403	17	)	)	PUNCT
ejpam-5827	403	18	⊆	⊆	NUM
ejpam-5827	403	19	τp⟨i⟩l(h	τp⟨i⟩l(h	NUM
ejpam-5827	403	20	)	)	PUNCT
ejpam-5827	403	21	.	.	PUNCT
ejpam-5827	404	1	(	(	PUNCT
ejpam-5827	404	2	v	v	NOUN
ejpam-5827	404	3	)	)	PUNCT
ejpam-5827	404	4	τp⟨i⟩u(h	τp⟨i⟩u(h	NUM
ejpam-5827	404	5	)	)	PUNCT
ejpam-5827	405	1	⊆	⊆	NUM
ejpam-5827	405	2	τp⟨r⟩u(h	τp⟨r⟩u(h	NUM
ejpam-5827	405	3	)	)	PUNCT
ejpam-5827	405	4	⊆	⊆	NUM
ejpam-5827	405	5	τp⟨u⟩u(h	τp⟨u⟩u(h	NUM
ejpam-5827	405	6	)	)	PUNCT
ejpam-5827	405	7	and	and	CCONJ
ejpam-5827	405	8	τp⟨i⟩u(h	τp⟨i⟩u(h	NUM
ejpam-5827	405	9	)	)	PUNCT
ejpam-5827	405	10	⊆	⊆	X
ejpam-5827	405	11	τp⟨l⟩u(h	τp⟨l⟩u(h	NUM
ejpam-5827	405	12	)	)	PUNCT
ejpam-5827	405	13	⊆	⊆	NUM
ejpam-5827	405	14	τp⟨u⟩u(h	τp⟨u⟩u(h	NUM
ejpam-5827	405	15	)	)	PUNCT
ejpam-5827	405	16	.	.	PUNCT
ejpam-5827	406	1	(	(	PUNCT
ejpam-5827	406	2	vi	vi	NOUN
ejpam-5827	406	3	)	)	PUNCT
ejpam-5827	406	4	τp⟨u⟩σ(h	τp⟨u⟩σ(h	NOUN
ejpam-5827	406	5	)	)	PUNCT
ejpam-5827	406	6	≤	≤	NUM
ejpam-5827	406	7	τp⟨r⟩σ(h	τp⟨r⟩σ(h	NOUN
ejpam-5827	406	8	)	)	PUNCT
ejpam-5827	406	9	≤	≤	NUM
ejpam-5827	406	10	τp⟨i⟩σ(h	τp⟨i⟩σ(h	NOUN
ejpam-5827	406	11	)	)	PUNCT
ejpam-5827	406	12	and	and	CCONJ
ejpam-5827	406	13	τp⟨u⟩σ(h	τp⟨u⟩σ(h	NOUN
ejpam-5827	406	14	)	)	PUNCT
ejpam-5827	406	15	≤	≤	NUM
ejpam-5827	406	16	τp⟨l⟩σ(h	τp⟨l⟩σ(h	NOUN
ejpam-5827	406	17	)	)	PUNCT
ejpam-5827	406	18	≤	≤	NUM
ejpam-5827	406	19	τp⟨i⟩σ(h	τp⟨i⟩σ(h	NOUN
ejpam-5827	406	20	)	)	PUNCT
ejpam-5827	406	21	.	.	PUNCT
ejpam-5827	407	1	theorem	theorem	VERB
ejpam-5827	407	2	6	6	NUM
ejpam-5827	407	3	.	.	PUNCT
ejpam-5827	408	1	let	let	VERB
ejpam-5827	408	2	p	p	NOUN
ejpam-5827	408	3	and	and	CCONJ
ejpam-5827	408	4	p̃	p̃	PROPN
ejpam-5827	408	5	be	be	VERB
ejpam-5827	408	6	two	two	NUM
ejpam-5827	408	7	primals	primal	NOUN
ejpam-5827	408	8	on	on	ADP
ejpam-5827	408	9	two	two	NUM
ejpam-5827	408	10	κ	κ	NOUN
ejpam-5827	408	11	-	-	PUNCT
ejpam-5827	408	12	supra	supra	ADJ
ejpam-5827	408	13	topological	topological	ADJ
ejpam-5827	408	14	spaces	space	NOUN
ejpam-5827	408	15	(	(	PUNCT
ejpam-5827	408	16	v	v	NOUN
ejpam-5827	408	17	,	,	PUNCT
ejpam-5827	408	18	τpκ	τpκ	NOUN
ejpam-5827	408	19	)	)	PUNCT
ejpam-5827	408	20	and	and	CCONJ
ejpam-5827	408	21	(	(	PUNCT
ejpam-5827	408	22	v	v	NOUN
ejpam-5827	408	23	,	,	PUNCT
ejpam-5827	408	24	τ	τ	PROPN
ejpam-5827	408	25	p̃κ	p̃κ	NOUN
ejpam-5827	408	26	)	)	PUNCT
ejpam-5827	408	27	,	,	PUNCT
ejpam-5827	408	28	respectively	respectively	ADV
ejpam-5827	408	29	,	,	PUNCT
ejpam-5827	408	30	with	with	ADP
ejpam-5827	408	31	p	p	NOUN
ejpam-5827	408	32	⊆	⊆	NUM
ejpam-5827	408	33	p̃.	p̃.	NOUN
ejpam-5827	408	34	if	if	SCONJ
ejpam-5827	408	35	h	h	NOUN
ejpam-5827	408	36	⊆	⊆	NUM
ejpam-5827	408	37	v	v	NOUN
ejpam-5827	408	38	,	,	PUNCT
ejpam-5827	408	39	then	then	ADV
ejpam-5827	408	40	the	the	DET
ejpam-5827	408	41	following	following	ADJ
ejpam-5827	408	42	statements	statement	NOUN
ejpam-5827	408	43	hold	hold	VERB
ejpam-5827	408	44	:	:	PUNCT
ejpam-5827	408	45	(	(	PUNCT
ejpam-5827	408	46	i	i	NOUN
ejpam-5827	408	47	)	)	PUNCT
ejpam-5827	408	48	τpκ	τpκ	NOUN
ejpam-5827	408	49	l(h	l(h	PROPN
ejpam-5827	408	50	)	)	PUNCT
ejpam-5827	409	1	⊆	⊆	NUM
ejpam-5827	409	2	τ	τ	X
ejpam-5827	409	3	p̃κ	p̃κ	NOUN
ejpam-5827	409	4	l(h	l(h	PROPN
ejpam-5827	409	5	)	)	PUNCT
ejpam-5827	409	6	,	,	PUNCT
ejpam-5827	409	7	(	(	PUNCT
ejpam-5827	409	8	ii	ii	NOUN
ejpam-5827	409	9	)	)	PUNCT
ejpam-5827	409	10	τpκ	τpκ	NOUN
ejpam-5827	409	11	u(h	u(h	PROPN
ejpam-5827	409	12	)	)	PUNCT
ejpam-5827	409	13	⊇	⊇	PROPN
ejpam-5827	409	14	τ	τ	PROPN
ejpam-5827	409	15	p̃κ	p̃κ	NOUN
ejpam-5827	409	16	u(h	u(h	PROPN
ejpam-5827	409	17	)	)	PUNCT
ejpam-5827	409	18	,	,	PUNCT
ejpam-5827	409	19	(	(	PUNCT
ejpam-5827	409	20	iii	iii	X
ejpam-5827	409	21	)	)	PUNCT
ejpam-5827	409	22	τpκ	τpκ	NOUN
ejpam-5827	409	23	σ(h	σ(h	NOUN
ejpam-5827	409	24	)	)	PUNCT
ejpam-5827	409	25	≤	≤	NOUN
ejpam-5827	409	26	τ	τ	X
ejpam-5827	409	27	p̃κ	p̃κ	PROPN
ejpam-5827	409	28	σ(h	σ(h	PROPN
ejpam-5827	409	29	)	)	PUNCT
ejpam-5827	409	30	.	.	PUNCT
ejpam-5827	410	1	remark	remark	PROPN
ejpam-5827	410	2	13	13	NUM
ejpam-5827	410	3	.	.	PUNCT
ejpam-5827	410	4	example	example	NOUN
ejpam-5827	411	1	5	5	NUM
ejpam-5827	411	2	demonstrates	demonstrate	VERB
ejpam-5827	411	3	that	that	SCONJ
ejpam-5827	411	4	the	the	DET
ejpam-5827	411	5	converse	converse	NOUN
ejpam-5827	411	6	of	of	ADP
ejpam-5827	411	7	theorem	theorem	ADJ
ejpam-5827	411	8	6	6	NUM
ejpam-5827	411	9	fails	fail	VERB
ejpam-5827	411	10	in	in	ADP
ejpam-5827	411	11	general	general	ADJ
ejpam-5827	411	12	.	.	PUNCT
ejpam-5827	412	1	r.	r.	PROPN
ejpam-5827	412	2	a.	a.	PROPN
ejpam-5827	412	3	hosny	hosny	PROPN
ejpam-5827	412	4	,	,	PUNCT
ejpam-5827	412	5	m.	m.	PROPN
ejpam-5827	412	6	k.	k.	PROPN
ejpam-5827	413	1	el	el	PROPN
ejpam-5827	413	2	-	-	PROPN
ejpam-5827	413	3	bably	bably	ADV
ejpam-5827	413	4	,	,	PUNCT
ejpam-5827	413	5	m.	m.	NOUN
ejpam-5827	413	6	a.	a.	PROPN
ejpam-5827	413	7	el	el	PROPN
ejpam-5827	413	8	-	-	PROPN
ejpam-5827	413	9	gayar	gayar	PROPN
ejpam-5827	413	10	/	/	SYM
ejpam-5827	413	11	eur	eur	PROPN
ejpam-5827	413	12	.	.	PUNCT
ejpam-5827	414	1	j.	j.	PROPN
ejpam-5827	414	2	pure	pure	PROPN
ejpam-5827	414	3	appl	appl	PROPN
ejpam-5827	414	4	.	.	PROPN
ejpam-5827	414	5	math	math	PROPN
ejpam-5827	414	6	,	,	PUNCT
ejpam-5827	414	7	18	18	NUM
ejpam-5827	414	8	(	(	PUNCT
ejpam-5827	414	9	1	1	NUM
ejpam-5827	414	10	)	)	PUNCT
ejpam-5827	414	11	(	(	PUNCT
ejpam-5827	414	12	2025	2025	NUM
ejpam-5827	414	13	)	)	PUNCT
ejpam-5827	414	14	,	,	PUNCT
ejpam-5827	414	15	5827	5827	NUM
ejpam-5827	414	16	16	16	NUM
ejpam-5827	414	17	of	of	ADP
ejpam-5827	414	18	29	29	NUM
ejpam-5827	414	19	(	(	PUNCT
ejpam-5827	414	20	i	i	NOUN
ejpam-5827	414	21	)	)	PUNCT
ejpam-5827	414	22	suppose	suppose	VERB
ejpam-5827	414	23	that	that	SCONJ
ejpam-5827	414	24	κ	κ	PROPN
ejpam-5827	414	25	=	=	X
ejpam-5827	414	26	r.	r.	PROPN
ejpam-5827	414	27	let	let	VERB
ejpam-5827	414	28	h	h	NOUN
ejpam-5827	414	29	=	=	PRON
ejpam-5827	414	30	{	{	PUNCT
ejpam-5827	414	31	c	c	NOUN
ejpam-5827	414	32	}	}	PUNCT
ejpam-5827	414	33	,	,	PUNCT
ejpam-5827	414	34	then	then	ADV
ejpam-5827	414	35	τpκ	τpκ	NOUN
ejpam-5827	414	36	l(h	l(h	PROPN
ejpam-5827	414	37	)	)	PUNCT
ejpam-5827	414	38	=	=	NOUN
ejpam-5827	414	39	∅	∅	NOUN
ejpam-5827	414	40	,	,	PUNCT
ejpam-5827	414	41	τ	τ	X
ejpam-5827	414	42	p̃κ	p̃κ	NOUN
ejpam-5827	414	43	l(h	l(h	PROPN
ejpam-5827	414	44	)	)	PUNCT
ejpam-5827	414	45	=	=	PRON
ejpam-5827	414	46	{	{	PUNCT
ejpam-5827	414	47	c	c	NOUN
ejpam-5827	414	48	}	}	PUNCT
ejpam-5827	414	49	and	and	CCONJ
ejpam-5827	414	50	so	so	ADV
ejpam-5827	414	51	τ	τ	PROPN
ejpam-5827	414	52	p̃κ	p̃κ	NOUN
ejpam-5827	414	53	l(h	l(h	PROPN
ejpam-5827	414	54	)	)	PUNCT
ejpam-5827	414	55	⊈	⊈	PROPN
ejpam-5827	414	56	τpκ	τpκ	NOUN
ejpam-5827	414	57	l(h	l(h	PROPN
ejpam-5827	414	58	)	)	PUNCT
ejpam-5827	414	59	,	,	PUNCT
ejpam-5827	414	60	(	(	PUNCT
ejpam-5827	414	61	ii	ii	NOUN
ejpam-5827	414	62	)	)	PUNCT
ejpam-5827	414	63	suppose	suppose	VERB
ejpam-5827	414	64	that	that	SCONJ
ejpam-5827	414	65	κ	κ	PROPN
ejpam-5827	414	66	=	=	X
ejpam-5827	414	67	r.	r.	PROPN
ejpam-5827	414	68	let	let	VERB
ejpam-5827	414	69	h	h	NOUN
ejpam-5827	414	70	=	=	PUNCT
ejpam-5827	414	71	{	{	PUNCT
ejpam-5827	414	72	a	a	PRON
ejpam-5827	414	73	,	,	PUNCT
ejpam-5827	414	74	b	b	NOUN
ejpam-5827	414	75	,	,	PUNCT
ejpam-5827	414	76	d	d	NOUN
ejpam-5827	414	77	}	}	PUNCT
ejpam-5827	414	78	,	,	PUNCT
ejpam-5827	414	79	then	then	ADV
ejpam-5827	414	80	τpκ	τpκ	NOUN
ejpam-5827	414	81	u(h	u(h	ADJ
ejpam-5827	414	82	)	)	PUNCT
ejpam-5827	414	83	=	=	SYM
ejpam-5827	414	84	v	v	NOUN
ejpam-5827	414	85	,	,	PUNCT
ejpam-5827	414	86	τ	τ	PROPN
ejpam-5827	414	87	p̃κ	p̃κ	NOUN
ejpam-5827	414	88	u(h	u(h	PROPN
ejpam-5827	414	89	)	)	PUNCT
ejpam-5827	415	1	=	=	PRON
ejpam-5827	415	2	{	{	PUNCT
ejpam-5827	415	3	a	a	PRON
ejpam-5827	415	4	,	,	PUNCT
ejpam-5827	415	5	b	b	NOUN
ejpam-5827	415	6	,	,	PUNCT
ejpam-5827	415	7	d	d	NOUN
ejpam-5827	415	8	}	}	PUNCT
ejpam-5827	415	9	.	.	PUNCT
ejpam-5827	416	1	hence	hence	ADV
ejpam-5827	416	2	,	,	PUNCT
ejpam-5827	416	3	τpκ	τpκ	NOUN
ejpam-5827	416	4	u(h	u(h	PROPN
ejpam-5827	416	5	)	)	PUNCT
ejpam-5827	416	6	⊈	⊈	PROPN
ejpam-5827	417	1	τ	τ	X
ejpam-5827	417	2	p̃κ	p̃κ	NOUN
ejpam-5827	417	3	u(h	u(h	PROPN
ejpam-5827	417	4	)	)	PUNCT
ejpam-5827	417	5	,	,	PUNCT
ejpam-5827	417	6	(	(	PUNCT
ejpam-5827	417	7	iii	iii	X
ejpam-5827	417	8	)	)	PUNCT
ejpam-5827	417	9	suppose	suppose	VERB
ejpam-5827	417	10	that	that	SCONJ
ejpam-5827	417	11	κ	κ	PROPN
ejpam-5827	417	12	=	=	X
ejpam-5827	417	13	r.	r.	PROPN
ejpam-5827	417	14	let	let	VERB
ejpam-5827	417	15	h	h	NOUN
ejpam-5827	417	16	=	=	PRON
ejpam-5827	417	17	{	{	PUNCT
ejpam-5827	417	18	c	c	NOUN
ejpam-5827	417	19	}	}	PUNCT
ejpam-5827	417	20	,	,	PUNCT
ejpam-5827	417	21	then	then	ADV
ejpam-5827	417	22	τpκ	τpκ	X
ejpam-5827	417	23	σ(h	σ(h	NOUN
ejpam-5827	417	24	)	)	PUNCT
ejpam-5827	417	25	=	=	SYM
ejpam-5827	417	26	0	0	NUM
ejpam-5827	417	27	,	,	PUNCT
ejpam-5827	417	28	τ	τ	PROPN
ejpam-5827	417	29	p̃κ	p̃κ	PROPN
ejpam-5827	417	30	σ(h	σ(h	PROPN
ejpam-5827	417	31	)	)	PUNCT
ejpam-5827	417	32	=	=	SYM
ejpam-5827	417	33	1	1	NUM
ejpam-5827	417	34	hence	hence	ADV
ejpam-5827	417	35	,	,	PUNCT
ejpam-5827	417	36	τ	τ	PROPN
ejpam-5827	417	37	p̃κ	p̃κ	PROPN
ejpam-5827	417	38	σ(h	σ(h	PROPN
ejpam-5827	417	39	)	)	PUNCT
ejpam-5827	417	40	≮	≮	VERB
ejpam-5827	417	41	τpκ	τpκ	X
ejpam-5827	417	42	σ(h	σ(h	PROPN
ejpam-5827	417	43	)	)	PUNCT
ejpam-5827	417	44	.	.	PUNCT
ejpam-5827	418	1	example	example	NOUN
ejpam-5827	419	1	6	6	NUM
ejpam-5827	419	2	.	.	PUNCT
ejpam-5827	420	1	let	let	VERB
ejpam-5827	420	2	v	v	VERB
ejpam-5827	420	3	=	=	PUNCT
ejpam-5827	420	4	{	{	PUNCT
ejpam-5827	420	5	a	a	PRON
ejpam-5827	420	6	,	,	PUNCT
ejpam-5827	420	7	b	b	NOUN
ejpam-5827	420	8	,	,	PUNCT
ejpam-5827	420	9	c	c	NOUN
ejpam-5827	420	10	}	}	PUNCT
ejpam-5827	420	11	,	,	PUNCT
ejpam-5827	420	12	and	and	CCONJ
ejpam-5827	420	13	consider	consider	VERB
ejpam-5827	420	14	the	the	DET
ejpam-5827	420	15	primal	primal	ADJ
ejpam-5827	420	16	p	p	X
ejpam-5827	420	17	=	=	X
ejpam-5827	420	18	{	{	PUNCT
ejpam-5827	420	19	∅	∅	NOUN
ejpam-5827	420	20	,	,	PUNCT
ejpam-5827	420	21	{	{	PUNCT
ejpam-5827	420	22	a	a	X
ejpam-5827	420	23	}	}	PUNCT
ejpam-5827	420	24	,	,	PUNCT
ejpam-5827	420	25	{	{	PUNCT
ejpam-5827	420	26	b	b	NOUN
ejpam-5827	420	27	}	}	PUNCT
ejpam-5827	420	28	,	,	PUNCT
ejpam-5827	420	29	{	{	PUNCT
ejpam-5827	420	30	c	c	X
ejpam-5827	420	31	}	}	PUNCT
ejpam-5827	420	32	,	,	PUNCT
ejpam-5827	420	33	{	{	PUNCT
ejpam-5827	420	34	a	a	DET
ejpam-5827	420	35	,	,	PUNCT
ejpam-5827	420	36	b	b	NOUN
ejpam-5827	420	37	}	}	PUNCT
ejpam-5827	420	38	,	,	PUNCT
ejpam-5827	420	39	{	{	PUNCT
ejpam-5827	420	40	a	a	PRON
ejpam-5827	420	41	,	,	PUNCT
ejpam-5827	420	42	c	c	NOUN
ejpam-5827	420	43	}	}	PUNCT
ejpam-5827	420	44	}	}	PUNCT
ejpam-5827	420	45	.	.	PUNCT
ejpam-5827	421	1	if	if	SCONJ
ejpam-5827	421	2	r	r	NOUN
ejpam-5827	421	3	is	be	AUX
ejpam-5827	421	4	a	a	DET
ejpam-5827	421	5	binary	binary	ADJ
ejpam-5827	421	6	relation	relation	NOUN
ejpam-5827	421	7	on	on	ADP
ejpam-5827	421	8	v	v	NOUN
ejpam-5827	421	9	defined	define	VERB
ejpam-5827	421	10	as	as	ADP
ejpam-5827	421	11	r	r	NOUN
ejpam-5827	421	12	=	=	SYM
ejpam-5827	421	13	{	{	PUNCT
ejpam-5827	421	14	(	(	PUNCT
ejpam-5827	421	15	a	a	DET
ejpam-5827	421	16	,	,	PUNCT
ejpam-5827	421	17	b	b	NOUN
ejpam-5827	421	18	)	)	PUNCT
ejpam-5827	421	19	,	,	PUNCT
ejpam-5827	421	20	(	(	PUNCT
ejpam-5827	421	21	a	a	DET
ejpam-5827	421	22	,	,	PUNCT
ejpam-5827	421	23	c	c	NOUN
ejpam-5827	421	24	)	)	PUNCT
ejpam-5827	421	25	,	,	PUNCT
ejpam-5827	421	26	(	(	PUNCT
ejpam-5827	421	27	b	b	X
ejpam-5827	421	28	,	,	PUNCT
ejpam-5827	421	29	b	b	NOUN
ejpam-5827	421	30	)	)	PUNCT
ejpam-5827	421	31	,	,	PUNCT
ejpam-5827	421	32	(	(	PUNCT
ejpam-5827	421	33	b	b	X
ejpam-5827	421	34	,	,	PUNCT
ejpam-5827	421	35	c	c	NOUN
ejpam-5827	421	36	)	)	PUNCT
ejpam-5827	421	37	,	,	PUNCT
ejpam-5827	421	38	(	(	PUNCT
ejpam-5827	421	39	c	c	X
ejpam-5827	421	40	,	,	PUNCT
ejpam-5827	421	41	b	b	NOUN
ejpam-5827	421	42	)	)	PUNCT
ejpam-5827	421	43	}	}	PUNCT
ejpam-5827	421	44	,	,	PUNCT
ejpam-5827	421	45	then	then	ADV
ejpam-5827	421	46	the	the	DET
ejpam-5827	421	47	corresponding	corresponding	ADJ
ejpam-5827	421	48	neighborhoods	neighborhood	NOUN
ejpam-5827	421	49	are	be	AUX
ejpam-5827	421	50	determined	determine	VERB
ejpam-5827	421	51	as	as	SCONJ
ejpam-5827	421	52	follows	follow	VERB
ejpam-5827	421	53	:	:	PUNCT
ejpam-5827	421	54	right	right	ADJ
ejpam-5827	421	55	neighborhoods	neighborhood	NOUN
ejpam-5827	421	56	minimal	minimal	ADJ
ejpam-5827	421	57	neighborhoods	neighborhood	NOUN
ejpam-5827	421	58	maximal	maximal	ADJ
ejpam-5827	421	59	neighborhoods	neighborhood	NOUN
ejpam-5827	421	60	nr(a	nr(a	PUNCT
ejpam-5827	421	61	)	)	PUNCT
ejpam-5827	422	1	=	=	PUNCT
ejpam-5827	422	2	{	{	PUNCT
ejpam-5827	422	3	b	b	NOUN
ejpam-5827	422	4	,	,	PUNCT
ejpam-5827	422	5	c	c	NOUN
ejpam-5827	422	6	}	}	PUNCT
ejpam-5827	422	7	n⟨r⟩(a	n⟨r⟩(a	NUM
ejpam-5827	422	8	)	)	PUNCT
ejpam-5827	422	9	=	=	NOUN
ejpam-5827	422	10	∅	∅	NOUN
ejpam-5827	422	11	nm(a	nm(a	NOUN
ejpam-5827	422	12	)	)	PUNCT
ejpam-5827	422	13	=	=	SYM
ejpam-5827	422	14	∅	∅	NOUN
ejpam-5827	422	15	nr(b	nr(b	NUM
ejpam-5827	422	16	)	)	PUNCT
ejpam-5827	422	17	=	=	SYM
ejpam-5827	422	18	{	{	PUNCT
ejpam-5827	422	19	b	b	NOUN
ejpam-5827	422	20	,	,	PUNCT
ejpam-5827	422	21	c	c	NOUN
ejpam-5827	422	22	}	}	PUNCT
ejpam-5827	422	23	n⟨r⟩(b	n⟨r⟩(b	NUM
ejpam-5827	422	24	)	)	PUNCT
ejpam-5827	422	25	=	=	PRON
ejpam-5827	422	26	{	{	PUNCT
ejpam-5827	422	27	b	b	NOUN
ejpam-5827	422	28	}	}	PUNCT
ejpam-5827	422	29	nm(b	nm(b	NUM
ejpam-5827	422	30	)	)	PUNCT
ejpam-5827	422	31	=	=	PRON
ejpam-5827	422	32	{	{	PUNCT
ejpam-5827	422	33	b	b	NOUN
ejpam-5827	422	34	,	,	PUNCT
ejpam-5827	422	35	c	c	NOUN
ejpam-5827	422	36	}	}	PUNCT
ejpam-5827	422	37	nr(c	nr(c	ADJ
ejpam-5827	422	38	)	)	PUNCT
ejpam-5827	422	39	=	=	PRON
ejpam-5827	422	40	{	{	PUNCT
ejpam-5827	422	41	b	b	NOUN
ejpam-5827	422	42	}	}	PUNCT
ejpam-5827	422	43	n⟨r⟩(c	n⟨r⟩(c	PROPN
ejpam-5827	422	44	)	)	PUNCT
ejpam-5827	422	45	=	=	PRON
ejpam-5827	422	46	{	{	PUNCT
ejpam-5827	422	47	b	b	NOUN
ejpam-5827	422	48	,	,	PUNCT
ejpam-5827	422	49	c	c	NOUN
ejpam-5827	422	50	}	}	PUNCT
ejpam-5827	422	51	nm(c	nm(c	PUNCT
ejpam-5827	422	52	)	)	PUNCT
ejpam-5827	422	53	=	=	PRON
ejpam-5827	422	54	{	{	PUNCT
ejpam-5827	422	55	b	b	NOUN
ejpam-5827	422	56	,	,	PUNCT
ejpam-5827	422	57	c	c	NOUN
ejpam-5827	422	58	}	}	PUNCT
ejpam-5827	422	59	hence	hence	ADV
ejpam-5827	422	60	,	,	PUNCT
ejpam-5827	422	61	table	table	NOUN
ejpam-5827	422	62	1	1	NUM
ejpam-5827	422	63	explains	explain	VERB
ejpam-5827	422	64	comparative	comparative	ADJ
ejpam-5827	422	65	studies	study	NOUN
ejpam-5827	422	66	between	between	ADP
ejpam-5827	422	67	the	the	DET
ejpam-5827	422	68	previous	previous	ADJ
ejpam-5827	422	69	approaches	approach	NOUN
ejpam-5827	422	70	and	and	CCONJ
ejpam-5827	422	71	the	the	DET
ejpam-5827	422	72	proposed	propose	VERB
ejpam-5827	422	73	technique	technique	NOUN
ejpam-5827	422	74	.	.	PUNCT
ejpam-5827	423	1	table	table	NOUN
ejpam-5827	423	2	1	1	NUM
ejpam-5827	423	3	:	:	PUNCT
ejpam-5827	423	4	(	(	PUNCT
ejpam-5827	423	5	comparisons	comparison	NOUN
ejpam-5827	423	6	of	of	ADP
ejpam-5827	423	7	the	the	DET
ejpam-5827	423	8	boundary	boundary	ADJ
ejpam-5827	423	9	regions	region	NOUN
ejpam-5827	423	10	and	and	CCONJ
ejpam-5827	423	11	the	the	DET
ejpam-5827	423	12	accuracy	accuracy	NOUN
ejpam-5827	423	13	measures	measure	NOUN
ejpam-5827	423	14	among	among	ADP
ejpam-5827	423	15	different	different	ADJ
ejpam-5827	423	16	methods	method	NOUN
ejpam-5827	423	17	,	,	PUNCT
ejpam-5827	423	18	whenever	whenever	SCONJ
ejpam-5827	423	19	p	p	NOUN
ejpam-5827	423	20	=	=	PUNCT
ejpam-5827	423	21	{	{	PUNCT
ejpam-5827	423	22	∅	∅	NOUN
ejpam-5827	423	23	,	,	PUNCT
ejpam-5827	423	24	{	{	PUNCT
ejpam-5827	423	25	a	a	X
ejpam-5827	423	26	}	}	PUNCT
ejpam-5827	423	27	,	,	PUNCT
ejpam-5827	423	28	{	{	PUNCT
ejpam-5827	423	29	b	b	NOUN
ejpam-5827	423	30	}	}	PUNCT
ejpam-5827	423	31	,	,	PUNCT
ejpam-5827	423	32	{	{	PUNCT
ejpam-5827	423	33	c	c	X
ejpam-5827	423	34	}	}	PUNCT
ejpam-5827	423	35	,	,	PUNCT
ejpam-5827	423	36	{	{	PUNCT
ejpam-5827	423	37	a	a	DET
ejpam-5827	423	38	,	,	PUNCT
ejpam-5827	423	39	b	b	NOUN
ejpam-5827	423	40	}	}	PUNCT
ejpam-5827	423	41	,	,	PUNCT
ejpam-5827	423	42	{	{	PUNCT
ejpam-5827	423	43	a	a	PRON
ejpam-5827	423	44	,	,	PUNCT
ejpam-5827	423	45	c	c	NOUN
ejpam-5827	423	46	}	}	PUNCT
ejpam-5827	423	47	}	}	PUNCT
ejpam-5827	423	48	yao	yao	NOUN
ejpam-5827	423	49	allam	allam	PROPN
ejpam-5827	423	50	dai	dai	PROPN
ejpam-5827	423	51	abd	abd	PROPN
ejpam-5827	423	52	el	el	PROPN
ejpam-5827	423	53	-	-	PUNCT
ejpam-5827	423	54	monsef	monsef	ADJ
ejpam-5827	423	55	current	current	ADJ
ejpam-5827	423	56	method	method	NOUN
ejpam-5827	423	57	g	g	PROPN
ejpam-5827	423	58	⊆	⊆	NUM
ejpam-5827	423	59	v	v	NOUN
ejpam-5827	423	60	by(g	by(g	NOUN
ejpam-5827	423	61	)	)	PUNCT
ejpam-5827	423	62	σy(g	σy(g	NUM
ejpam-5827	423	63	)	)	PUNCT
ejpam-5827	423	64	ba(g	ba(g	NOUN
ejpam-5827	423	65	)	)	PUNCT
ejpam-5827	423	66	σa(g	σa(g	NOUN
ejpam-5827	423	67	)	)	PUNCT
ejpam-5827	423	68	bd(g	bd(g	NUM
ejpam-5827	423	69	)	)	PUNCT
ejpam-5827	423	70	σd(g	σd(g	NUM
ejpam-5827	423	71	)	)	PUNCT
ejpam-5827	423	72	τκb(g	τκb(g	NUM
ejpam-5827	423	73	)	)	PUNCT
ejpam-5827	423	74	τκσ(g	τκσ(g	NOUN
ejpam-5827	423	75	)	)	PUNCT
ejpam-5827	423	76	τpκ	τpκ	NOUN
ejpam-5827	423	77	b(g	b(g	NOUN
ejpam-5827	423	78	)	)	PUNCT
ejpam-5827	423	79	τpκ	τpκ	NOUN
ejpam-5827	423	80	σ(g	σ(g	NOUN
ejpam-5827	423	81	)	)	PUNCT
ejpam-5827	423	82	{	{	PUNCT
ejpam-5827	423	83	a	a	DET
ejpam-5827	423	84	}	}	PUNCT
ejpam-5827	423	85	∅	∅	NOUN
ejpam-5827	423	86	undef	undef	NOUN
ejpam-5827	423	87	.	.	PUNCT
ejpam-5827	424	1	∅	∅	NOUN
ejpam-5827	424	2	undef	undef	NOUN
ejpam-5827	424	3	.	.	PUNCT
ejpam-5827	425	1	∅	∅	NOUN
ejpam-5827	425	2	undef	undef	NOUN
ejpam-5827	425	3	.	.	PUNCT
ejpam-5827	426	1	{	{	PUNCT
ejpam-5827	426	2	a	a	X
ejpam-5827	426	3	}	}	PUNCT
ejpam-5827	426	4	0	0	NUM
ejpam-5827	426	5	{	{	PUNCT
ejpam-5827	426	6	a	a	NOUN
ejpam-5827	426	7	}	}	PUNCT
ejpam-5827	426	8	0	0	NUM
ejpam-5827	426	9	{	{	PUNCT
ejpam-5827	426	10	b	b	NOUN
ejpam-5827	426	11	}	}	PUNCT
ejpam-5827	426	12	{	{	PUNCT
ejpam-5827	426	13	a	a	PRON
ejpam-5827	426	14	,	,	PUNCT
ejpam-5827	426	15	b	b	NOUN
ejpam-5827	426	16	}	}	PUNCT
ejpam-5827	426	17	1/3	1/3	NUM
ejpam-5827	426	18	{	{	PUNCT
ejpam-5827	426	19	c	c	NOUN
ejpam-5827	426	20	}	}	SYM
ejpam-5827	426	21	1	1	NUM
ejpam-5827	426	22	∅	∅	NOUN
ejpam-5827	426	23	1/2	1/2	NUM
ejpam-5827	426	24	∅	∅	NOUN
ejpam-5827	426	25	0	0	NUM
ejpam-5827	426	26	∅	∅	NOUN
ejpam-5827	426	27	1	1	NUM
ejpam-5827	426	28	{	{	PUNCT
ejpam-5827	426	29	c	c	NOUN
ejpam-5827	426	30	}	}	PUNCT
ejpam-5827	426	31	{	{	PUNCT
ejpam-5827	426	32	a	a	PRON
ejpam-5827	426	33	,	,	PUNCT
ejpam-5827	426	34	b	b	NOUN
ejpam-5827	426	35	}	}	SYM
ejpam-5827	426	36	0	0	NUM
ejpam-5827	426	37	∅	∅	NOUN
ejpam-5827	426	38	1	1	NUM
ejpam-5827	426	39	∅	∅	NOUN
ejpam-5827	426	40	1/2	1/2	NUM
ejpam-5827	426	41	v	v	NOUN
ejpam-5827	426	42	0	0	NUM
ejpam-5827	426	43	∅	∅	NOUN
ejpam-5827	426	44	1	1	NUM
ejpam-5827	426	45	{	{	PUNCT
ejpam-5827	426	46	a	a	DET
ejpam-5827	426	47	,	,	PUNCT
ejpam-5827	426	48	b	b	NOUN
ejpam-5827	426	49	}	}	PUNCT
ejpam-5827	426	50	{	{	PUNCT
ejpam-5827	426	51	a	a	PRON
ejpam-5827	426	52	,	,	PUNCT
ejpam-5827	426	53	b	b	NOUN
ejpam-5827	426	54	}	}	PUNCT
ejpam-5827	426	55	1/3	1/3	NUM
ejpam-5827	426	56	{	{	PUNCT
ejpam-5827	426	57	c	c	NOUN
ejpam-5827	426	58	}	}	SYM
ejpam-5827	426	59	1	1	NUM
ejpam-5827	426	60	{	{	PUNCT
ejpam-5827	426	61	b	b	NOUN
ejpam-5827	426	62	,	,	PUNCT
ejpam-5827	426	63	c	c	NOUN
ejpam-5827	426	64	}	}	PUNCT
ejpam-5827	426	65	1/2	1/2	NUM
ejpam-5827	426	66	∅	∅	NOUN
ejpam-5827	426	67	0	0	NUM
ejpam-5827	426	68	∅	∅	NOUN
ejpam-5827	426	69	1	1	NUM
ejpam-5827	426	70	{	{	PUNCT
ejpam-5827	426	71	a	a	NOUN
ejpam-5827	426	72	,	,	PUNCT
ejpam-5827	426	73	c	c	NOUN
ejpam-5827	426	74	}	}	PUNCT
ejpam-5827	426	75	{	{	PUNCT
ejpam-5827	426	76	a	a	PRON
ejpam-5827	426	77	,	,	PUNCT
ejpam-5827	426	78	b	b	NOUN
ejpam-5827	426	79	}	}	SYM
ejpam-5827	426	80	0	0	NUM
ejpam-5827	426	81	∅	∅	NOUN
ejpam-5827	426	82	1	1	NUM
ejpam-5827	426	83	{	{	PUNCT
ejpam-5827	426	84	b	b	NOUN
ejpam-5827	426	85	,	,	PUNCT
ejpam-5827	426	86	c	c	NOUN
ejpam-5827	426	87	}	}	PUNCT
ejpam-5827	426	88	0.5	0.5	NUM
ejpam-5827	426	89	∅	∅	NOUN
ejpam-5827	426	90	0	0	NUM
ejpam-5827	426	91	∅	∅	NOUN
ejpam-5827	426	92	1	1	NUM
ejpam-5827	426	93	{	{	PUNCT
ejpam-5827	426	94	b	b	NOUN
ejpam-5827	426	95	,	,	PUNCT
ejpam-5827	426	96	c	c	NOUN
ejpam-5827	426	97	}	}	PUNCT
ejpam-5827	426	98	∅	∅	NOUN
ejpam-5827	426	99	1	1	NUM
ejpam-5827	426	100	∅	∅	ADP
ejpam-5827	426	101	1.5	1.5	NUM
ejpam-5827	426	102	{	{	PUNCT
ejpam-5827	426	103	a	a	DET
ejpam-5827	426	104	}	}	PUNCT
ejpam-5827	426	105	3/2	3/2	NUM
ejpam-5827	426	106	{	{	PUNCT
ejpam-5827	426	107	a	a	PRON
ejpam-5827	426	108	}	}	PUNCT
ejpam-5827	426	109	2/3	2/3	NUM
ejpam-5827	426	110	{	{	PUNCT
ejpam-5827	426	111	a	a	PRON
ejpam-5827	426	112	}	}	PUNCT
ejpam-5827	426	113	2/3	2/3	NUM
ejpam-5827	426	114	w	w	PROPN
ejpam-5827	426	115	∅	∅	NOUN
ejpam-5827	426	116	1	1	NUM
ejpam-5827	426	117	∅	∅	NOUN
ejpam-5827	426	118	1.5	1.5	NUM
ejpam-5827	426	119	∅	∅	NOUN
ejpam-5827	426	120	3/2	3/2	NUM
ejpam-5827	426	121	∅	∅	NOUN
ejpam-5827	426	122	1	1	NUM
ejpam-5827	426	123	∅	∅	NOUN
ejpam-5827	426	124	1	1	NUM
ejpam-5827	426	125	∅	∅	NOUN
ejpam-5827	426	126	∅	∅	NOUN
ejpam-5827	426	127	1	1	NUM
ejpam-5827	426	128	∅	∅	NOUN
ejpam-5827	426	129	undef	undef	NOUN
ejpam-5827	426	130	.	.	PUNCT
ejpam-5827	427	1	∅	∅	NOUN
ejpam-5827	427	2	undef	undef	NOUN
ejpam-5827	427	3	.	.	PUNCT
ejpam-5827	428	1	∅	∅	NOUN
ejpam-5827	428	2	1	1	NUM
ejpam-5827	428	3	∅	∅	NOUN
ejpam-5827	428	4	1	1	NUM
ejpam-5827	428	5	note	note	NOUN
ejpam-5827	428	6	:	:	PUNCT
ejpam-5827	428	7	”	"	PUNCT
ejpam-5827	428	8	undef	undef	NOUN
ejpam-5827	428	9	.	.	PUNCT
ejpam-5827	428	10	”	"	PUNCT
ejpam-5827	428	11	refers	refer	VERB
ejpam-5827	428	12	to	to	ADP
ejpam-5827	428	13	”	"	PUNCT
ejpam-5827	428	14	undefined	undefined	ADJ
ejpam-5827	428	15	quantity	quantity	NOUN
ejpam-5827	428	16	”	"	PUNCT
ejpam-5827	428	17	in	in	ADP
ejpam-5827	428	18	table	table	NOUN
ejpam-5827	428	19	1	1	NUM
ejpam-5827	428	20	4	4	NUM
ejpam-5827	428	21	.	.	PUNCT
ejpam-5827	428	22	bi	bi	ADJ
ejpam-5827	428	23	-	-	ADJ
ejpam-5827	428	24	primal	primal	ADJ
ejpam-5827	428	25	approximation	approximation	NOUN
ejpam-5827	428	26	spaces	space	VERB
ejpam-5827	428	27	this	this	DET
ejpam-5827	428	28	section	section	NOUN
ejpam-5827	428	29	introduces	introduce	VERB
ejpam-5827	428	30	a	a	DET
ejpam-5827	428	31	novel	novel	ADJ
ejpam-5827	428	32	type	type	NOUN
ejpam-5827	428	33	of	of	ADP
ejpam-5827	428	34	approximation	approximation	NOUN
ejpam-5827	428	35	space	space	NOUN
ejpam-5827	428	36	referred	refer	VERB
ejpam-5827	428	37	to	to	ADP
ejpam-5827	428	38	as	as	ADP
ejpam-5827	428	39	”	"	PUNCT
ejpam-5827	428	40	bi	bi	ADJ
ejpam-5827	428	41	-	-	ADJ
ejpam-5827	428	42	primal	primal	ADJ
ejpam-5827	428	43	approximation	approximation	NOUN
ejpam-5827	428	44	spaces	space	NOUN
ejpam-5827	428	45	.	.	PUNCT
ejpam-5827	428	46	”	"	PUNCT
ejpam-5827	429	1	these	these	DET
ejpam-5827	429	2	spaces	space	NOUN
ejpam-5827	429	3	are	be	AUX
ejpam-5827	429	4	distinguished	distinguish	VERB
ejpam-5827	429	5	by	by	ADP
ejpam-5827	429	6	the	the	DET
ejpam-5827	429	7	presence	presence	NOUN
ejpam-5827	429	8	of	of	ADP
ejpam-5827	429	9	two	two	NUM
ejpam-5827	429	10	distinct	distinct	ADJ
ejpam-5827	429	11	primal	primal	ADJ
ejpam-5827	429	12	sets	set	NOUN
ejpam-5827	429	13	,	,	PUNCT
ejpam-5827	429	14	each	each	PRON
ejpam-5827	429	15	offering	offer	VERB
ejpam-5827	429	16	a	a	DET
ejpam-5827	429	17	unique	unique	ADJ
ejpam-5827	429	18	framework	framework	NOUN
ejpam-5827	429	19	for	for	ADP
ejpam-5827	429	20	approximating	approximate	VERB
ejpam-5827	429	21	and	and	CCONJ
ejpam-5827	429	22	estimating	estimate	VERB
ejpam-5827	429	23	the	the	DET
ejpam-5827	429	24	properties	property	NOUN
ejpam-5827	429	25	of	of	ADP
ejpam-5827	429	26	sets	set	NOUN
ejpam-5827	429	27	.	.	PUNCT
ejpam-5827	430	1	the	the	DET
ejpam-5827	430	2	integration	integration	NOUN
ejpam-5827	430	3	of	of	ADP
ejpam-5827	430	4	these	these	DET
ejpam-5827	430	5	two	two	NUM
ejpam-5827	430	6	primals	primal	NOUN
ejpam-5827	430	7	allows	allow	VERB
ejpam-5827	430	8	for	for	ADP
ejpam-5827	430	9	multiple	multiple	ADJ
ejpam-5827	430	10	analytical	analytical	ADJ
ejpam-5827	430	11	perspectives	perspective	NOUN
ejpam-5827	430	12	,	,	PUNCT
ejpam-5827	430	13	giving	give	VERB
ejpam-5827	430	14	a	a	DET
ejpam-5827	430	15	more	more	ADV
ejpam-5827	430	16	flexible	flexible	ADJ
ejpam-5827	430	17	and	and	CCONJ
ejpam-5827	430	18	comprehensive	comprehensive	ADJ
ejpam-5827	430	19	approach	approach	NOUN
ejpam-5827	430	20	to	to	ADP
ejpam-5827	430	21	approximation	approximation	NOUN
ejpam-5827	430	22	theory	theory	NOUN
ejpam-5827	430	23	.	.	PUNCT
ejpam-5827	431	1	the	the	DET
ejpam-5827	431	2	importance	importance	NOUN
ejpam-5827	431	3	of	of	ADP
ejpam-5827	431	4	this	this	DET
ejpam-5827	431	5	methodology	methodology	NOUN
ejpam-5827	431	6	lies	lie	VERB
ejpam-5827	431	7	in	in	ADP
ejpam-5827	431	8	its	its	PRON
ejpam-5827	431	9	banking	banking	NOUN
ejpam-5827	431	10	on	on	ADP
ejpam-5827	431	11	primal	primal	ADJ
ejpam-5827	431	12	sets	set	NOUN
ejpam-5827	431	13	,	,	PUNCT
ejpam-5827	431	14	which	which	PRON
ejpam-5827	431	15	serve	serve	VERB
ejpam-5827	431	16	as	as	ADP
ejpam-5827	431	17	essential	essential	PROPN
ejpam-5827	431	18	r.	r.	PROPN
ejpam-5827	431	19	a.	a.	PROPN
ejpam-5827	431	20	hosny	hosny	PROPN
ejpam-5827	431	21	,	,	PUNCT
ejpam-5827	431	22	m.	m.	PROPN
ejpam-5827	431	23	k.	k.	PROPN
ejpam-5827	431	24	el	el	PROPN
ejpam-5827	431	25	-	-	PROPN
ejpam-5827	431	26	bably	bably	ADV
ejpam-5827	431	27	,	,	PUNCT
ejpam-5827	431	28	m.	m.	NOUN
ejpam-5827	431	29	a.	a.	PROPN
ejpam-5827	431	30	el	el	PROPN
ejpam-5827	431	31	-	-	PROPN
ejpam-5827	431	32	gayar	gayar	PROPN
ejpam-5827	431	33	/	/	SYM
ejpam-5827	431	34	eur	eur	PROPN
ejpam-5827	431	35	.	.	PUNCT
ejpam-5827	432	1	j.	j.	PROPN
ejpam-5827	432	2	pure	pure	PROPN
ejpam-5827	432	3	appl	appl	PROPN
ejpam-5827	432	4	.	.	PROPN
ejpam-5827	432	5	math	math	PROPN
ejpam-5827	432	6	,	,	PUNCT
ejpam-5827	432	7	18	18	NUM
ejpam-5827	432	8	(	(	PUNCT
ejpam-5827	432	9	1	1	NUM
ejpam-5827	432	10	)	)	PUNCT
ejpam-5827	432	11	(	(	PUNCT
ejpam-5827	432	12	2025	2025	NUM
ejpam-5827	432	13	)	)	PUNCT
ejpam-5827	432	14	,	,	PUNCT
ejpam-5827	432	15	5827	5827	NUM
ejpam-5827	432	16	17	17	NUM
ejpam-5827	432	17	of	of	ADP
ejpam-5827	432	18	29	29	NUM
ejpam-5827	432	19	topological	topological	ADJ
ejpam-5827	432	20	tools	tool	NOUN
ejpam-5827	432	21	.	.	PUNCT
ejpam-5827	433	1	by	by	ADP
ejpam-5827	433	2	incorporating	incorporate	VERB
ejpam-5827	433	3	two	two	NUM
ejpam-5827	433	4	primals	primal	NOUN
ejpam-5827	433	5	,	,	PUNCT
ejpam-5827	433	6	the	the	DET
ejpam-5827	433	7	framework	framework	NOUN
ejpam-5827	433	8	enriches	enrich	VERB
ejpam-5827	433	9	the	the	DET
ejpam-5827	433	10	analysis	analysis	NOUN
ejpam-5827	433	11	,	,	PUNCT
ejpam-5827	433	12	transcending	transcend	VERB
ejpam-5827	433	13	a	a	DET
ejpam-5827	433	14	singular	singular	ADJ
ejpam-5827	433	15	viewpoint	viewpoint	NOUN
ejpam-5827	433	16	.	.	PUNCT
ejpam-5827	434	1	additionally	additionally	ADV
ejpam-5827	434	2	,	,	PUNCT
ejpam-5827	434	3	the	the	DET
ejpam-5827	434	4	constructed	construct	VERB
ejpam-5827	434	5	approximations	approximation	NOUN
ejpam-5827	434	6	of	of	ADP
ejpam-5827	434	7	two	two	NUM
ejpam-5827	434	8	primals	primal	NOUN
ejpam-5827	434	9	are	be	AUX
ejpam-5827	434	10	more	more	ADV
ejpam-5827	434	11	accurate	accurate	ADJ
ejpam-5827	434	12	than	than	ADP
ejpam-5827	434	13	those	those	PRON
ejpam-5827	434	14	generated	generate	VERB
ejpam-5827	434	15	by	by	ADP
ejpam-5827	434	16	a	a	DET
ejpam-5827	434	17	single	single	ADJ
ejpam-5827	434	18	primal	primal	NOUN
ejpam-5827	434	19	,	,	PUNCT
ejpam-5827	434	20	without	without	ADP
ejpam-5827	434	21	affecting	affect	VERB
ejpam-5827	434	22	the	the	DET
ejpam-5827	434	23	basic	basic	ADJ
ejpam-5827	434	24	properties	property	NOUN
ejpam-5827	434	25	of	of	ADP
ejpam-5827	434	26	these	these	DET
ejpam-5827	434	27	approximations	approximation	NOUN
ejpam-5827	434	28	.	.	PUNCT
ejpam-5827	435	1	a	a	DET
ejpam-5827	435	2	key	key	ADJ
ejpam-5827	435	3	component	component	NOUN
ejpam-5827	435	4	of	of	ADP
ejpam-5827	435	5	this	this	DET
ejpam-5827	435	6	structure	structure	NOUN
ejpam-5827	435	7	is	be	AUX
ejpam-5827	435	8	the	the	DET
ejpam-5827	435	9	primal	primal	ADJ
ejpam-5827	435	10	set	set	NOUN
ejpam-5827	435	11	p	p	X
ejpam-5827	435	12	,	,	PUNCT
ejpam-5827	435	13	where	where	SCONJ
ejpam-5827	435	14	the	the	DET
ejpam-5827	435	15	specific	specific	ADJ
ejpam-5827	435	16	selection	selection	NOUN
ejpam-5827	435	17	of	of	ADP
ejpam-5827	435	18	these	these	DET
ejpam-5827	435	19	primals	primal	NOUN
ejpam-5827	435	20	directly	directly	ADV
ejpam-5827	435	21	influences	influence	VERB
ejpam-5827	435	22	the	the	DET
ejpam-5827	435	23	form	form	NOUN
ejpam-5827	435	24	of	of	ADP
ejpam-5827	435	25	the	the	DET
ejpam-5827	435	26	supra	supra	PROPN
ejpam-5827	435	27	topology	topology	NOUN
ejpam-5827	435	28	.	.	PUNCT
ejpam-5827	436	1	the	the	DET
ejpam-5827	436	2	union	union	NOUN
ejpam-5827	436	3	of	of	ADP
ejpam-5827	436	4	the	the	DET
ejpam-5827	436	5	primal	primal	ADJ
ejpam-5827	436	6	sets	set	NOUN
ejpam-5827	436	7	further	far	ADV
ejpam-5827	436	8	enhances	enhance	VERB
ejpam-5827	436	9	the	the	DET
ejpam-5827	436	10	flexibility	flexibility	NOUN
ejpam-5827	436	11	of	of	ADP
ejpam-5827	436	12	the	the	DET
ejpam-5827	436	13	structure	structure	NOUN
ejpam-5827	436	14	,	,	PUNCT
ejpam-5827	436	15	enabling	enable	VERB
ejpam-5827	436	16	the	the	DET
ejpam-5827	436	17	development	development	NOUN
ejpam-5827	436	18	of	of	ADP
ejpam-5827	436	19	various	various	ADJ
ejpam-5827	436	20	kinds	kind	NOUN
ejpam-5827	436	21	of	of	ADP
ejpam-5827	436	22	supra	supra	NOUN
ejpam-5827	436	23	topologies	topology	NOUN
ejpam-5827	436	24	based	base	VERB
ejpam-5827	436	25	on	on	ADP
ejpam-5827	436	26	the	the	DET
ejpam-5827	436	27	chosen	choose	VERB
ejpam-5827	436	28	primal	primal	NOUN
ejpam-5827	436	29	.	.	PUNCT
ejpam-5827	437	1	definition	definition	NOUN
ejpam-5827	437	2	16	16	NUM
ejpam-5827	437	3	.	.	PUNCT
ejpam-5827	438	1	the	the	PRON
ejpam-5827	438	2	quadrable	quadrable	ADJ
ejpam-5827	438	3	(	(	PUNCT
ejpam-5827	438	4	v	v	NOUN
ejpam-5827	438	5	,	,	PUNCT
ejpam-5827	438	6	r	r	NOUN
ejpam-5827	438	7	,	,	PUNCT
ejpam-5827	438	8	p	p	NOUN
ejpam-5827	438	9	,	,	PUNCT
ejpam-5827	438	10	p̃	p̃	PROPN
ejpam-5827	438	11	)	)	PUNCT
ejpam-5827	438	12	is	be	AUX
ejpam-5827	438	13	called	call	VERB
ejpam-5827	438	14	a	a	DET
ejpam-5827	438	15	bi	bi	ADJ
ejpam-5827	438	16	-	-	ADJ
ejpam-5827	438	17	primal	primal	ADJ
ejpam-5827	438	18	approximation	approximation	NOUN
ejpam-5827	438	19	space	space	NOUN
ejpam-5827	438	20	where	where	SCONJ
ejpam-5827	438	21	r	r	NOUN
ejpam-5827	438	22	is	be	AUX
ejpam-5827	438	23	a	a	DET
ejpam-5827	438	24	binary	binary	ADJ
ejpam-5827	438	25	relation	relation	NOUN
ejpam-5827	438	26	on	on	ADP
ejpam-5827	438	27	v	v	NOUN
ejpam-5827	438	28	,	,	PUNCT
ejpam-5827	438	29	and	and	CCONJ
ejpam-5827	438	30	p	p	X
ejpam-5827	438	31	,	,	PUNCT
ejpam-5827	438	32	p̃	p̃	PROPN
ejpam-5827	438	33	are	be	AUX
ejpam-5827	438	34	two	two	NUM
ejpam-5827	438	35	primals	primal	NOUN
ejpam-5827	438	36	on	on	ADP
ejpam-5827	438	37	v.	v.	CCONJ
ejpam-5827	438	38	theorem	theorem	ADJ
ejpam-5827	438	39	7	7	X
ejpam-5827	438	40	.	.	PUNCT
ejpam-5827	439	1	let	let	VERB
ejpam-5827	439	2	(	(	PUNCT
ejpam-5827	439	3	v	v	NOUN
ejpam-5827	439	4	,	,	PUNCT
ejpam-5827	439	5	r	r	NOUN
ejpam-5827	439	6	,	,	PUNCT
ejpam-5827	439	7	p	p	NOUN
ejpam-5827	439	8	,	,	PUNCT
ejpam-5827	439	9	p̃	p̃	PROPN
ejpam-5827	439	10	)	)	PUNCT
ejpam-5827	439	11	be	be	VERB
ejpam-5827	439	12	a	a	DET
ejpam-5827	439	13	bi	bi	ADJ
ejpam-5827	439	14	-	-	ADJ
ejpam-5827	439	15	primal	primal	ADJ
ejpam-5827	439	16	approximation	approximation	NOUN
ejpam-5827	439	17	space	space	NOUN
ejpam-5827	439	18	.	.	PUNCT
ejpam-5827	440	1	then	then	ADV
ejpam-5827	440	2	,	,	PUNCT
ejpam-5827	440	3	τp∪p̃	τp∪p̃	ADP
ejpam-5827	440	4	κ	κ	NOUN
ejpam-5827	440	5	=	=	PUNCT
ejpam-5827	440	6	τpκ	τpκ	NOUN
ejpam-5827	440	7	∪τ	∪τ	PROPN
ejpam-5827	440	8	p̃κ	p̃κ	NOUN
ejpam-5827	440	9	,	,	PUNCT
ejpam-5827	440	10	∀	∀	X
ejpam-5827	440	11	κ	κ	NOUN
ejpam-5827	440	12	.	.	PUNCT
ejpam-5827	440	13	proof	proof	NOUN
ejpam-5827	440	14	.	.	PUNCT
ejpam-5827	441	1	since	since	SCONJ
ejpam-5827	441	2	p	p	NOUN
ejpam-5827	441	3	⊆	⊆	NUM
ejpam-5827	441	4	p	p	NOUN
ejpam-5827	441	5	∪	∪	ADP
ejpam-5827	441	6	p̃	p̃	PROPN
ejpam-5827	441	7	,	,	PUNCT
ejpam-5827	441	8	and	and	CCONJ
ejpam-5827	441	9	p̃	p̃	PROPN
ejpam-5827	441	10	⊆	⊆	NUM
ejpam-5827	441	11	p	p	NOUN
ejpam-5827	441	12	∪	∪	ADP
ejpam-5827	441	13	p̃	p̃	PROPN
ejpam-5827	441	14	,	,	PUNCT
ejpam-5827	441	15	then	then	ADV
ejpam-5827	441	16	by	by	ADP
ejpam-5827	441	17	proposition	proposition	NOUN
ejpam-5827	441	18	3	3	NUM
ejpam-5827	441	19	τpκ	τpκ	NOUN
ejpam-5827	441	20	∪	∪	ADP
ejpam-5827	441	21	τ	τ	PROPN
ejpam-5827	441	22	p̃κ	p̃κ	NOUN
ejpam-5827	441	23	⊆	⊆	NUM
ejpam-5827	441	24	τp∪p̃	τp∪p̃	ADP
ejpam-5827	441	25	κ	κ	PROPN
ejpam-5827	441	26	.	.	PUNCT
ejpam-5827	442	1	let	let	VERB
ejpam-5827	442	2	h	h	NOUN
ejpam-5827	442	3	∈	∈	PROPN
ejpam-5827	442	4	τp∪p̃	τp∪p̃	ADP
ejpam-5827	442	5	κ	κ	PROPN
ejpam-5827	442	6	.	.	PUNCT
ejpam-5827	443	1	then	then	ADV
ejpam-5827	443	2	nκ(z	nκ(z	NUM
ejpam-5827	443	3	)	)	PUNCT
ejpam-5827	444	1	−	−	PROPN
ejpam-5827	444	2	h	h	PROPN
ejpam-5827	444	3	∈p	∈p	PROPN
ejpam-5827	444	4	∪	∪	ADP
ejpam-5827	444	5	p̃	p̃	PROPN
ejpam-5827	444	6	,	,	PUNCT
ejpam-5827	444	7	∀z	∀z	NOUN
ejpam-5827	444	8	∈h	∈h	NOUN
ejpam-5827	444	9	.	.	PUNCT
ejpam-5827	445	1	hence	hence	ADV
ejpam-5827	445	2	,	,	PUNCT
ejpam-5827	445	3	nκ(z	nκ(z	NUM
ejpam-5827	445	4	)	)	PUNCT
ejpam-5827	445	5	−	−	PROPN
ejpam-5827	445	6	h	h	PROPN
ejpam-5827	445	7	∈p	∈p	PROPN
ejpam-5827	445	8	,	,	PUNCT
ejpam-5827	445	9	∀z	∀z	X
ejpam-5827	445	10	∈h	∈h	NOUN
ejpam-5827	445	11	or	or	CCONJ
ejpam-5827	445	12	nκ(z)−h	nκ(z)−h	NOUN
ejpam-5827	445	13	∈p̃	∈p̃	NOUN
ejpam-5827	445	14	,	,	PUNCT
ejpam-5827	445	15	∀z	∀z	X
ejpam-5827	445	16	∈h	∈h	NOUN
ejpam-5827	445	17	.	.	PUNCT
ejpam-5827	446	1	so	so	ADV
ejpam-5827	446	2	τp∪p̃	τp∪p̃	SCONJ
ejpam-5827	446	3	κ	κ	ADP
ejpam-5827	446	4	⊆	⊆	NUM
ejpam-5827	446	5	τpκ	τpκ	NOUN
ejpam-5827	446	6	∪	∪	NOUN
ejpam-5827	446	7	τ	τ	PROPN
ejpam-5827	446	8	p̃κ	p̃κ	NOUN
ejpam-5827	446	9	.	.	PUNCT
ejpam-5827	447	1	consequently	consequently	ADV
ejpam-5827	447	2	,	,	PUNCT
ejpam-5827	447	3	τp∪p̃	τp∪p̃	ADP
ejpam-5827	447	4	κ	κ	NOUN
ejpam-5827	447	5	=	=	PUNCT
ejpam-5827	447	6	τpκ	τpκ	NOUN
ejpam-5827	447	7	∪	∪	X
ejpam-5827	447	8	τ	τ	PROPN
ejpam-5827	447	9	p̃κ	p̃κ	NOUN
ejpam-5827	447	10	.	.	PUNCT
ejpam-5827	448	1	definition	definition	NOUN
ejpam-5827	448	2	17	17	NUM
ejpam-5827	448	3	.	.	PUNCT
ejpam-5827	449	1	let	let	VERB
ejpam-5827	449	2	τp∪p̃	τp∪p̃	SCONJ
ejpam-5827	449	3	κ	κ	AUX
ejpam-5827	449	4	be	be	AUX
ejpam-5827	449	5	a	a	DET
ejpam-5827	449	6	κ	κ	NOUN
ejpam-5827	449	7	-	-	PUNCT
ejpam-5827	449	8	supra	supra	ADJ
ejpam-5827	449	9	topology	topology	NOUN
ejpam-5827	449	10	generated	generate	VERB
ejpam-5827	449	11	by	by	ADP
ejpam-5827	449	12	κ	κ	ADV
ejpam-5827	449	13	-	-	PUNCT
ejpam-5827	449	14	ns	ns	ADJ
ejpam-5827	449	15	and	and	CCONJ
ejpam-5827	449	16	primals	primal	NOUN
ejpam-5827	449	17	p	p	NOUN
ejpam-5827	449	18	,	,	PUNCT
ejpam-5827	449	19	p̃.	p̃.	NOUN
ejpam-5827	449	20	then	then	ADV
ejpam-5827	449	21	the	the	DET
ejpam-5827	449	22	lower	low	ADJ
ejpam-5827	449	23	and	and	CCONJ
ejpam-5827	449	24	upper	upper	ADJ
ejpam-5827	449	25	approximations	approximation	NOUN
ejpam-5827	449	26	,	,	PUNCT
ejpam-5827	449	27	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	449	28	κ	κ	X
ejpam-5827	449	29	(	(	PUNCT
ejpam-5827	449	30	h	h	NOUN
ejpam-5827	449	31	)	)	PUNCT
ejpam-5827	449	32	,	,	PUNCT
ejpam-5827	449	33	up∪p̃	up∪p̃	VERB
ejpam-5827	449	34	κ	κ	X
ejpam-5827	449	35	(	(	PUNCT
ejpam-5827	449	36	h	h	NOUN
ejpam-5827	449	37	)	)	PUNCT
ejpam-5827	449	38	of	of	ADP
ejpam-5827	449	39	a	a	DET
ejpam-5827	449	40	set	set	ADJ
ejpam-5827	449	41	h	h	NOUN
ejpam-5827	449	42	are	be	AUX
ejpam-5827	449	43	assigned	assign	VERB
ejpam-5827	449	44	respectively	respectively	ADV
ejpam-5827	449	45	for	for	ADP
ejpam-5827	449	46	each	each	DET
ejpam-5827	449	47	κ	κ	NOUN
ejpam-5827	449	48	as	as	ADP
ejpam-5827	449	49	:	:	PUNCT
ejpam-5827	449	50	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	449	51	κ	κ	X
ejpam-5827	449	52	(	(	PUNCT
ejpam-5827	449	53	h	h	NOUN
ejpam-5827	449	54	)	)	PUNCT
ejpam-5827	449	55	=	=	PUNCT
ejpam-5827	450	1	∪{w	∪{w	PROPN
ejpam-5827	450	2	∈τp∪p̃	∈τp∪p̃	NOUN
ejpam-5827	450	3	κ	κ	NOUN
ejpam-5827	450	4	:	:	PUNCT
ejpam-5827	450	5	w	w	PROPN
ejpam-5827	450	6	⊆	⊆	NUM
ejpam-5827	450	7	h	h	NOUN
ejpam-5827	450	8	}	}	PUNCT
ejpam-5827	450	9	,	,	PUNCT
ejpam-5827	450	10	up∪p̃	up∪p̃	VERB
ejpam-5827	450	11	κ	κ	X
ejpam-5827	450	12	(	(	PUNCT
ejpam-5827	450	13	h	h	NOUN
ejpam-5827	450	14	)	)	PUNCT
ejpam-5827	450	15	=	=	PUNCT
ejpam-5827	450	16	∩{f	∩{f	NOUN
ejpam-5827	450	17	∈υp∪p̃	∈υp∪p̃	NOUN
ejpam-5827	450	18	κ	κ	NOUN
ejpam-5827	450	19	:	:	PUNCT
ejpam-5827	450	20	h	h	NOUN
ejpam-5827	450	21	⊆	⊆	NUM
ejpam-5827	450	22	f	f	X
ejpam-5827	450	23	}	}	PUNCT
ejpam-5827	450	24	.	.	PUNCT
ejpam-5827	451	1	using	use	VERB
ejpam-5827	451	2	theorem	theorem	NOUN
ejpam-5827	451	3	7	7	NUM
ejpam-5827	451	4	,	,	PUNCT
ejpam-5827	451	5	definition	definition	NOUN
ejpam-5827	451	6	17	17	NUM
ejpam-5827	451	7	can	can	AUX
ejpam-5827	451	8	be	be	AUX
ejpam-5827	451	9	restated	restate	VERB
ejpam-5827	451	10	as	as	SCONJ
ejpam-5827	451	11	follows	follow	VERB
ejpam-5827	451	12	:	:	PUNCT
ejpam-5827	451	13	definition	definition	NOUN
ejpam-5827	451	14	18	18	NUM
ejpam-5827	451	15	.	.	PUNCT
ejpam-5827	452	1	let	let	AUX
ejpam-5827	452	2	(	(	PUNCT
ejpam-5827	452	3	v	v	NOUN
ejpam-5827	452	4	,	,	PUNCT
ejpam-5827	452	5	r	r	NOUN
ejpam-5827	452	6	,	,	PUNCT
ejpam-5827	452	7	p	p	NOUN
ejpam-5827	452	8	,	,	PUNCT
ejpam-5827	452	9	p̃	p̃	PROPN
ejpam-5827	452	10	)	)	PUNCT
ejpam-5827	452	11	be	be	VERB
ejpam-5827	452	12	a	a	DET
ejpam-5827	452	13	bi	bi	ADJ
ejpam-5827	452	14	-	-	ADJ
ejpam-5827	452	15	primal	primal	ADJ
ejpam-5827	452	16	approximation	approximation	NOUN
ejpam-5827	452	17	space	space	NOUN
ejpam-5827	452	18	.	.	PUNCT
ejpam-5827	453	1	if	if	SCONJ
ejpam-5827	453	2	h	h	PROPN
ejpam-5827	453	3	⊆	⊆	NUM
ejpam-5827	453	4	v	v	NOUN
ejpam-5827	453	5	,	,	PUNCT
ejpam-5827	453	6	then	then	ADV
ejpam-5827	453	7	the	the	DET
ejpam-5827	453	8	lower	low	ADJ
ejpam-5827	453	9	and	and	CCONJ
ejpam-5827	453	10	upper	upper	ADJ
ejpam-5827	453	11	approximations	approximation	NOUN
ejpam-5827	453	12	,	,	PUNCT
ejpam-5827	453	13	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	453	14	κ	κ	X
ejpam-5827	453	15	(	(	PUNCT
ejpam-5827	453	16	h	h	NOUN
ejpam-5827	453	17	)	)	PUNCT
ejpam-5827	453	18	,	,	PUNCT
ejpam-5827	453	19	up∪p̃	up∪p̃	VERB
ejpam-5827	453	20	κ	κ	X
ejpam-5827	453	21	(	(	PUNCT
ejpam-5827	453	22	h	h	NOUN
ejpam-5827	453	23	)	)	PUNCT
ejpam-5827	453	24	are	be	AUX
ejpam-5827	453	25	defined	define	VERB
ejpam-5827	453	26	,	,	PUNCT
ejpam-5827	453	27	respectively	respectively	ADV
ejpam-5827	453	28	,	,	PUNCT
ejpam-5827	453	29	as	as	ADP
ejpam-5827	453	30	:	:	PUNCT
ejpam-5827	453	31	lp∪p̃	lp∪p̃	NOUN
ejpam-5827	453	32	κ	κ	X
ejpam-5827	453	33	(	(	PUNCT
ejpam-5827	453	34	h	h	NOUN
ejpam-5827	453	35	)	)	PUNCT
ejpam-5827	453	36	=	=	SYM
ejpam-5827	453	37	τpκ	τpκ	NOUN
ejpam-5827	453	38	l(h	l(h	PROPN
ejpam-5827	453	39	)	)	PUNCT
ejpam-5827	453	40	∪	∪	ADP
ejpam-5827	453	41	τ	τ	PROPN
ejpam-5827	453	42	p̃κ	p̃κ	PROPN
ejpam-5827	453	43	l(h	l(h	PROPN
ejpam-5827	453	44	)	)	PUNCT
ejpam-5827	453	45	up∪p̃	up∪p̃	NOUN
ejpam-5827	453	46	κ	κ	X
ejpam-5827	453	47	(	(	PUNCT
ejpam-5827	453	48	h	h	NOUN
ejpam-5827	453	49	)	)	PUNCT
ejpam-5827	453	50	=	=	NOUN
ejpam-5827	453	51	τpκ	τpκ	NOUN
ejpam-5827	453	52	u(h	u(h	ADJ
ejpam-5827	453	53	)	)	PUNCT
ejpam-5827	453	54	∩	∩	NOUN
ejpam-5827	453	55	τ	τ	PROPN
ejpam-5827	453	56	p̃κ	p̃κ	X
ejpam-5827	453	57	u(h	u(h	PROPN
ejpam-5827	453	58	)	)	PUNCT
ejpam-5827	453	59	example	example	NOUN
ejpam-5827	454	1	7	7	NUM
ejpam-5827	454	2	.	.	PUNCT
ejpam-5827	455	1	let	let	AUX
ejpam-5827	455	2	r	r	NOUN
ejpam-5827	455	3	=	=	PRON
ejpam-5827	455	4	{	{	PUNCT
ejpam-5827	455	5	(	(	PUNCT
ejpam-5827	455	6	a	a	PRON
ejpam-5827	455	7	,	,	PUNCT
ejpam-5827	455	8	a	a	NOUN
ejpam-5827	455	9	)	)	PUNCT
ejpam-5827	455	10	,	,	PUNCT
ejpam-5827	455	11	(	(	PUNCT
ejpam-5827	455	12	a	a	DET
ejpam-5827	455	13	,	,	PUNCT
ejpam-5827	455	14	b	b	NOUN
ejpam-5827	455	15	)	)	PUNCT
ejpam-5827	455	16	,	,	PUNCT
ejpam-5827	455	17	(	(	PUNCT
ejpam-5827	455	18	a	a	DET
ejpam-5827	455	19	,	,	PUNCT
ejpam-5827	455	20	c	c	NOUN
ejpam-5827	455	21	)	)	PUNCT
ejpam-5827	455	22	,	,	PUNCT
ejpam-5827	455	23	(	(	PUNCT
ejpam-5827	455	24	b	b	X
ejpam-5827	455	25	,	,	PUNCT
ejpam-5827	455	26	c	c	NOUN
ejpam-5827	455	27	)	)	PUNCT
ejpam-5827	455	28	,	,	PUNCT
ejpam-5827	455	29	(	(	PUNCT
ejpam-5827	455	30	c	c	X
ejpam-5827	455	31	,	,	PUNCT
ejpam-5827	455	32	d	d	NOUN
ejpam-5827	455	33	)	)	PUNCT
ejpam-5827	455	34	,	,	PUNCT
ejpam-5827	455	35	(	(	PUNCT
ejpam-5827	455	36	d	d	X
ejpam-5827	455	37	,	,	PUNCT
ejpam-5827	455	38	c	c	NOUN
ejpam-5827	455	39	)	)	PUNCT
ejpam-5827	455	40	}	}	PUNCT
ejpam-5827	455	41	be	be	AUX
ejpam-5827	455	42	an	an	DET
ejpam-5827	455	43	arbitrary	arbitrary	ADJ
ejpam-5827	455	44	relation	relation	NOUN
ejpam-5827	455	45	on	on	ADP
ejpam-5827	455	46	v	v	NOUN
ejpam-5827	455	47	=	=	PUNCT
ejpam-5827	455	48	{	{	PUNCT
ejpam-5827	455	49	a	a	PRON
ejpam-5827	455	50	,	,	PUNCT
ejpam-5827	455	51	b	b	NOUN
ejpam-5827	455	52	,	,	PUNCT
ejpam-5827	455	53	c	c	NOUN
ejpam-5827	455	54	,	,	PUNCT
ejpam-5827	455	55	d	d	NOUN
ejpam-5827	455	56	}	}	PUNCT
ejpam-5827	455	57	.	.	PUNCT
ejpam-5827	456	1	if	if	SCONJ
ejpam-5827	456	2	p	p	NOUN
ejpam-5827	456	3	=	=	PUNCT
ejpam-5827	456	4	{	{	PUNCT
ejpam-5827	456	5	∅	∅	NOUN
ejpam-5827	456	6	,	,	PUNCT
ejpam-5827	456	7	{	{	PUNCT
ejpam-5827	456	8	a	a	X
ejpam-5827	456	9	}	}	PUNCT
ejpam-5827	456	10	,	,	PUNCT
ejpam-5827	456	11	{	{	PUNCT
ejpam-5827	456	12	b	b	NOUN
ejpam-5827	456	13	}	}	PUNCT
ejpam-5827	456	14	,	,	PUNCT
ejpam-5827	456	15	{	{	PUNCT
ejpam-5827	456	16	d	d	X
ejpam-5827	456	17	}	}	PUNCT
ejpam-5827	456	18	,	,	PUNCT
ejpam-5827	456	19	{	{	PUNCT
ejpam-5827	456	20	a	a	DET
ejpam-5827	456	21	,	,	PUNCT
ejpam-5827	456	22	b	b	NOUN
ejpam-5827	456	23	}	}	PUNCT
ejpam-5827	456	24	,	,	PUNCT
ejpam-5827	456	25	{	{	PUNCT
ejpam-5827	456	26	b	b	X
ejpam-5827	456	27	,	,	PUNCT
ejpam-5827	456	28	d	d	NOUN
ejpam-5827	456	29	}	}	PUNCT
ejpam-5827	456	30	,	,	PUNCT
ejpam-5827	456	31	{	{	PUNCT
ejpam-5827	456	32	a	a	DET
ejpam-5827	456	33	,	,	PUNCT
ejpam-5827	456	34	d	d	NOUN
ejpam-5827	456	35	}	}	PUNCT
ejpam-5827	456	36	,	,	PUNCT
ejpam-5827	456	37	{	{	PUNCT
ejpam-5827	456	38	a	a	DET
ejpam-5827	456	39	,	,	PUNCT
ejpam-5827	456	40	b	b	NOUN
ejpam-5827	456	41	,	,	PUNCT
ejpam-5827	456	42	d	d	NOUN
ejpam-5827	456	43	}	}	PUNCT
ejpam-5827	456	44	}	}	PUNCT
ejpam-5827	456	45	,	,	PUNCT
ejpam-5827	456	46	then	then	ADV
ejpam-5827	456	47	τpr	τpr	NOUN
ejpam-5827	456	48	=	=	SYM
ejpam-5827	456	49	{	{	PUNCT
ejpam-5827	456	50	∅,v	∅,v	X
ejpam-5827	456	51	,	,	PUNCT
ejpam-5827	456	52	{	{	PUNCT
ejpam-5827	456	53	c	c	NOUN
ejpam-5827	456	54	}	}	PUNCT
ejpam-5827	456	55	,	,	PUNCT
ejpam-5827	456	56	{	{	PUNCT
ejpam-5827	456	57	a	a	X
ejpam-5827	456	58	,	,	PUNCT
ejpam-5827	456	59	c	c	NOUN
ejpam-5827	456	60	}	}	PUNCT
ejpam-5827	456	61	,	,	PUNCT
ejpam-5827	456	62	{	{	PUNCT
ejpam-5827	456	63	b	b	X
ejpam-5827	456	64	,	,	PUNCT
ejpam-5827	456	65	c	c	NOUN
ejpam-5827	456	66	}	}	PUNCT
ejpam-5827	456	67	,	,	PUNCT
ejpam-5827	456	68	{	{	PUNCT
ejpam-5827	456	69	c	c	X
ejpam-5827	456	70	,	,	PUNCT
ejpam-5827	456	71	d	d	NOUN
ejpam-5827	456	72	}	}	PUNCT
ejpam-5827	456	73	,	,	PUNCT
ejpam-5827	456	74	{	{	PUNCT
ejpam-5827	456	75	a	a	DET
ejpam-5827	456	76	,	,	PUNCT
ejpam-5827	456	77	b	b	NOUN
ejpam-5827	456	78	,	,	PUNCT
ejpam-5827	456	79	c	c	NOUN
ejpam-5827	456	80	}	}	PUNCT
ejpam-5827	456	81	,	,	PUNCT
ejpam-5827	456	82	{	{	PUNCT
ejpam-5827	456	83	a	a	PRON
ejpam-5827	456	84	,	,	PUNCT
ejpam-5827	456	85	c	c	NOUN
ejpam-5827	456	86	,	,	PUNCT
ejpam-5827	456	87	d	d	NOUN
ejpam-5827	456	88	}	}	PUNCT
ejpam-5827	456	89	,	,	PUNCT
ejpam-5827	456	90	{	{	PUNCT
ejpam-5827	456	91	b	b	X
ejpam-5827	456	92	,	,	PUNCT
ejpam-5827	456	93	c	c	NOUN
ejpam-5827	456	94	,	,	PUNCT
ejpam-5827	456	95	d	d	NOUN
ejpam-5827	456	96	}	}	PUNCT
ejpam-5827	456	97	}	}	PUNCT
ejpam-5827	456	98	.	.	PUNCT
ejpam-5827	457	1	if	if	SCONJ
ejpam-5827	457	2	p̃	p̃	PROPN
ejpam-5827	457	3	=	=	SYM
ejpam-5827	457	4	{	{	PUNCT
ejpam-5827	457	5	∅	∅	NOUN
ejpam-5827	457	6	,	,	PUNCT
ejpam-5827	457	7	{	{	PUNCT
ejpam-5827	457	8	a	a	X
ejpam-5827	457	9	}	}	PUNCT
ejpam-5827	457	10	,	,	PUNCT
ejpam-5827	457	11	{	{	PUNCT
ejpam-5827	457	12	b	b	NOUN
ejpam-5827	457	13	}	}	PUNCT
ejpam-5827	457	14	,	,	PUNCT
ejpam-5827	457	15	{	{	PUNCT
ejpam-5827	457	16	c	c	X
ejpam-5827	457	17	}	}	PUNCT
ejpam-5827	457	18	,	,	PUNCT
ejpam-5827	457	19	{	{	PUNCT
ejpam-5827	457	20	a	a	DET
ejpam-5827	457	21	,	,	PUNCT
ejpam-5827	457	22	b	b	NOUN
ejpam-5827	457	23	}	}	PUNCT
ejpam-5827	457	24	,	,	PUNCT
ejpam-5827	457	25	{	{	PUNCT
ejpam-5827	457	26	b	b	X
ejpam-5827	457	27	,	,	PUNCT
ejpam-5827	457	28	c	c	NOUN
ejpam-5827	457	29	}	}	PUNCT
ejpam-5827	457	30	,	,	PUNCT
ejpam-5827	457	31	{	{	PUNCT
ejpam-5827	457	32	a	a	X
ejpam-5827	457	33	,	,	PUNCT
ejpam-5827	457	34	c	c	NOUN
ejpam-5827	457	35	}	}	PUNCT
ejpam-5827	457	36	,	,	PUNCT
ejpam-5827	457	37	{	{	PUNCT
ejpam-5827	457	38	a	a	DET
ejpam-5827	457	39	,	,	PUNCT
ejpam-5827	457	40	b	b	NOUN
ejpam-5827	457	41	,	,	PUNCT
ejpam-5827	457	42	c	c	NOUN
ejpam-5827	457	43	}	}	PUNCT
ejpam-5827	457	44	}	}	PUNCT
ejpam-5827	457	45	,	,	PUNCT
ejpam-5827	457	46	then	then	ADV
ejpam-5827	457	47	τ	τ	PROPN
ejpam-5827	457	48	p̃r	p̃r	NOUN
ejpam-5827	457	49	=	=	PUNCT
ejpam-5827	457	50	{	{	PUNCT
ejpam-5827	457	51	∅,v	∅,v	X
ejpam-5827	457	52	,	,	PUNCT
ejpam-5827	457	53	{	{	PUNCT
ejpam-5827	457	54	a	a	X
ejpam-5827	457	55	}	}	PUNCT
ejpam-5827	457	56	,	,	PUNCT
ejpam-5827	457	57	{	{	PUNCT
ejpam-5827	457	58	b	b	NOUN
ejpam-5827	457	59	}	}	PUNCT
ejpam-5827	457	60	,	,	PUNCT
ejpam-5827	457	61	{	{	PUNCT
ejpam-5827	457	62	d	d	X
ejpam-5827	457	63	}	}	PUNCT
ejpam-5827	457	64	,	,	PUNCT
ejpam-5827	457	65	{	{	PUNCT
ejpam-5827	457	66	a	a	DET
ejpam-5827	457	67	,	,	PUNCT
ejpam-5827	457	68	b	b	NOUN
ejpam-5827	457	69	}	}	PUNCT
ejpam-5827	457	70	,	,	PUNCT
ejpam-5827	457	71	{	{	PUNCT
ejpam-5827	457	72	b	b	X
ejpam-5827	457	73	,	,	PUNCT
ejpam-5827	457	74	d	d	NOUN
ejpam-5827	457	75	}	}	PUNCT
ejpam-5827	457	76	,	,	PUNCT
ejpam-5827	457	77	{	{	PUNCT
ejpam-5827	457	78	a	a	PRON
ejpam-5827	457	79	,	,	PUNCT
ejpam-5827	457	80	d	d	NOUN
ejpam-5827	457	81	}	}	PUNCT
ejpam-5827	457	82	,	,	PUNCT
ejpam-5827	457	83	{	{	PUNCT
ejpam-5827	457	84	a	a	PRON
ejpam-5827	457	85	,	,	PUNCT
ejpam-5827	457	86	b	b	NOUN
ejpam-5827	457	87	,	,	PUNCT
ejpam-5827	457	88	d	d	NOUN
ejpam-5827	457	89	}	}	PUNCT
ejpam-5827	457	90	,	,	PUNCT
ejpam-5827	457	91	{	{	PUNCT
ejpam-5827	457	92	c	c	X
ejpam-5827	457	93	,	,	PUNCT
ejpam-5827	457	94	d	d	NOUN
ejpam-5827	457	95	}	}	PUNCT
ejpam-5827	457	96	,	,	PUNCT
ejpam-5827	457	97	{	{	PUNCT
ejpam-5827	457	98	a	a	PRON
ejpam-5827	457	99	,	,	PUNCT
ejpam-5827	457	100	c	c	NOUN
ejpam-5827	457	101	,	,	PUNCT
ejpam-5827	457	102	d	d	NOUN
ejpam-5827	457	103	}	}	PUNCT
ejpam-5827	457	104	,	,	PUNCT
ejpam-5827	457	105	{	{	PUNCT
ejpam-5827	457	106	b	b	X
ejpam-5827	457	107	,	,	PUNCT
ejpam-5827	457	108	c	c	NOUN
ejpam-5827	457	109	,	,	PUNCT
ejpam-5827	457	110	d	d	NOUN
ejpam-5827	457	111	}	}	PUNCT
ejpam-5827	457	112	}	}	PUNCT
ejpam-5827	457	113	.	.	PUNCT
ejpam-5827	458	1	r.	r.	PROPN
ejpam-5827	458	2	a.	a.	PROPN
ejpam-5827	458	3	hosny	hosny	PROPN
ejpam-5827	458	4	,	,	PUNCT
ejpam-5827	458	5	m.	m.	PROPN
ejpam-5827	458	6	k.	k.	PROPN
ejpam-5827	459	1	el	el	PROPN
ejpam-5827	459	2	-	-	PROPN
ejpam-5827	459	3	bably	bably	ADV
ejpam-5827	459	4	,	,	PUNCT
ejpam-5827	459	5	m.	m.	NOUN
ejpam-5827	459	6	a.	a.	PROPN
ejpam-5827	459	7	el	el	PROPN
ejpam-5827	459	8	-	-	PROPN
ejpam-5827	459	9	gayar	gayar	PROPN
ejpam-5827	459	10	/	/	SYM
ejpam-5827	459	11	eur	eur	PROPN
ejpam-5827	459	12	.	.	PUNCT
ejpam-5827	460	1	j.	j.	PROPN
ejpam-5827	460	2	pure	pure	PROPN
ejpam-5827	460	3	appl	appl	PROPN
ejpam-5827	460	4	.	.	PROPN
ejpam-5827	460	5	math	math	PROPN
ejpam-5827	460	6	,	,	PUNCT
ejpam-5827	460	7	18	18	NUM
ejpam-5827	460	8	(	(	PUNCT
ejpam-5827	460	9	1	1	NUM
ejpam-5827	460	10	)	)	PUNCT
ejpam-5827	460	11	(	(	PUNCT
ejpam-5827	460	12	2025	2025	NUM
ejpam-5827	460	13	)	)	PUNCT
ejpam-5827	460	14	,	,	PUNCT
ejpam-5827	460	15	5827	5827	NUM
ejpam-5827	460	16	18	18	NUM
ejpam-5827	460	17	of	of	ADP
ejpam-5827	460	18	29	29	NUM
ejpam-5827	460	19	if	if	SCONJ
ejpam-5827	460	20	p	p	NOUN
ejpam-5827	460	21	∪	∪	VERB
ejpam-5827	460	22	p̃	p̃	PROPN
ejpam-5827	460	23	=	=	SYM
ejpam-5827	460	24	2v	2v	PROPN
ejpam-5827	460	25	\	\	PROPN
ejpam-5827	460	26	{	{	PUNCT
ejpam-5827	460	27	v	v	NOUN
ejpam-5827	460	28	,	,	PUNCT
ejpam-5827	460	29	{	{	PUNCT
ejpam-5827	460	30	a	a	PRON
ejpam-5827	460	31	,	,	PUNCT
ejpam-5827	460	32	c	c	NOUN
ejpam-5827	460	33	,	,	PUNCT
ejpam-5827	460	34	d	d	NOUN
ejpam-5827	460	35	}	}	PUNCT
ejpam-5827	460	36	,	,	PUNCT
ejpam-5827	460	37	{	{	PUNCT
ejpam-5827	460	38	b	b	X
ejpam-5827	460	39	,	,	PUNCT
ejpam-5827	460	40	c	c	NOUN
ejpam-5827	460	41	,	,	PUNCT
ejpam-5827	460	42	d	d	NOUN
ejpam-5827	460	43	}	}	PUNCT
ejpam-5827	460	44	,	,	PUNCT
ejpam-5827	460	45	{	{	PUNCT
ejpam-5827	460	46	c	c	X
ejpam-5827	460	47	,	,	PUNCT
ejpam-5827	460	48	d	d	NOUN
ejpam-5827	460	49	}	}	PUNCT
ejpam-5827	460	50	}	}	PUNCT
ejpam-5827	460	51	,	,	PUNCT
ejpam-5827	460	52	then	then	ADV
ejpam-5827	460	53	τp∪p̃	τp∪p̃	ADP
ejpam-5827	460	54	r	r	NOUN
ejpam-5827	460	55	=	=	SYM
ejpam-5827	460	56	2v	2v	PROPN
ejpam-5827	460	57	.	.	PUNCT
ejpam-5827	461	1	remark	remark	PROPN
ejpam-5827	461	2	14	14	NUM
ejpam-5827	461	3	.	.	PUNCT
ejpam-5827	462	1	the	the	DET
ejpam-5827	462	2	present	present	ADJ
ejpam-5827	462	3	operators	operator	NOUN
ejpam-5827	462	4	introduced	introduce	VERB
ejpam-5827	462	5	in	in	ADP
ejpam-5827	462	6	definition	definition	NOUN
ejpam-5827	462	7	18	18	NUM
ejpam-5827	462	8	can	can	AUX
ejpam-5827	462	9	be	be	AUX
ejpam-5827	462	10	viewed	view	VERB
ejpam-5827	462	11	as	as	ADP
ejpam-5827	462	12	a	a	DET
ejpam-5827	462	13	real	real	ADJ
ejpam-5827	462	14	generalization	generalization	NOUN
ejpam-5827	462	15	of	of	ADP
ejpam-5827	462	16	the	the	DET
ejpam-5827	462	17	operators	operator	NOUN
ejpam-5827	462	18	offered	offer	VERB
ejpam-5827	462	19	in	in	ADP
ejpam-5827	462	20	definition	definition	NOUN
ejpam-5827	462	21	14	14	NUM
ejpam-5827	462	22	.	.	PUNCT
ejpam-5827	463	1	because	because	SCONJ
ejpam-5827	463	2	the	the	DET
ejpam-5827	463	3	two	two	NUM
ejpam-5827	463	4	definitions	definition	NOUN
ejpam-5827	463	5	are	be	AUX
ejpam-5827	463	6	coincide	coincide	ADJ
ejpam-5827	463	7	,	,	PUNCT
ejpam-5827	463	8	if	if	SCONJ
ejpam-5827	463	9	one	one	NUM
ejpam-5827	463	10	of	of	ADP
ejpam-5827	463	11	the	the	DET
ejpam-5827	463	12	following	follow	VERB
ejpam-5827	463	13	conditions	condition	NOUN
ejpam-5827	463	14	is	be	AUX
ejpam-5827	463	15	held	hold	VERB
ejpam-5827	463	16	:	:	PUNCT
ejpam-5827	463	17	(	(	PUNCT
ejpam-5827	463	18	i	i	NOUN
ejpam-5827	463	19	)	)	PUNCT
ejpam-5827	464	1	p	p	X
ejpam-5827	464	2	⊆	⊆	NUM
ejpam-5827	464	3	p̃	p̃	PROPN
ejpam-5827	464	4	or	or	CCONJ
ejpam-5827	464	5	p	p	NOUN
ejpam-5827	464	6	⊇	⊇	ADJ
ejpam-5827	464	7	p̃.	p̃.	PROPN
ejpam-5827	464	8	(	(	PUNCT
ejpam-5827	464	9	ii	ii	NOUN
ejpam-5827	464	10	)	)	PUNCT
ejpam-5827	464	11	p	p	NOUN
ejpam-5827	464	12	⊆	⊆	NUM
ejpam-5827	464	13	p̃	p̃	PROPN
ejpam-5827	464	14	and	and	CCONJ
ejpam-5827	464	15	p	p	NOUN
ejpam-5827	464	16	⊇	⊇	PROPN
ejpam-5827	464	17	p̃	p̃	PROPN
ejpam-5827	464	18	i.e	i.e	PRON
ejpam-5827	464	19	p	p	X
ejpam-5827	464	20	=	=	NOUN
ejpam-5827	464	21	p̃.	p̃.	NOUN
ejpam-5827	464	22	if	if	SCONJ
ejpam-5827	464	23	τpκ	τpκ	NOUN
ejpam-5827	464	24	l(h	l(h	PROPN
ejpam-5827	464	25	)	)	PUNCT
ejpam-5827	464	26	(	(	PUNCT
ejpam-5827	464	27	resp	resp	NOUN
ejpam-5827	464	28	.	.	PUNCT
ejpam-5827	464	29	τpκ	τpκ	PROPN
ejpam-5827	464	30	u(h	u(h	PROPN
ejpam-5827	464	31	)	)	PUNCT
ejpam-5827	464	32	)	)	PUNCT
ejpam-5827	464	33	and	and	CCONJ
ejpam-5827	464	34	τ	τ	PROPN
ejpam-5827	464	35	p̃κ	p̃κ	NOUN
ejpam-5827	464	36	l(h	l(h	PROPN
ejpam-5827	464	37	)	)	PUNCT
ejpam-5827	464	38	(	(	PUNCT
ejpam-5827	464	39	resp	resp	NOUN
ejpam-5827	464	40	.	.	PUNCT
ejpam-5827	465	1	τ	τ	PROPN
ejpam-5827	465	2	p̃κ	p̃κ	NOUN
ejpam-5827	465	3	u(h	u(h	PROPN
ejpam-5827	465	4	)	)	PUNCT
ejpam-5827	465	5	)	)	PUNCT
ejpam-5827	465	6	preserve	preserve	VERB
ejpam-5827	465	7	certain	certain	ADJ
ejpam-5827	465	8	structural	structural	ADJ
ejpam-5827	465	9	properties	property	NOUN
ejpam-5827	465	10	of	of	ADP
ejpam-5827	465	11	h	h	NOUN
ejpam-5827	465	12	(	(	PUNCT
ejpam-5827	465	13	see	see	VERB
ejpam-5827	465	14	proposition	proposition	NOUN
ejpam-5827	465	15	6	6	NUM
ejpam-5827	465	16	)	)	PUNCT
ejpam-5827	465	17	,	,	PUNCT
ejpam-5827	465	18	then	then	ADV
ejpam-5827	465	19	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	465	20	κ	κ	PROPN
ejpam-5827	465	21	(	(	PUNCT
ejpam-5827	465	22	h	h	NOUN
ejpam-5827	465	23	)	)	PUNCT
ejpam-5827	465	24	(	(	PUNCT
ejpam-5827	465	25	resp	resp	NOUN
ejpam-5827	465	26	.	.	PUNCT
ejpam-5827	466	1	up∪p̃	up∪p̃	NOUN
ejpam-5827	466	2	κ	κ	X
ejpam-5827	466	3	(	(	PUNCT
ejpam-5827	466	4	h	h	NOUN
ejpam-5827	466	5	)	)	PUNCT
ejpam-5827	466	6	)	)	PUNCT
ejpam-5827	466	7	might	might	AUX
ejpam-5827	466	8	retain	retain	VERB
ejpam-5827	466	9	those	those	DET
ejpam-5827	466	10	properties	property	NOUN
ejpam-5827	466	11	.	.	PUNCT
ejpam-5827	467	1	according	accord	VERB
ejpam-5827	467	2	to	to	ADP
ejpam-5827	467	3	definition	definition	NOUN
ejpam-5827	467	4	18	18	NUM
ejpam-5827	467	5	and	and	CCONJ
ejpam-5827	467	6	proposition	proposition	NOUN
ejpam-5827	467	7	6	6	NUM
ejpam-5827	467	8	,	,	PUNCT
ejpam-5827	467	9	the	the	DET
ejpam-5827	467	10	proof	proof	NOUN
ejpam-5827	467	11	of	of	ADP
ejpam-5827	467	12	the	the	DET
ejpam-5827	467	13	next	next	ADJ
ejpam-5827	467	14	proposition	proposition	NOUN
ejpam-5827	467	15	is	be	AUX
ejpam-5827	467	16	simple	simple	ADJ
ejpam-5827	467	17	.	.	PUNCT
ejpam-5827	468	1	proposition	proposition	NOUN
ejpam-5827	468	2	9	9	NUM
ejpam-5827	468	3	.	.	PUNCT
ejpam-5827	469	1	let	let	AUX
ejpam-5827	469	2	(	(	PUNCT
ejpam-5827	469	3	v	v	NOUN
ejpam-5827	469	4	,	,	PUNCT
ejpam-5827	469	5	r	r	NOUN
ejpam-5827	469	6	,	,	PUNCT
ejpam-5827	469	7	p	p	NOUN
ejpam-5827	469	8	,	,	PUNCT
ejpam-5827	469	9	p̃	p̃	PROPN
ejpam-5827	469	10	)	)	PUNCT
ejpam-5827	469	11	be	be	VERB
ejpam-5827	469	12	a	a	DET
ejpam-5827	469	13	bi	bi	ADJ
ejpam-5827	469	14	-	-	ADJ
ejpam-5827	469	15	primal	primal	ADJ
ejpam-5827	469	16	approximation	approximation	NOUN
ejpam-5827	469	17	space	space	NOUN
ejpam-5827	469	18	.	.	PUNCT
ejpam-5827	470	1	if	if	SCONJ
ejpam-5827	470	2	h	h	NOUN
ejpam-5827	470	3	,	,	PUNCT
ejpam-5827	470	4	h́	h́	PROPN
ejpam-5827	470	5	are	be	AUX
ejpam-5827	470	6	subsets	subset	NOUN
ejpam-5827	470	7	of	of	ADP
ejpam-5827	470	8	v	v	NOUN
ejpam-5827	470	9	,	,	PUNCT
ejpam-5827	470	10	then	then	ADV
ejpam-5827	470	11	the	the	DET
ejpam-5827	470	12	following	follow	VERB
ejpam-5827	470	13	properties	property	NOUN
ejpam-5827	470	14	hold	hold	VERB
ejpam-5827	470	15	:	:	PUNCT
ejpam-5827	470	16	(	(	PUNCT
ejpam-5827	470	17	l1	l1	PROPN
ejpam-5827	470	18	)	)	PUNCT
ejpam-5827	470	19	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	470	20	κ	κ	X
ejpam-5827	470	21	(	(	PUNCT
ejpam-5827	470	22	h	h	NOUN
ejpam-5827	470	23	)	)	PUNCT
ejpam-5827	470	24	⊆	⊆	NUM
ejpam-5827	470	25	h	h	NOUN
ejpam-5827	470	26	(	(	PUNCT
ejpam-5827	470	27	u1	u1	NOUN
ejpam-5827	470	28	)	)	PUNCT
ejpam-5827	470	29	h	h	NOUN
ejpam-5827	471	1	⊆	⊆	NUM
ejpam-5827	471	2	up∪p̃	up∪p̃	NOUN
ejpam-5827	471	3	κ	κ	X
ejpam-5827	471	4	(	(	PUNCT
ejpam-5827	471	5	h	h	NOUN
ejpam-5827	471	6	)	)	PUNCT
ejpam-5827	471	7	(	(	PUNCT
ejpam-5827	471	8	l2	l2	NOUN
ejpam-5827	471	9	)	)	PUNCT
ejpam-5827	471	10	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	471	11	κ	κ	X
ejpam-5827	471	12	(	(	PUNCT
ejpam-5827	471	13	∅	∅	NOUN
ejpam-5827	471	14	)	)	PUNCT
ejpam-5827	471	15	=	=	NOUN
ejpam-5827	471	16	∅	∅	NOUN
ejpam-5827	471	17	(	(	PUNCT
ejpam-5827	471	18	u2	u2	NOUN
ejpam-5827	471	19	)	)	PUNCT
ejpam-5827	471	20	up∪p̃	up∪p̃	NOUN
ejpam-5827	471	21	κ	κ	X
ejpam-5827	471	22	(	(	PUNCT
ejpam-5827	471	23	∅	∅	NOUN
ejpam-5827	471	24	)	)	PUNCT
ejpam-5827	471	25	=	=	NOUN
ejpam-5827	471	26	∅	∅	NOUN
ejpam-5827	471	27	(	(	PUNCT
ejpam-5827	471	28	l3	l3	PROPN
ejpam-5827	471	29	)	)	PUNCT
ejpam-5827	471	30	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	471	31	κ	κ	X
ejpam-5827	471	32	(	(	PUNCT
ejpam-5827	471	33	v	v	NOUN
ejpam-5827	471	34	)	)	PUNCT
ejpam-5827	471	35	=	=	SYM
ejpam-5827	471	36	v	v	X
ejpam-5827	471	37	(	(	PUNCT
ejpam-5827	471	38	u3	u3	NOUN
ejpam-5827	471	39	)	)	PUNCT
ejpam-5827	471	40	up∪p̃	up∪p̃	NOUN
ejpam-5827	471	41	κ	κ	X
ejpam-5827	471	42	(	(	PUNCT
ejpam-5827	471	43	v	v	NOUN
ejpam-5827	471	44	)	)	PUNCT
ejpam-5827	471	45	=	=	SYM
ejpam-5827	471	46	v	v	X
ejpam-5827	471	47	(	(	PUNCT
ejpam-5827	471	48	l4	l4	PROPN
ejpam-5827	471	49	)	)	PUNCT
ejpam-5827	471	50	if	if	SCONJ
ejpam-5827	471	51	h	h	PROPN
ejpam-5827	471	52	⊆	⊆	NUM
ejpam-5827	471	53	h́	h́	NOUN
ejpam-5827	471	54	,	,	PUNCT
ejpam-5827	471	55	then	then	ADV
ejpam-5827	471	56	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	471	57	κ	κ	PROPN
ejpam-5827	471	58	(	(	PUNCT
ejpam-5827	471	59	h	h	NOUN
ejpam-5827	471	60	)	)	PUNCT
ejpam-5827	471	61	⊆	⊆	NUM
ejpam-5827	471	62	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	471	63	κ	κ	X
ejpam-5827	471	64	(	(	PUNCT
ejpam-5827	471	65	h́	h́	NOUN
ejpam-5827	471	66	)	)	PUNCT
ejpam-5827	471	67	(	(	PUNCT
ejpam-5827	471	68	u4	u4	PROPN
ejpam-5827	471	69	)	)	PUNCT
ejpam-5827	471	70	if	if	SCONJ
ejpam-5827	471	71	h	h	PROPN
ejpam-5827	471	72	⊆	⊆	NUM
ejpam-5827	471	73	h́	h́	NOUN
ejpam-5827	471	74	,	,	PUNCT
ejpam-5827	471	75	then	then	ADV
ejpam-5827	471	76	up∪p̃	up∪p̃	VERB
ejpam-5827	471	77	κ	κ	X
ejpam-5827	471	78	(	(	PUNCT
ejpam-5827	471	79	h	h	NOUN
ejpam-5827	471	80	)	)	PUNCT
ejpam-5827	471	81	⊆	⊆	NUM
ejpam-5827	471	82	up∪p̃	up∪p̃	NOUN
ejpam-5827	471	83	κ	κ	X
ejpam-5827	471	84	(	(	PUNCT
ejpam-5827	471	85	h́	h́	NOUN
ejpam-5827	471	86	)	)	PUNCT
ejpam-5827	471	87	(	(	PUNCT
ejpam-5827	471	88	l5	l5	PROPN
ejpam-5827	471	89	)	)	PUNCT
ejpam-5827	471	90	lp∪p̃	lp∪p̃	NOUN
ejpam-5827	471	91	κ	κ	X
ejpam-5827	471	92	(	(	PUNCT
ejpam-5827	471	93	h	h	PROPN
ejpam-5827	471	94	∩	∩	ADJ
ejpam-5827	471	95	h́	h́	PROPN
ejpam-5827	471	96	)	)	PUNCT
ejpam-5827	471	97	⊆	⊆	NUM
ejpam-5827	471	98	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	471	99	κ	κ	X
ejpam-5827	471	100	(	(	PUNCT
ejpam-5827	471	101	h	h	NOUN
ejpam-5827	471	102	)	)	PUNCT
ejpam-5827	471	103	∩	∩	PROPN
ejpam-5827	471	104	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	471	105	κ	κ	X
ejpam-5827	471	106	(	(	PUNCT
ejpam-5827	471	107	h́	h́	NOUN
ejpam-5827	471	108	)	)	PUNCT
ejpam-5827	471	109	(	(	PUNCT
ejpam-5827	471	110	u5	u5	NOUN
ejpam-5827	471	111	)	)	PUNCT
ejpam-5827	471	112	up∪p̃	up∪p̃	NOUN
ejpam-5827	471	113	κ	κ	X
ejpam-5827	471	114	(	(	PUNCT
ejpam-5827	471	115	h	h	PROPN
ejpam-5827	471	116	∩	∩	ADJ
ejpam-5827	471	117	h́	h́	NOUN
ejpam-5827	471	118	)	)	PUNCT
ejpam-5827	471	119	⊆	⊆	NUM
ejpam-5827	471	120	up∪p̃	up∪p̃	NOUN
ejpam-5827	471	121	κ	κ	X
ejpam-5827	471	122	(	(	PUNCT
ejpam-5827	471	123	h	h	NOUN
ejpam-5827	471	124	)	)	PUNCT
ejpam-5827	471	125	∩	∩	ADJ
ejpam-5827	471	126	up∪p̃	up∪p̃	X
ejpam-5827	471	127	κ	κ	X
ejpam-5827	471	128	(	(	PUNCT
ejpam-5827	471	129	h́	h́	NOUN
ejpam-5827	471	130	)	)	PUNCT
ejpam-5827	471	131	(	(	PUNCT
ejpam-5827	471	132	l6	l6	PROPN
ejpam-5827	471	133	)	)	PUNCT
ejpam-5827	471	134	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	471	135	κ	κ	X
ejpam-5827	471	136	(	(	PUNCT
ejpam-5827	471	137	h	h	PROPN
ejpam-5827	471	138	∪	∪	ADP
ejpam-5827	471	139	h́	h́	PROPN
ejpam-5827	471	140	)	)	PUNCT
ejpam-5827	471	141	⊇	⊇	PROPN
ejpam-5827	471	142	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	471	143	κ	κ	PROPN
ejpam-5827	471	144	(	(	PUNCT
ejpam-5827	471	145	h	h	NOUN
ejpam-5827	471	146	)	)	PUNCT
ejpam-5827	471	147	∪	∪	ADP
ejpam-5827	471	148	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	471	149	κ	κ	PROPN
ejpam-5827	471	150	(	(	PUNCT
ejpam-5827	471	151	h́	h́	NOUN
ejpam-5827	471	152	)	)	PUNCT
ejpam-5827	471	153	(	(	PUNCT
ejpam-5827	471	154	u6	u6	NOUN
ejpam-5827	471	155	)	)	PUNCT
ejpam-5827	471	156	up∪p̃	up∪p̃	NOUN
ejpam-5827	471	157	κ	κ	X
ejpam-5827	471	158	(	(	PUNCT
ejpam-5827	471	159	h	h	PROPN
ejpam-5827	471	160	∪	∪	ADP
ejpam-5827	471	161	h́	h́	PROPN
ejpam-5827	471	162	)	)	PUNCT
ejpam-5827	471	163	⊇	⊇	PROPN
ejpam-5827	471	164	up∪p̃	up∪p̃	PROPN
ejpam-5827	471	165	κ	κ	X
ejpam-5827	471	166	(	(	PUNCT
ejpam-5827	471	167	h	h	NOUN
ejpam-5827	471	168	)	)	PUNCT
ejpam-5827	471	169	∪	∪	ADP
ejpam-5827	471	170	up∪p̃	up∪p̃	NOUN
ejpam-5827	471	171	κ	κ	X
ejpam-5827	471	172	(	(	PUNCT
ejpam-5827	471	173	h́	h́	NOUN
ejpam-5827	471	174	)	)	PUNCT
ejpam-5827	471	175	(	(	PUNCT
ejpam-5827	471	176	l7	l7	PROPN
ejpam-5827	471	177	)	)	PUNCT
ejpam-5827	471	178	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	471	179	κ	κ	X
ejpam-5827	471	180	(	(	PUNCT
ejpam-5827	471	181	h	h	NOUN
ejpam-5827	471	182	)	)	PUNCT
ejpam-5827	471	183	=	=	NOUN
ejpam-5827	472	1	[	[	X
ejpam-5827	472	2	up∪p̃	up∪p̃	X
ejpam-5827	472	3	κ	κ	X
ejpam-5827	472	4	(	(	PUNCT
ejpam-5827	472	5	hc)]c	hc)]c	PROPN
ejpam-5827	472	6	(	(	PUNCT
ejpam-5827	472	7	u7	u7	PROPN
ejpam-5827	472	8	)	)	PUNCT
ejpam-5827	472	9	up∪p̃	up∪p̃	PROPN
ejpam-5827	472	10	κ	κ	X
ejpam-5827	472	11	(	(	PUNCT
ejpam-5827	472	12	h	h	NOUN
ejpam-5827	472	13	)	)	PUNCT
ejpam-5827	472	14	=	=	PUNCT
ejpam-5827	473	1	[	[	X
ejpam-5827	473	2	lp∪p̃	lp∪p̃	NOUN
ejpam-5827	473	3	κ	κ	X
ejpam-5827	473	4	(	(	PUNCT
ejpam-5827	473	5	hc)]c	hc)]c	PROPN
ejpam-5827	473	6	(	(	PUNCT
ejpam-5827	473	7	l8	l8	PROPN
ejpam-5827	473	8	)	)	PUNCT
ejpam-5827	473	9	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	473	10	κ	κ	X
ejpam-5827	473	11	(	(	PUNCT
ejpam-5827	473	12	lp∪p̃	lp∪p̃	NOUN
ejpam-5827	473	13	κ	κ	X
ejpam-5827	473	14	(	(	PUNCT
ejpam-5827	473	15	h	h	NOUN
ejpam-5827	473	16	)	)	PUNCT
ejpam-5827	473	17	)	)	PUNCT
ejpam-5827	474	1	⊆	⊆	NUM
ejpam-5827	474	2	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	474	3	κ	κ	X
ejpam-5827	474	4	(	(	PUNCT
ejpam-5827	474	5	h	h	NOUN
ejpam-5827	474	6	)	)	PUNCT
ejpam-5827	474	7	(	(	PUNCT
ejpam-5827	474	8	u8	u8	PROPN
ejpam-5827	474	9	)	)	PUNCT
ejpam-5827	474	10	up∪p̃	up∪p̃	NOUN
ejpam-5827	474	11	κ	κ	X
ejpam-5827	474	12	(	(	PUNCT
ejpam-5827	474	13	up∪p̃	up∪p̃	NOUN
ejpam-5827	474	14	κ	κ	X
ejpam-5827	474	15	(	(	PUNCT
ejpam-5827	474	16	h	h	NOUN
ejpam-5827	474	17	)	)	PUNCT
ejpam-5827	474	18	)	)	PUNCT
ejpam-5827	475	1	⊇	⊇	PROPN
ejpam-5827	475	2	up∪p̃	up∪p̃	PROPN
ejpam-5827	475	3	κ	κ	X
ejpam-5827	475	4	(	(	PUNCT
ejpam-5827	475	5	h	h	NOUN
ejpam-5827	475	6	)	)	PUNCT
ejpam-5827	475	7	.	.	PUNCT
ejpam-5827	476	1	remark	remark	PROPN
ejpam-5827	476	2	15	15	NUM
ejpam-5827	476	3	.	.	PUNCT
ejpam-5827	476	4	example	example	NOUN
ejpam-5827	477	1	5	5	NUM
ejpam-5827	477	2	demonstrates	demonstrate	VERB
ejpam-5827	477	3	that	that	SCONJ
ejpam-5827	477	4	the	the	DET
ejpam-5827	477	5	converse	converse	NOUN
ejpam-5827	477	6	of	of	ADP
ejpam-5827	477	7	(	(	PUNCT
ejpam-5827	477	8	l1	l1	PROPN
ejpam-5827	477	9	)	)	PUNCT
ejpam-5827	477	10	,	,	PUNCT
ejpam-5827	477	11	(	(	PUNCT
ejpam-5827	477	12	l4	l4	PROPN
ejpam-5827	477	13	)	)	PUNCT
ejpam-5827	477	14	,	,	PUNCT
ejpam-5827	477	15	(	(	PUNCT
ejpam-5827	477	16	l5	l5	PROPN
ejpam-5827	477	17	)	)	PUNCT
ejpam-5827	477	18	,	,	PUNCT
ejpam-5827	477	19	(	(	PUNCT
ejpam-5827	477	20	l6	l6	PROPN
ejpam-5827	477	21	)	)	PUNCT
ejpam-5827	477	22	(	(	PUNCT
ejpam-5827	477	23	resp	resp	NOUN
ejpam-5827	477	24	.	.	PUNCT
ejpam-5827	478	1	(	(	PUNCT
ejpam-5827	478	2	u1	u1	NOUN
ejpam-5827	478	3	)	)	PUNCT
ejpam-5827	478	4	,	,	PUNCT
ejpam-5827	478	5	(	(	PUNCT
ejpam-5827	478	6	u4	u4	PROPN
ejpam-5827	478	7	)	)	PUNCT
ejpam-5827	478	8	,	,	PUNCT
ejpam-5827	478	9	(	(	PUNCT
ejpam-5827	478	10	u5	u5	NOUN
ejpam-5827	478	11	)	)	PUNCT
ejpam-5827	478	12	,	,	PUNCT
ejpam-5827	478	13	(	(	PUNCT
ejpam-5827	478	14	u6	u6	NOUN
ejpam-5827	478	15	)	)	PUNCT
ejpam-5827	478	16	)	)	PUNCT
ejpam-5827	479	1	for	for	ADP
ejpam-5827	479	2	proposition	proposition	NOUN
ejpam-5827	479	3	9	9	NUM
ejpam-5827	479	4	fails	fail	VERB
ejpam-5827	479	5	in	in	ADP
ejpam-5827	479	6	general	general	ADJ
ejpam-5827	479	7	.	.	PUNCT
ejpam-5827	480	1	(	(	PUNCT
ejpam-5827	480	2	l1	l1	PROPN
ejpam-5827	480	3	)	)	PUNCT
ejpam-5827	480	4	suppose	suppose	VERB
ejpam-5827	480	5	that	that	SCONJ
ejpam-5827	480	6	κ	κ	PROPN
ejpam-5827	480	7	=	=	X
ejpam-5827	480	8	u.	u.	NOUN
ejpam-5827	480	9	let	let	VERB
ejpam-5827	480	10	h	h	NOUN
ejpam-5827	480	11	=	=	PUNCT
ejpam-5827	480	12	{	{	PUNCT
ejpam-5827	480	13	a	a	X
ejpam-5827	480	14	,	,	PUNCT
ejpam-5827	480	15	c	c	NOUN
ejpam-5827	480	16	}	}	PUNCT
ejpam-5827	480	17	,	,	PUNCT
ejpam-5827	480	18	then	then	ADV
ejpam-5827	480	19	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	480	20	κ	κ	PROPN
ejpam-5827	480	21	(	(	PUNCT
ejpam-5827	480	22	h	h	NOUN
ejpam-5827	480	23	)	)	PUNCT
ejpam-5827	480	24	=	=	NOUN
ejpam-5827	480	25	{	{	PUNCT
ejpam-5827	480	26	a	a	NOUN
ejpam-5827	480	27	}	}	PUNCT
ejpam-5827	480	28	and	and	CCONJ
ejpam-5827	480	29	so	so	ADV
ejpam-5827	480	30	h	h	NOUN
ejpam-5827	480	31	⊈	⊈	PROPN
ejpam-5827	480	32	lp∪p̃	lp∪p̃	NOUN
ejpam-5827	480	33	κ	κ	X
ejpam-5827	480	34	(	(	PUNCT
ejpam-5827	480	35	h	h	NOUN
ejpam-5827	480	36	)	)	PUNCT
ejpam-5827	480	37	,	,	PUNCT
ejpam-5827	480	38	(	(	PUNCT
ejpam-5827	480	39	l4	l4	PROPN
ejpam-5827	480	40	)	)	PUNCT
ejpam-5827	480	41	suppose	suppose	VERB
ejpam-5827	480	42	that	that	SCONJ
ejpam-5827	480	43	κ	κ	PROPN
ejpam-5827	480	44	=	=	X
ejpam-5827	480	45	u.	u.	NOUN
ejpam-5827	480	46	let	let	VERB
ejpam-5827	480	47	h	h	NOUN
ejpam-5827	480	48	=	=	PUNCT
ejpam-5827	480	49	{	{	PUNCT
ejpam-5827	480	50	c	c	NOUN
ejpam-5827	480	51	}	}	PUNCT
ejpam-5827	480	52	,	,	PUNCT
ejpam-5827	481	1	h́	h́	NOUN
ejpam-5827	481	2	=	=	PUNCT
ejpam-5827	481	3	{	{	PUNCT
ejpam-5827	481	4	b	b	NOUN
ejpam-5827	481	5	}	}	PUNCT
ejpam-5827	481	6	,	,	PUNCT
ejpam-5827	481	7	then	then	ADV
ejpam-5827	481	8	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	481	9	κ	κ	PROPN
ejpam-5827	481	10	(	(	PUNCT
ejpam-5827	481	11	h	h	NOUN
ejpam-5827	481	12	)	)	PUNCT
ejpam-5827	481	13	=	=	NOUN
ejpam-5827	481	14	∅	∅	NOUN
ejpam-5827	481	15	,	,	PUNCT
ejpam-5827	481	16	and	and	CCONJ
ejpam-5827	481	17	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	481	18	κ	κ	PROPN
ejpam-5827	481	19	(	(	PUNCT
ejpam-5827	481	20	h́	h́	NOUN
ejpam-5827	481	21	)	)	PUNCT
ejpam-5827	481	22	=	=	PRON
ejpam-5827	481	23	{	{	PUNCT
ejpam-5827	481	24	b	b	NOUN
ejpam-5827	481	25	}	}	PUNCT
ejpam-5827	481	26	.	.	PUNCT
ejpam-5827	482	1	then	then	ADV
ejpam-5827	482	2	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	482	3	κ	κ	PROPN
ejpam-5827	482	4	(	(	PUNCT
ejpam-5827	482	5	h	h	NOUN
ejpam-5827	482	6	)	)	PUNCT
ejpam-5827	482	7	⊆	⊆	NUM
ejpam-5827	482	8	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	482	9	κ	κ	X
ejpam-5827	482	10	(	(	PUNCT
ejpam-5827	482	11	h́	h́	NOUN
ejpam-5827	482	12	)	)	PUNCT
ejpam-5827	482	13	,	,	PUNCT
ejpam-5827	482	14	and	and	CCONJ
ejpam-5827	482	15	h	h	NOUN
ejpam-5827	482	16	⊈	⊈	PROPN
ejpam-5827	482	17	h́	h́	NOUN
ejpam-5827	482	18	,	,	PUNCT
ejpam-5827	482	19	(	(	PUNCT
ejpam-5827	482	20	l5	l5	PROPN
ejpam-5827	482	21	)	)	PUNCT
ejpam-5827	482	22	suppose	suppose	VERB
ejpam-5827	482	23	that	that	SCONJ
ejpam-5827	482	24	κ	κ	PROPN
ejpam-5827	482	25	=	=	X
ejpam-5827	482	26	u.	u.	NOUN
ejpam-5827	482	27	let	let	VERB
ejpam-5827	482	28	h	h	NOUN
ejpam-5827	482	29	=	=	PUNCT
ejpam-5827	482	30	{	{	PUNCT
ejpam-5827	482	31	a	a	DET
ejpam-5827	482	32	,	,	PUNCT
ejpam-5827	482	33	b	b	NOUN
ejpam-5827	482	34	,	,	PUNCT
ejpam-5827	482	35	c	c	NOUN
ejpam-5827	482	36	}	}	PUNCT
ejpam-5827	482	37	,	,	PUNCT
ejpam-5827	482	38	h́	h́	NOUN
ejpam-5827	482	39	=	=	PUNCT
ejpam-5827	482	40	{	{	PUNCT
ejpam-5827	482	41	a	a	X
ejpam-5827	482	42	,	,	PUNCT
ejpam-5827	482	43	c	c	NOUN
ejpam-5827	482	44	,	,	PUNCT
ejpam-5827	482	45	d	d	NOUN
ejpam-5827	482	46	}	}	PUNCT
ejpam-5827	482	47	,	,	PUNCT
ejpam-5827	482	48	then	then	ADV
ejpam-5827	482	49	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	482	50	κ	κ	PROPN
ejpam-5827	482	51	(	(	PUNCT
ejpam-5827	482	52	h	h	NOUN
ejpam-5827	482	53	)	)	PUNCT
ejpam-5827	482	54	=	=	NOUN
ejpam-5827	482	55	{	{	PUNCT
ejpam-5827	482	56	a	a	DET
ejpam-5827	482	57	,	,	PUNCT
ejpam-5827	482	58	b	b	NOUN
ejpam-5827	482	59	,	,	PUNCT
ejpam-5827	482	60	c	c	NOUN
ejpam-5827	482	61	}	}	PUNCT
ejpam-5827	482	62	,	,	PUNCT
ejpam-5827	482	63	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	482	64	κ	κ	X
ejpam-5827	482	65	(	(	PUNCT
ejpam-5827	482	66	h́	h́	NOUN
ejpam-5827	482	67	)	)	PUNCT
ejpam-5827	482	68	=	=	PRON
ejpam-5827	482	69	{	{	PUNCT
ejpam-5827	482	70	a	a	X
ejpam-5827	482	71	,	,	PUNCT
ejpam-5827	482	72	c	c	NOUN
ejpam-5827	482	73	,	,	PUNCT
ejpam-5827	482	74	d	d	NOUN
ejpam-5827	482	75	}	}	PUNCT
ejpam-5827	482	76	,	,	PUNCT
ejpam-5827	482	77	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	482	78	κ	κ	X
ejpam-5827	482	79	(	(	PUNCT
ejpam-5827	482	80	h)∩lp∪p̃	h)∩lp∪p̃	PROPN
ejpam-5827	482	81	κ	κ	X
ejpam-5827	482	82	(	(	PUNCT
ejpam-5827	482	83	h́	h́	NOUN
ejpam-5827	482	84	)	)	PUNCT
ejpam-5827	482	85	=	=	PRON
ejpam-5827	482	86	{	{	PUNCT
ejpam-5827	482	87	a	a	X
ejpam-5827	482	88	,	,	PUNCT
ejpam-5827	482	89	c	c	NOUN
ejpam-5827	482	90	}	}	PUNCT
ejpam-5827	482	91	and	and	CCONJ
ejpam-5827	482	92	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	482	93	κ	κ	PROPN
ejpam-5827	482	94	(	(	PUNCT
ejpam-5827	482	95	h∩h́	h∩h́	PROPN
ejpam-5827	482	96	)	)	PUNCT
ejpam-5827	483	1	=	=	PRON
ejpam-5827	483	2	{	{	PUNCT
ejpam-5827	483	3	a	a	NOUN
ejpam-5827	483	4	}	}	PUNCT
ejpam-5827	483	5	.	.	PUNCT
ejpam-5827	484	1	hence	hence	ADV
ejpam-5827	484	2	,	,	PUNCT
ejpam-5827	484	3	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	484	4	κ	κ	X
ejpam-5827	484	5	(	(	PUNCT
ejpam-5827	484	6	h	h	PROPN
ejpam-5827	484	7	∩	∩	ADJ
ejpam-5827	484	8	h́	h́	NOUN
ejpam-5827	484	9	)	)	PUNCT
ejpam-5827	484	10	̸=	̸=	PROPN
ejpam-5827	484	11	lp∪p̃	lp∪p̃	NOUN
ejpam-5827	484	12	κ	κ	X
ejpam-5827	484	13	(	(	PUNCT
ejpam-5827	484	14	h	h	NOUN
ejpam-5827	484	15	)	)	PUNCT
ejpam-5827	484	16	∩	∩	PROPN
ejpam-5827	484	17	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	484	18	κ	κ	X
ejpam-5827	484	19	(	(	PUNCT
ejpam-5827	484	20	h́	h́	NOUN
ejpam-5827	484	21	)	)	PUNCT
ejpam-5827	484	22	,	,	PUNCT
ejpam-5827	484	23	(	(	PUNCT
ejpam-5827	484	24	l6	l6	PROPN
ejpam-5827	484	25	)	)	PUNCT
ejpam-5827	484	26	suppose	suppose	VERB
ejpam-5827	484	27	that	that	SCONJ
ejpam-5827	484	28	κ	κ	PROPN
ejpam-5827	484	29	=	=	X
ejpam-5827	484	30	u.	u.	NOUN
ejpam-5827	484	31	let	let	VERB
ejpam-5827	484	32	h	h	NOUN
ejpam-5827	484	33	=	=	PUNCT
ejpam-5827	484	34	{	{	PUNCT
ejpam-5827	484	35	b	b	NOUN
ejpam-5827	484	36	}	}	PUNCT
ejpam-5827	484	37	,	,	PUNCT
ejpam-5827	484	38	h́	h́	NOUN
ejpam-5827	484	39	=	=	PUNCT
ejpam-5827	484	40	{	{	PUNCT
ejpam-5827	484	41	c	c	NOUN
ejpam-5827	484	42	}	}	PUNCT
ejpam-5827	484	43	,	,	PUNCT
ejpam-5827	484	44	then	then	ADV
ejpam-5827	484	45	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	484	46	κ	κ	PROPN
ejpam-5827	484	47	(	(	PUNCT
ejpam-5827	484	48	h	h	NOUN
ejpam-5827	484	49	)	)	PUNCT
ejpam-5827	484	50	=	=	NOUN
ejpam-5827	484	51	{	{	PUNCT
ejpam-5827	484	52	b	b	NOUN
ejpam-5827	484	53	}	}	PUNCT
ejpam-5827	484	54	,	,	PUNCT
ejpam-5827	484	55	and	and	CCONJ
ejpam-5827	484	56	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	484	57	κ	κ	PROPN
ejpam-5827	484	58	(	(	PUNCT
ejpam-5827	484	59	h́	h́	NOUN
ejpam-5827	484	60	)	)	PUNCT
ejpam-5827	484	61	=	=	PUNCT
ejpam-5827	484	62	∅.	∅.	VERB
ejpam-5827	484	63	so	so	ADV
ejpam-5827	484	64	,	,	PUNCT
ejpam-5827	484	65	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	484	66	κ	κ	X
ejpam-5827	484	67	(	(	PUNCT
ejpam-5827	484	68	h	h	PROPN
ejpam-5827	484	69	∪	∪	PROPN
ejpam-5827	484	70	h́	h́	PROPN
ejpam-5827	484	71	)	)	PUNCT
ejpam-5827	484	72	=	=	PRON
ejpam-5827	484	73	{	{	PUNCT
ejpam-5827	484	74	b	b	NOUN
ejpam-5827	484	75	,	,	PUNCT
ejpam-5827	484	76	c	c	NOUN
ejpam-5827	484	77	}	}	PUNCT
ejpam-5827	484	78	,	,	PUNCT
ejpam-5827	484	79	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	484	80	κ	κ	X
ejpam-5827	484	81	(	(	PUNCT
ejpam-5827	484	82	h	h	NOUN
ejpam-5827	484	83	)	)	PUNCT
ejpam-5827	484	84	∪	∪	ADP
ejpam-5827	484	85	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	484	86	κ	κ	PROPN
ejpam-5827	484	87	(	(	PUNCT
ejpam-5827	484	88	h́	h́	NOUN
ejpam-5827	484	89	)	)	PUNCT
ejpam-5827	484	90	=	=	PRON
ejpam-5827	484	91	{	{	PUNCT
ejpam-5827	484	92	b	b	NOUN
ejpam-5827	484	93	}	}	PUNCT
ejpam-5827	484	94	.	.	PUNCT
ejpam-5827	485	1	then	then	ADV
ejpam-5827	485	2	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	485	3	κ	κ	X
ejpam-5827	485	4	(	(	PUNCT
ejpam-5827	485	5	h	h	PROPN
ejpam-5827	485	6	∪	∪	ADP
ejpam-5827	485	7	h́	h́	NOUN
ejpam-5827	485	8	)	)	PUNCT
ejpam-5827	485	9	̸=	̸=	PROPN
ejpam-5827	485	10	lp∪p̃	lp∪p̃	NOUN
ejpam-5827	485	11	κ	κ	X
ejpam-5827	485	12	(	(	PUNCT
ejpam-5827	485	13	h	h	NOUN
ejpam-5827	485	14	)	)	PUNCT
ejpam-5827	485	15	∪	∪	ADP
ejpam-5827	485	16	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	485	17	κ	κ	PROPN
ejpam-5827	485	18	(	(	PUNCT
ejpam-5827	485	19	h́	h́	NOUN
ejpam-5827	485	20	)	)	PUNCT
ejpam-5827	485	21	.	.	PUNCT
ejpam-5827	486	1	r.	r.	PROPN
ejpam-5827	486	2	a.	a.	PROPN
ejpam-5827	486	3	hosny	hosny	PROPN
ejpam-5827	486	4	,	,	PUNCT
ejpam-5827	486	5	m.	m.	PROPN
ejpam-5827	486	6	k.	k.	PROPN
ejpam-5827	487	1	el	el	PROPN
ejpam-5827	487	2	-	-	PROPN
ejpam-5827	487	3	bably	bably	ADV
ejpam-5827	487	4	,	,	PUNCT
ejpam-5827	487	5	m.	m.	NOUN
ejpam-5827	487	6	a.	a.	PROPN
ejpam-5827	487	7	el	el	PROPN
ejpam-5827	487	8	-	-	PROPN
ejpam-5827	487	9	gayar	gayar	PROPN
ejpam-5827	487	10	/	/	SYM
ejpam-5827	487	11	eur	eur	PROPN
ejpam-5827	487	12	.	.	PUNCT
ejpam-5827	488	1	j.	j.	PROPN
ejpam-5827	488	2	pure	pure	PROPN
ejpam-5827	488	3	appl	appl	PROPN
ejpam-5827	488	4	.	.	PROPN
ejpam-5827	488	5	math	math	PROPN
ejpam-5827	488	6	,	,	PUNCT
ejpam-5827	488	7	18	18	NUM
ejpam-5827	488	8	(	(	PUNCT
ejpam-5827	488	9	1	1	NUM
ejpam-5827	488	10	)	)	PUNCT
ejpam-5827	488	11	(	(	PUNCT
ejpam-5827	488	12	2025	2025	NUM
ejpam-5827	488	13	)	)	PUNCT
ejpam-5827	488	14	,	,	PUNCT
ejpam-5827	488	15	5827	5827	NUM
ejpam-5827	488	16	19	19	NUM
ejpam-5827	488	17	of	of	ADP
ejpam-5827	488	18	29	29	NUM
ejpam-5827	488	19	proposition	proposition	NOUN
ejpam-5827	488	20	10	10	NUM
ejpam-5827	488	21	.	.	PUNCT
ejpam-5827	489	1	let	let	AUX
ejpam-5827	489	2	(	(	PUNCT
ejpam-5827	489	3	v	v	NOUN
ejpam-5827	489	4	,	,	PUNCT
ejpam-5827	489	5	r	r	NOUN
ejpam-5827	489	6	,	,	PUNCT
ejpam-5827	489	7	p	p	NOUN
ejpam-5827	489	8	,	,	PUNCT
ejpam-5827	489	9	p̃	p̃	PROPN
ejpam-5827	489	10	)	)	PUNCT
ejpam-5827	489	11	be	be	VERB
ejpam-5827	489	12	a	a	DET
ejpam-5827	489	13	bi	bi	ADJ
ejpam-5827	489	14	-	-	ADJ
ejpam-5827	489	15	primal	primal	ADJ
ejpam-5827	489	16	approximation	approximation	NOUN
ejpam-5827	489	17	space	space	NOUN
ejpam-5827	489	18	.	.	PUNCT
ejpam-5827	490	1	if	if	SCONJ
ejpam-5827	490	2	r	r	NOUN
ejpam-5827	490	3	is	be	AUX
ejpam-5827	490	4	a	a	DET
ejpam-5827	490	5	preorder	preorder	NOUN
ejpam-5827	490	6	relation	relation	NOUN
ejpam-5827	490	7	,	,	PUNCT
ejpam-5827	490	8	then	then	ADV
ejpam-5827	490	9	for	for	ADP
ejpam-5827	490	10	any	any	DET
ejpam-5827	490	11	w	w	PROPN
ejpam-5827	490	12	∈	∈	PROPN
ejpam-5827	490	13	v	v	NOUN
ejpam-5827	490	14	:	:	PUNCT
ejpam-5827	490	15	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	490	16	κ	κ	X
ejpam-5827	490	17	(	(	PUNCT
ejpam-5827	490	18	nκ(w	nκ(w	NOUN
ejpam-5827	490	19	)	)	PUNCT
ejpam-5827	490	20	)	)	PUNCT
ejpam-5827	491	1	=	=	SYM
ejpam-5827	491	2	nκ(w	nκ(w	NOUN
ejpam-5827	491	3	)	)	PUNCT
ejpam-5827	491	4	,	,	PUNCT
ejpam-5827	491	5	for	for	ADP
ejpam-5827	491	6	each	each	DET
ejpam-5827	491	7	κ	κ	PROPN
ejpam-5827	491	8	∈	∈	PROPN
ejpam-5827	491	9	{	{	PUNCT
ejpam-5827	491	10	r	r	NOUN
ejpam-5827	491	11	,	,	PUNCT
ejpam-5827	491	12	l	l	NOUN
ejpam-5827	491	13	,	,	PUNCT
ejpam-5827	491	14	i	i	PRON
ejpam-5827	491	15	,	,	PUNCT
ejpam-5827	491	16	⟨r⟩	⟨r⟩	PROPN
ejpam-5827	491	17	,	,	PUNCT
ejpam-5827	491	18	⟨l⟩	⟨l⟩	PROPN
ejpam-5827	491	19	,	,	PUNCT
ejpam-5827	491	20	⟨i⟩	⟨i⟩	PROPN
ejpam-5827	491	21	,	,	PUNCT
ejpam-5827	491	22	u	u	NOUN
ejpam-5827	491	23	,	,	PUNCT
ejpam-5827	491	24	⟨u⟩	⟨u⟩	PROPN
ejpam-5827	491	25	}	}	PUNCT
ejpam-5827	491	26	.	.	PUNCT
ejpam-5827	492	1	proof	proof	NOUN
ejpam-5827	492	2	.	.	PUNCT
ejpam-5827	493	1	according	accord	VERB
ejpam-5827	493	2	to	to	ADP
ejpam-5827	493	3	proposition	proposition	NOUN
ejpam-5827	493	4	7	7	NUM
ejpam-5827	493	5	,	,	PUNCT
ejpam-5827	493	6	the	the	DET
ejpam-5827	493	7	proof	proof	NOUN
ejpam-5827	493	8	is	be	AUX
ejpam-5827	493	9	obvious	obvious	ADJ
ejpam-5827	493	10	.	.	PUNCT
ejpam-5827	494	1	remark	remark	NOUN
ejpam-5827	494	2	16	16	NUM
ejpam-5827	494	3	.	.	PUNCT
ejpam-5827	495	1	according	accord	VERB
ejpam-5827	495	2	to	to	ADP
ejpam-5827	495	3	example	example	NOUN
ejpam-5827	495	4	5	5	NUM
ejpam-5827	495	5	illustrates	illustrate	VERB
ejpam-5827	495	6	that	that	SCONJ
ejpam-5827	495	7	the	the	DET
ejpam-5827	495	8	conditions	condition	NOUN
ejpam-5827	495	9	of	of	ADP
ejpam-5827	495	10	reflexivity	reflexivity	NOUN
ejpam-5827	495	11	and	and	CCONJ
ejpam-5827	495	12	transitivity	transitivity	NOUN
ejpam-5827	495	13	in	in	ADP
ejpam-5827	495	14	proposition	proposition	NOUN
ejpam-5827	495	15	7	7	NUM
ejpam-5827	495	16	are	be	AUX
ejpam-5827	495	17	indeed	indeed	ADV
ejpam-5827	495	18	strict	strict	ADJ
ejpam-5827	495	19	.	.	PUNCT
ejpam-5827	496	1	let	let	VERB
ejpam-5827	496	2	w	w	PROPN
ejpam-5827	496	3	=	=	PROPN
ejpam-5827	496	4	b.	b.	PROPN
ejpam-5827	496	5	then	then	ADV
ejpam-5827	496	6	nu(w	nu(w	NOUN
ejpam-5827	496	7	)	)	PUNCT
ejpam-5827	497	1	=	=	PRON
ejpam-5827	497	2	{	{	PUNCT
ejpam-5827	497	3	a	a	X
ejpam-5827	497	4	,	,	PUNCT
ejpam-5827	497	5	c	c	NOUN
ejpam-5827	497	6	}	}	PUNCT
ejpam-5827	497	7	,	,	PUNCT
ejpam-5827	497	8	lp∪p̃	lp∪p̃	NOUN
ejpam-5827	497	9	u	u	NOUN
ejpam-5827	497	10	(	(	PUNCT
ejpam-5827	497	11	nu(w	nu(w	NOUN
ejpam-5827	497	12	)	)	PUNCT
ejpam-5827	497	13	)	)	PUNCT
ejpam-5827	498	1	=	=	PRON
ejpam-5827	499	1	{	{	PUNCT
ejpam-5827	499	2	a	a	X
ejpam-5827	499	3	}	}	PUNCT
ejpam-5827	499	4	.	.	PUNCT
ejpam-5827	500	1	hence	hence	ADV
ejpam-5827	500	2	,	,	PUNCT
ejpam-5827	500	3	nu(w	nu(w	NUM
ejpam-5827	500	4	)	)	PUNCT
ejpam-5827	500	5	⊈	⊈	PROPN
ejpam-5827	500	6	lp∪p̃	lp∪p̃	NOUN
ejpam-5827	500	7	u	u	NOUN
ejpam-5827	500	8	(	(	PUNCT
ejpam-5827	500	9	nu(w	nu(w	NOUN
ejpam-5827	500	10	)	)	PUNCT
ejpam-5827	500	11	)	)	PUNCT
ejpam-5827	500	12	.	.	PUNCT
ejpam-5827	501	1	proposition	proposition	NOUN
ejpam-5827	501	2	11	11	NUM
ejpam-5827	501	3	.	.	PUNCT
ejpam-5827	502	1	let	let	AUX
ejpam-5827	502	2	(	(	PUNCT
ejpam-5827	502	3	v	v	NOUN
ejpam-5827	502	4	,	,	PUNCT
ejpam-5827	502	5	r	r	NOUN
ejpam-5827	502	6	,	,	PUNCT
ejpam-5827	502	7	p	p	NOUN
ejpam-5827	502	8	,	,	PUNCT
ejpam-5827	502	9	p̃	p̃	PROPN
ejpam-5827	502	10	)	)	PUNCT
ejpam-5827	502	11	be	be	VERB
ejpam-5827	502	12	a	a	DET
ejpam-5827	502	13	bi	bi	ADJ
ejpam-5827	502	14	-	-	ADJ
ejpam-5827	502	15	primal	primal	ADJ
ejpam-5827	502	16	approximation	approximation	NOUN
ejpam-5827	502	17	space	space	NOUN
ejpam-5827	502	18	.	.	PUNCT
ejpam-5827	503	1	if	if	SCONJ
ejpam-5827	503	2	h	h	NOUN
ejpam-5827	503	3	is	be	AUX
ejpam-5827	503	4	a	a	DET
ejpam-5827	503	5	subset	subset	NOUN
ejpam-5827	503	6	of	of	ADP
ejpam-5827	503	7	v	v	NOUN
ejpam-5827	503	8	,	,	PUNCT
ejpam-5827	503	9	then	then	ADV
ejpam-5827	503	10	(	(	PUNCT
ejpam-5827	503	11	i	i	NOUN
ejpam-5827	503	12	)	)	PUNCT
ejpam-5827	503	13	τpκ	τpκ	NOUN
ejpam-5827	503	14	l(h	l(h	PROPN
ejpam-5827	503	15	)	)	PUNCT
ejpam-5827	503	16	⊆	⊆	NUM
ejpam-5827	503	17	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	503	18	κ	κ	X
ejpam-5827	503	19	(	(	PUNCT
ejpam-5827	503	20	h	h	NOUN
ejpam-5827	503	21	)	)	PUNCT
ejpam-5827	503	22	and	and	CCONJ
ejpam-5827	503	23	τ	τ	PROPN
ejpam-5827	503	24	p̃κ	p̃κ	NOUN
ejpam-5827	503	25	l(h	l(h	PROPN
ejpam-5827	503	26	)	)	PUNCT
ejpam-5827	503	27	⊆	⊆	NUM
ejpam-5827	503	28	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	503	29	κ	κ	X
ejpam-5827	503	30	(	(	PUNCT
ejpam-5827	503	31	h	h	NOUN
ejpam-5827	503	32	)	)	PUNCT
ejpam-5827	503	33	.	.	PUNCT
ejpam-5827	504	1	(	(	PUNCT
ejpam-5827	504	2	ii	ii	X
ejpam-5827	504	3	)	)	PUNCT
ejpam-5827	504	4	up∪p̃	up∪p̃	NOUN
ejpam-5827	504	5	κ	κ	X
ejpam-5827	504	6	(	(	PUNCT
ejpam-5827	504	7	h	h	NOUN
ejpam-5827	504	8	)	)	PUNCT
ejpam-5827	504	9	⊆	⊆	NUM
ejpam-5827	504	10	τpκ	τpκ	NOUN
ejpam-5827	504	11	u(h	u(h	PROPN
ejpam-5827	504	12	)	)	PUNCT
ejpam-5827	504	13	and	and	CCONJ
ejpam-5827	504	14	up∪p̃	up∪p̃	X
ejpam-5827	504	15	κ	κ	X
ejpam-5827	504	16	(	(	PUNCT
ejpam-5827	504	17	h	h	NOUN
ejpam-5827	504	18	)	)	PUNCT
ejpam-5827	504	19	⊆	⊆	NUM
ejpam-5827	504	20	τ	τ	X
ejpam-5827	504	21	p̃κ	p̃κ	NOUN
ejpam-5827	504	22	u(h	u(h	PROPN
ejpam-5827	504	23	)	)	PUNCT
ejpam-5827	504	24	.	.	PUNCT
ejpam-5827	505	1	(	(	PUNCT
ejpam-5827	505	2	iii	iii	X
ejpam-5827	505	3	)	)	PUNCT
ejpam-5827	505	4	τpκ	τpκ	NOUN
ejpam-5827	505	5	σ(h	σ(h	NOUN
ejpam-5827	505	6	)	)	PUNCT
ejpam-5827	505	7	≤	≤	NUM
ejpam-5827	506	1	σp∪p̃	σp∪p̃	NOUN
ejpam-5827	506	2	κ	κ	X
ejpam-5827	506	3	(	(	PUNCT
ejpam-5827	506	4	h	h	NOUN
ejpam-5827	506	5	)	)	PUNCT
ejpam-5827	506	6	and	and	CCONJ
ejpam-5827	506	7	τ	τ	PROPN
ejpam-5827	506	8	p̃κ	p̃κ	PROPN
ejpam-5827	506	9	σ(h	σ(h	PROPN
ejpam-5827	506	10	)	)	PUNCT
ejpam-5827	506	11	≤	≤	NUM
ejpam-5827	506	12	σp∪p̃	σp∪p̃	NOUN
ejpam-5827	506	13	κ	κ	X
ejpam-5827	506	14	(	(	PUNCT
ejpam-5827	506	15	h	h	NOUN
ejpam-5827	506	16	)	)	PUNCT
ejpam-5827	506	17	.	.	PUNCT
ejpam-5827	507	1	proof	proof	NOUN
ejpam-5827	507	2	.	.	PUNCT
ejpam-5827	508	1	direct	direct	ADJ
ejpam-5827	508	2	to	to	PART
ejpam-5827	508	3	prove	prove	VERB
ejpam-5827	508	4	.	.	PUNCT
ejpam-5827	509	1	remark	remark	PROPN
ejpam-5827	509	2	17	17	NUM
ejpam-5827	509	3	.	.	PUNCT
ejpam-5827	509	4	example	example	NOUN
ejpam-5827	510	1	5	5	NUM
ejpam-5827	510	2	demonstrates	demonstrate	VERB
ejpam-5827	510	3	that	that	SCONJ
ejpam-5827	510	4	the	the	DET
ejpam-5827	510	5	converse	converse	NOUN
ejpam-5827	510	6	of	of	ADP
ejpam-5827	510	7	proposition	proposition	NOUN
ejpam-5827	510	8	11	11	NUM
ejpam-5827	510	9	fails	fail	VERB
ejpam-5827	510	10	in	in	ADP
ejpam-5827	510	11	general	general	ADJ
ejpam-5827	510	12	.	.	PUNCT
ejpam-5827	511	1	(	(	PUNCT
ejpam-5827	511	2	i	i	NOUN
ejpam-5827	511	3	)	)	PUNCT
ejpam-5827	511	4	suppose	suppose	VERB
ejpam-5827	511	5	that	that	SCONJ
ejpam-5827	511	6	κ	κ	PROPN
ejpam-5827	511	7	=	=	X
ejpam-5827	511	8	u.	u.	NOUN
ejpam-5827	511	9	let	let	VERB
ejpam-5827	511	10	h	h	NOUN
ejpam-5827	511	11	=	=	PUNCT
ejpam-5827	511	12	{	{	PUNCT
ejpam-5827	511	13	b	b	NOUN
ejpam-5827	511	14	,	,	PUNCT
ejpam-5827	511	15	c	c	NOUN
ejpam-5827	511	16	}	}	PUNCT
ejpam-5827	511	17	,	,	PUNCT
ejpam-5827	511	18	then	then	ADV
ejpam-5827	511	19	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	511	20	κ	κ	PROPN
ejpam-5827	511	21	(	(	PUNCT
ejpam-5827	511	22	h	h	NOUN
ejpam-5827	511	23	)	)	PUNCT
ejpam-5827	511	24	=	=	NOUN
ejpam-5827	511	25	{	{	PUNCT
ejpam-5827	511	26	b	b	NOUN
ejpam-5827	511	27	,	,	PUNCT
ejpam-5827	511	28	c	c	NOUN
ejpam-5827	511	29	}	}	PUNCT
ejpam-5827	511	30	,	,	PUNCT
ejpam-5827	511	31	τpκ	τpκ	NOUN
ejpam-5827	511	32	l(h	l(h	PROPN
ejpam-5827	511	33	)	)	PUNCT
ejpam-5827	511	34	=	=	PRON
ejpam-5827	511	35	{	{	PUNCT
ejpam-5827	511	36	b	b	NOUN
ejpam-5827	511	37	}	}	PUNCT
ejpam-5827	511	38	.	.	PUNCT
ejpam-5827	512	1	hence	hence	ADV
ejpam-5827	512	2	,	,	PUNCT
ejpam-5827	512	3	lp∪p̃	lp∪p̃	PROPN
ejpam-5827	512	4	κ	κ	X
ejpam-5827	512	5	(	(	PUNCT
ejpam-5827	512	6	h	h	NOUN
ejpam-5827	512	7	)	)	PUNCT
ejpam-5827	512	8	⊈	⊈	PROPN
ejpam-5827	512	9	τpκ	τpκ	NOUN
ejpam-5827	512	10	l(h	l(h	PROPN
ejpam-5827	512	11	)	)	PUNCT
ejpam-5827	512	12	.	.	PUNCT
ejpam-5827	513	1	(	(	PUNCT
ejpam-5827	513	2	ii	ii	NOUN
ejpam-5827	513	3	)	)	PUNCT
ejpam-5827	513	4	suppose	suppose	VERB
ejpam-5827	513	5	that	that	SCONJ
ejpam-5827	513	6	κ	κ	PROPN
ejpam-5827	513	7	=	=	X
ejpam-5827	513	8	u.	u.	NOUN
ejpam-5827	513	9	let	let	VERB
ejpam-5827	513	10	h	h	NOUN
ejpam-5827	513	11	=	=	PUNCT
ejpam-5827	513	12	{	{	PUNCT
ejpam-5827	513	13	d	d	NOUN
ejpam-5827	513	14	}	}	PUNCT
ejpam-5827	513	15	,	,	PUNCT
ejpam-5827	513	16	then	then	ADV
ejpam-5827	513	17	up∪p̃	up∪p̃	VERB
ejpam-5827	513	18	κ	κ	X
ejpam-5827	513	19	(	(	PUNCT
ejpam-5827	513	20	h	h	NOUN
ejpam-5827	513	21	)	)	PUNCT
ejpam-5827	513	22	=	=	NOUN
ejpam-5827	513	23	{	{	PUNCT
ejpam-5827	513	24	d	d	NOUN
ejpam-5827	513	25	}	}	PUNCT
ejpam-5827	513	26	,	,	PUNCT
ejpam-5827	513	27	τpκ	τpκ	NOUN
ejpam-5827	513	28	u(h	u(h	ADJ
ejpam-5827	513	29	)	)	PUNCT
ejpam-5827	513	30	=	=	PRON
ejpam-5827	513	31	{	{	PUNCT
ejpam-5827	513	32	c	c	NOUN
ejpam-5827	513	33	,	,	PUNCT
ejpam-5827	513	34	d	d	NOUN
ejpam-5827	513	35	}	}	PUNCT
ejpam-5827	513	36	.	.	PUNCT
ejpam-5827	514	1	hence	hence	ADV
ejpam-5827	514	2	,	,	PUNCT
ejpam-5827	514	3	up∪p̃	up∪p̃	VERB
ejpam-5827	514	4	κ	κ	X
ejpam-5827	514	5	(	(	PUNCT
ejpam-5827	514	6	h	h	NOUN
ejpam-5827	514	7	)	)	PUNCT
ejpam-5827	514	8	⊉	⊉	NOUN
ejpam-5827	514	9	τpκ	τpκ	NOUN
ejpam-5827	514	10	u(h	u(h	PROPN
ejpam-5827	514	11	)	)	PUNCT
ejpam-5827	514	12	.	.	PUNCT
ejpam-5827	515	1	(	(	PUNCT
ejpam-5827	515	2	iii	iii	X
ejpam-5827	515	3	)	)	PUNCT
ejpam-5827	515	4	suppose	suppose	VERB
ejpam-5827	515	5	that	that	SCONJ
ejpam-5827	515	6	κ	κ	PROPN
ejpam-5827	515	7	=	=	X
ejpam-5827	515	8	u.	u.	NOUN
ejpam-5827	515	9	let	let	VERB
ejpam-5827	515	10	h	h	NOUN
ejpam-5827	515	11	=	=	PUNCT
ejpam-5827	515	12	{	{	PUNCT
ejpam-5827	515	13	d	d	NOUN
ejpam-5827	515	14	}	}	PUNCT
ejpam-5827	515	15	,	,	PUNCT
ejpam-5827	515	16	then	then	ADV
ejpam-5827	515	17	τpκ	τpκ	X
ejpam-5827	515	18	σ(h	σ(h	NOUN
ejpam-5827	515	19	)	)	PUNCT
ejpam-5827	515	20	=	=	SYM
ejpam-5827	515	21	1	1	NUM
ejpam-5827	515	22	2	2	NUM
ejpam-5827	515	23	,	,	PUNCT
ejpam-5827	515	24	σ	σ	PROPN
ejpam-5827	515	25	p∪p̃	p∪p̃	PROPN
ejpam-5827	515	26	κ	κ	X
ejpam-5827	515	27	(	(	PUNCT
ejpam-5827	515	28	h	h	NOUN
ejpam-5827	515	29	)	)	PUNCT
ejpam-5827	515	30	=	=	SYM
ejpam-5827	516	1	1	1	X
ejpam-5827	516	2	.	.	PUNCT
ejpam-5827	517	1	hence	hence	ADV
ejpam-5827	517	2	,	,	PUNCT
ejpam-5827	517	3	τpκ	τpκ	X
ejpam-5827	517	4	σ(h	σ(h	NOUN
ejpam-5827	517	5	)	)	PUNCT
ejpam-5827	517	6	≯	≯	VERB
ejpam-5827	517	7	σp∪p̃	σp∪p̃	NOUN
ejpam-5827	517	8	κ	κ	PROPN
ejpam-5827	517	9	(	(	PUNCT
ejpam-5827	517	10	h	h	NOUN
ejpam-5827	517	11	)	)	PUNCT
ejpam-5827	517	12	.	.	PUNCT
ejpam-5827	518	1	5	5	X
ejpam-5827	518	2	.	.	X
ejpam-5827	518	3	application	application	NOUN
ejpam-5827	518	4	the	the	DET
ejpam-5827	518	5	present	present	ADJ
ejpam-5827	518	6	section	section	NOUN
ejpam-5827	518	7	is	be	AUX
ejpam-5827	518	8	devoted	devote	VERB
ejpam-5827	518	9	to	to	ADP
ejpam-5827	518	10	providing	provide	VERB
ejpam-5827	518	11	an	an	DET
ejpam-5827	518	12	interesting	interesting	ADJ
ejpam-5827	518	13	real	real	ADJ
ejpam-5827	518	14	-	-	PUNCT
ejpam-5827	518	15	life	life	NOUN
ejpam-5827	518	16	application	application	NOUN
ejpam-5827	518	17	to	to	PART
ejpam-5827	518	18	demonstrate	demonstrate	VERB
ejpam-5827	518	19	the	the	DET
ejpam-5827	518	20	importance	importance	NOUN
ejpam-5827	518	21	of	of	ADP
ejpam-5827	518	22	primal	primal	ADJ
ejpam-5827	518	23	approximation	approximation	NOUN
ejpam-5827	518	24	spaces	space	NOUN
ejpam-5827	518	25	in	in	ADP
ejpam-5827	518	26	decision	decision	NOUN
ejpam-5827	518	27	-	-	PUNCT
ejpam-5827	518	28	making	make	VERB
ejpam-5827	518	29	problems	problem	NOUN
ejpam-5827	518	30	and	and	CCONJ
ejpam-5827	518	31	to	to	PART
ejpam-5827	518	32	identify	identify	VERB
ejpam-5827	518	33	their	their	PRON
ejpam-5827	518	34	differences	difference	NOUN
ejpam-5827	518	35	from	from	ADP
ejpam-5827	518	36	other	other	ADJ
ejpam-5827	518	37	methods	method	NOUN
ejpam-5827	518	38	,	,	PUNCT
ejpam-5827	518	39	such	such	ADJ
ejpam-5827	518	40	as	as	ADP
ejpam-5827	518	41	ideal	ideal	ADJ
ejpam-5827	518	42	rough	rough	ADJ
ejpam-5827	518	43	sets	set	NOUN
ejpam-5827	518	44	.	.	PUNCT
ejpam-5827	519	1	5.1	5.1	NUM
ejpam-5827	519	2	.	.	PUNCT
ejpam-5827	520	1	experimental	experimental	ADJ
ejpam-5827	520	2	outcomes	outcome	NOUN
ejpam-5827	520	3	and	and	CCONJ
ejpam-5827	520	4	medical	medical	ADJ
ejpam-5827	520	5	decision	decision	NOUN
ejpam-5827	520	6	table	table	NOUN
ejpam-5827	520	7	this	this	DET
ejpam-5827	520	8	section	section	NOUN
ejpam-5827	520	9	provides	provide	VERB
ejpam-5827	520	10	an	an	DET
ejpam-5827	520	11	analysis	analysis	NOUN
ejpam-5827	520	12	of	of	ADP
ejpam-5827	520	13	the	the	DET
ejpam-5827	520	14	computed	compute	VERB
ejpam-5827	520	15	results	result	NOUN
ejpam-5827	520	16	derived	derive	VERB
ejpam-5827	520	17	from	from	ADP
ejpam-5827	520	18	examinations	examination	NOUN
ejpam-5827	520	19	administered	administer	VERB
ejpam-5827	520	20	to	to	ADP
ejpam-5827	520	21	five	five	NUM
ejpam-5827	520	22	students	student	NOUN
ejpam-5827	520	23	across	across	ADP
ejpam-5827	520	24	four	four	NUM
ejpam-5827	520	25	subjects	subject	NOUN
ejpam-5827	520	26	,	,	PUNCT
ejpam-5827	520	27	using	use	VERB
ejpam-5827	520	28	the	the	DET
ejpam-5827	520	29	current	current	ADJ
ejpam-5827	520	30	approach	approach	NOUN
ejpam-5827	520	31	.	.	PUNCT
ejpam-5827	521	1	the	the	DET
ejpam-5827	521	2	data	datum	NOUN
ejpam-5827	521	3	,	,	PUNCT
ejpam-5827	521	4	originally	originally	ADV
ejpam-5827	521	5	presented	present	VERB
ejpam-5827	521	6	in	in	ADP
ejpam-5827	521	7	[	[	X
ejpam-5827	521	8	11	11	NUM
ejpam-5827	521	9	]	]	PUNCT
ejpam-5827	521	10	,	,	PUNCT
ejpam-5827	521	11	contained	contain	VERB
ejpam-5827	521	12	inaccuracies	inaccuracy	NOUN
ejpam-5827	521	13	which	which	PRON
ejpam-5827	521	14	are	be	AUX
ejpam-5827	521	15	addressed	address	VERB
ejpam-5827	521	16	and	and	CCONJ
ejpam-5827	521	17	corrected	correct	VERB
ejpam-5827	521	18	in	in	ADP
ejpam-5827	521	19	this	this	DET
ejpam-5827	521	20	analysis	analysis	NOUN
ejpam-5827	521	21	.	.	PUNCT
ejpam-5827	522	1	the	the	DET
ejpam-5827	522	2	evaluation	evaluation	NOUN
ejpam-5827	522	3	focuses	focus	VERB
ejpam-5827	522	4	on	on	ADP
ejpam-5827	522	5	student	student	NOUN
ejpam-5827	522	6	performance	performance	NOUN
ejpam-5827	522	7	in	in	ADP
ejpam-5827	522	8	biology	biology	NOUN
ejpam-5827	522	9	,	,	PUNCT
ejpam-5827	522	10	chemistry	chemistry	NOUN
ejpam-5827	522	11	,	,	PUNCT
ejpam-5827	522	12	mathematics	mathematic	NOUN
ejpam-5827	522	13	,	,	PUNCT
ejpam-5827	522	14	and	and	CCONJ
ejpam-5827	522	15	physics	physics	NOUN
ejpam-5827	522	16	.	.	PUNCT
ejpam-5827	523	1	the	the	DET
ejpam-5827	523	2	five	five	NUM
ejpam-5827	523	3	students	student	NOUN
ejpam-5827	523	4	,	,	PUNCT
ejpam-5827	523	5	denoted	denote	VERB
ejpam-5827	523	6	as	as	ADP
ejpam-5827	523	7	v	v	NOUN
ejpam-5827	523	8	=	=	PUNCT
ejpam-5827	523	9	{	{	PUNCT
ejpam-5827	523	10	ϵ1	ϵ1	ADJ
ejpam-5827	523	11	,	,	PUNCT
ejpam-5827	523	12	ϵ2	ϵ2	ADJ
ejpam-5827	523	13	,	,	PUNCT
ejpam-5827	523	14	ϵ3	ϵ3	PROPN
ejpam-5827	523	15	,	,	PUNCT
ejpam-5827	523	16	ϵ4	ϵ4	PROPN
ejpam-5827	523	17	,	,	PUNCT
ejpam-5827	523	18	ϵ5	ϵ5	PROPN
ejpam-5827	523	19	}	}	PUNCT
ejpam-5827	523	20	,	,	PUNCT
ejpam-5827	523	21	were	be	AUX
ejpam-5827	523	22	assessed	assess	VERB
ejpam-5827	523	23	in	in	ADP
ejpam-5827	523	24	these	these	DET
ejpam-5827	523	25	academic	academic	ADJ
ejpam-5827	523	26	disciplines	discipline	NOUN
ejpam-5827	523	27	.	.	PUNCT
ejpam-5827	524	1	the	the	DET
ejpam-5827	524	2	results	result	NOUN
ejpam-5827	524	3	of	of	ADP
ejpam-5827	524	4	the	the	DET
ejpam-5827	524	5	assessments	assessment	NOUN
ejpam-5827	524	6	are	be	AUX
ejpam-5827	524	7	classified	classify	VERB
ejpam-5827	524	8	into	into	ADP
ejpam-5827	524	9	r.	r.	PROPN
ejpam-5827	524	10	a.	a.	PROPN
ejpam-5827	524	11	hosny	hosny	PROPN
ejpam-5827	524	12	,	,	PUNCT
ejpam-5827	524	13	m.	m.	PROPN
ejpam-5827	524	14	k.	k.	PROPN
ejpam-5827	525	1	el	el	PROPN
ejpam-5827	525	2	-	-	PROPN
ejpam-5827	525	3	bably	bably	ADV
ejpam-5827	525	4	,	,	PUNCT
ejpam-5827	525	5	m.	m.	NOUN
ejpam-5827	525	6	a.	a.	PROPN
ejpam-5827	525	7	el	el	PROPN
ejpam-5827	525	8	-	-	PROPN
ejpam-5827	525	9	gayar	gayar	PROPN
ejpam-5827	525	10	/	/	SYM
ejpam-5827	525	11	eur	eur	PROPN
ejpam-5827	525	12	.	.	PUNCT
ejpam-5827	526	1	j.	j.	PROPN
ejpam-5827	526	2	pure	pure	PROPN
ejpam-5827	526	3	appl	appl	PROPN
ejpam-5827	526	4	.	.	PROPN
ejpam-5827	526	5	math	math	PROPN
ejpam-5827	526	6	,	,	PUNCT
ejpam-5827	526	7	18	18	NUM
ejpam-5827	526	8	(	(	PUNCT
ejpam-5827	526	9	1	1	NUM
ejpam-5827	526	10	)	)	PUNCT
ejpam-5827	526	11	(	(	PUNCT
ejpam-5827	526	12	2025	2025	NUM
ejpam-5827	526	13	)	)	PUNCT
ejpam-5827	526	14	,	,	PUNCT
ejpam-5827	526	15	5827	5827	NUM
ejpam-5827	526	16	20	20	NUM
ejpam-5827	526	17	of	of	ADP
ejpam-5827	526	18	29	29	NUM
ejpam-5827	526	19	figure	figure	NOUN
ejpam-5827	526	20	1	1	NUM
ejpam-5827	526	21	:	:	PUNCT
ejpam-5827	526	22	graphical	graphical	ADJ
ejpam-5827	526	23	representation	representation	NOUN
ejpam-5827	526	24	.	.	PUNCT
ejpam-5827	527	1	five	five	NUM
ejpam-5827	527	2	distinct	distinct	ADJ
ejpam-5827	527	3	levels	level	NOUN
ejpam-5827	527	4	or	or	CCONJ
ejpam-5827	527	5	ranks	rank	NOUN
ejpam-5827	527	6	,	,	PUNCT
ejpam-5827	527	7	illustrated	illustrate	VERB
ejpam-5827	527	8	in	in	ADP
ejpam-5827	527	9	figure	figure	NOUN
ejpam-5827	527	10	1	1	NUM
ejpam-5827	527	11	(	(	PUNCT
ejpam-5827	527	12	fig	fig	NOUN
ejpam-5827	527	13	.	.	PUNCT
ejpam-5827	527	14	1	1	NUM
ejpam-5827	527	15	)	)	PUNCT
ejpam-5827	527	16	.	.	PUNCT
ejpam-5827	528	1	the	the	DET
ejpam-5827	528	2	hierarchical	hierarchical	ADJ
ejpam-5827	528	3	arrangement	arrangement	NOUN
ejpam-5827	528	4	of	of	ADP
ejpam-5827	528	5	these	these	DET
ejpam-5827	528	6	ranks	rank	NOUN
ejpam-5827	528	7	is	be	AUX
ejpam-5827	528	8	as	as	SCONJ
ejpam-5827	528	9	follows	follow	VERB
ejpam-5827	528	10	:	:	PUNCT
ejpam-5827	528	11	excellent	excellent	ADJ
ejpam-5827	528	12	>	>	X
ejpam-5827	528	13	very	very	ADV
ejpam-5827	528	14	good	good	ADJ
ejpam-5827	528	15	>	>	X
ejpam-5827	528	16	good	good	ADJ
ejpam-5827	528	17	>	>	X
ejpam-5827	528	18	fair	fair	PROPN
ejpam-5827	528	19	>	>	X
ejpam-5827	528	20	failed	fail	VERB
ejpam-5827	528	21	,	,	PUNCT
ejpam-5827	528	22	where	where	SCONJ
ejpam-5827	528	23	the	the	DET
ejpam-5827	528	24	symbol	symbol	NOUN
ejpam-5827	528	25	>	>	X
ejpam-5827	528	26	denotes	denote	NOUN
ejpam-5827	528	27	”	"	PUNCT
ejpam-5827	528	28	greater	great	ADJ
ejpam-5827	528	29	than	than	ADP
ejpam-5827	528	30	”	"	PUNCT
ejpam-5827	528	31	.	.	PUNCT
ejpam-5827	529	1	the	the	DET
ejpam-5827	529	2	relational	relational	ADJ
ejpam-5827	529	3	structure	structure	NOUN
ejpam-5827	529	4	defining	define	VERB
ejpam-5827	529	5	associations	association	NOUN
ejpam-5827	529	6	among	among	ADP
ejpam-5827	529	7	students	student	NOUN
ejpam-5827	529	8	is	be	AUX
ejpam-5827	529	9	established	establish	VERB
ejpam-5827	529	10	as	as	SCONJ
ejpam-5827	529	11	follows	follow	VERB
ejpam-5827	529	12	:	:	PUNCT
ejpam-5827	529	13	wrz	wrz	SCONJ
ejpam-5827	529	14	if	if	SCONJ
ejpam-5827	529	15	and	and	CCONJ
ejpam-5827	529	16	only	only	ADV
ejpam-5827	529	17	if	if	SCONJ
ejpam-5827	529	18	student	student	NOUN
ejpam-5827	529	19	w	w	PROPN
ejpam-5827	529	20	possesses	possesse	NOUN
ejpam-5827	529	21	at	at	ADV
ejpam-5827	529	22	least	least	ADV
ejpam-5827	529	23	two	two	NUM
ejpam-5827	529	24	subjects	subject	NOUN
ejpam-5827	529	25	with	with	ADP
ejpam-5827	529	26	a	a	DET
ejpam-5827	529	27	rank	rank	NOUN
ejpam-5827	529	28	superior	superior	NOUN
ejpam-5827	529	29	to	to	ADP
ejpam-5827	529	30	that	that	PRON
ejpam-5827	529	31	of	of	ADP
ejpam-5827	529	32	the	the	DET
ejpam-5827	529	33	corresponding	corresponding	ADJ
ejpam-5827	529	34	subjects	subject	NOUN
ejpam-5827	529	35	of	of	ADP
ejpam-5827	529	36	student	student	NOUN
ejpam-5827	529	37	z.	z.	PROPN
ejpam-5827	529	38	for	for	ADP
ejpam-5827	529	39	instance	instance	NOUN
ejpam-5827	529	40	,	,	PUNCT
ejpam-5827	529	41	ϵ4rϵ3	ϵ4rϵ3	PROPN
ejpam-5827	529	42	is	be	AUX
ejpam-5827	529	43	valid	valid	ADJ
ejpam-5827	529	44	due	due	ADP
ejpam-5827	529	45	to	to	ADP
ejpam-5827	529	46	the	the	DET
ejpam-5827	529	47	higher	high	ADJ
ejpam-5827	529	48	ranks	rank	NOUN
ejpam-5827	529	49	of	of	ADP
ejpam-5827	529	50	student	student	NOUN
ejpam-5827	529	51	ϵ4	ϵ4	PROPN
ejpam-5827	529	52	in	in	ADP
ejpam-5827	529	53	biology	biology	NOUN
ejpam-5827	529	54	,	,	PUNCT
ejpam-5827	529	55	mathematics	mathematic	NOUN
ejpam-5827	529	56	,	,	PUNCT
ejpam-5827	529	57	and	and	CCONJ
ejpam-5827	529	58	physics	physics	NOUN
ejpam-5827	529	59	compared	compare	VERB
ejpam-5827	529	60	to	to	ADP
ejpam-5827	529	61	those	those	PRON
ejpam-5827	529	62	of	of	ADP
ejpam-5827	529	63	student	student	NOUN
ejpam-5827	529	64	ϵ3	ϵ3	PROPN
ejpam-5827	529	65	in	in	ADP
ejpam-5827	529	66	the	the	DET
ejpam-5827	529	67	same	same	ADJ
ejpam-5827	529	68	subjects	subject	NOUN
ejpam-5827	529	69	.	.	PUNCT
ejpam-5827	530	1	however	however	ADV
ejpam-5827	530	2	,	,	PUNCT
ejpam-5827	530	3	the	the	DET
ejpam-5827	530	4	pair	pair	NOUN
ejpam-5827	530	5	(	(	PUNCT
ejpam-5827	530	6	ϵ3	ϵ3	PROPN
ejpam-5827	530	7	,	,	PUNCT
ejpam-5827	530	8	ϵ4	ϵ4	PROPN
ejpam-5827	530	9	)	)	PUNCT
ejpam-5827	530	10	does	do	AUX
ejpam-5827	530	11	not	not	PART
ejpam-5827	530	12	belong	belong	VERB
ejpam-5827	530	13	to	to	ADP
ejpam-5827	530	14	r	r	NOUN
ejpam-5827	530	15	as	as	ADP
ejpam-5827	530	16	student	student	NOUN
ejpam-5827	530	17	ϵ3	ϵ3	PROPN
ejpam-5827	530	18	only	only	ADV
ejpam-5827	530	19	has	have	VERB
ejpam-5827	530	20	one	one	NUM
ejpam-5827	530	21	subject	subject	NOUN
ejpam-5827	530	22	with	with	ADP
ejpam-5827	530	23	a	a	DET
ejpam-5827	530	24	rank	rank	NOUN
ejpam-5827	530	25	higher	high	ADJ
ejpam-5827	530	26	than	than	ADP
ejpam-5827	530	27	that	that	PRON
ejpam-5827	530	28	of	of	ADP
ejpam-5827	530	29	student	student	NOUN
ejpam-5827	530	30	ϵ4	ϵ4	PROPN
ejpam-5827	530	31	.	.	PUNCT
ejpam-5827	531	1	the	the	DET
ejpam-5827	531	2	construction	construction	NOUN
ejpam-5827	531	3	of	of	ADP
ejpam-5827	531	4	the	the	DET
ejpam-5827	531	5	approximation	approximation	NOUN
ejpam-5827	531	6	space	space	NOUN
ejpam-5827	531	7	for	for	ADP
ejpam-5827	531	8	the	the	DET
ejpam-5827	531	9	student	student	NOUN
ejpam-5827	531	10	’s	’s	PART
ejpam-5827	531	11	information	information	NOUN
ejpam-5827	531	12	system	system	NOUN
ejpam-5827	531	13	begins	begin	VERB
ejpam-5827	531	14	with	with	ADP
ejpam-5827	531	15	the	the	DET
ejpam-5827	531	16	conversion	conversion	NOUN
ejpam-5827	531	17	of	of	ADP
ejpam-5827	531	18	table	table	NOUN
ejpam-5827	531	19	2	2	NUM
ejpam-5827	531	20	into	into	ADP
ejpam-5827	531	21	the	the	DET
ejpam-5827	531	22	binary	binary	PROPN
ejpam-5827	531	23	relation	relation	NOUN
ejpam-5827	531	24	r	r	NOUN
ejpam-5827	531	25	=	=	PRON
ejpam-5827	531	26	{	{	PUNCT
ejpam-5827	531	27	(	(	PUNCT
ejpam-5827	531	28	ϵ1	ϵ1	ADJ
ejpam-5827	531	29	,	,	PUNCT
ejpam-5827	531	30	ϵ3	ϵ3	PROPN
ejpam-5827	531	31	)	)	PUNCT
ejpam-5827	531	32	,	,	PUNCT
ejpam-5827	531	33	(	(	PUNCT
ejpam-5827	531	34	ϵ2	ϵ2	ADJ
ejpam-5827	531	35	,	,	PUNCT
ejpam-5827	531	36	ϵ1	ϵ1	ADJ
ejpam-5827	531	37	)	)	PUNCT
ejpam-5827	531	38	,	,	PUNCT
ejpam-5827	531	39	(	(	PUNCT
ejpam-5827	531	40	ϵ2	ϵ2	ADJ
ejpam-5827	531	41	,	,	PUNCT
ejpam-5827	531	42	ϵ4	ϵ4	PROPN
ejpam-5827	531	43	)	)	PUNCT
ejpam-5827	531	44	,	,	PUNCT
ejpam-5827	531	45	(	(	PUNCT
ejpam-5827	531	46	ϵ2	ϵ2	ADJ
ejpam-5827	531	47	,	,	PUNCT
ejpam-5827	531	48	ϵ5	ϵ5	PROPN
ejpam-5827	531	49	)	)	PUNCT
ejpam-5827	531	50	,	,	PUNCT
ejpam-5827	531	51	(	(	PUNCT
ejpam-5827	531	52	ϵ3	ϵ3	ADV
ejpam-5827	531	53	,	,	PUNCT
ejpam-5827	531	54	ϵ1	ϵ1	ADJ
ejpam-5827	531	55	)	)	PUNCT
ejpam-5827	531	56	,	,	PUNCT
ejpam-5827	531	57	(	(	PUNCT
ejpam-5827	531	58	ϵ4	ϵ4	INTJ
ejpam-5827	531	59	,	,	PUNCT
ejpam-5827	531	60	ϵ2	ϵ2	PROPN
ejpam-5827	531	61	)	)	PUNCT
ejpam-5827	531	62	,	,	PUNCT
ejpam-5827	531	63	(	(	PUNCT
ejpam-5827	531	64	ϵ4	ϵ4	INTJ
ejpam-5827	531	65	,	,	PUNCT
ejpam-5827	531	66	ϵ3	ϵ3	PROPN
ejpam-5827	531	67	)	)	PUNCT
ejpam-5827	531	68	,	,	PUNCT
ejpam-5827	531	69	(	(	PUNCT
ejpam-5827	531	70	ϵ5	ϵ5	PROPN
ejpam-5827	531	71	,	,	PUNCT
ejpam-5827	531	72	ϵ3	ϵ3	PROPN
ejpam-5827	531	73	)	)	PUNCT
ejpam-5827	531	74	}	}	PUNCT
ejpam-5827	531	75	.	.	PUNCT
ejpam-5827	532	1	table	table	NOUN
ejpam-5827	532	2	2	2	NUM
ejpam-5827	532	3	:	:	PUNCT
ejpam-5827	532	4	the	the	DET
ejpam-5827	532	5	information	information	NOUN
ejpam-5827	532	6	system	system	NOUN
ejpam-5827	532	7	pertaining	pertain	VERB
ejpam-5827	532	8	to	to	ADP
ejpam-5827	532	9	students	student	NOUN
ejpam-5827	532	10	’	'	PUNCT
ejpam-5827	532	11	academic	academic	ADJ
ejpam-5827	532	12	standings	standing	NOUN
ejpam-5827	532	13	in	in	ADP
ejpam-5827	532	14	each	each	DET
ejpam-5827	532	15	subject	subject	ADJ
ejpam-5827	532	16	biology	biology	NOUN
ejpam-5827	532	17	chemistry	chemistry	NOUN
ejpam-5827	532	18	mathematics	mathematics	PROPN
ejpam-5827	532	19	physics	physics	PROPN
ejpam-5827	532	20	ϵ1	ϵ1	VERB
ejpam-5827	532	21	good	good	ADJ
ejpam-5827	532	22	fair	fair	ADJ
ejpam-5827	532	23	excellent	excellent	ADJ
ejpam-5827	532	24	excellent	excellent	ADJ
ejpam-5827	532	25	ϵ2	ϵ2	NOUN
ejpam-5827	532	26	v.	v.	ADP
ejpam-5827	532	27	good	good	ADJ
ejpam-5827	533	1	good	good	ADJ
ejpam-5827	533	2	excellent	excellent	ADJ
ejpam-5827	533	3	fair	fair	ADJ
ejpam-5827	534	1	ϵ3	ϵ3	INTJ
ejpam-5827	534	2	v.	v.	ADP
ejpam-5827	534	3	good	good	ADJ
ejpam-5827	534	4	good	good	PROPN
ejpam-5827	534	5	failed	fail	VERB
ejpam-5827	534	6	good	good	ADJ
ejpam-5827	534	7	ϵ4	ϵ4	PROPN
ejpam-5827	535	1	excellent	excellent	ADJ
ejpam-5827	535	2	fair	fair	ADV
ejpam-5827	535	3	v.	v.	ADP
ejpam-5827	535	4	good	good	ADJ
ejpam-5827	536	1	excellent	excellent	ADJ
ejpam-5827	536	2	ϵ5	ϵ5	PROPN
ejpam-5827	537	1	v.	v.	CCONJ
ejpam-5827	537	2	good	good	PROPN
ejpam-5827	537	3	fair	fair	ADJ
ejpam-5827	538	1	v.	v.	ADP
ejpam-5827	538	2	good	good	ADJ
ejpam-5827	538	3	excellent	excellent	ADJ
ejpam-5827	538	4	the	the	DET
ejpam-5827	538	5	graphical	graphical	ADJ
ejpam-5827	538	6	representation	representation	NOUN
ejpam-5827	538	7	shown	show	VERB
ejpam-5827	538	8	in	in	ADP
ejpam-5827	538	9	figure	figure	NOUN
ejpam-5827	538	10	1	1	NUM
ejpam-5827	538	11	(	(	PUNCT
ejpam-5827	538	12	fig	fig	NOUN
ejpam-5827	538	13	.	.	NOUN
ejpam-5827	539	1	1	1	NUM
ejpam-5827	539	2	)	)	PUNCT
ejpam-5827	539	3	is	be	AUX
ejpam-5827	539	4	instrumental	instrumental	ADJ
ejpam-5827	539	5	for	for	ADP
ejpam-5827	539	6	analyzing	analyze	VERB
ejpam-5827	539	7	the	the	DET
ejpam-5827	539	8	relative	relative	ADJ
ejpam-5827	539	9	performance	performance	NOUN
ejpam-5827	539	10	and	and	CCONJ
ejpam-5827	539	11	ranking	ranking	NOUN
ejpam-5827	539	12	of	of	ADP
ejpam-5827	539	13	students	student	NOUN
ejpam-5827	539	14	,	,	PUNCT
ejpam-5827	539	15	allowing	allow	VERB
ejpam-5827	539	16	educators	educator	NOUN
ejpam-5827	539	17	to	to	PART
ejpam-5827	539	18	effectively	effectively	ADV
ejpam-5827	539	19	target	target	VERB
ejpam-5827	539	20	interventions	intervention	NOUN
ejpam-5827	539	21	or	or	CCONJ
ejpam-5827	539	22	recognitions	recognition	NOUN
ejpam-5827	539	23	.	.	PUNCT
ejpam-5827	540	1	additionally	additionally	ADV
ejpam-5827	540	2	,	,	PUNCT
ejpam-5827	540	3	the	the	DET
ejpam-5827	540	4	κ	κ	NOUN
ejpam-5827	540	5	-	-	NOUN
ejpam-5827	540	6	neighborhoods	neighborhood	NOUN
ejpam-5827	540	7	for	for	ADP
ejpam-5827	540	8	each	each	DET
ejpam-5827	540	9	κ	κ	NOUN
ejpam-5827	540	10	can	can	AUX
ejpam-5827	540	11	be	be	AUX
ejpam-5827	540	12	depicted	depict	VERB
ejpam-5827	540	13	,	,	PUNCT
ejpam-5827	540	14	as	as	SCONJ
ejpam-5827	540	15	illustrated	illustrate	VERB
ejpam-5827	540	16	in	in	ADP
ejpam-5827	540	17	figure	figure	NOUN
ejpam-5827	540	18	1	1	NUM
ejpam-5827	540	19	(	(	PUNCT
ejpam-5827	540	20	fig	fig	NOUN
ejpam-5827	540	21	.	.	PUNCT
ejpam-5827	541	1	2	2	NUM
ejpam-5827	541	2	)	)	PUNCT
ejpam-5827	541	3	,	,	PUNCT
ejpam-5827	541	4	which	which	PRON
ejpam-5827	541	5	specifically	specifically	ADV
ejpam-5827	541	6	shows	show	VERB
ejpam-5827	541	7	the	the	DET
ejpam-5827	541	8	right	right	ADJ
ejpam-5827	541	9	neighborhoods	neighborhood	NOUN
ejpam-5827	541	10	.	.	PUNCT
ejpam-5827	542	1	r.	r.	PROPN
ejpam-5827	542	2	a.	a.	PROPN
ejpam-5827	542	3	hosny	hosny	PROPN
ejpam-5827	542	4	,	,	PUNCT
ejpam-5827	542	5	m.	m.	PROPN
ejpam-5827	542	6	k.	k.	PROPN
ejpam-5827	543	1	el	el	PROPN
ejpam-5827	543	2	-	-	PROPN
ejpam-5827	543	3	bably	bably	ADV
ejpam-5827	543	4	,	,	PUNCT
ejpam-5827	543	5	m.	m.	NOUN
ejpam-5827	543	6	a.	a.	PROPN
ejpam-5827	543	7	el	el	PROPN
ejpam-5827	543	8	-	-	PROPN
ejpam-5827	543	9	gayar	gayar	PROPN
ejpam-5827	543	10	/	/	SYM
ejpam-5827	543	11	eur	eur	PROPN
ejpam-5827	543	12	.	.	PUNCT
ejpam-5827	544	1	j.	j.	PROPN
ejpam-5827	544	2	pure	pure	PROPN
ejpam-5827	544	3	appl	appl	PROPN
ejpam-5827	544	4	.	.	PROPN
ejpam-5827	544	5	math	math	PROPN
ejpam-5827	544	6	,	,	PUNCT
ejpam-5827	544	7	18	18	NUM
ejpam-5827	544	8	(	(	PUNCT
ejpam-5827	544	9	1	1	NUM
ejpam-5827	544	10	)	)	PUNCT
ejpam-5827	544	11	(	(	PUNCT
ejpam-5827	544	12	2025	2025	NUM
ejpam-5827	544	13	)	)	PUNCT
ejpam-5827	544	14	,	,	PUNCT
ejpam-5827	544	15	5827	5827	NUM
ejpam-5827	544	16	21	21	NUM
ejpam-5827	544	17	of	of	ADP
ejpam-5827	544	18	29	29	NUM
ejpam-5827	544	19	thus	thus	ADV
ejpam-5827	544	20	,	,	PUNCT
ejpam-5827	544	21	the	the	DET
ejpam-5827	544	22	generated	generate	VERB
ejpam-5827	544	23	topologies	topology	NOUN
ejpam-5827	544	24	are	be	AUX
ejpam-5827	544	25	:	:	PUNCT
ejpam-5827	544	26	table	table	NOUN
ejpam-5827	544	27	3	3	NUM
ejpam-5827	544	28	:	:	PUNCT
ejpam-5827	544	29	neighborhoods	neighborhood	NOUN
ejpam-5827	544	30	of	of	ADP
ejpam-5827	544	31	each	each	DET
ejpam-5827	544	32	student	student	NOUN
ejpam-5827	544	33	nr	nr	PROPN
ejpam-5827	544	34	(	(	PUNCT
ejpam-5827	544	35	.	.	PUNCT
ejpam-5827	544	36	)	)	PUNCT
ejpam-5827	545	1	nl	nl	PROPN
ejpam-5827	545	2	(	(	PUNCT
ejpam-5827	545	3	.	.	PUNCT
ejpam-5827	545	4	)	)	PUNCT
ejpam-5827	546	1	ni	ni	PROPN
ejpam-5827	546	2	(	(	PUNCT
ejpam-5827	546	3	.	.	PUNCT
ejpam-5827	546	4	)	)	PUNCT
ejpam-5827	547	1	nu	nu	PROPN
ejpam-5827	547	2	(	(	PUNCT
ejpam-5827	547	3	.	.	PUNCT
ejpam-5827	547	4	)	)	PUNCT
ejpam-5827	548	1	n⟨r⟩	n⟨r⟩	ADV
ejpam-5827	548	2	(	(	PUNCT
ejpam-5827	548	3	.	.	PUNCT
ejpam-5827	548	4	)	)	PUNCT
ejpam-5827	549	1	n⟨l⟩	n⟨l⟩	NOUN
ejpam-5827	549	2	(	(	PUNCT
ejpam-5827	549	3	.	.	PUNCT
ejpam-5827	549	4	)	)	PUNCT
ejpam-5827	550	1	n⟨i⟩	n⟨i⟩	PROPN
ejpam-5827	550	2	(	(	PUNCT
ejpam-5827	550	3	.	.	PUNCT
ejpam-5827	550	4	)	)	PUNCT
ejpam-5827	551	1	n⟨u⟩	n⟨u⟩	NOUN
ejpam-5827	551	2	(	(	PUNCT
ejpam-5827	551	3	.	.	PUNCT
ejpam-5827	551	4	)	)	PUNCT
ejpam-5827	552	1	ϵ1	ϵ1	PROPN
ejpam-5827	552	2	{	{	PUNCT
ejpam-5827	552	3	ϵ3	ϵ3	PROPN
ejpam-5827	552	4	}	}	PUNCT
ejpam-5827	552	5	{	{	PUNCT
ejpam-5827	552	6	ϵ2	ϵ2	ADJ
ejpam-5827	552	7	,	,	PUNCT
ejpam-5827	552	8	ϵ3	ϵ3	PROPN
ejpam-5827	552	9	}	}	PUNCT
ejpam-5827	552	10	{	{	PUNCT
ejpam-5827	552	11	ϵ3	ϵ3	PROPN
ejpam-5827	552	12	}	}	PUNCT
ejpam-5827	552	13	{	{	PUNCT
ejpam-5827	552	14	ϵ2	ϵ2	ADJ
ejpam-5827	552	15	,	,	PUNCT
ejpam-5827	552	16	ϵ3	ϵ3	PROPN
ejpam-5827	552	17	}	}	PUNCT
ejpam-5827	552	18	{	{	PUNCT
ejpam-5827	552	19	ϵ1	ϵ1	ADJ
ejpam-5827	552	20	}	}	PUNCT
ejpam-5827	552	21	{	{	PUNCT
ejpam-5827	552	22	ϵ1	ϵ1	ADJ
ejpam-5827	552	23	,	,	PUNCT
ejpam-5827	552	24	ϵ4	ϵ4	PROPN
ejpam-5827	552	25	,	,	PUNCT
ejpam-5827	552	26	ϵ5	ϵ5	PROPN
ejpam-5827	552	27	}	}	PUNCT
ejpam-5827	552	28	{	{	PUNCT
ejpam-5827	552	29	ϵ1	ϵ1	ADJ
ejpam-5827	552	30	}	}	PUNCT
ejpam-5827	552	31	{	{	PUNCT
ejpam-5827	552	32	ϵ1	ϵ1	ADJ
ejpam-5827	552	33	,	,	PUNCT
ejpam-5827	552	34	ϵ4	ϵ4	PROPN
ejpam-5827	552	35	,	,	PUNCT
ejpam-5827	552	36	ϵ5	ϵ5	PROPN
ejpam-5827	552	37	}	}	PUNCT
ejpam-5827	552	38	ϵ2	ϵ2	PROPN
ejpam-5827	552	39	{	{	PUNCT
ejpam-5827	552	40	ϵ1	ϵ1	ADJ
ejpam-5827	552	41	,	,	PUNCT
ejpam-5827	552	42	ϵ4	ϵ4	PROPN
ejpam-5827	552	43	,	,	PUNCT
ejpam-5827	552	44	ϵ5	ϵ5	PROPN
ejpam-5827	552	45	}	}	PUNCT
ejpam-5827	552	46	{	{	PUNCT
ejpam-5827	552	47	ϵ4	ϵ4	NOUN
ejpam-5827	552	48	}	}	PUNCT
ejpam-5827	552	49	{	{	PUNCT
ejpam-5827	552	50	ϵ4	ϵ4	NOUN
ejpam-5827	552	51	}	}	PUNCT
ejpam-5827	552	52	{	{	PUNCT
ejpam-5827	552	53	ϵ1	ϵ1	ADJ
ejpam-5827	552	54	,	,	PUNCT
ejpam-5827	552	55	ϵ4	ϵ4	PROPN
ejpam-5827	552	56	,	,	PUNCT
ejpam-5827	552	57	ϵ5	ϵ5	PROPN
ejpam-5827	552	58	}	}	PUNCT
ejpam-5827	552	59	{	{	PUNCT
ejpam-5827	552	60	ϵ2	ϵ2	ADJ
ejpam-5827	552	61	,	,	PUNCT
ejpam-5827	552	62	ϵ3	ϵ3	PROPN
ejpam-5827	552	63	}	}	PUNCT
ejpam-5827	552	64	{	{	PUNCT
ejpam-5827	552	65	ϵ2	ϵ2	PROPN
ejpam-5827	552	66	}	}	PUNCT
ejpam-5827	552	67	{	{	PUNCT
ejpam-5827	552	68	ϵ2	ϵ2	PROPN
ejpam-5827	552	69	}	}	PUNCT
ejpam-5827	552	70	{	{	PUNCT
ejpam-5827	552	71	ϵ2	ϵ2	ADJ
ejpam-5827	552	72	,	,	PUNCT
ejpam-5827	552	73	ϵ3	ϵ3	PROPN
ejpam-5827	552	74	}	}	PUNCT
ejpam-5827	552	75	ϵ3	ϵ3	PROPN
ejpam-5827	552	76	{	{	PUNCT
ejpam-5827	552	77	ϵ1	ϵ1	ADJ
ejpam-5827	552	78	}	}	PUNCT
ejpam-5827	552	79	{	{	PUNCT
ejpam-5827	552	80	ϵ1	ϵ1	ADJ
ejpam-5827	552	81	,	,	PUNCT
ejpam-5827	552	82	ϵ4	ϵ4	PROPN
ejpam-5827	552	83	,	,	PUNCT
ejpam-5827	552	84	ϵ5	ϵ5	PROPN
ejpam-5827	552	85	}	}	PUNCT
ejpam-5827	552	86	{	{	PUNCT
ejpam-5827	552	87	ϵ1	ϵ1	ADJ
ejpam-5827	552	88	}	}	PUNCT
ejpam-5827	552	89	{	{	PUNCT
ejpam-5827	552	90	ϵ1	ϵ1	ADJ
ejpam-5827	552	91	,	,	PUNCT
ejpam-5827	552	92	ϵ4	ϵ4	PROPN
ejpam-5827	552	93	,	,	PUNCT
ejpam-5827	552	94	ϵ5	ϵ5	PROPN
ejpam-5827	552	95	}	}	PUNCT
ejpam-5827	552	96	{	{	PUNCT
ejpam-5827	552	97	ϵ3	ϵ3	PROPN
ejpam-5827	552	98	}	}	PUNCT
ejpam-5827	552	99	{	{	PUNCT
ejpam-5827	552	100	ϵ2	ϵ2	ADJ
ejpam-5827	552	101	,	,	PUNCT
ejpam-5827	552	102	ϵ3	ϵ3	PROPN
ejpam-5827	552	103	}	}	PUNCT
ejpam-5827	552	104	{	{	PUNCT
ejpam-5827	552	105	ϵ3	ϵ3	PROPN
ejpam-5827	552	106	}	}	PUNCT
ejpam-5827	552	107	{	{	PUNCT
ejpam-5827	552	108	ϵ2	ϵ2	ADJ
ejpam-5827	552	109	,	,	PUNCT
ejpam-5827	552	110	ϵ3	ϵ3	PROPN
ejpam-5827	552	111	}	}	PUNCT
ejpam-5827	552	112	ϵ4	ϵ4	NOUN
ejpam-5827	552	113	{	{	PUNCT
ejpam-5827	552	114	ϵ2	ϵ2	ADJ
ejpam-5827	552	115	,	,	PUNCT
ejpam-5827	552	116	ϵ3	ϵ3	PROPN
ejpam-5827	552	117	}	}	PUNCT
ejpam-5827	552	118	{	{	PUNCT
ejpam-5827	552	119	ϵ2	ϵ2	PROPN
ejpam-5827	552	120	}	}	PUNCT
ejpam-5827	552	121	{	{	PUNCT
ejpam-5827	552	122	ϵ2	ϵ2	PROPN
ejpam-5827	552	123	}	}	PUNCT
ejpam-5827	552	124	{	{	PUNCT
ejpam-5827	552	125	ϵ2	ϵ2	ADJ
ejpam-5827	552	126	,	,	PUNCT
ejpam-5827	552	127	ϵ3	ϵ3	PROPN
ejpam-5827	552	128	}	}	PUNCT
ejpam-5827	552	129	{	{	PUNCT
ejpam-5827	552	130	ϵ1	ϵ1	ADJ
ejpam-5827	552	131	,	,	PUNCT
ejpam-5827	552	132	ϵ4	ϵ4	PROPN
ejpam-5827	552	133	,	,	PUNCT
ejpam-5827	552	134	ϵ5	ϵ5	PROPN
ejpam-5827	552	135	}	}	PUNCT
ejpam-5827	552	136	{	{	PUNCT
ejpam-5827	552	137	ϵ4	ϵ4	NOUN
ejpam-5827	552	138	}	}	PUNCT
ejpam-5827	552	139	{	{	PUNCT
ejpam-5827	552	140	ϵ4	ϵ4	NOUN
ejpam-5827	552	141	}	}	PUNCT
ejpam-5827	552	142	{	{	PUNCT
ejpam-5827	552	143	ϵ1	ϵ1	ADJ
ejpam-5827	552	144	,	,	PUNCT
ejpam-5827	552	145	ϵ4	ϵ4	PROPN
ejpam-5827	552	146	,	,	PUNCT
ejpam-5827	552	147	ϵ5	ϵ5	PROPN
ejpam-5827	552	148	}	}	PUNCT
ejpam-5827	552	149	ϵ5	ϵ5	PROPN
ejpam-5827	552	150	{	{	PUNCT
ejpam-5827	552	151	ϵ3	ϵ3	PROPN
ejpam-5827	552	152	}	}	PUNCT
ejpam-5827	552	153	{	{	PUNCT
ejpam-5827	552	154	ϵ2	ϵ2	NOUN
ejpam-5827	552	155	}	}	PUNCT
ejpam-5827	552	156	∅	∅	NOUN
ejpam-5827	552	157	{	{	PUNCT
ejpam-5827	552	158	ϵ2	ϵ2	ADJ
ejpam-5827	552	159	,	,	PUNCT
ejpam-5827	552	160	ϵ3	ϵ3	PROPN
ejpam-5827	552	161	}	}	PUNCT
ejpam-5827	552	162	{	{	PUNCT
ejpam-5827	552	163	ϵ1	ϵ1	ADJ
ejpam-5827	552	164	,	,	PUNCT
ejpam-5827	552	165	ϵ4	ϵ4	PROPN
ejpam-5827	552	166	,	,	PUNCT
ejpam-5827	552	167	ϵ5	ϵ5	PROPN
ejpam-5827	552	168	}	}	PUNCT
ejpam-5827	552	169	{	{	PUNCT
ejpam-5827	552	170	ϵ1	ϵ1	ADJ
ejpam-5827	552	171	,	,	PUNCT
ejpam-5827	552	172	ϵ4	ϵ4	PROPN
ejpam-5827	552	173	,	,	PUNCT
ejpam-5827	552	174	ϵ5	ϵ5	PROPN
ejpam-5827	552	175	}	}	PUNCT
ejpam-5827	552	176	{	{	PUNCT
ejpam-5827	552	177	ϵ1	ϵ1	ADJ
ejpam-5827	552	178	,	,	PUNCT
ejpam-5827	552	179	ϵ4	ϵ4	PROPN
ejpam-5827	552	180	,	,	PUNCT
ejpam-5827	552	181	ϵ5	ϵ5	PROPN
ejpam-5827	552	182	}	}	PUNCT
ejpam-5827	552	183	{	{	PUNCT
ejpam-5827	552	184	ϵ1	ϵ1	ADJ
ejpam-5827	552	185	,	,	PUNCT
ejpam-5827	552	186	ϵ4	ϵ4	PROPN
ejpam-5827	552	187	,	,	PUNCT
ejpam-5827	552	188	ϵ5	ϵ5	PROPN
ejpam-5827	552	189	}	}	PUNCT
ejpam-5827	552	190	τr	τr	ADP
ejpam-5827	553	1	=	=	PRON
ejpam-5827	553	2	{	{	PUNCT
ejpam-5827	553	3	∅,v	∅,v	X
ejpam-5827	553	4	,	,	PUNCT
ejpam-5827	553	5	{	{	PUNCT
ejpam-5827	553	6	ϵ1	ϵ1	ADJ
ejpam-5827	553	7	,	,	PUNCT
ejpam-5827	553	8	ϵ3	ϵ3	PROPN
ejpam-5827	553	9	}	}	PUNCT
ejpam-5827	553	10	,	,	PUNCT
ejpam-5827	553	11	{	{	PUNCT
ejpam-5827	553	12	ϵ1	ϵ1	ADJ
ejpam-5827	553	13	,	,	PUNCT
ejpam-5827	553	14	ϵ3	ϵ3	PROPN
ejpam-5827	553	15	,	,	PUNCT
ejpam-5827	553	16	ϵ5	ϵ5	PROPN
ejpam-5827	553	17	}	}	PUNCT
ejpam-5827	553	18	}	}	PUNCT
ejpam-5827	553	19	.	.	PUNCT
ejpam-5827	554	1	τl	τl	PUNCT
ejpam-5827	555	1	=	=	X
ejpam-5827	555	2	{	{	PUNCT
ejpam-5827	555	3	∅,v	∅,v	X
ejpam-5827	555	4	,	,	PUNCT
ejpam-5827	555	5	{	{	PUNCT
ejpam-5827	555	6	ϵ2	ϵ2	ADJ
ejpam-5827	555	7	,	,	PUNCT
ejpam-5827	555	8	ϵ4	ϵ4	PROPN
ejpam-5827	555	9	}	}	PUNCT
ejpam-5827	555	10	,	,	PUNCT
ejpam-5827	555	11	{	{	PUNCT
ejpam-5827	555	12	ϵ2	ϵ2	ADJ
ejpam-5827	555	13	,	,	PUNCT
ejpam-5827	555	14	ϵ4	ϵ4	PROPN
ejpam-5827	555	15	,	,	PUNCT
ejpam-5827	555	16	ϵ5	ϵ5	PROPN
ejpam-5827	555	17	}	}	PUNCT
ejpam-5827	555	18	}	}	PUNCT
ejpam-5827	555	19	.	.	PUNCT
ejpam-5827	556	1	τi	τi	VERB
ejpam-5827	557	1	=	=	SYM
ejpam-5827	557	2	{	{	PUNCT
ejpam-5827	557	3	∅,v	∅,v	X
ejpam-5827	557	4	,	,	PUNCT
ejpam-5827	557	5	{	{	PUNCT
ejpam-5827	557	6	ϵ5	ϵ5	PROPN
ejpam-5827	557	7	}	}	PUNCT
ejpam-5827	557	8	,	,	PUNCT
ejpam-5827	557	9	{	{	PUNCT
ejpam-5827	557	10	ϵ1	ϵ1	ADJ
ejpam-5827	557	11	,	,	PUNCT
ejpam-5827	557	12	ϵ3	ϵ3	PROPN
ejpam-5827	557	13	}	}	PUNCT
ejpam-5827	557	14	,	,	PUNCT
ejpam-5827	557	15	{	{	PUNCT
ejpam-5827	557	16	ϵ2	ϵ2	ADJ
ejpam-5827	557	17	,	,	PUNCT
ejpam-5827	557	18	ϵ4	ϵ4	PROPN
ejpam-5827	557	19	}	}	PUNCT
ejpam-5827	557	20	,	,	PUNCT
ejpam-5827	557	21	{	{	PUNCT
ejpam-5827	557	22	ϵ2	ϵ2	ADJ
ejpam-5827	557	23	,	,	PUNCT
ejpam-5827	557	24	ϵ4	ϵ4	PROPN
ejpam-5827	557	25	,	,	PUNCT
ejpam-5827	557	26	ϵ5	ϵ5	PROPN
ejpam-5827	557	27	}	}	PUNCT
ejpam-5827	557	28	,	,	PUNCT
ejpam-5827	557	29	{	{	PUNCT
ejpam-5827	557	30	ϵ1	ϵ1	ADJ
ejpam-5827	557	31	,	,	PUNCT
ejpam-5827	557	32	ϵ3	ϵ3	PROPN
ejpam-5827	557	33	,	,	PUNCT
ejpam-5827	557	34	ϵ5	ϵ5	PROPN
ejpam-5827	557	35	}	}	PUNCT
ejpam-5827	557	36	,	,	PUNCT
ejpam-5827	557	37	{	{	PUNCT
ejpam-5827	557	38	ϵ1	ϵ1	ADJ
ejpam-5827	557	39	,	,	PUNCT
ejpam-5827	557	40	ϵ2	ϵ2	ADJ
ejpam-5827	557	41	,	,	PUNCT
ejpam-5827	557	42	ϵ3	ϵ3	PROPN
ejpam-5827	557	43	,	,	PUNCT
ejpam-5827	557	44	ϵ4	ϵ4	NOUN
ejpam-5827	557	45	}	}	PUNCT
ejpam-5827	557	46	}	}	PUNCT
ejpam-5827	557	47	.	.	PUNCT
ejpam-5827	558	1	τu	τu	PUNCT
ejpam-5827	558	2	=	=	X
ejpam-5827	558	3	{	{	PUNCT
ejpam-5827	558	4	∅,v	∅,v	NOUN
ejpam-5827	558	5	}	}	PUNCT
ejpam-5827	558	6	.	.	PUNCT
ejpam-5827	559	1	τ⟨r⟩	τ⟨r⟩	PUNCT
ejpam-5827	559	2	=	=	SYM
ejpam-5827	559	3	{	{	PUNCT
ejpam-5827	559	4	∅,v	∅,v	X
ejpam-5827	559	5	,	,	PUNCT
ejpam-5827	559	6	{	{	PUNCT
ejpam-5827	559	7	ϵ1	ϵ1	ADJ
ejpam-5827	559	8	}	}	PUNCT
ejpam-5827	559	9	,	,	PUNCT
ejpam-5827	559	10	{	{	PUNCT
ejpam-5827	559	11	ϵ2	ϵ2	PROPN
ejpam-5827	559	12	}	}	PUNCT
ejpam-5827	559	13	,	,	PUNCT
ejpam-5827	559	14	{	{	PUNCT
ejpam-5827	559	15	ϵ3	ϵ3	PROPN
ejpam-5827	559	16	}	}	PUNCT
ejpam-5827	559	17	,	,	PUNCT
ejpam-5827	559	18	{	{	PUNCT
ejpam-5827	559	19	ϵ1	ϵ1	ADJ
ejpam-5827	559	20	,	,	PUNCT
ejpam-5827	559	21	ϵ2	ϵ2	ADJ
ejpam-5827	559	22	}	}	PUNCT
ejpam-5827	559	23	,	,	PUNCT
ejpam-5827	559	24	{	{	PUNCT
ejpam-5827	559	25	ϵ1	ϵ1	ADJ
ejpam-5827	559	26	,	,	PUNCT
ejpam-5827	559	27	ϵ3	ϵ3	PROPN
ejpam-5827	559	28	}	}	PUNCT
ejpam-5827	559	29	,	,	PUNCT
ejpam-5827	559	30	{	{	PUNCT
ejpam-5827	559	31	ϵ2	ϵ2	ADJ
ejpam-5827	559	32	,	,	PUNCT
ejpam-5827	559	33	ϵ3	ϵ3	PROPN
ejpam-5827	559	34	}	}	PUNCT
ejpam-5827	559	35	,	,	PUNCT
ejpam-5827	559	36	{	{	PUNCT
ejpam-5827	559	37	ϵ4	ϵ4	NOUN
ejpam-5827	559	38	,	,	PUNCT
ejpam-5827	559	39	ϵ5	ϵ5	PROPN
ejpam-5827	559	40	}	}	PUNCT
ejpam-5827	559	41	,	,	PUNCT
ejpam-5827	559	42	{	{	PUNCT
ejpam-5827	559	43	ϵ1	ϵ1	ADJ
ejpam-5827	559	44	,	,	PUNCT
ejpam-5827	559	45	ϵ2	ϵ2	ADJ
ejpam-5827	559	46	,	,	PUNCT
ejpam-5827	559	47	ϵ3	ϵ3	PROPN
ejpam-5827	559	48	}	}	PUNCT
ejpam-5827	559	49	,	,	PUNCT
ejpam-5827	559	50	{	{	PUNCT
ejpam-5827	559	51	ϵ1	ϵ1	ADJ
ejpam-5827	559	52	,	,	PUNCT
ejpam-5827	559	53	ϵ4	ϵ4	PROPN
ejpam-5827	559	54	,	,	PUNCT
ejpam-5827	559	55	ϵ5	ϵ5	PROPN
ejpam-5827	559	56	}	}	PUNCT
ejpam-5827	559	57	,	,	PUNCT
ejpam-5827	559	58	{	{	PUNCT
ejpam-5827	559	59	ϵ2	ϵ2	ADJ
ejpam-5827	559	60	,	,	PUNCT
ejpam-5827	559	61	ϵ4	ϵ4	PROPN
ejpam-5827	559	62	,	,	PUNCT
ejpam-5827	559	63	ϵ5	ϵ5	PROPN
ejpam-5827	559	64	}	}	PUNCT
ejpam-5827	559	65	,	,	PUNCT
ejpam-5827	559	66	{	{	PUNCT
ejpam-5827	559	67	ϵ3	ϵ3	PROPN
ejpam-5827	559	68	,	,	PUNCT
ejpam-5827	559	69	ϵ4	ϵ4	PROPN
ejpam-5827	559	70	,	,	PUNCT
ejpam-5827	559	71	ϵ5	ϵ5	PROPN
ejpam-5827	559	72	}	}	PUNCT
ejpam-5827	559	73	,	,	PUNCT
ejpam-5827	559	74	{	{	PUNCT
ejpam-5827	559	75	ϵ1	ϵ1	ADJ
ejpam-5827	559	76	,	,	PUNCT
ejpam-5827	559	77	ϵ2	ϵ2	ADJ
ejpam-5827	559	78	,	,	PUNCT
ejpam-5827	559	79	ϵ4	ϵ4	PROPN
ejpam-5827	559	80	,	,	PUNCT
ejpam-5827	559	81	ϵ5	ϵ5	PROPN
ejpam-5827	559	82	}	}	PUNCT
ejpam-5827	559	83	,	,	PUNCT
ejpam-5827	559	84	{	{	PUNCT
ejpam-5827	559	85	ϵ1	ϵ1	ADJ
ejpam-5827	559	86	,	,	PUNCT
ejpam-5827	559	87	ϵ3	ϵ3	PROPN
ejpam-5827	559	88	,	,	PUNCT
ejpam-5827	559	89	ϵ4	ϵ4	PROPN
ejpam-5827	559	90	,	,	PUNCT
ejpam-5827	559	91	ϵ5	ϵ5	PROPN
ejpam-5827	559	92	}	}	PUNCT
ejpam-5827	559	93	,	,	PUNCT
ejpam-5827	559	94	{	{	PUNCT
ejpam-5827	559	95	ϵ2	ϵ2	ADJ
ejpam-5827	559	96	,	,	PUNCT
ejpam-5827	559	97	ϵ3	ϵ3	PROPN
ejpam-5827	559	98	,	,	PUNCT
ejpam-5827	559	99	ϵ4	ϵ4	PROPN
ejpam-5827	559	100	,	,	PUNCT
ejpam-5827	559	101	ϵ5	ϵ5	PROPN
ejpam-5827	559	102	}	}	PUNCT
ejpam-5827	559	103	}	}	PUNCT
ejpam-5827	559	104	.	.	PUNCT
ejpam-5827	560	1	τ⟨l⟩	τ⟨l⟩	NOUN
ejpam-5827	560	2	=	=	SYM
ejpam-5827	560	3	{	{	PUNCT
ejpam-5827	560	4	∅,v	∅,v	X
ejpam-5827	560	5	,	,	PUNCT
ejpam-5827	560	6	{	{	PUNCT
ejpam-5827	560	7	ϵ2	ϵ2	PROPN
ejpam-5827	560	8	}	}	PUNCT
ejpam-5827	560	9	,	,	PUNCT
ejpam-5827	560	10	{	{	PUNCT
ejpam-5827	560	11	ϵ3	ϵ3	PROPN
ejpam-5827	560	12	}	}	PUNCT
ejpam-5827	560	13	,	,	PUNCT
ejpam-5827	560	14	{	{	PUNCT
ejpam-5827	560	15	ϵ4	ϵ4	NOUN
ejpam-5827	560	16	}	}	PUNCT
ejpam-5827	560	17	,	,	PUNCT
ejpam-5827	560	18	{	{	PUNCT
ejpam-5827	560	19	ϵ2	ϵ2	ADJ
ejpam-5827	560	20	,	,	PUNCT
ejpam-5827	560	21	ϵ3	ϵ3	PROPN
ejpam-5827	560	22	}	}	PUNCT
ejpam-5827	560	23	,	,	PUNCT
ejpam-5827	560	24	{	{	PUNCT
ejpam-5827	560	25	ϵ2	ϵ2	ADJ
ejpam-5827	560	26	,	,	PUNCT
ejpam-5827	560	27	ϵ4	ϵ4	PROPN
ejpam-5827	560	28	}	}	PUNCT
ejpam-5827	560	29	,	,	PUNCT
ejpam-5827	560	30	{	{	PUNCT
ejpam-5827	560	31	ϵ3	ϵ3	PROPN
ejpam-5827	560	32	,	,	PUNCT
ejpam-5827	560	33	ϵ4	ϵ4	PROPN
ejpam-5827	560	34	}	}	PUNCT
ejpam-5827	560	35	,	,	PUNCT
ejpam-5827	560	36	{	{	PUNCT
ejpam-5827	560	37	ϵ4	ϵ4	NOUN
ejpam-5827	560	38	,	,	PUNCT
ejpam-5827	560	39	ϵ5	ϵ5	PROPN
ejpam-5827	560	40	}	}	PUNCT
ejpam-5827	560	41	,	,	PUNCT
ejpam-5827	560	42	{	{	PUNCT
ejpam-5827	560	43	ϵ1	ϵ1	ADJ
ejpam-5827	560	44	,	,	PUNCT
ejpam-5827	560	45	ϵ4	ϵ4	PROPN
ejpam-5827	560	46	,	,	PUNCT
ejpam-5827	560	47	ϵ5	ϵ5	PROPN
ejpam-5827	560	48	}	}	PUNCT
ejpam-5827	560	49	,	,	PUNCT
ejpam-5827	560	50	{	{	PUNCT
ejpam-5827	560	51	ϵ2	ϵ2	ADJ
ejpam-5827	560	52	,	,	PUNCT
ejpam-5827	560	53	ϵ3	ϵ3	PROPN
ejpam-5827	560	54	,	,	PUNCT
ejpam-5827	560	55	ϵ4	ϵ4	PROPN
ejpam-5827	560	56	}	}	PUNCT
ejpam-5827	560	57	,	,	PUNCT
ejpam-5827	560	58	{	{	PUNCT
ejpam-5827	560	59	ϵ2	ϵ2	ADJ
ejpam-5827	560	60	,	,	PUNCT
ejpam-5827	560	61	ϵ4	ϵ4	PROPN
ejpam-5827	560	62	,	,	PUNCT
ejpam-5827	560	63	ϵ5	ϵ5	PROPN
ejpam-5827	560	64	}	}	PUNCT
ejpam-5827	560	65	,	,	PUNCT
ejpam-5827	560	66	{	{	PUNCT
ejpam-5827	560	67	ϵ3	ϵ3	PROPN
ejpam-5827	560	68	,	,	PUNCT
ejpam-5827	560	69	ϵ4	ϵ4	PROPN
ejpam-5827	560	70	,	,	PUNCT
ejpam-5827	560	71	ϵ5	ϵ5	PROPN
ejpam-5827	560	72	}	}	PUNCT
ejpam-5827	560	73	,	,	PUNCT
ejpam-5827	560	74	{	{	PUNCT
ejpam-5827	560	75	ϵ1	ϵ1	ADJ
ejpam-5827	560	76	,	,	PUNCT
ejpam-5827	560	77	ϵ2	ϵ2	ADJ
ejpam-5827	560	78	,	,	PUNCT
ejpam-5827	560	79	ϵ4	ϵ4	PROPN
ejpam-5827	560	80	,	,	PUNCT
ejpam-5827	560	81	ϵ5	ϵ5	PROPN
ejpam-5827	560	82	}	}	PUNCT
ejpam-5827	560	83	,	,	PUNCT
ejpam-5827	560	84	{	{	PUNCT
ejpam-5827	560	85	ϵ1	ϵ1	ADJ
ejpam-5827	560	86	,	,	PUNCT
ejpam-5827	560	87	ϵ3	ϵ3	PROPN
ejpam-5827	560	88	,	,	PUNCT
ejpam-5827	560	89	ϵ4	ϵ4	PROPN
ejpam-5827	560	90	,	,	PUNCT
ejpam-5827	560	91	ϵ5	ϵ5	PROPN
ejpam-5827	560	92	}	}	PUNCT
ejpam-5827	560	93	,	,	PUNCT
ejpam-5827	560	94	{	{	PUNCT
ejpam-5827	560	95	ϵ2	ϵ2	ADJ
ejpam-5827	560	96	,	,	PUNCT
ejpam-5827	560	97	ϵ3	ϵ3	PROPN
ejpam-5827	560	98	,	,	PUNCT
ejpam-5827	560	99	ϵ4	ϵ4	PROPN
ejpam-5827	560	100	,	,	PUNCT
ejpam-5827	560	101	ϵ5	ϵ5	PROPN
ejpam-5827	560	102	}	}	PUNCT
ejpam-5827	560	103	}	}	PUNCT
ejpam-5827	560	104	.	.	PUNCT
ejpam-5827	561	1	τ⟨i⟩	τ⟨i⟩	PROPN
ejpam-5827	561	2	=	=	SYM
ejpam-5827	561	3	{	{	PUNCT
ejpam-5827	561	4	∅,v	∅,v	X
ejpam-5827	561	5	,	,	PUNCT
ejpam-5827	561	6	{	{	PUNCT
ejpam-5827	561	7	ϵ1	ϵ1	ADJ
ejpam-5827	561	8	}	}	PUNCT
ejpam-5827	561	9	,	,	PUNCT
ejpam-5827	561	10	{	{	PUNCT
ejpam-5827	561	11	ϵ2	ϵ2	PROPN
ejpam-5827	561	12	}	}	PUNCT
ejpam-5827	561	13	,	,	PUNCT
ejpam-5827	561	14	{	{	PUNCT
ejpam-5827	561	15	ϵ3	ϵ3	PROPN
ejpam-5827	561	16	}	}	PUNCT
ejpam-5827	561	17	,	,	PUNCT
ejpam-5827	561	18	{	{	PUNCT
ejpam-5827	561	19	ϵ4	ϵ4	NOUN
ejpam-5827	561	20	}	}	PUNCT
ejpam-5827	561	21	,	,	PUNCT
ejpam-5827	561	22	{	{	PUNCT
ejpam-5827	561	23	ϵ1	ϵ1	ADJ
ejpam-5827	561	24	,	,	PUNCT
ejpam-5827	561	25	ϵ2	ϵ2	ADJ
ejpam-5827	561	26	}	}	PUNCT
ejpam-5827	561	27	,	,	PUNCT
ejpam-5827	561	28	{	{	PUNCT
ejpam-5827	561	29	ϵ1	ϵ1	ADJ
ejpam-5827	561	30	,	,	PUNCT
ejpam-5827	561	31	ϵ3	ϵ3	PROPN
ejpam-5827	561	32	}	}	PUNCT
ejpam-5827	561	33	,	,	PUNCT
ejpam-5827	561	34	{	{	PUNCT
ejpam-5827	561	35	ϵ1	ϵ1	ADJ
ejpam-5827	561	36	,	,	PUNCT
ejpam-5827	561	37	ϵ4	ϵ4	PROPN
ejpam-5827	561	38	}	}	PUNCT
ejpam-5827	561	39	,	,	PUNCT
ejpam-5827	561	40	{	{	PUNCT
ejpam-5827	561	41	ϵ2	ϵ2	ADJ
ejpam-5827	561	42	,	,	PUNCT
ejpam-5827	561	43	ϵ3	ϵ3	PROPN
ejpam-5827	561	44	}	}	PUNCT
ejpam-5827	561	45	,	,	PUNCT
ejpam-5827	561	46	{	{	PUNCT
ejpam-5827	561	47	ϵ2	ϵ2	ADJ
ejpam-5827	561	48	,	,	PUNCT
ejpam-5827	561	49	ϵ4	ϵ4	PROPN
ejpam-5827	561	50	}	}	PUNCT
ejpam-5827	561	51	,	,	PUNCT
ejpam-5827	561	52	{	{	PUNCT
ejpam-5827	561	53	ϵ3	ϵ3	PROPN
ejpam-5827	561	54	,	,	PUNCT
ejpam-5827	561	55	ϵ4	ϵ4	PROPN
ejpam-5827	561	56	}	}	PUNCT
ejpam-5827	561	57	,	,	PUNCT
ejpam-5827	561	58	{	{	PUNCT
ejpam-5827	561	59	ϵ4	ϵ4	NOUN
ejpam-5827	561	60	,	,	PUNCT
ejpam-5827	561	61	ϵ5	ϵ5	PROPN
ejpam-5827	561	62	}	}	PUNCT
ejpam-5827	561	63	,	,	PUNCT
ejpam-5827	561	64	{	{	PUNCT
ejpam-5827	561	65	ϵ1	ϵ1	ADJ
ejpam-5827	561	66	,	,	PUNCT
ejpam-5827	561	67	ϵ2	ϵ2	ADJ
ejpam-5827	561	68	,	,	PUNCT
ejpam-5827	561	69	ϵ3	ϵ3	PROPN
ejpam-5827	561	70	}	}	PUNCT
ejpam-5827	561	71	,	,	PUNCT
ejpam-5827	561	72	{	{	PUNCT
ejpam-5827	561	73	ϵ1	ϵ1	ADJ
ejpam-5827	561	74	,	,	PUNCT
ejpam-5827	561	75	ϵ2	ϵ2	ADJ
ejpam-5827	561	76	,	,	PUNCT
ejpam-5827	561	77	ϵ4	ϵ4	PROPN
ejpam-5827	561	78	}	}	PUNCT
ejpam-5827	561	79	,	,	PUNCT
ejpam-5827	561	80	{	{	PUNCT
ejpam-5827	561	81	ϵ1	ϵ1	ADJ
ejpam-5827	561	82	,	,	PUNCT
ejpam-5827	561	83	ϵ3	ϵ3	PROPN
ejpam-5827	561	84	,	,	PUNCT
ejpam-5827	561	85	ϵ4	ϵ4	PROPN
ejpam-5827	561	86	}	}	PUNCT
ejpam-5827	561	87	,	,	PUNCT
ejpam-5827	561	88	{	{	PUNCT
ejpam-5827	561	89	ϵ1	ϵ1	ADJ
ejpam-5827	561	90	,	,	PUNCT
ejpam-5827	561	91	ϵ4	ϵ4	PROPN
ejpam-5827	561	92	,	,	PUNCT
ejpam-5827	561	93	ϵ5	ϵ5	PROPN
ejpam-5827	561	94	}	}	PUNCT
ejpam-5827	561	95	,	,	PUNCT
ejpam-5827	561	96	{	{	PUNCT
ejpam-5827	561	97	ϵ2	ϵ2	ADJ
ejpam-5827	561	98	,	,	PUNCT
ejpam-5827	561	99	ϵ3	ϵ3	PROPN
ejpam-5827	561	100	,	,	PUNCT
ejpam-5827	561	101	ϵ4	ϵ4	PROPN
ejpam-5827	561	102	}	}	PUNCT
ejpam-5827	561	103	,	,	PUNCT
ejpam-5827	561	104	{	{	PUNCT
ejpam-5827	561	105	ϵ2	ϵ2	ADJ
ejpam-5827	561	106	,	,	PUNCT
ejpam-5827	561	107	ϵ4	ϵ4	PROPN
ejpam-5827	561	108	,	,	PUNCT
ejpam-5827	561	109	ϵ5	ϵ5	PROPN
ejpam-5827	561	110	}	}	PUNCT
ejpam-5827	561	111	,	,	PUNCT
ejpam-5827	561	112	{	{	PUNCT
ejpam-5827	561	113	ϵ3	ϵ3	PROPN
ejpam-5827	561	114	,	,	PUNCT
ejpam-5827	561	115	ϵ4	ϵ4	PROPN
ejpam-5827	561	116	,	,	PUNCT
ejpam-5827	561	117	ϵ5	ϵ5	PROPN
ejpam-5827	561	118	}	}	PUNCT
ejpam-5827	561	119	,	,	PUNCT
ejpam-5827	561	120	{	{	PUNCT
ejpam-5827	561	121	ϵ1	ϵ1	ADJ
ejpam-5827	561	122	,	,	PUNCT
ejpam-5827	561	123	ϵ2	ϵ2	ADJ
ejpam-5827	561	124	,	,	PUNCT
ejpam-5827	561	125	ϵ3	ϵ3	PROPN
ejpam-5827	561	126	,	,	PUNCT
ejpam-5827	561	127	ϵ4	ϵ4	PROPN
ejpam-5827	561	128	}	}	PUNCT
ejpam-5827	561	129	,	,	PUNCT
ejpam-5827	561	130	{	{	PUNCT
ejpam-5827	561	131	ϵ1	ϵ1	ADJ
ejpam-5827	561	132	,	,	PUNCT
ejpam-5827	561	133	ϵ2	ϵ2	ADJ
ejpam-5827	561	134	,	,	PUNCT
ejpam-5827	561	135	ϵ4	ϵ4	PROPN
ejpam-5827	561	136	,	,	PUNCT
ejpam-5827	561	137	ϵ5	ϵ5	PROPN
ejpam-5827	561	138	}	}	PUNCT
ejpam-5827	561	139	,	,	PUNCT
ejpam-5827	561	140	{	{	PUNCT
ejpam-5827	561	141	ϵ1	ϵ1	ADJ
ejpam-5827	561	142	,	,	PUNCT
ejpam-5827	561	143	ϵ3	ϵ3	PROPN
ejpam-5827	561	144	,	,	PUNCT
ejpam-5827	561	145	ϵ4	ϵ4	PROPN
ejpam-5827	561	146	,	,	PUNCT
ejpam-5827	561	147	ϵ5	ϵ5	PROPN
ejpam-5827	561	148	}	}	PUNCT
ejpam-5827	561	149	,	,	PUNCT
ejpam-5827	561	150	{	{	PUNCT
ejpam-5827	561	151	ϵ2	ϵ2	ADJ
ejpam-5827	561	152	,	,	PUNCT
ejpam-5827	561	153	ϵ3	ϵ3	PROPN
ejpam-5827	561	154	,	,	PUNCT
ejpam-5827	561	155	ϵ4	ϵ4	PROPN
ejpam-5827	561	156	,	,	PUNCT
ejpam-5827	561	157	ϵ5	ϵ5	PROPN
ejpam-5827	561	158	}	}	PUNCT
ejpam-5827	561	159	}	}	PUNCT
ejpam-5827	561	160	.	.	PUNCT
ejpam-5827	562	1	τ⟨u⟩	τ⟨u⟩	NOUN
ejpam-5827	562	2	=	=	SYM
ejpam-5827	562	3	{	{	PUNCT
ejpam-5827	562	4	∅,v	∅,v	X
ejpam-5827	562	5	,	,	PUNCT
ejpam-5827	562	6	{	{	PUNCT
ejpam-5827	562	7	ϵ2	ϵ2	PROPN
ejpam-5827	562	8	}	}	PUNCT
ejpam-5827	562	9	,	,	PUNCT
ejpam-5827	562	10	{	{	PUNCT
ejpam-5827	562	11	ϵ3	ϵ3	PROPN
ejpam-5827	562	12	}	}	PUNCT
ejpam-5827	562	13	,	,	PUNCT
ejpam-5827	562	14	{	{	PUNCT
ejpam-5827	562	15	ϵ2	ϵ2	ADJ
ejpam-5827	562	16	,	,	PUNCT
ejpam-5827	562	17	ϵ3	ϵ3	PROPN
ejpam-5827	562	18	}	}	PUNCT
ejpam-5827	562	19	,	,	PUNCT
ejpam-5827	562	20	{	{	PUNCT
ejpam-5827	562	21	ϵ4	ϵ4	NOUN
ejpam-5827	562	22	,	,	PUNCT
ejpam-5827	562	23	ϵ5	ϵ5	PROPN
ejpam-5827	562	24	}	}	PUNCT
ejpam-5827	562	25	,	,	PUNCT
ejpam-5827	562	26	{	{	PUNCT
ejpam-5827	562	27	ϵ1	ϵ1	ADJ
ejpam-5827	562	28	,	,	PUNCT
ejpam-5827	562	29	ϵ4	ϵ4	PROPN
ejpam-5827	562	30	,	,	PUNCT
ejpam-5827	562	31	ϵ5	ϵ5	PROPN
ejpam-5827	562	32	}	}	PUNCT
ejpam-5827	562	33	,	,	PUNCT
ejpam-5827	562	34	{	{	PUNCT
ejpam-5827	562	35	ϵ2	ϵ2	ADJ
ejpam-5827	562	36	,	,	PUNCT
ejpam-5827	562	37	ϵ3	ϵ3	PROPN
ejpam-5827	562	38	,	,	PUNCT
ejpam-5827	562	39	ϵ5	ϵ5	PROPN
ejpam-5827	562	40	}	}	PUNCT
ejpam-5827	562	41	,	,	PUNCT
ejpam-5827	562	42	{	{	PUNCT
ejpam-5827	562	43	ϵ2	ϵ2	ADJ
ejpam-5827	562	44	,	,	PUNCT
ejpam-5827	562	45	ϵ4	ϵ4	PROPN
ejpam-5827	562	46	,	,	PUNCT
ejpam-5827	562	47	ϵ5	ϵ5	PROPN
ejpam-5827	562	48	}	}	PUNCT
ejpam-5827	562	49	,	,	PUNCT
ejpam-5827	562	50	{	{	PUNCT
ejpam-5827	562	51	ϵ3	ϵ3	PROPN
ejpam-5827	562	52	,	,	PUNCT
ejpam-5827	562	53	ϵ4	ϵ4	PROPN
ejpam-5827	562	54	,	,	PUNCT
ejpam-5827	562	55	ϵ5	ϵ5	PROPN
ejpam-5827	562	56	}	}	PUNCT
ejpam-5827	562	57	,	,	PUNCT
ejpam-5827	562	58	{	{	PUNCT
ejpam-5827	562	59	ϵ1	ϵ1	ADJ
ejpam-5827	562	60	,	,	PUNCT
ejpam-5827	562	61	ϵ2	ϵ2	ADJ
ejpam-5827	562	62	,	,	PUNCT
ejpam-5827	562	63	ϵ4	ϵ4	PROPN
ejpam-5827	562	64	,	,	PUNCT
ejpam-5827	562	65	ϵ5	ϵ5	PROPN
ejpam-5827	562	66	}	}	PUNCT
ejpam-5827	562	67	,	,	PUNCT
ejpam-5827	562	68	{	{	PUNCT
ejpam-5827	562	69	ϵ1	ϵ1	ADJ
ejpam-5827	562	70	,	,	PUNCT
ejpam-5827	562	71	ϵ3	ϵ3	PROPN
ejpam-5827	562	72	,	,	PUNCT
ejpam-5827	562	73	ϵ4	ϵ4	PROPN
ejpam-5827	562	74	,	,	PUNCT
ejpam-5827	562	75	ϵ5	ϵ5	PROPN
ejpam-5827	562	76	}	}	PUNCT
ejpam-5827	562	77	,	,	PUNCT
ejpam-5827	562	78	{	{	PUNCT
ejpam-5827	562	79	ϵ2	ϵ2	ADJ
ejpam-5827	562	80	,	,	PUNCT
ejpam-5827	562	81	ϵ3	ϵ3	PROPN
ejpam-5827	562	82	,	,	PUNCT
ejpam-5827	562	83	ϵ4	ϵ4	PROPN
ejpam-5827	562	84	,	,	PUNCT
ejpam-5827	562	85	ϵ5	ϵ5	PROPN
ejpam-5827	562	86	}	}	PUNCT
ejpam-5827	562	87	}	}	PUNCT
ejpam-5827	562	88	.	.	PUNCT
ejpam-5827	563	1	let	let	VERB
ejpam-5827	563	2	p	p	NOUN
ejpam-5827	563	3	=	=	PROPN
ejpam-5827	563	4	2v\{v	2v\{v	PROPN
ejpam-5827	563	5	,	,	PUNCT
ejpam-5827	563	6	{	{	PUNCT
ejpam-5827	563	7	ϵ1	ϵ1	ADJ
ejpam-5827	563	8	,	,	PUNCT
ejpam-5827	563	9	ϵ4	ϵ4	PROPN
ejpam-5827	563	10	,	,	PUNCT
ejpam-5827	563	11	ϵ5	ϵ5	PROPN
ejpam-5827	563	12	}	}	PUNCT
ejpam-5827	563	13	,	,	PUNCT
ejpam-5827	563	14	{	{	PUNCT
ejpam-5827	563	15	ϵ1	ϵ1	ADJ
ejpam-5827	563	16	,	,	PUNCT
ejpam-5827	563	17	ϵ2	ϵ2	ADJ
ejpam-5827	563	18	,	,	PUNCT
ejpam-5827	563	19	ϵ4	ϵ4	PROPN
ejpam-5827	563	20	,	,	PUNCT
ejpam-5827	563	21	ϵ5	ϵ5	PROPN
ejpam-5827	563	22	}	}	PUNCT
ejpam-5827	563	23	,	,	PUNCT
ejpam-5827	563	24	{	{	PUNCT
ejpam-5827	563	25	ϵ1	ϵ1	ADJ
ejpam-5827	563	26	,	,	PUNCT
ejpam-5827	563	27	ϵ3	ϵ3	PROPN
ejpam-5827	563	28	,	,	PUNCT
ejpam-5827	563	29	ϵ4	ϵ4	PROPN
ejpam-5827	563	30	,	,	PUNCT
ejpam-5827	563	31	ϵ5	ϵ5	PROPN
ejpam-5827	563	32	}	}	PUNCT
ejpam-5827	563	33	}	}	PUNCT
ejpam-5827	563	34	,	,	PUNCT
ejpam-5827	563	35	and	and	CCONJ
ejpam-5827	563	36	p̃	p̃	PROPN
ejpam-5827	563	37	=	=	SYM
ejpam-5827	563	38	2v\{v	2v\{v	PROPN
ejpam-5827	563	39	,	,	PUNCT
ejpam-5827	563	40	{	{	PUNCT
ejpam-5827	563	41	ϵ2	ϵ2	ADJ
ejpam-5827	563	42	,	,	PUNCT
ejpam-5827	563	43	ϵ3	ϵ3	PROPN
ejpam-5827	563	44	}	}	PUNCT
ejpam-5827	563	45	,	,	PUNCT
ejpam-5827	563	46	{	{	PUNCT
ejpam-5827	563	47	ϵ1	ϵ1	ADJ
ejpam-5827	563	48	,	,	PUNCT
ejpam-5827	563	49	ϵ2	ϵ2	ADJ
ejpam-5827	563	50	,	,	PUNCT
ejpam-5827	563	51	ϵ3	ϵ3	PROPN
ejpam-5827	563	52	}	}	PUNCT
ejpam-5827	563	53	,	,	PUNCT
ejpam-5827	563	54	{	{	PUNCT
ejpam-5827	563	55	ϵ2	ϵ2	ADJ
ejpam-5827	563	56	,	,	PUNCT
ejpam-5827	563	57	ϵ3	ϵ3	PROPN
ejpam-5827	563	58	,	,	PUNCT
ejpam-5827	563	59	ϵ4	ϵ4	PROPN
ejpam-5827	563	60	}	}	PUNCT
ejpam-5827	563	61	,	,	PUNCT
ejpam-5827	563	62	{	{	PUNCT
ejpam-5827	563	63	ϵ2	ϵ2	ADJ
ejpam-5827	563	64	,	,	PUNCT
ejpam-5827	563	65	ϵ3	ϵ3	PROPN
ejpam-5827	563	66	,	,	PUNCT
ejpam-5827	563	67	ϵ5	ϵ5	PROPN
ejpam-5827	563	68	}	}	PUNCT
ejpam-5827	563	69	,	,	PUNCT
ejpam-5827	563	70	{	{	PUNCT
ejpam-5827	563	71	ϵ1	ϵ1	ADJ
ejpam-5827	563	72	,	,	PUNCT
ejpam-5827	563	73	ϵ2	ϵ2	ADJ
ejpam-5827	563	74	,	,	PUNCT
ejpam-5827	563	75	ϵ3	ϵ3	PROPN
ejpam-5827	563	76	,	,	PUNCT
ejpam-5827	563	77	ϵ4	ϵ4	PROPN
ejpam-5827	563	78	}	}	PUNCT
ejpam-5827	563	79	,	,	PUNCT
ejpam-5827	563	80	{	{	PUNCT
ejpam-5827	563	81	ϵ1	ϵ1	ADJ
ejpam-5827	563	82	,	,	PUNCT
ejpam-5827	563	83	ϵ2	ϵ2	ADJ
ejpam-5827	563	84	,	,	PUNCT
ejpam-5827	563	85	ϵ3	ϵ3	PROPN
ejpam-5827	563	86	,	,	PUNCT
ejpam-5827	563	87	ϵ5	ϵ5	PROPN
ejpam-5827	563	88	}	}	PUNCT
ejpam-5827	563	89	,	,	PUNCT
ejpam-5827	563	90	{	{	PUNCT
ejpam-5827	563	91	ϵ2	ϵ2	ADJ
ejpam-5827	563	92	,	,	PUNCT
ejpam-5827	563	93	ϵ3	ϵ3	PROPN
ejpam-5827	563	94	,	,	PUNCT
ejpam-5827	563	95	ϵ4	ϵ4	PROPN
ejpam-5827	563	96	,	,	PUNCT
ejpam-5827	563	97	ϵ5	ϵ5	PROPN
ejpam-5827	563	98	}	}	PUNCT
ejpam-5827	563	99	}	}	PUNCT
ejpam-5827	563	100	be	be	AUX
ejpam-5827	563	101	two	two	NUM
ejpam-5827	563	102	primals	primal	NOUN
ejpam-5827	563	103	on	on	ADP
ejpam-5827	563	104	v.	v.	ADP
ejpam-5827	563	105	then	then	ADV
ejpam-5827	563	106	,	,	PUNCT
ejpam-5827	563	107	τpr	τpr	NOUN
ejpam-5827	563	108	=	=	X
ejpam-5827	563	109	{	{	PUNCT
ejpam-5827	563	110	∅,v	∅,v	X
ejpam-5827	563	111	,	,	PUNCT
ejpam-5827	563	112	{	{	PUNCT
ejpam-5827	563	113	ϵ1	ϵ1	ADJ
ejpam-5827	563	114	}	}	PUNCT
ejpam-5827	563	115	,	,	PUNCT
ejpam-5827	563	116	{	{	PUNCT
ejpam-5827	563	117	ϵ3	ϵ3	PROPN
ejpam-5827	563	118	}	}	PUNCT
ejpam-5827	563	119	,	,	PUNCT
ejpam-5827	563	120	{	{	PUNCT
ejpam-5827	563	121	ϵ4	ϵ4	NOUN
ejpam-5827	563	122	}	}	PUNCT
ejpam-5827	563	123	,	,	PUNCT
ejpam-5827	563	124	{	{	PUNCT
ejpam-5827	563	125	ϵ5	ϵ5	PROPN
ejpam-5827	563	126	}	}	PUNCT
ejpam-5827	563	127	,	,	PUNCT
ejpam-5827	563	128	{	{	PUNCT
ejpam-5827	563	129	ϵ1	ϵ1	ADJ
ejpam-5827	563	130	,	,	PUNCT
ejpam-5827	563	131	ϵ2	ϵ2	ADJ
ejpam-5827	563	132	}	}	PUNCT
ejpam-5827	563	133	,	,	PUNCT
ejpam-5827	563	134	{	{	PUNCT
ejpam-5827	563	135	ϵ1	ϵ1	ADJ
ejpam-5827	563	136	,	,	PUNCT
ejpam-5827	563	137	ϵ3	ϵ3	PROPN
ejpam-5827	563	138	}	}	PUNCT
ejpam-5827	563	139	,	,	PUNCT
ejpam-5827	563	140	{	{	PUNCT
ejpam-5827	563	141	ϵ1	ϵ1	ADJ
ejpam-5827	563	142	,	,	PUNCT
ejpam-5827	563	143	ϵ4	ϵ4	PROPN
ejpam-5827	563	144	}	}	PUNCT
ejpam-5827	563	145	,	,	PUNCT
ejpam-5827	563	146	{	{	PUNCT
ejpam-5827	563	147	ϵ1	ϵ1	ADJ
ejpam-5827	563	148	,	,	PUNCT
ejpam-5827	563	149	ϵ5	ϵ5	PROPN
ejpam-5827	563	150	}	}	PUNCT
ejpam-5827	563	151	,	,	PUNCT
ejpam-5827	563	152	{	{	PUNCT
ejpam-5827	563	153	ϵ2	ϵ2	ADJ
ejpam-5827	563	154	,	,	PUNCT
ejpam-5827	563	155	ϵ4	ϵ4	PROPN
ejpam-5827	563	156	}	}	PUNCT
ejpam-5827	563	157	,	,	PUNCT
ejpam-5827	563	158	{	{	PUNCT
ejpam-5827	563	159	ϵ2	ϵ2	ADJ
ejpam-5827	563	160	,	,	PUNCT
ejpam-5827	563	161	ϵ5	ϵ5	PROPN
ejpam-5827	563	162	}	}	PUNCT
ejpam-5827	563	163	,	,	PUNCT
ejpam-5827	563	164	{	{	PUNCT
ejpam-5827	563	165	ϵ3	ϵ3	PROPN
ejpam-5827	563	166	,	,	PUNCT
ejpam-5827	563	167	ϵ4	ϵ4	PROPN
ejpam-5827	563	168	}	}	PUNCT
ejpam-5827	563	169	,	,	PUNCT
ejpam-5827	563	170	{	{	PUNCT
ejpam-5827	563	171	ϵ3	ϵ3	PROPN
ejpam-5827	563	172	,	,	PUNCT
ejpam-5827	563	173	ϵ5	ϵ5	PROPN
ejpam-5827	563	174	}	}	PUNCT
ejpam-5827	563	175	,	,	PUNCT
ejpam-5827	563	176	{	{	PUNCT
ejpam-5827	563	177	ϵ4	ϵ4	NOUN
ejpam-5827	563	178	,	,	PUNCT
ejpam-5827	563	179	ϵ5	ϵ5	PROPN
ejpam-5827	563	180	}	}	PUNCT
ejpam-5827	563	181	,	,	PUNCT
ejpam-5827	563	182	{	{	PUNCT
ejpam-5827	563	183	ϵ1	ϵ1	ADJ
ejpam-5827	563	184	,	,	PUNCT
ejpam-5827	563	185	ϵ2	ϵ2	ADJ
ejpam-5827	563	186	,	,	PUNCT
ejpam-5827	563	187	ϵ3	ϵ3	PROPN
ejpam-5827	563	188	}	}	PUNCT
ejpam-5827	563	189	,	,	PUNCT
ejpam-5827	563	190	{	{	PUNCT
ejpam-5827	563	191	ϵ1	ϵ1	ADJ
ejpam-5827	563	192	,	,	PUNCT
ejpam-5827	563	193	ϵ2	ϵ2	ADJ
ejpam-5827	563	194	,	,	PUNCT
ejpam-5827	563	195	ϵ4	ϵ4	PROPN
ejpam-5827	563	196	}	}	PUNCT
ejpam-5827	563	197	,	,	PUNCT
ejpam-5827	563	198	{	{	PUNCT
ejpam-5827	563	199	ϵ1	ϵ1	ADJ
ejpam-5827	563	200	,	,	PUNCT
ejpam-5827	563	201	ϵ2	ϵ2	ADJ
ejpam-5827	563	202	,	,	PUNCT
ejpam-5827	563	203	ϵ5	ϵ5	PROPN
ejpam-5827	563	204	}	}	PUNCT
ejpam-5827	563	205	,	,	PUNCT
ejpam-5827	563	206	{	{	PUNCT
ejpam-5827	563	207	ϵ1	ϵ1	ADJ
ejpam-5827	563	208	,	,	PUNCT
ejpam-5827	563	209	ϵ3	ϵ3	PROPN
ejpam-5827	563	210	,	,	PUNCT
ejpam-5827	563	211	ϵ4	ϵ4	PROPN
ejpam-5827	563	212	}	}	PUNCT
ejpam-5827	563	213	,	,	PUNCT
ejpam-5827	563	214	{	{	PUNCT
ejpam-5827	563	215	ϵ1	ϵ1	ADJ
ejpam-5827	563	216	,	,	PUNCT
ejpam-5827	563	217	ϵ3	ϵ3	PROPN
ejpam-5827	563	218	,	,	PUNCT
ejpam-5827	563	219	ϵ5	ϵ5	PROPN
ejpam-5827	563	220	}	}	PUNCT
ejpam-5827	563	221	,	,	PUNCT
ejpam-5827	563	222	{	{	PUNCT
ejpam-5827	563	223	ϵ1	ϵ1	ADJ
ejpam-5827	563	224	,	,	PUNCT
ejpam-5827	563	225	ϵ4	ϵ4	PROPN
ejpam-5827	563	226	,	,	PUNCT
ejpam-5827	563	227	ϵ5	ϵ5	PROPN
ejpam-5827	563	228	}	}	PUNCT
ejpam-5827	563	229	,	,	PUNCT
ejpam-5827	563	230	{	{	PUNCT
ejpam-5827	563	231	ϵ2	ϵ2	ADJ
ejpam-5827	563	232	,	,	PUNCT
ejpam-5827	563	233	ϵ3	ϵ3	PROPN
ejpam-5827	563	234	,	,	PUNCT
ejpam-5827	563	235	ϵ4	ϵ4	PROPN
ejpam-5827	563	236	}	}	PUNCT
ejpam-5827	563	237	,	,	PUNCT
ejpam-5827	563	238	{	{	PUNCT
ejpam-5827	563	239	ϵ2	ϵ2	ADJ
ejpam-5827	563	240	,	,	PUNCT
ejpam-5827	563	241	ϵ3	ϵ3	PROPN
ejpam-5827	563	242	,	,	PUNCT
ejpam-5827	563	243	ϵ5	ϵ5	PROPN
ejpam-5827	563	244	}	}	PUNCT
ejpam-5827	563	245	,	,	PUNCT
ejpam-5827	563	246	{	{	PUNCT
ejpam-5827	563	247	ϵ2	ϵ2	ADJ
ejpam-5827	563	248	,	,	PUNCT
ejpam-5827	563	249	ϵ4	ϵ4	PROPN
ejpam-5827	563	250	,	,	PUNCT
ejpam-5827	563	251	ϵ5	ϵ5	PROPN
ejpam-5827	563	252	}	}	PUNCT
ejpam-5827	563	253	,	,	PUNCT
ejpam-5827	563	254	{	{	PUNCT
ejpam-5827	563	255	ϵ3	ϵ3	PROPN
ejpam-5827	563	256	,	,	PUNCT
ejpam-5827	563	257	ϵ4	ϵ4	PROPN
ejpam-5827	563	258	,	,	PUNCT
ejpam-5827	563	259	ϵ5	ϵ5	PROPN
ejpam-5827	563	260	}	}	PUNCT
ejpam-5827	563	261	,	,	PUNCT
ejpam-5827	563	262	{	{	PUNCT
ejpam-5827	563	263	ϵ1	ϵ1	ADJ
ejpam-5827	563	264	,	,	PUNCT
ejpam-5827	563	265	ϵ2	ϵ2	ADJ
ejpam-5827	563	266	,	,	PUNCT
ejpam-5827	563	267	ϵ3	ϵ3	PROPN
ejpam-5827	563	268	,	,	PUNCT
ejpam-5827	563	269	ϵ4	ϵ4	PROPN
ejpam-5827	563	270	}	}	PUNCT
ejpam-5827	563	271	,	,	PUNCT
ejpam-5827	563	272	{	{	PUNCT
ejpam-5827	563	273	ϵ1	ϵ1	ADJ
ejpam-5827	563	274	,	,	PUNCT
ejpam-5827	563	275	ϵ2	ϵ2	ADJ
ejpam-5827	563	276	,	,	PUNCT
ejpam-5827	563	277	ϵ3	ϵ3	PROPN
ejpam-5827	563	278	,	,	PUNCT
ejpam-5827	563	279	ϵ5	ϵ5	PROPN
ejpam-5827	563	280	}	}	PUNCT
ejpam-5827	563	281	,	,	PUNCT
ejpam-5827	563	282	{	{	PUNCT
ejpam-5827	563	283	ϵ1	ϵ1	ADJ
ejpam-5827	563	284	,	,	PUNCT
ejpam-5827	563	285	ϵ2	ϵ2	ADJ
ejpam-5827	563	286	,	,	PUNCT
ejpam-5827	563	287	ϵ4	ϵ4	PROPN
ejpam-5827	563	288	,	,	PUNCT
ejpam-5827	563	289	ϵ5	ϵ5	PROPN
ejpam-5827	563	290	}	}	PUNCT
ejpam-5827	563	291	,	,	PUNCT
ejpam-5827	563	292	{	{	PUNCT
ejpam-5827	563	293	ϵ1	ϵ1	ADJ
ejpam-5827	563	294	,	,	PUNCT
ejpam-5827	563	295	ϵ3	ϵ3	PROPN
ejpam-5827	563	296	,	,	PUNCT
ejpam-5827	563	297	ϵ4	ϵ4	PROPN
ejpam-5827	563	298	,	,	PUNCT
ejpam-5827	563	299	ϵ5	ϵ5	PROPN
ejpam-5827	563	300	}	}	PUNCT
ejpam-5827	563	301	,	,	PUNCT
ejpam-5827	563	302	{	{	PUNCT
ejpam-5827	563	303	ϵ2	ϵ2	ADJ
ejpam-5827	563	304	,	,	PUNCT
ejpam-5827	563	305	ϵ3	ϵ3	PROPN
ejpam-5827	563	306	,	,	PUNCT
ejpam-5827	563	307	ϵ4	ϵ4	PROPN
ejpam-5827	563	308	,	,	PUNCT
ejpam-5827	563	309	ϵ5	ϵ5	PROPN
ejpam-5827	563	310	}	}	PUNCT
ejpam-5827	563	311	}	}	PUNCT
ejpam-5827	563	312	.	.	PUNCT
ejpam-5827	564	1	τpl	τpl	PROPN
ejpam-5827	564	2	=	=	PUNCT
ejpam-5827	564	3	{	{	PUNCT
ejpam-5827	564	4	∅,v	∅,v	X
ejpam-5827	564	5	,	,	PUNCT
ejpam-5827	564	6	{	{	PUNCT
ejpam-5827	564	7	ϵ1	ϵ1	ADJ
ejpam-5827	564	8	}	}	PUNCT
ejpam-5827	564	9	,	,	PUNCT
ejpam-5827	564	10	{	{	PUNCT
ejpam-5827	564	11	ϵ2	ϵ2	PROPN
ejpam-5827	564	12	}	}	PUNCT
ejpam-5827	564	13	,	,	PUNCT
ejpam-5827	564	14	{	{	PUNCT
ejpam-5827	564	15	ϵ4	ϵ4	NOUN
ejpam-5827	564	16	}	}	PUNCT
ejpam-5827	564	17	,	,	PUNCT
ejpam-5827	564	18	{	{	PUNCT
ejpam-5827	564	19	ϵ5	ϵ5	PROPN
ejpam-5827	564	20	}	}	PUNCT
ejpam-5827	564	21	,	,	PUNCT
ejpam-5827	564	22	{	{	PUNCT
ejpam-5827	564	23	ϵ1	ϵ1	ADJ
ejpam-5827	564	24	,	,	PUNCT
ejpam-5827	564	25	ϵ2	ϵ2	ADJ
ejpam-5827	564	26	}	}	PUNCT
ejpam-5827	564	27	,	,	PUNCT
ejpam-5827	564	28	{	{	PUNCT
ejpam-5827	564	29	ϵ1	ϵ1	ADJ
ejpam-5827	564	30	,	,	PUNCT
ejpam-5827	564	31	ϵ3	ϵ3	PROPN
ejpam-5827	564	32	}	}	PUNCT
ejpam-5827	564	33	,	,	PUNCT
ejpam-5827	564	34	{	{	PUNCT
ejpam-5827	564	35	ϵ1	ϵ1	ADJ
ejpam-5827	564	36	,	,	PUNCT
ejpam-5827	564	37	ϵ4	ϵ4	PROPN
ejpam-5827	564	38	}	}	PUNCT
ejpam-5827	564	39	,	,	PUNCT
ejpam-5827	564	40	{	{	PUNCT
ejpam-5827	564	41	ϵ1	ϵ1	ADJ
ejpam-5827	564	42	,	,	PUNCT
ejpam-5827	564	43	ϵ5	ϵ5	PROPN
ejpam-5827	564	44	}	}	PUNCT
ejpam-5827	564	45	,	,	PUNCT
ejpam-5827	564	46	{	{	PUNCT
ejpam-5827	564	47	ϵ2	ϵ2	ADJ
ejpam-5827	564	48	,	,	PUNCT
ejpam-5827	564	49	ϵ4	ϵ4	PROPN
ejpam-5827	564	50	}	}	PUNCT
ejpam-5827	564	51	,	,	PUNCT
ejpam-5827	564	52	{	{	PUNCT
ejpam-5827	564	53	ϵ2	ϵ2	ADJ
ejpam-5827	564	54	,	,	PUNCT
ejpam-5827	564	55	ϵ5	ϵ5	PROPN
ejpam-5827	564	56	}	}	PUNCT
ejpam-5827	564	57	,	,	PUNCT
ejpam-5827	564	58	{	{	PUNCT
ejpam-5827	564	59	ϵ3	ϵ3	PROPN
ejpam-5827	564	60	,	,	PUNCT
ejpam-5827	564	61	ϵ4	ϵ4	PROPN
ejpam-5827	564	62	}	}	PUNCT
ejpam-5827	564	63	,	,	PUNCT
ejpam-5827	564	64	{	{	PUNCT
ejpam-5827	564	65	ϵ3	ϵ3	PROPN
ejpam-5827	564	66	,	,	PUNCT
ejpam-5827	564	67	ϵ5	ϵ5	PROPN
ejpam-5827	564	68	}	}	PUNCT
ejpam-5827	564	69	,	,	PUNCT
ejpam-5827	564	70	{	{	PUNCT
ejpam-5827	564	71	ϵ4	ϵ4	NOUN
ejpam-5827	564	72	,	,	PUNCT
ejpam-5827	564	73	ϵ5	ϵ5	PROPN
ejpam-5827	564	74	}	}	PUNCT
ejpam-5827	564	75	,	,	PUNCT
ejpam-5827	564	76	{	{	PUNCT
ejpam-5827	564	77	ϵ1	ϵ1	ADJ
ejpam-5827	564	78	,	,	PUNCT
ejpam-5827	564	79	ϵ2	ϵ2	ADJ
ejpam-5827	564	80	,	,	PUNCT
ejpam-5827	564	81	ϵ3	ϵ3	PROPN
ejpam-5827	564	82	}	}	PUNCT
ejpam-5827	564	83	,	,	PUNCT
ejpam-5827	564	84	{	{	PUNCT
ejpam-5827	564	85	ϵ1	ϵ1	ADJ
ejpam-5827	564	86	,	,	PUNCT
ejpam-5827	564	87	ϵ2	ϵ2	ADJ
ejpam-5827	564	88	,	,	PUNCT
ejpam-5827	564	89	ϵ4	ϵ4	PROPN
ejpam-5827	564	90	}	}	PUNCT
ejpam-5827	564	91	,	,	PUNCT
ejpam-5827	564	92	{	{	PUNCT
ejpam-5827	564	93	ϵ1	ϵ1	ADJ
ejpam-5827	564	94	,	,	PUNCT
ejpam-5827	564	95	ϵ2	ϵ2	ADJ
ejpam-5827	564	96	,	,	PUNCT
ejpam-5827	564	97	ϵ5	ϵ5	PROPN
ejpam-5827	564	98	}	}	PUNCT
ejpam-5827	564	99	,	,	PUNCT
ejpam-5827	564	100	{	{	PUNCT
ejpam-5827	564	101	ϵ1	ϵ1	ADJ
ejpam-5827	564	102	,	,	PUNCT
ejpam-5827	564	103	ϵ3	ϵ3	PROPN
ejpam-5827	564	104	,	,	PUNCT
ejpam-5827	564	105	ϵ4	ϵ4	PROPN
ejpam-5827	564	106	}	}	PUNCT
ejpam-5827	564	107	,	,	PUNCT
ejpam-5827	564	108	{	{	PUNCT
ejpam-5827	564	109	ϵ1	ϵ1	ADJ
ejpam-5827	564	110	,	,	PUNCT
ejpam-5827	564	111	ϵ3	ϵ3	PROPN
ejpam-5827	564	112	,	,	PUNCT
ejpam-5827	564	113	ϵ5	ϵ5	PROPN
ejpam-5827	564	114	}	}	PUNCT
ejpam-5827	564	115	,	,	PUNCT
ejpam-5827	564	116	{	{	PUNCT
ejpam-5827	564	117	ϵ1	ϵ1	ADJ
ejpam-5827	564	118	,	,	PUNCT
ejpam-5827	564	119	ϵ4	ϵ4	PROPN
ejpam-5827	564	120	,	,	PUNCT
ejpam-5827	564	121	ϵ5	ϵ5	PROPN
ejpam-5827	564	122	}	}	PUNCT
ejpam-5827	564	123	,	,	PUNCT
ejpam-5827	564	124	{	{	PUNCT
ejpam-5827	564	125	ϵ2	ϵ2	ADJ
ejpam-5827	564	126	,	,	PUNCT
ejpam-5827	564	127	ϵ3	ϵ3	PROPN
ejpam-5827	564	128	,	,	PUNCT
ejpam-5827	564	129	ϵ4	ϵ4	PROPN
ejpam-5827	564	130	}	}	PUNCT
ejpam-5827	564	131	,	,	PUNCT
ejpam-5827	564	132	{	{	PUNCT
ejpam-5827	564	133	ϵ2	ϵ2	ADJ
ejpam-5827	564	134	,	,	PUNCT
ejpam-5827	564	135	ϵ3	ϵ3	PROPN
ejpam-5827	564	136	,	,	PUNCT
ejpam-5827	564	137	ϵ5	ϵ5	PROPN
ejpam-5827	564	138	}	}	PUNCT
ejpam-5827	564	139	,	,	PUNCT
ejpam-5827	564	140	{	{	PUNCT
ejpam-5827	564	141	ϵ2	ϵ2	ADJ
ejpam-5827	564	142	,	,	PUNCT
ejpam-5827	564	143	ϵ4	ϵ4	PROPN
ejpam-5827	564	144	,	,	PUNCT
ejpam-5827	564	145	ϵ5	ϵ5	PROPN
ejpam-5827	564	146	}	}	PUNCT
ejpam-5827	564	147	,	,	PUNCT
ejpam-5827	564	148	{	{	PUNCT
ejpam-5827	564	149	ϵ3	ϵ3	PROPN
ejpam-5827	564	150	,	,	PUNCT
ejpam-5827	564	151	ϵ4	ϵ4	PROPN
ejpam-5827	564	152	,	,	PUNCT
ejpam-5827	564	153	ϵ5	ϵ5	PROPN
ejpam-5827	564	154	}	}	PUNCT
ejpam-5827	564	155	,	,	PUNCT
ejpam-5827	564	156	{	{	PUNCT
ejpam-5827	564	157	ϵ1	ϵ1	ADJ
ejpam-5827	564	158	,	,	PUNCT
ejpam-5827	564	159	ϵ2	ϵ2	ADJ
ejpam-5827	564	160	,	,	PUNCT
ejpam-5827	564	161	ϵ3	ϵ3	PROPN
ejpam-5827	564	162	,	,	PUNCT
ejpam-5827	564	163	ϵ4	ϵ4	PROPN
ejpam-5827	564	164	}	}	PUNCT
ejpam-5827	564	165	,	,	PUNCT
ejpam-5827	564	166	{	{	PUNCT
ejpam-5827	564	167	ϵ1	ϵ1	ADJ
ejpam-5827	564	168	,	,	PUNCT
ejpam-5827	564	169	ϵ2	ϵ2	ADJ
ejpam-5827	564	170	,	,	PUNCT
ejpam-5827	564	171	ϵ3	ϵ3	PROPN
ejpam-5827	564	172	,	,	PUNCT
ejpam-5827	564	173	ϵ5	ϵ5	PROPN
ejpam-5827	564	174	}	}	PUNCT
ejpam-5827	564	175	,	,	PUNCT
ejpam-5827	564	176	{	{	PUNCT
ejpam-5827	564	177	ϵ1	ϵ1	ADJ
ejpam-5827	564	178	,	,	PUNCT
ejpam-5827	564	179	ϵ2	ϵ2	ADJ
ejpam-5827	564	180	,	,	PUNCT
ejpam-5827	564	181	ϵ4	ϵ4	PROPN
ejpam-5827	564	182	,	,	PUNCT
ejpam-5827	564	183	ϵ5	ϵ5	PROPN
ejpam-5827	564	184	}	}	PUNCT
ejpam-5827	564	185	,	,	PUNCT
ejpam-5827	564	186	{	{	PUNCT
ejpam-5827	564	187	ϵ1	ϵ1	ADJ
ejpam-5827	564	188	,	,	PUNCT
ejpam-5827	564	189	ϵ3	ϵ3	PROPN
ejpam-5827	564	190	,	,	PUNCT
ejpam-5827	564	191	ϵ4	ϵ4	PROPN
ejpam-5827	564	192	,	,	PUNCT
ejpam-5827	564	193	ϵ5	ϵ5	PROPN
ejpam-5827	564	194	}	}	PUNCT
ejpam-5827	564	195	,	,	PUNCT
ejpam-5827	564	196	{	{	PUNCT
ejpam-5827	564	197	ϵ2	ϵ2	ADJ
ejpam-5827	564	198	,	,	PUNCT
ejpam-5827	564	199	ϵ3	ϵ3	PROPN
ejpam-5827	564	200	,	,	PUNCT
ejpam-5827	564	201	ϵ4	ϵ4	PROPN
ejpam-5827	564	202	,	,	PUNCT
ejpam-5827	564	203	ϵ5	ϵ5	PROPN
ejpam-5827	564	204	}	}	PUNCT
ejpam-5827	564	205	}	}	PUNCT
ejpam-5827	564	206	.	.	PUNCT
ejpam-5827	565	1	τpi	τpi	PROPN
ejpam-5827	566	1	=	=	SYM
ejpam-5827	566	2	2v	2v	PROPN
ejpam-5827	566	3	.	.	PUNCT
ejpam-5827	567	1	τpu	τpu	PROPN
ejpam-5827	567	2	=	=	SYM
ejpam-5827	567	3	{	{	PUNCT
ejpam-5827	567	4	∅,v	∅,v	X
ejpam-5827	567	5	,	,	PUNCT
ejpam-5827	567	6	{	{	PUNCT
ejpam-5827	567	7	ϵ1	ϵ1	ADJ
ejpam-5827	567	8	}	}	PUNCT
ejpam-5827	567	9	,	,	PUNCT
ejpam-5827	567	10	{	{	PUNCT
ejpam-5827	567	11	ϵ4	ϵ4	NOUN
ejpam-5827	567	12	}	}	PUNCT
ejpam-5827	567	13	,	,	PUNCT
ejpam-5827	567	14	{	{	PUNCT
ejpam-5827	567	15	ϵ5	ϵ5	PROPN
ejpam-5827	567	16	}	}	PUNCT
ejpam-5827	567	17	,	,	PUNCT
ejpam-5827	567	18	{	{	PUNCT
ejpam-5827	567	19	ϵ1	ϵ1	ADJ
ejpam-5827	567	20	,	,	PUNCT
ejpam-5827	567	21	ϵ2	ϵ2	ADJ
ejpam-5827	567	22	}	}	PUNCT
ejpam-5827	567	23	,	,	PUNCT
ejpam-5827	567	24	{	{	PUNCT
ejpam-5827	567	25	ϵ1	ϵ1	ADJ
ejpam-5827	567	26	,	,	PUNCT
ejpam-5827	567	27	ϵ3	ϵ3	PROPN
ejpam-5827	567	28	}	}	PUNCT
ejpam-5827	567	29	,	,	PUNCT
ejpam-5827	567	30	{	{	PUNCT
ejpam-5827	567	31	ϵ1	ϵ1	ADJ
ejpam-5827	567	32	,	,	PUNCT
ejpam-5827	567	33	ϵ4	ϵ4	PROPN
ejpam-5827	567	34	}	}	PUNCT
ejpam-5827	567	35	,	,	PUNCT
ejpam-5827	567	36	{	{	PUNCT
ejpam-5827	567	37	ϵ1	ϵ1	ADJ
ejpam-5827	567	38	,	,	PUNCT
ejpam-5827	567	39	ϵ5	ϵ5	PROPN
ejpam-5827	567	40	}	}	PUNCT
ejpam-5827	567	41	,	,	PUNCT
ejpam-5827	567	42	{	{	PUNCT
ejpam-5827	567	43	ϵ2	ϵ2	ADJ
ejpam-5827	567	44	,	,	PUNCT
ejpam-5827	567	45	ϵ4	ϵ4	PROPN
ejpam-5827	567	46	}	}	PUNCT
ejpam-5827	567	47	,	,	PUNCT
ejpam-5827	567	48	{	{	PUNCT
ejpam-5827	567	49	ϵ2	ϵ2	ADJ
ejpam-5827	567	50	,	,	PUNCT
ejpam-5827	567	51	ϵ5	ϵ5	PROPN
ejpam-5827	567	52	}	}	PUNCT
ejpam-5827	567	53	,	,	PUNCT
ejpam-5827	567	54	{	{	PUNCT
ejpam-5827	567	55	ϵ3	ϵ3	PROPN
ejpam-5827	567	56	,	,	PUNCT
ejpam-5827	567	57	ϵ4	ϵ4	PROPN
ejpam-5827	567	58	}	}	PUNCT
ejpam-5827	567	59	,	,	PUNCT
ejpam-5827	567	60	{	{	PUNCT
ejpam-5827	567	61	ϵ3	ϵ3	PROPN
ejpam-5827	567	62	,	,	PUNCT
ejpam-5827	567	63	ϵ5	ϵ5	PROPN
ejpam-5827	567	64	}	}	PUNCT
ejpam-5827	567	65	,	,	PUNCT
ejpam-5827	567	66	{	{	PUNCT
ejpam-5827	567	67	ϵ4	ϵ4	NOUN
ejpam-5827	567	68	,	,	PUNCT
ejpam-5827	567	69	ϵ5	ϵ5	PROPN
ejpam-5827	567	70	}	}	PUNCT
ejpam-5827	567	71	,	,	PUNCT
ejpam-5827	567	72	{	{	PUNCT
ejpam-5827	567	73	ϵ1	ϵ1	ADJ
ejpam-5827	567	74	,	,	PUNCT
ejpam-5827	567	75	ϵ2	ϵ2	ADJ
ejpam-5827	567	76	,	,	PUNCT
ejpam-5827	567	77	ϵ3	ϵ3	PROPN
ejpam-5827	567	78	}	}	PUNCT
ejpam-5827	567	79	,	,	PUNCT
ejpam-5827	567	80	{	{	PUNCT
ejpam-5827	567	81	ϵ1	ϵ1	ADJ
ejpam-5827	567	82	,	,	PUNCT
ejpam-5827	567	83	ϵ2	ϵ2	ADJ
ejpam-5827	567	84	,	,	PUNCT
ejpam-5827	567	85	ϵ4	ϵ4	PROPN
ejpam-5827	567	86	}	}	PUNCT
ejpam-5827	567	87	,	,	PUNCT
ejpam-5827	567	88	{	{	PUNCT
ejpam-5827	567	89	ϵ1	ϵ1	ADJ
ejpam-5827	567	90	,	,	PUNCT
ejpam-5827	567	91	ϵ2	ϵ2	ADJ
ejpam-5827	567	92	,	,	PUNCT
ejpam-5827	567	93	ϵ5	ϵ5	PROPN
ejpam-5827	567	94	}	}	PUNCT
ejpam-5827	567	95	,	,	PUNCT
ejpam-5827	567	96	{	{	PUNCT
ejpam-5827	567	97	ϵ1	ϵ1	ADJ
ejpam-5827	567	98	,	,	PUNCT
ejpam-5827	567	99	ϵ3	ϵ3	PROPN
ejpam-5827	567	100	,	,	PUNCT
ejpam-5827	567	101	ϵ4	ϵ4	PROPN
ejpam-5827	567	102	}	}	PUNCT
ejpam-5827	567	103	,	,	PUNCT
ejpam-5827	567	104	{	{	PUNCT
ejpam-5827	567	105	ϵ1	ϵ1	ADJ
ejpam-5827	567	106	,	,	PUNCT
ejpam-5827	567	107	ϵ3	ϵ3	PROPN
ejpam-5827	567	108	,	,	PUNCT
ejpam-5827	567	109	ϵ5	ϵ5	PROPN
ejpam-5827	567	110	}	}	PUNCT
ejpam-5827	567	111	,	,	PUNCT
ejpam-5827	567	112	{	{	PUNCT
ejpam-5827	567	113	ϵ1	ϵ1	ADJ
ejpam-5827	567	114	,	,	PUNCT
ejpam-5827	567	115	ϵ4	ϵ4	PROPN
ejpam-5827	567	116	,	,	PUNCT
ejpam-5827	567	117	ϵ5	ϵ5	PROPN
ejpam-5827	567	118	}	}	PUNCT
ejpam-5827	567	119	,	,	PUNCT
ejpam-5827	567	120	{	{	PUNCT
ejpam-5827	567	121	ϵ2	ϵ2	ADJ
ejpam-5827	567	122	,	,	PUNCT
ejpam-5827	567	123	ϵ3	ϵ3	PROPN
ejpam-5827	567	124	,	,	PUNCT
ejpam-5827	567	125	ϵ4	ϵ4	PROPN
ejpam-5827	567	126	}	}	PUNCT
ejpam-5827	567	127	,	,	PUNCT
ejpam-5827	567	128	{	{	PUNCT
ejpam-5827	567	129	ϵ2	ϵ2	ADJ
ejpam-5827	567	130	,	,	PUNCT
ejpam-5827	567	131	ϵ3	ϵ3	PROPN
ejpam-5827	567	132	,	,	PUNCT
ejpam-5827	567	133	ϵ5	ϵ5	PROPN
ejpam-5827	567	134	}	}	PUNCT
ejpam-5827	567	135	,	,	PUNCT
ejpam-5827	567	136	{	{	PUNCT
ejpam-5827	567	137	ϵ2	ϵ2	ADJ
ejpam-5827	567	138	,	,	PUNCT
ejpam-5827	567	139	ϵ4	ϵ4	PROPN
ejpam-5827	567	140	,	,	PUNCT
ejpam-5827	567	141	ϵ5	ϵ5	PROPN
ejpam-5827	567	142	}	}	PUNCT
ejpam-5827	567	143	,	,	PUNCT
ejpam-5827	567	144	{	{	PUNCT
ejpam-5827	567	145	ϵ3	ϵ3	PROPN
ejpam-5827	567	146	,	,	PUNCT
ejpam-5827	567	147	ϵ4	ϵ4	PROPN
ejpam-5827	567	148	,	,	PUNCT
ejpam-5827	567	149	ϵ5	ϵ5	PROPN
ejpam-5827	567	150	}	}	PUNCT
ejpam-5827	567	151	,	,	PUNCT
ejpam-5827	567	152	{	{	PUNCT
ejpam-5827	567	153	ϵ1	ϵ1	ADJ
ejpam-5827	567	154	,	,	PUNCT
ejpam-5827	567	155	ϵ2	ϵ2	ADJ
ejpam-5827	567	156	,	,	PUNCT
ejpam-5827	567	157	ϵ3	ϵ3	PROPN
ejpam-5827	567	158	,	,	PUNCT
ejpam-5827	567	159	ϵ4	ϵ4	PROPN
ejpam-5827	567	160	}	}	PUNCT
ejpam-5827	567	161	,	,	PUNCT
ejpam-5827	567	162	{	{	PUNCT
ejpam-5827	567	163	ϵ1	ϵ1	ADJ
ejpam-5827	567	164	,	,	PUNCT
ejpam-5827	567	165	ϵ2	ϵ2	ADJ
ejpam-5827	567	166	,	,	PUNCT
ejpam-5827	567	167	ϵ3	ϵ3	PROPN
ejpam-5827	567	168	,	,	PUNCT
ejpam-5827	567	169	ϵ5	ϵ5	PROPN
ejpam-5827	567	170	}	}	PUNCT
ejpam-5827	567	171	,	,	PUNCT
ejpam-5827	567	172	{	{	PUNCT
ejpam-5827	567	173	ϵ1	ϵ1	ADJ
ejpam-5827	567	174	,	,	PUNCT
ejpam-5827	567	175	ϵ2	ϵ2	ADJ
ejpam-5827	567	176	,	,	PUNCT
ejpam-5827	567	177	ϵ4	ϵ4	PROPN
ejpam-5827	567	178	,	,	PUNCT
ejpam-5827	567	179	ϵ5	ϵ5	PROPN
ejpam-5827	567	180	}	}	PUNCT
ejpam-5827	567	181	,	,	PUNCT
ejpam-5827	567	182	{	{	PUNCT
ejpam-5827	567	183	ϵ1	ϵ1	ADJ
ejpam-5827	567	184	,	,	PUNCT
ejpam-5827	567	185	ϵ3	ϵ3	PROPN
ejpam-5827	567	186	,	,	PUNCT
ejpam-5827	567	187	ϵ4	ϵ4	PROPN
ejpam-5827	567	188	,	,	PUNCT
ejpam-5827	567	189	ϵ5	ϵ5	PROPN
ejpam-5827	567	190	}	}	PUNCT
ejpam-5827	567	191	,	,	PUNCT
ejpam-5827	567	192	{	{	PUNCT
ejpam-5827	567	193	ϵ2	ϵ2	ADJ
ejpam-5827	567	194	,	,	PUNCT
ejpam-5827	567	195	ϵ3	ϵ3	PROPN
ejpam-5827	567	196	,	,	PUNCT
ejpam-5827	567	197	ϵ4	ϵ4	PROPN
ejpam-5827	567	198	,	,	PUNCT
ejpam-5827	567	199	ϵ5	ϵ5	PROPN
ejpam-5827	567	200	}	}	PUNCT
ejpam-5827	567	201	}	}	PUNCT
ejpam-5827	567	202	.	.	PUNCT
ejpam-5827	568	1	τp⟨r⟩	τp⟨r⟩	X
ejpam-5827	569	1	=	=	PUNCT
ejpam-5827	569	2	τp⟨l⟩	τp⟨l⟩	PUNCT
ejpam-5827	569	3	=	=	PUNCT
ejpam-5827	569	4	τp⟨i⟩	τp⟨i⟩	PROPN
ejpam-5827	569	5	=	=	PUNCT
ejpam-5827	569	6	τp⟨u⟩	τp⟨u⟩	PROPN
ejpam-5827	569	7	=	=	SYM
ejpam-5827	569	8	2v	2v	PROPN
ejpam-5827	569	9	.	.	PUNCT
ejpam-5827	570	1	τ	τ	PROPN
ejpam-5827	570	2	p̃r	p̃r	NOUN
ejpam-5827	570	3	=	=	PUNCT
ejpam-5827	570	4	{	{	PUNCT
ejpam-5827	570	5	∅,v	∅,v	X
ejpam-5827	570	6	,	,	PUNCT
ejpam-5827	570	7	{	{	PUNCT
ejpam-5827	570	8	ϵ1	ϵ1	ADJ
ejpam-5827	570	9	}	}	PUNCT
ejpam-5827	570	10	,	,	PUNCT
ejpam-5827	570	11	{	{	PUNCT
ejpam-5827	570	12	ϵ2	ϵ2	PROPN
ejpam-5827	570	13	}	}	PUNCT
ejpam-5827	570	14	,	,	PUNCT
ejpam-5827	570	15	{	{	PUNCT
ejpam-5827	570	16	ϵ3	ϵ3	PROPN
ejpam-5827	570	17	}	}	PUNCT
ejpam-5827	570	18	,	,	PUNCT
ejpam-5827	570	19	{	{	PUNCT
ejpam-5827	570	20	ϵ5	ϵ5	PROPN
ejpam-5827	570	21	}	}	PUNCT
ejpam-5827	570	22	,	,	PUNCT
ejpam-5827	570	23	{	{	PUNCT
ejpam-5827	570	24	ϵ1	ϵ1	ADJ
ejpam-5827	570	25	,	,	PUNCT
ejpam-5827	570	26	ϵ2	ϵ2	ADJ
ejpam-5827	570	27	}	}	PUNCT
ejpam-5827	570	28	,	,	PUNCT
ejpam-5827	570	29	{	{	PUNCT
ejpam-5827	570	30	ϵ1	ϵ1	ADJ
ejpam-5827	570	31	,	,	PUNCT
ejpam-5827	570	32	ϵ3	ϵ3	PROPN
ejpam-5827	570	33	}	}	PUNCT
ejpam-5827	570	34	,	,	PUNCT
ejpam-5827	570	35	{	{	PUNCT
ejpam-5827	570	36	ϵ1	ϵ1	ADJ
ejpam-5827	570	37	,	,	PUNCT
ejpam-5827	570	38	ϵ5	ϵ5	PROPN
ejpam-5827	570	39	}	}	PUNCT
ejpam-5827	570	40	,	,	PUNCT
ejpam-5827	570	41	{	{	PUNCT
ejpam-5827	570	42	ϵ2	ϵ2	ADJ
ejpam-5827	570	43	,	,	PUNCT
ejpam-5827	570	44	ϵ3	ϵ3	PROPN
ejpam-5827	570	45	}	}	PUNCT
ejpam-5827	570	46	,	,	PUNCT
ejpam-5827	570	47	{	{	PUNCT
ejpam-5827	570	48	ϵ2	ϵ2	ADJ
ejpam-5827	570	49	,	,	PUNCT
ejpam-5827	570	50	ϵ4	ϵ4	PROPN
ejpam-5827	570	51	}	}	PUNCT
ejpam-5827	570	52	,	,	PUNCT
ejpam-5827	570	53	{	{	PUNCT
ejpam-5827	570	54	ϵ2	ϵ2	ADJ
ejpam-5827	570	55	,	,	PUNCT
ejpam-5827	570	56	ϵ5	ϵ5	PROPN
ejpam-5827	570	57	}	}	PUNCT
ejpam-5827	570	58	,	,	PUNCT
ejpam-5827	570	59	{	{	PUNCT
ejpam-5827	570	60	ϵ3	ϵ3	PROPN
ejpam-5827	570	61	,	,	PUNCT
ejpam-5827	570	62	ϵ4	ϵ4	PROPN
ejpam-5827	570	63	}	}	PUNCT
ejpam-5827	570	64	,	,	PUNCT
ejpam-5827	570	65	{	{	PUNCT
ejpam-5827	570	66	ϵ3	ϵ3	PROPN
ejpam-5827	570	67	,	,	PUNCT
ejpam-5827	570	68	ϵ5	ϵ5	PROPN
ejpam-5827	570	69	}	}	PUNCT
ejpam-5827	570	70	,	,	PUNCT
ejpam-5827	570	71	{	{	PUNCT
ejpam-5827	570	72	ϵ1	ϵ1	ADJ
ejpam-5827	570	73	,	,	PUNCT
ejpam-5827	570	74	ϵ2	ϵ2	ADJ
ejpam-5827	570	75	,	,	PUNCT
ejpam-5827	570	76	ϵ3	ϵ3	PROPN
ejpam-5827	570	77	}	}	PUNCT
ejpam-5827	570	78	,	,	PUNCT
ejpam-5827	570	79	{	{	PUNCT
ejpam-5827	570	80	ϵ1	ϵ1	ADJ
ejpam-5827	570	81	,	,	PUNCT
ejpam-5827	570	82	ϵ2	ϵ2	ADJ
ejpam-5827	570	83	,	,	PUNCT
ejpam-5827	570	84	ϵ4	ϵ4	PROPN
ejpam-5827	570	85	}	}	PUNCT
ejpam-5827	570	86	,	,	PUNCT
ejpam-5827	570	87	{	{	PUNCT
ejpam-5827	570	88	ϵ1	ϵ1	ADJ
ejpam-5827	570	89	,	,	PUNCT
ejpam-5827	570	90	ϵ2	ϵ2	ADJ
ejpam-5827	570	91	,	,	PUNCT
ejpam-5827	570	92	ϵ5	ϵ5	PROPN
ejpam-5827	570	93	}	}	PUNCT
ejpam-5827	570	94	,	,	PUNCT
ejpam-5827	570	95	{	{	PUNCT
ejpam-5827	570	96	ϵ1	ϵ1	ADJ
ejpam-5827	570	97	,	,	PUNCT
ejpam-5827	570	98	ϵ3	ϵ3	PROPN
ejpam-5827	570	99	,	,	PUNCT
ejpam-5827	570	100	ϵ4	ϵ4	PROPN
ejpam-5827	570	101	}	}	PUNCT
ejpam-5827	570	102	,	,	PUNCT
ejpam-5827	570	103	{	{	PUNCT
ejpam-5827	570	104	ϵ1	ϵ1	ADJ
ejpam-5827	570	105	,	,	PUNCT
ejpam-5827	570	106	ϵ3	ϵ3	PROPN
ejpam-5827	570	107	,	,	PUNCT
ejpam-5827	570	108	ϵ5	ϵ5	PROPN
ejpam-5827	570	109	}	}	PUNCT
ejpam-5827	570	110	,	,	PUNCT
ejpam-5827	570	111	{	{	PUNCT
ejpam-5827	570	112	ϵ2	ϵ2	ADJ
ejpam-5827	570	113	,	,	PUNCT
ejpam-5827	570	114	ϵ3	ϵ3	PROPN
ejpam-5827	570	115	,	,	PUNCT
ejpam-5827	570	116	ϵ4	ϵ4	PROPN
ejpam-5827	570	117	}	}	PUNCT
ejpam-5827	570	118	,	,	PUNCT
ejpam-5827	570	119	{	{	PUNCT
ejpam-5827	570	120	ϵ2	ϵ2	ADJ
ejpam-5827	570	121	,	,	PUNCT
ejpam-5827	570	122	ϵ3	ϵ3	PROPN
ejpam-5827	570	123	,	,	PUNCT
ejpam-5827	570	124	ϵ5	ϵ5	PROPN
ejpam-5827	570	125	}	}	PUNCT
ejpam-5827	570	126	,	,	PUNCT
ejpam-5827	570	127	{	{	PUNCT
ejpam-5827	570	128	ϵ2	ϵ2	ADJ
ejpam-5827	570	129	,	,	PUNCT
ejpam-5827	570	130	ϵ4	ϵ4	PROPN
ejpam-5827	570	131	,	,	PUNCT
ejpam-5827	570	132	ϵ5	ϵ5	PROPN
ejpam-5827	570	133	}	}	PUNCT
ejpam-5827	570	134	,	,	PUNCT
ejpam-5827	570	135	{	{	PUNCT
ejpam-5827	570	136	ϵ3	ϵ3	PROPN
ejpam-5827	570	137	,	,	PUNCT
ejpam-5827	570	138	ϵ4	ϵ4	PROPN
ejpam-5827	570	139	,	,	PUNCT
ejpam-5827	570	140	ϵ5	ϵ5	PROPN
ejpam-5827	570	141	}	}	PUNCT
ejpam-5827	570	142	,	,	PUNCT
ejpam-5827	570	143	{	{	PUNCT
ejpam-5827	570	144	ϵ1	ϵ1	ADJ
ejpam-5827	570	145	,	,	PUNCT
ejpam-5827	570	146	ϵ2	ϵ2	ADJ
ejpam-5827	570	147	,	,	PUNCT
ejpam-5827	570	148	ϵ3	ϵ3	PROPN
ejpam-5827	570	149	,	,	PUNCT
ejpam-5827	570	150	ϵ4	ϵ4	PROPN
ejpam-5827	570	151	}	}	PUNCT
ejpam-5827	570	152	,	,	PUNCT
ejpam-5827	570	153	{	{	PUNCT
ejpam-5827	570	154	ϵ1	ϵ1	ADJ
ejpam-5827	570	155	,	,	PUNCT
ejpam-5827	570	156	ϵ2	ϵ2	ADJ
ejpam-5827	570	157	,	,	PUNCT
ejpam-5827	570	158	ϵ3	ϵ3	PROPN
ejpam-5827	570	159	,	,	PUNCT
ejpam-5827	570	160	ϵ5	ϵ5	PROPN
ejpam-5827	570	161	}	}	PUNCT
ejpam-5827	570	162	,	,	PUNCT
ejpam-5827	570	163	{	{	PUNCT
ejpam-5827	570	164	ϵ1	ϵ1	ADJ
ejpam-5827	570	165	,	,	PUNCT
ejpam-5827	570	166	ϵ2	ϵ2	ADJ
ejpam-5827	570	167	,	,	PUNCT
ejpam-5827	570	168	ϵ4	ϵ4	PROPN
ejpam-5827	570	169	,	,	PUNCT
ejpam-5827	570	170	ϵ5	ϵ5	PROPN
ejpam-5827	570	171	}	}	PUNCT
ejpam-5827	570	172	,	,	PUNCT
ejpam-5827	570	173	{	{	PUNCT
ejpam-5827	570	174	ϵ1	ϵ1	ADJ
ejpam-5827	570	175	,	,	PUNCT
ejpam-5827	570	176	ϵ3	ϵ3	PROPN
ejpam-5827	570	177	,	,	PUNCT
ejpam-5827	570	178	ϵ4	ϵ4	PROPN
ejpam-5827	570	179	,	,	PUNCT
ejpam-5827	570	180	ϵ5	ϵ5	PROPN
ejpam-5827	570	181	}	}	PUNCT
ejpam-5827	570	182	,	,	PUNCT
ejpam-5827	570	183	{	{	PUNCT
ejpam-5827	570	184	ϵ2	ϵ2	ADJ
ejpam-5827	570	185	,	,	PUNCT
ejpam-5827	570	186	ϵ3	ϵ3	PROPN
ejpam-5827	570	187	,	,	PUNCT
ejpam-5827	570	188	ϵ4	ϵ4	PROPN
ejpam-5827	570	189	,	,	PUNCT
ejpam-5827	570	190	ϵ5	ϵ5	PROPN
ejpam-5827	570	191	}	}	PUNCT
ejpam-5827	570	192	}	}	PUNCT
ejpam-5827	570	193	.	.	PUNCT
ejpam-5827	571	1	τ	τ	PROPN
ejpam-5827	571	2	p̃l	p̃l	PROPN
ejpam-5827	571	3	=	=	X
ejpam-5827	571	4	{	{	PUNCT
ejpam-5827	571	5	∅,v	∅,v	X
ejpam-5827	571	6	,	,	PUNCT
ejpam-5827	571	7	{	{	PUNCT
ejpam-5827	571	8	ϵ2	ϵ2	PROPN
ejpam-5827	571	9	}	}	PUNCT
ejpam-5827	571	10	,	,	PUNCT
ejpam-5827	571	11	{	{	PUNCT
ejpam-5827	571	12	ϵ3	ϵ3	PROPN
ejpam-5827	571	13	}	}	PUNCT
ejpam-5827	571	14	,	,	PUNCT
ejpam-5827	571	15	{	{	PUNCT
ejpam-5827	571	16	ϵ4	ϵ4	NOUN
ejpam-5827	571	17	}	}	PUNCT
ejpam-5827	571	18	,	,	PUNCT
ejpam-5827	571	19	{	{	PUNCT
ejpam-5827	571	20	ϵ5	ϵ5	PROPN
ejpam-5827	571	21	}	}	PUNCT
ejpam-5827	571	22	,	,	PUNCT
ejpam-5827	571	23	{	{	PUNCT
ejpam-5827	571	24	ϵ1	ϵ1	ADJ
ejpam-5827	571	25	,	,	PUNCT
ejpam-5827	571	26	ϵ2	ϵ2	ADJ
ejpam-5827	571	27	}	}	PUNCT
ejpam-5827	571	28	,	,	PUNCT
ejpam-5827	571	29	{	{	PUNCT
ejpam-5827	571	30	ϵ1	ϵ1	ADJ
ejpam-5827	571	31	,	,	PUNCT
ejpam-5827	571	32	ϵ3	ϵ3	PROPN
ejpam-5827	571	33	}	}	PUNCT
ejpam-5827	571	34	,	,	PUNCT
ejpam-5827	571	35	{	{	PUNCT
ejpam-5827	571	36	ϵ2	ϵ2	ADJ
ejpam-5827	571	37	,	,	PUNCT
ejpam-5827	571	38	ϵ3	ϵ3	PROPN
ejpam-5827	571	39	}	}	PUNCT
ejpam-5827	571	40	,	,	PUNCT
ejpam-5827	571	41	{	{	PUNCT
ejpam-5827	571	42	ϵ2	ϵ2	ADJ
ejpam-5827	571	43	,	,	PUNCT
ejpam-5827	571	44	ϵ4	ϵ4	PROPN
ejpam-5827	571	45	}	}	PUNCT
ejpam-5827	571	46	,	,	PUNCT
ejpam-5827	571	47	{	{	PUNCT
ejpam-5827	571	48	ϵ2	ϵ2	ADJ
ejpam-5827	571	49	,	,	PUNCT
ejpam-5827	571	50	ϵ5	ϵ5	PROPN
ejpam-5827	571	51	}	}	PUNCT
ejpam-5827	571	52	,	,	PUNCT
ejpam-5827	571	53	{	{	PUNCT
ejpam-5827	571	54	ϵ3	ϵ3	PROPN
ejpam-5827	571	55	,	,	PUNCT
ejpam-5827	571	56	ϵ4	ϵ4	PROPN
ejpam-5827	571	57	}	}	PUNCT
ejpam-5827	571	58	,	,	PUNCT
ejpam-5827	571	59	{	{	PUNCT
ejpam-5827	571	60	ϵ3	ϵ3	PROPN
ejpam-5827	571	61	,	,	PUNCT
ejpam-5827	571	62	ϵ5	ϵ5	PROPN
ejpam-5827	571	63	}	}	PUNCT
ejpam-5827	571	64	,	,	PUNCT
ejpam-5827	571	65	{	{	PUNCT
ejpam-5827	571	66	ϵ4	ϵ4	NOUN
ejpam-5827	571	67	,	,	PUNCT
ejpam-5827	571	68	ϵ5	ϵ5	PROPN
ejpam-5827	571	69	}	}	PUNCT
ejpam-5827	571	70	,	,	PUNCT
ejpam-5827	571	71	{	{	PUNCT
ejpam-5827	571	72	ϵ1	ϵ1	ADJ
ejpam-5827	571	73	,	,	PUNCT
ejpam-5827	571	74	ϵ2	ϵ2	ADJ
ejpam-5827	571	75	,	,	PUNCT
ejpam-5827	571	76	ϵ3	ϵ3	PROPN
ejpam-5827	571	77	}	}	PUNCT
ejpam-5827	571	78	,	,	PUNCT
ejpam-5827	571	79	{	{	PUNCT
ejpam-5827	571	80	ϵ1	ϵ1	ADJ
ejpam-5827	571	81	,	,	PUNCT
ejpam-5827	571	82	ϵ2	ϵ2	ADJ
ejpam-5827	571	83	,	,	PUNCT
ejpam-5827	571	84	ϵ4	ϵ4	PROPN
ejpam-5827	571	85	}	}	PUNCT
ejpam-5827	571	86	,	,	PUNCT
ejpam-5827	571	87	{	{	PUNCT
ejpam-5827	571	88	ϵ1	ϵ1	ADJ
ejpam-5827	571	89	,	,	PUNCT
ejpam-5827	571	90	ϵ2	ϵ2	ADJ
ejpam-5827	571	91	,	,	PUNCT
ejpam-5827	571	92	ϵ5	ϵ5	PROPN
ejpam-5827	571	93	}	}	PUNCT
ejpam-5827	571	94	,	,	PUNCT
ejpam-5827	571	95	{	{	PUNCT
ejpam-5827	571	96	ϵ1	ϵ1	ADJ
ejpam-5827	571	97	,	,	PUNCT
ejpam-5827	571	98	ϵ3	ϵ3	PROPN
ejpam-5827	571	99	,	,	PUNCT
ejpam-5827	571	100	ϵ4	ϵ4	PROPN
ejpam-5827	571	101	}	}	PUNCT
ejpam-5827	571	102	,	,	PUNCT
ejpam-5827	571	103	{	{	PUNCT
ejpam-5827	571	104	ϵ1	ϵ1	ADJ
ejpam-5827	571	105	,	,	PUNCT
ejpam-5827	571	106	ϵ3	ϵ3	PROPN
ejpam-5827	571	107	,	,	PUNCT
ejpam-5827	571	108	ϵ5	ϵ5	PROPN
ejpam-5827	571	109	}	}	PUNCT
ejpam-5827	571	110	,	,	PUNCT
ejpam-5827	571	111	{	{	PUNCT
ejpam-5827	571	112	ϵ2	ϵ2	ADJ
ejpam-5827	571	113	,	,	PUNCT
ejpam-5827	571	114	ϵ3	ϵ3	PROPN
ejpam-5827	571	115	,	,	PUNCT
ejpam-5827	571	116	ϵ4	ϵ4	PROPN
ejpam-5827	571	117	}	}	PUNCT
ejpam-5827	571	118	,	,	PUNCT
ejpam-5827	571	119	{	{	PUNCT
ejpam-5827	571	120	ϵ2	ϵ2	ADJ
ejpam-5827	571	121	,	,	PUNCT
ejpam-5827	571	122	ϵ3	ϵ3	PROPN
ejpam-5827	571	123	,	,	PUNCT
ejpam-5827	571	124	ϵ5	ϵ5	PROPN
ejpam-5827	571	125	}	}	PUNCT
ejpam-5827	571	126	,	,	PUNCT
ejpam-5827	571	127	{	{	PUNCT
ejpam-5827	571	128	ϵ2	ϵ2	ADJ
ejpam-5827	571	129	,	,	PUNCT
ejpam-5827	571	130	ϵ4	ϵ4	PROPN
ejpam-5827	571	131	,	,	PUNCT
ejpam-5827	571	132	ϵ5	ϵ5	PROPN
ejpam-5827	571	133	}	}	PUNCT
ejpam-5827	571	134	,	,	PUNCT
ejpam-5827	571	135	{	{	PUNCT
ejpam-5827	571	136	ϵ3	ϵ3	PROPN
ejpam-5827	571	137	,	,	PUNCT
ejpam-5827	571	138	ϵ4	ϵ4	PROPN
ejpam-5827	571	139	,	,	PUNCT
ejpam-5827	571	140	ϵ5	ϵ5	PROPN
ejpam-5827	571	141	}	}	PUNCT
ejpam-5827	571	142	,	,	PUNCT
ejpam-5827	571	143	r.	r.	PROPN
ejpam-5827	571	144	a.	a.	PROPN
ejpam-5827	571	145	hosny	hosny	PROPN
ejpam-5827	571	146	,	,	PUNCT
ejpam-5827	571	147	m.	m.	PROPN
ejpam-5827	571	148	k.	k.	PROPN
ejpam-5827	571	149	el	el	PROPN
ejpam-5827	571	150	-	-	PROPN
ejpam-5827	571	151	bably	bably	ADV
ejpam-5827	571	152	,	,	PUNCT
ejpam-5827	571	153	m.	m.	NOUN
ejpam-5827	571	154	a.	a.	PROPN
ejpam-5827	571	155	el	el	PROPN
ejpam-5827	571	156	-	-	PROPN
ejpam-5827	571	157	gayar	gayar	PROPN
ejpam-5827	571	158	/	/	SYM
ejpam-5827	571	159	eur	eur	PROPN
ejpam-5827	571	160	.	.	PUNCT
ejpam-5827	572	1	j.	j.	PROPN
ejpam-5827	572	2	pure	pure	PROPN
ejpam-5827	572	3	appl	appl	PROPN
ejpam-5827	572	4	.	.	PROPN
ejpam-5827	572	5	math	math	PROPN
ejpam-5827	572	6	,	,	PUNCT
ejpam-5827	572	7	18	18	NUM
ejpam-5827	572	8	(	(	PUNCT
ejpam-5827	572	9	1	1	NUM
ejpam-5827	572	10	)	)	PUNCT
ejpam-5827	572	11	(	(	PUNCT
ejpam-5827	572	12	2025	2025	NUM
ejpam-5827	572	13	)	)	PUNCT
ejpam-5827	572	14	,	,	PUNCT
ejpam-5827	572	15	5827	5827	NUM
ejpam-5827	572	16	22	22	NUM
ejpam-5827	572	17	of	of	ADP
ejpam-5827	572	18	29	29	NUM
ejpam-5827	572	19	{	{	PUNCT
ejpam-5827	572	20	ϵ1	ϵ1	ADJ
ejpam-5827	572	21	,	,	PUNCT
ejpam-5827	572	22	ϵ2	ϵ2	ADJ
ejpam-5827	572	23	,	,	PUNCT
ejpam-5827	572	24	ϵ3	ϵ3	PROPN
ejpam-5827	572	25	,	,	PUNCT
ejpam-5827	572	26	ϵ4	ϵ4	PROPN
ejpam-5827	572	27	}	}	PUNCT
ejpam-5827	572	28	,	,	PUNCT
ejpam-5827	572	29	{	{	PUNCT
ejpam-5827	572	30	ϵ1	ϵ1	ADJ
ejpam-5827	572	31	,	,	PUNCT
ejpam-5827	572	32	ϵ2	ϵ2	ADJ
ejpam-5827	572	33	,	,	PUNCT
ejpam-5827	572	34	ϵ3	ϵ3	PROPN
ejpam-5827	572	35	,	,	PUNCT
ejpam-5827	572	36	ϵ5	ϵ5	PROPN
ejpam-5827	572	37	}	}	PUNCT
ejpam-5827	572	38	,	,	PUNCT
ejpam-5827	572	39	{	{	PUNCT
ejpam-5827	572	40	ϵ1	ϵ1	ADJ
ejpam-5827	572	41	,	,	PUNCT
ejpam-5827	572	42	ϵ2	ϵ2	ADJ
ejpam-5827	572	43	,	,	PUNCT
ejpam-5827	572	44	ϵ4	ϵ4	PROPN
ejpam-5827	572	45	,	,	PUNCT
ejpam-5827	572	46	ϵ5	ϵ5	PROPN
ejpam-5827	572	47	}	}	PUNCT
ejpam-5827	572	48	,	,	PUNCT
ejpam-5827	572	49	{	{	PUNCT
ejpam-5827	572	50	ϵ1	ϵ1	ADJ
ejpam-5827	572	51	,	,	PUNCT
ejpam-5827	572	52	ϵ3	ϵ3	PROPN
ejpam-5827	572	53	,	,	PUNCT
ejpam-5827	572	54	ϵ4	ϵ4	PROPN
ejpam-5827	572	55	,	,	PUNCT
ejpam-5827	572	56	ϵ5	ϵ5	PROPN
ejpam-5827	572	57	}	}	PUNCT
ejpam-5827	572	58	,	,	PUNCT
ejpam-5827	572	59	{	{	PUNCT
ejpam-5827	572	60	ϵ2	ϵ2	ADJ
ejpam-5827	572	61	,	,	PUNCT
ejpam-5827	572	62	ϵ3	ϵ3	PROPN
ejpam-5827	572	63	,	,	PUNCT
ejpam-5827	572	64	ϵ4	ϵ4	PROPN
ejpam-5827	572	65	,	,	PUNCT
ejpam-5827	572	66	ϵ5	ϵ5	PROPN
ejpam-5827	572	67	}	}	PUNCT
ejpam-5827	572	68	}	}	PUNCT
ejpam-5827	572	69	.	.	PUNCT
ejpam-5827	573	1	τ	τ	PROPN
ejpam-5827	573	2	p̃i	p̃i	NOUN
ejpam-5827	573	3	=	=	SYM
ejpam-5827	573	4	2v	2v	PROPN
ejpam-5827	573	5	.	.	PUNCT
ejpam-5827	574	1	τ	τ	X
ejpam-5827	574	2	p̃u	p̃u	PROPN
ejpam-5827	574	3	=	=	NOUN
ejpam-5827	574	4	{	{	PUNCT
ejpam-5827	574	5	∅,v	∅,v	X
ejpam-5827	574	6	,	,	PUNCT
ejpam-5827	574	7	{	{	PUNCT
ejpam-5827	574	8	ϵ2	ϵ2	PROPN
ejpam-5827	574	9	}	}	PUNCT
ejpam-5827	574	10	,	,	PUNCT
ejpam-5827	574	11	{	{	PUNCT
ejpam-5827	574	12	ϵ3	ϵ3	PROPN
ejpam-5827	574	13	}	}	PUNCT
ejpam-5827	574	14	,	,	PUNCT
ejpam-5827	574	15	{	{	PUNCT
ejpam-5827	574	16	ϵ1	ϵ1	ADJ
ejpam-5827	574	17	,	,	PUNCT
ejpam-5827	574	18	ϵ2	ϵ2	ADJ
ejpam-5827	574	19	}	}	PUNCT
ejpam-5827	574	20	,	,	PUNCT
ejpam-5827	574	21	{	{	PUNCT
ejpam-5827	574	22	ϵ1	ϵ1	ADJ
ejpam-5827	574	23	,	,	PUNCT
ejpam-5827	574	24	ϵ3	ϵ3	PROPN
ejpam-5827	574	25	}	}	PUNCT
ejpam-5827	574	26	,	,	PUNCT
ejpam-5827	574	27	{	{	PUNCT
ejpam-5827	574	28	ϵ2	ϵ2	ADJ
ejpam-5827	574	29	,	,	PUNCT
ejpam-5827	574	30	ϵ3	ϵ3	PROPN
ejpam-5827	574	31	}	}	PUNCT
ejpam-5827	574	32	,	,	PUNCT
ejpam-5827	574	33	{	{	PUNCT
ejpam-5827	574	34	ϵ2	ϵ2	ADJ
ejpam-5827	574	35	,	,	PUNCT
ejpam-5827	574	36	ϵ4	ϵ4	PROPN
ejpam-5827	574	37	}	}	PUNCT
ejpam-5827	574	38	,	,	PUNCT
ejpam-5827	574	39	{	{	PUNCT
ejpam-5827	574	40	ϵ2	ϵ2	ADJ
ejpam-5827	574	41	,	,	PUNCT
ejpam-5827	574	42	ϵ5	ϵ5	PROPN
ejpam-5827	574	43	}	}	PUNCT
ejpam-5827	574	44	,	,	PUNCT
ejpam-5827	574	45	{	{	PUNCT
ejpam-5827	574	46	ϵ3	ϵ3	PROPN
ejpam-5827	574	47	,	,	PUNCT
ejpam-5827	574	48	ϵ4	ϵ4	PROPN
ejpam-5827	574	49	}	}	PUNCT
ejpam-5827	574	50	,	,	PUNCT
ejpam-5827	574	51	{	{	PUNCT
ejpam-5827	574	52	ϵ3	ϵ3	PROPN
ejpam-5827	574	53	,	,	PUNCT
ejpam-5827	574	54	ϵ5	ϵ5	PROPN
ejpam-5827	574	55	}	}	PUNCT
ejpam-5827	574	56	,	,	PUNCT
ejpam-5827	574	57	{	{	PUNCT
ejpam-5827	574	58	ϵ1	ϵ1	ADJ
ejpam-5827	574	59	,	,	PUNCT
ejpam-5827	574	60	ϵ2	ϵ2	ADJ
ejpam-5827	574	61	,	,	PUNCT
ejpam-5827	574	62	ϵ3	ϵ3	PROPN
ejpam-5827	574	63	}	}	PUNCT
ejpam-5827	574	64	,	,	PUNCT
ejpam-5827	574	65	{	{	PUNCT
ejpam-5827	574	66	ϵ1	ϵ1	ADJ
ejpam-5827	574	67	,	,	PUNCT
ejpam-5827	574	68	ϵ2	ϵ2	ADJ
ejpam-5827	574	69	,	,	PUNCT
ejpam-5827	574	70	ϵ4	ϵ4	PROPN
ejpam-5827	574	71	}	}	PUNCT
ejpam-5827	574	72	,	,	PUNCT
ejpam-5827	574	73	{	{	PUNCT
ejpam-5827	574	74	ϵ1	ϵ1	ADJ
ejpam-5827	574	75	,	,	PUNCT
ejpam-5827	574	76	ϵ2	ϵ2	ADJ
ejpam-5827	574	77	,	,	PUNCT
ejpam-5827	574	78	ϵ5	ϵ5	PROPN
ejpam-5827	574	79	}	}	PUNCT
ejpam-5827	574	80	,	,	PUNCT
ejpam-5827	574	81	{	{	PUNCT
ejpam-5827	574	82	ϵ1	ϵ1	ADJ
ejpam-5827	574	83	,	,	PUNCT
ejpam-5827	574	84	ϵ3	ϵ3	PROPN
ejpam-5827	574	85	,	,	PUNCT
ejpam-5827	574	86	ϵ4	ϵ4	PROPN
ejpam-5827	574	87	}	}	PUNCT
ejpam-5827	574	88	,	,	PUNCT
ejpam-5827	574	89	{	{	PUNCT
ejpam-5827	574	90	ϵ1	ϵ1	ADJ
ejpam-5827	574	91	,	,	PUNCT
ejpam-5827	574	92	ϵ3	ϵ3	PROPN
ejpam-5827	574	93	,	,	PUNCT
ejpam-5827	574	94	ϵ5	ϵ5	PROPN
ejpam-5827	574	95	}	}	PUNCT
ejpam-5827	574	96	,	,	PUNCT
ejpam-5827	574	97	{	{	PUNCT
ejpam-5827	574	98	ϵ2	ϵ2	ADJ
ejpam-5827	574	99	,	,	PUNCT
ejpam-5827	574	100	ϵ3	ϵ3	PROPN
ejpam-5827	574	101	,	,	PUNCT
ejpam-5827	574	102	ϵ4	ϵ4	PROPN
ejpam-5827	574	103	}	}	PUNCT
ejpam-5827	574	104	,	,	PUNCT
ejpam-5827	574	105	{	{	PUNCT
ejpam-5827	574	106	ϵ2	ϵ2	ADJ
ejpam-5827	574	107	,	,	PUNCT
ejpam-5827	574	108	ϵ3	ϵ3	PROPN
ejpam-5827	574	109	,	,	PUNCT
ejpam-5827	574	110	ϵ5	ϵ5	PROPN
ejpam-5827	574	111	}	}	PUNCT
ejpam-5827	574	112	,	,	PUNCT
ejpam-5827	574	113	{	{	PUNCT
ejpam-5827	574	114	ϵ2	ϵ2	ADJ
ejpam-5827	574	115	,	,	PUNCT
ejpam-5827	574	116	ϵ4	ϵ4	PROPN
ejpam-5827	574	117	,	,	PUNCT
ejpam-5827	574	118	ϵ5	ϵ5	PROPN
ejpam-5827	574	119	}	}	PUNCT
ejpam-5827	574	120	,	,	PUNCT
ejpam-5827	574	121	{	{	PUNCT
ejpam-5827	574	122	ϵ3	ϵ3	PROPN
ejpam-5827	574	123	,	,	PUNCT
ejpam-5827	574	124	ϵ4	ϵ4	PROPN
ejpam-5827	574	125	,	,	PUNCT
ejpam-5827	574	126	ϵ5	ϵ5	PROPN
ejpam-5827	574	127	}	}	PUNCT
ejpam-5827	574	128	,	,	PUNCT
ejpam-5827	574	129	{	{	PUNCT
ejpam-5827	574	130	ϵ1	ϵ1	ADJ
ejpam-5827	574	131	,	,	PUNCT
ejpam-5827	574	132	ϵ2	ϵ2	ADJ
ejpam-5827	574	133	,	,	PUNCT
ejpam-5827	574	134	ϵ3	ϵ3	PROPN
ejpam-5827	574	135	,	,	PUNCT
ejpam-5827	574	136	ϵ4	ϵ4	PROPN
ejpam-5827	574	137	}	}	PUNCT
ejpam-5827	574	138	,	,	PUNCT
ejpam-5827	574	139	{	{	PUNCT
ejpam-5827	574	140	ϵ1	ϵ1	ADJ
ejpam-5827	574	141	,	,	PUNCT
ejpam-5827	574	142	ϵ2	ϵ2	ADJ
ejpam-5827	574	143	,	,	PUNCT
ejpam-5827	574	144	ϵ3	ϵ3	PROPN
ejpam-5827	574	145	,	,	PUNCT
ejpam-5827	574	146	ϵ5	ϵ5	PROPN
ejpam-5827	574	147	}	}	PUNCT
ejpam-5827	574	148	,	,	PUNCT
ejpam-5827	574	149	{	{	PUNCT
ejpam-5827	574	150	ϵ1	ϵ1	ADJ
ejpam-5827	574	151	,	,	PUNCT
ejpam-5827	574	152	ϵ2	ϵ2	ADJ
ejpam-5827	574	153	,	,	PUNCT
ejpam-5827	574	154	ϵ4	ϵ4	PROPN
ejpam-5827	574	155	,	,	PUNCT
ejpam-5827	574	156	ϵ5	ϵ5	PROPN
ejpam-5827	574	157	}	}	PUNCT
ejpam-5827	574	158	,	,	PUNCT
ejpam-5827	574	159	{	{	PUNCT
ejpam-5827	574	160	ϵ1	ϵ1	ADJ
ejpam-5827	574	161	,	,	PUNCT
ejpam-5827	574	162	ϵ3	ϵ3	PROPN
ejpam-5827	574	163	,	,	PUNCT
ejpam-5827	574	164	ϵ4	ϵ4	PROPN
ejpam-5827	574	165	,	,	PUNCT
ejpam-5827	574	166	ϵ5	ϵ5	PROPN
ejpam-5827	574	167	}	}	PUNCT
ejpam-5827	574	168	,	,	PUNCT
ejpam-5827	574	169	{	{	PUNCT
ejpam-5827	574	170	ϵ2	ϵ2	ADJ
ejpam-5827	574	171	,	,	PUNCT
ejpam-5827	574	172	ϵ3	ϵ3	PROPN
ejpam-5827	574	173	,	,	PUNCT
ejpam-5827	574	174	ϵ4	ϵ4	PROPN
ejpam-5827	574	175	,	,	PUNCT
ejpam-5827	574	176	ϵ5	ϵ5	PROPN
ejpam-5827	574	177	}	}	PUNCT
ejpam-5827	574	178	}	}	PUNCT
ejpam-5827	574	179	.	.	PUNCT
ejpam-5827	575	1	τ	τ	PROPN
ejpam-5827	575	2	p̃⟨r⟩	p̃⟨r⟩	NOUN
ejpam-5827	575	3	=	=	PUNCT
ejpam-5827	575	4	τ	τ	X
ejpam-5827	575	5	p̃⟨l⟩	p̃⟨l⟩	NOUN
ejpam-5827	575	6	=	=	PROPN
ejpam-5827	575	7	τ	τ	PROPN
ejpam-5827	575	8	p̃⟨i⟩	p̃⟨i⟩	NOUN
ejpam-5827	575	9	=	=	SYM
ejpam-5827	575	10	τ	τ	PROPN
ejpam-5827	575	11	p̃⟨u⟩	p̃⟨u⟩	NOUN
ejpam-5827	575	12	=	=	SYM
ejpam-5827	575	13	2v	2v	PROPN
ejpam-5827	575	14	.	.	PUNCT
ejpam-5827	576	1	note	note	VERB
ejpam-5827	576	2	that	that	SCONJ
ejpam-5827	576	3	:	:	PUNCT
ejpam-5827	576	4	p̃	p̃	PROPN
ejpam-5827	576	5	is	be	AUX
ejpam-5827	576	6	not	not	PART
ejpam-5827	576	7	ideal	ideal	ADJ
ejpam-5827	576	8	.	.	PUNCT
ejpam-5827	577	1	let	let	VERB
ejpam-5827	577	2	i	i	PRON
ejpam-5827	577	3	=	=	PUNCT
ejpam-5827	577	4	{	{	PUNCT
ejpam-5827	577	5	∅	∅	NOUN
ejpam-5827	577	6	,	,	PUNCT
ejpam-5827	577	7	{	{	PUNCT
ejpam-5827	577	8	ϵ1	ϵ1	ADJ
ejpam-5827	577	9	}	}	PUNCT
ejpam-5827	577	10	,	,	PUNCT
ejpam-5827	577	11	{	{	PUNCT
ejpam-5827	577	12	ϵ2	ϵ2	PROPN
ejpam-5827	577	13	}	}	PUNCT
ejpam-5827	577	14	,	,	PUNCT
ejpam-5827	577	15	{	{	PUNCT
ejpam-5827	577	16	ϵ3	ϵ3	PROPN
ejpam-5827	577	17	}	}	PUNCT
ejpam-5827	577	18	,	,	PUNCT
ejpam-5827	577	19	{	{	PUNCT
ejpam-5827	577	20	ϵ1	ϵ1	ADJ
ejpam-5827	577	21	,	,	PUNCT
ejpam-5827	577	22	ϵ2	ϵ2	ADJ
ejpam-5827	577	23	}	}	PUNCT
ejpam-5827	577	24	,	,	PUNCT
ejpam-5827	577	25	{	{	PUNCT
ejpam-5827	577	26	ϵ1	ϵ1	ADJ
ejpam-5827	577	27	,	,	PUNCT
ejpam-5827	577	28	ϵ3	ϵ3	PROPN
ejpam-5827	577	29	}	}	PUNCT
ejpam-5827	577	30	,	,	PUNCT
ejpam-5827	577	31	{	{	PUNCT
ejpam-5827	577	32	ϵ2	ϵ2	ADJ
ejpam-5827	577	33	,	,	PUNCT
ejpam-5827	577	34	ϵ3	ϵ3	PROPN
ejpam-5827	577	35	}	}	PUNCT
ejpam-5827	577	36	,	,	PUNCT
ejpam-5827	577	37	{	{	PUNCT
ejpam-5827	577	38	ϵ1	ϵ1	ADJ
ejpam-5827	577	39	,	,	PUNCT
ejpam-5827	577	40	ϵ2	ϵ2	ADJ
ejpam-5827	577	41	,	,	PUNCT
ejpam-5827	577	42	ϵ3	ϵ3	PROPN
ejpam-5827	577	43	}	}	PUNCT
ejpam-5827	577	44	}	}	PUNCT
ejpam-5827	577	45	be	be	AUX
ejpam-5827	577	46	an	an	DET
ejpam-5827	577	47	ideal	ideal	NOUN
ejpam-5827	577	48	on	on	ADP
ejpam-5827	578	1	v.	v.	ADV
ejpam-5827	578	2	then	then	ADV
ejpam-5827	578	3	,	,	PUNCT
ejpam-5827	578	4	τir	τir	X
ejpam-5827	578	5	=	=	X
ejpam-5827	578	6	{	{	PUNCT
ejpam-5827	578	7	∅,v	∅,v	X
ejpam-5827	578	8	,	,	PUNCT
ejpam-5827	578	9	{	{	PUNCT
ejpam-5827	578	10	ϵ1	ϵ1	ADJ
ejpam-5827	578	11	}	}	PUNCT
ejpam-5827	578	12	,	,	PUNCT
ejpam-5827	578	13	{	{	PUNCT
ejpam-5827	578	14	ϵ3	ϵ3	PROPN
ejpam-5827	578	15	}	}	PUNCT
ejpam-5827	578	16	,	,	PUNCT
ejpam-5827	578	17	{	{	PUNCT
ejpam-5827	578	18	ϵ4	ϵ4	NOUN
ejpam-5827	578	19	}	}	PUNCT
ejpam-5827	578	20	,	,	PUNCT
ejpam-5827	578	21	{	{	PUNCT
ejpam-5827	578	22	ϵ5	ϵ5	PROPN
ejpam-5827	578	23	}	}	PUNCT
ejpam-5827	578	24	,	,	PUNCT
ejpam-5827	578	25	{	{	PUNCT
ejpam-5827	578	26	ϵ1	ϵ1	ADJ
ejpam-5827	578	27	,	,	PUNCT
ejpam-5827	578	28	ϵ3	ϵ3	PROPN
ejpam-5827	578	29	}	}	PUNCT
ejpam-5827	578	30	,	,	PUNCT
ejpam-5827	578	31	{	{	PUNCT
ejpam-5827	578	32	ϵ1	ϵ1	ADJ
ejpam-5827	578	33	,	,	PUNCT
ejpam-5827	578	34	ϵ4	ϵ4	PROPN
ejpam-5827	578	35	}	}	PUNCT
ejpam-5827	578	36	,	,	PUNCT
ejpam-5827	578	37	{	{	PUNCT
ejpam-5827	578	38	ϵ1	ϵ1	ADJ
ejpam-5827	578	39	,	,	PUNCT
ejpam-5827	578	40	ϵ5	ϵ5	PROPN
ejpam-5827	578	41	}	}	PUNCT
ejpam-5827	578	42	,	,	PUNCT
ejpam-5827	578	43	{	{	PUNCT
ejpam-5827	578	44	ϵ3	ϵ3	PROPN
ejpam-5827	578	45	,	,	PUNCT
ejpam-5827	578	46	ϵ4	ϵ4	PROPN
ejpam-5827	578	47	}	}	PUNCT
ejpam-5827	578	48	,	,	PUNCT
ejpam-5827	578	49	{	{	PUNCT
ejpam-5827	578	50	ϵ3	ϵ3	PROPN
ejpam-5827	578	51	,	,	PUNCT
ejpam-5827	578	52	ϵ5	ϵ5	PROPN
ejpam-5827	578	53	}	}	PUNCT
ejpam-5827	578	54	,	,	PUNCT
ejpam-5827	578	55	{	{	PUNCT
ejpam-5827	578	56	ϵ4	ϵ4	NOUN
ejpam-5827	578	57	,	,	PUNCT
ejpam-5827	578	58	ϵ5	ϵ5	PROPN
ejpam-5827	578	59	}	}	PUNCT
ejpam-5827	578	60	,	,	PUNCT
ejpam-5827	578	61	{	{	PUNCT
ejpam-5827	578	62	ϵ1	ϵ1	ADJ
ejpam-5827	578	63	,	,	PUNCT
ejpam-5827	578	64	ϵ3	ϵ3	PROPN
ejpam-5827	578	65	,	,	PUNCT
ejpam-5827	578	66	ϵ4	ϵ4	PROPN
ejpam-5827	578	67	}	}	PUNCT
ejpam-5827	578	68	,	,	PUNCT
ejpam-5827	578	69	{	{	PUNCT
ejpam-5827	578	70	ϵ1	ϵ1	ADJ
ejpam-5827	578	71	,	,	PUNCT
ejpam-5827	578	72	ϵ3	ϵ3	PROPN
ejpam-5827	578	73	,	,	PUNCT
ejpam-5827	578	74	ϵ5	ϵ5	PROPN
ejpam-5827	578	75	}	}	PUNCT
ejpam-5827	578	76	,	,	PUNCT
ejpam-5827	578	77	{	{	PUNCT
ejpam-5827	578	78	ϵ1	ϵ1	ADJ
ejpam-5827	578	79	,	,	PUNCT
ejpam-5827	578	80	ϵ4	ϵ4	PROPN
ejpam-5827	578	81	,	,	PUNCT
ejpam-5827	578	82	ϵ5	ϵ5	PROPN
ejpam-5827	578	83	}	}	PUNCT
ejpam-5827	578	84	,	,	PUNCT
ejpam-5827	578	85	{	{	PUNCT
ejpam-5827	578	86	ϵ2	ϵ2	ADJ
ejpam-5827	578	87	,	,	PUNCT
ejpam-5827	578	88	ϵ4	ϵ4	PROPN
ejpam-5827	578	89	,	,	PUNCT
ejpam-5827	578	90	ϵ5	ϵ5	PROPN
ejpam-5827	578	91	}	}	PUNCT
ejpam-5827	578	92	,	,	PUNCT
ejpam-5827	578	93	{	{	PUNCT
ejpam-5827	578	94	ϵ3	ϵ3	PROPN
ejpam-5827	578	95	,	,	PUNCT
ejpam-5827	578	96	ϵ4	ϵ4	PROPN
ejpam-5827	578	97	,	,	PUNCT
ejpam-5827	578	98	ϵ5	ϵ5	PROPN
ejpam-5827	578	99	}	}	PUNCT
ejpam-5827	578	100	,	,	PUNCT
ejpam-5827	578	101	{	{	PUNCT
ejpam-5827	578	102	ϵ1	ϵ1	ADJ
ejpam-5827	578	103	,	,	PUNCT
ejpam-5827	578	104	ϵ2	ϵ2	ADJ
ejpam-5827	578	105	,	,	PUNCT
ejpam-5827	578	106	ϵ4	ϵ4	PROPN
ejpam-5827	578	107	,	,	PUNCT
ejpam-5827	578	108	ϵ5	ϵ5	PROPN
ejpam-5827	578	109	}	}	PUNCT
ejpam-5827	578	110	,	,	PUNCT
ejpam-5827	578	111	{	{	PUNCT
ejpam-5827	578	112	ϵ1	ϵ1	ADJ
ejpam-5827	578	113	,	,	PUNCT
ejpam-5827	578	114	ϵ3	ϵ3	PROPN
ejpam-5827	578	115	,	,	PUNCT
ejpam-5827	578	116	ϵ4	ϵ4	PROPN
ejpam-5827	578	117	,	,	PUNCT
ejpam-5827	578	118	ϵ5	ϵ5	PROPN
ejpam-5827	578	119	}	}	PUNCT
ejpam-5827	578	120	,	,	PUNCT
ejpam-5827	578	121	{	{	PUNCT
ejpam-5827	578	122	ϵ2	ϵ2	ADJ
ejpam-5827	578	123	,	,	PUNCT
ejpam-5827	578	124	ϵ3	ϵ3	PROPN
ejpam-5827	578	125	,	,	PUNCT
ejpam-5827	578	126	ϵ4	ϵ4	PROPN
ejpam-5827	578	127	,	,	PUNCT
ejpam-5827	578	128	ϵ5	ϵ5	PROPN
ejpam-5827	578	129	}	}	PUNCT
ejpam-5827	578	130	}	}	PUNCT
ejpam-5827	578	131	.	.	PUNCT
ejpam-5827	579	1	τil	τil	NOUN
ejpam-5827	579	2	=	=	SYM
ejpam-5827	579	3	{	{	PUNCT
ejpam-5827	579	4	∅,v	∅,v	X
ejpam-5827	579	5	,	,	PUNCT
ejpam-5827	579	6	{	{	PUNCT
ejpam-5827	579	7	ϵ1	ϵ1	ADJ
ejpam-5827	579	8	}	}	PUNCT
ejpam-5827	579	9	,	,	PUNCT
ejpam-5827	579	10	{	{	PUNCT
ejpam-5827	579	11	ϵ4	ϵ4	NOUN
ejpam-5827	579	12	}	}	PUNCT
ejpam-5827	579	13	,	,	PUNCT
ejpam-5827	579	14	{	{	PUNCT
ejpam-5827	579	15	ϵ5	ϵ5	PROPN
ejpam-5827	579	16	}	}	PUNCT
ejpam-5827	579	17	,	,	PUNCT
ejpam-5827	579	18	{	{	PUNCT
ejpam-5827	579	19	ϵ1	ϵ1	ADJ
ejpam-5827	579	20	,	,	PUNCT
ejpam-5827	579	21	ϵ4	ϵ4	PROPN
ejpam-5827	579	22	}	}	PUNCT
ejpam-5827	579	23	,	,	PUNCT
ejpam-5827	579	24	{	{	PUNCT
ejpam-5827	579	25	ϵ1	ϵ1	ADJ
ejpam-5827	579	26	,	,	PUNCT
ejpam-5827	579	27	ϵ5	ϵ5	PROPN
ejpam-5827	579	28	}	}	PUNCT
ejpam-5827	579	29	,	,	PUNCT
ejpam-5827	579	30	{	{	PUNCT
ejpam-5827	579	31	ϵ2	ϵ2	ADJ
ejpam-5827	579	32	,	,	PUNCT
ejpam-5827	579	33	ϵ4	ϵ4	PROPN
ejpam-5827	579	34	}	}	PUNCT
ejpam-5827	579	35	,	,	PUNCT
ejpam-5827	579	36	{	{	PUNCT
ejpam-5827	579	37	ϵ4	ϵ4	NOUN
ejpam-5827	579	38	,	,	PUNCT
ejpam-5827	579	39	ϵ5	ϵ5	PROPN
ejpam-5827	579	40	}	}	PUNCT
ejpam-5827	579	41	,	,	PUNCT
ejpam-5827	579	42	{	{	PUNCT
ejpam-5827	579	43	ϵ1	ϵ1	ADJ
ejpam-5827	579	44	,	,	PUNCT
ejpam-5827	579	45	ϵ2	ϵ2	ADJ
ejpam-5827	579	46	,	,	PUNCT
ejpam-5827	579	47	ϵ4	ϵ4	PROPN
ejpam-5827	579	48	}	}	PUNCT
ejpam-5827	579	49	,	,	PUNCT
ejpam-5827	579	50	{	{	PUNCT
ejpam-5827	579	51	ϵ1	ϵ1	ADJ
ejpam-5827	579	52	,	,	PUNCT
ejpam-5827	579	53	ϵ4	ϵ4	PROPN
ejpam-5827	579	54	,	,	PUNCT
ejpam-5827	579	55	ϵ5	ϵ5	PROPN
ejpam-5827	579	56	}	}	PUNCT
ejpam-5827	579	57	,	,	PUNCT
ejpam-5827	579	58	{	{	PUNCT
ejpam-5827	579	59	ϵ2	ϵ2	ADJ
ejpam-5827	579	60	,	,	PUNCT
ejpam-5827	579	61	ϵ4	ϵ4	PROPN
ejpam-5827	579	62	,	,	PUNCT
ejpam-5827	579	63	ϵ5	ϵ5	PROPN
ejpam-5827	579	64	}	}	PUNCT
ejpam-5827	579	65	,	,	PUNCT
ejpam-5827	579	66	{	{	PUNCT
ejpam-5827	579	67	ϵ3	ϵ3	PROPN
ejpam-5827	579	68	,	,	PUNCT
ejpam-5827	579	69	ϵ4	ϵ4	PROPN
ejpam-5827	579	70	,	,	PUNCT
ejpam-5827	579	71	ϵ5	ϵ5	PROPN
ejpam-5827	579	72	}	}	PUNCT
ejpam-5827	579	73	,	,	PUNCT
ejpam-5827	579	74	{	{	PUNCT
ejpam-5827	579	75	ϵ1	ϵ1	ADJ
ejpam-5827	579	76	,	,	PUNCT
ejpam-5827	579	77	ϵ2	ϵ2	ADJ
ejpam-5827	579	78	,	,	PUNCT
ejpam-5827	579	79	ϵ4	ϵ4	PROPN
ejpam-5827	579	80	,	,	PUNCT
ejpam-5827	579	81	ϵ5	ϵ5	PROPN
ejpam-5827	579	82	}	}	PUNCT
ejpam-5827	579	83	,	,	PUNCT
ejpam-5827	579	84	{	{	PUNCT
ejpam-5827	579	85	ϵ1	ϵ1	ADJ
ejpam-5827	579	86	,	,	PUNCT
ejpam-5827	579	87	ϵ3	ϵ3	PROPN
ejpam-5827	579	88	,	,	PUNCT
ejpam-5827	579	89	ϵ4	ϵ4	PROPN
ejpam-5827	579	90	,	,	PUNCT
ejpam-5827	579	91	ϵ5	ϵ5	PROPN
ejpam-5827	579	92	}	}	PUNCT
ejpam-5827	579	93	,	,	PUNCT
ejpam-5827	579	94	{	{	PUNCT
ejpam-5827	579	95	ϵ2	ϵ2	ADJ
ejpam-5827	579	96	,	,	PUNCT
ejpam-5827	579	97	ϵ3	ϵ3	PROPN
ejpam-5827	579	98	,	,	PUNCT
ejpam-5827	579	99	ϵ4	ϵ4	PROPN
ejpam-5827	579	100	,	,	PUNCT
ejpam-5827	579	101	ϵ5	ϵ5	PROPN
ejpam-5827	579	102	}	}	PUNCT
ejpam-5827	579	103	}	}	PUNCT
ejpam-5827	579	104	.	.	PUNCT
ejpam-5827	580	1	τii	τii	NUM
ejpam-5827	580	2	=	=	SYM
ejpam-5827	580	3	{	{	PUNCT
ejpam-5827	580	4	∅,v	∅,v	X
ejpam-5827	580	5	,	,	PUNCT
ejpam-5827	580	6	{	{	PUNCT
ejpam-5827	580	7	ϵ1	ϵ1	ADJ
ejpam-5827	580	8	}	}	PUNCT
ejpam-5827	580	9	,	,	PUNCT
ejpam-5827	580	10	{	{	PUNCT
ejpam-5827	580	11	ϵ3	ϵ3	PROPN
ejpam-5827	580	12	}	}	PUNCT
ejpam-5827	580	13	,	,	PUNCT
ejpam-5827	580	14	{	{	PUNCT
ejpam-5827	580	15	ϵ4	ϵ4	NOUN
ejpam-5827	580	16	}	}	PUNCT
ejpam-5827	580	17	,	,	PUNCT
ejpam-5827	580	18	{	{	PUNCT
ejpam-5827	580	19	ϵ5	ϵ5	PROPN
ejpam-5827	580	20	}	}	PUNCT
ejpam-5827	580	21	,	,	PUNCT
ejpam-5827	580	22	{	{	PUNCT
ejpam-5827	580	23	ϵ1	ϵ1	ADJ
ejpam-5827	580	24	,	,	PUNCT
ejpam-5827	580	25	ϵ3	ϵ3	PROPN
ejpam-5827	580	26	}	}	PUNCT
ejpam-5827	580	27	,	,	PUNCT
ejpam-5827	580	28	{	{	PUNCT
ejpam-5827	580	29	ϵ1	ϵ1	ADJ
ejpam-5827	580	30	,	,	PUNCT
ejpam-5827	580	31	ϵ4	ϵ4	PROPN
ejpam-5827	580	32	}	}	PUNCT
ejpam-5827	580	33	,	,	PUNCT
ejpam-5827	580	34	{	{	PUNCT
ejpam-5827	580	35	ϵ1	ϵ1	ADJ
ejpam-5827	580	36	,	,	PUNCT
ejpam-5827	580	37	ϵ5	ϵ5	PROPN
ejpam-5827	580	38	}	}	PUNCT
ejpam-5827	580	39	,	,	PUNCT
ejpam-5827	580	40	{	{	PUNCT
ejpam-5827	580	41	ϵ2	ϵ2	ADJ
ejpam-5827	580	42	,	,	PUNCT
ejpam-5827	580	43	ϵ4	ϵ4	PROPN
ejpam-5827	580	44	}	}	PUNCT
ejpam-5827	580	45	,	,	PUNCT
ejpam-5827	580	46	{	{	PUNCT
ejpam-5827	580	47	ϵ3	ϵ3	PROPN
ejpam-5827	580	48	,	,	PUNCT
ejpam-5827	580	49	ϵ4	ϵ4	PROPN
ejpam-5827	580	50	}	}	PUNCT
ejpam-5827	580	51	,	,	PUNCT
ejpam-5827	580	52	{	{	PUNCT
ejpam-5827	580	53	ϵ3	ϵ3	PROPN
ejpam-5827	580	54	,	,	PUNCT
ejpam-5827	580	55	ϵ5	ϵ5	PROPN
ejpam-5827	580	56	}	}	PUNCT
ejpam-5827	580	57	,	,	PUNCT
ejpam-5827	580	58	{	{	PUNCT
ejpam-5827	580	59	ϵ4	ϵ4	NOUN
ejpam-5827	580	60	,	,	PUNCT
ejpam-5827	580	61	ϵ5	ϵ5	PROPN
ejpam-5827	580	62	}	}	PUNCT
ejpam-5827	580	63	,	,	PUNCT
ejpam-5827	580	64	{	{	PUNCT
ejpam-5827	580	65	ϵ1	ϵ1	ADJ
ejpam-5827	580	66	,	,	PUNCT
ejpam-5827	580	67	ϵ2	ϵ2	ADJ
ejpam-5827	580	68	,	,	PUNCT
ejpam-5827	580	69	ϵ4	ϵ4	PROPN
ejpam-5827	580	70	}	}	PUNCT
ejpam-5827	580	71	,	,	PUNCT
ejpam-5827	580	72	{	{	PUNCT
ejpam-5827	580	73	ϵ1	ϵ1	ADJ
ejpam-5827	580	74	,	,	PUNCT
ejpam-5827	580	75	ϵ3	ϵ3	PROPN
ejpam-5827	580	76	,	,	PUNCT
ejpam-5827	580	77	ϵ4	ϵ4	PROPN
ejpam-5827	580	78	}	}	PUNCT
ejpam-5827	580	79	,	,	PUNCT
ejpam-5827	580	80	{	{	PUNCT
ejpam-5827	580	81	ϵ1	ϵ1	ADJ
ejpam-5827	580	82	,	,	PUNCT
ejpam-5827	580	83	ϵ3	ϵ3	PROPN
ejpam-5827	580	84	,	,	PUNCT
ejpam-5827	580	85	ϵ5	ϵ5	PROPN
ejpam-5827	580	86	}	}	PUNCT
ejpam-5827	580	87	,	,	PUNCT
ejpam-5827	580	88	{	{	PUNCT
ejpam-5827	580	89	ϵ1	ϵ1	ADJ
ejpam-5827	580	90	,	,	PUNCT
ejpam-5827	580	91	ϵ4	ϵ4	PROPN
ejpam-5827	580	92	,	,	PUNCT
ejpam-5827	580	93	ϵ5	ϵ5	PROPN
ejpam-5827	580	94	}	}	PUNCT
ejpam-5827	580	95	,	,	PUNCT
ejpam-5827	580	96	{	{	PUNCT
ejpam-5827	580	97	ϵ2	ϵ2	ADJ
ejpam-5827	580	98	,	,	PUNCT
ejpam-5827	580	99	ϵ3	ϵ3	PROPN
ejpam-5827	580	100	,	,	PUNCT
ejpam-5827	580	101	ϵ4	ϵ4	PROPN
ejpam-5827	580	102	}	}	PUNCT
ejpam-5827	580	103	,	,	PUNCT
ejpam-5827	580	104	{	{	PUNCT
ejpam-5827	580	105	ϵ2	ϵ2	ADJ
ejpam-5827	580	106	,	,	PUNCT
ejpam-5827	580	107	ϵ4	ϵ4	PROPN
ejpam-5827	580	108	,	,	PUNCT
ejpam-5827	580	109	ϵ5	ϵ5	PROPN
ejpam-5827	580	110	}	}	PUNCT
ejpam-5827	580	111	,	,	PUNCT
ejpam-5827	580	112	{	{	PUNCT
ejpam-5827	580	113	ϵ3	ϵ3	PROPN
ejpam-5827	580	114	,	,	PUNCT
ejpam-5827	580	115	ϵ4	ϵ4	PROPN
ejpam-5827	580	116	,	,	PUNCT
ejpam-5827	580	117	ϵ5	ϵ5	PROPN
ejpam-5827	580	118	}	}	PUNCT
ejpam-5827	580	119	,	,	PUNCT
ejpam-5827	580	120	{	{	PUNCT
ejpam-5827	580	121	ϵ1	ϵ1	ADJ
ejpam-5827	580	122	,	,	PUNCT
ejpam-5827	580	123	ϵ2	ϵ2	ADJ
ejpam-5827	580	124	,	,	PUNCT
ejpam-5827	580	125	ϵ3	ϵ3	PROPN
ejpam-5827	580	126	,	,	PUNCT
ejpam-5827	580	127	ϵ4	ϵ4	PROPN
ejpam-5827	580	128	}	}	PUNCT
ejpam-5827	580	129	,	,	PUNCT
ejpam-5827	580	130	{	{	PUNCT
ejpam-5827	580	131	ϵ1	ϵ1	ADJ
ejpam-5827	580	132	,	,	PUNCT
ejpam-5827	580	133	ϵ2	ϵ2	ADJ
ejpam-5827	580	134	,	,	PUNCT
ejpam-5827	580	135	ϵ4	ϵ4	PROPN
ejpam-5827	580	136	,	,	PUNCT
ejpam-5827	580	137	ϵ5	ϵ5	PROPN
ejpam-5827	580	138	}	}	PUNCT
ejpam-5827	580	139	,	,	PUNCT
ejpam-5827	580	140	{	{	PUNCT
ejpam-5827	580	141	ϵ1	ϵ1	ADJ
ejpam-5827	580	142	,	,	PUNCT
ejpam-5827	580	143	ϵ3	ϵ3	PROPN
ejpam-5827	580	144	,	,	PUNCT
ejpam-5827	580	145	ϵ4	ϵ4	PROPN
ejpam-5827	580	146	,	,	PUNCT
ejpam-5827	580	147	ϵ5	ϵ5	PROPN
ejpam-5827	580	148	}	}	PUNCT
ejpam-5827	580	149	,	,	PUNCT
ejpam-5827	580	150	{	{	PUNCT
ejpam-5827	580	151	ϵ2	ϵ2	ADJ
ejpam-5827	580	152	,	,	PUNCT
ejpam-5827	580	153	ϵ3	ϵ3	PROPN
ejpam-5827	580	154	,	,	PUNCT
ejpam-5827	580	155	ϵ4	ϵ4	PROPN
ejpam-5827	580	156	,	,	PUNCT
ejpam-5827	580	157	ϵ5	ϵ5	PROPN
ejpam-5827	580	158	}	}	PUNCT
ejpam-5827	580	159	}	}	PUNCT
ejpam-5827	580	160	.	.	PUNCT
ejpam-5827	581	1	τiu	τiu	PROPN
ejpam-5827	581	2	=	=	PRON
ejpam-5827	581	3	{	{	PUNCT
ejpam-5827	581	4	∅,v	∅,v	X
ejpam-5827	581	5	,	,	PUNCT
ejpam-5827	581	6	{	{	PUNCT
ejpam-5827	581	7	ϵ1	ϵ1	ADJ
ejpam-5827	581	8	}	}	PUNCT
ejpam-5827	581	9	,	,	PUNCT
ejpam-5827	581	10	{	{	PUNCT
ejpam-5827	581	11	ϵ4	ϵ4	NOUN
ejpam-5827	581	12	}	}	PUNCT
ejpam-5827	581	13	,	,	PUNCT
ejpam-5827	581	14	{	{	PUNCT
ejpam-5827	581	15	ϵ5	ϵ5	PROPN
ejpam-5827	581	16	}	}	PUNCT
ejpam-5827	581	17	,	,	PUNCT
ejpam-5827	581	18	{	{	PUNCT
ejpam-5827	581	19	ϵ1	ϵ1	ADJ
ejpam-5827	581	20	,	,	PUNCT
ejpam-5827	581	21	ϵ4	ϵ4	PROPN
ejpam-5827	581	22	}	}	PUNCT
ejpam-5827	581	23	,	,	PUNCT
ejpam-5827	581	24	{	{	PUNCT
ejpam-5827	581	25	ϵ1	ϵ1	ADJ
ejpam-5827	581	26	,	,	PUNCT
ejpam-5827	581	27	ϵ5	ϵ5	PROPN
ejpam-5827	581	28	}	}	PUNCT
ejpam-5827	581	29	,	,	PUNCT
ejpam-5827	581	30	{	{	PUNCT
ejpam-5827	581	31	ϵ4	ϵ4	NOUN
ejpam-5827	581	32	,	,	PUNCT
ejpam-5827	581	33	ϵ5	ϵ5	PROPN
ejpam-5827	581	34	}	}	PUNCT
ejpam-5827	581	35	,	,	PUNCT
ejpam-5827	581	36	{	{	PUNCT
ejpam-5827	581	37	ϵ1	ϵ1	ADJ
ejpam-5827	581	38	,	,	PUNCT
ejpam-5827	581	39	ϵ4	ϵ4	PROPN
ejpam-5827	581	40	,	,	PUNCT
ejpam-5827	581	41	ϵ5	ϵ5	PROPN
ejpam-5827	581	42	}	}	PUNCT
ejpam-5827	581	43	,	,	PUNCT
ejpam-5827	581	44	{	{	PUNCT
ejpam-5827	581	45	ϵ2	ϵ2	ADJ
ejpam-5827	581	46	,	,	PUNCT
ejpam-5827	581	47	ϵ4	ϵ4	PROPN
ejpam-5827	581	48	,	,	PUNCT
ejpam-5827	581	49	ϵ5	ϵ5	PROPN
ejpam-5827	581	50	}	}	PUNCT
ejpam-5827	581	51	,	,	PUNCT
ejpam-5827	581	52	{	{	PUNCT
ejpam-5827	581	53	ϵ3	ϵ3	PROPN
ejpam-5827	581	54	,	,	PUNCT
ejpam-5827	581	55	ϵ4	ϵ4	PROPN
ejpam-5827	581	56	,	,	PUNCT
ejpam-5827	581	57	ϵ5	ϵ5	PROPN
ejpam-5827	581	58	}	}	PUNCT
ejpam-5827	581	59	,	,	PUNCT
ejpam-5827	581	60	{	{	PUNCT
ejpam-5827	581	61	ϵ1	ϵ1	ADJ
ejpam-5827	581	62	,	,	PUNCT
ejpam-5827	581	63	ϵ2	ϵ2	ADJ
ejpam-5827	581	64	,	,	PUNCT
ejpam-5827	581	65	ϵ4	ϵ4	PROPN
ejpam-5827	581	66	,	,	PUNCT
ejpam-5827	581	67	ϵ5	ϵ5	PROPN
ejpam-5827	581	68	}	}	PUNCT
ejpam-5827	581	69	,	,	PUNCT
ejpam-5827	581	70	{	{	PUNCT
ejpam-5827	581	71	ϵ1	ϵ1	ADJ
ejpam-5827	581	72	,	,	PUNCT
ejpam-5827	581	73	ϵ3	ϵ3	PROPN
ejpam-5827	581	74	,	,	PUNCT
ejpam-5827	581	75	ϵ4	ϵ4	PROPN
ejpam-5827	581	76	,	,	PUNCT
ejpam-5827	581	77	ϵ5	ϵ5	PROPN
ejpam-5827	581	78	}	}	PUNCT
ejpam-5827	581	79	,	,	PUNCT
ejpam-5827	581	80	{	{	PUNCT
ejpam-5827	581	81	ϵ2	ϵ2	ADJ
ejpam-5827	581	82	,	,	PUNCT
ejpam-5827	581	83	ϵ3	ϵ3	PROPN
ejpam-5827	581	84	,	,	PUNCT
ejpam-5827	581	85	ϵ4	ϵ4	PROPN
ejpam-5827	581	86	,	,	PUNCT
ejpam-5827	581	87	ϵ5	ϵ5	PROPN
ejpam-5827	581	88	}	}	PUNCT
ejpam-5827	581	89	}	}	PUNCT
ejpam-5827	581	90	.	.	PUNCT
ejpam-5827	582	1	τi⟨r⟩	τi⟨r⟩	NOUN
ejpam-5827	582	2	=	=	PRON
ejpam-5827	582	3	{	{	PUNCT
ejpam-5827	582	4	∅,v	∅,v	X
ejpam-5827	582	5	,	,	PUNCT
ejpam-5827	582	6	{	{	PUNCT
ejpam-5827	582	7	ϵ1	ϵ1	ADJ
ejpam-5827	582	8	}	}	PUNCT
ejpam-5827	582	9	,	,	PUNCT
ejpam-5827	582	10	{	{	PUNCT
ejpam-5827	582	11	ϵ2	ϵ2	PROPN
ejpam-5827	582	12	}	}	PUNCT
ejpam-5827	582	13	,	,	PUNCT
ejpam-5827	582	14	{	{	PUNCT
ejpam-5827	582	15	ϵ3	ϵ3	PROPN
ejpam-5827	582	16	}	}	PUNCT
ejpam-5827	582	17	,	,	PUNCT
ejpam-5827	582	18	{	{	PUNCT
ejpam-5827	582	19	ϵ1	ϵ1	ADJ
ejpam-5827	582	20	,	,	PUNCT
ejpam-5827	582	21	ϵ2	ϵ2	ADJ
ejpam-5827	582	22	}	}	PUNCT
ejpam-5827	582	23	,	,	PUNCT
ejpam-5827	582	24	{	{	PUNCT
ejpam-5827	582	25	ϵ1	ϵ1	ADJ
ejpam-5827	582	26	,	,	PUNCT
ejpam-5827	582	27	ϵ3	ϵ3	PROPN
ejpam-5827	582	28	}	}	PUNCT
ejpam-5827	582	29	,	,	PUNCT
ejpam-5827	582	30	{	{	PUNCT
ejpam-5827	582	31	ϵ2	ϵ2	ADJ
ejpam-5827	582	32	,	,	PUNCT
ejpam-5827	582	33	ϵ3	ϵ3	PROPN
ejpam-5827	582	34	}	}	PUNCT
ejpam-5827	582	35	,	,	PUNCT
ejpam-5827	582	36	{	{	PUNCT
ejpam-5827	582	37	ϵ4	ϵ4	NOUN
ejpam-5827	582	38	,	,	PUNCT
ejpam-5827	582	39	ϵ5	ϵ5	PROPN
ejpam-5827	582	40	}	}	PUNCT
ejpam-5827	582	41	,	,	PUNCT
ejpam-5827	582	42	{	{	PUNCT
ejpam-5827	582	43	ϵ1	ϵ1	ADJ
ejpam-5827	582	44	,	,	PUNCT
ejpam-5827	582	45	ϵ2	ϵ2	ADJ
ejpam-5827	582	46	,	,	PUNCT
ejpam-5827	582	47	ϵ3	ϵ3	PROPN
ejpam-5827	582	48	}	}	PUNCT
ejpam-5827	582	49	,	,	PUNCT
ejpam-5827	582	50	{	{	PUNCT
ejpam-5827	582	51	ϵ1	ϵ1	ADJ
ejpam-5827	582	52	,	,	PUNCT
ejpam-5827	582	53	ϵ4	ϵ4	PROPN
ejpam-5827	582	54	,	,	PUNCT
ejpam-5827	582	55	ϵ5	ϵ5	PROPN
ejpam-5827	582	56	}	}	PUNCT
ejpam-5827	582	57	,	,	PUNCT
ejpam-5827	582	58	{	{	PUNCT
ejpam-5827	582	59	ϵ2	ϵ2	ADJ
ejpam-5827	582	60	,	,	PUNCT
ejpam-5827	582	61	ϵ4	ϵ4	PROPN
ejpam-5827	582	62	,	,	PUNCT
ejpam-5827	582	63	ϵ5	ϵ5	PROPN
ejpam-5827	582	64	}	}	PUNCT
ejpam-5827	582	65	,	,	PUNCT
ejpam-5827	582	66	{	{	PUNCT
ejpam-5827	582	67	ϵ3	ϵ3	PROPN
ejpam-5827	582	68	,	,	PUNCT
ejpam-5827	582	69	ϵ4	ϵ4	PROPN
ejpam-5827	582	70	,	,	PUNCT
ejpam-5827	582	71	ϵ5	ϵ5	PROPN
ejpam-5827	582	72	}	}	PUNCT
ejpam-5827	582	73	,	,	PUNCT
ejpam-5827	582	74	{	{	PUNCT
ejpam-5827	582	75	ϵ1	ϵ1	ADJ
ejpam-5827	582	76	,	,	PUNCT
ejpam-5827	582	77	ϵ2	ϵ2	ADJ
ejpam-5827	582	78	,	,	PUNCT
ejpam-5827	582	79	ϵ4	ϵ4	PROPN
ejpam-5827	582	80	,	,	PUNCT
ejpam-5827	582	81	ϵ5	ϵ5	PROPN
ejpam-5827	582	82	}	}	PUNCT
ejpam-5827	582	83	,	,	PUNCT
ejpam-5827	582	84	{	{	PUNCT
ejpam-5827	582	85	ϵ1	ϵ1	ADJ
ejpam-5827	582	86	,	,	PUNCT
ejpam-5827	582	87	ϵ3	ϵ3	PROPN
ejpam-5827	582	88	,	,	PUNCT
ejpam-5827	582	89	ϵ4	ϵ4	PROPN
ejpam-5827	582	90	,	,	PUNCT
ejpam-5827	582	91	ϵ5	ϵ5	PROPN
ejpam-5827	582	92	}	}	PUNCT
ejpam-5827	582	93	,	,	PUNCT
ejpam-5827	582	94	{	{	PUNCT
ejpam-5827	582	95	ϵ2	ϵ2	ADJ
ejpam-5827	582	96	,	,	PUNCT
ejpam-5827	582	97	ϵ3	ϵ3	PROPN
ejpam-5827	582	98	,	,	PUNCT
ejpam-5827	582	99	ϵ4	ϵ4	PROPN
ejpam-5827	582	100	,	,	PUNCT
ejpam-5827	582	101	ϵ5	ϵ5	PROPN
ejpam-5827	582	102	}	}	PUNCT
ejpam-5827	582	103	}	}	PUNCT
ejpam-5827	582	104	.	.	PUNCT
ejpam-5827	583	1	τi⟨l⟩	τi⟨l⟩	PUNCT
ejpam-5827	583	2	=	=	PRON
ejpam-5827	583	3	{	{	PUNCT
ejpam-5827	583	4	∅,v	∅,v	X
ejpam-5827	583	5	,	,	PUNCT
ejpam-5827	583	6	{	{	PUNCT
ejpam-5827	583	7	ϵ2	ϵ2	PROPN
ejpam-5827	583	8	}	}	PUNCT
ejpam-5827	583	9	,	,	PUNCT
ejpam-5827	583	10	{	{	PUNCT
ejpam-5827	583	11	ϵ3	ϵ3	PROPN
ejpam-5827	583	12	}	}	PUNCT
ejpam-5827	583	13	,	,	PUNCT
ejpam-5827	583	14	{	{	PUNCT
ejpam-5827	583	15	ϵ4	ϵ4	NOUN
ejpam-5827	583	16	}	}	PUNCT
ejpam-5827	583	17	,	,	PUNCT
ejpam-5827	583	18	{	{	PUNCT
ejpam-5827	583	19	ϵ2	ϵ2	ADJ
ejpam-5827	583	20	,	,	PUNCT
ejpam-5827	583	21	ϵ3	ϵ3	PROPN
ejpam-5827	583	22	}	}	PUNCT
ejpam-5827	583	23	,	,	PUNCT
ejpam-5827	583	24	{	{	PUNCT
ejpam-5827	583	25	ϵ2	ϵ2	ADJ
ejpam-5827	583	26	,	,	PUNCT
ejpam-5827	583	27	ϵ4	ϵ4	PROPN
ejpam-5827	583	28	}	}	PUNCT
ejpam-5827	583	29	,	,	PUNCT
ejpam-5827	583	30	{	{	PUNCT
ejpam-5827	583	31	ϵ3	ϵ3	PROPN
ejpam-5827	583	32	,	,	PUNCT
ejpam-5827	583	33	ϵ4	ϵ4	PROPN
ejpam-5827	583	34	}	}	PUNCT
ejpam-5827	583	35	,	,	PUNCT
ejpam-5827	583	36	{	{	PUNCT
ejpam-5827	583	37	ϵ4	ϵ4	NOUN
ejpam-5827	583	38	,	,	PUNCT
ejpam-5827	583	39	ϵ5	ϵ5	PROPN
ejpam-5827	583	40	}	}	PUNCT
ejpam-5827	583	41	,	,	PUNCT
ejpam-5827	583	42	{	{	PUNCT
ejpam-5827	583	43	ϵ2	ϵ2	ADJ
ejpam-5827	583	44	,	,	PUNCT
ejpam-5827	583	45	ϵ3	ϵ3	PROPN
ejpam-5827	583	46	,	,	PUNCT
ejpam-5827	583	47	ϵ4	ϵ4	PROPN
ejpam-5827	583	48	}	}	PUNCT
ejpam-5827	583	49	,	,	PUNCT
ejpam-5827	583	50	{	{	PUNCT
ejpam-5827	583	51	ϵ1	ϵ1	ADJ
ejpam-5827	583	52	,	,	PUNCT
ejpam-5827	583	53	ϵ4	ϵ4	PROPN
ejpam-5827	583	54	,	,	PUNCT
ejpam-5827	583	55	ϵ5	ϵ5	PROPN
ejpam-5827	583	56	}	}	PUNCT
ejpam-5827	583	57	,	,	PUNCT
ejpam-5827	583	58	{	{	PUNCT
ejpam-5827	583	59	ϵ2	ϵ2	ADJ
ejpam-5827	583	60	,	,	PUNCT
ejpam-5827	583	61	ϵ4	ϵ4	PROPN
ejpam-5827	583	62	,	,	PUNCT
ejpam-5827	583	63	ϵ5	ϵ5	PROPN
ejpam-5827	583	64	}	}	PUNCT
ejpam-5827	583	65	,	,	PUNCT
ejpam-5827	583	66	{	{	PUNCT
ejpam-5827	583	67	ϵ3	ϵ3	PROPN
ejpam-5827	583	68	,	,	PUNCT
ejpam-5827	583	69	ϵ4	ϵ4	PROPN
ejpam-5827	583	70	,	,	PUNCT
ejpam-5827	583	71	ϵ5	ϵ5	PROPN
ejpam-5827	583	72	}	}	PUNCT
ejpam-5827	583	73	,	,	PUNCT
ejpam-5827	583	74	{	{	PUNCT
ejpam-5827	583	75	ϵ1	ϵ1	ADJ
ejpam-5827	583	76	,	,	PUNCT
ejpam-5827	583	77	ϵ2	ϵ2	ADJ
ejpam-5827	583	78	,	,	PUNCT
ejpam-5827	583	79	ϵ4	ϵ4	PROPN
ejpam-5827	583	80	,	,	PUNCT
ejpam-5827	583	81	ϵ5	ϵ5	PROPN
ejpam-5827	583	82	}	}	PUNCT
ejpam-5827	583	83	,	,	PUNCT
ejpam-5827	583	84	{	{	PUNCT
ejpam-5827	583	85	ϵ1	ϵ1	ADJ
ejpam-5827	583	86	,	,	PUNCT
ejpam-5827	583	87	ϵ3	ϵ3	PROPN
ejpam-5827	583	88	,	,	PUNCT
ejpam-5827	583	89	ϵ4	ϵ4	PROPN
ejpam-5827	583	90	,	,	PUNCT
ejpam-5827	583	91	ϵ5	ϵ5	PROPN
ejpam-5827	583	92	}	}	PUNCT
ejpam-5827	583	93	,	,	PUNCT
ejpam-5827	583	94	{	{	PUNCT
ejpam-5827	583	95	ϵ2	ϵ2	ADJ
ejpam-5827	583	96	,	,	PUNCT
ejpam-5827	583	97	ϵ3	ϵ3	PROPN
ejpam-5827	583	98	,	,	PUNCT
ejpam-5827	583	99	ϵ4	ϵ4	PROPN
ejpam-5827	583	100	,	,	PUNCT
ejpam-5827	583	101	ϵ5	ϵ5	PROPN
ejpam-5827	583	102	}	}	PUNCT
ejpam-5827	583	103	}	}	PUNCT
ejpam-5827	583	104	.	.	PUNCT
ejpam-5827	584	1	τi⟨i⟩	τi⟨i⟩	PROPN
ejpam-5827	585	1	=	=	X
ejpam-5827	585	2	{	{	PUNCT
ejpam-5827	585	3	∅,v	∅,v	X
ejpam-5827	585	4	,	,	PUNCT
ejpam-5827	585	5	{	{	PUNCT
ejpam-5827	585	6	ϵ1	ϵ1	ADJ
ejpam-5827	585	7	}	}	PUNCT
ejpam-5827	585	8	,	,	PUNCT
ejpam-5827	585	9	{	{	PUNCT
ejpam-5827	585	10	ϵ2	ϵ2	PROPN
ejpam-5827	585	11	}	}	PUNCT
ejpam-5827	585	12	,	,	PUNCT
ejpam-5827	585	13	{	{	PUNCT
ejpam-5827	585	14	ϵ3	ϵ3	PROPN
ejpam-5827	585	15	}	}	PUNCT
ejpam-5827	585	16	,	,	PUNCT
ejpam-5827	585	17	{	{	PUNCT
ejpam-5827	585	18	ϵ4	ϵ4	NOUN
ejpam-5827	585	19	}	}	PUNCT
ejpam-5827	585	20	,	,	PUNCT
ejpam-5827	585	21	{	{	PUNCT
ejpam-5827	585	22	ϵ1	ϵ1	ADJ
ejpam-5827	585	23	,	,	PUNCT
ejpam-5827	585	24	ϵ2	ϵ2	ADJ
ejpam-5827	585	25	}	}	PUNCT
ejpam-5827	585	26	,	,	PUNCT
ejpam-5827	585	27	{	{	PUNCT
ejpam-5827	585	28	ϵ1	ϵ1	ADJ
ejpam-5827	585	29	,	,	PUNCT
ejpam-5827	585	30	ϵ3	ϵ3	PROPN
ejpam-5827	585	31	}	}	PUNCT
ejpam-5827	585	32	,	,	PUNCT
ejpam-5827	585	33	{	{	PUNCT
ejpam-5827	585	34	ϵ1	ϵ1	ADJ
ejpam-5827	585	35	,	,	PUNCT
ejpam-5827	585	36	ϵ4	ϵ4	PROPN
ejpam-5827	585	37	}	}	PUNCT
ejpam-5827	585	38	,	,	PUNCT
ejpam-5827	585	39	{	{	PUNCT
ejpam-5827	585	40	ϵ2	ϵ2	ADJ
ejpam-5827	585	41	,	,	PUNCT
ejpam-5827	585	42	ϵ3	ϵ3	PROPN
ejpam-5827	585	43	}	}	PUNCT
ejpam-5827	585	44	,	,	PUNCT
ejpam-5827	585	45	{	{	PUNCT
ejpam-5827	585	46	ϵ2	ϵ2	ADJ
ejpam-5827	585	47	,	,	PUNCT
ejpam-5827	585	48	ϵ4	ϵ4	PROPN
ejpam-5827	585	49	}	}	PUNCT
ejpam-5827	585	50	,	,	PUNCT
ejpam-5827	585	51	{	{	PUNCT
ejpam-5827	585	52	ϵ3	ϵ3	PROPN
ejpam-5827	585	53	,	,	PUNCT
ejpam-5827	585	54	ϵ4	ϵ4	PROPN
ejpam-5827	585	55	}	}	PUNCT
ejpam-5827	585	56	,	,	PUNCT
ejpam-5827	585	57	{	{	PUNCT
ejpam-5827	585	58	ϵ4	ϵ4	NOUN
ejpam-5827	585	59	,	,	PUNCT
ejpam-5827	585	60	ϵ5	ϵ5	PROPN
ejpam-5827	585	61	}	}	PUNCT
ejpam-5827	585	62	,	,	PUNCT
ejpam-5827	585	63	{	{	PUNCT
ejpam-5827	585	64	ϵ1	ϵ1	ADJ
ejpam-5827	585	65	,	,	PUNCT
ejpam-5827	585	66	ϵ2	ϵ2	ADJ
ejpam-5827	585	67	,	,	PUNCT
ejpam-5827	585	68	ϵ3	ϵ3	PROPN
ejpam-5827	585	69	}	}	PUNCT
ejpam-5827	585	70	,	,	PUNCT
ejpam-5827	585	71	{	{	PUNCT
ejpam-5827	585	72	ϵ1	ϵ1	ADJ
ejpam-5827	585	73	,	,	PUNCT
ejpam-5827	585	74	ϵ2	ϵ2	ADJ
ejpam-5827	585	75	,	,	PUNCT
ejpam-5827	585	76	ϵ4	ϵ4	PROPN
ejpam-5827	585	77	}	}	PUNCT
ejpam-5827	585	78	,	,	PUNCT
ejpam-5827	585	79	{	{	PUNCT
ejpam-5827	585	80	ϵ1	ϵ1	ADJ
ejpam-5827	585	81	,	,	PUNCT
ejpam-5827	585	82	ϵ3	ϵ3	PROPN
ejpam-5827	585	83	,	,	PUNCT
ejpam-5827	585	84	ϵ4	ϵ4	PROPN
ejpam-5827	585	85	}	}	PUNCT
ejpam-5827	585	86	,	,	PUNCT
ejpam-5827	585	87	{	{	PUNCT
ejpam-5827	585	88	ϵ1	ϵ1	ADJ
ejpam-5827	585	89	,	,	PUNCT
ejpam-5827	585	90	ϵ4	ϵ4	PROPN
ejpam-5827	585	91	,	,	PUNCT
ejpam-5827	585	92	ϵ5	ϵ5	PROPN
ejpam-5827	585	93	}	}	PUNCT
ejpam-5827	585	94	,	,	PUNCT
ejpam-5827	585	95	{	{	PUNCT
ejpam-5827	585	96	ϵ2	ϵ2	ADJ
ejpam-5827	585	97	,	,	PUNCT
ejpam-5827	585	98	ϵ4	ϵ4	PROPN
ejpam-5827	585	99	,	,	PUNCT
ejpam-5827	585	100	ϵ5	ϵ5	PROPN
ejpam-5827	585	101	}	}	PUNCT
ejpam-5827	585	102	,	,	PUNCT
ejpam-5827	585	103	{	{	PUNCT
ejpam-5827	585	104	ϵ3	ϵ3	PROPN
ejpam-5827	585	105	,	,	PUNCT
ejpam-5827	585	106	ϵ4	ϵ4	PROPN
ejpam-5827	585	107	,	,	PUNCT
ejpam-5827	585	108	ϵ5	ϵ5	PROPN
ejpam-5827	585	109	}	}	PUNCT
ejpam-5827	585	110	,	,	PUNCT
ejpam-5827	585	111	{	{	PUNCT
ejpam-5827	585	112	ϵ2	ϵ2	ADJ
ejpam-5827	585	113	,	,	PUNCT
ejpam-5827	585	114	ϵ3	ϵ3	PROPN
ejpam-5827	585	115	,	,	PUNCT
ejpam-5827	585	116	ϵ4	ϵ4	PROPN
ejpam-5827	585	117	}	}	PUNCT
ejpam-5827	585	118	,	,	PUNCT
ejpam-5827	585	119	{	{	PUNCT
ejpam-5827	585	120	ϵ1	ϵ1	ADJ
ejpam-5827	585	121	,	,	PUNCT
ejpam-5827	585	122	ϵ2	ϵ2	ADJ
ejpam-5827	585	123	,	,	PUNCT
ejpam-5827	585	124	ϵ3	ϵ3	PROPN
ejpam-5827	585	125	,	,	PUNCT
ejpam-5827	585	126	ϵ4	ϵ4	PROPN
ejpam-5827	585	127	}	}	PUNCT
ejpam-5827	585	128	,	,	PUNCT
ejpam-5827	585	129	{	{	PUNCT
ejpam-5827	585	130	ϵ1	ϵ1	ADJ
ejpam-5827	585	131	,	,	PUNCT
ejpam-5827	585	132	ϵ2	ϵ2	ADJ
ejpam-5827	585	133	,	,	PUNCT
ejpam-5827	585	134	ϵ4	ϵ4	PROPN
ejpam-5827	585	135	,	,	PUNCT
ejpam-5827	585	136	ϵ5	ϵ5	PROPN
ejpam-5827	585	137	}	}	PUNCT
ejpam-5827	585	138	,	,	PUNCT
ejpam-5827	585	139	{	{	PUNCT
ejpam-5827	585	140	ϵ1	ϵ1	ADJ
ejpam-5827	585	141	,	,	PUNCT
ejpam-5827	585	142	ϵ3	ϵ3	PROPN
ejpam-5827	585	143	,	,	PUNCT
ejpam-5827	585	144	ϵ4	ϵ4	PROPN
ejpam-5827	585	145	,	,	PUNCT
ejpam-5827	585	146	ϵ5	ϵ5	PROPN
ejpam-5827	585	147	}	}	PUNCT
ejpam-5827	585	148	,	,	PUNCT
ejpam-5827	585	149	{	{	PUNCT
ejpam-5827	585	150	ϵ2	ϵ2	ADJ
ejpam-5827	585	151	,	,	PUNCT
ejpam-5827	585	152	ϵ3	ϵ3	PROPN
ejpam-5827	585	153	,	,	PUNCT
ejpam-5827	585	154	ϵ4	ϵ4	PROPN
ejpam-5827	585	155	,	,	PUNCT
ejpam-5827	585	156	ϵ5	ϵ5	PROPN
ejpam-5827	585	157	}	}	PUNCT
ejpam-5827	585	158	}	}	PUNCT
ejpam-5827	585	159	.	.	PUNCT
ejpam-5827	586	1	τi⟨u⟩	τi⟨u⟩	VERB
ejpam-5827	586	2	=	=	SYM
ejpam-5827	586	3	{	{	PUNCT
ejpam-5827	586	4	∅,v	∅,v	X
ejpam-5827	586	5	,	,	PUNCT
ejpam-5827	586	6	{	{	PUNCT
ejpam-5827	586	7	ϵ2	ϵ2	PROPN
ejpam-5827	586	8	}	}	PUNCT
ejpam-5827	586	9	,	,	PUNCT
ejpam-5827	586	10	{	{	PUNCT
ejpam-5827	586	11	ϵ3	ϵ3	PROPN
ejpam-5827	586	12	}	}	PUNCT
ejpam-5827	586	13	,	,	PUNCT
ejpam-5827	586	14	{	{	PUNCT
ejpam-5827	586	15	ϵ2	ϵ2	ADJ
ejpam-5827	586	16	,	,	PUNCT
ejpam-5827	586	17	ϵ3	ϵ3	PROPN
ejpam-5827	586	18	}	}	PUNCT
ejpam-5827	586	19	,	,	PUNCT
ejpam-5827	586	20	{	{	PUNCT
ejpam-5827	586	21	ϵ4	ϵ4	NOUN
ejpam-5827	586	22	,	,	PUNCT
ejpam-5827	586	23	ϵ5	ϵ5	PROPN
ejpam-5827	586	24	}	}	PUNCT
ejpam-5827	586	25	,	,	PUNCT
ejpam-5827	586	26	{	{	PUNCT
ejpam-5827	586	27	ϵ1	ϵ1	ADJ
ejpam-5827	586	28	,	,	PUNCT
ejpam-5827	586	29	ϵ4	ϵ4	PROPN
ejpam-5827	586	30	,	,	PUNCT
ejpam-5827	586	31	ϵ5	ϵ5	PROPN
ejpam-5827	586	32	}	}	PUNCT
ejpam-5827	586	33	,	,	PUNCT
ejpam-5827	586	34	{	{	PUNCT
ejpam-5827	586	35	ϵ2	ϵ2	ADJ
ejpam-5827	586	36	,	,	PUNCT
ejpam-5827	586	37	ϵ4	ϵ4	PROPN
ejpam-5827	586	38	,	,	PUNCT
ejpam-5827	586	39	ϵ5	ϵ5	PROPN
ejpam-5827	586	40	}	}	PUNCT
ejpam-5827	586	41	,	,	PUNCT
ejpam-5827	586	42	{	{	PUNCT
ejpam-5827	586	43	ϵ3	ϵ3	PROPN
ejpam-5827	586	44	,	,	PUNCT
ejpam-5827	586	45	ϵ4	ϵ4	PROPN
ejpam-5827	586	46	,	,	PUNCT
ejpam-5827	586	47	ϵ5	ϵ5	PROPN
ejpam-5827	586	48	}	}	PUNCT
ejpam-5827	586	49	,	,	PUNCT
ejpam-5827	586	50	{	{	PUNCT
ejpam-5827	586	51	ϵ2	ϵ2	ADJ
ejpam-5827	586	52	,	,	PUNCT
ejpam-5827	586	53	ϵ3	ϵ3	PROPN
ejpam-5827	586	54	,	,	PUNCT
ejpam-5827	586	55	ϵ4	ϵ4	PROPN
ejpam-5827	586	56	,	,	PUNCT
ejpam-5827	586	57	ϵ5	ϵ5	PROPN
ejpam-5827	586	58	}	}	PUNCT
ejpam-5827	586	59	,	,	PUNCT
ejpam-5827	586	60	{	{	PUNCT
ejpam-5827	586	61	ϵ1	ϵ1	ADJ
ejpam-5827	586	62	,	,	PUNCT
ejpam-5827	586	63	ϵ2	ϵ2	ADJ
ejpam-5827	586	64	,	,	PUNCT
ejpam-5827	586	65	ϵ4	ϵ4	PROPN
ejpam-5827	586	66	,	,	PUNCT
ejpam-5827	586	67	ϵ5	ϵ5	PROPN
ejpam-5827	586	68	}	}	PUNCT
ejpam-5827	586	69	,	,	PUNCT
ejpam-5827	586	70	{	{	PUNCT
ejpam-5827	586	71	ϵ1	ϵ1	ADJ
ejpam-5827	586	72	,	,	PUNCT
ejpam-5827	586	73	ϵ3	ϵ3	PROPN
ejpam-5827	586	74	,	,	PUNCT
ejpam-5827	586	75	ϵ4	ϵ4	PROPN
ejpam-5827	586	76	,	,	PUNCT
ejpam-5827	586	77	ϵ5	ϵ5	PROPN
ejpam-5827	586	78	}	}	PUNCT
ejpam-5827	586	79	}	}	PUNCT
ejpam-5827	586	80	.	.	PUNCT
ejpam-5827	587	1	suppose	suppose	VERB
ejpam-5827	587	2	that	that	SCONJ
ejpam-5827	587	3	h	h	NOUN
ejpam-5827	587	4	=	=	PRON
ejpam-5827	587	5	{	{	PUNCT
ejpam-5827	587	6	ϵ1	ϵ1	ADJ
ejpam-5827	587	7	,	,	PUNCT
ejpam-5827	587	8	ϵ5	ϵ5	PROPN
ejpam-5827	587	9	}	}	PUNCT
ejpam-5827	587	10	.	.	PUNCT
ejpam-5827	588	1	then	then	ADV
ejpam-5827	588	2	,	,	PUNCT
ejpam-5827	588	3	table	table	NOUN
ejpam-5827	588	4	4	4	NUM
ejpam-5827	588	5	:	:	PUNCT
ejpam-5827	588	6	lower	low	ADJ
ejpam-5827	588	7	,	,	PUNCT
ejpam-5827	588	8	upper	upper	ADJ
ejpam-5827	588	9	approximation	approximation	NOUN
ejpam-5827	588	10	,	,	PUNCT
ejpam-5827	588	11	and	and	CCONJ
ejpam-5827	588	12	accuracy	accuracy	NOUN
ejpam-5827	588	13	degree	degree	NOUN
ejpam-5827	588	14	with	with	ADP
ejpam-5827	588	15	τκ	τκ	PROPN
ejpam-5827	588	16	κ	κ	NOUN
ejpam-5827	588	17	r	r	NOUN
ejpam-5827	588	18	l	l	NOUN
ejpam-5827	589	1	i	i	PRON
ejpam-5827	589	2	u	u	NOUN
ejpam-5827	589	3	⟨r⟩	⟨r⟩	X
ejpam-5827	589	4	⟨l⟩	⟨l⟩	PROPN
ejpam-5827	589	5	⟨i⟩	⟨i⟩	PROPN
ejpam-5827	589	6	⟨u⟩	⟨u⟩	PROPN
ejpam-5827	589	7	τκl(h	τκl(h	NUM
ejpam-5827	589	8	)	)	PUNCT
ejpam-5827	589	9	∅	∅	NOUN
ejpam-5827	589	10	∅	∅	NOUN
ejpam-5827	589	11	{	{	PUNCT
ejpam-5827	589	12	ϵ5	ϵ5	PROPN
ejpam-5827	589	13	}	}	PUNCT
ejpam-5827	589	14	∅	∅	NOUN
ejpam-5827	589	15	{	{	PUNCT
ejpam-5827	589	16	ϵ1	ϵ1	ADJ
ejpam-5827	589	17	}	}	PUNCT
ejpam-5827	589	18	∅	∅	NOUN
ejpam-5827	589	19	{	{	PUNCT
ejpam-5827	589	20	ϵ1	ϵ1	ADJ
ejpam-5827	589	21	}	}	PUNCT
ejpam-5827	589	22	∅	∅	NOUN
ejpam-5827	589	23	τκu(h	τκu(h	PROPN
ejpam-5827	589	24	)	)	PUNCT
ejpam-5827	589	25	v	v	NOUN
ejpam-5827	589	26	{	{	PUNCT
ejpam-5827	589	27	ϵ1	ϵ1	ADJ
ejpam-5827	589	28	,	,	PUNCT
ejpam-5827	589	29	ϵ3	ϵ3	PROPN
ejpam-5827	589	30	,	,	PUNCT
ejpam-5827	589	31	ϵ5	ϵ5	PROPN
ejpam-5827	589	32	}	}	PUNCT
ejpam-5827	589	33	{	{	PUNCT
ejpam-5827	589	34	ϵ1	ϵ1	ADJ
ejpam-5827	589	35	,	,	PUNCT
ejpam-5827	589	36	ϵ3	ϵ3	PROPN
ejpam-5827	589	37	,	,	PUNCT
ejpam-5827	589	38	ϵ5	ϵ5	PROPN
ejpam-5827	589	39	}	}	PUNCT
ejpam-5827	589	40	v	v	NOUN
ejpam-5827	589	41	{	{	PUNCT
ejpam-5827	589	42	ϵ1	ϵ1	ADJ
ejpam-5827	589	43	,	,	PUNCT
ejpam-5827	589	44	ϵ4	ϵ4	PROPN
ejpam-5827	589	45	,	,	PUNCT
ejpam-5827	589	46	ϵ5	ϵ5	PROPN
ejpam-5827	589	47	}	}	PUNCT
ejpam-5827	589	48	{	{	PUNCT
ejpam-5827	589	49	ϵ1	ϵ1	ADJ
ejpam-5827	589	50	,	,	PUNCT
ejpam-5827	589	51	ϵ5	ϵ5	PROPN
ejpam-5827	589	52	}	}	PUNCT
ejpam-5827	589	53	{	{	PUNCT
ejpam-5827	589	54	ϵ1	ϵ1	ADJ
ejpam-5827	589	55	,	,	PUNCT
ejpam-5827	589	56	ϵ5	ϵ5	PROPN
ejpam-5827	589	57	}	}	PUNCT
ejpam-5827	589	58	{	{	PUNCT
ejpam-5827	589	59	ϵ1	ϵ1	ADJ
ejpam-5827	589	60	,	,	PUNCT
ejpam-5827	589	61	ϵ4	ϵ4	PROPN
ejpam-5827	589	62	,	,	PUNCT
ejpam-5827	589	63	ϵ5	ϵ5	PROPN
ejpam-5827	589	64	}	}	PUNCT
ejpam-5827	589	65	τκσ(h	τκσ(h	PROPN
ejpam-5827	589	66	)	)	PUNCT
ejpam-5827	589	67	0	0	NUM
ejpam-5827	589	68	0	0	NUM
ejpam-5827	589	69	1	1	NUM
ejpam-5827	589	70	3	3	NUM
ejpam-5827	589	71	0	0	NUM
ejpam-5827	589	72	1	1	NUM
ejpam-5827	589	73	3	3	NUM
ejpam-5827	589	74	0	0	NUM
ejpam-5827	589	75	1	1	NUM
ejpam-5827	589	76	2	2	NUM
ejpam-5827	589	77	0	0	NUM
ejpam-5827	589	78	table	table	NOUN
ejpam-5827	589	79	5	5	NUM
ejpam-5827	589	80	:	:	PUNCT
ejpam-5827	589	81	lower	low	ADJ
ejpam-5827	589	82	,	,	PUNCT
ejpam-5827	589	83	upper	upper	ADJ
ejpam-5827	589	84	approximation	approximation	NOUN
ejpam-5827	589	85	,	,	PUNCT
ejpam-5827	589	86	and	and	CCONJ
ejpam-5827	589	87	accuracy	accuracy	NOUN
ejpam-5827	589	88	degree	degree	NOUN
ejpam-5827	589	89	with	with	ADP
ejpam-5827	589	90	τp	τp	PRON
ejpam-5827	589	91	κ	κ	PROPN
ejpam-5827	589	92	κ	κ	PROPN
ejpam-5827	589	93	r	r	NOUN
ejpam-5827	589	94	l	l	NOUN
ejpam-5827	590	1	i	i	PRON
ejpam-5827	590	2	u	u	NOUN
ejpam-5827	591	1	⟨r⟩	⟨r⟩	X
ejpam-5827	591	2	⟨l⟩	⟨l⟩	PROPN
ejpam-5827	591	3	⟨i⟩	⟨i⟩	PROPN
ejpam-5827	591	4	⟨u⟩	⟨u⟩	PROPN
ejpam-5827	591	5	τpκ	τpκ	NOUN
ejpam-5827	591	6	l(h	l(h	PROPN
ejpam-5827	591	7	)	)	PUNCT
ejpam-5827	591	8	{	{	PUNCT
ejpam-5827	591	9	ϵ1	ϵ1	ADJ
ejpam-5827	591	10	,	,	PUNCT
ejpam-5827	591	11	ϵ5	ϵ5	PROPN
ejpam-5827	591	12	}	}	PUNCT
ejpam-5827	591	13	{	{	PUNCT
ejpam-5827	591	14	ϵ1	ϵ1	ADJ
ejpam-5827	591	15	,	,	PUNCT
ejpam-5827	591	16	ϵ5	ϵ5	PROPN
ejpam-5827	591	17	}	}	PUNCT
ejpam-5827	591	18	{	{	PUNCT
ejpam-5827	591	19	ϵ1	ϵ1	ADJ
ejpam-5827	591	20	,	,	PUNCT
ejpam-5827	591	21	ϵ5	ϵ5	PROPN
ejpam-5827	591	22	}	}	PUNCT
ejpam-5827	591	23	{	{	PUNCT
ejpam-5827	591	24	ϵ1	ϵ1	ADJ
ejpam-5827	591	25	,	,	PUNCT
ejpam-5827	591	26	ϵ5	ϵ5	PROPN
ejpam-5827	591	27	}	}	PUNCT
ejpam-5827	591	28	{	{	PUNCT
ejpam-5827	591	29	ϵ1	ϵ1	ADJ
ejpam-5827	591	30	,	,	PUNCT
ejpam-5827	591	31	ϵ5	ϵ5	PROPN
ejpam-5827	591	32	}	}	PUNCT
ejpam-5827	591	33	{	{	PUNCT
ejpam-5827	591	34	ϵ1	ϵ1	ADJ
ejpam-5827	591	35	,	,	PUNCT
ejpam-5827	591	36	ϵ5	ϵ5	PROPN
ejpam-5827	591	37	}	}	PUNCT
ejpam-5827	591	38	{	{	PUNCT
ejpam-5827	591	39	ϵ1	ϵ1	ADJ
ejpam-5827	591	40	,	,	PUNCT
ejpam-5827	591	41	ϵ5	ϵ5	PROPN
ejpam-5827	591	42	}	}	PUNCT
ejpam-5827	591	43	{	{	PUNCT
ejpam-5827	591	44	ϵ1	ϵ1	ADJ
ejpam-5827	591	45	,	,	PUNCT
ejpam-5827	591	46	ϵ5	ϵ5	PROPN
ejpam-5827	591	47	}	}	PUNCT
ejpam-5827	591	48	τpκ	τpκ	NOUN
ejpam-5827	591	49	u(h	u(h	PROPN
ejpam-5827	591	50	)	)	PUNCT
ejpam-5827	591	51	{	{	PUNCT
ejpam-5827	591	52	ϵ1	ϵ1	ADJ
ejpam-5827	591	53	,	,	PUNCT
ejpam-5827	591	54	ϵ5	ϵ5	PROPN
ejpam-5827	591	55	}	}	PUNCT
ejpam-5827	591	56	{	{	PUNCT
ejpam-5827	591	57	ϵ1	ϵ1	ADJ
ejpam-5827	591	58	,	,	PUNCT
ejpam-5827	591	59	ϵ5	ϵ5	PROPN
ejpam-5827	591	60	}	}	PUNCT
ejpam-5827	591	61	{	{	PUNCT
ejpam-5827	591	62	ϵ1	ϵ1	ADJ
ejpam-5827	591	63	,	,	PUNCT
ejpam-5827	591	64	ϵ5	ϵ5	PROPN
ejpam-5827	591	65	}	}	PUNCT
ejpam-5827	591	66	{	{	PUNCT
ejpam-5827	591	67	ϵ1	ϵ1	ADJ
ejpam-5827	591	68	,	,	PUNCT
ejpam-5827	591	69	ϵ5	ϵ5	PROPN
ejpam-5827	591	70	}	}	PUNCT
ejpam-5827	591	71	{	{	PUNCT
ejpam-5827	591	72	ϵ1	ϵ1	ADJ
ejpam-5827	591	73	,	,	PUNCT
ejpam-5827	591	74	ϵ5	ϵ5	PROPN
ejpam-5827	591	75	}	}	PUNCT
ejpam-5827	591	76	{	{	PUNCT
ejpam-5827	591	77	ϵ1	ϵ1	ADJ
ejpam-5827	591	78	,	,	PUNCT
ejpam-5827	591	79	ϵ5	ϵ5	PROPN
ejpam-5827	591	80	}	}	PUNCT
ejpam-5827	591	81	{	{	PUNCT
ejpam-5827	591	82	ϵ1	ϵ1	ADJ
ejpam-5827	591	83	,	,	PUNCT
ejpam-5827	591	84	ϵ5	ϵ5	PROPN
ejpam-5827	591	85	}	}	PUNCT
ejpam-5827	591	86	{	{	PUNCT
ejpam-5827	591	87	ϵ1	ϵ1	ADJ
ejpam-5827	591	88	,	,	PUNCT
ejpam-5827	591	89	ϵ5	ϵ5	PROPN
ejpam-5827	591	90	}	}	PUNCT
ejpam-5827	591	91	τpκ	τpκ	NOUN
ejpam-5827	591	92	σ(h	σ(h	PROPN
ejpam-5827	591	93	)	)	PUNCT
ejpam-5827	591	94	1	1	NUM
ejpam-5827	591	95	1	1	NUM
ejpam-5827	591	96	1	1	NUM
ejpam-5827	591	97	1	1	NUM
ejpam-5827	591	98	1	1	NUM
ejpam-5827	591	99	1	1	NUM
ejpam-5827	591	100	1	1	NUM
ejpam-5827	591	101	1	1	NUM
ejpam-5827	591	102	r.	r.	PROPN
ejpam-5827	591	103	a.	a.	PROPN
ejpam-5827	591	104	hosny	hosny	PROPN
ejpam-5827	591	105	,	,	PUNCT
ejpam-5827	591	106	m.	m.	PROPN
ejpam-5827	591	107	k.	k.	PROPN
ejpam-5827	592	1	el	el	PROPN
ejpam-5827	592	2	-	-	PROPN
ejpam-5827	592	3	bably	bably	ADV
ejpam-5827	592	4	,	,	PUNCT
ejpam-5827	592	5	m.	m.	NOUN
ejpam-5827	592	6	a.	a.	PROPN
ejpam-5827	592	7	el	el	PROPN
ejpam-5827	592	8	-	-	PROPN
ejpam-5827	592	9	gayar	gayar	PROPN
ejpam-5827	592	10	/	/	SYM
ejpam-5827	592	11	eur	eur	PROPN
ejpam-5827	592	12	.	.	PUNCT
ejpam-5827	593	1	j.	j.	PROPN
ejpam-5827	593	2	pure	pure	PROPN
ejpam-5827	593	3	appl	appl	PROPN
ejpam-5827	593	4	.	.	PROPN
ejpam-5827	593	5	math	math	PROPN
ejpam-5827	593	6	,	,	PUNCT
ejpam-5827	593	7	18	18	NUM
ejpam-5827	593	8	(	(	PUNCT
ejpam-5827	593	9	1	1	NUM
ejpam-5827	593	10	)	)	PUNCT
ejpam-5827	593	11	(	(	PUNCT
ejpam-5827	593	12	2025	2025	NUM
ejpam-5827	593	13	)	)	PUNCT
ejpam-5827	593	14	,	,	PUNCT
ejpam-5827	593	15	5827	5827	NUM
ejpam-5827	593	16	23	23	NUM
ejpam-5827	593	17	of	of	ADP
ejpam-5827	593	18	29	29	NUM
ejpam-5827	593	19	table	table	NOUN
ejpam-5827	593	20	6	6	NUM
ejpam-5827	593	21	:	:	PUNCT
ejpam-5827	593	22	lower	low	ADJ
ejpam-5827	593	23	,	,	PUNCT
ejpam-5827	593	24	upper	upper	ADJ
ejpam-5827	593	25	approximation	approximation	NOUN
ejpam-5827	593	26	,	,	PUNCT
ejpam-5827	593	27	and	and	CCONJ
ejpam-5827	593	28	accuracy	accuracy	NOUN
ejpam-5827	593	29	degree	degree	NOUN
ejpam-5827	593	30	with	with	ADP
ejpam-5827	593	31	τ	τ	PROPN
ejpam-5827	593	32	p̃	p̃	PROPN
ejpam-5827	593	33	κ	κ	X
ejpam-5827	593	34	κ	κ	NOUN
ejpam-5827	593	35	r	r	NOUN
ejpam-5827	593	36	l	l	NOUN
ejpam-5827	594	1	i	i	PRON
ejpam-5827	594	2	u	u	NOUN
ejpam-5827	594	3	⟨r⟩	⟨r⟩	X
ejpam-5827	594	4	⟨l⟩	⟨l⟩	PROPN
ejpam-5827	594	5	⟨i⟩	⟨i⟩	PROPN
ejpam-5827	594	6	⟨u⟩	⟨u⟩	PROPN
ejpam-5827	594	7	τ	τ	PROPN
ejpam-5827	594	8	p̃κ	p̃κ	NOUN
ejpam-5827	594	9	l(h	l(h	PROPN
ejpam-5827	594	10	)	)	PUNCT
ejpam-5827	594	11	{	{	PUNCT
ejpam-5827	594	12	ϵ1	ϵ1	ADJ
ejpam-5827	594	13	,	,	PUNCT
ejpam-5827	594	14	ϵ5	ϵ5	PROPN
ejpam-5827	594	15	}	}	PUNCT
ejpam-5827	594	16	{	{	PUNCT
ejpam-5827	594	17	ϵ5	ϵ5	PROPN
ejpam-5827	594	18	}	}	PUNCT
ejpam-5827	594	19	{	{	PUNCT
ejpam-5827	594	20	ϵ1	ϵ1	ADJ
ejpam-5827	594	21	,	,	PUNCT
ejpam-5827	594	22	ϵ5	ϵ5	PROPN
ejpam-5827	594	23	}	}	PUNCT
ejpam-5827	594	24	∅	∅	NOUN
ejpam-5827	594	25	{	{	PUNCT
ejpam-5827	594	26	ϵ1	ϵ1	ADJ
ejpam-5827	594	27	,	,	PUNCT
ejpam-5827	594	28	ϵ5	ϵ5	PROPN
ejpam-5827	594	29	}	}	PUNCT
ejpam-5827	594	30	{	{	PUNCT
ejpam-5827	594	31	ϵ1	ϵ1	ADJ
ejpam-5827	594	32	,	,	PUNCT
ejpam-5827	594	33	ϵ5	ϵ5	PROPN
ejpam-5827	594	34	}	}	PUNCT
ejpam-5827	594	35	{	{	PUNCT
ejpam-5827	594	36	ϵ1	ϵ1	ADJ
ejpam-5827	594	37	,	,	PUNCT
ejpam-5827	594	38	ϵ5	ϵ5	PROPN
ejpam-5827	594	39	}	}	PUNCT
ejpam-5827	594	40	{	{	PUNCT
ejpam-5827	594	41	ϵ1	ϵ1	ADJ
ejpam-5827	594	42	,	,	PUNCT
ejpam-5827	594	43	ϵ5	ϵ5	PROPN
ejpam-5827	594	44	}	}	PUNCT
ejpam-5827	594	45	τ	τ	PROPN
ejpam-5827	594	46	p̃κ	p̃κ	NOUN
ejpam-5827	594	47	u(h	u(h	PROPN
ejpam-5827	594	48	)	)	PUNCT
ejpam-5827	594	49	{	{	PUNCT
ejpam-5827	594	50	ϵ1	ϵ1	ADJ
ejpam-5827	594	51	,	,	PUNCT
ejpam-5827	594	52	ϵ5	ϵ5	PROPN
ejpam-5827	594	53	}	}	PUNCT
ejpam-5827	594	54	{	{	PUNCT
ejpam-5827	594	55	ϵ1	ϵ1	ADJ
ejpam-5827	594	56	,	,	PUNCT
ejpam-5827	594	57	ϵ5	ϵ5	PROPN
ejpam-5827	594	58	}	}	PUNCT
ejpam-5827	594	59	{	{	PUNCT
ejpam-5827	594	60	ϵ1	ϵ1	ADJ
ejpam-5827	594	61	,	,	PUNCT
ejpam-5827	594	62	ϵ5	ϵ5	PROPN
ejpam-5827	594	63	}	}	PUNCT
ejpam-5827	594	64	{	{	PUNCT
ejpam-5827	594	65	ϵ1	ϵ1	ADJ
ejpam-5827	594	66	,	,	PUNCT
ejpam-5827	594	67	ϵ5	ϵ5	PROPN
ejpam-5827	594	68	}	}	PUNCT
ejpam-5827	594	69	{	{	PUNCT
ejpam-5827	594	70	ϵ1	ϵ1	ADJ
ejpam-5827	594	71	,	,	PUNCT
ejpam-5827	594	72	ϵ5	ϵ5	PROPN
ejpam-5827	594	73	}	}	PUNCT
ejpam-5827	594	74	{	{	PUNCT
ejpam-5827	594	75	ϵ1	ϵ1	ADJ
ejpam-5827	594	76	,	,	PUNCT
ejpam-5827	594	77	ϵ5	ϵ5	PROPN
ejpam-5827	594	78	}	}	PUNCT
ejpam-5827	594	79	{	{	PUNCT
ejpam-5827	594	80	ϵ1	ϵ1	ADJ
ejpam-5827	594	81	,	,	PUNCT
ejpam-5827	594	82	ϵ5	ϵ5	PROPN
ejpam-5827	594	83	}	}	PUNCT
ejpam-5827	594	84	{	{	PUNCT
ejpam-5827	594	85	ϵ1	ϵ1	ADJ
ejpam-5827	594	86	,	,	PUNCT
ejpam-5827	594	87	ϵ5	ϵ5	PROPN
ejpam-5827	594	88	}	}	PUNCT
ejpam-5827	594	89	τ	τ	PROPN
ejpam-5827	594	90	p̃κ	p̃κ	PROPN
ejpam-5827	594	91	σ(h	σ(h	PROPN
ejpam-5827	594	92	)	)	PUNCT
ejpam-5827	594	93	1	1	NUM
ejpam-5827	594	94	1	1	NUM
ejpam-5827	594	95	2	2	NUM
ejpam-5827	594	96	1	1	NUM
ejpam-5827	594	97	0	0	NUM
ejpam-5827	594	98	1	1	NUM
ejpam-5827	594	99	1	1	NUM
ejpam-5827	594	100	1	1	NUM
ejpam-5827	594	101	1	1	NUM
ejpam-5827	594	102	table	table	NOUN
ejpam-5827	594	103	7	7	NUM
ejpam-5827	594	104	:	:	PUNCT
ejpam-5827	594	105	lower	low	ADJ
ejpam-5827	594	106	,	,	PUNCT
ejpam-5827	594	107	upper	upper	ADJ
ejpam-5827	594	108	approximation	approximation	NOUN
ejpam-5827	594	109	,	,	PUNCT
ejpam-5827	594	110	and	and	CCONJ
ejpam-5827	594	111	accuracy	accuracy	NOUN
ejpam-5827	594	112	degree	degree	NOUN
ejpam-5827	594	113	with	with	ADP
ejpam-5827	594	114	τp∪p̃	τp∪p̃	ADP
ejpam-5827	594	115	κ	κ	PROPN
ejpam-5827	594	116	κ	κ	PROPN
ejpam-5827	594	117	r	r	NOUN
ejpam-5827	594	118	l	l	NOUN
ejpam-5827	595	1	i	i	PRON
ejpam-5827	595	2	u	u	NOUN
ejpam-5827	596	1	⟨r⟩	⟨r⟩	X
ejpam-5827	596	2	⟨l⟩	⟨l⟩	PROPN
ejpam-5827	596	3	⟨i⟩	⟨i⟩	PROPN
ejpam-5827	596	4	⟨u⟩	⟨u⟩	PROPN
ejpam-5827	596	5	τp∪p̃	τp∪p̃	ADP
ejpam-5827	596	6	κ	κ	PROPN
ejpam-5827	596	7	l(h	l(h	PROPN
ejpam-5827	596	8	)	)	PUNCT
ejpam-5827	596	9	{	{	PUNCT
ejpam-5827	596	10	ϵ1	ϵ1	ADJ
ejpam-5827	596	11	,	,	PUNCT
ejpam-5827	596	12	ϵ5	ϵ5	PROPN
ejpam-5827	596	13	}	}	PUNCT
ejpam-5827	596	14	{	{	PUNCT
ejpam-5827	596	15	ϵ1	ϵ1	ADJ
ejpam-5827	596	16	,	,	PUNCT
ejpam-5827	596	17	ϵ5	ϵ5	PROPN
ejpam-5827	596	18	}	}	PUNCT
ejpam-5827	596	19	{	{	PUNCT
ejpam-5827	596	20	ϵ1	ϵ1	ADJ
ejpam-5827	596	21	,	,	PUNCT
ejpam-5827	596	22	ϵ5	ϵ5	PROPN
ejpam-5827	596	23	}	}	PUNCT
ejpam-5827	596	24	{	{	PUNCT
ejpam-5827	596	25	ϵ1	ϵ1	ADJ
ejpam-5827	596	26	,	,	PUNCT
ejpam-5827	596	27	ϵ5	ϵ5	PROPN
ejpam-5827	596	28	}	}	PUNCT
ejpam-5827	596	29	{	{	PUNCT
ejpam-5827	596	30	ϵ1	ϵ1	ADJ
ejpam-5827	596	31	,	,	PUNCT
ejpam-5827	596	32	ϵ5	ϵ5	PROPN
ejpam-5827	596	33	}	}	PUNCT
ejpam-5827	596	34	{	{	PUNCT
ejpam-5827	596	35	ϵ1	ϵ1	ADJ
ejpam-5827	596	36	,	,	PUNCT
ejpam-5827	596	37	ϵ5	ϵ5	PROPN
ejpam-5827	596	38	}	}	PUNCT
ejpam-5827	596	39	{	{	PUNCT
ejpam-5827	596	40	ϵ1	ϵ1	ADJ
ejpam-5827	596	41	,	,	PUNCT
ejpam-5827	596	42	ϵ5	ϵ5	PROPN
ejpam-5827	596	43	}	}	PUNCT
ejpam-5827	596	44	{	{	PUNCT
ejpam-5827	596	45	ϵ1	ϵ1	ADJ
ejpam-5827	596	46	,	,	PUNCT
ejpam-5827	596	47	ϵ5	ϵ5	PROPN
ejpam-5827	596	48	}	}	PUNCT
ejpam-5827	596	49	τp∪p̃	τp∪p̃	ADP
ejpam-5827	596	50	κ	κ	PROPN
ejpam-5827	596	51	u(h	u(h	PROPN
ejpam-5827	596	52	)	)	PUNCT
ejpam-5827	596	53	{	{	PUNCT
ejpam-5827	596	54	ϵ1	ϵ1	ADJ
ejpam-5827	596	55	,	,	PUNCT
ejpam-5827	596	56	ϵ5	ϵ5	PROPN
ejpam-5827	596	57	}	}	PUNCT
ejpam-5827	596	58	{	{	PUNCT
ejpam-5827	596	59	ϵ1	ϵ1	ADJ
ejpam-5827	596	60	,	,	PUNCT
ejpam-5827	596	61	ϵ5	ϵ5	PROPN
ejpam-5827	596	62	}	}	PUNCT
ejpam-5827	596	63	{	{	PUNCT
ejpam-5827	596	64	ϵ1	ϵ1	ADJ
ejpam-5827	596	65	,	,	PUNCT
ejpam-5827	596	66	ϵ5	ϵ5	PROPN
ejpam-5827	596	67	}	}	PUNCT
ejpam-5827	596	68	{	{	PUNCT
ejpam-5827	596	69	ϵ1	ϵ1	ADJ
ejpam-5827	596	70	,	,	PUNCT
ejpam-5827	596	71	ϵ5	ϵ5	PROPN
ejpam-5827	596	72	}	}	PUNCT
ejpam-5827	596	73	{	{	PUNCT
ejpam-5827	596	74	ϵ1	ϵ1	ADJ
ejpam-5827	596	75	,	,	PUNCT
ejpam-5827	596	76	ϵ5	ϵ5	PROPN
ejpam-5827	596	77	}	}	PUNCT
ejpam-5827	596	78	{	{	PUNCT
ejpam-5827	596	79	ϵ1	ϵ1	ADJ
ejpam-5827	596	80	,	,	PUNCT
ejpam-5827	596	81	ϵ5	ϵ5	PROPN
ejpam-5827	596	82	}	}	PUNCT
ejpam-5827	596	83	{	{	PUNCT
ejpam-5827	596	84	ϵ1	ϵ1	ADJ
ejpam-5827	596	85	,	,	PUNCT
ejpam-5827	596	86	ϵ5	ϵ5	PROPN
ejpam-5827	596	87	}	}	PUNCT
ejpam-5827	596	88	{	{	PUNCT
ejpam-5827	596	89	ϵ1	ϵ1	ADJ
ejpam-5827	596	90	,	,	PUNCT
ejpam-5827	596	91	ϵ5	ϵ5	PROPN
ejpam-5827	596	92	}	}	PUNCT
ejpam-5827	596	93	τp∪p̃	τp∪p̃	ADP
ejpam-5827	596	94	κ	κ	PROPN
ejpam-5827	596	95	σ(h	σ(h	PROPN
ejpam-5827	596	96	)	)	PUNCT
ejpam-5827	596	97	1	1	NUM
ejpam-5827	596	98	1	1	NUM
ejpam-5827	596	99	1	1	NUM
ejpam-5827	596	100	1	1	NUM
ejpam-5827	596	101	1	1	NUM
ejpam-5827	596	102	1	1	NUM
ejpam-5827	596	103	1	1	NUM
ejpam-5827	596	104	1	1	NUM
ejpam-5827	596	105	6	6	NUM
ejpam-5827	596	106	.	.	PUNCT
ejpam-5827	597	1	conclusions	conclusion	NOUN
ejpam-5827	597	2	and	and	CCONJ
ejpam-5827	597	3	future	future	ADJ
ejpam-5827	597	4	works	work	NOUN
ejpam-5827	597	5	in	in	ADP
ejpam-5827	597	6	this	this	DET
ejpam-5827	597	7	study	study	NOUN
ejpam-5827	597	8	,	,	PUNCT
ejpam-5827	597	9	we	we	PRON
ejpam-5827	597	10	have	have	AUX
ejpam-5827	597	11	offered	offer	VERB
ejpam-5827	597	12	a	a	DET
ejpam-5827	597	13	novel	novel	ADJ
ejpam-5827	597	14	framework	framework	NOUN
ejpam-5827	597	15	for	for	ADP
ejpam-5827	597	16	approximate	approximate	ADJ
ejpam-5827	597	17	rough	rough	ADJ
ejpam-5827	597	18	sets	set	NOUN
ejpam-5827	597	19	by	by	ADP
ejpam-5827	597	20	introducing	introduce	VERB
ejpam-5827	597	21	the	the	DET
ejpam-5827	597	22	concept	concept	NOUN
ejpam-5827	597	23	of	of	ADP
ejpam-5827	597	24	”	"	PUNCT
ejpam-5827	597	25	primal	primal	ADJ
ejpam-5827	597	26	”	"	PUNCT
ejpam-5827	597	27	and	and	CCONJ
ejpam-5827	597	28	exploring	explore	VERB
ejpam-5827	597	29	bi	bi	ADJ
ejpam-5827	597	30	-	-	ADJ
ejpam-5827	597	31	primal	primal	ADJ
ejpam-5827	597	32	approximation	approximation	NOUN
ejpam-5827	597	33	spaces	space	NOUN
ejpam-5827	597	34	.	.	PUNCT
ejpam-5827	598	1	the	the	DET
ejpam-5827	598	2	findings	finding	NOUN
ejpam-5827	598	3	indicate	indicate	VERB
ejpam-5827	598	4	that	that	SCONJ
ejpam-5827	598	5	these	these	DET
ejpam-5827	598	6	new	new	ADJ
ejpam-5827	598	7	structures	structure	NOUN
ejpam-5827	598	8	effectively	effectively	ADV
ejpam-5827	598	9	address	address	VERB
ejpam-5827	598	10	the	the	DET
ejpam-5827	598	11	drawbacks	drawback	NOUN
ejpam-5827	598	12	of	of	ADP
ejpam-5827	598	13	traditional	traditional	ADJ
ejpam-5827	598	14	rough	rough	ADJ
ejpam-5827	598	15	set	set	NOUN
ejpam-5827	598	16	models	model	NOUN
ejpam-5827	598	17	,	,	PUNCT
ejpam-5827	598	18	especially	especially	ADV
ejpam-5827	598	19	those	those	PRON
ejpam-5827	598	20	arising	arise	VERB
ejpam-5827	598	21	from	from	ADP
ejpam-5827	598	22	rigid	rigid	ADJ
ejpam-5827	598	23	topological	topological	ADJ
ejpam-5827	598	24	conditions	condition	NOUN
ejpam-5827	598	25	.	.	PUNCT
ejpam-5827	599	1	by	by	ADP
ejpam-5827	599	2	employing	employ	VERB
ejpam-5827	599	3	κ	κ	NOUN
ejpam-5827	599	4	-	-	NOUN
ejpam-5827	599	5	neighborhoods	neighborhood	NOUN
ejpam-5827	599	6	and	and	CCONJ
ejpam-5827	599	7	primal	primal	ADJ
ejpam-5827	599	8	,	,	PUNCT
ejpam-5827	599	9	we	we	PRON
ejpam-5827	599	10	have	have	AUX
ejpam-5827	599	11	established	establish	VERB
ejpam-5827	599	12	methods	method	NOUN
ejpam-5827	599	13	for	for	ADP
ejpam-5827	599	14	generating	generate	VERB
ejpam-5827	599	15	diverse	diverse	ADJ
ejpam-5827	599	16	supratopologies	supratopologie	NOUN
ejpam-5827	599	17	that	that	PRON
ejpam-5827	599	18	not	not	PART
ejpam-5827	599	19	only	only	ADV
ejpam-5827	599	20	enhance	enhance	VERB
ejpam-5827	599	21	flexibility	flexibility	NOUN
ejpam-5827	599	22	but	but	CCONJ
ejpam-5827	599	23	also	also	ADV
ejpam-5827	599	24	allow	allow	VERB
ejpam-5827	599	25	for	for	ADP
ejpam-5827	599	26	a	a	DET
ejpam-5827	599	27	broader	broad	ADJ
ejpam-5827	599	28	range	range	NOUN
ejpam-5827	599	29	of	of	ADP
ejpam-5827	599	30	real	real	ADJ
ejpam-5827	599	31	-	-	PUNCT
ejpam-5827	599	32	world	world	NOUN
ejpam-5827	599	33	applications	application	NOUN
ejpam-5827	599	34	.	.	PUNCT
ejpam-5827	600	1	the	the	DET
ejpam-5827	600	2	approach	approach	NOUN
ejpam-5827	600	3	of	of	ADP
ejpam-5827	600	4	supra	supra	ADJ
ejpam-5827	600	5	-	-	PUNCT
ejpam-5827	600	6	topological	topological	ADJ
ejpam-5827	600	7	structures	structure	NOUN
ejpam-5827	600	8	used	use	VERB
ejpam-5827	600	9	to	to	PART
ejpam-5827	600	10	develop	develop	VERB
ejpam-5827	600	11	new	new	ADJ
ejpam-5827	600	12	models	model	NOUN
ejpam-5827	600	13	of	of	ADP
ejpam-5827	600	14	rough	rough	ADJ
ejpam-5827	600	15	set	set	NOUN
ejpam-5827	600	16	theory	theory	NOUN
ejpam-5827	600	17	in	in	ADP
ejpam-5827	600	18	this	this	DET
ejpam-5827	600	19	manuscript	manuscript	NOUN
ejpam-5827	600	20	is	be	AUX
ejpam-5827	600	21	more	more	ADV
ejpam-5827	600	22	adjustable	adjustable	ADJ
ejpam-5827	600	23	than	than	ADP
ejpam-5827	600	24	traditional	traditional	ADJ
ejpam-5827	600	25	topological	topological	ADJ
ejpam-5827	600	26	structures	structure	NOUN
ejpam-5827	600	27	.	.	PUNCT
ejpam-5827	601	1	this	this	DET
ejpam-5827	601	2	flexibility	flexibility	NOUN
ejpam-5827	601	3	allows	allow	VERB
ejpam-5827	601	4	for	for	ADP
ejpam-5827	601	5	a	a	DET
ejpam-5827	601	6	broader	broad	ADJ
ejpam-5827	601	7	scope	scope	NOUN
ejpam-5827	601	8	in	in	ADP
ejpam-5827	601	9	describing	describe	VERB
ejpam-5827	601	10	various	various	ADJ
ejpam-5827	601	11	phenomena	phenomenon	NOUN
ejpam-5827	601	12	,	,	PUNCT
ejpam-5827	601	13	as	as	SCONJ
ejpam-5827	601	14	it	it	PRON
ejpam-5827	601	15	removes	remove	VERB
ejpam-5827	601	16	the	the	DET
ejpam-5827	601	17	need	need	NOUN
ejpam-5827	601	18	for	for	ADP
ejpam-5827	601	19	an	an	DET
ejpam-5827	601	20	intersection	intersection	NOUN
ejpam-5827	601	21	condition	condition	NOUN
ejpam-5827	601	22	that	that	PRON
ejpam-5827	601	23	may	may	AUX
ejpam-5827	601	24	not	not	PART
ejpam-5827	601	25	be	be	AUX
ejpam-5827	601	26	suitable	suitable	ADJ
ejpam-5827	601	27	in	in	ADP
ejpam-5827	601	28	certain	certain	ADJ
ejpam-5827	601	29	contexts	context	NOUN
ejpam-5827	601	30	.	.	PUNCT
ejpam-5827	602	1	for	for	ADP
ejpam-5827	602	2	instance	instance	NOUN
ejpam-5827	602	3	,	,	PUNCT
ejpam-5827	602	4	in	in	ADP
ejpam-5827	602	5	the	the	DET
ejpam-5827	602	6	provided	provide	VERB
ejpam-5827	602	7	application	application	NOUN
ejpam-5827	602	8	,	,	PUNCT
ejpam-5827	602	9	we	we	PRON
ejpam-5827	602	10	demonstrated	demonstrate	VERB
ejpam-5827	602	11	how	how	SCONJ
ejpam-5827	602	12	the	the	DET
ejpam-5827	602	13	generated	generate	VERB
ejpam-5827	602	14	supra	supra	NOUN
ejpam-5827	602	15	-	-	PUNCT
ejpam-5827	602	16	topologies	topology	NOUN
ejpam-5827	602	17	aided	aid	VERB
ejpam-5827	602	18	in	in	ADP
ejpam-5827	602	19	more	more	ADV
ejpam-5827	602	20	accurate	accurate	ADJ
ejpam-5827	602	21	decision	decision	NOUN
ejpam-5827	602	22	-	-	PUNCT
ejpam-5827	602	23	making	making	NOUN
ejpam-5827	602	24	by	by	ADP
ejpam-5827	602	25	avoiding	avoid	VERB
ejpam-5827	602	26	common	common	ADJ
ejpam-5827	602	27	levels	level	NOUN
ejpam-5827	602	28	,	,	PUNCT
ejpam-5827	602	29	thereby	thereby	ADV
ejpam-5827	602	30	providing	provide	VERB
ejpam-5827	602	31	more	more	ADV
ejpam-5827	602	32	precise	precise	ADJ
ejpam-5827	602	33	decisions	decision	NOUN
ejpam-5827	602	34	.	.	PUNCT
ejpam-5827	603	1	the	the	DET
ejpam-5827	603	2	introduction	introduction	NOUN
ejpam-5827	603	3	of	of	ADP
ejpam-5827	603	4	bi	bi	ADJ
ejpam-5827	603	5	-	-	ADJ
ejpam-5827	603	6	primal	primal	ADJ
ejpam-5827	603	7	approximation	approximation	NOUN
ejpam-5827	603	8	spaces	space	NOUN
ejpam-5827	603	9	underlines	underline	VERB
ejpam-5827	603	10	a	a	DET
ejpam-5827	603	11	significant	significant	ADJ
ejpam-5827	603	12	advancement	advancement	NOUN
ejpam-5827	603	13	in	in	ADP
ejpam-5827	603	14	rough	rough	ADJ
ejpam-5827	603	15	set	set	NOUN
ejpam-5827	603	16	theory	theory	NOUN
ejpam-5827	603	17	.	.	PUNCT
ejpam-5827	604	1	our	our	PRON
ejpam-5827	604	2	investigation	investigation	NOUN
ejpam-5827	604	3	into	into	ADP
ejpam-5827	604	4	the	the	DET
ejpam-5827	604	5	distinct	distinct	ADJ
ejpam-5827	604	6	methods	method	NOUN
ejpam-5827	604	7	associated	associate	VERB
ejpam-5827	604	8	with	with	ADP
ejpam-5827	604	9	these	these	DET
ejpam-5827	604	10	spaces	space	NOUN
ejpam-5827	604	11	reveals	reveal	VERB
ejpam-5827	604	12	their	their	PRON
ejpam-5827	604	13	potential	potential	NOUN
ejpam-5827	604	14	for	for	ADP
ejpam-5827	604	15	offering	offer	VERB
ejpam-5827	604	16	solutions	solution	NOUN
ejpam-5827	604	17	to	to	ADP
ejpam-5827	604	18	complex	complex	ADJ
ejpam-5827	604	19	decision	decision	NOUN
ejpam-5827	604	20	-	-	PUNCT
ejpam-5827	604	21	making	make	VERB
ejpam-5827	604	22	problems	problem	NOUN
ejpam-5827	604	23	.	.	PUNCT
ejpam-5827	605	1	notably	notably	ADV
ejpam-5827	605	2	,	,	PUNCT
ejpam-5827	605	3	these	these	DET
ejpam-5827	605	4	approaches	approach	NOUN
ejpam-5827	605	5	enable	enable	VERB
ejpam-5827	605	6	the	the	DET
ejpam-5827	605	7	modeling	modeling	NOUN
ejpam-5827	605	8	of	of	ADP
ejpam-5827	605	9	scenarios	scenario	NOUN
ejpam-5827	605	10	where	where	SCONJ
ejpam-5827	605	11	existing	exist	VERB
ejpam-5827	605	12	methods	method	NOUN
ejpam-5827	605	13	based	base	VERB
ejpam-5827	605	14	on	on	ADP
ejpam-5827	605	15	ideals	ideal	NOUN
ejpam-5827	605	16	may	may	AUX
ejpam-5827	605	17	fall	fall	VERB
ejpam-5827	605	18	short	short	ADJ
ejpam-5827	605	19	.	.	PUNCT
ejpam-5827	606	1	for	for	ADP
ejpam-5827	606	2	instance	instance	NOUN
ejpam-5827	606	3	,	,	PUNCT
ejpam-5827	606	4	the	the	DET
ejpam-5827	606	5	elimination	elimination	NOUN
ejpam-5827	606	6	of	of	ADP
ejpam-5827	606	7	the	the	DET
ejpam-5827	606	8	finite	finite	ADJ
ejpam-5827	606	9	intersection	intersection	NOUN
ejpam-5827	606	10	condition	condition	NOUN
ejpam-5827	606	11	in	in	ADP
ejpam-5827	606	12	topological	topological	ADJ
ejpam-5827	606	13	rough	rough	ADJ
ejpam-5827	606	14	models	model	NOUN
ejpam-5827	606	15	not	not	PART
ejpam-5827	606	16	only	only	ADV
ejpam-5827	606	17	widens	widen	VERB
ejpam-5827	606	18	the	the	DET
ejpam-5827	606	19	applicability	applicability	NOUN
ejpam-5827	606	20	of	of	ADP
ejpam-5827	606	21	the	the	DET
ejpam-5827	606	22	framework	framework	NOUN
ejpam-5827	606	23	but	but	CCONJ
ejpam-5827	606	24	also	also	ADV
ejpam-5827	606	25	facilitates	facilitate	VERB
ejpam-5827	606	26	a	a	DET
ejpam-5827	606	27	more	more	ADV
ejpam-5827	606	28	nuanced	nuanced	ADJ
ejpam-5827	606	29	understanding	understanding	NOUN
ejpam-5827	606	30	of	of	ADP
ejpam-5827	606	31	the	the	DET
ejpam-5827	606	32	relationships	relationship	NOUN
ejpam-5827	606	33	between	between	ADP
ejpam-5827	606	34	various	various	ADJ
ejpam-5827	606	35	attributes	attribute	NOUN
ejpam-5827	606	36	table	table	NOUN
ejpam-5827	606	37	8	8	NUM
ejpam-5827	606	38	:	:	PUNCT
ejpam-5827	606	39	lower	low	ADJ
ejpam-5827	606	40	,	,	PUNCT
ejpam-5827	606	41	upper	upper	ADJ
ejpam-5827	606	42	approximation	approximation	NOUN
ejpam-5827	606	43	,	,	PUNCT
ejpam-5827	606	44	and	and	CCONJ
ejpam-5827	606	45	accuracy	accuracy	NOUN
ejpam-5827	606	46	degree	degree	NOUN
ejpam-5827	606	47	with	with	ADP
ejpam-5827	606	48	τi	τi	PROPN
ejpam-5827	606	49	κ	κ	PROPN
ejpam-5827	606	50	κ	κ	PROPN
ejpam-5827	606	51	r	r	NOUN
ejpam-5827	606	52	l	l	NOUN
ejpam-5827	607	1	i	i	PRON
ejpam-5827	607	2	u	u	NOUN
ejpam-5827	608	1	⟨r⟩	⟨r⟩	X
ejpam-5827	608	2	⟨l⟩	⟨l⟩	PROPN
ejpam-5827	608	3	⟨i⟩	⟨i⟩	PROPN
ejpam-5827	608	4	⟨u⟩	⟨u⟩	PROPN
ejpam-5827	608	5	τiκl(h	τiκl(h	NUM
ejpam-5827	608	6	)	)	PUNCT
ejpam-5827	608	7	{	{	PUNCT
ejpam-5827	608	8	ϵ1	ϵ1	ADJ
ejpam-5827	608	9	,	,	PUNCT
ejpam-5827	608	10	ϵ5	ϵ5	PROPN
ejpam-5827	608	11	}	}	PUNCT
ejpam-5827	608	12	{	{	PUNCT
ejpam-5827	608	13	ϵ1	ϵ1	ADJ
ejpam-5827	608	14	,	,	PUNCT
ejpam-5827	608	15	ϵ5	ϵ5	PROPN
ejpam-5827	608	16	}	}	PUNCT
ejpam-5827	608	17	{	{	PUNCT
ejpam-5827	608	18	ϵ1	ϵ1	ADJ
ejpam-5827	608	19	,	,	PUNCT
ejpam-5827	608	20	ϵ5	ϵ5	PROPN
ejpam-5827	608	21	}	}	PUNCT
ejpam-5827	608	22	{	{	PUNCT
ejpam-5827	608	23	ϵ1	ϵ1	ADJ
ejpam-5827	608	24	,	,	PUNCT
ejpam-5827	608	25	ϵ5	ϵ5	PROPN
ejpam-5827	608	26	}	}	PUNCT
ejpam-5827	608	27	{	{	PUNCT
ejpam-5827	608	28	ϵ1	ϵ1	ADJ
ejpam-5827	608	29	}	}	PUNCT
ejpam-5827	608	30	{	{	PUNCT
ejpam-5827	608	31	ϵ5	ϵ5	PROPN
ejpam-5827	608	32	}	}	PUNCT
ejpam-5827	608	33	{	{	PUNCT
ejpam-5827	608	34	ϵ1	ϵ1	ADJ
ejpam-5827	608	35	}	}	PUNCT
ejpam-5827	608	36	∅	∅	NOUN
ejpam-5827	608	37	τiκu(h	τiκu(h	NOUN
ejpam-5827	608	38	)	)	PUNCT
ejpam-5827	608	39	{	{	PUNCT
ejpam-5827	608	40	ϵ1	ϵ1	ADJ
ejpam-5827	608	41	,	,	PUNCT
ejpam-5827	608	42	ϵ2	ϵ2	ADJ
ejpam-5827	608	43	,	,	PUNCT
ejpam-5827	608	44	ϵ5	ϵ5	PROPN
ejpam-5827	608	45	}	}	PUNCT
ejpam-5827	608	46	{	{	PUNCT
ejpam-5827	608	47	ϵ1	ϵ1	ADJ
ejpam-5827	608	48	,	,	PUNCT
ejpam-5827	608	49	ϵ3	ϵ3	PROPN
ejpam-5827	608	50	,	,	PUNCT
ejpam-5827	608	51	ϵ5	ϵ5	PROPN
ejpam-5827	608	52	}	}	PUNCT
ejpam-5827	608	53	{	{	PUNCT
ejpam-5827	608	54	ϵ1	ϵ1	ADJ
ejpam-5827	608	55	,	,	PUNCT
ejpam-5827	608	56	ϵ5	ϵ5	PROPN
ejpam-5827	608	57	}	}	PUNCT
ejpam-5827	608	58	{	{	PUNCT
ejpam-5827	608	59	ϵ1	ϵ1	ADJ
ejpam-5827	608	60	,	,	PUNCT
ejpam-5827	608	61	ϵ2	ϵ2	ADJ
ejpam-5827	608	62	,	,	PUNCT
ejpam-5827	608	63	ϵ3	ϵ3	PROPN
ejpam-5827	608	64	,	,	PUNCT
ejpam-5827	608	65	ϵ5	ϵ5	PROPN
ejpam-5827	608	66	}	}	PUNCT
ejpam-5827	608	67	{	{	PUNCT
ejpam-5827	608	68	ϵ1	ϵ1	ADJ
ejpam-5827	608	69	,	,	PUNCT
ejpam-5827	608	70	ϵ4	ϵ4	PROPN
ejpam-5827	608	71	,	,	PUNCT
ejpam-5827	608	72	ϵ5	ϵ5	PROPN
ejpam-5827	608	73	}	}	PUNCT
ejpam-5827	608	74	{	{	PUNCT
ejpam-5827	608	75	ϵ1	ϵ1	ADJ
ejpam-5827	608	76	,	,	PUNCT
ejpam-5827	608	77	ϵ3	ϵ3	PROPN
ejpam-5827	608	78	,	,	PUNCT
ejpam-5827	608	79	ϵ5	ϵ5	PROPN
ejpam-5827	608	80	}	}	PUNCT
ejpam-5827	608	81	{	{	PUNCT
ejpam-5827	608	82	ϵ1	ϵ1	ADJ
ejpam-5827	608	83	,	,	PUNCT
ejpam-5827	608	84	ϵ5	ϵ5	PROPN
ejpam-5827	608	85	}	}	PUNCT
ejpam-5827	608	86	{	{	PUNCT
ejpam-5827	608	87	ϵ1	ϵ1	ADJ
ejpam-5827	608	88	,	,	PUNCT
ejpam-5827	608	89	ϵ5	ϵ5	PROPN
ejpam-5827	608	90	}	}	PUNCT
ejpam-5827	608	91	τiκ	τiκ	PROPN
ejpam-5827	608	92	σ(h	σ(h	PROPN
ejpam-5827	608	93	)	)	PUNCT
ejpam-5827	608	94	2	2	NUM
ejpam-5827	608	95	3	3	NUM
ejpam-5827	608	96	2	2	NUM
ejpam-5827	608	97	3	3	NUM
ejpam-5827	608	98	1	1	NUM
ejpam-5827	608	99	1	1	NUM
ejpam-5827	608	100	2	2	NUM
ejpam-5827	608	101	1	1	NUM
ejpam-5827	608	102	3	3	NUM
ejpam-5827	608	103	1	1	NUM
ejpam-5827	608	104	3	3	NUM
ejpam-5827	608	105	1	1	NUM
ejpam-5827	608	106	2	2	NUM
ejpam-5827	608	107	0	0	NUM
ejpam-5827	608	108	r.	r.	PROPN
ejpam-5827	608	109	a.	a.	PROPN
ejpam-5827	608	110	hosny	hosny	PROPN
ejpam-5827	608	111	,	,	PUNCT
ejpam-5827	608	112	m.	m.	PROPN
ejpam-5827	608	113	k.	k.	PROPN
ejpam-5827	609	1	el	el	PROPN
ejpam-5827	609	2	-	-	PROPN
ejpam-5827	609	3	bably	bably	ADV
ejpam-5827	609	4	,	,	PUNCT
ejpam-5827	609	5	m.	m.	NOUN
ejpam-5827	609	6	a.	a.	PROPN
ejpam-5827	609	7	el	el	PROPN
ejpam-5827	609	8	-	-	PROPN
ejpam-5827	609	9	gayar	gayar	PROPN
ejpam-5827	609	10	/	/	SYM
ejpam-5827	609	11	eur	eur	PROPN
ejpam-5827	609	12	.	.	PUNCT
ejpam-5827	610	1	j.	j.	PROPN
ejpam-5827	610	2	pure	pure	PROPN
ejpam-5827	610	3	appl	appl	PROPN
ejpam-5827	610	4	.	.	PROPN
ejpam-5827	610	5	math	math	PROPN
ejpam-5827	610	6	,	,	PUNCT
ejpam-5827	610	7	18	18	NUM
ejpam-5827	610	8	(	(	PUNCT
ejpam-5827	610	9	1	1	NUM
ejpam-5827	610	10	)	)	PUNCT
ejpam-5827	610	11	(	(	PUNCT
ejpam-5827	610	12	2025	2025	NUM
ejpam-5827	610	13	)	)	PUNCT
ejpam-5827	610	14	,	,	PUNCT
ejpam-5827	610	15	5827	5827	NUM
ejpam-5827	610	16	24	24	NUM
ejpam-5827	610	17	of	of	ADP
ejpam-5827	610	18	29	29	NUM
ejpam-5827	610	19	involved	involve	VERB
ejpam-5827	610	20	in	in	ADP
ejpam-5827	610	21	decision	decision	NOUN
ejpam-5827	610	22	-	-	PUNCT
ejpam-5827	610	23	making	make	VERB
ejpam-5827	610	24	processes	process	NOUN
ejpam-5827	610	25	.	.	PUNCT
ejpam-5827	611	1	additionally	additionally	ADV
ejpam-5827	611	2	,	,	PUNCT
ejpam-5827	611	3	we	we	PRON
ejpam-5827	611	4	illustrated	illustrate	VERB
ejpam-5827	611	5	that	that	SCONJ
ejpam-5827	611	6	the	the	DET
ejpam-5827	611	7	constructed	construct	VERB
ejpam-5827	611	8	approximations	approximation	NOUN
ejpam-5827	611	9	of	of	ADP
ejpam-5827	611	10	two	two	NUM
ejpam-5827	611	11	primals	primal	NOUN
ejpam-5827	611	12	are	be	AUX
ejpam-5827	611	13	more	more	ADV
ejpam-5827	611	14	accurate	accurate	ADJ
ejpam-5827	611	15	than	than	ADP
ejpam-5827	611	16	those	those	PRON
ejpam-5827	611	17	generated	generate	VERB
ejpam-5827	611	18	by	by	ADP
ejpam-5827	611	19	a	a	DET
ejpam-5827	611	20	single	single	ADJ
ejpam-5827	611	21	primal	primal	NOUN
ejpam-5827	611	22	,	,	PUNCT
ejpam-5827	611	23	without	without	ADP
ejpam-5827	611	24	affecting	affect	VERB
ejpam-5827	611	25	the	the	DET
ejpam-5827	611	26	basic	basic	ADJ
ejpam-5827	611	27	properties	property	NOUN
ejpam-5827	611	28	of	of	ADP
ejpam-5827	611	29	these	these	DET
ejpam-5827	611	30	approximations	approximation	NOUN
ejpam-5827	611	31	.	.	PUNCT
ejpam-5827	612	1	moreover	moreover	ADV
ejpam-5827	612	2	,	,	PUNCT
ejpam-5827	612	3	our	our	PRON
ejpam-5827	612	4	practical	practical	ADJ
ejpam-5827	612	5	example	example	NOUN
ejpam-5827	612	6	demonstrates	demonstrate	VERB
ejpam-5827	612	7	the	the	DET
ejpam-5827	612	8	efficacy	efficacy	NOUN
ejpam-5827	612	9	of	of	ADP
ejpam-5827	612	10	the	the	DET
ejpam-5827	612	11	proposed	propose	VERB
ejpam-5827	612	12	methods	method	NOUN
ejpam-5827	612	13	in	in	ADP
ejpam-5827	612	14	real	real	ADJ
ejpam-5827	612	15	-	-	PUNCT
ejpam-5827	612	16	world	world	NOUN
ejpam-5827	612	17	applications	application	NOUN
ejpam-5827	612	18	,	,	PUNCT
ejpam-5827	612	19	underlining	underline	VERB
ejpam-5827	612	20	the	the	DET
ejpam-5827	612	21	ability	ability	NOUN
ejpam-5827	612	22	of	of	ADP
ejpam-5827	612	23	primals	primal	NOUN
ejpam-5827	612	24	to	to	PART
ejpam-5827	612	25	streamline	streamline	VERB
ejpam-5827	612	26	the	the	DET
ejpam-5827	612	27	evaluation	evaluation	NOUN
ejpam-5827	612	28	of	of	ADP
ejpam-5827	612	29	candidates	candidate	NOUN
ejpam-5827	612	30	against	against	ADP
ejpam-5827	612	31	multiple	multiple	ADJ
ejpam-5827	612	32	criteria	criterion	NOUN
ejpam-5827	612	33	.	.	PUNCT
ejpam-5827	613	1	this	this	DET
ejpam-5827	613	2	refined	refined	ADJ
ejpam-5827	613	3	approach	approach	NOUN
ejpam-5827	613	4	reduces	reduce	VERB
ejpam-5827	613	5	uncertainty	uncertainty	NOUN
ejpam-5827	613	6	by	by	ADP
ejpam-5827	613	7	focusing	focus	VERB
ejpam-5827	613	8	on	on	ADP
ejpam-5827	613	9	the	the	DET
ejpam-5827	613	10	most	most	ADV
ejpam-5827	613	11	pertinent	pertinent	ADJ
ejpam-5827	613	12	attributes	attribute	NOUN
ejpam-5827	613	13	,	,	PUNCT
ejpam-5827	613	14	thereby	thereby	ADV
ejpam-5827	613	15	simplifying	simplify	VERB
ejpam-5827	613	16	the	the	DET
ejpam-5827	613	17	selection	selection	NOUN
ejpam-5827	613	18	process	process	NOUN
ejpam-5827	613	19	in	in	ADP
ejpam-5827	613	20	competitive	competitive	ADJ
ejpam-5827	613	21	scenarios	scenario	NOUN
ejpam-5827	613	22	.	.	PUNCT
ejpam-5827	614	1	the	the	DET
ejpam-5827	614	2	implications	implication	NOUN
ejpam-5827	614	3	of	of	ADP
ejpam-5827	614	4	this	this	DET
ejpam-5827	614	5	research	research	NOUN
ejpam-5827	614	6	extend	extend	VERB
ejpam-5827	614	7	beyond	beyond	ADP
ejpam-5827	614	8	rough	rough	ADJ
ejpam-5827	614	9	set	set	NOUN
ejpam-5827	614	10	theory	theory	NOUN
ejpam-5827	614	11	;	;	PUNCT
ejpam-5827	614	12	they	they	PRON
ejpam-5827	614	13	provide	provide	VERB
ejpam-5827	614	14	new	new	ADJ
ejpam-5827	614	15	aspects	aspect	NOUN
ejpam-5827	614	16	for	for	ADP
ejpam-5827	614	17	query	query	NOUN
ejpam-5827	614	18	into	into	ADP
ejpam-5827	614	19	the	the	DET
ejpam-5827	614	20	interplay	interplay	NOUN
ejpam-5827	614	21	between	between	ADP
ejpam-5827	614	22	topological	topological	ADJ
ejpam-5827	614	23	constructs	construct	NOUN
ejpam-5827	614	24	and	and	CCONJ
ejpam-5827	614	25	the	the	DET
ejpam-5827	614	26	handling	handling	NOUN
ejpam-5827	614	27	of	of	ADP
ejpam-5827	614	28	imprecision	imprecision	NOUN
ejpam-5827	614	29	in	in	ADP
ejpam-5827	614	30	diverse	diverse	ADJ
ejpam-5827	614	31	fields	field	NOUN
ejpam-5827	614	32	such	such	ADJ
ejpam-5827	614	33	as	as	ADP
ejpam-5827	614	34	artificial	artificial	ADJ
ejpam-5827	614	35	intelligence	intelligence	NOUN
ejpam-5827	614	36	,	,	PUNCT
ejpam-5827	614	37	engineering	engineering	NOUN
ejpam-5827	614	38	,	,	PUNCT
ejpam-5827	614	39	and	and	CCONJ
ejpam-5827	614	40	medical	medical	ADJ
ejpam-5827	614	41	science	science	NOUN
ejpam-5827	614	42	.	.	PUNCT
ejpam-5827	615	1	future	future	ADJ
ejpam-5827	615	2	research	research	NOUN
ejpam-5827	615	3	may	may	AUX
ejpam-5827	615	4	build	build	VERB
ejpam-5827	615	5	upon	upon	SCONJ
ejpam-5827	615	6	these	these	DET
ejpam-5827	615	7	foundations	foundation	NOUN
ejpam-5827	615	8	by	by	ADP
ejpam-5827	615	9	exploring	explore	VERB
ejpam-5827	615	10	additional	additional	ADJ
ejpam-5827	615	11	applications	application	NOUN
ejpam-5827	615	12	of	of	ADP
ejpam-5827	615	13	primal	primal	ADJ
ejpam-5827	615	14	and	and	CCONJ
ejpam-5827	615	15	bi	bi	ADJ
ejpam-5827	615	16	-	-	ADJ
ejpam-5827	615	17	primal	primal	ADJ
ejpam-5827	615	18	spaces	space	NOUN
ejpam-5827	615	19	,	,	PUNCT
ejpam-5827	615	20	further	far	ADV
ejpam-5827	615	21	enriching	enrich	VERB
ejpam-5827	615	22	the	the	DET
ejpam-5827	615	23	theoretical	theoretical	ADJ
ejpam-5827	615	24	landscape	landscape	NOUN
ejpam-5827	615	25	of	of	ADP
ejpam-5827	615	26	rough	rough	ADJ
ejpam-5827	615	27	set	set	NOUN
ejpam-5827	615	28	modeling	modeling	NOUN
ejpam-5827	615	29	.	.	PUNCT
ejpam-5827	616	1	in	in	ADP
ejpam-5827	616	2	summary	summary	NOUN
ejpam-5827	616	3	,	,	PUNCT
ejpam-5827	616	4	the	the	DET
ejpam-5827	616	5	contributions	contribution	NOUN
ejpam-5827	616	6	of	of	ADP
ejpam-5827	616	7	this	this	DET
ejpam-5827	616	8	paper	paper	NOUN
ejpam-5827	616	9	underscore	underscore	VERB
ejpam-5827	616	10	the	the	DET
ejpam-5827	616	11	importance	importance	NOUN
ejpam-5827	616	12	of	of	ADP
ejpam-5827	616	13	flexible	flexible	ADJ
ejpam-5827	616	14	mathematical	mathematical	ADJ
ejpam-5827	616	15	frameworks	framework	NOUN
ejpam-5827	616	16	in	in	ADP
ejpam-5827	616	17	addressing	address	VERB
ejpam-5827	616	18	the	the	DET
ejpam-5827	616	19	complexities	complexity	NOUN
ejpam-5827	616	20	of	of	ADP
ejpam-5827	616	21	real	real	ADJ
ejpam-5827	616	22	-	-	PUNCT
ejpam-5827	616	23	life	life	NOUN
ejpam-5827	616	24	problems	problem	NOUN
ejpam-5827	616	25	.	.	PUNCT
ejpam-5827	617	1	by	by	ADP
ejpam-5827	617	2	relaxing	relax	VERB
ejpam-5827	617	3	traditional	traditional	ADJ
ejpam-5827	617	4	constraints	constraint	NOUN
ejpam-5827	617	5	and	and	CCONJ
ejpam-5827	617	6	introducing	introduce	VERB
ejpam-5827	617	7	innovative	innovative	ADJ
ejpam-5827	617	8	concepts	concept	NOUN
ejpam-5827	617	9	,	,	PUNCT
ejpam-5827	617	10	we	we	PRON
ejpam-5827	617	11	pave	pave	VERB
ejpam-5827	617	12	the	the	DET
ejpam-5827	617	13	way	way	NOUN
ejpam-5827	617	14	for	for	ADP
ejpam-5827	617	15	more	more	ADV
ejpam-5827	617	16	adaptive	adaptive	ADJ
ejpam-5827	617	17	and	and	CCONJ
ejpam-5827	617	18	effective	effective	ADJ
ejpam-5827	617	19	solutions	solution	NOUN
ejpam-5827	617	20	in	in	ADP
ejpam-5827	617	21	the	the	DET
ejpam-5827	617	22	realm	realm	NOUN
ejpam-5827	617	23	of	of	ADP
ejpam-5827	617	24	decision	decision	NOUN
ejpam-5827	617	25	-	-	PUNCT
ejpam-5827	617	26	making	making	NOUN
ejpam-5827	617	27	.	.	PUNCT
ejpam-5827	618	1	promising	promise	VERB
ejpam-5827	618	2	directions	direction	NOUN
ejpam-5827	618	3	for	for	ADP
ejpam-5827	618	4	future	future	ADJ
ejpam-5827	618	5	research	research	NOUN
ejpam-5827	618	6	include	include	VERB
ejpam-5827	618	7	the	the	DET
ejpam-5827	618	8	following	follow	VERB
ejpam-5827	618	9	:	:	PUNCT
ejpam-5827	619	1	1	1	X
ejpam-5827	619	2	.	.	X
ejpam-5827	619	3	investigating	investigate	VERB
ejpam-5827	619	4	practical	practical	ADJ
ejpam-5827	619	5	applications	application	NOUN
ejpam-5827	619	6	:	:	PUNCT
ejpam-5827	619	7	applying	apply	VERB
ejpam-5827	619	8	these	these	DET
ejpam-5827	619	9	newly	newly	ADV
ejpam-5827	619	10	developed	develop	VERB
ejpam-5827	619	11	approximations	approximation	NOUN
ejpam-5827	619	12	to	to	ADP
ejpam-5827	619	13	various	various	ADJ
ejpam-5827	619	14	real	real	ADJ
ejpam-5827	619	15	-	-	PUNCT
ejpam-5827	619	16	world	world	NOUN
ejpam-5827	619	17	scenarios	scenario	NOUN
ejpam-5827	619	18	,	,	PUNCT
ejpam-5827	619	19	as	as	SCONJ
ejpam-5827	619	20	demonstrated	demonstrate	VERB
ejpam-5827	619	21	in	in	ADP
ejpam-5827	619	22	[	[	X
ejpam-5827	619	23	23	23	NUM
ejpam-5827	619	24	,	,	PUNCT
ejpam-5827	619	25	30	30	NUM
ejpam-5827	619	26	]	]	PUNCT
ejpam-5827	619	27	.	.	PUNCT
ejpam-5827	620	1	2	2	X
ejpam-5827	620	2	.	.	X
ejpam-5827	620	3	incorporating	incorporate	VERB
ejpam-5827	620	4	novel	novel	ADJ
ejpam-5827	620	5	neighborhoods	neighborhood	NOUN
ejpam-5827	620	6	:	:	PUNCT
ejpam-5827	620	7	advancing	advance	VERB
ejpam-5827	620	8	current	current	ADJ
ejpam-5827	620	9	techniques	technique	NOUN
ejpam-5827	620	10	by	by	ADP
ejpam-5827	620	11	utilizing	utilize	VERB
ejpam-5827	620	12	new	new	ADJ
ejpam-5827	620	13	neighborhood	neighborhood	NOUN
ejpam-5827	620	14	structures	structure	NOUN
ejpam-5827	620	15	(	(	PUNCT
ejpam-5827	620	16	maximal	maximal	ADJ
ejpam-5827	620	17	neighborhoods	neighborhood	NOUN
ejpam-5827	620	18	[	[	X
ejpam-5827	620	19	20	20	NUM
ejpam-5827	620	20	]	]	PUNCT
ejpam-5827	620	21	,	,	PUNCT
ejpam-5827	620	22	basic	basic	ADJ
ejpam-5827	620	23	-	-	PUNCT
ejpam-5827	620	24	neighborhoods	neighborhood	NOUN
ejpam-5827	620	25	[	[	X
ejpam-5827	620	26	7	7	NUM
ejpam-5827	620	27	,	,	PUNCT
ejpam-5827	620	28	31	31	NUM
ejpam-5827	620	29	,	,	PUNCT
ejpam-5827	620	30	71	71	NUM
ejpam-5827	620	31	,	,	PUNCT
ejpam-5827	620	32	72	72	NUM
ejpam-5827	620	33	]	]	PUNCT
ejpam-5827	620	34	,	,	PUNCT
ejpam-5827	620	35	initial	initial	ADJ
ejpam-5827	620	36	-	-	PUNCT
ejpam-5827	620	37	neighborhoods	neighborhood	NOUN
ejpam-5827	620	38	[	[	X
ejpam-5827	620	39	62	62	NUM
ejpam-5827	620	40	]	]	PUNCT
ejpam-5827	620	41	,	,	PUNCT
ejpam-5827	620	42	and	and	CCONJ
ejpam-5827	620	43	adhesion	adhesion	NOUN
ejpam-5827	620	44	neighborhoods	neighborhood	NOUN
ejpam-5827	620	45	[	[	X
ejpam-5827	620	46	17	17	NUM
ejpam-5827	620	47	,	,	PUNCT
ejpam-5827	620	48	25	25	NUM
ejpam-5827	620	49	]	]	PUNCT
ejpam-5827	620	50	)	)	PUNCT
ejpam-5827	620	51	.	.	PUNCT
ejpam-5827	621	1	3	3	X
ejpam-5827	621	2	.	.	X
ejpam-5827	621	3	expanding	expand	VERB
ejpam-5827	621	4	with	with	ADP
ejpam-5827	621	5	near	near	ADJ
ejpam-5827	621	6	open	open	ADJ
ejpam-5827	621	7	sets	set	NOUN
ejpam-5827	621	8	:	:	PUNCT
ejpam-5827	621	9	building	build	VERB
ejpam-5827	621	10	on	on	ADP
ejpam-5827	621	11	the	the	DET
ejpam-5827	621	12	current	current	ADJ
ejpam-5827	621	13	results	result	NOUN
ejpam-5827	621	14	by	by	ADP
ejpam-5827	621	15	introducing	introduce	VERB
ejpam-5827	621	16	near	near	ADP
ejpam-5827	621	17	open	open	ADJ
ejpam-5827	621	18	sets	set	NOUN
ejpam-5827	621	19	,	,	PUNCT
ejpam-5827	621	20	as	as	SCONJ
ejpam-5827	621	21	discussed	discuss	VERB
ejpam-5827	621	22	in	in	ADP
ejpam-5827	621	23	[	[	X
ejpam-5827	621	24	29	29	NUM
ejpam-5827	621	25	,	,	PUNCT
ejpam-5827	621	26	36	36	NUM
ejpam-5827	621	27	,	,	PUNCT
ejpam-5827	621	28	39	39	NUM
ejpam-5827	621	29	,	,	PUNCT
ejpam-5827	621	30	40	40	NUM
ejpam-5827	621	31	]	]	PUNCT
ejpam-5827	621	32	.	.	PUNCT
ejpam-5827	622	1	4	4	X
ejpam-5827	622	2	.	.	X
ejpam-5827	622	3	extending	extend	VERB
ejpam-5827	622	4	to	to	ADP
ejpam-5827	622	5	broader	broad	ADJ
ejpam-5827	622	6	fields	field	NOUN
ejpam-5827	622	7	:	:	PUNCT
ejpam-5827	622	8	widening	widen	VERB
ejpam-5827	622	9	the	the	DET
ejpam-5827	622	10	scope	scope	NOUN
ejpam-5827	622	11	of	of	ADP
ejpam-5827	622	12	this	this	DET
ejpam-5827	622	13	study	study	NOUN
ejpam-5827	622	14	to	to	PART
ejpam-5827	622	15	encompass	encompass	VERB
ejpam-5827	622	16	rough	rough	ADJ
ejpam-5827	622	17	fuzzy	fuzzy	ADJ
ejpam-5827	622	18	methods	method	NOUN
ejpam-5827	622	19	and	and	CCONJ
ejpam-5827	622	20	other	other	ADJ
ejpam-5827	622	21	related	related	ADJ
ejpam-5827	622	22	fields	field	NOUN
ejpam-5827	622	23	,	,	PUNCT
ejpam-5827	622	24	in	in	ADP
ejpam-5827	622	25	alignment	alignment	NOUN
ejpam-5827	622	26	with	with	ADP
ejpam-5827	622	27	[	[	X
ejpam-5827	622	28	8	8	NUM
ejpam-5827	622	29	,	,	PUNCT
ejpam-5827	622	30	33	33	NUM
ejpam-5827	622	31	,	,	PUNCT
ejpam-5827	622	32	34	34	NUM
ejpam-5827	622	33	,	,	PUNCT
ejpam-5827	622	34	54	54	NUM
ejpam-5827	622	35	,	,	PUNCT
ejpam-5827	622	36	68	68	NUM
ejpam-5827	622	37	,	,	PUNCT
ejpam-5827	622	38	69	69	NUM
ejpam-5827	622	39	]	]	PUNCT
ejpam-5827	622	40	,	,	PUNCT
ejpam-5827	622	41	soft	soft	ADJ
ejpam-5827	622	42	topological	topological	ADJ
ejpam-5827	622	43	spaces	space	NOUN
ejpam-5827	622	44	[	[	X
ejpam-5827	622	45	10	10	NUM
ejpam-5827	622	46	,	,	PUNCT
ejpam-5827	622	47	14	14	NUM
ejpam-5827	622	48	,	,	PUNCT
ejpam-5827	622	49	15	15	NUM
ejpam-5827	622	50	,	,	PUNCT
ejpam-5827	622	51	61	61	NUM
ejpam-5827	622	52	]	]	PUNCT
ejpam-5827	622	53	and	and	CCONJ
ejpam-5827	622	54	decision	decision	NOUN
ejpam-5827	622	55	-	-	PUNCT
ejpam-5827	622	56	making	make	VERB
ejpam-5827	622	57	problems	problem	NOUN
ejpam-5827	622	58	in	in	ADP
ejpam-5827	622	59	[	[	X
ejpam-5827	622	60	16	16	NUM
ejpam-5827	622	61	,	,	PUNCT
ejpam-5827	622	62	57	57	NUM
ejpam-5827	622	63	]	]	PUNCT
ejpam-5827	622	64	.	.	PUNCT
ejpam-5827	623	1	acknowledgements	acknowledgement	NOUN
ejpam-5827	623	2	the	the	DET
ejpam-5827	623	3	authors	author	NOUN
ejpam-5827	623	4	would	would	AUX
ejpam-5827	623	5	like	like	VERB
ejpam-5827	623	6	to	to	PART
ejpam-5827	623	7	extend	extend	VERB
ejpam-5827	623	8	their	their	PRON
ejpam-5827	623	9	deepest	deep	ADJ
ejpam-5827	623	10	gratitude	gratitude	NOUN
ejpam-5827	623	11	to	to	ADP
ejpam-5827	623	12	the	the	DET
ejpam-5827	623	13	editor	editor	NOUN
ejpam-5827	623	14	-	-	PUNCT
ejpam-5827	623	15	in	in	ADP
ejpam-5827	623	16	-	-	PUNCT
ejpam-5827	623	17	chief	chief	NOUN
ejpam-5827	623	18	,	,	PUNCT
ejpam-5827	623	19	and	and	CCONJ
ejpam-5827	623	20	the	the	DET
ejpam-5827	623	21	reviewers	reviewer	NOUN
ejpam-5827	623	22	for	for	ADP
ejpam-5827	623	23	their	their	PRON
ejpam-5827	623	24	insightful	insightful	ADJ
ejpam-5827	623	25	comments	comment	NOUN
ejpam-5827	623	26	and	and	CCONJ
ejpam-5827	623	27	suggestions	suggestion	NOUN
ejpam-5827	623	28	,	,	PUNCT
ejpam-5827	623	29	which	which	PRON
ejpam-5827	623	30	were	be	AUX
ejpam-5827	623	31	instrumental	instrumental	ADJ
ejpam-5827	623	32	in	in	ADP
ejpam-5827	623	33	refining	refining	NOUN
ejpam-5827	623	34	and	and	CCONJ
ejpam-5827	623	35	improving	improve	VERB
ejpam-5827	623	36	the	the	DET
ejpam-5827	623	37	quality	quality	NOUN
ejpam-5827	623	38	of	of	ADP
ejpam-5827	623	39	this	this	DET
ejpam-5827	623	40	work	work	NOUN
ejpam-5827	623	41	.	.	PUNCT
ejpam-5827	624	1	special	special	ADJ
ejpam-5827	624	2	thanks	thank	NOUN
ejpam-5827	624	3	are	be	AUX
ejpam-5827	624	4	also	also	ADV
ejpam-5827	624	5	due	due	ADJ
ejpam-5827	624	6	to	to	ADP
ejpam-5827	624	7	our	our	PRON
ejpam-5827	624	8	esteemed	esteemed	ADJ
ejpam-5827	624	9	colleagues	colleague	NOUN
ejpam-5827	624	10	at	at	ADP
ejpam-5827	624	11	the	the	DET
ejpam-5827	624	12	egyptian	egyptian	ADJ
ejpam-5827	624	13	school	school	NOUN
ejpam-5827	624	14	of	of	ADP
ejpam-5827	624	15	topology	topology	NOUN
ejpam-5827	624	16	(	(	PUNCT
ejpam-5827	624	17	in	in	ADP
ejpam-5827	624	18	tanta	tanta	PROPN
ejpam-5827	624	19	,	,	PUNCT
ejpam-5827	624	20	egypt	egypt	PROPN
ejpam-5827	624	21	)	)	PUNCT
ejpam-5827	624	22	,	,	PUNCT
ejpam-5827	624	23	established	establish	VERB
ejpam-5827	624	24	by	by	ADP
ejpam-5827	624	25	prof	prof	PROPN
ejpam-5827	624	26	.	.	PUNCT
ejpam-5827	625	1	a.	a.	PROPN
ejpam-5827	625	2	s.	s.	PROPN
ejpam-5827	625	3	mashhour	mashhour	PROPN
ejpam-5827	625	4	and	and	CCONJ
ejpam-5827	625	5	prof	prof	PROPN
ejpam-5827	625	6	.	.	PUNCT
ejpam-5827	626	1	m.	m.	PROPN
ejpam-5827	626	2	e.	e.	PROPN
ejpam-5827	626	3	abd	abd	PROPN
ejpam-5827	627	1	el	el	PROPN
ejpam-5827	627	2	-	-	PROPN
ejpam-5827	627	3	monsef	monsef	ADJ
ejpam-5827	627	4	,	,	PUNCT
ejpam-5827	627	5	and	and	CCONJ
ejpam-5827	627	6	led	lead	VERB
ejpam-5827	627	7	by	by	ADP
ejpam-5827	627	8	prof	prof	PROPN
ejpam-5827	627	9	.	.	PUNCT
ejpam-5827	627	10	a.	a.	PROPN
ejpam-5827	627	11	m.	m.	PROPN
ejpam-5827	627	12	kozae	kozae	PROPN
ejpam-5827	627	13	.	.	PUNCT
ejpam-5827	628	1	this	this	DET
ejpam-5827	628	2	institution	institution	NOUN
ejpam-5827	628	3	has	have	AUX
ejpam-5827	628	4	fostered	foster	VERB
ejpam-5827	628	5	numerous	numerous	ADJ
ejpam-5827	628	6	distinguished	distinguished	ADJ
ejpam-5827	628	7	researchers	researcher	NOUN
ejpam-5827	628	8	both	both	CCONJ
ejpam-5827	628	9	within	within	ADP
ejpam-5827	628	10	egypt	egypt	PROPN
ejpam-5827	628	11	and	and	CCONJ
ejpam-5827	628	12	internationally	internationally	ADV
ejpam-5827	628	13	,	,	PUNCT
ejpam-5827	628	14	including	include	VERB
ejpam-5827	628	15	scholars	scholar	NOUN
ejpam-5827	628	16	from	from	ADP
ejpam-5827	628	17	yemen	yemen	PROPN
ejpam-5827	628	18	,	,	PUNCT
ejpam-5827	628	19	palestine	palestine	PROPN
ejpam-5827	628	20	,	,	PUNCT
ejpam-5827	628	21	jordan	jordan	PROPN
ejpam-5827	628	22	,	,	PUNCT
ejpam-5827	628	23	and	and	CCONJ
ejpam-5827	628	24	saudi	saudi	PROPN
ejpam-5827	628	25	arabia	arabia	PROPN
ejpam-5827	628	26	.	.	PUNCT
ejpam-5827	629	1	the	the	DET
ejpam-5827	629	2	authors	author	NOUN
ejpam-5827	629	3	are	be	AUX
ejpam-5827	629	4	particularly	particularly	ADV
ejpam-5827	629	5	thankful	thankful	ADJ
ejpam-5827	629	6	for	for	ADP
ejpam-5827	629	7	the	the	DET
ejpam-5827	629	8	school	school	NOUN
ejpam-5827	629	9	’s	’s	PART
ejpam-5827	629	10	unwavering	unwavering	ADJ
ejpam-5827	629	11	support	support	NOUN
ejpam-5827	629	12	,	,	PUNCT
ejpam-5827	629	13	encouragement	encouragement	NOUN
ejpam-5827	629	14	,	,	PUNCT
ejpam-5827	629	15	and	and	CCONJ
ejpam-5827	629	16	the	the	DET
ejpam-5827	629	17	enriching	enriching	ADJ
ejpam-5827	629	18	discussions	discussion	NOUN
ejpam-5827	629	19	that	that	PRON
ejpam-5827	629	20	contributed	contribute	VERB
ejpam-5827	629	21	to	to	ADP
ejpam-5827	629	22	this	this	DET
ejpam-5827	629	23	research	research	NOUN
ejpam-5827	629	24	.	.	PUNCT
ejpam-5827	630	1	finally	finally	ADV
ejpam-5827	630	2	,	,	PUNCT
ejpam-5827	630	3	this	this	DET
ejpam-5827	630	4	work	work	NOUN
ejpam-5827	630	5	is	be	AUX
ejpam-5827	630	6	dedicated	dedicate	VERB
ejpam-5827	630	7	to	to	ADP
ejpam-5827	630	8	the	the	DET
ejpam-5827	630	9	memory	memory	NOUN
ejpam-5827	630	10	of	of	ADP
ejpam-5827	630	11	prof	prof	PROPN
ejpam-5827	630	12	.	.	PUNCT
ejpam-5827	631	1	a.	a.	PROPN
ejpam-5827	631	2	s.	s.	PROPN
ejpam-5827	631	3	mashhour	mashhour	PROPN
ejpam-5827	631	4	,	,	PUNCT
ejpam-5827	631	5	prof	prof	PROPN
ejpam-5827	631	6	.	.	PUNCT
ejpam-5827	632	1	m.	m.	PROPN
ejpam-5827	632	2	e.	e.	PROPN
ejpam-5827	632	3	abd	abd	PROPN
ejpam-5827	633	1	el	el	PROPN
ejpam-5827	633	2	-	-	PROPN
ejpam-5827	633	3	monsef	monsef	ADJ
ejpam-5827	633	4	,	,	PUNCT
ejpam-5827	633	5	and	and	CCONJ
ejpam-5827	633	6	prof	prof	PROPN
ejpam-5827	633	7	.	.	PUNCT
ejpam-5827	633	8	a.	a.	PROPN
ejpam-5827	633	9	kandil	kandil	PROPN
ejpam-5827	633	10	”	"	PUNCT
ejpam-5827	633	11	may	may	AUX
ejpam-5827	633	12	god	god	PROPN
ejpam-5827	633	13	’s	’s	PART
ejpam-5827	633	14	mercy	mercy	NOUN
ejpam-5827	633	15	be	be	AUX
ejpam-5827	633	16	upon	upon	SCONJ
ejpam-5827	633	17	them	they	PRON
ejpam-5827	633	18	”	"	PUNCT
ejpam-5827	633	19	.	.	PUNCT
ejpam-5827	634	1	conflict	conflict	NOUN
ejpam-5827	634	2	of	of	ADP
ejpam-5827	634	3	interest	interest	NOUN
ejpam-5827	634	4	:	:	PUNCT
ejpam-5827	634	5	the	the	DET
ejpam-5827	634	6	authors	author	NOUN
ejpam-5827	634	7	declare	declare	VERB
ejpam-5827	634	8	that	that	SCONJ
ejpam-5827	634	9	there	there	PRON
ejpam-5827	634	10	is	be	VERB
ejpam-5827	634	11	no	no	DET
ejpam-5827	634	12	conflict	conflict	NOUN
ejpam-5827	634	13	of	of	ADP
ejpam-5827	634	14	interest	interest	NOUN
ejpam-5827	634	15	.	.	PUNCT
ejpam-5827	635	1	r.	r.	PROPN
ejpam-5827	635	2	a.	a.	PROPN
ejpam-5827	635	3	hosny	hosny	PROPN
ejpam-5827	635	4	,	,	PUNCT
ejpam-5827	635	5	m.	m.	PROPN
ejpam-5827	635	6	k.	k.	PROPN
ejpam-5827	636	1	el	el	PROPN
ejpam-5827	636	2	-	-	PROPN
ejpam-5827	636	3	bably	bably	ADV
ejpam-5827	636	4	,	,	PUNCT
ejpam-5827	636	5	m.	m.	NOUN
ejpam-5827	636	6	a.	a.	PROPN
ejpam-5827	636	7	el	el	PROPN
ejpam-5827	636	8	-	-	PROPN
ejpam-5827	636	9	gayar	gayar	PROPN
ejpam-5827	636	10	/	/	SYM
ejpam-5827	636	11	eur	eur	PROPN
ejpam-5827	636	12	.	.	PUNCT
ejpam-5827	637	1	j.	j.	PROPN
ejpam-5827	637	2	pure	pure	PROPN
ejpam-5827	637	3	appl	appl	PROPN
ejpam-5827	637	4	.	.	PROPN
ejpam-5827	637	5	math	math	PROPN
ejpam-5827	637	6	,	,	PUNCT
ejpam-5827	637	7	18	18	NUM
ejpam-5827	637	8	(	(	PUNCT
ejpam-5827	637	9	1	1	NUM
ejpam-5827	637	10	)	)	PUNCT
ejpam-5827	637	11	(	(	PUNCT
ejpam-5827	637	12	2025	2025	NUM
ejpam-5827	637	13	)	)	PUNCT
ejpam-5827	637	14	,	,	PUNCT
ejpam-5827	637	15	5827	5827	NUM
ejpam-5827	637	16	25	25	NUM
ejpam-5827	637	17	of	of	ADP
ejpam-5827	637	18	29	29	NUM
ejpam-5827	637	19	references	reference	NOUN
ejpam-5827	637	20	[	[	X
ejpam-5827	637	21	1	1	NUM
ejpam-5827	637	22	]	]	PUNCT
ejpam-5827	637	23	e.	e.	PROPN
ejpam-5827	637	24	a.	a.	PROPN
ejpam-5827	637	25	abo	abo	PROPN
ejpam-5827	637	26	-	-	PUNCT
ejpam-5827	637	27	tabl	tabl	NOUN
ejpam-5827	637	28	.	.	PUNCT
ejpam-5827	638	1	topological	topological	ADJ
ejpam-5827	638	2	approaches	approach	NOUN
ejpam-5827	638	3	to	to	ADP
ejpam-5827	638	4	generalized	generalized	ADJ
ejpam-5827	638	5	definitions	definition	NOUN
ejpam-5827	638	6	of	of	ADP
ejpam-5827	638	7	rough	rough	ADJ
ejpam-5827	638	8	multiset	multiset	ADJ
ejpam-5827	638	9	approximations	approximation	NOUN
ejpam-5827	638	10	.	.	PUNCT
ejpam-5827	639	1	[	[	X
ejpam-5827	639	2	2	2	X
ejpam-5827	639	3	]	]	PUNCT
ejpam-5827	639	4	e.	e.	PROPN
ejpam-5827	639	5	a.	a.	PROPN
ejpam-5827	639	6	abo	abo	PROPN
ejpam-5827	639	7	-	-	PUNCT
ejpam-5827	639	8	tabl	tabl	NOUN
ejpam-5827	639	9	.	.	PUNCT
ejpam-5827	640	1	a	a	DET
ejpam-5827	640	2	comparison	comparison	NOUN
ejpam-5827	640	3	of	of	ADP
ejpam-5827	640	4	two	two	NUM
ejpam-5827	640	5	kinds	kind	NOUN
ejpam-5827	640	6	of	of	ADP
ejpam-5827	640	7	definitions	definition	NOUN
ejpam-5827	640	8	of	of	ADP
ejpam-5827	640	9	rough	rough	ADJ
ejpam-5827	640	10	approximations	approximation	NOUN
ejpam-5827	640	11	based	base	VERB
ejpam-5827	640	12	on	on	ADP
ejpam-5827	640	13	a	a	DET
ejpam-5827	640	14	similarity	similarity	NOUN
ejpam-5827	640	15	relation	relation	NOUN
ejpam-5827	640	16	.	.	PUNCT
ejpam-5827	641	1	inform	inform	NOUN
ejpam-5827	641	2	.	.	PUNCT
ejpam-5827	642	1	sci	sci	PROPN
ejpam-5827	642	2	.	.	PROPN
ejpam-5827	642	3	,	,	PUNCT
ejpam-5827	642	4	181(12):2587–2596	181(12):2587–2596	NUM
ejpam-5827	642	5	,	,	PUNCT
ejpam-5827	642	6	2011	2011	NUM
ejpam-5827	642	7	.	.	PUNCT
ejpam-5827	643	1	[	[	X
ejpam-5827	643	2	3	3	X
ejpam-5827	643	3	]	]	X
ejpam-5827	643	4	e.	e.	PROPN
ejpam-5827	643	5	a.	a.	PROPN
ejpam-5827	643	6	abo	abo	PROPN
ejpam-5827	643	7	-	-	PUNCT
ejpam-5827	643	8	tabl	tabl	NOUN
ejpam-5827	643	9	.	.	PUNCT
ejpam-5827	644	1	rough	rough	ADJ
ejpam-5827	644	2	sets	set	NOUN
ejpam-5827	644	3	and	and	CCONJ
ejpam-5827	644	4	topological	topological	ADJ
ejpam-5827	644	5	spaces	space	NOUN
ejpam-5827	644	6	based	base	VERB
ejpam-5827	644	7	on	on	ADP
ejpam-5827	644	8	similarity	similarity	NOUN
ejpam-5827	644	9	.	.	PUNCT
ejpam-5827	645	1	int	int	NOUN
ejpam-5827	645	2	.	.	PUNCT
ejpam-5827	646	1	j.	j.	PROPN
ejpam-5827	646	2	mach	mach	PROPN
ejpam-5827	646	3	.	.	PUNCT
ejpam-5827	647	1	learn	learn	VERB
ejpam-5827	647	2	.	.	PUNCT
ejpam-5827	648	1	cybern	cybern	PROPN
ejpam-5827	648	2	.	.	PROPN
ejpam-5827	648	3	,	,	PUNCT
ejpam-5827	648	4	4:451–458	4:451–458	NOUN
ejpam-5827	648	5	,	,	PUNCT
ejpam-5827	648	6	2013	2013	NUM
ejpam-5827	648	7	.	.	PUNCT
ejpam-5827	649	1	[	[	X
ejpam-5827	649	2	4	4	X
ejpam-5827	649	3	]	]	PUNCT
ejpam-5827	649	4	e.	e.	PROPN
ejpam-5827	649	5	a.	a.	PROPN
ejpam-5827	649	6	abo	abo	PROPN
ejpam-5827	649	7	-	-	PUNCT
ejpam-5827	649	8	tabl	tabl	NOUN
ejpam-5827	649	9	and	and	CCONJ
ejpam-5827	649	10	m.	m.	NOUN
ejpam-5827	649	11	k.	k.	PROPN
ejpam-5827	650	1	el	el	PROPN
ejpam-5827	650	2	-	-	PROPN
ejpam-5827	650	3	bably	bably	ADV
ejpam-5827	650	4	.	.	PUNCT
ejpam-5827	651	1	rough	rough	ADJ
ejpam-5827	651	2	topological	topological	ADJ
ejpam-5827	651	3	structure	structure	NOUN
ejpam-5827	651	4	based	base	VERB
ejpam-5827	651	5	on	on	ADP
ejpam-5827	651	6	reflexivity	reflexivity	NOUN
ejpam-5827	651	7	with	with	ADP
ejpam-5827	651	8	some	some	DET
ejpam-5827	651	9	applications	application	NOUN
ejpam-5827	651	10	.	.	PUNCT
ejpam-5827	652	1	aims	aim	VERB
ejpam-5827	652	2	mathematics	mathematic	NOUN
ejpam-5827	652	3	.	.	PUNCT
ejpam-5827	652	4	,	,	PUNCT
ejpam-5827	652	5	7(6):9911–9999	7(6):9911–9999	PROPN
ejpam-5827	652	6	,	,	PUNCT
ejpam-5827	652	7	2022	2022	NUM
ejpam-5827	652	8	.	.	PUNCT
ejpam-5827	653	1	[	[	X
ejpam-5827	653	2	5	5	NUM
ejpam-5827	653	3	]	]	PUNCT
ejpam-5827	653	4	r.	r.	PROPN
ejpam-5827	653	5	abu	abu	PROPN
ejpam-5827	653	6	-	-	PUNCT
ejpam-5827	653	7	gdairi	gdairi	PROPN
ejpam-5827	653	8	,	,	PUNCT
ejpam-5827	653	9	a.	a.	PROPN
ejpam-5827	653	10	a.	a.	PROPN
ejpam-5827	653	11	el	el	PROPN
ejpam-5827	653	12	-	-	PUNCT
ejpam-5827	653	13	atik	atik	PROPN
ejpam-5827	653	14	,	,	PUNCT
ejpam-5827	653	15	and	and	CCONJ
ejpam-5827	653	16	m.	m.	PROPN
ejpam-5827	653	17	k.	k.	PROPN
ejpam-5827	653	18	el	el	PROPN
ejpam-5827	653	19	-	-	PROPN
ejpam-5827	653	20	bably	bably	ADV
ejpam-5827	653	21	.	.	PUNCT
ejpam-5827	654	1	topological	topological	ADJ
ejpam-5827	654	2	visualization	visualization	NOUN
ejpam-5827	654	3	and	and	CCONJ
ejpam-5827	654	4	graph	graph	VERB
ejpam-5827	654	5	analysis	analysis	NOUN
ejpam-5827	654	6	of	of	ADP
ejpam-5827	654	7	rough	rough	ADJ
ejpam-5827	654	8	sets	set	NOUN
ejpam-5827	654	9	via	via	ADP
ejpam-5827	654	10	neighborhoods	neighborhood	NOUN
ejpam-5827	654	11	:	:	PUNCT
ejpam-5827	654	12	a	a	DET
ejpam-5827	654	13	medical	medical	ADJ
ejpam-5827	654	14	application	application	NOUN
ejpam-5827	654	15	using	use	VERB
ejpam-5827	654	16	human	human	ADJ
ejpam-5827	654	17	heart	heart	NOUN
ejpam-5827	654	18	data	datum	NOUN
ejpam-5827	654	19	.	.	PUNCT
ejpam-5827	655	1	aims	aim	VERB
ejpam-5827	655	2	math	math	NOUN
ejpam-5827	655	3	.	.	PUNCT
ejpam-5827	655	4	,	,	PUNCT
ejpam-5827	655	5	8(11):26945–26967	8(11):26945–26967	NUM
ejpam-5827	655	6	,	,	PUNCT
ejpam-5827	655	7	2023	2023	NUM
ejpam-5827	655	8	.	.	PUNCT
ejpam-5827	656	1	[	[	X
ejpam-5827	656	2	6	6	NUM
ejpam-5827	656	3	]	]	PUNCT
ejpam-5827	656	4	r.	r.	PROPN
ejpam-5827	656	5	abu	abu	PROPN
ejpam-5827	656	6	-	-	PUNCT
ejpam-5827	656	7	gdairi	gdairi	PROPN
ejpam-5827	656	8	and	and	CCONJ
ejpam-5827	656	9	m.	m.	PROPN
ejpam-5827	656	10	k.	k.	PROPN
ejpam-5827	656	11	el	el	PROPN
ejpam-5827	656	12	-	-	PROPN
ejpam-5827	656	13	bably	bably	ADV
ejpam-5827	656	14	.	.	PUNCT
ejpam-5827	657	1	the	the	DET
ejpam-5827	657	2	accurate	accurate	ADJ
ejpam-5827	657	3	diagnosis	diagnosis	NOUN
ejpam-5827	657	4	for	for	ADP
ejpam-5827	657	5	covid19	covid19	NOUN
ejpam-5827	657	6	variants	variant	NOUN
ejpam-5827	657	7	using	use	VERB
ejpam-5827	657	8	nearly	nearly	ADV
ejpam-5827	657	9	initial	initial	ADJ
ejpam-5827	657	10	-	-	PUNCT
ejpam-5827	657	11	rough	rough	ADJ
ejpam-5827	657	12	sets	set	NOUN
ejpam-5827	657	13	.	.	PUNCT
ejpam-5827	658	1	heliyon	heliyon	NOUN
ejpam-5827	658	2	.	.	PUNCT
ejpam-5827	658	3	,	,	PUNCT
ejpam-5827	658	4	10(10	10(10	NUM
ejpam-5827	658	5	)	)	PUNCT
ejpam-5827	658	6	,	,	PUNCT
ejpam-5827	658	7	2024	2024	NUM
ejpam-5827	658	8	.	.	PUNCT
ejpam-5827	659	1	https://doi.org/10.1016/j.heliyon.2024.e31288	https://doi.org/10.1016/j.heliyon.2024.e31288	PUNCT
ejpam-5827	659	2	.	.	PUNCT
ejpam-5827	660	1	[	[	X
ejpam-5827	660	2	7	7	X
ejpam-5827	660	3	]	]	X
ejpam-5827	660	4	r.	r.	PROPN
ejpam-5827	660	5	abu	abu	PROPN
ejpam-5827	660	6	-	-	PUNCT
ejpam-5827	660	7	gdairi	gdairi	PROPN
ejpam-5827	660	8	,	,	PUNCT
ejpam-5827	660	9	m.	m.	NOUN
ejpam-5827	660	10	a.	a.	PROPN
ejpam-5827	660	11	el	el	PROPN
ejpam-5827	660	12	-	-	PUNCT
ejpam-5827	660	13	gayar	gayar	PROPN
ejpam-5827	660	14	,	,	PUNCT
ejpam-5827	660	15	m.	m.	NOUN
ejpam-5827	660	16	k.	k.	PROPN
ejpam-5827	660	17	el	el	PROPN
ejpam-5827	660	18	-	-	PROPN
ejpam-5827	660	19	bably	bably	ADV
ejpam-5827	660	20	,	,	PUNCT
ejpam-5827	660	21	and	and	CCONJ
ejpam-5827	660	22	k.	k.	PROPN
ejpam-5827	660	23	k.	k.	PROPN
ejpam-5827	660	24	fleifel	fleifel	PROPN
ejpam-5827	660	25	.	.	PUNCT
ejpam-5827	661	1	two	two	NUM
ejpam-5827	661	2	different	different	ADJ
ejpam-5827	661	3	views	view	NOUN
ejpam-5827	661	4	for	for	ADP
ejpam-5827	661	5	generalized	generalized	ADJ
ejpam-5827	661	6	rough	rough	ADJ
ejpam-5827	661	7	sets	set	NOUN
ejpam-5827	661	8	with	with	ADP
ejpam-5827	661	9	applications	application	NOUN
ejpam-5827	661	10	.	.	PUNCT
ejpam-5827	662	1	math	math	NOUN
ejpam-5827	662	2	.	.	PUNCT
ejpam-5827	662	3	,	,	PUNCT
ejpam-5827	662	4	9	9	NUM
ejpam-5827	662	5	,	,	PUNCT
ejpam-5827	662	6	2021	2021	NUM
ejpam-5827	662	7	.	.	PUNCT
ejpam-5827	663	1	https://doi.org/10.3390/math9182275	https://doi.org/10.3390/math9182275	PROPN
ejpam-5827	663	2	.	.	PUNCT
ejpam-5827	664	1	[	[	X
ejpam-5827	664	2	8	8	NUM
ejpam-5827	664	3	]	]	X
ejpam-5827	664	4	r.	r.	PROPN
ejpam-5827	664	5	abu	abu	PROPN
ejpam-5827	664	6	-	-	PUNCT
ejpam-5827	664	7	gdairi	gdairi	PROPN
ejpam-5827	664	8	,	,	PUNCT
ejpam-5827	664	9	a.	a.	NOUN
ejpam-5827	664	10	a.	a.	NOUN
ejpam-5827	664	11	nasef	nasef	PROPN
ejpam-5827	664	12	,	,	PUNCT
ejpam-5827	664	13	m.	m.	NOUN
ejpam-5827	664	14	a.	a.	PROPN
ejpam-5827	664	15	el	el	PROPN
ejpam-5827	664	16	-	-	PROPN
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ejpam-5827	664	18	,	,	PUNCT
ejpam-5827	664	19	and	and	CCONJ
ejpam-5827	664	20	m.	m.	PROPN
ejpam-5827	664	21	k.	k.	PROPN
ejpam-5827	664	22	el	el	PROPN
ejpam-5827	664	23	-	-	PROPN
ejpam-5827	664	24	bably	bably	ADV
ejpam-5827	664	25	.	.	PUNCT
ejpam-5827	665	1	on	on	ADP
ejpam-5827	665	2	fuzzy	fuzzy	ADJ
ejpam-5827	665	3	point	point	NOUN
ejpam-5827	665	4	applications	application	NOUN
ejpam-5827	665	5	of	of	ADP
ejpam-5827	665	6	fuzzy	fuzzy	ADJ
ejpam-5827	665	7	topological	topological	ADJ
ejpam-5827	665	8	spaces	space	NOUN
ejpam-5827	665	9	.	.	PUNCT
ejpam-5827	666	1	int	int	NOUN
ejpam-5827	666	2	.	.	PUNCT
ejpam-5827	667	1	j.	j.	PROPN
ejpam-5827	667	2	fuzz	fuzz	PROPN
ejpam-5827	667	3	.	.	PUNCT
ejpam-5827	668	1	log	log	PROPN
ejpam-5827	668	2	.	.	PUNCT
ejpam-5827	669	1	intell	intell	PROPN
ejpam-5827	669	2	,	,	PUNCT
ejpam-5827	669	3	syst	syst	PROPN
ejpam-5827	669	4	.	.	PUNCT
ejpam-5827	669	5	,	,	PUNCT
ejpam-5827	669	6	23(2):162–172	23(2):162–172	PROPN
ejpam-5827	669	7	,	,	PUNCT
ejpam-5827	669	8	2023	2023	NUM
ejpam-5827	669	9	.	.	PUNCT
ejpam-5827	670	1	[	[	X
ejpam-5827	670	2	9	9	NUM
ejpam-5827	670	3	]	]	PUNCT
ejpam-5827	670	4	s.	s.	PROPN
ejpam-5827	670	5	acharjee	acharjee	PROPN
ejpam-5827	670	6	,	,	PUNCT
ejpam-5827	670	7	m.	m.	NOUN
ejpam-5827	670	8	özkoç	özkoç	PROPN
ejpam-5827	670	9	,	,	PUNCT
ejpam-5827	670	10	and	and	CCONJ
ejpam-5827	670	11	f.	f.	PROPN
ejpam-5827	670	12	y.	y.	PROPN
ejpam-5827	670	13	issaka	issaka	PROPN
ejpam-5827	670	14	.	.	PUNCT
ejpam-5827	671	1	primal	primal	ADJ
ejpam-5827	671	2	topological	topological	ADJ
ejpam-5827	671	3	spaces	space	NOUN
ejpam-5827	671	4	.	.	PUNCT
ejpam-5827	672	1	arxiv	arxiv	PROPN
ejpam-5827	672	2	preprint	preprint	PROPN
ejpam-5827	672	3	arxiv:2209.12676	arxiv:2209.12676	PUNCT
ejpam-5827	672	4	,	,	PUNCT
ejpam-5827	672	5	pages	page	NOUN
ejpam-5827	672	6	1–9	1–9	NUM
ejpam-5827	672	7	,	,	PUNCT
ejpam-5827	672	8	2022	2022	NUM
ejpam-5827	672	9	.	.	PUNCT
ejpam-5827	673	1	https://doi.org/10.48550/arxiv.2209.12676	https://doi.org/10.48550/arxiv.2209.12676	PROPN
ejpam-5827	673	2	.	.	PUNCT
ejpam-5827	674	1	[	[	X
ejpam-5827	674	2	10	10	NUM
ejpam-5827	674	3	]	]	PUNCT
ejpam-5827	674	4	j.	j.	PROPN
ejpam-5827	674	5	al	al	PROPN
ejpam-5827	674	6	-	-	PUNCT
ejpam-5827	674	7	mufarrij	mufarrij	PROPN
ejpam-5827	674	8	and	and	CCONJ
ejpam-5827	674	9	s.	s.	PROPN
ejpam-5827	674	10	saleh	saleh	PROPN
ejpam-5827	674	11	.	.	PUNCT
ejpam-5827	675	1	new	new	ADJ
ejpam-5827	675	2	results	result	NOUN
ejpam-5827	675	3	on	on	ADP
ejpam-5827	675	4	soft	soft	ADJ
ejpam-5827	675	5	generalized	generalized	ADJ
ejpam-5827	675	6	topological	topological	ADJ
ejpam-5827	675	7	spaces	space	NOUN
ejpam-5827	675	8	.	.	PUNCT
ejpam-5827	676	1	j.	j.	PROPN
ejpam-5827	676	2	math	math	PROPN
ejpam-5827	676	3	.	.	PUNCT
ejpam-5827	677	1	comput	comput	NOUN
ejpam-5827	677	2	.	.	PUNCT
ejpam-5827	678	1	sci	sci	PROPN
ejpam-5827	678	2	.	.	PROPN
ejpam-5827	678	3	,	,	PUNCT
ejpam-5827	678	4	32(01):43–53	32(01):43–53	NOUN
ejpam-5827	678	5	,	,	PUNCT
ejpam-5827	678	6	2023	2023	NUM
ejpam-5827	678	7	.	.	PUNCT
ejpam-5827	679	1	[	[	X
ejpam-5827	679	2	11	11	NUM
ejpam-5827	679	3	]	]	PUNCT
ejpam-5827	679	4	t.	t.	PROPN
ejpam-5827	679	5	m.	m.	PROPN
ejpam-5827	679	6	al	al	PROPN
ejpam-5827	679	7	-	-	PUNCT
ejpam-5827	679	8	shami	shami	PROPN
ejpam-5827	679	9	and	and	CCONJ
ejpam-5827	679	10	m.	m.	PROPN
ejpam-5827	679	11	hosny	hosny	PROPN
ejpam-5827	679	12	.	.	PUNCT
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ejpam-5827	680	2	of	of	ADP
ejpam-5827	680	3	approximation	approximation	NOUN
ejpam-5827	680	4	spaces	space	NOUN
ejpam-5827	680	5	using	use	VERB
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ejpam-5827	680	7	left	leave	VERB
ejpam-5827	680	8	neighborhoods	neighborhood	NOUN
ejpam-5827	680	9	and	and	CCONJ
ejpam-5827	680	10	ideals	ideal	NOUN
ejpam-5827	680	11	.	.	PUNCT
ejpam-5827	681	1	ieee	ieee	NOUN
ejpam-5827	681	2	access	access	NOUN
ejpam-5827	681	3	,	,	PUNCT
ejpam-5827	681	4	10:79379–79393	10:79379–79393	NUM
ejpam-5827	681	5	,	,	PUNCT
ejpam-5827	681	6	2022	2022	NUM
ejpam-5827	681	7	.	.	PUNCT
ejpam-5827	682	1	[	[	X
ejpam-5827	682	2	12	12	NUM
ejpam-5827	682	3	]	]	PUNCT
ejpam-5827	682	4	a.	a.	NOUN
ejpam-5827	682	5	a.	a.	PROPN
ejpam-5827	682	6	allam	allam	PROPN
ejpam-5827	682	7	,	,	PUNCT
ejpam-5827	682	8	m.	m.	PROPN
ejpam-5827	682	9	y.	y.	PROPN
ejpam-5827	682	10	bakeir	bakeir	PROPN
ejpam-5827	682	11	,	,	PUNCT
ejpam-5827	682	12	and	and	CCONJ
ejpam-5827	682	13	e.	e.	PROPN
ejpam-5827	682	14	a.	a.	PROPN
ejpam-5827	682	15	abo	abo	PROPN
ejpam-5827	682	16	-	-	PUNCT
ejpam-5827	682	17	tabl	tabl	NOUN
ejpam-5827	682	18	.	.	PUNCT
ejpam-5827	683	1	new	new	ADJ
ejpam-5827	683	2	approach	approach	NOUN
ejpam-5827	683	3	for	for	ADP
ejpam-5827	683	4	basic	basic	ADJ
ejpam-5827	683	5	rough	rough	ADJ
ejpam-5827	683	6	set	set	NOUN
ejpam-5827	683	7	concepts	concept	NOUN
ejpam-5827	683	8	,	,	PUNCT
ejpam-5827	683	9	in	in	ADP
ejpam-5827	683	10	:	:	PUNCT
ejpam-5827	683	11	rough	rough	ADJ
ejpam-5827	683	12	sets	set	NOUN
ejpam-5827	683	13	,	,	PUNCT
ejpam-5827	683	14	fuzzy	fuzzy	ADJ
ejpam-5827	683	15	sets	set	NOUN
ejpam-5827	683	16	,	,	PUNCT
ejpam-5827	683	17	data	datum	NOUN
ejpam-5827	683	18	mining	mining	NOUN
ejpam-5827	683	19	,	,	PUNCT
ejpam-5827	683	20	and	and	CCONJ
ejpam-5827	683	21	granular	granular	ADJ
ejpam-5827	683	22	computing	computing	NOUN
ejpam-5827	683	23	.	.	PUNCT
ejpam-5827	684	1	berlin	berlin	PROPN
ejpam-5827	684	2	,	,	PUNCT
ejpam-5827	684	3	heidelberg	heidelberg	PROPN
ejpam-5827	684	4	,	,	PUNCT
ejpam-5827	684	5	springer	springer	NOUN
ejpam-5827	684	6	,	,	PUNCT
ejpam-5827	684	7	2005	2005	NUM
ejpam-5827	684	8	.	.	PUNCT
ejpam-5827	685	1	[	[	X
ejpam-5827	685	2	13	13	NUM
ejpam-5827	685	3	]	]	PUNCT
ejpam-5827	685	4	a.	a.	NOUN
ejpam-5827	685	5	a.	a.	PROPN
ejpam-5827	685	6	allam	allam	PROPN
ejpam-5827	685	7	,	,	PUNCT
ejpam-5827	685	8	m.	m.	PROPN
ejpam-5827	685	9	y.	y.	PROPN
ejpam-5827	685	10	bakeir	bakeir	PROPN
ejpam-5827	685	11	,	,	PUNCT
ejpam-5827	685	12	and	and	CCONJ
ejpam-5827	685	13	e.	e.	PROPN
ejpam-5827	685	14	a.	a.	PROPN
ejpam-5827	685	15	abo	abo	PROPN
ejpam-5827	685	16	-	-	PUNCT
ejpam-5827	685	17	tabl	tabl	NOUN
ejpam-5827	685	18	.	.	PUNCT
ejpam-5827	686	1	new	new	ADJ
ejpam-5827	686	2	approach	approach	NOUN
ejpam-5827	686	3	for	for	ADP
ejpam-5827	686	4	basic	basic	ADJ
ejpam-5827	686	5	rough	rough	ADJ
ejpam-5827	686	6	set	set	NOUN
ejpam-5827	686	7	concepts	concept	NOUN
ejpam-5827	686	8	,	,	PUNCT
ejpam-5827	686	9	in	in	ADP
ejpam-5827	686	10	:	:	PUNCT
ejpam-5827	686	11	rough	rough	ADJ
ejpam-5827	686	12	sets	set	NOUN
ejpam-5827	686	13	,	,	PUNCT
ejpam-5827	686	14	fuzzy	fuzzy	ADJ
ejpam-5827	686	15	sets	set	NOUN
ejpam-5827	686	16	,	,	PUNCT
ejpam-5827	686	17	data	datum	NOUN
ejpam-5827	686	18	mining	mining	NOUN
ejpam-5827	686	19	,	,	PUNCT
ejpam-5827	686	20	and	and	CCONJ
ejpam-5827	686	21	granular	granular	ADJ
ejpam-5827	686	22	computing	computing	NOUN
ejpam-5827	686	23	.	.	PUNCT
ejpam-5827	687	1	acta	acta	PROPN
ejpam-5827	687	2	math	math	PROPN
ejpam-5827	687	3	.	.	PUNCT
ejpam-5827	688	1	acad	acad	PROPN
ejpam-5827	688	2	.	.	PUNCT
ejpam-5827	689	1	paedagog	paedagog	PROPN
ejpam-5827	689	2	.	.	PUNCT
ejpam-5827	690	1	nyiregyháziensis	nyiregyháziensis	NOUN
ejpam-5827	690	2	,	,	PUNCT
ejpam-5827	690	3	22(3):285–304	22(3):285–304	PROPN
ejpam-5827	690	4	,	,	PUNCT
ejpam-5827	690	5	2006	2006	NUM
ejpam-5827	690	6	.	.	PUNCT
ejpam-5827	691	1	[	[	X
ejpam-5827	691	2	14	14	NUM
ejpam-5827	691	3	]	]	PUNCT
ejpam-5827	691	4	z.	z.	PROPN
ejpam-5827	691	5	a.	a.	PROPN
ejpam-5827	691	6	ameen	ameen	PROPN
ejpam-5827	691	7	and	and	CCONJ
ejpam-5827	691	8	b.	b.	PROPN
ejpam-5827	691	9	a.	a.	PROPN
ejpam-5827	691	10	asaad	asaad	PROPN
ejpam-5827	691	11	.	.	PUNCT
ejpam-5827	692	1	methods	method	NOUN
ejpam-5827	692	2	of	of	ADP
ejpam-5827	692	3	generating	generate	VERB
ejpam-5827	692	4	soft	soft	ADJ
ejpam-5827	692	5	topologies	topology	NOUN
ejpam-5827	692	6	and	and	CCONJ
ejpam-5827	692	7	soft	soft	ADJ
ejpam-5827	692	8	separation	separation	NOUN
ejpam-5827	692	9	axioms	axiom	NOUN
ejpam-5827	692	10	.	.	PUNCT
ejpam-5827	693	1	eur	eur	PROPN
ejpam-5827	693	2	.	.	PUNCT
ejpam-5827	694	1	j.	j.	PROPN
ejpam-5827	694	2	pure	pure	PROPN
ejpam-5827	694	3	appl	appl	PROPN
ejpam-5827	694	4	.	.	PUNCT
ejpam-5827	694	5	math	math	PROPN
ejpam-5827	694	6	.	.	PUNCT
ejpam-5827	694	7	,	,	PUNCT
ejpam-5827	694	8	17(2):1168–1182	17(2):1168–1182	PROPN
ejpam-5827	694	9	,	,	PUNCT
ejpam-5827	694	10	2023	2023	NUM
ejpam-5827	694	11	.	.	PUNCT
ejpam-5827	695	1	[	[	X
ejpam-5827	695	2	15	15	NUM
ejpam-5827	695	3	]	]	X
ejpam-5827	695	4	b.	b.	PROPN
ejpam-5827	695	5	a.	a.	PROPN
ejpam-5827	695	6	asaad	asaad	PROPN
ejpam-5827	695	7	.	.	PUNCT
ejpam-5827	696	1	results	result	NOUN
ejpam-5827	696	2	on	on	ADP
ejpam-5827	696	3	soft	soft	ADJ
ejpam-5827	696	4	extremally	extremally	ADV
ejpam-5827	696	5	disconnectedness	disconnectedness	NOUN
ejpam-5827	696	6	of	of	ADP
ejpam-5827	696	7	soft	soft	ADJ
ejpam-5827	696	8	topological	topological	ADJ
ejpam-5827	696	9	spaces	space	NOUN
ejpam-5827	696	10	.	.	PUNCT
ejpam-5827	697	1	j.	j.	PROPN
ejpam-5827	697	2	math	math	PROPN
ejpam-5827	697	3	.	.	PUNCT
ejpam-5827	698	1	comput	comput	NOUN
ejpam-5827	698	2	.	.	PUNCT
ejpam-5827	699	1	sci	sci	PROPN
ejpam-5827	699	2	.	.	PROPN
ejpam-5827	699	3	,	,	PUNCT
ejpam-5827	699	4	17(4):448–464	17(4):448–464	PROPN
ejpam-5827	699	5	,	,	PUNCT
ejpam-5827	699	6	2017	2017	NUM
ejpam-5827	699	7	.	.	PUNCT
ejpam-5827	700	1	[	[	X
ejpam-5827	700	2	16	16	NUM
ejpam-5827	700	3	]	]	X
ejpam-5827	700	4	b.	b.	PROPN
ejpam-5827	700	5	a.	a.	PROPN
ejpam-5827	700	6	asaad	asaad	PROPN
ejpam-5827	700	7	,	,	PUNCT
ejpam-5827	700	8	s.	s.	PROPN
ejpam-5827	700	9	y.	y.	PROPN
ejpam-5827	700	10	musa	musa	PROPN
ejpam-5827	700	11	,	,	PUNCT
ejpam-5827	700	12	and	and	CCONJ
ejpam-5827	700	13	ameen	ameen	PROPN
ejpam-5827	700	14	z.	z.	PROPN
ejpam-5827	700	15	a.	a.	NOUN
ejpam-5827	700	16	fuzzy	fuzzy	PROPN
ejpam-5827	700	17	bipolar	bipolar	ADJ
ejpam-5827	700	18	hypersoft	hypersoft	NOUN
ejpam-5827	700	19	sets	set	VERB
ejpam-5827	700	20	:	:	PUNCT
ejpam-5827	700	21	a	a	DET
ejpam-5827	700	22	novel	novel	ADJ
ejpam-5827	700	23	approach	approach	NOUN
ejpam-5827	700	24	for	for	ADP
ejpam-5827	700	25	decision	decision	NOUN
ejpam-5827	700	26	-	-	PUNCT
ejpam-5827	700	27	making	make	VERB
ejpam-5827	700	28	applications	application	NOUN
ejpam-5827	700	29	.	.	PUNCT
ejpam-5827	701	1	math	math	NOUN
ejpam-5827	701	2	.	.	PUNCT
ejpam-5827	702	1	comput	comput	NOUN
ejpam-5827	702	2	.	.	PUNCT
ejpam-5827	703	1	appl	appl	PROPN
ejpam-5827	703	2	.	.	PROPN
ejpam-5827	703	3	,	,	PUNCT
ejpam-5827	703	4	29(4):50	29(4):50	NUM
ejpam-5827	703	5	,	,	PUNCT
ejpam-5827	703	6	2024	2024	NUM
ejpam-5827	703	7	.	.	PUNCT
ejpam-5827	704	1	[	[	X
ejpam-5827	704	2	17	17	NUM
ejpam-5827	704	3	]	]	PUNCT
ejpam-5827	704	4	m.	m.	NOUN
ejpam-5827	704	5	atef	atef	PROPN
ejpam-5827	704	6	,	,	PUNCT
ejpam-5827	704	7	a.	a.	PROPN
ejpam-5827	704	8	m.	m.	PROPN
ejpam-5827	704	9	khalil	khalil	PROPN
ejpam-5827	704	10	,	,	PUNCT
ejpam-5827	704	11	s.-g	s.-g	PROPN
ejpam-5827	704	12	.	.	PUNCT
ejpam-5827	705	1	li	li	PROPN
ejpam-5827	705	2	,	,	PUNCT
ejpam-5827	705	3	a.	a.	PROPN
ejpam-5827	705	4	a.	a.	PROPN
ejpam-5827	705	5	azzam	azzam	PROPN
ejpam-5827	705	6	,	,	PUNCT
ejpam-5827	705	7	and	and	CCONJ
ejpam-5827	705	8	a.	a.	PROPN
ejpam-5827	705	9	a.	a.	PROPN
ejpam-5827	705	10	atik	atik	PROPN
ejpam-5827	705	11	.	.	PUNCT
ejpam-5827	706	1	comparison	comparison	NOUN
ejpam-5827	706	2	of	of	ADP
ejpam-5827	706	3	six	six	NUM
ejpam-5827	706	4	types	type	NOUN
ejpam-5827	706	5	of	of	ADP
ejpam-5827	706	6	rough	rough	ADJ
ejpam-5827	706	7	approximations	approximation	NOUN
ejpam-5827	706	8	based	base	VERB
ejpam-5827	706	9	on	on	ADP
ejpam-5827	706	10	j	j	PROPN
ejpam-5827	706	11	-	-	PUNCT
ejpam-5827	706	12	neighborhood	neighborhood	NOUN
ejpam-5827	706	13	space	space	NOUN
ejpam-5827	706	14	and	and	CCONJ
ejpam-5827	706	15	j	j	NOUN
ejpam-5827	706	16	-	-	PUNCT
ejpam-5827	706	17	adhesion	adhesion	NOUN
ejpam-5827	706	18	neighborhood	neighborhood	NOUN
ejpam-5827	706	19	space	space	NOUN
ejpam-5827	706	20	.	.	PUNCT
ejpam-5827	707	1	j.	j.	PROPN
ejpam-5827	707	2	intell	intell	PROPN
ejpam-5827	707	3	.	.	PUNCT
ejpam-5827	708	1	fuzzy	fuzzy	ADJ
ejpam-5827	708	2	syst	syst	PROPN
ejpam-5827	708	3	.	.	PUNCT
ejpam-5827	708	4	,	,	PUNCT
ejpam-5827	708	5	39:4515–4531	39:4515–4531	NUM
ejpam-5827	708	6	,	,	PUNCT
ejpam-5827	708	7	2020	2020	NUM
ejpam-5827	708	8	.	.	PUNCT
ejpam-5827	709	1	r.	r.	PROPN
ejpam-5827	709	2	a.	a.	PROPN
ejpam-5827	709	3	hosny	hosny	PROPN
ejpam-5827	709	4	,	,	PUNCT
ejpam-5827	709	5	m.	m.	PROPN
ejpam-5827	709	6	k.	k.	PROPN
ejpam-5827	710	1	el	el	PROPN
ejpam-5827	710	2	-	-	PROPN
ejpam-5827	710	3	bably	bably	ADV
ejpam-5827	710	4	,	,	PUNCT
ejpam-5827	710	5	m.	m.	NOUN
ejpam-5827	710	6	a.	a.	PROPN
ejpam-5827	710	7	el	el	PROPN
ejpam-5827	710	8	-	-	PROPN
ejpam-5827	710	9	gayar	gayar	PROPN
ejpam-5827	710	10	/	/	SYM
ejpam-5827	710	11	eur	eur	PROPN
ejpam-5827	710	12	.	.	PUNCT
ejpam-5827	711	1	j.	j.	PROPN
ejpam-5827	711	2	pure	pure	PROPN
ejpam-5827	711	3	appl	appl	PROPN
ejpam-5827	711	4	.	.	PROPN
ejpam-5827	711	5	math	math	PROPN
ejpam-5827	711	6	,	,	PUNCT
ejpam-5827	711	7	18	18	NUM
ejpam-5827	711	8	(	(	PUNCT
ejpam-5827	711	9	1	1	NUM
ejpam-5827	711	10	)	)	PUNCT
ejpam-5827	711	11	(	(	PUNCT
ejpam-5827	711	12	2025	2025	NUM
ejpam-5827	711	13	)	)	PUNCT
ejpam-5827	711	14	,	,	PUNCT
ejpam-5827	711	15	5827	5827	NUM
ejpam-5827	711	16	26	26	NUM
ejpam-5827	711	17	of	of	ADP
ejpam-5827	711	18	29	29	NUM
ejpam-5827	711	19	[	[	SYM
ejpam-5827	711	20	18	18	NUM
ejpam-5827	711	21	]	]	PUNCT
ejpam-5827	711	22	m.	m.	NOUN
ejpam-5827	711	23	atef	atef	PROPN
ejpam-5827	711	24	,	,	PUNCT
ejpam-5827	711	25	s.	s.	PROPN
ejpam-5827	711	26	nada	nada	PROPN
ejpam-5827	711	27	,	,	PUNCT
ejpam-5827	711	28	and	and	CCONJ
ejpam-5827	711	29	a.	a.	PROPN
ejpam-5827	711	30	s.	s.	PROPN
ejpam-5827	711	31	nawar	nawar	PROPN
ejpam-5827	711	32	.	.	PUNCT
ejpam-5827	712	1	covering	cover	VERB
ejpam-5827	712	2	soft	soft	ADJ
ejpam-5827	712	3	rough	rough	ADJ
ejpam-5827	712	4	sets	set	NOUN
ejpam-5827	712	5	and	and	CCONJ
ejpam-5827	712	6	its	its	PRON
ejpam-5827	712	7	topological	topological	ADJ
ejpam-5827	712	8	properties	property	NOUN
ejpam-5827	712	9	with	with	ADP
ejpam-5827	712	10	application	application	NOUN
ejpam-5827	712	11	.	.	PUNCT
ejpam-5827	713	1	soft	soft	ADJ
ejpam-5827	713	2	comput	comput	NOUN
ejpam-5827	713	3	.	.	PUNCT
ejpam-5827	713	4	,	,	PUNCT
ejpam-5827	714	1	27(8):4451–4461	27(8):4451–4461	NUM
ejpam-5827	714	2	,	,	PUNCT
ejpam-5827	714	3	2023	2023	NUM
ejpam-5827	714	4	.	.	PUNCT
ejpam-5827	715	1	[	[	X
ejpam-5827	715	2	19	19	NUM
ejpam-5827	715	3	]	]	X
ejpam-5827	715	4	g.	g.	NOUN
ejpam-5827	715	5	choquet	choquet	PROPN
ejpam-5827	715	6	.	.	PUNCT
ejpam-5827	716	1	sur	sur	PROPN
ejpam-5827	716	2	les	les	PROPN
ejpam-5827	716	3	notions	notion	NOUN
ejpam-5827	716	4	de	de	X
ejpam-5827	716	5	filtre	filtre	NOUN
ejpam-5827	716	6	et	et	NOUN
ejpam-5827	716	7	de	de	NOUN
ejpam-5827	716	8	grille	grille	NOUN
ejpam-5827	716	9	.	.	PUNCT
ejpam-5827	717	1	comptes	compte	VERB
ejpam-5827	717	2	rendus	rendus	PROPN
ejpam-5827	717	3	acad	acad	PROPN
ejpam-5827	717	4	.	.	PUNCT
ejpam-5827	718	1	sci	sci	PROPN
ejpam-5827	718	2	.	.	PROPN
ejpam-5827	718	3	paris	paris	PROPN
ejpam-5827	718	4	,	,	PUNCT
ejpam-5827	718	5	224:171–173	224:171–173	NUM
ejpam-5827	718	6	,	,	PUNCT
ejpam-5827	718	7	1947	1947	NUM
ejpam-5827	718	8	.	.	PUNCT
ejpam-5827	719	1	https://doi.org/10.1155/2023/4723233	https://doi.org/10.1155/2023/4723233	PROPN
ejpam-5827	719	2	.	.	PUNCT
ejpam-5827	720	1	[	[	X
ejpam-5827	720	2	20	20	NUM
ejpam-5827	720	3	]	]	PUNCT
ejpam-5827	720	4	j.	j.	PROPN
ejpam-5827	720	5	h.	h.	PROPN
ejpam-5827	720	6	dai	dai	PROPN
ejpam-5827	720	7	,	,	PUNCT
ejpam-5827	720	8	s.	s.	PROPN
ejpam-5827	720	9	c.	c.	PROPN
ejpam-5827	720	10	gao	gao	PROPN
ejpam-5827	720	11	,	,	PUNCT
ejpam-5827	720	12	and	and	CCONJ
ejpam-5827	720	13	g.	g.	PROPN
ejpam-5827	720	14	j.	j.	PROPN
ejpam-5827	720	15	zheng	zheng	PROPN
ejpam-5827	720	16	.	.	PUNCT
ejpam-5827	721	1	generalized	generalize	VERB
ejpam-5827	721	2	rough	rough	ADJ
ejpam-5827	721	3	set	set	NOUN
ejpam-5827	721	4	models	model	NOUN
ejpam-5827	721	5	determined	determine	VERB
ejpam-5827	721	6	by	by	ADP
ejpam-5827	721	7	multiple	multiple	ADJ
ejpam-5827	721	8	neighborhoods	neighborhood	NOUN
ejpam-5827	721	9	generated	generate	VERB
ejpam-5827	721	10	from	from	ADP
ejpam-5827	721	11	a	a	DET
ejpam-5827	721	12	similarity	similarity	NOUN
ejpam-5827	721	13	relation	relation	NOUN
ejpam-5827	721	14	.	.	PUNCT
ejpam-5827	722	1	soft	soft	ADJ
ejpam-5827	722	2	comput	comput	NOUN
ejpam-5827	722	3	.	.	PUNCT
ejpam-5827	722	4	,	,	PUNCT
ejpam-5827	722	5	22:2081	22:2081	NUM
ejpam-5827	722	6	–	–	PUNCT
ejpam-5827	722	7	2094	2094	NUM
ejpam-5827	722	8	,	,	PUNCT
ejpam-5827	722	9	2018	2018	NUM
ejpam-5827	722	10	.	.	PUNCT
ejpam-5827	723	1	[	[	X
ejpam-5827	723	2	21	21	NUM
ejpam-5827	723	3	]	]	PUNCT
ejpam-5827	723	4	m.	m.	NOUN
ejpam-5827	723	5	k.	k.	PROPN
ejpam-5827	724	1	el	el	PROPN
ejpam-5827	724	2	-	-	PROPN
ejpam-5827	724	3	bably	bably	PROPN
ejpam-5827	724	4	.	.	PUNCT
ejpam-5827	725	1	generalized	generalized	ADJ
ejpam-5827	725	2	approximation	approximation	NOUN
ejpam-5827	725	3	spaces	space	NOUN
ejpam-5827	725	4	.	.	PUNCT
ejpam-5827	726	1	m.	m.	PROPN
ejpam-5827	726	2	sc	sc	PROPN
ejpam-5827	726	3	.	.	PUNCT
ejpam-5827	727	1	thesis	thesis	PROPN
ejpam-5827	727	2	,	,	PUNCT
ejpam-5827	727	3	tanta	tanta	PROPN
ejpam-5827	727	4	university	university	PROPN
ejpam-5827	727	5	,	,	PUNCT
ejpam-5827	727	6	egypt	egypt	PROPN
ejpam-5827	727	7	,	,	PUNCT
ejpam-5827	727	8	2008	2008	NUM
ejpam-5827	727	9	.	.	PUNCT
ejpam-5827	728	1	[	[	X
ejpam-5827	728	2	22	22	NUM
ejpam-5827	728	3	]	]	PUNCT
ejpam-5827	728	4	m.	m.	NOUN
ejpam-5827	728	5	k.	k.	PROPN
ejpam-5827	729	1	el	el	PROPN
ejpam-5827	729	2	-	-	PROPN
ejpam-5827	729	3	bably	bably	PROPN
ejpam-5827	729	4	and	and	CCONJ
ejpam-5827	729	5	e.	e.	PROPN
ejpam-5827	729	6	a.	a.	PROPN
ejpam-5827	729	7	abo	abo	PROPN
ejpam-5827	729	8	-	-	PUNCT
ejpam-5827	729	9	tabl	tabl	NOUN
ejpam-5827	729	10	.	.	PUNCT
ejpam-5827	730	1	a	a	DET
ejpam-5827	730	2	topological	topological	ADJ
ejpam-5827	730	3	reduction	reduction	NOUN
ejpam-5827	730	4	for	for	ADP
ejpam-5827	730	5	predicting	predict	VERB
ejpam-5827	730	6	of	of	ADP
ejpam-5827	730	7	a	a	DET
ejpam-5827	730	8	lung	lung	NOUN
ejpam-5827	730	9	cancer	cancer	NOUN
ejpam-5827	730	10	disease	disease	NOUN
ejpam-5827	730	11	based	base	VERB
ejpam-5827	730	12	on	on	ADP
ejpam-5827	730	13	generalized	generalized	ADJ
ejpam-5827	730	14	rough	rough	ADJ
ejpam-5827	730	15	sets	set	NOUN
ejpam-5827	730	16	.	.	PUNCT
ejpam-5827	731	1	j.	j.	PROPN
ejpam-5827	731	2	intell	intell	PROPN
ejpam-5827	731	3	.	.	PUNCT
ejpam-5827	732	1	fuzzy	fuzzy	ADJ
ejpam-5827	732	2	syst	syst	PROPN
ejpam-5827	732	3	.	.	PUNCT
ejpam-5827	732	4	,	,	PUNCT
ejpam-5827	732	5	41:335–346	41:335–346	NUM
ejpam-5827	732	6	,	,	PUNCT
ejpam-5827	732	7	2021	2021	NUM
ejpam-5827	732	8	.	.	PUNCT
ejpam-5827	733	1	[	[	X
ejpam-5827	733	2	23	23	NUM
ejpam-5827	733	3	]	]	PUNCT
ejpam-5827	733	4	m.	m.	NOUN
ejpam-5827	733	5	k.	k.	PROPN
ejpam-5827	734	1	el	el	PROPN
ejpam-5827	734	2	-	-	PROPN
ejpam-5827	734	3	bably	bably	PROPN
ejpam-5827	734	4	,	,	PUNCT
ejpam-5827	734	5	r.	r.	PROPN
ejpam-5827	734	6	abu	abu	PROPN
ejpam-5827	734	7	-	-	PUNCT
ejpam-5827	734	8	gdairi	gdairi	PROPN
ejpam-5827	734	9	,	,	PUNCT
ejpam-5827	734	10	and	and	CCONJ
ejpam-5827	734	11	m.	m.	PROPN
ejpam-5827	734	12	a.	a.	PROPN
ejpam-5827	734	13	el	el	PROPN
ejpam-5827	734	14	-	-	PROPN
ejpam-5827	734	15	gayar	gayar	NOUN
ejpam-5827	734	16	.	.	PUNCT
ejpam-5827	735	1	medical	medical	ADJ
ejpam-5827	735	2	diagnosis	diagnosis	NOUN
ejpam-5827	735	3	for	for	ADP
ejpam-5827	735	4	the	the	DET
ejpam-5827	735	5	problem	problem	NOUN
ejpam-5827	735	6	of	of	ADP
ejpam-5827	735	7	chikungunya	chikungunya	NOUN
ejpam-5827	735	8	disease	disease	NOUN
ejpam-5827	735	9	using	use	VERB
ejpam-5827	735	10	soft	soft	ADJ
ejpam-5827	735	11	rough	rough	ADJ
ejpam-5827	735	12	sets	set	NOUN
ejpam-5827	735	13	.	.	PUNCT
ejpam-5827	736	1	aims	aim	VERB
ejpam-5827	736	2	math	math	NOUN
ejpam-5827	736	3	.	.	PUNCT
ejpam-5827	736	4	,	,	PUNCT
ejpam-5827	736	5	8:9082–9105	8:9082–9105	NUM
ejpam-5827	736	6	,	,	PUNCT
ejpam-5827	736	7	2023	2023	NUM
ejpam-5827	736	8	.	.	PUNCT
ejpam-5827	737	1	[	[	X
ejpam-5827	737	2	24	24	NUM
ejpam-5827	737	3	]	]	PUNCT
ejpam-5827	737	4	m.	m.	NOUN
ejpam-5827	737	5	k.	k.	PROPN
ejpam-5827	738	1	el	el	PROPN
ejpam-5827	738	2	-	-	PROPN
ejpam-5827	738	3	bably	bably	PROPN
ejpam-5827	738	4	,	,	PUNCT
ejpam-5827	738	5	r.	r.	PROPN
ejpam-5827	738	6	abu	abu	PROPN
ejpam-5827	738	7	-	-	PUNCT
ejpam-5827	738	8	gdairi	gdairi	PROPN
ejpam-5827	738	9	,	,	PUNCT
ejpam-5827	738	10	k.	k.	PROPN
ejpam-5827	738	11	k.	k.	PROPN
ejpam-5827	738	12	fleifel	fleifel	PROPN
ejpam-5827	738	13	,	,	PUNCT
ejpam-5827	738	14	and	and	CCONJ
ejpam-5827	738	15	m.	m.	NOUN
ejpam-5827	738	16	a.	a.	PROPN
ejpam-5827	738	17	el	el	PROPN
ejpam-5827	738	18	-	-	PROPN
ejpam-5827	738	19	gayar	gayar	NOUN
ejpam-5827	738	20	.	.	PUNCT
ejpam-5827	739	1	exploring	explore	VERB
ejpam-5827	739	2	β	β	NOUN
ejpam-5827	739	3	-	-	ADJ
ejpam-5827	739	4	basic	basic	ADJ
ejpam-5827	739	5	rough	rough	ADJ
ejpam-5827	739	6	sets	set	NOUN
ejpam-5827	739	7	and	and	CCONJ
ejpam-5827	739	8	their	their	PRON
ejpam-5827	739	9	applications	application	NOUN
ejpam-5827	739	10	in	in	ADP
ejpam-5827	739	11	medicine	medicine	NOUN
ejpam-5827	739	12	.	.	PUNCT
ejpam-5827	740	1	eur	eur	PROPN
ejpam-5827	740	2	.	.	PUNCT
ejpam-5827	741	1	j.	j.	PROPN
ejpam-5827	741	2	pure	pure	PROPN
ejpam-5827	741	3	appl	appl	PROPN
ejpam-5827	741	4	.	.	PUNCT
ejpam-5827	741	5	math	math	PROPN
ejpam-5827	741	6	.	.	PUNCT
ejpam-5827	741	7	,	,	PUNCT
ejpam-5827	742	1	17(4):3743	17(4):3743	NUM
ejpam-5827	742	2	–	–	PUNCT
ejpam-5827	742	3	3771	3771	NUM
ejpam-5827	742	4	,	,	PUNCT
ejpam-5827	742	5	2024	2024	NUM
ejpam-5827	742	6	.	.	PUNCT
ejpam-5827	743	1	[	[	X
ejpam-5827	743	2	25	25	NUM
ejpam-5827	743	3	]	]	PUNCT
ejpam-5827	743	4	m.	m.	NOUN
ejpam-5827	743	5	k.	k.	PROPN
ejpam-5827	744	1	el	el	PROPN
ejpam-5827	744	2	-	-	PROPN
ejpam-5827	744	3	bably	bably	ADV
ejpam-5827	744	4	,	,	PUNCT
ejpam-5827	744	5	t.	t.	PROPN
ejpam-5827	744	6	m.	m.	PROPN
ejpam-5827	744	7	al	al	PROPN
ejpam-5827	744	8	-	-	PUNCT
ejpam-5827	744	9	shami	shami	PROPN
ejpam-5827	744	10	,	,	PUNCT
ejpam-5827	744	11	a.	a.	PROPN
ejpam-5827	744	12	s.	s.	PROPN
ejpam-5827	744	13	nawar	nawar	PROPN
ejpam-5827	744	14	,	,	PUNCT
ejpam-5827	744	15	and	and	CCONJ
ejpam-5827	744	16	a.	a.	NOUN
ejpam-5827	744	17	mhemdi	mhemdi	PROPN
ejpam-5827	744	18	.	.	PUNCT
ejpam-5827	745	1	corrigendum	corrigendum	NOUN
ejpam-5827	745	2	to	to	PART
ejpam-5827	745	3	“	"	PUNCT
ejpam-5827	745	4	comparison	comparison	NOUN
ejpam-5827	745	5	of	of	ADP
ejpam-5827	745	6	six	six	NUM
ejpam-5827	745	7	types	type	NOUN
ejpam-5827	745	8	of	of	ADP
ejpam-5827	745	9	rough	rough	ADJ
ejpam-5827	745	10	approximations	approximation	NOUN
ejpam-5827	745	11	based	base	VERB
ejpam-5827	745	12	on	on	ADP
ejpam-5827	745	13	j	j	PROPN
ejpam-5827	745	14	-	-	PUNCT
ejpam-5827	745	15	neighborhood	neighborhood	NOUN
ejpam-5827	745	16	space	space	NOUN
ejpam-5827	745	17	and	and	CCONJ
ejpam-5827	745	18	j	j	NOUN
ejpam-5827	745	19	-	-	PUNCT
ejpam-5827	745	20	adhesion	adhesion	NOUN
ejpam-5827	745	21	neighborhood	neighborhood	NOUN
ejpam-5827	745	22	space	space	NOUN
ejpam-5827	745	23	.	.	PUNCT
ejpam-5827	746	1	j.	j.	PROPN
ejpam-5827	746	2	intell	intell	PROPN
ejpam-5827	746	3	.	.	PUNCT
ejpam-5827	747	1	fuzzy	fuzzy	ADJ
ejpam-5827	747	2	syst	syst	PROPN
ejpam-5827	747	3	.	.	PUNCT
ejpam-5827	747	4	,	,	PUNCT
ejpam-5827	747	5	41:7353–7361	41:7353–7361	PROPN
ejpam-5827	747	6	,	,	PUNCT
ejpam-5827	747	7	2021	2021	NUM
ejpam-5827	747	8	.	.	PUNCT
ejpam-5827	748	1	[	[	X
ejpam-5827	748	2	26	26	NUM
ejpam-5827	748	3	]	]	PUNCT
ejpam-5827	748	4	m.	m.	NOUN
ejpam-5827	748	5	k.	k.	PROPN
ejpam-5827	749	1	el	el	PROPN
ejpam-5827	749	2	-	-	PROPN
ejpam-5827	749	3	bably	bably	ADV
ejpam-5827	749	4	,	,	PUNCT
ejpam-5827	749	5	m.	m.	NOUN
ejpam-5827	749	6	i.	i.	PROPN
ejpam-5827	749	7	ali	ali	PROPN
ejpam-5827	749	8	,	,	PUNCT
ejpam-5827	749	9	and	and	CCONJ
ejpam-5827	749	10	e.	e.	PROPN
ejpam-5827	749	11	a.	a.	PROPN
ejpam-5827	749	12	abo	abo	PROPN
ejpam-5827	749	13	-	-	PUNCT
ejpam-5827	749	14	tabl	tabl	NOUN
ejpam-5827	749	15	.	.	PUNCT
ejpam-5827	750	1	new	new	ADJ
ejpam-5827	750	2	topological	topological	ADJ
ejpam-5827	750	3	approaches	approach	NOUN
ejpam-5827	750	4	to	to	ADP
ejpam-5827	750	5	generalized	generalize	VERB
ejpam-5827	750	6	soft	soft	ADJ
ejpam-5827	750	7	rough	rough	ADJ
ejpam-5827	750	8	approximations	approximation	NOUN
ejpam-5827	750	9	with	with	ADP
ejpam-5827	750	10	medical	medical	ADJ
ejpam-5827	750	11	applications	application	NOUN
ejpam-5827	750	12	.	.	PUNCT
ejpam-5827	751	1	j.	j.	PROPN
ejpam-5827	751	2	math	math	PROPN
ejpam-5827	751	3	.	.	PROPN
ejpam-5827	751	4	,	,	PUNCT
ejpam-5827	751	5	2021:2559495	2021:2559495	NUM
ejpam-5827	751	6	,	,	PUNCT
ejpam-5827	751	7	2021	2021	NUM
ejpam-5827	751	8	.	.	PUNCT
ejpam-5827	752	1	[	[	X
ejpam-5827	752	2	27	27	NUM
ejpam-5827	752	3	]	]	PUNCT
ejpam-5827	752	4	m.	m.	NOUN
ejpam-5827	752	5	k.	k.	PROPN
ejpam-5827	753	1	el	el	PROPN
ejpam-5827	753	2	-	-	PROPN
ejpam-5827	753	3	bably	bably	PROPN
ejpam-5827	753	4	and	and	CCONJ
ejpam-5827	753	5	a.	a.	NOUN
ejpam-5827	753	6	a.	a.	PROPN
ejpam-5827	753	7	el	el	PROPN
ejpam-5827	753	8	atik	atik	PROPN
ejpam-5827	753	9	.	.	PUNCT
ejpam-5827	754	1	soft	soft	ADJ
ejpam-5827	754	2	β	β	NOUN
ejpam-5827	754	3	-	-	ADJ
ejpam-5827	754	4	rough	rough	ADJ
ejpam-5827	754	5	sets	set	NOUN
ejpam-5827	754	6	and	and	CCONJ
ejpam-5827	754	7	their	their	PRON
ejpam-5827	754	8	application	application	NOUN
ejpam-5827	754	9	to	to	PART
ejpam-5827	754	10	determine	determine	VERB
ejpam-5827	754	11	covid-19	covid-19	PROPN
ejpam-5827	754	12	.	.	PROPN
ejpam-5827	754	13	turk	turk	PROPN
ejpam-5827	754	14	.	.	PUNCT
ejpam-5827	755	1	j.	j.	PROPN
ejpam-5827	755	2	math	math	PROPN
ejpam-5827	755	3	.	.	PUNCT
ejpam-5827	755	4	,	,	PUNCT
ejpam-5827	755	5	45(3):1133–1148	45(3):1133–1148	NUM
ejpam-5827	755	6	,	,	PUNCT
ejpam-5827	755	7	2021	2021	NUM
ejpam-5827	755	8	.	.	PUNCT
ejpam-5827	756	1	[	[	X
ejpam-5827	756	2	28	28	NUM
ejpam-5827	756	3	]	]	X
ejpam-5827	756	4	m.	m.	NOUN
ejpam-5827	756	5	k.	k.	PROPN
ejpam-5827	757	1	el	el	PROPN
ejpam-5827	757	2	-	-	PROPN
ejpam-5827	757	3	bably	bably	PROPN
ejpam-5827	757	4	and	and	CCONJ
ejpam-5827	757	5	m.	m.	NOUN
ejpam-5827	757	6	el	el	PROPN
ejpam-5827	757	7	-	-	PUNCT
ejpam-5827	757	8	sayed	say	VERB
ejpam-5827	757	9	.	.	PUNCT
ejpam-5827	758	1	three	three	NUM
ejpam-5827	758	2	methods	method	NOUN
ejpam-5827	758	3	to	to	PART
ejpam-5827	758	4	generalize	generalize	VERB
ejpam-5827	758	5	pawlak	pawlak	ADJ
ejpam-5827	758	6	approximations	approximation	NOUN
ejpam-5827	758	7	via	via	ADP
ejpam-5827	758	8	simply	simply	ADV
ejpam-5827	758	9	open	open	ADJ
ejpam-5827	758	10	concepts	concept	NOUN
ejpam-5827	758	11	with	with	ADP
ejpam-5827	758	12	economic	economic	ADJ
ejpam-5827	758	13	applications	application	NOUN
ejpam-5827	758	14	.	.	PUNCT
ejpam-5827	759	1	soft	soft	ADJ
ejpam-5827	759	2	comput	comput	NOUN
ejpam-5827	759	3	.	.	PUNCT
ejpam-5827	759	4	,	,	PUNCT
ejpam-5827	759	5	26:4685–4700	26:4685–4700	NUM
ejpam-5827	759	6	,	,	PUNCT
ejpam-5827	759	7	2022	2022	NUM
ejpam-5827	759	8	.	.	PUNCT
ejpam-5827	760	1	[	[	X
ejpam-5827	760	2	29	29	NUM
ejpam-5827	760	3	]	]	PUNCT
ejpam-5827	760	4	m.	m.	NOUN
ejpam-5827	760	5	k.	k.	PROPN
ejpam-5827	761	1	el	el	PROPN
ejpam-5827	761	2	-	-	PROPN
ejpam-5827	761	3	bably	bably	PROPN
ejpam-5827	761	4	and	and	CCONJ
ejpam-5827	761	5	k.	k.	PROPN
ejpam-5827	761	6	k.	k.	PROPN
ejpam-5827	761	7	fleifel	fleifel	PROPN
ejpam-5827	761	8	.	.	PUNCT
ejpam-5827	762	1	some	some	DET
ejpam-5827	762	2	topological	topological	ADJ
ejpam-5827	762	3	structures	structure	NOUN
ejpam-5827	762	4	by	by	ADP
ejpam-5827	762	5	relations	relation	NOUN
ejpam-5827	762	6	.	.	PUNCT
ejpam-5827	763	1	j.	j.	PROPN
ejpam-5827	763	2	comput	comput	PROPN
ejpam-5827	763	3	.	.	PUNCT
ejpam-5827	764	1	theor	theor	PROPN
ejpam-5827	764	2	.	.	PUNCT
ejpam-5827	765	1	nanosci	nanosci	PROPN
ejpam-5827	765	2	.	.	PUNCT
ejpam-5827	765	3	,	,	PUNCT
ejpam-5827	765	4	14(8):4104–4113	14(8):4104–4113	NUM
ejpam-5827	765	5	,	,	PUNCT
ejpam-5827	765	6	2017	2017	NUM
ejpam-5827	765	7	.	.	PUNCT
ejpam-5827	766	1	[	[	X
ejpam-5827	766	2	30	30	NUM
ejpam-5827	766	3	]	]	X
ejpam-5827	766	4	m.	m.	NOUN
ejpam-5827	766	5	a.	a.	PROPN
ejpam-5827	766	6	el	el	PROPN
ejpam-5827	766	7	-	-	PROPN
ejpam-5827	766	8	gayar	gayar	PROPN
ejpam-5827	766	9	and	and	CCONJ
ejpam-5827	766	10	r.	r.	PROPN
ejpam-5827	766	11	abu	abu	PROPN
ejpam-5827	766	12	-	-	PUNCT
ejpam-5827	766	13	gdairi	gdairi	PROPN
ejpam-5827	766	14	.	.	PUNCT
ejpam-5827	767	1	extension	extension	NOUN
ejpam-5827	767	2	of	of	ADP
ejpam-5827	767	3	topological	topological	ADJ
ejpam-5827	767	4	structures	structure	NOUN
ejpam-5827	767	5	using	use	VERB
ejpam-5827	767	6	lattices	lattice	NOUN
ejpam-5827	767	7	and	and	CCONJ
ejpam-5827	767	8	rough	rough	ADJ
ejpam-5827	767	9	sets	set	NOUN
ejpam-5827	767	10	.	.	PUNCT
ejpam-5827	768	1	aims	aim	VERB
ejpam-5827	768	2	math	math	NOUN
ejpam-5827	768	3	.	.	PUNCT
ejpam-5827	768	4	,	,	PUNCT
ejpam-5827	768	5	9(3):7552–7569	9(3):7552–7569	NUM
ejpam-5827	768	6	,	,	PUNCT
ejpam-5827	768	7	2024	2024	NUM
ejpam-5827	768	8	.	.	PUNCT
ejpam-5827	769	1	[	[	X
ejpam-5827	769	2	31	31	NUM
ejpam-5827	769	3	]	]	PUNCT
ejpam-5827	769	4	m.	m.	NOUN
ejpam-5827	769	5	a.	a.	PROPN
ejpam-5827	769	6	el	el	PROPN
ejpam-5827	769	7	-	-	PROPN
ejpam-5827	769	8	gayar	gayar	PROPN
ejpam-5827	769	9	,	,	PUNCT
ejpam-5827	769	10	r.	r.	PROPN
ejpam-5827	769	11	abu	abu	PROPN
ejpam-5827	769	12	-	-	PUNCT
ejpam-5827	769	13	gdairi	gdairi	PROPN
ejpam-5827	769	14	,	,	PUNCT
ejpam-5827	769	15	m.	m.	PROPN
ejpam-5827	769	16	k.	k.	PROPN
ejpam-5827	770	1	el	el	PROPN
ejpam-5827	770	2	-	-	PROPN
ejpam-5827	770	3	bably	bably	ADV
ejpam-5827	770	4	,	,	PUNCT
ejpam-5827	770	5	and	and	CCONJ
ejpam-5827	770	6	d.	d.	PROPN
ejpam-5827	770	7	i.	i.	PROPN
ejpam-5827	770	8	taher	taher	PROPN
ejpam-5827	770	9	.	.	PUNCT
ejpam-5827	771	1	economic	economic	ADJ
ejpam-5827	771	2	decision	decision	NOUN
ejpam-5827	771	3	-	-	PUNCT
ejpam-5827	771	4	making	making	NOUN
ejpam-5827	771	5	using	use	VERB
ejpam-5827	771	6	rough	rough	ADJ
ejpam-5827	771	7	topological	topological	ADJ
ejpam-5827	771	8	structures	structure	NOUN
ejpam-5827	771	9	.	.	PUNCT
ejpam-5827	772	1	j.	j.	PROPN
ejpam-5827	772	2	math	math	PROPN
ejpam-5827	772	3	.	.	PROPN
ejpam-5827	772	4	,	,	PUNCT
ejpam-5827	772	5	2023(4723233):10	2023(4723233):10	NUM
ejpam-5827	772	6	,	,	PUNCT
ejpam-5827	772	7	2023	2023	NUM
ejpam-5827	772	8	.	.	PUNCT
ejpam-5827	773	1	https://doi.org/10.1155/2023/4723233	https://doi.org/10.1155/2023/4723233	PROPN
ejpam-5827	773	2	.	.	PUNCT
ejpam-5827	774	1	[	[	X
ejpam-5827	774	2	32	32	NUM
ejpam-5827	774	3	]	]	PUNCT
ejpam-5827	774	4	m.	m.	NOUN
ejpam-5827	774	5	a.	a.	PROPN
ejpam-5827	774	6	el	el	PROPN
ejpam-5827	774	7	-	-	PROPN
ejpam-5827	774	8	gayar	gayar	PROPN
ejpam-5827	774	9	and	and	CCONJ
ejpam-5827	774	10	a.	a.	PROPN
ejpam-5827	774	11	el	el	PROPN
ejpam-5827	774	12	atik	atik	PROPN
ejpam-5827	774	13	.	.	PUNCT
ejpam-5827	775	1	topological	topological	ADJ
ejpam-5827	775	2	models	model	NOUN
ejpam-5827	775	3	of	of	ADP
ejpam-5827	775	4	rough	rough	ADJ
ejpam-5827	775	5	sets	set	NOUN
ejpam-5827	775	6	and	and	CCONJ
ejpam-5827	775	7	decision	decision	NOUN
ejpam-5827	775	8	making	making	NOUN
ejpam-5827	775	9	of	of	ADP
ejpam-5827	775	10	covid-19	covid-19	PROPN
ejpam-5827	775	11	.	.	PUNCT
ejpam-5827	775	12	complexity	complexity	NOUN
ejpam-5827	775	13	.	.	PUNCT
ejpam-5827	775	14	,	,	PUNCT
ejpam-5827	775	15	2022	2022	NUM
ejpam-5827	775	16	,	,	PUNCT
ejpam-5827	775	17	2022	2022	NUM
ejpam-5827	775	18	.	.	PUNCT
ejpam-5827	776	1	https://doi.org/10.1155/2022/2989236	https://doi.org/10.1155/2022/2989236	PROPN
ejpam-5827	776	2	.	.	PUNCT
ejpam-5827	777	1	[	[	X
ejpam-5827	777	2	33	33	NUM
ejpam-5827	777	3	]	]	PUNCT
ejpam-5827	777	4	m.	m.	PROPN
ejpam-5827	777	5	e.	e.	PROPN
ejpam-5827	777	6	abd	abd	PROPN
ejpam-5827	778	1	el	el	PROPN
ejpam-5827	778	2	-	-	PUNCT
ejpam-5827	778	3	monsef	monsef	ADJ
ejpam-5827	778	4	,	,	PUNCT
ejpam-5827	778	5	m.	m.	NOUN
ejpam-5827	778	6	a.	a.	PROPN
ejpam-5827	778	7	el	el	PROPN
ejpam-5827	778	8	-	-	PROPN
ejpam-5827	778	9	gayar	gayar	NOUN
ejpam-5827	778	10	,	,	PUNCT
ejpam-5827	778	11	and	and	CCONJ
ejpam-5827	778	12	r.	r.	PROPN
ejpam-5827	778	13	m.	m.	PROPN
ejpam-5827	778	14	aqeel	aqeel	PROPN
ejpam-5827	778	15	.	.	PUNCT
ejpam-5827	779	1	on	on	ADP
ejpam-5827	779	2	relationships	relationship	NOUN
ejpam-5827	779	3	between	between	ADP
ejpam-5827	779	4	revised	revise	VERB
ejpam-5827	779	5	rough	rough	ADJ
ejpam-5827	779	6	fuzzy	fuzzy	ADJ
ejpam-5827	779	7	approximation	approximation	NOUN
ejpam-5827	779	8	operators	operator	NOUN
ejpam-5827	779	9	and	and	CCONJ
ejpam-5827	779	10	fuzzy	fuzzy	ADJ
ejpam-5827	779	11	topological	topological	ADJ
ejpam-5827	779	12	spaces	space	NOUN
ejpam-5827	779	13	.	.	PUNCT
ejpam-5827	780	1	int	int	NOUN
ejpam-5827	780	2	.	.	PUNCT
ejpam-5827	781	1	j.	j.	PROPN
ejpam-5827	781	2	granul	granul	PROPN
ejpam-5827	781	3	.	.	PUNCT
ejpam-5827	782	1	comput	comput	NOUN
ejpam-5827	782	2	.	.	PUNCT
ejpam-5827	783	1	rough	rough	ADJ
ejpam-5827	783	2	sets	set	NOUN
ejpam-5827	783	3	intell	intell	PROPN
ejpam-5827	783	4	.	.	PUNCT
ejpam-5827	784	1	syst	syst	PROPN
ejpam-5827	784	2	.	.	PUNCT
ejpam-5827	784	3	,	,	PUNCT
ejpam-5827	784	4	3:257–271	3:257–271	NUM
ejpam-5827	784	5	,	,	PUNCT
ejpam-5827	784	6	2014	2014	NUM
ejpam-5827	784	7	.	.	PUNCT
ejpam-5827	785	1	[	[	X
ejpam-5827	785	2	34	34	NUM
ejpam-5827	785	3	]	]	PUNCT
ejpam-5827	785	4	m.	m.	NOUN
ejpam-5827	785	5	e.	e.	PROPN
ejpam-5827	785	6	abd	abd	PROPN
ejpam-5827	786	1	el	el	PROPN
ejpam-5827	786	2	-	-	PUNCT
ejpam-5827	786	3	monsef	monsef	ADJ
ejpam-5827	786	4	,	,	PUNCT
ejpam-5827	786	5	m.	m.	NOUN
ejpam-5827	786	6	a.	a.	PROPN
ejpam-5827	786	7	el	el	PROPN
ejpam-5827	786	8	-	-	PROPN
ejpam-5827	786	9	gayar	gayar	NOUN
ejpam-5827	786	10	,	,	PUNCT
ejpam-5827	786	11	and	and	CCONJ
ejpam-5827	786	12	r.	r.	PROPN
ejpam-5827	786	13	m.	m.	PROPN
ejpam-5827	786	14	aqeel	aqeel	PROPN
ejpam-5827	786	15	.	.	PUNCT
ejpam-5827	787	1	a	a	DET
ejpam-5827	787	2	comparison	comparison	NOUN
ejpam-5827	787	3	of	of	ADP
ejpam-5827	787	4	three	three	NUM
ejpam-5827	787	5	types	type	NOUN
ejpam-5827	787	6	of	of	ADP
ejpam-5827	787	7	rough	rough	ADJ
ejpam-5827	787	8	fuzzy	fuzzy	ADJ
ejpam-5827	787	9	sets	set	NOUN
ejpam-5827	787	10	based	base	VERB
ejpam-5827	787	11	on	on	ADP
ejpam-5827	787	12	two	two	NUM
ejpam-5827	787	13	universal	universal	ADJ
ejpam-5827	787	14	sets	set	NOUN
ejpam-5827	787	15	.	.	PUNCT
ejpam-5827	788	1	int	int	NOUN
ejpam-5827	788	2	.	.	PUNCT
ejpam-5827	789	1	j.	j.	PROPN
ejpam-5827	789	2	mach	mach	PROPN
ejpam-5827	789	3	.	.	PUNCT
ejpam-5827	790	1	learn	learn	VERB
ejpam-5827	790	2	.	.	PUNCT
ejpam-5827	791	1	cybern	cybern	PROPN
ejpam-5827	791	2	.	.	PROPN
ejpam-5827	791	3	,	,	PUNCT
ejpam-5827	791	4	r.	r.	PROPN
ejpam-5827	791	5	a.	a.	PROPN
ejpam-5827	791	6	hosny	hosny	PROPN
ejpam-5827	791	7	,	,	PUNCT
ejpam-5827	791	8	m.	m.	PROPN
ejpam-5827	791	9	k.	k.	PROPN
ejpam-5827	792	1	el	el	PROPN
ejpam-5827	792	2	-	-	PROPN
ejpam-5827	792	3	bably	bably	ADV
ejpam-5827	792	4	,	,	PUNCT
ejpam-5827	792	5	m.	m.	NOUN
ejpam-5827	792	6	a.	a.	PROPN
ejpam-5827	792	7	el	el	PROPN
ejpam-5827	792	8	-	-	PROPN
ejpam-5827	792	9	gayar	gayar	PROPN
ejpam-5827	792	10	/	/	SYM
ejpam-5827	792	11	eur	eur	PROPN
ejpam-5827	792	12	.	.	PUNCT
ejpam-5827	793	1	j.	j.	PROPN
ejpam-5827	793	2	pure	pure	PROPN
ejpam-5827	793	3	appl	appl	PROPN
ejpam-5827	793	4	.	.	PROPN
ejpam-5827	793	5	math	math	PROPN
ejpam-5827	793	6	,	,	PUNCT
ejpam-5827	793	7	18	18	NUM
ejpam-5827	793	8	(	(	PUNCT
ejpam-5827	793	9	1	1	NUM
ejpam-5827	793	10	)	)	PUNCT
ejpam-5827	793	11	(	(	PUNCT
ejpam-5827	793	12	2025	2025	NUM
ejpam-5827	793	13	)	)	PUNCT
ejpam-5827	793	14	,	,	PUNCT
ejpam-5827	793	15	5827	5827	NUM
ejpam-5827	793	16	27	27	NUM
ejpam-5827	793	17	of	of	ADP
ejpam-5827	793	18	29	29	NUM
ejpam-5827	793	19	8:343–353	8:343–353	NUM
ejpam-5827	793	20	,	,	PUNCT
ejpam-5827	793	21	2017	2017	NUM
ejpam-5827	793	22	.	.	PUNCT
ejpam-5827	794	1	[	[	X
ejpam-5827	794	2	35	35	NUM
ejpam-5827	794	3	]	]	PUNCT
ejpam-5827	794	4	m.	m.	NOUN
ejpam-5827	794	5	e.	e.	PROPN
ejpam-5827	794	6	abd	abd	PROPN
ejpam-5827	795	1	el	el	PROPN
ejpam-5827	795	2	-	-	PROPN
ejpam-5827	795	3	monsef	monsef	ADJ
ejpam-5827	795	4	,	,	PUNCT
ejpam-5827	795	5	o.	o.	PROPN
ejpam-5827	795	6	a.	a.	NOUN
ejpam-5827	795	7	embaby	embaby	PROPN
ejpam-5827	795	8	,	,	PUNCT
ejpam-5827	795	9	and	and	CCONJ
ejpam-5827	795	10	m.	m.	PROPN
ejpam-5827	795	11	k.	k.	PROPN
ejpam-5827	796	1	el	el	PROPN
ejpam-5827	796	2	-	-	PROPN
ejpam-5827	796	3	bably	bably	ADV
ejpam-5827	796	4	.	.	PUNCT
ejpam-5827	797	1	comparison	comparison	NOUN
ejpam-5827	797	2	between	between	ADP
ejpam-5827	797	3	rough	rough	ADJ
ejpam-5827	797	4	set	set	VERB
ejpam-5827	797	5	approximations	approximation	NOUN
ejpam-5827	797	6	based	base	VERB
ejpam-5827	797	7	on	on	ADP
ejpam-5827	797	8	different	different	ADJ
ejpam-5827	797	9	topologies	topology	NOUN
ejpam-5827	797	10	.	.	PUNCT
ejpam-5827	798	1	int	int	NOUN
ejpam-5827	798	2	.	.	PUNCT
ejpam-5827	799	1	j.	j.	PROPN
ejpam-5827	799	2	granul	granul	PROPN
ejpam-5827	799	3	.	.	PUNCT
ejpam-5827	800	1	comput	comput	PROPN
ejpam-5827	800	2	.	.	PUNCT
ejpam-5827	801	1	,	,	PUNCT
ejpam-5827	801	2	rough	rough	ADJ
ejpam-5827	801	3	sets	set	NOUN
ejpam-5827	801	4	intell	intell	PROPN
ejpam-5827	801	5	.	.	PUNCT
ejpam-5827	802	1	syst	syst	PROPN
ejpam-5827	802	2	.	.	PROPN
ejpam-5827	802	3	,	,	PUNCT
ejpam-5827	802	4	3:292–305	3:292–305	NUM
ejpam-5827	802	5	,	,	PUNCT
ejpam-5827	802	6	2014	2014	NUM
ejpam-5827	802	7	.	.	PUNCT
ejpam-5827	803	1	[	[	X
ejpam-5827	803	2	36	36	NUM
ejpam-5827	803	3	]	]	PUNCT
ejpam-5827	803	4	m.	m.	PROPN
ejpam-5827	803	5	e.	e.	PROPN
ejpam-5827	803	6	abd	abd	PROPN
ejpam-5827	804	1	el	el	PROPN
ejpam-5827	804	2	-	-	PROPN
ejpam-5827	804	3	monsef	monsef	ADJ
ejpam-5827	804	4	,	,	PUNCT
ejpam-5827	804	5	a.	a.	NOUN
ejpam-5827	804	6	m.	m.	NOUN
ejpam-5827	804	7	kozae	kozae	PROPN
ejpam-5827	804	8	,	,	PUNCT
ejpam-5827	804	9	and	and	CCONJ
ejpam-5827	805	1	m.	m.	PROPN
ejpam-5827	805	2	k.	k.	PROPN
ejpam-5827	805	3	el	el	PROPN
ejpam-5827	805	4	-	-	PROPN
ejpam-5827	805	5	bably	bably	ADV
ejpam-5827	805	6	.	.	PUNCT
ejpam-5827	806	1	generalized	generalize	VERB
ejpam-5827	806	2	covering	cover	VERB
ejpam-5827	806	3	approximation	approximation	NOUN
ejpam-5827	806	4	space	space	NOUN
ejpam-5827	806	5	and	and	CCONJ
ejpam-5827	806	6	near	near	ADP
ejpam-5827	806	7	concepts	concept	NOUN
ejpam-5827	806	8	with	with	ADP
ejpam-5827	806	9	some	some	DET
ejpam-5827	806	10	applications	application	NOUN
ejpam-5827	806	11	.	.	PUNCT
ejpam-5827	807	1	appl	appl	PROPN
ejpam-5827	807	2	.	.	PUNCT
ejpam-5827	808	1	comput	comput	NOUN
ejpam-5827	808	2	.	.	PUNCT
ejpam-5827	809	1	inform	inform	NOUN
ejpam-5827	809	2	.	.	PUNCT
ejpam-5827	809	3	,	,	PUNCT
ejpam-5827	809	4	12(1):51–69	12(1):51–69	NUM
ejpam-5827	809	5	,	,	PUNCT
ejpam-5827	809	6	2016	2016	NUM
ejpam-5827	809	7	.	.	PUNCT
ejpam-5827	810	1	[	[	X
ejpam-5827	810	2	37	37	NUM
ejpam-5827	810	3	]	]	PUNCT
ejpam-5827	810	4	m.	m.	NOUN
ejpam-5827	810	5	abd	abd	PROPN
ejpam-5827	810	6	elaziz	elaziz	PROPN
ejpam-5827	810	7	,	,	PUNCT
ejpam-5827	810	8	h.	h.	PROPN
ejpam-5827	810	9	m.	m.	PROPN
ejpam-5827	810	10	abu	abu	PROPN
ejpam-5827	810	11	-	-	PUNCT
ejpam-5827	810	12	donia	donia	PROPN
ejpam-5827	810	13	,	,	PUNCT
ejpam-5827	810	14	r.	r.	PROPN
ejpam-5827	810	15	a.	a.	PROPN
ejpam-5827	810	16	hosny	hosny	PROPN
ejpam-5827	810	17	,	,	PUNCT
ejpam-5827	810	18	s.	s.	PROPN
ejpam-5827	810	19	l.	l.	PROPN
ejpam-5827	810	20	hazae	hazae	PROPN
ejpam-5827	810	21	,	,	PUNCT
ejpam-5827	810	22	and	and	CCONJ
ejpam-5827	810	23	r.	r.	PROPN
ejpam-5827	810	24	a.	a.	PROPN
ejpam-5827	810	25	ibrahim	ibrahim	PROPN
ejpam-5827	810	26	.	.	PUNCT
ejpam-5827	810	27	improved	improve	VERB
ejpam-5827	810	28	evolutionary	evolutionary	ADJ
ejpam-5827	810	29	-	-	PUNCT
ejpam-5827	810	30	based	base	VERB
ejpam-5827	810	31	feature	feature	NOUN
ejpam-5827	810	32	selection	selection	NOUN
ejpam-5827	810	33	technique	technique	NOUN
ejpam-5827	810	34	using	use	VERB
ejpam-5827	810	35	extension	extension	NOUN
ejpam-5827	810	36	of	of	ADP
ejpam-5827	810	37	knowledge	knowledge	NOUN
ejpam-5827	810	38	based	base	VERB
ejpam-5827	810	39	on	on	ADP
ejpam-5827	810	40	the	the	DET
ejpam-5827	810	41	rough	rough	ADJ
ejpam-5827	810	42	approximations	approximation	NOUN
ejpam-5827	810	43	.	.	PUNCT
ejpam-5827	811	1	inf	inf	PROPN
ejpam-5827	811	2	.	.	PUNCT
ejpam-5827	812	1	sci	sci	PROPN
ejpam-5827	812	2	.	.	PROPN
ejpam-5827	812	3	,	,	PUNCT
ejpam-5827	812	4	594:76–94	594:76–94	NUM
ejpam-5827	812	5	,	,	PUNCT
ejpam-5827	812	6	2022	2022	NUM
ejpam-5827	812	7	.	.	PUNCT
ejpam-5827	813	1	[	[	X
ejpam-5827	813	2	38	38	NUM
ejpam-5827	813	3	]	]	X
ejpam-5827	813	4	o.	o.	PROPN
ejpam-5827	813	5	a.	a.	NOUN
ejpam-5827	813	6	embaby	embaby	PROPN
ejpam-5827	813	7	and	and	CCONJ
ejpam-5827	813	8	n.	n.	PROPN
ejpam-5827	813	9	toumi	toumi	PROPN
ejpam-5827	813	10	.	.	PUNCT
ejpam-5827	814	1	a	a	DET
ejpam-5827	814	2	method	method	NOUN
ejpam-5827	814	3	for	for	ADP
ejpam-5827	814	4	improving	improve	VERB
ejpam-5827	814	5	rough	rough	ADJ
ejpam-5827	814	6	set	set	NOUN
ejpam-5827	814	7	approximation	approximation	NOUN
ejpam-5827	814	8	accuracy	accuracy	NOUN
ejpam-5827	814	9	in	in	ADP
ejpam-5827	814	10	terms	term	NOUN
ejpam-5827	814	11	of	of	ADP
ejpam-5827	814	12	j	j	PROPN
ejpam-5827	814	13	-	-	PUNCT
ejpam-5827	814	14	neighborhood	neighborhood	NOUN
ejpam-5827	814	15	spaces	space	NOUN
ejpam-5827	814	16	.	.	PUNCT
ejpam-5827	815	1	delta	delta	PROPN
ejpam-5827	815	2	j.	j.	PROPN
ejpam-5827	815	3	sci	sci	PROPN
ejpam-5827	815	4	.	.	PROPN
ejpam-5827	815	5	,	,	PUNCT
ejpam-5827	815	6	38(1):43–52	38(1):43–52	NUM
ejpam-5827	815	7	,	,	PUNCT
ejpam-5827	815	8	2017	2017	NUM
ejpam-5827	815	9	.	.	PUNCT
ejpam-5827	816	1	[	[	X
ejpam-5827	816	2	39	39	NUM
ejpam-5827	816	3	]	]	PUNCT
ejpam-5827	816	4	r.	r.	PROPN
ejpam-5827	816	5	b.	b.	PROPN
ejpam-5827	816	6	esmaeel	esmaeel	PROPN
ejpam-5827	816	7	and	and	CCONJ
ejpam-5827	816	8	m.	m.	NOUN
ejpam-5827	816	9	o.	o.	PROPN
ejpam-5827	816	10	mustafa	mustafa	PROPN
ejpam-5827	816	11	.	.	PUNCT
ejpam-5827	817	1	on	on	ADP
ejpam-5827	817	2	nano	nano	NOUN
ejpam-5827	817	3	topological	topological	ADJ
ejpam-5827	817	4	spaces	space	NOUN
ejpam-5827	817	5	with	with	ADP
ejpam-5827	817	6	grill	grill	ADV
ejpam-5827	817	7	-	-	PUNCT
ejpam-5827	817	8	generalized	generalize	VERB
ejpam-5827	817	9	open	open	ADJ
ejpam-5827	817	10	and	and	CCONJ
ejpam-5827	817	11	closed	closed	ADJ
ejpam-5827	817	12	sets	set	NOUN
ejpam-5827	817	13	.	.	PUNCT
ejpam-5827	818	1	in	in	ADP
ejpam-5827	818	2	aip	aip	PROPN
ejpam-5827	818	3	conf	conf	PROPN
ejpam-5827	818	4	.	.	PUNCT
ejpam-5827	819	1	proc	proc	PROPN
ejpam-5827	819	2	.	.	PROPN
ejpam-5827	819	3	,	,	PUNCT
ejpam-5827	819	4	page	page	NOUN
ejpam-5827	819	5	2414	2414	NUM
ejpam-5827	819	6	,	,	PUNCT
ejpam-5827	819	7	aip	aip	PROPN
ejpam-5827	819	8	conf	conf	PROPN
ejpam-5827	819	9	.	.	PUNCT
ejpam-5827	820	1	proc	proc	PROPN
ejpam-5827	820	2	.	.	PROPN
ejpam-5827	820	3	,	,	PUNCT
ejpam-5827	820	4	2023	2023	NUM
ejpam-5827	820	5	.	.	PUNCT
ejpam-5827	821	1	aip	aip	PROPN
ejpam-5827	821	2	conf	conf	PROPN
ejpam-5827	821	3	.	.	PUNCT
ejpam-5827	822	1	proc	proc	PROPN
ejpam-5827	822	2	.	.	PUNCT
ejpam-5827	823	1	https://doi.org/10.1063/5.0117062	https://doi.org/10.1063/5.0117062	X
ejpam-5827	823	2	.	.	PUNCT
ejpam-5827	824	1	[	[	X
ejpam-5827	824	2	40	40	NUM
ejpam-5827	824	3	]	]	PUNCT
ejpam-5827	824	4	r.	r.	PROPN
ejpam-5827	824	5	b.	b.	PROPN
ejpam-5827	824	6	esmaeel	esmaeel	PROPN
ejpam-5827	824	7	and	and	CCONJ
ejpam-5827	824	8	n.	n.	PROPN
ejpam-5827	824	9	m.	m.	NOUN
ejpam-5827	824	10	shahadhuh	shahadhuh	PROPN
ejpam-5827	824	11	.	.	PUNCT
ejpam-5827	825	1	on	on	ADP
ejpam-5827	825	2	nano	nano	NOUN
ejpam-5827	825	3	topological	topological	ADJ
ejpam-5827	825	4	spaces	space	NOUN
ejpam-5827	825	5	with	with	ADP
ejpam-5827	825	6	grill	grill	ADV
ejpam-5827	825	7	-	-	PUNCT
ejpam-5827	825	8	generalized	generalize	VERB
ejpam-5827	825	9	open	open	ADJ
ejpam-5827	825	10	and	and	CCONJ
ejpam-5827	825	11	closed	closed	ADJ
ejpam-5827	825	12	sets	set	NOUN
ejpam-5827	825	13	on	on	ADP
ejpam-5827	825	14	grill	grill	NOUN
ejpam-5827	825	15	-	-	PUNCT
ejpam-5827	825	16	semi	semi	ADJ
ejpam-5827	825	17	-	-	ADJ
ejpam-5827	825	18	p	p	ADJ
ejpam-5827	825	19	-	-	PUNCT
ejpam-5827	825	20	separation	separation	NOUN
ejpam-5827	825	21	axioms	axiom	NOUN
ejpam-5827	825	22	.	.	PUNCT
ejpam-5827	826	1	in	in	ADP
ejpam-5827	826	2	aip	aip	PROPN
ejpam-5827	826	3	conf	conf	PROPN
ejpam-5827	826	4	.	.	PUNCT
ejpam-5827	827	1	proc	proc	PROPN
ejpam-5827	827	2	.	.	PROPN
ejpam-5827	827	3	,	,	PUNCT
ejpam-5827	827	4	page	page	NOUN
ejpam-5827	827	5	2414	2414	NUM
ejpam-5827	827	6	,	,	PUNCT
ejpam-5827	827	7	aip	aip	PROPN
ejpam-5827	827	8	conf	conf	PROPN
ejpam-5827	827	9	.	.	PUNCT
ejpam-5827	828	1	proc	proc	PROPN
ejpam-5827	828	2	.	.	PROPN
ejpam-5827	828	3	,	,	PUNCT
ejpam-5827	828	4	2023	2023	NUM
ejpam-5827	828	5	.	.	PUNCT
ejpam-5827	829	1	aip	aip	PROPN
ejpam-5827	829	2	conf	conf	PROPN
ejpam-5827	829	3	.	.	PUNCT
ejpam-5827	830	1	proc	proc	PROPN
ejpam-5827	830	2	.	.	PUNCT
ejpam-5827	831	1	https://doi.org/10.1063/5.0117064	https://doi.org/10.1063/5.0117064	NOUN
ejpam-5827	831	2	.	.	PUNCT
ejpam-5827	832	1	[	[	X
ejpam-5827	832	2	41	41	NUM
ejpam-5827	832	3	]	]	PUNCT
ejpam-5827	832	4	m.	m.	PROPN
ejpam-5827	832	5	hosny	hosny	PROPN
ejpam-5827	832	6	.	.	PUNCT
ejpam-5827	833	1	idealization	idealization	NOUN
ejpam-5827	833	2	of	of	ADP
ejpam-5827	833	3	j	j	NOUN
ejpam-5827	833	4	-	-	PUNCT
ejpam-5827	833	5	approximation	approximation	NOUN
ejpam-5827	833	6	spaces	space	NOUN
ejpam-5827	833	7	.	.	PUNCT
ejpam-5827	834	1	filomat	filomat	NOUN
ejpam-5827	834	2	,	,	PUNCT
ejpam-5827	834	3	34(2):287—-301	34(2):287—-301	PROPN
ejpam-5827	834	4	,	,	PUNCT
ejpam-5827	834	5	2020	2020	NUM
ejpam-5827	834	6	.	.	PUNCT
ejpam-5827	835	1	[	[	X
ejpam-5827	835	2	42	42	NUM
ejpam-5827	835	3	]	]	PUNCT
ejpam-5827	835	4	r.	r.	PROPN
ejpam-5827	835	5	a.	a.	PROPN
ejpam-5827	835	6	hosny	hosny	PROPN
ejpam-5827	835	7	,	,	PUNCT
ejpam-5827	835	8	m.	m.	NOUN
ejpam-5827	835	9	abdelaziz	abdelaziz	PROPN
ejpam-5827	835	10	,	,	PUNCT
ejpam-5827	835	11	and	and	CCONJ
ejpam-5827	835	12	r.	r.	PROPN
ejpam-5827	835	13	a.	a.	PROPN
ejpam-5827	835	14	ibrahim	ibrahim	PROPN
ejpam-5827	835	15	.	.	PUNCT
ejpam-5827	836	1	enhanced	enhance	VERB
ejpam-5827	836	2	feature	feature	NOUN
ejpam-5827	836	3	selection	selection	NOUN
ejpam-5827	836	4	based	base	VERB
ejpam-5827	836	5	on	on	ADP
ejpam-5827	836	6	integration	integration	NOUN
ejpam-5827	836	7	containment	containment	NOUN
ejpam-5827	836	8	neighborhoods	neighborhood	NOUN
ejpam-5827	836	9	rough	rough	ADJ
ejpam-5827	836	10	set	set	VERB
ejpam-5827	836	11	approximations	approximation	NOUN
ejpam-5827	836	12	and	and	CCONJ
ejpam-5827	836	13	binary	binary	ADJ
ejpam-5827	836	14	honey	honey	NOUN
ejpam-5827	836	15	badger	badger	PROPN
ejpam-5827	836	16	optimization	optimization	NOUN
ejpam-5827	836	17	.	.	PUNCT
ejpam-5827	837	1	comput	comput	NOUN
ejpam-5827	837	2	.	.	PUNCT
ejpam-5827	838	1	intell	intell	PROPN
ejpam-5827	838	2	.	.	PUNCT
ejpam-5827	839	1	neurosci	neurosci	PROPN
ejpam-5827	839	2	.	.	PUNCT
ejpam-5827	839	3	,	,	PUNCT
ejpam-5827	839	4	2022	2022	NUM
ejpam-5827	839	5	,	,	PUNCT
ejpam-5827	839	6	article	article	NOUN
ejpam-5827	839	7	i	i	NOUN
ejpam-5827	839	8	d	d	PROPN
ejpam-5827	839	9	3991870:17	3991870:17	NUM
ejpam-5827	839	10	pages	page	NOUN
ejpam-5827	839	11	,	,	PUNCT
ejpam-5827	839	12	2022	2022	NUM
ejpam-5827	839	13	.	.	PUNCT
ejpam-5827	840	1	[	[	X
ejpam-5827	840	2	43	43	NUM
ejpam-5827	840	3	]	]	X
ejpam-5827	840	4	r.	r.	PROPN
ejpam-5827	840	5	a.	a.	PROPN
ejpam-5827	840	6	hosny	hosny	PROPN
ejpam-5827	840	7	,	,	PUNCT
ejpam-5827	840	8	r.	r.	PROPN
ejpam-5827	840	9	abu	abu	PROPN
ejpam-5827	840	10	-	-	PUNCT
ejpam-5827	840	11	gdairi	gdairi	PROPN
ejpam-5827	840	12	,	,	PUNCT
ejpam-5827	840	13	and	and	CCONJ
ejpam-5827	840	14	m.	m.	PROPN
ejpam-5827	840	15	k.	k.	PROPN
ejpam-5827	841	1	el	el	PROPN
ejpam-5827	841	2	-	-	PROPN
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ejpam-5827	841	4	.	.	PUNCT
ejpam-5827	842	1	enhancing	enhance	VERB
ejpam-5827	842	2	dengue	dengue	NOUN
ejpam-5827	842	3	fever	fever	NOUN
ejpam-5827	842	4	diagnosis	diagnosis	NOUN
ejpam-5827	842	5	with	with	ADP
ejpam-5827	842	6	generalized	generalized	ADJ
ejpam-5827	842	7	rough	rough	ADJ
ejpam-5827	842	8	sets	set	NOUN
ejpam-5827	842	9	:	:	PUNCT
ejpam-5827	842	10	utilizing	utilize	VERB
ejpam-5827	842	11	initial	initial	ADJ
ejpam-5827	842	12	-	-	PUNCT
ejpam-5827	842	13	neighborhoods	neighborhood	NOUN
ejpam-5827	842	14	and	and	CCONJ
ejpam-5827	842	15	ideals	ideal	NOUN
ejpam-5827	842	16	.	.	PUNCT
ejpam-5827	843	1	alex	alex	PROPN
ejpam-5827	843	2	.	.	PUNCT
ejpam-5827	844	1	eng	eng	PROPN
ejpam-5827	844	2	.	.	PUNCT
ejpam-5827	845	1	j.	j.	PROPN
ejpam-5827	845	2	,	,	PUNCT
ejpam-5827	845	3	94:68–79	94:68–79	PROPN
ejpam-5827	845	4	,	,	PUNCT
ejpam-5827	845	5	2024	2024	NUM
ejpam-5827	845	6	.	.	PUNCT
ejpam-5827	846	1	[	[	X
ejpam-5827	846	2	44	44	NUM
ejpam-5827	846	3	]	]	PUNCT
ejpam-5827	846	4	r.	r.	PROPN
ejpam-5827	846	5	a.	a.	PROPN
ejpam-5827	846	6	hosny	hosny	PROPN
ejpam-5827	846	7	,	,	PUNCT
ejpam-5827	846	8	m.	m.	PROPN
ejpam-5827	846	9	k.	k.	PROPN
ejpam-5827	846	10	el	el	PROPN
ejpam-5827	846	11	-	-	PROPN
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ejpam-5827	846	13	,	,	PUNCT
ejpam-5827	846	14	and	and	CCONJ
ejpam-5827	846	15	a.	a.	PROPN
ejpam-5827	846	16	s.	s.	PROPN
ejpam-5827	846	17	nawar	nawar	PROPN
ejpam-5827	846	18	.	.	PUNCT
ejpam-5827	847	1	some	some	DET
ejpam-5827	847	2	modifications	modification	NOUN
ejpam-5827	847	3	and	and	CCONJ
ejpam-5827	847	4	improvements	improvement	NOUN
ejpam-5827	847	5	to	to	ADP
ejpam-5827	847	6	idealization	idealization	NOUN
ejpam-5827	847	7	of	of	ADP
ejpam-5827	847	8	j	j	NOUN
ejpam-5827	847	9	-	-	PUNCT
ejpam-5827	847	10	approximation	approximation	NOUN
ejpam-5827	847	11	spaces	space	NOUN
ejpam-5827	847	12	.	.	PUNCT
ejpam-5827	848	1	j.	j.	PROPN
ejpam-5827	848	2	adv	adv	PROPN
ejpam-5827	848	3	.	.	PUNCT
ejpam-5827	848	4	stud	stud	PROPN
ejpam-5827	848	5	.	.	PUNCT
ejpam-5827	849	1	topol	topol	PROPN
ejpam-5827	849	2	.	.	PROPN
ejpam-5827	849	3	,	,	PUNCT
ejpam-5827	849	4	1–2:1–7	1–2:1–7	NUM
ejpam-5827	849	5	,	,	PUNCT
ejpam-5827	849	6	2022	2022	NUM
ejpam-5827	849	7	.	.	PUNCT
ejpam-5827	850	1	[	[	X
ejpam-5827	850	2	45	45	NUM
ejpam-5827	850	3	]	]	PUNCT
ejpam-5827	850	4	r.	r.	PROPN
ejpam-5827	850	5	a.	a.	PROPN
ejpam-5827	850	6	hosny	hosny	PROPN
ejpam-5827	850	7	,	,	PUNCT
ejpam-5827	850	8	n.	n.	PROPN
ejpam-5827	850	9	m.	m.	PROPN
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ejpam-5827	850	11	,	,	PUNCT
ejpam-5827	850	12	and	and	CCONJ
ejpam-5827	850	13	m.	m.	PROPN
ejpam-5827	850	14	k.	k.	PROPN
ejpam-5827	851	1	el	el	PROPN
ejpam-5827	851	2	-	-	PROPN
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ejpam-5827	851	4	.	.	PUNCT
ejpam-5827	852	1	essential	essential	ADJ
ejpam-5827	852	2	corrigenda	corrigenda	ADV
ejpam-5827	852	3	to	to	ADP
ejpam-5827	852	4	”	"	PUNCT
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ejpam-5827	852	6	approximation	approximation	NOUN
ejpam-5827	852	7	spaces	space	NOUN
ejpam-5827	852	8	generation	generation	NOUN
ejpam-5827	852	9	from	from	ADP
ejpam-5827	852	10	ij	ij	NOUN
ejpam-5827	852	11	-	-	PUNCT
ejpam-5827	852	12	neighborhoods	neighborhood	NOUN
ejpam-5827	852	13	and	and	CCONJ
ejpam-5827	852	14	ideals	ideal	NOUN
ejpam-5827	852	15	with	with	ADP
ejpam-5827	852	16	application	application	NOUN
ejpam-5827	852	17	to	to	ADP
ejpam-5827	852	18	chikungunya	chikungunya	NOUN
ejpam-5827	852	19	disease	disease	NOUN
ejpam-5827	852	20	”	"	PUNCT
ejpam-5827	852	21	.	.	PUNCT
ejpam-5827	853	1	arxiv	arxiv	PROPN
ejpam-5827	853	2	preprint	preprint	PROPN
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ejpam-5827	853	4	,	,	PUNCT
ejpam-5827	853	5	pages	page	NOUN
ejpam-5827	853	6	1–12	1–12	PROPN
ejpam-5827	853	7	,	,	PUNCT
ejpam-5827	853	8	2024	2024	NUM
ejpam-5827	853	9	.	.	PUNCT
ejpam-5827	854	1	https://doi.org/10.48550/arxiv.2412.05284	https://doi.org/10.48550/arxiv.2412.05284	PROPN
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ejpam-5827	855	1	[	[	X
ejpam-5827	855	2	46	46	NUM
ejpam-5827	855	3	]	]	X
ejpam-5827	855	4	a.	a.	NOUN
ejpam-5827	855	5	kandil	kandil	PROPN
ejpam-5827	855	6	,	,	PUNCT
ejpam-5827	855	7	m.	m.	NOUN
ejpam-5827	855	8	m.	m.	NOUN
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ejpam-5827	855	10	,	,	PUNCT
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ejpam-5827	855	12	a.	a.	NOUN
ejpam-5827	855	13	zakaria	zakaria	PROPN
ejpam-5827	855	14	.	.	PUNCT
ejpam-5827	856	1	generalized	generalize	VERB
ejpam-5827	856	2	rough	rough	ADJ
ejpam-5827	856	3	sets	set	NOUN
ejpam-5827	856	4	via	via	ADP
ejpam-5827	856	5	ideals	ideal	NOUN
ejpam-5827	856	6	.	.	PUNCT
ejpam-5827	857	1	ann	ann	PROPN
ejpam-5827	857	2	.	.	PUNCT
ejpam-5827	857	3	fuzzy	fuzzy	ADJ
ejpam-5827	857	4	math	math	NOUN
ejpam-5827	857	5	.	.	PUNCT
ejpam-5827	858	1	inform	inform	NOUN
ejpam-5827	858	2	.	.	PUNCT
ejpam-5827	858	3	,	,	PUNCT
ejpam-5827	858	4	5(3):525–532	5(3):525–532	PROPN
ejpam-5827	858	5	,	,	PUNCT
ejpam-5827	858	6	2013	2013	NUM
ejpam-5827	858	7	.	.	PUNCT
ejpam-5827	859	1	[	[	X
ejpam-5827	859	2	47	47	NUM
ejpam-5827	859	3	]	]	PUNCT
ejpam-5827	859	4	a.	a.	NOUN
ejpam-5827	859	5	kandil	kandil	PROPN
ejpam-5827	859	6	,	,	PUNCT
ejpam-5827	859	7	m.	m.	NOUN
ejpam-5827	859	8	m.	m.	NOUN
ejpam-5827	859	9	yakout	yakout	PROPN
ejpam-5827	859	10	,	,	PUNCT
ejpam-5827	859	11	and	and	CCONJ
ejpam-5827	859	12	a.	a.	NOUN
ejpam-5827	859	13	zakaria	zakaria	PROPN
ejpam-5827	859	14	.	.	PUNCT
ejpam-5827	860	1	new	new	ADJ
ejpam-5827	860	2	approaches	approach	NOUN
ejpam-5827	860	3	of	of	ADP
ejpam-5827	860	4	rough	rough	ADJ
ejpam-5827	860	5	sets	set	NOUN
ejpam-5827	860	6	via	via	ADP
ejpam-5827	860	7	ideals	ideal	NOUN
ejpam-5827	860	8	.	.	PUNCT
ejpam-5827	861	1	in	in	ADP
ejpam-5827	861	2	handbook	handbook	NOUN
ejpam-5827	861	3	of	of	ADP
ejpam-5827	861	4	research	research	NOUN
ejpam-5827	861	5	on	on	ADP
ejpam-5827	861	6	generalized	generalized	ADJ
ejpam-5827	861	7	and	and	CCONJ
ejpam-5827	861	8	hybrid	hybrid	ADJ
ejpam-5827	861	9	set	set	NOUN
ejpam-5827	861	10	structures	structure	NOUN
ejpam-5827	861	11	and	and	CCONJ
ejpam-5827	861	12	applications	application	NOUN
ejpam-5827	861	13	for	for	ADP
ejpam-5827	861	14	soft	soft	ADJ
ejpam-5827	861	15	computing	computing	NOUN
ejpam-5827	861	16	,	,	PUNCT
ejpam-5827	861	17	pages	page	NOUN
ejpam-5827	861	18	247–264	247–264	NUM
ejpam-5827	861	19	.	.	PUNCT
ejpam-5827	862	1	igi	igi	PROPN
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ejpam-5827	862	3	,	,	PUNCT
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ejpam-5827	862	5	.	.	PUNCT
ejpam-5827	863	1	[	[	X
ejpam-5827	863	2	48	48	NUM
ejpam-5827	863	3	]	]	PUNCT
ejpam-5827	863	4	a.	a.	NOUN
ejpam-5827	863	5	a.	a.	NOUN
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ejpam-5827	863	9	m.	m.	PROPN
ejpam-5827	863	10	k.	k.	PROPN
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ejpam-5827	863	12	-	-	PROPN
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ejpam-5827	863	14	.	.	PUNCT
ejpam-5827	864	1	topological	topological	ADJ
ejpam-5827	864	2	approach	approach	NOUN
ejpam-5827	864	3	to	to	ADP
ejpam-5827	864	4	tolerance	tolerance	NOUN
ejpam-5827	864	5	space	space	NOUN
ejpam-5827	864	6	.	.	PUNCT
ejpam-5827	865	1	alex	alex	PROPN
ejpam-5827	865	2	.	.	PUNCT
ejpam-5827	866	1	eng	eng	PROPN
ejpam-5827	866	2	.	.	PUNCT
ejpam-5827	867	1	j.	j.	PROPN
ejpam-5827	867	2	,	,	PUNCT
ejpam-5827	867	3	47(6):575–580	47(6):575–580	NOUN
ejpam-5827	867	4	,	,	PUNCT
ejpam-5827	867	5	2008	2008	NUM
ejpam-5827	867	6	.	.	PUNCT
ejpam-5827	868	1	[	[	X
ejpam-5827	868	2	49	49	NUM
ejpam-5827	868	3	]	]	PUNCT
ejpam-5827	868	4	a.	a.	NOUN
ejpam-5827	868	5	a.	a.	NOUN
ejpam-5827	868	6	abo	abo	PROPN
ejpam-5827	868	7	khadra	khadra	PROPN
ejpam-5827	868	8	,	,	PUNCT
ejpam-5827	868	9	b.	b.	PROPN
ejpam-5827	868	10	m.	m.	PROPN
ejpam-5827	868	11	taher	taher	PROPN
ejpam-5827	868	12	,	,	PUNCT
ejpam-5827	868	13	and	and	CCONJ
ejpam-5827	868	14	m.	m.	PROPN
ejpam-5827	868	15	k.	k.	PROPN
ejpam-5827	869	1	el	el	PROPN
ejpam-5827	869	2	-	-	PROPN
ejpam-5827	869	3	bably	bably	ADV
ejpam-5827	869	4	.	.	PUNCT
ejpam-5827	870	1	generalization	generalization	NOUN
ejpam-5827	870	2	of	of	ADP
ejpam-5827	870	3	pawlak	pawlak	ADJ
ejpam-5827	870	4	approximation	approximation	NOUN
ejpam-5827	870	5	space	space	NOUN
ejpam-5827	870	6	.	.	PUNCT
ejpam-5827	871	1	in	in	ADP
ejpam-5827	871	2	proceeding	proceeding	NOUN
ejpam-5827	871	3	of	of	ADP
ejpam-5827	871	4	the	the	DET
ejpam-5827	871	5	international	international	ADJ
ejpam-5827	871	6	conference	conference	NOUN
ejpam-5827	871	7	on	on	ADP
ejpam-5827	871	8	mathematics	mathematic	NOUN
ejpam-5827	871	9	:	:	PUNCT
ejpam-5827	871	10	trends	trend	NOUN
ejpam-5827	871	11	and	and	CCONJ
ejpam-5827	871	12	developments	development	NOUN
ejpam-5827	871	13	,	,	PUNCT
ejpam-5827	871	14	the	the	DET
ejpam-5827	871	15	egyptian	egyptian	PROPN
ejpam-5827	871	16	mathematical	mathematical	ADJ
ejpam-5827	871	17	society	society	NOUN
ejpam-5827	871	18	,	,	PUNCT
ejpam-5827	871	19	volume	volume	NOUN
ejpam-5827	871	20	3	3	NUM
ejpam-5827	871	21	,	,	PUNCT
ejpam-5827	871	22	pages	page	NOUN
ejpam-5827	871	23	335	335	NUM
ejpam-5827	871	24	–	–	PUNCT
ejpam-5827	871	25	r.	r.	PROPN
ejpam-5827	871	26	a.	a.	PROPN
ejpam-5827	871	27	hosny	hosny	PROPN
ejpam-5827	871	28	,	,	PUNCT
ejpam-5827	871	29	m.	m.	PROPN
ejpam-5827	871	30	k.	k.	PROPN
ejpam-5827	872	1	el	el	PROPN
ejpam-5827	872	2	-	-	PROPN
ejpam-5827	872	3	bably	bably	ADV
ejpam-5827	872	4	,	,	PUNCT
ejpam-5827	872	5	m.	m.	NOUN
ejpam-5827	872	6	a.	a.	PROPN
ejpam-5827	872	7	el	el	PROPN
ejpam-5827	872	8	-	-	PROPN
ejpam-5827	872	9	gayar	gayar	PROPN
ejpam-5827	872	10	/	/	SYM
ejpam-5827	872	11	eur	eur	PROPN
ejpam-5827	872	12	.	.	PUNCT
ejpam-5827	873	1	j.	j.	PROPN
ejpam-5827	873	2	pure	pure	PROPN
ejpam-5827	873	3	appl	appl	PROPN
ejpam-5827	873	4	.	.	PROPN
ejpam-5827	873	5	math	math	PROPN
ejpam-5827	873	6	,	,	PUNCT
ejpam-5827	873	7	18	18	NUM
ejpam-5827	873	8	(	(	PUNCT
ejpam-5827	873	9	1	1	NUM
ejpam-5827	873	10	)	)	PUNCT
ejpam-5827	873	11	(	(	PUNCT
ejpam-5827	873	12	2025	2025	NUM
ejpam-5827	873	13	)	)	PUNCT
ejpam-5827	873	14	,	,	PUNCT
ejpam-5827	873	15	5827	5827	NUM
ejpam-5827	873	16	28	28	NUM
ejpam-5827	873	17	of	of	ADP
ejpam-5827	873	18	29	29	NUM
ejpam-5827	873	19	346	346	NUM
ejpam-5827	873	20	,	,	PUNCT
ejpam-5827	873	21	2007	2007	NUM
ejpam-5827	873	22	.	.	PUNCT
ejpam-5827	874	1	[	[	X
ejpam-5827	874	2	50	50	NUM
ejpam-5827	874	3	]	]	PUNCT
ejpam-5827	874	4	m.	m.	NOUN
ejpam-5827	874	5	kondo	kondo	PROPN
ejpam-5827	874	6	and	and	CCONJ
ejpam-5827	874	7	w.	w.	PROPN
ejpam-5827	874	8	a.	a.	PROPN
ejpam-5827	874	9	dudek	dudek	PROPN
ejpam-5827	874	10	.	.	PUNCT
ejpam-5827	875	1	topological	topological	ADJ
ejpam-5827	875	2	structures	structure	NOUN
ejpam-5827	875	3	of	of	ADP
ejpam-5827	875	4	rough	rough	ADJ
ejpam-5827	875	5	sets	set	NOUN
ejpam-5827	875	6	induced	induce	VERB
ejpam-5827	875	7	by	by	ADP
ejpam-5827	875	8	equivalence	equivalence	NOUN
ejpam-5827	875	9	relations	relation	NOUN
ejpam-5827	875	10	.	.	PUNCT
ejpam-5827	876	1	j.	j.	PROPN
ejpam-5827	876	2	adv	adv	PROPN
ejpam-5827	876	3	.	.	PUNCT
ejpam-5827	877	1	comput	comput	PROPN
ejpam-5827	877	2	.	.	PUNCT
ejpam-5827	878	1	intell	intell	PROPN
ejpam-5827	878	2	.	.	PUNCT
ejpam-5827	879	1	intell	intell	PROPN
ejpam-5827	879	2	.	.	PUNCT
ejpam-5827	880	1	inform	inform	NOUN
ejpam-5827	880	2	.	.	PUNCT
ejpam-5827	880	3	,	,	PUNCT
ejpam-5827	880	4	10(5):621–624	10(5):621–624	NUM
ejpam-5827	880	5	,	,	PUNCT
ejpam-5827	880	6	2006	2006	NUM
ejpam-5827	880	7	.	.	PUNCT
ejpam-5827	881	1	[	[	X
ejpam-5827	881	2	51	51	NUM
ejpam-5827	881	3	]	]	PUNCT
ejpam-5827	881	4	a.	a.	NOUN
ejpam-5827	881	5	m.	m.	NOUN
ejpam-5827	881	6	kozae	kozae	PROPN
ejpam-5827	881	7	,	,	PUNCT
ejpam-5827	881	8	m.	m.	NOUN
ejpam-5827	881	9	shokry	shokry	PROPN
ejpam-5827	881	10	,	,	PUNCT
ejpam-5827	881	11	and	and	CCONJ
ejpam-5827	881	12	m.	m.	PROPN
ejpam-5827	881	13	zidan	zidan	PROPN
ejpam-5827	881	14	.	.	PUNCT
ejpam-5827	882	1	supra	supra	PROPN
ejpam-5827	882	2	topologies	topology	NOUN
ejpam-5827	882	3	for	for	ADP
ejpam-5827	882	4	digital	digital	ADJ
ejpam-5827	882	5	plane	plane	NOUN
ejpam-5827	882	6	.	.	PUNCT
ejpam-5827	883	1	aascit	aascit	PROPN
ejpam-5827	883	2	commun	commun	PROPN
ejpam-5827	883	3	.	.	PROPN
ejpam-5827	883	4	,	,	PUNCT
ejpam-5827	883	5	3(1):1–10	3(1):1–10	NUM
ejpam-5827	883	6	,	,	PUNCT
ejpam-5827	883	7	2016	2016	NUM
ejpam-5827	883	8	.	.	PUNCT
ejpam-5827	884	1	[	[	X
ejpam-5827	884	2	52	52	NUM
ejpam-5827	884	3	]	]	PUNCT
ejpam-5827	884	4	k.	k.	PROPN
ejpam-5827	884	5	kuratowski	kuratowski	PROPN
ejpam-5827	884	6	.	.	PUNCT
ejpam-5827	885	1	topology	topology	NOUN
ejpam-5827	885	2	:	:	PUNCT
ejpam-5827	885	3	volume	volume	NOUN
ejpam-5827	885	4	i.	i.	PROPN
ejpam-5827	885	5	dordrecht	dordrecht	PROPN
ejpam-5827	885	6	,	,	PUNCT
ejpam-5827	885	7	new	new	PROPN
ejpam-5827	885	8	york	york	PROPN
ejpam-5827	885	9	,	,	PUNCT
ejpam-5827	885	10	1966	1966	NUM
ejpam-5827	885	11	.	.	PUNCT
ejpam-5827	886	1	[	[	X
ejpam-5827	886	2	53	53	NUM
ejpam-5827	886	3	]	]	PUNCT
ejpam-5827	886	4	e.	e.	PROPN
ejpam-5827	886	5	f.	f.	PROPN
ejpam-5827	886	6	lashin	lashin	PROPN
ejpam-5827	886	7	,	,	PUNCT
ejpam-5827	886	8	a.	a.	NOUN
ejpam-5827	886	9	m.	m.	NOUN
ejpam-5827	886	10	kozae	kozae	PROPN
ejpam-5827	886	11	,	,	PUNCT
ejpam-5827	886	12	a.	a.	NOUN
ejpam-5827	886	13	a.	a.	NOUN
ejpam-5827	886	14	abo	abo	PROPN
ejpam-5827	886	15	khadra	khadra	NOUN
ejpam-5827	886	16	,	,	PUNCT
ejpam-5827	886	17	and	and	CCONJ
ejpam-5827	886	18	t.	t.	PROPN
ejpam-5827	886	19	medhat	medhat	PROPN
ejpam-5827	886	20	.	.	PUNCT
ejpam-5827	887	1	rough	rough	ADJ
ejpam-5827	887	2	set	set	NOUN
ejpam-5827	887	3	theory	theory	NOUN
ejpam-5827	887	4	for	for	ADP
ejpam-5827	887	5	topological	topological	ADJ
ejpam-5827	887	6	spaces	space	NOUN
ejpam-5827	887	7	.	.	PUNCT
ejpam-5827	888	1	int	int	NOUN
ejpam-5827	888	2	.	.	PUNCT
ejpam-5827	889	1	j.	j.	PROPN
ejpam-5827	889	2	approx	approx	PROPN
ejpam-5827	889	3	.	.	PUNCT
ejpam-5827	890	1	reason	reason	NOUN
ejpam-5827	890	2	.	.	PUNCT
ejpam-5827	890	3	,	,	PUNCT
ejpam-5827	890	4	40:35–43	40:35–43	NUM
ejpam-5827	890	5	,	,	PUNCT
ejpam-5827	890	6	2005	2005	NUM
ejpam-5827	890	7	.	.	PUNCT
ejpam-5827	891	1	[	[	X
ejpam-5827	891	2	54	54	NUM
ejpam-5827	891	3	]	]	X
ejpam-5827	891	4	h.	h.	PROPN
ejpam-5827	891	5	lu	lu	PROPN
ejpam-5827	891	6	,	,	PUNCT
ejpam-5827	891	7	a.	a.	PROPN
ejpam-5827	891	8	m.	m.	PROPN
ejpam-5827	891	9	khalil	khalil	PROPN
ejpam-5827	891	10	,	,	PUNCT
ejpam-5827	891	11	w.d	w.d	PROPN
ejpam-5827	891	12	.	.	PROPN
ejpam-5827	891	13	alharbi	alharbi	PROPN
ejpam-5827	891	14	,	,	PUNCT
ejpam-5827	891	15	and	and	CCONJ
ejpam-5827	891	16	m.	m.	PROPN
ejpam-5827	891	17	a.	a.	PROPN
ejpam-5827	891	18	el	el	PROPN
ejpam-5827	891	19	-	-	PROPN
ejpam-5827	891	20	gayar	gayar	NOUN
ejpam-5827	891	21	.	.	PUNCT
ejpam-5827	892	1	a	a	DET
ejpam-5827	892	2	new	new	ADJ
ejpam-5827	892	3	type	type	NOUN
ejpam-5827	892	4	of	of	ADP
ejpam-5827	892	5	generalized	generalized	ADJ
ejpam-5827	892	6	picture	picture	NOUN
ejpam-5827	892	7	fuzzy	fuzzy	ADJ
ejpam-5827	892	8	soft	soft	ADJ
ejpam-5827	892	9	set	set	NOUN
ejpam-5827	892	10	and	and	CCONJ
ejpam-5827	892	11	its	its	PRON
ejpam-5827	892	12	application	application	NOUN
ejpam-5827	892	13	in	in	ADP
ejpam-5827	892	14	decision	decision	NOUN
ejpam-5827	892	15	making	making	NOUN
ejpam-5827	892	16	.	.	PUNCT
ejpam-5827	893	1	j.	j.	PROPN
ejpam-5827	893	2	intell	intell	PROPN
ejpam-5827	893	3	.	.	PUNCT
ejpam-5827	894	1	fuzzy	fuzzy	ADJ
ejpam-5827	894	2	syst	syst	PROPN
ejpam-5827	894	3	.	.	PUNCT
ejpam-5827	894	4	,	,	PUNCT
ejpam-5827	894	5	40:12459–12475	40:12459–12475	PROPN
ejpam-5827	894	6	,	,	PUNCT
ejpam-5827	894	7	2021	2021	NUM
ejpam-5827	894	8	.	.	PUNCT
ejpam-5827	895	1	[	[	X
ejpam-5827	895	2	55	55	NUM
ejpam-5827	895	3	]	]	PUNCT
ejpam-5827	895	4	h.	h.	PROPN
ejpam-5827	895	5	maki	maki	PROPN
ejpam-5827	895	6	,	,	PUNCT
ejpam-5827	895	7	j.	j.	PROPN
ejpam-5827	895	8	umehara	umehara	PROPN
ejpam-5827	895	9	,	,	PUNCT
ejpam-5827	895	10	and	and	CCONJ
ejpam-5827	895	11	t.	t.	PROPN
ejpam-5827	895	12	noiri	noiri	PROPN
ejpam-5827	895	13	.	.	PUNCT
ejpam-5827	896	1	every	every	DET
ejpam-5827	896	2	topological	topological	ADJ
ejpam-5827	896	3	space	space	NOUN
ejpam-5827	896	4	is	be	AUX
ejpam-5827	896	5	pret12	pret12	NOUN
ejpam-5827	896	6	.	.	PUNCT
ejpam-5827	897	1	mem	mem	PROPN
ejpam-5827	897	2	.	.	PUNCT
ejpam-5827	897	3	fac	fac	PROPN
ejpam-5827	897	4	.	.	PUNCT
ejpam-5827	897	5	sci	sci	PROPN
ejpam-5827	897	6	.	.	PROPN
ejpam-5827	897	7	kochi	kochi	PROPN
ejpam-5827	897	8	univ	univ	PROPN
ejpam-5827	897	9	.	.	PUNCT
ejpam-5827	897	10	ser	ser	PROPN
ejpam-5827	897	11	.	.	PUNCT
ejpam-5827	898	1	a	a	DET
ejpam-5827	898	2	math	math	NOUN
ejpam-5827	898	3	.	.	PUNCT
ejpam-5827	898	4	,	,	PUNCT
ejpam-5827	898	5	17:33–42	17:33–42	PROPN
ejpam-5827	898	6	,	,	PUNCT
ejpam-5827	898	7	1996	1996	NUM
ejpam-5827	898	8	.	.	PUNCT
ejpam-5827	899	1	[	[	X
ejpam-5827	899	2	56	56	NUM
ejpam-5827	899	3	]	]	PUNCT
ejpam-5827	899	4	a.	a.	NOUN
ejpam-5827	899	5	s.	s.	PROPN
ejpam-5827	899	6	mashhour	mashhour	PROPN
ejpam-5827	899	7	.	.	PUNCT
ejpam-5827	900	1	on	on	ADP
ejpam-5827	900	2	supratopological	supratopological	ADJ
ejpam-5827	900	3	spaces	space	NOUN
ejpam-5827	900	4	.	.	PUNCT
ejpam-5827	901	1	indian	indian	PROPN
ejpam-5827	901	2	j.	j.	PROPN
ejpam-5827	901	3	pure	pure	PROPN
ejpam-5827	901	4	appl	appl	PROPN
ejpam-5827	901	5	.	.	PUNCT
ejpam-5827	901	6	math	math	PROPN
ejpam-5827	901	7	.	.	PUNCT
ejpam-5827	901	8	,	,	PUNCT
ejpam-5827	901	9	14:502–510	14:502–510	NUM
ejpam-5827	901	10	,	,	PUNCT
ejpam-5827	901	11	1983	1983	NUM
ejpam-5827	901	12	.	.	PUNCT
ejpam-5827	902	1	[	[	X
ejpam-5827	902	2	57	57	NUM
ejpam-5827	902	3	]	]	PUNCT
ejpam-5827	902	4	s.	s.	PROPN
ejpam-5827	902	5	y.	y.	PROPN
ejpam-5827	902	6	musa	musa	PROPN
ejpam-5827	902	7	and	and	CCONJ
ejpam-5827	902	8	b.	b.	PROPN
ejpam-5827	902	9	a.	a.	PROPN
ejpam-5827	902	10	asaad	asaad	PROPN
ejpam-5827	902	11	.	.	PUNCT
ejpam-5827	903	1	bipolar	bipolar	ADJ
ejpam-5827	903	2	m	m	ADJ
ejpam-5827	903	3	-	-	PUNCT
ejpam-5827	903	4	parametrized	parametrized	ADJ
ejpam-5827	903	5	n	n	CCONJ
ejpam-5827	903	6	-	-	PUNCT
ejpam-5827	903	7	soft	soft	ADJ
ejpam-5827	903	8	sets	set	NOUN
ejpam-5827	903	9	:	:	PUNCT
ejpam-5827	903	10	a	a	DET
ejpam-5827	903	11	gateway	gateway	NOUN
ejpam-5827	903	12	to	to	PART
ejpam-5827	903	13	informed	informed	VERB
ejpam-5827	903	14	decision	decision	NOUN
ejpam-5827	903	15	-	-	PUNCT
ejpam-5827	903	16	making	making	NOUN
ejpam-5827	903	17	.	.	PUNCT
ejpam-5827	904	1	j.	j.	PROPN
ejpam-5827	904	2	math	math	PROPN
ejpam-5827	904	3	.	.	PUNCT
ejpam-5827	905	1	comput	comput	NOUN
ejpam-5827	905	2	.	.	PUNCT
ejpam-5827	906	1	sci	sci	PROPN
ejpam-5827	906	2	.	.	PROPN
ejpam-5827	906	3	,	,	PUNCT
ejpam-5827	906	4	36(1):121–141	36(1):121–141	NUM
ejpam-5827	906	5	,	,	PUNCT
ejpam-5827	906	6	2025	2025	NUM
ejpam-5827	906	7	.	.	PUNCT
ejpam-5827	907	1	[	[	X
ejpam-5827	907	2	58	58	NUM
ejpam-5827	907	3	]	]	PUNCT
ejpam-5827	907	4	a.	a.	PROPN
ejpam-5827	907	5	s.	s.	PROPN
ejpam-5827	907	6	nawar	nawar	PROPN
ejpam-5827	907	7	,	,	PUNCT
ejpam-5827	907	8	m.a	m.a	PROPN
ejpam-5827	907	9	.	.	PROPN
ejpam-5827	907	10	el	el	PROPN
ejpam-5827	907	11	-	-	PUNCT
ejpam-5827	907	12	gayar	gayar	PROPN
ejpam-5827	907	13	,	,	PUNCT
ejpam-5827	907	14	m.	m.	NOUN
ejpam-5827	907	15	k.	k.	PROPN
ejpam-5827	908	1	el	el	PROPN
ejpam-5827	908	2	-	-	PROPN
ejpam-5827	908	3	bably	bably	ADV
ejpam-5827	908	4	,	,	PUNCT
ejpam-5827	908	5	and	and	CCONJ
ejpam-5827	908	6	r.	r.	PROPN
ejpam-5827	908	7	a.	a.	PROPN
ejpam-5827	908	8	hosny	hosny	PROPN
ejpam-5827	908	9	.	.	PUNCT
ejpam-5827	909	1	θβ	θβ	NOUN
ejpam-5827	909	2	-	-	PUNCT
ejpam-5827	909	3	ideal	ideal	NOUN
ejpam-5827	909	4	approximation	approximation	NOUN
ejpam-5827	909	5	spaces	space	NOUN
ejpam-5827	909	6	and	and	CCONJ
ejpam-5827	909	7	their	their	PRON
ejpam-5827	909	8	applications	application	NOUN
ejpam-5827	909	9	.	.	PUNCT
ejpam-5827	910	1	aims	aim	VERB
ejpam-5827	910	2	mathematics	mathematic	NOUN
ejpam-5827	910	3	.	.	PUNCT
ejpam-5827	910	4	,	,	PUNCT
ejpam-5827	911	1	7(2):2479–2497	7(2):2479–2497	NUM
ejpam-5827	911	2	,	,	PUNCT
ejpam-5827	911	3	2022	2022	NUM
ejpam-5827	911	4	.	.	PUNCT
ejpam-5827	912	1	[	[	X
ejpam-5827	912	2	59	59	NUM
ejpam-5827	912	3	]	]	PUNCT
ejpam-5827	912	4	z.	z.	PROPN
ejpam-5827	912	5	pawlak	pawlak	PROPN
ejpam-5827	912	6	.	.	PUNCT
ejpam-5827	913	1	rough	rough	ADJ
ejpam-5827	913	2	sets	set	NOUN
ejpam-5827	913	3	.	.	PUNCT
ejpam-5827	914	1	int	int	NOUN
ejpam-5827	914	2	.	.	PUNCT
ejpam-5827	915	1	j.	j.	PROPN
ejpam-5827	915	2	inform	inform	PROPN
ejpam-5827	915	3	.	.	PUNCT
ejpam-5827	916	1	comput	comput	NOUN
ejpam-5827	916	2	.	.	PUNCT
ejpam-5827	917	1	sci	sci	PROPN
ejpam-5827	917	2	.	.	PROPN
ejpam-5827	917	3	,	,	PUNCT
ejpam-5827	917	4	11:341–356	11:341–356	NUM
ejpam-5827	917	5	,	,	PUNCT
ejpam-5827	917	6	1982	1982	NUM
ejpam-5827	917	7	.	.	PUNCT
ejpam-5827	918	1	[	[	X
ejpam-5827	918	2	60	60	NUM
ejpam-5827	918	3	]	]	PUNCT
ejpam-5827	918	4	k.	k.	PROPN
ejpam-5827	918	5	qin	qin	PROPN
ejpam-5827	918	6	,	,	PUNCT
ejpam-5827	918	7	j.	j.	PROPN
ejpam-5827	918	8	yang	yang	PROPN
ejpam-5827	918	9	,	,	PUNCT
ejpam-5827	918	10	and	and	CCONJ
ejpam-5827	918	11	z.	z.	PROPN
ejpam-5827	918	12	pei	pei	PROPN
ejpam-5827	918	13	.	.	PROPN
ejpam-5827	919	1	generalized	generalize	VERB
ejpam-5827	919	2	rough	rough	ADJ
ejpam-5827	919	3	sets	set	NOUN
ejpam-5827	919	4	based	base	VERB
ejpam-5827	919	5	on	on	ADP
ejpam-5827	919	6	reflexive	reflexive	ADJ
ejpam-5827	919	7	and	and	CCONJ
ejpam-5827	919	8	transitive	transitive	ADJ
ejpam-5827	919	9	relations	relation	NOUN
ejpam-5827	919	10	.	.	PUNCT
ejpam-5827	920	1	inf	inf	PROPN
ejpam-5827	920	2	.	.	PUNCT
ejpam-5827	921	1	sci	sci	PROPN
ejpam-5827	921	2	.	.	PROPN
ejpam-5827	921	3	,	,	PUNCT
ejpam-5827	921	4	178:4138–4141	178:4138–4141	NUM
ejpam-5827	921	5	,	,	PUNCT
ejpam-5827	921	6	2008	2008	NUM
ejpam-5827	921	7	.	.	PUNCT
ejpam-5827	922	1	[	[	X
ejpam-5827	922	2	61	61	NUM
ejpam-5827	922	3	]	]	PUNCT
ejpam-5827	922	4	s.	s.	PROPN
ejpam-5827	922	5	saleh	saleh	PROPN
ejpam-5827	922	6	,	,	PUNCT
ejpam-5827	922	7	l.	l.	PROPN
ejpam-5827	922	8	r.	r.	PROPN
ejpam-5827	922	9	flaih	flaih	PROPN
ejpam-5827	922	10	,	,	PUNCT
ejpam-5827	922	11	and	and	CCONJ
ejpam-5827	922	12	k.	k.	PROPN
ejpam-5827	922	13	f.	f.	PROPN
ejpam-5827	922	14	jasim	jasim	PROPN
ejpam-5827	922	15	.	.	PUNCT
ejpam-5827	923	1	some	some	DET
ejpam-5827	923	2	applications	application	NOUN
ejpam-5827	923	3	of	of	ADP
ejpam-5827	923	4	soft∂-closed	soft∂-closed	ADJ
ejpam-5827	923	5	sets	set	NOUN
ejpam-5827	923	6	in	in	ADP
ejpam-5827	923	7	soft	soft	ADJ
ejpam-5827	923	8	closure	closure	NOUN
ejpam-5827	923	9	spaces	space	NOUN
ejpam-5827	923	10	.	.	PUNCT
ejpam-5827	924	1	commun	commun	PROPN
ejpam-5827	924	2	.	.	PUNCT
ejpam-5827	925	1	math	math	PROPN
ejpam-5827	925	2	.	.	PUNCT
ejpam-5827	926	1	appl	appl	PROPN
ejpam-5827	926	2	.	.	PROPN
ejpam-5827	926	3	,	,	PUNCT
ejpam-5827	926	4	14(2):481–492	14(2):481–492	PROPN
ejpam-5827	926	5	,	,	PUNCT
ejpam-5827	926	6	2023	2023	NUM
ejpam-5827	926	7	.	.	PUNCT
ejpam-5827	927	1	[	[	X
ejpam-5827	927	2	62	62	NUM
ejpam-5827	927	3	]	]	PUNCT
ejpam-5827	927	4	m.	m.	NOUN
ejpam-5827	927	5	el	el	PROPN
ejpam-5827	927	6	sayed	say	VERB
ejpam-5827	927	7	,	,	PUNCT
ejpam-5827	927	8	m.	m.	NOUN
ejpam-5827	927	9	a.	a.	PROPN
ejpam-5827	927	10	el	el	PROPN
ejpam-5827	927	11	safty	safty	PROPN
ejpam-5827	927	12	,	,	PUNCT
ejpam-5827	927	13	and	and	CCONJ
ejpam-5827	927	14	m.	m.	PROPN
ejpam-5827	927	15	k.	k.	PROPN
ejpam-5827	928	1	el	el	PROPN
ejpam-5827	928	2	-	-	PROPN
ejpam-5827	928	3	bably	bably	ADV
ejpam-5827	928	4	.	.	PUNCT
ejpam-5827	929	1	topological	topological	ADJ
ejpam-5827	929	2	approach	approach	NOUN
ejpam-5827	929	3	for	for	ADP
ejpam-5827	929	4	decisionmaking	decisionmake	VERB
ejpam-5827	929	5	of	of	ADP
ejpam-5827	929	6	covid-19	covid-19	PROPN
ejpam-5827	929	7	infection	infection	NOUN
ejpam-5827	929	8	via	via	ADP
ejpam-5827	929	9	a	a	DET
ejpam-5827	929	10	nano	nano	NOUN
ejpam-5827	929	11	-	-	PUNCT
ejpam-5827	929	12	topology	topology	NOUN
ejpam-5827	929	13	model	model	NOUN
ejpam-5827	929	14	.	.	PUNCT
ejpam-5827	930	1	aims	aim	VERB
ejpam-5827	930	2	math	math	NOUN
ejpam-5827	930	3	.	.	PUNCT
ejpam-5827	930	4	,	,	PUNCT
ejpam-5827	930	5	6:7872–7894	6:7872–7894	NUM
ejpam-5827	930	6	,	,	PUNCT
ejpam-5827	930	7	2021	2021	NUM
ejpam-5827	930	8	.	.	PUNCT
ejpam-5827	931	1	[	[	X
ejpam-5827	931	2	63	63	NUM
ejpam-5827	931	3	]	]	PUNCT
ejpam-5827	931	4	t.	t.	PROPN
ejpam-5827	931	5	k.	k.	PROPN
ejpam-5827	931	6	sheeja	sheeja	PROPN
ejpam-5827	931	7	and	and	CCONJ
ejpam-5827	931	8	s.	s.	PROPN
ejpam-5827	931	9	kuriakose	kuriakose	PROPN
ejpam-5827	931	10	.	.	PUNCT
ejpam-5827	932	1	rough	rough	ADJ
ejpam-5827	932	2	topology	topology	NOUN
ejpam-5827	932	3	on	on	ADP
ejpam-5827	932	4	approximation	approximation	NOUN
ejpam-5827	932	5	spaces	space	NOUN
ejpam-5827	932	6	.	.	PUNCT
ejpam-5827	933	1	int	int	NOUN
ejpam-5827	933	2	.	.	PUNCT
ejpam-5827	934	1	j.	j.	PROPN
ejpam-5827	934	2	adv	adv	PROPN
ejpam-5827	934	3	.	.	PUNCT
ejpam-5827	935	1	res	re	NOUN
ejpam-5827	935	2	.	.	PUNCT
ejpam-5827	936	1	comput	comput	PROPN
ejpam-5827	936	2	.	.	PUNCT
ejpam-5827	937	1	sci	sci	PROPN
ejpam-5827	937	2	.	.	PROPN
ejpam-5827	937	3	,	,	PUNCT
ejpam-5827	937	4	8(9	8(9	NUM
ejpam-5827	937	5	)	)	PUNCT
ejpam-5827	937	6	,	,	PUNCT
ejpam-5827	937	7	2017	2017	NUM
ejpam-5827	937	8	.	.	PUNCT
ejpam-5827	938	1	https://doi.org/10.26483/ijarcs.v8i9.5028	https://doi.org/10.26483/ijarcs.v8i9.5028	ADJ
ejpam-5827	938	2	.	.	PUNCT
ejpam-5827	939	1	[	[	X
ejpam-5827	939	2	64	64	NUM
ejpam-5827	939	3	]	]	PUNCT
ejpam-5827	940	1	p.	p.	NOUN
ejpam-5827	940	2	k.	k.	PROPN
ejpam-5827	941	1	singh	singh	PROPN
ejpam-5827	941	2	and	and	CCONJ
ejpam-5827	941	3	s.	s.	PROPN
ejpam-5827	941	4	tiwari	tiwari	PROPN
ejpam-5827	941	5	.	.	PUNCT
ejpam-5827	942	1	topological	topological	ADJ
ejpam-5827	942	2	structures	structure	NOUN
ejpam-5827	942	3	in	in	ADP
ejpam-5827	942	4	rough	rough	ADJ
ejpam-5827	942	5	set	set	NOUN
ejpam-5827	942	6	theory	theory	NOUN
ejpam-5827	942	7	a	a	DET
ejpam-5827	942	8	survey	survey	NOUN
ejpam-5827	942	9	.	.	PUNCT
ejpam-5827	943	1	hacet	hacet	PROPN
ejpam-5827	943	2	.	.	PUNCT
ejpam-5827	944	1	j.	j.	PROPN
ejpam-5827	944	2	math	math	PROPN
ejpam-5827	944	3	.	.	PUNCT
ejpam-5827	945	1	stat	stat	PROPN
ejpam-5827	945	2	.	.	PUNCT
ejpam-5827	945	3	,	,	PUNCT
ejpam-5827	945	4	49(4):1270–1294	49(4):1270–1294	NUM
ejpam-5827	945	5	,	,	PUNCT
ejpam-5827	945	6	2020	2020	NUM
ejpam-5827	945	7	.	.	PUNCT
ejpam-5827	946	1	[	[	X
ejpam-5827	946	2	65	65	NUM
ejpam-5827	946	3	]	]	X
ejpam-5827	946	4	a.	a.	NOUN
ejpam-5827	946	5	skowron	skowron	PROPN
ejpam-5827	946	6	.	.	PUNCT
ejpam-5827	947	1	on	on	ADP
ejpam-5827	947	2	topology	topology	NOUN
ejpam-5827	947	3	in	in	ADP
ejpam-5827	947	4	information	information	NOUN
ejpam-5827	947	5	system	system	NOUN
ejpam-5827	947	6	.	.	PUNCT
ejpam-5827	948	1	bull	bull	NOUN
ejpam-5827	948	2	.	.	PUNCT
ejpam-5827	949	1	pol	pol	PROPN
ejpam-5827	949	2	.	.	PUNCT
ejpam-5827	950	1	acad	acad	PROPN
ejpam-5827	950	2	.	.	PUNCT
ejpam-5827	951	1	sci	sci	PROPN
ejpam-5827	951	2	.	.	PROPN
ejpam-5827	951	3	math	math	PROPN
ejpam-5827	951	4	.	.	PUNCT
ejpam-5827	951	5	,	,	PUNCT
ejpam-5827	951	6	36:477	36:477	NUM
ejpam-5827	951	7	–	–	PUNCT
ejpam-5827	951	8	480	480	NUM
ejpam-5827	951	9	,	,	PUNCT
ejpam-5827	951	10	1988	1988	NUM
ejpam-5827	951	11	.	.	PUNCT
ejpam-5827	952	1	[	[	X
ejpam-5827	952	2	66	66	NUM
ejpam-5827	952	3	]	]	PUNCT
ejpam-5827	952	4	a.	a.	NOUN
ejpam-5827	952	5	skowron	skowron	NOUN
ejpam-5827	952	6	and	and	CCONJ
ejpam-5827	952	7	j.	j.	PROPN
ejpam-5827	952	8	stepaniuk	stepaniuk	PROPN
ejpam-5827	952	9	.	.	PUNCT
ejpam-5827	953	1	tolerance	tolerance	NOUN
ejpam-5827	953	2	approximation	approximation	NOUN
ejpam-5827	953	3	spaces	space	NOUN
ejpam-5827	953	4	.	.	PUNCT
ejpam-5827	954	1	fundam	fundam	ADJ
ejpam-5827	954	2	.	.	PUNCT
ejpam-5827	954	3	inform	inform	NOUN
ejpam-5827	954	4	.	.	PUNCT
ejpam-5827	954	5	,	,	PUNCT
ejpam-5827	954	6	27(2):245–253	27(2):245–253	PROPN
ejpam-5827	954	7	,	,	PUNCT
ejpam-5827	954	8	1996	1996	NUM
ejpam-5827	954	9	.	.	PUNCT
ejpam-5827	955	1	[	[	X
ejpam-5827	955	2	67	67	NUM
ejpam-5827	955	3	]	]	X
ejpam-5827	955	4	r.	r.	PROPN
ejpam-5827	955	5	slowinski	slowinski	PROPN
ejpam-5827	955	6	and	and	CCONJ
ejpam-5827	955	7	d.	d.	PROPN
ejpam-5827	955	8	vanderpooten	vanderpooten	NOUN
ejpam-5827	955	9	.	.	PUNCT
ejpam-5827	956	1	a	a	DET
ejpam-5827	956	2	generalized	generalized	ADJ
ejpam-5827	956	3	definition	definition	NOUN
ejpam-5827	956	4	of	of	ADP
ejpam-5827	956	5	rough	rough	ADJ
ejpam-5827	956	6	approximations	approximation	NOUN
ejpam-5827	956	7	based	base	VERB
ejpam-5827	956	8	on	on	ADP
ejpam-5827	956	9	similarity	similarity	NOUN
ejpam-5827	956	10	.	.	PUNCT
ejpam-5827	957	1	ieee	ieee	PROPN
ejpam-5827	957	2	trans	trans	PROPN
ejpam-5827	957	3	.	.	PROPN
ejpam-5827	958	1	knowl	knowl	PROPN
ejpam-5827	958	2	.	.	PUNCT
ejpam-5827	959	1	data	data	PROPN
ejpam-5827	959	2	eng	eng	PROPN
ejpam-5827	959	3	.	.	PROPN
ejpam-5827	959	4	,	,	PUNCT
ejpam-5827	959	5	12(2):331–336	12(2):331–336	PROPN
ejpam-5827	959	6	,	,	PUNCT
ejpam-5827	959	7	2000	2000	NUM
ejpam-5827	959	8	.	.	PUNCT
ejpam-5827	960	1	[	[	X
ejpam-5827	960	2	68	68	NUM
ejpam-5827	960	3	]	]	PUNCT
ejpam-5827	960	4	i.	i.	PROPN
ejpam-5827	960	5	m.	m.	PROPN
ejpam-5827	960	6	taha	taha	PROPN
ejpam-5827	960	7	.	.	PUNCT
ejpam-5827	961	1	some	some	DET
ejpam-5827	961	2	new	new	ADJ
ejpam-5827	961	3	separation	separation	NOUN
ejpam-5827	961	4	axioms	axiom	VERB
ejpam-5827	961	5	in	in	ADP
ejpam-5827	961	6	fuzzy	fuzzy	ADJ
ejpam-5827	961	7	soft	soft	ADJ
ejpam-5827	961	8	topological	topological	ADJ
ejpam-5827	961	9	spaces	space	NOUN
ejpam-5827	961	10	.	.	PUNCT
ejpam-5827	962	1	filomat	filomat	PROPN
ejpam-5827	962	2	.	.	PROPN
ejpam-5827	962	3	,	,	PUNCT
ejpam-5827	962	4	35(6):1775–1783	35(6):1775–1783	NOUN
ejpam-5827	962	5	,	,	PUNCT
ejpam-5827	962	6	2021	2021	NUM
ejpam-5827	962	7	.	.	PUNCT
ejpam-5827	963	1	[	[	X
ejpam-5827	963	2	69	69	NUM
ejpam-5827	963	3	]	]	PUNCT
ejpam-5827	963	4	i.	i.	PROPN
ejpam-5827	963	5	m.	m.	PROPN
ejpam-5827	963	6	taha	taha	PROPN
ejpam-5827	963	7	.	.	PUNCT
ejpam-5827	964	1	some	some	DET
ejpam-5827	964	2	new	new	ADJ
ejpam-5827	964	3	results	result	NOUN
ejpam-5827	964	4	on	on	ADP
ejpam-5827	964	5	fuzzy	fuzzy	ADJ
ejpam-5827	964	6	soft	soft	ADJ
ejpam-5827	964	7	r	r	NOUN
ejpam-5827	964	8	-	-	PUNCT
ejpam-5827	964	9	minimal	minimal	ADJ
ejpam-5827	964	10	spaces	space	NOUN
ejpam-5827	964	11	.	.	PUNCT
ejpam-5827	965	1	aims	aim	VERB
ejpam-5827	965	2	mathematics	mathematic	NOUN
ejpam-5827	965	3	.	.	PUNCT
ejpam-5827	965	4	,	,	PUNCT
ejpam-5827	966	1	7(7):12458–12470	7(7):12458–12470	PROPN
ejpam-5827	966	2	,	,	PUNCT
ejpam-5827	966	3	2022	2022	NUM
ejpam-5827	966	4	.	.	PUNCT
ejpam-5827	967	1	[	[	X
ejpam-5827	967	2	70	70	NUM
ejpam-5827	967	3	]	]	X
ejpam-5827	967	4	i.	i.	PROPN
ejpam-5827	967	5	m.	m.	PROPN
ejpam-5827	967	6	taha	taha	PROPN
ejpam-5827	967	7	.	.	PUNCT
ejpam-5827	968	1	some	some	DET
ejpam-5827	968	2	properties	property	NOUN
ejpam-5827	968	3	of	of	ADP
ejpam-5827	968	4	(	(	PUNCT
ejpam-5827	968	5	r	r	NOUN
ejpam-5827	968	6	,	,	PUNCT
ejpam-5827	968	7	s)-generalized	s)-generalized	ADJ
ejpam-5827	968	8	fuzzy	fuzzy	ADJ
ejpam-5827	968	9	semi	semi	ADJ
ejpam-5827	968	10	-	-	ADJ
ejpam-5827	968	11	closed	closed	ADJ
ejpam-5827	968	12	sets	set	NOUN
ejpam-5827	968	13	and	and	CCONJ
ejpam-5827	968	14	some	some	DET
ejpam-5827	968	15	applications	application	NOUN
ejpam-5827	968	16	.	.	PUNCT
ejpam-5827	969	1	j.	j.	PROPN
ejpam-5827	969	2	math	math	PROPN
ejpam-5827	969	3	.	.	PUNCT
ejpam-5827	970	1	comput	comput	NOUN
ejpam-5827	970	2	.	.	PUNCT
ejpam-5827	971	1	sci	sci	PROPN
ejpam-5827	971	2	.	.	PROPN
ejpam-5827	971	3	,	,	PUNCT
ejpam-5827	971	4	27(2):164–175	27(2):164–175	PROPN
ejpam-5827	971	5	,	,	PUNCT
ejpam-5827	971	6	2022	2022	NUM
ejpam-5827	971	7	.	.	PUNCT
ejpam-5827	972	1	r.	r.	PROPN
ejpam-5827	972	2	a.	a.	PROPN
ejpam-5827	972	3	hosny	hosny	PROPN
ejpam-5827	972	4	,	,	PUNCT
ejpam-5827	972	5	m.	m.	PROPN
ejpam-5827	972	6	k.	k.	PROPN
ejpam-5827	973	1	el	el	PROPN
ejpam-5827	973	2	-	-	PROPN
ejpam-5827	973	3	bably	bably	ADV
ejpam-5827	973	4	,	,	PUNCT
ejpam-5827	973	5	m.	m.	NOUN
ejpam-5827	973	6	a.	a.	PROPN
ejpam-5827	973	7	el	el	PROPN
ejpam-5827	973	8	-	-	PROPN
ejpam-5827	973	9	gayar	gayar	PROPN
ejpam-5827	973	10	/	/	SYM
ejpam-5827	973	11	eur	eur	PROPN
ejpam-5827	973	12	.	.	PUNCT
ejpam-5827	974	1	j.	j.	PROPN
ejpam-5827	974	2	pure	pure	PROPN
ejpam-5827	974	3	appl	appl	PROPN
ejpam-5827	974	4	.	.	PROPN
ejpam-5827	974	5	math	math	PROPN
ejpam-5827	974	6	,	,	PUNCT
ejpam-5827	974	7	18	18	NUM
ejpam-5827	974	8	(	(	PUNCT
ejpam-5827	974	9	1	1	NUM
ejpam-5827	974	10	)	)	PUNCT
ejpam-5827	974	11	(	(	PUNCT
ejpam-5827	974	12	2025	2025	NUM
ejpam-5827	974	13	)	)	PUNCT
ejpam-5827	974	14	,	,	PUNCT
ejpam-5827	974	15	5827	5827	NUM
ejpam-5827	974	16	29	29	NUM
ejpam-5827	974	17	of	of	ADP
ejpam-5827	974	18	29	29	NUM
ejpam-5827	974	19	[	[	SYM
ejpam-5827	974	20	71	71	NUM
ejpam-5827	974	21	]	]	X
ejpam-5827	974	22	d.	d.	PROPN
ejpam-5827	974	23	i.	i.	PROPN
ejpam-5827	974	24	taher	taher	PROPN
ejpam-5827	974	25	,	,	PUNCT
ejpam-5827	974	26	r.	r.	PROPN
ejpam-5827	974	27	abu	abu	PROPN
ejpam-5827	974	28	-	-	PUNCT
ejpam-5827	974	29	gdairi	gdairi	PROPN
ejpam-5827	974	30	,	,	PUNCT
ejpam-5827	974	31	m.	m.	PROPN
ejpam-5827	974	32	k.	k.	PROPN
ejpam-5827	975	1	el	el	PROPN
ejpam-5827	975	2	-	-	PROPN
ejpam-5827	975	3	bably	bably	ADV
ejpam-5827	975	4	,	,	PUNCT
ejpam-5827	975	5	and	and	CCONJ
ejpam-5827	975	6	m.	m.	PROPN
ejpam-5827	975	7	a.	a.	PROPN
ejpam-5827	975	8	el	el	PROPN
ejpam-5827	975	9	-	-	PUNCT
ejpam-5827	975	10	gayar	gayar	NOUN
ejpam-5827	975	11	.	.	PUNCT
ejpam-5827	976	1	correction	correction	NOUN
ejpam-5827	976	2	:	:	PUNCT
ejpam-5827	976	3	decision	decision	NOUN
ejpam-5827	976	4	-	-	PUNCT
ejpam-5827	976	5	making	making	NOUN
ejpam-5827	976	6	in	in	ADP
ejpam-5827	976	7	diagnosing	diagnose	VERB
ejpam-5827	976	8	heart	heart	NOUN
ejpam-5827	976	9	failure	failure	NOUN
ejpam-5827	976	10	problems	problem	NOUN
ejpam-5827	976	11	using	use	VERB
ejpam-5827	976	12	basic	basic	ADJ
ejpam-5827	976	13	rough	rough	ADJ
ejpam-5827	976	14	sets	set	NOUN
ejpam-5827	976	15	.	.	PUNCT
ejpam-5827	977	1	aims	aim	VERB
ejpam-5827	977	2	math	math	NOUN
ejpam-5827	977	3	.	.	PUNCT
ejpam-5827	977	4	,	,	PUNCT
ejpam-5827	977	5	9(12):34270–34271	9(12):34270–34271	NUM
ejpam-5827	977	6	,	,	PUNCT
ejpam-5827	977	7	2024	2024	NUM
ejpam-5827	977	8	.	.	PUNCT
ejpam-5827	978	1	[	[	X
ejpam-5827	978	2	72	72	NUM
ejpam-5827	978	3	]	]	X
ejpam-5827	978	4	d.	d.	PROPN
ejpam-5827	978	5	i.	i.	PROPN
ejpam-5827	978	6	taher	taher	PROPN
ejpam-5827	978	7	,	,	PUNCT
ejpam-5827	978	8	r.	r.	PROPN
ejpam-5827	978	9	abu	abu	PROPN
ejpam-5827	978	10	-	-	PUNCT
ejpam-5827	978	11	gdairi	gdairi	PROPN
ejpam-5827	978	12	,	,	PUNCT
ejpam-5827	978	13	m.	m.	PROPN
ejpam-5827	978	14	k.	k.	PROPN
ejpam-5827	979	1	el	el	PROPN
ejpam-5827	979	2	-	-	PROPN
ejpam-5827	979	3	bably	bably	ADV
ejpam-5827	979	4	,	,	PUNCT
ejpam-5827	979	5	and	and	CCONJ
ejpam-5827	979	6	m.	m.	PROPN
ejpam-5827	979	7	a.	a.	PROPN
ejpam-5827	979	8	el	el	PROPN
ejpam-5827	979	9	-	-	PUNCT
ejpam-5827	979	10	gayar	gayar	NOUN
ejpam-5827	979	11	.	.	PUNCT
ejpam-5827	980	1	decision	decision	NOUN
ejpam-5827	980	2	-	-	PUNCT
ejpam-5827	980	3	making	making	NOUN
ejpam-5827	980	4	in	in	ADP
ejpam-5827	980	5	diagnosing	diagnose	VERB
ejpam-5827	980	6	heart	heart	NOUN
ejpam-5827	980	7	failure	failure	NOUN
ejpam-5827	980	8	problems	problem	NOUN
ejpam-5827	980	9	using	use	VERB
ejpam-5827	980	10	basic	basic	ADJ
ejpam-5827	980	11	rough	rough	ADJ
ejpam-5827	980	12	sets	set	NOUN
ejpam-5827	980	13	.	.	PUNCT
ejpam-5827	981	1	aims	aim	VERB
ejpam-5827	981	2	math	math	NOUN
ejpam-5827	981	3	.	.	PUNCT
ejpam-5827	981	4	,	,	PUNCT
ejpam-5827	981	5	9(8):21816	9(8):21816	NUM
ejpam-5827	981	6	–	–	PUNCT
ejpam-5827	981	7	21847	21847	NUM
ejpam-5827	981	8	,	,	PUNCT
ejpam-5827	981	9	2024	2024	NUM
ejpam-5827	981	10	.	.	PUNCT
ejpam-5827	982	1	[	[	X
ejpam-5827	982	2	73	73	NUM
ejpam-5827	982	3	]	]	X
ejpam-5827	982	4	y.	y.	PROPN
ejpam-5827	982	5	y.	y.	PROPN
ejpam-5827	982	6	yao	yao	PROPN
ejpam-5827	982	7	.	.	PUNCT
ejpam-5827	983	1	two	two	NUM
ejpam-5827	983	2	views	view	NOUN
ejpam-5827	983	3	of	of	ADP
ejpam-5827	983	4	the	the	DET
ejpam-5827	983	5	theory	theory	NOUN
ejpam-5827	983	6	of	of	ADP
ejpam-5827	983	7	rough	rough	ADJ
ejpam-5827	983	8	sets	set	NOUN
ejpam-5827	983	9	in	in	ADP
ejpam-5827	983	10	finite	finite	ADJ
ejpam-5827	983	11	universes	universe	NOUN
ejpam-5827	983	12	.	.	PUNCT
ejpam-5827	984	1	int	int	NOUN
ejpam-5827	984	2	.	.	PUNCT
ejpam-5827	985	1	j.	j.	PROPN
ejpam-5827	985	2	approx	approx	PROPN
ejpam-5827	985	3	.	.	PUNCT
ejpam-5827	986	1	reason	reason	NOUN
ejpam-5827	986	2	.	.	PUNCT
ejpam-5827	986	3	,	,	PUNCT
ejpam-5827	986	4	15(4):291–317	15(4):291–317	NUM
ejpam-5827	986	5	,	,	PUNCT
ejpam-5827	986	6	1996	1996	NUM
ejpam-5827	986	7	.	.	PUNCT
ejpam-5827	987	1	[	[	X
ejpam-5827	987	2	74	74	NUM
ejpam-5827	987	3	]	]	PUNCT
ejpam-5827	987	4	w.	w.	PROPN
ejpam-5827	987	5	zhu	zhu	PROPN
ejpam-5827	987	6	.	.	PUNCT
ejpam-5827	988	1	topological	topological	ADJ
ejpam-5827	988	2	approaches	approach	NOUN
ejpam-5827	988	3	to	to	ADP
ejpam-5827	988	4	covering	cover	VERB
ejpam-5827	988	5	rough	rough	ADJ
ejpam-5827	988	6	sets	set	NOUN
ejpam-5827	988	7	.	.	PUNCT
ejpam-5827	989	1	inf	inf	PROPN
ejpam-5827	989	2	.	.	PUNCT
ejpam-5827	990	1	sci	sci	PROPN
ejpam-5827	990	2	.	.	PROPN
ejpam-5827	990	3	,	,	PUNCT
ejpam-5827	990	4	177(6):1499–1508	177(6):1499–1508	NUM
ejpam-5827	990	5	,	,	PUNCT
ejpam-5827	990	6	2007	2007	NUM
ejpam-5827	990	7	.	.	PUNCT