id	sid	tid	token	lemma	pos
ejpam-6358	1	1	european	european	PROPN
ejpam-6358	1	2	journal	journal	PROPN
ejpam-6358	1	3	of	of	ADP
ejpam-6358	1	4	pure	pure	ADJ
ejpam-6358	1	5	and	and	CCONJ
ejpam-6358	1	6	applied	applied	ADJ
ejpam-6358	1	7	mathematics	mathematic	NOUN
ejpam-6358	1	8	2025	2025	NUM
ejpam-6358	1	9	,	,	PUNCT
ejpam-6358	1	10	vol	vol	NOUN
ejpam-6358	1	11	.	.	PROPN
ejpam-6358	1	12	18	18	NUM
ejpam-6358	1	13	,	,	PUNCT
ejpam-6358	1	14	issue	issue	NOUN
ejpam-6358	1	15	4	4	NUM
ejpam-6358	1	16	,	,	PUNCT
ejpam-6358	1	17	article	article	NOUN
ejpam-6358	1	18	number	number	NOUN
ejpam-6358	1	19	6358	6358	NUM
ejpam-6358	1	20	issn	issn	VERB
ejpam-6358	1	21	1307	1307	NUM
ejpam-6358	1	22	-	-	SYM
ejpam-6358	1	23	5543	5543	NUM
ejpam-6358	1	24	–	–	PUNCT
ejpam-6358	1	25	ejpam.com	ejpam.com	X
ejpam-6358	1	26	published	publish	VERB
ejpam-6358	1	27	by	by	ADP
ejpam-6358	1	28	new	new	PROPN
ejpam-6358	1	29	york	york	PROPN
ejpam-6358	1	30	business	business	PROPN
ejpam-6358	1	31	global	global	ADJ
ejpam-6358	1	32	theoretical	theoretical	ADJ
ejpam-6358	1	33	advances	advance	NOUN
ejpam-6358	1	34	and	and	CCONJ
ejpam-6358	1	35	improvements	improvement	NOUN
ejpam-6358	1	36	of	of	ADP
ejpam-6358	1	37	“	"	PUNCT
ejpam-6358	1	38	generalized	generalized	ADJ
ejpam-6358	1	39	approximation	approximation	NOUN
ejpam-6358	1	40	spaces	space	NOUN
ejpam-6358	1	41	generation	generation	NOUN
ejpam-6358	1	42	from	from	ADP
ejpam-6358	1	43	ij	ij	NOUN
ejpam-6358	1	44	-	-	PUNCT
ejpam-6358	1	45	neighborhoods	neighborhood	NOUN
ejpam-6358	1	46	and	and	CCONJ
ejpam-6358	1	47	ideals	ideal	NOUN
ejpam-6358	1	48	with	with	ADP
ejpam-6358	1	49	application	application	NOUN
ejpam-6358	1	50	to	to	ADP
ejpam-6358	1	51	chikungunya	chikungunya	NOUN
ejpam-6358	1	52	disease	disease	NOUN
ejpam-6358	1	53	”	"	PUNCT
ejpam-6358	1	54	rodyna	rodyna	PROPN
ejpam-6358	1	55	a.	a.	NOUN
ejpam-6358	1	56	hosny1	hosny1	PROPN
ejpam-6358	1	57	,	,	PUNCT
ejpam-6358	1	58	naglaa	naglaa	PROPN
ejpam-6358	1	59	m.	m.	NOUN
ejpam-6358	1	60	madbouly2	madbouly2	PROPN
ejpam-6358	1	61	,	,	PUNCT
ejpam-6358	2	1	mostafa	mostafa	PROPN
ejpam-6358	2	2	k.	k.	PROPN
ejpam-6358	2	3	el	el	PROPN
ejpam-6358	2	4	-	-	PUNCT
ejpam-6358	2	5	bably3,4,∗	bably3,4,∗	ADJ
ejpam-6358	2	6	1	1	NUM
ejpam-6358	2	7	department	department	NOUN
ejpam-6358	2	8	of	of	ADP
ejpam-6358	2	9	mathematics	mathematic	NOUN
ejpam-6358	2	10	,	,	PUNCT
ejpam-6358	2	11	faculty	faculty	NOUN
ejpam-6358	2	12	of	of	ADP
ejpam-6358	2	13	science	science	NOUN
ejpam-6358	2	14	,	,	PUNCT
ejpam-6358	2	15	zagazig	zagazig	PROPN
ejpam-6358	2	16	university	university	PROPN
ejpam-6358	2	17	,	,	PUNCT
ejpam-6358	2	18	zagazig	zagazig	PROPN
ejpam-6358	2	19	44519	44519	NUM
ejpam-6358	2	20	,	,	PUNCT
ejpam-6358	2	21	egypt	egypt	PROPN
ejpam-6358	2	22	2	2	NUM
ejpam-6358	2	23	mathematics	mathematics	PROPN
ejpam-6358	2	24	department	department	NOUN
ejpam-6358	2	25	,	,	PUNCT
ejpam-6358	2	26	faculty	faculty	NOUN
ejpam-6358	2	27	of	of	ADP
ejpam-6358	2	28	science	science	NOUN
ejpam-6358	2	29	,	,	PUNCT
ejpam-6358	2	30	helwan	helwan	PROPN
ejpam-6358	2	31	university	university	PROPN
ejpam-6358	2	32	,	,	PUNCT
ejpam-6358	2	33	helwan	helwan	PROPN
ejpam-6358	2	34	11795	11795	NUM
ejpam-6358	2	35	,	,	PUNCT
ejpam-6358	2	36	egypt	egypt	PROPN
ejpam-6358	2	37	3	3	NUM
ejpam-6358	2	38	department	department	NOUN
ejpam-6358	2	39	of	of	ADP
ejpam-6358	2	40	mathematics	mathematic	NOUN
ejpam-6358	2	41	,	,	PUNCT
ejpam-6358	2	42	faculty	faculty	NOUN
ejpam-6358	2	43	of	of	ADP
ejpam-6358	2	44	science	science	NOUN
ejpam-6358	2	45	,	,	PUNCT
ejpam-6358	2	46	tanta	tanta	PROPN
ejpam-6358	2	47	university	university	PROPN
ejpam-6358	2	48	,	,	PUNCT
ejpam-6358	2	49	tanta	tanta	PROPN
ejpam-6358	2	50	31527	31527	NUM
ejpam-6358	2	51	,	,	PUNCT
ejpam-6358	2	52	egypt	egypt	PROPN
ejpam-6358	2	53	4	4	NUM
ejpam-6358	2	54	jadara	jadara	PROPN
ejpam-6358	2	55	university	university	PROPN
ejpam-6358	2	56	research	research	NOUN
ejpam-6358	2	57	center	center	NOUN
ejpam-6358	2	58	,	,	PUNCT
ejpam-6358	2	59	jadara	jadara	PROPN
ejpam-6358	2	60	university	university	PROPN
ejpam-6358	2	61	,	,	PUNCT
ejpam-6358	2	62	irbid	irbid	VERB
ejpam-6358	2	63	21110	21110	NUM
ejpam-6358	2	64	,	,	PUNCT
ejpam-6358	2	65	jordan	jordan	PROPN
ejpam-6358	2	66	abstract	abstract	PROPN
ejpam-6358	2	67	.	.	PUNCT
ejpam-6358	3	1	in	in	ADP
ejpam-6358	3	2	their	their	PRON
ejpam-6358	3	3	article	article	NOUN
ejpam-6358	3	4	,	,	PUNCT
ejpam-6358	3	5	“	"	PUNCT
ejpam-6358	3	6	generalized	generalized	ADJ
ejpam-6358	3	7	approximation	approximation	NOUN
ejpam-6358	3	8	spaces	space	NOUN
ejpam-6358	3	9	generation	generation	NOUN
ejpam-6358	3	10	from	from	ADP
ejpam-6358	3	11	ij	ij	NOUN
ejpam-6358	3	12	-	-	PUNCT
ejpam-6358	3	13	neighborhoods	neighborhood	NOUN
ejpam-6358	3	14	and	and	CCONJ
ejpam-6358	3	15	ideals	ideal	NOUN
ejpam-6358	3	16	with	with	ADP
ejpam-6358	3	17	application	application	NOUN
ejpam-6358	3	18	to	to	ADP
ejpam-6358	3	19	chikungunya	chikungunya	NOUN
ejpam-6358	3	20	disease	disease	NOUN
ejpam-6358	3	21	,	,	PUNCT
ejpam-6358	3	22	”	"	PUNCT
ejpam-6358	3	23	published	publish	VERB
ejpam-6358	3	24	in	in	ADP
ejpam-6358	3	25	aims	aim	NOUN
ejpam-6358	3	26	mathematics	mathematic	NOUN
ejpam-6358	3	27	,	,	PUNCT
ejpam-6358	3	28	9(4	9(4	NUM
ejpam-6358	3	29	)	)	PUNCT
ejpam-6358	3	30	(	(	PUNCT
ejpam-6358	3	31	2024	2024	NUM
ejpam-6358	3	32	)	)	PUNCT
ejpam-6358	3	33	,	,	PUNCT
ejpam-6358	3	34	10050–10077	10050–10077	NUM
ejpam-6358	3	35	,	,	PUNCT
ejpam-6358	3	36	t.	t.	PROPN
ejpam-6358	3	37	m.	m.	PROPN
ejpam-6358	3	38	al	al	PROPN
ejpam-6358	3	39	-	-	PUNCT
ejpam-6358	3	40	shami	shami	PROPN
ejpam-6358	3	41	and	and	CCONJ
ejpam-6358	3	42	m.	m.	PROPN
ejpam-6358	3	43	hosny	hosny	PROPN
ejpam-6358	3	44	introduced	introduce	VERB
ejpam-6358	3	45	a	a	DET
ejpam-6358	3	46	novel	novel	ADJ
ejpam-6358	3	47	framework	framework	NOUN
ejpam-6358	3	48	for	for	ADP
ejpam-6358	3	49	constructing	construct	VERB
ejpam-6358	3	50	generalized	generalized	ADJ
ejpam-6358	3	51	approximation	approximation	NOUN
ejpam-6358	3	52	spaces	space	NOUN
ejpam-6358	3	53	utilizing	utilize	VERB
ejpam-6358	3	54	ij	ij	NOUN
ejpam-6358	3	55	-	-	PUNCT
ejpam-6358	3	56	neighborhoods	neighborhood	NOUN
ejpam-6358	3	57	and	and	CCONJ
ejpam-6358	3	58	ideals	ideal	NOUN
ejpam-6358	3	59	.	.	PUNCT
ejpam-6358	4	1	this	this	DET
ejpam-6358	4	2	current	current	ADJ
ejpam-6358	4	3	paper	paper	NOUN
ejpam-6358	4	4	undertakes	undertake	VERB
ejpam-6358	4	5	a	a	DET
ejpam-6358	4	6	critical	critical	ADJ
ejpam-6358	4	7	validation	validation	NOUN
ejpam-6358	4	8	of	of	ADP
ejpam-6358	4	9	the	the	DET
ejpam-6358	4	10	published	publish	VERB
ejpam-6358	4	11	work	work	NOUN
ejpam-6358	4	12	.	.	PUNCT
ejpam-6358	5	1	our	our	PRON
ejpam-6358	5	2	detailed	detailed	ADJ
ejpam-6358	5	3	investigation	investigation	NOUN
ejpam-6358	5	4	indicates	indicate	VERB
ejpam-6358	5	5	that	that	SCONJ
ejpam-6358	5	6	several	several	ADJ
ejpam-6358	5	7	core	core	NOUN
ejpam-6358	5	8	propositions	proposition	NOUN
ejpam-6358	5	9	and	and	CCONJ
ejpam-6358	5	10	methodological	methodological	ADJ
ejpam-6358	5	11	instances	instance	NOUN
ejpam-6358	5	12	require	require	VERB
ejpam-6358	5	13	careful	careful	ADJ
ejpam-6358	5	14	re	re	NOUN
ejpam-6358	5	15	-	-	NOUN
ejpam-6358	5	16	examination	examination	NOUN
ejpam-6358	5	17	and	and	CCONJ
ejpam-6358	5	18	precision	precision	NOUN
ejpam-6358	5	19	,	,	PUNCT
ejpam-6358	5	20	including	include	VERB
ejpam-6358	5	21	the	the	DET
ejpam-6358	5	22	formulation	formulation	NOUN
ejpam-6358	5	23	of	of	ADP
ejpam-6358	5	24	key	key	ADJ
ejpam-6358	5	25	results	result	NOUN
ejpam-6358	5	26	,	,	PUNCT
ejpam-6358	5	27	underlying	underlying	ADJ
ejpam-6358	5	28	derivations	derivation	NOUN
ejpam-6358	5	29	,	,	PUNCT
ejpam-6358	5	30	and	and	CCONJ
ejpam-6358	5	31	illustrative	illustrative	ADJ
ejpam-6358	5	32	examples	example	NOUN
ejpam-6358	5	33	.	.	PUNCT
ejpam-6358	6	1	to	to	PART
ejpam-6358	6	2	address	address	VERB
ejpam-6358	6	3	these	these	DET
ejpam-6358	6	4	areas	area	NOUN
ejpam-6358	6	5	,	,	PUNCT
ejpam-6358	6	6	we	we	PRON
ejpam-6358	6	7	provide	provide	VERB
ejpam-6358	6	8	rigorous	rigorous	ADJ
ejpam-6358	6	9	counterexamples	counterexample	NOUN
ejpam-6358	6	10	that	that	PRON
ejpam-6358	6	11	highlight	highlight	VERB
ejpam-6358	6	12	where	where	SCONJ
ejpam-6358	6	13	further	further	ADJ
ejpam-6358	6	14	theoretical	theoretical	ADJ
ejpam-6358	6	15	refinement	refinement	NOUN
ejpam-6358	6	16	is	be	AUX
ejpam-6358	6	17	necessary	necessary	ADJ
ejpam-6358	6	18	.	.	PUNCT
ejpam-6358	7	1	we	we	PRON
ejpam-6358	7	2	subsequently	subsequently	ADV
ejpam-6358	7	3	correct	correct	VERB
ejpam-6358	7	4	and	and	CCONJ
ejpam-6358	7	5	formally	formally	ADV
ejpam-6358	7	6	refine	refine	VERB
ejpam-6358	7	7	the	the	DET
ejpam-6358	7	8	established	establish	VERB
ejpam-6358	7	9	findings	finding	NOUN
ejpam-6358	7	10	,	,	PUNCT
ejpam-6358	7	11	offer	offer	VERB
ejpam-6358	7	12	enhanced	enhance	VERB
ejpam-6358	7	13	mathematical	mathematical	ADJ
ejpam-6358	7	14	formulations	formulation	NOUN
ejpam-6358	7	15	for	for	ADP
ejpam-6358	7	16	critical	critical	ADJ
ejpam-6358	7	17	concepts	concept	NOUN
ejpam-6358	7	18	,	,	PUNCT
ejpam-6358	7	19	and	and	CCONJ
ejpam-6358	7	20	present	present	VERB
ejpam-6358	7	21	new	new	ADJ
ejpam-6358	7	22	properties	property	NOUN
ejpam-6358	7	23	and	and	CCONJ
ejpam-6358	7	24	clarifications	clarification	NOUN
ejpam-6358	7	25	.	.	PUNCT
ejpam-6358	8	1	the	the	DET
ejpam-6358	8	2	goal	goal	NOUN
ejpam-6358	8	3	of	of	ADP
ejpam-6358	8	4	this	this	DET
ejpam-6358	8	5	paper	paper	NOUN
ejpam-6358	8	6	is	be	AUX
ejpam-6358	8	7	to	to	PART
ejpam-6358	8	8	strengthen	strengthen	VERB
ejpam-6358	8	9	the	the	DET
ejpam-6358	8	10	theoretical	theoretical	ADJ
ejpam-6358	8	11	foundation	foundation	NOUN
ejpam-6358	8	12	of	of	ADP
ejpam-6358	8	13	these	these	DET
ejpam-6358	8	14	generalized	generalized	ADJ
ejpam-6358	8	15	approximation	approximation	NOUN
ejpam-6358	8	16	spaces	space	NOUN
ejpam-6358	8	17	,	,	PUNCT
ejpam-6358	8	18	ensuring	ensure	VERB
ejpam-6358	8	19	maximal	maximal	ADJ
ejpam-6358	8	20	rigor	rigor	NOUN
ejpam-6358	8	21	and	and	CCONJ
ejpam-6358	8	22	practical	practical	ADJ
ejpam-6358	8	23	applicability	applicability	NOUN
ejpam-6358	8	24	for	for	ADP
ejpam-6358	8	25	future	future	ADJ
ejpam-6358	8	26	research	research	NOUN
ejpam-6358	8	27	in	in	ADP
ejpam-6358	8	28	the	the	DET
ejpam-6358	8	29	field	field	NOUN
ejpam-6358	8	30	.	.	PUNCT
ejpam-6358	9	1	2020	2020	NUM
ejpam-6358	9	2	mathematics	mathematic	NOUN
ejpam-6358	9	3	subject	subject	NOUN
ejpam-6358	9	4	classifications	classification	NOUN
ejpam-6358	9	5	:	:	PUNCT
ejpam-6358	9	6	03e72	03e72	NUM
ejpam-6358	9	7	,	,	PUNCT
ejpam-6358	9	8	54a05	54a05	NUM
ejpam-6358	9	9	,	,	PUNCT
ejpam-6358	9	10	68t30	68t30	NUM
ejpam-6358	9	11	,	,	PUNCT
ejpam-6358	9	12	91b06	91b06	NUM
ejpam-6358	9	13	key	key	ADJ
ejpam-6358	9	14	words	word	NOUN
ejpam-6358	9	15	and	and	CCONJ
ejpam-6358	9	16	phrases	phrase	NOUN
ejpam-6358	9	17	:	:	PUNCT
ejpam-6358	9	18	ij	ij	NOUN
ejpam-6358	9	19	-	-	NOUN
ejpam-6358	9	20	neighborhoods	neighborhood	NOUN
ejpam-6358	9	21	,	,	PUNCT
ejpam-6358	9	22	ikj	ikj	PROPN
ejpam-6358	9	23	-neighborhoods	-neighborhood	NOUN
ejpam-6358	9	24	,	,	PUNCT
ejpam-6358	9	25	approximation	approximation	NOUN
ejpam-6358	9	26	operators	operator	NOUN
ejpam-6358	9	27	,	,	PUNCT
ejpam-6358	9	28	rough	rough	ADJ
ejpam-6358	9	29	sets	set	NOUN
ejpam-6358	9	30	,	,	PUNCT
ejpam-6358	9	31	topology	topology	NOUN
ejpam-6358	9	32	∗corresponding	∗corresponding	NOUN
ejpam-6358	9	33	author	author	NOUN
ejpam-6358	9	34	.	.	PUNCT
ejpam-6358	10	1	doi	doi	NOUN
ejpam-6358	10	2	:	:	PUNCT
ejpam-6358	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6358	https://doi.org/10.29020/nybg.ejpam.v18i4.6358	PROPN
ejpam-6358	10	4	email	email	NOUN
ejpam-6358	10	5	addresses	address	NOUN
ejpam-6358	10	6	:	:	PUNCT
ejpam-6358	10	7	hrodyna@yahoo.com	hrodyna@yahoo.com	X
ejpam-6358	10	8	(	(	PUNCT
ejpam-6358	10	9	r.	r.	PROPN
ejpam-6358	10	10	a.	a.	PROPN
ejpam-6358	10	11	hosny	hosny	PROPN
ejpam-6358	10	12	)	)	PUNCT
ejpam-6358	10	13	,	,	PUNCT
ejpam-6358	10	14	naglaa.madbouly@science.helwan.edu.eg	naglaa.madbouly@science.helwan.edu.eg	X
ejpam-6358	10	15	(	(	PUNCT
ejpam-6358	10	16	n.	n.	PROPN
ejpam-6358	10	17	m.	m.	PROPN
ejpam-6358	10	18	madbouly	madbouly	PROPN
ejpam-6358	10	19	)	)	PUNCT
ejpam-6358	10	20	,	,	PUNCT
ejpam-6358	10	21	mkamel_bably@yahoo.com	mkamel_bably@yahoo.com	X
ejpam-6358	10	22	(	(	PUNCT
ejpam-6358	10	23	m.	m.	PROPN
ejpam-6358	10	24	k.	k.	PROPN
ejpam-6358	11	1	el	el	PROPN
ejpam-6358	11	2	-	-	PROPN
ejpam-6358	11	3	bably	bably	ADV
ejpam-6358	11	4	)	)	PUNCT
ejpam-6358	11	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6358	12	1	1	1	NUM
ejpam-6358	12	2	copyright	copyright	NOUN
ejpam-6358	12	3	:	:	PUNCT
ejpam-6358	12	4	©	©	PROPN
ejpam-6358	12	5	2025	2025	NUM
ejpam-6358	12	6	the	the	DET
ejpam-6358	12	7	author(s	author(s	NOUN
ejpam-6358	12	8	)	)	PUNCT
ejpam-6358	12	9	.	.	PUNCT
ejpam-6358	13	1	(	(	PUNCT
ejpam-6358	13	2	cc	cc	NOUN
ejpam-6358	13	3	by	by	ADP
ejpam-6358	13	4	-	-	PUNCT
ejpam-6358	13	5	nc	nc	PROPN
ejpam-6358	13	6	4.0	4.0	NUM
ejpam-6358	13	7	)	)	PUNCT
ejpam-6358	13	8	r.	r.	PROPN
ejpam-6358	13	9	a.	a.	PROPN
ejpam-6358	13	10	hosny	hosny	PROPN
ejpam-6358	13	11	et	et	PROPN
ejpam-6358	13	12	al	al	PROPN
ejpam-6358	13	13	.	.	PUNCT
ejpam-6358	13	14	/	/	SYM
ejpam-6358	13	15	eur	eur	PROPN
ejpam-6358	13	16	.	.	PUNCT
ejpam-6358	14	1	j.	j.	PROPN
ejpam-6358	14	2	pure	pure	PROPN
ejpam-6358	14	3	appl	appl	PROPN
ejpam-6358	14	4	.	.	PROPN
ejpam-6358	14	5	math	math	PROPN
ejpam-6358	14	6	,	,	PUNCT
ejpam-6358	14	7	18	18	NUM
ejpam-6358	14	8	(	(	PUNCT
ejpam-6358	14	9	4	4	NUM
ejpam-6358	14	10	)	)	PUNCT
ejpam-6358	14	11	(	(	PUNCT
ejpam-6358	14	12	2025	2025	NUM
ejpam-6358	14	13	)	)	PUNCT
ejpam-6358	14	14	,	,	PUNCT
ejpam-6358	14	15	6358	6358	NUM
ejpam-6358	14	16	2	2	NUM
ejpam-6358	14	17	of	of	ADP
ejpam-6358	14	18	24	24	NUM
ejpam-6358	14	19	1	1	NUM
ejpam-6358	14	20	.	.	PUNCT
ejpam-6358	15	1	introduction	introduction	NOUN
ejpam-6358	15	2	•	•	NUM
ejpam-6358	15	3	literature	literature	PROPN
ejpam-6358	15	4	review	review	PROPN
ejpam-6358	15	5	:	:	PUNCT
ejpam-6358	15	6	the	the	DET
ejpam-6358	15	7	theory	theory	NOUN
ejpam-6358	15	8	of	of	ADP
ejpam-6358	15	9	rough	rough	ADJ
ejpam-6358	15	10	sets	set	NOUN
ejpam-6358	15	11	is	be	AUX
ejpam-6358	15	12	a	a	DET
ejpam-6358	15	13	significant	significant	ADJ
ejpam-6358	15	14	and	and	CCONJ
ejpam-6358	15	15	effective	effective	ADJ
ejpam-6358	15	16	methodology	methodology	NOUN
ejpam-6358	15	17	for	for	ADP
ejpam-6358	15	18	handling	handle	VERB
ejpam-6358	15	19	uncertainty	uncertainty	NOUN
ejpam-6358	15	20	and	and	CCONJ
ejpam-6358	15	21	ambiguity	ambiguity	NOUN
ejpam-6358	15	22	in	in	ADP
ejpam-6358	15	23	data	datum	NOUN
ejpam-6358	15	24	,	,	PUNCT
ejpam-6358	15	25	as	as	ADV
ejpam-6358	15	26	well	well	ADV
ejpam-6358	15	27	as	as	ADP
ejpam-6358	15	28	for	for	ADP
ejpam-6358	15	29	analyzing	analyze	VERB
ejpam-6358	15	30	and	and	CCONJ
ejpam-6358	15	31	extracting	extract	VERB
ejpam-6358	15	32	knowledge	knowledge	NOUN
ejpam-6358	15	33	from	from	ADP
ejpam-6358	15	34	it	it	PRON
ejpam-6358	15	35	.	.	PUNCT
ejpam-6358	16	1	introduced	introduce	VERB
ejpam-6358	16	2	by	by	ADP
ejpam-6358	16	3	pawlak	pawlak	ADJ
ejpam-6358	16	4	in	in	ADP
ejpam-6358	16	5	1982	1982	NUM
ejpam-6358	16	6	[	[	X
ejpam-6358	16	7	1	1	NUM
ejpam-6358	16	8	,	,	PUNCT
ejpam-6358	16	9	2	2	NUM
ejpam-6358	16	10	]	]	PUNCT
ejpam-6358	16	11	,	,	PUNCT
ejpam-6358	16	12	this	this	DET
ejpam-6358	16	13	theory	theory	NOUN
ejpam-6358	16	14	has	have	AUX
ejpam-6358	16	15	served	serve	VERB
ejpam-6358	16	16	as	as	ADP
ejpam-6358	16	17	a	a	DET
ejpam-6358	16	18	foundational	foundational	ADJ
ejpam-6358	16	19	framework	framework	NOUN
ejpam-6358	16	20	for	for	ADP
ejpam-6358	16	21	effective	effective	ADJ
ejpam-6358	16	22	solutions	solution	NOUN
ejpam-6358	16	23	to	to	ADP
ejpam-6358	16	24	decision	decision	NOUN
ejpam-6358	16	25	-	-	PUNCT
ejpam-6358	16	26	making	make	VERB
ejpam-6358	16	27	problems	problem	NOUN
ejpam-6358	16	28	.	.	PUNCT
ejpam-6358	17	1	despite	despite	SCONJ
ejpam-6358	17	2	its	its	PRON
ejpam-6358	17	3	strengths	strength	NOUN
ejpam-6358	17	4	,	,	PUNCT
ejpam-6358	17	5	the	the	DET
ejpam-6358	17	6	constraints	constraint	NOUN
ejpam-6358	17	7	of	of	ADP
ejpam-6358	17	8	equivalence	equivalence	NOUN
ejpam-6358	17	9	relation	relation	NOUN
ejpam-6358	17	10	conditions	condition	NOUN
ejpam-6358	17	11	central	central	ADJ
ejpam-6358	17	12	to	to	ADP
ejpam-6358	17	13	this	this	DET
ejpam-6358	17	14	approach	approach	NOUN
ejpam-6358	17	15	have	have	AUX
ejpam-6358	17	16	led	lead	VERB
ejpam-6358	17	17	many	many	ADJ
ejpam-6358	17	18	researchers	researcher	NOUN
ejpam-6358	17	19	to	to	PART
ejpam-6358	17	20	propose	propose	VERB
ejpam-6358	17	21	generalizations	generalization	NOUN
ejpam-6358	17	22	and	and	CCONJ
ejpam-6358	17	23	extensions	extension	NOUN
ejpam-6358	17	24	to	to	PART
ejpam-6358	17	25	broaden	broaden	VERB
ejpam-6358	17	26	its	its	PRON
ejpam-6358	17	27	applications	application	NOUN
ejpam-6358	17	28	.	.	PUNCT
ejpam-6358	18	1	several	several	ADJ
ejpam-6358	18	2	avenues	avenue	NOUN
ejpam-6358	18	3	have	have	AUX
ejpam-6358	18	4	been	be	AUX
ejpam-6358	18	5	explored	explore	VERB
ejpam-6358	18	6	in	in	ADP
ejpam-6358	18	7	this	this	DET
ejpam-6358	18	8	regard	regard	NOUN
ejpam-6358	18	9	.	.	PUNCT
ejpam-6358	19	1	for	for	ADP
ejpam-6358	19	2	instance	instance	NOUN
ejpam-6358	19	3	,	,	PUNCT
ejpam-6358	19	4	yao	yao	PROPN
ejpam-6358	20	1	[	[	X
ejpam-6358	20	2	3	3	NUM
ejpam-6358	20	3	]	]	PUNCT
ejpam-6358	20	4	extended	extend	VERB
ejpam-6358	20	5	the	the	DET
ejpam-6358	20	6	concept	concept	NOUN
ejpam-6358	20	7	of	of	ADP
ejpam-6358	20	8	an	an	DET
ejpam-6358	20	9	equivalence	equivalence	NOUN
ejpam-6358	20	10	relation	relation	NOUN
ejpam-6358	20	11	to	to	ADP
ejpam-6358	20	12	a	a	DET
ejpam-6358	20	13	more	more	ADV
ejpam-6358	20	14	general	general	ADJ
ejpam-6358	20	15	binary	binary	NOUN
ejpam-6358	20	16	relation	relation	PROPN
ejpam-6358	20	17	,	,	PUNCT
ejpam-6358	20	18	introducing	introduce	VERB
ejpam-6358	20	19	the	the	DET
ejpam-6358	20	20	notions	notion	NOUN
ejpam-6358	20	21	of	of	ADP
ejpam-6358	20	22	right	right	NOUN
ejpam-6358	20	23	and	and	CCONJ
ejpam-6358	20	24	left	leave	VERB
ejpam-6358	20	25	neighborhoods	neighborhood	NOUN
ejpam-6358	20	26	derived	derive	VERB
ejpam-6358	20	27	from	from	ADP
ejpam-6358	20	28	the	the	DET
ejpam-6358	20	29	concepts	concept	NOUN
ejpam-6358	20	30	of	of	ADP
ejpam-6358	20	31	afterand	afterand	NOUN
ejpam-6358	20	32	beforesets	beforeset	NOUN
ejpam-6358	20	33	,	,	PUNCT
ejpam-6358	20	34	which	which	PRON
ejpam-6358	20	35	were	be	AUX
ejpam-6358	20	36	defined	define	VERB
ejpam-6358	20	37	in	in	ADP
ejpam-6358	20	38	[	[	X
ejpam-6358	20	39	4	4	NUM
ejpam-6358	20	40	]	]	PUNCT
ejpam-6358	20	41	.	.	PUNCT
ejpam-6358	21	1	similarly	similarly	ADV
ejpam-6358	21	2	,	,	PUNCT
ejpam-6358	21	3	allam	allam	PROPN
ejpam-6358	21	4	et	et	PROPN
ejpam-6358	21	5	al	al	PROPN
ejpam-6358	21	6	.	.	PUNCT
ejpam-6358	22	1	[	[	X
ejpam-6358	22	2	5	5	NUM
ejpam-6358	22	3	,	,	PUNCT
ejpam-6358	22	4	6	6	NUM
ejpam-6358	22	5	]	]	PUNCT
ejpam-6358	22	6	proposed	propose	VERB
ejpam-6358	22	7	minimal	minimal	ADJ
ejpam-6358	22	8	right	right	NOUN
ejpam-6358	22	9	and	and	CCONJ
ejpam-6358	22	10	minimal	minimal	ADJ
ejpam-6358	22	11	left	leave	VERB
ejpam-6358	22	12	neighborhoods	neighborhood	NOUN
ejpam-6358	22	13	to	to	PART
ejpam-6358	22	14	generate	generate	VERB
ejpam-6358	22	15	new	new	ADJ
ejpam-6358	22	16	approximations	approximation	NOUN
ejpam-6358	22	17	that	that	PRON
ejpam-6358	22	18	generalize	generalize	VERB
ejpam-6358	22	19	pawlak	pawlak	ADJ
ejpam-6358	22	20	’s	’s	PART
ejpam-6358	22	21	rough	rough	ADJ
ejpam-6358	22	22	set	set	NOUN
ejpam-6358	22	23	theory	theory	NOUN
ejpam-6358	22	24	.	.	PUNCT
ejpam-6358	23	1	in	in	ADP
ejpam-6358	23	2	2007	2007	NUM
ejpam-6358	23	3	,	,	PUNCT
ejpam-6358	23	4	abo	abo	NOUN
ejpam-6358	23	5	khadra	khadra	NOUN
ejpam-6358	23	6	et	et	PROPN
ejpam-6358	23	7	al	al	PROPN
ejpam-6358	23	8	.	.	PUNCT
ejpam-6358	24	1	[	[	X
ejpam-6358	24	2	7	7	X
ejpam-6358	24	3	]	]	PUNCT
ejpam-6358	24	4	introduced	introduce	VERB
ejpam-6358	24	5	a	a	DET
ejpam-6358	24	6	technique	technique	NOUN
ejpam-6358	24	7	to	to	PART
ejpam-6358	24	8	generalize	generalize	VERB
ejpam-6358	24	9	pawlak	pawlak	ADJ
ejpam-6358	24	10	’s	’s	PART
ejpam-6358	24	11	approximation	approximation	NOUN
ejpam-6358	24	12	space	space	NOUN
ejpam-6358	24	13	using	use	VERB
ejpam-6358	24	14	binary	binary	ADJ
ejpam-6358	24	15	relations	relation	NOUN
ejpam-6358	24	16	.	.	PUNCT
ejpam-6358	25	1	this	this	DET
ejpam-6358	25	2	method	method	NOUN
ejpam-6358	25	3	constructs	construct	VERB
ejpam-6358	25	4	dual	dual	ADJ
ejpam-6358	25	5	topologies	topology	NOUN
ejpam-6358	25	6	directly	directly	ADV
ejpam-6358	25	7	from	from	ADP
ejpam-6358	25	8	right	right	ADJ
ejpam-6358	25	9	and	and	CCONJ
ejpam-6358	25	10	left	leave	VERB
ejpam-6358	25	11	neighborhoods	neighborhood	NOUN
ejpam-6358	25	12	,	,	PUNCT
ejpam-6358	25	13	without	without	ADP
ejpam-6358	25	14	modifying	modify	VERB
ejpam-6358	25	15	the	the	DET
ejpam-6358	25	16	data	datum	NOUN
ejpam-6358	25	17	within	within	ADP
ejpam-6358	25	18	the	the	DET
ejpam-6358	25	19	information	information	NOUN
ejpam-6358	25	20	system	system	NOUN
ejpam-6358	25	21	.	.	PUNCT
ejpam-6358	26	1	it	it	PRON
ejpam-6358	26	2	asserts	assert	VERB
ejpam-6358	26	3	that	that	SCONJ
ejpam-6358	26	4	the	the	DET
ejpam-6358	26	5	class	class	NOUN
ejpam-6358	26	6	t	t	NOUN
ejpam-6358	26	7	=	=	PUNCT
ejpam-6358	26	8	{	{	PUNCT
ejpam-6358	26	9	a	a	DET
ejpam-6358	26	10	⊆	⊆	NUM
ejpam-6358	26	11	u	u	NOUN
ejpam-6358	26	12	:	:	PUNCT
ejpam-6358	26	13	℧	℧	PROPN
ejpam-6358	26	14	(	(	PUNCT
ejpam-6358	26	15	s	s	NOUN
ejpam-6358	26	16	)	)	PUNCT
ejpam-6358	26	17	⊆	⊆	PROPN
ejpam-6358	26	18	a	a	PRON
ejpam-6358	26	19	,	,	PUNCT
ejpam-6358	26	20	∀s	∀s	PROPN
ejpam-6358	26	21	∈	∈	PROPN
ejpam-6358	26	22	a	a	DET
ejpam-6358	26	23	}	}	PUNCT
ejpam-6358	26	24	forms	form	VERB
ejpam-6358	26	25	a	a	DET
ejpam-6358	26	26	topology	topology	NOUN
ejpam-6358	26	27	on	on	ADP
ejpam-6358	26	28	u	u	PROPN
ejpam-6358	26	29	,	,	PUNCT
ejpam-6358	26	30	where	where	SCONJ
ejpam-6358	26	31	u	u	PRON
ejpam-6358	26	32	represents	represent	VERB
ejpam-6358	26	33	the	the	DET
ejpam-6358	26	34	universe	universe	NOUN
ejpam-6358	26	35	and	and	CCONJ
ejpam-6358	26	36	℧	℧	PROPN
ejpam-6358	26	37	(	(	PUNCT
ejpam-6358	26	38	s	s	X
ejpam-6358	26	39	)	)	PUNCT
ejpam-6358	26	40	is	be	AUX
ejpam-6358	26	41	the	the	DET
ejpam-6358	26	42	neighborhood	neighborhood	NOUN
ejpam-6358	26	43	of	of	ADP
ejpam-6358	26	44	s.	s.	PROPN
ejpam-6358	26	45	by	by	ADP
ejpam-6358	26	46	defining	define	VERB
ejpam-6358	26	47	these	these	DET
ejpam-6358	26	48	neighborhoods	neighborhood	NOUN
ejpam-6358	26	49	,	,	PUNCT
ejpam-6358	26	50	various	various	ADJ
ejpam-6358	26	51	topologies	topology	NOUN
ejpam-6358	26	52	on	on	ADP
ejpam-6358	26	53	u	u	NOUN
ejpam-6358	26	54	can	can	AUX
ejpam-6358	26	55	be	be	AUX
ejpam-6358	26	56	generated	generate	VERB
ejpam-6358	26	57	.	.	PUNCT
ejpam-6358	27	1	this	this	DET
ejpam-6358	27	2	technique	technique	NOUN
ejpam-6358	27	3	was	be	AUX
ejpam-6358	27	4	expanded	expand	VERB
ejpam-6358	27	5	in	in	ADP
ejpam-6358	27	6	el	el	PROPN
ejpam-6358	27	7	-	-	PUNCT
ejpam-6358	27	8	bably	bably	PROPN
ejpam-6358	27	9	’s	’s	PART
ejpam-6358	27	10	2008	2008	NUM
ejpam-6358	27	11	master	master	NOUN
ejpam-6358	27	12	’s	’s	PART
ejpam-6358	27	13	thesis	thesis	NOUN
ejpam-6358	28	1	[	[	X
ejpam-6358	28	2	8	8	NUM
ejpam-6358	28	3	]	]	PUNCT
ejpam-6358	28	4	,	,	PUNCT
ejpam-6358	28	5	which	which	PRON
ejpam-6358	28	6	examined	examine	VERB
ejpam-6358	28	7	additional	additional	ADJ
ejpam-6358	28	8	topological	topological	ADJ
ejpam-6358	28	9	structures	structure	NOUN
ejpam-6358	28	10	and	and	CCONJ
ejpam-6358	28	11	rough	rough	ADJ
ejpam-6358	28	12	set	set	NOUN
ejpam-6358	28	13	theory	theory	NOUN
ejpam-6358	28	14	generalizations	generalization	NOUN
ejpam-6358	28	15	.	.	PUNCT
ejpam-6358	29	1	later	later	ADV
ejpam-6358	29	2	,	,	PUNCT
ejpam-6358	29	3	abd	abd	PROPN
ejpam-6358	29	4	el	el	PROPN
ejpam-6358	29	5	-	-	PROPN
ejpam-6358	29	6	monsef	monsef	PROPN
ejpam-6358	29	7	et	et	PROPN
ejpam-6358	29	8	al	al	PROPN
ejpam-6358	29	9	.	.	PUNCT
ejpam-6358	30	1	[	[	X
ejpam-6358	30	2	9	9	NUM
ejpam-6358	30	3	]	]	PUNCT
ejpam-6358	30	4	extended	extend	VERB
ejpam-6358	30	5	the	the	DET
ejpam-6358	30	6	work	work	NOUN
ejpam-6358	30	7	of	of	ADP
ejpam-6358	30	8	[	[	X
ejpam-6358	30	9	7	7	NUM
ejpam-6358	30	10	,	,	PUNCT
ejpam-6358	30	11	8	8	NUM
ejpam-6358	30	12	]	]	PUNCT
ejpam-6358	30	13	by	by	ADP
ejpam-6358	30	14	introducing	introduce	VERB
ejpam-6358	30	15	a	a	DET
ejpam-6358	30	16	new	new	ADJ
ejpam-6358	30	17	space	space	NOUN
ejpam-6358	30	18	called	call	VERB
ejpam-6358	30	19	jneighborhood	jneighborhood	ADJ
ejpam-6358	30	20	space	space	NOUN
ejpam-6358	30	21	(	(	PUNCT
ejpam-6358	30	22	j	j	NOUN
ejpam-6358	30	23	-	-	PUNCT
ejpam-6358	30	24	ns	ns	NUM
ejpam-6358	30	25	)	)	PUNCT
ejpam-6358	30	26	,	,	PUNCT
ejpam-6358	30	27	constructed	construct	VERB
ejpam-6358	30	28	by	by	ADP
ejpam-6358	30	29	defining	define	VERB
ejpam-6358	30	30	union	union	NOUN
ejpam-6358	30	31	and	and	CCONJ
ejpam-6358	30	32	intersection	intersection	NOUN
ejpam-6358	30	33	neighborhoods	neighborhood	NOUN
ejpam-6358	30	34	from	from	ADP
ejpam-6358	30	35	right	right	ADJ
ejpam-6358	30	36	and	and	CCONJ
ejpam-6358	30	37	minimal	minimal	ADJ
ejpam-6358	30	38	right	right	ADJ
ejpam-6358	30	39	neighborhoods	neighborhood	NOUN
ejpam-6358	30	40	.	.	PUNCT
ejpam-6358	31	1	this	this	DET
ejpam-6358	31	2	development	development	NOUN
ejpam-6358	31	3	led	lead	VERB
ejpam-6358	31	4	to	to	ADP
ejpam-6358	31	5	eight	eight	NUM
ejpam-6358	31	6	types	type	NOUN
ejpam-6358	31	7	of	of	ADP
ejpam-6358	31	8	neighborhoods	neighborhood	NOUN
ejpam-6358	31	9	derived	derive	VERB
ejpam-6358	31	10	from	from	ADP
ejpam-6358	31	11	binary	binary	ADJ
ejpam-6358	31	12	relations	relation	NOUN
ejpam-6358	31	13	,	,	PUNCT
ejpam-6358	31	14	which	which	PRON
ejpam-6358	31	15	have	have	AUX
ejpam-6358	31	16	been	be	AUX
ejpam-6358	31	17	widely	widely	ADV
ejpam-6358	31	18	used	use	VERB
ejpam-6358	31	19	in	in	ADP
ejpam-6358	31	20	recent	recent	ADJ
ejpam-6358	31	21	studies	study	NOUN
ejpam-6358	31	22	to	to	PART
ejpam-6358	31	23	define	define	VERB
ejpam-6358	31	24	neighborhoods	neighborhood	NOUN
ejpam-6358	31	25	based	base	VERB
ejpam-6358	31	26	on	on	ADP
ejpam-6358	31	27	these	these	DET
ejpam-6358	31	28	concepts	concept	NOUN
ejpam-6358	31	29	(	(	PUNCT
ejpam-6358	31	30	e.g.	e.g.	ADV
ejpam-6358	31	31	,	,	PUNCT
ejpam-6358	31	32	[	[	X
ejpam-6358	31	33	10	10	NUM
ejpam-6358	31	34	,	,	PUNCT
ejpam-6358	31	35	11	11	NUM
ejpam-6358	31	36	]	]	NUM
ejpam-6358	31	37	)	)	PUNCT
ejpam-6358	31	38	,	,	PUNCT
ejpam-6358	31	39	as	as	ADV
ejpam-6358	31	40	well	well	ADV
ejpam-6358	31	41	as	as	ADP
ejpam-6358	31	42	ej	ej	NOUN
ejpam-6358	31	43	-	-	NOUN
ejpam-6358	31	44	neighborhoods	neighborhood	NOUN
ejpam-6358	31	45	[	[	X
ejpam-6358	31	46	12	12	NUM
ejpam-6358	31	47	,	,	PUNCT
ejpam-6358	31	48	13	13	NUM
ejpam-6358	31	49	]	]	PUNCT
ejpam-6358	31	50	and	and	CCONJ
ejpam-6358	31	51	initial	initial	ADJ
ejpam-6358	31	52	neighborhoods	neighborhood	NOUN
ejpam-6358	31	53	[	[	X
ejpam-6358	31	54	14	14	NUM
ejpam-6358	31	55	,	,	PUNCT
ejpam-6358	31	56	15	15	NUM
ejpam-6358	31	57	]	]	PUNCT
ejpam-6358	31	58	.	.	PUNCT
ejpam-6358	32	1	yao	yao	NOUN
ejpam-6358	33	1	[	[	X
ejpam-6358	33	2	3	3	X
ejpam-6358	33	3	]	]	PUNCT
ejpam-6358	33	4	presented	present	VERB
ejpam-6358	33	5	a	a	DET
ejpam-6358	33	6	special	special	ADJ
ejpam-6358	33	7	class	class	NOUN
ejpam-6358	33	8	of	of	ADP
ejpam-6358	33	9	neighborhood	neighborhood	NOUN
ejpam-6358	33	10	systems	system	NOUN
ejpam-6358	33	11	,	,	PUNCT
ejpam-6358	33	12	termed	term	VERB
ejpam-6358	33	13	1	1	NUM
ejpam-6358	33	14	-	-	PUNCT
ejpam-6358	33	15	neighborhood	neighborhood	NOUN
ejpam-6358	33	16	systems	system	NOUN
ejpam-6358	33	17	,	,	PUNCT
ejpam-6358	33	18	which	which	PRON
ejpam-6358	33	19	combine	combine	VERB
ejpam-6358	33	20	right	right	ADV
ejpam-6358	33	21	and	and	CCONJ
ejpam-6358	33	22	left	leave	VERB
ejpam-6358	33	23	neighborhoods	neighborhood	NOUN
ejpam-6358	33	24	without	without	ADP
ejpam-6358	33	25	studying	study	VERB
ejpam-6358	33	26	topological	topological	ADJ
ejpam-6358	33	27	structures	structure	NOUN
ejpam-6358	33	28	.	.	PUNCT
ejpam-6358	34	1	kozae	kozae	PROPN
ejpam-6358	34	2	et	et	PROPN
ejpam-6358	34	3	al	al	PROPN
ejpam-6358	34	4	.	.	PUNCT
ejpam-6358	35	1	[	[	X
ejpam-6358	35	2	16	16	NUM
ejpam-6358	35	3	]	]	PUNCT
ejpam-6358	35	4	further	far	ADV
ejpam-6358	35	5	proposed	propose	VERB
ejpam-6358	35	6	r	r	NOUN
ejpam-6358	35	7	<	<	X
ejpam-6358	35	8	x	x	X
ejpam-6358	35	9	>	>	X
ejpam-6358	35	10	r	r	NOUN
ejpam-6358	35	11	as	as	ADP
ejpam-6358	35	12	the	the	DET
ejpam-6358	35	13	intersection	intersection	NOUN
ejpam-6358	35	14	of	of	ADP
ejpam-6358	35	15	minimal	minimal	ADJ
ejpam-6358	35	16	right	right	NOUN
ejpam-6358	35	17	and	and	CCONJ
ejpam-6358	35	18	left	leave	VERB
ejpam-6358	35	19	neighborhoods	neighborhood	NOUN
ejpam-6358	35	20	to	to	PART
ejpam-6358	35	21	define	define	VERB
ejpam-6358	35	22	rough	rough	ADJ
ejpam-6358	35	23	sets	set	NOUN
ejpam-6358	35	24	,	,	PUNCT
ejpam-6358	35	25	building	build	VERB
ejpam-6358	35	26	on	on	ADP
ejpam-6358	35	27	the	the	DET
ejpam-6358	35	28	works	work	NOUN
ejpam-6358	35	29	in	in	ADP
ejpam-6358	35	30	[	[	X
ejpam-6358	35	31	5	5	NUM
ejpam-6358	35	32	,	,	PUNCT
ejpam-6358	35	33	6	6	NUM
ejpam-6358	35	34	]	]	PUNCT
ejpam-6358	35	35	.	.	PUNCT
ejpam-6358	36	1	in	in	ADP
ejpam-6358	36	2	a	a	DET
ejpam-6358	36	3	subsequent	subsequent	ADJ
ejpam-6358	36	4	study	study	NOUN
ejpam-6358	36	5	,	,	PUNCT
ejpam-6358	36	6	atef	atef	PROPN
ejpam-6358	36	7	et	et	PROPN
ejpam-6358	36	8	al	al	PROPN
ejpam-6358	36	9	.	.	PUNCT
ejpam-6358	37	1	[	[	X
ejpam-6358	37	2	17	17	NUM
ejpam-6358	37	3	]	]	PUNCT
ejpam-6358	37	4	introduced	introduce	VERB
ejpam-6358	37	5	the	the	DET
ejpam-6358	37	6	j	j	NOUN
ejpam-6358	37	7	-	-	PUNCT
ejpam-6358	37	8	adhesion	adhesion	NOUN
ejpam-6358	37	9	neighborhood	neighborhood	NOUN
ejpam-6358	37	10	space	space	NOUN
ejpam-6358	37	11	,	,	PUNCT
ejpam-6358	37	12	highlighting	highlight	VERB
ejpam-6358	37	13	the	the	DET
ejpam-6358	37	14	potential	potential	NOUN
ejpam-6358	37	15	of	of	ADP
ejpam-6358	37	16	j	j	PROPN
ejpam-6358	37	17	-	-	PROPN
ejpam-6358	37	18	ns	ns	ADJ
ejpam-6358	37	19	to	to	PART
ejpam-6358	37	20	extend	extend	VERB
ejpam-6358	37	21	concepts	concept	NOUN
ejpam-6358	37	22	related	relate	VERB
ejpam-6358	37	23	to	to	ADP
ejpam-6358	37	24	adhesion	adhesion	NOUN
ejpam-6358	37	25	sets	set	NOUN
ejpam-6358	37	26	.	.	PUNCT
ejpam-6358	38	1	later	later	ADV
ejpam-6358	38	2	,	,	PUNCT
ejpam-6358	38	3	el	el	PROPN
ejpam-6358	38	4	-	-	ADJ
ejpam-6358	38	5	bably	bably	PROPN
ejpam-6358	38	6	et	et	PROPN
ejpam-6358	38	7	al	al	PROPN
ejpam-6358	38	8	.	.	PUNCT
ejpam-6358	39	1	[	[	X
ejpam-6358	39	2	18	18	NUM
ejpam-6358	39	3	]	]	PUNCT
ejpam-6358	39	4	addressed	address	VERB
ejpam-6358	39	5	inconsistencies	inconsistency	NOUN
ejpam-6358	39	6	in	in	ADP
ejpam-6358	39	7	the	the	DET
ejpam-6358	39	8	findings	finding	NOUN
ejpam-6358	39	9	of	of	ADP
ejpam-6358	39	10	atef	atef	PROPN
ejpam-6358	39	11	et	et	PROPN
ejpam-6358	39	12	al	al	PROPN
ejpam-6358	39	13	.	.	PROPN
ejpam-6358	39	14	,	,	PUNCT
ejpam-6358	39	15	providing	provide	VERB
ejpam-6358	39	16	corrected	correct	VERB
ejpam-6358	39	17	results	result	NOUN
ejpam-6358	39	18	and	and	CCONJ
ejpam-6358	39	19	additional	additional	ADJ
ejpam-6358	39	20	insights	insight	NOUN
ejpam-6358	39	21	into	into	ADP
ejpam-6358	39	22	j	j	NOUN
ejpam-6358	39	23	-	-	PUNCT
ejpam-6358	39	24	adhesion	adhesion	NOUN
ejpam-6358	39	25	neighborhoods	neighborhood	NOUN
ejpam-6358	39	26	.	.	PUNCT
ejpam-6358	40	1	their	their	PRON
ejpam-6358	40	2	approach	approach	NOUN
ejpam-6358	40	3	is	be	AUX
ejpam-6358	40	4	based	base	VERB
ejpam-6358	40	5	on	on	ADP
ejpam-6358	40	6	the	the	DET
ejpam-6358	40	7	concept	concept	NOUN
ejpam-6358	40	8	of	of	ADP
ejpam-6358	40	9	”	"	PUNCT
ejpam-6358	40	10	adhesion	adhesion	NOUN
ejpam-6358	40	11	sets	set	NOUN
ejpam-6358	40	12	”	"	PUNCT
ejpam-6358	40	13	proposed	propose	VERB
ejpam-6358	40	14	by	by	ADP
ejpam-6358	40	15	ma	ma	PROPN
ejpam-6358	40	16	in	in	ADP
ejpam-6358	40	17	2012	2012	NUM
ejpam-6358	40	18	[	[	X
ejpam-6358	40	19	19	19	NUM
ejpam-6358	40	20	]	]	PUNCT
ejpam-6358	40	21	,	,	PUNCT
ejpam-6358	40	22	which	which	PRON
ejpam-6358	40	23	is	be	AUX
ejpam-6358	40	24	relevant	relevant	ADJ
ejpam-6358	40	25	to	to	ADP
ejpam-6358	40	26	the	the	DET
ejpam-6358	40	27	theory	theory	NOUN
ejpam-6358	40	28	of	of	ADP
ejpam-6358	40	29	covering	cover	VERB
ejpam-6358	40	30	rough	rough	ADJ
ejpam-6358	40	31	sets	set	NOUN
ejpam-6358	40	32	.	.	PUNCT
ejpam-6358	41	1	additionally	additionally	ADV
ejpam-6358	41	2	,	,	PUNCT
ejpam-6358	41	3	nawar	nawar	NOUN
ejpam-6358	41	4	et	et	PROPN
ejpam-6358	41	5	al	al	PROPN
ejpam-6358	41	6	.	.	PUNCT
ejpam-6358	42	1	[	[	X
ejpam-6358	42	2	20	20	NUM
ejpam-6358	42	3	]	]	PUNCT
ejpam-6358	42	4	introduced	introduce	VERB
ejpam-6358	42	5	j	j	NOUN
ejpam-6358	42	6	-	-	PUNCT
ejpam-6358	42	7	adhesion	adhesion	NOUN
ejpam-6358	42	8	r.	r.	PROPN
ejpam-6358	42	9	a.	a.	PROPN
ejpam-6358	42	10	hosny	hosny	PROPN
ejpam-6358	42	11	et	et	PROPN
ejpam-6358	42	12	al	al	PROPN
ejpam-6358	42	13	.	.	PUNCT
ejpam-6358	42	14	/	/	SYM
ejpam-6358	42	15	eur	eur	PROPN
ejpam-6358	42	16	.	.	PUNCT
ejpam-6358	43	1	j.	j.	PROPN
ejpam-6358	43	2	pure	pure	PROPN
ejpam-6358	43	3	appl	appl	PROPN
ejpam-6358	43	4	.	.	PROPN
ejpam-6358	43	5	math	math	PROPN
ejpam-6358	43	6	,	,	PUNCT
ejpam-6358	43	7	18	18	NUM
ejpam-6358	43	8	(	(	PUNCT
ejpam-6358	43	9	4	4	NUM
ejpam-6358	43	10	)	)	PUNCT
ejpam-6358	43	11	(	(	PUNCT
ejpam-6358	43	12	2025	2025	NUM
ejpam-6358	43	13	)	)	PUNCT
ejpam-6358	43	14	,	,	PUNCT
ejpam-6358	43	15	6358	6358	NUM
ejpam-6358	43	16	3	3	NUM
ejpam-6358	43	17	of	of	ADP
ejpam-6358	43	18	24	24	NUM
ejpam-6358	43	19	neighborhoods	neighborhood	NOUN
ejpam-6358	43	20	in	in	ADP
ejpam-6358	43	21	covering	covering	NOUN
ejpam-6358	43	22	-	-	PUNCT
ejpam-6358	43	23	based	base	VERB
ejpam-6358	43	24	rough	rough	ADJ
ejpam-6358	43	25	sets	set	NOUN
ejpam-6358	43	26	,	,	PUNCT
ejpam-6358	43	27	based	base	VERB
ejpam-6358	43	28	on	on	ADP
ejpam-6358	43	29	the	the	DET
ejpam-6358	43	30	generalized	generalized	ADJ
ejpam-6358	43	31	covering	covering	NOUN
ejpam-6358	43	32	approximation	approximation	NOUN
ejpam-6358	43	33	space	space	NOUN
ejpam-6358	43	34	of	of	ADP
ejpam-6358	43	35	abd	abd	PROPN
ejpam-6358	43	36	el	el	PROPN
ejpam-6358	43	37	-	-	PROPN
ejpam-6358	43	38	monsef	monsef	PROPN
ejpam-6358	43	39	et	et	PROPN
ejpam-6358	43	40	al	al	PROPN
ejpam-6358	43	41	.	.	PUNCT
ejpam-6358	44	1	[	[	X
ejpam-6358	44	2	21	21	NUM
ejpam-6358	44	3	]	]	PUNCT
ejpam-6358	44	4	.	.	PUNCT
ejpam-6358	45	1	core	core	ADJ
ejpam-6358	45	2	neighborhood	neighborhood	NOUN
ejpam-6358	45	3	ideas	idea	NOUN
ejpam-6358	45	4	from	from	ADP
ejpam-6358	45	5	[	[	X
ejpam-6358	45	6	22	22	NUM
ejpam-6358	45	7	,	,	PUNCT
ejpam-6358	45	8	23	23	NUM
ejpam-6358	45	9	]	]	PUNCT
ejpam-6358	45	10	were	be	AUX
ejpam-6358	45	11	also	also	ADV
ejpam-6358	45	12	extended	extend	VERB
ejpam-6358	45	13	in	in	ADP
ejpam-6358	45	14	[	[	X
ejpam-6358	45	15	24	24	NUM
ejpam-6358	45	16	]	]	PUNCT
ejpam-6358	45	17	using	use	VERB
ejpam-6358	45	18	techniques	technique	NOUN
ejpam-6358	45	19	from	from	ADP
ejpam-6358	45	20	[	[	X
ejpam-6358	45	21	7	7	NUM
ejpam-6358	45	22	,	,	PUNCT
ejpam-6358	45	23	9	9	NUM
ejpam-6358	45	24	]	]	PUNCT
ejpam-6358	45	25	.	.	PUNCT
ejpam-6358	46	1	furthermore	furthermore	ADV
ejpam-6358	46	2	,	,	PUNCT
ejpam-6358	46	3	el	el	PROPN
ejpam-6358	46	4	-	-	ADJ
ejpam-6358	46	5	bably	bably	PROPN
ejpam-6358	46	6	and	and	CCONJ
ejpam-6358	46	7	al	al	PROPN
ejpam-6358	46	8	-	-	PUNCT
ejpam-6358	46	9	shami	shami	PROPN
ejpam-6358	46	10	[	[	X
ejpam-6358	46	11	25	25	NUM
ejpam-6358	46	12	]	]	PUNCT
ejpam-6358	46	13	introduced	introduce	VERB
ejpam-6358	46	14	core	core	NOUN
ejpam-6358	46	15	minimal	minimal	ADJ
ejpam-6358	46	16	neighborhoods	neighborhood	NOUN
ejpam-6358	46	17	through	through	ADP
ejpam-6358	46	18	binary	binary	ADJ
ejpam-6358	46	19	relations	relation	NOUN
ejpam-6358	46	20	,	,	PUNCT
ejpam-6358	46	21	extending	extend	VERB
ejpam-6358	46	22	pawlak	pawlak	ADJ
ejpam-6358	46	23	rough	rough	ADJ
ejpam-6358	46	24	sets	set	NOUN
ejpam-6358	46	25	to	to	ADP
ejpam-6358	46	26	generalized	generalized	ADJ
ejpam-6358	46	27	types	type	NOUN
ejpam-6358	46	28	for	for	ADP
ejpam-6358	46	29	applications	application	NOUN
ejpam-6358	46	30	,	,	PUNCT
ejpam-6358	46	31	such	such	ADJ
ejpam-6358	46	32	as	as	ADP
ejpam-6358	46	33	in	in	ADP
ejpam-6358	46	34	lung	lung	NOUN
ejpam-6358	46	35	cancer	cancer	NOUN
ejpam-6358	46	36	research	research	NOUN
ejpam-6358	46	37	.	.	PUNCT
ejpam-6358	47	1	on	on	ADP
ejpam-6358	47	2	the	the	DET
ejpam-6358	47	3	other	other	ADJ
ejpam-6358	47	4	hand	hand	NOUN
ejpam-6358	47	5	,	,	PUNCT
ejpam-6358	47	6	the	the	DET
ejpam-6358	47	7	application	application	NOUN
ejpam-6358	47	8	of	of	ADP
ejpam-6358	47	9	neighborhood	neighborhood	NOUN
ejpam-6358	47	10	concepts	concept	NOUN
ejpam-6358	47	11	has	have	AUX
ejpam-6358	47	12	expanded	expand	VERB
ejpam-6358	47	13	in	in	ADP
ejpam-6358	47	14	new	new	ADJ
ejpam-6358	47	15	directions	direction	NOUN
ejpam-6358	47	16	,	,	PUNCT
ejpam-6358	47	17	such	such	ADJ
ejpam-6358	47	18	as	as	ADP
ejpam-6358	47	19	advanced	advanced	ADJ
ejpam-6358	47	20	neighborhood	neighborhood	NOUN
ejpam-6358	47	21	-	-	PUNCT
ejpam-6358	47	22	based	base	VERB
ejpam-6358	47	23	methods	method	NOUN
ejpam-6358	47	24	used	use	VERB
ejpam-6358	47	25	for	for	ADP
ejpam-6358	47	26	feature	feature	NOUN
ejpam-6358	47	27	selection	selection	NOUN
ejpam-6358	47	28	—	—	PUNCT
ejpam-6358	47	29	for	for	ADP
ejpam-6358	47	30	example	example	NOUN
ejpam-6358	47	31	,	,	PUNCT
ejpam-6358	47	32	an	an	DET
ejpam-6358	47	33	enhanced	enhance	VERB
ejpam-6358	47	34	evolutionary	evolutionary	ADJ
ejpam-6358	47	35	feature	feature	NOUN
ejpam-6358	47	36	selection	selection	NOUN
ejpam-6358	47	37	method	method	NOUN
ejpam-6358	47	38	based	base	VERB
ejpam-6358	47	39	on	on	ADP
ejpam-6358	47	40	extended	extended	ADJ
ejpam-6358	47	41	knowledge	knowledge	NOUN
ejpam-6358	47	42	from	from	ADP
ejpam-6358	47	43	rough	rough	ADJ
ejpam-6358	47	44	approximations	approximation	NOUN
ejpam-6358	47	45	[	[	X
ejpam-6358	47	46	26	26	NUM
ejpam-6358	47	47	]	]	PUNCT
ejpam-6358	47	48	.	.	PUNCT
ejpam-6358	48	1	studies	study	NOUN
ejpam-6358	48	2	such	such	ADJ
ejpam-6358	48	3	as	as	ADP
ejpam-6358	48	4	an	an	DET
ejpam-6358	48	5	efficient	efficient	ADJ
ejpam-6358	48	6	approach	approach	NOUN
ejpam-6358	48	7	to	to	ADP
ejpam-6358	48	8	neighborhood	neighborhood	NOUN
ejpam-6358	48	9	learning	learning	NOUN
ejpam-6358	48	10	in	in	ADP
ejpam-6358	48	11	big	big	ADJ
ejpam-6358	48	12	data	datum	NOUN
ejpam-6358	48	13	and	and	CCONJ
ejpam-6358	48	14	its	its	PRON
ejpam-6358	48	15	application	application	NOUN
ejpam-6358	48	16	to	to	ADP
ejpam-6358	48	17	medical	medical	ADJ
ejpam-6358	48	18	diagnosis	diagnosis	NOUN
ejpam-6358	48	19	[	[	X
ejpam-6358	48	20	27	27	NUM
ejpam-6358	48	21	,	,	PUNCT
ejpam-6358	48	22	28	28	NUM
ejpam-6358	48	23	]	]	PUNCT
ejpam-6358	48	24	and	and	CCONJ
ejpam-6358	48	25	neighborhood	neighborhood	NOUN
ejpam-6358	48	26	combination	combination	NOUN
ejpam-6358	48	27	entropy	entropy	NOUN
ejpam-6358	48	28	and	and	CCONJ
ejpam-6358	48	29	multi	multi	ADJ
ejpam-6358	48	30	-	-	ADJ
ejpam-6358	48	31	scale	scale	ADJ
ejpam-6358	48	32	information	information	NOUN
ejpam-6358	48	33	fusion	fusion	NOUN
ejpam-6358	48	34	-	-	PUNCT
ejpam-6358	48	35	based	base	VERB
ejpam-6358	48	36	multiple	multiple	ADJ
ejpam-6358	48	37	correlations	correlation	NOUN
ejpam-6358	48	38	for	for	ADP
ejpam-6358	48	39	unsupervised	unsupervised	ADJ
ejpam-6358	48	40	attribute	attribute	NOUN
ejpam-6358	48	41	selection	selection	NOUN
ejpam-6358	48	42	[	[	X
ejpam-6358	48	43	29	29	NUM
ejpam-6358	48	44	,	,	PUNCT
ejpam-6358	48	45	30	30	NUM
ejpam-6358	48	46	]	]	PUNCT
ejpam-6358	48	47	have	have	AUX
ejpam-6358	48	48	also	also	ADV
ejpam-6358	48	49	employed	employ	VERB
ejpam-6358	48	50	these	these	DET
ejpam-6358	48	51	methods	method	NOUN
ejpam-6358	48	52	for	for	ADP
ejpam-6358	48	53	feature	feature	NOUN
ejpam-6358	48	54	selection	selection	NOUN
ejpam-6358	48	55	.	.	PUNCT
ejpam-6358	49	1	in	in	ADP
ejpam-6358	49	2	addition	addition	NOUN
ejpam-6358	49	3	,	,	PUNCT
ejpam-6358	49	4	nmf	nmf	NOUN
ejpam-6358	49	5	-	-	PUNCT
ejpam-6358	49	6	based	base	VERB
ejpam-6358	49	7	deep	deep	ADJ
ejpam-6358	49	8	representation	representation	NOUN
ejpam-6358	49	9	algorithms	algorithm	NOUN
ejpam-6358	49	10	and	and	CCONJ
ejpam-6358	49	11	deep	deep	ADJ
ejpam-6358	49	12	learning	learning	NOUN
ejpam-6358	49	13	algorithms	algorithm	NOUN
ejpam-6358	49	14	based	base	VERB
ejpam-6358	49	15	on	on	ADP
ejpam-6358	49	16	nmf	nmf	PROPN
ejpam-6358	49	17	for	for	ADP
ejpam-6358	49	18	multi	multi	ADJ
ejpam-6358	49	19	-	-	ADJ
ejpam-6358	49	20	view	view	NOUN
ejpam-6358	49	21	clustering	cluster	VERB
ejpam-6358	49	22	[	[	X
ejpam-6358	49	23	31	31	NUM
ejpam-6358	49	24	,	,	PUNCT
ejpam-6358	49	25	32	32	NUM
ejpam-6358	49	26	]	]	PUNCT
ejpam-6358	49	27	have	have	AUX
ejpam-6358	49	28	further	far	ADV
ejpam-6358	49	29	demonstrated	demonstrate	VERB
ejpam-6358	49	30	their	their	PRON
ejpam-6358	49	31	usefulness	usefulness	NOUN
ejpam-6358	49	32	in	in	ADP
ejpam-6358	49	33	this	this	DET
ejpam-6358	49	34	context	context	NOUN
ejpam-6358	49	35	.	.	PUNCT
ejpam-6358	50	1	furthermore	furthermore	ADV
ejpam-6358	50	2	,	,	PUNCT
ejpam-6358	50	3	these	these	DET
ejpam-6358	50	4	approaches	approach	NOUN
ejpam-6358	50	5	have	have	AUX
ejpam-6358	50	6	been	be	AUX
ejpam-6358	50	7	applied	apply	VERB
ejpam-6358	50	8	to	to	ADP
ejpam-6358	50	9	decisionmaking	decisionmake	VERB
ejpam-6358	50	10	problems	problem	NOUN
ejpam-6358	50	11	[	[	X
ejpam-6358	50	12	33	33	NUM
ejpam-6358	50	13	,	,	PUNCT
ejpam-6358	50	14	34	34	NUM
ejpam-6358	50	15	]	]	PUNCT
ejpam-6358	50	16	,	,	PUNCT
ejpam-6358	50	17	θβ	θβ	NOUN
ejpam-6358	50	18	-	-	PUNCT
ejpam-6358	50	19	ideal	ideal	NOUN
ejpam-6358	50	20	approximation	approximation	NOUN
ejpam-6358	50	21	spaces	space	NOUN
ejpam-6358	50	22	[	[	X
ejpam-6358	50	23	35	35	NUM
ejpam-6358	50	24	,	,	PUNCT
ejpam-6358	50	25	36	36	NUM
ejpam-6358	50	26	]	]	PUNCT
ejpam-6358	50	27	,	,	PUNCT
ejpam-6358	50	28	primal	primal	ADJ
ejpam-6358	50	29	approximation	approximation	NOUN
ejpam-6358	50	30	spaces	space	NOUN
ejpam-6358	51	1	[	[	X
ejpam-6358	51	2	37	37	NUM
ejpam-6358	51	3	,	,	PUNCT
ejpam-6358	51	4	38	38	NUM
ejpam-6358	51	5	]	]	PUNCT
ejpam-6358	51	6	,	,	PUNCT
ejpam-6358	51	7	and	and	CCONJ
ejpam-6358	51	8	medical	medical	ADJ
ejpam-6358	51	9	applications	application	NOUN
ejpam-6358	51	10	[	[	X
ejpam-6358	51	11	14	14	NUM
ejpam-6358	51	12	,	,	PUNCT
ejpam-6358	51	13	39	39	NUM
ejpam-6358	51	14	]	]	PUNCT
ejpam-6358	51	15	.	.	PUNCT
ejpam-6358	52	1	•	•	NUM
ejpam-6358	52	2	motivations	motivation	NOUN
ejpam-6358	52	3	and	and	CCONJ
ejpam-6358	52	4	objectives	objective	NOUN
ejpam-6358	52	5	:	:	PUNCT
ejpam-6358	52	6	recently	recently	ADV
ejpam-6358	52	7	,	,	PUNCT
ejpam-6358	52	8	t.	t.	PROPN
ejpam-6358	52	9	m.	m.	PROPN
ejpam-6358	52	10	al	al	PROPN
ejpam-6358	52	11	-	-	PUNCT
ejpam-6358	52	12	shami	shami	PROPN
ejpam-6358	52	13	and	and	CCONJ
ejpam-6358	52	14	m.	m.	PROPN
ejpam-6358	52	15	hosny	hosny	PROPN
ejpam-6358	53	1	[	[	X
ejpam-6358	53	2	40	40	NUM
ejpam-6358	53	3	]	]	PUNCT
ejpam-6358	53	4	introduced	introduce	VERB
ejpam-6358	53	5	a	a	DET
ejpam-6358	53	6	new	new	ADJ
ejpam-6358	53	7	type	type	NOUN
ejpam-6358	53	8	of	of	ADP
ejpam-6358	53	9	neighborhood	neighborhood	NOUN
ejpam-6358	53	10	based	base	VERB
ejpam-6358	53	11	on	on	ADP
ejpam-6358	53	12	the	the	DET
ejpam-6358	53	13	ij	ij	ADJ
ejpam-6358	53	14	-	-	PUNCT
ejpam-6358	53	15	neighborhood	neighborhood	NOUN
ejpam-6358	53	16	concept	concept	NOUN
ejpam-6358	53	17	[	[	X
ejpam-6358	53	18	12	12	NUM
ejpam-6358	53	19	]	]	PUNCT
ejpam-6358	53	20	.	.	PUNCT
ejpam-6358	54	1	by	by	ADP
ejpam-6358	54	2	utilizing	utilize	VERB
ejpam-6358	54	3	the	the	DET
ejpam-6358	54	4	definitions	definition	NOUN
ejpam-6358	54	5	of	of	ADP
ejpam-6358	54	6	intersection	intersection	NOUN
ejpam-6358	54	7	and	and	CCONJ
ejpam-6358	54	8	union	union	NOUN
ejpam-6358	54	9	neighborhoods	neighborhood	NOUN
ejpam-6358	54	10	proposed	propose	VERB
ejpam-6358	54	11	by	by	ADP
ejpam-6358	54	12	abd	abd	PROPN
ejpam-6358	54	13	el	el	PROPN
ejpam-6358	54	14	-	-	PROPN
ejpam-6358	54	15	monsef	monsef	PROPN
ejpam-6358	54	16	et	et	PROPN
ejpam-6358	54	17	al	al	PROPN
ejpam-6358	54	18	.	.	PUNCT
ejpam-6358	55	1	[	[	X
ejpam-6358	55	2	9	9	NUM
ejpam-6358	55	3	]	]	PUNCT
ejpam-6358	55	4	,	,	PUNCT
ejpam-6358	55	5	they	they	PRON
ejpam-6358	55	6	constructed	construct	VERB
ejpam-6358	55	7	eight	eight	NUM
ejpam-6358	55	8	novel	novel	ADJ
ejpam-6358	55	9	neighborhoods	neighborhood	NOUN
ejpam-6358	55	10	,	,	PUNCT
ejpam-6358	55	11	examined	examine	VERB
ejpam-6358	55	12	their	their	PRON
ejpam-6358	55	13	properties	property	NOUN
ejpam-6358	55	14	and	and	CCONJ
ejpam-6358	55	15	interrelationships	interrelationship	NOUN
ejpam-6358	55	16	,	,	PUNCT
ejpam-6358	55	17	and	and	CCONJ
ejpam-6358	55	18	presented	present	VERB
ejpam-6358	55	19	theoretical	theoretical	ADJ
ejpam-6358	55	20	results	result	NOUN
ejpam-6358	55	21	supported	support	VERB
ejpam-6358	55	22	by	by	ADP
ejpam-6358	55	23	illustrative	illustrative	ADJ
ejpam-6358	55	24	examples	example	NOUN
ejpam-6358	55	25	.	.	PUNCT
ejpam-6358	56	1	they	they	PRON
ejpam-6358	56	2	further	far	ADV
ejpam-6358	56	3	developed	develop	VERB
ejpam-6358	56	4	various	various	ADJ
ejpam-6358	56	5	rough	rough	ADJ
ejpam-6358	56	6	set	set	VERB
ejpam-6358	56	7	approximations	approximation	NOUN
ejpam-6358	56	8	based	base	VERB
ejpam-6358	56	9	on	on	ADP
ejpam-6358	56	10	ikj	ikj	PROPN
ejpam-6358	56	11	-neighborhoods	-neighborhood	NOUN
ejpam-6358	56	12	,	,	PUNCT
ejpam-6358	56	13	demonstrating	demonstrate	VERB
ejpam-6358	56	14	their	their	PRON
ejpam-6358	56	15	potential	potential	NOUN
ejpam-6358	56	16	through	through	ADP
ejpam-6358	56	17	a	a	DET
ejpam-6358	56	18	medical	medical	ADJ
ejpam-6358	56	19	case	case	NOUN
ejpam-6358	56	20	study	study	NOUN
ejpam-6358	56	21	.	.	PUNCT
ejpam-6358	57	1	however	however	ADV
ejpam-6358	57	2	,	,	PUNCT
ejpam-6358	57	3	the	the	DET
ejpam-6358	57	4	objective	objective	NOUN
ejpam-6358	57	5	of	of	ADP
ejpam-6358	57	6	their	their	PRON
ejpam-6358	57	7	study	study	NOUN
ejpam-6358	57	8	was	be	AUX
ejpam-6358	57	9	not	not	PART
ejpam-6358	57	10	achieved	achieve	VERB
ejpam-6358	57	11	due	due	ADP
ejpam-6358	57	12	to	to	ADP
ejpam-6358	57	13	several	several	ADJ
ejpam-6358	57	14	fundamental	fundamental	ADJ
ejpam-6358	57	15	errors	error	NOUN
ejpam-6358	57	16	and	and	CCONJ
ejpam-6358	57	17	a	a	DET
ejpam-6358	57	18	lack	lack	NOUN
ejpam-6358	57	19	of	of	ADP
ejpam-6358	57	20	precision	precision	NOUN
ejpam-6358	57	21	.	.	PUNCT
ejpam-6358	58	1	this	this	DET
ejpam-6358	58	2	paper	paper	NOUN
ejpam-6358	58	3	aims	aim	VERB
ejpam-6358	58	4	to	to	PART
ejpam-6358	58	5	address	address	VERB
ejpam-6358	58	6	the	the	DET
ejpam-6358	58	7	errors	error	NOUN
ejpam-6358	58	8	,	,	PUNCT
ejpam-6358	58	9	inconsistencies	inconsistency	NOUN
ejpam-6358	58	10	,	,	PUNCT
ejpam-6358	58	11	and	and	CCONJ
ejpam-6358	58	12	inaccuracies	inaccuracy	NOUN
ejpam-6358	58	13	identified	identify	VERB
ejpam-6358	58	14	in	in	ADP
ejpam-6358	58	15	their	their	PRON
ejpam-6358	58	16	work	work	NOUN
ejpam-6358	58	17	.	.	PUNCT
ejpam-6358	59	1	the	the	DET
ejpam-6358	59	2	primary	primary	ADJ
ejpam-6358	59	3	objectives	objective	NOUN
ejpam-6358	59	4	of	of	ADP
ejpam-6358	59	5	our	our	PRON
ejpam-6358	59	6	study	study	NOUN
ejpam-6358	59	7	are	be	AUX
ejpam-6358	59	8	as	as	SCONJ
ejpam-6358	59	9	follows	follow	VERB
ejpam-6358	59	10	:	:	PUNCT
ejpam-6358	59	11	(	(	PUNCT
ejpam-6358	59	12	i	i	NOUN
ejpam-6358	59	13	)	)	PUNCT
ejpam-6358	59	14	identify	identify	VERB
ejpam-6358	59	15	and	and	CCONJ
ejpam-6358	59	16	highlight	highlight	VERB
ejpam-6358	59	17	the	the	DET
ejpam-6358	59	18	errors	error	NOUN
ejpam-6358	59	19	in	in	ADP
ejpam-6358	59	20	results	result	NOUN
ejpam-6358	59	21	such	such	ADJ
ejpam-6358	59	22	as	as	ADP
ejpam-6358	59	23	theorem	theorem	ADJ
ejpam-6358	59	24	3.4	3.4	NUM
ejpam-6358	59	25	,	,	PUNCT
ejpam-6358	59	26	proposition	proposition	NOUN
ejpam-6358	59	27	4.3	4.3	NUM
ejpam-6358	59	28	,	,	PUNCT
ejpam-6358	59	29	and	and	CCONJ
ejpam-6358	59	30	proposition	proposition	NOUN
ejpam-6358	59	31	5.4	5.4	NUM
ejpam-6358	59	32	.	.	PUNCT
ejpam-6358	60	1	(	(	PUNCT
ejpam-6358	60	2	ii	ii	NOUN
ejpam-6358	60	3	)	)	PUNCT
ejpam-6358	60	4	provide	provide	VERB
ejpam-6358	60	5	counterexamples	counterexample	NOUN
ejpam-6358	60	6	to	to	PART
ejpam-6358	60	7	demonstrate	demonstrate	VERB
ejpam-6358	60	8	inaccuracies	inaccuracy	NOUN
ejpam-6358	60	9	in	in	ADP
ejpam-6358	60	10	their	their	PRON
ejpam-6358	60	11	findings	finding	NOUN
ejpam-6358	60	12	,	,	PUNCT
ejpam-6358	60	13	such	such	ADJ
ejpam-6358	60	14	as	as	ADP
ejpam-6358	60	15	examples	example	NOUN
ejpam-6358	60	16	1	1	NUM
ejpam-6358	60	17	,	,	PUNCT
ejpam-6358	60	18	2	2	NUM
ejpam-6358	60	19	,	,	PUNCT
ejpam-6358	60	20	3	3	NUM
ejpam-6358	60	21	,	,	PUNCT
ejpam-6358	60	22	4	4	NUM
ejpam-6358	60	23	,	,	PUNCT
ejpam-6358	60	24	5	5	NUM
ejpam-6358	60	25	,	,	PUNCT
ejpam-6358	60	26	and	and	CCONJ
ejpam-6358	60	27	6	6	NUM
ejpam-6358	60	28	.	.	PUNCT
ejpam-6358	60	29	(	(	PUNCT
ejpam-6358	60	30	iii	iii	X
ejpam-6358	60	31	)	)	PUNCT
ejpam-6358	60	32	correct	correct	VERB
ejpam-6358	60	33	the	the	DET
ejpam-6358	60	34	erroneous	erroneous	ADJ
ejpam-6358	60	35	results	result	NOUN
ejpam-6358	60	36	,	,	PUNCT
ejpam-6358	60	37	definitions	definition	NOUN
ejpam-6358	60	38	,	,	PUNCT
ejpam-6358	60	39	and	and	CCONJ
ejpam-6358	60	40	properties	property	NOUN
ejpam-6358	60	41	introduced	introduce	VERB
ejpam-6358	60	42	in	in	ADP
ejpam-6358	60	43	their	their	PRON
ejpam-6358	60	44	research	research	NOUN
ejpam-6358	60	45	.	.	PUNCT
ejpam-6358	61	1	(	(	PUNCT
ejpam-6358	61	2	iv	iv	X
ejpam-6358	61	3	)	)	PUNCT
ejpam-6358	61	4	rectify	rectify	VERB
ejpam-6358	61	5	the	the	DET
ejpam-6358	61	6	incorrect	incorrect	ADJ
ejpam-6358	61	7	examples	example	NOUN
ejpam-6358	61	8	and	and	CCONJ
ejpam-6358	61	9	flawed	flaw	VERB
ejpam-6358	61	10	proofs	proof	NOUN
ejpam-6358	61	11	presented	present	VERB
ejpam-6358	61	12	in	in	ADP
ejpam-6358	61	13	their	their	PRON
ejpam-6358	61	14	paper	paper	NOUN
ejpam-6358	61	15	.	.	PUNCT
ejpam-6358	62	1	(	(	PUNCT
ejpam-6358	62	2	v	v	NOUN
ejpam-6358	62	3	)	)	PUNCT
ejpam-6358	62	4	enhance	enhance	VERB
ejpam-6358	62	5	the	the	DET
ejpam-6358	62	6	understanding	understanding	NOUN
ejpam-6358	62	7	of	of	ADP
ejpam-6358	62	8	the	the	DET
ejpam-6358	62	9	research	research	NOUN
ejpam-6358	62	10	topic	topic	NOUN
ejpam-6358	62	11	by	by	ADP
ejpam-6358	62	12	presenting	present	VERB
ejpam-6358	62	13	corrected	correct	VERB
ejpam-6358	62	14	results	result	NOUN
ejpam-6358	62	15	and	and	CCONJ
ejpam-6358	62	16	expanding	expand	VERB
ejpam-6358	62	17	the	the	DET
ejpam-6358	62	18	scope	scope	NOUN
ejpam-6358	62	19	of	of	ADP
ejpam-6358	62	20	potential	potential	ADJ
ejpam-6358	62	21	applications	application	NOUN
ejpam-6358	62	22	.	.	PUNCT
ejpam-6358	63	1	r.	r.	PROPN
ejpam-6358	63	2	a.	a.	PROPN
ejpam-6358	63	3	hosny	hosny	PROPN
ejpam-6358	63	4	et	et	PROPN
ejpam-6358	63	5	al	al	PROPN
ejpam-6358	63	6	.	.	PUNCT
ejpam-6358	63	7	/	/	SYM
ejpam-6358	63	8	eur	eur	PROPN
ejpam-6358	63	9	.	.	PUNCT
ejpam-6358	64	1	j.	j.	PROPN
ejpam-6358	64	2	pure	pure	PROPN
ejpam-6358	64	3	appl	appl	PROPN
ejpam-6358	64	4	.	.	PROPN
ejpam-6358	64	5	math	math	PROPN
ejpam-6358	64	6	,	,	PUNCT
ejpam-6358	64	7	18	18	NUM
ejpam-6358	64	8	(	(	PUNCT
ejpam-6358	64	9	4	4	NUM
ejpam-6358	64	10	)	)	PUNCT
ejpam-6358	64	11	(	(	PUNCT
ejpam-6358	64	12	2025	2025	NUM
ejpam-6358	64	13	)	)	PUNCT
ejpam-6358	64	14	,	,	PUNCT
ejpam-6358	64	15	6358	6358	NUM
ejpam-6358	64	16	4	4	NUM
ejpam-6358	64	17	of	of	ADP
ejpam-6358	64	18	24	24	NUM
ejpam-6358	64	19	(	(	PUNCT
ejpam-6358	64	20	vi	vi	NOUN
ejpam-6358	64	21	)	)	PUNCT
ejpam-6358	64	22	contribute	contribute	VERB
ejpam-6358	64	23	to	to	ADP
ejpam-6358	64	24	the	the	DET
ejpam-6358	64	25	advancement	advancement	NOUN
ejpam-6358	64	26	of	of	ADP
ejpam-6358	64	27	rough	rough	ADJ
ejpam-6358	64	28	set	set	NOUN
ejpam-6358	64	29	theory	theory	NOUN
ejpam-6358	64	30	and	and	CCONJ
ejpam-6358	64	31	methodologies	methodology	NOUN
ejpam-6358	64	32	through	through	ADP
ejpam-6358	64	33	refined	refined	ADJ
ejpam-6358	64	34	neighborhood	neighborhood	NOUN
ejpam-6358	64	35	concepts	concept	NOUN
ejpam-6358	64	36	.	.	PUNCT
ejpam-6358	65	1	•	•	NUM
ejpam-6358	65	2	organization	organization	NOUN
ejpam-6358	65	3	of	of	ADP
ejpam-6358	65	4	the	the	DET
ejpam-6358	65	5	manuscript	manuscript	NOUN
ejpam-6358	65	6	:	:	PUNCT
ejpam-6358	65	7	the	the	DET
ejpam-6358	65	8	remainder	remainder	NOUN
ejpam-6358	65	9	of	of	ADP
ejpam-6358	65	10	this	this	DET
ejpam-6358	65	11	paper	paper	NOUN
ejpam-6358	65	12	is	be	AUX
ejpam-6358	65	13	organized	organize	VERB
ejpam-6358	65	14	as	as	SCONJ
ejpam-6358	65	15	follows	follow	VERB
ejpam-6358	65	16	:	:	PUNCT
ejpam-6358	65	17	section	section	NOUN
ejpam-6358	65	18	2	2	NUM
ejpam-6358	65	19	presents	present	VERB
ejpam-6358	65	20	essential	essential	ADJ
ejpam-6358	65	21	concepts	concept	NOUN
ejpam-6358	65	22	and	and	CCONJ
ejpam-6358	65	23	foundational	foundational	ADJ
ejpam-6358	65	24	results	result	NOUN
ejpam-6358	65	25	necessary	necessary	ADJ
ejpam-6358	65	26	for	for	ADP
ejpam-6358	65	27	understanding	understand	VERB
ejpam-6358	65	28	the	the	DET
ejpam-6358	65	29	manuscript	manuscript	NOUN
ejpam-6358	65	30	.	.	PUNCT
ejpam-6358	66	1	this	this	PRON
ejpam-6358	66	2	includes	include	VERB
ejpam-6358	66	3	corrections	correction	NOUN
ejpam-6358	66	4	to	to	ADP
ejpam-6358	66	5	inaccurate	inaccurate	ADJ
ejpam-6358	66	6	definitions	definition	NOUN
ejpam-6358	66	7	,	,	PUNCT
ejpam-6358	66	8	results	result	NOUN
ejpam-6358	66	9	,	,	PUNCT
ejpam-6358	66	10	and	and	CCONJ
ejpam-6358	66	11	citations	citation	NOUN
ejpam-6358	66	12	from	from	ADP
ejpam-6358	66	13	[	[	X
ejpam-6358	66	14	40	40	NUM
ejpam-6358	66	15	]	]	PUNCT
ejpam-6358	66	16	to	to	PART
ejpam-6358	66	17	ensure	ensure	VERB
ejpam-6358	66	18	coherence	coherence	NOUN
ejpam-6358	66	19	.	.	PUNCT
ejpam-6358	67	1	section	section	NOUN
ejpam-6358	67	2	3	3	NUM
ejpam-6358	67	3	systematically	systematically	ADV
ejpam-6358	67	4	identifies	identify	VERB
ejpam-6358	67	5	and	and	CCONJ
ejpam-6358	67	6	analyzes	analyze	VERB
ejpam-6358	67	7	the	the	DET
ejpam-6358	67	8	errors	error	NOUN
ejpam-6358	67	9	in	in	ADP
ejpam-6358	67	10	[	[	X
ejpam-6358	67	11	40	40	NUM
ejpam-6358	67	12	]	]	PUNCT
ejpam-6358	67	13	,	,	PUNCT
ejpam-6358	67	14	addressing	address	VERB
ejpam-6358	67	15	inaccuracies	inaccuracy	NOUN
ejpam-6358	67	16	in	in	ADP
ejpam-6358	67	17	results	result	NOUN
ejpam-6358	67	18	,	,	PUNCT
ejpam-6358	67	19	definitions	definition	NOUN
ejpam-6358	67	20	,	,	PUNCT
ejpam-6358	67	21	and	and	CCONJ
ejpam-6358	67	22	examples	example	NOUN
ejpam-6358	67	23	,	,	PUNCT
ejpam-6358	67	24	along	along	ADP
ejpam-6358	67	25	with	with	ADP
ejpam-6358	67	26	the	the	DET
ejpam-6358	67	27	corresponding	correspond	VERB
ejpam-6358	67	28	corrections	correction	NOUN
ejpam-6358	67	29	.	.	PUNCT
ejpam-6358	68	1	finally	finally	ADV
ejpam-6358	68	2	,	,	PUNCT
ejpam-6358	68	3	section	section	NOUN
ejpam-6358	68	4	4	4	NUM
ejpam-6358	68	5	provides	provide	VERB
ejpam-6358	68	6	a	a	DET
ejpam-6358	68	7	summary	summary	NOUN
ejpam-6358	68	8	of	of	ADP
ejpam-6358	68	9	our	our	PRON
ejpam-6358	68	10	findings	finding	NOUN
ejpam-6358	68	11	and	and	CCONJ
ejpam-6358	68	12	a	a	DET
ejpam-6358	68	13	concluding	conclude	VERB
ejpam-6358	68	14	discussion	discussion	NOUN
ejpam-6358	68	15	.	.	PUNCT
ejpam-6358	69	1	2	2	X
ejpam-6358	69	2	.	.	X
ejpam-6358	69	3	preliminaries	preliminary	NOUN
ejpam-6358	69	4	this	this	DET
ejpam-6358	69	5	section	section	NOUN
ejpam-6358	69	6	establishes	establish	VERB
ejpam-6358	69	7	fundamental	fundamental	ADJ
ejpam-6358	69	8	concepts	concept	NOUN
ejpam-6358	69	9	and	and	CCONJ
ejpam-6358	69	10	key	key	ADJ
ejpam-6358	69	11	results	result	NOUN
ejpam-6358	69	12	necessary	necessary	ADJ
ejpam-6358	69	13	for	for	ADP
ejpam-6358	69	14	understanding	understand	VERB
ejpam-6358	69	15	both	both	CCONJ
ejpam-6358	69	16	the	the	DET
ejpam-6358	69	17	study	study	NOUN
ejpam-6358	69	18	and	and	CCONJ
ejpam-6358	69	19	the	the	DET
ejpam-6358	69	20	manuscript	manuscript	NOUN
ejpam-6358	69	21	’s	’s	PART
ejpam-6358	69	22	content	content	NOUN
ejpam-6358	69	23	.	.	PUNCT
ejpam-6358	70	1	a	a	DET
ejpam-6358	70	2	primary	primary	ADJ
ejpam-6358	70	3	objective	objective	NOUN
ejpam-6358	70	4	is	be	AUX
ejpam-6358	70	5	to	to	PART
ejpam-6358	70	6	rectify	rectify	VERB
ejpam-6358	70	7	inaccuracies	inaccuracy	NOUN
ejpam-6358	70	8	in	in	ADP
ejpam-6358	70	9	definitions	definition	NOUN
ejpam-6358	70	10	and	and	CCONJ
ejpam-6358	70	11	results	result	NOUN
ejpam-6358	70	12	,	,	PUNCT
ejpam-6358	70	13	as	as	ADV
ejpam-6358	70	14	well	well	ADV
ejpam-6358	70	15	as	as	ADP
ejpam-6358	70	16	to	to	PART
ejpam-6358	70	17	correct	correct	VERB
ejpam-6358	70	18	erroneous	erroneous	ADJ
ejpam-6358	70	19	citations	citation	NOUN
ejpam-6358	70	20	of	of	ADP
ejpam-6358	70	21	key	key	ADJ
ejpam-6358	70	22	concepts	concept	NOUN
ejpam-6358	70	23	from	from	ADP
ejpam-6358	70	24	[	[	X
ejpam-6358	70	25	40	40	NUM
ejpam-6358	70	26	]	]	PUNCT
ejpam-6358	70	27	,	,	PUNCT
ejpam-6358	70	28	ensuring	ensure	VERB
ejpam-6358	70	29	clarity	clarity	NOUN
ejpam-6358	70	30	and	and	CCONJ
ejpam-6358	70	31	coherence	coherence	NOUN
ejpam-6358	70	32	throughout	throughout	ADP
ejpam-6358	70	33	the	the	DET
ejpam-6358	70	34	discussion	discussion	NOUN
ejpam-6358	70	35	.	.	PUNCT
ejpam-6358	71	1	a	a	DET
ejpam-6358	71	2	well	well	ADV
ejpam-6358	71	3	-	-	PUNCT
ejpam-6358	71	4	established	establish	VERB
ejpam-6358	71	5	fact	fact	NOUN
ejpam-6358	71	6	is	be	AUX
ejpam-6358	71	7	that	that	SCONJ
ejpam-6358	71	8	a	a	DET
ejpam-6358	71	9	binary	binary	ADJ
ejpam-6358	71	10	relation	relation	NOUN
ejpam-6358	71	11	r	r	NOUN
ejpam-6358	71	12	on	on	ADP
ejpam-6358	71	13	a	a	DET
ejpam-6358	71	14	nonempty	nonempty	ADJ
ejpam-6358	71	15	set	set	VERB
ejpam-6358	71	16	(	(	PUNCT
ejpam-6358	71	17	universe	universe	NOUN
ejpam-6358	71	18	)	)	PUNCT
ejpam-6358	71	19	u	u	NOUN
ejpam-6358	71	20	is	be	AUX
ejpam-6358	71	21	a	a	DET
ejpam-6358	71	22	subset	subset	NOUN
ejpam-6358	71	23	of	of	ADP
ejpam-6358	71	24	u	u	NOUN
ejpam-6358	71	25	×u	×u	X
ejpam-6358	71	26	.	.	PUNCT
ejpam-6358	72	1	throughout	throughout	ADP
ejpam-6358	72	2	this	this	DET
ejpam-6358	72	3	work	work	NOUN
ejpam-6358	72	4	,	,	PUNCT
ejpam-6358	72	5	we	we	PRON
ejpam-6358	72	6	assume	assume	VERB
ejpam-6358	72	7	u	u	PRON
ejpam-6358	72	8	to	to	PART
ejpam-6358	72	9	be	be	AUX
ejpam-6358	72	10	a	a	DET
ejpam-6358	72	11	nonempty	nonempty	ADJ
ejpam-6358	72	12	finite	finite	NOUN
ejpam-6358	72	13	set	set	NOUN
ejpam-6358	72	14	,	,	PUNCT
ejpam-6358	72	15	with	with	ADP
ejpam-6358	72	16	r	r	NOUN
ejpam-6358	72	17	representing	represent	VERB
ejpam-6358	72	18	an	an	DET
ejpam-6358	72	19	arbitrary	arbitrary	ADJ
ejpam-6358	72	20	relation	relation	NOUN
ejpam-6358	72	21	unless	unless	SCONJ
ejpam-6358	72	22	specified	specify	VERB
ejpam-6358	72	23	otherwise	otherwise	ADV
ejpam-6358	72	24	.	.	PUNCT
ejpam-6358	73	1	for	for	ADP
ejpam-6358	73	2	s	s	PROPN
ejpam-6358	73	3	,	,	PUNCT
ejpam-6358	73	4	t	t	PROPN
ejpam-6358	73	5	∈	∈	PROPN
ejpam-6358	73	6	u	u	PROPN
ejpam-6358	73	7	,	,	PUNCT
ejpam-6358	73	8	we	we	PRON
ejpam-6358	73	9	write	write	VERB
ejpam-6358	73	10	srt	srt	NOUN
ejpam-6358	73	11	if	if	SCONJ
ejpam-6358	73	12	(	(	PUNCT
ejpam-6358	73	13	s	s	PROPN
ejpam-6358	73	14	,	,	PUNCT
ejpam-6358	73	15	t	t	PROPN
ejpam-6358	73	16	)	)	PUNCT
ejpam-6358	73	17	∈	∈	PROPN
ejpam-6358	73	18	r.	r.	PROPN
ejpam-6358	73	19	several	several	ADJ
ejpam-6358	73	20	key	key	ADJ
ejpam-6358	73	21	concepts	concept	NOUN
ejpam-6358	73	22	in	in	ADP
ejpam-6358	73	23	[	[	X
ejpam-6358	73	24	40	40	NUM
ejpam-6358	73	25	]	]	PUNCT
ejpam-6358	73	26	were	be	AUX
ejpam-6358	73	27	inaccurately	inaccurately	ADV
ejpam-6358	73	28	presented	present	VERB
ejpam-6358	73	29	.	.	PUNCT
ejpam-6358	74	1	below	below	ADV
ejpam-6358	74	2	,	,	PUNCT
ejpam-6358	74	3	we	we	PRON
ejpam-6358	74	4	provide	provide	VERB
ejpam-6358	74	5	the	the	DET
ejpam-6358	74	6	corrected	correct	VERB
ejpam-6358	74	7	definitions	definition	NOUN
ejpam-6358	74	8	to	to	PART
ejpam-6358	74	9	ensure	ensure	VERB
ejpam-6358	74	10	precision	precision	NOUN
ejpam-6358	74	11	and	and	CCONJ
ejpam-6358	74	12	correctness	correctness	NOUN
ejpam-6358	74	13	.	.	PUNCT
ejpam-6358	75	1	definition	definition	NOUN
ejpam-6358	75	2	1	1	NUM
ejpam-6358	75	3	.	.	PUNCT
ejpam-6358	76	1	[	[	X
ejpam-6358	76	2	3	3	NUM
ejpam-6358	76	3	,	,	PUNCT
ejpam-6358	76	4	4	4	NUM
ejpam-6358	76	5	]	]	PUNCT
ejpam-6358	76	6	a	a	DET
ejpam-6358	76	7	relation	relation	NOUN
ejpam-6358	76	8	r	r	NOUN
ejpam-6358	76	9	on	on	ADP
ejpam-6358	76	10	u	u	NOUN
ejpam-6358	76	11	is	be	AUX
ejpam-6358	76	12	classified	classify	VERB
ejpam-6358	76	13	as	as	SCONJ
ejpam-6358	76	14	follows	follow	VERB
ejpam-6358	76	15	:	:	PUNCT
ejpam-6358	76	16	(	(	PUNCT
ejpam-6358	76	17	i	i	NOUN
ejpam-6358	76	18	)	)	PUNCT
ejpam-6358	76	19	serial	serial	NOUN
ejpam-6358	76	20	:	:	PUNCT
ejpam-6358	76	21	for	for	ADP
ejpam-6358	76	22	each	each	DET
ejpam-6358	76	23	s	s	X
ejpam-6358	76	24	∈	∈	PROPN
ejpam-6358	76	25	u	u	NOUN
ejpam-6358	76	26	,	,	PUNCT
ejpam-6358	76	27	there	there	PRON
ejpam-6358	76	28	exists	exist	VERB
ejpam-6358	76	29	t	t	PROPN
ejpam-6358	76	30	∈	∈	PROPN
ejpam-6358	76	31	u	u	NOUN
ejpam-6358	76	32	such	such	ADJ
ejpam-6358	76	33	that	that	DET
ejpam-6358	76	34	srt	srt	NOUN
ejpam-6358	76	35	.	.	PUNCT
ejpam-6358	77	1	(	(	PUNCT
ejpam-6358	77	2	ii	ii	NOUN
ejpam-6358	77	3	)	)	PUNCT
ejpam-6358	77	4	reflexive	reflexive	VERB
ejpam-6358	77	5	:	:	PUNCT
ejpam-6358	77	6	for	for	ADP
ejpam-6358	77	7	all	all	DET
ejpam-6358	77	8	s	s	PART
ejpam-6358	77	9	∈	∈	PROPN
ejpam-6358	77	10	u	u	NOUN
ejpam-6358	77	11	,	,	PUNCT
ejpam-6358	77	12	srs	srs	PROPN
ejpam-6358	77	13	.	.	PROPN
ejpam-6358	77	14	(	(	PUNCT
ejpam-6358	77	15	iii	iii	NOUN
ejpam-6358	77	16	)	)	PUNCT
ejpam-6358	77	17	symmetric	symmetric	NOUN
ejpam-6358	77	18	:	:	PUNCT
ejpam-6358	77	19	for	for	ADP
ejpam-6358	77	20	all	all	DET
ejpam-6358	77	21	s	s	PROPN
ejpam-6358	77	22	,	,	PUNCT
ejpam-6358	77	23	t	t	PROPN
ejpam-6358	77	24	∈	∈	PROPN
ejpam-6358	77	25	u	u	PROPN
ejpam-6358	77	26	,	,	PUNCT
ejpam-6358	77	27	srt	srt	VERB
ejpam-6358	77	28	if	if	SCONJ
ejpam-6358	77	29	and	and	CCONJ
ejpam-6358	77	30	only	only	ADV
ejpam-6358	77	31	if	if	SCONJ
ejpam-6358	77	32	trs	trs	PROPN
ejpam-6358	77	33	.	.	PUNCT
ejpam-6358	78	1	(	(	PUNCT
ejpam-6358	78	2	iv	iv	X
ejpam-6358	78	3	)	)	PUNCT
ejpam-6358	78	4	transitive	transitive	ADJ
ejpam-6358	78	5	:	:	PUNCT
ejpam-6358	78	6	for	for	ADP
ejpam-6358	78	7	all	all	PRON
ejpam-6358	78	8	s	s	PROPN
ejpam-6358	78	9	,	,	PUNCT
ejpam-6358	78	10	t	t	PROPN
ejpam-6358	78	11	,	,	PUNCT
ejpam-6358	78	12	p	p	PROPN
ejpam-6358	78	13	∈	∈	PROPN
ejpam-6358	78	14	u	u	NOUN
ejpam-6358	78	15	,	,	PUNCT
ejpam-6358	78	16	if	if	SCONJ
ejpam-6358	78	17	srp	srp	PROPN
ejpam-6358	78	18	and	and	CCONJ
ejpam-6358	78	19	prt	prt	PROPN
ejpam-6358	78	20	,	,	PUNCT
ejpam-6358	78	21	then	then	ADV
ejpam-6358	78	22	srt	srt	NOUN
ejpam-6358	78	23	.	.	PUNCT
ejpam-6358	79	1	(	(	PUNCT
ejpam-6358	79	2	v	v	NOUN
ejpam-6358	79	3	)	)	PUNCT
ejpam-6358	79	4	preorder	preorder	NOUN
ejpam-6358	79	5	(	(	PUNCT
ejpam-6358	79	6	or	or	CCONJ
ejpam-6358	79	7	quasi	quasi	ADJ
ejpam-6358	79	8	-	-	NOUN
ejpam-6358	79	9	order	order	NOUN
ejpam-6358	79	10	):	):	PUNCT
ejpam-6358	79	11	r	r	NOUN
ejpam-6358	79	12	is	be	AUX
ejpam-6358	79	13	reflexive	reflexive	ADJ
ejpam-6358	79	14	and	and	CCONJ
ejpam-6358	79	15	transitive	transitive	ADJ
ejpam-6358	79	16	.	.	PUNCT
ejpam-6358	80	1	(	(	PUNCT
ejpam-6358	80	2	vi	vi	NOUN
ejpam-6358	80	3	)	)	PUNCT
ejpam-6358	80	4	equivalence	equivalence	NOUN
ejpam-6358	80	5	relation	relation	NOUN
ejpam-6358	80	6	:	:	PUNCT
ejpam-6358	81	1	r	r	NOUN
ejpam-6358	81	2	is	be	AUX
ejpam-6358	81	3	reflexive	reflexive	ADJ
ejpam-6358	81	4	,	,	PUNCT
ejpam-6358	81	5	symmetric	symmetric	ADJ
ejpam-6358	81	6	,	,	PUNCT
ejpam-6358	81	7	and	and	CCONJ
ejpam-6358	81	8	transitive	transitive	ADJ
ejpam-6358	81	9	.	.	PUNCT
ejpam-6358	82	1	in	in	ADP
ejpam-6358	82	2	[	[	X
ejpam-6358	82	3	40	40	NUM
ejpam-6358	82	4	]	]	PUNCT
ejpam-6358	82	5	,	,	PUNCT
ejpam-6358	82	6	the	the	DET
ejpam-6358	82	7	authors	author	NOUN
ejpam-6358	82	8	presented	present	VERB
ejpam-6358	82	9	definition	definition	NOUN
ejpam-6358	82	10	2.2	2.2	NUM
ejpam-6358	82	11	;	;	PUNCT
ejpam-6358	82	12	however	however	ADV
ejpam-6358	82	13	,	,	PUNCT
ejpam-6358	82	14	they	they	PRON
ejpam-6358	82	15	omitted	omit	VERB
ejpam-6358	82	16	the	the	DET
ejpam-6358	82	17	essential	essential	ADJ
ejpam-6358	82	18	concepts	concept	NOUN
ejpam-6358	82	19	of	of	ADP
ejpam-6358	82	20	intersection	intersection	NOUN
ejpam-6358	82	21	(	(	PUNCT
ejpam-6358	82	22	and	and	CCONJ
ejpam-6358	82	23	minimal	minimal	ADJ
ejpam-6358	82	24	intersection	intersection	NOUN
ejpam-6358	82	25	)	)	PUNCT
ejpam-6358	82	26	neighborhoods	neighborhood	NOUN
ejpam-6358	82	27	as	as	ADV
ejpam-6358	82	28	well	well	ADV
ejpam-6358	82	29	as	as	ADP
ejpam-6358	82	30	union	union	NOUN
ejpam-6358	82	31	(	(	PUNCT
ejpam-6358	82	32	and	and	CCONJ
ejpam-6358	82	33	minimal	minimal	ADJ
ejpam-6358	82	34	union	union	NOUN
ejpam-6358	82	35	)	)	PUNCT
ejpam-6358	82	36	neighborhoods	neighborhood	NOUN
ejpam-6358	82	37	,	,	PUNCT
ejpam-6358	82	38	which	which	PRON
ejpam-6358	82	39	are	be	AUX
ejpam-6358	82	40	fundamental	fundamental	ADJ
ejpam-6358	82	41	to	to	ADP
ejpam-6358	82	42	their	their	PRON
ejpam-6358	82	43	definitions	definition	NOUN
ejpam-6358	82	44	and	and	CCONJ
ejpam-6358	82	45	results	result	NOUN
ejpam-6358	82	46	.	.	PUNCT
ejpam-6358	83	1	to	to	PART
ejpam-6358	83	2	rectify	rectify	VERB
ejpam-6358	83	3	this	this	PRON
ejpam-6358	83	4	,	,	PUNCT
ejpam-6358	83	5	we	we	PRON
ejpam-6358	83	6	provide	provide	VERB
ejpam-6358	83	7	the	the	DET
ejpam-6358	83	8	necessary	necessary	ADJ
ejpam-6358	83	9	definitions	definition	NOUN
ejpam-6358	83	10	below	below	ADV
ejpam-6358	83	11	.	.	PUNCT
ejpam-6358	84	1	definition	definition	NOUN
ejpam-6358	84	2	2	2	NUM
ejpam-6358	84	3	.	.	PUNCT
ejpam-6358	85	1	let	let	VERB
ejpam-6358	85	2	r	r	PRON
ejpam-6358	85	3	be	be	AUX
ejpam-6358	85	4	a	a	DET
ejpam-6358	85	5	binary	binary	ADJ
ejpam-6358	85	6	relation	relation	NOUN
ejpam-6358	85	7	on	on	ADP
ejpam-6358	85	8	a	a	DET
ejpam-6358	85	9	set	set	ADJ
ejpam-6358	85	10	u	u	NOUN
ejpam-6358	85	11	,	,	PUNCT
ejpam-6358	85	12	and	and	CCONJ
ejpam-6358	85	13	let	let	VERB
ejpam-6358	85	14	s	s	PRON
ejpam-6358	85	15	∈	∈	PROPN
ejpam-6358	85	16	u	u	NOUN
ejpam-6358	85	17	.	.	PUNCT
ejpam-6358	86	1	the	the	DET
ejpam-6358	86	2	following	follow	VERB
ejpam-6358	86	3	types	type	NOUN
ejpam-6358	86	4	of	of	ADP
ejpam-6358	86	5	neighborhoods	neighborhood	NOUN
ejpam-6358	86	6	,	,	PUNCT
ejpam-6358	86	7	based	base	VERB
ejpam-6358	86	8	on	on	ADP
ejpam-6358	86	9	r	r	NOUN
ejpam-6358	86	10	,	,	PUNCT
ejpam-6358	86	11	are	be	AUX
ejpam-6358	86	12	defined	define	VERB
ejpam-6358	86	13	:	:	PUNCT
ejpam-6358	86	14	r.	r.	PROPN
ejpam-6358	86	15	a.	a.	PROPN
ejpam-6358	86	16	hosny	hosny	PROPN
ejpam-6358	86	17	et	et	PROPN
ejpam-6358	86	18	al	al	PROPN
ejpam-6358	86	19	.	.	PUNCT
ejpam-6358	86	20	/	/	SYM
ejpam-6358	86	21	eur	eur	PROPN
ejpam-6358	86	22	.	.	PUNCT
ejpam-6358	87	1	j.	j.	PROPN
ejpam-6358	87	2	pure	pure	PROPN
ejpam-6358	87	3	appl	appl	PROPN
ejpam-6358	87	4	.	.	PROPN
ejpam-6358	87	5	math	math	PROPN
ejpam-6358	87	6	,	,	PUNCT
ejpam-6358	87	7	18	18	NUM
ejpam-6358	87	8	(	(	PUNCT
ejpam-6358	87	9	4	4	NUM
ejpam-6358	87	10	)	)	PUNCT
ejpam-6358	87	11	(	(	PUNCT
ejpam-6358	87	12	2025	2025	NUM
ejpam-6358	87	13	)	)	PUNCT
ejpam-6358	87	14	,	,	PUNCT
ejpam-6358	87	15	6358	6358	NUM
ejpam-6358	87	16	5	5	NUM
ejpam-6358	87	17	of	of	ADP
ejpam-6358	87	18	24	24	NUM
ejpam-6358	87	19	(	(	PUNCT
ejpam-6358	87	20	i	i	NOUN
ejpam-6358	87	21	)	)	PUNCT
ejpam-6358	87	22	after	after	ADP
ejpam-6358	87	23	(	(	PUNCT
ejpam-6358	87	24	right	right	ADJ
ejpam-6358	87	25	)	)	PUNCT
ejpam-6358	87	26	neighborhood	neighborhood	NOUN
ejpam-6358	88	1	[	[	X
ejpam-6358	88	2	3	3	NUM
ejpam-6358	88	3	,	,	PUNCT
ejpam-6358	88	4	4	4	NUM
ejpam-6358	88	5	]	]	NUM
ejpam-6358	88	6	:	:	PUNCT
ejpam-6358	88	7	ωa(s	ωa(s	X
ejpam-6358	88	8	)	)	PUNCT
ejpam-6358	88	9	=	=	SYM
ejpam-6358	88	10	{	{	PUNCT
ejpam-6358	88	11	t	t	NOUN
ejpam-6358	88	12	∈	∈	PROPN
ejpam-6358	88	13	u	u	NOUN
ejpam-6358	88	14	:	:	PUNCT
ejpam-6358	88	15	srt	srt	NOUN
ejpam-6358	88	16	}	}	PUNCT
ejpam-6358	88	17	.	.	PUNCT
ejpam-6358	89	1	(	(	PUNCT
ejpam-6358	89	2	ii	ii	NOUN
ejpam-6358	89	3	)	)	PUNCT
ejpam-6358	89	4	before	before	ADP
ejpam-6358	89	5	(	(	PUNCT
ejpam-6358	89	6	left	left	ADJ
ejpam-6358	89	7	)	)	PUNCT
ejpam-6358	89	8	neighborhood	neighborhood	NOUN
ejpam-6358	90	1	[	[	X
ejpam-6358	90	2	3	3	NUM
ejpam-6358	90	3	,	,	PUNCT
ejpam-6358	90	4	4	4	NUM
ejpam-6358	90	5	]	]	NUM
ejpam-6358	90	6	:	:	PUNCT
ejpam-6358	90	7	ωb(s	ωb(s	NUM
ejpam-6358	90	8	)	)	PUNCT
ejpam-6358	90	9	=	=	PRON
ejpam-6358	90	10	{	{	PUNCT
ejpam-6358	90	11	t	t	PROPN
ejpam-6358	90	12	∈	∈	PROPN
ejpam-6358	90	13	u	u	NOUN
ejpam-6358	90	14	:	:	PUNCT
ejpam-6358	90	15	trs	trs	PROPN
ejpam-6358	90	16	}	}	PUNCT
ejpam-6358	90	17	.	.	PUNCT
ejpam-6358	91	1	(	(	PUNCT
ejpam-6358	91	2	iii	iii	X
ejpam-6358	91	3	)	)	PUNCT
ejpam-6358	91	4	minimal	minimal	ADJ
ejpam-6358	91	5	-	-	PUNCT
ejpam-6358	91	6	after	after	ADP
ejpam-6358	91	7	neighborhood	neighborhood	NOUN
ejpam-6358	91	8	[	[	X
ejpam-6358	91	9	5	5	NUM
ejpam-6358	91	10	,	,	PUNCT
ejpam-6358	91	11	6	6	NUM
ejpam-6358	91	12	]	]	PUNCT
ejpam-6358	91	13	:	:	PUNCT
ejpam-6358	91	14	ω	ω	X
ejpam-6358	91	15	<	<	X
ejpam-6358	91	16	a>(s	a>(s	X
ejpam-6358	91	17	)	)	PUNCT
ejpam-6358	91	18	=	=	NOUN
ejpam-6358	91	19	∩	∩	X
ejpam-6358	91	20	{	{	PUNCT
ejpam-6358	91	21	ωa(p	ωa(p	PROPN
ejpam-6358	91	22	)	)	PUNCT
ejpam-6358	91	23	:	:	PUNCT
ejpam-6358	92	1	s	s	X
ejpam-6358	92	2	∈	∈	PROPN
ejpam-6358	92	3	ωa(p	ωa(p	NUM
ejpam-6358	92	4	)	)	PUNCT
ejpam-6358	92	5	}	}	PUNCT
ejpam-6358	92	6	.	.	PUNCT
ejpam-6358	93	1	(	(	PUNCT
ejpam-6358	93	2	iv	iv	X
ejpam-6358	93	3	)	)	PUNCT
ejpam-6358	93	4	minimal	minimal	ADJ
ejpam-6358	93	5	-	-	PUNCT
ejpam-6358	93	6	before	before	ADP
ejpam-6358	93	7	neighborhood	neighborhood	NOUN
ejpam-6358	93	8	[	[	X
ejpam-6358	93	9	6	6	NUM
ejpam-6358	93	10	]	]	SYM
ejpam-6358	93	11	:	:	PUNCT
ejpam-6358	93	12	ω	ω	NUM
ejpam-6358	93	13	<	<	X
ejpam-6358	93	14	b>(s	b>(s	X
ejpam-6358	93	15	)	)	PUNCT
ejpam-6358	94	1	=	=	NOUN
ejpam-6358	94	2	∩	∩	NOUN
ejpam-6358	94	3	{	{	PUNCT
ejpam-6358	94	4	ωb(p	ωb(p	X
ejpam-6358	94	5	)	)	PUNCT
ejpam-6358	94	6	:	:	PUNCT
ejpam-6358	94	7	s	s	VERB
ejpam-6358	94	8	∈	∈	NOUN
ejpam-6358	94	9	ωb(p	ωb(p	NOUN
ejpam-6358	94	10	)	)	PUNCT
ejpam-6358	94	11	}	}	PUNCT
ejpam-6358	94	12	.	.	PUNCT
ejpam-6358	95	1	(	(	PUNCT
ejpam-6358	95	2	v	v	NOUN
ejpam-6358	95	3	)	)	PUNCT
ejpam-6358	95	4	intersection	intersection	NOUN
ejpam-6358	95	5	neighborhood	neighborhood	NOUN
ejpam-6358	96	1	[	[	X
ejpam-6358	96	2	3	3	NUM
ejpam-6358	96	3	,	,	PUNCT
ejpam-6358	96	4	9	9	NUM
ejpam-6358	96	5	]	]	NUM
ejpam-6358	96	6	:	:	PUNCT
ejpam-6358	96	7	ωi(s	ωi(s	X
ejpam-6358	96	8	)	)	PUNCT
ejpam-6358	96	9	=	=	SYM
ejpam-6358	96	10	ωa(s	ωa(	NOUN
ejpam-6358	96	11	)	)	PUNCT
ejpam-6358	96	12	∩	∩	NOUN
ejpam-6358	96	13	ωb(s	ωb(	NOUN
ejpam-6358	96	14	)	)	PUNCT
ejpam-6358	96	15	.	.	PUNCT
ejpam-6358	97	1	(	(	PUNCT
ejpam-6358	97	2	vi	vi	X
ejpam-6358	97	3	)	)	PUNCT
ejpam-6358	97	4	union	union	NOUN
ejpam-6358	97	5	neighborhood	neighborhood	NOUN
ejpam-6358	98	1	[	[	X
ejpam-6358	98	2	3	3	NUM
ejpam-6358	98	3	,	,	PUNCT
ejpam-6358	98	4	9	9	NUM
ejpam-6358	98	5	]	]	NUM
ejpam-6358	98	6	:	:	PUNCT
ejpam-6358	98	7	ωu(s	ωu(s	NUM
ejpam-6358	98	8	)	)	PUNCT
ejpam-6358	98	9	=	=	SYM
ejpam-6358	98	10	ωa(s	ωa(	NOUN
ejpam-6358	98	11	)	)	PUNCT
ejpam-6358	98	12	∪	∪	ADP
ejpam-6358	98	13	ωb(s	ωb(	NOUN
ejpam-6358	98	14	)	)	PUNCT
ejpam-6358	98	15	.	.	PUNCT
ejpam-6358	99	1	(	(	PUNCT
ejpam-6358	99	2	vii	vii	PROPN
ejpam-6358	99	3	)	)	PUNCT
ejpam-6358	99	4	minimal	minimal	ADJ
ejpam-6358	99	5	-	-	PUNCT
ejpam-6358	99	6	intersection	intersection	NOUN
ejpam-6358	99	7	neighborhood	neighborhood	NOUN
ejpam-6358	100	1	[	[	X
ejpam-6358	100	2	9	9	NUM
ejpam-6358	100	3	,	,	PUNCT
ejpam-6358	100	4	16	16	NUM
ejpam-6358	100	5	]	]	SYM
ejpam-6358	100	6	:	:	PUNCT
ejpam-6358	100	7	ω	ω	NUM
ejpam-6358	100	8	<	<	X
ejpam-6358	100	9	i>(s	i>(s	NOUN
ejpam-6358	100	10	)	)	PUNCT
ejpam-6358	101	1	=	=	PUNCT
ejpam-6358	101	2	ω	ω	PROPN
ejpam-6358	101	3	<	<	X
ejpam-6358	101	4	a>(s	a>(s	X
ejpam-6358	101	5	)	)	PUNCT
ejpam-6358	101	6	∩	∩	PROPN
ejpam-6358	101	7	ω	ω	X
ejpam-6358	101	8	<	<	X
ejpam-6358	101	9	b>(s	b>(s	PRON
ejpam-6358	101	10	)	)	PUNCT
ejpam-6358	101	11	.	.	PUNCT
ejpam-6358	102	1	(	(	PUNCT
ejpam-6358	102	2	viii	viii	NOUN
ejpam-6358	102	3	)	)	PUNCT
ejpam-6358	102	4	minimal	minimal	ADJ
ejpam-6358	102	5	-	-	PUNCT
ejpam-6358	102	6	union	union	NOUN
ejpam-6358	102	7	neighborhood	neighborhood	NOUN
ejpam-6358	103	1	[	[	X
ejpam-6358	103	2	9	9	NUM
ejpam-6358	103	3	]	]	SYM
ejpam-6358	103	4	:	:	PUNCT
ejpam-6358	103	5	ω	ω	NUM
ejpam-6358	103	6	<	<	X
ejpam-6358	103	7	u>(s	u>(s	X
ejpam-6358	103	8	)	)	PUNCT
ejpam-6358	103	9	=	=	PUNCT
ejpam-6358	103	10	ω	ω	PROPN
ejpam-6358	103	11	<	<	X
ejpam-6358	103	12	a>(s	a>(s	X
ejpam-6358	103	13	)	)	PUNCT
ejpam-6358	103	14	∪	∪	X
ejpam-6358	103	15	ω	ω	X
ejpam-6358	103	16	<	<	X
ejpam-6358	103	17	b>(s	b>(s	PRON
ejpam-6358	103	18	)	)	PUNCT
ejpam-6358	103	19	.	.	PUNCT
ejpam-6358	104	1	for	for	ADP
ejpam-6358	104	2	simplicity	simplicity	NOUN
ejpam-6358	104	3	,	,	PUNCT
ejpam-6358	104	4	the	the	DET
ejpam-6358	104	5	set	set	NOUN
ejpam-6358	104	6	{	{	PUNCT
ejpam-6358	104	7	a	a	DET
ejpam-6358	104	8	,	,	PUNCT
ejpam-6358	104	9	b	b	NOUN
ejpam-6358	104	10	,	,	PUNCT
ejpam-6358	104	11	<	<	X
ejpam-6358	104	12	a	a	X
ejpam-6358	104	13	>	>	X
ejpam-6358	104	14	,	,	PUNCT
ejpam-6358	104	15	<	<	X
ejpam-6358	104	16	b	b	X
ejpam-6358	104	17	>	>	X
ejpam-6358	104	18	,	,	PUNCT
ejpam-6358	104	19	i	i	PRON
ejpam-6358	104	20	,	,	PUNCT
ejpam-6358	104	21	u	u	NOUN
ejpam-6358	104	22	,	,	PUNCT
ejpam-6358	104	23	<	<	X
ejpam-6358	104	24	i	i	X
ejpam-6358	104	25	>	>	X
ejpam-6358	104	26	,	,	PUNCT
ejpam-6358	104	27	<	<	X
ejpam-6358	104	28	u	u	X
ejpam-6358	104	29	>	>	X
ejpam-6358	104	30	}	}	PUNCT
ejpam-6358	104	31	will	will	AUX
ejpam-6358	104	32	be	be	AUX
ejpam-6358	104	33	collectively	collectively	ADV
ejpam-6358	104	34	denoted	denote	VERB
ejpam-6358	104	35	by	by	ADP
ejpam-6358	104	36	ω	ω	PROPN
ejpam-6358	104	37	.	.	PUNCT
ejpam-6358	105	1	definition	definition	NOUN
ejpam-6358	105	2	3	3	NUM
ejpam-6358	105	3	.	.	PUNCT
ejpam-6358	106	1	[	[	X
ejpam-6358	106	2	3	3	NUM
ejpam-6358	106	3	,	,	PUNCT
ejpam-6358	106	4	5	5	NUM
ejpam-6358	106	5	,	,	PUNCT
ejpam-6358	106	6	16	16	NUM
ejpam-6358	106	7	]	]	PUNCT
ejpam-6358	106	8	let	let	VERB
ejpam-6358	106	9	r	r	PRON
ejpam-6358	106	10	be	be	AUX
ejpam-6358	106	11	a	a	DET
ejpam-6358	106	12	binary	binary	ADJ
ejpam-6358	106	13	relation	relation	NOUN
ejpam-6358	106	14	on	on	ADP
ejpam-6358	106	15	a	a	DET
ejpam-6358	106	16	finite	finite	ADJ
ejpam-6358	106	17	universe	universe	NOUN
ejpam-6358	106	18	u	u	NOUN
ejpam-6358	106	19	,	,	PUNCT
ejpam-6358	106	20	and	and	CCONJ
ejpam-6358	106	21	let	let	VERB
ejpam-6358	106	22	f	f	PROPN
ejpam-6358	106	23	⊆	⊆	NUM
ejpam-6358	106	24	u	u	NOUN
ejpam-6358	106	25	be	be	VERB
ejpam-6358	106	26	a	a	DET
ejpam-6358	106	27	nonempty	nonempty	NOUN
ejpam-6358	106	28	subset	subset	NOUN
ejpam-6358	106	29	.	.	PUNCT
ejpam-6358	107	1	for	for	ADP
ejpam-6358	107	2	each	each	DET
ejpam-6358	107	3	j	j	PROPN
ejpam-6358	107	4	∈	∈	PROPN
ejpam-6358	107	5	ω	ω	PROPN
ejpam-6358	107	6	,	,	PUNCT
ejpam-6358	107	7	the	the	DET
ejpam-6358	107	8	approximation	approximation	NOUN
ejpam-6358	107	9	operators	operator	NOUN
ejpam-6358	107	10	based	base	VERB
ejpam-6358	107	11	on	on	ADP
ejpam-6358	107	12	the	the	DET
ejpam-6358	107	13	ωjneighborhoods	ωjneighborhood	NOUN
ejpam-6358	107	14	are	be	AUX
ejpam-6358	107	15	defined	define	VERB
ejpam-6358	107	16	as	as	ADP
ejpam-6358	107	17	:	:	PUNCT
ejpam-6358	107	18	�	�	PROPN
ejpam-6358	107	19	lower	low	ADJ
ejpam-6358	107	20	approximation	approximation	NOUN
ejpam-6358	107	21	:	:	PUNCT
ejpam-6358	108	1	r	r	NOUN
ejpam-6358	108	2	ωj	ωj	ADP
ejpam-6358	108	3	⋆	⋆	NOUN
ejpam-6358	108	4	(	(	PUNCT
ejpam-6358	108	5	f	f	NOUN
ejpam-6358	108	6	)	)	PUNCT
ejpam-6358	108	7	=	=	PRON
ejpam-6358	108	8	{	{	PUNCT
ejpam-6358	108	9	s	s	NOUN
ejpam-6358	108	10	∈	∈	PROPN
ejpam-6358	108	11	u	u	NOUN
ejpam-6358	108	12	:	:	PUNCT
ejpam-6358	108	13	ωj(s	ωj(s	NUM
ejpam-6358	108	14	)	)	PUNCT
ejpam-6358	108	15	⊆	⊆	NUM
ejpam-6358	108	16	f	f	X
ejpam-6358	108	17	}	}	PUNCT
ejpam-6358	108	18	.	.	PUNCT
ejpam-6358	109	1	�	�	PROPN
ejpam-6358	109	2	upper	upper	ADJ
ejpam-6358	109	3	approximation	approximation	NOUN
ejpam-6358	109	4	:	:	PUNCT
ejpam-6358	109	5	r⋆ωj	r⋆ωj	PROPN
ejpam-6358	109	6	(	(	PUNCT
ejpam-6358	109	7	f	f	X
ejpam-6358	109	8	)	)	PUNCT
ejpam-6358	109	9	=	=	PRON
ejpam-6358	109	10	{	{	PUNCT
ejpam-6358	109	11	s	s	NOUN
ejpam-6358	109	12	∈	∈	PROPN
ejpam-6358	109	13	u	u	NOUN
ejpam-6358	109	14	:	:	PUNCT
ejpam-6358	109	15	ωj(s	ωj(s	NUM
ejpam-6358	109	16	)	)	PUNCT
ejpam-6358	109	17	∩	∩	NOUN
ejpam-6358	109	18	f	f	PROPN
ejpam-6358	109	19	̸=	̸=	PROPN
ejpam-6358	109	20	∅	∅	NOUN
ejpam-6358	109	21	}	}	PUNCT
ejpam-6358	109	22	.	.	PUNCT
ejpam-6358	110	1	�	�	PROPN
ejpam-6358	110	2	boundary	boundary	PROPN
ejpam-6358	110	3	region	region	NOUN
ejpam-6358	110	4	:	:	PUNCT
ejpam-6358	110	5	bnd	bnd	NOUN
ejpam-6358	110	6	⋆ωj	⋆ωj	PROPN
ejpam-6358	111	1	r	r	NOUN
ejpam-6358	111	2	(	(	PUNCT
ejpam-6358	111	3	f	f	PROPN
ejpam-6358	111	4	)	)	PUNCT
ejpam-6358	111	5	=	=	SYM
ejpam-6358	112	1	r⋆ωj	r⋆ωj	INTJ
ejpam-6358	112	2	(	(	PUNCT
ejpam-6358	112	3	f	f	PROPN
ejpam-6358	112	4	)	)	PUNCT
ejpam-6358	112	5	\rωj	\rωj	PROPN
ejpam-6358	112	6	⋆	⋆	X
ejpam-6358	112	7	(	(	PUNCT
ejpam-6358	112	8	f	f	PROPN
ejpam-6358	112	9	)	)	PUNCT
ejpam-6358	112	10	.	.	PUNCT
ejpam-6358	113	1	�	�	PROPN
ejpam-6358	113	2	accuracy	accuracy	NOUN
ejpam-6358	113	3	measure	measure	NOUN
ejpam-6358	113	4	:	:	PUNCT
ejpam-6358	114	1	acc	acc	PROPN
ejpam-6358	114	2	⋆ωj	⋆ωj	PROPN
ejpam-6358	114	3	r	r	NOUN
ejpam-6358	114	4	(	(	PUNCT
ejpam-6358	114	5	f	f	PROPN
ejpam-6358	114	6	)	)	PUNCT
ejpam-6358	114	7	=	=	SYM
ejpam-6358	115	1	|r	|r	PROPN
ejpam-6358	115	2	ωj	ωj	INTJ
ejpam-6358	115	3	⋆	⋆	X
ejpam-6358	115	4	(	(	PUNCT
ejpam-6358	115	5	f	f	NOUN
ejpam-6358	115	6	)	)	PUNCT
ejpam-6358	115	7	∩f	∩f	NOUN
ejpam-6358	115	8	|	|	ADV
ejpam-6358	116	1	|r⋆ωj	|r⋆ωj	INTJ
ejpam-6358	116	2	(	(	PUNCT
ejpam-6358	116	3	f	f	NOUN
ejpam-6358	116	4	)	)	PUNCT
ejpam-6358	116	5	∪f	∪f	PROPN
ejpam-6358	117	1	|	|	ADV
ejpam-6358	117	2	,	,	PUNCT
ejpam-6358	117	3	provided	provide	VERB
ejpam-6358	117	4	that	that	SCONJ
ejpam-6358	117	5	|	|	ADV
ejpam-6358	117	6	r⋆ωj	r⋆ωj	NOUN
ejpam-6358	117	7	(	(	PUNCT
ejpam-6358	117	8	f	f	PROPN
ejpam-6358	117	9	)	)	PUNCT
ejpam-6358	117	10	∪	∪	ADP
ejpam-6358	117	11	f	f	PROPN
ejpam-6358	117	12	|̸=	|̸=	NUM
ejpam-6358	117	13	0	0	NUM
ejpam-6358	117	14	.	.	PUNCT
ejpam-6358	118	1	the	the	DET
ejpam-6358	118	2	following	follow	VERB
ejpam-6358	118	3	definition	definition	NOUN
ejpam-6358	118	4	presents	present	VERB
ejpam-6358	118	5	an	an	DET
ejpam-6358	118	6	interesting	interesting	ADJ
ejpam-6358	118	7	application	application	NOUN
ejpam-6358	118	8	of	of	ADP
ejpam-6358	118	9	j	j	PROPN
ejpam-6358	118	10	-	-	PUNCT
ejpam-6358	118	11	ns	ns	ADJ
ejpam-6358	118	12	,	,	PUNCT
ejpam-6358	118	13	as	as	SCONJ
ejpam-6358	118	14	defined	define	VERB
ejpam-6358	118	15	by	by	ADP
ejpam-6358	118	16	[	[	X
ejpam-6358	118	17	17	17	NUM
ejpam-6358	118	18	,	,	PUNCT
ejpam-6358	118	19	18	18	NUM
ejpam-6358	118	20	]	]	PUNCT
ejpam-6358	118	21	.	.	PUNCT
ejpam-6358	119	1	in	in	ADP
ejpam-6358	119	2	this	this	DET
ejpam-6358	119	3	definition	definition	NOUN
ejpam-6358	119	4	,	,	PUNCT
ejpam-6358	119	5	the	the	DET
ejpam-6358	119	6	ωj	ωj	ADP
ejpam-6358	119	7	-	-	PUNCT
ejpam-6358	119	8	neighborhoods	neighborhood	NOUN
ejpam-6358	119	9	are	be	AUX
ejpam-6358	119	10	extended	extend	VERB
ejpam-6358	119	11	to	to	ADP
ejpam-6358	119	12	generalized	generalize	VERB
ejpam-6358	119	13	neighborhoods	neighborhood	NOUN
ejpam-6358	119	14	called	call	VERB
ejpam-6358	119	15	”	"	PUNCT
ejpam-6358	119	16	adhesion	adhesion	NOUN
ejpam-6358	119	17	-	-	PUNCT
ejpam-6358	119	18	neighborhoods	neighborhood	NOUN
ejpam-6358	119	19	”	"	PUNCT
ejpam-6358	119	20	(	(	PUNCT
ejpam-6358	119	21	denoted	denote	VERB
ejpam-6358	119	22	as	as	ADP
ejpam-6358	119	23	ρj	ρj	NOUN
ejpam-6358	119	24	-	-	NOUN
ejpam-6358	119	25	neighborhoods	neighborhood	NOUN
ejpam-6358	119	26	)	)	PUNCT
ejpam-6358	119	27	.	.	PUNCT
ejpam-6358	120	1	these	these	DET
ejpam-6358	120	2	generalized	generalize	VERB
ejpam-6358	120	3	neighborhoods	neighborhood	NOUN
ejpam-6358	120	4	are	be	AUX
ejpam-6358	120	5	utilized	utilize	VERB
ejpam-6358	120	6	in	in	ADP
ejpam-6358	120	7	identifying	identify	VERB
ejpam-6358	120	8	generalized	generalized	ADJ
ejpam-6358	120	9	rough	rough	ADJ
ejpam-6358	120	10	sets	set	NOUN
ejpam-6358	120	11	,	,	PUNCT
ejpam-6358	120	12	which	which	PRON
ejpam-6358	120	13	serve	serve	VERB
ejpam-6358	120	14	as	as	ADP
ejpam-6358	120	15	generalizations	generalization	NOUN
ejpam-6358	120	16	of	of	ADP
ejpam-6358	120	17	pawlak	pawlak	ADJ
ejpam-6358	120	18	’s	’s	PART
ejpam-6358	120	19	models	model	NOUN
ejpam-6358	120	20	and	and	CCONJ
ejpam-6358	120	21	their	their	PRON
ejpam-6358	120	22	extensions	extension	NOUN
ejpam-6358	120	23	.	.	PUNCT
ejpam-6358	121	1	definition	definition	NOUN
ejpam-6358	121	2	4	4	NUM
ejpam-6358	121	3	.	.	PUNCT
ejpam-6358	122	1	[	[	X
ejpam-6358	122	2	17	17	NUM
ejpam-6358	122	3	,	,	PUNCT
ejpam-6358	122	4	18	18	NUM
ejpam-6358	122	5	,	,	PUNCT
ejpam-6358	122	6	20	20	NUM
ejpam-6358	122	7	]	]	PUNCT
ejpam-6358	122	8	let	let	VERB
ejpam-6358	122	9	r	r	PRON
ejpam-6358	122	10	be	be	AUX
ejpam-6358	122	11	a	a	DET
ejpam-6358	122	12	binary	binary	ADJ
ejpam-6358	122	13	relation	relation	NOUN
ejpam-6358	122	14	on	on	ADP
ejpam-6358	122	15	a	a	DET
ejpam-6358	122	16	set	set	ADJ
ejpam-6358	122	17	u	u	NOUN
ejpam-6358	122	18	,	,	PUNCT
ejpam-6358	122	19	and	and	CCONJ
ejpam-6358	122	20	let	let	VERB
ejpam-6358	122	21	s	s	PRON
ejpam-6358	122	22	∈	∈	PROPN
ejpam-6358	122	23	u	u	NOUN
ejpam-6358	122	24	.	.	PUNCT
ejpam-6358	123	1	the	the	DET
ejpam-6358	123	2	ρj	ρj	NOUN
ejpam-6358	123	3	-	-	PUNCT
ejpam-6358	123	4	neighborhood	neighborhood	NOUN
ejpam-6358	123	5	of	of	ADP
ejpam-6358	123	6	s	s	NOUN
ejpam-6358	123	7	collects	collect	VERB
ejpam-6358	123	8	all	all	DET
ejpam-6358	123	9	elements	element	NOUN
ejpam-6358	123	10	that	that	PRON
ejpam-6358	123	11	share	share	VERB
ejpam-6358	123	12	the	the	DET
ejpam-6358	123	13	same	same	ADJ
ejpam-6358	123	14	ωj	ωj	NOUN
ejpam-6358	123	15	-	-	PUNCT
ejpam-6358	123	16	neighborhood	neighborhood	NOUN
ejpam-6358	123	17	.	.	PUNCT
ejpam-6358	124	1	for	for	ADP
ejpam-6358	124	2	each	each	DET
ejpam-6358	124	3	j	j	PROPN
ejpam-6358	124	4	∈	∈	PROPN
ejpam-6358	124	5	ω	ω	PROPN
ejpam-6358	124	6	,	,	PUNCT
ejpam-6358	124	7	the	the	DET
ejpam-6358	124	8	neighborhoods	neighborhood	NOUN
ejpam-6358	124	9	are	be	AUX
ejpam-6358	124	10	defined	define	VERB
ejpam-6358	124	11	as	as	SCONJ
ejpam-6358	124	12	follows	follow	VERB
ejpam-6358	124	13	:	:	PUNCT
ejpam-6358	125	1	r.	r.	PROPN
ejpam-6358	125	2	a.	a.	PROPN
ejpam-6358	125	3	hosny	hosny	PROPN
ejpam-6358	125	4	et	et	PROPN
ejpam-6358	125	5	al	al	PROPN
ejpam-6358	125	6	.	.	PUNCT
ejpam-6358	125	7	/	/	SYM
ejpam-6358	125	8	eur	eur	PROPN
ejpam-6358	125	9	.	.	PUNCT
ejpam-6358	126	1	j.	j.	PROPN
ejpam-6358	126	2	pure	pure	PROPN
ejpam-6358	126	3	appl	appl	PROPN
ejpam-6358	126	4	.	.	PROPN
ejpam-6358	126	5	math	math	PROPN
ejpam-6358	126	6	,	,	PUNCT
ejpam-6358	126	7	18	18	NUM
ejpam-6358	126	8	(	(	PUNCT
ejpam-6358	126	9	4	4	NUM
ejpam-6358	126	10	)	)	PUNCT
ejpam-6358	126	11	(	(	PUNCT
ejpam-6358	126	12	2025	2025	NUM
ejpam-6358	126	13	)	)	PUNCT
ejpam-6358	126	14	,	,	PUNCT
ejpam-6358	126	15	6358	6358	NUM
ejpam-6358	126	16	6	6	NUM
ejpam-6358	126	17	of	of	ADP
ejpam-6358	126	18	24	24	NUM
ejpam-6358	126	19	(	(	PUNCT
ejpam-6358	126	20	i	i	NOUN
ejpam-6358	126	21	)	)	PUNCT
ejpam-6358	126	22	after	after	ADP
ejpam-6358	126	23	ρ	ρ	NOUN
ejpam-6358	126	24	-	-	PUNCT
ejpam-6358	126	25	neighborhood	neighborhood	NOUN
ejpam-6358	126	26	:	:	PUNCT
ejpam-6358	126	27	ρa(s	ρa(s	NUM
ejpam-6358	126	28	)	)	PUNCT
ejpam-6358	126	29	=	=	SYM
ejpam-6358	126	30	{	{	PUNCT
ejpam-6358	126	31	t	t	PROPN
ejpam-6358	126	32	∈	∈	PROPN
ejpam-6358	126	33	u	u	NOUN
ejpam-6358	126	34	:	:	PUNCT
ejpam-6358	126	35	ωa(t	ωa(t	NUM
ejpam-6358	126	36	)	)	PUNCT
ejpam-6358	126	37	=	=	SYM
ejpam-6358	126	38	ωa(s	ωa(	NOUN
ejpam-6358	126	39	)	)	PUNCT
ejpam-6358	126	40	}	}	PUNCT
ejpam-6358	126	41	.	.	PUNCT
ejpam-6358	127	1	(	(	PUNCT
ejpam-6358	127	2	ii	ii	NOUN
ejpam-6358	127	3	)	)	PUNCT
ejpam-6358	127	4	before	before	ADP
ejpam-6358	127	5	ρ	ρ	NOUN
ejpam-6358	127	6	-	-	PUNCT
ejpam-6358	127	7	neighborhood	neighborhood	NOUN
ejpam-6358	127	8	:	:	PUNCT
ejpam-6358	127	9	ρb(s	ρb(	NOUN
ejpam-6358	127	10	)	)	PUNCT
ejpam-6358	128	1	=	=	PRON
ejpam-6358	128	2	{	{	PUNCT
ejpam-6358	128	3	t	t	PROPN
ejpam-6358	128	4	∈	∈	PROPN
ejpam-6358	128	5	u	u	NOUN
ejpam-6358	128	6	:	:	PUNCT
ejpam-6358	128	7	ωb(t	ωb(t	NUM
ejpam-6358	128	8	)	)	PUNCT
ejpam-6358	128	9	=	=	SYM
ejpam-6358	128	10	ωb(s	ωb(	NOUN
ejpam-6358	128	11	)	)	PUNCT
ejpam-6358	128	12	}	}	PUNCT
ejpam-6358	128	13	.	.	PUNCT
ejpam-6358	129	1	(	(	PUNCT
ejpam-6358	129	2	iii	iii	X
ejpam-6358	129	3	)	)	PUNCT
ejpam-6358	129	4	intersection	intersection	NOUN
ejpam-6358	129	5	ρ	ρ	NOUN
ejpam-6358	129	6	-	-	PUNCT
ejpam-6358	129	7	neighborhood	neighborhood	NOUN
ejpam-6358	129	8	:	:	PUNCT
ejpam-6358	129	9	ρi(s	ρi(s	NUM
ejpam-6358	129	10	)	)	PUNCT
ejpam-6358	129	11	=	=	SYM
ejpam-6358	129	12	ρa(s	ρa(	NOUN
ejpam-6358	129	13	)	)	PUNCT
ejpam-6358	129	14	∩	∩	NOUN
ejpam-6358	129	15	ρb(s	ρb(	NOUN
ejpam-6358	129	16	)	)	PUNCT
ejpam-6358	129	17	.	.	PUNCT
ejpam-6358	130	1	(	(	PUNCT
ejpam-6358	130	2	iv	iv	X
ejpam-6358	130	3	)	)	PUNCT
ejpam-6358	130	4	union	union	NOUN
ejpam-6358	130	5	ρ	ρ	PROPN
ejpam-6358	130	6	-	-	PUNCT
ejpam-6358	130	7	neighborhood	neighborhood	NOUN
ejpam-6358	130	8	:	:	PUNCT
ejpam-6358	130	9	ρu(s	ρu(s	NUM
ejpam-6358	130	10	)	)	PUNCT
ejpam-6358	130	11	=	=	SYM
ejpam-6358	130	12	ρa(s	ρa(	NOUN
ejpam-6358	130	13	)	)	PUNCT
ejpam-6358	130	14	∪	∪	ADP
ejpam-6358	130	15	ρb(s	ρb(	NOUN
ejpam-6358	130	16	)	)	PUNCT
ejpam-6358	130	17	.	.	PUNCT
ejpam-6358	131	1	(	(	PUNCT
ejpam-6358	131	2	v	v	NOUN
ejpam-6358	131	3	)	)	PUNCT
ejpam-6358	131	4	minimal	minimal	ADJ
ejpam-6358	131	5	-	-	PUNCT
ejpam-6358	131	6	after	after	ADP
ejpam-6358	131	7	ρ	ρ	NOUN
ejpam-6358	131	8	-	-	PUNCT
ejpam-6358	131	9	neighborhood	neighborhood	NOUN
ejpam-6358	131	10	:	:	PUNCT
ejpam-6358	132	1	ρ	ρ	PROPN
ejpam-6358	132	2	<	<	X
ejpam-6358	132	3	a>(s	a>(s	X
ejpam-6358	132	4	)	)	PUNCT
ejpam-6358	132	5	=	=	PRON
ejpam-6358	132	6	{	{	PUNCT
ejpam-6358	132	7	t	t	NOUN
ejpam-6358	132	8	∈	∈	PROPN
ejpam-6358	132	9	u	u	NOUN
ejpam-6358	132	10	:	:	PUNCT
ejpam-6358	132	11	ω	ω	X
ejpam-6358	132	12	<	<	X
ejpam-6358	132	13	a>(t	a>(t	X
ejpam-6358	132	14	)	)	PUNCT
ejpam-6358	132	15	=	=	PUNCT
ejpam-6358	132	16	ω	ω	PROPN
ejpam-6358	132	17	<	<	X
ejpam-6358	132	18	a>(s	a>(s	X
ejpam-6358	132	19	)	)	PUNCT
ejpam-6358	132	20	}	}	PUNCT
ejpam-6358	132	21	.	.	PUNCT
ejpam-6358	133	1	(	(	PUNCT
ejpam-6358	133	2	vi	vi	NOUN
ejpam-6358	133	3	)	)	PUNCT
ejpam-6358	133	4	minimal	minimal	ADJ
ejpam-6358	133	5	-	-	PUNCT
ejpam-6358	133	6	before	before	ADP
ejpam-6358	133	7	ρ	ρ	NOUN
ejpam-6358	133	8	-	-	PUNCT
ejpam-6358	133	9	neighborhood	neighborhood	NOUN
ejpam-6358	133	10	:	:	PUNCT
ejpam-6358	134	1	ρ	ρ	X
ejpam-6358	134	2	<	<	X
ejpam-6358	134	3	b>(s	b>(s	PRON
ejpam-6358	134	4	)	)	PUNCT
ejpam-6358	135	1	=	=	PRON
ejpam-6358	135	2	{	{	PUNCT
ejpam-6358	135	3	t	t	PROPN
ejpam-6358	135	4	∈	∈	PROPN
ejpam-6358	135	5	u	u	NOUN
ejpam-6358	135	6	:	:	PUNCT
ejpam-6358	135	7	ω	ω	NUM
ejpam-6358	135	8	<	<	NOUN
ejpam-6358	135	9	b>(t	b>(t	X
ejpam-6358	135	10	)	)	PUNCT
ejpam-6358	135	11	=	=	SYM
ejpam-6358	135	12	ω	ω	PROPN
ejpam-6358	135	13	<	<	X
ejpam-6358	135	14	b>(s	b>(s	PRON
ejpam-6358	135	15	)	)	PUNCT
ejpam-6358	135	16	}	}	PUNCT
ejpam-6358	135	17	.	.	PUNCT
ejpam-6358	136	1	(	(	PUNCT
ejpam-6358	136	2	vii	vii	PROPN
ejpam-6358	136	3	)	)	PUNCT
ejpam-6358	136	4	minimal	minimal	ADJ
ejpam-6358	136	5	-	-	PUNCT
ejpam-6358	136	6	intersection	intersection	NOUN
ejpam-6358	136	7	ρ	ρ	NOUN
ejpam-6358	136	8	-	-	PUNCT
ejpam-6358	136	9	neighborhood	neighborhood	NOUN
ejpam-6358	136	10	:	:	PUNCT
ejpam-6358	137	1	ρ	ρ	NOUN
ejpam-6358	137	2	<	<	NOUN
ejpam-6358	137	3	i>(s	i>(s	NOUN
ejpam-6358	137	4	)	)	PUNCT
ejpam-6358	137	5	=	=	SYM
ejpam-6358	138	1	ρ	ρ	PROPN
ejpam-6358	138	2	<	<	NOUN
ejpam-6358	138	3	a>(s	a>(s	X
ejpam-6358	138	4	)	)	PUNCT
ejpam-6358	138	5	∩	∩	NOUN
ejpam-6358	138	6	ρ	ρ	PROPN
ejpam-6358	138	7	<	<	X
ejpam-6358	138	8	b>(s	b>(s	PRON
ejpam-6358	138	9	)	)	PUNCT
ejpam-6358	138	10	.	.	PUNCT
ejpam-6358	139	1	(	(	PUNCT
ejpam-6358	139	2	viii	viii	NOUN
ejpam-6358	139	3	)	)	PUNCT
ejpam-6358	139	4	minimal	minimal	PROPN
ejpam-6358	139	5	-	-	PUNCT
ejpam-6358	139	6	union	union	NOUN
ejpam-6358	139	7	ρ	ρ	NOUN
ejpam-6358	139	8	-	-	PUNCT
ejpam-6358	139	9	neighborhood	neighborhood	NOUN
ejpam-6358	139	10	:	:	PUNCT
ejpam-6358	139	11	ρ	ρ	NOUN
ejpam-6358	139	12	<	<	NOUN
ejpam-6358	139	13	u>(s	u>(s	NOUN
ejpam-6358	139	14	)	)	PUNCT
ejpam-6358	139	15	=	=	PUNCT
ejpam-6358	140	1	ρ	ρ	PROPN
ejpam-6358	140	2	<	<	X
ejpam-6358	140	3	a>(s	a>(s	X
ejpam-6358	140	4	)	)	PUNCT
ejpam-6358	140	5	∪	∪	X
ejpam-6358	140	6	ρ	ρ	PROPN
ejpam-6358	140	7	<	<	X
ejpam-6358	140	8	b>(s	b>(s	PRON
ejpam-6358	140	9	)	)	PUNCT
ejpam-6358	140	10	.	.	PUNCT
ejpam-6358	141	1	definition	definition	NOUN
ejpam-6358	141	2	5	5	NUM
ejpam-6358	141	3	.	.	PUNCT
ejpam-6358	142	1	[	[	X
ejpam-6358	142	2	17	17	NUM
ejpam-6358	142	3	,	,	PUNCT
ejpam-6358	142	4	18	18	NUM
ejpam-6358	142	5	,	,	PUNCT
ejpam-6358	142	6	20	20	NUM
ejpam-6358	142	7	]	]	PUNCT
ejpam-6358	142	8	let	let	VERB
ejpam-6358	142	9	f	f	PROPN
ejpam-6358	142	10	⊆	⊆	NUM
ejpam-6358	142	11	u	u	NOUN
ejpam-6358	142	12	be	be	VERB
ejpam-6358	142	13	a	a	DET
ejpam-6358	142	14	nonempty	nonempty	NOUN
ejpam-6358	142	15	subset	subset	NOUN
ejpam-6358	142	16	,	,	PUNCT
ejpam-6358	142	17	and	and	CCONJ
ejpam-6358	142	18	let	let	VERB
ejpam-6358	142	19	j	j	PROPN
ejpam-6358	142	20	∈	∈	PROPN
ejpam-6358	142	21	ω	ω	PROPN
ejpam-6358	142	22	.	.	PUNCT
ejpam-6358	143	1	the	the	DET
ejpam-6358	143	2	approximation	approximation	NOUN
ejpam-6358	143	3	operators	operator	NOUN
ejpam-6358	143	4	based	base	VERB
ejpam-6358	143	5	on	on	ADP
ejpam-6358	143	6	ρj	ρj	NOUN
ejpam-6358	143	7	-	-	NOUN
ejpam-6358	143	8	neighborhoods	neighborhood	NOUN
ejpam-6358	143	9	are	be	AUX
ejpam-6358	143	10	defined	define	VERB
ejpam-6358	143	11	as	as	SCONJ
ejpam-6358	143	12	follows	follow	VERB
ejpam-6358	143	13	:	:	PUNCT
ejpam-6358	143	14	�	�	PROPN
ejpam-6358	143	15	lower	low	ADJ
ejpam-6358	143	16	approximation	approximation	NOUN
ejpam-6358	143	17	:	:	PUNCT
ejpam-6358	144	1	r	r	NOUN
ejpam-6358	144	2	ρj	ρj	NOUN
ejpam-6358	144	3	⋆	⋆	X
ejpam-6358	144	4	(	(	PUNCT
ejpam-6358	144	5	f	f	NOUN
ejpam-6358	144	6	)	)	PUNCT
ejpam-6358	144	7	=	=	PRON
ejpam-6358	144	8	{	{	PUNCT
ejpam-6358	144	9	s	s	NOUN
ejpam-6358	144	10	∈	∈	PROPN
ejpam-6358	144	11	u	u	NOUN
ejpam-6358	144	12	:	:	PUNCT
ejpam-6358	144	13	ρj(s	ρj(s	NUM
ejpam-6358	144	14	)	)	PUNCT
ejpam-6358	144	15	⊆	⊆	NUM
ejpam-6358	144	16	f	f	X
ejpam-6358	144	17	}	}	PUNCT
ejpam-6358	144	18	.	.	PUNCT
ejpam-6358	145	1	�	�	PROPN
ejpam-6358	145	2	upper	upper	ADJ
ejpam-6358	145	3	approximation	approximation	NOUN
ejpam-6358	145	4	:	:	PUNCT
ejpam-6358	145	5	r⋆ρj	r⋆ρj	NOUN
ejpam-6358	145	6	(	(	PUNCT
ejpam-6358	145	7	f	f	X
ejpam-6358	145	8	)	)	PUNCT
ejpam-6358	145	9	=	=	PRON
ejpam-6358	145	10	{	{	PUNCT
ejpam-6358	145	11	s	s	NOUN
ejpam-6358	145	12	∈	∈	PROPN
ejpam-6358	145	13	u	u	NOUN
ejpam-6358	145	14	:	:	PUNCT
ejpam-6358	145	15	ρj(s	ρj(s	NUM
ejpam-6358	145	16	)	)	PUNCT
ejpam-6358	145	17	∩	∩	NOUN
ejpam-6358	145	18	f	f	PROPN
ejpam-6358	145	19	̸=	̸=	PROPN
ejpam-6358	145	20	∅	∅	NOUN
ejpam-6358	145	21	}	}	PUNCT
ejpam-6358	145	22	.	.	PUNCT
ejpam-6358	146	1	�	�	PROPN
ejpam-6358	146	2	boundary	boundary	PROPN
ejpam-6358	146	3	region	region	NOUN
ejpam-6358	146	4	:	:	PUNCT
ejpam-6358	147	1	bnd	bnd	NOUN
ejpam-6358	147	2	⋆ρj	⋆ρj	NOUN
ejpam-6358	148	1	r	r	NOUN
ejpam-6358	148	2	(	(	PUNCT
ejpam-6358	148	3	f	f	NOUN
ejpam-6358	148	4	)	)	PUNCT
ejpam-6358	149	1	=	=	PUNCT
ejpam-6358	149	2	r⋆ρj	r⋆ρj	NOUN
ejpam-6358	149	3	(	(	PUNCT
ejpam-6358	149	4	f	f	PROPN
ejpam-6358	149	5	)	)	PUNCT
ejpam-6358	149	6	\rρj	\rρj	ADJ
ejpam-6358	149	7	⋆	⋆	X
ejpam-6358	149	8	(	(	PUNCT
ejpam-6358	149	9	f	f	PROPN
ejpam-6358	149	10	)	)	PUNCT
ejpam-6358	149	11	.	.	PUNCT
ejpam-6358	150	1	�	�	PROPN
ejpam-6358	150	2	accuracy	accuracy	NOUN
ejpam-6358	150	3	measure	measure	NOUN
ejpam-6358	150	4	:	:	PUNCT
ejpam-6358	150	5	acc	acc	PROPN
ejpam-6358	151	1	⋆ρj	⋆ρj	INTJ
ejpam-6358	151	2	r	r	NOUN
ejpam-6358	151	3	(	(	PUNCT
ejpam-6358	151	4	f	f	NOUN
ejpam-6358	151	5	)	)	PUNCT
ejpam-6358	151	6	=	=	SYM
ejpam-6358	152	1	|r	|r	PROPN
ejpam-6358	153	1	ρj	ρj	INTJ
ejpam-6358	153	2	⋆	⋆	X
ejpam-6358	153	3	(	(	PUNCT
ejpam-6358	153	4	f	f	NOUN
ejpam-6358	153	5	)	)	PUNCT
ejpam-6358	153	6	|	|	ADV
ejpam-6358	153	7	|r⋆ρj	|r⋆ρj	NOUN
ejpam-6358	153	8	(	(	PUNCT
ejpam-6358	153	9	f	f	X
ejpam-6358	153	10	)	)	PUNCT
ejpam-6358	153	11	|	|	ADV
ejpam-6358	153	12	,	,	PUNCT
ejpam-6358	153	13	where	where	SCONJ
ejpam-6358	153	14	|	|	ADV
ejpam-6358	153	15	r⋆ρj	r⋆ρj	NOUN
ejpam-6358	153	16	(	(	PUNCT
ejpam-6358	153	17	f	f	PROPN
ejpam-6358	153	18	)	)	PUNCT
ejpam-6358	153	19	|̸=	|̸=	NOUN
ejpam-6358	153	20	0	0	NUM
ejpam-6358	153	21	.	.	PUNCT
ejpam-6358	154	1	the	the	DET
ejpam-6358	154	2	following	follow	VERB
ejpam-6358	154	3	definition	definition	NOUN
ejpam-6358	154	4	introduces	introduce	VERB
ejpam-6358	154	5	a	a	DET
ejpam-6358	154	6	significant	significant	ADJ
ejpam-6358	154	7	extension	extension	NOUN
ejpam-6358	154	8	of	of	ADP
ejpam-6358	154	9	the	the	DET
ejpam-6358	154	10	j	j	PROPN
ejpam-6358	154	11	-	-	PUNCT
ejpam-6358	154	12	ns	ns	ADJ
ejpam-6358	154	13	concept	concept	NOUN
ejpam-6358	154	14	,	,	PUNCT
ejpam-6358	154	15	as	as	SCONJ
ejpam-6358	154	16	proposed	propose	VERB
ejpam-6358	154	17	in	in	ADP
ejpam-6358	154	18	[	[	X
ejpam-6358	154	19	12	12	NUM
ejpam-6358	154	20	]	]	PUNCT
ejpam-6358	154	21	.	.	PUNCT
ejpam-6358	155	1	it	it	PRON
ejpam-6358	155	2	generalizes	generalize	VERB
ejpam-6358	155	3	the	the	DET
ejpam-6358	155	4	notion	notion	NOUN
ejpam-6358	155	5	of	of	ADP
ejpam-6358	155	6	ωj	ωj	NOUN
ejpam-6358	155	7	-	-	PUNCT
ejpam-6358	155	8	neighborhoods	neighborhood	NOUN
ejpam-6358	155	9	into	into	ADP
ejpam-6358	155	10	a	a	DET
ejpam-6358	155	11	broader	broad	ADJ
ejpam-6358	155	12	framework	framework	NOUN
ejpam-6358	155	13	known	know	VERB
ejpam-6358	155	14	as	as	ADP
ejpam-6358	155	15	ij	ij	NOUN
ejpam-6358	155	16	-	-	NOUN
ejpam-6358	155	17	neighborhoods	neighborhood	NOUN
ejpam-6358	155	18	,	,	PUNCT
ejpam-6358	155	19	for	for	ADP
ejpam-6358	155	20	each	each	DET
ejpam-6358	155	21	j	j	PROPN
ejpam-6358	155	22	∈	∈	PROPN
ejpam-6358	155	23	ω	ω	PROPN
ejpam-6358	155	24	.	.	PUNCT
ejpam-6358	156	1	these	these	DET
ejpam-6358	156	2	generalized	generalize	VERB
ejpam-6358	156	3	neighborhoods	neighborhood	NOUN
ejpam-6358	156	4	are	be	AUX
ejpam-6358	156	5	employed	employ	VERB
ejpam-6358	156	6	to	to	PART
ejpam-6358	156	7	define	define	VERB
ejpam-6358	156	8	more	more	ADV
ejpam-6358	156	9	flexible	flexible	ADJ
ejpam-6358	156	10	rough	rough	ADJ
ejpam-6358	156	11	set	set	NOUN
ejpam-6358	156	12	models	model	NOUN
ejpam-6358	156	13	that	that	PRON
ejpam-6358	156	14	extend	extend	VERB
ejpam-6358	156	15	beyond	beyond	ADP
ejpam-6358	156	16	pawlak	pawlak	ADJ
ejpam-6358	156	17	’s	’s	PART
ejpam-6358	156	18	classical	classical	ADJ
ejpam-6358	156	19	framework	framework	NOUN
ejpam-6358	156	20	and	and	CCONJ
ejpam-6358	156	21	support	support	VERB
ejpam-6358	156	22	diverse	diverse	ADJ
ejpam-6358	156	23	applications	application	NOUN
ejpam-6358	156	24	,	,	PUNCT
ejpam-6358	156	25	such	such	ADJ
ejpam-6358	156	26	as	as	ADP
ejpam-6358	156	27	those	those	PRON
ejpam-6358	156	28	discussed	discuss	VERB
ejpam-6358	156	29	in	in	ADP
ejpam-6358	156	30	[	[	X
ejpam-6358	156	31	40	40	NUM
ejpam-6358	156	32	]	]	PUNCT
ejpam-6358	156	33	.	.	PUNCT
ejpam-6358	157	1	definition	definition	NOUN
ejpam-6358	157	2	6	6	NUM
ejpam-6358	157	3	.	.	PUNCT
ejpam-6358	158	1	[	[	X
ejpam-6358	158	2	12	12	NUM
ejpam-6358	158	3	]	]	PUNCT
ejpam-6358	158	4	the	the	DET
ejpam-6358	158	5	subsequent	subsequent	ADJ
ejpam-6358	158	6	ij	ij	NOUN
ejpam-6358	158	7	-	-	NOUN
ejpam-6358	158	8	neighborhoods	neighborhood	NOUN
ejpam-6358	158	9	of	of	ADP
ejpam-6358	158	10	an	an	DET
ejpam-6358	158	11	element	element	NOUN
ejpam-6358	158	12	s	s	PART
ejpam-6358	158	13	∈	∈	PROPN
ejpam-6358	158	14	u	u	NOUN
ejpam-6358	158	15	,	,	PUNCT
ejpam-6358	158	16	derived	derive	VERB
ejpam-6358	158	17	from	from	ADP
ejpam-6358	158	18	a	a	DET
ejpam-6358	158	19	relation	relation	NOUN
ejpam-6358	158	20	r	r	NOUN
ejpam-6358	158	21	,	,	PUNCT
ejpam-6358	158	22	are	be	AUX
ejpam-6358	158	23	specified	specify	VERB
ejpam-6358	158	24	as	as	SCONJ
ejpam-6358	158	25	follows	follow	VERB
ejpam-6358	158	26	:	:	PUNCT
ejpam-6358	158	27	(	(	PUNCT
ejpam-6358	158	28	i	i	NOUN
ejpam-6358	158	29	)	)	PUNCT
ejpam-6358	158	30	after	after	ADP
ejpam-6358	158	31	i	i	NOUN
ejpam-6358	158	32	-	-	PUNCT
ejpam-6358	158	33	neighborhood	neighborhood	NOUN
ejpam-6358	158	34	:	:	PUNCT
ejpam-6358	158	35	ia(s	ia(s	NUM
ejpam-6358	158	36	)	)	PUNCT
ejpam-6358	158	37	=	=	SYM
ejpam-6358	158	38	{	{	PUNCT
ejpam-6358	158	39	t	t	PROPN
ejpam-6358	158	40	∈	∈	PROPN
ejpam-6358	158	41	u	u	NOUN
ejpam-6358	158	42	:	:	PUNCT
ejpam-6358	158	43	ωa(t	ωa(t	NUM
ejpam-6358	158	44	)	)	PUNCT
ejpam-6358	158	45	∩	∩	NOUN
ejpam-6358	158	46	ωa(s	ωa(	NOUN
ejpam-6358	158	47	)	)	PUNCT
ejpam-6358	158	48	̸=	̸=	PROPN
ejpam-6358	158	49	∅	∅	NOUN
ejpam-6358	158	50	}	}	PUNCT
ejpam-6358	158	51	.	.	PUNCT
ejpam-6358	159	1	(	(	PUNCT
ejpam-6358	159	2	ii	ii	NOUN
ejpam-6358	159	3	)	)	PUNCT
ejpam-6358	159	4	before	before	ADP
ejpam-6358	159	5	i	i	NOUN
ejpam-6358	159	6	-	-	PUNCT
ejpam-6358	159	7	neighborhood	neighborhood	NOUN
ejpam-6358	159	8	:	:	PUNCT
ejpam-6358	159	9	ib(s	ib(	NOUN
ejpam-6358	159	10	)	)	PUNCT
ejpam-6358	160	1	=	=	PRON
ejpam-6358	160	2	{	{	PUNCT
ejpam-6358	160	3	t	t	PROPN
ejpam-6358	160	4	∈	∈	PROPN
ejpam-6358	160	5	u	u	NOUN
ejpam-6358	160	6	:	:	PUNCT
ejpam-6358	160	7	ωb(t	ωb(t	NUM
ejpam-6358	160	8	)	)	PUNCT
ejpam-6358	160	9	∩	∩	NOUN
ejpam-6358	160	10	ωb(s	ωb(	NOUN
ejpam-6358	160	11	)	)	PUNCT
ejpam-6358	160	12	̸=	̸=	NOUN
ejpam-6358	160	13	∅	∅	NOUN
ejpam-6358	160	14	}	}	PUNCT
ejpam-6358	160	15	.	.	PUNCT
ejpam-6358	161	1	r.	r.	PROPN
ejpam-6358	161	2	a.	a.	PROPN
ejpam-6358	161	3	hosny	hosny	PROPN
ejpam-6358	161	4	et	et	PROPN
ejpam-6358	161	5	al	al	PROPN
ejpam-6358	161	6	.	.	PUNCT
ejpam-6358	161	7	/	/	SYM
ejpam-6358	161	8	eur	eur	PROPN
ejpam-6358	161	9	.	.	PUNCT
ejpam-6358	162	1	j.	j.	PROPN
ejpam-6358	162	2	pure	pure	PROPN
ejpam-6358	162	3	appl	appl	PROPN
ejpam-6358	162	4	.	.	PROPN
ejpam-6358	162	5	math	math	PROPN
ejpam-6358	162	6	,	,	PUNCT
ejpam-6358	162	7	18	18	NUM
ejpam-6358	162	8	(	(	PUNCT
ejpam-6358	162	9	4	4	NUM
ejpam-6358	162	10	)	)	PUNCT
ejpam-6358	162	11	(	(	PUNCT
ejpam-6358	162	12	2025	2025	NUM
ejpam-6358	162	13	)	)	PUNCT
ejpam-6358	162	14	,	,	PUNCT
ejpam-6358	162	15	6358	6358	NUM
ejpam-6358	162	16	7	7	NUM
ejpam-6358	162	17	of	of	ADP
ejpam-6358	162	18	24	24	NUM
ejpam-6358	162	19	(	(	PUNCT
ejpam-6358	162	20	iii	iii	NOUN
ejpam-6358	162	21	)	)	PUNCT
ejpam-6358	162	22	intersection	intersection	NOUN
ejpam-6358	162	23	i	i	NOUN
ejpam-6358	162	24	-	-	PUNCT
ejpam-6358	162	25	neighborhood	neighborhood	NOUN
ejpam-6358	162	26	:	:	PUNCT
ejpam-6358	162	27	ii(s	ii(s	NUM
ejpam-6358	162	28	)	)	PUNCT
ejpam-6358	162	29	=	=	SYM
ejpam-6358	162	30	ia(s	ia(s	PRON
ejpam-6358	162	31	)	)	PUNCT
ejpam-6358	162	32	∩	∩	NOUN
ejpam-6358	162	33	ib(s	ib(	NOUN
ejpam-6358	162	34	)	)	PUNCT
ejpam-6358	162	35	.	.	PUNCT
ejpam-6358	163	1	(	(	PUNCT
ejpam-6358	163	2	iv	iv	X
ejpam-6358	163	3	)	)	PUNCT
ejpam-6358	163	4	union	union	NOUN
ejpam-6358	163	5	i	i	PROPN
ejpam-6358	163	6	-	-	PUNCT
ejpam-6358	163	7	neighborhood	neighborhood	NOUN
ejpam-6358	163	8	:	:	PUNCT
ejpam-6358	163	9	iu(s	iu(s	NUM
ejpam-6358	163	10	)	)	PUNCT
ejpam-6358	163	11	=	=	SYM
ejpam-6358	163	12	ia(s	ia(s	PRON
ejpam-6358	163	13	)	)	PUNCT
ejpam-6358	163	14	∪	∪	ADP
ejpam-6358	163	15	ib(s	ib(	NOUN
ejpam-6358	163	16	)	)	PUNCT
ejpam-6358	163	17	.	.	PUNCT
ejpam-6358	164	1	(	(	PUNCT
ejpam-6358	164	2	v	v	NOUN
ejpam-6358	164	3	)	)	PUNCT
ejpam-6358	164	4	minimal	minimal	ADJ
ejpam-6358	164	5	-	-	PUNCT
ejpam-6358	164	6	after	after	ADP
ejpam-6358	164	7	i	i	NOUN
ejpam-6358	164	8	-	-	PUNCT
ejpam-6358	164	9	neighborhood	neighborhood	NOUN
ejpam-6358	164	10	:	:	PUNCT
ejpam-6358	165	1	i	i	PRON
ejpam-6358	165	2	<	<	X
ejpam-6358	165	3	a>(s	a>(s	X
ejpam-6358	165	4	)	)	PUNCT
ejpam-6358	165	5	=	=	PRON
ejpam-6358	165	6	{	{	PUNCT
ejpam-6358	165	7	t	t	NOUN
ejpam-6358	165	8	∈	∈	PROPN
ejpam-6358	165	9	u	u	NOUN
ejpam-6358	165	10	:	:	PUNCT
ejpam-6358	165	11	ω	ω	X
ejpam-6358	165	12	<	<	X
ejpam-6358	165	13	a>(t	a>(t	NOUN
ejpam-6358	165	14	)	)	PUNCT
ejpam-6358	165	15	∩	∩	NOUN
ejpam-6358	165	16	ω	ω	PROPN
ejpam-6358	165	17	<	<	X
ejpam-6358	165	18	a>(s	a>(s	X
ejpam-6358	165	19	)	)	PUNCT
ejpam-6358	165	20	̸=	̸=	PROPN
ejpam-6358	165	21	∅	∅	NOUN
ejpam-6358	165	22	}	}	PUNCT
ejpam-6358	165	23	.	.	PUNCT
ejpam-6358	166	1	(	(	PUNCT
ejpam-6358	166	2	vi	vi	NOUN
ejpam-6358	166	3	)	)	PUNCT
ejpam-6358	166	4	minimal	minimal	ADJ
ejpam-6358	166	5	-	-	PUNCT
ejpam-6358	166	6	before	before	ADP
ejpam-6358	166	7	i	i	NOUN
ejpam-6358	166	8	-	-	PUNCT
ejpam-6358	166	9	neighborhood	neighborhood	NOUN
ejpam-6358	166	10	:	:	PUNCT
ejpam-6358	167	1	i	i	PRON
ejpam-6358	167	2	<	<	X
ejpam-6358	167	3	b>(s	b>(s	PRON
ejpam-6358	167	4	)	)	PUNCT
ejpam-6358	168	1	=	=	PRON
ejpam-6358	168	2	{	{	PUNCT
ejpam-6358	168	3	t	t	PROPN
ejpam-6358	168	4	∈	∈	PROPN
ejpam-6358	168	5	u	u	NOUN
ejpam-6358	168	6	:	:	PUNCT
ejpam-6358	168	7	ω	ω	NUM
ejpam-6358	168	8	<	<	NOUN
ejpam-6358	168	9	b>(t	b>(t	NOUN
ejpam-6358	168	10	)	)	PUNCT
ejpam-6358	168	11	∩	∩	NOUN
ejpam-6358	168	12	ω	ω	NOUN
ejpam-6358	168	13	<	<	X
ejpam-6358	168	14	b>(s	b>(s	PRON
ejpam-6358	168	15	)	)	PUNCT
ejpam-6358	168	16	̸=	̸=	PROPN
ejpam-6358	168	17	∅	∅	NOUN
ejpam-6358	168	18	}	}	PUNCT
ejpam-6358	168	19	.	.	PUNCT
ejpam-6358	169	1	(	(	PUNCT
ejpam-6358	169	2	vii	vii	PROPN
ejpam-6358	169	3	)	)	PUNCT
ejpam-6358	169	4	minimal	minimal	ADJ
ejpam-6358	169	5	-	-	PUNCT
ejpam-6358	169	6	intersection	intersection	NOUN
ejpam-6358	169	7	i	i	NOUN
ejpam-6358	169	8	-	-	PUNCT
ejpam-6358	169	9	neighborhood	neighborhood	NOUN
ejpam-6358	169	10	:	:	PUNCT
ejpam-6358	170	1	i	i	PRON
ejpam-6358	170	2	<	<	X
ejpam-6358	170	3	i>(s	i>(s	NOUN
ejpam-6358	170	4	)	)	PUNCT
ejpam-6358	171	1	=	=	PUNCT
ejpam-6358	172	1	i	i	PRON
ejpam-6358	172	2	<	<	X
ejpam-6358	172	3	a>(s	a>(s	X
ejpam-6358	172	4	)	)	PUNCT
ejpam-6358	172	5	∩	∩	NOUN
ejpam-6358	172	6	i	i	PRON
ejpam-6358	172	7	<	<	X
ejpam-6358	172	8	b>(s	b>(s	PRON
ejpam-6358	172	9	)	)	PUNCT
ejpam-6358	172	10	.	.	PUNCT
ejpam-6358	173	1	(	(	PUNCT
ejpam-6358	173	2	viii	viii	NOUN
ejpam-6358	173	3	)	)	PUNCT
ejpam-6358	173	4	minimal	minimal	PROPN
ejpam-6358	173	5	-	-	PUNCT
ejpam-6358	173	6	union	union	NOUN
ejpam-6358	173	7	i	i	PROPN
ejpam-6358	173	8	-	-	PUNCT
ejpam-6358	173	9	neighborhood	neighborhood	NOUN
ejpam-6358	173	10	:	:	PUNCT
ejpam-6358	174	1	i	i	PRON
ejpam-6358	174	2	<	<	X
ejpam-6358	174	3	u>(s	u>(s	X
ejpam-6358	174	4	)	)	PUNCT
ejpam-6358	174	5	=	=	PUNCT
ejpam-6358	175	1	i	i	PRON
ejpam-6358	175	2	<	<	X
ejpam-6358	175	3	a>(s	a>(s	X
ejpam-6358	175	4	)	)	PUNCT
ejpam-6358	175	5	∪	∪	ADP
ejpam-6358	175	6	i	i	PRON
ejpam-6358	175	7	<	<	X
ejpam-6358	175	8	b>(s	b>(s	PRON
ejpam-6358	175	9	)	)	PUNCT
ejpam-6358	175	10	.	.	PUNCT
ejpam-6358	176	1	in	in	ADP
ejpam-6358	176	2	[	[	X
ejpam-6358	176	3	12	12	NUM
ejpam-6358	176	4	]	]	PUNCT
ejpam-6358	176	5	,	,	PUNCT
ejpam-6358	176	6	ij	ij	NOUN
ejpam-6358	176	7	-	-	NOUN
ejpam-6358	176	8	neighborhoods	neighborhood	NOUN
ejpam-6358	176	9	were	be	AUX
ejpam-6358	176	10	examined	examine	VERB
ejpam-6358	176	11	under	under	ADP
ejpam-6358	176	12	the	the	DET
ejpam-6358	176	13	designation	designation	NOUN
ejpam-6358	176	14	“	"	PUNCT
ejpam-6358	176	15	ej	ej	PROPN
ejpam-6358	176	16	-	-	PUNCT
ejpam-6358	176	17	neighborhoods	neighborhood	NOUN
ejpam-6358	176	18	”	"	PUNCT
ejpam-6358	176	19	,	,	PUNCT
ejpam-6358	177	1	j	j	PROPN
ejpam-6358	177	2	∈	∈	PROPN
ejpam-6358	177	3	ω	ω	PROPN
ejpam-6358	177	4	.	.	PUNCT
ejpam-6358	178	1	definition	definition	NOUN
ejpam-6358	178	2	7	7	NUM
ejpam-6358	178	3	.	.	PUNCT
ejpam-6358	179	1	[	[	X
ejpam-6358	179	2	12	12	NUM
ejpam-6358	179	3	]	]	PUNCT
ejpam-6358	179	4	for	for	ADP
ejpam-6358	179	5	ij	ij	NOUN
ejpam-6358	179	6	-	-	NOUN
ejpam-6358	179	7	neighborhoods	neighborhood	NOUN
ejpam-6358	179	8	and	and	CCONJ
ejpam-6358	179	9	for	for	ADP
ejpam-6358	179	10	each	each	DET
ejpam-6358	179	11	j	j	PROPN
ejpam-6358	179	12	∈	∈	PROPN
ejpam-6358	179	13	ω	ω	PROPN
ejpam-6358	179	14	,	,	PUNCT
ejpam-6358	179	15	the	the	DET
ejpam-6358	179	16	approximation	approximation	NOUN
ejpam-6358	179	17	operators	operator	NOUN
ejpam-6358	179	18	(	(	PUNCT
ejpam-6358	179	19	both	both	CCONJ
ejpam-6358	179	20	lower	low	ADJ
ejpam-6358	179	21	and	and	CCONJ
ejpam-6358	179	22	upper	upper	ADJ
ejpam-6358	179	23	)	)	PUNCT
ejpam-6358	179	24	,	,	PUNCT
ejpam-6358	179	25	boundary	boundary	ADJ
ejpam-6358	179	26	region	region	NOUN
ejpam-6358	179	27	,	,	PUNCT
ejpam-6358	179	28	and	and	CCONJ
ejpam-6358	179	29	accuracy	accuracy	NOUN
ejpam-6358	179	30	measure	measure	NOUN
ejpam-6358	179	31	for	for	ADP
ejpam-6358	179	32	a	a	DET
ejpam-6358	179	33	nonempty	nonempty	NOUN
ejpam-6358	179	34	subset	subset	VERB
ejpam-6358	179	35	f	f	PROPN
ejpam-6358	179	36	of	of	ADP
ejpam-6358	179	37	u	u	PROPN
ejpam-6358	179	38	are	be	AUX
ejpam-6358	179	39	defined	define	VERB
ejpam-6358	179	40	as	as	SCONJ
ejpam-6358	179	41	follows	follow	VERB
ejpam-6358	179	42	:	:	PUNCT
ejpam-6358	179	43	�	�	PROPN
ejpam-6358	179	44	lower	low	ADJ
ejpam-6358	179	45	approximation	approximation	NOUN
ejpam-6358	179	46	:	:	PUNCT
ejpam-6358	180	1	r	r	NOUN
ejpam-6358	180	2	ij	ij	X
ejpam-6358	180	3	⋆	⋆	X
ejpam-6358	180	4	(	(	PUNCT
ejpam-6358	180	5	f	f	NOUN
ejpam-6358	180	6	)	)	PUNCT
ejpam-6358	180	7	=	=	PRON
ejpam-6358	180	8	{	{	PUNCT
ejpam-6358	180	9	s	s	NOUN
ejpam-6358	180	10	∈	∈	PROPN
ejpam-6358	180	11	u	u	NOUN
ejpam-6358	180	12	:	:	PUNCT
ejpam-6358	180	13	ij(s	ij(s	NUM
ejpam-6358	180	14	)	)	PUNCT
ejpam-6358	180	15	⊆	⊆	NUM
ejpam-6358	180	16	f	f	X
ejpam-6358	180	17	}	}	PUNCT
ejpam-6358	180	18	.	.	PUNCT
ejpam-6358	181	1	�	�	PROPN
ejpam-6358	181	2	upper	upper	ADJ
ejpam-6358	181	3	approximation	approximation	NOUN
ejpam-6358	181	4	:	:	PUNCT
ejpam-6358	181	5	r⋆ij	r⋆ij	PROPN
ejpam-6358	181	6	(	(	PUNCT
ejpam-6358	181	7	f	f	X
ejpam-6358	181	8	)	)	PUNCT
ejpam-6358	181	9	=	=	PRON
ejpam-6358	181	10	{	{	PUNCT
ejpam-6358	181	11	s	s	NOUN
ejpam-6358	181	12	∈	∈	PROPN
ejpam-6358	181	13	u	u	NOUN
ejpam-6358	181	14	:	:	PUNCT
ejpam-6358	181	15	ij(s	ij(s	NOUN
ejpam-6358	181	16	)	)	PUNCT
ejpam-6358	181	17	∩	∩	NOUN
ejpam-6358	181	18	f	f	PROPN
ejpam-6358	181	19	̸=	̸=	PROPN
ejpam-6358	181	20	∅	∅	NOUN
ejpam-6358	181	21	}	}	PUNCT
ejpam-6358	181	22	.	.	PUNCT
ejpam-6358	182	1	�	�	PROPN
ejpam-6358	182	2	boundary	boundary	PROPN
ejpam-6358	182	3	region	region	NOUN
ejpam-6358	182	4	:	:	PUNCT
ejpam-6358	183	1	bnd	bnd	NOUN
ejpam-6358	183	2	⋆ij	⋆ij	PROPN
ejpam-6358	183	3	r	r	NOUN
ejpam-6358	183	4	(	(	PUNCT
ejpam-6358	183	5	f	f	PROPN
ejpam-6358	183	6	)	)	PUNCT
ejpam-6358	184	1	=	=	SYM
ejpam-6358	184	2	r⋆ij	r⋆ij	PROPN
ejpam-6358	184	3	(	(	PUNCT
ejpam-6358	184	4	f	f	PROPN
ejpam-6358	184	5	)	)	PUNCT
ejpam-6358	184	6	\rij	\rij	PROPN
ejpam-6358	184	7	⋆	⋆	X
ejpam-6358	184	8	(	(	PUNCT
ejpam-6358	184	9	f	f	PROPN
ejpam-6358	184	10	)	)	PUNCT
ejpam-6358	184	11	.	.	PUNCT
ejpam-6358	185	1	�	�	PROPN
ejpam-6358	185	2	accuracy	accuracy	NOUN
ejpam-6358	185	3	measure	measure	NOUN
ejpam-6358	185	4	:	:	PUNCT
ejpam-6358	185	5	acc	acc	PROPN
ejpam-6358	185	6	⋆ij	⋆ij	PROPN
ejpam-6358	186	1	r	r	PROPN
ejpam-6358	186	2	(	(	PUNCT
ejpam-6358	186	3	f	f	PROPN
ejpam-6358	186	4	)	)	PUNCT
ejpam-6358	186	5	=	=	SYM
ejpam-6358	187	1	|r	|r	X
ejpam-6358	188	1	ij	ij	INTJ
ejpam-6358	188	2	⋆	⋆	X
ejpam-6358	188	3	(	(	PUNCT
ejpam-6358	188	4	f	f	NOUN
ejpam-6358	188	5	)	)	PUNCT
ejpam-6358	188	6	∩f	∩f	PROPN
ejpam-6358	188	7	|	|	ADV
ejpam-6358	188	8	|r⋆ij	|r⋆ij	INTJ
ejpam-6358	189	1	(	(	PUNCT
ejpam-6358	189	2	f	f	PROPN
ejpam-6358	189	3	)	)	PUNCT
ejpam-6358	189	4	∪f	∪f	PROPN
ejpam-6358	190	1	|	|	ADV
ejpam-6358	190	2	,	,	PUNCT
ejpam-6358	190	3	where	where	SCONJ
ejpam-6358	190	4	|	|	ADV
ejpam-6358	190	5	r⋆ij	r⋆ij	NOUN
ejpam-6358	190	6	(	(	PUNCT
ejpam-6358	190	7	f	f	NOUN
ejpam-6358	190	8	)	)	PUNCT
ejpam-6358	190	9	∪	∪	ADP
ejpam-6358	190	10	f	f	PROPN
ejpam-6358	190	11	|̸=	|̸=	NUM
ejpam-6358	190	12	0	0	NUM
ejpam-6358	190	13	.	.	PUNCT
ejpam-6358	191	1	definition	definition	NOUN
ejpam-6358	191	2	8	8	NUM
ejpam-6358	191	3	.	.	PUNCT
ejpam-6358	192	1	[	[	X
ejpam-6358	192	2	41	41	NUM
ejpam-6358	192	3	]	]	X
ejpam-6358	192	4	an	an	DET
ejpam-6358	192	5	ideal	ideal	NOUN
ejpam-6358	192	6	k	k	NOUN
ejpam-6358	192	7	on	on	ADP
ejpam-6358	192	8	a	a	DET
ejpam-6358	192	9	nonempty	nonempty	ADV
ejpam-6358	192	10	set	set	VERB
ejpam-6358	192	11	u	u	NOUN
ejpam-6358	192	12	is	be	AUX
ejpam-6358	192	13	a	a	DET
ejpam-6358	192	14	nonempty	nonempty	ADJ
ejpam-6358	192	15	collection	collection	NOUN
ejpam-6358	192	16	of	of	ADP
ejpam-6358	192	17	subsets	subset	NOUN
ejpam-6358	192	18	of	of	ADP
ejpam-6358	192	19	u	u	PRON
ejpam-6358	192	20	that	that	PRON
ejpam-6358	192	21	is	be	AUX
ejpam-6358	192	22	closed	close	VERB
ejpam-6358	192	23	under	under	ADP
ejpam-6358	192	24	finite	finite	ADJ
ejpam-6358	192	25	unions	union	NOUN
ejpam-6358	192	26	and	and	CCONJ
ejpam-6358	192	27	contains	contain	VERB
ejpam-6358	192	28	all	all	DET
ejpam-6358	192	29	subsets	subset	NOUN
ejpam-6358	192	30	of	of	ADP
ejpam-6358	192	31	its	its	PRON
ejpam-6358	192	32	elements	element	NOUN
ejpam-6358	192	33	.	.	PUNCT
ejpam-6358	193	1	by	by	ADP
ejpam-6358	193	2	using	use	VERB
ejpam-6358	193	3	the	the	DET
ejpam-6358	193	4	concept	concept	NOUN
ejpam-6358	193	5	of	of	ADP
ejpam-6358	193	6	ideals	ideal	NOUN
ejpam-6358	193	7	,	,	PUNCT
ejpam-6358	193	8	r.	r.	PROPN
ejpam-6358	193	9	a.	a.	PROPN
ejpam-6358	193	10	hosny	hosny	PROPN
ejpam-6358	193	11	et	et	PROPN
ejpam-6358	193	12	al	al	PROPN
ejpam-6358	193	13	.	.	PUNCT
ejpam-6358	194	1	[	[	X
ejpam-6358	194	2	13	13	NUM
ejpam-6358	194	3	]	]	PUNCT
ejpam-6358	194	4	have	have	AUX
ejpam-6358	194	5	succeeded	succeed	VERB
ejpam-6358	194	6	in	in	ADP
ejpam-6358	194	7	proposing	propose	VERB
ejpam-6358	194	8	a	a	DET
ejpam-6358	194	9	notable	notable	ADJ
ejpam-6358	194	10	application	application	NOUN
ejpam-6358	194	11	of	of	ADP
ejpam-6358	194	12	j	j	PROPN
ejpam-6358	194	13	-	-	PUNCT
ejpam-6358	194	14	ns	ns	PROPN
ejpam-6358	194	15	.	.	PUNCT
ejpam-6358	195	1	in	in	ADP
ejpam-6358	195	2	this	this	DET
ejpam-6358	195	3	context	context	NOUN
ejpam-6358	195	4	,	,	PUNCT
ejpam-6358	195	5	the	the	DET
ejpam-6358	195	6	concept	concept	NOUN
ejpam-6358	195	7	of	of	ADP
ejpam-6358	195	8	”	"	PUNCT
ejpam-6358	195	9	ij	ij	NOUN
ejpam-6358	195	10	-	-	PUNCT
ejpam-6358	195	11	neighborhoods	neighborhood	NOUN
ejpam-6358	195	12	”	"	PUNCT
ejpam-6358	195	13	was	be	AUX
ejpam-6358	195	14	used	use	VERB
ejpam-6358	195	15	alongside	alongside	ADP
ejpam-6358	195	16	the	the	DET
ejpam-6358	195	17	topological	topological	ADJ
ejpam-6358	195	18	structure	structure	NOUN
ejpam-6358	195	19	of	of	ADP
ejpam-6358	195	20	”	"	PUNCT
ejpam-6358	195	21	ideals	ideal	NOUN
ejpam-6358	195	22	”	"	PUNCT
ejpam-6358	195	23	to	to	PART
ejpam-6358	195	24	play	play	VERB
ejpam-6358	195	25	a	a	DET
ejpam-6358	195	26	crucial	crucial	ADJ
ejpam-6358	195	27	role	role	NOUN
ejpam-6358	195	28	in	in	ADP
ejpam-6358	195	29	the	the	DET
ejpam-6358	195	30	identification	identification	NOUN
ejpam-6358	195	31	of	of	ADP
ejpam-6358	195	32	generalized	generalized	ADJ
ejpam-6358	195	33	rough	rough	ADJ
ejpam-6358	195	34	sets	set	NOUN
ejpam-6358	195	35	,	,	PUNCT
ejpam-6358	195	36	which	which	PRON
ejpam-6358	195	37	encompass	encompass	VERB
ejpam-6358	195	38	and	and	CCONJ
ejpam-6358	195	39	extend	extend	VERB
ejpam-6358	195	40	pawlak	pawlak	ADJ
ejpam-6358	195	41	’s	’s	PART
ejpam-6358	195	42	models	model	NOUN
ejpam-6358	195	43	and	and	CCONJ
ejpam-6358	195	44	their	their	PRON
ejpam-6358	195	45	variations	variation	NOUN
ejpam-6358	195	46	.	.	PUNCT
ejpam-6358	196	1	furthermore	furthermore	ADV
ejpam-6358	196	2	,	,	PUNCT
ejpam-6358	196	3	they	they	PRON
ejpam-6358	196	4	find	find	VERB
ejpam-6358	196	5	applications	application	NOUN
ejpam-6358	196	6	in	in	ADP
ejpam-6358	196	7	diverse	diverse	ADJ
ejpam-6358	196	8	settings	setting	NOUN
ejpam-6358	196	9	.	.	PUNCT
ejpam-6358	197	1	definition	definition	NOUN
ejpam-6358	197	2	9	9	NUM
ejpam-6358	197	3	.	.	PUNCT
ejpam-6358	198	1	[	[	X
ejpam-6358	198	2	13	13	NUM
ejpam-6358	198	3	]	]	PUNCT
ejpam-6358	198	4	let	let	VERB
ejpam-6358	198	5	r	r	PRON
ejpam-6358	198	6	be	be	AUX
ejpam-6358	198	7	a	a	DET
ejpam-6358	198	8	binary	binary	ADJ
ejpam-6358	198	9	relation	relation	NOUN
ejpam-6358	198	10	and	and	CCONJ
ejpam-6358	198	11	k	k	X
ejpam-6358	198	12	an	an	DET
ejpam-6358	198	13	ideal	ideal	NOUN
ejpam-6358	198	14	on	on	ADP
ejpam-6358	198	15	a	a	DET
ejpam-6358	198	16	nonempty	nonempty	ADV
ejpam-6358	198	17	set	set	VERB
ejpam-6358	198	18	u	u	NOUN
ejpam-6358	198	19	.	.	PUNCT
ejpam-6358	199	1	the	the	DET
ejpam-6358	199	2	approximation	approximation	NOUN
ejpam-6358	199	3	operators	operator	NOUN
ejpam-6358	199	4	(	(	PUNCT
ejpam-6358	199	5	lower	low	ADJ
ejpam-6358	199	6	and	and	CCONJ
ejpam-6358	199	7	upper	upper	ADJ
ejpam-6358	199	8	)	)	PUNCT
ejpam-6358	199	9	,	,	PUNCT
ejpam-6358	199	10	boundary	boundary	ADJ
ejpam-6358	199	11	region	region	NOUN
ejpam-6358	199	12	,	,	PUNCT
ejpam-6358	199	13	and	and	CCONJ
ejpam-6358	199	14	accuracy	accuracy	NOUN
ejpam-6358	199	15	measure	measure	NOUN
ejpam-6358	199	16	of	of	ADP
ejpam-6358	199	17	a	a	DET
ejpam-6358	199	18	nonempty	nonempty	NOUN
ejpam-6358	199	19	subset	subset	VERB
ejpam-6358	199	20	f	f	PROPN
ejpam-6358	199	21	of	of	ADP
ejpam-6358	199	22	u	u	PROPN
ejpam-6358	199	23	,	,	PUNCT
ejpam-6358	199	24	derived	derive	VERB
ejpam-6358	199	25	from	from	ADP
ejpam-6358	199	26	r	r	NOUN
ejpam-6358	199	27	and	and	CCONJ
ejpam-6358	199	28	k	k	PROPN
ejpam-6358	199	29	using	use	VERB
ejpam-6358	199	30	ij	ij	NOUN
ejpam-6358	199	31	-	-	NOUN
ejpam-6358	199	32	neighborhoods	neighborhood	NOUN
ejpam-6358	199	33	,	,	PUNCT
ejpam-6358	199	34	are	be	AUX
ejpam-6358	199	35	defined	define	VERB
ejpam-6358	199	36	as	as	SCONJ
ejpam-6358	199	37	follows	follow	VERB
ejpam-6358	199	38	:	:	PUNCT
ejpam-6358	200	1	r.	r.	PROPN
ejpam-6358	200	2	a.	a.	PROPN
ejpam-6358	200	3	hosny	hosny	PROPN
ejpam-6358	200	4	et	et	PROPN
ejpam-6358	200	5	al	al	PROPN
ejpam-6358	200	6	.	.	PUNCT
ejpam-6358	200	7	/	/	SYM
ejpam-6358	200	8	eur	eur	PROPN
ejpam-6358	200	9	.	.	PUNCT
ejpam-6358	201	1	j.	j.	PROPN
ejpam-6358	201	2	pure	pure	PROPN
ejpam-6358	201	3	appl	appl	PROPN
ejpam-6358	201	4	.	.	PROPN
ejpam-6358	201	5	math	math	PROPN
ejpam-6358	201	6	,	,	PUNCT
ejpam-6358	201	7	18	18	NUM
ejpam-6358	201	8	(	(	PUNCT
ejpam-6358	201	9	4	4	NUM
ejpam-6358	201	10	)	)	PUNCT
ejpam-6358	201	11	(	(	PUNCT
ejpam-6358	201	12	2025	2025	NUM
ejpam-6358	201	13	)	)	PUNCT
ejpam-6358	201	14	,	,	PUNCT
ejpam-6358	201	15	6358	6358	NUM
ejpam-6358	201	16	8	8	NUM
ejpam-6358	201	17	of	of	ADP
ejpam-6358	201	18	24	24	NUM
ejpam-6358	201	19	�	�	PROPN
ejpam-6358	201	20	lower	low	ADJ
ejpam-6358	201	21	approximation	approximation	NOUN
ejpam-6358	201	22	:	:	PUNCT
ejpam-6358	202	1	l	l	NOUN
ejpam-6358	202	2	ij	ij	X
ejpam-6358	202	3	⋆	⋆	X
ejpam-6358	202	4	(	(	PUNCT
ejpam-6358	202	5	f	f	NOUN
ejpam-6358	202	6	)	)	PUNCT
ejpam-6358	202	7	=	=	PRON
ejpam-6358	202	8	{	{	PUNCT
ejpam-6358	202	9	s	s	NOUN
ejpam-6358	202	10	∈	∈	PROPN
ejpam-6358	202	11	u	u	NOUN
ejpam-6358	202	12	:	:	PUNCT
ejpam-6358	202	13	ij(s	ij(s	X
ejpam-6358	202	14	)	)	PUNCT
ejpam-6358	202	15	\	\	PUNCT
ejpam-6358	203	1	f	f	PROPN
ejpam-6358	203	2	∈	∈	PROPN
ejpam-6358	203	3	k	k	NOUN
ejpam-6358	203	4	}	}	PUNCT
ejpam-6358	203	5	.	.	PUNCT
ejpam-6358	204	1	�	�	PROPN
ejpam-6358	204	2	upper	upper	ADJ
ejpam-6358	204	3	approximation	approximation	NOUN
ejpam-6358	204	4	:	:	PUNCT
ejpam-6358	204	5	u⋆ij	u⋆ij	PROPN
ejpam-6358	204	6	(	(	PUNCT
ejpam-6358	204	7	f	f	X
ejpam-6358	204	8	)	)	PUNCT
ejpam-6358	204	9	=	=	PRON
ejpam-6358	204	10	{	{	PUNCT
ejpam-6358	204	11	s	s	NOUN
ejpam-6358	204	12	∈	∈	PROPN
ejpam-6358	204	13	u	u	NOUN
ejpam-6358	204	14	:	:	PUNCT
ejpam-6358	204	15	ij(s	ij(s	NOUN
ejpam-6358	204	16	)	)	PUNCT
ejpam-6358	204	17	∩	∩	PROPN
ejpam-6358	204	18	f	f	PROPN
ejpam-6358	204	19	̸∈	̸∈	PROPN
ejpam-6358	204	20	k	k	PROPN
ejpam-6358	204	21	}	}	PUNCT
ejpam-6358	204	22	.	.	PUNCT
ejpam-6358	205	1	�	�	PROPN
ejpam-6358	205	2	boundary	boundary	ADJ
ejpam-6358	205	3	region	region	NOUN
ejpam-6358	205	4	:	:	PUNCT
ejpam-6358	205	5	△	△	X
ejpam-6358	205	6	⋆ij	⋆ij	NOUN
ejpam-6358	205	7	r	r	NOUN
ejpam-6358	205	8	(	(	PUNCT
ejpam-6358	205	9	f	f	PROPN
ejpam-6358	205	10	)	)	PUNCT
ejpam-6358	206	1	=	=	SYM
ejpam-6358	206	2	u⋆ij	u⋆ij	INTJ
ejpam-6358	206	3	(	(	PUNCT
ejpam-6358	206	4	f	f	PROPN
ejpam-6358	206	5	)	)	PUNCT
ejpam-6358	206	6	\	\	PROPN
ejpam-6358	207	1	lij	lij	PROPN
ejpam-6358	207	2	⋆	⋆	X
ejpam-6358	207	3	(	(	PUNCT
ejpam-6358	207	4	f	f	PROPN
ejpam-6358	207	5	)	)	PUNCT
ejpam-6358	207	6	.	.	PUNCT
ejpam-6358	208	1	�	�	PROPN
ejpam-6358	208	2	accuracy	accuracy	NOUN
ejpam-6358	208	3	measure	measure	NOUN
ejpam-6358	208	4	:	:	PUNCT
ejpam-6358	209	1	m	m	VERB
ejpam-6358	209	2	⋆ikj	⋆ikj	X
ejpam-6358	209	3	r	r	NOUN
ejpam-6358	209	4	(	(	PUNCT
ejpam-6358	209	5	f	f	PROPN
ejpam-6358	209	6	)	)	PUNCT
ejpam-6358	210	1	=	=	NOUN
ejpam-6358	210	2	|l	|l	PROPN
ejpam-6358	210	3	ij	ij	X
ejpam-6358	210	4	⋆	⋆	X
ejpam-6358	210	5	(	(	PUNCT
ejpam-6358	210	6	f	f	NOUN
ejpam-6358	210	7	)	)	PUNCT
ejpam-6358	210	8	∩f	∩f	PROPN
ejpam-6358	210	9	|	|	ADV
ejpam-6358	210	10	|u⋆ij	|u⋆ij	VERB
ejpam-6358	210	11	(	(	PUNCT
ejpam-6358	210	12	f	f	NOUN
ejpam-6358	210	13	)	)	PUNCT
ejpam-6358	210	14	∪f	∪f	PROPN
ejpam-6358	211	1	|	|	ADV
ejpam-6358	211	2	,	,	PUNCT
ejpam-6358	211	3	where	where	SCONJ
ejpam-6358	211	4	|	|	ADV
ejpam-6358	211	5	u⋆ij	u⋆ij	INTJ
ejpam-6358	211	6	(	(	PUNCT
ejpam-6358	211	7	f	f	PROPN
ejpam-6358	211	8	)	)	PUNCT
ejpam-6358	211	9	∪	∪	ADP
ejpam-6358	211	10	f	f	PROPN
ejpam-6358	211	11	|̸=	|̸=	NUM
ejpam-6358	211	12	0	0	NUM
ejpam-6358	211	13	.	.	PUNCT
ejpam-6358	212	1	definition	definition	NOUN
ejpam-6358	212	2	10	10	NUM
ejpam-6358	212	3	.	.	PUNCT
ejpam-6358	213	1	[	[	X
ejpam-6358	213	2	40	40	NUM
ejpam-6358	213	3	]	]	PUNCT
ejpam-6358	213	4	let	let	VERB
ejpam-6358	213	5	r	r	PRON
ejpam-6358	213	6	be	be	AUX
ejpam-6358	213	7	a	a	DET
ejpam-6358	213	8	relation	relation	NOUN
ejpam-6358	213	9	on	on	ADP
ejpam-6358	213	10	u	u	NOUN
ejpam-6358	213	11	,	,	PUNCT
ejpam-6358	213	12	and	and	CCONJ
ejpam-6358	213	13	let	let	VERB
ejpam-6358	213	14	k	k	PRON
ejpam-6358	213	15	be	be	AUX
ejpam-6358	213	16	an	an	DET
ejpam-6358	213	17	ideal	ideal	NOUN
ejpam-6358	213	18	on	on	ADP
ejpam-6358	213	19	u	u	PROPN
ejpam-6358	213	20	.	.	PUNCT
ejpam-6358	214	1	the	the	DET
ejpam-6358	214	2	ikj	ikj	PROPN
ejpam-6358	214	3	neighborhoods	neighborhood	NOUN
ejpam-6358	214	4	of	of	ADP
ejpam-6358	214	5	an	an	DET
ejpam-6358	214	6	element	element	NOUN
ejpam-6358	214	7	s	s	PART
ejpam-6358	214	8	∈	∈	NOUN
ejpam-6358	214	9	u	u	NOUN
ejpam-6358	214	10	are	be	AUX
ejpam-6358	214	11	specified	specify	VERB
ejpam-6358	214	12	as	as	SCONJ
ejpam-6358	214	13	follows	follow	VERB
ejpam-6358	214	14	:	:	PUNCT
ejpam-6358	214	15	(	(	PUNCT
ejpam-6358	214	16	i	i	NOUN
ejpam-6358	214	17	)	)	PUNCT
ejpam-6358	214	18	ika	ika	PROPN
ejpam-6358	214	19	(	(	PUNCT
ejpam-6358	214	20	s	s	NOUN
ejpam-6358	214	21	)	)	PUNCT
ejpam-6358	214	22	=	=	SYM
ejpam-6358	214	23	{	{	PUNCT
ejpam-6358	214	24	t	t	PROPN
ejpam-6358	214	25	∈	∈	PROPN
ejpam-6358	214	26	u	u	NOUN
ejpam-6358	214	27	:	:	PUNCT
ejpam-6358	214	28	ωa(t	ωa(t	NUM
ejpam-6358	214	29	)	)	PUNCT
ejpam-6358	214	30	∩	∩	NOUN
ejpam-6358	214	31	ωa(s	ωa(	NOUN
ejpam-6358	214	32	)	)	PUNCT
ejpam-6358	214	33	̸∈	̸∈	PROPN
ejpam-6358	214	34	k	k	PROPN
ejpam-6358	214	35	}	}	PUNCT
ejpam-6358	214	36	.	.	PUNCT
ejpam-6358	215	1	(	(	PUNCT
ejpam-6358	215	2	ii	ii	NOUN
ejpam-6358	215	3	)	)	PUNCT
ejpam-6358	215	4	ikb	ikb	PROPN
ejpam-6358	215	5	(	(	PUNCT
ejpam-6358	215	6	s	s	X
ejpam-6358	215	7	)	)	PUNCT
ejpam-6358	215	8	=	=	SYM
ejpam-6358	215	9	{	{	PUNCT
ejpam-6358	215	10	t	t	PROPN
ejpam-6358	215	11	∈	∈	PROPN
ejpam-6358	215	12	u	u	NOUN
ejpam-6358	215	13	:	:	PUNCT
ejpam-6358	215	14	ωb(t	ωb(t	NUM
ejpam-6358	215	15	)	)	PUNCT
ejpam-6358	215	16	∩	∩	NOUN
ejpam-6358	215	17	ωb(s	ωb(	NOUN
ejpam-6358	215	18	)	)	PUNCT
ejpam-6358	215	19	̸∈	̸∈	PROPN
ejpam-6358	215	20	k	k	PROPN
ejpam-6358	215	21	}	}	PUNCT
ejpam-6358	215	22	.	.	PUNCT
ejpam-6358	216	1	(	(	PUNCT
ejpam-6358	216	2	iii	iii	X
ejpam-6358	216	3	)	)	PUNCT
ejpam-6358	216	4	iki	iki	PROPN
ejpam-6358	216	5	(	(	PUNCT
ejpam-6358	216	6	s	s	NOUN
ejpam-6358	216	7	)	)	PUNCT
ejpam-6358	216	8	=	=	SYM
ejpam-6358	216	9	ika	ika	X
ejpam-6358	216	10	(	(	PUNCT
ejpam-6358	216	11	s	s	NOUN
ejpam-6358	216	12	)	)	PUNCT
ejpam-6358	216	13	∩	∩	ADJ
ejpam-6358	216	14	ikb	ikb	PROPN
ejpam-6358	216	15	(	(	PUNCT
ejpam-6358	216	16	s	s	NOUN
ejpam-6358	216	17	)	)	PUNCT
ejpam-6358	216	18	.	.	PUNCT
ejpam-6358	217	1	(	(	PUNCT
ejpam-6358	217	2	iv	iv	X
ejpam-6358	217	3	)	)	PUNCT
ejpam-6358	217	4	iku	iku	PROPN
ejpam-6358	217	5	(	(	PUNCT
ejpam-6358	217	6	s	s	NOUN
ejpam-6358	217	7	)	)	PUNCT
ejpam-6358	217	8	=	=	SYM
ejpam-6358	217	9	ika	ika	X
ejpam-6358	217	10	(	(	PUNCT
ejpam-6358	217	11	s	s	NOUN
ejpam-6358	217	12	)	)	PUNCT
ejpam-6358	217	13	∪	∪	NOUN
ejpam-6358	217	14	ikb	ikb	PROPN
ejpam-6358	217	15	(	(	PUNCT
ejpam-6358	217	16	s	s	NOUN
ejpam-6358	217	17	)	)	PUNCT
ejpam-6358	217	18	.	.	PUNCT
ejpam-6358	218	1	(	(	PUNCT
ejpam-6358	218	2	v	v	NOUN
ejpam-6358	218	3	)	)	PUNCT
ejpam-6358	218	4	ik	ik	PROPN
ejpam-6358	218	5	<	<	X
ejpam-6358	218	6	a>(s	a>(s	X
ejpam-6358	218	7	)	)	PUNCT
ejpam-6358	218	8	=	=	PRON
ejpam-6358	219	1	{	{	PUNCT
ejpam-6358	219	2	t	t	NOUN
ejpam-6358	219	3	∈	∈	PROPN
ejpam-6358	219	4	u	u	NOUN
ejpam-6358	219	5	:	:	PUNCT
ejpam-6358	219	6	ω	ω	X
ejpam-6358	219	7	<	<	X
ejpam-6358	219	8	a>(t	a>(t	NOUN
ejpam-6358	219	9	)	)	PUNCT
ejpam-6358	219	10	∩	∩	NOUN
ejpam-6358	219	11	ω	ω	PROPN
ejpam-6358	219	12	<	<	X
ejpam-6358	219	13	a>(s	a>(s	X
ejpam-6358	219	14	)	)	PUNCT
ejpam-6358	219	15	̸∈	̸∈	PROPN
ejpam-6358	219	16	k	k	PROPN
ejpam-6358	219	17	}	}	PUNCT
ejpam-6358	219	18	.	.	PUNCT
ejpam-6358	220	1	(	(	PUNCT
ejpam-6358	220	2	vi	vi	X
ejpam-6358	220	3	)	)	PUNCT
ejpam-6358	220	4	ik	ik	X
ejpam-6358	220	5	<	<	X
ejpam-6358	220	6	b>(s	b>(s	X
ejpam-6358	220	7	)	)	PUNCT
ejpam-6358	221	1	=	=	PRON
ejpam-6358	221	2	{	{	PUNCT
ejpam-6358	221	3	t	t	PROPN
ejpam-6358	221	4	∈	∈	PROPN
ejpam-6358	221	5	u	u	NOUN
ejpam-6358	221	6	:	:	PUNCT
ejpam-6358	221	7	ω	ω	NUM
ejpam-6358	221	8	<	<	NOUN
ejpam-6358	221	9	b>(t	b>(t	NOUN
ejpam-6358	221	10	)	)	PUNCT
ejpam-6358	221	11	∩	∩	NOUN
ejpam-6358	221	12	ω	ω	NOUN
ejpam-6358	221	13	<	<	X
ejpam-6358	221	14	b>(s	b>(s	X
ejpam-6358	221	15	)	)	PUNCT
ejpam-6358	221	16	̸∈	̸∈	PROPN
ejpam-6358	221	17	k	k	PROPN
ejpam-6358	221	18	}	}	PUNCT
ejpam-6358	221	19	.	.	PUNCT
ejpam-6358	222	1	(	(	PUNCT
ejpam-6358	222	2	vii	vii	PROPN
ejpam-6358	222	3	)	)	PUNCT
ejpam-6358	222	4	ik	ik	PROPN
ejpam-6358	222	5	<	<	X
ejpam-6358	222	6	i>(s	i>(s	NOUN
ejpam-6358	222	7	)	)	PUNCT
ejpam-6358	222	8	=	=	PUNCT
ejpam-6358	222	9	ik	ik	X
ejpam-6358	222	10	<	<	X
ejpam-6358	222	11	a>(s	a>(s	X
ejpam-6358	222	12	)	)	PUNCT
ejpam-6358	222	13	∩	∩	NOUN
ejpam-6358	222	14	ik	ik	PROPN
ejpam-6358	222	15	<	<	X
ejpam-6358	222	16	b>(s	b>(s	PRON
ejpam-6358	222	17	)	)	PUNCT
ejpam-6358	222	18	.	.	PUNCT
ejpam-6358	223	1	(	(	PUNCT
ejpam-6358	223	2	viii	viii	NOUN
ejpam-6358	223	3	)	)	PUNCT
ejpam-6358	223	4	ik	ik	ADP
ejpam-6358	223	5	<	<	X
ejpam-6358	223	6	u>(s	u>(s	X
ejpam-6358	223	7	)	)	PUNCT
ejpam-6358	223	8	=	=	PUNCT
ejpam-6358	224	1	ik	ik	X
ejpam-6358	224	2	<	<	X
ejpam-6358	224	3	a>(s	a>(s	X
ejpam-6358	224	4	)	)	PUNCT
ejpam-6358	224	5	∪	∪	ADP
ejpam-6358	224	6	ik	ik	PROPN
ejpam-6358	224	7	<	<	X
ejpam-6358	224	8	b>(s	b>(s	PRON
ejpam-6358	224	9	)	)	PUNCT
ejpam-6358	224	10	.	.	PUNCT
ejpam-6358	225	1	note	note	VERB
ejpam-6358	225	2	that	that	SCONJ
ejpam-6358	225	3	if	if	SCONJ
ejpam-6358	225	4	the	the	DET
ejpam-6358	225	5	ideal	ideal	NOUN
ejpam-6358	225	6	is	be	AUX
ejpam-6358	225	7	given	give	VERB
ejpam-6358	225	8	by	by	ADP
ejpam-6358	225	9	k	k	PROPN
ejpam-6358	225	10	=	=	PUNCT
ejpam-6358	225	11	{	{	PUNCT
ejpam-6358	225	12	∅	∅	NOUN
ejpam-6358	225	13	}	}	PUNCT
ejpam-6358	225	14	,	,	PUNCT
ejpam-6358	225	15	then	then	ADV
ejpam-6358	225	16	definition	definition	NOUN
ejpam-6358	225	17	10	10	NUM
ejpam-6358	225	18	reduces	reduce	VERB
ejpam-6358	225	19	to	to	ADP
ejpam-6358	225	20	definition	definition	NOUN
ejpam-6358	225	21	6	6	NUM
ejpam-6358	225	22	.	.	PUNCT
ejpam-6358	226	1	as	as	ADP
ejpam-6358	226	2	a	a	DET
ejpam-6358	226	3	result	result	NOUN
ejpam-6358	226	4	,	,	PUNCT
ejpam-6358	226	5	the	the	DET
ejpam-6358	226	6	work	work	NOUN
ejpam-6358	226	7	presented	present	VERB
ejpam-6358	226	8	in	in	ADP
ejpam-6358	226	9	[	[	X
ejpam-6358	226	10	40	40	NUM
ejpam-6358	226	11	]	]	PUNCT
ejpam-6358	226	12	can	can	AUX
ejpam-6358	226	13	be	be	AUX
ejpam-6358	226	14	regarded	regard	VERB
ejpam-6358	226	15	as	as	ADP
ejpam-6358	226	16	a	a	DET
ejpam-6358	226	17	genuine	genuine	ADJ
ejpam-6358	226	18	extension	extension	NOUN
ejpam-6358	226	19	of	of	ADP
ejpam-6358	226	20	the	the	DET
ejpam-6358	226	21	results	result	NOUN
ejpam-6358	226	22	established	establish	VERB
ejpam-6358	226	23	in	in	ADP
ejpam-6358	226	24	[	[	X
ejpam-6358	226	25	12	12	NUM
ejpam-6358	226	26	]	]	PUNCT
ejpam-6358	226	27	.	.	PUNCT
ejpam-6358	227	1	furthermore	furthermore	ADV
ejpam-6358	227	2	,	,	PUNCT
ejpam-6358	227	3	the	the	DET
ejpam-6358	227	4	notion	notion	NOUN
ejpam-6358	227	5	of	of	ADP
ejpam-6358	227	6	the	the	DET
ejpam-6358	227	7	”	"	PUNCT
ejpam-6358	227	8	i	i	NOUN
ejpam-6358	227	9	-	-	PUNCT
ejpam-6358	227	10	generalized	generalize	VERB
ejpam-6358	227	11	approximation	approximation	NOUN
ejpam-6358	227	12	space	space	NOUN
ejpam-6358	227	13	”	"	PUNCT
ejpam-6358	227	14	(	(	PUNCT
ejpam-6358	227	15	corrected	correct	VERB
ejpam-6358	227	16	and	and	CCONJ
ejpam-6358	227	17	abbreviated	abbreviate	VERB
ejpam-6358	227	18	as	as	ADP
ejpam-6358	227	19	ij	ij	NOUN
ejpam-6358	227	20	-	-	PUNCT
ejpam-6358	227	21	g	g	NOUN
ejpam-6358	227	22	approximation	approximation	NOUN
ejpam-6358	227	23	space	space	NOUN
ejpam-6358	227	24	)	)	PUNCT
ejpam-6358	227	25	was	be	AUX
ejpam-6358	227	26	not	not	PART
ejpam-6358	227	27	explicitly	explicitly	ADV
ejpam-6358	227	28	defined	define	VERB
ejpam-6358	227	29	in	in	ADP
ejpam-6358	227	30	[	[	X
ejpam-6358	227	31	40	40	NUM
ejpam-6358	227	32	]	]	PUNCT
ejpam-6358	227	33	,	,	PUNCT
ejpam-6358	227	34	despite	despite	SCONJ
ejpam-6358	227	35	being	be	AUX
ejpam-6358	227	36	referenced	reference	VERB
ejpam-6358	227	37	throughout	throughout	ADP
ejpam-6358	227	38	various	various	ADJ
ejpam-6358	227	39	definitions	definition	NOUN
ejpam-6358	227	40	and	and	CCONJ
ejpam-6358	227	41	results	result	NOUN
ejpam-6358	227	42	.	.	PUNCT
ejpam-6358	228	1	to	to	PART
ejpam-6358	228	2	address	address	VERB
ejpam-6358	228	3	this	this	DET
ejpam-6358	228	4	gap	gap	NOUN
ejpam-6358	228	5	,	,	PUNCT
ejpam-6358	228	6	we	we	PRON
ejpam-6358	228	7	formally	formally	ADV
ejpam-6358	228	8	introduce	introduce	VERB
ejpam-6358	228	9	it	it	PRON
ejpam-6358	228	10	as	as	SCONJ
ejpam-6358	228	11	follows	follow	VERB
ejpam-6358	228	12	:	:	PUNCT
ejpam-6358	228	13	definition	definition	NOUN
ejpam-6358	228	14	11	11	NUM
ejpam-6358	228	15	.	.	PUNCT
ejpam-6358	229	1	let	let	VERB
ejpam-6358	229	2	r	r	PRON
ejpam-6358	229	3	be	be	AUX
ejpam-6358	229	4	a	a	DET
ejpam-6358	229	5	relation	relation	NOUN
ejpam-6358	229	6	on	on	ADP
ejpam-6358	229	7	u	u	PROPN
ejpam-6358	229	8	,	,	PUNCT
ejpam-6358	229	9	and	and	CCONJ
ejpam-6358	229	10	k	k	PROPN
ejpam-6358	229	11	be	be	AUX
ejpam-6358	229	12	an	an	DET
ejpam-6358	229	13	ideal	ideal	NOUN
ejpam-6358	229	14	on	on	ADP
ejpam-6358	229	15	u	u	PROPN
ejpam-6358	229	16	.	.	PUNCT
ejpam-6358	230	1	the	the	DET
ejpam-6358	230	2	triplet	triplet	NOUN
ejpam-6358	230	3	(	(	PUNCT
ejpam-6358	230	4	u	u	NOUN
ejpam-6358	230	5	,	,	PUNCT
ejpam-6358	230	6	r	r	NOUN
ejpam-6358	230	7	,	,	PUNCT
ejpam-6358	230	8	k	k	NOUN
ejpam-6358	230	9	)	)	PUNCT
ejpam-6358	230	10	is	be	AUX
ejpam-6358	230	11	named	name	VERB
ejpam-6358	230	12	an	an	DET
ejpam-6358	230	13	ij	ij	ADJ
ejpam-6358	230	14	-	-	PUNCT
ejpam-6358	230	15	g	g	NOUN
ejpam-6358	230	16	approximation	approximation	NOUN
ejpam-6358	230	17	space	space	NOUN
ejpam-6358	230	18	.	.	PUNCT
ejpam-6358	231	1	r.	r.	PROPN
ejpam-6358	231	2	a.	a.	PROPN
ejpam-6358	231	3	hosny	hosny	PROPN
ejpam-6358	231	4	et	et	PROPN
ejpam-6358	231	5	al	al	PROPN
ejpam-6358	231	6	.	.	PUNCT
ejpam-6358	231	7	/	/	SYM
ejpam-6358	231	8	eur	eur	PROPN
ejpam-6358	231	9	.	.	PUNCT
ejpam-6358	232	1	j.	j.	PROPN
ejpam-6358	232	2	pure	pure	PROPN
ejpam-6358	232	3	appl	appl	PROPN
ejpam-6358	232	4	.	.	PROPN
ejpam-6358	232	5	math	math	PROPN
ejpam-6358	232	6	,	,	PUNCT
ejpam-6358	232	7	18	18	NUM
ejpam-6358	232	8	(	(	PUNCT
ejpam-6358	232	9	4	4	NUM
ejpam-6358	232	10	)	)	PUNCT
ejpam-6358	232	11	(	(	PUNCT
ejpam-6358	232	12	2025	2025	NUM
ejpam-6358	232	13	)	)	PUNCT
ejpam-6358	232	14	,	,	PUNCT
ejpam-6358	232	15	6358	6358	NUM
ejpam-6358	232	16	9	9	NUM
ejpam-6358	232	17	of	of	ADP
ejpam-6358	232	18	24	24	NUM
ejpam-6358	232	19	theorem	theorem	NOUN
ejpam-6358	232	20	1	1	NUM
ejpam-6358	232	21	.	.	PUNCT
ejpam-6358	233	1	[	[	X
ejpam-6358	233	2	40	40	NUM
ejpam-6358	233	3	]	]	PUNCT
ejpam-6358	233	4	let	let	VERB
ejpam-6358	233	5	(	(	PUNCT
ejpam-6358	233	6	u	u	NOUN
ejpam-6358	233	7	,	,	PUNCT
ejpam-6358	233	8	r	r	NOUN
ejpam-6358	233	9	,	,	PUNCT
ejpam-6358	233	10	k	k	NOUN
ejpam-6358	233	11	)	)	PUNCT
ejpam-6358	233	12	be	be	VERB
ejpam-6358	233	13	an	an	DET
ejpam-6358	233	14	ij	ij	ADJ
ejpam-6358	233	15	-	-	PUNCT
ejpam-6358	233	16	g	g	NOUN
ejpam-6358	233	17	approximation	approximation	NOUN
ejpam-6358	233	18	space	space	NOUN
ejpam-6358	233	19	,	,	PUNCT
ejpam-6358	233	20	and	and	CCONJ
ejpam-6358	233	21	let	let	VERB
ejpam-6358	233	22	s	s	PRON
ejpam-6358	233	23	∈	∈	PROPN
ejpam-6358	233	24	u	u	NOUN
ejpam-6358	233	25	.	.	PUNCT
ejpam-6358	234	1	if	if	SCONJ
ejpam-6358	234	2	r	r	NOUN
ejpam-6358	234	3	is	be	AUX
ejpam-6358	234	4	reflexive	reflexive	ADJ
ejpam-6358	234	5	,	,	PUNCT
ejpam-6358	234	6	then	then	ADV
ejpam-6358	234	7	for	for	ADP
ejpam-6358	234	8	each	each	DET
ejpam-6358	234	9	j	j	PROPN
ejpam-6358	234	10	∈	∈	PROPN
ejpam-6358	234	11	{	{	PUNCT
ejpam-6358	234	12	a	a	PROPN
ejpam-6358	234	13	,	,	PUNCT
ejpam-6358	234	14	b	b	NOUN
ejpam-6358	234	15	,	,	PUNCT
ejpam-6358	234	16	i	i	PRON
ejpam-6358	234	17	,	,	PUNCT
ejpam-6358	234	18	u	u	NOUN
ejpam-6358	234	19	}	}	PUNCT
ejpam-6358	234	20	,	,	PUNCT
ejpam-6358	234	21	the	the	DET
ejpam-6358	234	22	following	follow	VERB
ejpam-6358	234	23	inclusion	inclusion	NOUN
ejpam-6358	234	24	holds	hold	VERB
ejpam-6358	234	25	:	:	PUNCT
ejpam-6358	234	26	ik	ik	PROPN
ejpam-6358	234	27	<	<	X
ejpam-6358	234	28	j>(s	j>(s	X
ejpam-6358	234	29	)	)	PUNCT
ejpam-6358	234	30	⊆	⊆	NUM
ejpam-6358	234	31	ikj	ikj	X
ejpam-6358	234	32	(	(	PUNCT
ejpam-6358	234	33	s	s	NOUN
ejpam-6358	234	34	)	)	PUNCT
ejpam-6358	234	35	.	.	PUNCT
ejpam-6358	235	1	definition	definition	NOUN
ejpam-6358	235	2	12	12	NUM
ejpam-6358	235	3	.	.	PUNCT
ejpam-6358	236	1	[	[	X
ejpam-6358	236	2	40	40	NUM
ejpam-6358	236	3	]	]	PUNCT
ejpam-6358	236	4	let	let	VERB
ejpam-6358	236	5	r	r	PRON
ejpam-6358	236	6	be	be	AUX
ejpam-6358	236	7	a	a	DET
ejpam-6358	236	8	binary	binary	ADJ
ejpam-6358	236	9	relation	relation	NOUN
ejpam-6358	236	10	and	and	CCONJ
ejpam-6358	236	11	k	k	X
ejpam-6358	236	12	an	an	DET
ejpam-6358	236	13	ideal	ideal	NOUN
ejpam-6358	236	14	on	on	ADP
ejpam-6358	236	15	a	a	DET
ejpam-6358	236	16	nonempty	nonempty	ADV
ejpam-6358	236	17	set	set	VERB
ejpam-6358	236	18	u	u	NOUN
ejpam-6358	236	19	.	.	PUNCT
ejpam-6358	237	1	the	the	DET
ejpam-6358	237	2	improved	improved	ADJ
ejpam-6358	237	3	operators	operator	NOUN
ejpam-6358	237	4	(	(	PUNCT
ejpam-6358	237	5	lower	low	ADJ
ejpam-6358	237	6	and	and	CCONJ
ejpam-6358	237	7	upper	upper	ADJ
ejpam-6358	237	8	)	)	PUNCT
ejpam-6358	237	9	,	,	PUNCT
ejpam-6358	237	10	boundary	boundary	ADJ
ejpam-6358	237	11	region	region	NOUN
ejpam-6358	237	12	,	,	PUNCT
ejpam-6358	237	13	and	and	CCONJ
ejpam-6358	237	14	accuracy	accuracy	NOUN
ejpam-6358	237	15	measure	measure	NOUN
ejpam-6358	237	16	of	of	ADP
ejpam-6358	237	17	a	a	DET
ejpam-6358	237	18	nonempty	nonempty	NOUN
ejpam-6358	237	19	subset	subset	VERB
ejpam-6358	237	20	f	f	PROPN
ejpam-6358	237	21	of	of	ADP
ejpam-6358	237	22	u	u	PROPN
ejpam-6358	237	23	,	,	PUNCT
ejpam-6358	237	24	derived	derive	VERB
ejpam-6358	237	25	from	from	ADP
ejpam-6358	237	26	r	r	NOUN
ejpam-6358	237	27	and	and	CCONJ
ejpam-6358	237	28	k	k	NOUN
ejpam-6358	237	29	,	,	PUNCT
ejpam-6358	237	30	are	be	AUX
ejpam-6358	237	31	defined	define	VERB
ejpam-6358	237	32	as	as	SCONJ
ejpam-6358	237	33	follows	follow	VERB
ejpam-6358	237	34	:	:	PUNCT
ejpam-6358	237	35	�	�	PROPN
ejpam-6358	237	36	lower	low	ADJ
ejpam-6358	237	37	approximation	approximation	NOUN
ejpam-6358	237	38	:	:	PUNCT
ejpam-6358	238	1	r	r	NOUN
ejpam-6358	238	2	ikj	ikj	NOUN
ejpam-6358	238	3	⋆	⋆	X
ejpam-6358	238	4	(	(	PUNCT
ejpam-6358	238	5	f	f	PROPN
ejpam-6358	238	6	)	)	PUNCT
ejpam-6358	238	7	=	=	PRON
ejpam-6358	238	8	{	{	PUNCT
ejpam-6358	238	9	s	s	NOUN
ejpam-6358	238	10	∈	∈	PROPN
ejpam-6358	238	11	u	u	NOUN
ejpam-6358	238	12	:	:	PUNCT
ejpam-6358	238	13	ikj	ikj	PROPN
ejpam-6358	238	14	(	(	PUNCT
ejpam-6358	238	15	s	s	NOUN
ejpam-6358	238	16	)	)	PUNCT
ejpam-6358	238	17	\	\	NOUN
ejpam-6358	238	18	f	f	PROPN
ejpam-6358	238	19	∈	∈	PROPN
ejpam-6358	238	20	k	k	NOUN
ejpam-6358	238	21	}	}	PUNCT
ejpam-6358	238	22	.	.	PUNCT
ejpam-6358	239	1	�	�	PROPN
ejpam-6358	239	2	upper	upper	ADJ
ejpam-6358	239	3	approximation	approximation	NOUN
ejpam-6358	239	4	:	:	PUNCT
ejpam-6358	239	5	r⋆ikj	r⋆ikj	PROPN
ejpam-6358	239	6	(	(	PUNCT
ejpam-6358	239	7	f	f	PROPN
ejpam-6358	239	8	)	)	PUNCT
ejpam-6358	239	9	=	=	PRON
ejpam-6358	239	10	{	{	PUNCT
ejpam-6358	239	11	s	s	NOUN
ejpam-6358	239	12	∈	∈	PROPN
ejpam-6358	239	13	u	u	NOUN
ejpam-6358	239	14	:	:	PUNCT
ejpam-6358	239	15	ikj	ikj	PROPN
ejpam-6358	239	16	(	(	PUNCT
ejpam-6358	239	17	s	s	NOUN
ejpam-6358	239	18	)	)	PUNCT
ejpam-6358	239	19	∩	∩	NOUN
ejpam-6358	239	20	f	f	PROPN
ejpam-6358	239	21	̸∈	̸∈	PROPN
ejpam-6358	239	22	k	k	PROPN
ejpam-6358	239	23	}	}	PUNCT
ejpam-6358	239	24	.	.	PUNCT
ejpam-6358	240	1	�	�	PROPN
ejpam-6358	240	2	boundary	boundary	ADJ
ejpam-6358	240	3	region	region	NOUN
ejpam-6358	240	4	:	:	PUNCT
ejpam-6358	241	1	bnd	bnd	NOUN
ejpam-6358	241	2	⋆ikj	⋆ikj	PROPN
ejpam-6358	242	1	r	r	NOUN
ejpam-6358	242	2	(	(	PUNCT
ejpam-6358	242	3	f	f	PROPN
ejpam-6358	242	4	)	)	PUNCT
ejpam-6358	243	1	=	=	SYM
ejpam-6358	243	2	r⋆ikj	r⋆ikj	PROPN
ejpam-6358	243	3	(	(	PUNCT
ejpam-6358	243	4	f	f	PROPN
ejpam-6358	243	5	)	)	PUNCT
ejpam-6358	243	6	\r	\r	PROPN
ejpam-6358	243	7	ikj	ikj	PROPN
ejpam-6358	243	8	⋆	⋆	X
ejpam-6358	243	9	(	(	PUNCT
ejpam-6358	243	10	f	f	PROPN
ejpam-6358	243	11	)	)	PUNCT
ejpam-6358	243	12	.	.	PUNCT
ejpam-6358	244	1	�	�	PROPN
ejpam-6358	244	2	accuracy	accuracy	NOUN
ejpam-6358	244	3	measure	measure	NOUN
ejpam-6358	244	4	:	:	PUNCT
ejpam-6358	244	5	acc	acc	PROPN
ejpam-6358	245	1	⋆ikj	⋆ikj	PROPN
ejpam-6358	245	2	r	r	PROPN
ejpam-6358	245	3	(	(	PUNCT
ejpam-6358	245	4	f	f	PROPN
ejpam-6358	245	5	)	)	PUNCT
ejpam-6358	246	1	=	=	SYM
ejpam-6358	247	1	|r	|r	PROPN
ejpam-6358	247	2	ikj	ikj	PROPN
ejpam-6358	247	3	⋆	⋆	X
ejpam-6358	247	4	(	(	PUNCT
ejpam-6358	247	5	f	f	PROPN
ejpam-6358	247	6	)	)	PUNCT
ejpam-6358	247	7	∩f	∩f	PROPN
ejpam-6358	248	1	|	|	ADV
ejpam-6358	248	2	|r⋆ik	|r⋆ik	PROPN
ejpam-6358	248	3	j	j	PROPN
ejpam-6358	248	4	(	(	PUNCT
ejpam-6358	248	5	f	f	PROPN
ejpam-6358	248	6	)	)	PUNCT
ejpam-6358	248	7	∪f	∪f	PROPN
ejpam-6358	249	1	|	|	ADV
ejpam-6358	249	2	,	,	PUNCT
ejpam-6358	249	3	where	where	SCONJ
ejpam-6358	249	4	|	|	ADV
ejpam-6358	249	5	r⋆ikj	r⋆ikj	PROPN
ejpam-6358	249	6	(	(	PUNCT
ejpam-6358	249	7	f	f	PROPN
ejpam-6358	249	8	)	)	PUNCT
ejpam-6358	249	9	∪	∪	ADP
ejpam-6358	249	10	f	f	PROPN
ejpam-6358	249	11	|̸=	|̸=	PROPN
ejpam-6358	249	12	0	0	NUM
ejpam-6358	249	13	.	.	PUNCT
ejpam-6358	249	14	remark	remark	PROPN
ejpam-6358	249	15	1	1	NUM
ejpam-6358	249	16	.	.	PUNCT
ejpam-6358	250	1	(	(	PUNCT
ejpam-6358	250	2	i	i	NOUN
ejpam-6358	250	3	)	)	PUNCT
ejpam-6358	250	4	according	accord	VERB
ejpam-6358	250	5	to	to	ADP
ejpam-6358	250	6	the	the	DET
ejpam-6358	250	7	principles	principle	NOUN
ejpam-6358	250	8	of	of	ADP
ejpam-6358	250	9	pawlak	pawlak	ADJ
ejpam-6358	250	10	’s	’s	PART
ejpam-6358	250	11	rough	rough	ADJ
ejpam-6358	250	12	set	set	NOUN
ejpam-6358	250	13	theory	theory	NOUN
ejpam-6358	250	14	,	,	PUNCT
ejpam-6358	250	15	as	as	SCONJ
ejpam-6358	250	16	established	establish	VERB
ejpam-6358	250	17	in	in	ADP
ejpam-6358	250	18	[	[	X
ejpam-6358	250	19	1	1	NUM
ejpam-6358	250	20	]	]	PUNCT
ejpam-6358	250	21	,	,	PUNCT
ejpam-6358	250	22	a	a	DET
ejpam-6358	250	23	set	set	NOUN
ejpam-6358	250	24	is	be	AUX
ejpam-6358	250	25	considered	consider	VERB
ejpam-6358	250	26	definable	definable	ADJ
ejpam-6358	250	27	(	(	PUNCT
ejpam-6358	250	28	or	or	CCONJ
ejpam-6358	250	29	exact	exact	ADJ
ejpam-6358	250	30	)	)	PUNCT
ejpam-6358	250	31	if	if	SCONJ
ejpam-6358	250	32	its	its	PRON
ejpam-6358	250	33	lower	low	ADJ
ejpam-6358	250	34	and	and	CCONJ
ejpam-6358	250	35	upper	upper	ADJ
ejpam-6358	250	36	approximations	approximation	NOUN
ejpam-6358	250	37	coincide	coincide	NOUN
ejpam-6358	250	38	.	.	PUNCT
ejpam-6358	251	1	in	in	ADP
ejpam-6358	251	2	particular	particular	ADJ
ejpam-6358	251	3	,	,	PUNCT
ejpam-6358	251	4	if	if	SCONJ
ejpam-6358	251	5	the	the	DET
ejpam-6358	251	6	lower	low	ADJ
ejpam-6358	251	7	approximation	approximation	NOUN
ejpam-6358	251	8	of	of	ADP
ejpam-6358	251	9	the	the	DET
ejpam-6358	251	10	empty	empty	ADJ
ejpam-6358	251	11	set	set	VERB
ejpam-6358	251	12	∅	∅	NOUN
ejpam-6358	251	13	is	be	AUX
ejpam-6358	251	14	equal	equal	ADJ
ejpam-6358	251	15	to	to	ADP
ejpam-6358	251	16	its	its	PRON
ejpam-6358	251	17	upper	upper	ADJ
ejpam-6358	251	18	approximation	approximation	NOUN
ejpam-6358	251	19	,	,	PUNCT
ejpam-6358	251	20	which	which	PRON
ejpam-6358	251	21	is	be	AUX
ejpam-6358	251	22	also	also	ADV
ejpam-6358	251	23	∅	∅	NOUN
ejpam-6358	251	24	,	,	PUNCT
ejpam-6358	251	25	then	then	ADV
ejpam-6358	251	26	∅	∅	NOUN
ejpam-6358	251	27	is	be	AUX
ejpam-6358	251	28	a	a	DET
ejpam-6358	251	29	definable	definable	ADJ
ejpam-6358	251	30	set	set	NOUN
ejpam-6358	251	31	,	,	PUNCT
ejpam-6358	251	32	and	and	CCONJ
ejpam-6358	251	33	its	its	PRON
ejpam-6358	251	34	accuracy	accuracy	NOUN
ejpam-6358	251	35	measure	measure	NOUN
ejpam-6358	251	36	is	be	AUX
ejpam-6358	251	37	1	1	NUM
ejpam-6358	251	38	.	.	PUNCT
ejpam-6358	252	1	conversely	conversely	ADV
ejpam-6358	252	2	,	,	PUNCT
ejpam-6358	252	3	if	if	SCONJ
ejpam-6358	252	4	this	this	DET
ejpam-6358	252	5	condition	condition	NOUN
ejpam-6358	252	6	is	be	AUX
ejpam-6358	252	7	not	not	PART
ejpam-6358	252	8	satisfied	satisfied	ADJ
ejpam-6358	252	9	,	,	PUNCT
ejpam-6358	252	10	∅	∅	NOUN
ejpam-6358	252	11	is	be	AUX
ejpam-6358	252	12	classified	classify	VERB
ejpam-6358	252	13	as	as	ADP
ejpam-6358	252	14	an	an	DET
ejpam-6358	252	15	undefinable	undefinable	ADJ
ejpam-6358	252	16	(	(	PUNCT
ejpam-6358	252	17	or	or	CCONJ
ejpam-6358	252	18	rough	rough	ADJ
ejpam-6358	252	19	)	)	PUNCT
ejpam-6358	252	20	set	set	NOUN
ejpam-6358	252	21	,	,	PUNCT
ejpam-6358	252	22	meaning	mean	VERB
ejpam-6358	252	23	its	its	PRON
ejpam-6358	252	24	accuracy	accuracy	NOUN
ejpam-6358	252	25	measure	measure	NOUN
ejpam-6358	252	26	differs	differ	VERB
ejpam-6358	252	27	from	from	ADP
ejpam-6358	252	28	1	1	NUM
ejpam-6358	252	29	.	.	PUNCT
ejpam-6358	253	1	additionally	additionally	ADV
ejpam-6358	253	2	,	,	PUNCT
ejpam-6358	253	3	the	the	DET
ejpam-6358	253	4	definition	definition	NOUN
ejpam-6358	253	5	of	of	ADP
ejpam-6358	253	6	the	the	DET
ejpam-6358	253	7	accuracy	accuracy	NOUN
ejpam-6358	253	8	measure	measure	NOUN
ejpam-6358	253	9	requires	require	VERB
ejpam-6358	253	10	that	that	SCONJ
ejpam-6358	253	11	the	the	DET
ejpam-6358	253	12	upper	upper	ADJ
ejpam-6358	253	13	approximation	approximation	NOUN
ejpam-6358	253	14	be	be	AUX
ejpam-6358	253	15	nonempty	nonempty	ADJ
ejpam-6358	253	16	to	to	PART
ejpam-6358	253	17	avoid	avoid	VERB
ejpam-6358	253	18	division	division	NOUN
ejpam-6358	253	19	by	by	ADP
ejpam-6358	253	20	zero	zero	NUM
ejpam-6358	253	21	.	.	PUNCT
ejpam-6358	254	1	therefore	therefore	ADV
ejpam-6358	254	2	,	,	PUNCT
ejpam-6358	254	3	if	if	SCONJ
ejpam-6358	254	4	the	the	DET
ejpam-6358	254	5	upper	upper	ADJ
ejpam-6358	254	6	approximation	approximation	NOUN
ejpam-6358	254	7	of	of	ADP
ejpam-6358	254	8	∅	∅	NOUN
ejpam-6358	254	9	is	be	AUX
ejpam-6358	254	10	itself	itself	PRON
ejpam-6358	254	11	∅	∅	NOUN
ejpam-6358	254	12	,	,	PUNCT
ejpam-6358	254	13	the	the	DET
ejpam-6358	254	14	accuracy	accuracy	NOUN
ejpam-6358	254	15	measure	measure	NOUN
ejpam-6358	254	16	in	in	ADP
ejpam-6358	254	17	this	this	DET
ejpam-6358	254	18	case	case	NOUN
ejpam-6358	254	19	is	be	AUX
ejpam-6358	254	20	considered	consider	VERB
ejpam-6358	254	21	as	as	ADP
ejpam-6358	254	22	an	an	DET
ejpam-6358	254	23	indefinite	indefinite	ADJ
ejpam-6358	254	24	quantity	quantity	NOUN
ejpam-6358	254	25	.	.	PUNCT
ejpam-6358	255	1	(	(	PUNCT
ejpam-6358	255	2	ii	ii	NOUN
ejpam-6358	255	3	)	)	PUNCT
ejpam-6358	255	4	accordingly	accordingly	ADV
ejpam-6358	255	5	,	,	PUNCT
ejpam-6358	255	6	in	in	ADP
ejpam-6358	255	7	definition	definition	NOUN
ejpam-6358	255	8	12	12	NUM
ejpam-6358	255	9	,	,	PUNCT
ejpam-6358	255	10	the	the	DET
ejpam-6358	255	11	empty	empty	ADJ
ejpam-6358	255	12	set	set	ADJ
ejpam-6358	255	13	∅	∅	NOUN
ejpam-6358	255	14	is	be	AUX
ejpam-6358	255	15	definable	definable	ADJ
ejpam-6358	255	16	if	if	SCONJ
ejpam-6358	255	17	r	r	NOUN
ejpam-6358	255	18	ikj	ikj	X
ejpam-6358	255	19	⋆	⋆	X
ejpam-6358	255	20	(	(	PUNCT
ejpam-6358	255	21	∅	∅	NOUN
ejpam-6358	255	22	)	)	PUNCT
ejpam-6358	255	23	=	=	SYM
ejpam-6358	255	24	r⋆ikj	r⋆ikj	PROPN
ejpam-6358	255	25	(	(	PUNCT
ejpam-6358	255	26	∅	∅	NOUN
ejpam-6358	255	27	)	)	PUNCT
ejpam-6358	255	28	=	=	SYM
ejpam-6358	255	29	∅	∅	NOUN
ejpam-6358	255	30	,	,	PUNCT
ejpam-6358	255	31	which	which	PRON
ejpam-6358	255	32	implies	imply	VERB
ejpam-6358	255	33	that	that	SCONJ
ejpam-6358	255	34	acc	acc	PROPN
ejpam-6358	255	35	⋆ikj	⋆ikj	PROPN
ejpam-6358	255	36	r	r	NOUN
ejpam-6358	255	37	(	(	PUNCT
ejpam-6358	255	38	∅	∅	NOUN
ejpam-6358	255	39	)	)	PUNCT
ejpam-6358	255	40	=	=	SYM
ejpam-6358	255	41	1	1	X
ejpam-6358	255	42	.	.	PUNCT
ejpam-6358	255	43	r.	r.	PROPN
ejpam-6358	255	44	a.	a.	PROPN
ejpam-6358	255	45	hosny	hosny	PROPN
ejpam-6358	255	46	et	et	PROPN
ejpam-6358	255	47	al	al	PROPN
ejpam-6358	255	48	.	.	PUNCT
ejpam-6358	255	49	/	/	SYM
ejpam-6358	255	50	eur	eur	PROPN
ejpam-6358	255	51	.	.	PUNCT
ejpam-6358	256	1	j.	j.	PROPN
ejpam-6358	256	2	pure	pure	PROPN
ejpam-6358	256	3	appl	appl	PROPN
ejpam-6358	256	4	.	.	PROPN
ejpam-6358	256	5	math	math	PROPN
ejpam-6358	256	6	,	,	PUNCT
ejpam-6358	256	7	18	18	NUM
ejpam-6358	256	8	(	(	PUNCT
ejpam-6358	256	9	4	4	NUM
ejpam-6358	256	10	)	)	PUNCT
ejpam-6358	256	11	(	(	PUNCT
ejpam-6358	256	12	2025	2025	NUM
ejpam-6358	256	13	)	)	PUNCT
ejpam-6358	256	14	,	,	PUNCT
ejpam-6358	256	15	6358	6358	NUM
ejpam-6358	256	16	10	10	NUM
ejpam-6358	256	17	of	of	ADP
ejpam-6358	256	18	24	24	NUM
ejpam-6358	256	19	otherwise	otherwise	ADV
ejpam-6358	256	20	,	,	PUNCT
ejpam-6358	256	21	∅	∅	NOUN
ejpam-6358	256	22	is	be	AUX
ejpam-6358	256	23	an	an	DET
ejpam-6358	256	24	undefinable	undefinable	ADJ
ejpam-6358	256	25	(	(	PUNCT
ejpam-6358	256	26	rough	rough	ADJ
ejpam-6358	256	27	)	)	PUNCT
ejpam-6358	256	28	set	set	NOUN
ejpam-6358	256	29	,	,	PUNCT
ejpam-6358	256	30	and	and	CCONJ
ejpam-6358	256	31	the	the	DET
ejpam-6358	256	32	accuracy	accuracy	NOUN
ejpam-6358	256	33	measure	measure	NOUN
ejpam-6358	256	34	acc	acc	PROPN
ejpam-6358	256	35	⋆ikj	⋆ikj	PROPN
ejpam-6358	256	36	r	r	X
ejpam-6358	256	37	(	(	PUNCT
ejpam-6358	256	38	∅	∅	NOUN
ejpam-6358	256	39	)	)	PUNCT
ejpam-6358	256	40	is	be	AUX
ejpam-6358	256	41	considered	consider	VERB
ejpam-6358	256	42	an	an	DET
ejpam-6358	256	43	indefinite	indefinite	ADJ
ejpam-6358	256	44	quantity	quantity	NOUN
ejpam-6358	256	45	.	.	PUNCT
ejpam-6358	257	1	theorem	theorem	ADJ
ejpam-6358	257	2	2	2	NUM
ejpam-6358	257	3	presents	present	VERB
ejpam-6358	257	4	a	a	DET
ejpam-6358	257	5	significant	significant	ADJ
ejpam-6358	257	6	result	result	NOUN
ejpam-6358	257	7	for	for	ADP
ejpam-6358	257	8	deriving	derive	VERB
ejpam-6358	257	9	a	a	DET
ejpam-6358	257	10	general	general	ADJ
ejpam-6358	257	11	topology	topology	NOUN
ejpam-6358	257	12	from	from	ADP
ejpam-6358	257	13	an	an	DET
ejpam-6358	257	14	arbitrary	arbitrary	ADJ
ejpam-6358	257	15	neighborhood	neighborhood	NOUN
ejpam-6358	257	16	system	system	NOUN
ejpam-6358	257	17	.	.	PUNCT
ejpam-6358	258	1	this	this	DET
ejpam-6358	258	2	method	method	NOUN
ejpam-6358	258	3	was	be	AUX
ejpam-6358	258	4	initially	initially	ADV
ejpam-6358	258	5	proposed	propose	VERB
ejpam-6358	258	6	by	by	ADP
ejpam-6358	258	7	abo	abo	PROPN
ejpam-6358	258	8	khadra	khadra	NOUN
ejpam-6358	258	9	et	et	PROPN
ejpam-6358	258	10	al	al	PROPN
ejpam-6358	258	11	.	.	PROPN
ejpam-6358	259	1	(	(	PUNCT
ejpam-6358	259	2	2007	2007	NUM
ejpam-6358	259	3	)	)	PUNCT
ejpam-6358	260	1	[	[	X
ejpam-6358	260	2	7	7	X
ejpam-6358	260	3	]	]	PUNCT
ejpam-6358	260	4	and	and	CCONJ
ejpam-6358	260	5	later	later	ADV
ejpam-6358	260	6	extended	extend	VERB
ejpam-6358	260	7	by	by	ADP
ejpam-6358	260	8	abd	abd	PROPN
ejpam-6358	260	9	el	el	PROPN
ejpam-6358	260	10	-	-	PROPN
ejpam-6358	260	11	monsef	monsef	PROPN
ejpam-6358	260	12	et	et	PROPN
ejpam-6358	260	13	al	al	PROPN
ejpam-6358	260	14	.	.	PROPN
ejpam-6358	260	15	(	(	PUNCT
ejpam-6358	260	16	2014	2014	NUM
ejpam-6358	260	17	)	)	PUNCT
ejpam-6358	261	1	[	[	X
ejpam-6358	261	2	9	9	NUM
ejpam-6358	261	3	]	]	PUNCT
ejpam-6358	261	4	.	.	PUNCT
ejpam-6358	262	1	since	since	SCONJ
ejpam-6358	262	2	then	then	ADV
ejpam-6358	262	3	,	,	PUNCT
ejpam-6358	262	4	this	this	DET
ejpam-6358	262	5	approach	approach	NOUN
ejpam-6358	262	6	has	have	AUX
ejpam-6358	262	7	been	be	AUX
ejpam-6358	262	8	widely	widely	ADV
ejpam-6358	262	9	adopted	adopt	VERB
ejpam-6358	262	10	by	by	ADP
ejpam-6358	262	11	researchers	researcher	NOUN
ejpam-6358	262	12	to	to	PART
ejpam-6358	262	13	construct	construct	VERB
ejpam-6358	262	14	various	various	ADJ
ejpam-6358	262	15	topological	topological	ADJ
ejpam-6358	262	16	frameworks	framework	NOUN
ejpam-6358	262	17	,	,	PUNCT
ejpam-6358	262	18	as	as	SCONJ
ejpam-6358	262	19	demonstrated	demonstrate	VERB
ejpam-6358	262	20	in	in	ADP
ejpam-6358	262	21	theorem	theorem	ADJ
ejpam-6358	262	22	2	2	NUM
ejpam-6358	262	23	.	.	PUNCT
ejpam-6358	262	24	theorem	theorem	NOUN
ejpam-6358	262	25	2	2	NUM
ejpam-6358	262	26	.	.	PUNCT
ejpam-6358	262	27	let	let	VERB
ejpam-6358	262	28	u	u	PRON
ejpam-6358	262	29	be	be	AUX
ejpam-6358	262	30	a	a	DET
ejpam-6358	262	31	universal	universal	ADJ
ejpam-6358	262	32	set	set	NOUN
ejpam-6358	262	33	and	and	CCONJ
ejpam-6358	262	34	let	let	VERB
ejpam-6358	262	35	j	j	PROPN
ejpam-6358	262	36	∈	∈	PROPN
ejpam-6358	262	37	ω	ω	PROPN
ejpam-6358	262	38	.	.	PUNCT
ejpam-6358	263	1	then	then	ADV
ejpam-6358	263	2	,	,	PUNCT
ejpam-6358	263	3	(	(	PUNCT
ejpam-6358	263	4	i	i	NOUN
ejpam-6358	263	5	)	)	PUNCT
ejpam-6358	263	6	fundamental	fundamental	ADJ
ejpam-6358	263	7	method	method	NOUN
ejpam-6358	263	8	[	[	X
ejpam-6358	263	9	7	7	NUM
ejpam-6358	263	10	,	,	PUNCT
ejpam-6358	263	11	9	9	NUM
ejpam-6358	263	12	]	]	PUNCT
ejpam-6358	263	13	:	:	PUNCT
ejpam-6358	263	14	the	the	DET
ejpam-6358	263	15	collection	collection	NOUN
ejpam-6358	263	16	⊤ωj	⊤ωj	PROPN
ejpam-6358	264	1	=	=	SYM
ejpam-6358	265	1	{	{	PUNCT
ejpam-6358	265	2	f	f	PROPN
ejpam-6358	265	3	⊆	⊆	NUM
ejpam-6358	265	4	u	u	NOUN
ejpam-6358	265	5	:	:	PUNCT
ejpam-6358	265	6	ωj(s	ωj(s	NUM
ejpam-6358	265	7	)	)	PUNCT
ejpam-6358	265	8	⊆	⊆	NUM
ejpam-6358	265	9	f	f	NOUN
ejpam-6358	265	10	,	,	PUNCT
ejpam-6358	265	11	∀s	∀s	PROPN
ejpam-6358	265	12	∈	∈	PROPN
ejpam-6358	265	13	f	f	X
ejpam-6358	265	14	}	}	PUNCT
ejpam-6358	265	15	forms	form	VERB
ejpam-6358	265	16	a	a	DET
ejpam-6358	265	17	topology	topology	NOUN
ejpam-6358	265	18	on	on	ADP
ejpam-6358	265	19	u	u	PROPN
ejpam-6358	265	20	.	.	PUNCT
ejpam-6358	266	1	(	(	PUNCT
ejpam-6358	266	2	ii	ii	NOUN
ejpam-6358	266	3	)	)	PUNCT
ejpam-6358	266	4	adhesion	adhesion	NOUN
ejpam-6358	266	5	topologies	topology	NOUN
ejpam-6358	266	6	[	[	X
ejpam-6358	266	7	17	17	NUM
ejpam-6358	266	8	,	,	PUNCT
ejpam-6358	266	9	18	18	NUM
ejpam-6358	266	10	,	,	PUNCT
ejpam-6358	266	11	20	20	NUM
ejpam-6358	266	12	]	]	PUNCT
ejpam-6358	266	13	:	:	PUNCT
ejpam-6358	266	14	the	the	DET
ejpam-6358	266	15	collection	collection	NOUN
ejpam-6358	266	16	⊤ρj	⊤ρj	NOUN
ejpam-6358	266	17	=	=	PUNCT
ejpam-6358	266	18	{	{	PUNCT
ejpam-6358	266	19	f	f	PROPN
ejpam-6358	266	20	⊆	⊆	NUM
ejpam-6358	266	21	u	u	NOUN
ejpam-6358	266	22	:	:	PUNCT
ejpam-6358	266	23	ρj(s	ρj(s	NUM
ejpam-6358	266	24	)	)	PUNCT
ejpam-6358	266	25	⊆	⊆	NUM
ejpam-6358	266	26	f	f	NOUN
ejpam-6358	266	27	,	,	PUNCT
ejpam-6358	266	28	∀s	∀s	PROPN
ejpam-6358	266	29	∈	∈	PROPN
ejpam-6358	266	30	f	f	X
ejpam-6358	266	31	}	}	PUNCT
ejpam-6358	266	32	defines	define	VERB
ejpam-6358	266	33	a	a	DET
ejpam-6358	266	34	topology	topology	NOUN
ejpam-6358	266	35	on	on	ADP
ejpam-6358	266	36	u	u	PROPN
ejpam-6358	266	37	.	.	PUNCT
ejpam-6358	267	1	(	(	PUNCT
ejpam-6358	267	2	iii	iii	NOUN
ejpam-6358	267	3	)	)	PUNCT
ejpam-6358	267	4	ij	ij	NOUN
ejpam-6358	267	5	-	-	PUNCT
ejpam-6358	267	6	topologies	topology	NOUN
ejpam-6358	267	7	[	[	X
ejpam-6358	267	8	12	12	NUM
ejpam-6358	267	9	]	]	X
ejpam-6358	267	10	:	:	PUNCT
ejpam-6358	267	11	the	the	DET
ejpam-6358	267	12	collection	collection	NOUN
ejpam-6358	267	13	⊤ij	⊤ij	PROPN
ejpam-6358	268	1	=	=	PUNCT
ejpam-6358	268	2	{	{	PUNCT
ejpam-6358	268	3	f	f	PROPN
ejpam-6358	268	4	⊆	⊆	NUM
ejpam-6358	268	5	u	u	NOUN
ejpam-6358	268	6	:	:	PUNCT
ejpam-6358	268	7	ij(s	ij(s	NUM
ejpam-6358	268	8	)	)	PUNCT
ejpam-6358	268	9	⊆	⊆	NUM
ejpam-6358	268	10	f	f	NOUN
ejpam-6358	268	11	,	,	PUNCT
ejpam-6358	268	12	∀s	∀s	PROPN
ejpam-6358	268	13	∈	∈	PROPN
ejpam-6358	268	14	f	f	AUX
ejpam-6358	268	15	}	}	PUNCT
ejpam-6358	268	16	constitutes	constitute	VERB
ejpam-6358	268	17	a	a	DET
ejpam-6358	268	18	topology	topology	NOUN
ejpam-6358	268	19	on	on	ADP
ejpam-6358	268	20	u	u	PROPN
ejpam-6358	268	21	.	.	PUNCT
ejpam-6358	269	1	definition	definition	NOUN
ejpam-6358	269	2	13	13	NUM
ejpam-6358	269	3	.	.	PUNCT
ejpam-6358	270	1	[	[	X
ejpam-6358	270	2	12	12	NUM
ejpam-6358	270	3	]	]	PUNCT
ejpam-6358	270	4	let	let	VERB
ejpam-6358	270	5	⊤ij	⊤ij	PROPN
ejpam-6358	270	6	be	be	AUX
ejpam-6358	270	7	a	a	DET
ejpam-6358	270	8	topology	topology	NOUN
ejpam-6358	270	9	on	on	ADP
ejpam-6358	270	10	u	u	NOUN
ejpam-6358	270	11	as	as	SCONJ
ejpam-6358	270	12	defined	define	VERB
ejpam-6358	270	13	in	in	ADP
ejpam-6358	270	14	the	the	DET
ejpam-6358	270	15	theorem	theorem	NOUN
ejpam-6358	270	16	above	above	ADV
ejpam-6358	270	17	,	,	PUNCT
ejpam-6358	270	18	for	for	ADP
ejpam-6358	270	19	all	all	DET
ejpam-6358	270	20	j	j	PROPN
ejpam-6358	270	21	∈	∈	PROPN
ejpam-6358	270	22	ω	ω	PROPN
ejpam-6358	270	23	,	,	PUNCT
ejpam-6358	270	24	and	and	CCONJ
ejpam-6358	270	25	let	let	VERB
ejpam-6358	270	26	f	f	PROPN
ejpam-6358	270	27	⊆	⊆	NUM
ejpam-6358	270	28	u	u	NOUN
ejpam-6358	270	29	.	.	PUNCT
ejpam-6358	271	1	the	the	DET
ejpam-6358	271	2	interior	interior	ADJ
ejpam-6358	271	3	and	and	CCONJ
ejpam-6358	271	4	closure	closure	NOUN
ejpam-6358	271	5	operators	operator	NOUN
ejpam-6358	271	6	of	of	ADP
ejpam-6358	271	7	f	f	PROPN
ejpam-6358	271	8	in	in	ADP
ejpam-6358	271	9	the	the	DET
ejpam-6358	271	10	topological	topological	ADJ
ejpam-6358	271	11	space	space	NOUN
ejpam-6358	271	12	(	(	PUNCT
ejpam-6358	271	13	u,⊤ij	u,⊤ij	PROPN
ejpam-6358	271	14	)	)	PUNCT
ejpam-6358	271	15	,	,	PUNCT
ejpam-6358	271	16	denoted	denote	VERB
ejpam-6358	271	17	by	by	ADP
ejpam-6358	271	18	⊤ij	⊤ij	PROPN
ejpam-6358	271	19	(	(	PUNCT
ejpam-6358	271	20	f	f	PROPN
ejpam-6358	271	21	)	)	PUNCT
ejpam-6358	271	22	and	and	CCONJ
ejpam-6358	271	23	⊤ij	⊤ij	PROPN
ejpam-6358	271	24	(	(	PUNCT
ejpam-6358	271	25	f	f	PROPN
ejpam-6358	271	26	)	)	PUNCT
ejpam-6358	271	27	,	,	PUNCT
ejpam-6358	271	28	are	be	AUX
ejpam-6358	271	29	referred	refer	VERB
ejpam-6358	271	30	to	to	ADP
ejpam-6358	271	31	as	as	ADP
ejpam-6358	271	32	the	the	DET
ejpam-6358	271	33	⊤ij	⊤ij	PROPN
ejpam-6358	271	34	-lower	-lower	PROPN
ejpam-6358	271	35	approximation	approximation	NOUN
ejpam-6358	271	36	and	and	CCONJ
ejpam-6358	271	37	⊤ij	⊤ij	PROPN
ejpam-6358	271	38	-upper	-upper	NOUN
ejpam-6358	271	39	approximation	approximation	NOUN
ejpam-6358	271	40	,	,	PUNCT
ejpam-6358	271	41	respectively	respectively	ADV
ejpam-6358	271	42	.	.	PUNCT
ejpam-6358	272	1	definition	definition	NOUN
ejpam-6358	272	2	14	14	NUM
ejpam-6358	272	3	.	.	PUNCT
ejpam-6358	273	1	[	[	X
ejpam-6358	273	2	12	12	NUM
ejpam-6358	273	3	]	]	PUNCT
ejpam-6358	273	4	the	the	DET
ejpam-6358	273	5	⊤ij	⊤ij	PROPN
ejpam-6358	273	6	-boundary	-boundary	ADJ
ejpam-6358	273	7	and	and	CCONJ
ejpam-6358	273	8	⊤ij	⊤ij	PROPN
ejpam-6358	273	9	-accuracy	-accuracy	NOUN
ejpam-6358	273	10	of	of	ADP
ejpam-6358	273	11	a	a	DET
ejpam-6358	273	12	subset	subset	NOUN
ejpam-6358	273	13	f	f	NOUN
ejpam-6358	273	14	in	in	ADP
ejpam-6358	273	15	a	a	DET
ejpam-6358	273	16	topological	topological	ADJ
ejpam-6358	273	17	space	space	NOUN
ejpam-6358	273	18	(	(	PUNCT
ejpam-6358	273	19	u,⊤ij	u,⊤ij	X
ejpam-6358	273	20	)	)	PUNCT
ejpam-6358	273	21	are	be	AUX
ejpam-6358	273	22	given	give	VERB
ejpam-6358	273	23	as	as	SCONJ
ejpam-6358	273	24	follows	follow	VERB
ejpam-6358	273	25	:	:	PUNCT
ejpam-6358	273	26	�	�	PROPN
ejpam-6358	273	27	the	the	DET
ejpam-6358	273	28	⊤ij	⊤ij	PROPN
ejpam-6358	273	29	-boundary	-boundary	PROPN
ejpam-6358	273	30	of	of	ADP
ejpam-6358	273	31	f	f	PROPN
ejpam-6358	273	32	is	be	AUX
ejpam-6358	273	33	given	give	VERB
ejpam-6358	273	34	by	by	ADP
ejpam-6358	273	35	:	:	PUNCT
ejpam-6358	273	36	bnd⊤ij	bnd⊤ij	PROPN
ejpam-6358	273	37	(	(	PUNCT
ejpam-6358	273	38	f	f	X
ejpam-6358	273	39	)	)	PUNCT
ejpam-6358	274	1	=	=	SYM
ejpam-6358	274	2	⊤ij	⊤ij	PROPN
ejpam-6358	274	3	(	(	PUNCT
ejpam-6358	274	4	f	f	PROPN
ejpam-6358	274	5	)	)	PUNCT
ejpam-6358	274	6	\	\	PROPN
ejpam-6358	275	1	⊤ij	⊤ij	PROPN
ejpam-6358	275	2	(	(	PUNCT
ejpam-6358	275	3	f	f	PROPN
ejpam-6358	275	4	)	)	PUNCT
ejpam-6358	275	5	�	�	PROPN
ejpam-6358	275	6	the	the	DET
ejpam-6358	275	7	⊤ij	⊤ij	PROPN
ejpam-6358	275	8	-accuracy	-accuracy	NOUN
ejpam-6358	275	9	of	of	ADP
ejpam-6358	275	10	f	f	PROPN
ejpam-6358	275	11	is	be	AUX
ejpam-6358	275	12	given	give	VERB
ejpam-6358	275	13	by	by	ADP
ejpam-6358	275	14	:	:	PUNCT
ejpam-6358	275	15	acc⊤ij	acc⊤ij	PROPN
ejpam-6358	275	16	(	(	PUNCT
ejpam-6358	275	17	f	f	PROPN
ejpam-6358	275	18	)	)	PUNCT
ejpam-6358	275	19	=	=	SYM
ejpam-6358	276	1	|⊤ij	|⊤ij	PROPN
ejpam-6358	276	2	(	(	PUNCT
ejpam-6358	276	3	f	f	X
ejpam-6358	276	4	)	)	PUNCT
ejpam-6358	276	5	|	|	ADV
ejpam-6358	276	6	|⊤ij	|⊤ij	PROPN
ejpam-6358	276	7	(	(	PUNCT
ejpam-6358	276	8	f	f	X
ejpam-6358	276	9	)	)	PUNCT
ejpam-6358	276	10	|	|	ADV
ejpam-6358	276	11	,	,	PUNCT
ejpam-6358	276	12	where	where	SCONJ
ejpam-6358	276	13	|⊤ij	|⊤ij	PROPN
ejpam-6358	276	14	(	(	PUNCT
ejpam-6358	276	15	f	f	X
ejpam-6358	276	16	)	)	PUNCT
ejpam-6358	276	17	|	|	ADV
ejpam-6358	276	18	̸=	̸=	PROPN
ejpam-6358	276	19	0	0	NUM
ejpam-6358	276	20	.	.	PUNCT
ejpam-6358	277	1	r.	r.	PROPN
ejpam-6358	277	2	a.	a.	PROPN
ejpam-6358	277	3	hosny	hosny	PROPN
ejpam-6358	277	4	et	et	PROPN
ejpam-6358	277	5	al	al	PROPN
ejpam-6358	277	6	.	.	PUNCT
ejpam-6358	277	7	/	/	SYM
ejpam-6358	277	8	eur	eur	PROPN
ejpam-6358	277	9	.	.	PUNCT
ejpam-6358	278	1	j.	j.	PROPN
ejpam-6358	278	2	pure	pure	PROPN
ejpam-6358	278	3	appl	appl	PROPN
ejpam-6358	278	4	.	.	PROPN
ejpam-6358	278	5	math	math	PROPN
ejpam-6358	278	6	,	,	PUNCT
ejpam-6358	278	7	18	18	NUM
ejpam-6358	278	8	(	(	PUNCT
ejpam-6358	278	9	4	4	NUM
ejpam-6358	278	10	)	)	PUNCT
ejpam-6358	278	11	(	(	PUNCT
ejpam-6358	278	12	2025	2025	NUM
ejpam-6358	278	13	)	)	PUNCT
ejpam-6358	278	14	,	,	PUNCT
ejpam-6358	278	15	6358	6358	NUM
ejpam-6358	278	16	11	11	NUM
ejpam-6358	278	17	of	of	ADP
ejpam-6358	278	18	24	24	NUM
ejpam-6358	278	19	theorem	theorem	NOUN
ejpam-6358	278	20	3	3	NUM
ejpam-6358	278	21	.	.	PUNCT
ejpam-6358	279	1	[	[	X
ejpam-6358	279	2	40	40	NUM
ejpam-6358	279	3	]	]	PUNCT
ejpam-6358	279	4	let	let	VERB
ejpam-6358	279	5	(	(	PUNCT
ejpam-6358	279	6	u	u	NOUN
ejpam-6358	279	7	,	,	PUNCT
ejpam-6358	279	8	r	r	NOUN
ejpam-6358	279	9	,	,	PUNCT
ejpam-6358	279	10	k	k	NOUN
ejpam-6358	279	11	)	)	PUNCT
ejpam-6358	279	12	be	be	VERB
ejpam-6358	279	13	an	an	DET
ejpam-6358	279	14	ij	ij	ADJ
ejpam-6358	279	15	-	-	PUNCT
ejpam-6358	279	16	g	g	NOUN
ejpam-6358	279	17	approximation	approximation	NOUN
ejpam-6358	279	18	space	space	NOUN
ejpam-6358	279	19	,	,	PUNCT
ejpam-6358	279	20	and	and	CCONJ
ejpam-6358	279	21	let	let	VERB
ejpam-6358	279	22	s	s	PRON
ejpam-6358	279	23	∈	∈	PROPN
ejpam-6358	279	24	u	u	NOUN
ejpam-6358	279	25	.	.	PUNCT
ejpam-6358	280	1	for	for	ADP
ejpam-6358	280	2	all	all	DET
ejpam-6358	280	3	j	j	PROPN
ejpam-6358	280	4	∈	∈	PROPN
ejpam-6358	280	5	ω	ω	PROPN
ejpam-6358	280	6	,	,	PUNCT
ejpam-6358	280	7	the	the	DET
ejpam-6358	280	8	collection	collection	NOUN
ejpam-6358	280	9	τ	τ	X
ejpam-6358	280	10	i	i	NOUN
ejpam-6358	280	11	k	k	PROPN
ejpam-6358	280	12	j	j	PROPN
ejpam-6358	281	1	=	=	PRON
ejpam-6358	281	2	{	{	PUNCT
ejpam-6358	281	3	f	f	PROPN
ejpam-6358	281	4	⊆	⊆	NUM
ejpam-6358	281	5	u	u	NOUN
ejpam-6358	281	6	:	:	PUNCT
ejpam-6358	281	7	ikj	ikj	PROPN
ejpam-6358	281	8	(	(	PUNCT
ejpam-6358	281	9	s	s	NOUN
ejpam-6358	281	10	)	)	PUNCT
ejpam-6358	281	11	\	\	NOUN
ejpam-6358	282	1	f	f	PROPN
ejpam-6358	282	2	∈	∈	PROPN
ejpam-6358	282	3	k	k	PROPN
ejpam-6358	282	4	,	,	PUNCT
ejpam-6358	282	5	∀s	∀s	PROPN
ejpam-6358	282	6	∈	∈	PROPN
ejpam-6358	282	7	f	f	X
ejpam-6358	282	8	}	}	PUNCT
ejpam-6358	282	9	forms	form	VERB
ejpam-6358	282	10	a	a	DET
ejpam-6358	282	11	topology	topology	NOUN
ejpam-6358	282	12	on	on	ADP
ejpam-6358	282	13	u	u	PROPN
ejpam-6358	282	14	.	.	PUNCT
ejpam-6358	283	1	if	if	SCONJ
ejpam-6358	283	2	k	k	PROPN
ejpam-6358	283	3	=	=	PRON
ejpam-6358	283	4	{	{	PUNCT
ejpam-6358	283	5	∅	∅	NOUN
ejpam-6358	283	6	}	}	PUNCT
ejpam-6358	283	7	in	in	ADP
ejpam-6358	283	8	theorem	theorem	ADJ
ejpam-6358	283	9	5.2	5.2	NUM
ejpam-6358	284	1	[	[	X
ejpam-6358	284	2	40	40	NUM
ejpam-6358	284	3	]	]	PUNCT
ejpam-6358	284	4	,	,	PUNCT
ejpam-6358	284	5	then	then	ADV
ejpam-6358	284	6	the	the	DET
ejpam-6358	284	7	resulting	result	VERB
ejpam-6358	284	8	topologies	topology	NOUN
ejpam-6358	284	9	coincide	coincide	VERB
ejpam-6358	284	10	with	with	ADP
ejpam-6358	284	11	those	those	PRON
ejpam-6358	284	12	established	establish	VERB
ejpam-6358	284	13	in	in	ADP
ejpam-6358	284	14	theorem	theorem	ADJ
ejpam-6358	284	15	2.11	2.11	NUM
ejpam-6358	284	16	of	of	ADP
ejpam-6358	284	17	[	[	X
ejpam-6358	284	18	12	12	NUM
ejpam-6358	284	19	]	]	PUNCT
ejpam-6358	284	20	.	.	PUNCT
ejpam-6358	285	1	consequently	consequently	ADV
ejpam-6358	285	2	,	,	PUNCT
ejpam-6358	285	3	the	the	DET
ejpam-6358	285	4	findings	finding	NOUN
ejpam-6358	285	5	in	in	ADP
ejpam-6358	285	6	[	[	X
ejpam-6358	285	7	40	40	NUM
ejpam-6358	285	8	]	]	PUNCT
ejpam-6358	285	9	serves	serve	VERB
ejpam-6358	285	10	as	as	ADP
ejpam-6358	285	11	a	a	DET
ejpam-6358	285	12	meaningful	meaningful	ADJ
ejpam-6358	285	13	extension	extension	NOUN
ejpam-6358	285	14	of	of	ADP
ejpam-6358	285	15	the	the	DET
ejpam-6358	285	16	work	work	NOUN
ejpam-6358	285	17	in	in	ADP
ejpam-6358	285	18	[	[	X
ejpam-6358	285	19	12	12	NUM
ejpam-6358	285	20	]	]	PUNCT
ejpam-6358	285	21	.	.	PUNCT
ejpam-6358	286	1	theorem	theorem	ADJ
ejpam-6358	286	2	4	4	NUM
ejpam-6358	286	3	.	.	PUNCT
ejpam-6358	287	1	[	[	X
ejpam-6358	287	2	42	42	NUM
ejpam-6358	287	3	]	]	PUNCT
ejpam-6358	287	4	let	let	VERB
ejpam-6358	287	5	(	(	PUNCT
ejpam-6358	287	6	u	u	NOUN
ejpam-6358	287	7	,	,	PUNCT
ejpam-6358	287	8	r	r	NOUN
ejpam-6358	287	9	,	,	PUNCT
ejpam-6358	287	10	k	k	NOUN
ejpam-6358	287	11	)	)	PUNCT
ejpam-6358	287	12	be	be	AUX
ejpam-6358	287	13	an	an	DET
ejpam-6358	287	14	ρj	ρj	NOUN
ejpam-6358	287	15	-	-	PUNCT
ejpam-6358	287	16	g	g	NOUN
ejpam-6358	287	17	approximation	approximation	NOUN
ejpam-6358	287	18	space	space	NOUN
ejpam-6358	287	19	and	and	CCONJ
ejpam-6358	287	20	s	s	NOUN
ejpam-6358	287	21	∈	∈	PROPN
ejpam-6358	287	22	u	u	NOUN
ejpam-6358	287	23	.	.	PUNCT
ejpam-6358	288	1	then	then	ADV
ejpam-6358	288	2	,	,	PUNCT
ejpam-6358	288	3	for	for	ADP
ejpam-6358	288	4	all	all	DET
ejpam-6358	288	5	j	j	PROPN
ejpam-6358	288	6	∈	∈	PROPN
ejpam-6358	288	7	ω	ω	PROPN
ejpam-6358	288	8	,	,	PUNCT
ejpam-6358	288	9	the	the	DET
ejpam-6358	288	10	collection	collection	NOUN
ejpam-6358	288	11	τρ	τρ	ADP
ejpam-6358	288	12	k	k	PROPN
ejpam-6358	288	13	j	j	PROPN
ejpam-6358	288	14	=	=	PRON
ejpam-6358	288	15	{	{	PUNCT
ejpam-6358	288	16	f	f	PROPN
ejpam-6358	288	17	⊆	⊆	NUM
ejpam-6358	288	18	u	u	NOUN
ejpam-6358	288	19	:	:	PUNCT
ejpam-6358	288	20	ρj(s	ρj(s	NUM
ejpam-6358	288	21	)	)	PUNCT
ejpam-6358	288	22	\	\	X
ejpam-6358	289	1	f	f	PROPN
ejpam-6358	289	2	∈	∈	PROPN
ejpam-6358	289	3	k	k	PROPN
ejpam-6358	289	4	,	,	PUNCT
ejpam-6358	289	5	∀s	∀s	PROPN
ejpam-6358	289	6	∈	∈	PROPN
ejpam-6358	289	7	f	f	AUX
ejpam-6358	289	8	}	}	PUNCT
ejpam-6358	289	9	constitutes	constitute	VERB
ejpam-6358	289	10	a	a	DET
ejpam-6358	289	11	topology	topology	NOUN
ejpam-6358	289	12	on	on	ADP
ejpam-6358	289	13	u	u	PROPN
ejpam-6358	289	14	.	.	PUNCT
ejpam-6358	290	1	3	3	X
ejpam-6358	290	2	.	.	X
ejpam-6358	290	3	main	main	ADJ
ejpam-6358	290	4	results	result	NOUN
ejpam-6358	290	5	this	this	DET
ejpam-6358	290	6	section	section	NOUN
ejpam-6358	290	7	constitutes	constitute	VERB
ejpam-6358	290	8	the	the	DET
ejpam-6358	290	9	core	core	NOUN
ejpam-6358	290	10	of	of	ADP
ejpam-6358	290	11	our	our	PRON
ejpam-6358	290	12	research	research	NOUN
ejpam-6358	290	13	,	,	PUNCT
ejpam-6358	290	14	where	where	SCONJ
ejpam-6358	290	15	we	we	PRON
ejpam-6358	290	16	critically	critically	ADV
ejpam-6358	290	17	examine	examine	VERB
ejpam-6358	290	18	the	the	DET
ejpam-6358	290	19	errors	error	NOUN
ejpam-6358	290	20	identified	identify	VERB
ejpam-6358	290	21	in	in	ADP
ejpam-6358	290	22	the	the	DET
ejpam-6358	290	23	study	study	NOUN
ejpam-6358	290	24	by	by	ADP
ejpam-6358	290	25	t.	t.	PROPN
ejpam-6358	290	26	al	al	PROPN
ejpam-6358	290	27	-	-	PUNCT
ejpam-6358	290	28	shami	shami	PROPN
ejpam-6358	290	29	and	and	CCONJ
ejpam-6358	290	30	m.	m.	PROPN
ejpam-6358	290	31	hosny	hosny	PROPN
ejpam-6358	291	1	[	[	X
ejpam-6358	291	2	40	40	NUM
ejpam-6358	291	3	]	]	PUNCT
ejpam-6358	291	4	.	.	PUNCT
ejpam-6358	292	1	we	we	PRON
ejpam-6358	292	2	provide	provide	VERB
ejpam-6358	292	3	multiple	multiple	ADJ
ejpam-6358	292	4	counterexamples	counterexample	NOUN
ejpam-6358	292	5	to	to	PART
ejpam-6358	292	6	substantiate	substantiate	VERB
ejpam-6358	292	7	these	these	DET
ejpam-6358	292	8	inaccuracies	inaccuracy	NOUN
ejpam-6358	292	9	and	and	CCONJ
ejpam-6358	292	10	propose	propose	VERB
ejpam-6358	292	11	necessary	necessary	ADJ
ejpam-6358	292	12	corrections	correction	NOUN
ejpam-6358	292	13	.	.	PUNCT
ejpam-6358	293	1	additionally	additionally	ADV
ejpam-6358	293	2	,	,	PUNCT
ejpam-6358	293	3	we	we	PRON
ejpam-6358	293	4	refine	refine	VERB
ejpam-6358	293	5	and	and	CCONJ
ejpam-6358	293	6	amend	amend	VERB
ejpam-6358	293	7	errors	error	NOUN
ejpam-6358	293	8	in	in	ADP
ejpam-6358	293	9	the	the	DET
ejpam-6358	293	10	proofs	proof	NOUN
ejpam-6358	293	11	of	of	ADP
ejpam-6358	293	12	certain	certain	ADJ
ejpam-6358	293	13	results	result	NOUN
ejpam-6358	293	14	while	while	SCONJ
ejpam-6358	293	15	addressing	address	VERB
ejpam-6358	293	16	inconsistencies	inconsistency	NOUN
ejpam-6358	293	17	in	in	ADP
ejpam-6358	293	18	the	the	DET
ejpam-6358	293	19	examples	example	NOUN
ejpam-6358	293	20	and	and	CCONJ
ejpam-6358	293	21	comparison	comparison	NOUN
ejpam-6358	293	22	tables	table	NOUN
ejpam-6358	293	23	presented	present	VERB
ejpam-6358	293	24	in	in	ADP
ejpam-6358	293	25	their	their	PRON
ejpam-6358	293	26	study	study	NOUN
ejpam-6358	293	27	.	.	PUNCT
ejpam-6358	294	1	the	the	DET
ejpam-6358	294	2	following	follow	VERB
ejpam-6358	294	3	theorem	theorem	NOUN
ejpam-6358	294	4	,	,	PUNCT
ejpam-6358	294	5	originally	originally	ADV
ejpam-6358	294	6	stated	state	VERB
ejpam-6358	294	7	as	as	ADP
ejpam-6358	294	8	theorem	theorem	VERB
ejpam-6358	294	9	3.4	3.4	NUM
ejpam-6358	294	10	in	in	ADP
ejpam-6358	294	11	[	[	X
ejpam-6358	294	12	40	40	NUM
ejpam-6358	294	13	]	]	PUNCT
ejpam-6358	294	14	,	,	PUNCT
ejpam-6358	294	15	contains	contain	VERB
ejpam-6358	294	16	errors	error	NOUN
ejpam-6358	294	17	requiring	require	VERB
ejpam-6358	294	18	correction	correction	NOUN
ejpam-6358	294	19	.	.	PUNCT
ejpam-6358	295	1	theorem	theorem	NOUN
ejpam-6358	295	2	5	5	NUM
ejpam-6358	295	3	.	.	PUNCT
ejpam-6358	296	1	[	[	X
ejpam-6358	296	2	40	40	NUM
ejpam-6358	296	3	]	]	PUNCT
ejpam-6358	296	4	let	let	VERB
ejpam-6358	296	5	(	(	PUNCT
ejpam-6358	296	6	u	u	NOUN
ejpam-6358	296	7	,	,	PUNCT
ejpam-6358	296	8	r	r	NOUN
ejpam-6358	296	9	,	,	PUNCT
ejpam-6358	296	10	k	k	NOUN
ejpam-6358	296	11	)	)	PUNCT
ejpam-6358	296	12	be	be	VERB
ejpam-6358	296	13	an	an	DET
ejpam-6358	296	14	ij	ij	ADJ
ejpam-6358	296	15	-	-	PUNCT
ejpam-6358	296	16	g	g	NOUN
ejpam-6358	296	17	approximation	approximation	NOUN
ejpam-6358	296	18	space	space	NOUN
ejpam-6358	296	19	.	.	PUNCT
ejpam-6358	297	1	if	if	SCONJ
ejpam-6358	297	2	s	s	X
ejpam-6358	297	3	∈	∈	PROPN
ejpam-6358	297	4	u	u	NOUN
ejpam-6358	297	5	,	,	PUNCT
ejpam-6358	297	6	then	then	ADV
ejpam-6358	297	7	the	the	DET
ejpam-6358	297	8	following	follow	VERB
ejpam-6358	297	9	properties	property	NOUN
ejpam-6358	297	10	hold	hold	VERB
ejpam-6358	297	11	:	:	PUNCT
ejpam-6358	297	12	(	(	PUNCT
ejpam-6358	297	13	i	i	NOUN
ejpam-6358	297	14	)	)	PUNCT
ejpam-6358	297	15	iki	iki	PROPN
ejpam-6358	297	16	(	(	PUNCT
ejpam-6358	297	17	s	s	NOUN
ejpam-6358	297	18	)	)	PUNCT
ejpam-6358	297	19	⊆	⊆	NUM
ejpam-6358	297	20	ika	ika	X
ejpam-6358	297	21	(	(	PUNCT
ejpam-6358	297	22	s	s	NOUN
ejpam-6358	297	23	)	)	PUNCT
ejpam-6358	297	24	∩	∩	ADJ
ejpam-6358	297	25	ikb	ikb	PROPN
ejpam-6358	297	26	(	(	PUNCT
ejpam-6358	297	27	s	s	NOUN
ejpam-6358	297	28	)	)	PUNCT
ejpam-6358	297	29	⊆	⊆	NUM
ejpam-6358	297	30	ika	ika	X
ejpam-6358	297	31	(	(	PUNCT
ejpam-6358	297	32	s	s	NOUN
ejpam-6358	297	33	)	)	PUNCT
ejpam-6358	297	34	∪	∪	NOUN
ejpam-6358	297	35	ikb	ikb	PROPN
ejpam-6358	297	36	(	(	PUNCT
ejpam-6358	297	37	s	s	NOUN
ejpam-6358	297	38	)	)	PUNCT
ejpam-6358	297	39	⊆	⊆	NUM
ejpam-6358	297	40	iku	iku	PROPN
ejpam-6358	297	41	(	(	PUNCT
ejpam-6358	297	42	s	s	NOUN
ejpam-6358	297	43	)	)	PUNCT
ejpam-6358	297	44	.	.	PUNCT
ejpam-6358	298	1	(	(	PUNCT
ejpam-6358	298	2	ii	ii	X
ejpam-6358	298	3	)	)	PUNCT
ejpam-6358	298	4	ik	ik	PROPN
ejpam-6358	298	5	<	<	X
ejpam-6358	298	6	i>(s	i>(s	NOUN
ejpam-6358	298	7	)	)	PUNCT
ejpam-6358	298	8	⊆	⊆	NUM
ejpam-6358	298	9	ik	ik	X
ejpam-6358	298	10	<	<	X
ejpam-6358	298	11	a>(s	a>(s	X
ejpam-6358	298	12	)	)	PUNCT
ejpam-6358	298	13	∩	∩	NOUN
ejpam-6358	298	14	ik	ik	PROPN
ejpam-6358	298	15	<	<	X
ejpam-6358	298	16	b>(s	b>(s	PRON
ejpam-6358	298	17	)	)	PUNCT
ejpam-6358	298	18	⊆	⊆	NUM
ejpam-6358	298	19	ik	ik	X
ejpam-6358	298	20	<	<	X
ejpam-6358	298	21	a>(s	a>(s	X
ejpam-6358	298	22	)	)	PUNCT
ejpam-6358	298	23	∪	∪	ADP
ejpam-6358	298	24	ik	ik	PROPN
ejpam-6358	298	25	<	<	X
ejpam-6358	298	26	b>(s	b>(s	PRON
ejpam-6358	298	27	)	)	PUNCT
ejpam-6358	298	28	⊆	⊆	NUM
ejpam-6358	298	29	ik	ik	X
ejpam-6358	298	30	<	<	X
ejpam-6358	298	31	u>(s	u>(s	NUM
ejpam-6358	298	32	)	)	PUNCT
ejpam-6358	298	33	.	.	PUNCT
ejpam-6358	299	1	(	(	PUNCT
ejpam-6358	299	2	iii	iii	X
ejpam-6358	299	3	)	)	PUNCT
ejpam-6358	299	4	if	if	SCONJ
ejpam-6358	299	5	r	r	NOUN
ejpam-6358	299	6	is	be	AUX
ejpam-6358	299	7	reflexive	reflexive	ADJ
ejpam-6358	299	8	,	,	PUNCT
ejpam-6358	299	9	then	then	ADV
ejpam-6358	299	10	ρj(s	ρj(s	NUM
ejpam-6358	299	11	)	)	PUNCT
ejpam-6358	299	12	∪	∪	ADP
ejpam-6358	299	13	ωj(s	ωj(s	NUM
ejpam-6358	299	14	)	)	PUNCT
ejpam-6358	299	15	⊆	⊆	NUM
ejpam-6358	299	16	ikj	ikj	X
ejpam-6358	299	17	(	(	PUNCT
ejpam-6358	299	18	s	s	NOUN
ejpam-6358	299	19	)	)	PUNCT
ejpam-6358	299	20	for	for	ADP
ejpam-6358	299	21	all	all	DET
ejpam-6358	299	22	j	j	PROPN
ejpam-6358	299	23	∈	∈	PROPN
ejpam-6358	299	24	ω	ω	PROPN
ejpam-6358	299	25	.	.	PUNCT
ejpam-6358	299	26	(	(	PUNCT
ejpam-6358	299	27	iv	iv	X
ejpam-6358	299	28	)	)	PUNCT
ejpam-6358	299	29	if	if	SCONJ
ejpam-6358	299	30	r	r	NOUN
ejpam-6358	299	31	is	be	AUX
ejpam-6358	299	32	serial	serial	ADJ
ejpam-6358	299	33	,	,	PUNCT
ejpam-6358	299	34	then	then	ADV
ejpam-6358	299	35	ρj(s	ρj(s	NUM
ejpam-6358	299	36	)	)	PUNCT
ejpam-6358	299	37	⊆	⊆	NUM
ejpam-6358	299	38	ikj	ikj	X
ejpam-6358	299	39	(	(	PUNCT
ejpam-6358	299	40	s	s	NOUN
ejpam-6358	299	41	)	)	PUNCT
ejpam-6358	299	42	for	for	ADP
ejpam-6358	299	43	all	all	DET
ejpam-6358	299	44	j	j	PROPN
ejpam-6358	299	45	∈	∈	PROPN
ejpam-6358	299	46	ω	ω	PROPN
ejpam-6358	299	47	.	.	PUNCT
ejpam-6358	299	48	(	(	PUNCT
ejpam-6358	299	49	v	v	NOUN
ejpam-6358	299	50	)	)	PUNCT
ejpam-6358	299	51	if	if	SCONJ
ejpam-6358	299	52	r	r	NOUN
ejpam-6358	299	53	is	be	AUX
ejpam-6358	299	54	transitive	transitive	ADJ
ejpam-6358	299	55	,	,	PUNCT
ejpam-6358	299	56	then	then	ADV
ejpam-6358	299	57	ikj	ikj	PROPN
ejpam-6358	299	58	(	(	PUNCT
ejpam-6358	299	59	s	s	NOUN
ejpam-6358	299	60	)	)	PUNCT
ejpam-6358	299	61	⊆	⊆	NUM
ejpam-6358	299	62	ik	ik	PROPN
ejpam-6358	299	63	<	<	X
ejpam-6358	299	64	j>(s	j>(s	NUM
ejpam-6358	299	65	)	)	PUNCT
ejpam-6358	299	66	for	for	ADP
ejpam-6358	299	67	each	each	DET
ejpam-6358	299	68	j	j	PROPN
ejpam-6358	299	69	∈	∈	PROPN
ejpam-6358	299	70	{	{	PUNCT
ejpam-6358	299	71	a	a	PROPN
ejpam-6358	299	72	,	,	PUNCT
ejpam-6358	299	73	b	b	NOUN
ejpam-6358	299	74	,	,	PUNCT
ejpam-6358	299	75	i	i	PRON
ejpam-6358	299	76	,	,	PUNCT
ejpam-6358	299	77	u	u	NOUN
ejpam-6358	299	78	}	}	PUNCT
ejpam-6358	299	79	.	.	PUNCT
ejpam-6358	300	1	remark	remark	PROPN
ejpam-6358	300	2	2	2	NUM
ejpam-6358	300	3	.	.	PUNCT
ejpam-6358	301	1	firstly	firstly	ADV
ejpam-6358	301	2	,	,	PUNCT
ejpam-6358	301	3	statements	statement	NOUN
ejpam-6358	301	4	(	(	PUNCT
ejpam-6358	301	5	1	1	NUM
ejpam-6358	301	6	)	)	PUNCT
ejpam-6358	301	7	and	and	CCONJ
ejpam-6358	301	8	(	(	PUNCT
ejpam-6358	301	9	2	2	X
ejpam-6358	301	10	)	)	PUNCT
ejpam-6358	301	11	are	be	AUX
ejpam-6358	301	12	incorrect	incorrect	ADJ
ejpam-6358	301	13	,	,	PUNCT
ejpam-6358	301	14	as	as	SCONJ
ejpam-6358	301	15	the	the	DET
ejpam-6358	301	16	equalities	equality	NOUN
ejpam-6358	301	17	can	can	AUX
ejpam-6358	301	18	not	not	PART
ejpam-6358	301	19	be	be	AUX
ejpam-6358	301	20	replaced	replace	VERB
ejpam-6358	301	21	by	by	ADP
ejpam-6358	301	22	subset	subset	ADJ
ejpam-6358	301	23	symbols	symbol	NOUN
ejpam-6358	301	24	according	accord	VERB
ejpam-6358	301	25	to	to	ADP
ejpam-6358	301	26	definition	definition	NOUN
ejpam-6358	301	27	2	2	NUM
ejpam-6358	301	28	.	.	PUNCT
ejpam-6358	302	1	the	the	DET
ejpam-6358	302	2	following	follow	VERB
ejpam-6358	302	3	examples	example	NOUN
ejpam-6358	302	4	demonstrate	demonstrate	VERB
ejpam-6358	302	5	errors	error	NOUN
ejpam-6358	302	6	in	in	ADP
ejpam-6358	302	7	the	the	DET
ejpam-6358	302	8	remaining	remain	VERB
ejpam-6358	302	9	statements	statement	NOUN
ejpam-6358	302	10	of	of	ADP
ejpam-6358	302	11	the	the	DET
ejpam-6358	302	12	preceding	precede	VERB
ejpam-6358	302	13	theorem	theorem	PROPN
ejpam-6358	302	14	.	.	PROPN
ejpam-6358	302	15	example	example	NOUN
ejpam-6358	302	16	1	1	NUM
ejpam-6358	302	17	.	.	X
ejpam-6358	303	1	consider	consider	VERB
ejpam-6358	303	2	u	u	PRON
ejpam-6358	303	3	=	=	X
ejpam-6358	303	4	{	{	PUNCT
ejpam-6358	303	5	p	p	X
ejpam-6358	303	6	,	,	PUNCT
ejpam-6358	303	7	q	q	ADJ
ejpam-6358	303	8	,	,	PUNCT
ejpam-6358	303	9	s	s	PROPN
ejpam-6358	303	10	,	,	PUNCT
ejpam-6358	303	11	t	t	PROPN
ejpam-6358	303	12	}	}	PUNCT
ejpam-6358	303	13	and	and	CCONJ
ejpam-6358	303	14	the	the	DET
ejpam-6358	303	15	reflexive	reflexive	PROPN
ejpam-6358	303	16	relation	relation	PROPN
ejpam-6358	303	17	r.	r.	PROPN
ejpam-6358	303	18	a.	a.	PROPN
ejpam-6358	303	19	hosny	hosny	PROPN
ejpam-6358	303	20	et	et	PROPN
ejpam-6358	303	21	al	al	PROPN
ejpam-6358	303	22	.	.	PUNCT
ejpam-6358	303	23	/	/	SYM
ejpam-6358	303	24	eur	eur	PROPN
ejpam-6358	303	25	.	.	PUNCT
ejpam-6358	304	1	j.	j.	PROPN
ejpam-6358	304	2	pure	pure	PROPN
ejpam-6358	304	3	appl	appl	PROPN
ejpam-6358	304	4	.	.	PROPN
ejpam-6358	304	5	math	math	PROPN
ejpam-6358	304	6	,	,	PUNCT
ejpam-6358	304	7	18	18	NUM
ejpam-6358	304	8	(	(	PUNCT
ejpam-6358	304	9	4	4	NUM
ejpam-6358	304	10	)	)	PUNCT
ejpam-6358	304	11	(	(	PUNCT
ejpam-6358	304	12	2025	2025	NUM
ejpam-6358	304	13	)	)	PUNCT
ejpam-6358	304	14	,	,	PUNCT
ejpam-6358	304	15	6358	6358	NUM
ejpam-6358	304	16	12	12	NUM
ejpam-6358	304	17	of	of	ADP
ejpam-6358	304	18	24	24	NUM
ejpam-6358	304	19	r	r	NOUN
ejpam-6358	304	20	=	=	PUNCT
ejpam-6358	304	21	{	{	PUNCT
ejpam-6358	304	22	(	(	PUNCT
ejpam-6358	304	23	p	p	X
ejpam-6358	304	24	,	,	PUNCT
ejpam-6358	304	25	s	s	PART
ejpam-6358	304	26	)	)	PUNCT
ejpam-6358	304	27	,	,	PUNCT
ejpam-6358	304	28	(	(	PUNCT
ejpam-6358	304	29	p	p	X
ejpam-6358	304	30	,	,	PUNCT
ejpam-6358	304	31	t	t	PROPN
ejpam-6358	304	32	)	)	PUNCT
ejpam-6358	304	33	,	,	PUNCT
ejpam-6358	304	34	(	(	PUNCT
ejpam-6358	304	35	q	q	X
ejpam-6358	304	36	,	,	PUNCT
ejpam-6358	304	37	t	t	PROPN
ejpam-6358	304	38	)	)	PUNCT
ejpam-6358	304	39	,	,	PUNCT
ejpam-6358	304	40	(	(	PUNCT
ejpam-6358	304	41	t	t	PROPN
ejpam-6358	304	42	,	,	PUNCT
ejpam-6358	304	43	q	q	NOUN
ejpam-6358	304	44	)	)	PUNCT
ejpam-6358	304	45	,	,	PUNCT
ejpam-6358	304	46	(	(	PUNCT
ejpam-6358	304	47	p	p	X
ejpam-6358	304	48	,	,	PUNCT
ejpam-6358	304	49	p	p	NOUN
ejpam-6358	304	50	)	)	PUNCT
ejpam-6358	304	51	,	,	PUNCT
ejpam-6358	304	52	(	(	PUNCT
ejpam-6358	304	53	q	q	X
ejpam-6358	304	54	,	,	PUNCT
ejpam-6358	304	55	q	q	NOUN
ejpam-6358	304	56	)	)	PUNCT
ejpam-6358	304	57	,	,	PUNCT
ejpam-6358	304	58	(	(	PUNCT
ejpam-6358	304	59	s	s	X
ejpam-6358	304	60	,	,	PUNCT
ejpam-6358	304	61	s	s	PART
ejpam-6358	304	62	)	)	PUNCT
ejpam-6358	304	63	,	,	PUNCT
ejpam-6358	304	64	(	(	PUNCT
ejpam-6358	304	65	t	t	PROPN
ejpam-6358	304	66	,	,	PUNCT
ejpam-6358	304	67	t	t	PROPN
ejpam-6358	304	68	)	)	PUNCT
ejpam-6358	304	69	}	}	PUNCT
ejpam-6358	304	70	on	on	ADP
ejpam-6358	304	71	u	u	NOUN
ejpam-6358	304	72	.	.	PUNCT
ejpam-6358	305	1	the	the	DET
ejpam-6358	305	2	associated	associate	VERB
ejpam-6358	305	3	neighborhoods	neighborhood	NOUN
ejpam-6358	305	4	for	for	ADP
ejpam-6358	305	5	the	the	DET
ejpam-6358	305	6	element	element	NOUN
ejpam-6358	305	7	t	t	PROPN
ejpam-6358	305	8	are	be	AUX
ejpam-6358	305	9	given	give	VERB
ejpam-6358	305	10	as	as	SCONJ
ejpam-6358	305	11	follows	follow	VERB
ejpam-6358	305	12	:	:	PUNCT
ejpam-6358	305	13	�	�	PROPN
ejpam-6358	305	14	ωa(t	ωa(t	PUNCT
ejpam-6358	305	15	)	)	PUNCT
ejpam-6358	305	16	=	=	PRON
ejpam-6358	305	17	{	{	PUNCT
ejpam-6358	305	18	q	q	PROPN
ejpam-6358	305	19	,	,	PUNCT
ejpam-6358	305	20	t	t	PROPN
ejpam-6358	305	21	}	}	PUNCT
ejpam-6358	305	22	,	,	PUNCT
ejpam-6358	305	23	ωb(t	ωb(t	NUM
ejpam-6358	305	24	)	)	PUNCT
ejpam-6358	305	25	=	=	PRON
ejpam-6358	305	26	{	{	PUNCT
ejpam-6358	305	27	p	p	X
ejpam-6358	305	28	,	,	PUNCT
ejpam-6358	305	29	q	q	X
ejpam-6358	305	30	,	,	PUNCT
ejpam-6358	305	31	t	t	PROPN
ejpam-6358	305	32	}	}	PUNCT
ejpam-6358	305	33	,	,	PUNCT
ejpam-6358	305	34	ωi(t	ωi(t	PUNCT
ejpam-6358	305	35	)	)	PUNCT
ejpam-6358	305	36	=	=	PRON
ejpam-6358	305	37	{	{	PUNCT
ejpam-6358	305	38	q	q	PROPN
ejpam-6358	305	39	,	,	PUNCT
ejpam-6358	305	40	t	t	PROPN
ejpam-6358	305	41	}	}	PUNCT
ejpam-6358	305	42	,	,	PUNCT
ejpam-6358	305	43	ωu(t	ωu(t	NOUN
ejpam-6358	305	44	)	)	PUNCT
ejpam-6358	305	45	=	=	PRON
ejpam-6358	305	46	{	{	PUNCT
ejpam-6358	305	47	p	p	X
ejpam-6358	305	48	,	,	PUNCT
ejpam-6358	305	49	q	q	X
ejpam-6358	305	50	,	,	PUNCT
ejpam-6358	305	51	t	t	PROPN
ejpam-6358	305	52	}	}	PUNCT
ejpam-6358	305	53	,	,	PUNCT
ejpam-6358	305	54	�	�	PROPN
ejpam-6358	305	55	ω	ω	PROPN
ejpam-6358	305	56	<	<	X
ejpam-6358	305	57	a>(t	a>(t	X
ejpam-6358	305	58	)	)	PUNCT
ejpam-6358	305	59	=	=	NUM
ejpam-6358	305	60	{	{	PUNCT
ejpam-6358	305	61	t	t	PROPN
ejpam-6358	305	62	}	}	PUNCT
ejpam-6358	305	63	,	,	PUNCT
ejpam-6358	305	64	ω	ω	NOUN
ejpam-6358	305	65	<	<	NOUN
ejpam-6358	305	66	b>(t	b>(t	NOUN
ejpam-6358	305	67	)	)	PUNCT
ejpam-6358	305	68	=	=	SYM
ejpam-6358	305	69	{	{	PUNCT
ejpam-6358	305	70	q	q	PROPN
ejpam-6358	305	71	,	,	PUNCT
ejpam-6358	305	72	t	t	PROPN
ejpam-6358	305	73	}	}	PUNCT
ejpam-6358	305	74	,	,	PUNCT
ejpam-6358	306	1	ω	ω	X
ejpam-6358	306	2	<	<	X
ejpam-6358	306	3	i>(t	i>(t	NOUN
ejpam-6358	306	4	)	)	PUNCT
ejpam-6358	306	5	=	=	SYM
ejpam-6358	306	6	{	{	PUNCT
ejpam-6358	306	7	t	t	PROPN
ejpam-6358	306	8	}	}	PUNCT
ejpam-6358	306	9	,	,	PUNCT
ejpam-6358	307	1	ω	ω	X
ejpam-6358	307	2	<	<	X
ejpam-6358	307	3	u>(t	u>(t	NOUN
ejpam-6358	307	4	)	)	PUNCT
ejpam-6358	307	5	=	=	SYM
ejpam-6358	307	6	{	{	PUNCT
ejpam-6358	307	7	q	q	PROPN
ejpam-6358	307	8	,	,	PUNCT
ejpam-6358	307	9	t	t	PROPN
ejpam-6358	307	10	}	}	PUNCT
ejpam-6358	307	11	,	,	PUNCT
ejpam-6358	307	12	�	�	PROPN
ejpam-6358	307	13	ρa(t	ρa(t	NUM
ejpam-6358	307	14	)	)	PUNCT
ejpam-6358	307	15	=	=	PRON
ejpam-6358	307	16	{	{	PUNCT
ejpam-6358	307	17	q	q	PROPN
ejpam-6358	307	18	,	,	PUNCT
ejpam-6358	307	19	t	t	PROPN
ejpam-6358	307	20	}	}	PUNCT
ejpam-6358	307	21	,	,	PUNCT
ejpam-6358	307	22	ρb(t	ρb(t	NUM
ejpam-6358	307	23	)	)	PUNCT
ejpam-6358	307	24	=	=	PRON
ejpam-6358	307	25	{	{	PUNCT
ejpam-6358	307	26	t	t	NOUN
ejpam-6358	307	27	}	}	PUNCT
ejpam-6358	307	28	,	,	PUNCT
ejpam-6358	307	29	ρi(t	ρi(t	NUM
ejpam-6358	307	30	)	)	PUNCT
ejpam-6358	307	31	=	=	PRON
ejpam-6358	307	32	{	{	PUNCT
ejpam-6358	307	33	t	t	NOUN
ejpam-6358	307	34	}	}	PUNCT
ejpam-6358	307	35	,	,	PUNCT
ejpam-6358	307	36	ρu(t	ρu(t	NUM
ejpam-6358	307	37	)	)	PUNCT
ejpam-6358	307	38	=	=	PRON
ejpam-6358	307	39	{	{	PUNCT
ejpam-6358	307	40	q	q	PROPN
ejpam-6358	307	41	,	,	PUNCT
ejpam-6358	307	42	t	t	PROPN
ejpam-6358	307	43	}	}	PUNCT
ejpam-6358	307	44	,	,	PUNCT
ejpam-6358	307	45	�	�	PROPN
ejpam-6358	307	46	ρ	ρ	PROPN
ejpam-6358	307	47	<	<	NOUN
ejpam-6358	307	48	a>(t	a>(t	NOUN
ejpam-6358	307	49	)	)	PUNCT
ejpam-6358	307	50	=	=	NUM
ejpam-6358	307	51	{	{	PUNCT
ejpam-6358	307	52	t	t	PROPN
ejpam-6358	307	53	}	}	PUNCT
ejpam-6358	307	54	,	,	PUNCT
ejpam-6358	307	55	ρ	ρ	NOUN
ejpam-6358	307	56	<	<	NOUN
ejpam-6358	307	57	b>(t	b>(t	NOUN
ejpam-6358	307	58	)	)	PUNCT
ejpam-6358	308	1	=	=	SYM
ejpam-6358	308	2	{	{	PUNCT
ejpam-6358	308	3	q	q	PROPN
ejpam-6358	308	4	,	,	PUNCT
ejpam-6358	308	5	t	t	PROPN
ejpam-6358	308	6	}	}	PUNCT
ejpam-6358	308	7	,	,	PUNCT
ejpam-6358	308	8	ρ	ρ	NOUN
ejpam-6358	308	9	<	<	X
ejpam-6358	308	10	i>(t	i>(t	NOUN
ejpam-6358	308	11	)	)	PUNCT
ejpam-6358	308	12	=	=	SYM
ejpam-6358	308	13	{	{	PUNCT
ejpam-6358	308	14	t	t	PROPN
ejpam-6358	308	15	}	}	PUNCT
ejpam-6358	308	16	,	,	PUNCT
ejpam-6358	308	17	ρ	ρ	PROPN
ejpam-6358	308	18	<	<	X
ejpam-6358	308	19	u>(t	u>(t	NOUN
ejpam-6358	308	20	)	)	PUNCT
ejpam-6358	308	21	=	=	SYM
ejpam-6358	308	22	{	{	PUNCT
ejpam-6358	308	23	q	q	PROPN
ejpam-6358	308	24	,	,	PUNCT
ejpam-6358	308	25	t	t	PROPN
ejpam-6358	308	26	}	}	PUNCT
ejpam-6358	308	27	.	.	PUNCT
ejpam-6358	309	1	now	now	ADV
ejpam-6358	309	2	,	,	PUNCT
ejpam-6358	309	3	let	let	VERB
ejpam-6358	309	4	k	k	X
ejpam-6358	309	5	=	=	PRON
ejpam-6358	309	6	{	{	PUNCT
ejpam-6358	309	7	∅	∅	NOUN
ejpam-6358	309	8	,	,	PUNCT
ejpam-6358	309	9	{	{	PUNCT
ejpam-6358	309	10	t	t	NOUN
ejpam-6358	309	11	}	}	PUNCT
ejpam-6358	309	12	}	}	PUNCT
ejpam-6358	309	13	.	.	PUNCT
ejpam-6358	310	1	the	the	DET
ejpam-6358	310	2	corresponding	correspond	VERB
ejpam-6358	310	3	ikj	ikj	PROPN
ejpam-6358	310	4	-neighborhoods	-neighborhood	NOUN
ejpam-6358	310	5	are	be	AUX
ejpam-6358	310	6	:	:	PUNCT
ejpam-6358	310	7	�	�	PROPN
ejpam-6358	310	8	ika	ika	PROPN
ejpam-6358	310	9	(	(	PUNCT
ejpam-6358	310	10	t	t	PROPN
ejpam-6358	310	11	)	)	PUNCT
ejpam-6358	310	12	=	=	PRON
ejpam-6358	311	1	{	{	PUNCT
ejpam-6358	311	2	q	q	PROPN
ejpam-6358	311	3	,	,	PUNCT
ejpam-6358	311	4	t	t	PROPN
ejpam-6358	311	5	}	}	PUNCT
ejpam-6358	311	6	,	,	PUNCT
ejpam-6358	311	7	ikb	ikb	PROPN
ejpam-6358	311	8	(	(	PUNCT
ejpam-6358	311	9	t	t	NOUN
ejpam-6358	311	10	)	)	PUNCT
ejpam-6358	311	11	=	=	SYM
ejpam-6358	311	12	u	u	PROPN
ejpam-6358	311	13	,	,	PUNCT
ejpam-6358	311	14	iki	iki	PROPN
ejpam-6358	311	15	(	(	PUNCT
ejpam-6358	311	16	t	t	PROPN
ejpam-6358	311	17	)	)	PUNCT
ejpam-6358	311	18	=	=	PRON
ejpam-6358	311	19	{	{	PUNCT
ejpam-6358	311	20	q	q	PROPN
ejpam-6358	311	21	,	,	PUNCT
ejpam-6358	311	22	t	t	PROPN
ejpam-6358	311	23	}	}	PUNCT
ejpam-6358	311	24	,	,	PUNCT
ejpam-6358	311	25	iku	iku	PROPN
ejpam-6358	311	26	(	(	PUNCT
ejpam-6358	311	27	t	t	PROPN
ejpam-6358	311	28	)	)	PUNCT
ejpam-6358	311	29	=	=	SYM
ejpam-6358	311	30	u	u	PROPN
ejpam-6358	311	31	.	.	PUNCT
ejpam-6358	311	32	�	�	PROPN
ejpam-6358	311	33	ik	ik	PRON
ejpam-6358	311	34	<	<	X
ejpam-6358	311	35	a>(t	a>(t	NOUN
ejpam-6358	311	36	)	)	PUNCT
ejpam-6358	311	37	=	=	SYM
ejpam-6358	311	38	∅	∅	NOUN
ejpam-6358	311	39	,	,	PUNCT
ejpam-6358	311	40	ik	ik	X
ejpam-6358	311	41	<	<	X
ejpam-6358	311	42	b>(t	b>(t	NOUN
ejpam-6358	311	43	)	)	PUNCT
ejpam-6358	311	44	=	=	SYM
ejpam-6358	311	45	{	{	PUNCT
ejpam-6358	311	46	q	q	PROPN
ejpam-6358	311	47	,	,	PUNCT
ejpam-6358	311	48	t	t	PROPN
ejpam-6358	311	49	}	}	PUNCT
ejpam-6358	311	50	.	.	PUNCT
ejpam-6358	312	1	ik	ik	X
ejpam-6358	312	2	<	<	X
ejpam-6358	312	3	i>(t	i>(t	NOUN
ejpam-6358	312	4	)	)	PUNCT
ejpam-6358	312	5	=	=	SYM
ejpam-6358	312	6	∅	∅	NOUN
ejpam-6358	312	7	,	,	PUNCT
ejpam-6358	312	8	ik	ik	X
ejpam-6358	312	9	<	<	X
ejpam-6358	312	10	u>(t	u>(t	NOUN
ejpam-6358	312	11	)	)	PUNCT
ejpam-6358	312	12	=	=	SYM
ejpam-6358	312	13	{	{	PUNCT
ejpam-6358	312	14	q	q	PROPN
ejpam-6358	312	15	,	,	PUNCT
ejpam-6358	312	16	t	t	PROPN
ejpam-6358	312	17	}	}	PUNCT
ejpam-6358	312	18	.	.	PUNCT
ejpam-6358	313	1	it	it	PRON
ejpam-6358	313	2	is	be	AUX
ejpam-6358	313	3	evident	evident	ADJ
ejpam-6358	313	4	that	that	SCONJ
ejpam-6358	313	5	for	for	ADP
ejpam-6358	313	6	j	j	PROPN
ejpam-6358	313	7	∈	∈	PROPN
ejpam-6358	313	8	{	{	PUNCT
ejpam-6358	313	9	<	<	X
ejpam-6358	313	10	a	a	X
ejpam-6358	313	11	>	>	X
ejpam-6358	313	12	,	,	PUNCT
ejpam-6358	313	13	<	<	X
ejpam-6358	313	14	i	i	X
ejpam-6358	313	15	>	>	X
ejpam-6358	313	16	}	}	PUNCT
ejpam-6358	313	17	,	,	PUNCT
ejpam-6358	313	18	neither	neither	CCONJ
ejpam-6358	313	19	ρj(t	ρj(t	NUM
ejpam-6358	313	20	)	)	PUNCT
ejpam-6358	313	21	⊆	⊆	NUM
ejpam-6358	313	22	ikj	ikj	X
ejpam-6358	313	23	(	(	PUNCT
ejpam-6358	313	24	t	t	PROPN
ejpam-6358	313	25	)	)	PUNCT
ejpam-6358	313	26	nor	nor	CCONJ
ejpam-6358	313	27	ωj(t	ωj(t	NUM
ejpam-6358	313	28	)	)	PUNCT
ejpam-6358	313	29	⊆	⊆	NUM
ejpam-6358	313	30	ikj	ikj	X
ejpam-6358	313	31	(	(	PUNCT
ejpam-6358	313	32	t	t	PROPN
ejpam-6358	313	33	)	)	PUNCT
ejpam-6358	313	34	,	,	PUNCT
ejpam-6358	313	35	thereby	thereby	ADV
ejpam-6358	313	36	demonstrating	demonstrate	VERB
ejpam-6358	313	37	a	a	DET
ejpam-6358	313	38	counterexample	counterexample	NOUN
ejpam-6358	313	39	to	to	ADP
ejpam-6358	313	40	the	the	DET
ejpam-6358	313	41	corresponding	correspond	VERB
ejpam-6358	313	42	claims	claim	NOUN
ejpam-6358	313	43	.	.	PUNCT
ejpam-6358	314	1	example	example	NOUN
ejpam-6358	314	2	2	2	NUM
ejpam-6358	314	3	.	.	X
ejpam-6358	314	4	consider	consider	VERB
ejpam-6358	314	5	the	the	DET
ejpam-6358	314	6	set	set	NOUN
ejpam-6358	314	7	u	u	NOUN
ejpam-6358	314	8	=	=	PUNCT
ejpam-6358	314	9	{	{	PUNCT
ejpam-6358	314	10	p	p	X
ejpam-6358	314	11	,	,	PUNCT
ejpam-6358	314	12	q	q	ADJ
ejpam-6358	314	13	,	,	PUNCT
ejpam-6358	314	14	s	s	PROPN
ejpam-6358	314	15	,	,	PUNCT
ejpam-6358	314	16	t	t	PROPN
ejpam-6358	314	17	}	}	PUNCT
ejpam-6358	314	18	with	with	ADP
ejpam-6358	314	19	the	the	DET
ejpam-6358	314	20	serial	serial	ADJ
ejpam-6358	314	21	relation	relation	NOUN
ejpam-6358	314	22	r	r	NOUN
ejpam-6358	314	23	=	=	SYM
ejpam-6358	314	24	{	{	PUNCT
ejpam-6358	314	25	(	(	PUNCT
ejpam-6358	314	26	p	p	X
ejpam-6358	314	27	,	,	PUNCT
ejpam-6358	314	28	p	p	NOUN
ejpam-6358	314	29	)	)	PUNCT
ejpam-6358	314	30	,	,	PUNCT
ejpam-6358	314	31	(	(	PUNCT
ejpam-6358	314	32	s	s	X
ejpam-6358	314	33	,	,	PUNCT
ejpam-6358	314	34	p	p	NOUN
ejpam-6358	314	35	)	)	PUNCT
ejpam-6358	314	36	,	,	PUNCT
ejpam-6358	314	37	(	(	PUNCT
ejpam-6358	314	38	t	t	PROPN
ejpam-6358	314	39	,	,	PUNCT
ejpam-6358	314	40	p	p	NOUN
ejpam-6358	314	41	)	)	PUNCT
ejpam-6358	314	42	,	,	PUNCT
ejpam-6358	314	43	(	(	PUNCT
ejpam-6358	314	44	q	q	X
ejpam-6358	314	45	,	,	PUNCT
ejpam-6358	314	46	t	t	PROPN
ejpam-6358	314	47	)	)	PUNCT
ejpam-6358	314	48	,	,	PUNCT
ejpam-6358	314	49	(	(	PUNCT
ejpam-6358	314	50	t	t	PROPN
ejpam-6358	314	51	,	,	PUNCT
ejpam-6358	314	52	q	q	NOUN
ejpam-6358	314	53	)	)	PUNCT
ejpam-6358	314	54	,	,	PUNCT
ejpam-6358	314	55	(	(	PUNCT
ejpam-6358	314	56	t	t	PROPN
ejpam-6358	314	57	,	,	PUNCT
ejpam-6358	314	58	t	t	PROPN
ejpam-6358	314	59	)	)	PUNCT
ejpam-6358	314	60	}	}	PUNCT
ejpam-6358	314	61	.	.	PUNCT
ejpam-6358	315	1	the	the	DET
ejpam-6358	315	2	corresponding	correspond	VERB
ejpam-6358	315	3	neighborhoods	neighborhood	NOUN
ejpam-6358	315	4	under	under	ADP
ejpam-6358	315	5	ωa	ωa	ADJ
ejpam-6358	315	6	,	,	PUNCT
ejpam-6358	315	7	ρa	ρa	ADP
ejpam-6358	315	8	,	,	PUNCT
ejpam-6358	315	9	ia	ia	PROPN
ejpam-6358	315	10	are	be	AUX
ejpam-6358	315	11	given	give	VERB
ejpam-6358	315	12	as	as	SCONJ
ejpam-6358	315	13	follows	follow	VERB
ejpam-6358	315	14	:	:	PUNCT
ejpam-6358	315	15	�	�	PROPN
ejpam-6358	315	16	ωa(p	ωa(p	NUM
ejpam-6358	315	17	)	)	PUNCT
ejpam-6358	315	18	=	=	PRON
ejpam-6358	315	19	{	{	PUNCT
ejpam-6358	315	20	p	p	X
ejpam-6358	315	21	}	}	PUNCT
ejpam-6358	315	22	,	,	PUNCT
ejpam-6358	315	23	ωa(q	ωa(q	NUM
ejpam-6358	315	24	)	)	PUNCT
ejpam-6358	316	1	=	=	PRON
ejpam-6358	316	2	{	{	PUNCT
ejpam-6358	316	3	t	t	NOUN
ejpam-6358	316	4	}	}	PUNCT
ejpam-6358	316	5	,	,	PUNCT
ejpam-6358	316	6	ωa(s	ωa(s	NUM
ejpam-6358	316	7	)	)	PUNCT
ejpam-6358	316	8	=	=	SYM
ejpam-6358	316	9	{	{	PUNCT
ejpam-6358	316	10	p	p	X
ejpam-6358	316	11	}	}	PUNCT
ejpam-6358	316	12	,	,	PUNCT
ejpam-6358	316	13	ωa(t	ωa(t	NUM
ejpam-6358	316	14	)	)	PUNCT
ejpam-6358	316	15	=	=	PRON
ejpam-6358	316	16	{	{	PUNCT
ejpam-6358	316	17	p	p	X
ejpam-6358	316	18	,	,	PUNCT
ejpam-6358	316	19	q	q	X
ejpam-6358	316	20	,	,	PUNCT
ejpam-6358	316	21	t	t	PROPN
ejpam-6358	316	22	}	}	PUNCT
ejpam-6358	316	23	.	.	PUNCT
ejpam-6358	317	1	�	�	PROPN
ejpam-6358	317	2	ρa(p	ρa(p	NUM
ejpam-6358	317	3	)	)	PUNCT
ejpam-6358	318	1	=	=	PRON
ejpam-6358	318	2	{	{	PUNCT
ejpam-6358	318	3	p	p	X
ejpam-6358	318	4	,	,	PUNCT
ejpam-6358	318	5	s	s	PART
ejpam-6358	318	6	}	}	PUNCT
ejpam-6358	318	7	,	,	PUNCT
ejpam-6358	318	8	ρa(q	ρa(q	NOUN
ejpam-6358	318	9	)	)	PUNCT
ejpam-6358	318	10	=	=	PRON
ejpam-6358	318	11	{	{	PUNCT
ejpam-6358	318	12	q	q	X
ejpam-6358	318	13	}	}	PUNCT
ejpam-6358	318	14	,	,	PUNCT
ejpam-6358	318	15	ρa(s	ρa(s	NUM
ejpam-6358	318	16	)	)	PUNCT
ejpam-6358	319	1	=	=	PRON
ejpam-6358	319	2	{	{	PUNCT
ejpam-6358	319	3	p	p	X
ejpam-6358	319	4	,	,	PUNCT
ejpam-6358	319	5	s	s	PART
ejpam-6358	319	6	}	}	PUNCT
ejpam-6358	319	7	,	,	PUNCT
ejpam-6358	319	8	ρa(t	ρa(t	NUM
ejpam-6358	319	9	)	)	PUNCT
ejpam-6358	319	10	=	=	PRON
ejpam-6358	319	11	{	{	PUNCT
ejpam-6358	319	12	t	t	NOUN
ejpam-6358	319	13	}	}	PUNCT
ejpam-6358	319	14	.	.	PUNCT
ejpam-6358	320	1	�	�	PROPN
ejpam-6358	320	2	ia(p	ia(p	NUM
ejpam-6358	320	3	)	)	PUNCT
ejpam-6358	320	4	=	=	PRON
ejpam-6358	320	5	{	{	PUNCT
ejpam-6358	320	6	p	p	X
ejpam-6358	320	7	,	,	PUNCT
ejpam-6358	320	8	s	s	PROPN
ejpam-6358	320	9	,	,	PUNCT
ejpam-6358	320	10	t	t	PROPN
ejpam-6358	320	11	}	}	PUNCT
ejpam-6358	320	12	,	,	PUNCT
ejpam-6358	320	13	ia(q	ia(q	NOUN
ejpam-6358	320	14	)	)	PUNCT
ejpam-6358	320	15	=	=	PRON
ejpam-6358	320	16	{	{	PUNCT
ejpam-6358	320	17	q	q	PROPN
ejpam-6358	320	18	,	,	PUNCT
ejpam-6358	320	19	t	t	PROPN
ejpam-6358	320	20	}	}	PUNCT
ejpam-6358	320	21	,	,	PUNCT
ejpam-6358	320	22	ia(s	ia(s	NUM
ejpam-6358	320	23	)	)	PUNCT
ejpam-6358	320	24	=	=	PRON
ejpam-6358	320	25	{	{	PUNCT
ejpam-6358	320	26	p	p	X
ejpam-6358	320	27	,	,	PUNCT
ejpam-6358	320	28	s	s	PROPN
ejpam-6358	320	29	,	,	PUNCT
ejpam-6358	320	30	t	t	PROPN
ejpam-6358	320	31	}	}	PUNCT
ejpam-6358	320	32	,	,	PUNCT
ejpam-6358	320	33	ia(t	ia(t	PUNCT
ejpam-6358	320	34	)	)	PUNCT
ejpam-6358	321	1	=	=	SYM
ejpam-6358	321	2	u	u	NOUN
ejpam-6358	321	3	.	.	PUNCT
ejpam-6358	322	1	now	now	ADV
ejpam-6358	322	2	,	,	PUNCT
ejpam-6358	322	3	let	let	VERB
ejpam-6358	322	4	k	k	X
ejpam-6358	322	5	=	=	PRON
ejpam-6358	322	6	{	{	PUNCT
ejpam-6358	322	7	∅	∅	NOUN
ejpam-6358	322	8	,	,	PUNCT
ejpam-6358	322	9	{	{	PUNCT
ejpam-6358	322	10	t	t	NOUN
ejpam-6358	322	11	}	}	PUNCT
ejpam-6358	322	12	}	}	PUNCT
ejpam-6358	322	13	,	,	PUNCT
ejpam-6358	322	14	then	then	ADV
ejpam-6358	322	15	the	the	DET
ejpam-6358	322	16	ika	ika	NOUN
ejpam-6358	322	17	-neighborhoods	-neighborhood	NOUN
ejpam-6358	322	18	are	be	AUX
ejpam-6358	322	19	:	:	PUNCT
ejpam-6358	322	20	�	�	PROPN
ejpam-6358	322	21	ika	ika	PROPN
ejpam-6358	322	22	(	(	PUNCT
ejpam-6358	322	23	p	p	NOUN
ejpam-6358	322	24	)	)	PUNCT
ejpam-6358	322	25	=	=	SYM
ejpam-6358	322	26	{	{	PUNCT
ejpam-6358	322	27	p	p	X
ejpam-6358	322	28	,	,	PUNCT
ejpam-6358	322	29	s	s	PROPN
ejpam-6358	322	30	,	,	PUNCT
ejpam-6358	322	31	t	t	PROPN
ejpam-6358	322	32	}	}	PUNCT
ejpam-6358	322	33	,	,	PUNCT
ejpam-6358	322	34	ika	ika	X
ejpam-6358	322	35	(	(	PUNCT
ejpam-6358	322	36	q	q	NOUN
ejpam-6358	322	37	)	)	PUNCT
ejpam-6358	322	38	=	=	NOUN
ejpam-6358	322	39	∅	∅	NOUN
ejpam-6358	322	40	,	,	PUNCT
ejpam-6358	322	41	ika	ika	X
ejpam-6358	322	42	(	(	PUNCT
ejpam-6358	322	43	s	s	NOUN
ejpam-6358	322	44	)	)	PUNCT
ejpam-6358	322	45	=	=	SYM
ejpam-6358	322	46	{	{	PUNCT
ejpam-6358	322	47	p	p	X
ejpam-6358	322	48	,	,	PUNCT
ejpam-6358	322	49	s	s	PROPN
ejpam-6358	322	50	,	,	PUNCT
ejpam-6358	322	51	t	t	PROPN
ejpam-6358	322	52	}	}	PUNCT
ejpam-6358	322	53	,	,	PUNCT
ejpam-6358	322	54	ika	ika	X
ejpam-6358	322	55	(	(	PUNCT
ejpam-6358	322	56	t	t	PROPN
ejpam-6358	322	57	)	)	PUNCT
ejpam-6358	322	58	=	=	PRON
ejpam-6358	323	1	{	{	PUNCT
ejpam-6358	323	2	p	p	X
ejpam-6358	323	3	,	,	PUNCT
ejpam-6358	323	4	s	s	PROPN
ejpam-6358	323	5	,	,	PUNCT
ejpam-6358	323	6	t	t	PROPN
ejpam-6358	323	7	}	}	PUNCT
ejpam-6358	323	8	.	.	PUNCT
ejpam-6358	324	1	it	it	PRON
ejpam-6358	324	2	is	be	AUX
ejpam-6358	324	3	evident	evident	ADJ
ejpam-6358	324	4	that	that	SCONJ
ejpam-6358	324	5	ρa(q	ρa(q	NOUN
ejpam-6358	324	6	)	)	PUNCT
ejpam-6358	324	7	⊈	⊈	PROPN
ejpam-6358	324	8	ika	ika	X
ejpam-6358	324	9	(	(	PUNCT
ejpam-6358	324	10	q	q	NOUN
ejpam-6358	324	11	)	)	PUNCT
ejpam-6358	324	12	,	,	PUNCT
ejpam-6358	324	13	thereby	thereby	ADV
ejpam-6358	324	14	demonstrating	demonstrate	VERB
ejpam-6358	324	15	a	a	DET
ejpam-6358	324	16	counterexample	counterexample	NOUN
ejpam-6358	324	17	to	to	ADP
ejpam-6358	324	18	the	the	DET
ejpam-6358	324	19	claim	claim	NOUN
ejpam-6358	324	20	.	.	PUNCT
ejpam-6358	325	1	example	example	NOUN
ejpam-6358	326	1	3	3	X
ejpam-6358	326	2	.	.	X
ejpam-6358	326	3	consider	consider	VERB
ejpam-6358	326	4	u	u	PRON
ejpam-6358	326	5	=	=	X
ejpam-6358	326	6	{	{	PUNCT
ejpam-6358	326	7	p	p	X
ejpam-6358	326	8	,	,	PUNCT
ejpam-6358	326	9	q	q	ADJ
ejpam-6358	326	10	,	,	PUNCT
ejpam-6358	326	11	s	s	PROPN
ejpam-6358	326	12	,	,	PUNCT
ejpam-6358	326	13	t	t	PROPN
ejpam-6358	326	14	}	}	PUNCT
ejpam-6358	326	15	with	with	ADP
ejpam-6358	326	16	the	the	DET
ejpam-6358	326	17	transitive	transitive	ADJ
ejpam-6358	326	18	relation	relation	NOUN
ejpam-6358	326	19	r	r	NOUN
ejpam-6358	326	20	=	=	PRON
ejpam-6358	326	21	{	{	PUNCT
ejpam-6358	326	22	(	(	PUNCT
ejpam-6358	326	23	p	p	X
ejpam-6358	326	24	,	,	PUNCT
ejpam-6358	326	25	s	s	PART
ejpam-6358	326	26	)	)	PUNCT
ejpam-6358	326	27	,	,	PUNCT
ejpam-6358	326	28	(	(	PUNCT
ejpam-6358	326	29	p	p	X
ejpam-6358	326	30	,	,	PUNCT
ejpam-6358	326	31	t	t	PROPN
ejpam-6358	326	32	)	)	PUNCT
ejpam-6358	326	33	,	,	PUNCT
ejpam-6358	326	34	(	(	PUNCT
ejpam-6358	326	35	p	p	X
ejpam-6358	326	36	,	,	PUNCT
ejpam-6358	326	37	q	q	NOUN
ejpam-6358	326	38	)	)	PUNCT
ejpam-6358	326	39	,	,	PUNCT
ejpam-6358	326	40	(	(	PUNCT
ejpam-6358	326	41	t	t	PROPN
ejpam-6358	326	42	,	,	PUNCT
ejpam-6358	326	43	q	q	NOUN
ejpam-6358	326	44	)	)	PUNCT
ejpam-6358	326	45	,	,	PUNCT
ejpam-6358	326	46	(	(	PUNCT
ejpam-6358	326	47	t	t	PROPN
ejpam-6358	326	48	,	,	PUNCT
ejpam-6358	326	49	t	t	PROPN
ejpam-6358	326	50	)	)	PUNCT
ejpam-6358	326	51	}	}	PUNCT
ejpam-6358	326	52	.	.	PUNCT
ejpam-6358	327	1	the	the	DET
ejpam-6358	327	2	corresponding	correspond	VERB
ejpam-6358	327	3	neighborhoods	neighborhood	NOUN
ejpam-6358	327	4	under	under	ADP
ejpam-6358	327	5	ωb	ωb	PROPN
ejpam-6358	327	6	,	,	PUNCT
ejpam-6358	327	7	ω	ω	NOUN
ejpam-6358	327	8	<	<	X
ejpam-6358	327	9	b	b	X
ejpam-6358	327	10	>	>	X
ejpam-6358	327	11	,	,	PUNCT
ejpam-6358	327	12	ρb	ρb	PROPN
ejpam-6358	327	13	,	,	PUNCT
ejpam-6358	327	14	ρ	ρ	NOUN
ejpam-6358	327	15	<	<	X
ejpam-6358	327	16	b	b	X
ejpam-6358	327	17	>	>	X
ejpam-6358	327	18	are	be	AUX
ejpam-6358	327	19	as	as	SCONJ
ejpam-6358	327	20	follows	follow	VERB
ejpam-6358	327	21	:	:	PUNCT
ejpam-6358	327	22	�	�	PROPN
ejpam-6358	327	23	ωb(p	ωb(p	PART
ejpam-6358	327	24	)	)	PUNCT
ejpam-6358	327	25	=	=	SYM
ejpam-6358	327	26	∅	∅	NOUN
ejpam-6358	327	27	,	,	PUNCT
ejpam-6358	327	28	ωb(q	ωb(q	NUM
ejpam-6358	327	29	)	)	PUNCT
ejpam-6358	327	30	=	=	SYM
ejpam-6358	327	31	{	{	PUNCT
ejpam-6358	327	32	p	p	X
ejpam-6358	327	33	,	,	PUNCT
ejpam-6358	327	34	t	t	PROPN
ejpam-6358	327	35	}	}	PUNCT
ejpam-6358	327	36	,	,	PUNCT
ejpam-6358	327	37	ωb(s	ωb(	NOUN
ejpam-6358	327	38	)	)	PUNCT
ejpam-6358	328	1	=	=	PRON
ejpam-6358	328	2	{	{	PUNCT
ejpam-6358	328	3	p	p	X
ejpam-6358	328	4	}	}	PUNCT
ejpam-6358	328	5	,	,	PUNCT
ejpam-6358	328	6	ωb(t	ωb(t	NUM
ejpam-6358	328	7	)	)	PUNCT
ejpam-6358	328	8	=	=	PRON
ejpam-6358	328	9	{	{	PUNCT
ejpam-6358	328	10	p	p	X
ejpam-6358	328	11	,	,	PUNCT
ejpam-6358	328	12	t	t	PROPN
ejpam-6358	328	13	}	}	PUNCT
ejpam-6358	328	14	.	.	PUNCT
ejpam-6358	329	1	�	�	PROPN
ejpam-6358	329	2	ω	ω	PROPN
ejpam-6358	329	3	<	<	X
ejpam-6358	329	4	b>(p	b>(p	NUM
ejpam-6358	329	5	)	)	PUNCT
ejpam-6358	330	1	=	=	PRON
ejpam-6358	330	2	{	{	PUNCT
ejpam-6358	330	3	p	p	X
ejpam-6358	330	4	}	}	PUNCT
ejpam-6358	330	5	,	,	PUNCT
ejpam-6358	330	6	ω	ω	PROPN
ejpam-6358	330	7	<	<	X
ejpam-6358	330	8	b>(q	b>(q	X
ejpam-6358	330	9	)	)	PUNCT
ejpam-6358	331	1	=	=	NOUN
ejpam-6358	331	2	∅	∅	NOUN
ejpam-6358	331	3	,	,	PUNCT
ejpam-6358	331	4	ω	ω	NOUN
ejpam-6358	331	5	<	<	X
ejpam-6358	331	6	b>(s	b>(s	X
ejpam-6358	331	7	)	)	PUNCT
ejpam-6358	332	1	=	=	NOUN
ejpam-6358	332	2	∅	∅	NOUN
ejpam-6358	332	3	,	,	PUNCT
ejpam-6358	332	4	ω	ω	NOUN
ejpam-6358	332	5	<	<	NOUN
ejpam-6358	332	6	b>(t	b>(t	NOUN
ejpam-6358	332	7	)	)	PUNCT
ejpam-6358	332	8	=	=	SYM
ejpam-6358	332	9	{	{	PUNCT
ejpam-6358	332	10	p	p	X
ejpam-6358	332	11	,	,	PUNCT
ejpam-6358	332	12	t	t	PROPN
ejpam-6358	332	13	}	}	PUNCT
ejpam-6358	332	14	.	.	PUNCT
ejpam-6358	333	1	�	�	PROPN
ejpam-6358	333	2	ρb(p	ρb(p	NUM
ejpam-6358	333	3	)	)	PUNCT
ejpam-6358	334	1	=	=	PRON
ejpam-6358	334	2	{	{	PUNCT
ejpam-6358	334	3	p	p	X
ejpam-6358	334	4	}	}	PUNCT
ejpam-6358	334	5	,	,	PUNCT
ejpam-6358	334	6	ρb(q	ρb(q	NUM
ejpam-6358	334	7	)	)	PUNCT
ejpam-6358	334	8	=	=	PRON
ejpam-6358	334	9	{	{	PUNCT
ejpam-6358	334	10	q	q	PROPN
ejpam-6358	334	11	,	,	PUNCT
ejpam-6358	334	12	t	t	PROPN
ejpam-6358	334	13	}	}	PUNCT
ejpam-6358	334	14	,	,	PUNCT
ejpam-6358	334	15	ρb(s	ρb(	NOUN
ejpam-6358	334	16	)	)	PUNCT
ejpam-6358	334	17	=	=	PRON
ejpam-6358	334	18	{	{	PUNCT
ejpam-6358	334	19	s	s	NOUN
ejpam-6358	334	20	}	}	PUNCT
ejpam-6358	334	21	,	,	PUNCT
ejpam-6358	334	22	ρb(t	ρb(t	NUM
ejpam-6358	334	23	)	)	PUNCT
ejpam-6358	334	24	=	=	PRON
ejpam-6358	334	25	{	{	PUNCT
ejpam-6358	334	26	q	q	PROPN
ejpam-6358	334	27	,	,	PUNCT
ejpam-6358	334	28	t	t	PROPN
ejpam-6358	334	29	}	}	PUNCT
ejpam-6358	334	30	.	.	PUNCT
ejpam-6358	335	1	�	�	PROPN
ejpam-6358	335	2	ρ	ρ	PROPN
ejpam-6358	335	3	<	<	X
ejpam-6358	335	4	b>(p	b>(p	NUM
ejpam-6358	335	5	)	)	PUNCT
ejpam-6358	336	1	=	=	PRON
ejpam-6358	336	2	{	{	PUNCT
ejpam-6358	336	3	p	p	NOUN
ejpam-6358	336	4	}	}	PUNCT
ejpam-6358	336	5	,	,	PUNCT
ejpam-6358	336	6	ρ	ρ	PROPN
ejpam-6358	336	7	<	<	NOUN
ejpam-6358	336	8	b>(q	b>(q	PROPN
ejpam-6358	336	9	)	)	PUNCT
ejpam-6358	336	10	=	=	PRON
ejpam-6358	337	1	{	{	PUNCT
ejpam-6358	337	2	q	q	X
ejpam-6358	337	3	,	,	PUNCT
ejpam-6358	337	4	s	s	PART
ejpam-6358	337	5	}	}	PUNCT
ejpam-6358	337	6	,	,	PUNCT
ejpam-6358	337	7	ρ	ρ	PROPN
ejpam-6358	337	8	<	<	X
ejpam-6358	337	9	b>(s	b>(s	PRON
ejpam-6358	337	10	)	)	PUNCT
ejpam-6358	338	1	=	=	PRON
ejpam-6358	338	2	{	{	PUNCT
ejpam-6358	338	3	q	q	X
ejpam-6358	338	4	,	,	PUNCT
ejpam-6358	338	5	s	s	PART
ejpam-6358	338	6	}	}	PUNCT
ejpam-6358	338	7	,	,	PUNCT
ejpam-6358	338	8	ρ	ρ	NOUN
ejpam-6358	338	9	<	<	NOUN
ejpam-6358	338	10	b>(t	b>(t	NOUN
ejpam-6358	338	11	)	)	PUNCT
ejpam-6358	338	12	=	=	SYM
ejpam-6358	338	13	{	{	PUNCT
ejpam-6358	338	14	t	t	NOUN
ejpam-6358	338	15	}	}	PUNCT
ejpam-6358	338	16	.	.	PUNCT
ejpam-6358	339	1	r.	r.	PROPN
ejpam-6358	339	2	a.	a.	PROPN
ejpam-6358	339	3	hosny	hosny	PROPN
ejpam-6358	339	4	et	et	PROPN
ejpam-6358	339	5	al	al	PROPN
ejpam-6358	339	6	.	.	PUNCT
ejpam-6358	339	7	/	/	SYM
ejpam-6358	339	8	eur	eur	PROPN
ejpam-6358	339	9	.	.	PUNCT
ejpam-6358	340	1	j.	j.	PROPN
ejpam-6358	340	2	pure	pure	PROPN
ejpam-6358	340	3	appl	appl	PROPN
ejpam-6358	340	4	.	.	PROPN
ejpam-6358	340	5	math	math	PROPN
ejpam-6358	340	6	,	,	PUNCT
ejpam-6358	340	7	18	18	NUM
ejpam-6358	340	8	(	(	PUNCT
ejpam-6358	340	9	4	4	NUM
ejpam-6358	340	10	)	)	PUNCT
ejpam-6358	340	11	(	(	PUNCT
ejpam-6358	340	12	2025	2025	NUM
ejpam-6358	340	13	)	)	PUNCT
ejpam-6358	340	14	,	,	PUNCT
ejpam-6358	340	15	6358	6358	NUM
ejpam-6358	340	16	13	13	NUM
ejpam-6358	340	17	of	of	ADP
ejpam-6358	340	18	24	24	NUM
ejpam-6358	340	19	now	now	ADV
ejpam-6358	340	20	,	,	PUNCT
ejpam-6358	340	21	let	let	VERB
ejpam-6358	340	22	k	k	X
ejpam-6358	340	23	=	=	PRON
ejpam-6358	340	24	{	{	PUNCT
ejpam-6358	340	25	∅	∅	NOUN
ejpam-6358	340	26	,	,	PUNCT
ejpam-6358	340	27	{	{	PUNCT
ejpam-6358	340	28	t	t	NOUN
ejpam-6358	340	29	}	}	PUNCT
ejpam-6358	340	30	}	}	PUNCT
ejpam-6358	340	31	.	.	PUNCT
ejpam-6358	341	1	the	the	DET
ejpam-6358	341	2	corresponding	correspond	VERB
ejpam-6358	341	3	ikb	ikb	PROPN
ejpam-6358	341	4	and	and	CCONJ
ejpam-6358	341	5	ik	ik	NOUN
ejpam-6358	341	6	<	<	X
ejpam-6358	341	7	b>-neighborhoods	b>-neighborhood	NOUN
ejpam-6358	341	8	are	be	AUX
ejpam-6358	341	9	:	:	PUNCT
ejpam-6358	341	10	�	�	PROPN
ejpam-6358	341	11	ikb	ikb	PROPN
ejpam-6358	341	12	(	(	PUNCT
ejpam-6358	341	13	p	p	NOUN
ejpam-6358	341	14	)	)	PUNCT
ejpam-6358	341	15	=	=	NOUN
ejpam-6358	341	16	∅	∅	NOUN
ejpam-6358	341	17	,	,	PUNCT
ejpam-6358	341	18	ikb	ikb	PROPN
ejpam-6358	341	19	(	(	PUNCT
ejpam-6358	341	20	q	q	X
ejpam-6358	341	21	)	)	PUNCT
ejpam-6358	341	22	=	=	SYM
ejpam-6358	341	23	{	{	PUNCT
ejpam-6358	341	24	q	q	X
ejpam-6358	341	25	,	,	PUNCT
ejpam-6358	341	26	s	s	PROPN
ejpam-6358	341	27	,	,	PUNCT
ejpam-6358	341	28	t	t	PROPN
ejpam-6358	341	29	}	}	PUNCT
ejpam-6358	341	30	,	,	PUNCT
ejpam-6358	341	31	ikb	ikb	PROPN
ejpam-6358	341	32	(	(	PUNCT
ejpam-6358	341	33	s	s	NOUN
ejpam-6358	341	34	)	)	PUNCT
ejpam-6358	341	35	=	=	SYM
ejpam-6358	341	36	{	{	PUNCT
ejpam-6358	341	37	q	q	X
ejpam-6358	341	38	,	,	PUNCT
ejpam-6358	341	39	s	s	PROPN
ejpam-6358	341	40	,	,	PUNCT
ejpam-6358	341	41	t	t	PROPN
ejpam-6358	341	42	}	}	PUNCT
ejpam-6358	341	43	,	,	PUNCT
ejpam-6358	341	44	ikb	ikb	PROPN
ejpam-6358	341	45	(	(	PUNCT
ejpam-6358	341	46	t	t	NOUN
ejpam-6358	341	47	)	)	PUNCT
ejpam-6358	341	48	=	=	PRON
ejpam-6358	342	1	{	{	PUNCT
ejpam-6358	342	2	q	q	X
ejpam-6358	342	3	,	,	PUNCT
ejpam-6358	342	4	s	s	PROPN
ejpam-6358	342	5	,	,	PUNCT
ejpam-6358	342	6	t	t	PROPN
ejpam-6358	342	7	}	}	PUNCT
ejpam-6358	342	8	.	.	PUNCT
ejpam-6358	343	1	�	�	PROPN
ejpam-6358	343	2	ik	ik	PROPN
ejpam-6358	343	3	<	<	X
ejpam-6358	343	4	b>(p	b>(p	NUM
ejpam-6358	343	5	)	)	PUNCT
ejpam-6358	344	1	=	=	PRON
ejpam-6358	344	2	{	{	PUNCT
ejpam-6358	344	3	p	p	X
ejpam-6358	344	4	,	,	PUNCT
ejpam-6358	344	5	t	t	PROPN
ejpam-6358	344	6	}	}	PUNCT
ejpam-6358	344	7	,	,	PUNCT
ejpam-6358	344	8	ik	ik	X
ejpam-6358	344	9	<	<	X
ejpam-6358	344	10	b>(q	b>(q	X
ejpam-6358	344	11	)	)	PUNCT
ejpam-6358	344	12	=	=	NOUN
ejpam-6358	344	13	∅	∅	NOUN
ejpam-6358	344	14	,	,	PUNCT
ejpam-6358	344	15	ik	ik	X
ejpam-6358	344	16	<	<	X
ejpam-6358	344	17	b>(s	b>(s	PRON
ejpam-6358	344	18	)	)	PUNCT
ejpam-6358	344	19	=	=	NOUN
ejpam-6358	344	20	∅	∅	NOUN
ejpam-6358	344	21	,	,	PUNCT
ejpam-6358	344	22	ik	ik	X
ejpam-6358	344	23	<	<	X
ejpam-6358	344	24	b>(t	b>(t	NOUN
ejpam-6358	344	25	)	)	PUNCT
ejpam-6358	344	26	=	=	SYM
ejpam-6358	344	27	{	{	PUNCT
ejpam-6358	344	28	p	p	X
ejpam-6358	344	29	,	,	PUNCT
ejpam-6358	344	30	t	t	PROPN
ejpam-6358	344	31	}	}	PUNCT
ejpam-6358	344	32	.	.	PUNCT
ejpam-6358	345	1	consequently	consequently	ADV
ejpam-6358	345	2	,	,	PUNCT
ejpam-6358	345	3	ikj	ikj	PROPN
ejpam-6358	345	4	(	(	PUNCT
ejpam-6358	345	5	x	x	NOUN
ejpam-6358	345	6	)	)	PUNCT
ejpam-6358	345	7	̸=	̸=	PROPN
ejpam-6358	345	8	ik	ik	PROPN
ejpam-6358	345	9	<	<	NOUN
ejpam-6358	345	10	j>(x	j>(x	X
ejpam-6358	345	11	)	)	PUNCT
ejpam-6358	345	12	,	,	PUNCT
ejpam-6358	345	13	∀x	∀x	VERB
ejpam-6358	345	14	∈	∈	PROPN
ejpam-6358	345	15	u	u	NOUN
ejpam-6358	345	16	.	.	PUNCT
ejpam-6358	346	1	this	this	PRON
ejpam-6358	346	2	demonstrates	demonstrate	VERB
ejpam-6358	346	3	a	a	DET
ejpam-6358	346	4	discrepancy	discrepancy	NOUN
ejpam-6358	346	5	between	between	ADP
ejpam-6358	346	6	ikj	ikj	PROPN
ejpam-6358	346	7	and	and	CCONJ
ejpam-6358	346	8	ik	ik	PROPN
ejpam-6358	346	9	<	<	X
ejpam-6358	346	10	j	j	X
ejpam-6358	346	11	>	>	X
ejpam-6358	346	12	contradicting	contradict	VERB
ejpam-6358	346	13	any	any	DET
ejpam-6358	346	14	assumption	assumption	NOUN
ejpam-6358	346	15	of	of	ADP
ejpam-6358	346	16	their	their	PRON
ejpam-6358	346	17	equivalence	equivalence	NOUN
ejpam-6358	346	18	.	.	PUNCT
ejpam-6358	347	1	example	example	NOUN
ejpam-6358	348	1	4	4	NUM
ejpam-6358	348	2	.	.	PUNCT
ejpam-6358	348	3	consider	consider	VERB
ejpam-6358	348	4	u	u	PRON
ejpam-6358	348	5	=	=	X
ejpam-6358	348	6	{	{	PUNCT
ejpam-6358	348	7	p	p	X
ejpam-6358	348	8	,	,	PUNCT
ejpam-6358	348	9	q	q	ADJ
ejpam-6358	348	10	,	,	PUNCT
ejpam-6358	348	11	s	s	AUX
ejpam-6358	348	12	}	}	PUNCT
ejpam-6358	348	13	equipped	equip	VERB
ejpam-6358	348	14	with	with	ADP
ejpam-6358	348	15	the	the	DET
ejpam-6358	348	16	preorder	preorder	NOUN
ejpam-6358	348	17	relation	relation	NOUN
ejpam-6358	348	18	r	r	NOUN
ejpam-6358	348	19	=	=	PUNCT
ejpam-6358	348	20	{	{	PUNCT
ejpam-6358	348	21	(	(	PUNCT
ejpam-6358	348	22	p	p	X
ejpam-6358	348	23	,	,	PUNCT
ejpam-6358	348	24	p	p	NOUN
ejpam-6358	348	25	)	)	PUNCT
ejpam-6358	348	26	,	,	PUNCT
ejpam-6358	348	27	(	(	PUNCT
ejpam-6358	348	28	q	q	X
ejpam-6358	348	29	,	,	PUNCT
ejpam-6358	348	30	q	q	NOUN
ejpam-6358	348	31	)	)	PUNCT
ejpam-6358	348	32	,	,	PUNCT
ejpam-6358	348	33	(	(	PUNCT
ejpam-6358	348	34	s	s	X
ejpam-6358	348	35	,	,	PUNCT
ejpam-6358	348	36	s	s	PART
ejpam-6358	348	37	)	)	PUNCT
ejpam-6358	348	38	,	,	PUNCT
ejpam-6358	348	39	(	(	PUNCT
ejpam-6358	348	40	p	p	X
ejpam-6358	348	41	,	,	PUNCT
ejpam-6358	348	42	q	q	NOUN
ejpam-6358	348	43	)	)	PUNCT
ejpam-6358	348	44	,	,	PUNCT
ejpam-6358	348	45	(	(	PUNCT
ejpam-6358	348	46	p	p	X
ejpam-6358	348	47	,	,	PUNCT
ejpam-6358	348	48	s	s	PART
ejpam-6358	348	49	)	)	PUNCT
ejpam-6358	348	50	,	,	PUNCT
ejpam-6358	348	51	(	(	PUNCT
ejpam-6358	348	52	q	q	X
ejpam-6358	348	53	,	,	PUNCT
ejpam-6358	348	54	s	s	NOUN
ejpam-6358	348	55	)	)	PUNCT
ejpam-6358	348	56	}	}	PUNCT
ejpam-6358	348	57	.	.	PUNCT
ejpam-6358	349	1	the	the	DET
ejpam-6358	349	2	corresponding	correspond	VERB
ejpam-6358	349	3	neighborhoods	neighborhood	NOUN
ejpam-6358	349	4	under	under	ADP
ejpam-6358	349	5	ωa	ωa	ADJ
ejpam-6358	349	6	,	,	PUNCT
ejpam-6358	349	7	ρa	ρa	PRON
ejpam-6358	349	8	are	be	AUX
ejpam-6358	349	9	given	give	VERB
ejpam-6358	349	10	by	by	ADP
ejpam-6358	349	11	:	:	PUNCT
ejpam-6358	349	12	�	�	PROPN
ejpam-6358	349	13	ωa(p	ωa(p	NUM
ejpam-6358	349	14	)	)	PUNCT
ejpam-6358	349	15	=	=	SYM
ejpam-6358	349	16	u	u	NOUN
ejpam-6358	349	17	,	,	PUNCT
ejpam-6358	349	18	ωa(q	ωa(q	PUNCT
ejpam-6358	349	19	)	)	PUNCT
ejpam-6358	349	20	=	=	PRON
ejpam-6358	349	21	{	{	PUNCT
ejpam-6358	349	22	q	q	X
ejpam-6358	349	23	,	,	PUNCT
ejpam-6358	349	24	s	s	PART
ejpam-6358	349	25	}	}	PUNCT
ejpam-6358	349	26	,	,	PUNCT
ejpam-6358	349	27	ωa(s	ωa(	NOUN
ejpam-6358	349	28	)	)	PUNCT
ejpam-6358	349	29	=	=	SYM
ejpam-6358	349	30	{	{	PUNCT
ejpam-6358	349	31	s	s	PROPN
ejpam-6358	349	32	}	}	PUNCT
ejpam-6358	349	33	.	.	PUNCT
ejpam-6358	350	1	�	�	PROPN
ejpam-6358	350	2	ρa(p	ρa(p	NUM
ejpam-6358	350	3	)	)	PUNCT
ejpam-6358	351	1	=	=	PRON
ejpam-6358	351	2	{	{	PUNCT
ejpam-6358	351	3	p	p	X
ejpam-6358	351	4	}	}	PUNCT
ejpam-6358	351	5	,	,	PUNCT
ejpam-6358	351	6	ρa(q	ρa(q	NOUN
ejpam-6358	351	7	)	)	PUNCT
ejpam-6358	351	8	=	=	PRON
ejpam-6358	351	9	{	{	PUNCT
ejpam-6358	351	10	q	q	X
ejpam-6358	351	11	}	}	PUNCT
ejpam-6358	351	12	,	,	PUNCT
ejpam-6358	351	13	and	and	CCONJ
ejpam-6358	351	14	ρa(s	ρa(s	NUM
ejpam-6358	351	15	)	)	PUNCT
ejpam-6358	352	1	=	=	PRON
ejpam-6358	352	2	{	{	PUNCT
ejpam-6358	352	3	s	s	NOUN
ejpam-6358	352	4	}	}	PUNCT
ejpam-6358	352	5	.	.	PUNCT
ejpam-6358	353	1	now	now	ADV
ejpam-6358	353	2	,	,	PUNCT
ejpam-6358	353	3	let	let	VERB
ejpam-6358	353	4	k	k	X
ejpam-6358	353	5	=	=	PRON
ejpam-6358	353	6	{	{	PUNCT
ejpam-6358	353	7	∅	∅	NOUN
ejpam-6358	353	8	,	,	PUNCT
ejpam-6358	353	9	{	{	PUNCT
ejpam-6358	353	10	s	s	NOUN
ejpam-6358	353	11	}	}	PUNCT
ejpam-6358	353	12	}	}	PUNCT
ejpam-6358	353	13	.	.	PUNCT
ejpam-6358	354	1	the	the	DET
ejpam-6358	354	2	corresponding	correspond	VERB
ejpam-6358	354	3	neighborhoods	neighborhood	NOUN
ejpam-6358	354	4	under	under	ADP
ejpam-6358	354	5	ika	ika	PROPN
ejpam-6358	354	6	are	be	AUX
ejpam-6358	354	7	given	give	VERB
ejpam-6358	354	8	by	by	ADP
ejpam-6358	354	9	:	:	PUNCT
ejpam-6358	354	10	�	�	PROPN
ejpam-6358	354	11	ika	ika	PROPN
ejpam-6358	354	12	(	(	PUNCT
ejpam-6358	354	13	p	p	NOUN
ejpam-6358	354	14	)	)	PUNCT
ejpam-6358	354	15	=	=	PUNCT
ejpam-6358	354	16	{	{	PUNCT
ejpam-6358	354	17	p	p	X
ejpam-6358	354	18	,	,	PUNCT
ejpam-6358	354	19	q	q	ADJ
ejpam-6358	354	20	}	}	PUNCT
ejpam-6358	354	21	,	,	PUNCT
ejpam-6358	354	22	ika	ika	X
ejpam-6358	354	23	(	(	PUNCT
ejpam-6358	354	24	q	q	X
ejpam-6358	354	25	)	)	PUNCT
ejpam-6358	354	26	=	=	SYM
ejpam-6358	354	27	{	{	PUNCT
ejpam-6358	354	28	p	p	X
ejpam-6358	354	29	,	,	PUNCT
ejpam-6358	354	30	q	q	ADJ
ejpam-6358	354	31	}	}	PUNCT
ejpam-6358	354	32	,	,	PUNCT
ejpam-6358	354	33	ika	ika	X
ejpam-6358	354	34	(	(	PUNCT
ejpam-6358	354	35	s	s	NOUN
ejpam-6358	354	36	)	)	PUNCT
ejpam-6358	354	37	=	=	PUNCT
ejpam-6358	354	38	∅.	∅.	NOUN
ejpam-6358	354	39	it	it	PRON
ejpam-6358	354	40	follows	follow	VERB
ejpam-6358	354	41	that	that	PRON
ejpam-6358	354	42	ωa(x	ωa(x	NOUN
ejpam-6358	354	43	)	)	PUNCT
ejpam-6358	354	44	⊈	⊈	PROPN
ejpam-6358	354	45	ika	ika	X
ejpam-6358	354	46	(	(	PUNCT
ejpam-6358	354	47	x	x	NOUN
ejpam-6358	354	48	)	)	PUNCT
ejpam-6358	354	49	,	,	PUNCT
ejpam-6358	354	50	for	for	ADP
ejpam-6358	354	51	all	all	DET
ejpam-6358	354	52	x	x	SYM
ejpam-6358	354	53	∈	∈	PROPN
ejpam-6358	354	54	u	u	NOUN
ejpam-6358	354	55	.	.	PUNCT
ejpam-6358	355	1	additionally	additionally	ADV
ejpam-6358	355	2	,	,	PUNCT
ejpam-6358	355	3	ρa(s	ρa(s	NUM
ejpam-6358	355	4	)	)	PUNCT
ejpam-6358	355	5	⊈	⊈	PROPN
ejpam-6358	355	6	ika	ika	X
ejpam-6358	355	7	(	(	PUNCT
ejpam-6358	355	8	s	s	NOUN
ejpam-6358	355	9	)	)	PUNCT
ejpam-6358	355	10	.	.	PUNCT
ejpam-6358	356	1	remark	remark	PROPN
ejpam-6358	356	2	3	3	NUM
ejpam-6358	356	3	.	.	PUNCT
ejpam-6358	357	1	(	(	PUNCT
ejpam-6358	357	2	i	i	NOUN
ejpam-6358	357	3	)	)	PUNCT
ejpam-6358	357	4	for	for	ADP
ejpam-6358	357	5	all	all	DET
ejpam-6358	357	6	j	j	PROPN
ejpam-6358	357	7	∈	∈	PROPN
ejpam-6358	357	8	ω	ω	PROPN
ejpam-6358	357	9	,	,	PUNCT
ejpam-6358	357	10	and	and	CCONJ
ejpam-6358	357	11	x	x	X
ejpam-6358	357	12	∈	∈	PROPN
ejpam-6358	357	13	u	u	NOUN
ejpam-6358	357	14	,	,	PUNCT
ejpam-6358	357	15	the	the	DET
ejpam-6358	357	16	inclusion	inclusion	NOUN
ejpam-6358	357	17	ρj(x	ρj(x	NOUN
ejpam-6358	357	18	)	)	PUNCT
ejpam-6358	357	19	⊆	⊆	NUM
ejpam-6358	357	20	ikj	ikj	X
ejpam-6358	357	21	(	(	PUNCT
ejpam-6358	357	22	x	x	X
ejpam-6358	357	23	)	)	PUNCT
ejpam-6358	357	24	does	do	AUX
ejpam-6358	357	25	not	not	PART
ejpam-6358	357	26	necessarily	necessarily	ADV
ejpam-6358	357	27	hold	hold	VERB
ejpam-6358	357	28	when	when	SCONJ
ejpam-6358	357	29	r	r	NOUN
ejpam-6358	357	30	is	be	AUX
ejpam-6358	357	31	serial	serial	ADJ
ejpam-6358	357	32	,	,	PUNCT
ejpam-6358	357	33	reflexive	reflexive	ADJ
ejpam-6358	357	34	,	,	PUNCT
ejpam-6358	357	35	symmetric	symmetric	ADJ
ejpam-6358	357	36	,	,	PUNCT
ejpam-6358	357	37	transitive	transitive	ADJ
ejpam-6358	357	38	,	,	PUNCT
ejpam-6358	357	39	a	a	DET
ejpam-6358	357	40	preorder	preorder	NOUN
ejpam-6358	357	41	,	,	PUNCT
ejpam-6358	357	42	or	or	CCONJ
ejpam-6358	357	43	a	a	DET
ejpam-6358	357	44	similarity	similarity	NOUN
ejpam-6358	357	45	relation	relation	NOUN
ejpam-6358	357	46	,	,	PUNCT
ejpam-6358	357	47	as	as	SCONJ
ejpam-6358	357	48	demonstrated	demonstrate	VERB
ejpam-6358	357	49	in	in	ADP
ejpam-6358	357	50	examples	example	NOUN
ejpam-6358	357	51	1	1	NUM
ejpam-6358	357	52	,	,	PUNCT
ejpam-6358	357	53	2	2	NUM
ejpam-6358	357	54	,	,	PUNCT
ejpam-6358	357	55	3	3	NUM
ejpam-6358	357	56	,	,	PUNCT
ejpam-6358	357	57	and	and	CCONJ
ejpam-6358	357	58	4	4	NUM
ejpam-6358	357	59	.	.	PUNCT
ejpam-6358	357	60	(	(	PUNCT
ejpam-6358	357	61	ii	ii	NOUN
ejpam-6358	357	62	)	)	PUNCT
ejpam-6358	357	63	for	for	ADP
ejpam-6358	357	64	all	all	DET
ejpam-6358	357	65	j	j	PROPN
ejpam-6358	357	66	∈	∈	PROPN
ejpam-6358	357	67	ω	ω	PROPN
ejpam-6358	357	68	and	and	CCONJ
ejpam-6358	357	69	x	x	NOUN
ejpam-6358	357	70	,	,	PUNCT
ejpam-6358	357	71	y	y	PROPN
ejpam-6358	357	72	∈	∈	PROPN
ejpam-6358	357	73	u	u	PROPN
ejpam-6358	357	74	,	,	PUNCT
ejpam-6358	357	75	the	the	DET
ejpam-6358	357	76	condition	condition	NOUN
ejpam-6358	357	77	ωj(x	ωj(x	NUM
ejpam-6358	357	78	)	)	PUNCT
ejpam-6358	357	79	∩	∩	NOUN
ejpam-6358	357	80	ωj(y	ωj(y	PUNCT
ejpam-6358	357	81	)	)	PUNCT
ejpam-6358	357	82	̸=	̸=	NOUN
ejpam-6358	357	83	∅	∅	NOUN
ejpam-6358	357	84	does	do	AUX
ejpam-6358	357	85	not	not	PART
ejpam-6358	357	86	imply	imply	VERB
ejpam-6358	357	87	that	that	PRON
ejpam-6358	357	88	ωj(x	ωj(x	PUNCT
ejpam-6358	357	89	)	)	PUNCT
ejpam-6358	357	90	∩	∩	NOUN
ejpam-6358	357	91	ωj(y	ωj(y	NUM
ejpam-6358	357	92	)	)	PUNCT
ejpam-6358	357	93	̸∈	̸∈	PROPN
ejpam-6358	357	94	k	k	PROPN
ejpam-6358	357	95	,	,	PUNCT
ejpam-6358	357	96	as	as	SCONJ
ejpam-6358	357	97	shown	show	VERB
ejpam-6358	357	98	in	in	ADP
ejpam-6358	357	99	examples	example	NOUN
ejpam-6358	357	100	1	1	NUM
ejpam-6358	357	101	,	,	PUNCT
ejpam-6358	357	102	2	2	NUM
ejpam-6358	357	103	,	,	PUNCT
ejpam-6358	357	104	3	3	NUM
ejpam-6358	357	105	,	,	PUNCT
ejpam-6358	357	106	and	and	CCONJ
ejpam-6358	357	107	4	4	NUM
ejpam-6358	357	108	.	.	PUNCT
ejpam-6358	357	109	(	(	PUNCT
ejpam-6358	357	110	iii	iii	NOUN
ejpam-6358	357	111	)	)	PUNCT
ejpam-6358	357	112	for	for	ADP
ejpam-6358	357	113	all	all	DET
ejpam-6358	357	114	j	j	PROPN
ejpam-6358	357	115	∈	∈	PROPN
ejpam-6358	357	116	ω	ω	PROPN
ejpam-6358	357	117	and	and	CCONJ
ejpam-6358	357	118	x	x	NOUN
ejpam-6358	357	119	,	,	PUNCT
ejpam-6358	357	120	y	y	PROPN
ejpam-6358	357	121	∈	∈	PROPN
ejpam-6358	357	122	u	u	PROPN
ejpam-6358	357	123	,	,	PUNCT
ejpam-6358	357	124	the	the	DET
ejpam-6358	357	125	intersection	intersection	NOUN
ejpam-6358	357	126	ikj	ikj	NOUN
ejpam-6358	357	127	(	(	PUNCT
ejpam-6358	357	128	x	x	NOUN
ejpam-6358	357	129	)	)	PUNCT
ejpam-6358	357	130	∩	∩	ADJ
ejpam-6358	357	131	ikj(y	ikj(y	PROPN
ejpam-6358	357	132	)	)	PUNCT
ejpam-6358	357	133	̸=	̸=	PROPN
ejpam-6358	357	134	∅	∅	NOUN
ejpam-6358	357	135	does	do	AUX
ejpam-6358	357	136	not	not	PART
ejpam-6358	357	137	necessarily	necessarily	ADV
ejpam-6358	357	138	imply	imply	VERB
ejpam-6358	357	139	that	that	SCONJ
ejpam-6358	357	140	ikj	ikj	PROPN
ejpam-6358	357	141	(	(	PUNCT
ejpam-6358	357	142	x	x	NOUN
ejpam-6358	357	143	)	)	PUNCT
ejpam-6358	357	144	∩	∩	ADJ
ejpam-6358	357	145	ikj	ikj	PROPN
ejpam-6358	357	146	(	(	PUNCT
ejpam-6358	357	147	y	y	NOUN
ejpam-6358	357	148	)	)	PUNCT
ejpam-6358	357	149	̸∈	̸∈	PROPN
ejpam-6358	357	150	k	k	PROPN
ejpam-6358	357	151	,	,	PUNCT
ejpam-6358	357	152	as	as	SCONJ
ejpam-6358	357	153	evidenced	evidence	VERB
ejpam-6358	357	154	in	in	ADP
ejpam-6358	357	155	examples	example	NOUN
ejpam-6358	357	156	1	1	NUM
ejpam-6358	357	157	,	,	PUNCT
ejpam-6358	357	158	2	2	NUM
ejpam-6358	357	159	,	,	PUNCT
ejpam-6358	357	160	3	3	NUM
ejpam-6358	357	161	,	,	PUNCT
ejpam-6358	357	162	and	and	CCONJ
ejpam-6358	357	163	4	4	X
ejpam-6358	357	164	.	.	PUNCT
ejpam-6358	357	165	accordingly	accordingly	ADV
ejpam-6358	357	166	,	,	PUNCT
ejpam-6358	357	167	the	the	DET
ejpam-6358	357	168	revised	revise	VERB
ejpam-6358	357	169	formulation	formulation	NOUN
ejpam-6358	357	170	of	of	ADP
ejpam-6358	357	171	theorem	theorem	NOUN
ejpam-6358	357	172	3.4	3.4	NUM
ejpam-6358	357	173	from	from	ADP
ejpam-6358	357	174	[	[	X
ejpam-6358	357	175	40	40	NUM
ejpam-6358	357	176	]	]	PUNCT
ejpam-6358	357	177	is	be	AUX
ejpam-6358	357	178	stated	state	VERB
ejpam-6358	357	179	as	as	SCONJ
ejpam-6358	357	180	follows	follow	VERB
ejpam-6358	357	181	:	:	PUNCT
ejpam-6358	357	182	theorem	theorem	NOUN
ejpam-6358	357	183	6	6	NUM
ejpam-6358	357	184	.	.	PUNCT
ejpam-6358	358	1	let	let	VERB
ejpam-6358	358	2	(	(	PUNCT
ejpam-6358	358	3	u	u	NOUN
ejpam-6358	358	4	,	,	PUNCT
ejpam-6358	358	5	r	r	NOUN
ejpam-6358	358	6	,	,	PUNCT
ejpam-6358	358	7	k	k	NOUN
ejpam-6358	358	8	)	)	PUNCT
ejpam-6358	358	9	be	be	VERB
ejpam-6358	358	10	an	an	DET
ejpam-6358	358	11	ij	ij	ADJ
ejpam-6358	358	12	-	-	PUNCT
ejpam-6358	358	13	g	g	NOUN
ejpam-6358	358	14	approximation	approximation	NOUN
ejpam-6358	358	15	space	space	NOUN
ejpam-6358	358	16	,	,	PUNCT
ejpam-6358	358	17	and	and	CCONJ
ejpam-6358	358	18	let	let	VERB
ejpam-6358	358	19	s	s	NOUN
ejpam-6358	358	20	,	,	PUNCT
ejpam-6358	358	21	t	t	PROPN
ejpam-6358	358	22	∈	∈	PROPN
ejpam-6358	358	23	u	u	PROPN
ejpam-6358	358	24	.	.	PUNCT
ejpam-6358	359	1	the	the	DET
ejpam-6358	359	2	following	follow	VERB
ejpam-6358	359	3	statements	statement	NOUN
ejpam-6358	359	4	are	be	AUX
ejpam-6358	359	5	valid	valid	ADJ
ejpam-6358	359	6	:	:	PUNCT
ejpam-6358	359	7	(	(	PUNCT
ejpam-6358	359	8	i	i	NOUN
ejpam-6358	359	9	)	)	PUNCT
ejpam-6358	359	10	for	for	ADP
ejpam-6358	359	11	all	all	DET
ejpam-6358	359	12	j	j	PROPN
ejpam-6358	359	13	∈	∈	PROPN
ejpam-6358	359	14	ω	ω	PROPN
ejpam-6358	359	15	,	,	PUNCT
ejpam-6358	359	16	t	t	PROPN
ejpam-6358	359	17	∈	∈	PROPN
ejpam-6358	359	18	ikj	ikj	PROPN
ejpam-6358	359	19	(	(	PUNCT
ejpam-6358	359	20	s	s	NOUN
ejpam-6358	359	21	)	)	PUNCT
ejpam-6358	359	22	if	if	SCONJ
ejpam-6358	359	23	and	and	CCONJ
ejpam-6358	359	24	only	only	ADV
ejpam-6358	359	25	if	if	SCONJ
ejpam-6358	359	26	s	s	X
ejpam-6358	359	27	∈	∈	PROPN
ejpam-6358	359	28	ikj	ikj	PROPN
ejpam-6358	359	29	(	(	PUNCT
ejpam-6358	359	30	t	t	PROPN
ejpam-6358	359	31	)	)	PUNCT
ejpam-6358	359	32	.	.	PUNCT
ejpam-6358	360	1	(	(	PUNCT
ejpam-6358	360	2	ii	ii	NOUN
ejpam-6358	360	3	)	)	PUNCT
ejpam-6358	360	4	if	if	SCONJ
ejpam-6358	360	5	r	r	NOUN
ejpam-6358	360	6	is	be	AUX
ejpam-6358	360	7	reflexive	reflexive	ADJ
ejpam-6358	360	8	,	,	PUNCT
ejpam-6358	360	9	then	then	ADV
ejpam-6358	360	10	ik	ik	PROPN
ejpam-6358	360	11	<	<	X
ejpam-6358	360	12	j>(s	j>(s	X
ejpam-6358	360	13	)	)	PUNCT
ejpam-6358	360	14	⊆	⊆	NUM
ejpam-6358	360	15	ikj	ikj	X
ejpam-6358	360	16	(	(	PUNCT
ejpam-6358	360	17	s	s	NOUN
ejpam-6358	360	18	)	)	PUNCT
ejpam-6358	360	19	,	,	PUNCT
ejpam-6358	360	20	for	for	ADP
ejpam-6358	360	21	each	each	DET
ejpam-6358	360	22	j	j	PROPN
ejpam-6358	360	23	∈	∈	PROPN
ejpam-6358	360	24	{	{	PUNCT
ejpam-6358	360	25	a	a	PROPN
ejpam-6358	360	26	,	,	PUNCT
ejpam-6358	360	27	b	b	NOUN
ejpam-6358	360	28	,	,	PUNCT
ejpam-6358	360	29	i	i	PRON
ejpam-6358	360	30	,	,	PUNCT
ejpam-6358	360	31	u	u	NOUN
ejpam-6358	360	32	}	}	PUNCT
ejpam-6358	360	33	.	.	PUNCT
ejpam-6358	361	1	(	(	PUNCT
ejpam-6358	361	2	iii	iii	X
ejpam-6358	361	3	)	)	PUNCT
ejpam-6358	361	4	if	if	SCONJ
ejpam-6358	361	5	r	r	NOUN
ejpam-6358	361	6	is	be	AUX
ejpam-6358	361	7	preorder	preorder	NOUN
ejpam-6358	361	8	,	,	PUNCT
ejpam-6358	361	9	then	then	ADV
ejpam-6358	361	10	ik	ik	PROPN
ejpam-6358	361	11	<	<	X
ejpam-6358	361	12	j>(s	j>(s	X
ejpam-6358	361	13	)	)	PUNCT
ejpam-6358	361	14	=	=	SYM
ejpam-6358	361	15	ikj	ikj	PROPN
ejpam-6358	361	16	(	(	PUNCT
ejpam-6358	361	17	s	s	NOUN
ejpam-6358	361	18	)	)	PUNCT
ejpam-6358	361	19	,	,	PUNCT
ejpam-6358	361	20	for	for	ADP
ejpam-6358	361	21	each	each	DET
ejpam-6358	361	22	j	j	PROPN
ejpam-6358	361	23	∈	∈	PROPN
ejpam-6358	361	24	{	{	PUNCT
ejpam-6358	361	25	a	a	PROPN
ejpam-6358	361	26	,	,	PUNCT
ejpam-6358	361	27	b	b	NOUN
ejpam-6358	361	28	,	,	PUNCT
ejpam-6358	361	29	i	i	PRON
ejpam-6358	361	30	,	,	PUNCT
ejpam-6358	361	31	u	u	NOUN
ejpam-6358	361	32	}	}	PUNCT
ejpam-6358	361	33	.	.	PUNCT
ejpam-6358	362	1	(	(	PUNCT
ejpam-6358	362	2	iv	iv	X
ejpam-6358	362	3	)	)	PUNCT
ejpam-6358	362	4	if	if	SCONJ
ejpam-6358	362	5	r	r	NOUN
ejpam-6358	362	6	is	be	AUX
ejpam-6358	362	7	reflexive	reflexive	ADJ
ejpam-6358	362	8	,	,	PUNCT
ejpam-6358	362	9	then	then	ADV
ejpam-6358	362	10	for	for	ADP
ejpam-6358	362	11	all	all	DET
ejpam-6358	362	12	j	j	PROPN
ejpam-6358	362	13	∈	∈	PROPN
ejpam-6358	362	14	ω	ω	PROPN
ejpam-6358	362	15	,	,	PUNCT
ejpam-6358	362	16	the	the	DET
ejpam-6358	362	17	following	follow	VERB
ejpam-6358	362	18	equalities	equality	NOUN
ejpam-6358	362	19	hold	hold	VERB
ejpam-6358	362	20	:	:	PUNCT
ejpam-6358	363	1	r.	r.	PROPN
ejpam-6358	363	2	a.	a.	PROPN
ejpam-6358	363	3	hosny	hosny	PROPN
ejpam-6358	363	4	et	et	PROPN
ejpam-6358	363	5	al	al	PROPN
ejpam-6358	363	6	.	.	PUNCT
ejpam-6358	363	7	/	/	SYM
ejpam-6358	363	8	eur	eur	PROPN
ejpam-6358	363	9	.	.	PUNCT
ejpam-6358	364	1	j.	j.	PROPN
ejpam-6358	364	2	pure	pure	PROPN
ejpam-6358	364	3	appl	appl	PROPN
ejpam-6358	364	4	.	.	PROPN
ejpam-6358	364	5	math	math	PROPN
ejpam-6358	364	6	,	,	PUNCT
ejpam-6358	364	7	18	18	NUM
ejpam-6358	364	8	(	(	PUNCT
ejpam-6358	364	9	4	4	NUM
ejpam-6358	364	10	)	)	PUNCT
ejpam-6358	364	11	(	(	PUNCT
ejpam-6358	364	12	2025	2025	NUM
ejpam-6358	364	13	)	)	PUNCT
ejpam-6358	364	14	,	,	PUNCT
ejpam-6358	364	15	6358	6358	NUM
ejpam-6358	364	16	14	14	NUM
ejpam-6358	364	17	of	of	ADP
ejpam-6358	364	18	24	24	NUM
ejpam-6358	364	19	ρj(s	ρj(s	NUM
ejpam-6358	364	20	)	)	PUNCT
ejpam-6358	364	21	∩	∩	NOUN
ejpam-6358	364	22	ωj(s	ωj(s	NUM
ejpam-6358	364	23	)	)	PUNCT
ejpam-6358	364	24	=	=	SYM
ejpam-6358	364	25	ρj(s	ρj(s	NUM
ejpam-6358	364	26	)	)	PUNCT
ejpam-6358	364	27	and	and	CCONJ
ejpam-6358	364	28	ρj(s	ρj(s	NUM
ejpam-6358	364	29	)	)	PUNCT
ejpam-6358	364	30	∪	∪	ADP
ejpam-6358	364	31	ωj(s	ωj(s	NUM
ejpam-6358	364	32	)	)	PUNCT
ejpam-6358	364	33	=	=	SYM
ejpam-6358	364	34	ωj(s	ωj(s	NUM
ejpam-6358	364	35	)	)	PUNCT
ejpam-6358	364	36	.	.	PUNCT
ejpam-6358	365	1	(	(	PUNCT
ejpam-6358	365	2	v	v	NOUN
ejpam-6358	365	3	)	)	PUNCT
ejpam-6358	365	4	if	if	SCONJ
ejpam-6358	365	5	r	r	NOUN
ejpam-6358	365	6	is	be	AUX
ejpam-6358	365	7	symmetric	symmetric	ADJ
ejpam-6358	365	8	,	,	PUNCT
ejpam-6358	365	9	then	then	ADV
ejpam-6358	365	10	iki	iki	PROPN
ejpam-6358	365	11	(	(	PUNCT
ejpam-6358	365	12	s	s	NOUN
ejpam-6358	365	13	)	)	PUNCT
ejpam-6358	365	14	=	=	SYM
ejpam-6358	365	15	ika	ika	X
ejpam-6358	365	16	(	(	PUNCT
ejpam-6358	365	17	s	s	NOUN
ejpam-6358	365	18	)	)	PUNCT
ejpam-6358	365	19	=	=	PRON
ejpam-6358	365	20	ikb	ikb	PROPN
ejpam-6358	365	21	(	(	PUNCT
ejpam-6358	365	22	s	s	NOUN
ejpam-6358	365	23	)	)	PUNCT
ejpam-6358	365	24	=	=	SYM
ejpam-6358	365	25	iku	iku	PROPN
ejpam-6358	365	26	(	(	PUNCT
ejpam-6358	365	27	s	s	NOUN
ejpam-6358	365	28	)	)	PUNCT
ejpam-6358	365	29	and	and	CCONJ
ejpam-6358	365	30	ik	ik	ADP
ejpam-6358	365	31	<	<	NOUN
ejpam-6358	365	32	i>(s	i>(s	NOUN
ejpam-6358	365	33	)	)	PUNCT
ejpam-6358	365	34	=	=	PUNCT
ejpam-6358	366	1	ik	ik	X
ejpam-6358	366	2	<	<	X
ejpam-6358	366	3	a>(s	a>(s	X
ejpam-6358	366	4	)	)	PUNCT
ejpam-6358	366	5	=	=	PUNCT
ejpam-6358	367	1	ik	ik	X
ejpam-6358	367	2	<	<	X
ejpam-6358	367	3	b>(s	b>(s	PRON
ejpam-6358	367	4	)	)	PUNCT
ejpam-6358	367	5	=	=	PUNCT
ejpam-6358	368	1	ik	ik	X
ejpam-6358	368	2	<	<	X
ejpam-6358	368	3	u>(s	u>(s	NUM
ejpam-6358	368	4	)	)	PUNCT
ejpam-6358	368	5	.	.	PUNCT
ejpam-6358	369	1	proof	proof	NOUN
ejpam-6358	369	2	.	.	PUNCT
ejpam-6358	370	1	the	the	DET
ejpam-6358	370	2	proofs	proof	NOUN
ejpam-6358	370	3	of	of	ADP
ejpam-6358	370	4	statements	statement	NOUN
ejpam-6358	370	5	1	1	NUM
ejpam-6358	370	6	,	,	PUNCT
ejpam-6358	370	7	2	2	NUM
ejpam-6358	370	8	,	,	PUNCT
ejpam-6358	370	9	and	and	CCONJ
ejpam-6358	370	10	5	5	NUM
ejpam-6358	370	11	can	can	AUX
ejpam-6358	370	12	be	be	AUX
ejpam-6358	370	13	found	find	VERB
ejpam-6358	370	14	in	in	ADP
ejpam-6358	370	15	[	[	X
ejpam-6358	370	16	40	40	NUM
ejpam-6358	370	17	]	]	PUNCT
ejpam-6358	370	18	.	.	PUNCT
ejpam-6358	371	1	we	we	PRON
ejpam-6358	371	2	now	now	ADV
ejpam-6358	371	3	proceed	proceed	VERB
ejpam-6358	371	4	to	to	PART
ejpam-6358	371	5	establish	establish	VERB
ejpam-6358	371	6	the	the	DET
ejpam-6358	371	7	remaining	remain	VERB
ejpam-6358	371	8	assertions	assertion	NOUN
ejpam-6358	371	9	that	that	PRON
ejpam-6358	371	10	are	be	AUX
ejpam-6358	371	11	not	not	PART
ejpam-6358	371	12	explicitly	explicitly	ADV
ejpam-6358	371	13	stated	state	VERB
ejpam-6358	371	14	in	in	ADP
ejpam-6358	371	15	[	[	X
ejpam-6358	371	16	40	40	NUM
ejpam-6358	371	17	]	]	PUNCT
ejpam-6358	371	18	,	,	PUNCT
ejpam-6358	371	19	as	as	SCONJ
ejpam-6358	371	20	follows	follow	VERB
ejpam-6358	371	21	:	:	PUNCT
ejpam-6358	371	22	3	3	X
ejpam-6358	371	23	.	.	PUNCT
ejpam-6358	371	24	according	accord	VERB
ejpam-6358	371	25	to	to	ADP
ejpam-6358	371	26	[	[	X
ejpam-6358	371	27	43	43	NUM
ejpam-6358	371	28	]	]	X
ejpam-6358	371	29	,	,	PUNCT
ejpam-6358	371	30	since	since	SCONJ
ejpam-6358	371	31	r	r	NOUN
ejpam-6358	371	32	is	be	AUX
ejpam-6358	371	33	a	a	DET
ejpam-6358	371	34	preorder	preorder	NOUN
ejpam-6358	371	35	,	,	PUNCT
ejpam-6358	371	36	it	it	PRON
ejpam-6358	371	37	follows	follow	VERB
ejpam-6358	371	38	that	that	SCONJ
ejpam-6358	371	39	ω	ω	PROPN
ejpam-6358	371	40	<	<	X
ejpam-6358	371	41	j>(s	j>(s	X
ejpam-6358	371	42	)	)	PUNCT
ejpam-6358	371	43	=	=	SYM
ejpam-6358	372	1	ωj(s	ωj(s	NUM
ejpam-6358	372	2	)	)	PUNCT
ejpam-6358	372	3	for	for	ADP
ejpam-6358	372	4	all	all	DET
ejpam-6358	372	5	j	j	PROPN
ejpam-6358	372	6	∈	∈	PROPN
ejpam-6358	372	7	ω	ω	PROPN
ejpam-6358	372	8	.	.	PUNCT
ejpam-6358	373	1	therefore	therefore	ADV
ejpam-6358	373	2	,	,	PUNCT
ejpam-6358	373	3	by	by	ADP
ejpam-6358	373	4	applying	apply	VERB
ejpam-6358	373	5	statements	statement	NOUN
ejpam-6358	373	6	1	1	NUM
ejpam-6358	373	7	and	and	CCONJ
ejpam-6358	373	8	2	2	NUM
ejpam-6358	373	9	,	,	PUNCT
ejpam-6358	373	10	we	we	PRON
ejpam-6358	373	11	conclude	conclude	VERB
ejpam-6358	373	12	that	that	SCONJ
ejpam-6358	373	13	ik	ik	PROPN
ejpam-6358	373	14	<	<	X
ejpam-6358	373	15	j>(s	j>(s	X
ejpam-6358	373	16	)	)	PUNCT
ejpam-6358	373	17	=	=	SYM
ejpam-6358	373	18	ikj	ikj	PROPN
ejpam-6358	373	19	(	(	PUNCT
ejpam-6358	373	20	s	s	NOUN
ejpam-6358	373	21	)	)	PUNCT
ejpam-6358	373	22	.	.	PUNCT
ejpam-6358	374	1	4	4	X
ejpam-6358	374	2	.	.	X
ejpam-6358	374	3	as	as	SCONJ
ejpam-6358	374	4	noted	note	VERB
ejpam-6358	374	5	in	in	ADP
ejpam-6358	374	6	[	[	X
ejpam-6358	374	7	18	18	NUM
ejpam-6358	374	8	]	]	PUNCT
ejpam-6358	374	9	,	,	PUNCT
ejpam-6358	374	10	the	the	DET
ejpam-6358	374	11	reflexivity	reflexivity	NOUN
ejpam-6358	374	12	of	of	ADP
ejpam-6358	374	13	r	r	NOUN
ejpam-6358	374	14	ensures	ensure	VERB
ejpam-6358	374	15	that	that	PRON
ejpam-6358	374	16	ρj(s	ρj(s	X
ejpam-6358	374	17	)	)	PUNCT
ejpam-6358	374	18	⊆	⊆	NUM
ejpam-6358	374	19	ωj(s	ωj(s	NUM
ejpam-6358	374	20	)	)	PUNCT
ejpam-6358	374	21	for	for	ADP
ejpam-6358	374	22	all	all	DET
ejpam-6358	374	23	j	j	PROPN
ejpam-6358	374	24	∈	∈	PROPN
ejpam-6358	374	25	ω	ω	PROPN
ejpam-6358	374	26	.	.	PUNCT
ejpam-6358	375	1	thus	thus	ADV
ejpam-6358	375	2	,	,	PUNCT
ejpam-6358	375	3	it	it	PRON
ejpam-6358	375	4	follows	follow	VERB
ejpam-6358	375	5	that	that	SCONJ
ejpam-6358	375	6	ρj(s	ρj(s	NUM
ejpam-6358	375	7	)	)	PUNCT
ejpam-6358	375	8	∩	∩	NOUN
ejpam-6358	375	9	ωj(s	ωj(s	NUM
ejpam-6358	375	10	)	)	PUNCT
ejpam-6358	375	11	=	=	SYM
ejpam-6358	375	12	ρj(s	ρj(s	NUM
ejpam-6358	375	13	)	)	PUNCT
ejpam-6358	375	14	and	and	CCONJ
ejpam-6358	375	15	ρj(s	ρj(s	NUM
ejpam-6358	375	16	)	)	PUNCT
ejpam-6358	375	17	∪	∪	ADP
ejpam-6358	375	18	ωj(s	ωj(s	NUM
ejpam-6358	375	19	)	)	PUNCT
ejpam-6358	375	20	=	=	SYM
ejpam-6358	375	21	ωj(s	ωj(s	NUM
ejpam-6358	375	22	)	)	PUNCT
ejpam-6358	375	23	,	,	PUNCT
ejpam-6358	375	24	for	for	ADP
ejpam-6358	375	25	all	all	DET
ejpam-6358	375	26	j	j	PROPN
ejpam-6358	375	27	∈	∈	PROPN
ejpam-6358	375	28	ω	ω	PROPN
ejpam-6358	375	29	.	.	PUNCT
ejpam-6358	376	1	as	as	SCONJ
ejpam-6358	376	2	noted	note	VERB
ejpam-6358	376	3	in	in	ADP
ejpam-6358	376	4	remark	remark	NOUN
ejpam-6358	376	5	3	3	NUM
ejpam-6358	376	6	,	,	PUNCT
ejpam-6358	376	7	the	the	DET
ejpam-6358	376	8	proof	proof	NOUN
ejpam-6358	376	9	of	of	ADP
ejpam-6358	376	10	item	item	NOUN
ejpam-6358	376	11	(	(	PUNCT
ejpam-6358	376	12	8)	8)	NUM
ejpam-6358	376	13	in	in	ADP
ejpam-6358	376	14	theorem	theorem	NOUN
ejpam-6358	376	15	3.4	3.4	NUM
ejpam-6358	376	16	from	from	ADP
ejpam-6358	376	17	[	[	X
ejpam-6358	376	18	40	40	NUM
ejpam-6358	376	19	]	]	PUNCT
ejpam-6358	376	20	contains	contain	VERB
ejpam-6358	376	21	inaccuracies	inaccuracy	NOUN
ejpam-6358	376	22	.	.	PUNCT
ejpam-6358	377	1	to	to	PART
ejpam-6358	377	2	address	address	VERB
ejpam-6358	377	3	this	this	PRON
ejpam-6358	377	4	,	,	PUNCT
ejpam-6358	377	5	we	we	PRON
ejpam-6358	377	6	present	present	VERB
ejpam-6358	377	7	the	the	DET
ejpam-6358	377	8	following	follow	VERB
ejpam-6358	377	9	lemma	lemma	PROPN
ejpam-6358	377	10	,	,	PUNCT
ejpam-6358	377	11	accompanied	accompany	VERB
ejpam-6358	377	12	by	by	ADP
ejpam-6358	377	13	a	a	DET
ejpam-6358	377	14	detailed	detailed	ADJ
ejpam-6358	377	15	proof	proof	NOUN
ejpam-6358	377	16	—	—	PUNCT
ejpam-6358	377	17	absent	absent	ADJ
ejpam-6358	377	18	in	in	ADP
ejpam-6358	377	19	[	[	PUNCT
ejpam-6358	377	20	40]—which	40]—which	PROPN
ejpam-6358	377	21	serves	serve	VERB
ejpam-6358	377	22	both	both	PRON
ejpam-6358	377	23	as	as	ADP
ejpam-6358	377	24	a	a	DET
ejpam-6358	377	25	correction	correction	NOUN
ejpam-6358	377	26	to	to	PART
ejpam-6358	377	27	item	item	VERB
ejpam-6358	377	28	(	(	PUNCT
ejpam-6358	377	29	8)	8)	NUM
ejpam-6358	377	30	of	of	ADP
ejpam-6358	377	31	theorem	theorem	NOUN
ejpam-6358	377	32	3.4	3.4	NUM
ejpam-6358	377	33	in	in	ADP
ejpam-6358	377	34	[	[	X
ejpam-6358	377	35	40	40	NUM
ejpam-6358	377	36	]	]	PUNCT
ejpam-6358	377	37	and	and	CCONJ
ejpam-6358	377	38	as	as	ADP
ejpam-6358	377	39	a	a	DET
ejpam-6358	377	40	supporting	support	VERB
ejpam-6358	377	41	result	result	NOUN
ejpam-6358	377	42	for	for	ADP
ejpam-6358	377	43	the	the	DET
ejpam-6358	377	44	proof	proof	NOUN
ejpam-6358	377	45	of	of	ADP
ejpam-6358	377	46	theorem	theorem	ADJ
ejpam-6358	377	47	7	7	NUM
ejpam-6358	377	48	:	:	PUNCT
ejpam-6358	377	49	lemma	lemma	PROPN
ejpam-6358	377	50	1	1	X
ejpam-6358	377	51	.	.	PUNCT
ejpam-6358	378	1	let	let	VERB
ejpam-6358	378	2	r	r	PRON
ejpam-6358	378	3	be	be	AUX
ejpam-6358	378	4	a	a	DET
ejpam-6358	378	5	symmetric	symmetric	ADJ
ejpam-6358	378	6	and	and	CCONJ
ejpam-6358	378	7	transitive	transitive	ADJ
ejpam-6358	378	8	relation	relation	NOUN
ejpam-6358	378	9	on	on	ADP
ejpam-6358	378	10	u	u	PROPN
ejpam-6358	378	11	.	.	PUNCT
ejpam-6358	379	1	then	then	ADV
ejpam-6358	379	2	,	,	PUNCT
ejpam-6358	379	3	for	for	ADP
ejpam-6358	379	4	all	all	DET
ejpam-6358	379	5	s	s	PROPN
ejpam-6358	379	6	,	,	PUNCT
ejpam-6358	379	7	t	t	PROPN
ejpam-6358	379	8	∈	∈	PROPN
ejpam-6358	379	9	u	u	NOUN
ejpam-6358	379	10	and	and	CCONJ
ejpam-6358	379	11	each	each	DET
ejpam-6358	379	12	j	j	PROPN
ejpam-6358	379	13	∈	∈	PROPN
ejpam-6358	379	14	ω	ω	PROPN
ejpam-6358	379	15	,	,	PUNCT
ejpam-6358	379	16	ωj(s	ωj(s	NUM
ejpam-6358	379	17	)	)	PUNCT
ejpam-6358	379	18	∩	∩	NOUN
ejpam-6358	379	19	ωj(t	ωj(t	NUM
ejpam-6358	379	20	)	)	PUNCT
ejpam-6358	379	21	̸=	̸=	NOUN
ejpam-6358	379	22	∅	∅	NOUN
ejpam-6358	379	23	if	if	SCONJ
ejpam-6358	379	24	and	and	CCONJ
ejpam-6358	379	25	only	only	ADV
ejpam-6358	379	26	if	if	SCONJ
ejpam-6358	379	27	ωj(s	ωj(	NOUN
ejpam-6358	379	28	)	)	PUNCT
ejpam-6358	379	29	=	=	SYM
ejpam-6358	379	30	ωj(t	ωj(t	NUM
ejpam-6358	379	31	)	)	PUNCT
ejpam-6358	379	32	.	.	PUNCT
ejpam-6358	380	1	proof	proof	NOUN
ejpam-6358	380	2	.	.	PUNCT
ejpam-6358	381	1	we	we	PRON
ejpam-6358	381	2	prove	prove	VERB
ejpam-6358	381	3	the	the	DET
ejpam-6358	381	4	case	case	NOUN
ejpam-6358	381	5	j	j	NOUN
ejpam-6358	381	6	=	=	PUNCT
ejpam-6358	381	7	a	a	PROPN
ejpam-6358	381	8	;	;	PUNCT
ejpam-6358	381	9	the	the	DET
ejpam-6358	381	10	argument	argument	NOUN
ejpam-6358	381	11	for	for	ADP
ejpam-6358	381	12	other	other	ADJ
ejpam-6358	381	13	values	value	NOUN
ejpam-6358	381	14	of	of	ADP
ejpam-6358	381	15	j	j	PROPN
ejpam-6358	381	16	is	be	AUX
ejpam-6358	381	17	identical	identical	ADJ
ejpam-6358	381	18	.	.	PUNCT
ejpam-6358	382	1	assume	assume	VERB
ejpam-6358	382	2	ωa(s	ωa(	NOUN
ejpam-6358	382	3	)	)	PUNCT
ejpam-6358	382	4	∩	∩	NOUN
ejpam-6358	382	5	ωa(t	ωa(t	NUM
ejpam-6358	382	6	)	)	PUNCT
ejpam-6358	382	7	̸=	̸=	NOUN
ejpam-6358	382	8	∅	∅	NOUN
ejpam-6358	382	9	,	,	PUNCT
ejpam-6358	382	10	and	and	CCONJ
ejpam-6358	382	11	let	let	VERB
ejpam-6358	382	12	q	q	PROPN
ejpam-6358	382	13	∈	∈	PROPN
ejpam-6358	382	14	ωa(s	ωa(	NOUN
ejpam-6358	382	15	)	)	PUNCT
ejpam-6358	382	16	∩	∩	NOUN
ejpam-6358	382	17	ωa(t	ωa(t	NUM
ejpam-6358	382	18	)	)	PUNCT
ejpam-6358	382	19	.	.	PUNCT
ejpam-6358	383	1	it	it	PRON
ejpam-6358	383	2	suffices	suffice	VERB
ejpam-6358	383	3	to	to	PART
ejpam-6358	383	4	show	show	VERB
ejpam-6358	383	5	that	that	SCONJ
ejpam-6358	383	6	ωa(s	ωa(	NOUN
ejpam-6358	383	7	)	)	PUNCT
ejpam-6358	383	8	=	=	SYM
ejpam-6358	383	9	ωa(q	ωa(q	X
ejpam-6358	383	10	)	)	PUNCT
ejpam-6358	383	11	and	and	CCONJ
ejpam-6358	383	12	ωa(t	ωa(t	NUM
ejpam-6358	383	13	)	)	PUNCT
ejpam-6358	383	14	=	=	SYM
ejpam-6358	383	15	ωa(q	ωa(q	NOUN
ejpam-6358	383	16	)	)	PUNCT
ejpam-6358	383	17	.	.	PUNCT
ejpam-6358	384	1	(	(	PUNCT
ejpam-6358	384	2	i	i	NOUN
ejpam-6358	384	3	)	)	PUNCT
ejpam-6358	384	4	ωa(s	ωa(	NOUN
ejpam-6358	384	5	)	)	PUNCT
ejpam-6358	384	6	=	=	SYM
ejpam-6358	384	7	ωa(q	ωa(q	NOUN
ejpam-6358	384	8	)	)	PUNCT
ejpam-6358	384	9	.	.	PUNCT
ejpam-6358	385	1	since	since	SCONJ
ejpam-6358	385	2	q	q	PROPN
ejpam-6358	385	3	∈	∈	PROPN
ejpam-6358	385	4	ωa(s	ωa(	NOUN
ejpam-6358	385	5	)	)	PUNCT
ejpam-6358	385	6	,	,	PUNCT
ejpam-6358	385	7	we	we	PRON
ejpam-6358	385	8	have	have	VERB
ejpam-6358	385	9	srq	srq	NOUN
ejpam-6358	385	10	,	,	PUNCT
ejpam-6358	385	11	(	(	PUNCT
ejpam-6358	385	12	1	1	X
ejpam-6358	385	13	)	)	PUNCT
ejpam-6358	385	14	qrs	qrs	NOUN
ejpam-6358	385	15	(	(	PUNCT
ejpam-6358	385	16	by	by	ADP
ejpam-6358	385	17	the	the	DET
ejpam-6358	385	18	symmetry	symmetry	NOUN
ejpam-6358	385	19	of	of	ADP
ejpam-6358	385	20	r	r	NOUN
ejpam-6358	385	21	)	)	PUNCT
ejpam-6358	385	22	.	.	PUNCT
ejpam-6358	386	1	(	(	PUNCT
ejpam-6358	386	2	2	2	X
ejpam-6358	386	3	)	)	PUNCT
ejpam-6358	386	4	if	if	SCONJ
ejpam-6358	386	5	x	x	PUNCT
ejpam-6358	386	6	∈	∈	NOUN
ejpam-6358	386	7	ωa(q	ωa(q	NOUN
ejpam-6358	386	8	)	)	PUNCT
ejpam-6358	386	9	,	,	PUNCT
ejpam-6358	386	10	then	then	ADV
ejpam-6358	386	11	qrx	qrx	VERB
ejpam-6358	386	12	,	,	PUNCT
ejpam-6358	386	13	and	and	CCONJ
ejpam-6358	386	14	by	by	ADP
ejpam-6358	386	15	(	(	PUNCT
ejpam-6358	386	16	1	1	NUM
ejpam-6358	386	17	)	)	PUNCT
ejpam-6358	386	18	and	and	CCONJ
ejpam-6358	386	19	the	the	DET
ejpam-6358	386	20	transitivity	transitivity	NOUN
ejpam-6358	386	21	of	of	ADP
ejpam-6358	386	22	r	r	NOUN
ejpam-6358	386	23	,	,	PUNCT
ejpam-6358	386	24	it	it	PRON
ejpam-6358	386	25	follows	follow	VERB
ejpam-6358	386	26	that	that	SCONJ
ejpam-6358	386	27	srx	srx	NOUN
ejpam-6358	386	28	,	,	PUNCT
ejpam-6358	386	29	so	so	ADV
ejpam-6358	386	30	x	x	SYM
ejpam-6358	386	31	∈	∈	NOUN
ejpam-6358	386	32	ωa(s	ωa(	NOUN
ejpam-6358	386	33	)	)	PUNCT
ejpam-6358	386	34	.	.	PUNCT
ejpam-6358	387	1	hence	hence	ADV
ejpam-6358	387	2	,	,	PUNCT
ejpam-6358	387	3	ωa(q	ωa(q	NOUN
ejpam-6358	387	4	)	)	PUNCT
ejpam-6358	387	5	⊆	⊆	NUM
ejpam-6358	387	6	ωa(s	ωa(s	NUM
ejpam-6358	387	7	)	)	PUNCT
ejpam-6358	387	8	.	.	PUNCT
ejpam-6358	388	1	r.	r.	PROPN
ejpam-6358	388	2	a.	a.	PROPN
ejpam-6358	388	3	hosny	hosny	PROPN
ejpam-6358	388	4	et	et	PROPN
ejpam-6358	388	5	al	al	PROPN
ejpam-6358	388	6	.	.	PUNCT
ejpam-6358	388	7	/	/	SYM
ejpam-6358	388	8	eur	eur	PROPN
ejpam-6358	388	9	.	.	PUNCT
ejpam-6358	389	1	j.	j.	PROPN
ejpam-6358	389	2	pure	pure	PROPN
ejpam-6358	389	3	appl	appl	PROPN
ejpam-6358	389	4	.	.	PROPN
ejpam-6358	389	5	math	math	PROPN
ejpam-6358	389	6	,	,	PUNCT
ejpam-6358	389	7	18	18	NUM
ejpam-6358	389	8	(	(	PUNCT
ejpam-6358	389	9	4	4	NUM
ejpam-6358	389	10	)	)	PUNCT
ejpam-6358	389	11	(	(	PUNCT
ejpam-6358	389	12	2025	2025	NUM
ejpam-6358	389	13	)	)	PUNCT
ejpam-6358	389	14	,	,	PUNCT
ejpam-6358	389	15	6358	6358	NUM
ejpam-6358	389	16	15	15	NUM
ejpam-6358	389	17	of	of	ADP
ejpam-6358	389	18	24	24	NUM
ejpam-6358	389	19	conversely	conversely	ADV
ejpam-6358	389	20	,	,	PUNCT
ejpam-6358	389	21	if	if	SCONJ
ejpam-6358	389	22	y	y	PROPN
ejpam-6358	389	23	∈	∈	PROPN
ejpam-6358	389	24	ωa(s	ωa(	NOUN
ejpam-6358	389	25	)	)	PUNCT
ejpam-6358	389	26	,	,	PUNCT
ejpam-6358	389	27	then	then	ADV
ejpam-6358	389	28	sry	sry	INTJ
ejpam-6358	389	29	,	,	PUNCT
ejpam-6358	389	30	and	and	CCONJ
ejpam-6358	389	31	by	by	ADP
ejpam-6358	389	32	(	(	PUNCT
ejpam-6358	389	33	2	2	NUM
ejpam-6358	389	34	)	)	PUNCT
ejpam-6358	389	35	and	and	CCONJ
ejpam-6358	389	36	transitivity	transitivity	NOUN
ejpam-6358	389	37	,	,	PUNCT
ejpam-6358	389	38	qry	qry	NOUN
ejpam-6358	389	39	,	,	PUNCT
ejpam-6358	389	40	so	so	ADV
ejpam-6358	389	41	y	y	PROPN
ejpam-6358	389	42	∈	∈	PROPN
ejpam-6358	389	43	ωa(q	ωa(q	NUM
ejpam-6358	389	44	)	)	PUNCT
ejpam-6358	389	45	.	.	PUNCT
ejpam-6358	390	1	thus	thus	ADV
ejpam-6358	390	2	,	,	PUNCT
ejpam-6358	390	3	ωa(s	ωa(	NOUN
ejpam-6358	390	4	)	)	PUNCT
ejpam-6358	390	5	⊆	⊆	NUM
ejpam-6358	390	6	ωa(q	ωa(q	NUM
ejpam-6358	390	7	)	)	PUNCT
ejpam-6358	390	8	,	,	PUNCT
ejpam-6358	390	9	and	and	CCONJ
ejpam-6358	390	10	therefore	therefore	ADV
ejpam-6358	390	11	ωa(s	ωa(s	NUM
ejpam-6358	390	12	)	)	PUNCT
ejpam-6358	390	13	=	=	SYM
ejpam-6358	391	1	ωa(q	ωa(q	NOUN
ejpam-6358	391	2	)	)	PUNCT
ejpam-6358	391	3	.	.	PUNCT
ejpam-6358	392	1	(	(	PUNCT
ejpam-6358	392	2	ii	ii	NOUN
ejpam-6358	392	3	)	)	PUNCT
ejpam-6358	392	4	ωa(t	ωa(t	PUNCT
ejpam-6358	392	5	)	)	PUNCT
ejpam-6358	392	6	=	=	SYM
ejpam-6358	392	7	ωa(q	ωa(q	NOUN
ejpam-6358	392	8	)	)	PUNCT
ejpam-6358	392	9	.	.	PUNCT
ejpam-6358	393	1	the	the	DET
ejpam-6358	393	2	same	same	ADJ
ejpam-6358	393	3	reasoning	reasoning	NOUN
ejpam-6358	393	4	applies	apply	VERB
ejpam-6358	393	5	,	,	PUNCT
ejpam-6358	393	6	since	since	SCONJ
ejpam-6358	393	7	q	q	PROPN
ejpam-6358	393	8	∈	∈	PROPN
ejpam-6358	393	9	ωa(t	ωa(t	PUNCT
ejpam-6358	393	10	)	)	PUNCT
ejpam-6358	393	11	implies	imply	VERB
ejpam-6358	393	12	trq	trq	NOUN
ejpam-6358	393	13	and	and	CCONJ
ejpam-6358	393	14	qrt	qrt	NOUN
ejpam-6358	393	15	,	,	PUNCT
ejpam-6358	393	16	and	and	CCONJ
ejpam-6358	393	17	the	the	DET
ejpam-6358	393	18	transitivity	transitivity	NOUN
ejpam-6358	393	19	argument	argument	NOUN
ejpam-6358	393	20	shows	show	VERB
ejpam-6358	393	21	that	that	PRON
ejpam-6358	393	22	ωa(t	ωa(t	PUNCT
ejpam-6358	393	23	)	)	PUNCT
ejpam-6358	393	24	=	=	SYM
ejpam-6358	393	25	ωa(q	ωa(q	NOUN
ejpam-6358	393	26	)	)	PUNCT
ejpam-6358	393	27	.	.	PUNCT
ejpam-6358	394	1	(	(	PUNCT
ejpam-6358	394	2	iii	iii	X
ejpam-6358	394	3	)	)	PUNCT
ejpam-6358	394	4	converse	converse	NOUN
ejpam-6358	394	5	direction	direction	NOUN
ejpam-6358	394	6	.	.	PUNCT
ejpam-6358	395	1	on	on	ADP
ejpam-6358	395	2	the	the	DET
ejpam-6358	395	3	other	other	ADJ
ejpam-6358	395	4	hand	hand	NOUN
ejpam-6358	395	5	,	,	PUNCT
ejpam-6358	395	6	it	it	PRON
ejpam-6358	395	7	is	be	AUX
ejpam-6358	395	8	easy	easy	ADJ
ejpam-6358	395	9	to	to	PART
ejpam-6358	395	10	see	see	VERB
ejpam-6358	395	11	,	,	PUNCT
ejpam-6358	395	12	using	use	VERB
ejpam-6358	395	13	the	the	DET
ejpam-6358	395	14	same	same	ADJ
ejpam-6358	395	15	reasoning	reasoning	NOUN
ejpam-6358	395	16	,	,	PUNCT
ejpam-6358	395	17	that	that	SCONJ
ejpam-6358	395	18	if	if	SCONJ
ejpam-6358	395	19	ωj(s	ωj(s	NUM
ejpam-6358	395	20	)	)	PUNCT
ejpam-6358	395	21	=	=	SYM
ejpam-6358	395	22	ωj(t	ωj(t	NUM
ejpam-6358	395	23	)	)	PUNCT
ejpam-6358	395	24	,	,	PUNCT
ejpam-6358	395	25	then	then	ADV
ejpam-6358	395	26	ωj(s	ωj(s	NUM
ejpam-6358	395	27	)	)	PUNCT
ejpam-6358	395	28	∩	∩	NOUN
ejpam-6358	395	29	ωj(t	ωj(t	NUM
ejpam-6358	395	30	)	)	PUNCT
ejpam-6358	395	31	̸=	̸=	PROPN
ejpam-6358	395	32	∅.	∅.	ADP
ejpam-6358	395	33	now	now	ADV
ejpam-6358	395	34	,	,	PUNCT
ejpam-6358	395	35	the	the	DET
ejpam-6358	395	36	proof	proof	NOUN
ejpam-6358	395	37	of	of	ADP
ejpam-6358	395	38	item	item	NOUN
ejpam-6358	395	39	(	(	PUNCT
ejpam-6358	395	40	8)	8)	NUM
ejpam-6358	395	41	in	in	ADP
ejpam-6358	395	42	theorem	theorem	NOUN
ejpam-6358	395	43	3.4	3.4	NUM
ejpam-6358	395	44	from	from	ADP
ejpam-6358	395	45	[	[	X
ejpam-6358	395	46	40	40	NUM
ejpam-6358	395	47	]	]	PUNCT
ejpam-6358	395	48	contains	contain	VERB
ejpam-6358	395	49	errors	error	NOUN
ejpam-6358	395	50	.	.	PUNCT
ejpam-6358	396	1	therefore	therefore	ADV
ejpam-6358	396	2	,	,	PUNCT
ejpam-6358	396	3	we	we	PRON
ejpam-6358	396	4	provide	provide	VERB
ejpam-6358	396	5	a	a	DET
ejpam-6358	396	6	revised	revise	VERB
ejpam-6358	396	7	and	and	CCONJ
ejpam-6358	396	8	corrected	correct	VERB
ejpam-6358	396	9	version	version	NOUN
ejpam-6358	396	10	as	as	SCONJ
ejpam-6358	396	11	follows	follow	VERB
ejpam-6358	396	12	:	:	PUNCT
ejpam-6358	396	13	theorem	theorem	NOUN
ejpam-6358	396	14	7	7	NUM
ejpam-6358	396	15	.	.	PUNCT
ejpam-6358	397	1	[	[	X
ejpam-6358	397	2	40	40	NUM
ejpam-6358	397	3	]	]	PUNCT
ejpam-6358	397	4	let	let	VERB
ejpam-6358	397	5	r	r	PRON
ejpam-6358	397	6	be	be	AUX
ejpam-6358	397	7	a	a	DET
ejpam-6358	397	8	symmetric	symmetric	ADJ
ejpam-6358	397	9	and	and	CCONJ
ejpam-6358	397	10	transitive	transitive	ADJ
ejpam-6358	397	11	relation	relation	NOUN
ejpam-6358	397	12	on	on	ADP
ejpam-6358	397	13	u	u	NOUN
ejpam-6358	397	14	,	,	PUNCT
ejpam-6358	397	15	and	and	CCONJ
ejpam-6358	397	16	let	let	VERB
ejpam-6358	397	17	k	k	PRON
ejpam-6358	397	18	be	be	AUX
ejpam-6358	397	19	an	an	DET
ejpam-6358	397	20	ideal	ideal	NOUN
ejpam-6358	397	21	on	on	ADP
ejpam-6358	397	22	u	u	PROPN
ejpam-6358	397	23	.	.	PUNCT
ejpam-6358	398	1	for	for	ADP
ejpam-6358	398	2	any	any	DET
ejpam-6358	398	3	s	s	X
ejpam-6358	398	4	∈	∈	PROPN
ejpam-6358	398	5	u	u	NOUN
ejpam-6358	398	6	and	and	CCONJ
ejpam-6358	398	7	j	j	PROPN
ejpam-6358	398	8	∈	∈	PROPN
ejpam-6358	398	9	ω	ω	PROPN
ejpam-6358	398	10	,	,	PUNCT
ejpam-6358	398	11	the	the	DET
ejpam-6358	398	12	following	follow	VERB
ejpam-6358	398	13	hold	hold	NOUN
ejpam-6358	398	14	:	:	PUNCT
ejpam-6358	398	15	(	(	PUNCT
ejpam-6358	398	16	i	i	NOUN
ejpam-6358	398	17	)	)	PUNCT
ejpam-6358	398	18	ikj	ikj	PROPN
ejpam-6358	398	19	(	(	PUNCT
ejpam-6358	398	20	s	s	NOUN
ejpam-6358	398	21	)	)	PUNCT
ejpam-6358	398	22	⊆	⊆	NUM
ejpam-6358	398	23	ωj(s	ωj(s	NUM
ejpam-6358	398	24	)	)	PUNCT
ejpam-6358	398	25	.	.	PUNCT
ejpam-6358	399	1	(	(	PUNCT
ejpam-6358	399	2	ii	ii	X
ejpam-6358	399	3	)	)	PUNCT
ejpam-6358	399	4	if	if	SCONJ
ejpam-6358	399	5	s	s	PROPN
ejpam-6358	399	6	∈	∈	PROPN
ejpam-6358	399	7	ikj	ikj	PROPN
ejpam-6358	399	8	(	(	PUNCT
ejpam-6358	399	9	t	t	PROPN
ejpam-6358	399	10	)	)	PUNCT
ejpam-6358	399	11	then	then	ADV
ejpam-6358	399	12	ikj	ikj	PROPN
ejpam-6358	399	13	(	(	PUNCT
ejpam-6358	399	14	s	s	PROPN
ejpam-6358	399	15	)	)	PUNCT
ejpam-6358	399	16	⊆	⊆	NUM
ejpam-6358	399	17	ikj	ikj	X
ejpam-6358	399	18	(	(	PUNCT
ejpam-6358	399	19	t	t	PROPN
ejpam-6358	399	20	)	)	PUNCT
ejpam-6358	399	21	.	.	PUNCT
ejpam-6358	400	1	proof	proof	NOUN
ejpam-6358	400	2	.	.	PUNCT
ejpam-6358	401	1	we	we	PRON
ejpam-6358	401	2	again	again	ADV
ejpam-6358	401	3	treat	treat	VERB
ejpam-6358	401	4	the	the	DET
ejpam-6358	401	5	case	case	NOUN
ejpam-6358	401	6	j	j	NOUN
ejpam-6358	401	7	=	=	PUNCT
ejpam-6358	401	8	a.	a.	NOUN
ejpam-6358	401	9	1	1	NUM
ejpam-6358	401	10	.	.	PUNCT
ejpam-6358	402	1	let	let	VERB
ejpam-6358	402	2	p	p	PROPN
ejpam-6358	402	3	∈	∈	PROPN
ejpam-6358	402	4	ika	ika	X
ejpam-6358	402	5	(	(	PUNCT
ejpam-6358	402	6	s	s	NOUN
ejpam-6358	402	7	)	)	PUNCT
ejpam-6358	402	8	.	.	PUNCT
ejpam-6358	403	1	by	by	ADP
ejpam-6358	403	2	definition	definition	NOUN
ejpam-6358	403	3	,	,	PUNCT
ejpam-6358	403	4	ωa(p	ωa(p	NUM
ejpam-6358	403	5	)	)	PUNCT
ejpam-6358	403	6	∩	∩	NOUN
ejpam-6358	403	7	ωa(s	ωa(	NOUN
ejpam-6358	403	8	)	)	PUNCT
ejpam-6358	403	9	̸∈	̸∈	PROPN
ejpam-6358	403	10	k	k	PROPN
ejpam-6358	403	11	,	,	PUNCT
ejpam-6358	403	12	so	so	ADV
ejpam-6358	403	13	in	in	ADP
ejpam-6358	403	14	particular	particular	ADJ
ejpam-6358	403	15	ωa(p	ωa(p	NUM
ejpam-6358	403	16	)	)	PUNCT
ejpam-6358	403	17	∩	∩	NOUN
ejpam-6358	403	18	ωa(s	ωa(	NOUN
ejpam-6358	403	19	)	)	PUNCT
ejpam-6358	403	20	̸=	̸=	PROPN
ejpam-6358	403	21	∅.	∅.	ADV
ejpam-6358	403	22	hence	hence	ADV
ejpam-6358	403	23	there	there	ADV
ejpam-6358	403	24	exists	exist	VERB
ejpam-6358	403	25	q	q	PROPN
ejpam-6358	403	26	∈	∈	PROPN
ejpam-6358	403	27	ωa(p	ωa(p	PRON
ejpam-6358	403	28	)	)	PUNCT
ejpam-6358	403	29	∩	∩	NOUN
ejpam-6358	403	30	ωa(s	ωa(	NOUN
ejpam-6358	403	31	)	)	PUNCT
ejpam-6358	403	32	with	with	ADP
ejpam-6358	403	33	prq	prq	PROPN
ejpam-6358	403	34	and	and	CCONJ
ejpam-6358	403	35	srq	srq	PROPN
ejpam-6358	403	36	.	.	PUNCT
ejpam-6358	404	1	symmetry	symmetry	NOUN
ejpam-6358	404	2	and	and	CCONJ
ejpam-6358	404	3	transitivity	transitivity	NOUN
ejpam-6358	404	4	of	of	ADP
ejpam-6358	404	5	r	r	NOUN
ejpam-6358	404	6	imply	imply	VERB
ejpam-6358	404	7	srp	srp	PROPN
ejpam-6358	404	8	,	,	PUNCT
ejpam-6358	404	9	i.e.	i.e.	X
ejpam-6358	404	10	p	p	PRON
ejpam-6358	404	11	∈	∈	PROPN
ejpam-6358	404	12	ωa(s	ωa(	NOUN
ejpam-6358	404	13	)	)	PUNCT
ejpam-6358	404	14	.	.	PUNCT
ejpam-6358	405	1	thus	thus	ADV
ejpam-6358	405	2	ika	ika	X
ejpam-6358	405	3	(	(	PUNCT
ejpam-6358	405	4	s	s	NOUN
ejpam-6358	405	5	)	)	PUNCT
ejpam-6358	405	6	⊆	⊆	NUM
ejpam-6358	405	7	ωa(s	ωa(s	NUM
ejpam-6358	405	8	)	)	PUNCT
ejpam-6358	405	9	.	.	PUNCT
ejpam-6358	406	1	2	2	X
ejpam-6358	406	2	.	.	X
ejpam-6358	406	3	suppose	suppose	VERB
ejpam-6358	406	4	s	s	X
ejpam-6358	406	5	∈	∈	PROPN
ejpam-6358	406	6	ika	ika	X
ejpam-6358	406	7	(	(	PUNCT
ejpam-6358	406	8	t	t	PROPN
ejpam-6358	406	9	)	)	PUNCT
ejpam-6358	406	10	,	,	PUNCT
ejpam-6358	406	11	so	so	ADV
ejpam-6358	406	12	ωa(s	ωa(	NOUN
ejpam-6358	406	13	)	)	PUNCT
ejpam-6358	406	14	∩	∩	NOUN
ejpam-6358	406	15	ωa(t	ωa(t	NUM
ejpam-6358	406	16	)	)	PUNCT
ejpam-6358	406	17	̸∈	̸∈	PROPN
ejpam-6358	406	18	k	k	PROPN
ejpam-6358	406	19	=	=	PROPN
ejpam-6358	406	20	⇒	⇒	NOUN
ejpam-6358	406	21	ωa(s	ωa(s	NUM
ejpam-6358	406	22	)	)	PUNCT
ejpam-6358	406	23	∩	∩	NOUN
ejpam-6358	406	24	ωa(t	ωa(t	NUM
ejpam-6358	406	25	)	)	PUNCT
ejpam-6358	406	26	̸=	̸=	PROPN
ejpam-6358	406	27	∅.	∅.	PRON
ejpam-6358	406	28	by	by	ADP
ejpam-6358	406	29	lemma	lemma	PROPN
ejpam-6358	406	30	1	1	NUM
ejpam-6358	406	31	,	,	PUNCT
ejpam-6358	406	32	ωa(s	ωa(s	NUM
ejpam-6358	406	33	)	)	PUNCT
ejpam-6358	406	34	=	=	SYM
ejpam-6358	406	35	ωa(t	ωa(t	X
ejpam-6358	406	36	)	)	PUNCT
ejpam-6358	406	37	and	and	CCONJ
ejpam-6358	406	38	hence	hence	ADV
ejpam-6358	406	39	ωa(s	ωa(s	NUM
ejpam-6358	406	40	)	)	PUNCT
ejpam-6358	406	41	̸∈	̸∈	PROPN
ejpam-6358	406	42	k	k	PROPN
ejpam-6358	406	43	,	,	PUNCT
ejpam-6358	406	44	ωa(t	ωa(t	NUM
ejpam-6358	406	45	)	)	PUNCT
ejpam-6358	406	46	̸∈	̸∈	PROPN
ejpam-6358	406	47	k.	k.	PROPN
ejpam-6358	406	48	now	now	ADV
ejpam-6358	406	49	let	let	VERB
ejpam-6358	406	50	p	p	PROPN
ejpam-6358	406	51	∈	∈	PROPN
ejpam-6358	406	52	ika	ika	X
ejpam-6358	406	53	(	(	PUNCT
ejpam-6358	406	54	s	s	NOUN
ejpam-6358	406	55	)	)	PUNCT
ejpam-6358	406	56	,	,	PUNCT
ejpam-6358	406	57	so	so	CCONJ
ejpam-6358	406	58	ωa(p	ωa(p	NUM
ejpam-6358	406	59	)	)	PUNCT
ejpam-6358	406	60	∩	∩	NOUN
ejpam-6358	406	61	ωa(s	ωa(	NOUN
ejpam-6358	406	62	)	)	PUNCT
ejpam-6358	406	63	̸∈	̸∈	PROPN
ejpam-6358	406	64	k	k	PROPN
ejpam-6358	406	65	=	=	PROPN
ejpam-6358	406	66	⇒	⇒	PROPN
ejpam-6358	406	67	ωa(p	ωa(p	NUM
ejpam-6358	406	68	)	)	PUNCT
ejpam-6358	406	69	∩	∩	NOUN
ejpam-6358	406	70	ωa(s	ωa(	NOUN
ejpam-6358	406	71	)	)	PUNCT
ejpam-6358	406	72	̸=	̸=	PROPN
ejpam-6358	406	73	∅.	∅.	PRON
ejpam-6358	406	74	again	again	ADV
ejpam-6358	406	75	by	by	ADP
ejpam-6358	406	76	lemma	lemma	PROPN
ejpam-6358	406	77	1	1	NUM
ejpam-6358	406	78	,	,	PUNCT
ejpam-6358	406	79	ωa(p	ωa(p	NUM
ejpam-6358	406	80	)	)	PUNCT
ejpam-6358	406	81	=	=	SYM
ejpam-6358	406	82	ωa(s	ωa(	NOUN
ejpam-6358	406	83	)	)	PUNCT
ejpam-6358	406	84	.	.	PUNCT
ejpam-6358	407	1	therefore	therefore	ADV
ejpam-6358	407	2	ωa(p	ωa(p	NUM
ejpam-6358	407	3	)	)	PUNCT
ejpam-6358	407	4	∩	∩	NOUN
ejpam-6358	407	5	ωa(t	ωa(t	NUM
ejpam-6358	407	6	)	)	PUNCT
ejpam-6358	407	7	=	=	SYM
ejpam-6358	407	8	ωa(s	ωa(s	X
ejpam-6358	407	9	)	)	PUNCT
ejpam-6358	407	10	̸∈	̸∈	PROPN
ejpam-6358	407	11	k	k	PROPN
ejpam-6358	407	12	,	,	PUNCT
ejpam-6358	407	13	and	and	CCONJ
ejpam-6358	407	14	hence	hence	ADV
ejpam-6358	407	15	p	p	X
ejpam-6358	407	16	∈	∈	PROPN
ejpam-6358	407	17	ika	ika	X
ejpam-6358	407	18	(	(	PUNCT
ejpam-6358	407	19	t	t	PROPN
ejpam-6358	407	20	)	)	PUNCT
ejpam-6358	407	21	,	,	PUNCT
ejpam-6358	407	22	completing	complete	VERB
ejpam-6358	407	23	the	the	DET
ejpam-6358	407	24	proof	proof	NOUN
ejpam-6358	407	25	.	.	PUNCT
ejpam-6358	408	1	r.	r.	PROPN
ejpam-6358	408	2	a.	a.	PROPN
ejpam-6358	408	3	hosny	hosny	PROPN
ejpam-6358	408	4	et	et	PROPN
ejpam-6358	408	5	al	al	PROPN
ejpam-6358	408	6	.	.	PUNCT
ejpam-6358	408	7	/	/	SYM
ejpam-6358	408	8	eur	eur	PROPN
ejpam-6358	408	9	.	.	PUNCT
ejpam-6358	409	1	j.	j.	PROPN
ejpam-6358	409	2	pure	pure	PROPN
ejpam-6358	409	3	appl	appl	PROPN
ejpam-6358	409	4	.	.	PROPN
ejpam-6358	409	5	math	math	PROPN
ejpam-6358	409	6	,	,	PUNCT
ejpam-6358	409	7	18	18	NUM
ejpam-6358	409	8	(	(	PUNCT
ejpam-6358	409	9	4	4	NUM
ejpam-6358	409	10	)	)	PUNCT
ejpam-6358	409	11	(	(	PUNCT
ejpam-6358	409	12	2025	2025	NUM
ejpam-6358	409	13	)	)	PUNCT
ejpam-6358	409	14	,	,	PUNCT
ejpam-6358	409	15	6358	6358	NUM
ejpam-6358	409	16	16	16	NUM
ejpam-6358	409	17	of	of	ADP
ejpam-6358	409	18	24	24	NUM
ejpam-6358	409	19	the	the	DET
ejpam-6358	409	20	converse	converse	NOUN
ejpam-6358	409	21	of	of	ADP
ejpam-6358	409	22	theorem	theorem	ADJ
ejpam-6358	409	23	7	7	NUM
ejpam-6358	409	24	(	(	PUNCT
ejpam-6358	409	25	1	1	NUM
ejpam-6358	409	26	)	)	PUNCT
ejpam-6358	409	27	does	do	AUX
ejpam-6358	409	28	not	not	PART
ejpam-6358	409	29	hold	hold	VERB
ejpam-6358	409	30	in	in	ADP
ejpam-6358	409	31	general	general	ADJ
ejpam-6358	409	32	,	,	PUNCT
ejpam-6358	409	33	as	as	SCONJ
ejpam-6358	409	34	demonstrated	demonstrate	VERB
ejpam-6358	409	35	by	by	ADP
ejpam-6358	409	36	the	the	DET
ejpam-6358	409	37	following	follow	VERB
ejpam-6358	409	38	example	example	NOUN
ejpam-6358	409	39	.	.	PUNCT
ejpam-6358	410	1	example	example	NOUN
ejpam-6358	410	2	5	5	NUM
ejpam-6358	410	3	.	.	PUNCT
ejpam-6358	411	1	consider	consider	VERB
ejpam-6358	411	2	the	the	DET
ejpam-6358	411	3	set	set	NOUN
ejpam-6358	411	4	u	u	NOUN
ejpam-6358	411	5	=	=	PUNCT
ejpam-6358	411	6	{	{	PUNCT
ejpam-6358	411	7	p	p	X
ejpam-6358	411	8	,	,	PUNCT
ejpam-6358	411	9	q	q	ADJ
ejpam-6358	411	10	,	,	PUNCT
ejpam-6358	411	11	s	s	PROPN
ejpam-6358	411	12	,	,	PUNCT
ejpam-6358	411	13	t	t	PROPN
ejpam-6358	411	14	}	}	PUNCT
ejpam-6358	411	15	with	with	ADP
ejpam-6358	411	16	the	the	DET
ejpam-6358	411	17	relation	relation	NOUN
ejpam-6358	411	18	r	r	NOUN
ejpam-6358	411	19	=	=	SYM
ejpam-6358	411	20	{	{	PUNCT
ejpam-6358	411	21	(	(	PUNCT
ejpam-6358	411	22	t	t	PROPN
ejpam-6358	411	23	,	,	PUNCT
ejpam-6358	411	24	t	t	PROPN
ejpam-6358	411	25	)	)	PUNCT
ejpam-6358	411	26	}	}	PUNCT
ejpam-6358	411	27	,	,	PUNCT
ejpam-6358	411	28	which	which	PRON
ejpam-6358	411	29	is	be	AUX
ejpam-6358	411	30	both	both	CCONJ
ejpam-6358	411	31	symmetric	symmetric	ADJ
ejpam-6358	411	32	and	and	CCONJ
ejpam-6358	411	33	transitive	transitive	ADJ
ejpam-6358	411	34	.	.	PUNCT
ejpam-6358	412	1	let	let	VERB
ejpam-6358	412	2	k	k	NOUN
ejpam-6358	412	3	=	=	PRON
ejpam-6358	412	4	{	{	PUNCT
ejpam-6358	412	5	∅	∅	NOUN
ejpam-6358	412	6	,	,	PUNCT
ejpam-6358	412	7	{	{	PUNCT
ejpam-6358	412	8	t	t	NOUN
ejpam-6358	412	9	}	}	PUNCT
ejpam-6358	412	10	}	}	PUNCT
ejpam-6358	412	11	be	be	AUX
ejpam-6358	412	12	an	an	DET
ejpam-6358	412	13	ideal	ideal	NOUN
ejpam-6358	412	14	on	on	ADP
ejpam-6358	412	15	u	u	PROPN
ejpam-6358	412	16	.	.	PUNCT
ejpam-6358	413	1	then	then	ADV
ejpam-6358	413	2	,	,	PUNCT
ejpam-6358	413	3	we	we	PRON
ejpam-6358	413	4	obtain	obtain	VERB
ejpam-6358	413	5	ωa(t	ωa(t	PUNCT
ejpam-6358	413	6	)	)	PUNCT
ejpam-6358	413	7	=	=	PRON
ejpam-6358	413	8	{	{	PUNCT
ejpam-6358	413	9	t	t	NOUN
ejpam-6358	413	10	}	}	PUNCT
ejpam-6358	413	11	and	and	CCONJ
ejpam-6358	413	12	ika	ika	PROPN
ejpam-6358	413	13	(	(	PUNCT
ejpam-6358	413	14	t	t	PROPN
ejpam-6358	413	15	)	)	PUNCT
ejpam-6358	413	16	=	=	PUNCT
ejpam-6358	413	17	∅.	∅.	ADP
ejpam-6358	413	18	consequently	consequently	ADV
ejpam-6358	413	19	,	,	PUNCT
ejpam-6358	413	20	it	it	PRON
ejpam-6358	413	21	follows	follow	VERB
ejpam-6358	413	22	that	that	PRON
ejpam-6358	413	23	ωa(t	ωa(t	PUNCT
ejpam-6358	413	24	)	)	PUNCT
ejpam-6358	413	25	⊈	⊈	PROPN
ejpam-6358	413	26	ika	ika	X
ejpam-6358	413	27	(	(	PUNCT
ejpam-6358	413	28	t	t	PROPN
ejpam-6358	413	29	)	)	PUNCT
ejpam-6358	413	30	.	.	PUNCT
ejpam-6358	414	1	table	table	NOUN
ejpam-6358	414	2	1	1	NUM
ejpam-6358	414	3	in	in	ADP
ejpam-6358	414	4	[	[	X
ejpam-6358	414	5	40	40	NUM
ejpam-6358	414	6	]	]	PUNCT
ejpam-6358	414	7	introduces	introduce	VERB
ejpam-6358	414	8	various	various	ADJ
ejpam-6358	414	9	kinds	kind	NOUN
ejpam-6358	414	10	of	of	ADP
ejpam-6358	414	11	neighborhoods	neighborhood	NOUN
ejpam-6358	414	12	,	,	PUNCT
ejpam-6358	414	13	including	include	VERB
ejpam-6358	414	14	ωj	ωj	NOUN
ejpam-6358	414	15	-	-	PUNCT
ejpam-6358	414	16	neighborhoods	neighborhood	NOUN
ejpam-6358	414	17	,	,	PUNCT
ejpam-6358	414	18	ρj	ρj	NOUN
ejpam-6358	414	19	-	-	NOUN
ejpam-6358	414	20	neighborhoods	neighborhood	NOUN
ejpam-6358	414	21	,	,	PUNCT
ejpam-6358	414	22	ij	ij	NOUN
ejpam-6358	414	23	-	-	NOUN
ejpam-6358	414	24	neighborhoods	neighborhood	NOUN
ejpam-6358	414	25	,	,	PUNCT
ejpam-6358	414	26	and	and	CCONJ
ejpam-6358	414	27	ikj	ikj	PROPN
ejpam-6358	414	28	-neighborhoods	-neighborhood	NOUN
ejpam-6358	414	29	,	,	PUNCT
ejpam-6358	414	30	for	for	ADP
ejpam-6358	414	31	each	each	DET
ejpam-6358	414	32	j	j	PROPN
ejpam-6358	414	33	∈	∈	PROPN
ejpam-6358	414	34	ω	ω	PROPN
ejpam-6358	414	35	.	.	PUNCT
ejpam-6358	415	1	in	in	ADP
ejpam-6358	415	2	this	this	DET
ejpam-6358	415	3	work	work	NOUN
ejpam-6358	415	4	,	,	PUNCT
ejpam-6358	415	5	we	we	PRON
ejpam-6358	415	6	address	address	VERB
ejpam-6358	415	7	and	and	CCONJ
ejpam-6358	415	8	correct	correct	VERB
ejpam-6358	415	9	several	several	ADJ
ejpam-6358	415	10	errors	error	NOUN
ejpam-6358	415	11	in	in	ADP
ejpam-6358	415	12	table	table	NOUN
ejpam-6358	415	13	1	1	NUM
ejpam-6358	415	14	,	,	PUNCT
ejpam-6358	415	15	that	that	PRON
ejpam-6358	415	16	create	create	VERB
ejpam-6358	415	17	ambiguity	ambiguity	NOUN
ejpam-6358	415	18	in	in	ADP
ejpam-6358	415	19	the	the	DET
ejpam-6358	415	20	intended	intended	ADJ
ejpam-6358	415	21	meaning	meaning	NOUN
ejpam-6358	415	22	.	.	PUNCT
ejpam-6358	416	1	specifically	specifically	ADV
ejpam-6358	416	2	,	,	PUNCT
ejpam-6358	416	3	while	while	SCONJ
ejpam-6358	416	4	a	a	DET
ejpam-6358	416	5	neighborhood	neighborhood	NOUN
ejpam-6358	416	6	of	of	ADP
ejpam-6358	416	7	a	a	DET
ejpam-6358	416	8	point	point	NOUN
ejpam-6358	416	9	in	in	ADP
ejpam-6358	416	10	the	the	DET
ejpam-6358	416	11	universe	universe	NOUN
ejpam-6358	416	12	can	can	AUX
ejpam-6358	416	13	be	be	AUX
ejpam-6358	416	14	equal	equal	ADJ
ejpam-6358	416	15	to	to	ADP
ejpam-6358	416	16	the	the	DET
ejpam-6358	416	17	empty	empty	ADJ
ejpam-6358	416	18	set	set	NOUN
ejpam-6358	416	19	,	,	PUNCT
ejpam-6358	416	20	it	it	PRON
ejpam-6358	416	21	should	should	AUX
ejpam-6358	416	22	not	not	PART
ejpam-6358	416	23	be	be	AUX
ejpam-6358	416	24	represented	represent	VERB
ejpam-6358	416	25	as	as	ADP
ejpam-6358	416	26	{	{	PUNCT
ejpam-6358	416	27	∅	∅	NOUN
ejpam-6358	416	28	}	}	PUNCT
ejpam-6358	416	29	.	.	PUNCT
ejpam-6358	417	1	furthermore	furthermore	ADV
ejpam-6358	417	2	,	,	PUNCT
ejpam-6358	417	3	table	table	NOUN
ejpam-6358	417	4	2	2	NUM
ejpam-6358	417	5	in	in	ADP
ejpam-6358	417	6	[	[	X
ejpam-6358	417	7	40	40	NUM
ejpam-6358	417	8	]	]	PUNCT
ejpam-6358	417	9	provides	provide	VERB
ejpam-6358	417	10	a	a	DET
ejpam-6358	417	11	comparative	comparative	ADJ
ejpam-6358	417	12	analysis	analysis	NOUN
ejpam-6358	417	13	of	of	ADP
ejpam-6358	417	14	the	the	DET
ejpam-6358	417	15	lower	low	ADJ
ejpam-6358	417	16	and	and	CCONJ
ejpam-6358	417	17	upper	upper	ADJ
ejpam-6358	417	18	operators	operator	NOUN
ejpam-6358	417	19	,	,	PUNCT
ejpam-6358	417	20	as	as	ADV
ejpam-6358	417	21	well	well	ADV
ejpam-6358	417	22	as	as	ADP
ejpam-6358	417	23	accuracy	accuracy	NOUN
ejpam-6358	417	24	measure	measure	NOUN
ejpam-6358	417	25	results	result	VERB
ejpam-6358	417	26	for	for	ADP
ejpam-6358	417	27	any	any	DET
ejpam-6358	417	28	subset	subset	NOUN
ejpam-6358	417	29	of	of	ADP
ejpam-6358	417	30	u	u	NOUN
ejpam-6358	417	31	,	,	PUNCT
ejpam-6358	417	32	with	with	ADP
ejpam-6358	417	33	respect	respect	NOUN
ejpam-6358	417	34	to	to	ADP
ejpam-6358	417	35	{	{	PUNCT
ejpam-6358	417	36	a	a	PRON
ejpam-6358	417	37	,	,	PUNCT
ejpam-6358	417	38	b	b	NOUN
ejpam-6358	417	39	,	,	PUNCT
ejpam-6358	417	40	i	i	PRON
ejpam-6358	417	41	,	,	PUNCT
ejpam-6358	417	42	u	u	NOUN
ejpam-6358	417	43	}	}	PUNCT
ejpam-6358	417	44	.	.	PUNCT
ejpam-6358	418	1	according	accord	VERB
ejpam-6358	418	2	to	to	ADP
ejpam-6358	418	3	remark	remark	NOUN
ejpam-6358	418	4	1	1	NUM
ejpam-6358	418	5	,	,	PUNCT
ejpam-6358	418	6	we	we	PRON
ejpam-6358	418	7	identify	identify	VERB
ejpam-6358	418	8	and	and	CCONJ
ejpam-6358	418	9	clarify	clarify	VERB
ejpam-6358	418	10	several	several	ADJ
ejpam-6358	418	11	observations	observation	NOUN
ejpam-6358	418	12	and	and	CCONJ
ejpam-6358	418	13	necessary	necessary	ADJ
ejpam-6358	418	14	corrections	correction	NOUN
ejpam-6358	418	15	related	relate	VERB
ejpam-6358	418	16	to	to	ADP
ejpam-6358	418	17	this	this	DET
ejpam-6358	418	18	table	table	NOUN
ejpam-6358	418	19	.	.	PUNCT
ejpam-6358	419	1	(	(	PUNCT
ejpam-6358	419	2	i	i	NOUN
ejpam-6358	419	3	)	)	PUNCT
ejpam-6358	419	4	since	since	SCONJ
ejpam-6358	419	5	r	r	NOUN
ejpam-6358	419	6	ika	ika	X
ejpam-6358	419	7	⋆	⋆	X
ejpam-6358	419	8	(	(	PUNCT
ejpam-6358	419	9	∅	∅	NOUN
ejpam-6358	419	10	)	)	PUNCT
ejpam-6358	419	11	=	=	SYM
ejpam-6358	419	12	{	{	PUNCT
ejpam-6358	419	13	q	q	X
ejpam-6358	419	14	,	,	PUNCT
ejpam-6358	419	15	s	s	PROPN
ejpam-6358	419	16	,	,	PUNCT
ejpam-6358	419	17	t	t	PROPN
ejpam-6358	419	18	}	}	PUNCT
ejpam-6358	419	19	,	,	PUNCT
ejpam-6358	419	20	it	it	PRON
ejpam-6358	419	21	follows	follow	VERB
ejpam-6358	419	22	that	that	SCONJ
ejpam-6358	419	23	r⋆ika	r⋆ika	PROPN
ejpam-6358	419	24	(	(	PUNCT
ejpam-6358	419	25	∅	∅	NOUN
ejpam-6358	419	26	)	)	PUNCT
ejpam-6358	419	27	=	=	PUNCT
ejpam-6358	419	28	∅.	∅.	ADP
ejpam-6358	419	29	consequently	consequently	ADV
ejpam-6358	419	30	,	,	PUNCT
ejpam-6358	419	31	acc	acc	PROPN
ejpam-6358	419	32	⋆ika	⋆ika	X
ejpam-6358	419	33	r	r	X
ejpam-6358	419	34	(	(	PUNCT
ejpam-6358	419	35	∅	∅	NOUN
ejpam-6358	419	36	)	)	PUNCT
ejpam-6358	419	37	is	be	AUX
ejpam-6358	419	38	not	not	PART
ejpam-6358	419	39	zero	zero	NUM
ejpam-6358	419	40	but	but	CCONJ
ejpam-6358	419	41	rather	rather	ADV
ejpam-6358	419	42	an	an	DET
ejpam-6358	419	43	indefinite	indefinite	ADJ
ejpam-6358	419	44	quantity	quantity	NOUN
ejpam-6358	419	45	.	.	PUNCT
ejpam-6358	420	1	by	by	ADP
ejpam-6358	420	2	the	the	DET
ejpam-6358	420	3	same	same	ADJ
ejpam-6358	420	4	manner	manner	NOUN
ejpam-6358	420	5	,	,	PUNCT
ejpam-6358	420	6	acc	acc	PROPN
ejpam-6358	420	7	⋆ikb	⋆ikb	PROPN
ejpam-6358	420	8	r	r	NOUN
ejpam-6358	420	9	(	(	PUNCT
ejpam-6358	420	10	∅	∅	NOUN
ejpam-6358	420	11	)	)	PUNCT
ejpam-6358	420	12	,	,	PUNCT
ejpam-6358	420	13	acc	acc	PROPN
ejpam-6358	420	14	⋆iki	⋆iki	PROPN
ejpam-6358	420	15	r	r	NOUN
ejpam-6358	420	16	(	(	PUNCT
ejpam-6358	420	17	∅	∅	NOUN
ejpam-6358	420	18	)	)	PUNCT
ejpam-6358	420	19	,	,	PUNCT
ejpam-6358	420	20	and	and	CCONJ
ejpam-6358	420	21	acc	acc	PROPN
ejpam-6358	420	22	⋆iku	⋆iku	NOUN
ejpam-6358	420	23	r	r	NOUN
ejpam-6358	420	24	(	(	PUNCT
ejpam-6358	420	25	{	{	PUNCT
ejpam-6358	420	26	p	p	NOUN
ejpam-6358	420	27	}	}	PUNCT
ejpam-6358	420	28	)	)	PUNCT
ejpam-6358	420	29	should	should	AUX
ejpam-6358	420	30	also	also	ADV
ejpam-6358	420	31	be	be	AUX
ejpam-6358	420	32	considered	consider	VERB
ejpam-6358	420	33	indefinite	indefinite	ADJ
ejpam-6358	420	34	quantities	quantity	NOUN
ejpam-6358	420	35	.	.	PUNCT
ejpam-6358	421	1	(	(	PUNCT
ejpam-6358	421	2	ii	ii	NOUN
ejpam-6358	421	3	)	)	PUNCT
ejpam-6358	421	4	since	since	SCONJ
ejpam-6358	421	5	r	r	NOUN
ejpam-6358	421	6	iku	iku	PROPN
ejpam-6358	421	7	⋆	⋆	X
ejpam-6358	421	8	(	(	PUNCT
ejpam-6358	421	9	∅	∅	NOUN
ejpam-6358	421	10	)	)	PUNCT
ejpam-6358	421	11	=	=	SYM
ejpam-6358	422	1	r⋆iku	r⋆iku	ADJ
ejpam-6358	422	2	(	(	PUNCT
ejpam-6358	422	3	∅	∅	NOUN
ejpam-6358	422	4	)	)	PUNCT
ejpam-6358	422	5	=	=	NOUN
ejpam-6358	422	6	∅	∅	NOUN
ejpam-6358	422	7	,	,	PUNCT
ejpam-6358	422	8	it	it	PRON
ejpam-6358	422	9	follows	follow	VERB
ejpam-6358	422	10	that	that	SCONJ
ejpam-6358	422	11	acc	acc	PROPN
ejpam-6358	422	12	⋆iku	⋆iku	NOUN
ejpam-6358	422	13	r	r	NOUN
ejpam-6358	422	14	(	(	PUNCT
ejpam-6358	422	15	∅	∅	NOUN
ejpam-6358	422	16	)	)	PUNCT
ejpam-6358	422	17	should	should	AUX
ejpam-6358	422	18	be	be	AUX
ejpam-6358	422	19	1	1	NUM
ejpam-6358	422	20	,	,	PUNCT
ejpam-6358	422	21	not	not	PART
ejpam-6358	422	22	zero	zero	NUM
ejpam-6358	422	23	.	.	PUNCT
ejpam-6358	423	1	(	(	PUNCT
ejpam-6358	423	2	iii	iii	NOUN
ejpam-6358	423	3	)	)	PUNCT
ejpam-6358	423	4	given	give	VERB
ejpam-6358	423	5	that	that	SCONJ
ejpam-6358	423	6	r	r	NOUN
ejpam-6358	423	7	ikb	ikb	NOUN
ejpam-6358	423	8	⋆	⋆	NOUN
ejpam-6358	423	9	(	(	PUNCT
ejpam-6358	423	10	∅	∅	NOUN
ejpam-6358	423	11	)	)	PUNCT
ejpam-6358	423	12	=	=	PUNCT
ejpam-6358	423	13	{	{	PUNCT
ejpam-6358	423	14	q	q	X
ejpam-6358	423	15	}	}	PUNCT
ejpam-6358	423	16	,	,	PUNCT
ejpam-6358	423	17	which	which	PRON
ejpam-6358	423	18	is	be	AUX
ejpam-6358	423	19	not	not	PART
ejpam-6358	423	20	equal	equal	ADJ
ejpam-6358	423	21	to	to	ADP
ejpam-6358	423	22	∅	∅	NOUN
ejpam-6358	423	23	,	,	PUNCT
ejpam-6358	423	24	it	it	PRON
ejpam-6358	423	25	follows	follow	VERB
ejpam-6358	423	26	that	that	SCONJ
ejpam-6358	423	27	acc	acc	PROPN
ejpam-6358	424	1	⋆ikb	⋆ikb	PROPN
ejpam-6358	424	2	r	r	NOUN
ejpam-6358	424	3	(	(	PUNCT
ejpam-6358	424	4	∅	∅	NOUN
ejpam-6358	424	5	)	)	PUNCT
ejpam-6358	424	6	is	be	AUX
ejpam-6358	424	7	also	also	ADV
ejpam-6358	424	8	an	an	DET
ejpam-6358	424	9	indefinite	indefinite	ADJ
ejpam-6358	424	10	quantity	quantity	NOUN
ejpam-6358	424	11	.	.	PUNCT
ejpam-6358	425	1	(	(	PUNCT
ejpam-6358	425	2	iv	iv	X
ejpam-6358	425	3	)	)	PUNCT
ejpam-6358	425	4	acc	acc	NOUN
ejpam-6358	425	5	⋆iki	⋆iki	PROPN
ejpam-6358	425	6	r	r	NOUN
ejpam-6358	425	7	(	(	PUNCT
ejpam-6358	425	8	∅	∅	NOUN
ejpam-6358	425	9	)	)	PUNCT
ejpam-6358	425	10	=	=	SYM
ejpam-6358	425	11	1	1	X
ejpam-6358	425	12	.	.	PUNCT
ejpam-6358	425	13	(	(	PUNCT
ejpam-6358	425	14	v	v	NOUN
ejpam-6358	425	15	)	)	PUNCT
ejpam-6358	425	16	since	since	SCONJ
ejpam-6358	425	17	r	r	NOUN
ejpam-6358	425	18	iku	iku	PROPN
ejpam-6358	425	19	⋆	⋆	X
ejpam-6358	425	20	(	(	PUNCT
ejpam-6358	425	21	{	{	PUNCT
ejpam-6358	425	22	p	p	NOUN
ejpam-6358	425	23	}	}	PUNCT
ejpam-6358	425	24	)	)	PUNCT
ejpam-6358	425	25	=	=	PRON
ejpam-6358	425	26	{	{	PUNCT
ejpam-6358	425	27	q	q	X
ejpam-6358	425	28	}	}	PUNCT
ejpam-6358	425	29	,	,	PUNCT
ejpam-6358	425	30	this	this	DET
ejpam-6358	425	31	set	set	NOUN
ejpam-6358	425	32	is	be	AUX
ejpam-6358	425	33	nonempty	nonempty	ADJ
ejpam-6358	425	34	.	.	PUNCT
ejpam-6358	426	1	item	item	NOUN
ejpam-6358	426	2	(	(	PUNCT
ejpam-6358	426	3	3	3	NUM
ejpam-6358	426	4	)	)	PUNCT
ejpam-6358	426	5	of	of	ADP
ejpam-6358	426	6	proposition	proposition	NOUN
ejpam-6358	426	7	4.3	4.3	NUM
ejpam-6358	426	8	in	in	ADP
ejpam-6358	426	9	[	[	X
ejpam-6358	426	10	40	40	NUM
ejpam-6358	426	11	]	]	PUNCT
ejpam-6358	426	12	,	,	PUNCT
ejpam-6358	426	13	which	which	PRON
ejpam-6358	426	14	asserts	assert	VERB
ejpam-6358	426	15	that	that	SCONJ
ejpam-6358	426	16	r⋆ika	r⋆ika	PROPN
ejpam-6358	426	17	(	(	PUNCT
ejpam-6358	426	18	u	u	NOUN
ejpam-6358	426	19	)	)	PUNCT
ejpam-6358	426	20	⊇	⊇	PROPN
ejpam-6358	426	21	u	u	NOUN
ejpam-6358	426	22	,	,	PUNCT
ejpam-6358	426	23	is	be	AUX
ejpam-6358	426	24	incorrect	incorrect	ADJ
ejpam-6358	426	25	.	.	PUNCT
ejpam-6358	427	1	as	as	SCONJ
ejpam-6358	427	2	illustrated	illustrate	VERB
ejpam-6358	427	3	in	in	ADP
ejpam-6358	427	4	table	table	NOUN
ejpam-6358	427	5	2	2	NUM
ejpam-6358	427	6	of	of	ADP
ejpam-6358	427	7	[	[	X
ejpam-6358	427	8	40	40	NUM
ejpam-6358	427	9	]	]	PUNCT
ejpam-6358	427	10	,	,	PUNCT
ejpam-6358	427	11	it	it	PRON
ejpam-6358	427	12	is	be	AUX
ejpam-6358	427	13	observed	observe	VERB
ejpam-6358	427	14	that	that	SCONJ
ejpam-6358	427	15	r⋆ika	r⋆ika	PROPN
ejpam-6358	427	16	(	(	PUNCT
ejpam-6358	427	17	u	u	NOUN
ejpam-6358	427	18	)	)	PUNCT
ejpam-6358	427	19	=	=	PUNCT
ejpam-6358	427	20	{	{	PUNCT
ejpam-6358	427	21	p	p	X
ejpam-6358	427	22	}	}	PUNCT
ejpam-6358	427	23	,	,	PUNCT
ejpam-6358	427	24	which	which	PRON
ejpam-6358	427	25	does	do	AUX
ejpam-6358	427	26	not	not	PART
ejpam-6358	427	27	satisfy	satisfy	VERB
ejpam-6358	427	28	r⋆ika	r⋆ika	PROPN
ejpam-6358	427	29	(	(	PUNCT
ejpam-6358	427	30	u	u	NOUN
ejpam-6358	427	31	)	)	PUNCT
ejpam-6358	427	32	⊇	⊇	PROPN
ejpam-6358	427	33	u	u	NOUN
ejpam-6358	427	34	.	.	PUNCT
ejpam-6358	428	1	consequently	consequently	ADV
ejpam-6358	428	2	,	,	PUNCT
ejpam-6358	428	3	several	several	ADJ
ejpam-6358	428	4	observations	observation	NOUN
ejpam-6358	428	5	and	and	CCONJ
ejpam-6358	428	6	necessary	necessary	ADJ
ejpam-6358	428	7	corrections	correction	NOUN
ejpam-6358	428	8	have	have	AUX
ejpam-6358	428	9	been	be	AUX
ejpam-6358	428	10	recorded	record	VERB
ejpam-6358	428	11	based	base	VERB
ejpam-6358	428	12	on	on	ADP
ejpam-6358	428	13	this	this	DET
ejpam-6358	428	14	table	table	NOUN
ejpam-6358	428	15	.	.	PUNCT
ejpam-6358	429	1	remark	remark	NOUN
ejpam-6358	429	2	4.4	4.4	NUM
ejpam-6358	429	3	in	in	ADP
ejpam-6358	429	4	[	[	X
ejpam-6358	429	5	40	40	NUM
ejpam-6358	429	6	]	]	PUNCT
ejpam-6358	429	7	further	far	ADV
ejpam-6358	429	8	asserts	assert	VERB
ejpam-6358	429	9	that	that	SCONJ
ejpam-6358	429	10	the	the	DET
ejpam-6358	429	11	inclusion	inclusion	NOUN
ejpam-6358	429	12	relations	relation	NOUN
ejpam-6358	429	13	in	in	ADP
ejpam-6358	429	14	proposition	proposition	NOUN
ejpam-6358	429	15	4.3	4.3	NUM
ejpam-6358	429	16	(	(	PUNCT
ejpam-6358	429	17	3	3	NUM
ejpam-6358	429	18	)	)	PUNCT
ejpam-6358	429	19	are	be	AUX
ejpam-6358	429	20	generally	generally	ADV
ejpam-6358	429	21	proper	proper	ADJ
ejpam-6358	429	22	.	.	PUNCT
ejpam-6358	430	1	however	however	ADV
ejpam-6358	430	2	,	,	PUNCT
ejpam-6358	430	3	this	this	DET
ejpam-6358	430	4	claim	claim	NOUN
ejpam-6358	430	5	is	be	AUX
ejpam-6358	430	6	also	also	ADV
ejpam-6358	430	7	inaccurate	inaccurate	ADJ
ejpam-6358	430	8	,	,	PUNCT
ejpam-6358	430	9	as	as	ADP
ejpam-6358	430	10	the	the	DET
ejpam-6358	430	11	inclusion	inclusion	NOUN
ejpam-6358	430	12	r⋆ika	r⋆ika	X
ejpam-6358	430	13	(	(	PUNCT
ejpam-6358	430	14	u	u	NOUN
ejpam-6358	430	15	)	)	PUNCT
ejpam-6358	430	16	⊆	⊆	NUM
ejpam-6358	430	17	u	u	NOUN
ejpam-6358	430	18	does	do	AUX
ejpam-6358	430	19	not	not	PART
ejpam-6358	430	20	hold	hold	VERB
ejpam-6358	430	21	in	in	ADP
ejpam-6358	430	22	this	this	DET
ejpam-6358	430	23	context	context	NOUN
ejpam-6358	430	24	.	.	PUNCT
ejpam-6358	431	1	according	accord	VERB
ejpam-6358	431	2	to	to	ADP
ejpam-6358	431	3	remark	remark	NOUN
ejpam-6358	431	4	1	1	NUM
ejpam-6358	431	5	,	,	PUNCT
ejpam-6358	431	6	table	table	NOUN
ejpam-6358	431	7	3	3	NUM
ejpam-6358	431	8	in	in	ADP
ejpam-6358	431	9	[	[	X
ejpam-6358	431	10	40	40	NUM
ejpam-6358	431	11	]	]	PUNCT
ejpam-6358	431	12	provides	provide	VERB
ejpam-6358	431	13	a	a	DET
ejpam-6358	431	14	comparative	comparative	ADJ
ejpam-6358	431	15	analysis	analysis	NOUN
ejpam-6358	431	16	between	between	ADP
ejpam-6358	431	17	the	the	DET
ejpam-6358	431	18	results	result	NOUN
ejpam-6358	431	19	derived	derive	VERB
ejpam-6358	431	20	from	from	ADP
ejpam-6358	431	21	the	the	DET
ejpam-6358	431	22	proposed	propose	VERB
ejpam-6358	431	23	definition	definition	NOUN
ejpam-6358	431	24	4.1	4.1	NUM
ejpam-6358	431	25	in	in	ADP
ejpam-6358	431	26	[	[	X
ejpam-6358	431	27	40	40	NUM
ejpam-6358	431	28	]	]	PUNCT
ejpam-6358	431	29	and	and	CCONJ
ejpam-6358	432	1	those	those	DET
ejpam-6358	432	2	obtained	obtain	VERB
ejpam-6358	432	3	from	from	ADP
ejpam-6358	432	4	definition	definition	NOUN
ejpam-6358	432	5	2.7	2.7	NUM
ejpam-6358	432	6	in	in	ADP
ejpam-6358	432	7	[	[	X
ejpam-6358	432	8	12	12	NUM
ejpam-6358	432	9	]	]	PUNCT
ejpam-6358	432	10	for	for	ADP
ejpam-6358	432	11	the	the	DET
ejpam-6358	432	12	case	case	NOUN
ejpam-6358	432	13	j	j	NOUN
ejpam-6358	432	14	=	=	PUNCT
ejpam-6358	432	15	a.	a.	NOUN
ejpam-6358	432	16	this	this	DET
ejpam-6358	432	17	comparison	comparison	NOUN
ejpam-6358	432	18	reveals	reveal	VERB
ejpam-6358	432	19	several	several	ADJ
ejpam-6358	432	20	observations	observation	NOUN
ejpam-6358	432	21	and	and	CCONJ
ejpam-6358	432	22	necessary	necessary	ADJ
ejpam-6358	432	23	corrections	correction	NOUN
ejpam-6358	432	24	,	,	PUNCT
ejpam-6358	432	25	as	as	SCONJ
ejpam-6358	432	26	outlined	outline	VERB
ejpam-6358	432	27	below	below	ADV
ejpam-6358	432	28	:	:	PUNCT
ejpam-6358	433	1	r.	r.	PROPN
ejpam-6358	433	2	a.	a.	PROPN
ejpam-6358	433	3	hosny	hosny	PROPN
ejpam-6358	433	4	et	et	PROPN
ejpam-6358	433	5	al	al	PROPN
ejpam-6358	433	6	.	.	PUNCT
ejpam-6358	433	7	/	/	SYM
ejpam-6358	433	8	eur	eur	PROPN
ejpam-6358	433	9	.	.	PUNCT
ejpam-6358	434	1	j.	j.	PROPN
ejpam-6358	434	2	pure	pure	PROPN
ejpam-6358	434	3	appl	appl	PROPN
ejpam-6358	434	4	.	.	PROPN
ejpam-6358	434	5	math	math	PROPN
ejpam-6358	434	6	,	,	PUNCT
ejpam-6358	434	7	18	18	NUM
ejpam-6358	434	8	(	(	PUNCT
ejpam-6358	434	9	4	4	NUM
ejpam-6358	434	10	)	)	PUNCT
ejpam-6358	434	11	(	(	PUNCT
ejpam-6358	434	12	2025	2025	NUM
ejpam-6358	434	13	)	)	PUNCT
ejpam-6358	434	14	,	,	PUNCT
ejpam-6358	434	15	6358	6358	NUM
ejpam-6358	434	16	17	17	NUM
ejpam-6358	434	17	of	of	ADP
ejpam-6358	434	18	24	24	NUM
ejpam-6358	434	19	(	(	PUNCT
ejpam-6358	434	20	i	i	NOUN
ejpam-6358	434	21	)	)	PUNCT
ejpam-6358	434	22	given	give	VERB
ejpam-6358	434	23	that	that	DET
ejpam-6358	434	24	rika	rika	X
ejpam-6358	434	25	⋆	⋆	X
ejpam-6358	434	26	(	(	PUNCT
ejpam-6358	434	27	∅	∅	NOUN
ejpam-6358	434	28	)	)	PUNCT
ejpam-6358	434	29	=	=	SYM
ejpam-6358	434	30	{	{	PUNCT
ejpam-6358	434	31	q	q	X
ejpam-6358	434	32	,	,	PUNCT
ejpam-6358	434	33	s	s	PROPN
ejpam-6358	434	34	,	,	PUNCT
ejpam-6358	434	35	t	t	PROPN
ejpam-6358	434	36	}	}	PUNCT
ejpam-6358	434	37	,	,	PUNCT
ejpam-6358	434	38	r⋆ika	r⋆ika	X
ejpam-6358	434	39	(	(	PUNCT
ejpam-6358	434	40	∅	∅	NOUN
ejpam-6358	434	41	)	)	PUNCT
ejpam-6358	434	42	=	=	NOUN
ejpam-6358	434	43	∅	∅	NOUN
ejpam-6358	435	1	,	,	PUNCT
ejpam-6358	435	2	it	it	PRON
ejpam-6358	435	3	follows	follow	VERB
ejpam-6358	435	4	that	that	SCONJ
ejpam-6358	435	5	acc	acc	PROPN
ejpam-6358	435	6	⋆ika	⋆ika	ADP
ejpam-6358	435	7	r	r	X
ejpam-6358	435	8	(	(	PUNCT
ejpam-6358	435	9	∅	∅	NOUN
ejpam-6358	435	10	)	)	PUNCT
ejpam-6358	435	11	is	be	AUX
ejpam-6358	435	12	not	not	PART
ejpam-6358	435	13	zero	zero	NUM
ejpam-6358	435	14	but	but	CCONJ
ejpam-6358	435	15	an	an	DET
ejpam-6358	435	16	indefinite	indefinite	ADJ
ejpam-6358	435	17	quantity	quantity	NOUN
ejpam-6358	435	18	.	.	PUNCT
ejpam-6358	436	1	(	(	PUNCT
ejpam-6358	436	2	ii	ii	NOUN
ejpam-6358	436	3	)	)	PUNCT
ejpam-6358	436	4	acc⋆ia	acc⋆ia	PROPN
ejpam-6358	436	5	r	r	NOUN
ejpam-6358	436	6	(	(	PUNCT
ejpam-6358	436	7	∅	∅	NOUN
ejpam-6358	436	8	)	)	PUNCT
ejpam-6358	436	9	should	should	AUX
ejpam-6358	436	10	be	be	AUX
ejpam-6358	436	11	1	1	NUM
ejpam-6358	436	12	,	,	PUNCT
ejpam-6358	436	13	not	not	PART
ejpam-6358	436	14	zero	zero	NUM
ejpam-6358	436	15	.	.	PUNCT
ejpam-6358	437	1	according	accord	VERB
ejpam-6358	437	2	to	to	ADP
ejpam-6358	437	3	remark	remark	NOUN
ejpam-6358	437	4	1	1	NUM
ejpam-6358	437	5	,	,	PUNCT
ejpam-6358	437	6	table	table	NOUN
ejpam-6358	437	7	4	4	NUM
ejpam-6358	437	8	in	in	ADP
ejpam-6358	437	9	[	[	X
ejpam-6358	437	10	40	40	NUM
ejpam-6358	437	11	]	]	PUNCT
ejpam-6358	437	12	presents	present	VERB
ejpam-6358	437	13	a	a	DET
ejpam-6358	437	14	comparative	comparative	ADJ
ejpam-6358	437	15	analysis	analysis	NOUN
ejpam-6358	437	16	of	of	ADP
ejpam-6358	437	17	results	result	NOUN
ejpam-6358	437	18	derived	derive	VERB
ejpam-6358	437	19	from	from	ADP
ejpam-6358	437	20	the	the	DET
ejpam-6358	437	21	proposed	propose	VERB
ejpam-6358	437	22	definition	definition	NOUN
ejpam-6358	437	23	4.1	4.1	NUM
ejpam-6358	437	24	from	from	ADP
ejpam-6358	437	25	[	[	X
ejpam-6358	437	26	40	40	NUM
ejpam-6358	437	27	]	]	PUNCT
ejpam-6358	437	28	,	,	PUNCT
ejpam-6358	437	29	alongside	alongside	ADP
ejpam-6358	437	30	those	those	PRON
ejpam-6358	437	31	of	of	ADP
ejpam-6358	437	32	definition	definition	NOUN
ejpam-6358	437	33	2	2	NUM
ejpam-6358	437	34	from	from	ADP
ejpam-6358	437	35	[	[	X
ejpam-6358	437	36	3	3	NUM
ejpam-6358	437	37	]	]	PUNCT
ejpam-6358	437	38	,	,	PUNCT
ejpam-6358	437	39	definition	definition	NOUN
ejpam-6358	437	40	3	3	NUM
ejpam-6358	437	41	from	from	ADP
ejpam-6358	437	42	[	[	X
ejpam-6358	437	43	5	5	NUM
ejpam-6358	437	44	]	]	PUNCT
ejpam-6358	437	45	and	and	CCONJ
ejpam-6358	437	46	definitions	definition	NOUN
ejpam-6358	437	47	4.3	4.3	NUM
ejpam-6358	437	48	,	,	PUNCT
ejpam-6358	437	49	4.5	4.5	NUM
ejpam-6358	437	50	in	in	ADP
ejpam-6358	437	51	[	[	X
ejpam-6358	437	52	17	17	NUM
ejpam-6358	437	53	]	]	PUNCT
ejpam-6358	437	54	for	for	ADP
ejpam-6358	437	55	the	the	DET
ejpam-6358	437	56	case	case	NOUN
ejpam-6358	437	57	j	j	PROPN
ejpam-6358	437	58	=	=	PROPN
ejpam-6358	437	59	b.	b.	PROPN
ejpam-6358	437	60	several	several	ADJ
ejpam-6358	437	61	omissions	omission	NOUN
ejpam-6358	437	62	and	and	CCONJ
ejpam-6358	437	63	errors	error	NOUN
ejpam-6358	437	64	were	be	AUX
ejpam-6358	437	65	identified	identify	VERB
ejpam-6358	437	66	in	in	ADP
ejpam-6358	437	67	this	this	DET
ejpam-6358	437	68	comparison	comparison	NOUN
ejpam-6358	437	69	,	,	PUNCT
ejpam-6358	437	70	as	as	SCONJ
ejpam-6358	437	71	outlined	outline	VERB
ejpam-6358	437	72	below	below	ADV
ejpam-6358	437	73	.	.	PUNCT
ejpam-6358	438	1	(	(	PUNCT
ejpam-6358	438	2	i	i	NOUN
ejpam-6358	438	3	)	)	PUNCT
ejpam-6358	438	4	since	since	SCONJ
ejpam-6358	438	5	r	r	PRON
ejpam-6358	438	6	ikb	ikb	ADV
ejpam-6358	438	7	⋆	⋆	NOUN
ejpam-6358	438	8	(	(	PUNCT
ejpam-6358	438	9	∅	∅	NOUN
ejpam-6358	438	10	)	)	PUNCT
ejpam-6358	438	11	=	=	PUNCT
ejpam-6358	438	12	{	{	PUNCT
ejpam-6358	438	13	q	q	X
ejpam-6358	438	14	}	}	PUNCT
ejpam-6358	438	15	,	,	PUNCT
ejpam-6358	438	16	which	which	PRON
ejpam-6358	438	17	is	be	AUX
ejpam-6358	438	18	not	not	PART
ejpam-6358	438	19	equal	equal	ADJ
ejpam-6358	438	20	to	to	ADP
ejpam-6358	438	21	∅	∅	NOUN
ejpam-6358	438	22	,	,	PUNCT
ejpam-6358	438	23	it	it	PRON
ejpam-6358	438	24	follows	follow	VERB
ejpam-6358	438	25	that	that	SCONJ
ejpam-6358	438	26	∅	∅	NOUN
ejpam-6358	438	27	is	be	AUX
ejpam-6358	438	28	rough	rough	ADJ
ejpam-6358	438	29	,	,	PUNCT
ejpam-6358	438	30	implying	imply	VERB
ejpam-6358	438	31	that	that	SCONJ
ejpam-6358	438	32	acc	acc	PROPN
ejpam-6358	438	33	⋆ikb	⋆ikb	PROPN
ejpam-6358	438	34	r	r	NOUN
ejpam-6358	438	35	(	(	PUNCT
ejpam-6358	438	36	∅	∅	NOUN
ejpam-6358	438	37	)	)	PUNCT
ejpam-6358	438	38	is	be	AUX
ejpam-6358	438	39	undefined	undefined	ADJ
ejpam-6358	438	40	.	.	PUNCT
ejpam-6358	439	1	(	(	PUNCT
ejpam-6358	439	2	ii	ii	X
ejpam-6358	439	3	)	)	PUNCT
ejpam-6358	439	4	rwb	rwb	PROPN
ejpam-6358	439	5	⋆	⋆	X
ejpam-6358	439	6	(	(	PUNCT
ejpam-6358	439	7	∅	∅	NOUN
ejpam-6358	439	8	)	)	PUNCT
ejpam-6358	439	9	=	=	NOUN
ejpam-6358	439	10	∅	∅	NOUN
ejpam-6358	439	11	,	,	PUNCT
ejpam-6358	439	12	rather	rather	ADV
ejpam-6358	439	13	than	than	ADP
ejpam-6358	439	14	{	{	PUNCT
ejpam-6358	439	15	q	q	NOUN
ejpam-6358	439	16	}	}	PUNCT
ejpam-6358	439	17	.	.	PUNCT
ejpam-6358	440	1	thus	thus	ADV
ejpam-6358	440	2	,	,	PUNCT
ejpam-6358	440	3	rwb	rwb	PROPN
ejpam-6358	440	4	⋆	⋆	X
ejpam-6358	440	5	(	(	PUNCT
ejpam-6358	440	6	∅	∅	NOUN
ejpam-6358	440	7	)	)	PUNCT
ejpam-6358	440	8	=	=	SYM
ejpam-6358	440	9	r⋆ωb(∅	r⋆ωb(∅	X
ejpam-6358	440	10	)	)	PUNCT
ejpam-6358	440	11	=	=	NOUN
ejpam-6358	440	12	∅	∅	NOUN
ejpam-6358	440	13	,	,	PUNCT
ejpam-6358	440	14	indicating	indicate	VERB
ejpam-6358	440	15	that	that	SCONJ
ejpam-6358	440	16	∅	∅	NOUN
ejpam-6358	440	17	is	be	AUX
ejpam-6358	440	18	exact	exact	ADJ
ejpam-6358	440	19	and	and	CCONJ
ejpam-6358	440	20	hence	hence	ADV
ejpam-6358	440	21	acc⋆wb	acc⋆wb	NOUN
ejpam-6358	440	22	r	r	NOUN
ejpam-6358	440	23	(	(	PUNCT
ejpam-6358	440	24	∅	∅	NOUN
ejpam-6358	440	25	)	)	PUNCT
ejpam-6358	440	26	=	=	SYM
ejpam-6358	440	27	1	1	X
ejpam-6358	440	28	.	.	PUNCT
ejpam-6358	440	29	(	(	PUNCT
ejpam-6358	440	30	iii	iii	X
ejpam-6358	440	31	)	)	PUNCT
ejpam-6358	440	32	rwb	rwb	PROPN
ejpam-6358	440	33	⋆	⋆	X
ejpam-6358	440	34	(	(	PUNCT
ejpam-6358	440	35	{	{	PUNCT
ejpam-6358	440	36	p	p	NOUN
ejpam-6358	440	37	}	}	PUNCT
ejpam-6358	440	38	)	)	PUNCT
ejpam-6358	441	1	=	=	PRON
ejpam-6358	441	2	{	{	PUNCT
ejpam-6358	441	3	p	p	X
ejpam-6358	441	4	,	,	PUNCT
ejpam-6358	441	5	s	s	PART
ejpam-6358	441	6	}	}	PUNCT
ejpam-6358	441	7	,	,	PUNCT
ejpam-6358	441	8	which	which	PRON
ejpam-6358	441	9	differs	differ	VERB
ejpam-6358	441	10	from	from	ADP
ejpam-6358	441	11	{	{	PUNCT
ejpam-6358	441	12	p	p	X
ejpam-6358	441	13	,	,	PUNCT
ejpam-6358	441	14	q	q	ADJ
ejpam-6358	441	15	,	,	PUNCT
ejpam-6358	441	16	s	s	PART
ejpam-6358	441	17	}	}	PUNCT
ejpam-6358	441	18	.	.	PUNCT
ejpam-6358	442	1	(	(	PUNCT
ejpam-6358	442	2	iv	iv	X
ejpam-6358	442	3	)	)	PUNCT
ejpam-6358	442	4	rwb	rwb	PROPN
ejpam-6358	442	5	⋆	⋆	X
ejpam-6358	442	6	(	(	PUNCT
ejpam-6358	442	7	{	{	PUNCT
ejpam-6358	442	8	q	q	NOUN
ejpam-6358	442	9	}	}	PUNCT
ejpam-6358	442	10	)	)	PUNCT
ejpam-6358	443	1	=	=	SYM
ejpam-6358	443	2	∅	∅	NOUN
ejpam-6358	443	3	,	,	PUNCT
ejpam-6358	443	4	rather	rather	ADV
ejpam-6358	443	5	than	than	ADP
ejpam-6358	443	6	{	{	PUNCT
ejpam-6358	443	7	q	q	NOUN
ejpam-6358	443	8	}	}	PUNCT
ejpam-6358	443	9	,	,	PUNCT
ejpam-6358	443	10	and	and	CCONJ
ejpam-6358	443	11	consequently	consequently	ADV
ejpam-6358	443	12	,	,	PUNCT
ejpam-6358	443	13	acc⋆wb	acc⋆wb	NOUN
ejpam-6358	443	14	r	r	NOUN
ejpam-6358	443	15	(	(	PUNCT
ejpam-6358	443	16	{	{	PUNCT
ejpam-6358	443	17	q	q	NOUN
ejpam-6358	443	18	}	}	PUNCT
ejpam-6358	443	19	)	)	PUNCT
ejpam-6358	443	20	=	=	SYM
ejpam-6358	443	21	0	0	X
ejpam-6358	443	22	.	.	PUNCT
ejpam-6358	444	1	(	(	PUNCT
ejpam-6358	444	2	v	v	NOUN
ejpam-6358	444	3	)	)	PUNCT
ejpam-6358	444	4	rwb	rwb	PROPN
ejpam-6358	444	5	⋆	⋆	X
ejpam-6358	444	6	(	(	PUNCT
ejpam-6358	444	7	{	{	PUNCT
ejpam-6358	444	8	s	s	NOUN
ejpam-6358	444	9	}	}	PUNCT
ejpam-6358	444	10	)	)	PUNCT
ejpam-6358	445	1	=	=	NOUN
ejpam-6358	445	2	∅	∅	NOUN
ejpam-6358	445	3	,	,	PUNCT
ejpam-6358	445	4	differing	differ	VERB
ejpam-6358	445	5	from	from	ADP
ejpam-6358	445	6	{	{	PUNCT
ejpam-6358	445	7	q	q	NOUN
ejpam-6358	445	8	}	}	PUNCT
ejpam-6358	445	9	.	.	PUNCT
ejpam-6358	446	1	(	(	PUNCT
ejpam-6358	446	2	vi	vi	X
ejpam-6358	446	3	)	)	PUNCT
ejpam-6358	446	4	rwb	rwb	X
ejpam-6358	446	5	⋆	⋆	X
ejpam-6358	446	6	(	(	PUNCT
ejpam-6358	446	7	{	{	PUNCT
ejpam-6358	446	8	p	p	X
ejpam-6358	446	9	,	,	PUNCT
ejpam-6358	446	10	q	q	NOUN
ejpam-6358	446	11	}	}	PUNCT
ejpam-6358	446	12	)	)	PUNCT
ejpam-6358	446	13	=	=	PRON
ejpam-6358	447	1	{	{	PUNCT
ejpam-6358	447	2	p	p	X
ejpam-6358	447	3	,	,	PUNCT
ejpam-6358	447	4	s	s	PART
ejpam-6358	447	5	}	}	PUNCT
ejpam-6358	447	6	,	,	PUNCT
ejpam-6358	447	7	which	which	PRON
ejpam-6358	447	8	is	be	AUX
ejpam-6358	447	9	not	not	PART
ejpam-6358	447	10	equal	equal	ADJ
ejpam-6358	447	11	to	to	ADP
ejpam-6358	447	12	u	u	PRON
ejpam-6358	447	13	.	.	PUNCT
ejpam-6358	448	1	also	also	ADV
ejpam-6358	448	2	,	,	PUNCT
ejpam-6358	448	3	acc⋆ωb	acc⋆ωb	ADV
ejpam-6358	448	4	r	r	X
ejpam-6358	448	5	(	(	PUNCT
ejpam-6358	448	6	{	{	PUNCT
ejpam-6358	448	7	p	p	X
ejpam-6358	448	8	,	,	PUNCT
ejpam-6358	448	9	q	q	NOUN
ejpam-6358	448	10	}	}	PUNCT
ejpam-6358	448	11	)	)	PUNCT
ejpam-6358	448	12	=	=	SYM
ejpam-6358	448	13	1	1	NUM
ejpam-6358	448	14	4	4	NUM
ejpam-6358	448	15	.	.	PUNCT
ejpam-6358	449	1	(	(	PUNCT
ejpam-6358	449	2	vii	vii	PROPN
ejpam-6358	449	3	)	)	PUNCT
ejpam-6358	449	4	rwb	rwb	PROPN
ejpam-6358	449	5	⋆	⋆	X
ejpam-6358	449	6	(	(	PUNCT
ejpam-6358	449	7	{	{	PUNCT
ejpam-6358	449	8	p	p	X
ejpam-6358	449	9	,	,	PUNCT
ejpam-6358	449	10	s	s	NOUN
ejpam-6358	449	11	}	}	PUNCT
ejpam-6358	449	12	)	)	PUNCT
ejpam-6358	449	13	=	=	PRON
ejpam-6358	449	14	{	{	PUNCT
ejpam-6358	449	15	p	p	X
ejpam-6358	449	16	,	,	PUNCT
ejpam-6358	449	17	s	s	PART
ejpam-6358	449	18	}	}	PUNCT
ejpam-6358	449	19	,	,	PUNCT
ejpam-6358	449	20	differing	differ	VERB
ejpam-6358	449	21	from	from	ADP
ejpam-6358	449	22	{	{	PUNCT
ejpam-6358	449	23	p	p	X
ejpam-6358	449	24	,	,	PUNCT
ejpam-6358	449	25	q	q	ADJ
ejpam-6358	449	26	,	,	PUNCT
ejpam-6358	449	27	s	s	PART
ejpam-6358	449	28	}	}	PUNCT
ejpam-6358	449	29	.	.	PUNCT
ejpam-6358	450	1	(	(	PUNCT
ejpam-6358	450	2	viii	viii	NOUN
ejpam-6358	450	3	)	)	PUNCT
ejpam-6358	450	4	rwb	rwb	PROPN
ejpam-6358	450	5	⋆	⋆	X
ejpam-6358	450	6	(	(	PUNCT
ejpam-6358	450	7	{	{	PUNCT
ejpam-6358	450	8	q	q	NOUN
ejpam-6358	450	9	,	,	PUNCT
ejpam-6358	450	10	s	s	NOUN
ejpam-6358	450	11	}	}	PUNCT
ejpam-6358	450	12	)	)	PUNCT
ejpam-6358	451	1	=	=	SYM
ejpam-6358	451	2	∅	∅	NOUN
ejpam-6358	451	3	,	,	PUNCT
ejpam-6358	451	4	which	which	PRON
ejpam-6358	451	5	does	do	AUX
ejpam-6358	451	6	not	not	PART
ejpam-6358	451	7	equal	equal	VERB
ejpam-6358	451	8	to	to	ADP
ejpam-6358	451	9	{	{	PUNCT
ejpam-6358	451	10	q	q	NOUN
ejpam-6358	451	11	}	}	PUNCT
ejpam-6358	451	12	.	.	PUNCT
ejpam-6358	452	1	furthermore	furthermore	ADV
ejpam-6358	452	2	,	,	PUNCT
ejpam-6358	452	3	acc⋆wb	acc⋆wb	NOUN
ejpam-6358	452	4	r	r	NOUN
ejpam-6358	452	5	(	(	PUNCT
ejpam-6358	452	6	{	{	PUNCT
ejpam-6358	452	7	q	q	NOUN
ejpam-6358	452	8	,	,	PUNCT
ejpam-6358	452	9	s	s	NOUN
ejpam-6358	452	10	}	}	PUNCT
ejpam-6358	452	11	)	)	PUNCT
ejpam-6358	452	12	=	=	SYM
ejpam-6358	453	1	0	0	X
ejpam-6358	453	2	.	.	PUNCT
ejpam-6358	453	3	(	(	PUNCT
ejpam-6358	453	4	ix	ix	INTJ
ejpam-6358	453	5	)	)	PUNCT
ejpam-6358	453	6	rwb	rwb	PROPN
ejpam-6358	453	7	⋆	⋆	X
ejpam-6358	453	8	(	(	PUNCT
ejpam-6358	453	9	{	{	PUNCT
ejpam-6358	453	10	p	p	X
ejpam-6358	453	11	,	,	PUNCT
ejpam-6358	453	12	q	q	ADJ
ejpam-6358	453	13	,	,	PUNCT
ejpam-6358	453	14	s	s	NOUN
ejpam-6358	453	15	}	}	PUNCT
ejpam-6358	453	16	)	)	PUNCT
ejpam-6358	453	17	=	=	PRON
ejpam-6358	454	1	{	{	PUNCT
ejpam-6358	454	2	p	p	X
ejpam-6358	454	3	,	,	PUNCT
ejpam-6358	454	4	s	s	PART
ejpam-6358	454	5	}	}	PUNCT
ejpam-6358	454	6	,	,	PUNCT
ejpam-6358	454	7	differing	differ	VERB
ejpam-6358	454	8	from	from	ADP
ejpam-6358	454	9	u	u	PROPN
ejpam-6358	454	10	.	.	PUNCT
ejpam-6358	455	1	moreover	moreover	ADV
ejpam-6358	455	2	,	,	PUNCT
ejpam-6358	455	3	acc⋆wb	acc⋆wb	NOUN
ejpam-6358	455	4	r	r	NOUN
ejpam-6358	455	5	(	(	PUNCT
ejpam-6358	455	6	{	{	PUNCT
ejpam-6358	455	7	p	p	X
ejpam-6358	455	8	,	,	PUNCT
ejpam-6358	455	9	q	q	ADJ
ejpam-6358	455	10	,	,	PUNCT
ejpam-6358	455	11	s	s	NOUN
ejpam-6358	455	12	}	}	PUNCT
ejpam-6358	455	13	)	)	PUNCT
ejpam-6358	455	14	=	=	SYM
ejpam-6358	455	15	1	1	NUM
ejpam-6358	455	16	2	2	NUM
ejpam-6358	455	17	.	.	PUNCT
ejpam-6358	456	1	(	(	PUNCT
ejpam-6358	456	2	x	x	X
ejpam-6358	456	3	)	)	PUNCT
ejpam-6358	456	4	rρb	rρb	NOUN
ejpam-6358	456	5	⋆	⋆	X
ejpam-6358	456	6	(	(	PUNCT
ejpam-6358	456	7	∅	∅	NOUN
ejpam-6358	456	8	)	)	PUNCT
ejpam-6358	456	9	=	=	NOUN
ejpam-6358	456	10	∅	∅	NOUN
ejpam-6358	456	11	,	,	PUNCT
ejpam-6358	456	12	differing	differ	VERB
ejpam-6358	456	13	from	from	ADP
ejpam-6358	456	14	{	{	PUNCT
ejpam-6358	456	15	t	t	NOUN
ejpam-6358	456	16	}	}	PUNCT
ejpam-6358	456	17	.	.	PUNCT
ejpam-6358	457	1	therefore	therefore	ADV
ejpam-6358	457	2	,	,	PUNCT
ejpam-6358	457	3	rρb	rρb	PROPN
ejpam-6358	457	4	⋆	⋆	X
ejpam-6358	457	5	(	(	PUNCT
ejpam-6358	457	6	∅	∅	NOUN
ejpam-6358	457	7	)	)	PUNCT
ejpam-6358	457	8	=	=	SYM
ejpam-6358	457	9	r⋆ρb(∅	r⋆ρb(∅	PROPN
ejpam-6358	457	10	)	)	PUNCT
ejpam-6358	457	11	=	=	NOUN
ejpam-6358	457	12	∅	∅	NOUN
ejpam-6358	457	13	,	,	PUNCT
ejpam-6358	457	14	implying	imply	VERB
ejpam-6358	457	15	that	that	SCONJ
ejpam-6358	457	16	∅	∅	NOUN
ejpam-6358	457	17	is	be	AUX
ejpam-6358	457	18	an	an	DET
ejpam-6358	457	19	exact	exact	ADJ
ejpam-6358	457	20	set	set	NOUN
ejpam-6358	457	21	,	,	PUNCT
ejpam-6358	457	22	and	and	CCONJ
ejpam-6358	457	23	hence	hence	ADV
ejpam-6358	457	24	acc⋆ρb	acc⋆ρb	VERB
ejpam-6358	457	25	r	r	NOUN
ejpam-6358	457	26	(	(	PUNCT
ejpam-6358	457	27	∅	∅	NOUN
ejpam-6358	457	28	)	)	PUNCT
ejpam-6358	457	29	=	=	SYM
ejpam-6358	457	30	1	1	X
ejpam-6358	457	31	.	.	PUNCT
ejpam-6358	457	32	(	(	PUNCT
ejpam-6358	457	33	xi	xi	NOUN
ejpam-6358	457	34	)	)	PUNCT
ejpam-6358	457	35	r⋆ρb(u	r⋆ρb(u	PROPN
ejpam-6358	457	36	)	)	PUNCT
ejpam-6358	457	37	=	=	SYM
ejpam-6358	457	38	u	u	NOUN
ejpam-6358	457	39	,	,	PUNCT
ejpam-6358	457	40	rather	rather	ADV
ejpam-6358	457	41	than	than	ADP
ejpam-6358	457	42	{	{	PUNCT
ejpam-6358	457	43	p	p	X
ejpam-6358	457	44	,	,	PUNCT
ejpam-6358	457	45	q	q	X
ejpam-6358	457	46	,	,	PUNCT
ejpam-6358	457	47	s	s	PART
ejpam-6358	457	48	}	}	PUNCT
ejpam-6358	457	49	.	.	PUNCT
ejpam-6358	458	1	(	(	PUNCT
ejpam-6358	458	2	xii	xii	NOUN
ejpam-6358	458	3	)	)	PUNCT
ejpam-6358	458	4	rρb	rρb	NOUN
ejpam-6358	458	5	⋆	⋆	X
ejpam-6358	458	6	(	(	PUNCT
ejpam-6358	458	7	{	{	PUNCT
ejpam-6358	458	8	p	p	NOUN
ejpam-6358	458	9	}	}	PUNCT
ejpam-6358	458	10	)	)	PUNCT
ejpam-6358	459	1	=	=	SYM
ejpam-6358	459	2	∅	∅	NOUN
ejpam-6358	459	3	,	,	PUNCT
ejpam-6358	459	4	instead	instead	ADV
ejpam-6358	459	5	of	of	ADP
ejpam-6358	459	6	{	{	PUNCT
ejpam-6358	459	7	t	t	NOUN
ejpam-6358	459	8	}	}	PUNCT
ejpam-6358	459	9	,	,	PUNCT
ejpam-6358	459	10	while	while	SCONJ
ejpam-6358	459	11	r⋆ρb({p	r⋆ρb({p	NOUN
ejpam-6358	459	12	}	}	PUNCT
ejpam-6358	459	13	)	)	PUNCT
ejpam-6358	459	14	=	=	PRON
ejpam-6358	459	15	{	{	PUNCT
ejpam-6358	459	16	p	p	X
ejpam-6358	459	17	,	,	PUNCT
ejpam-6358	459	18	s	s	PART
ejpam-6358	459	19	}	}	PUNCT
ejpam-6358	459	20	,	,	PUNCT
ejpam-6358	459	21	differing	differ	VERB
ejpam-6358	459	22	from	from	ADP
ejpam-6358	459	23	{	{	PUNCT
ejpam-6358	459	24	p	p	X
ejpam-6358	459	25	,	,	PUNCT
ejpam-6358	459	26	q	q	NOUN
ejpam-6358	459	27	}	}	PUNCT
ejpam-6358	459	28	.	.	PUNCT
ejpam-6358	460	1	(	(	PUNCT
ejpam-6358	460	2	xiii	xiii	PROPN
ejpam-6358	460	3	)	)	PUNCT
ejpam-6358	460	4	rρb	rρb	NOUN
ejpam-6358	460	5	⋆	⋆	X
ejpam-6358	460	6	(	(	PUNCT
ejpam-6358	460	7	{	{	PUNCT
ejpam-6358	460	8	q	q	NOUN
ejpam-6358	460	9	}	}	PUNCT
ejpam-6358	460	10	)	)	PUNCT
ejpam-6358	461	1	=	=	PRON
ejpam-6358	461	2	{	{	PUNCT
ejpam-6358	461	3	q	q	X
ejpam-6358	461	4	}	}	PUNCT
ejpam-6358	461	5	,	,	PUNCT
ejpam-6358	461	6	not	not	PART
ejpam-6358	461	7	{	{	PUNCT
ejpam-6358	461	8	q	q	ADJ
ejpam-6358	461	9	,	,	PUNCT
ejpam-6358	461	10	t	t	PROPN
ejpam-6358	461	11	}	}	PUNCT
ejpam-6358	461	12	.	.	PUNCT
ejpam-6358	462	1	(	(	PUNCT
ejpam-6358	462	2	xiv	xiv	PROPN
ejpam-6358	462	3	)	)	PUNCT
ejpam-6358	462	4	rρb	rρb	PROPN
ejpam-6358	462	5	⋆	⋆	X
ejpam-6358	462	6	(	(	PUNCT
ejpam-6358	462	7	{	{	PUNCT
ejpam-6358	462	8	s	s	NOUN
ejpam-6358	462	9	}	}	PUNCT
ejpam-6358	462	10	)	)	PUNCT
ejpam-6358	463	1	=	=	SYM
ejpam-6358	463	2	∅	∅	NOUN
ejpam-6358	463	3	,	,	PUNCT
ejpam-6358	463	4	rather	rather	ADV
ejpam-6358	463	5	than	than	ADP
ejpam-6358	463	6	{	{	PUNCT
ejpam-6358	463	7	t	t	NOUN
ejpam-6358	463	8	}	}	PUNCT
ejpam-6358	463	9	.	.	PUNCT
ejpam-6358	464	1	(	(	PUNCT
ejpam-6358	464	2	xv	xv	X
ejpam-6358	464	3	)	)	PUNCT
ejpam-6358	464	4	r⋆ρb({t	r⋆ρb({t	PROPN
ejpam-6358	464	5	}	}	PUNCT
ejpam-6358	464	6	)	)	PUNCT
ejpam-6358	465	1	=	=	SYM
ejpam-6358	465	2	{	{	PUNCT
ejpam-6358	465	3	t	t	NOUN
ejpam-6358	465	4	}	}	PUNCT
ejpam-6358	465	5	,	,	PUNCT
ejpam-6358	465	6	not	not	PART
ejpam-6358	465	7	∅.	∅.	VERB
ejpam-6358	465	8	(	(	PUNCT
ejpam-6358	465	9	xvi	xvi	NOUN
ejpam-6358	465	10	)	)	PUNCT
ejpam-6358	465	11	rρb	rρb	NOUN
ejpam-6358	465	12	⋆	⋆	X
ejpam-6358	465	13	(	(	PUNCT
ejpam-6358	465	14	{	{	PUNCT
ejpam-6358	465	15	p	p	X
ejpam-6358	465	16	,	,	PUNCT
ejpam-6358	465	17	q	q	NOUN
ejpam-6358	465	18	}	}	PUNCT
ejpam-6358	465	19	)	)	PUNCT
ejpam-6358	465	20	=	=	PRON
ejpam-6358	466	1	{	{	PUNCT
ejpam-6358	466	2	q	q	X
ejpam-6358	466	3	}	}	PUNCT
ejpam-6358	466	4	,	,	PUNCT
ejpam-6358	466	5	rather	rather	ADV
ejpam-6358	466	6	than	than	ADP
ejpam-6358	466	7	{	{	PUNCT
ejpam-6358	466	8	q	q	NOUN
ejpam-6358	466	9	,	,	PUNCT
ejpam-6358	466	10	t	t	PROPN
ejpam-6358	466	11	}	}	PUNCT
ejpam-6358	466	12	.	.	PUNCT
ejpam-6358	467	1	(	(	PUNCT
ejpam-6358	467	2	xvii	xvii	PROPN
ejpam-6358	467	3	)	)	PUNCT
ejpam-6358	467	4	rρb	rρb	PROPN
ejpam-6358	467	5	⋆	⋆	X
ejpam-6358	467	6	(	(	PUNCT
ejpam-6358	467	7	{	{	PUNCT
ejpam-6358	467	8	p	p	X
ejpam-6358	467	9	,	,	PUNCT
ejpam-6358	467	10	s	s	NOUN
ejpam-6358	467	11	}	}	PUNCT
ejpam-6358	467	12	)	)	PUNCT
ejpam-6358	468	1	=	=	PRON
ejpam-6358	468	2	{	{	PUNCT
ejpam-6358	468	3	p	p	X
ejpam-6358	468	4	,	,	PUNCT
ejpam-6358	468	5	s	s	PART
ejpam-6358	468	6	}	}	PUNCT
ejpam-6358	468	7	,	,	PUNCT
ejpam-6358	468	8	differing	differ	VERB
ejpam-6358	468	9	from	from	ADP
ejpam-6358	468	10	{	{	PUNCT
ejpam-6358	468	11	p	p	X
ejpam-6358	468	12	,	,	PUNCT
ejpam-6358	468	13	s	s	PROPN
ejpam-6358	468	14	,	,	PUNCT
ejpam-6358	468	15	t	t	PROPN
ejpam-6358	468	16	}	}	PUNCT
ejpam-6358	468	17	.	.	PUNCT
ejpam-6358	469	1	(	(	PUNCT
ejpam-6358	469	2	xviii	xviii	PROPN
ejpam-6358	469	3	)	)	PUNCT
ejpam-6358	469	4	rρb	rρb	NOUN
ejpam-6358	469	5	⋆	⋆	X
ejpam-6358	469	6	(	(	PUNCT
ejpam-6358	469	7	{	{	PUNCT
ejpam-6358	469	8	p	p	X
ejpam-6358	469	9	,	,	PUNCT
ejpam-6358	469	10	t	t	PROPN
ejpam-6358	469	11	}	}	PUNCT
ejpam-6358	469	12	)	)	PUNCT
ejpam-6358	470	1	=	=	PRON
ejpam-6358	470	2	{	{	PUNCT
ejpam-6358	470	3	t	t	NOUN
ejpam-6358	470	4	}	}	PUNCT
ejpam-6358	470	5	,	,	PUNCT
ejpam-6358	470	6	rather	rather	ADV
ejpam-6358	470	7	than	than	ADP
ejpam-6358	470	8	{	{	PUNCT
ejpam-6358	470	9	p	p	X
ejpam-6358	470	10	,	,	PUNCT
ejpam-6358	470	11	s	s	PROPN
ejpam-6358	470	12	,	,	PUNCT
ejpam-6358	470	13	t	t	PROPN
ejpam-6358	470	14	}	}	PUNCT
ejpam-6358	470	15	,	,	PUNCT
ejpam-6358	470	16	while	while	SCONJ
ejpam-6358	470	17	r⋆ρb({p	r⋆ρb({p	NOUN
ejpam-6358	470	18	,	,	PUNCT
ejpam-6358	470	19	t	t	NOUN
ejpam-6358	470	20	}	}	PUNCT
ejpam-6358	470	21	)	)	PUNCT
ejpam-6358	471	1	=	=	PRON
ejpam-6358	471	2	{	{	PUNCT
ejpam-6358	471	3	p	p	X
ejpam-6358	471	4	,	,	PUNCT
ejpam-6358	471	5	s	s	PROPN
ejpam-6358	471	6	,	,	PUNCT
ejpam-6358	471	7	t	t	PROPN
ejpam-6358	471	8	}	}	PUNCT
ejpam-6358	471	9	,	,	PUNCT
ejpam-6358	471	10	differing	differ	VERB
ejpam-6358	471	11	from	from	ADP
ejpam-6358	471	12	{	{	PUNCT
ejpam-6358	471	13	p	p	X
ejpam-6358	471	14	,	,	PUNCT
ejpam-6358	471	15	s	s	PART
ejpam-6358	471	16	}	}	PUNCT
ejpam-6358	471	17	.	.	PUNCT
ejpam-6358	472	1	in	in	ADP
ejpam-6358	472	2	addition	addition	NOUN
ejpam-6358	472	3	,	,	PUNCT
ejpam-6358	472	4	acc⋆ρb	acc⋆ρb	ADJ
ejpam-6358	472	5	r	r	NOUN
ejpam-6358	472	6	(	(	PUNCT
ejpam-6358	472	7	{	{	PUNCT
ejpam-6358	472	8	p	p	X
ejpam-6358	472	9	,	,	PUNCT
ejpam-6358	472	10	t	t	PROPN
ejpam-6358	472	11	}	}	PUNCT
ejpam-6358	472	12	)	)	PUNCT
ejpam-6358	472	13	=	=	SYM
ejpam-6358	472	14	1	1	NUM
ejpam-6358	472	15	3	3	NUM
ejpam-6358	472	16	.	.	PUNCT
ejpam-6358	473	1	r.	r.	PROPN
ejpam-6358	473	2	a.	a.	PROPN
ejpam-6358	473	3	hosny	hosny	PROPN
ejpam-6358	473	4	et	et	PROPN
ejpam-6358	473	5	al	al	PROPN
ejpam-6358	473	6	.	.	PUNCT
ejpam-6358	473	7	/	/	SYM
ejpam-6358	473	8	eur	eur	PROPN
ejpam-6358	473	9	.	.	PUNCT
ejpam-6358	474	1	j.	j.	PROPN
ejpam-6358	474	2	pure	pure	PROPN
ejpam-6358	474	3	appl	appl	PROPN
ejpam-6358	474	4	.	.	PROPN
ejpam-6358	474	5	math	math	PROPN
ejpam-6358	474	6	,	,	PUNCT
ejpam-6358	474	7	18	18	NUM
ejpam-6358	474	8	(	(	PUNCT
ejpam-6358	474	9	4	4	NUM
ejpam-6358	474	10	)	)	PUNCT
ejpam-6358	474	11	(	(	PUNCT
ejpam-6358	474	12	2025	2025	NUM
ejpam-6358	474	13	)	)	PUNCT
ejpam-6358	474	14	,	,	PUNCT
ejpam-6358	474	15	6358	6358	NUM
ejpam-6358	474	16	18	18	NUM
ejpam-6358	474	17	of	of	ADP
ejpam-6358	474	18	24	24	NUM
ejpam-6358	474	19	(	(	PUNCT
ejpam-6358	474	20	xix	xix	NOUN
ejpam-6358	474	21	)	)	PUNCT
ejpam-6358	474	22	rρb	rρb	NOUN
ejpam-6358	474	23	⋆	⋆	X
ejpam-6358	474	24	(	(	PUNCT
ejpam-6358	474	25	{	{	PUNCT
ejpam-6358	474	26	q	q	NOUN
ejpam-6358	474	27	,	,	PUNCT
ejpam-6358	474	28	s	s	NOUN
ejpam-6358	474	29	}	}	PUNCT
ejpam-6358	474	30	)	)	PUNCT
ejpam-6358	474	31	=	=	PRON
ejpam-6358	474	32	{	{	PUNCT
ejpam-6358	474	33	q	q	X
ejpam-6358	474	34	}	}	PUNCT
ejpam-6358	474	35	,	,	PUNCT
ejpam-6358	474	36	which	which	PRON
ejpam-6358	474	37	does	do	AUX
ejpam-6358	474	38	not	not	PART
ejpam-6358	474	39	equal	equal	VERB
ejpam-6358	474	40	to	to	ADP
ejpam-6358	474	41	{	{	PUNCT
ejpam-6358	474	42	q	q	PROPN
ejpam-6358	474	43	,	,	PUNCT
ejpam-6358	474	44	t	t	PROPN
ejpam-6358	474	45	}	}	PUNCT
ejpam-6358	474	46	.	.	PUNCT
ejpam-6358	475	1	(	(	PUNCT
ejpam-6358	475	2	xx	xx	X
ejpam-6358	475	3	)	)	PUNCT
ejpam-6358	475	4	r⋆ρb({q	r⋆ρb({q	PROPN
ejpam-6358	475	5	,	,	PUNCT
ejpam-6358	475	6	t	t	NOUN
ejpam-6358	475	7	}	}	PUNCT
ejpam-6358	475	8	)	)	PUNCT
ejpam-6358	476	1	=	=	PRON
ejpam-6358	476	2	{	{	PUNCT
ejpam-6358	476	3	q	q	PROPN
ejpam-6358	476	4	,	,	PUNCT
ejpam-6358	476	5	t	t	PROPN
ejpam-6358	476	6	}	}	PUNCT
ejpam-6358	476	7	,	,	PUNCT
ejpam-6358	476	8	rather	rather	ADV
ejpam-6358	476	9	than	than	ADP
ejpam-6358	476	10	{	{	PUNCT
ejpam-6358	476	11	q	q	NOUN
ejpam-6358	476	12	}	}	PUNCT
ejpam-6358	476	13	.	.	PUNCT
ejpam-6358	477	1	(	(	PUNCT
ejpam-6358	477	2	xxi	xxi	PROPN
ejpam-6358	477	3	)	)	PUNCT
ejpam-6358	477	4	r⋆ρb({s	r⋆ρb({s	PROPN
ejpam-6358	477	5	,	,	PUNCT
ejpam-6358	477	6	t	t	NOUN
ejpam-6358	477	7	}	}	PUNCT
ejpam-6358	477	8	)	)	PUNCT
ejpam-6358	478	1	=	=	PRON
ejpam-6358	478	2	{	{	PUNCT
ejpam-6358	478	3	p	p	X
ejpam-6358	478	4	,	,	PUNCT
ejpam-6358	478	5	s	s	PROPN
ejpam-6358	478	6	,	,	PUNCT
ejpam-6358	478	7	t	t	PROPN
ejpam-6358	478	8	}	}	PUNCT
ejpam-6358	478	9	,	,	PUNCT
ejpam-6358	478	10	not	not	PART
ejpam-6358	478	11	{	{	PUNCT
ejpam-6358	478	12	p	p	X
ejpam-6358	478	13	,	,	PUNCT
ejpam-6358	478	14	s	s	PART
ejpam-6358	478	15	}	}	PUNCT
ejpam-6358	478	16	.	.	PUNCT
ejpam-6358	479	1	(	(	PUNCT
ejpam-6358	479	2	xxii	xxii	NOUN
ejpam-6358	479	3	)	)	PUNCT
ejpam-6358	479	4	rρb	rρb	NOUN
ejpam-6358	479	5	⋆	⋆	X
ejpam-6358	479	6	(	(	PUNCT
ejpam-6358	479	7	{	{	PUNCT
ejpam-6358	479	8	p	p	X
ejpam-6358	479	9	,	,	PUNCT
ejpam-6358	479	10	q	q	ADJ
ejpam-6358	479	11	,	,	PUNCT
ejpam-6358	479	12	s	s	NOUN
ejpam-6358	479	13	}	}	PUNCT
ejpam-6358	479	14	)	)	PUNCT
ejpam-6358	480	1	=	=	PRON
ejpam-6358	480	2	{	{	PUNCT
ejpam-6358	480	3	p	p	X
ejpam-6358	480	4	,	,	PUNCT
ejpam-6358	480	5	q	q	X
ejpam-6358	480	6	,	,	PUNCT
ejpam-6358	480	7	s	s	PART
ejpam-6358	480	8	}	}	PUNCT
ejpam-6358	480	9	,	,	PUNCT
ejpam-6358	480	10	differing	differ	VERB
ejpam-6358	480	11	from	from	ADP
ejpam-6358	480	12	u	u	PROPN
ejpam-6358	480	13	.	.	PUNCT
ejpam-6358	481	1	(	(	PUNCT
ejpam-6358	481	2	xxiii	xxiii	PROPN
ejpam-6358	481	3	)	)	PUNCT
ejpam-6358	481	4	r⋆ρb({p	r⋆ρb({p	NOUN
ejpam-6358	481	5	,	,	PUNCT
ejpam-6358	481	6	q	q	NOUN
ejpam-6358	481	7	,	,	PUNCT
ejpam-6358	481	8	t	t	PROPN
ejpam-6358	481	9	}	}	PUNCT
ejpam-6358	481	10	)	)	PUNCT
ejpam-6358	482	1	=	=	SYM
ejpam-6358	482	2	u	u	NOUN
ejpam-6358	482	3	,	,	PUNCT
ejpam-6358	482	4	instead	instead	ADV
ejpam-6358	482	5	of	of	ADP
ejpam-6358	482	6	{	{	PUNCT
ejpam-6358	482	7	p	p	X
ejpam-6358	482	8	,	,	PUNCT
ejpam-6358	482	9	q	q	NOUN
ejpam-6358	482	10	}	}	PUNCT
ejpam-6358	482	11	.	.	PUNCT
ejpam-6358	483	1	additionally	additionally	ADV
ejpam-6358	483	2	,	,	PUNCT
ejpam-6358	483	3	acc⋆ρb	acc⋆ρb	ADJ
ejpam-6358	483	4	r	r	NOUN
ejpam-6358	483	5	(	(	PUNCT
ejpam-6358	483	6	{	{	PUNCT
ejpam-6358	483	7	p	p	X
ejpam-6358	483	8	,	,	PUNCT
ejpam-6358	483	9	q	q	NOUN
ejpam-6358	483	10	,	,	PUNCT
ejpam-6358	483	11	t	t	PROPN
ejpam-6358	483	12	}	}	PUNCT
ejpam-6358	483	13	)	)	PUNCT
ejpam-6358	483	14	=	=	SYM
ejpam-6358	483	15	1	1	NUM
ejpam-6358	483	16	2	2	NUM
ejpam-6358	483	17	.	.	PUNCT
ejpam-6358	484	1	(	(	PUNCT
ejpam-6358	484	2	xxiv	xxiv	NUM
ejpam-6358	484	3	)	)	PUNCT
ejpam-6358	484	4	rρb	rρb	PROPN
ejpam-6358	484	5	⋆	⋆	X
ejpam-6358	484	6	(	(	PUNCT
ejpam-6358	484	7	{	{	PUNCT
ejpam-6358	484	8	p	p	X
ejpam-6358	484	9	,	,	PUNCT
ejpam-6358	484	10	s	s	PROPN
ejpam-6358	484	11	,	,	PUNCT
ejpam-6358	484	12	t	t	NOUN
ejpam-6358	484	13	}	}	PUNCT
ejpam-6358	484	14	)	)	PUNCT
ejpam-6358	485	1	=	=	PRON
ejpam-6358	485	2	{	{	PUNCT
ejpam-6358	485	3	p	p	X
ejpam-6358	485	4	,	,	PUNCT
ejpam-6358	485	5	s	s	PROPN
ejpam-6358	485	6	,	,	PUNCT
ejpam-6358	485	7	t	t	PROPN
ejpam-6358	485	8	}	}	PUNCT
ejpam-6358	485	9	,	,	PUNCT
ejpam-6358	485	10	rather	rather	ADV
ejpam-6358	485	11	than	than	ADP
ejpam-6358	485	12	{	{	PUNCT
ejpam-6358	485	13	p	p	X
ejpam-6358	485	14	,	,	PUNCT
ejpam-6358	485	15	s	s	PART
ejpam-6358	485	16	}	}	PUNCT
ejpam-6358	485	17	,	,	PUNCT
ejpam-6358	485	18	and	and	CCONJ
ejpam-6358	485	19	r⋆ρb({p	r⋆ρb({p	NOUN
ejpam-6358	485	20	,	,	PUNCT
ejpam-6358	485	21	s	s	PROPN
ejpam-6358	485	22	,	,	PUNCT
ejpam-6358	485	23	t	t	NOUN
ejpam-6358	485	24	}	}	PUNCT
ejpam-6358	485	25	)	)	PUNCT
ejpam-6358	486	1	=	=	PRON
ejpam-6358	486	2	{	{	PUNCT
ejpam-6358	486	3	p	p	X
ejpam-6358	486	4	,	,	PUNCT
ejpam-6358	486	5	s	s	PROPN
ejpam-6358	486	6	,	,	PUNCT
ejpam-6358	486	7	t	t	PROPN
ejpam-6358	486	8	}	}	PUNCT
ejpam-6358	486	9	,	,	PUNCT
ejpam-6358	486	10	differing	differ	VERB
ejpam-6358	486	11	from	from	ADP
ejpam-6358	486	12	{	{	PUNCT
ejpam-6358	486	13	p	p	X
ejpam-6358	486	14	,	,	PUNCT
ejpam-6358	486	15	s	s	PART
ejpam-6358	486	16	}	}	PUNCT
ejpam-6358	486	17	.	.	PUNCT
ejpam-6358	487	1	moreover	moreover	ADV
ejpam-6358	487	2	,	,	PUNCT
ejpam-6358	487	3	acc⋆ρb	acc⋆ρb	ADJ
ejpam-6358	487	4	r	r	NOUN
ejpam-6358	487	5	(	(	PUNCT
ejpam-6358	487	6	{	{	PUNCT
ejpam-6358	487	7	p	p	X
ejpam-6358	487	8	,	,	PUNCT
ejpam-6358	487	9	s	s	PROPN
ejpam-6358	487	10	,	,	PUNCT
ejpam-6358	487	11	t	t	NOUN
ejpam-6358	487	12	}	}	PUNCT
ejpam-6358	487	13	)	)	PUNCT
ejpam-6358	487	14	=	=	SYM
ejpam-6358	487	15	1	1	X
ejpam-6358	487	16	.	.	PUNCT
ejpam-6358	487	17	(	(	PUNCT
ejpam-6358	487	18	xxv	xxv	PROPN
ejpam-6358	487	19	)	)	PUNCT
ejpam-6358	487	20	r⋆ρb({q	r⋆ρb({q	PROPN
ejpam-6358	487	21	,	,	PUNCT
ejpam-6358	487	22	s	s	PROPN
ejpam-6358	487	23	,	,	PUNCT
ejpam-6358	487	24	t	t	NOUN
ejpam-6358	487	25	}	}	PUNCT
ejpam-6358	487	26	)	)	PUNCT
ejpam-6358	487	27	=	=	SYM
ejpam-6358	487	28	u	u	NOUN
ejpam-6358	487	29	,	,	PUNCT
ejpam-6358	487	30	differing	differ	VERB
ejpam-6358	487	31	from	from	ADP
ejpam-6358	487	32	{	{	PUNCT
ejpam-6358	487	33	p	p	X
ejpam-6358	487	34	,	,	PUNCT
ejpam-6358	487	35	q	q	ADJ
ejpam-6358	487	36	}	}	PUNCT
ejpam-6358	487	37	.	.	PUNCT
ejpam-6358	488	1	remark	remark	PROPN
ejpam-6358	488	2	4	4	NUM
ejpam-6358	488	3	.	.	PUNCT
ejpam-6358	489	1	in	in	ADP
ejpam-6358	489	2	the	the	DET
ejpam-6358	489	3	proof	proof	NOUN
ejpam-6358	489	4	of	of	ADP
ejpam-6358	489	5	theorem	theorem	ADJ
ejpam-6358	489	6	5.1	5.1	NUM
ejpam-6358	489	7	in	in	ADP
ejpam-6358	489	8	[	[	X
ejpam-6358	489	9	40	40	NUM
ejpam-6358	489	10	]	]	PUNCT
ejpam-6358	489	11	,	,	PUNCT
ejpam-6358	489	12	the	the	DET
ejpam-6358	489	13	symbol	symbol	NOUN
ejpam-6358	489	14	i	i	PRON
ejpam-6358	489	15	should	should	AUX
ejpam-6358	489	16	be	be	AUX
ejpam-6358	489	17	modified	modify	VERB
ejpam-6358	489	18	into	into	ADP
ejpam-6358	489	19	the	the	DET
ejpam-6358	489	20	symbol	symbol	NOUN
ejpam-6358	489	21	k.	k.	PROPN
ejpam-6358	489	22	items	item	NOUN
ejpam-6358	489	23	(	(	PUNCT
ejpam-6358	489	24	5	5	NUM
ejpam-6358	489	25	)	)	PUNCT
ejpam-6358	489	26	and	and	CCONJ
ejpam-6358	489	27	(	(	PUNCT
ejpam-6358	489	28	8)	8)	NUM
ejpam-6358	489	29	of	of	ADP
ejpam-6358	489	30	proposition	proposition	NOUN
ejpam-6358	489	31	5.4	5.4	NUM
ejpam-6358	489	32	in	in	ADP
ejpam-6358	489	33	[	[	X
ejpam-6358	489	34	40	40	NUM
ejpam-6358	489	35	]	]	PUNCT
ejpam-6358	489	36	are	be	AUX
ejpam-6358	489	37	not	not	PART
ejpam-6358	489	38	generally	generally	ADV
ejpam-6358	489	39	valid	valid	ADJ
ejpam-6358	489	40	,	,	PUNCT
ejpam-6358	489	41	as	as	SCONJ
ejpam-6358	489	42	evidenced	evidence	VERB
ejpam-6358	489	43	by	by	ADP
ejpam-6358	489	44	the	the	DET
ejpam-6358	489	45	following	follow	VERB
ejpam-6358	489	46	example	example	NOUN
ejpam-6358	489	47	.	.	PUNCT
ejpam-6358	490	1	example	example	NOUN
ejpam-6358	491	1	6	6	NUM
ejpam-6358	491	2	.	.	PUNCT
ejpam-6358	491	3	consider	consider	VERB
ejpam-6358	491	4	the	the	DET
ejpam-6358	491	5	reflexive	reflexive	ADJ
ejpam-6358	491	6	relation	relation	NOUN
ejpam-6358	491	7	r	r	NOUN
ejpam-6358	491	8	=	=	PRON
ejpam-6358	491	9	{	{	PUNCT
ejpam-6358	491	10	(	(	PUNCT
ejpam-6358	491	11	p	p	X
ejpam-6358	491	12	,	,	PUNCT
ejpam-6358	491	13	p	p	NOUN
ejpam-6358	491	14	)	)	PUNCT
ejpam-6358	491	15	,	,	PUNCT
ejpam-6358	491	16	(	(	PUNCT
ejpam-6358	491	17	p	p	X
ejpam-6358	491	18	,	,	PUNCT
ejpam-6358	491	19	s	s	PART
ejpam-6358	491	20	)	)	PUNCT
ejpam-6358	491	21	,	,	PUNCT
ejpam-6358	491	22	(	(	PUNCT
ejpam-6358	491	23	p	p	X
ejpam-6358	491	24	,	,	PUNCT
ejpam-6358	491	25	t	t	PROPN
ejpam-6358	491	26	)	)	PUNCT
ejpam-6358	491	27	,	,	PUNCT
ejpam-6358	491	28	(	(	PUNCT
ejpam-6358	491	29	q	q	X
ejpam-6358	491	30	,	,	PUNCT
ejpam-6358	491	31	t	t	PROPN
ejpam-6358	491	32	)	)	PUNCT
ejpam-6358	491	33	,	,	PUNCT
ejpam-6358	491	34	(	(	PUNCT
ejpam-6358	491	35	q	q	X
ejpam-6358	491	36	,	,	PUNCT
ejpam-6358	491	37	q	q	NOUN
ejpam-6358	491	38	)	)	PUNCT
ejpam-6358	491	39	,	,	PUNCT
ejpam-6358	491	40	(	(	PUNCT
ejpam-6358	491	41	s	s	X
ejpam-6358	491	42	,	,	PUNCT
ejpam-6358	491	43	s	s	PART
ejpam-6358	491	44	)	)	PUNCT
ejpam-6358	491	45	,	,	PUNCT
ejpam-6358	491	46	(	(	PUNCT
ejpam-6358	491	47	t	t	PROPN
ejpam-6358	491	48	,	,	PUNCT
ejpam-6358	491	49	q	q	NOUN
ejpam-6358	491	50	)	)	PUNCT
ejpam-6358	491	51	,	,	PUNCT
ejpam-6358	491	52	(	(	PUNCT
ejpam-6358	491	53	t	t	PROPN
ejpam-6358	491	54	,	,	PUNCT
ejpam-6358	491	55	t	t	PROPN
ejpam-6358	491	56	)	)	PUNCT
ejpam-6358	491	57	}	}	PUNCT
ejpam-6358	491	58	on	on	ADP
ejpam-6358	491	59	u	u	NOUN
ejpam-6358	491	60	=	=	PUNCT
ejpam-6358	491	61	{	{	PUNCT
ejpam-6358	491	62	p	p	X
ejpam-6358	491	63	,	,	PUNCT
ejpam-6358	491	64	q	q	ADJ
ejpam-6358	491	65	,	,	PUNCT
ejpam-6358	491	66	s	s	PROPN
ejpam-6358	491	67	,	,	PUNCT
ejpam-6358	491	68	t	t	PROPN
ejpam-6358	491	69	}	}	PUNCT
ejpam-6358	491	70	.	.	PUNCT
ejpam-6358	492	1	if	if	SCONJ
ejpam-6358	492	2	the	the	DET
ejpam-6358	492	3	ideal	ideal	NOUN
ejpam-6358	492	4	is	be	AUX
ejpam-6358	492	5	given	give	VERB
ejpam-6358	492	6	by	by	ADP
ejpam-6358	492	7	k	k	PROPN
ejpam-6358	492	8	=	=	PUNCT
ejpam-6358	492	9	{	{	PUNCT
ejpam-6358	492	10	∅	∅	NOUN
ejpam-6358	492	11	,	,	PUNCT
ejpam-6358	492	12	{	{	PUNCT
ejpam-6358	492	13	s	s	X
ejpam-6358	492	14	}	}	PUNCT
ejpam-6358	492	15	,	,	PUNCT
ejpam-6358	492	16	{	{	PUNCT
ejpam-6358	492	17	t	t	NOUN
ejpam-6358	492	18	}	}	PUNCT
ejpam-6358	492	19	,	,	PUNCT
ejpam-6358	492	20	{	{	PUNCT
ejpam-6358	492	21	s	s	PROPN
ejpam-6358	492	22	,	,	PUNCT
ejpam-6358	492	23	t	t	PROPN
ejpam-6358	492	24	}	}	PUNCT
ejpam-6358	492	25	}	}	PUNCT
ejpam-6358	492	26	,	,	PUNCT
ejpam-6358	492	27	then	then	ADV
ejpam-6358	492	28	the	the	DET
ejpam-6358	492	29	associated	associated	ADJ
ejpam-6358	492	30	topologies	topology	NOUN
ejpam-6358	492	31	are	be	AUX
ejpam-6358	492	32	as	as	SCONJ
ejpam-6358	492	33	follows	follow	VERB
ejpam-6358	492	34	:	:	PUNCT
ejpam-6358	492	35	τ	τ	PROPN
ejpam-6358	493	1	i	i	PRON
ejpam-6358	493	2	k	k	X
ejpam-6358	494	1	<	<	X
ejpam-6358	494	2	a	a	X
ejpam-6358	494	3	>	>	X
ejpam-6358	494	4	=	=	SYM
ejpam-6358	494	5	2u	2u	NOUN
ejpam-6358	494	6	(	(	PUNCT
ejpam-6358	494	7	the	the	DET
ejpam-6358	494	8	power	power	NOUN
ejpam-6358	494	9	set	set	NOUN
ejpam-6358	494	10	of	of	ADP
ejpam-6358	494	11	u	u	NOUN
ejpam-6358	494	12	)	)	PUNCT
ejpam-6358	494	13	,	,	PUNCT
ejpam-6358	494	14	τ	τ	PROPN
ejpam-6358	495	1	i	i	VERB
ejpam-6358	495	2	k	k	PROPN
ejpam-6358	496	1	a	a	X
ejpam-6358	496	2	=	=	X
ejpam-6358	496	3	{	{	PUNCT
ejpam-6358	496	4	{	{	PUNCT
ejpam-6358	496	5	p	p	X
ejpam-6358	496	6	}	}	PUNCT
ejpam-6358	496	7	,	,	PUNCT
ejpam-6358	496	8	{	{	PUNCT
ejpam-6358	496	9	q	q	X
ejpam-6358	496	10	}	}	PUNCT
ejpam-6358	496	11	,	,	PUNCT
ejpam-6358	496	12	{	{	PUNCT
ejpam-6358	496	13	s	s	X
ejpam-6358	496	14	}	}	PUNCT
ejpam-6358	496	15	,	,	PUNCT
ejpam-6358	496	16	{	{	PUNCT
ejpam-6358	496	17	p	p	X
ejpam-6358	496	18	,	,	PUNCT
ejpam-6358	496	19	q	q	NOUN
ejpam-6358	496	20	}	}	PUNCT
ejpam-6358	496	21	,	,	PUNCT
ejpam-6358	496	22	{	{	PUNCT
ejpam-6358	496	23	p	p	X
ejpam-6358	496	24	,	,	PUNCT
ejpam-6358	496	25	s	s	PART
ejpam-6358	496	26	}	}	PUNCT
ejpam-6358	496	27	,	,	PUNCT
ejpam-6358	496	28	{	{	PUNCT
ejpam-6358	496	29	q	q	X
ejpam-6358	496	30	,	,	PUNCT
ejpam-6358	496	31	s	s	PART
ejpam-6358	496	32	}	}	PUNCT
ejpam-6358	496	33	,	,	PUNCT
ejpam-6358	496	34	{	{	PUNCT
ejpam-6358	496	35	q	q	NOUN
ejpam-6358	496	36	,	,	PUNCT
ejpam-6358	496	37	t	t	PROPN
ejpam-6358	496	38	}	}	PUNCT
ejpam-6358	496	39	,	,	PUNCT
ejpam-6358	496	40	{	{	PUNCT
ejpam-6358	496	41	p	p	X
ejpam-6358	496	42	,	,	PUNCT
ejpam-6358	496	43	q	q	X
ejpam-6358	496	44	,	,	PUNCT
ejpam-6358	496	45	s	s	PART
ejpam-6358	496	46	}	}	PUNCT
ejpam-6358	496	47	,	,	PUNCT
ejpam-6358	496	48	{	{	PUNCT
ejpam-6358	496	49	p	p	X
ejpam-6358	496	50	,	,	PUNCT
ejpam-6358	496	51	q	q	X
ejpam-6358	496	52	,	,	PUNCT
ejpam-6358	496	53	t	t	PROPN
ejpam-6358	496	54	}	}	PUNCT
ejpam-6358	496	55	,	,	PUNCT
ejpam-6358	496	56	{	{	PUNCT
ejpam-6358	496	57	q	q	X
ejpam-6358	496	58	,	,	PUNCT
ejpam-6358	496	59	s	s	PROPN
ejpam-6358	496	60	,	,	PUNCT
ejpam-6358	496	61	t	t	PROPN
ejpam-6358	496	62	}	}	PUNCT
ejpam-6358	496	63	,	,	PUNCT
ejpam-6358	496	64	∅	∅	NOUN
ejpam-6358	496	65	,	,	PUNCT
ejpam-6358	496	66	u	u	NOUN
ejpam-6358	496	67	}	}	PUNCT
ejpam-6358	496	68	.	.	PUNCT
ejpam-6358	497	1	thus	thus	ADV
ejpam-6358	497	2	,	,	PUNCT
ejpam-6358	497	3	we	we	PRON
ejpam-6358	497	4	observe	observe	VERB
ejpam-6358	497	5	that	that	SCONJ
ejpam-6358	497	6	τ	τ	PROPN
ejpam-6358	497	7	ik	ik	PROPN
ejpam-6358	497	8	<	<	X
ejpam-6358	497	9	a	a	X
ejpam-6358	497	10	>	>	X
ejpam-6358	497	11	⊈	⊈	PROPN
ejpam-6358	498	1	τ	τ	X
ejpam-6358	499	1	i	i	PRON
ejpam-6358	499	2	k	k	PROPN
ejpam-6358	499	3	a	a	X
ejpam-6358	499	4	.	.	PUNCT
ejpam-6358	500	1	the	the	DET
ejpam-6358	500	2	next	next	ADJ
ejpam-6358	500	3	proposition	proposition	NOUN
ejpam-6358	500	4	presents	present	VERB
ejpam-6358	500	5	a	a	DET
ejpam-6358	500	6	revised	revised	ADJ
ejpam-6358	500	7	formulation	formulation	NOUN
ejpam-6358	500	8	to	to	PART
ejpam-6358	500	9	rectify	rectify	VERB
ejpam-6358	500	10	item	item	NOUN
ejpam-6358	500	11	(	(	PUNCT
ejpam-6358	500	12	5	5	NUM
ejpam-6358	500	13	)	)	PUNCT
ejpam-6358	500	14	of	of	ADP
ejpam-6358	500	15	proposition	proposition	NOUN
ejpam-6358	500	16	5.4	5.4	NUM
ejpam-6358	500	17	in	in	ADP
ejpam-6358	500	18	[	[	X
ejpam-6358	500	19	40	40	NUM
ejpam-6358	500	20	]	]	NOUN
ejpam-6358	500	21	:	:	PUNCT
ejpam-6358	500	22	proposition	proposition	NOUN
ejpam-6358	500	23	1	1	X
ejpam-6358	500	24	.	.	PUNCT
ejpam-6358	501	1	let	let	VERB
ejpam-6358	501	2	(	(	PUNCT
ejpam-6358	501	3	u	u	NOUN
ejpam-6358	501	4	,	,	PUNCT
ejpam-6358	501	5	r	r	NOUN
ejpam-6358	501	6	,	,	PUNCT
ejpam-6358	501	7	k	k	NOUN
ejpam-6358	501	8	)	)	PUNCT
ejpam-6358	501	9	be	be	VERB
ejpam-6358	501	10	an	an	DET
ejpam-6358	501	11	ij	ij	ADJ
ejpam-6358	501	12	-	-	PUNCT
ejpam-6358	501	13	g	g	NOUN
ejpam-6358	501	14	approximation	approximation	NOUN
ejpam-6358	501	15	space	space	NOUN
ejpam-6358	501	16	,	,	PUNCT
ejpam-6358	501	17	and	and	CCONJ
ejpam-6358	501	18	let	let	VERB
ejpam-6358	501	19	s	s	PRON
ejpam-6358	501	20	∈	∈	PROPN
ejpam-6358	501	21	u	u	NOUN
ejpam-6358	501	22	.	.	PUNCT
ejpam-6358	502	1	if	if	SCONJ
ejpam-6358	502	2	r	r	NOUN
ejpam-6358	502	3	is	be	AUX
ejpam-6358	502	4	reflexive	reflexive	ADJ
ejpam-6358	502	5	,	,	PUNCT
ejpam-6358	502	6	then	then	ADV
ejpam-6358	502	7	for	for	ADP
ejpam-6358	502	8	each	each	DET
ejpam-6358	502	9	j	j	PROPN
ejpam-6358	502	10	∈	∈	PROPN
ejpam-6358	502	11	{	{	PUNCT
ejpam-6358	502	12	a	a	PROPN
ejpam-6358	502	13	,	,	PUNCT
ejpam-6358	502	14	b	b	NOUN
ejpam-6358	502	15	,	,	PUNCT
ejpam-6358	502	16	i	i	PRON
ejpam-6358	502	17	,	,	PUNCT
ejpam-6358	502	18	u	u	NOUN
ejpam-6358	502	19	}	}	PUNCT
ejpam-6358	502	20	,	,	PUNCT
ejpam-6358	502	21	the	the	DET
ejpam-6358	502	22	inclusion	inclusion	NOUN
ejpam-6358	502	23	τ	τ	X
ejpam-6358	503	1	i	i	NOUN
ejpam-6358	503	2	k	k	PROPN
ejpam-6358	503	3	j	j	PROPN
ejpam-6358	504	1	⊆	⊆	NUM
ejpam-6358	504	2	τ	τ	X
ejpam-6358	505	1	i	i	PRON
ejpam-6358	505	2	k	k	PROPN
ejpam-6358	506	1	<	<	X
ejpam-6358	506	2	j	j	X
ejpam-6358	506	3	>	>	X
ejpam-6358	506	4	holds	hold	NOUN
ejpam-6358	506	5	.	.	PUNCT
ejpam-6358	507	1	proof	proof	NOUN
ejpam-6358	507	2	.	.	PUNCT
ejpam-6358	508	1	let	let	VERB
ejpam-6358	508	2	f	f	PRON
ejpam-6358	508	3	∈	∈	PROPN
ejpam-6358	508	4	τ	τ	X
ejpam-6358	508	5	i	i	PROPN
ejpam-6358	508	6	k	k	PROPN
ejpam-6358	508	7	j	j	PROPN
ejpam-6358	508	8	and	and	CCONJ
ejpam-6358	508	9	suppose	suppose	VERB
ejpam-6358	508	10	s	s	X
ejpam-6358	508	11	∈	∈	PROPN
ejpam-6358	508	12	f	f	X
ejpam-6358	508	13	.	.	PUNCT
ejpam-6358	509	1	by	by	ADP
ejpam-6358	509	2	definition	definition	NOUN
ejpam-6358	509	3	,	,	PUNCT
ejpam-6358	509	4	this	this	PRON
ejpam-6358	509	5	implies	imply	VERB
ejpam-6358	509	6	that	that	SCONJ
ejpam-6358	509	7	ikj	ikj	PROPN
ejpam-6358	509	8	(	(	PUNCT
ejpam-6358	509	9	s	s	NOUN
ejpam-6358	509	10	)	)	PUNCT
ejpam-6358	509	11	\f	\f	PUNCT
ejpam-6358	509	12	∈	∈	PROPN
ejpam-6358	509	13	k.	k.	PROPN
ejpam-6358	509	14	since	since	SCONJ
ejpam-6358	509	15	r	r	NOUN
ejpam-6358	509	16	is	be	AUX
ejpam-6358	509	17	reflexive	reflexive	ADJ
ejpam-6358	509	18	,	,	PUNCT
ejpam-6358	509	19	it	it	PRON
ejpam-6358	509	20	follows	follow	VERB
ejpam-6358	509	21	from	from	ADP
ejpam-6358	509	22	theorem	theorem	ADJ
ejpam-6358	509	23	1	1	NUM
ejpam-6358	510	1	that	that	SCONJ
ejpam-6358	510	2	ik	ik	PROPN
ejpam-6358	510	3	<	<	X
ejpam-6358	510	4	j>(s	j>(s	X
ejpam-6358	510	5	)	)	PUNCT
ejpam-6358	510	6	⊆	⊆	NUM
ejpam-6358	510	7	ikj	ikj	X
ejpam-6358	510	8	(	(	PUNCT
ejpam-6358	510	9	s	s	NOUN
ejpam-6358	510	10	)	)	PUNCT
ejpam-6358	510	11	.	.	PUNCT
ejpam-6358	511	1	therefore	therefore	ADV
ejpam-6358	511	2	,	,	PUNCT
ejpam-6358	511	3	we	we	PRON
ejpam-6358	511	4	obtain	obtain	VERB
ejpam-6358	511	5	ik	ik	PROPN
ejpam-6358	511	6	<	<	X
ejpam-6358	511	7	j>(s	j>(s	X
ejpam-6358	511	8	)	)	PUNCT
ejpam-6358	511	9	\	\	PUNCT
ejpam-6358	512	1	f	f	PROPN
ejpam-6358	512	2	∈	∈	PROPN
ejpam-6358	512	3	k	k	PROPN
ejpam-6358	512	4	,	,	PUNCT
ejpam-6358	512	5	which	which	PRON
ejpam-6358	512	6	implies	imply	VERB
ejpam-6358	512	7	that	that	SCONJ
ejpam-6358	512	8	f	f	PROPN
ejpam-6358	512	9	∈	∈	PROPN
ejpam-6358	512	10	τ	τ	X
ejpam-6358	513	1	i	i	NOUN
ejpam-6358	513	2	k	k	PROPN
ejpam-6358	513	3	<	<	X
ejpam-6358	513	4	j	j	X
ejpam-6358	513	5	>	>	X
ejpam-6358	513	6	.	.	PUNCT
ejpam-6358	514	1	thus	thus	ADV
ejpam-6358	514	2	,	,	PUNCT
ejpam-6358	514	3	the	the	DET
ejpam-6358	514	4	desired	desire	VERB
ejpam-6358	514	5	inclusion	inclusion	NOUN
ejpam-6358	514	6	holds	hold	VERB
ejpam-6358	514	7	.	.	PUNCT
ejpam-6358	515	1	remark	remark	PROPN
ejpam-6358	515	2	5	5	NUM
ejpam-6358	515	3	.	.	PUNCT
ejpam-6358	516	1	if	if	SCONJ
ejpam-6358	516	2	r	r	NOUN
ejpam-6358	516	3	is	be	AUX
ejpam-6358	516	4	reflexive	reflexive	ADJ
ejpam-6358	516	5	,	,	PUNCT
ejpam-6358	516	6	then	then	ADV
ejpam-6358	516	7	for	for	ADP
ejpam-6358	516	8	every	every	DET
ejpam-6358	516	9	x	x	SYM
ejpam-6358	516	10	∈	∈	PROPN
ejpam-6358	516	11	u	u	NOUN
ejpam-6358	516	12	and	and	CCONJ
ejpam-6358	516	13	for	for	ADP
ejpam-6358	516	14	all	all	DET
ejpam-6358	516	15	j	j	PROPN
ejpam-6358	516	16	∈	∈	PROPN
ejpam-6358	516	17	ω	ω	PROPN
ejpam-6358	516	18	,	,	PUNCT
ejpam-6358	516	19	the	the	DET
ejpam-6358	516	20	inclusion	inclusion	NOUN
ejpam-6358	516	21	ρj(x	ρj(x	NOUN
ejpam-6358	516	22	)	)	PUNCT
ejpam-6358	516	23	⊆	⊆	NUM
ejpam-6358	516	24	ikj	ikj	X
ejpam-6358	516	25	(	(	PUNCT
ejpam-6358	516	26	x	x	X
ejpam-6358	516	27	)	)	PUNCT
ejpam-6358	516	28	does	do	AUX
ejpam-6358	516	29	not	not	PART
ejpam-6358	516	30	hold	hold	VERB
ejpam-6358	516	31	in	in	ADP
ejpam-6358	516	32	general	general	ADJ
ejpam-6358	516	33	.	.	PUNCT
ejpam-6358	517	1	as	as	ADP
ejpam-6358	517	2	a	a	DET
ejpam-6358	517	3	result	result	NOUN
ejpam-6358	517	4	,	,	PUNCT
ejpam-6358	517	5	it	it	PRON
ejpam-6358	517	6	follows	follow	VERB
ejpam-6358	517	7	that	that	SCONJ
ejpam-6358	517	8	τρ	τρ	ADP
ejpam-6358	517	9	k	k	PROPN
ejpam-6358	517	10	j	j	PROPN
ejpam-6358	517	11	⊈	⊈	PROPN
ejpam-6358	518	1	τ	τ	X
ejpam-6358	518	2	i	i	NOUN
ejpam-6358	518	3	k	k	PROPN
ejpam-6358	518	4	j	j	PROPN
ejpam-6358	518	5	∀j	∀j	PROPN
ejpam-6358	518	6	∈	∈	PROPN
ejpam-6358	518	7	ω	ω	PROPN
ejpam-6358	518	8	.	.	PUNCT
ejpam-6358	518	9	r.	r.	PROPN
ejpam-6358	518	10	a.	a.	PROPN
ejpam-6358	518	11	hosny	hosny	PROPN
ejpam-6358	518	12	et	et	PROPN
ejpam-6358	518	13	al	al	PROPN
ejpam-6358	518	14	.	.	PUNCT
ejpam-6358	518	15	/	/	SYM
ejpam-6358	518	16	eur	eur	PROPN
ejpam-6358	518	17	.	.	PUNCT
ejpam-6358	519	1	j.	j.	PROPN
ejpam-6358	519	2	pure	pure	PROPN
ejpam-6358	519	3	appl	appl	PROPN
ejpam-6358	519	4	.	.	PROPN
ejpam-6358	519	5	math	math	PROPN
ejpam-6358	519	6	,	,	PUNCT
ejpam-6358	519	7	18	18	NUM
ejpam-6358	519	8	(	(	PUNCT
ejpam-6358	519	9	4	4	NUM
ejpam-6358	519	10	)	)	PUNCT
ejpam-6358	519	11	(	(	PUNCT
ejpam-6358	519	12	2025	2025	NUM
ejpam-6358	519	13	)	)	PUNCT
ejpam-6358	519	14	,	,	PUNCT
ejpam-6358	519	15	6358	6358	NUM
ejpam-6358	519	16	19	19	NUM
ejpam-6358	519	17	of	of	ADP
ejpam-6358	519	18	24	24	NUM
ejpam-6358	519	19	according	accord	VERB
ejpam-6358	519	20	to	to	ADP
ejpam-6358	519	21	remark	remark	NOUN
ejpam-6358	519	22	1	1	NUM
ejpam-6358	519	23	,	,	PUNCT
ejpam-6358	519	24	table	table	NOUN
ejpam-6358	519	25	5	5	NUM
ejpam-6358	519	26	in	in	ADP
ejpam-6358	519	27	[	[	X
ejpam-6358	519	28	40	40	NUM
ejpam-6358	519	29	]	]	PUNCT
ejpam-6358	519	30	presents	present	VERB
ejpam-6358	519	31	a	a	DET
ejpam-6358	519	32	comparative	comparative	ADJ
ejpam-6358	519	33	analysis	analysis	NOUN
ejpam-6358	519	34	of	of	ADP
ejpam-6358	519	35	the	the	DET
ejpam-6358	519	36	boundary	boundary	ADJ
ejpam-6358	519	37	region	region	NOUN
ejpam-6358	519	38	and	and	CCONJ
ejpam-6358	519	39	accuracy	accuracy	NOUN
ejpam-6358	519	40	measure	measure	NOUN
ejpam-6358	519	41	results	result	VERB
ejpam-6358	519	42	for	for	ADP
ejpam-6358	519	43	a	a	DET
ejpam-6358	519	44	set	set	NOUN
ejpam-6358	519	45	f	f	PROPN
ejpam-6358	519	46	based	base	VERB
ejpam-6358	519	47	on	on	ADP
ejpam-6358	519	48	definition	definition	NOUN
ejpam-6358	519	49	5.7	5.7	NUM
ejpam-6358	519	50	in	in	ADP
ejpam-6358	519	51	[	[	X
ejpam-6358	519	52	40	40	NUM
ejpam-6358	519	53	]	]	PUNCT
ejpam-6358	519	54	,	,	PUNCT
ejpam-6358	519	55	where	where	SCONJ
ejpam-6358	519	56	j	j	PROPN
ejpam-6358	519	57	∈	∈	PROPN
ejpam-6358	519	58	{	{	PUNCT
ejpam-6358	519	59	a	a	PROPN
ejpam-6358	519	60	,	,	PUNCT
ejpam-6358	519	61	b	b	NOUN
ejpam-6358	519	62	,	,	PUNCT
ejpam-6358	519	63	i	i	PRON
ejpam-6358	519	64	,	,	PUNCT
ejpam-6358	519	65	u	u	NOUN
ejpam-6358	519	66	}	}	PUNCT
ejpam-6358	519	67	.	.	PUNCT
ejpam-6358	520	1	the	the	DET
ejpam-6358	520	2	values	value	NOUN
ejpam-6358	520	3	of	of	ADP
ejpam-6358	520	4	accτ	accτ	NOUN
ejpam-6358	520	5	i	i	PROPN
ejpam-6358	520	6	k	k	PROPN
ejpam-6358	520	7	a	a	DET
ejpam-6358	520	8	r	r	NOUN
ejpam-6358	520	9	(	(	PUNCT
ejpam-6358	520	10	∅	∅	NOUN
ejpam-6358	520	11	)	)	PUNCT
ejpam-6358	520	12	(	(	PUNCT
ejpam-6358	520	13	and	and	CCONJ
ejpam-6358	520	14	similarly	similarly	ADV
ejpam-6358	520	15	accτ	accτ	NOUN
ejpam-6358	521	1	i	i	NOUN
ejpam-6358	521	2	k	k	PROPN
ejpam-6358	522	1	b	b	X
ejpam-6358	522	2	r	r	NOUN
ejpam-6358	522	3	(	(	PUNCT
ejpam-6358	522	4	∅	∅	NOUN
ejpam-6358	522	5	)	)	PUNCT
ejpam-6358	522	6	,	,	PUNCT
ejpam-6358	522	7	accτ	accτ	PROPN
ejpam-6358	523	1	i	i	PROPN
ejpam-6358	523	2	k	k	PROPN
ejpam-6358	524	1	i	i	PRON
ejpam-6358	524	2	r	r	NOUN
ejpam-6358	524	3	(	(	PUNCT
ejpam-6358	524	4	∅	∅	NOUN
ejpam-6358	524	5	)	)	PUNCT
ejpam-6358	524	6	,	,	PUNCT
ejpam-6358	524	7	andaccτ	andaccτ	NOUN
ejpam-6358	525	1	i	i	NOUN
ejpam-6358	525	2	k	k	NOUN
ejpam-6358	526	1	u	u	NOUN
ejpam-6358	526	2	r	r	NOUN
ejpam-6358	526	3	(	(	PUNCT
ejpam-6358	526	4	∅	∅	NOUN
ejpam-6358	526	5	)	)	PUNCT
ejpam-6358	526	6	)	)	PUNCT
ejpam-6358	526	7	should	should	AUX
ejpam-6358	526	8	be	be	AUX
ejpam-6358	526	9	1	1	NUM
ejpam-6358	526	10	,	,	PUNCT
ejpam-6358	526	11	rather	rather	ADV
ejpam-6358	526	12	than	than	ADP
ejpam-6358	526	13	0	0	NUM
ejpam-6358	526	14	.	.	PUNCT
ejpam-6358	527	1	besides	besides	SCONJ
ejpam-6358	527	2	,	,	PUNCT
ejpam-6358	527	3	the	the	DET
ejpam-6358	527	4	indices	index	NOUN
ejpam-6358	527	5	j	j	PROPN
ejpam-6358	527	6	=	=	SYM
ejpam-6358	527	7	r	r	PROPN
ejpam-6358	527	8	,	,	PUNCT
ejpam-6358	527	9	j	j	PROPN
ejpam-6358	527	10	=	=	SYM
ejpam-6358	527	11	l	l	PROPN
ejpam-6358	527	12	have	have	AUX
ejpam-6358	527	13	been	be	AUX
ejpam-6358	527	14	revised	revise	VERB
ejpam-6358	527	15	to	to	ADP
ejpam-6358	527	16	j	j	PROPN
ejpam-6358	527	17	=	=	PUNCT
ejpam-6358	527	18	a	a	PROPN
ejpam-6358	527	19	,	,	PUNCT
ejpam-6358	527	20	j	j	PROPN
ejpam-6358	527	21	=	=	SYM
ejpam-6358	527	22	b	b	PROPN
ejpam-6358	527	23	respectively	respectively	ADV
ejpam-6358	527	24	.	.	PUNCT
ejpam-6358	528	1	table	table	NOUN
ejpam-6358	528	2	6	6	NUM
ejpam-6358	528	3	in	in	ADP
ejpam-6358	528	4	[	[	X
ejpam-6358	528	5	40	40	NUM
ejpam-6358	528	6	]	]	PUNCT
ejpam-6358	528	7	presents	present	VERB
ejpam-6358	528	8	a	a	DET
ejpam-6358	528	9	comparison	comparison	NOUN
ejpam-6358	528	10	of	of	ADP
ejpam-6358	528	11	the	the	DET
ejpam-6358	528	12	boundary	boundary	ADJ
ejpam-6358	528	13	region	region	NOUN
ejpam-6358	528	14	and	and	CCONJ
ejpam-6358	528	15	accuracy	accuracy	NOUN
ejpam-6358	528	16	measure	measure	NOUN
ejpam-6358	528	17	results	result	VERB
ejpam-6358	528	18	for	for	ADP
ejpam-6358	528	19	a	a	DET
ejpam-6358	528	20	set	set	NOUN
ejpam-6358	528	21	f	f	PROPN
ejpam-6358	528	22	based	base	VERB
ejpam-6358	528	23	on	on	ADP
ejpam-6358	528	24	the	the	DET
ejpam-6358	528	25	proposed	propose	VERB
ejpam-6358	528	26	definition	definition	NOUN
ejpam-6358	528	27	5.7	5.7	NUM
ejpam-6358	528	28	and	and	CCONJ
ejpam-6358	528	29	definition	definition	NOUN
ejpam-6358	528	30	2.13	2.13	NUM
ejpam-6358	528	31	from	from	ADP
ejpam-6358	528	32	[	[	X
ejpam-6358	528	33	12	12	NUM
ejpam-6358	528	34	]	]	PUNCT
ejpam-6358	528	35	for	for	ADP
ejpam-6358	528	36	j	j	NOUN
ejpam-6358	528	37	=	=	PUNCT
ejpam-6358	528	38	a.	a.	NOUN
ejpam-6358	528	39	the	the	DET
ejpam-6358	528	40	notation	notation	NOUN
ejpam-6358	528	41	τ	τ	PROPN
ejpam-6358	528	42	ib(l	ib(l	NUM
ejpam-6358	528	43	)	)	PUNCT
ejpam-6358	528	44	(	(	PUNCT
ejpam-6358	528	45	and	and	CCONJ
ejpam-6358	528	46	similarly	similarly	ADV
ejpam-6358	528	47	τ	τ	PROPN
ejpam-6358	528	48	ib(l	ib(l	NUM
ejpam-6358	528	49	)	)	PUNCT
ejpam-6358	528	50	,	,	PUNCT
ejpam-6358	528	51	bndτ	bndτ	NOUN
ejpam-6358	528	52	ib	ib	NOUN
ejpam-6358	528	53	(	(	PUNCT
ejpam-6358	528	54	l	l	NOUN
ejpam-6358	528	55	)	)	PUNCT
ejpam-6358	528	56	,	,	PUNCT
ejpam-6358	528	57	accτ	accτ	PROPN
ejpam-6358	528	58	ib	ib	PROPN
ejpam-6358	528	59	(	(	PUNCT
ejpam-6358	528	60	l	l	NOUN
ejpam-6358	528	61	)	)	PUNCT
ejpam-6358	528	62	)	)	PUNCT
ejpam-6358	528	63	should	should	AUX
ejpam-6358	528	64	be	be	AUX
ejpam-6358	528	65	corrected	correct	VERB
ejpam-6358	528	66	to	to	ADP
ejpam-6358	528	67	τ	τ	PROPN
ejpam-6358	528	68	ia(l	ia(l	NOUN
ejpam-6358	528	69	)	)	PUNCT
ejpam-6358	528	70	(	(	PUNCT
ejpam-6358	528	71	and	and	CCONJ
ejpam-6358	528	72	similarly	similarly	ADV
ejpam-6358	528	73	τ	τ	X
ejpam-6358	528	74	ia(l	ia(l	NOUN
ejpam-6358	528	75	)	)	PUNCT
ejpam-6358	528	76	,	,	PUNCT
ejpam-6358	528	77	bndτ	bndτ	NOUN
ejpam-6358	528	78	ia	ia	PROPN
ejpam-6358	528	79	(	(	PUNCT
ejpam-6358	528	80	l	l	NOUN
ejpam-6358	528	81	)	)	PUNCT
ejpam-6358	528	82	,	,	PUNCT
ejpam-6358	528	83	accτ	accτ	PROPN
ejpam-6358	528	84	ia	ia	PROPN
ejpam-6358	528	85	(	(	PUNCT
ejpam-6358	528	86	l	l	NOUN
ejpam-6358	528	87	)	)	PUNCT
ejpam-6358	528	88	)	)	PUNCT
ejpam-6358	528	89	.	.	PUNCT
ejpam-6358	529	1	additionally	additionally	ADV
ejpam-6358	529	2	,	,	PUNCT
ejpam-6358	529	3	the	the	DET
ejpam-6358	529	4	values	value	NOUN
ejpam-6358	529	5	of	of	ADP
ejpam-6358	529	6	accτ	accτ	NOUN
ejpam-6358	530	1	i	i	PROPN
ejpam-6358	530	2	k	k	PROPN
ejpam-6358	531	1	a	a	DET
ejpam-6358	531	2	r	r	NOUN
ejpam-6358	531	3	(	(	PUNCT
ejpam-6358	531	4	∅	∅	NOUN
ejpam-6358	531	5	)	)	PUNCT
ejpam-6358	531	6	,	,	PUNCT
ejpam-6358	531	7	and	and	CCONJ
ejpam-6358	531	8	accτ	accτ	PROPN
ejpam-6358	531	9	ia	ia	PROPN
ejpam-6358	531	10	r	r	PROPN
ejpam-6358	531	11	(	(	PUNCT
ejpam-6358	531	12	∅	∅	NOUN
ejpam-6358	531	13	)	)	PUNCT
ejpam-6358	531	14	should	should	AUX
ejpam-6358	531	15	be	be	AUX
ejpam-6358	531	16	considered	consider	VERB
ejpam-6358	531	17	indefinite	indefinite	ADJ
ejpam-6358	531	18	.	.	PUNCT
ejpam-6358	532	1	4	4	X
ejpam-6358	532	2	.	.	X
ejpam-6358	532	3	conclusion	conclusion	NOUN
ejpam-6358	532	4	and	and	CCONJ
ejpam-6358	532	5	discussion	discussion	NOUN
ejpam-6358	532	6	this	this	DET
ejpam-6358	532	7	paper	paper	NOUN
ejpam-6358	532	8	presents	present	VERB
ejpam-6358	532	9	a	a	DET
ejpam-6358	532	10	systematic	systematic	ADJ
ejpam-6358	532	11	critique	critique	NOUN
ejpam-6358	532	12	of	of	ADP
ejpam-6358	532	13	the	the	DET
ejpam-6358	532	14	work	work	NOUN
ejpam-6358	532	15	by	by	ADP
ejpam-6358	532	16	t.	t.	PROPN
ejpam-6358	532	17	m.	m.	PROPN
ejpam-6358	532	18	al	al	PROPN
ejpam-6358	532	19	-	-	PUNCT
ejpam-6358	532	20	shami	shami	PROPN
ejpam-6358	532	21	and	and	CCONJ
ejpam-6358	532	22	m.	m.	PROPN
ejpam-6358	532	23	hosny	hosny	PROPN
ejpam-6358	533	1	[	[	X
ejpam-6358	533	2	40	40	NUM
ejpam-6358	533	3	]	]	PUNCT
ejpam-6358	533	4	,	,	PUNCT
ejpam-6358	533	5	identifying	identify	VERB
ejpam-6358	533	6	and	and	CCONJ
ejpam-6358	533	7	resolving	resolve	VERB
ejpam-6358	533	8	fundamental	fundamental	ADJ
ejpam-6358	533	9	flaws	flaw	NOUN
ejpam-6358	533	10	in	in	ADP
ejpam-6358	533	11	their	their	PRON
ejpam-6358	533	12	formalization	formalization	NOUN
ejpam-6358	533	13	of	of	ADP
ejpam-6358	533	14	ikj	ikj	PROPN
ejpam-6358	533	15	neighborhoods	neighborhood	NOUN
ejpam-6358	533	16	within	within	ADP
ejpam-6358	533	17	rough	rough	ADJ
ejpam-6358	533	18	set	set	NOUN
ejpam-6358	533	19	theory	theory	NOUN
ejpam-6358	533	20	.	.	PUNCT
ejpam-6358	534	1	through	through	ADP
ejpam-6358	534	2	rigorous	rigorous	ADJ
ejpam-6358	534	3	analysis	analysis	NOUN
ejpam-6358	534	4	,	,	PUNCT
ejpam-6358	534	5	counterexamples	counterexample	NOUN
ejpam-6358	534	6	,	,	PUNCT
ejpam-6358	534	7	and	and	CCONJ
ejpam-6358	534	8	reconstructed	reconstructed	ADJ
ejpam-6358	534	9	proofs	proof	NOUN
ejpam-6358	534	10	,	,	PUNCT
ejpam-6358	534	11	we	we	PRON
ejpam-6358	534	12	have	have	AUX
ejpam-6358	534	13	thoroughly	thoroughly	ADV
ejpam-6358	534	14	examined	examine	VERB
ejpam-6358	534	15	and	and	CCONJ
ejpam-6358	534	16	rectified	rectify	VERB
ejpam-6358	534	17	critical	critical	ADJ
ejpam-6358	534	18	inaccuracies	inaccuracy	NOUN
ejpam-6358	534	19	in	in	ADP
ejpam-6358	534	20	their	their	PRON
ejpam-6358	534	21	definitions	definition	NOUN
ejpam-6358	534	22	,	,	PUNCT
ejpam-6358	534	23	theoretical	theoretical	ADJ
ejpam-6358	534	24	results	result	NOUN
ejpam-6358	534	25	,	,	PUNCT
ejpam-6358	534	26	and	and	CCONJ
ejpam-6358	534	27	illustrative	illustrative	ADJ
ejpam-6358	534	28	examples	example	NOUN
ejpam-6358	534	29	.	.	PUNCT
ejpam-6358	535	1	the	the	DET
ejpam-6358	535	2	proposed	propose	VERB
ejpam-6358	535	3	corrections	correction	NOUN
ejpam-6358	535	4	provide	provide	VERB
ejpam-6358	535	5	dual	dual	ADJ
ejpam-6358	535	6	benefits	benefit	NOUN
ejpam-6358	535	7	:	:	PUNCT
ejpam-6358	535	8	they	they	PRON
ejpam-6358	535	9	strengthen	strengthen	VERB
ejpam-6358	535	10	the	the	DET
ejpam-6358	535	11	theoretical	theoretical	ADJ
ejpam-6358	535	12	foundations	foundation	NOUN
ejpam-6358	535	13	of	of	ADP
ejpam-6358	535	14	neighborhood	neighborhood	NOUN
ejpam-6358	535	15	systems	system	NOUN
ejpam-6358	535	16	while	while	SCONJ
ejpam-6358	535	17	enhancing	enhance	VERB
ejpam-6358	535	18	their	their	PRON
ejpam-6358	535	19	practical	practical	ADJ
ejpam-6358	535	20	applicability	applicability	NOUN
ejpam-6358	535	21	within	within	ADP
ejpam-6358	535	22	rough	rough	ADJ
ejpam-6358	535	23	set	set	NOUN
ejpam-6358	535	24	–	–	PUNCT
ejpam-6358	535	25	based	base	VERB
ejpam-6358	535	26	frameworks	framework	NOUN
ejpam-6358	535	27	.	.	PUNCT
ejpam-6358	536	1	our	our	PRON
ejpam-6358	536	2	primary	primary	ADJ
ejpam-6358	536	3	contribution	contribution	NOUN
ejpam-6358	536	4	lies	lie	VERB
ejpam-6358	536	5	in	in	ADP
ejpam-6358	536	6	dismantling	dismantle	VERB
ejpam-6358	536	7	the	the	DET
ejpam-6358	536	8	problematic	problematic	ADJ
ejpam-6358	536	9	claims	claim	NOUN
ejpam-6358	536	10	of	of	ADP
ejpam-6358	536	11	the	the	DET
ejpam-6358	536	12	original	original	ADJ
ejpam-6358	536	13	work	work	NOUN
ejpam-6358	536	14	through	through	ADP
ejpam-6358	536	15	comprehensive	comprehensive	ADJ
ejpam-6358	536	16	error	error	NOUN
ejpam-6358	536	17	identification	identification	NOUN
ejpam-6358	536	18	and	and	CCONJ
ejpam-6358	536	19	replacement	replacement	NOUN
ejpam-6358	536	20	with	with	ADP
ejpam-6358	536	21	validated	validated	ADJ
ejpam-6358	536	22	and	and	CCONJ
ejpam-6358	536	23	consistent	consistent	ADJ
ejpam-6358	536	24	alternatives	alternative	NOUN
ejpam-6358	536	25	.	.	PUNCT
ejpam-6358	537	1	the	the	DET
ejpam-6358	537	2	revised	revise	VERB
ejpam-6358	537	3	framework	framework	NOUN
ejpam-6358	537	4	substantially	substantially	ADV
ejpam-6358	537	5	improves	improve	VERB
ejpam-6358	537	6	the	the	DET
ejpam-6358	537	7	internal	internal	ADJ
ejpam-6358	537	8	coherence	coherence	NOUN
ejpam-6358	537	9	and	and	CCONJ
ejpam-6358	537	10	reliability	reliability	NOUN
ejpam-6358	537	11	of	of	ADP
ejpam-6358	537	12	neighborhood	neighborhood	NOUN
ejpam-6358	537	13	-	-	PUNCT
ejpam-6358	537	14	based	base	VERB
ejpam-6358	537	15	approximation	approximation	NOUN
ejpam-6358	537	16	methods	method	NOUN
ejpam-6358	537	17	,	,	PUNCT
ejpam-6358	537	18	particularly	particularly	ADV
ejpam-6358	537	19	through	through	ADP
ejpam-6358	537	20	corrected	correct	VERB
ejpam-6358	537	21	examples	example	NOUN
ejpam-6358	537	22	that	that	PRON
ejpam-6358	537	23	now	now	ADV
ejpam-6358	537	24	accurately	accurately	ADV
ejpam-6358	537	25	support	support	VERB
ejpam-6358	537	26	the	the	DET
ejpam-6358	537	27	theoretical	theoretical	ADJ
ejpam-6358	537	28	propositions	proposition	NOUN
ejpam-6358	537	29	.	.	PUNCT
ejpam-6358	538	1	moreover	moreover	ADV
ejpam-6358	538	2	,	,	PUNCT
ejpam-6358	538	3	the	the	DET
ejpam-6358	538	4	refined	refined	ADJ
ejpam-6358	538	5	methodology	methodology	NOUN
ejpam-6358	538	6	paves	pave	VERB
ejpam-6358	538	7	the	the	DET
ejpam-6358	538	8	way	way	NOUN
ejpam-6358	538	9	for	for	ADP
ejpam-6358	538	10	new	new	ADJ
ejpam-6358	538	11	research	research	NOUN
ejpam-6358	538	12	directions	direction	NOUN
ejpam-6358	538	13	in	in	ADP
ejpam-6358	538	14	uncertainty	uncertainty	NOUN
ejpam-6358	538	15	quantification	quantification	NOUN
ejpam-6358	538	16	,	,	PUNCT
ejpam-6358	538	17	offering	offer	VERB
ejpam-6358	538	18	researchers	researcher	NOUN
ejpam-6358	538	19	more	more	ADV
ejpam-6358	538	20	robust	robust	ADJ
ejpam-6358	538	21	analytical	analytical	ADJ
ejpam-6358	538	22	tools	tool	NOUN
ejpam-6358	538	23	for	for	ADP
ejpam-6358	538	24	complex	complex	ADJ
ejpam-6358	538	25	data	datum	NOUN
ejpam-6358	538	26	interpretation	interpretation	NOUN
ejpam-6358	538	27	,	,	PUNCT
ejpam-6358	538	28	as	as	SCONJ
ejpam-6358	538	29	demonstrated	demonstrate	VERB
ejpam-6358	538	30	through	through	ADP
ejpam-6358	538	31	improved	improve	VERB
ejpam-6358	538	32	medical	medical	ADJ
ejpam-6358	538	33	application	application	NOUN
ejpam-6358	538	34	scenarios	scenario	NOUN
ejpam-6358	538	35	.	.	PUNCT
ejpam-6358	539	1	in	in	ADP
ejpam-6358	539	2	this	this	DET
ejpam-6358	539	3	study	study	NOUN
ejpam-6358	539	4	,	,	PUNCT
ejpam-6358	539	5	several	several	ADJ
ejpam-6358	539	6	major	major	ADJ
ejpam-6358	539	7	errors	error	NOUN
ejpam-6358	539	8	have	have	AUX
ejpam-6358	539	9	been	be	AUX
ejpam-6358	539	10	identified	identify	VERB
ejpam-6358	539	11	in	in	ADP
ejpam-6358	539	12	theorem	theorem	NOUN
ejpam-6358	539	13	3.4	3.4	NUM
ejpam-6358	539	14	,	,	PUNCT
ejpam-6358	539	15	proposition	proposition	NOUN
ejpam-6358	539	16	4.3	4.3	NUM
ejpam-6358	539	17	,	,	PUNCT
ejpam-6358	539	18	and	and	CCONJ
ejpam-6358	539	19	proposition	proposition	NOUN
ejpam-6358	539	20	5.4	5.4	NUM
ejpam-6358	539	21	of	of	ADP
ejpam-6358	539	22	[	[	X
ejpam-6358	539	23	40	40	NUM
ejpam-6358	539	24	]	]	PUNCT
ejpam-6358	539	25	.	.	PUNCT
ejpam-6358	540	1	these	these	DET
ejpam-6358	540	2	inaccuracies	inaccuracy	NOUN
ejpam-6358	540	3	were	be	AUX
ejpam-6358	540	4	demonstrated	demonstrate	VERB
ejpam-6358	540	5	through	through	ADP
ejpam-6358	540	6	various	various	ADJ
ejpam-6358	540	7	examples	example	NOUN
ejpam-6358	540	8	,	,	PUNCT
ejpam-6358	540	9	including	include	VERB
ejpam-6358	540	10	examples	example	NOUN
ejpam-6358	540	11	1	1	NUM
ejpam-6358	540	12	,	,	PUNCT
ejpam-6358	540	13	2	2	NUM
ejpam-6358	540	14	,	,	PUNCT
ejpam-6358	540	15	3	3	NUM
ejpam-6358	540	16	,	,	PUNCT
ejpam-6358	540	17	4	4	NUM
ejpam-6358	540	18	,	,	PUNCT
ejpam-6358	540	19	5	5	NUM
ejpam-6358	540	20	,	,	PUNCT
ejpam-6358	540	21	and	and	CCONJ
ejpam-6358	540	22	6	6	NUM
ejpam-6358	540	23	.	.	X
ejpam-6358	540	24	corrections	correction	NOUN
ejpam-6358	540	25	and	and	CCONJ
ejpam-6358	540	26	clarifications	clarification	NOUN
ejpam-6358	540	27	were	be	AUX
ejpam-6358	540	28	subsequently	subsequently	ADV
ejpam-6358	540	29	provided	provide	VERB
ejpam-6358	540	30	,	,	PUNCT
ejpam-6358	540	31	such	such	ADJ
ejpam-6358	540	32	as	as	ADP
ejpam-6358	540	33	the	the	DET
ejpam-6358	540	34	revised	revise	VERB
ejpam-6358	540	35	proof	proof	NOUN
ejpam-6358	540	36	of	of	ADP
ejpam-6358	540	37	theorem	theorem	ADJ
ejpam-6358	540	38	3.4	3.4	NUM
ejpam-6358	540	39	,	,	PUNCT
ejpam-6358	540	40	which	which	PRON
ejpam-6358	540	41	is	be	AUX
ejpam-6358	540	42	now	now	ADV
ejpam-6358	540	43	accurately	accurately	ADV
ejpam-6358	540	44	reformulated	reformulate	VERB
ejpam-6358	540	45	and	and	CCONJ
ejpam-6358	540	46	presented	present	VERB
ejpam-6358	540	47	in	in	ADP
ejpam-6358	540	48	theorems	theorem	NOUN
ejpam-6358	540	49	6	6	NUM
ejpam-6358	540	50	and	and	CCONJ
ejpam-6358	540	51	7	7	NUM
ejpam-6358	540	52	of	of	ADP
ejpam-6358	540	53	this	this	DET
ejpam-6358	540	54	paper	paper	NOUN
ejpam-6358	540	55	.	.	PUNCT
ejpam-6358	541	1	additional	additional	ADJ
ejpam-6358	541	2	corrected	correct	VERB
ejpam-6358	541	3	versions	version	NOUN
ejpam-6358	541	4	of	of	ADP
ejpam-6358	541	5	erroneous	erroneous	ADJ
ejpam-6358	541	6	results	result	NOUN
ejpam-6358	541	7	,	,	PUNCT
ejpam-6358	541	8	including	include	VERB
ejpam-6358	541	9	theorem	theorem	VERB
ejpam-6358	541	10	6	6	NUM
ejpam-6358	541	11	and	and	CCONJ
ejpam-6358	541	12	proposition	proposition	NOUN
ejpam-6358	541	13	1	1	NUM
ejpam-6358	541	14	,	,	PUNCT
ejpam-6358	541	15	have	have	AUX
ejpam-6358	541	16	also	also	ADV
ejpam-6358	541	17	been	be	AUX
ejpam-6358	541	18	proposed	propose	VERB
ejpam-6358	541	19	.	.	PUNCT
ejpam-6358	542	1	errors	error	NOUN
ejpam-6358	542	2	within	within	ADP
ejpam-6358	542	3	several	several	ADJ
ejpam-6358	542	4	concepts	concept	NOUN
ejpam-6358	542	5	,	,	PUNCT
ejpam-6358	542	6	definitions	definition	NOUN
ejpam-6358	542	7	,	,	PUNCT
ejpam-6358	542	8	examples	example	NOUN
ejpam-6358	542	9	,	,	PUNCT
ejpam-6358	542	10	and	and	CCONJ
ejpam-6358	542	11	tables	table	NOUN
ejpam-6358	542	12	from	from	ADP
ejpam-6358	542	13	[	[	X
ejpam-6358	542	14	40	40	NUM
ejpam-6358	542	15	]	]	PUNCT
ejpam-6358	542	16	have	have	AUX
ejpam-6358	542	17	been	be	AUX
ejpam-6358	542	18	thoroughly	thoroughly	ADV
ejpam-6358	542	19	identified	identify	VERB
ejpam-6358	542	20	and	and	CCONJ
ejpam-6358	542	21	corrected	correct	VERB
ejpam-6358	542	22	.	.	PUNCT
ejpam-6358	543	1	these	these	PRON
ejpam-6358	543	2	include	include	VERB
ejpam-6358	543	3	revisions	revision	NOUN
ejpam-6358	543	4	to	to	ADP
ejpam-6358	543	5	definitions	definition	NOUN
ejpam-6358	543	6	1	1	NUM
ejpam-6358	543	7	,	,	PUNCT
ejpam-6358	543	8	2	2	NUM
ejpam-6358	543	9	,	,	PUNCT
ejpam-6358	543	10	11	11	NUM
ejpam-6358	543	11	,	,	PUNCT
ejpam-6358	543	12	and	and	CCONJ
ejpam-6358	543	13	12	12	NUM
ejpam-6358	543	14	,	,	PUNCT
ejpam-6358	543	15	as	as	ADV
ejpam-6358	543	16	well	well	ADV
ejpam-6358	543	17	as	as	ADP
ejpam-6358	543	18	major	major	ADJ
ejpam-6358	543	19	modifications	modification	NOUN
ejpam-6358	543	20	to	to	ADP
ejpam-6358	543	21	five	five	NUM
ejpam-6358	543	22	tables	table	NOUN
ejpam-6358	543	23	and	and	CCONJ
ejpam-6358	543	24	the	the	DET
ejpam-6358	543	25	resolution	resolution	NOUN
ejpam-6358	543	26	of	of	ADP
ejpam-6358	543	27	twenty	twenty	NUM
ejpam-6358	543	28	-	-	PUNCT
ejpam-6358	543	29	five	five	NUM
ejpam-6358	543	30	distinct	distinct	ADJ
ejpam-6358	543	31	inconsistencies	inconsistency	NOUN
ejpam-6358	543	32	across	across	ADP
ejpam-6358	543	33	multiple	multiple	ADJ
ejpam-6358	543	34	examples	example	NOUN
ejpam-6358	543	35	.	.	PUNCT
ejpam-6358	544	1	furthermore	furthermore	ADV
ejpam-6358	544	2	,	,	PUNCT
ejpam-6358	544	3	new	new	ADJ
ejpam-6358	544	4	theoretical	theoretical	ADJ
ejpam-6358	544	5	results	result	NOUN
ejpam-6358	544	6	and	and	CCONJ
ejpam-6358	544	7	properties	property	NOUN
ejpam-6358	544	8	,	,	PUNCT
ejpam-6358	544	9	including	include	VERB
ejpam-6358	544	10	remark	remark	NOUN
ejpam-6358	544	11	3	3	NUM
ejpam-6358	544	12	and	and	CCONJ
ejpam-6358	544	13	lemma	lemma	PROPN
ejpam-6358	544	14	1	1	NUM
ejpam-6358	544	15	,	,	PUNCT
ejpam-6358	544	16	have	have	AUX
ejpam-6358	544	17	been	be	AUX
ejpam-6358	544	18	introduced	introduce	VERB
ejpam-6358	544	19	and	and	CCONJ
ejpam-6358	544	20	justified	justify	VERB
ejpam-6358	544	21	to	to	PART
ejpam-6358	544	22	reinforce	reinforce	VERB
ejpam-6358	544	23	the	the	DET
ejpam-6358	544	24	consistency	consistency	NOUN
ejpam-6358	544	25	of	of	ADP
ejpam-6358	544	26	the	the	DET
ejpam-6358	544	27	proposed	propose	VERB
ejpam-6358	544	28	framework	framework	NOUN
ejpam-6358	544	29	.	.	PUNCT
ejpam-6358	545	1	r.	r.	PROPN
ejpam-6358	545	2	a.	a.	PROPN
ejpam-6358	545	3	hosny	hosny	PROPN
ejpam-6358	545	4	et	et	PROPN
ejpam-6358	545	5	al	al	PROPN
ejpam-6358	545	6	.	.	PUNCT
ejpam-6358	545	7	/	/	SYM
ejpam-6358	545	8	eur	eur	PROPN
ejpam-6358	545	9	.	.	PUNCT
ejpam-6358	546	1	j.	j.	PROPN
ejpam-6358	546	2	pure	pure	PROPN
ejpam-6358	546	3	appl	appl	PROPN
ejpam-6358	546	4	.	.	PROPN
ejpam-6358	546	5	math	math	PROPN
ejpam-6358	546	6	,	,	PUNCT
ejpam-6358	546	7	18	18	NUM
ejpam-6358	546	8	(	(	PUNCT
ejpam-6358	546	9	4	4	NUM
ejpam-6358	546	10	)	)	PUNCT
ejpam-6358	546	11	(	(	PUNCT
ejpam-6358	546	12	2025	2025	NUM
ejpam-6358	546	13	)	)	PUNCT
ejpam-6358	546	14	,	,	PUNCT
ejpam-6358	546	15	6358	6358	NUM
ejpam-6358	546	16	20	20	NUM
ejpam-6358	546	17	of	of	ADP
ejpam-6358	546	18	24	24	NUM
ejpam-6358	546	19	overall	overall	ADJ
ejpam-6358	547	1	,	,	PUNCT
ejpam-6358	547	2	the	the	DET
ejpam-6358	547	3	findings	finding	NOUN
ejpam-6358	547	4	of	of	ADP
ejpam-6358	547	5	this	this	DET
ejpam-6358	547	6	study	study	NOUN
ejpam-6358	547	7	highlight	highlight	VERB
ejpam-6358	547	8	the	the	DET
ejpam-6358	547	9	necessity	necessity	NOUN
ejpam-6358	547	10	of	of	ADP
ejpam-6358	547	11	critically	critically	ADV
ejpam-6358	547	12	examining	examine	VERB
ejpam-6358	547	13	recently	recently	ADV
ejpam-6358	547	14	proposed	propose	VERB
ejpam-6358	547	15	methodologies	methodology	NOUN
ejpam-6358	547	16	and	and	CCONJ
ejpam-6358	547	17	results	result	NOUN
ejpam-6358	547	18	in	in	ADP
ejpam-6358	547	19	evolving	evolve	VERB
ejpam-6358	547	20	fields	field	NOUN
ejpam-6358	547	21	such	such	ADJ
ejpam-6358	547	22	as	as	ADP
ejpam-6358	547	23	rough	rough	ADJ
ejpam-6358	547	24	set	set	NOUN
ejpam-6358	547	25	theory	theory	NOUN
ejpam-6358	547	26	.	.	PUNCT
ejpam-6358	548	1	the	the	DET
ejpam-6358	548	2	corrections	correction	NOUN
ejpam-6358	548	3	and	and	CCONJ
ejpam-6358	548	4	refinements	refinement	NOUN
ejpam-6358	548	5	provided	provide	VERB
ejpam-6358	548	6	herein	herein	NOUN
ejpam-6358	548	7	ensure	ensure	VERB
ejpam-6358	548	8	that	that	SCONJ
ejpam-6358	548	9	the	the	DET
ejpam-6358	548	10	theoretical	theoretical	ADJ
ejpam-6358	548	11	basis	basis	NOUN
ejpam-6358	548	12	of	of	ADP
ejpam-6358	548	13	neighborhood	neighborhood	NOUN
ejpam-6358	548	14	systems	system	NOUN
ejpam-6358	548	15	remains	remain	VERB
ejpam-6358	548	16	sound	sound	ADJ
ejpam-6358	548	17	,	,	PUNCT
ejpam-6358	548	18	rigorous	rigorous	ADJ
ejpam-6358	548	19	,	,	PUNCT
ejpam-6358	548	20	and	and	CCONJ
ejpam-6358	548	21	dependable	dependable	ADJ
ejpam-6358	548	22	for	for	ADP
ejpam-6358	548	23	subsequent	subsequent	ADJ
ejpam-6358	548	24	research	research	NOUN
ejpam-6358	548	25	and	and	CCONJ
ejpam-6358	548	26	applications	application	NOUN
ejpam-6358	548	27	.	.	PUNCT
ejpam-6358	549	1	moreover	moreover	ADV
ejpam-6358	549	2	,	,	PUNCT
ejpam-6358	549	3	the	the	DET
ejpam-6358	549	4	enhanced	enhanced	ADJ
ejpam-6358	549	5	understanding	understanding	NOUN
ejpam-6358	549	6	of	of	ADP
ejpam-6358	549	7	neighborhood	neighborhood	NOUN
ejpam-6358	549	8	-	-	PUNCT
ejpam-6358	549	9	based	base	VERB
ejpam-6358	549	10	rough	rough	ADJ
ejpam-6358	549	11	approximations	approximation	NOUN
ejpam-6358	549	12	broadens	broaden	VERB
ejpam-6358	549	13	their	their	PRON
ejpam-6358	549	14	applicability	applicability	NOUN
ejpam-6358	549	15	in	in	ADP
ejpam-6358	549	16	decision	decision	NOUN
ejpam-6358	549	17	-	-	PUNCT
ejpam-6358	549	18	making	making	NOUN
ejpam-6358	549	19	,	,	PUNCT
ejpam-6358	549	20	data	datum	NOUN
ejpam-6358	549	21	analysis	analysis	NOUN
ejpam-6358	549	22	,	,	PUNCT
ejpam-6358	549	23	and	and	CCONJ
ejpam-6358	549	24	knowledge	knowledge	NOUN
ejpam-6358	549	25	discovery	discovery	NOUN
ejpam-6358	549	26	across	across	ADP
ejpam-6358	549	27	diverse	diverse	ADJ
ejpam-6358	549	28	scientific	scientific	ADJ
ejpam-6358	549	29	and	and	CCONJ
ejpam-6358	549	30	engineering	engineering	NOUN
ejpam-6358	549	31	domains	domain	NOUN
ejpam-6358	549	32	.	.	PUNCT
ejpam-6358	550	1	in	in	ADP
ejpam-6358	550	2	our	our	PRON
ejpam-6358	550	3	future	future	ADJ
ejpam-6358	550	4	work	work	NOUN
ejpam-6358	550	5	,	,	PUNCT
ejpam-6358	550	6	we	we	PRON
ejpam-6358	550	7	will	will	AUX
ejpam-6358	550	8	apply	apply	VERB
ejpam-6358	550	9	the	the	DET
ejpam-6358	550	10	techniques	technique	NOUN
ejpam-6358	550	11	introduced	introduce	VERB
ejpam-6358	550	12	in	in	ADP
ejpam-6358	550	13	the	the	DET
ejpam-6358	550	14	present	present	ADJ
ejpam-6358	550	15	paper	paper	NOUN
ejpam-6358	550	16	to	to	ADP
ejpam-6358	550	17	various	various	ADJ
ejpam-6358	550	18	fields	field	NOUN
ejpam-6358	550	19	,	,	PUNCT
ejpam-6358	550	20	such	such	ADJ
ejpam-6358	550	21	as	as	ADP
ejpam-6358	550	22	applications	application	NOUN
ejpam-6358	550	23	of	of	ADP
ejpam-6358	550	24	fuzzy	fuzzy	ADJ
ejpam-6358	550	25	topological	topological	ADJ
ejpam-6358	550	26	spaces	space	NOUN
ejpam-6358	550	27	[	[	X
ejpam-6358	550	28	44	44	NUM
ejpam-6358	550	29	]	]	PUNCT
ejpam-6358	550	30	,	,	PUNCT
ejpam-6358	550	31	rough	rough	ADJ
ejpam-6358	550	32	lattices	lattice	NOUN
ejpam-6358	550	33	[	[	X
ejpam-6358	550	34	45	45	NUM
ejpam-6358	550	35	]	]	PUNCT
ejpam-6358	550	36	,	,	PUNCT
ejpam-6358	550	37	the	the	DET
ejpam-6358	550	38	study	study	NOUN
ejpam-6358	550	39	of	of	ADP
ejpam-6358	550	40	sc	sc	NOUN
ejpam-6358	550	41	-	-	PUNCT
ejpam-6358	550	42	compactness	compactness	NOUN
ejpam-6358	550	43	of	of	ADP
ejpam-6358	550	44	rough	rough	ADJ
ejpam-6358	550	45	sets	set	NOUN
ejpam-6358	550	46	using	use	VERB
ejpam-6358	550	47	ideal	ideal	ADJ
ejpam-6358	550	48	neighborhoods	neighborhood	NOUN
ejpam-6358	550	49	[	[	X
ejpam-6358	550	50	46	46	NUM
ejpam-6358	550	51	]	]	PUNCT
ejpam-6358	550	52	,	,	PUNCT
ejpam-6358	550	53	and	and	CCONJ
ejpam-6358	550	54	the	the	DET
ejpam-6358	550	55	improvement	improvement	NOUN
ejpam-6358	550	56	of	of	ADP
ejpam-6358	550	57	rough	rough	ADJ
ejpam-6358	550	58	approximation	approximation	NOUN
ejpam-6358	550	59	and	and	CCONJ
ejpam-6358	550	60	ideal	ideal	ADJ
ejpam-6358	550	61	methods	method	NOUN
ejpam-6358	550	62	introduced	introduce	VERB
ejpam-6358	550	63	in	in	ADP
ejpam-6358	550	64	[	[	X
ejpam-6358	550	65	47	47	NUM
ejpam-6358	550	66	]	]	PUNCT
ejpam-6358	550	67	.	.	PUNCT
ejpam-6358	551	1	finally	finally	ADV
ejpam-6358	551	2	,	,	PUNCT
ejpam-6358	551	3	to	to	PART
ejpam-6358	551	4	facilitate	facilitate	VERB
ejpam-6358	551	5	easy	easy	ADJ
ejpam-6358	551	6	reference	reference	NOUN
ejpam-6358	551	7	,	,	PUNCT
ejpam-6358	551	8	we	we	PRON
ejpam-6358	551	9	provide	provide	VERB
ejpam-6358	551	10	a	a	DET
ejpam-6358	551	11	nomenclature	nomenclature	NOUN
ejpam-6358	551	12	section	section	NOUN
ejpam-6358	551	13	listing	list	VERB
ejpam-6358	551	14	the	the	DET
ejpam-6358	551	15	symbols	symbol	NOUN
ejpam-6358	551	16	along	along	ADP
ejpam-6358	551	17	with	with	ADP
ejpam-6358	551	18	their	their	PRON
ejpam-6358	551	19	abbreviations	abbreviation	NOUN
ejpam-6358	551	20	.	.	PUNCT
ejpam-6358	552	1	list	list	NOUN
ejpam-6358	552	2	of	of	ADP
ejpam-6358	552	3	symbols	symbol	NOUN
ejpam-6358	552	4	and	and	CCONJ
ejpam-6358	552	5	abbreviations	abbreviation	NOUN
ejpam-6358	552	6	u	u	NOUN
ejpam-6358	552	7	a	a	DET
ejpam-6358	552	8	nonempty	nonempty	ADJ
ejpam-6358	552	9	universe	universe	NOUN
ejpam-6358	552	10	set	set	NOUN
ejpam-6358	552	11	.	.	PUNCT
ejpam-6358	553	1	∅	∅	NOUN
ejpam-6358	553	2	the	the	DET
ejpam-6358	553	3	empty	empty	ADJ
ejpam-6358	553	4	set	set	NOUN
ejpam-6358	553	5	.	.	PUNCT
ejpam-6358	554	1	k	k	X
ejpam-6358	555	1	the	the	DET
ejpam-6358	555	2	ideal	ideal	NOUN
ejpam-6358	555	3	.	.	PUNCT
ejpam-6358	556	1	j	j	PROPN
ejpam-6358	556	2	-	-	PUNCT
ejpam-6358	556	3	ns	ns	INTJ
ejpam-6358	556	4	j	j	PROPN
ejpam-6358	556	5	-	-	PUNCT
ejpam-6358	556	6	neighborhood	neighborhood	NOUN
ejpam-6358	556	7	space	space	NOUN
ejpam-6358	556	8	,	,	PUNCT
ejpam-6358	556	9	for	for	ADP
ejpam-6358	556	10	each	each	DET
ejpam-6358	556	11	j	j	PROPN
ejpam-6358	556	12	∈	∈	PROPN
ejpam-6358	556	13	ω	ω	PROPN
ejpam-6358	556	14	,	,	PUNCT
ejpam-6358	556	15	where	where	SCONJ
ejpam-6358	556	16	ω	ω	X
ejpam-6358	556	17	=	=	X
ejpam-6358	556	18	{	{	PUNCT
ejpam-6358	556	19	a	a	DET
ejpam-6358	556	20	,	,	PUNCT
ejpam-6358	556	21	b	b	NOUN
ejpam-6358	556	22	,	,	PUNCT
ejpam-6358	556	23	<	<	X
ejpam-6358	556	24	a	a	X
ejpam-6358	556	25	>	>	X
ejpam-6358	556	26	,	,	PUNCT
ejpam-6358	556	27	<	<	X
ejpam-6358	556	28	b	b	X
ejpam-6358	556	29	>	>	X
ejpam-6358	556	30	,	,	PUNCT
ejpam-6358	556	31	i	i	PRON
ejpam-6358	556	32	,	,	PUNCT
ejpam-6358	556	33	u	u	NOUN
ejpam-6358	556	34	,	,	PUNCT
ejpam-6358	556	35	<	<	X
ejpam-6358	556	36	i	i	X
ejpam-6358	556	37	>	>	X
ejpam-6358	556	38	,	,	PUNCT
ejpam-6358	556	39	<	<	X
ejpam-6358	556	40	u	u	X
ejpam-6358	556	41	>	>	X
ejpam-6358	556	42	}	}	PUNCT
ejpam-6358	556	43	.	.	PUNCT
ejpam-6358	557	1	ωj(s	ωj(s	NUM
ejpam-6358	557	2	)	)	PUNCT
ejpam-6358	558	1	the	the	DET
ejpam-6358	558	2	j	j	PROPN
ejpam-6358	558	3	-	-	PUNCT
ejpam-6358	558	4	neighborhood	neighborhood	NOUN
ejpam-6358	558	5	of	of	ADP
ejpam-6358	558	6	a	a	DET
ejpam-6358	558	7	point	point	NOUN
ejpam-6358	558	8	s	s	ADP
ejpam-6358	558	9	,	,	PUNCT
ejpam-6358	558	10	for	for	ADP
ejpam-6358	558	11	each	each	DET
ejpam-6358	558	12	j	j	PROPN
ejpam-6358	558	13	∈	∈	PROPN
ejpam-6358	558	14	ω	ω	PROPN
ejpam-6358	558	15	.	.	PROPN
ejpam-6358	558	16	ρj(s	ρj(s	NUM
ejpam-6358	558	17	)	)	PUNCT
ejpam-6358	558	18	the	the	DET
ejpam-6358	558	19	ρj	ρj	NOUN
ejpam-6358	558	20	-	-	PUNCT
ejpam-6358	558	21	neighborhood	neighborhood	NOUN
ejpam-6358	558	22	of	of	ADP
ejpam-6358	558	23	a	a	DET
ejpam-6358	558	24	point	point	NOUN
ejpam-6358	558	25	s	s	ADP
ejpam-6358	558	26	,	,	PUNCT
ejpam-6358	558	27	for	for	ADP
ejpam-6358	558	28	each	each	DET
ejpam-6358	558	29	j	j	PROPN
ejpam-6358	558	30	∈	∈	PROPN
ejpam-6358	558	31	ω	ω	PROPN
ejpam-6358	558	32	.	.	PUNCT
ejpam-6358	558	33	ij(s	ij(s	PROPN
ejpam-6358	558	34	)	)	PUNCT
ejpam-6358	559	1	the	the	DET
ejpam-6358	559	2	ij	ij	NOUN
ejpam-6358	559	3	-	-	PUNCT
ejpam-6358	559	4	neighborhood	neighborhood	NOUN
ejpam-6358	559	5	of	of	ADP
ejpam-6358	559	6	a	a	DET
ejpam-6358	559	7	point	point	NOUN
ejpam-6358	559	8	s	s	ADP
ejpam-6358	559	9	,	,	PUNCT
ejpam-6358	559	10	for	for	ADP
ejpam-6358	559	11	each	each	DET
ejpam-6358	559	12	j	j	PROPN
ejpam-6358	559	13	∈	∈	PROPN
ejpam-6358	559	14	ω	ω	PROPN
ejpam-6358	559	15	.	.	PROPN
ejpam-6358	559	16	ikj	ikj	PROPN
ejpam-6358	559	17	(	(	PUNCT
ejpam-6358	559	18	s	s	PROPN
ejpam-6358	559	19	)	)	PUNCT
ejpam-6358	559	20	the	the	DET
ejpam-6358	559	21	ikj	ikj	PROPN
ejpam-6358	559	22	-neighborhood	-neighborhood	PROPN
ejpam-6358	559	23	of	of	ADP
ejpam-6358	559	24	a	a	DET
ejpam-6358	559	25	point	point	NOUN
ejpam-6358	559	26	s	s	ADP
ejpam-6358	559	27	,	,	PUNCT
ejpam-6358	559	28	for	for	ADP
ejpam-6358	559	29	each	each	DET
ejpam-6358	559	30	j	j	PROPN
ejpam-6358	559	31	∈	∈	PROPN
ejpam-6358	559	32	ω	ω	PROPN
ejpam-6358	559	33	.	.	PUNCT
ejpam-6358	560	1	ij	ij	PROPN
ejpam-6358	560	2	-	-	PUNCT
ejpam-6358	560	3	g	g	NOUN
ejpam-6358	560	4	approximation	approximation	NOUN
ejpam-6358	560	5	space	space	NOUN
ejpam-6358	560	6	ij	ij	ADJ
ejpam-6358	560	7	-	-	PUNCT
ejpam-6358	560	8	generalized	generalized	ADJ
ejpam-6358	560	9	approximation	approximation	NOUN
ejpam-6358	560	10	space	space	NOUN
ejpam-6358	560	11	.	.	PUNCT
ejpam-6358	561	1	⊤hj	⊤hj	PROPN
ejpam-6358	561	2	hj	hj	PROPN
ejpam-6358	561	3	-	-	PUNCT
ejpam-6358	561	4	topology	topology	NOUN
ejpam-6358	561	5	generated	generate	VERB
ejpam-6358	561	6	by	by	ADP
ejpam-6358	561	7	hj	hj	PROPN
ejpam-6358	561	8	-	-	PUNCT
ejpam-6358	561	9	neighborhood	neighborhood	NOUN
ejpam-6358	561	10	,	,	PUNCT
ejpam-6358	561	11	where	where	SCONJ
ejpam-6358	561	12	h	h	NOUN
ejpam-6358	561	13	∈	∈	PROPN
ejpam-6358	561	14	{	{	PUNCT
ejpam-6358	561	15	ω	ω	PROPN
ejpam-6358	561	16	,	,	PUNCT
ejpam-6358	561	17	ρ	ρ	PROPN
ejpam-6358	561	18	,	,	PUNCT
ejpam-6358	561	19	i	i	PRON
ejpam-6358	561	20	,	,	PUNCT
ejpam-6358	561	21	ik	ik	PROPN
ejpam-6358	561	22	}	}	PUNCT
ejpam-6358	561	23	.	.	PUNCT
ejpam-6358	562	1	r	r	NOUN
ejpam-6358	562	2	hj	hj	PROPN
ejpam-6358	562	3	⋆	⋆	X
ejpam-6358	562	4	(	(	PUNCT
ejpam-6358	562	5	f	f	PROPN
ejpam-6358	562	6	)	)	PUNCT
ejpam-6358	562	7	the	the	DET
ejpam-6358	562	8	lower	low	ADJ
ejpam-6358	562	9	approximation	approximation	NOUN
ejpam-6358	562	10	of	of	ADP
ejpam-6358	562	11	a	a	DET
ejpam-6358	562	12	subset	subset	NOUN
ejpam-6358	562	13	f	f	PROPN
ejpam-6358	562	14	⊆	⊆	NUM
ejpam-6358	562	15	u	u	NOUN
ejpam-6358	562	16	,	,	PUNCT
ejpam-6358	562	17	where	where	SCONJ
ejpam-6358	562	18	h	h	PROPN
ejpam-6358	562	19	∈	∈	PROPN
ejpam-6358	562	20	{	{	PUNCT
ejpam-6358	562	21	ω	ω	PROPN
ejpam-6358	562	22	,	,	PUNCT
ejpam-6358	562	23	ρ	ρ	PROPN
ejpam-6358	562	24	,	,	PUNCT
ejpam-6358	562	25	i	i	PRON
ejpam-6358	562	26	,	,	PUNCT
ejpam-6358	562	27	ik	ik	PROPN
ejpam-6358	562	28	}	}	PUNCT
ejpam-6358	562	29	.	.	PUNCT
ejpam-6358	563	1	r⋆hj	r⋆hj	PROPN
ejpam-6358	563	2	(	(	PUNCT
ejpam-6358	563	3	f	f	X
ejpam-6358	563	4	)	)	PUNCT
ejpam-6358	563	5	the	the	DET
ejpam-6358	563	6	upper	upper	ADJ
ejpam-6358	563	7	approximation	approximation	NOUN
ejpam-6358	563	8	of	of	ADP
ejpam-6358	563	9	a	a	DET
ejpam-6358	563	10	subset	subset	NOUN
ejpam-6358	563	11	f	f	PROPN
ejpam-6358	563	12	⊆	⊆	NUM
ejpam-6358	563	13	u	u	NOUN
ejpam-6358	563	14	,	,	PUNCT
ejpam-6358	563	15	where	where	SCONJ
ejpam-6358	563	16	h	h	PROPN
ejpam-6358	563	17	∈	∈	PROPN
ejpam-6358	563	18	{	{	PUNCT
ejpam-6358	563	19	ω	ω	PROPN
ejpam-6358	563	20	,	,	PUNCT
ejpam-6358	563	21	ρ	ρ	PROPN
ejpam-6358	563	22	,	,	PUNCT
ejpam-6358	563	23	i	i	PRON
ejpam-6358	563	24	,	,	PUNCT
ejpam-6358	563	25	ik	ik	PROPN
ejpam-6358	563	26	}	}	PUNCT
ejpam-6358	563	27	.	.	PUNCT
ejpam-6358	564	1	bnd	bnd	NOUN
ejpam-6358	564	2	⋆hj	⋆hj	PROPN
ejpam-6358	564	3	r	r	NOUN
ejpam-6358	564	4	(	(	PUNCT
ejpam-6358	564	5	f	f	PROPN
ejpam-6358	564	6	)	)	PUNCT
ejpam-6358	564	7	the	the	DET
ejpam-6358	564	8	boundary	boundary	ADJ
ejpam-6358	564	9	region	region	NOUN
ejpam-6358	564	10	of	of	ADP
ejpam-6358	564	11	a	a	DET
ejpam-6358	564	12	subset	subset	NOUN
ejpam-6358	564	13	f	f	PROPN
ejpam-6358	564	14	⊆	⊆	NUM
ejpam-6358	564	15	u	u	NOUN
ejpam-6358	564	16	,	,	PUNCT
ejpam-6358	564	17	where	where	SCONJ
ejpam-6358	564	18	h	h	PROPN
ejpam-6358	564	19	∈	∈	PROPN
ejpam-6358	564	20	{	{	PUNCT
ejpam-6358	564	21	ω	ω	PROPN
ejpam-6358	564	22	,	,	PUNCT
ejpam-6358	564	23	ρ	ρ	PROPN
ejpam-6358	564	24	,	,	PUNCT
ejpam-6358	564	25	i	i	PRON
ejpam-6358	564	26	,	,	PUNCT
ejpam-6358	564	27	ik	ik	PROPN
ejpam-6358	564	28	}	}	PUNCT
ejpam-6358	564	29	.	.	PUNCT
ejpam-6358	565	1	acc	acc	PROPN
ejpam-6358	565	2	⋆hj	⋆hj	PROPN
ejpam-6358	565	3	r	r	PROPN
ejpam-6358	565	4	(	(	PUNCT
ejpam-6358	565	5	f	f	PROPN
ejpam-6358	565	6	)	)	PUNCT
ejpam-6358	565	7	the	the	DET
ejpam-6358	565	8	accuracy	accuracy	NOUN
ejpam-6358	565	9	measure	measure	NOUN
ejpam-6358	565	10	of	of	ADP
ejpam-6358	565	11	a	a	DET
ejpam-6358	565	12	subset	subset	NOUN
ejpam-6358	565	13	f	f	PROPN
ejpam-6358	565	14	⊆	⊆	NUM
ejpam-6358	565	15	u	u	NOUN
ejpam-6358	565	16	,	,	PUNCT
ejpam-6358	565	17	where	where	SCONJ
ejpam-6358	565	18	h	h	PROPN
ejpam-6358	565	19	∈	∈	PROPN
ejpam-6358	565	20	{	{	PUNCT
ejpam-6358	565	21	ω	ω	PROPN
ejpam-6358	565	22	,	,	PUNCT
ejpam-6358	565	23	ρ	ρ	PROPN
ejpam-6358	565	24	,	,	PUNCT
ejpam-6358	565	25	i	i	PRON
ejpam-6358	565	26	,	,	PUNCT
ejpam-6358	565	27	ik	ik	PROPN
ejpam-6358	565	28	}	}	PUNCT
ejpam-6358	565	29	.	.	PUNCT
ejpam-6358	566	1	acknowledgements	acknowledgement	NOUN
ejpam-6358	566	2	the	the	DET
ejpam-6358	566	3	authors	author	NOUN
ejpam-6358	566	4	would	would	AUX
ejpam-6358	566	5	like	like	VERB
ejpam-6358	566	6	to	to	PART
ejpam-6358	566	7	extend	extend	VERB
ejpam-6358	566	8	their	their	PRON
ejpam-6358	566	9	deepest	deep	ADJ
ejpam-6358	566	10	gratitude	gratitude	NOUN
ejpam-6358	566	11	to	to	ADP
ejpam-6358	566	12	the	the	DET
ejpam-6358	566	13	editor	editor	NOUN
ejpam-6358	566	14	-	-	PUNCT
ejpam-6358	566	15	in	in	ADP
ejpam-6358	566	16	-	-	PUNCT
ejpam-6358	566	17	chief	chief	NOUN
ejpam-6358	566	18	,	,	PUNCT
ejpam-6358	566	19	the	the	DET
ejpam-6358	566	20	section	section	NOUN
ejpam-6358	566	21	editor	editor	NOUN
ejpam-6358	566	22	,	,	PUNCT
ejpam-6358	566	23	and	and	CCONJ
ejpam-6358	566	24	the	the	DET
ejpam-6358	566	25	reviewers	reviewer	NOUN
ejpam-6358	566	26	for	for	ADP
ejpam-6358	566	27	their	their	PRON
ejpam-6358	566	28	insightful	insightful	ADJ
ejpam-6358	566	29	comments	comment	NOUN
ejpam-6358	566	30	and	and	CCONJ
ejpam-6358	566	31	suggestions	suggestion	NOUN
ejpam-6358	566	32	,	,	PUNCT
ejpam-6358	566	33	which	which	PRON
ejpam-6358	566	34	were	be	AUX
ejpam-6358	566	35	instrumental	instrumental	ADJ
ejpam-6358	566	36	in	in	ADP
ejpam-6358	566	37	refining	refining	NOUN
ejpam-6358	566	38	and	and	CCONJ
ejpam-6358	566	39	improving	improve	VERB
ejpam-6358	566	40	the	the	DET
ejpam-6358	566	41	quality	quality	NOUN
ejpam-6358	566	42	of	of	ADP
ejpam-6358	566	43	this	this	DET
ejpam-6358	566	44	work	work	NOUN
ejpam-6358	566	45	.	.	PUNCT
ejpam-6358	567	1	special	special	ADJ
ejpam-6358	567	2	thanks	thank	NOUN
ejpam-6358	567	3	are	be	AUX
ejpam-6358	567	4	also	also	ADV
ejpam-6358	567	5	due	due	ADJ
ejpam-6358	567	6	to	to	ADP
ejpam-6358	567	7	our	our	PRON
ejpam-6358	567	8	esteemed	esteemed	ADJ
ejpam-6358	567	9	colleagues	colleague	NOUN
ejpam-6358	567	10	at	at	ADP
ejpam-6358	567	11	the	the	DET
ejpam-6358	567	12	egyptian	egyptian	ADJ
ejpam-6358	567	13	school	school	NOUN
ejpam-6358	567	14	of	of	ADP
ejpam-6358	567	15	topology	topology	NOUN
ejpam-6358	567	16	(	(	PUNCT
ejpam-6358	567	17	in	in	ADP
ejpam-6358	567	18	tanta	tanta	PROPN
ejpam-6358	567	19	,	,	PUNCT
ejpam-6358	567	20	egypt	egypt	PROPN
ejpam-6358	567	21	)	)	PUNCT
ejpam-6358	567	22	,	,	PUNCT
ejpam-6358	567	23	established	establish	VERB
ejpam-6358	567	24	by	by	ADP
ejpam-6358	567	25	prof	prof	PROPN
ejpam-6358	567	26	.	.	PUNCT
ejpam-6358	568	1	a.	a.	PROPN
ejpam-6358	568	2	s.	s.	PROPN
ejpam-6358	568	3	mashhour	mashhour	PROPN
ejpam-6358	568	4	and	and	CCONJ
ejpam-6358	568	5	prof	prof	PROPN
ejpam-6358	568	6	.	.	PUNCT
ejpam-6358	569	1	m.	m.	PROPN
ejpam-6358	569	2	e.	e.	PROPN
ejpam-6358	569	3	abd	abd	PROPN
ejpam-6358	570	1	el	el	PROPN
ejpam-6358	570	2	-	-	PROPN
ejpam-6358	570	3	monsef	monsef	ADJ
ejpam-6358	570	4	,	,	PUNCT
ejpam-6358	570	5	and	and	CCONJ
ejpam-6358	570	6	led	lead	VERB
ejpam-6358	570	7	by	by	ADP
ejpam-6358	570	8	prof	prof	PROPN
ejpam-6358	570	9	.	.	PUNCT
ejpam-6358	570	10	a.	a.	PROPN
ejpam-6358	570	11	m.	m.	PROPN
ejpam-6358	570	12	kozae	kozae	PROPN
ejpam-6358	570	13	.	.	PUNCT
ejpam-6358	571	1	this	this	DET
ejpam-6358	571	2	institution	institution	NOUN
ejpam-6358	571	3	has	have	AUX
ejpam-6358	571	4	fostered	foster	VERB
ejpam-6358	571	5	numerous	numerous	ADJ
ejpam-6358	571	6	distinguished	distinguished	ADJ
ejpam-6358	571	7	researchers	researcher	NOUN
ejpam-6358	571	8	both	both	CCONJ
ejpam-6358	571	9	within	within	ADP
ejpam-6358	571	10	egypt	egypt	PROPN
ejpam-6358	571	11	and	and	CCONJ
ejpam-6358	571	12	internationally	internationally	ADV
ejpam-6358	571	13	,	,	PUNCT
ejpam-6358	571	14	including	include	VERB
ejpam-6358	571	15	scholars	scholar	NOUN
ejpam-6358	571	16	from	from	ADP
ejpam-6358	571	17	yemen	yemen	PROPN
ejpam-6358	571	18	,	,	PUNCT
ejpam-6358	571	19	palestine	palestine	PROPN
ejpam-6358	571	20	,	,	PUNCT
ejpam-6358	571	21	jordan	jordan	PROPN
ejpam-6358	571	22	,	,	PUNCT
ejpam-6358	571	23	and	and	CCONJ
ejpam-6358	571	24	saudi	saudi	PROPN
ejpam-6358	571	25	arabia	arabia	PROPN
ejpam-6358	571	26	.	.	PUNCT
ejpam-6358	572	1	the	the	DET
ejpam-6358	572	2	authors	author	NOUN
ejpam-6358	572	3	are	be	AUX
ejpam-6358	572	4	particularly	particularly	ADV
ejpam-6358	572	5	thankful	thankful	ADJ
ejpam-6358	572	6	for	for	ADP
ejpam-6358	572	7	the	the	DET
ejpam-6358	572	8	school	school	NOUN
ejpam-6358	572	9	’s	’s	PART
ejpam-6358	572	10	unwavering	unwavering	ADJ
ejpam-6358	572	11	support	support	NOUN
ejpam-6358	572	12	,	,	PUNCT
ejpam-6358	573	1	r.	r.	PROPN
ejpam-6358	573	2	a.	a.	PROPN
ejpam-6358	573	3	hosny	hosny	PROPN
ejpam-6358	573	4	et	et	PROPN
ejpam-6358	573	5	al	al	PROPN
ejpam-6358	573	6	.	.	PUNCT
ejpam-6358	573	7	/	/	SYM
ejpam-6358	573	8	eur	eur	PROPN
ejpam-6358	573	9	.	.	PUNCT
ejpam-6358	574	1	j.	j.	PROPN
ejpam-6358	574	2	pure	pure	PROPN
ejpam-6358	574	3	appl	appl	PROPN
ejpam-6358	574	4	.	.	PROPN
ejpam-6358	574	5	math	math	PROPN
ejpam-6358	574	6	,	,	PUNCT
ejpam-6358	574	7	18	18	NUM
ejpam-6358	574	8	(	(	PUNCT
ejpam-6358	574	9	4	4	NUM
ejpam-6358	574	10	)	)	PUNCT
ejpam-6358	574	11	(	(	PUNCT
ejpam-6358	574	12	2025	2025	NUM
ejpam-6358	574	13	)	)	PUNCT
ejpam-6358	574	14	,	,	PUNCT
ejpam-6358	574	15	6358	6358	NUM
ejpam-6358	574	16	21	21	NUM
ejpam-6358	574	17	of	of	ADP
ejpam-6358	574	18	24	24	NUM
ejpam-6358	574	19	encouragement	encouragement	NOUN
ejpam-6358	574	20	,	,	PUNCT
ejpam-6358	574	21	and	and	CCONJ
ejpam-6358	574	22	the	the	DET
ejpam-6358	574	23	enriching	enriching	ADJ
ejpam-6358	574	24	discussions	discussion	NOUN
ejpam-6358	574	25	that	that	PRON
ejpam-6358	574	26	contributed	contribute	VERB
ejpam-6358	574	27	to	to	ADP
ejpam-6358	574	28	this	this	DET
ejpam-6358	574	29	research	research	NOUN
ejpam-6358	574	30	.	.	PUNCT
ejpam-6358	575	1	finally	finally	ADV
ejpam-6358	575	2	,	,	PUNCT
ejpam-6358	575	3	this	this	DET
ejpam-6358	575	4	work	work	NOUN
ejpam-6358	575	5	is	be	AUX
ejpam-6358	575	6	dedicated	dedicate	VERB
ejpam-6358	575	7	to	to	ADP
ejpam-6358	575	8	the	the	DET
ejpam-6358	575	9	memory	memory	NOUN
ejpam-6358	575	10	of	of	ADP
ejpam-6358	575	11	prof	prof	PROPN
ejpam-6358	575	12	.	.	PUNCT
ejpam-6358	576	1	a.	a.	PROPN
ejpam-6358	576	2	s.	s.	PROPN
ejpam-6358	576	3	mashhour	mashhour	PROPN
ejpam-6358	576	4	,	,	PUNCT
ejpam-6358	576	5	and	and	CCONJ
ejpam-6358	576	6	prof	prof	PROPN
ejpam-6358	576	7	.	.	PUNCT
ejpam-6358	576	8	m.	m.	PROPN
ejpam-6358	576	9	e.	e.	PROPN
ejpam-6358	576	10	abd	abd	PROPN
ejpam-6358	576	11	el	el	PROPN
ejpam-6358	576	12	-	-	PROPN
ejpam-6358	576	13	monsef	monsef	ADJ
ejpam-6358	576	14	—	—	PUNCT
ejpam-6358	576	15	may	may	AUX
ejpam-6358	576	16	god	god	PROPN
ejpam-6358	576	17	’s	’s	PART
ejpam-6358	576	18	mercy	mercy	NOUN
ejpam-6358	576	19	be	be	AUX
ejpam-6358	576	20	upon	upon	SCONJ
ejpam-6358	576	21	them	they	PRON
ejpam-6358	576	22	.	.	PUNCT
ejpam-6358	577	1	we	we	PRON
ejpam-6358	577	2	also	also	ADV
ejpam-6358	577	3	dedicate	dedicate	VERB
ejpam-6358	577	4	this	this	DET
ejpam-6358	577	5	work	work	NOUN
ejpam-6358	577	6	to	to	ADP
ejpam-6358	577	7	the	the	DET
ejpam-6358	577	8	memory	memory	NOUN
ejpam-6358	577	9	of	of	ADP
ejpam-6358	577	10	our	our	PRON
ejpam-6358	577	11	dear	dear	ADJ
ejpam-6358	577	12	friend	friend	NOUN
ejpam-6358	577	13	and	and	CCONJ
ejpam-6358	577	14	long	long	ADJ
ejpam-6358	577	15	-	-	PUNCT
ejpam-6358	577	16	time	time	NOUN
ejpam-6358	577	17	collaborator	collaborator	NOUN
ejpam-6358	577	18	in	in	ADP
ejpam-6358	577	19	fruitful	fruitful	ADJ
ejpam-6358	577	20	scientific	scientific	ADJ
ejpam-6358	577	21	research	research	NOUN
ejpam-6358	577	22	,	,	PUNCT
ejpam-6358	577	23	prof	prof	PROPN
ejpam-6358	577	24	.	.	PUNCT
ejpam-6358	578	1	r.	r.	PROPN
ejpam-6358	578	2	abu	abu	PROPN
ejpam-6358	578	3	-	-	PUNCT
ejpam-6358	578	4	gdairi	gdairi	PROPN
ejpam-6358	578	5	,	,	PUNCT
ejpam-6358	578	6	who	who	PRON
ejpam-6358	578	7	passed	pass	VERB
ejpam-6358	578	8	away	away	ADV
ejpam-6358	578	9	in	in	ADP
ejpam-6358	578	10	june	june	PROPN
ejpam-6358	578	11	2025	2025	NUM
ejpam-6358	578	12	.	.	PUNCT
ejpam-6358	579	1	use	use	NOUN
ejpam-6358	579	2	of	of	ADP
ejpam-6358	579	3	ai	ai	ADJ
ejpam-6358	579	4	tools	tool	NOUN
ejpam-6358	579	5	declaration	declaration	NOUN
ejpam-6358	579	6	:	:	PUNCT
ejpam-6358	579	7	the	the	DET
ejpam-6358	579	8	authors	author	NOUN
ejpam-6358	579	9	declare	declare	VERB
ejpam-6358	579	10	that	that	SCONJ
ejpam-6358	579	11	they	they	PRON
ejpam-6358	579	12	have	have	AUX
ejpam-6358	579	13	not	not	PART
ejpam-6358	579	14	used	use	VERB
ejpam-6358	579	15	artificial	artificial	ADJ
ejpam-6358	579	16	intelligence	intelligence	NOUN
ejpam-6358	579	17	(	(	PUNCT
ejpam-6358	579	18	ai	ai	NOUN
ejpam-6358	579	19	)	)	PUNCT
ejpam-6358	579	20	tools	tool	NOUN
ejpam-6358	579	21	in	in	ADP
ejpam-6358	579	22	the	the	DET
ejpam-6358	579	23	creation	creation	NOUN
ejpam-6358	579	24	of	of	ADP
ejpam-6358	579	25	the	the	DET
ejpam-6358	579	26	content	content	NOUN
ejpam-6358	579	27	of	of	ADP
ejpam-6358	579	28	this	this	DET
ejpam-6358	579	29	article	article	NOUN
ejpam-6358	579	30	.	.	PUNCT
ejpam-6358	580	1	however	however	ADV
ejpam-6358	580	2	,	,	PUNCT
ejpam-6358	580	3	ai	ai	VERB
ejpam-6358	580	4	tools	tool	NOUN
ejpam-6358	580	5	have	have	AUX
ejpam-6358	580	6	been	be	AUX
ejpam-6358	580	7	utilized	utilize	VERB
ejpam-6358	580	8	solely	solely	ADV
ejpam-6358	580	9	for	for	ADP
ejpam-6358	580	10	grammar	grammar	NOUN
ejpam-6358	580	11	and	and	CCONJ
ejpam-6358	580	12	spelling	spelling	NOUN
ejpam-6358	580	13	correction	correction	NOUN
ejpam-6358	580	14	support	support	NOUN
ejpam-6358	580	15	.	.	PUNCT
ejpam-6358	581	1	all	all	DET
ejpam-6358	581	2	the	the	DET
ejpam-6358	581	3	information	information	NOUN
ejpam-6358	581	4	and	and	CCONJ
ejpam-6358	581	5	data	datum	NOUN
ejpam-6358	581	6	in	in	ADP
ejpam-6358	581	7	this	this	DET
ejpam-6358	581	8	paper	paper	NOUN
ejpam-6358	581	9	have	have	AUX
ejpam-6358	581	10	been	be	AUX
ejpam-6358	581	11	ethically	ethically	ADV
ejpam-6358	581	12	reviewed	review	VERB
ejpam-6358	581	13	,	,	PUNCT
ejpam-6358	581	14	edited	edit	VERB
ejpam-6358	581	15	,	,	PUNCT
ejpam-6358	581	16	and	and	CCONJ
ejpam-6358	581	17	studied	study	VERB
ejpam-6358	581	18	.	.	PUNCT
ejpam-6358	582	1	no	no	DET
ejpam-6358	582	2	ai	ai	NOUN
ejpam-6358	582	3	-	-	PUNCT
ejpam-6358	582	4	generated	generate	VERB
ejpam-6358	582	5	data	datum	NOUN
ejpam-6358	582	6	or	or	CCONJ
ejpam-6358	582	7	results	result	NOUN
ejpam-6358	582	8	are	be	AUX
ejpam-6358	582	9	included	include	VERB
ejpam-6358	582	10	.	.	PUNCT
ejpam-6358	583	1	availability	availability	NOUN
ejpam-6358	583	2	of	of	ADP
ejpam-6358	583	3	data	datum	NOUN
ejpam-6358	583	4	and	and	CCONJ
ejpam-6358	583	5	material	material	NOUN
ejpam-6358	583	6	not	not	PART
ejpam-6358	583	7	applicable	applicable	ADJ
ejpam-6358	583	8	.	.	PUNCT
ejpam-6358	584	1	competing	compete	VERB
ejpam-6358	584	2	interests	interest	NOUN
ejpam-6358	584	3	the	the	DET
ejpam-6358	584	4	authors	author	NOUN
ejpam-6358	584	5	declare	declare	VERB
ejpam-6358	584	6	that	that	SCONJ
ejpam-6358	584	7	they	they	PRON
ejpam-6358	584	8	have	have	VERB
ejpam-6358	584	9	no	no	DET
ejpam-6358	584	10	competing	compete	VERB
ejpam-6358	584	11	interests	interest	NOUN
ejpam-6358	584	12	.	.	PUNCT
ejpam-6358	585	1	funding	fund	VERB
ejpam-6358	585	2	there	there	PRON
ejpam-6358	585	3	is	be	VERB
ejpam-6358	585	4	no	no	DET
ejpam-6358	585	5	funding	funding	NOUN
ejpam-6358	585	6	available	available	ADJ
ejpam-6358	585	7	.	.	PUNCT
ejpam-6358	586	1	references	reference	NOUN
ejpam-6358	586	2	[	[	X
ejpam-6358	586	3	1	1	NUM
ejpam-6358	586	4	]	]	PUNCT
ejpam-6358	586	5	z.	z.	PROPN
ejpam-6358	586	6	pawlak	pawlak	PROPN
ejpam-6358	586	7	.	.	PUNCT
ejpam-6358	587	1	rough	rough	ADJ
ejpam-6358	587	2	sets	set	NOUN
ejpam-6358	587	3	.	.	PUNCT
ejpam-6358	588	1	international	international	ADJ
ejpam-6358	588	2	journal	journal	NOUN
ejpam-6358	588	3	of	of	ADP
ejpam-6358	588	4	information	information	NOUN
ejpam-6358	588	5	and	and	CCONJ
ejpam-6358	588	6	computer	computer	NOUN
ejpam-6358	588	7	sciences	science	NOUN
ejpam-6358	588	8	,	,	PUNCT
ejpam-6358	588	9	11:341–356	11:341–356	NUM
ejpam-6358	588	10	,	,	PUNCT
ejpam-6358	588	11	1982	1982	NUM
ejpam-6358	588	12	.	.	PUNCT
ejpam-6358	589	1	[	[	X
ejpam-6358	589	2	2	2	NUM
ejpam-6358	589	3	]	]	PUNCT
ejpam-6358	589	4	z.	z.	PROPN
ejpam-6358	589	5	pawlak	pawlak	PROPN
ejpam-6358	589	6	.	.	PUNCT
ejpam-6358	590	1	rough	rough	ADJ
ejpam-6358	590	2	sets	set	NOUN
ejpam-6358	590	3	:	:	PUNCT
ejpam-6358	590	4	theoretical	theoretical	ADJ
ejpam-6358	590	5	aspects	aspect	NOUN
ejpam-6358	590	6	of	of	ADP
ejpam-6358	590	7	reasoning	reasoning	NOUN
ejpam-6358	590	8	about	about	ADP
ejpam-6358	590	9	data	datum	NOUN
ejpam-6358	590	10	.	.	PUNCT
ejpam-6358	591	1	springer	springer	PROPN
ejpam-6358	591	2	,	,	PUNCT
ejpam-6358	591	3	dordrecht	dordrecht	PROPN
ejpam-6358	591	4	,	,	PUNCT
ejpam-6358	591	5	1991	1991	NUM
ejpam-6358	591	6	.	.	PUNCT
ejpam-6358	592	1	[	[	X
ejpam-6358	592	2	3	3	X
ejpam-6358	592	3	]	]	X
ejpam-6358	592	4	y.	y.	PROPN
ejpam-6358	592	5	y.	y.	PROPN
ejpam-6358	592	6	yao	yao	PROPN
ejpam-6358	592	7	.	.	PUNCT
ejpam-6358	593	1	two	two	NUM
ejpam-6358	593	2	views	view	NOUN
ejpam-6358	593	3	of	of	ADP
ejpam-6358	593	4	the	the	DET
ejpam-6358	593	5	theory	theory	NOUN
ejpam-6358	593	6	of	of	ADP
ejpam-6358	593	7	rough	rough	ADJ
ejpam-6358	593	8	sets	set	NOUN
ejpam-6358	593	9	in	in	ADP
ejpam-6358	593	10	finite	finite	ADJ
ejpam-6358	593	11	universes	universe	NOUN
ejpam-6358	593	12	.	.	PUNCT
ejpam-6358	594	1	international	international	ADJ
ejpam-6358	594	2	journal	journal	PROPN
ejpam-6358	594	3	of	of	ADP
ejpam-6358	594	4	approximate	approximate	ADJ
ejpam-6358	594	5	reasoning	reasoning	NOUN
ejpam-6358	594	6	,	,	PUNCT
ejpam-6358	594	7	15:291–317	15:291–317	NUM
ejpam-6358	594	8	,	,	PUNCT
ejpam-6358	594	9	1996	1996	NUM
ejpam-6358	594	10	.	.	PUNCT
ejpam-6358	595	1	[	[	X
ejpam-6358	595	2	4	4	X
ejpam-6358	595	3	]	]	X
ejpam-6358	595	4	b.	b.	PROPN
ejpam-6358	595	5	de	de	X
ejpam-6358	595	6	baets	baet	NOUN
ejpam-6358	595	7	and	and	CCONJ
ejpam-6358	595	8	e.	e.	PROPN
ejpam-6358	595	9	kerre	kerre	PROPN
ejpam-6358	595	10	.	.	PUNCT
ejpam-6358	596	1	a	a	DET
ejpam-6358	596	2	revision	revision	NOUN
ejpam-6358	596	3	of	of	ADP
ejpam-6358	596	4	bandler	bandler	NOUN
ejpam-6358	596	5	-	-	PUNCT
ejpam-6358	596	6	kohout	kohout	NOUN
ejpam-6358	596	7	compositions	composition	NOUN
ejpam-6358	596	8	of	of	ADP
ejpam-6358	596	9	relations	relation	NOUN
ejpam-6358	596	10	.	.	PUNCT
ejpam-6358	597	1	mathematica	mathematica	PROPN
ejpam-6358	597	2	pannonica	pannonica	PROPN
ejpam-6358	597	3	,	,	PUNCT
ejpam-6358	597	4	4:59–78	4:59–78	NUM
ejpam-6358	597	5	,	,	PUNCT
ejpam-6358	597	6	1993	1993	NUM
ejpam-6358	597	7	.	.	PUNCT
ejpam-6358	598	1	[	[	X
ejpam-6358	598	2	5	5	NUM
ejpam-6358	598	3	]	]	PUNCT
ejpam-6358	598	4	a.	a.	NOUN
ejpam-6358	598	5	a.	a.	PROPN
ejpam-6358	598	6	allam	allam	PROPN
ejpam-6358	598	7	,	,	PUNCT
ejpam-6358	598	8	m.	m.	PROPN
ejpam-6358	598	9	y.	y.	PROPN
ejpam-6358	598	10	bakeir	bakeir	PROPN
ejpam-6358	598	11	,	,	PUNCT
ejpam-6358	598	12	and	and	CCONJ
ejpam-6358	598	13	e.	e.	PROPN
ejpam-6358	598	14	a.	a.	PROPN
ejpam-6358	598	15	abo	abo	PROPN
ejpam-6358	598	16	-	-	PUNCT
ejpam-6358	598	17	tabl	tabl	NOUN
ejpam-6358	598	18	.	.	PUNCT
ejpam-6358	599	1	new	new	ADJ
ejpam-6358	599	2	approach	approach	NOUN
ejpam-6358	599	3	for	for	ADP
ejpam-6358	599	4	basic	basic	ADJ
ejpam-6358	599	5	rough	rough	ADJ
ejpam-6358	599	6	set	set	NOUN
ejpam-6358	599	7	concepts	concept	NOUN
ejpam-6358	599	8	.	.	PUNCT
ejpam-6358	600	1	in	in	ADP
ejpam-6358	600	2	rough	rough	ADJ
ejpam-6358	600	3	sets	set	NOUN
ejpam-6358	600	4	,	,	PUNCT
ejpam-6358	600	5	fuzzy	fuzzy	ADJ
ejpam-6358	600	6	sets	set	NOUN
ejpam-6358	600	7	,	,	PUNCT
ejpam-6358	600	8	data	datum	NOUN
ejpam-6358	600	9	mining	mining	NOUN
ejpam-6358	600	10	,	,	PUNCT
ejpam-6358	600	11	and	and	CCONJ
ejpam-6358	600	12	granular	granular	ADJ
ejpam-6358	600	13	computing	computing	NOUN
ejpam-6358	600	14	,	,	PUNCT
ejpam-6358	600	15	pages	page	NOUN
ejpam-6358	600	16	64–73	64–73	NUM
ejpam-6358	600	17	,	,	PUNCT
ejpam-6358	600	18	berlin	berlin	PROPN
ejpam-6358	600	19	,	,	PUNCT
ejpam-6358	600	20	heidelberg	heidelberg	PROPN
ejpam-6358	600	21	,	,	PUNCT
ejpam-6358	600	22	2005	2005	NUM
ejpam-6358	600	23	.	.	PUNCT
ejpam-6358	600	24	springer	springer	NOUN
ejpam-6358	600	25	.	.	PUNCT
ejpam-6358	601	1	[	[	X
ejpam-6358	601	2	6	6	NUM
ejpam-6358	601	3	]	]	PUNCT
ejpam-6358	601	4	a.	a.	NOUN
ejpam-6358	601	5	a.	a.	PROPN
ejpam-6358	601	6	allam	allam	PROPN
ejpam-6358	601	7	,	,	PUNCT
ejpam-6358	601	8	m.	m.	PROPN
ejpam-6358	601	9	y.	y.	PROPN
ejpam-6358	601	10	bakeir	bakeir	PROPN
ejpam-6358	601	11	,	,	PUNCT
ejpam-6358	601	12	and	and	CCONJ
ejpam-6358	601	13	e.	e.	PROPN
ejpam-6358	601	14	a.	a.	PROPN
ejpam-6358	601	15	abo	abo	PROPN
ejpam-6358	601	16	-	-	PUNCT
ejpam-6358	601	17	tabl	tabl	NOUN
ejpam-6358	601	18	.	.	PUNCT
ejpam-6358	602	1	new	new	ADJ
ejpam-6358	602	2	approach	approach	NOUN
ejpam-6358	602	3	for	for	ADP
ejpam-6358	602	4	closure	closure	NOUN
ejpam-6358	602	5	spaces	space	NOUN
ejpam-6358	602	6	by	by	ADP
ejpam-6358	602	7	relations	relation	NOUN
ejpam-6358	602	8	.	.	PUNCT
ejpam-6358	603	1	acta	acta	PROPN
ejpam-6358	603	2	mathematica	mathematica	PROPN
ejpam-6358	603	3	academiae	academiae	PROPN
ejpam-6358	603	4	paedagogicae	paedagogicae	ADJ
ejpam-6358	603	5	nyíregyháziensis	nyíregyháziensis	NOUN
ejpam-6358	603	6	,	,	PUNCT
ejpam-6358	603	7	22(3):285	22(3):285	NUM
ejpam-6358	603	8	–	–	PUNCT
ejpam-6358	603	9	304	304	NUM
ejpam-6358	603	10	,	,	PUNCT
ejpam-6358	603	11	2006	2006	NUM
ejpam-6358	603	12	.	.	PUNCT
ejpam-6358	604	1	[	[	X
ejpam-6358	604	2	7	7	X
ejpam-6358	604	3	]	]	PUNCT
ejpam-6358	604	4	a.	a.	NOUN
ejpam-6358	604	5	a.	a.	NOUN
ejpam-6358	604	6	abo	abo	PROPN
ejpam-6358	604	7	khadra	khadra	PROPN
ejpam-6358	604	8	,	,	PUNCT
ejpam-6358	604	9	b.	b.	PROPN
ejpam-6358	604	10	m.	m.	PROPN
ejpam-6358	604	11	taher	taher	PROPN
ejpam-6358	604	12	,	,	PUNCT
ejpam-6358	604	13	and	and	CCONJ
ejpam-6358	604	14	m.	m.	PROPN
ejpam-6358	604	15	k.	k.	PROPN
ejpam-6358	605	1	el	el	PROPN
ejpam-6358	605	2	-	-	PROPN
ejpam-6358	605	3	bably	bably	ADV
ejpam-6358	605	4	.	.	PUNCT
ejpam-6358	606	1	generalization	generalization	NOUN
ejpam-6358	606	2	of	of	ADP
ejpam-6358	606	3	pawlak	pawlak	ADJ
ejpam-6358	606	4	approximation	approximation	NOUN
ejpam-6358	606	5	space	space	NOUN
ejpam-6358	606	6	.	.	PUNCT
ejpam-6358	607	1	in	in	ADP
ejpam-6358	607	2	proceedings	proceeding	NOUN
ejpam-6358	607	3	of	of	ADP
ejpam-6358	607	4	the	the	DET
ejpam-6358	607	5	international	international	ADJ
ejpam-6358	607	6	conference	conference	NOUN
ejpam-6358	607	7	on	on	ADP
ejpam-6358	607	8	mathematics	mathematic	NOUN
ejpam-6358	607	9	:	:	PUNCT
ejpam-6358	607	10	trends	trend	NOUN
ejpam-6358	607	11	and	and	CCONJ
ejpam-6358	607	12	developments	development	NOUN
ejpam-6358	607	13	,	,	PUNCT
ejpam-6358	607	14	volume	volume	NOUN
ejpam-6358	607	15	3	3	NUM
ejpam-6358	607	16	,	,	PUNCT
ejpam-6358	607	17	pages	page	NOUN
ejpam-6358	607	18	335–346	335–346	NUM
ejpam-6358	607	19	,	,	PUNCT
ejpam-6358	607	20	tanta	tanta	PROPN
ejpam-6358	607	21	,	,	PUNCT
ejpam-6358	607	22	egypt	egypt	PROPN
ejpam-6358	607	23	,	,	PUNCT
ejpam-6358	607	24	2007	2007	NUM
ejpam-6358	607	25	.	.	PUNCT
ejpam-6358	608	1	egyptian	egyptian	PROPN
ejpam-6358	608	2	mathematical	mathematical	ADJ
ejpam-6358	608	3	society	society	NOUN
ejpam-6358	608	4	.	.	PUNCT
ejpam-6358	609	1	[	[	X
ejpam-6358	609	2	8	8	NUM
ejpam-6358	609	3	]	]	PUNCT
ejpam-6358	609	4	m.	m.	NOUN
ejpam-6358	609	5	k.	k.	PROPN
ejpam-6358	610	1	el	el	PROPN
ejpam-6358	610	2	-	-	PROPN
ejpam-6358	610	3	bably	bably	PROPN
ejpam-6358	610	4	.	.	PUNCT
ejpam-6358	611	1	generalized	generalized	ADJ
ejpam-6358	611	2	approximation	approximation	NOUN
ejpam-6358	611	3	spaces	space	NOUN
ejpam-6358	611	4	.	.	PUNCT
ejpam-6358	612	1	m.sc	m.sc	PROPN
ejpam-6358	612	2	.	.	PUNCT
ejpam-6358	613	1	thesis	thesis	PROPN
ejpam-6358	613	2	,	,	PUNCT
ejpam-6358	613	3	tanta	tanta	PROPN
ejpam-6358	613	4	university	university	PROPN
ejpam-6358	613	5	,	,	PUNCT
ejpam-6358	613	6	tanta	tanta	PROPN
ejpam-6358	613	7	,	,	PUNCT
ejpam-6358	613	8	egypt	egypt	PROPN
ejpam-6358	613	9	,	,	PUNCT
ejpam-6358	613	10	2008	2008	NUM
ejpam-6358	613	11	.	.	PUNCT
ejpam-6358	614	1	[	[	X
ejpam-6358	614	2	9	9	NUM
ejpam-6358	614	3	]	]	PUNCT
ejpam-6358	614	4	m.	m.	NOUN
ejpam-6358	614	5	e.	e.	PROPN
ejpam-6358	614	6	abd	abd	PROPN
ejpam-6358	615	1	el	el	PROPN
ejpam-6358	615	2	-	-	PROPN
ejpam-6358	615	3	monsef	monsef	ADJ
ejpam-6358	615	4	,	,	PUNCT
ejpam-6358	615	5	o.	o.	PROPN
ejpam-6358	615	6	a.	a.	NOUN
ejpam-6358	615	7	embaby	embaby	PROPN
ejpam-6358	615	8	,	,	PUNCT
ejpam-6358	615	9	and	and	CCONJ
ejpam-6358	615	10	m.	m.	PROPN
ejpam-6358	615	11	k.	k.	PROPN
ejpam-6358	616	1	el	el	PROPN
ejpam-6358	616	2	-	-	PROPN
ejpam-6358	616	3	bably	bably	ADV
ejpam-6358	616	4	.	.	PUNCT
ejpam-6358	617	1	comparison	comparison	NOUN
ejpam-6358	617	2	between	between	ADP
ejpam-6358	617	3	rough	rough	ADJ
ejpam-6358	617	4	set	set	VERB
ejpam-6358	617	5	approximations	approximation	NOUN
ejpam-6358	617	6	based	base	VERB
ejpam-6358	617	7	on	on	ADP
ejpam-6358	617	8	different	different	ADJ
ejpam-6358	617	9	topologies	topology	NOUN
ejpam-6358	617	10	.	.	PUNCT
ejpam-6358	618	1	international	international	ADJ
ejpam-6358	618	2	journal	journal	NOUN
ejpam-6358	618	3	of	of	ADP
ejpam-6358	618	4	granular	granular	ADJ
ejpam-6358	618	5	computing	computing	NOUN
ejpam-6358	618	6	,	,	PUNCT
ejpam-6358	618	7	rough	rough	ADJ
ejpam-6358	618	8	sets	set	NOUN
ejpam-6358	618	9	and	and	CCONJ
ejpam-6358	618	10	intelligent	intelligent	ADJ
ejpam-6358	618	11	systems	system	NOUN
ejpam-6358	618	12	,	,	PUNCT
ejpam-6358	618	13	3(4):292–305	3(4):292–305	NUM
ejpam-6358	618	14	,	,	PUNCT
ejpam-6358	618	15	2014	2014	NUM
ejpam-6358	618	16	.	.	PUNCT
ejpam-6358	619	1	[	[	X
ejpam-6358	619	2	10	10	NUM
ejpam-6358	619	3	]	]	X
ejpam-6358	619	4	r.	r.	PROPN
ejpam-6358	619	5	a.	a.	PROPN
ejpam-6358	619	6	hosny	hosny	PROPN
ejpam-6358	619	7	,	,	PUNCT
ejpam-6358	619	8	r.	r.	PROPN
ejpam-6358	619	9	abu	abu	PROPN
ejpam-6358	619	10	-	-	PUNCT
ejpam-6358	619	11	gdairi	gdairi	PROPN
ejpam-6358	619	12	,	,	PUNCT
ejpam-6358	619	13	and	and	CCONJ
ejpam-6358	619	14	m.	m.	PROPN
ejpam-6358	619	15	k.	k.	PROPN
ejpam-6358	620	1	el	el	PROPN
ejpam-6358	620	2	-	-	PROPN
ejpam-6358	620	3	bably	bably	ADV
ejpam-6358	620	4	.	.	PUNCT
ejpam-6358	621	1	approximations	approximation	NOUN
ejpam-6358	621	2	by	by	ADP
ejpam-6358	621	3	ideal	ideal	ADJ
ejpam-6358	621	4	minir	minir	NOUN
ejpam-6358	621	5	.	.	PUNCT
ejpam-6358	622	1	a.	a.	PROPN
ejpam-6358	622	2	hosny	hosny	PROPN
ejpam-6358	622	3	et	et	PROPN
ejpam-6358	622	4	al	al	PROPN
ejpam-6358	622	5	.	.	PUNCT
ejpam-6358	622	6	/	/	SYM
ejpam-6358	622	7	eur	eur	PROPN
ejpam-6358	622	8	.	.	PUNCT
ejpam-6358	623	1	j.	j.	PROPN
ejpam-6358	623	2	pure	pure	PROPN
ejpam-6358	623	3	appl	appl	PROPN
ejpam-6358	623	4	.	.	PROPN
ejpam-6358	623	5	math	math	PROPN
ejpam-6358	623	6	,	,	PUNCT
ejpam-6358	623	7	18	18	NUM
ejpam-6358	623	8	(	(	PUNCT
ejpam-6358	623	9	4	4	NUM
ejpam-6358	623	10	)	)	PUNCT
ejpam-6358	623	11	(	(	PUNCT
ejpam-6358	623	12	2025	2025	NUM
ejpam-6358	623	13	)	)	PUNCT
ejpam-6358	623	14	,	,	PUNCT
ejpam-6358	623	15	6358	6358	NUM
ejpam-6358	623	16	22	22	NUM
ejpam-6358	623	17	of	of	ADP
ejpam-6358	623	18	24	24	NUM
ejpam-6358	623	19	mal	mal	ADJ
ejpam-6358	623	20	structure	structure	NOUN
ejpam-6358	623	21	with	with	ADP
ejpam-6358	623	22	chemical	chemical	ADJ
ejpam-6358	623	23	application	application	NOUN
ejpam-6358	623	24	.	.	PUNCT
ejpam-6358	624	1	intelligent	intelligent	ADJ
ejpam-6358	624	2	automation	automation	NOUN
ejpam-6358	624	3	&	&	CCONJ
ejpam-6358	624	4	soft	soft	ADJ
ejpam-6358	624	5	computing	computing	NOUN
ejpam-6358	624	6	,	,	PUNCT
ejpam-6358	624	7	36(3):3073–3085	36(3):3073–3085	NUM
ejpam-6358	624	8	,	,	PUNCT
ejpam-6358	624	9	2023	2023	NUM
ejpam-6358	624	10	.	.	PUNCT
ejpam-6358	625	1	[	[	X
ejpam-6358	625	2	11	11	NUM
ejpam-6358	625	3	]	]	X
ejpam-6358	625	4	r.	r.	PROPN
ejpam-6358	625	5	a.	a.	PROPN
ejpam-6358	625	6	hosny	hosny	PROPN
ejpam-6358	625	7	,	,	PUNCT
ejpam-6358	625	8	r.	r.	PROPN
ejpam-6358	625	9	abu	abu	PROPN
ejpam-6358	625	10	-	-	PUNCT
ejpam-6358	625	11	gdairi	gdairi	PROPN
ejpam-6358	625	12	,	,	PUNCT
ejpam-6358	625	13	and	and	CCONJ
ejpam-6358	625	14	m.	m.	PROPN
ejpam-6358	625	15	k.	k.	PROPN
ejpam-6358	626	1	el	el	PROPN
ejpam-6358	626	2	-	-	PROPN
ejpam-6358	626	3	bably	bably	ADV
ejpam-6358	626	4	.	.	PUNCT
ejpam-6358	627	1	enhancing	enhance	VERB
ejpam-6358	627	2	dengue	dengue	NOUN
ejpam-6358	627	3	fever	fever	NOUN
ejpam-6358	627	4	diagnosis	diagnosis	NOUN
ejpam-6358	627	5	with	with	ADP
ejpam-6358	627	6	generalized	generalized	ADJ
ejpam-6358	627	7	rough	rough	ADJ
ejpam-6358	627	8	sets	set	NOUN
ejpam-6358	627	9	:	:	PUNCT
ejpam-6358	627	10	utilizing	utilize	VERB
ejpam-6358	627	11	initial	initial	ADJ
ejpam-6358	627	12	-	-	PUNCT
ejpam-6358	627	13	neighborhoods	neighborhood	NOUN
ejpam-6358	627	14	and	and	CCONJ
ejpam-6358	627	15	ideals	ideal	NOUN
ejpam-6358	627	16	.	.	PUNCT
ejpam-6358	628	1	alexandria	alexandria	PROPN
ejpam-6358	628	2	engineering	engineering	PROPN
ejpam-6358	628	3	journal	journal	PROPN
ejpam-6358	628	4	,	,	PUNCT
ejpam-6358	628	5	94:68–79	94:68–79	ADV
ejpam-6358	628	6	,	,	PUNCT
ejpam-6358	628	7	2024	2024	NUM
ejpam-6358	628	8	.	.	PUNCT
ejpam-6358	629	1	[	[	X
ejpam-6358	629	2	12	12	NUM
ejpam-6358	629	3	]	]	PUNCT
ejpam-6358	629	4	t.	t.	PROPN
ejpam-6358	629	5	m.	m.	PROPN
ejpam-6358	629	6	al	al	PROPN
ejpam-6358	629	7	-	-	PUNCT
ejpam-6358	629	8	shami	shami	PROPN
ejpam-6358	629	9	,	,	PUNCT
ejpam-6358	629	10	w.	w.	PROPN
ejpam-6358	629	11	q.	q.	PROPN
ejpam-6358	629	12	fu	fu	PROPN
ejpam-6358	629	13	,	,	PUNCT
ejpam-6358	629	14	and	and	CCONJ
ejpam-6358	629	15	e.	e.	PROPN
ejpam-6358	629	16	a.	a.	PROPN
ejpam-6358	629	17	abo	abo	PROPN
ejpam-6358	629	18	-	-	PUNCT
ejpam-6358	629	19	tabl	tabl	NOUN
ejpam-6358	629	20	.	.	PUNCT
ejpam-6358	630	1	new	new	ADJ
ejpam-6358	630	2	rough	rough	ADJ
ejpam-6358	630	3	approximations	approximation	NOUN
ejpam-6358	630	4	based	base	VERB
ejpam-6358	630	5	on	on	ADP
ejpam-6358	630	6	e	e	NOUN
ejpam-6358	630	7	-	-	NOUN
ejpam-6358	630	8	neighborhoods	neighborhood	NOUN
ejpam-6358	630	9	.	.	PUNCT
ejpam-6358	631	1	complexity	complexity	NOUN
ejpam-6358	631	2	,	,	PUNCT
ejpam-6358	631	3	2021:6666853	2021:6666853	NUM
ejpam-6358	631	4	,	,	PUNCT
ejpam-6358	631	5	2021	2021	NUM
ejpam-6358	631	6	.	.	PUNCT
ejpam-6358	632	1	[	[	X
ejpam-6358	632	2	13	13	NUM
ejpam-6358	632	3	]	]	PUNCT
ejpam-6358	632	4	r.	r.	PROPN
ejpam-6358	632	5	a.	a.	PROPN
ejpam-6358	632	6	hosny	hosny	PROPN
ejpam-6358	632	7	,	,	PUNCT
ejpam-6358	632	8	b.	b.	PROPN
ejpam-6358	632	9	a.	a.	PROPN
ejpam-6358	632	10	asaad	asaad	PROPN
ejpam-6358	632	11	,	,	PUNCT
ejpam-6358	632	12	a.	a.	NOUN
ejpam-6358	632	13	a.	a.	PROPN
ejpam-6358	632	14	azzam	azzam	PROPN
ejpam-6358	632	15	,	,	PUNCT
ejpam-6358	632	16	and	and	CCONJ
ejpam-6358	632	17	t.	t.	PROPN
ejpam-6358	632	18	m.	m.	PROPN
ejpam-6358	632	19	al	al	PROPN
ejpam-6358	632	20	-	-	PUNCT
ejpam-6358	632	21	shami	shami	PROPN
ejpam-6358	632	22	.	.	PUNCT
ejpam-6358	633	1	various	various	ADJ
ejpam-6358	633	2	topologies	topology	NOUN
ejpam-6358	633	3	generated	generate	VERB
ejpam-6358	633	4	from	from	ADP
ejpam-6358	633	5	ej	ej	NOUN
ejpam-6358	633	6	-	-	PUNCT
ejpam-6358	633	7	neighbourhoods	neighbourhood	NOUN
ejpam-6358	633	8	via	via	ADP
ejpam-6358	633	9	ideals	ideal	NOUN
ejpam-6358	633	10	.	.	PUNCT
ejpam-6358	634	1	complexity	complexity	NOUN
ejpam-6358	634	2	,	,	PUNCT
ejpam-6358	634	3	2021:4149368	2021:4149368	NUM
ejpam-6358	634	4	,	,	PUNCT
ejpam-6358	634	5	2021	2021	NUM
ejpam-6358	634	6	.	.	PUNCT
ejpam-6358	635	1	[	[	X
ejpam-6358	635	2	14	14	NUM
ejpam-6358	635	3	]	]	PUNCT
ejpam-6358	635	4	m.	m.	NOUN
ejpam-6358	635	5	k.	k.	PROPN
ejpam-6358	636	1	el	el	PROPN
ejpam-6358	636	2	-	-	PROPN
ejpam-6358	636	3	bably	bably	PROPN
ejpam-6358	636	4	,	,	PUNCT
ejpam-6358	636	5	r.	r.	PROPN
ejpam-6358	636	6	a.	a.	PROPN
ejpam-6358	636	7	hosny	hosny	PROPN
ejpam-6358	636	8	,	,	PUNCT
ejpam-6358	636	9	and	and	CCONJ
ejpam-6358	636	10	m.	m.	PROPN
ejpam-6358	636	11	a.	a.	PROPN
ejpam-6358	636	12	el	el	PROPN
ejpam-6358	636	13	-	-	PROPN
ejpam-6358	636	14	gayar	gayar	NOUN
ejpam-6358	636	15	.	.	PUNCT
ejpam-6358	637	1	innovative	innovative	ADJ
ejpam-6358	637	2	rough	rough	ADJ
ejpam-6358	637	3	set	set	NOUN
ejpam-6358	637	4	approaches	approach	NOUN
ejpam-6358	637	5	using	use	VERB
ejpam-6358	637	6	novel	novel	ADJ
ejpam-6358	637	7	initial	initial	ADJ
ejpam-6358	637	8	-	-	PUNCT
ejpam-6358	637	9	neighborhood	neighborhood	NOUN
ejpam-6358	637	10	systems	system	NOUN
ejpam-6358	637	11	:	:	PUNCT
ejpam-6358	637	12	applications	application	NOUN
ejpam-6358	637	13	in	in	ADP
ejpam-6358	637	14	medical	medical	ADJ
ejpam-6358	637	15	diagnosis	diagnosis	NOUN
ejpam-6358	637	16	of	of	ADP
ejpam-6358	637	17	covid-19	covid-19	PROPN
ejpam-6358	637	18	variants	variant	NOUN
ejpam-6358	637	19	.	.	PUNCT
ejpam-6358	638	1	information	information	NOUN
ejpam-6358	638	2	sciences	sciences	PROPN
ejpam-6358	638	3	,	,	PUNCT
ejpam-6358	638	4	708:122044	708:122044	NUM
ejpam-6358	638	5	,	,	PUNCT
ejpam-6358	638	6	2025	2025	NUM
ejpam-6358	638	7	.	.	PUNCT
ejpam-6358	639	1	[	[	X
ejpam-6358	639	2	15	15	NUM
ejpam-6358	639	3	]	]	X
ejpam-6358	639	4	m.	m.	NOUN
ejpam-6358	639	5	el	el	PROPN
ejpam-6358	639	6	sayed	say	VERB
ejpam-6358	639	7	,	,	PUNCT
ejpam-6358	639	8	m.	m.	PROPN
ejpam-6358	639	9	k.	k.	PROPN
ejpam-6358	640	1	el	el	PROPN
ejpam-6358	640	2	-	-	PROPN
ejpam-6358	640	3	bably	bably	ADV
ejpam-6358	640	4	,	,	PUNCT
ejpam-6358	640	5	and	and	CCONJ
ejpam-6358	640	6	m.	m.	NOUN
ejpam-6358	640	7	a.	a.	PROPN
ejpam-6358	640	8	el	el	PROPN
ejpam-6358	640	9	safty	safty	PROPN
ejpam-6358	640	10	.	.	PUNCT
ejpam-6358	641	1	topological	topological	ADJ
ejpam-6358	641	2	approach	approach	NOUN
ejpam-6358	641	3	for	for	ADP
ejpam-6358	641	4	decisionmaking	decisionmake	VERB
ejpam-6358	641	5	of	of	ADP
ejpam-6358	641	6	covid-19	covid-19	PROPN
ejpam-6358	641	7	infection	infection	NOUN
ejpam-6358	641	8	via	via	ADP
ejpam-6358	641	9	a	a	DET
ejpam-6358	641	10	nano	nano	NOUN
ejpam-6358	641	11	-	-	PUNCT
ejpam-6358	641	12	topology	topology	NOUN
ejpam-6358	641	13	model	model	NOUN
ejpam-6358	641	14	.	.	PUNCT
ejpam-6358	642	1	aims	aim	VERB
ejpam-6358	642	2	mathematics	mathematic	NOUN
ejpam-6358	642	3	,	,	PUNCT
ejpam-6358	642	4	6(7):7872–7894	6(7):7872–7894	PROPN
ejpam-6358	642	5	,	,	PUNCT
ejpam-6358	642	6	2021	2021	NUM
ejpam-6358	642	7	.	.	PUNCT
ejpam-6358	643	1	[	[	X
ejpam-6358	643	2	16	16	NUM
ejpam-6358	643	3	]	]	PUNCT
ejpam-6358	643	4	a.	a.	NOUN
ejpam-6358	643	5	m.	m.	NOUN
ejpam-6358	643	6	kozae	kozae	PROPN
ejpam-6358	643	7	,	,	PUNCT
ejpam-6358	643	8	s.	s.	PROPN
ejpam-6358	643	9	a.	a.	PROPN
ejpam-6358	643	10	el	el	PROPN
ejpam-6358	643	11	-	-	PUNCT
ejpam-6358	643	12	sheikh	sheikh	NOUN
ejpam-6358	643	13	,	,	PUNCT
ejpam-6358	643	14	and	and	CCONJ
ejpam-6358	643	15	m.	m.	PROPN
ejpam-6358	643	16	hosny	hosny	PROPN
ejpam-6358	643	17	.	.	PUNCT
ejpam-6358	644	1	on	on	ADP
ejpam-6358	644	2	generalized	generalize	VERB
ejpam-6358	644	3	rough	rough	ADJ
ejpam-6358	644	4	sets	set	NOUN
ejpam-6358	644	5	and	and	CCONJ
ejpam-6358	644	6	closure	closure	NOUN
ejpam-6358	644	7	spaces	space	NOUN
ejpam-6358	644	8	.	.	PUNCT
ejpam-6358	645	1	international	international	ADJ
ejpam-6358	645	2	journal	journal	PROPN
ejpam-6358	645	3	of	of	ADP
ejpam-6358	645	4	applied	apply	VERB
ejpam-6358	645	5	mathematics	mathematic	NOUN
ejpam-6358	645	6	,	,	PUNCT
ejpam-6358	645	7	23:997–1023	23:997–1023	NUM
ejpam-6358	645	8	,	,	PUNCT
ejpam-6358	645	9	2010	2010	NUM
ejpam-6358	645	10	.	.	PUNCT
ejpam-6358	646	1	[	[	X
ejpam-6358	646	2	17	17	NUM
ejpam-6358	646	3	]	]	PUNCT
ejpam-6358	646	4	m.	m.	NOUN
ejpam-6358	646	5	atef	atef	PROPN
ejpam-6358	646	6	,	,	PUNCT
ejpam-6358	646	7	a.	a.	PROPN
ejpam-6358	646	8	m.	m.	PROPN
ejpam-6358	646	9	khalil	khalil	PROPN
ejpam-6358	646	10	,	,	PUNCT
ejpam-6358	646	11	s.-g	s.-g	PROPN
ejpam-6358	646	12	.	.	PUNCT
ejpam-6358	647	1	li	li	PROPN
ejpam-6358	647	2	,	,	PUNCT
ejpam-6358	647	3	a.	a.	PROPN
ejpam-6358	647	4	a.	a.	PROPN
ejpam-6358	647	5	azzam	azzam	PROPN
ejpam-6358	647	6	,	,	PUNCT
ejpam-6358	647	7	and	and	CCONJ
ejpam-6358	647	8	a.	a.	PROPN
ejpam-6358	647	9	a.	a.	PROPN
ejpam-6358	647	10	atik	atik	PROPN
ejpam-6358	647	11	.	.	PUNCT
ejpam-6358	648	1	comparison	comparison	NOUN
ejpam-6358	648	2	of	of	ADP
ejpam-6358	648	3	six	six	NUM
ejpam-6358	648	4	types	type	NOUN
ejpam-6358	648	5	of	of	ADP
ejpam-6358	648	6	rough	rough	ADJ
ejpam-6358	648	7	approximations	approximation	NOUN
ejpam-6358	648	8	based	base	VERB
ejpam-6358	648	9	on	on	ADP
ejpam-6358	648	10	j	j	PROPN
ejpam-6358	648	11	-	-	PUNCT
ejpam-6358	648	12	neighborhood	neighborhood	NOUN
ejpam-6358	648	13	space	space	NOUN
ejpam-6358	648	14	and	and	CCONJ
ejpam-6358	648	15	j	j	NOUN
ejpam-6358	648	16	-	-	PUNCT
ejpam-6358	648	17	adhesion	adhesion	NOUN
ejpam-6358	648	18	neighborhood	neighborhood	NOUN
ejpam-6358	648	19	space	space	NOUN
ejpam-6358	648	20	.	.	PUNCT
ejpam-6358	649	1	journal	journal	NOUN
ejpam-6358	649	2	of	of	ADP
ejpam-6358	649	3	intelligent	intelligent	ADJ
ejpam-6358	649	4	&	&	CCONJ
ejpam-6358	649	5	fuzzy	fuzzy	ADJ
ejpam-6358	649	6	systems	system	NOUN
ejpam-6358	649	7	,	,	PUNCT
ejpam-6358	649	8	39:4515–4531	39:4515–4531	NUM
ejpam-6358	649	9	,	,	PUNCT
ejpam-6358	649	10	2020	2020	NUM
ejpam-6358	649	11	.	.	PUNCT
ejpam-6358	650	1	[	[	X
ejpam-6358	650	2	18	18	NUM
ejpam-6358	650	3	]	]	PUNCT
ejpam-6358	650	4	m.	m.	NOUN
ejpam-6358	650	5	k.	k.	PROPN
ejpam-6358	651	1	el	el	PROPN
ejpam-6358	651	2	-	-	PROPN
ejpam-6358	651	3	bably	bably	ADV
ejpam-6358	651	4	,	,	PUNCT
ejpam-6358	651	5	t.	t.	PROPN
ejpam-6358	651	6	m.	m.	PROPN
ejpam-6358	651	7	al	al	PROPN
ejpam-6358	651	8	-	-	PUNCT
ejpam-6358	651	9	shami	shami	PROPN
ejpam-6358	651	10	,	,	PUNCT
ejpam-6358	651	11	a.	a.	PROPN
ejpam-6358	651	12	s.	s.	PROPN
ejpam-6358	651	13	nawar	nawar	PROPN
ejpam-6358	651	14	,	,	PUNCT
ejpam-6358	651	15	and	and	CCONJ
ejpam-6358	651	16	a.	a.	NOUN
ejpam-6358	651	17	mhemdi	mhemdi	PROPN
ejpam-6358	651	18	.	.	PUNCT
ejpam-6358	652	1	corrigendum	corrigendum	NOUN
ejpam-6358	652	2	to	to	PART
ejpam-6358	652	3	“	"	PUNCT
ejpam-6358	652	4	comparison	comparison	NOUN
ejpam-6358	652	5	of	of	ADP
ejpam-6358	652	6	six	six	NUM
ejpam-6358	652	7	types	type	NOUN
ejpam-6358	652	8	of	of	ADP
ejpam-6358	652	9	rough	rough	ADJ
ejpam-6358	652	10	approximations	approximation	NOUN
ejpam-6358	652	11	based	base	VERB
ejpam-6358	652	12	on	on	ADP
ejpam-6358	652	13	j	j	PROPN
ejpam-6358	652	14	-	-	PUNCT
ejpam-6358	652	15	neighborhood	neighborhood	NOUN
ejpam-6358	652	16	space	space	NOUN
ejpam-6358	652	17	and	and	CCONJ
ejpam-6358	652	18	j	j	NOUN
ejpam-6358	652	19	-	-	PUNCT
ejpam-6358	652	20	adhesion	adhesion	NOUN
ejpam-6358	652	21	neighborhood	neighborhood	NOUN
ejpam-6358	652	22	space	space	NOUN
ejpam-6358	652	23	”	"	PUNCT
ejpam-6358	652	24	.	.	PUNCT
ejpam-6358	653	1	journal	journal	PROPN
ejpam-6358	653	2	of	of	ADP
ejpam-6358	653	3	intelligent	intelligent	ADJ
ejpam-6358	653	4	&	&	CCONJ
ejpam-6358	653	5	fuzzy	fuzzy	ADJ
ejpam-6358	653	6	systems	system	NOUN
ejpam-6358	653	7	,	,	PUNCT
ejpam-6358	653	8	41:7353	41:7353	NUM
ejpam-6358	653	9	–	–	PUNCT
ejpam-6358	653	10	7361	7361	NUM
ejpam-6358	653	11	,	,	PUNCT
ejpam-6358	653	12	2021	2021	NUM
ejpam-6358	653	13	.	.	PUNCT
ejpam-6358	654	1	[	[	X
ejpam-6358	654	2	19	19	NUM
ejpam-6358	654	3	]	]	PUNCT
ejpam-6358	654	4	l.	l.	PROPN
ejpam-6358	654	5	ma	ma	PROPN
ejpam-6358	654	6	.	.	PROPN
ejpam-6358	655	1	on	on	ADP
ejpam-6358	655	2	some	some	DET
ejpam-6358	655	3	types	type	NOUN
ejpam-6358	655	4	of	of	ADP
ejpam-6358	655	5	neighborhood	neighborhood	NOUN
ejpam-6358	655	6	-	-	PUNCT
ejpam-6358	655	7	related	relate	VERB
ejpam-6358	655	8	covering	cover	VERB
ejpam-6358	655	9	rough	rough	ADJ
ejpam-6358	655	10	sets	set	NOUN
ejpam-6358	655	11	.	.	PUNCT
ejpam-6358	656	1	international	international	ADJ
ejpam-6358	656	2	journal	journal	PROPN
ejpam-6358	656	3	of	of	ADP
ejpam-6358	656	4	approximate	approximate	ADJ
ejpam-6358	656	5	reasoning	reasoning	NOUN
ejpam-6358	656	6	,	,	PUNCT
ejpam-6358	656	7	53:901–911	53:901–911	PROPN
ejpam-6358	656	8	,	,	PUNCT
ejpam-6358	656	9	2012	2012	NUM
ejpam-6358	656	10	.	.	PUNCT
ejpam-6358	657	1	[	[	X
ejpam-6358	657	2	20	20	NUM
ejpam-6358	657	3	]	]	PUNCT
ejpam-6358	657	4	a.	a.	PROPN
ejpam-6358	657	5	s.	s.	PROPN
ejpam-6358	657	6	nawar	nawar	PROPN
ejpam-6358	657	7	,	,	PUNCT
ejpam-6358	657	8	m.	m.	PROPN
ejpam-6358	657	9	k.	k.	PROPN
ejpam-6358	658	1	el	el	PROPN
ejpam-6358	658	2	-	-	PROPN
ejpam-6358	658	3	bably	bably	ADV
ejpam-6358	658	4	,	,	PUNCT
ejpam-6358	658	5	and	and	CCONJ
ejpam-6358	658	6	a.	a.	NOUN
ejpam-6358	658	7	a.	a.	PROPN
ejpam-6358	658	8	el	el	PROPN
ejpam-6358	658	9	atik	atik	PROPN
ejpam-6358	658	10	.	.	PUNCT
ejpam-6358	659	1	certain	certain	ADJ
ejpam-6358	659	2	types	type	NOUN
ejpam-6358	659	3	of	of	ADP
ejpam-6358	659	4	coverings	covering	NOUN
ejpam-6358	659	5	based	base	VERB
ejpam-6358	659	6	rough	rough	ADJ
ejpam-6358	659	7	sets	set	NOUN
ejpam-6358	659	8	with	with	ADP
ejpam-6358	659	9	application	application	NOUN
ejpam-6358	659	10	.	.	PUNCT
ejpam-6358	660	1	journal	journal	NOUN
ejpam-6358	660	2	of	of	ADP
ejpam-6358	660	3	intelligent	intelligent	ADJ
ejpam-6358	660	4	&	&	CCONJ
ejpam-6358	660	5	fuzzy	fuzzy	ADJ
ejpam-6358	660	6	systems	system	NOUN
ejpam-6358	660	7	,	,	PUNCT
ejpam-6358	660	8	39(3):3085–3098	39(3):3085–3098	NUM
ejpam-6358	660	9	,	,	PUNCT
ejpam-6358	660	10	2021	2021	NUM
ejpam-6358	660	11	.	.	PUNCT
ejpam-6358	661	1	[	[	X
ejpam-6358	661	2	21	21	NUM
ejpam-6358	661	3	]	]	PUNCT
ejpam-6358	661	4	m.	m.	PROPN
ejpam-6358	661	5	e.	e.	PROPN
ejpam-6358	661	6	abd	abd	PROPN
ejpam-6358	662	1	el	el	PROPN
ejpam-6358	662	2	-	-	PROPN
ejpam-6358	662	3	monsef	monsef	ADJ
ejpam-6358	662	4	,	,	PUNCT
ejpam-6358	662	5	a.	a.	NOUN
ejpam-6358	662	6	m.	m.	NOUN
ejpam-6358	662	7	kozae	kozae	PROPN
ejpam-6358	662	8	,	,	PUNCT
ejpam-6358	662	9	and	and	CCONJ
ejpam-6358	663	1	m.	m.	PROPN
ejpam-6358	663	2	k.	k.	PROPN
ejpam-6358	663	3	el	el	PROPN
ejpam-6358	663	4	-	-	PROPN
ejpam-6358	663	5	bably	bably	ADV
ejpam-6358	663	6	.	.	PUNCT
ejpam-6358	664	1	on	on	ADP
ejpam-6358	664	2	generalizing	generalize	VERB
ejpam-6358	664	3	covering	cover	VERB
ejpam-6358	664	4	approximation	approximation	NOUN
ejpam-6358	664	5	space	space	NOUN
ejpam-6358	664	6	.	.	PUNCT
ejpam-6358	665	1	journal	journal	NOUN
ejpam-6358	665	2	of	of	ADP
ejpam-6358	665	3	the	the	DET
ejpam-6358	665	4	egyptian	egyptian	PROPN
ejpam-6358	665	5	mathematical	mathematical	PROPN
ejpam-6358	665	6	society	society	NOUN
ejpam-6358	665	7	,	,	PUNCT
ejpam-6358	665	8	23(3):535–545	23(3):535–545	NOUN
ejpam-6358	665	9	,	,	PUNCT
ejpam-6358	665	10	2015	2015	NUM
ejpam-6358	665	11	.	.	PUNCT
ejpam-6358	666	1	[	[	X
ejpam-6358	666	2	22	22	NUM
ejpam-6358	666	3	]	]	PUNCT
ejpam-6358	666	4	h.	h.	PROPN
ejpam-6358	666	5	hung	hung	PROPN
ejpam-6358	666	6	.	.	PUNCT
ejpam-6358	667	1	symmetric	symmetric	PROPN
ejpam-6358	667	2	and	and	CCONJ
ejpam-6358	667	3	tufted	tufte	VERB
ejpam-6358	667	4	assignments	assignment	NOUN
ejpam-6358	667	5	of	of	ADP
ejpam-6358	667	6	neighborhoods	neighborhood	NOUN
ejpam-6358	667	7	and	and	CCONJ
ejpam-6358	667	8	metrization	metrization	NOUN
ejpam-6358	667	9	.	.	PUNCT
ejpam-6358	668	1	topological	topological	ADJ
ejpam-6358	668	2	applications	application	NOUN
ejpam-6358	668	3	,	,	PUNCT
ejpam-6358	668	4	155:2137–2142	155:2137–2142	NUM
ejpam-6358	668	5	,	,	PUNCT
ejpam-6358	668	6	2008	2008	NUM
ejpam-6358	668	7	.	.	PUNCT
ejpam-6358	669	1	[	[	X
ejpam-6358	669	2	23	23	NUM
ejpam-6358	669	3	]	]	PUNCT
ejpam-6358	669	4	z.	z.	PROPN
ejpam-6358	669	5	y.	y.	PROPN
ejpam-6358	669	6	xiaole	xiaole	PROPN
ejpam-6358	669	7	and	and	CCONJ
ejpam-6358	669	8	z.	z.	PROPN
ejpam-6358	669	9	yun	yun	PROPN
ejpam-6358	669	10	.	.	PUNCT
ejpam-6358	670	1	a	a	DET
ejpam-6358	670	2	study	study	NOUN
ejpam-6358	670	3	of	of	ADP
ejpam-6358	670	4	rough	rough	ADJ
ejpam-6358	670	5	sets	set	NOUN
ejpam-6358	670	6	based	base	VERB
ejpam-6358	670	7	on	on	ADP
ejpam-6358	670	8	1	1	NUM
ejpam-6358	670	9	-	-	PUNCT
ejpam-6358	670	10	neighborhood	neighborhood	NOUN
ejpam-6358	670	11	systems	system	NOUN
ejpam-6358	670	12	.	.	PUNCT
ejpam-6358	671	1	information	information	NOUN
ejpam-6358	671	2	sciences	sciences	PROPN
ejpam-6358	671	3	,	,	PUNCT
ejpam-6358	671	4	248:103–113	248:103–113	NUM
ejpam-6358	671	5	,	,	PUNCT
ejpam-6358	671	6	2013	2013	NUM
ejpam-6358	671	7	.	.	PUNCT
ejpam-6358	672	1	[	[	X
ejpam-6358	672	2	24	24	NUM
ejpam-6358	672	3	]	]	X
ejpam-6358	672	4	r.	r.	PROPN
ejpam-6358	672	5	mareay	mareay	PROPN
ejpam-6358	672	6	.	.	PUNCT
ejpam-6358	673	1	generalized	generalize	VERB
ejpam-6358	673	2	rough	rough	ADJ
ejpam-6358	673	3	sets	set	NOUN
ejpam-6358	673	4	based	base	VERB
ejpam-6358	673	5	on	on	ADP
ejpam-6358	673	6	neighborhood	neighborhood	NOUN
ejpam-6358	673	7	systems	system	NOUN
ejpam-6358	673	8	and	and	CCONJ
ejpam-6358	673	9	topological	topological	ADJ
ejpam-6358	673	10	spaces	space	NOUN
ejpam-6358	673	11	.	.	PUNCT
ejpam-6358	674	1	journal	journal	NOUN
ejpam-6358	674	2	of	of	ADP
ejpam-6358	674	3	the	the	DET
ejpam-6358	674	4	egyptian	egyptian	PROPN
ejpam-6358	674	5	mathematical	mathematical	PROPN
ejpam-6358	674	6	society	society	NOUN
ejpam-6358	674	7	,	,	PUNCT
ejpam-6358	674	8	24:603–608	24:603–608	PROPN
ejpam-6358	674	9	,	,	PUNCT
ejpam-6358	674	10	2016	2016	NUM
ejpam-6358	674	11	.	.	PUNCT
ejpam-6358	675	1	[	[	X
ejpam-6358	675	2	25	25	NUM
ejpam-6358	675	3	]	]	PUNCT
ejpam-6358	675	4	m.	m.	NOUN
ejpam-6358	675	5	k.	k.	PROPN
ejpam-6358	676	1	el	el	PROPN
ejpam-6358	676	2	-	-	PROPN
ejpam-6358	676	3	bably	bably	PROPN
ejpam-6358	676	4	and	and	CCONJ
ejpam-6358	676	5	t.	t.	PROPN
ejpam-6358	676	6	m.	m.	PROPN
ejpam-6358	676	7	al	al	PROPN
ejpam-6358	676	8	-	-	PUNCT
ejpam-6358	676	9	shami	shami	PROPN
ejpam-6358	676	10	.	.	PUNCT
ejpam-6358	677	1	different	different	ADJ
ejpam-6358	677	2	kinds	kind	NOUN
ejpam-6358	677	3	of	of	ADP
ejpam-6358	677	4	generalized	generalized	ADJ
ejpam-6358	677	5	rough	rough	ADJ
ejpam-6358	677	6	sets	set	NOUN
ejpam-6358	677	7	based	base	VERB
ejpam-6358	677	8	on	on	ADP
ejpam-6358	677	9	neighborhoods	neighborhood	NOUN
ejpam-6358	677	10	with	with	ADP
ejpam-6358	677	11	a	a	DET
ejpam-6358	677	12	medical	medical	ADJ
ejpam-6358	677	13	application	application	NOUN
ejpam-6358	677	14	.	.	PUNCT
ejpam-6358	678	1	international	international	ADJ
ejpam-6358	678	2	journal	journal	NOUN
ejpam-6358	678	3	of	of	ADP
ejpam-6358	678	4	biomathematics	biomathematic	NOUN
ejpam-6358	678	5	,	,	PUNCT
ejpam-6358	678	6	14(08):2150086	14(08):2150086	NUM
ejpam-6358	678	7	,	,	PUNCT
ejpam-6358	678	8	2021	2021	NUM
ejpam-6358	678	9	.	.	PUNCT
ejpam-6358	679	1	[	[	X
ejpam-6358	679	2	26	26	NUM
ejpam-6358	679	3	]	]	PUNCT
ejpam-6358	679	4	m.	m.	NOUN
ejpam-6358	679	5	abdelaziz	abdelaziz	PROPN
ejpam-6358	679	6	,	,	PUNCT
ejpam-6358	679	7	h.	h.	PROPN
ejpam-6358	679	8	m.	m.	PROPN
ejpam-6358	679	9	abu	abu	PROPN
ejpam-6358	679	10	-	-	PUNCT
ejpam-6358	679	11	donia	donia	PROPN
ejpam-6358	679	12	,	,	PUNCT
ejpam-6358	679	13	r.	r.	PROPN
ejpam-6358	679	14	a.	a.	PROPN
ejpam-6358	679	15	hosny	hosny	PROPN
ejpam-6358	679	16	,	,	PUNCT
ejpam-6358	679	17	s.	s.	PROPN
ejpam-6358	679	18	l.	l.	PROPN
ejpam-6358	679	19	hazae	hazae	PROPN
ejpam-6358	679	20	,	,	PUNCT
ejpam-6358	679	21	and	and	CCONJ
ejpam-6358	679	22	r.	r.	PROPN
ejpam-6358	679	23	a.	a.	PROPN
ejpam-6358	679	24	ibrahim	ibrahim	PROPN
ejpam-6358	679	25	.	.	PUNCT
ejpam-6358	679	26	improved	improve	VERB
ejpam-6358	679	27	evolutionary	evolutionary	ADJ
ejpam-6358	679	28	-	-	PUNCT
ejpam-6358	679	29	based	base	VERB
ejpam-6358	679	30	feature	feature	NOUN
ejpam-6358	679	31	selection	selection	NOUN
ejpam-6358	679	32	technique	technique	NOUN
ejpam-6358	679	33	using	use	VERB
ejpam-6358	679	34	extension	extension	NOUN
ejpam-6358	679	35	of	of	ADP
ejpam-6358	679	36	knowledge	knowledge	PROPN
ejpam-6358	679	37	r.	r.	PROPN
ejpam-6358	679	38	a.	a.	PROPN
ejpam-6358	679	39	hosny	hosny	PROPN
ejpam-6358	679	40	et	et	PROPN
ejpam-6358	679	41	al	al	PROPN
ejpam-6358	679	42	.	.	PUNCT
ejpam-6358	679	43	/	/	SYM
ejpam-6358	679	44	eur	eur	PROPN
ejpam-6358	679	45	.	.	PUNCT
ejpam-6358	680	1	j.	j.	PROPN
ejpam-6358	680	2	pure	pure	PROPN
ejpam-6358	680	3	appl	appl	PROPN
ejpam-6358	680	4	.	.	PROPN
ejpam-6358	680	5	math	math	PROPN
ejpam-6358	680	6	,	,	PUNCT
ejpam-6358	680	7	18	18	NUM
ejpam-6358	680	8	(	(	PUNCT
ejpam-6358	680	9	4	4	NUM
ejpam-6358	680	10	)	)	PUNCT
ejpam-6358	680	11	(	(	PUNCT
ejpam-6358	680	12	2025	2025	NUM
ejpam-6358	680	13	)	)	PUNCT
ejpam-6358	680	14	,	,	PUNCT
ejpam-6358	680	15	6358	6358	NUM
ejpam-6358	680	16	23	23	NUM
ejpam-6358	680	17	of	of	ADP
ejpam-6358	680	18	24	24	NUM
ejpam-6358	680	19	based	base	VERB
ejpam-6358	680	20	on	on	ADP
ejpam-6358	680	21	the	the	DET
ejpam-6358	680	22	rough	rough	ADJ
ejpam-6358	680	23	approximations	approximation	NOUN
ejpam-6358	680	24	.	.	PUNCT
ejpam-6358	681	1	information	information	NOUN
ejpam-6358	681	2	sciences	sciences	PROPN
ejpam-6358	681	3	,	,	PUNCT
ejpam-6358	681	4	594:76–94	594:76–94	NUM
ejpam-6358	681	5	,	,	PUNCT
ejpam-6358	681	6	2022	2022	NUM
ejpam-6358	681	7	.	.	PUNCT
ejpam-6358	682	1	[	[	X
ejpam-6358	682	2	27	27	NUM
ejpam-6358	682	3	]	]	PUNCT
ejpam-6358	682	4	keyu	keyu	PROPN
ejpam-6358	682	5	liu	liu	PROPN
ejpam-6358	682	6	,	,	PUNCT
ejpam-6358	682	7	tianrui	tianrui	PROPN
ejpam-6358	682	8	li	li	PROPN
ejpam-6358	682	9	,	,	PUNCT
ejpam-6358	682	10	xibei	xibei	PROPN
ejpam-6358	682	11	yang	yang	PROPN
ejpam-6358	682	12	,	,	PUNCT
ejpam-6358	682	13	xin	xin	PROPN
ejpam-6358	682	14	yang	yang	PROPN
ejpam-6358	682	15	,	,	PUNCT
ejpam-6358	682	16	dun	dun	PROPN
ejpam-6358	682	17	liu	liu	PROPN
ejpam-6358	682	18	,	,	PUNCT
ejpam-6358	682	19	pengfei	pengfei	PROPN
ejpam-6358	682	20	zhang	zhang	PROPN
ejpam-6358	682	21	,	,	PUNCT
ejpam-6358	682	22	and	and	CCONJ
ejpam-6358	682	23	jie	jie	PROPN
ejpam-6358	682	24	wang	wang	PROPN
ejpam-6358	682	25	.	.	PUNCT
ejpam-6358	682	26	granular	granular	ADJ
ejpam-6358	682	27	cabin	cabin	NOUN
ejpam-6358	682	28	:	:	PUNCT
ejpam-6358	682	29	an	an	DET
ejpam-6358	682	30	efficient	efficient	ADJ
ejpam-6358	682	31	solution	solution	NOUN
ejpam-6358	682	32	to	to	ADP
ejpam-6358	682	33	neighborhood	neighborhood	NOUN
ejpam-6358	682	34	learning	learning	NOUN
ejpam-6358	682	35	in	in	ADP
ejpam-6358	682	36	big	big	ADJ
ejpam-6358	682	37	data	datum	NOUN
ejpam-6358	682	38	.	.	PUNCT
ejpam-6358	683	1	information	information	NOUN
ejpam-6358	683	2	sciences	sciences	PROPN
ejpam-6358	683	3	,	,	PUNCT
ejpam-6358	683	4	583:189–201	583:189–201	NUM
ejpam-6358	683	5	,	,	PUNCT
ejpam-6358	683	6	2022	2022	NUM
ejpam-6358	683	7	.	.	PUNCT
ejpam-6358	684	1	[	[	X
ejpam-6358	684	2	28	28	NUM
ejpam-6358	684	3	]	]	PUNCT
ejpam-6358	684	4	j.	j.	PROPN
ejpam-6358	684	5	xiao	xiao	PROPN
ejpam-6358	684	6	,	,	PUNCT
ejpam-6358	684	7	q.	q.	PROPN
ejpam-6358	684	8	zhang	zhang	PROPN
ejpam-6358	684	9	,	,	PUNCT
ejpam-6358	684	10	z.	z.	PROPN
ejpam-6358	684	11	ai	ai	PROPN
ejpam-6358	684	12	,	,	PUNCT
ejpam-6358	684	13	and	and	CCONJ
ejpam-6358	684	14	g.	g.	PROPN
ejpam-6358	684	15	wang	wang	PROPN
ejpam-6358	684	16	.	.	PUNCT
ejpam-6358	685	1	a	a	DET
ejpam-6358	685	2	fast	fast	ADJ
ejpam-6358	685	3	neighborhood	neighborhood	NOUN
ejpam-6358	685	4	classifier	classifier	NOUN
ejpam-6358	685	5	based	base	VERB
ejpam-6358	685	6	on	on	ADP
ejpam-6358	685	7	hash	hash	NOUN
ejpam-6358	685	8	bucket	bucket	NOUN
ejpam-6358	685	9	with	with	ADP
ejpam-6358	685	10	application	application	NOUN
ejpam-6358	685	11	to	to	ADP
ejpam-6358	685	12	medical	medical	ADJ
ejpam-6358	685	13	diagnosis	diagnosis	NOUN
ejpam-6358	685	14	.	.	PUNCT
ejpam-6358	686	1	international	international	ADJ
ejpam-6358	686	2	journal	journal	PROPN
ejpam-6358	686	3	of	of	ADP
ejpam-6358	686	4	approximate	approximate	ADJ
ejpam-6358	686	5	reasoning	reasoning	NOUN
ejpam-6358	686	6	,	,	PUNCT
ejpam-6358	686	7	148:117–132	148:117–132	NUM
ejpam-6358	686	8	,	,	PUNCT
ejpam-6358	686	9	2022	2022	NUM
ejpam-6358	686	10	.	.	PUNCT
ejpam-6358	687	1	[	[	X
ejpam-6358	687	2	29	29	NUM
ejpam-6358	687	3	]	]	PUNCT
ejpam-6358	687	4	p.	p.	PROPN
ejpam-6358	687	5	zhang	zhang	PROPN
ejpam-6358	687	6	,	,	PUNCT
ejpam-6358	687	7	t.	t.	PROPN
ejpam-6358	687	8	li	li	PROPN
ejpam-6358	687	9	,	,	PUNCT
ejpam-6358	687	10	z.	z.	PROPN
ejpam-6358	687	11	yuan	yuan	PROPN
ejpam-6358	687	12	,	,	PUNCT
ejpam-6358	687	13	c.	c.	PROPN
ejpam-6358	687	14	luo	luo	PROPN
ejpam-6358	687	15	,	,	PUNCT
ejpam-6358	687	16	k.	k.	PROPN
ejpam-6358	687	17	liu	liu	PROPN
ejpam-6358	687	18	,	,	PUNCT
ejpam-6358	687	19	and	and	CCONJ
ejpam-6358	687	20	x.	x.	PROPN
ejpam-6358	687	21	yang	yang	PROPN
ejpam-6358	687	22	.	.	PROPN
ejpam-6358	687	23	heterogeneous	heterogeneous	ADJ
ejpam-6358	687	24	feature	feature	NOUN
ejpam-6358	687	25	selection	selection	NOUN
ejpam-6358	687	26	based	base	VERB
ejpam-6358	687	27	on	on	ADP
ejpam-6358	687	28	neighborhood	neighborhood	NOUN
ejpam-6358	687	29	combination	combination	NOUN
ejpam-6358	687	30	entropy	entropy	NOUN
ejpam-6358	687	31	.	.	PUNCT
ejpam-6358	688	1	ieee	ieee	NOUN
ejpam-6358	688	2	transactions	transaction	NOUN
ejpam-6358	688	3	on	on	ADP
ejpam-6358	688	4	neural	neural	ADJ
ejpam-6358	688	5	networks	network	NOUN
ejpam-6358	688	6	and	and	CCONJ
ejpam-6358	688	7	learning	learning	NOUN
ejpam-6358	688	8	systems	system	NOUN
ejpam-6358	688	9	,	,	PUNCT
ejpam-6358	688	10	35(3):3514–3527	35(3):3514–3527	NUM
ejpam-6358	688	11	,	,	PUNCT
ejpam-6358	688	12	2022	2022	NUM
ejpam-6358	688	13	.	.	PUNCT
ejpam-6358	689	1	[	[	X
ejpam-6358	689	2	30	30	NUM
ejpam-6358	689	3	]	]	PUNCT
ejpam-6358	689	4	p.	p.	PROPN
ejpam-6358	689	5	zhang	zhang	PROPN
ejpam-6358	689	6	,	,	PUNCT
ejpam-6358	689	7	d.	d.	PROPN
ejpam-6358	689	8	wang	wang	PROPN
ejpam-6358	689	9	,	,	PUNCT
ejpam-6358	689	10	z.	z.	PROPN
ejpam-6358	689	11	yu	yu	PROPN
ejpam-6358	689	12	,	,	PUNCT
ejpam-6358	689	13	y.	y.	PROPN
ejpam-6358	689	14	zhang	zhang	PROPN
ejpam-6358	689	15	,	,	PUNCT
ejpam-6358	689	16	t.	t.	PROPN
ejpam-6358	689	17	jiang	jiang	PROPN
ejpam-6358	689	18	,	,	PUNCT
ejpam-6358	689	19	and	and	CCONJ
ejpam-6358	689	20	t.	t.	PROPN
ejpam-6358	689	21	li	li	PROPN
ejpam-6358	689	22	.	.	PUNCT
ejpam-6358	690	1	a	a	DET
ejpam-6358	690	2	multi	multi	ADJ
ejpam-6358	690	3	-	-	ADJ
ejpam-6358	690	4	scale	scale	ADJ
ejpam-6358	690	5	information	information	NOUN
ejpam-6358	690	6	fusion	fusion	NOUN
ejpam-6358	690	7	-	-	PUNCT
ejpam-6358	690	8	based	base	VERB
ejpam-6358	690	9	multiple	multiple	ADJ
ejpam-6358	690	10	correlations	correlation	NOUN
ejpam-6358	690	11	for	for	ADP
ejpam-6358	690	12	unsupervised	unsupervised	ADJ
ejpam-6358	690	13	attribute	attribute	NOUN
ejpam-6358	690	14	selection	selection	NOUN
ejpam-6358	690	15	.	.	PUNCT
ejpam-6358	691	1	information	information	NOUN
ejpam-6358	691	2	fusion	fusion	NOUN
ejpam-6358	691	3	,	,	PUNCT
ejpam-6358	691	4	106:102276	106:102276	NUM
ejpam-6358	691	5	,	,	PUNCT
ejpam-6358	691	6	2024	2024	NUM
ejpam-6358	691	7	.	.	PUNCT
ejpam-6358	692	1	[	[	X
ejpam-6358	692	2	31	31	NUM
ejpam-6358	692	3	]	]	X
ejpam-6358	692	4	d.	d.	PROPN
ejpam-6358	692	5	wang	wang	PROPN
ejpam-6358	692	6	,	,	PUNCT
ejpam-6358	692	7	z.	z.	PROPN
ejpam-6358	692	8	li	li	PROPN
ejpam-6358	692	9	,	,	PUNCT
ejpam-6358	692	10	s.	s.	PROPN
ejpam-6358	692	11	yang	yang	PROPN
ejpam-6358	692	12	,	,	PUNCT
ejpam-6358	692	13	t.	t.	PROPN
ejpam-6358	692	14	ren	ren	PROPN
ejpam-6358	692	15	,	,	PUNCT
ejpam-6358	692	16	p.	p.	PROPN
ejpam-6358	692	17	zhang	zhang	PROPN
ejpam-6358	692	18	,	,	PUNCT
ejpam-6358	692	19	p.	p.	PROPN
ejpam-6358	692	20	deng	deng	PROPN
ejpam-6358	692	21	,	,	PUNCT
ejpam-6358	692	22	and	and	CCONJ
ejpam-6358	692	23	t.	t.	PROPN
ejpam-6358	692	24	li	li	PROPN
ejpam-6358	692	25	.	.	PUNCT
ejpam-6358	693	1	ndridc	ndridc	NOUN
ejpam-6358	693	2	:	:	PUNCT
ejpam-6358	693	3	nmfbased	nmfbased	ADJ
ejpam-6358	693	4	deep	deep	ADJ
ejpam-6358	693	5	representation	representation	NOUN
ejpam-6358	693	6	algorithm	algorithm	NOUN
ejpam-6358	693	7	for	for	ADP
ejpam-6358	693	8	incomplete	incomplete	ADJ
ejpam-6358	693	9	data	datum	NOUN
ejpam-6358	693	10	clustering	cluster	VERB
ejpam-6358	693	11	.	.	PUNCT
ejpam-6358	694	1	knowledge	knowledge	NOUN
ejpam-6358	694	2	-	-	PUNCT
ejpam-6358	694	3	based	base	VERB
ejpam-6358	694	4	systems	system	NOUN
ejpam-6358	694	5	,	,	PUNCT
ejpam-6358	694	6	324:113771	324:113771	NUM
ejpam-6358	694	7	,	,	PUNCT
ejpam-6358	694	8	2025	2025	NUM
ejpam-6358	694	9	.	.	PUNCT
ejpam-6358	695	1	[	[	X
ejpam-6358	695	2	32	32	NUM
ejpam-6358	695	3	]	]	PUNCT
ejpam-6358	695	4	d.	d.	PROPN
ejpam-6358	695	5	wang	wang	PROPN
ejpam-6358	695	6	,	,	PUNCT
ejpam-6358	695	7	t.	t.	PROPN
ejpam-6358	695	8	li	li	PROPN
ejpam-6358	695	9	,	,	PUNCT
ejpam-6358	695	10	p.	p.	PROPN
ejpam-6358	695	11	deng	deng	PROPN
ejpam-6358	695	12	,	,	PUNCT
ejpam-6358	695	13	j.	j.	PROPN
ejpam-6358	695	14	liu	liu	PROPN
ejpam-6358	695	15	,	,	PUNCT
ejpam-6358	695	16	w.	w.	PROPN
ejpam-6358	695	17	huang	huang	PROPN
ejpam-6358	695	18	,	,	PUNCT
ejpam-6358	695	19	and	and	CCONJ
ejpam-6358	695	20	f.	f.	PROPN
ejpam-6358	695	21	zhang	zhang	PROPN
ejpam-6358	695	22	.	.	PUNCT
ejpam-6358	696	1	a	a	DET
ejpam-6358	696	2	generalized	generalized	ADJ
ejpam-6358	696	3	deep	deep	ADJ
ejpam-6358	696	4	learning	learning	NOUN
ejpam-6358	696	5	algorithm	algorithm	NOUN
ejpam-6358	696	6	based	base	VERB
ejpam-6358	696	7	on	on	ADP
ejpam-6358	696	8	nmf	nmf	PROPN
ejpam-6358	696	9	for	for	ADP
ejpam-6358	696	10	multi	multi	ADJ
ejpam-6358	696	11	-	-	ADJ
ejpam-6358	696	12	view	view	ADJ
ejpam-6358	696	13	clustering	clustering	NOUN
ejpam-6358	696	14	.	.	PUNCT
ejpam-6358	697	1	ieee	ieee	NOUN
ejpam-6358	697	2	transactions	transaction	NOUN
ejpam-6358	697	3	on	on	ADP
ejpam-6358	697	4	big	big	ADJ
ejpam-6358	697	5	data	datum	NOUN
ejpam-6358	697	6	,	,	PUNCT
ejpam-6358	697	7	9(1):328–340	9(1):328–340	NUM
ejpam-6358	697	8	,	,	PUNCT
ejpam-6358	697	9	2023	2023	NUM
ejpam-6358	697	10	.	.	PUNCT
ejpam-6358	698	1	[	[	X
ejpam-6358	698	2	33	33	NUM
ejpam-6358	698	3	]	]	X
ejpam-6358	698	4	d.	d.	PROPN
ejpam-6358	698	5	i.	i.	PROPN
ejpam-6358	698	6	taher	taher	PROPN
ejpam-6358	698	7	,	,	PUNCT
ejpam-6358	698	8	r.	r.	PROPN
ejpam-6358	698	9	abu	abu	PROPN
ejpam-6358	698	10	-	-	PUNCT
ejpam-6358	698	11	gdairi	gdairi	PROPN
ejpam-6358	698	12	,	,	PUNCT
ejpam-6358	698	13	m.	m.	PROPN
ejpam-6358	698	14	k.	k.	PROPN
ejpam-6358	699	1	el	el	PROPN
ejpam-6358	699	2	-	-	PROPN
ejpam-6358	699	3	bably	bably	ADV
ejpam-6358	699	4	,	,	PUNCT
ejpam-6358	699	5	and	and	CCONJ
ejpam-6358	699	6	m.	m.	PROPN
ejpam-6358	699	7	a.	a.	PROPN
ejpam-6358	699	8	el	el	PROPN
ejpam-6358	699	9	-	-	PUNCT
ejpam-6358	699	10	gayar	gayar	NOUN
ejpam-6358	699	11	.	.	PUNCT
ejpam-6358	700	1	correction	correction	NOUN
ejpam-6358	700	2	:	:	PUNCT
ejpam-6358	700	3	decision	decision	NOUN
ejpam-6358	700	4	-	-	PUNCT
ejpam-6358	700	5	making	making	NOUN
ejpam-6358	700	6	in	in	ADP
ejpam-6358	700	7	diagnosing	diagnose	VERB
ejpam-6358	700	8	heart	heart	NOUN
ejpam-6358	700	9	failure	failure	NOUN
ejpam-6358	700	10	problems	problem	NOUN
ejpam-6358	700	11	using	use	VERB
ejpam-6358	700	12	basic	basic	ADJ
ejpam-6358	700	13	rough	rough	ADJ
ejpam-6358	700	14	sets	set	NOUN
ejpam-6358	700	15	.	.	PUNCT
ejpam-6358	701	1	aims	aim	VERB
ejpam-6358	701	2	mathematics	mathematic	NOUN
ejpam-6358	701	3	,	,	PUNCT
ejpam-6358	701	4	9(12):34270–34271	9(12):34270–34271	NUM
ejpam-6358	701	5	,	,	PUNCT
ejpam-6358	701	6	2024	2024	NUM
ejpam-6358	701	7	.	.	PUNCT
ejpam-6358	702	1	[	[	X
ejpam-6358	702	2	34	34	NUM
ejpam-6358	702	3	]	]	X
ejpam-6358	702	4	d.	d.	PROPN
ejpam-6358	702	5	i.	i.	PROPN
ejpam-6358	702	6	taher	taher	PROPN
ejpam-6358	702	7	,	,	PUNCT
ejpam-6358	702	8	r.	r.	PROPN
ejpam-6358	702	9	abu	abu	PROPN
ejpam-6358	702	10	-	-	PUNCT
ejpam-6358	702	11	gdairi	gdairi	PROPN
ejpam-6358	702	12	,	,	PUNCT
ejpam-6358	702	13	m.	m.	PROPN
ejpam-6358	702	14	k.	k.	PROPN
ejpam-6358	703	1	el	el	PROPN
ejpam-6358	703	2	-	-	PROPN
ejpam-6358	703	3	bably	bably	ADV
ejpam-6358	703	4	,	,	PUNCT
ejpam-6358	703	5	and	and	CCONJ
ejpam-6358	703	6	m.	m.	PROPN
ejpam-6358	703	7	a.	a.	PROPN
ejpam-6358	703	8	el	el	PROPN
ejpam-6358	703	9	-	-	PUNCT
ejpam-6358	703	10	gayar	gayar	NOUN
ejpam-6358	703	11	.	.	PUNCT
ejpam-6358	704	1	decision	decision	NOUN
ejpam-6358	704	2	-	-	PUNCT
ejpam-6358	704	3	making	making	NOUN
ejpam-6358	704	4	in	in	ADP
ejpam-6358	704	5	diagnosing	diagnose	VERB
ejpam-6358	704	6	heart	heart	NOUN
ejpam-6358	704	7	failure	failure	NOUN
ejpam-6358	704	8	problems	problem	NOUN
ejpam-6358	704	9	using	use	VERB
ejpam-6358	704	10	basic	basic	ADJ
ejpam-6358	704	11	rough	rough	ADJ
ejpam-6358	704	12	sets	set	NOUN
ejpam-6358	704	13	.	.	PUNCT
ejpam-6358	705	1	aims	aim	VERB
ejpam-6358	705	2	mathematics	mathematic	NOUN
ejpam-6358	705	3	,	,	PUNCT
ejpam-6358	705	4	9(8):21816–21847	9(8):21816–21847	PROPN
ejpam-6358	705	5	,	,	PUNCT
ejpam-6358	705	6	2024	2024	NUM
ejpam-6358	705	7	.	.	PUNCT
ejpam-6358	706	1	[	[	X
ejpam-6358	706	2	35	35	NUM
ejpam-6358	706	3	]	]	PUNCT
ejpam-6358	706	4	m.	m.	NOUN
ejpam-6358	706	5	k.	k.	PROPN
ejpam-6358	707	1	el	el	PROPN
ejpam-6358	707	2	-	-	PROPN
ejpam-6358	707	3	bably	bably	ADV
ejpam-6358	707	4	,	,	PUNCT
ejpam-6358	707	5	a.	a.	PROPN
ejpam-6358	707	6	s.	s.	PROPN
ejpam-6358	707	7	nawar	nawar	PROPN
ejpam-6358	707	8	,	,	PUNCT
ejpam-6358	707	9	m.	m.	NOUN
ejpam-6358	707	10	a.	a.	PROPN
ejpam-6358	707	11	el	el	PROPN
ejpam-6358	707	12	-	-	PROPN
ejpam-6358	707	13	gayar	gayar	NOUN
ejpam-6358	707	14	,	,	PUNCT
ejpam-6358	707	15	and	and	CCONJ
ejpam-6358	707	16	r.	r.	PROPN
ejpam-6358	707	17	a.	a.	PROPN
ejpam-6358	707	18	hosny	hosny	PROPN
ejpam-6358	707	19	.	.	PUNCT
ejpam-6358	708	1	theoretical	theoretical	ADJ
ejpam-6358	708	2	refinements	refinement	NOUN
ejpam-6358	708	3	and	and	CCONJ
ejpam-6358	708	4	practical	practical	ADJ
ejpam-6358	708	5	implications	implication	NOUN
ejpam-6358	708	6	of	of	ADP
ejpam-6358	708	7	θβ	θβ	NOUN
ejpam-6358	708	8	-	-	PUNCT
ejpam-6358	708	9	ideal	ideal	NOUN
ejpam-6358	708	10	rough	rough	ADJ
ejpam-6358	708	11	approximations	approximation	NOUN
ejpam-6358	708	12	.	.	PUNCT
ejpam-6358	709	1	annals	annal	NOUN
ejpam-6358	709	2	of	of	ADP
ejpam-6358	709	3	fuzzy	fuzzy	ADJ
ejpam-6358	709	4	mathematics	mathematic	NOUN
ejpam-6358	709	5	and	and	CCONJ
ejpam-6358	709	6	informatics	informatic	NOUN
ejpam-6358	709	7	,	,	PUNCT
ejpam-6358	709	8	30(2):113–131	30(2):113–131	PROPN
ejpam-6358	709	9	,	,	PUNCT
ejpam-6358	709	10	2025	2025	NUM
ejpam-6358	709	11	.	.	PUNCT
ejpam-6358	710	1	[	[	X
ejpam-6358	710	2	36	36	NUM
ejpam-6358	710	3	]	]	PUNCT
ejpam-6358	710	4	a.	a.	PROPN
ejpam-6358	710	5	s.	s.	PROPN
ejpam-6358	710	6	nawar	nawar	PROPN
ejpam-6358	710	7	,	,	PUNCT
ejpam-6358	710	8	m.	m.	NOUN
ejpam-6358	710	9	a.	a.	PROPN
ejpam-6358	710	10	el	el	PROPN
ejpam-6358	710	11	-	-	PUNCT
ejpam-6358	710	12	gayar	gayar	PROPN
ejpam-6358	710	13	,	,	PUNCT
ejpam-6358	710	14	m.	m.	NOUN
ejpam-6358	710	15	k.	k.	PROPN
ejpam-6358	711	1	el	el	PROPN
ejpam-6358	711	2	-	-	PROPN
ejpam-6358	711	3	bably	bably	ADV
ejpam-6358	711	4	,	,	PUNCT
ejpam-6358	711	5	and	and	CCONJ
ejpam-6358	711	6	r.	r.	PROPN
ejpam-6358	711	7	a.	a.	PROPN
ejpam-6358	711	8	hosny	hosny	PROPN
ejpam-6358	711	9	.	.	PUNCT
ejpam-6358	712	1	θβ	θβ	NOUN
ejpam-6358	712	2	-	-	PUNCT
ejpam-6358	712	3	ideal	ideal	NOUN
ejpam-6358	712	4	approximation	approximation	NOUN
ejpam-6358	712	5	spaces	space	NOUN
ejpam-6358	712	6	and	and	CCONJ
ejpam-6358	712	7	their	their	PRON
ejpam-6358	712	8	applications	application	NOUN
ejpam-6358	712	9	.	.	PUNCT
ejpam-6358	713	1	aims	aim	VERB
ejpam-6358	713	2	mathematics	mathematic	NOUN
ejpam-6358	713	3	,	,	PUNCT
ejpam-6358	713	4	7(2):2479–2497	7(2):2479–2497	NUM
ejpam-6358	713	5	,	,	PUNCT
ejpam-6358	713	6	2022	2022	NUM
ejpam-6358	713	7	.	.	PUNCT
ejpam-6358	714	1	[	[	X
ejpam-6358	714	2	37	37	NUM
ejpam-6358	714	3	]	]	X
ejpam-6358	714	4	r.	r.	PROPN
ejpam-6358	714	5	a.	a.	PROPN
ejpam-6358	714	6	hosny	hosny	PROPN
ejpam-6358	714	7	and	and	CCONJ
ejpam-6358	714	8	m.	m.	PROPN
ejpam-6358	714	9	k.	k.	PROPN
ejpam-6358	714	10	el	el	PROPN
ejpam-6358	714	11	-	-	PROPN
ejpam-6358	714	12	bably	bably	ADV
ejpam-6358	714	13	.	.	PUNCT
ejpam-6358	715	1	generating	generate	VERB
ejpam-6358	715	2	minimal	minimal	ADJ
ejpam-6358	715	3	topologies	topology	NOUN
ejpam-6358	715	4	from	from	ADP
ejpam-6358	715	5	κneighborhoods	κneighborhood	NOUN
ejpam-6358	715	6	and	and	CCONJ
ejpam-6358	715	7	primals	primal	NOUN
ejpam-6358	715	8	.	.	PUNCT
ejpam-6358	716	1	mathematical	mathematical	ADJ
ejpam-6358	716	2	system	system	NOUN
ejpam-6358	716	3	science	science	NOUN
ejpam-6358	716	4	,	,	PUNCT
ejpam-6358	716	5	3(1):19	3(1):19	NUM
ejpam-6358	716	6	pages	page	NOUN
ejpam-6358	716	7	,	,	PUNCT
ejpam-6358	716	8	2025	2025	NUM
ejpam-6358	716	9	.	.	PUNCT
ejpam-6358	717	1	[	[	X
ejpam-6358	717	2	38	38	NUM
ejpam-6358	717	3	]	]	PUNCT
ejpam-6358	717	4	r.	r.	PROPN
ejpam-6358	717	5	a.	a.	PROPN
ejpam-6358	717	6	hosny	hosny	PROPN
ejpam-6358	717	7	,	,	PUNCT
ejpam-6358	717	8	m.	m.	PROPN
ejpam-6358	717	9	k.	k.	PROPN
ejpam-6358	717	10	el	el	PROPN
ejpam-6358	717	11	-	-	PROPN
ejpam-6358	717	12	bably	bably	ADV
ejpam-6358	717	13	,	,	PUNCT
ejpam-6358	717	14	and	and	CCONJ
ejpam-6358	717	15	m.	m.	PROPN
ejpam-6358	717	16	a.	a.	PROPN
ejpam-6358	717	17	el	el	PROPN
ejpam-6358	717	18	-	-	PROPN
ejpam-6358	717	19	gayar	gayar	NOUN
ejpam-6358	717	20	.	.	PUNCT
ejpam-6358	718	1	primal	primal	ADJ
ejpam-6358	718	2	approximation	approximation	NOUN
ejpam-6358	718	3	spaces	space	NOUN
ejpam-6358	718	4	by	by	ADP
ejpam-6358	718	5	κ	κ	NOUN
ejpam-6358	718	6	-	-	PUNCT
ejpam-6358	718	7	neighborhoods	neighborhood	NOUN
ejpam-6358	718	8	with	with	ADP
ejpam-6358	718	9	applications	application	NOUN
ejpam-6358	718	10	.	.	PUNCT
ejpam-6358	719	1	european	european	ADJ
ejpam-6358	719	2	journal	journal	PROPN
ejpam-6358	719	3	of	of	ADP
ejpam-6358	719	4	pure	pure	ADJ
ejpam-6358	719	5	and	and	CCONJ
ejpam-6358	719	6	applied	applied	ADJ
ejpam-6358	719	7	mathematics	mathematic	NOUN
ejpam-6358	719	8	,	,	PUNCT
ejpam-6358	719	9	18(1):5827	18(1):5827	NUM
ejpam-6358	719	10	,	,	PUNCT
ejpam-6358	719	11	2025	2025	NUM
ejpam-6358	719	12	.	.	PUNCT
ejpam-6358	720	1	[	[	X
ejpam-6358	720	2	39	39	NUM
ejpam-6358	720	3	]	]	PUNCT
ejpam-6358	720	4	m.	m.	NOUN
ejpam-6358	720	5	k.	k.	PROPN
ejpam-6358	721	1	el	el	PROPN
ejpam-6358	721	2	-	-	PROPN
ejpam-6358	721	3	bably	bably	PROPN
ejpam-6358	721	4	,	,	PUNCT
ejpam-6358	721	5	r.	r.	PROPN
ejpam-6358	721	6	abu	abu	PROPN
ejpam-6358	721	7	-	-	PUNCT
ejpam-6358	721	8	gdairi	gdairi	PROPN
ejpam-6358	721	9	,	,	PUNCT
ejpam-6358	721	10	k.	k.	PROPN
ejpam-6358	721	11	k.	k.	PROPN
ejpam-6358	721	12	fleifel	fleifel	PROPN
ejpam-6358	721	13	,	,	PUNCT
ejpam-6358	721	14	and	and	CCONJ
ejpam-6358	721	15	m.	m.	NOUN
ejpam-6358	721	16	a.	a.	PROPN
ejpam-6358	721	17	el	el	PROPN
ejpam-6358	721	18	-	-	PROPN
ejpam-6358	721	19	gayar	gayar	NOUN
ejpam-6358	721	20	.	.	PUNCT
ejpam-6358	722	1	exploring	explore	VERB
ejpam-6358	722	2	β	β	NOUN
ejpam-6358	722	3	-	-	ADJ
ejpam-6358	722	4	basic	basic	ADJ
ejpam-6358	722	5	rough	rough	ADJ
ejpam-6358	722	6	sets	set	NOUN
ejpam-6358	722	7	and	and	CCONJ
ejpam-6358	722	8	their	their	PRON
ejpam-6358	722	9	applications	application	NOUN
ejpam-6358	722	10	in	in	ADP
ejpam-6358	722	11	medicine	medicine	NOUN
ejpam-6358	722	12	.	.	PUNCT
ejpam-6358	723	1	european	european	ADJ
ejpam-6358	723	2	journal	journal	PROPN
ejpam-6358	723	3	of	of	ADP
ejpam-6358	723	4	pure	pure	ADJ
ejpam-6358	723	5	and	and	CCONJ
ejpam-6358	723	6	applied	applied	ADJ
ejpam-6358	723	7	mathematics	mathematic	NOUN
ejpam-6358	723	8	,	,	PUNCT
ejpam-6358	723	9	17(4):3743–3771	17(4):3743–3771	NUM
ejpam-6358	723	10	,	,	PUNCT
ejpam-6358	723	11	2024	2024	NUM
ejpam-6358	723	12	.	.	PUNCT
ejpam-6358	724	1	[	[	X
ejpam-6358	724	2	40	40	NUM
ejpam-6358	724	3	]	]	PUNCT
ejpam-6358	724	4	t.	t.	PROPN
ejpam-6358	724	5	m.	m.	PROPN
ejpam-6358	724	6	al	al	PROPN
ejpam-6358	724	7	-	-	PUNCT
ejpam-6358	724	8	shami	shami	PROPN
ejpam-6358	724	9	and	and	CCONJ
ejpam-6358	724	10	m.	m.	PROPN
ejpam-6358	724	11	hosny	hosny	PROPN
ejpam-6358	724	12	.	.	PUNCT
ejpam-6358	725	1	generalized	generalized	ADJ
ejpam-6358	725	2	approximation	approximation	NOUN
ejpam-6358	725	3	spaces	space	NOUN
ejpam-6358	725	4	generation	generation	NOUN
ejpam-6358	725	5	from	from	ADP
ejpam-6358	725	6	ij	ij	NOUN
ejpam-6358	725	7	-	-	PUNCT
ejpam-6358	725	8	neighborhoods	neighborhood	NOUN
ejpam-6358	725	9	and	and	CCONJ
ejpam-6358	725	10	ideals	ideal	NOUN
ejpam-6358	725	11	with	with	ADP
ejpam-6358	725	12	application	application	NOUN
ejpam-6358	725	13	to	to	ADP
ejpam-6358	725	14	chikungunya	chikungunya	NOUN
ejpam-6358	725	15	disease	disease	NOUN
ejpam-6358	725	16	.	.	PUNCT
ejpam-6358	726	1	aims	aim	VERB
ejpam-6358	726	2	mathematics	mathematic	NOUN
ejpam-6358	726	3	,	,	PUNCT
ejpam-6358	726	4	9(4):10050–10077	9(4):10050–10077	NUM
ejpam-6358	726	5	,	,	PUNCT
ejpam-6358	726	6	2024	2024	NUM
ejpam-6358	726	7	.	.	PUNCT
ejpam-6358	727	1	[	[	X
ejpam-6358	727	2	41	41	NUM
ejpam-6358	727	3	]	]	PUNCT
ejpam-6358	727	4	k.	k.	PROPN
ejpam-6358	727	5	kuratowski	kuratowski	PROPN
ejpam-6358	727	6	.	.	PUNCT
ejpam-6358	728	1	topology	topology	NOUN
ejpam-6358	728	2	vol	vol	NOUN
ejpam-6358	728	3	.	.	PUNCT
ejpam-6358	728	4	i.	i.	PROPN
ejpam-6358	728	5	academic	academic	PROPN
ejpam-6358	728	6	press	press	PROPN
ejpam-6358	728	7	,	,	PUNCT
ejpam-6358	728	8	new	new	PROPN
ejpam-6358	728	9	york	york	PROPN
ejpam-6358	728	10	,	,	PUNCT
ejpam-6358	728	11	1966	1966	NUM
ejpam-6358	728	12	.	.	PUNCT
ejpam-6358	729	1	[	[	X
ejpam-6358	729	2	42	42	NUM
ejpam-6358	729	3	]	]	PUNCT
ejpam-6358	729	4	t.	t.	PROPN
ejpam-6358	729	5	m.	m.	PROPN
ejpam-6358	729	6	al	al	PROPN
ejpam-6358	729	7	-	-	PUNCT
ejpam-6358	729	8	shami	shami	PROPN
ejpam-6358	729	9	,	,	PUNCT
ejpam-6358	729	10	h.	h.	PROPN
ejpam-6358	729	11	işık	işık	PROPN
ejpam-6358	729	12	,	,	PUNCT
ejpam-6358	729	13	a.	a.	PROPN
ejpam-6358	729	14	s.	s.	PROPN
ejpam-6358	729	15	nawar	nawar	PROPN
ejpam-6358	729	16	,	,	PUNCT
ejpam-6358	729	17	and	and	CCONJ
ejpam-6358	729	18	r.	r.	PROPN
ejpam-6358	729	19	a.	a.	PROPN
ejpam-6358	729	20	hosny	hosny	PROPN
ejpam-6358	729	21	.	.	PUNCT
ejpam-6358	730	1	some	some	DET
ejpam-6358	730	2	topological	topological	ADJ
ejpam-6358	730	3	approaches	approach	NOUN
ejpam-6358	730	4	r.	r.	PROPN
ejpam-6358	730	5	a.	a.	PROPN
ejpam-6358	730	6	hosny	hosny	PROPN
ejpam-6358	730	7	et	et	PROPN
ejpam-6358	731	1	al	al	PROPN
ejpam-6358	731	2	.	.	PUNCT
ejpam-6358	731	3	/	/	SYM
ejpam-6358	731	4	eur	eur	PROPN
ejpam-6358	731	5	.	.	PUNCT
ejpam-6358	732	1	j.	j.	PROPN
ejpam-6358	732	2	pure	pure	PROPN
ejpam-6358	732	3	appl	appl	PROPN
ejpam-6358	732	4	.	.	PROPN
ejpam-6358	732	5	math	math	PROPN
ejpam-6358	732	6	,	,	PUNCT
ejpam-6358	732	7	18	18	NUM
ejpam-6358	732	8	(	(	PUNCT
ejpam-6358	732	9	4	4	NUM
ejpam-6358	732	10	)	)	PUNCT
ejpam-6358	732	11	(	(	PUNCT
ejpam-6358	732	12	2025	2025	NUM
ejpam-6358	732	13	)	)	PUNCT
ejpam-6358	732	14	,	,	PUNCT
ejpam-6358	732	15	6358	6358	NUM
ejpam-6358	732	16	24	24	NUM
ejpam-6358	732	17	of	of	ADP
ejpam-6358	732	18	24	24	NUM
ejpam-6358	732	19	for	for	ADP
ejpam-6358	732	20	generalized	generalize	VERB
ejpam-6358	732	21	rough	rough	ADJ
ejpam-6358	732	22	sets	set	NOUN
ejpam-6358	732	23	via	via	ADP
ejpam-6358	732	24	ideals	ideal	NOUN
ejpam-6358	732	25	.	.	PUNCT
ejpam-6358	733	1	mathematical	mathematical	ADJ
ejpam-6358	733	2	problems	problem	NOUN
ejpam-6358	733	3	in	in	ADP
ejpam-6358	733	4	engineering	engineering	NOUN
ejpam-6358	733	5	,	,	PUNCT
ejpam-6358	733	6	2021	2021	NUM
ejpam-6358	733	7	:	:	PUNCT
ejpam-6358	733	8	article	article	NOUN
ejpam-6358	733	9	i	i	PROPN
ejpam-6358	733	10	d	d	PROPN
ejpam-6358	733	11	5642982	5642982	NUM
ejpam-6358	733	12	,	,	PUNCT
ejpam-6358	733	13	11	11	NUM
ejpam-6358	733	14	pages	page	NOUN
ejpam-6358	733	15	,	,	PUNCT
ejpam-6358	733	16	2021	2021	NUM
ejpam-6358	733	17	.	.	PUNCT
ejpam-6358	734	1	[	[	X
ejpam-6358	734	2	43	43	NUM
ejpam-6358	734	3	]	]	X
ejpam-6358	734	4	r.	r.	PROPN
ejpam-6358	734	5	abu	abu	PROPN
ejpam-6358	734	6	-	-	PUNCT
ejpam-6358	734	7	gdairi	gdairi	PROPN
ejpam-6358	734	8	and	and	CCONJ
ejpam-6358	734	9	m.	m.	PROPN
ejpam-6358	734	10	k.	k.	PROPN
ejpam-6358	734	11	el	el	PROPN
ejpam-6358	734	12	-	-	PROPN
ejpam-6358	734	13	bably	bably	ADV
ejpam-6358	734	14	.	.	PUNCT
ejpam-6358	735	1	the	the	DET
ejpam-6358	735	2	accurate	accurate	ADJ
ejpam-6358	735	3	diagnosis	diagnosis	NOUN
ejpam-6358	735	4	for	for	ADP
ejpam-6358	735	5	covid-19	covid-19	PROPN
ejpam-6358	735	6	variants	variant	NOUN
ejpam-6358	735	7	using	use	VERB
ejpam-6358	735	8	nearly	nearly	ADV
ejpam-6358	735	9	initial	initial	ADJ
ejpam-6358	735	10	-	-	PUNCT
ejpam-6358	735	11	rough	rough	ADJ
ejpam-6358	735	12	sets	set	NOUN
ejpam-6358	735	13	.	.	PUNCT
ejpam-6358	736	1	heliyon	heliyon	NOUN
ejpam-6358	736	2	,	,	PUNCT
ejpam-6358	736	3	10(10):e31288	10(10):e31288	NUM
ejpam-6358	736	4	,	,	PUNCT
ejpam-6358	736	5	2024	2024	NUM
ejpam-6358	736	6	.	.	PUNCT
ejpam-6358	737	1	[	[	X
ejpam-6358	737	2	44	44	NUM
ejpam-6358	737	3	]	]	PUNCT
ejpam-6358	737	4	r.	r.	PROPN
ejpam-6358	737	5	abu	abu	PROPN
ejpam-6358	737	6	-	-	PUNCT
ejpam-6358	737	7	gdairi	gdairi	PROPN
ejpam-6358	737	8	,	,	PUNCT
ejpam-6358	737	9	a.	a.	NOUN
ejpam-6358	737	10	a.	a.	NOUN
ejpam-6358	737	11	nasef	nasef	PROPN
ejpam-6358	737	12	,	,	PUNCT
ejpam-6358	737	13	m.	m.	NOUN
ejpam-6358	737	14	a.	a.	PROPN
ejpam-6358	737	15	el	el	PROPN
ejpam-6358	737	16	-	-	PROPN
ejpam-6358	737	17	gayar	gayar	NOUN
ejpam-6358	737	18	,	,	PUNCT
ejpam-6358	737	19	and	and	CCONJ
ejpam-6358	737	20	m.	m.	PROPN
ejpam-6358	737	21	k.	k.	PROPN
ejpam-6358	738	1	el	el	PROPN
ejpam-6358	738	2	-	-	PROPN
ejpam-6358	738	3	bably	bably	ADV
ejpam-6358	738	4	.	.	PUNCT
ejpam-6358	739	1	on	on	ADP
ejpam-6358	739	2	fuzzy	fuzzy	ADJ
ejpam-6358	739	3	point	point	NOUN
ejpam-6358	739	4	applications	application	NOUN
ejpam-6358	739	5	of	of	ADP
ejpam-6358	739	6	fuzzy	fuzzy	ADJ
ejpam-6358	739	7	topological	topological	ADJ
ejpam-6358	739	8	spaces	space	NOUN
ejpam-6358	739	9	.	.	PUNCT
ejpam-6358	740	1	international	international	ADJ
ejpam-6358	740	2	journal	journal	NOUN
ejpam-6358	740	3	of	of	ADP
ejpam-6358	740	4	fuzzy	fuzzy	ADJ
ejpam-6358	740	5	logic	logic	NOUN
ejpam-6358	740	6	and	and	CCONJ
ejpam-6358	740	7	intelligent	intelligent	ADJ
ejpam-6358	740	8	systems	system	NOUN
ejpam-6358	740	9	,	,	PUNCT
ejpam-6358	740	10	23(2):162–172	23(2):162–172	PROPN
ejpam-6358	740	11	,	,	PUNCT
ejpam-6358	740	12	2023	2023	NUM
ejpam-6358	740	13	.	.	PUNCT
ejpam-6358	741	1	[	[	X
ejpam-6358	741	2	45	45	NUM
ejpam-6358	741	3	]	]	PUNCT
ejpam-6358	741	4	m.	m.	NOUN
ejpam-6358	741	5	a.	a.	PROPN
ejpam-6358	741	6	el	el	PROPN
ejpam-6358	741	7	-	-	PROPN
ejpam-6358	741	8	gayar	gayar	PROPN
ejpam-6358	741	9	and	and	CCONJ
ejpam-6358	741	10	r.	r.	PROPN
ejpam-6358	741	11	abu	abu	PROPN
ejpam-6358	741	12	-	-	PUNCT
ejpam-6358	741	13	gdairi	gdairi	PROPN
ejpam-6358	741	14	.	.	PUNCT
ejpam-6358	742	1	extension	extension	NOUN
ejpam-6358	742	2	of	of	ADP
ejpam-6358	742	3	topological	topological	ADJ
ejpam-6358	742	4	structures	structure	NOUN
ejpam-6358	742	5	using	use	VERB
ejpam-6358	742	6	lattices	lattice	NOUN
ejpam-6358	742	7	and	and	CCONJ
ejpam-6358	742	8	rough	rough	ADJ
ejpam-6358	742	9	sets	set	NOUN
ejpam-6358	742	10	.	.	PUNCT
ejpam-6358	743	1	aims	aim	VERB
ejpam-6358	743	2	mathematics	mathematic	NOUN
ejpam-6358	743	3	,	,	PUNCT
ejpam-6358	743	4	9(3):7552–7569	9(3):7552–7569	NUM
ejpam-6358	743	5	,	,	PUNCT
ejpam-6358	743	6	2024	2024	NUM
ejpam-6358	743	7	.	.	PUNCT
ejpam-6358	744	1	[	[	X
ejpam-6358	744	2	46	46	NUM
ejpam-6358	744	3	]	]	PUNCT
ejpam-6358	744	4	a.	a.	NOUN
ejpam-6358	744	5	a.	a.	NOUN
ejpam-6358	744	6	nasef	nasef	PROPN
ejpam-6358	744	7	,	,	PUNCT
ejpam-6358	744	8	m.	m.	PROPN
ejpam-6358	744	9	k.	k.	PROPN
ejpam-6358	745	1	el	el	PROPN
ejpam-6358	745	2	-	-	PROPN
ejpam-6358	745	3	bably	bably	ADV
ejpam-6358	745	4	,	,	PUNCT
ejpam-6358	745	5	and	and	CCONJ
ejpam-6358	745	6	m.	m.	PROPN
ejpam-6358	745	7	a.	a.	PROPN
ejpam-6358	745	8	el	el	PROPN
ejpam-6358	745	9	-	-	PROPN
ejpam-6358	745	10	gayar	gayar	NOUN
ejpam-6358	745	11	.	.	PUNCT
ejpam-6358	746	1	on	on	ADP
ejpam-6358	746	2	sc	sc	ADJ
ejpam-6358	746	3	-	-	ADJ
ejpam-6358	746	4	compact	compact	ADJ
ejpam-6358	746	5	spaces	space	NOUN
ejpam-6358	746	6	and	and	CCONJ
ejpam-6358	746	7	their	their	PRON
ejpam-6358	746	8	relations	relation	NOUN
ejpam-6358	746	9	to	to	AUX
ejpam-6358	746	10	semi	semi	ADJ
ejpam-6358	746	11	-	-	ADJ
ejpam-6358	746	12	compact	compact	ADJ
ejpam-6358	746	13	and	and	CCONJ
ejpam-6358	746	14	s	s	NOUN
ejpam-6358	746	15	-	-	PUNCT
ejpam-6358	746	16	closed	closed	ADJ
ejpam-6358	746	17	spaces	space	NOUN
ejpam-6358	746	18	.	.	PUNCT
ejpam-6358	747	1	advances	advance	NOUN
ejpam-6358	747	2	in	in	ADP
ejpam-6358	747	3	basic	basic	ADJ
ejpam-6358	747	4	and	and	CCONJ
ejpam-6358	747	5	applied	applied	ADJ
ejpam-6358	747	6	sciences	science	NOUN
ejpam-6358	747	7	,	,	PUNCT
ejpam-6358	747	8	5(1):29–37	5(1):29–37	NUM
ejpam-6358	747	9	,	,	PUNCT
ejpam-6358	747	10	2025	2025	NUM
ejpam-6358	747	11	.	.	PUNCT
ejpam-6358	748	1	[	[	X
ejpam-6358	748	2	47	47	NUM
ejpam-6358	748	3	]	]	X
ejpam-6358	748	4	r.	r.	PROPN
ejpam-6358	748	5	a.	a.	PROPN
ejpam-6358	748	6	hosny	hosny	PROPN
ejpam-6358	748	7	,	,	PUNCT
ejpam-6358	748	8	t.	t.	PROPN
ejpam-6358	748	9	m.	m.	PROPN
ejpam-6358	748	10	al	al	PROPN
ejpam-6358	748	11	-	-	PUNCT
ejpam-6358	748	12	shami	shami	PROPN
ejpam-6358	748	13	,	,	PUNCT
ejpam-6358	748	14	a.	a.	PROPN
ejpam-6358	748	15	a.	a.	NOUN
ejpam-6358	748	16	azzam	azzam	PROPN
ejpam-6358	748	17	,	,	PUNCT
ejpam-6358	748	18	and	and	CCONJ
ejpam-6358	748	19	a.	a.	PROPN
ejpam-6358	748	20	s.	s.	PROPN
ejpam-6358	748	21	nawar	nawar	PROPN
ejpam-6358	748	22	.	.	PUNCT
ejpam-6358	749	1	knowledge	knowledge	NOUN
ejpam-6358	749	2	based	base	VERB
ejpam-6358	749	3	on	on	ADP
ejpam-6358	749	4	rough	rough	ADJ
ejpam-6358	749	5	approximations	approximation	NOUN
ejpam-6358	749	6	and	and	CCONJ
ejpam-6358	749	7	ideals	ideal	NOUN
ejpam-6358	749	8	.	.	PUNCT
ejpam-6358	750	1	mathematical	mathematical	ADJ
ejpam-6358	750	2	problems	problem	NOUN
ejpam-6358	750	3	in	in	ADP
ejpam-6358	750	4	engineering	engineering	NOUN
ejpam-6358	750	5	,	,	PUNCT
ejpam-6358	750	6	2022	2022	NUM
ejpam-6358	750	7	:	:	PUNCT
ejpam-6358	750	8	article	article	NOUN
ejpam-6358	750	9	i	i	PROPN
ejpam-6358	750	10	d	d	PROPN
ejpam-6358	750	11	3766286	3766286	NUM
ejpam-6358	750	12	,	,	PUNCT
ejpam-6358	750	13	12	12	NUM
ejpam-6358	750	14	pages	page	NOUN
ejpam-6358	750	15	,	,	PUNCT
ejpam-6358	750	16	2022	2022	NUM
ejpam-6358	750	17	.	.	PUNCT
ejpam-6358	751	1	introduction	introduction	NOUN
ejpam-6358	751	2	preliminaries	preliminary	NOUN
ejpam-6358	751	3	main	main	ADJ
ejpam-6358	751	4	results	result	NOUN
ejpam-6358	751	5	conclusion	conclusion	NOUN
ejpam-6358	751	6	and	and	CCONJ
ejpam-6358	751	7	discussion	discussion	NOUN