id	sid	tid	token	lemma	pos
ejpam-6997	1	1	european	european	PROPN
ejpam-6997	1	2	journal	journal	PROPN
ejpam-6997	1	3	of	of	ADP
ejpam-6997	1	4	pure	pure	ADJ
ejpam-6997	1	5	and	and	CCONJ
ejpam-6997	1	6	applied	applied	ADJ
ejpam-6997	1	7	mathematics	mathematic	NOUN
ejpam-6997	1	8	2025	2025	NUM
ejpam-6997	1	9	,	,	PUNCT
ejpam-6997	1	10	vol	vol	NOUN
ejpam-6997	1	11	.	.	PROPN
ejpam-6997	1	12	18	18	NUM
ejpam-6997	1	13	,	,	PUNCT
ejpam-6997	1	14	issue	issue	NOUN
ejpam-6997	1	15	4	4	NUM
ejpam-6997	1	16	,	,	PUNCT
ejpam-6997	1	17	article	article	NOUN
ejpam-6997	1	18	number	number	NOUN
ejpam-6997	1	19	6997	6997	NUM
ejpam-6997	1	20	issn	issn	PROPN
ejpam-6997	1	21	1307	1307	NUM
ejpam-6997	1	22	-	-	SYM
ejpam-6997	1	23	5543	5543	NUM
ejpam-6997	1	24	–	–	PUNCT
ejpam-6997	1	25	ejpam.com	ejpam.com	X
ejpam-6997	1	26	published	publish	VERB
ejpam-6997	1	27	by	by	ADP
ejpam-6997	1	28	new	new	PROPN
ejpam-6997	1	29	york	york	PROPN
ejpam-6997	1	30	business	business	PROPN
ejpam-6997	1	31	global	global	ADJ
ejpam-6997	1	32	improving	improve	VERB
ejpam-6997	1	33	cardinality	cardinality	NOUN
ejpam-6997	1	34	rough	rough	ADJ
ejpam-6997	1	35	neighborhoods	neighborhood	NOUN
ejpam-6997	1	36	via	via	ADP
ejpam-6997	1	37	grills	grill	NOUN
ejpam-6997	1	38	and	and	CCONJ
ejpam-6997	1	39	their	their	PRON
ejpam-6997	1	40	applications	application	NOUN
ejpam-6997	1	41	a.	a.	NOUN
ejpam-6997	1	42	a.	a.	NOUN
ejpam-6997	1	43	azzam1,∗	azzam1,∗	PROPN
ejpam-6997	1	44	,	,	PUNCT
ejpam-6997	1	45	m.	m.	NOUN
ejpam-6997	1	46	aldawood1	aldawood1	PROPN
ejpam-6997	1	47	,	,	PUNCT
ejpam-6997	1	48	b.	b.	PROPN
ejpam-6997	2	1	alreshidi1	alreshidi1	PROPN
ejpam-6997	2	2	1	1	NUM
ejpam-6997	2	3	mathematics	mathematic	NOUN
ejpam-6997	2	4	department	department	NOUN
ejpam-6997	2	5	,	,	PUNCT
ejpam-6997	2	6	faculty	faculty	NOUN
ejpam-6997	2	7	of	of	ADP
ejpam-6997	2	8	science	science	NOUN
ejpam-6997	2	9	and	and	CCONJ
ejpam-6997	2	10	humanities	humanity	NOUN
ejpam-6997	2	11	,	,	PUNCT
ejpam-6997	2	12	prince	prince	PROPN
ejpam-6997	2	13	sattam	sattam	PROPN
ejpam-6997	2	14	bin	bin	PROPN
ejpam-6997	2	15	abdulaziz	abdulaziz	PROPN
ejpam-6997	2	16	university	university	PROPN
ejpam-6997	2	17	,	,	PUNCT
ejpam-6997	2	18	al	al	PROPN
ejpam-6997	2	19	-	-	PUNCT
ejpam-6997	2	20	kharj	kharj	PROPN
ejpam-6997	2	21	11942	11942	NUM
ejpam-6997	2	22	,	,	PUNCT
ejpam-6997	2	23	saudi	saudi	PROPN
ejpam-6997	2	24	arabia	arabia	PROPN
ejpam-6997	2	25	abstract	abstract	NOUN
ejpam-6997	2	26	.	.	PUNCT
ejpam-6997	3	1	in	in	ADP
ejpam-6997	3	2	order	order	NOUN
ejpam-6997	3	3	to	to	PART
ejpam-6997	3	4	solve	solve	VERB
ejpam-6997	3	5	problems	problem	NOUN
ejpam-6997	3	6	and	and	CCONJ
ejpam-6997	3	7	provide	provide	VERB
ejpam-6997	3	8	practical	practical	ADJ
ejpam-6997	3	9	solutions	solution	NOUN
ejpam-6997	3	10	,	,	PUNCT
ejpam-6997	3	11	researchers	researcher	NOUN
ejpam-6997	3	12	attempt	attempt	VERB
ejpam-6997	3	13	to	to	PART
ejpam-6997	3	14	accurately	accurately	ADV
ejpam-6997	3	15	describe	describe	VERB
ejpam-6997	3	16	societal	societal	ADJ
ejpam-6997	3	17	difficulties	difficulty	NOUN
ejpam-6997	3	18	and	and	CCONJ
ejpam-6997	3	19	obstacles	obstacle	NOUN
ejpam-6997	3	20	.	.	PUNCT
ejpam-6997	4	1	an	an	DET
ejpam-6997	4	2	efficient	efficient	ADJ
ejpam-6997	4	3	method	method	NOUN
ejpam-6997	4	4	for	for	ADP
ejpam-6997	4	5	handling	handle	VERB
ejpam-6997	4	6	complicated	complicated	ADJ
ejpam-6997	4	7	real	real	ADJ
ejpam-6997	4	8	-	-	PUNCT
ejpam-6997	4	9	world	world	NOUN
ejpam-6997	4	10	data	datum	NOUN
ejpam-6997	4	11	is	be	AUX
ejpam-6997	4	12	rough	rough	ADJ
ejpam-6997	4	13	set	set	NOUN
ejpam-6997	4	14	theory	theory	NOUN
ejpam-6997	4	15	.	.	PUNCT
ejpam-6997	5	1	the	the	DET
ejpam-6997	5	2	method	method	NOUN
ejpam-6997	5	3	finds	finds	AUX
ejpam-6997	5	4	confirmed	confirm	VERB
ejpam-6997	5	5	and	and	CCONJ
ejpam-6997	5	6	likely	likely	ADJ
ejpam-6997	5	7	data	datum	NOUN
ejpam-6997	5	8	from	from	ADP
ejpam-6997	5	9	subsets	subset	NOUN
ejpam-6997	5	10	using	use	VERB
ejpam-6997	5	11	rough	rough	ADJ
ejpam-6997	5	12	approximation	approximation	NOUN
ejpam-6997	5	13	operators	operator	NOUN
ejpam-6997	5	14	.	.	PUNCT
ejpam-6997	6	1	in	in	ADP
ejpam-6997	6	2	order	order	NOUN
ejpam-6997	6	3	to	to	PART
ejpam-6997	6	4	increase	increase	VERB
ejpam-6997	6	5	accuracy	accuracy	NOUN
ejpam-6997	6	6	while	while	SCONJ
ejpam-6997	6	7	following	follow	VERB
ejpam-6997	6	8	pawlak	pawlak	ADJ
ejpam-6997	6	9	’s	’s	PART
ejpam-6997	6	10	conventional	conventional	ADJ
ejpam-6997	6	11	approximation	approximation	NOUN
ejpam-6997	6	12	axioms	axiom	NOUN
ejpam-6997	6	13	,	,	PUNCT
ejpam-6997	6	14	earlier	early	ADJ
ejpam-6997	6	15	research	research	NOUN
ejpam-6997	6	16	has	have	AUX
ejpam-6997	6	17	created	create	VERB
ejpam-6997	6	18	rough	rough	ADJ
ejpam-6997	6	19	approximation	approximation	NOUN
ejpam-6997	6	20	models	model	NOUN
ejpam-6997	6	21	based	base	VERB
ejpam-6997	6	22	on	on	ADP
ejpam-6997	6	23	neighborhood	neighborhood	NOUN
ejpam-6997	6	24	systems	system	NOUN
ejpam-6997	6	25	.	.	PUNCT
ejpam-6997	7	1	based	base	VERB
ejpam-6997	7	2	on	on	ADP
ejpam-6997	7	3	cardinality	cardinality	PROPN
ejpam-6997	7	4	rough	rough	ADJ
ejpam-6997	7	5	neighborhoods	neighborhood	NOUN
ejpam-6997	7	6	and	and	CCONJ
ejpam-6997	7	7	grills	grill	NOUN
ejpam-6997	7	8	,	,	PUNCT
ejpam-6997	7	9	we	we	PRON
ejpam-6997	7	10	present	present	VERB
ejpam-6997	7	11	new	new	ADJ
ejpam-6997	7	12	rough	rough	ADJ
ejpam-6997	7	13	set	set	NOUN
ejpam-6997	7	14	notions	notion	NOUN
ejpam-6997	7	15	in	in	ADP
ejpam-6997	7	16	this	this	DET
ejpam-6997	7	17	study	study	NOUN
ejpam-6997	7	18	.	.	PUNCT
ejpam-6997	8	1	these	these	DET
ejpam-6997	8	2	models	model	NOUN
ejpam-6997	8	3	are	be	AUX
ejpam-6997	8	4	a	a	DET
ejpam-6997	8	5	suitable	suitable	ADJ
ejpam-6997	8	6	approach	approach	NOUN
ejpam-6997	8	7	for	for	ADP
ejpam-6997	8	8	a	a	DET
ejpam-6997	8	9	number	number	NOUN
ejpam-6997	8	10	of	of	ADP
ejpam-6997	8	11	scenarios	scenario	NOUN
ejpam-6997	8	12	,	,	PUNCT
ejpam-6997	8	13	including	include	VERB
ejpam-6997	8	14	computational	computational	ADJ
ejpam-6997	8	15	analysis	analysis	NOUN
ejpam-6997	8	16	,	,	PUNCT
ejpam-6997	8	17	comparisons	comparison	NOUN
ejpam-6997	8	18	on	on	ADP
ejpam-6997	8	19	medical	medical	ADJ
ejpam-6997	8	20	datasets	dataset	NOUN
ejpam-6997	8	21	,	,	PUNCT
ejpam-6997	8	22	real	real	ADJ
ejpam-6997	8	23	-	-	PUNCT
ejpam-6997	8	24	world	world	NOUN
ejpam-6997	8	25	data	datum	NOUN
ejpam-6997	8	26	analysis	analysis	NOUN
ejpam-6997	8	27	challenges	challenge	NOUN
ejpam-6997	8	28	,	,	PUNCT
ejpam-6997	8	29	and	and	CCONJ
ejpam-6997	8	30	classification	classification	NOUN
ejpam-6997	8	31	accuracy	accuracy	NOUN
ejpam-6997	8	32	metrics	metric	NOUN
ejpam-6997	8	33	.	.	PUNCT
ejpam-6997	9	1	we	we	PRON
ejpam-6997	9	2	thoroughly	thoroughly	ADV
ejpam-6997	9	3	examine	examine	VERB
ejpam-6997	9	4	the	the	DET
ejpam-6997	9	5	fundamental	fundamental	ADJ
ejpam-6997	9	6	components	component	NOUN
ejpam-6997	9	7	of	of	ADP
ejpam-6997	9	8	these	these	DET
ejpam-6997	9	9	ideas	idea	NOUN
ejpam-6997	9	10	and	and	CCONJ
ejpam-6997	9	11	clarify	clarify	VERB
ejpam-6997	9	12	how	how	SCONJ
ejpam-6997	9	13	they	they	PRON
ejpam-6997	9	14	relate	relate	VERB
ejpam-6997	9	15	to	to	ADP
ejpam-6997	9	16	each	each	DET
ejpam-6997	9	17	other	other	ADJ
ejpam-6997	9	18	and	and	CCONJ
ejpam-6997	9	19	to	to	ADP
ejpam-6997	9	20	earlier	early	ADV
ejpam-6997	9	21	paradigms	paradigms	PROPN
ejpam-6997	9	22	.	.	PUNCT
ejpam-6997	10	1	next	next	ADV
ejpam-6997	10	2	,	,	PUNCT
ejpam-6997	10	3	we	we	PRON
ejpam-6997	10	4	describe	describe	VERB
ejpam-6997	10	5	the	the	DET
ejpam-6997	10	6	boundary	boundary	ADJ
ejpam-6997	10	7	regions	region	NOUN
ejpam-6997	10	8	and	and	CCONJ
ejpam-6997	10	9	assess	assess	VERB
ejpam-6997	10	10	the	the	DET
ejpam-6997	10	11	accuracy	accuracy	NOUN
ejpam-6997	10	12	of	of	ADP
ejpam-6997	10	13	the	the	DET
ejpam-6997	10	14	data	datum	NOUN
ejpam-6997	10	15	using	use	VERB
ejpam-6997	10	16	a	a	DET
ejpam-6997	10	17	topological	topological	ADJ
ejpam-6997	10	18	technique	technique	NOUN
ejpam-6997	10	19	.	.	PUNCT
ejpam-6997	11	1	additionally	additionally	ADV
ejpam-6997	11	2	,	,	PUNCT
ejpam-6997	11	3	we	we	PRON
ejpam-6997	11	4	look	look	VERB
ejpam-6997	11	5	at	at	ADP
ejpam-6997	11	6	how	how	SCONJ
ejpam-6997	11	7	well	well	ADV
ejpam-6997	11	8	our	our	PRON
ejpam-6997	11	9	models	model	NOUN
ejpam-6997	11	10	handle	handle	VERB
ejpam-6997	11	11	heart	heart	NOUN
ejpam-6997	11	12	failure	failure	NOUN
ejpam-6997	11	13	disease	disease	NOUN
ejpam-6997	11	14	in	in	ADP
ejpam-6997	11	15	certain	certain	ADJ
ejpam-6997	11	16	individuals	individual	NOUN
ejpam-6997	11	17	and	and	CCONJ
ejpam-6997	11	18	come	come	VERB
ejpam-6997	11	19	to	to	ADP
ejpam-6997	11	20	the	the	DET
ejpam-6997	11	21	conclusion	conclusion	NOUN
ejpam-6997	11	22	that	that	SCONJ
ejpam-6997	11	23	the	the	DET
ejpam-6997	11	24	suggested	suggest	VERB
ejpam-6997	11	25	rough	rough	ADJ
ejpam-6997	11	26	set	set	NOUN
ejpam-6997	11	27	concepts	concept	NOUN
ejpam-6997	11	28	improve	improve	VERB
ejpam-6997	11	29	upon	upon	SCONJ
ejpam-6997	11	30	the	the	DET
ejpam-6997	11	31	characteristics	characteristic	NOUN
ejpam-6997	11	32	of	of	ADP
ejpam-6997	11	33	the	the	DET
ejpam-6997	11	34	earlier	early	ADJ
ejpam-6997	11	35	approach	approach	NOUN
ejpam-6997	11	36	spaces	space	VERB
ejpam-6997	11	37	.	.	PUNCT
ejpam-6997	12	1	finally	finally	ADV
ejpam-6997	12	2	,	,	PUNCT
ejpam-6997	12	3	we	we	PRON
ejpam-6997	12	4	identify	identify	VERB
ejpam-6997	12	5	the	the	DET
ejpam-6997	12	6	shortcomings	shortcoming	NOUN
ejpam-6997	12	7	of	of	ADP
ejpam-6997	12	8	the	the	DET
ejpam-6997	12	9	current	current	ADJ
ejpam-6997	12	10	concepts	concept	NOUN
ejpam-6997	12	11	and	and	CCONJ
ejpam-6997	12	12	show	show	VERB
ejpam-6997	12	13	their	their	PRON
ejpam-6997	12	14	advantages	advantage	NOUN
ejpam-6997	12	15	in	in	ADP
ejpam-6997	12	16	terms	term	NOUN
ejpam-6997	12	17	of	of	ADP
ejpam-6997	12	18	extending	extend	VERB
ejpam-6997	12	19	the	the	DET
ejpam-6997	12	20	verified	verified	ADJ
ejpam-6997	12	21	information	information	NOUN
ejpam-6997	12	22	gleaned	glean	VERB
ejpam-6997	12	23	from	from	ADP
ejpam-6997	12	24	subsets	subset	NOUN
ejpam-6997	12	25	of	of	ADP
ejpam-6997	12	26	data	datum	NOUN
ejpam-6997	12	27	while	while	SCONJ
ejpam-6997	12	28	preserving	preserve	VERB
ejpam-6997	12	29	the	the	DET
ejpam-6997	12	30	key	key	ADJ
ejpam-6997	12	31	elements	element	NOUN
ejpam-6997	12	32	of	of	ADP
ejpam-6997	12	33	pawlak	pawlak	ADJ
ejpam-6997	12	34	’s	’s	PART
ejpam-6997	12	35	original	original	ADJ
ejpam-6997	12	36	paradigms	paradigms	NOUN
ejpam-6997	12	37	that	that	PRON
ejpam-6997	12	38	were	be	AUX
ejpam-6997	12	39	destroyed	destroy	VERB
ejpam-6997	12	40	by	by	ADP
ejpam-6997	12	41	the	the	DET
ejpam-6997	12	42	models	model	NOUN
ejpam-6997	12	43	that	that	PRON
ejpam-6997	12	44	went	go	VERB
ejpam-6997	12	45	before	before	ADP
ejpam-6997	12	46	them	they	PRON
ejpam-6997	12	47	.	.	PUNCT
ejpam-6997	13	1	2020	2020	NUM
ejpam-6997	13	2	mathematics	mathematic	NOUN
ejpam-6997	13	3	subject	subject	NOUN
ejpam-6997	13	4	classifications	classification	NOUN
ejpam-6997	13	5	:	:	PUNCT
ejpam-6997	13	6	54d80	54d80	NUM
ejpam-6997	13	7	,	,	PUNCT
ejpam-6997	13	8	54c55	54c55	NUM
ejpam-6997	13	9	,	,	PUNCT
ejpam-6997	13	10	54a25	54a25	NUM
ejpam-6997	13	11	,	,	PUNCT
ejpam-6997	13	12	54a05	54a05	NUM
ejpam-6997	13	13	key	key	ADJ
ejpam-6997	13	14	words	word	NOUN
ejpam-6997	13	15	and	and	CCONJ
ejpam-6997	13	16	phrases	phrase	NOUN
ejpam-6997	13	17	:	:	PUNCT
ejpam-6997	13	18	lower	low	ADJ
ejpam-6997	13	19	/	/	SYM
ejpam-6997	13	20	upper	upper	ADJ
ejpam-6997	13	21	approximation	approximation	NOUN
ejpam-6997	13	22	,	,	PUNCT
ejpam-6997	13	23	grill	grill	NOUN
ejpam-6997	13	24	,	,	PUNCT
ejpam-6997	13	25	neighborhood	neighborhood	NOUN
ejpam-6997	13	26	,	,	PUNCT
ejpam-6997	13	27	rough	rough	ADJ
ejpam-6997	13	28	set	set	NOUN
ejpam-6997	13	29	1	1	NUM
ejpam-6997	13	30	.	.	PUNCT
ejpam-6997	14	1	introduction	introduction	NOUN
ejpam-6997	14	2	rough	rough	ADJ
ejpam-6997	14	3	sets	set	NOUN
ejpam-6997	14	4	theory	theory	NOUN
ejpam-6997	14	5	(	(	PUNCT
ejpam-6997	14	6	rsst	rsst	NOUN
ejpam-6997	14	7	)	)	PUNCT
ejpam-6997	14	8	applications	application	NOUN
ejpam-6997	14	9	to	to	PART
ejpam-6997	14	10	knowledge	knowledge	VERB
ejpam-6997	14	11	discovery	discovery	NOUN
ejpam-6997	14	12	entail	entail	NOUN
ejpam-6997	14	13	gathering	gather	VERB
ejpam-6997	14	14	actual	actual	ADJ
ejpam-6997	14	15	data	datum	NOUN
ejpam-6997	14	16	and	and	CCONJ
ejpam-6997	14	17	using	use	VERB
ejpam-6997	14	18	it	it	PRON
ejpam-6997	14	19	to	to	PART
ejpam-6997	14	20	create	create	VERB
ejpam-6997	14	21	classification	classification	NOUN
ejpam-6997	14	22	models	model	NOUN
ejpam-6997	14	23	according	accord	VERB
ejpam-6997	14	24	to	to	ADP
ejpam-6997	14	25	the	the	DET
ejpam-6997	14	26	data	datum	NOUN
ejpam-6997	14	27	[	[	X
ejpam-6997	14	28	1	1	NUM
ejpam-6997	14	29	,	,	PUNCT
ejpam-6997	14	30	2	2	NUM
ejpam-6997	14	31	]	]	PUNCT
ejpam-6997	14	32	.	.	PUNCT
ejpam-6997	15	1	each	each	PRON
ejpam-6997	15	2	subset	subset	VERB
ejpam-6997	15	3	in	in	ADP
ejpam-6997	15	4	this	this	DET
ejpam-6997	15	5	theory	theory	NOUN
ejpam-6997	15	6	corresponds	correspond	VERB
ejpam-6997	15	7	to	to	ADP
ejpam-6997	15	8	two	two	NUM
ejpam-6997	15	9	distinct	distinct	ADJ
ejpam-6997	15	10	sets	set	NOUN
ejpam-6997	15	11	that	that	PRON
ejpam-6997	15	12	are	be	AUX
ejpam-6997	15	13	derived	derive	VERB
ejpam-6997	15	14	from	from	ADP
ejpam-6997	15	15	an	an	DET
ejpam-6997	15	16	equivalence	equivalence	NOUN
ejpam-6997	15	17	relation	relation	NOUN
ejpam-6997	15	18	(	(	PUNCT
ejpam-6997	15	19	eqr	eqr	PROPN
ejpam-6997	15	20	)	)	PUNCT
ejpam-6997	15	21	and	and	CCONJ
ejpam-6997	15	22	are	be	AUX
ejpam-6997	15	23	referred	refer	VERB
ejpam-6997	15	24	to	to	ADP
ejpam-6997	15	25	as	as	ADP
ejpam-6997	15	26	the	the	DET
ejpam-6997	15	27	lower	low	ADJ
ejpam-6997	15	28	(	(	PUNCT
ejpam-6997	15	29	lw	lw	NOUN
ejpam-6997	15	30	)	)	PUNCT
ejpam-6997	15	31	and	and	CCONJ
ejpam-6997	15	32	upper	upper	ADJ
ejpam-6997	15	33	(	(	PUNCT
ejpam-6997	15	34	up	up	ADJ
ejpam-6997	15	35	)	)	PUNCT
ejpam-6997	15	36	approximations	approximation	NOUN
ejpam-6997	15	37	(	(	PUNCT
ejpam-6997	15	38	aps	ap	NOUN
ejpam-6997	15	39	)	)	PUNCT
ejpam-6997	15	40	.	.	PUNCT
ejpam-6997	16	1	many	many	ADJ
ejpam-6997	16	2	researchers	researcher	NOUN
ejpam-6997	16	3	have	have	AUX
ejpam-6997	16	4	substituted	substitute	VERB
ejpam-6997	16	5	different	different	ADJ
ejpam-6997	16	6	kinds	kind	NOUN
ejpam-6997	16	7	of	of	ADP
ejpam-6997	16	8	relations	relation	NOUN
ejpam-6997	16	9	for	for	ADP
ejpam-6997	16	10	the	the	DET
ejpam-6997	16	11	eqr	eqr	NOUN
ejpam-6997	16	12	in	in	ADP
ejpam-6997	16	13	order	order	NOUN
ejpam-6997	16	14	to	to	PART
ejpam-6997	16	15	expand	expand	VERB
ejpam-6997	16	16	the	the	DET
ejpam-6997	16	17	∗corresponding	∗corresponding	NOUN
ejpam-6997	16	18	author	author	NOUN
ejpam-6997	16	19	.	.	PUNCT
ejpam-6997	17	1	doi	doi	NOUN
ejpam-6997	17	2	:	:	PUNCT
ejpam-6997	17	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6997	https://doi.org/10.29020/nybg.ejpam.v18i4.6997	VERB
ejpam-6997	17	4	email	email	NOUN
ejpam-6997	17	5	addresses	address	NOUN
ejpam-6997	17	6	:	:	PUNCT
ejpam-6997	17	7	azzam0911@yahoo.com	azzam0911@yahoo.com	X
ejpam-6997	17	8	(	(	PUNCT
ejpam-6997	17	9	a.	a.	NOUN
ejpam-6997	17	10	a.	a.	PROPN
ejpam-6997	17	11	azzam	azzam	PROPN
ejpam-6997	17	12	)	)	PUNCT
ejpam-6997	17	13	,	,	PUNCT
ejpam-6997	17	14	m.aldawood@psau.edu.sa	m.aldawood@psau.edu.sa	PROPN
ejpam-6997	17	15	(	(	PUNCT
ejpam-6997	17	16	m.	m.	NOUN
ejpam-6997	17	17	aldawood	aldawood	PROPN
ejpam-6997	17	18	)	)	PUNCT
ejpam-6997	17	19	,	,	PUNCT
ejpam-6997	18	1	b.alreshidi@psau.edu.sa	b.alreshidi@psau.edu.sa	PROPN
ejpam-6997	18	2	(	(	PUNCT
ejpam-6997	18	3	b.	b.	PROPN
ejpam-6997	18	4	alreshidi	alreshidi	PROPN
ejpam-6997	18	5	)	)	PUNCT
ejpam-6997	18	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6997	19	1	1	1	NUM
ejpam-6997	19	2	copyright	copyright	NOUN
ejpam-6997	19	3	:	:	PUNCT
ejpam-6997	19	4	©	©	PROPN
ejpam-6997	19	5	2025	2025	NUM
ejpam-6997	19	6	the	the	DET
ejpam-6997	19	7	author(s	author(s	NOUN
ejpam-6997	19	8	)	)	PUNCT
ejpam-6997	19	9	.	.	PUNCT
ejpam-6997	20	1	(	(	PUNCT
ejpam-6997	20	2	cc	cc	NOUN
ejpam-6997	20	3	by	by	ADP
ejpam-6997	20	4	-	-	PUNCT
ejpam-6997	20	5	nc	nc	PROPN
ejpam-6997	20	6	4.0	4.0	NUM
ejpam-6997	20	7	)	)	PUNCT
ejpam-6997	20	8	a.	a.	NOUN
ejpam-6997	20	9	a.	a.	PROPN
ejpam-6997	20	10	azzam	azzam	PROPN
ejpam-6997	20	11	,	,	PUNCT
ejpam-6997	20	12	m.	m.	NOUN
ejpam-6997	20	13	aldawood	aldawood	PROPN
ejpam-6997	20	14	,	,	PUNCT
ejpam-6997	20	15	b.	b.	PROPN
ejpam-6997	20	16	alreshidi	alreshidi	PROPN
ejpam-6997	20	17	/	/	SYM
ejpam-6997	20	18	eur	eur	PROPN
ejpam-6997	20	19	.	.	PUNCT
ejpam-6997	21	1	j.	j.	PROPN
ejpam-6997	21	2	pure	pure	PROPN
ejpam-6997	21	3	appl	appl	PROPN
ejpam-6997	21	4	.	.	PROPN
ejpam-6997	21	5	math	math	PROPN
ejpam-6997	21	6	,	,	PUNCT
ejpam-6997	21	7	18	18	NUM
ejpam-6997	21	8	(	(	PUNCT
ejpam-6997	21	9	4	4	NUM
ejpam-6997	21	10	)	)	PUNCT
ejpam-6997	21	11	(	(	PUNCT
ejpam-6997	21	12	2025	2025	NUM
ejpam-6997	21	13	)	)	PUNCT
ejpam-6997	21	14	,	,	PUNCT
ejpam-6997	21	15	6997	6997	NUM
ejpam-6997	21	16	2	2	NUM
ejpam-6997	21	17	of	of	ADP
ejpam-6997	21	18	31	31	NUM
ejpam-6997	21	19	applications	application	NOUN
ejpam-6997	21	20	of	of	ADP
ejpam-6997	21	21	rsst	rsst	NOUN
ejpam-6997	21	22	[	[	X
ejpam-6997	21	23	3–11	3–11	NOUN
ejpam-6997	21	24	]	]	PUNCT
ejpam-6997	21	25	.	.	PUNCT
ejpam-6997	22	1	as	as	ADP
ejpam-6997	22	2	a	a	DET
ejpam-6997	22	3	result	result	NOUN
ejpam-6997	22	4	,	,	PUNCT
ejpam-6997	22	5	equivalence	equivalence	NOUN
ejpam-6997	22	6	classes	class	NOUN
ejpam-6997	22	7	were	be	AUX
ejpam-6997	22	8	replaced	replace	VERB
ejpam-6997	22	9	with	with	ADP
ejpam-6997	22	10	various	various	ADJ
ejpam-6997	22	11	neighborhood	neighborhood	NOUN
ejpam-6997	22	12	(	(	PUNCT
ejpam-6997	22	13	nbd	nbd	PROPN
ejpam-6997	22	14	)	)	PUNCT
ejpam-6997	22	15	representations	representation	NOUN
ejpam-6997	22	16	of	of	ADP
ejpam-6997	22	17	blocks	block	NOUN
ejpam-6997	22	18	or	or	CCONJ
ejpam-6997	22	19	granular	granular	ADJ
ejpam-6997	22	20	computing	computing	NOUN
ejpam-6997	22	21	to	to	PART
ejpam-6997	22	22	characterize	characterize	VERB
ejpam-6997	22	23	systems	system	NOUN
ejpam-6997	22	24	of	of	ADP
ejpam-6997	22	25	information	information	NOUN
ejpam-6997	22	26	.	.	PUNCT
ejpam-6997	23	1	these	these	DET
ejpam-6997	23	2	neighborhoods	neighborhood	NOUN
ejpam-6997	23	3	(	(	PUNCT
ejpam-6997	23	4	nbds	nbds	NOUN
ejpam-6997	23	5	)	)	PUNCT
ejpam-6997	23	6	include	include	VERB
ejpam-6997	23	7	union	union	NOUN
ejpam-6997	23	8	,	,	PUNCT
ejpam-6997	23	9	intersection	intersection	NOUN
ejpam-6997	23	10	,	,	PUNCT
ejpam-6997	23	11	and	and	CCONJ
ejpam-6997	23	12	right	right	ADJ
ejpam-6997	23	13	and	and	CCONJ
ejpam-6997	23	14	left	leave	VERB
ejpam-6997	23	15	nbds	nbds	NOUN
ejpam-6997	24	1	[	[	X
ejpam-6997	24	2	12–15	12–15	NUM
ejpam-6997	24	3	]	]	PUNCT
ejpam-6997	24	4	,	,	PUNCT
ejpam-6997	24	5	equal	equal	ADJ
ejpam-6997	24	6	nbds	nbds	NOUN
ejpam-6997	25	1	[	[	X
ejpam-6997	25	2	16	16	NUM
ejpam-6997	25	3	,	,	PUNCT
ejpam-6997	25	4	17	17	NUM
ejpam-6997	25	5	]	]	PUNCT
ejpam-6997	25	6	,	,	PUNCT
ejpam-6997	25	7	rough	rough	ADJ
ejpam-6997	25	8	nbd	nbd	PROPN
ejpam-6997	25	9	ideal	ideal	NOUN
ejpam-6997	26	1	[	[	X
ejpam-6997	26	2	18	18	NUM
ejpam-6997	26	3	]	]	PUNCT
ejpam-6997	26	4	.	.	PUNCT
ejpam-6997	27	1	the	the	DET
ejpam-6997	27	2	researchers	researcher	NOUN
ejpam-6997	27	3	demonstrated	demonstrate	VERB
ejpam-6997	27	4	their	their	PRON
ejpam-6997	27	5	usefulness	usefulness	NOUN
ejpam-6997	27	6	in	in	ADP
ejpam-6997	27	7	handling	handle	VERB
ejpam-6997	27	8	actual	actual	ADJ
ejpam-6997	27	9	situations	situation	NOUN
ejpam-6997	27	10	involving	involve	VERB
ejpam-6997	27	11	social	social	ADJ
ejpam-6997	27	12	difficulties	difficulty	NOUN
ejpam-6997	27	13	,	,	PUNCT
ejpam-6997	27	14	economics	economic	NOUN
ejpam-6997	27	15	,	,	PUNCT
ejpam-6997	27	16	and	and	CCONJ
ejpam-6997	27	17	medical	medical	ADJ
ejpam-6997	27	18	and	and	CCONJ
ejpam-6997	27	19	in	in	ADP
ejpam-6997	27	20	helping	help	VERB
ejpam-6997	27	21	decision	decision	NOUN
ejpam-6997	27	22	-	-	PUNCT
ejpam-6997	27	23	makers	maker	NOUN
ejpam-6997	27	24	make	make	VERB
ejpam-6997	27	25	wise	wise	ADJ
ejpam-6997	27	26	choices	choice	NOUN
ejpam-6997	27	27	.	.	PUNCT
ejpam-6997	28	1	in	in	ADP
ejpam-6997	28	2	other	other	ADJ
ejpam-6997	28	3	words	word	NOUN
ejpam-6997	28	4	,	,	PUNCT
ejpam-6997	28	5	they	they	PRON
ejpam-6997	28	6	provide	provide	VERB
ejpam-6997	28	7	a	a	DET
ejpam-6997	28	8	broad	broad	ADJ
ejpam-6997	28	9	framework	framework	NOUN
ejpam-6997	28	10	devoid	devoid	ADJ
ejpam-6997	28	11	of	of	ADP
ejpam-6997	28	12	limitations	limitation	NOUN
ejpam-6997	28	13	on	on	ADP
ejpam-6997	28	14	the	the	DET
ejpam-6997	28	15	kind	kind	NOUN
ejpam-6997	28	16	of	of	ADP
ejpam-6997	28	17	binary	binary	ADJ
ejpam-6997	28	18	relationships	relationship	NOUN
ejpam-6997	28	19	.	.	PUNCT
ejpam-6997	29	1	notably	notably	ADV
ejpam-6997	29	2	,	,	PUNCT
ejpam-6997	29	3	rsst	rsst	NOUN
ejpam-6997	29	4	has	have	AUX
ejpam-6997	29	5	demonstrated	demonstrate	VERB
ejpam-6997	29	6	its	its	PRON
ejpam-6997	29	7	usefulness	usefulness	NOUN
ejpam-6997	29	8	as	as	ADP
ejpam-6997	29	9	a	a	DET
ejpam-6997	29	10	crucial	crucial	ADJ
ejpam-6997	29	11	instrument	instrument	NOUN
ejpam-6997	29	12	for	for	ADP
ejpam-6997	29	13	characterizing	characterize	VERB
ejpam-6997	29	14	information	information	NOUN
ejpam-6997	29	15	content	content	NOUN
ejpam-6997	29	16	across	across	ADP
ejpam-6997	29	17	numerous	numerous	ADJ
ejpam-6997	29	18	frameworks	framework	NOUN
ejpam-6997	29	19	and	and	CCONJ
ejpam-6997	29	20	applications	application	NOUN
ejpam-6997	29	21	in	in	ADP
ejpam-6997	29	22	numerous	numerous	ADJ
ejpam-6997	29	23	fields	field	NOUN
ejpam-6997	29	24	[	[	X
ejpam-6997	29	25	19–26	19–26	NOUN
ejpam-6997	29	26	]	]	PUNCT
ejpam-6997	29	27	.	.	PUNCT
ejpam-6997	30	1	in	in	ADP
ejpam-6997	30	2	[	[	X
ejpam-6997	30	3	27	27	NUM
ejpam-6997	30	4	]	]	PUNCT
ejpam-6997	30	5	,	,	PUNCT
ejpam-6997	30	6	the	the	DET
ejpam-6997	30	7	topological	topological	ADJ
ejpam-6997	30	8	characteristics	characteristic	NOUN
ejpam-6997	30	9	of	of	ADP
ejpam-6997	30	10	rss	rss	NOUN
ejpam-6997	30	11	were	be	AUX
ejpam-6997	30	12	examined	examine	VERB
ejpam-6997	30	13	.	.	PUNCT
ejpam-6997	31	1	as	as	ADP
ejpam-6997	31	2	a	a	DET
ejpam-6997	31	3	result	result	NOUN
ejpam-6997	31	4	,	,	PUNCT
ejpam-6997	31	5	topological	topological	ADJ
ejpam-6997	31	6	and	and	CCONJ
ejpam-6997	31	7	rough	rough	ADJ
ejpam-6997	31	8	set	set	NOUN
ejpam-6997	31	9	(	(	PUNCT
ejpam-6997	31	10	rs	rs	NOUN
ejpam-6997	31	11	)	)	PUNCT
ejpam-6997	31	12	theories	theory	NOUN
ejpam-6997	31	13	were	be	AUX
ejpam-6997	31	14	combined	combine	VERB
ejpam-6997	31	15	,	,	PUNCT
ejpam-6997	31	16	and	and	CCONJ
ejpam-6997	31	17	this	this	PRON
ejpam-6997	31	18	became	become	VERB
ejpam-6997	31	19	the	the	DET
ejpam-6997	31	20	main	main	ADJ
ejpam-6997	31	21	topic	topic	NOUN
ejpam-6997	31	22	of	of	ADP
ejpam-6997	31	23	several	several	ADJ
ejpam-6997	31	24	works	work	NOUN
ejpam-6997	31	25	[	[	X
ejpam-6997	31	26	14	14	NUM
ejpam-6997	31	27	,	,	PUNCT
ejpam-6997	31	28	28–32	28–32	NUM
ejpam-6997	31	29	]	]	PUNCT
ejpam-6997	31	30	.	.	PUNCT
ejpam-6997	32	1	additionally	additionally	ADV
ejpam-6997	32	2	,	,	PUNCT
ejpam-6997	32	3	this	this	DET
ejpam-6997	32	4	relationship	relationship	NOUN
ejpam-6997	32	5	involved	involve	VERB
ejpam-6997	32	6	topological	topological	ADJ
ejpam-6997	32	7	generalizations	generalization	NOUN
ejpam-6997	32	8	,	,	PUNCT
ejpam-6997	32	9	including	include	VERB
ejpam-6997	32	10	minimal	minimal	ADJ
ejpam-6997	32	11	structures	structure	NOUN
ejpam-6997	32	12	[	[	X
ejpam-6997	32	13	33	33	NUM
ejpam-6997	32	14	]	]	PUNCT
ejpam-6997	32	15	,	,	PUNCT
ejpam-6997	32	16	supra	supra	ADJ
ejpam-6997	32	17	topology	topology	NOUN
ejpam-6997	33	1	[	[	X
ejpam-6997	33	2	34	34	NUM
ejpam-6997	33	3	]	]	PUNCT
ejpam-6997	33	4	,	,	PUNCT
ejpam-6997	33	5	infra	infra	NOUN
ejpam-6997	33	6	topology	topology	NOUN
ejpam-6997	34	1	[	[	X
ejpam-6997	34	2	35	35	NUM
ejpam-6997	34	3	]	]	PUNCT
ejpam-6997	34	4	,	,	PUNCT
ejpam-6997	34	5	nano	nano	NOUN
ejpam-6997	34	6	-	-	PUNCT
ejpam-6997	34	7	topology	topology	NOUN
ejpam-6997	34	8	[	[	X
ejpam-6997	34	9	36	36	NUM
ejpam-6997	34	10	]	]	PUNCT
ejpam-6997	34	11	,	,	PUNCT
ejpam-6997	34	12	and	and	CCONJ
ejpam-6997	34	13	bitopology	bitopology	NOUN
ejpam-6997	35	1	[	[	X
ejpam-6997	35	2	37	37	NUM
ejpam-6997	35	3	]	]	PUNCT
ejpam-6997	35	4	.	.	PUNCT
ejpam-6997	36	1	we	we	PRON
ejpam-6997	36	2	direct	direct	VERB
ejpam-6997	36	3	readers	reader	NOUN
ejpam-6997	36	4	to	to	ADP
ejpam-6997	36	5	[	[	X
ejpam-6997	36	6	38	38	NUM
ejpam-6997	36	7	,	,	PUNCT
ejpam-6997	36	8	39	39	NUM
ejpam-6997	36	9	]	]	PUNCT
ejpam-6997	36	10	for	for	ADP
ejpam-6997	36	11	a	a	DET
ejpam-6997	36	12	comprehensive	comprehensive	ADJ
ejpam-6997	36	13	summary	summary	NOUN
ejpam-6997	36	14	of	of	ADP
ejpam-6997	36	15	the	the	DET
ejpam-6997	36	16	works	work	NOUN
ejpam-6997	36	17	examining	examine	VERB
ejpam-6997	36	18	the	the	DET
ejpam-6997	36	19	connections	connection	NOUN
ejpam-6997	36	20	between	between	ADP
ejpam-6997	36	21	rsst	rsst	NOUN
ejpam-6997	36	22	and	and	CCONJ
ejpam-6997	36	23	topology	topology	NOUN
ejpam-6997	36	24	.	.	PUNCT
ejpam-6997	37	1	the	the	DET
ejpam-6997	37	2	symmetry	symmetry	NOUN
ejpam-6997	37	3	between	between	ADP
ejpam-6997	37	4	closure	closure	NOUN
ejpam-6997	37	5	and	and	CCONJ
ejpam-6997	37	6	interior	interior	ADJ
ejpam-6997	37	7	topological	topological	ADJ
ejpam-6997	37	8	operators	operator	NOUN
ejpam-6997	37	9	with	with	ADP
ejpam-6997	37	10	lw	lw	PROPN
ejpam-6997	37	11	and	and	CCONJ
ejpam-6997	37	12	up	up	ADP
ejpam-6997	37	13	-	-	PUNCT
ejpam-6997	37	14	aps	ap	NOUN
ejpam-6997	37	15	,	,	PUNCT
ejpam-6997	37	16	as	as	ADV
ejpam-6997	37	17	well	well	ADV
ejpam-6997	37	18	,	,	PUNCT
ejpam-6997	37	19	allows	allow	VERB
ejpam-6997	37	20	us	we	PRON
ejpam-6997	37	21	to	to	PART
ejpam-6997	37	22	give	give	VERB
ejpam-6997	37	23	abstract	abstract	ADJ
ejpam-6997	37	24	conceptions	conception	NOUN
ejpam-6997	37	25	meaningful	meaningful	ADJ
ejpam-6997	37	26	meanings	meaning	NOUN
ejpam-6997	37	27	and	and	CCONJ
ejpam-6997	37	28	employ	employ	VERB
ejpam-6997	37	29	abstract	abstract	ADJ
ejpam-6997	37	30	methods	method	NOUN
ejpam-6997	37	31	to	to	PART
ejpam-6997	37	32	convey	convey	VERB
ejpam-6997	37	33	knowledge	knowledge	NOUN
ejpam-6997	37	34	extracted	extract	VERB
ejpam-6997	37	35	from	from	ADP
ejpam-6997	37	36	systems	system	NOUN
ejpam-6997	37	37	of	of	ADP
ejpam-6997	37	38	data	datum	NOUN
ejpam-6997	37	39	.	.	PUNCT
ejpam-6997	38	1	the	the	DET
ejpam-6997	38	2	concept	concept	NOUN
ejpam-6997	38	3	of	of	ADP
ejpam-6997	38	4	two	two	NUM
ejpam-6997	38	5	operators	operator	NOUN
ejpam-6997	38	6	,	,	PUNCT
ejpam-6997	38	7	ξ	ξ	PROPN
ejpam-6997	38	8	and	and	CCONJ
ejpam-6997	38	9	ζ	ζ	NOUN
ejpam-6997	38	10	,	,	PUNCT
ejpam-6997	38	11	is	be	AUX
ejpam-6997	38	12	the	the	DET
ejpam-6997	38	13	foundation	foundation	NOUN
ejpam-6997	38	14	of	of	ADP
ejpam-6997	38	15	grill	grill	ADJ
ejpam-6997	38	16	topological	topological	ADJ
ejpam-6997	38	17	spaces	space	NOUN
ejpam-6997	38	18	.	.	PUNCT
ejpam-6997	39	1	choquet	choquet	PROPN
ejpam-6997	39	2	was	be	AUX
ejpam-6997	39	3	the	the	DET
ejpam-6997	39	4	first	first	ADJ
ejpam-6997	39	5	to	to	PART
ejpam-6997	39	6	propose	propose	VERB
ejpam-6997	39	7	this	this	DET
ejpam-6997	39	8	concept	concept	NOUN
ejpam-6997	39	9	[	[	X
ejpam-6997	39	10	40	40	NUM
ejpam-6997	39	11	]	]	PUNCT
ejpam-6997	39	12	.	.	PUNCT
ejpam-6997	40	1	some	some	DET
ejpam-6997	40	2	similarities	similarity	NOUN
ejpam-6997	40	3	between	between	ADP
ejpam-6997	40	4	the	the	DET
ejpam-6997	40	5	choquat	choquat	ADJ
ejpam-6997	40	6	notion	notion	NOUN
ejpam-6997	40	7	and	and	CCONJ
ejpam-6997	40	8	ideals	ideal	NOUN
ejpam-6997	40	9	,	,	PUNCT
ejpam-6997	40	10	nets	net	NOUN
ejpam-6997	40	11	,	,	PUNCT
ejpam-6997	40	12	and	and	CCONJ
ejpam-6997	40	13	filters	filter	NOUN
ejpam-6997	40	14	have	have	AUX
ejpam-6997	40	15	been	be	AUX
ejpam-6997	40	16	found	find	VERB
ejpam-6997	40	17	.	.	PUNCT
ejpam-6997	41	1	[	[	X
ejpam-6997	41	2	41	41	NUM
ejpam-6997	41	3	]	]	PUNCT
ejpam-6997	41	4	and	and	CCONJ
ejpam-6997	41	5	[	[	X
ejpam-6997	41	6	18	18	NUM
ejpam-6997	41	7	]	]	PUNCT
ejpam-6997	41	8	have	have	AUX
ejpam-6997	41	9	addressed	address	VERB
ejpam-6997	41	10	a	a	DET
ejpam-6997	41	11	number	number	NOUN
ejpam-6997	41	12	of	of	ADP
ejpam-6997	41	13	hypotheses	hypothesis	NOUN
ejpam-6997	41	14	and	and	CCONJ
ejpam-6997	41	15	aspects	aspect	NOUN
ejpam-6997	41	16	.	.	PUNCT
ejpam-6997	42	1	it	it	PRON
ejpam-6997	42	2	contributes	contribute	VERB
ejpam-6997	42	3	to	to	ADP
ejpam-6997	42	4	the	the	DET
ejpam-6997	42	5	expansion	expansion	NOUN
ejpam-6997	42	6	of	of	ADP
ejpam-6997	42	7	the	the	DET
ejpam-6997	42	8	topological	topological	ADJ
ejpam-6997	42	9	form	form	NOUN
ejpam-6997	42	10	,	,	PUNCT
ejpam-6997	42	11	which	which	PRON
ejpam-6997	42	12	is	be	AUX
ejpam-6997	42	13	used	use	VERB
ejpam-6997	42	14	to	to	PART
ejpam-6997	42	15	measure	measure	VERB
ejpam-6997	42	16	attributes	attribute	NOUN
ejpam-6997	42	17	like	like	ADP
ejpam-6997	42	18	love	love	NOUN
ejpam-6997	42	19	,	,	PUNCT
ejpam-6997	42	20	intelligence	intelligence	NOUN
ejpam-6997	42	21	,	,	PUNCT
ejpam-6997	42	22	beauty	beauty	NOUN
ejpam-6997	42	23	,	,	PUNCT
ejpam-6997	42	24	and	and	CCONJ
ejpam-6997	42	25	educational	educational	ADJ
ejpam-6997	42	26	attainment	attainment	NOUN
ejpam-6997	42	27	rather	rather	ADV
ejpam-6997	42	28	than	than	ADP
ejpam-6997	42	29	numbers	number	NOUN
ejpam-6997	42	30	.	.	PUNCT
ejpam-6997	43	1	furthermore	furthermore	ADV
ejpam-6997	43	2	,	,	PUNCT
ejpam-6997	43	3	it	it	PRON
ejpam-6997	43	4	extends	extend	VERB
ejpam-6997	43	5	the	the	DET
ejpam-6997	43	6	topological	topological	ADJ
ejpam-6997	43	7	structure	structure	NOUN
ejpam-6997	43	8	(	(	PUNCT
ejpam-6997	43	9	tsr	tsr	PROPN
ejpam-6997	43	10	)	)	PUNCT
ejpam-6997	43	11	by	by	ADP
ejpam-6997	43	12	using	use	VERB
ejpam-6997	43	13	the	the	DET
ejpam-6997	43	14	idea	idea	NOUN
ejpam-6997	43	15	of	of	ADP
ejpam-6997	43	16	grill	grill	NOUN
ejpam-6997	43	17	alterations	alteration	NOUN
ejpam-6997	43	18	in	in	ADP
ejpam-6997	43	19	the	the	DET
ejpam-6997	43	20	boundary	boundary	ADJ
ejpam-6997	43	21	region	region	NOUN
ejpam-6997	43	22	(	(	PUNCT
ejpam-6997	43	23	br	br	NOUN
ejpam-6997	43	24	)	)	PUNCT
ejpam-6997	43	25	,	,	PUNCT
ejpam-6997	43	26	up	up	ADP
ejpam-6997	43	27	,	,	PUNCT
ejpam-6997	43	28	and	and	CCONJ
ejpam-6997	43	29	lw	lw	NOUN
ejpam-6997	43	30	-	-	PUNCT
ejpam-6997	43	31	aps	ap	NOUN
ejpam-6997	43	32	,	,	PUNCT
ejpam-6997	43	33	opening	open	VERB
ejpam-6997	43	34	up	up	ADP
ejpam-6997	43	35	new	new	ADJ
ejpam-6997	43	36	boundaries	boundary	NOUN
ejpam-6997	43	37	in	in	ADP
ejpam-6997	43	38	nano	nano	NOUN
ejpam-6997	43	39	topological	topological	ADJ
ejpam-6997	43	40	spaces	space	NOUN
ejpam-6997	43	41	[	[	X
ejpam-6997	43	42	42	42	NUM
ejpam-6997	43	43	]	]	PUNCT
ejpam-6997	43	44	.	.	PUNCT
ejpam-6997	44	1	grills	grill	NOUN
ejpam-6997	44	2	are	be	AUX
ejpam-6997	44	3	effective	effective	ADJ
ejpam-6997	44	4	for	for	ADP
ejpam-6997	44	5	analyzing	analyze	VERB
ejpam-6997	44	6	raw	raw	ADJ
ejpam-6997	44	7	datasets	dataset	NOUN
ejpam-6997	44	8	,	,	PUNCT
ejpam-6997	44	9	especially	especially	ADV
ejpam-6997	44	10	for	for	ADP
ejpam-6997	44	11	eliminating	eliminate	VERB
ejpam-6997	44	12	ambiguity	ambiguity	NOUN
ejpam-6997	44	13	.	.	PUNCT
ejpam-6997	45	1	consequently	consequently	ADV
ejpam-6997	45	2	,	,	PUNCT
ejpam-6997	45	3	a	a	DET
ejpam-6997	45	4	principal	principal	ADJ
ejpam-6997	45	5	impetus	impetus	NOUN
ejpam-6997	45	6	for	for	ADP
ejpam-6997	45	7	this	this	DET
ejpam-6997	45	8	endeavor	endeavor	NOUN
ejpam-6997	45	9	is	be	AUX
ejpam-6997	45	10	the	the	DET
ejpam-6997	45	11	implementation	implementation	NOUN
ejpam-6997	45	12	of	of	ADP
ejpam-6997	45	13	novel	novel	ADJ
ejpam-6997	45	14	grill	grill	NOUN
ejpam-6997	45	15	-	-	PUNCT
ejpam-6997	45	16	based	base	VERB
ejpam-6997	45	17	rs	rs	NOUN
ejpam-6997	45	18	methodologies	methodology	NOUN
ejpam-6997	45	19	.	.	PUNCT
ejpam-6997	46	1	to	to	PART
ejpam-6997	46	2	put	put	VERB
ejpam-6997	46	3	it	it	PRON
ejpam-6997	46	4	another	another	DET
ejpam-6997	46	5	way	way	NOUN
ejpam-6997	46	6	,	,	PUNCT
ejpam-6997	46	7	it	it	PRON
ejpam-6997	46	8	creates	create	VERB
ejpam-6997	46	9	a	a	DET
ejpam-6997	46	10	special	special	ADJ
ejpam-6997	46	11	situation	situation	NOUN
ejpam-6997	46	12	for	for	ADP
ejpam-6997	46	13	its	its	PRON
ejpam-6997	46	14	generic	generic	ADJ
ejpam-6997	46	15	rs	rs	NOUN
ejpam-6997	46	16	model	model	NOUN
ejpam-6997	46	17	counterparts	counterpart	NOUN
ejpam-6997	46	18	when	when	SCONJ
ejpam-6997	46	19	the	the	DET
ejpam-6997	46	20	grill	grill	NOUN
ejpam-6997	46	21	is	be	AUX
ejpam-6997	46	22	the	the	DET
ejpam-6997	46	23	universal	universal	ADJ
ejpam-6997	46	24	set	set	NOUN
ejpam-6997	46	25	.	.	PUNCT
ejpam-6997	47	1	because	because	SCONJ
ejpam-6997	47	2	of	of	ADP
ejpam-6997	47	3	this	this	PRON
ejpam-6997	47	4	,	,	PUNCT
ejpam-6997	47	5	a	a	DET
ejpam-6997	47	6	few	few	ADJ
ejpam-6997	47	7	intriguing	intriguing	ADJ
ejpam-6997	47	8	studies	study	NOUN
ejpam-6997	47	9	examined	examine	VERB
ejpam-6997	47	10	the	the	DET
ejpam-6997	47	11	rst	rst	NOUN
ejpam-6997	47	12	that	that	PRON
ejpam-6997	47	13	grills	grill	VERB
ejpam-6997	47	14	describe	describe	NOUN
ejpam-6997	47	15	.	.	PUNCT
ejpam-6997	48	1	this	this	DET
ejpam-6997	48	2	paper	paper	NOUN
ejpam-6997	48	3	is	be	AUX
ejpam-6997	48	4	laid	lay	VERB
ejpam-6997	48	5	out	out	ADP
ejpam-6997	48	6	as	as	SCONJ
ejpam-6997	48	7	follows	follow	VERB
ejpam-6997	48	8	.	.	PUNCT
ejpam-6997	49	1	in	in	ADP
ejpam-6997	49	2	order	order	NOUN
ejpam-6997	49	3	to	to	PART
ejpam-6997	49	4	explain	explain	VERB
ejpam-6997	49	5	why	why	SCONJ
ejpam-6997	49	6	this	this	DET
ejpam-6997	49	7	study	study	NOUN
ejpam-6997	49	8	is	be	AUX
ejpam-6997	49	9	necessary	necessary	ADJ
ejpam-6997	49	10	,	,	PUNCT
ejpam-6997	49	11	we	we	PRON
ejpam-6997	49	12	refer	refer	VERB
ejpam-6997	49	13	to	to	ADP
ejpam-6997	49	14	the	the	DET
ejpam-6997	49	15	earlier	early	ADJ
ejpam-6997	49	16	types	type	NOUN
ejpam-6997	49	17	of	of	ADP
ejpam-6997	49	18	r	r	NOUN
ejpam-6997	49	19	nbds	nbds	NOUN
ejpam-6997	49	20	and	and	CCONJ
ejpam-6997	49	21	the	the	DET
ejpam-6997	49	22	key	key	ADJ
ejpam-6997	49	23	ideas	idea	NOUN
ejpam-6997	49	24	associated	associate	VERB
ejpam-6997	49	25	with	with	ADP
ejpam-6997	49	26	them	they	PRON
ejpam-6997	49	27	in	in	ADP
ejpam-6997	49	28	the	the	DET
ejpam-6997	49	29	following	follow	VERB
ejpam-6997	49	30	section	section	NOUN
ejpam-6997	49	31	.	.	PUNCT
ejpam-6997	50	1	we	we	PRON
ejpam-6997	50	2	then	then	ADV
ejpam-6997	50	3	divide	divide	VERB
ejpam-6997	50	4	sect	sect	NOUN
ejpam-6997	50	5	.	.	PUNCT
ejpam-6997	51	1	3	3	NUM
ejpam-6997	51	2	into	into	ADP
ejpam-6997	51	3	two	two	NUM
ejpam-6997	51	4	subsections	subsection	NOUN
ejpam-6997	51	5	,	,	PUNCT
ejpam-6997	51	6	each	each	PRON
ejpam-6997	51	7	of	of	ADP
ejpam-6997	51	8	which	which	PRON
ejpam-6997	51	9	has	have	VERB
ejpam-6997	51	10	two	two	NUM
ejpam-6997	51	11	new	new	ADJ
ejpam-6997	51	12	ap	ap	PROPN
ejpam-6997	51	13	spaces	space	NOUN
ejpam-6997	51	14	based	base	VERB
ejpam-6997	51	15	on	on	ADP
ejpam-6997	51	16	cardinality	cardinality	PROPN
ejpam-6997	51	17	rough	rough	ADJ
ejpam-6997	51	18	nbds	nbds	NOUN
ejpam-6997	51	19	via	via	ADP
ejpam-6997	51	20	grills	grill	NOUN
ejpam-6997	51	21	.	.	PUNCT
ejpam-6997	52	1	we	we	PRON
ejpam-6997	52	2	present	present	VERB
ejpam-6997	52	3	a	a	DET
ejpam-6997	52	4	new	new	ADJ
ejpam-6997	52	5	kind	kind	NOUN
ejpam-6997	52	6	of	of	ADP
ejpam-6997	52	7	ap	ap	PROPN
ejpam-6997	52	8	space	space	NOUN
ejpam-6997	52	9	and	and	CCONJ
ejpam-6997	52	10	examine	examine	VERB
ejpam-6997	52	11	its	its	PRON
ejpam-6997	52	12	primary	primary	ADJ
ejpam-6997	52	13	characteristics	characteristic	NOUN
ejpam-6997	52	14	in	in	ADP
ejpam-6997	52	15	sect	sect	NOUN
ejpam-6997	52	16	.	.	PUNCT
ejpam-6997	53	1	3.1	3.1	NUM
ejpam-6997	53	2	.	.	PUNCT
ejpam-6997	53	3	to	to	PART
ejpam-6997	53	4	deal	deal	VERB
ejpam-6997	53	5	with	with	ADP
ejpam-6997	53	6	irrational	irrational	ADJ
ejpam-6997	53	7	traits	trait	NOUN
ejpam-6997	53	8	and	and	CCONJ
ejpam-6997	53	9	ambiguous	ambiguous	ADJ
ejpam-6997	53	10	situations	situation	NOUN
ejpam-6997	53	11	,	,	PUNCT
ejpam-6997	53	12	in	in	ADP
ejpam-6997	53	13	sect	sect	NOUN
ejpam-6997	53	14	.	.	PUNCT
ejpam-6997	54	1	3.2	3.2	NUM
ejpam-6997	54	2	,	,	PUNCT
ejpam-6997	54	3	we	we	PRON
ejpam-6997	54	4	modified	modify	VERB
ejpam-6997	54	5	the	the	DET
ejpam-6997	54	6	prior	prior	ADJ
ejpam-6997	54	7	method	method	NOUN
ejpam-6997	54	8	and	and	CCONJ
ejpam-6997	54	9	demonstrate	demonstrate	VERB
ejpam-6997	54	10	the	the	DET
ejpam-6997	54	11	advantages	advantage	NOUN
ejpam-6997	54	12	of	of	ADP
ejpam-6997	54	13	the	the	DET
ejpam-6997	54	14	new	new	ADJ
ejpam-6997	54	15	one	one	NUM
ejpam-6997	54	16	.	.	PUNCT
ejpam-6997	55	1	the	the	DET
ejpam-6997	55	2	objective	objective	NOUN
ejpam-6997	55	3	of	of	ADP
ejpam-6997	55	4	sect	sect	NOUN
ejpam-6997	55	5	.	.	PUNCT
ejpam-6997	56	1	4	4	NUM
ejpam-6997	56	2	is	be	AUX
ejpam-6997	56	3	to	to	PART
ejpam-6997	56	4	investigate	investigate	VERB
ejpam-6997	56	5	the	the	DET
ejpam-6997	56	6	suggested	suggest	VERB
ejpam-6997	56	7	rs	rs	NOUN
ejpam-6997	56	8	models	model	NOUN
ejpam-6997	56	9	from	from	ADP
ejpam-6997	56	10	a	a	DET
ejpam-6997	56	11	topological	topological	ADJ
ejpam-6997	56	12	perspective	perspective	NOUN
ejpam-6997	56	13	.	.	PUNCT
ejpam-6997	57	1	in	in	ADP
ejpam-6997	57	2	sect	sect	NOUN
ejpam-6997	57	3	.	.	PUNCT
ejpam-6997	58	1	5	5	NUM
ejpam-6997	58	2	,	,	PUNCT
ejpam-6997	58	3	we	we	PRON
ejpam-6997	58	4	demonstrate	demonstrate	VERB
ejpam-6997	58	5	the	the	DET
ejpam-6997	58	6	effectiveness	effectiveness	NOUN
ejpam-6997	58	7	of	of	ADP
ejpam-6997	58	8	the	the	DET
ejpam-6997	58	9	provided	provide	VERB
ejpam-6997	58	10	models	model	NOUN
ejpam-6997	58	11	in	in	ADP
ejpam-6997	58	12	handling	handle	VERB
ejpam-6997	58	13	a	a	DET
ejpam-6997	58	14	medical	medical	ADJ
ejpam-6997	58	15	scenario	scenario	NOUN
ejpam-6997	58	16	involving	involve	VERB
ejpam-6997	58	17	the	the	DET
ejpam-6997	58	18	treatment	treatment	NOUN
ejpam-6997	58	19	of	of	ADP
ejpam-6997	58	20	heart	heart	NOUN
ejpam-6997	58	21	failure	failure	NOUN
ejpam-6997	58	22	.	.	PUNCT
ejpam-6997	59	1	we	we	PRON
ejpam-6997	59	2	also	also	ADV
ejpam-6997	59	3	highlight	highlight	VERB
ejpam-6997	59	4	how	how	SCONJ
ejpam-6997	59	5	our	our	PRON
ejpam-6997	59	6	method	method	NOUN
ejpam-6997	59	7	enhances	enhance	VERB
ejpam-6997	59	8	making	make	VERB
ejpam-6997	59	9	choices	choice	NOUN
ejpam-6997	59	10	and	and	CCONJ
ejpam-6997	59	11	how	how	SCONJ
ejpam-6997	59	12	we	we	PRON
ejpam-6997	59	13	apply	apply	VERB
ejpam-6997	59	14	a	a	DET
ejpam-6997	59	15	topological	topological	ADJ
ejpam-6997	59	16	approach	approach	NOUN
ejpam-6997	59	17	motivated	motivate	VERB
ejpam-6997	59	18	by	by	ADP
ejpam-6997	59	19	this	this	DET
ejpam-6997	59	20	method	method	NOUN
ejpam-6997	59	21	to	to	PART
ejpam-6997	59	22	determine	determine	VERB
ejpam-6997	59	23	the	the	DET
ejpam-6997	59	24	most	most	ADV
ejpam-6997	59	25	important	important	ADJ
ejpam-6997	59	26	characteristics	characteristic	NOUN
ejpam-6997	59	27	or	or	CCONJ
ejpam-6997	59	28	symptoms	symptom	NOUN
ejpam-6997	59	29	for	for	ADP
ejpam-6997	59	30	making	make	VERB
ejpam-6997	59	31	choices	choice	NOUN
ejpam-6997	59	32	.	.	PUNCT
ejpam-6997	60	1	finally	finally	ADV
ejpam-6997	60	2	,	,	PUNCT
ejpam-6997	60	3	in	in	ADP
ejpam-6997	60	4	sect	sect	NOUN
ejpam-6997	60	5	.	.	PUNCT
ejpam-6997	61	1	6	6	NUM
ejpam-6997	61	2	we	we	PRON
ejpam-6997	61	3	address	address	VERB
ejpam-6997	61	4	the	the	DET
ejpam-6997	61	5	benefits	benefit	NOUN
ejpam-6997	61	6	and	and	CCONJ
ejpam-6997	61	7	drawbacks	drawback	NOUN
ejpam-6997	61	8	of	of	ADP
ejpam-6997	61	9	the	the	DET
ejpam-6997	61	10	current	current	ADJ
ejpam-6997	61	11	models	model	NOUN
ejpam-6997	61	12	and	and	CCONJ
ejpam-6997	61	13	highlight	highlight	VERB
ejpam-6997	61	14	the	the	DET
ejpam-6997	61	15	key	key	ADJ
ejpam-6997	61	16	findings	finding	NOUN
ejpam-6997	61	17	of	of	ADP
ejpam-6997	61	18	this	this	DET
ejpam-6997	61	19	work	work	NOUN
ejpam-6997	61	20	with	with	ADP
ejpam-6997	61	21	a	a	DET
ejpam-6997	61	22	proposal	proposal	NOUN
ejpam-6997	61	23	for	for	ADP
ejpam-6997	61	24	further	further	ADJ
ejpam-6997	61	25	research	research	NOUN
ejpam-6997	61	26	,	,	PUNCT
ejpam-6997	61	27	respectively	respectively	ADV
ejpam-6997	61	28	.	.	PUNCT
ejpam-6997	61	29	a.	a.	PROPN
ejpam-6997	61	30	a.	a.	PROPN
ejpam-6997	61	31	azzam	azzam	PROPN
ejpam-6997	61	32	,	,	PUNCT
ejpam-6997	61	33	m.	m.	NOUN
ejpam-6997	61	34	aldawood	aldawood	PROPN
ejpam-6997	61	35	,	,	PUNCT
ejpam-6997	61	36	b.	b.	PROPN
ejpam-6997	61	37	alreshidi	alreshidi	PROPN
ejpam-6997	61	38	/	/	SYM
ejpam-6997	61	39	eur	eur	PROPN
ejpam-6997	61	40	.	.	PUNCT
ejpam-6997	62	1	j.	j.	PROPN
ejpam-6997	62	2	pure	pure	PROPN
ejpam-6997	62	3	appl	appl	PROPN
ejpam-6997	62	4	.	.	PROPN
ejpam-6997	62	5	math	math	PROPN
ejpam-6997	62	6	,	,	PUNCT
ejpam-6997	62	7	18	18	NUM
ejpam-6997	62	8	(	(	PUNCT
ejpam-6997	62	9	4	4	NUM
ejpam-6997	62	10	)	)	PUNCT
ejpam-6997	62	11	(	(	PUNCT
ejpam-6997	62	12	2025	2025	NUM
ejpam-6997	62	13	)	)	PUNCT
ejpam-6997	62	14	,	,	PUNCT
ejpam-6997	62	15	6997	6997	NUM
ejpam-6997	62	16	3	3	NUM
ejpam-6997	62	17	of	of	ADP
ejpam-6997	62	18	31	31	NUM
ejpam-6997	62	19	2	2	NUM
ejpam-6997	62	20	.	.	PUNCT
ejpam-6997	62	21	preliminaries	preliminary	NOUN
ejpam-6997	62	22	this	this	DET
ejpam-6997	62	23	part	part	NOUN
ejpam-6997	62	24	was	be	AUX
ejpam-6997	62	25	devoted	devote	VERB
ejpam-6997	62	26	to	to	ADP
ejpam-6997	62	27	reviewing	review	VERB
ejpam-6997	62	28	the	the	DET
ejpam-6997	62	29	key	key	ADJ
ejpam-6997	62	30	terms	term	NOUN
ejpam-6997	62	31	and	and	CCONJ
ejpam-6997	62	32	findings	finding	NOUN
ejpam-6997	62	33	and	and	CCONJ
ejpam-6997	62	34	explaining	explain	VERB
ejpam-6997	62	35	the	the	DET
ejpam-6997	62	36	advantages	advantage	NOUN
ejpam-6997	62	37	of	of	ADP
ejpam-6997	62	38	hybridizing	hybridizing	NOUN
ejpam-6997	62	39	grills	grill	NOUN
ejpam-6997	62	40	with	with	ADP
ejpam-6997	62	41	cardinal	cardinal	ADJ
ejpam-6997	62	42	rough	rough	ADJ
ejpam-6997	62	43	nbds	nbds	NOUN
ejpam-6997	62	44	in	in	ADP
ejpam-6997	62	45	order	order	NOUN
ejpam-6997	62	46	to	to	PART
ejpam-6997	62	47	improve	improve	VERB
ejpam-6997	62	48	accuracy	accuracy	NOUN
ejpam-6997	62	49	.	.	PUNCT
ejpam-6997	63	1	2.1	2.1	NUM
ejpam-6997	63	2	.	.	PUNCT
ejpam-6997	63	3	conventional	conventional	ADJ
ejpam-6997	63	4	approximation	approximation	NOUN
ejpam-6997	63	5	space	space	NOUN
ejpam-6997	63	6	definition	definition	NOUN
ejpam-6997	63	7	1	1	NUM
ejpam-6997	63	8	.	.	PUNCT
ejpam-6997	64	1	[	[	X
ejpam-6997	64	2	1	1	X
ejpam-6997	64	3	]	]	PUNCT
ejpam-6997	64	4	let	let	VERB
ejpam-6997	64	5	ℵ	ℵ	PART
ejpam-6997	64	6	represent	represent	VERB
ejpam-6997	64	7	a	a	DET
ejpam-6997	64	8	universe	universe	NOUN
ejpam-6997	64	9	,	,	PUNCT
ejpam-6997	64	10	which	which	PRON
ejpam-6997	64	11	is	be	AUX
ejpam-6997	64	12	a	a	DET
ejpam-6997	64	13	finite	finite	NOUN
ejpam-6997	64	14	,	,	PUNCT
ejpam-6997	64	15	nonempty	nonempty	NOUN
ejpam-6997	64	16	set	set	VERB
ejpam-6997	64	17	.	.	PUNCT
ejpam-6997	65	1	one	one	NUM
ejpam-6997	65	2	way	way	NOUN
ejpam-6997	65	3	to	to	PART
ejpam-6997	65	4	describe	describe	VERB
ejpam-6997	65	5	a	a	DET
ejpam-6997	65	6	binary	binary	ADJ
ejpam-6997	65	7	relation	relation	NOUN
ejpam-6997	65	8	on	on	ADP
ejpam-6997	65	9	ℵ	ℵ	NOUN
ejpam-6997	65	10	is	be	AUX
ejpam-6997	65	11	as	as	ADP
ejpam-6997	65	12	a	a	DET
ejpam-6997	65	13	subcollection	subcollection	NOUN
ejpam-6997	65	14	of	of	ADP
ejpam-6997	65	15	ℵ×ℵ.	ℵ×ℵ.	PROPN
ejpam-6997	65	16	a	a	DET
ejpam-6997	65	17	binary	binary	PROPN
ejpam-6997	65	18	relation	relation	NOUN
ejpam-6997	65	19	γ	γ	NOUN
ejpam-6997	65	20	on	on	ADP
ejpam-6997	65	21	ℵ	ℵ	PRON
ejpam-6997	65	22	is	be	AUX
ejpam-6997	65	23	a	a	DET
ejpam-6997	65	24	subclass	subclass	ADJ
ejpam-6997	65	25	γ	γ	NOUN
ejpam-6997	65	26	of	of	ADP
ejpam-6997	65	27	ℵ×ℵ.	ℵ×ℵ.	PROPN
ejpam-6997	65	28	to	to	PART
ejpam-6997	65	29	indicate	indicate	VERB
ejpam-6997	65	30	that	that	SCONJ
ejpam-6997	65	31	(	(	PUNCT
ejpam-6997	65	32	b	b	NOUN
ejpam-6997	65	33	,	,	PUNCT
ejpam-6997	65	34	n	n	CCONJ
ejpam-6997	65	35	)	)	PUNCT
ejpam-6997	65	36	is	be	AUX
ejpam-6997	65	37	an	an	DET
ejpam-6997	65	38	element	element	NOUN
ejpam-6997	65	39	of	of	ADP
ejpam-6997	65	40	γ	γ	PROPN
ejpam-6997	65	41	,	,	PUNCT
ejpam-6997	65	42	we	we	PRON
ejpam-6997	65	43	write	write	VERB
ejpam-6997	65	44	bγn	bγn	NOUN
ejpam-6997	65	45	.	.	PUNCT
ejpam-6997	66	1	if	if	SCONJ
ejpam-6997	66	2	a	a	DET
ejpam-6997	66	3	relation	relation	NOUN
ejpam-6997	66	4	γ	γ	VERB
ejpam-6997	66	5	on	on	ADP
ejpam-6997	66	6	ℵ	ℵ	NOUN
ejpam-6997	66	7	is	be	AUX
ejpam-6997	66	8	reflexive	reflexive	ADJ
ejpam-6997	66	9	(	(	PUNCT
ejpam-6997	66	10	i.e.	i.e.	X
ejpam-6997	66	11	,	,	PUNCT
ejpam-6997	66	12	bγb	bγb	VERB
ejpam-6997	66	13	for	for	ADP
ejpam-6997	66	14	all	all	DET
ejpam-6997	66	15	b	b	NOUN
ejpam-6997	66	16	∈	∈	PROPN
ejpam-6997	66	17	ℵ	ℵ	NOUN
ejpam-6997	66	18	)	)	PUNCT
ejpam-6997	66	19	,	,	PUNCT
ejpam-6997	66	20	symmetric	symmetric	ADJ
ejpam-6997	66	21	(	(	PUNCT
ejpam-6997	66	22	bγn	bγn	NOUN
ejpam-6997	66	23	⇔	⇔	PROPN
ejpam-6997	66	24	nγb	nγb	PROPN
ejpam-6997	66	25	)	)	PUNCT
ejpam-6997	66	26	,	,	PUNCT
ejpam-6997	66	27	and	and	CCONJ
ejpam-6997	66	28	transitive	transitive	ADJ
ejpam-6997	66	29	(	(	PUNCT
ejpam-6997	66	30	i.e.	i.e.	X
ejpam-6997	66	31	,bγm	,bγm	PUNCT
ejpam-6997	66	32	when	when	SCONJ
ejpam-6997	66	33	bγn	bγn	NOUN
ejpam-6997	66	34	and	and	CCONJ
ejpam-6997	66	35	nγm	nγm	NOUN
ejpam-6997	66	36	)	)	PUNCT
ejpam-6997	66	37	,	,	PUNCT
ejpam-6997	66	38	we	we	PRON
ejpam-6997	66	39	call	call	VERB
ejpam-6997	66	40	it	it	PRON
ejpam-6997	66	41	an	an	DET
ejpam-6997	66	42	equivalence	equivalence	NOUN
ejpam-6997	66	43	.	.	PUNCT
ejpam-6997	67	1	furthermore	furthermore	ADV
ejpam-6997	67	2	,	,	PUNCT
ejpam-6997	67	3	a	a	DET
ejpam-6997	67	4	relation	relation	NOUN
ejpam-6997	67	5	is	be	AUX
ejpam-6997	67	6	referred	refer	VERB
ejpam-6997	67	7	to	to	ADP
ejpam-6997	67	8	as	as	ADV
ejpam-6997	67	9	comparable	comparable	ADJ
ejpam-6997	67	10	if	if	SCONJ
ejpam-6997	67	11	it	it	PRON
ejpam-6997	67	12	fulfills	fulfill	VERB
ejpam-6997	67	13	bγn	bγn	NOUN
ejpam-6997	67	14	or	or	CCONJ
ejpam-6997	67	15	nγb	nγb	VERB
ejpam-6997	67	16	for	for	ADP
ejpam-6997	67	17	any	any	DET
ejpam-6997	67	18	b	b	NOUN
ejpam-6997	67	19	,	,	PUNCT
ejpam-6997	67	20	n	n	PRON
ejpam-6997	67	21	∈	∈	NOUN
ejpam-6997	67	22	ℵ.	ℵ.	NOUN
ejpam-6997	67	23	definition	definition	NOUN
ejpam-6997	67	24	2	2	NUM
ejpam-6997	67	25	.	.	PUNCT
ejpam-6997	68	1	[	[	X
ejpam-6997	68	2	1	1	X
ejpam-6997	68	3	]	]	PUNCT
ejpam-6997	68	4	let	let	VERB
ejpam-6997	68	5	γ	γ	PRON
ejpam-6997	68	6	represent	represent	VERB
ejpam-6997	68	7	an	an	DET
ejpam-6997	68	8	eqr	eqr	NOUN
ejpam-6997	68	9	on	on	ADP
ejpam-6997	68	10	ℵ	ℵ	NOUN
ejpam-6997	68	11	,	,	PUNCT
ejpam-6997	68	12	and	and	CCONJ
ejpam-6997	68	13	∆	∆	PROPN
ejpam-6997	68	14	⊑	⊑	PRON
ejpam-6997	68	15	ℵ	ℵ	PROPN
ejpam-6997	68	16	so	so	ADV
ejpam-6997	68	17	,	,	PUNCT
ejpam-6997	68	18	the	the	DET
ejpam-6997	68	19	lw	lw	NOUN
ejpam-6997	68	20	and	and	CCONJ
ejpam-6997	68	21	up	up	ADP
ejpam-6997	68	22	-	-	PUNCT
ejpam-6997	68	23	aps	ap	NOUN
ejpam-6997	68	24	of	of	ADP
ejpam-6997	68	25	∆	∆	PROPN
ejpam-6997	68	26	will	will	AUX
ejpam-6997	68	27	be	be	AUX
ejpam-6997	68	28	represented	represent	VERB
ejpam-6997	68	29	as	as	ADP
ejpam-6997	68	30	:	:	PUNCT
ejpam-6997	68	31	γ(∆	γ(∆	NUM
ejpam-6997	68	32	)	)	PUNCT
ejpam-6997	69	1	=	=	PUNCT
ejpam-6997	69	2	⊔{d	⊔{d	NUM
ejpam-6997	69	3	∈	∈	PROPN
ejpam-6997	69	4	ℵ	ℵ	ADP
ejpam-6997	69	5	γ	γ	NOUN
ejpam-6997	69	6	:	:	PUNCT
ejpam-6997	69	7	d	d	X
ejpam-6997	69	8	⊑	⊑	PRON
ejpam-6997	69	9	∆	∆	PROPN
ejpam-6997	69	10	}	}	PUNCT
ejpam-6997	69	11	.	.	PUNCT
ejpam-6997	70	1	γ(∆	γ(∆	NUM
ejpam-6997	70	2	)	)	PUNCT
ejpam-6997	71	1	=	=	PUNCT
ejpam-6997	71	2	⊔{d	⊔{d	NUM
ejpam-6997	71	3	∈	∈	PROPN
ejpam-6997	71	4	ℵ	ℵ	ADP
ejpam-6997	71	5	γ	γ	NOUN
ejpam-6997	71	6	:	:	PUNCT
ejpam-6997	71	7	d	d	SYM
ejpam-6997	71	8	⊓	⊓	PROPN
ejpam-6997	71	9	∆	∆	PROPN
ejpam-6997	71	10	̸=	̸=	PROPN
ejpam-6997	71	11	ϕ	ϕ	PROPN
ejpam-6997	71	12	}	}	PUNCT
ejpam-6997	71	13	notation	notation	NOUN
ejpam-6997	71	14	ℵ	ℵ	NOUN
ejpam-6997	71	15	γ	γ	X
ejpam-6997	71	16	represents	represent	VERB
ejpam-6997	71	17	the	the	DET
ejpam-6997	71	18	family	family	NOUN
ejpam-6997	71	19	that	that	PRON
ejpam-6997	71	20	includes	include	VERB
ejpam-6997	71	21	all	all	DET
ejpam-6997	71	22	equivalency	equivalency	NOUN
ejpam-6997	71	23	classes	class	NOUN
ejpam-6997	71	24	brought	bring	VERB
ejpam-6997	71	25	to	to	ADP
ejpam-6997	71	26	by	by	ADP
ejpam-6997	71	27	the	the	DET
ejpam-6997	71	28	relation	relation	NOUN
ejpam-6997	71	29	γ	γ	PROPN
ejpam-6997	71	30	.	.	PROPN
ejpam-6997	71	31	henceforth	henceforth	ADV
ejpam-6997	71	32	referred	refer	VERB
ejpam-6997	71	33	to	to	ADP
ejpam-6997	71	34	as	as	SCONJ
ejpam-6997	71	35	an	an	DET
ejpam-6997	71	36	ap	ap	PROPN
ejpam-6997	71	37	space	space	NOUN
ejpam-6997	71	38	is	be	AUX
ejpam-6997	71	39	the	the	DET
ejpam-6997	71	40	pair	pair	NOUN
ejpam-6997	71	41	(	(	PUNCT
ejpam-6997	71	42	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	71	43	)	)	PUNCT
ejpam-6997	71	44	.	.	PUNCT
ejpam-6997	72	1	it	it	PRON
ejpam-6997	72	2	is	be	AUX
ejpam-6997	72	3	described	describe	VERB
ejpam-6997	72	4	as	as	SCONJ
ejpam-6997	72	5	follows	follow	VERB
ejpam-6997	72	6	if	if	SCONJ
ejpam-6997	72	7	γ(∆	γ(∆	NUM
ejpam-6997	72	8	)	)	PUNCT
ejpam-6997	72	9	and	and	CCONJ
ejpam-6997	72	10	γ(∆	γ(∆	NUM
ejpam-6997	72	11	)	)	PUNCT
ejpam-6997	72	12	are	be	AUX
ejpam-6997	72	13	not	not	PART
ejpam-6997	72	14	equal	equal	ADJ
ejpam-6997	72	15	,	,	PUNCT
ejpam-6997	72	16	∆	∆	PROPN
ejpam-6997	72	17	is	be	AUX
ejpam-6997	72	18	said	say	VERB
ejpam-6997	72	19	to	to	PART
ejpam-6997	72	20	be	be	AUX
ejpam-6997	72	21	rough	rough	ADJ
ejpam-6997	72	22	.	.	PUNCT
ejpam-6997	73	1	on	on	ADP
ejpam-6997	73	2	the	the	DET
ejpam-6997	73	3	other	other	ADJ
ejpam-6997	73	4	hand	hand	NOUN
ejpam-6997	73	5	,	,	PUNCT
ejpam-6997	73	6	a	a	DET
ejpam-6997	73	7	subset	subset	NOUN
ejpam-6997	73	8	∆	∆	PROPN
ejpam-6997	73	9	is	be	AUX
ejpam-6997	73	10	said	say	VERB
ejpam-6997	73	11	to	to	PART
ejpam-6997	73	12	be	be	AUX
ejpam-6997	73	13	exact	exact	ADJ
ejpam-6997	73	14	if	if	SCONJ
ejpam-6997	73	15	γ(∆	γ(∆	NUM
ejpam-6997	73	16	)	)	PUNCT
ejpam-6997	73	17	=	=	SYM
ejpam-6997	73	18	γ(∆	γ(∆	NUM
ejpam-6997	73	19	)	)	PUNCT
ejpam-6997	73	20	.	.	PUNCT
ejpam-6997	74	1	the	the	DET
ejpam-6997	74	2	following	follow	VERB
ejpam-6997	74	3	proposition	proposition	NOUN
ejpam-6997	74	4	lists	list	VERB
ejpam-6997	74	5	the	the	DET
ejpam-6997	74	6	main	main	ADJ
ejpam-6997	74	7	characteristics	characteristic	NOUN
ejpam-6997	74	8	of	of	ADP
ejpam-6997	74	9	the	the	DET
ejpam-6997	74	10	conventional	conventional	ADJ
ejpam-6997	74	11	rs	rs	NOUN
ejpam-6997	74	12	model	model	NOUN
ejpam-6997	74	13	.	.	PUNCT
ejpam-6997	75	1	proposition	proposition	NOUN
ejpam-6997	75	2	1	1	NUM
ejpam-6997	75	3	.	.	PUNCT
ejpam-6997	76	1	[	[	X
ejpam-6997	76	2	1	1	NUM
ejpam-6997	76	3	,	,	PUNCT
ejpam-6997	76	4	2	2	NUM
ejpam-6997	76	5	]	]	PUNCT
ejpam-6997	76	6	examine	examine	VERB
ejpam-6997	76	7	the	the	DET
ejpam-6997	76	8	definition	definition	NOUN
ejpam-6997	76	9	of	of	ADP
ejpam-6997	76	10	an	an	DET
ejpam-6997	76	11	eqr	eqr	NOUN
ejpam-6997	76	12	γ	γ	X
ejpam-6997	76	13	on	on	ADP
ejpam-6997	76	14	ℵ.	ℵ.	PROPN
ejpam-6997	76	15	the	the	DET
ejpam-6997	76	16	following	follow	VERB
ejpam-6997	76	17	properties	property	NOUN
ejpam-6997	76	18	are	be	AUX
ejpam-6997	76	19	true	true	ADJ
ejpam-6997	76	20	for	for	ADP
ejpam-6997	76	21	sets	set	NOUN
ejpam-6997	76	22	d	d	PROPN
ejpam-6997	76	23	and	and	CCONJ
ejpam-6997	76	24	∆	∆	NUM
ejpam-6997	76	25	:	:	PUNCT
ejpam-6997	76	26	(	(	PUNCT
ejpam-6997	76	27	l1	l1	PROPN
ejpam-6997	76	28	)	)	PUNCT
ejpam-6997	76	29	γ(d	γ(d	PROPN
ejpam-6997	76	30	)	)	PUNCT
ejpam-6997	77	1	⊑	⊑	PROPN
ejpam-6997	77	2	d.	d.	PROPN
ejpam-6997	77	3	(	(	PUNCT
ejpam-6997	77	4	l2	l2	PROPN
ejpam-6997	77	5	)	)	PUNCT
ejpam-6997	77	6	γ(ℵ	γ(ℵ	PROPN
ejpam-6997	77	7	)	)	PUNCT
ejpam-6997	78	1	=	=	PUNCT
ejpam-6997	78	2	ℵ.	ℵ.	PROPN
ejpam-6997	78	3	(	(	PUNCT
ejpam-6997	78	4	l3	l3	PROPN
ejpam-6997	78	5	)	)	PUNCT
ejpam-6997	78	6	γ(ϕ	γ(ϕ	PROPN
ejpam-6997	78	7	)	)	PUNCT
ejpam-6997	79	1	=	=	SYM
ejpam-6997	79	2	ϕ.	ϕ.	PROPN
ejpam-6997	79	3	(	(	PUNCT
ejpam-6997	79	4	l4	l4	PROPN
ejpam-6997	79	5	)	)	PUNCT
ejpam-6997	79	6	γ(d	γ(d	PROPN
ejpam-6997	79	7	)	)	PUNCT
ejpam-6997	79	8	⊑	⊑	X
ejpam-6997	79	9	γ(∆	γ(∆	NUM
ejpam-6997	79	10	)	)	PUNCT
ejpam-6997	79	11	whenever	whenever	SCONJ
ejpam-6997	79	12	d	d	PROPN
ejpam-6997	79	13	⊑	⊑	X
ejpam-6997	79	14	∆.	∆.	X
ejpam-6997	79	15	(	(	PUNCT
ejpam-6997	79	16	l5	l5	PROPN
ejpam-6997	79	17	)	)	PUNCT
ejpam-6997	79	18	γ((d	γ((d	NOUN
ejpam-6997	79	19	)	)	PUNCT
ejpam-6997	80	1	⊓	⊓	PROPN
ejpam-6997	80	2	∆	∆	X
ejpam-6997	80	3	)	)	PUNCT
ejpam-6997	80	4	=	=	SYM
ejpam-6997	80	5	γ(d	γ(d	NOUN
ejpam-6997	80	6	)	)	PUNCT
ejpam-6997	80	7	⊓	⊓	PROPN
ejpam-6997	80	8	γ(∆	γ(∆	NUM
ejpam-6997	80	9	)	)	PUNCT
ejpam-6997	80	10	.	.	PUNCT
ejpam-6997	81	1	(	(	PUNCT
ejpam-6997	81	2	l6	l6	PROPN
ejpam-6997	81	3	)	)	PUNCT
ejpam-6997	81	4	γ(d	γ(d	PROPN
ejpam-6997	81	5	)	)	PUNCT
ejpam-6997	81	6	⊔	⊔	NUM
ejpam-6997	81	7	γ(∆	γ(∆	NUM
ejpam-6997	81	8	)	)	PUNCT
ejpam-6997	81	9	⊑	⊑	X
ejpam-6997	82	1	γ(d	γ(d	X
ejpam-6997	82	2	⊔	⊔	NUM
ejpam-6997	82	3	∆	∆	PROPN
ejpam-6997	82	4	)	)	PUNCT
ejpam-6997	82	5	.	.	PUNCT
ejpam-6997	83	1	a.	a.	PROPN
ejpam-6997	83	2	a.	a.	PROPN
ejpam-6997	83	3	azzam	azzam	PROPN
ejpam-6997	83	4	,	,	PUNCT
ejpam-6997	83	5	m.	m.	NOUN
ejpam-6997	83	6	aldawood	aldawood	PROPN
ejpam-6997	83	7	,	,	PUNCT
ejpam-6997	83	8	b.	b.	PROPN
ejpam-6997	83	9	alreshidi	alreshidi	PROPN
ejpam-6997	83	10	/	/	SYM
ejpam-6997	83	11	eur	eur	PROPN
ejpam-6997	83	12	.	.	PUNCT
ejpam-6997	84	1	j.	j.	PROPN
ejpam-6997	84	2	pure	pure	PROPN
ejpam-6997	84	3	appl	appl	PROPN
ejpam-6997	84	4	.	.	PROPN
ejpam-6997	84	5	math	math	PROPN
ejpam-6997	84	6	,	,	PUNCT
ejpam-6997	84	7	18	18	NUM
ejpam-6997	84	8	(	(	PUNCT
ejpam-6997	84	9	4	4	NUM
ejpam-6997	84	10	)	)	PUNCT
ejpam-6997	84	11	(	(	PUNCT
ejpam-6997	84	12	2025	2025	NUM
ejpam-6997	84	13	)	)	PUNCT
ejpam-6997	84	14	,	,	PUNCT
ejpam-6997	84	15	6997	6997	NUM
ejpam-6997	84	16	4	4	NUM
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ejpam-6997	84	18	31	31	NUM
ejpam-6997	84	19	(	(	PUNCT
ejpam-6997	84	20	l7	l7	PROPN
ejpam-6997	84	21	)	)	PUNCT
ejpam-6997	84	22	γ(dc	γ(dc	PROPN
ejpam-6997	84	23	)	)	PUNCT
ejpam-6997	84	24	=	=	SYM
ejpam-6997	84	25	(	(	PUNCT
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ejpam-6997	85	3	)	)	PUNCT
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ejpam-6997	85	5	)	)	PUNCT
ejpam-6997	85	6	)	)	PUNCT
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ejpam-6997	86	3	)	)	PUNCT
ejpam-6997	86	4	.	.	PUNCT
ejpam-6997	87	1	(	(	PUNCT
ejpam-6997	87	2	l9	l9	PROPN
ejpam-6997	87	3	)	)	PUNCT
ejpam-6997	87	4	γ((γ(d))c	γ((γ(d))c	PROPN
ejpam-6997	87	5	)	)	PUNCT
ejpam-6997	88	1	=	=	SYM
ejpam-6997	88	2	(	(	PUNCT
ejpam-6997	88	3	γ(d))c	γ(d))c	PROPN
ejpam-6997	88	4	.	.	PUNCT
ejpam-6997	89	1	(	(	PUNCT
ejpam-6997	89	2	l10	l10	PROPN
ejpam-6997	89	3	)	)	PUNCT
ejpam-6997	89	4	γ(∆	γ(∆	NUM
ejpam-6997	89	5	)	)	PUNCT
ejpam-6997	89	6	=	=	PUNCT
ejpam-6997	90	1	∆,∀∆	∆,∀∆	NUM
ejpam-6997	90	2	∈	∈	PROPN
ejpam-6997	90	3	ℵ	ℵ	NOUN
ejpam-6997	90	4	γ	γ	X
ejpam-6997	90	5	.	.	PUNCT
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ejpam-6997	91	2	u1	u1	NOUN
ejpam-6997	91	3	)	)	PUNCT
ejpam-6997	92	1	d	d	ADP
ejpam-6997	92	2	⊑	⊑	PRON
ejpam-6997	92	3	γ(d	γ(d	PROPN
ejpam-6997	92	4	)	)	PUNCT
ejpam-6997	92	5	.	.	PUNCT
ejpam-6997	93	1	(	(	PUNCT
ejpam-6997	93	2	u2	u2	NOUN
ejpam-6997	93	3	)	)	PUNCT
ejpam-6997	93	4	γ(ℵ	γ(ℵ	PROPN
ejpam-6997	93	5	)	)	PUNCT
ejpam-6997	94	1	=	=	PUNCT
ejpam-6997	94	2	ℵ.	ℵ.	PROPN
ejpam-6997	94	3	(	(	PUNCT
ejpam-6997	94	4	u3	u3	PROPN
ejpam-6997	94	5	)	)	PUNCT
ejpam-6997	94	6	γ(ϕ	γ(ϕ	PROPN
ejpam-6997	94	7	)	)	PUNCT
ejpam-6997	95	1	=	=	SYM
ejpam-6997	95	2	ϕ.	ϕ.	PROPN
ejpam-6997	95	3	(	(	PUNCT
ejpam-6997	95	4	u4	u4	PROPN
ejpam-6997	95	5	)	)	PUNCT
ejpam-6997	95	6	if	if	SCONJ
ejpam-6997	95	7	d	d	PROPN
ejpam-6997	95	8	⊑	⊑	PRON
ejpam-6997	95	9	∆	∆	PROPN
ejpam-6997	95	10	,	,	PUNCT
ejpam-6997	95	11	then	then	ADV
ejpam-6997	95	12	γ(d	γ(d	PROPN
ejpam-6997	95	13	)	)	PUNCT
ejpam-6997	95	14	⊑	⊑	PROPN
ejpam-6997	95	15	γ(∆	γ(∆	NUM
ejpam-6997	95	16	)	)	PUNCT
ejpam-6997	95	17	.	.	PUNCT
ejpam-6997	96	1	(	(	PUNCT
ejpam-6997	96	2	u5	u5	NOUN
ejpam-6997	96	3	)	)	PUNCT
ejpam-6997	96	4	γ(d	γ(d	PROPN
ejpam-6997	96	5	⊓	⊓	PROPN
ejpam-6997	96	6	∆	∆	X
ejpam-6997	96	7	)	)	PUNCT
ejpam-6997	96	8	⊑	⊑	PRON
ejpam-6997	96	9	γ(d	γ(d	PROPN
ejpam-6997	96	10	)	)	PUNCT
ejpam-6997	96	11	⊓ap	⊓ap	NOUN
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ejpam-6997	96	13	∆	∆	PROPN
ejpam-6997	96	14	)	)	PUNCT
ejpam-6997	96	15	.	.	PUNCT
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ejpam-6997	97	2	u6	u6	NOUN
ejpam-6997	97	3	)	)	PUNCT
ejpam-6997	97	4	γ(d	γ(d	PROPN
ejpam-6997	97	5	⊔	⊔	NUM
ejpam-6997	97	6	∆	∆	PROPN
ejpam-6997	97	7	)	)	PUNCT
ejpam-6997	98	1	=	=	SYM
ejpam-6997	98	2	γ(d	γ(d	PROPN
ejpam-6997	98	3	)	)	PUNCT
ejpam-6997	98	4	⊔	⊔	NUM
ejpam-6997	98	5	γ(∆	γ(∆	NUM
ejpam-6997	98	6	)	)	PUNCT
ejpam-6997	98	7	.	.	PUNCT
ejpam-6997	99	1	(	(	PUNCT
ejpam-6997	99	2	u7	u7	PROPN
ejpam-6997	99	3	)	)	PUNCT
ejpam-6997	99	4	γ(dc	γ(dc	PROPN
ejpam-6997	99	5	)	)	PUNCT
ejpam-6997	99	6	=	=	SYM
ejpam-6997	99	7	(	(	PUNCT
ejpam-6997	99	8	γ(d))c	γ(d))c	PROPN
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ejpam-6997	100	3	)	)	PUNCT
ejpam-6997	100	4	γ(γ(d	γ(γ(d	PROPN
ejpam-6997	100	5	)	)	PUNCT
ejpam-6997	100	6	)	)	PUNCT
ejpam-6997	101	1	=	=	SYM
ejpam-6997	101	2	γ(d	γ(d	PROPN
ejpam-6997	101	3	)	)	PUNCT
ejpam-6997	101	4	.	.	PUNCT
ejpam-6997	102	1	(	(	PUNCT
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ejpam-6997	102	3	)	)	PUNCT
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ejpam-6997	103	2	(	(	PUNCT
ejpam-6997	103	3	γ(d))c	γ(d))c	PROPN
ejpam-6997	103	4	.	.	PUNCT
ejpam-6997	104	1	(	(	PUNCT
ejpam-6997	104	2	u10	u10	PROPN
ejpam-6997	104	3	)	)	PUNCT
ejpam-6997	104	4	γ(∆	γ(∆	NUM
ejpam-6997	104	5	)	)	PUNCT
ejpam-6997	105	1	=	=	PUNCT
ejpam-6997	105	2	∆,∀∆	∆,∀∆	NUM
ejpam-6997	105	3	∈	∈	PROPN
ejpam-6997	105	4	ℵ	ℵ	NOUN
ejpam-6997	105	5	γ	γ	X
ejpam-6997	105	6	.	.	PUNCT
ejpam-6997	106	1	numerous	numerous	ADJ
ejpam-6997	106	2	methods	method	NOUN
ejpam-6997	106	3	have	have	AUX
ejpam-6997	106	4	been	be	AUX
ejpam-6997	106	5	used	use	VERB
ejpam-6997	106	6	to	to	PART
ejpam-6997	106	7	expand	expand	VERB
ejpam-6997	106	8	traditional	traditional	ADJ
ejpam-6997	106	9	theory	theory	NOUN
ejpam-6997	106	10	[	[	X
ejpam-6997	106	11	26	26	NUM
ejpam-6997	106	12	]	]	PUNCT
ejpam-6997	106	13	,	,	PUNCT
ejpam-6997	106	14	and	and	CCONJ
ejpam-6997	106	15	the	the	DET
ejpam-6997	106	16	validity	validity	NOUN
ejpam-6997	106	17	of	of	ADP
ejpam-6997	106	18	these	these	DET
ejpam-6997	106	19	traits	trait	NOUN
ejpam-6997	106	20	has	have	AUX
ejpam-6997	106	21	been	be	AUX
ejpam-6997	106	22	well	well	ADV
ejpam-6997	106	23	validated	validate	VERB
ejpam-6997	106	24	.	.	PUNCT
ejpam-6997	107	1	regretfully	regretfully	ADV
ejpam-6997	107	2	,	,	PUNCT
ejpam-6997	107	3	it	it	PRON
ejpam-6997	107	4	has	have	AUX
ejpam-6997	107	5	been	be	AUX
ejpam-6997	107	6	discovered	discover	VERB
ejpam-6997	107	7	that	that	SCONJ
ejpam-6997	107	8	some	some	DET
ejpam-6997	107	9	qualities	quality	NOUN
ejpam-6997	107	10	are	be	AUX
ejpam-6997	107	11	questionable	questionable	ADJ
ejpam-6997	107	12	.	.	PUNCT
ejpam-6997	108	1	however	however	ADV
ejpam-6997	108	2	,	,	PUNCT
ejpam-6997	108	3	it	it	PRON
ejpam-6997	108	4	is	be	AUX
ejpam-6997	108	5	seen	see	VERB
ejpam-6997	108	6	to	to	PART
ejpam-6997	108	7	be	be	AUX
ejpam-6997	108	8	beneficial	beneficial	ADJ
ejpam-6997	108	9	in	in	ADP
ejpam-6997	108	10	these	these	DET
ejpam-6997	108	11	approaches	approach	NOUN
ejpam-6997	108	12	to	to	PART
ejpam-6997	108	13	acquire	acquire	VERB
ejpam-6997	108	14	as	as	ADV
ejpam-6997	108	15	many	many	ADJ
ejpam-6997	108	16	of	of	ADP
ejpam-6997	108	17	these	these	DET
ejpam-6997	108	18	traits	trait	NOUN
ejpam-6997	108	19	as	as	SCONJ
ejpam-6997	108	20	is	be	AUX
ejpam-6997	108	21	practical	practical	ADJ
ejpam-6997	108	22	.	.	PUNCT
ejpam-6997	109	1	definition	definition	NOUN
ejpam-6997	109	2	3	3	NUM
ejpam-6997	109	3	.	.	PUNCT
ejpam-6997	110	1	[	[	X
ejpam-6997	110	2	1	1	NUM
ejpam-6997	110	3	,	,	PUNCT
ejpam-6997	110	4	2	2	NUM
ejpam-6997	110	5	]	]	PUNCT
ejpam-6997	110	6	the	the	DET
ejpam-6997	110	7	σ	σ	NOUN
ejpam-6997	110	8	-	-	PUNCT
ejpam-6997	110	9	accuracy	accuracy	NOUN
ejpam-6997	110	10	and	and	CCONJ
ejpam-6997	110	11	ℜ-roughness	ℜ-roughness	PROPN
ejpam-6997	110	12	criteria	criterion	NOUN
ejpam-6997	110	13	of	of	ADP
ejpam-6997	110	14	∆	∆	PROPN
ejpam-6997	110	15	are	be	AUX
ejpam-6997	110	16	ascertained	ascertain	VERB
ejpam-6997	110	17	by	by	ADP
ejpam-6997	110	18	taking	take	VERB
ejpam-6997	110	19	an	an	DET
ejpam-6997	110	20	eqr	eqr	NOUN
ejpam-6997	110	21	γ	γ	NOUN
ejpam-6997	110	22	on	on	ADP
ejpam-6997	110	23	ℵ	ℵ	NOUN
ejpam-6997	110	24	into	into	ADP
ejpam-6997	110	25	consideration	consideration	NOUN
ejpam-6997	110	26	:	:	PUNCT
ejpam-6997	110	27	σ(∆	σ(∆	X
ejpam-6997	110	28	)	)	PUNCT
ejpam-6997	110	29	=	=	SYM
ejpam-6997	110	30	|γ(∆)|	|γ(∆)|	NOUN
ejpam-6997	110	31	|γ(∆)|	|γ(∆)|	NOUN
ejpam-6997	110	32	,	,	PUNCT
ejpam-6997	110	33	|γ(∆)|	|γ(∆)|	PROPN
ejpam-6997	110	34	̸=	̸=	PROPN
ejpam-6997	110	35	0	0	NUM
ejpam-6997	110	36	.	.	PUNCT
ejpam-6997	110	37	ℜ(∆	ℜ(∆	ADV
ejpam-6997	110	38	)	)	PUNCT
ejpam-6997	111	1	=	=	SYM
ejpam-6997	111	2	1	1	NUM
ejpam-6997	111	3	−	−	PROPN
ejpam-6997	111	4	σ(∆	σ(∆	PROPN
ejpam-6997	111	5	)	)	PUNCT
ejpam-6997	111	6	.	.	PUNCT
ejpam-6997	112	1	the	the	DET
ejpam-6997	112	2	equivalency	equivalency	NOUN
ejpam-6997	112	3	relations	relation	NOUN
ejpam-6997	112	4	are	be	AUX
ejpam-6997	112	5	not	not	PART
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ejpam-6997	112	7	in	in	ADP
ejpam-6997	112	8	many	many	ADJ
ejpam-6997	112	9	situations	situation	NOUN
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ejpam-6997	113	2	,	,	PUNCT
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ejpam-6997	113	4	relationships	relationship	NOUN
ejpam-6997	113	5	than	than	ADP
ejpam-6997	113	6	full	full	ADJ
ejpam-6997	113	7	equivalency	equivalency	NOUN
ejpam-6997	113	8	have	have	AUX
ejpam-6997	113	9	been	be	AUX
ejpam-6997	113	10	used	use	VERB
ejpam-6997	113	11	to	to	PART
ejpam-6997	113	12	augment	augment	VERB
ejpam-6997	113	13	the	the	DET
ejpam-6997	113	14	traditional	traditional	ADJ
ejpam-6997	113	15	approach	approach	NOUN
ejpam-6997	113	16	.	.	PUNCT
ejpam-6997	114	1	a.	a.	NOUN
ejpam-6997	114	2	a.	a.	PROPN
ejpam-6997	114	3	azzam	azzam	PROPN
ejpam-6997	114	4	,	,	PUNCT
ejpam-6997	114	5	m.	m.	NOUN
ejpam-6997	114	6	aldawood	aldawood	PROPN
ejpam-6997	114	7	,	,	PUNCT
ejpam-6997	114	8	b.	b.	PROPN
ejpam-6997	114	9	alreshidi	alreshidi	PROPN
ejpam-6997	114	10	/	/	SYM
ejpam-6997	114	11	eur	eur	PROPN
ejpam-6997	114	12	.	.	PUNCT
ejpam-6997	115	1	j.	j.	PROPN
ejpam-6997	115	2	pure	pure	PROPN
ejpam-6997	115	3	appl	appl	PROPN
ejpam-6997	115	4	.	.	PROPN
ejpam-6997	115	5	math	math	PROPN
ejpam-6997	115	6	,	,	PUNCT
ejpam-6997	115	7	18	18	NUM
ejpam-6997	115	8	(	(	PUNCT
ejpam-6997	115	9	4	4	NUM
ejpam-6997	115	10	)	)	PUNCT
ejpam-6997	115	11	(	(	PUNCT
ejpam-6997	115	12	2025	2025	NUM
ejpam-6997	115	13	)	)	PUNCT
ejpam-6997	115	14	,	,	PUNCT
ejpam-6997	115	15	6997	6997	NUM
ejpam-6997	115	16	5	5	NUM
ejpam-6997	115	17	of	of	ADP
ejpam-6997	115	18	31	31	NUM
ejpam-6997	115	19	2.2	2.2	NUM
ejpam-6997	115	20	.	.	PUNCT
ejpam-6997	116	1	ϱ-neighborhood	ϱ-neighborhood	NOUN
ejpam-6997	116	2	space	space	NOUN
ejpam-6997	116	3	types	type	NOUN
ejpam-6997	116	4	definition	definition	NOUN
ejpam-6997	116	5	4	4	NUM
ejpam-6997	116	6	.	.	PUNCT
ejpam-6997	117	1	[	[	X
ejpam-6997	117	2	13	13	NUM
ejpam-6997	117	3	,	,	PUNCT
ejpam-6997	117	4	15	15	NUM
ejpam-6997	117	5	,	,	PUNCT
ejpam-6997	117	6	43	43	NUM
ejpam-6997	117	7	,	,	PUNCT
ejpam-6997	117	8	44	44	NUM
ejpam-6997	117	9	]	]	PUNCT
ejpam-6997	117	10	in	in	ADP
ejpam-6997	117	11	an	an	DET
ejpam-6997	117	12	arbitrary	arbitrary	ADJ
ejpam-6997	117	13	relation	relation	NOUN
ejpam-6997	117	14	γ	γ	X
ejpam-6997	117	15	on	on	ADP
ejpam-6997	117	16	ℵ.	ℵ.	PROPN
ejpam-6997	117	17	where	where	SCONJ
ejpam-6997	117	18	ϱ	ϱ	ADP
ejpam-6997	117	19	∈	∈	PROPN
ejpam-6997	117	20	{	{	PUNCT
ejpam-6997	117	21	r	r	NOUN
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ejpam-6997	117	26	,	,	PUNCT
ejpam-6997	117	27	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	117	28	,	,	PUNCT
ejpam-6997	117	29	i	i	PRON
ejpam-6997	117	30	,	,	PUNCT
ejpam-6997	117	31	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	117	32	,	,	PUNCT
ejpam-6997	117	33	u	u	NOUN
ejpam-6997	117	34	,	,	PUNCT
ejpam-6997	117	35	⟨u⟩	⟨u⟩	PROPN
ejpam-6997	117	36	}	}	PUNCT
ejpam-6997	117	37	,	,	PUNCT
ejpam-6997	117	38	the	the	DET
ejpam-6997	117	39	ϱ-nbds	ϱ-nbds	NOUN
ejpam-6997	117	40	of	of	ADP
ejpam-6997	117	41	an	an	DET
ejpam-6997	117	42	e	e	PROPN
ejpam-6997	117	43	∈	∈	PROPN
ejpam-6997	117	44	ℵ	ℵ	NOUN
ejpam-6997	117	45	(	(	PUNCT
ejpam-6997	117	46	denoted	denote	VERB
ejpam-6997	117	47	by	by	ADP
ejpam-6997	117	48	mϱ(e	mϱ(e	NOUN
ejpam-6997	117	49	)	)	PUNCT
ejpam-6997	117	50	)	)	PUNCT
ejpam-6997	117	51	are	be	AUX
ejpam-6997	117	52	defined	define	VERB
ejpam-6997	117	53	as	as	SCONJ
ejpam-6997	117	54	follows	follow	VERB
ejpam-6997	117	55	:	:	PUNCT
ejpam-6997	117	56	(	(	PUNCT
ejpam-6997	117	57	1	1	X
ejpam-6997	117	58	)	)	PUNCT
ejpam-6997	117	59	mr(e	mr(e	NOUN
ejpam-6997	117	60	)	)	PUNCT
ejpam-6997	118	1	=	=	PRON
ejpam-6997	119	1	{	{	PUNCT
ejpam-6997	119	2	π	π	PROPN
ejpam-6997	119	3	∈	∈	PROPN
ejpam-6997	119	4	ℵ	ℵ	NOUN
ejpam-6997	119	5	:	:	PUNCT
ejpam-6997	119	6	eγπ	eγπ	NOUN
ejpam-6997	119	7	}	}	PUNCT
ejpam-6997	119	8	.	.	PUNCT
ejpam-6997	120	1	(	(	PUNCT
ejpam-6997	120	2	2	2	NUM
ejpam-6997	120	3	)	)	PUNCT
ejpam-6997	120	4	ml(e	ml(e	NUM
ejpam-6997	120	5	)	)	PUNCT
ejpam-6997	120	6	=	=	PRON
ejpam-6997	121	1	{	{	PUNCT
ejpam-6997	121	2	π	π	PROPN
ejpam-6997	121	3	∈	∈	PROPN
ejpam-6997	121	4	ℵ	ℵ	X
ejpam-6997	121	5	:	:	PUNCT
ejpam-6997	121	6	πγe	πγe	NOUN
ejpam-6997	121	7	}	}	PUNCT
ejpam-6997	121	8	.	.	PUNCT
ejpam-6997	122	1	(	(	PUNCT
ejpam-6997	122	2	3	3	X
ejpam-6997	122	3	)	)	PUNCT
ejpam-6997	122	4	m⟨r⟩(e	m⟨r⟩(e	PROPN
ejpam-6997	122	5	)	)	PUNCT
ejpam-6997	123	1	=	=	PRON
ejpam-6997	123	2	{	{	PUNCT
ejpam-6997	123	3	⊓e∈mr(π)mr(π	⊓e∈mr(π)mr(π	PROPN
ejpam-6997	123	4	)	)	PUNCT
ejpam-6997	123	5	:	:	PUNCT
ejpam-6997	124	1	∃	∃	PROPN
ejpam-6997	124	2	mr(π	mr(π	PUNCT
ejpam-6997	124	3	)	)	PUNCT
ejpam-6997	124	4	containing	contain	VERB
ejpam-6997	124	5	e	e	NOUN
ejpam-6997	124	6	,	,	PUNCT
ejpam-6997	124	7	ϕ	ϕ	X
ejpam-6997	124	8	:	:	PUNCT
ejpam-6997	124	9	otherwise	otherwise	ADV
ejpam-6997	124	10	.	.	PUNCT
ejpam-6997	125	1	(	(	PUNCT
ejpam-6997	125	2	4	4	X
ejpam-6997	125	3	)	)	PUNCT
ejpam-6997	125	4	m⟨l⟩(e	m⟨l⟩(e	NOUN
ejpam-6997	125	5	)	)	PUNCT
ejpam-6997	125	6	=	=	PRON
ejpam-6997	125	7	{	{	PUNCT
ejpam-6997	125	8	⊓e∈ml(π)ml(π	⊓e∈ml(π)ml(π	PROPN
ejpam-6997	125	9	)	)	PUNCT
ejpam-6997	125	10	:	:	PUNCT
ejpam-6997	126	1	∃	∃	PROPN
ejpam-6997	126	2	ml(π	ml(π	PROPN
ejpam-6997	126	3	)	)	PUNCT
ejpam-6997	126	4	containing	contain	VERB
ejpam-6997	126	5	e	e	NOUN
ejpam-6997	126	6	,	,	PUNCT
ejpam-6997	126	7	ϕ	ϕ	X
ejpam-6997	126	8	:	:	PUNCT
ejpam-6997	126	9	otherwise	otherwise	ADV
ejpam-6997	126	10	.	.	PUNCT
ejpam-6997	126	11	.	.	PUNCT
ejpam-6997	127	1	(	(	PUNCT
ejpam-6997	127	2	5	5	NUM
ejpam-6997	127	3	)	)	PUNCT
ejpam-6997	127	4	mi(e	mi(e	NOUN
ejpam-6997	127	5	)	)	PUNCT
ejpam-6997	127	6	=	=	SYM
ejpam-6997	127	7	mr(e	mr(e	NOUN
ejpam-6997	127	8	)	)	PUNCT
ejpam-6997	128	1	⊓ml(e	⊓ml(e	PROPN
ejpam-6997	128	2	)	)	PUNCT
ejpam-6997	128	3	.	.	PUNCT
ejpam-6997	129	1	(	(	PUNCT
ejpam-6997	129	2	6	6	NUM
ejpam-6997	129	3	)	)	PUNCT
ejpam-6997	129	4	mu(e	mu(e	NOUN
ejpam-6997	129	5	)	)	PUNCT
ejpam-6997	129	6	=	=	SYM
ejpam-6997	129	7	mr(e	mr(e	NOUN
ejpam-6997	129	8	)	)	PUNCT
ejpam-6997	129	9	⊔ml(e	⊔ml(e	NOUN
ejpam-6997	129	10	)	)	PUNCT
ejpam-6997	129	11	.	.	PUNCT
ejpam-6997	130	1	(	(	PUNCT
ejpam-6997	130	2	7	7	X
ejpam-6997	130	3	)	)	PUNCT
ejpam-6997	130	4	m⟨i⟩(e	m⟨i⟩(e	NOUN
ejpam-6997	130	5	)	)	PUNCT
ejpam-6997	130	6	=	=	SYM
ejpam-6997	130	7	m⟨r⟩(e	m⟨r⟩(e	PROPN
ejpam-6997	130	8	)	)	PUNCT
ejpam-6997	130	9	⊓m⟨l⟩(e	⊓m⟨l⟩(e	NOUN
ejpam-6997	130	10	)	)	PUNCT
ejpam-6997	130	11	.	.	PUNCT
ejpam-6997	131	1	(	(	PUNCT
ejpam-6997	131	2	8)	8)	NUM
ejpam-6997	131	3	m⟨u⟩(e	m⟨u⟩(e	NUM
ejpam-6997	131	4	)	)	PUNCT
ejpam-6997	131	5	=	=	SYM
ejpam-6997	131	6	m⟨r⟩(e	m⟨r⟩(e	PROPN
ejpam-6997	131	7	)	)	PUNCT
ejpam-6997	131	8	⊔m⟨l⟩(e	⊔m⟨l⟩(e	NOUN
ejpam-6997	131	9	)	)	PUNCT
ejpam-6997	131	10	.	.	PUNCT
ejpam-6997	132	1	from	from	ADP
ejpam-6997	132	2	now	now	ADV
ejpam-6997	132	3	on	on	ADV
ejpam-6997	132	4	,	,	PUNCT
ejpam-6997	132	5	unless	unless	SCONJ
ejpam-6997	132	6	otherwise	otherwise	ADV
ejpam-6997	132	7	noted	note	VERB
ejpam-6997	132	8	,	,	PUNCT
ejpam-6997	132	9	we	we	PRON
ejpam-6997	132	10	shall	shall	AUX
ejpam-6997	132	11	take	take	VERB
ejpam-6997	132	12	into	into	ADP
ejpam-6997	132	13	ϱ	ϱ	NOUN
ejpam-6997	132	14	=	=	SYM
ejpam-6997	132	15	{	{	PUNCT
ejpam-6997	132	16	r	r	NOUN
ejpam-6997	132	17	,	,	PUNCT
ejpam-6997	132	18	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	132	19	,	,	PUNCT
ejpam-6997	132	20	l	l	NOUN
ejpam-6997	132	21	,	,	PUNCT
ejpam-6997	132	22	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	132	23	,	,	PUNCT
ejpam-6997	132	24	i	i	PRON
ejpam-6997	132	25	,	,	PUNCT
ejpam-6997	132	26	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	132	27	,	,	PUNCT
ejpam-6997	132	28	u	u	NOUN
ejpam-6997	132	29	,	,	PUNCT
ejpam-6997	132	30	⟨u⟩	⟨u⟩	PROPN
ejpam-6997	132	31	}	}	PUNCT
ejpam-6997	132	32	.	.	PUNCT
ejpam-6997	133	1	definition	definition	NOUN
ejpam-6997	133	2	5	5	NUM
ejpam-6997	133	3	.	.	PUNCT
ejpam-6997	134	1	[	[	X
ejpam-6997	134	2	43	43	NUM
ejpam-6997	134	3	]	]	PUNCT
ejpam-6997	134	4	let	let	VERB
ejpam-6997	134	5	us	we	PRON
ejpam-6997	134	6	examine	examine	VERB
ejpam-6997	134	7	a	a	DET
ejpam-6997	134	8	relation	relation	NOUN
ejpam-6997	134	9	γ	γ	NOUN
ejpam-6997	134	10	on	on	ADP
ejpam-6997	134	11	ℵ	ℵ	NOUN
ejpam-6997	134	12	and	and	CCONJ
ejpam-6997	134	13	demonstrate	demonstrate	VERB
ejpam-6997	134	14	a	a	DET
ejpam-6997	134	15	mapping	mapping	NOUN
ejpam-6997	134	16	ξϱ	ξϱ	NOUN
ejpam-6997	134	17	from	from	ADP
ejpam-6997	134	18	ℵ	ℵ	NOUN
ejpam-6997	134	19	to	to	ADP
ejpam-6997	134	20	2ℵ	2ℵ	NUM
ejpam-6997	134	21	that	that	PRON
ejpam-6997	134	22	connects	connect	VERB
ejpam-6997	134	23	each	each	DET
ejpam-6997	134	24	member	member	NOUN
ejpam-6997	134	25	of	of	ADP
ejpam-6997	134	26	ℵ	ℵ	NOUN
ejpam-6997	134	27	to	to	ADP
ejpam-6997	134	28	its	its	PRON
ejpam-6997	134	29	ϱ-nbd	ϱ-nbd	NOUN
ejpam-6997	134	30	in	in	ADP
ejpam-6997	134	31	2ℵ.	2ℵ.	NUM
ejpam-6997	134	32	the	the	DET
ejpam-6997	134	33	triple	triple	ADJ
ejpam-6997	134	34	(	(	PUNCT
ejpam-6997	134	35	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	134	36	,	,	PUNCT
ejpam-6997	134	37	ξϱ	ξϱ	NOUN
ejpam-6997	134	38	)	)	PUNCT
ejpam-6997	134	39	,	,	PUNCT
ejpam-6997	134	40	shortened	shorten	VERB
ejpam-6997	134	41	to	to	ADP
ejpam-6997	134	42	ϱ-ns	ϱ-ns	NOUN
ejpam-6997	134	43	,	,	PUNCT
ejpam-6997	134	44	is	be	AUX
ejpam-6997	134	45	hence	hence	ADV
ejpam-6997	134	46	referred	refer	VERB
ejpam-6997	134	47	to	to	ADP
ejpam-6997	134	48	as	as	ADP
ejpam-6997	134	49	a	a	DET
ejpam-6997	134	50	ϱ-nbd	ϱ-nbd	NOUN
ejpam-6997	134	51	space	space	NOUN
ejpam-6997	134	52	.	.	PUNCT
ejpam-6997	135	1	we	we	PRON
ejpam-6997	135	2	used	use	VERB
ejpam-6997	135	3	the	the	DET
ejpam-6997	135	4	aforementioned	aforementioned	ADJ
ejpam-6997	135	5	nbds	nbds	NOUN
ejpam-6997	135	6	to	to	PART
ejpam-6997	135	7	develop	develop	VERB
ejpam-6997	135	8	new	new	ADJ
ejpam-6997	135	9	lw	lw	NOUN
ejpam-6997	135	10	and	and	CCONJ
ejpam-6997	135	11	up	up	ADP
ejpam-6997	135	12	-	-	PUNCT
ejpam-6997	135	13	ap	ap	NOUN
ejpam-6997	135	14	,	,	PUNCT
ejpam-6997	135	15	as	as	ADV
ejpam-6997	135	16	well	well	ADV
ejpam-6997	135	17	as	as	ADP
ejpam-6997	135	18	accuracy	accuracy	NOUN
ejpam-6997	135	19	(	(	PUNCT
ejpam-6997	135	20	roughness	roughness	NOUN
ejpam-6997	135	21	)	)	PUNCT
ejpam-6997	135	22	requirements	requirement	NOUN
ejpam-6997	135	23	.	.	PUNCT
ejpam-6997	136	1	to	to	PART
ejpam-6997	136	2	improve	improve	VERB
ejpam-6997	136	3	ap	ap	PROPN
ejpam-6997	136	4	quality	quality	NOUN
ejpam-6997	136	5	and	and	CCONJ
ejpam-6997	136	6	accuracy	accuracy	NOUN
ejpam-6997	136	7	,	,	PUNCT
ejpam-6997	136	8	we	we	PRON
ejpam-6997	136	9	compared	compare	VERB
ejpam-6997	136	10	several	several	ADJ
ejpam-6997	136	11	types	type	NOUN
ejpam-6997	136	12	of	of	ADP
ejpam-6997	136	13	nbds	nbds	NOUN
ejpam-6997	136	14	.	.	PUNCT
ejpam-6997	137	1	definition	definition	NOUN
ejpam-6997	137	2	6	6	NUM
ejpam-6997	137	3	.	.	PUNCT
ejpam-6997	138	1	[	[	X
ejpam-6997	138	2	13	13	NUM
ejpam-6997	138	3	,	,	PUNCT
ejpam-6997	138	4	15	15	NUM
ejpam-6997	138	5	,	,	PUNCT
ejpam-6997	138	6	43	43	NUM
ejpam-6997	138	7	,	,	PUNCT
ejpam-6997	138	8	44	44	NUM
ejpam-6997	138	9	]	]	PUNCT
ejpam-6997	138	10	the	the	DET
ejpam-6997	138	11	lw	lw	NOUN
ejpam-6997	138	12	and	and	CCONJ
ejpam-6997	138	13	up	up	ADP
ejpam-6997	138	14	-	-	PUNCT
ejpam-6997	138	15	ap	ap	NOUN
ejpam-6997	138	16	of	of	ADP
ejpam-6997	138	17	each	each	DET
ejpam-6997	138	18	subset	subset	NOUN
ejpam-6997	138	19	∆	∆	PROPN
ejpam-6997	138	20	in	in	ADP
ejpam-6997	138	21	relative	relative	ADJ
ejpam-6997	138	22	to	to	ADP
ejpam-6997	138	23	mϱ(e)nbds	mϱ(e)nbds	NOUN
ejpam-6997	138	24	are	be	AUX
ejpam-6997	138	25	introduced	introduce	VERB
ejpam-6997	138	26	as	as	SCONJ
ejpam-6997	138	27	follows	follow	VERB
ejpam-6997	138	28	:	:	PUNCT
ejpam-6997	138	29	mmϱ(∆	mmϱ(∆	NUM
ejpam-6997	138	30	)	)	PUNCT
ejpam-6997	138	31	=	=	PRON
ejpam-6997	138	32	{	{	PUNCT
ejpam-6997	138	33	e	e	NOUN
ejpam-6997	138	34	∈	∈	PROPN
ejpam-6997	138	35	ℵ	ℵ	NOUN
ejpam-6997	138	36	:	:	PUNCT
ejpam-6997	138	37	mϱ(e	mϱ(e	X
ejpam-6997	138	38	)	)	PUNCT
ejpam-6997	138	39	⊑	⊑	PRON
ejpam-6997	138	40	∆	∆	PROPN
ejpam-6997	138	41	}	}	PUNCT
ejpam-6997	138	42	.	.	PUNCT
ejpam-6997	139	1	mmϱ(∆	mmϱ(∆	NUM
ejpam-6997	139	2	)	)	PUNCT
ejpam-6997	140	1	=	=	PRON
ejpam-6997	140	2	{	{	PUNCT
ejpam-6997	140	3	e	e	NOUN
ejpam-6997	140	4	∈	∈	PROPN
ejpam-6997	140	5	ℵ	ℵ	NOUN
ejpam-6997	140	6	:	:	PUNCT
ejpam-6997	140	7	mϱ(e	mϱ(e	X
ejpam-6997	140	8	)	)	PUNCT
ejpam-6997	141	1	⊓	⊓	PROPN
ejpam-6997	141	2	∆	∆	PROPN
ejpam-6997	141	3	̸=	̸=	PROPN
ejpam-6997	141	4	ϕ	ϕ	NOUN
ejpam-6997	141	5	}	}	PUNCT
ejpam-6997	141	6	.	.	PUNCT
ejpam-6997	141	7	definition	definition	NOUN
ejpam-6997	141	8	7	7	NUM
ejpam-6997	141	9	.	.	PUNCT
ejpam-6997	142	1	[	[	X
ejpam-6997	142	2	12	12	NUM
ejpam-6997	142	3	,	,	PUNCT
ejpam-6997	142	4	13	13	NUM
ejpam-6997	142	5	,	,	PUNCT
ejpam-6997	142	6	15	15	NUM
ejpam-6997	142	7	]	]	PUNCT
ejpam-6997	142	8	the	the	DET
ejpam-6997	142	9	σmϱ-accuracy	σmϱ-accuracy	ADJ
ejpam-6997	142	10	and	and	CCONJ
ejpam-6997	142	11	ℜmϱ-roughness	ℜmϱ-roughness	ADJ
ejpam-6997	142	12	criteria	criterion	NOUN
ejpam-6997	142	13	of	of	ADP
ejpam-6997	142	14	nonempty	nonempty	ADV
ejpam-6997	142	15	set	set	VERB
ejpam-6997	142	16	∆	∆	PROPN
ejpam-6997	142	17	in	in	ADP
ejpam-6997	142	18	regarding	regard	VERB
ejpam-6997	142	19	to	to	ADP
ejpam-6997	142	20	γ	γ	NOUN
ejpam-6997	142	21	are	be	AUX
ejpam-6997	142	22	computed	compute	VERB
ejpam-6997	142	23	as	as	ADP
ejpam-6997	142	24	:	:	PUNCT
ejpam-6997	142	25	a.	a.	NOUN
ejpam-6997	142	26	a.	a.	PROPN
ejpam-6997	142	27	azzam	azzam	PROPN
ejpam-6997	142	28	,	,	PUNCT
ejpam-6997	142	29	m.	m.	NOUN
ejpam-6997	142	30	aldawood	aldawood	PROPN
ejpam-6997	142	31	,	,	PUNCT
ejpam-6997	142	32	b.	b.	PROPN
ejpam-6997	142	33	alreshidi	alreshidi	PROPN
ejpam-6997	142	34	/	/	SYM
ejpam-6997	142	35	eur	eur	PROPN
ejpam-6997	142	36	.	.	PUNCT
ejpam-6997	143	1	j.	j.	PROPN
ejpam-6997	143	2	pure	pure	PROPN
ejpam-6997	143	3	appl	appl	PROPN
ejpam-6997	143	4	.	.	PROPN
ejpam-6997	143	5	math	math	PROPN
ejpam-6997	143	6	,	,	PUNCT
ejpam-6997	143	7	18	18	NUM
ejpam-6997	143	8	(	(	PUNCT
ejpam-6997	143	9	4	4	NUM
ejpam-6997	143	10	)	)	PUNCT
ejpam-6997	143	11	(	(	PUNCT
ejpam-6997	143	12	2025	2025	NUM
ejpam-6997	143	13	)	)	PUNCT
ejpam-6997	143	14	,	,	PUNCT
ejpam-6997	143	15	6997	6997	NUM
ejpam-6997	143	16	6	6	NUM
ejpam-6997	143	17	of	of	ADP
ejpam-6997	143	18	31	31	NUM
ejpam-6997	143	19	σmϱ(∆	σmϱ(∆	NOUN
ejpam-6997	143	20	)	)	PUNCT
ejpam-6997	144	1	=	=	VERB
ejpam-6997	144	2	|mmϱ(∆)⊓∆|	|mmϱ(∆)⊓∆|	PROPN
ejpam-6997	144	3	|mmϱ(∆)⊔∆|	|mmϱ(∆)⊔∆|	PROPN
ejpam-6997	144	4	,	,	PUNCT
ejpam-6997	144	5	and	and	CCONJ
ejpam-6997	144	6	ℜmϱ(∆	ℜmϱ(∆	NUM
ejpam-6997	144	7	)	)	PUNCT
ejpam-6997	144	8	=	=	SYM
ejpam-6997	144	9	1	1	NUM
ejpam-6997	144	10	−	−	NUM
ejpam-6997	144	11	σmϱ(∆	σmϱ(∆	NUM
ejpam-6997	144	12	)	)	PUNCT
ejpam-6997	144	13	.	.	PUNCT
ejpam-6997	145	1	definition	definition	NOUN
ejpam-6997	145	2	8	8	NUM
ejpam-6997	145	3	.	.	PUNCT
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ejpam-6997	146	2	1	1	NUM
ejpam-6997	146	3	,	,	PUNCT
ejpam-6997	146	4	2	2	NUM
ejpam-6997	146	5	]	]	PUNCT
ejpam-6997	146	6	let	let	VERB
ejpam-6997	146	7	γ1	γ1	NOUN
ejpam-6997	146	8	and	and	CCONJ
ejpam-6997	146	9	γ2	γ2	PROPN
ejpam-6997	146	10	be	be	AUX
ejpam-6997	146	11	relations	relation	NOUN
ejpam-6997	146	12	on	on	ADP
ejpam-6997	146	13	ℵ	ℵ	DET
ejpam-6997	146	14	such	such	ADJ
ejpam-6997	146	15	that	that	DET
ejpam-6997	146	16	γ1	γ1	PROPN
ejpam-6997	146	17	⊑	⊑	PROPN
ejpam-6997	146	18	γ2	γ2	PROPN
ejpam-6997	146	19	.	.	PUNCT
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ejpam-6997	147	2	monotonicity	monotonicity	NOUN
ejpam-6997	147	3	property	property	NOUN
ejpam-6997	147	4	in	in	ADP
ejpam-6997	147	5	accuracy	accuracy	NOUN
ejpam-6997	147	6	and	and	CCONJ
ejpam-6997	147	7	roughness	roughness	NOUN
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ejpam-6997	147	9	any	any	DET
ejpam-6997	147	10	set	set	NOUN
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ejpam-6997	147	12	demonstrated	demonstrate	VERB
ejpam-6997	147	13	by	by	ADP
ejpam-6997	147	14	ap	ap	PROPN
ejpam-6997	147	15	obtained	obtain	VERB
ejpam-6997	147	16	from	from	ADP
ejpam-6997	147	17	m	m	PROPN
ejpam-6997	147	18	-nbds	-nbds	NOUN
ejpam-6997	147	19	,	,	PUNCT
ejpam-6997	147	20	σmϱ1(∆	σmϱ1(∆	NOUN
ejpam-6997	147	21	)	)	PUNCT
ejpam-6997	147	22	≥	≥	NOUN
ejpam-6997	147	23	σmϱ2(∆	σmϱ2(∆	NOUN
ejpam-6997	147	24	)	)	PUNCT
ejpam-6997	147	25	,	,	PUNCT
ejpam-6997	147	26	and	and	CCONJ
ejpam-6997	147	27	ℜmϱ1(∆	ℜmϱ1(∆	VERB
ejpam-6997	147	28	)	)	PUNCT
ejpam-6997	147	29	≤	≤	NUM
ejpam-6997	147	30	ℜmϱ2(∆	ℜmϱ2(∆	NOUN
ejpam-6997	147	31	)	)	PUNCT
ejpam-6997	147	32	,	,	PUNCT
ejpam-6997	147	33	in	in	ADP
ejpam-6997	147	34	that	that	DET
ejpam-6997	147	35	order	order	NOUN
ejpam-6997	147	36	.	.	PUNCT
ejpam-6997	148	1	definition	definition	NOUN
ejpam-6997	148	2	9	9	NUM
ejpam-6997	148	3	.	.	PUNCT
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ejpam-6997	149	2	16	16	NUM
ejpam-6997	149	3	,	,	PUNCT
ejpam-6997	149	4	17	17	NUM
ejpam-6997	149	5	]	]	PUNCT
ejpam-6997	149	6	let	let	VERB
ejpam-6997	149	7	us	we	PRON
ejpam-6997	149	8	examine	examine	VERB
ejpam-6997	149	9	a	a	DET
ejpam-6997	149	10	relation	relation	NOUN
ejpam-6997	149	11	γ	γ	X
ejpam-6997	149	12	on	on	ADP
ejpam-6997	149	13	ℵ.	ℵ.	PROPN
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ejpam-6997	150	2	h	h	NOUN
ejpam-6997	150	3	-	-	PUNCT
ejpam-6997	150	4	nbds	nbds	NOUN
ejpam-6997	150	5	of	of	ADP
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ejpam-6997	150	7	element	element	NOUN
ejpam-6997	150	8	e	e	NOUN
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ejpam-6997	150	10	ℵ	ℵ	NOUN
ejpam-6997	150	11	for	for	ADP
ejpam-6997	150	12	each	each	DET
ejpam-6997	150	13	ϱ	ϱ	NOUN
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ejpam-6997	150	15	expressed	express	VERB
ejpam-6997	150	16	as	as	SCONJ
ejpam-6997	150	17	follows	follow	VERB
ejpam-6997	150	18	:	:	PUNCT
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ejpam-6997	150	20	1	1	X
ejpam-6997	150	21	)	)	PUNCT
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ejpam-6997	150	23	)	)	PUNCT
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ejpam-6997	151	5	ℵ	ℵ	NOUN
ejpam-6997	151	6	:	:	PUNCT
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ejpam-6997	152	3	)	)	PUNCT
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ejpam-6997	152	5	)	)	PUNCT
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ejpam-6997	153	1	{	{	PUNCT
ejpam-6997	153	2	π	π	PROPN
ejpam-6997	153	3	∈	∈	PROPN
ejpam-6997	153	4	ℵ	ℵ	NOUN
ejpam-6997	153	5	:	:	PUNCT
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ejpam-6997	154	2	3	3	X
ejpam-6997	154	3	)	)	PUNCT
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ejpam-6997	154	5	)	)	PUNCT
ejpam-6997	155	1	=	=	SYM
ejpam-6997	155	2	hr(e	hr(e	NOUN
ejpam-6997	155	3	)	)	PUNCT
ejpam-6997	155	4	⊓hl(e	⊓hl(e	NUM
ejpam-6997	155	5	)	)	PUNCT
ejpam-6997	155	6	.	.	PUNCT
ejpam-6997	156	1	(	(	PUNCT
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ejpam-6997	156	3	)	)	PUNCT
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ejpam-6997	156	7	hr(e	hr(e	NOUN
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ejpam-6997	157	1	(	(	PUNCT
ejpam-6997	157	2	5	5	X
ejpam-6997	157	3	)	)	PUNCT
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ejpam-6997	157	7	{	{	PUNCT
ejpam-6997	157	8	π	π	PROPN
ejpam-6997	157	9	∈	∈	PROPN
ejpam-6997	157	10	ℵ	ℵ	X
ejpam-6997	157	11	:	:	PUNCT
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ejpam-6997	158	2	6	6	NUM
ejpam-6997	158	3	)	)	PUNCT
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ejpam-6997	159	2	π	π	PROPN
ejpam-6997	159	3	∈	∈	PROPN
ejpam-6997	159	4	ℵ	ℵ	NOUN
ejpam-6997	159	5	:	:	PUNCT
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ejpam-6997	160	2	7	7	X
ejpam-6997	160	3	)	)	PUNCT
ejpam-6997	160	4	h⟨i⟩(e	h⟨i⟩(e	NOUN
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ejpam-6997	160	10	)	)	PUNCT
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ejpam-6997	161	4	)	)	PUNCT
ejpam-6997	161	5	=	=	SYM
ejpam-6997	161	6	h⟨r⟩(e	h⟨r⟩(e	NOUN
ejpam-6997	161	7	)	)	PUNCT
ejpam-6997	161	8	⊔h⟨l⟩(e	⊔h⟨l⟩(e	NOUN
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ejpam-6997	161	10	.	.	PUNCT
ejpam-6997	162	1	definition	definition	NOUN
ejpam-6997	162	2	10	10	NUM
ejpam-6997	162	3	.	.	PUNCT
ejpam-6997	163	1	[	[	X
ejpam-6997	163	2	29	29	NUM
ejpam-6997	163	3	]	]	PUNCT
ejpam-6997	163	4	let	let	VERB
ejpam-6997	163	5	us	we	PRON
ejpam-6997	163	6	examine	examine	VERB
ejpam-6997	163	7	a	a	DET
ejpam-6997	163	8	relation	relation	NOUN
ejpam-6997	163	9	γ	γ	X
ejpam-6997	163	10	on	on	ADP
ejpam-6997	163	11	ℵ.	ℵ.	PROPN
ejpam-6997	164	1	the	the	DET
ejpam-6997	164	2	k	k	NOUN
ejpam-6997	164	3	-	-	NOUN
ejpam-6997	164	4	nbds	nbds	NOUN
ejpam-6997	164	5	of	of	ADP
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ejpam-6997	164	8	e	e	NOUN
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ejpam-6997	164	15	expressed	express	VERB
ejpam-6997	164	16	as	as	SCONJ
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ejpam-6997	164	18	:	:	PUNCT
ejpam-6997	164	19	(	(	PUNCT
ejpam-6997	164	20	1	1	X
ejpam-6997	164	21	)	)	PUNCT
ejpam-6997	164	22	kr(e	kr(e	NOUN
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ejpam-6997	164	24	⊑	⊑	X
ejpam-6997	164	25	{	{	PUNCT
ejpam-6997	164	26	π	π	PROPN
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ejpam-6997	164	28	ℵ	ℵ	NOUN
ejpam-6997	164	29	:	:	PUNCT
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ejpam-6997	167	2	π	π	PROPN
ejpam-6997	167	3	∈	∈	PROPN
ejpam-6997	167	4	ℵ	ℵ	NOUN
ejpam-6997	167	5	:	:	PUNCT
ejpam-6997	167	6	ml(π	ml(π	NOUN
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ejpam-6997	167	9	ml(e	ml(e	NOUN
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ejpam-6997	173	3	)	)	PUNCT
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ejpam-6997	173	8	π	π	PROPN
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ejpam-6997	173	10	ℵ	ℵ	NOUN
ejpam-6997	173	11	:	:	PUNCT
ejpam-6997	173	12	m⟨l⟩(π	m⟨l⟩(π	NUM
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ejpam-6997	173	14	⊑	⊑	PRON
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ejpam-6997	176	26	⊔	⊔	NOUN
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ejpam-6997	176	28	)	)	PUNCT
ejpam-6997	176	29	.	.	PUNCT
ejpam-6997	177	1	definition	definition	NOUN
ejpam-6997	177	2	11	11	NUM
ejpam-6997	177	3	.	.	PUNCT
ejpam-6997	178	1	[	[	X
ejpam-6997	178	2	45	45	NUM
ejpam-6997	178	3	]	]	PUNCT
ejpam-6997	178	4	let	let	VERB
ejpam-6997	178	5	us	we	PRON
ejpam-6997	178	6	examine	examine	VERB
ejpam-6997	178	7	a	a	DET
ejpam-6997	178	8	relation	relation	NOUN
ejpam-6997	178	9	γ	γ	X
ejpam-6997	178	10	on	on	ADP
ejpam-6997	178	11	ℵ.	ℵ.	PROPN
ejpam-6997	178	12	the	the	DET
ejpam-6997	178	13	∦-nbds	∦-nbds	NOUN
ejpam-6997	178	14	of	of	ADP
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ejpam-6997	178	20	for	for	ADP
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ejpam-6997	178	22	ϱ	ϱ	NOUN
ejpam-6997	178	23	are	be	AUX
ejpam-6997	178	24	expressed	express	VERB
ejpam-6997	178	25	as	as	SCONJ
ejpam-6997	178	26	follows	follow	VERB
ejpam-6997	178	27	:	:	PUNCT
ejpam-6997	178	28	(	(	PUNCT
ejpam-6997	178	29	1	1	NUM
ejpam-6997	178	30	)	)	PUNCT
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ejpam-6997	178	32	)	)	PUNCT
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ejpam-6997	179	4	ℵ	ℵ	NOUN
ejpam-6997	179	5	:	:	PUNCT
ejpam-6997	179	6	mr(e	mr(e	NOUN
ejpam-6997	179	7	)	)	PUNCT
ejpam-6997	179	8	⊑	⊑	PRON
ejpam-6997	179	9	mr(π	mr(π	PUNCT
ejpam-6997	179	10	)	)	PUNCT
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ejpam-6997	181	4	ℵ	ℵ	NOUN
ejpam-6997	181	5	:	:	PUNCT
ejpam-6997	181	6	ml(e	ml(e	NUM
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ejpam-6997	181	9	ml(π	ml(π	NOUN
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ejpam-6997	182	3	)	)	PUNCT
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ejpam-6997	182	5	)	)	PUNCT
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ejpam-6997	183	1	(	(	PUNCT
ejpam-6997	183	2	4	4	NUM
ejpam-6997	183	3	)	)	PUNCT
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ejpam-6997	183	5	)	)	PUNCT
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ejpam-6997	183	7	∦r(e	∦r(e	NOUN
ejpam-6997	183	8	)	)	PUNCT
ejpam-6997	183	9	⊔	⊔	NUM
ejpam-6997	183	10	∦l(e	∦l(e	NOUN
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ejpam-6997	184	1	(	(	PUNCT
ejpam-6997	184	2	5	5	NUM
ejpam-6997	184	3	)	)	PUNCT
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ejpam-6997	184	5	)	)	PUNCT
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ejpam-6997	185	1	{	{	PUNCT
ejpam-6997	185	2	π	π	PROPN
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ejpam-6997	185	4	ℵ	ℵ	X
ejpam-6997	185	5	:	:	PUNCT
ejpam-6997	185	6	m⟨r⟩(e	m⟨r⟩(e	NUM
ejpam-6997	185	7	)	)	PUNCT
ejpam-6997	185	8	⊑	⊑	PRON
ejpam-6997	185	9	m⟨r⟩(π	m⟨r⟩(π	NOUN
ejpam-6997	185	10	)	)	PUNCT
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ejpam-6997	186	2	6	6	NUM
ejpam-6997	186	3	)	)	PUNCT
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ejpam-6997	186	5	)	)	PUNCT
ejpam-6997	186	6	=	=	SYM
ejpam-6997	187	1	{	{	PUNCT
ejpam-6997	187	2	π	π	PROPN
ejpam-6997	187	3	∈	∈	PROPN
ejpam-6997	187	4	ℵ	ℵ	NOUN
ejpam-6997	187	5	:	:	PUNCT
ejpam-6997	187	6	m⟨l⟩(e	m⟨l⟩(e	NOUN
ejpam-6997	187	7	)	)	PUNCT
ejpam-6997	187	8	⊑	⊑	PRON
ejpam-6997	187	9	m⟨l⟩(π	m⟨l⟩(π	PROPN
ejpam-6997	187	10	)	)	PUNCT
ejpam-6997	187	11	}	}	PUNCT
ejpam-6997	187	12	.	.	PUNCT
ejpam-6997	188	1	(	(	PUNCT
ejpam-6997	188	2	7	7	NUM
ejpam-6997	188	3	)	)	PUNCT
ejpam-6997	188	4	∦⟨i⟩(e	∦⟨i⟩(e	NOUN
ejpam-6997	188	5	)	)	PUNCT
ejpam-6997	188	6	=	=	SYM
ejpam-6997	188	7	∦⟨r⟩(e	∦⟨r⟩(e	X
ejpam-6997	188	8	)	)	PUNCT
ejpam-6997	188	9	⊓	⊓	PROPN
ejpam-6997	188	10	∦⟨l⟩(e	∦⟨l⟩(e	NUM
ejpam-6997	188	11	)	)	PUNCT
ejpam-6997	188	12	.	.	PUNCT
ejpam-6997	189	1	(	(	PUNCT
ejpam-6997	189	2	8)	8)	NUM
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ejpam-6997	189	4	)	)	PUNCT
ejpam-6997	189	5	=	=	SYM
ejpam-6997	189	6	∦⟨r⟩(e	∦⟨r⟩(e	X
ejpam-6997	189	7	)	)	PUNCT
ejpam-6997	189	8	⊔	⊔	NUM
ejpam-6997	189	9	∦⟨l⟩(e	∦⟨l⟩(e	NOUN
ejpam-6997	189	10	)	)	PUNCT
ejpam-6997	189	11	.	.	PUNCT
ejpam-6997	190	1	2.3	2.3	NUM
ejpam-6997	190	2	.	.	PUNCT
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ejpam-6997	191	2	ϱ-neighborhood	ϱ-neighborhood	PROPN
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ejpam-6997	191	4	this	this	DET
ejpam-6997	191	5	section	section	NOUN
ejpam-6997	191	6	is	be	AUX
ejpam-6997	191	7	dedicated	dedicate	VERB
ejpam-6997	191	8	to	to	ADP
ejpam-6997	191	9	introducing	introduce	VERB
ejpam-6997	191	10	the	the	DET
ejpam-6997	191	11	concept	concept	NOUN
ejpam-6997	191	12	of	of	ADP
ejpam-6997	191	13	cardinality	cardinality	PROPN
ejpam-6997	191	14	nbds	nbds	NOUN
ejpam-6997	191	15	,	,	PUNCT
ejpam-6997	191	16	in	in	ADP
ejpam-6997	191	17	accordance	accordance	NOUN
ejpam-6997	191	18	with	with	ADP
ejpam-6997	191	19	any	any	DET
ejpam-6997	191	20	binary	binary	ADJ
ejpam-6997	191	21	relation	relation	NOUN
ejpam-6997	191	22	.	.	PUNCT
ejpam-6997	192	1	the	the	DET
ejpam-6997	192	2	goal	goal	NOUN
ejpam-6997	192	3	of	of	ADP
ejpam-6997	192	4	studying	study	VERB
ejpam-6997	192	5	cardinality	cardinality	NOUN
ejpam-6997	192	6	nbds	nbds	NOUN
ejpam-6997	192	7	is	be	AUX
ejpam-6997	192	8	to	to	PART
ejpam-6997	192	9	address	address	VERB
ejpam-6997	192	10	specific	specific	ADJ
ejpam-6997	192	11	situations	situation	NOUN
ejpam-6997	192	12	where	where	SCONJ
ejpam-6997	192	13	the	the	DET
ejpam-6997	192	14	number	number	NOUN
ejpam-6997	192	15	of	of	ADP
ejpam-6997	192	16	members	member	NOUN
ejpam-6997	192	17	in	in	ADP
ejpam-6997	192	18	mϱ-nbds	mϱ-nbds	NOUN
ejpam-6997	192	19	affects	affect	VERB
ejpam-6997	192	20	the	the	DET
ejpam-6997	192	21	situation	situation	NOUN
ejpam-6997	192	22	.	.	PUNCT
ejpam-6997	193	1	we	we	PRON
ejpam-6997	193	2	’ll	’ll	AUX
ejpam-6997	193	3	examine	examine	VERB
ejpam-6997	193	4	their	their	PRON
ejpam-6997	193	5	primary	primary	ADJ
ejpam-6997	193	6	characteristics	characteristic	NOUN
ejpam-6997	193	7	and	and	CCONJ
ejpam-6997	193	8	identify	identify	VERB
ejpam-6997	193	9	the	the	DET
ejpam-6997	193	10	circumstances	circumstance	NOUN
ejpam-6997	193	11	in	in	ADP
ejpam-6997	193	12	which	which	PRON
ejpam-6997	193	13	some	some	PRON
ejpam-6997	193	14	of	of	ADP
ejpam-6997	193	15	them	they	PRON
ejpam-6997	193	16	are	be	AUX
ejpam-6997	193	17	the	the	DET
ejpam-6997	193	18	same	same	ADJ
ejpam-6997	193	19	.	.	PUNCT
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ejpam-6997	194	2	examples	example	NOUN
ejpam-6997	194	3	are	be	AUX
ejpam-6997	194	4	offered	offer	VERB
ejpam-6997	194	5	to	to	PART
ejpam-6997	194	6	bolster	bolster	VERB
ejpam-6997	194	7	the	the	DET
ejpam-6997	194	8	links	link	NOUN
ejpam-6997	194	9	and	and	CCONJ
ejpam-6997	194	10	outcomes	outcome	NOUN
ejpam-6997	194	11	obtained	obtain	VERB
ejpam-6997	194	12	.	.	PUNCT
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ejpam-6997	195	4	mϱ	mϱ	PROPN
ejpam-6997	195	5	(	(	PUNCT
ejpam-6997	195	6	.	.	PUNCT
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ejpam-6997	195	11	|mϱ(.)|	|mϱ(.)|	PROPN
ejpam-6997	195	12	for	for	ADP
ejpam-6997	195	13	each	each	PRON
ejpam-6997	195	14	ϱ	ϱ	PROPN
ejpam-6997	195	15	∈	∈	PROPN
ejpam-6997	195	16	{	{	PUNCT
ejpam-6997	195	17	r	r	NOUN
ejpam-6997	195	18	,	,	PUNCT
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ejpam-6997	195	22	,	,	PUNCT
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ejpam-6997	195	25	i	i	PRON
ejpam-6997	195	26	,	,	PUNCT
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ejpam-6997	195	28	,	,	PUNCT
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ejpam-6997	195	30	,	,	PUNCT
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ejpam-6997	195	32	}	}	PUNCT
ejpam-6997	195	33	.	.	PUNCT
ejpam-6997	196	1	definition	definition	NOUN
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ejpam-6997	197	2	46	46	NUM
ejpam-6997	197	3	]	]	PUNCT
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ejpam-6997	197	12	e	e	PROPN
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ejpam-6997	197	17	by	by	ADP
ejpam-6997	197	18	cϱ(e	cϱ(e	NOUN
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ejpam-6997	197	22	found	find	VERB
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ejpam-6997	197	33	(	(	PUNCT
ejpam-6997	197	34	1	1	X
ejpam-6997	197	35	)	)	PUNCT
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ejpam-6997	202	2	3	3	X
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ejpam-6997	204	3	)	)	PUNCT
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ejpam-6997	205	1	{	{	PUNCT
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ejpam-6997	234	11	a	a	DET
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ejpam-6997	237	2	46	46	NUM
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ejpam-6997	237	11	a	a	DET
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ejpam-6997	238	7	b	b	X
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ejpam-6997	240	11	a	a	DET
ejpam-6997	240	12	ϱ-ns	ϱ-ns	NOUN
ejpam-6997	240	13	and	and	CCONJ
ejpam-6997	240	14	e	e	PROPN
ejpam-6997	240	15	∈	∈	PROPN
ejpam-6997	240	16	ℵ.	ℵ.	PROPN
ejpam-6997	241	1	then	then	ADV
ejpam-6997	241	2	,	,	PUNCT
ejpam-6997	241	3	e	e	PROPN
ejpam-6997	241	4	∈	∈	PROPN
ejpam-6997	241	5	cϱ(b	cϱ(b	NOUN
ejpam-6997	241	6	)	)	PUNCT
ejpam-6997	241	7	iff	iff	PROPN
ejpam-6997	241	8	cϱ(e	cϱ(e	PUNCT
ejpam-6997	241	9	)	)	PUNCT
ejpam-6997	241	10	=	=	SYM
ejpam-6997	241	11	cϱ(b	cϱ(b	NOUN
ejpam-6997	241	12	)	)	PUNCT
ejpam-6997	241	13	,	,	PUNCT
ejpam-6997	241	14	in	in	ADP
ejpam-6997	241	15	the	the	DET
ejpam-6997	241	16	cases	case	NOUN
ejpam-6997	241	17	of	of	ADP
ejpam-6997	241	18	ϱ	ϱ	ADP
ejpam-6997	241	19	∈	∈	PROPN
ejpam-6997	241	20	{	{	PUNCT
ejpam-6997	241	21	r	r	NOUN
ejpam-6997	241	22	,	,	PUNCT
ejpam-6997	241	23	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	241	24	,	,	PUNCT
ejpam-6997	241	25	l	l	NOUN
ejpam-6997	241	26	,	,	PUNCT
ejpam-6997	241	27	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	241	28	,	,	PUNCT
ejpam-6997	241	29	i	i	PRON
ejpam-6997	241	30	,	,	PUNCT
ejpam-6997	241	31	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	241	32	}	}	PUNCT
ejpam-6997	241	33	.	.	PUNCT
ejpam-6997	242	1	corollary	corollary	ADJ
ejpam-6997	242	2	3	3	NUM
ejpam-6997	242	3	.	.	PUNCT
ejpam-6997	243	1	[	[	X
ejpam-6997	243	2	46	46	NUM
ejpam-6997	243	3	]	]	PUNCT
ejpam-6997	243	4	in	in	ADP
ejpam-6997	243	5	the	the	DET
ejpam-6997	243	6	instances	instance	NOUN
ejpam-6997	243	7	of	of	ADP
ejpam-6997	243	8	ϱ	ϱ	ADP
ejpam-6997	243	9	∈	∈	PROPN
ejpam-6997	243	10	{	{	PUNCT
ejpam-6997	243	11	r	r	NOUN
ejpam-6997	243	12	,	,	PUNCT
ejpam-6997	243	13	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	243	14	,	,	PUNCT
ejpam-6997	243	15	l	l	NOUN
ejpam-6997	243	16	,	,	PUNCT
ejpam-6997	243	17	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	243	18	,	,	PUNCT
ejpam-6997	243	19	i	i	PRON
ejpam-6997	243	20	,	,	PUNCT
ejpam-6997	243	21	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	243	22	}	}	PUNCT
ejpam-6997	243	23	,	,	PUNCT
ejpam-6997	243	24	the	the	DET
ejpam-6997	243	25	relation	relation	NOUN
ejpam-6997	243	26	γ	γ	X
ejpam-6997	243	27	where	where	SCONJ
ejpam-6997	243	28	bγe	bγe	PROPN
ejpam-6997	243	29	⇔	⇔	PROPN
ejpam-6997	243	30	b	b	PROPN
ejpam-6997	243	31	∈	∈	PROPN
ejpam-6997	243	32	cϱ(e	cϱ(e	PUNCT
ejpam-6997	243	33	)	)	PUNCT
ejpam-6997	243	34	is	be	AUX
ejpam-6997	243	35	an	an	DET
ejpam-6997	243	36	equivalence	equivalence	NOUN
ejpam-6997	243	37	.	.	PUNCT
ejpam-6997	244	1	a.	a.	NOUN
ejpam-6997	244	2	a.	a.	PROPN
ejpam-6997	244	3	azzam	azzam	PROPN
ejpam-6997	244	4	,	,	PUNCT
ejpam-6997	244	5	m.	m.	NOUN
ejpam-6997	244	6	aldawood	aldawood	PROPN
ejpam-6997	244	7	,	,	PUNCT
ejpam-6997	244	8	b.	b.	PROPN
ejpam-6997	244	9	alreshidi	alreshidi	PROPN
ejpam-6997	244	10	/	/	SYM
ejpam-6997	244	11	eur	eur	PROPN
ejpam-6997	244	12	.	.	PUNCT
ejpam-6997	245	1	j.	j.	PROPN
ejpam-6997	245	2	pure	pure	PROPN
ejpam-6997	245	3	appl	appl	PROPN
ejpam-6997	245	4	.	.	PROPN
ejpam-6997	245	5	math	math	PROPN
ejpam-6997	245	6	,	,	PUNCT
ejpam-6997	245	7	18	18	NUM
ejpam-6997	245	8	(	(	PUNCT
ejpam-6997	245	9	4	4	NUM
ejpam-6997	245	10	)	)	PUNCT
ejpam-6997	245	11	(	(	PUNCT
ejpam-6997	245	12	2025	2025	NUM
ejpam-6997	245	13	)	)	PUNCT
ejpam-6997	245	14	,	,	PUNCT
ejpam-6997	245	15	6997	6997	NUM
ejpam-6997	245	16	9	9	NUM
ejpam-6997	245	17	of	of	ADP
ejpam-6997	245	18	31	31	NUM
ejpam-6997	245	19	corollary	corollary	ADJ
ejpam-6997	245	20	4	4	NUM
ejpam-6997	245	21	.	.	PUNCT
ejpam-6997	246	1	[	[	X
ejpam-6997	246	2	46	46	NUM
ejpam-6997	246	3	]	]	PUNCT
ejpam-6997	246	4	under	under	ADP
ejpam-6997	246	5	a	a	DET
ejpam-6997	246	6	symmetric	symmetric	ADJ
ejpam-6997	246	7	relation	relation	NOUN
ejpam-6997	246	8	,	,	PUNCT
ejpam-6997	246	9	the	the	DET
ejpam-6997	246	10	cardinality	cardinality	NOUN
ejpam-6997	246	11	nbds	nbds	NOUN
ejpam-6997	246	12	create	create	VERB
ejpam-6997	246	13	a	a	DET
ejpam-6997	246	14	partition	partition	NOUN
ejpam-6997	246	15	for	for	ADP
ejpam-6997	246	16	ℵ	ℵ	NOUN
ejpam-6997	246	17	for	for	ADP
ejpam-6997	246	18	each	each	DET
ejpam-6997	246	19	ϱ.	ϱ.	ADJ
ejpam-6997	246	20	proposition	proposition	NOUN
ejpam-6997	246	21	7	7	NUM
ejpam-6997	246	22	.	.	PUNCT
ejpam-6997	247	1	[	[	X
ejpam-6997	247	2	46	46	NUM
ejpam-6997	247	3	]	]	SYM
ejpam-6997	247	4	cϱ	cϱ	X
ejpam-6997	247	5	=	=	SYM
ejpam-6997	247	6	c⟨ϱ⟩	c⟨ϱ⟩	PROPN
ejpam-6997	247	7	for	for	ADP
ejpam-6997	247	8	ϱ	ϱ	PROPN
ejpam-6997	247	9	belongs	belong	VERB
ejpam-6997	247	10	to	to	ADP
ejpam-6997	247	11	{	{	PUNCT
ejpam-6997	247	12	r	r	NOUN
ejpam-6997	247	13	,	,	PUNCT
ejpam-6997	247	14	l	l	NOUN
ejpam-6997	247	15	,	,	PUNCT
ejpam-6997	247	16	i	i	PRON
ejpam-6997	247	17	,	,	PUNCT
ejpam-6997	247	18	u	u	NOUN
ejpam-6997	247	19	}	}	PUNCT
ejpam-6997	247	20	,	,	PUNCT
ejpam-6997	247	21	if	if	SCONJ
ejpam-6997	247	22	γ	γ	NOUN
ejpam-6997	247	23	is	be	AUX
ejpam-6997	247	24	a	a	DET
ejpam-6997	247	25	preorder	preorder	NOUN
ejpam-6997	247	26	relation	relation	NOUN
ejpam-6997	247	27	on	on	ADP
ejpam-6997	247	28	ℵ.	ℵ.	PROPN
ejpam-6997	247	29	proposition	proposition	NOUN
ejpam-6997	247	30	8	8	NUM
ejpam-6997	247	31	.	.	PUNCT
ejpam-6997	248	1	[	[	X
ejpam-6997	248	2	46	46	NUM
ejpam-6997	248	3	]	]	X
ejpam-6997	248	4	let	let	VERB
ejpam-6997	248	5	(	(	PUNCT
ejpam-6997	248	6	ℵ,γ	ℵ,γ	VERB
ejpam-6997	248	7	,	,	PUNCT
ejpam-6997	248	8	ξϱ	ξϱ	NOUN
ejpam-6997	248	9	)	)	PUNCT
ejpam-6997	248	10	be	be	VERB
ejpam-6997	248	11	a	a	DET
ejpam-6997	248	12	ϱ-ns	ϱ-ns	NOUN
ejpam-6997	248	13	.	.	PUNCT
ejpam-6997	249	1	if	if	SCONJ
ejpam-6997	249	2	e	e	PROPN
ejpam-6997	249	3	∈	∈	PROPN
ejpam-6997	249	4	ℵ	ℵ	NOUN
ejpam-6997	249	5	,	,	PUNCT
ejpam-6997	249	6	then	then	ADV
ejpam-6997	249	7	∦ϱ(e	∦ϱ(e	NOUN
ejpam-6997	249	8	)	)	PUNCT
ejpam-6997	249	9	⊑	⊑	PROPN
ejpam-6997	249	10	cϱ(e)∀ϱ.	cϱ(e)∀ϱ.	VERB
ejpam-6997	249	11	definition	definition	NOUN
ejpam-6997	249	12	13	13	NUM
ejpam-6997	249	13	.	.	PUNCT
ejpam-6997	250	1	[	[	X
ejpam-6997	250	2	46	46	NUM
ejpam-6997	250	3	]	]	X
ejpam-6997	250	4	let	let	VERB
ejpam-6997	250	5	(	(	PUNCT
ejpam-6997	250	6	ℵ,γ	ℵ,γ	VERB
ejpam-6997	250	7	,	,	PUNCT
ejpam-6997	250	8	ξϱ	ξϱ	NOUN
ejpam-6997	250	9	)	)	PUNCT
ejpam-6997	250	10	be	be	VERB
ejpam-6997	250	11	a	a	DET
ejpam-6997	250	12	ϱ-ns	ϱ-ns	NOUN
ejpam-6997	250	13	.	.	PUNCT
ejpam-6997	251	1	based	base	VERB
ejpam-6997	251	2	on	on	ADP
ejpam-6997	251	3	cardinality	cardinality	PROPN
ejpam-6997	251	4	nbds	nbds	NOUN
ejpam-6997	251	5	,	,	PUNCT
ejpam-6997	251	6	the	the	DET
ejpam-6997	251	7	cϱ-lw	cϱ-lw	PROPN
ejpam-6997	251	8	-	-	PUNCT
ejpam-6997	251	9	ap	ap	PROPN
ejpam-6997	251	10	mcϱ(∆	mcϱ(∆	PROPN
ejpam-6997	251	11	)	)	PUNCT
ejpam-6997	251	12	,	,	PUNCT
ejpam-6997	251	13	and	and	CCONJ
ejpam-6997	251	14	cϱ-up	cϱ-up	PROPN
ejpam-6997	251	15	-	-	PUNCT
ejpam-6997	251	16	ap	ap	PROPN
ejpam-6997	251	17	mcϱ(∆	mcϱ(∆	PROPN
ejpam-6997	251	18	)	)	PUNCT
ejpam-6997	251	19	of	of	ADP
ejpam-6997	251	20	a	a	DET
ejpam-6997	251	21	set	set	NOUN
ejpam-6997	251	22	∆	∆	PROPN
ejpam-6997	251	23	,	,	PUNCT
ejpam-6997	251	24	assigned	assign	VERB
ejpam-6997	251	25	as	as	ADP
ejpam-6997	251	26	:	:	PUNCT
ejpam-6997	251	27	mcϱ(∆	mcϱ(∆	NUM
ejpam-6997	251	28	)	)	PUNCT
ejpam-6997	251	29	=	=	PRON
ejpam-6997	251	30	{	{	PUNCT
ejpam-6997	251	31	b	b	PROPN
ejpam-6997	251	32	∈	∈	PROPN
ejpam-6997	251	33	ℵ	ℵ	NOUN
ejpam-6997	251	34	:	:	PUNCT
ejpam-6997	251	35	cϱ(b	cϱ(b	NOUN
ejpam-6997	251	36	)	)	PUNCT
ejpam-6997	251	37	⊑	⊑	PRON
ejpam-6997	251	38	∆	∆	PROPN
ejpam-6997	251	39	}	}	PUNCT
ejpam-6997	251	40	.	.	PUNCT
ejpam-6997	252	1	mcϱ(∆	mcϱ(∆	X
ejpam-6997	252	2	)	)	PUNCT
ejpam-6997	253	1	=	=	PRON
ejpam-6997	253	2	{	{	PUNCT
ejpam-6997	253	3	b	b	PROPN
ejpam-6997	253	4	∈	∈	PROPN
ejpam-6997	253	5	ℵ	ℵ	NOUN
ejpam-6997	253	6	:	:	PUNCT
ejpam-6997	253	7	cϱ(b	cϱ(b	NOUN
ejpam-6997	253	8	)	)	PUNCT
ejpam-6997	254	1	⊓	⊓	PROPN
ejpam-6997	254	2	∆	∆	PROPN
ejpam-6997	254	3	̸=	̸=	PROPN
ejpam-6997	254	4	ϕ	ϕ	NOUN
ejpam-6997	254	5	}	}	PUNCT
ejpam-6997	254	6	.	.	PUNCT
ejpam-6997	255	1	definition	definition	NOUN
ejpam-6997	255	2	14	14	NUM
ejpam-6997	255	3	.	.	PUNCT
ejpam-6997	256	1	[	[	X
ejpam-6997	256	2	46	46	NUM
ejpam-6997	256	3	]	]	X
ejpam-6997	256	4	the	the	DET
ejpam-6997	256	5	cϱ-boundary	cϱ-boundary	ADJ
ejpam-6997	256	6	,	,	PUNCT
ejpam-6997	256	7	cϱ-positive	cϱ-positive	ADJ
ejpam-6997	256	8	,	,	PUNCT
ejpam-6997	256	9	cϱ-negative	cϱ-negative	ADJ
ejpam-6997	256	10	regions	region	NOUN
ejpam-6997	256	11	of	of	ADP
ejpam-6997	256	12	a	a	DET
ejpam-6997	256	13	subset	subset	NOUN
ejpam-6997	256	14	∆	∆	PROPN
ejpam-6997	256	15	within	within	ADP
ejpam-6997	256	16	a	a	DET
ejpam-6997	256	17	ϱ-ns	ϱ-ns	ADV
ejpam-6997	256	18	(	(	PUNCT
ejpam-6997	256	19	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	256	20	,	,	PUNCT
ejpam-6997	256	21	ξϱ	ξϱ	NOUN
ejpam-6997	256	22	)	)	PUNCT
ejpam-6997	256	23	are	be	AUX
ejpam-6997	256	24	identified	identify	VERB
ejpam-6997	256	25	respectively	respectively	ADV
ejpam-6997	256	26	as	as	ADP
ejpam-6997	256	27	:	:	PUNCT
ejpam-6997	256	28	bcϱ(∆	bcϱ(∆	NUM
ejpam-6997	256	29	)	)	PUNCT
ejpam-6997	256	30	=	=	SYM
ejpam-6997	256	31	mcϱ(∆)\mcϱ(∆	mcϱ(∆)\mcϱ(∆	NOUN
ejpam-6997	256	32	)	)	PUNCT
ejpam-6997	256	33	.	.	PUNCT
ejpam-6997	257	1	pcϱ(∆	pcϱ(∆	X
ejpam-6997	257	2	)	)	PUNCT
ejpam-6997	258	1	=	=	SYM
ejpam-6997	258	2	mcϱ(∆	mcϱ(∆	NUM
ejpam-6997	258	3	)	)	PUNCT
ejpam-6997	258	4	.	.	PUNCT
ejpam-6997	259	1	n	n	CCONJ
ejpam-6997	259	2	cϱ(∆	cϱ(∆	NOUN
ejpam-6997	259	3	)	)	PUNCT
ejpam-6997	259	4	=	=	PUNCT
ejpam-6997	260	1	ℵ\mcϱ(∆	ℵ\mcϱ(∆	PROPN
ejpam-6997	260	2	)	)	PUNCT
ejpam-6997	260	3	.	.	PUNCT
ejpam-6997	261	1	definition	definition	NOUN
ejpam-6997	261	2	15	15	NUM
ejpam-6997	261	3	.	.	PUNCT
ejpam-6997	262	1	[	[	X
ejpam-6997	262	2	46	46	NUM
ejpam-6997	262	3	]	]	PUNCT
ejpam-6997	262	4	the	the	DET
ejpam-6997	262	5	cϱ-accuracy	cϱ-accuracy	NOUN
ejpam-6997	262	6	and	and	CCONJ
ejpam-6997	262	7	cϱ-roughness	cϱ-roughness	NOUN
ejpam-6997	262	8	criteria	criterion	NOUN
ejpam-6997	262	9	of	of	ADP
ejpam-6997	262	10	∆	∆	PROPN
ejpam-6997	262	11	̸=	̸=	PROPN
ejpam-6997	262	12	ϕ	ϕ	NOUN
ejpam-6997	262	13	of	of	ADP
ejpam-6997	262	14	a	a	DET
ejpam-6997	262	15	ϱ-ns	ϱ-ns	ADV
ejpam-6997	262	16	(	(	PUNCT
ejpam-6997	262	17	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	262	18	,	,	PUNCT
ejpam-6997	262	19	ξϱ	ξϱ	NOUN
ejpam-6997	262	20	)	)	PUNCT
ejpam-6997	262	21	are	be	AUX
ejpam-6997	262	22	identified	identify	VERB
ejpam-6997	262	23	respectively	respectively	ADV
ejpam-6997	262	24	as	as	ADP
ejpam-6997	262	25	:	:	PUNCT
ejpam-6997	262	26	σcϱ(∆	σcϱ(∆	NUM
ejpam-6997	262	27	)	)	PUNCT
ejpam-6997	262	28	=	=	SYM
ejpam-6997	263	1	|mcϱ	|mcϱ	NOUN
ejpam-6997	263	2	(	(	PUNCT
ejpam-6997	263	3	∆)|	∆)|	NOUN
ejpam-6997	263	4	|mcϱ	|mcϱ	NUM
ejpam-6997	263	5	(	(	PUNCT
ejpam-6997	263	6	∆)|	∆)|	NOUN
ejpam-6997	263	7	,	,	PUNCT
ejpam-6997	263	8	|m	|m	NOUN
ejpam-6997	263	9	cϱ(∆)|	cϱ(∆)|	PROPN
ejpam-6997	263	10	̸=	̸=	PROPN
ejpam-6997	263	11	0	0	NUM
ejpam-6997	263	12	.	.	PUNCT
ejpam-6997	263	13	ℜcϱ(∆	ℜcϱ(∆	NUM
ejpam-6997	263	14	)	)	PUNCT
ejpam-6997	263	15	=	=	SYM
ejpam-6997	263	16	1	1	NUM
ejpam-6997	263	17	−	−	NOUN
ejpam-6997	263	18	σcϱ(∆	σcϱ(∆	PROPN
ejpam-6997	263	19	)	)	PUNCT
ejpam-6997	263	20	.	.	PUNCT
ejpam-6997	264	1	theorem	theorem	NOUN
ejpam-6997	264	2	1	1	NUM
ejpam-6997	264	3	.	.	PUNCT
ejpam-6997	265	1	[	[	X
ejpam-6997	265	2	46	46	NUM
ejpam-6997	265	3	]	]	X
ejpam-6997	265	4	let	let	VERB
ejpam-6997	265	5	(	(	PUNCT
ejpam-6997	265	6	ℵ,γ	ℵ,γ	VERB
ejpam-6997	265	7	,	,	PUNCT
ejpam-6997	265	8	ξϱ	ξϱ	NOUN
ejpam-6997	265	9	)	)	PUNCT
ejpam-6997	265	10	be	be	VERB
ejpam-6997	265	11	a	a	DET
ejpam-6997	265	12	ϱ-ns	ϱ-ns	NOUN
ejpam-6997	265	13	.	.	PUNCT
ejpam-6997	266	1	based	base	VERB
ejpam-6997	266	2	on	on	ADP
ejpam-6997	266	3	cardinality	cardinality	PROPN
ejpam-6997	266	4	nbds	nbds	NOUN
ejpam-6997	266	5	,	,	PUNCT
ejpam-6997	266	6	the	the	DET
ejpam-6997	266	7	family	family	NOUN
ejpam-6997	266	8	τcϱ	τcϱ	NOUN
ejpam-6997	266	9	=	=	PUNCT
ejpam-6997	266	10	{	{	PUNCT
ejpam-6997	266	11	∆	∆	PROPN
ejpam-6997	266	12	⊑	⊑	PRON
ejpam-6997	266	13	ℵ	ℵ	X
ejpam-6997	266	14	:	:	PUNCT
ejpam-6997	266	15	∀e	∀e	PROPN
ejpam-6997	266	16	∈	∈	PROPN
ejpam-6997	266	17	∆	∆	PROPN
ejpam-6997	266	18	,	,	PUNCT
ejpam-6997	266	19	cϱ(e	cϱ(e	PUNCT
ejpam-6997	266	20	)	)	PUNCT
ejpam-6997	266	21	⊑	⊑	PRON
ejpam-6997	266	22	∆	∆	X
ejpam-6997	266	23	}	}	PUNCT
ejpam-6997	266	24	is	be	AUX
ejpam-6997	266	25	a	a	DET
ejpam-6997	266	26	topology	topology	NOUN
ejpam-6997	266	27	on	on	ADP
ejpam-6997	266	28	ℵ	ℵ	NOUN
ejpam-6997	266	29	,	,	PUNCT
ejpam-6997	266	30	for	for	ADP
ejpam-6997	266	31	each	each	DET
ejpam-6997	266	32	ϱ.	ϱ.	NOUN
ejpam-6997	266	33	lemma	lemma	PROPN
ejpam-6997	267	1	1	1	NUM
ejpam-6997	267	2	.	.	PUNCT
ejpam-6997	268	1	[	[	X
ejpam-6997	268	2	46	46	NUM
ejpam-6997	268	3	]	]	X
ejpam-6997	268	4	let	let	VERB
ejpam-6997	268	5	(	(	PUNCT
ejpam-6997	268	6	ℵ,γ	ℵ,γ	VERB
ejpam-6997	268	7	,	,	PUNCT
ejpam-6997	268	8	ξϱ	ξϱ	NOUN
ejpam-6997	268	9	)	)	PUNCT
ejpam-6997	268	10	be	be	VERB
ejpam-6997	268	11	a	a	DET
ejpam-6997	268	12	ϱ-ns	ϱ-ns	NOUN
ejpam-6997	268	13	and	and	CCONJ
ejpam-6997	268	14	e	e	ADP
ejpam-6997	268	15	∈	∈	PROPN
ejpam-6997	268	16	ℵ.	ℵ.	PROPN
ejpam-6997	269	1	if	if	SCONJ
ejpam-6997	269	2	ϱ	ϱ	ADP
ejpam-6997	269	3	∈	∈	PROPN
ejpam-6997	269	4	{	{	PUNCT
ejpam-6997	269	5	r	r	NOUN
ejpam-6997	269	6	,	,	PUNCT
ejpam-6997	269	7	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	269	8	,	,	PUNCT
ejpam-6997	269	9	l	l	NOUN
ejpam-6997	269	10	,	,	PUNCT
ejpam-6997	269	11	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	269	12	,	,	PUNCT
ejpam-6997	269	13	i	i	PRON
ejpam-6997	269	14	,	,	PUNCT
ejpam-6997	269	15	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	269	16	}	}	PUNCT
ejpam-6997	269	17	,	,	PUNCT
ejpam-6997	269	18	then	then	ADV
ejpam-6997	269	19	cϱ(e	cϱ(e	PUNCT
ejpam-6997	269	20	)	)	PUNCT
ejpam-6997	269	21	is	be	AUX
ejpam-6997	269	22	τcϱ-open	τcϱ-open	ADJ
ejpam-6997	269	23	set	set	NOUN
ejpam-6997	269	24	.	.	PUNCT
ejpam-6997	270	1	definition	definition	NOUN
ejpam-6997	270	2	16	16	NUM
ejpam-6997	270	3	.	.	PUNCT
ejpam-6997	271	1	[	[	X
ejpam-6997	271	2	42	42	NUM
ejpam-6997	271	3	]	]	PUNCT
ejpam-6997	271	4	a	a	DET
ejpam-6997	271	5	nonempty	nonempty	ADJ
ejpam-6997	271	6	subcollection	subcollection	NOUN
ejpam-6997	271	7	g	g	PROPN
ejpam-6997	271	8	⊑	⊑	PROPN
ejpam-6997	271	9	2ℵ	2ℵ	PROPN
ejpam-6997	271	10	is	be	AUX
ejpam-6997	271	11	defined	define	VERB
ejpam-6997	271	12	as	as	ADP
ejpam-6997	271	13	a	a	DET
ejpam-6997	271	14	grill	grill	NOUN
ejpam-6997	271	15	on	on	ADP
ejpam-6997	271	16	ℵ	ℵ	NOUN
ejpam-6997	271	17	if	if	SCONJ
ejpam-6997	271	18	the	the	DET
ejpam-6997	271	19	following	following	NOUN
ejpam-6997	271	20	are	be	AUX
ejpam-6997	271	21	satisfied	satisfied	ADJ
ejpam-6997	271	22	:	:	PUNCT
ejpam-6997	271	23	ϕ	ϕ	X
ejpam-6997	271	24	/∈	/∈	PUNCT
ejpam-6997	272	1	g	g	NOUN
ejpam-6997	272	2	h	h	NOUN
ejpam-6997	272	3	∈	∈	PROPN
ejpam-6997	272	4	g	g	PROPN
ejpam-6997	272	5	,	,	PUNCT
ejpam-6997	272	6	h	h	PROPN
ejpam-6997	273	1	⊑	⊑	X
ejpam-6997	273	2	j	j	PROPN
ejpam-6997	273	3	⊑	⊑	X
ejpam-6997	273	4	ℵ	ℵ	ADJ
ejpam-6997	273	5	leads	lead	VERB
ejpam-6997	273	6	to	to	ADP
ejpam-6997	273	7	j	j	PROPN
ejpam-6997	273	8	∈	∈	PROPN
ejpam-6997	273	9	g	g	PROPN
ejpam-6997	273	10	,	,	PUNCT
ejpam-6997	273	11	if	if	SCONJ
ejpam-6997	273	12	h	h	PROPN
ejpam-6997	273	13	⊔	⊔	X
ejpam-6997	273	14	j	j	PROPN
ejpam-6997	273	15	∈	∈	PROPN
ejpam-6997	273	16	g	g	PROPN
ejpam-6997	273	17	for	for	ADP
ejpam-6997	273	18	h	h	NOUN
ejpam-6997	273	19	,	,	PUNCT
ejpam-6997	273	20	j	j	PROPN
ejpam-6997	273	21	⊑	⊑	X
ejpam-6997	273	22	ℵ	ℵ	PROPN
ejpam-6997	273	23	,	,	PUNCT
ejpam-6997	273	24	then	then	ADV
ejpam-6997	273	25	h	h	PROPN
ejpam-6997	273	26	∈	∈	PROPN
ejpam-6997	273	27	g	g	PROPN
ejpam-6997	273	28	or	or	CCONJ
ejpam-6997	273	29	j	j	PROPN
ejpam-6997	273	30	∈	∈	PROPN
ejpam-6997	273	31	g.	g.	PROPN
ejpam-6997	273	32	3	3	NUM
ejpam-6997	273	33	.	.	PUNCT
ejpam-6997	273	34	grills	grill	NOUN
ejpam-6997	273	35	and	and	CCONJ
ejpam-6997	273	36	cardinality	cardinality	NOUN
ejpam-6997	273	37	create	create	VERB
ejpam-6997	273	38	new	new	ADJ
ejpam-6997	273	39	rough	rough	ADJ
ejpam-6997	273	40	-	-	PUNCT
ejpam-6997	273	41	set	set	VERB
ejpam-6997	273	42	paradigms	paradigm	NOUN
ejpam-6997	273	43	in	in	ADP
ejpam-6997	273	44	neighborhoods	neighborhood	NOUN
ejpam-6997	273	45	this	this	DET
ejpam-6997	273	46	section	section	NOUN
ejpam-6997	273	47	aims	aim	VERB
ejpam-6997	273	48	to	to	PART
ejpam-6997	273	49	delineate	delineate	VERB
ejpam-6997	273	50	and	and	CCONJ
ejpam-6997	273	51	examine	examine	VERB
ejpam-6997	273	52	novel	novel	ADJ
ejpam-6997	273	53	r	r	NOUN
ejpam-6997	273	54	-	-	PUNCT
ejpam-6997	273	55	ap	ap	PROPN
ejpam-6997	273	56	spaces	space	NOUN
ejpam-6997	273	57	generated	generate	VERB
ejpam-6997	273	58	by	by	ADP
ejpam-6997	273	59	cardinality	cardinality	PROPN
ejpam-6997	273	60	nbds	nbds	NOUN
ejpam-6997	273	61	and	and	CCONJ
ejpam-6997	273	62	grills	grill	NOUN
ejpam-6997	273	63	,	,	PUNCT
ejpam-6997	273	64	with	with	ADP
ejpam-6997	273	65	an	an	DET
ejpam-6997	273	66	emphasis	emphasis	NOUN
ejpam-6997	273	67	on	on	ADP
ejpam-6997	273	68	establishing	establish	VERB
ejpam-6997	273	69	new	new	ADJ
ejpam-6997	273	70	areas	area	NOUN
ejpam-6997	273	71	and	and	CCONJ
ejpam-6997	273	72	standards	standard	NOUN
ejpam-6997	273	73	for	for	ADP
ejpam-6997	273	74	accuracy	accuracy	NOUN
ejpam-6997	273	75	and	and	CCONJ
ejpam-6997	273	76	roughness	roughness	NOUN
ejpam-6997	273	77	.	.	PUNCT
ejpam-6997	274	1	a.	a.	NOUN
ejpam-6997	274	2	a.	a.	PROPN
ejpam-6997	274	3	azzam	azzam	PROPN
ejpam-6997	274	4	,	,	PUNCT
ejpam-6997	274	5	m.	m.	NOUN
ejpam-6997	274	6	aldawood	aldawood	PROPN
ejpam-6997	274	7	,	,	PUNCT
ejpam-6997	274	8	b.	b.	PROPN
ejpam-6997	274	9	alreshidi	alreshidi	PROPN
ejpam-6997	274	10	/	/	SYM
ejpam-6997	274	11	eur	eur	PROPN
ejpam-6997	274	12	.	.	PUNCT
ejpam-6997	275	1	j.	j.	PROPN
ejpam-6997	275	2	pure	pure	PROPN
ejpam-6997	275	3	appl	appl	PROPN
ejpam-6997	275	4	.	.	PROPN
ejpam-6997	275	5	math	math	PROPN
ejpam-6997	275	6	,	,	PUNCT
ejpam-6997	275	7	18	18	NUM
ejpam-6997	275	8	(	(	PUNCT
ejpam-6997	275	9	4	4	NUM
ejpam-6997	275	10	)	)	PUNCT
ejpam-6997	275	11	(	(	PUNCT
ejpam-6997	275	12	2025	2025	NUM
ejpam-6997	275	13	)	)	PUNCT
ejpam-6997	275	14	,	,	PUNCT
ejpam-6997	275	15	6997	6997	NUM
ejpam-6997	275	16	10	10	NUM
ejpam-6997	275	17	of	of	ADP
ejpam-6997	275	18	31	31	NUM
ejpam-6997	275	19	3.1	3.1	NUM
ejpam-6997	275	20	.	.	PUNCT
ejpam-6997	276	1	the	the	DET
ejpam-6997	276	2	initial	initial	ADJ
ejpam-6997	276	3	class	class	NOUN
ejpam-6997	276	4	of	of	ADP
ejpam-6997	276	5	rs	rs	ADJ
ejpam-6997	276	6	paradigms	paradigms	NOUN
ejpam-6997	276	7	this	this	DET
ejpam-6997	276	8	section	section	NOUN
ejpam-6997	276	9	is	be	AUX
ejpam-6997	276	10	devoted	devote	VERB
ejpam-6997	276	11	to	to	ADP
ejpam-6997	276	12	presenting	present	VERB
ejpam-6997	276	13	novel	novel	ADJ
ejpam-6997	276	14	rs	rs	NOUN
ejpam-6997	276	15	paradigms	paradigm	NOUN
ejpam-6997	276	16	that	that	PRON
ejpam-6997	276	17	are	be	AUX
ejpam-6997	276	18	influenced	influence	VERB
ejpam-6997	276	19	by	by	ADP
ejpam-6997	276	20	the	the	DET
ejpam-6997	276	21	concepts	concept	NOUN
ejpam-6997	276	22	of	of	ADP
ejpam-6997	276	23	grills	grill	NOUN
ejpam-6997	276	24	and	and	CCONJ
ejpam-6997	276	25	cardinality	cardinality	PROPN
ejpam-6997	276	26	nbds	nbds	NOUN
ejpam-6997	276	27	.	.	PUNCT
ejpam-6997	277	1	we	we	PRON
ejpam-6997	277	2	demonstrate	demonstrate	VERB
ejpam-6997	277	3	that	that	SCONJ
ejpam-6997	277	4	,	,	PUNCT
ejpam-6997	277	5	in	in	ADP
ejpam-6997	277	6	contrast	contrast	NOUN
ejpam-6997	277	7	to	to	ADP
ejpam-6997	277	8	the	the	DET
ejpam-6997	277	9	earlier	early	ADJ
ejpam-6997	277	10	models	model	NOUN
ejpam-6997	277	11	of	of	ADP
ejpam-6997	277	12	rss	rss	NOUN
ejpam-6997	277	13	,	,	PUNCT
ejpam-6997	277	14	in	in	ADP
ejpam-6997	277	15	these	these	DET
ejpam-6997	277	16	paradigms	paradigm	NOUN
ejpam-6997	277	17	,	,	PUNCT
ejpam-6997	277	18	the	the	DET
ejpam-6997	277	19	lw	lw	PROPN
ejpam-6997	277	20	-	-	PUNCT
ejpam-6997	277	21	ap	ap	PROPN
ejpam-6997	277	22	is	be	AUX
ejpam-6997	277	23	amplified	amplify	VERB
ejpam-6997	277	24	and	and	CCONJ
ejpam-6997	277	25	the	the	DET
ejpam-6997	277	26	up	up	NOUN
ejpam-6997	277	27	-	-	PUNCT
ejpam-6997	277	28	ap	ap	PROPN
ejpam-6997	277	29	is	be	AUX
ejpam-6997	277	30	minified	minify	VERB
ejpam-6997	277	31	.	.	PUNCT
ejpam-6997	278	1	on	on	ADP
ejpam-6997	278	2	the	the	DET
ejpam-6997	278	3	other	other	ADJ
ejpam-6997	278	4	hand	hand	NOUN
ejpam-6997	278	5	,	,	PUNCT
ejpam-6997	278	6	we	we	PRON
ejpam-6997	278	7	talk	talk	VERB
ejpam-6997	278	8	about	about	ADP
ejpam-6997	278	9	the	the	DET
ejpam-6997	278	10	current	current	ADJ
ejpam-6997	278	11	models	model	NOUN
ejpam-6997	278	12	’	'	PUNCT
ejpam-6997	278	13	flaws	flaw	NOUN
ejpam-6997	278	14	.	.	PUNCT
ejpam-6997	279	1	definition	definition	NOUN
ejpam-6997	279	2	17	17	NUM
ejpam-6997	279	3	.	.	PUNCT
ejpam-6997	280	1	let	let	AUX
ejpam-6997	280	2	(	(	PUNCT
ejpam-6997	280	3	ℵ,γ	ℵ,γ	VERB
ejpam-6997	280	4	,	,	PUNCT
ejpam-6997	280	5	ξϱ	ξϱ	NOUN
ejpam-6997	280	6	)	)	PUNCT
ejpam-6997	280	7	be	be	VERB
ejpam-6997	280	8	a	a	DET
ejpam-6997	280	9	ϱ-ns	ϱ-ns	NOUN
ejpam-6997	280	10	and	and	CCONJ
ejpam-6997	280	11	g	g	PROPN
ejpam-6997	280	12	be	be	AUX
ejpam-6997	280	13	a	a	DET
ejpam-6997	280	14	grill	grill	NOUN
ejpam-6997	280	15	on	on	ADP
ejpam-6997	280	16	ℵ.	ℵ.	PROPN
ejpam-6997	281	1	the	the	DET
ejpam-6997	281	2	pair	pair	NOUN
ejpam-6997	281	3	(	(	PUNCT
ejpam-6997	281	4	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	281	5	(	(	PUNCT
ejpam-6997	281	6	∆),gm̃cϱ	∆),gm̃cϱ	NOUN
ejpam-6997	281	7	(	(	PUNCT
ejpam-6997	281	8	∆	∆	PROPN
ejpam-6997	281	9	)	)	PUNCT
ejpam-6997	281	10	)	)	PUNCT
ejpam-6997	281	11	represents	represent	VERB
ejpam-6997	281	12	lw	lw	PROPN
ejpam-6997	281	13	,	,	PUNCT
ejpam-6997	281	14	and	and	CCONJ
ejpam-6997	281	15	up	up	ADP
ejpam-6997	281	16	-	-	PUNCT
ejpam-6997	281	17	ap	ap	NOUN
ejpam-6997	281	18	of	of	ADP
ejpam-6997	281	19	a	a	DET
ejpam-6997	281	20	subset	subset	NOUN
ejpam-6997	281	21	∆	∆	PROPN
ejpam-6997	281	22	with	with	ADP
ejpam-6997	281	23	respect	respect	NOUN
ejpam-6997	281	24	to	to	ADP
ejpam-6997	281	25	grills	grill	NOUN
ejpam-6997	281	26	and	and	CCONJ
ejpam-6997	281	27	cardinality	cardinality	PROPN
ejpam-6997	281	28	nbds	nbds	NOUN
ejpam-6997	281	29	,	,	PUNCT
ejpam-6997	281	30	and	and	CCONJ
ejpam-6997	281	31	they	they	PRON
ejpam-6997	281	32	are	be	AUX
ejpam-6997	281	33	calculated	calculate	VERB
ejpam-6997	281	34	by	by	ADP
ejpam-6997	281	35	:	:	PUNCT
ejpam-6997	281	36	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	281	37	(	(	PUNCT
ejpam-6997	281	38	∆	∆	PROPN
ejpam-6997	281	39	)	)	PUNCT
ejpam-6997	282	1	=	=	PRON
ejpam-6997	282	2	{	{	PUNCT
ejpam-6997	282	3	b	b	PROPN
ejpam-6997	282	4	∈	∈	PROPN
ejpam-6997	282	5	ℵ	ℵ	NOUN
ejpam-6997	282	6	:	:	PUNCT
ejpam-6997	282	7	cϱ(b	cϱ(b	NOUN
ejpam-6997	282	8	)	)	PUNCT
ejpam-6997	283	1	⊓	⊓	PROPN
ejpam-6997	283	2	∆c	∆c	NOUN
ejpam-6997	283	3	/∈	/∈	PUNCT
ejpam-6997	283	4	g	g	NOUN
ejpam-6997	283	5	}	}	PUNCT
ejpam-6997	283	6	,	,	PUNCT
ejpam-6997	283	7	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	283	8	(	(	PUNCT
ejpam-6997	283	9	∆	∆	PROPN
ejpam-6997	283	10	)	)	PUNCT
ejpam-6997	284	1	=	=	PRON
ejpam-6997	284	2	{	{	PUNCT
ejpam-6997	284	3	b	b	PROPN
ejpam-6997	284	4	∈	∈	PROPN
ejpam-6997	284	5	ℵ	ℵ	NOUN
ejpam-6997	284	6	:	:	PUNCT
ejpam-6997	284	7	cϱ(b	cϱ(b	NOUN
ejpam-6997	284	8	)	)	PUNCT
ejpam-6997	285	1	⊓	⊓	NOUN
ejpam-6997	285	2	∆	∆	PRON
ejpam-6997	285	3	∈	∈	PROPN
ejpam-6997	285	4	g	g	NOUN
ejpam-6997	285	5	}	}	PUNCT
ejpam-6997	285	6	remark	remark	NOUN
ejpam-6997	285	7	1	1	NUM
ejpam-6997	285	8	.	.	PUNCT
ejpam-6997	286	1	if	if	SCONJ
ejpam-6997	286	2	g	g	NOUN
ejpam-6997	286	3	=	=	SYM
ejpam-6997	286	4	ℵ	ℵ	NOUN
ejpam-6997	286	5	in	in	ADP
ejpam-6997	286	6	definition	definition	NOUN
ejpam-6997	286	7	3.1	3.1	NUM
ejpam-6997	286	8	then	then	ADV
ejpam-6997	286	9	,	,	PUNCT
ejpam-6997	286	10	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	286	11	(	(	PUNCT
ejpam-6997	286	12	∆	∆	PROPN
ejpam-6997	286	13	)	)	PUNCT
ejpam-6997	287	1	=	=	SYM
ejpam-6997	287	2	ϕ.	ϕ.	PROPN
ejpam-6997	287	3	theorem	theorem	VERB
ejpam-6997	287	4	2	2	X
ejpam-6997	287	5	.	.	X
ejpam-6997	288	1	let	let	AUX
ejpam-6997	288	2	(	(	PUNCT
ejpam-6997	288	3	ℵ,γ	ℵ,γ	VERB
ejpam-6997	288	4	,	,	PUNCT
ejpam-6997	288	5	ξϱ	ξϱ	NOUN
ejpam-6997	288	6	)	)	PUNCT
ejpam-6997	288	7	be	be	VERB
ejpam-6997	288	8	a	a	DET
ejpam-6997	288	9	ϱ-ns	ϱ-ns	NOUN
ejpam-6997	288	10	and	and	CCONJ
ejpam-6997	288	11	g	g	PROPN
ejpam-6997	288	12	be	be	AUX
ejpam-6997	288	13	a	a	DET
ejpam-6997	288	14	grill	grill	NOUN
ejpam-6997	288	15	on	on	ADP
ejpam-6997	288	16	ℵ.	ℵ.	PROPN
ejpam-6997	289	1	if	if	SCONJ
ejpam-6997	289	2	∆	∆	PROPN
ejpam-6997	289	3	,	,	PUNCT
ejpam-6997	289	4	d	d	X
ejpam-6997	289	5	⊑	⊑	PRON
ejpam-6997	289	6	ℵ	ℵ	X
ejpam-6997	289	7	,	,	PUNCT
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ejpam-6997	289	9	∀ϱ	∀ϱ	PROPN
ejpam-6997	289	10	the	the	DET
ejpam-6997	289	11	next	next	ADJ
ejpam-6997	289	12	statement	statement	NOUN
ejpam-6997	289	13	hold	hold	VERB
ejpam-6997	289	14	true	true	ADJ
ejpam-6997	289	15	.	.	PUNCT
ejpam-6997	290	1	(	(	PUNCT
ejpam-6997	290	2	1	1	X
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ejpam-6997	290	5	(	(	PUNCT
ejpam-6997	290	6	ℵ	ℵ	NOUN
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ejpam-6997	290	8	=	=	SYM
ejpam-6997	290	9	ℵ	ℵ	NOUN
ejpam-6997	290	10	and	and	CCONJ
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ejpam-6997	290	12	(	(	PUNCT
ejpam-6997	290	13	ϕ	ϕ	NOUN
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ejpam-6997	290	15	=	=	SYM
ejpam-6997	290	16	ϕ.	ϕ.	NOUN
ejpam-6997	290	17	(	(	PUNCT
ejpam-6997	290	18	2	2	NUM
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ejpam-6997	291	2	d	d	PROPN
ejpam-6997	291	3	⊑	⊑	DET
ejpam-6997	291	4	∆	∆	PROPN
ejpam-6997	291	5	,	,	PUNCT
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ejpam-6997	291	8	(	(	PUNCT
ejpam-6997	291	9	d	d	X
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ejpam-6997	291	11	⊑	⊑	PRON
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ejpam-6997	291	13	(	(	PUNCT
ejpam-6997	291	14	∆	∆	PROPN
ejpam-6997	291	15	)	)	PUNCT
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ejpam-6997	291	18	(	(	PUNCT
ejpam-6997	291	19	d	d	X
ejpam-6997	291	20	)	)	PUNCT
ejpam-6997	291	21	⊑	⊑	PRON
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ejpam-6997	291	23	(	(	PUNCT
ejpam-6997	291	24	∆	∆	PROPN
ejpam-6997	291	25	)	)	PUNCT
ejpam-6997	291	26	.	.	PUNCT
ejpam-6997	292	1	(	(	PUNCT
ejpam-6997	292	2	3	3	X
ejpam-6997	292	3	)	)	PUNCT
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ejpam-6997	292	5	(	(	PUNCT
ejpam-6997	292	6	d	d	X
ejpam-6997	292	7	⊓	⊓	PROPN
ejpam-6997	292	8	∆	∆	X
ejpam-6997	292	9	)	)	PUNCT
ejpam-6997	293	1	=	=	SYM
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ejpam-6997	293	3	(	(	PUNCT
ejpam-6997	293	4	d	d	X
ejpam-6997	293	5	)	)	PUNCT
ejpam-6997	293	6	⊓	⊓	PROPN
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ejpam-6997	293	8	(	(	PUNCT
ejpam-6997	293	9	∆	∆	PROPN
ejpam-6997	293	10	)	)	PUNCT
ejpam-6997	293	11	and	and	CCONJ
ejpam-6997	293	12	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	293	13	(	(	PUNCT
ejpam-6997	293	14	d	d	NOUN
ejpam-6997	293	15	⊔	⊔	NUM
ejpam-6997	293	16	∆	∆	PROPN
ejpam-6997	293	17	)	)	PUNCT
ejpam-6997	294	1	=	=	SYM
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ejpam-6997	294	3	(	(	PUNCT
ejpam-6997	294	4	d	d	NOUN
ejpam-6997	294	5	)	)	PUNCT
ejpam-6997	294	6	⊔	⊔	NUM
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ejpam-6997	294	8	(	(	PUNCT
ejpam-6997	294	9	∆	∆	PROPN
ejpam-6997	294	10	)	)	PUNCT
ejpam-6997	294	11	.	.	PUNCT
ejpam-6997	295	1	(	(	PUNCT
ejpam-6997	295	2	4	4	X
ejpam-6997	295	3	)	)	PUNCT
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ejpam-6997	295	5	(	(	PUNCT
ejpam-6997	295	6	∆c	∆c	NOUN
ejpam-6997	295	7	)	)	PUNCT
ejpam-6997	295	8	=	=	SYM
ejpam-6997	295	9	(	(	PUNCT
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ejpam-6997	295	11	(	(	PUNCT
ejpam-6997	295	12	∆))c	∆))c	PROPN
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ejpam-6997	295	15	(	(	PUNCT
ejpam-6997	295	16	∆c	∆c	NOUN
ejpam-6997	295	17	)	)	PUNCT
ejpam-6997	295	18	=	=	SYM
ejpam-6997	295	19	(	(	PUNCT
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ejpam-6997	295	21	(	(	PUNCT
ejpam-6997	295	22	∆))c	∆))c	PROPN
ejpam-6997	295	23	.	.	PUNCT
ejpam-6997	296	1	(	(	PUNCT
ejpam-6997	296	2	5	5	NUM
ejpam-6997	296	3	)	)	PUNCT
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ejpam-6997	296	5	∆c	∆c	PROPN
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ejpam-6997	296	7	g	g	NOUN
ejpam-6997	296	8	,	,	PUNCT
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ejpam-6997	296	11	(	(	PUNCT
ejpam-6997	296	12	∆	∆	PROPN
ejpam-6997	296	13	)	)	PUNCT
ejpam-6997	296	14	=	=	SYM
ejpam-6997	296	15	ℵ	ℵ	NOUN
ejpam-6997	296	16	and	and	CCONJ
ejpam-6997	296	17	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	296	18	(	(	PUNCT
ejpam-6997	296	19	∆c	∆c	PROPN
ejpam-6997	296	20	)	)	PUNCT
ejpam-6997	297	1	=	=	SYM
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ejpam-6997	297	3	(	(	PUNCT
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ejpam-6997	297	5	)	)	PUNCT
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ejpam-6997	297	7	(	(	PUNCT
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ejpam-6997	297	9	(	(	PUNCT
ejpam-6997	297	10	∆	∆	PROPN
ejpam-6997	297	11	)	)	PUNCT
ejpam-6997	297	12	)	)	PUNCT
ejpam-6997	298	1	⊒	⊒	PROPN
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ejpam-6997	298	3	(	(	PUNCT
ejpam-6997	298	4	∆	∆	PROPN
ejpam-6997	298	5	)	)	PUNCT
ejpam-6997	298	6	and	and	CCONJ
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ejpam-6997	298	8	(	(	PUNCT
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ejpam-6997	298	10	(	(	PUNCT
ejpam-6997	298	11	∆	∆	PROPN
ejpam-6997	298	12	)	)	PUNCT
ejpam-6997	298	13	)	)	PUNCT
ejpam-6997	299	1	⊑	⊑	PRON
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ejpam-6997	299	3	(	(	PUNCT
ejpam-6997	299	4	∆	∆	PROPN
ejpam-6997	299	5	)	)	PUNCT
ejpam-6997	299	6	,	,	PUNCT
ejpam-6997	299	7	∀ϱ	∀ϱ	PROPN
ejpam-6997	299	8	∈	∈	PROPN
ejpam-6997	299	9	{	{	PUNCT
ejpam-6997	299	10	r	r	NOUN
ejpam-6997	299	11	,	,	PUNCT
ejpam-6997	299	12	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	299	13	,	,	PUNCT
ejpam-6997	299	14	l	l	NOUN
ejpam-6997	299	15	,	,	PUNCT
ejpam-6997	299	16	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	299	17	,	,	PUNCT
ejpam-6997	299	18	i	i	PRON
ejpam-6997	299	19	,	,	PUNCT
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ejpam-6997	299	22	.	.	PUNCT
ejpam-6997	300	1	(	(	PUNCT
ejpam-6997	300	2	7	7	X
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ejpam-6997	300	5	(	(	PUNCT
ejpam-6997	300	6	cϱ(n	cϱ(n	NUM
ejpam-6997	300	7	)	)	PUNCT
ejpam-6997	300	8	)	)	PUNCT
ejpam-6997	301	1	⊒	⊒	NOUN
ejpam-6997	301	2	cϱ(n	cϱ(n	X
ejpam-6997	301	3	)	)	PUNCT
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ejpam-6997	301	5	∈	∈	PROPN
ejpam-6997	301	6	{	{	PUNCT
ejpam-6997	301	7	r	r	NOUN
ejpam-6997	301	8	,	,	PUNCT
ejpam-6997	301	9	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	301	10	,	,	PUNCT
ejpam-6997	301	11	l	l	NOUN
ejpam-6997	301	12	,	,	PUNCT
ejpam-6997	301	13	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	301	14	,	,	PUNCT
ejpam-6997	301	15	i	i	PRON
ejpam-6997	301	16	,	,	PUNCT
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ejpam-6997	301	18	}	}	PUNCT
ejpam-6997	301	19	.	.	PUNCT
ejpam-6997	302	1	proof	proof	NOUN
ejpam-6997	302	2	.	.	PUNCT
ejpam-6997	303	1	(	(	PUNCT
ejpam-6997	303	2	1	1	X
ejpam-6997	303	3	)	)	PUNCT
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ejpam-6997	303	5	(	(	PUNCT
ejpam-6997	303	6	ℵ	ℵ	NOUN
ejpam-6997	303	7	)	)	PUNCT
ejpam-6997	303	8	=	=	SYM
ejpam-6997	303	9	{	{	PUNCT
ejpam-6997	303	10	b	b	PROPN
ejpam-6997	303	11	∈	∈	PROPN
ejpam-6997	303	12	ℵ	ℵ	NOUN
ejpam-6997	303	13	:	:	PUNCT
ejpam-6997	303	14	cϱ(b	cϱ(b	NOUN
ejpam-6997	303	15	)	)	PUNCT
ejpam-6997	303	16	\	\	PROPN
ejpam-6997	303	17	ℵ	ℵ	PROPN
ejpam-6997	303	18	=	=	SYM
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ejpam-6997	304	1	g	g	NOUN
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ejpam-6997	304	3	=	=	SYM
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ejpam-6997	304	7	(	(	PUNCT
ejpam-6997	304	8	ϕ	ϕ	NOUN
ejpam-6997	304	9	)	)	PUNCT
ejpam-6997	304	10	=	=	SYM
ejpam-6997	305	1	{	{	PUNCT
ejpam-6997	305	2	b	b	PROPN
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ejpam-6997	305	4	ℵ	ℵ	NOUN
ejpam-6997	305	5	:	:	PUNCT
ejpam-6997	305	6	cϱ(b	cϱ(b	NOUN
ejpam-6997	305	7	)	)	PUNCT
ejpam-6997	306	1	⊓	⊓	PROPN
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ejpam-6997	306	6	=	=	SYM
ejpam-6997	306	7	ϕ.	ϕ.	NOUN
ejpam-6997	306	8	(	(	PUNCT
ejpam-6997	306	9	2	2	X
ejpam-6997	306	10	)	)	PUNCT
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ejpam-6997	307	12	(	(	PUNCT
ejpam-6997	307	13	d	d	PROPN
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ejpam-6997	308	1	⊑	⊑	PRON
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ejpam-6997	309	8	(	(	PUNCT
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ejpam-6997	309	11	⊓	⊓	PROPN
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ejpam-6997	309	13	(	(	PUNCT
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ejpam-6997	310	3	∈	∈	PROPN
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ejpam-6997	310	5	(	(	PUNCT
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ejpam-6997	310	9	b	b	X
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ejpam-6997	310	12	(	(	PUNCT
ejpam-6997	310	13	∆	∆	PROPN
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ejpam-6997	310	23	∈	∈	PROPN
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ejpam-6997	311	7	∈	∈	PROPN
ejpam-6997	311	8	g.	g.	PROPN
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ejpam-6997	311	11	b	b	PROPN
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ejpam-6997	311	14	(	(	PUNCT
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ejpam-6997	311	17	∆	∆	X
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ejpam-6997	312	1	hence	hence	ADV
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ejpam-6997	312	4	(	(	PUNCT
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ejpam-6997	312	9	(	(	PUNCT
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ejpam-6997	312	14	(	(	PUNCT
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ejpam-6997	312	17	∆	∆	X
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ejpam-6997	313	13	aldawood	aldawood	PROPN
ejpam-6997	313	14	,	,	PUNCT
ejpam-6997	313	15	b.	b.	PROPN
ejpam-6997	313	16	alreshidi	alreshidi	PROPN
ejpam-6997	313	17	/	/	SYM
ejpam-6997	313	18	eur	eur	PROPN
ejpam-6997	313	19	.	.	PUNCT
ejpam-6997	314	1	j.	j.	PROPN
ejpam-6997	314	2	pure	pure	PROPN
ejpam-6997	314	3	appl	appl	PROPN
ejpam-6997	314	4	.	.	PROPN
ejpam-6997	314	5	math	math	PROPN
ejpam-6997	314	6	,	,	PUNCT
ejpam-6997	314	7	18	18	NUM
ejpam-6997	314	8	(	(	PUNCT
ejpam-6997	314	9	4	4	NUM
ejpam-6997	314	10	)	)	PUNCT
ejpam-6997	314	11	(	(	PUNCT
ejpam-6997	314	12	2025	2025	NUM
ejpam-6997	314	13	)	)	PUNCT
ejpam-6997	314	14	,	,	PUNCT
ejpam-6997	314	15	6997	6997	NUM
ejpam-6997	314	16	11	11	NUM
ejpam-6997	314	17	of	of	ADP
ejpam-6997	314	18	31	31	NUM
ejpam-6997	314	19	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	314	20	(	(	PUNCT
ejpam-6997	314	21	d	d	NOUN
ejpam-6997	314	22	⊔	⊔	NUM
ejpam-6997	314	23	∆	∆	PROPN
ejpam-6997	314	24	)	)	PUNCT
ejpam-6997	315	1	=	=	SYM
ejpam-6997	315	2	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	315	3	(	(	PUNCT
ejpam-6997	315	4	d	d	NOUN
ejpam-6997	315	5	)	)	PUNCT
ejpam-6997	315	6	⊔	⊔	NUM
ejpam-6997	315	7	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	315	8	(	(	PUNCT
ejpam-6997	315	9	∆	∆	PROPN
ejpam-6997	315	10	)	)	PUNCT
ejpam-6997	315	11	.	.	PUNCT
ejpam-6997	316	1	(	(	PUNCT
ejpam-6997	316	2	4	4	X
ejpam-6997	316	3	)	)	PUNCT
ejpam-6997	316	4	b	b	NOUN
ejpam-6997	316	5	∈	∈	NOUN
ejpam-6997	316	6	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	316	7	(	(	PUNCT
ejpam-6997	316	8	∆c	∆c	PROPN
ejpam-6997	316	9	)	)	PUNCT
ejpam-6997	316	10	⇔	⇔	PROPN
ejpam-6997	316	11	cϱ(b)\∆c	cϱ(b)\∆c	PROPN
ejpam-6997	316	12	∈	∈	PROPN
ejpam-6997	316	13	g	g	PROPN
ejpam-6997	316	14	⇔	⇔	X
ejpam-6997	316	15	cϱ(b	cϱ(b	NOUN
ejpam-6997	316	16	)	)	PUNCT
ejpam-6997	317	1	⊓	⊓	NOUN
ejpam-6997	317	2	∆	∆	PROPN
ejpam-6997	317	3	∈	∈	PROPN
ejpam-6997	317	4	g	g	PROPN
ejpam-6997	317	5	⇔	⇔	PROPN
ejpam-6997	317	6	b	b	PROPN
ejpam-6997	317	7	̸=	̸=	PROPN
ejpam-6997	317	8	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	317	9	(	(	PUNCT
ejpam-6997	317	10	∆	∆	PROPN
ejpam-6997	317	11	)	)	PUNCT
ejpam-6997	317	12	⇔	⇔	PROPN
ejpam-6997	317	13	b	b	X
ejpam-6997	317	14	∈	∈	PROPN
ejpam-6997	317	15	(	(	PUNCT
ejpam-6997	317	16	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	317	17	(	(	PUNCT
ejpam-6997	317	18	∆))c	∆))c	PROPN
ejpam-6997	317	19	.	.	PUNCT
ejpam-6997	318	1	likewise	likewise	ADV
ejpam-6997	318	2	,	,	PUNCT
ejpam-6997	318	3	it	it	PRON
ejpam-6997	318	4	can	can	AUX
ejpam-6997	318	5	be	be	AUX
ejpam-6997	318	6	demonstrated	demonstrate	VERB
ejpam-6997	318	7	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	318	8	(	(	PUNCT
ejpam-6997	318	9	∆c	∆c	NOUN
ejpam-6997	318	10	)	)	PUNCT
ejpam-6997	318	11	=	=	SYM
ejpam-6997	318	12	(	(	PUNCT
ejpam-6997	318	13	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	318	14	(	(	PUNCT
ejpam-6997	318	15	∆))c	∆))c	PROPN
ejpam-6997	318	16	.	.	PUNCT
ejpam-6997	319	1	let	let	VERB
ejpam-6997	319	2	b	b	NOUN
ejpam-6997	319	3	∈	∈	PROPN
ejpam-6997	319	4	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	319	5	(	(	PUNCT
ejpam-6997	319	6	∆c	∆c	PROPN
ejpam-6997	319	7	)	)	PUNCT
ejpam-6997	319	8	⇒	⇒	NOUN
ejpam-6997	319	9	cϱ(b)\∆c	cϱ(b)\∆c	PROPN
ejpam-6997	319	10	/∈	/∈	PUNCT
ejpam-6997	320	1	g	g	PROPN
ejpam-6997	320	2	⇔	⇔	PROPN
ejpam-6997	320	3	cϱ(b	cϱ(b	NOUN
ejpam-6997	320	4	)	)	PUNCT
ejpam-6997	321	1	⊓	⊓	PROPN
ejpam-6997	321	2	∆	∆	X
ejpam-6997	321	3	/∈	/∈	PUNCT
ejpam-6997	322	1	g	g	PROPN
ejpam-6997	322	2	⇔	⇔	PROPN
ejpam-6997	322	3	b	b	PROPN
ejpam-6997	322	4	∈	∈	PROPN
ejpam-6997	322	5	(	(	PUNCT
ejpam-6997	322	6	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	322	7	(	(	PUNCT
ejpam-6997	322	8	∆))c	∆))c	PROPN
ejpam-6997	322	9	.	.	PUNCT
ejpam-6997	322	10	(	(	PUNCT
ejpam-6997	322	11	5	5	X
ejpam-6997	322	12	)	)	PUNCT
ejpam-6997	322	13	let	let	VERB
ejpam-6997	322	14	∆c	∆c	PROPN
ejpam-6997	322	15	∈	∈	PROPN
ejpam-6997	322	16	g.	g.	NOUN
ejpam-6997	322	17	for	for	ADP
ejpam-6997	322	18	any	any	DET
ejpam-6997	322	19	b	b	PROPN
ejpam-6997	322	20	∈	∈	PROPN
ejpam-6997	322	21	ℵ	ℵ	NOUN
ejpam-6997	322	22	,	,	PUNCT
ejpam-6997	322	23	cϱ(b)\∆	cϱ(b)\∆	NOUN
ejpam-6997	322	24	=	=	PUNCT
ejpam-6997	322	25	cϱ(b	cϱ(b	NOUN
ejpam-6997	322	26	)	)	PUNCT
ejpam-6997	323	1	⊓	⊓	PROPN
ejpam-6997	323	2	∆c	∆c	PROPN
ejpam-6997	323	3	∈	∈	PROPN
ejpam-6997	323	4	g.	g.	NOUN
ejpam-6997	323	5	hence	hence	ADV
ejpam-6997	323	6	,	,	PUNCT
ejpam-6997	323	7	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	323	8	(	(	PUNCT
ejpam-6997	323	9	∆	∆	PROPN
ejpam-6997	323	10	)	)	PUNCT
ejpam-6997	323	11	=	=	PUNCT
ejpam-6997	324	1	ℵ.	ℵ.	PROPN
ejpam-6997	324	2	from	from	ADP
ejpam-6997	324	3	(	(	PUNCT
ejpam-6997	324	4	4	4	NUM
ejpam-6997	324	5	)	)	PUNCT
ejpam-6997	324	6	,	,	PUNCT
ejpam-6997	324	7	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	324	8	(	(	PUNCT
ejpam-6997	324	9	∆c	∆c	PROPN
ejpam-6997	324	10	)	)	PUNCT
ejpam-6997	325	1	=	=	SYM
ejpam-6997	325	2	ϕ.	ϕ.	NOUN
ejpam-6997	325	3	(	(	PUNCT
ejpam-6997	325	4	6	6	X
ejpam-6997	325	5	)	)	PUNCT
ejpam-6997	325	6	suppose	suppose	VERB
ejpam-6997	325	7	ϱ	ϱ	ADP
ejpam-6997	325	8	∈	∈	PROPN
ejpam-6997	325	9	{	{	PUNCT
ejpam-6997	325	10	r	r	NOUN
ejpam-6997	325	11	,	,	PUNCT
ejpam-6997	325	12	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	325	13	,	,	PUNCT
ejpam-6997	325	14	l	l	NOUN
ejpam-6997	325	15	,	,	PUNCT
ejpam-6997	325	16	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	325	17	,	,	PUNCT
ejpam-6997	325	18	i	i	PRON
ejpam-6997	325	19	,	,	PUNCT
ejpam-6997	325	20	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	325	21	}	}	PUNCT
ejpam-6997	325	22	.	.	PUNCT
ejpam-6997	326	1	we	we	PRON
ejpam-6997	326	2	will	will	AUX
ejpam-6997	326	3	just	just	ADV
ejpam-6997	326	4	demonstrate	demonstrate	VERB
ejpam-6997	326	5	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	326	6	(	(	PUNCT
ejpam-6997	326	7	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	326	8	(	(	PUNCT
ejpam-6997	326	9	∆	∆	PROPN
ejpam-6997	326	10	)	)	PUNCT
ejpam-6997	326	11	)	)	PUNCT
ejpam-6997	326	12	⊑	⊑	DET
ejpam-6997	326	13	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	326	14	(	(	PUNCT
ejpam-6997	326	15	∆	∆	PROPN
ejpam-6997	326	16	)	)	PUNCT
ejpam-6997	326	17	.	.	PUNCT
ejpam-6997	327	1	let	let	VERB
ejpam-6997	327	2	b	b	NOUN
ejpam-6997	327	3	∈	∈	PROPN
ejpam-6997	327	4	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	327	5	(	(	PUNCT
ejpam-6997	327	6	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	327	7	(	(	PUNCT
ejpam-6997	327	8	∆	∆	PROPN
ejpam-6997	327	9	)	)	PUNCT
ejpam-6997	327	10	)	)	PUNCT
ejpam-6997	327	11	,	,	PUNCT
ejpam-6997	327	12	then	then	ADV
ejpam-6997	327	13	cϱ(b)⊓gm̃cϱ	cϱ(b)⊓gm̃cϱ	NOUN
ejpam-6997	327	14	(	(	PUNCT
ejpam-6997	327	15	∆	∆	PROPN
ejpam-6997	327	16	)	)	PUNCT
ejpam-6997	327	17	∈	∈	PROPN
ejpam-6997	327	18	g.	g.	NOUN
ejpam-6997	327	19	hence	hence	ADV
ejpam-6997	327	20	,	,	PUNCT
ejpam-6997	327	21	cϱ(b)⊓gm̃cϱ	cϱ(b)⊓gm̃cϱ	NOUN
ejpam-6997	327	22	(	(	PUNCT
ejpam-6997	327	23	∆	∆	X
ejpam-6997	327	24	)	)	PUNCT
ejpam-6997	327	25	̸=	̸=	PROPN
ejpam-6997	327	26	ϕ	ϕ	NOUN
ejpam-6997	327	27	i.e.	i.e.	X
ejpam-6997	327	28	there	there	PRON
ejpam-6997	327	29	exists	exist	VERB
ejpam-6997	327	30	m	m	PROPN
ejpam-6997	327	31	∈	∈	PROPN
ejpam-6997	327	32	ℵ	ℵ	PROPN
ejpam-6997	327	33	s.t	s.t	PROPN
ejpam-6997	327	34	.	.	PROPN
ejpam-6997	327	35	m	m	PROPN
ejpam-6997	327	36	∈	∈	NOUN
ejpam-6997	327	37	cϱ(b	cϱ(b	NOUN
ejpam-6997	327	38	)	)	PUNCT
ejpam-6997	327	39	,	,	PUNCT
ejpam-6997	327	40	and	and	CCONJ
ejpam-6997	327	41	m	m	PROPN
ejpam-6997	327	42	∈	∈	NOUN
ejpam-6997	327	43	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	327	44	(	(	PUNCT
ejpam-6997	327	45	∆	∆	PROPN
ejpam-6997	327	46	)	)	PUNCT
ejpam-6997	327	47	.	.	PUNCT
ejpam-6997	328	1	this	this	DET
ejpam-6997	328	2	results	result	VERB
ejpam-6997	328	3	in	in	ADP
ejpam-6997	328	4	that	that	DET
ejpam-6997	328	5	cϱ(m)⊓∆	cϱ(m)⊓∆	PROPN
ejpam-6997	328	6	∈	∈	PROPN
ejpam-6997	328	7	g.	g.	NOUN
ejpam-6997	328	8	considering	consider	VERB
ejpam-6997	328	9	corollary	corollary	ADJ
ejpam-6997	328	10	2.20	2.20	NUM
ejpam-6997	328	11	,	,	PUNCT
ejpam-6997	328	12	cϱ(m	cϱ(m	X
ejpam-6997	328	13	)	)	PUNCT
ejpam-6997	328	14	=	=	SYM
ejpam-6997	328	15	cϱ(b	cϱ(b	NOUN
ejpam-6997	328	16	)	)	PUNCT
ejpam-6997	328	17	.	.	PUNCT
ejpam-6997	329	1	consequently	consequently	ADV
ejpam-6997	329	2	,	,	PUNCT
ejpam-6997	329	3	cϱ(b)⊓∆	cϱ(b)⊓∆	PROPN
ejpam-6997	329	4	∈	∈	PROPN
ejpam-6997	329	5	g	g	PROPN
ejpam-6997	329	6	and	and	CCONJ
ejpam-6997	329	7	so	so	ADV
ejpam-6997	329	8	b	b	PROPN
ejpam-6997	329	9	∈	∈	PROPN
ejpam-6997	329	10	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	329	11	(	(	PUNCT
ejpam-6997	329	12	∆	∆	PROPN
ejpam-6997	329	13	)	)	PUNCT
ejpam-6997	329	14	.	.	PUNCT
ejpam-6997	330	1	(	(	PUNCT
ejpam-6997	330	2	7	7	X
ejpam-6997	330	3	)	)	PUNCT
ejpam-6997	330	4	suppose	suppose	VERB
ejpam-6997	330	5	ϱ	ϱ	ADP
ejpam-6997	330	6	∈	∈	PROPN
ejpam-6997	330	7	{	{	PUNCT
ejpam-6997	330	8	r	r	NOUN
ejpam-6997	330	9	,	,	PUNCT
ejpam-6997	330	10	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	330	11	,	,	PUNCT
ejpam-6997	330	12	l	l	NOUN
ejpam-6997	330	13	,	,	PUNCT
ejpam-6997	330	14	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	330	15	,	,	PUNCT
ejpam-6997	330	16	i	i	PRON
ejpam-6997	330	17	,	,	PUNCT
ejpam-6997	330	18	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	330	19	}	}	PUNCT
ejpam-6997	330	20	.	.	PUNCT
ejpam-6997	331	1	let	let	VERB
ejpam-6997	331	2	b	b	X
ejpam-6997	331	3	∈	∈	PROPN
ejpam-6997	331	4	cϱ(n	cϱ(n	X
ejpam-6997	331	5	)	)	PUNCT
ejpam-6997	331	6	.	.	PUNCT
ejpam-6997	332	1	in	in	ADP
ejpam-6997	332	2	line	line	NOUN
ejpam-6997	332	3	with	with	ADP
ejpam-6997	332	4	corollary	corollary	ADJ
ejpam-6997	332	5	2.20	2.20	NUM
ejpam-6997	332	6	,	,	PUNCT
ejpam-6997	332	7	cϱ(n	cϱ(n	X
ejpam-6997	332	8	)	)	PUNCT
ejpam-6997	332	9	=	=	SYM
ejpam-6997	332	10	cϱ(b	cϱ(b	NOUN
ejpam-6997	332	11	)	)	PUNCT
ejpam-6997	332	12	.	.	PUNCT
ejpam-6997	333	1	then	then	ADV
ejpam-6997	333	2	,	,	PUNCT
ejpam-6997	333	3	cϱ(b)\cϱ(n	cϱ(b)\cϱ(n	ADJ
ejpam-6997	333	4	)	)	PUNCT
ejpam-6997	334	1	̸=	̸=	PROPN
ejpam-6997	334	2	ϕ	ϕ	PROPN
ejpam-6997	334	3	∈	∈	PROPN
ejpam-6997	334	4	g	g	NOUN
ejpam-6997	334	5	,	,	PUNCT
ejpam-6997	334	6	and	and	CCONJ
ejpam-6997	334	7	so	so	ADV
ejpam-6997	334	8	b	b	PROPN
ejpam-6997	334	9	∈	∈	PROPN
ejpam-6997	334	10	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	334	11	(	(	PUNCT
ejpam-6997	334	12	cϱ(n	cϱ(n	NUM
ejpam-6997	334	13	)	)	PUNCT
ejpam-6997	334	14	)	)	PUNCT
ejpam-6997	334	15	,	,	PUNCT
ejpam-6997	334	16	and	and	CCONJ
ejpam-6997	334	17	cϱ(n	cϱ(n	NUM
ejpam-6997	334	18	)	)	PUNCT
ejpam-6997	334	19	⊑	⊑	PRON
ejpam-6997	334	20	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	334	21	(	(	PUNCT
ejpam-6997	334	22	cϱ(n	cϱ(n	NUM
ejpam-6997	334	23	)	)	PUNCT
ejpam-6997	334	24	)	)	PUNCT
ejpam-6997	334	25	.	.	PUNCT
ejpam-6997	335	1	it	it	PRON
ejpam-6997	335	2	is	be	AUX
ejpam-6997	335	3	clear	clear	ADJ
ejpam-6997	335	4	that	that	SCONJ
ejpam-6997	335	5	the	the	DET
ejpam-6997	335	6	following	follow	VERB
ejpam-6997	335	7	implication	implication	NOUN
ejpam-6997	335	8	follows	follow	VERB
ejpam-6997	335	9	from	from	ADP
ejpam-6997	335	10	points	point	NOUN
ejpam-6997	335	11	(	(	PUNCT
ejpam-6997	335	12	2	2	NUM
ejpam-6997	335	13	)	)	PUNCT
ejpam-6997	335	14	of	of	ADP
ejpam-6997	335	15	theorem	theorem	ADJ
ejpam-6997	335	16	3.3	3.3	NUM
ejpam-6997	335	17	.	.	PUNCT
ejpam-6997	336	1	corollary	corollary	ADJ
ejpam-6997	336	2	5	5	NUM
ejpam-6997	336	3	.	.	PUNCT
ejpam-6997	337	1	a	a	DET
ejpam-6997	337	2	grill	grill	NOUN
ejpam-6997	337	3	on	on	ADP
ejpam-6997	337	4	a	a	DET
ejpam-6997	337	5	ϱ-ns	ϱ-ns	ADV
ejpam-6997	337	6	(	(	PUNCT
ejpam-6997	337	7	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	337	8	,	,	PUNCT
ejpam-6997	337	9	ξϱ	ξϱ	NOUN
ejpam-6997	337	10	)	)	PUNCT
ejpam-6997	337	11	is	be	AUX
ejpam-6997	337	12	denoted	denote	VERB
ejpam-6997	337	13	by	by	ADP
ejpam-6997	337	14	g.	g.	PROPN
ejpam-6997	337	15	for	for	ADP
ejpam-6997	337	16	any	any	DET
ejpam-6997	337	17	ϱ	ϱ	NOUN
ejpam-6997	337	18	,	,	PUNCT
ejpam-6997	337	19	the	the	DET
ejpam-6997	337	20	following	follow	VERB
ejpam-6997	337	21	ideas	idea	NOUN
ejpam-6997	337	22	are	be	AUX
ejpam-6997	337	23	true	true	ADJ
ejpam-6997	337	24	if	if	SCONJ
ejpam-6997	337	25	d,∆	d,∆	NOUN
ejpam-6997	337	26	⊑	⊑	PRON
ejpam-6997	337	27	ℵ	ℵ	NOUN
ejpam-6997	337	28	:	:	PUNCT
ejpam-6997	337	29	(	(	PUNCT
ejpam-6997	337	30	1	1	X
ejpam-6997	337	31	)	)	PUNCT
ejpam-6997	337	32	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	337	33	(	(	PUNCT
ejpam-6997	337	34	d	d	NOUN
ejpam-6997	337	35	)	)	PUNCT
ejpam-6997	337	36	⊔	⊔	NUM
ejpam-6997	337	37	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	337	38	(	(	PUNCT
ejpam-6997	337	39	∆	∆	PROPN
ejpam-6997	337	40	)	)	PUNCT
ejpam-6997	337	41	⊑	⊑	PRON
ejpam-6997	337	42	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	337	43	(	(	PUNCT
ejpam-6997	337	44	d	d	PROPN
ejpam-6997	337	45	⊔	⊔	NUM
ejpam-6997	337	46	ℵ	ℵ	NOUN
ejpam-6997	337	47	)	)	PUNCT
ejpam-6997	337	48	.	.	PUNCT
ejpam-6997	338	1	(	(	PUNCT
ejpam-6997	338	2	2	2	X
ejpam-6997	338	3	)	)	PUNCT
ejpam-6997	338	4	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	338	5	(	(	PUNCT
ejpam-6997	338	6	d	d	PROPN
ejpam-6997	338	7	⊓	⊓	PROPN
ejpam-6997	338	8	∆	∆	X
ejpam-6997	338	9	)	)	PUNCT
ejpam-6997	338	10	⊑	⊑	PRON
ejpam-6997	338	11	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	338	12	(	(	PUNCT
ejpam-6997	338	13	d	d	X
ejpam-6997	338	14	)	)	PUNCT
ejpam-6997	338	15	⊓	⊓	PROPN
ejpam-6997	338	16	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	338	17	(	(	PUNCT
ejpam-6997	338	18	∆	∆	PROPN
ejpam-6997	338	19	)	)	PUNCT
ejpam-6997	338	20	.	.	PUNCT
ejpam-6997	339	1	proposition	proposition	NOUN
ejpam-6997	339	2	9	9	NUM
ejpam-6997	339	3	.	.	PUNCT
ejpam-6997	340	1	let	let	VERB
ejpam-6997	340	2	g	g	PRON
ejpam-6997	340	3	be	be	AUX
ejpam-6997	340	4	a	a	DET
ejpam-6997	340	5	grill	grill	NOUN
ejpam-6997	340	6	on	on	ADP
ejpam-6997	340	7	a	a	DET
ejpam-6997	340	8	ϱ-ns	ϱ-ns	ADV
ejpam-6997	340	9	(	(	PUNCT
ejpam-6997	340	10	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	340	11	,	,	PUNCT
ejpam-6997	340	12	ξϱ	ξϱ	NOUN
ejpam-6997	340	13	)	)	PUNCT
ejpam-6997	340	14	.	.	PUNCT
ejpam-6997	341	1	if	if	SCONJ
ejpam-6997	341	2	d,∆	d,∆	NOUN
ejpam-6997	341	3	⊑	⊑	PRON
ejpam-6997	341	4	ℵ	ℵ	NOUN
ejpam-6997	341	5	,	,	PUNCT
ejpam-6997	341	6	then	then	ADV
ejpam-6997	341	7	(	(	PUNCT
ejpam-6997	341	8	1	1	X
ejpam-6997	341	9	)	)	PUNCT
ejpam-6997	341	10	gm̃cu	gm̃cu	NOUN
ejpam-6997	341	11	(	(	PUNCT
ejpam-6997	341	12	∆	∆	PROPN
ejpam-6997	341	13	)	)	PUNCT
ejpam-6997	341	14	⊑	⊑	X
ejpam-6997	341	15	gm̃cr	gm̃cr	NOUN
ejpam-6997	341	16	(	(	PUNCT
ejpam-6997	341	17	∆	∆	X
ejpam-6997	341	18	)	)	PUNCT
ejpam-6997	342	1	⊓	⊓	NOUN
ejpam-6997	342	2	gm̃cl	gm̃cl	VERB
ejpam-6997	342	3	(	(	PUNCT
ejpam-6997	342	4	∆	∆	X
ejpam-6997	342	5	)	)	PUNCT
ejpam-6997	342	6	⊑	⊑	X
ejpam-6997	342	7	gm̃cr	gm̃cr	NOUN
ejpam-6997	342	8	(	(	PUNCT
ejpam-6997	342	9	∆	∆	PROPN
ejpam-6997	342	10	)	)	PUNCT
ejpam-6997	342	11	⊔	⊔	NUM
ejpam-6997	342	12	gm̃cl	gm̃cl	NOUN
ejpam-6997	342	13	(	(	PUNCT
ejpam-6997	342	14	∆	∆	PROPN
ejpam-6997	342	15	)	)	PUNCT
ejpam-6997	342	16	⊑	⊑	X
ejpam-6997	342	17	gm̃ci	gm̃ci	PROPN
ejpam-6997	342	18	(	(	PUNCT
ejpam-6997	342	19	∆	∆	PROPN
ejpam-6997	342	20	)	)	PUNCT
ejpam-6997	342	21	.	.	PUNCT
ejpam-6997	343	1	(	(	PUNCT
ejpam-6997	343	2	2	2	X
ejpam-6997	343	3	)	)	PUNCT
ejpam-6997	343	4	gm̃ci	gm̃ci	PROPN
ejpam-6997	343	5	(	(	PUNCT
ejpam-6997	343	6	∆	∆	PROPN
ejpam-6997	343	7	)	)	PUNCT
ejpam-6997	343	8	⊑	⊑	X
ejpam-6997	343	9	gm̃cr	gm̃cr	NOUN
ejpam-6997	343	10	(	(	PUNCT
ejpam-6997	343	11	∆	∆	X
ejpam-6997	343	12	)	)	PUNCT
ejpam-6997	344	1	⊓	⊓	NOUN
ejpam-6997	344	2	gm̃cl	gm̃cl	VERB
ejpam-6997	344	3	(	(	PUNCT
ejpam-6997	344	4	∆	∆	X
ejpam-6997	344	5	)	)	PUNCT
ejpam-6997	344	6	⊑	⊑	X
ejpam-6997	344	7	gm̃cr	gm̃cr	NOUN
ejpam-6997	344	8	(	(	PUNCT
ejpam-6997	344	9	∆	∆	PROPN
ejpam-6997	344	10	)	)	PUNCT
ejpam-6997	344	11	⊔	⊔	NUM
ejpam-6997	344	12	gm̃cl	gm̃cl	NOUN
ejpam-6997	344	13	(	(	PUNCT
ejpam-6997	344	14	∆	∆	X
ejpam-6997	344	15	)	)	PUNCT
ejpam-6997	345	1	⊑	⊑	PRON
ejpam-6997	345	2	gm̃cu	gm̃cu	NOUN
ejpam-6997	345	3	(	(	PUNCT
ejpam-6997	345	4	∆	∆	PROPN
ejpam-6997	345	5	)	)	PUNCT
ejpam-6997	345	6	.	.	PUNCT
ejpam-6997	346	1	(	(	PUNCT
ejpam-6997	346	2	3	3	X
ejpam-6997	346	3	)	)	PUNCT
ejpam-6997	346	4	gm̃c⟨u⟩	gm̃c⟨u⟩	NOUN
ejpam-6997	346	5	(	(	PUNCT
ejpam-6997	346	6	∆	∆	X
ejpam-6997	346	7	)	)	PUNCT
ejpam-6997	347	1	⊑	⊑	X
ejpam-6997	347	2	gm̃c⟨r⟩	gm̃c⟨r⟩	X
ejpam-6997	347	3	(	(	PUNCT
ejpam-6997	347	4	∆	∆	X
ejpam-6997	347	5	)	)	PUNCT
ejpam-6997	348	1	⊓	⊓	PROPN
ejpam-6997	348	2	gm̃c⟨l⟩	gm̃c⟨l⟩	X
ejpam-6997	348	3	(	(	PUNCT
ejpam-6997	348	4	∆	∆	PROPN
ejpam-6997	348	5	)	)	PUNCT
ejpam-6997	348	6	⊑	⊑	X
ejpam-6997	348	7	gm̃c⟨r⟩	gm̃c⟨r⟩	X
ejpam-6997	348	8	(	(	PUNCT
ejpam-6997	348	9	∆	∆	PROPN
ejpam-6997	348	10	)	)	PUNCT
ejpam-6997	348	11	⊔	⊔	PROPN
ejpam-6997	348	12	gm̃c⟨l⟩	gm̃c⟨l⟩	PROPN
ejpam-6997	348	13	(	(	PUNCT
ejpam-6997	348	14	∆	∆	PROPN
ejpam-6997	348	15	)	)	PUNCT
ejpam-6997	348	16	⊑	⊑	X
ejpam-6997	348	17	gm̃c⟨i⟩	gm̃c⟨i⟩	X
ejpam-6997	348	18	(	(	PUNCT
ejpam-6997	348	19	∆	∆	PROPN
ejpam-6997	348	20	)	)	PUNCT
ejpam-6997	348	21	.	.	PUNCT
ejpam-6997	349	1	(	(	PUNCT
ejpam-6997	349	2	4	4	X
ejpam-6997	349	3	)	)	PUNCT
ejpam-6997	349	4	gm̃c⟨i⟩	gm̃c⟨i⟩	NOUN
ejpam-6997	349	5	(	(	PUNCT
ejpam-6997	349	6	∆	∆	X
ejpam-6997	349	7	)	)	PUNCT
ejpam-6997	350	1	⊑	⊑	X
ejpam-6997	350	2	gm̃c⟨r⟩	gm̃c⟨r⟩	X
ejpam-6997	350	3	(	(	PUNCT
ejpam-6997	350	4	∆	∆	X
ejpam-6997	350	5	)	)	PUNCT
ejpam-6997	351	1	⊓	⊓	PROPN
ejpam-6997	351	2	gm̃c⟨l⟩	gm̃c⟨l⟩	X
ejpam-6997	351	3	(	(	PUNCT
ejpam-6997	351	4	∆	∆	PROPN
ejpam-6997	351	5	)	)	PUNCT
ejpam-6997	351	6	⊑	⊑	X
ejpam-6997	351	7	gm̃c⟨r⟩	gm̃c⟨r⟩	X
ejpam-6997	351	8	(	(	PUNCT
ejpam-6997	351	9	∆	∆	PROPN
ejpam-6997	351	10	)	)	PUNCT
ejpam-6997	351	11	⊔	⊔	PROPN
ejpam-6997	351	12	gm̃c⟨l⟩	gm̃c⟨l⟩	PROPN
ejpam-6997	351	13	(	(	PUNCT
ejpam-6997	351	14	∆	∆	PROPN
ejpam-6997	351	15	)	)	PUNCT
ejpam-6997	351	16	⊑	⊑	PRON
ejpam-6997	351	17	gm̃c⟨u⟩	gm̃c⟨u⟩	X
ejpam-6997	351	18	(	(	PUNCT
ejpam-6997	351	19	∆	∆	PROPN
ejpam-6997	351	20	)	)	PUNCT
ejpam-6997	351	21	.	.	PUNCT
ejpam-6997	352	1	proof	proof	NOUN
ejpam-6997	352	2	.	.	PUNCT
ejpam-6997	353	1	this	this	PRON
ejpam-6997	353	2	derives	derive	VERB
ejpam-6997	353	3	from	from	ADP
ejpam-6997	353	4	proposition	proposition	NOUN
ejpam-6997	353	5	2.14	2.14	NUM
ejpam-6997	353	6	(	(	PUNCT
ejpam-6997	353	7	1	1	NUM
ejpam-6997	353	8	)	)	PUNCT
ejpam-6997	353	9	.	.	PUNCT
ejpam-6997	354	1	a.	a.	PROPN
ejpam-6997	354	2	a.	a.	PROPN
ejpam-6997	354	3	azzam	azzam	PROPN
ejpam-6997	354	4	,	,	PUNCT
ejpam-6997	354	5	m.	m.	NOUN
ejpam-6997	354	6	aldawood	aldawood	PROPN
ejpam-6997	354	7	,	,	PUNCT
ejpam-6997	354	8	b.	b.	PROPN
ejpam-6997	354	9	alreshidi	alreshidi	PROPN
ejpam-6997	354	10	/	/	SYM
ejpam-6997	354	11	eur	eur	PROPN
ejpam-6997	354	12	.	.	PUNCT
ejpam-6997	355	1	j.	j.	PROPN
ejpam-6997	355	2	pure	pure	PROPN
ejpam-6997	355	3	appl	appl	PROPN
ejpam-6997	355	4	.	.	PROPN
ejpam-6997	355	5	math	math	PROPN
ejpam-6997	355	6	,	,	PUNCT
ejpam-6997	355	7	18	18	NUM
ejpam-6997	355	8	(	(	PUNCT
ejpam-6997	355	9	4	4	NUM
ejpam-6997	355	10	)	)	PUNCT
ejpam-6997	355	11	(	(	PUNCT
ejpam-6997	355	12	2025	2025	NUM
ejpam-6997	355	13	)	)	PUNCT
ejpam-6997	355	14	,	,	PUNCT
ejpam-6997	355	15	6997	6997	NUM
ejpam-6997	355	16	12	12	NUM
ejpam-6997	355	17	of	of	ADP
ejpam-6997	355	18	31	31	NUM
ejpam-6997	355	19	proposition	proposition	NOUN
ejpam-6997	355	20	10	10	NUM
ejpam-6997	355	21	.	.	PUNCT
ejpam-6997	356	1	on	on	ADP
ejpam-6997	356	2	a	a	DET
ejpam-6997	356	3	ϱ-ns	ϱ-ns	ADV
ejpam-6997	356	4	(	(	PUNCT
ejpam-6997	356	5	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	356	6	,	,	PUNCT
ejpam-6997	356	7	ξϱ	ξϱ	NOUN
ejpam-6997	356	8	)	)	PUNCT
ejpam-6997	356	9	,	,	PUNCT
ejpam-6997	356	10	let	let	VERB
ejpam-6997	356	11	g	g	PRON
ejpam-6997	356	12	be	be	AUX
ejpam-6997	356	13	a	a	DET
ejpam-6997	356	14	grill	grill	NOUN
ejpam-6997	356	15	,	,	PUNCT
ejpam-6997	356	16	and	and	CCONJ
ejpam-6997	356	17	let	let	VERB
ejpam-6997	356	18	γ	γ	NOUN
ejpam-6997	356	19	be	be	AUX
ejpam-6997	356	20	a	a	DET
ejpam-6997	356	21	symmetric	symmetric	ADJ
ejpam-6997	356	22	relation	relation	NOUN
ejpam-6997	356	23	.	.	PUNCT
ejpam-6997	357	1	then	then	ADV
ejpam-6997	357	2	,	,	PUNCT
ejpam-6997	357	3	∀∆	∀∆	X
ejpam-6997	357	4	⊑	⊑	X
ejpam-6997	357	5	ℵ	ℵ	X
ejpam-6997	357	6	,	,	PUNCT
ejpam-6997	357	7	all	all	DET
ejpam-6997	357	8	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	357	9	(	(	PUNCT
ejpam-6997	357	10	∆)(gm̃cϱ	∆)(gm̃cϱ	X
ejpam-6997	357	11	(	(	PUNCT
ejpam-6997	357	12	∆	∆	PROPN
ejpam-6997	357	13	)	)	PUNCT
ejpam-6997	357	14	)	)	PUNCT
ejpam-6997	357	15	are	be	AUX
ejpam-6997	357	16	equal	equal	ADJ
ejpam-6997	357	17	.	.	PUNCT
ejpam-6997	358	1	proof	proof	NOUN
ejpam-6997	358	2	.	.	PUNCT
ejpam-6997	359	1	this	this	PRON
ejpam-6997	359	2	derives	derive	VERB
ejpam-6997	359	3	from	from	ADP
ejpam-6997	359	4	proposition	proposition	NOUN
ejpam-6997	359	5	2.14(2	2.14(2	NUM
ejpam-6997	359	6	)	)	PUNCT
ejpam-6997	359	7	.	.	PUNCT
ejpam-6997	360	1	to	to	PART
ejpam-6997	360	2	demonstrate	demonstrate	VERB
ejpam-6997	360	3	this	this	PRON
ejpam-6997	360	4	,	,	PUNCT
ejpam-6997	360	5	we	we	PRON
ejpam-6997	360	6	provide	provide	VERB
ejpam-6997	360	7	the	the	DET
ejpam-6997	360	8	following	follow	VERB
ejpam-6997	360	9	example	example	NOUN
ejpam-6997	360	10	:	:	PUNCT
ejpam-6997	360	11	(	(	PUNCT
ejpam-6997	360	12	1	1	X
ejpam-6997	360	13	)	)	PUNCT
ejpam-6997	360	14	in	in	ADP
ejpam-6997	360	15	general	general	ADJ
ejpam-6997	360	16	,	,	PUNCT
ejpam-6997	360	17	the	the	DET
ejpam-6997	360	18	opposite	opposite	NOUN
ejpam-6997	360	19	of	of	ADP
ejpam-6997	360	20	items	item	NOUN
ejpam-6997	360	21	(	(	PUNCT
ejpam-6997	360	22	2	2	NUM
ejpam-6997	360	23	)	)	PUNCT
ejpam-6997	360	24	,	,	PUNCT
ejpam-6997	360	25	(	(	PUNCT
ejpam-6997	360	26	6	6	NUM
ejpam-6997	360	27	)	)	PUNCT
ejpam-6997	360	28	,	,	PUNCT
ejpam-6997	360	29	and	and	CCONJ
ejpam-6997	360	30	(	(	PUNCT
ejpam-6997	360	31	7	7	X
ejpam-6997	360	32	)	)	PUNCT
ejpam-6997	360	33	in	in	ADP
ejpam-6997	360	34	theorem	theorem	ADJ
ejpam-6997	360	35	3.3	3.3	NUM
ejpam-6997	360	36	is	be	AUX
ejpam-6997	360	37	not	not	PART
ejpam-6997	360	38	successful	successful	ADJ
ejpam-6997	360	39	,	,	PUNCT
ejpam-6997	360	40	(	(	PUNCT
ejpam-6997	360	41	2	2	X
ejpam-6997	360	42	)	)	PUNCT
ejpam-6997	360	43	corollary	corollary	NOUN
ejpam-6997	360	44	3.4	3.4	NUM
ejpam-6997	360	45	’s	’s	PART
ejpam-6997	360	46	converse	converse	NOUN
ejpam-6997	360	47	is	be	AUX
ejpam-6997	360	48	n’t	not	PART
ejpam-6997	360	49	always	always	ADV
ejpam-6997	360	50	true	true	ADJ
ejpam-6997	360	51	,	,	PUNCT
ejpam-6997	360	52	(	(	PUNCT
ejpam-6997	360	53	3	3	X
ejpam-6997	360	54	)	)	PUNCT
ejpam-6997	360	55	the	the	DET
ejpam-6997	360	56	subsets	subset	NOUN
ejpam-6997	360	57	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	360	58	(	(	PUNCT
ejpam-6997	360	59	cϱ(b	cϱ(b	NOUN
ejpam-6997	360	60	)	)	PUNCT
ejpam-6997	360	61	)	)	PUNCT
ejpam-6997	360	62	and	and	CCONJ
ejpam-6997	360	63	cϱ(b	cϱ(b	NOUN
ejpam-6997	360	64	)	)	PUNCT
ejpam-6997	360	65	are	be	AUX
ejpam-6997	360	66	independent	independent	ADJ
ejpam-6997	360	67	of	of	ADP
ejpam-6997	360	68	one	one	NUM
ejpam-6997	360	69	another	another	DET
ejpam-6997	360	70	in	in	ADP
ejpam-6997	360	71	the	the	DET
ejpam-6997	360	72	case	case	NOUN
ejpam-6997	360	73	of	of	ADP
ejpam-6997	360	74	ϱ	ϱ	PROPN
ejpam-6997	360	75	∈	∈	PROPN
ejpam-6997	360	76	{	{	PUNCT
ejpam-6997	360	77	u	u	NOUN
ejpam-6997	360	78	,	,	PUNCT
ejpam-6997	360	79	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	360	80	}	}	PUNCT
ejpam-6997	360	81	,	,	PUNCT
ejpam-6997	360	82	(	(	PUNCT
ejpam-6997	360	83	4	4	X
ejpam-6997	360	84	)	)	PUNCT
ejpam-6997	360	85	proposition	proposition	NOUN
ejpam-6997	360	86	3.5	3.5	NUM
ejpam-6997	360	87	’s	’s	NOUN
ejpam-6997	360	88	opposite	opposite	ADJ
ejpam-6997	360	89	need	need	AUX
ejpam-6997	360	90	not	not	PART
ejpam-6997	360	91	be	be	AUX
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ejpam-6997	365	17	1	1	X
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ejpam-6997	372	450	{	{	PUNCT
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ejpam-6997	372	454	,	,	PUNCT
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ejpam-6997	372	458	n	n	X
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ejpam-6997	372	460	e	e	NOUN
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ejpam-6997	372	463	{	{	PUNCT
ejpam-6997	372	464	b	b	NOUN
ejpam-6997	372	465	,	,	PUNCT
ejpam-6997	372	466	n	n	CCONJ
ejpam-6997	372	467	}	}	PUNCT
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ejpam-6997	372	473	,	,	PUNCT
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ejpam-6997	372	478	,	,	PUNCT
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ejpam-6997	372	480	,	,	PUNCT
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ejpam-6997	372	485	}	}	PUNCT
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ejpam-6997	372	491	,	,	PUNCT
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ejpam-6997	372	495	b	b	PROPN
ejpam-6997	372	496	,	,	PUNCT
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ejpam-6997	372	498	,	,	PUNCT
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ejpam-6997	372	502	b	b	PROPN
ejpam-6997	372	503	,	,	PUNCT
ejpam-6997	372	504	m	m	PROPN
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ejpam-6997	372	594	ℵ	ℵ	ADJ
ejpam-6997	372	595	ℵ	ℵ	NOUN
ejpam-6997	372	596	ℵ	ℵ	NOUN
ejpam-6997	372	597	ℵ	ℵ	NOUN
ejpam-6997	372	598	ℵ	ℵ	NOUN
ejpam-6997	372	599	ℵ	ℵ	NOUN
ejpam-6997	372	600	ℵ	ℵ	NOUN
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ejpam-6997	372	602	ℵ	ℵ	NOUN
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ejpam-6997	372	604	ϕ	ϕ	X
ejpam-6997	372	605	ϕ	ϕ	X
ejpam-6997	372	606	ϕ	ϕ	X
ejpam-6997	372	607	ϕ	ϕ	X
ejpam-6997	372	608	ϕ	ϕ	X
ejpam-6997	372	609	ϕ	ϕ	X
ejpam-6997	372	610	ϕ	ϕ	X
ejpam-6997	372	611	ϕ	ϕ	X
ejpam-6997	372	612	ϕ	ϕ	X
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ejpam-6997	372	614	primary	primary	ADJ
ejpam-6997	372	615	benefit	benefit	NOUN
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ejpam-6997	372	640	-	-	PUNCT
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ejpam-6997	372	646	-	-	PUNCT
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ejpam-6997	375	11	,	,	PUNCT
ejpam-6997	375	12	ξϱ	ξϱ	NOUN
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ejpam-6997	376	10	1	1	X
ejpam-6997	376	11	)	)	PUNCT
ejpam-6997	376	12	mcϱ(d	mcϱ(d	PROPN
ejpam-6997	376	13	)	)	PUNCT
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ejpam-6997	376	16	(	(	PUNCT
ejpam-6997	376	17	d	d	NOUN
ejpam-6997	376	18	)	)	PUNCT
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ejpam-6997	376	21	2	2	X
ejpam-6997	376	22	)	)	PUNCT
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ejpam-6997	376	30	mcϱ(d	mcϱ(d	PROPN
ejpam-6997	376	31	)	)	PUNCT
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ejpam-6997	378	2	π	π	PROPN
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ejpam-6997	378	4	mcϱ(d	mcϱ(d	PROPN
ejpam-6997	378	5	)	)	PUNCT
ejpam-6997	378	6	.	.	PUNCT
ejpam-6997	379	1	then	then	ADV
ejpam-6997	379	2	,	,	PUNCT
ejpam-6997	379	3	cϱ(π	cϱ(π	NOUN
ejpam-6997	379	4	)	)	PUNCT
ejpam-6997	379	5	⊑	⊑	PROPN
ejpam-6997	380	1	d	d	NOUN
ejpam-6997	380	2	,	,	PUNCT
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ejpam-6997	380	4	cϱ(π	cϱ(π	NOUN
ejpam-6997	380	5	)	)	PUNCT
ejpam-6997	380	6	⊓dc	⊓dc	PROPN
ejpam-6997	380	7	/∈	/∈	PUNCT
ejpam-6997	381	1	g.	g.	PROPN
ejpam-6997	381	2	currently	currently	ADV
ejpam-6997	381	3	,	,	PUNCT
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ejpam-6997	381	5	have	have	VERB
ejpam-6997	381	6	π	π	PROPN
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ejpam-6997	381	9	(	(	PUNCT
ejpam-6997	381	10	d	d	NOUN
ejpam-6997	381	11	)	)	PUNCT
ejpam-6997	381	12	.	.	PUNCT
ejpam-6997	382	1	hence	hence	ADV
ejpam-6997	382	2	,	,	PUNCT
ejpam-6997	382	3	mcϱ(d	mcϱ(d	PROPN
ejpam-6997	382	4	)	)	PUNCT
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ejpam-6997	383	2	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	383	3	(	(	PUNCT
ejpam-6997	383	4	d	d	NOUN
ejpam-6997	383	5	)	)	PUNCT
ejpam-6997	383	6	.	.	PUNCT
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ejpam-6997	385	16	we	we	PRON
ejpam-6997	385	17	shall	shall	AUX
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ejpam-6997	385	19	an	an	DET
ejpam-6997	385	20	example	example	NOUN
ejpam-6997	385	21	.	.	PUNCT
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ejpam-6997	387	1	2	2	NUM
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ejpam-6997	387	9	.	.	PUNCT
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ejpam-6997	388	3	mcϱ(d	mcϱ(d	PROPN
ejpam-6997	388	4	)	)	PUNCT
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ejpam-6997	404	5	cϱ(π	cϱ(π	NOUN
ejpam-6997	404	6	)	)	PUNCT
ejpam-6997	404	7	)	)	PUNCT
ejpam-6997	405	1	⊈	⊈	PROPN
ejpam-6997	405	2	cϱ(π)∀ϱ.	cϱ(π)∀ϱ.	PROPN
ejpam-6997	405	3	example	example	NOUN
ejpam-6997	405	4	3.11	3.11	NUM
ejpam-6997	405	5	illustrates	illustrate	VERB
ejpam-6997	405	6	property	property	NOUN
ejpam-6997	405	7	(	(	PUNCT
ejpam-6997	405	8	1	1	NUM
ejpam-6997	405	9	→	→	SYM
ejpam-6997	405	10	5	5	NUM
ejpam-6997	405	11	)	)	PUNCT
ejpam-6997	405	12	of	of	ADP
ejpam-6997	405	13	remark	remark	NOUN
ejpam-6997	405	14	3.10	3.10	NUM
ejpam-6997	405	15	example	example	NOUN
ejpam-6997	405	16	3	3	NUM
ejpam-6997	405	17	.	.	PUNCT
ejpam-6997	406	1	in	in	ADP
ejpam-6997	406	2	example	example	NOUN
ejpam-6997	406	3	3.7	3.7	NUM
ejpam-6997	406	4	.	.	PUNCT
ejpam-6997	407	1	let	let	VERB
ejpam-6997	407	2	g	g	NOUN
ejpam-6997	407	3	=	=	PRON
ejpam-6997	407	4	{	{	PUNCT
ejpam-6997	407	5	{	{	PUNCT
ejpam-6997	407	6	b	b	NOUN
ejpam-6997	407	7	}	}	PUNCT
ejpam-6997	407	8	,	,	PUNCT
ejpam-6997	407	9	{	{	PUNCT
ejpam-6997	407	10	b	b	NOUN
ejpam-6997	407	11	,	,	PUNCT
ejpam-6997	407	12	e	e	NOUN
ejpam-6997	407	13	}	}	PUNCT
ejpam-6997	407	14	,	,	PUNCT
ejpam-6997	407	15	{	{	PUNCT
ejpam-6997	407	16	b	b	NOUN
ejpam-6997	407	17	,	,	PUNCT
ejpam-6997	407	18	n	n	CCONJ
ejpam-6997	407	19	}	}	PUNCT
ejpam-6997	407	20	,	,	PUNCT
ejpam-6997	407	21	{	{	PUNCT
ejpam-6997	407	22	b	b	X
ejpam-6997	407	23	,	,	PUNCT
ejpam-6997	407	24	m	m	NOUN
ejpam-6997	407	25	}	}	PUNCT
ejpam-6997	407	26	,	,	PUNCT
ejpam-6997	407	27	{	{	PUNCT
ejpam-6997	407	28	b	b	NOUN
ejpam-6997	407	29	,	,	PUNCT
ejpam-6997	407	30	e	e	NOUN
ejpam-6997	407	31	,	,	PUNCT
ejpam-6997	407	32	n	n	CCONJ
ejpam-6997	407	33	}	}	PUNCT
ejpam-6997	407	34	,	,	PUNCT
ejpam-6997	407	35	{	{	PUNCT
ejpam-6997	407	36	b	b	NOUN
ejpam-6997	407	37	,	,	PUNCT
ejpam-6997	407	38	e	e	NOUN
ejpam-6997	407	39	,	,	PUNCT
ejpam-6997	407	40	m	m	VERB
ejpam-6997	407	41	}	}	PUNCT
ejpam-6997	407	42	,	,	PUNCT
ejpam-6997	407	43	{	{	PUNCT
ejpam-6997	407	44	b	b	NOUN
ejpam-6997	407	45	,	,	PUNCT
ejpam-6997	407	46	n	n	CCONJ
ejpam-6997	407	47	,	,	PUNCT
ejpam-6997	407	48	m},ℵ	m},ℵ	NOUN
ejpam-6997	407	49	}	}	PUNCT
ejpam-6997	407	50	be	be	AUX
ejpam-6997	407	51	a	a	DET
ejpam-6997	407	52	grill	grill	NOUN
ejpam-6997	407	53	on	on	ADP
ejpam-6997	407	54	a	a	DET
ejpam-6997	407	55	ϱ-ns	ϱ-ns	ADV
ejpam-6997	407	56	(	(	PUNCT
ejpam-6997	407	57	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	407	58	,	,	PUNCT
ejpam-6997	407	59	ξϱ	ξϱ	NOUN
ejpam-6997	407	60	)	)	PUNCT
ejpam-6997	407	61	(	(	PUNCT
ejpam-6997	407	62	1	1	X
ejpam-6997	407	63	)	)	PUNCT
ejpam-6997	407	64	if	if	SCONJ
ejpam-6997	407	65	∆	∆	VERB
ejpam-6997	407	66	=	=	PRON
ejpam-6997	407	67	{	{	PUNCT
ejpam-6997	407	68	b	b	PROPN
ejpam-6997	407	69	,	,	PUNCT
ejpam-6997	407	70	n	n	CCONJ
ejpam-6997	407	71	,	,	PUNCT
ejpam-6997	407	72	m	m	NOUN
ejpam-6997	407	73	}	}	PUNCT
ejpam-6997	407	74	,	,	PUNCT
ejpam-6997	407	75	then	then	ADV
ejpam-6997	407	76	gm̃cr	gm̃cr	NOUN
ejpam-6997	407	77	(	(	PUNCT
ejpam-6997	407	78	∆	∆	PROPN
ejpam-6997	407	79	)	)	PUNCT
ejpam-6997	408	1	=	=	SYM
ejpam-6997	408	2	ℵ	ℵ	PRON
ejpam-6997	408	3	⊈	⊈	NUM
ejpam-6997	408	4	∆	∆	X
ejpam-6997	408	5	,	,	PUNCT
ejpam-6997	408	6	(	(	PUNCT
ejpam-6997	408	7	2	2	X
ejpam-6997	408	8	)	)	PUNCT
ejpam-6997	408	9	if	if	SCONJ
ejpam-6997	408	10	∆	∆	VERB
ejpam-6997	408	11	=	=	PRON
ejpam-6997	408	12	{	{	PUNCT
ejpam-6997	408	13	b	b	NOUN
ejpam-6997	408	14	,	,	PUNCT
ejpam-6997	408	15	e	e	NOUN
ejpam-6997	408	16	}	}	PUNCT
ejpam-6997	408	17	,	,	PUNCT
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ejpam-6997	408	19	∆	∆	PROPN
ejpam-6997	408	20	⊈	⊈	PROPN
ejpam-6997	408	21	{	{	PUNCT
ejpam-6997	408	22	b	b	NOUN
ejpam-6997	408	23	,	,	PUNCT
ejpam-6997	408	24	m	m	NOUN
ejpam-6997	408	25	}	}	PUNCT
ejpam-6997	408	26	=	=	PUNCT
ejpam-6997	408	27	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	408	28	(	(	PUNCT
ejpam-6997	408	29	{	{	PUNCT
ejpam-6997	408	30	∆	∆	X
ejpam-6997	408	31	}	}	PUNCT
ejpam-6997	408	32	)	)	PUNCT
ejpam-6997	408	33	.	.	PUNCT
ejpam-6997	409	1	(	(	PUNCT
ejpam-6997	409	2	3	3	X
ejpam-6997	409	3	)	)	PUNCT
ejpam-6997	409	4	gm̃cr	gm̃cr	NOUN
ejpam-6997	409	5	(	(	PUNCT
ejpam-6997	409	6	ϕ	ϕ	NOUN
ejpam-6997	409	7	)	)	PUNCT
ejpam-6997	409	8	=	=	SYM
ejpam-6997	409	9	{	{	PUNCT
ejpam-6997	409	10	n	n	X
ejpam-6997	409	11	,	,	PUNCT
ejpam-6997	409	12	e	e	NOUN
ejpam-6997	409	13	}	}	PUNCT
ejpam-6997	409	14	̸=	̸=	PROPN
ejpam-6997	409	15	ϕ.	ϕ.	NOUN
ejpam-6997	409	16	(	(	PUNCT
ejpam-6997	409	17	4	4	X
ejpam-6997	409	18	)	)	PUNCT
ejpam-6997	409	19	gm̃cr	gm̃cr	NOUN
ejpam-6997	409	20	(	(	PUNCT
ejpam-6997	409	21	ℵ	ℵ	NOUN
ejpam-6997	409	22	)	)	PUNCT
ejpam-6997	409	23	=	=	SYM
ejpam-6997	409	24	{	{	PUNCT
ejpam-6997	409	25	b	b	PROPN
ejpam-6997	409	26	,	,	PUNCT
ejpam-6997	409	27	m	m	VERB
ejpam-6997	409	28	}	}	PUNCT
ejpam-6997	409	29	̸=	̸=	PROPN
ejpam-6997	409	30	ℵ.	ℵ.	NOUN
ejpam-6997	409	31	(	(	PUNCT
ejpam-6997	409	32	5	5	X
ejpam-6997	409	33	)	)	PUNCT
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ejpam-6997	409	35	(	(	PUNCT
ejpam-6997	409	36	{	{	PUNCT
ejpam-6997	409	37	n	n	CCONJ
ejpam-6997	409	38	}	}	PUNCT
ejpam-6997	409	39	)	)	PUNCT
ejpam-6997	409	40	=	=	PRON
ejpam-6997	409	41	{	{	PUNCT
ejpam-6997	409	42	n	n	X
ejpam-6997	409	43	,	,	PUNCT
ejpam-6997	409	44	e	e	NOUN
ejpam-6997	409	45	}	}	PUNCT
ejpam-6997	409	46	⊈	⊈	PROPN
ejpam-6997	409	47	{	{	PUNCT
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ejpam-6997	409	49	(	(	PUNCT
ejpam-6997	409	50	{	{	PUNCT
ejpam-6997	409	51	n	n	CCONJ
ejpam-6997	409	52	}	}	PUNCT
ejpam-6997	409	53	)	)	PUNCT
ejpam-6997	409	54	=	=	PRON
ejpam-6997	409	55	{	{	PUNCT
ejpam-6997	409	56	n	n	X
ejpam-6997	409	57	,	,	PUNCT
ejpam-6997	409	58	m	m	PROPN
ejpam-6997	409	59	,	,	PUNCT
ejpam-6997	409	60	e	e	NOUN
ejpam-6997	409	61	}	}	PUNCT
ejpam-6997	409	62	⊈	⊈	PROPN
ejpam-6997	409	63	{	{	PUNCT
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ejpam-6997	409	65	(	(	PUNCT
ejpam-6997	409	66	{	{	PUNCT
ejpam-6997	409	67	e	e	NOUN
ejpam-6997	409	68	}	}	PUNCT
ejpam-6997	409	69	)	)	PUNCT
ejpam-6997	409	70	=	=	SYM
ejpam-6997	409	71	{	{	PUNCT
ejpam-6997	409	72	n	n	X
ejpam-6997	409	73	,	,	PUNCT
ejpam-6997	409	74	e	e	NOUN
ejpam-6997	409	75	}	}	PUNCT
ejpam-6997	409	76	⊈	⊈	PROPN
ejpam-6997	409	77	{	{	PUNCT
ejpam-6997	409	78	e	e	NOUN
ejpam-6997	409	79	}	}	PUNCT
ejpam-6997	409	80	.	.	PUNCT
ejpam-6997	410	1	hence	hence	ADV
ejpam-6997	410	2	,	,	PUNCT
ejpam-6997	410	3	∀π	∀π	PROPN
ejpam-6997	410	4	∈	∈	PROPN
ejpam-6997	410	5	ℵ,gm̃cϱ	ℵ,gm̃cϱ	PROPN
ejpam-6997	410	6	(	(	PUNCT
ejpam-6997	410	7	{	{	PUNCT
ejpam-6997	410	8	π	π	NOUN
ejpam-6997	410	9	}	}	PUNCT
ejpam-6997	410	10	)	)	PUNCT
ejpam-6997	410	11	⊈	⊈	PROPN
ejpam-6997	410	12	cϱ({π	cϱ({π	NOUN
ejpam-6997	410	13	}	}	PUNCT
ejpam-6997	410	14	)	)	PUNCT
ejpam-6997	410	15	a.	a.	NOUN
ejpam-6997	410	16	a.	a.	PROPN
ejpam-6997	410	17	azzam	azzam	PROPN
ejpam-6997	410	18	,	,	PUNCT
ejpam-6997	410	19	m.	m.	NOUN
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ejpam-6997	410	21	,	,	PUNCT
ejpam-6997	410	22	b.	b.	PROPN
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ejpam-6997	410	26	.	.	PUNCT
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ejpam-6997	411	2	pure	pure	PROPN
ejpam-6997	411	3	appl	appl	PROPN
ejpam-6997	411	4	.	.	PROPN
ejpam-6997	411	5	math	math	PROPN
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ejpam-6997	411	8	(	(	PUNCT
ejpam-6997	411	9	4	4	NUM
ejpam-6997	411	10	)	)	PUNCT
ejpam-6997	411	11	(	(	PUNCT
ejpam-6997	411	12	2025	2025	NUM
ejpam-6997	411	13	)	)	PUNCT
ejpam-6997	411	14	,	,	PUNCT
ejpam-6997	411	15	6997	6997	NUM
ejpam-6997	411	16	15	15	NUM
ejpam-6997	411	17	of	of	ADP
ejpam-6997	411	18	31	31	NUM
ejpam-6997	411	19	(	(	PUNCT
ejpam-6997	411	20	6	6	NUM
ejpam-6997	411	21	)	)	PUNCT
ejpam-6997	411	22	gm̃c⟨r⟩	gm̃c⟨r⟩	NOUN
ejpam-6997	411	23	(	(	PUNCT
ejpam-6997	411	24	gm̃c⟨r⟩	gm̃c⟨r⟩	X
ejpam-6997	411	25	(	(	PUNCT
ejpam-6997	411	26	{	{	PUNCT
ejpam-6997	411	27	e	e	NOUN
ejpam-6997	411	28	}	}	PUNCT
ejpam-6997	411	29	)	)	PUNCT
ejpam-6997	411	30	)	)	PUNCT
ejpam-6997	412	1	=	=	PRON
ejpam-6997	412	2	{	{	PUNCT
ejpam-6997	412	3	n	n	X
ejpam-6997	412	4	,	,	PUNCT
ejpam-6997	412	5	e	e	NOUN
ejpam-6997	412	6	}	}	PUNCT
ejpam-6997	412	7	̸=	̸=	PROPN
ejpam-6997	412	8	{	{	PUNCT
ejpam-6997	412	9	n	n	CCONJ
ejpam-6997	412	10	,	,	PUNCT
ejpam-6997	412	11	m	m	PROPN
ejpam-6997	412	12	,	,	PUNCT
ejpam-6997	412	13	e	e	NOUN
ejpam-6997	412	14	}	}	PUNCT
ejpam-6997	412	15	=	=	SYM
ejpam-6997	412	16	gm̃c⟨r⟩	gm̃c⟨r⟩	X
ejpam-6997	412	17	(	(	PUNCT
ejpam-6997	412	18	{	{	PUNCT
ejpam-6997	412	19	e	e	NOUN
ejpam-6997	412	20	}	}	PUNCT
ejpam-6997	412	21	)	)	PUNCT
ejpam-6997	412	22	.	.	PUNCT
ejpam-6997	413	1	proposition	proposition	NOUN
ejpam-6997	413	2	11	11	NUM
ejpam-6997	413	3	.	.	PUNCT
ejpam-6997	414	1	let	let	VERB
ejpam-6997	414	2	g	g	NOUN
ejpam-6997	414	3	,	,	PUNCT
ejpam-6997	414	4	j	j	PROPN
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ejpam-6997	414	6	grills	grill	VERB
ejpam-6997	414	7	on	on	ADP
ejpam-6997	414	8	a	a	DET
ejpam-6997	414	9	ϱ-ns	ϱ-ns	ADV
ejpam-6997	414	10	(	(	PUNCT
ejpam-6997	414	11	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	414	12	,	,	PUNCT
ejpam-6997	414	13	ξϱ	ξϱ	NOUN
ejpam-6997	414	14	)	)	PUNCT
ejpam-6997	414	15	.	.	PUNCT
ejpam-6997	415	1	if	if	SCONJ
ejpam-6997	415	2	d,∆	d,∆	NOUN
ejpam-6997	415	3	⊑	⊑	PRON
ejpam-6997	415	4	ℵ	ℵ	NOUN
ejpam-6997	415	5	,	,	PUNCT
ejpam-6997	415	6	g	g	PROPN
ejpam-6997	415	7	⊑	⊑	X
ejpam-6997	415	8	j	j	PROPN
ejpam-6997	415	9	then	then	ADV
ejpam-6997	415	10	,	,	PUNCT
ejpam-6997	415	11	the	the	DET
ejpam-6997	415	12	following	follow	VERB
ejpam-6997	415	13	claims	claim	NOUN
ejpam-6997	415	14	are	be	AUX
ejpam-6997	415	15	true	true	ADJ
ejpam-6997	415	16	for	for	ADP
ejpam-6997	415	17	all	all	DET
ejpam-6997	415	18	ϱ.	ϱ.	NOUN
ejpam-6997	415	19	(	(	PUNCT
ejpam-6997	415	20	1	1	X
ejpam-6997	415	21	)	)	PUNCT
ejpam-6997	415	22	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	415	23	(	(	PUNCT
ejpam-6997	415	24	d	d	X
ejpam-6997	415	25	)	)	PUNCT
ejpam-6997	415	26	⊑	⊑	PRON
ejpam-6997	415	27	jm̃cϱ	jm̃cϱ	NOUN
ejpam-6997	415	28	(	(	PUNCT
ejpam-6997	415	29	d	d	NOUN
ejpam-6997	415	30	)	)	PUNCT
ejpam-6997	415	31	.	.	PUNCT
ejpam-6997	416	1	(	(	PUNCT
ejpam-6997	416	2	2	2	X
ejpam-6997	416	3	)	)	PUNCT
ejpam-6997	416	4	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	416	5	(	(	PUNCT
ejpam-6997	416	6	d	d	X
ejpam-6997	416	7	)	)	PUNCT
ejpam-6997	416	8	⊑	⊑	PRON
ejpam-6997	416	9	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	416	10	(	(	PUNCT
ejpam-6997	416	11	d	d	NOUN
ejpam-6997	416	12	)	)	PUNCT
ejpam-6997	416	13	.	.	PUNCT
ejpam-6997	417	1	proof	proof	NOUN
ejpam-6997	417	2	.	.	PUNCT
ejpam-6997	418	1	this	this	PRON
ejpam-6997	418	2	is	be	AUX
ejpam-6997	418	3	evident	evident	ADJ
ejpam-6997	418	4	.	.	PUNCT
ejpam-6997	419	1	remark	remark	NOUN
ejpam-6997	419	2	3	3	NUM
ejpam-6997	419	3	.	.	PUNCT
ejpam-6997	420	1	let	let	VERB
ejpam-6997	420	2	g	g	NOUN
ejpam-6997	420	3	=	=	PRON
ejpam-6997	420	4	{	{	PUNCT
ejpam-6997	420	5	{	{	PUNCT
ejpam-6997	420	6	b	b	NOUN
ejpam-6997	420	7	}	}	PUNCT
ejpam-6997	420	8	,	,	PUNCT
ejpam-6997	420	9	{	{	PUNCT
ejpam-6997	420	10	b	b	NOUN
ejpam-6997	420	11	,	,	PUNCT
ejpam-6997	420	12	e	e	NOUN
ejpam-6997	420	13	}	}	PUNCT
ejpam-6997	420	14	,	,	PUNCT
ejpam-6997	420	15	{	{	PUNCT
ejpam-6997	420	16	b	b	NOUN
ejpam-6997	420	17	,	,	PUNCT
ejpam-6997	420	18	n	n	CCONJ
ejpam-6997	420	19	}	}	PUNCT
ejpam-6997	420	20	,	,	PUNCT
ejpam-6997	420	21	{	{	PUNCT
ejpam-6997	420	22	b	b	X
ejpam-6997	420	23	,	,	PUNCT
ejpam-6997	420	24	m	m	NOUN
ejpam-6997	420	25	}	}	PUNCT
ejpam-6997	420	26	,	,	PUNCT
ejpam-6997	420	27	{	{	PUNCT
ejpam-6997	420	28	b	b	NOUN
ejpam-6997	420	29	,	,	PUNCT
ejpam-6997	420	30	e	e	NOUN
ejpam-6997	420	31	,	,	PUNCT
ejpam-6997	420	32	n	n	CCONJ
ejpam-6997	420	33	}	}	PUNCT
ejpam-6997	420	34	,	,	PUNCT
ejpam-6997	420	35	{	{	PUNCT
ejpam-6997	420	36	b	b	NOUN
ejpam-6997	420	37	,	,	PUNCT
ejpam-6997	420	38	e	e	NOUN
ejpam-6997	420	39	,	,	PUNCT
ejpam-6997	420	40	m	m	VERB
ejpam-6997	420	41	}	}	PUNCT
ejpam-6997	420	42	,	,	PUNCT
ejpam-6997	420	43	{	{	PUNCT
ejpam-6997	420	44	b	b	NOUN
ejpam-6997	420	45	,	,	PUNCT
ejpam-6997	420	46	n	n	CCONJ
ejpam-6997	420	47	,	,	PUNCT
ejpam-6997	420	48	m},ℵ	m},ℵ	NOUN
ejpam-6997	420	49	}	}	PUNCT
ejpam-6997	420	50	,	,	PUNCT
ejpam-6997	420	51	and	and	CCONJ
ejpam-6997	420	52	j	j	PROPN
ejpam-6997	420	53	=	=	SYM
ejpam-6997	420	54	2ℵ\ϕ	2ℵ\ϕ	NUM
ejpam-6997	420	55	be	be	AUX
ejpam-6997	420	56	grills	grill	NOUN
ejpam-6997	420	57	on	on	ADP
ejpam-6997	420	58	a	a	DET
ejpam-6997	420	59	ϱ-ns	ϱ-ns	ADV
ejpam-6997	420	60	(	(	PUNCT
ejpam-6997	420	61	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	420	62	,	,	PUNCT
ejpam-6997	420	63	ξϱ	ξϱ	NOUN
ejpam-6997	420	64	)	)	PUNCT
ejpam-6997	420	65	.	.	PUNCT
ejpam-6997	421	1	(	(	PUNCT
ejpam-6997	421	2	1	1	X
ejpam-6997	421	3	)	)	PUNCT
ejpam-6997	421	4	if	if	SCONJ
ejpam-6997	421	5	d	d	NOUN
ejpam-6997	421	6	=	=	PRON
ejpam-6997	421	7	{	{	PUNCT
ejpam-6997	421	8	b	b	NOUN
ejpam-6997	421	9	}	}	PUNCT
ejpam-6997	421	10	,	,	PUNCT
ejpam-6997	421	11	then	then	ADV
ejpam-6997	421	12	gm̃cr	gm̃cr	NOUN
ejpam-6997	421	13	(	(	PUNCT
ejpam-6997	421	14	d	d	X
ejpam-6997	421	15	)	)	PUNCT
ejpam-6997	421	16	=	=	SYM
ejpam-6997	421	17	ℵ	ℵ	ADP
ejpam-6997	421	18	⊈	⊈	PROPN
ejpam-6997	421	19	ϕ	ϕ	NOUN
ejpam-6997	421	20	=	=	X
ejpam-6997	421	21	jm̃cr	jm̃cr	PROPN
ejpam-6997	421	22	(	(	PUNCT
ejpam-6997	421	23	d	d	NOUN
ejpam-6997	421	24	)	)	PUNCT
ejpam-6997	421	25	.	.	PUNCT
ejpam-6997	422	1	(	(	PUNCT
ejpam-6997	422	2	2	2	X
ejpam-6997	422	3	)	)	PUNCT
ejpam-6997	422	4	if	if	SCONJ
ejpam-6997	422	5	d	d	NOUN
ejpam-6997	422	6	=	=	PRON
ejpam-6997	422	7	{	{	PUNCT
ejpam-6997	422	8	b	b	NOUN
ejpam-6997	422	9	,	,	PUNCT
ejpam-6997	422	10	n	n	CCONJ
ejpam-6997	422	11	}	}	PUNCT
ejpam-6997	422	12	,	,	PUNCT
ejpam-6997	422	13	then	then	ADV
ejpam-6997	422	14	gm̃cr	gm̃cr	NOUN
ejpam-6997	422	15	(	(	PUNCT
ejpam-6997	422	16	d	d	X
ejpam-6997	422	17	)	)	PUNCT
ejpam-6997	422	18	=	=	SYM
ejpam-6997	422	19	{	{	PUNCT
ejpam-6997	422	20	b	b	PROPN
ejpam-6997	422	21	,	,	PUNCT
ejpam-6997	422	22	n	n	CCONJ
ejpam-6997	422	23	,	,	PUNCT
ejpam-6997	422	24	m	m	VERB
ejpam-6997	422	25	}	}	PUNCT
ejpam-6997	422	26	⊈	⊈	PROPN
ejpam-6997	422	27	{	{	PUNCT
ejpam-6997	422	28	b	b	NOUN
ejpam-6997	422	29	,	,	PUNCT
ejpam-6997	422	30	m	m	NOUN
ejpam-6997	422	31	}	}	PUNCT
ejpam-6997	422	32	=	=	SYM
ejpam-6997	423	1	gm̃cr	gm̃cr	NOUN
ejpam-6997	423	2	(	(	PUNCT
ejpam-6997	423	3	d	d	NOUN
ejpam-6997	423	4	)	)	PUNCT
ejpam-6997	423	5	.	.	PUNCT
ejpam-6997	424	1	3.2	3.2	NUM
ejpam-6997	424	2	.	.	PUNCT
ejpam-6997	425	1	the	the	DET
ejpam-6997	425	2	second	second	ADJ
ejpam-6997	425	3	class	class	NOUN
ejpam-6997	425	4	of	of	ADP
ejpam-6997	425	5	rs	rs	NOUN
ejpam-6997	425	6	paradigms	paradigm	VERB
ejpam-6997	425	7	some	some	DET
ejpam-6997	425	8	drawbacks	drawback	NOUN
ejpam-6997	425	9	and	and	CCONJ
ejpam-6997	425	10	unacceptable	unacceptable	ADJ
ejpam-6997	425	11	characteristics	characteristic	NOUN
ejpam-6997	425	12	of	of	ADP
ejpam-6997	425	13	the	the	DET
ejpam-6997	425	14	first	first	ADJ
ejpam-6997	425	15	category	category	NOUN
ejpam-6997	425	16	of	of	ADP
ejpam-6997	425	17	rs	rs	ADJ
ejpam-6997	425	18	paradigms	paradigm	NOUN
ejpam-6997	425	19	include	include	VERB
ejpam-6997	425	20	:	:	PUNCT
ejpam-6997	425	21	the	the	DET
ejpam-6997	425	22	property	property	NOUN
ejpam-6997	425	23	that	that	PRON
ejpam-6997	425	24	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	425	25	(	(	PUNCT
ejpam-6997	425	26	d	d	NOUN
ejpam-6997	425	27	)	)	PUNCT
ejpam-6997	426	1	⊆	⊆	NUM
ejpam-6997	426	2	d	d	SYM
ejpam-6997	426	3	⊆	⊆	NUM
ejpam-6997	426	4	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	426	5	(	(	PUNCT
ejpam-6997	426	6	{	{	PUNCT
ejpam-6997	426	7	d	d	NOUN
ejpam-6997	426	8	}	}	PUNCT
ejpam-6997	426	9	)	)	PUNCT
ejpam-6997	426	10	does	do	AUX
ejpam-6997	426	11	not	not	PART
ejpam-6997	426	12	apply	apply	VERB
ejpam-6997	426	13	to	to	ADP
ejpam-6997	426	14	all	all	DET
ejpam-6997	426	15	subsets	subset	NOUN
ejpam-6997	426	16	,	,	PUNCT
ejpam-6997	426	17	consequently	consequently	ADV
ejpam-6997	426	18	,	,	PUNCT
ejpam-6997	426	19	particularly	particularly	ADV
ejpam-6997	426	20	when	when	SCONJ
ejpam-6997	426	21	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	426	22	(	(	PUNCT
ejpam-6997	426	23	ϕ	ϕ	NOUN
ejpam-6997	426	24	)	)	PUNCT
ejpam-6997	426	25	̸=	̸=	PROPN
ejpam-6997	426	26	ϕ	ϕ	NOUN
ejpam-6997	426	27	and	and	CCONJ
ejpam-6997	426	28	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	426	29	(	(	PUNCT
ejpam-6997	426	30	ℵ	ℵ	NOUN
ejpam-6997	426	31	)	)	PUNCT
ejpam-6997	426	32	̸=	̸=	PROPN
ejpam-6997	426	33	ℵ	ℵ	NOUN
ejpam-6997	426	34	,	,	PUNCT
ejpam-6997	426	35	results	result	NOUN
ejpam-6997	426	36	in	in	ADP
ejpam-6997	426	37	irrational	irrational	ADJ
ejpam-6997	426	38	descriptions	description	NOUN
ejpam-6997	426	39	of	of	ADP
ejpam-6997	426	40	those	those	DET
ejpam-6997	426	41	basic	basic	ADJ
ejpam-6997	426	42	set	set	NOUN
ejpam-6997	426	43	models	model	NOUN
ejpam-6997	426	44	or	or	CCONJ
ejpam-6997	426	45	mistrust	mistrust	NOUN
ejpam-6997	426	46	of	of	ADP
ejpam-6997	426	47	the	the	DET
ejpam-6997	426	48	information	information	NOUN
ejpam-6997	426	49	gleaned	glean	VERB
ejpam-6997	426	50	from	from	ADP
ejpam-6997	426	51	them	they	PRON
ejpam-6997	426	52	.	.	PUNCT
ejpam-6997	427	1	since	since	SCONJ
ejpam-6997	427	2	the	the	DET
ejpam-6997	427	3	original	original	ADJ
ejpam-6997	427	4	accuracy	accuracy	NOUN
ejpam-6997	427	5	measure	measure	NOUN
ejpam-6997	427	6	formula	formula	NOUN
ejpam-6997	427	7	yields	yield	VERB
ejpam-6997	427	8	values	value	NOUN
ejpam-6997	427	9	greater	great	ADJ
ejpam-6997	427	10	than	than	ADP
ejpam-6997	427	11	one	one	NUM
ejpam-6997	427	12	or	or	CCONJ
ejpam-6997	427	13	undefined	undefined	ADJ
ejpam-6997	427	14	cases	case	NOUN
ejpam-6997	427	15	for	for	ADP
ejpam-6997	427	16	certain	certain	ADJ
ejpam-6997	427	17	subsets	subset	NOUN
ejpam-6997	427	18	,	,	PUNCT
ejpam-6997	427	19	we	we	PRON
ejpam-6997	427	20	are	be	AUX
ejpam-6997	427	21	unable	unable	ADJ
ejpam-6997	427	22	to	to	PART
ejpam-6997	427	23	apply	apply	VERB
ejpam-6997	427	24	it	it	PRON
ejpam-6997	427	25	,	,	PUNCT
ejpam-6997	427	26	i.e.	i.e.	X
ejpam-6997	427	27	in	in	ADP
ejpam-6997	427	28	example	example	NOUN
ejpam-6997	427	29	3.11	3.11	NUM
ejpam-6997	427	30	,	,	PUNCT
ejpam-6997	427	31	we	we	PRON
ejpam-6997	427	32	have	have	VERB
ejpam-6997	427	33	|gm̃cr	|gm̃cr	NOUN
ejpam-6997	427	34	(	(	PUNCT
ejpam-6997	427	35	{	{	PUNCT
ejpam-6997	427	36	b})|	b})|	VERB
ejpam-6997	427	37	|gm̃cr	|gm̃cr	X
ejpam-6997	427	38	(	(	PUNCT
ejpam-6997	427	39	{	{	PUNCT
ejpam-6997	427	40	b})|	b})|	VERB
ejpam-6997	427	41	=	=	SYM
ejpam-6997	427	42	4	4	NUM
ejpam-6997	427	43	2	2	NUM
ejpam-6997	427	44	>	>	SYM
ejpam-6997	427	45	1	1	NUM
ejpam-6997	427	46	,	,	PUNCT
ejpam-6997	427	47	and	and	CCONJ
ejpam-6997	427	48	|gm̃cr	|gm̃cr	PROPN
ejpam-6997	427	49	(	(	PUNCT
ejpam-6997	427	50	ϕ)|	ϕ)|	VERB
ejpam-6997	427	51	|gm̃cr	|gm̃cr	PROPN
ejpam-6997	427	52	(	(	PUNCT
ejpam-6997	427	53	ϕ)|	ϕ)|	NOUN
ejpam-6997	427	54	=	=	SYM
ejpam-6997	427	55	2	2	NUM
ejpam-6997	427	56	0	0	NUM
ejpam-6997	427	57	.	.	PUNCT
ejpam-6997	428	1	these	these	DET
ejpam-6997	428	2	situations	situation	NOUN
ejpam-6997	428	3	have	have	VERB
ejpam-6997	428	4	little	little	ADJ
ejpam-6997	428	5	practical	practical	ADJ
ejpam-6997	428	6	significance	significance	NOUN
ejpam-6997	428	7	and	and	CCONJ
ejpam-6997	428	8	are	be	AUX
ejpam-6997	428	9	worthless	worthless	ADJ
ejpam-6997	428	10	.	.	PUNCT
ejpam-6997	429	1	this	this	DET
ejpam-6997	429	2	section	section	NOUN
ejpam-6997	429	3	aims	aim	VERB
ejpam-6997	429	4	to	to	PART
ejpam-6997	429	5	improve	improve	VERB
ejpam-6997	429	6	the	the	DET
ejpam-6997	429	7	initial	initial	ADJ
ejpam-6997	429	8	rs	rs	NOUN
ejpam-6997	429	9	paradigm	paradigm	NOUN
ejpam-6997	429	10	by	by	ADP
ejpam-6997	429	11	enhancing	enhance	VERB
ejpam-6997	429	12	lw	lw	PROPN
ejpam-6997	429	13	-	-	PUNCT
ejpam-6997	429	14	ap	ap	PROPN
ejpam-6997	429	15	and	and	CCONJ
ejpam-6997	429	16	up	up	ADP
ejpam-6997	429	17	-	-	PUNCT
ejpam-6997	429	18	ap	ap	NOUN
ejpam-6997	429	19	,	,	PUNCT
ejpam-6997	429	20	while	while	SCONJ
ejpam-6997	429	21	maintaining	maintain	VERB
ejpam-6997	429	22	its	its	PRON
ejpam-6997	429	23	advantages	advantage	NOUN
ejpam-6997	429	24	.	.	PUNCT
ejpam-6997	430	1	definition	definition	NOUN
ejpam-6997	430	2	18	18	NUM
ejpam-6997	430	3	.	.	PUNCT
ejpam-6997	431	1	let	let	VERB
ejpam-6997	431	2	g	g	PRON
ejpam-6997	431	3	be	be	AUX
ejpam-6997	431	4	a	a	DET
ejpam-6997	431	5	grill	grill	NOUN
ejpam-6997	431	6	on	on	ADP
ejpam-6997	431	7	a	a	DET
ejpam-6997	431	8	ϱ-ns	ϱ-ns	ADV
ejpam-6997	431	9	(	(	PUNCT
ejpam-6997	431	10	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	431	11	,	,	PUNCT
ejpam-6997	431	12	ξϱ	ξϱ	NOUN
ejpam-6997	431	13	)	)	PUNCT
ejpam-6997	431	14	.	.	PUNCT
ejpam-6997	432	1	based	base	VERB
ejpam-6997	432	2	on	on	ADP
ejpam-6997	432	3	grills	grill	NOUN
ejpam-6997	432	4	and	and	CCONJ
ejpam-6997	432	5	cardinality	cardinality	PROPN
ejpam-6997	432	6	nbds	nbds	NOUN
ejpam-6997	432	7	,	,	PUNCT
ejpam-6997	432	8	the	the	DET
ejpam-6997	432	9	gcϱlw	gcϱlw	PROPN
ejpam-6997	432	10	−ap	−ap	PROPN
ejpam-6997	432	11	(	(	PUNCT
ejpam-6997	432	12	gmcϱ	gmcϱ	NOUN
ejpam-6997	432	13	(	(	PUNCT
ejpam-6997	432	14	)	)	PUNCT
ejpam-6997	432	15	)	)	PUNCT
ejpam-6997	432	16	,	,	PUNCT
ejpam-6997	432	17	and	and	CCONJ
ejpam-6997	432	18	gcϱup	gcϱup	PROPN
ejpam-6997	432	19	-	-	PUNCT
ejpam-6997	432	20	ap	ap	PROPN
ejpam-6997	432	21	gmcϱ	gmcϱ	PROPN
ejpam-6997	432	22	(	(	PUNCT
ejpam-6997	432	23	)	)	PUNCT
ejpam-6997	432	24	of	of	ADP
ejpam-6997	432	25	∆	∆	PROPN
ejpam-6997	432	26	⊑	⊑	DET
ejpam-6997	432	27	ℵ	ℵ	NOUN
ejpam-6997	432	28	are	be	AUX
ejpam-6997	432	29	respectively	respectively	ADV
ejpam-6997	432	30	computed	compute	VERB
ejpam-6997	432	31	by	by	ADP
ejpam-6997	432	32	:	:	PUNCT
ejpam-6997	432	33	gmcϱ	gmcϱ	NOUN
ejpam-6997	432	34	(	(	PUNCT
ejpam-6997	432	35	∆	∆	PROPN
ejpam-6997	432	36	)	)	PUNCT
ejpam-6997	433	1	=	=	PRON
ejpam-6997	433	2	{	{	PUNCT
ejpam-6997	433	3	δ	δ	PROPN
ejpam-6997	433	4	∈	∈	PROPN
ejpam-6997	433	5	∆	∆	X
ejpam-6997	433	6	:	:	PUNCT
ejpam-6997	433	7	cϱ(δ	cϱ(δ	X
ejpam-6997	433	8	)	)	PUNCT
ejpam-6997	434	1	⊓	⊓	PROPN
ejpam-6997	434	2	∆c	∆c	NOUN
ejpam-6997	434	3	/∈	/∈	PUNCT
ejpam-6997	434	4	g	g	NOUN
ejpam-6997	434	5	}	}	PUNCT
ejpam-6997	434	6	gmcϱ	gmcϱ	NOUN
ejpam-6997	434	7	(	(	PUNCT
ejpam-6997	434	8	∆	∆	X
ejpam-6997	434	9	)	)	PUNCT
ejpam-6997	435	1	=	=	SYM
ejpam-6997	435	2	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	435	3	(	(	PUNCT
ejpam-6997	435	4	∆	∆	PROPN
ejpam-6997	435	5	)	)	PUNCT
ejpam-6997	436	1	⊔	⊔	PROPN
ejpam-6997	436	2	∆	∆	PROPN
ejpam-6997	436	3	a.	a.	NOUN
ejpam-6997	436	4	a.	a.	PROPN
ejpam-6997	436	5	azzam	azzam	PROPN
ejpam-6997	436	6	,	,	PUNCT
ejpam-6997	436	7	m.	m.	NOUN
ejpam-6997	436	8	aldawood	aldawood	PROPN
ejpam-6997	436	9	,	,	PUNCT
ejpam-6997	436	10	b.	b.	PROPN
ejpam-6997	436	11	alreshidi	alreshidi	PROPN
ejpam-6997	436	12	/	/	SYM
ejpam-6997	436	13	eur	eur	PROPN
ejpam-6997	436	14	.	.	PUNCT
ejpam-6997	437	1	j.	j.	PROPN
ejpam-6997	437	2	pure	pure	PROPN
ejpam-6997	437	3	appl	appl	PROPN
ejpam-6997	437	4	.	.	PROPN
ejpam-6997	437	5	math	math	PROPN
ejpam-6997	437	6	,	,	PUNCT
ejpam-6997	437	7	18	18	NUM
ejpam-6997	437	8	(	(	PUNCT
ejpam-6997	437	9	4	4	NUM
ejpam-6997	437	10	)	)	PUNCT
ejpam-6997	437	11	(	(	PUNCT
ejpam-6997	437	12	2025	2025	NUM
ejpam-6997	437	13	)	)	PUNCT
ejpam-6997	437	14	,	,	PUNCT
ejpam-6997	437	15	6997	6997	NUM
ejpam-6997	437	16	16	16	NUM
ejpam-6997	437	17	of	of	ADP
ejpam-6997	437	18	31	31	NUM
ejpam-6997	437	19	definition	definition	NOUN
ejpam-6997	437	20	19	19	NUM
ejpam-6997	437	21	.	.	PUNCT
ejpam-6997	438	1	the	the	DET
ejpam-6997	438	2	gcϱ-boundary	gcϱ-boundary	ADJ
ejpam-6997	438	3	,	,	PUNCT
ejpam-6997	438	4	gcϱ-positive	gcϱ-positive	ADJ
ejpam-6997	438	5	,	,	PUNCT
ejpam-6997	438	6	and	and	CCONJ
ejpam-6997	438	7	gcϱ-negative	gcϱ-negative	ADJ
ejpam-6997	438	8	regions	region	NOUN
ejpam-6997	438	9	of	of	ADP
ejpam-6997	438	10	a	a	DET
ejpam-6997	438	11	subset	subset	NOUN
ejpam-6997	438	12	∆	∆	PROPN
ejpam-6997	438	13	within	within	ADP
ejpam-6997	438	14	a	a	DET
ejpam-6997	438	15	ϱ-ns	ϱ-ns	ADV
ejpam-6997	438	16	(	(	PUNCT
ejpam-6997	438	17	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	438	18	,	,	PUNCT
ejpam-6997	438	19	ξϱ	ξϱ	NOUN
ejpam-6997	438	20	)	)	PUNCT
ejpam-6997	438	21	with	with	ADP
ejpam-6997	438	22	grill	grill	NOUN
ejpam-6997	438	23	g	g	NOUN
ejpam-6997	438	24	on	on	ADP
ejpam-6997	438	25	ℵ	ℵ	NOUN
ejpam-6997	438	26	are	be	AUX
ejpam-6997	438	27	respectively	respectively	ADV
ejpam-6997	438	28	computed	compute	VERB
ejpam-6997	438	29	by	by	ADP
ejpam-6997	438	30	:	:	PUNCT
ejpam-6997	438	31	gbcϱ	gbcϱ	NOUN
ejpam-6997	438	32	(	(	PUNCT
ejpam-6997	438	33	∆	∆	X
ejpam-6997	438	34	)	)	PUNCT
ejpam-6997	439	1	=	=	VERB
ejpam-6997	439	2	gmcϱ	gmcϱ	NOUN
ejpam-6997	439	3	(	(	PUNCT
ejpam-6997	439	4	∆	∆	PROPN
ejpam-6997	439	5	)	)	PUNCT
ejpam-6997	439	6	\	\	PROPN
ejpam-6997	439	7	gmcϱ	gmcϱ	NOUN
ejpam-6997	439	8	(	(	PUNCT
ejpam-6997	439	9	∆	∆	PROPN
ejpam-6997	439	10	)	)	PUNCT
ejpam-6997	439	11	gpcϱ	gpcϱ	NOUN
ejpam-6997	439	12	(	(	PUNCT
ejpam-6997	439	13	∆	∆	X
ejpam-6997	439	14	)	)	PUNCT
ejpam-6997	440	1	=	=	VERB
ejpam-6997	440	2	gmcϱ	gmcϱ	NOUN
ejpam-6997	440	3	(	(	PUNCT
ejpam-6997	440	4	∆	∆	PROPN
ejpam-6997	440	5	)	)	PUNCT
ejpam-6997	440	6	gncϱ	gncϱ	NOUN
ejpam-6997	440	7	(	(	PUNCT
ejpam-6997	440	8	∆	∆	X
ejpam-6997	440	9	)	)	PUNCT
ejpam-6997	440	10	=	=	SYM
ejpam-6997	440	11	ℵ\gmcϱ	ℵ\gmcϱ	ADJ
ejpam-6997	440	12	(	(	PUNCT
ejpam-6997	440	13	∆	∆	PROPN
ejpam-6997	440	14	)	)	PUNCT
ejpam-6997	441	1	the	the	DET
ejpam-6997	441	2	following	follow	VERB
ejpam-6997	441	3	measurements	measurement	NOUN
ejpam-6997	441	4	can	can	AUX
ejpam-6997	441	5	be	be	AUX
ejpam-6997	441	6	used	use	VERB
ejpam-6997	441	7	to	to	PART
ejpam-6997	441	8	numerically	numerically	ADV
ejpam-6997	441	9	characterize	characterize	VERB
ejpam-6997	441	10	rss	rss	NOUN
ejpam-6997	441	11	in	in	ADP
ejpam-6997	441	12	relation	relation	NOUN
ejpam-6997	441	13	to	to	PART
ejpam-6997	441	14	cϱ-nbds	cϱ-nbds	VERB
ejpam-6997	441	15	and	and	CCONJ
ejpam-6997	441	16	grills	grill	NOUN
ejpam-6997	441	17	.	.	PUNCT
ejpam-6997	442	1	definition	definition	NOUN
ejpam-6997	442	2	20	20	NUM
ejpam-6997	442	3	.	.	PUNCT
ejpam-6997	443	1	the	the	DET
ejpam-6997	443	2	gcϱ-accuracy	gcϱ-accuracy	NOUN
ejpam-6997	443	3	,	,	PUNCT
ejpam-6997	443	4	and	and	CCONJ
ejpam-6997	443	5	gcϱ-roughness	gcϱ-roughness	ADJ
ejpam-6997	443	6	criteria	criterion	NOUN
ejpam-6997	443	7	of	of	ADP
ejpam-6997	443	8	∆	∆	PROPN
ejpam-6997	443	9	̸=	̸=	PROPN
ejpam-6997	443	10	of	of	ADP
ejpam-6997	443	11	a	a	DET
ejpam-6997	443	12	ϱ-ns	ϱ-ns	ADV
ejpam-6997	443	13	(	(	PUNCT
ejpam-6997	443	14	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	443	15	,	,	PUNCT
ejpam-6997	443	16	ξϱ	ξϱ	NOUN
ejpam-6997	443	17	)	)	PUNCT
ejpam-6997	443	18	with	with	ADP
ejpam-6997	443	19	grill	grill	NOUN
ejpam-6997	443	20	g	g	NOUN
ejpam-6997	443	21	on	on	ADP
ejpam-6997	443	22	ℵ	ℵ	NOUN
ejpam-6997	443	23	are	be	AUX
ejpam-6997	443	24	provided	provide	VERB
ejpam-6997	443	25	,	,	PUNCT
ejpam-6997	443	26	respectively	respectively	ADV
ejpam-6997	443	27	,	,	PUNCT
ejpam-6997	443	28	by	by	ADP
ejpam-6997	443	29	:	:	PUNCT
ejpam-6997	443	30	gacϱ	gacϱ	NOUN
ejpam-6997	443	31	(	(	PUNCT
ejpam-6997	443	32	∆	∆	PROPN
ejpam-6997	443	33	)	)	PUNCT
ejpam-6997	443	34	=	=	SYM
ejpam-6997	444	1	|gmcϱ	|gmcϱ	ADJ
ejpam-6997	444	2	(	(	PUNCT
ejpam-6997	444	3	∆)|	∆)|	NOUN
ejpam-6997	444	4	|g	|g	PART
ejpam-6997	444	5	mcϱ	mcϱ	ADJ
ejpam-6997	444	6	(	(	PUNCT
ejpam-6997	444	7	∆)|	∆)|	NOUN
ejpam-6997	444	8	,	,	PUNCT
ejpam-6997	444	9	|gmcϱ	|gmcϱ	ADJ
ejpam-6997	444	10	(	(	PUNCT
ejpam-6997	444	11	∆)|	∆)|	NOUN
ejpam-6997	444	12	̸=	̸=	PROPN
ejpam-6997	444	13	0	0	NUM
ejpam-6997	444	14	.	.	PUNCT
ejpam-6997	445	1	grcϱ	grcϱ	NOUN
ejpam-6997	445	2	(	(	PUNCT
ejpam-6997	445	3	∆	∆	PROPN
ejpam-6997	445	4	)	)	PUNCT
ejpam-6997	445	5	=	=	SYM
ejpam-6997	445	6	1	1	NUM
ejpam-6997	445	7	−	−	PROPN
ejpam-6997	445	8	gacϱ	gacϱ	NOUN
ejpam-6997	445	9	(	(	PUNCT
ejpam-6997	445	10	∆	∆	PROPN
ejpam-6997	445	11	)	)	PUNCT
ejpam-6997	445	12	.	.	PUNCT
ejpam-6997	446	1	the	the	DET
ejpam-6997	446	2	statement	statement	NOUN
ejpam-6997	446	3	of	of	ADP
ejpam-6997	446	4	pawlak	pawlak	ADJ
ejpam-6997	446	5	’s	’s	PART
ejpam-6997	446	6	properties	property	NOUN
ejpam-6997	446	7	using	use	VERB
ejpam-6997	446	8	the	the	DET
ejpam-6997	446	9	gcϱ-lw	gcϱ-lw	ADJ
ejpam-6997	446	10	and	and	CCONJ
ejpam-6997	446	11	gcϱ-up	gcϱ-up	PROPN
ejpam-6997	446	12	-	-	PUNCT
ejpam-6997	446	13	ap	ap	PROPN
ejpam-6997	446	14	will	will	AUX
ejpam-6997	446	15	be	be	AUX
ejpam-6997	446	16	looked	look	VERB
ejpam-6997	446	17	at	at	ADP
ejpam-6997	446	18	in	in	ADP
ejpam-6997	446	19	the	the	DET
ejpam-6997	446	20	following	follow	VERB
ejpam-6997	446	21	theorem	theorem	NOUN
ejpam-6997	446	22	.	.	PUNCT
ejpam-6997	446	23	theorem	theorem	NOUN
ejpam-6997	446	24	4	4	NUM
ejpam-6997	446	25	.	.	X
ejpam-6997	446	26	for	for	ADP
ejpam-6997	446	27	a	a	DET
ejpam-6997	446	28	ϱ-ns	ϱ-ns	ADV
ejpam-6997	446	29	(	(	PUNCT
ejpam-6997	446	30	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	446	31	,	,	PUNCT
ejpam-6997	446	32	ξϱ	ξϱ	NOUN
ejpam-6997	446	33	)	)	PUNCT
ejpam-6997	446	34	and	and	CCONJ
ejpam-6997	446	35	d,∆	d,∆	VERB
ejpam-6997	446	36	⊑	⊑	PRON
ejpam-6997	446	37	ℵ	ℵ	NOUN
ejpam-6997	446	38	,	,	PUNCT
ejpam-6997	446	39	let	let	VERB
ejpam-6997	446	40	g	g	NOUN
ejpam-6997	446	41	=	=	NOUN
ejpam-6997	446	42	2ℵ\ϕ	2ℵ\ϕ	NUM
ejpam-6997	446	43	be	be	AUX
ejpam-6997	446	44	a	a	DET
ejpam-6997	446	45	grill	grill	NOUN
ejpam-6997	446	46	.	.	PUNCT
ejpam-6997	447	1	next	next	ADV
ejpam-6997	447	2	,	,	PUNCT
ejpam-6997	447	3	we	we	PRON
ejpam-6997	447	4	have	have	VERB
ejpam-6997	447	5	the	the	DET
ejpam-6997	447	6	properties	property	NOUN
ejpam-6997	447	7	listed	list	VERB
ejpam-6997	447	8	below	below	ADV
ejpam-6997	447	9	.	.	PUNCT
ejpam-6997	448	1	(	(	PUNCT
ejpam-6997	448	2	1	1	X
ejpam-6997	448	3	)	)	PUNCT
ejpam-6997	448	4	gmcϱ	gmcϱ	NOUN
ejpam-6997	448	5	(	(	PUNCT
ejpam-6997	448	6	∆	∆	PROPN
ejpam-6997	448	7	)	)	PUNCT
ejpam-6997	448	8	⊑	⊑	PART
ejpam-6997	448	9	∆	∆	PROPN
ejpam-6997	448	10	⊑	⊑	PART
ejpam-6997	448	11	gmcϱ	gmcϱ	VERB
ejpam-6997	448	12	(	(	PUNCT
ejpam-6997	448	13	∆	∆	PROPN
ejpam-6997	448	14	)	)	PUNCT
ejpam-6997	448	15	.	.	PUNCT
ejpam-6997	449	1	(	(	PUNCT
ejpam-6997	449	2	2	2	X
ejpam-6997	449	3	)	)	PUNCT
ejpam-6997	449	4	gmcϱ	gmcϱ	NOUN
ejpam-6997	449	5	(	(	PUNCT
ejpam-6997	449	6	ϕ	ϕ	NOUN
ejpam-6997	449	7	)	)	PUNCT
ejpam-6997	449	8	=	=	SYM
ejpam-6997	449	9	ϕ	ϕ	NOUN
ejpam-6997	449	10	,	,	PUNCT
ejpam-6997	449	11	and	and	CCONJ
ejpam-6997	449	12	gmcϱ	gmcϱ	NOUN
ejpam-6997	449	13	(	(	PUNCT
ejpam-6997	449	14	ϕ	ϕ	NOUN
ejpam-6997	449	15	)	)	PUNCT
ejpam-6997	449	16	=	=	SYM
ejpam-6997	450	1	ϕ.	ϕ.	NOUN
ejpam-6997	450	2	(	(	PUNCT
ejpam-6997	450	3	3	3	X
ejpam-6997	450	4	)	)	PUNCT
ejpam-6997	450	5	gmcϱ	gmcϱ	NOUN
ejpam-6997	450	6	(	(	PUNCT
ejpam-6997	450	7	ℵ	ℵ	NOUN
ejpam-6997	450	8	)	)	PUNCT
ejpam-6997	450	9	=	=	SYM
ejpam-6997	450	10	ℵ	ℵ	NOUN
ejpam-6997	450	11	,	,	PUNCT
ejpam-6997	450	12	and	and	CCONJ
ejpam-6997	450	13	gmcϱ	gmcϱ	NOUN
ejpam-6997	450	14	(	(	PUNCT
ejpam-6997	450	15	ℵ	ℵ	NOUN
ejpam-6997	450	16	)	)	PUNCT
ejpam-6997	450	17	=	=	PUNCT
ejpam-6997	450	18	ℵ.	ℵ.	NOUN
ejpam-6997	450	19	(	(	PUNCT
ejpam-6997	450	20	4	4	X
ejpam-6997	450	21	)	)	PUNCT
ejpam-6997	450	22	if	if	SCONJ
ejpam-6997	450	23	d	d	PROPN
ejpam-6997	450	24	⊑	⊑	PRON
ejpam-6997	450	25	∆	∆	PROPN
ejpam-6997	450	26	,	,	PUNCT
ejpam-6997	450	27	then	then	ADV
ejpam-6997	450	28	gmcϱ	gmcϱ	VERB
ejpam-6997	450	29	(	(	PUNCT
ejpam-6997	450	30	d	d	NOUN
ejpam-6997	450	31	)	)	PUNCT
ejpam-6997	450	32	⊑	⊑	PRON
ejpam-6997	450	33	gmcϱ	gmcϱ	VERB
ejpam-6997	450	34	(	(	PUNCT
ejpam-6997	450	35	∆	∆	PROPN
ejpam-6997	450	36	)	)	PUNCT
ejpam-6997	450	37	,	,	PUNCT
ejpam-6997	450	38	and	and	CCONJ
ejpam-6997	450	39	gmcϱ	gmcϱ	VERB
ejpam-6997	450	40	(	(	PUNCT
ejpam-6997	450	41	d	d	NOUN
ejpam-6997	450	42	)	)	PUNCT
ejpam-6997	450	43	⊑	⊑	PRON
ejpam-6997	450	44	gmcϱ	gmcϱ	VERB
ejpam-6997	450	45	(	(	PUNCT
ejpam-6997	450	46	∆	∆	PROPN
ejpam-6997	450	47	)	)	PUNCT
ejpam-6997	450	48	.	.	PUNCT
ejpam-6997	451	1	(	(	PUNCT
ejpam-6997	451	2	5	5	X
ejpam-6997	451	3	)	)	PUNCT
ejpam-6997	451	4	gmcϱ	gmcϱ	NOUN
ejpam-6997	451	5	(	(	PUNCT
ejpam-6997	451	6	gmcϱ	gmcϱ	PROPN
ejpam-6997	451	7	(	(	PUNCT
ejpam-6997	451	8	∆	∆	PROPN
ejpam-6997	451	9	)	)	PUNCT
ejpam-6997	451	10	)	)	PUNCT
ejpam-6997	452	1	=	=	PRON
ejpam-6997	452	2	gmcϱ	gmcϱ	NOUN
ejpam-6997	452	3	(	(	PUNCT
ejpam-6997	452	4	∆	∆	PROPN
ejpam-6997	452	5	)	)	PUNCT
ejpam-6997	452	6	for	for	ADP
ejpam-6997	452	7	ϱ	ϱ	PROPN
ejpam-6997	452	8	∈	∈	PROPN
ejpam-6997	452	9	{	{	PUNCT
ejpam-6997	452	10	r	r	NOUN
ejpam-6997	452	11	,	,	PUNCT
ejpam-6997	452	12	l	l	NOUN
ejpam-6997	452	13	,	,	PUNCT
ejpam-6997	452	14	i	i	PRON
ejpam-6997	452	15	,	,	PUNCT
ejpam-6997	452	16	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	452	17	,	,	PUNCT
ejpam-6997	452	18	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	452	19	}	}	PUNCT
ejpam-6997	452	20	.	.	PUNCT
ejpam-6997	453	1	(	(	PUNCT
ejpam-6997	453	2	6	6	X
ejpam-6997	453	3	)	)	PUNCT
ejpam-6997	453	4	gmcϱ	gmcϱ	NOUN
ejpam-6997	453	5	(	(	PUNCT
ejpam-6997	453	6	gmcϱ	gmcϱ	PROPN
ejpam-6997	453	7	(	(	PUNCT
ejpam-6997	453	8	∆	∆	PROPN
ejpam-6997	453	9	)	)	PUNCT
ejpam-6997	453	10	)	)	PUNCT
ejpam-6997	454	1	⊑	⊑	PROPN
ejpam-6997	454	2	gmcϱ	gmcϱ	VERB
ejpam-6997	454	3	(	(	PUNCT
ejpam-6997	454	4	∆	∆	PROPN
ejpam-6997	454	5	)	)	PUNCT
ejpam-6997	454	6	for	for	ADP
ejpam-6997	454	7	ϱ	ϱ	PROPN
ejpam-6997	454	8	∈	∈	PROPN
ejpam-6997	454	9	{	{	PUNCT
ejpam-6997	454	10	u	u	NOUN
ejpam-6997	454	11	,	,	PUNCT
ejpam-6997	454	12	⟨u⟩	⟨u⟩	PROPN
ejpam-6997	454	13	,	,	PUNCT
ejpam-6997	454	14	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	454	15	}	}	PUNCT
ejpam-6997	454	16	.	.	PUNCT
ejpam-6997	455	1	(	(	PUNCT
ejpam-6997	455	2	7	7	X
ejpam-6997	455	3	)	)	PUNCT
ejpam-6997	455	4	let	let	VERB
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ejpam-6997	455	7	ℵ.	ℵ.	PROPN
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ejpam-6997	455	9	gmcϱ	gmcϱ	VERB
ejpam-6997	455	10	(	(	PUNCT
ejpam-6997	455	11	cϱ(π	cϱ(π	NOUN
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ejpam-6997	455	13	)	)	PUNCT
ejpam-6997	456	1	=	=	SYM
ejpam-6997	456	2	cϱ(π	cϱ(π	NOUN
ejpam-6997	456	3	)	)	PUNCT
ejpam-6997	456	4	for	for	ADP
ejpam-6997	456	5	ϱ	ϱ	PROPN
ejpam-6997	456	6	∈	∈	PROPN
ejpam-6997	456	7	{	{	PUNCT
ejpam-6997	456	8	r	r	NOUN
ejpam-6997	456	9	,	,	PUNCT
ejpam-6997	456	10	l	l	NOUN
ejpam-6997	456	11	,	,	PUNCT
ejpam-6997	456	12	i	i	PRON
ejpam-6997	456	13	,	,	PUNCT
ejpam-6997	456	14	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	456	15	,	,	PUNCT
ejpam-6997	456	16	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	456	17	}	}	PUNCT
ejpam-6997	456	18	.	.	PUNCT
ejpam-6997	457	1	(	(	PUNCT
ejpam-6997	457	2	8)	8)	NUM
ejpam-6997	457	3	let	let	VERB
ejpam-6997	457	4	π	π	PROPN
ejpam-6997	457	5	∈	∈	PROPN
ejpam-6997	457	6	ℵ.	ℵ.	PROPN
ejpam-6997	457	7	then	then	ADV
ejpam-6997	457	8	gmcϱ	gmcϱ	VERB
ejpam-6997	457	9	(	(	PUNCT
ejpam-6997	457	10	cϱ(π	cϱ(π	NOUN
ejpam-6997	457	11	)	)	PUNCT
ejpam-6997	457	12	)	)	PUNCT
ejpam-6997	457	13	⊑	⊑	PRON
ejpam-6997	457	14	cϱ(π	cϱ(π	NOUN
ejpam-6997	457	15	)	)	PUNCT
ejpam-6997	457	16	for	for	ADP
ejpam-6997	457	17	ϱ	ϱ	PROPN
ejpam-6997	457	18	∈	∈	PROPN
ejpam-6997	457	19	{	{	PUNCT
ejpam-6997	457	20	u	u	NOUN
ejpam-6997	457	21	,	,	PUNCT
ejpam-6997	457	22	⟨u⟩	⟨u⟩	PROPN
ejpam-6997	457	23	,	,	PUNCT
ejpam-6997	457	24	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	457	25	}	}	PUNCT
ejpam-6997	457	26	.	.	PUNCT
ejpam-6997	458	1	a.	a.	PROPN
ejpam-6997	458	2	a.	a.	PROPN
ejpam-6997	458	3	azzam	azzam	PROPN
ejpam-6997	458	4	,	,	PUNCT
ejpam-6997	458	5	m.	m.	NOUN
ejpam-6997	458	6	aldawood	aldawood	PROPN
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ejpam-6997	458	9	alreshidi	alreshidi	PROPN
ejpam-6997	458	10	/	/	SYM
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ejpam-6997	458	12	.	.	PUNCT
ejpam-6997	459	1	j.	j.	PROPN
ejpam-6997	459	2	pure	pure	PROPN
ejpam-6997	459	3	appl	appl	PROPN
ejpam-6997	459	4	.	.	PROPN
ejpam-6997	459	5	math	math	PROPN
ejpam-6997	459	6	,	,	PUNCT
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ejpam-6997	459	8	(	(	PUNCT
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ejpam-6997	459	10	)	)	PUNCT
ejpam-6997	459	11	(	(	PUNCT
ejpam-6997	459	12	2025	2025	NUM
ejpam-6997	459	13	)	)	PUNCT
ejpam-6997	459	14	,	,	PUNCT
ejpam-6997	459	15	6997	6997	NUM
ejpam-6997	459	16	17	17	NUM
ejpam-6997	459	17	of	of	ADP
ejpam-6997	459	18	31	31	NUM
ejpam-6997	459	19	(	(	PUNCT
ejpam-6997	459	20	9	9	NUM
ejpam-6997	459	21	)	)	PUNCT
ejpam-6997	459	22	mcϱ(mcϱ(∆	mcϱ(mcϱ(∆	ADJ
ejpam-6997	459	23	)	)	PUNCT
ejpam-6997	459	24	)	)	PUNCT
ejpam-6997	460	1	=	=	PUNCT
ejpam-6997	460	2	mcϱ(∆	mcϱ(∆	X
ejpam-6997	460	3	)	)	PUNCT
ejpam-6997	460	4	for	for	ADP
ejpam-6997	460	5	ϱ	ϱ	PROPN
ejpam-6997	460	6	∈	∈	PROPN
ejpam-6997	460	7	{	{	PUNCT
ejpam-6997	460	8	r	r	NOUN
ejpam-6997	460	9	,	,	PUNCT
ejpam-6997	460	10	l	l	NOUN
ejpam-6997	460	11	,	,	PUNCT
ejpam-6997	460	12	i	i	PRON
ejpam-6997	460	13	,	,	PUNCT
ejpam-6997	460	14	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	460	15	,	,	PUNCT
ejpam-6997	460	16	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	460	17	}	}	PUNCT
ejpam-6997	460	18	.	.	PUNCT
ejpam-6997	461	1	(	(	PUNCT
ejpam-6997	461	2	10	10	NUM
ejpam-6997	461	3	)	)	PUNCT
ejpam-6997	461	4	mcϱ(mcϱ(∆	mcϱ(mcϱ(∆	ADJ
ejpam-6997	461	5	)	)	PUNCT
ejpam-6997	461	6	)	)	PUNCT
ejpam-6997	462	1	⊒	⊒	X
ejpam-6997	462	2	mcϱ(∆	mcϱ(∆	NUM
ejpam-6997	462	3	)	)	PUNCT
ejpam-6997	462	4	for	for	ADP
ejpam-6997	462	5	ϱ	ϱ	PROPN
ejpam-6997	462	6	∈	∈	PROPN
ejpam-6997	462	7	{	{	PUNCT
ejpam-6997	462	8	u	u	NOUN
ejpam-6997	462	9	,	,	PUNCT
ejpam-6997	462	10	⟨u⟩	⟨u⟩	PROPN
ejpam-6997	462	11	,	,	PUNCT
ejpam-6997	462	12	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	462	13	}	}	PUNCT
ejpam-6997	462	14	.	.	PUNCT
ejpam-6997	463	1	(	(	PUNCT
ejpam-6997	463	2	11	11	NUM
ejpam-6997	463	3	)	)	PUNCT
ejpam-6997	463	4	gmcϱ	gmcϱ	NOUN
ejpam-6997	463	5	(	(	PUNCT
ejpam-6997	463	6	d	d	NOUN
ejpam-6997	463	7	)	)	PUNCT
ejpam-6997	463	8	⊓	⊓	PROPN
ejpam-6997	463	9	gmcϱ	gmcϱ	VERB
ejpam-6997	463	10	(	(	PUNCT
ejpam-6997	463	11	∆	∆	X
ejpam-6997	463	12	)	)	PUNCT
ejpam-6997	464	1	=	=	VERB
ejpam-6997	464	2	gmcϱ	gmcϱ	VERB
ejpam-6997	464	3	(	(	PUNCT
ejpam-6997	464	4	d	d	PROPN
ejpam-6997	464	5	⊓	⊓	PROPN
ejpam-6997	464	6	∆	∆	X
ejpam-6997	464	7	)	)	PUNCT
ejpam-6997	464	8	for	for	ADP
ejpam-6997	464	9	ϱ.	ϱ.	NOUN
ejpam-6997	464	10	(	(	PUNCT
ejpam-6997	464	11	12	12	NUM
ejpam-6997	464	12	)	)	PUNCT
ejpam-6997	464	13	gmcϱ	gmcϱ	NOUN
ejpam-6997	464	14	(	(	PUNCT
ejpam-6997	464	15	d	d	NOUN
ejpam-6997	464	16	)	)	PUNCT
ejpam-6997	464	17	⊔	⊔	PROPN
ejpam-6997	464	18	gmcϱ	gmcϱ	NOUN
ejpam-6997	464	19	(	(	PUNCT
ejpam-6997	464	20	∆	∆	X
ejpam-6997	464	21	)	)	PUNCT
ejpam-6997	464	22	=	=	VERB
ejpam-6997	464	23	gmcϱ	gmcϱ	VERB
ejpam-6997	464	24	(	(	PUNCT
ejpam-6997	464	25	d	d	NOUN
ejpam-6997	464	26	⊔	⊔	NUM
ejpam-6997	464	27	∆	∆	PROPN
ejpam-6997	464	28	)	)	PUNCT
ejpam-6997	464	29	for	for	ADP
ejpam-6997	464	30	ϱ.	ϱ.	NOUN
ejpam-6997	464	31	proof	proof	NOUN
ejpam-6997	464	32	.	.	PUNCT
ejpam-6997	465	1	validating	validate	VERB
ejpam-6997	465	2	(	(	PUNCT
ejpam-6997	465	3	1	1	NUM
ejpam-6997	465	4	)	)	PUNCT
ejpam-6997	465	5	,	,	PUNCT
ejpam-6997	465	6	(	(	PUNCT
ejpam-6997	465	7	2	2	NUM
ejpam-6997	465	8	)	)	PUNCT
ejpam-6997	465	9	,	,	PUNCT
ejpam-6997	465	10	(	(	PUNCT
ejpam-6997	465	11	3	3	NUM
ejpam-6997	465	12	)	)	PUNCT
ejpam-6997	465	13	,	,	PUNCT
ejpam-6997	465	14	(	(	PUNCT
ejpam-6997	465	15	4	4	NUM
ejpam-6997	465	16	)	)	PUNCT
ejpam-6997	465	17	,	,	PUNCT
ejpam-6997	465	18	(	(	PUNCT
ejpam-6997	465	19	11	11	NUM
ejpam-6997	465	20	)	)	PUNCT
ejpam-6997	465	21	,	,	PUNCT
ejpam-6997	465	22	and	and	CCONJ
ejpam-6997	465	23	(	(	PUNCT
ejpam-6997	465	24	12	12	NUM
ejpam-6997	465	25	)	)	PUNCT
ejpam-6997	465	26	is	be	AUX
ejpam-6997	465	27	simple	simple	ADJ
ejpam-6997	465	28	in	in	ADP
ejpam-6997	465	29	accordance	accordance	NOUN
ejpam-6997	465	30	with	with	ADP
ejpam-6997	465	31	definition	definition	NOUN
ejpam-6997	465	32	3.14	3.14	NUM
ejpam-6997	465	33	.	.	PUNCT
ejpam-6997	466	1	(	(	PUNCT
ejpam-6997	466	2	5	5	X
ejpam-6997	466	3	)	)	PUNCT
ejpam-6997	466	4	let	let	VERB
ejpam-6997	466	5	ϱ	ϱ	PART
ejpam-6997	466	6	be	be	AUX
ejpam-6997	466	7	a	a	DET
ejpam-6997	466	8	member	member	NOUN
ejpam-6997	466	9	of	of	ADP
ejpam-6997	466	10	{	{	PUNCT
ejpam-6997	466	11	r	r	NOUN
ejpam-6997	466	12	,	,	PUNCT
ejpam-6997	466	13	l	l	NOUN
ejpam-6997	466	14	,	,	PUNCT
ejpam-6997	466	15	i	i	PRON
ejpam-6997	466	16	,	,	PUNCT
ejpam-6997	466	17	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	466	18	,	,	PUNCT
ejpam-6997	466	19	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	466	20	}	}	PUNCT
ejpam-6997	466	21	.	.	PUNCT
ejpam-6997	467	1	using	use	VERB
ejpam-6997	467	2	the	the	DET
ejpam-6997	467	3	current	current	ADJ
ejpam-6997	467	4	theorem	theorem	NOUN
ejpam-6997	467	5	’s	’s	PART
ejpam-6997	467	6	characteristics	characteristic	NOUN
ejpam-6997	467	7	(	(	PUNCT
ejpam-6997	467	8	1	1	NUM
ejpam-6997	467	9	)	)	PUNCT
ejpam-6997	467	10	and	and	CCONJ
ejpam-6997	467	11	(	(	PUNCT
ejpam-6997	467	12	4	4	NUM
ejpam-6997	467	13	)	)	PUNCT
ejpam-6997	467	14	,	,	PUNCT
ejpam-6997	467	15	gmcϱ	gmcϱ	NOUN
ejpam-6997	467	16	(	(	PUNCT
ejpam-6997	467	17	gmcϱ	gmcϱ	PROPN
ejpam-6997	467	18	(	(	PUNCT
ejpam-6997	467	19	∆	∆	PROPN
ejpam-6997	467	20	)	)	PUNCT
ejpam-6997	467	21	)	)	PUNCT
ejpam-6997	467	22	⊑	⊑	PROPN
ejpam-6997	467	23	gmcϱ	gmcϱ	VERB
ejpam-6997	467	24	(	(	PUNCT
ejpam-6997	467	25	∆	∆	PROPN
ejpam-6997	467	26	)	)	PUNCT
ejpam-6997	467	27	.	.	PUNCT
ejpam-6997	468	1	the	the	DET
ejpam-6997	468	2	gmcϱ	gmcϱ	NOUN
ejpam-6997	468	3	(	(	PUNCT
ejpam-6997	468	4	gmcϱ	gmcϱ	PROPN
ejpam-6997	468	5	(	(	PUNCT
ejpam-6997	468	6	∆	∆	PROPN
ejpam-6997	468	7	)	)	PUNCT
ejpam-6997	468	8	)	)	PUNCT
ejpam-6997	469	1	=	=	PRON
ejpam-6997	469	2	gmcϱ	gmcϱ	NOUN
ejpam-6997	469	3	(	(	PUNCT
ejpam-6997	469	4	∆	∆	PROPN
ejpam-6997	469	5	)	)	PUNCT
ejpam-6997	469	6	is	be	AUX
ejpam-6997	469	7	the	the	DET
ejpam-6997	469	8	result	result	NOUN
ejpam-6997	469	9	of	of	ADP
ejpam-6997	469	10	utilizing	utilize	VERB
ejpam-6997	469	11	(	(	PUNCT
ejpam-6997	469	12	6	6	NUM
ejpam-6997	469	13	)	)	PUNCT
ejpam-6997	469	14	of	of	ADP
ejpam-6997	469	15	theorem	theorem	ADJ
ejpam-6997	469	16	3.3	3.3	NUM
ejpam-6997	469	17	to	to	PART
ejpam-6997	469	18	show	show	VERB
ejpam-6997	469	19	the	the	DET
ejpam-6997	469	20	other	other	ADJ
ejpam-6997	469	21	direction	direction	NOUN
ejpam-6997	469	22	.	.	PUNCT
ejpam-6997	470	1	(	(	PUNCT
ejpam-6997	470	2	6	6	X
ejpam-6997	470	3	)	)	PUNCT
ejpam-6997	470	4	let	let	VERB
ejpam-6997	470	5	ϱ	ϱ	ADP
ejpam-6997	470	6	∈	∈	PROPN
ejpam-6997	470	7	{	{	PUNCT
ejpam-6997	470	8	u	u	NOUN
ejpam-6997	470	9	,	,	PUNCT
ejpam-6997	470	10	⟨u⟩	⟨u⟩	PROPN
ejpam-6997	470	11	,	,	PUNCT
ejpam-6997	470	12	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	470	13	}	}	PUNCT
ejpam-6997	470	14	.	.	PUNCT
ejpam-6997	471	1	using	use	VERB
ejpam-6997	471	2	the	the	DET
ejpam-6997	471	3	current	current	ADJ
ejpam-6997	471	4	theorem	theorem	NOUN
ejpam-6997	471	5	’s	’s	PART
ejpam-6997	471	6	characteristics	characteristic	NOUN
ejpam-6997	471	7	(	(	PUNCT
ejpam-6997	471	8	1	1	NUM
ejpam-6997	471	9	)	)	PUNCT
ejpam-6997	471	10	and	and	CCONJ
ejpam-6997	471	11	(	(	PUNCT
ejpam-6997	471	12	4	4	NUM
ejpam-6997	471	13	)	)	PUNCT
ejpam-6997	471	14	,	,	PUNCT
ejpam-6997	471	15	gmcϱ	gmcϱ	NOUN
ejpam-6997	471	16	(	(	PUNCT
ejpam-6997	471	17	gmcϱ	gmcϱ	PROPN
ejpam-6997	471	18	(	(	PUNCT
ejpam-6997	471	19	∆	∆	PROPN
ejpam-6997	471	20	)	)	PUNCT
ejpam-6997	471	21	)	)	PUNCT
ejpam-6997	471	22	⊑	⊑	PROPN
ejpam-6997	471	23	gmcϱ	gmcϱ	VERB
ejpam-6997	471	24	(	(	PUNCT
ejpam-6997	471	25	∆	∆	PROPN
ejpam-6997	471	26	)	)	PUNCT
ejpam-6997	471	27	.	.	PUNCT
ejpam-6997	472	1	(	(	PUNCT
ejpam-6997	472	2	7	7	X
ejpam-6997	472	3	)	)	PUNCT
ejpam-6997	472	4	let	let	VERB
ejpam-6997	472	5	ϱ	ϱ	ADP
ejpam-6997	472	6	∈	∈	PROPN
ejpam-6997	472	7	{	{	PUNCT
ejpam-6997	472	8	r	r	NOUN
ejpam-6997	472	9	,	,	PUNCT
ejpam-6997	472	10	l	l	NOUN
ejpam-6997	472	11	,	,	PUNCT
ejpam-6997	472	12	i	i	PRON
ejpam-6997	472	13	,	,	PUNCT
ejpam-6997	472	14	⟨l⟩	⟨l⟩	PROPN
ejpam-6997	472	15	,	,	PUNCT
ejpam-6997	472	16	⟨i⟩	⟨i⟩	PROPN
ejpam-6997	472	17	}	}	PUNCT
ejpam-6997	472	18	.	.	PUNCT
ejpam-6997	473	1	applying	apply	VERB
ejpam-6997	473	2	the	the	DET
ejpam-6997	473	3	current	current	ADJ
ejpam-6997	473	4	theorem	theorem	NOUN
ejpam-6997	473	5	’s	’s	PART
ejpam-6997	473	6	property	property	NOUN
ejpam-6997	473	7	(	(	PUNCT
ejpam-6997	473	8	1	1	NUM
ejpam-6997	473	9	)	)	PUNCT
ejpam-6997	473	10	,	,	PUNCT
ejpam-6997	473	11	we	we	PRON
ejpam-6997	473	12	have	have	AUX
ejpam-6997	473	13	gmcϱ	gmcϱ	VERB
ejpam-6997	473	14	(	(	PUNCT
ejpam-6997	473	15	cϱ(π	cϱ(π	NOUN
ejpam-6997	473	16	)	)	PUNCT
ejpam-6997	473	17	)	)	PUNCT
ejpam-6997	473	18	⊑	⊑	PRON
ejpam-6997	473	19	cϱ(π	cϱ(π	NOUN
ejpam-6997	473	20	)	)	PUNCT
ejpam-6997	473	21	,	,	PUNCT
ejpam-6997	473	22	∀π	∀π	PROPN
ejpam-6997	473	23	∈	∈	PROPN
ejpam-6997	473	24	ℵ.	ℵ.	PROPN
ejpam-6997	473	25	theorem	theorem	VERB
ejpam-6997	473	26	2	2	NUM
ejpam-6997	473	27	’s	’s	PART
ejpam-6997	473	28	(	(	PUNCT
ejpam-6997	473	29	7	7	NUM
ejpam-6997	473	30	)	)	PUNCT
ejpam-6997	473	31	is	be	AUX
ejpam-6997	473	32	used	use	VERB
ejpam-6997	473	33	to	to	PART
ejpam-6997	473	34	demonstrate	demonstrate	VERB
ejpam-6997	473	35	the	the	DET
ejpam-6997	473	36	opposite	opposite	ADJ
ejpam-6997	473	37	direction	direction	NOUN
ejpam-6997	473	38	.	.	PUNCT
ejpam-6997	474	1	thus	thus	ADV
ejpam-6997	474	2	,	,	PUNCT
ejpam-6997	474	3	gmcϱ	gmcϱ	NOUN
ejpam-6997	474	4	(	(	PUNCT
ejpam-6997	474	5	cϱ(π	cϱ(π	NOUN
ejpam-6997	474	6	)	)	PUNCT
ejpam-6997	474	7	)	)	PUNCT
ejpam-6997	475	1	=	=	SYM
ejpam-6997	475	2	cϱ(π	cϱ(π	NOUN
ejpam-6997	475	3	)	)	PUNCT
ejpam-6997	475	4	.	.	PUNCT
ejpam-6997	476	1	(	(	PUNCT
ejpam-6997	476	2	8)	8)	NUM
ejpam-6997	476	3	assume	assume	VERB
ejpam-6997	476	4	that	that	SCONJ
ejpam-6997	476	5	ϱ	ϱ	ADP
ejpam-6997	476	6	∈	∈	PROPN
ejpam-6997	476	7	{	{	PUNCT
ejpam-6997	476	8	u	u	NOUN
ejpam-6997	476	9	,	,	PUNCT
ejpam-6997	476	10	⟨u⟩	⟨u⟩	PROPN
ejpam-6997	476	11	,	,	PUNCT
ejpam-6997	476	12	⟨r⟩	⟨r⟩	PROPN
ejpam-6997	476	13	}	}	PUNCT
ejpam-6997	476	14	.	.	PUNCT
ejpam-6997	477	1	by	by	ADP
ejpam-6997	477	2	property	property	NOUN
ejpam-6997	477	3	(	(	PUNCT
ejpam-6997	477	4	1	1	NUM
ejpam-6997	477	5	)	)	PUNCT
ejpam-6997	477	6	of	of	ADP
ejpam-6997	477	7	the	the	DET
ejpam-6997	477	8	current	current	ADJ
ejpam-6997	477	9	theorem	theorem	NOUN
ejpam-6997	477	10	,	,	PUNCT
ejpam-6997	477	11	we	we	PRON
ejpam-6997	477	12	,	,	PUNCT
ejpam-6997	477	13	have	have	AUX
ejpam-6997	477	14	gmcϱ	gmcϱ	VERB
ejpam-6997	477	15	(	(	PUNCT
ejpam-6997	477	16	cϱ(π	cϱ(π	NOUN
ejpam-6997	477	17	)	)	PUNCT
ejpam-6997	477	18	)	)	PUNCT
ejpam-6997	478	1	⊑	⊑	PROPN
ejpam-6997	479	1	cϱ(π)∀π	cϱ(π)∀π	NOUN
ejpam-6997	479	2	∈	∈	PROPN
ejpam-6997	479	3	ℵ.	ℵ.	NOUN
ejpam-6997	480	1	(	(	PUNCT
ejpam-6997	480	2	9	9	X
ejpam-6997	480	3	)	)	PUNCT
ejpam-6997	480	4	identical	identical	ADJ
ejpam-6997	480	5	to	to	ADP
ejpam-6997	480	6	evidence	evidence	NOUN
ejpam-6997	480	7	of	of	ADP
ejpam-6997	480	8	property	property	NOUN
ejpam-6997	480	9	(	(	PUNCT
ejpam-6997	480	10	5	5	NUM
ejpam-6997	480	11	)	)	PUNCT
ejpam-6997	480	12	.	.	PUNCT
ejpam-6997	481	1	(	(	PUNCT
ejpam-6997	481	2	10	10	NUM
ejpam-6997	481	3	)	)	PUNCT
ejpam-6997	481	4	identical	identical	ADJ
ejpam-6997	481	5	to	to	ADP
ejpam-6997	481	6	evidence	evidence	NOUN
ejpam-6997	481	7	of	of	ADP
ejpam-6997	481	8	property	property	NOUN
ejpam-6997	481	9	(	(	PUNCT
ejpam-6997	481	10	5	5	NUM
ejpam-6997	481	11	)	)	PUNCT
ejpam-6997	481	12	.	.	PUNCT
ejpam-6997	482	1	proposition	proposition	NOUN
ejpam-6997	482	2	12	12	NUM
ejpam-6997	482	3	.	.	PUNCT
ejpam-6997	483	1	for	for	ADP
ejpam-6997	483	2	a	a	DET
ejpam-6997	483	3	ϱ-ns	ϱ-ns	ADV
ejpam-6997	483	4	(	(	PUNCT
ejpam-6997	483	5	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	483	6	,	,	PUNCT
ejpam-6997	483	7	ξϱ	ξϱ	NOUN
ejpam-6997	483	8	)	)	PUNCT
ejpam-6997	483	9	and	and	CCONJ
ejpam-6997	483	10	∆	∆	PROPN
ejpam-6997	483	11	⊑	⊑	PRON
ejpam-6997	483	12	ℵ	ℵ	NOUN
ejpam-6997	483	13	,	,	PUNCT
ejpam-6997	483	14	let	let	VERB
ejpam-6997	483	15	g	g	PRON
ejpam-6997	483	16	be	be	AUX
ejpam-6997	483	17	a	a	DET
ejpam-6997	483	18	grill	grill	NOUN
ejpam-6997	483	19	,	,	PUNCT
ejpam-6997	483	20	then	then	ADV
ejpam-6997	483	21	(	(	PUNCT
ejpam-6997	483	22	1	1	X
ejpam-6997	483	23	)	)	PUNCT
ejpam-6997	483	24	gmcu	gmcu	NOUN
ejpam-6997	483	25	(	(	PUNCT
ejpam-6997	483	26	∆	∆	PROPN
ejpam-6997	483	27	)	)	PUNCT
ejpam-6997	483	28	⊑	⊑	X
ejpam-6997	483	29	gmcr	gmcr	X
ejpam-6997	483	30	(	(	PUNCT
ejpam-6997	483	31	∆	∆	X
ejpam-6997	483	32	)	)	PUNCT
ejpam-6997	483	33	⊓	⊓	PROPN
ejpam-6997	483	34	gmcl	gmcl	NOUN
ejpam-6997	483	35	(	(	PUNCT
ejpam-6997	483	36	∆	∆	PROPN
ejpam-6997	483	37	)	)	PUNCT
ejpam-6997	484	1	⊑	⊑	X
ejpam-6997	484	2	gmcr	gmcr	X
ejpam-6997	484	3	(	(	PUNCT
ejpam-6997	484	4	∆	∆	X
ejpam-6997	484	5	)	)	PUNCT
ejpam-6997	484	6	⊔	⊔	PROPN
ejpam-6997	484	7	gmcl	gmcl	NOUN
ejpam-6997	484	8	(	(	PUNCT
ejpam-6997	484	9	∆	∆	PROPN
ejpam-6997	484	10	)	)	PUNCT
ejpam-6997	484	11	⊑	⊑	PRON
ejpam-6997	484	12	gmci	gmci	VERB
ejpam-6997	484	13	(	(	PUNCT
ejpam-6997	484	14	∆	∆	PROPN
ejpam-6997	484	15	)	)	PUNCT
ejpam-6997	484	16	.	.	PUNCT
ejpam-6997	485	1	(	(	PUNCT
ejpam-6997	485	2	2	2	X
ejpam-6997	485	3	)	)	PUNCT
ejpam-6997	485	4	gmci	gmci	NOUN
ejpam-6997	485	5	(	(	PUNCT
ejpam-6997	485	6	∆	∆	PROPN
ejpam-6997	485	7	)	)	PUNCT
ejpam-6997	486	1	⊑	⊑	X
ejpam-6997	486	2	gmcr	gmcr	X
ejpam-6997	486	3	(	(	PUNCT
ejpam-6997	486	4	∆	∆	X
ejpam-6997	486	5	)	)	PUNCT
ejpam-6997	487	1	⊓	⊓	PROPN
ejpam-6997	487	2	gmcl	gmcl	NOUN
ejpam-6997	487	3	(	(	PUNCT
ejpam-6997	487	4	∆	∆	PROPN
ejpam-6997	487	5	)	)	PUNCT
ejpam-6997	487	6	⊑	⊑	X
ejpam-6997	487	7	gmcr	gmcr	X
ejpam-6997	487	8	(	(	PUNCT
ejpam-6997	487	9	∆	∆	X
ejpam-6997	487	10	)	)	PUNCT
ejpam-6997	487	11	⊔	⊔	PROPN
ejpam-6997	487	12	gmcl	gmcl	NOUN
ejpam-6997	487	13	(	(	PUNCT
ejpam-6997	487	14	∆	∆	PROPN
ejpam-6997	487	15	)	)	PUNCT
ejpam-6997	487	16	⊑	⊑	PRON
ejpam-6997	487	17	gmcu	gmcu	NOUN
ejpam-6997	487	18	(	(	PUNCT
ejpam-6997	487	19	∆	∆	PROPN
ejpam-6997	487	20	)	)	PUNCT
ejpam-6997	487	21	.	.	PUNCT
ejpam-6997	488	1	(	(	PUNCT
ejpam-6997	488	2	3	3	X
ejpam-6997	488	3	)	)	PUNCT
ejpam-6997	488	4	gmc⟨u⟩	gmc⟨u⟩	NOUN
ejpam-6997	488	5	(	(	PUNCT
ejpam-6997	488	6	∆	∆	X
ejpam-6997	488	7	)	)	PUNCT
ejpam-6997	489	1	⊑	⊑	X
ejpam-6997	489	2	gmc⟨r⟩	gmc⟨r⟩	X
ejpam-6997	489	3	(	(	PUNCT
ejpam-6997	489	4	∆	∆	X
ejpam-6997	489	5	)	)	PUNCT
ejpam-6997	490	1	⊓	⊓	PROPN
ejpam-6997	490	2	gmc⟨l⟩	gmc⟨l⟩	X
ejpam-6997	490	3	(	(	PUNCT
ejpam-6997	490	4	∆	∆	PROPN
ejpam-6997	490	5	)	)	PUNCT
ejpam-6997	490	6	⊑	⊑	X
ejpam-6997	490	7	gmc⟨r⟩	gmc⟨r⟩	X
ejpam-6997	490	8	(	(	PUNCT
ejpam-6997	490	9	∆	∆	X
ejpam-6997	490	10	)	)	PUNCT
ejpam-6997	490	11	⊔	⊔	PROPN
ejpam-6997	490	12	gmc⟨l⟩	gmc⟨l⟩	NOUN
ejpam-6997	490	13	(	(	PUNCT
ejpam-6997	490	14	∆	∆	PROPN
ejpam-6997	490	15	)	)	PUNCT
ejpam-6997	490	16	⊑	⊑	X
ejpam-6997	490	17	gmc⟨i⟩	gmc⟨i⟩	X
ejpam-6997	490	18	(	(	PUNCT
ejpam-6997	490	19	∆	∆	PROPN
ejpam-6997	490	20	)	)	PUNCT
ejpam-6997	490	21	.	.	PUNCT
ejpam-6997	491	1	(	(	PUNCT
ejpam-6997	491	2	4	4	X
ejpam-6997	491	3	)	)	PUNCT
ejpam-6997	491	4	gmc⟨i⟩	gmc⟨i⟩	NOUN
ejpam-6997	491	5	(	(	PUNCT
ejpam-6997	491	6	∆	∆	X
ejpam-6997	491	7	)	)	PUNCT
ejpam-6997	492	1	⊑	⊑	X
ejpam-6997	492	2	gmc⟨r⟩	gmc⟨r⟩	X
ejpam-6997	492	3	(	(	PUNCT
ejpam-6997	492	4	∆	∆	X
ejpam-6997	492	5	)	)	PUNCT
ejpam-6997	493	1	⊓	⊓	PROPN
ejpam-6997	493	2	gmc⟨l⟩	gmc⟨l⟩	X
ejpam-6997	493	3	(	(	PUNCT
ejpam-6997	493	4	∆	∆	PROPN
ejpam-6997	493	5	)	)	PUNCT
ejpam-6997	493	6	⊑	⊑	X
ejpam-6997	493	7	gmc⟨r⟩	gmc⟨r⟩	X
ejpam-6997	493	8	(	(	PUNCT
ejpam-6997	493	9	∆	∆	X
ejpam-6997	493	10	)	)	PUNCT
ejpam-6997	493	11	⊔	⊔	PROPN
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ejpam-6997	493	13	(	(	PUNCT
ejpam-6997	493	14	∆	∆	PROPN
ejpam-6997	493	15	)	)	PUNCT
ejpam-6997	494	1	⊑	⊑	PROPN
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ejpam-6997	494	3	(	(	PUNCT
ejpam-6997	494	4	∆	∆	PROPN
ejpam-6997	494	5	)	)	PUNCT
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ejpam-6997	495	2	.	.	PUNCT
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ejpam-6997	496	3	definition	definition	NOUN
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ejpam-6997	496	7	3.5	3.5	NUM
ejpam-6997	496	8	.	.	PUNCT
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ejpam-6997	498	4	(	(	PUNCT
ejpam-6997	498	5	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	498	6	,	,	PUNCT
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ejpam-6997	498	8	)	)	PUNCT
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ejpam-6997	498	10	∆	∆	PROPN
ejpam-6997	498	11	⊑	⊑	PRON
ejpam-6997	498	12	ℵ	ℵ	NOUN
ejpam-6997	498	13	,	,	PUNCT
ejpam-6997	498	14	let	let	VERB
ejpam-6997	498	15	g	g	PRON
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ejpam-6997	498	21	a.	a.	PROPN
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ejpam-6997	498	24	,	,	PUNCT
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ejpam-6997	498	32	.	.	PUNCT
ejpam-6997	499	1	j.	j.	PROPN
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ejpam-6997	499	4	.	.	PROPN
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ejpam-6997	499	6	,	,	PUNCT
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ejpam-6997	499	8	(	(	PUNCT
ejpam-6997	499	9	4	4	NUM
ejpam-6997	499	10	)	)	PUNCT
ejpam-6997	499	11	(	(	PUNCT
ejpam-6997	499	12	2025	2025	NUM
ejpam-6997	499	13	)	)	PUNCT
ejpam-6997	499	14	,	,	PUNCT
ejpam-6997	499	15	6997	6997	NUM
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ejpam-6997	499	18	31	31	NUM
ejpam-6997	499	19	(	(	PUNCT
ejpam-6997	499	20	1	1	X
ejpam-6997	499	21	)	)	PUNCT
ejpam-6997	499	22	gacu	gacu	NOUN
ejpam-6997	499	23	(	(	PUNCT
ejpam-6997	499	24	∆	∆	PROPN
ejpam-6997	499	25	)	)	PUNCT
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ejpam-6997	499	28	(	(	PUNCT
ejpam-6997	499	29	∆	∆	PROPN
ejpam-6997	499	30	)	)	PUNCT
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ejpam-6997	499	33	(	(	PUNCT
ejpam-6997	499	34	∆	∆	PROPN
ejpam-6997	499	35	)	)	PUNCT
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ejpam-6997	500	1	(	(	PUNCT
ejpam-6997	500	2	2	2	X
ejpam-6997	500	3	)	)	PUNCT
ejpam-6997	500	4	gacu	gacu	NOUN
ejpam-6997	500	5	(	(	PUNCT
ejpam-6997	500	6	∆	∆	PROPN
ejpam-6997	500	7	)	)	PUNCT
ejpam-6997	500	8	≤	≤	NOUN
ejpam-6997	500	9	gacl	gacl	NOUN
ejpam-6997	500	10	(	(	PUNCT
ejpam-6997	500	11	∆	∆	PROPN
ejpam-6997	500	12	)	)	PUNCT
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ejpam-6997	500	15	(	(	PUNCT
ejpam-6997	500	16	∆	∆	PROPN
ejpam-6997	500	17	)	)	PUNCT
ejpam-6997	500	18	.	.	PUNCT
ejpam-6997	501	1	(	(	PUNCT
ejpam-6997	501	2	3	3	X
ejpam-6997	501	3	)	)	PUNCT
ejpam-6997	501	4	gac⟨u⟩	gac⟨u⟩	NOUN
ejpam-6997	501	5	(	(	PUNCT
ejpam-6997	501	6	∆	∆	X
ejpam-6997	501	7	)	)	PUNCT
ejpam-6997	501	8	≤	≤	NUM
ejpam-6997	501	9	gac⟨r⟩	gac⟨r⟩	PUNCT
ejpam-6997	501	10	(	(	PUNCT
ejpam-6997	501	11	∆	∆	X
ejpam-6997	501	12	)	)	PUNCT
ejpam-6997	501	13	≤	≤	NUM
ejpam-6997	501	14	gac⟨i⟩	gac⟨i⟩	NOUN
ejpam-6997	501	15	(	(	PUNCT
ejpam-6997	501	16	∆	∆	PROPN
ejpam-6997	501	17	)	)	PUNCT
ejpam-6997	501	18	.	.	PUNCT
ejpam-6997	502	1	(	(	PUNCT
ejpam-6997	502	2	4	4	X
ejpam-6997	502	3	)	)	PUNCT
ejpam-6997	502	4	gac⟨u⟩	gac⟨u⟩	NOUN
ejpam-6997	502	5	(	(	PUNCT
ejpam-6997	502	6	∆	∆	X
ejpam-6997	502	7	)	)	PUNCT
ejpam-6997	502	8	≤	≤	NUM
ejpam-6997	503	1	gac⟨l⟩	gac⟨l⟩	X
ejpam-6997	503	2	(	(	PUNCT
ejpam-6997	503	3	∆	∆	PROPN
ejpam-6997	503	4	)	)	PUNCT
ejpam-6997	503	5	≤	≤	NUM
ejpam-6997	503	6	gac⟨i⟩	gac⟨i⟩	NOUN
ejpam-6997	503	7	(	(	PUNCT
ejpam-6997	503	8	∆	∆	PROPN
ejpam-6997	503	9	)	)	PUNCT
ejpam-6997	503	10	.	.	PUNCT
ejpam-6997	504	1	proposition	proposition	NOUN
ejpam-6997	504	2	13	13	NUM
ejpam-6997	504	3	.	.	PUNCT
ejpam-6997	505	1	if	if	SCONJ
ejpam-6997	505	2	∆	∆	PROPN
ejpam-6997	505	3	is	be	AUX
ejpam-6997	505	4	a	a	DET
ejpam-6997	505	5	nonempty	nonempty	ADJ
ejpam-6997	505	6	subset	subset	NOUN
ejpam-6997	505	7	of	of	ADP
ejpam-6997	505	8	ℵ	ℵ	NOUN
ejpam-6997	505	9	,	,	PUNCT
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ejpam-6997	505	11	for	for	ADP
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ejpam-6997	505	13	ϱ	ϱ	NOUN
ejpam-6997	505	14	,	,	PUNCT
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ejpam-6997	505	18	(	(	PUNCT
ejpam-6997	505	19	∆	∆	PROPN
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ejpam-6997	507	7	(	(	PUNCT
ejpam-6997	507	8	∆	∆	PROPN
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ejpam-6997	507	10	⊑	⊑	PART
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ejpam-6997	507	12	⊑	⊑	PART
ejpam-6997	507	13	gmcϱ	gmcϱ	VERB
ejpam-6997	507	14	(	(	PUNCT
ejpam-6997	507	15	∆	∆	PROPN
ejpam-6997	507	16	)	)	PUNCT
ejpam-6997	507	17	.	.	PUNCT
ejpam-6997	508	1	definition	definition	NOUN
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ejpam-6997	508	3	.	.	PUNCT
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ejpam-6997	509	6	∆	∆	PROPN
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ejpam-6997	509	10	(	(	PUNCT
ejpam-6997	509	11	∆	∆	PROPN
ejpam-6997	509	12	)	)	PUNCT
ejpam-6997	510	1	=	=	SYM
ejpam-6997	510	2	1	1	X
ejpam-6997	510	3	.	.	X
ejpam-6997	510	4	otherwise	otherwise	ADV
ejpam-6997	510	5	it	it	PRON
ejpam-6997	510	6	’s	’	VERB
ejpam-6997	510	7	known	know	VERB
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ejpam-6997	511	8	fails	fail	VERB
ejpam-6997	511	9	,	,	PUNCT
ejpam-6997	511	10	as	as	SCONJ
ejpam-6997	511	11	the	the	DET
ejpam-6997	511	12	following	follow	VERB
ejpam-6997	511	13	example	example	NOUN
ejpam-6997	511	14	shows	show	NOUN
ejpam-6997	511	15	.	.	PUNCT
ejpam-6997	512	1	example	example	NOUN
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ejpam-6997	512	7	3.11	3.11	NUM
ejpam-6997	512	8	.	.	PUNCT
ejpam-6997	513	1	tables	table	NOUN
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ejpam-6997	513	10	(	(	PUNCT
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ejpam-6997	513	18	:	:	PUNCT
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ejpam-6997	513	20	(	(	PUNCT
ejpam-6997	513	21	∆	∆	PROPN
ejpam-6997	513	22	)	)	PUNCT
ejpam-6997	513	23	for	for	ADP
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ejpam-6997	513	26	{	{	PUNCT
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ejpam-6997	521	22	1	1	NUM
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ejpam-6997	521	29	1	1	NUM
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ejpam-6997	521	141	1	1	NUM
ejpam-6997	521	142	1	1	NUM
ejpam-6997	521	143	ℵ	ℵ	SYM
ejpam-6997	521	144	1	1	NUM
ejpam-6997	521	145	1	1	NUM
ejpam-6997	521	146	1	1	NUM
ejpam-6997	521	147	1	1	NUM
ejpam-6997	521	148	(	(	PUNCT
ejpam-6997	521	149	1	1	NUM
ejpam-6997	521	150	)	)	PUNCT
ejpam-6997	521	151	mcϱ(d	mcϱ(d	PROPN
ejpam-6997	521	152	)	)	PUNCT
ejpam-6997	521	153	⊑	⊑	PRON
ejpam-6997	521	154	gmcϱ	gmcϱ	VERB
ejpam-6997	521	155	(	(	PUNCT
ejpam-6997	521	156	d	d	NOUN
ejpam-6997	521	157	)	)	PUNCT
ejpam-6997	521	158	.	.	PUNCT
ejpam-6997	522	1	(	(	PUNCT
ejpam-6997	522	2	2	2	X
ejpam-6997	522	3	)	)	PUNCT
ejpam-6997	522	4	gmcϱ	gmcϱ	NOUN
ejpam-6997	522	5	(	(	PUNCT
ejpam-6997	522	6	d	d	NOUN
ejpam-6997	522	7	)	)	PUNCT
ejpam-6997	522	8	⊑	⊑	PRON
ejpam-6997	522	9	mcϱ(d	mcϱ(d	PROPN
ejpam-6997	522	10	)	)	PUNCT
ejpam-6997	522	11	.	.	PUNCT
ejpam-6997	523	1	proof	proof	NOUN
ejpam-6997	523	2	.	.	PUNCT
ejpam-6997	524	1	by	by	ADP
ejpam-6997	524	2	using	use	VERB
ejpam-6997	524	3	theorem	theorem	NOUN
ejpam-6997	524	4	3.8	3.8	NUM
ejpam-6997	524	5	,	,	PUNCT
ejpam-6997	524	6	then	then	ADV
ejpam-6997	524	7	mcϱ(d	mcϱ(d	PROPN
ejpam-6997	524	8	)	)	PUNCT
ejpam-6997	524	9	⊑	⊑	PRON
ejpam-6997	524	10	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	524	11	(	(	PUNCT
ejpam-6997	524	12	d	d	NOUN
ejpam-6997	524	13	)	)	PUNCT
ejpam-6997	524	14	.	.	PUNCT
ejpam-6997	525	1	since	since	SCONJ
ejpam-6997	525	2	mcϱ(d	mcϱ(d	PROPN
ejpam-6997	525	3	)	)	PUNCT
ejpam-6997	525	4	⊑	⊑	PROPN
ejpam-6997	525	5	d	d	X
ejpam-6997	525	6	,	,	PUNCT
ejpam-6997	525	7	then	then	ADV
ejpam-6997	525	8	mcϱ(d	mcϱ(d	PROPN
ejpam-6997	525	9	)	)	PUNCT
ejpam-6997	525	10	⊑	⊑	PRON
ejpam-6997	525	11	gmcϱ	gmcϱ	VERB
ejpam-6997	525	12	(	(	PUNCT
ejpam-6997	525	13	d	d	NOUN
ejpam-6997	525	14	)	)	PUNCT
ejpam-6997	525	15	.	.	PUNCT
ejpam-6997	526	1	it	it	PRON
ejpam-6997	526	2	is	be	AUX
ejpam-6997	526	3	possible	possible	ADJ
ejpam-6997	526	4	to	to	PART
ejpam-6997	526	5	prove	prove	VERB
ejpam-6997	526	6	the	the	DET
ejpam-6997	526	7	second	second	ADJ
ejpam-6997	526	8	statement	statement	NOUN
ejpam-6997	526	9	by	by	ADP
ejpam-6997	526	10	following	follow	VERB
ejpam-6997	526	11	the	the	DET
ejpam-6997	526	12	same	same	ADJ
ejpam-6997	526	13	logic	logic	NOUN
ejpam-6997	526	14	.	.	PUNCT
ejpam-6997	527	1	corollary	corollary	ADJ
ejpam-6997	527	2	7	7	NUM
ejpam-6997	527	3	.	.	PUNCT
ejpam-6997	528	1	for	for	ADP
ejpam-6997	528	2	a	a	DET
ejpam-6997	528	3	ϱ-ns	ϱ-ns	ADV
ejpam-6997	528	4	(	(	PUNCT
ejpam-6997	528	5	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	528	6	,	,	PUNCT
ejpam-6997	528	7	ξϱ	ξϱ	NOUN
ejpam-6997	528	8	)	)	PUNCT
ejpam-6997	528	9	and	and	CCONJ
ejpam-6997	528	10	d	d	X
ejpam-6997	528	11	⊑	⊑	PRON
ejpam-6997	528	12	ℵ	ℵ	X
ejpam-6997	528	13	,	,	PUNCT
ejpam-6997	528	14	let	let	VERB
ejpam-6997	528	15	g	g	PRON
ejpam-6997	528	16	be	be	AUX
ejpam-6997	528	17	a	a	DET
ejpam-6997	528	18	grill	grill	NOUN
ejpam-6997	528	19	,	,	PUNCT
ejpam-6997	528	20	then	then	ADV
ejpam-6997	528	21	acϱ(d	acϱ(d	NUM
ejpam-6997	528	22	)	)	PUNCT
ejpam-6997	528	23	≤	≤	NOUN
ejpam-6997	528	24	gacϱ	gacϱ	NOUN
ejpam-6997	528	25	(	(	PUNCT
ejpam-6997	528	26	∆)∀ϱ.	∆)∀ϱ.	VERB
ejpam-6997	528	27	to	to	PART
ejpam-6997	528	28	demonstrate	demonstrate	VERB
ejpam-6997	528	29	that	that	SCONJ
ejpam-6997	528	30	the	the	DET
ejpam-6997	528	31	inverse	inverse	NOUN
ejpam-6997	528	32	of	of	ADP
ejpam-6997	528	33	the	the	DET
ejpam-6997	528	34	aforementioned	aforementioned	ADJ
ejpam-6997	528	35	theorem	theorem	NOUN
ejpam-6997	528	36	and	and	CCONJ
ejpam-6997	528	37	corollary	corollary	ADJ
ejpam-6997	528	38	fails	fail	NOUN
ejpam-6997	528	39	,	,	PUNCT
ejpam-6997	528	40	use	use	VERB
ejpam-6997	528	41	the	the	DET
ejpam-6997	528	42	following	follow	VERB
ejpam-6997	528	43	example	example	NOUN
ejpam-6997	528	44	.	.	PUNCT
ejpam-6997	529	1	example	example	NOUN
ejpam-6997	529	2	5	5	NUM
ejpam-6997	529	3	.	.	PUNCT
ejpam-6997	530	1	extending	extend	VERB
ejpam-6997	530	2	from	from	ADP
ejpam-6997	530	3	example	example	NOUN
ejpam-6997	530	4	3.11	3.11	NUM
ejpam-6997	530	5	.	.	PUNCT
ejpam-6997	531	1	if	if	SCONJ
ejpam-6997	531	2	∆	∆	PROPN
ejpam-6997	531	3	=	=	PRON
ejpam-6997	531	4	{	{	PUNCT
ejpam-6997	531	5	b	b	PROPN
ejpam-6997	531	6	,	,	PUNCT
ejpam-6997	531	7	n	n	CCONJ
ejpam-6997	531	8	}	}	PUNCT
ejpam-6997	531	9	,	,	PUNCT
ejpam-6997	531	10	then	then	ADV
ejpam-6997	531	11	gmcϱ	gmcϱ	VERB
ejpam-6997	531	12	(	(	PUNCT
ejpam-6997	531	13	∆),gmcϱ	∆),gmcϱ	NOUN
ejpam-6997	531	14	(	(	PUNCT
ejpam-6997	531	15	∆	∆	PROPN
ejpam-6997	531	16	)	)	PUNCT
ejpam-6997	531	17	,	,	PUNCT
ejpam-6997	531	18	and	and	CCONJ
ejpam-6997	531	19	gacϱ	gacϱ	NOUN
ejpam-6997	531	20	(	(	PUNCT
ejpam-6997	531	21	∆	∆	PROPN
ejpam-6997	531	22	)	)	PUNCT
ejpam-6997	531	23	are	be	AUX
ejpam-6997	531	24	computed	compute	VERB
ejpam-6997	531	25	for	for	ADP
ejpam-6997	531	26	ϱ	ϱ	PROPN
ejpam-6997	531	27	∈	∈	PROPN
ejpam-6997	531	28	{	{	PUNCT
ejpam-6997	531	29	r	r	NOUN
ejpam-6997	531	30	,	,	PUNCT
ejpam-6997	531	31	u	u	NOUN
ejpam-6997	531	32	}	}	PUNCT
ejpam-6997	531	33	as	as	SCONJ
ejpam-6997	531	34	follows	follow	VERB
ejpam-6997	531	35	:	:	PUNCT
ejpam-6997	531	36	(	(	PUNCT
ejpam-6997	531	37	1	1	X
ejpam-6997	531	38	)	)	PUNCT
ejpam-6997	531	39	gmcϱ	gmcϱ	NOUN
ejpam-6997	531	40	(	(	PUNCT
ejpam-6997	531	41	∆	∆	PROPN
ejpam-6997	531	42	)	)	PUNCT
ejpam-6997	532	1	=	=	PRON
ejpam-6997	532	2	{	{	PUNCT
ejpam-6997	532	3	b	b	NOUN
ejpam-6997	532	4	,	,	PUNCT
ejpam-6997	532	5	n	n	CCONJ
ejpam-6997	532	6	}	}	PUNCT
ejpam-6997	532	7	,	,	PUNCT
ejpam-6997	532	8	gmcϱ	gmcϱ	NOUN
ejpam-6997	532	9	(	(	PUNCT
ejpam-6997	532	10	∆	∆	PROPN
ejpam-6997	532	11	)	)	PUNCT
ejpam-6997	532	12	=	=	PRON
ejpam-6997	532	13	{	{	PUNCT
ejpam-6997	532	14	b	b	NOUN
ejpam-6997	532	15	,	,	PUNCT
ejpam-6997	532	16	n	n	CCONJ
ejpam-6997	532	17	}	}	PUNCT
ejpam-6997	532	18	,	,	PUNCT
ejpam-6997	532	19	and	and	CCONJ
ejpam-6997	532	20	gacϱ	gacϱ	NOUN
ejpam-6997	532	21	(	(	PUNCT
ejpam-6997	532	22	∆	∆	PROPN
ejpam-6997	532	23	)	)	PUNCT
ejpam-6997	533	1	=	=	SYM
ejpam-6997	533	2	1	1	X
ejpam-6997	533	3	.	.	PUNCT
ejpam-6997	533	4	(	(	PUNCT
ejpam-6997	533	5	2	2	NUM
ejpam-6997	533	6	)	)	PUNCT
ejpam-6997	533	7	mcϱ(∆	mcϱ(∆	NUM
ejpam-6997	533	8	)	)	PUNCT
ejpam-6997	533	9	=	=	PRON
ejpam-6997	533	10	{	{	PUNCT
ejpam-6997	533	11	n	n	CCONJ
ejpam-6997	533	12	}	}	PUNCT
ejpam-6997	533	13	,	,	PUNCT
ejpam-6997	533	14	mcϱ(∆	mcϱ(∆	X
ejpam-6997	533	15	)	)	PUNCT
ejpam-6997	533	16	=	=	PRON
ejpam-6997	533	17	{	{	PUNCT
ejpam-6997	533	18	b	b	NOUN
ejpam-6997	533	19	,	,	PUNCT
ejpam-6997	533	20	n	n	CCONJ
ejpam-6997	533	21	,	,	PUNCT
ejpam-6997	533	22	m	m	NOUN
ejpam-6997	533	23	}	}	PUNCT
ejpam-6997	533	24	,	,	PUNCT
ejpam-6997	533	25	and	and	CCONJ
ejpam-6997	533	26	gacϱ	gacϱ	NOUN
ejpam-6997	533	27	(	(	PUNCT
ejpam-6997	533	28	∆	∆	PROPN
ejpam-6997	533	29	)	)	PUNCT
ejpam-6997	533	30	=	=	SYM
ejpam-6997	533	31	1	1	NUM
ejpam-6997	533	32	3	3	NUM
ejpam-6997	533	33	.	.	PUNCT
ejpam-6997	534	1	proposition	proposition	NOUN
ejpam-6997	534	2	14	14	NUM
ejpam-6997	534	3	.	.	PUNCT
ejpam-6997	535	1	for	for	ADP
ejpam-6997	535	2	any	any	DET
ejpam-6997	535	3	ϱ	ϱ	NOUN
ejpam-6997	535	4	,	,	PUNCT
ejpam-6997	535	5	suppose	suppose	VERB
ejpam-6997	535	6	that	that	SCONJ
ejpam-6997	535	7	g	g	PROPN
ejpam-6997	535	8	is	be	AUX
ejpam-6997	535	9	a	a	DET
ejpam-6997	535	10	grill	grill	NOUN
ejpam-6997	535	11	on	on	ADP
ejpam-6997	535	12	a	a	DET
ejpam-6997	535	13	ϱ-ns	ϱ-ns	ADV
ejpam-6997	535	14	(	(	PUNCT
ejpam-6997	535	15	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	535	16	,	,	PUNCT
ejpam-6997	535	17	ξϱ	ξϱ	NOUN
ejpam-6997	535	18	)	)	PUNCT
ejpam-6997	535	19	.	.	PUNCT
ejpam-6997	536	1	if	if	SCONJ
ejpam-6997	536	2	∆	∆	PROPN
ejpam-6997	536	3	⊑	⊑	DET
ejpam-6997	536	4	ℵ	ℵ	NOUN
ejpam-6997	536	5	,	,	PUNCT
ejpam-6997	536	6	then	then	ADV
ejpam-6997	536	7	a.	a.	PROPN
ejpam-6997	536	8	a.	a.	PROPN
ejpam-6997	536	9	azzam	azzam	PROPN
ejpam-6997	536	10	,	,	PUNCT
ejpam-6997	536	11	m.	m.	NOUN
ejpam-6997	536	12	aldawood	aldawood	PROPN
ejpam-6997	536	13	,	,	PUNCT
ejpam-6997	536	14	b.	b.	PROPN
ejpam-6997	536	15	alreshidi	alreshidi	PROPN
ejpam-6997	536	16	/	/	SYM
ejpam-6997	536	17	eur	eur	PROPN
ejpam-6997	536	18	.	.	PUNCT
ejpam-6997	537	1	j.	j.	PROPN
ejpam-6997	537	2	pure	pure	PROPN
ejpam-6997	537	3	appl	appl	PROPN
ejpam-6997	537	4	.	.	PROPN
ejpam-6997	537	5	math	math	PROPN
ejpam-6997	537	6	,	,	PUNCT
ejpam-6997	537	7	18	18	NUM
ejpam-6997	537	8	(	(	PUNCT
ejpam-6997	537	9	4	4	NUM
ejpam-6997	537	10	)	)	PUNCT
ejpam-6997	537	11	(	(	PUNCT
ejpam-6997	537	12	2025	2025	NUM
ejpam-6997	537	13	)	)	PUNCT
ejpam-6997	537	14	,	,	PUNCT
ejpam-6997	537	15	6997	6997	NUM
ejpam-6997	537	16	20	20	NUM
ejpam-6997	537	17	of	of	ADP
ejpam-6997	537	18	31	31	NUM
ejpam-6997	537	19	(	(	PUNCT
ejpam-6997	537	20	1	1	NUM
ejpam-6997	537	21	)	)	PUNCT
ejpam-6997	537	22	gmcϱ	gmcϱ	NOUN
ejpam-6997	537	23	(	(	PUNCT
ejpam-6997	537	24	∆	∆	PROPN
ejpam-6997	537	25	)	)	PUNCT
ejpam-6997	537	26	⊑	⊑	PRON
ejpam-6997	537	27	gm∦ϱ	gm∦ϱ	PROPN
ejpam-6997	537	28	(	(	PUNCT
ejpam-6997	537	29	∆	∆	PROPN
ejpam-6997	537	30	)	)	PUNCT
ejpam-6997	537	31	.	.	PUNCT
ejpam-6997	538	1	(	(	PUNCT
ejpam-6997	538	2	2	2	X
ejpam-6997	538	3	)	)	PUNCT
ejpam-6997	538	4	gm∦ϱ	gm∦ϱ	NOUN
ejpam-6997	538	5	(	(	PUNCT
ejpam-6997	538	6	∆	∆	PROPN
ejpam-6997	538	7	)	)	PUNCT
ejpam-6997	539	1	⊑	⊑	PROPN
ejpam-6997	539	2	gmcϱ	gmcϱ	VERB
ejpam-6997	539	3	(	(	PUNCT
ejpam-6997	539	4	∆	∆	PROPN
ejpam-6997	539	5	)	)	PUNCT
ejpam-6997	539	6	.	.	PUNCT
ejpam-6997	540	1	(	(	PUNCT
ejpam-6997	540	2	3	3	X
ejpam-6997	540	3	)	)	PUNCT
ejpam-6997	540	4	gacϱ	gacϱ	NOUN
ejpam-6997	540	5	(	(	PUNCT
ejpam-6997	540	6	∆	∆	PROPN
ejpam-6997	540	7	)	)	PUNCT
ejpam-6997	540	8	≤	≤	NUM
ejpam-6997	540	9	ga∦ϱ	ga∦ϱ	NOUN
ejpam-6997	540	10	(	(	PUNCT
ejpam-6997	540	11	∆	∆	PROPN
ejpam-6997	540	12	)	)	PUNCT
ejpam-6997	540	13	.	.	PUNCT
ejpam-6997	541	1	proof	proof	NOUN
ejpam-6997	541	2	.	.	PUNCT
ejpam-6997	542	1	(	(	PUNCT
ejpam-6997	542	2	1	1	X
ejpam-6997	542	3	)	)	PUNCT
ejpam-6997	542	4	let	let	VERB
ejpam-6997	542	5	δ	δ	PROPN
ejpam-6997	542	6	∈	∈	PROPN
ejpam-6997	542	7	gmcϱ	gmcϱ	NOUN
ejpam-6997	542	8	(	(	PUNCT
ejpam-6997	542	9	∆	∆	PROPN
ejpam-6997	542	10	)	)	PUNCT
ejpam-6997	542	11	,	,	PUNCT
ejpam-6997	542	12	then	then	ADV
ejpam-6997	542	13	cϱ(δ	cϱ(δ	PUNCT
ejpam-6997	542	14	)	)	PUNCT
ejpam-6997	543	1	⊓	⊓	PROPN
ejpam-6997	543	2	∆c	∆c	NOUN
ejpam-6997	543	3	/∈	/∈	PUNCT
ejpam-6997	543	4	g	g	PROPN
ejpam-6997	543	5	(	(	PUNCT
ejpam-6997	543	6	by	by	ADP
ejpam-6997	543	7	definition	definition	NOUN
ejpam-6997	543	8	4.1	4.1	NUM
ejpam-6997	543	9	)	)	PUNCT
ejpam-6997	543	10	,	,	PUNCT
ejpam-6997	543	11	∦ϱ(δ	∦ϱ(δ	NOUN
ejpam-6997	543	12	)	)	PUNCT
ejpam-6997	543	13	⊓	⊓	PROPN
ejpam-6997	543	14	∆c	∆c	PROPN
ejpam-6997	543	15	/∈	/∈	PUNCT
ejpam-6997	544	1	g.	g.	NOUN
ejpam-6997	544	2	this	this	PRON
ejpam-6997	544	3	is	be	AUX
ejpam-6997	544	4	show	show	NOUN
ejpam-6997	544	5	that	that	SCONJ
ejpam-6997	544	6	δ	δ	PROPN
ejpam-6997	544	7	∈	∈	PROPN
ejpam-6997	544	8	gm∦ϱ	gm∦ϱ	PROPN
ejpam-6997	544	9	(	(	PUNCT
ejpam-6997	544	10	∆	∆	PROPN
ejpam-6997	544	11	)	)	PUNCT
ejpam-6997	544	12	.	.	PUNCT
ejpam-6997	545	1	(	(	PUNCT
ejpam-6997	545	2	2	2	X
ejpam-6997	545	3	)	)	PUNCT
ejpam-6997	545	4	let	let	VERB
ejpam-6997	545	5	δ	δ	PROPN
ejpam-6997	545	6	∈	∈	PROPN
ejpam-6997	545	7	gm∦ϱ	gm∦ϱ	PROPN
ejpam-6997	545	8	(	(	PUNCT
ejpam-6997	545	9	∆	∆	PROPN
ejpam-6997	545	10	)	)	PUNCT
ejpam-6997	545	11	,	,	PUNCT
ejpam-6997	545	12	i.e.	i.e.	X
ejpam-6997	545	13	,	,	PUNCT
ejpam-6997	545	14	∦ϱ	∦ϱ	PUNCT
ejpam-6997	546	1	⊓	⊓	PROPN
ejpam-6997	546	2	∆	∆	PROPN
ejpam-6997	546	3	∈	∈	PROPN
ejpam-6997	546	4	g	g	NOUN
ejpam-6997	546	5	,	,	PUNCT
ejpam-6997	546	6	hence	hence	ADV
ejpam-6997	546	7	,	,	PUNCT
ejpam-6997	546	8	cϱ	cϱ	AUX
ejpam-6997	546	9	⊓	⊓	PROPN
ejpam-6997	546	10	∆	∆	X
ejpam-6997	546	11	∈	∈	PROPN
ejpam-6997	546	12	g	g	PROPN
ejpam-6997	546	13	,	,	PUNCT
ejpam-6997	546	14	δ	δ	PROPN
ejpam-6997	546	15	∈	∈	PROPN
ejpam-6997	546	16	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	546	17	(	(	PUNCT
ejpam-6997	546	18	∆	∆	PROPN
ejpam-6997	546	19	)	)	PUNCT
ejpam-6997	546	20	.	.	PUNCT
ejpam-6997	547	1	so	so	ADV
ejpam-6997	547	2	,	,	PUNCT
ejpam-6997	547	3	δ	δ	PROPN
ejpam-6997	547	4	∈	∈	PROPN
ejpam-6997	547	5	gmcϱ	gmcϱ	NOUN
ejpam-6997	547	6	(	(	PUNCT
ejpam-6997	547	7	∆),(by	∆),(by	NOUN
ejpam-6997	547	8	definition	definition	NOUN
ejpam-6997	547	9	3.14	3.14	NUM
ejpam-6997	547	10	)	)	PUNCT
ejpam-6997	547	11	.	.	PUNCT
ejpam-6997	548	1	(	(	PUNCT
ejpam-6997	548	2	3	3	X
ejpam-6997	548	3	)	)	PUNCT
ejpam-6997	548	4	the	the	DET
ejpam-6997	548	5	evidence	evidence	NOUN
ejpam-6997	548	6	is	be	AUX
ejpam-6997	548	7	obvious	obvious	ADJ
ejpam-6997	548	8	.	.	PUNCT
ejpam-6997	549	1	remark	remark	NOUN
ejpam-6997	549	2	4	4	NUM
ejpam-6997	549	3	.	.	PUNCT
ejpam-6997	550	1	let	let	VERB
ejpam-6997	550	2	g1	g1	PROPN
ejpam-6997	550	3	,	,	PUNCT
ejpam-6997	550	4	and	and	CCONJ
ejpam-6997	550	5	g2	g2	PROPN
ejpam-6997	550	6	be	be	AUX
ejpam-6997	550	7	grills	grill	NOUN
ejpam-6997	550	8	on	on	ADP
ejpam-6997	550	9	a	a	DET
ejpam-6997	550	10	ϱ-ns	ϱ-ns	ADV
ejpam-6997	550	11	(	(	PUNCT
ejpam-6997	550	12	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	550	13	,	,	PUNCT
ejpam-6997	550	14	ξϱ	ξϱ	NOUN
ejpam-6997	550	15	)	)	PUNCT
ejpam-6997	550	16	,	,	PUNCT
ejpam-6997	550	17	∆	∆	PROPN
ejpam-6997	550	18	⊑	⊑	X
ejpam-6997	551	1	ℵ.	ℵ.	PROPN
ejpam-6997	551	2	if	if	SCONJ
ejpam-6997	551	3	g1	g1	PROPN
ejpam-6997	551	4	⊑	⊑	DET
ejpam-6997	551	5	g2	g2	PROPN
ejpam-6997	551	6	then	then	ADV
ejpam-6997	551	7	{	{	PUNCT
ejpam-6997	551	8	g1}acϱ	g1}acϱ	PROPN
ejpam-6997	551	9	(	(	PUNCT
ejpam-6997	551	10	∆	∆	PROPN
ejpam-6997	551	11	)	)	PUNCT
ejpam-6997	551	12	≥	≥	NOUN
ejpam-6997	551	13	{	{	PUNCT
ejpam-6997	551	14	g2}acϱ	g2}acϱ	NOUN
ejpam-6997	551	15	,	,	PUNCT
ejpam-6997	551	16	for	for	ADP
ejpam-6997	551	17	each	each	DET
ejpam-6997	551	18	ϱ.	ϱ.	NOUN
ejpam-6997	551	19	4	4	NUM
ejpam-6997	551	20	.	.	PUNCT
ejpam-6997	551	21	various	various	ADJ
ejpam-6997	551	22	topologies	topology	NOUN
ejpam-6997	551	23	created	create	VERB
ejpam-6997	551	24	using	use	VERB
ejpam-6997	551	25	grills	grill	NOUN
ejpam-6997	551	26	and	and	CCONJ
ejpam-6997	551	27	cardinality	cardinality	NOUN
ejpam-6997	551	28	nbds	nbds	NOUN
ejpam-6997	551	29	in	in	ADP
ejpam-6997	551	30	this	this	DET
ejpam-6997	551	31	section	section	NOUN
ejpam-6997	551	32	,	,	PUNCT
ejpam-6997	551	33	for	for	ADP
ejpam-6997	551	34	any	any	DET
ejpam-6997	551	35	given	give	VERB
ejpam-6997	551	36	relation	relation	NOUN
ejpam-6997	551	37	,	,	PUNCT
ejpam-6997	551	38	we	we	PRON
ejpam-6997	551	39	use	use	VERB
ejpam-6997	551	40	grills	grill	NOUN
ejpam-6997	551	41	and	and	CCONJ
ejpam-6997	551	42	cardinal	cardinal	ADJ
ejpam-6997	551	43	nbds	nbds	NOUN
ejpam-6997	551	44	to	to	PART
ejpam-6997	551	45	build	build	VERB
ejpam-6997	551	46	a	a	DET
ejpam-6997	551	47	variety	variety	NOUN
ejpam-6997	551	48	of	of	ADP
ejpam-6997	551	49	topologies	topology	NOUN
ejpam-6997	551	50	that	that	PRON
ejpam-6997	551	51	are	be	AUX
ejpam-6997	551	52	finer	fine	ADJ
ejpam-6997	551	53	than	than	ADP
ejpam-6997	551	54	those	those	PRON
ejpam-6997	551	55	previously	previously	ADV
ejpam-6997	551	56	produced	produce	VERB
ejpam-6997	551	57	by	by	ADP
ejpam-6997	551	58	cardinal	cardinal	ADJ
ejpam-6997	551	59	nbds	nbds	NOUN
ejpam-6997	551	60	as	as	SCONJ
ejpam-6997	551	61	detailed	detailed	ADJ
ejpam-6997	551	62	in	in	ADP
ejpam-6997	551	63	[	[	X
ejpam-6997	551	64	46	46	NUM
ejpam-6997	551	65	]	]	PUNCT
ejpam-6997	551	66	.	.	PUNCT
ejpam-6997	552	1	theorem	theorem	ADJ
ejpam-6997	552	2	6	6	NUM
ejpam-6997	552	3	.	.	PUNCT
ejpam-6997	553	1	for	for	ADP
ejpam-6997	553	2	a	a	DET
ejpam-6997	553	3	ϱ-ns	ϱ-ns	ADV
ejpam-6997	553	4	(	(	PUNCT
ejpam-6997	553	5	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	553	6	,	,	PUNCT
ejpam-6997	553	7	ξϱ	ξϱ	NOUN
ejpam-6997	553	8	)	)	PUNCT
ejpam-6997	553	9	,	,	PUNCT
ejpam-6997	553	10	let	let	VERB
ejpam-6997	553	11	g	g	PRON
ejpam-6997	553	12	be	be	AUX
ejpam-6997	553	13	a	a	DET
ejpam-6997	553	14	grill	grill	NOUN
ejpam-6997	553	15	.	.	PUNCT
ejpam-6997	554	1	the	the	DET
ejpam-6997	554	2	family	family	NOUN
ejpam-6997	554	3	gψcϱ	gψcϱ	NOUN
ejpam-6997	554	4	=	=	PRON
ejpam-6997	554	5	{	{	PUNCT
ejpam-6997	554	6	∆	∆	PROPN
ejpam-6997	554	7	⊑	⊑	PRON
ejpam-6997	554	8	ℵ	ℵ	X
ejpam-6997	554	9	:	:	PUNCT
ejpam-6997	554	10	∀δ	∀δ	X
ejpam-6997	554	11	∈	∈	NOUN
ejpam-6997	554	12	∆	∆	X
ejpam-6997	554	13	,	,	PUNCT
ejpam-6997	554	14	cϱ(δ	cϱ(δ	NOUN
ejpam-6997	554	15	)	)	PUNCT
ejpam-6997	555	1	⊓	⊓	PROPN
ejpam-6997	555	2	∆c	∆c	NOUN
ejpam-6997	555	3	/∈	/∈	PUNCT
ejpam-6997	556	1	g	g	NOUN
ejpam-6997	556	2	}	}	PUNCT
ejpam-6997	556	3	a	a	DET
ejpam-6997	556	4	topology	topology	NOUN
ejpam-6997	556	5	on	on	ADP
ejpam-6997	556	6	ℵ.	ℵ.	PROPN
ejpam-6997	556	7	proof	proof	PROPN
ejpam-6997	556	8	.	.	PUNCT
ejpam-6997	557	1	first	first	ADV
ejpam-6997	557	2	,	,	PUNCT
ejpam-6997	557	3	for	for	ADP
ejpam-6997	557	4	any	any	DET
ejpam-6997	557	5	ϱ	ϱ	NOUN
ejpam-6997	557	6	,	,	PUNCT
ejpam-6997	557	7	it	it	PRON
ejpam-6997	557	8	is	be	AUX
ejpam-6997	557	9	obvious	obvious	ADJ
ejpam-6997	557	10	that	that	SCONJ
ejpam-6997	557	11	ℵ	ℵ	NOUN
ejpam-6997	557	12	,	,	PUNCT
ejpam-6997	557	13	ϕ	ϕ	PROPN
ejpam-6997	557	14	∈	∈	PROPN
ejpam-6997	557	15	gψcϱ	gψcϱ	NOUN
ejpam-6997	557	16	.	.	PUNCT
ejpam-6997	558	1	second	second	ADV
ejpam-6997	558	2	,	,	PUNCT
ejpam-6997	558	3	define	define	VERB
ejpam-6997	558	4	∆1,∆2	∆1,∆2	ADJ
ejpam-6997	558	5	as	as	ADP
ejpam-6997	558	6	elements	element	NOUN
ejpam-6997	558	7	of	of	ADP
ejpam-6997	558	8	gψcϱ	gψcϱ	NOUN
ejpam-6997	558	9	,	,	PUNCT
ejpam-6997	558	10	and	and	CCONJ
ejpam-6997	558	11	δ	δ	PROPN
ejpam-6997	558	12	∈	∈	PROPN
ejpam-6997	558	13	∆1	∆1	NUM
ejpam-6997	558	14	⊓	⊓	PROPN
ejpam-6997	558	15	∆2	∆2	PROPN
ejpam-6997	558	16	.	.	PUNCT
ejpam-6997	559	1	then	then	ADV
ejpam-6997	559	2	cϱ(δ	cϱ(δ	PUNCT
ejpam-6997	559	3	)	)	PUNCT
ejpam-6997	559	4	⊓	⊓	PROPN
ejpam-6997	559	5	∆c	∆c	NOUN
ejpam-6997	559	6	1	1	NUM
ejpam-6997	559	7	/∈	/∈	SYM
ejpam-6997	559	8	g	g	NOUN
ejpam-6997	559	9	,	,	PUNCT
ejpam-6997	559	10	and	and	CCONJ
ejpam-6997	559	11	cϱ(δ	cϱ(δ	NOUN
ejpam-6997	559	12	)	)	PUNCT
ejpam-6997	559	13	⊓	⊓	PROPN
ejpam-6997	559	14	∆c	∆c	NOUN
ejpam-6997	559	15	2	2	NUM
ejpam-6997	559	16	/∈	/∈	NOUN
ejpam-6997	559	17	g.	g.	NOUN
ejpam-6997	559	18	hence	hence	ADV
ejpam-6997	559	19	,	,	PUNCT
ejpam-6997	559	20	cϱ(δ	cϱ(δ	NOUN
ejpam-6997	559	21	)	)	PUNCT
ejpam-6997	559	22	⊓	⊓	PROPN
ejpam-6997	559	23	(	(	PUNCT
ejpam-6997	559	24	∆1	∆1	NUM
ejpam-6997	559	25	⊓	⊓	PROPN
ejpam-6997	559	26	∆2	∆2	NOUN
ejpam-6997	559	27	)	)	PUNCT
ejpam-6997	559	28	c	c	PROPN
ejpam-6997	559	29	/∈	/∈	PUNCT
ejpam-6997	560	1	g.	g.	NOUN
ejpam-6997	560	2	this	this	PRON
ejpam-6997	560	3	implies	imply	VERB
ejpam-6997	560	4	that	that	SCONJ
ejpam-6997	560	5	∆1	∆1	NUM
ejpam-6997	560	6	⊓	⊓	PROPN
ejpam-6997	560	7	∆2	∆2	PROPN
ejpam-6997	560	8	∈	∈	PROPN
ejpam-6997	560	9	gψcϱ	gψcϱ	NOUN
ejpam-6997	560	10	.	.	PUNCT
ejpam-6997	561	1	lastly	lastly	ADV
ejpam-6997	561	2	,	,	PUNCT
ejpam-6997	561	3	for	for	ADP
ejpam-6997	561	4	each	each	DET
ejpam-6997	561	5	i	i	PRON
ejpam-6997	561	6	∈	∈	PROPN
ejpam-6997	562	1	i	i	PRON
ejpam-6997	562	2	,	,	PUNCT
ejpam-6997	562	3	assume	assume	VERB
ejpam-6997	562	4	that	that	SCONJ
ejpam-6997	562	5	∆i	∆i	PROPN
ejpam-6997	562	6	belonged	belong	VERB
ejpam-6997	562	7	to	to	PART
ejpam-6997	562	8	gψcϱ	gψcϱ	VERB
ejpam-6997	562	9	.	.	PUNCT
ejpam-6997	563	1	let	let	VERB
ejpam-6997	563	2	δ	δ	PROPN
ejpam-6997	563	3	∈	∈	PROPN
ejpam-6997	563	4	⊔i∈i∆i	⊔i∈i∆i	PROPN
ejpam-6997	563	5	,	,	PUNCT
ejpam-6997	563	6	then	then	ADV
ejpam-6997	563	7	there	there	PRON
ejpam-6997	563	8	is	be	VERB
ejpam-6997	563	9	i0	i0	PROPN
ejpam-6997	563	10	∈	∈	PROPN
ejpam-6997	563	11	i	i	PRON
ejpam-6997	563	12	s.t	s.t	PROPN
ejpam-6997	563	13	.	.	PUNCT
ejpam-6997	563	14	δ	δ	PROPN
ejpam-6997	563	15	∈	∈	PROPN
ejpam-6997	563	16	∆i0	∆i0	PROPN
ejpam-6997	563	17	and	and	CCONJ
ejpam-6997	563	18	cϱ(δ)⊓∆c	cϱ(δ)⊓∆c	NOUN
ejpam-6997	563	19	i0	i0	PROPN
ejpam-6997	563	20	/∈	/∈	PUNCT
ejpam-6997	564	1	g.	g.	NOUN
ejpam-6997	564	2	since	since	SCONJ
ejpam-6997	564	3	∆i0	∆i0	PROPN
ejpam-6997	564	4	⊑	⊑	PRON
ejpam-6997	564	5	⊔i∈i∆i	⊔i∈i∆i	PROPN
ejpam-6997	564	6	.	.	PUNCT
ejpam-6997	565	1	then	then	ADV
ejpam-6997	565	2	,	,	PUNCT
ejpam-6997	565	3	cϱ(δ)⊓	cϱ(δ)⊓	PROPN
ejpam-6997	565	4	(	(	PUNCT
ejpam-6997	565	5	⊔i∈i∆i	⊔i∈i∆i	PROPN
ejpam-6997	565	6	)	)	PUNCT
ejpam-6997	565	7	c	c	NOUN
ejpam-6997	565	8	/∈	/∈	PUNCT
ejpam-6997	566	1	g	g	NOUN
ejpam-6997	566	2	,	,	PUNCT
ejpam-6997	566	3	and	and	CCONJ
ejpam-6997	566	4	⊔i∈i∆i	⊔i∈i∆i	PROPN
ejpam-6997	566	5	∈	∈	PROPN
ejpam-6997	566	6	gψcϱ	gψcϱ	NOUN
ejpam-6997	566	7	.	.	PUNCT
ejpam-6997	567	1	the	the	DET
ejpam-6997	567	2	gψcϱ	gψcϱ	NOUN
ejpam-6997	567	3	-open	-open	NOUN
ejpam-6997	567	4	sets	set	NOUN
ejpam-6997	567	5	are	be	AUX
ejpam-6997	567	6	the	the	DET
ejpam-6997	567	7	members	member	NOUN
ejpam-6997	567	8	of	of	ADP
ejpam-6997	567	9	gψcϱ	gψcϱ	NOUN
ejpam-6997	567	10	,	,	PUNCT
ejpam-6997	567	11	and	and	CCONJ
ejpam-6997	567	12	the	the	DET
ejpam-6997	567	13	gψcϱ	gψcϱ	NOUN
ejpam-6997	567	14	-closed	-close	VERB
ejpam-6997	567	15	sets	set	NOUN
ejpam-6997	567	16	are	be	AUX
ejpam-6997	567	17	its	its	PRON
ejpam-6997	567	18	complement	complement	NOUN
ejpam-6997	567	19	.	.	PUNCT
ejpam-6997	568	1	proposition	proposition	NOUN
ejpam-6997	568	2	15	15	NUM
ejpam-6997	568	3	.	.	PUNCT
ejpam-6997	569	1	for	for	ADP
ejpam-6997	569	2	any	any	DET
ejpam-6997	569	3	ϱ	ϱ	NOUN
ejpam-6997	569	4	,	,	PUNCT
ejpam-6997	569	5	suppose	suppose	VERB
ejpam-6997	569	6	that	that	SCONJ
ejpam-6997	569	7	g	g	PROPN
ejpam-6997	569	8	is	be	AUX
ejpam-6997	569	9	a	a	DET
ejpam-6997	569	10	grill	grill	NOUN
ejpam-6997	569	11	on	on	ADP
ejpam-6997	569	12	a	a	DET
ejpam-6997	569	13	ϱ-ns	ϱ-ns	ADV
ejpam-6997	569	14	(	(	PUNCT
ejpam-6997	569	15	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	569	16	,	,	PUNCT
ejpam-6997	569	17	ξϱ	ξϱ	NOUN
ejpam-6997	569	18	)	)	PUNCT
ejpam-6997	569	19	.	.	PUNCT
ejpam-6997	570	1	then	then	ADV
ejpam-6997	570	2	(	(	PUNCT
ejpam-6997	570	3	1	1	X
ejpam-6997	570	4	)	)	PUNCT
ejpam-6997	570	5	for	for	ADP
ejpam-6997	570	6	each	each	DET
ejpam-6997	570	7	ϱ	ϱ	NOUN
ejpam-6997	570	8	,	,	PUNCT
ejpam-6997	570	9	ψcϱ	ψcϱ	NOUN
ejpam-6997	570	10	⊑	⊑	PRON
ejpam-6997	570	11	gψcϱ	gψcϱ	NOUN
ejpam-6997	570	12	.	.	PUNCT
ejpam-6997	571	1	(	(	PUNCT
ejpam-6997	571	2	2	2	X
ejpam-6997	571	3	)	)	PUNCT
ejpam-6997	571	4	for	for	ADP
ejpam-6997	571	5	each	each	DET
ejpam-6997	571	6	ϱ	ϱ	NOUN
ejpam-6997	571	7	,	,	PUNCT
ejpam-6997	571	8	gψcϱ	gψcϱ	NOUN
ejpam-6997	571	9	⊑	⊑	NOUN
ejpam-6997	571	10	gψ∦ϱ	gψ∦ϱ	VERB
ejpam-6997	571	11	.	.	PUNCT
ejpam-6997	572	1	proof	proof	NOUN
ejpam-6997	572	2	.	.	PUNCT
ejpam-6997	573	1	(	(	PUNCT
ejpam-6997	573	2	1	1	NUM
ejpam-6997	573	3	)	)	PUNCT
ejpam-6997	573	4	cϱ(e	cϱ(e	PUNCT
ejpam-6997	573	5	)	)	PUNCT
ejpam-6997	573	6	⊓dc	⊓dc	PROPN
ejpam-6997	573	7	/∈	/∈	PUNCT
ejpam-6997	574	1	g	g	PROPN
ejpam-6997	574	2	∀e	∀e	PROPN
ejpam-6997	574	3	∈	∈	PROPN
ejpam-6997	574	4	d	d	NOUN
ejpam-6997	574	5	is	be	AUX
ejpam-6997	574	6	implied	imply	VERB
ejpam-6997	574	7	by	by	ADP
ejpam-6997	574	8	the	the	DET
ejpam-6997	574	9	fact	fact	NOUN
ejpam-6997	574	10	that	that	SCONJ
ejpam-6997	574	11	cϱ(e	cϱ(e	ADP
ejpam-6997	574	12	)	)	PUNCT
ejpam-6997	574	13	⊑	⊑	X
ejpam-6997	574	14	d	d	X
ejpam-6997	574	15	∀e	∀e	PROPN
ejpam-6997	574	16	∈	∈	PROPN
ejpam-6997	574	17	d.	d.	NOUN
ejpam-6997	574	18	(	(	PUNCT
ejpam-6997	574	19	2	2	NUM
ejpam-6997	574	20	)	)	PUNCT
ejpam-6997	574	21	according	accord	VERB
ejpam-6997	574	22	to	to	ADP
ejpam-6997	574	23	proposition	proposition	NOUN
ejpam-6997	574	24	2.24	2.24	NUM
ejpam-6997	574	25	,	,	PUNCT
ejpam-6997	574	26	for	for	ADP
ejpam-6997	574	27	any	any	DET
ejpam-6997	574	28	ϱ	ϱ	NOUN
ejpam-6997	574	29	,	,	PUNCT
ejpam-6997	574	30	we	we	PRON
ejpam-6997	574	31	have	have	AUX
ejpam-6997	574	32	∥ϱ(e	∥ϱ(e	NOUN
ejpam-6997	574	33	)	)	PUNCT
ejpam-6997	574	34	⊑	⊑	PRON
ejpam-6997	574	35	cϱ(e	cϱ(e	NOUN
ejpam-6997	574	36	)	)	PUNCT
ejpam-6997	574	37	.	.	PUNCT
ejpam-6997	575	1	therefore	therefore	ADV
ejpam-6997	575	2	,	,	PUNCT
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ejpam-6997	575	4	the	the	DET
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ejpam-6997	575	6	property	property	NOUN
ejpam-6997	575	7	,	,	PUNCT
ejpam-6997	575	8	we	we	PRON
ejpam-6997	575	9	determine	determine	VERB
ejpam-6997	575	10	that	that	PRON
ejpam-6997	575	11	cϱ(e	cϱ(e	PUNCT
ejpam-6997	575	12	)	)	PUNCT
ejpam-6997	575	13	⊓dc	⊓dc	PROPN
ejpam-6997	575	14	/∈	/∈	PUNCT
ejpam-6997	575	15	g.	g.	PROPN
ejpam-6997	575	16	a.	a.	PROPN
ejpam-6997	575	17	a.	a.	PROPN
ejpam-6997	575	18	azzam	azzam	PROPN
ejpam-6997	575	19	,	,	PUNCT
ejpam-6997	575	20	m.	m.	NOUN
ejpam-6997	575	21	aldawood	aldawood	PROPN
ejpam-6997	575	22	,	,	PUNCT
ejpam-6997	575	23	b.	b.	PROPN
ejpam-6997	575	24	alreshidi	alreshidi	PROPN
ejpam-6997	575	25	/	/	SYM
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ejpam-6997	575	27	.	.	PUNCT
ejpam-6997	576	1	j.	j.	PROPN
ejpam-6997	576	2	pure	pure	PROPN
ejpam-6997	576	3	appl	appl	PROPN
ejpam-6997	576	4	.	.	PROPN
ejpam-6997	576	5	math	math	PROPN
ejpam-6997	576	6	,	,	PUNCT
ejpam-6997	576	7	18	18	NUM
ejpam-6997	576	8	(	(	PUNCT
ejpam-6997	576	9	4	4	NUM
ejpam-6997	576	10	)	)	PUNCT
ejpam-6997	576	11	(	(	PUNCT
ejpam-6997	576	12	2025	2025	NUM
ejpam-6997	576	13	)	)	PUNCT
ejpam-6997	576	14	,	,	PUNCT
ejpam-6997	576	15	6997	6997	NUM
ejpam-6997	576	16	21	21	NUM
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ejpam-6997	576	18	31	31	NUM
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ejpam-6997	576	20	6	6	NUM
ejpam-6997	576	21	.	.	PUNCT
ejpam-6997	577	1	from	from	ADP
ejpam-6997	577	2	example	example	NOUN
ejpam-6997	577	3	3.11	3.11	NUM
ejpam-6997	577	4	,	,	PUNCT
ejpam-6997	577	5	we	we	PRON
ejpam-6997	577	6	have	have	VERB
ejpam-6997	577	7	:	:	PUNCT
ejpam-6997	577	8	ψcr	ψcr	ADV
ejpam-6997	577	9	=	=	PUNCT
ejpam-6997	577	10	{	{	PUNCT
ejpam-6997	577	11	{	{	PUNCT
ejpam-6997	577	12	n	n	CCONJ
ejpam-6997	577	13	}	}	PUNCT
ejpam-6997	577	14	,	,	PUNCT
ejpam-6997	577	15	{	{	PUNCT
ejpam-6997	577	16	e	e	NOUN
ejpam-6997	577	17	}	}	PUNCT
ejpam-6997	577	18	,	,	PUNCT
ejpam-6997	577	19	{	{	PUNCT
ejpam-6997	577	20	n	n	X
ejpam-6997	577	21	,	,	PUNCT
ejpam-6997	577	22	e	e	NOUN
ejpam-6997	577	23	}	}	PUNCT
ejpam-6997	577	24	,	,	PUNCT
ejpam-6997	577	25	{	{	PUNCT
ejpam-6997	577	26	b	b	X
ejpam-6997	577	27	,	,	PUNCT
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ejpam-6997	577	29	}	}	PUNCT
ejpam-6997	577	30	,	,	PUNCT
ejpam-6997	577	31	{	{	PUNCT
ejpam-6997	577	32	b	b	NOUN
ejpam-6997	577	33	,	,	PUNCT
ejpam-6997	577	34	m	m	PROPN
ejpam-6997	577	35	,	,	PUNCT
ejpam-6997	577	36	n	n	CCONJ
ejpam-6997	577	37	}	}	PUNCT
ejpam-6997	577	38	,	,	PUNCT
ejpam-6997	577	39	{	{	PUNCT
ejpam-6997	577	40	b	b	NOUN
ejpam-6997	577	41	,	,	PUNCT
ejpam-6997	577	42	m	m	PROPN
ejpam-6997	577	43	,	,	PUNCT
ejpam-6997	577	44	e},ℵ	e},ℵ	PROPN
ejpam-6997	577	45	,	,	PUNCT
ejpam-6997	577	46	ϕ	ϕ	NOUN
ejpam-6997	577	47	}	}	PUNCT
ejpam-6997	577	48	.	.	PUNCT
ejpam-6997	578	1	gψcr	gψcr	NOUN
ejpam-6997	578	2	=	=	PRON
ejpam-6997	578	3	{	{	PUNCT
ejpam-6997	578	4	{	{	PUNCT
ejpam-6997	578	5	n	n	CCONJ
ejpam-6997	578	6	}	}	PUNCT
ejpam-6997	578	7	,	,	PUNCT
ejpam-6997	578	8	{	{	PUNCT
ejpam-6997	578	9	b	b	X
ejpam-6997	578	10	}	}	PUNCT
ejpam-6997	578	11	,	,	PUNCT
ejpam-6997	578	12	{	{	PUNCT
ejpam-6997	578	13	e	e	NOUN
ejpam-6997	578	14	}	}	PUNCT
ejpam-6997	578	15	,	,	PUNCT
ejpam-6997	578	16	{	{	PUNCT
ejpam-6997	578	17	b	b	NOUN
ejpam-6997	578	18	,	,	PUNCT
ejpam-6997	578	19	n	n	CCONJ
ejpam-6997	578	20	}	}	PUNCT
ejpam-6997	578	21	,	,	PUNCT
ejpam-6997	578	22	{	{	PUNCT
ejpam-6997	578	23	b	b	X
ejpam-6997	578	24	,	,	PUNCT
ejpam-6997	578	25	m	m	NOUN
ejpam-6997	578	26	}	}	PUNCT
ejpam-6997	578	27	,	,	PUNCT
ejpam-6997	578	28	{	{	PUNCT
ejpam-6997	578	29	b	b	NOUN
ejpam-6997	578	30	,	,	PUNCT
ejpam-6997	578	31	e	e	NOUN
ejpam-6997	578	32	}	}	PUNCT
ejpam-6997	578	33	,	,	PUNCT
ejpam-6997	578	34	{	{	PUNCT
ejpam-6997	578	35	n	n	X
ejpam-6997	578	36	,	,	PUNCT
ejpam-6997	578	37	e	e	NOUN
ejpam-6997	578	38	}	}	PUNCT
ejpam-6997	578	39	,	,	PUNCT
ejpam-6997	578	40	{	{	PUNCT
ejpam-6997	578	41	b	b	NOUN
ejpam-6997	578	42	,	,	PUNCT
ejpam-6997	578	43	m	m	PROPN
ejpam-6997	578	44	,	,	PUNCT
ejpam-6997	578	45	n	n	CCONJ
ejpam-6997	578	46	}	}	PUNCT
ejpam-6997	578	47	,	,	PUNCT
ejpam-6997	578	48	{	{	PUNCT
ejpam-6997	578	49	b	b	NOUN
ejpam-6997	578	50	,	,	PUNCT
ejpam-6997	578	51	n	n	CCONJ
ejpam-6997	578	52	,	,	PUNCT
ejpam-6997	578	53	e	e	NOUN
ejpam-6997	578	54	}	}	PUNCT
ejpam-6997	578	55	,	,	PUNCT
ejpam-6997	578	56	{	{	PUNCT
ejpam-6997	578	57	b	b	NOUN
ejpam-6997	578	58	,	,	PUNCT
ejpam-6997	578	59	m	m	PROPN
ejpam-6997	578	60	,	,	PUNCT
ejpam-6997	578	61	e},ℵ	e},ℵ	PROPN
ejpam-6997	578	62	,	,	PUNCT
ejpam-6997	578	63	ϕ	ϕ	NOUN
ejpam-6997	578	64	}	}	PUNCT
ejpam-6997	578	65	.	.	PUNCT
ejpam-6997	579	1	ψcl	ψcl	NOUN
ejpam-6997	579	2	=	=	PUNCT
ejpam-6997	579	3	{	{	PUNCT
ejpam-6997	579	4	{	{	PUNCT
ejpam-6997	579	5	n	n	CCONJ
ejpam-6997	579	6	}	}	PUNCT
ejpam-6997	579	7	,	,	PUNCT
ejpam-6997	579	8	{	{	PUNCT
ejpam-6997	579	9	b	b	X
ejpam-6997	579	10	}	}	PUNCT
ejpam-6997	579	11	,	,	PUNCT
ejpam-6997	579	12	{	{	PUNCT
ejpam-6997	579	13	m	m	NOUN
ejpam-6997	579	14	,	,	PUNCT
ejpam-6997	579	15	e	e	NOUN
ejpam-6997	579	16	}	}	PUNCT
ejpam-6997	579	17	,	,	PUNCT
ejpam-6997	579	18	{	{	PUNCT
ejpam-6997	579	19	b	b	NOUN
ejpam-6997	579	20	,	,	PUNCT
ejpam-6997	579	21	n	n	CCONJ
ejpam-6997	579	22	}	}	PUNCT
ejpam-6997	579	23	,	,	PUNCT
ejpam-6997	579	24	{	{	PUNCT
ejpam-6997	579	25	b	b	NOUN
ejpam-6997	579	26	,	,	PUNCT
ejpam-6997	579	27	m	m	PROPN
ejpam-6997	579	28	,	,	PUNCT
ejpam-6997	579	29	e	e	NOUN
ejpam-6997	579	30	}	}	PUNCT
ejpam-6997	579	31	,	,	PUNCT
ejpam-6997	579	32	{	{	PUNCT
ejpam-6997	579	33	n	n	CCONJ
ejpam-6997	579	34	,	,	PUNCT
ejpam-6997	579	35	m	m	PROPN
ejpam-6997	579	36	,	,	PUNCT
ejpam-6997	579	37	e},ℵ	e},ℵ	PROPN
ejpam-6997	579	38	,	,	PUNCT
ejpam-6997	579	39	ϕ	ϕ	NOUN
ejpam-6997	579	40	}	}	PUNCT
ejpam-6997	579	41	.	.	PUNCT
ejpam-6997	580	1	gψcl	gψcl	NOUN
ejpam-6997	580	2	=	=	NOUN
ejpam-6997	580	3	2ℵ.	2ℵ.	NUM
ejpam-6997	580	4	ψci	ψci	NOUN
ejpam-6997	580	5	=	=	SYM
ejpam-6997	580	6	2ℵ.	2ℵ.	NUM
ejpam-6997	580	7	gψci	gψci	NOUN
ejpam-6997	580	8	=	=	SYM
ejpam-6997	580	9	2ℵ.	2ℵ.	NUM
ejpam-6997	580	10	ψcu	ψcu	NOUN
ejpam-6997	580	11	=	=	SYM
ejpam-6997	580	12	{	{	PUNCT
ejpam-6997	580	13	{	{	PUNCT
ejpam-6997	580	14	n	n	CCONJ
ejpam-6997	580	15	}	}	PUNCT
ejpam-6997	580	16	,	,	PUNCT
ejpam-6997	580	17	{	{	PUNCT
ejpam-6997	580	18	b	b	NOUN
ejpam-6997	580	19	,	,	PUNCT
ejpam-6997	580	20	m	m	PROPN
ejpam-6997	580	21	,	,	PUNCT
ejpam-6997	580	22	e},ℵ	e},ℵ	PROPN
ejpam-6997	580	23	,	,	PUNCT
ejpam-6997	580	24	ϕ	ϕ	NOUN
ejpam-6997	580	25	}	}	PUNCT
ejpam-6997	580	26	.	.	PUNCT
ejpam-6997	581	1	gψcu	gψcu	NOUN
ejpam-6997	581	2	=	=	PUNCT
ejpam-6997	581	3	{	{	PUNCT
ejpam-6997	581	4	{	{	PUNCT
ejpam-6997	581	5	n	n	CCONJ
ejpam-6997	581	6	}	}	PUNCT
ejpam-6997	581	7	,	,	PUNCT
ejpam-6997	581	8	{	{	PUNCT
ejpam-6997	581	9	b	b	X
ejpam-6997	581	10	}	}	PUNCT
ejpam-6997	581	11	,	,	PUNCT
ejpam-6997	581	12	{	{	PUNCT
ejpam-6997	581	13	e	e	NOUN
ejpam-6997	581	14	}	}	PUNCT
ejpam-6997	581	15	,	,	PUNCT
ejpam-6997	581	16	{	{	PUNCT
ejpam-6997	581	17	b	b	NOUN
ejpam-6997	581	18	,	,	PUNCT
ejpam-6997	581	19	n	n	CCONJ
ejpam-6997	581	20	}	}	PUNCT
ejpam-6997	581	21	,	,	PUNCT
ejpam-6997	581	22	{	{	PUNCT
ejpam-6997	581	23	b	b	X
ejpam-6997	581	24	,	,	PUNCT
ejpam-6997	581	25	m	m	NOUN
ejpam-6997	581	26	}	}	PUNCT
ejpam-6997	581	27	,	,	PUNCT
ejpam-6997	581	28	{	{	PUNCT
ejpam-6997	581	29	b	b	NOUN
ejpam-6997	581	30	,	,	PUNCT
ejpam-6997	581	31	e	e	NOUN
ejpam-6997	581	32	}	}	PUNCT
ejpam-6997	581	33	,	,	PUNCT
ejpam-6997	581	34	{	{	PUNCT
ejpam-6997	581	35	n	n	X
ejpam-6997	581	36	,	,	PUNCT
ejpam-6997	581	37	e	e	NOUN
ejpam-6997	581	38	}	}	PUNCT
ejpam-6997	581	39	,	,	PUNCT
ejpam-6997	581	40	{	{	PUNCT
ejpam-6997	581	41	b	b	NOUN
ejpam-6997	581	42	,	,	PUNCT
ejpam-6997	581	43	m	m	PROPN
ejpam-6997	581	44	,	,	PUNCT
ejpam-6997	581	45	n	n	CCONJ
ejpam-6997	581	46	}	}	PUNCT
ejpam-6997	581	47	,	,	PUNCT
ejpam-6997	581	48	{	{	PUNCT
ejpam-6997	581	49	b	b	NOUN
ejpam-6997	581	50	,	,	PUNCT
ejpam-6997	581	51	n	n	CCONJ
ejpam-6997	581	52	,	,	PUNCT
ejpam-6997	581	53	e	e	NOUN
ejpam-6997	581	54	}	}	PUNCT
ejpam-6997	581	55	,	,	PUNCT
ejpam-6997	581	56	{	{	PUNCT
ejpam-6997	581	57	b	b	NOUN
ejpam-6997	581	58	,	,	PUNCT
ejpam-6997	581	59	m	m	PROPN
ejpam-6997	581	60	,	,	PUNCT
ejpam-6997	581	61	e},ℵ	e},ℵ	PROPN
ejpam-6997	581	62	,	,	PUNCT
ejpam-6997	581	63	ϕ	ϕ	NOUN
ejpam-6997	581	64	}	}	PUNCT
ejpam-6997	581	65	.	.	PUNCT
ejpam-6997	582	1	ψc⟨r⟩	ψc⟨r⟩	NOUN
ejpam-6997	582	2	=	=	PRON
ejpam-6997	582	3	{	{	PUNCT
ejpam-6997	582	4	{	{	PUNCT
ejpam-6997	582	5	b	b	NOUN
ejpam-6997	582	6	}	}	PUNCT
ejpam-6997	582	7	,	,	PUNCT
ejpam-6997	582	8	{	{	PUNCT
ejpam-6997	582	9	m	m	VERB
ejpam-6997	582	10	}	}	PUNCT
ejpam-6997	582	11	,	,	PUNCT
ejpam-6997	582	12	{	{	PUNCT
ejpam-6997	582	13	n	n	X
ejpam-6997	582	14	,	,	PUNCT
ejpam-6997	582	15	e	e	NOUN
ejpam-6997	582	16	}	}	PUNCT
ejpam-6997	582	17	,	,	PUNCT
ejpam-6997	582	18	{	{	PUNCT
ejpam-6997	582	19	b	b	X
ejpam-6997	582	20	,	,	PUNCT
ejpam-6997	582	21	m	m	NOUN
ejpam-6997	582	22	}	}	PUNCT
ejpam-6997	582	23	,	,	PUNCT
ejpam-6997	582	24	{	{	PUNCT
ejpam-6997	582	25	b	b	NOUN
ejpam-6997	582	26	,	,	PUNCT
ejpam-6997	582	27	n	n	CCONJ
ejpam-6997	582	28	,	,	PUNCT
ejpam-6997	582	29	e	e	NOUN
ejpam-6997	582	30	}	}	PUNCT
ejpam-6997	582	31	,	,	PUNCT
ejpam-6997	582	32	{	{	PUNCT
ejpam-6997	582	33	n	n	CCONJ
ejpam-6997	582	34	,	,	PUNCT
ejpam-6997	582	35	m	m	PROPN
ejpam-6997	582	36	,	,	PUNCT
ejpam-6997	582	37	e},ℵ	e},ℵ	PROPN
ejpam-6997	582	38	,	,	PUNCT
ejpam-6997	582	39	ϕ	ϕ	NOUN
ejpam-6997	582	40	}	}	PUNCT
ejpam-6997	582	41	.	.	PUNCT
ejpam-6997	583	1	gψc⟨r⟩	gψc⟨r⟩	X
ejpam-6997	583	2	=	=	NOUN
ejpam-6997	583	3	2ℵ.	2ℵ.	NUM
ejpam-6997	583	4	ψc⟨l⟩	ψc⟨l⟩	NOUN
ejpam-6997	583	5	=	=	X
ejpam-6997	583	6	{	{	PUNCT
ejpam-6997	583	7	{	{	PUNCT
ejpam-6997	583	8	b	b	NOUN
ejpam-6997	583	9	}	}	PUNCT
ejpam-6997	583	10	,	,	PUNCT
ejpam-6997	583	11	{	{	PUNCT
ejpam-6997	583	12	e	e	NOUN
ejpam-6997	583	13	}	}	PUNCT
ejpam-6997	583	14	,	,	PUNCT
ejpam-6997	583	15	{	{	PUNCT
ejpam-6997	583	16	n	n	X
ejpam-6997	583	17	,	,	PUNCT
ejpam-6997	583	18	m	m	NOUN
ejpam-6997	583	19	}	}	PUNCT
ejpam-6997	583	20	,	,	PUNCT
ejpam-6997	583	21	{	{	PUNCT
ejpam-6997	583	22	b	b	NOUN
ejpam-6997	583	23	,	,	PUNCT
ejpam-6997	583	24	e	e	NOUN
ejpam-6997	583	25	}	}	PUNCT
ejpam-6997	583	26	,	,	PUNCT
ejpam-6997	583	27	{	{	PUNCT
ejpam-6997	583	28	n	n	CCONJ
ejpam-6997	583	29	,	,	PUNCT
ejpam-6997	583	30	m	m	PROPN
ejpam-6997	583	31	,	,	PUNCT
ejpam-6997	583	32	e	e	NOUN
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ejpam-6997	583	34	,	,	PUNCT
ejpam-6997	583	35	{	{	PUNCT
ejpam-6997	583	36	n	n	CCONJ
ejpam-6997	583	37	,	,	PUNCT
ejpam-6997	583	38	m	m	PROPN
ejpam-6997	583	39	,	,	PUNCT
ejpam-6997	583	40	b},ℵ	b},ℵ	PROPN
ejpam-6997	583	41	,	,	PUNCT
ejpam-6997	583	42	ϕ	ϕ	NOUN
ejpam-6997	583	43	}	}	PUNCT
ejpam-6997	583	44	.	.	PUNCT
ejpam-6997	583	45	gψc⟨l⟩	gψc⟨l⟩	X
ejpam-6997	584	1	=	=	NOUN
ejpam-6997	584	2	2ℵ.	2ℵ.	NUM
ejpam-6997	584	3	ψc⟨i⟩	ψc⟨i⟩	PROPN
ejpam-6997	584	4	=	=	SYM
ejpam-6997	584	5	2ℵ.	2ℵ.	NUM
ejpam-6997	584	6	gψc⟨i⟩	gψc⟨i⟩	NOUN
ejpam-6997	585	1	=	=	NOUN
ejpam-6997	585	2	2ℵ.	2ℵ.	NUM
ejpam-6997	585	3	ψc⟨u⟩	ψc⟨u⟩	NOUN
ejpam-6997	585	4	=	=	SYM
ejpam-6997	585	5	{	{	PUNCT
ejpam-6997	585	6	{	{	PUNCT
ejpam-6997	585	7	b	b	NOUN
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ejpam-6997	585	9	,	,	PUNCT
ejpam-6997	585	10	{	{	PUNCT
ejpam-6997	585	11	n	n	CCONJ
ejpam-6997	585	12	,	,	PUNCT
ejpam-6997	585	13	m	m	PROPN
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ejpam-6997	585	17	,	,	PUNCT
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ejpam-6997	585	20	.	.	PUNCT
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ejpam-6997	586	2	=	=	SYM
ejpam-6997	586	3	2ℵ.	2ℵ.	NUM
ejpam-6997	586	4	lemma	lemma	PROPN
ejpam-6997	586	5	2	2	NUM
ejpam-6997	586	6	.	.	PUNCT
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ejpam-6997	587	2	g	g	NOUN
ejpam-6997	587	3	,	,	PUNCT
ejpam-6997	587	4	j	j	PROPN
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ejpam-6997	587	6	grills	grill	VERB
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ejpam-6997	587	8	a	a	DET
ejpam-6997	587	9	ϱ-ns	ϱ-ns	ADV
ejpam-6997	587	10	(	(	PUNCT
ejpam-6997	587	11	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	587	12	,	,	PUNCT
ejpam-6997	587	13	ξϱ	ξϱ	NOUN
ejpam-6997	587	14	)	)	PUNCT
ejpam-6997	587	15	such	such	ADJ
ejpam-6997	587	16	that	that	SCONJ
ejpam-6997	587	17	g	g	PROPN
ejpam-6997	587	18	⊑	⊑	PROPN
ejpam-6997	587	19	j	j	PROPN
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ejpam-6997	587	22	ϱ.	ϱ.	NOUN
ejpam-6997	587	23	jψcϱ	jψcϱ	NOUN
ejpam-6997	587	24	⊑	⊑	DET
ejpam-6997	587	25	gψcϱ	gψcϱ	NOUN
ejpam-6997	587	26	follows	follow	VERB
ejpam-6997	587	27	.	.	PUNCT
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ejpam-6997	588	2	.	.	PUNCT
ejpam-6997	589	1	straight	straight	ADV
ejpam-6997	589	2	to	to	PART
ejpam-6997	589	3	prove	prove	VERB
ejpam-6997	589	4	.	.	PUNCT
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ejpam-6997	590	2	following	follow	VERB
ejpam-6997	590	3	example	example	NOUN
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ejpam-6997	590	5	that	that	SCONJ
ejpam-6997	590	6	lemma	lemma	PROPN
ejpam-6997	590	7	4.4	4.4	NUM
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ejpam-6997	591	2	7	7	NUM
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ejpam-6997	592	2	with	with	ADP
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ejpam-6997	592	4	3.11	3.11	NUM
ejpam-6997	592	5	.	.	PUNCT
ejpam-6997	593	1	let	let	VERB
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ejpam-6997	593	4	{	{	PUNCT
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ejpam-6997	593	6	b	b	NOUN
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ejpam-6997	593	8	,	,	PUNCT
ejpam-6997	593	9	{	{	PUNCT
ejpam-6997	593	10	b	b	NOUN
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ejpam-6997	593	14	,	,	PUNCT
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ejpam-6997	593	16	b	b	NOUN
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ejpam-6997	593	20	,	,	PUNCT
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ejpam-6997	593	22	b	b	X
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ejpam-6997	593	26	,	,	PUNCT
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ejpam-6997	593	28	b	b	NOUN
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ejpam-6997	593	34	,	,	PUNCT
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ejpam-6997	593	36	b	b	NOUN
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ejpam-6997	593	40	m	m	VERB
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ejpam-6997	593	42	,	,	PUNCT
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ejpam-6997	593	44	b	b	NOUN
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ejpam-6997	593	47	,	,	PUNCT
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ejpam-6997	593	50	,	,	PUNCT
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ejpam-6997	593	52	j	j	PROPN
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ejpam-6997	593	54	2ℵ\ϕ	2ℵ\ϕ	NUM
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ejpam-6997	593	57	ϱ	ϱ	X
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ejpam-6997	593	60	a.	a.	PROPN
ejpam-6997	593	61	a.	a.	PROPN
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ejpam-6997	593	63	,	,	PUNCT
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ejpam-6997	593	71	.	.	PUNCT
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ejpam-6997	594	6	,	,	PUNCT
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ejpam-6997	594	8	(	(	PUNCT
ejpam-6997	594	9	4	4	NUM
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ejpam-6997	594	12	2025	2025	NUM
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ejpam-6997	594	18	31	31	NUM
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ejpam-6997	594	20	,	,	PUNCT
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ejpam-6997	594	22	=	=	PRON
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ejpam-6997	594	33	e	e	NOUN
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ejpam-6997	594	41	,	,	PUNCT
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ejpam-6997	594	43	b	b	X
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ejpam-6997	594	47	,	,	PUNCT
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ejpam-6997	594	49	b	b	NOUN
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ejpam-6997	594	53	,	,	PUNCT
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ejpam-6997	594	55	n	n	X
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ejpam-6997	594	59	,	,	PUNCT
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ejpam-6997	594	75	,	,	PUNCT
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ejpam-6997	594	77	b	b	NOUN
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ejpam-6997	594	88	n	n	CCONJ
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ejpam-6997	594	94	,	,	PUNCT
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ejpam-6997	594	96	b	b	X
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ejpam-6997	594	100	,	,	PUNCT
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ejpam-6997	594	102	n	n	X
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ejpam-6997	594	106	,	,	PUNCT
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ejpam-6997	594	124	=	=	PUNCT
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ejpam-6997	594	126	.	.	PUNCT
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ejpam-6997	595	2	7	7	NUM
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ejpam-6997	595	6	the	the	DET
ejpam-6997	595	7	following	follow	VERB
ejpam-6997	595	8	relations	relation	NOUN
ejpam-6997	595	9	:	:	PUNCT
ejpam-6997	595	10	(	(	PUNCT
ejpam-6997	595	11	1	1	X
ejpam-6997	595	12	)	)	PUNCT
ejpam-6997	595	13	gψcu	gψcu	NOUN
ejpam-6997	595	14	⊑	⊑	PRON
ejpam-6997	595	15	gψcr	gψcr	PROPN
ejpam-6997	595	16	⊓	⊓	PROPN
ejpam-6997	595	17	gψcl	gψcl	VERB
ejpam-6997	595	18	⊑	⊑	DET
ejpam-6997	595	19	gψcr	gψcr	PROPN
ejpam-6997	595	20	⊔	⊔	PROPN
ejpam-6997	595	21	gψcl	gψcl	VERB
ejpam-6997	595	22	⊑	⊑	DET
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ejpam-6997	595	24	.	.	PUNCT
ejpam-6997	596	1	(	(	PUNCT
ejpam-6997	596	2	2	2	X
ejpam-6997	596	3	)	)	PUNCT
ejpam-6997	596	4	gψc⟨u⟩	gψc⟨u⟩	NOUN
ejpam-6997	596	5	⊑	⊑	X
ejpam-6997	597	1	gψc⟨r⟩	gψc⟨r⟩	PROPN
ejpam-6997	597	2	⊓	⊓	PROPN
ejpam-6997	597	3	gψc⟨l⟩	gψc⟨l⟩	PROPN
ejpam-6997	597	4	⊑	⊑	X
ejpam-6997	597	5	gψc⟨r⟩	gψc⟨r⟩	PROPN
ejpam-6997	597	6	⊔	⊔	PROPN
ejpam-6997	597	7	gψc⟨l⟩	gψc⟨l⟩	PROPN
ejpam-6997	597	8	⊑	⊑	PRON
ejpam-6997	597	9	gψc⟨i⟩	gψc⟨i⟩	PROPN
ejpam-6997	597	10	.	.	PUNCT
ejpam-6997	598	1	proof	proof	NOUN
ejpam-6997	598	2	.	.	PUNCT
ejpam-6997	599	1	proposition	proposition	NOUN
ejpam-6997	599	2	2.14	2.14	NUM
ejpam-6997	599	3	’s	’s	PART
ejpam-6997	599	4	first	first	ADJ
ejpam-6997	599	5	item	item	NOUN
ejpam-6997	599	6	justifies	justify	VERB
ejpam-6997	599	7	these	these	DET
ejpam-6997	599	8	relationships	relationship	NOUN
ejpam-6997	599	9	.	.	PUNCT
ejpam-6997	600	1	example	example	NOUN
ejpam-6997	600	2	4.3	4.3	NUM
ejpam-6997	600	3	displays	display	NOUN
ejpam-6997	600	4	that	that	PRON
ejpam-6997	600	5	gψcr	gψcr	NOUN
ejpam-6997	600	6	̸=	̸=	PROPN
ejpam-6997	600	7	gψcl	gψcl	VERB
ejpam-6997	600	8	,	,	PUNCT
ejpam-6997	600	9	gψcr	gψcr	NOUN
ejpam-6997	600	10	̸=	̸=	PROPN
ejpam-6997	600	11	gψci	gψci	NOUN
ejpam-6997	600	12	,	,	PUNCT
ejpam-6997	600	13	gψcu	gψcu	PROPN
ejpam-6997	600	14	̸=	̸=	PROPN
ejpam-6997	600	15	gψcl	gψcl	VERB
ejpam-6997	600	16	,	,	PUNCT
ejpam-6997	600	17	gψcu	gψcu	PROPN
ejpam-6997	600	18	̸=	̸=	PROPN
ejpam-6997	600	19	gψci	gψci	NOUN
ejpam-6997	600	20	,	,	PUNCT
ejpam-6997	600	21	gψcr	gψcr	NOUN
ejpam-6997	600	22	=	=	NOUN
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ejpam-6997	600	24	,	,	PUNCT
ejpam-6997	600	25	gψci	gψci	NOUN
ejpam-6997	600	26	=	=	PUNCT
ejpam-6997	600	27	gψcl	gψcl	NOUN
ejpam-6997	600	28	,	,	PUNCT
ejpam-6997	600	29	and	and	CCONJ
ejpam-6997	600	30	gψc⟨u⟩	gψc⟨u⟩	NOUN
ejpam-6997	600	31	=	=	SYM
ejpam-6997	600	32	gψc⟨r⟩	gψc⟨r⟩	NOUN
ejpam-6997	600	33	=	=	SYM
ejpam-6997	600	34	gψc⟨l⟩	gψc⟨l⟩	PROPN
ejpam-6997	601	1	=	=	NOUN
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ejpam-6997	602	8	using	use	VERB
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ejpam-6997	602	10	based	base	VERB
ejpam-6997	602	11	on	on	ADP
ejpam-6997	602	12	grills	grill	NOUN
ejpam-6997	602	13	and	and	CCONJ
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ejpam-6997	602	15	nbds	nbds	NOUN
ejpam-6997	602	16	.	.	PUNCT
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ejpam-6997	603	10	be	be	AUX
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ejpam-6997	604	3	.	.	PUNCT
ejpam-6997	605	1	let	let	VERB
ejpam-6997	605	2	gψcϱ	gψcϱ	NOUN
ejpam-6997	605	3	represent	represent	VERB
ejpam-6997	605	4	a	a	DET
ejpam-6997	605	5	topology	topology	NOUN
ejpam-6997	605	6	induced	induce	VERB
ejpam-6997	605	7	by	by	ADP
ejpam-6997	605	8	grills	grill	NOUN
ejpam-6997	605	9	and	and	CCONJ
ejpam-6997	605	10	cardinality	cardinality	PROPN
ejpam-6997	605	11	nbds	nbds	NOUN
ejpam-6997	605	12	.	.	PUNCT
ejpam-6997	606	1	then	then	ADV
ejpam-6997	606	2	,	,	PUNCT
ejpam-6997	606	3	for	for	ADP
ejpam-6997	606	4	each	each	DET
ejpam-6997	606	5	ϱ	ϱ	PROPN
ejpam-6997	606	6	,	,	PUNCT
ejpam-6997	606	7	lw	lw	NOUN
ejpam-6997	606	8	and	and	CCONJ
ejpam-6997	606	9	up	up	ADP
ejpam-6997	606	10	-	-	PUNCT
ejpam-6997	606	11	ap	ap	NOUN
ejpam-6997	606	12	of	of	ADP
ejpam-6997	606	13	a	a	DET
ejpam-6997	606	14	st	st	PROPN
ejpam-6997	606	15	∆	∆	PROPN
ejpam-6997	606	16	⊑	⊑	DET
ejpam-6997	606	17	ℵ	ℵ	NOUN
ejpam-6997	606	18	are	be	AUX
ejpam-6997	606	19	respectively	respectively	ADV
ejpam-6997	606	20	given	give	VERB
ejpam-6997	606	21	by	by	ADP
ejpam-6997	606	22	:	:	PUNCT
ejpam-6997	606	23	gξϱ(∆	gξϱ(∆	NUM
ejpam-6997	606	24	)	)	PUNCT
ejpam-6997	606	25	=	=	SYM
ejpam-6997	606	26	gintcϱ	gintcϱ	NOUN
ejpam-6997	606	27	(	(	PUNCT
ejpam-6997	606	28	∆	∆	PROPN
ejpam-6997	606	29	)	)	PUNCT
ejpam-6997	606	30	,	,	PUNCT
ejpam-6997	606	31	gξϱ(∆	gξϱ(∆	X
ejpam-6997	606	32	)	)	PUNCT
ejpam-6997	606	33	=	=	SYM
ejpam-6997	606	34	gclcϱ	gclcϱ	X
ejpam-6997	606	35	(	(	PUNCT
ejpam-6997	606	36	∆	∆	PROPN
ejpam-6997	606	37	)	)	PUNCT
ejpam-6997	606	38	,	,	PUNCT
ejpam-6997	606	39	where	where	SCONJ
ejpam-6997	606	40	gintcϱ	gintcϱ	PROPN
ejpam-6997	606	41	(	(	PUNCT
ejpam-6997	606	42	∆	∆	PROPN
ejpam-6997	606	43	)	)	PUNCT
ejpam-6997	606	44	,	,	PUNCT
ejpam-6997	606	45	gclcϱ	gclcϱ	NOUN
ejpam-6997	606	46	(	(	PUNCT
ejpam-6997	606	47	∆	∆	PROPN
ejpam-6997	606	48	)	)	PUNCT
ejpam-6997	606	49	respectively	respectively	ADV
ejpam-6997	606	50	represent	represent	VERB
ejpam-6997	606	51	the	the	DET
ejpam-6997	606	52	interior	interior	NOUN
ejpam-6997	606	53	and	and	CCONJ
ejpam-6997	606	54	closure	closure	NOUN
ejpam-6997	606	55	of	of	ADP
ejpam-6997	606	56	a	a	DET
ejpam-6997	606	57	set	set	NOUN
ejpam-6997	606	58	∆	∆	PROPN
ejpam-6997	606	59	with	with	ADP
ejpam-6997	606	60	respect	respect	NOUN
ejpam-6997	606	61	the	the	DET
ejpam-6997	606	62	topology	topology	NOUN
ejpam-6997	606	63	gψcϱ	gψcϱ	NOUN
ejpam-6997	606	64	.	.	PUNCT
ejpam-6997	607	1	furthermore	furthermore	ADV
ejpam-6997	607	2	,	,	PUNCT
ejpam-6997	607	3	∆	∆	PROPN
ejpam-6997	607	4	’s	’s	PART
ejpam-6997	607	5	accuracy	accuracy	NOUN
ejpam-6997	607	6	criterion	criterion	NOUN
ejpam-6997	607	7	is	be	AUX
ejpam-6997	607	8	set	set	VERB
ejpam-6997	607	9	as	as	SCONJ
ejpam-6997	607	10	follows	follow	VERB
ejpam-6997	607	11	:	:	PUNCT
ejpam-6997	607	12	gλξϱ	gλξϱ	NOUN
ejpam-6997	607	13	(	(	PUNCT
ejpam-6997	607	14	∆	∆	X
ejpam-6997	607	15	)	)	PUNCT
ejpam-6997	608	1	=	=	SYM
ejpam-6997	608	2	|gξϱ	|gξϱ	NOUN
ejpam-6997	608	3	(	(	PUNCT
ejpam-6997	608	4	∆)|	∆)|	NOUN
ejpam-6997	608	5	|gξϱ	|gξϱ	NOUN
ejpam-6997	608	6	(	(	PUNCT
ejpam-6997	608	7	∆)|	∆)|	NOUN
ejpam-6997	608	8	,	,	PUNCT
ejpam-6997	608	9	|gξϱ(∆)|	|gξϱ(∆)|	VERB
ejpam-6997	608	10	̸=	̸=	PROPN
ejpam-6997	608	11	0	0	NUM
ejpam-6997	608	12	.	.	NOUN
ejpam-6997	608	13	0	0	NUM
ejpam-6997	609	1	≤	≤	NOUN
ejpam-6997	609	2	gλξϱ	gλξϱ	NOUN
ejpam-6997	609	3	≤	≤	ADJ
ejpam-6997	609	4	1	1	NUM
ejpam-6997	609	5	is	be	AUX
ejpam-6997	609	6	clearly	clearly	ADV
ejpam-6997	609	7	.	.	PUNCT
ejpam-6997	610	1	∆	∆	PROPN
ejpam-6997	610	2	is	be	AUX
ejpam-6997	610	3	called	call	VERB
ejpam-6997	610	4	a	a	DET
ejpam-6997	610	5	gcϱ-exact	gcϱ-exact	NOUN
ejpam-6997	610	6	set	set	NOUN
ejpam-6997	610	7	if	if	SCONJ
ejpam-6997	610	8	gλξϱ	gλξϱ	NOUN
ejpam-6997	610	9	(	(	PUNCT
ejpam-6997	610	10	∆	∆	X
ejpam-6997	610	11	)	)	PUNCT
ejpam-6997	611	1	=	=	SYM
ejpam-6997	611	2	1	1	X
ejpam-6997	611	3	.	.	PUNCT
ejpam-6997	612	1	on	on	ADP
ejpam-6997	612	2	the	the	DET
ejpam-6997	612	3	other	other	ADJ
ejpam-6997	612	4	hand	hand	NOUN
ejpam-6997	612	5	,	,	PUNCT
ejpam-6997	612	6	∆	∆	PROPN
ejpam-6997	612	7	is	be	AUX
ejpam-6997	612	8	referred	refer	VERB
ejpam-6997	612	9	to	to	ADP
ejpam-6997	612	10	as	as	ADP
ejpam-6997	612	11	a	a	DET
ejpam-6997	612	12	gcϱ-rs	gcϱ-rs	PROPN
ejpam-6997	612	13	.	.	PUNCT
ejpam-6997	613	1	concerning	concern	VERB
ejpam-6997	613	2	to	to	ADP
ejpam-6997	613	3	definition	definition	NOUN
ejpam-6997	613	4	4.7	4.7	NUM
ejpam-6997	613	5	,	,	PUNCT
ejpam-6997	613	6	the	the	DET
ejpam-6997	613	7	following	follow	VERB
ejpam-6997	613	8	results	result	NOUN
ejpam-6997	613	9	can	can	AUX
ejpam-6997	613	10	be	be	AUX
ejpam-6997	613	11	proven	prove	VERB
ejpam-6997	613	12	using	use	VERB
ejpam-6997	613	13	the	the	DET
ejpam-6997	613	14	topological	topological	ADJ
ejpam-6997	613	15	characteristics	characteristic	NOUN
ejpam-6997	613	16	of	of	ADP
ejpam-6997	613	17	interior	interior	ADJ
ejpam-6997	613	18	and	and	CCONJ
ejpam-6997	613	19	closure	closure	NOUN
ejpam-6997	613	20	operators	operator	NOUN
ejpam-6997	613	21	.	.	PUNCT
ejpam-6997	614	1	it	it	PRON
ejpam-6997	614	2	is	be	AUX
ejpam-6997	614	3	noteworthy	noteworthy	ADJ
ejpam-6997	614	4	that	that	SCONJ
ejpam-6997	614	5	certain	certain	ADJ
ejpam-6997	614	6	properties	property	NOUN
ejpam-6997	614	7	absent	absent	ADJ
ejpam-6997	614	8	in	in	ADP
ejpam-6997	614	9	the	the	DET
ejpam-6997	614	10	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	615	1	-,gm̃cϱ	-,gm̃cϱ	PUNCT
ejpam-6997	615	2	-ap	-ap	VERB
ejpam-6997	615	3	are	be	AUX
ejpam-6997	615	4	still	still	ADV
ejpam-6997	615	5	valid	valid	ADJ
ejpam-6997	615	6	for	for	ADP
ejpam-6997	615	7	the	the	DET
ejpam-6997	615	8	gξϱ-	gξϱ-	NOUN
ejpam-6997	615	9	,	,	PUNCT
ejpam-6997	615	10	gξϱ-ap	gξϱ-ap	PROPN
ejpam-6997	615	11	that	that	SCONJ
ejpam-6997	615	12	as	as	ADP
ejpam-6997	615	13	item	item	NOUN
ejpam-6997	615	14	(	(	PUNCT
ejpam-6997	615	15	1	1	NUM
ejpam-6997	615	16	)	)	PUNCT
ejpam-6997	615	17	of	of	ADP
ejpam-6997	615	18	theorem	theorem	ADJ
ejpam-6997	615	19	3.3	3.3	NUM
ejpam-6997	615	20	.	.	PUNCT
ejpam-6997	616	1	theorem	theorem	VERB
ejpam-6997	616	2	8	8	NUM
ejpam-6997	616	3	.	.	PUNCT
ejpam-6997	617	1	for	for	ADP
ejpam-6997	617	2	each	each	DET
ejpam-6997	617	3	ϱ	ϱ	NOUN
ejpam-6997	617	4	,	,	PUNCT
ejpam-6997	617	5	let	let	VERB
ejpam-6997	617	6	gψcϱ	gψcϱ	NOUN
ejpam-6997	617	7	represent	represent	VERB
ejpam-6997	617	8	a	a	DET
ejpam-6997	617	9	topology	topology	NOUN
ejpam-6997	617	10	induced	induce	VERB
ejpam-6997	617	11	by	by	ADP
ejpam-6997	617	12	grills	grill	NOUN
ejpam-6997	617	13	and	and	CCONJ
ejpam-6997	617	14	cardinality	cardinality	PROPN
ejpam-6997	617	15	nbds	nbds	NOUN
ejpam-6997	617	16	,	,	PUNCT
ejpam-6997	617	17	and	and	CCONJ
ejpam-6997	617	18	let	let	VERB
ejpam-6997	617	19	d,∆	d,∆	PRON
ejpam-6997	617	20	⊑	⊑	PRON
ejpam-6997	617	21	ℵ.	ℵ.	PROPN
ejpam-6997	618	1	next	next	ADV
ejpam-6997	618	2	are	be	AUX
ejpam-6997	618	3	the	the	DET
ejpam-6997	618	4	following	follow	VERB
ejpam-6997	618	5	properties	property	NOUN
ejpam-6997	618	6	:	:	PUNCT
ejpam-6997	618	7	(	(	PUNCT
ejpam-6997	618	8	1	1	X
ejpam-6997	618	9	)	)	PUNCT
ejpam-6997	618	10	gξϱ(∆	gξϱ(∆	NUM
ejpam-6997	618	11	)	)	PUNCT
ejpam-6997	619	1	⊑	⊑	X
ejpam-6997	619	2	∆.	∆.	X
ejpam-6997	619	3	(	(	PUNCT
ejpam-6997	619	4	2	2	X
ejpam-6997	619	5	)	)	PUNCT
ejpam-6997	619	6	gξϱ(ϕ	gξϱ(ϕ	PROPN
ejpam-6997	619	7	)	)	PUNCT
ejpam-6997	620	1	=	=	SYM
ejpam-6997	620	2	ϕ.	ϕ.	NOUN
ejpam-6997	620	3	(	(	PUNCT
ejpam-6997	620	4	3	3	NUM
ejpam-6997	620	5	)	)	PUNCT
ejpam-6997	620	6	gξϱ(ℵ	gξϱ(ℵ	PROPN
ejpam-6997	620	7	)	)	PUNCT
ejpam-6997	620	8	=	=	SYM
ejpam-6997	620	9	ℵ.	ℵ.	NOUN
ejpam-6997	620	10	(	(	PUNCT
ejpam-6997	620	11	4	4	X
ejpam-6997	620	12	)	)	PUNCT
ejpam-6997	621	1	if	if	SCONJ
ejpam-6997	621	2	d	d	PROPN
ejpam-6997	621	3	⊑	⊑	PRON
ejpam-6997	621	4	∆	∆	PROPN
ejpam-6997	621	5	,	,	PUNCT
ejpam-6997	621	6	then	then	ADV
ejpam-6997	621	7	gξϱ(d	gξϱ(d	PROPN
ejpam-6997	621	8	)	)	PUNCT
ejpam-6997	621	9	⊑	⊑	PRON
ejpam-6997	621	10	gξϱ(∆	gξϱ(∆	PROPN
ejpam-6997	621	11	)	)	PUNCT
ejpam-6997	621	12	.	.	PUNCT
ejpam-6997	622	1	(	(	PUNCT
ejpam-6997	622	2	5	5	X
ejpam-6997	622	3	)	)	PUNCT
ejpam-6997	622	4	gξϱ(d	gξϱ(d	PROPN
ejpam-6997	622	5	⊓	⊓	PROPN
ejpam-6997	622	6	∆	∆	X
ejpam-6997	622	7	)	)	PUNCT
ejpam-6997	623	1	=	=	SYM
ejpam-6997	623	2	gξϱ(d	gξϱ(d	X
ejpam-6997	623	3	)	)	PUNCT
ejpam-6997	623	4	⊓	⊓	PROPN
ejpam-6997	623	5	gξϱ(∆	gξϱ(∆	NUM
ejpam-6997	623	6	)	)	PUNCT
ejpam-6997	623	7	.	.	PUNCT
ejpam-6997	624	1	(	(	PUNCT
ejpam-6997	624	2	6	6	NUM
ejpam-6997	624	3	)	)	PUNCT
ejpam-6997	624	4	gξϱ(∆c	gξϱ(∆c	NOUN
ejpam-6997	624	5	)	)	PUNCT
ejpam-6997	624	6	=	=	SYM
ejpam-6997	624	7	(	(	PUNCT
ejpam-6997	624	8	gξϱ(∆))c	gξϱ(∆))c	PROPN
ejpam-6997	624	9	.	.	PUNCT
ejpam-6997	625	1	(	(	PUNCT
ejpam-6997	625	2	7	7	X
ejpam-6997	625	3	)	)	PUNCT
ejpam-6997	625	4	gξϱ(gξϱ(∆	gξϱ(gξϱ(∆	NOUN
ejpam-6997	625	5	)	)	PUNCT
ejpam-6997	625	6	)	)	PUNCT
ejpam-6997	626	1	=	=	PUNCT
ejpam-6997	626	2	gξϱ(∆	gξϱ(∆	X
ejpam-6997	626	3	)	)	PUNCT
ejpam-6997	626	4	∀ϱ.	∀ϱ.	NUM
ejpam-6997	626	5	a.	a.	NOUN
ejpam-6997	626	6	a.	a.	PROPN
ejpam-6997	626	7	azzam	azzam	PROPN
ejpam-6997	626	8	,	,	PUNCT
ejpam-6997	626	9	m.	m.	NOUN
ejpam-6997	626	10	aldawood	aldawood	PROPN
ejpam-6997	626	11	,	,	PUNCT
ejpam-6997	626	12	b.	b.	PROPN
ejpam-6997	626	13	alreshidi	alreshidi	PROPN
ejpam-6997	626	14	/	/	SYM
ejpam-6997	626	15	eur	eur	PROPN
ejpam-6997	626	16	.	.	PUNCT
ejpam-6997	627	1	j.	j.	PROPN
ejpam-6997	627	2	pure	pure	PROPN
ejpam-6997	627	3	appl	appl	PROPN
ejpam-6997	627	4	.	.	PROPN
ejpam-6997	627	5	math	math	PROPN
ejpam-6997	627	6	,	,	PUNCT
ejpam-6997	627	7	18	18	NUM
ejpam-6997	627	8	(	(	PUNCT
ejpam-6997	627	9	4	4	NUM
ejpam-6997	627	10	)	)	PUNCT
ejpam-6997	627	11	(	(	PUNCT
ejpam-6997	627	12	2025	2025	NUM
ejpam-6997	627	13	)	)	PUNCT
ejpam-6997	627	14	,	,	PUNCT
ejpam-6997	627	15	6997	6997	NUM
ejpam-6997	627	16	23	23	NUM
ejpam-6997	627	17	of	of	ADP
ejpam-6997	627	18	31	31	NUM
ejpam-6997	627	19	proof	proof	NOUN
ejpam-6997	627	20	.	.	PUNCT
ejpam-6997	628	1	these	these	DET
ejpam-6997	628	2	connections	connection	NOUN
ejpam-6997	628	3	are	be	AUX
ejpam-6997	628	4	true	true	ADJ
ejpam-6997	628	5	because	because	SCONJ
ejpam-6997	628	6	they	they	PRON
ejpam-6997	628	7	correspond	correspond	VERB
ejpam-6997	628	8	to	to	ADP
ejpam-6997	628	9	interior	interior	ADJ
ejpam-6997	628	10	topology	topology	NOUN
ejpam-6997	628	11	and	and	CCONJ
ejpam-6997	628	12	lw	lw	PROPN
ejpam-6997	628	13	-	-	PUNCT
ejpam-6997	628	14	ap	ap	PROPN
ejpam-6997	628	15	operators	operator	NOUN
ejpam-6997	628	16	.	.	PUNCT
ejpam-6997	629	1	corollary	corollary	ADJ
ejpam-6997	629	2	8	8	NUM
ejpam-6997	629	3	.	.	PUNCT
ejpam-6997	630	1	for	for	ADP
ejpam-6997	630	2	each	each	DET
ejpam-6997	630	3	ϱ	ϱ	NOUN
ejpam-6997	630	4	,	,	PUNCT
ejpam-6997	630	5	let	let	VERB
ejpam-6997	630	6	gψcϱ	gψcϱ	NOUN
ejpam-6997	630	7	represent	represent	VERB
ejpam-6997	630	8	a	a	DET
ejpam-6997	630	9	topology	topology	NOUN
ejpam-6997	630	10	induced	induce	VERB
ejpam-6997	630	11	by	by	ADP
ejpam-6997	630	12	grills	grill	NOUN
ejpam-6997	630	13	and	and	CCONJ
ejpam-6997	630	14	cardinality	cardinality	PROPN
ejpam-6997	630	15	nbds	nbds	NOUN
ejpam-6997	630	16	.	.	PUNCT
ejpam-6997	631	1	then	then	ADV
ejpam-6997	631	2	,	,	PUNCT
ejpam-6997	631	3	gξϱ(d	gξϱ(d	PROPN
ejpam-6997	631	4	)	)	PUNCT
ejpam-6997	631	5	⊔	⊔	NOUN
ejpam-6997	631	6	gξϱ(∆	gξϱ(∆	PUNCT
ejpam-6997	631	7	)	)	PUNCT
ejpam-6997	632	1	⊑	⊑	PROPN
ejpam-6997	633	1	gξϱ(d	gξϱ(d	PROPN
ejpam-6997	633	2	⊔	⊔	NUM
ejpam-6997	633	3	∆	∆	PROPN
ejpam-6997	633	4	)	)	PUNCT
ejpam-6997	633	5	for	for	ADP
ejpam-6997	633	6	any	any	DET
ejpam-6997	633	7	d,∆	d,∆	NOUN
ejpam-6997	633	8	⊑	⊑	X
ejpam-6997	633	9	ℵ.	ℵ.	PROPN
ejpam-6997	633	10	theorem	theorem	VERB
ejpam-6997	633	11	9	9	NUM
ejpam-6997	633	12	.	.	PUNCT
ejpam-6997	634	1	for	for	ADP
ejpam-6997	634	2	each	each	DET
ejpam-6997	634	3	ϱ	ϱ	NOUN
ejpam-6997	634	4	,	,	PUNCT
ejpam-6997	634	5	let	let	VERB
ejpam-6997	634	6	gψcϱ	gψcϱ	NOUN
ejpam-6997	634	7	represent	represent	VERB
ejpam-6997	634	8	a	a	DET
ejpam-6997	634	9	topology	topology	NOUN
ejpam-6997	634	10	induced	induce	VERB
ejpam-6997	634	11	by	by	ADP
ejpam-6997	634	12	grills	grill	NOUN
ejpam-6997	634	13	and	and	CCONJ
ejpam-6997	634	14	cardinality	cardinality	PROPN
ejpam-6997	634	15	nbds	nbds	NOUN
ejpam-6997	634	16	,	,	PUNCT
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ejpam-6997	634	18	let	let	VERB
ejpam-6997	634	19	d,∆	d,∆	PRON
ejpam-6997	634	20	⊑	⊑	PRON
ejpam-6997	634	21	ℵ.	ℵ.	PROPN
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ejpam-6997	635	2	are	be	AUX
ejpam-6997	635	3	the	the	DET
ejpam-6997	635	4	following	follow	VERB
ejpam-6997	635	5	properties	property	NOUN
ejpam-6997	635	6	:	:	PUNCT
ejpam-6997	635	7	(	(	PUNCT
ejpam-6997	635	8	1	1	X
ejpam-6997	635	9	)	)	PUNCT
ejpam-6997	635	10	∆	∆	PROPN
ejpam-6997	635	11	⊑	⊑	PRON
ejpam-6997	635	12	gξϱ(∆	gξϱ(∆	PROPN
ejpam-6997	635	13	)	)	PUNCT
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ejpam-6997	636	3	)	)	PUNCT
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ejpam-6997	637	5	)	)	PUNCT
ejpam-6997	637	6	gξϱ(ℵ	gξϱ(ℵ	PROPN
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ejpam-6997	637	8	=	=	SYM
ejpam-6997	637	9	ℵ.	ℵ.	NOUN
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ejpam-6997	637	11	4	4	X
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ejpam-6997	638	4	ℵ	ℵ	NOUN
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ejpam-6997	638	7	gξϱ(d	gξϱ(d	PROPN
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ejpam-6997	639	2	5	5	X
ejpam-6997	639	3	)	)	PUNCT
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ejpam-6997	639	6	∆	∆	PROPN
ejpam-6997	639	7	)	)	PUNCT
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ejpam-6997	640	3	)	)	PUNCT
ejpam-6997	640	4	⊔	⊔	NOUN
ejpam-6997	640	5	gξϱ(∆	gξϱ(∆	PROPN
ejpam-6997	640	6	)	)	PUNCT
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ejpam-6997	641	2	6	6	NUM
ejpam-6997	641	3	)	)	PUNCT
ejpam-6997	641	4	gξϱ(∆c	gξϱ(∆c	NOUN
ejpam-6997	641	5	)	)	PUNCT
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ejpam-6997	641	8	gξϱ(∆))c	gξϱ(∆))c	PROPN
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ejpam-6997	642	2	7	7	X
ejpam-6997	642	3	)	)	PUNCT
ejpam-6997	642	4	gξϱ(gξϱ(∆	gξϱ(gξϱ(∆	NOUN
ejpam-6997	642	5	)	)	PUNCT
ejpam-6997	642	6	)	)	PUNCT
ejpam-6997	643	1	=	=	PUNCT
ejpam-6997	643	2	gξϱ(∆	gξϱ(∆	X
ejpam-6997	643	3	)	)	PUNCT
ejpam-6997	643	4	∀ϱ.	∀ϱ.	NUM
ejpam-6997	643	5	proof	proof	NOUN
ejpam-6997	643	6	.	.	PUNCT
ejpam-6997	644	1	these	these	DET
ejpam-6997	644	2	connections	connection	NOUN
ejpam-6997	644	3	are	be	AUX
ejpam-6997	644	4	true	true	ADJ
ejpam-6997	644	5	because	because	SCONJ
ejpam-6997	644	6	they	they	PRON
ejpam-6997	644	7	correspond	correspond	VERB
ejpam-6997	644	8	to	to	ADP
ejpam-6997	644	9	closure	closure	NOUN
ejpam-6997	644	10	topology	topology	NOUN
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ejpam-6997	644	12	up	up	ADP
ejpam-6997	644	13	-	-	PUNCT
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ejpam-6997	644	15	operators	operator	NOUN
ejpam-6997	644	16	.	.	PUNCT
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ejpam-6997	645	2	9	9	NUM
ejpam-6997	645	3	.	.	PUNCT
ejpam-6997	646	1	for	for	ADP
ejpam-6997	646	2	each	each	DET
ejpam-6997	646	3	ϱ	ϱ	NOUN
ejpam-6997	646	4	,	,	PUNCT
ejpam-6997	646	5	let	let	VERB
ejpam-6997	646	6	gψcϱ	gψcϱ	NOUN
ejpam-6997	646	7	represent	represent	VERB
ejpam-6997	646	8	a	a	DET
ejpam-6997	646	9	topology	topology	NOUN
ejpam-6997	646	10	induced	induce	VERB
ejpam-6997	646	11	by	by	ADP
ejpam-6997	646	12	grills	grill	NOUN
ejpam-6997	646	13	and	and	CCONJ
ejpam-6997	646	14	cardinality	cardinality	PROPN
ejpam-6997	646	15	nbds	nbds	NOUN
ejpam-6997	646	16	.	.	PUNCT
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ejpam-6997	647	2	,	,	PUNCT
ejpam-6997	647	3	gξϱ(d	gξϱ(d	PROPN
ejpam-6997	647	4	⊓	⊓	PROPN
ejpam-6997	647	5	∆	∆	X
ejpam-6997	647	6	)	)	PUNCT
ejpam-6997	648	1	⊑	⊑	PRON
ejpam-6997	648	2	gξϱ(d	gξϱ(d	X
ejpam-6997	648	3	)	)	PUNCT
ejpam-6997	648	4	⊓	⊓	PROPN
ejpam-6997	648	5	gξϱ(∆	gξϱ(∆	X
ejpam-6997	648	6	)	)	PUNCT
ejpam-6997	648	7	for	for	ADP
ejpam-6997	648	8	any	any	DET
ejpam-6997	648	9	d,∆	d,∆	NOUN
ejpam-6997	648	10	⊑	⊑	X
ejpam-6997	648	11	ℵ.	ℵ.	PROPN
ejpam-6997	648	12	proposition	proposition	NOUN
ejpam-6997	648	13	16	16	NUM
ejpam-6997	648	14	.	.	PUNCT
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ejpam-6997	649	2	ϕ	ϕ	PROPN
ejpam-6997	649	3	̸=	̸=	PROPN
ejpam-6997	649	4	∆	∆	PROPN
ejpam-6997	649	5	⊑	⊑	PRON
ejpam-6997	649	6	ℵ	ℵ	NOUN
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ejpam-6997	649	8	0	0	NUM
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ejpam-6997	649	10	gλξϱ	gλξϱ	NOUN
ejpam-6997	649	11	(	(	PUNCT
ejpam-6997	649	12	∆	∆	X
ejpam-6997	649	13	)	)	PUNCT
ejpam-6997	649	14	≤	≤	NUM
ejpam-6997	649	15	1	1	NUM
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ejpam-6997	649	19	(	(	PUNCT
ejpam-6997	649	20	ℵ	ℵ	NOUN
ejpam-6997	649	21	)	)	PUNCT
ejpam-6997	649	22	=	=	SYM
ejpam-6997	649	23	1	1	NUM
ejpam-6997	649	24	for	for	ADP
ejpam-6997	649	25	each	each	DET
ejpam-6997	649	26	ϱ.	ϱ.	ADJ
ejpam-6997	649	27	proposition	proposition	NOUN
ejpam-6997	649	28	17	17	NUM
ejpam-6997	649	29	.	.	PUNCT
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ejpam-6997	650	2	following	follow	VERB
ejpam-6997	650	3	inclusion	inclusion	NOUN
ejpam-6997	650	4	relations	relation	NOUN
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ejpam-6997	650	8	any	any	DET
ejpam-6997	650	9	subset	subset	NOUN
ejpam-6997	650	10	d	d	NOUN
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ejpam-6997	650	12	a	a	DET
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ejpam-6997	650	14	space	space	NOUN
ejpam-6997	650	15	(	(	PUNCT
ejpam-6997	650	16	ℵ,gψcϱ	ℵ,gψcϱ	NOUN
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ejpam-6997	650	18	(	(	PUNCT
ejpam-6997	650	19	1	1	X
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ejpam-6997	650	21	gξu(d	gξu(d	PROPN
ejpam-6997	650	22	)	)	PUNCT
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ejpam-6997	651	2	gξr(d	gξr(d	PROPN
ejpam-6997	651	3	)	)	PUNCT
ejpam-6997	651	4	⊓	⊓	PROPN
ejpam-6997	651	5	gξl(d	gξl(d	NUM
ejpam-6997	651	6	)	)	PUNCT
ejpam-6997	651	7	⊑	⊑	PRON
ejpam-6997	651	8	gξr(d	gξr(d	PROPN
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ejpam-6997	651	10	⊔	⊔	PROPN
ejpam-6997	651	11	gξl(d	gξl(d	PROPN
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ejpam-6997	651	13	⊑	⊑	PROPN
ejpam-6997	651	14	gξi(d	gξi(d	PROPN
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ejpam-6997	652	2	2	2	X
ejpam-6997	652	3	)	)	PUNCT
ejpam-6997	652	4	gξl(d	gξl(d	PROPN
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ejpam-6997	652	7	gξr(d	gξr(d	PROPN
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ejpam-6997	652	9	⊓	⊓	PROPN
ejpam-6997	652	10	gξi(d	gξi(d	PROPN
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ejpam-6997	652	13	gξr(d	gξr(d	PROPN
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ejpam-6997	652	18	⊑	⊑	PRON
ejpam-6997	652	19	gξu(d	gξu(d	PROPN
ejpam-6997	652	20	)	)	PUNCT
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ejpam-6997	653	8	)	)	PUNCT
ejpam-6997	653	9	=	=	SYM
ejpam-6997	653	10	gξ⟨l⟩(d	gξ⟨l⟩(d	NOUN
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ejpam-6997	653	12	=	=	SYM
ejpam-6997	653	13	gξ⟨i⟩(d	gξ⟨i⟩(d	NOUN
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ejpam-6997	653	15	.	.	PUNCT
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ejpam-6997	654	2	4	4	X
ejpam-6997	654	3	)	)	PUNCT
ejpam-6997	654	4	gξ⟨u⟩(d	gξ⟨u⟩(d	NOUN
ejpam-6997	654	5	)	)	PUNCT
ejpam-6997	654	6	=	=	SYM
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ejpam-6997	654	9	=	=	SYM
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ejpam-6997	654	12	=	=	SYM
ejpam-6997	654	13	gξ⟨i⟩(d	gξ⟨i⟩(d	NOUN
ejpam-6997	654	14	)	)	PUNCT
ejpam-6997	654	15	.	.	PUNCT
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ejpam-6997	655	2	10	10	NUM
ejpam-6997	655	3	.	.	PUNCT
ejpam-6997	656	1	the	the	DET
ejpam-6997	656	2	following	follow	VERB
ejpam-6997	656	3	inequalities	inequality	NOUN
ejpam-6997	656	4	are	be	AUX
ejpam-6997	656	5	valid	valid	ADJ
ejpam-6997	656	6	for	for	ADP
ejpam-6997	656	7	any	any	DET
ejpam-6997	656	8	nonempty	nonempty	NOUN
ejpam-6997	656	9	subset	subset	VERB
ejpam-6997	656	10	d	d	NOUN
ejpam-6997	656	11	of	of	ADP
ejpam-6997	656	12	a	a	DET
ejpam-6997	656	13	topological	topological	ADJ
ejpam-6997	656	14	space	space	NOUN
ejpam-6997	656	15	(	(	PUNCT
ejpam-6997	656	16	ℵ,gψcϱ	ℵ,gψcϱ	NOUN
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ejpam-6997	656	19	a.	a.	PROPN
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ejpam-6997	656	22	m.	m.	NOUN
ejpam-6997	656	23	aldawood	aldawood	PROPN
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ejpam-6997	656	27	/	/	SYM
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ejpam-6997	657	2	pure	pure	PROPN
ejpam-6997	657	3	appl	appl	PROPN
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ejpam-6997	657	11	(	(	PUNCT
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ejpam-6997	657	15	6997	6997	NUM
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ejpam-6997	657	18	31	31	NUM
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ejpam-6997	660	2	(	(	PUNCT
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ejpam-6997	660	10	=	=	SYM
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ejpam-6997	661	2	approaches	approach	NOUN
ejpam-6997	661	3	covered	cover	VERB
ejpam-6997	661	4	in	in	ADP
ejpam-6997	661	5	the	the	DET
ejpam-6997	661	6	preceding	precede	VERB
ejpam-6997	661	7	section	section	NOUN
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ejpam-6997	661	9	now	now	ADV
ejpam-6997	661	10	be	be	AUX
ejpam-6997	661	11	compared	compare	VERB
ejpam-6997	661	12	with	with	ADP
ejpam-6997	661	13	the	the	DET
ejpam-6997	661	14	ap	ap	PROPN
ejpam-6997	661	15	and	and	CCONJ
ejpam-6997	661	16	accuracy	accuracy	NOUN
ejpam-6997	661	17	standards	standard	NOUN
ejpam-6997	661	18	described	describe	VERB
ejpam-6997	661	19	in	in	ADP
ejpam-6997	661	20	this	this	DET
ejpam-6997	661	21	section	section	NOUN
ejpam-6997	661	22	,	,	PUNCT
ejpam-6997	661	23	which	which	PRON
ejpam-6997	661	24	are	be	AUX
ejpam-6997	661	25	based	base	VERB
ejpam-6997	661	26	on	on	ADP
ejpam-6997	661	27	topological	topological	ADJ
ejpam-6997	661	28	spaces	space	NOUN
ejpam-6997	661	29	.	.	PUNCT
ejpam-6997	662	1	proposition	proposition	NOUN
ejpam-6997	662	2	18	18	NUM
ejpam-6997	662	3	.	.	PUNCT
ejpam-6997	663	1	the	the	DET
ejpam-6997	663	2	relations	relation	NOUN
ejpam-6997	663	3	for	for	ADP
ejpam-6997	663	4	each	each	DET
ejpam-6997	663	5	ϱ	ϱ	NOUN
ejpam-6997	663	6	and	and	CCONJ
ejpam-6997	663	7	d	d	X
ejpam-6997	663	8	⊑	⊑	DET
ejpam-6997	663	9	ℵ	ℵ	NOUN
ejpam-6997	663	10	are	be	AUX
ejpam-6997	663	11	as	as	SCONJ
ejpam-6997	663	12	follows	follow	VERB
ejpam-6997	663	13	:	:	PUNCT
ejpam-6997	663	14	(	(	PUNCT
ejpam-6997	663	15	1	1	X
ejpam-6997	663	16	)	)	PUNCT
ejpam-6997	663	17	gξϱ(d	gξϱ(d	PROPN
ejpam-6997	663	18	)	)	PUNCT
ejpam-6997	663	19	⊑	⊑	PRON
ejpam-6997	663	20	gmcϱ	gmcϱ	VERB
ejpam-6997	663	21	(	(	PUNCT
ejpam-6997	663	22	d	d	NOUN
ejpam-6997	663	23	)	)	PUNCT
ejpam-6997	663	24	.	.	PUNCT
ejpam-6997	664	1	(	(	PUNCT
ejpam-6997	664	2	2	2	X
ejpam-6997	664	3	)	)	PUNCT
ejpam-6997	664	4	gmcϱ	gmcϱ	NOUN
ejpam-6997	664	5	(	(	PUNCT
ejpam-6997	664	6	d	d	NOUN
ejpam-6997	664	7	)	)	PUNCT
ejpam-6997	664	8	⊑	⊑	PRON
ejpam-6997	664	9	gξϱ(d	gξϱ(d	PROPN
ejpam-6997	664	10	)	)	PUNCT
ejpam-6997	664	11	.	.	PUNCT
ejpam-6997	665	1	proof	proof	NOUN
ejpam-6997	665	2	.	.	PUNCT
ejpam-6997	666	1	(	(	PUNCT
ejpam-6997	666	2	1	1	X
ejpam-6997	666	3	)	)	PUNCT
ejpam-6997	666	4	let	let	VERB
ejpam-6997	666	5	b	b	NOUN
ejpam-6997	666	6	∈	∈	PROPN
ejpam-6997	666	7	gξϱ(d	gξϱ(d	PROPN
ejpam-6997	666	8	)	)	PUNCT
ejpam-6997	666	9	.	.	PUNCT
ejpam-6997	667	1	then	then	ADV
ejpam-6997	667	2	we	we	PRON
ejpam-6997	667	3	find	find	VERB
ejpam-6997	667	4	a	a	DET
ejpam-6997	667	5	subset	subset	NOUN
ejpam-6997	667	6	v	v	ADP
ejpam-6997	667	7	∈	∈	PROPN
ejpam-6997	667	8	gψcϱ	gψcϱ	NOUN
ejpam-6997	667	9	with	with	ADP
ejpam-6997	667	10	b	b	PROPN
ejpam-6997	667	11	∈	∈	PROPN
ejpam-6997	667	12	v	v	ADP
ejpam-6997	667	13	⊑	⊑	X
ejpam-6997	667	14	d.	d.	PROPN
ejpam-6997	667	15	we	we	PRON
ejpam-6997	667	16	derive	derive	VERB
ejpam-6997	667	17	cϱ(b	cϱ(b	NOUN
ejpam-6997	667	18	)	)	PUNCT
ejpam-6997	668	1	⊓	⊓	NOUN
ejpam-6997	668	2	v	v	ADP
ejpam-6997	668	3	c	c	NOUN
ejpam-6997	668	4	/∈	/∈	PUNCT
ejpam-6997	669	1	g	g	NOUN
ejpam-6997	669	2	from	from	ADP
ejpam-6997	669	3	the	the	DET
ejpam-6997	669	4	topology	topology	NOUN
ejpam-6997	669	5	structuring	structuring	NOUN
ejpam-6997	669	6	method	method	NOUN
ejpam-6997	669	7	.	.	PUNCT
ejpam-6997	670	1	now	now	ADV
ejpam-6997	670	2	,	,	PUNCT
ejpam-6997	670	3	we	we	PRON
ejpam-6997	670	4	get	get	VERB
ejpam-6997	670	5	cϱ(b	cϱ(b	NOUN
ejpam-6997	670	6	)	)	PUNCT
ejpam-6997	670	7	⊓dc	⊓dc	PROPN
ejpam-6997	670	8	/∈	/∈	VERB
ejpam-6997	671	1	g	g	NOUN
ejpam-6997	671	2	since	since	SCONJ
ejpam-6997	671	3	v	v	ADP
ejpam-6997	671	4	⊑	⊑	PROPN
ejpam-6997	671	5	d.	d.	PROPN
ejpam-6997	671	6	hence	hence	ADV
ejpam-6997	671	7	,	,	PUNCT
ejpam-6997	671	8	b	b	PROPN
ejpam-6997	671	9	∈	∈	PROPN
ejpam-6997	671	10	gm̃cϱ	gm̃cϱ	NOUN
ejpam-6997	671	11	(	(	PUNCT
ejpam-6997	671	12	d	d	NOUN
ejpam-6997	671	13	)	)	PUNCT
ejpam-6997	671	14	.	.	PUNCT
ejpam-6997	672	1	since	since	SCONJ
ejpam-6997	672	2	b	b	PROPN
ejpam-6997	672	3	∈	∈	PROPN
ejpam-6997	672	4	d	d	NOUN
ejpam-6997	672	5	,	,	PUNCT
ejpam-6997	672	6	then	then	ADV
ejpam-6997	672	7	b	b	PROPN
ejpam-6997	672	8	∈	∈	PROPN
ejpam-6997	672	9	gmcϱ	gmcϱ	NOUN
ejpam-6997	672	10	(	(	PUNCT
ejpam-6997	672	11	d	d	NOUN
ejpam-6997	672	12	)	)	PUNCT
ejpam-6997	672	13	,	,	PUNCT
ejpam-6997	672	14	and	and	CCONJ
ejpam-6997	672	15	gξϱ(d	gξϱ(d	NUM
ejpam-6997	672	16	)	)	PUNCT
ejpam-6997	672	17	⊑	⊑	PROPN
ejpam-6997	672	18	gmcϱ	gmcϱ	VERB
ejpam-6997	672	19	(	(	PUNCT
ejpam-6997	672	20	d	d	NOUN
ejpam-6997	672	21	)	)	PUNCT
ejpam-6997	672	22	.	.	PUNCT
ejpam-6997	673	1	by	by	ADP
ejpam-6997	673	2	the	the	DET
ejpam-6997	673	3	same	same	ADJ
ejpam-6997	673	4	manner	manner	NOUN
ejpam-6997	673	5	,	,	PUNCT
ejpam-6997	673	6	one	one	PRON
ejpam-6997	673	7	can	can	AUX
ejpam-6997	673	8	prove	prove	VERB
ejpam-6997	673	9	(	(	PUNCT
ejpam-6997	673	10	2	2	NUM
ejpam-6997	673	11	)	)	PUNCT
ejpam-6997	673	12	.	.	PUNCT
ejpam-6997	674	1	the	the	DET
ejpam-6997	674	2	converse	converse	NOUN
ejpam-6997	674	3	of	of	ADP
ejpam-6997	674	4	proposition	proposition	NOUN
ejpam-6997	674	5	4.15	4.15	NUM
ejpam-6997	674	6	need	need	AUX
ejpam-6997	674	7	not	not	PART
ejpam-6997	674	8	be	be	AUX
ejpam-6997	674	9	true	true	ADJ
ejpam-6997	674	10	,	,	PUNCT
ejpam-6997	674	11	refer	refer	VERB
ejpam-6997	674	12	to	to	ADP
ejpam-6997	674	13	table	table	NOUN
ejpam-6997	674	14	2	2	NUM
ejpam-6997	674	15	and	and	CCONJ
ejpam-6997	674	16	example	example	NOUN
ejpam-6997	674	17	4.3	4.3	NUM
ejpam-6997	674	18	.	.	PUNCT
ejpam-6997	675	1	suppose	suppose	VERB
ejpam-6997	675	2	that	that	SCONJ
ejpam-6997	675	3	σ	σ	NOUN
ejpam-6997	675	4	=	=	PUNCT
ejpam-6997	675	5	r	r	NOUN
ejpam-6997	675	6	and	and	CCONJ
ejpam-6997	675	7	d	d	NOUN
ejpam-6997	675	8	=	=	SYM
ejpam-6997	675	9	{	{	PUNCT
ejpam-6997	675	10	b	b	NOUN
ejpam-6997	675	11	,	,	PUNCT
ejpam-6997	675	12	n	n	CCONJ
ejpam-6997	675	13	}	}	PUNCT
ejpam-6997	675	14	.	.	PUNCT
ejpam-6997	676	1	then	then	ADV
ejpam-6997	676	2	gmcϱ	gmcϱ	VERB
ejpam-6997	676	3	(	(	PUNCT
ejpam-6997	676	4	d	d	NOUN
ejpam-6997	676	5	)	)	PUNCT
ejpam-6997	676	6	=	=	SYM
ejpam-6997	676	7	ℵ	ℵ	NOUN
ejpam-6997	676	8	,	,	PUNCT
ejpam-6997	676	9	gξϱ(d	gξϱ(d	PROPN
ejpam-6997	676	10	)	)	PUNCT
ejpam-6997	676	11	=	=	PRON
ejpam-6997	676	12	{	{	PUNCT
ejpam-6997	676	13	b	b	NOUN
ejpam-6997	676	14	,	,	PUNCT
ejpam-6997	676	15	n	n	CCONJ
ejpam-6997	676	16	}	}	PUNCT
ejpam-6997	676	17	.	.	PUNCT
ejpam-6997	677	1	hence	hence	ADV
ejpam-6997	677	2	,	,	PUNCT
ejpam-6997	677	3	the	the	DET
ejpam-6997	677	4	opposite	opposite	NOUN
ejpam-6997	677	5	is	be	AUX
ejpam-6997	677	6	therefore	therefore	ADV
ejpam-6997	677	7	untrue	untrue	ADJ
ejpam-6997	677	8	.	.	PUNCT
ejpam-6997	678	1	corollary	corollary	ADJ
ejpam-6997	678	2	11	11	NUM
ejpam-6997	678	3	.	.	PUNCT
ejpam-6997	679	1	for	for	ADP
ejpam-6997	679	2	any	any	DET
ejpam-6997	679	3	ϱ	ϱ	NOUN
ejpam-6997	679	4	,	,	PUNCT
ejpam-6997	679	5	suppose	suppose	VERB
ejpam-6997	679	6	that	that	SCONJ
ejpam-6997	679	7	g	g	PROPN
ejpam-6997	679	8	is	be	AUX
ejpam-6997	679	9	a	a	DET
ejpam-6997	679	10	grill	grill	NOUN
ejpam-6997	679	11	on	on	ADP
ejpam-6997	679	12	a	a	DET
ejpam-6997	679	13	ϱ-ns	ϱ-ns	ADV
ejpam-6997	679	14	(	(	PUNCT
ejpam-6997	679	15	ℵ,γ	ℵ,γ	NOUN
ejpam-6997	679	16	,	,	PUNCT
ejpam-6997	679	17	ξϱ	ξϱ	NOUN
ejpam-6997	679	18	)	)	PUNCT
ejpam-6997	679	19	.	.	PUNCT
ejpam-6997	680	1	if	if	SCONJ
ejpam-6997	680	2	d	d	PROPN
ejpam-6997	680	3	⊑	⊑	X
ejpam-6997	680	4	ℵ	ℵ	NOUN
ejpam-6997	680	5	,	,	PUNCT
ejpam-6997	680	6	then	then	ADV
ejpam-6997	680	7	gλξϱ	gλξϱ	NOUN
ejpam-6997	680	8	(	(	PUNCT
ejpam-6997	680	9	d	d	NOUN
ejpam-6997	680	10	)	)	PUNCT
ejpam-6997	680	11	≤	≤	NOUN
ejpam-6997	680	12	gacϱ	gacϱ	NOUN
ejpam-6997	680	13	(	(	PUNCT
ejpam-6997	680	14	d	d	NOUN
ejpam-6997	680	15	)	)	PUNCT
ejpam-6997	680	16	.	.	PUNCT
ejpam-6997	681	1	5	5	X
ejpam-6997	681	2	.	.	X
ejpam-6997	681	3	diagnostic	diagnostic	ADJ
ejpam-6997	681	4	analysis	analysis	NOUN
ejpam-6997	681	5	of	of	ADP
ejpam-6997	681	6	heart	heart	NOUN
ejpam-6997	681	7	failure	failure	NOUN
ejpam-6997	681	8	as	as	ADP
ejpam-6997	681	9	a	a	DET
ejpam-6997	681	10	medical	medical	ADJ
ejpam-6997	681	11	application	application	NOUN
ejpam-6997	681	12	in	in	ADP
ejpam-6997	681	13	this	this	DET
ejpam-6997	681	14	section	section	NOUN
ejpam-6997	681	15	,	,	PUNCT
ejpam-6997	681	16	we	we	PRON
ejpam-6997	681	17	assess	assess	VERB
ejpam-6997	681	18	the	the	DET
ejpam-6997	681	19	efficiency	efficiency	NOUN
ejpam-6997	681	20	of	of	ADP
ejpam-6997	681	21	suggested	suggest	VERB
ejpam-6997	681	22	models	model	NOUN
ejpam-6997	681	23	in	in	ADP
ejpam-6997	681	24	managing	manage	VERB
ejpam-6997	681	25	heart	heart	NOUN
ejpam-6997	681	26	failure	failure	NOUN
ejpam-6997	681	27	information	information	NOUN
ejpam-6997	681	28	systems	system	NOUN
ejpam-6997	681	29	for	for	ADP
ejpam-6997	681	30	specific	specific	ADJ
ejpam-6997	681	31	patients	patient	NOUN
ejpam-6997	681	32	[	[	X
ejpam-6997	681	33	47	47	NUM
ejpam-6997	681	34	]	]	PUNCT
ejpam-6997	681	35	.	.	PUNCT
ejpam-6997	682	1	we	we	PRON
ejpam-6997	682	2	demonstrate	demonstrate	VERB
ejpam-6997	682	3	how	how	SCONJ
ejpam-6997	682	4	the	the	DET
ejpam-6997	682	5	current	current	ADJ
ejpam-6997	682	6	approach	approach	NOUN
ejpam-6997	682	7	improves	improve	VERB
ejpam-6997	682	8	decision	decision	NOUN
ejpam-6997	682	9	-	-	PUNCT
ejpam-6997	682	10	making	making	NOUN
ejpam-6997	682	11	and	and	CCONJ
ejpam-6997	682	12	how	how	SCONJ
ejpam-6997	682	13	we	we	PRON
ejpam-6997	682	14	use	use	VERB
ejpam-6997	682	15	a	a	DET
ejpam-6997	682	16	topological	topological	ADJ
ejpam-6997	682	17	strategy	strategy	NOUN
ejpam-6997	682	18	to	to	PART
ejpam-6997	682	19	pinpoint	pinpoint	VERB
ejpam-6997	682	20	the	the	DET
ejpam-6997	682	21	most	most	ADV
ejpam-6997	682	22	important	important	ADJ
ejpam-6997	682	23	symptoms	symptom	NOUN
ejpam-6997	682	24	for	for	ADP
ejpam-6997	682	25	identifying	identify	VERB
ejpam-6997	682	26	heart	heart	NOUN
ejpam-6997	682	27	failure	failure	NOUN
ejpam-6997	682	28	disease	disease	NOUN
ejpam-6997	682	29	.	.	PUNCT
ejpam-6997	683	1	the	the	DET
ejpam-6997	683	2	investigation	investigation	NOUN
ejpam-6997	683	3	that	that	PRON
ejpam-6997	683	4	follows	follow	VERB
ejpam-6997	683	5	leads	lead	VERB
ejpam-6997	683	6	us	we	PRON
ejpam-6997	683	7	to	to	ADP
ejpam-6997	683	8	the	the	DET
ejpam-6997	683	9	conclusion	conclusion	NOUN
ejpam-6997	683	10	that	that	SCONJ
ejpam-6997	683	11	the	the	DET
ejpam-6997	683	12	suggested	suggest	VERB
ejpam-6997	683	13	rs	rs	PROPN
ejpam-6997	683	14	paradigms	paradigm	NOUN
ejpam-6997	683	15	perform	perform	VERB
ejpam-6997	683	16	better	well	ADJ
ejpam-6997	683	17	than	than	ADP
ejpam-6997	683	18	their	their	PRON
ejpam-6997	683	19	counterparts	counterpart	NOUN
ejpam-6997	683	20	that	that	PRON
ejpam-6997	683	21	are	be	AUX
ejpam-6997	683	22	based	base	VERB
ejpam-6997	683	23	on	on	ADP
ejpam-6997	683	24	cardinality	cardinality	PROPN
ejpam-6997	683	25	nbds	nbds	NOUN
ejpam-6997	683	26	without	without	ADP
ejpam-6997	683	27	grills	grill	NOUN
ejpam-6997	683	28	.	.	PUNCT
ejpam-6997	684	1	we	we	PRON
ejpam-6997	684	2	also	also	ADV
ejpam-6997	684	3	make	make	VERB
ejpam-6997	684	4	reference	reference	NOUN
ejpam-6997	684	5	to	to	ADP
ejpam-6997	684	6	the	the	DET
ejpam-6997	684	7	restrictions	restriction	NOUN
ejpam-6997	684	8	connected	connect	VERB
ejpam-6997	684	9	to	to	ADP
ejpam-6997	684	10	the	the	DET
ejpam-6997	684	11	approach	approach	NOUN
ejpam-6997	684	12	described	describe	VERB
ejpam-6997	684	13	in	in	ADP
ejpam-6997	684	14	sec	sec	PROPN
ejpam-6997	684	15	.	.	PROPN
ejpam-6997	685	1	3.1	3.1	NUM
ejpam-6997	685	2	.	.	PUNCT
ejpam-6997	685	3	table	table	NOUN
ejpam-6997	685	4	6	6	NUM
ejpam-6997	685	5	shows	show	VERB
ejpam-6997	685	6	data	datum	NOUN
ejpam-6997	685	7	for	for	ADP
ejpam-6997	685	8	eight	eight	NUM
ejpam-6997	685	9	patients	patient	NOUN
ejpam-6997	685	10	(	(	PUNCT
ejpam-6997	685	11	ℵ	ℵ	NOUN
ejpam-6997	685	12	=	=	SYM
ejpam-6997	685	13	{	{	PUNCT
ejpam-6997	685	14	p1	p1	PROPN
ejpam-6997	685	15	,	,	PUNCT
ejpam-6997	685	16	p2	p2	NOUN
ejpam-6997	685	17	,	,	PUNCT
ejpam-6997	685	18	p3	p3	NOUN
ejpam-6997	685	19	,	,	PUNCT
ejpam-6997	685	20	p4	p4	ADJ
ejpam-6997	685	21	,	,	PUNCT
ejpam-6997	685	22	p5	p5	ADJ
ejpam-6997	685	23	,	,	PUNCT
ejpam-6997	685	24	p6	p6	PROPN
ejpam-6997	685	25	,	,	PUNCT
ejpam-6997	685	26	p7	p7	ADJ
ejpam-6997	685	27	,	,	PUNCT
ejpam-6997	685	28	p8	p8	PROPN
ejpam-6997	685	29	}	}	PUNCT
ejpam-6997	685	30	)	)	PUNCT
ejpam-6997	685	31	and	and	CCONJ
ejpam-6997	685	32	their	their	PRON
ejpam-6997	685	33	associated	associated	ADJ
ejpam-6997	685	34	symptoms	symptom	NOUN
ejpam-6997	685	35	(	(	PUNCT
ejpam-6997	685	36	conditional	conditional	ADJ
ejpam-6997	685	37	attributes	attribute	NOUN
ejpam-6997	685	38	):	):	PUNCT
ejpam-6997	685	39	breathlessness	breathlessness	NOUN
ejpam-6997	685	40	(	(	PUNCT
ejpam-6997	685	41	br	br	NOUN
ejpam-6997	685	42	)	)	PUNCT
ejpam-6997	685	43	,	,	PUNCT
ejpam-6997	685	44	orthopnea	orthopnea	PROPN
ejpam-6997	685	45	(	(	PUNCT
ejpam-6997	685	46	or	or	CCONJ
ejpam-6997	685	47	)	)	PUNCT
ejpam-6997	685	48	,	,	PUNCT
ejpam-6997	685	49	paroxysmal	paroxysmal	ADJ
ejpam-6997	685	50	nocturnal	nocturnal	ADJ
ejpam-6997	685	51	dyspnea	dyspnea	NOUN
ejpam-6997	685	52	(	(	PUNCT
ejpam-6997	685	53	pnd	pnd	NOUN
ejpam-6997	685	54	)	)	PUNCT
ejpam-6997	685	55	,	,	PUNCT
ejpam-6997	685	56	impaired	impair	VERB
ejpam-6997	685	57	exercise	exercise	NOUN
ejpam-6997	685	58	tolerance	tolerance	NOUN
ejpam-6997	685	59	(	(	PUNCT
ejpam-6997	685	60	iet	iet	PROPN
ejpam-6997	685	61	)	)	PUNCT
ejpam-6997	685	62	,	,	PUNCT
ejpam-6997	685	63	and	and	CCONJ
ejpam-6997	685	64	ankle	ankle	NOUN
ejpam-6997	685	65	swelling	swelling	NOUN
ejpam-6997	685	66	(	(	PUNCT
ejpam-6997	685	67	as	as	ADP
ejpam-6997	685	68	)	)	PUNCT
ejpam-6997	685	69	.	.	PUNCT
ejpam-6997	686	1	heart	heart	NOUN
ejpam-6997	686	2	failure	failure	NOUN
ejpam-6997	686	3	is	be	AUX
ejpam-6997	686	4	regarded	regard	VERB
ejpam-6997	686	5	as	as	ADP
ejpam-6997	686	6	the	the	DET
ejpam-6997	686	7	deciding	decide	VERB
ejpam-6997	686	8	attribute	attribute	NOUN
ejpam-6997	686	9	.	.	PUNCT
ejpam-6997	687	1	we	we	PRON
ejpam-6997	687	2	add	add	VERB
ejpam-6997	687	3	a	a	DET
ejpam-6997	687	4	value	value	NOUN
ejpam-6997	687	5	of	of	ADP
ejpam-6997	687	6	s+	s+	NUM
ejpam-6997	687	7	or	or	CCONJ
ejpam-6997	687	8	s−	s−	PROPN
ejpam-6997	687	9	to	to	ADP
ejpam-6997	687	10	each	each	DET
ejpam-6997	687	11	conditional	conditional	ADJ
ejpam-6997	687	12	property	property	NOUN
ejpam-6997	687	13	(	(	PUNCT
ejpam-6997	687	14	symptom	symptom	NOUN
ejpam-6997	687	15	)	)	PUNCT
ejpam-6997	687	16	to	to	PART
ejpam-6997	687	17	indicate	indicate	VERB
ejpam-6997	687	18	whether	whether	SCONJ
ejpam-6997	687	19	the	the	DET
ejpam-6997	687	20	patient	patient	NOUN
ejpam-6997	687	21	has	have	VERB
ejpam-6997	687	22	the	the	DET
ejpam-6997	687	23	symptom	symptom	NOUN
ejpam-6997	687	24	or	or	CCONJ
ejpam-6997	687	25	not	not	PART
ejpam-6997	687	26	.	.	PUNCT
ejpam-6997	688	1	in	in	ADP
ejpam-6997	688	2	a	a	DET
ejpam-6997	688	3	similar	similar	ADJ
ejpam-6997	688	4	manner	manner	NOUN
ejpam-6997	688	5	,	,	PUNCT
ejpam-6997	688	6	the	the	DET
ejpam-6997	688	7	decision	decision	NOUN
ejpam-6997	688	8	attribute	attribute	NOUN
ejpam-6997	688	9	is	be	AUX
ejpam-6997	688	10	labeled	label	VERB
ejpam-6997	688	11	with	with	ADP
ejpam-6997	688	12	+	+	PROPN
ejpam-6997	688	13	+	+	NOUN
ejpam-6997	688	14	or	or	CCONJ
ejpam-6997	688	15	−−	−−	NOUN
ejpam-6997	688	16	to	to	PART
ejpam-6997	688	17	indicate	indicate	VERB
ejpam-6997	688	18	a	a	DET
ejpam-6997	688	19	heart	heart	NOUN
ejpam-6997	688	20	failure	failure	NOUN
ejpam-6997	688	21	report	report	NOUN
ejpam-6997	688	22	that	that	PRON
ejpam-6997	688	23	is	be	AUX
ejpam-6997	688	24	positive	positive	ADJ
ejpam-6997	688	25	or	or	CCONJ
ejpam-6997	688	26	negative	negative	ADJ
ejpam-6997	688	27	.	.	PUNCT
ejpam-6997	689	1	suppose	suppose	VERB
ejpam-6997	689	2	the	the	DET
ejpam-6997	689	3	system	system	NOUN
ejpam-6997	689	4	’s	’s	PART
ejpam-6997	689	5	expert	expert	NOUN
ejpam-6997	689	6	proposed	propose	VERB
ejpam-6997	689	7	the	the	DET
ejpam-6997	689	8	next	next	ADJ
ejpam-6997	689	9	relation	relation	NOUN
ejpam-6997	689	10	γ	γ	NOUN
ejpam-6997	689	11	on	on	ADP
ejpam-6997	689	12	the	the	DET
ejpam-6997	689	13	set	set	NOUN
ejpam-6997	689	14	of	of	ADP
ejpam-6997	689	15	patients	patient	NOUN
ejpam-6997	689	16	ℵ	ℵ	VERB
ejpam-6997	689	17	to	to	PART
ejpam-6997	689	18	describe	describe	VERB
ejpam-6997	689	19	the	the	DET
ejpam-6997	689	20	links	link	NOUN
ejpam-6997	689	21	between	between	ADP
ejpam-6997	689	22	them	they	PRON
ejpam-6997	689	23	based	base	VERB
ejpam-6997	689	24	on	on	ADP
ejpam-6997	689	25	their	their	PRON
ejpam-6997	689	26	symptoms	symptom	NOUN
ejpam-6997	689	27	:	:	PUNCT
ejpam-6997	689	28	a.	a.	NOUN
ejpam-6997	689	29	a.	a.	PROPN
ejpam-6997	689	30	azzam	azzam	PROPN
ejpam-6997	689	31	,	,	PUNCT
ejpam-6997	689	32	m.	m.	NOUN
ejpam-6997	689	33	aldawood	aldawood	PROPN
ejpam-6997	689	34	,	,	PUNCT
ejpam-6997	689	35	b.	b.	PROPN
ejpam-6997	689	36	alreshidi	alreshidi	PROPN
ejpam-6997	689	37	/	/	SYM
ejpam-6997	689	38	eur	eur	PROPN
ejpam-6997	689	39	.	.	PUNCT
ejpam-6997	690	1	j.	j.	PROPN
ejpam-6997	690	2	pure	pure	PROPN
ejpam-6997	690	3	appl	appl	PROPN
ejpam-6997	690	4	.	.	PROPN
ejpam-6997	690	5	math	math	PROPN
ejpam-6997	690	6	,	,	PUNCT
ejpam-6997	690	7	18	18	NUM
ejpam-6997	690	8	(	(	PUNCT
ejpam-6997	690	9	4	4	NUM
ejpam-6997	690	10	)	)	PUNCT
ejpam-6997	690	11	(	(	PUNCT
ejpam-6997	690	12	2025	2025	NUM
ejpam-6997	690	13	)	)	PUNCT
ejpam-6997	690	14	,	,	PUNCT
ejpam-6997	690	15	6997	6997	NUM
ejpam-6997	690	16	25	25	NUM
ejpam-6997	690	17	of	of	ADP
ejpam-6997	690	18	31	31	NUM
ejpam-6997	690	19	table	table	NOUN
ejpam-6997	690	20	6	6	NUM
ejpam-6997	690	21	:	:	PUNCT
ejpam-6997	690	22	information	information	NOUN
ejpam-6997	690	23	system	system	NOUN
ejpam-6997	690	24	for	for	ADP
ejpam-6997	690	25	heart	heart	NOUN
ejpam-6997	690	26	failure	failure	NOUN
ejpam-6997	690	27	patients	patient	NOUN
ejpam-6997	690	28	br	br	VERB
ejpam-6997	690	29	or	or	CCONJ
ejpam-6997	690	30	pnd	pnd	NOUN
ejpam-6997	690	31	iet	iet	PROPN
ejpam-6997	690	32	as	as	ADP
ejpam-6997	690	33	decision	decision	NOUN
ejpam-6997	690	34	.	.	PUNCT
ejpam-6997	691	1	p1	p1	NOUN
ejpam-6997	691	2	s+	s+	PUNCT
ejpam-6997	691	3	s+	s+	NUM
ejpam-6997	691	4	s+	s+	ADV
ejpam-6997	691	5	s+	s+	ADV
ejpam-6997	691	6	s−	s−	PROPN
ejpam-6997	691	7	+	+	PROPN
ejpam-6997	691	8	+	+	PROPN
ejpam-6997	691	9	p2	p2	PROPN
ejpam-6997	691	10	s−	s−	PROPN
ejpam-6997	691	11	s−	s−	PROPN
ejpam-6997	691	12	s−	s−	PROPN
ejpam-6997	691	13	s+	s+	PUNCT
ejpam-6997	691	14	s+	s+	PUNCT
ejpam-6997	691	15	−−	−−	PROPN
ejpam-6997	691	16	p3	p3	PROPN
ejpam-6997	691	17	s+	s+	PUNCT
ejpam-6997	691	18	s+	s+	ADV
ejpam-6997	691	19	s+	s+	NUM
ejpam-6997	691	20	s+	s+	NUM
ejpam-6997	691	21	s+	s+	PUNCT
ejpam-6997	691	22	+	+	PROPN
ejpam-6997	691	23	+	+	X
ejpam-6997	691	24	p4	p4	ADJ
ejpam-6997	691	25	s−	s−	PROPN
ejpam-6997	691	26	s−	s−	PROPN
ejpam-6997	691	27	s−	s−	PROPN
ejpam-6997	691	28	s+	s+	PUNCT
ejpam-6997	691	29	s−	s−	PROPN
ejpam-6997	691	30	−−	−−	NOUN
ejpam-6997	691	31	p5	p5	ADJ
ejpam-6997	691	32	s+	s+	PUNCT
ejpam-6997	691	33	s−	s−	PROPN
ejpam-6997	691	34	s−	s−	PROPN
ejpam-6997	691	35	s+	s+	PUNCT
ejpam-6997	691	36	s+	s+	PUNCT
ejpam-6997	691	37	−−	−−	NOUN
ejpam-6997	691	38	p6	p6	VERB
ejpam-6997	691	39	s−	s−	PROPN
ejpam-6997	691	40	s−	s−	PROPN
ejpam-6997	691	41	s−	s−	PROPN
ejpam-6997	691	42	s+	s+	PUNCT
ejpam-6997	691	43	s−	s−	PROPN
ejpam-6997	691	44	−−	−−	NOUN
ejpam-6997	691	45	p7	p7	PROPN
ejpam-6997	691	46	s+	s+	PUNCT
ejpam-6997	691	47	s+	s+	PUNCT
ejpam-6997	691	48	s+	s+	NUM
ejpam-6997	691	49	s+	s+	NUM
ejpam-6997	691	50	s+	s+	PUNCT
ejpam-6997	692	1	+	+	PUNCT
ejpam-6997	692	2	+	+	X
ejpam-6997	692	3	p8	p8	ADJ
ejpam-6997	692	4	s+	s+	PUNCT
ejpam-6997	692	5	s+	s+	PUNCT
ejpam-6997	692	6	s−	s−	PROPN
ejpam-6997	692	7	s+	s+	PUNCT
ejpam-6997	692	8	s+	s+	ADV
ejpam-6997	692	9	+	+	PROPN
ejpam-6997	692	10	+	+	PROPN
ejpam-6997	692	11	prγpt	prγpt	PROPN
ejpam-6997	692	12	⇔	⇔	PROPN
ejpam-6997	692	13	there	there	PRON
ejpam-6997	692	14	are	be	VERB
ejpam-6997	692	15	more	more	ADJ
ejpam-6997	692	16	than	than	ADP
ejpam-6997	692	17	two	two	NUM
ejpam-6997	692	18	frequent	frequent	ADJ
ejpam-6997	692	19	positive	positive	ADJ
ejpam-6997	692	20	symptoms	symptom	NOUN
ejpam-6997	692	21	that	that	PRON
ejpam-6997	692	22	distinguish	distinguish	VERB
ejpam-6997	692	23	pr	pr	NOUN
ejpam-6997	692	24	from	from	ADP
ejpam-6997	692	25	pt	pt	PROPN
ejpam-6997	692	26	.	.	PROPN
ejpam-6997	692	27	then	then	ADV
ejpam-6997	692	28	,	,	PUNCT
ejpam-6997	692	29	γ	γ	X
ejpam-6997	692	30	=	=	SYM
ejpam-6997	692	31	{	{	PUNCT
ejpam-6997	692	32	(	(	PUNCT
ejpam-6997	692	33	p1	p1	PROPN
ejpam-6997	692	34	,	,	PUNCT
ejpam-6997	692	35	p1	p1	PROPN
ejpam-6997	692	36	)	)	PUNCT
ejpam-6997	692	37	,	,	PUNCT
ejpam-6997	692	38	(	(	PUNCT
ejpam-6997	692	39	p3	p3	PROPN
ejpam-6997	692	40	,	,	PUNCT
ejpam-6997	692	41	p3	p3	PROPN
ejpam-6997	692	42	)	)	PUNCT
ejpam-6997	692	43	,	,	PUNCT
ejpam-6997	692	44	(	(	PUNCT
ejpam-6997	692	45	p5	p5	ADJ
ejpam-6997	692	46	,	,	PUNCT
ejpam-6997	692	47	p5	p5	ADJ
ejpam-6997	692	48	)	)	PUNCT
ejpam-6997	692	49	,	,	PUNCT
ejpam-6997	692	50	(	(	PUNCT
ejpam-6997	692	51	p7	p7	ADJ
ejpam-6997	692	52	,	,	PUNCT
ejpam-6997	692	53	p7	p7	ADJ
ejpam-6997	692	54	)	)	PUNCT
ejpam-6997	692	55	,	,	PUNCT
ejpam-6997	692	56	(	(	PUNCT
ejpam-6997	692	57	p8	p8	PROPN
ejpam-6997	692	58	,	,	PUNCT
ejpam-6997	692	59	p8	p8	PROPN
ejpam-6997	692	60	)	)	PUNCT
ejpam-6997	692	61	,	,	PUNCT
ejpam-6997	692	62	(	(	PUNCT
ejpam-6997	692	63	p1	p1	NOUN
ejpam-6997	692	64	,	,	PUNCT
ejpam-6997	692	65	p3	p3	PROPN
ejpam-6997	692	66	)	)	PUNCT
ejpam-6997	692	67	,	,	PUNCT
ejpam-6997	692	68	(	(	PUNCT
ejpam-6997	692	69	p3	p3	PROPN
ejpam-6997	692	70	,	,	PUNCT
ejpam-6997	692	71	p1	p1	PROPN
ejpam-6997	692	72	)	)	PUNCT
ejpam-6997	692	73	,	,	PUNCT
ejpam-6997	692	74	(	(	PUNCT
ejpam-6997	692	75	p1	p1	NOUN
ejpam-6997	692	76	,	,	PUNCT
ejpam-6997	692	77	p7	p7	NOUN
ejpam-6997	692	78	)	)	PUNCT
ejpam-6997	692	79	,	,	PUNCT
ejpam-6997	692	80	(	(	PUNCT
ejpam-6997	692	81	p7	p7	PROPN
ejpam-6997	692	82	,	,	PUNCT
ejpam-6997	692	83	p1	p1	PROPN
ejpam-6997	692	84	)	)	PUNCT
ejpam-6997	692	85	,	,	PUNCT
ejpam-6997	692	86	(	(	PUNCT
ejpam-6997	692	87	p1	p1	NOUN
ejpam-6997	692	88	,	,	PUNCT
ejpam-6997	692	89	p8	p8	PROPN
ejpam-6997	692	90	)	)	PUNCT
ejpam-6997	692	91	,	,	PUNCT
ejpam-6997	692	92	(	(	PUNCT
ejpam-6997	692	93	p8	p8	PROPN
ejpam-6997	692	94	,	,	PUNCT
ejpam-6997	692	95	p1	p1	PROPN
ejpam-6997	692	96	)	)	PUNCT
ejpam-6997	692	97	,	,	PUNCT
ejpam-6997	692	98	(	(	PUNCT
ejpam-6997	692	99	p3	p3	NOUN
ejpam-6997	692	100	,	,	PUNCT
ejpam-6997	692	101	p5	p5	ADJ
ejpam-6997	692	102	)	)	PUNCT
ejpam-6997	692	103	,	,	PUNCT
ejpam-6997	692	104	(	(	PUNCT
ejpam-6997	692	105	p5	p5	PROPN
ejpam-6997	692	106	,	,	PUNCT
ejpam-6997	692	107	p3	p3	PROPN
ejpam-6997	692	108	)	)	PUNCT
ejpam-6997	692	109	,	,	PUNCT
ejpam-6997	692	110	(	(	PUNCT
ejpam-6997	692	111	p3	p3	PROPN
ejpam-6997	692	112	,	,	PUNCT
ejpam-6997	692	113	p7	p7	PROPN
ejpam-6997	692	114	)	)	PUNCT
ejpam-6997	692	115	,	,	PUNCT
ejpam-6997	692	116	(	(	PUNCT
ejpam-6997	692	117	p7	p7	PROPN
ejpam-6997	692	118	,	,	PUNCT
ejpam-6997	692	119	p3	p3	PROPN
ejpam-6997	692	120	)	)	PUNCT
ejpam-6997	692	121	,	,	PUNCT
ejpam-6997	692	122	(	(	PUNCT
ejpam-6997	692	123	p3	p3	PROPN
ejpam-6997	692	124	,	,	PUNCT
ejpam-6997	692	125	p8	p8	PROPN
ejpam-6997	692	126	)	)	PUNCT
ejpam-6997	692	127	,	,	PUNCT
ejpam-6997	692	128	(	(	PUNCT
ejpam-6997	692	129	p8	p8	PROPN
ejpam-6997	692	130	,	,	PUNCT
ejpam-6997	692	131	p3	p3	PROPN
ejpam-6997	692	132	)	)	PUNCT
ejpam-6997	692	133	,	,	PUNCT
ejpam-6997	692	134	(	(	PUNCT
ejpam-6997	692	135	p5	p5	ADJ
ejpam-6997	692	136	,	,	PUNCT
ejpam-6997	692	137	p7	p7	ADJ
ejpam-6997	692	138	)	)	PUNCT
ejpam-6997	692	139	,	,	PUNCT
ejpam-6997	692	140	(	(	PUNCT
ejpam-6997	692	141	p7	p7	ADJ
ejpam-6997	692	142	,	,	PUNCT
ejpam-6997	692	143	p5	p5	ADJ
ejpam-6997	692	144	)	)	PUNCT
ejpam-6997	692	145	,	,	PUNCT
ejpam-6997	692	146	(	(	PUNCT
ejpam-6997	692	147	p5	p5	ADJ
ejpam-6997	692	148	,	,	PUNCT
ejpam-6997	692	149	p8	p8	PROPN
ejpam-6997	692	150	)	)	PUNCT
ejpam-6997	692	151	,	,	PUNCT
ejpam-6997	692	152	(	(	PUNCT
ejpam-6997	692	153	p8	p8	ADJ
ejpam-6997	692	154	,	,	PUNCT
ejpam-6997	692	155	p5	p5	ADJ
ejpam-6997	692	156	)	)	PUNCT
ejpam-6997	692	157	,	,	PUNCT
ejpam-6997	692	158	(	(	PUNCT
ejpam-6997	692	159	p7	p7	PROPN
ejpam-6997	692	160	,	,	PUNCT
ejpam-6997	692	161	p8	p8	PROPN
ejpam-6997	692	162	)	)	PUNCT
ejpam-6997	692	163	,	,	PUNCT
ejpam-6997	692	164	(	(	PUNCT
ejpam-6997	692	165	p8	p8	PROPN
ejpam-6997	692	166	,	,	PUNCT
ejpam-6997	692	167	p7	p7	ADJ
ejpam-6997	692	168	)	)	PUNCT
ejpam-6997	692	169	}	}	PUNCT
ejpam-6997	692	170	.	.	PUNCT
ejpam-6997	693	1	note	note	VERB
ejpam-6997	693	2	that	that	SCONJ
ejpam-6997	693	3	γ	γ	PROPN
ejpam-6997	693	4	is	be	AUX
ejpam-6997	693	5	a	a	DET
ejpam-6997	693	6	symmetric	symmetric	ADJ
ejpam-6997	693	7	relation	relation	NOUN
ejpam-6997	693	8	that	that	PRON
ejpam-6997	693	9	is	be	AUX
ejpam-6997	693	10	neither	neither	CCONJ
ejpam-6997	693	11	transitive	transitive	ADJ
ejpam-6997	693	12	nor	nor	CCONJ
ejpam-6997	693	13	reflexive	reflexive	ADJ
ejpam-6997	693	14	.	.	PUNCT
ejpam-6997	694	1	we	we	PRON
ejpam-6997	694	2	start	start	VERB
ejpam-6997	694	3	by	by	ADP
ejpam-6997	694	4	building	build	VERB
ejpam-6997	694	5	the	the	DET
ejpam-6997	694	6	cϱ-nbd	cϱ-nbd	PROPN
ejpam-6997	694	7	systems	system	NOUN
ejpam-6997	694	8	in	in	ADP
ejpam-6997	694	9	order	order	NOUN
ejpam-6997	694	10	to	to	PART
ejpam-6997	694	11	process	process	VERB
ejpam-6997	694	12	the	the	DET
ejpam-6997	694	13	data	datum	NOUN
ejpam-6997	694	14	that	that	PRON
ejpam-6997	694	15	is	be	AUX
ejpam-6997	694	16	described	describe	VERB
ejpam-6997	694	17	by	by	ADP
ejpam-6997	694	18	the	the	DET
ejpam-6997	694	19	specified	specified	ADJ
ejpam-6997	694	20	relation	relation	NOUN
ejpam-6997	694	21	.	.	PUNCT
ejpam-6997	695	1	as	as	SCONJ
ejpam-6997	695	2	stated	state	VERB
ejpam-6997	695	3	in	in	ADP
ejpam-6997	695	4	proposition	proposition	NOUN
ejpam-6997	695	5	2.14	2.14	NUM
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ejpam-6997	695	11	cϱ-nbds	cϱ-nbds	NOUN
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ejpam-6997	695	14	because	because	SCONJ
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ejpam-6997	695	17	symmetry	symmetry	NOUN
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ejpam-6997	695	19	the	the	DET
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ejpam-6997	697	64	p1	p1	NOUN
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ejpam-6997	697	78	p1	p1	NOUN
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ejpam-6997	700	5	)	)	PUNCT
ejpam-6997	700	6	=	=	SYM
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ejpam-6997	701	6	=	=	SYM
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ejpam-6997	703	8	=	=	SYM
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ejpam-6997	705	3	showed	show	VERB
ejpam-6997	705	4	our	our	PRON
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ejpam-6997	705	8	.	.	PUNCT
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ejpam-6997	706	2	(	(	PUNCT
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ejpam-6997	707	4	2	2	X
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ejpam-6997	707	7	(	(	PUNCT
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ejpam-6997	708	4	3	3	X
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ejpam-6997	708	7	(	(	PUNCT
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ejpam-6997	709	1	gmcϱ	gmcϱ	NOUN
ejpam-6997	709	2	(	(	PUNCT
ejpam-6997	709	3	∆	∆	PROPN
ejpam-6997	709	4	)	)	PUNCT
ejpam-6997	709	5	\	\	PROPN
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ejpam-6997	709	7	(	(	PUNCT
ejpam-6997	709	8	d	d	NOUN
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ejpam-6997	709	10	=	=	SYM
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ejpam-6997	709	12	,	,	PUNCT
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ejpam-6997	709	14	(	(	PUNCT
ejpam-6997	709	15	4	4	X
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ejpam-6997	709	17	gacϱ	gacϱ	NOUN
ejpam-6997	709	18	(	(	PUNCT
ejpam-6997	709	19	d	d	NOUN
ejpam-6997	709	20	)	)	PUNCT
ejpam-6997	709	21	=	=	PUNCT
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ejpam-6997	709	23	(	(	PUNCT
ejpam-6997	709	24	d)|	d)|	PROPN
ejpam-6997	709	25	|g	|g	PROPN
ejpam-6997	709	26	mcϱ	mcϱ	PROPN
ejpam-6997	709	27	(	(	PUNCT
ejpam-6997	709	28	d)|	d)|	NOUN
ejpam-6997	709	29	=	=	SYM
ejpam-6997	709	30	1	1	X
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ejpam-6997	709	33	of	of	ADP
ejpam-6997	709	34	topology	topology	NOUN
ejpam-6997	709	35	developed	develop	VERB
ejpam-6997	709	36	in	in	ADP
ejpam-6997	709	37	sect.4	sect.4	PROPN
ejpam-6997	709	38	.	.	PUNCT
ejpam-6997	710	1	in	in	ADP
ejpam-6997	710	2	order	order	NOUN
ejpam-6997	710	3	to	to	PART
ejpam-6997	710	4	use	use	VERB
ejpam-6997	710	5	these	these	DET
ejpam-6997	710	6	models	model	NOUN
ejpam-6997	710	7	,	,	PUNCT
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ejpam-6997	710	9	first	first	ADV
ejpam-6997	710	10	set	set	VERB
ejpam-6997	710	11	up	up	ADP
ejpam-6997	710	12	a	a	DET
ejpam-6997	710	13	topology	topology	NOUN
ejpam-6997	710	14	as	as	SCONJ
ejpam-6997	710	15	shown	show	VERB
ejpam-6997	710	16	in	in	ADP
ejpam-6997	710	17	table	table	NOUN
ejpam-6997	710	18	7	7	NUM
ejpam-6997	710	19	:	:	PUNCT
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ejpam-6997	710	21	7	7	NUM
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ejpam-6997	710	25	each	each	DET
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ejpam-6997	711	2	p2	p2	PROPN
ejpam-6997	711	3	p3	p3	PROPN
ejpam-6997	711	4	p4	p4	ADJ
ejpam-6997	711	5	p5	p5	ADJ
ejpam-6997	711	6	p6	p6	ADJ
ejpam-6997	711	7	p7	p7	PROPN
ejpam-6997	711	8	p8	p8	PROPN
ejpam-6997	711	9	mr	mr	PROPN
ejpam-6997	711	10	(	(	PUNCT
ejpam-6997	711	11	)	)	PUNCT
ejpam-6997	711	12	{	{	PUNCT
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ejpam-6997	711	18	,	,	PUNCT
ejpam-6997	711	19	p8	p8	PROPN
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ejpam-6997	711	21	ϕ	ϕ	PROPN
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ejpam-6997	711	23	p1	p1	PROPN
ejpam-6997	711	24	,	,	PUNCT
ejpam-6997	711	25	p3	p3	PROPN
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ejpam-6997	711	27	p5	p5	ADJ
ejpam-6997	711	28	,	,	PUNCT
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ejpam-6997	711	30	,	,	PUNCT
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ejpam-6997	711	36	,	,	PUNCT
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ejpam-6997	711	38	,	,	PUNCT
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ejpam-6997	711	40	,	,	PUNCT
ejpam-6997	711	41	p8	p8	PROPN
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ejpam-6997	711	50	,	,	PUNCT
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ejpam-6997	711	52	,	,	PUNCT
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ejpam-6997	711	78	ϕ	ϕ	PROPN
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ejpam-6997	711	81	,	,	PUNCT
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ejpam-6997	711	86	ϕ	ϕ	PROPN
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ejpam-6997	711	88	p3	p3	PROPN
ejpam-6997	711	89	,	,	PUNCT
ejpam-6997	711	90	p5	p5	ADJ
ejpam-6997	711	91	,	,	PUNCT
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ejpam-6997	711	104	{	{	PUNCT
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ejpam-6997	711	113	)	)	PUNCT
ejpam-6997	711	114	{	{	PUNCT
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ejpam-6997	711	127	p3	p3	PROPN
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ejpam-6997	711	131	p8	p8	PROPN
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ejpam-6997	711	207	,	,	PUNCT
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ejpam-6997	711	210	p5	p5	ADJ
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ejpam-6997	713	15	=	=	SYM
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ejpam-6997	713	17	(	(	PUNCT
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ejpam-6997	713	20	=	=	SYM
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ejpam-6997	713	28	)	)	PUNCT
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ejpam-6997	713	31	(	(	PUNCT
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ejpam-6997	713	33	(	(	PUNCT
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ejpam-6997	714	1	=	=	SYM
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ejpam-6997	714	3	(	(	PUNCT
ejpam-6997	714	4	∆)|	∆)|	NOUN
ejpam-6997	714	5	|gξϱ	|gξϱ	NOUN
ejpam-6997	714	6	(	(	PUNCT
ejpam-6997	714	7	∆)|	∆)|	NOUN
ejpam-6997	714	8	=	=	SYM
ejpam-6997	714	9	1	1	X
ejpam-6997	714	10	.	.	PUNCT
ejpam-6997	715	1	it	it	PRON
ejpam-6997	715	2	is	be	AUX
ejpam-6997	715	3	clear	clear	ADJ
ejpam-6997	715	4	from	from	ADP
ejpam-6997	715	5	the	the	DET
ejpam-6997	715	6	aforementioned	aforementioned	ADJ
ejpam-6997	715	7	results	result	NOUN
ejpam-6997	715	8	that	that	SCONJ
ejpam-6997	715	9	these	these	DET
ejpam-6997	715	10	calculations	calculation	NOUN
ejpam-6997	715	11	support	support	VERB
ejpam-6997	715	12	the	the	DET
ejpam-6997	715	13	conclusions	conclusion	NOUN
ejpam-6997	715	14	made	make	VERB
ejpam-6997	715	15	in	in	ADP
ejpam-6997	715	16	theorem	theorem	ADJ
ejpam-6997	715	17	3.23	3.23	NUM
ejpam-6997	715	18	and	and	CCONJ
ejpam-6997	715	19	corollary	corollary	ADJ
ejpam-6997	715	20	3.24	3.24	NUM
ejpam-6997	715	21	.	.	PUNCT
ejpam-6997	716	1	in	in	ADP
ejpam-6997	716	2	summary	summary	NOUN
ejpam-6997	716	3	,	,	PUNCT
ejpam-6997	716	4	it	it	PRON
ejpam-6997	716	5	can	can	AUX
ejpam-6997	716	6	be	be	AUX
ejpam-6997	716	7	observed	observe	VERB
ejpam-6997	716	8	that	that	SCONJ
ejpam-6997	716	9	,	,	PUNCT
ejpam-6997	716	10	in	in	ADP
ejpam-6997	716	11	contrast	contrast	NOUN
ejpam-6997	716	12	to	to	ADP
ejpam-6997	716	13	the	the	DET
ejpam-6997	716	14	rs	rs	NOUN
ejpam-6997	716	15	models	model	NOUN
ejpam-6997	716	16	discussed	discuss	VERB
ejpam-6997	716	17	by	by	ADP
ejpam-6997	716	18	[	[	X
ejpam-6997	716	19	46	46	NUM
ejpam-6997	716	20	]	]	PUNCT
ejpam-6997	716	21	,	,	PUNCT
ejpam-6997	716	22	the	the	DET
ejpam-6997	716	23	models	model	NOUN
ejpam-6997	716	24	suggested	suggest	VERB
ejpam-6997	716	25	in	in	ADP
ejpam-6997	716	26	sec	sec	PROPN
ejpam-6997	716	27	.	.	PROPN
ejpam-6997	716	28	3.2	3.2	NUM
ejpam-6997	716	29	improve	improve	VERB
ejpam-6997	716	30	the	the	DET
ejpam-6997	716	31	accuracy	accuracy	NOUN
ejpam-6997	716	32	measures	measure	NOUN
ejpam-6997	716	33	of	of	ADP
ejpam-6997	716	34	subsets	subset	NOUN
ejpam-6997	716	35	by	by	ADP
ejpam-6997	716	36	strengthening	strengthen	VERB
ejpam-6997	716	37	the	the	DET
ejpam-6997	716	38	lw	lw	NOUN
ejpam-6997	716	39	,	,	PUNCT
ejpam-6997	716	40	and	and	CCONJ
ejpam-6997	716	41	up	up	ADP
ejpam-6997	716	42	-	-	PUNCT
ejpam-6997	716	43	ap	ap	NOUN
ejpam-6997	716	44	.	.	PUNCT
ejpam-6997	717	1	furthermore	furthermore	ADV
ejpam-6997	717	2	,	,	PUNCT
ejpam-6997	717	3	the	the	DET
ejpam-6997	717	4	rs	rs	ADJ
ejpam-6997	717	5	paradigms	paradigm	NOUN
ejpam-6997	717	6	shown	show	VERB
ejpam-6997	717	7	in	in	ADP
ejpam-6997	717	8	sec	sec	PROPN
ejpam-6997	717	9	.	.	PROPN
ejpam-6997	717	10	3.2	3.2	NUM
ejpam-6997	717	11	produce	produce	VERB
ejpam-6997	717	12	the	the	DET
ejpam-6997	717	13	same	same	ADJ
ejpam-6997	717	14	ap	ap	PROPN
ejpam-6997	717	15	spaces	space	VERB
ejpam-6997	717	16	as	as	ADP
ejpam-6997	717	17	those	those	PRON
ejpam-6997	717	18	shown	show	VERB
ejpam-6997	717	19	in	in	ADP
ejpam-6997	717	20	sec	sec	PROPN
ejpam-6997	717	21	.	.	PROPN
ejpam-6997	717	22	4	4	NUM
ejpam-6997	717	23	due	due	ADP
ejpam-6997	717	24	to	to	ADP
ejpam-6997	717	25	the	the	DET
ejpam-6997	717	26	topological	topological	ADJ
ejpam-6997	717	27	technique	technique	NOUN
ejpam-6997	717	28	.	.	PUNCT
ejpam-6997	718	1	the	the	DET
ejpam-6997	718	2	computations	computation	NOUN
ejpam-6997	718	3	from	from	ADP
ejpam-6997	718	4	the	the	DET
ejpam-6997	718	5	four	four	NUM
ejpam-6997	718	6	rs	rs	NOUN
ejpam-6997	718	7	models	model	NOUN
ejpam-6997	718	8	discussed	discuss	VERB
ejpam-6997	718	9	above	above	ADV
ejpam-6997	718	10	will	will	AUX
ejpam-6997	718	11	be	be	AUX
ejpam-6997	718	12	compared	compare	VERB
ejpam-6997	718	13	.	.	PUNCT
ejpam-6997	719	1	we	we	PRON
ejpam-6997	719	2	discovered	discover	VERB
ejpam-6997	719	3	that	that	SCONJ
ejpam-6997	719	4	the	the	DET
ejpam-6997	719	5	greatest	great	ADJ
ejpam-6997	719	6	estimates	estimate	NOUN
ejpam-6997	719	7	(	(	PUNCT
ejpam-6997	719	8	lw	lw	NOUN
ejpam-6997	719	9	and	and	CCONJ
ejpam-6997	719	10	up	up	ADV
ejpam-6997	719	11	)	)	PUNCT
ejpam-6997	719	12	are	be	AUX
ejpam-6997	719	13	produced	produce	VERB
ejpam-6997	719	14	by	by	ADP
ejpam-6997	719	15	the	the	DET
ejpam-6997	719	16	model	model	NOUN
ejpam-6997	719	17	shown	show	VERB
ejpam-6997	719	18	in	in	ADP
ejpam-6997	719	19	sec	sec	PROPN
ejpam-6997	719	20	.	.	PROPN
ejpam-6997	719	21	3.2	3.2	NUM
ejpam-6997	719	22	.	.	PUNCT
ejpam-6997	720	1	it	it	PRON
ejpam-6997	720	2	is	be	AUX
ejpam-6997	720	3	important	important	ADJ
ejpam-6997	720	4	to	to	PART
ejpam-6997	720	5	note	note	VERB
ejpam-6997	720	6	that	that	DET
ejpam-6997	720	7	model	model	NOUN
ejpam-6997	720	8	3.1	3.1	NUM
ejpam-6997	720	9	has	have	VERB
ejpam-6997	720	10	certain	certain	ADJ
ejpam-6997	720	11	shortcomings	shortcoming	NOUN
ejpam-6997	720	12	,	,	PUNCT
ejpam-6997	720	13	including	include	VERB
ejpam-6997	720	14	the	the	DET
ejpam-6997	720	15	inability	inability	NOUN
ejpam-6997	720	16	to	to	PART
ejpam-6997	720	17	preserve	preserve	VERB
ejpam-6997	720	18	the	the	DET
ejpam-6997	720	19	essential	essential	ADJ
ejpam-6997	720	20	elements	element	NOUN
ejpam-6997	720	21	of	of	ADP
ejpam-6997	720	22	ap	ap	PROPN
ejpam-6997	720	23	procedures	procedure	NOUN
ejpam-6997	720	24	and	and	CCONJ
ejpam-6997	720	25	excessive	excessive	ADJ
ejpam-6997	720	26	accuracy	accuracy	NOUN
ejpam-6997	720	27	of	of	ADP
ejpam-6997	720	28	measurements	measurement	NOUN
ejpam-6997	720	29	.	.	PUNCT
ejpam-6997	721	1	in	in	ADP
ejpam-6997	721	2	the	the	DET
ejpam-6997	721	3	remaining	remain	VERB
ejpam-6997	721	4	portion	portion	NOUN
ejpam-6997	721	5	of	of	ADP
ejpam-6997	721	6	this	this	DET
ejpam-6997	721	7	part	part	NOUN
ejpam-6997	721	8	,	,	PUNCT
ejpam-6997	721	9	we	we	PRON
ejpam-6997	721	10	determine	determine	VERB
ejpam-6997	721	11	the	the	DET
ejpam-6997	721	12	primary	primary	ADJ
ejpam-6997	721	13	symptoms	symptom	NOUN
ejpam-6997	721	14	for	for	ADP
ejpam-6997	721	15	determining	determine	VERB
ejpam-6997	721	16	whether	whether	SCONJ
ejpam-6997	721	17	a	a	DET
ejpam-6997	721	18	patient	patient	NOUN
ejpam-6997	721	19	has	have	VERB
ejpam-6997	721	20	heart	heart	NOUN
ejpam-6997	721	21	failure	failure	NOUN
ejpam-6997	721	22	disease	disease	NOUN
ejpam-6997	721	23	by	by	ADP
ejpam-6997	721	24	using	use	VERB
ejpam-6997	721	25	the	the	DET
ejpam-6997	721	26	topological	topological	ADJ
ejpam-6997	721	27	spaces	space	NOUN
ejpam-6997	721	28	that	that	PRON
ejpam-6997	721	29	were	be	AUX
ejpam-6997	721	30	previously	previously	ADV
ejpam-6997	721	31	created	create	VERB
ejpam-6997	721	32	using	use	VERB
ejpam-6997	721	33	grills	grill	NOUN
ejpam-6997	721	34	and	and	CCONJ
ejpam-6997	721	35	cardinality	cardinality	PROPN
ejpam-6997	721	36	nbds	nbds	NOUN
ejpam-6997	721	37	.	.	PUNCT
ejpam-6997	722	1	the	the	DET
ejpam-6997	722	2	initial	initial	ADJ
ejpam-6997	722	3	topology	topology	NOUN
ejpam-6997	722	4	is	be	AUX
ejpam-6997	722	5	:	:	PUNCT
ejpam-6997	722	6	a.	a.	NOUN
ejpam-6997	722	7	a.	a.	PROPN
ejpam-6997	722	8	azzam	azzam	PROPN
ejpam-6997	722	9	,	,	PUNCT
ejpam-6997	722	10	m.	m.	NOUN
ejpam-6997	722	11	aldawood	aldawood	PROPN
ejpam-6997	722	12	,	,	PUNCT
ejpam-6997	722	13	b.	b.	PROPN
ejpam-6997	722	14	alreshidi	alreshidi	PROPN
ejpam-6997	722	15	/	/	SYM
ejpam-6997	722	16	eur	eur	PROPN
ejpam-6997	722	17	.	.	PUNCT
ejpam-6997	723	1	j.	j.	PROPN
ejpam-6997	723	2	pure	pure	PROPN
ejpam-6997	723	3	appl	appl	PROPN
ejpam-6997	723	4	.	.	PROPN
ejpam-6997	723	5	math	math	PROPN
ejpam-6997	723	6	,	,	PUNCT
ejpam-6997	723	7	18	18	NUM
ejpam-6997	723	8	(	(	PUNCT
ejpam-6997	723	9	4	4	NUM
ejpam-6997	723	10	)	)	PUNCT
ejpam-6997	723	11	(	(	PUNCT
ejpam-6997	723	12	2025	2025	NUM
ejpam-6997	723	13	)	)	PUNCT
ejpam-6997	723	14	,	,	PUNCT
ejpam-6997	723	15	6997	6997	NUM
ejpam-6997	723	16	27	27	NUM
ejpam-6997	723	17	of	of	ADP
ejpam-6997	723	18	31	31	NUM
ejpam-6997	723	19	gψcϱ	gψcϱ	NOUN
ejpam-6997	723	20	=	=	SYM
ejpam-6997	723	21	{	{	PUNCT
ejpam-6997	723	22	ϕ,ℵ	ϕ,ℵ	NOUN
ejpam-6997	723	23	,	,	PUNCT
ejpam-6997	723	24	{	{	PUNCT
ejpam-6997	723	25	p1	p1	NOUN
ejpam-6997	723	26	,	,	PUNCT
ejpam-6997	723	27	p5	p5	PROPN
ejpam-6997	723	28	}	}	PUNCT
ejpam-6997	723	29	,	,	PUNCT
ejpam-6997	723	30	{	{	PUNCT
ejpam-6997	723	31	p2	p2	NOUN
ejpam-6997	723	32	,	,	PUNCT
ejpam-6997	723	33	p4	p4	ADJ
ejpam-6997	723	34	,	,	PUNCT
ejpam-6997	723	35	p6	p6	PROPN
ejpam-6997	723	36	}	}	PUNCT
ejpam-6997	723	37	,	,	PUNCT
ejpam-6997	723	38	{	{	PUNCT
ejpam-6997	723	39	p3	p3	PROPN
ejpam-6997	723	40	,	,	PUNCT
ejpam-6997	723	41	p7	p7	PROPN
ejpam-6997	723	42	,	,	PUNCT
ejpam-6997	723	43	p8	p8	PROPN
ejpam-6997	723	44	}	}	PUNCT
ejpam-6997	723	45	,	,	PUNCT
ejpam-6997	723	46	{	{	PUNCT
ejpam-6997	723	47	p1	p1	NOUN
ejpam-6997	723	48	,	,	PUNCT
ejpam-6997	723	49	p2	p2	NOUN
ejpam-6997	723	50	,	,	PUNCT
ejpam-6997	723	51	p4	p4	ADJ
ejpam-6997	723	52	,	,	PUNCT
ejpam-6997	723	53	p5	p5	ADJ
ejpam-6997	723	54	,	,	PUNCT
ejpam-6997	723	55	p6	p6	PROPN
ejpam-6997	723	56	}	}	PUNCT
ejpam-6997	723	57	,	,	PUNCT
ejpam-6997	723	58	{	{	PUNCT
ejpam-6997	723	59	p1	p1	NOUN
ejpam-6997	723	60	,	,	PUNCT
ejpam-6997	723	61	p3	p3	PROPN
ejpam-6997	723	62	,	,	PUNCT
ejpam-6997	723	63	p5	p5	ADJ
ejpam-6997	723	64	,	,	PUNCT
ejpam-6997	723	65	p7	p7	ADJ
ejpam-6997	723	66	,	,	PUNCT
ejpam-6997	723	67	p8	p8	PROPN
ejpam-6997	723	68	}	}	PUNCT
ejpam-6997	723	69	,	,	PUNCT
ejpam-6997	723	70	{	{	PUNCT
ejpam-6997	723	71	p2	p2	NOUN
ejpam-6997	723	72	,	,	PUNCT
ejpam-6997	723	73	p3	p3	NOUN
ejpam-6997	723	74	,	,	PUNCT
ejpam-6997	723	75	p4	p4	ADJ
ejpam-6997	723	76	,	,	PUNCT
ejpam-6997	723	77	p6	p6	PROPN
ejpam-6997	723	78	,	,	PUNCT
ejpam-6997	723	79	p7	p7	PROPN
ejpam-6997	723	80	,	,	PUNCT
ejpam-6997	723	81	p8	p8	PROPN
ejpam-6997	723	82	}	}	PUNCT
ejpam-6997	723	83	}	}	PUNCT
ejpam-6997	723	84	.	.	PUNCT
ejpam-6997	724	1	next	next	ADV
ejpam-6997	724	2	,	,	PUNCT
ejpam-6997	724	3	we	we	PRON
ejpam-6997	724	4	will	will	AUX
ejpam-6997	724	5	contrast	contrast	VERB
ejpam-6997	724	6	the	the	DET
ejpam-6997	724	7	topologies	topology	NOUN
ejpam-6997	724	8	produced	produce	VERB
ejpam-6997	724	9	from	from	ADP
ejpam-6997	724	10	the	the	DET
ejpam-6997	724	11	same	same	ADJ
ejpam-6997	724	12	database	database	NOUN
ejpam-6997	724	13	after	after	ADP
ejpam-6997	724	14	eliminating	eliminate	VERB
ejpam-6997	724	15	each	each	DET
ejpam-6997	724	16	symptom	symptom	NOUN
ejpam-6997	724	17	separately	separately	ADV
ejpam-6997	724	18	with	with	ADP
ejpam-6997	724	19	the	the	DET
ejpam-6997	724	20	initial	initial	ADJ
ejpam-6997	724	21	topology	topology	NOUN
ejpam-6997	724	22	created	create	VERB
ejpam-6997	724	23	from	from	ADP
ejpam-6997	724	24	the	the	DET
ejpam-6997	724	25	patient	patient	ADJ
ejpam-6997	724	26	information	information	NOUN
ejpam-6997	724	27	system	system	NOUN
ejpam-6997	724	28	shown	show	VERB
ejpam-6997	724	29	in	in	ADP
ejpam-6997	724	30	table	table	NOUN
ejpam-6997	724	31	6	6	NUM
ejpam-6997	724	32	.	.	PUNCT
ejpam-6997	725	1	this	this	DET
ejpam-6997	725	2	procedure	procedure	NOUN
ejpam-6997	725	3	will	will	AUX
ejpam-6997	725	4	be	be	AUX
ejpam-6997	725	5	carried	carry	VERB
ejpam-6997	725	6	out	out	ADP
ejpam-6997	725	7	once	once	ADV
ejpam-6997	725	8	again	again	ADV
ejpam-6997	725	9	for	for	ADP
ejpam-6997	725	10	every	every	DET
ejpam-6997	725	11	symptom	symptom	NOUN
ejpam-6997	725	12	.	.	PUNCT
ejpam-6997	726	1	(	(	PUNCT
ejpam-6997	726	2	1	1	X
ejpam-6997	726	3	)	)	PUNCT
ejpam-6997	726	4	if	if	SCONJ
ejpam-6997	726	5	the	the	DET
ejpam-6997	726	6	symptom	symptom	NOUN
ejpam-6997	726	7	”	"	PUNCT
ejpam-6997	726	8	breathlessness	breathlessness	NOUN
ejpam-6997	726	9	”	"	PUNCT
ejpam-6997	726	10	is	be	AUX
ejpam-6997	726	11	removed	remove	VERB
ejpam-6997	726	12	from	from	ADP
ejpam-6997	726	13	the	the	DET
ejpam-6997	726	14	input	input	NOUN
ejpam-6997	726	15	attributes	attribute	VERB
ejpam-6997	726	16	,	,	PUNCT
ejpam-6997	726	17	then	then	ADV
ejpam-6997	726	18	γbr	γbr	NOUN
ejpam-6997	726	19	=	=	PRON
ejpam-6997	726	20	{	{	PUNCT
ejpam-6997	726	21	(	(	PUNCT
ejpam-6997	726	22	p1	p1	PROPN
ejpam-6997	726	23	,	,	PUNCT
ejpam-6997	726	24	p1	p1	PROPN
ejpam-6997	726	25	)	)	PUNCT
ejpam-6997	726	26	,	,	PUNCT
ejpam-6997	726	27	(	(	PUNCT
ejpam-6997	726	28	p3	p3	PROPN
ejpam-6997	726	29	,	,	PUNCT
ejpam-6997	726	30	p3	p3	PROPN
ejpam-6997	726	31	)	)	PUNCT
ejpam-6997	726	32	,	,	PUNCT
ejpam-6997	726	33	(	(	PUNCT
ejpam-6997	726	34	p7	p7	ADJ
ejpam-6997	726	35	,	,	PUNCT
ejpam-6997	726	36	p7	p7	ADJ
ejpam-6997	726	37	)	)	PUNCT
ejpam-6997	726	38	,	,	PUNCT
ejpam-6997	726	39	(	(	PUNCT
ejpam-6997	726	40	p8	p8	PROPN
ejpam-6997	726	41	,	,	PUNCT
ejpam-6997	726	42	p8	p8	PROPN
ejpam-6997	726	43	)	)	PUNCT
ejpam-6997	726	44	,	,	PUNCT
ejpam-6997	726	45	(	(	PUNCT
ejpam-6997	726	46	p1	p1	NOUN
ejpam-6997	726	47	,	,	PUNCT
ejpam-6997	726	48	p3	p3	PROPN
ejpam-6997	726	49	)	)	PUNCT
ejpam-6997	726	50	,	,	PUNCT
ejpam-6997	726	51	(	(	PUNCT
ejpam-6997	726	52	p3	p3	PROPN
ejpam-6997	726	53	,	,	PUNCT
ejpam-6997	726	54	p1	p1	PROPN
ejpam-6997	726	55	)	)	PUNCT
ejpam-6997	726	56	,	,	PUNCT
ejpam-6997	726	57	(	(	PUNCT
ejpam-6997	726	58	p1	p1	NOUN
ejpam-6997	726	59	,	,	PUNCT
ejpam-6997	726	60	p7	p7	NOUN
ejpam-6997	726	61	)	)	PUNCT
ejpam-6997	726	62	,	,	PUNCT
ejpam-6997	726	63	(	(	PUNCT
ejpam-6997	726	64	p7	p7	PROPN
ejpam-6997	726	65	,	,	PUNCT
ejpam-6997	726	66	p1	p1	PROPN
ejpam-6997	726	67	)	)	PUNCT
ejpam-6997	726	68	,	,	PUNCT
ejpam-6997	726	69	(	(	PUNCT
ejpam-6997	726	70	p3	p3	PROPN
ejpam-6997	726	71	,	,	PUNCT
ejpam-6997	726	72	p7	p7	PROPN
ejpam-6997	726	73	)	)	PUNCT
ejpam-6997	726	74	,	,	PUNCT
ejpam-6997	726	75	(	(	PUNCT
ejpam-6997	726	76	p7	p7	PROPN
ejpam-6997	726	77	,	,	PUNCT
ejpam-6997	726	78	p3	p3	PROPN
ejpam-6997	726	79	)	)	PUNCT
ejpam-6997	726	80	,	,	PUNCT
ejpam-6997	726	81	(	(	PUNCT
ejpam-6997	726	82	p3	p3	PROPN
ejpam-6997	726	83	,	,	PUNCT
ejpam-6997	726	84	p8	p8	PROPN
ejpam-6997	726	85	)	)	PUNCT
ejpam-6997	726	86	,	,	PUNCT
ejpam-6997	726	87	(	(	PUNCT
ejpam-6997	726	88	p8	p8	PROPN
ejpam-6997	726	89	,	,	PUNCT
ejpam-6997	726	90	p3	p3	PROPN
ejpam-6997	726	91	)	)	PUNCT
ejpam-6997	726	92	,	,	PUNCT
ejpam-6997	726	93	(	(	PUNCT
ejpam-6997	726	94	p7	p7	PROPN
ejpam-6997	726	95	,	,	PUNCT
ejpam-6997	726	96	p8	p8	PROPN
ejpam-6997	726	97	)	)	PUNCT
ejpam-6997	726	98	,	,	PUNCT
ejpam-6997	726	99	(	(	PUNCT
ejpam-6997	726	100	p8	p8	PROPN
ejpam-6997	726	101	,	,	PUNCT
ejpam-6997	726	102	p7	p7	ADJ
ejpam-6997	726	103	)	)	PUNCT
ejpam-6997	726	104	}	}	PUNCT
ejpam-6997	726	105	.	.	PUNCT
ejpam-6997	727	1	it	it	PRON
ejpam-6997	727	2	is	be	AUX
ejpam-6997	727	3	clear	clear	ADJ
ejpam-6997	727	4	that	that	SCONJ
ejpam-6997	727	5	gψcϱ	gψcϱ	NOUN
ejpam-6997	727	6	-br	-br	ADP
ejpam-6997	727	7	̸=	̸=	PROPN
ejpam-6997	727	8	gψcϱ	gψcϱ	NOUN
ejpam-6997	727	9	.	.	PUNCT
ejpam-6997	728	1	(	(	PUNCT
ejpam-6997	728	2	2	2	X
ejpam-6997	728	3	)	)	PUNCT
ejpam-6997	728	4	if	if	SCONJ
ejpam-6997	728	5	the	the	DET
ejpam-6997	728	6	symptom	symptom	NOUN
ejpam-6997	728	7	”	"	PUNCT
ejpam-6997	728	8	orthopnea	orthopnea	PROPN
ejpam-6997	728	9	”	"	PUNCT
ejpam-6997	728	10	is	be	AUX
ejpam-6997	728	11	removed	remove	VERB
ejpam-6997	728	12	from	from	ADP
ejpam-6997	728	13	the	the	DET
ejpam-6997	728	14	input	input	NOUN
ejpam-6997	728	15	attributes	attribute	VERB
ejpam-6997	728	16	,	,	PUNCT
ejpam-6997	728	17	then	then	ADV
ejpam-6997	728	18	γor	γor	PROPN
ejpam-6997	728	19	=	=	SYM
ejpam-6997	728	20	γ	γ	X
ejpam-6997	728	21	.	.	PUNCT
ejpam-6997	728	22	consequently	consequently	ADV
ejpam-6997	728	23	,	,	PUNCT
ejpam-6997	728	24	gψcϱ	gψcϱ	NOUN
ejpam-6997	728	25	-br	-br	NOUN
ejpam-6997	728	26	=	=	SYM
ejpam-6997	728	27	gψcϱ	gψcϱ	NOUN
ejpam-6997	728	28	.	.	PUNCT
ejpam-6997	729	1	(	(	PUNCT
ejpam-6997	729	2	3	3	X
ejpam-6997	729	3	)	)	PUNCT
ejpam-6997	729	4	if	if	SCONJ
ejpam-6997	729	5	the	the	DET
ejpam-6997	729	6	symptom	symptom	NOUN
ejpam-6997	729	7	”	"	PUNCT
ejpam-6997	729	8	paroxysmal	paroxysmal	ADJ
ejpam-6997	729	9	nocturnal	nocturnal	ADJ
ejpam-6997	729	10	dyspnea	dyspnea	NOUN
ejpam-6997	729	11	”	"	PUNCT
ejpam-6997	729	12	is	be	AUX
ejpam-6997	729	13	removed	remove	VERB
ejpam-6997	729	14	from	from	ADP
ejpam-6997	729	15	the	the	DET
ejpam-6997	729	16	input	input	NOUN
ejpam-6997	729	17	attributes	attribute	VERB
ejpam-6997	729	18	,	,	PUNCT
ejpam-6997	729	19	then	then	ADV
ejpam-6997	729	20	γpnd	γpnd	NOUN
ejpam-6997	729	21	=	=	SYM
ejpam-6997	729	22	γ	γ	X
ejpam-6997	729	23	.	.	PUNCT
ejpam-6997	729	24	consequently	consequently	ADV
ejpam-6997	729	25	,	,	PUNCT
ejpam-6997	729	26	gψcϱ	gψcϱ	NOUN
ejpam-6997	729	27	-pnd	-pnd	PUNCT
ejpam-6997	729	28	=	=	SYM
ejpam-6997	729	29	gψcϱ	gψcϱ	NOUN
ejpam-6997	729	30	.	.	PUNCT
ejpam-6997	730	1	(	(	PUNCT
ejpam-6997	730	2	4	4	X
ejpam-6997	730	3	)	)	PUNCT
ejpam-6997	730	4	if	if	SCONJ
ejpam-6997	730	5	the	the	DET
ejpam-6997	730	6	symptom	symptom	NOUN
ejpam-6997	730	7	”	"	PUNCT
ejpam-6997	730	8	impaired	impaired	ADJ
ejpam-6997	730	9	exercise	exercise	NOUN
ejpam-6997	730	10	tolerance	tolerance	NOUN
ejpam-6997	730	11	”	"	PUNCT
ejpam-6997	730	12	is	be	AUX
ejpam-6997	730	13	removed	remove	VERB
ejpam-6997	730	14	from	from	ADP
ejpam-6997	730	15	the	the	DET
ejpam-6997	730	16	input	input	NOUN
ejpam-6997	730	17	attributes	attribute	VERB
ejpam-6997	730	18	,	,	PUNCT
ejpam-6997	730	19	then	then	ADV
ejpam-6997	730	20	γiet	γiet	PROPN
ejpam-6997	730	21	̸=	̸=	PROPN
ejpam-6997	730	22	γ	γ	NOUN
ejpam-6997	730	23	.	.	PUNCT
ejpam-6997	730	24	consequently	consequently	ADV
ejpam-6997	730	25	,	,	PUNCT
ejpam-6997	730	26	gψcϱ	gψcϱ	NOUN
ejpam-6997	730	27	-pnd	-pnd	PUNCT
ejpam-6997	730	28	̸=	̸=	PROPN
ejpam-6997	730	29	gψcϱ	gψcϱ	NOUN
ejpam-6997	730	30	.	.	PUNCT
ejpam-6997	731	1	(	(	PUNCT
ejpam-6997	731	2	5	5	X
ejpam-6997	731	3	)	)	PUNCT
ejpam-6997	731	4	if	if	SCONJ
ejpam-6997	731	5	the	the	DET
ejpam-6997	731	6	symptom	symptom	NOUN
ejpam-6997	731	7	”	"	PUNCT
ejpam-6997	731	8	ankle	ankle	NOUN
ejpam-6997	731	9	swelling	swelling	NOUN
ejpam-6997	731	10	”	"	PUNCT
ejpam-6997	731	11	is	be	AUX
ejpam-6997	731	12	removed	remove	VERB
ejpam-6997	731	13	from	from	ADP
ejpam-6997	731	14	the	the	DET
ejpam-6997	731	15	input	input	NOUN
ejpam-6997	731	16	attributes	attribute	VERB
ejpam-6997	731	17	,	,	PUNCT
ejpam-6997	731	18	then	then	ADV
ejpam-6997	731	19	γas	γa	VERB
ejpam-6997	731	20	̸=	̸=	PROPN
ejpam-6997	731	21	γ	γ	NOUN
ejpam-6997	731	22	.	.	PUNCT
ejpam-6997	732	1	consequently	consequently	ADV
ejpam-6997	732	2	,	,	PUNCT
ejpam-6997	732	3	gψcϱ	gψcϱ	NOUN
ejpam-6997	732	4	-pnd	-pnd	SYM
ejpam-6997	732	5	̸=	̸=	PROPN
ejpam-6997	732	6	gψcϱ	gψcϱ	NOUN
ejpam-6997	732	7	.	.	PUNCT
ejpam-6997	733	1	the	the	DET
ejpam-6997	733	2	computations	computation	NOUN
ejpam-6997	733	3	indicate	indicate	VERB
ejpam-6997	733	4	that	that	SCONJ
ejpam-6997	733	5	the	the	DET
ejpam-6997	733	6	main	main	ADJ
ejpam-6997	733	7	symptoms	symptom	NOUN
ejpam-6997	733	8	are	be	AUX
ejpam-6997	733	9	br	br	PROPN
ejpam-6997	733	10	,	,	PUNCT
ejpam-6997	733	11	iet	iet	PROPN
ejpam-6997	733	12	,	,	PUNCT
ejpam-6997	733	13	and	and	CCONJ
ejpam-6997	733	14	as	as	SCONJ
ejpam-6997	733	15	.	.	PROPN
ejpam-6997	733	16	stated	state	VERB
ejpam-6997	733	17	differently	differently	ADV
ejpam-6997	733	18	,	,	PUNCT
ejpam-6997	733	19	these	these	DET
ejpam-6997	733	20	symptoms	symptom	NOUN
ejpam-6997	733	21	are	be	AUX
ejpam-6997	733	22	recognized	recognize	VERB
ejpam-6997	733	23	as	as	ADP
ejpam-6997	733	24	the	the	DET
ejpam-6997	733	25	primary	primary	ADJ
ejpam-6997	733	26	markers	marker	NOUN
ejpam-6997	733	27	for	for	ADP
ejpam-6997	733	28	identifying	identify	VERB
ejpam-6997	733	29	if	if	SCONJ
ejpam-6997	733	30	a	a	DET
ejpam-6997	733	31	patient	patient	NOUN
ejpam-6997	733	32	has	have	VERB
ejpam-6997	733	33	heart	heart	NOUN
ejpam-6997	733	34	failure	failure	NOUN
ejpam-6997	733	35	disease	disease	NOUN
ejpam-6997	733	36	.	.	PUNCT
ejpam-6997	734	1	on	on	ADP
ejpam-6997	734	2	the	the	DET
ejpam-6997	734	3	other	other	ADJ
ejpam-6997	734	4	hand	hand	NOUN
ejpam-6997	734	5	,	,	PUNCT
ejpam-6997	734	6	eliminating	eliminate	VERB
ejpam-6997	734	7	the	the	PRON
ejpam-6997	734	8	or	or	CCONJ
ejpam-6997	734	9	and	and	CCONJ
ejpam-6997	734	10	br	br	PROPN
ejpam-6997	734	11	symptom	symptom	NOUN
ejpam-6997	734	12	does	do	AUX
ejpam-6997	734	13	not	not	PART
ejpam-6997	734	14	change	change	VERB
ejpam-6997	734	15	the	the	DET
ejpam-6997	734	16	topology	topology	NOUN
ejpam-6997	734	17	’s	’s	PART
ejpam-6997	734	18	structure	structure	NOUN
ejpam-6997	734	19	;	;	PUNCT
ejpam-6997	734	20	as	as	ADP
ejpam-6997	734	21	a	a	DET
ejpam-6997	734	22	result	result	NOUN
ejpam-6997	734	23	,	,	PUNCT
ejpam-6997	734	24	it	it	PRON
ejpam-6997	734	25	can	can	AUX
ejpam-6997	734	26	be	be	AUX
ejpam-6997	734	27	skipped	skip	VERB
ejpam-6997	734	28	during	during	ADP
ejpam-6997	734	29	tests	test	NOUN
ejpam-6997	734	30	.	.	PUNCT
ejpam-6997	735	1	6	6	X
ejpam-6997	735	2	.	.	X
ejpam-6997	735	3	conclusion	conclusion	NOUN
ejpam-6997	735	4	and	and	CCONJ
ejpam-6997	735	5	future	future	ADJ
ejpam-6997	735	6	work	work	NOUN
ejpam-6997	735	7	rsst	rsst	NOUN
ejpam-6997	735	8	,	,	PUNCT
ejpam-6997	735	9	proposed	propose	VERB
ejpam-6997	735	10	by	by	ADP
ejpam-6997	735	11	pawlak	pawlak	ADJ
ejpam-6997	735	12	in	in	ADP
ejpam-6997	735	13	1982	1982	NUM
ejpam-6997	735	14	,	,	PUNCT
ejpam-6997	735	15	is	be	AUX
ejpam-6997	735	16	a	a	DET
ejpam-6997	735	17	powerful	powerful	ADJ
ejpam-6997	735	18	tool	tool	NOUN
ejpam-6997	735	19	for	for	ADP
ejpam-6997	735	20	handling	handle	VERB
ejpam-6997	735	21	inaccurate	inaccurate	ADJ
ejpam-6997	735	22	and	and	CCONJ
ejpam-6997	735	23	confusing	confusing	ADJ
ejpam-6997	735	24	information	information	NOUN
ejpam-6997	735	25	.	.	PUNCT
ejpam-6997	736	1	the	the	DET
ejpam-6997	736	2	capacity	capacity	NOUN
ejpam-6997	736	3	of	of	ADP
ejpam-6997	736	4	rst	rst	PROPN
ejpam-6997	736	5	to	to	PART
ejpam-6997	736	6	represent	represent	VERB
ejpam-6997	736	7	data	datum	NOUN
ejpam-6997	736	8	using	use	VERB
ejpam-6997	736	9	granular	granular	ADJ
ejpam-6997	736	10	structure	structure	NOUN
ejpam-6997	736	11	without	without	ADP
ejpam-6997	736	12	having	have	VERB
ejpam-6997	736	13	any	any	DET
ejpam-6997	736	14	a	a	DET
ejpam-6997	736	15	priori	priori	ADJ
ejpam-6997	736	16	knowledge	knowledge	NOUN
ejpam-6997	736	17	outside	outside	ADP
ejpam-6997	736	18	of	of	ADP
ejpam-6997	736	19	the	the	DET
ejpam-6997	736	20	data	datum	NOUN
ejpam-6997	736	21	set	set	VERB
ejpam-6997	736	22	itself	itself	PRON
ejpam-6997	736	23	is	be	AUX
ejpam-6997	736	24	one	one	NUM
ejpam-6997	736	25	of	of	ADP
ejpam-6997	736	26	its	its	PRON
ejpam-6997	736	27	main	main	ADJ
ejpam-6997	736	28	advantages	advantage	NOUN
ejpam-6997	736	29	.	.	PUNCT
ejpam-6997	737	1	as	as	SCONJ
ejpam-6997	737	2	is	be	AUX
ejpam-6997	737	3	well	well	ADV
ejpam-6997	737	4	known	know	VERB
ejpam-6997	737	5	,	,	PUNCT
ejpam-6997	737	6	neighborhood	neighborhood	NOUN
ejpam-6997	737	7	systems	system	NOUN
ejpam-6997	737	8	modeled	model	VERB
ejpam-6997	737	9	after	after	SCONJ
ejpam-6997	737	10	arbitrary	arbitrary	ADJ
ejpam-6997	737	11	relations	relation	NOUN
ejpam-6997	737	12	have	have	AUX
ejpam-6997	737	13	been	be	AUX
ejpam-6997	737	14	used	use	VERB
ejpam-6997	737	15	to	to	PART
ejpam-6997	737	16	update	update	VERB
ejpam-6997	737	17	the	the	DET
ejpam-6997	737	18	detail	detail	NOUN
ejpam-6997	737	19	that	that	PRON
ejpam-6997	737	20	equivalency	equivalency	NOUN
ejpam-6997	737	21	classes	class	NOUN
ejpam-6997	737	22	reflect	reflect	VERB
ejpam-6997	737	23	.	.	PUNCT
ejpam-6997	738	1	this	this	PRON
ejpam-6997	738	2	helps	help	VERB
ejpam-6997	738	3	to	to	PART
ejpam-6997	738	4	eliminate	eliminate	VERB
ejpam-6997	738	5	a	a	DET
ejpam-6997	738	6	rigid	rigid	ADJ
ejpam-6997	738	7	constraint	constraint	NOUN
ejpam-6997	738	8	of	of	ADP
ejpam-6997	738	9	an	an	DET
ejpam-6997	738	10	equivalence	equivalence	NOUN
ejpam-6997	738	11	relation	relation	NOUN
ejpam-6997	738	12	.	.	PUNCT
ejpam-6997	739	1	recent	recent	ADJ
ejpam-6997	739	2	models	model	NOUN
ejpam-6997	739	3	have	have	AUX
ejpam-6997	739	4	failed	fail	VERB
ejpam-6997	739	5	to	to	PART
ejpam-6997	739	6	maintain	maintain	VERB
ejpam-6997	739	7	the	the	DET
ejpam-6997	739	8	original	original	ADJ
ejpam-6997	739	9	paradigm	paradigm	NOUN
ejpam-6997	739	10	’s	’s	PART
ejpam-6997	739	11	major	major	ADJ
ejpam-6997	739	12	elements	element	NOUN
ejpam-6997	739	13	and	and	CCONJ
ejpam-6997	739	14	have	have	AUX
ejpam-6997	739	15	flawed	flaw	VERB
ejpam-6997	739	16	formulas	formula	NOUN
ejpam-6997	739	17	for	for	ADP
ejpam-6997	739	18	measuring	measure	VERB
ejpam-6997	739	19	proven	prove	VERB
ejpam-6997	739	20	and	and	CCONJ
ejpam-6997	739	21	potential	potential	ADJ
ejpam-6997	739	22	knowledge	knowledge	NOUN
ejpam-6997	739	23	.	.	PUNCT
ejpam-6997	740	1	in	in	ADP
ejpam-6997	740	2	this	this	DET
ejpam-6997	740	3	work	work	NOUN
ejpam-6997	740	4	,	,	PUNCT
ejpam-6997	740	5	we	we	PRON
ejpam-6997	740	6	provide	provide	VERB
ejpam-6997	740	7	new	new	ADJ
ejpam-6997	740	8	kinds	kind	NOUN
ejpam-6997	740	9	of	of	ADP
ejpam-6997	740	10	generalized	generalized	ADJ
ejpam-6997	740	11	ap	ap	PROPN
ejpam-6997	740	12	spaces	space	NOUN
ejpam-6997	740	13	that	that	PRON
ejpam-6997	740	14	are	be	AUX
ejpam-6997	740	15	inspired	inspire	VERB
ejpam-6997	740	16	by	by	ADP
ejpam-6997	740	17	the	the	DET
ejpam-6997	740	18	concepts	concept	NOUN
ejpam-6997	740	19	of	of	ADP
ejpam-6997	740	20	cardinality	cardinality	PROPN
ejpam-6997	740	21	nbds	nbds	NOUN
ejpam-6997	740	22	and	and	CCONJ
ejpam-6997	740	23	grills	grill	NOUN
ejpam-6997	740	24	.	.	PUNCT
ejpam-6997	741	1	the	the	DET
ejpam-6997	741	2	first	first	ADJ
ejpam-6997	741	3	kind	kind	NOUN
ejpam-6997	741	4	has	have	AUX
ejpam-6997	741	5	proven	prove	VERB
ejpam-6997	741	6	to	to	PART
ejpam-6997	741	7	be	be	AUX
ejpam-6997	741	8	effective	effective	ADJ
ejpam-6997	741	9	in	in	ADP
ejpam-6997	741	10	extracting	extract	VERB
ejpam-6997	741	11	as	as	ADV
ejpam-6997	741	12	many	many	ADJ
ejpam-6997	741	13	details	detail	NOUN
ejpam-6997	741	14	as	as	ADP
ejpam-6997	741	15	possible	possible	ADJ
ejpam-6997	741	16	from	from	ADP
ejpam-6997	741	17	dataset	dataset	ADJ
ejpam-6997	741	18	subsets	subset	NOUN
ejpam-6997	741	19	.	.	PUNCT
ejpam-6997	742	1	nevertheless	nevertheless	ADV
ejpam-6997	742	2	,	,	PUNCT
ejpam-6997	742	3	it	it	PRON
ejpam-6997	742	4	has	have	VERB
ejpam-6997	742	5	flaws	flaw	NOUN
ejpam-6997	742	6	in	in	ADP
ejpam-6997	742	7	that	that	SCONJ
ejpam-6997	742	8	it	it	PRON
ejpam-6997	742	9	violates	violate	VERB
ejpam-6997	742	10	certain	certain	ADJ
ejpam-6997	742	11	of	of	ADP
ejpam-6997	742	12	the	the	DET
ejpam-6997	742	13	original	original	ADJ
ejpam-6997	742	14	model	model	NOUN
ejpam-6997	742	15	’s	’s	PART
ejpam-6997	742	16	characteristics	characteristic	NOUN
ejpam-6997	742	17	.	.	PUNCT
ejpam-6997	743	1	in	in	ADP
ejpam-6997	743	2	order	order	NOUN
ejpam-6997	743	3	to	to	PART
ejpam-6997	743	4	get	get	VERB
ejpam-6997	743	5	over	over	ADP
ejpam-6997	743	6	this	this	DET
ejpam-6997	743	7	problem	problem	NOUN
ejpam-6997	743	8	,	,	PUNCT
ejpam-6997	743	9	we	we	PRON
ejpam-6997	743	10	have	have	AUX
ejpam-6997	743	11	introduced	introduce	VERB
ejpam-6997	743	12	the	the	DET
ejpam-6997	743	13	second	second	ADJ
ejpam-6997	743	14	kind	kind	NOUN
ejpam-6997	743	15	of	of	ADP
ejpam-6997	743	16	ap	ap	PROPN
ejpam-6997	743	17	space	space	NOUN
ejpam-6997	743	18	,	,	PUNCT
ejpam-6997	743	19	which	which	PRON
ejpam-6997	743	20	maintains	maintain	VERB
ejpam-6997	743	21	the	the	DET
ejpam-6997	743	22	features	feature	NOUN
ejpam-6997	743	23	of	of	ADP
ejpam-6997	743	24	the	the	DET
ejpam-6997	743	25	original	original	ADJ
ejpam-6997	743	26	model	model	NOUN
ejpam-6997	743	27	while	while	SCONJ
ejpam-6997	743	28	appreciably	appreciably	ADV
ejpam-6997	743	29	expanding	expand	VERB
ejpam-6997	743	30	the	the	DET
ejpam-6997	743	31	knowledge	knowledge	NOUN
ejpam-6997	743	32	that	that	PRON
ejpam-6997	743	33	has	have	AUX
ejpam-6997	743	34	been	be	AUX
ejpam-6997	743	35	gathered	gather	VERB
ejpam-6997	743	36	.	.	PUNCT
ejpam-6997	744	1	to	to	PART
ejpam-6997	744	2	improve	improve	VERB
ejpam-6997	744	3	the	the	DET
ejpam-6997	744	4	ap	ap	PROPN
ejpam-6997	744	5	operators	operator	NOUN
ejpam-6997	744	6	,	,	PUNCT
ejpam-6997	744	7	we	we	PRON
ejpam-6997	744	8	inferred	infer	VERB
ejpam-6997	744	9	the	the	DET
ejpam-6997	744	10	associated	associated	ADJ
ejpam-6997	744	11	positive	positive	ADJ
ejpam-6997	744	12	properties	property	NOUN
ejpam-6997	744	13	of	of	ADP
ejpam-6997	744	14	these	these	DET
ejpam-6997	744	15	models	model	NOUN
ejpam-6997	744	16	and	and	CCONJ
ejpam-6997	744	17	verified	verify	VERB
ejpam-6997	744	18	their	their	PRON
ejpam-6997	744	19	validity	validity	NOUN
ejpam-6997	744	20	.	.	PUNCT
ejpam-6997	745	1	the	the	DET
ejpam-6997	745	2	suggested	suggest	VERB
ejpam-6997	745	3	crude	crude	NOUN
ejpam-6997	745	4	set	set	NOUN
ejpam-6997	745	5	model	model	NOUN
ejpam-6997	745	6	is	be	AUX
ejpam-6997	745	7	then	then	ADV
ejpam-6997	745	8	represented	represent	VERB
ejpam-6997	745	9	a.	a.	NOUN
ejpam-6997	745	10	a.	a.	PROPN
ejpam-6997	745	11	azzam	azzam	PROPN
ejpam-6997	745	12	,	,	PUNCT
ejpam-6997	745	13	m.	m.	NOUN
ejpam-6997	745	14	aldawood	aldawood	PROPN
ejpam-6997	745	15	,	,	PUNCT
ejpam-6997	745	16	b.	b.	PROPN
ejpam-6997	745	17	alreshidi	alreshidi	PROPN
ejpam-6997	745	18	/	/	SYM
ejpam-6997	745	19	eur	eur	PROPN
ejpam-6997	745	20	.	.	PUNCT
ejpam-6997	746	1	j.	j.	PROPN
ejpam-6997	746	2	pure	pure	PROPN
ejpam-6997	746	3	appl	appl	PROPN
ejpam-6997	746	4	.	.	PROPN
ejpam-6997	746	5	math	math	PROPN
ejpam-6997	746	6	,	,	PUNCT
ejpam-6997	746	7	18	18	NUM
ejpam-6997	746	8	(	(	PUNCT
ejpam-6997	746	9	4	4	NUM
ejpam-6997	746	10	)	)	PUNCT
ejpam-6997	746	11	(	(	PUNCT
ejpam-6997	746	12	2025	2025	NUM
ejpam-6997	746	13	)	)	PUNCT
ejpam-6997	746	14	,	,	PUNCT
ejpam-6997	746	15	6997	6997	NUM
ejpam-6997	746	16	28	28	NUM
ejpam-6997	746	17	of	of	ADP
ejpam-6997	746	18	31	31	NUM
ejpam-6997	746	19	by	by	ADP
ejpam-6997	746	20	a	a	DET
ejpam-6997	746	21	topological	topological	ADJ
ejpam-6997	746	22	frame	frame	NOUN
ejpam-6997	746	23	that	that	PRON
ejpam-6997	746	24	we	we	PRON
ejpam-6997	746	25	have	have	AUX
ejpam-6997	746	26	constructed	construct	VERB
ejpam-6997	746	27	.	.	PUNCT
ejpam-6997	747	1	we	we	PRON
ejpam-6997	747	2	have	have	AUX
ejpam-6997	747	3	presented	present	VERB
ejpam-6997	747	4	the	the	DET
ejpam-6997	747	5	crude	crude	ADJ
ejpam-6997	747	6	topological	topological	PROPN
ejpam-6997	747	7	model	model	NOUN
ejpam-6997	747	8	’s	’s	PART
ejpam-6997	747	9	characteristics	characteristic	NOUN
ejpam-6997	747	10	and	and	CCONJ
ejpam-6997	747	11	clarified	clarify	VERB
ejpam-6997	747	12	how	how	SCONJ
ejpam-6997	747	13	it	it	PRON
ejpam-6997	747	14	differs	differ	VERB
ejpam-6997	747	15	from	from	ADP
ejpam-6997	747	16	its	its	PRON
ejpam-6997	747	17	counterpart	counterpart	NOUN
ejpam-6997	747	18	that	that	PRON
ejpam-6997	747	19	is	be	AUX
ejpam-6997	747	20	defined	define	VERB
ejpam-6997	747	21	without	without	ADP
ejpam-6997	747	22	a	a	DET
ejpam-6997	747	23	grill	grill	ADJ
ejpam-6997	747	24	structure	structure	NOUN
ejpam-6997	747	25	.	.	PUNCT
ejpam-6997	748	1	we	we	PRON
ejpam-6997	748	2	may	may	AUX
ejpam-6997	748	3	conclude	conclude	VERB
ejpam-6997	748	4	that	that	SCONJ
ejpam-6997	748	5	the	the	DET
ejpam-6997	748	6	rs	rs	NOUN
ejpam-6997	748	7	models	model	NOUN
ejpam-6997	748	8	used	use	VERB
ejpam-6997	748	9	here	here	ADV
ejpam-6997	748	10	perform	perform	VERB
ejpam-6997	748	11	better	well	ADV
ejpam-6997	748	12	than	than	ADP
ejpam-6997	748	13	the	the	DET
ejpam-6997	748	14	current	current	ADJ
ejpam-6997	748	15	models	model	NOUN
ejpam-6997	748	16	based	base	VERB
ejpam-6997	748	17	on	on	ADP
ejpam-6997	748	18	the	the	DET
ejpam-6997	748	19	analysis	analysis	NOUN
ejpam-6997	748	20	presented	present	VERB
ejpam-6997	748	21	in	in	ADP
ejpam-6997	748	22	the	the	DET
ejpam-6997	748	23	medical	medical	ADJ
ejpam-6997	748	24	case	case	NOUN
ejpam-6997	748	25	of	of	ADP
ejpam-6997	748	26	heart	heart	NOUN
ejpam-6997	748	27	failure	failure	NOUN
ejpam-6997	748	28	condition	condition	NOUN
ejpam-6997	748	29	.	.	PUNCT
ejpam-6997	749	1	here	here	ADV
ejpam-6997	749	2	is	be	AUX
ejpam-6997	749	3	our	our	PRON
ejpam-6997	749	4	strategy	strategy	NOUN
ejpam-6997	749	5	for	for	ADP
ejpam-6997	749	6	the	the	DET
ejpam-6997	749	7	future	future	NOUN
ejpam-6997	749	8	:	:	PUNCT
ejpam-6997	749	9	†	†	X
ejpam-6997	749	10	to	to	PART
ejpam-6997	749	11	improve	improve	VERB
ejpam-6997	749	12	accuracy	accuracy	NOUN
ejpam-6997	749	13	,	,	PUNCT
ejpam-6997	749	14	the	the	DET
ejpam-6997	749	15	existing	exist	VERB
ejpam-6997	749	16	models	model	NOUN
ejpam-6997	749	17	are	be	AUX
ejpam-6997	749	18	being	be	AUX
ejpam-6997	749	19	expanded	expand	VERB
ejpam-6997	749	20	using	use	VERB
ejpam-6997	749	21	various	various	ADJ
ejpam-6997	749	22	relations	relation	NOUN
ejpam-6997	749	23	.	.	PUNCT
ejpam-6997	749	24	‡	‡	PUNCT
ejpam-6997	750	1	in	in	ADP
ejpam-6997	750	2	connection	connection	NOUN
ejpam-6997	750	3	with	with	ADP
ejpam-6997	750	4	the	the	DET
ejpam-6997	750	5	concepts	concept	NOUN
ejpam-6997	750	6	that	that	PRON
ejpam-6997	750	7	were	be	AUX
ejpam-6997	750	8	given	give	VERB
ejpam-6997	750	9	,	,	PUNCT
ejpam-6997	750	10	the	the	DET
ejpam-6997	750	11	concepts	concept	NOUN
ejpam-6997	750	12	of	of	ADP
ejpam-6997	750	13	soft	soft	ADJ
ejpam-6997	750	14	and	and	CCONJ
ejpam-6997	750	15	pythagorean	pythagorean	VERB
ejpam-6997	750	16	fuzzy	fuzzy	ADJ
ejpam-6997	750	17	soft	soft	ADJ
ejpam-6997	750	18	settings	setting	NOUN
ejpam-6997	750	19	will	will	AUX
ejpam-6997	750	20	be	be	AUX
ejpam-6997	750	21	discussed	discuss	VERB
ejpam-6997	750	22	.	.	PUNCT
ejpam-6997	751	1	†‡	†‡	NOUN
ejpam-6997	751	2	investigate	investigate	VERB
ejpam-6997	751	3	innovative	innovative	ADJ
ejpam-6997	751	4	rough	rough	ADJ
ejpam-6997	751	5	set	set	NOUN
ejpam-6997	751	6	models	model	NOUN
ejpam-6997	751	7	produced	produce	VERB
ejpam-6997	751	8	by	by	ADP
ejpam-6997	751	9	cϱ-neighborhoods	cϱ-neighborhood	NOUN
ejpam-6997	751	10	and	and	CCONJ
ejpam-6997	751	11	a	a	DET
ejpam-6997	751	12	grill	grill	NOUN
ejpam-6997	751	13	structure	structure	NOUN
ejpam-6997	751	14	created	create	VERB
ejpam-6997	751	15	by	by	ADP
ejpam-6997	751	16	two	two	NUM
ejpam-6997	751	17	grills	grill	NOUN
ejpam-6997	751	18	,	,	PUNCT
ejpam-6997	751	19	g∗	g∗	NOUN
ejpam-6997	751	20	and	and	CCONJ
ejpam-6997	751	21	g∗∗	g∗∗	PROPN
ejpam-6997	751	22	,	,	PUNCT
ejpam-6997	751	23	as	as	SCONJ
ejpam-6997	751	24	outlined	outline	VERB
ejpam-6997	751	25	below	below	ADV
ejpam-6997	751	26	.	.	PUNCT
ejpam-6997	752	1	g	g	NOUN
ejpam-6997	752	2	.	.	PUNCT
ejpam-6997	753	1	=	=	PRON
ejpam-6997	753	2	{	{	PUNCT
ejpam-6997	754	1	x	x	X
ejpam-6997	754	2	⊔	⊔	NOUN
ejpam-6997	754	3	y	y	NOUN
ejpam-6997	754	4	:	:	PUNCT
ejpam-6997	754	5	x	x	SYM
ejpam-6997	754	6	∈	∈	PROPN
ejpam-6997	754	7	g∗	g∗	PROPN
ejpam-6997	754	8	,	,	PUNCT
ejpam-6997	754	9	y	y	PROPN
ejpam-6997	754	10	∈	∈	PROPN
ejpam-6997	754	11	g∗∗	g∗∗	PROPN
ejpam-6997	754	12	}	}	PUNCT
ejpam-6997	754	13	.	.	PUNCT
ejpam-6997	755	1	‡‡	‡‡	NOUN
ejpam-6997	755	2	in	in	ADP
ejpam-6997	755	3	connection	connection	NOUN
ejpam-6997	755	4	with	with	ADP
ejpam-6997	755	5	the	the	DET
ejpam-6997	755	6	concepts	concept	NOUN
ejpam-6997	755	7	that	that	PRON
ejpam-6997	755	8	were	be	AUX
ejpam-6997	755	9	given	give	VERB
ejpam-6997	755	10	,	,	PUNCT
ejpam-6997	755	11	the	the	DET
ejpam-6997	755	12	concepts	concept	NOUN
ejpam-6997	755	13	of	of	ADP
ejpam-6997	755	14	soft	soft	ADJ
ejpam-6997	755	15	and	and	CCONJ
ejpam-6997	755	16	picture	picture	NOUN
ejpam-6997	755	17	fuzzy	fuzzy	ADJ
ejpam-6997	755	18	soft	soft	ADJ
ejpam-6997	755	19	settings	setting	NOUN
ejpam-6997	755	20	will	will	AUX
ejpam-6997	755	21	be	be	AUX
ejpam-6997	755	22	discussed	discuss	VERB
ejpam-6997	755	23	.	.	PUNCT
ejpam-6997	756	1	acknowledgements	acknowledgement	NOUN
ejpam-6997	756	2	the	the	DET
ejpam-6997	756	3	authors	author	NOUN
ejpam-6997	756	4	extend	extend	VERB
ejpam-6997	756	5	their	their	PRON
ejpam-6997	756	6	appreciation	appreciation	NOUN
ejpam-6997	756	7	to	to	ADP
ejpam-6997	756	8	prince	prince	PROPN
ejpam-6997	756	9	sattam	sattam	PROPN
ejpam-6997	756	10	bin	bin	PROPN
ejpam-6997	756	11	abdulaziz	abdulaziz	PROPN
ejpam-6997	756	12	university	university	PROPN
ejpam-6997	756	13	for	for	ADP
ejpam-6997	756	14	funding	fund	VERB
ejpam-6997	756	15	this	this	DET
ejpam-6997	756	16	research	research	NOUN
ejpam-6997	756	17	work	work	NOUN
ejpam-6997	756	18	through	through	ADP
ejpam-6997	756	19	the	the	DET
ejpam-6997	756	20	project	project	NOUN
ejpam-6997	756	21	number	number	NOUN
ejpam-6997	756	22	(	(	PUNCT
ejpam-6997	756	23	psau/2025/01/34111	psau/2025/01/34111	PROPN
ejpam-6997	756	24	)	)	PUNCT
ejpam-6997	756	25	.	.	PUNCT
ejpam-6997	757	1	conflict	conflict	NOUN
ejpam-6997	757	2	of	of	ADP
ejpam-6997	757	3	interest	interest	NOUN
ejpam-6997	757	4	regarding	regard	VERB
ejpam-6997	757	5	the	the	DET
ejpam-6997	757	6	publishing	publishing	NOUN
ejpam-6997	757	7	of	of	ADP
ejpam-6997	757	8	this	this	DET
ejpam-6997	757	9	work	work	NOUN
ejpam-6997	757	10	,	,	PUNCT
ejpam-6997	757	11	the	the	DET
ejpam-6997	757	12	authors	author	NOUN
ejpam-6997	757	13	affirm	affirm	VERB
ejpam-6997	757	14	that	that	SCONJ
ejpam-6997	757	15	they	they	PRON
ejpam-6997	757	16	have	have	VERB
ejpam-6997	757	17	no	no	DET
ejpam-6997	757	18	conflicts	conflict	NOUN
ejpam-6997	757	19	of	of	ADP
ejpam-6997	757	20	interest	interest	NOUN
ejpam-6997	757	21	.	.	PUNCT
ejpam-6997	758	1	references	reference	NOUN
ejpam-6997	758	2	[	[	X
ejpam-6997	758	3	1	1	NUM
ejpam-6997	758	4	]	]	PUNCT
ejpam-6997	758	5	zdzis	zdzis	NOUN
ejpam-6997	758	6	law	law	NOUN
ejpam-6997	758	7	pawlak	pawlak	NOUN
ejpam-6997	758	8	.	.	PUNCT
ejpam-6997	759	1	rough	rough	ADJ
ejpam-6997	759	2	sets	set	NOUN
ejpam-6997	759	3	.	.	PUNCT
ejpam-6997	760	1	international	international	ADJ
ejpam-6997	760	2	journal	journal	PROPN
ejpam-6997	760	3	of	of	ADP
ejpam-6997	760	4	computer	computer	PROPN
ejpam-6997	760	5	&	&	CCONJ
ejpam-6997	760	6	information	information	PROPN
ejpam-6997	760	7	sciences	sciences	PROPN
ejpam-6997	760	8	,	,	PUNCT
ejpam-6997	760	9	11(5):341–356	11(5):341–356	NUM
ejpam-6997	760	10	,	,	PUNCT
ejpam-6997	760	11	1982	1982	NUM
ejpam-6997	760	12	.	.	PUNCT
ejpam-6997	761	1	[	[	X
ejpam-6997	761	2	2	2	NUM
ejpam-6997	761	3	]	]	PUNCT
ejpam-6997	761	4	zdzislaw	zdzislaw	NOUN
ejpam-6997	761	5	pawlak	pawlak	ADJ
ejpam-6997	761	6	.	.	PUNCT
ejpam-6997	762	1	rough	rough	ADJ
ejpam-6997	762	2	sets	set	NOUN
ejpam-6997	762	3	and	and	CCONJ
ejpam-6997	762	4	decision	decision	NOUN
ejpam-6997	762	5	analysis	analysis	NOUN
ejpam-6997	762	6	.	.	PUNCT
ejpam-6997	763	1	infor	infor	NOUN
ejpam-6997	763	2	:	:	PUNCT
ejpam-6997	763	3	information	information	NOUN
ejpam-6997	763	4	systems	system	NOUN
ejpam-6997	763	5	and	and	CCONJ
ejpam-6997	763	6	operational	operational	ADJ
ejpam-6997	763	7	research	research	NOUN
ejpam-6997	763	8	,	,	PUNCT
ejpam-6997	763	9	38(3):132–144	38(3):132–144	NUM
ejpam-6997	763	10	,	,	PUNCT
ejpam-6997	763	11	2000	2000	NUM
ejpam-6997	763	12	.	.	PUNCT
ejpam-6997	764	1	[	[	X
ejpam-6997	764	2	3	3	NUM
ejpam-6997	764	3	]	]	SYM
ejpam-6997	764	4	ea	ea	X
ejpam-6997	764	5	abo	abo	NOUN
ejpam-6997	764	6	-	-	PUNCT
ejpam-6997	764	7	tabl	tabl	NOUN
ejpam-6997	764	8	.	.	PUNCT
ejpam-6997	765	1	a	a	DET
ejpam-6997	765	2	comparison	comparison	NOUN
ejpam-6997	765	3	of	of	ADP
ejpam-6997	765	4	two	two	NUM
ejpam-6997	765	5	kinds	kind	NOUN
ejpam-6997	765	6	of	of	ADP
ejpam-6997	765	7	definitions	definition	NOUN
ejpam-6997	765	8	of	of	ADP
ejpam-6997	765	9	rough	rough	ADJ
ejpam-6997	765	10	approximations	approximation	NOUN
ejpam-6997	765	11	based	base	VERB
ejpam-6997	765	12	on	on	ADP
ejpam-6997	765	13	a	a	DET
ejpam-6997	765	14	similarity	similarity	NOUN
ejpam-6997	765	15	relation	relation	NOUN
ejpam-6997	765	16	.	.	PUNCT
ejpam-6997	766	1	information	information	NOUN
ejpam-6997	766	2	sciences	sciences	PROPN
ejpam-6997	766	3	,	,	PUNCT
ejpam-6997	766	4	181(12):2587–2596	181(12):2587–2596	NUM
ejpam-6997	766	5	,	,	PUNCT
ejpam-6997	766	6	2011	2011	NUM
ejpam-6997	766	7	.	.	PUNCT
ejpam-6997	767	1	[	[	X
ejpam-6997	767	2	4	4	NUM
ejpam-6997	767	3	]	]	SYM
ejpam-6997	767	4	b	b	X
ejpam-6997	767	5	almarri	almarri	NOUN
ejpam-6997	767	6	and	and	CCONJ
ejpam-6997	767	7	aa	aa	PROPN
ejpam-6997	767	8	azzam	azzam	PROPN
ejpam-6997	767	9	.	.	PUNCT
ejpam-6997	768	1	energy	energy	NOUN
ejpam-6997	768	2	saving	save	VERB
ejpam-6997	768	3	via	via	ADP
ejpam-6997	768	4	a	a	DET
ejpam-6997	768	5	minimal	minimal	ADJ
ejpam-6997	768	6	structure	structure	NOUN
ejpam-6997	768	7	.	.	PUNCT
ejpam-6997	769	1	mathematical	mathematical	ADJ
ejpam-6997	769	2	problems	problem	NOUN
ejpam-6997	769	3	in	in	ADP
ejpam-6997	769	4	engineering	engineering	NOUN
ejpam-6997	769	5	,	,	PUNCT
ejpam-6997	769	6	2022(1):5450344	2022(1):5450344	NOUN
ejpam-6997	769	7	,	,	PUNCT
ejpam-6997	769	8	2022	2022	NUM
ejpam-6997	769	9	.	.	PUNCT
ejpam-6997	770	1	[	[	X
ejpam-6997	770	2	5	5	NUM
ejpam-6997	770	3	]	]	PUNCT
ejpam-6997	770	4	jianhua	jianhua	PROPN
ejpam-6997	770	5	dai	dai	PROPN
ejpam-6997	770	6	,	,	PUNCT
ejpam-6997	770	7	shuaichao	shuaichao	PROPN
ejpam-6997	770	8	gao	gao	PROPN
ejpam-6997	770	9	,	,	PUNCT
ejpam-6997	770	10	and	and	CCONJ
ejpam-6997	770	11	guojie	guojie	PROPN
ejpam-6997	770	12	zheng	zheng	PROPN
ejpam-6997	770	13	.	.	PUNCT
ejpam-6997	771	1	generalized	generalize	VERB
ejpam-6997	771	2	rough	rough	ADJ
ejpam-6997	771	3	set	set	NOUN
ejpam-6997	771	4	models	model	NOUN
ejpam-6997	771	5	determined	determine	VERB
ejpam-6997	771	6	by	by	ADP
ejpam-6997	771	7	multiple	multiple	ADJ
ejpam-6997	771	8	neighborhoods	neighborhood	NOUN
ejpam-6997	771	9	generated	generate	VERB
ejpam-6997	771	10	from	from	ADP
ejpam-6997	771	11	a	a	DET
ejpam-6997	771	12	similarity	similarity	NOUN
ejpam-6997	771	13	relation	relation	NOUN
ejpam-6997	771	14	.	.	PUNCT
ejpam-6997	772	1	soft	soft	ADJ
ejpam-6997	772	2	computing	computing	NOUN
ejpam-6997	772	3	,	,	PUNCT
ejpam-6997	772	4	22(7):2081–2094	22(7):2081–2094	NUM
ejpam-6997	772	5	,	,	PUNCT
ejpam-6997	772	6	2018	2018	NUM
ejpam-6997	772	7	.	.	PUNCT
ejpam-6997	773	1	[	[	X
ejpam-6997	773	2	6	6	NUM
ejpam-6997	773	3	]	]	X
ejpam-6997	773	4	tareq	tareq	PROPN
ejpam-6997	773	5	m	m	PROPN
ejpam-6997	773	6	al	al	PROPN
ejpam-6997	773	7	-	-	PUNCT
ejpam-6997	773	8	shami	shami	PROPN
ejpam-6997	773	9	,	,	PUNCT
ejpam-6997	773	10	wen	wen	PROPN
ejpam-6997	773	11	qing	qing	PROPN
ejpam-6997	773	12	fu	fu	PROPN
ejpam-6997	773	13	,	,	PUNCT
ejpam-6997	773	14	and	and	CCONJ
ejpam-6997	773	15	ea	ea	ADP
ejpam-6997	773	16	abo	abo	NOUN
ejpam-6997	773	17	-	-	PUNCT
ejpam-6997	773	18	tabl	tabl	NOUN
ejpam-6997	773	19	.	.	PUNCT
ejpam-6997	774	1	new	new	ADJ
ejpam-6997	774	2	rough	rough	ADJ
ejpam-6997	774	3	approximations	approximation	NOUN
ejpam-6997	774	4	based	base	VERB
ejpam-6997	774	5	on	on	ADP
ejpam-6997	774	6	e	e	NOUN
ejpam-6997	774	7	-	-	NOUN
ejpam-6997	774	8	neighborhoods	neighborhood	NOUN
ejpam-6997	774	9	.	.	PUNCT
ejpam-6997	775	1	complexity	complexity	NOUN
ejpam-6997	775	2	,	,	PUNCT
ejpam-6997	775	3	2021(1):6666853	2021(1):6666853	NOUN
ejpam-6997	775	4	,	,	PUNCT
ejpam-6997	775	5	2021	2021	NUM
ejpam-6997	775	6	.	.	PUNCT
ejpam-6997	776	1	[	[	X
ejpam-6997	776	2	7	7	X
ejpam-6997	776	3	]	]	X
ejpam-6997	776	4	aa	aa	PROPN
ejpam-6997	776	5	azzam	azzam	PROPN
ejpam-6997	776	6	.	.	PUNCT
ejpam-6997	777	1	a	a	DET
ejpam-6997	777	2	topological	topological	ADJ
ejpam-6997	777	3	tool	tool	NOUN
ejpam-6997	777	4	to	to	PART
ejpam-6997	777	5	develop	develop	VERB
ejpam-6997	777	6	novel	novel	ADJ
ejpam-6997	777	7	rough	rough	ADJ
ejpam-6997	777	8	set	set	NOUN
ejpam-6997	777	9	.	.	PUNCT
ejpam-6997	778	1	journal	journal	NOUN
ejpam-6997	778	2	of	of	ADP
ejpam-6997	778	3	mathematics	mathematic	NOUN
ejpam-6997	778	4	and	and	CCONJ
ejpam-6997	778	5	computer	computer	NOUN
ejpam-6997	778	6	science	science	NOUN
ejpam-6997	778	7	,	,	PUNCT
ejpam-6997	778	8	33(2):204–216	33(2):204–216	NUM
ejpam-6997	778	9	,	,	PUNCT
ejpam-6997	778	10	2024	2024	NUM
ejpam-6997	778	11	.	.	PUNCT
ejpam-6997	779	1	a.	a.	NOUN
ejpam-6997	779	2	a.	a.	PROPN
ejpam-6997	779	3	azzam	azzam	PROPN
ejpam-6997	779	4	,	,	PUNCT
ejpam-6997	779	5	m.	m.	NOUN
ejpam-6997	779	6	aldawood	aldawood	PROPN
ejpam-6997	779	7	,	,	PUNCT
ejpam-6997	779	8	b.	b.	PROPN
ejpam-6997	779	9	alreshidi	alreshidi	PROPN
ejpam-6997	779	10	/	/	SYM
ejpam-6997	779	11	eur	eur	PROPN
ejpam-6997	779	12	.	.	PUNCT
ejpam-6997	780	1	j.	j.	PROPN
ejpam-6997	780	2	pure	pure	PROPN
ejpam-6997	780	3	appl	appl	PROPN
ejpam-6997	780	4	.	.	PROPN
ejpam-6997	780	5	math	math	PROPN
ejpam-6997	780	6	,	,	PUNCT
ejpam-6997	780	7	18	18	NUM
ejpam-6997	780	8	(	(	PUNCT
ejpam-6997	780	9	4	4	NUM
ejpam-6997	780	10	)	)	PUNCT
ejpam-6997	780	11	(	(	PUNCT
ejpam-6997	780	12	2025	2025	NUM
ejpam-6997	780	13	)	)	PUNCT
ejpam-6997	780	14	,	,	PUNCT
ejpam-6997	780	15	6997	6997	NUM
ejpam-6997	780	16	29	29	NUM
ejpam-6997	780	17	of	of	ADP
ejpam-6997	780	18	31	31	NUM
ejpam-6997	780	19	[	[	SYM
ejpam-6997	780	20	8	8	NUM
ejpam-6997	780	21	]	]	X
ejpam-6997	780	22	jianhua	jianhua	PROPN
ejpam-6997	780	23	dai	dai	PROPN
ejpam-6997	780	24	and	and	CCONJ
ejpam-6997	780	25	qing	qing	PROPN
ejpam-6997	780	26	xu	xu	PROPN
ejpam-6997	780	27	.	.	PUNCT
ejpam-6997	781	1	approximations	approximation	NOUN
ejpam-6997	781	2	and	and	CCONJ
ejpam-6997	781	3	uncertainty	uncertainty	NOUN
ejpam-6997	781	4	measures	measure	NOUN
ejpam-6997	781	5	in	in	ADP
ejpam-6997	781	6	incomplete	incomplete	ADJ
ejpam-6997	781	7	information	information	NOUN
ejpam-6997	781	8	systems	system	NOUN
ejpam-6997	781	9	.	.	PUNCT
ejpam-6997	782	1	information	information	NOUN
ejpam-6997	782	2	sciences	sciences	PROPN
ejpam-6997	782	3	,	,	PUNCT
ejpam-6997	782	4	198:62–80	198:62–80	PROPN
ejpam-6997	782	5	,	,	PUNCT
ejpam-6997	782	6	2012	2012	NUM
ejpam-6997	782	7	.	.	PUNCT
ejpam-6997	783	1	[	[	X
ejpam-6997	783	2	9	9	NUM
ejpam-6997	783	3	]	]	PUNCT
ejpam-6997	783	4	keyun	keyun	PROPN
ejpam-6997	783	5	qin	qin	PROPN
ejpam-6997	783	6	,	,	PUNCT
ejpam-6997	783	7	jilin	jilin	PROPN
ejpam-6997	783	8	yang	yang	PROPN
ejpam-6997	783	9	,	,	PUNCT
ejpam-6997	783	10	and	and	CCONJ
ejpam-6997	783	11	zheng	zheng	PROPN
ejpam-6997	783	12	pei	pei	PROPN
ejpam-6997	783	13	.	.	PROPN
ejpam-6997	784	1	generalized	generalize	VERB
ejpam-6997	784	2	rough	rough	ADJ
ejpam-6997	784	3	sets	set	NOUN
ejpam-6997	784	4	based	base	VERB
ejpam-6997	784	5	on	on	ADP
ejpam-6997	784	6	reflexive	reflexive	ADJ
ejpam-6997	784	7	and	and	CCONJ
ejpam-6997	784	8	transitive	transitive	ADJ
ejpam-6997	784	9	relations	relation	NOUN
ejpam-6997	784	10	.	.	PUNCT
ejpam-6997	785	1	information	information	NOUN
ejpam-6997	785	2	sciences	sciences	PROPN
ejpam-6997	785	3	,	,	PUNCT
ejpam-6997	785	4	178(21):4138–4141	178(21):4138–4141	NUM
ejpam-6997	785	5	,	,	PUNCT
ejpam-6997	785	6	2008	2008	NUM
ejpam-6997	785	7	.	.	PUNCT
ejpam-6997	786	1	[	[	X
ejpam-6997	786	2	10	10	NUM
ejpam-6997	786	3	]	]	X
ejpam-6997	786	4	roman	roman	ADJ
ejpam-6997	786	5	slowinski	slowinski	NOUN
ejpam-6997	786	6	and	and	CCONJ
ejpam-6997	786	7	daniel	daniel	PROPN
ejpam-6997	786	8	vanderpooten	vanderpooten	NOUN
ejpam-6997	786	9	.	.	PUNCT
ejpam-6997	787	1	a	a	DET
ejpam-6997	787	2	generalized	generalized	ADJ
ejpam-6997	787	3	definition	definition	NOUN
ejpam-6997	787	4	of	of	ADP
ejpam-6997	787	5	rough	rough	ADJ
ejpam-6997	787	6	approximations	approximation	NOUN
ejpam-6997	787	7	based	base	VERB
ejpam-6997	787	8	on	on	ADP
ejpam-6997	787	9	similarity	similarity	NOUN
ejpam-6997	787	10	.	.	PUNCT
ejpam-6997	788	1	ieee	ieee	NOUN
ejpam-6997	788	2	transactions	transaction	NOUN
ejpam-6997	788	3	on	on	ADP
ejpam-6997	788	4	knowledge	knowledge	NOUN
ejpam-6997	788	5	and	and	CCONJ
ejpam-6997	788	6	data	datum	NOUN
ejpam-6997	788	7	engineering	engineering	NOUN
ejpam-6997	788	8	,	,	PUNCT
ejpam-6997	788	9	12(2):331–336	12(2):331–336	PROPN
ejpam-6997	788	10	,	,	PUNCT
ejpam-6997	788	11	2002	2002	NUM
ejpam-6997	788	12	.	.	PUNCT
ejpam-6997	789	1	[	[	X
ejpam-6997	789	2	11	11	NUM
ejpam-6997	789	3	]	]	X
ejpam-6997	789	4	hua	hua	PROPN
ejpam-6997	789	5	-	-	PROPN
ejpam-6997	789	6	peng	peng	PROPN
ejpam-6997	789	7	zhang	zhang	PROPN
ejpam-6997	789	8	,	,	PUNCT
ejpam-6997	789	9	yao	yao	PROPN
ejpam-6997	789	10	ouyang	ouyang	PROPN
ejpam-6997	789	11	,	,	PUNCT
ejpam-6997	789	12	and	and	CCONJ
ejpam-6997	789	13	zhudeng	zhudeng	PROPN
ejpam-6997	789	14	wang	wang	PROPN
ejpam-6997	789	15	.	.	PUNCT
ejpam-6997	790	1	note	note	VERB
ejpam-6997	790	2	on	on	ADP
ejpam-6997	790	3	“	"	PUNCT
ejpam-6997	790	4	generalized	generalize	VERB
ejpam-6997	790	5	rough	rough	ADJ
ejpam-6997	790	6	sets	set	NOUN
ejpam-6997	790	7	based	base	VERB
ejpam-6997	790	8	on	on	ADP
ejpam-6997	790	9	reflexive	reflexive	ADJ
ejpam-6997	790	10	and	and	CCONJ
ejpam-6997	790	11	transitive	transitive	ADJ
ejpam-6997	790	12	relations	relation	NOUN
ejpam-6997	790	13	”	"	PUNCT
ejpam-6997	790	14	.	.	PUNCT
ejpam-6997	791	1	information	information	NOUN
ejpam-6997	791	2	sciences	sciences	PROPN
ejpam-6997	791	3	,	,	PUNCT
ejpam-6997	791	4	179(4):471–473	179(4):471–473	NUM
ejpam-6997	791	5	,	,	PUNCT
ejpam-6997	791	6	2009	2009	NUM
ejpam-6997	791	7	.	.	PUNCT
ejpam-6997	792	1	[	[	X
ejpam-6997	792	2	12	12	NUM
ejpam-6997	792	3	]	]	X
ejpam-6997	792	4	aa	aa	PROPN
ejpam-6997	792	5	allam	allam	PROPN
ejpam-6997	792	6	,	,	PUNCT
ejpam-6997	792	7	my	my	PRON
ejpam-6997	792	8	bakeir	bakeir	NOUN
ejpam-6997	792	9	,	,	PUNCT
ejpam-6997	792	10	and	and	CCONJ
ejpam-6997	792	11	ea	ea	ADP
ejpam-6997	792	12	abo	abo	NOUN
ejpam-6997	792	13	-	-	PUNCT
ejpam-6997	792	14	tabl	tabl	NOUN
ejpam-6997	792	15	.	.	PUNCT
ejpam-6997	793	1	new	new	ADJ
ejpam-6997	793	2	approach	approach	NOUN
ejpam-6997	793	3	for	for	ADP
ejpam-6997	793	4	basic	basic	ADJ
ejpam-6997	793	5	rough	rough	ADJ
ejpam-6997	793	6	set	set	NOUN
ejpam-6997	793	7	concepts	concept	NOUN
ejpam-6997	793	8	.	.	PUNCT
ejpam-6997	794	1	in	in	ADP
ejpam-6997	794	2	international	international	ADJ
ejpam-6997	794	3	workshop	workshop	NOUN
ejpam-6997	794	4	on	on	ADP
ejpam-6997	794	5	rough	rough	ADJ
ejpam-6997	794	6	sets	set	NOUN
ejpam-6997	794	7	,	,	PUNCT
ejpam-6997	794	8	fuzzy	fuzzy	ADJ
ejpam-6997	794	9	sets	set	NOUN
ejpam-6997	794	10	,	,	PUNCT
ejpam-6997	794	11	data	datum	NOUN
ejpam-6997	794	12	mining	mining	NOUN
ejpam-6997	794	13	,	,	PUNCT
ejpam-6997	794	14	and	and	CCONJ
ejpam-6997	794	15	granularsoft	granularsoft	ADJ
ejpam-6997	794	16	computing	computing	NOUN
ejpam-6997	794	17	,	,	PUNCT
ejpam-6997	794	18	pages	page	NOUN
ejpam-6997	794	19	64–73	64–73	NUM
ejpam-6997	794	20	.	.	PUNCT
ejpam-6997	794	21	springer	springer	NOUN
ejpam-6997	794	22	,	,	PUNCT
ejpam-6997	794	23	2005	2005	NUM
ejpam-6997	794	24	.	.	PUNCT
ejpam-6997	795	1	[	[	X
ejpam-6997	795	2	13	13	NUM
ejpam-6997	795	3	]	]	X
ejpam-6997	795	4	aa	aa	PROPN
ejpam-6997	795	5	allam	allam	PROPN
ejpam-6997	795	6	,	,	PUNCT
ejpam-6997	795	7	my	my	PRON
ejpam-6997	795	8	bakeir	bakeir	NOUN
ejpam-6997	795	9	,	,	PUNCT
ejpam-6997	795	10	and	and	CCONJ
ejpam-6997	795	11	ea	ea	ADP
ejpam-6997	795	12	abo	abo	NOUN
ejpam-6997	795	13	-	-	PUNCT
ejpam-6997	795	14	tabl	tabl	NOUN
ejpam-6997	795	15	.	.	PUNCT
ejpam-6997	796	1	new	new	ADJ
ejpam-6997	796	2	approach	approach	NOUN
ejpam-6997	796	3	for	for	ADP
ejpam-6997	796	4	closure	closure	NOUN
ejpam-6997	796	5	spaces	space	NOUN
ejpam-6997	796	6	by	by	ADP
ejpam-6997	796	7	relations	relation	NOUN
ejpam-6997	796	8	.	.	PUNCT
ejpam-6997	797	1	acta	acta	PROPN
ejpam-6997	797	2	mathematica	mathematica	PROPN
ejpam-6997	797	3	academiae	academiae	PROPN
ejpam-6997	797	4	paedagogicae	paedagogicae	VERB
ejpam-6997	797	5	nyiregyháziensis	nyiregyháziensis	NOUN
ejpam-6997	797	6	,	,	PUNCT
ejpam-6997	797	7	22(3):285	22(3):285	NUM
ejpam-6997	797	8	–	–	PUNCT
ejpam-6997	797	9	304	304	NUM
ejpam-6997	797	10	,	,	PUNCT
ejpam-6997	797	11	2006	2006	NUM
ejpam-6997	797	12	.	.	PUNCT
ejpam-6997	798	1	[	[	X
ejpam-6997	798	2	14	14	NUM
ejpam-6997	798	3	]	]	X
ejpam-6997	798	4	huishan	huishan	PROPN
ejpam-6997	798	5	wu	wu	PROPN
ejpam-6997	798	6	and	and	CCONJ
ejpam-6997	798	7	guilong	guilong	PROPN
ejpam-6997	798	8	liu	liu	PROPN
ejpam-6997	798	9	.	.	PUNCT
ejpam-6997	799	1	the	the	DET
ejpam-6997	799	2	relationships	relationship	NOUN
ejpam-6997	799	3	between	between	ADP
ejpam-6997	799	4	topologies	topology	NOUN
ejpam-6997	799	5	and	and	CCONJ
ejpam-6997	799	6	generalized	generalize	VERB
ejpam-6997	799	7	rough	rough	ADJ
ejpam-6997	799	8	sets	set	NOUN
ejpam-6997	799	9	.	.	PUNCT
ejpam-6997	800	1	international	international	ADJ
ejpam-6997	800	2	journal	journal	PROPN
ejpam-6997	800	3	of	of	ADP
ejpam-6997	800	4	approximate	approximate	ADJ
ejpam-6997	800	5	reasoning	reasoning	NOUN
ejpam-6997	800	6	,	,	PUNCT
ejpam-6997	800	7	119:313–324	119:313–324	NUM
ejpam-6997	800	8	,	,	PUNCT
ejpam-6997	800	9	2020	2020	NUM
ejpam-6997	800	10	.	.	PUNCT
ejpam-6997	801	1	[	[	X
ejpam-6997	801	2	15	15	NUM
ejpam-6997	801	3	]	]	X
ejpam-6997	801	4	yy	yy	PROPN
ejpam-6997	801	5	yao	yao	PROPN
ejpam-6997	801	6	.	.	PUNCT
ejpam-6997	802	1	two	two	NUM
ejpam-6997	802	2	views	view	NOUN
ejpam-6997	802	3	of	of	ADP
ejpam-6997	802	4	the	the	DET
ejpam-6997	802	5	theory	theory	NOUN
ejpam-6997	802	6	of	of	ADP
ejpam-6997	802	7	rough	rough	ADJ
ejpam-6997	802	8	sets	set	NOUN
ejpam-6997	802	9	in	in	ADP
ejpam-6997	802	10	finite	finite	ADJ
ejpam-6997	802	11	universes	universe	NOUN
ejpam-6997	802	12	.	.	PUNCT
ejpam-6997	803	1	international	international	ADJ
ejpam-6997	803	2	journal	journal	PROPN
ejpam-6997	803	3	of	of	ADP
ejpam-6997	803	4	approximate	approximate	ADJ
ejpam-6997	803	5	reasoning	reasoning	NOUN
ejpam-6997	803	6	,	,	PUNCT
ejpam-6997	803	7	15(4):291–317	15(4):291–317	NUM
ejpam-6997	803	8	,	,	PUNCT
ejpam-6997	803	9	1996	1996	NUM
ejpam-6997	803	10	.	.	PUNCT
ejpam-6997	804	1	[	[	X
ejpam-6997	804	2	16	16	NUM
ejpam-6997	804	3	]	]	X
ejpam-6997	804	4	mohammed	mohammed	PROPN
ejpam-6997	804	5	atef	atef	PROPN
ejpam-6997	804	6	,	,	PUNCT
ejpam-6997	804	7	ahmed	ahmed	PROPN
ejpam-6997	804	8	mostafa	mostafa	PROPN
ejpam-6997	804	9	khalil	khalil	PROPN
ejpam-6997	804	10	,	,	PUNCT
ejpam-6997	804	11	sheng	sheng	PROPN
ejpam-6997	804	12	-	-	PUNCT
ejpam-6997	804	13	gang	gang	NOUN
ejpam-6997	804	14	li	li	PROPN
ejpam-6997	804	15	,	,	PUNCT
ejpam-6997	804	16	aa	aa	PROPN
ejpam-6997	804	17	azzam	azzam	PROPN
ejpam-6997	804	18	,	,	PUNCT
ejpam-6997	804	19	and	and	CCONJ
ejpam-6997	804	20	abd	abd	PROPN
ejpam-6997	804	21	el	el	PROPN
ejpam-6997	804	22	fattah	fattah	PROPN
ejpam-6997	804	23	el	el	PROPN
ejpam-6997	804	24	atik	atik	PROPN
ejpam-6997	804	25	.	.	PUNCT
ejpam-6997	805	1	comparison	comparison	NOUN
ejpam-6997	805	2	of	of	ADP
ejpam-6997	805	3	six	six	NUM
ejpam-6997	805	4	types	type	NOUN
ejpam-6997	805	5	of	of	ADP
ejpam-6997	805	6	rough	rough	ADJ
ejpam-6997	805	7	approximations	approximation	NOUN
ejpam-6997	805	8	based	base	VERB
ejpam-6997	805	9	on	on	ADP
ejpam-6997	805	10	jneighborhood	jneighborhood	ADJ
ejpam-6997	805	11	space	space	NOUN
ejpam-6997	805	12	and	and	CCONJ
ejpam-6997	805	13	j	j	NOUN
ejpam-6997	805	14	-	-	PUNCT
ejpam-6997	805	15	adhesion	adhesion	NOUN
ejpam-6997	805	16	neighborhood	neighborhood	NOUN
ejpam-6997	805	17	space	space	NOUN
ejpam-6997	805	18	.	.	PUNCT
ejpam-6997	806	1	journal	journal	NOUN
ejpam-6997	806	2	of	of	ADP
ejpam-6997	806	3	intelligent	intelligent	ADJ
ejpam-6997	806	4	&	&	CCONJ
ejpam-6997	806	5	fuzzy	fuzzy	ADJ
ejpam-6997	806	6	systems	system	NOUN
ejpam-6997	806	7	,	,	PUNCT
ejpam-6997	806	8	39(3):4515–4531	39(3):4515–4531	NUM
ejpam-6997	806	9	,	,	PUNCT
ejpam-6997	806	10	2020	2020	NUM
ejpam-6997	806	11	.	.	PUNCT
ejpam-6997	807	1	[	[	X
ejpam-6997	807	2	17	17	NUM
ejpam-6997	807	3	]	]	X
ejpam-6997	807	4	r	r	NOUN
ejpam-6997	807	5	mareay	mareay	NOUN
ejpam-6997	807	6	.	.	PUNCT
ejpam-6997	808	1	generalized	generalize	VERB
ejpam-6997	808	2	rough	rough	ADJ
ejpam-6997	808	3	sets	set	NOUN
ejpam-6997	808	4	based	base	VERB
ejpam-6997	808	5	on	on	ADP
ejpam-6997	808	6	neighborhood	neighborhood	NOUN
ejpam-6997	808	7	systems	system	NOUN
ejpam-6997	808	8	and	and	CCONJ
ejpam-6997	808	9	topological	topological	ADJ
ejpam-6997	808	10	spaces	space	NOUN
ejpam-6997	808	11	.	.	PUNCT
ejpam-6997	809	1	journal	journal	NOUN
ejpam-6997	809	2	of	of	ADP
ejpam-6997	809	3	the	the	DET
ejpam-6997	809	4	egyptian	egyptian	PROPN
ejpam-6997	809	5	mathematical	mathematical	PROPN
ejpam-6997	809	6	society	society	NOUN
ejpam-6997	809	7	,	,	PUNCT
ejpam-6997	809	8	24(4):603–608	24(4):603–608	PROPN
ejpam-6997	809	9	,	,	PUNCT
ejpam-6997	809	10	2016	2016	NUM
ejpam-6997	809	11	.	.	PUNCT
ejpam-6997	810	1	[	[	X
ejpam-6997	810	2	18	18	NUM
ejpam-6997	810	3	]	]	X
ejpam-6997	810	4	abdel	abdel	PROPN
ejpam-6997	810	5	fatah	fatah	PROPN
ejpam-6997	810	6	a	a	PROPN
ejpam-6997	810	7	azzam	azzam	PROPN
ejpam-6997	810	8	.	.	PUNCT
ejpam-6997	811	1	rough	rough	ADJ
ejpam-6997	811	2	neighborhood	neighborhood	NOUN
ejpam-6997	811	3	ideal	ideal	NOUN
ejpam-6997	811	4	and	and	CCONJ
ejpam-6997	811	5	its	its	PRON
ejpam-6997	811	6	applications	application	NOUN
ejpam-6997	811	7	.	.	PUNCT
ejpam-6997	812	1	international	international	ADJ
ejpam-6997	812	2	journal	journal	NOUN
ejpam-6997	812	3	of	of	ADP
ejpam-6997	812	4	fuzzy	fuzzy	ADJ
ejpam-6997	812	5	logic	logic	NOUN
ejpam-6997	812	6	and	and	CCONJ
ejpam-6997	812	7	intelligent	intelligent	ADJ
ejpam-6997	812	8	systems	system	NOUN
ejpam-6997	812	9	,	,	PUNCT
ejpam-6997	812	10	24(1):43–49	24(1):43–49	NUM
ejpam-6997	812	11	,	,	PUNCT
ejpam-6997	812	12	2024	2024	NUM
ejpam-6997	812	13	.	.	PUNCT
ejpam-6997	813	1	[	[	X
ejpam-6997	813	2	19	19	NUM
ejpam-6997	813	3	]	]	PUNCT
ejpam-6997	813	4	mohamed	mohamed	PROPN
ejpam-6997	813	5	abd	abd	PROPN
ejpam-6997	813	6	elaziz	elaziz	PROPN
ejpam-6997	813	7	,	,	PUNCT
ejpam-6997	813	8	hassan	hassan	PROPN
ejpam-6997	813	9	m	m	PROPN
ejpam-6997	813	10	abu	abu	PROPN
ejpam-6997	813	11	-	-	PUNCT
ejpam-6997	813	12	donia	donia	PROPN
ejpam-6997	813	13	,	,	PUNCT
ejpam-6997	813	14	rodyna	rodyna	PROPN
ejpam-6997	813	15	a	a	DET
ejpam-6997	813	16	hosny	hosny	PROPN
ejpam-6997	813	17	,	,	PUNCT
ejpam-6997	813	18	saeed	saeed	PROPN
ejpam-6997	813	19	l	l	PROPN
ejpam-6997	813	20	hazae	hazae	PROPN
ejpam-6997	813	21	,	,	PUNCT
ejpam-6997	813	22	and	and	CCONJ
ejpam-6997	813	23	rehab	rehab	PROPN
ejpam-6997	813	24	ali	ali	PROPN
ejpam-6997	813	25	ibrahim	ibrahim	PROPN
ejpam-6997	813	26	.	.	PUNCT
ejpam-6997	814	1	improved	improve	VERB
ejpam-6997	814	2	evolutionary	evolutionary	ADJ
ejpam-6997	814	3	-	-	PUNCT
ejpam-6997	814	4	based	base	VERB
ejpam-6997	814	5	feature	feature	NOUN
ejpam-6997	814	6	selection	selection	NOUN
ejpam-6997	814	7	technique	technique	NOUN
ejpam-6997	814	8	using	use	VERB
ejpam-6997	814	9	extension	extension	NOUN
ejpam-6997	814	10	of	of	ADP
ejpam-6997	814	11	knowledge	knowledge	NOUN
ejpam-6997	814	12	based	base	VERB
ejpam-6997	814	13	on	on	ADP
ejpam-6997	814	14	the	the	DET
ejpam-6997	814	15	rough	rough	ADJ
ejpam-6997	814	16	approximations	approximation	NOUN
ejpam-6997	814	17	.	.	PUNCT
ejpam-6997	815	1	information	information	NOUN
ejpam-6997	815	2	sciences	sciences	PROPN
ejpam-6997	815	3	,	,	PUNCT
ejpam-6997	815	4	594:76–94	594:76–94	NUM
ejpam-6997	815	5	,	,	PUNCT
ejpam-6997	815	6	2022	2022	NUM
ejpam-6997	815	7	.	.	PUNCT
ejpam-6997	816	1	[	[	X
ejpam-6997	816	2	20	20	NUM
ejpam-6997	816	3	]	]	X
ejpam-6997	816	4	seiki	seiki	PROPN
ejpam-6997	816	5	akama	akama	PROPN
ejpam-6997	816	6	,	,	PUNCT
ejpam-6997	816	7	tetsuya	tetsuya	PROPN
ejpam-6997	816	8	murai	murai	PROPN
ejpam-6997	816	9	,	,	PUNCT
ejpam-6997	816	10	and	and	CCONJ
ejpam-6997	816	11	yasuo	yasuo	PROPN
ejpam-6997	816	12	kudo	kudo	PROPN
ejpam-6997	816	13	.	.	PROPN
ejpam-6997	816	14	reasoning	reasoning	NOUN
ejpam-6997	816	15	with	with	ADP
ejpam-6997	816	16	rough	rough	ADJ
ejpam-6997	816	17	sets	set	NOUN
ejpam-6997	816	18	.	.	PUNCT
ejpam-6997	817	1	logical	logical	ADJ
ejpam-6997	817	2	approaches	approach	NOUN
ejpam-6997	817	3	to	to	ADP
ejpam-6997	817	4	granularity	granularity	NOUN
ejpam-6997	817	5	-	-	PUNCT
ejpam-6997	817	6	based	base	VERB
ejpam-6997	817	7	framework	framework	NOUN
ejpam-6997	817	8	,	,	PUNCT
ejpam-6997	817	9	2018	2018	NUM
ejpam-6997	817	10	.	.	PUNCT
ejpam-6997	818	1	[	[	X
ejpam-6997	818	2	21	21	NUM
ejpam-6997	818	3	]	]	X
ejpam-6997	818	4	mona	mona	PROPN
ejpam-6997	818	5	hosny	hosny	PROPN
ejpam-6997	818	6	and	and	CCONJ
ejpam-6997	818	7	tareq	tareq	PROPN
ejpam-6997	818	8	m	m	PROPN
ejpam-6997	818	9	al	al	PROPN
ejpam-6997	818	10	-	-	PUNCT
ejpam-6997	818	11	shami	shami	PROPN
ejpam-6997	818	12	.	.	PUNCT
ejpam-6997	819	1	rough	rough	ADJ
ejpam-6997	819	2	set	set	NOUN
ejpam-6997	819	3	models	model	NOUN
ejpam-6997	819	4	in	in	ADP
ejpam-6997	819	5	a	a	DET
ejpam-6997	819	6	more	more	ADV
ejpam-6997	819	7	general	general	ADJ
ejpam-6997	819	8	manner	manner	NOUN
ejpam-6997	819	9	with	with	ADP
ejpam-6997	819	10	applications	application	NOUN
ejpam-6997	819	11	.	.	PUNCT
ejpam-6997	820	1	aims	aim	VERB
ejpam-6997	820	2	math	math	NOUN
ejpam-6997	820	3	,	,	PUNCT
ejpam-6997	820	4	7(10):18971–19017	7(10):18971–19017	NUM
ejpam-6997	820	5	,	,	PUNCT
ejpam-6997	820	6	2022	2022	NUM
ejpam-6997	820	7	.	.	PUNCT
ejpam-6997	821	1	[	[	X
ejpam-6997	821	2	22	22	NUM
ejpam-6997	821	3	]	]	PUNCT
ejpam-6997	821	4	rodyna	rodyna	NOUN
ejpam-6997	821	5	a	a	DET
ejpam-6997	821	6	hosny	hosny	PROPN
ejpam-6997	821	7	,	,	PUNCT
ejpam-6997	821	8	mohamed	mohamed	PROPN
ejpam-6997	821	9	abd	abd	PROPN
ejpam-6997	821	10	elaziz	elaziz	PROPN
ejpam-6997	821	11	,	,	PUNCT
ejpam-6997	821	12	and	and	CCONJ
ejpam-6997	821	13	rehab	rehab	PROPN
ejpam-6997	821	14	ali	ali	PROPN
ejpam-6997	821	15	ibrahim	ibrahim	PROPN
ejpam-6997	821	16	.	.	PUNCT
ejpam-6997	822	1	enhanced	enhance	VERB
ejpam-6997	822	2	feature	feature	NOUN
ejpam-6997	822	3	selection	selection	NOUN
ejpam-6997	822	4	based	base	VERB
ejpam-6997	822	5	on	on	ADP
ejpam-6997	822	6	integration	integration	NOUN
ejpam-6997	822	7	containment	containment	NOUN
ejpam-6997	822	8	neighborhoods	neighborhood	NOUN
ejpam-6997	822	9	rough	rough	ADJ
ejpam-6997	822	10	set	set	VERB
ejpam-6997	822	11	approximations	approximation	NOUN
ejpam-6997	822	12	and	and	CCONJ
ejpam-6997	822	13	binary	binary	ADJ
ejpam-6997	822	14	honey	honey	NOUN
ejpam-6997	822	15	badger	badger	PROPN
ejpam-6997	822	16	optimization	optimization	NOUN
ejpam-6997	822	17	.	.	PUNCT
ejpam-6997	823	1	computational	computational	ADJ
ejpam-6997	823	2	intelligence	intelligence	NOUN
ejpam-6997	823	3	and	and	CCONJ
ejpam-6997	823	4	neuroscience	neuroscience	NOUN
ejpam-6997	823	5	,	,	PUNCT
ejpam-6997	823	6	2022(1):3991870	2022(1):3991870	NOUN
ejpam-6997	823	7	,	,	PUNCT
ejpam-6997	823	8	2022	2022	NUM
ejpam-6997	823	9	.	.	PUNCT
ejpam-6997	824	1	[	[	X
ejpam-6997	824	2	23	23	NUM
ejpam-6997	824	3	]	]	PUNCT
ejpam-6997	824	4	rodyna	rodyna	NOUN
ejpam-6997	824	5	a	a	DET
ejpam-6997	824	6	hosny	hosny	PROPN
ejpam-6997	824	7	,	,	PUNCT
ejpam-6997	824	8	tareq	tareq	PROPN
ejpam-6997	824	9	m	m	PROPN
ejpam-6997	824	10	al	al	PROPN
ejpam-6997	824	11	-	-	PUNCT
ejpam-6997	824	12	shami	shami	PROPN
ejpam-6997	824	13	,	,	PUNCT
ejpam-6997	824	14	aa	aa	PROPN
ejpam-6997	824	15	azzam	azzam	PROPN
ejpam-6997	824	16	,	,	PUNCT
ejpam-6997	824	17	and	and	CCONJ
ejpam-6997	824	18	ashraf	ashraf	PROPN
ejpam-6997	824	19	s	s	PART
ejpam-6997	824	20	nawar	nawar	NOUN
ejpam-6997	824	21	.	.	PUNCT
ejpam-6997	825	1	knowledge	knowledge	NOUN
ejpam-6997	825	2	based	base	VERB
ejpam-6997	825	3	on	on	ADP
ejpam-6997	825	4	rough	rough	ADJ
ejpam-6997	825	5	approximations	approximation	NOUN
ejpam-6997	825	6	and	and	CCONJ
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ejpam-6997	825	8	.	.	PUNCT
ejpam-6997	826	1	mathematical	mathematical	ADJ
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ejpam-6997	826	3	in	in	ADP
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ejpam-6997	826	5	,	,	PUNCT
ejpam-6997	826	6	2022(1):3766286	2022(1):3766286	NUM
ejpam-6997	826	7	,	,	PUNCT
ejpam-6997	826	8	2022	2022	NUM
ejpam-6997	826	9	.	.	PUNCT
ejpam-6997	827	1	a.	a.	NOUN
ejpam-6997	827	2	a.	a.	PROPN
ejpam-6997	827	3	azzam	azzam	PROPN
ejpam-6997	827	4	,	,	PUNCT
ejpam-6997	827	5	m.	m.	NOUN
ejpam-6997	827	6	aldawood	aldawood	PROPN
ejpam-6997	827	7	,	,	PUNCT
ejpam-6997	827	8	b.	b.	PROPN
ejpam-6997	827	9	alreshidi	alreshidi	PROPN
ejpam-6997	827	10	/	/	SYM
ejpam-6997	827	11	eur	eur	PROPN
ejpam-6997	827	12	.	.	PUNCT
ejpam-6997	828	1	j.	j.	PROPN
ejpam-6997	828	2	pure	pure	PROPN
ejpam-6997	828	3	appl	appl	PROPN
ejpam-6997	828	4	.	.	PROPN
ejpam-6997	828	5	math	math	PROPN
ejpam-6997	828	6	,	,	PUNCT
ejpam-6997	828	7	18	18	NUM
ejpam-6997	828	8	(	(	PUNCT
ejpam-6997	828	9	4	4	NUM
ejpam-6997	828	10	)	)	PUNCT
ejpam-6997	828	11	(	(	PUNCT
ejpam-6997	828	12	2025	2025	NUM
ejpam-6997	828	13	)	)	PUNCT
ejpam-6997	828	14	,	,	PUNCT
ejpam-6997	828	15	6997	6997	NUM
ejpam-6997	828	16	30	30	NUM
ejpam-6997	828	17	of	of	ADP
ejpam-6997	828	18	31	31	NUM
ejpam-6997	829	1	[	[	X
ejpam-6997	829	2	24	24	NUM
ejpam-6997	829	3	]	]	X
ejpam-6997	829	4	mona	mona	PROPN
ejpam-6997	829	5	hosny	hosny	PROPN
ejpam-6997	829	6	.	.	PUNCT
ejpam-6997	830	1	generalization	generalization	NOUN
ejpam-6997	830	2	of	of	ADP
ejpam-6997	830	3	rough	rough	ADJ
ejpam-6997	830	4	sets	set	NOUN
ejpam-6997	830	5	using	use	VERB
ejpam-6997	830	6	maximal	maximal	ADJ
ejpam-6997	830	7	right	right	ADJ
ejpam-6997	830	8	neighborhood	neighborhood	NOUN
ejpam-6997	830	9	systems	system	NOUN
ejpam-6997	830	10	and	and	CCONJ
ejpam-6997	830	11	ideals	ideal	NOUN
ejpam-6997	830	12	with	with	ADP
ejpam-6997	830	13	medical	medical	ADJ
ejpam-6997	830	14	applications	application	NOUN
ejpam-6997	830	15	.	.	PUNCT
ejpam-6997	831	1	aims	aim	VERB
ejpam-6997	831	2	math	math	NOUN
ejpam-6997	831	3	,	,	PUNCT
ejpam-6997	831	4	7(7):13104–13138	7(7):13104–13138	PROPN
ejpam-6997	831	5	,	,	PUNCT
ejpam-6997	831	6	2022	2022	NUM
ejpam-6997	831	7	.	.	PUNCT
ejpam-6997	832	1	[	[	X
ejpam-6997	832	2	25	25	NUM
ejpam-6997	832	3	]	]	X
ejpam-6997	832	4	marzena	marzena	PROPN
ejpam-6997	832	5	kryszkiewicz	kryszkiewicz	NOUN
ejpam-6997	832	6	.	.	PUNCT
ejpam-6997	833	1	rough	rough	ADJ
ejpam-6997	833	2	set	set	NOUN
ejpam-6997	833	3	approach	approach	NOUN
ejpam-6997	833	4	to	to	ADP
ejpam-6997	833	5	incomplete	incomplete	ADJ
ejpam-6997	833	6	information	information	NOUN
ejpam-6997	833	7	systems	system	NOUN
ejpam-6997	833	8	.	.	PUNCT
ejpam-6997	834	1	information	information	NOUN
ejpam-6997	834	2	sciences	sciences	PROPN
ejpam-6997	834	3	,	,	PUNCT
ejpam-6997	834	4	112(1	112(1	NUM
ejpam-6997	834	5	-	-	SYM
ejpam-6997	834	6	4):39–49	4):39–49	NUM
ejpam-6997	834	7	,	,	PUNCT
ejpam-6997	834	8	1998	1998	NUM
ejpam-6997	834	9	.	.	PUNCT
ejpam-6997	835	1	[	[	X
ejpam-6997	835	2	26	26	NUM
ejpam-6997	835	3	]	]	PUNCT
ejpam-6997	835	4	roshdey	roshdey	ADJ
ejpam-6997	835	5	mareay	mareay	NOUN
ejpam-6997	835	6	.	.	PUNCT
ejpam-6997	836	1	soft	soft	ADJ
ejpam-6997	836	2	rough	rough	ADJ
ejpam-6997	836	3	sets	set	NOUN
ejpam-6997	836	4	based	base	VERB
ejpam-6997	836	5	on	on	ADP
ejpam-6997	836	6	covering	covering	NOUN
ejpam-6997	836	7	and	and	CCONJ
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ejpam-6997	836	9	applications	application	NOUN
ejpam-6997	836	10	.	.	PUNCT
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ejpam-6997	837	2	of	of	ADP
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ejpam-6997	837	4	in	in	ADP
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ejpam-6997	837	6	,	,	PUNCT
ejpam-6997	837	7	14(1):4	14(1):4	NUM
ejpam-6997	837	8	,	,	PUNCT
ejpam-6997	837	9	2024	2024	NUM
ejpam-6997	837	10	.	.	PUNCT
ejpam-6997	838	1	[	[	X
ejpam-6997	838	2	27	27	NUM
ejpam-6997	838	3	]	]	X
ejpam-6997	838	4	antoni	antoni	NOUN
ejpam-6997	838	5	wiweger	wiweger	NOUN
ejpam-6997	838	6	.	.	PUNCT
ejpam-6997	839	1	on	on	ADP
ejpam-6997	839	2	topological	topological	ADJ
ejpam-6997	839	3	rough	rough	ADJ
ejpam-6997	839	4	sets	set	NOUN
ejpam-6997	839	5	.	.	PUNCT
ejpam-6997	840	1	bulletin	bulletin	NOUN
ejpam-6997	840	2	of	of	ADP
ejpam-6997	840	3	the	the	DET
ejpam-6997	840	4	polish	polish	PROPN
ejpam-6997	840	5	academy	academy	PROPN
ejpam-6997	840	6	of	of	ADP
ejpam-6997	840	7	sciences	sciences	PROPN
ejpam-6997	840	8	.	.	PUNCT
ejpam-6997	841	1	mathematics	mathematic	NOUN
ejpam-6997	841	2	,	,	PUNCT
ejpam-6997	841	3	37(1	37(1	NOUN
ejpam-6997	841	4	-	-	PUNCT
ejpam-6997	841	5	6):89–93	6):89–93	NOUN
ejpam-6997	841	6	,	,	PUNCT
ejpam-6997	841	7	1989	1989	NUM
ejpam-6997	841	8	.	.	PUNCT
ejpam-6997	842	1	[	[	X
ejpam-6997	842	2	28	28	NUM
ejpam-6997	842	3	]	]	SYM
ejpam-6997	842	4	ea	ea	X
ejpam-6997	842	5	abo	abo	NOUN
ejpam-6997	842	6	-	-	PUNCT
ejpam-6997	842	7	tabl	tabl	NOUN
ejpam-6997	842	8	.	.	PUNCT
ejpam-6997	843	1	rough	rough	ADJ
ejpam-6997	843	2	sets	set	NOUN
ejpam-6997	843	3	and	and	CCONJ
ejpam-6997	843	4	topological	topological	ADJ
ejpam-6997	843	5	spaces	space	NOUN
ejpam-6997	843	6	based	base	VERB
ejpam-6997	843	7	on	on	ADP
ejpam-6997	843	8	similarity	similarity	NOUN
ejpam-6997	843	9	.	.	PUNCT
ejpam-6997	844	1	international	international	ADJ
ejpam-6997	844	2	journal	journal	PROPN
ejpam-6997	844	3	of	of	ADP
ejpam-6997	844	4	machine	machine	NOUN
ejpam-6997	844	5	learning	learning	NOUN
ejpam-6997	844	6	and	and	CCONJ
ejpam-6997	844	7	cybernetics	cybernetic	NOUN
ejpam-6997	844	8	,	,	PUNCT
ejpam-6997	844	9	4(5):451–458	4(5):451–458	NOUN
ejpam-6997	844	10	,	,	PUNCT
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ejpam-6997	844	12	.	.	PUNCT
ejpam-6997	845	1	[	[	X
ejpam-6997	845	2	29	29	NUM
ejpam-6997	845	3	]	]	X
ejpam-6997	845	4	tareq	tareq	PROPN
ejpam-6997	845	5	m	m	PROPN
ejpam-6997	845	6	al	al	PROPN
ejpam-6997	845	7	-	-	PUNCT
ejpam-6997	845	8	shami	shami	PROPN
ejpam-6997	845	9	.	.	PUNCT
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ejpam-6997	846	2	of	of	ADP
ejpam-6997	846	3	the	the	DET
ejpam-6997	846	4	approximations	approximation	NOUN
ejpam-6997	846	5	and	and	CCONJ
ejpam-6997	846	6	accuracy	accuracy	NOUN
ejpam-6997	846	7	measure	measure	NOUN
ejpam-6997	846	8	of	of	ADP
ejpam-6997	846	9	a	a	DET
ejpam-6997	846	10	rough	rough	ADJ
ejpam-6997	846	11	set	set	NOUN
ejpam-6997	846	12	using	use	VERB
ejpam-6997	846	13	somewhere	somewhere	ADV
ejpam-6997	846	14	dense	dense	ADJ
ejpam-6997	846	15	sets	set	NOUN
ejpam-6997	846	16	.	.	PUNCT
ejpam-6997	847	1	soft	soft	ADJ
ejpam-6997	847	2	computing	computing	NOUN
ejpam-6997	847	3	,	,	PUNCT
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ejpam-6997	847	5	,	,	PUNCT
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ejpam-6997	847	7	.	.	PUNCT
ejpam-6997	848	1	[	[	X
ejpam-6997	848	2	30	30	NUM
ejpam-6997	848	3	]	]	X
ejpam-6997	848	4	tareq	tareq	PROPN
ejpam-6997	848	5	m	m	PROPN
ejpam-6997	848	6	al	al	PROPN
ejpam-6997	848	7	-	-	PUNCT
ejpam-6997	848	8	shami	shami	PROPN
ejpam-6997	848	9	.	.	PUNCT
ejpam-6997	849	1	topological	topological	ADJ
ejpam-6997	849	2	approach	approach	NOUN
ejpam-6997	849	3	to	to	PART
ejpam-6997	849	4	generate	generate	VERB
ejpam-6997	849	5	new	new	ADJ
ejpam-6997	849	6	rough	rough	ADJ
ejpam-6997	849	7	set	set	NOUN
ejpam-6997	849	8	models	model	NOUN
ejpam-6997	849	9	.	.	PUNCT
ejpam-6997	850	1	complex	complex	ADJ
ejpam-6997	850	2	&	&	CCONJ
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ejpam-6997	850	4	systems	system	NOUN
ejpam-6997	850	5	,	,	PUNCT
ejpam-6997	850	6	8(5):4101–4113	8(5):4101–4113	NOUN
ejpam-6997	850	7	,	,	PUNCT
ejpam-6997	850	8	2022	2022	NUM
ejpam-6997	850	9	.	.	PUNCT
ejpam-6997	851	1	[	[	X
ejpam-6997	851	2	31	31	NUM
ejpam-6997	851	3	]	]	PUNCT
ejpam-6997	851	4	ef	ef	X
ejpam-6997	851	5	lashin	lashin	NOUN
ejpam-6997	851	6	,	,	PUNCT
ejpam-6997	851	7	am	be	AUX
ejpam-6997	851	8	kozae	kozae	NOUN
ejpam-6997	851	9	,	,	PUNCT
ejpam-6997	851	10	aa	aa	NOUN
ejpam-6997	851	11	abo	abo	NOUN
ejpam-6997	851	12	khadra	khadra	NOUN
ejpam-6997	851	13	,	,	PUNCT
ejpam-6997	851	14	and	and	CCONJ
ejpam-6997	851	15	tamer	tame	ADJ
ejpam-6997	851	16	medhat	medhat	PROPN
ejpam-6997	851	17	.	.	PUNCT
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ejpam-6997	852	4	for	for	ADP
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ejpam-6997	852	7	.	.	PUNCT
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ejpam-6997	853	6	,	,	PUNCT
ejpam-6997	853	7	40(1	40(1	NUM
ejpam-6997	853	8	-	-	SYM
ejpam-6997	853	9	2):35–43	2):35–43	NUM
ejpam-6997	853	10	,	,	PUNCT
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ejpam-6997	853	12	.	.	PUNCT
ejpam-6997	854	1	[	[	X
ejpam-6997	854	2	32	32	NUM
ejpam-6997	854	3	]	]	PUNCT
ejpam-6997	854	4	as	as	ADP
ejpam-6997	854	5	salama	salama	NOUN
ejpam-6997	854	6	.	.	PUNCT
ejpam-6997	855	1	topological	topological	ADJ
ejpam-6997	855	2	solution	solution	NOUN
ejpam-6997	855	3	of	of	ADP
ejpam-6997	855	4	missing	miss	VERB
ejpam-6997	855	5	attribute	attribute	NOUN
ejpam-6997	855	6	values	value	NOUN
ejpam-6997	855	7	problem	problem	NOUN
ejpam-6997	855	8	in	in	ADP
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ejpam-6997	855	10	information	information	NOUN
ejpam-6997	855	11	tables	table	NOUN
ejpam-6997	855	12	.	.	PUNCT
ejpam-6997	856	1	information	information	NOUN
ejpam-6997	856	2	sciences	sciences	PROPN
ejpam-6997	856	3	,	,	PUNCT
ejpam-6997	856	4	180(5):631–639	180(5):631–639	PROPN
ejpam-6997	856	5	,	,	PUNCT
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ejpam-6997	856	7	.	.	PUNCT
ejpam-6997	857	1	[	[	X
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ejpam-6997	857	3	]	]	PUNCT
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ejpam-6997	857	6	-	-	PROPN
ejpam-6997	857	7	sharkasy	sharkasy	PROPN
ejpam-6997	857	8	.	.	PUNCT
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ejpam-6997	858	4	space	space	NOUN
ejpam-6997	858	5	and	and	CCONJ
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ejpam-6997	858	8	its	its	PRON
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ejpam-6997	858	10	.	.	PUNCT
ejpam-6997	859	1	journal	journal	NOUN
ejpam-6997	859	2	of	of	ADP
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ejpam-6997	859	4	&	&	CCONJ
ejpam-6997	859	5	fuzzy	fuzzy	ADJ
ejpam-6997	859	6	systems	system	NOUN
ejpam-6997	859	7	,	,	PUNCT
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ejpam-6997	859	9	,	,	PUNCT
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ejpam-6997	859	11	.	.	PUNCT
ejpam-6997	860	1	[	[	X
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ejpam-6997	860	3	]	]	X
ejpam-6997	860	4	tareq	tareq	PROPN
ejpam-6997	860	5	m	m	PROPN
ejpam-6997	860	6	al	al	PROPN
ejpam-6997	860	7	-	-	PUNCT
ejpam-6997	860	8	shami	shami	PROPN
ejpam-6997	860	9	and	and	CCONJ
ejpam-6997	860	10	ibtesam	ibtesam	PROPN
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ejpam-6997	860	12	.	.	PUNCT
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ejpam-6997	861	8	.	.	PUNCT
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ejpam-6997	862	4	,	,	PUNCT
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ejpam-6997	862	6	,	,	PUNCT
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ejpam-6997	862	8	.	.	PUNCT
ejpam-6997	863	1	[	[	X
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ejpam-6997	863	4	tareq	tareq	PROPN
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ejpam-6997	863	7	-	-	PUNCT
ejpam-6997	863	8	shami	shami	PROPN
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ejpam-6997	863	12	.	.	PUNCT
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ejpam-6997	863	24	-	-	PUNCT
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ejpam-6997	863	27	.	.	PUNCT
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ejpam-6997	864	3	,	,	PUNCT
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ejpam-6997	864	7	.	.	PUNCT
ejpam-6997	865	1	[	[	X
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ejpam-6997	865	6	,	,	PUNCT
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ejpam-6997	865	9	,	,	PUNCT
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ejpam-6997	865	13	-	-	PUNCT
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ejpam-6997	865	16	and	and	CCONJ
ejpam-6997	865	17	m	m	PROPN
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ejpam-6997	866	5	-	-	PUNCT
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ejpam-6997	868	1	[	[	X
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ejpam-6997	868	3	]	]	PUNCT
ejpam-6997	868	4	as	as	ADP
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ejpam-6997	868	6	.	.	PUNCT
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ejpam-6997	869	14	systems	system	NOUN
ejpam-6997	869	15	.	.	PUNCT
ejpam-6997	870	1	filomat	filomat	PROPN
ejpam-6997	870	2	,	,	PUNCT
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ejpam-6997	870	6	.	.	PUNCT
ejpam-6997	871	1	[	[	X
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ejpam-6997	871	4	pankaj	pankaj	PROPN
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ejpam-6997	872	7	:	:	PUNCT
ejpam-6997	872	8	a	a	DET
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ejpam-6997	872	10	.	.	PUNCT
ejpam-6997	873	1	hacettepe	hacettepe	ADJ
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ejpam-6997	873	5	and	and	CCONJ
ejpam-6997	873	6	statistics	statistic	NOUN
ejpam-6997	873	7	,	,	PUNCT
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ejpam-6997	873	9	,	,	PUNCT
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ejpam-6997	873	11	.	.	PUNCT
ejpam-6997	874	1	[	[	X
ejpam-6997	874	2	39	39	NUM
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ejpam-6997	874	5	-	-	PUNCT
ejpam-6997	874	6	lan	lan	PROPN
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ejpam-6997	874	8	,	,	PUNCT
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ejpam-6997	874	13	changqing	changqe	VERB
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ejpam-6997	875	1	topological	topological	ADJ
ejpam-6997	875	2	structure	structure	NOUN
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ejpam-6997	875	4	relation	relation	NOUN
ejpam-6997	875	5	-	-	PUNCT
ejpam-6997	875	6	based	base	VERB
ejpam-6997	875	7	generalized	generalize	VERB
ejpam-6997	875	8	rough	rough	ADJ
ejpam-6997	875	9	sets	set	NOUN
ejpam-6997	875	10	.	.	PUNCT
ejpam-6997	876	1	fundamenta	fundamenta	PROPN
ejpam-6997	876	2	informaticae	informaticae	PROPN
ejpam-6997	876	3	,	,	PUNCT
ejpam-6997	876	4	147(4):477–491	147(4):477–491	NUM
ejpam-6997	876	5	,	,	PUNCT
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ejpam-6997	876	7	.	.	PUNCT
ejpam-6997	877	1	[	[	X
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ejpam-6997	877	3	]	]	X
ejpam-6997	877	4	g	g	PROPN
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ejpam-6997	877	6	.	.	PUNCT
ejpam-6997	878	1	sur	sur	PROPN
ejpam-6997	878	2	les	les	PROPN
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ejpam-6997	878	4	de	de	X
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ejpam-6997	878	6	et	et	PROPN
ejpam-6997	878	7	,	,	PUNCT
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ejpam-6997	878	9	.	.	PUNCT
ejpam-6997	879	1	[	[	X
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ejpam-6997	879	4	aa	aa	PROPN
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ejpam-6997	879	6	.	.	PUNCT
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ejpam-6997	880	10	.	.	PUNCT
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ejpam-6997	881	2	j.	j.	PROPN
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ejpam-6997	881	5	.	.	PUNCT
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ejpam-6997	881	7	,	,	PUNCT
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ejpam-6997	881	11	.	.	PUNCT
ejpam-6997	882	1	[	[	X
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ejpam-6997	882	4	aa	aa	PROPN
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ejpam-6997	882	6	.	.	PUNCT
ejpam-6997	882	7	grill	grill	PROPN
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ejpam-6997	882	13	nano	nano	NOUN
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ejpam-6997	882	17	.	.	PUNCT
ejpam-6997	883	1	journal	journal	NOUN
ejpam-6997	883	2	of	of	ADP
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ejpam-6997	883	7	,	,	PUNCT
ejpam-6997	883	8	25(2):164–166	25(2):164–166	PROPN
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ejpam-6997	883	11	.	.	PUNCT
ejpam-6997	884	1	[	[	X
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ejpam-6997	884	3	]	]	PUNCT
ejpam-6997	884	4	as	as	ADP
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ejpam-6997	884	6	and	and	CCONJ
ejpam-6997	884	7	mohamed	mohamed	PROPN
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ejpam-6997	884	9	ezzat	ezzat	PROPN
ejpam-6997	884	10	abd	abd	PROPN
ejpam-6997	884	11	el	el	PROPN
ejpam-6997	884	12	-	-	PUNCT
ejpam-6997	884	13	monsef	monsef	ADJ
ejpam-6997	884	14	.	.	PUNCT
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ejpam-6997	885	3	approach	approach	NOUN
ejpam-6997	885	4	of	of	ADP
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ejpam-6997	885	6	set	set	NOUN
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ejpam-6997	885	8	.	.	PUNCT
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ejpam-6997	886	6	,	,	PUNCT
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ejpam-6997	886	8	,	,	PUNCT
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ejpam-6997	886	10	.	.	PUNCT
ejpam-6997	887	1	a.	a.	PROPN
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ejpam-6997	887	7	,	,	PUNCT
ejpam-6997	887	8	b.	b.	PROPN
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ejpam-6997	887	10	/	/	SYM
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ejpam-6997	887	12	.	.	PUNCT
ejpam-6997	888	1	j.	j.	PROPN
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ejpam-6997	888	6	,	,	PUNCT
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ejpam-6997	888	8	(	(	PUNCT
ejpam-6997	888	9	4	4	NUM
ejpam-6997	888	10	)	)	PUNCT
ejpam-6997	888	11	(	(	PUNCT
ejpam-6997	888	12	2025	2025	NUM
ejpam-6997	888	13	)	)	PUNCT
ejpam-6997	888	14	,	,	PUNCT
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ejpam-6997	888	19	[	[	SYM
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ejpam-6997	888	22	yi	yi	PROPN
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ejpam-6997	888	25	.	.	PUNCT
ejpam-6997	889	1	relational	relational	ADJ
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ejpam-6997	889	3	of	of	ADP
ejpam-6997	889	4	neighborhood	neighborhood	NOUN
ejpam-6997	889	5	operators	operator	NOUN
ejpam-6997	889	6	and	and	CCONJ
ejpam-6997	889	7	rough	rough	ADJ
ejpam-6997	889	8	set	set	NOUN
ejpam-6997	889	9	approximation	approximation	NOUN
ejpam-6997	889	10	operators	operator	NOUN
ejpam-6997	889	11	.	.	PUNCT
ejpam-6997	890	1	information	information	NOUN
ejpam-6997	890	2	sciences	science	NOUN
ejpam-6997	890	3	,	,	PUNCT
ejpam-6997	890	4	111(1	111(1	NUM
ejpam-6997	890	5	-	-	SYM
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ejpam-6997	890	7	,	,	PUNCT
ejpam-6997	890	8	1998	1998	NUM
ejpam-6997	890	9	.	.	PUNCT
ejpam-6997	891	1	[	[	X
ejpam-6997	891	2	45	45	NUM
ejpam-6997	891	3	]	]	X
ejpam-6997	891	4	tareq	tareq	PROPN
ejpam-6997	891	5	m	m	PROPN
ejpam-6997	891	6	al	al	PROPN
ejpam-6997	891	7	-	-	PUNCT
ejpam-6997	891	8	shami	shami	PROPN
ejpam-6997	891	9	and	and	CCONJ
ejpam-6997	891	10	davide	davide	PROPN
ejpam-6997	891	11	ciucci	ciucci	PROPN
ejpam-6997	891	12	.	.	PUNCT
ejpam-6997	892	1	subset	subset	ADJ
ejpam-6997	892	2	neighborhood	neighborhood	NOUN
ejpam-6997	892	3	rough	rough	ADJ
ejpam-6997	892	4	sets	set	NOUN
ejpam-6997	892	5	.	.	PUNCT
ejpam-6997	893	1	knowledgebased	knowledgebased	ADJ
ejpam-6997	893	2	systems	system	NOUN
ejpam-6997	893	3	,	,	PUNCT
ejpam-6997	893	4	237:107868	237:107868	NUM
ejpam-6997	893	5	,	,	PUNCT
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ejpam-6997	893	7	.	.	PUNCT
ejpam-6997	894	1	[	[	X
ejpam-6997	894	2	46	46	NUM
ejpam-6997	894	3	]	]	X
ejpam-6997	894	4	tareq	tareq	PROPN
ejpam-6997	894	5	m	m	PROPN
ejpam-6997	894	6	al	al	PROPN
ejpam-6997	894	7	-	-	PUNCT
ejpam-6997	894	8	shami	shami	PROPN
ejpam-6997	894	9	,	,	PUNCT
ejpam-6997	894	10	rodyna	rodyna	VERB
ejpam-6997	894	11	a	a	DET
ejpam-6997	894	12	hosny	hosny	PROPN
ejpam-6997	894	13	,	,	PUNCT
ejpam-6997	894	14	abdelwaheb	abdelwaheb	PROPN
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ejpam-6997	894	16	,	,	PUNCT
ejpam-6997	894	17	and	and	CCONJ
ejpam-6997	894	18	m	m	PROPN
ejpam-6997	894	19	hosny	hosny	PROPN
ejpam-6997	894	20	.	.	PUNCT
ejpam-6997	895	1	cardinality	cardinality	PROPN
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ejpam-6997	895	3	neighborhoods	neighborhood	NOUN
ejpam-6997	895	4	with	with	ADP
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ejpam-6997	895	6	.	.	PUNCT
ejpam-6997	896	1	aims	aim	VERB
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ejpam-6997	896	3	,	,	PUNCT
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ejpam-6997	896	5	,	,	PUNCT
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ejpam-6997	896	7	.	.	PUNCT
ejpam-6997	897	1	[	[	X
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ejpam-6997	897	4	aa	aa	PROPN
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ejpam-6997	897	6	,	,	PUNCT
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ejpam-6997	897	13	-	-	PUNCT
ejpam-6997	897	14	gang	gang	PROPN
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ejpam-6997	897	19	via	via	ADP
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ejpam-6997	897	22	structure	structure	NOUN
ejpam-6997	897	23	.	.	PUNCT
ejpam-6997	898	1	journal	journal	NOUN
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ejpam-6997	898	4	&	&	CCONJ
ejpam-6997	898	5	fuzzy	fuzzy	ADJ
ejpam-6997	898	6	systems	system	NOUN
ejpam-6997	898	7	,	,	PUNCT
ejpam-6997	898	8	39(3):4723	39(3):4723	NUM
ejpam-6997	898	9	–	–	PUNCT
ejpam-6997	898	10	4730	4730	NUM
ejpam-6997	898	11	,	,	PUNCT
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ejpam-6997	898	13	.	.	PUNCT