id	sid	tid	token	lemma	pos
ejpam-5392	1	1	european	european	PROPN
ejpam-5392	1	2	journal	journal	PROPN
ejpam-5392	1	3	of	of	ADP
ejpam-5392	1	4	pure	pure	ADJ
ejpam-5392	1	5	and	and	CCONJ
ejpam-5392	1	6	applied	apply	VERB
ejpam-5392	1	7	mathematics	mathematic	NOUN
ejpam-5392	1	8	vol	vol	NOUN
ejpam-5392	1	9	.	.	PROPN
ejpam-5392	2	1	17	17	NUM
ejpam-5392	2	2	,	,	PUNCT
ejpam-5392	2	3	no	no	INTJ
ejpam-5392	2	4	.	.	NOUN
ejpam-5392	2	5	4	4	NUM
ejpam-5392	2	6	,	,	PUNCT
ejpam-5392	2	7	2024	2024	NUM
ejpam-5392	2	8	,	,	PUNCT
ejpam-5392	2	9	3436	3436	NUM
ejpam-5392	2	10	-	-	SYM
ejpam-5392	2	11	3463	3463	NUM
ejpam-5392	2	12	issn	issn	PROPN
ejpam-5392	2	13	1307	1307	NUM
ejpam-5392	2	14	-	-	SYM
ejpam-5392	2	15	5543	5543	NUM
ejpam-5392	2	16	–	–	PUNCT
ejpam-5392	2	17	ejpam.com	ejpam.com	X
ejpam-5392	2	18	published	publish	VERB
ejpam-5392	2	19	by	by	ADP
ejpam-5392	2	20	new	new	PROPN
ejpam-5392	2	21	york	york	PROPN
ejpam-5392	2	22	business	business	PROPN
ejpam-5392	2	23	global	global	ADJ
ejpam-5392	2	24	employing	employ	VERB
ejpam-5392	2	25	a	a	DET
ejpam-5392	2	26	generalization	generalization	NOUN
ejpam-5392	2	27	of	of	ADP
ejpam-5392	2	28	open	open	ADJ
ejpam-5392	2	29	sets	set	NOUN
ejpam-5392	2	30	defined	define	VERB
ejpam-5392	2	31	by	by	ADP
ejpam-5392	2	32	ideals	ideal	NOUN
ejpam-5392	2	33	to	to	PART
ejpam-5392	2	34	initiate	initiate	VERB
ejpam-5392	2	35	novel	novel	ADJ
ejpam-5392	2	36	rough	rough	ADJ
ejpam-5392	2	37	approximation	approximation	NOUN
ejpam-5392	2	38	spaces	space	NOUN
ejpam-5392	2	39	with	with	ADP
ejpam-5392	2	40	a	a	DET
ejpam-5392	2	41	chemical	chemical	NOUN
ejpam-5392	2	42	application	application	NOUN
ejpam-5392	2	43	m.	m.	NOUN
ejpam-5392	2	44	hosny1,2	hosny1,2	PROPN
ejpam-5392	2	45	,	,	PUNCT
ejpam-5392	2	46	tareq	tareq	PROPN
ejpam-5392	2	47	m.	m.	PROPN
ejpam-5392	2	48	al	al	PROPN
ejpam-5392	2	49	-	-	PUNCT
ejpam-5392	2	50	shami3,4,∗	shami3,4,∗	ADJ
ejpam-5392	2	51	1	1	NUM
ejpam-5392	2	52	department	department	NOUN
ejpam-5392	2	53	of	of	ADP
ejpam-5392	2	54	mathematics	mathematic	NOUN
ejpam-5392	2	55	,	,	PUNCT
ejpam-5392	2	56	college	college	NOUN
ejpam-5392	2	57	of	of	ADP
ejpam-5392	2	58	science	science	NOUN
ejpam-5392	2	59	,	,	PUNCT
ejpam-5392	2	60	king	king	PROPN
ejpam-5392	2	61	khalid	khalid	PROPN
ejpam-5392	2	62	university	university	PROPN
ejpam-5392	2	63	,	,	PUNCT
ejpam-5392	2	64	abha	abha	NOUN
ejpam-5392	2	65	,	,	PUNCT
ejpam-5392	2	66	61413	61413	NUM
ejpam-5392	2	67	,	,	PUNCT
ejpam-5392	2	68	saudi	saudi	PROPN
ejpam-5392	2	69	arabia	arabia	PROPN
ejpam-5392	2	70	2	2	NUM
ejpam-5392	2	71	department	department	NOUN
ejpam-5392	2	72	of	of	ADP
ejpam-5392	2	73	mathematics	mathematic	NOUN
ejpam-5392	2	74	,	,	PUNCT
ejpam-5392	2	75	faculty	faculty	NOUN
ejpam-5392	2	76	of	of	ADP
ejpam-5392	2	77	education	education	NOUN
ejpam-5392	2	78	,	,	PUNCT
ejpam-5392	2	79	ain	ain	PROPN
ejpam-5392	2	80	shams	shams	PROPN
ejpam-5392	2	81	university	university	PROPN
ejpam-5392	2	82	,	,	PUNCT
ejpam-5392	2	83	roxy	roxy	PROPN
ejpam-5392	2	84	11341	11341	NUM
ejpam-5392	2	85	,	,	PUNCT
ejpam-5392	2	86	cairo	cairo	PROPN
ejpam-5392	2	87	,	,	PUNCT
ejpam-5392	2	88	egypt	egypt	PROPN
ejpam-5392	2	89	3	3	NUM
ejpam-5392	2	90	department	department	NOUN
ejpam-5392	2	91	of	of	ADP
ejpam-5392	2	92	engineering	engineering	NOUN
ejpam-5392	2	93	mathematics	mathematics	PROPN
ejpam-5392	2	94	&	&	CCONJ
ejpam-5392	2	95	physics	physics	PROPN
ejpam-5392	2	96	,	,	PUNCT
ejpam-5392	2	97	faculty	faculty	NOUN
ejpam-5392	2	98	of	of	ADP
ejpam-5392	2	99	engineering	engineering	NOUN
ejpam-5392	2	100	&	&	CCONJ
ejpam-5392	2	101	technology	technology	PROPN
ejpam-5392	2	102	,	,	PUNCT
ejpam-5392	2	103	future	future	ADJ
ejpam-5392	2	104	university	university	NOUN
ejpam-5392	2	105	,	,	PUNCT
ejpam-5392	2	106	new	new	ADJ
ejpam-5392	2	107	cairo	cairo	PROPN
ejpam-5392	2	108	,	,	PUNCT
ejpam-5392	2	109	egypt	egypt	PROPN
ejpam-5392	2	110	4	4	NUM
ejpam-5392	2	111	jadara	jadara	PROPN
ejpam-5392	2	112	university	university	PROPN
ejpam-5392	2	113	research	research	NOUN
ejpam-5392	2	114	center	center	NOUN
ejpam-5392	2	115	,	,	PUNCT
ejpam-5392	2	116	jadara	jadara	PROPN
ejpam-5392	2	117	university	university	PROPN
ejpam-5392	2	118	,	,	PUNCT
ejpam-5392	2	119	jordan	jordan	PROPN
ejpam-5392	2	120	abstract	abstract	PROPN
ejpam-5392	2	121	.	.	PUNCT
ejpam-5392	3	1	a	a	DET
ejpam-5392	3	2	close	close	ADJ
ejpam-5392	3	3	similarity	similarity	NOUN
ejpam-5392	3	4	and	and	CCONJ
ejpam-5392	3	5	analogy	analogy	NOUN
ejpam-5392	3	6	between	between	ADP
ejpam-5392	3	7	rough	rough	ADJ
ejpam-5392	3	8	set	set	NOUN
ejpam-5392	3	9	theory	theory	NOUN
ejpam-5392	3	10	and	and	CCONJ
ejpam-5392	3	11	topology	topology	NOUN
ejpam-5392	3	12	is	be	AUX
ejpam-5392	3	13	attributed	attribute	VERB
ejpam-5392	3	14	to	to	ADP
ejpam-5392	3	15	the	the	DET
ejpam-5392	3	16	corresponding	corresponding	ADJ
ejpam-5392	3	17	behavior	behavior	NOUN
ejpam-5392	3	18	of	of	ADP
ejpam-5392	3	19	lower	low	ADJ
ejpam-5392	3	20	and	and	CCONJ
ejpam-5392	3	21	upper	upper	ADJ
ejpam-5392	3	22	rough	rough	ADJ
ejpam-5392	3	23	approximations	approximation	NOUN
ejpam-5392	3	24	with	with	ADP
ejpam-5392	3	25	interior	interior	ADJ
ejpam-5392	3	26	and	and	CCONJ
ejpam-5392	3	27	closure	closure	NOUN
ejpam-5392	3	28	topological	topological	ADJ
ejpam-5392	3	29	operators	operator	NOUN
ejpam-5392	3	30	,	,	PUNCT
ejpam-5392	3	31	respectively	respectively	ADV
ejpam-5392	3	32	.	.	PUNCT
ejpam-5392	4	1	this	this	DET
ejpam-5392	4	2	relation	relation	NOUN
ejpam-5392	4	3	motivates	motivate	VERB
ejpam-5392	4	4	joint	joint	ADJ
ejpam-5392	4	5	studies	study	NOUN
ejpam-5392	4	6	between	between	ADP
ejpam-5392	4	7	topology	topology	NOUN
ejpam-5392	4	8	and	and	CCONJ
ejpam-5392	4	9	this	this	DET
ejpam-5392	4	10	theory	theory	NOUN
ejpam-5392	4	11	.	.	PUNCT
ejpam-5392	5	1	we	we	PRON
ejpam-5392	5	2	endeavor	endeavor	VERB
ejpam-5392	5	3	by	by	ADP
ejpam-5392	5	4	rough	rough	ADJ
ejpam-5392	5	5	set	set	NOUN
ejpam-5392	5	6	theory	theory	NOUN
ejpam-5392	5	7	to	to	PART
ejpam-5392	5	8	enlarge	enlarge	VERB
ejpam-5392	5	9	the	the	DET
ejpam-5392	5	10	knowledge	knowledge	NOUN
ejpam-5392	5	11	we	we	PRON
ejpam-5392	5	12	obtain	obtain	VERB
ejpam-5392	5	13	from	from	ADP
ejpam-5392	5	14	the	the	DET
ejpam-5392	5	15	information	information	NOUN
ejpam-5392	5	16	systems	system	NOUN
ejpam-5392	5	17	,	,	PUNCT
ejpam-5392	5	18	for	for	ADP
ejpam-5392	5	19	this	this	DET
ejpam-5392	5	20	reason	reason	NOUN
ejpam-5392	5	21	,	,	PUNCT
ejpam-5392	5	22	we	we	PRON
ejpam-5392	5	23	apply	apply	VERB
ejpam-5392	5	24	the	the	DET
ejpam-5392	5	25	abstract	abstract	ADJ
ejpam-5392	5	26	concept	concept	NOUN
ejpam-5392	5	27	of	of	ADP
ejpam-5392	5	28	ideal	ideal	ADJ
ejpam-5392	5	29	structures	structure	NOUN
ejpam-5392	5	30	to	to	PART
ejpam-5392	5	31	build	build	VERB
ejpam-5392	5	32	new	new	ADJ
ejpam-5392	5	33	generalized	generalized	ADJ
ejpam-5392	5	34	approximation	approximation	NOUN
ejpam-5392	5	35	spaces	space	NOUN
ejpam-5392	5	36	with	with	ADP
ejpam-5392	5	37	less	less	ADJ
ejpam-5392	5	38	vagueness	vagueness	NOUN
ejpam-5392	5	39	.	.	PUNCT
ejpam-5392	6	1	in	in	ADP
ejpam-5392	6	2	the	the	DET
ejpam-5392	6	3	present	present	ADJ
ejpam-5392	6	4	work	work	NOUN
ejpam-5392	6	5	,	,	PUNCT
ejpam-5392	6	6	we	we	PRON
ejpam-5392	6	7	employ	employ	VERB
ejpam-5392	6	8	a	a	DET
ejpam-5392	6	9	novel	novel	ADJ
ejpam-5392	6	10	type	type	NOUN
ejpam-5392	6	11	of	of	ADP
ejpam-5392	6	12	nearly	nearly	ADV
ejpam-5392	6	13	open	open	ADJ
ejpam-5392	6	14	sets	set	NOUN
ejpam-5392	6	15	in	in	ADP
ejpam-5392	6	16	topology	topology	NOUN
ejpam-5392	6	17	so	so	ADV
ejpam-5392	6	18	-	-	PUNCT
ejpam-5392	6	19	called	call	VERB
ejpam-5392	6	20	“	"	PUNCT
ejpam-5392	6	21	l	l	NOUN
ejpam-5392	6	22	-	-	PUNCT
ejpam-5392	6	23	θβλ	θβλ	NOUN
ejpam-5392	6	24	-	-	PUNCT
ejpam-5392	6	25	open	open	ADJ
ejpam-5392	6	26	”	"	PUNCT
ejpam-5392	6	27	with	with	ADP
ejpam-5392	6	28	an	an	DET
ejpam-5392	6	29	ideal	ideal	ADJ
ejpam-5392	6	30	structure	structure	NOUN
ejpam-5392	6	31	to	to	PART
ejpam-5392	6	32	introduce	introduce	VERB
ejpam-5392	6	33	novel	novel	ADJ
ejpam-5392	6	34	approximation	approximation	NOUN
ejpam-5392	6	35	spaces	space	NOUN
ejpam-5392	6	36	satisfying	satisfy	VERB
ejpam-5392	6	37	the	the	DET
ejpam-5392	6	38	desired	desire	VERB
ejpam-5392	6	39	properties	property	NOUN
ejpam-5392	6	40	concerning	concern	VERB
ejpam-5392	6	41	shrinking	shrink	VERB
ejpam-5392	6	42	the	the	DET
ejpam-5392	6	43	boundary	boundary	ADJ
ejpam-5392	6	44	region	region	NOUN
ejpam-5392	6	45	of	of	ADP
ejpam-5392	6	46	uncertainty	uncertainty	NOUN
ejpam-5392	6	47	and	and	CCONJ
ejpam-5392	6	48	expanding	expand	VERB
ejpam-5392	6	49	the	the	DET
ejpam-5392	6	50	domain	domain	NOUN
ejpam-5392	6	51	of	of	ADP
ejpam-5392	6	52	confirmed	confirm	VERB
ejpam-5392	6	53	information	information	NOUN
ejpam-5392	6	54	.	.	PUNCT
ejpam-5392	7	1	we	we	PRON
ejpam-5392	7	2	set	set	VERB
ejpam-5392	7	3	up	up	ADP
ejpam-5392	7	4	the	the	DET
ejpam-5392	7	5	fundamentals	fundamental	NOUN
ejpam-5392	7	6	of	of	ADP
ejpam-5392	7	7	the	the	DET
ejpam-5392	7	8	proposed	propose	VERB
ejpam-5392	7	9	rough	rough	ADJ
ejpam-5392	7	10	paradigms	paradigm	NOUN
ejpam-5392	7	11	and	and	CCONJ
ejpam-5392	7	12	demonstrate	demonstrate	VERB
ejpam-5392	7	13	their	their	PRON
ejpam-5392	7	14	superiority	superiority	NOUN
ejpam-5392	7	15	over	over	ADP
ejpam-5392	7	16	the	the	DET
ejpam-5392	7	17	preceding	precede	VERB
ejpam-5392	7	18	paradigms	paradigm	NOUN
ejpam-5392	7	19	induced	induce	VERB
ejpam-5392	7	20	by	by	ADP
ejpam-5392	7	21	some	some	DET
ejpam-5392	7	22	nearly	nearly	ADV
ejpam-5392	7	23	open	open	ADJ
ejpam-5392	7	24	sets	set	NOUN
ejpam-5392	7	25	.	.	PUNCT
ejpam-5392	8	1	two	two	NUM
ejpam-5392	8	2	algorithms	algorithm	NOUN
ejpam-5392	8	3	are	be	AUX
ejpam-5392	8	4	furnished	furnish	VERB
ejpam-5392	8	5	to	to	PART
ejpam-5392	8	6	illustrate	illustrate	VERB
ejpam-5392	8	7	the	the	DET
ejpam-5392	8	8	way	way	NOUN
ejpam-5392	8	9	of	of	ADP
ejpam-5392	8	10	specifying	specify	VERB
ejpam-5392	8	11	the	the	DET
ejpam-5392	8	12	family	family	NOUN
ejpam-5392	8	13	of	of	ADP
ejpam-5392	8	14	l	l	PROPN
ejpam-5392	8	15	-	-	PUNCT
ejpam-5392	8	16	θβλ	θβλ	NOUN
ejpam-5392	8	17	-	-	PUNCT
ejpam-5392	8	18	open	open	ADJ
ejpam-5392	8	19	sets	set	NOUN
ejpam-5392	8	20	and	and	CCONJ
ejpam-5392	8	21	exploring	explore	VERB
ejpam-5392	8	22	whether	whether	SCONJ
ejpam-5392	8	23	a	a	DET
ejpam-5392	8	24	subset	subset	NOUN
ejpam-5392	8	25	is	be	AUX
ejpam-5392	8	26	l	l	NOUN
ejpam-5392	8	27	-	-	PUNCT
ejpam-5392	8	28	θβλ	θβλ	NOUN
ejpam-5392	8	29	-	-	PUNCT
ejpam-5392	8	30	definable	definable	ADJ
ejpam-5392	8	31	or	or	CCONJ
ejpam-5392	8	32	l	l	NOUN
ejpam-5392	8	33	-	-	PUNCT
ejpam-5392	8	34	θβλ	θβλ	NOUN
ejpam-5392	8	35	-	-	PUNCT
ejpam-5392	8	36	rough	rough	ADJ
ejpam-5392	8	37	.	.	PUNCT
ejpam-5392	9	1	then	then	ADV
ejpam-5392	9	2	,	,	PUNCT
ejpam-5392	9	3	we	we	PRON
ejpam-5392	9	4	put	put	VERB
ejpam-5392	9	5	forward	forward	ADV
ejpam-5392	9	6	the	the	DET
ejpam-5392	9	7	concepts	concept	NOUN
ejpam-5392	9	8	of	of	ADP
ejpam-5392	9	9	rough	rough	ADJ
ejpam-5392	9	10	membership	membership	NOUN
ejpam-5392	9	11	relations	relation	NOUN
ejpam-5392	9	12	and	and	CCONJ
ejpam-5392	9	13	functions	function	NOUN
ejpam-5392	9	14	and	and	CCONJ
ejpam-5392	9	15	uncover	uncover	VERB
ejpam-5392	9	16	their	their	PRON
ejpam-5392	9	17	core	core	NOUN
ejpam-5392	9	18	characterizations	characterization	NOUN
ejpam-5392	9	19	.	.	PUNCT
ejpam-5392	10	1	finally	finally	ADV
ejpam-5392	10	2	,	,	PUNCT
ejpam-5392	10	3	we	we	PRON
ejpam-5392	10	4	examine	examine	VERB
ejpam-5392	10	5	the	the	DET
ejpam-5392	10	6	proposed	propose	VERB
ejpam-5392	10	7	models	model	NOUN
ejpam-5392	10	8	to	to	PART
ejpam-5392	10	9	model	model	VERB
ejpam-5392	10	10	a	a	DET
ejpam-5392	10	11	real	real	ADJ
ejpam-5392	10	12	situation	situation	NOUN
ejpam-5392	10	13	in	in	ADP
ejpam-5392	10	14	the	the	DET
ejpam-5392	10	15	chemistry	chemistry	NOUN
ejpam-5392	10	16	field	field	NOUN
ejpam-5392	10	17	and	and	CCONJ
ejpam-5392	10	18	clarify	clarify	VERB
ejpam-5392	10	19	how	how	SCONJ
ejpam-5392	10	20	our	our	PRON
ejpam-5392	10	21	models	model	NOUN
ejpam-5392	10	22	improve	improve	VERB
ejpam-5392	10	23	the	the	DET
ejpam-5392	10	24	outcomes	outcome	NOUN
ejpam-5392	10	25	of	of	ADP
ejpam-5392	10	26	generalized	generalized	ADJ
ejpam-5392	10	27	approximation	approximation	NOUN
ejpam-5392	10	28	spaces	space	NOUN
ejpam-5392	10	29	over	over	ADP
ejpam-5392	10	30	the	the	DET
ejpam-5392	10	31	previous	previous	ADJ
ejpam-5392	10	32	models	model	NOUN
ejpam-5392	10	33	.	.	PUNCT
ejpam-5392	11	1	2020	2020	NUM
ejpam-5392	11	2	mathematics	mathematic	NOUN
ejpam-5392	11	3	subject	subject	NOUN
ejpam-5392	11	4	classifications	classification	NOUN
ejpam-5392	11	5	:	:	PUNCT
ejpam-5392	11	6	03e99	03e99	NUM
ejpam-5392	11	7	,	,	PUNCT
ejpam-5392	11	8	54a05	54a05	NUM
ejpam-5392	11	9	,	,	PUNCT
ejpam-5392	11	10	54e99	54e99	DET
ejpam-5392	11	11	key	key	ADJ
ejpam-5392	11	12	words	word	NOUN
ejpam-5392	11	13	and	and	CCONJ
ejpam-5392	11	14	phrases	phrase	NOUN
ejpam-5392	11	15	:	:	PUNCT
ejpam-5392	11	16	rough	rough	ADJ
ejpam-5392	11	17	set	set	NOUN
ejpam-5392	11	18	,	,	PUNCT
ejpam-5392	11	19	topology	topology	NOUN
ejpam-5392	11	20	,	,	PUNCT
ejpam-5392	11	21	ideal	ideal	ADJ
ejpam-5392	11	22	,	,	PUNCT
ejpam-5392	11	23	l	l	NOUN
ejpam-5392	11	24	-	-	NOUN
ejpam-5392	11	25	θβλo	θβλo	VERB
ejpam-5392	11	26	-	-	ADJ
ejpam-5392	11	27	open	open	ADJ
ejpam-5392	11	28	set	set	NOUN
ejpam-5392	11	29	∗corresponding	∗corresponde	VERB
ejpam-5392	11	30	author	author	NOUN
ejpam-5392	11	31	.	.	PUNCT
ejpam-5392	12	1	doi	doi	NOUN
ejpam-5392	12	2	:	:	PUNCT
ejpam-5392	12	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5392	https://doi.org/10.29020/nybg.ejpam.v17i4.5392	NOUN
ejpam-5392	12	4	email	email	NOUN
ejpam-5392	12	5	addresses	address	NOUN
ejpam-5392	12	6	:	:	PUNCT
ejpam-5392	12	7	maly@kku.edu.sa	maly@kku.edu.sa	PROPN
ejpam-5392	12	8	(	(	PUNCT
ejpam-5392	12	9	m.	m.	PROPN
ejpam-5392	12	10	hosny	hosny	PROPN
ejpam-5392	12	11	)	)	PUNCT
ejpam-5392	12	12	,	,	PUNCT
ejpam-5392	12	13	tareqalshami83@gmail.com	tareqalshami83@gmail.com	X
ejpam-5392	12	14	(	(	PUNCT
ejpam-5392	12	15	t.m	t.m	PROPN
ejpam-5392	12	16	.	.	PROPN
ejpam-5392	12	17	al	al	PROPN
ejpam-5392	12	18	-	-	PUNCT
ejpam-5392	12	19	shami	shami	PROPN
ejpam-5392	12	20	)	)	PUNCT
ejpam-5392	12	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5392	13	1	3436	3436	NUM
ejpam-5392	13	2	copyright	copyright	NOUN
ejpam-5392	13	3	:	:	PUNCT
ejpam-5392	13	4	©	©	PROPN
ejpam-5392	13	5	2024	2024	NUM
ejpam-5392	13	6	the	the	DET
ejpam-5392	13	7	author(s	author(s	NOUN
ejpam-5392	13	8	)	)	PUNCT
ejpam-5392	13	9	.	.	PUNCT
ejpam-5392	14	1	(	(	PUNCT
ejpam-5392	14	2	cc	cc	NOUN
ejpam-5392	14	3	by	by	ADP
ejpam-5392	14	4	-	-	PUNCT
ejpam-5392	14	5	nc	nc	PROPN
ejpam-5392	14	6	4.0	4.0	NUM
ejpam-5392	14	7	)	)	PUNCT
ejpam-5392	14	8	m.	m.	NOUN
ejpam-5392	14	9	hosny	hosny	PROPN
ejpam-5392	14	10	,	,	PUNCT
ejpam-5392	14	11	t.m	t.m	PROPN
ejpam-5392	14	12	.	.	PROPN
ejpam-5392	14	13	al	al	PROPN
ejpam-5392	14	14	-	-	PUNCT
ejpam-5392	14	15	shami	shami	PROPN
ejpam-5392	14	16	/	/	PUNCT
ejpam-5392	14	17	eur	eur	PROPN
ejpam-5392	14	18	.	.	PUNCT
ejpam-5392	15	1	j.	j.	PROPN
ejpam-5392	15	2	pure	pure	PROPN
ejpam-5392	15	3	appl	appl	PROPN
ejpam-5392	15	4	.	.	PROPN
ejpam-5392	15	5	math	math	PROPN
ejpam-5392	15	6	,	,	PUNCT
ejpam-5392	15	7	17	17	NUM
ejpam-5392	15	8	(	(	PUNCT
ejpam-5392	15	9	4	4	NUM
ejpam-5392	15	10	)	)	PUNCT
ejpam-5392	15	11	(	(	PUNCT
ejpam-5392	15	12	2024	2024	NUM
ejpam-5392	15	13	)	)	PUNCT
ejpam-5392	15	14	,	,	PUNCT
ejpam-5392	15	15	3436	3436	NUM
ejpam-5392	15	16	-	-	SYM
ejpam-5392	15	17	3463	3463	NUM
ejpam-5392	15	18	3437	3437	NUM
ejpam-5392	15	19	1	1	NUM
ejpam-5392	15	20	.	.	PUNCT
ejpam-5392	16	1	introduction	introduction	NOUN
ejpam-5392	16	2	nowadays	nowadays	ADV
ejpam-5392	16	3	,	,	PUNCT
ejpam-5392	16	4	one	one	PRON
ejpam-5392	16	5	can	can	AUX
ejpam-5392	16	6	see	see	VERB
ejpam-5392	16	7	a	a	DET
ejpam-5392	16	8	rapid	rapid	ADJ
ejpam-5392	16	9	growth	growth	NOUN
ejpam-5392	16	10	of	of	ADP
ejpam-5392	16	11	interest	interest	NOUN
ejpam-5392	16	12	in	in	ADP
ejpam-5392	16	13	the	the	DET
ejpam-5392	16	14	theory	theory	NOUN
ejpam-5392	16	15	of	of	ADP
ejpam-5392	16	16	rough	rough	ADJ
ejpam-5392	16	17	sets	set	NOUN
ejpam-5392	16	18	and	and	CCONJ
ejpam-5392	16	19	its	its	PRON
ejpam-5392	16	20	applications	application	NOUN
ejpam-5392	16	21	,	,	PUNCT
ejpam-5392	16	22	evident	evident	ADJ
ejpam-5392	16	23	from	from	ADP
ejpam-5392	16	24	the	the	DET
ejpam-5392	16	25	number	number	NOUN
ejpam-5392	16	26	of	of	ADP
ejpam-5392	16	27	international	international	ADJ
ejpam-5392	16	28	conferences	conference	NOUN
ejpam-5392	16	29	and	and	CCONJ
ejpam-5392	16	30	workshops	workshop	NOUN
ejpam-5392	16	31	dedicated	dedicate	VERB
ejpam-5392	16	32	to	to	ADP
ejpam-5392	16	33	investigating	investigate	VERB
ejpam-5392	16	34	the	the	DET
ejpam-5392	16	35	progression	progression	NOUN
ejpam-5392	16	36	of	of	ADP
ejpam-5392	16	37	rough	rough	ADJ
ejpam-5392	16	38	set	set	NOUN
ejpam-5392	16	39	theory	theory	NOUN
ejpam-5392	16	40	,	,	PUNCT
ejpam-5392	16	41	as	as	ADV
ejpam-5392	16	42	well	well	ADV
ejpam-5392	16	43	as	as	ADP
ejpam-5392	16	44	the	the	DET
ejpam-5392	16	45	high	high	ADJ
ejpam-5392	16	46	-	-	PUNCT
ejpam-5392	16	47	quality	quality	NOUN
ejpam-5392	16	48	papers	paper	NOUN
ejpam-5392	16	49	published	publish	VERB
ejpam-5392	16	50	as	as	ADP
ejpam-5392	16	51	a	a	DET
ejpam-5392	16	52	result	result	NOUN
ejpam-5392	16	53	of	of	ADP
ejpam-5392	16	54	this	this	DET
ejpam-5392	16	55	attention	attention	NOUN
ejpam-5392	16	56	.	.	PUNCT
ejpam-5392	17	1	this	this	DET
ejpam-5392	17	2	theory	theory	NOUN
ejpam-5392	17	3	was	be	AUX
ejpam-5392	17	4	initiated	initiate	VERB
ejpam-5392	17	5	by	by	ADP
ejpam-5392	17	6	pawlak	pawlak	ADJ
ejpam-5392	17	7	[	[	X
ejpam-5392	17	8	40	40	NUM
ejpam-5392	17	9	,	,	PUNCT
ejpam-5392	17	10	41	41	NUM
ejpam-5392	17	11	]	]	PUNCT
ejpam-5392	17	12	in	in	ADP
ejpam-5392	17	13	the	the	DET
ejpam-5392	17	14	early	early	ADJ
ejpam-5392	17	15	1980s	1980	NOUN
ejpam-5392	17	16	as	as	ADP
ejpam-5392	17	17	a	a	DET
ejpam-5392	17	18	non	non	ADJ
ejpam-5392	17	19	-	-	ADJ
ejpam-5392	17	20	statistical	statistical	ADJ
ejpam-5392	17	21	technique	technique	NOUN
ejpam-5392	17	22	to	to	PART
ejpam-5392	17	23	analyze	analyze	VERB
ejpam-5392	17	24	data	datum	NOUN
ejpam-5392	17	25	tables	table	NOUN
ejpam-5392	17	26	acquired	acquire	VERB
ejpam-5392	17	27	from	from	ADP
ejpam-5392	17	28	human	human	ADJ
ejpam-5392	17	29	experts	expert	NOUN
ejpam-5392	17	30	or	or	CCONJ
ejpam-5392	17	31	measurements	measurement	NOUN
ejpam-5392	17	32	.	.	PUNCT
ejpam-5392	18	1	the	the	DET
ejpam-5392	18	2	philosophy	philosophy	NOUN
ejpam-5392	18	3	of	of	ADP
ejpam-5392	18	4	rough	rough	ADJ
ejpam-5392	18	5	set	set	NOUN
ejpam-5392	18	6	theory	theory	NOUN
ejpam-5392	18	7	in	in	ADP
ejpam-5392	18	8	addressing	address	VERB
ejpam-5392	18	9	the	the	DET
ejpam-5392	18	10	complex	complex	ADJ
ejpam-5392	18	11	problems	problem	NOUN
ejpam-5392	18	12	individuals	individual	NOUN
ejpam-5392	18	13	face	face	VERB
ejpam-5392	18	14	in	in	ADP
ejpam-5392	18	15	practical	practical	ADJ
ejpam-5392	18	16	life	life	NOUN
ejpam-5392	18	17	is	be	AUX
ejpam-5392	18	18	based	base	VERB
ejpam-5392	18	19	on	on	ADP
ejpam-5392	18	20	dividing	divide	VERB
ejpam-5392	18	21	a	a	DET
ejpam-5392	18	22	set	set	NOUN
ejpam-5392	18	23	of	of	ADP
ejpam-5392	18	24	data	datum	NOUN
ejpam-5392	18	25	containing	contain	VERB
ejpam-5392	18	26	uncertainty	uncertainty	NOUN
ejpam-5392	18	27	into	into	ADP
ejpam-5392	18	28	three	three	NUM
ejpam-5392	18	29	regions	region	NOUN
ejpam-5392	18	30	.	.	PUNCT
ejpam-5392	19	1	the	the	DET
ejpam-5392	19	2	first	first	ADJ
ejpam-5392	19	3	region	region	NOUN
ejpam-5392	19	4	includes	include	VERB
ejpam-5392	19	5	the	the	DET
ejpam-5392	19	6	confirmed	confirm	VERB
ejpam-5392	19	7	information	information	NOUN
ejpam-5392	19	8	extracted	extract	VERB
ejpam-5392	19	9	from	from	ADP
ejpam-5392	19	10	this	this	DET
ejpam-5392	19	11	set	set	NOUN
ejpam-5392	19	12	,	,	PUNCT
ejpam-5392	19	13	terminologically	terminologically	ADV
ejpam-5392	19	14	known	know	VERB
ejpam-5392	19	15	as	as	ADP
ejpam-5392	19	16	the	the	DET
ejpam-5392	19	17	lower	low	ADJ
ejpam-5392	19	18	approximation	approximation	NOUN
ejpam-5392	19	19	.	.	PUNCT
ejpam-5392	20	1	the	the	DET
ejpam-5392	20	2	second	second	ADJ
ejpam-5392	20	3	region	region	NOUN
ejpam-5392	20	4	represents	represent	VERB
ejpam-5392	20	5	the	the	DET
ejpam-5392	20	6	information	information	NOUN
ejpam-5392	20	7	for	for	ADP
ejpam-5392	20	8	which	which	PRON
ejpam-5392	20	9	we	we	PRON
ejpam-5392	20	10	can	can	AUX
ejpam-5392	20	11	not	not	PART
ejpam-5392	20	12	determine	determine	VERB
ejpam-5392	20	13	its	its	PRON
ejpam-5392	20	14	belonging	belonging	NOUN
ejpam-5392	20	15	or	or	CCONJ
ejpam-5392	20	16	non	non	ADJ
ejpam-5392	20	17	-	-	ADJ
ejpam-5392	20	18	belonging	belonging	ADJ
ejpam-5392	20	19	to	to	ADP
ejpam-5392	20	20	the	the	DET
ejpam-5392	20	21	set	set	NOUN
ejpam-5392	20	22	,	,	PUNCT
ejpam-5392	20	23	known	know	VERB
ejpam-5392	20	24	as	as	ADP
ejpam-5392	20	25	the	the	DET
ejpam-5392	20	26	upper	upper	ADJ
ejpam-5392	20	27	approximation	approximation	NOUN
ejpam-5392	20	28	.	.	PUNCT
ejpam-5392	21	1	the	the	DET
ejpam-5392	21	2	third	third	ADJ
ejpam-5392	21	3	region	region	NOUN
ejpam-5392	21	4	,	,	PUNCT
ejpam-5392	21	5	known	know	VERB
ejpam-5392	21	6	as	as	ADP
ejpam-5392	21	7	the	the	DET
ejpam-5392	21	8	boundary	boundary	ADJ
ejpam-5392	21	9	region	region	NOUN
ejpam-5392	21	10	,	,	PUNCT
ejpam-5392	21	11	is	be	AUX
ejpam-5392	21	12	defined	define	VERB
ejpam-5392	21	13	as	as	ADP
ejpam-5392	21	14	the	the	DET
ejpam-5392	21	15	difference	difference	NOUN
ejpam-5392	21	16	between	between	ADP
ejpam-5392	21	17	the	the	DET
ejpam-5392	21	18	upper	upper	ADJ
ejpam-5392	21	19	approximation	approximation	NOUN
ejpam-5392	21	20	and	and	CCONJ
ejpam-5392	21	21	the	the	DET
ejpam-5392	21	22	lower	low	ADJ
ejpam-5392	21	23	approximation	approximation	NOUN
ejpam-5392	21	24	.	.	PUNCT
ejpam-5392	22	1	rough	rough	ADJ
ejpam-5392	22	2	set	set	NOUN
ejpam-5392	22	3	theory	theory	NOUN
ejpam-5392	22	4	begins	begin	VERB
ejpam-5392	22	5	with	with	ADP
ejpam-5392	22	6	the	the	DET
ejpam-5392	22	7	concept	concept	NOUN
ejpam-5392	22	8	of	of	ADP
ejpam-5392	22	9	an	an	DET
ejpam-5392	22	10	equivalence	equivalence	NOUN
ejpam-5392	22	11	relationship	relationship	NOUN
ejpam-5392	22	12	,	,	PUNCT
ejpam-5392	22	13	which	which	PRON
ejpam-5392	22	14	is	be	AUX
ejpam-5392	22	15	a	a	DET
ejpam-5392	22	16	strict	strict	ADJ
ejpam-5392	22	17	term	term	NOUN
ejpam-5392	22	18	when	when	SCONJ
ejpam-5392	22	19	modeling	model	VERB
ejpam-5392	22	20	many	many	ADJ
ejpam-5392	22	21	realistic	realistic	ADJ
ejpam-5392	22	22	problems	problem	NOUN
ejpam-5392	22	23	.	.	PUNCT
ejpam-5392	23	1	this	this	DET
ejpam-5392	23	2	strictness	strictness	NOUN
ejpam-5392	23	3	prompted	prompt	VERB
ejpam-5392	23	4	many	many	ADJ
ejpam-5392	23	5	researchers	researcher	NOUN
ejpam-5392	23	6	and	and	CCONJ
ejpam-5392	23	7	authors	author	NOUN
ejpam-5392	23	8	to	to	PART
ejpam-5392	23	9	search	search	VERB
ejpam-5392	23	10	for	for	ADP
ejpam-5392	23	11	alternative	alternative	ADJ
ejpam-5392	23	12	methods	method	NOUN
ejpam-5392	23	13	to	to	ADP
ejpam-5392	23	14	the	the	DET
ejpam-5392	23	15	equivalence	equivalence	NOUN
ejpam-5392	23	16	classes	class	NOUN
ejpam-5392	23	17	,	,	PUNCT
ejpam-5392	23	18	leading	lead	VERB
ejpam-5392	23	19	to	to	ADP
ejpam-5392	23	20	the	the	DET
ejpam-5392	23	21	development	development	NOUN
ejpam-5392	23	22	of	of	ADP
ejpam-5392	23	23	the	the	DET
ejpam-5392	23	24	neighborhood	neighborhood	NOUN
ejpam-5392	23	25	idea	idea	NOUN
ejpam-5392	23	26	.	.	PUNCT
ejpam-5392	24	1	initially	initially	ADV
ejpam-5392	24	2	defined	define	VERB
ejpam-5392	24	3	by	by	ADP
ejpam-5392	24	4	yao	yao	PROPN
ejpam-5392	24	5	,	,	PUNCT
ejpam-5392	24	6	he	he	PRON
ejpam-5392	24	7	[	[	X
ejpam-5392	24	8	50	50	NUM
ejpam-5392	24	9	,	,	PUNCT
ejpam-5392	24	10	51	51	NUM
ejpam-5392	24	11	]	]	PUNCT
ejpam-5392	24	12	formulated	formulate	VERB
ejpam-5392	24	13	the	the	DET
ejpam-5392	24	14	concepts	concept	NOUN
ejpam-5392	24	15	of	of	ADP
ejpam-5392	24	16	right	right	ADJ
ejpam-5392	24	17	neighborhoods	neighborhood	NOUN
ejpam-5392	24	18	and	and	CCONJ
ejpam-5392	24	19	left	leave	VERB
ejpam-5392	24	20	neighborhoods	neighborhood	NOUN
ejpam-5392	24	21	as	as	ADP
ejpam-5392	24	22	the	the	DET
ejpam-5392	24	23	equivalents	equivalent	NOUN
ejpam-5392	24	24	of	of	ADP
ejpam-5392	24	25	the	the	DET
ejpam-5392	24	26	equivalence	equivalence	NOUN
ejpam-5392	24	27	classes	class	NOUN
ejpam-5392	24	28	derived	derive	VERB
ejpam-5392	24	29	from	from	ADP
ejpam-5392	24	30	pawlak	pawlak	ADJ
ejpam-5392	24	31	’s	’s	PART
ejpam-5392	24	32	original	original	ADJ
ejpam-5392	24	33	model	model	NOUN
ejpam-5392	24	34	.	.	PUNCT
ejpam-5392	25	1	over	over	ADP
ejpam-5392	25	2	time	time	NOUN
ejpam-5392	25	3	,	,	PUNCT
ejpam-5392	25	4	with	with	ADP
ejpam-5392	25	5	the	the	DET
ejpam-5392	25	6	desire	desire	NOUN
ejpam-5392	25	7	to	to	PART
ejpam-5392	25	8	increase	increase	VERB
ejpam-5392	25	9	the	the	DET
ejpam-5392	25	10	confirmed	confirmed	ADJ
ejpam-5392	25	11	information	information	NOUN
ejpam-5392	25	12	,	,	PUNCT
ejpam-5392	25	13	other	other	ADJ
ejpam-5392	25	14	models	model	NOUN
ejpam-5392	25	15	were	be	AUX
ejpam-5392	25	16	proposed	propose	VERB
ejpam-5392	25	17	to	to	PART
ejpam-5392	25	18	improve	improve	VERB
ejpam-5392	25	19	the	the	DET
ejpam-5392	25	20	approximation	approximation	NOUN
ejpam-5392	25	21	operators	operator	NOUN
ejpam-5392	25	22	and	and	CCONJ
ejpam-5392	25	23	accuracy	accuracy	NOUN
ejpam-5392	25	24	measures	measure	NOUN
ejpam-5392	25	25	.	.	PUNCT
ejpam-5392	26	1	for	for	ADP
ejpam-5392	26	2	instance	instance	NOUN
ejpam-5392	26	3	,	,	PUNCT
ejpam-5392	26	4	rough	rough	ADJ
ejpam-5392	26	5	set	set	NOUN
ejpam-5392	26	6	paradigms	paradigm	NOUN
ejpam-5392	26	7	introduced	introduce	VERB
ejpam-5392	26	8	by	by	ADP
ejpam-5392	26	9	using	use	VERB
ejpam-5392	26	10	minimal	minimal	ADJ
ejpam-5392	26	11	neighborhoods	neighborhood	NOUN
ejpam-5392	26	12	[	[	X
ejpam-5392	26	13	3	3	NUM
ejpam-5392	26	14	]	]	PUNCT
ejpam-5392	26	15	,	,	PUNCT
ejpam-5392	26	16	containment	containment	NOUN
ejpam-5392	26	17	neighborhoods	neighborhood	NOUN
ejpam-5392	27	1	[	[	X
ejpam-5392	27	2	5	5	NUM
ejpam-5392	27	3	]	]	PUNCT
ejpam-5392	27	4	,	,	PUNCT
ejpam-5392	27	5	maximal	maximal	ADJ
ejpam-5392	27	6	neighborhoods	neighborhood	NOUN
ejpam-5392	27	7	[	[	X
ejpam-5392	27	8	8	8	NUM
ejpam-5392	27	9	,	,	PUNCT
ejpam-5392	27	10	16	16	NUM
ejpam-5392	27	11	]	]	PUNCT
ejpam-5392	27	12	,	,	PUNCT
ejpam-5392	27	13	subset	subset	VERB
ejpam-5392	27	14	neighborhoods	neighborhood	NOUN
ejpam-5392	27	15	[	[	X
ejpam-5392	27	16	10	10	NUM
ejpam-5392	27	17	,	,	PUNCT
ejpam-5392	27	18	52	52	NUM
ejpam-5392	27	19	]	]	PUNCT
ejpam-5392	27	20	,	,	PUNCT
ejpam-5392	27	21	adhesion	adhesion	NOUN
ejpam-5392	27	22	neighborhoods	neighborhood	NOUN
ejpam-5392	27	23	[	[	X
ejpam-5392	27	24	36	36	NUM
ejpam-5392	27	25	]	]	PUNCT
ejpam-5392	27	26	,	,	PUNCT
ejpam-5392	27	27	etcetera	etcetera	PROPN
ejpam-5392	27	28	.	.	PUNCT
ejpam-5392	28	1	attention	attention	NOUN
ejpam-5392	28	2	was	be	AUX
ejpam-5392	28	3	paid	pay	VERB
ejpam-5392	28	4	early	early	ADV
ejpam-5392	28	5	by	by	ADP
ejpam-5392	28	6	[	[	X
ejpam-5392	28	7	48	48	NUM
ejpam-5392	28	8	]	]	PUNCT
ejpam-5392	28	9	to	to	ADP
ejpam-5392	28	10	the	the	DET
ejpam-5392	28	11	similarity	similarity	NOUN
ejpam-5392	28	12	between	between	ADP
ejpam-5392	28	13	the	the	DET
ejpam-5392	28	14	behaviors	behavior	NOUN
ejpam-5392	28	15	of	of	ADP
ejpam-5392	28	16	lower	low	ADJ
ejpam-5392	28	17	and	and	CCONJ
ejpam-5392	28	18	upper	upper	ADJ
ejpam-5392	28	19	rough	rough	ADJ
ejpam-5392	28	20	approximations	approximation	NOUN
ejpam-5392	28	21	and	and	CCONJ
ejpam-5392	28	22	interior	interior	ADJ
ejpam-5392	28	23	and	and	CCONJ
ejpam-5392	28	24	closure	closure	NOUN
ejpam-5392	28	25	topological	topological	ADJ
ejpam-5392	28	26	operators	operator	NOUN
ejpam-5392	28	27	.	.	PUNCT
ejpam-5392	29	1	therefore	therefore	ADV
ejpam-5392	29	2	,	,	PUNCT
ejpam-5392	29	3	topological	topological	ADJ
ejpam-5392	29	4	structures	structure	NOUN
ejpam-5392	29	5	have	have	AUX
ejpam-5392	29	6	been	be	AUX
ejpam-5392	29	7	proposed	propose	VERB
ejpam-5392	29	8	to	to	PART
ejpam-5392	29	9	study	study	VERB
ejpam-5392	29	10	information	information	NOUN
ejpam-5392	29	11	systems	system	NOUN
ejpam-5392	29	12	and	and	CCONJ
ejpam-5392	29	13	apply	apply	VERB
ejpam-5392	29	14	topological	topological	ADJ
ejpam-5392	29	15	operators	operator	NOUN
ejpam-5392	29	16	as	as	ADP
ejpam-5392	29	17	alternative	alternative	ADJ
ejpam-5392	29	18	tools	tool	NOUN
ejpam-5392	29	19	for	for	ADP
ejpam-5392	29	20	these	these	DET
ejpam-5392	29	21	approximations	approximation	NOUN
ejpam-5392	29	22	;	;	PUNCT
ejpam-5392	29	23	see	see	VERB
ejpam-5392	29	24	,	,	PUNCT
ejpam-5392	29	25	for	for	ADP
ejpam-5392	29	26	instance	instance	NOUN
ejpam-5392	29	27	[	[	X
ejpam-5392	29	28	4	4	NUM
ejpam-5392	29	29	,	,	PUNCT
ejpam-5392	29	30	17	17	NUM
ejpam-5392	29	31	,	,	PUNCT
ejpam-5392	29	32	22	22	NUM
ejpam-5392	29	33	,	,	PUNCT
ejpam-5392	29	34	34	34	NUM
ejpam-5392	29	35	,	,	PUNCT
ejpam-5392	29	36	43	43	NUM
ejpam-5392	29	37	,	,	PUNCT
ejpam-5392	29	38	46	46	NUM
ejpam-5392	29	39	,	,	PUNCT
ejpam-5392	29	40	49	49	NUM
ejpam-5392	29	41	,	,	PUNCT
ejpam-5392	29	42	53	53	NUM
ejpam-5392	29	43	]	]	PUNCT
ejpam-5392	29	44	.	.	PUNCT
ejpam-5392	30	1	diverse	diverse	ADJ
ejpam-5392	30	2	techniques	technique	NOUN
ejpam-5392	30	3	have	have	AUX
ejpam-5392	30	4	been	be	AUX
ejpam-5392	30	5	introduced	introduce	VERB
ejpam-5392	30	6	to	to	PART
ejpam-5392	30	7	create	create	VERB
ejpam-5392	30	8	topological	topological	ADJ
ejpam-5392	30	9	spaces	space	NOUN
ejpam-5392	30	10	utilizing	utilize	VERB
ejpam-5392	30	11	neighborhood	neighborhood	NOUN
ejpam-5392	30	12	systems	system	NOUN
ejpam-5392	30	13	.	.	PUNCT
ejpam-5392	31	1	for	for	ADP
ejpam-5392	31	2	example	example	NOUN
ejpam-5392	31	3	,	,	PUNCT
ejpam-5392	31	4	one	one	PRON
ejpam-5392	31	5	can	can	AUX
ejpam-5392	31	6	take	take	VERB
ejpam-5392	31	7	the	the	DET
ejpam-5392	31	8	neighborhood	neighborhood	NOUN
ejpam-5392	31	9	of	of	ADP
ejpam-5392	31	10	each	each	DET
ejpam-5392	31	11	point	point	NOUN
ejpam-5392	31	12	as	as	ADP
ejpam-5392	31	13	a	a	DET
ejpam-5392	31	14	subbase	subbase	NOUN
ejpam-5392	31	15	of	of	ADP
ejpam-5392	31	16	a	a	DET
ejpam-5392	31	17	topology	topology	NOUN
ejpam-5392	31	18	[	[	X
ejpam-5392	31	19	33	33	NUM
ejpam-5392	31	20	]	]	PUNCT
ejpam-5392	31	21	or	or	CCONJ
ejpam-5392	31	22	initiate	initiate	VERB
ejpam-5392	31	23	the	the	DET
ejpam-5392	31	24	topology	topology	NOUN
ejpam-5392	31	25	using	use	VERB
ejpam-5392	31	26	the	the	DET
ejpam-5392	31	27	following	follow	VERB
ejpam-5392	31	28	formula	formula	NOUN
ejpam-5392	31	29	:	:	PUNCT
ejpam-5392	31	30	ϑλ	ϑλ	PART
ejpam-5392	31	31	=	=	PUNCT
ejpam-5392	31	32	{	{	PUNCT
ejpam-5392	31	33	v	v	ADP
ejpam-5392	31	34	⊆	⊆	NUM
ejpam-5392	31	35	x	x	SYM
ejpam-5392	31	36	:	:	PUNCT
ejpam-5392	31	37	∀y	∀y	NUM
ejpam-5392	31	38	∈	∈	PROPN
ejpam-5392	31	39	v	v	NOUN
ejpam-5392	31	40	,	,	PUNCT
ejpam-5392	31	41	gλ(y	gλ(y	NUM
ejpam-5392	31	42	)	)	PUNCT
ejpam-5392	31	43	⊆	⊆	NUM
ejpam-5392	31	44	v	v	NOUN
ejpam-5392	31	45	}	}	PUNCT
ejpam-5392	31	46	[	[	X
ejpam-5392	31	47	45	45	NUM
ejpam-5392	31	48	]	]	PUNCT
ejpam-5392	31	49	.	.	PUNCT
ejpam-5392	32	1	to	to	PART
ejpam-5392	32	2	develop	develop	VERB
ejpam-5392	32	3	decision	decision	NOUN
ejpam-5392	32	4	-	-	PUNCT
ejpam-5392	32	5	making	make	VERB
ejpam-5392	32	6	methods	method	NOUN
ejpam-5392	32	7	for	for	ADP
ejpam-5392	32	8	information	information	NOUN
ejpam-5392	32	9	systems	system	NOUN
ejpam-5392	32	10	from	from	ADP
ejpam-5392	32	11	a	a	DET
ejpam-5392	32	12	topological	topological	ADJ
ejpam-5392	32	13	standpoint	standpoint	NOUN
ejpam-5392	32	14	,	,	PUNCT
ejpam-5392	32	15	several	several	ADJ
ejpam-5392	32	16	authors	author	NOUN
ejpam-5392	32	17	have	have	AUX
ejpam-5392	32	18	employed	employ	VERB
ejpam-5392	32	19	abstract	abstract	ADJ
ejpam-5392	32	20	topological	topological	ADJ
ejpam-5392	32	21	principles	principle	NOUN
ejpam-5392	32	22	and	and	CCONJ
ejpam-5392	32	23	their	their	PRON
ejpam-5392	32	24	generalizations	generalization	NOUN
ejpam-5392	32	25	,	,	PUNCT
ejpam-5392	32	26	such	such	ADJ
ejpam-5392	32	27	as	as	ADP
ejpam-5392	32	28	nearly	nearly	ADV
ejpam-5392	32	29	open	open	ADJ
ejpam-5392	32	30	sets	set	NOUN
ejpam-5392	32	31	[	[	X
ejpam-5392	32	32	1	1	NUM
ejpam-5392	32	33	,	,	PUNCT
ejpam-5392	32	34	2	2	NUM
ejpam-5392	32	35	,	,	PUNCT
ejpam-5392	32	36	6	6	NUM
ejpam-5392	32	37	,	,	PUNCT
ejpam-5392	32	38	7	7	NUM
ejpam-5392	32	39	]	]	PUNCT
ejpam-5392	32	40	,	,	PUNCT
ejpam-5392	32	41	supra	supra	ADJ
ejpam-5392	32	42	topology	topology	NOUN
ejpam-5392	33	1	[	[	X
ejpam-5392	33	2	9	9	NUM
ejpam-5392	33	3	]	]	PUNCT
ejpam-5392	33	4	,	,	PUNCT
ejpam-5392	33	5	minimal	minimal	ADJ
ejpam-5392	33	6	structures	structure	NOUN
ejpam-5392	33	7	[	[	X
ejpam-5392	33	8	18	18	NUM
ejpam-5392	33	9	]	]	PUNCT
ejpam-5392	33	10	,	,	PUNCT
ejpam-5392	33	11	infra	infra	NOUN
ejpam-5392	33	12	topology	topology	NOUN
ejpam-5392	34	1	[	[	X
ejpam-5392	34	2	13	13	NUM
ejpam-5392	34	3	]	]	PUNCT
ejpam-5392	34	4	,	,	PUNCT
ejpam-5392	34	5	and	and	CCONJ
ejpam-5392	34	6	bitopology	bitopology	NOUN
ejpam-5392	34	7	[	[	X
ejpam-5392	34	8	44	44	NUM
ejpam-5392	34	9	]	]	PUNCT
ejpam-5392	34	10	.	.	PUNCT
ejpam-5392	35	1	the	the	DET
ejpam-5392	35	2	authors	author	NOUN
ejpam-5392	35	3	of	of	ADP
ejpam-5392	35	4	[	[	X
ejpam-5392	35	5	32	32	NUM
ejpam-5392	35	6	,	,	PUNCT
ejpam-5392	35	7	47	47	NUM
ejpam-5392	35	8	]	]	PUNCT
ejpam-5392	35	9	put	put	VERB
ejpam-5392	35	10	forward	forward	ADV
ejpam-5392	35	11	the	the	DET
ejpam-5392	35	12	notion	notion	NOUN
ejpam-5392	35	13	of	of	ADP
ejpam-5392	35	14	ideal	ideal	NOUN
ejpam-5392	35	15	over	over	ADP
ejpam-5392	35	16	a	a	DET
ejpam-5392	35	17	set	set	NOUN
ejpam-5392	35	18	x	x	PUNCT
ejpam-5392	35	19	as	as	ADP
ejpam-5392	35	20	a	a	DET
ejpam-5392	35	21	nonempty	nonempty	ADJ
ejpam-5392	35	22	subcollection	subcollection	NOUN
ejpam-5392	35	23	of	of	ADP
ejpam-5392	35	24	the	the	DET
ejpam-5392	35	25	power	power	NOUN
ejpam-5392	35	26	set	set	NOUN
ejpam-5392	35	27	of	of	ADP
ejpam-5392	35	28	x	x	PRON
ejpam-5392	35	29	which	which	PRON
ejpam-5392	35	30	is	be	AUX
ejpam-5392	35	31	closed	close	VERB
ejpam-5392	35	32	under	under	ADP
ejpam-5392	35	33	finite	finite	ADJ
ejpam-5392	35	34	union	union	NOUN
ejpam-5392	35	35	and	and	CCONJ
ejpam-5392	35	36	hereditary	hereditary	ADJ
ejpam-5392	35	37	property	property	NOUN
ejpam-5392	35	38	.	.	PUNCT
ejpam-5392	36	1	in	in	ADP
ejpam-5392	36	2	[	[	X
ejpam-5392	36	3	28	28	NUM
ejpam-5392	36	4	]	]	PUNCT
ejpam-5392	36	5	,	,	PUNCT
ejpam-5392	36	6	new	new	ADJ
ejpam-5392	36	7	topologies	topology	NOUN
ejpam-5392	36	8	are	be	AUX
ejpam-5392	36	9	derived	derive	VERB
ejpam-5392	36	10	from	from	ADP
ejpam-5392	36	11	an	an	DET
ejpam-5392	36	12	old	old	ADJ
ejpam-5392	36	13	one	one	NOUN
ejpam-5392	36	14	using	use	VERB
ejpam-5392	36	15	ideals	ideal	NOUN
ejpam-5392	36	16	.	.	PUNCT
ejpam-5392	37	1	with	with	ADP
ejpam-5392	37	2	a	a	DET
ejpam-5392	37	3	strong	strong	ADJ
ejpam-5392	37	4	desire	desire	NOUN
ejpam-5392	37	5	to	to	PART
ejpam-5392	37	6	increase	increase	VERB
ejpam-5392	37	7	the	the	DET
ejpam-5392	37	8	amount	amount	NOUN
ejpam-5392	37	9	of	of	ADP
ejpam-5392	37	10	confirmed	confirm	VERB
ejpam-5392	37	11	information	information	NOUN
ejpam-5392	37	12	,	,	PUNCT
ejpam-5392	37	13	which	which	PRON
ejpam-5392	37	14	gives	give	VERB
ejpam-5392	37	15	the	the	DET
ejpam-5392	37	16	decision	decision	NOUN
ejpam-5392	37	17	-	-	PUNCT
ejpam-5392	37	18	maker	maker	NOUN
ejpam-5392	37	19	a	a	DET
ejpam-5392	37	20	greater	great	ADJ
ejpam-5392	37	21	opportunity	opportunity	NOUN
ejpam-5392	37	22	to	to	PART
ejpam-5392	37	23	make	make	VERB
ejpam-5392	37	24	more	more	ADV
ejpam-5392	37	25	accurate	accurate	ADJ
ejpam-5392	37	26	decisions	decision	NOUN
ejpam-5392	37	27	,	,	PUNCT
ejpam-5392	37	28	the	the	DET
ejpam-5392	37	29	ideal	ideal	ADJ
ejpam-5392	37	30	structure	structure	NOUN
ejpam-5392	37	31	was	be	AUX
ejpam-5392	37	32	integrated	integrate	VERB
ejpam-5392	37	33	into	into	ADP
ejpam-5392	37	34	generalized	generalized	ADJ
ejpam-5392	37	35	approximation	approximation	NOUN
ejpam-5392	37	36	spaces	space	NOUN
ejpam-5392	37	37	.	.	PUNCT
ejpam-5392	38	1	the	the	DET
ejpam-5392	38	2	concept	concept	NOUN
ejpam-5392	38	3	was	be	AUX
ejpam-5392	38	4	first	first	ADV
ejpam-5392	38	5	employed	employ	VERB
ejpam-5392	38	6	by	by	ADP
ejpam-5392	38	7	kandil	kandil	PROPN
ejpam-5392	38	8	et	et	PROPN
ejpam-5392	38	9	al	al	PROPN
ejpam-5392	38	10	.	.	PUNCT
ejpam-5392	39	1	[	[	X
ejpam-5392	39	2	29	29	NUM
ejpam-5392	39	3	]	]	PUNCT
ejpam-5392	39	4	.	.	PUNCT
ejpam-5392	40	1	this	this	DET
ejpam-5392	40	2	concept	concept	NOUN
ejpam-5392	40	3	was	be	AUX
ejpam-5392	40	4	later	later	ADV
ejpam-5392	40	5	exploited	exploit	VERB
ejpam-5392	40	6	by	by	ADP
ejpam-5392	40	7	researchers	researcher	NOUN
ejpam-5392	40	8	in	in	ADP
ejpam-5392	40	9	the	the	DET
ejpam-5392	40	10	study	study	NOUN
ejpam-5392	40	11	of	of	ADP
ejpam-5392	40	12	information	information	NOUN
ejpam-5392	40	13	systems	system	NOUN
ejpam-5392	40	14	,	,	PUNCT
ejpam-5392	40	15	explaining	explain	VERB
ejpam-5392	40	16	the	the	DET
ejpam-5392	40	17	advantages	advantage	NOUN
ejpam-5392	40	18	of	of	ADP
ejpam-5392	40	19	this	this	DET
ejpam-5392	40	20	tool	tool	NOUN
ejpam-5392	40	21	in	in	ADP
ejpam-5392	40	22	various	various	ADJ
ejpam-5392	40	23	ways	way	NOUN
ejpam-5392	40	24	,	,	PUNCT
ejpam-5392	40	25	including	include	VERB
ejpam-5392	40	26	topological	topological	ADJ
ejpam-5392	40	27	approaches	approach	NOUN
ejpam-5392	40	28	,	,	PUNCT
ejpam-5392	40	29	m.	m.	PROPN
ejpam-5392	40	30	hosny	hosny	PROPN
ejpam-5392	40	31	,	,	PUNCT
ejpam-5392	40	32	t.m	t.m	PROPN
ejpam-5392	40	33	.	.	PROPN
ejpam-5392	40	34	al	al	PROPN
ejpam-5392	40	35	-	-	PUNCT
ejpam-5392	40	36	shami	shami	PROPN
ejpam-5392	40	37	/	/	PUNCT
ejpam-5392	40	38	eur	eur	PROPN
ejpam-5392	40	39	.	.	PUNCT
ejpam-5392	41	1	j.	j.	PROPN
ejpam-5392	41	2	pure	pure	PROPN
ejpam-5392	41	3	appl	appl	PROPN
ejpam-5392	41	4	.	.	PROPN
ejpam-5392	41	5	math	math	PROPN
ejpam-5392	41	6	,	,	PUNCT
ejpam-5392	41	7	17	17	NUM
ejpam-5392	41	8	(	(	PUNCT
ejpam-5392	41	9	4	4	NUM
ejpam-5392	41	10	)	)	PUNCT
ejpam-5392	41	11	(	(	PUNCT
ejpam-5392	41	12	2024	2024	NUM
ejpam-5392	41	13	)	)	PUNCT
ejpam-5392	41	14	,	,	PUNCT
ejpam-5392	41	15	3436	3436	NUM
ejpam-5392	41	16	-	-	SYM
ejpam-5392	41	17	3463	3463	NUM
ejpam-5392	41	18	3438	3438	NUM
ejpam-5392	41	19	as	as	SCONJ
ejpam-5392	41	20	illustrated	illustrate	VERB
ejpam-5392	41	21	in	in	ADP
ejpam-5392	41	22	many	many	ADJ
ejpam-5392	41	23	published	publish	VERB
ejpam-5392	41	24	manuscripts	manuscript	NOUN
ejpam-5392	41	25	[	[	X
ejpam-5392	41	26	11	11	NUM
ejpam-5392	41	27	,	,	PUNCT
ejpam-5392	41	28	12	12	NUM
ejpam-5392	41	29	,	,	PUNCT
ejpam-5392	41	30	14	14	NUM
ejpam-5392	41	31	,	,	PUNCT
ejpam-5392	41	32	21	21	NUM
ejpam-5392	41	33	,	,	PUNCT
ejpam-5392	41	34	23	23	NUM
ejpam-5392	41	35	,	,	PUNCT
ejpam-5392	41	36	24	24	NUM
ejpam-5392	41	37	,	,	PUNCT
ejpam-5392	41	38	27	27	NUM
ejpam-5392	41	39	,	,	PUNCT
ejpam-5392	41	40	39	39	NUM
ejpam-5392	41	41	]	]	PUNCT
ejpam-5392	41	42	.	.	PUNCT
ejpam-5392	42	1	researchers	researcher	NOUN
ejpam-5392	42	2	have	have	VERB
ejpam-5392	42	3	the	the	DET
ejpam-5392	42	4	freedom	freedom	NOUN
ejpam-5392	42	5	to	to	PART
ejpam-5392	42	6	choose	choose	VERB
ejpam-5392	42	7	the	the	DET
ejpam-5392	42	8	tool	tool	NOUN
ejpam-5392	42	9	that	that	PRON
ejpam-5392	42	10	is	be	AUX
ejpam-5392	42	11	most	most	ADV
ejpam-5392	42	12	efficient	efficient	ADJ
ejpam-5392	42	13	for	for	ADP
ejpam-5392	42	14	addressing	address	VERB
ejpam-5392	42	15	the	the	DET
ejpam-5392	42	16	problem	problem	NOUN
ejpam-5392	42	17	and	and	CCONJ
ejpam-5392	42	18	achieving	achieve	VERB
ejpam-5392	42	19	the	the	DET
ejpam-5392	42	20	greatest	great	ADJ
ejpam-5392	42	21	possible	possible	ADJ
ejpam-5392	42	22	amount	amount	NOUN
ejpam-5392	42	23	of	of	ADP
ejpam-5392	42	24	desired	desire	VERB
ejpam-5392	42	25	characteristics	characteristic	NOUN
ejpam-5392	42	26	of	of	ADP
ejpam-5392	42	27	pawlak	pawlak	ADJ
ejpam-5392	42	28	paradigms	paradigm	NOUN
ejpam-5392	42	29	.	.	PUNCT
ejpam-5392	43	1	michael	michael	PROPN
ejpam-5392	44	1	[	[	X
ejpam-5392	44	2	38	38	NUM
ejpam-5392	44	3	]	]	PUNCT
ejpam-5392	44	4	came	come	VERB
ejpam-5392	44	5	up	up	ADP
ejpam-5392	44	6	with	with	ADP
ejpam-5392	44	7	a	a	DET
ejpam-5392	44	8	brilliant	brilliant	ADJ
ejpam-5392	44	9	idea	idea	NOUN
ejpam-5392	44	10	to	to	PART
ejpam-5392	44	11	enlarge	enlarge	VERB
ejpam-5392	44	12	a	a	DET
ejpam-5392	44	13	family	family	NOUN
ejpam-5392	44	14	of	of	ADP
ejpam-5392	44	15	semi	semi	ADJ
ejpam-5392	44	16	-	-	ADJ
ejpam-5392	44	17	open	open	ADJ
ejpam-5392	44	18	sets	set	NOUN
ejpam-5392	44	19	using	use	VERB
ejpam-5392	44	20	ideals	ideal	NOUN
ejpam-5392	44	21	,	,	PUNCT
ejpam-5392	44	22	then	then	ADV
ejpam-5392	44	23	some	some	DET
ejpam-5392	44	24	authors	author	NOUN
ejpam-5392	44	25	[	[	X
ejpam-5392	44	26	25	25	NUM
ejpam-5392	44	27	,	,	PUNCT
ejpam-5392	44	28	26	26	NUM
ejpam-5392	44	29	]	]	PUNCT
ejpam-5392	44	30	followed	follow	VERB
ejpam-5392	44	31	this	this	DET
ejpam-5392	44	32	technique	technique	NOUN
ejpam-5392	44	33	to	to	PART
ejpam-5392	44	34	aggrandize	aggrandize	VERB
ejpam-5392	44	35	the	the	DET
ejpam-5392	44	36	classes	class	NOUN
ejpam-5392	44	37	of	of	ADP
ejpam-5392	44	38	α	α	NOUN
ejpam-5392	44	39	-	-	ADJ
ejpam-5392	44	40	open	open	ADJ
ejpam-5392	44	41	,	,	PUNCT
ejpam-5392	44	42	β	β	NOUN
ejpam-5392	44	43	-	-	ADJ
ejpam-5392	44	44	open	open	ADJ
ejpam-5392	44	45	,	,	PUNCT
ejpam-5392	44	46	and	and	CCONJ
ejpam-5392	44	47	pre	pre	ADJ
ejpam-5392	44	48	-	-	ADJ
ejpam-5392	44	49	open	open	ADJ
ejpam-5392	44	50	sets	set	NOUN
ejpam-5392	44	51	.	.	PUNCT
ejpam-5392	45	1	this	this	DET
ejpam-5392	45	2	work	work	NOUN
ejpam-5392	45	3	deals	deal	VERB
ejpam-5392	45	4	with	with	ADP
ejpam-5392	45	5	generalized	generalized	ADJ
ejpam-5392	45	6	approximation	approximation	NOUN
ejpam-5392	45	7	spaces	space	NOUN
ejpam-5392	45	8	using	use	VERB
ejpam-5392	45	9	a	a	DET
ejpam-5392	45	10	topological	topological	ADJ
ejpam-5392	45	11	approach	approach	NOUN
ejpam-5392	45	12	and	and	CCONJ
ejpam-5392	45	13	enhances	enhance	VERB
ejpam-5392	45	14	the	the	DET
ejpam-5392	45	15	prominence	prominence	NOUN
ejpam-5392	45	16	of	of	ADP
ejpam-5392	45	17	using	use	VERB
ejpam-5392	45	18	ideals	ideal	NOUN
ejpam-5392	45	19	via	via	ADP
ejpam-5392	45	20	rough	rough	ADJ
ejpam-5392	45	21	set	set	NOUN
ejpam-5392	45	22	theory	theory	NOUN
ejpam-5392	45	23	studies	study	NOUN
ejpam-5392	45	24	,	,	PUNCT
ejpam-5392	45	25	as	as	ADP
ejpam-5392	45	26	a	a	DET
ejpam-5392	45	27	tool	tool	NOUN
ejpam-5392	45	28	to	to	PART
ejpam-5392	45	29	demystify	demystify	VERB
ejpam-5392	45	30	the	the	DET
ejpam-5392	45	31	data	datum	NOUN
ejpam-5392	45	32	.	.	PUNCT
ejpam-5392	46	1	we	we	PRON
ejpam-5392	46	2	suggest	suggest	VERB
ejpam-5392	46	3	a	a	DET
ejpam-5392	46	4	broader	broad	ADJ
ejpam-5392	46	5	general	general	ADJ
ejpam-5392	46	6	framework	framework	NOUN
ejpam-5392	46	7	of	of	ADP
ejpam-5392	46	8	topological	topological	ADJ
ejpam-5392	46	9	approximation	approximation	NOUN
ejpam-5392	46	10	spaces	space	NOUN
ejpam-5392	46	11	via	via	ADP
ejpam-5392	46	12	ideals	ideal	NOUN
ejpam-5392	46	13	,	,	PUNCT
ejpam-5392	46	14	satisfying	satisfy	VERB
ejpam-5392	46	15	the	the	DET
ejpam-5392	46	16	desirable	desirable	ADJ
ejpam-5392	46	17	characteristics	characteristic	NOUN
ejpam-5392	46	18	of	of	ADP
ejpam-5392	46	19	original	original	ADJ
ejpam-5392	46	20	models	model	NOUN
ejpam-5392	46	21	and	and	CCONJ
ejpam-5392	46	22	enhancing	enhance	VERB
ejpam-5392	46	23	decision	decision	NOUN
ejpam-5392	46	24	reliability	reliability	NOUN
ejpam-5392	46	25	.	.	PUNCT
ejpam-5392	47	1	the	the	DET
ejpam-5392	47	2	presentation	presentation	NOUN
ejpam-5392	47	3	of	of	ADP
ejpam-5392	47	4	this	this	DET
ejpam-5392	47	5	article	article	NOUN
ejpam-5392	47	6	is	be	AUX
ejpam-5392	47	7	organized	organize	VERB
ejpam-5392	47	8	as	as	SCONJ
ejpam-5392	47	9	follows	follow	VERB
ejpam-5392	47	10	:	:	PUNCT
ejpam-5392	47	11	section	section	NOUN
ejpam-5392	47	12	2	2	NUM
ejpam-5392	47	13	covers	cover	VERB
ejpam-5392	47	14	the	the	DET
ejpam-5392	47	15	fundamentals	fundamental	NOUN
ejpam-5392	47	16	required	require	VERB
ejpam-5392	47	17	to	to	PART
ejpam-5392	47	18	make	make	VERB
ejpam-5392	47	19	the	the	DET
ejpam-5392	47	20	paper	paper	NOUN
ejpam-5392	47	21	self	self	NOUN
ejpam-5392	47	22	-	-	PUNCT
ejpam-5392	47	23	contained	contain	VERB
ejpam-5392	47	24	.	.	PUNCT
ejpam-5392	48	1	then	then	ADV
ejpam-5392	48	2	,	,	PUNCT
ejpam-5392	48	3	in	in	ADP
ejpam-5392	48	4	section	section	NOUN
ejpam-5392	48	5	3	3	NUM
ejpam-5392	48	6	,	,	PUNCT
ejpam-5392	48	7	we	we	PRON
ejpam-5392	48	8	define	define	VERB
ejpam-5392	48	9	a	a	DET
ejpam-5392	48	10	new	new	ADJ
ejpam-5392	48	11	class	class	NOUN
ejpam-5392	48	12	of	of	ADP
ejpam-5392	48	13	nearly	nearly	ADV
ejpam-5392	48	14	open	open	ADJ
ejpam-5392	48	15	sets	set	NOUN
ejpam-5392	48	16	,	,	PUNCT
ejpam-5392	48	17	namely	namely	ADV
ejpam-5392	48	18	,	,	PUNCT
ejpam-5392	48	19	l	l	NOUN
ejpam-5392	48	20	-	-	PUNCT
ejpam-5392	48	21	θβλ	θβλ	NOUN
ejpam-5392	48	22	-	-	PUNCT
ejpam-5392	48	23	open	open	ADJ
ejpam-5392	48	24	sets	set	NOUN
ejpam-5392	48	25	,	,	PUNCT
ejpam-5392	48	26	which	which	PRON
ejpam-5392	48	27	is	be	AUX
ejpam-5392	48	28	strictly	strictly	ADV
ejpam-5392	48	29	stronger	strong	ADJ
ejpam-5392	48	30	than	than	ADP
ejpam-5392	48	31	the	the	DET
ejpam-5392	48	32	class	class	NOUN
ejpam-5392	48	33	of	of	ADP
ejpam-5392	48	34	l	l	PROPN
ejpam-5392	48	35	-	-	PUNCT
ejpam-5392	48	36	βλ	βλ	ADJ
ejpam-5392	48	37	-	-	PUNCT
ejpam-5392	48	38	open	open	ADJ
ejpam-5392	48	39	sets	set	NOUN
ejpam-5392	48	40	.	.	PUNCT
ejpam-5392	49	1	we	we	PRON
ejpam-5392	49	2	draw	draw	VERB
ejpam-5392	49	3	the	the	DET
ejpam-5392	49	4	main	main	ADJ
ejpam-5392	49	5	properties	property	NOUN
ejpam-5392	49	6	of	of	ADP
ejpam-5392	49	7	this	this	DET
ejpam-5392	49	8	class	class	NOUN
ejpam-5392	49	9	and	and	CCONJ
ejpam-5392	49	10	articulate	articulate	VERB
ejpam-5392	49	11	its	its	PRON
ejpam-5392	49	12	relationships	relationship	NOUN
ejpam-5392	49	13	with	with	ADP
ejpam-5392	49	14	the	the	DET
ejpam-5392	49	15	preceding	precede	VERB
ejpam-5392	49	16	ones	one	NOUN
ejpam-5392	49	17	with	with	ADP
ejpam-5392	49	18	the	the	DET
ejpam-5392	49	19	aid	aid	NOUN
ejpam-5392	49	20	of	of	ADP
ejpam-5392	49	21	examples	example	NOUN
ejpam-5392	49	22	.	.	PUNCT
ejpam-5392	50	1	section	section	NOUN
ejpam-5392	50	2	4	4	NUM
ejpam-5392	50	3	is	be	AUX
ejpam-5392	50	4	devoted	devote	VERB
ejpam-5392	50	5	to	to	ADP
ejpam-5392	50	6	constructing	construct	VERB
ejpam-5392	50	7	rough	rough	ADJ
ejpam-5392	50	8	set	set	NOUN
ejpam-5392	50	9	models	model	NOUN
ejpam-5392	50	10	utilizing	utilize	VERB
ejpam-5392	50	11	the	the	DET
ejpam-5392	50	12	class	class	NOUN
ejpam-5392	50	13	of	of	ADP
ejpam-5392	50	14	l	l	NOUN
ejpam-5392	50	15	-	-	PUNCT
ejpam-5392	50	16	θβλ	θβλ	NOUN
ejpam-5392	50	17	-	-	PUNCT
ejpam-5392	50	18	open	open	ADJ
ejpam-5392	50	19	sets	set	NOUN
ejpam-5392	50	20	.	.	PUNCT
ejpam-5392	51	1	we	we	PRON
ejpam-5392	51	2	compare	compare	VERB
ejpam-5392	51	3	the	the	DET
ejpam-5392	51	4	approximation	approximation	NOUN
ejpam-5392	51	5	operators	operator	NOUN
ejpam-5392	51	6	,	,	PUNCT
ejpam-5392	51	7	boundary	boundary	ADJ
ejpam-5392	51	8	regions	region	NOUN
ejpam-5392	51	9	,	,	PUNCT
ejpam-5392	51	10	and	and	CCONJ
ejpam-5392	51	11	accuracy	accuracy	NOUN
ejpam-5392	51	12	values	value	NOUN
ejpam-5392	51	13	of	of	ADP
ejpam-5392	51	14	the	the	DET
ejpam-5392	51	15	proposed	propose	VERB
ejpam-5392	51	16	paradigms	paradigm	NOUN
ejpam-5392	51	17	with	with	ADP
ejpam-5392	51	18	those	those	PRON
ejpam-5392	51	19	presented	present	VERB
ejpam-5392	51	20	in	in	ADP
ejpam-5392	51	21	other	other	ADJ
ejpam-5392	51	22	studies	study	NOUN
ejpam-5392	51	23	.	.	PUNCT
ejpam-5392	52	1	in	in	ADP
ejpam-5392	52	2	section	section	NOUN
ejpam-5392	52	3	5	5	NUM
ejpam-5392	52	4	,	,	PUNCT
ejpam-5392	52	5	we	we	PRON
ejpam-5392	52	6	display	display	VERB
ejpam-5392	52	7	a	a	DET
ejpam-5392	52	8	new	new	ADJ
ejpam-5392	52	9	type	type	NOUN
ejpam-5392	52	10	of	of	ADP
ejpam-5392	52	11	rough	rough	ADJ
ejpam-5392	52	12	membership	membership	NOUN
ejpam-5392	52	13	functions	function	NOUN
ejpam-5392	52	14	and	and	CCONJ
ejpam-5392	52	15	apply	apply	VERB
ejpam-5392	52	16	to	to	PART
ejpam-5392	52	17	describe	describe	VERB
ejpam-5392	52	18	the	the	DET
ejpam-5392	52	19	main	main	ADJ
ejpam-5392	52	20	concepts	concept	NOUN
ejpam-5392	52	21	of	of	ADP
ejpam-5392	52	22	the	the	DET
ejpam-5392	52	23	proposed	propose	VERB
ejpam-5392	52	24	rough	rough	ADJ
ejpam-5392	52	25	set	set	NOUN
ejpam-5392	52	26	models	model	NOUN
ejpam-5392	52	27	.	.	PUNCT
ejpam-5392	53	1	we	we	PRON
ejpam-5392	53	2	provide	provide	VERB
ejpam-5392	53	3	a	a	DET
ejpam-5392	53	4	practical	practical	ADJ
ejpam-5392	53	5	example	example	NOUN
ejpam-5392	53	6	in	in	ADP
ejpam-5392	53	7	section	section	NOUN
ejpam-5392	53	8	6	6	NUM
ejpam-5392	53	9	to	to	PART
ejpam-5392	53	10	illustrate	illustrate	VERB
ejpam-5392	53	11	the	the	DET
ejpam-5392	53	12	superiority	superiority	NOUN
ejpam-5392	53	13	of	of	ADP
ejpam-5392	53	14	the	the	DET
ejpam-5392	53	15	current	current	ADJ
ejpam-5392	53	16	models	model	NOUN
ejpam-5392	53	17	over	over	ADP
ejpam-5392	53	18	the	the	DET
ejpam-5392	53	19	former	former	ADJ
ejpam-5392	53	20	models	model	NOUN
ejpam-5392	53	21	and	and	CCONJ
ejpam-5392	53	22	their	their	PRON
ejpam-5392	53	23	applicability	applicability	NOUN
ejpam-5392	53	24	in	in	ADP
ejpam-5392	53	25	addressing	address	VERB
ejpam-5392	53	26	realistic	realistic	ADJ
ejpam-5392	53	27	problems	problem	NOUN
ejpam-5392	53	28	.	.	PUNCT
ejpam-5392	54	1	lastly	lastly	ADV
ejpam-5392	54	2	,	,	PUNCT
ejpam-5392	54	3	we	we	PRON
ejpam-5392	54	4	draw	draw	VERB
ejpam-5392	54	5	conclusions	conclusion	NOUN
ejpam-5392	54	6	from	from	ADP
ejpam-5392	54	7	the	the	DET
ejpam-5392	54	8	present	present	ADJ
ejpam-5392	54	9	study	study	NOUN
ejpam-5392	54	10	and	and	CCONJ
ejpam-5392	54	11	summarize	summarize	VERB
ejpam-5392	54	12	its	its	PRON
ejpam-5392	54	13	most	most	ADV
ejpam-5392	54	14	important	important	ADJ
ejpam-5392	54	15	findings	finding	NOUN
ejpam-5392	54	16	in	in	ADP
ejpam-5392	54	17	section	section	NOUN
ejpam-5392	54	18	7	7	NUM
ejpam-5392	54	19	.	.	PUNCT
ejpam-5392	55	1	the	the	DET
ejpam-5392	55	2	presentation	presentation	NOUN
ejpam-5392	55	3	of	of	ADP
ejpam-5392	55	4	this	this	DET
ejpam-5392	55	5	article	article	NOUN
ejpam-5392	55	6	is	be	AUX
ejpam-5392	55	7	organized	organize	VERB
ejpam-5392	55	8	as	as	SCONJ
ejpam-5392	55	9	follows	follow	VERB
ejpam-5392	55	10	:	:	PUNCT
ejpam-5392	55	11	section	section	NOUN
ejpam-5392	55	12	2	2	NUM
ejpam-5392	55	13	covers	cover	VERB
ejpam-5392	55	14	the	the	DET
ejpam-5392	55	15	fundamentals	fundamental	NOUN
ejpam-5392	55	16	required	require	VERB
ejpam-5392	55	17	to	to	PART
ejpam-5392	55	18	make	make	VERB
ejpam-5392	55	19	the	the	DET
ejpam-5392	55	20	paper	paper	NOUN
ejpam-5392	55	21	self	self	NOUN
ejpam-5392	55	22	-	-	PUNCT
ejpam-5392	55	23	contained	contain	VERB
ejpam-5392	55	24	.	.	PUNCT
ejpam-5392	56	1	then	then	ADV
ejpam-5392	56	2	,	,	PUNCT
ejpam-5392	56	3	in	in	ADP
ejpam-5392	56	4	section	section	NOUN
ejpam-5392	56	5	3	3	NUM
ejpam-5392	56	6	,	,	PUNCT
ejpam-5392	56	7	we	we	PRON
ejpam-5392	56	8	define	define	VERB
ejpam-5392	56	9	a	a	DET
ejpam-5392	56	10	new	new	ADJ
ejpam-5392	56	11	class	class	NOUN
ejpam-5392	56	12	of	of	ADP
ejpam-5392	56	13	nearly	nearly	ADV
ejpam-5392	56	14	open	open	ADJ
ejpam-5392	56	15	sets	set	NOUN
ejpam-5392	56	16	,	,	PUNCT
ejpam-5392	56	17	namely	namely	ADV
ejpam-5392	56	18	,	,	PUNCT
ejpam-5392	56	19	l	l	NOUN
ejpam-5392	56	20	-	-	PUNCT
ejpam-5392	56	21	θβλ	θβλ	NOUN
ejpam-5392	56	22	-	-	PUNCT
ejpam-5392	56	23	open	open	ADJ
ejpam-5392	56	24	sets	set	NOUN
ejpam-5392	56	25	,	,	PUNCT
ejpam-5392	56	26	which	which	PRON
ejpam-5392	56	27	is	be	AUX
ejpam-5392	56	28	strictly	strictly	ADV
ejpam-5392	56	29	stronger	strong	ADJ
ejpam-5392	56	30	than	than	ADP
ejpam-5392	56	31	the	the	DET
ejpam-5392	56	32	class	class	NOUN
ejpam-5392	56	33	of	of	ADP
ejpam-5392	56	34	l	l	PROPN
ejpam-5392	56	35	-	-	PUNCT
ejpam-5392	56	36	βλ	βλ	ADJ
ejpam-5392	56	37	-	-	PUNCT
ejpam-5392	56	38	open	open	ADJ
ejpam-5392	56	39	sets	set	NOUN
ejpam-5392	56	40	.	.	PUNCT
ejpam-5392	57	1	we	we	PRON
ejpam-5392	57	2	draw	draw	VERB
ejpam-5392	57	3	the	the	DET
ejpam-5392	57	4	main	main	ADJ
ejpam-5392	57	5	properties	property	NOUN
ejpam-5392	57	6	of	of	ADP
ejpam-5392	57	7	this	this	DET
ejpam-5392	57	8	class	class	NOUN
ejpam-5392	57	9	and	and	CCONJ
ejpam-5392	57	10	articulate	articulate	VERB
ejpam-5392	57	11	its	its	PRON
ejpam-5392	57	12	relationships	relationship	NOUN
ejpam-5392	57	13	with	with	ADP
ejpam-5392	57	14	the	the	DET
ejpam-5392	57	15	preceding	precede	VERB
ejpam-5392	57	16	ones	one	NOUN
ejpam-5392	57	17	with	with	ADP
ejpam-5392	57	18	the	the	DET
ejpam-5392	57	19	aid	aid	NOUN
ejpam-5392	57	20	of	of	ADP
ejpam-5392	57	21	examples	example	NOUN
ejpam-5392	57	22	.	.	PUNCT
ejpam-5392	58	1	section	section	NOUN
ejpam-5392	58	2	4	4	NUM
ejpam-5392	58	3	focuses	focus	VERB
ejpam-5392	58	4	on	on	ADP
ejpam-5392	58	5	developing	develop	VERB
ejpam-5392	58	6	rough	rough	ADJ
ejpam-5392	58	7	set	set	NOUN
ejpam-5392	58	8	models	model	NOUN
ejpam-5392	58	9	using	use	VERB
ejpam-5392	58	10	the	the	DET
ejpam-5392	58	11	l	l	NOUN
ejpam-5392	58	12	-	-	PUNCT
ejpam-5392	58	13	θβλ	θβλ	NOUN
ejpam-5392	58	14	-	-	PUNCT
ejpam-5392	58	15	open	open	ADJ
ejpam-5392	58	16	sets	set	NOUN
ejpam-5392	58	17	.	.	PUNCT
ejpam-5392	59	1	we	we	PRON
ejpam-5392	59	2	compare	compare	VERB
ejpam-5392	59	3	the	the	DET
ejpam-5392	59	4	approximation	approximation	NOUN
ejpam-5392	59	5	operators	operator	NOUN
ejpam-5392	59	6	,	,	PUNCT
ejpam-5392	59	7	boundary	boundary	ADJ
ejpam-5392	59	8	regions	region	NOUN
ejpam-5392	59	9	,	,	PUNCT
ejpam-5392	59	10	and	and	CCONJ
ejpam-5392	59	11	accuracy	accuracy	NOUN
ejpam-5392	59	12	values	value	NOUN
ejpam-5392	59	13	of	of	ADP
ejpam-5392	59	14	the	the	DET
ejpam-5392	59	15	proposed	propose	VERB
ejpam-5392	59	16	models	model	NOUN
ejpam-5392	59	17	with	with	ADP
ejpam-5392	59	18	those	those	PRON
ejpam-5392	59	19	in	in	ADP
ejpam-5392	59	20	existing	exist	VERB
ejpam-5392	59	21	studies	study	NOUN
ejpam-5392	59	22	.	.	PUNCT
ejpam-5392	60	1	in	in	ADP
ejpam-5392	60	2	section	section	NOUN
ejpam-5392	60	3	5	5	NUM
ejpam-5392	60	4	,	,	PUNCT
ejpam-5392	60	5	we	we	PRON
ejpam-5392	60	6	introduce	introduce	VERB
ejpam-5392	60	7	a	a	DET
ejpam-5392	60	8	new	new	ADJ
ejpam-5392	60	9	type	type	NOUN
ejpam-5392	60	10	of	of	ADP
ejpam-5392	60	11	rough	rough	ADJ
ejpam-5392	60	12	membership	membership	NOUN
ejpam-5392	60	13	functions	function	NOUN
ejpam-5392	60	14	and	and	CCONJ
ejpam-5392	60	15	apply	apply	VERB
ejpam-5392	60	16	them	they	PRON
ejpam-5392	60	17	to	to	PART
ejpam-5392	60	18	explain	explain	VERB
ejpam-5392	60	19	the	the	DET
ejpam-5392	60	20	central	central	ADJ
ejpam-5392	60	21	concepts	concept	NOUN
ejpam-5392	60	22	of	of	ADP
ejpam-5392	60	23	the	the	DET
ejpam-5392	60	24	proposed	propose	VERB
ejpam-5392	60	25	rough	rough	ADJ
ejpam-5392	60	26	set	set	NOUN
ejpam-5392	60	27	models	model	NOUN
ejpam-5392	60	28	.	.	PUNCT
ejpam-5392	61	1	section	section	NOUN
ejpam-5392	61	2	6	6	NUM
ejpam-5392	61	3	provides	provide	VERB
ejpam-5392	61	4	a	a	DET
ejpam-5392	61	5	practical	practical	ADJ
ejpam-5392	61	6	example	example	NOUN
ejpam-5392	61	7	that	that	PRON
ejpam-5392	61	8	demonstrates	demonstrate	VERB
ejpam-5392	61	9	the	the	DET
ejpam-5392	61	10	advantages	advantage	NOUN
ejpam-5392	61	11	of	of	ADP
ejpam-5392	61	12	the	the	DET
ejpam-5392	61	13	current	current	ADJ
ejpam-5392	61	14	models	model	NOUN
ejpam-5392	61	15	over	over	ADP
ejpam-5392	61	16	previous	previous	ADJ
ejpam-5392	61	17	ones	one	NOUN
ejpam-5392	61	18	and	and	CCONJ
ejpam-5392	61	19	their	their	PRON
ejpam-5392	61	20	effectiveness	effectiveness	NOUN
ejpam-5392	61	21	in	in	ADP
ejpam-5392	61	22	solving	solve	VERB
ejpam-5392	61	23	real	real	ADJ
ejpam-5392	61	24	-	-	PUNCT
ejpam-5392	61	25	world	world	NOUN
ejpam-5392	61	26	problems	problem	NOUN
ejpam-5392	61	27	.	.	PUNCT
ejpam-5392	62	1	finally	finally	ADV
ejpam-5392	62	2	,	,	PUNCT
ejpam-5392	62	3	in	in	ADP
ejpam-5392	62	4	section	section	NOUN
ejpam-5392	62	5	7	7	NUM
ejpam-5392	62	6	,	,	PUNCT
ejpam-5392	62	7	we	we	PRON
ejpam-5392	62	8	conclude	conclude	VERB
ejpam-5392	62	9	the	the	DET
ejpam-5392	62	10	study	study	NOUN
ejpam-5392	62	11	by	by	ADP
ejpam-5392	62	12	summarizing	summarize	VERB
ejpam-5392	62	13	its	its	PRON
ejpam-5392	62	14	key	key	ADJ
ejpam-5392	62	15	findings	finding	NOUN
ejpam-5392	62	16	.	.	PUNCT
ejpam-5392	63	1	2	2	X
ejpam-5392	63	2	.	.	X
ejpam-5392	63	3	preliminaries	preliminary	NOUN
ejpam-5392	63	4	in	in	ADP
ejpam-5392	63	5	this	this	DET
ejpam-5392	63	6	segment	segment	NOUN
ejpam-5392	63	7	,	,	PUNCT
ejpam-5392	63	8	we	we	PRON
ejpam-5392	63	9	cover	cover	VERB
ejpam-5392	63	10	the	the	DET
ejpam-5392	63	11	main	main	ADJ
ejpam-5392	63	12	contributions	contribution	NOUN
ejpam-5392	63	13	via	via	ADP
ejpam-5392	63	14	topological	topological	ADJ
ejpam-5392	63	15	(	(	PUNCT
ejpam-5392	63	16	generalized	generalized	ADJ
ejpam-5392	63	17	)	)	PUNCT
ejpam-5392	63	18	approximation	approximation	NOUN
ejpam-5392	63	19	spaces	space	NOUN
ejpam-5392	63	20	that	that	PRON
ejpam-5392	63	21	are	be	AUX
ejpam-5392	63	22	required	require	VERB
ejpam-5392	63	23	to	to	PART
ejpam-5392	63	24	understand	understand	VERB
ejpam-5392	63	25	the	the	DET
ejpam-5392	63	26	main	main	ADJ
ejpam-5392	63	27	contributions	contribution	NOUN
ejpam-5392	63	28	and	and	CCONJ
ejpam-5392	63	29	significance	significance	NOUN
ejpam-5392	63	30	of	of	ADP
ejpam-5392	63	31	this	this	DET
ejpam-5392	63	32	manuscript	manuscript	NOUN
ejpam-5392	63	33	.	.	PUNCT
ejpam-5392	64	1	definition	definition	NOUN
ejpam-5392	64	2	1	1	NUM
ejpam-5392	64	3	.	.	PUNCT
ejpam-5392	65	1	[	[	X
ejpam-5392	65	2	32	32	NUM
ejpam-5392	65	3	,	,	PUNCT
ejpam-5392	65	4	47	47	NUM
ejpam-5392	65	5	]	]	PUNCT
ejpam-5392	65	6	an	an	DET
ejpam-5392	65	7	ideal	ideal	ADJ
ejpam-5392	65	8	l	l	NOUN
ejpam-5392	65	9	over	over	ADP
ejpam-5392	65	10	the	the	DET
ejpam-5392	65	11	universe	universe	NOUN
ejpam-5392	65	12	x	x	PUNCT
ejpam-5392	65	13	̸=	̸=	NOUN
ejpam-5392	65	14	∅	∅	NOUN
ejpam-5392	65	15	is	be	AUX
ejpam-5392	65	16	a	a	DET
ejpam-5392	65	17	subfamily	subfamily	NOUN
ejpam-5392	65	18	of	of	ADP
ejpam-5392	65	19	the	the	DET
ejpam-5392	65	20	power	power	NOUN
ejpam-5392	65	21	set	set	NOUN
ejpam-5392	65	22	of	of	ADP
ejpam-5392	65	23	x	x	PUNCT
ejpam-5392	65	24	satisfying	satisfy	VERB
ejpam-5392	65	25	the	the	DET
ejpam-5392	65	26	below	below	ADJ
ejpam-5392	65	27	terms	term	NOUN
ejpam-5392	65	28	.	.	PUNCT
ejpam-5392	66	1	m.	m.	PROPN
ejpam-5392	66	2	hosny	hosny	PROPN
ejpam-5392	66	3	,	,	PUNCT
ejpam-5392	66	4	t.m	t.m	PROPN
ejpam-5392	66	5	.	.	PROPN
ejpam-5392	66	6	al	al	PROPN
ejpam-5392	66	7	-	-	PUNCT
ejpam-5392	66	8	shami	shami	PROPN
ejpam-5392	66	9	/	/	PUNCT
ejpam-5392	66	10	eur	eur	PROPN
ejpam-5392	66	11	.	.	PUNCT
ejpam-5392	67	1	j.	j.	PROPN
ejpam-5392	67	2	pure	pure	PROPN
ejpam-5392	67	3	appl	appl	PROPN
ejpam-5392	67	4	.	.	PROPN
ejpam-5392	67	5	math	math	PROPN
ejpam-5392	67	6	,	,	PUNCT
ejpam-5392	67	7	17	17	NUM
ejpam-5392	67	8	(	(	PUNCT
ejpam-5392	67	9	4	4	NUM
ejpam-5392	67	10	)	)	PUNCT
ejpam-5392	67	11	(	(	PUNCT
ejpam-5392	67	12	2024	2024	NUM
ejpam-5392	67	13	)	)	PUNCT
ejpam-5392	67	14	,	,	PUNCT
ejpam-5392	67	15	3436	3436	NUM
ejpam-5392	67	16	-	-	SYM
ejpam-5392	67	17	3463	3463	NUM
ejpam-5392	67	18	3439	3439	NUM
ejpam-5392	67	19	(	(	PUNCT
ejpam-5392	67	20	i	i	NOUN
ejpam-5392	67	21	)	)	PUNCT
ejpam-5392	67	22	v	v	ADP
ejpam-5392	67	23	∈	∈	PROPN
ejpam-5392	67	24	l	l	NOUN
ejpam-5392	67	25	and	and	CCONJ
ejpam-5392	67	26	z	z	NOUN
ejpam-5392	67	27	∈	∈	PROPN
ejpam-5392	67	28	l	l	NOUN
ejpam-5392	67	29	⇒	⇒	NOUN
ejpam-5392	67	30	v	v	X
ejpam-5392	67	31	∪	∪	PROPN
ejpam-5392	67	32	z	z	PROPN
ejpam-5392	67	33	∈	∈	PROPN
ejpam-5392	67	34	l.	l.	PROPN
ejpam-5392	67	35	(	(	PUNCT
ejpam-5392	67	36	ii	ii	PROPN
ejpam-5392	67	37	)	)	PUNCT
ejpam-5392	67	38	v	v	ADP
ejpam-5392	67	39	∈	∈	PROPN
ejpam-5392	67	40	l	l	NOUN
ejpam-5392	67	41	and	and	CCONJ
ejpam-5392	67	42	z	z	PROPN
ejpam-5392	67	43	⊆	⊆	NUM
ejpam-5392	67	44	v	v	ADP
ejpam-5392	67	45	⇒	⇒	NOUN
ejpam-5392	67	46	z	z	PROPN
ejpam-5392	67	47	∈	∈	PROPN
ejpam-5392	67	48	l.	l.	NOUN
ejpam-5392	67	49	through	through	ADP
ejpam-5392	67	50	this	this	DET
ejpam-5392	67	51	content	content	NOUN
ejpam-5392	67	52	,	,	PUNCT
ejpam-5392	67	53	x	x	PRON
ejpam-5392	67	54	indicates	indicate	VERB
ejpam-5392	67	55	for	for	ADP
ejpam-5392	67	56	a	a	DET
ejpam-5392	67	57	finite	finite	NOUN
ejpam-5392	67	58	nonempty	nonempty	ADV
ejpam-5392	67	59	set	set	VERB
ejpam-5392	67	60	.	.	PUNCT
ejpam-5392	68	1	definition	definition	NOUN
ejpam-5392	68	2	2	2	NUM
ejpam-5392	68	3	.	.	PUNCT
ejpam-5392	69	1	[	[	X
ejpam-5392	69	2	9	9	NUM
ejpam-5392	69	3	]	]	PUNCT
ejpam-5392	69	4	let	let	VERB
ejpam-5392	69	5	r	r	PRON
ejpam-5392	69	6	be	be	AUX
ejpam-5392	69	7	a	a	DET
ejpam-5392	69	8	binary	binary	ADJ
ejpam-5392	69	9	relation	relation	NOUN
ejpam-5392	69	10	on	on	ADP
ejpam-5392	69	11	x.	x.	NOUN
ejpam-5392	69	12	then	then	ADV
ejpam-5392	69	13	,	,	PUNCT
ejpam-5392	69	14	the	the	DET
ejpam-5392	69	15	λ	λ	NOUN
ejpam-5392	69	16	-	-	NOUN
ejpam-5392	69	17	neighborhood	neighborhood	NOUN
ejpam-5392	69	18	of	of	ADP
ejpam-5392	69	19	an	an	DET
ejpam-5392	69	20	element	element	NOUN
ejpam-5392	69	21	y	y	PROPN
ejpam-5392	69	22	in	in	ADP
ejpam-5392	69	23	x	x	PRON
ejpam-5392	69	24	,	,	PUNCT
ejpam-5392	69	25	symbolized	symbolize	VERB
ejpam-5392	69	26	by	by	ADP
ejpam-5392	69	27	gλ(y	gλ(y	PROPN
ejpam-5392	69	28	)	)	PUNCT
ejpam-5392	69	29	,	,	PUNCT
ejpam-5392	69	30	λ	λ	PROPN
ejpam-5392	69	31	∈	∈	PROPN
ejpam-5392	69	32	{	{	PUNCT
ejpam-5392	69	33	a	a	PRON
ejpam-5392	69	34	,	,	PUNCT
ejpam-5392	69	35	b	b	NOUN
ejpam-5392	69	36	,	,	PUNCT
ejpam-5392	69	37	â	â	ADJ
ejpam-5392	69	38	,	,	PUNCT
ejpam-5392	69	39	b̂	b̂	PROPN
ejpam-5392	69	40	,	,	PUNCT
ejpam-5392	69	41	i	i	PRON
ejpam-5392	69	42	,	,	PUNCT
ejpam-5392	69	43	u	u	PROPN
ejpam-5392	69	44	,	,	PUNCT
ejpam-5392	69	45	î	î	X
ejpam-5392	69	46	,	,	PUNCT
ejpam-5392	69	47	û	û	NUM
ejpam-5392	69	48	}	}	PUNCT
ejpam-5392	69	49	,	,	PUNCT
ejpam-5392	69	50	is	be	AUX
ejpam-5392	69	51	given	give	VERB
ejpam-5392	69	52	by	by	ADP
ejpam-5392	69	53	:	:	PUNCT
ejpam-5392	69	54	(	(	PUNCT
ejpam-5392	69	55	i	i	NOUN
ejpam-5392	69	56	)	)	PUNCT
ejpam-5392	69	57	ga(y	ga(y	NOUN
ejpam-5392	69	58	)	)	PUNCT
ejpam-5392	69	59	=	=	PRON
ejpam-5392	70	1	{	{	PUNCT
ejpam-5392	70	2	x	x	PUNCT
ejpam-5392	70	3	∈	∈	PROPN
ejpam-5392	70	4	x	x	X
ejpam-5392	70	5	:	:	PUNCT
ejpam-5392	70	6	yrx	yrx	NOUN
ejpam-5392	70	7	}	}	PUNCT
ejpam-5392	70	8	.	.	PUNCT
ejpam-5392	71	1	(	(	PUNCT
ejpam-5392	71	2	ii	ii	NOUN
ejpam-5392	71	3	)	)	PUNCT
ejpam-5392	71	4	gb(y	gb(y	ADV
ejpam-5392	71	5	)	)	PUNCT
ejpam-5392	72	1	=	=	PRON
ejpam-5392	72	2	{	{	PUNCT
ejpam-5392	72	3	x	x	PUNCT
ejpam-5392	72	4	∈	∈	PROPN
ejpam-5392	72	5	x	x	X
ejpam-5392	72	6	:	:	PUNCT
ejpam-5392	72	7	xry	xry	X
ejpam-5392	72	8	}	}	PUNCT
ejpam-5392	72	9	.	.	PUNCT
ejpam-5392	73	1	(	(	PUNCT
ejpam-5392	73	2	iii	iii	X
ejpam-5392	73	3	)	)	PUNCT
ejpam-5392	73	4	gâ(y	gâ(y	NOUN
ejpam-5392	73	5	)	)	PUNCT
ejpam-5392	73	6	=	=	SYM
ejpam-5392	74	1	∩y∈ga(x)ga(x	∩y∈ga(x)ga(x	NUM
ejpam-5392	74	2	)	)	PUNCT
ejpam-5392	74	3	,	,	PUNCT
ejpam-5392	74	4	or	or	CCONJ
ejpam-5392	74	5	gâ(y	gâ(y	NOUN
ejpam-5392	74	6	)	)	PUNCT
ejpam-5392	74	7	=	=	NOUN
ejpam-5392	74	8	∅	∅	NOUN
ejpam-5392	74	9	when	when	SCONJ
ejpam-5392	74	10	there	there	PRON
ejpam-5392	74	11	does	do	AUX
ejpam-5392	74	12	not	not	PART
ejpam-5392	74	13	exists	exist	VERB
ejpam-5392	74	14	ga(x	ga(x	NOUN
ejpam-5392	74	15	)	)	PUNCT
ejpam-5392	74	16	containing	contain	VERB
ejpam-5392	74	17	y.	y.	PROPN
ejpam-5392	74	18	(	(	PUNCT
ejpam-5392	74	19	iv	iv	X
ejpam-5392	74	20	)	)	PUNCT
ejpam-5392	74	21	gb̂(y	gb̂(y	NOUN
ejpam-5392	74	22	)	)	PUNCT
ejpam-5392	74	23	=	=	SYM
ejpam-5392	74	24	∩y∈gb(x)gb(x	∩y∈gb(x)gb(x	NUM
ejpam-5392	74	25	)	)	PUNCT
ejpam-5392	74	26	,	,	PUNCT
ejpam-5392	74	27	or	or	CCONJ
ejpam-5392	74	28	gb̂(y	gb̂(y	NOUN
ejpam-5392	74	29	)	)	PUNCT
ejpam-5392	74	30	=	=	NOUN
ejpam-5392	74	31	∅	∅	NOUN
ejpam-5392	74	32	when	when	SCONJ
ejpam-5392	74	33	there	there	PRON
ejpam-5392	74	34	does	do	AUX
ejpam-5392	74	35	not	not	PART
ejpam-5392	74	36	exists	exist	VERB
ejpam-5392	74	37	gb(x	gb(x	PUNCT
ejpam-5392	74	38	)	)	PUNCT
ejpam-5392	74	39	containing	contain	VERB
ejpam-5392	74	40	y.	y.	NOUN
ejpam-5392	74	41	(	(	PUNCT
ejpam-5392	74	42	v	v	NOUN
ejpam-5392	74	43	)	)	PUNCT
ejpam-5392	74	44	gi(y	gi(y	X
ejpam-5392	74	45	)	)	PUNCT
ejpam-5392	74	46	=	=	SYM
ejpam-5392	74	47	ga(y	ga(y	NOUN
ejpam-5392	74	48	)	)	PUNCT
ejpam-5392	74	49	∩gb(y	∩gb(y	PROPN
ejpam-5392	74	50	)	)	PUNCT
ejpam-5392	74	51	.	.	PUNCT
ejpam-5392	75	1	(	(	PUNCT
ejpam-5392	75	2	vi	vi	NOUN
ejpam-5392	75	3	)	)	PUNCT
ejpam-5392	75	4	gu(y	gu(y	NOUN
ejpam-5392	75	5	)	)	PUNCT
ejpam-5392	75	6	=	=	SYM
ejpam-5392	75	7	ga(y	ga(y	NOUN
ejpam-5392	75	8	)	)	PUNCT
ejpam-5392	75	9	∪gb(y	∪gb(y	ADJ
ejpam-5392	75	10	)	)	PUNCT
ejpam-5392	75	11	.	.	PUNCT
ejpam-5392	76	1	(	(	PUNCT
ejpam-5392	76	2	vii	vii	PROPN
ejpam-5392	76	3	)	)	PUNCT
ejpam-5392	76	4	gî(y	gî(y	PROPN
ejpam-5392	76	5	)	)	PUNCT
ejpam-5392	76	6	=	=	SYM
ejpam-5392	76	7	gâ(y	gâ(y	NOUN
ejpam-5392	76	8	)	)	PUNCT
ejpam-5392	76	9	∩gb̂(y	∩gb̂(y	NOUN
ejpam-5392	76	10	)	)	PUNCT
ejpam-5392	76	11	.	.	PUNCT
ejpam-5392	77	1	(	(	PUNCT
ejpam-5392	77	2	viii	viii	NOUN
ejpam-5392	77	3	)	)	PUNCT
ejpam-5392	77	4	gû(y	gû(y	NOUN
ejpam-5392	77	5	)	)	PUNCT
ejpam-5392	77	6	=	=	SYM
ejpam-5392	77	7	gâ(y	gâ(y	NOUN
ejpam-5392	77	8	)	)	PUNCT
ejpam-5392	77	9	∪gb̂(y	∪gb̂(y	NOUN
ejpam-5392	77	10	)	)	PUNCT
ejpam-5392	77	11	.	.	PUNCT
ejpam-5392	78	1	moving	move	VERB
ejpam-5392	78	2	forward	forward	ADV
ejpam-5392	78	3	,	,	PUNCT
ejpam-5392	78	4	we	we	PRON
ejpam-5392	78	5	utilize	utilize	VERB
ejpam-5392	78	6	this	this	DET
ejpam-5392	78	7	symbol	symbol	NOUN
ejpam-5392	78	8	λ	λ	NOUN
ejpam-5392	78	9	throughout	throughout	ADP
ejpam-5392	78	10	this	this	DET
ejpam-5392	78	11	manuscript	manuscript	NOUN
ejpam-5392	78	12	to	to	PART
ejpam-5392	78	13	refer	refer	VERB
ejpam-5392	78	14	to	to	ADP
ejpam-5392	78	15	the	the	DET
ejpam-5392	78	16	types	type	NOUN
ejpam-5392	78	17	of	of	ADP
ejpam-5392	78	18	neighbourhoods	neighbourhood	NOUN
ejpam-5392	78	19	of	of	ADP
ejpam-5392	78	20	{	{	PUNCT
ejpam-5392	78	21	a	a	PRON
ejpam-5392	78	22	,	,	PUNCT
ejpam-5392	78	23	b	b	NOUN
ejpam-5392	78	24	,	,	PUNCT
ejpam-5392	78	25	â	â	ADJ
ejpam-5392	78	26	,	,	PUNCT
ejpam-5392	78	27	b̂	b̂	PROPN
ejpam-5392	78	28	,	,	PUNCT
ejpam-5392	78	29	i	i	PRON
ejpam-5392	78	30	,	,	PUNCT
ejpam-5392	78	31	u	u	PROPN
ejpam-5392	78	32	,	,	PUNCT
ejpam-5392	78	33	î	î	X
ejpam-5392	78	34	,	,	PUNCT
ejpam-5392	78	35	û	û	NUM
ejpam-5392	78	36	}	}	PUNCT
ejpam-5392	78	37	.	.	PUNCT
ejpam-5392	79	1	definition	definition	NOUN
ejpam-5392	79	2	3	3	NUM
ejpam-5392	79	3	.	.	PUNCT
ejpam-5392	80	1	[	[	X
ejpam-5392	80	2	45	45	NUM
ejpam-5392	80	3	]	]	PUNCT
ejpam-5392	80	4	if	if	SCONJ
ejpam-5392	80	5	ξλ	ξλ	INTJ
ejpam-5392	80	6	:	:	PUNCT
ejpam-5392	80	7	x	x	X
ejpam-5392	80	8	→	→	X
ejpam-5392	80	9	p	p	X
ejpam-5392	80	10	(	(	PUNCT
ejpam-5392	80	11	x	x	X
ejpam-5392	80	12	)	)	PUNCT
ejpam-5392	80	13	is	be	AUX
ejpam-5392	80	14	a	a	DET
ejpam-5392	80	15	mapping	mapping	NOUN
ejpam-5392	80	16	that	that	PRON
ejpam-5392	80	17	assigns	assign	VERB
ejpam-5392	80	18	for	for	ADP
ejpam-5392	80	19	each	each	DET
ejpam-5392	80	20	y	y	PROPN
ejpam-5392	80	21	in	in	ADP
ejpam-5392	80	22	x	x	PROPN
ejpam-5392	80	23	a	a	DET
ejpam-5392	80	24	gλ	gλ	NOUN
ejpam-5392	80	25	in	in	ADP
ejpam-5392	80	26	p	p	X
ejpam-5392	80	27	(	(	PUNCT
ejpam-5392	80	28	x	x	NOUN
ejpam-5392	80	29	)	)	PUNCT
ejpam-5392	80	30	,	,	PUNCT
ejpam-5392	80	31	then	then	ADV
ejpam-5392	80	32	we	we	PRON
ejpam-5392	80	33	called	call	VERB
ejpam-5392	80	34	a	a	DET
ejpam-5392	80	35	3	3	NUM
ejpam-5392	80	36	-	-	PUNCT
ejpam-5392	80	37	tuple	tuple	NOUN
ejpam-5392	80	38	(	(	PUNCT
ejpam-5392	80	39	x	x	X
ejpam-5392	80	40	,	,	PUNCT
ejpam-5392	80	41	r	r	NOUN
ejpam-5392	80	42	,	,	PUNCT
ejpam-5392	80	43	ξλ	ξλ	PROPN
ejpam-5392	80	44	)	)	PUNCT
ejpam-5392	80	45	a	a	DET
ejpam-5392	80	46	gλ	gλ	NOUN
ejpam-5392	80	47	-	-	PUNCT
ejpam-5392	80	48	space	space	NOUN
ejpam-5392	80	49	.	.	PUNCT
ejpam-5392	81	1	theorem	theorem	NOUN
ejpam-5392	81	2	1	1	NUM
ejpam-5392	81	3	.	.	PUNCT
ejpam-5392	82	1	[	[	X
ejpam-5392	82	2	30	30	NUM
ejpam-5392	82	3	,	,	PUNCT
ejpam-5392	82	4	31	31	NUM
ejpam-5392	82	5	,	,	PUNCT
ejpam-5392	82	6	45	45	NUM
ejpam-5392	82	7	]	]	PUNCT
ejpam-5392	82	8	it	it	PRON
ejpam-5392	82	9	may	may	AUX
ejpam-5392	82	10	generate	generate	VERB
ejpam-5392	82	11	a	a	DET
ejpam-5392	82	12	topology	topology	NOUN
ejpam-5392	82	13	ϑλ	ϑλ	ADP
ejpam-5392	82	14	on	on	ADP
ejpam-5392	82	15	x	x	PUNCT
ejpam-5392	82	16	using	use	VERB
ejpam-5392	82	17	gλ	gλ	NOUN
ejpam-5392	82	18	-	-	PUNCT
ejpam-5392	82	19	neighbourhoods	neighbourhood	NOUN
ejpam-5392	82	20	by	by	ADP
ejpam-5392	82	21	the	the	DET
ejpam-5392	82	22	next	next	ADJ
ejpam-5392	82	23	formula	formula	NOUN
ejpam-5392	82	24	ϑλ	ϑλ	ADP
ejpam-5392	82	25	=	=	PUNCT
ejpam-5392	82	26	{	{	PUNCT
ejpam-5392	82	27	v	v	ADP
ejpam-5392	82	28	⊆	⊆	NUM
ejpam-5392	82	29	x	x	SYM
ejpam-5392	82	30	:	:	PUNCT
ejpam-5392	82	31	∀y	∀y	NUM
ejpam-5392	82	32	∈	∈	PROPN
ejpam-5392	82	33	v	v	NOUN
ejpam-5392	82	34	,	,	PUNCT
ejpam-5392	82	35	gλ(y	gλ(y	NUM
ejpam-5392	82	36	)	)	PUNCT
ejpam-5392	82	37	⊆	⊆	NUM
ejpam-5392	82	38	v	v	NOUN
ejpam-5392	82	39	}	}	PUNCT
ejpam-5392	82	40	every	every	DET
ejpam-5392	82	41	member	member	NOUN
ejpam-5392	82	42	of	of	ADP
ejpam-5392	82	43	ϑλ	ϑλ	PROPN
ejpam-5392	82	44	is	be	AUX
ejpam-5392	82	45	named	name	VERB
ejpam-5392	82	46	a	a	DET
ejpam-5392	82	47	λ	λ	NOUN
ejpam-5392	82	48	-	-	ADJ
ejpam-5392	82	49	open	open	ADJ
ejpam-5392	82	50	set	set	NOUN
ejpam-5392	82	51	and	and	CCONJ
ejpam-5392	82	52	we	we	PRON
ejpam-5392	82	53	call	call	VERB
ejpam-5392	82	54	a	a	DET
ejpam-5392	82	55	subset	subset	NOUN
ejpam-5392	82	56	a	a	DET
ejpam-5392	82	57	λ	λ	NOUN
ejpam-5392	82	58	-	-	ADJ
ejpam-5392	82	59	closed	closed	ADJ
ejpam-5392	82	60	set	set	NOUN
ejpam-5392	82	61	if	if	SCONJ
ejpam-5392	82	62	its	its	PRON
ejpam-5392	82	63	complement	complement	NOUN
ejpam-5392	82	64	is	be	AUX
ejpam-5392	82	65	a	a	DET
ejpam-5392	82	66	λ	λ	NOUN
ejpam-5392	82	67	-	-	ADJ
ejpam-5392	82	68	open	open	ADJ
ejpam-5392	82	69	set	set	NOUN
ejpam-5392	82	70	.	.	PUNCT
ejpam-5392	83	1	the	the	DET
ejpam-5392	83	2	class	class	NOUN
ejpam-5392	83	3	of	of	ADP
ejpam-5392	83	4	γλ	γλ	PROPN
ejpam-5392	83	5	is	be	AUX
ejpam-5392	83	6	given	give	VERB
ejpam-5392	83	7	by	by	ADP
ejpam-5392	83	8	γλ	γλ	PROPN
ejpam-5392	83	9	=	=	SYM
ejpam-5392	83	10	{	{	PUNCT
ejpam-5392	83	11	f	f	NOUN
ejpam-5392	83	12	⊆	⊆	NUM
ejpam-5392	83	13	x	x	X
ejpam-5392	83	14	:	:	PUNCT
ejpam-5392	83	15	f	f	X
ejpam-5392	83	16	′	′	NUM
ejpam-5392	83	17	∈	∈	PROPN
ejpam-5392	83	18	ϑλ	ϑλ	ADP
ejpam-5392	83	19	}	}	PUNCT
ejpam-5392	83	20	,	,	PUNCT
ejpam-5392	83	21	where	where	SCONJ
ejpam-5392	83	22	f	f	PROPN
ejpam-5392	83	23	′	′	NOUN
ejpam-5392	83	24	is	be	AUX
ejpam-5392	83	25	the	the	DET
ejpam-5392	83	26	complement	complement	NOUN
ejpam-5392	83	27	of	of	ADP
ejpam-5392	83	28	f	f	PROPN
ejpam-5392	83	29	.	.	PUNCT
ejpam-5392	84	1	definition	definition	NOUN
ejpam-5392	84	2	4	4	NUM
ejpam-5392	84	3	.	.	PUNCT
ejpam-5392	85	1	[	[	X
ejpam-5392	85	2	45	45	NUM
ejpam-5392	85	3	]	]	PUNCT
ejpam-5392	85	4	the	the	DET
ejpam-5392	85	5	λ	λ	NOUN
ejpam-5392	85	6	-	-	PUNCT
ejpam-5392	85	7	lower	low	ADJ
ejpam-5392	85	8	and	and	CCONJ
ejpam-5392	85	9	λ	λ	NOUN
ejpam-5392	85	10	-	-	ADJ
ejpam-5392	85	11	upper	upper	ADJ
ejpam-5392	85	12	approximations	approximation	NOUN
ejpam-5392	85	13	,	,	PUNCT
ejpam-5392	85	14	λ	λ	NOUN
ejpam-5392	85	15	-	-	ADJ
ejpam-5392	85	16	boundary	boundary	ADJ
ejpam-5392	85	17	region	region	NOUN
ejpam-5392	85	18	and	and	CCONJ
ejpam-5392	85	19	λaccuracy	λaccuracy	NOUN
ejpam-5392	85	20	of	of	ADP
ejpam-5392	85	21	v	v	ADP
ejpam-5392	85	22	⊆	⊆	NUM
ejpam-5392	85	23	x	x	NOUN
ejpam-5392	85	24	,	,	PUNCT
ejpam-5392	85	25	inspired	inspire	VERB
ejpam-5392	85	26	by	by	ADP
ejpam-5392	85	27	the	the	DET
ejpam-5392	85	28	topological	topological	ADJ
ejpam-5392	85	29	space	space	NOUN
ejpam-5392	85	30	(	(	PUNCT
ejpam-5392	85	31	x,ϑλ	x,ϑλ	PROPN
ejpam-5392	85	32	)	)	PUNCT
ejpam-5392	85	33	given	give	VERB
ejpam-5392	85	34	in	in	ADP
ejpam-5392	85	35	above	above	ADP
ejpam-5392	85	36	theorem	theorem	ADJ
ejpam-5392	85	37	,	,	PUNCT
ejpam-5392	85	38	are	be	AUX
ejpam-5392	85	39	respectively	respectively	ADV
ejpam-5392	85	40	formulated	formulate	VERB
ejpam-5392	85	41	by	by	ADP
ejpam-5392	85	42	the	the	DET
ejpam-5392	85	43	subsequent	subsequent	ADJ
ejpam-5392	85	44	formulas	formula	NOUN
ejpam-5392	85	45	:	:	PUNCT
ejpam-5392	85	46	rλ(v	rλ(v	NOUN
ejpam-5392	85	47	)	)	PUNCT
ejpam-5392	85	48	is	be	AUX
ejpam-5392	85	49	the	the	DET
ejpam-5392	85	50	union	union	NOUN
ejpam-5392	85	51	of	of	ADP
ejpam-5392	85	52	all	all	DET
ejpam-5392	85	53	λ	λ	NOUN
ejpam-5392	85	54	-	-	ADJ
ejpam-5392	85	55	open	open	ADJ
ejpam-5392	85	56	sets	set	NOUN
ejpam-5392	85	57	which	which	PRON
ejpam-5392	85	58	are	be	AUX
ejpam-5392	85	59	contained	contain	VERB
ejpam-5392	85	60	in	in	ADP
ejpam-5392	85	61	v	v	NOUN
ejpam-5392	85	62	;	;	PUNCT
ejpam-5392	85	63	that	that	PRON
ejpam-5392	85	64	is	be	AUX
ejpam-5392	85	65	v	v	NOUN
ejpam-5392	85	66	=	=	SYM
ejpam-5392	85	67	intλ(v	intλ(v	PROPN
ejpam-5392	85	68	)	)	PUNCT
ejpam-5392	85	69	,	,	PUNCT
ejpam-5392	85	70	where	where	SCONJ
ejpam-5392	85	71	intλ	intλ	PROPN
ejpam-5392	85	72	is	be	AUX
ejpam-5392	85	73	the	the	DET
ejpam-5392	85	74	topological	topological	ADJ
ejpam-5392	85	75	λ	λ	ADJ
ejpam-5392	85	76	-	-	ADJ
ejpam-5392	85	77	interior	interior	ADJ
ejpam-5392	85	78	operator	operator	NOUN
ejpam-5392	85	79	.	.	PUNCT
ejpam-5392	86	1	rλ(v	rλ(v	PROPN
ejpam-5392	86	2	)	)	PUNCT
ejpam-5392	86	3	is	be	AUX
ejpam-5392	86	4	the	the	DET
ejpam-5392	86	5	intersection	intersection	NOUN
ejpam-5392	86	6	of	of	ADP
ejpam-5392	86	7	all	all	DET
ejpam-5392	86	8	λ	λ	NOUN
ejpam-5392	86	9	-	-	ADJ
ejpam-5392	86	10	closed	closed	ADJ
ejpam-5392	86	11	sets	set	NOUN
ejpam-5392	86	12	containing	contain	VERB
ejpam-5392	86	13	v	v	NOUN
ejpam-5392	86	14	;	;	PUNCT
ejpam-5392	86	15	that	that	PRON
ejpam-5392	86	16	is	is	ADV
ejpam-5392	86	17	,	,	PUNCT
ejpam-5392	86	18	v	v	NOUN
ejpam-5392	86	19	=	=	SYM
ejpam-5392	86	20	clλ(v	clλ(v	PROPN
ejpam-5392	86	21	)	)	PUNCT
ejpam-5392	86	22	,	,	PUNCT
ejpam-5392	86	23	where	where	SCONJ
ejpam-5392	86	24	clλ	clλ	NOUN
ejpam-5392	86	25	is	be	AUX
ejpam-5392	86	26	the	the	DET
ejpam-5392	86	27	topological	topological	ADJ
ejpam-5392	86	28	λ	λ	PROPN
ejpam-5392	86	29	-	-	PUNCT
ejpam-5392	86	30	closure	closure	NOUN
ejpam-5392	86	31	operator	operator	NOUN
ejpam-5392	86	32	.	.	PUNCT
ejpam-5392	87	1	bndλ(v	bndλ(v	INTJ
ejpam-5392	87	2	)	)	PUNCT
ejpam-5392	88	1	=	=	PUNCT
ejpam-5392	88	2	rλ(v	rλ(v	X
ejpam-5392	88	3	)	)	PUNCT
ejpam-5392	88	4	−rλ(v	−rλ(v	PROPN
ejpam-5392	88	5	)	)	PUNCT
ejpam-5392	88	6	.	.	PUNCT
ejpam-5392	89	1	accλ(v	accλ(v	ADV
ejpam-5392	89	2	)	)	PUNCT
ejpam-5392	90	1	=	=	SYM
ejpam-5392	90	2	|rλ(v	|rλ(v	PROPN
ejpam-5392	90	3	)	)	PUNCT
ejpam-5392	90	4	|	|	ADV
ejpam-5392	90	5	|rλ(v	|rλ(v	PRON
ejpam-5392	90	6	)	)	PUNCT
ejpam-5392	91	1	|	|	ADV
ejpam-5392	91	2	,	,	PUNCT
ejpam-5392	91	3	for	for	ADP
ejpam-5392	91	4	each	each	DET
ejpam-5392	91	5	subset	subset	NOUN
ejpam-5392	91	6	v	v	ADP
ejpam-5392	91	7	̸=	̸=	PROPN
ejpam-5392	91	8	∅.	∅.	PRON
ejpam-5392	91	9	m.	m.	PROPN
ejpam-5392	91	10	hosny	hosny	PROPN
ejpam-5392	91	11	,	,	PUNCT
ejpam-5392	91	12	t.m	t.m	PROPN
ejpam-5392	91	13	.	.	PROPN
ejpam-5392	91	14	al	al	PROPN
ejpam-5392	91	15	-	-	PUNCT
ejpam-5392	91	16	shami	shami	PROPN
ejpam-5392	91	17	/	/	PUNCT
ejpam-5392	91	18	eur	eur	PROPN
ejpam-5392	91	19	.	.	PUNCT
ejpam-5392	92	1	j.	j.	PROPN
ejpam-5392	92	2	pure	pure	PROPN
ejpam-5392	92	3	appl	appl	PROPN
ejpam-5392	92	4	.	.	PROPN
ejpam-5392	92	5	math	math	PROPN
ejpam-5392	92	6	,	,	PUNCT
ejpam-5392	92	7	17	17	NUM
ejpam-5392	92	8	(	(	PUNCT
ejpam-5392	92	9	4	4	NUM
ejpam-5392	92	10	)	)	PUNCT
ejpam-5392	92	11	(	(	PUNCT
ejpam-5392	92	12	2024	2024	NUM
ejpam-5392	92	13	)	)	PUNCT
ejpam-5392	92	14	,	,	PUNCT
ejpam-5392	92	15	3436	3436	NUM
ejpam-5392	92	16	-	-	SYM
ejpam-5392	92	17	3463	3463	NUM
ejpam-5392	92	18	3440	3440	NUM
ejpam-5392	92	19	remember	remember	VERB
ejpam-5392	92	20	that	that	SCONJ
ejpam-5392	92	21	a	a	DET
ejpam-5392	92	22	subset	subset	NOUN
ejpam-5392	92	23	v	v	NOUN
ejpam-5392	92	24	is	be	AUX
ejpam-5392	92	25	named	name	VERB
ejpam-5392	92	26	λ	λ	NOUN
ejpam-5392	92	27	-	-	NOUN
ejpam-5392	92	28	exact	exact	ADJ
ejpam-5392	92	29	if	if	SCONJ
ejpam-5392	92	30	rλ(v	rλ(v	VERB
ejpam-5392	92	31	)	)	PUNCT
ejpam-5392	92	32	=	=	VERB
ejpam-5392	92	33	rλ(v	rλ(v	X
ejpam-5392	92	34	)	)	PUNCT
ejpam-5392	92	35	.	.	PUNCT
ejpam-5392	93	1	otherwise	otherwise	ADV
ejpam-5392	93	2	,	,	PUNCT
ejpam-5392	93	3	v	v	NOUN
ejpam-5392	93	4	is	be	AUX
ejpam-5392	93	5	λ	λ	NOUN
ejpam-5392	93	6	-	-	NOUN
ejpam-5392	93	7	rough	rough	ADJ
ejpam-5392	93	8	.	.	PUNCT
ejpam-5392	94	1	in	in	ADP
ejpam-5392	94	2	what	what	PRON
ejpam-5392	94	3	follows	follow	VERB
ejpam-5392	94	4	,	,	PUNCT
ejpam-5392	94	5	we	we	PRON
ejpam-5392	94	6	recall	recall	VERB
ejpam-5392	94	7	some	some	DET
ejpam-5392	94	8	definitions	definition	NOUN
ejpam-5392	94	9	of	of	ADP
ejpam-5392	94	10	λ	λ	NOUN
ejpam-5392	94	11	-	-	PUNCT
ejpam-5392	94	12	nearly	nearly	ADV
ejpam-5392	94	13	open	open	ADJ
ejpam-5392	94	14	sets	set	NOUN
ejpam-5392	94	15	.	.	PUNCT
ejpam-5392	95	1	definition	definition	NOUN
ejpam-5392	95	2	5	5	NUM
ejpam-5392	95	3	.	.	PUNCT
ejpam-5392	96	1	[	[	X
ejpam-5392	96	2	15	15	NUM
ejpam-5392	96	3	,	,	PUNCT
ejpam-5392	96	4	20	20	NUM
ejpam-5392	96	5	]	]	PUNCT
ejpam-5392	96	6	let	let	VERB
ejpam-5392	96	7	(	(	PUNCT
ejpam-5392	96	8	x	x	NOUN
ejpam-5392	96	9	,	,	PUNCT
ejpam-5392	96	10	r	r	NOUN
ejpam-5392	96	11	,	,	PUNCT
ejpam-5392	96	12	ξλ	ξλ	NOUN
ejpam-5392	96	13	)	)	PUNCT
ejpam-5392	96	14	be	be	AUX
ejpam-5392	96	15	a	a	DET
ejpam-5392	96	16	gλ	gλ	NOUN
ejpam-5392	96	17	-	-	PUNCT
ejpam-5392	96	18	space	space	NOUN
ejpam-5392	96	19	.	.	PUNCT
ejpam-5392	97	1	v	v	ADP
ejpam-5392	97	2	⊆	⊆	NUM
ejpam-5392	97	3	x	x	PUNCT
ejpam-5392	97	4	is	be	AUX
ejpam-5392	97	5	said	say	VERB
ejpam-5392	97	6	to	to	PART
ejpam-5392	97	7	be	be	AUX
ejpam-5392	97	8	(	(	PUNCT
ejpam-5392	97	9	i	i	NOUN
ejpam-5392	97	10	)	)	PUNCT
ejpam-5392	97	11	λ	λ	NOUN
ejpam-5392	97	12	-	-	NOUN
ejpam-5392	97	13	preopen	preopen	ADJ
ejpam-5392	97	14	(	(	PUNCT
ejpam-5392	97	15	pλ	pλ	ADJ
ejpam-5392	97	16	-	-	ADV
ejpam-5392	97	17	open	open	ADJ
ejpam-5392	97	18	)	)	PUNCT
ejpam-5392	97	19	,	,	PUNCT
ejpam-5392	97	20	if	if	SCONJ
ejpam-5392	97	21	intλ(clλ(v	intλ(clλ(v	ADJ
ejpam-5392	97	22	)	)	PUNCT
ejpam-5392	97	23	)	)	PUNCT
ejpam-5392	98	1	⊇	⊇	PROPN
ejpam-5392	98	2	v	v	NOUN
ejpam-5392	98	3	.	.	PUNCT
ejpam-5392	98	4	(	(	PUNCT
ejpam-5392	98	5	ii	ii	NOUN
ejpam-5392	98	6	)	)	PUNCT
ejpam-5392	98	7	λ	λ	NOUN
ejpam-5392	98	8	-	-	PUNCT
ejpam-5392	98	9	semiopen	semiopen	ADJ
ejpam-5392	98	10	(	(	PUNCT
ejpam-5392	98	11	sλ	sλ	NOUN
ejpam-5392	98	12	-	-	PUNCT
ejpam-5392	98	13	open	open	ADJ
ejpam-5392	98	14	)	)	PUNCT
ejpam-5392	98	15	,	,	PUNCT
ejpam-5392	98	16	if	if	SCONJ
ejpam-5392	98	17	clλ(intλ(v	clλ(intλ(v	VERB
ejpam-5392	98	18	)	)	PUNCT
ejpam-5392	98	19	)	)	PUNCT
ejpam-5392	99	1	⊇	⊇	PROPN
ejpam-5392	99	2	v	v	NOUN
ejpam-5392	99	3	.	.	PUNCT
ejpam-5392	100	1	(	(	PUNCT
ejpam-5392	100	2	iii	iii	X
ejpam-5392	100	3	)	)	PUNCT
ejpam-5392	100	4	αλ	αλ	ADV
ejpam-5392	100	5	-	-	PUNCT
ejpam-5392	100	6	open	open	ADJ
ejpam-5392	100	7	,	,	PUNCT
ejpam-5392	100	8	if	if	SCONJ
ejpam-5392	100	9	v	v	ADP
ejpam-5392	100	10	⊆	⊆	NUM
ejpam-5392	100	11	intλ[clλ(intλ(v	intλ[clλ(intλ(v	PROPN
ejpam-5392	100	12	)	)	PUNCT
ejpam-5392	100	13	)	)	PUNCT
ejpam-5392	101	1	]	]	PUNCT
ejpam-5392	101	2	.	.	PUNCT
ejpam-5392	102	1	(	(	PUNCT
ejpam-5392	102	2	iv	iv	X
ejpam-5392	102	3	)	)	PUNCT
ejpam-5392	102	4	βλ	βλ	ADJ
ejpam-5392	102	5	-	-	PUNCT
ejpam-5392	102	6	open	open	ADJ
ejpam-5392	102	7	(	(	PUNCT
ejpam-5392	102	8	semi	semi	ADV
ejpam-5392	102	9	preopen	preopen	ADJ
ejpam-5392	102	10	)	)	PUNCT
ejpam-5392	102	11	,	,	PUNCT
ejpam-5392	102	12	if	if	SCONJ
ejpam-5392	102	13	v	v	ADP
ejpam-5392	102	14	⊆	⊆	NUM
ejpam-5392	102	15	clλ[intλ(clλ(v	clλ[intλ(clλ(v	PROPN
ejpam-5392	102	16	)	)	PUNCT
ejpam-5392	102	17	)	)	PUNCT
ejpam-5392	102	18	]	]	PUNCT
ejpam-5392	102	19	.	.	PUNCT
ejpam-5392	103	1	(	(	PUNCT
ejpam-5392	103	2	v	v	NOUN
ejpam-5392	103	3	)	)	PUNCT
ejpam-5392	103	4	δβλ	δβλ	NOUN
ejpam-5392	103	5	-	-	PUNCT
ejpam-5392	103	6	open	open	ADJ
ejpam-5392	103	7	,	,	PUNCT
ejpam-5392	103	8	if	if	SCONJ
ejpam-5392	103	9	v	v	ADP
ejpam-5392	103	10	⊆	⊆	NUM
ejpam-5392	103	11	clλ[intλ(cl	clλ[intλ(cl	PROPN
ejpam-5392	103	12	δ	δ	PROPN
ejpam-5392	103	13	λ(v	λ(v	PROPN
ejpam-5392	103	14	)	)	PUNCT
ejpam-5392	103	15	)	)	PUNCT
ejpam-5392	104	1	]	]	PUNCT
ejpam-5392	104	2	,	,	PUNCT
ejpam-5392	104	3	where	where	SCONJ
ejpam-5392	104	4	clδλ(v	clδλ(v	PROPN
ejpam-5392	104	5	)	)	PUNCT
ejpam-5392	104	6	=	=	PRON
ejpam-5392	105	1	{	{	PUNCT
ejpam-5392	105	2	y	y	PROPN
ejpam-5392	105	3	∈	∈	PROPN
ejpam-5392	105	4	x	x	X
ejpam-5392	105	5	:	:	PUNCT
ejpam-5392	105	6	v	v	NUM
ejpam-5392	105	7	∩	∩	NOUN
ejpam-5392	105	8	intλ(clλ(g	intλ(clλ(g	NOUN
ejpam-5392	105	9	)	)	PUNCT
ejpam-5392	105	10	)	)	PUNCT
ejpam-5392	106	1	̸=	̸=	NOUN
ejpam-5392	106	2	∅	∅	NOUN
ejpam-5392	106	3	,	,	PUNCT
ejpam-5392	106	4	g	g	PROPN
ejpam-5392	106	5	∈	∈	PROPN
ejpam-5392	106	6	ϑλ	ϑλ	PROPN
ejpam-5392	106	7	and	and	CCONJ
ejpam-5392	106	8	y	y	PROPN
ejpam-5392	106	9	∈	∈	PROPN
ejpam-5392	106	10	g	g	PROPN
ejpam-5392	106	11	}	}	PUNCT
ejpam-5392	106	12	.	.	PUNCT
ejpam-5392	107	1	(	(	PUNCT
ejpam-5392	107	2	vi	vi	NOUN
ejpam-5392	107	3	)	)	PUNCT
ejpam-5392	107	4	∧	∧	NOUN
ejpam-5392	107	5	βλ	βλ	INTJ
ejpam-5392	107	6	-set	-set	ADJ
ejpam-5392	107	7	if	if	SCONJ
ejpam-5392	107	8	v	v	VERB
ejpam-5392	107	9	=	=	SYM
ejpam-5392	107	10	∧	∧	PROPN
ejpam-5392	107	11	βλ	βλ	X
ejpam-5392	107	12	(	(	PUNCT
ejpam-5392	107	13	v	v	NOUN
ejpam-5392	107	14	)	)	PUNCT
ejpam-5392	107	15	,	,	PUNCT
ejpam-5392	107	16	where	where	SCONJ
ejpam-5392	107	17	∧	∧	PROPN
ejpam-5392	107	18	βλ	βλ	X
ejpam-5392	107	19	(	(	PUNCT
ejpam-5392	107	20	v	v	NOUN
ejpam-5392	107	21	)	)	PUNCT
ejpam-5392	108	1	=	=	VERB
ejpam-5392	108	2	∩{g	∩{g	INTJ
ejpam-5392	108	3	:	:	PUNCT
ejpam-5392	108	4	v	v	ADP
ejpam-5392	108	5	⊆	⊆	NUM
ejpam-5392	108	6	g	g	NOUN
ejpam-5392	108	7	,	,	PUNCT
ejpam-5392	108	8	g	g	PROPN
ejpam-5392	108	9	∈	∈	PROPN
ejpam-5392	108	10	βλo(x	βλo(x	PROPN
ejpam-5392	108	11	)	)	PUNCT
ejpam-5392	108	12	}	}	PUNCT
ejpam-5392	108	13	.	.	PUNCT
ejpam-5392	109	1	the	the	DET
ejpam-5392	109	2	families	family	NOUN
ejpam-5392	109	3	of	of	ADP
ejpam-5392	109	4	λ	λ	NOUN
ejpam-5392	109	5	-	-	PUNCT
ejpam-5392	109	6	nearly	nearly	ADV
ejpam-5392	109	7	open	open	ADJ
ejpam-5392	109	8	subsets	subset	NOUN
ejpam-5392	109	9	of	of	ADP
ejpam-5392	109	10	x	x	SYM
ejpam-5392	109	11	are	be	AUX
ejpam-5392	109	12	assigned	assign	VERB
ejpam-5392	109	13	by	by	ADP
ejpam-5392	109	14	ηλo(x	ηλo(x	PROPN
ejpam-5392	109	15	)	)	PUNCT
ejpam-5392	109	16	,	,	PUNCT
ejpam-5392	109	17	where	where	SCONJ
ejpam-5392	109	18	η	η	PROPN
ejpam-5392	109	19	∈	∈	PROPN
ejpam-5392	109	20	{	{	PUNCT
ejpam-5392	109	21	α	α	NOUN
ejpam-5392	109	22	,	,	PUNCT
ejpam-5392	109	23	p	p	X
ejpam-5392	109	24	,	,	PUNCT
ejpam-5392	109	25	s	s	PROPN
ejpam-5392	109	26	,	,	PUNCT
ejpam-5392	109	27	β	β	X
ejpam-5392	109	28	,	,	PUNCT
ejpam-5392	109	29	δβ	δβ	NOUN
ejpam-5392	109	30	,	,	PUNCT
ejpam-5392	109	31	∧	∧	PROPN
ejpam-5392	109	32	β	β	NOUN
ejpam-5392	109	33	}	}	PUNCT
ejpam-5392	109	34	.	.	PUNCT
ejpam-5392	110	1	the	the	DET
ejpam-5392	110	2	complements	complement	NOUN
ejpam-5392	110	3	of	of	ADP
ejpam-5392	110	4	the	the	DET
ejpam-5392	110	5	λ	λ	NOUN
ejpam-5392	110	6	-	-	PUNCT
ejpam-5392	110	7	nearly	nearly	ADV
ejpam-5392	110	8	open	open	ADJ
ejpam-5392	110	9	sets	set	NOUN
ejpam-5392	110	10	are	be	AUX
ejpam-5392	110	11	known	know	VERB
ejpam-5392	110	12	as	as	ADP
ejpam-5392	110	13	λ	λ	NOUN
ejpam-5392	110	14	-	-	PUNCT
ejpam-5392	110	15	nearly	nearly	ADV
ejpam-5392	110	16	closed	closed	ADJ
ejpam-5392	110	17	sets	set	NOUN
ejpam-5392	110	18	and	and	CCONJ
ejpam-5392	110	19	denoted	denote	VERB
ejpam-5392	110	20	by	by	ADP
ejpam-5392	110	21	ηλc(x	ηλc(x	PROPN
ejpam-5392	110	22	)	)	PUNCT
ejpam-5392	110	23	.	.	PUNCT
ejpam-5392	111	1	henceforth	henceforth	ADV
ejpam-5392	111	2	,	,	PUNCT
ejpam-5392	111	3	we	we	PRON
ejpam-5392	111	4	mean	mean	VERB
ejpam-5392	111	5	by	by	ADP
ejpam-5392	111	6	η	η	PROPN
ejpam-5392	111	7	the	the	DET
ejpam-5392	111	8	elements	element	NOUN
ejpam-5392	111	9	of	of	ADP
ejpam-5392	111	10	the	the	DET
ejpam-5392	111	11	set	set	NOUN
ejpam-5392	111	12	{	{	PUNCT
ejpam-5392	111	13	p	p	X
ejpam-5392	111	14	,	,	PUNCT
ejpam-5392	111	15	s	s	PROPN
ejpam-5392	111	16	,	,	PUNCT
ejpam-5392	111	17	α	α	PROPN
ejpam-5392	111	18	,	,	PUNCT
ejpam-5392	111	19	β	β	NOUN
ejpam-5392	111	20	,	,	PUNCT
ejpam-5392	111	21	δβ	δβ	NOUN
ejpam-5392	111	22	,	,	PUNCT
ejpam-5392	111	23	∧	∧	PROPN
ejpam-5392	111	24	β	β	NOUN
ejpam-5392	111	25	}	}	PUNCT
ejpam-5392	111	26	,	,	PUNCT
ejpam-5392	111	27	unless	unless	SCONJ
ejpam-5392	111	28	otherwise	otherwise	ADV
ejpam-5392	111	29	stated	state	VERB
ejpam-5392	111	30	.	.	PUNCT
ejpam-5392	112	1	definition	definition	NOUN
ejpam-5392	112	2	6	6	NUM
ejpam-5392	112	3	.	.	PUNCT
ejpam-5392	113	1	[	[	X
ejpam-5392	113	2	15	15	NUM
ejpam-5392	113	3	,	,	PUNCT
ejpam-5392	113	4	20	20	NUM
ejpam-5392	113	5	]	]	PUNCT
ejpam-5392	113	6	let	let	VERB
ejpam-5392	113	7	(	(	PUNCT
ejpam-5392	113	8	x	x	NOUN
ejpam-5392	113	9	,	,	PUNCT
ejpam-5392	113	10	r	r	NOUN
ejpam-5392	113	11	,	,	PUNCT
ejpam-5392	113	12	ξλ	ξλ	NOUN
ejpam-5392	113	13	)	)	PUNCT
ejpam-5392	113	14	be	be	AUX
ejpam-5392	113	15	a	a	DET
ejpam-5392	113	16	gλ	gλ	NOUN
ejpam-5392	113	17	-	-	PUNCT
ejpam-5392	113	18	space	space	NOUN
ejpam-5392	113	19	and	and	CCONJ
ejpam-5392	113	20	v	v	ADP
ejpam-5392	113	21	⊆	⊆	NUM
ejpam-5392	113	22	x.	x.	NOUN
ejpam-5392	113	23	the	the	DET
ejpam-5392	113	24	ηλ	ηλ	NOUN
ejpam-5392	113	25	-	-	PUNCT
ejpam-5392	113	26	lower	low	ADJ
ejpam-5392	113	27	and	and	CCONJ
ejpam-5392	113	28	ηλ	ηλ	NOUN
ejpam-5392	113	29	-	-	PUNCT
ejpam-5392	113	30	upper	upper	ADJ
ejpam-5392	113	31	approximations	approximation	NOUN
ejpam-5392	113	32	,	,	PUNCT
ejpam-5392	113	33	ηλ	ηλ	ADJ
ejpam-5392	113	34	-	-	PUNCT
ejpam-5392	113	35	boundary	boundary	ADJ
ejpam-5392	113	36	regions	region	NOUN
ejpam-5392	113	37	and	and	CCONJ
ejpam-5392	113	38	ηλ	ηλ	NOUN
ejpam-5392	113	39	-	-	PUNCT
ejpam-5392	113	40	accuracy	accuracy	NOUN
ejpam-5392	113	41	of	of	ADP
ejpam-5392	113	42	v	v	NOUN
ejpam-5392	113	43	are	be	AUX
ejpam-5392	113	44	respectively	respectively	ADV
ejpam-5392	113	45	given	give	VERB
ejpam-5392	113	46	by	by	ADP
ejpam-5392	113	47	:	:	PUNCT
ejpam-5392	113	48	rη	rη	NOUN
ejpam-5392	113	49	λ(v	λ(v	PRON
ejpam-5392	113	50	)	)	PUNCT
ejpam-5392	114	1	=	=	PUNCT
ejpam-5392	114	2	∪{g	∪{g	PROPN
ejpam-5392	114	3	∈	∈	PROPN
ejpam-5392	114	4	ηλo(x	ηλo(x	PROPN
ejpam-5392	114	5	)	)	PUNCT
ejpam-5392	114	6	:	:	PUNCT
ejpam-5392	115	1	g	g	PROPN
ejpam-5392	115	2	⊆	⊆	NUM
ejpam-5392	115	3	v	v	NOUN
ejpam-5392	115	4	}	}	PUNCT
ejpam-5392	115	5	=	=	PUNCT
ejpam-5392	115	6	ηλ	ηλ	PROPN
ejpam-5392	115	7	-	-	ADJ
ejpam-5392	115	8	interior	interior	NOUN
ejpam-5392	115	9	of	of	ADP
ejpam-5392	115	10	v	v	NOUN
ejpam-5392	115	11	.	.	PUNCT
ejpam-5392	116	1	rη	rη	NOUN
ejpam-5392	116	2	λ(v	λ(v	PROPN
ejpam-5392	116	3	)	)	PUNCT
ejpam-5392	117	1	∩	∩	NOUN
ejpam-5392	117	2	{	{	PUNCT
ejpam-5392	117	3	h	h	NOUN
ejpam-5392	117	4	∈	∈	PROPN
ejpam-5392	117	5	ηλc(x	ηλc(x	PROPN
ejpam-5392	117	6	)	)	PUNCT
ejpam-5392	117	7	:	:	PUNCT
ejpam-5392	117	8	v	v	ADP
ejpam-5392	117	9	⊆	⊆	NUM
ejpam-5392	117	10	h	h	NOUN
ejpam-5392	117	11	}	}	PUNCT
ejpam-5392	117	12	=	=	SYM
ejpam-5392	117	13	ηλ	ηλ	NOUN
ejpam-5392	117	14	-	-	PUNCT
ejpam-5392	117	15	closure	closure	NOUN
ejpam-5392	117	16	of	of	ADP
ejpam-5392	117	17	v	v	NOUN
ejpam-5392	117	18	.	.	PUNCT
ejpam-5392	118	1	bndη	bndη	NOUN
ejpam-5392	118	2	λ(v	λ(v	PROPN
ejpam-5392	118	3	)	)	PUNCT
ejpam-5392	119	1	=	=	PUNCT
ejpam-5392	119	2	rη	rη	NOUN
ejpam-5392	119	3	λ(v	λ(v	PROPN
ejpam-5392	119	4	)	)	PUNCT
ejpam-5392	119	5	−rη	−rη	PROPN
ejpam-5392	119	6	λ(v	λ(v	PROPN
ejpam-5392	119	7	)	)	PUNCT
ejpam-5392	119	8	.	.	PUNCT
ejpam-5392	120	1	accηλ(v	accηλ(v	INTJ
ejpam-5392	120	2	)	)	PUNCT
ejpam-5392	121	1	=	=	SYM
ejpam-5392	122	1	|rη	|rη	PROPN
ejpam-5392	122	2	λ(v	λ(v	PROPN
ejpam-5392	122	3	)	)	PUNCT
ejpam-5392	122	4	|	|	ADV
ejpam-5392	122	5	|rη	|rη	NUM
ejpam-5392	122	6	λ(v	λ(v	PROPN
ejpam-5392	122	7	)	)	PUNCT
ejpam-5392	123	1	|	|	ADV
ejpam-5392	123	2	,	,	PUNCT
ejpam-5392	123	3	where	where	SCONJ
ejpam-5392	123	4	|rη	|rη	PRON
ejpam-5392	123	5	λ(v	λ(v	PROPN
ejpam-5392	123	6	)	)	PUNCT
ejpam-5392	123	7	|	|	ADV
ejpam-5392	123	8	=	=	NOUN
ejpam-5392	123	9	̸	̸	NUM
ejpam-5392	123	10	0	0	NUM
ejpam-5392	123	11	,	,	PUNCT
ejpam-5392	123	12	|rη	|rη	NUM
ejpam-5392	123	13	λ(v	λ(v	PROPN
ejpam-5392	123	14	)	)	PUNCT
ejpam-5392	123	15	|	|	ADV
ejpam-5392	123	16	denotes	denote	VERB
ejpam-5392	123	17	the	the	DET
ejpam-5392	123	18	cardinality	cardinality	NOUN
ejpam-5392	123	19	of	of	ADP
ejpam-5392	123	20	rη	rη	NOUN
ejpam-5392	123	21	λ(v	λ(v	PROPN
ejpam-5392	123	22	)	)	PUNCT
ejpam-5392	123	23	.	.	PUNCT
ejpam-5392	124	1	definition	definition	NOUN
ejpam-5392	124	2	7	7	NUM
ejpam-5392	124	3	.	.	PUNCT
ejpam-5392	125	1	[	[	X
ejpam-5392	125	2	20	20	NUM
ejpam-5392	125	3	]	]	PUNCT
ejpam-5392	125	4	a	a	DET
ejpam-5392	125	5	subset	subset	NOUN
ejpam-5392	125	6	v	v	NOUN
ejpam-5392	125	7	of	of	ADP
ejpam-5392	125	8	a	a	DET
ejpam-5392	125	9	gλ	gλ	NOUN
ejpam-5392	125	10	-	-	PUNCT
ejpam-5392	125	11	space	space	NOUN
ejpam-5392	125	12	(	(	PUNCT
ejpam-5392	125	13	x	x	NOUN
ejpam-5392	125	14	,	,	PUNCT
ejpam-5392	125	15	r	r	NOUN
ejpam-5392	125	16	,	,	PUNCT
ejpam-5392	125	17	ξλ	ξλ	NOUN
ejpam-5392	125	18	)	)	PUNCT
ejpam-5392	125	19	is	be	AUX
ejpam-5392	125	20	called	call	VERB
ejpam-5392	125	21	:	:	PUNCT
ejpam-5392	125	22	(	(	PUNCT
ejpam-5392	125	23	i	i	NOUN
ejpam-5392	125	24	)	)	PUNCT
ejpam-5392	125	25	δβλ	δβλ	NOUN
ejpam-5392	125	26	-	-	PUNCT
ejpam-5392	125	27	definable	definable	ADJ
ejpam-5392	125	28	(	(	PUNCT
ejpam-5392	125	29	δβλ	δβλ	NOUN
ejpam-5392	125	30	-	-	PUNCT
ejpam-5392	125	31	exact	exact	ADJ
ejpam-5392	125	32	)	)	PUNCT
ejpam-5392	126	1	if	if	SCONJ
ejpam-5392	126	2	rδβ	rδβ	NOUN
ejpam-5392	126	3	λ	λ	PROPN
ejpam-5392	126	4	(	(	PUNCT
ejpam-5392	126	5	v	v	NOUN
ejpam-5392	126	6	)	)	PUNCT
ejpam-5392	126	7	=	=	SYM
ejpam-5392	126	8	rδβ	rδβ	NOUN
ejpam-5392	126	9	λ	λ	PROPN
ejpam-5392	126	10	(	(	PUNCT
ejpam-5392	126	11	v	v	NOUN
ejpam-5392	126	12	)	)	PUNCT
ejpam-5392	126	13	or	or	CCONJ
ejpam-5392	126	14	bndδβ	bndδβ	NOUN
ejpam-5392	126	15	λ	λ	PROPN
ejpam-5392	126	16	(	(	PUNCT
ejpam-5392	126	17	v	v	NOUN
ejpam-5392	126	18	)	)	PUNCT
ejpam-5392	126	19	=	=	PUNCT
ejpam-5392	126	20	∅.	∅.	PRON
ejpam-5392	126	21	(	(	PUNCT
ejpam-5392	126	22	ii	ii	NOUN
ejpam-5392	126	23	)	)	PUNCT
ejpam-5392	126	24	δβλ	δβλ	NOUN
ejpam-5392	126	25	-	-	PUNCT
ejpam-5392	126	26	rough	rough	ADJ
ejpam-5392	126	27	if	if	SCONJ
ejpam-5392	126	28	rδβ	rδβ	NOUN
ejpam-5392	126	29	λ	λ	PROPN
ejpam-5392	126	30	(	(	PUNCT
ejpam-5392	126	31	v	v	NOUN
ejpam-5392	126	32	)	)	PUNCT
ejpam-5392	126	33	̸=	̸=	PROPN
ejpam-5392	126	34	rδβ	rδβ	NOUN
ejpam-5392	126	35	λ	λ	PROPN
ejpam-5392	126	36	(	(	PUNCT
ejpam-5392	126	37	v	v	NOUN
ejpam-5392	126	38	)	)	PUNCT
ejpam-5392	126	39	or	or	CCONJ
ejpam-5392	126	40	bndδβ	bndδβ	NOUN
ejpam-5392	126	41	λ	λ	PROPN
ejpam-5392	126	42	(	(	PUNCT
ejpam-5392	126	43	v	v	NOUN
ejpam-5392	126	44	)	)	PUNCT
ejpam-5392	126	45	̸=	̸=	PROPN
ejpam-5392	126	46	∅.	∅.	ADP
ejpam-5392	126	47	(	(	PUNCT
ejpam-5392	126	48	iii	iii	NOUN
ejpam-5392	126	49	)	)	PUNCT
ejpam-5392	126	50	∧	∧	NOUN
ejpam-5392	126	51	βλ	βλ	ADP
ejpam-5392	126	52	-definable	-definable	ADJ
ejpam-5392	126	53	(	(	PUNCT
ejpam-5392	126	54	∧	∧	NOUN
ejpam-5392	126	55	βλ	βλ	NOUN
ejpam-5392	126	56	-exact	-exact	NOUN
ejpam-5392	126	57	)	)	PUNCT
ejpam-5392	126	58	if	if	SCONJ
ejpam-5392	126	59	r	r	NOUN
ejpam-5392	126	60	∧	∧	PROPN
ejpam-5392	126	61	β	β	X
ejpam-5392	126	62	λ	λ	PROPN
ejpam-5392	126	63	(	(	PUNCT
ejpam-5392	126	64	v	v	NOUN
ejpam-5392	126	65	)	)	PUNCT
ejpam-5392	126	66	=	=	SYM
ejpam-5392	127	1	r	r	NOUN
ejpam-5392	127	2	∧	∧	PROPN
ejpam-5392	127	3	β	β	X
ejpam-5392	127	4	λ	λ	PROPN
ejpam-5392	127	5	(	(	PUNCT
ejpam-5392	127	6	v	v	NOUN
ejpam-5392	127	7	)	)	PUNCT
ejpam-5392	127	8	or	or	CCONJ
ejpam-5392	127	9	bnd	bnd	VERB
ejpam-5392	127	10	∧	∧	PROPN
ejpam-5392	127	11	β	β	X
ejpam-5392	127	12	λ	λ	PROPN
ejpam-5392	127	13	(	(	PUNCT
ejpam-5392	127	14	v	v	NOUN
ejpam-5392	127	15	)	)	PUNCT
ejpam-5392	127	16	=	=	PUNCT
ejpam-5392	127	17	∅.	∅.	X
ejpam-5392	127	18	(	(	PUNCT
ejpam-5392	127	19	iv	iv	X
ejpam-5392	127	20	)	)	PUNCT
ejpam-5392	127	21	∧	∧	NOUN
ejpam-5392	127	22	βλ	βλ	NOUN
ejpam-5392	127	23	-rough	-rough	PROPN
ejpam-5392	127	24	if	if	SCONJ
ejpam-5392	127	25	r	r	NOUN
ejpam-5392	127	26	∧	∧	PROPN
ejpam-5392	127	27	β	β	X
ejpam-5392	127	28	λ	λ	PROPN
ejpam-5392	127	29	(	(	PUNCT
ejpam-5392	127	30	v	v	NOUN
ejpam-5392	127	31	)	)	PUNCT
ejpam-5392	127	32	̸=	̸=	PROPN
ejpam-5392	127	33	r	r	NOUN
ejpam-5392	127	34	∧	∧	PROPN
ejpam-5392	127	35	β	β	X
ejpam-5392	127	36	λ	λ	PROPN
ejpam-5392	127	37	(	(	PUNCT
ejpam-5392	127	38	v	v	NOUN
ejpam-5392	127	39	)	)	PUNCT
ejpam-5392	127	40	or	or	CCONJ
ejpam-5392	127	41	bnd	bnd	VERB
ejpam-5392	127	42	∧	∧	PROPN
ejpam-5392	127	43	β	β	X
ejpam-5392	127	44	λ	λ	PROPN
ejpam-5392	127	45	(	(	PUNCT
ejpam-5392	127	46	v	v	NOUN
ejpam-5392	127	47	)	)	PUNCT
ejpam-5392	127	48	̸=	̸=	PROPN
ejpam-5392	127	49	∅.	∅.	PRON
ejpam-5392	127	50	definition	definition	NOUN
ejpam-5392	127	51	8	8	NUM
ejpam-5392	127	52	.	.	PUNCT
ejpam-5392	128	1	[	[	X
ejpam-5392	128	2	22	22	NUM
ejpam-5392	128	3	,	,	PUNCT
ejpam-5392	128	4	23	23	NUM
ejpam-5392	128	5	]	]	PUNCT
ejpam-5392	128	6	let	let	AUX
ejpam-5392	128	7	l	l	NOUN
ejpam-5392	128	8	be	be	AUX
ejpam-5392	128	9	an	an	DET
ejpam-5392	128	10	ideal	ideal	NOUN
ejpam-5392	128	11	on	on	ADP
ejpam-5392	128	12	x.	x.	NOUN
ejpam-5392	128	13	we	we	PRON
ejpam-5392	128	14	call	call	VERB
ejpam-5392	128	15	a	a	DET
ejpam-5392	128	16	subset	subset	NOUN
ejpam-5392	128	17	v	v	NOUN
ejpam-5392	128	18	of	of	ADP
ejpam-5392	128	19	a	a	DET
ejpam-5392	128	20	gλ	gλ	NOUN
ejpam-5392	128	21	-	-	PUNCT
ejpam-5392	128	22	space	space	NOUN
ejpam-5392	128	23	(	(	PUNCT
ejpam-5392	128	24	x	x	NOUN
ejpam-5392	128	25	,	,	PUNCT
ejpam-5392	128	26	r	r	NOUN
ejpam-5392	128	27	,	,	PUNCT
ejpam-5392	128	28	ξλ	ξλ	PROPN
ejpam-5392	128	29	):	):	PUNCT
ejpam-5392	128	30	m.	m.	PROPN
ejpam-5392	128	31	hosny	hosny	PROPN
ejpam-5392	128	32	,	,	PUNCT
ejpam-5392	128	33	t.m	t.m	PROPN
ejpam-5392	128	34	.	.	PROPN
ejpam-5392	128	35	al	al	PROPN
ejpam-5392	128	36	-	-	PUNCT
ejpam-5392	128	37	shami	shami	PROPN
ejpam-5392	128	38	/	/	PUNCT
ejpam-5392	128	39	eur	eur	PROPN
ejpam-5392	128	40	.	.	PUNCT
ejpam-5392	129	1	j.	j.	PROPN
ejpam-5392	129	2	pure	pure	PROPN
ejpam-5392	129	3	appl	appl	PROPN
ejpam-5392	129	4	.	.	PROPN
ejpam-5392	129	5	math	math	PROPN
ejpam-5392	129	6	,	,	PUNCT
ejpam-5392	129	7	17	17	NUM
ejpam-5392	129	8	(	(	PUNCT
ejpam-5392	129	9	4	4	NUM
ejpam-5392	129	10	)	)	PUNCT
ejpam-5392	129	11	(	(	PUNCT
ejpam-5392	129	12	2024	2024	NUM
ejpam-5392	129	13	)	)	PUNCT
ejpam-5392	129	14	,	,	PUNCT
ejpam-5392	129	15	3436	3436	NUM
ejpam-5392	129	16	-	-	SYM
ejpam-5392	129	17	3463	3463	NUM
ejpam-5392	129	18	3441	3441	NUM
ejpam-5392	129	19	(	(	PUNCT
ejpam-5392	129	20	i	i	NOUN
ejpam-5392	129	21	)	)	PUNCT
ejpam-5392	130	1	l	l	NOUN
ejpam-5392	130	2	-	-	PUNCT
ejpam-5392	130	3	αλ	αλ	DET
ejpam-5392	130	4	-	-	PUNCT
ejpam-5392	130	5	open	open	NOUN
ejpam-5392	130	6	providing	provide	VERB
ejpam-5392	130	7	that	that	SCONJ
ejpam-5392	130	8	there	there	PRON
ejpam-5392	130	9	exists	exist	VERB
ejpam-5392	130	10	g	g	PROPN
ejpam-5392	130	11	∈	∈	PROPN
ejpam-5392	130	12	ϑλ	ϑλ	ADP
ejpam-5392	130	13	s.t	s.t	PROPN
ejpam-5392	130	14	.	.	PUNCT
ejpam-5392	131	1	(	(	PUNCT
ejpam-5392	131	2	v	v	X
ejpam-5392	131	3	−intλ(clλ((g	−intλ(clλ((g	PROPN
ejpam-5392	131	4	)	)	PUNCT
ejpam-5392	131	5	)	)	PUNCT
ejpam-5392	132	1	∈	∈	PROPN
ejpam-5392	132	2	l	l	NOUN
ejpam-5392	132	3	and	and	CCONJ
ejpam-5392	132	4	(	(	PUNCT
ejpam-5392	132	5	g−v	g−v	PROPN
ejpam-5392	132	6	)	)	PUNCT
ejpam-5392	132	7	∈	∈	PROPN
ejpam-5392	133	1	l.	l.	PROPN
ejpam-5392	133	2	(	(	PUNCT
ejpam-5392	133	3	ii	ii	PROPN
ejpam-5392	133	4	)	)	PUNCT
ejpam-5392	133	5	l	l	NOUN
ejpam-5392	133	6	-	-	ADJ
ejpam-5392	133	7	pλ	pλ	ADJ
ejpam-5392	133	8	-	-	PUNCT
ejpam-5392	133	9	open	open	ADJ
ejpam-5392	133	10	providing	provide	VERB
ejpam-5392	133	11	that	that	SCONJ
ejpam-5392	133	12	there	there	PRON
ejpam-5392	133	13	exists	exist	VERB
ejpam-5392	133	14	g	g	PROPN
ejpam-5392	133	15	∈	∈	PROPN
ejpam-5392	133	16	ϑλ	ϑλ	ADP
ejpam-5392	133	17	s.t	s.t	PROPN
ejpam-5392	133	18	.	.	PUNCT
ejpam-5392	134	1	(	(	PUNCT
ejpam-5392	134	2	v	v	NOUN
ejpam-5392	134	3	−g	−g	NOUN
ejpam-5392	134	4	)	)	PUNCT
ejpam-5392	134	5	∈	∈	PROPN
ejpam-5392	134	6	l	l	NOUN
ejpam-5392	134	7	and	and	CCONJ
ejpam-5392	134	8	(	(	PUNCT
ejpam-5392	134	9	g−	g−	PRON
ejpam-5392	134	10	clλ(v	clλ(v	PROPN
ejpam-5392	134	11	)	)	PUNCT
ejpam-5392	134	12	)	)	PUNCT
ejpam-5392	135	1	∈	∈	PROPN
ejpam-5392	135	2	l.	l.	PROPN
ejpam-5392	135	3	(	(	PUNCT
ejpam-5392	135	4	iii	iii	NOUN
ejpam-5392	135	5	)	)	PUNCT
ejpam-5392	135	6	l	l	NOUN
ejpam-5392	135	7	-	-	PUNCT
ejpam-5392	135	8	sλ	sλ	NOUN
ejpam-5392	135	9	-	-	PUNCT
ejpam-5392	135	10	open	open	NOUN
ejpam-5392	135	11	providing	provide	VERB
ejpam-5392	135	12	that	that	SCONJ
ejpam-5392	135	13	there	there	PRON
ejpam-5392	135	14	exists	exist	VERB
ejpam-5392	135	15	g	g	PROPN
ejpam-5392	135	16	∈	∈	PROPN
ejpam-5392	135	17	ϑλ	ϑλ	ADP
ejpam-5392	135	18	s.t	s.t	PROPN
ejpam-5392	135	19	.	.	PUNCT
ejpam-5392	136	1	(	(	PUNCT
ejpam-5392	136	2	v	v	NUM
ejpam-5392	136	3	−clλ(g	−clλ(g	NOUN
ejpam-5392	136	4	)	)	PUNCT
ejpam-5392	136	5	)	)	PUNCT
ejpam-5392	137	1	∈	∈	PROPN
ejpam-5392	137	2	l	l	NOUN
ejpam-5392	137	3	and	and	CCONJ
ejpam-5392	137	4	(	(	PUNCT
ejpam-5392	137	5	g−v	g−v	PROPN
ejpam-5392	137	6	)	)	PUNCT
ejpam-5392	137	7	∈	∈	PROPN
ejpam-5392	137	8	l.	l.	PROPN
ejpam-5392	137	9	(	(	PUNCT
ejpam-5392	137	10	iv	iv	X
ejpam-5392	137	11	)	)	PUNCT
ejpam-5392	137	12	l	l	NOUN
ejpam-5392	137	13	-	-	PUNCT
ejpam-5392	137	14	βλ	βλ	ADJ
ejpam-5392	137	15	-	-	ADJ
ejpam-5392	137	16	open	open	ADJ
ejpam-5392	137	17	providing	provide	VERB
ejpam-5392	137	18	that	that	SCONJ
ejpam-5392	137	19	there	there	PRON
ejpam-5392	137	20	exists	exist	VERB
ejpam-5392	137	21	g	g	PROPN
ejpam-5392	137	22	∈	∈	PROPN
ejpam-5392	137	23	ϑλ	ϑλ	ADP
ejpam-5392	137	24	s.t	s.t	PROPN
ejpam-5392	137	25	.	.	PUNCT
ejpam-5392	138	1	(	(	PUNCT
ejpam-5392	138	2	v	v	NUM
ejpam-5392	138	3	−clλ(g	−clλ(g	NOUN
ejpam-5392	138	4	)	)	PUNCT
ejpam-5392	138	5	)	)	PUNCT
ejpam-5392	139	1	∈	∈	PROPN
ejpam-5392	139	2	l	l	NOUN
ejpam-5392	139	3	and	and	CCONJ
ejpam-5392	139	4	(	(	PUNCT
ejpam-5392	139	5	g−clλ(v	g−clλ(v	NUM
ejpam-5392	139	6	)	)	PUNCT
ejpam-5392	139	7	)	)	PUNCT
ejpam-5392	140	1	∈	∈	PROPN
ejpam-5392	140	2	l.	l.	NOUN
ejpam-5392	140	3	(	(	PUNCT
ejpam-5392	140	4	v	v	NOUN
ejpam-5392	140	5	)	)	PUNCT
ejpam-5392	140	6	l	l	NOUN
ejpam-5392	140	7	-	-	ADJ
ejpam-5392	140	8	δβλ	δβλ	NOUN
ejpam-5392	140	9	-	-	PUNCT
ejpam-5392	140	10	open	open	ADJ
ejpam-5392	140	11	providing	provide	VERB
ejpam-5392	140	12	that	that	SCONJ
ejpam-5392	140	13	there	there	PRON
ejpam-5392	140	14	exists	exist	VERB
ejpam-5392	140	15	g	g	PROPN
ejpam-5392	140	16	∈	∈	PROPN
ejpam-5392	140	17	ϑλ	ϑλ	ADP
ejpam-5392	140	18	s.t	s.t	PROPN
ejpam-5392	140	19	.	.	PUNCT
ejpam-5392	141	1	(	(	PUNCT
ejpam-5392	141	2	v	v	NUM
ejpam-5392	141	3	−clλ(g	−clλ(g	NOUN
ejpam-5392	141	4	)	)	PUNCT
ejpam-5392	141	5	)	)	PUNCT
ejpam-5392	142	1	∈	∈	PROPN
ejpam-5392	142	2	l	l	NOUN
ejpam-5392	142	3	and	and	CCONJ
ejpam-5392	142	4	(	(	PUNCT
ejpam-5392	142	5	g−clδλ(v	g−clδλ(v	PROPN
ejpam-5392	142	6	)	)	PUNCT
ejpam-5392	142	7	)	)	PUNCT
ejpam-5392	143	1	∈	∈	PROPN
ejpam-5392	143	2	l.	l.	PROPN
ejpam-5392	143	3	(	(	PUNCT
ejpam-5392	143	4	vi	vi	PROPN
ejpam-5392	143	5	)	)	PUNCT
ejpam-5392	143	6	l∧	l∧	NOUN
ejpam-5392	143	7	βλ	βλ	PUNCT
ejpam-5392	143	8	-set	-set	ADJ
ejpam-5392	143	9	,	,	PUNCT
ejpam-5392	143	10	if	if	SCONJ
ejpam-5392	143	11	v	v	ADP
ejpam-5392	143	12	=	=	SYM
ejpam-5392	143	13	l	l	NOUN
ejpam-5392	143	14	−	−	PROPN
ejpam-5392	143	15	∧	∧	NOUN
ejpam-5392	143	16	βλ	βλ	INTJ
ejpam-5392	143	17	(	(	PUNCT
ejpam-5392	143	18	v	v	NOUN
ejpam-5392	143	19	)	)	PUNCT
ejpam-5392	143	20	,	,	PUNCT
ejpam-5392	143	21	where	where	SCONJ
ejpam-5392	143	22	l∧	l∧	ADV
ejpam-5392	143	23	βλ	βλ	PROPN
ejpam-5392	143	24	(	(	PUNCT
ejpam-5392	143	25	v	v	NOUN
ejpam-5392	143	26	)	)	PUNCT
ejpam-5392	143	27	=	=	VERB
ejpam-5392	143	28	∩{g	∩{g	INTJ
ejpam-5392	143	29	:	:	PUNCT
ejpam-5392	143	30	v	v	ADP
ejpam-5392	143	31	⊆	⊆	NUM
ejpam-5392	143	32	g	g	NOUN
ejpam-5392	143	33	,	,	PUNCT
ejpam-5392	143	34	g	g	PROPN
ejpam-5392	143	35	∈	∈	PROPN
ejpam-5392	143	36	l	l	PROPN
ejpam-5392	143	37	-	-	PUNCT
ejpam-5392	143	38	βλo(x	βλo(x	PROPN
ejpam-5392	143	39	)	)	PUNCT
ejpam-5392	143	40	}	}	PUNCT
ejpam-5392	143	41	.	.	PUNCT
ejpam-5392	144	1	these	these	DET
ejpam-5392	144	2	sets	set	NOUN
ejpam-5392	144	3	are	be	AUX
ejpam-5392	144	4	called	call	VERB
ejpam-5392	144	5	l	l	NOUN
ejpam-5392	144	6	-	-	PUNCT
ejpam-5392	144	7	λ	λ	VERB
ejpam-5392	144	8	-	-	PUNCT
ejpam-5392	144	9	nearly	nearly	ADV
ejpam-5392	144	10	open	open	ADJ
ejpam-5392	144	11	sets	set	NOUN
ejpam-5392	144	12	,	,	PUNCT
ejpam-5392	144	13	the	the	DET
ejpam-5392	144	14	complement	complement	NOUN
ejpam-5392	144	15	of	of	ADP
ejpam-5392	144	16	the	the	DET
ejpam-5392	144	17	l	l	NOUN
ejpam-5392	144	18	-	-	NOUN
ejpam-5392	144	19	λ	λ	VERB
ejpam-5392	144	20	-	-	PUNCT
ejpam-5392	144	21	nearly	nearly	ADV
ejpam-5392	144	22	open	open	ADJ
ejpam-5392	144	23	sets	set	NOUN
ejpam-5392	144	24	is	be	AUX
ejpam-5392	144	25	called	call	VERB
ejpam-5392	144	26	l	l	NOUN
ejpam-5392	144	27	-	-	PUNCT
ejpam-5392	144	28	λ	λ	VERB
ejpam-5392	144	29	-	-	PUNCT
ejpam-5392	144	30	nearly	nearly	ADV
ejpam-5392	144	31	closed	closed	ADJ
ejpam-5392	144	32	sets	set	NOUN
ejpam-5392	144	33	,	,	PUNCT
ejpam-5392	144	34	the	the	DET
ejpam-5392	144	35	families	family	NOUN
ejpam-5392	144	36	of	of	ADP
ejpam-5392	144	37	l	l	PROPN
ejpam-5392	144	38	-	-	NOUN
ejpam-5392	144	39	λ	λ	VERB
ejpam-5392	144	40	-	-	PUNCT
ejpam-5392	144	41	nearly	nearly	ADV
ejpam-5392	144	42	open	open	ADJ
ejpam-5392	144	43	sets	set	NOUN
ejpam-5392	144	44	of	of	ADP
ejpam-5392	144	45	x	x	PUNCT
ejpam-5392	144	46	denoted	denote	VERB
ejpam-5392	144	47	by	by	ADP
ejpam-5392	144	48	l	l	PROPN
ejpam-5392	144	49	-	-	PUNCT
ejpam-5392	144	50	ηλo(x	ηλo(x	PROPN
ejpam-5392	144	51	)	)	PUNCT
ejpam-5392	144	52	and	and	CCONJ
ejpam-5392	144	53	the	the	DET
ejpam-5392	144	54	families	family	NOUN
ejpam-5392	144	55	of	of	ADP
ejpam-5392	144	56	l	l	PROPN
ejpam-5392	144	57	-	-	PUNCT
ejpam-5392	144	58	λ	λ	VERB
ejpam-5392	144	59	-	-	PUNCT
ejpam-5392	144	60	nearly	nearly	ADV
ejpam-5392	144	61	closed	closed	ADJ
ejpam-5392	144	62	sets	set	NOUN
ejpam-5392	144	63	of	of	ADP
ejpam-5392	144	64	x	x	PUNCT
ejpam-5392	144	65	denoted	denote	VERB
ejpam-5392	144	66	by	by	ADP
ejpam-5392	144	67	l	l	NOUN
ejpam-5392	144	68	-	-	PUNCT
ejpam-5392	144	69	ηλc(x	ηλc(x	NOUN
ejpam-5392	144	70	)	)	PUNCT
ejpam-5392	144	71	.	.	PUNCT
ejpam-5392	145	1	proposition	proposition	NOUN
ejpam-5392	145	2	1	1	NUM
ejpam-5392	145	3	.	.	PUNCT
ejpam-5392	146	1	[	[	X
ejpam-5392	146	2	23	23	NUM
ejpam-5392	146	3	]	]	PUNCT
ejpam-5392	146	4	(	(	PUNCT
ejpam-5392	146	5	i	i	NOUN
ejpam-5392	146	6	)	)	PUNCT
ejpam-5392	146	7	every	every	DET
ejpam-5392	146	8	δβλ	δβλ	NOUN
ejpam-5392	146	9	-	-	PUNCT
ejpam-5392	146	10	open	open	ADJ
ejpam-5392	146	11	is	be	AUX
ejpam-5392	146	12	l	l	ADJ
ejpam-5392	146	13	-	-	ADJ
ejpam-5392	146	14	δβλ	δβλ	NOUN
ejpam-5392	146	15	-	-	PUNCT
ejpam-5392	146	16	open	open	ADJ
ejpam-5392	146	17	.	.	PUNCT
ejpam-5392	147	1	(	(	PUNCT
ejpam-5392	147	2	ii	ii	NOUN
ejpam-5392	147	3	)	)	PUNCT
ejpam-5392	147	4	every	every	DET
ejpam-5392	147	5	∧	∧	PROPN
ejpam-5392	147	6	βλ	βλ	X
ejpam-5392	147	7	-set	-set	PROPN
ejpam-5392	147	8	is	be	AUX
ejpam-5392	147	9	l∧	l∧	ADJ
ejpam-5392	147	10	βλ	βλ	PRON
ejpam-5392	147	11	-set	-set	ADJ
ejpam-5392	147	12	.	.	PUNCT
ejpam-5392	148	1	proposition	proposition	NOUN
ejpam-5392	148	2	2	2	NUM
ejpam-5392	148	3	.	.	PUNCT
ejpam-5392	149	1	[	[	X
ejpam-5392	149	2	23	23	NUM
ejpam-5392	149	3	]	]	PUNCT
ejpam-5392	149	4	the	the	DET
ejpam-5392	149	5	next	next	ADJ
ejpam-5392	149	6	implications	implication	NOUN
ejpam-5392	149	7	hold	hold	VERB
ejpam-5392	149	8	true	true	ADJ
ejpam-5392	149	9	:	:	PUNCT
ejpam-5392	149	10	ϑλ(γλ	ϑλ(γλ	PROPN
ejpam-5392	149	11	)	)	PUNCT
ejpam-5392	149	12	⇒	⇒	NOUN
ejpam-5392	149	13	l	l	PROPN
ejpam-5392	149	14	-	-	PUNCT
ejpam-5392	149	15	αλo(l	αλo(l	NUM
ejpam-5392	149	16	-	-	PUNCT
ejpam-5392	149	17	αλc	αλc	NOUN
ejpam-5392	149	18	)	)	PUNCT
ejpam-5392	149	19	l	l	NOUN
ejpam-5392	149	20	-	-	PUNCT
ejpam-5392	149	21	pλo(l	pλo(l	VERB
ejpam-5392	149	22	-	-	PUNCT
ejpam-5392	149	23	pλc	pλc	NOUN
ejpam-5392	149	24	)	)	PUNCT
ejpam-5392	149	25	⇓	⇓	PROPN
ejpam-5392	149	26	⇓	⇓	PROPN
ejpam-5392	149	27	l	l	PROPN
ejpam-5392	149	28	-	-	PUNCT
ejpam-5392	149	29	sλo(l	sλo(l	PROPN
ejpam-5392	149	30	-	-	PUNCT
ejpam-5392	149	31	sλc	sλc	NOUN
ejpam-5392	149	32	)	)	PUNCT
ejpam-5392	149	33	⇒	⇒	NOUN
ejpam-5392	149	34	l	l	PROPN
ejpam-5392	149	35	-	-	PUNCT
ejpam-5392	149	36	βλo(l	βλo(l	SYM
ejpam-5392	149	37	-	-	PUNCT
ejpam-5392	149	38	βλc	βλc	NOUN
ejpam-5392	149	39	)	)	PUNCT
ejpam-5392	149	40	⇒	⇒	NOUN
ejpam-5392	149	41	l	l	PROPN
ejpam-5392	149	42	-	-	PUNCT
ejpam-5392	149	43	δβλo(l	δβλo(l	PROPN
ejpam-5392	149	44	-	-	PUNCT
ejpam-5392	149	45	δβλc	δβλc	NOUN
ejpam-5392	149	46	)	)	PUNCT
ejpam-5392	149	47	.	.	PUNCT
ejpam-5392	150	1	ϑλ(γλ	ϑλ(γλ	PROPN
ejpam-5392	150	2	)	)	PUNCT
ejpam-5392	151	1	⇒	⇒	NOUN
ejpam-5392	151	2	l	l	PROPN
ejpam-5392	151	3	-	-	PUNCT
ejpam-5392	151	4	αλo(l	αλo(l	NUM
ejpam-5392	151	5	-	-	PUNCT
ejpam-5392	151	6	αλc	αλc	NOUN
ejpam-5392	151	7	)	)	PUNCT
ejpam-5392	151	8	l	l	NOUN
ejpam-5392	151	9	-	-	PUNCT
ejpam-5392	151	10	pλo(l	pλo(l	VERB
ejpam-5392	151	11	-	-	PUNCT
ejpam-5392	151	12	pλc	pλc	NOUN
ejpam-5392	151	13	)	)	PUNCT
ejpam-5392	151	14	⇓	⇓	PROPN
ejpam-5392	151	15	⇓	⇓	PROPN
ejpam-5392	151	16	l	l	PROPN
ejpam-5392	151	17	-	-	PUNCT
ejpam-5392	151	18	sλo(l	sλo(l	PROPN
ejpam-5392	151	19	-	-	PUNCT
ejpam-5392	151	20	sλc	sλc	NOUN
ejpam-5392	151	21	)	)	PUNCT
ejpam-5392	151	22	⇒	⇒	NOUN
ejpam-5392	151	23	l	l	PROPN
ejpam-5392	151	24	-	-	PUNCT
ejpam-5392	151	25	βλo(l	βλo(l	SYM
ejpam-5392	151	26	-	-	PUNCT
ejpam-5392	151	27	βλc	βλc	NOUN
ejpam-5392	151	28	)	)	PUNCT
ejpam-5392	151	29	⇒	⇒	VERB
ejpam-5392	152	1	l∧	l∧	PROPN
ejpam-5392	152	2	βλo	βλo	PROPN
ejpam-5392	152	3	(	(	PUNCT
ejpam-5392	152	4	l∧	l∧	PROPN
ejpam-5392	152	5	βλc	βλc	PROPN
ejpam-5392	152	6	)	)	PUNCT
ejpam-5392	152	7	.	.	PUNCT
ejpam-5392	153	1	ϑλ(γλ	ϑλ(γλ	PROPN
ejpam-5392	153	2	)	)	PUNCT
ejpam-5392	153	3	⇒	⇒	NOUN
ejpam-5392	153	4	αλo(αλc	αλo(αλc	VERB
ejpam-5392	153	5	)	)	PUNCT
ejpam-5392	153	6	pλo(pλc	pλo(pλc	PROPN
ejpam-5392	153	7	)	)	PUNCT
ejpam-5392	153	8	⇓	⇓	PROPN
ejpam-5392	153	9	⇓	⇓	PROPN
ejpam-5392	153	10	sλo(sλc	sλo(sλc	ADV
ejpam-5392	153	11	)	)	PUNCT
ejpam-5392	153	12	⇒	⇒	PROPN
ejpam-5392	153	13	βλo(βλc	βλo(βλc	NOUN
ejpam-5392	153	14	)	)	PUNCT
ejpam-5392	153	15	⇒	⇒	PROPN
ejpam-5392	153	16	δβλo(δβλc	δβλo(δβλc	PROPN
ejpam-5392	153	17	)	)	PUNCT
ejpam-5392	153	18	.	.	PUNCT
ejpam-5392	154	1	ϑλ(γλ	ϑλ(γλ	PROPN
ejpam-5392	154	2	)	)	PUNCT
ejpam-5392	154	3	⇒	⇒	NOUN
ejpam-5392	154	4	αλo(αλc	αλo(αλc	VERB
ejpam-5392	154	5	)	)	PUNCT
ejpam-5392	154	6	pλo(pλc	pλo(pλc	PROPN
ejpam-5392	154	7	)	)	PUNCT
ejpam-5392	154	8	⇓	⇓	PROPN
ejpam-5392	154	9	⇓	⇓	PROPN
ejpam-5392	154	10	sλo(sλc	sλo(sλc	ADV
ejpam-5392	154	11	)	)	PUNCT
ejpam-5392	154	12	⇒	⇒	PROPN
ejpam-5392	154	13	βλo(βλc	βλo(βλc	NOUN
ejpam-5392	154	14	)	)	PUNCT
ejpam-5392	154	15	⇒	⇒	VERB
ejpam-5392	154	16	∧	∧	PROPN
ejpam-5392	154	17	βλo	βλo	PROPN
ejpam-5392	154	18	(	(	PUNCT
ejpam-5392	154	19	∧	∧	PROPN
ejpam-5392	154	20	βλc	βλc	ADJ
ejpam-5392	154	21	)	)	PUNCT
ejpam-5392	154	22	.	.	PUNCT
ejpam-5392	155	1	definition	definition	NOUN
ejpam-5392	155	2	9	9	NUM
ejpam-5392	155	3	.	.	PUNCT
ejpam-5392	156	1	[	[	X
ejpam-5392	156	2	22	22	NUM
ejpam-5392	156	3	,	,	PUNCT
ejpam-5392	156	4	23	23	NUM
ejpam-5392	156	5	]	]	PUNCT
ejpam-5392	156	6	the	the	DET
ejpam-5392	156	7	l	l	NOUN
ejpam-5392	156	8	-	-	PUNCT
ejpam-5392	156	9	ηλ	ηλ	NOUN
ejpam-5392	156	10	-	-	PUNCT
ejpam-5392	156	11	lower	low	ADJ
ejpam-5392	156	12	and	and	CCONJ
ejpam-5392	156	13	l	l	NOUN
ejpam-5392	156	14	-	-	PUNCT
ejpam-5392	156	15	ηλ	ηλ	ADJ
ejpam-5392	156	16	-	-	PUNCT
ejpam-5392	156	17	upper	upper	ADJ
ejpam-5392	156	18	approximations	approximation	NOUN
ejpam-5392	156	19	,	,	PUNCT
ejpam-5392	156	20	l	l	NOUN
ejpam-5392	156	21	-	-	PUNCT
ejpam-5392	156	22	ηλ	ηλ	ADJ
ejpam-5392	156	23	-	-	PUNCT
ejpam-5392	156	24	boundary	boundary	ADJ
ejpam-5392	156	25	regions	region	NOUN
ejpam-5392	156	26	and	and	CCONJ
ejpam-5392	156	27	l	l	NOUN
ejpam-5392	156	28	-	-	PUNCT
ejpam-5392	156	29	ηλ	ηλ	NOUN
ejpam-5392	156	30	-	-	PUNCT
ejpam-5392	156	31	accuracy	accuracy	NOUN
ejpam-5392	156	32	of	of	ADP
ejpam-5392	156	33	v	v	NOUN
ejpam-5392	156	34	are	be	AUX
ejpam-5392	156	35	respectively	respectively	ADV
ejpam-5392	156	36	given	give	VERB
ejpam-5392	156	37	by	by	ADP
ejpam-5392	156	38	:	:	PUNCT
ejpam-5392	156	39	rl−η	rl−η	PROPN
ejpam-5392	156	40	λ	λ	PROPN
ejpam-5392	156	41	(	(	PUNCT
ejpam-5392	156	42	v	v	NOUN
ejpam-5392	156	43	)	)	PUNCT
ejpam-5392	156	44	=	=	PUNCT
ejpam-5392	157	1	∪{g	∪{g	PROPN
ejpam-5392	157	2	∈	∈	PROPN
ejpam-5392	157	3	l	l	PROPN
ejpam-5392	157	4	-	-	PROPN
ejpam-5392	157	5	ηλo(x	ηλo(x	PROPN
ejpam-5392	157	6	)	)	PUNCT
ejpam-5392	157	7	:	:	PUNCT
ejpam-5392	158	1	g	g	PROPN
ejpam-5392	158	2	⊆	⊆	NUM
ejpam-5392	158	3	v	v	NOUN
ejpam-5392	158	4	}	}	PUNCT
ejpam-5392	158	5	=	=	PUNCT
ejpam-5392	158	6	l	l	NOUN
ejpam-5392	158	7	-	-	PUNCT
ejpam-5392	158	8	ηλ	ηλ	NOUN
ejpam-5392	158	9	-	-	ADJ
ejpam-5392	158	10	interior	interior	NOUN
ejpam-5392	158	11	of	of	ADP
ejpam-5392	158	12	v	v	NOUN
ejpam-5392	158	13	.	.	PUNCT
ejpam-5392	159	1	rl−η	rl−η	PROPN
ejpam-5392	159	2	λ	λ	PROPN
ejpam-5392	159	3	(	(	PUNCT
ejpam-5392	159	4	v	v	NOUN
ejpam-5392	159	5	)	)	PUNCT
ejpam-5392	159	6	=	=	VERB
ejpam-5392	160	1	∩{h	∩{h	PUNCT
ejpam-5392	160	2	∈	∈	PROPN
ejpam-5392	160	3	l	l	NOUN
ejpam-5392	160	4	-	-	PUNCT
ejpam-5392	160	5	ηλc(x	ηλc(x	NOUN
ejpam-5392	160	6	)	)	PUNCT
ejpam-5392	160	7	:	:	PUNCT
ejpam-5392	160	8	v	v	ADP
ejpam-5392	160	9	⊆	⊆	NUM
ejpam-5392	160	10	h	h	NOUN
ejpam-5392	160	11	}	}	PUNCT
ejpam-5392	160	12	=	=	SYM
ejpam-5392	160	13	l	l	NOUN
ejpam-5392	160	14	-	-	PUNCT
ejpam-5392	160	15	ηλ	ηλ	NOUN
ejpam-5392	160	16	-	-	PUNCT
ejpam-5392	160	17	closure	closure	NOUN
ejpam-5392	160	18	of	of	ADP
ejpam-5392	160	19	v	v	NOUN
ejpam-5392	160	20	.	.	PUNCT
ejpam-5392	161	1	bndl−η	bndl−η	PROPN
ejpam-5392	161	2	λ	λ	PROPN
ejpam-5392	161	3	(	(	PUNCT
ejpam-5392	161	4	v	v	NOUN
ejpam-5392	161	5	)	)	PUNCT
ejpam-5392	161	6	=	=	PUNCT
ejpam-5392	161	7	rl−η	rl−η	PROPN
ejpam-5392	161	8	λ	λ	PROPN
ejpam-5392	161	9	(	(	PUNCT
ejpam-5392	161	10	v	v	NOUN
ejpam-5392	161	11	)	)	PUNCT
ejpam-5392	161	12	−rl−η	−rl−η	VERB
ejpam-5392	161	13	λ	λ	PROPN
ejpam-5392	161	14	(	(	PUNCT
ejpam-5392	161	15	v	v	NOUN
ejpam-5392	161	16	)	)	PUNCT
ejpam-5392	161	17	.	.	PUNCT
ejpam-5392	162	1	accl−η	accl−η	NUM
ejpam-5392	162	2	λ	λ	PROPN
ejpam-5392	162	3	(	(	PUNCT
ejpam-5392	162	4	v	v	NOUN
ejpam-5392	162	5	)	)	PUNCT
ejpam-5392	162	6	=	=	VERB
ejpam-5392	162	7	|rl−η	|rl−η	NOUN
ejpam-5392	162	8	λ	λ	PROPN
ejpam-5392	162	9	(	(	PUNCT
ejpam-5392	162	10	v	v	NOUN
ejpam-5392	162	11	)	)	PUNCT
ejpam-5392	162	12	|	|	ADV
ejpam-5392	162	13	|rl−η	|rl−η	X
ejpam-5392	162	14	λ	λ	PROPN
ejpam-5392	162	15	(	(	PUNCT
ejpam-5392	162	16	v	v	NOUN
ejpam-5392	162	17	)	)	PUNCT
ejpam-5392	162	18	|	|	ADV
ejpam-5392	162	19	,	,	PUNCT
ejpam-5392	162	20	where	where	SCONJ
ejpam-5392	162	21	|rl−η	|rl−η	PROPN
ejpam-5392	162	22	λ	λ	PROPN
ejpam-5392	162	23	(	(	PUNCT
ejpam-5392	162	24	v	v	NOUN
ejpam-5392	162	25	)	)	PUNCT
ejpam-5392	162	26	|	|	ADV
ejpam-5392	162	27	=	=	NOUN
ejpam-5392	162	28	̸	̸	NUM
ejpam-5392	162	29	0	0	NUM
ejpam-5392	162	30	.	.	PUNCT
ejpam-5392	162	31	m.	m.	PROPN
ejpam-5392	162	32	hosny	hosny	PROPN
ejpam-5392	162	33	,	,	PUNCT
ejpam-5392	162	34	t.m	t.m	PROPN
ejpam-5392	162	35	.	.	PROPN
ejpam-5392	162	36	al	al	PROPN
ejpam-5392	162	37	-	-	PUNCT
ejpam-5392	162	38	shami	shami	PROPN
ejpam-5392	162	39	/	/	PUNCT
ejpam-5392	162	40	eur	eur	PROPN
ejpam-5392	162	41	.	.	PUNCT
ejpam-5392	163	1	j.	j.	PROPN
ejpam-5392	163	2	pure	pure	PROPN
ejpam-5392	163	3	appl	appl	PROPN
ejpam-5392	163	4	.	.	PROPN
ejpam-5392	163	5	math	math	PROPN
ejpam-5392	163	6	,	,	PUNCT
ejpam-5392	163	7	17	17	NUM
ejpam-5392	163	8	(	(	PUNCT
ejpam-5392	163	9	4	4	NUM
ejpam-5392	163	10	)	)	PUNCT
ejpam-5392	163	11	(	(	PUNCT
ejpam-5392	163	12	2024	2024	NUM
ejpam-5392	163	13	)	)	PUNCT
ejpam-5392	163	14	,	,	PUNCT
ejpam-5392	163	15	3436	3436	NUM
ejpam-5392	163	16	-	-	SYM
ejpam-5392	163	17	3463	3463	NUM
ejpam-5392	163	18	3442	3442	NUM
ejpam-5392	163	19	remember	remember	VERB
ejpam-5392	163	20	that	that	SCONJ
ejpam-5392	163	21	a	a	DET
ejpam-5392	163	22	subset	subset	NOUN
ejpam-5392	163	23	v	v	NOUN
ejpam-5392	163	24	is	be	AUX
ejpam-5392	163	25	called	call	VERB
ejpam-5392	163	26	an	an	DET
ejpam-5392	163	27	l	l	NOUN
ejpam-5392	163	28	-	-	PUNCT
ejpam-5392	163	29	ηλ	ηλ	AUX
ejpam-5392	163	30	-	-	PUNCT
ejpam-5392	163	31	definable	definable	ADJ
ejpam-5392	163	32	(	(	PUNCT
ejpam-5392	163	33	l	l	NOUN
ejpam-5392	163	34	-	-	PUNCT
ejpam-5392	163	35	ηλ	ηλ	NOUN
ejpam-5392	163	36	-	-	PUNCT
ejpam-5392	163	37	exact	exact	NOUN
ejpam-5392	163	38	)	)	PUNCT
ejpam-5392	163	39	set	set	VERB
ejpam-5392	163	40	if	if	SCONJ
ejpam-5392	163	41	r	r	NOUN
ejpam-5392	163	42	l−η	l−η	NOUN
ejpam-5392	163	43	λ	λ	PROPN
ejpam-5392	163	44	(	(	PUNCT
ejpam-5392	163	45	v	v	NOUN
ejpam-5392	163	46	)	)	PUNCT
ejpam-5392	163	47	=	=	PUNCT
ejpam-5392	163	48	rl−η	rl−η	PROPN
ejpam-5392	163	49	λ	λ	PROPN
ejpam-5392	163	50	(	(	PUNCT
ejpam-5392	163	51	v	v	NOUN
ejpam-5392	163	52	)	)	PUNCT
ejpam-5392	163	53	.	.	PUNCT
ejpam-5392	164	1	otherwise	otherwise	ADV
ejpam-5392	164	2	,	,	PUNCT
ejpam-5392	164	3	v	v	NOUN
ejpam-5392	164	4	is	be	AUX
ejpam-5392	164	5	an	an	DET
ejpam-5392	164	6	l	l	NOUN
ejpam-5392	164	7	-	-	PUNCT
ejpam-5392	164	8	ηλ	ηλ	ADJ
ejpam-5392	164	9	-	-	PUNCT
ejpam-5392	164	10	rough	rough	ADJ
ejpam-5392	164	11	set	set	NOUN
ejpam-5392	164	12	.	.	PUNCT
ejpam-5392	165	1	theorem	theorem	NOUN
ejpam-5392	165	2	2	2	NUM
ejpam-5392	165	3	.	.	PUNCT
ejpam-5392	166	1	[	[	X
ejpam-5392	166	2	23	23	NUM
ejpam-5392	166	3	]	]	PUNCT
ejpam-5392	166	4	for	for	ADP
ejpam-5392	166	5	a	a	DET
ejpam-5392	166	6	subset	subset	NOUN
ejpam-5392	166	7	v	v	NOUN
ejpam-5392	166	8	of	of	ADP
ejpam-5392	166	9	a	a	DET
ejpam-5392	166	10	gλ	gλ	NOUN
ejpam-5392	166	11	-	-	PUNCT
ejpam-5392	166	12	space	space	NOUN
ejpam-5392	166	13	(	(	PUNCT
ejpam-5392	166	14	x	x	NOUN
ejpam-5392	166	15	,	,	PUNCT
ejpam-5392	166	16	r	r	NOUN
ejpam-5392	166	17	,	,	PUNCT
ejpam-5392	166	18	ξλ	ξλ	PROPN
ejpam-5392	166	19	)	)	PUNCT
ejpam-5392	166	20	,	,	PUNCT
ejpam-5392	166	21	we	we	PRON
ejpam-5392	166	22	have	have	VERB
ejpam-5392	166	23	:	:	PUNCT
ejpam-5392	166	24	(	(	PUNCT
ejpam-5392	166	25	i	i	NOUN
ejpam-5392	166	26	)	)	PUNCT
ejpam-5392	166	27	rα	rα	ADV
ejpam-5392	166	28	λ(v	λ(v	PROPN
ejpam-5392	166	29	)	)	PUNCT
ejpam-5392	167	1	⊆	⊆	NUM
ejpam-5392	167	2	rp	rp	NOUN
ejpam-5392	167	3	λ(v	λ(v	PROPN
ejpam-5392	167	4	)	)	PUNCT
ejpam-5392	168	1	⊆	⊆	NUM
ejpam-5392	168	2	rγ	rγ	NOUN
ejpam-5392	168	3	λ(v	λ(v	ADV
ejpam-5392	168	4	)	)	PUNCT
ejpam-5392	169	1	⊆	⊆	NUM
ejpam-5392	169	2	rβ	rβ	ADP
ejpam-5392	169	3	λ(v	λ(v	PROPN
ejpam-5392	169	4	)	)	PUNCT
ejpam-5392	169	5	⊆	⊆	NUM
ejpam-5392	169	6	rδβ	rδβ	NOUN
ejpam-5392	169	7	λ	λ	PROPN
ejpam-5392	169	8	(	(	PUNCT
ejpam-5392	169	9	v	v	NOUN
ejpam-5392	169	10	)	)	PUNCT
ejpam-5392	169	11	⊆	⊆	NUM
ejpam-5392	169	12	rl−αβ	rl−αβ	X
ejpam-5392	169	13	λ	λ	PROPN
ejpam-5392	169	14	(	(	PUNCT
ejpam-5392	169	15	v	v	NOUN
ejpam-5392	169	16	)	)	PUNCT
ejpam-5392	169	17	.	.	PUNCT
ejpam-5392	170	1	(	(	PUNCT
ejpam-5392	170	2	ii	ii	NOUN
ejpam-5392	170	3	)	)	PUNCT
ejpam-5392	170	4	rα	rα	ADV
ejpam-5392	170	5	λ(v	λ(v	PROPN
ejpam-5392	170	6	)	)	PUNCT
ejpam-5392	171	1	⊆	⊆	NUM
ejpam-5392	171	2	rs	rs	NOUN
ejpam-5392	171	3	λ(v	λ(v	PROPN
ejpam-5392	171	4	)	)	PUNCT
ejpam-5392	172	1	⊆	⊆	NUM
ejpam-5392	172	2	rγ	rγ	NOUN
ejpam-5392	172	3	λ(v	λ(v	ADV
ejpam-5392	172	4	)	)	PUNCT
ejpam-5392	173	1	⊆	⊆	NUM
ejpam-5392	173	2	rβ	rβ	ADP
ejpam-5392	173	3	λ(v	λ(v	PROPN
ejpam-5392	173	4	)	)	PUNCT
ejpam-5392	173	5	⊆	⊆	NUM
ejpam-5392	173	6	rδβ	rδβ	NOUN
ejpam-5392	173	7	λ	λ	PROPN
ejpam-5392	173	8	(	(	PUNCT
ejpam-5392	173	9	v	v	NOUN
ejpam-5392	173	10	)	)	PUNCT
ejpam-5392	173	11	⊆	⊆	NUM
ejpam-5392	173	12	rl−αβ	rl−αβ	X
ejpam-5392	173	13	λ	λ	PROPN
ejpam-5392	173	14	(	(	PUNCT
ejpam-5392	173	15	v	v	NOUN
ejpam-5392	173	16	)	)	PUNCT
ejpam-5392	173	17	.	.	PUNCT
ejpam-5392	174	1	(	(	PUNCT
ejpam-5392	174	2	iii	iii	NOUN
ejpam-5392	174	3	)	)	PUNCT
ejpam-5392	174	4	rλ(v	rλ(v	VERB
ejpam-5392	174	5	)	)	PUNCT
ejpam-5392	175	1	⊆	⊆	NUM
ejpam-5392	175	2	rδβ	rδβ	NOUN
ejpam-5392	175	3	λ(v	λ(v	PROPN
ejpam-5392	175	4	)	)	PUNCT
ejpam-5392	176	1	⊆	⊆	NUM
ejpam-5392	176	2	rl−αβ	rl−αβ	X
ejpam-5392	176	3	λ	λ	PROPN
ejpam-5392	176	4	(	(	PUNCT
ejpam-5392	176	5	v	v	NOUN
ejpam-5392	176	6	)	)	PUNCT
ejpam-5392	176	7	.	.	PUNCT
ejpam-5392	177	1	(	(	PUNCT
ejpam-5392	177	2	iv	iv	X
ejpam-5392	177	3	)	)	PUNCT
ejpam-5392	177	4	rα	rα	ADV
ejpam-5392	177	5	λ(v	λ(v	PROPN
ejpam-5392	177	6	)	)	PUNCT
ejpam-5392	178	1	⊆	⊆	NUM
ejpam-5392	178	2	rp	rp	NOUN
ejpam-5392	178	3	λ(v	λ(v	PROPN
ejpam-5392	178	4	)	)	PUNCT
ejpam-5392	179	1	⊆	⊆	NUM
ejpam-5392	179	2	rγ	rγ	NOUN
ejpam-5392	179	3	λ(v	λ(v	ADV
ejpam-5392	179	4	)	)	PUNCT
ejpam-5392	180	1	⊆	⊆	NUM
ejpam-5392	180	2	rβ	rβ	ADP
ejpam-5392	180	3	λ(v	λ(v	PROPN
ejpam-5392	180	4	)	)	PUNCT
ejpam-5392	181	1	⊆	⊆	NUM
ejpam-5392	181	2	r	r	NOUN
ejpam-5392	181	3	∧	∧	PROPN
ejpam-5392	181	4	β	β	X
ejpam-5392	181	5	λ	λ	X
ejpam-5392	181	6	(	(	PUNCT
ejpam-5392	181	7	v	v	NOUN
ejpam-5392	181	8	)	)	PUNCT
ejpam-5392	181	9	⊆	⊆	NUM
ejpam-5392	181	10	rl−	rl−	PROPN
ejpam-5392	181	11	∧	∧	PROPN
ejpam-5392	181	12	βλ	βλ	X
ejpam-5392	181	13	(	(	PUNCT
ejpam-5392	181	14	v	v	NOUN
ejpam-5392	181	15	)	)	PUNCT
ejpam-5392	181	16	.	.	PUNCT
ejpam-5392	182	1	(	(	PUNCT
ejpam-5392	182	2	v	v	NOUN
ejpam-5392	182	3	)	)	PUNCT
ejpam-5392	182	4	rα	rα	ADV
ejpam-5392	182	5	λ(v	λ(v	PROPN
ejpam-5392	182	6	)	)	PUNCT
ejpam-5392	183	1	⊆	⊆	NUM
ejpam-5392	183	2	rs	rs	NOUN
ejpam-5392	183	3	λ(v	λ(v	PROPN
ejpam-5392	183	4	)	)	PUNCT
ejpam-5392	184	1	⊆	⊆	NUM
ejpam-5392	184	2	rγ	rγ	NOUN
ejpam-5392	184	3	λ(v	λ(v	ADV
ejpam-5392	184	4	)	)	PUNCT
ejpam-5392	185	1	⊆	⊆	NUM
ejpam-5392	185	2	rβ	rβ	ADP
ejpam-5392	185	3	λ(v	λ(v	PROPN
ejpam-5392	185	4	)	)	PUNCT
ejpam-5392	186	1	⊆	⊆	NUM
ejpam-5392	186	2	r	r	NOUN
ejpam-5392	186	3	∧	∧	PROPN
ejpam-5392	186	4	β	β	X
ejpam-5392	186	5	λ	λ	X
ejpam-5392	186	6	(	(	PUNCT
ejpam-5392	186	7	v	v	NOUN
ejpam-5392	186	8	)	)	PUNCT
ejpam-5392	186	9	⊆	⊆	NUM
ejpam-5392	186	10	rl−	rl−	PROPN
ejpam-5392	186	11	∧	∧	PROPN
ejpam-5392	186	12	βλ	βλ	X
ejpam-5392	186	13	(	(	PUNCT
ejpam-5392	186	14	v	v	NOUN
ejpam-5392	186	15	)	)	PUNCT
ejpam-5392	186	16	.	.	PUNCT
ejpam-5392	187	1	(	(	PUNCT
ejpam-5392	187	2	vi	vi	X
ejpam-5392	187	3	)	)	PUNCT
ejpam-5392	187	4	rλ(v	rλ(v	VERB
ejpam-5392	187	5	)	)	PUNCT
ejpam-5392	188	1	⊆	⊆	NUM
ejpam-5392	188	2	r	r	NOUN
ejpam-5392	188	3	∧	∧	PROPN
ejpam-5392	188	4	β	β	X
ejpam-5392	188	5	λ	λ	X
ejpam-5392	188	6	(	(	PUNCT
ejpam-5392	188	7	v	v	NOUN
ejpam-5392	188	8	)	)	PUNCT
ejpam-5392	188	9	⊆	⊆	NUM
ejpam-5392	188	10	rl−	rl−	PROPN
ejpam-5392	188	11	∧	∧	PROPN
ejpam-5392	188	12	βλ	βλ	X
ejpam-5392	188	13	(	(	PUNCT
ejpam-5392	188	14	v	v	NOUN
ejpam-5392	188	15	)	)	PUNCT
ejpam-5392	188	16	.	.	PUNCT
ejpam-5392	189	1	(	(	PUNCT
ejpam-5392	189	2	vii	vii	PROPN
ejpam-5392	189	3	)	)	PUNCT
ejpam-5392	189	4	rl−δβ	rl−δβ	PROPN
ejpam-5392	190	1	λ	λ	INTJ
ejpam-5392	190	2	(	(	PUNCT
ejpam-5392	190	3	v	v	NOUN
ejpam-5392	190	4	)	)	PUNCT
ejpam-5392	190	5	⊆	⊆	NUM
ejpam-5392	190	6	rδβ	rδβ	NOUN
ejpam-5392	190	7	λ	λ	PROPN
ejpam-5392	190	8	(	(	PUNCT
ejpam-5392	190	9	v	v	NOUN
ejpam-5392	190	10	)	)	PUNCT
ejpam-5392	190	11	⊆	⊆	NUM
ejpam-5392	190	12	rβ	rβ	ADP
ejpam-5392	190	13	λ(v	λ(v	PROPN
ejpam-5392	190	14	)	)	PUNCT
ejpam-5392	191	1	⊆	⊆	NUM
ejpam-5392	191	2	rγ	rγ	NOUN
ejpam-5392	191	3	λ(v	λ(v	ADV
ejpam-5392	191	4	)	)	PUNCT
ejpam-5392	192	1	⊆	⊆	NUM
ejpam-5392	192	2	rp	rp	NOUN
ejpam-5392	192	3	λ(v	λ(v	PROPN
ejpam-5392	192	4	)	)	PUNCT
ejpam-5392	193	1	⊆	⊆	NUM
ejpam-5392	193	2	rα	rα	ADV
ejpam-5392	193	3	λ(v	λ(v	PROPN
ejpam-5392	193	4	)	)	PUNCT
ejpam-5392	193	5	.	.	PUNCT
ejpam-5392	194	1	(	(	PUNCT
ejpam-5392	194	2	viii	viii	NOUN
ejpam-5392	194	3	)	)	PUNCT
ejpam-5392	194	4	rl−δβ	rl−δβ	PROPN
ejpam-5392	195	1	λ	λ	INTJ
ejpam-5392	195	2	(	(	PUNCT
ejpam-5392	195	3	v	v	NOUN
ejpam-5392	195	4	)	)	PUNCT
ejpam-5392	195	5	⊆	⊆	NUM
ejpam-5392	195	6	rδβ	rδβ	NOUN
ejpam-5392	195	7	λ	λ	PROPN
ejpam-5392	195	8	(	(	PUNCT
ejpam-5392	195	9	v	v	NOUN
ejpam-5392	195	10	)	)	PUNCT
ejpam-5392	195	11	⊆	⊆	NUM
ejpam-5392	195	12	rβ	rβ	ADP
ejpam-5392	195	13	λ(v	λ(v	PROPN
ejpam-5392	195	14	)	)	PUNCT
ejpam-5392	196	1	⊆	⊆	NUM
ejpam-5392	196	2	rγ	rγ	NOUN
ejpam-5392	196	3	λ(v	λ(v	ADV
ejpam-5392	196	4	)	)	PUNCT
ejpam-5392	197	1	⊆	⊆	NUM
ejpam-5392	197	2	rs	rs	NOUN
ejpam-5392	197	3	λ(v	λ(v	PROPN
ejpam-5392	197	4	)	)	PUNCT
ejpam-5392	198	1	⊆	⊆	NUM
ejpam-5392	198	2	rα	rα	ADV
ejpam-5392	198	3	λ(v	λ(v	PROPN
ejpam-5392	198	4	)	)	PUNCT
ejpam-5392	198	5	.	.	PUNCT
ejpam-5392	199	1	(	(	PUNCT
ejpam-5392	199	2	ix	ix	PROPN
ejpam-5392	199	3	)	)	PUNCT
ejpam-5392	199	4	rl−δβ	rl−δβ	PROPN
ejpam-5392	200	1	λ	λ	INTJ
ejpam-5392	200	2	(	(	PUNCT
ejpam-5392	200	3	v	v	NOUN
ejpam-5392	200	4	)	)	PUNCT
ejpam-5392	200	5	⊆	⊆	NUM
ejpam-5392	200	6	rδβ	rδβ	NOUN
ejpam-5392	200	7	λ(v	λ(v	PROPN
ejpam-5392	200	8	)	)	PUNCT
ejpam-5392	201	1	⊆	⊆	NUM
ejpam-5392	201	2	rλ(v	rλ(v	NUM
ejpam-5392	201	3	)	)	PUNCT
ejpam-5392	201	4	.	.	PUNCT
ejpam-5392	202	1	(	(	PUNCT
ejpam-5392	202	2	x	x	X
ejpam-5392	202	3	)	)	PUNCT
ejpam-5392	202	4	rl−	rl−	PROPN
ejpam-5392	202	5	∧	∧	PROPN
ejpam-5392	202	6	β	β	X
ejpam-5392	202	7	λ	λ	X
ejpam-5392	202	8	(	(	PUNCT
ejpam-5392	202	9	v	v	NOUN
ejpam-5392	202	10	)	)	PUNCT
ejpam-5392	203	1	⊆	⊆	NUM
ejpam-5392	203	2	r	r	NOUN
ejpam-5392	203	3	∧	∧	PROPN
ejpam-5392	203	4	β	β	X
ejpam-5392	203	5	λ	λ	X
ejpam-5392	203	6	(	(	PUNCT
ejpam-5392	203	7	v	v	NOUN
ejpam-5392	203	8	)	)	PUNCT
ejpam-5392	203	9	⊆	⊆	NUM
ejpam-5392	203	10	rβ	rβ	ADP
ejpam-5392	203	11	λ(v	λ(v	PROPN
ejpam-5392	203	12	)	)	PUNCT
ejpam-5392	204	1	⊆	⊆	NUM
ejpam-5392	204	2	rγ	rγ	NOUN
ejpam-5392	204	3	λ(v	λ(v	ADV
ejpam-5392	204	4	)	)	PUNCT
ejpam-5392	205	1	⊆	⊆	NUM
ejpam-5392	205	2	rp	rp	NOUN
ejpam-5392	205	3	λ(v	λ(v	PROPN
ejpam-5392	205	4	)	)	PUNCT
ejpam-5392	206	1	⊆	⊆	NUM
ejpam-5392	206	2	rα	rα	ADV
ejpam-5392	206	3	λ(v	λ(v	PROPN
ejpam-5392	206	4	)	)	PUNCT
ejpam-5392	206	5	.	.	PUNCT
ejpam-5392	207	1	(	(	PUNCT
ejpam-5392	207	2	xi	xi	X
ejpam-5392	207	3	)	)	PUNCT
ejpam-5392	207	4	rl−	rl−	PROPN
ejpam-5392	207	5	∧	∧	PROPN
ejpam-5392	207	6	β	β	X
ejpam-5392	207	7	λ	λ	X
ejpam-5392	207	8	(	(	PUNCT
ejpam-5392	207	9	v	v	NOUN
ejpam-5392	207	10	)	)	PUNCT
ejpam-5392	208	1	⊆	⊆	NUM
ejpam-5392	208	2	r	r	NOUN
ejpam-5392	208	3	∧	∧	PROPN
ejpam-5392	208	4	β	β	X
ejpam-5392	208	5	λ	λ	X
ejpam-5392	208	6	(	(	PUNCT
ejpam-5392	208	7	v	v	NOUN
ejpam-5392	208	8	)	)	PUNCT
ejpam-5392	208	9	⊆	⊆	NUM
ejpam-5392	208	10	rβ	rβ	ADP
ejpam-5392	208	11	λ(v	λ(v	PROPN
ejpam-5392	208	12	)	)	PUNCT
ejpam-5392	209	1	⊆	⊆	NUM
ejpam-5392	209	2	rγ	rγ	NOUN
ejpam-5392	209	3	λ(v	λ(v	ADV
ejpam-5392	209	4	)	)	PUNCT
ejpam-5392	210	1	⊆	⊆	NUM
ejpam-5392	210	2	rs	rs	NOUN
ejpam-5392	210	3	λ(v	λ(v	PROPN
ejpam-5392	210	4	)	)	PUNCT
ejpam-5392	211	1	⊆	⊆	NUM
ejpam-5392	211	2	rα	rα	ADV
ejpam-5392	211	3	λ(v	λ(v	PROPN
ejpam-5392	211	4	)	)	PUNCT
ejpam-5392	211	5	.	.	PUNCT
ejpam-5392	212	1	(	(	PUNCT
ejpam-5392	212	2	xii	xii	NOUN
ejpam-5392	212	3	)	)	PUNCT
ejpam-5392	212	4	rl−	rl−	PROPN
ejpam-5392	212	5	∧	∧	PROPN
ejpam-5392	212	6	β	β	X
ejpam-5392	212	7	λ	λ	X
ejpam-5392	212	8	(	(	PUNCT
ejpam-5392	212	9	v	v	NOUN
ejpam-5392	212	10	)	)	PUNCT
ejpam-5392	212	11	⊆	⊆	NUM
ejpam-5392	212	12	r	r	NOUN
ejpam-5392	212	13	∧	∧	PROPN
ejpam-5392	212	14	β	β	X
ejpam-5392	212	15	λ	λ	X
ejpam-5392	212	16	(	(	PUNCT
ejpam-5392	212	17	v	v	NOUN
ejpam-5392	212	18	)	)	PUNCT
ejpam-5392	212	19	⊆	⊆	NUM
ejpam-5392	212	20	rλ(v	rλ(v	NUM
ejpam-5392	212	21	)	)	PUNCT
ejpam-5392	212	22	.	.	PUNCT
ejpam-5392	213	1	when	when	SCONJ
ejpam-5392	213	2	we	we	PRON
ejpam-5392	213	3	combine	combine	VERB
ejpam-5392	213	4	an	an	DET
ejpam-5392	213	5	ideal	ideal	ADJ
ejpam-5392	213	6	l	l	NOUN
ejpam-5392	213	7	with	with	ADP
ejpam-5392	213	8	a	a	DET
ejpam-5392	213	9	gλ	gλ	NOUN
ejpam-5392	213	10	-	-	PUNCT
ejpam-5392	213	11	space	space	NOUN
ejpam-5392	213	12	(	(	PUNCT
ejpam-5392	213	13	x	x	NOUN
ejpam-5392	213	14	,	,	PUNCT
ejpam-5392	213	15	r	r	NOUN
ejpam-5392	213	16	,	,	PUNCT
ejpam-5392	213	17	ξλ	ξλ	PROPN
ejpam-5392	213	18	)	)	PUNCT
ejpam-5392	213	19	,	,	PUNCT
ejpam-5392	213	20	we	we	PRON
ejpam-5392	213	21	write	write	VERB
ejpam-5392	213	22	the	the	DET
ejpam-5392	213	23	quadruple	quadruple	NOUN
ejpam-5392	213	24	(	(	PUNCT
ejpam-5392	213	25	x	x	NOUN
ejpam-5392	213	26	,	,	PUNCT
ejpam-5392	213	27	r	r	NOUN
ejpam-5392	213	28	,	,	PUNCT
ejpam-5392	213	29	ξλ	ξλ	NOUN
ejpam-5392	213	30	,	,	PUNCT
ejpam-5392	213	31	l	l	NOUN
ejpam-5392	213	32	)	)	PUNCT
ejpam-5392	213	33	;	;	PUNCT
ejpam-5392	213	34	this	this	DET
ejpam-5392	213	35	quadruple	quadruple	NOUN
ejpam-5392	213	36	is	be	AUX
ejpam-5392	213	37	symbolized	symbolize	VERB
ejpam-5392	213	38	by	by	ADP
ejpam-5392	213	39	l	l	NOUN
ejpam-5392	213	40	−gλ	−gλ	NOUN
ejpam-5392	213	41	-	-	PUNCT
ejpam-5392	213	42	space	space	NOUN
ejpam-5392	213	43	.	.	PUNCT
ejpam-5392	214	1	proposition	proposition	NOUN
ejpam-5392	214	2	3	3	NUM
ejpam-5392	214	3	.	.	PUNCT
ejpam-5392	215	1	[	[	X
ejpam-5392	215	2	23	23	NUM
ejpam-5392	215	3	]	]	PUNCT
ejpam-5392	215	4	for	for	ADP
ejpam-5392	215	5	a	a	DET
ejpam-5392	215	6	subset	subset	NOUN
ejpam-5392	215	7	v	v	NOUN
ejpam-5392	215	8	of	of	ADP
ejpam-5392	215	9	an	an	DET
ejpam-5392	215	10	l	l	NOUN
ejpam-5392	215	11	−gλ	−gλ	NOUN
ejpam-5392	215	12	-	-	PUNCT
ejpam-5392	215	13	space	space	NOUN
ejpam-5392	215	14	(	(	PUNCT
ejpam-5392	215	15	x	x	NOUN
ejpam-5392	215	16	,	,	PUNCT
ejpam-5392	215	17	r	r	NOUN
ejpam-5392	215	18	,	,	PUNCT
ejpam-5392	215	19	ξλ	ξλ	NOUN
ejpam-5392	215	20	,	,	PUNCT
ejpam-5392	215	21	l	l	NOUN
ejpam-5392	215	22	)	)	PUNCT
ejpam-5392	215	23	,	,	PUNCT
ejpam-5392	215	24	we	we	PRON
ejpam-5392	215	25	have	have	VERB
ejpam-5392	215	26	:	:	PUNCT
ejpam-5392	215	27	(	(	PUNCT
ejpam-5392	215	28	i	i	NOUN
ejpam-5392	215	29	)	)	PUNCT
ejpam-5392	215	30	rl−p	rl−p	PROPN
ejpam-5392	215	31	λ	λ	PROPN
ejpam-5392	215	32	(	(	PUNCT
ejpam-5392	215	33	v	v	NOUN
ejpam-5392	215	34	)	)	PUNCT
ejpam-5392	215	35	⊆	⊆	NUM
ejpam-5392	215	36	rl−β	rl−β	NOUN
ejpam-5392	215	37	λ	λ	PROPN
ejpam-5392	215	38	(	(	PUNCT
ejpam-5392	215	39	v	v	NOUN
ejpam-5392	215	40	)	)	PUNCT
ejpam-5392	215	41	⊆	⊆	NUM
ejpam-5392	215	42	rl−δβλ(v	rl−δβλ(v	ADJ
ejpam-5392	215	43	)	)	PUNCT
ejpam-5392	215	44	.	.	PUNCT
ejpam-5392	216	1	(	(	PUNCT
ejpam-5392	216	2	ii	ii	NOUN
ejpam-5392	216	3	)	)	PUNCT
ejpam-5392	216	4	rl−α	rl−α	PROPN
ejpam-5392	216	5	λ	λ	PROPN
ejpam-5392	216	6	(	(	PUNCT
ejpam-5392	216	7	v	v	NOUN
ejpam-5392	216	8	)	)	PUNCT
ejpam-5392	216	9	⊆	⊆	NUM
ejpam-5392	216	10	rl−s	rl−s	PROPN
ejpam-5392	216	11	λ	λ	PROPN
ejpam-5392	216	12	(	(	PUNCT
ejpam-5392	216	13	v	v	NOUN
ejpam-5392	216	14	)	)	PUNCT
ejpam-5392	216	15	⊆	⊆	NUM
ejpam-5392	216	16	rl−β	rl−β	NOUN
ejpam-5392	216	17	λ	λ	PROPN
ejpam-5392	216	18	(	(	PUNCT
ejpam-5392	216	19	v	v	NOUN
ejpam-5392	216	20	)	)	PUNCT
ejpam-5392	216	21	⊆	⊆	NUM
ejpam-5392	216	22	rl−δβ	rl−δβ	X
ejpam-5392	217	1	λ	λ	INTJ
ejpam-5392	217	2	(	(	PUNCT
ejpam-5392	217	3	v	v	NOUN
ejpam-5392	217	4	)	)	PUNCT
ejpam-5392	217	5	.	.	PUNCT
ejpam-5392	218	1	(	(	PUNCT
ejpam-5392	218	2	iii	iii	X
ejpam-5392	218	3	)	)	PUNCT
ejpam-5392	218	4	rl−δβ	rl−δβ	PROPN
ejpam-5392	219	1	λ	λ	INTJ
ejpam-5392	219	2	(	(	PUNCT
ejpam-5392	219	3	v	v	NOUN
ejpam-5392	219	4	)	)	PUNCT
ejpam-5392	219	5	⊆	⊆	NUM
ejpam-5392	219	6	rl−β	rl−β	NOUN
ejpam-5392	219	7	λ	λ	PROPN
ejpam-5392	219	8	(	(	PUNCT
ejpam-5392	219	9	v	v	NOUN
ejpam-5392	219	10	)	)	PUNCT
ejpam-5392	219	11	⊆	⊆	NUM
ejpam-5392	219	12	rl−p	rl−p	PROPN
ejpam-5392	219	13	λ	λ	PROPN
ejpam-5392	219	14	(	(	PUNCT
ejpam-5392	219	15	v	v	NOUN
ejpam-5392	219	16	)	)	PUNCT
ejpam-5392	219	17	.	.	PUNCT
ejpam-5392	220	1	(	(	PUNCT
ejpam-5392	220	2	iv	iv	X
ejpam-5392	220	3	)	)	PUNCT
ejpam-5392	220	4	rl−δβ	rl−δβ	PROPN
ejpam-5392	221	1	λ	λ	INTJ
ejpam-5392	221	2	(	(	PUNCT
ejpam-5392	221	3	v	v	NOUN
ejpam-5392	221	4	)	)	PUNCT
ejpam-5392	221	5	⊆	⊆	NUM
ejpam-5392	221	6	rl−β	rl−β	NOUN
ejpam-5392	221	7	λ	λ	PROPN
ejpam-5392	221	8	(	(	PUNCT
ejpam-5392	221	9	v	v	NOUN
ejpam-5392	221	10	)	)	PUNCT
ejpam-5392	221	11	⊆	⊆	NUM
ejpam-5392	221	12	rl−s	rl−s	PROPN
ejpam-5392	221	13	λ	λ	PROPN
ejpam-5392	221	14	(	(	PUNCT
ejpam-5392	221	15	v	v	NOUN
ejpam-5392	221	16	)	)	PUNCT
ejpam-5392	221	17	⊆	⊆	NUM
ejpam-5392	221	18	rl−α	rl−α	PROPN
ejpam-5392	221	19	λ	λ	PROPN
ejpam-5392	221	20	(	(	PUNCT
ejpam-5392	221	21	v	v	NOUN
ejpam-5392	221	22	)	)	PUNCT
ejpam-5392	221	23	.	.	PUNCT
ejpam-5392	222	1	(	(	PUNCT
ejpam-5392	222	2	v	v	NOUN
ejpam-5392	222	3	)	)	PUNCT
ejpam-5392	222	4	rl−p	rl−p	NOUN
ejpam-5392	222	5	λ	λ	PROPN
ejpam-5392	222	6	(	(	PUNCT
ejpam-5392	222	7	v	v	NOUN
ejpam-5392	222	8	)	)	PUNCT
ejpam-5392	222	9	⊆	⊆	NUM
ejpam-5392	222	10	rl−β	rl−β	NOUN
ejpam-5392	222	11	λ	λ	PROPN
ejpam-5392	222	12	(	(	PUNCT
ejpam-5392	222	13	v	v	NOUN
ejpam-5392	222	14	)	)	PUNCT
ejpam-5392	222	15	⊆	⊆	NUM
ejpam-5392	222	16	rl−	rl−	PROPN
ejpam-5392	222	17	∧	∧	NOUN
ejpam-5392	222	18	βλ(v	βλ(v	NUM
ejpam-5392	222	19	)	)	PUNCT
ejpam-5392	222	20	.	.	PUNCT
ejpam-5392	223	1	(	(	PUNCT
ejpam-5392	223	2	vi	vi	NOUN
ejpam-5392	223	3	)	)	PUNCT
ejpam-5392	223	4	rl−α	rl−α	NOUN
ejpam-5392	223	5	λ	λ	PROPN
ejpam-5392	223	6	(	(	PUNCT
ejpam-5392	223	7	v	v	NOUN
ejpam-5392	223	8	)	)	PUNCT
ejpam-5392	223	9	⊆	⊆	NUM
ejpam-5392	223	10	rl−s	rl−s	PROPN
ejpam-5392	223	11	λ	λ	PROPN
ejpam-5392	223	12	(	(	PUNCT
ejpam-5392	223	13	v	v	NOUN
ejpam-5392	223	14	)	)	PUNCT
ejpam-5392	223	15	⊆	⊆	NUM
ejpam-5392	223	16	rl−β	rl−β	NOUN
ejpam-5392	223	17	λ	λ	PROPN
ejpam-5392	223	18	(	(	PUNCT
ejpam-5392	223	19	v	v	NOUN
ejpam-5392	223	20	)	)	PUNCT
ejpam-5392	223	21	⊆	⊆	NUM
ejpam-5392	223	22	rl−	rl−	PROPN
ejpam-5392	223	23	∧	∧	NOUN
ejpam-5392	223	24	βλ(v	βλ(v	PUNCT
ejpam-5392	223	25	)	)	PUNCT
ejpam-5392	223	26	.	.	PUNCT
ejpam-5392	224	1	(	(	PUNCT
ejpam-5392	224	2	vii	vii	PROPN
ejpam-5392	224	3	)	)	PUNCT
ejpam-5392	224	4	rl−	rl−	PROPN
ejpam-5392	224	5	∧	∧	NOUN
ejpam-5392	224	6	βλ(v	βλ(v	PUNCT
ejpam-5392	224	7	)	)	PUNCT
ejpam-5392	225	1	⊆	⊆	NUM
ejpam-5392	225	2	rl−β	rl−β	NOUN
ejpam-5392	225	3	λ	λ	PROPN
ejpam-5392	225	4	(	(	PUNCT
ejpam-5392	225	5	v	v	NOUN
ejpam-5392	225	6	)	)	PUNCT
ejpam-5392	225	7	⊆	⊆	NUM
ejpam-5392	225	8	rl−p	rl−p	PROPN
ejpam-5392	225	9	λ	λ	PROPN
ejpam-5392	225	10	(	(	PUNCT
ejpam-5392	225	11	v	v	NOUN
ejpam-5392	225	12	)	)	PUNCT
ejpam-5392	225	13	.	.	PUNCT
ejpam-5392	226	1	m.	m.	PROPN
ejpam-5392	226	2	hosny	hosny	PROPN
ejpam-5392	226	3	,	,	PUNCT
ejpam-5392	226	4	t.m	t.m	PROPN
ejpam-5392	226	5	.	.	PROPN
ejpam-5392	226	6	al	al	PROPN
ejpam-5392	226	7	-	-	PUNCT
ejpam-5392	226	8	shami	shami	PROPN
ejpam-5392	226	9	/	/	PUNCT
ejpam-5392	226	10	eur	eur	PROPN
ejpam-5392	226	11	.	.	PUNCT
ejpam-5392	227	1	j.	j.	PROPN
ejpam-5392	227	2	pure	pure	PROPN
ejpam-5392	227	3	appl	appl	PROPN
ejpam-5392	227	4	.	.	PROPN
ejpam-5392	227	5	math	math	PROPN
ejpam-5392	227	6	,	,	PUNCT
ejpam-5392	227	7	17	17	NUM
ejpam-5392	227	8	(	(	PUNCT
ejpam-5392	227	9	4	4	NUM
ejpam-5392	227	10	)	)	PUNCT
ejpam-5392	227	11	(	(	PUNCT
ejpam-5392	227	12	2024	2024	NUM
ejpam-5392	227	13	)	)	PUNCT
ejpam-5392	227	14	,	,	PUNCT
ejpam-5392	227	15	3436	3436	NUM
ejpam-5392	227	16	-	-	SYM
ejpam-5392	227	17	3463	3463	NUM
ejpam-5392	227	18	3443	3443	NUM
ejpam-5392	227	19	(	(	PUNCT
ejpam-5392	227	20	viii	viii	NOUN
ejpam-5392	227	21	)	)	PUNCT
ejpam-5392	227	22	rl−	rl−	NOUN
ejpam-5392	227	23	∧	∧	NOUN
ejpam-5392	227	24	βλ(v	βλ(v	PUNCT
ejpam-5392	227	25	)	)	PUNCT
ejpam-5392	227	26	⊆	⊆	NUM
ejpam-5392	227	27	rl−β	rl−β	NOUN
ejpam-5392	227	28	λ	λ	PROPN
ejpam-5392	227	29	(	(	PUNCT
ejpam-5392	227	30	v	v	NOUN
ejpam-5392	227	31	)	)	PUNCT
ejpam-5392	227	32	⊆	⊆	NUM
ejpam-5392	227	33	rl−s	rl−s	PROPN
ejpam-5392	227	34	λ	λ	PROPN
ejpam-5392	227	35	(	(	PUNCT
ejpam-5392	227	36	v	v	NOUN
ejpam-5392	227	37	)	)	PUNCT
ejpam-5392	227	38	⊆	⊆	NUM
ejpam-5392	227	39	rl−α	rl−α	PROPN
ejpam-5392	227	40	λ	λ	PROPN
ejpam-5392	227	41	(	(	PUNCT
ejpam-5392	227	42	v	v	NOUN
ejpam-5392	227	43	)	)	PUNCT
ejpam-5392	227	44	.	.	PUNCT
ejpam-5392	228	1	definition	definition	NOUN
ejpam-5392	228	2	10	10	NUM
ejpam-5392	228	3	.	.	PUNCT
ejpam-5392	229	1	let	let	AUX
ejpam-5392	229	2	(	(	PUNCT
ejpam-5392	229	3	x	x	NOUN
ejpam-5392	229	4	,	,	PUNCT
ejpam-5392	229	5	r	r	NOUN
ejpam-5392	229	6	,	,	PUNCT
ejpam-5392	229	7	ξλ	ξλ	NOUN
ejpam-5392	229	8	)	)	PUNCT
ejpam-5392	229	9	be	be	AUX
ejpam-5392	229	10	a	a	DET
ejpam-5392	229	11	gλ	gλ	NOUN
ejpam-5392	229	12	-	-	PUNCT
ejpam-5392	229	13	space	space	NOUN
ejpam-5392	229	14	and	and	CCONJ
ejpam-5392	229	15	v	v	ADP
ejpam-5392	229	16	⊆	⊆	NUM
ejpam-5392	229	17	x.	x.	NOUN
ejpam-5392	229	18	the	the	DET
ejpam-5392	229	19	θλ	θλ	NOUN
ejpam-5392	229	20	-	-	PUNCT
ejpam-5392	229	21	closure	closure	NOUN
ejpam-5392	229	22	is	be	AUX
ejpam-5392	229	23	given	give	VERB
ejpam-5392	229	24	by	by	ADP
ejpam-5392	229	25	clθλ(v	clθλ(v	PROPN
ejpam-5392	229	26	)	)	PUNCT
ejpam-5392	230	1	=	=	PRON
ejpam-5392	230	2	{	{	PUNCT
ejpam-5392	230	3	y	y	PROPN
ejpam-5392	230	4	∈	∈	PROPN
ejpam-5392	230	5	x	x	X
ejpam-5392	230	6	:	:	PUNCT
ejpam-5392	230	7	v	v	NUM
ejpam-5392	230	8	∩	∩	ADJ
ejpam-5392	230	9	clλ(g	clλ(g	PROPN
ejpam-5392	230	10	)	)	PUNCT
ejpam-5392	230	11	̸=	̸=	PROPN
ejpam-5392	230	12	∅	∅	NOUN
ejpam-5392	230	13	,	,	PUNCT
ejpam-5392	230	14	g	g	PROPN
ejpam-5392	230	15	∈	∈	PROPN
ejpam-5392	230	16	ϑλ	ϑλ	PROPN
ejpam-5392	230	17	and	and	CCONJ
ejpam-5392	230	18	y	y	PROPN
ejpam-5392	230	19	∈	∈	PROPN
ejpam-5392	230	20	g	g	PROPN
ejpam-5392	230	21	}	}	PUNCT
ejpam-5392	230	22	.	.	PUNCT
ejpam-5392	231	1	definition	definition	NOUN
ejpam-5392	231	2	11	11	NUM
ejpam-5392	231	3	.	.	PUNCT
ejpam-5392	232	1	[	[	X
ejpam-5392	232	2	42	42	NUM
ejpam-5392	232	3	]	]	PUNCT
ejpam-5392	232	4	the	the	DET
ejpam-5392	232	5	rough	rough	ADJ
ejpam-5392	232	6	membership	membership	NOUN
ejpam-5392	232	7	function	function	NOUN
ejpam-5392	232	8	of	of	ADP
ejpam-5392	232	9	a	a	DET
ejpam-5392	232	10	subset	subset	NOUN
ejpam-5392	232	11	v	v	NOUN
ejpam-5392	232	12	of	of	ADP
ejpam-5392	232	13	x	x	PUNCT
ejpam-5392	232	14	is	be	AUX
ejpam-5392	232	15	defined	define	VERB
ejpam-5392	232	16	,	,	PUNCT
ejpam-5392	232	17	under	under	ADP
ejpam-5392	232	18	an	an	DET
ejpam-5392	232	19	equivalence	equivalence	NOUN
ejpam-5392	232	20	relation	relation	NOUN
ejpam-5392	232	21	r	r	NOUN
ejpam-5392	232	22	on	on	ADP
ejpam-5392	232	23	x	x	SYM
ejpam-5392	232	24	,	,	PUNCT
ejpam-5392	232	25	as	as	SCONJ
ejpam-5392	232	26	µv	µv	PRON
ejpam-5392	232	27	:	:	PUNCT
ejpam-5392	232	28	x	x	X
ejpam-5392	232	29	→	→	PUNCT
ejpam-5392	233	1	[	[	X
ejpam-5392	233	2	0	0	NUM
ejpam-5392	233	3	,	,	PUNCT
ejpam-5392	233	4	1	1	NUM
ejpam-5392	233	5	]	]	PUNCT
ejpam-5392	233	6	,	,	PUNCT
ejpam-5392	233	7	where	where	SCONJ
ejpam-5392	233	8	µv	µv	PROPN
ejpam-5392	233	9	(	(	PUNCT
ejpam-5392	233	10	y	y	NOUN
ejpam-5392	233	11	)	)	PUNCT
ejpam-5392	233	12	=	=	SYM
ejpam-5392	233	13	|[y]r	|[y]r	NOUN
ejpam-5392	233	14	∩v	∩v	NOUN
ejpam-5392	233	15	|	|	ADV
ejpam-5392	233	16	|[y]r|	|[y]r|	NUM
ejpam-5392	233	17	,	,	PUNCT
ejpam-5392	233	18	y	y	PROPN
ejpam-5392	233	19	∈	∈	PROPN
ejpam-5392	233	20	x.	x.	NOUN
ejpam-5392	234	1	[	[	X
ejpam-5392	234	2	y]r	y]r	NOUN
ejpam-5392	234	3	denotes	denote	VERB
ejpam-5392	234	4	to	to	ADP
ejpam-5392	234	5	an	an	DET
ejpam-5392	234	6	equivalence	equivalence	NOUN
ejpam-5392	234	7	classes	class	NOUN
ejpam-5392	234	8	.	.	PUNCT
ejpam-5392	235	1	definition	definition	NOUN
ejpam-5392	235	2	12	12	NUM
ejpam-5392	235	3	.	.	PUNCT
ejpam-5392	236	1	[	[	X
ejpam-5392	236	2	23	23	NUM
ejpam-5392	236	3	]	]	PUNCT
ejpam-5392	236	4	the	the	DET
ejpam-5392	236	5	λ	λ	NOUN
ejpam-5392	236	6	-	-	ADJ
ejpam-5392	236	7	rough	rough	ADJ
ejpam-5392	236	8	membership	membership	NOUN
ejpam-5392	236	9	functions	function	NOUN
ejpam-5392	236	10	of	of	ADP
ejpam-5392	236	11	a	a	DET
ejpam-5392	236	12	subset	subset	NOUN
ejpam-5392	236	13	v	v	NOUN
ejpam-5392	236	14	of	of	ADP
ejpam-5392	236	15	x	x	PROPN
ejpam-5392	236	16	is	be	AUX
ejpam-5392	236	17	given	give	VERB
ejpam-5392	236	18	by	by	ADP
ejpam-5392	236	19	µλv	µλv	NOUN
ejpam-5392	236	20	→	→	PUNCT
ejpam-5392	237	1	[	[	X
ejpam-5392	237	2	0	0	NUM
ejpam-5392	237	3	,	,	PUNCT
ejpam-5392	237	4	1	1	NUM
ejpam-5392	237	5	]	]	PUNCT
ejpam-5392	237	6	,	,	PUNCT
ejpam-5392	237	7	where	where	SCONJ
ejpam-5392	237	8	µλv	µλv	PROPN
ejpam-5392	237	9	(	(	PUNCT
ejpam-5392	237	10	y	y	NOUN
ejpam-5392	237	11	)	)	PUNCT
ejpam-5392	237	12	=	=	SYM
ejpam-5392	237	13	|{∩gλ(y)}∩v	|{∩gλ(y)}∩v	NOUN
ejpam-5392	238	1	|	|	ADV
ejpam-5392	238	2	|∩gλ(y)|	|∩gλ(y)|	PROPN
ejpam-5392	238	3	.	.	PUNCT
ejpam-5392	239	1	definition	definition	NOUN
ejpam-5392	239	2	13	13	NUM
ejpam-5392	239	3	.	.	PUNCT
ejpam-5392	240	1	[	[	X
ejpam-5392	240	2	35	35	NUM
ejpam-5392	240	3	]	]	PUNCT
ejpam-5392	240	4	the	the	DET
ejpam-5392	240	5	λ	λ	NOUN
ejpam-5392	240	6	-	-	NOUN
ejpam-5392	240	7	rough	rough	ADJ
ejpam-5392	240	8	nearly	nearly	ADV
ejpam-5392	240	9	membership	membership	NOUN
ejpam-5392	240	10	function	function	NOUN
ejpam-5392	240	11	of	of	ADP
ejpam-5392	240	12	a	a	DET
ejpam-5392	240	13	subset	subset	NOUN
ejpam-5392	240	14	v	v	NOUN
ejpam-5392	240	15	of	of	ADP
ejpam-5392	240	16	x	x	PUNCT
ejpam-5392	240	17	is	be	AUX
ejpam-5392	240	18	defined	define	VERB
ejpam-5392	240	19	by	by	ADP
ejpam-5392	240	20	µηλv	µηλv	NOUN
ejpam-5392	240	21	→	→	SYM
ejpam-5392	240	22	[	[	X
ejpam-5392	240	23	0	0	NUM
ejpam-5392	240	24	,	,	PUNCT
ejpam-5392	240	25	1	1	NUM
ejpam-5392	240	26	]	]	PUNCT
ejpam-5392	240	27	as	as	SCONJ
ejpam-5392	240	28	follows	follow	VERB
ejpam-5392	240	29	µηλv	µηλv	NOUN
ejpam-5392	240	30	(	(	PUNCT
ejpam-5392	240	31	y	y	NOUN
ejpam-5392	240	32	)	)	PUNCT
ejpam-5392	240	33	=	=	PRON
ejpam-5392	240	34	{	{	PUNCT
ejpam-5392	240	35	1	1	NUM
ejpam-5392	240	36	:	:	SYM
ejpam-5392	240	37	1	1	NUM
ejpam-5392	240	38	∈	∈	NOUN
ejpam-5392	240	39	ψηλv	ψηλv	NOUN
ejpam-5392	240	40	(	(	PUNCT
ejpam-5392	240	41	y	y	NOUN
ejpam-5392	240	42	)	)	PUNCT
ejpam-5392	240	43	min(ψηλv	min(ψηλv	NOUN
ejpam-5392	240	44	(	(	PUNCT
ejpam-5392	240	45	y	y	NOUN
ejpam-5392	240	46	)	)	PUNCT
ejpam-5392	240	47	)	)	PUNCT
ejpam-5392	240	48	:	:	PUNCT
ejpam-5392	241	1	otherwise	otherwise	ADV
ejpam-5392	241	2	where	where	SCONJ
ejpam-5392	241	3	ψηλv	ψηλv	NOUN
ejpam-5392	241	4	(	(	PUNCT
ejpam-5392	241	5	y	y	NOUN
ejpam-5392	241	6	)	)	PUNCT
ejpam-5392	241	7	=	=	PRON
ejpam-5392	241	8	{	{	PUNCT
ejpam-5392	241	9	|ηλ(y)∩v	|ηλ(y)∩v	X
ejpam-5392	242	1	|	|	ADV
ejpam-5392	242	2	|ηλ(y)|	|ηλ(y)|	PROPN
ejpam-5392	242	3	:	:	PUNCT
ejpam-5392	242	4	y	y	PROPN
ejpam-5392	242	5	∈	∈	PROPN
ejpam-5392	242	6	ηλ(y	ηλ(y	X
ejpam-5392	242	7	)	)	PUNCT
ejpam-5392	242	8	and	and	CCONJ
ejpam-5392	242	9	ηλ(y	ηλ(y	ADV
ejpam-5392	242	10	)	)	PUNCT
ejpam-5392	242	11	∈	∈	PROPN
ejpam-5392	242	12	ηλo(x	ηλo(x	PROPN
ejpam-5392	242	13	)	)	PUNCT
ejpam-5392	242	14	}	}	PUNCT
ejpam-5392	242	15	,	,	PUNCT
ejpam-5392	242	16	η	η	PROPN
ejpam-5392	242	17	∈	∈	PROPN
ejpam-5392	242	18	{	{	PUNCT
ejpam-5392	242	19	α	α	NOUN
ejpam-5392	242	20	,	,	PUNCT
ejpam-5392	242	21	p	p	X
ejpam-5392	242	22	,	,	PUNCT
ejpam-5392	242	23	s	s	X
ejpam-5392	242	24	,	,	PUNCT
ejpam-5392	242	25	β	β	NOUN
ejpam-5392	242	26	}	}	PUNCT
ejpam-5392	242	27	.	.	PUNCT
ejpam-5392	243	1	definition	definition	NOUN
ejpam-5392	243	2	14	14	NUM
ejpam-5392	243	3	.	.	PUNCT
ejpam-5392	244	1	[	[	X
ejpam-5392	244	2	22	22	NUM
ejpam-5392	244	3	,	,	PUNCT
ejpam-5392	244	4	23	23	NUM
ejpam-5392	244	5	]	]	PUNCT
ejpam-5392	244	6	the	the	DET
ejpam-5392	244	7	l	l	NOUN
ejpam-5392	244	8	−	−	NOUN
ejpam-5392	244	9	λ	λ	NOUN
ejpam-5392	244	10	-	-	PUNCT
ejpam-5392	244	11	nearly	nearly	ADV
ejpam-5392	244	12	rough	rough	ADJ
ejpam-5392	244	13	membership	membership	NOUN
ejpam-5392	244	14	functions	function	NOUN
ejpam-5392	244	15	of	of	ADP
ejpam-5392	244	16	a	a	DET
ejpam-5392	244	17	subset	subset	NOUN
ejpam-5392	244	18	v	v	NOUN
ejpam-5392	244	19	of	of	ADP
ejpam-5392	244	20	x	x	PUNCT
ejpam-5392	244	21	is	be	AUX
ejpam-5392	244	22	defined	define	VERB
ejpam-5392	244	23	by	by	ADP
ejpam-5392	244	24	µl−ηλv	µl−ηλv	NOUN
ejpam-5392	244	25	→	→	SYM
ejpam-5392	245	1	[	[	X
ejpam-5392	245	2	0	0	NUM
ejpam-5392	245	3	,	,	PUNCT
ejpam-5392	245	4	1	1	NUM
ejpam-5392	245	5	]	]	PUNCT
ejpam-5392	245	6	,	,	PUNCT
ejpam-5392	245	7	as	as	SCONJ
ejpam-5392	245	8	follows	follow	VERB
ejpam-5392	245	9	µl−ηλv	µl−ηλv	X
ejpam-5392	245	10	(	(	PUNCT
ejpam-5392	245	11	y	y	NOUN
ejpam-5392	245	12	)	)	PUNCT
ejpam-5392	245	13	=	=	PRON
ejpam-5392	245	14	{	{	PUNCT
ejpam-5392	245	15	1	1	NUM
ejpam-5392	245	16	:	:	SYM
ejpam-5392	245	17	1	1	NUM
ejpam-5392	245	18	∈	∈	PROPN
ejpam-5392	245	19	ψl−ηλ	ψl−ηλ	NOUN
ejpam-5392	245	20	v	v	NOUN
ejpam-5392	245	21	(	(	PUNCT
ejpam-5392	245	22	y	y	NOUN
ejpam-5392	245	23	)	)	PUNCT
ejpam-5392	245	24	min(ψl−ηλ	min(ψl−ηλ	NOUN
ejpam-5392	245	25	v	v	NOUN
ejpam-5392	245	26	(	(	PUNCT
ejpam-5392	245	27	y	y	NOUN
ejpam-5392	245	28	)	)	PUNCT
ejpam-5392	245	29	)	)	PUNCT
ejpam-5392	245	30	)	)	PUNCT
ejpam-5392	246	1	:	:	PUNCT
ejpam-5392	246	2	otherwise	otherwise	ADV
ejpam-5392	246	3	where	where	SCONJ
ejpam-5392	246	4	ψl−ηλ	ψl−ηλ	NOUN
ejpam-5392	246	5	v	v	X
ejpam-5392	246	6	(	(	PUNCT
ejpam-5392	246	7	y	y	NOUN
ejpam-5392	246	8	)	)	PUNCT
ejpam-5392	246	9	=	=	PRON
ejpam-5392	246	10	{	{	PUNCT
ejpam-5392	246	11	|l−ηλ(y)∩v	|l−ηλ(y)∩v	PRON
ejpam-5392	246	12	|	|	ADV
ejpam-5392	246	13	|l−ηλ(y)|	|l−ηλ(y)|	ADV
ejpam-5392	246	14	:	:	PUNCT
ejpam-5392	246	15	y	y	PROPN
ejpam-5392	246	16	∈	∈	PROPN
ejpam-5392	246	17	l	l	NOUN
ejpam-5392	246	18	−	−	PROPN
ejpam-5392	246	19	ηλ(y	ηλ(y	NUM
ejpam-5392	246	20	)	)	PUNCT
ejpam-5392	246	21	and	and	CCONJ
ejpam-5392	246	22	l	l	NOUN
ejpam-5392	246	23	−	−	NOUN
ejpam-5392	246	24	ηλ(y	ηλ(y	PUNCT
ejpam-5392	246	25	)	)	PUNCT
ejpam-5392	246	26	∈	∈	PROPN
ejpam-5392	246	27	l	l	PROPN
ejpam-5392	246	28	-	-	PROPN
ejpam-5392	246	29	ηλo(x	ηλo(x	PROPN
ejpam-5392	246	30	)	)	PUNCT
ejpam-5392	246	31	}	}	PUNCT
ejpam-5392	246	32	.	.	PUNCT
ejpam-5392	247	1	lemma	lemma	PROPN
ejpam-5392	247	2	1	1	NUM
ejpam-5392	247	3	.	.	PUNCT
ejpam-5392	248	1	[	[	X
ejpam-5392	248	2	23	23	NUM
ejpam-5392	248	3	]	]	PUNCT
ejpam-5392	248	4	let	let	VERB
ejpam-5392	248	5	v	v	PART
ejpam-5392	248	6	be	be	AUX
ejpam-5392	248	7	a	a	DET
ejpam-5392	248	8	subset	subset	NOUN
ejpam-5392	248	9	of	of	ADP
ejpam-5392	248	10	an	an	DET
ejpam-5392	248	11	l	l	NOUN
ejpam-5392	248	12	−gλ	−gλ	NOUN
ejpam-5392	248	13	-	-	PUNCT
ejpam-5392	248	14	space	space	NOUN
ejpam-5392	248	15	(	(	PUNCT
ejpam-5392	248	16	x	x	NOUN
ejpam-5392	248	17	,	,	PUNCT
ejpam-5392	248	18	r	r	NOUN
ejpam-5392	248	19	,	,	PUNCT
ejpam-5392	248	20	ξλ	ξλ	NOUN
ejpam-5392	248	21	,	,	PUNCT
ejpam-5392	248	22	l	l	NOUN
ejpam-5392	248	23	)	)	PUNCT
ejpam-5392	248	24	.	.	PUNCT
ejpam-5392	249	1	then	then	ADV
ejpam-5392	249	2	(	(	PUNCT
ejpam-5392	249	3	i	i	NOUN
ejpam-5392	249	4	)	)	PUNCT
ejpam-5392	249	5	µλv	µλv	NOUN
ejpam-5392	249	6	(	(	PUNCT
ejpam-5392	249	7	y	y	NOUN
ejpam-5392	249	8	)	)	PUNCT
ejpam-5392	249	9	=	=	SYM
ejpam-5392	249	10	1	1	NUM
ejpam-5392	249	11	⇒	⇒	NOUN
ejpam-5392	249	12	µηλv	µηλv	NOUN
ejpam-5392	249	13	(	(	PUNCT
ejpam-5392	249	14	y	y	NOUN
ejpam-5392	249	15	)	)	PUNCT
ejpam-5392	249	16	=	=	SYM
ejpam-5392	249	17	1	1	NUM
ejpam-5392	249	18	⇒	⇒	NOUN
ejpam-5392	249	19	µl−ηλv	µl−ηλv	NOUN
ejpam-5392	249	20	(	(	PUNCT
ejpam-5392	249	21	y	y	NOUN
ejpam-5392	249	22	)	)	PUNCT
ejpam-5392	249	23	=	=	SYM
ejpam-5392	249	24	1	1	NUM
ejpam-5392	249	25	,	,	PUNCT
ejpam-5392	249	26	∀	∀	VERB
ejpam-5392	249	27	y	y	PROPN
ejpam-5392	249	28	∈	∈	PROPN
ejpam-5392	249	29	x.	x.	NOUN
ejpam-5392	249	30	(	(	PUNCT
ejpam-5392	249	31	ii	ii	NOUN
ejpam-5392	249	32	)	)	PUNCT
ejpam-5392	249	33	µλv	µλv	NOUN
ejpam-5392	249	34	(	(	PUNCT
ejpam-5392	249	35	y	y	NOUN
ejpam-5392	249	36	)	)	PUNCT
ejpam-5392	249	37	=	=	SYM
ejpam-5392	249	38	0	0	NUM
ejpam-5392	249	39	⇒	⇒	PROPN
ejpam-5392	249	40	µηλv	µηλv	PROPN
ejpam-5392	249	41	(	(	PUNCT
ejpam-5392	249	42	y	y	NOUN
ejpam-5392	249	43	)	)	PUNCT
ejpam-5392	249	44	=	=	SYM
ejpam-5392	249	45	0	0	NUM
ejpam-5392	249	46	⇒	⇒	NOUN
ejpam-5392	249	47	µl−ηλv	µl−ηλv	NOUN
ejpam-5392	249	48	(	(	PUNCT
ejpam-5392	249	49	y	y	NOUN
ejpam-5392	249	50	)	)	PUNCT
ejpam-5392	249	51	=	=	SYM
ejpam-5392	249	52	0	0	NUM
ejpam-5392	249	53	,	,	PUNCT
ejpam-5392	249	54	∀	∀	VERB
ejpam-5392	249	55	y	y	PROPN
ejpam-5392	249	56	∈	∈	PROPN
ejpam-5392	249	57	x.	x.	NOUN
ejpam-5392	249	58	definition	definition	NOUN
ejpam-5392	249	59	15	15	NUM
ejpam-5392	249	60	.	.	PUNCT
ejpam-5392	250	1	[	[	X
ejpam-5392	250	2	45	45	NUM
ejpam-5392	250	3	]	]	X
ejpam-5392	250	4	let	let	AUX
ejpam-5392	250	5	(	(	PUNCT
ejpam-5392	250	6	x	x	NOUN
ejpam-5392	250	7	,	,	PUNCT
ejpam-5392	250	8	r	r	NOUN
ejpam-5392	250	9	,	,	PUNCT
ejpam-5392	250	10	ξλ	ξλ	NOUN
ejpam-5392	250	11	)	)	PUNCT
ejpam-5392	250	12	be	be	AUX
ejpam-5392	250	13	a	a	DET
ejpam-5392	250	14	gλ	gλ	NOUN
ejpam-5392	250	15	-	-	PUNCT
ejpam-5392	250	16	space	space	NOUN
ejpam-5392	250	17	,	,	PUNCT
ejpam-5392	250	18	y	y	PROPN
ejpam-5392	250	19	∈	∈	PROPN
ejpam-5392	250	20	x	x	X
ejpam-5392	250	21	and	and	CCONJ
ejpam-5392	250	22	v	v	ADP
ejpam-5392	250	23	⊆	⊆	NUM
ejpam-5392	250	24	x	x	SYM
ejpam-5392	250	25	:	:	PUNCT
ejpam-5392	250	26	(	(	PUNCT
ejpam-5392	250	27	i	i	NOUN
ejpam-5392	250	28	)	)	PUNCT
ejpam-5392	250	29	if	if	SCONJ
ejpam-5392	250	30	y	y	PROPN
ejpam-5392	250	31	∈	∈	PROPN
ejpam-5392	250	32	rλ(v	rλ(v	VERB
ejpam-5392	250	33	)	)	PUNCT
ejpam-5392	250	34	,	,	PUNCT
ejpam-5392	250	35	then	then	ADV
ejpam-5392	250	36	y	y	PROPN
ejpam-5392	250	37	λ	λ	PROPN
ejpam-5392	250	38	-	-	PUNCT
ejpam-5392	250	39	certainly	certainly	ADV
ejpam-5392	250	40	belongs	belong	VERB
ejpam-5392	250	41	to	to	ADP
ejpam-5392	250	42	v	v	NUM
ejpam-5392	250	43	,	,	PUNCT
ejpam-5392	250	44	denoted	denote	VERB
ejpam-5392	250	45	by	by	ADP
ejpam-5392	250	46	y	y	PROPN
ejpam-5392	250	47	∈λv	∈λv	PROPN
ejpam-5392	250	48	.	.	PUNCT
ejpam-5392	251	1	(	(	PUNCT
ejpam-5392	251	2	ii	ii	NOUN
ejpam-5392	251	3	)	)	PUNCT
ejpam-5392	251	4	if	if	SCONJ
ejpam-5392	251	5	y	y	PROPN
ejpam-5392	251	6	∈	∈	PROPN
ejpam-5392	251	7	rλ(v	rλ(v	VERB
ejpam-5392	251	8	)	)	PUNCT
ejpam-5392	251	9	,	,	PUNCT
ejpam-5392	251	10	then	then	ADV
ejpam-5392	251	11	y	y	PROPN
ejpam-5392	251	12	λ	λ	PROPN
ejpam-5392	251	13	-	-	PUNCT
ejpam-5392	251	14	probably	probably	ADV
ejpam-5392	251	15	belongs	belong	VERB
ejpam-5392	251	16	to	to	ADP
ejpam-5392	251	17	v	v	NUM
ejpam-5392	251	18	,	,	PUNCT
ejpam-5392	251	19	denoted	denote	VERB
ejpam-5392	251	20	by	by	ADP
ejpam-5392	251	21	y	y	PROPN
ejpam-5392	251	22	∈λv	∈λv	PROPN
ejpam-5392	251	23	.	.	PUNCT
ejpam-5392	252	1	(	(	PUNCT
ejpam-5392	252	2	iii	iii	X
ejpam-5392	252	3	)	)	PUNCT
ejpam-5392	252	4	if	if	SCONJ
ejpam-5392	252	5	y	y	PROPN
ejpam-5392	252	6	∈	∈	PROPN
ejpam-5392	252	7	rη	rη	NOUN
ejpam-5392	252	8	λ(v	λ(v	PROPN
ejpam-5392	252	9	)	)	PUNCT
ejpam-5392	252	10	,	,	PUNCT
ejpam-5392	252	11	then	then	ADV
ejpam-5392	252	12	y	y	PROPN
ejpam-5392	252	13	λ	λ	PROPN
ejpam-5392	252	14	-	-	PUNCT
ejpam-5392	252	15	nearly	nearly	ADV
ejpam-5392	252	16	certainly	certainly	ADV
ejpam-5392	252	17	(	(	PUNCT
ejpam-5392	252	18	ηλ	ηλ	AUX
ejpam-5392	252	19	-	-	PUNCT
ejpam-5392	252	20	certainly	certainly	ADV
ejpam-5392	252	21	)	)	PUNCT
ejpam-5392	252	22	belongs	belong	VERB
ejpam-5392	252	23	to	to	ADP
ejpam-5392	252	24	v	v	NUM
ejpam-5392	252	25	,	,	PUNCT
ejpam-5392	252	26	denoted	denote	VERB
ejpam-5392	252	27	by	by	ADP
ejpam-5392	252	28	y	y	PROPN
ejpam-5392	252	29	∈ηλv	∈ηλv	PROPN
ejpam-5392	252	30	,	,	PUNCT
ejpam-5392	252	31	η	η	PROPN
ejpam-5392	252	32	∈	∈	PROPN
ejpam-5392	252	33	{	{	PUNCT
ejpam-5392	252	34	α	α	NOUN
ejpam-5392	252	35	,	,	PUNCT
ejpam-5392	252	36	p	p	X
ejpam-5392	252	37	,	,	PUNCT
ejpam-5392	252	38	s	s	X
ejpam-5392	252	39	,	,	PUNCT
ejpam-5392	252	40	β	β	NOUN
ejpam-5392	252	41	}	}	PUNCT
ejpam-5392	252	42	.	.	PUNCT
ejpam-5392	253	1	m.	m.	PROPN
ejpam-5392	253	2	hosny	hosny	PROPN
ejpam-5392	253	3	,	,	PUNCT
ejpam-5392	253	4	t.m	t.m	PROPN
ejpam-5392	253	5	.	.	PROPN
ejpam-5392	253	6	al	al	PROPN
ejpam-5392	253	7	-	-	PUNCT
ejpam-5392	253	8	shami	shami	PROPN
ejpam-5392	253	9	/	/	PUNCT
ejpam-5392	253	10	eur	eur	PROPN
ejpam-5392	253	11	.	.	PUNCT
ejpam-5392	254	1	j.	j.	PROPN
ejpam-5392	254	2	pure	pure	PROPN
ejpam-5392	254	3	appl	appl	PROPN
ejpam-5392	254	4	.	.	PROPN
ejpam-5392	254	5	math	math	PROPN
ejpam-5392	254	6	,	,	PUNCT
ejpam-5392	254	7	17	17	NUM
ejpam-5392	254	8	(	(	PUNCT
ejpam-5392	254	9	4	4	NUM
ejpam-5392	254	10	)	)	PUNCT
ejpam-5392	254	11	(	(	PUNCT
ejpam-5392	254	12	2024	2024	NUM
ejpam-5392	254	13	)	)	PUNCT
ejpam-5392	254	14	,	,	PUNCT
ejpam-5392	254	15	3436	3436	NUM
ejpam-5392	254	16	-	-	SYM
ejpam-5392	254	17	3463	3463	NUM
ejpam-5392	254	18	3444	3444	NUM
ejpam-5392	254	19	(	(	PUNCT
ejpam-5392	254	20	iv	iv	X
ejpam-5392	254	21	)	)	PUNCT
ejpam-5392	254	22	if	if	SCONJ
ejpam-5392	254	23	y	y	PROPN
ejpam-5392	254	24	∈	∈	PROPN
ejpam-5392	254	25	rη	rη	NOUN
ejpam-5392	254	26	λ(v	λ(v	PROPN
ejpam-5392	254	27	)	)	PUNCT
ejpam-5392	254	28	,	,	PUNCT
ejpam-5392	254	29	then	then	ADV
ejpam-5392	254	30	y	y	PROPN
ejpam-5392	254	31	λ	λ	PROPN
ejpam-5392	254	32	-	-	PUNCT
ejpam-5392	254	33	nearly	nearly	ADV
ejpam-5392	254	34	probably	probably	ADV
ejpam-5392	254	35	(	(	PUNCT
ejpam-5392	254	36	ηλ	ηλ	AUX
ejpam-5392	254	37	-	-	PUNCT
ejpam-5392	254	38	probably	probably	ADV
ejpam-5392	254	39	)	)	PUNCT
ejpam-5392	254	40	belongs	belong	VERB
ejpam-5392	254	41	to	to	ADP
ejpam-5392	254	42	v	v	NUM
ejpam-5392	254	43	,	,	PUNCT
ejpam-5392	254	44	denoted	denote	VERB
ejpam-5392	254	45	by	by	ADP
ejpam-5392	254	46	y	y	PROPN
ejpam-5392	254	47	∈ηλv	∈ηλv	PROPN
ejpam-5392	254	48	,	,	PUNCT
ejpam-5392	254	49	η	η	PROPN
ejpam-5392	254	50	∈	∈	PROPN
ejpam-5392	254	51	{	{	PUNCT
ejpam-5392	254	52	α	α	NOUN
ejpam-5392	254	53	,	,	PUNCT
ejpam-5392	254	54	p	p	X
ejpam-5392	254	55	,	,	PUNCT
ejpam-5392	254	56	s	s	X
ejpam-5392	254	57	,	,	PUNCT
ejpam-5392	254	58	β	β	NOUN
ejpam-5392	254	59	}	}	PUNCT
ejpam-5392	254	60	.	.	PUNCT
ejpam-5392	255	1	definition	definition	NOUN
ejpam-5392	255	2	16	16	NUM
ejpam-5392	255	3	.	.	PUNCT
ejpam-5392	256	1	[	[	X
ejpam-5392	256	2	23	23	NUM
ejpam-5392	256	3	]	]	X
ejpam-5392	256	4	let	let	AUX
ejpam-5392	256	5	(	(	PUNCT
ejpam-5392	256	6	x	x	NOUN
ejpam-5392	256	7	,	,	PUNCT
ejpam-5392	256	8	r	r	NOUN
ejpam-5392	256	9	,	,	PUNCT
ejpam-5392	256	10	ξλ	ξλ	NOUN
ejpam-5392	256	11	)	)	PUNCT
ejpam-5392	256	12	be	be	AUX
ejpam-5392	256	13	a	a	DET
ejpam-5392	256	14	gλ	gλ	NOUN
ejpam-5392	256	15	-	-	PUNCT
ejpam-5392	256	16	space	space	NOUN
ejpam-5392	256	17	,	,	PUNCT
ejpam-5392	256	18	y	y	PROPN
ejpam-5392	256	19	∈	∈	PROPN
ejpam-5392	256	20	x	x	X
ejpam-5392	256	21	and	and	CCONJ
ejpam-5392	256	22	v	v	SCONJ
ejpam-5392	256	23	⊆	⊆	NUM
ejpam-5392	256	24	x	x	SYM
ejpam-5392	256	25	:	:	PUNCT
ejpam-5392	256	26	(	(	PUNCT
ejpam-5392	256	27	i	i	NOUN
ejpam-5392	256	28	)	)	PUNCT
ejpam-5392	256	29	if	if	SCONJ
ejpam-5392	256	30	y	y	PROPN
ejpam-5392	256	31	∈	∈	PROPN
ejpam-5392	256	32	rl−η	rl−η	PROPN
ejpam-5392	256	33	λ	λ	PROPN
ejpam-5392	256	34	(	(	PUNCT
ejpam-5392	256	35	v	v	NOUN
ejpam-5392	256	36	)	)	PUNCT
ejpam-5392	256	37	,	,	PUNCT
ejpam-5392	256	38	then	then	ADV
ejpam-5392	256	39	y	y	PROPN
ejpam-5392	256	40	is	be	AUX
ejpam-5392	256	41	λ	λ	NOUN
ejpam-5392	256	42	-	-	PUNCT
ejpam-5392	256	43	nearly	nearly	ADV
ejpam-5392	256	44	certainly	certainly	ADV
ejpam-5392	256	45	with	with	ADP
ejpam-5392	256	46	respect	respect	NOUN
ejpam-5392	256	47	to	to	ADP
ejpam-5392	256	48	l	l	NOUN
ejpam-5392	256	49	(	(	PUNCT
ejpam-5392	256	50	l	l	NOUN
ejpam-5392	256	51	−	−	X
ejpam-5392	256	52	ηλ	ηλ	AUX
ejpam-5392	256	53	-	-	PUNCT
ejpam-5392	256	54	certainly	certainly	ADV
ejpam-5392	256	55	)	)	PUNCT
ejpam-5392	256	56	belongs	belong	VERB
ejpam-5392	256	57	to	to	ADP
ejpam-5392	256	58	v	v	NUM
ejpam-5392	256	59	,	,	PUNCT
ejpam-5392	256	60	denoted	denote	VERB
ejpam-5392	256	61	by	by	ADP
ejpam-5392	256	62	y	y	PROPN
ejpam-5392	256	63	∈l−η	∈l−η	NOUN
ejpam-5392	256	64	λ	λ	X
ejpam-5392	256	65	a.	a.	PROPN
ejpam-5392	256	66	(	(	PUNCT
ejpam-5392	256	67	ii	ii	PROPN
ejpam-5392	256	68	)	)	PUNCT
ejpam-5392	256	69	if	if	SCONJ
ejpam-5392	256	70	y	y	PROPN
ejpam-5392	256	71	∈	∈	PROPN
ejpam-5392	256	72	rl−η	rl−η	PROPN
ejpam-5392	256	73	λ	λ	PROPN
ejpam-5392	256	74	(	(	PUNCT
ejpam-5392	256	75	v	v	NOUN
ejpam-5392	256	76	)	)	PUNCT
ejpam-5392	256	77	,	,	PUNCT
ejpam-5392	256	78	then	then	ADV
ejpam-5392	256	79	y	y	PROPN
ejpam-5392	256	80	is	be	AUX
ejpam-5392	256	81	λ	λ	NOUN
ejpam-5392	256	82	-	-	PUNCT
ejpam-5392	256	83	nearly	nearly	ADV
ejpam-5392	256	84	probably	probably	ADV
ejpam-5392	256	85	with	with	ADP
ejpam-5392	256	86	respect	respect	NOUN
ejpam-5392	256	87	to	to	ADP
ejpam-5392	256	88	l	l	NOUN
ejpam-5392	256	89	(	(	PUNCT
ejpam-5392	256	90	briefly	briefly	ADV
ejpam-5392	256	91	l−ηλ	l−ηλ	NOUN
ejpam-5392	256	92	-	-	PUNCT
ejpam-5392	256	93	probably	probably	ADV
ejpam-5392	256	94	)	)	PUNCT
ejpam-5392	256	95	belongs	belong	VERB
ejpam-5392	256	96	to	to	ADP
ejpam-5392	256	97	v	v	NUM
ejpam-5392	256	98	,	,	PUNCT
ejpam-5392	256	99	denoted	denote	VERB
ejpam-5392	256	100	by	by	ADP
ejpam-5392	256	101	y	y	PROPN
ejpam-5392	256	102	∈l−η	∈l−η	NOUN
ejpam-5392	256	103	λ	λ	PROPN
ejpam-5392	256	104	a.	a.	NOUN
ejpam-5392	256	105	proposition	proposition	NOUN
ejpam-5392	256	106	4	4	NUM
ejpam-5392	256	107	.	.	PUNCT
ejpam-5392	257	1	[	[	X
ejpam-5392	257	2	23	23	NUM
ejpam-5392	257	3	]	]	PUNCT
ejpam-5392	257	4	the	the	DET
ejpam-5392	257	5	subsequent	subsequent	ADJ
ejpam-5392	257	6	properties	property	NOUN
ejpam-5392	257	7	hold	hold	VERB
ejpam-5392	257	8	true	true	ADJ
ejpam-5392	257	9	for	for	ADP
ejpam-5392	257	10	each	each	DET
ejpam-5392	257	11	subset	subset	NOUN
ejpam-5392	257	12	v	v	NOUN
ejpam-5392	257	13	.	.	PUNCT
ejpam-5392	258	1	(	(	PUNCT
ejpam-5392	258	2	i	i	NOUN
ejpam-5392	258	3	)	)	PUNCT
ejpam-5392	258	4	if	if	SCONJ
ejpam-5392	258	5	y	y	PROPN
ejpam-5392	258	6	∈λa⇒	∈λa⇒	PROPN
ejpam-5392	258	7	y	y	PROPN
ejpam-5392	258	8	∈ηλa⇒	∈ηλa⇒	PROPN
ejpam-5392	258	9	y	y	PROPN
ejpam-5392	258	10	∈l−η	∈l−η	VERB
ejpam-5392	258	11	λ	λ	X
ejpam-5392	258	12	a.	a.	PROPN
ejpam-5392	258	13	(	(	PUNCT
ejpam-5392	258	14	ii	ii	PROPN
ejpam-5392	258	15	)	)	PUNCT
ejpam-5392	258	16	if	if	SCONJ
ejpam-5392	258	17	y	y	PROPN
ejpam-5392	258	18	∈l−η	∈l−η	VERB
ejpam-5392	258	19	λ	λ	PROPN
ejpam-5392	258	20	a⇒	a⇒	PROPN
ejpam-5392	258	21	y	y	PROPN
ejpam-5392	258	22	∈ηλa⇒	∈ηλa⇒	PROPN
ejpam-5392	258	23	y	y	PROPN
ejpam-5392	258	24	∈λa	∈λa	PROPN
ejpam-5392	258	25	.	.	PUNCT
ejpam-5392	259	1	3	3	X
ejpam-5392	259	2	.	.	X
ejpam-5392	259	3	l	l	NOUN
ejpam-5392	259	4	-	-	PUNCT
ejpam-5392	259	5	θβλ	θβλ	NOUN
ejpam-5392	259	6	-	-	PUNCT
ejpam-5392	259	7	open	open	ADJ
ejpam-5392	259	8	sets	set	NOUN
ejpam-5392	259	9	this	this	DET
ejpam-5392	259	10	section	section	NOUN
ejpam-5392	259	11	aims	aim	VERB
ejpam-5392	259	12	to	to	PART
ejpam-5392	259	13	adopt	adopt	VERB
ejpam-5392	259	14	a	a	DET
ejpam-5392	259	15	fresh	fresh	ADJ
ejpam-5392	259	16	class	class	NOUN
ejpam-5392	259	17	of	of	ADP
ejpam-5392	259	18	nearly	nearly	ADV
ejpam-5392	259	19	open	open	ADJ
ejpam-5392	259	20	sets	set	NOUN
ejpam-5392	259	21	called	call	VERB
ejpam-5392	259	22	l	l	NOUN
ejpam-5392	259	23	-	-	PUNCT
ejpam-5392	259	24	θβλ	θβλ	NOUN
ejpam-5392	259	25	-	-	PUNCT
ejpam-5392	259	26	open	open	ADJ
ejpam-5392	259	27	sets	set	NOUN
ejpam-5392	259	28	,	,	PUNCT
ejpam-5392	259	29	serving	serve	VERB
ejpam-5392	259	30	as	as	ADP
ejpam-5392	259	31	an	an	DET
ejpam-5392	259	32	introduction	introduction	NOUN
ejpam-5392	259	33	to	to	ADP
ejpam-5392	259	34	building	build	VERB
ejpam-5392	259	35	rough	rough	ADJ
ejpam-5392	259	36	set	set	NOUN
ejpam-5392	259	37	paradigms	paradigm	NOUN
ejpam-5392	259	38	.	.	PUNCT
ejpam-5392	260	1	this	this	DET
ejpam-5392	260	2	type	type	NOUN
ejpam-5392	260	3	of	of	ADP
ejpam-5392	260	4	nearly	nearly	ADV
ejpam-5392	260	5	open	open	ADJ
ejpam-5392	260	6	sets	set	NOUN
ejpam-5392	260	7	is	be	AUX
ejpam-5392	260	8	established	establish	VERB
ejpam-5392	260	9	by	by	ADP
ejpam-5392	260	10	replacing	replace	VERB
ejpam-5392	260	11	the	the	DET
ejpam-5392	260	12	empty	empty	ADJ
ejpam-5392	260	13	difference	difference	NOUN
ejpam-5392	260	14	of	of	ADP
ejpam-5392	260	15	θβ	θβ	NOUN
ejpam-5392	260	16	-	-	PUNCT
ejpam-5392	260	17	open	open	ADJ
ejpam-5392	260	18	sets	set	NOUN
ejpam-5392	260	19	with	with	ADP
ejpam-5392	260	20	the	the	DET
ejpam-5392	260	21	belonging	belonging	NOUN
ejpam-5392	260	22	of	of	ADP
ejpam-5392	260	23	difference	difference	NOUN
ejpam-5392	260	24	to	to	ADP
ejpam-5392	260	25	the	the	DET
ejpam-5392	260	26	ideal	ideal	NOUN
ejpam-5392	260	27	,	,	PUNCT
ejpam-5392	260	28	which	which	PRON
ejpam-5392	260	29	enlarges	enlarge	VERB
ejpam-5392	260	30	the	the	DET
ejpam-5392	260	31	class	class	NOUN
ejpam-5392	260	32	of	of	ADP
ejpam-5392	260	33	θβ	θβ	NOUN
ejpam-5392	260	34	-	-	PUNCT
ejpam-5392	260	35	open	open	ADJ
ejpam-5392	260	36	sets	set	NOUN
ejpam-5392	260	37	.	.	PUNCT
ejpam-5392	261	1	we	we	PRON
ejpam-5392	261	2	conclude	conclude	VERB
ejpam-5392	261	3	the	the	DET
ejpam-5392	261	4	core	core	NOUN
ejpam-5392	261	5	characterizations	characterization	NOUN
ejpam-5392	261	6	of	of	ADP
ejpam-5392	261	7	this	this	DET
ejpam-5392	261	8	class	class	NOUN
ejpam-5392	261	9	and	and	CCONJ
ejpam-5392	261	10	elucidate	elucidate	VERB
ejpam-5392	261	11	its	its	PRON
ejpam-5392	261	12	relationship	relationship	NOUN
ejpam-5392	261	13	with	with	ADP
ejpam-5392	261	14	the	the	DET
ejpam-5392	261	15	forgoing	forgo	VERB
ejpam-5392	261	16	classes	class	NOUN
ejpam-5392	261	17	.	.	PUNCT
ejpam-5392	262	1	definition	definition	NOUN
ejpam-5392	262	2	17	17	NUM
ejpam-5392	262	3	.	.	PUNCT
ejpam-5392	263	1	a	a	DET
ejpam-5392	263	2	subset	subset	NOUN
ejpam-5392	263	3	v	v	NOUN
ejpam-5392	263	4	of	of	ADP
ejpam-5392	263	5	an	an	DET
ejpam-5392	263	6	l−gλ	l−gλ	ADJ
ejpam-5392	263	7	-	-	PUNCT
ejpam-5392	263	8	space	space	NOUN
ejpam-5392	263	9	(	(	PUNCT
ejpam-5392	263	10	x	x	NOUN
ejpam-5392	263	11	,	,	PUNCT
ejpam-5392	263	12	r	r	NOUN
ejpam-5392	263	13	,	,	PUNCT
ejpam-5392	263	14	ξλ	ξλ	NOUN
ejpam-5392	263	15	,	,	PUNCT
ejpam-5392	263	16	l	l	NOUN
ejpam-5392	263	17	)	)	PUNCT
ejpam-5392	263	18	is	be	AUX
ejpam-5392	263	19	called	call	VERB
ejpam-5392	263	20	l	l	NOUN
ejpam-5392	263	21	-	-	PUNCT
ejpam-5392	263	22	θβλ	θβλ	NOUN
ejpam-5392	263	23	-	-	PUNCT
ejpam-5392	263	24	open	open	NOUN
ejpam-5392	263	25	providing	provide	VERB
ejpam-5392	263	26	that	that	SCONJ
ejpam-5392	263	27	∃	∃	PROPN
ejpam-5392	263	28	g	g	PROPN
ejpam-5392	263	29	∈	∈	PROPN
ejpam-5392	263	30	ϑλ	ϑλ	ADP
ejpam-5392	263	31	s.t	s.t	PROPN
ejpam-5392	263	32	.	.	PUNCT
ejpam-5392	264	1	(	(	PUNCT
ejpam-5392	264	2	v	v	ADP
ejpam-5392	264	3	−	−	PROPN
ejpam-5392	264	4	clλ(g	clλ(g	PROPN
ejpam-5392	264	5	)	)	PUNCT
ejpam-5392	264	6	)	)	PUNCT
ejpam-5392	265	1	∈	∈	PROPN
ejpam-5392	265	2	l	l	NOUN
ejpam-5392	265	3	and	and	CCONJ
ejpam-5392	265	4	(	(	PUNCT
ejpam-5392	265	5	g	g	PROPN
ejpam-5392	265	6	−	−	PROPN
ejpam-5392	265	7	clθλ(v	clθλ(v	PROPN
ejpam-5392	265	8	)	)	PUNCT
ejpam-5392	265	9	)	)	PUNCT
ejpam-5392	266	1	∈	∈	PROPN
ejpam-5392	266	2	l.	l.	NOUN
ejpam-5392	266	3	we	we	PRON
ejpam-5392	266	4	call	call	VERB
ejpam-5392	266	5	a	a	DET
ejpam-5392	266	6	complement	complement	NOUN
ejpam-5392	266	7	of	of	ADP
ejpam-5392	266	8	a	a	DET
ejpam-5392	266	9	l	l	NOUN
ejpam-5392	266	10	-	-	PUNCT
ejpam-5392	266	11	θβλ	θβλ	NOUN
ejpam-5392	266	12	-	-	PUNCT
ejpam-5392	266	13	open	open	NOUN
ejpam-5392	266	14	set	set	VERB
ejpam-5392	266	15	an	an	DET
ejpam-5392	266	16	l	l	NOUN
ejpam-5392	266	17	-	-	PUNCT
ejpam-5392	266	18	θβλ	θβλ	NOUN
ejpam-5392	266	19	-	-	PUNCT
ejpam-5392	266	20	closed	close	VERB
ejpam-5392	266	21	set	set	NOUN
ejpam-5392	266	22	.	.	PUNCT
ejpam-5392	267	1	the	the	DET
ejpam-5392	267	2	classes	class	NOUN
ejpam-5392	267	3	of	of	ADP
ejpam-5392	267	4	all	all	DET
ejpam-5392	267	5	l	l	NOUN
ejpam-5392	267	6	-	-	PUNCT
ejpam-5392	267	7	θβλ	θβλ	NOUN
ejpam-5392	267	8	-	-	PUNCT
ejpam-5392	267	9	open	open	ADJ
ejpam-5392	267	10	and	and	CCONJ
ejpam-5392	267	11	l	l	NOUN
ejpam-5392	267	12	-	-	PUNCT
ejpam-5392	267	13	θβλ	θβλ	NOUN
ejpam-5392	267	14	-	-	PUNCT
ejpam-5392	267	15	closed	close	VERB
ejpam-5392	267	16	are	be	AUX
ejpam-5392	267	17	respectively	respectively	ADV
ejpam-5392	267	18	symbolized	symbolize	VERB
ejpam-5392	267	19	by	by	ADP
ejpam-5392	267	20	l	l	NOUN
ejpam-5392	267	21	-	-	PUNCT
ejpam-5392	267	22	θβλo(x	θβλo(x	NOUN
ejpam-5392	267	23	)	)	PUNCT
ejpam-5392	267	24	and	and	CCONJ
ejpam-5392	267	25	l	l	NOUN
ejpam-5392	267	26	-	-	NOUN
ejpam-5392	267	27	θβλc(x	θβλc(x	NOUN
ejpam-5392	267	28	)	)	PUNCT
ejpam-5392	267	29	.	.	PUNCT
ejpam-5392	268	1	example	example	NOUN
ejpam-5392	269	1	1	1	X
ejpam-5392	269	2	.	.	PUNCT
ejpam-5392	269	3	let	let	VERB
ejpam-5392	269	4	x	x	PUNCT
ejpam-5392	269	5	=	=	PRON
ejpam-5392	269	6	{	{	PUNCT
ejpam-5392	269	7	y1	y1	PROPN
ejpam-5392	269	8	,	,	PUNCT
ejpam-5392	269	9	y2	y2	PROPN
ejpam-5392	269	10	,	,	PUNCT
ejpam-5392	269	11	y3	y3	PROPN
ejpam-5392	269	12	,	,	PUNCT
ejpam-5392	269	13	y4	y4	PROPN
ejpam-5392	269	14	,	,	PUNCT
ejpam-5392	269	15	y5},l	y5},l	PROPN
ejpam-5392	269	16	=	=	PUNCT
ejpam-5392	269	17	{	{	PUNCT
ejpam-5392	269	18	∅	∅	NOUN
ejpam-5392	269	19	,	,	PUNCT
ejpam-5392	269	20	{	{	PUNCT
ejpam-5392	269	21	y3	y3	NOUN
ejpam-5392	269	22	}	}	PUNCT
ejpam-5392	269	23	}	}	PUNCT
ejpam-5392	269	24	,	,	PUNCT
ejpam-5392	269	25	and	and	CCONJ
ejpam-5392	269	26	r	r	NOUN
ejpam-5392	269	27	=	=	SYM
ejpam-5392	269	28	{	{	PUNCT
ejpam-5392	269	29	(	(	PUNCT
ejpam-5392	269	30	y1	y1	INTJ
ejpam-5392	269	31	,	,	PUNCT
ejpam-5392	269	32	y1	y1	PROPN
ejpam-5392	269	33	)	)	PUNCT
ejpam-5392	269	34	,	,	PUNCT
ejpam-5392	269	35	(	(	PUNCT
ejpam-5392	269	36	y1	y1	INTJ
ejpam-5392	269	37	,	,	PUNCT
ejpam-5392	269	38	y2	y2	PROPN
ejpam-5392	269	39	)	)	PUNCT
ejpam-5392	269	40	,	,	PUNCT
ejpam-5392	269	41	(	(	PUNCT
ejpam-5392	269	42	y2	y2	INTJ
ejpam-5392	269	43	,	,	PUNCT
ejpam-5392	269	44	y2	y2	PROPN
ejpam-5392	269	45	)	)	PUNCT
ejpam-5392	269	46	,	,	PUNCT
ejpam-5392	269	47	(	(	PUNCT
ejpam-5392	269	48	y3	y3	PROPN
ejpam-5392	269	49	,	,	PUNCT
ejpam-5392	269	50	y3	y3	PROPN
ejpam-5392	269	51	)	)	PUNCT
ejpam-5392	269	52	,	,	PUNCT
ejpam-5392	269	53	(	(	PUNCT
ejpam-5392	269	54	y3	y3	NOUN
ejpam-5392	269	55	,	,	PUNCT
ejpam-5392	269	56	y4	y4	NUM
ejpam-5392	269	57	)	)	PUNCT
ejpam-5392	269	58	,	,	PUNCT
ejpam-5392	269	59	(	(	PUNCT
ejpam-5392	269	60	y4	y4	PROPN
ejpam-5392	269	61	,	,	PUNCT
ejpam-5392	269	62	y3	y3	PROPN
ejpam-5392	269	63	)	)	PUNCT
ejpam-5392	269	64	,	,	PUNCT
ejpam-5392	269	65	(	(	PUNCT
ejpam-5392	269	66	y4	y4	PROPN
ejpam-5392	269	67	,	,	PUNCT
ejpam-5392	269	68	y4	y4	PROPN
ejpam-5392	269	69	)	)	PUNCT
ejpam-5392	269	70	,	,	PUNCT
ejpam-5392	269	71	(	(	PUNCT
ejpam-5392	269	72	y5	y5	NOUN
ejpam-5392	269	73	,	,	PUNCT
ejpam-5392	269	74	y2	y2	PROPN
ejpam-5392	269	75	)	)	PUNCT
ejpam-5392	269	76	,	,	PUNCT
ejpam-5392	269	77	(	(	PUNCT
ejpam-5392	269	78	y5	y5	NOUN
ejpam-5392	269	79	,	,	PUNCT
ejpam-5392	269	80	y3	y3	NOUN
ejpam-5392	269	81	)	)	PUNCT
ejpam-5392	269	82	,	,	PUNCT
ejpam-5392	269	83	(	(	PUNCT
ejpam-5392	269	84	y5	y5	NOUN
ejpam-5392	269	85	,	,	PUNCT
ejpam-5392	269	86	y4	y4	PROPN
ejpam-5392	269	87	)	)	PUNCT
ejpam-5392	269	88	}	}	PUNCT
ejpam-5392	269	89	.	.	PUNCT
ejpam-5392	270	1	then	then	ADV
ejpam-5392	270	2	,	,	PUNCT
ejpam-5392	270	3	the	the	DET
ejpam-5392	270	4	topology	topology	NOUN
ejpam-5392	270	5	generated	generate	VERB
ejpam-5392	270	6	by	by	ADP
ejpam-5392	270	7	a	a	DET
ejpam-5392	270	8	relation	relation	NOUN
ejpam-5392	270	9	r	r	NOUN
ejpam-5392	270	10	in	in	ADP
ejpam-5392	270	11	the	the	DET
ejpam-5392	270	12	case	case	NOUN
ejpam-5392	270	13	of	of	ADP
ejpam-5392	270	14	λ	λ	PROPN
ejpam-5392	270	15	=	=	PUNCT
ejpam-5392	270	16	a	a	PROPN
ejpam-5392	270	17	is	be	AUX
ejpam-5392	270	18	ϑa	ϑa	ADP
ejpam-5392	270	19	=	=	PUNCT
ejpam-5392	270	20	{	{	PUNCT
ejpam-5392	270	21	x	x	NOUN
ejpam-5392	270	22	,	,	PUNCT
ejpam-5392	270	23	∅	∅	NOUN
ejpam-5392	270	24	,	,	PUNCT
ejpam-5392	270	25	{	{	PUNCT
ejpam-5392	270	26	y2	y2	NOUN
ejpam-5392	270	27	}	}	PUNCT
ejpam-5392	270	28	,	,	PUNCT
ejpam-5392	270	29	{	{	PUNCT
ejpam-5392	270	30	y1	y1	NOUN
ejpam-5392	270	31	,	,	PUNCT
ejpam-5392	270	32	y2	y2	PROPN
ejpam-5392	270	33	}	}	PUNCT
ejpam-5392	270	34	,	,	PUNCT
ejpam-5392	270	35	{	{	PUNCT
ejpam-5392	270	36	y3	y3	NOUN
ejpam-5392	270	37	,	,	PUNCT
ejpam-5392	270	38	y4	y4	PROPN
ejpam-5392	270	39	}	}	PUNCT
ejpam-5392	270	40	,	,	PUNCT
ejpam-5392	270	41	{	{	PUNCT
ejpam-5392	270	42	y2	y2	PROPN
ejpam-5392	270	43	,	,	PUNCT
ejpam-5392	270	44	y3	y3	PROPN
ejpam-5392	270	45	,	,	PUNCT
ejpam-5392	270	46	y4	y4	PROPN
ejpam-5392	270	47	}	}	PUNCT
ejpam-5392	270	48	,	,	PUNCT
ejpam-5392	270	49	{	{	PUNCT
ejpam-5392	270	50	y	y	PROPN
ejpam-5392	270	51	,	,	PUNCT
ejpam-5392	270	52	y2	y2	PROPN
ejpam-5392	270	53	,	,	PUNCT
ejpam-5392	270	54	y3	y3	PROPN
ejpam-5392	270	55	,	,	PUNCT
ejpam-5392	270	56	y4	y4	PROPN
ejpam-5392	270	57	}	}	PUNCT
ejpam-5392	270	58	,	,	PUNCT
ejpam-5392	270	59	{	{	PUNCT
ejpam-5392	270	60	y2	y2	PROPN
ejpam-5392	270	61	,	,	PUNCT
ejpam-5392	270	62	y3	y3	PROPN
ejpam-5392	270	63	,	,	PUNCT
ejpam-5392	270	64	y4	y4	PROPN
ejpam-5392	270	65	,	,	PUNCT
ejpam-5392	270	66	y5	y5	PROPN
ejpam-5392	270	67	}	}	PUNCT
ejpam-5392	270	68	}	}	PUNCT
ejpam-5392	270	69	and	and	CCONJ
ejpam-5392	270	70	l	l	NOUN
ejpam-5392	270	71	-	-	PUNCT
ejpam-5392	270	72	θβao(x	θβao(x	NOUN
ejpam-5392	270	73	)	)	PUNCT
ejpam-5392	270	74	is	be	AUX
ejpam-5392	270	75	the	the	DET
ejpam-5392	270	76	power	power	NOUN
ejpam-5392	270	77	set	set	NOUN
ejpam-5392	270	78	of	of	ADP
ejpam-5392	270	79	x.	x.	NOUN
ejpam-5392	270	80	we	we	PRON
ejpam-5392	270	81	demonstrate	demonstrate	VERB
ejpam-5392	270	82	in	in	ADP
ejpam-5392	270	83	the	the	DET
ejpam-5392	270	84	next	next	ADJ
ejpam-5392	270	85	result	result	NOUN
ejpam-5392	270	86	that	that	SCONJ
ejpam-5392	270	87	the	the	DET
ejpam-5392	270	88	class	class	NOUN
ejpam-5392	270	89	of	of	ADP
ejpam-5392	270	90	l	l	NOUN
ejpam-5392	270	91	-	-	PUNCT
ejpam-5392	270	92	θβλ	θβλ	NOUN
ejpam-5392	270	93	-	-	PUNCT
ejpam-5392	270	94	open	open	ADJ
ejpam-5392	270	95	sets	set	NOUN
ejpam-5392	270	96	is	be	AUX
ejpam-5392	270	97	wider	wide	ADJ
ejpam-5392	270	98	than	than	ADP
ejpam-5392	270	99	the	the	DET
ejpam-5392	270	100	classes	class	NOUN
ejpam-5392	270	101	of	of	ADP
ejpam-5392	270	102	l	l	NOUN
ejpam-5392	270	103	-	-	ADJ
ejpam-5392	270	104	δβλ	δβλ	ADJ
ejpam-5392	270	105	-	-	PUNCT
ejpam-5392	270	106	open	open	ADJ
ejpam-5392	270	107	sets	set	NOUN
ejpam-5392	270	108	,	,	PUNCT
ejpam-5392	270	109	l∧	l∧	ADV
ejpam-5392	270	110	βλ	βλ	PUNCT
ejpam-5392	270	111	-sets	-set	NOUN
ejpam-5392	270	112	.	.	PUNCT
ejpam-5392	271	1	proposition	proposition	NOUN
ejpam-5392	271	2	5	5	NUM
ejpam-5392	271	3	.	.	PUNCT
ejpam-5392	272	1	(	(	PUNCT
ejpam-5392	272	2	i	i	NOUN
ejpam-5392	272	3	)	)	PUNCT
ejpam-5392	272	4	every	every	DET
ejpam-5392	272	5	l	l	NOUN
ejpam-5392	272	6	-	-	ADJ
ejpam-5392	272	7	δβλ	δβλ	ADJ
ejpam-5392	272	8	-	-	PUNCT
ejpam-5392	272	9	open	open	ADJ
ejpam-5392	272	10	set	set	NOUN
ejpam-5392	272	11	is	be	AUX
ejpam-5392	272	12	l	l	NOUN
ejpam-5392	272	13	-	-	PUNCT
ejpam-5392	272	14	θβλ	θβλ	NOUN
ejpam-5392	272	15	-	-	PUNCT
ejpam-5392	272	16	open	open	ADJ
ejpam-5392	272	17	set	set	NOUN
ejpam-5392	272	18	.	.	PUNCT
ejpam-5392	273	1	(	(	PUNCT
ejpam-5392	273	2	ii	ii	NOUN
ejpam-5392	273	3	)	)	PUNCT
ejpam-5392	273	4	every	every	DET
ejpam-5392	273	5	l∧	l∧	NOUN
ejpam-5392	273	6	βλ	βλ	PRON
ejpam-5392	273	7	-set	-set	PROPN
ejpam-5392	273	8	is	be	AUX
ejpam-5392	273	9	l	l	NOUN
ejpam-5392	273	10	-	-	PUNCT
ejpam-5392	273	11	θβλ	θβλ	NOUN
ejpam-5392	273	12	-	-	PUNCT
ejpam-5392	273	13	open	open	ADJ
ejpam-5392	273	14	set	set	NOUN
ejpam-5392	273	15	.	.	PUNCT
ejpam-5392	274	1	m.	m.	PROPN
ejpam-5392	274	2	hosny	hosny	PROPN
ejpam-5392	274	3	,	,	PUNCT
ejpam-5392	274	4	t.m	t.m	PROPN
ejpam-5392	274	5	.	.	PROPN
ejpam-5392	274	6	al	al	PROPN
ejpam-5392	274	7	-	-	PUNCT
ejpam-5392	274	8	shami	shami	PROPN
ejpam-5392	274	9	/	/	PUNCT
ejpam-5392	274	10	eur	eur	PROPN
ejpam-5392	274	11	.	.	PUNCT
ejpam-5392	275	1	j.	j.	PROPN
ejpam-5392	275	2	pure	pure	PROPN
ejpam-5392	275	3	appl	appl	PROPN
ejpam-5392	275	4	.	.	PROPN
ejpam-5392	275	5	math	math	PROPN
ejpam-5392	275	6	,	,	PUNCT
ejpam-5392	275	7	17	17	NUM
ejpam-5392	275	8	(	(	PUNCT
ejpam-5392	275	9	4	4	NUM
ejpam-5392	275	10	)	)	PUNCT
ejpam-5392	275	11	(	(	PUNCT
ejpam-5392	275	12	2024	2024	NUM
ejpam-5392	275	13	)	)	PUNCT
ejpam-5392	275	14	,	,	PUNCT
ejpam-5392	275	15	3436	3436	NUM
ejpam-5392	275	16	-	-	SYM
ejpam-5392	275	17	3463	3463	NUM
ejpam-5392	275	18	3445	3445	NUM
ejpam-5392	275	19	proof	proof	NOUN
ejpam-5392	275	20	.	.	PUNCT
ejpam-5392	276	1	it	it	PRON
ejpam-5392	276	2	is	be	AUX
ejpam-5392	276	3	evident	evident	ADJ
ejpam-5392	276	4	by	by	ADP
ejpam-5392	276	5	definitions	definition	NOUN
ejpam-5392	276	6	8	8	NUM
ejpam-5392	276	7	[	[	X
ejpam-5392	276	8	23	23	NUM
ejpam-5392	276	9	]	]	PUNCT
ejpam-5392	276	10	and	and	CCONJ
ejpam-5392	276	11	17	17	NUM
ejpam-5392	276	12	.	.	PUNCT
ejpam-5392	277	1	remark	remark	PROPN
ejpam-5392	277	2	1	1	NUM
ejpam-5392	277	3	.	.	PUNCT
ejpam-5392	277	4	example	example	NOUN
ejpam-5392	277	5	1	1	NUM
ejpam-5392	277	6	yields	yield	VERB
ejpam-5392	277	7	an	an	DET
ejpam-5392	277	8	evidence	evidence	NOUN
ejpam-5392	277	9	that	that	SCONJ
ejpam-5392	277	10	the	the	DET
ejpam-5392	277	11	converse	converse	NOUN
ejpam-5392	277	12	of	of	ADP
ejpam-5392	277	13	proposition	proposition	NOUN
ejpam-5392	277	14	5	5	NUM
ejpam-5392	277	15	fails	fail	VERB
ejpam-5392	277	16	.	.	PUNCT
ejpam-5392	278	1	by	by	ADP
ejpam-5392	278	2	this	this	DET
ejpam-5392	278	3	example	example	NOUN
ejpam-5392	278	4	,	,	PUNCT
ejpam-5392	278	5	we	we	PRON
ejpam-5392	278	6	remark	remark	VERB
ejpam-5392	278	7	that	that	SCONJ
ejpam-5392	278	8	l	l	NOUN
ejpam-5392	278	9	-	-	PUNCT
ejpam-5392	278	10	θβao(x	θβao(x	NOUN
ejpam-5392	278	11	)	)	PUNCT
ejpam-5392	278	12	=	=	SYM
ejpam-5392	279	1	p	p	X
ejpam-5392	279	2	(	(	PUNCT
ejpam-5392	279	3	x	x	NOUN
ejpam-5392	279	4	)	)	PUNCT
ejpam-5392	279	5	,	,	PUNCT
ejpam-5392	279	6	l	l	NOUN
ejpam-5392	279	7	-	-	PUNCT
ejpam-5392	279	8	δβao(x	δβao(x	ADJ
ejpam-5392	279	9	)	)	PUNCT
ejpam-5392	279	10	=	=	SYM
ejpam-5392	279	11	p	p	X
ejpam-5392	279	12	(	(	PUNCT
ejpam-5392	279	13	x)−{{y5	x)−{{y5	ADJ
ejpam-5392	279	14	}	}	PUNCT
ejpam-5392	279	15	}	}	PUNCT
ejpam-5392	279	16	,	,	PUNCT
ejpam-5392	279	17	and	and	CCONJ
ejpam-5392	279	18	l-∧	l-∧	PROPN
ejpam-5392	279	19	βa	βa	NUM
ejpam-5392	279	20	o(x	o(x	PROPN
ejpam-5392	279	21	)	)	PUNCT
ejpam-5392	279	22	=	=	PRON
ejpam-5392	279	23	{	{	PUNCT
ejpam-5392	279	24	x	x	NOUN
ejpam-5392	279	25	,	,	PUNCT
ejpam-5392	279	26	∅	∅	NOUN
ejpam-5392	279	27	,	,	PUNCT
ejpam-5392	279	28	{	{	PUNCT
ejpam-5392	279	29	y2	y2	NOUN
ejpam-5392	279	30	}	}	PUNCT
ejpam-5392	279	31	,	,	PUNCT
ejpam-5392	279	32	{	{	PUNCT
ejpam-5392	279	33	y3	y3	NOUN
ejpam-5392	279	34	}	}	PUNCT
ejpam-5392	279	35	,	,	PUNCT
ejpam-5392	279	36	{	{	PUNCT
ejpam-5392	279	37	y4	y4	X
ejpam-5392	279	38	}	}	PUNCT
ejpam-5392	279	39	,	,	PUNCT
ejpam-5392	279	40	{	{	PUNCT
ejpam-5392	279	41	y5	y5	NOUN
ejpam-5392	279	42	}	}	PUNCT
ejpam-5392	279	43	,	,	PUNCT
ejpam-5392	279	44	{	{	PUNCT
ejpam-5392	279	45	y1	y1	NOUN
ejpam-5392	279	46	,	,	PUNCT
ejpam-5392	279	47	y2	y2	PROPN
ejpam-5392	279	48	}	}	PUNCT
ejpam-5392	279	49	,	,	PUNCT
ejpam-5392	279	50	{	{	PUNCT
ejpam-5392	279	51	y2	y2	NOUN
ejpam-5392	279	52	,	,	PUNCT
ejpam-5392	279	53	y3	y3	PROPN
ejpam-5392	279	54	}	}	PUNCT
ejpam-5392	279	55	,	,	PUNCT
ejpam-5392	279	56	{	{	PUNCT
ejpam-5392	279	57	y2	y2	NOUN
ejpam-5392	279	58	,	,	PUNCT
ejpam-5392	279	59	y4	y4	PROPN
ejpam-5392	279	60	}	}	PUNCT
ejpam-5392	279	61	,	,	PUNCT
ejpam-5392	279	62	{	{	PUNCT
ejpam-5392	279	63	y2	y2	NOUN
ejpam-5392	279	64	,	,	PUNCT
ejpam-5392	279	65	y5	y5	PROPN
ejpam-5392	279	66	}	}	PUNCT
ejpam-5392	279	67	,	,	PUNCT
ejpam-5392	279	68	{	{	PUNCT
ejpam-5392	279	69	y3	y3	NOUN
ejpam-5392	279	70	,	,	PUNCT
ejpam-5392	279	71	y4	y4	PROPN
ejpam-5392	279	72	}	}	PUNCT
ejpam-5392	279	73	,	,	PUNCT
ejpam-5392	279	74	{	{	PUNCT
ejpam-5392	279	75	y3	y3	NOUN
ejpam-5392	279	76	,	,	PUNCT
ejpam-5392	279	77	y5	y5	PROPN
ejpam-5392	279	78	}	}	PUNCT
ejpam-5392	279	79	,	,	PUNCT
ejpam-5392	279	80	{	{	PUNCT
ejpam-5392	279	81	y4	y4	ADJ
ejpam-5392	279	82	,	,	PUNCT
ejpam-5392	279	83	y5	y5	PROPN
ejpam-5392	279	84	}	}	PUNCT
ejpam-5392	279	85	,	,	PUNCT
ejpam-5392	279	86	{	{	PUNCT
ejpam-5392	279	87	y	y	PROPN
ejpam-5392	279	88	,	,	PUNCT
ejpam-5392	279	89	y2	y2	PROPN
ejpam-5392	279	90	,	,	PUNCT
ejpam-5392	279	91	y3	y3	PROPN
ejpam-5392	279	92	}	}	PUNCT
ejpam-5392	279	93	,	,	PUNCT
ejpam-5392	279	94	{	{	PUNCT
ejpam-5392	279	95	y1	y1	NOUN
ejpam-5392	279	96	,	,	PUNCT
ejpam-5392	279	97	y2	y2	PROPN
ejpam-5392	279	98	,	,	PUNCT
ejpam-5392	279	99	y5	y5	PROPN
ejpam-5392	279	100	}	}	PUNCT
ejpam-5392	279	101	,	,	PUNCT
ejpam-5392	279	102	{	{	PUNCT
ejpam-5392	279	103	y1	y1	NOUN
ejpam-5392	279	104	,	,	PUNCT
ejpam-5392	279	105	y2	y2	PROPN
ejpam-5392	279	106	,	,	PUNCT
ejpam-5392	279	107	y4	y4	PROPN
ejpam-5392	279	108	}	}	PUNCT
ejpam-5392	279	109	,	,	PUNCT
ejpam-5392	279	110	{	{	PUNCT
ejpam-5392	279	111	y2	y2	PROPN
ejpam-5392	279	112	,	,	PUNCT
ejpam-5392	279	113	y3	y3	PROPN
ejpam-5392	279	114	,	,	PUNCT
ejpam-5392	279	115	y4	y4	PROPN
ejpam-5392	279	116	}	}	PUNCT
ejpam-5392	279	117	,	,	PUNCT
ejpam-5392	279	118	{	{	PUNCT
ejpam-5392	279	119	y2	y2	PROPN
ejpam-5392	279	120	,	,	PUNCT
ejpam-5392	279	121	y3	y3	NOUN
ejpam-5392	279	122	,	,	PUNCT
ejpam-5392	279	123	y5	y5	PROPN
ejpam-5392	279	124	}	}	PUNCT
ejpam-5392	279	125	,	,	PUNCT
ejpam-5392	279	126	{	{	PUNCT
ejpam-5392	279	127	y2	y2	PROPN
ejpam-5392	279	128	,	,	PUNCT
ejpam-5392	279	129	y4	y4	PROPN
ejpam-5392	279	130	,	,	PUNCT
ejpam-5392	279	131	y5	y5	PROPN
ejpam-5392	279	132	}	}	PUNCT
ejpam-5392	279	133	,	,	PUNCT
ejpam-5392	279	134	{	{	PUNCT
ejpam-5392	279	135	y3	y3	NOUN
ejpam-5392	279	136	,	,	PUNCT
ejpam-5392	279	137	y4	y4	NOUN
ejpam-5392	279	138	,	,	PUNCT
ejpam-5392	279	139	y5	y5	PROPN
ejpam-5392	279	140	}	}	PUNCT
ejpam-5392	279	141	,	,	PUNCT
ejpam-5392	279	142	{	{	PUNCT
ejpam-5392	279	143	y1	y1	NOUN
ejpam-5392	279	144	,	,	PUNCT
ejpam-5392	279	145	y2	y2	PROPN
ejpam-5392	279	146	,	,	PUNCT
ejpam-5392	279	147	y3	y3	PROPN
ejpam-5392	279	148	,	,	PUNCT
ejpam-5392	279	149	y4	y4	PROPN
ejpam-5392	279	150	}	}	PUNCT
ejpam-5392	279	151	,	,	PUNCT
ejpam-5392	279	152	{	{	PUNCT
ejpam-5392	279	153	y1	y1	NOUN
ejpam-5392	279	154	,	,	PUNCT
ejpam-5392	279	155	y2	y2	PROPN
ejpam-5392	279	156	,	,	PUNCT
ejpam-5392	279	157	y3	y3	NOUN
ejpam-5392	279	158	,	,	PUNCT
ejpam-5392	279	159	y5	y5	PROPN
ejpam-5392	279	160	}	}	PUNCT
ejpam-5392	279	161	,	,	PUNCT
ejpam-5392	279	162	{	{	PUNCT
ejpam-5392	279	163	y1	y1	NOUN
ejpam-5392	279	164	,	,	PUNCT
ejpam-5392	279	165	y2	y2	PROPN
ejpam-5392	279	166	,	,	PUNCT
ejpam-5392	279	167	y4	y4	PROPN
ejpam-5392	279	168	,	,	PUNCT
ejpam-5392	279	169	y5},{y2	y5},{y2	PROPN
ejpam-5392	279	170	,	,	PUNCT
ejpam-5392	279	171	y3	y3	PROPN
ejpam-5392	279	172	,	,	PUNCT
ejpam-5392	279	173	y4	y4	NOUN
ejpam-5392	279	174	,	,	PUNCT
ejpam-5392	279	175	y5	y5	NOUN
ejpam-5392	279	176	}	}	PUNCT
ejpam-5392	279	177	}	}	PUNCT
ejpam-5392	279	178	.	.	PUNCT
ejpam-5392	280	1	now	now	ADV
ejpam-5392	280	2	,	,	PUNCT
ejpam-5392	280	3	{	{	PUNCT
ejpam-5392	280	4	y5	y5	NOUN
ejpam-5392	280	5	}	}	PUNCT
ejpam-5392	280	6	is	be	AUX
ejpam-5392	280	7	an	an	DET
ejpam-5392	280	8	l	l	NOUN
ejpam-5392	280	9	-	-	ADJ
ejpam-5392	280	10	θβao(x)-open	θβao(x)-open	ADJ
ejpam-5392	280	11	set	set	NOUN
ejpam-5392	280	12	,	,	PUNCT
ejpam-5392	280	13	but	but	CCONJ
ejpam-5392	280	14	it	it	PRON
ejpam-5392	280	15	is	be	AUX
ejpam-5392	280	16	neither	neither	CCONJ
ejpam-5392	280	17	an	an	DET
ejpam-5392	280	18	l	l	NOUN
ejpam-5392	280	19	-	-	NOUN
ejpam-5392	280	20	δβao(x)-open	δβao(x)-open	NOUN
ejpam-5392	280	21	set	set	NOUN
ejpam-5392	280	22	nor	nor	CCONJ
ejpam-5392	280	23	an	an	DET
ejpam-5392	280	24	l∧	l∧	ADJ
ejpam-5392	280	25	βa	βa	INTJ
ejpam-5392	280	26	-set	-set	NOUN
ejpam-5392	280	27	.	.	PUNCT
ejpam-5392	281	1	also	also	ADV
ejpam-5392	281	2	,	,	PUNCT
ejpam-5392	281	3	the	the	DET
ejpam-5392	281	4	next	next	ADJ
ejpam-5392	281	5	result	result	NOUN
ejpam-5392	281	6	clarifies	clarify	VERB
ejpam-5392	281	7	that	that	SCONJ
ejpam-5392	281	8	the	the	DET
ejpam-5392	281	9	class	class	NOUN
ejpam-5392	281	10	of	of	ADP
ejpam-5392	281	11	l	l	NOUN
ejpam-5392	281	12	-	-	PUNCT
ejpam-5392	281	13	θβλ	θβλ	NOUN
ejpam-5392	281	14	-	-	PUNCT
ejpam-5392	281	15	open	open	ADJ
ejpam-5392	281	16	sets	set	NOUN
ejpam-5392	281	17	is	be	AUX
ejpam-5392	281	18	wider	wide	ADJ
ejpam-5392	281	19	than	than	ADP
ejpam-5392	281	20	the	the	DET
ejpam-5392	281	21	classes	class	NOUN
ejpam-5392	281	22	of	of	ADP
ejpam-5392	281	23	δβλ	δβλ	NOUN
ejpam-5392	281	24	-	-	PUNCT
ejpam-5392	281	25	open	open	ADJ
ejpam-5392	281	26	sets	set	NOUN
ejpam-5392	281	27	and	and	CCONJ
ejpam-5392	281	28	∧	∧	NOUN
ejpam-5392	281	29	βλ	βλ	NOUN
ejpam-5392	281	30	-sets	-set	NOUN
ejpam-5392	281	31	.	.	PUNCT
ejpam-5392	282	1	proposition	proposition	NOUN
ejpam-5392	282	2	6	6	NUM
ejpam-5392	282	3	.	.	PUNCT
ejpam-5392	283	1	(	(	PUNCT
ejpam-5392	283	2	i	i	NOUN
ejpam-5392	283	3	)	)	PUNCT
ejpam-5392	283	4	every	every	DET
ejpam-5392	283	5	δβλ	δβλ	NOUN
ejpam-5392	283	6	-	-	PUNCT
ejpam-5392	283	7	open	open	ADJ
ejpam-5392	283	8	set	set	NOUN
ejpam-5392	283	9	is	be	AUX
ejpam-5392	283	10	l	l	NOUN
ejpam-5392	283	11	-	-	PUNCT
ejpam-5392	283	12	θβλ	θβλ	NOUN
ejpam-5392	283	13	-	-	PUNCT
ejpam-5392	283	14	open	open	ADJ
ejpam-5392	283	15	set	set	NOUN
ejpam-5392	283	16	.	.	PUNCT
ejpam-5392	284	1	(	(	PUNCT
ejpam-5392	284	2	ii	ii	NOUN
ejpam-5392	284	3	)	)	PUNCT
ejpam-5392	284	4	every	every	DET
ejpam-5392	284	5	∧	∧	PROPN
ejpam-5392	284	6	βλ	βλ	X
ejpam-5392	284	7	-set	-set	PUNCT
ejpam-5392	284	8	is	be	AUX
ejpam-5392	284	9	l	l	NOUN
ejpam-5392	284	10	-	-	PUNCT
ejpam-5392	284	11	θβλ	θβλ	NOUN
ejpam-5392	284	12	-	-	PUNCT
ejpam-5392	284	13	open	open	ADJ
ejpam-5392	284	14	set	set	NOUN
ejpam-5392	284	15	.	.	PUNCT
ejpam-5392	285	1	proof	proof	NOUN
ejpam-5392	285	2	.	.	PUNCT
ejpam-5392	286	1	by	by	ADP
ejpam-5392	286	2	using	use	VERB
ejpam-5392	286	3	propositions	proposition	NOUN
ejpam-5392	286	4	1	1	NUM
ejpam-5392	286	5	[	[	X
ejpam-5392	286	6	23	23	NUM
ejpam-5392	286	7	]	]	PUNCT
ejpam-5392	286	8	and	and	CCONJ
ejpam-5392	286	9	5	5	NUM
ejpam-5392	286	10	.	.	NOUN
ejpam-5392	286	11	example	example	NOUN
ejpam-5392	286	12	2	2	NUM
ejpam-5392	286	13	.	.	PUNCT
ejpam-5392	287	1	let	let	VERB
ejpam-5392	287	2	x	x	PUNCT
ejpam-5392	287	3	=	=	PRON
ejpam-5392	287	4	{	{	PUNCT
ejpam-5392	287	5	y1	y1	PROPN
ejpam-5392	287	6	,	,	PUNCT
ejpam-5392	287	7	y2	y2	PROPN
ejpam-5392	287	8	,	,	PUNCT
ejpam-5392	287	9	y3	y3	PROPN
ejpam-5392	287	10	,	,	PUNCT
ejpam-5392	287	11	y4},l	y4},l	X
ejpam-5392	287	12	=	=	PUNCT
ejpam-5392	287	13	{	{	PUNCT
ejpam-5392	287	14	∅	∅	NOUN
ejpam-5392	287	15	,	,	PUNCT
ejpam-5392	287	16	{	{	PUNCT
ejpam-5392	287	17	y3	y3	NOUN
ejpam-5392	287	18	}	}	PUNCT
ejpam-5392	287	19	}	}	PUNCT
ejpam-5392	287	20	,	,	PUNCT
ejpam-5392	287	21	and	and	CCONJ
ejpam-5392	287	22	r	r	NOUN
ejpam-5392	287	23	=	=	SYM
ejpam-5392	287	24	{	{	PUNCT
ejpam-5392	287	25	(	(	PUNCT
ejpam-5392	287	26	y1	y1	INTJ
ejpam-5392	287	27	,	,	PUNCT
ejpam-5392	287	28	y1	y1	PROPN
ejpam-5392	287	29	)	)	PUNCT
ejpam-5392	287	30	,	,	PUNCT
ejpam-5392	287	31	(	(	PUNCT
ejpam-5392	287	32	y1	y1	INTJ
ejpam-5392	287	33	,	,	PUNCT
ejpam-5392	287	34	y2	y2	PROPN
ejpam-5392	287	35	)	)	PUNCT
ejpam-5392	287	36	,	,	PUNCT
ejpam-5392	287	37	(	(	PUNCT
ejpam-5392	287	38	y2	y2	INTJ
ejpam-5392	287	39	,	,	PUNCT
ejpam-5392	287	40	y1	y1	PROPN
ejpam-5392	287	41	)	)	PUNCT
ejpam-5392	287	42	,	,	PUNCT
ejpam-5392	287	43	(	(	PUNCT
ejpam-5392	287	44	y2	y2	INTJ
ejpam-5392	287	45	,	,	PUNCT
ejpam-5392	287	46	y2	y2	PROPN
ejpam-5392	287	47	)	)	PUNCT
ejpam-5392	287	48	,	,	PUNCT
ejpam-5392	287	49	(	(	PUNCT
ejpam-5392	287	50	y3	y3	PROPN
ejpam-5392	287	51	,	,	PUNCT
ejpam-5392	287	52	y3	y3	PROPN
ejpam-5392	287	53	)	)	PUNCT
ejpam-5392	287	54	,	,	PUNCT
ejpam-5392	287	55	(	(	PUNCT
ejpam-5392	287	56	y4	y4	PROPN
ejpam-5392	287	57	,	,	PUNCT
ejpam-5392	287	58	y3	y3	PROPN
ejpam-5392	287	59	)	)	PUNCT
ejpam-5392	287	60	,	,	PUNCT
ejpam-5392	287	61	(	(	PUNCT
ejpam-5392	287	62	y4	y4	PROPN
ejpam-5392	287	63	,	,	PUNCT
ejpam-5392	287	64	y4	y4	PROPN
ejpam-5392	287	65	)	)	PUNCT
ejpam-5392	287	66	)	)	PUNCT
ejpam-5392	287	67	}	}	PUNCT
ejpam-5392	287	68	.	.	PUNCT
ejpam-5392	288	1	then	then	ADV
ejpam-5392	288	2	,	,	PUNCT
ejpam-5392	288	3	the	the	DET
ejpam-5392	288	4	topology	topology	NOUN
ejpam-5392	288	5	generated	generate	VERB
ejpam-5392	288	6	by	by	ADP
ejpam-5392	288	7	a	a	DET
ejpam-5392	288	8	relation	relation	NOUN
ejpam-5392	288	9	r	r	NOUN
ejpam-5392	288	10	in	in	ADP
ejpam-5392	288	11	the	the	DET
ejpam-5392	288	12	case	case	NOUN
ejpam-5392	288	13	of	of	ADP
ejpam-5392	288	14	λ	λ	PROPN
ejpam-5392	288	15	=	=	PUNCT
ejpam-5392	288	16	a	a	PROPN
ejpam-5392	288	17	is	be	AUX
ejpam-5392	288	18	ϑa	ϑa	ADP
ejpam-5392	288	19	=	=	PUNCT
ejpam-5392	288	20	{	{	PUNCT
ejpam-5392	288	21	x	x	NOUN
ejpam-5392	288	22	,	,	PUNCT
ejpam-5392	288	23	∅	∅	NOUN
ejpam-5392	288	24	,	,	PUNCT
ejpam-5392	288	25	{	{	PUNCT
ejpam-5392	288	26	y3	y3	NOUN
ejpam-5392	288	27	}	}	PUNCT
ejpam-5392	288	28	,	,	PUNCT
ejpam-5392	288	29	{	{	PUNCT
ejpam-5392	288	30	y1	y1	NOUN
ejpam-5392	288	31	,	,	PUNCT
ejpam-5392	288	32	y2	y2	PROPN
ejpam-5392	288	33	}	}	PUNCT
ejpam-5392	288	34	,	,	PUNCT
ejpam-5392	288	35	{	{	PUNCT
ejpam-5392	288	36	y1	y1	NOUN
ejpam-5392	288	37	,	,	PUNCT
ejpam-5392	288	38	y2	y2	PROPN
ejpam-5392	288	39	,	,	PUNCT
ejpam-5392	288	40	y3	y3	NOUN
ejpam-5392	288	41	}	}	PUNCT
ejpam-5392	288	42	}	}	PUNCT
ejpam-5392	288	43	.	.	PUNCT
ejpam-5392	289	1	now	now	ADV
ejpam-5392	289	2	,	,	PUNCT
ejpam-5392	289	3	l	l	NOUN
ejpam-5392	289	4	-	-	PUNCT
ejpam-5392	289	5	θβao(x	θβao(x	NOUN
ejpam-5392	289	6	)	)	PUNCT
ejpam-5392	289	7	is	be	AUX
ejpam-5392	289	8	the	the	DET
ejpam-5392	289	9	power	power	NOUN
ejpam-5392	289	10	set	set	NOUN
ejpam-5392	289	11	of	of	ADP
ejpam-5392	289	12	x	x	PUNCT
ejpam-5392	289	13	and	and	CCONJ
ejpam-5392	289	14	δβao(x	δβao(x	PROPN
ejpam-5392	289	15	)	)	PUNCT
ejpam-5392	289	16	is	be	AUX
ejpam-5392	289	17	p	p	X
ejpam-5392	289	18	(	(	PUNCT
ejpam-5392	289	19	x)\{{y4	x)\{{y4	PROPN
ejpam-5392	289	20	}	}	PUNCT
ejpam-5392	289	21	}	}	PUNCT
ejpam-5392	289	22	.	.	PUNCT
ejpam-5392	290	1	one	one	PRON
ejpam-5392	290	2	can	can	AUX
ejpam-5392	290	3	check	check	VERB
ejpam-5392	290	4	that	that	PRON
ejpam-5392	290	5	{	{	PUNCT
ejpam-5392	290	6	y4	y4	X
ejpam-5392	290	7	}	}	PUNCT
ejpam-5392	290	8	is	be	AUX
ejpam-5392	290	9	an	an	DET
ejpam-5392	290	10	l	l	NOUN
ejpam-5392	290	11	-	-	ADJ
ejpam-5392	290	12	θβao(x)-open	θβao(x)-open	ADJ
ejpam-5392	290	13	set	set	NOUN
ejpam-5392	290	14	,	,	PUNCT
ejpam-5392	290	15	but	but	CCONJ
ejpam-5392	290	16	it	it	PRON
ejpam-5392	290	17	is	be	AUX
ejpam-5392	290	18	not	not	PART
ejpam-5392	290	19	δβao(x)-open	δβao(x)-open	NOUN
ejpam-5392	290	20	.	.	PUNCT
ejpam-5392	290	21	example	example	NOUN
ejpam-5392	291	1	3	3	X
ejpam-5392	291	2	.	.	PUNCT
ejpam-5392	291	3	let	let	VERB
ejpam-5392	291	4	x	x	PUNCT
ejpam-5392	291	5	=	=	PRON
ejpam-5392	291	6	{	{	PUNCT
ejpam-5392	291	7	y1	y1	PROPN
ejpam-5392	291	8	,	,	PUNCT
ejpam-5392	291	9	y2	y2	PROPN
ejpam-5392	291	10	,	,	PUNCT
ejpam-5392	291	11	y3	y3	PROPN
ejpam-5392	291	12	,	,	PUNCT
ejpam-5392	291	13	y4},l	y4},l	X
ejpam-5392	291	14	=	=	PUNCT
ejpam-5392	291	15	{	{	PUNCT
ejpam-5392	291	16	∅	∅	NOUN
ejpam-5392	291	17	,	,	PUNCT
ejpam-5392	291	18	{	{	PUNCT
ejpam-5392	291	19	y3	y3	NOUN
ejpam-5392	291	20	}	}	PUNCT
ejpam-5392	291	21	}	}	PUNCT
ejpam-5392	291	22	and	and	CCONJ
ejpam-5392	291	23	r	r	NOUN
ejpam-5392	291	24	=	=	SYM
ejpam-5392	291	25	{	{	PUNCT
ejpam-5392	291	26	(	(	PUNCT
ejpam-5392	291	27	y1	y1	INTJ
ejpam-5392	291	28	,	,	PUNCT
ejpam-5392	291	29	y1	y1	PROPN
ejpam-5392	291	30	)	)	PUNCT
ejpam-5392	291	31	,	,	PUNCT
ejpam-5392	291	32	(	(	PUNCT
ejpam-5392	291	33	y1	y1	X
ejpam-5392	291	34	,	,	PUNCT
ejpam-5392	291	35	y3	y3	PROPN
ejpam-5392	291	36	)	)	PUNCT
ejpam-5392	291	37	,	,	PUNCT
ejpam-5392	291	38	(	(	PUNCT
ejpam-5392	291	39	y2	y2	INTJ
ejpam-5392	291	40	,	,	PUNCT
ejpam-5392	291	41	y1	y1	PROPN
ejpam-5392	291	42	)	)	PUNCT
ejpam-5392	291	43	,	,	PUNCT
ejpam-5392	291	44	(	(	PUNCT
ejpam-5392	291	45	y2	y2	PROPN
ejpam-5392	291	46	,	,	PUNCT
ejpam-5392	291	47	y3	y3	PROPN
ejpam-5392	291	48	)	)	PUNCT
ejpam-5392	291	49	,	,	PUNCT
ejpam-5392	291	50	(	(	PUNCT
ejpam-5392	291	51	y3	y3	PROPN
ejpam-5392	291	52	,	,	PUNCT
ejpam-5392	291	53	y3	y3	PROPN
ejpam-5392	291	54	)	)	PUNCT
ejpam-5392	291	55	,	,	PUNCT
ejpam-5392	291	56	(	(	PUNCT
ejpam-5392	291	57	y4	y4	PROPN
ejpam-5392	291	58	,	,	PUNCT
ejpam-5392	291	59	y4	y4	PROPN
ejpam-5392	291	60	)	)	PUNCT
ejpam-5392	291	61	}	}	PUNCT
ejpam-5392	291	62	then	then	ADV
ejpam-5392	291	63	,	,	PUNCT
ejpam-5392	291	64	the	the	DET
ejpam-5392	291	65	topology	topology	NOUN
ejpam-5392	291	66	generated	generate	VERB
ejpam-5392	291	67	by	by	ADP
ejpam-5392	291	68	a	a	DET
ejpam-5392	291	69	relation	relation	NOUN
ejpam-5392	291	70	r	r	NOUN
ejpam-5392	291	71	in	in	ADP
ejpam-5392	291	72	the	the	DET
ejpam-5392	291	73	case	case	NOUN
ejpam-5392	291	74	of	of	ADP
ejpam-5392	291	75	λ	λ	PROPN
ejpam-5392	291	76	=	=	PUNCT
ejpam-5392	291	77	a	a	PROPN
ejpam-5392	291	78	is	be	AUX
ejpam-5392	291	79	ϑa	ϑa	ADP
ejpam-5392	291	80	=	=	PUNCT
ejpam-5392	291	81	{	{	PUNCT
ejpam-5392	291	82	x	x	NOUN
ejpam-5392	291	83	,	,	PUNCT
ejpam-5392	291	84	∅	∅	NOUN
ejpam-5392	291	85	,	,	PUNCT
ejpam-5392	291	86	{	{	PUNCT
ejpam-5392	291	87	y3	y3	NOUN
ejpam-5392	291	88	}	}	PUNCT
ejpam-5392	291	89	,	,	PUNCT
ejpam-5392	291	90	{	{	PUNCT
ejpam-5392	291	91	y4	y4	X
ejpam-5392	291	92	}	}	PUNCT
ejpam-5392	291	93	,	,	PUNCT
ejpam-5392	291	94	{	{	PUNCT
ejpam-5392	291	95	y1	y1	X
ejpam-5392	291	96	,	,	PUNCT
ejpam-5392	291	97	y3	y3	PROPN
ejpam-5392	291	98	}	}	PUNCT
ejpam-5392	291	99	,	,	PUNCT
ejpam-5392	291	100	{	{	PUNCT
ejpam-5392	291	101	y3	y3	NOUN
ejpam-5392	291	102	,	,	PUNCT
ejpam-5392	291	103	y4	y4	PROPN
ejpam-5392	291	104	}	}	PUNCT
ejpam-5392	291	105	,	,	PUNCT
ejpam-5392	291	106	{	{	PUNCT
ejpam-5392	291	107	y1	y1	X
ejpam-5392	291	108	,	,	PUNCT
ejpam-5392	291	109	y3	y3	PROPN
ejpam-5392	291	110	,	,	PUNCT
ejpam-5392	291	111	y4	y4	PROPN
ejpam-5392	291	112	}	}	PUNCT
ejpam-5392	291	113	}	}	PUNCT
ejpam-5392	291	114	.	.	PUNCT
ejpam-5392	292	1	note	note	VERB
ejpam-5392	292	2	that	that	SCONJ
ejpam-5392	292	3	l	l	NOUN
ejpam-5392	292	4	-	-	PUNCT
ejpam-5392	292	5	θβao(x	θβao(x	NOUN
ejpam-5392	292	6	)	)	PUNCT
ejpam-5392	292	7	=	=	SYM
ejpam-5392	293	1	p	p	X
ejpam-5392	293	2	(	(	PUNCT
ejpam-5392	293	3	x	x	NOUN
ejpam-5392	293	4	)	)	PUNCT
ejpam-5392	293	5	and	and	CCONJ
ejpam-5392	293	6	∧	∧	PROPN
ejpam-5392	293	7	βa	βa	INTJ
ejpam-5392	293	8	o(x	o(x	PROPN
ejpam-5392	293	9	)	)	PUNCT
ejpam-5392	293	10	=	=	PRON
ejpam-5392	293	11	{	{	PUNCT
ejpam-5392	293	12	x	x	NOUN
ejpam-5392	293	13	,	,	PUNCT
ejpam-5392	293	14	∅	∅	NOUN
ejpam-5392	293	15	,	,	PUNCT
ejpam-5392	293	16	{	{	PUNCT
ejpam-5392	293	17	y2	y2	NOUN
ejpam-5392	293	18	}	}	PUNCT
ejpam-5392	293	19	,	,	PUNCT
ejpam-5392	293	20	{	{	PUNCT
ejpam-5392	293	21	y3	y3	NOUN
ejpam-5392	293	22	}	}	PUNCT
ejpam-5392	293	23	,	,	PUNCT
ejpam-5392	293	24	{	{	PUNCT
ejpam-5392	293	25	y4	y4	X
ejpam-5392	293	26	}	}	PUNCT
ejpam-5392	293	27	,	,	PUNCT
ejpam-5392	293	28	{	{	PUNCT
ejpam-5392	293	29	y1	y1	X
ejpam-5392	293	30	,	,	PUNCT
ejpam-5392	293	31	y3	y3	PROPN
ejpam-5392	293	32	}	}	PUNCT
ejpam-5392	293	33	,	,	PUNCT
ejpam-5392	293	34	{	{	PUNCT
ejpam-5392	293	35	y2	y2	NOUN
ejpam-5392	293	36	,	,	PUNCT
ejpam-5392	293	37	y3	y3	PROPN
ejpam-5392	293	38	}	}	PUNCT
ejpam-5392	293	39	,	,	PUNCT
ejpam-5392	293	40	{	{	PUNCT
ejpam-5392	293	41	y2	y2	NOUN
ejpam-5392	293	42	,	,	PUNCT
ejpam-5392	293	43	y4	y4	PROPN
ejpam-5392	293	44	}	}	PUNCT
ejpam-5392	293	45	,	,	PUNCT
ejpam-5392	293	46	{	{	PUNCT
ejpam-5392	293	47	y3	y3	NOUN
ejpam-5392	293	48	,	,	PUNCT
ejpam-5392	293	49	y4	y4	PROPN
ejpam-5392	293	50	}	}	PUNCT
ejpam-5392	293	51	,	,	PUNCT
ejpam-5392	293	52	{	{	PUNCT
ejpam-5392	293	53	y1	y1	NOUN
ejpam-5392	293	54	,	,	PUNCT
ejpam-5392	293	55	y2	y2	PROPN
ejpam-5392	293	56	,	,	PUNCT
ejpam-5392	293	57	y3	y3	PROPN
ejpam-5392	293	58	}	}	PUNCT
ejpam-5392	293	59	,	,	PUNCT
ejpam-5392	293	60	{	{	PUNCT
ejpam-5392	293	61	y1	y1	X
ejpam-5392	293	62	,	,	PUNCT
ejpam-5392	293	63	y3	y3	PROPN
ejpam-5392	293	64	,	,	PUNCT
ejpam-5392	293	65	y4	y4	PROPN
ejpam-5392	293	66	}	}	PUNCT
ejpam-5392	293	67	,	,	PUNCT
ejpam-5392	293	68	{	{	PUNCT
ejpam-5392	293	69	y2	y2	PROPN
ejpam-5392	293	70	,	,	PUNCT
ejpam-5392	293	71	y3	y3	PROPN
ejpam-5392	293	72	,	,	PUNCT
ejpam-5392	293	73	y4	y4	PROPN
ejpam-5392	293	74	}	}	PUNCT
ejpam-5392	293	75	}	}	PUNCT
ejpam-5392	293	76	.	.	PUNCT
ejpam-5392	294	1	the	the	DET
ejpam-5392	294	2	next	next	ADJ
ejpam-5392	294	3	proposition	proposition	NOUN
ejpam-5392	294	4	elucidates	elucidate	VERB
ejpam-5392	294	5	that	that	SCONJ
ejpam-5392	294	6	the	the	DET
ejpam-5392	294	7	the	the	DET
ejpam-5392	294	8	class	class	NOUN
ejpam-5392	294	9	of	of	ADP
ejpam-5392	294	10	l	l	NOUN
ejpam-5392	294	11	-	-	PUNCT
ejpam-5392	294	12	θβλ	θβλ	NOUN
ejpam-5392	294	13	-	-	PUNCT
ejpam-5392	294	14	open	open	ADJ
ejpam-5392	294	15	sets	set	NOUN
ejpam-5392	294	16	is	be	AUX
ejpam-5392	294	17	proper	proper	ADJ
ejpam-5392	294	18	wider	wide	ADJ
ejpam-5392	294	19	than	than	ADP
ejpam-5392	294	20	the	the	DET
ejpam-5392	294	21	class	class	NOUN
ejpam-5392	294	22	of	of	ADP
ejpam-5392	294	23	l	l	PROPN
ejpam-5392	294	24	-	-	ADJ
ejpam-5392	294	25	δβλ	δβλ	ADJ
ejpam-5392	294	26	-	-	PUNCT
ejpam-5392	294	27	open	open	ADJ
ejpam-5392	294	28	sets	set	NOUN
ejpam-5392	294	29	.	.	PUNCT
ejpam-5392	295	1	therefore	therefore	ADV
ejpam-5392	295	2	,	,	PUNCT
ejpam-5392	295	3	the	the	DET
ejpam-5392	295	4	class	class	NOUN
ejpam-5392	295	5	of	of	ADP
ejpam-5392	295	6	l	l	NOUN
ejpam-5392	295	7	-	-	PUNCT
ejpam-5392	295	8	θβλ	θβλ	NOUN
ejpam-5392	295	9	-	-	PUNCT
ejpam-5392	295	10	open	open	ADJ
ejpam-5392	295	11	sets	set	NOUN
ejpam-5392	295	12	is	be	AUX
ejpam-5392	295	13	also	also	ADV
ejpam-5392	295	14	wider	wide	ADJ
ejpam-5392	295	15	than	than	ADP
ejpam-5392	295	16	the	the	DET
ejpam-5392	295	17	classes	class	NOUN
ejpam-5392	295	18	of	of	ADP
ejpam-5392	295	19	all	all	DET
ejpam-5392	295	20	l	l	NOUN
ejpam-5392	295	21	-	-	NOUN
ejpam-5392	295	22	λ	λ	NOUN
ejpam-5392	295	23	-	-	PUNCT
ejpam-5392	295	24	near	near	ADV
ejpam-5392	295	25	open	open	ADJ
ejpam-5392	295	26	sets	set	NOUN
ejpam-5392	295	27	introduced	introduce	VERB
ejpam-5392	295	28	in	in	ADP
ejpam-5392	295	29	definition	definition	NOUN
ejpam-5392	295	30	8	8	NUM
ejpam-5392	295	31	[	[	X
ejpam-5392	295	32	21	21	NUM
ejpam-5392	295	33	]	]	PUNCT
ejpam-5392	295	34	,	,	PUNCT
ejpam-5392	295	35	i.e.	i.e.	X
ejpam-5392	295	36	,	,	PUNCT
ejpam-5392	295	37	l	l	X
ejpam-5392	295	38	-	-	PUNCT
ejpam-5392	295	39	βλ	βλ	ADV
ejpam-5392	295	40	-	-	ADJ
ejpam-5392	295	41	open	open	ADJ
ejpam-5392	295	42	,	,	PUNCT
ejpam-5392	295	43	l	l	ADJ
ejpam-5392	295	44	-	-	ADJ
ejpam-5392	295	45	pλ	pλ	ADJ
ejpam-5392	295	46	-	-	ADJ
ejpam-5392	295	47	open	open	ADJ
ejpam-5392	295	48	,	,	PUNCT
ejpam-5392	295	49	l	l	NOUN
ejpam-5392	295	50	-	-	PUNCT
ejpam-5392	295	51	sλ	sλ	NOUN
ejpam-5392	295	52	-	-	PUNCT
ejpam-5392	295	53	open	open	ADJ
ejpam-5392	295	54	and	and	CCONJ
ejpam-5392	295	55	l	l	NOUN
ejpam-5392	295	56	-	-	PUNCT
ejpam-5392	295	57	αλ	αλ	PRON
ejpam-5392	295	58	-	-	PUNCT
ejpam-5392	295	59	open	open	ADJ
ejpam-5392	295	60	sets	set	NOUN
ejpam-5392	295	61	.	.	PUNCT
ejpam-5392	296	1	moreover	moreover	ADV
ejpam-5392	296	2	,	,	PUNCT
ejpam-5392	296	3	it	it	PRON
ejpam-5392	296	4	is	be	AUX
ejpam-5392	296	5	wider	wide	ADJ
ejpam-5392	296	6	than	than	ADP
ejpam-5392	296	7	the	the	DET
ejpam-5392	296	8	classes	class	NOUN
ejpam-5392	296	9	of	of	ADP
ejpam-5392	296	10	δβλ	δβλ	NOUN
ejpam-5392	296	11	-	-	PUNCT
ejpam-5392	296	12	open	open	ADJ
ejpam-5392	296	13	sets	set	NOUN
ejpam-5392	296	14	.	.	PUNCT
ejpam-5392	297	1	hence	hence	ADV
ejpam-5392	297	2	,	,	PUNCT
ejpam-5392	297	3	it	it	PRON
ejpam-5392	297	4	is	be	AUX
ejpam-5392	297	5	also	also	ADV
ejpam-5392	297	6	wider	wide	ADJ
ejpam-5392	297	7	than	than	ADP
ejpam-5392	297	8	all	all	DET
ejpam-5392	297	9	classes	class	NOUN
ejpam-5392	297	10	of	of	ADP
ejpam-5392	297	11	λ	λ	NOUN
ejpam-5392	297	12	-	-	PUNCT
ejpam-5392	297	13	near	near	ADV
ejpam-5392	297	14	open	open	ADJ
ejpam-5392	297	15	sets	set	NOUN
ejpam-5392	297	16	introduced	introduce	VERB
ejpam-5392	297	17	in	in	ADP
ejpam-5392	297	18	definition	definition	NOUN
ejpam-5392	297	19	5	5	NUM
ejpam-5392	297	20	[	[	X
ejpam-5392	297	21	15	15	NUM
ejpam-5392	297	22	]	]	PUNCT
ejpam-5392	297	23	,	,	PUNCT
ejpam-5392	297	24	i.e.	i.e.	X
ejpam-5392	297	25	,	,	PUNCT
ejpam-5392	297	26	βλ	βλ	ADJ
ejpam-5392	297	27	-	-	ADJ
ejpam-5392	297	28	open	open	ADJ
ejpam-5392	297	29	,	,	PUNCT
ejpam-5392	297	30	pλ	pλ	NOUN
ejpam-5392	297	31	-	-	ADJ
ejpam-5392	297	32	open	open	ADJ
ejpam-5392	297	33	,	,	PUNCT
ejpam-5392	297	34	sλ	sλ	NOUN
ejpam-5392	297	35	-	-	PUNCT
ejpam-5392	297	36	open	open	ADJ
ejpam-5392	297	37	and	and	CCONJ
ejpam-5392	297	38	αλ	αλ	PRON
ejpam-5392	297	39	-	-	PUNCT
ejpam-5392	297	40	open	open	ADJ
ejpam-5392	297	41	sets	set	NOUN
ejpam-5392	297	42	.	.	PUNCT
ejpam-5392	298	1	m.	m.	PROPN
ejpam-5392	298	2	hosny	hosny	PROPN
ejpam-5392	298	3	,	,	PUNCT
ejpam-5392	298	4	t.m	t.m	PROPN
ejpam-5392	298	5	.	.	PROPN
ejpam-5392	298	6	al	al	PROPN
ejpam-5392	298	7	-	-	PUNCT
ejpam-5392	298	8	shami	shami	PROPN
ejpam-5392	298	9	/	/	PUNCT
ejpam-5392	298	10	eur	eur	PROPN
ejpam-5392	298	11	.	.	PUNCT
ejpam-5392	299	1	j.	j.	PROPN
ejpam-5392	299	2	pure	pure	PROPN
ejpam-5392	299	3	appl	appl	PROPN
ejpam-5392	299	4	.	.	PROPN
ejpam-5392	299	5	math	math	PROPN
ejpam-5392	299	6	,	,	PUNCT
ejpam-5392	299	7	17	17	NUM
ejpam-5392	299	8	(	(	PUNCT
ejpam-5392	299	9	4	4	NUM
ejpam-5392	299	10	)	)	PUNCT
ejpam-5392	299	11	(	(	PUNCT
ejpam-5392	299	12	2024	2024	NUM
ejpam-5392	299	13	)	)	PUNCT
ejpam-5392	299	14	,	,	PUNCT
ejpam-5392	299	15	3436	3436	NUM
ejpam-5392	299	16	-	-	SYM
ejpam-5392	299	17	3463	3463	NUM
ejpam-5392	299	18	3446	3446	NUM
ejpam-5392	299	19	proposition	proposition	NOUN
ejpam-5392	299	20	7	7	NUM
ejpam-5392	299	21	.	.	PUNCT
ejpam-5392	300	1	the	the	DET
ejpam-5392	300	2	next	next	ADJ
ejpam-5392	300	3	implications	implication	NOUN
ejpam-5392	300	4	hold	hold	VERB
ejpam-5392	300	5	true	true	ADJ
ejpam-5392	300	6	:	:	PUNCT
ejpam-5392	300	7	ϑλ(γλ	ϑλ(γλ	PROPN
ejpam-5392	300	8	)	)	PUNCT
ejpam-5392	300	9	⇒	⇒	NOUN
ejpam-5392	300	10	l	l	PROPN
ejpam-5392	300	11	-	-	PUNCT
ejpam-5392	300	12	αλo(l	αλo(l	NUM
ejpam-5392	300	13	-	-	PUNCT
ejpam-5392	300	14	αλc	αλc	NOUN
ejpam-5392	300	15	)	)	PUNCT
ejpam-5392	300	16	l	l	NOUN
ejpam-5392	300	17	-	-	PUNCT
ejpam-5392	300	18	pλo(l	pλo(l	VERB
ejpam-5392	300	19	-	-	PUNCT
ejpam-5392	300	20	pλc	pλc	NOUN
ejpam-5392	300	21	)	)	PUNCT
ejpam-5392	300	22	⇓	⇓	PROPN
ejpam-5392	300	23	⇓	⇓	PROPN
ejpam-5392	300	24	l	l	PROPN
ejpam-5392	300	25	-	-	PUNCT
ejpam-5392	300	26	sλo(l	sλo(l	PROPN
ejpam-5392	300	27	-	-	PUNCT
ejpam-5392	300	28	sλc	sλc	NOUN
ejpam-5392	300	29	)	)	PUNCT
ejpam-5392	300	30	⇒	⇒	NOUN
ejpam-5392	300	31	l	l	PROPN
ejpam-5392	300	32	-	-	PUNCT
ejpam-5392	300	33	βλo(l	βλo(l	SYM
ejpam-5392	300	34	-	-	PUNCT
ejpam-5392	300	35	βλc	βλc	NOUN
ejpam-5392	300	36	)	)	PUNCT
ejpam-5392	300	37	⇒	⇒	NOUN
ejpam-5392	300	38	l	l	PROPN
ejpam-5392	300	39	-	-	PUNCT
ejpam-5392	300	40	δβλo(l	δβλo(l	PROPN
ejpam-5392	300	41	-	-	PUNCT
ejpam-5392	300	42	δβλc	δβλc	NOUN
ejpam-5392	300	43	)	)	PUNCT
ejpam-5392	300	44	⇓	⇓	PROPN
ejpam-5392	300	45	l	l	PROPN
ejpam-5392	300	46	-	-	PUNCT
ejpam-5392	300	47	θβλo(l	θβλo(l	VERB
ejpam-5392	300	48	-	-	PUNCT
ejpam-5392	300	49	θβλc	θβλc	NOUN
ejpam-5392	300	50	)	)	PUNCT
ejpam-5392	300	51	.	.	PUNCT
ejpam-5392	301	1	ϑλ(γλ	ϑλ(γλ	PROPN
ejpam-5392	301	2	)	)	PUNCT
ejpam-5392	302	1	⇒	⇒	NOUN
ejpam-5392	302	2	l	l	PROPN
ejpam-5392	302	3	-	-	PUNCT
ejpam-5392	302	4	αλo(l	αλo(l	NUM
ejpam-5392	302	5	-	-	PUNCT
ejpam-5392	302	6	αλc	αλc	NOUN
ejpam-5392	302	7	)	)	PUNCT
ejpam-5392	302	8	l	l	NOUN
ejpam-5392	302	9	-	-	PUNCT
ejpam-5392	302	10	pλo(l	pλo(l	VERB
ejpam-5392	302	11	-	-	PUNCT
ejpam-5392	302	12	pλc	pλc	NOUN
ejpam-5392	302	13	)	)	PUNCT
ejpam-5392	302	14	⇓	⇓	PROPN
ejpam-5392	302	15	⇓	⇓	PROPN
ejpam-5392	302	16	l	l	PROPN
ejpam-5392	302	17	-	-	PUNCT
ejpam-5392	302	18	sλo(l	sλo(l	PROPN
ejpam-5392	302	19	-	-	PUNCT
ejpam-5392	302	20	sλc	sλc	NOUN
ejpam-5392	302	21	)	)	PUNCT
ejpam-5392	302	22	⇒	⇒	NOUN
ejpam-5392	302	23	l	l	PROPN
ejpam-5392	302	24	-	-	PUNCT
ejpam-5392	302	25	βλo(l	βλo(l	SYM
ejpam-5392	302	26	-	-	PUNCT
ejpam-5392	302	27	βλc	βλc	NOUN
ejpam-5392	302	28	)	)	PUNCT
ejpam-5392	302	29	⇒	⇒	VERB
ejpam-5392	303	1	l∧	l∧	PROPN
ejpam-5392	303	2	βλo	βλo	PROPN
ejpam-5392	303	3	(	(	PUNCT
ejpam-5392	303	4	l∧	l∧	PROPN
ejpam-5392	303	5	βλc	βλc	PROPN
ejpam-5392	303	6	)	)	PUNCT
ejpam-5392	304	1	⇓	⇓	PROPN
ejpam-5392	304	2	l	l	PROPN
ejpam-5392	304	3	-	-	PUNCT
ejpam-5392	304	4	θβλo(l	θβλo(l	VERB
ejpam-5392	304	5	-	-	PUNCT
ejpam-5392	304	6	θβλc	θβλc	NOUN
ejpam-5392	304	7	)	)	PUNCT
ejpam-5392	304	8	.	.	PUNCT
ejpam-5392	305	1	ϑλ(γλ	ϑλ(γλ	PROPN
ejpam-5392	305	2	)	)	PUNCT
ejpam-5392	305	3	⇒	⇒	NOUN
ejpam-5392	305	4	αλo(αλc	αλo(αλc	VERB
ejpam-5392	305	5	)	)	PUNCT
ejpam-5392	305	6	pλo(pλc	pλo(pλc	PROPN
ejpam-5392	305	7	)	)	PUNCT
ejpam-5392	305	8	⇓	⇓	PROPN
ejpam-5392	305	9	⇓	⇓	PROPN
ejpam-5392	305	10	sλo(sλc	sλo(sλc	ADV
ejpam-5392	305	11	)	)	PUNCT
ejpam-5392	305	12	⇒	⇒	PROPN
ejpam-5392	305	13	βλo(βλc	βλo(βλc	NOUN
ejpam-5392	305	14	)	)	PUNCT
ejpam-5392	305	15	⇒	⇒	PROPN
ejpam-5392	305	16	δβλo(δβλc	δβλo(δβλc	PROPN
ejpam-5392	305	17	)	)	PUNCT
ejpam-5392	305	18	⇓	⇓	PROPN
ejpam-5392	305	19	l	l	PROPN
ejpam-5392	305	20	-	-	PUNCT
ejpam-5392	305	21	θβλo(l	θβλo(l	VERB
ejpam-5392	305	22	-	-	PUNCT
ejpam-5392	305	23	θβλc	θβλc	NOUN
ejpam-5392	305	24	)	)	PUNCT
ejpam-5392	305	25	.	.	PUNCT
ejpam-5392	306	1	ϑλ(γλ	ϑλ(γλ	PROPN
ejpam-5392	306	2	)	)	PUNCT
ejpam-5392	306	3	⇒	⇒	NOUN
ejpam-5392	306	4	αλo(αλc	αλo(αλc	VERB
ejpam-5392	306	5	)	)	PUNCT
ejpam-5392	306	6	pλo(pλc	pλo(pλc	PROPN
ejpam-5392	306	7	)	)	PUNCT
ejpam-5392	306	8	⇓	⇓	PROPN
ejpam-5392	306	9	⇓	⇓	PROPN
ejpam-5392	306	10	sλo(sλc	sλo(sλc	ADV
ejpam-5392	306	11	)	)	PUNCT
ejpam-5392	306	12	⇒	⇒	PROPN
ejpam-5392	306	13	βλo(βλc	βλo(βλc	NOUN
ejpam-5392	306	14	)	)	PUNCT
ejpam-5392	306	15	⇒	⇒	VERB
ejpam-5392	306	16	∧	∧	PROPN
ejpam-5392	306	17	βλo	βλo	PROPN
ejpam-5392	306	18	(	(	PUNCT
ejpam-5392	306	19	∧	∧	PROPN
ejpam-5392	306	20	βλc	βλc	ADJ
ejpam-5392	306	21	)	)	PUNCT
ejpam-5392	306	22	⇓	⇓	PROPN
ejpam-5392	306	23	l	l	PROPN
ejpam-5392	306	24	-	-	PUNCT
ejpam-5392	306	25	θβλo(l	θβλo(l	VERB
ejpam-5392	306	26	-	-	PUNCT
ejpam-5392	306	27	θβλc	θβλc	NOUN
ejpam-5392	306	28	)	)	PUNCT
ejpam-5392	306	29	.	.	PUNCT
ejpam-5392	307	1	proof	proof	NOUN
ejpam-5392	307	2	.	.	PUNCT
ejpam-5392	308	1	by	by	ADP
ejpam-5392	308	2	propositions	proposition	NOUN
ejpam-5392	308	3	2	2	NUM
ejpam-5392	308	4	[	[	X
ejpam-5392	308	5	23	23	NUM
ejpam-5392	308	6	]	]	PUNCT
ejpam-5392	308	7	,	,	PUNCT
ejpam-5392	308	8	5	5	NUM
ejpam-5392	308	9	,	,	PUNCT
ejpam-5392	308	10	6	6	NUM
ejpam-5392	308	11	the	the	DET
ejpam-5392	308	12	proof	proof	NOUN
ejpam-5392	308	13	is	be	AUX
ejpam-5392	308	14	obvious	obvious	ADJ
ejpam-5392	308	15	.	.	PUNCT
ejpam-5392	309	1	theorem	theorem	NOUN
ejpam-5392	309	2	3	3	NUM
ejpam-5392	309	3	.	.	PUNCT
ejpam-5392	310	1	the	the	DET
ejpam-5392	310	2	union	union	NOUN
ejpam-5392	310	3	of	of	ADP
ejpam-5392	310	4	two	two	NUM
ejpam-5392	310	5	l	l	NOUN
ejpam-5392	310	6	-	-	PUNCT
ejpam-5392	310	7	θβλ	θβλ	NOUN
ejpam-5392	310	8	-	-	PUNCT
ejpam-5392	310	9	open	open	ADJ
ejpam-5392	310	10	subsets	subset	NOUN
ejpam-5392	310	11	is	be	AUX
ejpam-5392	310	12	l	l	NOUN
ejpam-5392	310	13	-	-	PUNCT
ejpam-5392	310	14	θβλ	θβλ	NOUN
ejpam-5392	310	15	-	-	PUNCT
ejpam-5392	310	16	open	open	ADJ
ejpam-5392	310	17	.	.	PUNCT
ejpam-5392	311	1	that	that	PRON
ejpam-5392	311	2	is	is	ADV
ejpam-5392	311	3	,	,	PUNCT
ejpam-5392	311	4	the	the	DET
ejpam-5392	311	5	family	family	NOUN
ejpam-5392	311	6	of	of	ADP
ejpam-5392	311	7	l	l	PROPN
ejpam-5392	311	8	-	-	PUNCT
ejpam-5392	311	9	θβλ	θβλ	NOUN
ejpam-5392	311	10	-	-	PUNCT
ejpam-5392	311	11	open	open	ADJ
ejpam-5392	311	12	subsets	subset	NOUN
ejpam-5392	311	13	is	be	AUX
ejpam-5392	311	14	closed	close	VERB
ejpam-5392	311	15	under	under	ADP
ejpam-5392	311	16	finite	finite	PROPN
ejpam-5392	311	17	union	union	NOUN
ejpam-5392	311	18	.	.	PUNCT
ejpam-5392	312	1	proof	proof	NOUN
ejpam-5392	312	2	.	.	PUNCT
ejpam-5392	313	1	take	take	VERB
ejpam-5392	313	2	arbitrary	arbitrary	ADJ
ejpam-5392	313	3	two	two	NUM
ejpam-5392	313	4	l	l	NOUN
ejpam-5392	313	5	-	-	PUNCT
ejpam-5392	313	6	θβλ	θβλ	NOUN
ejpam-5392	313	7	-	-	PUNCT
ejpam-5392	313	8	open	open	ADJ
ejpam-5392	313	9	subsets	subset	NOUN
ejpam-5392	313	10	v	v	NOUN
ejpam-5392	313	11	and	and	CCONJ
ejpam-5392	313	12	w	w	NOUN
ejpam-5392	313	13	.	.	PUNCT
ejpam-5392	314	1	then	then	ADV
ejpam-5392	314	2	,	,	PUNCT
ejpam-5392	314	3	there	there	PRON
ejpam-5392	314	4	are	be	VERB
ejpam-5392	314	5	open	open	ADJ
ejpam-5392	314	6	sets	set	NOUN
ejpam-5392	314	7	g	g	NOUN
ejpam-5392	314	8	and	and	CCONJ
ejpam-5392	314	9	h	h	PROPN
ejpam-5392	314	10	s.t	s.t	PROPN
ejpam-5392	314	11	.	.	PUNCT
ejpam-5392	315	1	the	the	DET
ejpam-5392	315	2	four	four	NUM
ejpam-5392	315	3	sets	set	NOUN
ejpam-5392	315	4	(	(	PUNCT
ejpam-5392	315	5	v	v	NOUN
ejpam-5392	315	6	\	\	PROPN
ejpam-5392	315	7	clλ(g	clλ(g	PROPN
ejpam-5392	315	8	)	)	PUNCT
ejpam-5392	315	9	)	)	PUNCT
ejpam-5392	315	10	,	,	PUNCT
ejpam-5392	315	11	(	(	PUNCT
ejpam-5392	315	12	g	g	PROPN
ejpam-5392	315	13	\	\	PROPN
ejpam-5392	315	14	clθλ(v	clθλ(v	PROPN
ejpam-5392	315	15	)	)	PUNCT
ejpam-5392	315	16	)	)	PUNCT
ejpam-5392	315	17	,	,	PUNCT
ejpam-5392	315	18	(	(	PUNCT
ejpam-5392	315	19	w	w	NOUN
ejpam-5392	315	20	\	\	ADJ
ejpam-5392	315	21	clλ(h	clλ(h	NOUN
ejpam-5392	315	22	)	)	PUNCT
ejpam-5392	315	23	)	)	PUNCT
ejpam-5392	315	24	and	and	CCONJ
ejpam-5392	315	25	(	(	PUNCT
ejpam-5392	315	26	w	w	NOUN
ejpam-5392	315	27	−	−	PROPN
ejpam-5392	315	28	clθλ(b	clθλ(b	PROPN
ejpam-5392	315	29	)	)	PUNCT
ejpam-5392	315	30	)	)	PUNCT
ejpam-5392	315	31	belong	belong	VERB
ejpam-5392	315	32	to	to	ADP
ejpam-5392	315	33	l.	l.	PROPN
ejpam-5392	315	34	since	since	SCONJ
ejpam-5392	315	35	(	(	PUNCT
ejpam-5392	315	36	g\clθλ(v	g\clθλ(v	PROPN
ejpam-5392	315	37	∪w	∪w	NUM
ejpam-5392	315	38	)	)	PUNCT
ejpam-5392	315	39	)	)	PUNCT
ejpam-5392	316	1	⊆	⊆	NUM
ejpam-5392	316	2	(	(	PUNCT
ejpam-5392	316	3	g\clθλ(v	g\clθλ(v	NOUN
ejpam-5392	316	4	)	)	PUNCT
ejpam-5392	316	5	)	)	PUNCT
ejpam-5392	317	1	∈	∈	PROPN
ejpam-5392	317	2	l	l	NOUN
ejpam-5392	317	3	,	,	PUNCT
ejpam-5392	317	4	(	(	PUNCT
ejpam-5392	317	5	h	h	NOUN
ejpam-5392	317	6	\clθλ(v	\clθλ(v	X
ejpam-5392	317	7	∪w	∪w	NUM
ejpam-5392	317	8	)	)	PUNCT
ejpam-5392	317	9	)	)	PUNCT
ejpam-5392	318	1	⊆	⊆	NUM
ejpam-5392	318	2	(	(	PUNCT
ejpam-5392	318	3	h	h	NOUN
ejpam-5392	318	4	\clθλ(w	\clθλ(w	X
ejpam-5392	318	5	)	)	PUNCT
ejpam-5392	318	6	)	)	PUNCT
ejpam-5392	319	1	∈	∈	PROPN
ejpam-5392	319	2	l	l	NOUN
ejpam-5392	319	3	,	,	PUNCT
ejpam-5392	319	4	we	we	PRON
ejpam-5392	319	5	have	have	VERB
ejpam-5392	319	6	(	(	PUNCT
ejpam-5392	319	7	g\clθλ(v	g\clθλ(v	PROPN
ejpam-5392	319	8	∪w	∪w	NUM
ejpam-5392	319	9	)	)	PUNCT
ejpam-5392	319	10	)	)	PUNCT
ejpam-5392	319	11	∪	∪	ADV
ejpam-5392	319	12	(	(	PUNCT
ejpam-5392	319	13	h	h	NOUN
ejpam-5392	319	14	\clθλ(v	\clθλ(v	X
ejpam-5392	319	15	∪w	∪w	NUM
ejpam-5392	319	16	)	)	PUNCT
ejpam-5392	319	17	)	)	PUNCT
ejpam-5392	320	1	∈	∈	PROPN
ejpam-5392	320	2	l.	l.	NOUN
ejpam-5392	320	3	let	let	VERB
ejpam-5392	320	4	z	z	NOUN
ejpam-5392	320	5	=	=	SYM
ejpam-5392	320	6	g∪h	g∪h	NOUN
ejpam-5392	320	7	,	,	PUNCT
ejpam-5392	320	8	then	then	ADV
ejpam-5392	320	9	(	(	PUNCT
ejpam-5392	320	10	z−clθλ(v	z−clθλ(v	PROPN
ejpam-5392	320	11	∪w	∪w	NUM
ejpam-5392	320	12	)	)	PUNCT
ejpam-5392	320	13	)	)	PUNCT
ejpam-5392	321	1	∈	∈	PROPN
ejpam-5392	321	2	l.	l.	NOUN
ejpam-5392	321	3	also	also	ADV
ejpam-5392	321	4	,	,	PUNCT
ejpam-5392	321	5	(	(	PUNCT
ejpam-5392	321	6	v	v	NOUN
ejpam-5392	321	7	\	\	NOUN
ejpam-5392	321	8	clλ(z	clλ(z	PROPN
ejpam-5392	321	9	)	)	PUNCT
ejpam-5392	321	10	)	)	PUNCT
ejpam-5392	322	1	⊆	⊆	NUM
ejpam-5392	322	2	(	(	PUNCT
ejpam-5392	322	3	v	v	NOUN
ejpam-5392	322	4	\	\	PROPN
ejpam-5392	322	5	clλ(g	clλ(g	PROPN
ejpam-5392	322	6	)	)	PUNCT
ejpam-5392	322	7	)	)	PUNCT
ejpam-5392	323	1	∈	∈	PROPN
ejpam-5392	323	2	l	l	NOUN
ejpam-5392	323	3	and	and	CCONJ
ejpam-5392	323	4	(	(	PUNCT
ejpam-5392	323	5	w	w	PROPN
ejpam-5392	323	6	\	\	PROPN
ejpam-5392	323	7	clλ(z	clλ(z	PROPN
ejpam-5392	323	8	)	)	PUNCT
ejpam-5392	323	9	)	)	PUNCT
ejpam-5392	324	1	⊆	⊆	NUM
ejpam-5392	324	2	(	(	PUNCT
ejpam-5392	324	3	w	w	NOUN
ejpam-5392	324	4	\	\	ADJ
ejpam-5392	324	5	clλ(h	clλ(h	NOUN
ejpam-5392	324	6	)	)	PUNCT
ejpam-5392	324	7	)	)	PUNCT
ejpam-5392	325	1	∈	∈	PROPN
ejpam-5392	325	2	l.	l.	NOUN
ejpam-5392	325	3	then	then	ADV
ejpam-5392	325	4	,	,	PUNCT
ejpam-5392	325	5	(	(	PUNCT
ejpam-5392	325	6	v	v	NOUN
ejpam-5392	325	7	\	\	NOUN
ejpam-5392	325	8	clλ(z))∪	clλ(z))∪	PROPN
ejpam-5392	325	9	(	(	PUNCT
ejpam-5392	325	10	w	w	PROPN
ejpam-5392	325	11	\	\	PROPN
ejpam-5392	325	12	clλ(z	clλ(z	PROPN
ejpam-5392	325	13	)	)	PUNCT
ejpam-5392	325	14	)	)	PUNCT
ejpam-5392	326	1	⊆	⊆	NUM
ejpam-5392	326	2	(	(	PUNCT
ejpam-5392	326	3	v	v	NOUN
ejpam-5392	326	4	\	\	NOUN
ejpam-5392	326	5	clλ(g))∪	clλ(g))∪	PROPN
ejpam-5392	326	6	(	(	PUNCT
ejpam-5392	326	7	w	w	NOUN
ejpam-5392	326	8	\	\	ADJ
ejpam-5392	326	9	clλ(h	clλ(h	NOUN
ejpam-5392	326	10	)	)	PUNCT
ejpam-5392	326	11	)	)	PUNCT
ejpam-5392	327	1	∈	∈	PROPN
ejpam-5392	327	2	l	l	NOUN
ejpam-5392	328	1	and	and	CCONJ
ejpam-5392	328	2	so	so	ADV
ejpam-5392	328	3	(	(	PUNCT
ejpam-5392	328	4	(	(	PUNCT
ejpam-5392	328	5	v	v	NOUN
ejpam-5392	328	6	∪w	∪w	PROPN
ejpam-5392	328	7	)	)	PUNCT
ejpam-5392	328	8	\	\	PROPN
ejpam-5392	329	1	clλ(z	clλ(z	PROPN
ejpam-5392	329	2	)	)	PUNCT
ejpam-5392	329	3	)	)	PUNCT
ejpam-5392	330	1	⊆	⊆	NUM
ejpam-5392	330	2	(	(	PUNCT
ejpam-5392	330	3	v	v	NOUN
ejpam-5392	330	4	\	\	PROPN
ejpam-5392	330	5	clλ(g	clλ(g	PROPN
ejpam-5392	330	6	)	)	PUNCT
ejpam-5392	330	7	)	)	PUNCT
ejpam-5392	330	8	∪	∪	ADP
ejpam-5392	330	9	(	(	PUNCT
ejpam-5392	330	10	w	w	NOUN
ejpam-5392	330	11	\	\	ADJ
ejpam-5392	330	12	clλ(h	clλ(h	NOUN
ejpam-5392	330	13	)	)	PUNCT
ejpam-5392	330	14	)	)	PUNCT
ejpam-5392	331	1	∈	∈	PROPN
ejpam-5392	331	2	l.	l.	PROPN
ejpam-5392	331	3	hence	hence	ADV
ejpam-5392	331	4	,	,	PUNCT
ejpam-5392	331	5	v	v	PROPN
ejpam-5392	331	6	∪w	∪w	NUM
ejpam-5392	331	7	is	be	AUX
ejpam-5392	331	8	an	an	DET
ejpam-5392	331	9	l	l	NOUN
ejpam-5392	331	10	-	-	PUNCT
ejpam-5392	331	11	θβλ	θβλ	NOUN
ejpam-5392	331	12	-	-	PUNCT
ejpam-5392	331	13	open	open	ADJ
ejpam-5392	331	14	subset	subset	NOUN
ejpam-5392	331	15	.	.	PUNCT
ejpam-5392	332	1	m.	m.	PROPN
ejpam-5392	332	2	hosny	hosny	PROPN
ejpam-5392	332	3	,	,	PUNCT
ejpam-5392	332	4	t.m	t.m	PROPN
ejpam-5392	332	5	.	.	PROPN
ejpam-5392	332	6	al	al	PROPN
ejpam-5392	332	7	-	-	PUNCT
ejpam-5392	332	8	shami	shami	PROPN
ejpam-5392	332	9	/	/	PUNCT
ejpam-5392	332	10	eur	eur	PROPN
ejpam-5392	332	11	.	.	PUNCT
ejpam-5392	333	1	j.	j.	PROPN
ejpam-5392	333	2	pure	pure	PROPN
ejpam-5392	333	3	appl	appl	PROPN
ejpam-5392	333	4	.	.	PROPN
ejpam-5392	333	5	math	math	PROPN
ejpam-5392	333	6	,	,	PUNCT
ejpam-5392	333	7	17	17	NUM
ejpam-5392	333	8	(	(	PUNCT
ejpam-5392	333	9	4	4	NUM
ejpam-5392	333	10	)	)	PUNCT
ejpam-5392	333	11	(	(	PUNCT
ejpam-5392	333	12	2024	2024	NUM
ejpam-5392	333	13	)	)	PUNCT
ejpam-5392	333	14	,	,	PUNCT
ejpam-5392	333	15	3436	3436	NUM
ejpam-5392	333	16	-	-	SYM
ejpam-5392	333	17	3463	3463	NUM
ejpam-5392	333	18	3447	3447	NUM
ejpam-5392	333	19	in	in	ADP
ejpam-5392	333	20	algorithm	algorithm	NOUN
ejpam-5392	333	21	1	1	NUM
ejpam-5392	333	22	,	,	PUNCT
ejpam-5392	333	23	we	we	PRON
ejpam-5392	333	24	present	present	VERB
ejpam-5392	333	25	the	the	DET
ejpam-5392	333	26	steps	step	NOUN
ejpam-5392	333	27	to	to	PART
ejpam-5392	333	28	calculate	calculate	VERB
ejpam-5392	333	29	the	the	DET
ejpam-5392	333	30	family	family	NOUN
ejpam-5392	333	31	of	of	ADP
ejpam-5392	333	32	l	l	PROPN
ejpam-5392	333	33	-	-	PUNCT
ejpam-5392	333	34	θβλ	θβλ	NOUN
ejpam-5392	333	35	-	-	PUNCT
ejpam-5392	333	36	open	open	ADJ
ejpam-5392	333	37	subsets	subset	NOUN
ejpam-5392	333	38	.	.	PUNCT
ejpam-5392	334	1	input	input	NOUN
ejpam-5392	334	2	:	:	PUNCT
ejpam-5392	334	3	the	the	DET
ejpam-5392	334	4	universal	universal	ADJ
ejpam-5392	334	5	set	set	NOUN
ejpam-5392	334	6	x	x	NOUN
ejpam-5392	334	7	,	,	PUNCT
ejpam-5392	334	8	a	a	DET
ejpam-5392	334	9	relation	relation	NOUN
ejpam-5392	334	10	r	r	NOUN
ejpam-5392	334	11	,	,	PUNCT
ejpam-5392	334	12	and	and	CCONJ
ejpam-5392	334	13	an	an	DET
ejpam-5392	334	14	ideal	ideal	ADJ
ejpam-5392	334	15	l	l	NOUN
ejpam-5392	334	16	under	under	ADP
ejpam-5392	334	17	consideration	consideration	NOUN
ejpam-5392	334	18	.	.	PUNCT
ejpam-5392	335	1	output	output	NOUN
ejpam-5392	335	2	:	:	PUNCT
ejpam-5392	335	3	the	the	DET
ejpam-5392	335	4	family	family	NOUN
ejpam-5392	335	5	of	of	ADP
ejpam-5392	335	6	l	l	PROPN
ejpam-5392	335	7	-	-	PUNCT
ejpam-5392	335	8	θβλ	θβλ	NOUN
ejpam-5392	335	9	-	-	PUNCT
ejpam-5392	335	10	open	open	ADJ
ejpam-5392	335	11	subsets	subset	NOUN
ejpam-5392	335	12	.	.	PUNCT
ejpam-5392	336	1	1	1	NUM
ejpam-5392	336	2	ask	ask	VERB
ejpam-5392	336	3	the	the	DET
ejpam-5392	336	4	the	the	DET
ejpam-5392	336	5	expert(s	expert(s	NOUN
ejpam-5392	336	6	)	)	PUNCT
ejpam-5392	336	7	to	to	PART
ejpam-5392	336	8	give	give	VERB
ejpam-5392	336	9	a	a	DET
ejpam-5392	336	10	relation	relation	NOUN
ejpam-5392	336	11	l	l	NOUN
ejpam-5392	336	12	over	over	ADP
ejpam-5392	336	13	x	x	SYM
ejpam-5392	336	14	;	;	PUNCT
ejpam-5392	336	15	2	2	NUM
ejpam-5392	336	16	choose	choose	VERB
ejpam-5392	336	17	a	a	DET
ejpam-5392	336	18	λ	λ	NOUN
ejpam-5392	336	19	type	type	NOUN
ejpam-5392	336	20	;	;	PUNCT
ejpam-5392	336	21	3	3	NUM
ejpam-5392	336	22	for	for	ADP
ejpam-5392	336	23	every	every	DET
ejpam-5392	336	24	y	y	PROPN
ejpam-5392	336	25	∈	∈	PROPN
ejpam-5392	336	26	x	x	PRON
ejpam-5392	336	27	do	do	VERB
ejpam-5392	336	28	4	4	NUM
ejpam-5392	336	29	compute	compute	NOUN
ejpam-5392	336	30	gλ(y	gλ(y	NUM
ejpam-5392	336	31	)	)	PUNCT
ejpam-5392	336	32	5	5	NUM
ejpam-5392	336	33	end	end	NOUN
ejpam-5392	336	34	6	6	NUM
ejpam-5392	336	35	construct	construct	VERB
ejpam-5392	336	36	a	a	DET
ejpam-5392	336	37	topology	topology	NOUN
ejpam-5392	336	38	ϑλ	ϑλ	ADP
ejpam-5392	336	39	=	=	PUNCT
ejpam-5392	336	40	{	{	PUNCT
ejpam-5392	336	41	v	v	ADP
ejpam-5392	336	42	⊆	⊆	NUM
ejpam-5392	336	43	x	x	SYM
ejpam-5392	336	44	:	:	PUNCT
ejpam-5392	336	45	∀y	∀y	NUM
ejpam-5392	336	46	∈	∈	PROPN
ejpam-5392	336	47	v	v	NOUN
ejpam-5392	336	48	,	,	PUNCT
ejpam-5392	336	49	gλ(y	gλ(y	NUM
ejpam-5392	336	50	)	)	PUNCT
ejpam-5392	336	51	⊆	⊆	NUM
ejpam-5392	336	52	v	v	NOUN
ejpam-5392	336	53	}	}	PUNCT
ejpam-5392	336	54	on	on	ADP
ejpam-5392	336	55	x	x	SYM
ejpam-5392	336	56	;	;	PUNCT
ejpam-5392	336	57	7	7	NUM
ejpam-5392	336	58	initiate	initiate	NOUN
ejpam-5392	336	59	c1	c1	PROPN
ejpam-5392	336	60	=	=	PUNCT
ejpam-5392	336	61	{	{	PUNCT
ejpam-5392	336	62	clλ(v	clλ(v	PROPN
ejpam-5392	336	63	)	)	PUNCT
ejpam-5392	336	64	:	:	PUNCT
ejpam-5392	336	65	v	v	X
ejpam-5392	336	66	∈	∈	NOUN
ejpam-5392	336	67	ϑλ	ϑλ	ADP
ejpam-5392	336	68	}	}	PUNCT
ejpam-5392	336	69	;	;	PUNCT
ejpam-5392	336	70	8	8	NUM
ejpam-5392	336	71	construct	construct	VERB
ejpam-5392	336	72	a	a	DET
ejpam-5392	336	73	θ	θ	NOUN
ejpam-5392	336	74	-	-	PUNCT
ejpam-5392	336	75	topology	topology	NOUN
ejpam-5392	336	76	ϑθλ	ϑθλ	NOUN
ejpam-5392	336	77	=	=	PUNCT
ejpam-5392	336	78	{	{	PUNCT
ejpam-5392	336	79	v	v	NOUN
ejpam-5392	336	80	∈	∈	NOUN
ejpam-5392	336	81	ϑλ	ϑλ	ADP
ejpam-5392	336	82	:	:	PUNCT
ejpam-5392	336	83	intθλ(v	intθλ(v	PROPN
ejpam-5392	336	84	)	)	PUNCT
ejpam-5392	336	85	=	=	SYM
ejpam-5392	336	86	v	v	NOUN
ejpam-5392	336	87	}	}	PUNCT
ejpam-5392	336	88	;	;	PUNCT
ejpam-5392	336	89	9	9	NUM
ejpam-5392	336	90	define	define	VERB
ejpam-5392	336	91	f	f	PROPN
ejpam-5392	336	92	=	=	SYM
ejpam-5392	336	93	p	p	X
ejpam-5392	336	94	(	(	PUNCT
ejpam-5392	336	95	x	x	NOUN
ejpam-5392	336	96	)	)	PUNCT
ejpam-5392	336	97	\	\	PUNCT
ejpam-5392	336	98	ϑλ	ϑλ	ADP
ejpam-5392	336	99	;	;	PUNCT
ejpam-5392	336	100	10	10	NUM
ejpam-5392	336	101	initiate	initiate	VERB
ejpam-5392	336	102	c2	c2	PROPN
ejpam-5392	336	103	=	=	PUNCT
ejpam-5392	336	104	{	{	PUNCT
ejpam-5392	336	105	clθλ(w	clθλ(w	NOUN
ejpam-5392	336	106	)	)	PUNCT
ejpam-5392	336	107	:	:	PUNCT
ejpam-5392	336	108	w	w	X
ejpam-5392	336	109	∈	∈	PROPN
ejpam-5392	336	110	f	f	X
ejpam-5392	336	111	}	}	PUNCT
ejpam-5392	336	112	;	;	PUNCT
ejpam-5392	336	113	11	11	NUM
ejpam-5392	336	114	ask	ask	VERB
ejpam-5392	336	115	the	the	DET
ejpam-5392	336	116	the	the	DET
ejpam-5392	336	117	expert(s	expert(s	NOUN
ejpam-5392	336	118	)	)	PUNCT
ejpam-5392	336	119	to	to	PART
ejpam-5392	336	120	give	give	VERB
ejpam-5392	336	121	an	an	DET
ejpam-5392	336	122	ideal	ideal	ADJ
ejpam-5392	336	123	l	l	NOUN
ejpam-5392	336	124	over	over	ADP
ejpam-5392	336	125	x	x	SYM
ejpam-5392	336	126	;	;	PUNCT
ejpam-5392	336	127	12	12	NUM
ejpam-5392	336	128	for	for	ADP
ejpam-5392	336	129	every	every	DET
ejpam-5392	336	130	w	w	PROPN
ejpam-5392	336	131	∈	∈	PROPN
ejpam-5392	336	132	f	f	X
ejpam-5392	336	133	do	do	VERB
ejpam-5392	336	134	13	13	NUM
ejpam-5392	336	135	if	if	SCONJ
ejpam-5392	336	136	∃	∃	PROPN
ejpam-5392	336	137	v	v	PROPN
ejpam-5392	336	138	∈	∈	PROPN
ejpam-5392	336	139	ϑλ	ϑλ	ADP
ejpam-5392	336	140	s.t	s.t	PROPN
ejpam-5392	336	141	.	.	PUNCT
ejpam-5392	337	1	(	(	PUNCT
ejpam-5392	337	2	w	w	NOUN
ejpam-5392	337	3	\	\	ADJ
ejpam-5392	337	4	clλ(v	clλ(v	PROPN
ejpam-5392	337	5	)	)	PUNCT
ejpam-5392	337	6	)	)	PUNCT
ejpam-5392	338	1	∈	∈	PROPN
ejpam-5392	338	2	l	l	NOUN
ejpam-5392	338	3	and	and	CCONJ
ejpam-5392	338	4	(	(	PUNCT
ejpam-5392	338	5	v	v	NOUN
ejpam-5392	338	6	\	\	PROPN
ejpam-5392	338	7	clθλ(w	clθλ(w	NOUN
ejpam-5392	338	8	)	)	PUNCT
ejpam-5392	338	9	)	)	PUNCT
ejpam-5392	339	1	∈	∈	PROPN
ejpam-5392	340	1	l	l	NOUN
ejpam-5392	340	2	then	then	ADV
ejpam-5392	340	3	14	14	NUM
ejpam-5392	340	4	w	w	NOUN
ejpam-5392	340	5	is	be	AUX
ejpam-5392	340	6	an	an	DET
ejpam-5392	340	7	l	l	NOUN
ejpam-5392	340	8	-	-	PUNCT
ejpam-5392	340	9	θβλ	θβλ	NOUN
ejpam-5392	340	10	-	-	PUNCT
ejpam-5392	340	11	open	open	ADJ
ejpam-5392	340	12	set	set	NOUN
ejpam-5392	340	13	;	;	PUNCT
ejpam-5392	340	14	15	15	NUM
ejpam-5392	340	15	w	w	PROPN
ejpam-5392	340	16	∈	∈	PROPN
ejpam-5392	340	17	f∗	f∗	NOUN
ejpam-5392	340	18	16	16	NUM
ejpam-5392	340	19	else	else	ADV
ejpam-5392	340	20	17	17	NUM
ejpam-5392	340	21	w	w	NOUN
ejpam-5392	340	22	is	be	AUX
ejpam-5392	340	23	not	not	PART
ejpam-5392	340	24	an	an	DET
ejpam-5392	340	25	l	l	NOUN
ejpam-5392	340	26	-	-	PUNCT
ejpam-5392	340	27	θβλ	θβλ	NOUN
ejpam-5392	340	28	-	-	PUNCT
ejpam-5392	340	29	open	open	NOUN
ejpam-5392	340	30	set	set	VERB
ejpam-5392	340	31	18	18	NUM
ejpam-5392	340	32	end	end	NOUN
ejpam-5392	340	33	19	19	NUM
ejpam-5392	340	34	end	end	NOUN
ejpam-5392	340	35	20	20	NUM
ejpam-5392	340	36	l	l	NOUN
ejpam-5392	340	37	-	-	PUNCT
ejpam-5392	340	38	θβλo(x	θβλo(x	NOUN
ejpam-5392	340	39	)	)	PUNCT
ejpam-5392	340	40	=	=	PUNCT
ejpam-5392	340	41	ϑλ	ϑλ	ADP
ejpam-5392	340	42	∪	∪	ADP
ejpam-5392	340	43	f∗.	f∗.	NOUN
ejpam-5392	340	44	algorithm	algorithm	NOUN
ejpam-5392	340	45	1	1	NUM
ejpam-5392	340	46	:	:	PUNCT
ejpam-5392	340	47	determination	determination	NOUN
ejpam-5392	340	48	of	of	ADP
ejpam-5392	340	49	the	the	DET
ejpam-5392	340	50	family	family	NOUN
ejpam-5392	340	51	of	of	ADP
ejpam-5392	340	52	l	l	PROPN
ejpam-5392	340	53	-	-	PUNCT
ejpam-5392	340	54	θβλ	θβλ	NOUN
ejpam-5392	340	55	-	-	PUNCT
ejpam-5392	340	56	open	open	ADJ
ejpam-5392	340	57	subsets	subset	NOUN
ejpam-5392	340	58	4	4	NUM
ejpam-5392	340	59	.	.	PUNCT
ejpam-5392	340	60	approximations	approximation	NOUN
ejpam-5392	340	61	spaces	space	VERB
ejpam-5392	340	62	by	by	ADP
ejpam-5392	340	63	using	use	VERB
ejpam-5392	340	64	l	l	NOUN
ejpam-5392	340	65	-	-	PUNCT
ejpam-5392	340	66	θβλ	θβλ	NOUN
ejpam-5392	340	67	-	-	PUNCT
ejpam-5392	340	68	open	open	ADJ
ejpam-5392	340	69	sets	set	NOUN
ejpam-5392	340	70	herein	herein	NOUN
ejpam-5392	340	71	,	,	PUNCT
ejpam-5392	340	72	we	we	PRON
ejpam-5392	340	73	establish	establish	VERB
ejpam-5392	340	74	novel	novel	ADJ
ejpam-5392	340	75	rough	rough	ADJ
ejpam-5392	340	76	paradigms	paradigm	NOUN
ejpam-5392	340	77	inspired	inspire	VERB
ejpam-5392	340	78	by	by	ADP
ejpam-5392	340	79	the	the	DET
ejpam-5392	340	80	family	family	NOUN
ejpam-5392	340	81	of	of	ADP
ejpam-5392	340	82	l	l	PROPN
ejpam-5392	340	83	-	-	PUNCT
ejpam-5392	340	84	θβλ	θβλ	NOUN
ejpam-5392	340	85	-	-	PUNCT
ejpam-5392	340	86	open	open	ADJ
ejpam-5392	340	87	sets	set	NOUN
ejpam-5392	340	88	.	.	PUNCT
ejpam-5392	341	1	we	we	PRON
ejpam-5392	341	2	focus	focus	VERB
ejpam-5392	341	3	on	on	ADP
ejpam-5392	341	4	the	the	DET
ejpam-5392	341	5	role	role	NOUN
ejpam-5392	341	6	of	of	ADP
ejpam-5392	341	7	the	the	DET
ejpam-5392	341	8	proposed	propose	VERB
ejpam-5392	341	9	rough	rough	ADJ
ejpam-5392	341	10	paradigms	paradigm	NOUN
ejpam-5392	341	11	in	in	ADP
ejpam-5392	341	12	developing	develop	VERB
ejpam-5392	341	13	decision	decision	NOUN
ejpam-5392	341	14	-	-	PUNCT
ejpam-5392	341	15	making	make	VERB
ejpam-5392	341	16	methods	method	NOUN
ejpam-5392	341	17	through	through	ADP
ejpam-5392	341	18	the	the	DET
ejpam-5392	341	19	preservation	preservation	NOUN
ejpam-5392	341	20	of	of	ADP
ejpam-5392	341	21	most	most	ADJ
ejpam-5392	341	22	properties	property	NOUN
ejpam-5392	341	23	of	of	ADP
ejpam-5392	341	24	the	the	DET
ejpam-5392	341	25	standard	standard	ADJ
ejpam-5392	341	26	model	model	NOUN
ejpam-5392	341	27	given	give	VERB
ejpam-5392	341	28	by	by	ADP
ejpam-5392	341	29	pawlak	pawlak	ADJ
ejpam-5392	341	30	and	and	CCONJ
ejpam-5392	341	31	heighten	heighten	VERB
ejpam-5392	341	32	the	the	DET
ejpam-5392	341	33	accuracy	accuracy	NOUN
ejpam-5392	341	34	measures	measure	NOUN
ejpam-5392	341	35	of	of	ADP
ejpam-5392	341	36	extracted	extract	VERB
ejpam-5392	341	37	knowledge	knowledge	NOUN
ejpam-5392	341	38	compared	compare	VERB
ejpam-5392	341	39	to	to	ADP
ejpam-5392	341	40	paradigms	paradigm	NOUN
ejpam-5392	341	41	studied	study	VERB
ejpam-5392	341	42	in	in	ADP
ejpam-5392	341	43	the	the	DET
ejpam-5392	341	44	literature	literature	NOUN
ejpam-5392	341	45	.	.	PUNCT
ejpam-5392	342	1	additionally	additionally	ADV
ejpam-5392	342	2	,	,	PUNCT
ejpam-5392	342	3	we	we	PRON
ejpam-5392	342	4	make	make	VERB
ejpam-5392	342	5	comparisons	comparison	NOUN
ejpam-5392	342	6	between	between	ADP
ejpam-5392	342	7	the	the	DET
ejpam-5392	342	8	proposed	propose	VERB
ejpam-5392	342	9	models	model	NOUN
ejpam-5392	342	10	for	for	ADP
ejpam-5392	342	11	all	all	DET
ejpam-5392	342	12	cases	case	NOUN
ejpam-5392	342	13	of	of	ADP
ejpam-5392	342	14	λ	λ	PROPN
ejpam-5392	342	15	with	with	ADP
ejpam-5392	342	16	the	the	DET
ejpam-5392	342	17	assistance	assistance	NOUN
ejpam-5392	342	18	of	of	ADP
ejpam-5392	342	19	counterexamples	counterexample	NOUN
ejpam-5392	342	20	.	.	PUNCT
ejpam-5392	343	1	definition	definition	NOUN
ejpam-5392	343	2	18	18	NUM
ejpam-5392	343	3	.	.	PUNCT
ejpam-5392	344	1	let	let	VERB
ejpam-5392	344	2	v	v	PART
ejpam-5392	344	3	be	be	AUX
ejpam-5392	344	4	a	a	DET
ejpam-5392	344	5	subset	subset	NOUN
ejpam-5392	344	6	of	of	ADP
ejpam-5392	344	7	an	an	DET
ejpam-5392	344	8	l	l	NOUN
ejpam-5392	344	9	−	−	NOUN
ejpam-5392	344	10	gλ	gλ	NOUN
ejpam-5392	344	11	-	-	PUNCT
ejpam-5392	344	12	space	space	NOUN
ejpam-5392	344	13	(	(	PUNCT
ejpam-5392	344	14	x	x	NOUN
ejpam-5392	344	15	,	,	PUNCT
ejpam-5392	344	16	r	r	NOUN
ejpam-5392	344	17	,	,	PUNCT
ejpam-5392	344	18	ξλ	ξλ	NOUN
ejpam-5392	344	19	,	,	PUNCT
ejpam-5392	344	20	l	l	NOUN
ejpam-5392	344	21	)	)	PUNCT
ejpam-5392	344	22	.	.	PUNCT
ejpam-5392	345	1	we	we	PRON
ejpam-5392	345	2	respectively	respectively	ADV
ejpam-5392	345	3	define	define	VERB
ejpam-5392	345	4	the	the	DET
ejpam-5392	345	5	l	l	NOUN
ejpam-5392	345	6	-	-	PUNCT
ejpam-5392	345	7	θβλ	θβλ	NOUN
ejpam-5392	345	8	-	-	PUNCT
ejpam-5392	345	9	lower	low	ADJ
ejpam-5392	345	10	,	,	PUNCT
ejpam-5392	345	11	l	l	NOUN
ejpam-5392	345	12	-	-	PUNCT
ejpam-5392	345	13	θβλ	θβλ	NOUN
ejpam-5392	345	14	-	-	PUNCT
ejpam-5392	345	15	upper	upper	ADJ
ejpam-5392	345	16	approximations	approximation	NOUN
ejpam-5392	345	17	,	,	PUNCT
ejpam-5392	345	18	l	l	NOUN
ejpam-5392	345	19	-	-	PUNCT
ejpam-5392	345	20	θβλ	θβλ	NOUN
ejpam-5392	345	21	-	-	PUNCT
ejpam-5392	345	22	boundary	boundary	ADJ
ejpam-5392	345	23	regions	region	NOUN
ejpam-5392	345	24	and	and	CCONJ
ejpam-5392	345	25	l	l	NOUN
ejpam-5392	345	26	-	-	NOUN
ejpam-5392	345	27	θβλaccuracy	θβλaccuracy	NOUN
ejpam-5392	345	28	of	of	ADP
ejpam-5392	345	29	v	v	NOUN
ejpam-5392	345	30	as	as	SCONJ
ejpam-5392	345	31	follows	follow	VERB
ejpam-5392	345	32	:	:	PUNCT
ejpam-5392	345	33	rl−θβ	rl−θβ	PROPN
ejpam-5392	345	34	λ	λ	PROPN
ejpam-5392	345	35	(	(	PUNCT
ejpam-5392	345	36	v	v	NOUN
ejpam-5392	345	37	)	)	PUNCT
ejpam-5392	345	38	=	=	PUNCT
ejpam-5392	345	39	∪{g	∪{g	PROPN
ejpam-5392	345	40	∈	∈	PROPN
ejpam-5392	345	41	l	l	PROPN
ejpam-5392	345	42	-	-	PUNCT
ejpam-5392	345	43	θβλo(x	θβλo(x	NOUN
ejpam-5392	345	44	)	)	PUNCT
ejpam-5392	345	45	:	:	PUNCT
ejpam-5392	345	46	g	g	PROPN
ejpam-5392	345	47	⊆	⊆	NUM
ejpam-5392	345	48	a	a	DET
ejpam-5392	345	49	}	}	PUNCT
ejpam-5392	345	50	=	=	SYM
ejpam-5392	345	51	l	l	NOUN
ejpam-5392	345	52	-	-	PUNCT
ejpam-5392	345	53	θβλ	θβλ	NOUN
ejpam-5392	345	54	-	-	PUNCT
ejpam-5392	345	55	interior	interior	NOUN
ejpam-5392	345	56	of	of	ADP
ejpam-5392	345	57	v	v	NOUN
ejpam-5392	345	58	.	.	PUNCT
ejpam-5392	346	1	rl−θβ	rl−θβ	PROPN
ejpam-5392	346	2	λ	λ	PROPN
ejpam-5392	346	3	(	(	PUNCT
ejpam-5392	346	4	v	v	NOUN
ejpam-5392	346	5	)	)	PUNCT
ejpam-5392	346	6	=	=	VERB
ejpam-5392	346	7	∩{h	∩{h	PUNCT
ejpam-5392	346	8	∈	∈	PROPN
ejpam-5392	346	9	l	l	NOUN
ejpam-5392	346	10	-	-	NOUN
ejpam-5392	346	11	θβλc(x	θβλc(x	NOUN
ejpam-5392	346	12	)	)	PUNCT
ejpam-5392	346	13	:	:	PUNCT
ejpam-5392	346	14	v	v	ADP
ejpam-5392	346	15	⊆	⊆	NUM
ejpam-5392	346	16	h	h	NOUN
ejpam-5392	346	17	}	}	PUNCT
ejpam-5392	346	18	=	=	SYM
ejpam-5392	346	19	l	l	NOUN
ejpam-5392	346	20	-	-	PUNCT
ejpam-5392	346	21	θβλ	θβλ	NOUN
ejpam-5392	346	22	-	-	PUNCT
ejpam-5392	346	23	closure	closure	NOUN
ejpam-5392	346	24	of	of	ADP
ejpam-5392	346	25	v	v	NOUN
ejpam-5392	346	26	.	.	PUNCT
ejpam-5392	347	1	bndl−θβ	bndl−θβ	PROPN
ejpam-5392	348	1	λ	λ	INTJ
ejpam-5392	348	2	(	(	PUNCT
ejpam-5392	348	3	v	v	NOUN
ejpam-5392	348	4	)	)	PUNCT
ejpam-5392	348	5	=	=	SYM
ejpam-5392	348	6	rl−θβ	rl−θβ	PROPN
ejpam-5392	348	7	λ	λ	PROPN
ejpam-5392	348	8	(	(	PUNCT
ejpam-5392	348	9	v	v	NOUN
ejpam-5392	348	10	)	)	PUNCT
ejpam-5392	348	11	−rl−θβ	−rl−θβ	PROPN
ejpam-5392	348	12	λ	λ	PROPN
ejpam-5392	348	13	(	(	PUNCT
ejpam-5392	348	14	v	v	NOUN
ejpam-5392	348	15	)	)	PUNCT
ejpam-5392	348	16	.	.	PUNCT
ejpam-5392	349	1	accl−θβ	accl−θβ	PROPN
ejpam-5392	349	2	λ	λ	PROPN
ejpam-5392	349	3	(	(	PUNCT
ejpam-5392	349	4	v	v	NOUN
ejpam-5392	349	5	)	)	PUNCT
ejpam-5392	349	6	=	=	PUNCT
ejpam-5392	350	1	|rl−θβ	|rl−θβ	PROPN
ejpam-5392	350	2	λ	λ	PROPN
ejpam-5392	350	3	(	(	PUNCT
ejpam-5392	350	4	v	v	NOUN
ejpam-5392	350	5	)	)	PUNCT
ejpam-5392	350	6	|	|	ADV
ejpam-5392	350	7	|rl−θβ	|rl−θβ	PROPN
ejpam-5392	350	8	λ	λ	PROPN
ejpam-5392	350	9	(	(	PUNCT
ejpam-5392	350	10	v	v	NOUN
ejpam-5392	350	11	)	)	PUNCT
ejpam-5392	350	12	|	|	ADV
ejpam-5392	350	13	,	,	PUNCT
ejpam-5392	350	14	where	where	SCONJ
ejpam-5392	350	15	|rl−θβ	|rl−θβ	PROPN
ejpam-5392	350	16	λ	λ	PROPN
ejpam-5392	350	17	(	(	PUNCT
ejpam-5392	350	18	v	v	NOUN
ejpam-5392	350	19	)	)	PUNCT
ejpam-5392	350	20	|	|	ADV
ejpam-5392	350	21	=	=	NOUN
ejpam-5392	350	22	̸	̸	NUM
ejpam-5392	350	23	0	0	NUM
ejpam-5392	350	24	.	.	PUNCT
ejpam-5392	350	25	m.	m.	PROPN
ejpam-5392	350	26	hosny	hosny	PROPN
ejpam-5392	350	27	,	,	PUNCT
ejpam-5392	350	28	t.m	t.m	PROPN
ejpam-5392	350	29	.	.	PROPN
ejpam-5392	350	30	al	al	PROPN
ejpam-5392	350	31	-	-	PUNCT
ejpam-5392	350	32	shami	shami	PROPN
ejpam-5392	350	33	/	/	PUNCT
ejpam-5392	350	34	eur	eur	PROPN
ejpam-5392	350	35	.	.	PUNCT
ejpam-5392	351	1	j.	j.	PROPN
ejpam-5392	351	2	pure	pure	PROPN
ejpam-5392	351	3	appl	appl	PROPN
ejpam-5392	351	4	.	.	PROPN
ejpam-5392	351	5	math	math	PROPN
ejpam-5392	351	6	,	,	PUNCT
ejpam-5392	351	7	17	17	NUM
ejpam-5392	351	8	(	(	PUNCT
ejpam-5392	351	9	4	4	NUM
ejpam-5392	351	10	)	)	PUNCT
ejpam-5392	351	11	(	(	PUNCT
ejpam-5392	351	12	2024	2024	NUM
ejpam-5392	351	13	)	)	PUNCT
ejpam-5392	351	14	,	,	PUNCT
ejpam-5392	351	15	3436	3436	NUM
ejpam-5392	351	16	-	-	SYM
ejpam-5392	351	17	3463	3463	NUM
ejpam-5392	351	18	3448	3448	NUM
ejpam-5392	351	19	proposition	proposition	NOUN
ejpam-5392	351	20	8	8	NUM
ejpam-5392	351	21	.	.	PUNCT
ejpam-5392	352	1	let	let	VERB
ejpam-5392	352	2	v	v	NOUN
ejpam-5392	352	3	,	,	PUNCT
ejpam-5392	352	4	w	w	PROPN
ejpam-5392	352	5	be	be	VERB
ejpam-5392	352	6	subsets	subset	NOUN
ejpam-5392	352	7	of	of	ADP
ejpam-5392	352	8	an	an	DET
ejpam-5392	352	9	l	l	NOUN
ejpam-5392	352	10	−gλ	−gλ	NOUN
ejpam-5392	352	11	-	-	PUNCT
ejpam-5392	352	12	space	space	NOUN
ejpam-5392	352	13	(	(	PUNCT
ejpam-5392	352	14	x	x	NOUN
ejpam-5392	352	15	,	,	PUNCT
ejpam-5392	352	16	r	r	NOUN
ejpam-5392	352	17	,	,	PUNCT
ejpam-5392	352	18	ξλ	ξλ	NOUN
ejpam-5392	352	19	,	,	PUNCT
ejpam-5392	352	20	l	l	NOUN
ejpam-5392	352	21	)	)	PUNCT
ejpam-5392	352	22	.	.	PUNCT
ejpam-5392	353	1	then	then	ADV
ejpam-5392	353	2	,	,	PUNCT
ejpam-5392	353	3	(	(	PUNCT
ejpam-5392	353	4	i	i	NOUN
ejpam-5392	353	5	)	)	PUNCT
ejpam-5392	353	6	rl−θβ	rl−θβ	PROPN
ejpam-5392	353	7	λ	λ	PROPN
ejpam-5392	353	8	(	(	PUNCT
ejpam-5392	353	9	v	v	NOUN
ejpam-5392	353	10	)	)	PUNCT
ejpam-5392	353	11	⊆	⊆	NUM
ejpam-5392	353	12	v	v	ADP
ejpam-5392	353	13	⊆	⊆	NUM
ejpam-5392	353	14	rl−θβ	rl−θβ	PROPN
ejpam-5392	353	15	λ	λ	PROPN
ejpam-5392	353	16	(	(	PUNCT
ejpam-5392	353	17	v	v	NOUN
ejpam-5392	353	18	)	)	PUNCT
ejpam-5392	353	19	equality	equality	NOUN
ejpam-5392	353	20	hold	hold	VERB
ejpam-5392	353	21	if	if	SCONJ
ejpam-5392	353	22	v	v	NOUN
ejpam-5392	353	23	=	=	NOUN
ejpam-5392	353	24	∅	∅	NOUN
ejpam-5392	353	25	or	or	CCONJ
ejpam-5392	353	26	x.	x.	NOUN
ejpam-5392	353	27	(	(	PUNCT
ejpam-5392	353	28	ii	ii	PROPN
ejpam-5392	353	29	)	)	PUNCT
ejpam-5392	353	30	v	v	ADP
ejpam-5392	353	31	⊆w	⊆w	NOUN
ejpam-5392	353	32	⇒	⇒	NOUN
ejpam-5392	353	33	rl−θβ	rl−θβ	PROPN
ejpam-5392	353	34	λ	λ	PROPN
ejpam-5392	353	35	(	(	PUNCT
ejpam-5392	353	36	v	v	NOUN
ejpam-5392	353	37	)	)	PUNCT
ejpam-5392	353	38	⊆	⊆	NUM
ejpam-5392	353	39	rl−θβ	rl−θβ	PROPN
ejpam-5392	353	40	λ	λ	PROPN
ejpam-5392	353	41	(	(	PUNCT
ejpam-5392	353	42	w	w	PROPN
ejpam-5392	353	43	)	)	PUNCT
ejpam-5392	353	44	.	.	PUNCT
ejpam-5392	354	1	(	(	PUNCT
ejpam-5392	354	2	iii	iii	X
ejpam-5392	354	3	)	)	PUNCT
ejpam-5392	354	4	v	v	NOUN
ejpam-5392	354	5	⊆w	⊆w	NOUN
ejpam-5392	354	6	⇒	⇒	NOUN
ejpam-5392	354	7	rl−θβ	rl−θβ	PROPN
ejpam-5392	354	8	λ	λ	PROPN
ejpam-5392	354	9	(	(	PUNCT
ejpam-5392	354	10	v	v	NOUN
ejpam-5392	354	11	)	)	PUNCT
ejpam-5392	354	12	⊆	⊆	NUM
ejpam-5392	354	13	rl−θβ	rl−θβ	PROPN
ejpam-5392	354	14	λ	λ	PROPN
ejpam-5392	354	15	(	(	PUNCT
ejpam-5392	354	16	w	w	PROPN
ejpam-5392	354	17	)	)	PUNCT
ejpam-5392	354	18	.	.	PUNCT
ejpam-5392	355	1	(	(	PUNCT
ejpam-5392	355	2	iv	iv	X
ejpam-5392	355	3	)	)	PUNCT
ejpam-5392	355	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	355	5	λ	λ	PROPN
ejpam-5392	355	6	(	(	PUNCT
ejpam-5392	355	7	v	v	NOUN
ejpam-5392	355	8	∩w	∩w	NOUN
ejpam-5392	355	9	)	)	PUNCT
ejpam-5392	356	1	⊆	⊆	NUM
ejpam-5392	356	2	rl−θβ	rl−θβ	PROPN
ejpam-5392	356	3	λ	λ	PROPN
ejpam-5392	356	4	(	(	PUNCT
ejpam-5392	356	5	v	v	NOUN
ejpam-5392	356	6	)	)	PUNCT
ejpam-5392	356	7	∩rl−θβ	∩rl−θβ	NUM
ejpam-5392	356	8	λ	λ	INTJ
ejpam-5392	356	9	(	(	PUNCT
ejpam-5392	356	10	w	w	PROPN
ejpam-5392	356	11	)	)	PUNCT
ejpam-5392	356	12	.	.	PUNCT
ejpam-5392	357	1	(	(	PUNCT
ejpam-5392	357	2	v	v	NOUN
ejpam-5392	357	3	)	)	PUNCT
ejpam-5392	357	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	357	5	λ	λ	PROPN
ejpam-5392	357	6	(	(	PUNCT
ejpam-5392	357	7	v	v	NOUN
ejpam-5392	357	8	∪w	∪w	PROPN
ejpam-5392	357	9	)	)	PUNCT
ejpam-5392	358	1	⊇	⊇	PROPN
ejpam-5392	358	2	rl−θβ	rl−θβ	PROPN
ejpam-5392	358	3	λ	λ	PROPN
ejpam-5392	358	4	(	(	PUNCT
ejpam-5392	358	5	v	v	NOUN
ejpam-5392	358	6	)	)	PUNCT
ejpam-5392	358	7	∪rl−θβ	∪rl−θβ	NUM
ejpam-5392	359	1	λ	λ	INTJ
ejpam-5392	359	2	(	(	PUNCT
ejpam-5392	359	3	w	w	PROPN
ejpam-5392	359	4	)	)	PUNCT
ejpam-5392	359	5	.	.	PUNCT
ejpam-5392	360	1	(	(	PUNCT
ejpam-5392	360	2	vi	vi	NOUN
ejpam-5392	360	3	)	)	PUNCT
ejpam-5392	360	4	rl−θβ	rl−θβ	NOUN
ejpam-5392	360	5	λ	λ	PROPN
ejpam-5392	360	6	(	(	PUNCT
ejpam-5392	360	7	v	v	NOUN
ejpam-5392	360	8	∪w	∪w	PROPN
ejpam-5392	360	9	)	)	PUNCT
ejpam-5392	360	10	⊇	⊇	PROPN
ejpam-5392	360	11	rl−θβ	rl−θβ	PROPN
ejpam-5392	360	12	λ	λ	PROPN
ejpam-5392	360	13	(	(	PUNCT
ejpam-5392	360	14	v	v	NOUN
ejpam-5392	360	15	)	)	PUNCT
ejpam-5392	360	16	∪rl−θβ	∪rl−θβ	NUM
ejpam-5392	361	1	λ	λ	INTJ
ejpam-5392	361	2	(	(	PUNCT
ejpam-5392	361	3	w	w	PROPN
ejpam-5392	361	4	)	)	PUNCT
ejpam-5392	361	5	.	.	PUNCT
ejpam-5392	362	1	(	(	PUNCT
ejpam-5392	362	2	vii	vii	PROPN
ejpam-5392	362	3	)	)	PUNCT
ejpam-5392	362	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	362	5	λ	λ	PROPN
ejpam-5392	362	6	(	(	PUNCT
ejpam-5392	362	7	v	v	NOUN
ejpam-5392	362	8	∩w	∩w	NOUN
ejpam-5392	362	9	)	)	PUNCT
ejpam-5392	363	1	⊆	⊆	NUM
ejpam-5392	363	2	rl−θβ	rl−θβ	PROPN
ejpam-5392	363	3	λ	λ	PROPN
ejpam-5392	363	4	(	(	PUNCT
ejpam-5392	363	5	v	v	NOUN
ejpam-5392	363	6	)	)	PUNCT
ejpam-5392	363	7	∩rl−θβ	∩rl−θβ	NUM
ejpam-5392	363	8	λ	λ	INTJ
ejpam-5392	363	9	(	(	PUNCT
ejpam-5392	363	10	w	w	PROPN
ejpam-5392	363	11	)	)	PUNCT
ejpam-5392	363	12	.	.	PUNCT
ejpam-5392	364	1	(	(	PUNCT
ejpam-5392	364	2	viii	viii	NOUN
ejpam-5392	364	3	)	)	PUNCT
ejpam-5392	364	4	rl−θβ	rl−θβ	NOUN
ejpam-5392	364	5	λ	λ	PROPN
ejpam-5392	364	6	(	(	PUNCT
ejpam-5392	364	7	v	v	NOUN
ejpam-5392	364	8	)	)	PUNCT
ejpam-5392	364	9	=	=	SYM
ejpam-5392	365	1	(	(	PUNCT
ejpam-5392	365	2	rl−θβ	rl−θβ	PROPN
ejpam-5392	365	3	λ	λ	PROPN
ejpam-5392	365	4	(	(	PUNCT
ejpam-5392	365	5	v	v	NOUN
ejpam-5392	365	6	′	′	NUM
ejpam-5392	365	7	)	)	PUNCT
ejpam-5392	365	8	)	)	PUNCT
ejpam-5392	366	1	′	′	NOUN
ejpam-5392	366	2	,	,	PUNCT
ejpam-5392	366	3	rl−θβ	rl−θβ	PROPN
ejpam-5392	366	4	λ	λ	PROPN
ejpam-5392	366	5	(	(	PUNCT
ejpam-5392	366	6	v	v	NOUN
ejpam-5392	366	7	)	)	PUNCT
ejpam-5392	366	8	=	=	SYM
ejpam-5392	367	1	(	(	PUNCT
ejpam-5392	367	2	rl−θβ	rl−θβ	PROPN
ejpam-5392	367	3	λ	λ	PROPN
ejpam-5392	367	4	(	(	PUNCT
ejpam-5392	367	5	v	v	NOUN
ejpam-5392	367	6	′	′	NUM
ejpam-5392	367	7	)	)	PUNCT
ejpam-5392	367	8	)	)	PUNCT
ejpam-5392	368	1	′	′	X
ejpam-5392	368	2	.	.	PUNCT
ejpam-5392	369	1	(	(	PUNCT
ejpam-5392	369	2	ix	ix	ADJ
ejpam-5392	369	3	)	)	PUNCT
ejpam-5392	369	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	369	5	λ	λ	PROPN
ejpam-5392	369	6	(	(	PUNCT
ejpam-5392	369	7	rl−θβ	rl−θβ	PROPN
ejpam-5392	369	8	λ	λ	PROPN
ejpam-5392	369	9	(	(	PUNCT
ejpam-5392	369	10	v	v	NOUN
ejpam-5392	369	11	)	)	PUNCT
ejpam-5392	369	12	)	)	PUNCT
ejpam-5392	370	1	=	=	PUNCT
ejpam-5392	370	2	rl−θβ	rl−θβ	PROPN
ejpam-5392	370	3	λ	λ	PROPN
ejpam-5392	370	4	(	(	PUNCT
ejpam-5392	370	5	v	v	NOUN
ejpam-5392	370	6	)	)	PUNCT
ejpam-5392	370	7	.	.	PUNCT
ejpam-5392	371	1	(	(	PUNCT
ejpam-5392	371	2	x	x	X
ejpam-5392	371	3	)	)	PUNCT
ejpam-5392	371	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	371	5	λ	λ	PROPN
ejpam-5392	371	6	(	(	PUNCT
ejpam-5392	371	7	rl−θβ	rl−θβ	PROPN
ejpam-5392	371	8	λ	λ	PROPN
ejpam-5392	371	9	(	(	PUNCT
ejpam-5392	371	10	v	v	NOUN
ejpam-5392	371	11	)	)	PUNCT
ejpam-5392	371	12	)	)	PUNCT
ejpam-5392	372	1	=	=	PUNCT
ejpam-5392	372	2	rl−θβ	rl−θβ	PROPN
ejpam-5392	372	3	λ	λ	PROPN
ejpam-5392	372	4	(	(	PUNCT
ejpam-5392	372	5	v	v	NOUN
ejpam-5392	372	6	)	)	PUNCT
ejpam-5392	372	7	.	.	PUNCT
ejpam-5392	373	1	(	(	PUNCT
ejpam-5392	373	2	xi	xi	X
ejpam-5392	373	3	)	)	PUNCT
ejpam-5392	373	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	373	5	λ	λ	PROPN
ejpam-5392	373	6	(	(	PUNCT
ejpam-5392	373	7	rl−θβ	rl−θβ	PROPN
ejpam-5392	373	8	λ	λ	PROPN
ejpam-5392	373	9	(	(	PUNCT
ejpam-5392	373	10	v	v	NOUN
ejpam-5392	373	11	)	)	PUNCT
ejpam-5392	373	12	)	)	PUNCT
ejpam-5392	374	1	⊆	⊆	NUM
ejpam-5392	374	2	rl−θβ	rl−θβ	PROPN
ejpam-5392	374	3	λ	λ	PROPN
ejpam-5392	374	4	(	(	PUNCT
ejpam-5392	374	5	rl−θβ	rl−θβ	PROPN
ejpam-5392	374	6	λ	λ	PROPN
ejpam-5392	374	7	(	(	PUNCT
ejpam-5392	374	8	v	v	NOUN
ejpam-5392	374	9	)	)	PUNCT
ejpam-5392	374	10	)	)	PUNCT
ejpam-5392	374	11	.	.	PUNCT
ejpam-5392	375	1	(	(	PUNCT
ejpam-5392	375	2	xii	xii	NOUN
ejpam-5392	375	3	)	)	PUNCT
ejpam-5392	376	1	rl−θβ	rl−θβ	PROPN
ejpam-5392	376	2	λ	λ	PROPN
ejpam-5392	376	3	(	(	PUNCT
ejpam-5392	376	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	376	5	λ	λ	PROPN
ejpam-5392	376	6	(	(	PUNCT
ejpam-5392	376	7	v	v	NOUN
ejpam-5392	376	8	)	)	PUNCT
ejpam-5392	376	9	)	)	PUNCT
ejpam-5392	377	1	⊆	⊆	NUM
ejpam-5392	377	2	rl−θβ	rl−θβ	PROPN
ejpam-5392	377	3	λ	λ	PROPN
ejpam-5392	377	4	(	(	PUNCT
ejpam-5392	377	5	rl−θβ	rl−θβ	PROPN
ejpam-5392	377	6	λ	λ	PROPN
ejpam-5392	377	7	(	(	PUNCT
ejpam-5392	377	8	v	v	NOUN
ejpam-5392	377	9	)	)	PUNCT
ejpam-5392	377	10	)	)	PUNCT
ejpam-5392	377	11	.	.	PUNCT
ejpam-5392	378	1	proof	proof	NOUN
ejpam-5392	378	2	.	.	PUNCT
ejpam-5392	379	1	the	the	DET
ejpam-5392	379	2	proof	proof	NOUN
ejpam-5392	379	3	is	be	AUX
ejpam-5392	379	4	warranted	warrant	VERB
ejpam-5392	379	5	by	by	ADP
ejpam-5392	379	6	using	use	VERB
ejpam-5392	379	7	the	the	DET
ejpam-5392	379	8	properties	property	NOUN
ejpam-5392	379	9	of	of	ADP
ejpam-5392	379	10	l	l	NOUN
ejpam-5392	379	11	-	-	PUNCT
ejpam-5392	379	12	θβλ	θβλ	NOUN
ejpam-5392	379	13	-	-	PUNCT
ejpam-5392	379	14	interior	interior	ADJ
ejpam-5392	379	15	and	and	CCONJ
ejpam-5392	379	16	l	l	ADJ
ejpam-5392	379	17	-	-	PUNCT
ejpam-5392	379	18	θβλclosure	θβλclosure	NOUN
ejpam-5392	379	19	operators	operator	NOUN
ejpam-5392	379	20	.	.	PUNCT
ejpam-5392	380	1	definition	definition	NOUN
ejpam-5392	380	2	19	19	NUM
ejpam-5392	380	3	.	.	PUNCT
ejpam-5392	381	1	a	a	DET
ejpam-5392	381	2	subset	subset	NOUN
ejpam-5392	381	3	v	v	NOUN
ejpam-5392	381	4	of	of	ADP
ejpam-5392	381	5	an	an	DET
ejpam-5392	381	6	l−gλ	l−gλ	ADJ
ejpam-5392	381	7	-	-	PUNCT
ejpam-5392	381	8	space	space	NOUN
ejpam-5392	381	9	(	(	PUNCT
ejpam-5392	381	10	x	x	NOUN
ejpam-5392	381	11	,	,	PUNCT
ejpam-5392	381	12	r	r	NOUN
ejpam-5392	381	13	,	,	PUNCT
ejpam-5392	381	14	ξλ	ξλ	NOUN
ejpam-5392	381	15	,	,	PUNCT
ejpam-5392	381	16	l	l	NOUN
ejpam-5392	381	17	)	)	PUNCT
ejpam-5392	381	18	is	be	AUX
ejpam-5392	381	19	named	name	VERB
ejpam-5392	381	20	an	an	PRON
ejpam-5392	381	21	l	l	NOUN
ejpam-5392	381	22	-	-	PUNCT
ejpam-5392	381	23	θβλ	θβλ	NOUN
ejpam-5392	381	24	-	-	PUNCT
ejpam-5392	381	25	definable	definable	ADJ
ejpam-5392	381	26	(	(	PUNCT
ejpam-5392	381	27	an	an	DET
ejpam-5392	381	28	l	l	NOUN
ejpam-5392	381	29	-	-	PUNCT
ejpam-5392	381	30	θβλ	θβλ	NOUN
ejpam-5392	381	31	-	-	PUNCT
ejpam-5392	381	32	exact	exact	NOUN
ejpam-5392	381	33	)	)	PUNCT
ejpam-5392	381	34	set	set	VERB
ejpam-5392	381	35	if	if	SCONJ
ejpam-5392	381	36	rl−θβ	rl−θβ	PROPN
ejpam-5392	381	37	λ	λ	PROPN
ejpam-5392	381	38	(	(	PUNCT
ejpam-5392	381	39	v	v	NOUN
ejpam-5392	381	40	)	)	PUNCT
ejpam-5392	382	1	=	=	SYM
ejpam-5392	382	2	rl−θβ	rl−θβ	PROPN
ejpam-5392	382	3	λ	λ	PROPN
ejpam-5392	382	4	(	(	PUNCT
ejpam-5392	382	5	v	v	NOUN
ejpam-5392	382	6	)	)	PUNCT
ejpam-5392	382	7	.	.	PUNCT
ejpam-5392	383	1	otherwise	otherwise	ADV
ejpam-5392	383	2	,	,	PUNCT
ejpam-5392	383	3	v	v	NOUN
ejpam-5392	383	4	is	be	AUX
ejpam-5392	383	5	an	an	DET
ejpam-5392	383	6	l	l	NOUN
ejpam-5392	383	7	-	-	PUNCT
ejpam-5392	383	8	θβλ	θβλ	NOUN
ejpam-5392	383	9	-	-	PUNCT
ejpam-5392	383	10	rough	rough	ADJ
ejpam-5392	383	11	set	set	NOUN
ejpam-5392	383	12	.	.	PUNCT
ejpam-5392	384	1	in	in	ADP
ejpam-5392	384	2	example	example	NOUN
ejpam-5392	384	3	1	1	NUM
ejpam-5392	384	4	v	v	NOUN
ejpam-5392	384	5	=	=	PUNCT
ejpam-5392	384	6	{	{	PUNCT
ejpam-5392	384	7	y3	y3	NOUN
ejpam-5392	384	8	}	}	PUNCT
ejpam-5392	384	9	is	be	AUX
ejpam-5392	384	10	l	l	NOUN
ejpam-5392	384	11	-	-	ADJ
ejpam-5392	384	12	θβa	θβa	NOUN
ejpam-5392	384	13	-	-	PUNCT
ejpam-5392	384	14	exact	exact	ADJ
ejpam-5392	384	15	.	.	PUNCT
ejpam-5392	385	1	to	to	PART
ejpam-5392	385	2	articulate	articulate	VERB
ejpam-5392	385	3	the	the	DET
ejpam-5392	385	4	relationships	relationship	NOUN
ejpam-5392	385	5	between	between	ADP
ejpam-5392	385	6	the	the	DET
ejpam-5392	385	7	present	present	ADJ
ejpam-5392	385	8	rough	rough	ADJ
ejpam-5392	385	9	paradigms	paradigm	NOUN
ejpam-5392	385	10	(	(	PUNCT
ejpam-5392	385	11	definition	definition	NOUN
ejpam-5392	385	12	18	18	NUM
ejpam-5392	385	13	)	)	PUNCT
ejpam-5392	385	14	and	and	CCONJ
ejpam-5392	385	15	those	those	PRON
ejpam-5392	385	16	given	give	VERB
ejpam-5392	385	17	in	in	ADP
ejpam-5392	385	18	definition	definition	NOUN
ejpam-5392	385	19	9	9	NUM
ejpam-5392	385	20	[	[	X
ejpam-5392	385	21	22	22	NUM
ejpam-5392	385	22	,	,	PUNCT
ejpam-5392	385	23	23	23	NUM
ejpam-5392	385	24	]	]	PUNCT
ejpam-5392	385	25	,	,	PUNCT
ejpam-5392	385	26	we	we	PRON
ejpam-5392	385	27	provide	provide	VERB
ejpam-5392	385	28	the	the	DET
ejpam-5392	385	29	next	next	ADJ
ejpam-5392	385	30	two	two	NUM
ejpam-5392	385	31	results	result	NOUN
ejpam-5392	385	32	.	.	PUNCT
ejpam-5392	386	1	theorem	theorem	ADJ
ejpam-5392	386	2	4	4	NUM
ejpam-5392	386	3	.	.	PUNCT
ejpam-5392	387	1	let	let	VERB
ejpam-5392	387	2	v	v	PART
ejpam-5392	387	3	be	be	AUX
ejpam-5392	387	4	a	a	DET
ejpam-5392	387	5	subset	subset	NOUN
ejpam-5392	387	6	of	of	ADP
ejpam-5392	387	7	an	an	DET
ejpam-5392	387	8	l	l	NOUN
ejpam-5392	387	9	−gλ	−gλ	NOUN
ejpam-5392	387	10	-	-	PUNCT
ejpam-5392	387	11	space	space	NOUN
ejpam-5392	387	12	(	(	PUNCT
ejpam-5392	387	13	x	x	NOUN
ejpam-5392	387	14	,	,	PUNCT
ejpam-5392	387	15	r	r	NOUN
ejpam-5392	387	16	,	,	PUNCT
ejpam-5392	387	17	ξλ	ξλ	NOUN
ejpam-5392	387	18	,	,	PUNCT
ejpam-5392	387	19	l	l	NOUN
ejpam-5392	387	20	)	)	PUNCT
ejpam-5392	387	21	.	.	PUNCT
ejpam-5392	388	1	then	then	ADV
ejpam-5392	388	2	:	:	PUNCT
ejpam-5392	388	3	(	(	PUNCT
ejpam-5392	388	4	i	i	NOUN
ejpam-5392	388	5	)	)	PUNCT
ejpam-5392	388	6	rl−p	rl−p	PROPN
ejpam-5392	388	7	λ	λ	PROPN
ejpam-5392	388	8	(	(	PUNCT
ejpam-5392	388	9	v	v	NOUN
ejpam-5392	388	10	)	)	PUNCT
ejpam-5392	388	11	⊆	⊆	NUM
ejpam-5392	388	12	rl−β	rl−β	NOUN
ejpam-5392	388	13	λ	λ	PROPN
ejpam-5392	388	14	(	(	PUNCT
ejpam-5392	388	15	v	v	NOUN
ejpam-5392	388	16	)	)	PUNCT
ejpam-5392	388	17	⊆	⊆	NUM
ejpam-5392	388	18	rl−δβ	rl−δβ	X
ejpam-5392	389	1	λ	λ	INTJ
ejpam-5392	389	2	(	(	PUNCT
ejpam-5392	389	3	v	v	NOUN
ejpam-5392	389	4	)	)	PUNCT
ejpam-5392	389	5	⊆	⊆	NUM
ejpam-5392	389	6	rl−θβ	rl−θβ	PROPN
ejpam-5392	389	7	λ	λ	PROPN
ejpam-5392	389	8	(	(	PUNCT
ejpam-5392	389	9	v	v	NOUN
ejpam-5392	389	10	)	)	PUNCT
ejpam-5392	389	11	.	.	PUNCT
ejpam-5392	390	1	(	(	PUNCT
ejpam-5392	390	2	ii	ii	NOUN
ejpam-5392	390	3	)	)	PUNCT
ejpam-5392	390	4	rl−α	rl−α	PROPN
ejpam-5392	390	5	λ	λ	PROPN
ejpam-5392	390	6	(	(	PUNCT
ejpam-5392	390	7	v	v	NOUN
ejpam-5392	390	8	)	)	PUNCT
ejpam-5392	390	9	⊆	⊆	NUM
ejpam-5392	390	10	rl−s	rl−s	PROPN
ejpam-5392	390	11	λ	λ	PROPN
ejpam-5392	390	12	(	(	PUNCT
ejpam-5392	390	13	v	v	NOUN
ejpam-5392	390	14	)	)	PUNCT
ejpam-5392	390	15	⊆	⊆	NUM
ejpam-5392	390	16	rl−β	rl−β	NOUN
ejpam-5392	390	17	λ	λ	PROPN
ejpam-5392	390	18	(	(	PUNCT
ejpam-5392	390	19	v	v	NOUN
ejpam-5392	390	20	)	)	PUNCT
ejpam-5392	390	21	⊆	⊆	NUM
ejpam-5392	390	22	rl−δβ	rl−δβ	X
ejpam-5392	391	1	λ	λ	INTJ
ejpam-5392	391	2	(	(	PUNCT
ejpam-5392	391	3	v	v	NOUN
ejpam-5392	391	4	)	)	PUNCT
ejpam-5392	391	5	⊆	⊆	NUM
ejpam-5392	391	6	rl−θβ	rl−θβ	PROPN
ejpam-5392	391	7	λ	λ	PROPN
ejpam-5392	391	8	(	(	PUNCT
ejpam-5392	391	9	v	v	NOUN
ejpam-5392	391	10	)	)	PUNCT
ejpam-5392	391	11	.	.	PUNCT
ejpam-5392	392	1	(	(	PUNCT
ejpam-5392	392	2	iii	iii	X
ejpam-5392	392	3	)	)	PUNCT
ejpam-5392	392	4	rl−p	rl−p	NOUN
ejpam-5392	392	5	λ	λ	PROPN
ejpam-5392	392	6	(	(	PUNCT
ejpam-5392	392	7	v	v	NOUN
ejpam-5392	392	8	)	)	PUNCT
ejpam-5392	392	9	⊆	⊆	NUM
ejpam-5392	392	10	rl−β	rl−β	NOUN
ejpam-5392	392	11	λ	λ	PROPN
ejpam-5392	392	12	(	(	PUNCT
ejpam-5392	392	13	v	v	NOUN
ejpam-5392	392	14	)	)	PUNCT
ejpam-5392	392	15	⊆	⊆	NUM
ejpam-5392	392	16	rl−	rl−	PROPN
ejpam-5392	392	17	∧	∧	NOUN
ejpam-5392	392	18	βλ(v	βλ(v	PUNCT
ejpam-5392	392	19	)	)	PUNCT
ejpam-5392	392	20	⊆	⊆	NUM
ejpam-5392	392	21	rl−θβλ(v	rl−θβλ(v	PROPN
ejpam-5392	392	22	)	)	PUNCT
ejpam-5392	392	23	.	.	PUNCT
ejpam-5392	393	1	(	(	PUNCT
ejpam-5392	393	2	iv	iv	X
ejpam-5392	393	3	)	)	PUNCT
ejpam-5392	393	4	rl−α	rl−α	NOUN
ejpam-5392	393	5	λ	λ	PROPN
ejpam-5392	393	6	(	(	PUNCT
ejpam-5392	393	7	v	v	NOUN
ejpam-5392	393	8	)	)	PUNCT
ejpam-5392	393	9	⊆	⊆	NUM
ejpam-5392	393	10	rl−s	rl−s	PROPN
ejpam-5392	393	11	λ	λ	PROPN
ejpam-5392	393	12	(	(	PUNCT
ejpam-5392	393	13	v	v	NOUN
ejpam-5392	393	14	)	)	PUNCT
ejpam-5392	393	15	⊆	⊆	NUM
ejpam-5392	393	16	rl−β	rl−β	NOUN
ejpam-5392	393	17	λ	λ	PROPN
ejpam-5392	393	18	(	(	PUNCT
ejpam-5392	393	19	v	v	NOUN
ejpam-5392	393	20	)	)	PUNCT
ejpam-5392	393	21	⊆	⊆	NUM
ejpam-5392	393	22	rl−	rl−	PROPN
ejpam-5392	393	23	∧	∧	NOUN
ejpam-5392	393	24	βλ(v	βλ(v	PUNCT
ejpam-5392	393	25	)	)	PUNCT
ejpam-5392	393	26	⊆	⊆	NUM
ejpam-5392	393	27	rl−θβλ(v	rl−θβλ(v	PROPN
ejpam-5392	393	28	)	)	PUNCT
ejpam-5392	393	29	.	.	PUNCT
ejpam-5392	394	1	(	(	PUNCT
ejpam-5392	394	2	v	v	NOUN
ejpam-5392	394	3	)	)	PUNCT
ejpam-5392	394	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	394	5	λ	λ	PROPN
ejpam-5392	394	6	(	(	PUNCT
ejpam-5392	394	7	v	v	NOUN
ejpam-5392	394	8	)	)	PUNCT
ejpam-5392	394	9	⊆	⊆	NUM
ejpam-5392	394	10	rl−δβ	rl−δβ	X
ejpam-5392	395	1	λ	λ	INTJ
ejpam-5392	395	2	(	(	PUNCT
ejpam-5392	395	3	v	v	NOUN
ejpam-5392	395	4	)	)	PUNCT
ejpam-5392	395	5	⊆	⊆	NUM
ejpam-5392	395	6	rl−β	rl−β	NOUN
ejpam-5392	395	7	λ	λ	PROPN
ejpam-5392	395	8	(	(	PUNCT
ejpam-5392	395	9	v	v	NOUN
ejpam-5392	395	10	)	)	PUNCT
ejpam-5392	395	11	⊆	⊆	NUM
ejpam-5392	395	12	rl−p	rl−p	PROPN
ejpam-5392	395	13	λ	λ	PROPN
ejpam-5392	395	14	(	(	PUNCT
ejpam-5392	395	15	v	v	NOUN
ejpam-5392	395	16	)	)	PUNCT
ejpam-5392	395	17	.	.	PUNCT
ejpam-5392	396	1	m.	m.	PROPN
ejpam-5392	396	2	hosny	hosny	PROPN
ejpam-5392	396	3	,	,	PUNCT
ejpam-5392	396	4	t.m	t.m	PROPN
ejpam-5392	396	5	.	.	PROPN
ejpam-5392	396	6	al	al	PROPN
ejpam-5392	396	7	-	-	PUNCT
ejpam-5392	396	8	shami	shami	PROPN
ejpam-5392	396	9	/	/	PUNCT
ejpam-5392	396	10	eur	eur	PROPN
ejpam-5392	396	11	.	.	PUNCT
ejpam-5392	397	1	j.	j.	PROPN
ejpam-5392	397	2	pure	pure	PROPN
ejpam-5392	397	3	appl	appl	PROPN
ejpam-5392	397	4	.	.	PROPN
ejpam-5392	397	5	math	math	PROPN
ejpam-5392	397	6	,	,	PUNCT
ejpam-5392	397	7	17	17	NUM
ejpam-5392	397	8	(	(	PUNCT
ejpam-5392	397	9	4	4	NUM
ejpam-5392	397	10	)	)	PUNCT
ejpam-5392	397	11	(	(	PUNCT
ejpam-5392	397	12	2024	2024	NUM
ejpam-5392	397	13	)	)	PUNCT
ejpam-5392	397	14	,	,	PUNCT
ejpam-5392	397	15	3436	3436	NUM
ejpam-5392	397	16	-	-	SYM
ejpam-5392	397	17	3463	3463	NUM
ejpam-5392	397	18	3449	3449	NUM
ejpam-5392	397	19	(	(	PUNCT
ejpam-5392	397	20	vi	vi	NOUN
ejpam-5392	397	21	)	)	PUNCT
ejpam-5392	398	1	rl−θβ	rl−θβ	NOUN
ejpam-5392	398	2	λ	λ	PROPN
ejpam-5392	398	3	(	(	PUNCT
ejpam-5392	398	4	v	v	NOUN
ejpam-5392	398	5	)	)	PUNCT
ejpam-5392	398	6	⊆	⊆	NUM
ejpam-5392	398	7	rl−δβ	rl−δβ	X
ejpam-5392	399	1	λ	λ	INTJ
ejpam-5392	399	2	(	(	PUNCT
ejpam-5392	399	3	v	v	NOUN
ejpam-5392	399	4	)	)	PUNCT
ejpam-5392	399	5	⊆	⊆	NUM
ejpam-5392	399	6	rl−β	rl−β	NOUN
ejpam-5392	399	7	λ	λ	PROPN
ejpam-5392	399	8	(	(	PUNCT
ejpam-5392	399	9	v	v	NOUN
ejpam-5392	399	10	)	)	PUNCT
ejpam-5392	399	11	⊆	⊆	NUM
ejpam-5392	399	12	rl−s	rl−s	PROPN
ejpam-5392	399	13	λ	λ	PROPN
ejpam-5392	399	14	(	(	PUNCT
ejpam-5392	399	15	v	v	NOUN
ejpam-5392	399	16	)	)	PUNCT
ejpam-5392	399	17	⊆	⊆	NUM
ejpam-5392	399	18	rl−α	rl−α	PROPN
ejpam-5392	399	19	λ	λ	PROPN
ejpam-5392	399	20	(	(	PUNCT
ejpam-5392	399	21	v	v	NOUN
ejpam-5392	399	22	)	)	PUNCT
ejpam-5392	399	23	.	.	PUNCT
ejpam-5392	400	1	(	(	PUNCT
ejpam-5392	400	2	vii	vii	PROPN
ejpam-5392	400	3	)	)	PUNCT
ejpam-5392	400	4	rl−θβλ(v	rl−θβλ(v	PROPN
ejpam-5392	400	5	)	)	PUNCT
ejpam-5392	401	1	⊆	⊆	NUM
ejpam-5392	401	2	rl−	rl−	PROPN
ejpam-5392	401	3	∧	∧	NOUN
ejpam-5392	401	4	βλ(v	βλ(v	PUNCT
ejpam-5392	401	5	)	)	PUNCT
ejpam-5392	401	6	⊆	⊆	NUM
ejpam-5392	401	7	rl−β	rl−β	NOUN
ejpam-5392	401	8	λ	λ	PROPN
ejpam-5392	401	9	(	(	PUNCT
ejpam-5392	401	10	v	v	NOUN
ejpam-5392	401	11	)	)	PUNCT
ejpam-5392	401	12	⊆	⊆	NUM
ejpam-5392	401	13	rl−p	rl−p	PROPN
ejpam-5392	401	14	λ	λ	PROPN
ejpam-5392	401	15	(	(	PUNCT
ejpam-5392	401	16	v	v	NOUN
ejpam-5392	401	17	)	)	PUNCT
ejpam-5392	401	18	.	.	PUNCT
ejpam-5392	402	1	(	(	PUNCT
ejpam-5392	402	2	viii	viii	NOUN
ejpam-5392	402	3	)	)	PUNCT
ejpam-5392	402	4	rl−θβλ(v	rl−θβλ(v	PROPN
ejpam-5392	402	5	)	)	PUNCT
ejpam-5392	403	1	⊆	⊆	NUM
ejpam-5392	403	2	rl−	rl−	PROPN
ejpam-5392	403	3	∧	∧	NOUN
ejpam-5392	403	4	βλ(v	βλ(v	PUNCT
ejpam-5392	403	5	)	)	PUNCT
ejpam-5392	403	6	⊆	⊆	NUM
ejpam-5392	403	7	rl−β	rl−β	NOUN
ejpam-5392	403	8	λ	λ	PROPN
ejpam-5392	403	9	(	(	PUNCT
ejpam-5392	403	10	v	v	NOUN
ejpam-5392	403	11	)	)	PUNCT
ejpam-5392	403	12	⊆	⊆	NUM
ejpam-5392	403	13	rl−s	rl−s	PROPN
ejpam-5392	403	14	λ	λ	PROPN
ejpam-5392	403	15	(	(	PUNCT
ejpam-5392	403	16	v	v	NOUN
ejpam-5392	403	17	)	)	PUNCT
ejpam-5392	403	18	⊆	⊆	NUM
ejpam-5392	403	19	rl−α	rl−α	PROPN
ejpam-5392	403	20	λ	λ	PROPN
ejpam-5392	403	21	(	(	PUNCT
ejpam-5392	403	22	v	v	NOUN
ejpam-5392	403	23	)	)	PUNCT
ejpam-5392	403	24	.	.	PUNCT
ejpam-5392	404	1	proof	proof	NOUN
ejpam-5392	404	2	.	.	PUNCT
ejpam-5392	405	1	it	it	PRON
ejpam-5392	405	2	is	be	AUX
ejpam-5392	405	3	warranted	warrant	VERB
ejpam-5392	405	4	by	by	ADP
ejpam-5392	405	5	proposition	proposition	NOUN
ejpam-5392	405	6	3	3	NUM
ejpam-5392	405	7	.	.	PUNCT
ejpam-5392	405	8	corollary	corollary	ADJ
ejpam-5392	405	9	1	1	NUM
ejpam-5392	405	10	.	.	PUNCT
ejpam-5392	406	1	let	let	VERB
ejpam-5392	406	2	v	v	PART
ejpam-5392	406	3	be	be	AUX
ejpam-5392	406	4	a	a	DET
ejpam-5392	406	5	subset	subset	NOUN
ejpam-5392	406	6	of	of	ADP
ejpam-5392	406	7	an	an	DET
ejpam-5392	406	8	l	l	NOUN
ejpam-5392	406	9	−gλ	−gλ	NOUN
ejpam-5392	406	10	-	-	PUNCT
ejpam-5392	406	11	space	space	NOUN
ejpam-5392	406	12	(	(	PUNCT
ejpam-5392	406	13	x	x	NOUN
ejpam-5392	406	14	,	,	PUNCT
ejpam-5392	406	15	r	r	NOUN
ejpam-5392	406	16	,	,	PUNCT
ejpam-5392	406	17	ξλ	ξλ	NOUN
ejpam-5392	406	18	,	,	PUNCT
ejpam-5392	406	19	l	l	NOUN
ejpam-5392	406	20	)	)	PUNCT
ejpam-5392	406	21	.	.	PUNCT
ejpam-5392	407	1	then	then	ADV
ejpam-5392	407	2	:	:	PUNCT
ejpam-5392	407	3	(	(	PUNCT
ejpam-5392	407	4	i	i	NOUN
ejpam-5392	407	5	)	)	PUNCT
ejpam-5392	407	6	bndl−θβ	bndl−θβ	NOUN
ejpam-5392	408	1	λ	λ	INTJ
ejpam-5392	408	2	(	(	PUNCT
ejpam-5392	408	3	v	v	NOUN
ejpam-5392	408	4	)	)	PUNCT
ejpam-5392	408	5	⊆	⊆	NUM
ejpam-5392	408	6	bndl−δβ	bndl−δβ	NOUN
ejpam-5392	408	7	λ	λ	PROPN
ejpam-5392	408	8	(	(	PUNCT
ejpam-5392	408	9	v	v	NOUN
ejpam-5392	408	10	)	)	PUNCT
ejpam-5392	408	11	⊆	⊆	NUM
ejpam-5392	408	12	bndl−β	bndl−β	NOUN
ejpam-5392	408	13	λ	λ	PROPN
ejpam-5392	408	14	(	(	PUNCT
ejpam-5392	408	15	v	v	NOUN
ejpam-5392	408	16	)	)	PUNCT
ejpam-5392	408	17	⊆	⊆	NUM
ejpam-5392	408	18	bndl−p	bndl−p	X
ejpam-5392	408	19	λ	λ	PROPN
ejpam-5392	408	20	(	(	PUNCT
ejpam-5392	408	21	v	v	NOUN
ejpam-5392	408	22	)	)	PUNCT
ejpam-5392	408	23	.	.	PUNCT
ejpam-5392	409	1	(	(	PUNCT
ejpam-5392	409	2	ii	ii	NOUN
ejpam-5392	409	3	)	)	PUNCT
ejpam-5392	409	4	bndl−θβ	bndl−θβ	NOUN
ejpam-5392	410	1	λ	λ	INTJ
ejpam-5392	410	2	(	(	PUNCT
ejpam-5392	410	3	v	v	NOUN
ejpam-5392	410	4	)	)	PUNCT
ejpam-5392	410	5	⊆	⊆	NUM
ejpam-5392	410	6	bndl−δβ	bndl−δβ	NOUN
ejpam-5392	410	7	λ	λ	PROPN
ejpam-5392	410	8	(	(	PUNCT
ejpam-5392	410	9	v	v	NOUN
ejpam-5392	410	10	)	)	PUNCT
ejpam-5392	410	11	⊆	⊆	NUM
ejpam-5392	410	12	bndl−β	bndl−β	NOUN
ejpam-5392	410	13	λ	λ	PROPN
ejpam-5392	410	14	(	(	PUNCT
ejpam-5392	410	15	v	v	NOUN
ejpam-5392	410	16	)	)	PUNCT
ejpam-5392	410	17	⊆	⊆	NUM
ejpam-5392	410	18	bndl−s	bndl−s	NOUN
ejpam-5392	410	19	λ	λ	X
ejpam-5392	410	20	(	(	PUNCT
ejpam-5392	410	21	v	v	NOUN
ejpam-5392	410	22	)	)	PUNCT
ejpam-5392	410	23	⊆	⊆	NUM
ejpam-5392	410	24	bndl−α	bndl−α	PROPN
ejpam-5392	410	25	λ	λ	PROPN
ejpam-5392	410	26	(	(	PUNCT
ejpam-5392	410	27	v	v	NOUN
ejpam-5392	410	28	)	)	PUNCT
ejpam-5392	410	29	.	.	PUNCT
ejpam-5392	411	1	(	(	PUNCT
ejpam-5392	411	2	iii	iii	X
ejpam-5392	411	3	)	)	PUNCT
ejpam-5392	411	4	bndl−θβλ(v	bndl−θβλ(v	NOUN
ejpam-5392	411	5	)	)	PUNCT
ejpam-5392	412	1	⊆	⊆	NUM
ejpam-5392	412	2	bndl−	bndl−	VERB
ejpam-5392	412	3	∧	∧	NOUN
ejpam-5392	412	4	βλ(v	βλ(v	PUNCT
ejpam-5392	412	5	)	)	PUNCT
ejpam-5392	412	6	⊆	⊆	NUM
ejpam-5392	412	7	bndl−β	bndl−β	NOUN
ejpam-5392	412	8	λ	λ	PROPN
ejpam-5392	412	9	(	(	PUNCT
ejpam-5392	412	10	v	v	NOUN
ejpam-5392	412	11	)	)	PUNCT
ejpam-5392	412	12	⊆	⊆	NUM
ejpam-5392	412	13	bndl−p	bndl−p	X
ejpam-5392	412	14	λ	λ	PROPN
ejpam-5392	412	15	(	(	PUNCT
ejpam-5392	412	16	v	v	NOUN
ejpam-5392	412	17	)	)	PUNCT
ejpam-5392	412	18	.	.	PUNCT
ejpam-5392	413	1	(	(	PUNCT
ejpam-5392	413	2	iv	iv	X
ejpam-5392	413	3	)	)	PUNCT
ejpam-5392	413	4	bndl−θβλ(v	bndl−θβλ(v	NOUN
ejpam-5392	413	5	)	)	PUNCT
ejpam-5392	414	1	⊆	⊆	NUM
ejpam-5392	414	2	bndl−	bndl−	VERB
ejpam-5392	414	3	∧	∧	NOUN
ejpam-5392	414	4	βλ(v	βλ(v	PUNCT
ejpam-5392	414	5	)	)	PUNCT
ejpam-5392	414	6	⊆	⊆	NUM
ejpam-5392	414	7	bndl−β	bndl−β	NOUN
ejpam-5392	414	8	λ	λ	PROPN
ejpam-5392	414	9	(	(	PUNCT
ejpam-5392	414	10	v	v	NOUN
ejpam-5392	414	11	)	)	PUNCT
ejpam-5392	414	12	⊆	⊆	NUM
ejpam-5392	414	13	bndl−s	bndl−s	NOUN
ejpam-5392	414	14	λ	λ	X
ejpam-5392	414	15	(	(	PUNCT
ejpam-5392	414	16	v	v	NOUN
ejpam-5392	414	17	)	)	PUNCT
ejpam-5392	414	18	⊆	⊆	NUM
ejpam-5392	414	19	bndl−α	bndl−α	PROPN
ejpam-5392	414	20	λ	λ	PROPN
ejpam-5392	414	21	(	(	PUNCT
ejpam-5392	414	22	v	v	NOUN
ejpam-5392	414	23	)	)	PUNCT
ejpam-5392	414	24	.	.	PUNCT
ejpam-5392	415	1	(	(	PUNCT
ejpam-5392	415	2	v	v	NOUN
ejpam-5392	415	3	)	)	PUNCT
ejpam-5392	415	4	accl−p	accl−p	NOUN
ejpam-5392	415	5	λ	λ	PROPN
ejpam-5392	415	6	(	(	PUNCT
ejpam-5392	415	7	v	v	NOUN
ejpam-5392	415	8	)	)	PUNCT
ejpam-5392	415	9	⩽	⩽	NOUN
ejpam-5392	415	10	accl−β	accl−β	PROPN
ejpam-5392	415	11	λ	λ	PROPN
ejpam-5392	415	12	(	(	PUNCT
ejpam-5392	415	13	v	v	NOUN
ejpam-5392	415	14	)	)	PUNCT
ejpam-5392	415	15	⩽	⩽	NOUN
ejpam-5392	415	16	accl−δβ	accl−δβ	PROPN
ejpam-5392	415	17	λ	λ	PROPN
ejpam-5392	415	18	(	(	PUNCT
ejpam-5392	415	19	v	v	NOUN
ejpam-5392	415	20	)	)	PUNCT
ejpam-5392	415	21	⩽	⩽	ADJ
ejpam-5392	415	22	accl−θβ	accl−θβ	PROPN
ejpam-5392	415	23	λ	λ	PROPN
ejpam-5392	415	24	(	(	PUNCT
ejpam-5392	415	25	v	v	NOUN
ejpam-5392	415	26	)	)	PUNCT
ejpam-5392	415	27	.	.	PUNCT
ejpam-5392	416	1	(	(	PUNCT
ejpam-5392	416	2	vi	vi	X
ejpam-5392	416	3	)	)	PUNCT
ejpam-5392	416	4	accl−α	accl−α	NUM
ejpam-5392	416	5	λ	λ	PROPN
ejpam-5392	416	6	(	(	PUNCT
ejpam-5392	416	7	v	v	NOUN
ejpam-5392	416	8	)	)	PUNCT
ejpam-5392	416	9	⩽	⩽	NOUN
ejpam-5392	416	10	accl−s	accl−s	PROPN
ejpam-5392	416	11	λ	λ	PROPN
ejpam-5392	416	12	(	(	PUNCT
ejpam-5392	416	13	v	v	NOUN
ejpam-5392	416	14	)	)	PUNCT
ejpam-5392	416	15	⩽	⩽	NOUN
ejpam-5392	416	16	accl−β	accl−β	PROPN
ejpam-5392	416	17	λ	λ	PROPN
ejpam-5392	416	18	(	(	PUNCT
ejpam-5392	416	19	v	v	NOUN
ejpam-5392	416	20	)	)	PUNCT
ejpam-5392	416	21	⩽	⩽	NOUN
ejpam-5392	416	22	accl−δβ	accl−δβ	PROPN
ejpam-5392	416	23	λ	λ	PROPN
ejpam-5392	416	24	(	(	PUNCT
ejpam-5392	416	25	v	v	NOUN
ejpam-5392	416	26	)	)	PUNCT
ejpam-5392	416	27	⩽	⩽	ADJ
ejpam-5392	416	28	accl−θβ	accl−θβ	PROPN
ejpam-5392	416	29	λ	λ	PROPN
ejpam-5392	416	30	(	(	PUNCT
ejpam-5392	416	31	v	v	NOUN
ejpam-5392	416	32	)	)	PUNCT
ejpam-5392	416	33	.	.	PUNCT
ejpam-5392	417	1	(	(	PUNCT
ejpam-5392	417	2	vii	vii	PROPN
ejpam-5392	417	3	)	)	PUNCT
ejpam-5392	417	4	accl−p	accl−p	NOUN
ejpam-5392	417	5	λ	λ	PROPN
ejpam-5392	417	6	(	(	PUNCT
ejpam-5392	417	7	v	v	NOUN
ejpam-5392	417	8	)	)	PUNCT
ejpam-5392	417	9	⩽	⩽	NOUN
ejpam-5392	417	10	accl−β	accl−β	PROPN
ejpam-5392	417	11	λ	λ	PROPN
ejpam-5392	417	12	(	(	PUNCT
ejpam-5392	417	13	v	v	NOUN
ejpam-5392	417	14	)	)	PUNCT
ejpam-5392	417	15	⩽	⩽	ADJ
ejpam-5392	417	16	accl−	accl−	NOUN
ejpam-5392	417	17	∧	∧	PROPN
ejpam-5392	417	18	βλ(v	βλ(v	PUNCT
ejpam-5392	417	19	)	)	PUNCT
ejpam-5392	417	20	⩽	⩽	ADJ
ejpam-5392	417	21	accl−θβλ(v	accl−θβλ(v	ADP
ejpam-5392	417	22	)	)	PUNCT
ejpam-5392	417	23	.	.	PUNCT
ejpam-5392	418	1	(	(	PUNCT
ejpam-5392	418	2	viii	viii	NOUN
ejpam-5392	418	3	)	)	PUNCT
ejpam-5392	418	4	accl−α	accl−α	NUM
ejpam-5392	418	5	λ	λ	PROPN
ejpam-5392	418	6	(	(	PUNCT
ejpam-5392	418	7	v	v	NOUN
ejpam-5392	418	8	)	)	PUNCT
ejpam-5392	418	9	⩽	⩽	NOUN
ejpam-5392	418	10	accl−s	accl−s	PROPN
ejpam-5392	418	11	λ	λ	PROPN
ejpam-5392	418	12	(	(	PUNCT
ejpam-5392	418	13	v	v	NOUN
ejpam-5392	418	14	)	)	PUNCT
ejpam-5392	418	15	⩽	⩽	NOUN
ejpam-5392	418	16	accl−β	accl−β	PROPN
ejpam-5392	418	17	λ	λ	PROPN
ejpam-5392	418	18	(	(	PUNCT
ejpam-5392	418	19	v	v	NOUN
ejpam-5392	418	20	)	)	PUNCT
ejpam-5392	418	21	⩽	⩽	ADJ
ejpam-5392	418	22	accl−	accl−	NOUN
ejpam-5392	418	23	∧	∧	PROPN
ejpam-5392	418	24	βλ(v	βλ(v	PUNCT
ejpam-5392	418	25	)	)	PUNCT
ejpam-5392	418	26	⩽	⩽	ADJ
ejpam-5392	418	27	accl−θβλ(v	accl−θβλ(v	ADP
ejpam-5392	418	28	)	)	PUNCT
ejpam-5392	418	29	.	.	PUNCT
ejpam-5392	419	1	remark	remark	PROPN
ejpam-5392	419	2	2	2	NUM
ejpam-5392	419	3	.	.	PUNCT
ejpam-5392	420	1	by	by	ADP
ejpam-5392	420	2	example	example	NOUN
ejpam-5392	420	3	1	1	NUM
ejpam-5392	420	4	,	,	PUNCT
ejpam-5392	420	5	we	we	PRON
ejpam-5392	420	6	will	will	AUX
ejpam-5392	420	7	illustrate	illustrate	VERB
ejpam-5392	420	8	that	that	SCONJ
ejpam-5392	420	9	the	the	DET
ejpam-5392	420	10	converse	converse	NOUN
ejpam-5392	420	11	of	of	ADP
ejpam-5392	420	12	the	the	DET
ejpam-5392	420	13	implications	implication	NOUN
ejpam-5392	420	14	in	in	ADP
ejpam-5392	420	15	theorem	theorem	ADJ
ejpam-5392	420	16	4	4	NUM
ejpam-5392	420	17	and	and	CCONJ
ejpam-5392	420	18	corollary	corollary	ADJ
ejpam-5392	420	19	1	1	NUM
ejpam-5392	420	20	is	be	AUX
ejpam-5392	420	21	not	not	PART
ejpam-5392	420	22	always	always	ADV
ejpam-5392	420	23	true	true	ADJ
ejpam-5392	420	24	as	as	SCONJ
ejpam-5392	420	25	follows	follow	VERB
ejpam-5392	420	26	.	.	PUNCT
ejpam-5392	421	1	(	(	PUNCT
ejpam-5392	421	2	i	i	NOUN
ejpam-5392	421	3	)	)	PUNCT
ejpam-5392	421	4	if	if	SCONJ
ejpam-5392	421	5	v	v	NUM
ejpam-5392	421	6	=	=	SYM
ejpam-5392	421	7	{	{	PUNCT
ejpam-5392	421	8	y5	y5	NOUN
ejpam-5392	421	9	}	}	PUNCT
ejpam-5392	421	10	,	,	PUNCT
ejpam-5392	421	11	then	then	ADV
ejpam-5392	421	12	rl−θβ	rl−θβ	PROPN
ejpam-5392	421	13	a	a	DET
ejpam-5392	421	14	(	(	PUNCT
ejpam-5392	421	15	v	v	NOUN
ejpam-5392	421	16	)	)	PUNCT
ejpam-5392	421	17	=	=	SYM
ejpam-5392	421	18	a	a	PRON
ejpam-5392	421	19	,	,	PUNCT
ejpam-5392	421	20	rl−θβ	rl−θβ	PROPN
ejpam-5392	421	21	a	a	DET
ejpam-5392	421	22	(	(	PUNCT
ejpam-5392	421	23	v	v	NOUN
ejpam-5392	421	24	)	)	PUNCT
ejpam-5392	421	25	=	=	SYM
ejpam-5392	422	1	a	a	PROPN
ejpam-5392	422	2	,	,	PUNCT
ejpam-5392	422	3	bndl−θβ	bndl−θβ	PROPN
ejpam-5392	422	4	a	a	DET
ejpam-5392	422	5	(	(	PUNCT
ejpam-5392	422	6	v	v	NOUN
ejpam-5392	422	7	)	)	PUNCT
ejpam-5392	422	8	=	=	NOUN
ejpam-5392	423	1	∅	∅	NOUN
ejpam-5392	423	2	,	,	PUNCT
ejpam-5392	423	3	accl−θβ	accl−θβ	NOUN
ejpam-5392	423	4	a	a	DET
ejpam-5392	423	5	(	(	PUNCT
ejpam-5392	423	6	v	v	NOUN
ejpam-5392	423	7	)	)	PUNCT
ejpam-5392	423	8	=	=	SYM
ejpam-5392	423	9	1	1	NUM
ejpam-5392	423	10	,	,	PUNCT
ejpam-5392	423	11	and	and	CCONJ
ejpam-5392	423	12	rl−δβ	rl−δβ	PROPN
ejpam-5392	423	13	a	a	DET
ejpam-5392	423	14	(	(	PUNCT
ejpam-5392	423	15	v	v	NOUN
ejpam-5392	423	16	)	)	PUNCT
ejpam-5392	423	17	=	=	PUNCT
ejpam-5392	424	1	∅,rl−δβ	∅,rl−δβ	PROPN
ejpam-5392	424	2	a	a	DET
ejpam-5392	424	3	(	(	PUNCT
ejpam-5392	424	4	v	v	NOUN
ejpam-5392	424	5	)	)	PUNCT
ejpam-5392	424	6	=	=	SYM
ejpam-5392	424	7	a	a	PROPN
ejpam-5392	424	8	,	,	PUNCT
ejpam-5392	424	9	bndl−δβ	bndl−δβ	VERB
ejpam-5392	424	10	a	a	DET
ejpam-5392	424	11	(	(	PUNCT
ejpam-5392	424	12	v	v	NOUN
ejpam-5392	424	13	)	)	PUNCT
ejpam-5392	424	14	=	=	SYM
ejpam-5392	425	1	a	a	PRON
ejpam-5392	425	2	,	,	PUNCT
ejpam-5392	425	3	accl−δβ	accl−δβ	PROPN
ejpam-5392	425	4	a	a	DET
ejpam-5392	425	5	(	(	PUNCT
ejpam-5392	425	6	v	v	NOUN
ejpam-5392	425	7	)	)	PUNCT
ejpam-5392	425	8	=	=	SYM
ejpam-5392	426	1	0	0	X
ejpam-5392	426	2	.	.	PUNCT
ejpam-5392	426	3	(	(	PUNCT
ejpam-5392	426	4	ii	ii	NOUN
ejpam-5392	426	5	)	)	PUNCT
ejpam-5392	426	6	if	if	SCONJ
ejpam-5392	426	7	v	v	NOUN
ejpam-5392	426	8	=	=	SYM
ejpam-5392	426	9	{	{	PUNCT
ejpam-5392	426	10	y	y	NOUN
ejpam-5392	426	11	}	}	PUNCT
ejpam-5392	426	12	,	,	PUNCT
ejpam-5392	426	13	then	then	ADV
ejpam-5392	426	14	rl−θβ	rl−θβ	PROPN
ejpam-5392	426	15	a	a	DET
ejpam-5392	426	16	(	(	PUNCT
ejpam-5392	426	17	v	v	NOUN
ejpam-5392	426	18	)	)	PUNCT
ejpam-5392	426	19	=	=	SYM
ejpam-5392	426	20	a	a	PRON
ejpam-5392	426	21	,	,	PUNCT
ejpam-5392	426	22	rl−θβ	rl−θβ	PROPN
ejpam-5392	426	23	a	a	DET
ejpam-5392	426	24	(	(	PUNCT
ejpam-5392	426	25	v	v	NOUN
ejpam-5392	426	26	)	)	PUNCT
ejpam-5392	426	27	=	=	PUNCT
ejpam-5392	426	28	a	a	PRON
ejpam-5392	426	29	,	,	PUNCT
ejpam-5392	426	30	bndl−θβ	bndl−θβ	PROPN
ejpam-5392	426	31	a	a	DET
ejpam-5392	426	32	(	(	PUNCT
ejpam-5392	426	33	v	v	NOUN
ejpam-5392	426	34	)	)	PUNCT
ejpam-5392	426	35	=	=	NOUN
ejpam-5392	426	36	∅	∅	NOUN
ejpam-5392	426	37	,	,	PUNCT
ejpam-5392	426	38	accl−θβ	accl−θβ	NOUN
ejpam-5392	426	39	a	a	DET
ejpam-5392	426	40	(	(	PUNCT
ejpam-5392	426	41	v	v	NOUN
ejpam-5392	426	42	)	)	PUNCT
ejpam-5392	426	43	=	=	SYM
ejpam-5392	426	44	1	1	NUM
ejpam-5392	426	45	,	,	PUNCT
ejpam-5392	426	46	and	and	CCONJ
ejpam-5392	426	47	rl−	rl−	PROPN
ejpam-5392	426	48	∧	∧	PROPN
ejpam-5392	426	49	βa(v	βa(v	PUNCT
ejpam-5392	426	50	)	)	PUNCT
ejpam-5392	426	51	=	=	SYM
ejpam-5392	426	52	∅,rl−	∅,rl−	NOUN
ejpam-5392	426	53	∧	∧	PROPN
ejpam-5392	426	54	βa(v	βa(v	PUNCT
ejpam-5392	426	55	)	)	PUNCT
ejpam-5392	426	56	=	=	SYM
ejpam-5392	426	57	a	a	PRON
ejpam-5392	426	58	,	,	PUNCT
ejpam-5392	426	59	bndl−	bndl−	VERB
ejpam-5392	426	60	∧	∧	NOUN
ejpam-5392	426	61	βa(v	βa(v	PUNCT
ejpam-5392	426	62	)	)	PUNCT
ejpam-5392	426	63	=	=	SYM
ejpam-5392	426	64	a	a	PRON
ejpam-5392	426	65	,	,	PUNCT
ejpam-5392	426	66	accl−	accl−	NOUN
ejpam-5392	426	67	∧	∧	PROPN
ejpam-5392	426	68	βa(v	βa(v	PUNCT
ejpam-5392	426	69	)	)	PUNCT
ejpam-5392	426	70	=	=	SYM
ejpam-5392	426	71	0	0	X
ejpam-5392	426	72	.	.	PUNCT
ejpam-5392	426	73	corollary	corollary	ADJ
ejpam-5392	426	74	2	2	NUM
ejpam-5392	426	75	.	.	PUNCT
ejpam-5392	426	76	let	let	VERB
ejpam-5392	426	77	v	v	PART
ejpam-5392	426	78	be	be	AUX
ejpam-5392	426	79	a	a	DET
ejpam-5392	426	80	subset	subset	NOUN
ejpam-5392	426	81	of	of	ADP
ejpam-5392	426	82	an	an	DET
ejpam-5392	426	83	l	l	NOUN
ejpam-5392	426	84	−gλ	−gλ	NOUN
ejpam-5392	426	85	-	-	PUNCT
ejpam-5392	426	86	space	space	NOUN
ejpam-5392	426	87	(	(	PUNCT
ejpam-5392	426	88	x	x	NOUN
ejpam-5392	426	89	,	,	PUNCT
ejpam-5392	426	90	r	r	NOUN
ejpam-5392	426	91	,	,	PUNCT
ejpam-5392	426	92	ξλ	ξλ	NOUN
ejpam-5392	426	93	,	,	PUNCT
ejpam-5392	426	94	l	l	NOUN
ejpam-5392	426	95	)	)	PUNCT
ejpam-5392	426	96	.	.	PUNCT
ejpam-5392	427	1	then	then	ADV
ejpam-5392	427	2	:	:	PUNCT
ejpam-5392	427	3	(	(	PUNCT
ejpam-5392	427	4	i	i	NOUN
ejpam-5392	427	5	)	)	PUNCT
ejpam-5392	427	6	v	v	NOUN
ejpam-5392	427	7	is	be	AUX
ejpam-5392	427	8	l	l	NOUN
ejpam-5392	427	9	-	-	PUNCT
ejpam-5392	427	10	αλ	αλ	PRON
ejpam-5392	427	11	-	-	PUNCT
ejpam-5392	427	12	exact	exact	ADJ
ejpam-5392	427	13	⇒	⇒	NOUN
ejpam-5392	427	14	v	v	NOUN
ejpam-5392	427	15	is	be	AUX
ejpam-5392	427	16	l	l	NOUN
ejpam-5392	427	17	-	-	PUNCT
ejpam-5392	427	18	sλ	sλ	NOUN
ejpam-5392	427	19	-	-	PUNCT
ejpam-5392	427	20	exact	exact	ADJ
ejpam-5392	427	21	⇒	⇒	NOUN
ejpam-5392	427	22	v	v	NOUN
ejpam-5392	427	23	is	be	AUX
ejpam-5392	427	24	l	l	NOUN
ejpam-5392	427	25	-	-	ADJ
ejpam-5392	427	26	βλ	βλ	ADJ
ejpam-5392	427	27	-	-	PUNCT
ejpam-5392	427	28	exact	exact	ADJ
ejpam-5392	427	29	⇒	⇒	NOUN
ejpam-5392	427	30	v	v	NOUN
ejpam-5392	427	31	is	be	AUX
ejpam-5392	427	32	l	l	ADJ
ejpam-5392	427	33	-	-	ADJ
ejpam-5392	427	34	δβλ	δβλ	ADJ
ejpam-5392	427	35	-	-	PUNCT
ejpam-5392	427	36	exact	exact	ADJ
ejpam-5392	427	37	⇒	⇒	NOUN
ejpam-5392	427	38	v	v	NOUN
ejpam-5392	427	39	is	be	AUX
ejpam-5392	427	40	l	l	NOUN
ejpam-5392	427	41	-	-	PUNCT
ejpam-5392	427	42	θβλ	θβλ	NOUN
ejpam-5392	427	43	-	-	PUNCT
ejpam-5392	427	44	exact	exact	NOUN
ejpam-5392	427	45	.	.	PUNCT
ejpam-5392	428	1	(	(	PUNCT
ejpam-5392	428	2	ii	ii	NOUN
ejpam-5392	428	3	)	)	PUNCT
ejpam-5392	428	4	v	v	NOUN
ejpam-5392	428	5	is	be	AUX
ejpam-5392	428	6	l	l	ADJ
ejpam-5392	428	7	-	-	ADJ
ejpam-5392	428	8	pλ	pλ	ADJ
ejpam-5392	428	9	-	-	PUNCT
ejpam-5392	428	10	exact	exact	ADJ
ejpam-5392	428	11	⇒	⇒	NOUN
ejpam-5392	428	12	v	v	NOUN
ejpam-5392	428	13	is	be	AUX
ejpam-5392	428	14	l	l	NOUN
ejpam-5392	428	15	-	-	ADJ
ejpam-5392	428	16	βλ	βλ	ADJ
ejpam-5392	428	17	-	-	PUNCT
ejpam-5392	428	18	exact	exact	ADJ
ejpam-5392	428	19	⇒	⇒	NOUN
ejpam-5392	428	20	v	v	NOUN
ejpam-5392	428	21	is	be	AUX
ejpam-5392	428	22	l	l	ADJ
ejpam-5392	428	23	-	-	ADJ
ejpam-5392	428	24	δβλ	δβλ	ADJ
ejpam-5392	428	25	-	-	PUNCT
ejpam-5392	428	26	exact	exact	ADJ
ejpam-5392	428	27	⇒	⇒	NOUN
ejpam-5392	428	28	v	v	NOUN
ejpam-5392	428	29	is	be	AUX
ejpam-5392	428	30	l	l	NOUN
ejpam-5392	428	31	-	-	PUNCT
ejpam-5392	428	32	θβλ	θβλ	NOUN
ejpam-5392	428	33	-	-	PUNCT
ejpam-5392	428	34	exact	exact	NOUN
ejpam-5392	428	35	.	.	PUNCT
ejpam-5392	429	1	(	(	PUNCT
ejpam-5392	429	2	iii	iii	X
ejpam-5392	429	3	)	)	PUNCT
ejpam-5392	429	4	v	v	NOUN
ejpam-5392	429	5	is	be	AUX
ejpam-5392	429	6	λ	λ	NOUN
ejpam-5392	429	7	-	-	ADJ
ejpam-5392	429	8	exact	exact	ADJ
ejpam-5392	429	9	⇒	⇒	NOUN
ejpam-5392	429	10	v	v	NOUN
ejpam-5392	429	11	is	be	AUX
ejpam-5392	429	12	l	l	ADJ
ejpam-5392	429	13	-	-	PUNCT
ejpam-5392	429	14	αλ	αλ	PRON
ejpam-5392	429	15	-	-	PUNCT
ejpam-5392	429	16	exact	exact	ADJ
ejpam-5392	429	17	⇒	⇒	NOUN
ejpam-5392	429	18	v	v	NOUN
ejpam-5392	429	19	is	be	AUX
ejpam-5392	429	20	l	l	NOUN
ejpam-5392	429	21	-	-	PUNCT
ejpam-5392	429	22	sλ	sλ	NOUN
ejpam-5392	429	23	-	-	PUNCT
ejpam-5392	429	24	exact	exact	ADJ
ejpam-5392	429	25	⇒	⇒	NOUN
ejpam-5392	429	26	v	v	NOUN
ejpam-5392	429	27	is	be	AUX
ejpam-5392	429	28	l	l	NOUN
ejpam-5392	429	29	-	-	ADJ
ejpam-5392	429	30	βλ	βλ	ADJ
ejpam-5392	429	31	-	-	PUNCT
ejpam-5392	429	32	exact	exact	ADJ
ejpam-5392	429	33	⇒	⇒	NOUN
ejpam-5392	429	34	v	v	NOUN
ejpam-5392	429	35	is	be	AUX
ejpam-5392	429	36	l∧	l∧	ADJ
ejpam-5392	429	37	βλ	βλ	NOUN
ejpam-5392	429	38	-exact	-exact	ADJ
ejpam-5392	429	39	⇒	⇒	NOUN
ejpam-5392	429	40	v	v	NOUN
ejpam-5392	429	41	is	be	AUX
ejpam-5392	429	42	l	l	NOUN
ejpam-5392	429	43	-	-	PUNCT
ejpam-5392	429	44	θβλ	θβλ	NOUN
ejpam-5392	429	45	-	-	PUNCT
ejpam-5392	429	46	exact	exact	NOUN
ejpam-5392	429	47	.	.	PUNCT
ejpam-5392	430	1	(	(	PUNCT
ejpam-5392	430	2	iv	iv	X
ejpam-5392	430	3	)	)	PUNCT
ejpam-5392	430	4	v	v	NOUN
ejpam-5392	430	5	is	be	AUX
ejpam-5392	430	6	l	l	ADJ
ejpam-5392	430	7	-	-	ADJ
ejpam-5392	430	8	pλ	pλ	ADJ
ejpam-5392	430	9	-	-	PUNCT
ejpam-5392	430	10	exact	exact	ADJ
ejpam-5392	430	11	⇒	⇒	NOUN
ejpam-5392	430	12	v	v	NOUN
ejpam-5392	430	13	is	be	AUX
ejpam-5392	430	14	l	l	NOUN
ejpam-5392	430	15	-	-	ADJ
ejpam-5392	430	16	βλ	βλ	ADJ
ejpam-5392	430	17	-	-	PUNCT
ejpam-5392	430	18	exact	exact	ADJ
ejpam-5392	430	19	⇒	⇒	NOUN
ejpam-5392	430	20	v	v	NOUN
ejpam-5392	430	21	is	be	AUX
ejpam-5392	430	22	l∧	l∧	ADJ
ejpam-5392	430	23	βλ	βλ	NOUN
ejpam-5392	430	24	-exact	-exact	ADJ
ejpam-5392	430	25	⇒	⇒	NOUN
ejpam-5392	430	26	v	v	NOUN
ejpam-5392	430	27	is	be	AUX
ejpam-5392	430	28	l	l	NOUN
ejpam-5392	430	29	-	-	PUNCT
ejpam-5392	430	30	θβλ	θβλ	NOUN
ejpam-5392	430	31	-	-	PUNCT
ejpam-5392	430	32	exact	exact	NOUN
ejpam-5392	430	33	.	.	PUNCT
ejpam-5392	431	1	m.	m.	PROPN
ejpam-5392	431	2	hosny	hosny	PROPN
ejpam-5392	431	3	,	,	PUNCT
ejpam-5392	431	4	t.m	t.m	PROPN
ejpam-5392	431	5	.	.	PROPN
ejpam-5392	431	6	al	al	PROPN
ejpam-5392	431	7	-	-	PUNCT
ejpam-5392	431	8	shami	shami	PROPN
ejpam-5392	431	9	/	/	PUNCT
ejpam-5392	431	10	eur	eur	PROPN
ejpam-5392	431	11	.	.	PUNCT
ejpam-5392	432	1	j.	j.	PROPN
ejpam-5392	432	2	pure	pure	PROPN
ejpam-5392	432	3	appl	appl	PROPN
ejpam-5392	432	4	.	.	PROPN
ejpam-5392	432	5	math	math	PROPN
ejpam-5392	432	6	,	,	PUNCT
ejpam-5392	432	7	17	17	NUM
ejpam-5392	432	8	(	(	PUNCT
ejpam-5392	432	9	4	4	NUM
ejpam-5392	432	10	)	)	PUNCT
ejpam-5392	432	11	(	(	PUNCT
ejpam-5392	432	12	2024	2024	NUM
ejpam-5392	432	13	)	)	PUNCT
ejpam-5392	432	14	,	,	PUNCT
ejpam-5392	432	15	3436	3436	NUM
ejpam-5392	432	16	-	-	SYM
ejpam-5392	432	17	3463	3463	NUM
ejpam-5392	432	18	3450	3450	NUM
ejpam-5392	432	19	(	(	PUNCT
ejpam-5392	432	20	v	v	NOUN
ejpam-5392	432	21	)	)	PUNCT
ejpam-5392	432	22	v	v	NOUN
ejpam-5392	432	23	is	be	AUX
ejpam-5392	432	24	l	l	NOUN
ejpam-5392	432	25	-	-	PUNCT
ejpam-5392	432	26	θβλ	θβλ	NOUN
ejpam-5392	432	27	-	-	PUNCT
ejpam-5392	432	28	rough	rough	ADJ
ejpam-5392	432	29	⇒	⇒	NOUN
ejpam-5392	432	30	v	v	NOUN
ejpam-5392	432	31	is	be	AUX
ejpam-5392	432	32	l	l	ADJ
ejpam-5392	432	33	-	-	ADJ
ejpam-5392	432	34	δβλ	δβλ	ADJ
ejpam-5392	432	35	-	-	PUNCT
ejpam-5392	432	36	rough	rough	ADJ
ejpam-5392	432	37	⇒	⇒	NOUN
ejpam-5392	432	38	v	v	NOUN
ejpam-5392	432	39	is	be	AUX
ejpam-5392	432	40	l	l	NOUN
ejpam-5392	432	41	-	-	PUNCT
ejpam-5392	432	42	βλ	βλ	ADJ
ejpam-5392	432	43	-	-	PUNCT
ejpam-5392	432	44	rough	rough	ADJ
ejpam-5392	432	45	⇒	⇒	NOUN
ejpam-5392	432	46	v	v	NOUN
ejpam-5392	432	47	is	be	AUX
ejpam-5392	432	48	l	l	NOUN
ejpam-5392	432	49	-	-	PUNCT
ejpam-5392	432	50	sλ	sλ	NOUN
ejpam-5392	432	51	-	-	PUNCT
ejpam-5392	432	52	rough	rough	ADJ
ejpam-5392	432	53	⇒	⇒	NOUN
ejpam-5392	432	54	v	v	NOUN
ejpam-5392	432	55	is	be	AUX
ejpam-5392	432	56	l	l	ADJ
ejpam-5392	432	57	-	-	PUNCT
ejpam-5392	432	58	αλ	αλ	NUM
ejpam-5392	432	59	-	-	PUNCT
ejpam-5392	432	60	rough	rough	ADJ
ejpam-5392	432	61	.	.	PUNCT
ejpam-5392	433	1	(	(	PUNCT
ejpam-5392	433	2	vi	vi	NOUN
ejpam-5392	433	3	)	)	PUNCT
ejpam-5392	433	4	v	v	NOUN
ejpam-5392	433	5	is	be	AUX
ejpam-5392	433	6	l	l	NOUN
ejpam-5392	433	7	-	-	PUNCT
ejpam-5392	433	8	θβλ	θβλ	NOUN
ejpam-5392	433	9	-	-	PUNCT
ejpam-5392	433	10	rough	rough	ADJ
ejpam-5392	433	11	⇒	⇒	NOUN
ejpam-5392	433	12	v	v	NOUN
ejpam-5392	433	13	is	be	AUX
ejpam-5392	433	14	l	l	ADJ
ejpam-5392	433	15	-	-	ADJ
ejpam-5392	433	16	δβλ	δβλ	ADJ
ejpam-5392	433	17	-	-	PUNCT
ejpam-5392	433	18	rough	rough	ADJ
ejpam-5392	433	19	⇒	⇒	NOUN
ejpam-5392	433	20	v	v	NOUN
ejpam-5392	433	21	is	be	AUX
ejpam-5392	433	22	l	l	NOUN
ejpam-5392	433	23	-	-	PUNCT
ejpam-5392	433	24	βλ	βλ	ADJ
ejpam-5392	433	25	-	-	PUNCT
ejpam-5392	433	26	rough	rough	ADJ
ejpam-5392	433	27	⇒	⇒	NOUN
ejpam-5392	433	28	v	v	NOUN
ejpam-5392	433	29	is	be	AUX
ejpam-5392	433	30	l	l	ADJ
ejpam-5392	433	31	-	-	ADJ
ejpam-5392	433	32	pλ	pλ	ADJ
ejpam-5392	433	33	-	-	PUNCT
ejpam-5392	433	34	rough	rough	ADJ
ejpam-5392	433	35	.	.	PUNCT
ejpam-5392	434	1	(	(	PUNCT
ejpam-5392	434	2	vii	vii	PROPN
ejpam-5392	434	3	)	)	PUNCT
ejpam-5392	434	4	v	v	NOUN
ejpam-5392	434	5	is	be	AUX
ejpam-5392	434	6	l	l	NOUN
ejpam-5392	434	7	-	-	PUNCT
ejpam-5392	434	8	θβλ	θβλ	NOUN
ejpam-5392	434	9	-	-	PUNCT
ejpam-5392	434	10	rough	rough	ADJ
ejpam-5392	434	11	⇒	⇒	NOUN
ejpam-5392	434	12	v	v	NOUN
ejpam-5392	434	13	is	be	AUX
ejpam-5392	434	14	l∧	l∧	ADJ
ejpam-5392	434	15	βλ	βλ	NOUN
ejpam-5392	434	16	-rough	-rough	PROPN
ejpam-5392	434	17	⇒	⇒	NOUN
ejpam-5392	434	18	v	v	NOUN
ejpam-5392	434	19	is	be	AUX
ejpam-5392	434	20	l	l	NOUN
ejpam-5392	434	21	-	-	PUNCT
ejpam-5392	434	22	βλ	βλ	ADJ
ejpam-5392	434	23	-	-	PUNCT
ejpam-5392	434	24	rough	rough	ADJ
ejpam-5392	434	25	⇒	⇒	NOUN
ejpam-5392	434	26	v	v	NOUN
ejpam-5392	434	27	is	be	AUX
ejpam-5392	434	28	l	l	NOUN
ejpam-5392	434	29	-	-	PUNCT
ejpam-5392	434	30	sλ	sλ	NOUN
ejpam-5392	434	31	-	-	PUNCT
ejpam-5392	434	32	rough	rough	ADJ
ejpam-5392	434	33	⇒	⇒	NOUN
ejpam-5392	434	34	v	v	NOUN
ejpam-5392	434	35	is	be	AUX
ejpam-5392	434	36	l	l	ADJ
ejpam-5392	434	37	-	-	PUNCT
ejpam-5392	434	38	αλ	αλ	NUM
ejpam-5392	434	39	-	-	PUNCT
ejpam-5392	434	40	rough	rough	ADJ
ejpam-5392	434	41	.	.	PUNCT
ejpam-5392	435	1	(	(	PUNCT
ejpam-5392	435	2	vii	vii	PROPN
ejpam-5392	435	3	)	)	PUNCT
ejpam-5392	435	4	v	v	NOUN
ejpam-5392	435	5	is	be	AUX
ejpam-5392	435	6	l	l	NOUN
ejpam-5392	435	7	-	-	PUNCT
ejpam-5392	435	8	θβλ	θβλ	NOUN
ejpam-5392	435	9	-	-	PUNCT
ejpam-5392	435	10	rough	rough	ADJ
ejpam-5392	435	11	⇒	⇒	NOUN
ejpam-5392	435	12	v	v	NOUN
ejpam-5392	435	13	is	be	AUX
ejpam-5392	435	14	l∧	l∧	ADJ
ejpam-5392	435	15	βλ	βλ	NOUN
ejpam-5392	435	16	-rough	-rough	PROPN
ejpam-5392	435	17	⇒	⇒	NOUN
ejpam-5392	435	18	v	v	NOUN
ejpam-5392	435	19	is	be	AUX
ejpam-5392	435	20	l	l	NOUN
ejpam-5392	435	21	-	-	PUNCT
ejpam-5392	435	22	βλ	βλ	ADJ
ejpam-5392	435	23	-	-	PUNCT
ejpam-5392	435	24	rough	rough	ADJ
ejpam-5392	435	25	⇒	⇒	NOUN
ejpam-5392	435	26	v	v	NOUN
ejpam-5392	435	27	is	be	AUX
ejpam-5392	435	28	l	l	ADJ
ejpam-5392	435	29	-	-	ADJ
ejpam-5392	435	30	pλ	pλ	ADJ
ejpam-5392	435	31	-	-	PUNCT
ejpam-5392	435	32	rough	rough	ADJ
ejpam-5392	435	33	.	.	PUNCT
ejpam-5392	436	1	remark	remark	PROPN
ejpam-5392	436	2	3	3	NUM
ejpam-5392	436	3	.	.	PUNCT
ejpam-5392	437	1	by	by	ADP
ejpam-5392	437	2	example	example	NOUN
ejpam-5392	437	3	1	1	NUM
ejpam-5392	437	4	,	,	PUNCT
ejpam-5392	437	5	we	we	PRON
ejpam-5392	437	6	will	will	AUX
ejpam-5392	437	7	illustrate	illustrate	VERB
ejpam-5392	437	8	that	that	SCONJ
ejpam-5392	437	9	the	the	DET
ejpam-5392	437	10	converse	converse	NOUN
ejpam-5392	437	11	of	of	ADP
ejpam-5392	437	12	the	the	DET
ejpam-5392	437	13	implications	implication	NOUN
ejpam-5392	437	14	in	in	ADP
ejpam-5392	437	15	corollary	corollary	ADJ
ejpam-5392	437	16	2	2	NUM
ejpam-5392	437	17	fails	fail	VERB
ejpam-5392	437	18	.	.	PUNCT
ejpam-5392	438	1	(	(	PUNCT
ejpam-5392	438	2	i	i	NOUN
ejpam-5392	438	3	)	)	PUNCT
ejpam-5392	438	4	if	if	SCONJ
ejpam-5392	438	5	v	v	NUM
ejpam-5392	438	6	=	=	SYM
ejpam-5392	438	7	{	{	PUNCT
ejpam-5392	438	8	y5	y5	NOUN
ejpam-5392	438	9	}	}	PUNCT
ejpam-5392	438	10	,	,	PUNCT
ejpam-5392	438	11	then	then	ADV
ejpam-5392	438	12	it	it	PRON
ejpam-5392	438	13	is	be	AUX
ejpam-5392	438	14	l	l	NOUN
ejpam-5392	438	15	-	-	ADJ
ejpam-5392	438	16	θβa	θβa	NOUN
ejpam-5392	438	17	-	-	PUNCT
ejpam-5392	438	18	exact	exact	ADJ
ejpam-5392	438	19	,	,	PUNCT
ejpam-5392	438	20	but	but	CCONJ
ejpam-5392	438	21	it	it	PRON
ejpam-5392	438	22	is	be	AUX
ejpam-5392	438	23	not	not	PART
ejpam-5392	438	24	l	l	ADJ
ejpam-5392	438	25	-	-	ADJ
ejpam-5392	438	26	δβa	δβa	ADJ
ejpam-5392	438	27	-	-	PUNCT
ejpam-5392	438	28	exact	exact	NOUN
ejpam-5392	438	29	and	and	CCONJ
ejpam-5392	438	30	consequently	consequently	ADV
ejpam-5392	438	31	,	,	PUNCT
ejpam-5392	438	32	not	not	PART
ejpam-5392	438	33	l	l	NOUN
ejpam-5392	438	34	-	-	ADJ
ejpam-5392	438	35	βa	βa	ADJ
ejpam-5392	438	36	-	-	PUNCT
ejpam-5392	438	37	exact	exact	ADJ
ejpam-5392	438	38	,	,	PUNCT
ejpam-5392	438	39	not	not	PART
ejpam-5392	438	40	l	l	NOUN
ejpam-5392	438	41	-	-	PUNCT
ejpam-5392	438	42	sa	sa	NOUN
ejpam-5392	438	43	-	-	PUNCT
ejpam-5392	438	44	exact	exact	ADJ
ejpam-5392	438	45	,	,	PUNCT
ejpam-5392	438	46	not	not	PART
ejpam-5392	438	47	l	l	NOUN
ejpam-5392	438	48	-	-	PUNCT
ejpam-5392	438	49	αa	αa	ADP
ejpam-5392	438	50	-	-	PUNCT
ejpam-5392	438	51	exact	exact	ADJ
ejpam-5392	438	52	and	and	CCONJ
ejpam-5392	438	53	not	not	PART
ejpam-5392	438	54	l	l	NOUN
ejpam-5392	438	55	-	-	PROPN
ejpam-5392	438	56	pa	pa	NOUN
ejpam-5392	438	57	-	-	PUNCT
ejpam-5392	438	58	exact	exact	NOUN
ejpam-5392	438	59	.	.	PUNCT
ejpam-5392	439	1	(	(	PUNCT
ejpam-5392	439	2	ii	ii	NOUN
ejpam-5392	439	3	)	)	PUNCT
ejpam-5392	439	4	if	if	SCONJ
ejpam-5392	439	5	v	v	NOUN
ejpam-5392	439	6	=	=	SYM
ejpam-5392	439	7	{	{	PUNCT
ejpam-5392	439	8	y	y	NOUN
ejpam-5392	439	9	}	}	PUNCT
ejpam-5392	439	10	,	,	PUNCT
ejpam-5392	439	11	then	then	ADV
ejpam-5392	439	12	it	it	PRON
ejpam-5392	439	13	is	be	AUX
ejpam-5392	439	14	l	l	NOUN
ejpam-5392	439	15	-	-	ADJ
ejpam-5392	439	16	θβa	θβa	NOUN
ejpam-5392	439	17	-	-	PUNCT
ejpam-5392	439	18	exact	exact	ADJ
ejpam-5392	439	19	,	,	PUNCT
ejpam-5392	439	20	but	but	CCONJ
ejpam-5392	439	21	it	it	PRON
ejpam-5392	439	22	is	be	AUX
ejpam-5392	439	23	not	not	PART
ejpam-5392	439	24	l∧	l∧	ADJ
ejpam-5392	439	25	βa	βa	ADJ
ejpam-5392	439	26	-	-	PUNCT
ejpam-5392	439	27	exact	exact	ADJ
ejpam-5392	439	28	and	and	CCONJ
ejpam-5392	439	29	consequently	consequently	ADV
ejpam-5392	439	30	,	,	PUNCT
ejpam-5392	439	31	not	not	PART
ejpam-5392	439	32	l	l	NOUN
ejpam-5392	439	33	-	-	ADJ
ejpam-5392	439	34	βa	βa	ADJ
ejpam-5392	439	35	-	-	PUNCT
ejpam-5392	439	36	exact	exact	ADJ
ejpam-5392	439	37	,	,	PUNCT
ejpam-5392	439	38	not	not	PART
ejpam-5392	439	39	l	l	NOUN
ejpam-5392	439	40	-	-	PUNCT
ejpam-5392	439	41	sa	sa	NOUN
ejpam-5392	439	42	-	-	PUNCT
ejpam-5392	439	43	exact	exact	ADJ
ejpam-5392	439	44	,	,	PUNCT
ejpam-5392	439	45	not	not	PART
ejpam-5392	439	46	l	l	NOUN
ejpam-5392	439	47	-	-	PUNCT
ejpam-5392	439	48	αa	αa	ADP
ejpam-5392	439	49	-	-	PUNCT
ejpam-5392	439	50	exact	exact	ADJ
ejpam-5392	439	51	and	and	CCONJ
ejpam-5392	439	52	not	not	PART
ejpam-5392	439	53	l	l	NOUN
ejpam-5392	439	54	-	-	PROPN
ejpam-5392	439	55	pa	pa	NOUN
ejpam-5392	439	56	-	-	PUNCT
ejpam-5392	439	57	exact	exact	ADJ
ejpam-5392	439	58	.	.	PUNCT
ejpam-5392	440	1	we	we	PRON
ejpam-5392	440	2	elucidate	elucidate	VERB
ejpam-5392	440	3	the	the	DET
ejpam-5392	440	4	interrelations	interrelation	NOUN
ejpam-5392	440	5	between	between	ADP
ejpam-5392	440	6	the	the	DET
ejpam-5392	440	7	present	present	ADJ
ejpam-5392	440	8	rough	rough	ADJ
ejpam-5392	440	9	paradigms	paradigm	NOUN
ejpam-5392	440	10	(	(	PUNCT
ejpam-5392	440	11	definition	definition	NOUN
ejpam-5392	440	12	18	18	NUM
ejpam-5392	440	13	)	)	PUNCT
ejpam-5392	440	14	and	and	CCONJ
ejpam-5392	440	15	the	the	DET
ejpam-5392	440	16	those	those	PRON
ejpam-5392	440	17	displayed	display	VERB
ejpam-5392	440	18	in	in	ADP
ejpam-5392	440	19	definition	definition	NOUN
ejpam-5392	440	20	4	4	NUM
ejpam-5392	440	21	[	[	X
ejpam-5392	440	22	45	45	NUM
ejpam-5392	440	23	]	]	PUNCT
ejpam-5392	440	24	and	and	CCONJ
ejpam-5392	440	25	definition	definition	NOUN
ejpam-5392	440	26	6	6	NUM
ejpam-5392	440	27	[	[	SYM
ejpam-5392	440	28	15	15	NUM
ejpam-5392	440	29	,	,	PUNCT
ejpam-5392	440	30	20	20	NUM
ejpam-5392	440	31	]	]	PUNCT
ejpam-5392	440	32	.	.	PUNCT
ejpam-5392	441	1	theorem	theorem	NOUN
ejpam-5392	441	2	5	5	NUM
ejpam-5392	441	3	.	.	PUNCT
ejpam-5392	442	1	let	let	VERB
ejpam-5392	442	2	v	v	PART
ejpam-5392	442	3	be	be	AUX
ejpam-5392	442	4	a	a	DET
ejpam-5392	442	5	subset	subset	NOUN
ejpam-5392	442	6	of	of	ADP
ejpam-5392	442	7	an	an	DET
ejpam-5392	442	8	l	l	NOUN
ejpam-5392	442	9	−gλ	−gλ	NOUN
ejpam-5392	442	10	-	-	PUNCT
ejpam-5392	442	11	space	space	NOUN
ejpam-5392	442	12	(	(	PUNCT
ejpam-5392	442	13	x	x	NOUN
ejpam-5392	442	14	,	,	PUNCT
ejpam-5392	442	15	r	r	NOUN
ejpam-5392	442	16	,	,	PUNCT
ejpam-5392	442	17	ξλ	ξλ	NOUN
ejpam-5392	442	18	,	,	PUNCT
ejpam-5392	442	19	l	l	NOUN
ejpam-5392	442	20	)	)	PUNCT
ejpam-5392	442	21	.	.	PUNCT
ejpam-5392	443	1	then	then	ADV
ejpam-5392	443	2	:	:	PUNCT
ejpam-5392	443	3	(	(	PUNCT
ejpam-5392	443	4	i	i	NOUN
ejpam-5392	443	5	)	)	PUNCT
ejpam-5392	443	6	rα	rα	ADV
ejpam-5392	443	7	λ(v	λ(v	PROPN
ejpam-5392	443	8	)	)	PUNCT
ejpam-5392	444	1	⊆	⊆	NUM
ejpam-5392	444	2	rp	rp	NOUN
ejpam-5392	444	3	λ(v	λ(v	PROPN
ejpam-5392	444	4	)	)	PUNCT
ejpam-5392	445	1	⊆	⊆	NUM
ejpam-5392	445	2	rγ	rγ	NOUN
ejpam-5392	445	3	λ(v	λ(v	ADV
ejpam-5392	445	4	)	)	PUNCT
ejpam-5392	446	1	⊆	⊆	NUM
ejpam-5392	446	2	rβ	rβ	ADP
ejpam-5392	446	3	λ(v	λ(v	PROPN
ejpam-5392	446	4	)	)	PUNCT
ejpam-5392	446	5	⊆	⊆	NUM
ejpam-5392	446	6	rδβ	rδβ	NOUN
ejpam-5392	446	7	λ	λ	PROPN
ejpam-5392	446	8	(	(	PUNCT
ejpam-5392	446	9	v	v	NOUN
ejpam-5392	446	10	)	)	PUNCT
ejpam-5392	446	11	⊆	⊆	NUM
ejpam-5392	446	12	rl−θβ	rl−θβ	PROPN
ejpam-5392	446	13	λ	λ	PROPN
ejpam-5392	446	14	(	(	PUNCT
ejpam-5392	446	15	v	v	NOUN
ejpam-5392	446	16	)	)	PUNCT
ejpam-5392	446	17	.	.	PUNCT
ejpam-5392	447	1	(	(	PUNCT
ejpam-5392	447	2	ii	ii	NOUN
ejpam-5392	447	3	)	)	PUNCT
ejpam-5392	447	4	rα	rα	ADV
ejpam-5392	447	5	λ(v	λ(v	PROPN
ejpam-5392	447	6	)	)	PUNCT
ejpam-5392	448	1	⊆	⊆	NUM
ejpam-5392	448	2	rs	rs	NOUN
ejpam-5392	448	3	λ(v	λ(v	PROPN
ejpam-5392	448	4	)	)	PUNCT
ejpam-5392	449	1	⊆	⊆	NUM
ejpam-5392	449	2	rγ	rγ	NOUN
ejpam-5392	449	3	λ(v	λ(v	ADV
ejpam-5392	449	4	)	)	PUNCT
ejpam-5392	450	1	⊆	⊆	NUM
ejpam-5392	450	2	rβ	rβ	ADP
ejpam-5392	450	3	λ(v	λ(v	PROPN
ejpam-5392	450	4	)	)	PUNCT
ejpam-5392	450	5	⊆	⊆	NUM
ejpam-5392	450	6	rδβ	rδβ	NOUN
ejpam-5392	450	7	λ	λ	PROPN
ejpam-5392	450	8	(	(	PUNCT
ejpam-5392	450	9	v	v	NOUN
ejpam-5392	450	10	)	)	PUNCT
ejpam-5392	450	11	⊆	⊆	NUM
ejpam-5392	450	12	rl−θβ	rl−θβ	PROPN
ejpam-5392	450	13	λ	λ	PROPN
ejpam-5392	450	14	(	(	PUNCT
ejpam-5392	450	15	v	v	NOUN
ejpam-5392	450	16	)	)	PUNCT
ejpam-5392	450	17	.	.	PUNCT
ejpam-5392	451	1	(	(	PUNCT
ejpam-5392	451	2	iii	iii	X
ejpam-5392	451	3	)	)	PUNCT
ejpam-5392	451	4	rα	rα	ADV
ejpam-5392	451	5	λ(v	λ(v	PROPN
ejpam-5392	451	6	)	)	PUNCT
ejpam-5392	452	1	⊆	⊆	NUM
ejpam-5392	452	2	rp	rp	NOUN
ejpam-5392	452	3	λ(v	λ(v	PROPN
ejpam-5392	452	4	)	)	PUNCT
ejpam-5392	453	1	⊆	⊆	NUM
ejpam-5392	453	2	rγ	rγ	NOUN
ejpam-5392	453	3	λ(v	λ(v	ADV
ejpam-5392	453	4	)	)	PUNCT
ejpam-5392	454	1	⊆	⊆	NUM
ejpam-5392	454	2	rβ	rβ	ADP
ejpam-5392	454	3	λ(v	λ(v	PROPN
ejpam-5392	454	4	)	)	PUNCT
ejpam-5392	455	1	⊆	⊆	NUM
ejpam-5392	455	2	r	r	NOUN
ejpam-5392	455	3	∧	∧	PROPN
ejpam-5392	455	4	β	β	X
ejpam-5392	455	5	λ	λ	X
ejpam-5392	455	6	(	(	PUNCT
ejpam-5392	455	7	v	v	NOUN
ejpam-5392	455	8	)	)	PUNCT
ejpam-5392	455	9	⊆	⊆	NUM
ejpam-5392	455	10	rl−θβλ(v	rl−θβλ(v	PROPN
ejpam-5392	455	11	)	)	PUNCT
ejpam-5392	455	12	.	.	PUNCT
ejpam-5392	456	1	(	(	PUNCT
ejpam-5392	456	2	iv	iv	X
ejpam-5392	456	3	)	)	PUNCT
ejpam-5392	456	4	rα	rα	ADV
ejpam-5392	456	5	λ(v	λ(v	PROPN
ejpam-5392	456	6	)	)	PUNCT
ejpam-5392	457	1	⊆	⊆	NUM
ejpam-5392	457	2	rs	rs	NOUN
ejpam-5392	457	3	λ(v	λ(v	PROPN
ejpam-5392	457	4	)	)	PUNCT
ejpam-5392	458	1	⊆	⊆	NUM
ejpam-5392	458	2	rγ	rγ	NOUN
ejpam-5392	458	3	λ(v	λ(v	ADV
ejpam-5392	458	4	)	)	PUNCT
ejpam-5392	459	1	⊆	⊆	NUM
ejpam-5392	459	2	rβ	rβ	ADP
ejpam-5392	459	3	λ(v	λ(v	PROPN
ejpam-5392	459	4	)	)	PUNCT
ejpam-5392	460	1	⊆	⊆	NUM
ejpam-5392	460	2	r	r	NOUN
ejpam-5392	460	3	∧	∧	PROPN
ejpam-5392	460	4	βλ	βλ	X
ejpam-5392	460	5	(	(	PUNCT
ejpam-5392	460	6	v	v	NOUN
ejpam-5392	460	7	)	)	PUNCT
ejpam-5392	460	8	⊆	⊆	NUM
ejpam-5392	460	9	rl−θβλ(v	rl−θβλ(v	PROPN
ejpam-5392	460	10	)	)	PUNCT
ejpam-5392	460	11	.	.	PUNCT
ejpam-5392	461	1	(	(	PUNCT
ejpam-5392	461	2	v	v	NOUN
ejpam-5392	461	3	)	)	PUNCT
ejpam-5392	461	4	rλ(v	rλ(v	NOUN
ejpam-5392	461	5	)	)	PUNCT
ejpam-5392	462	1	⊆	⊆	NUM
ejpam-5392	462	2	rl−θβ	rl−θβ	PROPN
ejpam-5392	462	3	λ	λ	PROPN
ejpam-5392	462	4	(	(	PUNCT
ejpam-5392	462	5	v	v	NOUN
ejpam-5392	462	6	)	)	PUNCT
ejpam-5392	462	7	.	.	PUNCT
ejpam-5392	463	1	(	(	PUNCT
ejpam-5392	463	2	vi	vi	NOUN
ejpam-5392	463	3	)	)	PUNCT
ejpam-5392	463	4	rl−θβ	rl−θβ	NOUN
ejpam-5392	463	5	λ	λ	PROPN
ejpam-5392	463	6	(	(	PUNCT
ejpam-5392	463	7	v	v	NOUN
ejpam-5392	463	8	)	)	PUNCT
ejpam-5392	463	9	⊆	⊆	NUM
ejpam-5392	463	10	rδβ	rδβ	NOUN
ejpam-5392	463	11	λ	λ	PROPN
ejpam-5392	463	12	(	(	PUNCT
ejpam-5392	463	13	v	v	NOUN
ejpam-5392	463	14	)	)	PUNCT
ejpam-5392	463	15	⊆	⊆	NUM
ejpam-5392	463	16	rβ	rβ	ADP
ejpam-5392	463	17	λ(v	λ(v	PROPN
ejpam-5392	463	18	)	)	PUNCT
ejpam-5392	464	1	⊆	⊆	NUM
ejpam-5392	464	2	rγ	rγ	NOUN
ejpam-5392	464	3	λ(v	λ(v	ADV
ejpam-5392	464	4	)	)	PUNCT
ejpam-5392	465	1	⊆	⊆	NUM
ejpam-5392	465	2	rp	rp	NOUN
ejpam-5392	465	3	λ(v	λ(v	PROPN
ejpam-5392	465	4	)	)	PUNCT
ejpam-5392	466	1	⊆	⊆	NUM
ejpam-5392	466	2	rα	rα	ADV
ejpam-5392	466	3	λ(v	λ(v	PROPN
ejpam-5392	466	4	)	)	PUNCT
ejpam-5392	466	5	.	.	PUNCT
ejpam-5392	467	1	(	(	PUNCT
ejpam-5392	467	2	vii	vii	PROPN
ejpam-5392	467	3	)	)	PUNCT
ejpam-5392	467	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	467	5	λ	λ	PROPN
ejpam-5392	467	6	(	(	PUNCT
ejpam-5392	467	7	v	v	NOUN
ejpam-5392	467	8	)	)	PUNCT
ejpam-5392	467	9	⊆	⊆	NUM
ejpam-5392	467	10	rδβ	rδβ	NOUN
ejpam-5392	467	11	λ	λ	PROPN
ejpam-5392	467	12	(	(	PUNCT
ejpam-5392	467	13	v	v	NOUN
ejpam-5392	467	14	)	)	PUNCT
ejpam-5392	467	15	⊆	⊆	NUM
ejpam-5392	467	16	rβ	rβ	ADP
ejpam-5392	467	17	λ(v	λ(v	PROPN
ejpam-5392	467	18	)	)	PUNCT
ejpam-5392	468	1	⊆	⊆	NUM
ejpam-5392	468	2	rγ	rγ	NOUN
ejpam-5392	468	3	λ(v	λ(v	ADV
ejpam-5392	468	4	)	)	PUNCT
ejpam-5392	469	1	⊆	⊆	NUM
ejpam-5392	469	2	rs	rs	NOUN
ejpam-5392	469	3	λ(v	λ(v	PROPN
ejpam-5392	469	4	)	)	PUNCT
ejpam-5392	470	1	⊆	⊆	NUM
ejpam-5392	470	2	rα	rα	ADV
ejpam-5392	470	3	λ(v	λ(v	PROPN
ejpam-5392	470	4	)	)	PUNCT
ejpam-5392	470	5	.	.	PUNCT
ejpam-5392	471	1	(	(	PUNCT
ejpam-5392	471	2	viii	viii	NOUN
ejpam-5392	471	3	)	)	PUNCT
ejpam-5392	471	4	rl−θβλ(v	rl−θβλ(v	PROPN
ejpam-5392	471	5	)	)	PUNCT
ejpam-5392	472	1	⊆	⊆	NUM
ejpam-5392	472	2	r	r	NOUN
ejpam-5392	472	3	∧	∧	PROPN
ejpam-5392	472	4	β	β	X
ejpam-5392	472	5	λ	λ	X
ejpam-5392	472	6	(	(	PUNCT
ejpam-5392	472	7	v	v	NOUN
ejpam-5392	472	8	)	)	PUNCT
ejpam-5392	472	9	⊆	⊆	NUM
ejpam-5392	472	10	rβ	rβ	ADP
ejpam-5392	472	11	λ(v	λ(v	PROPN
ejpam-5392	472	12	)	)	PUNCT
ejpam-5392	473	1	⊆	⊆	NUM
ejpam-5392	473	2	rγ	rγ	NOUN
ejpam-5392	473	3	λ(v	λ(v	ADV
ejpam-5392	473	4	)	)	PUNCT
ejpam-5392	474	1	⊆	⊆	NUM
ejpam-5392	474	2	rp	rp	NOUN
ejpam-5392	474	3	λ(v	λ(v	PROPN
ejpam-5392	474	4	)	)	PUNCT
ejpam-5392	475	1	⊆	⊆	NUM
ejpam-5392	475	2	rα	rα	ADV
ejpam-5392	475	3	λ(v	λ(v	PROPN
ejpam-5392	475	4	)	)	PUNCT
ejpam-5392	475	5	.	.	PUNCT
ejpam-5392	476	1	(	(	PUNCT
ejpam-5392	476	2	ix	ix	X
ejpam-5392	476	3	)	)	PUNCT
ejpam-5392	476	4	rl−θβλ(v	rl−θβλ(v	PROPN
ejpam-5392	476	5	)	)	PUNCT
ejpam-5392	476	6	)	)	PUNCT
ejpam-5392	477	1	⊆	⊆	NUM
ejpam-5392	477	2	r	r	NOUN
ejpam-5392	477	3	∧	∧	PROPN
ejpam-5392	477	4	β	β	X
ejpam-5392	477	5	λ	λ	X
ejpam-5392	477	6	(	(	PUNCT
ejpam-5392	477	7	v	v	NOUN
ejpam-5392	477	8	)	)	PUNCT
ejpam-5392	477	9	⊆	⊆	NUM
ejpam-5392	477	10	rβ	rβ	ADP
ejpam-5392	477	11	λ(v	λ(v	PROPN
ejpam-5392	477	12	)	)	PUNCT
ejpam-5392	478	1	⊆	⊆	NUM
ejpam-5392	478	2	rγ	rγ	NOUN
ejpam-5392	478	3	λ(v	λ(v	ADV
ejpam-5392	478	4	)	)	PUNCT
ejpam-5392	479	1	⊆	⊆	NUM
ejpam-5392	479	2	rs	rs	NOUN
ejpam-5392	479	3	λ(v	λ(v	PROPN
ejpam-5392	479	4	)	)	PUNCT
ejpam-5392	480	1	⊆	⊆	NUM
ejpam-5392	480	2	rα	rα	ADV
ejpam-5392	480	3	λ(v	λ(v	PROPN
ejpam-5392	480	4	)	)	PUNCT
ejpam-5392	480	5	.	.	PUNCT
ejpam-5392	481	1	(	(	PUNCT
ejpam-5392	481	2	x	x	X
ejpam-5392	481	3	)	)	PUNCT
ejpam-5392	481	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	481	5	λ	λ	PROPN
ejpam-5392	481	6	(	(	PUNCT
ejpam-5392	481	7	v	v	NOUN
ejpam-5392	481	8	)	)	PUNCT
ejpam-5392	481	9	⊆	⊆	NUM
ejpam-5392	481	10	rλ(v	rλ(v	NUM
ejpam-5392	481	11	)	)	PUNCT
ejpam-5392	481	12	.	.	PUNCT
ejpam-5392	482	1	proof	proof	NOUN
ejpam-5392	482	2	.	.	PUNCT
ejpam-5392	483	1	(	(	PUNCT
ejpam-5392	483	2	i	i	NOUN
ejpam-5392	483	3	)	)	PUNCT
ejpam-5392	483	4	by	by	ADP
ejpam-5392	483	5	theorem	theorem	NOUN
ejpam-5392	483	6	2	2	NUM
ejpam-5392	483	7	[	[	X
ejpam-5392	483	8	23	23	NUM
ejpam-5392	483	9	]	]	PUNCT
ejpam-5392	483	10	,	,	PUNCT
ejpam-5392	483	11	rα	rα	ADV
ejpam-5392	483	12	λ(v	λ(v	PROPN
ejpam-5392	483	13	)	)	PUNCT
ejpam-5392	484	1	⊆	⊆	NUM
ejpam-5392	484	2	rp	rp	NOUN
ejpam-5392	484	3	λ(v	λ(v	PROPN
ejpam-5392	484	4	)	)	PUNCT
ejpam-5392	485	1	⊆	⊆	NUM
ejpam-5392	485	2	rγ	rγ	NOUN
ejpam-5392	485	3	λ(v	λ(v	ADV
ejpam-5392	485	4	)	)	PUNCT
ejpam-5392	486	1	⊆	⊆	NUM
ejpam-5392	486	2	rβ	rβ	ADP
ejpam-5392	486	3	λ(v	λ(v	PROPN
ejpam-5392	486	4	)	)	PUNCT
ejpam-5392	486	5	⊆	⊆	NUM
ejpam-5392	486	6	rδβ	rδβ	NOUN
ejpam-5392	486	7	λ	λ	PROPN
ejpam-5392	486	8	(	(	PUNCT
ejpam-5392	486	9	v	v	NOUN
ejpam-5392	486	10	)	)	PUNCT
ejpam-5392	486	11	and	and	CCONJ
ejpam-5392	486	12	rδβ	rδβ	VERB
ejpam-5392	486	13	λ	λ	PROPN
ejpam-5392	486	14	(	(	PUNCT
ejpam-5392	486	15	v	v	NOUN
ejpam-5392	486	16	)	)	PUNCT
ejpam-5392	486	17	)	)	PUNCT
ejpam-5392	487	1	=	=	PUNCT
ejpam-5392	487	2	∪{g	∪{g	PROPN
ejpam-5392	487	3	∈	∈	PROPN
ejpam-5392	487	4	δβλo(x	δβλo(x	PROPN
ejpam-5392	487	5	)	)	PUNCT
ejpam-5392	487	6	:	:	PUNCT
ejpam-5392	487	7	g	g	PROPN
ejpam-5392	487	8	⊆	⊆	NUM
ejpam-5392	487	9	a	a	DET
ejpam-5392	487	10	}	}	PUNCT
ejpam-5392	487	11	⊆	⊆	NUM
ejpam-5392	487	12	∪{g	∪{g	PROPN
ejpam-5392	487	13	∈	∈	PROPN
ejpam-5392	487	14	l	l	PROPN
ejpam-5392	487	15	-	-	PUNCT
ejpam-5392	487	16	θβλo(x	θβλo(x	NOUN
ejpam-5392	487	17	)	)	PUNCT
ejpam-5392	487	18	:	:	PUNCT
ejpam-5392	487	19	g	g	PROPN
ejpam-5392	487	20	⊆	⊆	NUM
ejpam-5392	487	21	a	a	DET
ejpam-5392	487	22	}	}	PUNCT
ejpam-5392	487	23	=	=	SYM
ejpam-5392	487	24	rl−θβ	rl−θβ	PROPN
ejpam-5392	487	25	λ	λ	PROPN
ejpam-5392	487	26	(	(	PUNCT
ejpam-5392	487	27	v	v	NOUN
ejpam-5392	487	28	)	)	PUNCT
ejpam-5392	487	29	(	(	PUNCT
ejpam-5392	487	30	by	by	ADP
ejpam-5392	487	31	proposition	proposition	NOUN
ejpam-5392	487	32	6	6	NUM
ejpam-5392	487	33	)	)	PUNCT
ejpam-5392	487	34	.	.	PUNCT
ejpam-5392	488	1	m.	m.	PROPN
ejpam-5392	488	2	hosny	hosny	PROPN
ejpam-5392	488	3	,	,	PUNCT
ejpam-5392	488	4	t.m	t.m	PROPN
ejpam-5392	488	5	.	.	PROPN
ejpam-5392	488	6	al	al	PROPN
ejpam-5392	488	7	-	-	PUNCT
ejpam-5392	488	8	shami	shami	PROPN
ejpam-5392	488	9	/	/	PUNCT
ejpam-5392	488	10	eur	eur	PROPN
ejpam-5392	488	11	.	.	PUNCT
ejpam-5392	489	1	j.	j.	PROPN
ejpam-5392	489	2	pure	pure	PROPN
ejpam-5392	489	3	appl	appl	PROPN
ejpam-5392	489	4	.	.	PROPN
ejpam-5392	489	5	math	math	PROPN
ejpam-5392	489	6	,	,	PUNCT
ejpam-5392	489	7	17	17	NUM
ejpam-5392	489	8	(	(	PUNCT
ejpam-5392	489	9	4	4	NUM
ejpam-5392	489	10	)	)	PUNCT
ejpam-5392	489	11	(	(	PUNCT
ejpam-5392	489	12	2024	2024	NUM
ejpam-5392	489	13	)	)	PUNCT
ejpam-5392	489	14	,	,	PUNCT
ejpam-5392	489	15	3436	3436	NUM
ejpam-5392	489	16	-	-	SYM
ejpam-5392	489	17	3463	3463	NUM
ejpam-5392	489	18	3451	3451	NUM
ejpam-5392	489	19	(	(	PUNCT
ejpam-5392	489	20	ii)–(iv	ii)–(iv	NOUN
ejpam-5392	489	21	)	)	PUNCT
ejpam-5392	489	22	it	it	PRON
ejpam-5392	489	23	is	be	AUX
ejpam-5392	489	24	similar	similar	ADJ
ejpam-5392	489	25	to	to	ADP
ejpam-5392	489	26	(	(	PUNCT
ejpam-5392	489	27	i	i	NOUN
ejpam-5392	489	28	)	)	PUNCT
ejpam-5392	489	29	.	.	PUNCT
ejpam-5392	490	1	(	(	PUNCT
ejpam-5392	490	2	v	v	NOUN
ejpam-5392	490	3	)	)	PUNCT
ejpam-5392	490	4	by	by	ADP
ejpam-5392	490	5	theorem	theorem	NOUN
ejpam-5392	490	6	2	2	NUM
ejpam-5392	491	1	[	[	X
ejpam-5392	491	2	23	23	NUM
ejpam-5392	491	3	]	]	PUNCT
ejpam-5392	491	4	,	,	PUNCT
ejpam-5392	491	5	rλ(v	rλ(v	X
ejpam-5392	491	6	)	)	PUNCT
ejpam-5392	492	1	⊆	⊆	NUM
ejpam-5392	492	2	rδβλ(v	rδβλ(v	PROPN
ejpam-5392	492	3	)	)	PUNCT
ejpam-5392	492	4	,	,	PUNCT
ejpam-5392	492	5	and	and	CCONJ
ejpam-5392	492	6	by	by	ADP
ejpam-5392	492	7	(	(	PUNCT
ejpam-5392	492	8	1	1	X
ejpam-5392	492	9	)	)	PUNCT
ejpam-5392	492	10	rδβλ(v	rδβλ(v	PROPN
ejpam-5392	492	11	)	)	PUNCT
ejpam-5392	492	12	⊆	⊆	NUM
ejpam-5392	492	13	rl−θβ	rl−θβ	PROPN
ejpam-5392	492	14	λ	λ	PROPN
ejpam-5392	492	15	(	(	PUNCT
ejpam-5392	492	16	v	v	NOUN
ejpam-5392	492	17	)	)	PUNCT
ejpam-5392	492	18	.	.	PUNCT
ejpam-5392	493	1	hence	hence	ADV
ejpam-5392	493	2	,	,	PUNCT
ejpam-5392	493	3	rλ(v	rλ(v	NOUN
ejpam-5392	493	4	)	)	PUNCT
ejpam-5392	493	5	⊆	⊆	NUM
ejpam-5392	493	6	rl−θβ	rl−θβ	PROPN
ejpam-5392	493	7	λ	λ	PROPN
ejpam-5392	493	8	(	(	PUNCT
ejpam-5392	493	9	v	v	NOUN
ejpam-5392	493	10	)	)	PUNCT
ejpam-5392	493	11	.	.	PUNCT
ejpam-5392	494	1	(	(	PUNCT
ejpam-5392	494	2	vi)–(x	vi)–(x	NOUN
ejpam-5392	494	3	)	)	PUNCT
ejpam-5392	494	4	they	they	PRON
ejpam-5392	494	5	are	be	AUX
ejpam-5392	494	6	similar	similar	ADJ
ejpam-5392	494	7	to	to	ADP
ejpam-5392	494	8	(	(	PUNCT
ejpam-5392	494	9	i)–(v	i)–(v	PROPN
ejpam-5392	494	10	)	)	PUNCT
ejpam-5392	494	11	.	.	PUNCT
ejpam-5392	495	1	the	the	DET
ejpam-5392	495	2	subsequent	subsequent	ADJ
ejpam-5392	495	3	corollary	corollary	ADJ
ejpam-5392	495	4	points	point	NOUN
ejpam-5392	495	5	out	out	ADP
ejpam-5392	495	6	that	that	SCONJ
ejpam-5392	495	7	the	the	PRON
ejpam-5392	495	8	greater	great	ADJ
ejpam-5392	495	9	the	the	DET
ejpam-5392	495	10	size	size	NOUN
ejpam-5392	495	11	of	of	ADP
ejpam-5392	495	12	the	the	DET
ejpam-5392	495	13	boundary	boundary	ADJ
ejpam-5392	495	14	region	region	NOUN
ejpam-5392	495	15	,	,	PUNCT
ejpam-5392	495	16	the	the	PRON
ejpam-5392	495	17	lower	low	ADJ
ejpam-5392	495	18	the	the	DET
ejpam-5392	495	19	accuracy	accuracy	NOUN
ejpam-5392	495	20	measures	measure	NOUN
ejpam-5392	495	21	.	.	PUNCT
ejpam-5392	496	1	corollary	corollary	ADJ
ejpam-5392	496	2	3	3	NUM
ejpam-5392	496	3	.	.	PUNCT
ejpam-5392	497	1	if	if	SCONJ
ejpam-5392	497	2	v	v	NOUN
ejpam-5392	497	3	is	be	AUX
ejpam-5392	497	4	a	a	DET
ejpam-5392	497	5	subset	subset	NOUN
ejpam-5392	497	6	of	of	ADP
ejpam-5392	497	7	an	an	DET
ejpam-5392	497	8	l−gλ	l−gλ	ADJ
ejpam-5392	497	9	-	-	PUNCT
ejpam-5392	497	10	space	space	NOUN
ejpam-5392	497	11	(	(	PUNCT
ejpam-5392	497	12	x	x	NOUN
ejpam-5392	497	13	,	,	PUNCT
ejpam-5392	497	14	r	r	NOUN
ejpam-5392	497	15	,	,	PUNCT
ejpam-5392	497	16	ξλ	ξλ	NOUN
ejpam-5392	497	17	,	,	PUNCT
ejpam-5392	497	18	l	l	NOUN
ejpam-5392	497	19	)	)	PUNCT
ejpam-5392	497	20	,	,	PUNCT
ejpam-5392	497	21	then	then	ADV
ejpam-5392	497	22	the	the	DET
ejpam-5392	497	23	next	next	ADJ
ejpam-5392	497	24	properties	property	NOUN
ejpam-5392	497	25	are	be	AUX
ejpam-5392	497	26	satisfied	satisfied	ADJ
ejpam-5392	497	27	.	.	PUNCT
ejpam-5392	498	1	(	(	PUNCT
ejpam-5392	498	2	i	i	NOUN
ejpam-5392	498	3	)	)	PUNCT
ejpam-5392	498	4	bndl−θβλ(v	bndl−θβλ(v	VERB
ejpam-5392	498	5	)	)	PUNCT
ejpam-5392	499	1	⊆	⊆	NUM
ejpam-5392	499	2	bndδβ	bndδβ	PROPN
ejpam-5392	499	3	λ	λ	PROPN
ejpam-5392	499	4	(	(	PUNCT
ejpam-5392	499	5	v	v	NOUN
ejpam-5392	499	6	)	)	PUNCT
ejpam-5392	499	7	⊆	⊆	NUM
ejpam-5392	499	8	bndβ	bndβ	NOUN
ejpam-5392	499	9	λ(v	λ(v	PROPN
ejpam-5392	499	10	)	)	PUNCT
ejpam-5392	499	11	⊆	⊆	NUM
ejpam-5392	499	12	bndγ	bndγ	NOUN
ejpam-5392	499	13	λ(v	λ(v	PROPN
ejpam-5392	499	14	)	)	PUNCT
ejpam-5392	500	1	⊆	⊆	NUM
ejpam-5392	500	2	bndp	bndp	NOUN
ejpam-5392	500	3	λ(v	λ(v	PROPN
ejpam-5392	500	4	)	)	PUNCT
ejpam-5392	501	1	⊆	⊆	NUM
ejpam-5392	501	2	bndα	bndα	ADJ
ejpam-5392	501	3	λ(v	λ(v	PROPN
ejpam-5392	501	4	)	)	PUNCT
ejpam-5392	501	5	.	.	PUNCT
ejpam-5392	502	1	(	(	PUNCT
ejpam-5392	502	2	ii	ii	NOUN
ejpam-5392	502	3	)	)	PUNCT
ejpam-5392	502	4	bndl−θβλ(v	bndl−θβλ(v	NOUN
ejpam-5392	502	5	)	)	PUNCT
ejpam-5392	503	1	⊆	⊆	NUM
ejpam-5392	503	2	bndδβ	bndδβ	PROPN
ejpam-5392	503	3	λ	λ	PROPN
ejpam-5392	503	4	(	(	PUNCT
ejpam-5392	503	5	v	v	NOUN
ejpam-5392	503	6	)	)	PUNCT
ejpam-5392	503	7	⊆	⊆	NUM
ejpam-5392	503	8	bndβ	bndβ	NOUN
ejpam-5392	503	9	λ(v	λ(v	PROPN
ejpam-5392	503	10	)	)	PUNCT
ejpam-5392	503	11	⊆	⊆	NUM
ejpam-5392	503	12	bndγ	bndγ	NOUN
ejpam-5392	503	13	λ(v	λ(v	PROPN
ejpam-5392	503	14	)	)	PUNCT
ejpam-5392	504	1	⊆	⊆	NUM
ejpam-5392	504	2	bnds	bnd	NOUN
ejpam-5392	504	3	λ(v	λ(v	PROPN
ejpam-5392	504	4	)	)	PUNCT
ejpam-5392	505	1	⊆	⊆	NUM
ejpam-5392	505	2	bndα	bndα	ADJ
ejpam-5392	505	3	λ(v	λ(v	PROPN
ejpam-5392	505	4	)	)	PUNCT
ejpam-5392	505	5	.	.	PUNCT
ejpam-5392	506	1	(	(	PUNCT
ejpam-5392	506	2	iii	iii	X
ejpam-5392	506	3	)	)	PUNCT
ejpam-5392	506	4	bndl−θβλ(v	bndl−θβλ(v	NOUN
ejpam-5392	506	5	)	)	PUNCT
ejpam-5392	507	1	⊆	⊆	NUM
ejpam-5392	507	2	bnd	bnd	PROPN
ejpam-5392	507	3	∧	∧	PROPN
ejpam-5392	507	4	β	β	X
ejpam-5392	507	5	λ	λ	PROPN
ejpam-5392	507	6	(	(	PUNCT
ejpam-5392	507	7	v	v	NOUN
ejpam-5392	507	8	)	)	PUNCT
ejpam-5392	507	9	⊆	⊆	NUM
ejpam-5392	507	10	bndβ	bndβ	NOUN
ejpam-5392	507	11	λ(v	λ(v	PROPN
ejpam-5392	507	12	)	)	PUNCT
ejpam-5392	508	1	⊆	⊆	NUM
ejpam-5392	508	2	bndγ	bndγ	NOUN
ejpam-5392	508	3	λ(v	λ(v	PROPN
ejpam-5392	508	4	)	)	PUNCT
ejpam-5392	509	1	⊆	⊆	NUM
ejpam-5392	509	2	bndp	bndp	NOUN
ejpam-5392	509	3	λ(v	λ(v	PROPN
ejpam-5392	509	4	)	)	PUNCT
ejpam-5392	510	1	⊆	⊆	NUM
ejpam-5392	510	2	bndα	bndα	ADJ
ejpam-5392	510	3	λ(v	λ(v	PROPN
ejpam-5392	510	4	)	)	PUNCT
ejpam-5392	510	5	.	.	PUNCT
ejpam-5392	511	1	(	(	PUNCT
ejpam-5392	511	2	iv	iv	X
ejpam-5392	511	3	)	)	PUNCT
ejpam-5392	511	4	bndl−θβλ(v	bndl−θβλ(v	NOUN
ejpam-5392	511	5	)	)	PUNCT
ejpam-5392	512	1	⊆	⊆	NUM
ejpam-5392	512	2	bnd	bnd	PROPN
ejpam-5392	512	3	∧	∧	PROPN
ejpam-5392	512	4	β	β	X
ejpam-5392	512	5	λ	λ	PROPN
ejpam-5392	512	6	(	(	PUNCT
ejpam-5392	512	7	v	v	NOUN
ejpam-5392	512	8	)	)	PUNCT
ejpam-5392	512	9	⊆	⊆	NUM
ejpam-5392	512	10	bndβ	bndβ	NOUN
ejpam-5392	512	11	λ(v	λ(v	PROPN
ejpam-5392	512	12	)	)	PUNCT
ejpam-5392	513	1	⊆	⊆	NUM
ejpam-5392	513	2	bndγ	bndγ	NOUN
ejpam-5392	513	3	λ(v	λ(v	PROPN
ejpam-5392	513	4	)	)	PUNCT
ejpam-5392	514	1	⊆	⊆	NUM
ejpam-5392	514	2	bnds	bnd	NOUN
ejpam-5392	514	3	λ(v	λ(v	PROPN
ejpam-5392	514	4	)	)	PUNCT
ejpam-5392	515	1	⊆	⊆	NUM
ejpam-5392	515	2	bndα	bndα	ADJ
ejpam-5392	515	3	λ(v	λ(v	PROPN
ejpam-5392	515	4	)	)	PUNCT
ejpam-5392	515	5	.	.	PUNCT
ejpam-5392	516	1	(	(	PUNCT
ejpam-5392	516	2	v	v	NOUN
ejpam-5392	516	3	)	)	PUNCT
ejpam-5392	516	4	bndl−θβ	bndl−θβ	NOUN
ejpam-5392	517	1	λ	λ	INTJ
ejpam-5392	517	2	(	(	PUNCT
ejpam-5392	517	3	v	v	NOUN
ejpam-5392	517	4	)	)	PUNCT
ejpam-5392	517	5	⊆	⊆	NUM
ejpam-5392	517	6	bndλ(v	bndλ(v	NOUN
ejpam-5392	517	7	)	)	PUNCT
ejpam-5392	517	8	.	.	PUNCT
ejpam-5392	518	1	(	(	PUNCT
ejpam-5392	518	2	vi	vi	X
ejpam-5392	518	3	)	)	PUNCT
ejpam-5392	518	4	accαλ(v	accαλ(v	PROPN
ejpam-5392	518	5	)	)	PUNCT
ejpam-5392	518	6	⩽	⩽	PROPN
ejpam-5392	518	7	accpλ(v	accpλ(v	PROPN
ejpam-5392	518	8	)	)	PUNCT
ejpam-5392	518	9	⩽	⩽	NOUN
ejpam-5392	518	10	accγλ(v	accγλ(v	ADV
ejpam-5392	518	11	)	)	PUNCT
ejpam-5392	518	12	⩽	⩽	PROPN
ejpam-5392	518	13	accβλ(v	accβλ(v	PROPN
ejpam-5392	518	14	)	)	PUNCT
ejpam-5392	518	15	⩽	⩽	ADV
ejpam-5392	518	16	accδβλ	accδβλ	ADJ
ejpam-5392	518	17	(	(	PUNCT
ejpam-5392	518	18	v	v	NOUN
ejpam-5392	518	19	)	)	PUNCT
ejpam-5392	518	20	⩽	⩽	ADJ
ejpam-5392	518	21	accl−θβ	accl−θβ	PROPN
ejpam-5392	518	22	λ	λ	PROPN
ejpam-5392	518	23	(	(	PUNCT
ejpam-5392	518	24	v	v	NOUN
ejpam-5392	518	25	)	)	PUNCT
ejpam-5392	518	26	.	.	PUNCT
ejpam-5392	519	1	(	(	PUNCT
ejpam-5392	519	2	vii	vii	PROPN
ejpam-5392	519	3	)	)	PUNCT
ejpam-5392	519	4	accαλ(v	accαλ(v	PROPN
ejpam-5392	519	5	)	)	PUNCT
ejpam-5392	519	6	⩽	⩽	PROPN
ejpam-5392	519	7	accsλ(v	accsλ(v	PROPN
ejpam-5392	519	8	)	)	PUNCT
ejpam-5392	519	9	⩽	⩽	NOUN
ejpam-5392	519	10	accγλ(v	accγλ(v	ADV
ejpam-5392	519	11	)	)	PUNCT
ejpam-5392	519	12	⩽	⩽	PROPN
ejpam-5392	519	13	accβλ(v	accβλ(v	PROPN
ejpam-5392	519	14	)	)	PUNCT
ejpam-5392	519	15	⩽	⩽	ADV
ejpam-5392	519	16	accδβλ	accδβλ	ADJ
ejpam-5392	519	17	(	(	PUNCT
ejpam-5392	519	18	v	v	NOUN
ejpam-5392	519	19	)	)	PUNCT
ejpam-5392	519	20	⩽	⩽	ADJ
ejpam-5392	519	21	accl−θβ	accl−θβ	PROPN
ejpam-5392	519	22	λ	λ	PROPN
ejpam-5392	519	23	(	(	PUNCT
ejpam-5392	519	24	v	v	NOUN
ejpam-5392	519	25	)	)	PUNCT
ejpam-5392	519	26	.	.	PUNCT
ejpam-5392	520	1	(	(	PUNCT
ejpam-5392	520	2	viii	viii	NOUN
ejpam-5392	520	3	)	)	PUNCT
ejpam-5392	520	4	accαλ(v	accαλ(v	PROPN
ejpam-5392	520	5	)	)	PUNCT
ejpam-5392	520	6	⩽	⩽	PROPN
ejpam-5392	520	7	accpλ(v	accpλ(v	PROPN
ejpam-5392	520	8	)	)	PUNCT
ejpam-5392	520	9	⩽	⩽	NOUN
ejpam-5392	520	10	accγλ(v	accγλ(v	ADV
ejpam-5392	520	11	)	)	PUNCT
ejpam-5392	520	12	⩽	⩽	PROPN
ejpam-5392	520	13	accβλ(v	accβλ(v	PROPN
ejpam-5392	520	14	)	)	PUNCT
ejpam-5392	521	1	⩽	⩽	ADJ
ejpam-5392	521	2	acc	acc	PROPN
ejpam-5392	521	3	∧	∧	PROPN
ejpam-5392	521	4	β	β	X
ejpam-5392	521	5	λ	λ	PROPN
ejpam-5392	521	6	(	(	PUNCT
ejpam-5392	521	7	v	v	NOUN
ejpam-5392	521	8	)	)	PUNCT
ejpam-5392	521	9	⩽	⩽	NOUN
ejpam-5392	521	10	acc	acc	PROPN
ejpam-5392	521	11	l−θβ	l−θβ	PROPN
ejpam-5392	521	12	λ	λ	PROPN
ejpam-5392	521	13	(	(	PUNCT
ejpam-5392	521	14	v	v	NOUN
ejpam-5392	521	15	)	)	PUNCT
ejpam-5392	521	16	.	.	PUNCT
ejpam-5392	522	1	(	(	PUNCT
ejpam-5392	522	2	ix	ix	CCONJ
ejpam-5392	522	3	)	)	PUNCT
ejpam-5392	522	4	accαλ(v	accαλ(v	PROPN
ejpam-5392	522	5	)	)	PUNCT
ejpam-5392	522	6	⩽	⩽	PROPN
ejpam-5392	522	7	accsλ(v	accsλ(v	PROPN
ejpam-5392	522	8	)	)	PUNCT
ejpam-5392	522	9	⩽	⩽	NOUN
ejpam-5392	522	10	accγλ(v	accγλ(v	ADV
ejpam-5392	522	11	)	)	PUNCT
ejpam-5392	522	12	⩽	⩽	PROPN
ejpam-5392	522	13	accβλ(v	accβλ(v	PROPN
ejpam-5392	522	14	)	)	PUNCT
ejpam-5392	523	1	⩽	⩽	ADJ
ejpam-5392	523	2	acc	acc	PROPN
ejpam-5392	523	3	∧	∧	PROPN
ejpam-5392	523	4	β	β	X
ejpam-5392	523	5	λ	λ	PROPN
ejpam-5392	523	6	(	(	PUNCT
ejpam-5392	523	7	v	v	NOUN
ejpam-5392	523	8	)	)	PUNCT
ejpam-5392	523	9	⩽	⩽	NOUN
ejpam-5392	523	10	acc	acc	PROPN
ejpam-5392	523	11	l−θβ	l−θβ	PROPN
ejpam-5392	523	12	λ	λ	PROPN
ejpam-5392	523	13	(	(	PUNCT
ejpam-5392	523	14	v	v	NOUN
ejpam-5392	523	15	)	)	PUNCT
ejpam-5392	523	16	.	.	PUNCT
ejpam-5392	524	1	(	(	PUNCT
ejpam-5392	524	2	x	x	X
ejpam-5392	524	3	)	)	PUNCT
ejpam-5392	524	4	accλ(v	accλ(v	PROPN
ejpam-5392	524	5	)	)	PUNCT
ejpam-5392	524	6	⩽	⩽	ADJ
ejpam-5392	524	7	accl−θβ	accl−θβ	PROPN
ejpam-5392	524	8	λ	λ	PROPN
ejpam-5392	524	9	(	(	PUNCT
ejpam-5392	524	10	v	v	NOUN
ejpam-5392	524	11	)	)	PUNCT
ejpam-5392	524	12	.	.	PUNCT
ejpam-5392	525	1	remark	remark	PROPN
ejpam-5392	525	2	4	4	NUM
ejpam-5392	525	3	.	.	PUNCT
ejpam-5392	526	1	the	the	DET
ejpam-5392	526	2	converse	converse	NOUN
ejpam-5392	526	3	of	of	ADP
ejpam-5392	526	4	the	the	DET
ejpam-5392	526	5	implications	implication	NOUN
ejpam-5392	526	6	in	in	ADP
ejpam-5392	526	7	theorem	theorem	ADJ
ejpam-5392	526	8	5	5	NUM
ejpam-5392	526	9	and	and	CCONJ
ejpam-5392	526	10	corollary	corollary	ADJ
ejpam-5392	526	11	3	3	NUM
ejpam-5392	526	12	is	be	AUX
ejpam-5392	526	13	not	not	PART
ejpam-5392	526	14	true	true	ADJ
ejpam-5392	526	15	in	in	ADP
ejpam-5392	526	16	general	general	ADJ
ejpam-5392	526	17	as	as	SCONJ
ejpam-5392	526	18	shown	show	VERB
ejpam-5392	526	19	in	in	ADP
ejpam-5392	526	20	(	(	PUNCT
ejpam-5392	526	21	i	i	NOUN
ejpam-5392	526	22	)	)	PUNCT
ejpam-5392	526	23	example	example	NOUN
ejpam-5392	527	1	2	2	NUM
ejpam-5392	527	2	,	,	PUNCT
ejpam-5392	527	3	if	if	SCONJ
ejpam-5392	527	4	v	v	ADJ
ejpam-5392	527	5	=	=	SYM
ejpam-5392	527	6	{	{	PUNCT
ejpam-5392	527	7	y4	y4	X
ejpam-5392	527	8	}	}	PUNCT
ejpam-5392	527	9	,	,	PUNCT
ejpam-5392	527	10	then	then	ADV
ejpam-5392	527	11	rl−θβ	rl−θβ	PROPN
ejpam-5392	527	12	a	a	DET
ejpam-5392	527	13	(	(	PUNCT
ejpam-5392	527	14	v	v	NOUN
ejpam-5392	527	15	)	)	PUNCT
ejpam-5392	527	16	=	=	SYM
ejpam-5392	527	17	a	a	PRON
ejpam-5392	527	18	,	,	PUNCT
ejpam-5392	527	19	rl−θβ	rl−θβ	PROPN
ejpam-5392	527	20	a	a	DET
ejpam-5392	527	21	(	(	PUNCT
ejpam-5392	527	22	v	v	NOUN
ejpam-5392	527	23	)	)	PUNCT
ejpam-5392	527	24	=	=	SYM
ejpam-5392	527	25	a	a	PROPN
ejpam-5392	527	26	,	,	PUNCT
ejpam-5392	527	27	bndl−θβ	bndl−θβ	PROPN
ejpam-5392	527	28	a	a	DET
ejpam-5392	527	29	(	(	PUNCT
ejpam-5392	527	30	v	v	NOUN
ejpam-5392	527	31	)	)	PUNCT
ejpam-5392	527	32	=	=	NOUN
ejpam-5392	527	33	∅	∅	NOUN
ejpam-5392	527	34	,	,	PUNCT
ejpam-5392	527	35	accl−θβ	accl−θβ	NOUN
ejpam-5392	527	36	a(v	a(v	ADV
ejpam-5392	527	37	)	)	PUNCT
ejpam-5392	527	38	=	=	SYM
ejpam-5392	527	39	1	1	NUM
ejpam-5392	527	40	,	,	PUNCT
ejpam-5392	527	41	and	and	CCONJ
ejpam-5392	527	42	rδβ	rδβ	VERB
ejpam-5392	527	43	a(v	a(v	ADV
ejpam-5392	527	44	)	)	PUNCT
ejpam-5392	527	45	=	=	SYM
ejpam-5392	527	46	∅	∅	NOUN
ejpam-5392	527	47	,	,	PUNCT
ejpam-5392	527	48	rδβ	rδβ	NOUN
ejpam-5392	527	49	a(v	a(v	PROPN
ejpam-5392	527	50	)	)	PUNCT
ejpam-5392	527	51	=	=	SYM
ejpam-5392	527	52	a	a	PRON
ejpam-5392	527	53	and	and	CCONJ
ejpam-5392	527	54	bndδβ	bndδβ	NOUN
ejpam-5392	527	55	a(v	a(v	PROPN
ejpam-5392	527	56	)	)	PUNCT
ejpam-5392	527	57	=	=	SYM
ejpam-5392	527	58	a	a	PRON
ejpam-5392	527	59	,	,	PUNCT
ejpam-5392	527	60	accδβa(v	accδβa(v	NOUN
ejpam-5392	527	61	)	)	PUNCT
ejpam-5392	527	62	=	=	SYM
ejpam-5392	527	63	0	0	X
ejpam-5392	527	64	.	.	PUNCT
ejpam-5392	527	65	(	(	PUNCT
ejpam-5392	527	66	ii	ii	NOUN
ejpam-5392	527	67	)	)	PUNCT
ejpam-5392	527	68	example	example	NOUN
ejpam-5392	527	69	3	3	NUM
ejpam-5392	527	70	,	,	PUNCT
ejpam-5392	527	71	if	if	SCONJ
ejpam-5392	527	72	v	v	ADJ
ejpam-5392	527	73	=	=	SYM
ejpam-5392	527	74	{	{	PUNCT
ejpam-5392	527	75	y	y	NOUN
ejpam-5392	527	76	}	}	PUNCT
ejpam-5392	527	77	,	,	PUNCT
ejpam-5392	527	78	then	then	ADV
ejpam-5392	527	79	rl−θβ	rl−θβ	PROPN
ejpam-5392	527	80	a	a	DET
ejpam-5392	527	81	(	(	PUNCT
ejpam-5392	527	82	v	v	NOUN
ejpam-5392	527	83	)	)	PUNCT
ejpam-5392	527	84	=	=	SYM
ejpam-5392	527	85	a	a	PRON
ejpam-5392	527	86	,	,	PUNCT
ejpam-5392	527	87	rl−θβ	rl−θβ	PROPN
ejpam-5392	527	88	a	a	DET
ejpam-5392	527	89	(	(	PUNCT
ejpam-5392	527	90	v	v	NOUN
ejpam-5392	527	91	)	)	PUNCT
ejpam-5392	527	92	=	=	PUNCT
ejpam-5392	527	93	a	a	PRON
ejpam-5392	527	94	,	,	PUNCT
ejpam-5392	527	95	bndl−θβ	bndl−θβ	PROPN
ejpam-5392	527	96	a	a	DET
ejpam-5392	527	97	(	(	PUNCT
ejpam-5392	527	98	v	v	NOUN
ejpam-5392	527	99	)	)	PUNCT
ejpam-5392	527	100	=	=	NOUN
ejpam-5392	527	101	∅	∅	NOUN
ejpam-5392	527	102	,	,	PUNCT
ejpam-5392	527	103	accl−θβ	accl−θβ	NOUN
ejpam-5392	527	104	a	a	DET
ejpam-5392	527	105	(	(	PUNCT
ejpam-5392	527	106	v	v	NOUN
ejpam-5392	527	107	)	)	PUNCT
ejpam-5392	527	108	=	=	SYM
ejpam-5392	527	109	1	1	NUM
ejpam-5392	527	110	,	,	PUNCT
ejpam-5392	527	111	and	and	CCONJ
ejpam-5392	527	112	rl−	rl−	PROPN
ejpam-5392	527	113	∧	∧	PROPN
ejpam-5392	527	114	βa(v	βa(v	PUNCT
ejpam-5392	527	115	)	)	PUNCT
ejpam-5392	527	116	=	=	SYM
ejpam-5392	527	117	∅,rl−	∅,rl−	NOUN
ejpam-5392	527	118	∧	∧	PROPN
ejpam-5392	527	119	βa(v	βa(v	PUNCT
ejpam-5392	527	120	)	)	PUNCT
ejpam-5392	527	121	=	=	SYM
ejpam-5392	527	122	a	a	PRON
ejpam-5392	527	123	,	,	PUNCT
ejpam-5392	527	124	bndl−	bndl−	VERB
ejpam-5392	527	125	∧	∧	NOUN
ejpam-5392	527	126	βa(v	βa(v	PUNCT
ejpam-5392	527	127	)	)	PUNCT
ejpam-5392	527	128	=	=	SYM
ejpam-5392	527	129	a	a	PRON
ejpam-5392	527	130	,	,	PUNCT
ejpam-5392	527	131	accl−	accl−	NOUN
ejpam-5392	527	132	∧	∧	PROPN
ejpam-5392	527	133	βa(v	βa(v	PUNCT
ejpam-5392	527	134	)	)	PUNCT
ejpam-5392	527	135	=	=	SYM
ejpam-5392	527	136	0	0	X
ejpam-5392	527	137	.	.	PUNCT
ejpam-5392	527	138	corollary	corollary	ADJ
ejpam-5392	527	139	4	4	NUM
ejpam-5392	527	140	.	.	PUNCT
ejpam-5392	527	141	for	for	ADP
ejpam-5392	527	142	a	a	DET
ejpam-5392	527	143	subset	subset	NOUN
ejpam-5392	527	144	v	v	NOUN
ejpam-5392	527	145	of	of	ADP
ejpam-5392	527	146	an	an	DET
ejpam-5392	527	147	l−gλ	l−gλ	ADJ
ejpam-5392	527	148	-	-	PUNCT
ejpam-5392	527	149	space	space	NOUN
ejpam-5392	527	150	(	(	PUNCT
ejpam-5392	527	151	x	x	NOUN
ejpam-5392	527	152	,	,	PUNCT
ejpam-5392	527	153	r	r	NOUN
ejpam-5392	527	154	,	,	PUNCT
ejpam-5392	527	155	ξλ	ξλ	NOUN
ejpam-5392	527	156	,	,	PUNCT
ejpam-5392	527	157	l	l	NOUN
ejpam-5392	527	158	)	)	PUNCT
ejpam-5392	527	159	,	,	PUNCT
ejpam-5392	527	160	we	we	PRON
ejpam-5392	527	161	have	have	VERB
ejpam-5392	527	162	the	the	DET
ejpam-5392	527	163	next	next	ADJ
ejpam-5392	527	164	results	result	NOUN
ejpam-5392	527	165	.	.	PUNCT
ejpam-5392	528	1	m.	m.	PROPN
ejpam-5392	528	2	hosny	hosny	PROPN
ejpam-5392	528	3	,	,	PUNCT
ejpam-5392	528	4	t.m	t.m	PROPN
ejpam-5392	528	5	.	.	PROPN
ejpam-5392	528	6	al	al	PROPN
ejpam-5392	528	7	-	-	PUNCT
ejpam-5392	528	8	shami	shami	PROPN
ejpam-5392	528	9	/	/	PUNCT
ejpam-5392	528	10	eur	eur	PROPN
ejpam-5392	528	11	.	.	PUNCT
ejpam-5392	529	1	j.	j.	PROPN
ejpam-5392	529	2	pure	pure	PROPN
ejpam-5392	529	3	appl	appl	PROPN
ejpam-5392	529	4	.	.	PROPN
ejpam-5392	529	5	math	math	PROPN
ejpam-5392	529	6	,	,	PUNCT
ejpam-5392	529	7	17	17	NUM
ejpam-5392	529	8	(	(	PUNCT
ejpam-5392	529	9	4	4	NUM
ejpam-5392	529	10	)	)	PUNCT
ejpam-5392	529	11	(	(	PUNCT
ejpam-5392	529	12	2024	2024	NUM
ejpam-5392	529	13	)	)	PUNCT
ejpam-5392	529	14	,	,	PUNCT
ejpam-5392	529	15	3436	3436	NUM
ejpam-5392	529	16	-	-	SYM
ejpam-5392	529	17	3463	3463	NUM
ejpam-5392	529	18	3452	3452	NUM
ejpam-5392	529	19	(	(	PUNCT
ejpam-5392	529	20	i	i	NOUN
ejpam-5392	529	21	)	)	PUNCT
ejpam-5392	529	22	v	v	NOUN
ejpam-5392	529	23	is	be	AUX
ejpam-5392	529	24	αλ	αλ	PRON
ejpam-5392	529	25	-	-	PUNCT
ejpam-5392	529	26	exact	exact	ADJ
ejpam-5392	529	27	⇒	⇒	NOUN
ejpam-5392	529	28	v	v	NOUN
ejpam-5392	529	29	is	be	AUX
ejpam-5392	529	30	sλ	sλ	NOUN
ejpam-5392	529	31	-	-	PUNCT
ejpam-5392	529	32	exact	exact	ADJ
ejpam-5392	529	33	⇒	⇒	NOUN
ejpam-5392	529	34	v	v	NOUN
ejpam-5392	529	35	is	be	AUX
ejpam-5392	529	36	βλ	βλ	ADJ
ejpam-5392	529	37	-	-	PUNCT
ejpam-5392	529	38	exact	exact	ADJ
ejpam-5392	529	39	⇒	⇒	NOUN
ejpam-5392	529	40	δβλ	δβλ	NOUN
ejpam-5392	529	41	-	-	PUNCT
ejpam-5392	529	42	exact	exact	ADJ
ejpam-5392	529	43	⇒	⇒	NOUN
ejpam-5392	529	44	v	v	NOUN
ejpam-5392	529	45	is	be	AUX
ejpam-5392	529	46	l	l	NOUN
ejpam-5392	529	47	-	-	PUNCT
ejpam-5392	529	48	θβλ	θβλ	NOUN
ejpam-5392	529	49	-	-	PUNCT
ejpam-5392	529	50	exact	exact	NOUN
ejpam-5392	529	51	.	.	PUNCT
ejpam-5392	530	1	(	(	PUNCT
ejpam-5392	530	2	ii	ii	NOUN
ejpam-5392	530	3	)	)	PUNCT
ejpam-5392	530	4	v	v	NOUN
ejpam-5392	530	5	is	be	AUX
ejpam-5392	530	6	pλ	pλ	ADJ
ejpam-5392	530	7	-	-	PUNCT
ejpam-5392	530	8	exact	exact	ADJ
ejpam-5392	530	9	⇒	⇒	NOUN
ejpam-5392	530	10	v	v	NOUN
ejpam-5392	530	11	is	be	AUX
ejpam-5392	530	12	βλ	βλ	ADJ
ejpam-5392	530	13	-	-	PUNCT
ejpam-5392	530	14	exact	exact	ADJ
ejpam-5392	530	15	⇒	⇒	NOUN
ejpam-5392	530	16	v	v	NOUN
ejpam-5392	530	17	is	be	AUX
ejpam-5392	530	18	δβλ	δβλ	NOUN
ejpam-5392	530	19	-	-	PUNCT
ejpam-5392	530	20	exact	exact	ADJ
ejpam-5392	530	21	⇒	⇒	NOUN
ejpam-5392	530	22	v	v	NOUN
ejpam-5392	530	23	is	be	AUX
ejpam-5392	530	24	l	l	NOUN
ejpam-5392	530	25	-	-	PUNCT
ejpam-5392	530	26	θβλ	θβλ	NOUN
ejpam-5392	530	27	-	-	PUNCT
ejpam-5392	530	28	exact	exact	NOUN
ejpam-5392	530	29	.	.	PUNCT
ejpam-5392	531	1	(	(	PUNCT
ejpam-5392	531	2	iii	iii	X
ejpam-5392	531	3	)	)	PUNCT
ejpam-5392	531	4	v	v	NOUN
ejpam-5392	531	5	is	be	AUX
ejpam-5392	531	6	αλ	αλ	PRON
ejpam-5392	531	7	-	-	PUNCT
ejpam-5392	531	8	exact	exact	ADJ
ejpam-5392	531	9	⇒	⇒	NOUN
ejpam-5392	531	10	v	v	NOUN
ejpam-5392	531	11	is	be	AUX
ejpam-5392	531	12	sλ	sλ	NOUN
ejpam-5392	531	13	-	-	PUNCT
ejpam-5392	531	14	exact	exact	ADJ
ejpam-5392	531	15	⇒	⇒	NOUN
ejpam-5392	531	16	v	v	NOUN
ejpam-5392	531	17	is	be	AUX
ejpam-5392	531	18	βλ	βλ	ADJ
ejpam-5392	531	19	-	-	PUNCT
ejpam-5392	531	20	exact	exact	ADJ
ejpam-5392	531	21	⇒	⇒	NOUN
ejpam-5392	531	22	v	v	NOUN
ejpam-5392	531	23	is	be	AUX
ejpam-5392	531	24	∧	∧	PROPN
ejpam-5392	531	25	βλ	βλ	NOUN
ejpam-5392	531	26	-exact	-exact	PROPN
ejpam-5392	531	27	⇒	⇒	NOUN
ejpam-5392	531	28	v	v	NOUN
ejpam-5392	531	29	is	be	AUX
ejpam-5392	531	30	l	l	NOUN
ejpam-5392	531	31	-	-	NOUN
ejpam-5392	531	32	θβλexact	θβλexact	NOUN
ejpam-5392	531	33	.	.	PUNCT
ejpam-5392	532	1	(	(	PUNCT
ejpam-5392	532	2	iv	iv	X
ejpam-5392	532	3	)	)	PUNCT
ejpam-5392	532	4	v	v	NOUN
ejpam-5392	532	5	is	be	AUX
ejpam-5392	532	6	pλ	pλ	ADJ
ejpam-5392	532	7	-	-	PUNCT
ejpam-5392	532	8	exact	exact	ADJ
ejpam-5392	532	9	⇒	⇒	NOUN
ejpam-5392	532	10	v	v	NOUN
ejpam-5392	532	11	is	be	AUX
ejpam-5392	532	12	βλ	βλ	ADJ
ejpam-5392	532	13	-	-	PUNCT
ejpam-5392	532	14	exact	exact	ADJ
ejpam-5392	532	15	⇒	⇒	NOUN
ejpam-5392	532	16	v	v	NOUN
ejpam-5392	532	17	is	be	AUX
ejpam-5392	532	18	∧	∧	PROPN
ejpam-5392	532	19	βλ	βλ	NOUN
ejpam-5392	532	20	-exact	-exact	PROPN
ejpam-5392	532	21	⇒	⇒	NOUN
ejpam-5392	532	22	v	v	NOUN
ejpam-5392	532	23	is	be	AUX
ejpam-5392	532	24	l	l	NOUN
ejpam-5392	532	25	-	-	PUNCT
ejpam-5392	532	26	θβλ	θβλ	NOUN
ejpam-5392	532	27	-	-	PUNCT
ejpam-5392	532	28	exact	exact	NOUN
ejpam-5392	532	29	.	.	PUNCT
ejpam-5392	533	1	(	(	PUNCT
ejpam-5392	533	2	v	v	NOUN
ejpam-5392	533	3	)	)	PUNCT
ejpam-5392	533	4	v	v	NOUN
ejpam-5392	533	5	is	be	AUX
ejpam-5392	533	6	λ	λ	NOUN
ejpam-5392	533	7	-	-	ADJ
ejpam-5392	533	8	exact	exact	ADJ
ejpam-5392	533	9	⇒	⇒	NOUN
ejpam-5392	533	10	v	v	NOUN
ejpam-5392	533	11	is	be	AUX
ejpam-5392	533	12	l	l	NOUN
ejpam-5392	533	13	-	-	PUNCT
ejpam-5392	533	14	θβλ	θβλ	NOUN
ejpam-5392	533	15	-	-	PUNCT
ejpam-5392	533	16	exact	exact	NOUN
ejpam-5392	533	17	.	.	PUNCT
ejpam-5392	534	1	(	(	PUNCT
ejpam-5392	534	2	vi	vi	NOUN
ejpam-5392	534	3	)	)	PUNCT
ejpam-5392	534	4	v	v	NOUN
ejpam-5392	534	5	is	be	AUX
ejpam-5392	534	6	l	l	NOUN
ejpam-5392	534	7	-	-	PUNCT
ejpam-5392	534	8	θβλ	θβλ	NOUN
ejpam-5392	534	9	-	-	PUNCT
ejpam-5392	534	10	rough	rough	ADJ
ejpam-5392	534	11	⇒	⇒	NOUN
ejpam-5392	534	12	v	v	NOUN
ejpam-5392	534	13	is	be	AUX
ejpam-5392	534	14	δβλ	δβλ	NOUN
ejpam-5392	534	15	-	-	PUNCT
ejpam-5392	534	16	rough	rough	ADJ
ejpam-5392	534	17	⇒	⇒	NOUN
ejpam-5392	534	18	v	v	NOUN
ejpam-5392	534	19	is	be	AUX
ejpam-5392	534	20	βλ	βλ	NOUN
ejpam-5392	534	21	-	-	ADJ
ejpam-5392	534	22	rough	rough	ADJ
ejpam-5392	534	23	⇒	⇒	NOUN
ejpam-5392	534	24	v	v	NOUN
ejpam-5392	534	25	is	be	AUX
ejpam-5392	534	26	sλ	sλ	NOUN
ejpam-5392	534	27	-	-	PUNCT
ejpam-5392	534	28	rough	rough	ADJ
ejpam-5392	534	29	⇒	⇒	NOUN
ejpam-5392	534	30	v	v	NOUN
ejpam-5392	534	31	is	be	AUX
ejpam-5392	534	32	αλ	αλ	PRON
ejpam-5392	534	33	-	-	PUNCT
ejpam-5392	534	34	rough	rough	ADJ
ejpam-5392	534	35	.	.	PUNCT
ejpam-5392	535	1	(	(	PUNCT
ejpam-5392	535	2	vii	vii	PROPN
ejpam-5392	535	3	)	)	PUNCT
ejpam-5392	535	4	v	v	NOUN
ejpam-5392	535	5	is	be	AUX
ejpam-5392	535	6	l	l	NOUN
ejpam-5392	535	7	-	-	PUNCT
ejpam-5392	535	8	θβλ	θβλ	NOUN
ejpam-5392	535	9	-	-	PUNCT
ejpam-5392	535	10	rough	rough	ADJ
ejpam-5392	535	11	⇒	⇒	NOUN
ejpam-5392	535	12	v	v	NOUN
ejpam-5392	535	13	is	be	AUX
ejpam-5392	535	14	δβλ	δβλ	NOUN
ejpam-5392	535	15	-	-	PUNCT
ejpam-5392	535	16	rough	rough	ADJ
ejpam-5392	535	17	⇒	⇒	NOUN
ejpam-5392	535	18	v	v	NOUN
ejpam-5392	535	19	is	be	AUX
ejpam-5392	535	20	βλ	βλ	NOUN
ejpam-5392	535	21	-	-	ADJ
ejpam-5392	535	22	rough	rough	ADJ
ejpam-5392	535	23	⇒	⇒	NOUN
ejpam-5392	535	24	v	v	NOUN
ejpam-5392	535	25	is	be	AUX
ejpam-5392	535	26	pλ	pλ	ADJ
ejpam-5392	535	27	-	-	ADV
ejpam-5392	535	28	rough	rough	ADJ
ejpam-5392	535	29	.	.	PUNCT
ejpam-5392	536	1	(	(	PUNCT
ejpam-5392	536	2	viii	viii	NOUN
ejpam-5392	536	3	)	)	PUNCT
ejpam-5392	536	4	v	v	NOUN
ejpam-5392	536	5	is	be	AUX
ejpam-5392	536	6	l	l	NOUN
ejpam-5392	536	7	-	-	PUNCT
ejpam-5392	536	8	θβλ	θβλ	NOUN
ejpam-5392	536	9	-	-	PUNCT
ejpam-5392	536	10	rough	rough	ADJ
ejpam-5392	536	11	⇒	⇒	NOUN
ejpam-5392	536	12	v	v	NOUN
ejpam-5392	536	13	is	be	AUX
ejpam-5392	536	14	∧	∧	PROPN
ejpam-5392	537	1	βλ	βλ	NOUN
ejpam-5392	537	2	-rough	-rough	PROPN
ejpam-5392	537	3	⇒	⇒	NOUN
ejpam-5392	537	4	v	v	NOUN
ejpam-5392	537	5	is	be	AUX
ejpam-5392	537	6	βλ	βλ	NOUN
ejpam-5392	537	7	-	-	ADJ
ejpam-5392	537	8	rough	rough	ADJ
ejpam-5392	537	9	⇒	⇒	NOUN
ejpam-5392	537	10	v	v	NOUN
ejpam-5392	537	11	is	be	AUX
ejpam-5392	537	12	sλ	sλ	NOUN
ejpam-5392	537	13	-	-	PUNCT
ejpam-5392	537	14	rough	rough	ADJ
ejpam-5392	537	15	⇒	⇒	NOUN
ejpam-5392	537	16	v	v	NOUN
ejpam-5392	537	17	is	be	AUX
ejpam-5392	537	18	αλ	αλ	PRON
ejpam-5392	537	19	-	-	PUNCT
ejpam-5392	537	20	rough	rough	ADJ
ejpam-5392	537	21	.	.	PUNCT
ejpam-5392	538	1	(	(	PUNCT
ejpam-5392	538	2	ix	ix	PROPN
ejpam-5392	538	3	)	)	PUNCT
ejpam-5392	538	4	v	v	NOUN
ejpam-5392	538	5	is	be	AUX
ejpam-5392	538	6	l	l	NOUN
ejpam-5392	538	7	-	-	PUNCT
ejpam-5392	538	8	θβλ	θβλ	NOUN
ejpam-5392	538	9	-	-	PUNCT
ejpam-5392	538	10	rough	rough	ADJ
ejpam-5392	538	11	⇒	⇒	NOUN
ejpam-5392	538	12	v	v	NOUN
ejpam-5392	538	13	is	be	AUX
ejpam-5392	538	14	∧	∧	PROPN
ejpam-5392	539	1	βλ	βλ	NOUN
ejpam-5392	539	2	-rough	-rough	PROPN
ejpam-5392	539	3	⇒	⇒	NOUN
ejpam-5392	539	4	v	v	NOUN
ejpam-5392	539	5	is	be	AUX
ejpam-5392	539	6	βλ	βλ	NOUN
ejpam-5392	539	7	-	-	ADJ
ejpam-5392	539	8	rough	rough	ADJ
ejpam-5392	539	9	⇒	⇒	NOUN
ejpam-5392	539	10	v	v	NOUN
ejpam-5392	539	11	is	be	AUX
ejpam-5392	539	12	pλ	pλ	ADJ
ejpam-5392	539	13	-	-	ADV
ejpam-5392	539	14	rough	rough	ADJ
ejpam-5392	539	15	.	.	PUNCT
ejpam-5392	540	1	(	(	PUNCT
ejpam-5392	540	2	x	x	X
ejpam-5392	540	3	)	)	PUNCT
ejpam-5392	540	4	v	v	NOUN
ejpam-5392	540	5	is	be	AUX
ejpam-5392	540	6	l	l	NOUN
ejpam-5392	540	7	-	-	PUNCT
ejpam-5392	540	8	θβλ	θβλ	NOUN
ejpam-5392	540	9	-	-	PUNCT
ejpam-5392	540	10	rough	rough	ADJ
ejpam-5392	540	11	⇒	⇒	NOUN
ejpam-5392	540	12	v	v	NOUN
ejpam-5392	540	13	is	be	AUX
ejpam-5392	540	14	λ	λ	NOUN
ejpam-5392	540	15	-	-	NOUN
ejpam-5392	540	16	rough	rough	ADJ
ejpam-5392	540	17	.	.	PUNCT
ejpam-5392	541	1	remark	remark	NOUN
ejpam-5392	541	2	5	5	NUM
ejpam-5392	541	3	.	.	PUNCT
ejpam-5392	542	1	the	the	DET
ejpam-5392	542	2	converse	converse	NOUN
ejpam-5392	542	3	of	of	ADP
ejpam-5392	542	4	corollary	corollary	ADJ
ejpam-5392	542	5	4	4	NUM
ejpam-5392	542	6	is	be	AUX
ejpam-5392	542	7	wrong	wrong	ADJ
ejpam-5392	542	8	in	in	ADP
ejpam-5392	542	9	general	general	ADJ
ejpam-5392	542	10	.	.	PUNCT
ejpam-5392	543	1	we	we	PRON
ejpam-5392	543	2	demonstrate	demonstrate	VERB
ejpam-5392	543	3	this	this	DET
ejpam-5392	543	4	claim	claim	NOUN
ejpam-5392	543	5	in	in	ADP
ejpam-5392	543	6	the	the	DET
ejpam-5392	543	7	following	following	NOUN
ejpam-5392	543	8	.	.	PUNCT
ejpam-5392	544	1	(	(	PUNCT
ejpam-5392	544	2	i	i	NOUN
ejpam-5392	544	3	)	)	PUNCT
ejpam-5392	544	4	example	example	NOUN
ejpam-5392	544	5	2	2	NUM
ejpam-5392	544	6	,	,	PUNCT
ejpam-5392	544	7	if	if	SCONJ
ejpam-5392	544	8	v	v	ADJ
ejpam-5392	544	9	=	=	SYM
ejpam-5392	544	10	{	{	PUNCT
ejpam-5392	544	11	y4	y4	X
ejpam-5392	544	12	}	}	PUNCT
ejpam-5392	544	13	,	,	PUNCT
ejpam-5392	544	14	then	then	ADV
ejpam-5392	544	15	it	it	PRON
ejpam-5392	544	16	is	be	AUX
ejpam-5392	544	17	l	l	NOUN
ejpam-5392	544	18	-	-	ADJ
ejpam-5392	544	19	θβa	θβa	NOUN
ejpam-5392	544	20	-	-	PUNCT
ejpam-5392	544	21	exact	exact	ADJ
ejpam-5392	544	22	,	,	PUNCT
ejpam-5392	544	23	but	but	CCONJ
ejpam-5392	544	24	it	it	PRON
ejpam-5392	544	25	is	be	AUX
ejpam-5392	544	26	neither	neither	CCONJ
ejpam-5392	544	27	δβa	δβa	ADJ
ejpam-5392	544	28	-	-	PUNCT
ejpam-5392	544	29	exact	exact	ADJ
ejpam-5392	544	30	nor	nor	CCONJ
ejpam-5392	544	31	r	r	NOUN
ejpam-5392	544	32	-	-	PUNCT
ejpam-5392	544	33	exact	exact	ADJ
ejpam-5392	544	34	.	.	PUNCT
ejpam-5392	545	1	(	(	PUNCT
ejpam-5392	545	2	ii	ii	NOUN
ejpam-5392	545	3	)	)	PUNCT
ejpam-5392	545	4	example	example	NOUN
ejpam-5392	545	5	3	3	NUM
ejpam-5392	545	6	,	,	PUNCT
ejpam-5392	545	7	if	if	SCONJ
ejpam-5392	545	8	v	v	ADJ
ejpam-5392	545	9	=	=	SYM
ejpam-5392	545	10	{	{	PUNCT
ejpam-5392	545	11	y	y	NOUN
ejpam-5392	545	12	}	}	PUNCT
ejpam-5392	545	13	,	,	PUNCT
ejpam-5392	545	14	then	then	ADV
ejpam-5392	545	15	it	it	PRON
ejpam-5392	545	16	is	be	AUX
ejpam-5392	545	17	l	l	NOUN
ejpam-5392	545	18	-	-	ADJ
ejpam-5392	545	19	θβa	θβa	NOUN
ejpam-5392	545	20	-	-	PUNCT
ejpam-5392	545	21	exact	exact	ADJ
ejpam-5392	545	22	,	,	PUNCT
ejpam-5392	545	23	but	but	CCONJ
ejpam-5392	545	24	it	it	PRON
ejpam-5392	545	25	is	be	AUX
ejpam-5392	545	26	neither	neither	CCONJ
ejpam-5392	545	27	∧	∧	PROPN
ejpam-5392	545	28	βa	βa	PUNCT
ejpam-5392	545	29	-exact	-exact	NOUN
ejpam-5392	545	30	nor	nor	CCONJ
ejpam-5392	545	31	a	a	DET
ejpam-5392	545	32	-	-	PUNCT
ejpam-5392	545	33	exact	exact	ADJ
ejpam-5392	545	34	.	.	PUNCT
ejpam-5392	546	1	remark	remark	NOUN
ejpam-5392	546	2	6	6	NUM
ejpam-5392	546	3	.	.	PUNCT
ejpam-5392	547	1	we	we	PRON
ejpam-5392	547	2	can	can	AUX
ejpam-5392	547	3	say	say	VERB
ejpam-5392	547	4	that	that	SCONJ
ejpam-5392	547	5	the	the	DET
ejpam-5392	547	6	present	present	ADJ
ejpam-5392	547	7	rough	rough	ADJ
ejpam-5392	547	8	set	set	NOUN
ejpam-5392	547	9	models	model	NOUN
ejpam-5392	547	10	(	(	PUNCT
ejpam-5392	547	11	definition	definition	NOUN
ejpam-5392	547	12	18	18	NUM
ejpam-5392	547	13	)	)	PUNCT
ejpam-5392	547	14	,	,	PUNCT
ejpam-5392	547	15	with	with	ADP
ejpam-5392	547	16	the	the	DET
ejpam-5392	547	17	comparison	comparison	NOUN
ejpam-5392	547	18	of	of	ADP
ejpam-5392	547	19	abd	abd	PROPN
ejpam-5392	547	20	el	el	PROPN
ejpam-5392	547	21	-	-	PROPN
ejpam-5392	547	22	monsef	monsef	PROPN
ejpam-5392	547	23	et	et	PROPN
ejpam-5392	547	24	al	al	PROPN
ejpam-5392	547	25	.	.	PROPN
ejpam-5392	547	26	’s	’s	PART
ejpam-5392	547	27	method	method	NOUN
ejpam-5392	547	28	4	4	NUM
ejpam-5392	547	29	[	[	SYM
ejpam-5392	547	30	45	45	NUM
ejpam-5392	547	31	]	]	PUNCT
ejpam-5392	547	32	,	,	PUNCT
ejpam-5392	547	33	amer	amer	PROPN
ejpam-5392	547	34	et	et	PROPN
ejpam-5392	547	35	al	al	PROPN
ejpam-5392	547	36	.	.	PROPN
ejpam-5392	547	37	’s	’s	PART
ejpam-5392	547	38	method	method	NOUN
ejpam-5392	547	39	[	[	X
ejpam-5392	547	40	15	15	NUM
ejpam-5392	547	41	]	]	PUNCT
ejpam-5392	547	42	and	and	CCONJ
ejpam-5392	547	43	hosny	hosny	PROPN
ejpam-5392	547	44	’s	’s	PART
ejpam-5392	547	45	method	method	NOUN
ejpam-5392	547	46	6	6	NUM
ejpam-5392	547	47	[	[	SYM
ejpam-5392	547	48	20	20	NUM
ejpam-5392	547	49	]	]	PUNCT
ejpam-5392	547	50	and	and	CCONJ
ejpam-5392	547	51	hosny	hosny	PROPN
ejpam-5392	547	52	’s	’s	PART
ejpam-5392	547	53	method	method	NOUN
ejpam-5392	547	54	9	9	NUM
ejpam-5392	548	1	[	[	SYM
ejpam-5392	548	2	22	22	NUM
ejpam-5392	548	3	,	,	PUNCT
ejpam-5392	548	4	23	23	NUM
ejpam-5392	548	5	]	]	PUNCT
ejpam-5392	548	6	,	,	PUNCT
ejpam-5392	548	7	enlarge	enlarge	VERB
ejpam-5392	548	8	the	the	DET
ejpam-5392	548	9	confirmed	confirm	VERB
ejpam-5392	548	10	knowledge	knowledge	NOUN
ejpam-5392	548	11	by	by	ADP
ejpam-5392	548	12	maximizing	maximize	VERB
ejpam-5392	548	13	the	the	DET
ejpam-5392	548	14	l	l	NOUN
ejpam-5392	548	15	-	-	PUNCT
ejpam-5392	548	16	θβλ	θβλ	NOUN
ejpam-5392	548	17	-	-	PUNCT
ejpam-5392	548	18	lower	low	ADJ
ejpam-5392	548	19	approximations	approximation	NOUN
ejpam-5392	548	20	and	and	CCONJ
ejpam-5392	548	21	minimizing	minimize	VERB
ejpam-5392	548	22	the	the	DET
ejpam-5392	548	23	l	l	NOUN
ejpam-5392	548	24	-	-	PUNCT
ejpam-5392	548	25	θβλ	θβλ	NOUN
ejpam-5392	548	26	-	-	PUNCT
ejpam-5392	548	27	upper	upper	ADJ
ejpam-5392	548	28	approximations	approximation	NOUN
ejpam-5392	548	29	as	as	SCONJ
ejpam-5392	548	30	illustrated	illustrate	VERB
ejpam-5392	548	31	in	in	ADP
ejpam-5392	548	32	theorems	theorem	NOUN
ejpam-5392	548	33	4	4	NUM
ejpam-5392	548	34	and	and	CCONJ
ejpam-5392	548	35	5	5	NUM
ejpam-5392	548	36	.	.	X
ejpam-5392	548	37	that	that	PRON
ejpam-5392	548	38	is	is	ADV
ejpam-5392	548	39	,	,	PUNCT
ejpam-5392	548	40	the	the	DET
ejpam-5392	548	41	present	present	ADJ
ejpam-5392	548	42	approach	approach	NOUN
ejpam-5392	548	43	successfully	successfully	ADV
ejpam-5392	548	44	shrinks	shrink	VERB
ejpam-5392	548	45	the	the	DET
ejpam-5392	548	46	boundary	boundary	ADJ
ejpam-5392	548	47	region	region	NOUN
ejpam-5392	548	48	,	,	PUNCT
ejpam-5392	548	49	which	which	PRON
ejpam-5392	548	50	refer	refer	VERB
ejpam-5392	548	51	to	to	ADP
ejpam-5392	548	52	size	size	NOUN
ejpam-5392	548	53	of	of	ADP
ejpam-5392	548	54	ambiguity	ambiguity	NOUN
ejpam-5392	548	55	.	.	PUNCT
ejpam-5392	549	1	furthemore	furthemore	NOUN
ejpam-5392	549	2	,	,	PUNCT
ejpam-5392	549	3	corollaries	corollary	NOUN
ejpam-5392	549	4	3	3	NUM
ejpam-5392	549	5	and	and	CCONJ
ejpam-5392	549	6	1	1	NUM
ejpam-5392	549	7	confirm	confirm	VERB
ejpam-5392	549	8	that	that	SCONJ
ejpam-5392	549	9	the	the	DET
ejpam-5392	549	10	our	our	PRON
ejpam-5392	549	11	accuracy	accuracy	NOUN
ejpam-5392	549	12	introduced	introduce	VERB
ejpam-5392	549	13	in	in	ADP
ejpam-5392	549	14	definition	definition	NOUN
ejpam-5392	549	15	18	18	NUM
ejpam-5392	549	16	is	be	AUX
ejpam-5392	549	17	greater	great	ADJ
ejpam-5392	549	18	than	than	ADP
ejpam-5392	549	19	the	the	DET
ejpam-5392	549	20	previous	previous	ADJ
ejpam-5392	549	21	ones	one	NOUN
ejpam-5392	549	22	in	in	ADP
ejpam-5392	549	23	definitions	definition	NOUN
ejpam-5392	549	24	4	4	NUM
ejpam-5392	549	25	[	[	X
ejpam-5392	549	26	15	15	NUM
ejpam-5392	549	27	]	]	PUNCT
ejpam-5392	549	28	,	,	PUNCT
ejpam-5392	549	29	6	6	NUM
ejpam-5392	549	30	[	[	SYM
ejpam-5392	549	31	15	15	NUM
ejpam-5392	549	32	,	,	PUNCT
ejpam-5392	549	33	20	20	NUM
ejpam-5392	549	34	]	]	PUNCT
ejpam-5392	549	35	and	and	CCONJ
ejpam-5392	549	36	9	9	NUM
ejpam-5392	549	37	[	[	SYM
ejpam-5392	549	38	22	22	NUM
ejpam-5392	549	39	,	,	PUNCT
ejpam-5392	549	40	23	23	NUM
ejpam-5392	549	41	]	]	PUNCT
ejpam-5392	549	42	.	.	PUNCT
ejpam-5392	550	1	in	in	ADP
ejpam-5392	550	2	algorithm	algorithm	NOUN
ejpam-5392	550	3	2	2	NUM
ejpam-5392	550	4	,	,	PUNCT
ejpam-5392	550	5	we	we	PRON
ejpam-5392	550	6	present	present	VERB
ejpam-5392	550	7	the	the	DET
ejpam-5392	550	8	steps	step	NOUN
ejpam-5392	550	9	to	to	PART
ejpam-5392	550	10	calculate	calculate	VERB
ejpam-5392	550	11	a	a	DET
ejpam-5392	550	12	subset	subset	NOUN
ejpam-5392	550	13	’s	’s	PART
ejpam-5392	550	14	boundary	boundary	ADJ
ejpam-5392	550	15	region	region	NOUN
ejpam-5392	550	16	and	and	CCONJ
ejpam-5392	550	17	accuracy	accuracy	NOUN
ejpam-5392	550	18	measure	measure	NOUN
ejpam-5392	550	19	and	and	CCONJ
ejpam-5392	550	20	determine	determine	VERB
ejpam-5392	550	21	whether	whether	SCONJ
ejpam-5392	550	22	an	an	DET
ejpam-5392	550	23	l	l	NOUN
ejpam-5392	550	24	-	-	PUNCT
ejpam-5392	550	25	θβλ	θβλ	NOUN
ejpam-5392	550	26	-	-	PUNCT
ejpam-5392	550	27	definable	definable	ADJ
ejpam-5392	550	28	set	set	NOUN
ejpam-5392	550	29	or	or	CCONJ
ejpam-5392	550	30	an	an	DET
ejpam-5392	550	31	l	l	NOUN
ejpam-5392	550	32	-	-	PUNCT
ejpam-5392	550	33	θβλ	θβλ	NOUN
ejpam-5392	550	34	-	-	PUNCT
ejpam-5392	550	35	rough	rough	ADJ
ejpam-5392	550	36	set	set	NOUN
ejpam-5392	550	37	.	.	PUNCT
ejpam-5392	551	1	m.	m.	PROPN
ejpam-5392	551	2	hosny	hosny	PROPN
ejpam-5392	551	3	,	,	PUNCT
ejpam-5392	551	4	t.m	t.m	PROPN
ejpam-5392	551	5	.	.	PROPN
ejpam-5392	551	6	al	al	PROPN
ejpam-5392	551	7	-	-	PUNCT
ejpam-5392	551	8	shami	shami	PROPN
ejpam-5392	551	9	/	/	PUNCT
ejpam-5392	551	10	eur	eur	PROPN
ejpam-5392	551	11	.	.	PUNCT
ejpam-5392	552	1	j.	j.	PROPN
ejpam-5392	552	2	pure	pure	PROPN
ejpam-5392	552	3	appl	appl	PROPN
ejpam-5392	552	4	.	.	PROPN
ejpam-5392	552	5	math	math	PROPN
ejpam-5392	552	6	,	,	PUNCT
ejpam-5392	552	7	17	17	NUM
ejpam-5392	552	8	(	(	PUNCT
ejpam-5392	552	9	4	4	NUM
ejpam-5392	552	10	)	)	PUNCT
ejpam-5392	552	11	(	(	PUNCT
ejpam-5392	552	12	2024	2024	NUM
ejpam-5392	552	13	)	)	PUNCT
ejpam-5392	552	14	,	,	PUNCT
ejpam-5392	552	15	3436	3436	NUM
ejpam-5392	552	16	-	-	SYM
ejpam-5392	552	17	3463	3463	NUM
ejpam-5392	552	18	3453	3453	NUM
ejpam-5392	552	19	input	input	NOUN
ejpam-5392	552	20	:	:	PUNCT
ejpam-5392	552	21	the	the	DET
ejpam-5392	552	22	universal	universal	ADJ
ejpam-5392	552	23	set	set	NOUN
ejpam-5392	552	24	x	x	NOUN
ejpam-5392	552	25	,	,	PUNCT
ejpam-5392	552	26	a	a	DET
ejpam-5392	552	27	relation	relation	NOUN
ejpam-5392	552	28	r	r	NOUN
ejpam-5392	552	29	,	,	PUNCT
ejpam-5392	552	30	and	and	CCONJ
ejpam-5392	552	31	an	an	DET
ejpam-5392	552	32	ideal	ideal	ADJ
ejpam-5392	552	33	l	l	NOUN
ejpam-5392	552	34	under	under	ADP
ejpam-5392	552	35	consideration	consideration	NOUN
ejpam-5392	552	36	.	.	PUNCT
ejpam-5392	553	1	output	output	NOUN
ejpam-5392	553	2	:	:	PUNCT
ejpam-5392	553	3	boundary	boundary	ADJ
ejpam-5392	553	4	region	region	NOUN
ejpam-5392	553	5	bndl−θβ	bndl−θβ	NOUN
ejpam-5392	553	6	λ	λ	NOUN
ejpam-5392	553	7	and	and	CCONJ
ejpam-5392	553	8	accuracy	accuracy	NOUN
ejpam-5392	553	9	measure	measure	NOUN
ejpam-5392	553	10	accl−θβ	accl−θβ	PROPN
ejpam-5392	553	11	λ	λ	PROPN
ejpam-5392	553	12	of	of	ADP
ejpam-5392	553	13	a	a	DET
ejpam-5392	553	14	subset	subset	NOUN
ejpam-5392	553	15	.	.	PUNCT
ejpam-5392	554	1	1	1	NUM
ejpam-5392	554	2	carry	carry	VERB
ejpam-5392	554	3	out	out	ADP
ejpam-5392	554	4	steps	step	NOUN
ejpam-5392	554	5	1–20	1–20	NOUN
ejpam-5392	554	6	given	give	VERB
ejpam-5392	554	7	in	in	ADP
ejpam-5392	554	8	algorithm	algorithm	NOUN
ejpam-5392	554	9	1	1	NUM
ejpam-5392	554	10	;	;	PUNCT
ejpam-5392	554	11	2	2	NUM
ejpam-5392	554	12	build	build	VERB
ejpam-5392	554	13	l	l	NOUN
ejpam-5392	554	14	-	-	NOUN
ejpam-5392	554	15	θβλc(x	θβλc(x	NOUN
ejpam-5392	554	16	)	)	PUNCT
ejpam-5392	554	17	=	=	NOUN
ejpam-5392	554	18	{	{	PUNCT
ejpam-5392	554	19	h	h	NOUN
ejpam-5392	554	20	⊆	⊆	NUM
ejpam-5392	554	21	x	x	X
ejpam-5392	554	22	:	:	PUNCT
ejpam-5392	554	23	hc	hc	PROPN
ejpam-5392	554	24	∈	∈	PROPN
ejpam-5392	554	25	l	l	PROPN
ejpam-5392	554	26	-	-	NOUN
ejpam-5392	554	27	θβλo(x	θβλo(x	NOUN
ejpam-5392	554	28	)	)	PUNCT
ejpam-5392	554	29	}	}	PUNCT
ejpam-5392	554	30	;	;	PUNCT
ejpam-5392	554	31	3	3	NUM
ejpam-5392	554	32	for	for	ADP
ejpam-5392	554	33	a	a	DET
ejpam-5392	554	34	subset	subset	NOUN
ejpam-5392	554	35	e	e	NOUN
ejpam-5392	554	36	⊆	⊆	NUM
ejpam-5392	554	37	x	x	SYM
ejpam-5392	554	38	do	do	AUX
ejpam-5392	554	39	4	4	NUM
ejpam-5392	554	40	compute	compute	NOUN
ejpam-5392	554	41	rl−θβ	rl−θβ	PROPN
ejpam-5392	554	42	λ	λ	PROPN
ejpam-5392	554	43	(	(	PUNCT
ejpam-5392	554	44	e	e	NOUN
ejpam-5392	554	45	)	)	PUNCT
ejpam-5392	554	46	=	=	PUNCT
ejpam-5392	554	47	∪{g	∪{g	PROPN
ejpam-5392	554	48	∈	∈	PROPN
ejpam-5392	554	49	l	l	PROPN
ejpam-5392	554	50	-	-	PUNCT
ejpam-5392	554	51	θβλo(x	θβλo(x	NOUN
ejpam-5392	554	52	)	)	PUNCT
ejpam-5392	554	53	:	:	PUNCT
ejpam-5392	554	54	g	g	PROPN
ejpam-5392	554	55	⊆	⊆	NUM
ejpam-5392	554	56	e	e	NOUN
ejpam-5392	554	57	}	}	PUNCT
ejpam-5392	554	58	;	;	PUNCT
ejpam-5392	554	59	5	5	NUM
ejpam-5392	554	60	compute	compute	NOUN
ejpam-5392	554	61	rl−θβ	rl−θβ	PROPN
ejpam-5392	554	62	λ	λ	PROPN
ejpam-5392	554	63	(	(	PUNCT
ejpam-5392	554	64	e	e	NOUN
ejpam-5392	554	65	)	)	PUNCT
ejpam-5392	554	66	=	=	SYM
ejpam-5392	554	67	∩{h	∩{h	PUNCT
ejpam-5392	554	68	∈	∈	PROPN
ejpam-5392	554	69	l	l	NOUN
ejpam-5392	554	70	-	-	NOUN
ejpam-5392	554	71	θβλc(x	θβλc(x	NOUN
ejpam-5392	554	72	)	)	PUNCT
ejpam-5392	554	73	:	:	PUNCT
ejpam-5392	555	1	e	e	X
ejpam-5392	555	2	⊆	⊆	NUM
ejpam-5392	555	3	h	h	NOUN
ejpam-5392	555	4	}	}	PUNCT
ejpam-5392	555	5	;	;	PUNCT
ejpam-5392	555	6	6	6	NUM
ejpam-5392	555	7	compute	compute	NOUN
ejpam-5392	555	8	bndl−θβ	bndl−θβ	NOUN
ejpam-5392	555	9	λ	λ	X
ejpam-5392	555	10	(	(	PUNCT
ejpam-5392	555	11	e	e	NOUN
ejpam-5392	555	12	)	)	PUNCT
ejpam-5392	555	13	=	=	SYM
ejpam-5392	556	1	rl−θβ	rl−θβ	PROPN
ejpam-5392	556	2	λ	λ	PROPN
ejpam-5392	556	3	(	(	PUNCT
ejpam-5392	556	4	e)−rl−θβ	e)−rl−θβ	NOUN
ejpam-5392	556	5	λ	λ	X
ejpam-5392	556	6	(	(	PUNCT
ejpam-5392	556	7	e	e	NOUN
ejpam-5392	556	8	)	)	PUNCT
ejpam-5392	556	9	;	;	PUNCT
ejpam-5392	556	10	7	7	NUM
ejpam-5392	556	11	compute	compute	NOUN
ejpam-5392	556	12	accl−θβ	accl−θβ	NOUN
ejpam-5392	556	13	λ	λ	PROPN
ejpam-5392	556	14	(	(	PUNCT
ejpam-5392	556	15	e	e	NOUN
ejpam-5392	556	16	)	)	PUNCT
ejpam-5392	556	17	=	=	SYM
ejpam-5392	556	18	|rl−θβ	|rl−θβ	PROPN
ejpam-5392	556	19	λ	λ	PROPN
ejpam-5392	556	20	(	(	PUNCT
ejpam-5392	556	21	e)|	e)|	INTJ
ejpam-5392	556	22	|rl−θβ	|rl−θβ	PROPN
ejpam-5392	556	23	λ	λ	PROPN
ejpam-5392	556	24	(	(	PUNCT
ejpam-5392	556	25	e)|	e)|	ADJ
ejpam-5392	556	26	8	8	NUM
ejpam-5392	556	27	end	end	NOUN
ejpam-5392	556	28	9	9	NUM
ejpam-5392	556	29	print	print	NOUN
ejpam-5392	556	30	bndl−θβ	bndl−θβ	NOUN
ejpam-5392	556	31	λ	λ	INTJ
ejpam-5392	556	32	(	(	PUNCT
ejpam-5392	556	33	e	e	NOUN
ejpam-5392	556	34	)	)	PUNCT
ejpam-5392	556	35	;	;	PUNCT
ejpam-5392	556	36	10	10	NUM
ejpam-5392	556	37	print	print	NOUN
ejpam-5392	556	38	accl−θβ	accl−θβ	PROPN
ejpam-5392	556	39	λ	λ	PROPN
ejpam-5392	556	40	(	(	PUNCT
ejpam-5392	556	41	e	e	NOUN
ejpam-5392	556	42	)	)	PUNCT
ejpam-5392	556	43	;	;	PUNCT
ejpam-5392	556	44	11	11	NUM
ejpam-5392	556	45	if	if	SCONJ
ejpam-5392	556	46	accl−θβ	accl−θβ	PROPN
ejpam-5392	556	47	λ	λ	X
ejpam-5392	556	48	(	(	PUNCT
ejpam-5392	556	49	e	e	NOUN
ejpam-5392	556	50	)	)	PUNCT
ejpam-5392	556	51	=	=	SYM
ejpam-5392	556	52	1	1	NUM
ejpam-5392	556	53	then	then	ADV
ejpam-5392	556	54	12	12	NUM
ejpam-5392	556	55	print	print	NOUN
ejpam-5392	556	56	e	e	NOUN
ejpam-5392	556	57	is	be	AUX
ejpam-5392	556	58	an	an	DET
ejpam-5392	556	59	l	l	NOUN
ejpam-5392	556	60	-	-	PUNCT
ejpam-5392	556	61	θβλ	θβλ	NOUN
ejpam-5392	556	62	-	-	PUNCT
ejpam-5392	556	63	definable	definable	ADJ
ejpam-5392	556	64	set	set	VERB
ejpam-5392	556	65	13	13	NUM
ejpam-5392	556	66	else	else	ADV
ejpam-5392	556	67	14	14	NUM
ejpam-5392	556	68	print	print	NOUN
ejpam-5392	556	69	e	e	NOUN
ejpam-5392	556	70	is	be	AUX
ejpam-5392	556	71	an	an	DET
ejpam-5392	556	72	l	l	NOUN
ejpam-5392	556	73	-	-	PUNCT
ejpam-5392	556	74	θβλ	θβλ	NOUN
ejpam-5392	556	75	-	-	PUNCT
ejpam-5392	556	76	rough	rough	NOUN
ejpam-5392	556	77	set	set	VERB
ejpam-5392	556	78	15	15	NUM
ejpam-5392	556	79	end	end	NOUN
ejpam-5392	556	80	algorithm	algorithm	NOUN
ejpam-5392	556	81	2	2	NUM
ejpam-5392	556	82	:	:	PUNCT
ejpam-5392	556	83	calculate	calculate	VERB
ejpam-5392	556	84	the	the	DET
ejpam-5392	556	85	boundary	boundary	ADJ
ejpam-5392	556	86	region	region	NOUN
ejpam-5392	556	87	and	and	CCONJ
ejpam-5392	556	88	accuracy	accuracy	NOUN
ejpam-5392	556	89	measure	measure	NOUN
ejpam-5392	556	90	of	of	ADP
ejpam-5392	556	91	a	a	DET
ejpam-5392	556	92	subset	subset	NOUN
ejpam-5392	556	93	5	5	NUM
ejpam-5392	556	94	.	.	PUNCT
ejpam-5392	557	1	l	l	NOUN
ejpam-5392	557	2	-	-	PUNCT
ejpam-5392	557	3	θβλ	θβλ	NOUN
ejpam-5392	557	4	-	-	PUNCT
ejpam-5392	557	5	rough	rough	ADJ
ejpam-5392	557	6	membership	membership	NOUN
ejpam-5392	557	7	functions	function	NOUN
ejpam-5392	557	8	in	in	ADP
ejpam-5392	557	9	this	this	DET
ejpam-5392	557	10	segment	segment	NOUN
ejpam-5392	557	11	,	,	PUNCT
ejpam-5392	557	12	we	we	PRON
ejpam-5392	557	13	introduce	introduce	VERB
ejpam-5392	557	14	the	the	DET
ejpam-5392	557	15	notion	notion	NOUN
ejpam-5392	557	16	of	of	ADP
ejpam-5392	557	17	l	l	NOUN
ejpam-5392	557	18	-	-	PUNCT
ejpam-5392	557	19	θβλ	θβλ	NOUN
ejpam-5392	557	20	-	-	PUNCT
ejpam-5392	557	21	rough	rough	ADJ
ejpam-5392	557	22	membership	membership	NOUN
ejpam-5392	557	23	functions	function	NOUN
ejpam-5392	557	24	as	as	ADP
ejpam-5392	557	25	a	a	DET
ejpam-5392	557	26	generalization	generalization	NOUN
ejpam-5392	557	27	of	of	ADP
ejpam-5392	557	28	classical	classical	ADJ
ejpam-5392	557	29	rough	rough	ADJ
ejpam-5392	557	30	membership	membership	NOUN
ejpam-5392	557	31	functions	function	NOUN
ejpam-5392	557	32	.	.	PUNCT
ejpam-5392	558	1	we	we	PRON
ejpam-5392	558	2	exploit	exploit	VERB
ejpam-5392	558	3	this	this	DET
ejpam-5392	558	4	notion	notion	NOUN
ejpam-5392	558	5	to	to	PART
ejpam-5392	558	6	describe	describe	VERB
ejpam-5392	558	7	the	the	DET
ejpam-5392	558	8	approximation	approximation	NOUN
ejpam-5392	558	9	operators	operator	NOUN
ejpam-5392	558	10	given	give	VERB
ejpam-5392	558	11	in	in	ADP
ejpam-5392	558	12	the	the	DET
ejpam-5392	558	13	preceding	precede	VERB
ejpam-5392	558	14	section	section	NOUN
ejpam-5392	558	15	.	.	PUNCT
ejpam-5392	559	1	definition	definition	NOUN
ejpam-5392	559	2	20	20	NUM
ejpam-5392	559	3	.	.	PUNCT
ejpam-5392	560	1	let	let	AUX
ejpam-5392	560	2	(	(	PUNCT
ejpam-5392	560	3	x	x	NOUN
ejpam-5392	560	4	,	,	PUNCT
ejpam-5392	560	5	r	r	NOUN
ejpam-5392	560	6	,	,	PUNCT
ejpam-5392	560	7	ξλ	ξλ	NOUN
ejpam-5392	560	8	,	,	PUNCT
ejpam-5392	560	9	l	l	NOUN
ejpam-5392	560	10	)	)	PUNCT
ejpam-5392	560	11	be	be	AUX
ejpam-5392	560	12	an	an	DET
ejpam-5392	560	13	l	l	NOUN
ejpam-5392	560	14	−gλ	−gλ	NOUN
ejpam-5392	560	15	-	-	PUNCT
ejpam-5392	560	16	space	space	NOUN
ejpam-5392	560	17	,	,	PUNCT
ejpam-5392	560	18	y	y	PROPN
ejpam-5392	560	19	∈	∈	PROPN
ejpam-5392	560	20	x	x	X
ejpam-5392	560	21	,	,	PUNCT
ejpam-5392	560	22	and	and	CCONJ
ejpam-5392	560	23	v	v	ADP
ejpam-5392	560	24	⊆	⊆	NUM
ejpam-5392	560	25	x.	x.	NOUN
ejpam-5392	560	26	(	(	PUNCT
ejpam-5392	560	27	i	i	NOUN
ejpam-5392	560	28	)	)	PUNCT
ejpam-5392	561	1	if	if	SCONJ
ejpam-5392	561	2	y	y	PROPN
ejpam-5392	561	3	∈	∈	PROPN
ejpam-5392	561	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	561	5	λ	λ	PROPN
ejpam-5392	561	6	(	(	PUNCT
ejpam-5392	561	7	v	v	NOUN
ejpam-5392	561	8	)	)	PUNCT
ejpam-5392	561	9	,	,	PUNCT
ejpam-5392	561	10	then	then	ADV
ejpam-5392	561	11	y	y	PROPN
ejpam-5392	561	12	is	be	AUX
ejpam-5392	561	13	λ	λ	PROPN
ejpam-5392	561	14	-	-	PUNCT
ejpam-5392	561	15	θβ	θβ	NOUN
ejpam-5392	561	16	-	-	PUNCT
ejpam-5392	561	17	certainly	certainly	ADV
ejpam-5392	561	18	with	with	ADP
ejpam-5392	561	19	respect	respect	NOUN
ejpam-5392	561	20	to	to	ADP
ejpam-5392	561	21	l	l	NOUN
ejpam-5392	561	22	(	(	PUNCT
ejpam-5392	561	23	l−θβλ	l−θβλ	NOUN
ejpam-5392	561	24	-	-	PUNCT
ejpam-5392	561	25	certainly	certainly	ADV
ejpam-5392	561	26	)	)	PUNCT
ejpam-5392	561	27	belongs	belong	VERB
ejpam-5392	561	28	to	to	ADP
ejpam-5392	561	29	v	v	NUM
ejpam-5392	561	30	,	,	PUNCT
ejpam-5392	561	31	denoted	denote	VERB
ejpam-5392	561	32	by	by	ADP
ejpam-5392	561	33	y	y	PROPN
ejpam-5392	561	34	∈l−θβλv	∈l−θβλv	ADV
ejpam-5392	561	35	.	.	PUNCT
ejpam-5392	562	1	(	(	PUNCT
ejpam-5392	562	2	ii	ii	NOUN
ejpam-5392	562	3	)	)	PUNCT
ejpam-5392	562	4	if	if	SCONJ
ejpam-5392	562	5	y	y	PROPN
ejpam-5392	562	6	∈	∈	PROPN
ejpam-5392	562	7	rl−θβ	rl−θβ	PROPN
ejpam-5392	562	8	λ	λ	PROPN
ejpam-5392	562	9	(	(	PUNCT
ejpam-5392	562	10	v	v	NOUN
ejpam-5392	562	11	)	)	PUNCT
ejpam-5392	562	12	,	,	PUNCT
ejpam-5392	562	13	then	then	ADV
ejpam-5392	562	14	y	y	PROPN
ejpam-5392	562	15	is	be	AUX
ejpam-5392	562	16	λ	λ	NOUN
ejpam-5392	562	17	-	-	PUNCT
ejpam-5392	562	18	θβ	θβ	NOUN
ejpam-5392	562	19	-	-	PUNCT
ejpam-5392	562	20	probably	probably	ADV
ejpam-5392	562	21	with	with	ADP
ejpam-5392	562	22	respect	respect	NOUN
ejpam-5392	562	23	to	to	ADP
ejpam-5392	562	24	l	l	NOUN
ejpam-5392	562	25	(	(	PUNCT
ejpam-5392	562	26	briefly	briefly	ADV
ejpam-5392	562	27	l−	l−	PROPN
ejpam-5392	562	28	θβλ	θβλ	NOUN
ejpam-5392	562	29	-	-	PUNCT
ejpam-5392	562	30	probably	probably	ADV
ejpam-5392	562	31	)	)	PUNCT
ejpam-5392	562	32	belongs	belong	VERB
ejpam-5392	562	33	to	to	ADP
ejpam-5392	562	34	v	v	NUM
ejpam-5392	562	35	,	,	PUNCT
ejpam-5392	562	36	denoted	denote	VERB
ejpam-5392	562	37	by	by	ADP
ejpam-5392	562	38	y	y	PROPN
ejpam-5392	562	39	∈l−θβλv	∈l−θβλv	ADV
ejpam-5392	562	40	.	.	PUNCT
ejpam-5392	563	1	it	it	PRON
ejpam-5392	563	2	is	be	AUX
ejpam-5392	563	3	called	call	VERB
ejpam-5392	563	4	λ	λ	NOUN
ejpam-5392	563	5	-	-	PUNCT
ejpam-5392	563	6	θβ	θβ	NOUN
ejpam-5392	563	7	-	-	PUNCT
ejpam-5392	563	8	strong	strong	ADJ
ejpam-5392	563	9	and	and	CCONJ
ejpam-5392	563	10	λ	λ	NOUN
ejpam-5392	563	11	-	-	PUNCT
ejpam-5392	563	12	θβ	θβ	ADP
ejpam-5392	563	13	-	-	PUNCT
ejpam-5392	563	14	weak	weak	ADJ
ejpam-5392	563	15	membership	membership	NOUN
ejpam-5392	563	16	relations	relation	NOUN
ejpam-5392	563	17	with	with	ADP
ejpam-5392	563	18	respect	respect	NOUN
ejpam-5392	563	19	to	to	ADP
ejpam-5392	563	20	l	l	NOUN
ejpam-5392	563	21	respectively	respectively	ADV
ejpam-5392	563	22	.	.	PUNCT
ejpam-5392	564	1	remark	remark	PROPN
ejpam-5392	564	2	7	7	NUM
ejpam-5392	564	3	.	.	PUNCT
ejpam-5392	565	1	according	accord	VERB
ejpam-5392	565	2	to	to	ADP
ejpam-5392	565	3	definition	definition	NOUN
ejpam-5392	565	4	18	18	NUM
ejpam-5392	565	5	,	,	PUNCT
ejpam-5392	565	6	the	the	DET
ejpam-5392	565	7	l	l	NOUN
ejpam-5392	565	8	-	-	PUNCT
ejpam-5392	565	9	θβλ	θβλ	NOUN
ejpam-5392	565	10	-	-	PUNCT
ejpam-5392	565	11	lower	low	ADJ
ejpam-5392	565	12	and	and	CCONJ
ejpam-5392	565	13	l	l	NOUN
ejpam-5392	565	14	-	-	PUNCT
ejpam-5392	565	15	θβλ	θβλ	NOUN
ejpam-5392	565	16	-	-	PUNCT
ejpam-5392	565	17	upper	upper	ADJ
ejpam-5392	565	18	approximations	approximation	NOUN
ejpam-5392	565	19	for	for	ADP
ejpam-5392	565	20	any	any	DET
ejpam-5392	565	21	v	v	ADP
ejpam-5392	565	22	⊆	⊆	NUM
ejpam-5392	565	23	x	x	PUNCT
ejpam-5392	565	24	can	can	AUX
ejpam-5392	565	25	be	be	AUX
ejpam-5392	565	26	written	write	VERB
ejpam-5392	565	27	as	as	ADP
ejpam-5392	565	28	:	:	PUNCT
ejpam-5392	565	29	(	(	PUNCT
ejpam-5392	565	30	i	i	NOUN
ejpam-5392	565	31	)	)	PUNCT
ejpam-5392	565	32	rl−θβ	rl−θβ	PROPN
ejpam-5392	565	33	λ	λ	PROPN
ejpam-5392	565	34	(	(	PUNCT
ejpam-5392	565	35	v	v	NOUN
ejpam-5392	565	36	)	)	PUNCT
ejpam-5392	565	37	=	=	PUNCT
ejpam-5392	566	1	{	{	PUNCT
ejpam-5392	566	2	y	y	PROPN
ejpam-5392	566	3	∈	∈	PROPN
ejpam-5392	566	4	x	x	X
ejpam-5392	566	5	:	:	PUNCT
ejpam-5392	566	6	y	y	PROPN
ejpam-5392	566	7	∈l−θβλv	∈l−θβλv	ADV
ejpam-5392	566	8	}	}	PUNCT
ejpam-5392	566	9	.	.	PUNCT
ejpam-5392	567	1	(	(	PUNCT
ejpam-5392	567	2	ii	ii	NOUN
ejpam-5392	567	3	)	)	PUNCT
ejpam-5392	567	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	567	5	λ	λ	PROPN
ejpam-5392	567	6	(	(	PUNCT
ejpam-5392	567	7	v	v	NOUN
ejpam-5392	567	8	)	)	PUNCT
ejpam-5392	567	9	=	=	PUNCT
ejpam-5392	567	10	{	{	PUNCT
ejpam-5392	567	11	y	y	PROPN
ejpam-5392	567	12	∈	∈	PROPN
ejpam-5392	567	13	x	x	X
ejpam-5392	567	14	:	:	PUNCT
ejpam-5392	567	15	y	y	PROPN
ejpam-5392	567	16	∈l−θβλv	∈l−θβλv	ADV
ejpam-5392	567	17	}	}	PUNCT
ejpam-5392	567	18	.	.	PUNCT
ejpam-5392	568	1	m.	m.	PROPN
ejpam-5392	568	2	hosny	hosny	PROPN
ejpam-5392	568	3	,	,	PUNCT
ejpam-5392	568	4	t.m	t.m	PROPN
ejpam-5392	568	5	.	.	PROPN
ejpam-5392	568	6	al	al	PROPN
ejpam-5392	568	7	-	-	PUNCT
ejpam-5392	568	8	shami	shami	PROPN
ejpam-5392	568	9	/	/	PUNCT
ejpam-5392	568	10	eur	eur	PROPN
ejpam-5392	568	11	.	.	PUNCT
ejpam-5392	569	1	j.	j.	PROPN
ejpam-5392	569	2	pure	pure	PROPN
ejpam-5392	569	3	appl	appl	PROPN
ejpam-5392	569	4	.	.	PROPN
ejpam-5392	569	5	math	math	PROPN
ejpam-5392	569	6	,	,	PUNCT
ejpam-5392	569	7	17	17	NUM
ejpam-5392	569	8	(	(	PUNCT
ejpam-5392	569	9	4	4	NUM
ejpam-5392	569	10	)	)	PUNCT
ejpam-5392	569	11	(	(	PUNCT
ejpam-5392	569	12	2024	2024	NUM
ejpam-5392	569	13	)	)	PUNCT
ejpam-5392	569	14	,	,	PUNCT
ejpam-5392	569	15	3436	3436	NUM
ejpam-5392	569	16	-	-	SYM
ejpam-5392	569	17	3463	3463	NUM
ejpam-5392	569	18	3454	3454	NUM
ejpam-5392	569	19	lemma	lemma	PROPN
ejpam-5392	569	20	2	2	NUM
ejpam-5392	569	21	.	.	PUNCT
ejpam-5392	570	1	let	let	AUX
ejpam-5392	570	2	(	(	PUNCT
ejpam-5392	570	3	x	x	NOUN
ejpam-5392	570	4	,	,	PUNCT
ejpam-5392	570	5	r	r	NOUN
ejpam-5392	570	6	,	,	PUNCT
ejpam-5392	570	7	ξλ	ξλ	NOUN
ejpam-5392	570	8	,	,	PUNCT
ejpam-5392	570	9	l	l	NOUN
ejpam-5392	570	10	)	)	PUNCT
ejpam-5392	570	11	be	be	AUX
ejpam-5392	570	12	an	an	DET
ejpam-5392	570	13	l	l	NOUN
ejpam-5392	570	14	−gλ	−gλ	NOUN
ejpam-5392	570	15	-	-	PUNCT
ejpam-5392	570	16	space	space	NOUN
ejpam-5392	570	17	and	and	CCONJ
ejpam-5392	570	18	v	v	ADP
ejpam-5392	570	19	⊆	⊆	NUM
ejpam-5392	570	20	x.	x.	NOUN
ejpam-5392	570	21	then	then	ADV
ejpam-5392	570	22	(	(	PUNCT
ejpam-5392	570	23	i	i	NOUN
ejpam-5392	570	24	)	)	PUNCT
ejpam-5392	570	25	if	if	SCONJ
ejpam-5392	570	26	y	y	PROPN
ejpam-5392	570	27	∈l−θβλv	∈l−θβλv	ADV
ejpam-5392	570	28	,	,	PUNCT
ejpam-5392	570	29	then	then	ADV
ejpam-5392	570	30	y	y	PROPN
ejpam-5392	570	31	∈	∈	PROPN
ejpam-5392	570	32	v	v	X
ejpam-5392	570	33	.	.	PUNCT
ejpam-5392	571	1	(	(	PUNCT
ejpam-5392	571	2	ii	ii	NOUN
ejpam-5392	571	3	)	)	PUNCT
ejpam-5392	571	4	if	if	SCONJ
ejpam-5392	571	5	y	y	PROPN
ejpam-5392	571	6	∈	∈	PROPN
ejpam-5392	571	7	v	v	ADP
ejpam-5392	571	8	,	,	PUNCT
ejpam-5392	571	9	then	then	ADV
ejpam-5392	571	10	y	y	PROPN
ejpam-5392	571	11	∈l−θβλv	∈l−θβλv	ADV
ejpam-5392	571	12	.	.	PUNCT
ejpam-5392	572	1	proof	proof	NOUN
ejpam-5392	572	2	.	.	PUNCT
ejpam-5392	573	1	straightforward	straightforward	ADJ
ejpam-5392	573	2	.	.	PUNCT
ejpam-5392	574	1	proposition	proposition	NOUN
ejpam-5392	574	2	9	9	NUM
ejpam-5392	574	3	.	.	PUNCT
ejpam-5392	575	1	let	let	AUX
ejpam-5392	575	2	(	(	PUNCT
ejpam-5392	575	3	x	x	NOUN
ejpam-5392	575	4	,	,	PUNCT
ejpam-5392	575	5	r	r	NOUN
ejpam-5392	575	6	,	,	PUNCT
ejpam-5392	575	7	ξλ	ξλ	NOUN
ejpam-5392	575	8	,	,	PUNCT
ejpam-5392	575	9	l	l	NOUN
ejpam-5392	575	10	)	)	PUNCT
ejpam-5392	575	11	be	be	AUX
ejpam-5392	575	12	an	an	DET
ejpam-5392	575	13	l	l	NOUN
ejpam-5392	575	14	−gλ	−gλ	NOUN
ejpam-5392	575	15	-	-	PUNCT
ejpam-5392	575	16	space	space	NOUN
ejpam-5392	575	17	and	and	CCONJ
ejpam-5392	575	18	v	v	ADP
ejpam-5392	575	19	⊆	⊆	NUM
ejpam-5392	575	20	x.	x.	NOUN
ejpam-5392	575	21	then	then	ADV
ejpam-5392	575	22	(	(	PUNCT
ejpam-5392	575	23	i	i	NOUN
ejpam-5392	575	24	)	)	PUNCT
ejpam-5392	575	25	if	if	SCONJ
ejpam-5392	575	26	y	y	PROPN
ejpam-5392	575	27	∈λa⇒	∈λa⇒	PROPN
ejpam-5392	575	28	y	y	PROPN
ejpam-5392	575	29	∈ηλa⇒	∈ηλa⇒	PROPN
ejpam-5392	575	30	y	y	PROPN
ejpam-5392	575	31	∈l−η	∈l−η	VERB
ejpam-5392	575	32	λ	λ	PROPN
ejpam-5392	575	33	v	v	ADJ
ejpam-5392	575	34	⇒	⇒	X
ejpam-5392	575	35	y	y	PROPN
ejpam-5392	575	36	∈l−θβλv	∈l−θβλv	ADV
ejpam-5392	575	37	.	.	PUNCT
ejpam-5392	576	1	(	(	PUNCT
ejpam-5392	576	2	ii	ii	NOUN
ejpam-5392	576	3	)	)	PUNCT
ejpam-5392	576	4	if	if	SCONJ
ejpam-5392	576	5	y	y	PROPN
ejpam-5392	576	6	∈l−θβλa⇒	∈l−θβλa⇒	PROPN
ejpam-5392	576	7	y	y	PROPN
ejpam-5392	576	8	∈l−η	∈l−η	VERB
ejpam-5392	576	9	λ	λ	PROPN
ejpam-5392	576	10	a⇒	a⇒	PROPN
ejpam-5392	576	11	y	y	PROPN
ejpam-5392	576	12	∈ηλa⇒	∈ηλa⇒	PROPN
ejpam-5392	576	13	y	y	PROPN
ejpam-5392	576	14	∈λv	∈λv	PROPN
ejpam-5392	576	15	.	.	PUNCT
ejpam-5392	577	1	proof	proof	NOUN
ejpam-5392	577	2	.	.	PUNCT
ejpam-5392	578	1	we	we	PRON
ejpam-5392	578	2	prove	prove	VERB
ejpam-5392	578	3	(	(	PUNCT
ejpam-5392	578	4	i	i	NOUN
ejpam-5392	578	5	)	)	PUNCT
ejpam-5392	578	6	and	and	CCONJ
ejpam-5392	578	7	the	the	DET
ejpam-5392	578	8	other	other	ADJ
ejpam-5392	578	9	similarly	similarly	ADV
ejpam-5392	578	10	.	.	PUNCT
ejpam-5392	579	1	y	y	PROPN
ejpam-5392	579	2	∈λa	∈λa	VERB
ejpam-5392	579	3	⇒	⇒	AUX
ejpam-5392	579	4	y	y	PROPN
ejpam-5392	579	5	∈ηλa	∈ηλa	SYM
ejpam-5392	579	6	⇒	⇒	PROPN
ejpam-5392	579	7	y	y	PROPN
ejpam-5392	579	8	∈l−η	∈l−η	VERB
ejpam-5392	579	9	λ	λ	PROPN
ejpam-5392	579	10	v	v	NUM
ejpam-5392	579	11	by	by	ADP
ejpam-5392	579	12	proposition	proposition	NOUN
ejpam-5392	579	13	4	4	NUM
ejpam-5392	579	14	.	.	PUNCT
ejpam-5392	580	1	let	let	VERB
ejpam-5392	580	2	y	y	PROPN
ejpam-5392	580	3	∈l−η	∈l−η	VERB
ejpam-5392	580	4	λ	λ	PROPN
ejpam-5392	580	5	v	v	NOUN
ejpam-5392	580	6	.	.	PUNCT
ejpam-5392	581	1	then	then	ADV
ejpam-5392	581	2	,	,	PUNCT
ejpam-5392	581	3	y	y	PROPN
ejpam-5392	581	4	∈	∈	PROPN
ejpam-5392	581	5	rl−η	rl−η	PROPN
ejpam-5392	581	6	λ	λ	PROPN
ejpam-5392	581	7	(	(	PUNCT
ejpam-5392	581	8	v	v	NOUN
ejpam-5392	581	9	)	)	PUNCT
ejpam-5392	581	10	⇒	⇒	VERB
ejpam-5392	581	11	y	y	PROPN
ejpam-5392	581	12	∈	∈	PROPN
ejpam-5392	581	13	rl−θβ	rl−θβ	PROPN
ejpam-5392	581	14	λ	λ	PROPN
ejpam-5392	581	15	(	(	PUNCT
ejpam-5392	581	16	v	v	NOUN
ejpam-5392	581	17	)	)	PUNCT
ejpam-5392	581	18	(	(	PUNCT
ejpam-5392	581	19	by	by	ADP
ejpam-5392	581	20	proposition	proposition	NOUN
ejpam-5392	581	21	4	4	NUM
ejpam-5392	581	22	)	)	PUNCT
ejpam-5392	581	23	⇒	⇒	VERB
ejpam-5392	581	24	y	y	PROPN
ejpam-5392	581	25	∈l−θβλv	∈l−θβλv	ADV
ejpam-5392	581	26	.	.	PUNCT
ejpam-5392	582	1	remark	remark	PROPN
ejpam-5392	582	2	8	8	NUM
ejpam-5392	582	3	.	.	PUNCT
ejpam-5392	583	1	the	the	DET
ejpam-5392	583	2	converse	converse	NOUN
ejpam-5392	583	3	of	of	ADP
ejpam-5392	583	4	proposition	proposition	NOUN
ejpam-5392	583	5	9	9	NUM
ejpam-5392	583	6	is	be	AUX
ejpam-5392	583	7	not	not	PART
ejpam-5392	583	8	true	true	ADJ
ejpam-5392	583	9	in	in	ADP
ejpam-5392	583	10	general	general	ADJ
ejpam-5392	583	11	,	,	PUNCT
ejpam-5392	583	12	as	as	SCONJ
ejpam-5392	583	13	it	it	PRON
ejpam-5392	583	14	is	be	AUX
ejpam-5392	583	15	shown	show	VERB
ejpam-5392	583	16	in	in	ADP
ejpam-5392	583	17	example	example	NOUN
ejpam-5392	583	18	1	1	NUM
ejpam-5392	583	19	(	(	PUNCT
ejpam-5392	583	20	i	i	NOUN
ejpam-5392	583	21	)	)	PUNCT
ejpam-5392	583	22	if	if	SCONJ
ejpam-5392	583	23	v	v	NUM
ejpam-5392	583	24	=	=	SYM
ejpam-5392	583	25	{	{	PUNCT
ejpam-5392	583	26	y5	y5	NOUN
ejpam-5392	583	27	}	}	PUNCT
ejpam-5392	583	28	,	,	PUNCT
ejpam-5392	583	29	then	then	ADV
ejpam-5392	583	30	y2	y2	PROPN
ejpam-5392	583	31	∈l−θβav	∈l−θβav	VERB
ejpam-5392	583	32	,	,	PUNCT
ejpam-5392	583	33	but	but	CCONJ
ejpam-5392	583	34	y2	y2	INTJ
ejpam-5392	583	35	∈l−δβav	∈l−δβav	INTJ
ejpam-5392	583	36	.	.	PUNCT
ejpam-5392	584	1	(	(	PUNCT
ejpam-5392	584	2	ii	ii	NOUN
ejpam-5392	584	3	)	)	PUNCT
ejpam-5392	584	4	if	if	SCONJ
ejpam-5392	584	5	v	v	NOUN
ejpam-5392	584	6	=	=	SYM
ejpam-5392	584	7	{	{	PUNCT
ejpam-5392	584	8	y1	y1	NOUN
ejpam-5392	584	9	}	}	PUNCT
ejpam-5392	584	10	,	,	PUNCT
ejpam-5392	584	11	then	then	ADV
ejpam-5392	584	12	y2	y2	PROPN
ejpam-5392	584	13	∈l−θβav	∈l−θβav	VERB
ejpam-5392	584	14	,	,	PUNCT
ejpam-5392	584	15	but	but	CCONJ
ejpam-5392	584	16	y2	y2	VERB
ejpam-5392	584	17	∈l−	∈l−	PROPN
ejpam-5392	584	18	∧	∧	PROPN
ejpam-5392	584	19	βav	βav	NOUN
ejpam-5392	584	20	.	.	PUNCT
ejpam-5392	585	1	definition	definition	NOUN
ejpam-5392	585	2	21	21	NUM
ejpam-5392	585	3	.	.	PUNCT
ejpam-5392	586	1	let	let	AUX
ejpam-5392	586	2	(	(	PUNCT
ejpam-5392	586	3	x	x	NOUN
ejpam-5392	586	4	,	,	PUNCT
ejpam-5392	586	5	r	r	NOUN
ejpam-5392	586	6	,	,	PUNCT
ejpam-5392	586	7	ξλ	ξλ	NOUN
ejpam-5392	586	8	)	)	PUNCT
ejpam-5392	586	9	be	be	AUX
ejpam-5392	586	10	a	a	DET
ejpam-5392	586	11	gλ	gλ	NOUN
ejpam-5392	586	12	-	-	PUNCT
ejpam-5392	586	13	space	space	NOUN
ejpam-5392	586	14	,	,	PUNCT
ejpam-5392	586	15	l	l	X
ejpam-5392	586	16	be	be	AUX
ejpam-5392	586	17	an	an	DET
ejpam-5392	586	18	ideal	ideal	NOUN
ejpam-5392	586	19	on	on	ADP
ejpam-5392	586	20	x	x	X
ejpam-5392	586	21	,	,	PUNCT
ejpam-5392	586	22	v	v	ADP
ejpam-5392	586	23	⊆	⊆	NUM
ejpam-5392	586	24	x	x	PUNCT
ejpam-5392	586	25	and	and	CCONJ
ejpam-5392	586	26	y	y	PROPN
ejpam-5392	586	27	∈	∈	PROPN
ejpam-5392	586	28	x.	x.	NOUN
ejpam-5392	587	1	the	the	DET
ejpam-5392	587	2	l	l	NOUN
ejpam-5392	587	3	−	−	PROPN
ejpam-5392	587	4	θβλ	θβλ	NOUN
ejpam-5392	587	5	-	-	PUNCT
ejpam-5392	587	6	rough	rough	ADJ
ejpam-5392	587	7	membership	membership	NOUN
ejpam-5392	587	8	functions	function	NOUN
ejpam-5392	587	9	of	of	ADP
ejpam-5392	587	10	v	v	NUM
ejpam-5392	587	11	are	be	AUX
ejpam-5392	587	12	defined	define	VERB
ejpam-5392	587	13	by	by	ADP
ejpam-5392	587	14	µ	µ	PRON
ejpam-5392	587	15	l−θβλ	l−θβλ	NOUN
ejpam-5392	587	16	v	v	NOUN
ejpam-5392	587	17	→	→	SYM
ejpam-5392	587	18	[	[	X
ejpam-5392	587	19	0	0	NUM
ejpam-5392	587	20	,	,	PUNCT
ejpam-5392	587	21	1	1	NUM
ejpam-5392	587	22	]	]	PUNCT
ejpam-5392	587	23	,	,	PUNCT
ejpam-5392	587	24	where	where	SCONJ
ejpam-5392	587	25	µ	µ	X
ejpam-5392	587	26	l−θβλ	l−θβλ	NOUN
ejpam-5392	587	27	v	v	ADP
ejpam-5392	587	28	(	(	PUNCT
ejpam-5392	587	29	y	y	NOUN
ejpam-5392	587	30	)	)	PUNCT
ejpam-5392	587	31	=	=	PRON
ejpam-5392	587	32	{	{	PUNCT
ejpam-5392	587	33	1	1	NUM
ejpam-5392	587	34	if	if	SCONJ
ejpam-5392	587	35	1∈ψl−θβλ	1∈ψl−θβλ	PROPN
ejpam-5392	587	36	v	v	ADP
ejpam-5392	587	37	(	(	PUNCT
ejpam-5392	587	38	y	y	NOUN
ejpam-5392	587	39	)	)	PUNCT
ejpam-5392	587	40	.	.	PUNCT
ejpam-5392	588	1	min(ψ	min(ψ	NOUN
ejpam-5392	588	2	l−θβλ	l−θβλ	ADJ
ejpam-5392	588	3	v	v	ADP
ejpam-5392	588	4	(	(	PUNCT
ejpam-5392	588	5	y	y	NOUN
ejpam-5392	588	6	)	)	PUNCT
ejpam-5392	588	7	)	)	PUNCT
ejpam-5392	588	8	otherwise	otherwise	ADV
ejpam-5392	588	9	.	.	PUNCT
ejpam-5392	588	10	}	}	PUNCT
ejpam-5392	588	11	.	.	PUNCT
ejpam-5392	589	1	and	and	CCONJ
ejpam-5392	589	2	ψ	ψ	X
ejpam-5392	589	3	l−θβλ	l−θβλ	ADJ
ejpam-5392	589	4	v	v	ADP
ejpam-5392	589	5	(	(	PUNCT
ejpam-5392	589	6	y	y	NOUN
ejpam-5392	589	7	)	)	PUNCT
ejpam-5392	589	8	=	=	SYM
ejpam-5392	590	1	|l−θβλ(y)∩v	|l−θβλ(y)∩v	PROPN
ejpam-5392	590	2	|	|	ADV
ejpam-5392	590	3	|l−θβλ(y)|	|l−θβλ(y)|	NUM
ejpam-5392	590	4	,	,	PUNCT
ejpam-5392	590	5	y	y	PROPN
ejpam-5392	590	6	∈	∈	PROPN
ejpam-5392	590	7	l	l	NOUN
ejpam-5392	591	1	−	−	NOUN
ejpam-5392	591	2	θβλ(y	θβλ(y	PROPN
ejpam-5392	591	3	)	)	PUNCT
ejpam-5392	591	4	,	,	PUNCT
ejpam-5392	591	5	l	l	NOUN
ejpam-5392	591	6	−	−	PROPN
ejpam-5392	591	7	θβλ(y	θβλ(y	PROPN
ejpam-5392	591	8	)	)	PUNCT
ejpam-5392	591	9	∈	∈	PROPN
ejpam-5392	591	10	l	l	PROPN
ejpam-5392	591	11	-	-	PUNCT
ejpam-5392	591	12	θβλo(x	θβλo(x	NOUN
ejpam-5392	591	13	)	)	PUNCT
ejpam-5392	591	14	.	.	PUNCT
ejpam-5392	592	1	remark	remark	NOUN
ejpam-5392	592	2	9	9	NUM
ejpam-5392	592	3	.	.	PUNCT
ejpam-5392	593	1	the	the	DET
ejpam-5392	593	2	l	l	NOUN
ejpam-5392	593	3	−	−	PROPN
ejpam-5392	593	4	θβλ	θβλ	NOUN
ejpam-5392	593	5	-	-	PUNCT
ejpam-5392	593	6	rough	rough	ADJ
ejpam-5392	593	7	membership	membership	NOUN
ejpam-5392	593	8	functions	function	NOUN
ejpam-5392	593	9	are	be	AUX
ejpam-5392	593	10	used	use	VERB
ejpam-5392	593	11	to	to	PART
ejpam-5392	593	12	define	define	VERB
ejpam-5392	593	13	the	the	DET
ejpam-5392	593	14	l	l	NOUN
ejpam-5392	593	15	-	-	PUNCT
ejpam-5392	593	16	θβλ	θβλ	NOUN
ejpam-5392	593	17	-	-	PUNCT
ejpam-5392	593	18	lower	low	ADJ
ejpam-5392	593	19	and	and	CCONJ
ejpam-5392	593	20	l	l	NOUN
ejpam-5392	593	21	-	-	PUNCT
ejpam-5392	593	22	θβλ	θβλ	NOUN
ejpam-5392	593	23	-	-	PUNCT
ejpam-5392	593	24	upper	upper	ADJ
ejpam-5392	593	25	approximations	approximation	NOUN
ejpam-5392	593	26	as	as	SCONJ
ejpam-5392	593	27	follows	follow	VERB
ejpam-5392	593	28	:	:	PUNCT
ejpam-5392	593	29	(	(	PUNCT
ejpam-5392	593	30	i	i	NOUN
ejpam-5392	593	31	)	)	PUNCT
ejpam-5392	594	1	rl−θβ	rl−θβ	PROPN
ejpam-5392	594	2	λ	λ	PROPN
ejpam-5392	594	3	(	(	PUNCT
ejpam-5392	594	4	v	v	NOUN
ejpam-5392	594	5	)	)	PUNCT
ejpam-5392	594	6	=	=	PUNCT
ejpam-5392	594	7	{	{	PUNCT
ejpam-5392	594	8	y	y	PROPN
ejpam-5392	594	9	∈	∈	PROPN
ejpam-5392	594	10	x	x	X
ejpam-5392	594	11	:	:	PUNCT
ejpam-5392	594	12	µ	µ	X
ejpam-5392	594	13	l−θβλ	l−θβλ	ADJ
ejpam-5392	594	14	v	v	ADP
ejpam-5392	594	15	(	(	PUNCT
ejpam-5392	594	16	y	y	NOUN
ejpam-5392	594	17	)	)	PUNCT
ejpam-5392	594	18	=	=	PUNCT
ejpam-5392	594	19	1	1	NUM
ejpam-5392	594	20	}	}	PUNCT
ejpam-5392	594	21	.	.	PUNCT
ejpam-5392	595	1	(	(	PUNCT
ejpam-5392	595	2	ii	ii	NOUN
ejpam-5392	595	3	)	)	PUNCT
ejpam-5392	595	4	rl−θβ	rl−θβ	PROPN
ejpam-5392	595	5	λ	λ	PROPN
ejpam-5392	595	6	(	(	PUNCT
ejpam-5392	595	7	v	v	NOUN
ejpam-5392	595	8	)	)	PUNCT
ejpam-5392	595	9	=	=	PUNCT
ejpam-5392	595	10	{	{	PUNCT
ejpam-5392	595	11	y	y	PROPN
ejpam-5392	595	12	∈	∈	PROPN
ejpam-5392	595	13	x	x	X
ejpam-5392	595	14	:	:	PUNCT
ejpam-5392	595	15	µ	µ	X
ejpam-5392	595	16	l−θβλ	l−θβλ	ADJ
ejpam-5392	595	17	v	v	ADP
ejpam-5392	595	18	(	(	PUNCT
ejpam-5392	595	19	y	y	NOUN
ejpam-5392	595	20	)	)	PUNCT
ejpam-5392	595	21	>	>	X
ejpam-5392	595	22	0	0	NUM
ejpam-5392	595	23	}	}	PUNCT
ejpam-5392	595	24	.	.	PUNCT
ejpam-5392	596	1	(	(	PUNCT
ejpam-5392	596	2	iii	iii	X
ejpam-5392	596	3	)	)	PUNCT
ejpam-5392	596	4	bndl−θβ	bndl−θβ	NOUN
ejpam-5392	597	1	λ	λ	PROPN
ejpam-5392	597	2	(	(	PUNCT
ejpam-5392	597	3	v	v	NOUN
ejpam-5392	597	4	)	)	PUNCT
ejpam-5392	597	5	=	=	PUNCT
ejpam-5392	597	6	{	{	PUNCT
ejpam-5392	597	7	y	y	PROPN
ejpam-5392	597	8	∈	∈	PROPN
ejpam-5392	597	9	x	x	PUNCT
ejpam-5392	597	10	:	:	PUNCT
ejpam-5392	597	11	0	0	NUM
ejpam-5392	597	12	<	<	X
ejpam-5392	597	13	µ	µ	X
ejpam-5392	597	14	l−θβλ	l−θβλ	NOUN
ejpam-5392	597	15	v	v	ADP
ejpam-5392	597	16	(	(	PUNCT
ejpam-5392	597	17	y	y	NOUN
ejpam-5392	597	18	)	)	PUNCT
ejpam-5392	597	19	<	<	X
ejpam-5392	597	20	1	1	NUM
ejpam-5392	597	21	}	}	PUNCT
ejpam-5392	597	22	.	.	PUNCT
ejpam-5392	598	1	proposition	proposition	NOUN
ejpam-5392	598	2	10	10	NUM
ejpam-5392	598	3	.	.	PUNCT
ejpam-5392	599	1	let	let	AUX
ejpam-5392	599	2	(	(	PUNCT
ejpam-5392	599	3	x	x	NOUN
ejpam-5392	599	4	,	,	PUNCT
ejpam-5392	599	5	r	r	NOUN
ejpam-5392	599	6	,	,	PUNCT
ejpam-5392	599	7	ξλ	ξλ	NOUN
ejpam-5392	599	8	,	,	PUNCT
ejpam-5392	599	9	l	l	NOUN
ejpam-5392	599	10	)	)	PUNCT
ejpam-5392	599	11	be	be	AUX
ejpam-5392	599	12	an	an	DET
ejpam-5392	599	13	l	l	NOUN
ejpam-5392	599	14	−gλ	−gλ	NOUN
ejpam-5392	599	15	-	-	PUNCT
ejpam-5392	599	16	space	space	NOUN
ejpam-5392	599	17	and	and	CCONJ
ejpam-5392	599	18	v	v	NOUN
ejpam-5392	599	19	,	,	PUNCT
ejpam-5392	599	20	w	w	PROPN
ejpam-5392	599	21	⊆	⊆	NUM
ejpam-5392	599	22	x.	x.	NOUN
ejpam-5392	599	23	then	then	ADV
ejpam-5392	599	24	(	(	PUNCT
ejpam-5392	599	25	i	i	NOUN
ejpam-5392	599	26	)	)	PUNCT
ejpam-5392	599	27	if	if	SCONJ
ejpam-5392	599	28	µ	µ	PRON
ejpam-5392	599	29	l−θβλ	l−θβλ	NOUN
ejpam-5392	599	30	v	v	ADP
ejpam-5392	599	31	(	(	PUNCT
ejpam-5392	599	32	y	y	NOUN
ejpam-5392	599	33	)	)	PUNCT
ejpam-5392	599	34	=	=	SYM
ejpam-5392	599	35	1	1	NUM
ejpam-5392	599	36	⇔	⇔	X
ejpam-5392	599	37	y	y	PROPN
ejpam-5392	599	38	∈l−θβλv	∈l−θβλv	ADV
ejpam-5392	599	39	.	.	PUNCT
ejpam-5392	600	1	(	(	PUNCT
ejpam-5392	600	2	ii	ii	NOUN
ejpam-5392	600	3	)	)	PUNCT
ejpam-5392	600	4	if	if	SCONJ
ejpam-5392	600	5	µ	µ	PRON
ejpam-5392	600	6	l−θβλ	l−θβλ	NOUN
ejpam-5392	600	7	v	v	ADP
ejpam-5392	600	8	(	(	PUNCT
ejpam-5392	600	9	y	y	NOUN
ejpam-5392	600	10	)	)	PUNCT
ejpam-5392	600	11	=	=	SYM
ejpam-5392	600	12	0	0	NUM
ejpam-5392	600	13	⇔	⇔	PROPN
ejpam-5392	600	14	y	y	PROPN
ejpam-5392	600	15	∈	∈	PROPN
ejpam-5392	600	16	x	x	PUNCT
ejpam-5392	600	17	−rl−θβ	−rl−θβ	NOUN
ejpam-5392	600	18	λ	λ	PROPN
ejpam-5392	600	19	(	(	PUNCT
ejpam-5392	600	20	v	v	NOUN
ejpam-5392	600	21	)	)	PUNCT
ejpam-5392	600	22	.	.	PUNCT
ejpam-5392	601	1	(	(	PUNCT
ejpam-5392	601	2	iii	iii	X
ejpam-5392	601	3	)	)	PUNCT
ejpam-5392	601	4	if	if	SCONJ
ejpam-5392	601	5	0	0	NUM
ejpam-5392	601	6	<	<	X
ejpam-5392	601	7	µ	µ	X
ejpam-5392	601	8	l−θβλ	l−θβλ	NOUN
ejpam-5392	601	9	v	v	ADP
ejpam-5392	601	10	(	(	PUNCT
ejpam-5392	601	11	y	y	NOUN
ejpam-5392	601	12	)	)	PUNCT
ejpam-5392	601	13	<	<	X
ejpam-5392	601	14	1	1	NUM
ejpam-5392	601	15	⇔	⇔	PROPN
ejpam-5392	601	16	y	y	PROPN
ejpam-5392	601	17	∈	∈	PROPN
ejpam-5392	601	18	bndl−θβ	bndl−θβ	NOUN
ejpam-5392	601	19	λ	λ	INTJ
ejpam-5392	601	20	(	(	PUNCT
ejpam-5392	601	21	v	v	NOUN
ejpam-5392	601	22	)	)	PUNCT
ejpam-5392	601	23	.	.	PUNCT
ejpam-5392	602	1	m.	m.	PROPN
ejpam-5392	602	2	hosny	hosny	PROPN
ejpam-5392	602	3	,	,	PUNCT
ejpam-5392	602	4	t.m	t.m	PROPN
ejpam-5392	602	5	.	.	PROPN
ejpam-5392	602	6	al	al	PROPN
ejpam-5392	602	7	-	-	PUNCT
ejpam-5392	602	8	shami	shami	PROPN
ejpam-5392	602	9	/	/	PUNCT
ejpam-5392	602	10	eur	eur	PROPN
ejpam-5392	602	11	.	.	PUNCT
ejpam-5392	603	1	j.	j.	PROPN
ejpam-5392	603	2	pure	pure	PROPN
ejpam-5392	603	3	appl	appl	PROPN
ejpam-5392	603	4	.	.	PROPN
ejpam-5392	603	5	math	math	PROPN
ejpam-5392	603	6	,	,	PUNCT
ejpam-5392	603	7	17	17	NUM
ejpam-5392	603	8	(	(	PUNCT
ejpam-5392	603	9	4	4	NUM
ejpam-5392	603	10	)	)	PUNCT
ejpam-5392	603	11	(	(	PUNCT
ejpam-5392	603	12	2024	2024	NUM
ejpam-5392	603	13	)	)	PUNCT
ejpam-5392	603	14	,	,	PUNCT
ejpam-5392	603	15	3436	3436	NUM
ejpam-5392	603	16	-	-	SYM
ejpam-5392	603	17	3463	3463	NUM
ejpam-5392	603	18	3455	3455	NUM
ejpam-5392	603	19	(	(	PUNCT
ejpam-5392	603	20	iv	iv	X
ejpam-5392	603	21	)	)	PUNCT
ejpam-5392	603	22	if	if	SCONJ
ejpam-5392	603	23	µ	µ	PRON
ejpam-5392	603	24	l−θβλ	l−θβλ	NOUN
ejpam-5392	603	25	a′	a′	PROPN
ejpam-5392	603	26	(	(	PUNCT
ejpam-5392	603	27	y	y	NOUN
ejpam-5392	603	28	)	)	PUNCT
ejpam-5392	603	29	=	=	SYM
ejpam-5392	604	1	1−	1−	NUM
ejpam-5392	604	2	µ	µ	NUM
ejpam-5392	604	3	l−θβλ	l−θβλ	NOUN
ejpam-5392	604	4	v	v	ADP
ejpam-5392	604	5	(	(	PUNCT
ejpam-5392	604	6	y	y	NOUN
ejpam-5392	604	7	)	)	PUNCT
ejpam-5392	604	8	,	,	PUNCT
ejpam-5392	604	9	∀	∀	PUNCT
ejpam-5392	604	10	y	y	PROPN
ejpam-5392	604	11	∈	∈	PROPN
ejpam-5392	604	12	x.	x.	NOUN
ejpam-5392	604	13	(	(	PUNCT
ejpam-5392	604	14	v	v	NOUN
ejpam-5392	604	15	)	)	PUNCT
ejpam-5392	604	16	if	if	SCONJ
ejpam-5392	604	17	µ	µ	PRON
ejpam-5392	604	18	l−θβλ	l−θβλ	NOUN
ejpam-5392	604	19	v	v	ADP
ejpam-5392	604	20	∪b	∪b	X
ejpam-5392	604	21	(	(	PUNCT
ejpam-5392	604	22	y	y	NOUN
ejpam-5392	604	23	)	)	PUNCT
ejpam-5392	604	24	≥	≥	NOUN
ejpam-5392	604	25	max(µ	max(µ	NOUN
ejpam-5392	604	26	l−θβλ	l−θβλ	ADJ
ejpam-5392	604	27	v	v	PROPN
ejpam-5392	604	28	(	(	PUNCT
ejpam-5392	604	29	y	y	NOUN
ejpam-5392	604	30	)	)	PUNCT
ejpam-5392	604	31	,	,	PUNCT
ejpam-5392	604	32	µ	µ	X
ejpam-5392	604	33	l−θβλ	l−θβλ	ADJ
ejpam-5392	604	34	b	b	PROPN
ejpam-5392	604	35	(	(	PUNCT
ejpam-5392	604	36	y	y	NOUN
ejpam-5392	604	37	)	)	PUNCT
ejpam-5392	604	38	)	)	PUNCT
ejpam-5392	604	39	,	,	PUNCT
ejpam-5392	604	40	∀	∀	PUNCT
ejpam-5392	604	41	y	y	PROPN
ejpam-5392	604	42	∈	∈	PROPN
ejpam-5392	604	43	x.	x.	NOUN
ejpam-5392	604	44	(	(	PUNCT
ejpam-5392	604	45	vi	vi	NOUN
ejpam-5392	604	46	)	)	PUNCT
ejpam-5392	604	47	if	if	SCONJ
ejpam-5392	604	48	µ	µ	PRON
ejpam-5392	604	49	l−θβλ	l−θβλ	NOUN
ejpam-5392	604	50	v	v	ADP
ejpam-5392	604	51	∩b	∩b	NOUN
ejpam-5392	604	52	(	(	PUNCT
ejpam-5392	604	53	y	y	NOUN
ejpam-5392	604	54	)	)	PUNCT
ejpam-5392	604	55	≤	≤	NOUN
ejpam-5392	604	56	min(µ	min(µ	NOUN
ejpam-5392	604	57	l−θβλ	l−θβλ	NOUN
ejpam-5392	604	58	v	v	PROPN
ejpam-5392	604	59	(	(	PUNCT
ejpam-5392	604	60	y	y	NOUN
ejpam-5392	604	61	)	)	PUNCT
ejpam-5392	604	62	,	,	PUNCT
ejpam-5392	604	63	µ	µ	X
ejpam-5392	604	64	l−θβλ	l−θβλ	ADJ
ejpam-5392	604	65	b	b	PROPN
ejpam-5392	604	66	(	(	PUNCT
ejpam-5392	604	67	y	y	NOUN
ejpam-5392	604	68	)	)	PUNCT
ejpam-5392	604	69	)	)	PUNCT
ejpam-5392	604	70	,	,	PUNCT
ejpam-5392	604	71	∀	∀	PUNCT
ejpam-5392	604	72	y	y	PROPN
ejpam-5392	604	73	∈	∈	PROPN
ejpam-5392	604	74	x.	x.	NOUN
ejpam-5392	604	75	proof	proof	NOUN
ejpam-5392	604	76	.	.	PUNCT
ejpam-5392	605	1	we	we	PRON
ejpam-5392	605	2	prove	prove	VERB
ejpam-5392	605	3	(	(	PUNCT
ejpam-5392	605	4	i	i	NOUN
ejpam-5392	605	5	)	)	PUNCT
ejpam-5392	605	6	,	,	PUNCT
ejpam-5392	605	7	and	and	CCONJ
ejpam-5392	605	8	the	the	DET
ejpam-5392	605	9	others	other	NOUN
ejpam-5392	605	10	similarly	similarly	ADV
ejpam-5392	605	11	.	.	PUNCT
ejpam-5392	606	1	y	y	PROPN
ejpam-5392	606	2	∈l−θβλv	∈l−θβλv	PROPN
ejpam-5392	606	3	⇔	⇔	PROPN
ejpam-5392	606	4	y	y	PROPN
ejpam-5392	606	5	∈	∈	PROPN
ejpam-5392	606	6	rl−θβ	rl−θβ	PROPN
ejpam-5392	606	7	λ	λ	PROPN
ejpam-5392	606	8	(	(	PUNCT
ejpam-5392	606	9	v	v	NOUN
ejpam-5392	606	10	)	)	PUNCT
ejpam-5392	606	11	.	.	PUNCT
ejpam-5392	607	1	since	since	SCONJ
ejpam-5392	607	2	rl−θβ	rl−θβ	PROPN
ejpam-5392	607	3	λ	λ	PROPN
ejpam-5392	607	4	(	(	PUNCT
ejpam-5392	607	5	v	v	NOUN
ejpam-5392	607	6	)	)	PUNCT
ejpam-5392	607	7	is	be	AUX
ejpam-5392	607	8	l−	l−	PROPN
ejpam-5392	607	9	θβλ	θβλ	NOUN
ejpam-5392	607	10	-	-	PUNCT
ejpam-5392	607	11	open	open	ADJ
ejpam-5392	607	12	set	set	NOUN
ejpam-5392	607	13	contained	contain	VERB
ejpam-5392	607	14	in	in	ADP
ejpam-5392	607	15	v	v	NUM
ejpam-5392	607	16	,	,	PUNCT
ejpam-5392	607	17	thus	thus	ADV
ejpam-5392	607	18	|rl−θβ	|rl−θβ	PROPN
ejpam-5392	607	19	λ	λ	PROPN
ejpam-5392	607	20	(	(	PUNCT
ejpam-5392	607	21	v	v	NOUN
ejpam-5392	607	22	)	)	PUNCT
ejpam-5392	607	23	∩v	∩v	NOUN
ejpam-5392	608	1	|	|	INTJ
ejpam-5392	608	2	|rl−θβ	|rl−θβ	PROPN
ejpam-5392	608	3	λ	λ	PROPN
ejpam-5392	608	4	(	(	PUNCT
ejpam-5392	608	5	v	v	NOUN
ejpam-5392	608	6	)	)	PUNCT
ejpam-5392	608	7	|	|	ADV
ejpam-5392	608	8	=	=	SYM
ejpam-5392	609	1	|rl−θβ	|rl−θβ	PROPN
ejpam-5392	609	2	λ	λ	PROPN
ejpam-5392	609	3	(	(	PUNCT
ejpam-5392	609	4	v	v	NOUN
ejpam-5392	609	5	)	)	PUNCT
ejpam-5392	609	6	|	|	ADV
ejpam-5392	609	7	|rl−θβ	|rl−θβ	PROPN
ejpam-5392	609	8	λ	λ	PROPN
ejpam-5392	609	9	(	(	PUNCT
ejpam-5392	609	10	v	v	NOUN
ejpam-5392	609	11	)	)	PUNCT
ejpam-5392	609	12	|	|	NOUN
ejpam-5392	609	13	=	=	SYM
ejpam-5392	609	14	1	1	X
ejpam-5392	609	15	.	.	PUNCT
ejpam-5392	610	1	then	then	ADV
ejpam-5392	610	2	,	,	PUNCT
ejpam-5392	610	3	1	1	NUM
ejpam-5392	610	4	∈	∈	NOUN
ejpam-5392	610	5	ψ	ψ	NOUN
ejpam-5392	610	6	l−θβλ	l−θβλ	NOUN
ejpam-5392	610	7	v	v	ADP
ejpam-5392	610	8	(	(	PUNCT
ejpam-5392	610	9	y	y	NOUN
ejpam-5392	610	10	)	)	PUNCT
ejpam-5392	610	11	and	and	CCONJ
ejpam-5392	610	12	accordingly	accordingly	ADV
ejpam-5392	610	13	µ	µ	PRON
ejpam-5392	610	14	l−θβλ	l−θβλ	NOUN
ejpam-5392	610	15	v	v	ADP
ejpam-5392	610	16	(	(	PUNCT
ejpam-5392	610	17	y	y	NOUN
ejpam-5392	610	18	)	)	PUNCT
ejpam-5392	610	19	=	=	SYM
ejpam-5392	610	20	1	1	X
ejpam-5392	610	21	.	.	PUNCT
ejpam-5392	610	22	in	in	ADP
ejpam-5392	610	23	the	the	DET
ejpam-5392	610	24	next	next	ADJ
ejpam-5392	610	25	,	,	PUNCT
ejpam-5392	610	26	we	we	PRON
ejpam-5392	610	27	prove	prove	VERB
ejpam-5392	610	28	an	an	DET
ejpam-5392	610	29	important	important	ADJ
ejpam-5392	610	30	result	result	NOUN
ejpam-5392	610	31	showing	show	VERB
ejpam-5392	610	32	the	the	DET
ejpam-5392	610	33	interrelations	interrelation	NOUN
ejpam-5392	610	34	between	between	ADP
ejpam-5392	610	35	the	the	DET
ejpam-5392	610	36	relations	relation	NOUN
ejpam-5392	610	37	of	of	ADP
ejpam-5392	610	38	λ	λ	NOUN
ejpam-5392	610	39	-	-	ADJ
ejpam-5392	610	40	rough	rough	ADJ
ejpam-5392	610	41	membership	membership	NOUN
ejpam-5392	610	42	[	[	X
ejpam-5392	610	43	35	35	NUM
ejpam-5392	610	44	]	]	SYM
ejpam-5392	610	45	12	12	NUM
ejpam-5392	610	46	,	,	PUNCT
ejpam-5392	610	47	λ	λ	NOUN
ejpam-5392	610	48	-	-	PUNCT
ejpam-5392	610	49	nearly	nearly	ADV
ejpam-5392	610	50	rough	rough	ADJ
ejpam-5392	610	51	membership	membership	NOUN
ejpam-5392	610	52	[	[	X
ejpam-5392	610	53	45	45	NUM
ejpam-5392	610	54	]	]	SYM
ejpam-5392	610	55	13	13	NUM
ejpam-5392	610	56	,	,	PUNCT
ejpam-5392	610	57	λ	λ	NOUN
ejpam-5392	610	58	-	-	PUNCT
ejpam-5392	610	59	nearly	nearly	ADV
ejpam-5392	610	60	rough	rough	ADJ
ejpam-5392	610	61	membership	membership	NOUN
ejpam-5392	610	62	w.r.t	w.r.t	NOUN
ejpam-5392	610	63	l	l	PROPN
ejpam-5392	611	1	[	[	X
ejpam-5392	611	2	22	22	NUM
ejpam-5392	611	3	,	,	PUNCT
ejpam-5392	611	4	23	23	NUM
ejpam-5392	611	5	]	]	SYM
ejpam-5392	611	6	14	14	NUM
ejpam-5392	611	7	,	,	PUNCT
ejpam-5392	611	8	and	and	CCONJ
ejpam-5392	611	9	l	l	NOUN
ejpam-5392	611	10	-	-	PUNCT
ejpam-5392	611	11	θβλ	θβλ	NOUN
ejpam-5392	611	12	-	-	PUNCT
ejpam-5392	611	13	rough	rough	ADJ
ejpam-5392	611	14	membership	membership	NOUN
ejpam-5392	611	15	functions	function	NOUN
ejpam-5392	611	16	.	.	PUNCT
ejpam-5392	612	1	lemma	lemma	PROPN
ejpam-5392	612	2	3	3	X
ejpam-5392	612	3	.	.	PUNCT
ejpam-5392	613	1	let	let	AUX
ejpam-5392	613	2	(	(	PUNCT
ejpam-5392	613	3	x	x	NOUN
ejpam-5392	613	4	,	,	PUNCT
ejpam-5392	613	5	r	r	NOUN
ejpam-5392	613	6	,	,	PUNCT
ejpam-5392	613	7	ξλ	ξλ	NOUN
ejpam-5392	613	8	,	,	PUNCT
ejpam-5392	613	9	l	l	NOUN
ejpam-5392	613	10	)	)	PUNCT
ejpam-5392	613	11	be	be	AUX
ejpam-5392	613	12	an	an	DET
ejpam-5392	613	13	l	l	NOUN
ejpam-5392	613	14	−gλ	−gλ	NOUN
ejpam-5392	613	15	-	-	PUNCT
ejpam-5392	613	16	space	space	NOUN
ejpam-5392	613	17	and	and	CCONJ
ejpam-5392	613	18	v	v	ADP
ejpam-5392	613	19	⊆	⊆	NUM
ejpam-5392	613	20	x.	x.	NOUN
ejpam-5392	613	21	then	then	ADV
ejpam-5392	613	22	(	(	PUNCT
ejpam-5392	613	23	i	i	NOUN
ejpam-5392	613	24	)	)	PUNCT
ejpam-5392	613	25	µλv	µλv	NOUN
ejpam-5392	613	26	(	(	PUNCT
ejpam-5392	613	27	y	y	NOUN
ejpam-5392	613	28	)	)	PUNCT
ejpam-5392	614	1	=	=	SYM
ejpam-5392	614	2	1	1	NUM
ejpam-5392	614	3	⇒	⇒	NOUN
ejpam-5392	614	4	µηλv	µηλv	NOUN
ejpam-5392	614	5	(	(	PUNCT
ejpam-5392	614	6	y	y	NOUN
ejpam-5392	614	7	)	)	PUNCT
ejpam-5392	614	8	=	=	SYM
ejpam-5392	614	9	1	1	NUM
ejpam-5392	614	10	⇒	⇒	NOUN
ejpam-5392	614	11	µl−ηλv	µl−ηλv	NOUN
ejpam-5392	614	12	(	(	PUNCT
ejpam-5392	614	13	y	y	NOUN
ejpam-5392	614	14	)	)	PUNCT
ejpam-5392	614	15	=	=	SYM
ejpam-5392	614	16	1	1	NUM
ejpam-5392	614	17	⇒	⇒	NOUN
ejpam-5392	614	18	µ	µ	NUM
ejpam-5392	614	19	l−θβλ	l−θβλ	NOUN
ejpam-5392	614	20	v	v	ADP
ejpam-5392	614	21	(	(	PUNCT
ejpam-5392	614	22	y	y	NOUN
ejpam-5392	614	23	)	)	PUNCT
ejpam-5392	614	24	=	=	SYM
ejpam-5392	614	25	1	1	NUM
ejpam-5392	614	26	,	,	PUNCT
ejpam-5392	614	27	∀	∀	VERB
ejpam-5392	614	28	y	y	PROPN
ejpam-5392	614	29	∈	∈	PROPN
ejpam-5392	614	30	x.	x.	NOUN
ejpam-5392	614	31	(	(	PUNCT
ejpam-5392	614	32	ii	ii	NOUN
ejpam-5392	614	33	)	)	PUNCT
ejpam-5392	614	34	µλv	µλv	NOUN
ejpam-5392	614	35	(	(	PUNCT
ejpam-5392	614	36	y	y	NOUN
ejpam-5392	614	37	)	)	PUNCT
ejpam-5392	614	38	=	=	SYM
ejpam-5392	614	39	0	0	NUM
ejpam-5392	614	40	⇒	⇒	PROPN
ejpam-5392	614	41	µηλv	µηλv	PROPN
ejpam-5392	614	42	(	(	PUNCT
ejpam-5392	614	43	y	y	NOUN
ejpam-5392	614	44	)	)	PUNCT
ejpam-5392	614	45	=	=	SYM
ejpam-5392	614	46	0	0	NUM
ejpam-5392	614	47	⇒	⇒	NOUN
ejpam-5392	614	48	µl−ηλv	µl−ηλv	NOUN
ejpam-5392	614	49	(	(	PUNCT
ejpam-5392	614	50	y	y	NOUN
ejpam-5392	614	51	)	)	PUNCT
ejpam-5392	614	52	=	=	SYM
ejpam-5392	614	53	0	0	NUM
ejpam-5392	614	54	⇒	⇒	PROPN
ejpam-5392	614	55	µ	µ	NUM
ejpam-5392	614	56	l−θβλ	l−θβλ	NOUN
ejpam-5392	614	57	v	v	ADP
ejpam-5392	614	58	(	(	PUNCT
ejpam-5392	614	59	y	y	NOUN
ejpam-5392	614	60	)	)	PUNCT
ejpam-5392	614	61	=	=	SYM
ejpam-5392	614	62	0	0	NUM
ejpam-5392	614	63	,	,	PUNCT
ejpam-5392	614	64	∀	∀	VERB
ejpam-5392	614	65	y	y	PROPN
ejpam-5392	614	66	∈	∈	PROPN
ejpam-5392	614	67	x.	x.	NOUN
ejpam-5392	614	68	proof	proof	NOUN
ejpam-5392	614	69	.	.	PUNCT
ejpam-5392	615	1	(	(	PUNCT
ejpam-5392	615	2	i	i	NOUN
ejpam-5392	615	3	)	)	PUNCT
ejpam-5392	615	4	µλv	µλv	NOUN
ejpam-5392	615	5	(	(	PUNCT
ejpam-5392	615	6	y	y	NOUN
ejpam-5392	615	7	)	)	PUNCT
ejpam-5392	615	8	=	=	SYM
ejpam-5392	615	9	1	1	NUM
ejpam-5392	615	10	⇒	⇒	NOUN
ejpam-5392	615	11	µηλv	µηλv	NOUN
ejpam-5392	615	12	(	(	PUNCT
ejpam-5392	615	13	y	y	NOUN
ejpam-5392	615	14	)	)	PUNCT
ejpam-5392	615	15	=	=	SYM
ejpam-5392	615	16	1	1	NUM
ejpam-5392	615	17	⇒	⇒	NOUN
ejpam-5392	615	18	µl−ηλv	µl−ηλv	NOUN
ejpam-5392	615	19	(	(	PUNCT
ejpam-5392	615	20	y	y	NOUN
ejpam-5392	615	21	)	)	PUNCT
ejpam-5392	615	22	=	=	SYM
ejpam-5392	615	23	1	1	NUM
ejpam-5392	615	24	directly	directly	ADV
ejpam-5392	615	25	from	from	ADP
ejpam-5392	615	26	lemma	lemma	PROPN
ejpam-5392	615	27	1	1	NUM
ejpam-5392	615	28	.	.	PUNCT
ejpam-5392	616	1	let	let	VERB
ejpam-5392	616	2	µl−ηλv	µl−ηλv	X
ejpam-5392	616	3	(	(	PUNCT
ejpam-5392	616	4	y	y	NOUN
ejpam-5392	616	5	)	)	PUNCT
ejpam-5392	616	6	=	=	SYM
ejpam-5392	616	7	1	1	NUM
ejpam-5392	616	8	,	,	PUNCT
ejpam-5392	616	9	then	then	ADV
ejpam-5392	616	10	y	y	PROPN
ejpam-5392	616	11	∈	∈	PROPN
ejpam-5392	616	12	rl−η	rl−η	PROPN
ejpam-5392	616	13	λ	λ	PROPN
ejpam-5392	616	14	(	(	PUNCT
ejpam-5392	616	15	v	v	NOUN
ejpam-5392	616	16	)	)	PUNCT
ejpam-5392	616	17	⇒	⇒	VERB
ejpam-5392	616	18	y	y	PROPN
ejpam-5392	616	19	∈	∈	PROPN
ejpam-5392	617	1	rl−θβ	rl−θβ	PROPN
ejpam-5392	617	2	λ	λ	PROPN
ejpam-5392	617	3	(	(	PUNCT
ejpam-5392	617	4	v	v	NOUN
ejpam-5392	617	5	)	)	PUNCT
ejpam-5392	617	6	⇒	⇒	NOUN
ejpam-5392	617	7	µ	µ	NUM
ejpam-5392	617	8	l−θβλ	l−θβλ	NOUN
ejpam-5392	617	9	v	v	ADP
ejpam-5392	617	10	(	(	PUNCT
ejpam-5392	617	11	y	y	NOUN
ejpam-5392	617	12	)	)	PUNCT
ejpam-5392	617	13	=	=	NOUN
ejpam-5392	618	1	1,∀	1,∀	NUM
ejpam-5392	618	2	y	y	SYM
ejpam-5392	618	3	∈	∈	PROPN
ejpam-5392	618	4	x.	x.	NOUN
ejpam-5392	618	5	(	(	PUNCT
ejpam-5392	618	6	ii	ii	NOUN
ejpam-5392	618	7	)	)	PUNCT
ejpam-5392	618	8	µλv	µλv	NOUN
ejpam-5392	618	9	(	(	PUNCT
ejpam-5392	618	10	y	y	NOUN
ejpam-5392	618	11	)	)	PUNCT
ejpam-5392	618	12	=	=	SYM
ejpam-5392	618	13	0	0	NUM
ejpam-5392	618	14	⇒	⇒	PROPN
ejpam-5392	618	15	µηλv	µηλv	PROPN
ejpam-5392	618	16	(	(	PUNCT
ejpam-5392	618	17	y	y	NOUN
ejpam-5392	618	18	)	)	PUNCT
ejpam-5392	618	19	=	=	SYM
ejpam-5392	618	20	0	0	NUM
ejpam-5392	618	21	⇒	⇒	NOUN
ejpam-5392	618	22	µl−ηλv	µl−ηλv	NOUN
ejpam-5392	618	23	(	(	PUNCT
ejpam-5392	618	24	y	y	NOUN
ejpam-5392	618	25	)	)	PUNCT
ejpam-5392	618	26	=	=	SYM
ejpam-5392	618	27	0	0	PUNCT
ejpam-5392	618	28	directly	directly	ADV
ejpam-5392	618	29	from	from	ADP
ejpam-5392	618	30	lemma	lemma	PROPN
ejpam-5392	618	31	1	1	NUM
ejpam-5392	618	32	.	.	PUNCT
ejpam-5392	619	1	let	let	VERB
ejpam-5392	619	2	µl−ηλv	µl−ηλv	X
ejpam-5392	619	3	(	(	PUNCT
ejpam-5392	619	4	y	y	NOUN
ejpam-5392	619	5	)	)	PUNCT
ejpam-5392	619	6	=	=	SYM
ejpam-5392	619	7	0	0	NUM
ejpam-5392	619	8	,	,	PUNCT
ejpam-5392	619	9	then	then	ADV
ejpam-5392	619	10	y	y	PROPN
ejpam-5392	619	11	∈	∈	PROPN
ejpam-5392	619	12	x	x	PUNCT
ejpam-5392	619	13	−rl−η	−rl−η	PROPN
ejpam-5392	619	14	λ	λ	PROPN
ejpam-5392	619	15	(	(	PUNCT
ejpam-5392	619	16	v	v	NOUN
ejpam-5392	619	17	)	)	PUNCT
ejpam-5392	619	18	⇒	⇒	VERB
ejpam-5392	619	19	y	y	PROPN
ejpam-5392	619	20	∈	∈	PROPN
ejpam-5392	620	1	x	x	PUNCT
ejpam-5392	620	2	−rl−θβ	−rl−θβ	NOUN
ejpam-5392	620	3	λ	λ	PROPN
ejpam-5392	620	4	(	(	PUNCT
ejpam-5392	620	5	v	v	NOUN
ejpam-5392	620	6	)	)	PUNCT
ejpam-5392	620	7	⇒	⇒	NOUN
ejpam-5392	620	8	µ	µ	NUM
ejpam-5392	620	9	l−θβλ	l−θβλ	NOUN
ejpam-5392	620	10	v	v	ADP
ejpam-5392	620	11	(	(	PUNCT
ejpam-5392	620	12	y	y	NOUN
ejpam-5392	620	13	)	)	PUNCT
ejpam-5392	620	14	=	=	SYM
ejpam-5392	620	15	0	0	NUM
ejpam-5392	620	16	,	,	PUNCT
ejpam-5392	620	17	∀	∀	VERB
ejpam-5392	620	18	y	y	PROPN
ejpam-5392	620	19	∈	∈	PROPN
ejpam-5392	620	20	x.	x.	NOUN
ejpam-5392	620	21	remark	remark	VERB
ejpam-5392	620	22	10	10	NUM
ejpam-5392	620	23	.	.	PUNCT
ejpam-5392	621	1	by	by	ADP
ejpam-5392	621	2	example	example	NOUN
ejpam-5392	621	3	1	1	NUM
ejpam-5392	621	4	,	,	PUNCT
ejpam-5392	621	5	one	one	PRON
ejpam-5392	621	6	can	can	AUX
ejpam-5392	621	7	see	see	VERB
ejpam-5392	621	8	that	that	SCONJ
ejpam-5392	621	9	the	the	DET
ejpam-5392	621	10	converse	converse	NOUN
ejpam-5392	621	11	of	of	ADP
ejpam-5392	621	12	lemma	lemma	PROPN
ejpam-5392	621	13	3	3	NUM
ejpam-5392	621	14	fails	fail	VERB
ejpam-5392	621	15	.	.	PUNCT
ejpam-5392	622	1	remark	remark	NOUN
ejpam-5392	622	2	11	11	NUM
ejpam-5392	622	3	.	.	PUNCT
ejpam-5392	623	1	according	accord	VERB
ejpam-5392	623	2	to	to	ADP
ejpam-5392	623	3	lemma	lemma	PROPN
ejpam-5392	623	4	3	3	NUM
ejpam-5392	623	5	,	,	PUNCT
ejpam-5392	623	6	the	the	DET
ejpam-5392	623	7	current	current	ADJ
ejpam-5392	623	8	definition	definition	NOUN
ejpam-5392	623	9	21	21	NUM
ejpam-5392	623	10	is	be	AUX
ejpam-5392	623	11	also	also	ADV
ejpam-5392	623	12	generalization	generalization	NOUN
ejpam-5392	623	13	of	of	ADP
ejpam-5392	623	14	the	the	DET
ejpam-5392	623	15	approaches	approach	NOUN
ejpam-5392	623	16	in	in	ADP
ejpam-5392	623	17	[	[	X
ejpam-5392	623	18	35	35	NUM
ejpam-5392	623	19	]	]	PUNCT
ejpam-5392	623	20	and	and	CCONJ
ejpam-5392	623	21	11	11	NUM
ejpam-5392	623	22	[	[	X
ejpam-5392	623	23	42	42	NUM
ejpam-5392	623	24	]	]	PUNCT
ejpam-5392	623	25	.	.	PUNCT
ejpam-5392	624	1	6	6	NUM
ejpam-5392	624	2	.	.	X
ejpam-5392	624	3	practical	practical	ADJ
ejpam-5392	624	4	application	application	NOUN
ejpam-5392	624	5	we	we	PRON
ejpam-5392	624	6	allocated	allocate	VERB
ejpam-5392	624	7	this	this	DET
ejpam-5392	624	8	part	part	NOUN
ejpam-5392	624	9	to	to	PART
ejpam-5392	624	10	examine	examine	VERB
ejpam-5392	624	11	the	the	DET
ejpam-5392	624	12	proposed	propose	VERB
ejpam-5392	624	13	models	model	NOUN
ejpam-5392	624	14	to	to	PART
ejpam-5392	624	15	cope	cope	VERB
ejpam-5392	624	16	with	with	ADP
ejpam-5392	624	17	a	a	DET
ejpam-5392	624	18	real	real	ADJ
ejpam-5392	624	19	situation	situation	NOUN
ejpam-5392	624	20	in	in	ADP
ejpam-5392	624	21	the	the	DET
ejpam-5392	624	22	field	field	NOUN
ejpam-5392	624	23	of	of	ADP
ejpam-5392	624	24	chemistry	chemistry	NOUN
ejpam-5392	624	25	.	.	PUNCT
ejpam-5392	625	1	we	we	PRON
ejpam-5392	625	2	explain	explain	VERB
ejpam-5392	625	3	how	how	SCONJ
ejpam-5392	625	4	our	our	PRON
ejpam-5392	625	5	models	model	NOUN
ejpam-5392	625	6	improve	improve	VERB
ejpam-5392	625	7	the	the	DET
ejpam-5392	625	8	outcomes	outcome	NOUN
ejpam-5392	625	9	of	of	ADP
ejpam-5392	625	10	generalized	generalized	ADJ
ejpam-5392	625	11	approximation	approximation	NOUN
ejpam-5392	625	12	spaces	space	NOUN
ejpam-5392	625	13	over	over	ADP
ejpam-5392	625	14	the	the	DET
ejpam-5392	625	15	previous	previous	ADJ
ejpam-5392	625	16	models	model	NOUN
ejpam-5392	625	17	displayed	display	VERB
ejpam-5392	625	18	in	in	ADP
ejpam-5392	625	19	[	[	X
ejpam-5392	625	20	15	15	NUM
ejpam-5392	625	21	,	,	PUNCT
ejpam-5392	625	22	22	22	NUM
ejpam-5392	625	23	,	,	PUNCT
ejpam-5392	625	24	23	23	NUM
ejpam-5392	625	25	,	,	PUNCT
ejpam-5392	625	26	45	45	NUM
ejpam-5392	625	27	]	]	PUNCT
ejpam-5392	625	28	.	.	PUNCT
ejpam-5392	626	1	the	the	DET
ejpam-5392	626	2	authors	author	NOUN
ejpam-5392	626	3	of	of	ADP
ejpam-5392	626	4	[	[	X
ejpam-5392	626	5	19	19	NUM
ejpam-5392	626	6	]	]	PUNCT
ejpam-5392	626	7	presented	present	VERB
ejpam-5392	626	8	information	information	NOUN
ejpam-5392	626	9	systems	system	NOUN
ejpam-5392	626	10	of	of	ADP
ejpam-5392	626	11	amino	amino	ADJ
ejpam-5392	626	12	acids	acid	NOUN
ejpam-5392	626	13	(	(	PUNCT
ejpam-5392	626	14	aas	aas	PROPN
ejpam-5392	626	15	)	)	PUNCT
ejpam-5392	626	16	with	with	ADP
ejpam-5392	626	17	some	some	DET
ejpam-5392	626	18	characterizations	characterization	NOUN
ejpam-5392	626	19	.	.	PUNCT
ejpam-5392	627	1	to	to	PART
ejpam-5392	627	2	facilitate	facilitate	VERB
ejpam-5392	627	3	the	the	DET
ejpam-5392	627	4	mathematical	mathematical	ADJ
ejpam-5392	627	5	computations	computation	NOUN
ejpam-5392	627	6	,	,	PUNCT
ejpam-5392	627	7	we	we	PRON
ejpam-5392	627	8	shall	shall	AUX
ejpam-5392	627	9	select	select	VERB
ejpam-5392	627	10	a	a	DET
ejpam-5392	627	11	sample	sample	NOUN
ejpam-5392	627	12	of	of	ADP
ejpam-5392	627	13	that	that	DET
ejpam-5392	627	14	information	information	NOUN
ejpam-5392	627	15	system	system	NOUN
ejpam-5392	627	16	as	as	SCONJ
ejpam-5392	627	17	given	give	VERB
ejpam-5392	627	18	in	in	ADP
ejpam-5392	627	19	table	table	NOUN
ejpam-5392	627	20	1	1	NUM
ejpam-5392	627	21	;	;	PUNCT
ejpam-5392	627	22	that	that	PRON
ejpam-5392	627	23	is	is	ADV
ejpam-5392	627	24	,	,	PUNCT
ejpam-5392	627	25	we	we	PRON
ejpam-5392	627	26	choose	choose	VERB
ejpam-5392	627	27	data	datum	NOUN
ejpam-5392	627	28	of	of	ADP
ejpam-5392	627	29	five	five	NUM
ejpam-5392	627	30	aas	aas	NOUN
ejpam-5392	627	31	,	,	PUNCT
ejpam-5392	627	32	say	say	INTJ
ejpam-5392	627	33	,	,	PUNCT
ejpam-5392	627	34	c	c	NOUN
ejpam-5392	627	35	=	=	SYM
ejpam-5392	627	36	{	{	PUNCT
ejpam-5392	627	37	y1	y1	PROPN
ejpam-5392	627	38	,	,	PUNCT
ejpam-5392	627	39	y2	y2	PROPN
ejpam-5392	627	40	,	,	PUNCT
ejpam-5392	627	41	y3	y3	PROPN
ejpam-5392	627	42	,	,	PUNCT
ejpam-5392	627	43	y4	y4	PROPN
ejpam-5392	627	44	,	,	PUNCT
ejpam-5392	627	45	y5	y5	PROPN
ejpam-5392	627	46	}	}	PUNCT
ejpam-5392	627	47	described	describe	VERB
ejpam-5392	627	48	by	by	ADP
ejpam-5392	627	49	five	five	NUM
ejpam-5392	627	50	attributes	attribute	NOUN
ejpam-5392	627	51	as	as	SCONJ
ejpam-5392	627	52	follows	follow	VERB
ejpam-5392	627	53	ν1	ν1	NOUN
ejpam-5392	627	54	is	be	AUX
ejpam-5392	627	55	pie	pie	NOUN
ejpam-5392	627	56	,	,	PUNCT
ejpam-5392	627	57	ν2	ν2	NOUN
ejpam-5392	627	58	is	be	AUX
ejpam-5392	627	59	surface	surface	NOUN
ejpam-5392	627	60	area	area	NOUN
ejpam-5392	627	61	(	(	PUNCT
ejpam-5392	627	62	sac	sac	NOUN
ejpam-5392	627	63	)	)	PUNCT
ejpam-5392	627	64	,	,	PUNCT
ejpam-5392	627	65	ν3	ν3	NOUN
ejpam-5392	627	66	is	be	AUX
ejpam-5392	627	67	molecular	molecular	ADJ
ejpam-5392	627	68	refractivity	refractivity	NOUN
ejpam-5392	627	69	(	(	PUNCT
ejpam-5392	627	70	mr	mr	PROPN
ejpam-5392	627	71	)	)	PUNCT
ejpam-5392	627	72	,	,	PUNCT
ejpam-5392	627	73	ν4	ν4	PROPN
ejpam-5392	627	74	is	be	AUX
ejpam-5392	627	75	side	side	ADJ
ejpam-5392	627	76	chain	chain	NOUN
ejpam-5392	627	77	polarity	polarity	NOUN
ejpam-5392	627	78	(	(	PUNCT
ejpam-5392	627	79	lam	lam	PROPN
ejpam-5392	627	80	)	)	PUNCT
ejpam-5392	627	81	,	,	PUNCT
ejpam-5392	627	82	and	and	CCONJ
ejpam-5392	627	83	ν5	ν5	NOUN
ejpam-5392	627	84	is	be	AUX
ejpam-5392	627	85	molecular	molecular	ADJ
ejpam-5392	627	86	volume	volume	NOUN
ejpam-5392	627	87	(	(	PUNCT
ejpam-5392	627	88	vol	vol	NOUN
ejpam-5392	627	89	)	)	PUNCT
ejpam-5392	627	90	.	.	PUNCT
ejpam-5392	628	1	m.	m.	PROPN
ejpam-5392	628	2	hosny	hosny	PROPN
ejpam-5392	628	3	,	,	PUNCT
ejpam-5392	628	4	t.m	t.m	PROPN
ejpam-5392	628	5	.	.	PROPN
ejpam-5392	628	6	al	al	PROPN
ejpam-5392	628	7	-	-	PUNCT
ejpam-5392	628	8	shami	shami	PROPN
ejpam-5392	628	9	/	/	PUNCT
ejpam-5392	628	10	eur	eur	PROPN
ejpam-5392	628	11	.	.	PUNCT
ejpam-5392	629	1	j.	j.	PROPN
ejpam-5392	629	2	pure	pure	PROPN
ejpam-5392	629	3	appl	appl	PROPN
ejpam-5392	629	4	.	.	PROPN
ejpam-5392	629	5	math	math	PROPN
ejpam-5392	629	6	,	,	PUNCT
ejpam-5392	629	7	17	17	NUM
ejpam-5392	629	8	(	(	PUNCT
ejpam-5392	629	9	4	4	NUM
ejpam-5392	629	10	)	)	PUNCT
ejpam-5392	629	11	(	(	PUNCT
ejpam-5392	629	12	2024	2024	NUM
ejpam-5392	629	13	)	)	PUNCT
ejpam-5392	629	14	,	,	PUNCT
ejpam-5392	629	15	3436	3436	NUM
ejpam-5392	629	16	-	-	SYM
ejpam-5392	629	17	3463	3463	NUM
ejpam-5392	629	18	3456	3456	NUM
ejpam-5392	629	19	table	table	NOUN
ejpam-5392	629	20	1	1	NUM
ejpam-5392	629	21	:	:	PUNCT
ejpam-5392	629	22	quantitative	quantitative	ADJ
ejpam-5392	629	23	attributes	attribute	NOUN
ejpam-5392	629	24	of	of	ADP
ejpam-5392	629	25	five	five	NUM
ejpam-5392	629	26	amino	amino	ADJ
ejpam-5392	629	27	acids	acid	NOUN
ejpam-5392	629	28	.	.	PUNCT
ejpam-5392	630	1	ν1	ν1	NOUN
ejpam-5392	630	2	ν2	ν2	ADP
ejpam-5392	630	3	ν3	ν3	PROPN
ejpam-5392	630	4	ν4	ν4	PROPN
ejpam-5392	630	5	ν5	ν5	PROPN
ejpam-5392	630	6	y1	y1	PROPN
ejpam-5392	630	7	0.23	0.23	NUM
ejpam-5392	630	8	254.2	254.2	NUM
ejpam-5392	630	9	2.126	2.126	NUM
ejpam-5392	630	10	-0.02	-0.02	NUM
ejpam-5392	630	11	82.2	82.2	NUM
ejpam-5392	630	12	y2	y2	NOUN
ejpam-5392	630	13	-0.48	-0.48	NOUN
ejpam-5392	630	14	303.6	303.6	NUM
ejpam-5392	630	15	2.994	2.994	NUM
ejpam-5392	630	16	-1.24	-1.24	NOUN
ejpam-5392	630	17	112.3	112.3	NUM
ejpam-5392	630	18	y3	y3	NOUN
ejpam-5392	630	19	-0.61	-0.61	NOUN
ejpam-5392	630	20	287.9	287.9	NUM
ejpam-5392	630	21	2.994	2.994	NUM
ejpam-5392	630	22	-1.08	-1.08	NUM
ejpam-5392	630	23	103.7	103.7	NUM
ejpam-5392	630	24	y4	y4	NOUN
ejpam-5392	630	25	0.45	0.45	NUM
ejpam-5392	630	26	282.9	282.9	NUM
ejpam-5392	630	27	2.933	2.933	NUM
ejpam-5392	630	28	-0.11	-0.11	NUM
ejpam-5392	630	29	99.1	99.1	NUM
ejpam-5392	630	30	y5	y5	NOUN
ejpam-5392	630	31	-0.11	-0.11	NUM
ejpam-5392	630	32	335.0	335.0	NUM
ejpam-5392	630	33	3.458	3.458	NUM
ejpam-5392	630	34	-0.19	-0.19	NOUN
ejpam-5392	630	35	127.5	127.5	NUM
ejpam-5392	630	36	table	table	NOUN
ejpam-5392	630	37	2	2	NUM
ejpam-5392	630	38	:	:	PUNCT
ejpam-5392	630	39	ga	ga	PROPN
ejpam-5392	630	40	of	of	ADP
ejpam-5392	630	41	each	each	DET
ejpam-5392	630	42	element	element	NOUN
ejpam-5392	630	43	of	of	ADP
ejpam-5392	630	44	c	c	PROPN
ejpam-5392	630	45	inspired	inspire	VERB
ejpam-5392	630	46	by	by	ADP
ejpam-5392	630	47	each	each	DET
ejpam-5392	630	48	relation	relation	NOUN
ejpam-5392	630	49	rk	rk	NOUN
ejpam-5392	630	50	.	.	PUNCT
ejpam-5392	630	51	g1a(yi	g1a(yi	NOUN
ejpam-5392	630	52	)	)	PUNCT
ejpam-5392	630	53	g2a(yi	g2a(yi	ADJ
ejpam-5392	630	54	)	)	PUNCT
ejpam-5392	630	55	g3a(yi	g3a(yi	NOUN
ejpam-5392	630	56	)	)	PUNCT
ejpam-5392	630	57	g4a(yi	g4a(yi	PROPN
ejpam-5392	630	58	)	)	PUNCT
ejpam-5392	630	59	g5a(yi	g5a(yi	NOUN
ejpam-5392	630	60	)	)	PUNCT
ejpam-5392	630	61	y1	y1	NOUN
ejpam-5392	630	62	{	{	PUNCT
ejpam-5392	630	63	y1	y1	PROPN
ejpam-5392	630	64	,	,	PUNCT
ejpam-5392	630	65	y4	y4	PROPN
ejpam-5392	630	66	}	}	PUNCT
ejpam-5392	630	67	c	c	PROPN
ejpam-5392	630	68	c	c	PROPN
ejpam-5392	630	69	{	{	PUNCT
ejpam-5392	630	70	y1	y1	PROPN
ejpam-5392	630	71	,	,	PUNCT
ejpam-5392	630	72	y4	y4	PROPN
ejpam-5392	630	73	,	,	PUNCT
ejpam-5392	630	74	y5	y5	PROPN
ejpam-5392	630	75	}	}	PUNCT
ejpam-5392	630	76	c	c	NOUN
ejpam-5392	631	1	y2	y2	INTJ
ejpam-5392	631	2	c	c	NOUN
ejpam-5392	631	3	{	{	PUNCT
ejpam-5392	631	4	y2	y2	PROPN
ejpam-5392	631	5	,	,	PUNCT
ejpam-5392	631	6	y5	y5	PROPN
ejpam-5392	631	7	}	}	PUNCT
ejpam-5392	631	8	{	{	PUNCT
ejpam-5392	631	9	y2	y2	PROPN
ejpam-5392	631	10	,	,	PUNCT
ejpam-5392	631	11	y3	y3	PROPN
ejpam-5392	631	12	,	,	PUNCT
ejpam-5392	631	13	y4	y4	NOUN
ejpam-5392	631	14	,	,	PUNCT
ejpam-5392	631	15	y5	y5	PROPN
ejpam-5392	631	16	}	}	PUNCT
ejpam-5392	631	17	c	c	NOUN
ejpam-5392	631	18	{	{	PUNCT
ejpam-5392	631	19	y2	y2	PROPN
ejpam-5392	631	20	,	,	PUNCT
ejpam-5392	631	21	y5	y5	NOUN
ejpam-5392	631	22	}	}	PUNCT
ejpam-5392	631	23	y3	y3	NOUN
ejpam-5392	631	24	c	c	PROPN
ejpam-5392	631	25	{	{	PUNCT
ejpam-5392	631	26	y2	y2	PROPN
ejpam-5392	631	27	,	,	PUNCT
ejpam-5392	631	28	y3	y3	PROPN
ejpam-5392	631	29	,	,	PUNCT
ejpam-5392	631	30	y4	y4	NOUN
ejpam-5392	631	31	,	,	PUNCT
ejpam-5392	631	32	y5	y5	PROPN
ejpam-5392	631	33	}	}	PUNCT
ejpam-5392	631	34	{	{	PUNCT
ejpam-5392	631	35	y2	y2	PROPN
ejpam-5392	631	36	,	,	PUNCT
ejpam-5392	631	37	y3	y3	PROPN
ejpam-5392	631	38	,	,	PUNCT
ejpam-5392	631	39	y4	y4	NOUN
ejpam-5392	631	40	,	,	PUNCT
ejpam-5392	631	41	y5	y5	PROPN
ejpam-5392	631	42	}	}	PUNCT
ejpam-5392	631	43	c	c	NOUN
ejpam-5392	631	44	{	{	PUNCT
ejpam-5392	631	45	y2	y2	PROPN
ejpam-5392	631	46	,	,	PUNCT
ejpam-5392	631	47	y3	y3	PROPN
ejpam-5392	631	48	,	,	PUNCT
ejpam-5392	631	49	y4	y4	NOUN
ejpam-5392	631	50	,	,	PUNCT
ejpam-5392	631	51	y5	y5	PROPN
ejpam-5392	631	52	}	}	PUNCT
ejpam-5392	631	53	y4	y4	PROPN
ejpam-5392	631	54	{	{	PUNCT
ejpam-5392	631	55	y4	y4	PROPN
ejpam-5392	631	56	}	}	PUNCT
ejpam-5392	631	57	{	{	PUNCT
ejpam-5392	631	58	y2	y2	PROPN
ejpam-5392	631	59	,	,	PUNCT
ejpam-5392	631	60	y3	y3	PROPN
ejpam-5392	631	61	,	,	PUNCT
ejpam-5392	631	62	y4	y4	NOUN
ejpam-5392	631	63	,	,	PUNCT
ejpam-5392	631	64	y5	y5	PROPN
ejpam-5392	631	65	}	}	PUNCT
ejpam-5392	631	66	{	{	PUNCT
ejpam-5392	631	67	y2	y2	PROPN
ejpam-5392	631	68	,	,	PUNCT
ejpam-5392	631	69	y3	y3	PROPN
ejpam-5392	631	70	,	,	PUNCT
ejpam-5392	631	71	y4	y4	NOUN
ejpam-5392	631	72	,	,	PUNCT
ejpam-5392	631	73	y5	y5	PROPN
ejpam-5392	631	74	}	}	PUNCT
ejpam-5392	631	75	{	{	PUNCT
ejpam-5392	631	76	y1	y1	PROPN
ejpam-5392	631	77	,	,	PUNCT
ejpam-5392	631	78	y4	y4	PROPN
ejpam-5392	631	79	,	,	PUNCT
ejpam-5392	631	80	y5	y5	PROPN
ejpam-5392	631	81	}	}	PUNCT
ejpam-5392	631	82	{	{	PUNCT
ejpam-5392	631	83	y2	y2	PROPN
ejpam-5392	631	84	,	,	PUNCT
ejpam-5392	631	85	y3	y3	PROPN
ejpam-5392	631	86	,	,	PUNCT
ejpam-5392	631	87	y4	y4	NOUN
ejpam-5392	631	88	,	,	PUNCT
ejpam-5392	631	89	y5	y5	NOUN
ejpam-5392	631	90	}	}	PUNCT
ejpam-5392	631	91	y5	y5	NOUN
ejpam-5392	631	92	{	{	PUNCT
ejpam-5392	631	93	y1	y1	PROPN
ejpam-5392	631	94	,	,	PUNCT
ejpam-5392	631	95	y4	y4	PROPN
ejpam-5392	631	96	,	,	PUNCT
ejpam-5392	631	97	y5	y5	PROPN
ejpam-5392	631	98	}	}	PUNCT
ejpam-5392	631	99	{	{	PUNCT
ejpam-5392	631	100	y5	y5	NOUN
ejpam-5392	631	101	}	}	PUNCT
ejpam-5392	631	102	{	{	PUNCT
ejpam-5392	631	103	y5	y5	NOUN
ejpam-5392	631	104	}	}	PUNCT
ejpam-5392	631	105	{	{	PUNCT
ejpam-5392	631	106	y1	y1	PROPN
ejpam-5392	631	107	,	,	PUNCT
ejpam-5392	631	108	y4	y4	PROPN
ejpam-5392	631	109	,	,	PUNCT
ejpam-5392	631	110	y5	y5	PROPN
ejpam-5392	631	111	}	}	PUNCT
ejpam-5392	631	112	{	{	PUNCT
ejpam-5392	631	113	y3	y3	NOUN
ejpam-5392	631	114	,	,	PUNCT
ejpam-5392	631	115	y5	y5	PROPN
ejpam-5392	631	116	}	}	PUNCT
ejpam-5392	631	117	let	let	VERB
ejpam-5392	631	118	us	we	PRON
ejpam-5392	631	119	take	take	VERB
ejpam-5392	631	120	relations	relation	NOUN
ejpam-5392	631	121	on	on	ADP
ejpam-5392	631	122	c	c	NOUN
ejpam-5392	631	123	as	as	ADP
ejpam-5392	631	124	:	:	PUNCT
ejpam-5392	631	125	rk	rk	NOUN
ejpam-5392	631	126	=	=	SYM
ejpam-5392	631	127	{	{	PUNCT
ejpam-5392	631	128	(	(	PUNCT
ejpam-5392	631	129	yi	yi	PROPN
ejpam-5392	631	130	,	,	PUNCT
ejpam-5392	631	131	yj	yj	PROPN
ejpam-5392	631	132	)	)	PUNCT
ejpam-5392	631	133	:	:	PUNCT
ejpam-5392	631	134	yi(νk	yi(νk	NOUN
ejpam-5392	631	135	)	)	PUNCT
ejpam-5392	631	136	−	−	PROPN
ejpam-5392	631	137	yj(νk	yj(νk	NOUN
ejpam-5392	631	138	)	)	PUNCT
ejpam-5392	631	139	<	<	X
ejpam-5392	631	140	σyk	σyk	PROPN
ejpam-5392	631	141	2	2	NUM
ejpam-5392	631	142	}	}	PUNCT
ejpam-5392	631	143	for	for	ADP
ejpam-5392	631	144	i	i	PROPN
ejpam-5392	631	145	,	,	PUNCT
ejpam-5392	631	146	j	j	PROPN
ejpam-5392	631	147	,	,	PUNCT
ejpam-5392	631	148	k	k	PROPN
ejpam-5392	631	149	=	=	SYM
ejpam-5392	631	150	1	1	NUM
ejpam-5392	631	151	,	,	PUNCT
ejpam-5392	631	152	2	2	NUM
ejpam-5392	631	153	,	,	PUNCT
ejpam-5392	631	154	3	3	NUM
ejpam-5392	631	155	,	,	PUNCT
ejpam-5392	631	156	4	4	NUM
ejpam-5392	631	157	,	,	PUNCT
ejpam-5392	631	158	5	5	NUM
ejpam-5392	631	159	s.t	s.t	PROPN
ejpam-5392	631	160	.	.	PROPN
ejpam-5392	631	161	σyk	σyk	PROPN
ejpam-5392	631	162	is	be	AUX
ejpam-5392	631	163	the	the	DET
ejpam-5392	631	164	standard	standard	ADJ
ejpam-5392	631	165	deviation	deviation	NOUN
ejpam-5392	631	166	of	of	ADP
ejpam-5392	631	167	the	the	DET
ejpam-5392	631	168	quantitative	quantitative	ADJ
ejpam-5392	631	169	attributes	attribute	NOUN
ejpam-5392	631	170	.	.	PUNCT
ejpam-5392	632	1	the	the	DET
ejpam-5392	632	2	right	right	ADJ
ejpam-5392	632	3	neighbourhood	neighbourhood	NOUN
ejpam-5392	632	4	gka	gka	NOUN
ejpam-5392	632	5	of	of	ADP
ejpam-5392	632	6	each	each	DET
ejpam-5392	632	7	element	element	NOUN
ejpam-5392	632	8	of	of	ADP
ejpam-5392	632	9	c	c	PROPN
ejpam-5392	632	10	generated	generate	VERB
ejpam-5392	632	11	by	by	ADP
ejpam-5392	632	12	each	each	DET
ejpam-5392	632	13	one	one	NUM
ejpam-5392	632	14	of	of	ADP
ejpam-5392	632	15	these	these	DET
ejpam-5392	632	16	relations	relation	NOUN
ejpam-5392	632	17	rk	rk	NOUN
ejpam-5392	632	18	is	be	AUX
ejpam-5392	632	19	presented	present	VERB
ejpam-5392	632	20	in	in	ADP
ejpam-5392	632	21	table	table	NOUN
ejpam-5392	632	22	2	2	NUM
ejpam-5392	632	23	.	.	PUNCT
ejpam-5392	633	1	now	now	ADV
ejpam-5392	633	2	,	,	PUNCT
ejpam-5392	633	3	we	we	PRON
ejpam-5392	633	4	associate	associate	VERB
ejpam-5392	633	5	each	each	DET
ejpam-5392	633	6	element	element	NOUN
ejpam-5392	633	7	of	of	ADP
ejpam-5392	633	8	c	c	PROPN
ejpam-5392	633	9	with	with	ADP
ejpam-5392	633	10	all	all	DET
ejpam-5392	633	11	its	its	PRON
ejpam-5392	633	12	ga	ga	NOUN
ejpam-5392	633	13	by	by	ADP
ejpam-5392	633	14	the	the	DET
ejpam-5392	633	15	following	follow	VERB
ejpam-5392	633	16	relation	relation	NOUN
ejpam-5392	633	17	ha(yi	ha(yi	PROPN
ejpam-5392	633	18	)	)	PUNCT
ejpam-5392	634	1	=	=	SYM
ejpam-5392	634	2	5⋂	5⋂	NUM
ejpam-5392	634	3	k=1	k=1	PROPN
ejpam-5392	634	4	gka(yi	gka(yi	PROPN
ejpam-5392	634	5	)	)	PUNCT
ejpam-5392	634	6	.	.	PUNCT
ejpam-5392	635	1	for	for	ADP
ejpam-5392	635	2	the	the	DET
ejpam-5392	635	3	sake	sake	NOUN
ejpam-5392	635	4	of	of	ADP
ejpam-5392	635	5	brevity	brevity	NOUN
ejpam-5392	635	6	,	,	PUNCT
ejpam-5392	635	7	we	we	PRON
ejpam-5392	635	8	conduct	conduct	VERB
ejpam-5392	635	9	the	the	DET
ejpam-5392	635	10	computation	computation	NOUN
ejpam-5392	635	11	for	for	ADP
ejpam-5392	635	12	four	four	NUM
ejpam-5392	635	13	aas	aas	PROPN
ejpam-5392	635	14	,	,	PUNCT
ejpam-5392	635	15	say	say	INTJ
ejpam-5392	635	16	,	,	PUNCT
ejpam-5392	635	17	y	y	PROPN
ejpam-5392	635	18	=	=	PUNCT
ejpam-5392	635	19	c	c	PROPN
ejpam-5392	635	20	\	\	PROPN
ejpam-5392	635	21	{	{	PUNCT
ejpam-5392	635	22	y5	y5	NOUN
ejpam-5392	635	23	}	}	PUNCT
ejpam-5392	635	24	=	=	SYM
ejpam-5392	635	25	{	{	PUNCT
ejpam-5392	635	26	y1	y1	NOUN
ejpam-5392	635	27	,	,	PUNCT
ejpam-5392	635	28	y2	y2	PROPN
ejpam-5392	635	29	,	,	PUNCT
ejpam-5392	635	30	y3	y3	PROPN
ejpam-5392	635	31	,	,	PUNCT
ejpam-5392	635	32	y4	y4	PROPN
ejpam-5392	635	33	}	}	PUNCT
ejpam-5392	635	34	.	.	PUNCT
ejpam-5392	636	1	therefore	therefore	ADV
ejpam-5392	636	2	,	,	PUNCT
ejpam-5392	636	3	we	we	PRON
ejpam-5392	636	4	first	first	ADV
ejpam-5392	636	5	reduce	reduce	VERB
ejpam-5392	636	6	table	table	NOUN
ejpam-5392	636	7	2	2	NUM
ejpam-5392	636	8	to	to	PART
ejpam-5392	636	9	table	table	NOUN
ejpam-5392	636	10	3	3	NUM
ejpam-5392	636	11	.	.	PUNCT
ejpam-5392	636	12	table	table	NOUN
ejpam-5392	636	13	3	3	NUM
ejpam-5392	636	14	:	:	PUNCT
ejpam-5392	636	15	ga	ga	PROPN
ejpam-5392	636	16	of	of	ADP
ejpam-5392	636	17	each	each	DET
ejpam-5392	636	18	element	element	NOUN
ejpam-5392	636	19	of	of	ADP
ejpam-5392	636	20	y	y	PROPN
ejpam-5392	636	21	inspired	inspire	VERB
ejpam-5392	636	22	by	by	ADP
ejpam-5392	636	23	each	each	DET
ejpam-5392	636	24	relation	relation	NOUN
ejpam-5392	636	25	rk	rk	NOUN
ejpam-5392	636	26	.	.	PUNCT
ejpam-5392	636	27	g1a(yi	g1a(yi	NOUN
ejpam-5392	636	28	)	)	PUNCT
ejpam-5392	636	29	g2a(yi	g2a(yi	ADJ
ejpam-5392	636	30	)	)	PUNCT
ejpam-5392	636	31	g3a(yi	g3a(yi	NOUN
ejpam-5392	636	32	)	)	PUNCT
ejpam-5392	636	33	g4a(yi	g4a(yi	PROPN
ejpam-5392	636	34	)	)	PUNCT
ejpam-5392	636	35	g5a(yi	g5a(yi	NOUN
ejpam-5392	636	36	)	)	PUNCT
ejpam-5392	636	37	y1	y1	NOUN
ejpam-5392	636	38	{	{	PUNCT
ejpam-5392	636	39	y1	y1	PROPN
ejpam-5392	636	40	,	,	PUNCT
ejpam-5392	636	41	y4	y4	PROPN
ejpam-5392	636	42	}	}	PUNCT
ejpam-5392	636	43	y	y	PROPN
ejpam-5392	636	44	y	y	PROPN
ejpam-5392	636	45	{	{	PUNCT
ejpam-5392	636	46	y1	y1	PROPN
ejpam-5392	636	47	,	,	PUNCT
ejpam-5392	636	48	y4	y4	PROPN
ejpam-5392	636	49	}	}	PUNCT
ejpam-5392	636	50	y	y	PROPN
ejpam-5392	637	1	y2	y2	INTJ
ejpam-5392	638	1	y	y	PROPN
ejpam-5392	638	2	{	{	PUNCT
ejpam-5392	638	3	y2	y2	PROPN
ejpam-5392	638	4	}	}	PUNCT
ejpam-5392	638	5	{	{	PUNCT
ejpam-5392	638	6	y2	y2	PROPN
ejpam-5392	638	7	,	,	PUNCT
ejpam-5392	638	8	y3	y3	PROPN
ejpam-5392	638	9	,	,	PUNCT
ejpam-5392	638	10	y4	y4	PROPN
ejpam-5392	638	11	}	}	PUNCT
ejpam-5392	638	12	y	y	PROPN
ejpam-5392	638	13	{	{	PUNCT
ejpam-5392	638	14	y2	y2	PROPN
ejpam-5392	638	15	}	}	PUNCT
ejpam-5392	638	16	y3	y3	NOUN
ejpam-5392	638	17	y	y	PROPN
ejpam-5392	638	18	{	{	PUNCT
ejpam-5392	638	19	y2	y2	PROPN
ejpam-5392	638	20	,	,	PUNCT
ejpam-5392	638	21	y3	y3	PROPN
ejpam-5392	638	22	,	,	PUNCT
ejpam-5392	638	23	y4	y4	PROPN
ejpam-5392	638	24	}	}	PUNCT
ejpam-5392	638	25	{	{	PUNCT
ejpam-5392	638	26	y2	y2	PROPN
ejpam-5392	638	27	,	,	PUNCT
ejpam-5392	638	28	y3	y3	PROPN
ejpam-5392	638	29	,	,	PUNCT
ejpam-5392	638	30	y4	y4	PROPN
ejpam-5392	638	31	}	}	PUNCT
ejpam-5392	638	32	y	y	PROPN
ejpam-5392	638	33	{	{	PUNCT
ejpam-5392	638	34	y2	y2	PROPN
ejpam-5392	638	35	,	,	PUNCT
ejpam-5392	638	36	y3	y3	PROPN
ejpam-5392	638	37	,	,	PUNCT
ejpam-5392	638	38	y4	y4	ADV
ejpam-5392	638	39	}	}	PUNCT
ejpam-5392	638	40	y4	y4	PROPN
ejpam-5392	638	41	{	{	PUNCT
ejpam-5392	638	42	y4	y4	PROPN
ejpam-5392	638	43	}	}	PUNCT
ejpam-5392	638	44	{	{	PUNCT
ejpam-5392	638	45	y2	y2	PROPN
ejpam-5392	638	46	,	,	PUNCT
ejpam-5392	638	47	y3	y3	PROPN
ejpam-5392	638	48	,	,	PUNCT
ejpam-5392	638	49	y4	y4	PROPN
ejpam-5392	638	50	}	}	PUNCT
ejpam-5392	638	51	{	{	PUNCT
ejpam-5392	638	52	y2	y2	PROPN
ejpam-5392	638	53	,	,	PUNCT
ejpam-5392	638	54	y3	y3	PROPN
ejpam-5392	638	55	,	,	PUNCT
ejpam-5392	638	56	y4	y4	PROPN
ejpam-5392	638	57	}	}	PUNCT
ejpam-5392	638	58	{	{	PUNCT
ejpam-5392	638	59	y1	y1	PROPN
ejpam-5392	638	60	,	,	PUNCT
ejpam-5392	638	61	y4	y4	PROPN
ejpam-5392	638	62	}	}	PUNCT
ejpam-5392	638	63	{	{	PUNCT
ejpam-5392	638	64	y2	y2	PROPN
ejpam-5392	638	65	,	,	PUNCT
ejpam-5392	638	66	y3	y3	PROPN
ejpam-5392	638	67	,	,	PUNCT
ejpam-5392	638	68	y4	y4	PROPN
ejpam-5392	638	69	}	}	PUNCT
ejpam-5392	638	70	now	now	ADV
ejpam-5392	638	71	,	,	PUNCT
ejpam-5392	638	72	we	we	PRON
ejpam-5392	638	73	associate	associate	VERB
ejpam-5392	638	74	each	each	DET
ejpam-5392	638	75	element	element	NOUN
ejpam-5392	638	76	of	of	ADP
ejpam-5392	638	77	y	y	PROPN
ejpam-5392	638	78	with	with	ADP
ejpam-5392	638	79	all	all	DET
ejpam-5392	638	80	its	its	PRON
ejpam-5392	638	81	ga	ga	NOUN
ejpam-5392	638	82	by	by	ADP
ejpam-5392	638	83	the	the	DET
ejpam-5392	638	84	following	follow	VERB
ejpam-5392	638	85	relation	relation	NOUN
ejpam-5392	638	86	ha(yi	ha(yi	PROPN
ejpam-5392	638	87	)	)	PUNCT
ejpam-5392	639	1	=	=	SYM
ejpam-5392	639	2	4⋂	4⋂	NOUN
ejpam-5392	640	1	k=1	k=1	PROPN
ejpam-5392	640	2	gka(yi	gka(yi	PROPN
ejpam-5392	640	3	)	)	PUNCT
ejpam-5392	640	4	.	.	PUNCT
ejpam-5392	641	1	accordingly	accordingly	ADV
ejpam-5392	641	2	,	,	PUNCT
ejpam-5392	641	3	we	we	PRON
ejpam-5392	641	4	obtain	obtain	VERB
ejpam-5392	641	5	the	the	DET
ejpam-5392	641	6	following	following	ADJ
ejpam-5392	641	7	neighbourhoods	neighbourhood	NOUN
ejpam-5392	641	8	:	:	PUNCT
ejpam-5392	641	9	•	•	NUM
ejpam-5392	641	10	ha(y1	ha(y1	PROPN
ejpam-5392	641	11	)	)	PUNCT
ejpam-5392	641	12	=	=	SYM
ejpam-5392	641	13	{	{	PUNCT
ejpam-5392	641	14	y1	y1	PROPN
ejpam-5392	641	15	,	,	PUNCT
ejpam-5392	641	16	y4	y4	PROPN
ejpam-5392	641	17	}	}	PUNCT
ejpam-5392	641	18	,	,	PUNCT
ejpam-5392	641	19	m.	m.	PROPN
ejpam-5392	641	20	hosny	hosny	PROPN
ejpam-5392	641	21	,	,	PUNCT
ejpam-5392	641	22	t.m	t.m	PROPN
ejpam-5392	641	23	.	.	PROPN
ejpam-5392	641	24	al	al	PROPN
ejpam-5392	641	25	-	-	PUNCT
ejpam-5392	641	26	shami	shami	PROPN
ejpam-5392	641	27	/	/	PUNCT
ejpam-5392	641	28	eur	eur	PROPN
ejpam-5392	641	29	.	.	PUNCT
ejpam-5392	642	1	j.	j.	PROPN
ejpam-5392	642	2	pure	pure	PROPN
ejpam-5392	642	3	appl	appl	PROPN
ejpam-5392	642	4	.	.	PROPN
ejpam-5392	642	5	math	math	PROPN
ejpam-5392	642	6	,	,	PUNCT
ejpam-5392	642	7	17	17	NUM
ejpam-5392	642	8	(	(	PUNCT
ejpam-5392	642	9	4	4	NUM
ejpam-5392	642	10	)	)	PUNCT
ejpam-5392	642	11	(	(	PUNCT
ejpam-5392	642	12	2024	2024	NUM
ejpam-5392	642	13	)	)	PUNCT
ejpam-5392	642	14	,	,	PUNCT
ejpam-5392	642	15	3436	3436	NUM
ejpam-5392	642	16	-	-	SYM
ejpam-5392	642	17	3463	3463	NUM
ejpam-5392	642	18	3457	3457	NUM
ejpam-5392	642	19	•	•	NUM
ejpam-5392	642	20	ha(y2	ha(y2	NOUN
ejpam-5392	642	21	)	)	PUNCT
ejpam-5392	642	22	=	=	PRON
ejpam-5392	642	23	{	{	PUNCT
ejpam-5392	642	24	y2	y2	NOUN
ejpam-5392	642	25	}	}	PUNCT
ejpam-5392	642	26	,	,	PUNCT
ejpam-5392	642	27	•	•	NUM
ejpam-5392	642	28	ha(y3	ha(y3	NOUN
ejpam-5392	642	29	)	)	PUNCT
ejpam-5392	642	30	=	=	PRON
ejpam-5392	642	31	{	{	PUNCT
ejpam-5392	642	32	y2	y2	PROPN
ejpam-5392	642	33	,	,	PUNCT
ejpam-5392	642	34	y3	y3	PROPN
ejpam-5392	642	35	,	,	PUNCT
ejpam-5392	642	36	y4	y4	PROPN
ejpam-5392	642	37	}	}	PUNCT
ejpam-5392	642	38	,	,	PUNCT
ejpam-5392	642	39	and	and	CCONJ
ejpam-5392	642	40	•	•	NUM
ejpam-5392	642	41	ha(y4	ha(y4	VERB
ejpam-5392	642	42	)	)	PUNCT
ejpam-5392	642	43	=	=	PRON
ejpam-5392	642	44	{	{	PUNCT
ejpam-5392	642	45	y4	y4	X
ejpam-5392	642	46	}	}	PUNCT
ejpam-5392	642	47	.	.	PUNCT
ejpam-5392	643	1	thus	thus	ADV
ejpam-5392	643	2	,	,	PUNCT
ejpam-5392	643	3	the	the	DET
ejpam-5392	643	4	topology	topology	NOUN
ejpam-5392	643	5	initiated	initiate	VERB
ejpam-5392	643	6	by	by	ADP
ejpam-5392	643	7	these	these	DET
ejpam-5392	643	8	neighbourhoods	neighbourhood	NOUN
ejpam-5392	643	9	(	(	PUNCT
ejpam-5392	643	10	using	use	VERB
ejpam-5392	643	11	the	the	DET
ejpam-5392	643	12	formula	formula	NOUN
ejpam-5392	643	13	ϑa	ϑa	ADP
ejpam-5392	643	14	=	=	NOUN
ejpam-5392	643	15	{	{	PUNCT
ejpam-5392	643	16	v	v	ADP
ejpam-5392	643	17	⊆	⊆	NUM
ejpam-5392	643	18	y	y	NOUN
ejpam-5392	643	19	:	:	PUNCT
ejpam-5392	643	20	∀y	∀y	PROPN
ejpam-5392	643	21	∈	∈	PROPN
ejpam-5392	643	22	v	v	NOUN
ejpam-5392	643	23	,	,	PUNCT
ejpam-5392	643	24	h(y	h(y	NOUN
ejpam-5392	643	25	)	)	PUNCT
ejpam-5392	643	26	⊆	⊆	NUM
ejpam-5392	643	27	v	v	NOUN
ejpam-5392	643	28	}	}	PUNCT
ejpam-5392	643	29	)	)	PUNCT
ejpam-5392	643	30	is	be	AUX
ejpam-5392	643	31	:	:	PUNCT
ejpam-5392	643	32	ϑa	ϑa	PROPN
ejpam-5392	643	33	=	=	PUNCT
ejpam-5392	643	34	{	{	PUNCT
ejpam-5392	643	35	∅,y	∅,y	PROPN
ejpam-5392	643	36	,	,	PUNCT
ejpam-5392	643	37	{	{	PUNCT
ejpam-5392	643	38	y2	y2	NOUN
ejpam-5392	643	39	}	}	PUNCT
ejpam-5392	643	40	,	,	PUNCT
ejpam-5392	643	41	{	{	PUNCT
ejpam-5392	643	42	y4	y4	X
ejpam-5392	643	43	}	}	PUNCT
ejpam-5392	643	44	,	,	PUNCT
ejpam-5392	643	45	{	{	PUNCT
ejpam-5392	643	46	y2	y2	NOUN
ejpam-5392	643	47	,	,	PUNCT
ejpam-5392	643	48	y4	y4	PROPN
ejpam-5392	643	49	}	}	PUNCT
ejpam-5392	643	50	,	,	PUNCT
ejpam-5392	643	51	{	{	PUNCT
ejpam-5392	643	52	y1	y1	NOUN
ejpam-5392	643	53	,	,	PUNCT
ejpam-5392	643	54	y4	y4	PROPN
ejpam-5392	643	55	}	}	PUNCT
ejpam-5392	643	56	,	,	PUNCT
ejpam-5392	643	57	{	{	PUNCT
ejpam-5392	643	58	y1	y1	NOUN
ejpam-5392	643	59	,	,	PUNCT
ejpam-5392	643	60	y2	y2	PROPN
ejpam-5392	643	61	,	,	PUNCT
ejpam-5392	643	62	y4	y4	PROPN
ejpam-5392	643	63	}	}	PUNCT
ejpam-5392	643	64	,	,	PUNCT
ejpam-5392	643	65	{	{	PUNCT
ejpam-5392	643	66	y2	y2	PROPN
ejpam-5392	643	67	,	,	PUNCT
ejpam-5392	643	68	y3	y3	PROPN
ejpam-5392	643	69	,	,	PUNCT
ejpam-5392	643	70	y4	y4	PROPN
ejpam-5392	643	71	}	}	PUNCT
ejpam-5392	643	72	}	}	PUNCT
ejpam-5392	643	73	.	.	PUNCT
ejpam-5392	644	1	the	the	DET
ejpam-5392	644	2	family	family	NOUN
ejpam-5392	644	3	of	of	ADP
ejpam-5392	644	4	all	all	DET
ejpam-5392	644	5	β	β	NOUN
ejpam-5392	644	6	-	-	ADJ
ejpam-5392	644	7	open	open	ADJ
ejpam-5392	644	8	,	,	PUNCT
ejpam-5392	644	9	δ	δ	NOUN
ejpam-5392	644	10	-	-	ADJ
ejpam-5392	644	11	open	open	ADJ
ejpam-5392	644	12	and	and	CCONJ
ejpam-5392	644	13	θ	θ	ADJ
ejpam-5392	644	14	-	-	ADJ
ejpam-5392	644	15	open	open	ADJ
ejpam-5392	644	16	subsets	subset	NOUN
ejpam-5392	644	17	of	of	ADP
ejpam-5392	644	18	this	this	DET
ejpam-5392	644	19	topology	topology	NOUN
ejpam-5392	644	20	respectively	respectively	ADV
ejpam-5392	644	21	are	be	AUX
ejpam-5392	644	22	:	:	PUNCT
ejpam-5392	644	23	βao(y	βao(y	X
ejpam-5392	644	24	)	)	PUNCT
ejpam-5392	644	25	=	=	PRON
ejpam-5392	644	26	{	{	PUNCT
ejpam-5392	644	27	∅,y	∅,y	PROPN
ejpam-5392	644	28	,	,	PUNCT
ejpam-5392	644	29	{	{	PUNCT
ejpam-5392	644	30	y2	y2	NOUN
ejpam-5392	644	31	}	}	PUNCT
ejpam-5392	644	32	,	,	PUNCT
ejpam-5392	644	33	{	{	PUNCT
ejpam-5392	644	34	y4	y4	X
ejpam-5392	644	35	}	}	PUNCT
ejpam-5392	644	36	,	,	PUNCT
ejpam-5392	644	37	{	{	PUNCT
ejpam-5392	644	38	y2	y2	NOUN
ejpam-5392	644	39	,	,	PUNCT
ejpam-5392	644	40	y4	y4	PROPN
ejpam-5392	644	41	}	}	PUNCT
ejpam-5392	644	42	,	,	PUNCT
ejpam-5392	644	43	{	{	PUNCT
ejpam-5392	644	44	y1	y1	NOUN
ejpam-5392	644	45	,	,	PUNCT
ejpam-5392	644	46	y4	y4	PROPN
ejpam-5392	644	47	}	}	PUNCT
ejpam-5392	644	48	,	,	PUNCT
ejpam-5392	644	49	{	{	PUNCT
ejpam-5392	644	50	y2	y2	NOUN
ejpam-5392	644	51	,	,	PUNCT
ejpam-5392	644	52	y3	y3	PROPN
ejpam-5392	644	53	}	}	PUNCT
ejpam-5392	644	54	,	,	PUNCT
ejpam-5392	644	55	{	{	PUNCT
ejpam-5392	644	56	y3	y3	NOUN
ejpam-5392	644	57	,	,	PUNCT
ejpam-5392	644	58	y4	y4	PROPN
ejpam-5392	644	59	}	}	PUNCT
ejpam-5392	644	60	,	,	PUNCT
ejpam-5392	644	61	{	{	PUNCT
ejpam-5392	644	62	y1	y1	NOUN
ejpam-5392	644	63	,	,	PUNCT
ejpam-5392	644	64	y2	y2	PROPN
ejpam-5392	644	65	,	,	PUNCT
ejpam-5392	644	66	y4	y4	PROPN
ejpam-5392	644	67	}	}	PUNCT
ejpam-5392	644	68	,	,	PUNCT
ejpam-5392	644	69	{	{	PUNCT
ejpam-5392	644	70	y1	y1	X
ejpam-5392	644	71	,	,	PUNCT
ejpam-5392	644	72	y3	y3	PROPN
ejpam-5392	644	73	,	,	PUNCT
ejpam-5392	644	74	y4	y4	PROPN
ejpam-5392	644	75	}	}	PUNCT
ejpam-5392	644	76	,	,	PUNCT
ejpam-5392	644	77	{	{	PUNCT
ejpam-5392	644	78	y2	y2	PROPN
ejpam-5392	644	79	,	,	PUNCT
ejpam-5392	644	80	y3	y3	PROPN
ejpam-5392	644	81	,	,	PUNCT
ejpam-5392	644	82	y4	y4	PROPN
ejpam-5392	644	83	}	}	PUNCT
ejpam-5392	644	84	}	}	PUNCT
ejpam-5392	644	85	,	,	PUNCT
ejpam-5392	644	86	δao(y	δao(y	PROPN
ejpam-5392	644	87	)	)	PUNCT
ejpam-5392	644	88	=	=	PRON
ejpam-5392	644	89	{	{	PUNCT
ejpam-5392	644	90	∅,y	∅,y	PROPN
ejpam-5392	644	91	,	,	PUNCT
ejpam-5392	644	92	{	{	PUNCT
ejpam-5392	644	93	y2	y2	NOUN
ejpam-5392	644	94	}	}	PUNCT
ejpam-5392	644	95	,	,	PUNCT
ejpam-5392	644	96	{	{	PUNCT
ejpam-5392	644	97	y1	y1	NOUN
ejpam-5392	644	98	,	,	PUNCT
ejpam-5392	644	99	y4	y4	PROPN
ejpam-5392	644	100	}	}	PUNCT
ejpam-5392	644	101	,	,	PUNCT
ejpam-5392	644	102	{	{	PUNCT
ejpam-5392	644	103	y1	y1	NOUN
ejpam-5392	644	104	,	,	PUNCT
ejpam-5392	644	105	y2	y2	PROPN
ejpam-5392	644	106	,	,	PUNCT
ejpam-5392	644	107	y4	y4	PROPN
ejpam-5392	644	108	}	}	PUNCT
ejpam-5392	644	109	}	}	PUNCT
ejpam-5392	644	110	,	,	PUNCT
ejpam-5392	644	111	and	and	CCONJ
ejpam-5392	644	112	θao(y	θao(y	NOUN
ejpam-5392	644	113	)	)	PUNCT
ejpam-5392	644	114	=	=	NOUN
ejpam-5392	644	115	{	{	PUNCT
ejpam-5392	644	116	∅,y	∅,y	PROPN
ejpam-5392	644	117	}	}	PUNCT
ejpam-5392	644	118	.	.	PUNCT
ejpam-5392	645	1	if	if	SCONJ
ejpam-5392	645	2	we	we	PRON
ejpam-5392	645	3	take	take	VERB
ejpam-5392	645	4	l	l	NOUN
ejpam-5392	645	5	=	=	SYM
ejpam-5392	645	6	{	{	PUNCT
ejpam-5392	645	7	∅	∅	NOUN
ejpam-5392	645	8	,	,	PUNCT
ejpam-5392	645	9	{	{	PUNCT
ejpam-5392	645	10	y1	y1	NOUN
ejpam-5392	645	11	}	}	PUNCT
ejpam-5392	645	12	}	}	PUNCT
ejpam-5392	645	13	as	as	ADP
ejpam-5392	645	14	an	an	DET
ejpam-5392	645	15	ideal	ideal	ADJ
ejpam-5392	645	16	structure	structure	NOUN
ejpam-5392	645	17	on	on	ADP
ejpam-5392	645	18	y	y	PROPN
ejpam-5392	645	19	,	,	PUNCT
ejpam-5392	645	20	then	then	ADV
ejpam-5392	645	21	we	we	PRON
ejpam-5392	645	22	find	find	VERB
ejpam-5392	645	23	the	the	DET
ejpam-5392	645	24	following	follow	VERB
ejpam-5392	645	25	:	:	PUNCT
ejpam-5392	645	26	•	•	NUM
ejpam-5392	645	27	l	l	NOUN
ejpam-5392	645	28	-	-	PUNCT
ejpam-5392	645	29	βao(y	βao(y	ADJ
ejpam-5392	645	30	)	)	PUNCT
ejpam-5392	645	31	=	=	PRON
ejpam-5392	645	32	{	{	PUNCT
ejpam-5392	645	33	∅,y	∅,y	PROPN
ejpam-5392	645	34	,	,	PUNCT
ejpam-5392	645	35	{	{	PUNCT
ejpam-5392	645	36	y2	y2	NOUN
ejpam-5392	645	37	}	}	PUNCT
ejpam-5392	645	38	,	,	PUNCT
ejpam-5392	645	39	{	{	PUNCT
ejpam-5392	645	40	y4	y4	X
ejpam-5392	645	41	}	}	PUNCT
ejpam-5392	645	42	,	,	PUNCT
ejpam-5392	645	43	{	{	PUNCT
ejpam-5392	645	44	y1	y1	NOUN
ejpam-5392	645	45	,	,	PUNCT
ejpam-5392	645	46	y2	y2	PROPN
ejpam-5392	645	47	}	}	PUNCT
ejpam-5392	645	48	,	,	PUNCT
ejpam-5392	645	49	{	{	PUNCT
ejpam-5392	645	50	y2	y2	INTJ
ejpam-5392	645	51	,	,	PUNCT
ejpam-5392	645	52	y4	y4	PROPN
ejpam-5392	645	53	}	}	PUNCT
ejpam-5392	645	54	,	,	PUNCT
ejpam-5392	645	55	{	{	PUNCT
ejpam-5392	645	56	y1	y1	NOUN
ejpam-5392	645	57	,	,	PUNCT
ejpam-5392	645	58	y4	y4	PROPN
ejpam-5392	645	59	}	}	PUNCT
ejpam-5392	645	60	,	,	PUNCT
ejpam-5392	645	61	{	{	PUNCT
ejpam-5392	645	62	y2	y2	NOUN
ejpam-5392	645	63	,	,	PUNCT
ejpam-5392	645	64	y3	y3	PROPN
ejpam-5392	645	65	}	}	PUNCT
ejpam-5392	645	66	,	,	PUNCT
ejpam-5392	645	67	{	{	PUNCT
ejpam-5392	645	68	y3	y3	NOUN
ejpam-5392	645	69	,	,	PUNCT
ejpam-5392	645	70	y4	y4	PROPN
ejpam-5392	645	71	}	}	PUNCT
ejpam-5392	645	72	,	,	PUNCT
ejpam-5392	645	73	{	{	PUNCT
ejpam-5392	645	74	y1	y1	NOUN
ejpam-5392	645	75	,	,	PUNCT
ejpam-5392	645	76	y2	y2	PROPN
ejpam-5392	645	77	,	,	PUNCT
ejpam-5392	645	78	y4	y4	PROPN
ejpam-5392	645	79	}	}	PUNCT
ejpam-5392	645	80	,	,	PUNCT
ejpam-5392	645	81	{	{	PUNCT
ejpam-5392	645	82	y1	y1	X
ejpam-5392	645	83	,	,	PUNCT
ejpam-5392	645	84	y3	y3	PROPN
ejpam-5392	645	85	,	,	PUNCT
ejpam-5392	645	86	y4	y4	PROPN
ejpam-5392	645	87	}	}	PUNCT
ejpam-5392	645	88	,	,	PUNCT
ejpam-5392	645	89	{	{	PUNCT
ejpam-5392	645	90	y2	y2	PROPN
ejpam-5392	645	91	,	,	PUNCT
ejpam-5392	645	92	y3	y3	PROPN
ejpam-5392	645	93	,	,	PUNCT
ejpam-5392	645	94	y4	y4	PROPN
ejpam-5392	645	95	}	}	PUNCT
ejpam-5392	645	96	,	,	PUNCT
ejpam-5392	645	97	{	{	PUNCT
ejpam-5392	645	98	y1	y1	NOUN
ejpam-5392	645	99	,	,	PUNCT
ejpam-5392	645	100	y2	y2	PROPN
ejpam-5392	645	101	,	,	PUNCT
ejpam-5392	645	102	y3	y3	NOUN
ejpam-5392	645	103	}	}	PUNCT
ejpam-5392	645	104	}	}	PUNCT
ejpam-5392	645	105	=	=	PUNCT
ejpam-5392	645	106	βao(y	βao(y	CCONJ
ejpam-5392	645	107	)	)	PUNCT
ejpam-5392	645	108	∪	∪	X
ejpam-5392	645	109	{	{	PUNCT
ejpam-5392	645	110	{	{	PUNCT
ejpam-5392	645	111	y1	y1	NOUN
ejpam-5392	645	112	,	,	PUNCT
ejpam-5392	645	113	y2	y2	PROPN
ejpam-5392	645	114	}	}	PUNCT
ejpam-5392	645	115	,	,	PUNCT
ejpam-5392	645	116	{	{	PUNCT
ejpam-5392	645	117	y1	y1	NOUN
ejpam-5392	645	118	,	,	PUNCT
ejpam-5392	645	119	y2	y2	PROPN
ejpam-5392	645	120	,	,	PUNCT
ejpam-5392	645	121	y3	y3	NOUN
ejpam-5392	645	122	}	}	PUNCT
ejpam-5392	645	123	}	}	PUNCT
ejpam-5392	645	124	,	,	PUNCT
ejpam-5392	645	125	•	•	NOUN
ejpam-5392	645	126	l	l	NOUN
ejpam-5392	645	127	-	-	PUNCT
ejpam-5392	645	128	δβao(y	δβao(y	ADJ
ejpam-5392	645	129	)	)	PUNCT
ejpam-5392	645	130	=	=	NOUN
ejpam-5392	645	131	{	{	PUNCT
ejpam-5392	645	132	∅,y	∅,y	PROPN
ejpam-5392	645	133	,	,	PUNCT
ejpam-5392	645	134	{	{	PUNCT
ejpam-5392	645	135	y1	y1	NOUN
ejpam-5392	645	136	}	}	PUNCT
ejpam-5392	645	137	,	,	PUNCT
ejpam-5392	645	138	{	{	PUNCT
ejpam-5392	645	139	y2	y2	NOUN
ejpam-5392	645	140	}	}	PUNCT
ejpam-5392	645	141	,	,	PUNCT
ejpam-5392	645	142	{	{	PUNCT
ejpam-5392	645	143	y4	y4	X
ejpam-5392	645	144	}	}	PUNCT
ejpam-5392	645	145	,	,	PUNCT
ejpam-5392	645	146	{	{	PUNCT
ejpam-5392	645	147	y1	y1	NOUN
ejpam-5392	645	148	,	,	PUNCT
ejpam-5392	645	149	y2	y2	PROPN
ejpam-5392	645	150	}	}	PUNCT
ejpam-5392	645	151	,	,	PUNCT
ejpam-5392	645	152	{	{	PUNCT
ejpam-5392	645	153	y2	y2	INTJ
ejpam-5392	645	154	,	,	PUNCT
ejpam-5392	645	155	y4	y4	PROPN
ejpam-5392	645	156	}	}	PUNCT
ejpam-5392	645	157	,	,	PUNCT
ejpam-5392	645	158	{	{	PUNCT
ejpam-5392	645	159	y1	y1	NOUN
ejpam-5392	645	160	,	,	PUNCT
ejpam-5392	645	161	y4	y4	PROPN
ejpam-5392	645	162	}	}	PUNCT
ejpam-5392	645	163	,	,	PUNCT
ejpam-5392	645	164	{	{	PUNCT
ejpam-5392	645	165	y2	y2	NOUN
ejpam-5392	645	166	,	,	PUNCT
ejpam-5392	645	167	y3	y3	PROPN
ejpam-5392	645	168	}	}	PUNCT
ejpam-5392	645	169	,	,	PUNCT
ejpam-5392	645	170	{	{	PUNCT
ejpam-5392	645	171	y3	y3	NOUN
ejpam-5392	645	172	,	,	PUNCT
ejpam-5392	645	173	y4	y4	PROPN
ejpam-5392	645	174	}	}	PUNCT
ejpam-5392	645	175	,	,	PUNCT
ejpam-5392	645	176	{	{	PUNCT
ejpam-5392	645	177	y1	y1	NOUN
ejpam-5392	645	178	,	,	PUNCT
ejpam-5392	645	179	y2	y2	PROPN
ejpam-5392	645	180	,	,	PUNCT
ejpam-5392	645	181	y4	y4	PROPN
ejpam-5392	645	182	}	}	PUNCT
ejpam-5392	645	183	,	,	PUNCT
ejpam-5392	645	184	{	{	PUNCT
ejpam-5392	645	185	y1	y1	X
ejpam-5392	645	186	,	,	PUNCT
ejpam-5392	645	187	y3	y3	PROPN
ejpam-5392	645	188	,	,	PUNCT
ejpam-5392	645	189	y4	y4	PROPN
ejpam-5392	645	190	}	}	PUNCT
ejpam-5392	645	191	,	,	PUNCT
ejpam-5392	645	192	{	{	PUNCT
ejpam-5392	645	193	y2	y2	PROPN
ejpam-5392	645	194	,	,	PUNCT
ejpam-5392	645	195	y3	y3	PROPN
ejpam-5392	645	196	,	,	PUNCT
ejpam-5392	645	197	y4	y4	PROPN
ejpam-5392	645	198	}	}	PUNCT
ejpam-5392	645	199	,	,	PUNCT
ejpam-5392	645	200	{	{	PUNCT
ejpam-5392	645	201	y1	y1	NOUN
ejpam-5392	645	202	,	,	PUNCT
ejpam-5392	645	203	y2	y2	PROPN
ejpam-5392	645	204	,	,	PUNCT
ejpam-5392	645	205	y3	y3	NOUN
ejpam-5392	645	206	}	}	PUNCT
ejpam-5392	645	207	}	}	PUNCT
ejpam-5392	645	208	=	=	SYM
ejpam-5392	645	209	l	l	NOUN
ejpam-5392	645	210	-	-	PUNCT
ejpam-5392	645	211	βao(y	βao(y	PROPN
ejpam-5392	645	212	)	)	PUNCT
ejpam-5392	645	213	∪	∪	X
ejpam-5392	645	214	{	{	PUNCT
ejpam-5392	645	215	{	{	PUNCT
ejpam-5392	645	216	y1	y1	NOUN
ejpam-5392	645	217	}	}	PUNCT
ejpam-5392	645	218	,	,	PUNCT
ejpam-5392	645	219	{	{	PUNCT
ejpam-5392	645	220	y1	y1	X
ejpam-5392	645	221	,	,	PUNCT
ejpam-5392	645	222	y3	y3	NOUN
ejpam-5392	645	223	}	}	PUNCT
ejpam-5392	645	224	}	}	PUNCT
ejpam-5392	645	225	,	,	PUNCT
ejpam-5392	645	226	and	and	CCONJ
ejpam-5392	645	227	•	•	NUM
ejpam-5392	645	228	l	l	NOUN
ejpam-5392	645	229	-	-	PUNCT
ejpam-5392	645	230	θβao(y	θβao(y	ADJ
ejpam-5392	645	231	)	)	PUNCT
ejpam-5392	645	232	=	=	SYM
ejpam-5392	645	233	p	p	X
ejpam-5392	645	234	(	(	PUNCT
ejpam-5392	645	235	y	y	NOUN
ejpam-5392	645	236	)	)	PUNCT
ejpam-5392	645	237	.	.	PUNCT
ejpam-5392	646	1	m.	m.	PROPN
ejpam-5392	646	2	hosny	hosny	PROPN
ejpam-5392	646	3	,	,	PUNCT
ejpam-5392	646	4	t.m	t.m	PROPN
ejpam-5392	646	5	.	.	PROPN
ejpam-5392	646	6	al	al	PROPN
ejpam-5392	646	7	-	-	PUNCT
ejpam-5392	646	8	shami	shami	PROPN
ejpam-5392	646	9	/	/	PUNCT
ejpam-5392	646	10	eur	eur	PROPN
ejpam-5392	646	11	.	.	PUNCT
ejpam-5392	647	1	j.	j.	PROPN
ejpam-5392	647	2	pure	pure	PROPN
ejpam-5392	647	3	appl	appl	PROPN
ejpam-5392	647	4	.	.	PROPN
ejpam-5392	647	5	math	math	PROPN
ejpam-5392	647	6	,	,	PUNCT
ejpam-5392	647	7	17	17	NUM
ejpam-5392	647	8	(	(	PUNCT
ejpam-5392	647	9	4	4	NUM
ejpam-5392	647	10	)	)	PUNCT
ejpam-5392	647	11	(	(	PUNCT
ejpam-5392	647	12	2024	2024	NUM
ejpam-5392	647	13	)	)	PUNCT
ejpam-5392	647	14	,	,	PUNCT
ejpam-5392	647	15	3436	3436	NUM
ejpam-5392	647	16	-	-	SYM
ejpam-5392	647	17	3463	3463	NUM
ejpam-5392	647	18	3458	3458	NUM
ejpam-5392	647	19	t	t	PROPN
ejpam-5392	647	20	ab	ab	X
ejpam-5392	647	21	le	le	PROPN
ejpam-5392	647	22	4	4	NUM
ejpam-5392	647	23	:	:	SYM
ejpam-5392	647	24	b	b	X
ejpam-5392	647	25	o	o	X
ejpam-5392	647	26	u	u	NOUN
ejpam-5392	647	27	n	n	PROPN
ejpam-5392	647	28	d	d	PROPN
ejpam-5392	647	29	ar	ar	PROPN
ejpam-5392	647	30	y	y	PROPN
ejpam-5392	647	31	re	re	PROPN
ejpam-5392	647	32	g	g	PROPN
ejpam-5392	647	33	io	io	PROPN
ejpam-5392	647	34	n	n	PROPN
ejpam-5392	647	35	s	s	PROPN
ejpam-5392	647	36	an	an	PRON
ejpam-5392	647	37	d	d	X
ejpam-5392	647	38	ac	ac	PROPN
ejpam-5392	647	39	cu	cu	PROPN
ejpam-5392	647	40	ra	ra	PROPN
ejpam-5392	648	1	cy	cy	PROPN
ejpam-5392	648	2	m	m	PROPN
ejpam-5392	648	3	ea	ea	PROPN
ejpam-5392	648	4	su	su	PROPN
ejpam-5392	648	5	re	re	PROPN
ejpam-5392	648	6	s	s	PROPN
ejpam-5392	648	7	ca	ca	PROPN
ejpam-5392	648	8	lc	lc	VERB
ejpam-5392	648	9	u	u	PROPN
ejpam-5392	648	10	la	la	X
ejpam-5392	648	11	te	te	PROPN
ejpam-5392	649	1	d	d	X
ejpam-5392	649	2	w	w	VERB
ejpam-5392	649	3	it	it	PRON
ejpam-5392	649	4	h	h	NOUN
ejpam-5392	649	5	re	re	VERB
ejpam-5392	649	6	sp	sp	ADP
ejpam-5392	649	7	ec	ec	PROPN
ejpam-5392	649	8	t	t	PROPN
ejpam-5392	649	9	to	to	ADP
ejpam-5392	649	10	a	a	DET
ejpam-5392	649	11	m	m	NOUN
ejpam-5392	649	12	er	er	INTJ
ejpam-5392	649	13	et	et	NOUN
ejpam-5392	649	14	al	al	PROPN
ejpam-5392	649	15	.	.	PUNCT
ejpam-5392	650	1	[	[	X
ejpam-5392	650	2	1	1	NUM
ejpam-5392	650	3	5	5	NUM
ejpam-5392	650	4	]	]	PUNCT
ejpam-5392	650	5	m	m	VERB
ejpam-5392	650	6	et	et	NOUN
ejpam-5392	650	7	h	h	NOUN
ejpam-5392	650	8	o	o	NOUN
ejpam-5392	651	1	d	d	NOUN
ejpam-5392	651	2	,	,	PUNCT
ejpam-5392	651	3	h	h	NOUN
ejpam-5392	652	1	o	o	X
ejpam-5392	652	2	sn	sn	INTJ
ejpam-5392	652	3	y	y	PROPN
ejpam-5392	653	1	[	[	X
ejpam-5392	653	2	2	2	NUM
ejpam-5392	653	3	3	3	NUM
ejpam-5392	653	4	]	]	PUNCT
ejpam-5392	653	5	m	m	VERB
ejpam-5392	653	6	et	et	NOUN
ejpam-5392	653	7	h	h	NOUN
ejpam-5392	653	8	o	o	PROPN
ejpam-5392	654	1	d	d	X
ejpam-5392	654	2	,	,	PUNCT
ejpam-5392	654	3	an	an	DET
ejpam-5392	654	4	d	d	X
ejpam-5392	654	5	th	th	X
ejpam-5392	654	6	e	e	NOUN
ejpam-5392	654	7	pr	pr	NOUN
ejpam-5392	654	8	es	es	VERB
ejpam-5392	654	9	en	en	PROPN
ejpam-5392	654	10	t	t	PROPN
ejpam-5392	654	11	m	m	NOUN
ejpam-5392	654	12	et	et	NOUN
ejpam-5392	654	13	h	h	NOUN
ejpam-5392	654	14	o	o	NOUN
ejpam-5392	655	1	d	d	INTJ
ejpam-5392	655	2	.	.	PUNCT
ejpam-5392	656	1	m	m	VERB
ejpam-5392	656	2	et	et	NOUN
ejpam-5392	656	3	h	h	NOUN
ejpam-5392	657	1	o	o	NOUN
ejpam-5392	658	1	d	d	X
ejpam-5392	658	2	s	s	VERB
ejpam-5392	658	3	a	a	PRON
ejpam-5392	658	4	m	m	NOUN
ejpam-5392	658	5	er	er	INTJ
ejpam-5392	658	6	et	et	NOUN
ejpam-5392	658	7	al	al	PROPN
ejpam-5392	658	8	.	.	PUNCT
ejpam-5392	659	1	m	m	VERB
ejpam-5392	659	2	et	et	NOUN
ejpam-5392	659	3	h	h	NOUN
ejpam-5392	660	1	o	o	X
ejpam-5392	660	2	d	d	X
ejpam-5392	660	3	β	β	X
ejpam-5392	660	4	a	a	PRON
ejpam-5392	660	5	o	o	X
ejpam-5392	660	6	(	(	PUNCT
ejpam-5392	660	7	y	y	PROPN
ejpam-5392	660	8	)	)	PUNCT
ejpam-5392	660	9	h	h	NOUN
ejpam-5392	660	10	os	os	NOUN
ejpam-5392	661	1	n	n	CCONJ
ejpam-5392	661	2	y	y	PROPN
ejpam-5392	661	3	m	m	VERB
ejpam-5392	661	4	et	et	NOUN
ejpam-5392	661	5	h	h	NOUN
ejpam-5392	661	6	o	o	NOUN
ejpam-5392	662	1	d	d	X
ejpam-5392	662	2	s	s	VERB
ejpam-5392	662	3	l	l	NOUN
ejpam-5392	662	4	-β	-β	PUNCT
ejpam-5392	662	5	a	a	DET
ejpam-5392	662	6	o	o	X
ejpam-5392	662	7	(	(	PUNCT
ejpam-5392	662	8	y	y	PROPN
ejpam-5392	662	9	)	)	PUNCT
ejpam-5392	662	10	h	h	NOUN
ejpam-5392	662	11	os	os	NOUN
ejpam-5392	663	1	n	n	CCONJ
ejpam-5392	663	2	y	y	PROPN
ejpam-5392	663	3	m	m	VERB
ejpam-5392	663	4	et	et	NOUN
ejpam-5392	663	5	h	h	NOUN
ejpam-5392	663	6	o	o	NOUN
ejpam-5392	664	1	d	d	X
ejpam-5392	664	2	s	s	VERB
ejpam-5392	664	3	l	l	NOUN
ejpam-5392	664	4	-δ	-δ	PUNCT
ejpam-5392	664	5	β	β	NOUN
ejpam-5392	664	6	a	a	PRON
ejpam-5392	664	7	o	o	X
ejpam-5392	664	8	(	(	PUNCT
ejpam-5392	664	9	y	y	PROPN
ejpam-5392	664	10	)	)	PUNCT
ejpam-5392	664	11	t	t	PROPN
ejpam-5392	665	1	h	h	NOUN
ejpam-5392	665	2	e	e	X
ejpam-5392	665	3	p	p	X
ejpam-5392	665	4	re	re	X
ejpam-5392	665	5	se	se	X
ejpam-5392	665	6	n	n	PROPN
ejpam-5392	665	7	t	t	PROPN
ejpam-5392	665	8	m	m	VERB
ejpam-5392	665	9	et	et	NOUN
ejpam-5392	665	10	h	h	NOUN
ejpam-5392	666	1	o	o	NOUN
ejpam-5392	667	1	d	d	X
ejpam-5392	667	2	l	l	NOUN
ejpam-5392	667	3	-θ	-θ	PUNCT
ejpam-5392	667	4	β	β	VERB
ejpam-5392	667	5	a	a	DET
ejpam-5392	667	6	o	o	X
ejpam-5392	667	7	(	(	PUNCT
ejpam-5392	667	8	y	y	PROPN
ejpam-5392	667	9	)	)	PUNCT
ejpam-5392	667	10	v	v	ADP
ejpam-5392	667	11	⊆	⊆	NUM
ejpam-5392	667	12	y	y	PROPN
ejpam-5392	667	13	b	b	PROPN
ejpam-5392	667	14	n	n	PROPN
ejpam-5392	667	15	d	d	PROPN
ejpam-5392	667	16	β	β	X
ejpam-5392	667	17	a	a	DET
ejpam-5392	667	18	(	(	PUNCT
ejpam-5392	667	19	v	v	NOUN
ejpam-5392	667	20	)	)	PUNCT
ejpam-5392	667	21	a	a	DET
ejpam-5392	667	22	c	c	NOUN
ejpam-5392	667	23	c	c	NOUN
ejpam-5392	667	24	β	β	X
ejpam-5392	667	25	a	a	DET
ejpam-5392	667	26	(	(	PUNCT
ejpam-5392	667	27	v	v	NOUN
ejpam-5392	667	28	)	)	PUNCT
ejpam-5392	667	29	b	b	PROPN
ejpam-5392	667	30	n	n	ADP
ejpam-5392	667	31	d	d	NOUN
ejpam-5392	667	32	l	l	NOUN
ejpam-5392	667	33	−	−	NOUN
ejpam-5392	667	34	β	β	NOUN
ejpam-5392	667	35	a	a	DET
ejpam-5392	667	36	(	(	PUNCT
ejpam-5392	667	37	v	v	NOUN
ejpam-5392	667	38	)	)	PUNCT
ejpam-5392	667	39	a	a	DET
ejpam-5392	667	40	c	c	NOUN
ejpam-5392	667	41	c	c	NOUN
ejpam-5392	667	42	l	l	NOUN
ejpam-5392	667	43	−	−	X
ejpam-5392	667	44	β	β	NOUN
ejpam-5392	667	45	a	a	DET
ejpam-5392	667	46	(	(	PUNCT
ejpam-5392	667	47	v	v	NOUN
ejpam-5392	667	48	)	)	PUNCT
ejpam-5392	667	49	b	b	PROPN
ejpam-5392	667	50	n	n	ADP
ejpam-5392	667	51	d	d	NOUN
ejpam-5392	667	52	l	l	NOUN
ejpam-5392	667	53	−	−	PROPN
ejpam-5392	667	54	δ	δ	X
ejpam-5392	667	55	β	β	X
ejpam-5392	667	56	a	a	X
ejpam-5392	667	57	(	(	PUNCT
ejpam-5392	667	58	v	v	NOUN
ejpam-5392	667	59	)	)	PUNCT
ejpam-5392	667	60	a	a	DET
ejpam-5392	667	61	c	c	NOUN
ejpam-5392	667	62	c	c	NOUN
ejpam-5392	667	63	l	l	NOUN
ejpam-5392	667	64	−	−	PROPN
ejpam-5392	668	1	δ	δ	X
ejpam-5392	668	2	β	β	X
ejpam-5392	668	3	a	a	X
ejpam-5392	668	4	(	(	PUNCT
ejpam-5392	668	5	v	v	NOUN
ejpam-5392	668	6	)	)	PUNCT
ejpam-5392	668	7	b	b	PROPN
ejpam-5392	668	8	n	n	ADP
ejpam-5392	668	9	d	d	NOUN
ejpam-5392	668	10	l	l	NOUN
ejpam-5392	668	11	−	−	PROPN
ejpam-5392	668	12	θ	θ	X
ejpam-5392	668	13	β	β	X
ejpam-5392	668	14	a	a	DET
ejpam-5392	668	15	(	(	PUNCT
ejpam-5392	668	16	v	v	NOUN
ejpam-5392	668	17	)	)	PUNCT
ejpam-5392	668	18	a	a	DET
ejpam-5392	668	19	c	c	NOUN
ejpam-5392	668	20	c	c	NOUN
ejpam-5392	668	21	l	l	NOUN
ejpam-5392	668	22	−	−	PROPN
ejpam-5392	668	23	θ	θ	X
ejpam-5392	668	24	β	β	X
ejpam-5392	668	25	a	a	DET
ejpam-5392	668	26	(	(	PUNCT
ejpam-5392	668	27	v	v	NOUN
ejpam-5392	668	28	)	)	PUNCT
ejpam-5392	668	29	{	{	PUNCT
ejpam-5392	668	30	y	y	PROPN
ejpam-5392	668	31	1	1	NUM
ejpam-5392	668	32	}	}	PUNCT
ejpam-5392	668	33	{	{	PUNCT
ejpam-5392	668	34	y	y	PROPN
ejpam-5392	668	35	1	1	NUM
ejpam-5392	668	36	}	}	PUNCT
ejpam-5392	668	37	0	0	NUM
ejpam-5392	668	38	{	{	PUNCT
ejpam-5392	668	39	y	y	PROPN
ejpam-5392	668	40	1	1	NUM
ejpam-5392	668	41	}	}	SYM
ejpam-5392	668	42	0	0	NUM
ejpam-5392	668	43	∅	∅	NOUN
ejpam-5392	668	44	1	1	NUM
ejpam-5392	668	45	∅	∅	NOUN
ejpam-5392	668	46	1	1	NUM
ejpam-5392	668	47	{	{	PUNCT
ejpam-5392	668	48	y	y	PROPN
ejpam-5392	668	49	2	2	NUM
ejpam-5392	668	50	}	}	PUNCT
ejpam-5392	668	51	∅	∅	NOUN
ejpam-5392	668	52	1	1	NUM
ejpam-5392	668	53	∅	∅	NOUN
ejpam-5392	668	54	1	1	NUM
ejpam-5392	668	55	∅	∅	NOUN
ejpam-5392	668	56	1	1	NUM
ejpam-5392	668	57	∅	∅	NOUN
ejpam-5392	668	58	1	1	NUM
ejpam-5392	668	59	{	{	PUNCT
ejpam-5392	668	60	y	y	PROPN
ejpam-5392	668	61	3	3	NUM
ejpam-5392	668	62	}	}	PUNCT
ejpam-5392	668	63	{	{	PUNCT
ejpam-5392	668	64	y	y	PROPN
ejpam-5392	668	65	3	3	NUM
ejpam-5392	668	66	}	}	PUNCT
ejpam-5392	668	67	0	0	NUM
ejpam-5392	668	68	{	{	PUNCT
ejpam-5392	668	69	y	y	PROPN
ejpam-5392	668	70	3	3	NUM
ejpam-5392	668	71	}	}	PUNCT
ejpam-5392	668	72	0	0	NUM
ejpam-5392	668	73	{	{	PUNCT
ejpam-5392	668	74	y	y	PROPN
ejpam-5392	668	75	3	3	NUM
ejpam-5392	668	76	}	}	SYM
ejpam-5392	668	77	0	0	NUM
ejpam-5392	668	78	∅	∅	NOUN
ejpam-5392	668	79	1	1	NUM
ejpam-5392	668	80	{	{	PUNCT
ejpam-5392	668	81	y	y	NOUN
ejpam-5392	668	82	4	4	NUM
ejpam-5392	668	83	}	}	PUNCT
ejpam-5392	668	84	{	{	PUNCT
ejpam-5392	668	85	y	y	PROPN
ejpam-5392	668	86	1	1	NUM
ejpam-5392	668	87	}	}	PUNCT
ejpam-5392	668	88	1/	1/	NUM
ejpam-5392	668	89	2	2	NUM
ejpam-5392	668	90	∅	∅	NOUN
ejpam-5392	668	91	1	1	NUM
ejpam-5392	668	92	∅	∅	NOUN
ejpam-5392	668	93	1	1	NUM
ejpam-5392	668	94	∅	∅	NOUN
ejpam-5392	668	95	1	1	NUM
ejpam-5392	668	96	{	{	PUNCT
ejpam-5392	668	97	y	y	PROPN
ejpam-5392	668	98	1	1	NUM
ejpam-5392	668	99	,	,	PUNCT
ejpam-5392	668	100	y	y	PROPN
ejpam-5392	668	101	2	2	NUM
ejpam-5392	668	102	}	}	PUNCT
ejpam-5392	668	103	{	{	PUNCT
ejpam-5392	668	104	y	y	PROPN
ejpam-5392	668	105	1	1	NUM
ejpam-5392	668	106	}	}	PUNCT
ejpam-5392	668	107	1/	1/	NUM
ejpam-5392	668	108	2	2	NUM
ejpam-5392	668	109	∅	∅	NOUN
ejpam-5392	668	110	1	1	NUM
ejpam-5392	668	111	∅	∅	NOUN
ejpam-5392	668	112	1	1	NUM
ejpam-5392	668	113	∅	∅	NOUN
ejpam-5392	668	114	1	1	NUM
ejpam-5392	668	115	{	{	PUNCT
ejpam-5392	668	116	y	y	PROPN
ejpam-5392	668	117	1	1	NUM
ejpam-5392	668	118	,	,	PUNCT
ejpam-5392	668	119	y	y	PROPN
ejpam-5392	668	120	3	3	NUM
ejpam-5392	668	121	}	}	PUNCT
ejpam-5392	668	122	{	{	PUNCT
ejpam-5392	668	123	y	y	PROPN
ejpam-5392	668	124	1	1	NUM
ejpam-5392	668	125	,	,	PUNCT
ejpam-5392	668	126	y	y	PROPN
ejpam-5392	668	127	3	3	NUM
ejpam-5392	668	128	}	}	PUNCT
ejpam-5392	668	129	0	0	NUM
ejpam-5392	669	1	{	{	PUNCT
ejpam-5392	669	2	y	y	PROPN
ejpam-5392	669	3	1	1	NUM
ejpam-5392	669	4	,	,	PUNCT
ejpam-5392	669	5	y	y	PROPN
ejpam-5392	669	6	3	3	NUM
ejpam-5392	669	7	}	}	PUNCT
ejpam-5392	669	8	0	0	NUM
ejpam-5392	669	9	{	{	PUNCT
ejpam-5392	669	10	y	y	NOUN
ejpam-5392	669	11	2	2	NUM
ejpam-5392	669	12	}	}	PUNCT
ejpam-5392	669	13	2/	2/	NUM
ejpam-5392	669	14	3	3	NUM
ejpam-5392	669	15	∅	∅	NOUN
ejpam-5392	669	16	1	1	NUM
ejpam-5392	669	17	{	{	PUNCT
ejpam-5392	669	18	y	y	PROPN
ejpam-5392	669	19	1	1	NUM
ejpam-5392	669	20	,	,	PUNCT
ejpam-5392	669	21	y	y	PROPN
ejpam-5392	669	22	4	4	NUM
ejpam-5392	669	23	}	}	PUNCT
ejpam-5392	669	24	∅	∅	NOUN
ejpam-5392	669	25	1	1	NUM
ejpam-5392	669	26	∅	∅	NOUN
ejpam-5392	669	27	1	1	NUM
ejpam-5392	669	28	∅	∅	NOUN
ejpam-5392	669	29	1	1	NUM
ejpam-5392	669	30	∅	∅	NOUN
ejpam-5392	669	31	1	1	NUM
ejpam-5392	669	32	{	{	PUNCT
ejpam-5392	669	33	y	y	PROPN
ejpam-5392	669	34	2	2	NUM
ejpam-5392	669	35	,	,	PUNCT
ejpam-5392	669	36	y	y	PROPN
ejpam-5392	669	37	3	3	NUM
ejpam-5392	669	38	}	}	PUNCT
ejpam-5392	669	39	∅	∅	NOUN
ejpam-5392	669	40	1	1	NUM
ejpam-5392	669	41	∅	∅	NOUN
ejpam-5392	669	42	1	1	NUM
ejpam-5392	669	43	∅	∅	NOUN
ejpam-5392	669	44	1	1	NUM
ejpam-5392	669	45	∅	∅	NOUN
ejpam-5392	669	46	1	1	NUM
ejpam-5392	669	47	{	{	PUNCT
ejpam-5392	669	48	y	y	PROPN
ejpam-5392	669	49	2	2	NUM
ejpam-5392	669	50	,	,	PUNCT
ejpam-5392	669	51	y	y	PROPN
ejpam-5392	669	52	4	4	NUM
ejpam-5392	669	53	}	}	PUNCT
ejpam-5392	669	54	{	{	PUNCT
ejpam-5392	669	55	y	y	PROPN
ejpam-5392	669	56	1	1	NUM
ejpam-5392	669	57	,	,	PUNCT
ejpam-5392	669	58	y	y	PROPN
ejpam-5392	669	59	3	3	NUM
ejpam-5392	669	60	}	}	PUNCT
ejpam-5392	669	61	1/	1/	NUM
ejpam-5392	669	62	4	4	NUM
ejpam-5392	669	63	{	{	PUNCT
ejpam-5392	669	64	y	y	PROPN
ejpam-5392	669	65	1	1	NUM
ejpam-5392	669	66	,	,	PUNCT
ejpam-5392	669	67	y	y	PROPN
ejpam-5392	669	68	3	3	NUM
ejpam-5392	669	69	}	}	SYM
ejpam-5392	669	70	1	1	NUM
ejpam-5392	669	71	/2	/2	NOUN
ejpam-5392	669	72	∅	∅	NOUN
ejpam-5392	669	73	1	1	NUM
ejpam-5392	669	74	∅	∅	NOUN
ejpam-5392	669	75	1	1	NUM
ejpam-5392	669	76	{	{	PUNCT
ejpam-5392	669	77	y	y	PROPN
ejpam-5392	669	78	3	3	NUM
ejpam-5392	669	79	,	,	PUNCT
ejpam-5392	669	80	y	y	PROPN
ejpam-5392	669	81	4	4	NUM
ejpam-5392	669	82	}	}	PUNCT
ejpam-5392	669	83	{	{	PUNCT
ejpam-5392	669	84	y	y	PROPN
ejpam-5392	669	85	1	1	NUM
ejpam-5392	669	86	}	}	PUNCT
ejpam-5392	669	87	1/	1/	NUM
ejpam-5392	669	88	3	3	NUM
ejpam-5392	669	89	∅	∅	NOUN
ejpam-5392	669	90	1	1	NUM
ejpam-5392	669	91	∅	∅	NOUN
ejpam-5392	669	92	1	1	NUM
ejpam-5392	669	93	∅	∅	NOUN
ejpam-5392	669	94	1	1	NUM
ejpam-5392	669	95	{	{	PUNCT
ejpam-5392	669	96	y	y	PROPN
ejpam-5392	669	97	1	1	NUM
ejpam-5392	669	98	,	,	PUNCT
ejpam-5392	669	99	y	y	PROPN
ejpam-5392	669	100	2	2	NUM
ejpam-5392	669	101	,	,	PUNCT
ejpam-5392	669	102	y	y	PROPN
ejpam-5392	669	103	3	3	NUM
ejpam-5392	669	104	}	}	PUNCT
ejpam-5392	669	105	{	{	PUNCT
ejpam-5392	669	106	y	y	PROPN
ejpam-5392	669	107	1	1	NUM
ejpam-5392	669	108	}	}	PUNCT
ejpam-5392	669	109	2/	2/	NUM
ejpam-5392	669	110	3	3	NUM
ejpam-5392	669	111	∅	∅	NOUN
ejpam-5392	669	112	1	1	NUM
ejpam-5392	669	113	∅	∅	NOUN
ejpam-5392	669	114	1	1	NUM
ejpam-5392	669	115	∅	∅	NOUN
ejpam-5392	669	116	1	1	NUM
ejpam-5392	669	117	{	{	PUNCT
ejpam-5392	669	118	y	y	PROPN
ejpam-5392	669	119	1	1	NUM
ejpam-5392	669	120	,	,	PUNCT
ejpam-5392	669	121	y	y	PROPN
ejpam-5392	669	122	2	2	NUM
ejpam-5392	669	123	,	,	PUNCT
ejpam-5392	669	124	y	y	PROPN
ejpam-5392	669	125	4	4	NUM
ejpam-5392	669	126	}	}	PUNCT
ejpam-5392	669	127	{	{	PUNCT
ejpam-5392	669	128	y	y	PROPN
ejpam-5392	669	129	3	3	NUM
ejpam-5392	669	130	}	}	PUNCT
ejpam-5392	669	131	3/	3/	NUM
ejpam-5392	669	132	4	4	NUM
ejpam-5392	669	133	{	{	PUNCT
ejpam-5392	669	134	y	y	PROPN
ejpam-5392	669	135	3	3	NUM
ejpam-5392	669	136	}	}	SYM
ejpam-5392	669	137	3	3	NUM
ejpam-5392	669	138	/4	/4	NOUN
ejpam-5392	669	139	{	{	PUNCT
ejpam-5392	669	140	y	y	PROPN
ejpam-5392	669	141	3	3	NUM
ejpam-5392	669	142	}	}	SYM
ejpam-5392	669	143	3	3	NUM
ejpam-5392	669	144	/4	/4	NOUN
ejpam-5392	669	145	∅	∅	NOUN
ejpam-5392	669	146	1	1	NUM
ejpam-5392	669	147	{	{	PUNCT
ejpam-5392	669	148	y	y	PROPN
ejpam-5392	669	149	1	1	NUM
ejpam-5392	669	150	,	,	PUNCT
ejpam-5392	669	151	y	y	PROPN
ejpam-5392	669	152	3	3	NUM
ejpam-5392	669	153	,	,	PUNCT
ejpam-5392	669	154	y	y	PROPN
ejpam-5392	669	155	4	4	NUM
ejpam-5392	669	156	}	}	PUNCT
ejpam-5392	669	157	∅	∅	NOUN
ejpam-5392	669	158	1	1	NUM
ejpam-5392	669	159	∅	∅	NOUN
ejpam-5392	669	160	1	1	NUM
ejpam-5392	669	161	∅	∅	NOUN
ejpam-5392	669	162	1	1	NUM
ejpam-5392	669	163	∅	∅	NOUN
ejpam-5392	669	164	1	1	NUM
ejpam-5392	669	165	{	{	PUNCT
ejpam-5392	669	166	y	y	PROPN
ejpam-5392	669	167	2	2	NUM
ejpam-5392	669	168	,	,	PUNCT
ejpam-5392	669	169	y	y	PROPN
ejpam-5392	669	170	3	3	NUM
ejpam-5392	669	171	,	,	PUNCT
ejpam-5392	669	172	y	y	PROPN
ejpam-5392	669	173	4	4	NUM
ejpam-5392	669	174	}	}	PUNCT
ejpam-5392	669	175	{	{	PUNCT
ejpam-5392	669	176	y	y	PROPN
ejpam-5392	669	177	1	1	NUM
ejpam-5392	669	178	}	}	PUNCT
ejpam-5392	669	179	3/	3/	NUM
ejpam-5392	669	180	4	4	NUM
ejpam-5392	669	181	{	{	PUNCT
ejpam-5392	669	182	y	y	PROPN
ejpam-5392	669	183	1	1	NUM
ejpam-5392	669	184	}	}	SYM
ejpam-5392	669	185	3	3	NUM
ejpam-5392	669	186	/4	/4	NOUN
ejpam-5392	669	187	∅	∅	NOUN
ejpam-5392	669	188	1	1	NUM
ejpam-5392	669	189	∅	∅	NOUN
ejpam-5392	669	190	1	1	NUM
ejpam-5392	669	191	m.	m.	NOUN
ejpam-5392	669	192	hosny	hosny	PROPN
ejpam-5392	669	193	,	,	PUNCT
ejpam-5392	669	194	t.m	t.m	PROPN
ejpam-5392	669	195	.	.	PROPN
ejpam-5392	669	196	al	al	PROPN
ejpam-5392	669	197	-	-	PUNCT
ejpam-5392	669	198	shami	shami	PROPN
ejpam-5392	669	199	/	/	PUNCT
ejpam-5392	669	200	eur	eur	PROPN
ejpam-5392	669	201	.	.	PUNCT
ejpam-5392	670	1	j.	j.	PROPN
ejpam-5392	670	2	pure	pure	PROPN
ejpam-5392	670	3	appl	appl	PROPN
ejpam-5392	670	4	.	.	PROPN
ejpam-5392	670	5	math	math	PROPN
ejpam-5392	670	6	,	,	PUNCT
ejpam-5392	670	7	17	17	NUM
ejpam-5392	670	8	(	(	PUNCT
ejpam-5392	670	9	4	4	NUM
ejpam-5392	670	10	)	)	PUNCT
ejpam-5392	670	11	(	(	PUNCT
ejpam-5392	670	12	2024	2024	NUM
ejpam-5392	670	13	)	)	PUNCT
ejpam-5392	670	14	,	,	PUNCT
ejpam-5392	670	15	3436	3436	NUM
ejpam-5392	670	16	-	-	SYM
ejpam-5392	670	17	3463	3463	NUM
ejpam-5392	670	18	3459	3459	NUM
ejpam-5392	670	19	according	accord	VERB
ejpam-5392	670	20	to	to	ADP
ejpam-5392	670	21	the	the	DET
ejpam-5392	670	22	computations	computation	NOUN
ejpam-5392	670	23	of	of	ADP
ejpam-5392	670	24	boundary	boundary	ADJ
ejpam-5392	670	25	regions	region	NOUN
ejpam-5392	670	26	and	and	CCONJ
ejpam-5392	670	27	accuracy	accuracy	NOUN
ejpam-5392	670	28	measures	measure	NOUN
ejpam-5392	670	29	of	of	ADP
ejpam-5392	670	30	subsets	subset	NOUN
ejpam-5392	670	31	displayed	display	VERB
ejpam-5392	670	32	in	in	ADP
ejpam-5392	670	33	table	table	NOUN
ejpam-5392	670	34	4	4	NUM
ejpam-5392	670	35	,	,	PUNCT
ejpam-5392	670	36	we	we	PRON
ejpam-5392	670	37	remark	remark	VERB
ejpam-5392	670	38	the	the	DET
ejpam-5392	670	39	following	follow	VERB
ejpam-5392	670	40	points	point	NOUN
ejpam-5392	670	41	:	:	PUNCT
ejpam-5392	670	42	there	there	PRON
ejpam-5392	670	43	are	be	VERB
ejpam-5392	670	44	different	different	ADJ
ejpam-5392	670	45	techniques	technique	NOUN
ejpam-5392	670	46	introduced	introduce	VERB
ejpam-5392	670	47	in	in	ADP
ejpam-5392	670	48	the	the	DET
ejpam-5392	670	49	literature	literature	NOUN
ejpam-5392	670	50	to	to	PART
ejpam-5392	670	51	approximate	approximate	ADJ
ejpam-5392	670	52	subsets	subset	NOUN
ejpam-5392	670	53	using	use	VERB
ejpam-5392	670	54	some	some	DET
ejpam-5392	670	55	forms	form	NOUN
ejpam-5392	670	56	of	of	ADP
ejpam-5392	670	57	subsets	subset	NOUN
ejpam-5392	670	58	of	of	ADP
ejpam-5392	670	59	topological	topological	ADJ
ejpam-5392	670	60	spaces	space	NOUN
ejpam-5392	670	61	.	.	PUNCT
ejpam-5392	671	1	our	our	PRON
ejpam-5392	671	2	rough	rough	ADJ
ejpam-5392	671	3	approximation	approximation	NOUN
ejpam-5392	671	4	space	space	NOUN
ejpam-5392	671	5	minimizes	minimize	VERB
ejpam-5392	671	6	the	the	DET
ejpam-5392	671	7	upper	upper	ADJ
ejpam-5392	671	8	approximation	approximation	NOUN
ejpam-5392	671	9	and	and	CCONJ
ejpam-5392	671	10	maximizes	maximize	VERB
ejpam-5392	671	11	the	the	DET
ejpam-5392	671	12	lower	low	ADJ
ejpam-5392	671	13	approximation	approximation	NOUN
ejpam-5392	671	14	,	,	PUNCT
ejpam-5392	671	15	which	which	PRON
ejpam-5392	671	16	leads	lead	VERB
ejpam-5392	671	17	to	to	ADP
ejpam-5392	671	18	downsizing	downsize	VERB
ejpam-5392	671	19	(	(	PUNCT
ejpam-5392	671	20	or	or	CCONJ
ejpam-5392	671	21	removing	remove	VERB
ejpam-5392	671	22	)	)	PUNCT
ejpam-5392	671	23	the	the	DET
ejpam-5392	671	24	boundary	boundary	ADJ
ejpam-5392	671	25	regions	region	NOUN
ejpam-5392	671	26	.	.	PUNCT
ejpam-5392	672	1	as	as	ADP
ejpam-5392	672	2	a	a	DET
ejpam-5392	672	3	result	result	NOUN
ejpam-5392	672	4	,	,	PUNCT
ejpam-5392	672	5	it	it	PRON
ejpam-5392	672	6	outperforms	outperform	VERB
ejpam-5392	672	7	other	other	ADJ
ejpam-5392	672	8	rough	rough	ADJ
ejpam-5392	672	9	models	model	NOUN
ejpam-5392	672	10	given	give	VERB
ejpam-5392	672	11	in	in	ADP
ejpam-5392	672	12	the	the	DET
ejpam-5392	672	13	published	publish	VERB
ejpam-5392	672	14	literature	literature	NOUN
ejpam-5392	672	15	like	like	ADP
ejpam-5392	672	16	[	[	X
ejpam-5392	672	17	15	15	NUM
ejpam-5392	672	18	,	,	PUNCT
ejpam-5392	672	19	22	22	NUM
ejpam-5392	672	20	,	,	PUNCT
ejpam-5392	672	21	23	23	NUM
ejpam-5392	672	22	,	,	PUNCT
ejpam-5392	672	23	45	45	NUM
ejpam-5392	672	24	]	]	PUNCT
ejpam-5392	672	25	,	,	PUNCT
ejpam-5392	672	26	which	which	PRON
ejpam-5392	672	27	makes	make	VERB
ejpam-5392	672	28	it	it	PRON
ejpam-5392	672	29	the	the	DET
ejpam-5392	672	30	most	most	ADV
ejpam-5392	672	31	refined	refined	ADJ
ejpam-5392	672	32	technique	technique	NOUN
ejpam-5392	672	33	.	.	PUNCT
ejpam-5392	673	1	for	for	ADP
ejpam-5392	673	2	instance	instance	NOUN
ejpam-5392	673	3	,	,	PUNCT
ejpam-5392	673	4	the	the	DET
ejpam-5392	673	5	above	above	ADJ
ejpam-5392	673	6	table	table	NOUN
ejpam-5392	673	7	shows	show	VERB
ejpam-5392	673	8	that	that	SCONJ
ejpam-5392	673	9	a	a	DET
ejpam-5392	673	10	subset	subset	NOUN
ejpam-5392	673	11	{	{	PUNCT
ejpam-5392	673	12	y3	y3	NOUN
ejpam-5392	673	13	}	}	PUNCT
ejpam-5392	673	14	is	be	AUX
ejpam-5392	673	15	considered	consider	VERB
ejpam-5392	673	16	a	a	DET
ejpam-5392	673	17	rough	rough	ADJ
ejpam-5392	673	18	set	set	NOUN
ejpam-5392	673	19	according	accord	VERB
ejpam-5392	673	20	to	to	ADP
ejpam-5392	673	21	the	the	DET
ejpam-5392	673	22	models	model	NOUN
ejpam-5392	673	23	of	of	ADP
ejpam-5392	673	24	[	[	X
ejpam-5392	673	25	15	15	NUM
ejpam-5392	673	26	,	,	PUNCT
ejpam-5392	673	27	22	22	NUM
ejpam-5392	673	28	,	,	PUNCT
ejpam-5392	673	29	23	23	NUM
ejpam-5392	673	30	,	,	PUNCT
ejpam-5392	673	31	45	45	NUM
ejpam-5392	673	32	]	]	PUNCT
ejpam-5392	673	33	,	,	PUNCT
ejpam-5392	673	34	whereas	whereas	SCONJ
ejpam-5392	673	35	this	this	DET
ejpam-5392	673	36	subset	subset	NOUN
ejpam-5392	673	37	and	and	CCONJ
ejpam-5392	673	38	all	all	DET
ejpam-5392	673	39	other	other	ADJ
ejpam-5392	673	40	subsets	subset	NOUN
ejpam-5392	673	41	are	be	AUX
ejpam-5392	673	42	exact	exact	ADJ
ejpam-5392	673	43	according	accord	VERB
ejpam-5392	673	44	to	to	ADP
ejpam-5392	673	45	the	the	DET
ejpam-5392	673	46	model	model	NOUN
ejpam-5392	673	47	investigated	investigate	VERB
ejpam-5392	673	48	herein	herein	NOUN
ejpam-5392	673	49	.	.	PUNCT
ejpam-5392	674	1	this	this	DET
ejpam-5392	674	2	observation	observation	NOUN
ejpam-5392	674	3	confirms	confirm	VERB
ejpam-5392	674	4	that	that	SCONJ
ejpam-5392	674	5	the	the	DET
ejpam-5392	674	6	current	current	ADJ
ejpam-5392	674	7	model	model	NOUN
ejpam-5392	674	8	is	be	AUX
ejpam-5392	674	9	more	more	ADV
ejpam-5392	674	10	beneficial	beneficial	ADJ
ejpam-5392	674	11	for	for	ADP
ejpam-5392	674	12	coping	cope	VERB
ejpam-5392	674	13	with	with	ADP
ejpam-5392	674	14	real	real	ADJ
ejpam-5392	674	15	-	-	PUNCT
ejpam-5392	674	16	life	life	NOUN
ejpam-5392	674	17	scenarios	scenario	NOUN
ejpam-5392	674	18	since	since	SCONJ
ejpam-5392	674	19	it	it	PRON
ejpam-5392	674	20	extracts	extract	VERB
ejpam-5392	674	21	a	a	DET
ejpam-5392	674	22	greater	great	ADJ
ejpam-5392	674	23	amount	amount	NOUN
ejpam-5392	674	24	of	of	ADP
ejpam-5392	674	25	information	information	NOUN
ejpam-5392	674	26	and	and	CCONJ
ejpam-5392	674	27	reduces	reduce	VERB
ejpam-5392	674	28	data	datum	NOUN
ejpam-5392	674	29	ambiguity	ambiguity	NOUN
ejpam-5392	674	30	.	.	PUNCT
ejpam-5392	675	1	furthermore	furthermore	ADV
ejpam-5392	675	2	,	,	PUNCT
ejpam-5392	675	3	the	the	DET
ejpam-5392	675	4	proposed	propose	VERB
ejpam-5392	675	5	paradigm	paradigm	NOUN
ejpam-5392	675	6	adheres	adhere	VERB
ejpam-5392	675	7	to	to	ADP
ejpam-5392	675	8	most	most	ADJ
ejpam-5392	675	9	properties	property	NOUN
ejpam-5392	675	10	of	of	ADP
ejpam-5392	675	11	pawlak	pawlak	ADJ
ejpam-5392	675	12	’s	’s	PART
ejpam-5392	675	13	model	model	NOUN
ejpam-5392	675	14	without	without	ADP
ejpam-5392	675	15	any	any	DET
ejpam-5392	675	16	restrictions	restriction	NOUN
ejpam-5392	675	17	,	,	PUNCT
ejpam-5392	675	18	as	as	SCONJ
ejpam-5392	675	19	demonstrated	demonstrate	VERB
ejpam-5392	675	20	in	in	ADP
ejpam-5392	675	21	proposition	proposition	NOUN
ejpam-5392	675	22	8	8	NUM
ejpam-5392	675	23	.	.	PUNCT
ejpam-5392	676	1	in	in	ADP
ejpam-5392	676	2	this	this	DET
ejpam-5392	676	3	regard	regard	NOUN
ejpam-5392	676	4	,	,	PUNCT
ejpam-5392	676	5	we	we	PRON
ejpam-5392	676	6	emphasize	emphasize	VERB
ejpam-5392	676	7	that	that	SCONJ
ejpam-5392	676	8	the	the	DET
ejpam-5392	676	9	methodology	methodology	NOUN
ejpam-5392	676	10	of	of	ADP
ejpam-5392	676	11	using	use	VERB
ejpam-5392	676	12	nearly	nearly	ADV
ejpam-5392	676	13	open	open	ADJ
ejpam-5392	676	14	sets	set	NOUN
ejpam-5392	676	15	in	in	ADP
ejpam-5392	676	16	topology	topology	NOUN
ejpam-5392	676	17	can	can	AUX
ejpam-5392	676	18	achieve	achieve	VERB
ejpam-5392	676	19	some	some	PRON
ejpam-5392	676	20	or	or	CCONJ
ejpam-5392	676	21	all	all	DET
ejpam-5392	676	22	properties	property	NOUN
ejpam-5392	676	23	of	of	ADP
ejpam-5392	676	24	the	the	DET
ejpam-5392	676	25	pawlak	pawlak	ADJ
ejpam-5392	676	26	model	model	NOUN
ejpam-5392	676	27	,	,	PUNCT
ejpam-5392	676	28	depending	depend	VERB
ejpam-5392	676	29	on	on	ADP
ejpam-5392	676	30	the	the	DET
ejpam-5392	676	31	frameworks	framework	NOUN
ejpam-5392	676	32	these	these	DET
ejpam-5392	676	33	families	family	NOUN
ejpam-5392	676	34	of	of	ADP
ejpam-5392	676	35	subsets	subset	NOUN
ejpam-5392	676	36	form	form	NOUN
ejpam-5392	676	37	,	,	PUNCT
ejpam-5392	676	38	whether	whether	SCONJ
ejpam-5392	676	39	they	they	PRON
ejpam-5392	676	40	are	be	AUX
ejpam-5392	676	41	topology	topology	NOUN
ejpam-5392	676	42	,	,	PUNCT
ejpam-5392	676	43	supra	supra	NOUN
ejpam-5392	676	44	topology	topology	NOUN
ejpam-5392	676	45	,	,	PUNCT
ejpam-5392	676	46	infra	infra	NOUN
ejpam-5392	676	47	topology	topology	NOUN
ejpam-5392	676	48	,	,	PUNCT
ejpam-5392	676	49	or	or	CCONJ
ejpam-5392	676	50	minimal	minimal	ADJ
ejpam-5392	676	51	structures	structure	NOUN
ejpam-5392	676	52	.	.	PUNCT
ejpam-5392	677	1	to	to	PART
ejpam-5392	677	2	elucidate	elucidate	VERB
ejpam-5392	677	3	this	this	DET
ejpam-5392	677	4	point	point	NOUN
ejpam-5392	677	5	,	,	PUNCT
ejpam-5392	677	6	we	we	PRON
ejpam-5392	677	7	note	note	VERB
ejpam-5392	677	8	that	that	SCONJ
ejpam-5392	677	9	the	the	DET
ejpam-5392	677	10	family	family	NOUN
ejpam-5392	677	11	of	of	ADP
ejpam-5392	677	12	α	α	NOUN
ejpam-5392	677	13	-	-	ADJ
ejpam-5392	677	14	open	open	ADJ
ejpam-5392	677	15	sets	set	NOUN
ejpam-5392	677	16	constitutes	constitute	VERB
ejpam-5392	677	17	a	a	DET
ejpam-5392	677	18	topology	topology	NOUN
ejpam-5392	677	19	.	.	PUNCT
ejpam-5392	678	1	thus	thus	ADV
ejpam-5392	678	2	,	,	PUNCT
ejpam-5392	678	3	rough	rough	ADJ
ejpam-5392	678	4	set	set	NOUN
ejpam-5392	678	5	models	model	NOUN
ejpam-5392	678	6	inspired	inspire	VERB
ejpam-5392	678	7	by	by	ADP
ejpam-5392	678	8	this	this	DET
ejpam-5392	678	9	family	family	NOUN
ejpam-5392	678	10	will	will	AUX
ejpam-5392	678	11	fulfill	fulfill	VERB
ejpam-5392	678	12	all	all	DET
ejpam-5392	678	13	the	the	DET
ejpam-5392	678	14	properties	property	NOUN
ejpam-5392	678	15	of	of	ADP
ejpam-5392	678	16	the	the	DET
ejpam-5392	678	17	pawlak	pawlak	ADJ
ejpam-5392	678	18	model	model	NOUN
ejpam-5392	678	19	.	.	PUNCT
ejpam-5392	679	1	in	in	ADP
ejpam-5392	679	2	contrast	contrast	NOUN
ejpam-5392	679	3	,	,	PUNCT
ejpam-5392	679	4	the	the	DET
ejpam-5392	679	5	family	family	NOUN
ejpam-5392	679	6	of	of	ADP
ejpam-5392	679	7	semi	semi	ADJ
ejpam-5392	679	8	-	-	ADJ
ejpam-5392	679	9	open	open	ADJ
ejpam-5392	679	10	sets	set	NOUN
ejpam-5392	679	11	constitutes	constitute	VERB
ejpam-5392	679	12	a	a	DET
ejpam-5392	679	13	supra	supra	ADJ
ejpam-5392	679	14	topology	topology	NOUN
ejpam-5392	679	15	.	.	PUNCT
ejpam-5392	680	1	therefore	therefore	ADV
ejpam-5392	680	2	,	,	PUNCT
ejpam-5392	680	3	rough	rough	ADJ
ejpam-5392	680	4	set	set	NOUN
ejpam-5392	680	5	models	model	NOUN
ejpam-5392	680	6	inspired	inspire	VERB
ejpam-5392	680	7	by	by	ADP
ejpam-5392	680	8	this	this	DET
ejpam-5392	680	9	family	family	NOUN
ejpam-5392	680	10	lose	lose	VERB
ejpam-5392	680	11	some	some	DET
ejpam-5392	680	12	properties	property	NOUN
ejpam-5392	680	13	of	of	ADP
ejpam-5392	680	14	the	the	DET
ejpam-5392	680	15	pawlak	pawlak	ADJ
ejpam-5392	680	16	model	model	NOUN
ejpam-5392	680	17	related	relate	VERB
ejpam-5392	680	18	to	to	ADP
ejpam-5392	680	19	the	the	DET
ejpam-5392	680	20	distribution	distribution	NOUN
ejpam-5392	680	21	of	of	ADP
ejpam-5392	680	22	the	the	DET
ejpam-5392	680	23	union	union	NOUN
ejpam-5392	680	24	and	and	CCONJ
ejpam-5392	680	25	intersection	intersection	NOUN
ejpam-5392	680	26	operators	operator	NOUN
ejpam-5392	680	27	to	to	ADP
ejpam-5392	680	28	the	the	DET
ejpam-5392	680	29	upper	upper	ADJ
ejpam-5392	680	30	and	and	CCONJ
ejpam-5392	680	31	lower	low	ADJ
ejpam-5392	680	32	approximations	approximation	NOUN
ejpam-5392	680	33	,	,	PUNCT
ejpam-5392	680	34	respectively	respectively	ADV
ejpam-5392	680	35	.	.	PUNCT
ejpam-5392	681	1	on	on	ADP
ejpam-5392	681	2	the	the	DET
ejpam-5392	681	3	other	other	ADJ
ejpam-5392	681	4	hand	hand	NOUN
ejpam-5392	681	5	,	,	PUNCT
ejpam-5392	681	6	we	we	PRON
ejpam-5392	681	7	find	find	VERB
ejpam-5392	681	8	that	that	SCONJ
ejpam-5392	681	9	families	family	NOUN
ejpam-5392	681	10	that	that	PRON
ejpam-5392	681	11	do	do	AUX
ejpam-5392	681	12	not	not	PART
ejpam-5392	681	13	achieve	achieve	VERB
ejpam-5392	681	14	all	all	DET
ejpam-5392	681	15	the	the	DET
ejpam-5392	681	16	properties	property	NOUN
ejpam-5392	681	17	of	of	ADP
ejpam-5392	681	18	the	the	DET
ejpam-5392	681	19	pawlak	pawlak	ADJ
ejpam-5392	681	20	model	model	NOUN
ejpam-5392	681	21	expand	expand	VERB
ejpam-5392	681	22	the	the	DET
ejpam-5392	681	23	confirmed	confirm	VERB
ejpam-5392	681	24	knowledge	knowledge	NOUN
ejpam-5392	681	25	and	and	CCONJ
ejpam-5392	681	26	produce	produce	VERB
ejpam-5392	681	27	a	a	DET
ejpam-5392	681	28	greater	great	ADJ
ejpam-5392	681	29	accuracy	accuracy	NOUN
ejpam-5392	681	30	measure	measure	NOUN
ejpam-5392	681	31	than	than	ADP
ejpam-5392	681	32	those	those	DET
ejpam-5392	681	33	families	family	NOUN
ejpam-5392	681	34	that	that	PRON
ejpam-5392	681	35	achieve	achieve	VERB
ejpam-5392	681	36	all	all	DET
ejpam-5392	681	37	the	the	DET
ejpam-5392	681	38	properties	property	NOUN
ejpam-5392	681	39	of	of	ADP
ejpam-5392	681	40	the	the	DET
ejpam-5392	681	41	pawlak	pawlak	ADJ
ejpam-5392	681	42	model	model	NOUN
ejpam-5392	681	43	.	.	PUNCT
ejpam-5392	682	1	7	7	X
ejpam-5392	682	2	.	.	X
ejpam-5392	682	3	conclusions	conclusion	NOUN
ejpam-5392	682	4	the	the	DET
ejpam-5392	682	5	notion	notion	NOUN
ejpam-5392	682	6	of	of	ADP
ejpam-5392	682	7	rough	rough	ADJ
ejpam-5392	682	8	neighborhoods	neighborhood	NOUN
ejpam-5392	682	9	was	be	AUX
ejpam-5392	682	10	introduced	introduce	VERB
ejpam-5392	682	11	in	in	ADP
ejpam-5392	682	12	the	the	DET
ejpam-5392	682	13	literature	literature	NOUN
ejpam-5392	682	14	with	with	ADP
ejpam-5392	682	15	the	the	DET
ejpam-5392	682	16	aim	aim	NOUN
ejpam-5392	682	17	of	of	ADP
ejpam-5392	682	18	removing	remove	VERB
ejpam-5392	682	19	the	the	DET
ejpam-5392	682	20	strict	strict	ADJ
ejpam-5392	682	21	term	term	NOUN
ejpam-5392	682	22	of	of	ADP
ejpam-5392	682	23	an	an	DET
ejpam-5392	682	24	equivalence	equivalence	NOUN
ejpam-5392	682	25	relation	relation	NOUN
ejpam-5392	682	26	that	that	PRON
ejpam-5392	682	27	limited	limit	VERB
ejpam-5392	682	28	the	the	DET
ejpam-5392	682	29	application	application	NOUN
ejpam-5392	682	30	of	of	ADP
ejpam-5392	682	31	the	the	DET
ejpam-5392	682	32	classical	classical	ADJ
ejpam-5392	682	33	rough	rough	ADJ
ejpam-5392	682	34	set	set	NOUN
ejpam-5392	682	35	models	model	NOUN
ejpam-5392	682	36	.	.	PUNCT
ejpam-5392	683	1	such	such	ADJ
ejpam-5392	683	2	rough	rough	ADJ
ejpam-5392	683	3	neighborhoods	neighborhood	NOUN
ejpam-5392	683	4	have	have	AUX
ejpam-5392	683	5	shown	show	VERB
ejpam-5392	683	6	to	to	PART
ejpam-5392	683	7	be	be	AUX
ejpam-5392	683	8	useful	useful	ADJ
ejpam-5392	683	9	in	in	ADP
ejpam-5392	683	10	several	several	ADJ
ejpam-5392	683	11	applications	application	NOUN
ejpam-5392	683	12	.	.	PUNCT
ejpam-5392	684	1	some	some	DET
ejpam-5392	684	2	formulas	formula	NOUN
ejpam-5392	684	3	have	have	AUX
ejpam-5392	684	4	been	be	AUX
ejpam-5392	684	5	proposed	propose	VERB
ejpam-5392	684	6	to	to	PART
ejpam-5392	684	7	institute	institute	VERB
ejpam-5392	684	8	a	a	DET
ejpam-5392	684	9	topology	topology	NOUN
ejpam-5392	684	10	from	from	ADP
ejpam-5392	684	11	these	these	DET
ejpam-5392	684	12	neighborhoods	neighborhood	NOUN
ejpam-5392	684	13	making	make	VERB
ejpam-5392	684	14	topological	topological	ADJ
ejpam-5392	684	15	spaces	space	NOUN
ejpam-5392	684	16	a	a	DET
ejpam-5392	684	17	vital	vital	ADJ
ejpam-5392	684	18	instrument	instrument	NOUN
ejpam-5392	684	19	to	to	PART
ejpam-5392	684	20	represent	represent	VERB
ejpam-5392	684	21	rough	rough	ADJ
ejpam-5392	684	22	approximation	approximation	NOUN
ejpam-5392	684	23	operators	operator	NOUN
ejpam-5392	684	24	and	and	CCONJ
ejpam-5392	684	25	analyze	analyze	VERB
ejpam-5392	684	26	information	information	NOUN
ejpam-5392	684	27	systems	system	NOUN
ejpam-5392	684	28	.	.	PUNCT
ejpam-5392	685	1	one	one	NUM
ejpam-5392	685	2	of	of	ADP
ejpam-5392	685	3	the	the	DET
ejpam-5392	685	4	important	important	ADJ
ejpam-5392	685	5	topological	topological	ADJ
ejpam-5392	685	6	tools	tool	NOUN
ejpam-5392	685	7	to	to	PART
ejpam-5392	685	8	reduce	reduce	VERB
ejpam-5392	685	9	the	the	DET
ejpam-5392	685	10	vagueness	vagueness	NOUN
ejpam-5392	685	11	of	of	ADP
ejpam-5392	685	12	knowledge	knowledge	NOUN
ejpam-5392	685	13	is	be	AUX
ejpam-5392	685	14	nearly	nearly	ADV
ejpam-5392	685	15	open	open	ADJ
ejpam-5392	685	16	sets	set	NOUN
ejpam-5392	685	17	.	.	PUNCT
ejpam-5392	686	1	despite	despite	SCONJ
ejpam-5392	686	2	this	this	DET
ejpam-5392	686	3	tool	tool	NOUN
ejpam-5392	686	4	being	be	AUX
ejpam-5392	686	5	applied	apply	VERB
ejpam-5392	686	6	by	by	ADP
ejpam-5392	686	7	many	many	ADJ
ejpam-5392	686	8	researchers	researcher	NOUN
ejpam-5392	686	9	,	,	PUNCT
ejpam-5392	686	10	there	there	PRON
ejpam-5392	686	11	remain	remain	VERB
ejpam-5392	686	12	other	other	ADJ
ejpam-5392	686	13	types	type	NOUN
ejpam-5392	686	14	that	that	PRON
ejpam-5392	686	15	should	should	AUX
ejpam-5392	686	16	be	be	AUX
ejpam-5392	686	17	investigated	investigate	VERB
ejpam-5392	686	18	.	.	PUNCT
ejpam-5392	687	1	this	this	DET
ejpam-5392	687	2	work	work	NOUN
ejpam-5392	687	3	goes	go	VERB
ejpam-5392	687	4	along	along	ADP
ejpam-5392	687	5	with	with	ADP
ejpam-5392	687	6	this	this	DET
ejpam-5392	687	7	line	line	NOUN
ejpam-5392	687	8	of	of	ADP
ejpam-5392	687	9	research	research	NOUN
ejpam-5392	687	10	.	.	PUNCT
ejpam-5392	688	1	we	we	PRON
ejpam-5392	688	2	have	have	AUX
ejpam-5392	688	3	studied	study	VERB
ejpam-5392	688	4	generalized	generalized	ADJ
ejpam-5392	688	5	approximation	approximation	NOUN
ejpam-5392	688	6	spaces	space	NOUN
ejpam-5392	688	7	using	use	VERB
ejpam-5392	688	8	the	the	DET
ejpam-5392	688	9	ideas	idea	NOUN
ejpam-5392	688	10	of	of	ADP
ejpam-5392	688	11	l	l	NOUN
ejpam-5392	688	12	-	-	PUNCT
ejpam-5392	688	13	θβλ	θβλ	NOUN
ejpam-5392	688	14	-	-	PUNCT
ejpam-5392	688	15	open	open	ADJ
ejpam-5392	688	16	sets	set	NOUN
ejpam-5392	688	17	and	and	CCONJ
ejpam-5392	688	18	ideal	ideal	ADJ
ejpam-5392	688	19	structures	structure	NOUN
ejpam-5392	688	20	.	.	PUNCT
ejpam-5392	689	1	we	we	PRON
ejpam-5392	689	2	have	have	AUX
ejpam-5392	689	3	explored	explore	VERB
ejpam-5392	689	4	their	their	PRON
ejpam-5392	689	5	structural	structural	ADJ
ejpam-5392	689	6	properties	property	NOUN
ejpam-5392	689	7	and	and	CCONJ
ejpam-5392	689	8	pointed	point	VERB
ejpam-5392	689	9	out	out	ADP
ejpam-5392	689	10	the	the	DET
ejpam-5392	689	11	importance	importance	NOUN
ejpam-5392	689	12	of	of	ADP
ejpam-5392	689	13	the	the	DET
ejpam-5392	689	14	present	present	ADJ
ejpam-5392	689	15	models	model	NOUN
ejpam-5392	689	16	in	in	ADP
ejpam-5392	689	17	maximizing	maximize	VERB
ejpam-5392	689	18	the	the	DET
ejpam-5392	689	19	domain	domain	NOUN
ejpam-5392	689	20	of	of	ADP
ejpam-5392	689	21	confirmed	confirm	VERB
ejpam-5392	689	22	information	information	NOUN
ejpam-5392	689	23	and	and	CCONJ
ejpam-5392	689	24	minimizing	minimize	VERB
ejpam-5392	689	25	the	the	DET
ejpam-5392	689	26	boundary	boundary	ADJ
ejpam-5392	689	27	region	region	NOUN
ejpam-5392	689	28	of	of	ADP
ejpam-5392	689	29	uncertainty	uncertainty	NOUN
ejpam-5392	689	30	.	.	PUNCT
ejpam-5392	690	1	therefore	therefore	ADV
ejpam-5392	690	2	,	,	PUNCT
ejpam-5392	690	3	this	this	DET
ejpam-5392	690	4	work	work	NOUN
ejpam-5392	690	5	is	be	AUX
ejpam-5392	690	6	a	a	DET
ejpam-5392	690	7	foundation	foundation	NOUN
ejpam-5392	690	8	for	for	ADP
ejpam-5392	690	9	handling	handle	VERB
ejpam-5392	690	10	complicated	complicated	ADJ
ejpam-5392	690	11	paradigms	paradigm	NOUN
ejpam-5392	690	12	in	in	ADP
ejpam-5392	690	13	decision	decision	NOUN
ejpam-5392	690	14	-	-	PUNCT
ejpam-5392	690	15	making	making	NOUN
ejpam-5392	690	16	.	.	PUNCT
ejpam-5392	691	1	we	we	PRON
ejpam-5392	691	2	also	also	ADV
ejpam-5392	691	3	showed	show	VERB
ejpam-5392	691	4	the	the	DET
ejpam-5392	691	5	superiority	superiority	NOUN
ejpam-5392	691	6	of	of	ADP
ejpam-5392	691	7	the	the	DET
ejpam-5392	691	8	proposed	propose	VERB
ejpam-5392	691	9	rough	rough	ADJ
ejpam-5392	691	10	paradigms	paradigm	NOUN
ejpam-5392	691	11	over	over	ADP
ejpam-5392	691	12	different	different	ADJ
ejpam-5392	691	13	kinds	kind	NOUN
ejpam-5392	691	14	of	of	ADP
ejpam-5392	691	15	preceding	precede	VERB
ejpam-5392	691	16	paradigms	paradigm	NOUN
ejpam-5392	691	17	induced	induce	VERB
ejpam-5392	691	18	by	by	ADP
ejpam-5392	691	19	some	some	DET
ejpam-5392	691	20	nearly	nearly	ADV
ejpam-5392	691	21	open	open	ADJ
ejpam-5392	691	22	sets	set	NOUN
ejpam-5392	691	23	.	.	PUNCT
ejpam-5392	692	1	to	to	PART
ejpam-5392	692	2	facilitate	facilitate	VERB
ejpam-5392	692	3	the	the	DET
ejpam-5392	692	4	references	reference	NOUN
ejpam-5392	692	5	3460	3460	NUM
ejpam-5392	692	6	way	way	NOUN
ejpam-5392	692	7	of	of	ADP
ejpam-5392	692	8	specifying	specify	VERB
ejpam-5392	692	9	the	the	DET
ejpam-5392	692	10	family	family	NOUN
ejpam-5392	692	11	of	of	ADP
ejpam-5392	692	12	l	l	PROPN
ejpam-5392	692	13	-	-	PUNCT
ejpam-5392	692	14	θβλ	θβλ	NOUN
ejpam-5392	692	15	-	-	PUNCT
ejpam-5392	692	16	open	open	ADJ
ejpam-5392	692	17	sets	set	NOUN
ejpam-5392	692	18	and	and	CCONJ
ejpam-5392	692	19	exploring	explore	VERB
ejpam-5392	692	20	whether	whether	SCONJ
ejpam-5392	692	21	a	a	DET
ejpam-5392	692	22	subset	subset	NOUN
ejpam-5392	692	23	is	be	AUX
ejpam-5392	692	24	l	l	NOUN
ejpam-5392	692	25	-	-	ADJ
ejpam-5392	692	26	θβλdefinable	θβλdefinable	ADJ
ejpam-5392	692	27	or	or	CCONJ
ejpam-5392	692	28	l	l	NOUN
ejpam-5392	692	29	-	-	PUNCT
ejpam-5392	692	30	θβλ	θβλ	NOUN
ejpam-5392	692	31	-	-	PUNCT
ejpam-5392	692	32	rough	rough	ADJ
ejpam-5392	692	33	,	,	PUNCT
ejpam-5392	692	34	we	we	PRON
ejpam-5392	692	35	have	have	AUX
ejpam-5392	692	36	initiated	initiate	VERB
ejpam-5392	692	37	two	two	NUM
ejpam-5392	692	38	algorithms	algorithm	NOUN
ejpam-5392	692	39	.	.	PUNCT
ejpam-5392	693	1	furthermore	furthermore	ADV
ejpam-5392	693	2	,	,	PUNCT
ejpam-5392	693	3	we	we	PRON
ejpam-5392	693	4	have	have	AUX
ejpam-5392	693	5	defined	define	VERB
ejpam-5392	693	6	the	the	DET
ejpam-5392	693	7	relations	relation	NOUN
ejpam-5392	693	8	and	and	CCONJ
ejpam-5392	693	9	functions	function	NOUN
ejpam-5392	693	10	of	of	ADP
ejpam-5392	693	11	rough	rough	ADJ
ejpam-5392	693	12	membership	membership	NOUN
ejpam-5392	693	13	and	and	CCONJ
ejpam-5392	693	14	established	establish	VERB
ejpam-5392	693	15	their	their	PRON
ejpam-5392	693	16	key	key	ADJ
ejpam-5392	693	17	aspects	aspect	NOUN
ejpam-5392	693	18	.	.	PUNCT
ejpam-5392	694	1	in	in	ADP
ejpam-5392	694	2	the	the	DET
ejpam-5392	694	3	end	end	NOUN
ejpam-5392	694	4	,	,	PUNCT
ejpam-5392	694	5	we	we	PRON
ejpam-5392	694	6	have	have	AUX
ejpam-5392	694	7	applied	apply	VERB
ejpam-5392	694	8	the	the	DET
ejpam-5392	694	9	current	current	ADJ
ejpam-5392	694	10	technique	technique	NOUN
ejpam-5392	694	11	in	in	ADP
ejpam-5392	694	12	a	a	DET
ejpam-5392	694	13	practical	practical	ADJ
ejpam-5392	694	14	situation	situation	NOUN
ejpam-5392	694	15	concerning	concern	VERB
ejpam-5392	694	16	classifying	classify	VERB
ejpam-5392	694	17	some	some	DET
ejpam-5392	694	18	chemical	chemical	ADJ
ejpam-5392	694	19	elements	element	NOUN
ejpam-5392	694	20	.	.	PUNCT
ejpam-5392	695	1	a	a	DET
ejpam-5392	695	2	promising	promising	ADJ
ejpam-5392	695	3	avenue	avenue	NOUN
ejpam-5392	695	4	for	for	ADP
ejpam-5392	695	5	upcoming	upcoming	ADJ
ejpam-5392	695	6	research	research	NOUN
ejpam-5392	695	7	incorporates	incorporate	VERB
ejpam-5392	695	8	extending	extend	VERB
ejpam-5392	695	9	the	the	DET
ejpam-5392	695	10	present	present	ADJ
ejpam-5392	695	11	rough	rough	ADJ
ejpam-5392	695	12	set	set	NOUN
ejpam-5392	695	13	paradigms	paradigm	NOUN
ejpam-5392	695	14	to	to	PART
ejpam-5392	695	15	involve	involve	VERB
ejpam-5392	695	16	fuzzy	fuzzy	ADJ
ejpam-5392	695	17	and	and	CCONJ
ejpam-5392	695	18	soft	soft	ADJ
ejpam-5392	695	19	settings	setting	NOUN
ejpam-5392	695	20	to	to	PART
ejpam-5392	695	21	enhance	enhance	VERB
ejpam-5392	695	22	its	its	PRON
ejpam-5392	695	23	ability	ability	NOUN
ejpam-5392	695	24	to	to	PART
ejpam-5392	695	25	handle	handle	VERB
ejpam-5392	695	26	uncertainty	uncertainty	NOUN
ejpam-5392	695	27	.	.	PUNCT
ejpam-5392	696	1	additionally	additionally	ADV
ejpam-5392	696	2	,	,	PUNCT
ejpam-5392	696	3	considering	consider	VERB
ejpam-5392	696	4	other	other	ADJ
ejpam-5392	696	5	approaches	approach	NOUN
ejpam-5392	696	6	like	like	ADP
ejpam-5392	696	7	generating	generate	VERB
ejpam-5392	696	8	topological	topological	ADJ
ejpam-5392	696	9	spaces	space	NOUN
ejpam-5392	696	10	by	by	ADP
ejpam-5392	696	11	ideals	ideal	NOUN
ejpam-5392	696	12	first	first	ADV
ejpam-5392	696	13	and	and	CCONJ
ejpam-5392	696	14	then	then	ADV
ejpam-5392	696	15	applying	apply	VERB
ejpam-5392	696	16	nearly	nearly	ADV
ejpam-5392	696	17	open	open	ADJ
ejpam-5392	696	18	subsets	subset	NOUN
ejpam-5392	696	19	of	of	ADP
ejpam-5392	696	20	these	these	DET
ejpam-5392	696	21	spaces	space	NOUN
ejpam-5392	696	22	,	,	PUNCT
ejpam-5392	696	23	could	could	AUX
ejpam-5392	696	24	further	far	ADV
ejpam-5392	696	25	refine	refine	VERB
ejpam-5392	696	26	the	the	DET
ejpam-5392	696	27	present	present	ADJ
ejpam-5392	696	28	paradigms	paradigms	NOUN
ejpam-5392	696	29	and	and	CCONJ
ejpam-5392	696	30	offer	offer	VERB
ejpam-5392	696	31	another	another	DET
ejpam-5392	696	32	technique	technique	NOUN
ejpam-5392	696	33	to	to	PART
ejpam-5392	696	34	address	address	VERB
ejpam-5392	696	35	imperfect	imperfect	ADJ
ejpam-5392	696	36	knowledge	knowledge	NOUN
ejpam-5392	696	37	.	.	PUNCT
ejpam-5392	697	1	moreover	moreover	ADV
ejpam-5392	697	2	,	,	PUNCT
ejpam-5392	697	3	discussing	discuss	VERB
ejpam-5392	697	4	the	the	DET
ejpam-5392	697	5	current	current	ADJ
ejpam-5392	697	6	approaches	approach	NOUN
ejpam-5392	697	7	in	in	ADP
ejpam-5392	697	8	generalizations	generalization	NOUN
ejpam-5392	697	9	of	of	ADP
ejpam-5392	697	10	topology	topology	NOUN
ejpam-5392	698	1	[	[	X
ejpam-5392	698	2	37	37	NUM
ejpam-5392	698	3	]	]	PUNCT
ejpam-5392	698	4	opens	open	VERB
ejpam-5392	698	5	avenues	avenue	NOUN
ejpam-5392	698	6	for	for	ADP
ejpam-5392	698	7	a	a	DET
ejpam-5392	698	8	deeper	deep	ADJ
ejpam-5392	698	9	comprehension	comprehension	NOUN
ejpam-5392	698	10	of	of	ADP
ejpam-5392	698	11	their	their	PRON
ejpam-5392	698	12	mathematical	mathematical	ADJ
ejpam-5392	698	13	foundations	foundation	NOUN
ejpam-5392	698	14	.	.	PUNCT
ejpam-5392	699	1	conflict	conflict	NOUN
ejpam-5392	699	2	of	of	ADP
ejpam-5392	699	3	interest	interest	NOUN
ejpam-5392	699	4	the	the	DET
ejpam-5392	699	5	authors	author	NOUN
ejpam-5392	699	6	declare	declare	VERB
ejpam-5392	699	7	that	that	SCONJ
ejpam-5392	699	8	there	there	PRON
ejpam-5392	699	9	is	be	VERB
ejpam-5392	699	10	no	no	DET
ejpam-5392	699	11	conflict	conflict	NOUN
ejpam-5392	699	12	of	of	ADP
ejpam-5392	699	13	interest	interest	NOUN
ejpam-5392	699	14	regarding	regard	VERB
ejpam-5392	699	15	the	the	DET
ejpam-5392	699	16	publication	publication	NOUN
ejpam-5392	699	17	of	of	ADP
ejpam-5392	699	18	this	this	DET
ejpam-5392	699	19	paper	paper	NOUN
ejpam-5392	699	20	.	.	PUNCT
ejpam-5392	700	1	references	reference	NOUN
ejpam-5392	700	2	[	[	X
ejpam-5392	700	3	1	1	NUM
ejpam-5392	700	4	]	]	PUNCT
ejpam-5392	700	5	h.	h.	PROPN
ejpam-5392	700	6	m.	m.	PROPN
ejpam-5392	700	7	abo	abo	PROPN
ejpam-5392	700	8	-	-	PUNCT
ejpam-5392	700	9	doniaa	doniaa	ADJ
ejpam-5392	700	10	and	and	CCONJ
ejpam-5392	700	11	a.	a.	NOUN
ejpam-5392	700	12	s.	s.	PROPN
ejpam-5392	700	13	salama	salama	PROPN
ejpam-5392	700	14	.	.	PUNCT
ejpam-5392	701	1	β	β	X
ejpam-5392	701	2	-	-	ADJ
ejpam-5392	701	3	approximation	approximation	NOUN
ejpam-5392	701	4	spaces	space	NOUN
ejpam-5392	701	5	.	.	PUNCT
ejpam-5392	702	1	journal	journal	NOUN
ejpam-5392	702	2	of	of	ADP
ejpam-5392	702	3	hybrid	hybrid	ADJ
ejpam-5392	702	4	computing	computing	NOUN
ejpam-5392	702	5	research	research	NOUN
ejpam-5392	702	6	,	,	PUNCT
ejpam-5392	702	7	1:1–15	1:1–15	NUM
ejpam-5392	702	8	,	,	PUNCT
ejpam-5392	702	9	2008	2008	NUM
ejpam-5392	702	10	.	.	PUNCT
ejpam-5392	703	1	[	[	X
ejpam-5392	703	2	2	2	X
ejpam-5392	703	3	]	]	PUNCT
ejpam-5392	703	4	h.	h.	PROPN
ejpam-5392	703	5	m.	m.	PROPN
ejpam-5392	703	6	abo	abo	PROPN
ejpam-5392	703	7	-	-	PUNCT
ejpam-5392	703	8	doniaa	doniaa	ADJ
ejpam-5392	703	9	and	and	CCONJ
ejpam-5392	703	10	a.	a.	NOUN
ejpam-5392	703	11	s.	s.	PROPN
ejpam-5392	703	12	salama	salama	PROPN
ejpam-5392	703	13	.	.	PUNCT
ejpam-5392	704	1	generalization	generalization	NOUN
ejpam-5392	704	2	of	of	ADP
ejpam-5392	704	3	pawlak	pawlak	ADJ
ejpam-5392	704	4	’s	’s	PART
ejpam-5392	704	5	rough	rough	ADJ
ejpam-5392	704	6	approximation	approximation	NOUN
ejpam-5392	704	7	spaces	space	NOUN
ejpam-5392	704	8	by	by	ADP
ejpam-5392	704	9	using	use	VERB
ejpam-5392	704	10	δβ	δβ	NOUN
ejpam-5392	704	11	-	-	PUNCT
ejpam-5392	704	12	open	open	ADJ
ejpam-5392	704	13	sets	set	NOUN
ejpam-5392	704	14	.	.	PUNCT
ejpam-5392	705	1	international	international	ADJ
ejpam-5392	705	2	journal	journal	PROPN
ejpam-5392	705	3	of	of	ADP
ejpam-5392	705	4	approximate	approximate	ADJ
ejpam-5392	705	5	reasoning	reasoning	NOUN
ejpam-5392	705	6	,	,	PUNCT
ejpam-5392	705	7	53:1094–1105	53:1094–1105	NUM
ejpam-5392	705	8	,	,	PUNCT
ejpam-5392	705	9	2012	2012	NUM
ejpam-5392	705	10	.	.	PUNCT
ejpam-5392	706	1	[	[	X
ejpam-5392	706	2	3	3	X
ejpam-5392	706	3	]	]	X
ejpam-5392	706	4	e.	e.	PROPN
ejpam-5392	706	5	a.	a.	PROPN
ejpam-5392	706	6	abo	abo	PROPN
ejpam-5392	706	7	-	-	PUNCT
ejpam-5392	706	8	tabl	tabl	NOUN
ejpam-5392	706	9	.	.	PUNCT
ejpam-5392	707	1	a	a	DET
ejpam-5392	707	2	comparison	comparison	NOUN
ejpam-5392	707	3	of	of	ADP
ejpam-5392	707	4	two	two	NUM
ejpam-5392	707	5	kinds	kind	NOUN
ejpam-5392	707	6	of	of	ADP
ejpam-5392	707	7	definitions	definition	NOUN
ejpam-5392	707	8	of	of	ADP
ejpam-5392	707	9	rough	rough	ADJ
ejpam-5392	707	10	approximations	approximation	NOUN
ejpam-5392	707	11	based	base	VERB
ejpam-5392	707	12	on	on	ADP
ejpam-5392	707	13	a	a	DET
ejpam-5392	707	14	similarity	similarity	NOUN
ejpam-5392	707	15	relation	relation	NOUN
ejpam-5392	707	16	.	.	PUNCT
ejpam-5392	708	1	information	information	NOUN
ejpam-5392	708	2	sciences	sciences	PROPN
ejpam-5392	708	3	,	,	PUNCT
ejpam-5392	708	4	181:2587–2596	181:2587–2596	NUM
ejpam-5392	708	5	,	,	PUNCT
ejpam-5392	708	6	2011	2011	NUM
ejpam-5392	708	7	.	.	PUNCT
ejpam-5392	709	1	[	[	X
ejpam-5392	709	2	4	4	X
ejpam-5392	709	3	]	]	PUNCT
ejpam-5392	709	4	e.	e.	PROPN
ejpam-5392	709	5	a.	a.	PROPN
ejpam-5392	709	6	abo	abo	PROPN
ejpam-5392	709	7	-	-	PUNCT
ejpam-5392	709	8	tabl	tabl	NOUN
ejpam-5392	709	9	.	.	PUNCT
ejpam-5392	710	1	rough	rough	ADJ
ejpam-5392	710	2	sets	set	NOUN
ejpam-5392	710	3	and	and	CCONJ
ejpam-5392	710	4	topological	topological	ADJ
ejpam-5392	710	5	spaces	space	NOUN
ejpam-5392	710	6	based	base	VERB
ejpam-5392	710	7	on	on	ADP
ejpam-5392	710	8	similarity	similarity	NOUN
ejpam-5392	710	9	.	.	PUNCT
ejpam-5392	711	1	international	international	ADJ
ejpam-5392	711	2	journal	journal	PROPN
ejpam-5392	711	3	of	of	ADP
ejpam-5392	711	4	machine	machine	NOUN
ejpam-5392	711	5	learning	learning	NOUN
ejpam-5392	711	6	and	and	CCONJ
ejpam-5392	711	7	cybernetics	cybernetic	NOUN
ejpam-5392	711	8	,	,	PUNCT
ejpam-5392	711	9	4:451–458	4:451–458	NOUN
ejpam-5392	711	10	,	,	PUNCT
ejpam-5392	711	11	2013	2013	NUM
ejpam-5392	711	12	.	.	PUNCT
ejpam-5392	712	1	[	[	X
ejpam-5392	712	2	5	5	X
ejpam-5392	712	3	]	]	PUNCT
ejpam-5392	712	4	t.	t.	PROPN
ejpam-5392	712	5	m.	m.	PROPN
ejpam-5392	712	6	al	al	PROPN
ejpam-5392	712	7	-	-	PUNCT
ejpam-5392	712	8	shami	shami	PROPN
ejpam-5392	712	9	.	.	PUNCT
ejpam-5392	713	1	an	an	DET
ejpam-5392	713	2	improvement	improvement	NOUN
ejpam-5392	713	3	of	of	ADP
ejpam-5392	713	4	rough	rough	ADJ
ejpam-5392	713	5	sets	set	NOUN
ejpam-5392	713	6	’	'	PUNCT
ejpam-5392	713	7	accuracy	accuracy	NOUN
ejpam-5392	713	8	measure	measure	NOUN
ejpam-5392	713	9	using	use	VERB
ejpam-5392	713	10	containment	containment	NOUN
ejpam-5392	713	11	neighborhoods	neighborhood	NOUN
ejpam-5392	713	12	with	with	ADP
ejpam-5392	713	13	a	a	DET
ejpam-5392	713	14	medical	medical	ADJ
ejpam-5392	713	15	application	application	NOUN
ejpam-5392	713	16	.	.	PUNCT
ejpam-5392	714	1	information	information	NOUN
ejpam-5392	714	2	sciences	sciences	PROPN
ejpam-5392	714	3	,	,	PUNCT
ejpam-5392	714	4	569:110–124	569:110–124	NUM
ejpam-5392	714	5	,	,	PUNCT
ejpam-5392	714	6	2021	2021	NUM
ejpam-5392	714	7	.	.	PUNCT
ejpam-5392	715	1	[	[	X
ejpam-5392	715	2	6	6	NUM
ejpam-5392	715	3	]	]	PUNCT
ejpam-5392	715	4	t.	t.	PROPN
ejpam-5392	715	5	m.	m.	PROPN
ejpam-5392	715	6	al	al	PROPN
ejpam-5392	715	7	-	-	PUNCT
ejpam-5392	715	8	shami	shami	PROPN
ejpam-5392	715	9	.	.	PUNCT
ejpam-5392	716	1	improvement	improvement	NOUN
ejpam-5392	716	2	of	of	ADP
ejpam-5392	716	3	the	the	DET
ejpam-5392	716	4	approximations	approximation	NOUN
ejpam-5392	716	5	and	and	CCONJ
ejpam-5392	716	6	accuracy	accuracy	NOUN
ejpam-5392	716	7	measure	measure	NOUN
ejpam-5392	716	8	of	of	ADP
ejpam-5392	716	9	a	a	DET
ejpam-5392	716	10	rough	rough	ADJ
ejpam-5392	716	11	set	set	NOUN
ejpam-5392	716	12	using	use	VERB
ejpam-5392	716	13	somewhere	somewhere	ADV
ejpam-5392	716	14	dense	dense	ADJ
ejpam-5392	716	15	sets	set	NOUN
ejpam-5392	716	16	.	.	PUNCT
ejpam-5392	717	1	soft	soft	ADJ
ejpam-5392	717	2	computing	computing	NOUN
ejpam-5392	717	3	,	,	PUNCT
ejpam-5392	717	4	25(23):14449–14460	25(23):14449–14460	NUM
ejpam-5392	717	5	,	,	PUNCT
ejpam-5392	717	6	2021	2021	NUM
ejpam-5392	717	7	.	.	PUNCT
ejpam-5392	718	1	[	[	X
ejpam-5392	718	2	7	7	X
ejpam-5392	718	3	]	]	PUNCT
ejpam-5392	718	4	t.	t.	PROPN
ejpam-5392	718	5	m.	m.	PROPN
ejpam-5392	718	6	al	al	PROPN
ejpam-5392	718	7	-	-	PUNCT
ejpam-5392	718	8	shami	shami	PROPN
ejpam-5392	718	9	.	.	PUNCT
ejpam-5392	719	1	topological	topological	ADJ
ejpam-5392	719	2	approach	approach	NOUN
ejpam-5392	719	3	to	to	PART
ejpam-5392	719	4	generate	generate	VERB
ejpam-5392	719	5	new	new	ADJ
ejpam-5392	719	6	rough	rough	ADJ
ejpam-5392	719	7	set	set	NOUN
ejpam-5392	719	8	models	model	NOUN
ejpam-5392	719	9	.	.	PUNCT
ejpam-5392	720	1	complex	complex	ADJ
ejpam-5392	720	2	&	&	CCONJ
ejpam-5392	720	3	intelligent	intelligent	ADJ
ejpam-5392	720	4	systems	system	NOUN
ejpam-5392	720	5	,	,	PUNCT
ejpam-5392	720	6	8:4101–4113	8:4101–4113	NUM
ejpam-5392	720	7	,	,	PUNCT
ejpam-5392	720	8	2022	2022	NUM
ejpam-5392	720	9	.	.	PUNCT
ejpam-5392	721	1	[	[	X
ejpam-5392	721	2	8	8	X
ejpam-5392	721	3	]	]	PUNCT
ejpam-5392	721	4	t.	t.	PROPN
ejpam-5392	721	5	m.	m.	PROPN
ejpam-5392	721	6	al	al	PROPN
ejpam-5392	721	7	-	-	PUNCT
ejpam-5392	721	8	shami	shami	PROPN
ejpam-5392	721	9	.	.	PUNCT
ejpam-5392	722	1	maximal	maximal	ADJ
ejpam-5392	722	2	rough	rough	ADJ
ejpam-5392	722	3	neighborhoods	neighborhood	NOUN
ejpam-5392	722	4	with	with	ADP
ejpam-5392	722	5	a	a	DET
ejpam-5392	722	6	medical	medical	ADJ
ejpam-5392	722	7	application	application	NOUN
ejpam-5392	722	8	.	.	PUNCT
ejpam-5392	723	1	journal	journal	PROPN
ejpam-5392	723	2	of	of	ADP
ejpam-5392	723	3	ambient	ambient	ADJ
ejpam-5392	723	4	intelligence	intelligence	NOUN
ejpam-5392	723	5	and	and	CCONJ
ejpam-5392	723	6	humanized	humanize	VERB
ejpam-5392	723	7	computing	computing	NOUN
ejpam-5392	723	8	,	,	PUNCT
ejpam-5392	723	9	14(12):16373–16384	14(12):16373–16384	NUM
ejpam-5392	723	10	,	,	PUNCT
ejpam-5392	723	11	2023	2023	NUM
ejpam-5392	723	12	.	.	PUNCT
ejpam-5392	724	1	references	reference	NOUN
ejpam-5392	724	2	3461	3461	NUM
ejpam-5392	724	3	[	[	X
ejpam-5392	724	4	9	9	NUM
ejpam-5392	724	5	]	]	PUNCT
ejpam-5392	724	6	t.	t.	PROPN
ejpam-5392	724	7	m.	m.	PROPN
ejpam-5392	724	8	al	al	PROPN
ejpam-5392	724	9	-	-	PUNCT
ejpam-5392	724	10	shami	shami	PROPN
ejpam-5392	724	11	and	and	CCONJ
ejpam-5392	724	12	i.	i.	PROPN
ejpam-5392	724	13	alshammari	alshammari	PROPN
ejpam-5392	724	14	.	.	PUNCT
ejpam-5392	725	1	rough	rough	ADJ
ejpam-5392	725	2	sets	set	NOUN
ejpam-5392	725	3	models	model	NOUN
ejpam-5392	725	4	inspired	inspire	VERB
ejpam-5392	725	5	by	by	ADP
ejpam-5392	725	6	supra	supra	ADJ
ejpam-5392	725	7	-	-	PUNCT
ejpam-5392	725	8	topology	topology	NOUN
ejpam-5392	725	9	structures	structure	NOUN
ejpam-5392	725	10	.	.	PUNCT
ejpam-5392	726	1	artificial	artificial	ADJ
ejpam-5392	726	2	intelligence	intelligence	NOUN
ejpam-5392	726	3	review	review	NOUN
ejpam-5392	726	4	,	,	PUNCT
ejpam-5392	726	5	56(7):6855–6883	56(7):6855–6883	NUM
ejpam-5392	726	6	,	,	PUNCT
ejpam-5392	726	7	2023	2023	NUM
ejpam-5392	726	8	.	.	PUNCT
ejpam-5392	727	1	[	[	X
ejpam-5392	727	2	10	10	NUM
ejpam-5392	727	3	]	]	PUNCT
ejpam-5392	727	4	t.	t.	PROPN
ejpam-5392	727	5	m.	m.	PROPN
ejpam-5392	727	6	al	al	PROPN
ejpam-5392	727	7	-	-	PUNCT
ejpam-5392	727	8	shami	shami	PROPN
ejpam-5392	727	9	and	and	CCONJ
ejpam-5392	727	10	d.	d.	PROPN
ejpam-5392	727	11	ciucci	ciucci	PROPN
ejpam-5392	727	12	.	.	PUNCT
ejpam-5392	728	1	subset	subset	ADJ
ejpam-5392	728	2	neighborhood	neighborhood	NOUN
ejpam-5392	728	3	rough	rough	ADJ
ejpam-5392	728	4	sets	set	NOUN
ejpam-5392	728	5	.	.	PUNCT
ejpam-5392	729	1	knowledge	knowledge	NOUN
ejpam-5392	729	2	-	-	PUNCT
ejpam-5392	729	3	based	base	VERB
ejpam-5392	729	4	systems	system	NOUN
ejpam-5392	729	5	,	,	PUNCT
ejpam-5392	729	6	237(5):107868	237(5):107868	NOUN
ejpam-5392	729	7	,	,	PUNCT
ejpam-5392	729	8	2022	2022	NUM
ejpam-5392	729	9	.	.	PUNCT
ejpam-5392	730	1	[	[	X
ejpam-5392	730	2	11	11	NUM
ejpam-5392	730	3	]	]	PUNCT
ejpam-5392	730	4	t.	t.	PROPN
ejpam-5392	730	5	m.	m.	PROPN
ejpam-5392	730	6	al	al	PROPN
ejpam-5392	730	7	-	-	PUNCT
ejpam-5392	730	8	shami	shami	PROPN
ejpam-5392	730	9	and	and	CCONJ
ejpam-5392	730	10	m.	m.	PROPN
ejpam-5392	730	11	hosny	hosny	PROPN
ejpam-5392	730	12	.	.	PUNCT
ejpam-5392	731	1	generalized	generalized	ADJ
ejpam-5392	731	2	approximation	approximation	NOUN
ejpam-5392	731	3	spaces	space	NOUN
ejpam-5392	731	4	generation	generation	NOUN
ejpam-5392	731	5	from	from	ADP
ejpam-5392	731	6	ij	ij	NOUN
ejpam-5392	731	7	-	-	PUNCT
ejpam-5392	731	8	neighborhoods	neighborhood	NOUN
ejpam-5392	731	9	and	and	CCONJ
ejpam-5392	731	10	ideals	ideal	NOUN
ejpam-5392	731	11	with	with	ADP
ejpam-5392	731	12	application	application	NOUN
ejpam-5392	731	13	to	to	ADP
ejpam-5392	731	14	chikungunya	chikungunya	NOUN
ejpam-5392	731	15	disease	disease	NOUN
ejpam-5392	731	16	.	.	PUNCT
ejpam-5392	732	1	aims	aim	VERB
ejpam-5392	732	2	mathematics	mathematic	NOUN
ejpam-5392	732	3	,	,	PUNCT
ejpam-5392	732	4	9(4):10050–10077	9(4):10050–10077	NUM
ejpam-5392	732	5	,	,	PUNCT
ejpam-5392	732	6	2024	2024	NUM
ejpam-5392	732	7	.	.	PUNCT
ejpam-5392	733	1	[	[	X
ejpam-5392	733	2	12	12	NUM
ejpam-5392	733	3	]	]	PUNCT
ejpam-5392	733	4	t.	t.	PROPN
ejpam-5392	733	5	m.	m.	PROPN
ejpam-5392	733	6	al	al	PROPN
ejpam-5392	733	7	-	-	PUNCT
ejpam-5392	733	8	shami	shami	PROPN
ejpam-5392	733	9	,	,	PUNCT
ejpam-5392	733	10	h.	h.	PROPN
ejpam-5392	733	11	işık	işık	PROPN
ejpam-5392	733	12	,	,	PUNCT
ejpam-5392	733	13	a.	a.	PROPN
ejpam-5392	733	14	s.	s.	PROPN
ejpam-5392	733	15	nawar	nawar	PROPN
ejpam-5392	733	16	,	,	PUNCT
ejpam-5392	733	17	and	and	CCONJ
ejpam-5392	733	18	r.	r.	PROPN
ejpam-5392	733	19	a.	a.	PROPN
ejpam-5392	733	20	hosny	hosny	PROPN
ejpam-5392	733	21	.	.	PUNCT
ejpam-5392	734	1	some	some	DET
ejpam-5392	734	2	topological	topological	ADJ
ejpam-5392	734	3	approaches	approach	NOUN
ejpam-5392	734	4	for	for	ADP
ejpam-5392	734	5	generalized	generalized	ADJ
ejpam-5392	734	6	rough	rough	ADJ
ejpam-5392	734	7	sets	set	NOUN
ejpam-5392	734	8	via	via	ADP
ejpam-5392	734	9	ideals	ideal	NOUN
ejpam-5392	734	10	.	.	PUNCT
ejpam-5392	735	1	mathematical	mathematical	ADJ
ejpam-5392	735	2	problems	problem	NOUN
ejpam-5392	735	3	in	in	ADP
ejpam-5392	735	4	engineering	engineering	NOUN
ejpam-5392	735	5	,	,	PUNCT
ejpam-5392	735	6	2021:5642982	2021:5642982	NUM
ejpam-5392	735	7	,	,	PUNCT
ejpam-5392	735	8	2021	2021	NUM
ejpam-5392	735	9	.	.	PUNCT
ejpam-5392	736	1	[	[	X
ejpam-5392	736	2	13	13	NUM
ejpam-5392	736	3	]	]	PUNCT
ejpam-5392	736	4	t.	t.	PROPN
ejpam-5392	736	5	m.	m.	PROPN
ejpam-5392	736	6	al	al	PROPN
ejpam-5392	736	7	-	-	PUNCT
ejpam-5392	736	8	shami	shami	PROPN
ejpam-5392	736	9	and	and	CCONJ
ejpam-5392	736	10	a.	a.	PROPN
ejpam-5392	736	11	mhemdi	mhemdi	PROPN
ejpam-5392	736	12	.	.	PUNCT
ejpam-5392	737	1	approximation	approximation	NOUN
ejpam-5392	737	2	operators	operator	NOUN
ejpam-5392	737	3	and	and	CCONJ
ejpam-5392	737	4	accuracy	accuracy	NOUN
ejpam-5392	737	5	measures	measure	NOUN
ejpam-5392	737	6	of	of	ADP
ejpam-5392	737	7	rough	rough	ADJ
ejpam-5392	737	8	sets	set	NOUN
ejpam-5392	737	9	from	from	ADP
ejpam-5392	737	10	an	an	DET
ejpam-5392	737	11	infra	infra	NOUN
ejpam-5392	737	12	-	-	PUNCT
ejpam-5392	737	13	topology	topology	NOUN
ejpam-5392	737	14	view	view	NOUN
ejpam-5392	737	15	.	.	PUNCT
ejpam-5392	738	1	soft	soft	ADJ
ejpam-5392	738	2	computing	computing	NOUN
ejpam-5392	738	3	,	,	PUNCT
ejpam-5392	738	4	27:1317–1330	27:1317–1330	NUM
ejpam-5392	738	5	,	,	PUNCT
ejpam-5392	738	6	2023	2023	NUM
ejpam-5392	738	7	.	.	PUNCT
ejpam-5392	739	1	[	[	X
ejpam-5392	739	2	14	14	NUM
ejpam-5392	739	3	]	]	PUNCT
ejpam-5392	739	4	t.	t.	PROPN
ejpam-5392	739	5	m.	m.	PROPN
ejpam-5392	739	6	al	al	PROPN
ejpam-5392	739	7	-	-	PUNCT
ejpam-5392	739	8	shami	shami	PROPN
ejpam-5392	739	9	and	and	CCONJ
ejpam-5392	739	10	a.	a.	NOUN
ejpam-5392	739	11	mhemdi	mhemdi	PROPN
ejpam-5392	739	12	.	.	PUNCT
ejpam-5392	740	1	overlapping	overlap	VERB
ejpam-5392	740	2	containment	containment	NOUN
ejpam-5392	740	3	rough	rough	ADJ
ejpam-5392	740	4	neighborhoods	neighborhood	NOUN
ejpam-5392	740	5	and	and	CCONJ
ejpam-5392	740	6	their	their	PRON
ejpam-5392	740	7	generalized	generalized	ADJ
ejpam-5392	740	8	approximation	approximation	NOUN
ejpam-5392	740	9	spaces	space	NOUN
ejpam-5392	740	10	with	with	ADP
ejpam-5392	740	11	applications	application	NOUN
ejpam-5392	740	12	.	.	PUNCT
ejpam-5392	741	1	journal	journal	NOUN
ejpam-5392	741	2	of	of	ADP
ejpam-5392	741	3	applied	apply	VERB
ejpam-5392	741	4	mathematics	mathematic	NOUN
ejpam-5392	741	5	and	and	CCONJ
ejpam-5392	741	6	computing	computing	NOUN
ejpam-5392	741	7	,	,	PUNCT
ejpam-5392	741	8	2024	2024	NUM
ejpam-5392	741	9	.	.	PUNCT
ejpam-5392	742	1	[	[	X
ejpam-5392	742	2	15	15	NUM
ejpam-5392	742	3	]	]	X
ejpam-5392	742	4	w.	w.	PROPN
ejpam-5392	742	5	s.	s.	PROPN
ejpam-5392	742	6	amer	amer	PROPN
ejpam-5392	742	7	,	,	PUNCT
ejpam-5392	742	8	m.	m.	NOUN
ejpam-5392	742	9	i.	i.	PROPN
ejpam-5392	742	10	abbas	abbas	PROPN
ejpam-5392	742	11	,	,	PUNCT
ejpam-5392	742	12	and	and	CCONJ
ejpam-5392	742	13	m.	m.	PROPN
ejpam-5392	742	14	k.	k.	PROPN
ejpam-5392	743	1	el	el	PROPN
ejpam-5392	743	2	-	-	PROPN
ejpam-5392	743	3	bably	bably	ADV
ejpam-5392	743	4	.	.	PUNCT
ejpam-5392	744	1	on	on	ADP
ejpam-5392	744	2	j	j	PROPN
ejpam-5392	744	3	-	-	PUNCT
ejpam-5392	744	4	nearly	nearly	ADV
ejpam-5392	744	5	concepts	concept	NOUN
ejpam-5392	744	6	in	in	ADP
ejpam-5392	744	7	rough	rough	ADJ
ejpam-5392	744	8	sets	set	NOUN
ejpam-5392	744	9	with	with	ADP
ejpam-5392	744	10	some	some	DET
ejpam-5392	744	11	applications	application	NOUN
ejpam-5392	744	12	.	.	PUNCT
ejpam-5392	745	1	international	international	ADJ
ejpam-5392	745	2	journal	journal	NOUN
ejpam-5392	745	3	of	of	ADP
ejpam-5392	745	4	fuzzy	fuzzy	ADJ
ejpam-5392	745	5	intelligence	intelligence	NOUN
ejpam-5392	745	6	systems	system	NOUN
ejpam-5392	745	7	,	,	PUNCT
ejpam-5392	745	8	32:1089	32:1089	NUM
ejpam-5392	745	9	–	–	PUNCT
ejpam-5392	745	10	1099	1099	NUM
ejpam-5392	745	11	,	,	PUNCT
ejpam-5392	745	12	2017	2017	NUM
ejpam-5392	745	13	.	.	PUNCT
ejpam-5392	746	1	[	[	X
ejpam-5392	746	2	16	16	NUM
ejpam-5392	746	3	]	]	PUNCT
ejpam-5392	746	4	j.	j.	PROPN
ejpam-5392	746	5	dai	dai	PROPN
ejpam-5392	746	6	,	,	PUNCT
ejpam-5392	746	7	s.	s.	PROPN
ejpam-5392	746	8	gao	gao	PROPN
ejpam-5392	746	9	,	,	PUNCT
ejpam-5392	746	10	and	and	CCONJ
ejpam-5392	746	11	g.	g.	PROPN
ejpam-5392	746	12	zheng	zheng	PROPN
ejpam-5392	746	13	.	.	PUNCT
ejpam-5392	747	1	generalized	generalize	VERB
ejpam-5392	747	2	rough	rough	ADJ
ejpam-5392	747	3	set	set	NOUN
ejpam-5392	747	4	models	model	NOUN
ejpam-5392	747	5	determined	determine	VERB
ejpam-5392	747	6	by	by	ADP
ejpam-5392	747	7	multiple	multiple	ADJ
ejpam-5392	747	8	neighborhoods	neighborhood	NOUN
ejpam-5392	747	9	generated	generate	VERB
ejpam-5392	747	10	from	from	ADP
ejpam-5392	747	11	a	a	DET
ejpam-5392	747	12	similarity	similarity	NOUN
ejpam-5392	747	13	relation	relation	NOUN
ejpam-5392	747	14	.	.	PUNCT
ejpam-5392	748	1	soft	soft	ADJ
ejpam-5392	748	2	computing	computing	NOUN
ejpam-5392	748	3	,	,	PUNCT
ejpam-5392	748	4	13:2081–2094	13:2081–2094	NUM
ejpam-5392	748	5	,	,	PUNCT
ejpam-5392	748	6	2018	2018	NUM
ejpam-5392	748	7	.	.	PUNCT
ejpam-5392	749	1	[	[	X
ejpam-5392	749	2	17	17	NUM
ejpam-5392	749	3	]	]	X
ejpam-5392	749	4	s.	s.	PROPN
ejpam-5392	749	5	demiralp	demiralp	PROPN
ejpam-5392	749	6	,	,	PUNCT
ejpam-5392	749	7	t.	t.	PROPN
ejpam-5392	749	8	m.	m.	PROPN
ejpam-5392	749	9	al	al	PROPN
ejpam-5392	749	10	-	-	PUNCT
ejpam-5392	749	11	shami	shami	PROPN
ejpam-5392	749	12	,	,	PUNCT
ejpam-5392	749	13	a.	a.	NOUN
ejpam-5392	749	14	m.	m.	PROPN
ejpam-5392	749	15	abd	abd	PROPN
ejpam-5392	749	16	el	el	PROPN
ejpam-5392	749	17	-	-	PROPN
ejpam-5392	749	18	latif	latif	PROPN
ejpam-5392	749	19	,	,	PUNCT
ejpam-5392	749	20	and	and	CCONJ
ejpam-5392	749	21	f.	f.	PROPN
ejpam-5392	749	22	a.	a.	PROPN
ejpam-5392	749	23	abu	abu	PROPN
ejpam-5392	749	24	shaheen	shaheen	PROPN
ejpam-5392	749	25	.	.	PUNCT
ejpam-5392	750	1	topologically	topologically	ADV
ejpam-5392	750	2	indistinguishable	indistinguishable	ADJ
ejpam-5392	750	3	relations	relation	NOUN
ejpam-5392	750	4	and	and	CCONJ
ejpam-5392	750	5	separation	separation	NOUN
ejpam-5392	750	6	axioms	axiom	NOUN
ejpam-5392	750	7	.	.	PUNCT
ejpam-5392	751	1	aims	aim	VERB
ejpam-5392	751	2	mathematics	mathematic	NOUN
ejpam-5392	751	3	,	,	PUNCT
ejpam-5392	751	4	9(6):15701–15723	9(6):15701–15723	PROPN
ejpam-5392	751	5	,	,	PUNCT
ejpam-5392	751	6	2024	2024	NUM
ejpam-5392	751	7	.	.	PUNCT
ejpam-5392	752	1	[	[	X
ejpam-5392	752	2	18	18	NUM
ejpam-5392	752	3	]	]	PUNCT
ejpam-5392	752	4	m.	m.	NOUN
ejpam-5392	752	5	m.	m.	PROPN
ejpam-5392	752	6	el	el	PROPN
ejpam-5392	752	7	-	-	PROPN
ejpam-5392	752	8	sharkasy	sharkasy	PROPN
ejpam-5392	752	9	.	.	PUNCT
ejpam-5392	753	1	minimal	minimal	ADJ
ejpam-5392	753	2	structure	structure	NOUN
ejpam-5392	753	3	approximation	approximation	NOUN
ejpam-5392	753	4	space	space	NOUN
ejpam-5392	753	5	and	and	CCONJ
ejpam-5392	753	6	some	some	PRON
ejpam-5392	753	7	of	of	ADP
ejpam-5392	753	8	its	its	PRON
ejpam-5392	753	9	applications	application	NOUN
ejpam-5392	753	10	.	.	PUNCT
ejpam-5392	754	1	journal	journal	NOUN
ejpam-5392	754	2	of	of	ADP
ejpam-5392	754	3	intelligent	intelligent	ADJ
ejpam-5392	754	4	&	&	CCONJ
ejpam-5392	754	5	fuzzy	fuzzy	ADJ
ejpam-5392	754	6	systems	system	NOUN
ejpam-5392	754	7	,	,	PUNCT
ejpam-5392	754	8	40(1):973–982	40(1):973–982	NOUN
ejpam-5392	754	9	,	,	PUNCT
ejpam-5392	754	10	2021	2021	NUM
ejpam-5392	754	11	.	.	PUNCT
ejpam-5392	755	1	[	[	X
ejpam-5392	755	2	19	19	NUM
ejpam-5392	755	3	]	]	X
ejpam-5392	755	4	n.	n.	PROPN
ejpam-5392	755	5	e.	e.	PROPN
ejpam-5392	755	6	el	el	PROPN
ejpam-5392	755	7	-	-	PUNCT
ejpam-5392	755	8	tayar	tayar	PROPN
ejpam-5392	755	9	,	,	PUNCT
ejpam-5392	755	10	r.	r.	PROPN
ejpam-5392	755	11	s.	s.	PROPN
ejpam-5392	755	12	tsai	tsai	PROPN
ejpam-5392	755	13	,	,	PUNCT
ejpam-5392	755	14	p.	p.	PROPN
ejpam-5392	755	15	a.	a.	NOUN
ejpam-5392	755	16	carrupt	carrupt	PROPN
ejpam-5392	755	17	,	,	PUNCT
ejpam-5392	755	18	and	and	CCONJ
ejpam-5392	755	19	b.	b.	PROPN
ejpam-5392	755	20	testa	testa	PROPN
ejpam-5392	755	21	.	.	PUNCT
ejpam-5392	756	1	octan-1	octan-1	NUM
ejpam-5392	756	2	-	-	PUNCT
ejpam-5392	756	3	ol	ol	ADP
ejpam-5392	756	4	-	-	PUNCT
ejpam-5392	756	5	water	water	NOUN
ejpam-5392	756	6	partition	partition	NOUN
ejpam-5392	756	7	coefficients	coefficient	NOUN
ejpam-5392	756	8	of	of	ADP
ejpam-5392	756	9	zwitterionic	zwitterionic	ADJ
ejpam-5392	756	10	α	α	NOUN
ejpam-5392	756	11	-	-	ADJ
ejpam-5392	756	12	amino	amino	ADJ
ejpam-5392	756	13	acids	acid	NOUN
ejpam-5392	756	14	.	.	PUNCT
ejpam-5392	757	1	determination	determination	NOUN
ejpam-5392	757	2	by	by	ADP
ejpam-5392	757	3	centrifugal	centrifugal	ADJ
ejpam-5392	757	4	partition	partition	NOUN
ejpam-5392	757	5	chromatography	chromatography	NOUN
ejpam-5392	757	6	and	and	CCONJ
ejpam-5392	757	7	factorization	factorization	NOUN
ejpam-5392	757	8	into	into	ADP
ejpam-5392	757	9	steric	steric	ADJ
ejpam-5392	757	10	/	/	SYM
ejpam-5392	757	11	hydrophobic	hydrophobic	NOUN
ejpam-5392	757	12	and	and	CCONJ
ejpam-5392	757	13	polar	polar	ADJ
ejpam-5392	757	14	components	component	NOUN
ejpam-5392	757	15	.	.	PUNCT
ejpam-5392	758	1	journal	journal	NOUN
ejpam-5392	758	2	of	of	ADP
ejpam-5392	758	3	the	the	DET
ejpam-5392	758	4	chemical	chemical	NOUN
ejpam-5392	758	5	society	society	NOUN
ejpam-5392	758	6	,	,	PUNCT
ejpam-5392	758	7	2:79–84	2:79–84	NOUN
ejpam-5392	758	8	,	,	PUNCT
ejpam-5392	758	9	1992	1992	NUM
ejpam-5392	758	10	.	.	PUNCT
ejpam-5392	759	1	[	[	X
ejpam-5392	759	2	20	20	NUM
ejpam-5392	759	3	]	]	PUNCT
ejpam-5392	759	4	m.	m.	PROPN
ejpam-5392	759	5	hosny	hosny	PROPN
ejpam-5392	759	6	.	.	PUNCT
ejpam-5392	760	1	on	on	ADP
ejpam-5392	760	2	generalization	generalization	NOUN
ejpam-5392	760	3	of	of	ADP
ejpam-5392	760	4	rough	rough	ADJ
ejpam-5392	760	5	sets	set	NOUN
ejpam-5392	760	6	by	by	ADP
ejpam-5392	760	7	using	use	VERB
ejpam-5392	760	8	two	two	NUM
ejpam-5392	760	9	different	different	ADJ
ejpam-5392	760	10	methods	method	NOUN
ejpam-5392	760	11	.	.	PUNCT
ejpam-5392	761	1	journal	journal	NOUN
ejpam-5392	761	2	of	of	ADP
ejpam-5392	761	3	intelligent	intelligent	ADJ
ejpam-5392	761	4	&	&	CCONJ
ejpam-5392	761	5	fuzzy	fuzzy	ADJ
ejpam-5392	761	6	systems	system	NOUN
ejpam-5392	761	7	,	,	PUNCT
ejpam-5392	761	8	35:979–993	35:979–993	NUM
ejpam-5392	761	9	,	,	PUNCT
ejpam-5392	761	10	2018	2018	NUM
ejpam-5392	761	11	.	.	PUNCT
ejpam-5392	762	1	[	[	X
ejpam-5392	762	2	21	21	NUM
ejpam-5392	762	3	]	]	X
ejpam-5392	762	4	m.	m.	PROPN
ejpam-5392	762	5	hosny	hosny	PROPN
ejpam-5392	762	6	.	.	PUNCT
ejpam-5392	763	1	idealization	idealization	NOUN
ejpam-5392	763	2	of	of	ADP
ejpam-5392	763	3	j	j	NOUN
ejpam-5392	763	4	-	-	PUNCT
ejpam-5392	763	5	approximation	approximation	NOUN
ejpam-5392	763	6	spaces	space	NOUN
ejpam-5392	763	7	.	.	PUNCT
ejpam-5392	764	1	filomat	filomat	NOUN
ejpam-5392	764	2	,	,	PUNCT
ejpam-5392	764	3	34:287–301	34:287–301	PROPN
ejpam-5392	764	4	,	,	PUNCT
ejpam-5392	764	5	2020	2020	NUM
ejpam-5392	764	6	.	.	PUNCT
ejpam-5392	765	1	[	[	X
ejpam-5392	765	2	22	22	NUM
ejpam-5392	765	3	]	]	PUNCT
ejpam-5392	765	4	m.	m.	PROPN
ejpam-5392	765	5	hosny	hosny	PROPN
ejpam-5392	765	6	.	.	PUNCT
ejpam-5392	766	1	topological	topological	ADJ
ejpam-5392	766	2	approach	approach	NOUN
ejpam-5392	766	3	for	for	ADP
ejpam-5392	766	4	rough	rough	ADJ
ejpam-5392	766	5	sets	set	NOUN
ejpam-5392	766	6	by	by	ADP
ejpam-5392	766	7	using	use	VERB
ejpam-5392	766	8	j	j	NOUN
ejpam-5392	766	9	-	-	PUNCT
ejpam-5392	766	10	nearly	nearly	ADV
ejpam-5392	766	11	concepts	concept	NOUN
ejpam-5392	766	12	via	via	ADP
ejpam-5392	766	13	ideals	ideal	NOUN
ejpam-5392	766	14	.	.	PUNCT
ejpam-5392	767	1	filomat	filomat	NOUN
ejpam-5392	767	2	,	,	PUNCT
ejpam-5392	767	3	34:273–286	34:273–286	NUM
ejpam-5392	767	4	,	,	PUNCT
ejpam-5392	767	5	2020	2020	NUM
ejpam-5392	767	6	.	.	PUNCT
ejpam-5392	768	1	references	reference	NOUN
ejpam-5392	768	2	3462	3462	NUM
ejpam-5392	768	3	[	[	X
ejpam-5392	768	4	23	23	NUM
ejpam-5392	768	5	]	]	PUNCT
ejpam-5392	768	6	m.	m.	PROPN
ejpam-5392	768	7	hosny	hosny	PROPN
ejpam-5392	768	8	.	.	PUNCT
ejpam-5392	769	1	rough	rough	ADJ
ejpam-5392	769	2	sets	set	NOUN
ejpam-5392	769	3	theory	theory	NOUN
ejpam-5392	769	4	via	via	ADP
ejpam-5392	769	5	new	new	ADJ
ejpam-5392	769	6	topological	topological	ADJ
ejpam-5392	769	7	notions	notion	NOUN
ejpam-5392	769	8	based	base	VERB
ejpam-5392	769	9	on	on	ADP
ejpam-5392	769	10	ideals	ideal	NOUN
ejpam-5392	769	11	and	and	CCONJ
ejpam-5392	769	12	applications	application	NOUN
ejpam-5392	769	13	.	.	PUNCT
ejpam-5392	770	1	aims	aim	VERB
ejpam-5392	770	2	mathematics	mathematic	NOUN
ejpam-5392	770	3	,	,	PUNCT
ejpam-5392	770	4	7:869–902	7:869–902	NUM
ejpam-5392	770	5	,	,	PUNCT
ejpam-5392	770	6	2021	2021	NUM
ejpam-5392	770	7	.	.	PUNCT
ejpam-5392	771	1	[	[	X
ejpam-5392	771	2	24	24	NUM
ejpam-5392	771	3	]	]	PUNCT
ejpam-5392	771	4	m.	m.	NOUN
ejpam-5392	771	5	hosny	hosny	PROPN
ejpam-5392	771	6	,	,	PUNCT
ejpam-5392	771	7	t.	t.	PROPN
ejpam-5392	771	8	m.	m.	PROPN
ejpam-5392	771	9	al	al	PROPN
ejpam-5392	771	10	-	-	PUNCT
ejpam-5392	771	11	shami	shami	PROPN
ejpam-5392	771	12	,	,	PUNCT
ejpam-5392	771	13	and	and	CCONJ
ejpam-5392	771	14	a.	a.	NOUN
ejpam-5392	771	15	mhemdi	mhemdi	PROPN
ejpam-5392	771	16	.	.	PUNCT
ejpam-5392	772	1	rough	rough	ADJ
ejpam-5392	772	2	approximation	approximation	NOUN
ejpam-5392	772	3	spaces	space	NOUN
ejpam-5392	772	4	via	via	ADP
ejpam-5392	772	5	maximal	maximal	ADJ
ejpam-5392	772	6	union	union	NOUN
ejpam-5392	772	7	neighborhoods	neighborhood	NOUN
ejpam-5392	772	8	and	and	CCONJ
ejpam-5392	772	9	ideals	ideal	NOUN
ejpam-5392	772	10	with	with	ADP
ejpam-5392	772	11	a	a	DET
ejpam-5392	772	12	medical	medical	ADJ
ejpam-5392	772	13	application	application	NOUN
ejpam-5392	772	14	.	.	PUNCT
ejpam-5392	773	1	journal	journal	NOUN
ejpam-5392	773	2	of	of	ADP
ejpam-5392	773	3	mathematics	mathematic	NOUN
ejpam-5392	773	4	,	,	PUNCT
ejpam-5392	773	5	2022:17	2022:17	NUM
ejpam-5392	773	6	pages	page	NOUN
ejpam-5392	773	7	,	,	PUNCT
ejpam-5392	773	8	2022	2022	NUM
ejpam-5392	773	9	.	.	PUNCT
ejpam-5392	774	1	[	[	X
ejpam-5392	774	2	25	25	NUM
ejpam-5392	774	3	]	]	X
ejpam-5392	774	4	r.	r.	PROPN
ejpam-5392	774	5	a.	a.	PROPN
ejpam-5392	774	6	hosny	hosny	PROPN
ejpam-5392	774	7	.	.	PUNCT
ejpam-5392	775	1	pre	pre	ADJ
ejpam-5392	775	2	-	-	ADJ
ejpam-5392	775	3	open	open	ADJ
ejpam-5392	775	4	sets	set	NOUN
ejpam-5392	775	5	with	with	ADP
ejpam-5392	775	6	ideal	ideal	ADJ
ejpam-5392	775	7	.	.	PUNCT
ejpam-5392	776	1	european	european	ADJ
ejpam-5392	776	2	journal	journal	PROPN
ejpam-5392	776	3	of	of	ADP
ejpam-5392	776	4	scientific	scientific	ADJ
ejpam-5392	776	5	research	research	NOUN
ejpam-5392	776	6	,	,	PUNCT
ejpam-5392	776	7	104(1):99–101	104(1):99–101	NUM
ejpam-5392	776	8	,	,	PUNCT
ejpam-5392	776	9	2013	2013	NUM
ejpam-5392	776	10	.	.	PUNCT
ejpam-5392	777	1	[	[	X
ejpam-5392	777	2	26	26	NUM
ejpam-5392	777	3	]	]	X
ejpam-5392	777	4	r.	r.	PROPN
ejpam-5392	777	5	a.	a.	PROPN
ejpam-5392	777	6	hosny	hosny	PROPN
ejpam-5392	777	7	and	and	CCONJ
ejpam-5392	777	8	d.	d.	PROPN
ejpam-5392	777	9	al	al	PROPN
ejpam-5392	777	10	-	-	PUNCT
ejpam-5392	777	11	kadi	kadi	PROPN
ejpam-5392	777	12	.	.	PUNCT
ejpam-5392	778	1	types	type	NOUN
ejpam-5392	778	2	of	of	ADP
ejpam-5392	778	3	generalized	generalized	ADJ
ejpam-5392	778	4	open	open	ADJ
ejpam-5392	778	5	sets	set	NOUN
ejpam-5392	778	6	with	with	ADP
ejpam-5392	778	7	ideal	ideal	ADJ
ejpam-5392	778	8	.	.	PUNCT
ejpam-5392	779	1	international	international	ADJ
ejpam-5392	779	2	journal	journal	PROPN
ejpam-5392	779	3	of	of	ADP
ejpam-5392	779	4	computer	computer	NOUN
ejpam-5392	779	5	applications	application	NOUN
ejpam-5392	779	6	,	,	PUNCT
ejpam-5392	779	7	80(4):11–14	80(4):11–14	NUM
ejpam-5392	779	8	,	,	PUNCT
ejpam-5392	779	9	2013	2013	NUM
ejpam-5392	779	10	.	.	PUNCT
ejpam-5392	780	1	[	[	X
ejpam-5392	780	2	27	27	NUM
ejpam-5392	780	3	]	]	X
ejpam-5392	780	4	r.	r.	PROPN
ejpam-5392	780	5	a.	a.	PROPN
ejpam-5392	780	6	hosny	hosny	PROPN
ejpam-5392	780	7	,	,	PUNCT
ejpam-5392	780	8	b.	b.	PROPN
ejpam-5392	780	9	a.	a.	PROPN
ejpam-5392	780	10	asaad	asaad	PROPN
ejpam-5392	780	11	,	,	PUNCT
ejpam-5392	780	12	a.	a.	NOUN
ejpam-5392	780	13	a.	a.	PROPN
ejpam-5392	780	14	azzam	azzam	PROPN
ejpam-5392	780	15	,	,	PUNCT
ejpam-5392	780	16	and	and	CCONJ
ejpam-5392	780	17	t.	t.	PROPN
ejpam-5392	780	18	m.	m.	PROPN
ejpam-5392	780	19	al	al	PROPN
ejpam-5392	780	20	-	-	PUNCT
ejpam-5392	780	21	shami	shami	PROPN
ejpam-5392	780	22	.	.	PUNCT
ejpam-5392	781	1	various	various	ADJ
ejpam-5392	781	2	topologies	topology	NOUN
ejpam-5392	781	3	generated	generate	VERB
ejpam-5392	781	4	from	from	ADP
ejpam-5392	781	5	ej	ej	NOUN
ejpam-5392	781	6	-	-	PUNCT
ejpam-5392	781	7	neighbourhoods	neighbourhood	NOUN
ejpam-5392	781	8	via	via	ADP
ejpam-5392	781	9	ideals	ideal	NOUN
ejpam-5392	781	10	.	.	PUNCT
ejpam-5392	782	1	complexity	complexity	NOUN
ejpam-5392	782	2	,	,	PUNCT
ejpam-5392	782	3	2021:4149368	2021:4149368	NUM
ejpam-5392	782	4	,	,	PUNCT
ejpam-5392	782	5	2021	2021	NUM
ejpam-5392	782	6	.	.	PUNCT
ejpam-5392	783	1	[	[	X
ejpam-5392	783	2	28	28	NUM
ejpam-5392	783	3	]	]	X
ejpam-5392	783	4	d.	d.	PROPN
ejpam-5392	783	5	jankovic	jankovic	PROPN
ejpam-5392	783	6	and	and	CCONJ
ejpam-5392	783	7	t.	t.	PROPN
ejpam-5392	783	8	r.	r.	PROPN
ejpam-5392	783	9	hamlet	hamlet	PROPN
ejpam-5392	783	10	.	.	PUNCT
ejpam-5392	784	1	new	new	ADJ
ejpam-5392	784	2	topologies	topology	NOUN
ejpam-5392	784	3	from	from	ADP
ejpam-5392	784	4	old	old	ADJ
ejpam-5392	784	5	via	via	ADP
ejpam-5392	784	6	ideals	ideal	NOUN
ejpam-5392	784	7	.	.	PUNCT
ejpam-5392	785	1	american	american	PROPN
ejpam-5392	785	2	mathematical	mathematical	PROPN
ejpam-5392	785	3	monthly	monthly	PROPN
ejpam-5392	785	4	,	,	PUNCT
ejpam-5392	785	5	97:295–310	97:295–310	PROPN
ejpam-5392	785	6	,	,	PUNCT
ejpam-5392	785	7	1990	1990	NUM
ejpam-5392	785	8	.	.	PUNCT
ejpam-5392	786	1	[	[	X
ejpam-5392	786	2	29	29	NUM
ejpam-5392	786	3	]	]	PUNCT
ejpam-5392	786	4	a.	a.	NOUN
ejpam-5392	786	5	kandil	kandil	PROPN
ejpam-5392	786	6	,	,	PUNCT
ejpam-5392	786	7	m.	m.	NOUN
ejpam-5392	786	8	m.	m.	NOUN
ejpam-5392	786	9	yakout	yakout	PROPN
ejpam-5392	786	10	,	,	PUNCT
ejpam-5392	786	11	and	and	CCONJ
ejpam-5392	786	12	a.	a.	NOUN
ejpam-5392	786	13	zakaria	zakaria	PROPN
ejpam-5392	786	14	.	.	PUNCT
ejpam-5392	787	1	generalized	generalize	VERB
ejpam-5392	787	2	rough	rough	ADJ
ejpam-5392	787	3	sets	set	NOUN
ejpam-5392	787	4	via	via	ADP
ejpam-5392	787	5	ideals	ideal	NOUN
ejpam-5392	787	6	.	.	PUNCT
ejpam-5392	788	1	annals	annal	NOUN
ejpam-5392	788	2	of	of	ADP
ejpam-5392	788	3	fuzzy	fuzzy	ADJ
ejpam-5392	788	4	mathematics	mathematic	NOUN
ejpam-5392	788	5	and	and	CCONJ
ejpam-5392	788	6	informatics	informatic	NOUN
ejpam-5392	788	7	,	,	PUNCT
ejpam-5392	788	8	5(3):525–532	5(3):525–532	PROPN
ejpam-5392	788	9	,	,	PUNCT
ejpam-5392	788	10	2013	2013	NUM
ejpam-5392	788	11	.	.	PUNCT
ejpam-5392	789	1	[	[	X
ejpam-5392	789	2	30	30	NUM
ejpam-5392	789	3	]	]	PUNCT
ejpam-5392	789	4	a.	a.	NOUN
ejpam-5392	789	5	m.	m.	NOUN
ejpam-5392	789	6	kozae	kozae	PROPN
ejpam-5392	789	7	,	,	PUNCT
ejpam-5392	789	8	s.	s.	PROPN
ejpam-5392	789	9	a.	a.	PROPN
ejpam-5392	789	10	el	el	PROPN
ejpam-5392	789	11	-	-	PUNCT
ejpam-5392	789	12	sheikh	sheikh	PROPN
ejpam-5392	789	13	,	,	PUNCT
ejpam-5392	789	14	e.	e.	PROPN
ejpam-5392	789	15	h.	h.	PROPN
ejpam-5392	789	16	aly	aly	PROPN
ejpam-5392	789	17	,	,	PUNCT
ejpam-5392	789	18	and	and	CCONJ
ejpam-5392	789	19	m.	m.	PROPN
ejpam-5392	789	20	hosny	hosny	PROPN
ejpam-5392	789	21	.	.	PUNCT
ejpam-5392	790	1	rough	rough	ADJ
ejpam-5392	790	2	sets	set	NOUN
ejpam-5392	790	3	and	and	CCONJ
ejpam-5392	790	4	its	its	PRON
ejpam-5392	790	5	applications	application	NOUN
ejpam-5392	790	6	in	in	ADP
ejpam-5392	790	7	a	a	DET
ejpam-5392	790	8	computer	computer	NOUN
ejpam-5392	790	9	network	network	NOUN
ejpam-5392	790	10	.	.	PUNCT
ejpam-5392	791	1	annals	annal	NOUN
ejpam-5392	791	2	of	of	ADP
ejpam-5392	791	3	fuzzy	fuzzy	ADJ
ejpam-5392	791	4	mathematics	mathematic	NOUN
ejpam-5392	791	5	and	and	CCONJ
ejpam-5392	791	6	informatics	informatic	NOUN
ejpam-5392	791	7	,	,	PUNCT
ejpam-5392	791	8	6(3):605–624	6(3):605–624	PRON
ejpam-5392	791	9	,	,	PUNCT
ejpam-5392	791	10	2013	2013	NUM
ejpam-5392	791	11	.	.	PUNCT
ejpam-5392	792	1	[	[	X
ejpam-5392	792	2	31	31	NUM
ejpam-5392	792	3	]	]	PUNCT
ejpam-5392	792	4	a.	a.	NOUN
ejpam-5392	792	5	m.	m.	NOUN
ejpam-5392	792	6	kozae	kozae	PROPN
ejpam-5392	792	7	,	,	PUNCT
ejpam-5392	792	8	s.	s.	PROPN
ejpam-5392	792	9	a.	a.	PROPN
ejpam-5392	792	10	el	el	PROPN
ejpam-5392	792	11	-	-	PUNCT
ejpam-5392	792	12	sheikh	sheikh	NOUN
ejpam-5392	792	13	,	,	PUNCT
ejpam-5392	792	14	and	and	CCONJ
ejpam-5392	792	15	m.	m.	PROPN
ejpam-5392	792	16	hosny	hosny	PROPN
ejpam-5392	792	17	.	.	PUNCT
ejpam-5392	793	1	on	on	ADP
ejpam-5392	793	2	generalized	generalize	VERB
ejpam-5392	793	3	rough	rough	ADJ
ejpam-5392	793	4	sets	set	NOUN
ejpam-5392	793	5	and	and	CCONJ
ejpam-5392	793	6	closure	closure	NOUN
ejpam-5392	793	7	spaces	space	NOUN
ejpam-5392	793	8	.	.	PUNCT
ejpam-5392	794	1	international	international	ADJ
ejpam-5392	794	2	journal	journal	PROPN
ejpam-5392	794	3	of	of	ADP
ejpam-5392	794	4	applied	apply	VERB
ejpam-5392	794	5	mathematics	mathematic	NOUN
ejpam-5392	794	6	,	,	PUNCT
ejpam-5392	794	7	23(6):997–1023	23(6):997–1023	NUM
ejpam-5392	794	8	,	,	PUNCT
ejpam-5392	794	9	2010	2010	NUM
ejpam-5392	794	10	.	.	PUNCT
ejpam-5392	795	1	[	[	X
ejpam-5392	795	2	32	32	NUM
ejpam-5392	795	3	]	]	PUNCT
ejpam-5392	795	4	k.	k.	PROPN
ejpam-5392	795	5	kuratowski	kuratowski	PROPN
ejpam-5392	795	6	.	.	PUNCT
ejpam-5392	796	1	topology	topology	NOUN
ejpam-5392	796	2	,	,	PUNCT
ejpam-5392	796	3	volume	volume	NOUN
ejpam-5392	796	4	i.	i.	PROPN
ejpam-5392	796	5	academic	academic	PROPN
ejpam-5392	796	6	press	press	PROPN
ejpam-5392	796	7	,	,	PUNCT
ejpam-5392	796	8	new	new	PROPN
ejpam-5392	796	9	york	york	PROPN
ejpam-5392	796	10	,	,	PUNCT
ejpam-5392	796	11	1966	1966	NUM
ejpam-5392	796	12	.	.	PUNCT
ejpam-5392	797	1	[	[	X
ejpam-5392	797	2	33	33	NUM
ejpam-5392	797	3	]	]	PUNCT
ejpam-5392	797	4	e.	e.	PROPN
ejpam-5392	797	5	f.	f.	PROPN
ejpam-5392	797	6	lashin	lashin	PROPN
ejpam-5392	797	7	,	,	PUNCT
ejpam-5392	797	8	a.	a.	NOUN
ejpam-5392	797	9	m.	m.	NOUN
ejpam-5392	797	10	kozae	kozae	PROPN
ejpam-5392	797	11	,	,	PUNCT
ejpam-5392	797	12	a.	a.	NOUN
ejpam-5392	797	13	a.	a.	NOUN
ejpam-5392	797	14	abo	abo	PROPN
ejpam-5392	797	15	khadra	khadra	NOUN
ejpam-5392	797	16	,	,	PUNCT
ejpam-5392	797	17	and	and	CCONJ
ejpam-5392	797	18	t.	t.	PROPN
ejpam-5392	797	19	medhat	medhat	PROPN
ejpam-5392	797	20	.	.	PUNCT
ejpam-5392	798	1	rough	rough	ADJ
ejpam-5392	798	2	set	set	NOUN
ejpam-5392	798	3	theory	theory	NOUN
ejpam-5392	798	4	for	for	ADP
ejpam-5392	798	5	topological	topological	ADJ
ejpam-5392	798	6	spaces	space	NOUN
ejpam-5392	798	7	.	.	PUNCT
ejpam-5392	799	1	international	international	ADJ
ejpam-5392	799	2	journal	journal	PROPN
ejpam-5392	799	3	of	of	ADP
ejpam-5392	799	4	approximate	approximate	ADJ
ejpam-5392	799	5	reasoning	reasoning	NOUN
ejpam-5392	799	6	,	,	PUNCT
ejpam-5392	799	7	40:35–43	40:35–43	NUM
ejpam-5392	799	8	,	,	PUNCT
ejpam-5392	799	9	2005	2005	NUM
ejpam-5392	799	10	.	.	PUNCT
ejpam-5392	800	1	[	[	X
ejpam-5392	800	2	34	34	NUM
ejpam-5392	800	3	]	]	PUNCT
ejpam-5392	800	4	z.	z.	PROPN
ejpam-5392	800	5	li	li	PROPN
ejpam-5392	800	6	,	,	PUNCT
ejpam-5392	800	7	t.	t.	PROPN
ejpam-5392	800	8	xie	xie	PROPN
ejpam-5392	800	9	,	,	PUNCT
ejpam-5392	800	10	and	and	CCONJ
ejpam-5392	800	11	q.	q.	PROPN
ejpam-5392	800	12	li	li	PROPN
ejpam-5392	800	13	.	.	PUNCT
ejpam-5392	800	14	topological	topological	ADJ
ejpam-5392	800	15	structure	structure	NOUN
ejpam-5392	800	16	of	of	ADP
ejpam-5392	800	17	generalized	generalized	ADJ
ejpam-5392	800	18	rough	rough	ADJ
ejpam-5392	800	19	sets	set	NOUN
ejpam-5392	800	20	.	.	PUNCT
ejpam-5392	801	1	computers	computer	NOUN
ejpam-5392	801	2	&	&	CCONJ
ejpam-5392	801	3	mathematics	mathematics	PROPN
ejpam-5392	801	4	with	with	ADP
ejpam-5392	801	5	applications	application	NOUN
ejpam-5392	801	6	,	,	PUNCT
ejpam-5392	801	7	63:1066–1071	63:1066–1071	PROPN
ejpam-5392	801	8	,	,	PUNCT
ejpam-5392	801	9	2012	2012	NUM
ejpam-5392	801	10	.	.	PUNCT
ejpam-5392	802	1	[	[	X
ejpam-5392	802	2	35	35	NUM
ejpam-5392	802	3	]	]	PUNCT
ejpam-5392	802	4	t.	t.	PROPN
ejpam-5392	802	5	y.	y.	PROPN
ejpam-5392	802	6	lin	lin	PROPN
ejpam-5392	802	7	.	.	PUNCT
ejpam-5392	803	1	granular	granular	ADJ
ejpam-5392	803	2	computing	computing	NOUN
ejpam-5392	803	3	on	on	ADP
ejpam-5392	803	4	binary	binary	ADJ
ejpam-5392	803	5	relation	relation	PROPN
ejpam-5392	804	1	i	i	PRON
ejpam-5392	804	2	:	:	PUNCT
ejpam-5392	804	3	data	datum	NOUN
ejpam-5392	804	4	mining	mining	NOUN
ejpam-5392	804	5	and	and	CCONJ
ejpam-5392	804	6	neighborhood	neighborhood	NOUN
ejpam-5392	804	7	systems	system	NOUN
ejpam-5392	804	8	.	.	PUNCT
ejpam-5392	805	1	in	in	ADP
ejpam-5392	805	2	l.	l.	PROPN
ejpam-5392	805	3	polkowski	polkowski	PROPN
ejpam-5392	805	4	and	and	CCONJ
ejpam-5392	805	5	a.	a.	NOUN
ejpam-5392	805	6	skowron	skowron	PROPN
ejpam-5392	805	7	,	,	PUNCT
ejpam-5392	805	8	editors	editor	NOUN
ejpam-5392	805	9	,	,	PUNCT
ejpam-5392	805	10	rough	rough	ADJ
ejpam-5392	805	11	sets	set	NOUN
ejpam-5392	805	12	in	in	ADP
ejpam-5392	805	13	knowledge	knowledge	NOUN
ejpam-5392	805	14	discovery	discovery	PROPN
ejpam-5392	805	15	1	1	NUM
ejpam-5392	805	16	,	,	PUNCT
ejpam-5392	805	17	pages	page	NOUN
ejpam-5392	805	18	107–121	107–121	NUM
ejpam-5392	805	19	.	.	PUNCT
ejpam-5392	806	1	physica	physica	NOUN
ejpam-5392	806	2	-	-	PUNCT
ejpam-5392	806	3	verlag	verlag	PROPN
ejpam-5392	806	4	,	,	PUNCT
ejpam-5392	806	5	heidelberg	heidelberg	PROPN
ejpam-5392	806	6	,	,	PUNCT
ejpam-5392	806	7	1998	1998	NUM
ejpam-5392	806	8	.	.	PUNCT
ejpam-5392	807	1	[	[	X
ejpam-5392	807	2	36	36	NUM
ejpam-5392	807	3	]	]	X
ejpam-5392	807	4	r.	r.	PROPN
ejpam-5392	807	5	mareay	mareay	PROPN
ejpam-5392	807	6	.	.	PUNCT
ejpam-5392	808	1	generalized	generalize	VERB
ejpam-5392	808	2	rough	rough	ADJ
ejpam-5392	808	3	sets	set	NOUN
ejpam-5392	808	4	based	base	VERB
ejpam-5392	808	5	on	on	ADP
ejpam-5392	808	6	neighborhood	neighborhood	NOUN
ejpam-5392	808	7	systems	system	NOUN
ejpam-5392	808	8	and	and	CCONJ
ejpam-5392	808	9	topological	topological	ADJ
ejpam-5392	808	10	spaces	space	NOUN
ejpam-5392	808	11	.	.	PUNCT
ejpam-5392	809	1	journal	journal	NOUN
ejpam-5392	809	2	of	of	ADP
ejpam-5392	809	3	the	the	DET
ejpam-5392	809	4	egyptian	egyptian	PROPN
ejpam-5392	809	5	mathematical	mathematical	PROPN
ejpam-5392	809	6	society	society	NOUN
ejpam-5392	809	7	,	,	PUNCT
ejpam-5392	809	8	24:603–608	24:603–608	PROPN
ejpam-5392	809	9	,	,	PUNCT
ejpam-5392	809	10	2016	2016	NUM
ejpam-5392	809	11	.	.	PUNCT
ejpam-5392	810	1	[	[	X
ejpam-5392	810	2	37	37	NUM
ejpam-5392	810	3	]	]	PUNCT
ejpam-5392	810	4	a.	a.	NOUN
ejpam-5392	810	5	mhemdi	mhemdi	PROPN
ejpam-5392	810	6	and	and	CCONJ
ejpam-5392	810	7	t.	t.	PROPN
ejpam-5392	810	8	m.	m.	PROPN
ejpam-5392	810	9	al	al	PROPN
ejpam-5392	810	10	-	-	PUNCT
ejpam-5392	810	11	shami	shami	PROPN
ejpam-5392	810	12	.	.	PUNCT
ejpam-5392	811	1	introduction	introduction	NOUN
ejpam-5392	811	2	to	to	ADP
ejpam-5392	811	3	temporal	temporal	ADJ
ejpam-5392	811	4	topology	topology	NOUN
ejpam-5392	811	5	.	.	PUNCT
ejpam-5392	812	1	journal	journal	PROPN
ejpam-5392	812	2	of	of	ADP
ejpam-5392	812	3	mathematics	mathematics	PROPN
ejpam-5392	812	4	and	and	CCONJ
ejpam-5392	812	5	computer	computer	NOUN
ejpam-5392	812	6	science	science	NOUN
ejpam-5392	812	7	,	,	PUNCT
ejpam-5392	812	8	34(3):205–216	34(3):205–216	PROPN
ejpam-5392	812	9	,	,	PUNCT
ejpam-5392	812	10	2024	2024	NUM
ejpam-5392	812	11	.	.	PUNCT
ejpam-5392	813	1	[	[	X
ejpam-5392	813	2	38	38	NUM
ejpam-5392	813	3	]	]	PUNCT
ejpam-5392	813	4	f.	f.	PROPN
ejpam-5392	813	5	i.	i.	PROPN
ejpam-5392	813	6	michael	michael	PROPN
ejpam-5392	813	7	.	.	PUNCT
ejpam-5392	814	1	on	on	ADP
ejpam-5392	814	2	semi	semi	ADJ
ejpam-5392	814	3	-	-	ADJ
ejpam-5392	814	4	open	open	ADJ
ejpam-5392	814	5	sets	set	NOUN
ejpam-5392	814	6	with	with	ADP
ejpam-5392	814	7	respect	respect	NOUN
ejpam-5392	814	8	to	to	ADP
ejpam-5392	814	9	an	an	DET
ejpam-5392	814	10	ideal	ideal	NOUN
ejpam-5392	814	11	.	.	PUNCT
ejpam-5392	815	1	european	european	ADJ
ejpam-5392	815	2	journal	journal	PROPN
ejpam-5392	815	3	of	of	ADP
ejpam-5392	815	4	pure	pure	ADJ
ejpam-5392	815	5	and	and	CCONJ
ejpam-5392	815	6	applied	applied	ADJ
ejpam-5392	815	7	mathematics	mathematic	NOUN
ejpam-5392	815	8	,	,	PUNCT
ejpam-5392	815	9	6(1):53–58	6(1):53–58	NUM
ejpam-5392	815	10	,	,	PUNCT
ejpam-5392	815	11	2013	2013	NUM
ejpam-5392	815	12	.	.	PUNCT
ejpam-5392	816	1	references	reference	NOUN
ejpam-5392	816	2	3463	3463	NUM
ejpam-5392	816	3	[	[	X
ejpam-5392	816	4	39	39	NUM
ejpam-5392	816	5	]	]	PUNCT
ejpam-5392	816	6	a.	a.	PROPN
ejpam-5392	816	7	s.	s.	PROPN
ejpam-5392	816	8	nawar	nawar	PROPN
ejpam-5392	816	9	.	.	PUNCT
ejpam-5392	817	1	approximations	approximation	NOUN
ejpam-5392	817	2	of	of	ADP
ejpam-5392	817	3	some	some	DET
ejpam-5392	817	4	near	near	ADP
ejpam-5392	817	5	open	open	ADJ
ejpam-5392	817	6	sets	set	NOUN
ejpam-5392	817	7	in	in	ADP
ejpam-5392	817	8	ideal	ideal	ADJ
ejpam-5392	817	9	topological	topological	ADJ
ejpam-5392	817	10	spaces	space	NOUN
ejpam-5392	817	11	.	.	PUNCT
ejpam-5392	818	1	journal	journal	NOUN
ejpam-5392	818	2	of	of	ADP
ejpam-5392	818	3	the	the	DET
ejpam-5392	818	4	egyptian	egyptian	PROPN
ejpam-5392	818	5	mathematical	mathematical	PROPN
ejpam-5392	818	6	society	society	NOUN
ejpam-5392	818	7	,	,	PUNCT
ejpam-5392	818	8	pages	page	NOUN
ejpam-5392	818	9	1–11	1–11	PROPN
ejpam-5392	818	10	,	,	PUNCT
ejpam-5392	818	11	2020	2020	NUM
ejpam-5392	818	12	.	.	PUNCT
ejpam-5392	819	1	[	[	X
ejpam-5392	819	2	40	40	NUM
ejpam-5392	819	3	]	]	PUNCT
ejpam-5392	819	4	z.	z.	PROPN
ejpam-5392	819	5	pawlak	pawlak	PROPN
ejpam-5392	819	6	.	.	PUNCT
ejpam-5392	820	1	rough	rough	ADJ
ejpam-5392	820	2	sets	set	NOUN
ejpam-5392	820	3	.	.	PUNCT
ejpam-5392	821	1	international	international	ADJ
ejpam-5392	821	2	journal	journal	NOUN
ejpam-5392	821	3	of	of	ADP
ejpam-5392	821	4	information	information	NOUN
ejpam-5392	821	5	and	and	CCONJ
ejpam-5392	821	6	computer	computer	NOUN
ejpam-5392	821	7	science	science	NOUN
ejpam-5392	821	8	,	,	PUNCT
ejpam-5392	821	9	11:341–356	11:341–356	NUM
ejpam-5392	821	10	,	,	PUNCT
ejpam-5392	821	11	1982	1982	NUM
ejpam-5392	821	12	.	.	PUNCT
ejpam-5392	822	1	[	[	X
ejpam-5392	822	2	41	41	NUM
ejpam-5392	822	3	]	]	PUNCT
ejpam-5392	822	4	z.	z.	PROPN
ejpam-5392	822	5	pawlak	pawlak	PROPN
ejpam-5392	822	6	.	.	PUNCT
ejpam-5392	823	1	rough	rough	ADJ
ejpam-5392	823	2	concept	concept	NOUN
ejpam-5392	823	3	analysis	analysis	NOUN
ejpam-5392	823	4	.	.	PUNCT
ejpam-5392	824	1	bulletin	bulletin	NOUN
ejpam-5392	824	2	of	of	ADP
ejpam-5392	824	3	the	the	DET
ejpam-5392	824	4	polish	polish	PROPN
ejpam-5392	824	5	academy	academy	PROPN
ejpam-5392	824	6	of	of	ADP
ejpam-5392	824	7	sciences	sciences	PROPN
ejpam-5392	824	8	mathematics	mathematic	NOUN
ejpam-5392	824	9	,	,	PUNCT
ejpam-5392	824	10	33:495–498	33:495–498	PROPN
ejpam-5392	824	11	,	,	PUNCT
ejpam-5392	824	12	1985	1985	NUM
ejpam-5392	824	13	.	.	PUNCT
ejpam-5392	825	1	[	[	X
ejpam-5392	825	2	42	42	NUM
ejpam-5392	825	3	]	]	PUNCT
ejpam-5392	825	4	z.	z.	PROPN
ejpam-5392	825	5	pawlak	pawlak	PROPN
ejpam-5392	825	6	and	and	CCONJ
ejpam-5392	825	7	a.	a.	NOUN
ejpam-5392	825	8	skowron	skowron	PROPN
ejpam-5392	825	9	.	.	PUNCT
ejpam-5392	826	1	rough	rough	ADJ
ejpam-5392	826	2	membership	membership	NOUN
ejpam-5392	826	3	function	function	NOUN
ejpam-5392	826	4	.	.	PUNCT
ejpam-5392	827	1	in	in	ADP
ejpam-5392	827	2	r.	r.	PROPN
ejpam-5392	827	3	e.	e.	PROPN
ejpam-5392	827	4	yeager	yeager	PROPN
ejpam-5392	827	5	,	,	PUNCT
ejpam-5392	827	6	m.	m.	NOUN
ejpam-5392	827	7	fedrizzi	fedrizzi	NOUN
ejpam-5392	827	8	,	,	PUNCT
ejpam-5392	827	9	and	and	CCONJ
ejpam-5392	827	10	j.	j.	PROPN
ejpam-5392	827	11	kacprzyk	kacprzyk	PROPN
ejpam-5392	827	12	,	,	PUNCT
ejpam-5392	827	13	editors	editor	NOUN
ejpam-5392	827	14	,	,	PUNCT
ejpam-5392	827	15	advances	advance	NOUN
ejpam-5392	827	16	in	in	ADP
ejpam-5392	827	17	the	the	DET
ejpam-5392	827	18	dempster	dempster	PROPN
ejpam-5392	827	19	-	-	PUNCT
ejpam-5392	827	20	schafer	schafer	PROPN
ejpam-5392	827	21	theory	theory	NOUN
ejpam-5392	827	22	of	of	ADP
ejpam-5392	827	23	evidence	evidence	NOUN
ejpam-5392	827	24	,	,	PUNCT
ejpam-5392	827	25	pages	page	NOUN
ejpam-5392	827	26	251–271	251–271	NUM
ejpam-5392	827	27	.	.	PUNCT
ejpam-5392	827	28	wiley	wiley	PROPN
ejpam-5392	827	29	,	,	PUNCT
ejpam-5392	827	30	new	new	PROPN
ejpam-5392	827	31	york	york	PROPN
ejpam-5392	827	32	,	,	PUNCT
ejpam-5392	827	33	1994	1994	NUM
ejpam-5392	827	34	.	.	PUNCT
ejpam-5392	828	1	[	[	X
ejpam-5392	828	2	43	43	NUM
ejpam-5392	828	3	]	]	PUNCT
ejpam-5392	828	4	z.	z.	PROPN
ejpam-5392	828	5	pei	pei	PROPN
ejpam-5392	828	6	,	,	PUNCT
ejpam-5392	828	7	d.	d.	PROPN
ejpam-5392	828	8	pei	pei	PROPN
ejpam-5392	828	9	,	,	PUNCT
ejpam-5392	828	10	and	and	CCONJ
ejpam-5392	828	11	li	li	PROPN
ejpam-5392	828	12	zheng	zheng	PROPN
ejpam-5392	828	13	.	.	PUNCT
ejpam-5392	829	1	topology	topology	NOUN
ejpam-5392	829	2	vs	vs	ADP
ejpam-5392	829	3	generalized	generalize	VERB
ejpam-5392	829	4	rough	rough	ADJ
ejpam-5392	829	5	sets	set	NOUN
ejpam-5392	829	6	.	.	PUNCT
ejpam-5392	830	1	international	international	ADJ
ejpam-5392	830	2	journal	journal	PROPN
ejpam-5392	830	3	of	of	ADP
ejpam-5392	830	4	approximate	approximate	ADJ
ejpam-5392	830	5	reasoning	reasoning	NOUN
ejpam-5392	830	6	,	,	PUNCT
ejpam-5392	830	7	52:231–239	52:231–239	PROPN
ejpam-5392	830	8	,	,	PUNCT
ejpam-5392	830	9	2011	2011	NUM
ejpam-5392	830	10	.	.	PUNCT
ejpam-5392	831	1	[	[	X
ejpam-5392	831	2	44	44	NUM
ejpam-5392	831	3	]	]	PUNCT
ejpam-5392	831	4	a.	a.	PROPN
ejpam-5392	831	5	s.	s.	PROPN
ejpam-5392	831	6	salama	salama	PROPN
ejpam-5392	831	7	.	.	PUNCT
ejpam-5392	832	1	bitopological	bitopological	ADJ
ejpam-5392	832	2	approximation	approximation	NOUN
ejpam-5392	832	3	space	space	NOUN
ejpam-5392	832	4	with	with	ADP
ejpam-5392	832	5	application	application	NOUN
ejpam-5392	832	6	to	to	ADP
ejpam-5392	832	7	data	data	NOUN
ejpam-5392	832	8	reduction	reduction	NOUN
ejpam-5392	832	9	in	in	ADP
ejpam-5392	832	10	multi	multi	ADJ
ejpam-5392	832	11	-	-	ADJ
ejpam-5392	832	12	valued	value	VERB
ejpam-5392	832	13	information	information	NOUN
ejpam-5392	832	14	systems	system	NOUN
ejpam-5392	832	15	.	.	PUNCT
ejpam-5392	833	1	filomat	filomat	PROPN
ejpam-5392	833	2	,	,	PUNCT
ejpam-5392	833	3	34(1):99–110	34(1):99–110	PROPN
ejpam-5392	833	4	,	,	PUNCT
ejpam-5392	833	5	2020	2020	NUM
ejpam-5392	833	6	.	.	PUNCT
ejpam-5392	834	1	[	[	X
ejpam-5392	834	2	45	45	NUM
ejpam-5392	834	3	]	]	PUNCT
ejpam-5392	834	4	a.	a.	NOUN
ejpam-5392	834	5	s.	s.	PROPN
ejpam-5392	834	6	salama	salama	PROPN
ejpam-5392	834	7	and	and	CCONJ
ejpam-5392	834	8	m.	m.	NOUN
ejpam-5392	834	9	m.	m.	PROPN
ejpam-5392	834	10	e.	e.	PROPN
ejpam-5392	834	11	abd	abd	PROPN
ejpam-5392	834	12	el	el	PROPN
ejpam-5392	834	13	-	-	PROPN
ejpam-5392	834	14	monsef	monsef	ADJ
ejpam-5392	834	15	.	.	PUNCT
ejpam-5392	835	1	new	new	ADJ
ejpam-5392	835	2	topological	topological	ADJ
ejpam-5392	835	3	approach	approach	NOUN
ejpam-5392	835	4	of	of	ADP
ejpam-5392	835	5	rough	rough	ADJ
ejpam-5392	835	6	set	set	NOUN
ejpam-5392	835	7	generalizations	generalization	NOUN
ejpam-5392	835	8	.	.	PUNCT
ejpam-5392	836	1	international	international	ADJ
ejpam-5392	836	2	journal	journal	NOUN
ejpam-5392	836	3	of	of	ADP
ejpam-5392	836	4	computer	computer	NOUN
ejpam-5392	836	5	mathematics	mathematic	NOUN
ejpam-5392	836	6	,	,	PUNCT
ejpam-5392	836	7	88(7):1347–1357	88(7):1347–1357	NUM
ejpam-5392	836	8	,	,	PUNCT
ejpam-5392	836	9	2011	2011	NUM
ejpam-5392	836	10	.	.	PUNCT
ejpam-5392	837	1	[	[	X
ejpam-5392	837	2	46	46	NUM
ejpam-5392	837	3	]	]	PUNCT
ejpam-5392	838	1	p.	p.	NOUN
ejpam-5392	838	2	k.	k.	PROPN
ejpam-5392	839	1	singh	singh	PROPN
ejpam-5392	839	2	and	and	CCONJ
ejpam-5392	839	3	s.	s.	PROPN
ejpam-5392	839	4	tiwari	tiwari	PROPN
ejpam-5392	839	5	.	.	PUNCT
ejpam-5392	840	1	topological	topological	ADJ
ejpam-5392	840	2	structures	structure	NOUN
ejpam-5392	840	3	in	in	ADP
ejpam-5392	840	4	rough	rough	ADJ
ejpam-5392	840	5	set	set	NOUN
ejpam-5392	840	6	theory	theory	NOUN
ejpam-5392	840	7	:	:	PUNCT
ejpam-5392	840	8	a	a	DET
ejpam-5392	840	9	survey	survey	NOUN
ejpam-5392	840	10	.	.	PUNCT
ejpam-5392	841	1	hacettepe	hacettepe	ADJ
ejpam-5392	841	2	journal	journal	PROPN
ejpam-5392	841	3	of	of	ADP
ejpam-5392	841	4	mathematics	mathematic	NOUN
ejpam-5392	841	5	and	and	CCONJ
ejpam-5392	841	6	statistics	statistic	NOUN
ejpam-5392	841	7	,	,	PUNCT
ejpam-5392	841	8	49(4):1270–1294	49(4):1270–1294	NUM
ejpam-5392	841	9	,	,	PUNCT
ejpam-5392	841	10	2020	2020	NUM
ejpam-5392	841	11	.	.	PUNCT
ejpam-5392	842	1	[	[	X
ejpam-5392	842	2	47	47	NUM
ejpam-5392	842	3	]	]	X
ejpam-5392	842	4	r.	r.	PROPN
ejpam-5392	842	5	vaidynathaswamy	vaidynathaswamy	PROPN
ejpam-5392	842	6	.	.	PUNCT
ejpam-5392	843	1	the	the	DET
ejpam-5392	843	2	localization	localization	NOUN
ejpam-5392	843	3	theory	theory	NOUN
ejpam-5392	843	4	in	in	ADP
ejpam-5392	843	5	set	set	NOUN
ejpam-5392	843	6	topology	topology	NOUN
ejpam-5392	843	7	.	.	PUNCT
ejpam-5392	844	1	proceedings	proceeding	NOUN
ejpam-5392	844	2	of	of	ADP
ejpam-5392	844	3	the	the	DET
ejpam-5392	844	4	indian	indian	PROPN
ejpam-5392	844	5	academy	academy	PROPN
ejpam-5392	844	6	of	of	ADP
ejpam-5392	844	7	sciences	sciences	PROPN
ejpam-5392	844	8	,	,	PUNCT
ejpam-5392	844	9	20:51–61	20:51–61	NUM
ejpam-5392	844	10	,	,	PUNCT
ejpam-5392	844	11	1944	1944	NUM
ejpam-5392	844	12	.	.	PUNCT
ejpam-5392	845	1	[	[	X
ejpam-5392	845	2	48	48	NUM
ejpam-5392	845	3	]	]	PUNCT
ejpam-5392	845	4	a.	a.	NOUN
ejpam-5392	845	5	wiweger	wiweger	NOUN
ejpam-5392	845	6	.	.	PUNCT
ejpam-5392	846	1	on	on	ADP
ejpam-5392	846	2	topological	topological	ADJ
ejpam-5392	846	3	rough	rough	ADJ
ejpam-5392	846	4	sets	set	NOUN
ejpam-5392	846	5	.	.	PUNCT
ejpam-5392	847	1	bulletin	bulletin	NOUN
ejpam-5392	847	2	of	of	ADP
ejpam-5392	847	3	the	the	DET
ejpam-5392	847	4	polish	polish	PROPN
ejpam-5392	847	5	academy	academy	PROPN
ejpam-5392	847	6	of	of	ADP
ejpam-5392	847	7	sciences	sciences	PROPN
ejpam-5392	847	8	mathematics	mathematics	PROPN
ejpam-5392	847	9	,	,	PUNCT
ejpam-5392	847	10	37:89–93	37:89–93	NUM
ejpam-5392	847	11	,	,	PUNCT
ejpam-5392	847	12	1989	1989	NUM
ejpam-5392	847	13	.	.	PUNCT
ejpam-5392	848	1	[	[	X
ejpam-5392	848	2	49	49	NUM
ejpam-5392	848	3	]	]	PUNCT
ejpam-5392	848	4	h.	h.	PROPN
ejpam-5392	848	5	wu	wu	PROPN
ejpam-5392	848	6	and	and	CCONJ
ejpam-5392	848	7	g.	g.	PROPN
ejpam-5392	848	8	liu	liu	PROPN
ejpam-5392	848	9	.	.	PUNCT
ejpam-5392	849	1	the	the	DET
ejpam-5392	849	2	relationships	relationship	NOUN
ejpam-5392	849	3	between	between	ADP
ejpam-5392	849	4	topologies	topology	NOUN
ejpam-5392	849	5	and	and	CCONJ
ejpam-5392	849	6	generalized	generalize	VERB
ejpam-5392	849	7	rough	rough	ADJ
ejpam-5392	849	8	sets	set	NOUN
ejpam-5392	849	9	.	.	PUNCT
ejpam-5392	850	1	international	international	ADJ
ejpam-5392	850	2	journal	journal	PROPN
ejpam-5392	850	3	of	of	ADP
ejpam-5392	850	4	approximate	approximate	ADJ
ejpam-5392	850	5	reasoning	reasoning	NOUN
ejpam-5392	850	6	,	,	PUNCT
ejpam-5392	850	7	119:313–324	119:313–324	NUM
ejpam-5392	850	8	,	,	PUNCT
ejpam-5392	850	9	2020	2020	NUM
ejpam-5392	850	10	.	.	PUNCT
ejpam-5392	851	1	[	[	X
ejpam-5392	851	2	50	50	NUM
ejpam-5392	851	3	]	]	X
ejpam-5392	851	4	y.	y.	PROPN
ejpam-5392	851	5	y.	y.	PROPN
ejpam-5392	851	6	yao	yao	PROPN
ejpam-5392	851	7	.	.	PUNCT
ejpam-5392	852	1	two	two	NUM
ejpam-5392	852	2	views	view	NOUN
ejpam-5392	852	3	of	of	ADP
ejpam-5392	852	4	the	the	DET
ejpam-5392	852	5	theory	theory	NOUN
ejpam-5392	852	6	of	of	ADP
ejpam-5392	852	7	rough	rough	ADJ
ejpam-5392	852	8	sets	set	NOUN
ejpam-5392	852	9	in	in	ADP
ejpam-5392	852	10	finite	finite	ADJ
ejpam-5392	852	11	universes	universe	NOUN
ejpam-5392	852	12	.	.	PUNCT
ejpam-5392	853	1	international	international	ADJ
ejpam-5392	853	2	journal	journal	PROPN
ejpam-5392	853	3	of	of	ADP
ejpam-5392	853	4	approximate	approximate	ADJ
ejpam-5392	853	5	reasoning	reasoning	NOUN
ejpam-5392	853	6	,	,	PUNCT
ejpam-5392	853	7	15:291–317	15:291–317	NUM
ejpam-5392	853	8	,	,	PUNCT
ejpam-5392	853	9	1996	1996	NUM
ejpam-5392	853	10	.	.	PUNCT
ejpam-5392	854	1	[	[	X
ejpam-5392	854	2	51	51	NUM
ejpam-5392	854	3	]	]	X
ejpam-5392	854	4	y.	y.	PROPN
ejpam-5392	854	5	y.	y.	PROPN
ejpam-5392	854	6	yao	yao	PROPN
ejpam-5392	854	7	.	.	PUNCT
ejpam-5392	855	1	relational	relational	ADJ
ejpam-5392	855	2	interpretations	interpretation	NOUN
ejpam-5392	855	3	of	of	ADP
ejpam-5392	855	4	neighborhood	neighborhood	NOUN
ejpam-5392	855	5	operators	operator	NOUN
ejpam-5392	855	6	and	and	CCONJ
ejpam-5392	855	7	rough	rough	ADJ
ejpam-5392	855	8	set	set	NOUN
ejpam-5392	855	9	approximation	approximation	NOUN
ejpam-5392	855	10	operators	operator	NOUN
ejpam-5392	855	11	.	.	PUNCT
ejpam-5392	856	1	information	information	NOUN
ejpam-5392	856	2	sciences	sciences	PROPN
ejpam-5392	856	3	,	,	PUNCT
ejpam-5392	856	4	119:239–259	119:239–259	NUM
ejpam-5392	856	5	,	,	PUNCT
ejpam-5392	856	6	1998	1998	NUM
ejpam-5392	856	7	.	.	PUNCT
ejpam-5392	857	1	[	[	X
ejpam-5392	857	2	52	52	NUM
ejpam-5392	857	3	]	]	PUNCT
ejpam-5392	857	4	e.	e.	PROPN
ejpam-5392	857	5	d.	d.	PROPN
ejpam-5392	857	6	yildirim	yildirim	PROPN
ejpam-5392	857	7	.	.	PUNCT
ejpam-5392	858	1	new	new	ADJ
ejpam-5392	858	2	topological	topological	ADJ
ejpam-5392	858	3	approaches	approach	NOUN
ejpam-5392	858	4	to	to	ADP
ejpam-5392	858	5	rough	rough	ADJ
ejpam-5392	858	6	sets	set	NOUN
ejpam-5392	858	7	via	via	ADP
ejpam-5392	858	8	subset	subset	ADJ
ejpam-5392	858	9	neighborhoods	neighborhood	NOUN
ejpam-5392	858	10	.	.	PUNCT
ejpam-5392	859	1	journal	journal	PROPN
ejpam-5392	859	2	of	of	ADP
ejpam-5392	859	3	mathematics	mathematic	NOUN
ejpam-5392	859	4	,	,	PUNCT
ejpam-5392	859	5	page	page	NOUN
ejpam-5392	859	6	10	10	NUM
ejpam-5392	859	7	pages	page	NOUN
ejpam-5392	859	8	,	,	PUNCT
ejpam-5392	859	9	2022	2022	NUM
ejpam-5392	859	10	.	.	PUNCT
ejpam-5392	860	1	[	[	X
ejpam-5392	860	2	53	53	NUM
ejpam-5392	860	3	]	]	X
ejpam-5392	860	4	y.	y.	PROPN
ejpam-5392	860	5	l.	l.	PROPN
ejpam-5392	860	6	zhang	zhang	PROPN
ejpam-5392	860	7	,	,	PUNCT
ejpam-5392	860	8	j.	j.	PROPN
ejpam-5392	860	9	li	li	PROPN
ejpam-5392	860	10	,	,	PUNCT
ejpam-5392	860	11	and	and	CCONJ
ejpam-5392	860	12	c.	c.	PROPN
ejpam-5392	860	13	li	li	PROPN
ejpam-5392	860	14	.	.	PUNCT
ejpam-5392	861	1	topological	topological	ADJ
ejpam-5392	861	2	structure	structure	NOUN
ejpam-5392	861	3	of	of	ADP
ejpam-5392	861	4	relational	relational	NOUN
ejpam-5392	861	5	-	-	PUNCT
ejpam-5392	861	6	based	base	VERB
ejpam-5392	861	7	generalized	generalized	ADJ
ejpam-5392	861	8	rough	rough	ADJ
ejpam-5392	861	9	sets	set	NOUN
ejpam-5392	861	10	.	.	PUNCT
ejpam-5392	862	1	fundamenta	fundamenta	PROPN
ejpam-5392	862	2	informaticae	informaticae	PROPN
ejpam-5392	862	3	,	,	PUNCT
ejpam-5392	862	4	147(4):477–491	147(4):477–491	NUM
ejpam-5392	862	5	,	,	PUNCT
ejpam-5392	862	6	2016	2016	NUM
ejpam-5392	862	7	.	.	PUNCT