id	sid	tid	token	lemma	pos
ejpam-7160	1	1	european	european	PROPN
ejpam-7160	1	2	journal	journal	PROPN
ejpam-7160	1	3	of	of	ADP
ejpam-7160	1	4	pure	pure	ADJ
ejpam-7160	1	5	and	and	CCONJ
ejpam-7160	1	6	applied	applied	ADJ
ejpam-7160	1	7	mathematics	mathematic	NOUN
ejpam-7160	1	8	2025	2025	NUM
ejpam-7160	1	9	,	,	PUNCT
ejpam-7160	1	10	vol	vol	NOUN
ejpam-7160	1	11	.	.	PROPN
ejpam-7160	1	12	18	18	NUM
ejpam-7160	1	13	,	,	PUNCT
ejpam-7160	1	14	issue	issue	NOUN
ejpam-7160	1	15	4	4	NUM
ejpam-7160	1	16	,	,	PUNCT
ejpam-7160	1	17	article	article	NOUN
ejpam-7160	1	18	number	number	NOUN
ejpam-7160	1	19	7160	7160	NUM
ejpam-7160	1	20	issn	issn	PROPN
ejpam-7160	1	21	1307	1307	NUM
ejpam-7160	1	22	-	-	SYM
ejpam-7160	1	23	5543	5543	NUM
ejpam-7160	1	24	–	–	PUNCT
ejpam-7160	1	25	ejpam.com	ejpam.com	X
ejpam-7160	1	26	published	publish	VERB
ejpam-7160	1	27	by	by	ADP
ejpam-7160	1	28	new	new	PROPN
ejpam-7160	1	29	york	york	PROPN
ejpam-7160	1	30	business	business	PROPN
ejpam-7160	1	31	global	global	PROPN
ejpam-7160	1	32	exploring	explore	VERB
ejpam-7160	1	33	the	the	DET
ejpam-7160	1	34	applications	application	NOUN
ejpam-7160	1	35	of	of	ADP
ejpam-7160	1	36	grill	grill	NOUN
ejpam-7160	1	37	rough	rough	ADJ
ejpam-7160	1	38	topological	topological	ADJ
ejpam-7160	1	39	structures	structure	NOUN
ejpam-7160	1	40	generated	generate	VERB
ejpam-7160	1	41	by	by	ADP
ejpam-7160	1	42	different	different	ADJ
ejpam-7160	1	43	minimal	minimal	ADJ
ejpam-7160	1	44	neighborhood	neighborhood	NOUN
ejpam-7160	1	45	types	type	NOUN
ejpam-7160	1	46	a.	a.	NOUN
ejpam-7160	1	47	a.	a.	NOUN
ejpam-7160	1	48	azzam1,∗	azzam1,∗	PROPN
ejpam-7160	1	49	,	,	PUNCT
ejpam-7160	1	50	b.	b.	PROPN
ejpam-7160	1	51	alreshidi1	alreshidi1	PROPN
ejpam-7160	1	52	,	,	PUNCT
ejpam-7160	1	53	m.	m.	NOUN
ejpam-7160	1	54	aldawood1	aldawood1	NOUN
ejpam-7160	1	55	1	1	NUM
ejpam-7160	1	56	mathematics	mathematics	PROPN
ejpam-7160	1	57	department	department	NOUN
ejpam-7160	1	58	,	,	PUNCT
ejpam-7160	1	59	faculty	faculty	NOUN
ejpam-7160	1	60	of	of	ADP
ejpam-7160	1	61	science	science	NOUN
ejpam-7160	1	62	and	and	CCONJ
ejpam-7160	1	63	humanities	humanity	NOUN
ejpam-7160	1	64	,	,	PUNCT
ejpam-7160	1	65	prince	prince	PROPN
ejpam-7160	1	66	sattam	sattam	PROPN
ejpam-7160	1	67	bin	bin	PROPN
ejpam-7160	1	68	abdulaziz	abdulaziz	PROPN
ejpam-7160	1	69	university	university	PROPN
ejpam-7160	1	70	,	,	PUNCT
ejpam-7160	1	71	alkharj	alkharj	VERB
ejpam-7160	1	72	11942	11942	NUM
ejpam-7160	1	73	,	,	PUNCT
ejpam-7160	1	74	saudi	saudi	PROPN
ejpam-7160	1	75	arabia	arabia	PROPN
ejpam-7160	1	76	abstract	abstract	NOUN
ejpam-7160	1	77	.	.	PUNCT
ejpam-7160	2	1	a	a	DET
ejpam-7160	2	2	variety	variety	NOUN
ejpam-7160	2	3	of	of	ADP
ejpam-7160	2	4	grill	grill	NOUN
ejpam-7160	2	5	-	-	PUNCT
ejpam-7160	2	6	based	base	VERB
ejpam-7160	2	7	topologies	topology	NOUN
ejpam-7160	2	8	are	be	AUX
ejpam-7160	2	9	developed	develop	VERB
ejpam-7160	2	10	and	and	CCONJ
ejpam-7160	2	11	contrasted	contrast	VERB
ejpam-7160	2	12	with	with	ADP
ejpam-7160	2	13	earlier	early	ADJ
ejpam-7160	2	14	topologies	topology	NOUN
ejpam-7160	2	15	.	.	PUNCT
ejpam-7160	3	1	the	the	DET
ejpam-7160	3	2	results	result	NOUN
ejpam-7160	3	3	demonstrate	demonstrate	VERB
ejpam-7160	3	4	that	that	SCONJ
ejpam-7160	3	5	the	the	DET
ejpam-7160	3	6	present	present	ADJ
ejpam-7160	3	7	ones	one	NOUN
ejpam-7160	3	8	exceed	exceed	VERB
ejpam-7160	3	9	their	their	PRON
ejpam-7160	3	10	predecessors	predecessor	NOUN
ejpam-7160	3	11	.	.	PUNCT
ejpam-7160	4	1	this	this	DET
ejpam-7160	4	2	study	study	NOUN
ejpam-7160	4	3	distinguishes	distinguish	VERB
ejpam-7160	4	4	itself	itself	PRON
ejpam-7160	4	5	by	by	ADP
ejpam-7160	4	6	highlighting	highlight	VERB
ejpam-7160	4	7	the	the	DET
ejpam-7160	4	8	advantages	advantage	NOUN
ejpam-7160	4	9	of	of	ADP
ejpam-7160	4	10	certain	certain	ADJ
ejpam-7160	4	11	topologies	topology	NOUN
ejpam-7160	4	12	and	and	CCONJ
ejpam-7160	4	13	identifying	identify	VERB
ejpam-7160	4	14	both	both	CCONJ
ejpam-7160	4	15	the	the	DET
ejpam-7160	4	16	minimum	minimum	ADJ
ejpam-7160	4	17	and	and	CCONJ
ejpam-7160	4	18	maximum	maximum	ADJ
ejpam-7160	4	19	values	value	NOUN
ejpam-7160	4	20	.	.	PUNCT
ejpam-7160	5	1	these	these	DET
ejpam-7160	5	2	structural	structural	ADJ
ejpam-7160	5	3	topologies	topology	NOUN
ejpam-7160	5	4	are	be	AUX
ejpam-7160	5	5	later	later	ADV
ejpam-7160	5	6	utilized	utilize	VERB
ejpam-7160	5	7	to	to	PART
ejpam-7160	5	8	conduct	conduct	VERB
ejpam-7160	5	9	a	a	DET
ejpam-7160	5	10	more	more	ADV
ejpam-7160	5	11	thorough	thorough	ADJ
ejpam-7160	5	12	investigation	investigation	NOUN
ejpam-7160	5	13	of	of	ADP
ejpam-7160	5	14	extended	extended	ADJ
ejpam-7160	5	15	rough	rough	ADJ
ejpam-7160	5	16	sets	set	NOUN
ejpam-7160	5	17	.	.	PUNCT
ejpam-7160	6	1	compared	compare	VERB
ejpam-7160	6	2	to	to	ADP
ejpam-7160	6	3	earlier	early	ADJ
ejpam-7160	6	4	models	model	NOUN
ejpam-7160	6	5	,	,	PUNCT
ejpam-7160	6	6	the	the	DET
ejpam-7160	6	7	suggested	suggest	VERB
ejpam-7160	6	8	approximate	approximate	ADJ
ejpam-7160	6	9	models	model	NOUN
ejpam-7160	6	10	reduce	reduce	VERB
ejpam-7160	6	11	vagueness	vagueness	NOUN
ejpam-7160	6	12	and	and	CCONJ
ejpam-7160	6	13	uncertainty	uncertainty	NOUN
ejpam-7160	6	14	,	,	PUNCT
ejpam-7160	6	15	which	which	PRON
ejpam-7160	6	16	makes	make	VERB
ejpam-7160	6	17	them	they	PRON
ejpam-7160	6	18	especially	especially	ADV
ejpam-7160	6	19	important	important	ADJ
ejpam-7160	6	20	when	when	SCONJ
ejpam-7160	6	21	applied	apply	VERB
ejpam-7160	6	22	to	to	ADP
ejpam-7160	6	23	rough	rough	ADJ
ejpam-7160	6	24	sets	set	NOUN
ejpam-7160	6	25	(	(	PUNCT
ejpam-7160	6	26	rhss	rhss	NOUN
ejpam-7160	6	27	)	)	PUNCT
ejpam-7160	6	28	.	.	PUNCT
ejpam-7160	7	1	furthermore	furthermore	ADV
ejpam-7160	7	2	,	,	PUNCT
ejpam-7160	7	3	the	the	DET
ejpam-7160	7	4	suggested	suggest	VERB
ejpam-7160	7	5	models	model	NOUN
ejpam-7160	7	6	differ	differ	VERB
ejpam-7160	7	7	from	from	ADP
ejpam-7160	7	8	their	their	PRON
ejpam-7160	7	9	predecessors	predecessor	NOUN
ejpam-7160	7	10	in	in	ADP
ejpam-7160	7	11	that	that	SCONJ
ejpam-7160	7	12	they	they	PRON
ejpam-7160	7	13	exhibit	exhibit	VERB
ejpam-7160	7	14	all	all	PRON
ejpam-7160	7	15	of	of	ADP
ejpam-7160	7	16	pawlak	pawlak	ADJ
ejpam-7160	7	17	’s	’s	PART
ejpam-7160	7	18	properties	property	NOUN
ejpam-7160	7	19	,	,	PUNCT
ejpam-7160	7	20	including	include	VERB
ejpam-7160	7	21	the	the	DET
ejpam-7160	7	22	capability	capability	NOUN
ejpam-7160	7	23	of	of	ADP
ejpam-7160	7	24	contrasting	contrast	VERB
ejpam-7160	7	25	various	various	ADJ
ejpam-7160	7	26	approximations	approximation	NOUN
ejpam-7160	7	27	(	(	PUNCT
ejpam-7160	7	28	aprs	aprs	NOUN
ejpam-7160	7	29	)	)	PUNCT
ejpam-7160	7	30	,	,	PUNCT
ejpam-7160	7	31	and	and	CCONJ
ejpam-7160	7	32	have	have	VERB
ejpam-7160	7	33	the	the	DET
ejpam-7160	7	34	quality	quality	NOUN
ejpam-7160	7	35	of	of	ADP
ejpam-7160	7	36	monotonicity	monotonicity	NOUN
ejpam-7160	7	37	across	across	ADP
ejpam-7160	7	38	all	all	DET
ejpam-7160	7	39	relations	relation	NOUN
ejpam-7160	7	40	.	.	PUNCT
ejpam-7160	8	1	in	in	ADP
ejpam-7160	8	2	addition	addition	NOUN
ejpam-7160	8	3	,	,	PUNCT
ejpam-7160	8	4	the	the	DET
ejpam-7160	8	5	importance	importance	NOUN
ejpam-7160	8	6	of	of	ADP
ejpam-7160	8	7	new	new	ADJ
ejpam-7160	8	8	discoveries	discovery	NOUN
ejpam-7160	8	9	was	be	AUX
ejpam-7160	8	10	highlighted	highlight	VERB
ejpam-7160	8	11	by	by	ADP
ejpam-7160	8	12	demonstrating	demonstrate	VERB
ejpam-7160	8	13	their	their	PRON
ejpam-7160	8	14	use	use	NOUN
ejpam-7160	8	15	for	for	ADP
ejpam-7160	8	16	human	human	ADJ
ejpam-7160	8	17	health	health	NOUN
ejpam-7160	8	18	.	.	PUNCT
ejpam-7160	9	1	besides	besides	SCONJ
ejpam-7160	9	2	examining	examine	VERB
ejpam-7160	9	3	its	its	PRON
ejpam-7160	9	4	limitations	limitation	NOUN
ejpam-7160	9	5	,	,	PUNCT
ejpam-7160	9	6	the	the	DET
ejpam-7160	9	7	benefits	benefit	NOUN
ejpam-7160	9	8	of	of	ADP
ejpam-7160	9	9	the	the	DET
ejpam-7160	9	10	chosen	choose	VERB
ejpam-7160	9	11	technique	technique	NOUN
ejpam-7160	9	12	were	be	AUX
ejpam-7160	9	13	assessed	assess	VERB
ejpam-7160	9	14	.	.	PUNCT
ejpam-7160	10	1	the	the	DET
ejpam-7160	10	2	paper	paper	NOUN
ejpam-7160	10	3	ends	end	VERB
ejpam-7160	10	4	with	with	ADP
ejpam-7160	10	5	a	a	DET
ejpam-7160	10	6	summary	summary	NOUN
ejpam-7160	10	7	of	of	ADP
ejpam-7160	10	8	the	the	DET
ejpam-7160	10	9	main	main	ADJ
ejpam-7160	10	10	ideas	idea	NOUN
ejpam-7160	10	11	of	of	ADP
ejpam-7160	10	12	the	the	DET
ejpam-7160	10	13	proposed	propose	VERB
ejpam-7160	10	14	methodology	methodology	NOUN
ejpam-7160	10	15	and	and	CCONJ
ejpam-7160	10	16	recommendations	recommendation	NOUN
ejpam-7160	10	17	for	for	ADP
ejpam-7160	10	18	future	future	ADJ
ejpam-7160	10	19	research	research	NOUN
ejpam-7160	10	20	paths	path	NOUN
ejpam-7160	10	21	.	.	PUNCT
ejpam-7160	11	1	2020	2020	NUM
ejpam-7160	11	2	mathematics	mathematic	NOUN
ejpam-7160	11	3	subject	subject	NOUN
ejpam-7160	11	4	classifications	classification	NOUN
ejpam-7160	11	5	:	:	PUNCT
ejpam-7160	11	6	54a05	54a05	NUM
ejpam-7160	11	7	,	,	PUNCT
ejpam-7160	11	8	54c55	54c55	NUM
ejpam-7160	11	9	,	,	PUNCT
ejpam-7160	11	10	54d80	54d80	NUM
ejpam-7160	11	11	key	key	ADJ
ejpam-7160	11	12	words	word	NOUN
ejpam-7160	11	13	and	and	CCONJ
ejpam-7160	11	14	phrases	phrase	NOUN
ejpam-7160	11	15	:	:	PUNCT
ejpam-7160	11	16	upper	upper	ADJ
ejpam-7160	11	17	-	-	PUNCT
ejpam-7160	11	18	lower	low	ADJ
ejpam-7160	11	19	apr	apr	NOUN
ejpam-7160	11	20	,	,	PUNCT
ejpam-7160	11	21	grill	grill	NOUN
ejpam-7160	11	22	,	,	PUNCT
ejpam-7160	11	23	minimal	minimal	ADJ
ejpam-7160	11	24	neighborhood	neighborhood	NOUN
ejpam-7160	11	25	,	,	PUNCT
ejpam-7160	11	26	(	(	PUNCT
ejpam-7160	11	27	rhss	rhss	ADV
ejpam-7160	11	28	)	)	PUNCT
ejpam-7160	11	29	1	1	X
ejpam-7160	11	30	.	.	X
ejpam-7160	11	31	introduction	introduction	NOUN
ejpam-7160	11	32	in	in	ADP
ejpam-7160	11	33	the	the	DET
ejpam-7160	11	34	1980s	1980	NOUN
ejpam-7160	11	35	,	,	PUNCT
ejpam-7160	11	36	pawlak	pawlak	ADJ
ejpam-7160	11	37	[	[	X
ejpam-7160	11	38	1	1	NUM
ejpam-7160	11	39	,	,	PUNCT
ejpam-7160	11	40	2	2	NUM
ejpam-7160	11	41	]	]	PUNCT
ejpam-7160	11	42	created	create	VERB
ejpam-7160	11	43	rough	rough	ADJ
ejpam-7160	11	44	set	set	NOUN
ejpam-7160	11	45	theory	theory	NOUN
ejpam-7160	11	46	(	(	PUNCT
ejpam-7160	11	47	rhst	rhst	NOUN
ejpam-7160	11	48	)	)	PUNCT
ejpam-7160	11	49	to	to	PART
ejpam-7160	11	50	deal	deal	VERB
ejpam-7160	11	51	with	with	ADP
ejpam-7160	11	52	uncertainty	uncertainty	NOUN
ejpam-7160	11	53	in	in	ADP
ejpam-7160	11	54	medical	medical	ADJ
ejpam-7160	11	55	and	and	CCONJ
ejpam-7160	11	56	technical	technical	ADJ
ejpam-7160	11	57	data	datum	NOUN
ejpam-7160	11	58	processing	processing	NOUN
ejpam-7160	11	59	,	,	PUNCT
ejpam-7160	11	60	as	as	ADV
ejpam-7160	11	61	well	well	ADV
ejpam-7160	11	62	as	as	ADP
ejpam-7160	11	63	other	other	ADJ
ejpam-7160	11	64	domains	domain	NOUN
ejpam-7160	11	65	.	.	PUNCT
ejpam-7160	12	1	it	it	PRON
ejpam-7160	12	2	is	be	AUX
ejpam-7160	12	3	very	very	ADV
ejpam-7160	12	4	beneficial	beneficial	ADJ
ejpam-7160	12	5	for	for	ADP
ejpam-7160	12	6	assessing	assess	VERB
ejpam-7160	12	7	inadequate	inadequate	ADJ
ejpam-7160	12	8	or	or	CCONJ
ejpam-7160	12	9	confusing	confusing	ADJ
ejpam-7160	12	10	information	information	NOUN
ejpam-7160	12	11	systems	system	NOUN
ejpam-7160	12	12	,	,	PUNCT
ejpam-7160	12	13	as	as	ADV
ejpam-7160	12	14	well	well	ADV
ejpam-7160	12	15	as	as	ADP
ejpam-7160	12	16	categorizing	categorize	VERB
ejpam-7160	12	17	data	datum	NOUN
ejpam-7160	12	18	.	.	PUNCT
ejpam-7160	13	1	according	accord	VERB
ejpam-7160	13	2	to	to	ADP
ejpam-7160	13	3	the	the	DET
ejpam-7160	13	4	facts	fact	NOUN
ejpam-7160	13	5	at	at	ADP
ejpam-7160	13	6	hand	hand	NOUN
ejpam-7160	13	7	,	,	PUNCT
ejpam-7160	13	8	each	each	DET
ejpam-7160	13	9	class	class	NOUN
ejpam-7160	13	10	comprises	comprise	VERB
ejpam-7160	13	11	a	a	DET
ejpam-7160	13	12	collection	collection	NOUN
ejpam-7160	13	13	of	of	ADP
ejpam-7160	13	14	items	item	NOUN
ejpam-7160	13	15	that	that	PRON
ejpam-7160	13	16	are	be	AUX
ejpam-7160	13	17	comparable	comparable	ADJ
ejpam-7160	13	18	to	to	ADP
ejpam-7160	13	19	one	one	NUM
ejpam-7160	13	20	another	another	DET
ejpam-7160	13	21	.	.	PUNCT
ejpam-7160	14	1	to	to	PART
ejpam-7160	14	2	deal	deal	VERB
ejpam-7160	14	3	with	with	ADP
ejpam-7160	14	4	uncertainty	uncertainty	NOUN
ejpam-7160	14	5	and	and	CCONJ
ejpam-7160	14	6	confusion	confusion	NOUN
ejpam-7160	14	7	,	,	PUNCT
ejpam-7160	14	8	the	the	DET
ejpam-7160	14	9	theory	theory	NOUN
ejpam-7160	14	10	makes	make	VERB
ejpam-7160	14	11	use	use	NOUN
ejpam-7160	14	12	of	of	ADP
ejpam-7160	14	13	two	two	NUM
ejpam-7160	14	14	main	main	ADJ
ejpam-7160	14	15	(	(	PUNCT
ejpam-7160	14	16	aprs	aprs	NOUN
ejpam-7160	14	17	)	)	PUNCT
ejpam-7160	14	18	.	.	PUNCT
ejpam-7160	15	1	in	in	ADP
ejpam-7160	15	2	situations	situation	NOUN
ejpam-7160	15	3	where	where	SCONJ
ejpam-7160	15	4	exact	exact	ADJ
ejpam-7160	15	5	limits	limit	NOUN
ejpam-7160	15	6	are	be	AUX
ejpam-7160	15	7	unclear	unclear	ADJ
ejpam-7160	15	8	,	,	PUNCT
ejpam-7160	15	9	this	this	DET
ejpam-7160	15	10	distinction	distinction	NOUN
ejpam-7160	15	11	aids	aid	VERB
ejpam-7160	15	12	in	in	ADP
ejpam-7160	15	13	data	datum	NOUN
ejpam-7160	15	14	management	management	NOUN
ejpam-7160	15	15	and	and	CCONJ
ejpam-7160	15	16	analysis	analysis	NOUN
ejpam-7160	15	17	.	.	PUNCT
ejpam-7160	16	1	through	through	ADP
ejpam-7160	16	2	(	(	PUNCT
ejpam-7160	16	3	aprs	aprs	NOUN
ejpam-7160	16	4	)	)	PUNCT
ejpam-7160	16	5	of	of	ADP
ejpam-7160	16	6	groups	group	NOUN
ejpam-7160	16	7	that	that	PRON
ejpam-7160	16	8	can	can	AUX
ejpam-7160	16	9	not	not	PART
ejpam-7160	16	10	be	be	AUX
ejpam-7160	16	11	properly	properly	ADV
ejpam-7160	16	12	specified	specify	VERB
ejpam-7160	16	13	,	,	PUNCT
ejpam-7160	16	14	it	it	PRON
ejpam-7160	16	15	also	also	ADV
ejpam-7160	16	16	offers	offer	VERB
ejpam-7160	16	17	a	a	DET
ejpam-7160	16	18	formal	formal	ADJ
ejpam-7160	16	19	method	method	NOUN
ejpam-7160	16	20	of	of	ADP
ejpam-7160	16	21	handling	handle	VERB
ejpam-7160	16	22	ambiguous	ambiguous	ADJ
ejpam-7160	16	23	or	or	CCONJ
ejpam-7160	16	24	incomplete	incomplete	ADJ
ejpam-7160	16	25	information	information	NOUN
ejpam-7160	16	26	.	.	PUNCT
ejpam-7160	17	1	rhst	rhst	NOUN
ejpam-7160	17	2	∗corresponding	∗corresponde	VERB
ejpam-7160	17	3	author	author	NOUN
ejpam-7160	17	4	.	.	PUNCT
ejpam-7160	18	1	doi	doi	NOUN
ejpam-7160	18	2	:	:	PUNCT
ejpam-7160	18	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7160	https://doi.org/10.29020/nybg.ejpam.v18i4.7160	PROPN
ejpam-7160	18	4	email	email	NOUN
ejpam-7160	18	5	addresses	address	VERB
ejpam-7160	18	6	:	:	PUNCT
ejpam-7160	18	7	azzam0911@yahoo.com	azzam0911@yahoo.com	X
ejpam-7160	18	8	(	(	PUNCT
ejpam-7160	18	9	a.	a.	NOUN
ejpam-7160	18	10	a.	a.	PROPN
ejpam-7160	18	11	azzam	azzam	PROPN
ejpam-7160	18	12	)	)	PUNCT
ejpam-7160	18	13	,	,	PUNCT
ejpam-7160	19	1	b.alreshidi@psau.edu.sa	b.alreshidi@psau.edu.sa	PROPN
ejpam-7160	19	2	(	(	PUNCT
ejpam-7160	19	3	b.	b.	PROPN
ejpam-7160	19	4	alreshidi	alreshidi	PROPN
ejpam-7160	19	5	)	)	PUNCT
ejpam-7160	19	6	,	,	PUNCT
ejpam-7160	19	7	m.aldawood@psau.edu.sa	m.aldawood@psau.edu.sa	PROPN
ejpam-7160	19	8	(	(	PUNCT
ejpam-7160	19	9	m.	m.	NOUN
ejpam-7160	19	10	aldawood	aldawood	PROPN
ejpam-7160	19	11	)	)	PUNCT
ejpam-7160	19	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-7160	20	1	1	1	NUM
ejpam-7160	20	2	copyright	copyright	NOUN
ejpam-7160	20	3	:	:	PUNCT
ejpam-7160	20	4	©	©	PROPN
ejpam-7160	20	5	2025	2025	NUM
ejpam-7160	20	6	the	the	DET
ejpam-7160	20	7	author(s	author(s	NOUN
ejpam-7160	20	8	)	)	PUNCT
ejpam-7160	20	9	.	.	PUNCT
ejpam-7160	21	1	(	(	PUNCT
ejpam-7160	21	2	cc	cc	NOUN
ejpam-7160	21	3	by	by	ADP
ejpam-7160	21	4	-	-	PUNCT
ejpam-7160	21	5	nc	nc	PROPN
ejpam-7160	21	6	4.0	4.0	NUM
ejpam-7160	21	7	)	)	PUNCT
ejpam-7160	21	8	a.	a.	NOUN
ejpam-7160	21	9	a.	a.	NOUN
ejpam-7160	21	10	azzam	azzam	PROPN
ejpam-7160	21	11	et	et	PROPN
ejpam-7160	21	12	al	al	PROPN
ejpam-7160	21	13	.	.	PUNCT
ejpam-7160	21	14	/	/	SYM
ejpam-7160	21	15	eur	eur	PROPN
ejpam-7160	21	16	.	.	PUNCT
ejpam-7160	22	1	j.	j.	PROPN
ejpam-7160	22	2	pure	pure	PROPN
ejpam-7160	22	3	appl	appl	PROPN
ejpam-7160	22	4	.	.	PROPN
ejpam-7160	22	5	math	math	PROPN
ejpam-7160	22	6	,	,	PUNCT
ejpam-7160	22	7	18	18	NUM
ejpam-7160	22	8	(	(	PUNCT
ejpam-7160	22	9	4	4	NUM
ejpam-7160	22	10	)	)	PUNCT
ejpam-7160	22	11	(	(	PUNCT
ejpam-7160	22	12	2025	2025	NUM
ejpam-7160	22	13	)	)	PUNCT
ejpam-7160	22	14	,	,	PUNCT
ejpam-7160	22	15	7160	7160	NUM
ejpam-7160	22	16	2	2	NUM
ejpam-7160	22	17	of	of	ADP
ejpam-7160	22	18	22	22	NUM
ejpam-7160	22	19	has	have	AUX
ejpam-7160	22	20	been	be	AUX
ejpam-7160	22	21	expanded	expand	VERB
ejpam-7160	22	22	in	in	ADP
ejpam-7160	22	23	a	a	DET
ejpam-7160	22	24	number	number	NOUN
ejpam-7160	22	25	of	of	ADP
ejpam-7160	22	26	ways	way	NOUN
ejpam-7160	22	27	to	to	PART
ejpam-7160	22	28	handle	handle	VERB
ejpam-7160	22	29	a	a	DET
ejpam-7160	22	30	greater	great	ADJ
ejpam-7160	22	31	variety	variety	NOUN
ejpam-7160	22	32	of	of	ADP
ejpam-7160	22	33	uncertainty	uncertainty	NOUN
ejpam-7160	22	34	and	and	CCONJ
ejpam-7160	22	35	complexity	complexity	NOUN
ejpam-7160	22	36	in	in	ADP
ejpam-7160	22	37	data	datum	NOUN
ejpam-7160	22	38	processing	processing	NOUN
ejpam-7160	22	39	[	[	X
ejpam-7160	22	40	3	3	NUM
ejpam-7160	22	41	-	-	SYM
ejpam-7160	22	42	6	6	NUM
ejpam-7160	22	43	]	]	PUNCT
ejpam-7160	22	44	.	.	PUNCT
ejpam-7160	23	1	although	although	SCONJ
ejpam-7160	23	2	the	the	DET
ejpam-7160	23	3	equivalence	equivalence	NOUN
ejpam-7160	23	4	relation	relation	NOUN
ejpam-7160	23	5	(	(	PUNCT
ejpam-7160	23	6	eqr	eqr	PROPN
ejpam-7160	23	7	)	)	PUNCT
ejpam-7160	23	8	is	be	AUX
ejpam-7160	23	9	the	the	DET
ejpam-7160	23	10	main	main	ADJ
ejpam-7160	23	11	emphasis	emphasis	NOUN
ejpam-7160	23	12	of	of	ADP
ejpam-7160	23	13	classic	classic	ADJ
ejpam-7160	23	14	rhst	rhst	NOUN
ejpam-7160	23	15	,	,	PUNCT
ejpam-7160	23	16	its	its	PRON
ejpam-7160	23	17	generalizations	generalization	NOUN
ejpam-7160	23	18	seek	seek	VERB
ejpam-7160	23	19	to	to	PART
ejpam-7160	23	20	improve	improve	VERB
ejpam-7160	23	21	and	and	CCONJ
ejpam-7160	23	22	broaden	broaden	VERB
ejpam-7160	23	23	this	this	DET
ejpam-7160	23	24	methodology	methodology	NOUN
ejpam-7160	23	25	to	to	PART
ejpam-7160	23	26	handle	handle	VERB
ejpam-7160	23	27	more	more	ADV
ejpam-7160	23	28	complicated	complicated	ADJ
ejpam-7160	23	29	kinds	kind	NOUN
ejpam-7160	23	30	of	of	ADP
ejpam-7160	23	31	data	datum	NOUN
ejpam-7160	23	32	and	and	CCONJ
ejpam-7160	23	33	do	do	VERB
ejpam-7160	23	34	away	away	ADV
ejpam-7160	23	35	with	with	ADP
ejpam-7160	23	36	the	the	DET
ejpam-7160	23	37	equivalency	equivalency	NOUN
ejpam-7160	23	38	requirement	requirement	NOUN
ejpam-7160	23	39	.	.	PUNCT
ejpam-7160	24	1	rhst	rhst	PROPN
ejpam-7160	24	2	can	can	AUX
ejpam-7160	24	3	now	now	ADV
ejpam-7160	24	4	handle	handle	VERB
ejpam-7160	24	5	a	a	DET
ejpam-7160	24	6	wider	wide	ADJ
ejpam-7160	24	7	variety	variety	NOUN
ejpam-7160	24	8	of	of	ADP
ejpam-7160	24	9	complicated	complicated	ADJ
ejpam-7160	24	10	and	and	CCONJ
ejpam-7160	24	11	varied	varied	ADJ
ejpam-7160	24	12	datasets	dataset	NOUN
ejpam-7160	24	13	thanks	thank	NOUN
ejpam-7160	24	14	to	to	ADP
ejpam-7160	24	15	these	these	DET
ejpam-7160	24	16	generalizations	generalization	NOUN
ejpam-7160	24	17	.	.	PUNCT
ejpam-7160	25	1	this	this	PRON
ejpam-7160	25	2	also	also	ADV
ejpam-7160	25	3	allows	allow	VERB
ejpam-7160	25	4	it	it	PRON
ejpam-7160	25	5	to	to	PART
ejpam-7160	25	6	be	be	AUX
ejpam-7160	25	7	used	use	VERB
ejpam-7160	25	8	for	for	ADP
ejpam-7160	25	9	a	a	DET
ejpam-7160	25	10	broader	broad	ADJ
ejpam-7160	25	11	range	range	NOUN
ejpam-7160	25	12	of	of	ADP
ejpam-7160	25	13	issues	issue	NOUN
ejpam-7160	25	14	in	in	ADP
ejpam-7160	25	15	domains	domain	NOUN
ejpam-7160	25	16	such	such	ADJ
ejpam-7160	25	17	as	as	ADP
ejpam-7160	25	18	data	datum	NOUN
ejpam-7160	25	19	analysis	analysis	NOUN
ejpam-7160	25	20	,	,	PUNCT
ejpam-7160	25	21	machine	machine	NOUN
ejpam-7160	25	22	learning	learning	NOUN
ejpam-7160	25	23	,	,	PUNCT
ejpam-7160	25	24	decision	decision	NOUN
ejpam-7160	25	25	support	support	NOUN
ejpam-7160	25	26	systems	system	NOUN
ejpam-7160	25	27	,	,	PUNCT
ejpam-7160	25	28	smart	smart	ADJ
ejpam-7160	25	29	cities	city	NOUN
ejpam-7160	25	30	,	,	PUNCT
ejpam-7160	25	31	and	and	CCONJ
ejpam-7160	25	32	medicine	medicine	NOUN
ejpam-7160	25	33	,	,	PUNCT
ejpam-7160	25	34	among	among	ADP
ejpam-7160	25	35	others	other	NOUN
ejpam-7160	25	36	.	.	PUNCT
ejpam-7160	26	1	practitioners	practitioner	NOUN
ejpam-7160	26	2	as	as	ADV
ejpam-7160	26	3	well	well	ADV
ejpam-7160	26	4	as	as	SCONJ
ejpam-7160	26	5	researchers	researcher	NOUN
ejpam-7160	26	6	can	can	AUX
ejpam-7160	26	7	obtain	obtain	VERB
ejpam-7160	26	8	more	more	ADV
ejpam-7160	26	9	precise	precise	ADJ
ejpam-7160	26	10	and	and	CCONJ
ejpam-7160	26	11	significant	significant	ADJ
ejpam-7160	26	12	insights	insight	NOUN
ejpam-7160	26	13	from	from	ADP
ejpam-7160	26	14	data	datum	NOUN
ejpam-7160	26	15	with	with	ADP
ejpam-7160	26	16	different	different	ADJ
ejpam-7160	26	17	levels	level	NOUN
ejpam-7160	26	18	of	of	ADP
ejpam-7160	26	19	uncertainty	uncertainty	NOUN
ejpam-7160	26	20	by	by	ADP
ejpam-7160	26	21	broadening	broaden	VERB
ejpam-7160	26	22	the	the	DET
ejpam-7160	26	23	use	use	NOUN
ejpam-7160	26	24	of	of	ADP
ejpam-7160	26	25	rhst	rhst	NOUN
ejpam-7160	26	26	,	,	PUNCT
ejpam-7160	26	27	which	which	PRON
ejpam-7160	26	28	also	also	ADV
ejpam-7160	26	29	makes	make	VERB
ejpam-7160	26	30	decision	decision	NOUN
ejpam-7160	26	31	-	-	PUNCT
ejpam-7160	26	32	making	making	NOUN
ejpam-7160	26	33	easier	easy	ADJ
ejpam-7160	26	34	.	.	PUNCT
ejpam-7160	27	1	topology	topology	NOUN
ejpam-7160	27	2	was	be	AUX
ejpam-7160	27	3	used	use	VERB
ejpam-7160	27	4	to	to	PART
ejpam-7160	27	5	achieve	achieve	VERB
ejpam-7160	27	6	one	one	NUM
ejpam-7160	27	7	of	of	ADP
ejpam-7160	27	8	these	these	DET
ejpam-7160	27	9	generalizations	generalization	NOUN
ejpam-7160	27	10	.	.	PUNCT
ejpam-7160	28	1	the	the	DET
ejpam-7160	28	2	connection	connection	NOUN
ejpam-7160	28	3	between	between	ADP
ejpam-7160	28	4	rough	rough	ADJ
ejpam-7160	28	5	sets	set	NOUN
ejpam-7160	28	6	(	(	PUNCT
ejpam-7160	28	7	rhss	rhss	ADJ
ejpam-7160	28	8	)	)	PUNCT
ejpam-7160	28	9	and	and	CCONJ
ejpam-7160	28	10	topology	topology	NOUN
ejpam-7160	28	11	was	be	AUX
ejpam-7160	28	12	initially	initially	ADV
ejpam-7160	28	13	identified	identify	VERB
ejpam-7160	28	14	by	by	ADP
ejpam-7160	28	15	[	[	X
ejpam-7160	28	16	7	7	NUM
ejpam-7160	28	17	,	,	PUNCT
ejpam-7160	28	18	8	8	NUM
ejpam-7160	28	19	]	]	PUNCT
ejpam-7160	28	20	.	.	PUNCT
ejpam-7160	29	1	here	here	ADV
ejpam-7160	29	2	,	,	PUNCT
ejpam-7160	29	3	the	the	DET
ejpam-7160	29	4	closure	closure	NOUN
ejpam-7160	29	5	is	be	AUX
ejpam-7160	29	6	linked	link	VERB
ejpam-7160	29	7	to	to	ADP
ejpam-7160	29	8	the	the	DET
ejpam-7160	29	9	upper	upper	ADJ
ejpam-7160	29	10	(	(	PUNCT
ejpam-7160	29	11	up	up	ADJ
ejpam-7160	29	12	)	)	PUNCT
ejpam-7160	29	13	approximation	approximation	NOUN
ejpam-7160	29	14	(	(	PUNCT
ejpam-7160	29	15	apr	apr	NOUN
ejpam-7160	29	16	)	)	PUNCT
ejpam-7160	29	17	,	,	PUNCT
ejpam-7160	29	18	whereas	whereas	SCONJ
ejpam-7160	29	19	the	the	DET
ejpam-7160	29	20	topological	topological	ADJ
ejpam-7160	29	21	notion	notion	NOUN
ejpam-7160	29	22	of	of	ADP
ejpam-7160	29	23	the	the	DET
ejpam-7160	29	24	interior	interior	NOUN
ejpam-7160	29	25	is	be	AUX
ejpam-7160	29	26	linked	link	VERB
ejpam-7160	29	27	to	to	ADP
ejpam-7160	29	28	the	the	DET
ejpam-7160	29	29	lower	low	ADJ
ejpam-7160	29	30	(	(	PUNCT
ejpam-7160	29	31	lw	lw	NOUN
ejpam-7160	29	32	)	)	PUNCT
ejpam-7160	29	33	apr	apr	VERB
ejpam-7160	30	1	[	[	X
ejpam-7160	30	2	9–14	9–14	X
ejpam-7160	30	3	]	]	X
ejpam-7160	30	4	.	.	PUNCT
ejpam-7160	31	1	a	a	DET
ejpam-7160	31	2	grill	grill	NOUN
ejpam-7160	31	3	is	be	AUX
ejpam-7160	31	4	a	a	DET
ejpam-7160	31	5	nonempty	nonempty	ADJ
ejpam-7160	31	6	collection	collection	NOUN
ejpam-7160	31	7	of	of	ADP
ejpam-7160	31	8	closed	closed	ADJ
ejpam-7160	31	9	sets	set	NOUN
ejpam-7160	31	10	with	with	ADP
ejpam-7160	31	11	hereditary	hereditary	ADJ
ejpam-7160	31	12	property	property	NOUN
ejpam-7160	31	13	and	and	CCONJ
ejpam-7160	31	14	limited	limited	ADJ
ejpam-7160	31	15	additivity	additivity	NOUN
ejpam-7160	31	16	[	[	X
ejpam-7160	31	17	15	15	NUM
ejpam-7160	31	18	]	]	PUNCT
ejpam-7160	31	19	.	.	PUNCT
ejpam-7160	32	1	this	this	DET
ejpam-7160	32	2	idea	idea	NOUN
ejpam-7160	32	3	was	be	AUX
ejpam-7160	32	4	first	first	ADV
ejpam-7160	32	5	put	put	VERB
ejpam-7160	32	6	forth	forth	ADV
ejpam-7160	32	7	by	by	ADP
ejpam-7160	32	8	choquet	choquet	NOUN
ejpam-7160	32	9	[	[	X
ejpam-7160	32	10	15	15	NUM
ejpam-7160	32	11	]	]	PUNCT
ejpam-7160	32	12	.	.	PUNCT
ejpam-7160	33	1	the	the	DET
ejpam-7160	33	2	grill	grill	NOUN
ejpam-7160	33	3	and	and	CCONJ
ejpam-7160	33	4	ideas	idea	NOUN
ejpam-7160	33	5	,	,	PUNCT
ejpam-7160	33	6	nets	net	NOUN
ejpam-7160	33	7	,	,	PUNCT
ejpam-7160	33	8	and	and	CCONJ
ejpam-7160	33	9	filters	filter	NOUN
ejpam-7160	33	10	have	have	VERB
ejpam-7160	33	11	a	a	DET
ejpam-7160	33	12	number	number	NOUN
ejpam-7160	33	13	of	of	ADP
ejpam-7160	33	14	similarities	similarity	NOUN
ejpam-7160	33	15	.	.	PUNCT
ejpam-7160	34	1	many	many	ADJ
ejpam-7160	34	2	theories	theory	NOUN
ejpam-7160	34	3	and	and	CCONJ
ejpam-7160	34	4	facets	facet	NOUN
ejpam-7160	34	5	have	have	AUX
ejpam-7160	34	6	been	be	AUX
ejpam-7160	34	7	covered	cover	VERB
ejpam-7160	34	8	by	by	ADP
ejpam-7160	34	9	[	[	X
ejpam-7160	34	10	16	16	NUM
ejpam-7160	34	11	,	,	PUNCT
ejpam-7160	34	12	17	17	NUM
ejpam-7160	34	13	]	]	PUNCT
ejpam-7160	34	14	and	and	CCONJ
ejpam-7160	34	15	[	[	X
ejpam-7160	34	16	18	18	NUM
ejpam-7160	34	17	]	]	PUNCT
ejpam-7160	34	18	.	.	PUNCT
ejpam-7160	35	1	it	it	PRON
ejpam-7160	35	2	facilitates	facilitate	VERB
ejpam-7160	35	3	the	the	DET
ejpam-7160	35	4	enhancement	enhancement	NOUN
ejpam-7160	35	5	of	of	ADP
ejpam-7160	35	6	the	the	DET
ejpam-7160	35	7	topological	topological	ADJ
ejpam-7160	35	8	framework	framework	NOUN
ejpam-7160	35	9	,	,	PUNCT
ejpam-7160	35	10	which	which	PRON
ejpam-7160	35	11	substitutes	substitute	VERB
ejpam-7160	35	12	numerical	numerical	ADJ
ejpam-7160	35	13	values	value	NOUN
ejpam-7160	35	14	for	for	ADP
ejpam-7160	35	15	evaluating	evaluate	VERB
ejpam-7160	35	16	attributes	attribute	NOUN
ejpam-7160	35	17	such	such	ADJ
ejpam-7160	35	18	as	as	ADP
ejpam-7160	35	19	affection	affection	NOUN
ejpam-7160	35	20	,	,	PUNCT
ejpam-7160	35	21	intellect	intellect	NOUN
ejpam-7160	35	22	,	,	PUNCT
ejpam-7160	35	23	aesthetic	aesthetic	ADJ
ejpam-7160	35	24	appeal	appeal	NOUN
ejpam-7160	35	25	,	,	PUNCT
ejpam-7160	35	26	and	and	CCONJ
ejpam-7160	35	27	academic	academic	ADJ
ejpam-7160	35	28	achievement	achievement	NOUN
ejpam-7160	35	29	.	.	PUNCT
ejpam-7160	36	1	furthermore	furthermore	ADV
ejpam-7160	36	2	,	,	PUNCT
ejpam-7160	36	3	by	by	ADP
ejpam-7160	36	4	employing	employ	VERB
ejpam-7160	36	5	the	the	DET
ejpam-7160	36	6	notion	notion	NOUN
ejpam-7160	36	7	of	of	ADP
ejpam-7160	36	8	grill	grill	ADJ
ejpam-7160	36	9	modifications	modification	NOUN
ejpam-7160	36	10	in	in	ADP
ejpam-7160	36	11	the	the	DET
ejpam-7160	36	12	border	border	NOUN
ejpam-7160	36	13	region	region	NOUN
ejpam-7160	36	14	(	(	PUNCT
ejpam-7160	36	15	br	br	NOUN
ejpam-7160	36	16	)	)	PUNCT
ejpam-7160	36	17	,	,	PUNCT
ejpam-7160	36	18	up	up	ADP
ejpam-7160	36	19	,	,	PUNCT
ejpam-7160	36	20	and	and	CCONJ
ejpam-7160	36	21	lw	lw	NOUN
ejpam-7160	36	22	-	-	PUNCT
ejpam-7160	36	23	aprs	aprs	NOUN
ejpam-7160	36	24	,	,	PUNCT
ejpam-7160	36	25	it	it	PRON
ejpam-7160	36	26	expands	expand	VERB
ejpam-7160	36	27	the	the	DET
ejpam-7160	36	28	topological	topological	ADJ
ejpam-7160	36	29	structure	structure	NOUN
ejpam-7160	36	30	and	and	CCONJ
ejpam-7160	36	31	creates	create	VERB
ejpam-7160	36	32	novel	novel	ADJ
ejpam-7160	36	33	limits	limit	NOUN
ejpam-7160	36	34	in	in	ADP
ejpam-7160	36	35	nano	nano	NOUN
ejpam-7160	36	36	topological	topological	ADJ
ejpam-7160	36	37	spaces	space	NOUN
ejpam-7160	36	38	[	[	X
ejpam-7160	36	39	17	17	NUM
ejpam-7160	36	40	]	]	PUNCT
ejpam-7160	36	41	.	.	PUNCT
ejpam-7160	37	1	when	when	SCONJ
ejpam-7160	37	2	it	it	PRON
ejpam-7160	37	3	comes	come	VERB
ejpam-7160	37	4	to	to	ADP
ejpam-7160	37	5	removing	remove	VERB
ejpam-7160	37	6	ambiguity	ambiguity	NOUN
ejpam-7160	37	7	from	from	ADP
ejpam-7160	37	8	raw	raw	ADJ
ejpam-7160	37	9	sets	set	NOUN
ejpam-7160	37	10	,	,	PUNCT
ejpam-7160	37	11	grills	grill	NOUN
ejpam-7160	37	12	are	be	AUX
ejpam-7160	37	13	proven	prove	VERB
ejpam-7160	37	14	to	to	PART
ejpam-7160	37	15	be	be	AUX
ejpam-7160	37	16	helpful	helpful	ADJ
ejpam-7160	37	17	[	[	X
ejpam-7160	37	18	19	19	NUM
ejpam-7160	37	19	,	,	PUNCT
ejpam-7160	37	20	20	20	NUM
ejpam-7160	37	21	]	]	PUNCT
ejpam-7160	37	22	.	.	PUNCT
ejpam-7160	38	1	therefore	therefore	ADV
ejpam-7160	38	2	,	,	PUNCT
ejpam-7160	38	3	the	the	DET
ejpam-7160	38	4	introduction	introduction	NOUN
ejpam-7160	38	5	of	of	ADP
ejpam-7160	38	6	novel	novel	ADJ
ejpam-7160	38	7	grill	grill	NOUN
ejpam-7160	38	8	-	-	PUNCT
ejpam-7160	38	9	based	base	VERB
ejpam-7160	38	10	rhs	rhs	PROPN
ejpam-7160	38	11	approaches	approach	NOUN
ejpam-7160	38	12	is	be	AUX
ejpam-7160	38	13	one	one	NUM
ejpam-7160	38	14	of	of	ADP
ejpam-7160	38	15	the	the	DET
ejpam-7160	38	16	main	main	ADJ
ejpam-7160	38	17	reasons	reason	NOUN
ejpam-7160	38	18	for	for	ADP
ejpam-7160	38	19	this	this	DET
ejpam-7160	38	20	effort	effort	NOUN
ejpam-7160	38	21	.	.	PUNCT
ejpam-7160	39	1	in	in	ADP
ejpam-7160	39	2	other	other	ADJ
ejpam-7160	39	3	words	word	NOUN
ejpam-7160	39	4	,	,	PUNCT
ejpam-7160	39	5	when	when	SCONJ
ejpam-7160	39	6	the	the	DET
ejpam-7160	39	7	grill	grill	NOUN
ejpam-7160	39	8	is	be	AUX
ejpam-7160	39	9	the	the	DET
ejpam-7160	39	10	universal	universal	ADJ
ejpam-7160	39	11	set	set	NOUN
ejpam-7160	39	12	,	,	PUNCT
ejpam-7160	39	13	it	it	PRON
ejpam-7160	39	14	generates	generate	VERB
ejpam-7160	39	15	a	a	DET
ejpam-7160	39	16	unique	unique	ADJ
ejpam-7160	39	17	scenario	scenario	NOUN
ejpam-7160	39	18	for	for	ADP
ejpam-7160	39	19	its	its	PRON
ejpam-7160	39	20	generic	generic	ADJ
ejpam-7160	39	21	rhs	rhs	PROPN
ejpam-7160	39	22	model	model	NOUN
ejpam-7160	39	23	counterparts	counterpart	NOUN
ejpam-7160	39	24	.	.	PUNCT
ejpam-7160	40	1	as	as	ADP
ejpam-7160	40	2	a	a	DET
ejpam-7160	40	3	result	result	NOUN
ejpam-7160	40	4	,	,	PUNCT
ejpam-7160	40	5	some	some	DET
ejpam-7160	40	6	interesting	interesting	ADJ
ejpam-7160	40	7	research	research	NOUN
ejpam-7160	40	8	looked	look	VERB
ejpam-7160	40	9	into	into	ADP
ejpam-7160	40	10	the	the	DET
ejpam-7160	40	11	rhst	rhst	NOUN
ejpam-7160	40	12	that	that	PRON
ejpam-7160	40	13	grills	grills	AUX
ejpam-7160	40	14	describe	describe	NOUN
ejpam-7160	40	15	[	[	X
ejpam-7160	40	16	21	21	NUM
ejpam-7160	40	17	]	]	PUNCT
ejpam-7160	40	18	.	.	PUNCT
ejpam-7160	41	1	neighborhoods	neighborhood	NOUN
ejpam-7160	41	2	(	(	PUNCT
ejpam-7160	41	3	nbs	nbs	PROPN
ejpam-7160	41	4	)	)	PUNCT
ejpam-7160	41	5	are	be	AUX
ejpam-7160	41	6	a	a	DET
ejpam-7160	41	7	fundamental	fundamental	ADJ
ejpam-7160	41	8	topological	topological	ADJ
ejpam-7160	41	9	notion	notion	NOUN
ejpam-7160	41	10	to	to	PART
ejpam-7160	41	11	understand	understand	VERB
ejpam-7160	41	12	and	and	CCONJ
ejpam-7160	41	13	evaluate	evaluate	VERB
ejpam-7160	41	14	set	set	NOUN
ejpam-7160	41	15	aprs	aprs	NOUN
ejpam-7160	41	16	.	.	PUNCT
ejpam-7160	42	1	nbs	nbs	PROPN
ejpam-7160	42	2	and	and	CCONJ
ejpam-7160	42	3	any	any	DET
ejpam-7160	42	4	relation	relation	NOUN
ejpam-7160	42	5	was	be	AUX
ejpam-7160	42	6	used	use	VERB
ejpam-7160	42	7	to	to	PART
ejpam-7160	42	8	generate	generate	VERB
ejpam-7160	42	9	apr	apr	NOUN
ejpam-7160	42	10	spaces	space	NOUN
ejpam-7160	42	11	in	in	ADP
ejpam-7160	42	12	[	[	X
ejpam-7160	42	13	22	22	NUM
ejpam-7160	42	14	,	,	PUNCT
ejpam-7160	42	15	23	23	NUM
ejpam-7160	42	16	]	]	PUNCT
ejpam-7160	42	17	.	.	PUNCT
ejpam-7160	43	1	neighborhood	neighborhood	NOUN
ejpam-7160	43	2	(	(	PUNCT
ejpam-7160	43	3	nb	nb	NOUN
ejpam-7160	43	4	)	)	PUNCT
ejpam-7160	43	5	systems	system	NOUN
ejpam-7160	43	6	are	be	AUX
ejpam-7160	43	7	used	use	VERB
ejpam-7160	43	8	to	to	PART
ejpam-7160	43	9	generalize	generalize	VERB
ejpam-7160	43	10	rhst	rhst	NOUN
ejpam-7160	43	11	by	by	ADP
ejpam-7160	43	12	describing	describe	VERB
ejpam-7160	43	13	aprs	aprs	NOUN
ejpam-7160	43	14	through	through	ADP
ejpam-7160	43	15	a	a	DET
ejpam-7160	43	16	nb	nb	NOUN
ejpam-7160	43	17	rather	rather	ADV
ejpam-7160	43	18	than	than	ADP
ejpam-7160	43	19	an	an	DET
ejpam-7160	43	20	equivalency	equivalency	NOUN
ejpam-7160	43	21	class	class	NOUN
ejpam-7160	43	22	.	.	PUNCT
ejpam-7160	44	1	some	some	PRON
ejpam-7160	44	2	of	of	ADP
ejpam-7160	44	3	the	the	DET
ejpam-7160	44	4	nb	nb	PROPN
ejpam-7160	44	5	types	type	NOUN
ejpam-7160	44	6	used	use	VERB
ejpam-7160	44	7	to	to	PART
ejpam-7160	44	8	define	define	VERB
ejpam-7160	44	9	the	the	DET
ejpam-7160	44	10	lw	lw	NOUN
ejpam-7160	44	11	and	and	CCONJ
ejpam-7160	44	12	up	up	ADP
ejpam-7160	44	13	-	-	PUNCT
ejpam-7160	44	14	apr	apr	NOUN
ejpam-7160	44	15	were	be	AUX
ejpam-7160	44	16	union	union	NOUN
ejpam-7160	44	17	,	,	PUNCT
ejpam-7160	44	18	intersection	intersection	NOUN
ejpam-7160	44	19	[	[	X
ejpam-7160	44	20	24	24	NUM
ejpam-7160	44	21	,	,	PUNCT
ejpam-7160	44	22	25	25	NUM
ejpam-7160	44	23	]	]	PUNCT
ejpam-7160	44	24	,	,	PUNCT
ejpam-7160	44	25	equal	equal	ADJ
ejpam-7160	44	26	nbs	nbs	PROPN
ejpam-7160	45	1	[	[	X
ejpam-7160	45	2	26	26	NUM
ejpam-7160	45	3	,	,	PUNCT
ejpam-7160	45	4	27	27	NUM
ejpam-7160	45	5	]	]	PUNCT
ejpam-7160	45	6	,	,	PUNCT
ejpam-7160	45	7	minimal	minimal	ADJ
ejpam-7160	45	8	and	and	CCONJ
ejpam-7160	45	9	maximal	maximal	ADJ
ejpam-7160	45	10	nbs	nbs	NOUN
ejpam-7160	46	1	[	[	X
ejpam-7160	46	2	28	28	NUM
ejpam-7160	46	3	,	,	PUNCT
ejpam-7160	46	4	29	29	NUM
ejpam-7160	46	5	]	]	PUNCT
ejpam-7160	46	6	,	,	PUNCT
ejpam-7160	46	7	cardinality	cardinality	PROPN
ejpam-7160	46	8	nbs	nbs	PROPN
ejpam-7160	46	9	[	[	X
ejpam-7160	46	10	30	30	NUM
ejpam-7160	46	11	,	,	PUNCT
ejpam-7160	46	12	31	31	NUM
ejpam-7160	46	13	]	]	PUNCT
ejpam-7160	46	14	,	,	PUNCT
ejpam-7160	46	15	right	right	ADJ
ejpam-7160	46	16	and	and	CCONJ
ejpam-7160	46	17	left	leave	VERB
ejpam-7160	46	18	nbs	nbs	PROPN
ejpam-7160	47	1	[	[	X
ejpam-7160	47	2	22	22	NUM
ejpam-7160	47	3	,	,	PUNCT
ejpam-7160	47	4	23	23	NUM
ejpam-7160	47	5	]	]	PUNCT
ejpam-7160	47	6	,	,	PUNCT
ejpam-7160	47	7	rough	rough	ADJ
ejpam-7160	47	8	nb	nb	PROPN
ejpam-7160	47	9	ideal	ideal	NOUN
ejpam-7160	48	1	[	[	X
ejpam-7160	48	2	32	32	NUM
ejpam-7160	48	3	]	]	PUNCT
ejpam-7160	48	4	,	,	PUNCT
ejpam-7160	48	5	and	and	CCONJ
ejpam-7160	48	6	nbs	nbs	PROPN
ejpam-7160	48	7	with	with	ADP
ejpam-7160	48	8	minimal	minimal	ADJ
ejpam-7160	48	9	left(mnl	left(mnl	NOUN
ejpam-7160	48	10	)	)	PUNCT
ejpam-7160	48	11	and	and	CCONJ
ejpam-7160	48	12	minimal	minimal	ADJ
ejpam-7160	48	13	right(mnr	right(mnr	NOUN
ejpam-7160	48	14	)	)	PUNCT
ejpam-7160	49	1	[	[	X
ejpam-7160	49	2	33	33	NUM
ejpam-7160	49	3	,	,	PUNCT
ejpam-7160	49	4	34	34	NUM
ejpam-7160	49	5	]	]	PUNCT
ejpam-7160	49	6	.	.	PUNCT
ejpam-7160	50	1	in	in	ADP
ejpam-7160	50	2	the	the	DET
ejpam-7160	50	3	interim	interim	ADJ
ejpam-7160	50	4	,	,	PUNCT
ejpam-7160	50	5	abo	abo	NOUN
ejpam-7160	50	6	-	-	PUNCT
ejpam-7160	50	7	tabl	tabl	NOUN
ejpam-7160	50	8	[	[	X
ejpam-7160	50	9	35	35	NUM
ejpam-7160	50	10	]	]	PUNCT
ejpam-7160	50	11	created	create	VERB
ejpam-7160	50	12	the	the	DET
ejpam-7160	50	13	apps	app	NOUN
ejpam-7160	50	14	using	use	VERB
ejpam-7160	50	15	mnr	mnr	PROPN
ejpam-7160	50	16	nbs	nbs	PROPN
ejpam-7160	50	17	,	,	PUNCT
ejpam-7160	50	18	which	which	PRON
ejpam-7160	50	19	are	be	AUX
ejpam-7160	50	20	created	create	VERB
ejpam-7160	50	21	using	use	VERB
ejpam-7160	50	22	reflexive	reflexive	ADJ
ejpam-7160	50	23	relations	relation	NOUN
ejpam-7160	50	24	(	(	PUNCT
ejpam-7160	50	25	rfr	rfr	PROPN
ejpam-7160	50	26	)	)	PUNCT
ejpam-7160	50	27	that	that	PRON
ejpam-7160	50	28	form	form	VERB
ejpam-7160	50	29	the	the	DET
ejpam-7160	50	30	basis	basis	NOUN
ejpam-7160	50	31	of	of	ADP
ejpam-7160	50	32	topological	topological	ADJ
ejpam-7160	50	33	space	space	NOUN
ejpam-7160	50	34	.	.	PUNCT
ejpam-7160	51	1	three	three	NUM
ejpam-7160	51	2	more	more	ADJ
ejpam-7160	51	3	apr	apr	NOUN
ejpam-7160	51	4	categories	category	NOUN
ejpam-7160	51	5	were	be	AUX
ejpam-7160	51	6	created	create	VERB
ejpam-7160	51	7	more	more	ADV
ejpam-7160	51	8	recently	recently	ADV
ejpam-7160	51	9	by	by	ADP
ejpam-7160	51	10	dai	dai	PROPN
ejpam-7160	51	11	et	et	PROPN
ejpam-7160	51	12	al	al	PROPN
ejpam-7160	51	13	.	.	PUNCT
ejpam-7160	52	1	[	[	X
ejpam-7160	52	2	36	36	NUM
ejpam-7160	52	3	]	]	PUNCT
ejpam-7160	52	4	via	via	ADP
ejpam-7160	52	5	maximal	maximal	ADJ
ejpam-7160	52	6	right	right	PROPN
ejpam-7160	52	7	nbs	nbs	PROPN
ejpam-7160	52	8	determined	determine	VERB
ejpam-7160	52	9	by	by	ADP
ejpam-7160	52	10	similarity	similarity	NOUN
ejpam-7160	52	11	relations	relation	NOUN
ejpam-7160	52	12	(	(	PUNCT
ejpam-7160	52	13	sir	sir	NOUN
ejpam-7160	52	14	)	)	PUNCT
ejpam-7160	52	15	.	.	PUNCT
ejpam-7160	53	1	stated	state	VERB
ejpam-7160	53	2	differently	differently	ADV
ejpam-7160	53	3	,	,	PUNCT
ejpam-7160	53	4	they	they	PRON
ejpam-7160	53	5	offer	offer	VERB
ejpam-7160	53	6	a	a	DET
ejpam-7160	53	7	broad	broad	ADJ
ejpam-7160	53	8	framework	framework	NOUN
ejpam-7160	53	9	that	that	PRON
ejpam-7160	53	10	is	be	AUX
ejpam-7160	53	11	unrestricted	unrestricted	ADJ
ejpam-7160	53	12	in	in	ADP
ejpam-7160	53	13	terms	term	NOUN
ejpam-7160	53	14	of	of	ADP
ejpam-7160	53	15	the	the	DET
ejpam-7160	53	16	types	type	NOUN
ejpam-7160	53	17	of	of	ADP
ejpam-7160	53	18	binary	binary	ADJ
ejpam-7160	53	19	relations	relation	NOUN
ejpam-7160	53	20	(	(	PUNCT
ejpam-7160	53	21	br	br	NOUN
ejpam-7160	53	22	)	)	PUNCT
ejpam-7160	53	23	that	that	PRON
ejpam-7160	53	24	can	can	AUX
ejpam-7160	53	25	be	be	AUX
ejpam-7160	53	26	established	establish	VERB
ejpam-7160	53	27	.	.	PUNCT
ejpam-7160	54	1	interestingly	interestingly	ADV
ejpam-7160	54	2	,	,	PUNCT
ejpam-7160	54	3	it	it	PRON
ejpam-7160	54	4	rhst	rhst	NOUN
ejpam-7160	54	5	has	have	AUX
ejpam-7160	54	6	proven	prove	VERB
ejpam-7160	54	7	to	to	PART
ejpam-7160	54	8	be	be	AUX
ejpam-7160	54	9	a	a	DET
ejpam-7160	54	10	valuable	valuable	ADJ
ejpam-7160	54	11	tool	tool	NOUN
ejpam-7160	54	12	for	for	ADP
ejpam-7160	54	13	describing	describe	VERB
ejpam-7160	54	14	information	information	NOUN
ejpam-7160	54	15	content	content	NOUN
ejpam-7160	54	16	in	in	ADP
ejpam-7160	54	17	a	a	DET
ejpam-7160	54	18	wide	wide	ADJ
ejpam-7160	54	19	range	range	NOUN
ejpam-7160	54	20	of	of	ADP
ejpam-7160	54	21	frameworks	framework	NOUN
ejpam-7160	54	22	and	and	CCONJ
ejpam-7160	54	23	applications	application	NOUN
ejpam-7160	54	24	in	in	ADP
ejpam-7160	54	25	a	a	DET
ejpam-7160	54	26	wide	wide	ADJ
ejpam-7160	54	27	range	range	NOUN
ejpam-7160	54	28	of	of	ADP
ejpam-7160	54	29	domains	domain	NOUN
ejpam-7160	54	30	[	[	PUNCT
ejpam-7160	54	31	37	37	NUM
ejpam-7160	54	32	-	-	SYM
ejpam-7160	54	33	41	41	NUM
ejpam-7160	54	34	]	]	PUNCT
ejpam-7160	54	35	.	.	PUNCT
ejpam-7160	55	1	the	the	DET
ejpam-7160	55	2	topological	topological	ADJ
ejpam-7160	55	3	properties	property	NOUN
ejpam-7160	55	4	rhss	rhss	ADV
ejpam-7160	55	5	were	be	AUX
ejpam-7160	55	6	studied	study	VERB
ejpam-7160	55	7	in	in	ADP
ejpam-7160	55	8	[	[	X
ejpam-7160	55	9	42	42	NUM
ejpam-7160	55	10	]	]	PUNCT
ejpam-7160	55	11	.	.	PUNCT
ejpam-7160	56	1	this	this	PRON
ejpam-7160	56	2	led	lead	VERB
ejpam-7160	56	3	to	to	ADP
ejpam-7160	56	4	the	the	DET
ejpam-7160	56	5	combination	combination	NOUN
ejpam-7160	56	6	of	of	ADP
ejpam-7160	56	7	topological	topological	ADJ
ejpam-7160	56	8	and	and	CCONJ
ejpam-7160	56	9	rhs	rhs	PROPN
ejpam-7160	56	10	theories	theory	NOUN
ejpam-7160	56	11	,	,	PUNCT
ejpam-7160	56	12	which	which	PRON
ejpam-7160	56	13	became	become	VERB
ejpam-7160	56	14	the	the	DET
ejpam-7160	56	15	focus	focus	NOUN
ejpam-7160	56	16	of	of	ADP
ejpam-7160	56	17	a	a	DET
ejpam-7160	56	18	number	number	NOUN
ejpam-7160	56	19	of	of	ADP
ejpam-7160	56	20	researchs	research	NOUN
ejpam-7160	56	21	[	[	X
ejpam-7160	56	22	43	43	NUM
ejpam-7160	56	23	-	-	SYM
ejpam-7160	56	24	47	47	NUM
ejpam-7160	56	25	]	]	PUNCT
ejpam-7160	56	26	.	.	PUNCT
ejpam-7160	57	1	furthermore	furthermore	ADV
ejpam-7160	57	2	,	,	PUNCT
ejpam-7160	57	3	topological	topological	ADJ
ejpam-7160	57	4	generalizations	generalization	NOUN
ejpam-7160	57	5	such	such	ADJ
ejpam-7160	57	6	as	as	ADP
ejpam-7160	57	7	minimal	minimal	ADJ
ejpam-7160	57	8	structures	structure	NOUN
ejpam-7160	57	9	[	[	X
ejpam-7160	57	10	48	48	NUM
ejpam-7160	57	11	]	]	PUNCT
ejpam-7160	57	12	,	,	PUNCT
ejpam-7160	57	13	supra	supra	ADJ
ejpam-7160	57	14	topology	topology	NOUN
ejpam-7160	58	1	[	[	X
ejpam-7160	58	2	49	49	NUM
ejpam-7160	58	3	]	]	PUNCT
ejpam-7160	58	4	,	,	PUNCT
ejpam-7160	58	5	infra	infra	NOUN
ejpam-7160	58	6	topology	topology	NOUN
ejpam-7160	58	7	[	[	X
ejpam-7160	58	8	50	50	NUM
ejpam-7160	58	9	]	]	PUNCT
ejpam-7160	58	10	,	,	PUNCT
ejpam-7160	58	11	nano	nano	NOUN
ejpam-7160	58	12	-	-	PUNCT
ejpam-7160	58	13	topology	topology	NOUN
ejpam-7160	58	14	[	[	X
ejpam-7160	58	15	17	17	NUM
ejpam-7160	58	16	]	]	PUNCT
ejpam-7160	58	17	,	,	PUNCT
ejpam-7160	58	18	and	and	CCONJ
ejpam-7160	58	19	bitopology	bitopology	NOUN
ejpam-7160	59	1	[	[	X
ejpam-7160	59	2	51	51	NUM
ejpam-7160	59	3	]	]	PUNCT
ejpam-7160	59	4	were	be	AUX
ejpam-7160	59	5	engaged	engage	VERB
ejpam-7160	59	6	in	in	ADP
ejpam-7160	59	7	this	this	DET
ejpam-7160	59	8	relationship	relationship	NOUN
ejpam-7160	59	9	,	,	PUNCT
ejpam-7160	59	10	and	and	CCONJ
ejpam-7160	59	11	rh	rh	NOUN
ejpam-7160	59	12	apr	apr	NOUN
ejpam-7160	59	13	spaces	space	NOUN
ejpam-7160	59	14	using	use	VERB
ejpam-7160	59	15	grills	grill	NOUN
ejpam-7160	59	16	a.	a.	NOUN
ejpam-7160	59	17	a.	a.	NOUN
ejpam-7160	59	18	azzam	azzam	PROPN
ejpam-7160	59	19	et	et	PROPN
ejpam-7160	59	20	al	al	PROPN
ejpam-7160	59	21	.	.	PUNCT
ejpam-7160	59	22	/	/	SYM
ejpam-7160	59	23	eur	eur	PROPN
ejpam-7160	59	24	.	.	PUNCT
ejpam-7160	60	1	j.	j.	PROPN
ejpam-7160	60	2	pure	pure	PROPN
ejpam-7160	60	3	appl	appl	PROPN
ejpam-7160	60	4	.	.	PROPN
ejpam-7160	60	5	math	math	PROPN
ejpam-7160	60	6	,	,	PUNCT
ejpam-7160	60	7	18	18	NUM
ejpam-7160	60	8	(	(	PUNCT
ejpam-7160	60	9	4	4	NUM
ejpam-7160	60	10	)	)	PUNCT
ejpam-7160	60	11	(	(	PUNCT
ejpam-7160	60	12	2025	2025	NUM
ejpam-7160	60	13	)	)	PUNCT
ejpam-7160	60	14	,	,	PUNCT
ejpam-7160	60	15	7160	7160	NUM
ejpam-7160	60	16	3	3	NUM
ejpam-7160	60	17	of	of	ADP
ejpam-7160	60	18	22	22	NUM
ejpam-7160	60	19	and	and	CCONJ
ejpam-7160	60	20	maximal	maximal	ADJ
ejpam-7160	60	21	rh	rh	PROPN
ejpam-7160	60	22	-	-	PUNCT
ejpam-7160	60	23	nbs	nbs	PROPN
ejpam-7160	60	24	[	[	X
ejpam-7160	60	25	18	18	NUM
ejpam-7160	60	26	]	]	PUNCT
ejpam-7160	60	27	.	.	PUNCT
ejpam-7160	61	1	this	this	DET
ejpam-7160	61	2	study	study	NOUN
ejpam-7160	61	3	investigates	investigate	VERB
ejpam-7160	61	4	the	the	DET
ejpam-7160	61	5	purpose	purpose	NOUN
ejpam-7160	61	6	behind	behind	ADP
ejpam-7160	61	7	the	the	DET
ejpam-7160	61	8	specialized	specialized	ADJ
ejpam-7160	61	9	expansion	expansion	NOUN
ejpam-7160	61	10	utilizing	utilize	VERB
ejpam-7160	61	11	grills	grill	NOUN
ejpam-7160	61	12	by	by	ADP
ejpam-7160	61	13	distinct	distinct	ADJ
ejpam-7160	61	14	forms	form	NOUN
ejpam-7160	61	15	of	of	ADP
ejpam-7160	61	16	minimal	minimal	ADJ
ejpam-7160	61	17	nbs	nbs	PROPN
ejpam-7160	61	18	to	to	PART
ejpam-7160	61	19	reduce	reduce	VERB
ejpam-7160	61	20	the	the	DET
ejpam-7160	61	21	boundary	boundary	ADJ
ejpam-7160	61	22	regions	region	NOUN
ejpam-7160	61	23	.	.	PUNCT
ejpam-7160	62	1	this	this	DET
ejpam-7160	62	2	work	work	NOUN
ejpam-7160	62	3	focuses	focus	VERB
ejpam-7160	62	4	on	on	ADP
ejpam-7160	62	5	building	build	VERB
ejpam-7160	62	6	different	different	ADJ
ejpam-7160	62	7	topologies	topology	NOUN
ejpam-7160	62	8	using	use	VERB
ejpam-7160	62	9	grills	grill	NOUN
ejpam-7160	62	10	and	and	CCONJ
ejpam-7160	62	11	highlights	highlight	NOUN
ejpam-7160	62	12	the	the	DET
ejpam-7160	62	13	linkages	linkage	NOUN
ejpam-7160	62	14	between	between	ADP
ejpam-7160	62	15	these	these	DET
ejpam-7160	62	16	topologies	topology	NOUN
ejpam-7160	62	17	and	and	CCONJ
ejpam-7160	62	18	rhss	rhss	PROPN
ejpam-7160	62	19	,	,	PUNCT
ejpam-7160	62	20	acknowledging	acknowledge	VERB
ejpam-7160	62	21	the	the	DET
ejpam-7160	62	22	crucial	crucial	ADJ
ejpam-7160	62	23	role	role	NOUN
ejpam-7160	62	24	grills	grill	VERB
ejpam-7160	62	25	play	play	NOUN
ejpam-7160	62	26	in	in	ADP
ejpam-7160	62	27	influencing	influence	VERB
ejpam-7160	62	28	topological	topological	ADJ
ejpam-7160	62	29	rhs	rhs	PROPN
ejpam-7160	62	30	difficulties	difficulty	NOUN
ejpam-7160	62	31	.	.	PUNCT
ejpam-7160	63	1	the	the	DET
ejpam-7160	63	2	six	six	NUM
ejpam-7160	63	3	sections	section	NOUN
ejpam-7160	63	4	that	that	PRON
ejpam-7160	63	5	make	make	VERB
ejpam-7160	63	6	up	up	ADP
ejpam-7160	63	7	this	this	DET
ejpam-7160	63	8	article	article	NOUN
ejpam-7160	63	9	are	be	AUX
ejpam-7160	63	10	presented	present	VERB
ejpam-7160	63	11	as	as	SCONJ
ejpam-7160	63	12	follows	follow	VERB
ejpam-7160	63	13	:	:	PUNCT
ejpam-7160	63	14	a	a	DET
ejpam-7160	63	15	list	list	NOUN
ejpam-7160	63	16	of	of	ADP
ejpam-7160	63	17	important	important	ADJ
ejpam-7160	63	18	definitions	definition	NOUN
ejpam-7160	63	19	is	be	AUX
ejpam-7160	63	20	provided	provide	VERB
ejpam-7160	63	21	in	in	ADP
ejpam-7160	63	22	section	section	NOUN
ejpam-7160	63	23	2	2	NUM
ejpam-7160	63	24	.	.	PUNCT
ejpam-7160	64	1	the	the	DET
ejpam-7160	64	2	many	many	ADJ
ejpam-7160	64	3	topologies	topology	NOUN
ejpam-7160	64	4	that	that	PRON
ejpam-7160	64	5	grills	grill	VERB
ejpam-7160	64	6	can	can	AUX
ejpam-7160	64	7	create	create	VERB
ejpam-7160	64	8	are	be	AUX
ejpam-7160	64	9	examined	examine	VERB
ejpam-7160	64	10	in	in	ADP
ejpam-7160	64	11	section	section	NOUN
ejpam-7160	64	12	3	3	NUM
ejpam-7160	64	13	.	.	PUNCT
ejpam-7160	65	1	unlike	unlike	ADP
ejpam-7160	65	2	previous	previous	ADJ
ejpam-7160	65	3	methods	method	NOUN
ejpam-7160	65	4	[	[	X
ejpam-7160	65	5	36	36	NUM
ejpam-7160	65	6	,	,	PUNCT
ejpam-7160	65	7	52	52	NUM
ejpam-7160	65	8	]	]	PUNCT
ejpam-7160	65	9	,	,	PUNCT
ejpam-7160	65	10	it	it	PRON
ejpam-7160	65	11	presents	present	VERB
ejpam-7160	65	12	comparisons	comparison	NOUN
ejpam-7160	65	13	among	among	ADP
ejpam-7160	65	14	diverse	diverse	ADJ
ejpam-7160	65	15	topologies	topology	NOUN
ejpam-7160	65	16	and	and	CCONJ
ejpam-7160	65	17	determines	determine	VERB
ejpam-7160	65	18	the	the	DET
ejpam-7160	65	19	smallest	small	ADJ
ejpam-7160	65	20	and	and	CCONJ
ejpam-7160	65	21	largest	large	ADJ
ejpam-7160	65	22	,	,	PUNCT
ejpam-7160	65	23	whereas	whereas	SCONJ
ejpam-7160	65	24	other	other	ADJ
ejpam-7160	65	25	methods	method	NOUN
ejpam-7160	65	26	just	just	ADV
ejpam-7160	65	27	compare	compare	VERB
ejpam-7160	65	28	topologies	topology	NOUN
ejpam-7160	65	29	within	within	ADP
ejpam-7160	65	30	distinct	distinct	ADJ
ejpam-7160	65	31	sets	set	NOUN
ejpam-7160	65	32	.	.	PUNCT
ejpam-7160	66	1	conditions	condition	NOUN
ejpam-7160	66	2	for	for	ADP
ejpam-7160	66	3	determining	determine	VERB
ejpam-7160	66	4	equivalencies	equivalencie	NOUN
ejpam-7160	66	5	between	between	ADP
ejpam-7160	66	6	these	these	DET
ejpam-7160	66	7	topologies	topology	NOUN
ejpam-7160	66	8	are	be	AUX
ejpam-7160	66	9	established	establish	VERB
ejpam-7160	66	10	in	in	ADP
ejpam-7160	66	11	the	the	DET
ejpam-7160	66	12	section	section	NOUN
ejpam-7160	66	13	’s	’s	PART
ejpam-7160	66	14	conclusion	conclusion	NOUN
ejpam-7160	66	15	.	.	PUNCT
ejpam-7160	67	1	section	section	NOUN
ejpam-7160	67	2	4	4	NUM
ejpam-7160	67	3	describes	describe	VERB
ejpam-7160	67	4	the	the	DET
ejpam-7160	67	5	attributes	attribute	NOUN
ejpam-7160	67	6	of	of	ADP
ejpam-7160	67	7	the	the	DET
ejpam-7160	67	8	new	new	ADJ
ejpam-7160	67	9	apps	app	NOUN
ejpam-7160	67	10	,	,	PUNCT
ejpam-7160	67	11	which	which	PRON
ejpam-7160	67	12	are	be	AUX
ejpam-7160	67	13	examined	examine	VERB
ejpam-7160	67	14	using	use	VERB
ejpam-7160	67	15	the	the	DET
ejpam-7160	67	16	recommended	recommend	VERB
ejpam-7160	67	17	topologies	topology	NOUN
ejpam-7160	67	18	.	.	PUNCT
ejpam-7160	68	1	in	in	ADP
ejpam-7160	68	2	contrast	contrast	NOUN
ejpam-7160	68	3	to	to	ADP
ejpam-7160	68	4	the	the	DET
ejpam-7160	68	5	previous	previous	ADJ
ejpam-7160	68	6	ones	one	NOUN
ejpam-7160	68	7	,	,	PUNCT
ejpam-7160	68	8	they	they	PRON
ejpam-7160	68	9	have	have	VERB
ejpam-7160	68	10	the	the	DET
ejpam-7160	68	11	property	property	NOUN
ejpam-7160	68	12	of	of	ADP
ejpam-7160	68	13	monotonicity	monotonicity	NOUN
ejpam-7160	68	14	and	and	CCONJ
ejpam-7160	68	15	satisfy	satisfy	VERB
ejpam-7160	68	16	all	all	PRON
ejpam-7160	68	17	of	of	ADP
ejpam-7160	68	18	pawlak	pawlak	ADJ
ejpam-7160	68	19	’s	’s	PART
ejpam-7160	68	20	properties	property	NOUN
ejpam-7160	68	21	without	without	ADP
ejpam-7160	68	22	limitations	limitation	NOUN
ejpam-7160	68	23	[	[	X
ejpam-7160	68	24	53	53	NUM
ejpam-7160	68	25	,	,	PUNCT
ejpam-7160	68	26	54	54	NUM
ejpam-7160	68	27	]	]	PUNCT
ejpam-7160	68	28	.	.	PUNCT
ejpam-7160	69	1	in	in	ADP
ejpam-7160	69	2	section	section	NOUN
ejpam-7160	69	3	5	5	NUM
ejpam-7160	69	4	,	,	PUNCT
ejpam-7160	69	5	a	a	DET
ejpam-7160	69	6	medical	medical	ADJ
ejpam-7160	69	7	use	use	NOUN
ejpam-7160	69	8	is	be	AUX
ejpam-7160	69	9	also	also	ADV
ejpam-7160	69	10	suggested	suggest	VERB
ejpam-7160	69	11	.	.	PUNCT
ejpam-7160	70	1	consequently	consequently	ADV
ejpam-7160	70	2	,	,	PUNCT
ejpam-7160	70	3	these	these	DET
ejpam-7160	70	4	techniques	technique	NOUN
ejpam-7160	70	5	make	make	VERB
ejpam-7160	70	6	it	it	PRON
ejpam-7160	70	7	simple	simple	ADJ
ejpam-7160	70	8	and	and	CCONJ
ejpam-7160	70	9	very	very	ADV
ejpam-7160	70	10	accurate	accurate	ADJ
ejpam-7160	70	11	for	for	SCONJ
ejpam-7160	70	12	medical	medical	ADJ
ejpam-7160	70	13	professionals	professional	NOUN
ejpam-7160	70	14	to	to	PART
ejpam-7160	70	15	diagnose	diagnose	VERB
ejpam-7160	70	16	heart	heart	NOUN
ejpam-7160	70	17	failure	failure	NOUN
ejpam-7160	70	18	.	.	PUNCT
ejpam-7160	71	1	the	the	DET
ejpam-7160	71	2	usefulness	usefulness	NOUN
ejpam-7160	71	3	and	and	CCONJ
ejpam-7160	71	4	effectiveness	effectiveness	NOUN
ejpam-7160	71	5	of	of	ADP
ejpam-7160	71	6	the	the	DET
ejpam-7160	71	7	suggested	suggest	VERB
ejpam-7160	71	8	models	model	NOUN
ejpam-7160	71	9	are	be	AUX
ejpam-7160	71	10	demonstrated	demonstrate	VERB
ejpam-7160	71	11	,	,	PUNCT
ejpam-7160	71	12	highlighting	highlight	VERB
ejpam-7160	71	13	the	the	DET
ejpam-7160	71	14	crucial	crucial	ADJ
ejpam-7160	71	15	part	part	NOUN
ejpam-7160	71	16	grills	grill	VERB
ejpam-7160	71	17	play	play	VERB
ejpam-7160	71	18	in	in	ADP
ejpam-7160	71	19	decisionmaking	decisionmake	VERB
ejpam-7160	71	20	.	.	PUNCT
ejpam-7160	72	1	consequently	consequently	ADV
ejpam-7160	72	2	,	,	PUNCT
ejpam-7160	72	3	these	these	DET
ejpam-7160	72	4	techniques	technique	NOUN
ejpam-7160	72	5	enable	enable	VERB
ejpam-7160	72	6	physicians	physician	NOUN
ejpam-7160	72	7	to	to	PART
ejpam-7160	72	8	make	make	VERB
ejpam-7160	72	9	a	a	DET
ejpam-7160	72	10	quick	quick	ADJ
ejpam-7160	72	11	and	and	CCONJ
ejpam-7160	72	12	accurate	accurate	ADJ
ejpam-7160	72	13	diagnosis	diagnosis	NOUN
ejpam-7160	72	14	of	of	ADP
ejpam-7160	72	15	heart	heart	NOUN
ejpam-7160	72	16	failure	failure	NOUN
ejpam-7160	72	17	.	.	PUNCT
ejpam-7160	73	1	the	the	DET
ejpam-7160	73	2	discussion	discussion	NOUN
ejpam-7160	73	3	is	be	AUX
ejpam-7160	73	4	in	in	ADP
ejpam-7160	73	5	section	section	NOUN
ejpam-7160	73	6	6	6	NUM
ejpam-7160	73	7	,	,	PUNCT
ejpam-7160	73	8	and	and	CCONJ
ejpam-7160	73	9	the	the	DET
ejpam-7160	73	10	conclusion	conclusion	NOUN
ejpam-7160	73	11	section	section	NOUN
ejpam-7160	73	12	marks	mark	VERB
ejpam-7160	73	13	the	the	DET
ejpam-7160	73	14	end	end	NOUN
ejpam-7160	73	15	of	of	ADP
ejpam-7160	73	16	this	this	DET
ejpam-7160	73	17	study	study	NOUN
ejpam-7160	73	18	.	.	PUNCT
ejpam-7160	74	1	2	2	X
ejpam-7160	74	2	.	.	X
ejpam-7160	74	3	preliminaries	preliminary	NOUN
ejpam-7160	74	4	definition	definition	NOUN
ejpam-7160	74	5	1	1	NUM
ejpam-7160	74	6	.	.	PUNCT
ejpam-7160	75	1	[	[	X
ejpam-7160	75	2	25	25	NUM
ejpam-7160	75	3	,	,	PUNCT
ejpam-7160	75	4	37	37	NUM
ejpam-7160	75	5	,	,	PUNCT
ejpam-7160	75	6	38	38	NUM
ejpam-7160	75	7	,	,	PUNCT
ejpam-7160	75	8	39	39	NUM
ejpam-7160	75	9	]	]	PUNCT
ejpam-7160	75	10	assume	assume	VERB
ejpam-7160	75	11	that	that	SCONJ
ejpam-7160	75	12	π1	π1	NOUN
ejpam-7160	75	13	∈	∈	PROPN
ejpam-7160	75	14	π	π	NOUN
ejpam-7160	75	15	and	and	CCONJ
ejpam-7160	75	16	let	let	VERB
ejpam-7160	75	17	×	×	NOUN
ejpam-7160	75	18	be	be	AUX
ejpam-7160	75	19	any	any	DET
ejpam-7160	75	20	(	(	PUNCT
ejpam-7160	75	21	bir	bir	NOUN
ejpam-7160	75	22	)	)	PUNCT
ejpam-7160	75	23	on	on	ADP
ejpam-7160	75	24	a	a	DET
ejpam-7160	75	25	finite	finite	NOUN
ejpam-7160	75	26	set	set	VERB
ejpam-7160	75	27	π	π	PROPN
ejpam-7160	75	28	̸=	̸=	PROPN
ejpam-7160	75	29	ϕ.	ϕ.	VERB
ejpam-7160	75	30	the	the	DET
ejpam-7160	75	31	subsequent	subsequent	ADJ
ejpam-7160	75	32	terms	term	NOUN
ejpam-7160	75	33	are	be	AUX
ejpam-7160	75	34	elucidated	elucidate	VERB
ejpam-7160	75	35	:	:	PUNCT
ejpam-7160	75	36	(	(	PUNCT
ejpam-7160	75	37	1	1	X
ejpam-7160	75	38	)	)	PUNCT
ejpam-7160	75	39	nr(π1	nr(π1	NOUN
ejpam-7160	75	40	)	)	PUNCT
ejpam-7160	75	41	=	=	SYM
ejpam-7160	75	42	{	{	PUNCT
ejpam-7160	75	43	π2	π2	NOUN
ejpam-7160	75	44	∈	∈	PROPN
ejpam-7160	75	45	π	π	NOUN
ejpam-7160	75	46	:	:	PUNCT
ejpam-7160	75	47	π1×π2	π1×π2	PROPN
ejpam-7160	75	48	}	}	PUNCT
ejpam-7160	75	49	.	.	PUNCT
ejpam-7160	76	1	(	(	PUNCT
ejpam-7160	76	2	2	2	X
ejpam-7160	76	3	)	)	PUNCT
ejpam-7160	76	4	nl(π1	nl(π1	X
ejpam-7160	76	5	)	)	PUNCT
ejpam-7160	77	1	=	=	SYM
ejpam-7160	77	2	{	{	PUNCT
ejpam-7160	77	3	π2	π2	NOUN
ejpam-7160	77	4	∈	∈	PROPN
ejpam-7160	77	5	π	π	NOUN
ejpam-7160	77	6	:	:	PUNCT
ejpam-7160	77	7	π2×π1	π2×π1	NOUN
ejpam-7160	77	8	}	}	PUNCT
ejpam-7160	77	9	.	.	PUNCT
ejpam-7160	78	1	(	(	PUNCT
ejpam-7160	78	2	3	3	X
ejpam-7160	78	3	)	)	PUNCT
ejpam-7160	78	4	n⟨r⟩(π1	n⟨r⟩(π1	PROPN
ejpam-7160	78	5	)	)	PUNCT
ejpam-7160	78	6	=	=	PRON
ejpam-7160	78	7	{	{	PUNCT
ejpam-7160	78	8	⊓π1∈nr(π2)nr(π2	⊓π1∈nr(π2)nr(π2	NUM
ejpam-7160	78	9	)	)	PUNCT
ejpam-7160	78	10	:	:	PUNCT
ejpam-7160	79	1	∃	∃	PROPN
ejpam-7160	79	2	nr(π2	nr(π2	NOUN
ejpam-7160	79	3	)	)	PUNCT
ejpam-7160	79	4	containing	contain	VERB
ejpam-7160	79	5	π1	π1	NOUN
ejpam-7160	79	6	,	,	PUNCT
ejpam-7160	79	7	ϕ	ϕ	NOUN
ejpam-7160	79	8	:	:	PUNCT
ejpam-7160	79	9	otherwise	otherwise	ADV
ejpam-7160	79	10	.	.	PUNCT
ejpam-7160	80	1	(	(	PUNCT
ejpam-7160	80	2	4	4	X
ejpam-7160	80	3	)	)	PUNCT
ejpam-7160	80	4	n⟨l⟩(π1	n⟨l⟩(π1	PROPN
ejpam-7160	80	5	)	)	PUNCT
ejpam-7160	80	6	=	=	PRON
ejpam-7160	80	7	{	{	PUNCT
ejpam-7160	80	8	⊓π1∈nl(π2)nl(π2	⊓π1∈nl(π2)nl(π2	NUM
ejpam-7160	80	9	)	)	PUNCT
ejpam-7160	80	10	:	:	PUNCT
ejpam-7160	80	11	∃	∃	PROPN
ejpam-7160	80	12	nl(π2	nl(π2	NOUN
ejpam-7160	80	13	)	)	PUNCT
ejpam-7160	80	14	containing	contain	VERB
ejpam-7160	80	15	π1	π1	NOUN
ejpam-7160	80	16	,	,	PUNCT
ejpam-7160	80	17	ϕ	ϕ	NOUN
ejpam-7160	80	18	:	:	PUNCT
ejpam-7160	80	19	otherwise	otherwise	ADV
ejpam-7160	80	20	.	.	PUNCT
ejpam-7160	80	21	.	.	PUNCT
ejpam-7160	81	1	(	(	PUNCT
ejpam-7160	81	2	5	5	NUM
ejpam-7160	81	3	)	)	PUNCT
ejpam-7160	81	4	ni(π1	ni(π1	X
ejpam-7160	81	5	)	)	PUNCT
ejpam-7160	81	6	=	=	SYM
ejpam-7160	81	7	nr(π1	nr(π1	NOUN
ejpam-7160	81	8	)	)	PUNCT
ejpam-7160	81	9	⊓nl(π1	⊓nl(π1	PRON
ejpam-7160	81	10	)	)	PUNCT
ejpam-7160	81	11	.	.	PUNCT
ejpam-7160	82	1	(	(	PUNCT
ejpam-7160	82	2	6	6	NUM
ejpam-7160	82	3	)	)	PUNCT
ejpam-7160	82	4	nu(π1	nu(π1	PRON
ejpam-7160	82	5	)	)	PUNCT
ejpam-7160	82	6	=	=	SYM
ejpam-7160	82	7	nr(π1	nr(π1	NOUN
ejpam-7160	82	8	)	)	PUNCT
ejpam-7160	82	9	⊔nl(π1	⊔nl(π1	NOUN
ejpam-7160	82	10	)	)	PUNCT
ejpam-7160	82	11	.	.	PUNCT
ejpam-7160	83	1	a.	a.	PROPN
ejpam-7160	83	2	a.	a.	PROPN
ejpam-7160	83	3	azzam	azzam	PROPN
ejpam-7160	83	4	et	et	PROPN
ejpam-7160	83	5	al	al	PROPN
ejpam-7160	83	6	.	.	PUNCT
ejpam-7160	83	7	/	/	SYM
ejpam-7160	83	8	eur	eur	PROPN
ejpam-7160	83	9	.	.	PUNCT
ejpam-7160	84	1	j.	j.	PROPN
ejpam-7160	84	2	pure	pure	PROPN
ejpam-7160	84	3	appl	appl	PROPN
ejpam-7160	84	4	.	.	PROPN
ejpam-7160	84	5	math	math	PROPN
ejpam-7160	84	6	,	,	PUNCT
ejpam-7160	84	7	18	18	NUM
ejpam-7160	84	8	(	(	PUNCT
ejpam-7160	84	9	4	4	NUM
ejpam-7160	84	10	)	)	PUNCT
ejpam-7160	84	11	(	(	PUNCT
ejpam-7160	84	12	2025	2025	NUM
ejpam-7160	84	13	)	)	PUNCT
ejpam-7160	84	14	,	,	PUNCT
ejpam-7160	84	15	7160	7160	NUM
ejpam-7160	84	16	4	4	NUM
ejpam-7160	84	17	of	of	ADP
ejpam-7160	84	18	22	22	NUM
ejpam-7160	84	19	(	(	PUNCT
ejpam-7160	84	20	7	7	NUM
ejpam-7160	84	21	)	)	PUNCT
ejpam-7160	84	22	n⟨i⟩(π1	n⟨i⟩(π1	PROPN
ejpam-7160	84	23	)	)	PUNCT
ejpam-7160	84	24	=	=	SYM
ejpam-7160	84	25	n⟨r⟩(π1	n⟨r⟩(π1	PROPN
ejpam-7160	84	26	)	)	PUNCT
ejpam-7160	84	27	⊓n⟨l⟩(π1	⊓n⟨l⟩(π1	PUNCT
ejpam-7160	84	28	)	)	PUNCT
ejpam-7160	84	29	.	.	PUNCT
ejpam-7160	85	1	(	(	PUNCT
ejpam-7160	85	2	8)	8)	NUM
ejpam-7160	85	3	n⟨u⟩(π1	n⟨u⟩(π1	PROPN
ejpam-7160	85	4	)	)	PUNCT
ejpam-7160	85	5	=	=	SYM
ejpam-7160	85	6	n⟨r⟩(π1	n⟨r⟩(π1	PROPN
ejpam-7160	85	7	)	)	PUNCT
ejpam-7160	85	8	⊔n⟨l⟩(π1	⊔n⟨l⟩(π1	PROPN
ejpam-7160	85	9	)	)	PUNCT
ejpam-7160	85	10	.	.	PUNCT
ejpam-7160	86	1	definition	definition	NOUN
ejpam-7160	86	2	2	2	NUM
ejpam-7160	86	3	.	.	PUNCT
ejpam-7160	87	1	[	[	X
ejpam-7160	87	2	25	25	NUM
ejpam-7160	87	3	]	]	PUNCT
ejpam-7160	87	4	the	the	DET
ejpam-7160	87	5	triple	triple	ADJ
ejpam-7160	87	6	(	(	PUNCT
ejpam-7160	87	7	π,×	π,×	PROPN
ejpam-7160	87	8	,	,	PUNCT
ejpam-7160	87	9	ζι	ζι	NOUN
ejpam-7160	87	10	)	)	PUNCT
ejpam-7160	87	11	is	be	AUX
ejpam-7160	87	12	referred	refer	VERB
ejpam-7160	87	13	to	to	ADP
ejpam-7160	87	14	as	as	ADP
ejpam-7160	87	15	a	a	DET
ejpam-7160	87	16	ι	ι	NOUN
ejpam-7160	87	17	-	-	PUNCT
ejpam-7160	87	18	nb	nb	NOUN
ejpam-7160	87	19	space	space	NOUN
ejpam-7160	87	20	(	(	PUNCT
ejpam-7160	87	21	shortened	shorten	VERB
ejpam-7160	87	22	to	to	ADP
ejpam-7160	87	23	ι	ι	VERB
ejpam-7160	87	24	-	-	PUNCT
ejpam-7160	87	25	ns	ns	NUM
ejpam-7160	87	26	)	)	PUNCT
ejpam-7160	87	27	.	.	PUNCT
ejpam-7160	88	1	ι	ι	X
ejpam-7160	88	2	∈	∈	PROPN
ejpam-7160	88	3	{	{	PUNCT
ejpam-7160	88	4	r	r	NOUN
ejpam-7160	88	5	,	,	PUNCT
ejpam-7160	88	6	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	88	7	,	,	PUNCT
ejpam-7160	88	8	l	l	NOUN
ejpam-7160	88	9	,	,	PUNCT
ejpam-7160	88	10	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	88	11	,	,	PUNCT
ejpam-7160	88	12	i	i	PRON
ejpam-7160	88	13	,	,	PUNCT
ejpam-7160	88	14	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	88	15	,	,	PUNCT
ejpam-7160	88	16	u	u	NOUN
ejpam-7160	88	17	,	,	PUNCT
ejpam-7160	88	18	⟨u⟩	⟨u⟩	PROPN
ejpam-7160	88	19	}	}	PUNCT
ejpam-7160	88	20	,	,	PUNCT
ejpam-7160	88	21	and	and	CCONJ
ejpam-7160	88	22	ζι	ζι	X
ejpam-7160	88	23	is	be	AUX
ejpam-7160	88	24	a	a	DET
ejpam-7160	88	25	map	map	NOUN
ejpam-7160	88	26	from	from	ADP
ejpam-7160	88	27	π	π	PROPN
ejpam-7160	88	28	to	to	ADP
ejpam-7160	88	29	2π	2π	PROPN
ejpam-7160	88	30	which	which	PRON
ejpam-7160	88	31	links	link	VERB
ejpam-7160	88	32	each	each	DET
ejpam-7160	88	33	member	member	NOUN
ejpam-7160	88	34	of	of	ADP
ejpam-7160	88	35	π	π	PROPN
ejpam-7160	88	36	to	to	ADP
ejpam-7160	88	37	its	its	PRON
ejpam-7160	88	38	ι	ι	ADV
ejpam-7160	88	39	-	-	PUNCT
ejpam-7160	88	40	ns	ns	ADJ
ejpam-7160	88	41	.	.	PUNCT
ejpam-7160	88	42	theorem	theorem	NOUN
ejpam-7160	88	43	1	1	NUM
ejpam-7160	88	44	.	.	PUNCT
ejpam-7160	89	1	[	[	X
ejpam-7160	89	2	16	16	NUM
ejpam-7160	89	3	]	]	PUNCT
ejpam-7160	89	4	for	for	ADP
ejpam-7160	89	5	a	a	DET
ejpam-7160	89	6	ι	ι	NOUN
ejpam-7160	89	7	-	-	PUNCT
ejpam-7160	89	8	ns	ns	INTJ
ejpam-7160	89	9	(	(	PUNCT
ejpam-7160	89	10	π,×	π,×	PROPN
ejpam-7160	89	11	,	,	PUNCT
ejpam-7160	89	12	ζι	ζι	NOUN
ejpam-7160	89	13	)	)	PUNCT
ejpam-7160	89	14	,	,	PUNCT
ejpam-7160	89	15	and	and	CCONJ
ejpam-7160	89	16	l	l	NOUN
ejpam-7160	89	17	be	be	AUX
ejpam-7160	89	18	a	a	DET
ejpam-7160	89	19	grill	grill	NOUN
ejpam-7160	89	20	.	.	PUNCT
ejpam-7160	90	1	the	the	DET
ejpam-7160	90	2	family	family	NOUN
ejpam-7160	90	3	τlnι	τlnι	NOUN
ejpam-7160	90	4	=	=	PUNCT
ejpam-7160	90	5	{	{	PUNCT
ejpam-7160	90	6	c	c	NOUN
ejpam-7160	90	7	⊑	⊑	X
ejpam-7160	90	8	π	π	X
ejpam-7160	90	9	:	:	PUNCT
ejpam-7160	90	10	∀π1	∀π1	VERB
ejpam-7160	90	11	∈	∈	PROPN
ejpam-7160	90	12	c	c	X
ejpam-7160	90	13	,	,	PUNCT
ejpam-7160	90	14	nι(π1	nι(π1	X
ejpam-7160	90	15	)	)	PUNCT
ejpam-7160	90	16	⊓	⊓	PROPN
ejpam-7160	90	17	cc	cc	NOUN
ejpam-7160	90	18	/∈	/∈	PUNCT
ejpam-7160	90	19	l	l	NOUN
ejpam-7160	90	20	}	}	PUNCT
ejpam-7160	90	21	a	a	DET
ejpam-7160	90	22	nl	nl	NOUN
ejpam-7160	90	23	ι	ι	PROPN
ejpam-7160	90	24	topology	topology	NOUN
ejpam-7160	90	25	on	on	ADP
ejpam-7160	90	26	π	π	PROPN
ejpam-7160	90	27	where	where	SCONJ
ejpam-7160	90	28	cc	cc	PROPN
ejpam-7160	90	29	represents	represent	VERB
ejpam-7160	90	30	c	c	PROPN
ejpam-7160	90	31	’s	’s	PART
ejpam-7160	90	32	complementary	complementary	ADJ
ejpam-7160	90	33	set	set	NOUN
ejpam-7160	90	34	.	.	PUNCT
ejpam-7160	91	1	definition	definition	NOUN
ejpam-7160	91	2	3	3	NUM
ejpam-7160	91	3	.	.	PUNCT
ejpam-7160	92	1	[	[	X
ejpam-7160	92	2	55	55	NUM
ejpam-7160	92	3	]	]	PUNCT
ejpam-7160	92	4	consider	consider	VERB
ejpam-7160	92	5	(	(	PUNCT
ejpam-7160	92	6	π,×	π,×	PROPN
ejpam-7160	92	7	,	,	PUNCT
ejpam-7160	92	8	ζι	ζι	NOUN
ejpam-7160	92	9	)	)	PUNCT
ejpam-7160	92	10	is	be	AUX
ejpam-7160	92	11	a	a	DET
ejpam-7160	92	12	ι	ι	NOUN
ejpam-7160	92	13	-	-	PUNCT
ejpam-7160	92	14	ns	ns	ADJ
ejpam-7160	92	15	,	,	PUNCT
ejpam-7160	92	16	and	and	CCONJ
ejpam-7160	92	17	l	l	NOUN
ejpam-7160	92	18	be	be	AUX
ejpam-7160	92	19	a	a	DET
ejpam-7160	92	20	grill	grill	NOUN
ejpam-7160	92	21	on	on	ADP
ejpam-7160	92	22	π	π	PROPN
ejpam-7160	92	23	.	.	PUNCT
ejpam-7160	93	1	the	the	DET
ejpam-7160	93	2	l	l	NOUN
ejpam-7160	93	3	-	-	ADJ
ejpam-7160	93	4	nι	nι	ADP
ejpam-7160	93	5	-	-	PUNCT
ejpam-7160	93	6	up	up	ADP
ejpam-7160	93	7	app	app	NOUN
ejpam-7160	93	8	×l	×l	PROPN
ejpam-7160	93	9	nι	nι	NOUN
ejpam-7160	93	10	,	,	PUNCT
ejpam-7160	93	11	and	and	CCONJ
ejpam-7160	93	12	l	l	NOUN
ejpam-7160	93	13	-	-	ADJ
ejpam-7160	93	14	nι	nι	ADJ
ejpam-7160	93	15	-	-	PUNCT
ejpam-7160	93	16	lo	lo	NOUN
ejpam-7160	93	17	app	app	NOUN
ejpam-7160	93	18	×l	×l	PROPN
ejpam-7160	93	19	nι	nι	PROPN
ejpam-7160	93	20	of	of	ADP
ejpam-7160	93	21	c	c	NOUN
ejpam-7160	93	22	⊑	⊑	X
ejpam-7160	93	23	π	π	PROPN
ejpam-7160	93	24	are	be	AUX
ejpam-7160	93	25	×l	×l	ADV
ejpam-7160	93	26	nι	nι	X
ejpam-7160	93	27	(	(	PUNCT
ejpam-7160	93	28	c	c	NOUN
ejpam-7160	93	29	)	)	PUNCT
ejpam-7160	93	30	=	=	SYM
ejpam-7160	94	1	⊓{y	⊓{y	ADJ
ejpam-7160	94	2	:	:	PUNCT
ejpam-7160	94	3	y	y	PROPN
ejpam-7160	94	4	c	c	PROPN
ejpam-7160	94	5	∈	∈	PROPN
ejpam-7160	94	6	τlnι	τlnι	NOUN
ejpam-7160	94	7	:	:	PUNCT
ejpam-7160	94	8	c	c	X
ejpam-7160	94	9	⊑	⊑	X
ejpam-7160	94	10	y	y	PROPN
ejpam-7160	94	11	}	}	PUNCT
ejpam-7160	94	12	=	=	PUNCT
ejpam-7160	94	13	cll	cll	PROPN
ejpam-7160	94	14	nι	nι	INTJ
ejpam-7160	94	15	(	(	PUNCT
ejpam-7160	94	16	c	c	NOUN
ejpam-7160	94	17	)	)	PUNCT
ejpam-7160	94	18	.	.	PUNCT
ejpam-7160	95	1	×l	×l	PROPN
ejpam-7160	95	2	nι	nι	INTJ
ejpam-7160	95	3	(	(	PUNCT
ejpam-7160	95	4	c	c	NOUN
ejpam-7160	95	5	)	)	PUNCT
ejpam-7160	95	6	=	=	SYM
ejpam-7160	95	7	⊔{g	⊔{g	PROPN
ejpam-7160	95	8	∈	∈	PROPN
ejpam-7160	95	9	τlnι	τlnι	NOUN
ejpam-7160	95	10	:	:	PUNCT
ejpam-7160	95	11	g	g	X
ejpam-7160	95	12	⊑	⊑	X
ejpam-7160	95	13	c	c	X
ejpam-7160	95	14	}	}	PUNCT
ejpam-7160	95	15	=	=	VERB
ejpam-7160	95	16	intlnι	intlnι	ADJ
ejpam-7160	95	17	(	(	PUNCT
ejpam-7160	95	18	c	c	NOUN
ejpam-7160	95	19	)	)	PUNCT
ejpam-7160	95	20	.	.	PUNCT
ejpam-7160	96	1	definition	definition	NOUN
ejpam-7160	96	2	4	4	NUM
ejpam-7160	96	3	.	.	PUNCT
ejpam-7160	97	1	[	[	X
ejpam-7160	97	2	56	56	NUM
ejpam-7160	97	3	]	]	PUNCT
ejpam-7160	97	4	let	let	VERB
ejpam-7160	97	5	the	the	DET
ejpam-7160	97	6	relation	relation	NOUN
ejpam-7160	97	7	×	×	NOUN
ejpam-7160	97	8	be	be	AUX
ejpam-7160	97	9	arbitrary	arbitrary	ADJ
ejpam-7160	97	10	(	(	PUNCT
ejpam-7160	97	11	arr	arr	NOUN
ejpam-7160	97	12	)	)	PUNCT
ejpam-7160	97	13	on	on	ADP
ejpam-7160	97	14	a	a	DET
ejpam-7160	97	15	universe	universe	ADJ
ejpam-7160	97	16	π	π	NOUN
ejpam-7160	97	17	.	.	PUNCT
ejpam-7160	98	1	the	the	DET
ejpam-7160	98	2	maximal	maximal	ADJ
ejpam-7160	98	3	right	right	ADJ
ejpam-7160	98	4	nb	nb	INTJ
ejpam-7160	98	5	of	of	ADP
ejpam-7160	98	6	an	an	DET
ejpam-7160	98	7	π1	π1	ADJ
ejpam-7160	98	8	∈	∈	NOUN
ejpam-7160	98	9	π	π	NOUN
ejpam-7160	98	10	is	be	AUX
ejpam-7160	98	11	delineated	delineated	ADJ
ejpam-7160	98	12	as	as	ADP
ejpam-7160	98	13	such	such	ADJ
ejpam-7160	98	14	.	.	PUNCT
ejpam-7160	99	1	mr(π1	mr(π1	X
ejpam-7160	99	2	)	)	PUNCT
ejpam-7160	100	1	=	=	PUNCT
ejpam-7160	100	2	⊔π1∈nr(π2)nr(π2	⊔π1∈nr(π2)nr(π2	PRON
ejpam-7160	100	3	)	)	PUNCT
ejpam-7160	100	4	definition	definition	NOUN
ejpam-7160	100	5	5	5	NUM
ejpam-7160	100	6	.	.	PUNCT
ejpam-7160	101	1	[	[	X
ejpam-7160	101	2	55	55	NUM
ejpam-7160	101	3	]	]	X
ejpam-7160	101	4	let	let	AUX
ejpam-7160	101	5	(	(	PUNCT
ejpam-7160	101	6	π,×	π,×	PROPN
ejpam-7160	101	7	,	,	PUNCT
ejpam-7160	101	8	ζι	ζι	X
ejpam-7160	101	9	)	)	PUNCT
ejpam-7160	101	10	be	be	AUX
ejpam-7160	101	11	a	a	DET
ejpam-7160	101	12	ι	ι	NOUN
ejpam-7160	101	13	-	-	PUNCT
ejpam-7160	101	14	ns	ns	NOUN
ejpam-7160	101	15	and	and	CCONJ
ejpam-7160	101	16	l	l	NOUN
ejpam-7160	101	17	be	be	AUX
ejpam-7160	101	18	a	a	DET
ejpam-7160	101	19	grill	grill	NOUN
ejpam-7160	101	20	on	on	ADP
ejpam-7160	101	21	π	π	PROPN
ejpam-7160	101	22	.	.	PUNCT
ejpam-7160	102	1	the	the	DET
ejpam-7160	102	2	nl∗	nl∗	NOUN
ejpam-7160	102	3	ι	ι	X
ejpam-7160	102	4	lower	low	ADJ
ejpam-7160	102	5	and	and	CCONJ
ejpam-7160	102	6	×l∗	×l∗	VERB
ejpam-7160	102	7	ι	ι	PROPN
ejpam-7160	102	8	-up	-up	INTJ
ejpam-7160	102	9	apps	app	NOUN
ejpam-7160	102	10	of	of	ADP
ejpam-7160	102	11	the	the	DET
ejpam-7160	102	12	set	set	NOUN
ejpam-7160	102	13	c	c	PROPN
ejpam-7160	102	14	delineated	delineate	VERB
ejpam-7160	102	15	as	as	ADP
ejpam-7160	102	16	such	such	ADJ
ejpam-7160	102	17	..	..	PUNCT
ejpam-7160	102	18	×l∗	×l∗	PROPN
ejpam-7160	102	19	mι	mι	INTJ
ejpam-7160	102	20	(	(	PUNCT
ejpam-7160	102	21	c	c	NOUN
ejpam-7160	102	22	)	)	PUNCT
ejpam-7160	102	23	=	=	PRON
ejpam-7160	103	1	{	{	PUNCT
ejpam-7160	103	2	π1	π1	NOUN
ejpam-7160	103	3	∈	∈	PROPN
ejpam-7160	103	4	π	π	NOUN
ejpam-7160	103	5	:	:	PUNCT
ejpam-7160	103	6	mι(π1	mι(π1	X
ejpam-7160	103	7	)	)	PUNCT
ejpam-7160	104	1	⊓	⊓	PROPN
ejpam-7160	104	2	cc	cc	NOUN
ejpam-7160	104	3	/∈	/∈	PUNCT
ejpam-7160	104	4	l	l	NOUN
ejpam-7160	104	5	}	}	PUNCT
ejpam-7160	104	6	.	.	PUNCT
ejpam-7160	105	1	×l∗	×l∗	VERB
ejpam-7160	105	2	mι	mι	INTJ
ejpam-7160	105	3	(	(	PUNCT
ejpam-7160	105	4	c	c	NOUN
ejpam-7160	105	5	)	)	PUNCT
ejpam-7160	105	6	=	=	PRON
ejpam-7160	105	7	{	{	PUNCT
ejpam-7160	105	8	π1	π1	NOUN
ejpam-7160	105	9	∈	∈	PROPN
ejpam-7160	105	10	π	π	NOUN
ejpam-7160	105	11	:	:	PUNCT
ejpam-7160	105	12	mι(π1	mι(π1	X
ejpam-7160	105	13	)	)	PUNCT
ejpam-7160	106	1	⊓	⊓	PROPN
ejpam-7160	106	2	c	c	NOUN
ejpam-7160	106	3	∈	∈	PROPN
ejpam-7160	106	4	l	l	NOUN
ejpam-7160	106	5	}	}	PUNCT
ejpam-7160	106	6	.	.	PUNCT
ejpam-7160	107	1	definition	definition	NOUN
ejpam-7160	107	2	6	6	NUM
ejpam-7160	107	3	.	.	PUNCT
ejpam-7160	108	1	[	[	X
ejpam-7160	108	2	55	55	NUM
ejpam-7160	108	3	]	]	X
ejpam-7160	108	4	let	let	AUX
ejpam-7160	108	5	(	(	PUNCT
ejpam-7160	108	6	π,×	π,×	PROPN
ejpam-7160	108	7	,	,	PUNCT
ejpam-7160	108	8	ζι	ζι	X
ejpam-7160	108	9	)	)	PUNCT
ejpam-7160	108	10	be	be	AUX
ejpam-7160	108	11	a	a	DET
ejpam-7160	108	12	ι	ι	NOUN
ejpam-7160	108	13	-	-	PUNCT
ejpam-7160	108	14	ns	ns	NOUN
ejpam-7160	108	15	and	and	CCONJ
ejpam-7160	108	16	l	l	NOUN
ejpam-7160	108	17	be	be	AUX
ejpam-7160	108	18	a	a	DET
ejpam-7160	108	19	grill	grill	NOUN
ejpam-7160	108	20	on	on	ADP
ejpam-7160	108	21	π	π	PROPN
ejpam-7160	108	22	.	.	PUNCT
ejpam-7160	109	1	the	the	DET
ejpam-7160	109	2	nl∗∗	nl∗∗	PROPN
ejpam-7160	109	3	ι	ι	PROPN
ejpam-7160	109	4	lo	lo	PROPN
ejpam-7160	109	5	and	and	CCONJ
ejpam-7160	109	6	×l∗∗	×l∗∗	NOUN
ejpam-7160	109	7	ι	ι	PROPN
ejpam-7160	109	8	-up	-up	NOUN
ejpam-7160	109	9	apps	app	NOUN
ejpam-7160	109	10	of	of	ADP
ejpam-7160	109	11	the	the	DET
ejpam-7160	109	12	set	set	NOUN
ejpam-7160	109	13	c	c	NOUN
ejpam-7160	109	14	is	be	AUX
ejpam-7160	109	15	delineated	delineated	ADJ
ejpam-7160	109	16	as	as	ADP
ejpam-7160	109	17	such	such	ADJ
ejpam-7160	109	18	.	.	PUNCT
ejpam-7160	110	1	×l∗∗	×l∗∗	NOUN
ejpam-7160	110	2	mι	mι	INTJ
ejpam-7160	110	3	(	(	PUNCT
ejpam-7160	110	4	c	c	NOUN
ejpam-7160	110	5	)	)	PUNCT
ejpam-7160	110	6	=	=	PRON
ejpam-7160	111	1	{	{	PUNCT
ejpam-7160	111	2	π1	π1	NOUN
ejpam-7160	111	3	∈	∈	PROPN
ejpam-7160	111	4	π	π	NOUN
ejpam-7160	111	5	:	:	PUNCT
ejpam-7160	111	6	mι(π1	mι(π1	X
ejpam-7160	111	7	)	)	PUNCT
ejpam-7160	112	1	⊓	⊓	PROPN
ejpam-7160	112	2	cc	cc	NOUN
ejpam-7160	112	3	/∈	/∈	PUNCT
ejpam-7160	112	4	l	l	NOUN
ejpam-7160	112	5	}	}	PUNCT
ejpam-7160	112	6	.	.	PUNCT
ejpam-7160	113	1	×l∗∗	×l∗∗	NOUN
ejpam-7160	113	2	mι	mι	INTJ
ejpam-7160	113	3	(	(	PUNCT
ejpam-7160	113	4	c	c	NOUN
ejpam-7160	113	5	)	)	PUNCT
ejpam-7160	113	6	=	=	PUNCT
ejpam-7160	114	1	c	c	PROPN
ejpam-7160	114	2	⊔	⊔	PROPN
ejpam-7160	114	3	×l∗	×l∗	VERB
ejpam-7160	114	4	mι	mι	PROPN
ejpam-7160	114	5	(	(	PUNCT
ejpam-7160	114	6	c	c	NOUN
ejpam-7160	114	7	)	)	PUNCT
ejpam-7160	114	8	.	.	PUNCT
ejpam-7160	115	1	definition	definition	NOUN
ejpam-7160	115	2	7	7	NUM
ejpam-7160	115	3	.	.	PUNCT
ejpam-7160	116	1	[	[	X
ejpam-7160	116	2	55	55	NUM
ejpam-7160	116	3	]	]	X
ejpam-7160	116	4	let	let	AUX
ejpam-7160	116	5	(	(	PUNCT
ejpam-7160	116	6	π,×	π,×	PROPN
ejpam-7160	116	7	,	,	PUNCT
ejpam-7160	116	8	ζι	ζι	X
ejpam-7160	116	9	)	)	PUNCT
ejpam-7160	116	10	be	be	AUX
ejpam-7160	116	11	a	a	DET
ejpam-7160	116	12	ι	ι	NOUN
ejpam-7160	116	13	-	-	PUNCT
ejpam-7160	116	14	ns	ns	NOUN
ejpam-7160	116	15	and	and	CCONJ
ejpam-7160	116	16	l	l	NOUN
ejpam-7160	116	17	be	be	AUX
ejpam-7160	116	18	a	a	DET
ejpam-7160	116	19	grill	grill	NOUN
ejpam-7160	116	20	on	on	ADP
ejpam-7160	116	21	π	π	PROPN
ejpam-7160	116	22	.	.	PUNCT
ejpam-7160	117	1	the	the	DET
ejpam-7160	117	2	nl∗∗∗	nl∗∗∗	PROPN
ejpam-7160	117	3	ι	ι	PROPN
ejpam-7160	117	4	lo	lo	PROPN
ejpam-7160	117	5	and	and	CCONJ
ejpam-7160	117	6	×l∗∗∗	×l∗∗∗	PROPN
ejpam-7160	117	7	ι	ι	PROPN
ejpam-7160	117	8	-up	-up	INTJ
ejpam-7160	117	9	apps	app	NOUN
ejpam-7160	117	10	of	of	ADP
ejpam-7160	117	11	the	the	DET
ejpam-7160	117	12	set	set	NOUN
ejpam-7160	117	13	c	c	PROPN
ejpam-7160	117	14	articulated	articulate	VERB
ejpam-7160	117	15	as	as	SCONJ
ejpam-7160	117	16	follows	follow	VERB
ejpam-7160	117	17	.	.	PUNCT
ejpam-7160	118	1	×l∗∗∗	×l∗∗∗	PROPN
ejpam-7160	118	2	mι	mι	PROPN
ejpam-7160	118	3	(	(	PUNCT
ejpam-7160	118	4	c	c	NOUN
ejpam-7160	118	5	)	)	PUNCT
ejpam-7160	118	6	=	=	SYM
ejpam-7160	118	7	⊔{mι(π1	⊔{mι(π1	PROPN
ejpam-7160	118	8	)	)	PUNCT
ejpam-7160	118	9	:	:	PUNCT
ejpam-7160	118	10	mι(π1	mι(π1	X
ejpam-7160	118	11	)	)	PUNCT
ejpam-7160	118	12	⊓	⊓	PROPN
ejpam-7160	118	13	cc	cc	ADP
ejpam-7160	118	14	∈	∈	PROPN
ejpam-7160	118	15	l	l	NOUN
ejpam-7160	118	16	}	}	PUNCT
ejpam-7160	118	17	.	.	PUNCT
ejpam-7160	119	1	×l∗∗∗	×l∗∗∗	PROPN
ejpam-7160	119	2	mι	mι	PROPN
ejpam-7160	119	3	(	(	PUNCT
ejpam-7160	119	4	c	c	NOUN
ejpam-7160	119	5	)	)	PUNCT
ejpam-7160	119	6	=	=	PUNCT
ejpam-7160	120	1	[	[	X
ejpam-7160	120	2	×l∗∗∗	×l∗∗∗	PROPN
ejpam-7160	120	3	mι	mι	INTJ
ejpam-7160	120	4	(	(	PUNCT
ejpam-7160	120	5	cc)]c	cc)]c	PROPN
ejpam-7160	120	6	.	.	PUNCT
ejpam-7160	120	7	a.	a.	PROPN
ejpam-7160	120	8	a.	a.	PROPN
ejpam-7160	120	9	azzam	azzam	PROPN
ejpam-7160	120	10	et	et	PROPN
ejpam-7160	120	11	al	al	PROPN
ejpam-7160	120	12	.	.	PUNCT
ejpam-7160	120	13	/	/	SYM
ejpam-7160	120	14	eur	eur	PROPN
ejpam-7160	120	15	.	.	PUNCT
ejpam-7160	121	1	j.	j.	PROPN
ejpam-7160	121	2	pure	pure	PROPN
ejpam-7160	121	3	appl	appl	PROPN
ejpam-7160	121	4	.	.	PROPN
ejpam-7160	121	5	math	math	PROPN
ejpam-7160	121	6	,	,	PUNCT
ejpam-7160	121	7	18	18	NUM
ejpam-7160	121	8	(	(	PUNCT
ejpam-7160	121	9	4	4	NUM
ejpam-7160	121	10	)	)	PUNCT
ejpam-7160	121	11	(	(	PUNCT
ejpam-7160	121	12	2025	2025	NUM
ejpam-7160	121	13	)	)	PUNCT
ejpam-7160	121	14	,	,	PUNCT
ejpam-7160	121	15	7160	7160	NUM
ejpam-7160	121	16	5	5	NUM
ejpam-7160	121	17	of	of	ADP
ejpam-7160	121	18	22	22	NUM
ejpam-7160	121	19	definition	definition	NOUN
ejpam-7160	121	20	8	8	NUM
ejpam-7160	121	21	.	.	PUNCT
ejpam-7160	122	1	[	[	X
ejpam-7160	122	2	52	52	NUM
ejpam-7160	122	3	]	]	PUNCT
ejpam-7160	122	4	assume	assume	VERB
ejpam-7160	122	5	that	that	SCONJ
ejpam-7160	122	6	π1	π1	NOUN
ejpam-7160	122	7	∈	∈	PROPN
ejpam-7160	122	8	π	π	NOUN
ejpam-7160	122	9	and	and	CCONJ
ejpam-7160	122	10	let	let	VERB
ejpam-7160	122	11	×	×	NOUN
ejpam-7160	122	12	be	be	AUX
ejpam-7160	122	13	a	a	DET
ejpam-7160	122	14	br	br	NOUN
ejpam-7160	122	15	on	on	ADP
ejpam-7160	122	16	a	a	DET
ejpam-7160	122	17	finite	finite	NOUN
ejpam-7160	122	18	set	set	VERB
ejpam-7160	122	19	π	π	PROPN
ejpam-7160	122	20	̸=	̸=	PROPN
ejpam-7160	122	21	ϕ.	ϕ.	VERB
ejpam-7160	122	22	the	the	DET
ejpam-7160	122	23	minimal	minimal	ADJ
ejpam-7160	122	24	nb(mn	nb(mn	PROPN
ejpam-7160	122	25	)	)	PUNCT
ejpam-7160	122	26	of	of	ADP
ejpam-7160	122	27	π1	π1	ADJ
ejpam-7160	122	28	∈	∈	PROPN
ejpam-7160	122	29	π	π	NOUN
ejpam-7160	122	30	are	be	AUX
ejpam-7160	122	31	as	as	SCONJ
ejpam-7160	122	32	follows	follow	VERB
ejpam-7160	122	33	:	:	PUNCT
ejpam-7160	122	34	(	(	PUNCT
ejpam-7160	122	35	i	i	NOUN
ejpam-7160	122	36	)	)	PUNCT
ejpam-7160	122	37	mn	mn	PROPN
ejpam-7160	122	38	r(π1	r(π1	PROPN
ejpam-7160	122	39	)	)	PUNCT
ejpam-7160	122	40	=	=	SYM
ejpam-7160	123	1	⊓π2{nr(π2	⊓π2{nr(π2	X
ejpam-7160	123	2	)	)	PUNCT
ejpam-7160	123	3	:	:	PUNCT
ejpam-7160	123	4	π2×π1	π2×π1	NOUN
ejpam-7160	123	5	}	}	PUNCT
ejpam-7160	123	6	.	.	PUNCT
ejpam-7160	124	1	(	(	PUNCT
ejpam-7160	124	2	2	2	X
ejpam-7160	124	3	)	)	PUNCT
ejpam-7160	124	4	mn	mn	PROPN
ejpam-7160	124	5	l(π1	l(π1	PROPN
ejpam-7160	124	6	)	)	PUNCT
ejpam-7160	125	1	=	=	PUNCT
ejpam-7160	125	2	⊓π2{nl(π2	⊓π2{nl(π2	NOUN
ejpam-7160	125	3	)	)	PUNCT
ejpam-7160	125	4	:	:	PUNCT
ejpam-7160	125	5	π1×π2	π1×π2	PROPN
ejpam-7160	125	6	}	}	PUNCT
ejpam-7160	125	7	.	.	PUNCT
ejpam-7160	126	1	(	(	PUNCT
ejpam-7160	126	2	3	3	X
ejpam-7160	126	3	)	)	PUNCT
ejpam-7160	126	4	mn	mn	PROPN
ejpam-7160	126	5	u(π1	u(π1	PROPN
ejpam-7160	126	6	)	)	PUNCT
ejpam-7160	127	1	=	=	SYM
ejpam-7160	127	2	mn	mn	PROPN
ejpam-7160	127	3	r(π1	r(π1	PROPN
ejpam-7160	127	4	)	)	PUNCT
ejpam-7160	127	5	⊔mn	⊔mn	PROPN
ejpam-7160	127	6	l(π1	l(π1	NUM
ejpam-7160	127	7	)	)	PUNCT
ejpam-7160	127	8	.	.	PUNCT
ejpam-7160	128	1	(	(	PUNCT
ejpam-7160	128	2	4	4	X
ejpam-7160	128	3	)	)	PUNCT
ejpam-7160	128	4	mn	mn	PROPN
ejpam-7160	128	5	i(π1	i(π1	PROPN
ejpam-7160	128	6	)	)	PUNCT
ejpam-7160	128	7	=	=	SYM
ejpam-7160	128	8	mn	mn	PROPN
ejpam-7160	128	9	r(π1	r(π1	PROPN
ejpam-7160	128	10	)	)	PUNCT
ejpam-7160	128	11	⊓mn	⊓mn	ADP
ejpam-7160	128	12	l(π1	l(π1	PRON
ejpam-7160	128	13	)	)	PUNCT
ejpam-7160	128	14	.	.	PUNCT
ejpam-7160	129	1	(	(	PUNCT
ejpam-7160	129	2	5	5	X
ejpam-7160	129	3	)	)	PUNCT
ejpam-7160	129	4	mn	mn	NOUN
ejpam-7160	129	5	⟨r⟩(π1	⟨r⟩(π1	NUM
ejpam-7160	129	6	)	)	PUNCT
ejpam-7160	130	1	=	=	PUNCT
ejpam-7160	130	2	⊓π1∈mn	⊓π1∈mn	PROPN
ejpam-7160	130	3	r(π2)mn	r(π2)mn	NOUN
ejpam-7160	130	4	r(π2	r(π2	NOUN
ejpam-7160	130	5	)	)	PUNCT
ejpam-7160	130	6	.	.	PUNCT
ejpam-7160	131	1	(	(	PUNCT
ejpam-7160	131	2	6	6	X
ejpam-7160	131	3	)	)	PUNCT
ejpam-7160	131	4	mn	mn	NOUN
ejpam-7160	131	5	⟨l⟩(π1	⟨l⟩(π1	NUM
ejpam-7160	131	6	)	)	PUNCT
ejpam-7160	132	1	=	=	PUNCT
ejpam-7160	132	2	⊓π1∈mn	⊓π1∈mn	PROPN
ejpam-7160	132	3	l(π2)mn	l(π2)mn	ADJ
ejpam-7160	132	4	l(π2	l(π2	NOUN
ejpam-7160	132	5	)	)	PUNCT
ejpam-7160	132	6	.	.	PUNCT
ejpam-7160	133	1	(	(	PUNCT
ejpam-7160	133	2	7	7	X
ejpam-7160	133	3	)	)	PUNCT
ejpam-7160	133	4	mn	mn	PROPN
ejpam-7160	133	5	⟨i⟩(π1	⟨i⟩(π1	NUM
ejpam-7160	133	6	)	)	PUNCT
ejpam-7160	134	1	=	=	SYM
ejpam-7160	134	2	mn	mn	PROPN
ejpam-7160	134	3	⟨r⟩(π1	⟨r⟩(π1	NUM
ejpam-7160	134	4	)	)	PUNCT
ejpam-7160	134	5	⊓mn	⊓mn	NUM
ejpam-7160	134	6	⟨l⟩(π1	⟨l⟩(π1	NUM
ejpam-7160	134	7	)	)	PUNCT
ejpam-7160	134	8	.	.	PUNCT
ejpam-7160	135	1	(	(	PUNCT
ejpam-7160	135	2	8)	8)	NUM
ejpam-7160	135	3	mn	mn	PROPN
ejpam-7160	135	4	⟨u⟩(π1	⟨u⟩(π1	NUM
ejpam-7160	135	5	)	)	PUNCT
ejpam-7160	135	6	=	=	SYM
ejpam-7160	135	7	mn	mn	PROPN
ejpam-7160	135	8	⟨r⟩(π1	⟨r⟩(π1	NUM
ejpam-7160	135	9	)	)	PUNCT
ejpam-7160	135	10	⊔mn	⊔mn	PROPN
ejpam-7160	135	11	⟨l⟩(π1	⟨l⟩(π1	NUM
ejpam-7160	135	12	)	)	PUNCT
ejpam-7160	135	13	.	.	PUNCT
ejpam-7160	136	1	definition	definition	NOUN
ejpam-7160	136	2	9	9	NUM
ejpam-7160	136	3	.	.	PUNCT
ejpam-7160	137	1	[	[	X
ejpam-7160	137	2	52	52	NUM
ejpam-7160	137	3	]	]	PUNCT
ejpam-7160	137	4	let	let	VERB
ejpam-7160	137	5	mn	mn	PROPN
ejpam-7160	137	6	ι(π1	ι(π1	PROPN
ejpam-7160	137	7	)	)	PUNCT
ejpam-7160	137	8	be	be	AUX
ejpam-7160	137	9	a	a	DET
ejpam-7160	137	10	mn	mn	NOUN
ejpam-7160	137	11	system	system	NOUN
ejpam-7160	137	12	with	with	ADP
ejpam-7160	137	13	br	br	PROPN
ejpam-7160	137	14	×	×	PROPN
ejpam-7160	137	15	,	,	PUNCT
ejpam-7160	137	16	where	where	SCONJ
ejpam-7160	137	17	π1	π1	PROPN
ejpam-7160	137	18	∈	∈	PROPN
ejpam-7160	137	19	π	π	PROPN
ejpam-7160	137	20	,	,	PUNCT
ejpam-7160	137	21	and	and	CCONJ
ejpam-7160	137	22	ι	ι	PRON
ejpam-7160	137	23	∈	∈	PROPN
ejpam-7160	137	24	{	{	PUNCT
ejpam-7160	137	25	r	r	NOUN
ejpam-7160	137	26	,	,	PUNCT
ejpam-7160	137	27	l	l	NOUN
ejpam-7160	137	28	,	,	PUNCT
ejpam-7160	137	29	u	u	NOUN
ejpam-7160	137	30	,	,	PUNCT
ejpam-7160	137	31	i	i	PROPN
ejpam-7160	137	32	}	}	PUNCT
ejpam-7160	137	33	.	.	PUNCT
ejpam-7160	138	1	then	then	ADV
ejpam-7160	138	2	,	,	PUNCT
ejpam-7160	138	3	(	(	PUNCT
ejpam-7160	138	4	π,×,mn	π,×,mn	ADV
ejpam-7160	138	5	ι	ι	PROPN
ejpam-7160	138	6	)	)	PUNCT
ejpam-7160	138	7	is	be	AUX
ejpam-7160	138	8	an	an	DET
ejpam-7160	138	9	app	app	NOUN
ejpam-7160	138	10	space	space	NOUN
ejpam-7160	138	11	(	(	PUNCT
ejpam-7160	138	12	shortly	shortly	ADV
ejpam-7160	138	13	,	,	PUNCT
ejpam-7160	138	14	mn	mn	PROPN
ejpam-7160	138	15	ι	ι	PROPN
ejpam-7160	138	16	-	-	PUNCT
ejpam-7160	138	17	app	app	NOUN
ejpam-7160	138	18	space	space	NOUN
ejpam-7160	138	19	)	)	PUNCT
ejpam-7160	138	20	.	.	PUNCT
ejpam-7160	139	1	lemma	lemma	PROPN
ejpam-7160	139	2	1	1	NUM
ejpam-7160	139	3	.	.	PUNCT
ejpam-7160	140	1	[	[	X
ejpam-7160	140	2	52	52	NUM
ejpam-7160	140	3	]	]	PUNCT
ejpam-7160	140	4	if	if	SCONJ
ejpam-7160	140	5	π2	π2	PROPN
ejpam-7160	140	6	∈	∈	PROPN
ejpam-7160	140	7	mn	mn	PROPN
ejpam-7160	140	8	ι(π1	ι(π1	PROPN
ejpam-7160	140	9	)	)	PUNCT
ejpam-7160	140	10	,	,	PUNCT
ejpam-7160	140	11	then	then	ADV
ejpam-7160	140	12	mn	mn	PROPN
ejpam-7160	140	13	ι(π2	ι(π2	NOUN
ejpam-7160	140	14	)	)	PUNCT
ejpam-7160	141	1	⊑	⊑	PROPN
ejpam-7160	141	2	mn	mn	PROPN
ejpam-7160	141	3	ι(π1	ι(π1	PROPN
ejpam-7160	141	4	)	)	PUNCT
ejpam-7160	141	5	,	,	PUNCT
ejpam-7160	141	6	where	where	SCONJ
ejpam-7160	141	7	π1	π1	NOUN
ejpam-7160	141	8	,	,	PUNCT
ejpam-7160	141	9	π2	π2	PROPN
ejpam-7160	141	10	∈	∈	PROPN
ejpam-7160	141	11	π	π	NOUN
ejpam-7160	141	12	,	,	PUNCT
ejpam-7160	141	13	and	and	CCONJ
ejpam-7160	141	14	ι	ι	PRON
ejpam-7160	141	15	∈	∈	PROPN
ejpam-7160	141	16	{	{	PUNCT
ejpam-7160	141	17	r	r	NOUN
ejpam-7160	141	18	,	,	PUNCT
ejpam-7160	141	19	l	l	NOUN
ejpam-7160	141	20	,	,	PUNCT
ejpam-7160	141	21	i	i	NOUN
ejpam-7160	141	22	}	}	PUNCT
ejpam-7160	141	23	.	.	PUNCT
ejpam-7160	142	1	lemma	lemma	PROPN
ejpam-7160	142	2	2	2	NUM
ejpam-7160	142	3	.	.	PUNCT
ejpam-7160	143	1	[	[	X
ejpam-7160	143	2	52	52	NUM
ejpam-7160	143	3	]	]	PUNCT
ejpam-7160	143	4	let	let	VERB
ejpam-7160	143	5	×	×	NOUN
ejpam-7160	143	6	be	be	AUX
ejpam-7160	143	7	a	a	DET
ejpam-7160	143	8	symmetric	symmetric	ADJ
ejpam-7160	143	9	relation	relation	NOUN
ejpam-7160	143	10	(	(	PUNCT
ejpam-7160	143	11	sr	sr	PROPN
ejpam-7160	143	12	)	)	PUNCT
ejpam-7160	143	13	and	and	CCONJ
ejpam-7160	143	14	π2	π2	PROPN
ejpam-7160	143	15	∈	∈	PROPN
ejpam-7160	143	16	mn	mn	PROPN
ejpam-7160	143	17	u(π1	u(π1	PROPN
ejpam-7160	143	18	)	)	PUNCT
ejpam-7160	143	19	.	.	PUNCT
ejpam-7160	144	1	then	then	ADV
ejpam-7160	144	2	,	,	PUNCT
ejpam-7160	144	3	mn	mn	PROPN
ejpam-7160	144	4	u(π2	u(π2	NOUN
ejpam-7160	144	5	)	)	PUNCT
ejpam-7160	144	6	⊑	⊑	PROPN
ejpam-7160	144	7	mn	mn	PROPN
ejpam-7160	144	8	u(π1	u(π1	PROPN
ejpam-7160	144	9	)	)	PUNCT
ejpam-7160	144	10	,	,	PUNCT
ejpam-7160	144	11	for	for	ADP
ejpam-7160	144	12	all	all	DET
ejpam-7160	144	13	π1	π1	NOUN
ejpam-7160	144	14	,	,	PUNCT
ejpam-7160	144	15	π2	π2	PROPN
ejpam-7160	144	16	∈	∈	PROPN
ejpam-7160	144	17	π	π	X
ejpam-7160	144	18	.	.	PUNCT
ejpam-7160	144	19	proposition	proposition	NOUN
ejpam-7160	144	20	1	1	NUM
ejpam-7160	144	21	.	.	PUNCT
ejpam-7160	145	1	[	[	X
ejpam-7160	145	2	52	52	NUM
ejpam-7160	145	3	]	]	PUNCT
ejpam-7160	145	4	if	if	SCONJ
ejpam-7160	145	5	×	×	NOUN
ejpam-7160	145	6	is	be	AUX
ejpam-7160	145	7	reflexive	reflexive	ADJ
ejpam-7160	145	8	relation(rr	relation(rr	NOUN
ejpam-7160	145	9	)	)	PUNCT
ejpam-7160	145	10	and	and	CCONJ
ejpam-7160	145	11	π2	π2	NUM
ejpam-7160	145	12	∈	∈	PROPN
ejpam-7160	145	13	π	π	NOUN
ejpam-7160	145	14	,	,	PUNCT
ejpam-7160	145	15	then	then	ADV
ejpam-7160	145	16	(	(	PUNCT
ejpam-7160	145	17	1	1	X
ejpam-7160	145	18	)	)	PUNCT
ejpam-7160	145	19	mn	mn	PROPN
ejpam-7160	145	20	r(π2	r(π2	NOUN
ejpam-7160	145	21	)	)	PUNCT
ejpam-7160	145	22	⊑	⊑	PART
ejpam-7160	145	23	nr(π2	nr(π2	NOUN
ejpam-7160	145	24	)	)	PUNCT
ejpam-7160	145	25	(	(	PUNCT
ejpam-7160	145	26	2	2	X
ejpam-7160	145	27	)	)	PUNCT
ejpam-7160	145	28	mn	mn	PROPN
ejpam-7160	145	29	l(π2	l(π2	NOUN
ejpam-7160	145	30	)	)	PUNCT
ejpam-7160	145	31	⊑	⊑	NOUN
ejpam-7160	145	32	nl(π2	nl(π2	NOUN
ejpam-7160	145	33	)	)	PUNCT
ejpam-7160	145	34	(	(	PUNCT
ejpam-7160	145	35	3	3	X
ejpam-7160	145	36	)	)	PUNCT
ejpam-7160	145	37	mn	mn	PROPN
ejpam-7160	145	38	i(π2	i(π2	NOUN
ejpam-7160	145	39	)	)	PUNCT
ejpam-7160	145	40	⊑	⊑	PART
ejpam-7160	145	41	nr(π2	nr(π2	NOUN
ejpam-7160	145	42	)	)	PUNCT
ejpam-7160	145	43	(	(	PUNCT
ejpam-7160	145	44	4	4	X
ejpam-7160	145	45	)	)	PUNCT
ejpam-7160	145	46	mn	mn	PROPN
ejpam-7160	145	47	i(π2	i(π2	NOUN
ejpam-7160	145	48	)	)	PUNCT
ejpam-7160	145	49	⊑	⊑	NOUN
ejpam-7160	145	50	nl(π2	nl(π2	NOUN
ejpam-7160	145	51	)	)	PUNCT
ejpam-7160	145	52	(	(	PUNCT
ejpam-7160	145	53	5	5	X
ejpam-7160	145	54	)	)	PUNCT
ejpam-7160	145	55	mn	mn	NOUN
ejpam-7160	145	56	u(π2	u(π2	NOUN
ejpam-7160	145	57	)	)	PUNCT
ejpam-7160	145	58	⊑	⊑	DET
ejpam-7160	145	59	nr(π2	nr(π2	NOUN
ejpam-7160	145	60	)	)	PUNCT
ejpam-7160	145	61	⊔nl(π2	⊔nl(π2	NOUN
ejpam-7160	145	62	)	)	PUNCT
ejpam-7160	145	63	definition	definition	NOUN
ejpam-7160	145	64	10	10	NUM
ejpam-7160	145	65	.	.	PUNCT
ejpam-7160	146	1	[	[	X
ejpam-7160	146	2	52	52	NUM
ejpam-7160	146	3	]	]	PUNCT
ejpam-7160	146	4	in	in	ADP
ejpam-7160	146	5	(	(	PUNCT
ejpam-7160	146	6	π,×,mn	π,×,mn	NOUN
ejpam-7160	146	7	ι	ι	PROPN
ejpam-7160	146	8	)	)	PUNCT
ejpam-7160	146	9	with	with	ADP
ejpam-7160	146	10	c	c	PROPN
ejpam-7160	146	11	⊑	⊑	X
ejpam-7160	146	12	π	π	PROPN
ejpam-7160	146	13	,	,	PUNCT
ejpam-7160	146	14	then	then	ADV
ejpam-7160	146	15	mn	mn	PROPN
ejpam-7160	146	16	ι	ι	PROPN
ejpam-7160	146	17	-	-	PUNCT
ejpam-7160	146	18	lower	low	ADJ
ejpam-7160	146	19	and	and	CCONJ
ejpam-7160	146	20	mn	mn	PROPN
ejpam-7160	146	21	ι	ι	PROPN
ejpam-7160	146	22	-	-	PUNCT
ejpam-7160	146	23	up	up	ADP
ejpam-7160	146	24	apps	app	NOUN
ejpam-7160	146	25	of	of	ADP
ejpam-7160	146	26	c	c	PROPN
ejpam-7160	146	27	are	be	AUX
ejpam-7160	146	28	defined	define	VERB
ejpam-7160	146	29	by	by	ADP
ejpam-7160	146	30	a.	a.	PROPN
ejpam-7160	146	31	a.	a.	PROPN
ejpam-7160	146	32	azzam	azzam	PROPN
ejpam-7160	146	33	et	et	PROPN
ejpam-7160	146	34	al	al	PROPN
ejpam-7160	146	35	.	.	PUNCT
ejpam-7160	146	36	/	/	SYM
ejpam-7160	146	37	eur	eur	PROPN
ejpam-7160	146	38	.	.	PUNCT
ejpam-7160	147	1	j.	j.	PROPN
ejpam-7160	147	2	pure	pure	PROPN
ejpam-7160	147	3	appl	appl	PROPN
ejpam-7160	147	4	.	.	PROPN
ejpam-7160	147	5	math	math	PROPN
ejpam-7160	147	6	,	,	PUNCT
ejpam-7160	147	7	18	18	NUM
ejpam-7160	147	8	(	(	PUNCT
ejpam-7160	147	9	4	4	NUM
ejpam-7160	147	10	)	)	PUNCT
ejpam-7160	147	11	(	(	PUNCT
ejpam-7160	147	12	2025	2025	NUM
ejpam-7160	147	13	)	)	PUNCT
ejpam-7160	147	14	,	,	PUNCT
ejpam-7160	147	15	7160	7160	NUM
ejpam-7160	147	16	6	6	NUM
ejpam-7160	147	17	of	of	ADP
ejpam-7160	147	18	22	22	NUM
ejpam-7160	147	19	×mn	×mn	ADJ
ejpam-7160	147	20	ι	ι	X
ejpam-7160	147	21	(	(	PUNCT
ejpam-7160	147	22	c	c	NOUN
ejpam-7160	147	23	)	)	PUNCT
ejpam-7160	147	24	=	=	PRON
ejpam-7160	147	25	{	{	PUNCT
ejpam-7160	147	26	π1	π1	NOUN
ejpam-7160	147	27	∈	∈	PROPN
ejpam-7160	147	28	π	π	NOUN
ejpam-7160	147	29	:	:	PUNCT
ejpam-7160	147	30	mn	mn	PROPN
ejpam-7160	147	31	ι(π1	ι(π1	PROPN
ejpam-7160	147	32	)	)	PUNCT
ejpam-7160	148	1	⊑	⊑	PROPN
ejpam-7160	148	2	c	c	X
ejpam-7160	148	3	}	}	PUNCT
ejpam-7160	148	4	.	.	PUNCT
ejpam-7160	149	1	×mn	×mn	ADV
ejpam-7160	149	2	ι(c	ι(c	PRON
ejpam-7160	149	3	)	)	PUNCT
ejpam-7160	149	4	=	=	PRON
ejpam-7160	150	1	{	{	PUNCT
ejpam-7160	150	2	π1	π1	NOUN
ejpam-7160	150	3	∈	∈	PROPN
ejpam-7160	150	4	π	π	NOUN
ejpam-7160	150	5	:	:	PUNCT
ejpam-7160	150	6	mn	mn	PROPN
ejpam-7160	150	7	ι(π1	ι(π1	PROPN
ejpam-7160	150	8	)	)	PUNCT
ejpam-7160	151	1	⊓	⊓	PROPN
ejpam-7160	151	2	c	c	PROPN
ejpam-7160	151	3	̸=	̸=	PROPN
ejpam-7160	151	4	ϕ	ϕ	PROPN
ejpam-7160	151	5	}	}	PUNCT
ejpam-7160	151	6	.	.	PUNCT
ejpam-7160	152	1	theorem	theorem	NOUN
ejpam-7160	152	2	2	2	NUM
ejpam-7160	152	3	.	.	PUNCT
ejpam-7160	153	1	[	[	X
ejpam-7160	153	2	52	52	NUM
ejpam-7160	153	3	]	]	PUNCT
ejpam-7160	153	4	if	if	SCONJ
ejpam-7160	153	5	(	(	PUNCT
ejpam-7160	153	6	π,×,mn	π,×,mn	NOUN
ejpam-7160	153	7	ι	ι	PROPN
ejpam-7160	153	8	)	)	PUNCT
ejpam-7160	153	9	is	be	AUX
ejpam-7160	153	10	a	a	DET
ejpam-7160	153	11	mn	mn	PROPN
ejpam-7160	153	12	ι	ι	PROPN
ejpam-7160	153	13	-	-	PUNCT
ejpam-7160	153	14	app	app	NOUN
ejpam-7160	153	15	space	space	NOUN
ejpam-7160	153	16	and	and	CCONJ
ejpam-7160	153	17	×	×	NOUN
ejpam-7160	153	18	is	be	AUX
ejpam-7160	153	19	a	a	DET
ejpam-7160	153	20	br	br	NOUN
ejpam-7160	153	21	,	,	PUNCT
ejpam-7160	153	22	the	the	DET
ejpam-7160	153	23	families	family	NOUN
ejpam-7160	153	24	τmn	τmn	VERB
ejpam-7160	153	25	ι	ι	X
ejpam-7160	154	1	=	=	X
ejpam-7160	154	2	{	{	PUNCT
ejpam-7160	154	3	c	c	NOUN
ejpam-7160	154	4	⊑	⊑	X
ejpam-7160	154	5	π	π	X
ejpam-7160	154	6	:	:	PUNCT
ejpam-7160	154	7	mn	mn	PROPN
ejpam-7160	154	8	ι(π1	ι(π1	PROPN
ejpam-7160	154	9	)	)	PUNCT
ejpam-7160	155	1	⊑	⊑	PROPN
ejpam-7160	155	2	c	c	X
ejpam-7160	155	3	,	,	PUNCT
ejpam-7160	155	4	π1	π1	ADJ
ejpam-7160	155	5	∈	∈	NOUN
ejpam-7160	155	6	c	c	AUX
ejpam-7160	155	7	}	}	PUNCT
ejpam-7160	155	8	are	be	AUX
ejpam-7160	155	9	topology	topology	NOUN
ejpam-7160	155	10	on	on	ADP
ejpam-7160	155	11	π	π	PROPN
ejpam-7160	155	12	,	,	PUNCT
ejpam-7160	155	13	∀ι	∀ι	ADP
ejpam-7160	155	14	∈	∈	PROPN
ejpam-7160	155	15	{	{	PUNCT
ejpam-7160	155	16	r	r	NOUN
ejpam-7160	155	17	,	,	PUNCT
ejpam-7160	155	18	l	l	NOUN
ejpam-7160	155	19	,	,	PUNCT
ejpam-7160	155	20	u	u	NOUN
ejpam-7160	155	21	,	,	PUNCT
ejpam-7160	155	22	i	i	PRON
ejpam-7160	155	23	,	,	PUNCT
ejpam-7160	155	24	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	155	25	,	,	PUNCT
ejpam-7160	155	26	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	155	27	,	,	PUNCT
ejpam-7160	155	28	⟨u⟩	⟨u⟩	PROPN
ejpam-7160	155	29	,	,	PUNCT
ejpam-7160	155	30	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	155	31	}	}	PUNCT
ejpam-7160	155	32	.	.	PUNCT
ejpam-7160	156	1	definition	definition	NOUN
ejpam-7160	156	2	11	11	NUM
ejpam-7160	156	3	.	.	PUNCT
ejpam-7160	157	1	[	[	X
ejpam-7160	157	2	52	52	NUM
ejpam-7160	157	3	]	]	PUNCT
ejpam-7160	157	4	let	let	VERB
ejpam-7160	157	5	(	(	PUNCT
ejpam-7160	157	6	π,×,mn	π,×,mn	ADV
ejpam-7160	157	7	ι	ι	AUX
ejpam-7160	157	8	)	)	PUNCT
ejpam-7160	157	9	be	be	VERB
ejpam-7160	157	10	a	a	DET
ejpam-7160	157	11	mn	mn	PROPN
ejpam-7160	157	12	ι	ι	PROPN
ejpam-7160	157	13	-	-	PUNCT
ejpam-7160	157	14	app	app	NOUN
ejpam-7160	157	15	space	space	NOUN
ejpam-7160	157	16	,	,	PUNCT
ejpam-7160	157	17	the	the	DET
ejpam-7160	157	18	mn	mn	PROPN
ejpam-7160	157	19	ι	ι	PROPN
ejpam-7160	157	20	-	-	PUNCT
ejpam-7160	157	21	lo	lo	PROPN
ejpam-7160	157	22	app	app	NOUN
ejpam-7160	157	23	,	,	PUNCT
ejpam-7160	157	24	mn	mn	PROPN
ejpam-7160	157	25	ι	ι	PROPN
ejpam-7160	157	26	-	-	PUNCT
ejpam-7160	157	27	up	up	NOUN
ejpam-7160	157	28	app	app	PROPN
ejpam-7160	157	29	,	,	PUNCT
ejpam-7160	157	30	mn	mn	PROPN
ejpam-7160	157	31	ι	ι	PROPN
ejpam-7160	157	32	-	-	PUNCT
ejpam-7160	157	33	accuracy	accuracy	NOUN
ejpam-7160	157	34	,	,	PUNCT
ejpam-7160	157	35	and	and	CCONJ
ejpam-7160	157	36	mn	mn	PROPN
ejpam-7160	157	37	ι	ι	PROPN
ejpam-7160	157	38	-	-	PUNCT
ejpam-7160	157	39	boundary	boundary	NOUN
ejpam-7160	157	40	of	of	ADP
ejpam-7160	157	41	c	c	NOUN
ejpam-7160	157	42	are	be	AUX
ejpam-7160	157	43	as	as	SCONJ
ejpam-7160	157	44	follows	follow	VERB
ejpam-7160	157	45	:	:	PUNCT
ejpam-7160	157	46	×mn	×mn	PROPN
ejpam-7160	157	47	ι	ι	X
ejpam-7160	157	48	(	(	PUNCT
ejpam-7160	157	49	c	c	NOUN
ejpam-7160	157	50	)	)	PUNCT
ejpam-7160	157	51	=	=	SYM
ejpam-7160	158	1	⊔{g	⊔{g	PROPN
ejpam-7160	158	2	∈	∈	PROPN
ejpam-7160	158	3	τmn	τmn	INTJ
ejpam-7160	159	1	ι	ι	X
ejpam-7160	159	2	:	:	PUNCT
ejpam-7160	159	3	g	g	X
ejpam-7160	159	4	⊑	⊑	X
ejpam-7160	159	5	c	c	X
ejpam-7160	159	6	}	}	PUNCT
ejpam-7160	159	7	=	=	SYM
ejpam-7160	159	8	intmn	intmn	NOUN
ejpam-7160	159	9	ι(c	ι(c	PROPN
ejpam-7160	159	10	)	)	PUNCT
ejpam-7160	159	11	,	,	PUNCT
ejpam-7160	159	12	×mn	×mn	ADV
ejpam-7160	159	13	ι(c	ι(c	PRON
ejpam-7160	159	14	)	)	PUNCT
ejpam-7160	159	15	=	=	PUNCT
ejpam-7160	160	1	⊓{y	⊓{y	ADJ
ejpam-7160	160	2	:	:	PUNCT
ejpam-7160	161	1	y	y	PROPN
ejpam-7160	161	2	c	c	PROPN
ejpam-7160	161	3	∈	∈	PROPN
ejpam-7160	161	4	τmn	τmn	INTJ
ejpam-7160	162	1	ι	ι	X
ejpam-7160	162	2	:	:	PUNCT
ejpam-7160	162	3	c	c	X
ejpam-7160	162	4	⊑	⊑	X
ejpam-7160	162	5	y	y	PROPN
ejpam-7160	162	6	}	}	PUNCT
ejpam-7160	162	7	=	=	PUNCT
ejpam-7160	162	8	clmn	clmn	NOUN
ejpam-7160	162	9	ι(c	ι(c	PROPN
ejpam-7160	162	10	)	)	PUNCT
ejpam-7160	162	11	,	,	PUNCT
ejpam-7160	162	12	amn	amn	PROPN
ejpam-7160	162	13	ι(c	ι(c	PROPN
ejpam-7160	162	14	)	)	PUNCT
ejpam-7160	163	1	=	=	SYM
ejpam-7160	163	2	|×mn	|×mn	PROPN
ejpam-7160	163	3	ι	ι	PROPN
ejpam-7160	163	4	(	(	PUNCT
ejpam-7160	163	5	c)|	c)|	PROPN
ejpam-7160	163	6	|×mn	|×mn	PROPN
ejpam-7160	164	1	ι	ι	PROPN
ejpam-7160	164	2	(	(	PUNCT
ejpam-7160	164	3	c)|	c)|	NOUN
ejpam-7160	164	4	,	,	PUNCT
ejpam-7160	164	5	where	where	SCONJ
ejpam-7160	164	6	c	c	X
ejpam-7160	164	7	̸=	̸=	PROPN
ejpam-7160	164	8	ϕ	ϕ	NOUN
ejpam-7160	164	9	,	,	PUNCT
ejpam-7160	164	10	bmn	bmn	NOUN
ejpam-7160	164	11	ι(c	ι(c	PROPN
ejpam-7160	164	12	)	)	PUNCT
ejpam-7160	164	13	=	=	VERB
ejpam-7160	164	14	×mn	×mn	VERB
ejpam-7160	164	15	ι(c)\×mn	ι(c)\×mn	NOUN
ejpam-7160	164	16	ι	ι	X
ejpam-7160	164	17	(	(	PUNCT
ejpam-7160	164	18	c	c	NOUN
ejpam-7160	164	19	)	)	PUNCT
ejpam-7160	164	20	.	.	PUNCT
ejpam-7160	165	1	3	3	X
ejpam-7160	165	2	.	.	X
ejpam-7160	165	3	grill	grill	NOUN
ejpam-7160	165	4	topology	topology	NOUN
ejpam-7160	165	5	induced	induce	VERB
ejpam-7160	165	6	by	by	ADP
ejpam-7160	165	7	various	various	ADJ
ejpam-7160	165	8	types	type	NOUN
ejpam-7160	165	9	of	of	ADP
ejpam-7160	165	10	minimum	minimum	ADJ
ejpam-7160	165	11	neighborhoods	neighborhood	NOUN
ejpam-7160	165	12	[	[	X
ejpam-7160	165	13	52	52	NUM
ejpam-7160	165	14	]	]	PUNCT
ejpam-7160	165	15	proposed	propose	VERB
ejpam-7160	165	16	topologies	topology	NOUN
ejpam-7160	165	17	based	base	VERB
ejpam-7160	165	18	on	on	ADP
ejpam-7160	165	19	right	right	ADJ
ejpam-7160	165	20	minimal	minimal	ADJ
ejpam-7160	165	21	nbds	nbds	NOUN
ejpam-7160	165	22	,	,	PUNCT
ejpam-7160	165	23	and	and	CCONJ
ejpam-7160	165	24	they	they	PRON
ejpam-7160	165	25	also	also	ADV
ejpam-7160	165	26	presented	present	VERB
ejpam-7160	165	27	three	three	NUM
ejpam-7160	165	28	other	other	ADJ
ejpam-7160	165	29	topologies	topology	NOUN
ejpam-7160	165	30	based	base	VERB
ejpam-7160	165	31	on	on	ADP
ejpam-7160	165	32	distinct	distinct	ADJ
ejpam-7160	165	33	minimal	minimal	ADJ
ejpam-7160	165	34	nbds	nbds	NOUN
ejpam-7160	165	35	.	.	PUNCT
ejpam-7160	166	1	this	this	DET
ejpam-7160	166	2	part	part	NOUN
ejpam-7160	166	3	looks	look	VERB
ejpam-7160	166	4	at	at	ADP
ejpam-7160	166	5	the	the	DET
ejpam-7160	166	6	links	link	NOUN
ejpam-7160	166	7	between	between	ADP
ejpam-7160	166	8	various	various	ADJ
ejpam-7160	166	9	topologies	topology	NOUN
ejpam-7160	166	10	and	and	CCONJ
ejpam-7160	166	11	generalizes	generalize	VERB
ejpam-7160	166	12	them	they	PRON
ejpam-7160	166	13	using	use	VERB
ejpam-7160	166	14	grills	grill	NOUN
ejpam-7160	166	15	.	.	PUNCT
ejpam-7160	167	1	as	as	ADP
ejpam-7160	167	2	a	a	DET
ejpam-7160	167	3	conceptual	conceptual	ADJ
ejpam-7160	167	4	extension	extension	NOUN
ejpam-7160	167	5	of	of	ADP
ejpam-7160	167	6	the	the	DET
ejpam-7160	167	7	topologies	topology	NOUN
ejpam-7160	167	8	in	in	ADP
ejpam-7160	167	9	[	[	X
ejpam-7160	167	10	52	52	NUM
ejpam-7160	167	11	]	]	PUNCT
ejpam-7160	167	12	,	,	PUNCT
ejpam-7160	167	13	theorem	theorem	VERB
ejpam-7160	167	14	3.5	3.5	NUM
ejpam-7160	167	15	creates	create	VERB
ejpam-7160	167	16	the	the	DET
ejpam-7160	167	17	topologies	topology	NOUN
ejpam-7160	167	18	by	by	ADP
ejpam-7160	167	19	combining	combine	VERB
ejpam-7160	167	20	the	the	DET
ejpam-7160	167	21	minimal	minimal	ADJ
ejpam-7160	167	22	nbds	nbds	NOUN
ejpam-7160	167	23	and	and	CCONJ
ejpam-7160	167	24	grills	grill	NOUN
ejpam-7160	167	25	.	.	PUNCT
ejpam-7160	168	1	also	also	ADV
ejpam-7160	168	2	,	,	PUNCT
ejpam-7160	168	3	this	this	DET
ejpam-7160	168	4	section	section	NOUN
ejpam-7160	168	5	’s	’s	PART
ejpam-7160	168	6	objective	objective	NOUN
ejpam-7160	168	7	is	be	AUX
ejpam-7160	168	8	to	to	PART
ejpam-7160	168	9	provide	provide	VERB
ejpam-7160	168	10	three	three	NUM
ejpam-7160	168	11	types	type	NOUN
ejpam-7160	168	12	of	of	ADP
ejpam-7160	168	13	rh	rh	PROPN
ejpam-7160	168	14	app	app	PROPN
ejpam-7160	168	15	extensions	extension	NOUN
ejpam-7160	168	16	.	.	PUNCT
ejpam-7160	169	1	definition	definition	NOUN
ejpam-7160	169	2	12	12	NUM
ejpam-7160	169	3	.	.	PUNCT
ejpam-7160	170	1	let	let	VERB
ejpam-7160	170	2	(	(	PUNCT
ejpam-7160	170	3	π,×,mn	π,×,mn	ADV
ejpam-7160	170	4	ι	ι	AUX
ejpam-7160	170	5	)	)	PUNCT
ejpam-7160	170	6	be	be	VERB
ejpam-7160	170	7	a	a	DET
ejpam-7160	170	8	mn	mn	PROPN
ejpam-7160	170	9	ι	ι	PROPN
ejpam-7160	170	10	-	-	PUNCT
ejpam-7160	170	11	app	app	NOUN
ejpam-7160	170	12	space	space	NOUN
ejpam-7160	170	13	and	and	CCONJ
ejpam-7160	170	14	l	l	NOUN
ejpam-7160	170	15	be	be	AUX
ejpam-7160	170	16	a	a	DET
ejpam-7160	170	17	grill	grill	NOUN
ejpam-7160	170	18	on	on	ADP
ejpam-7160	170	19	π	π	PROPN
ejpam-7160	170	20	.	.	PUNCT
ejpam-7160	171	1	the	the	DET
ejpam-7160	171	2	mnl∗	mnl∗	NOUN
ejpam-7160	171	3	ι	ι	PROPN
ejpam-7160	171	4	lo	lo	NOUN
ejpam-7160	171	5	and	and	CCONJ
ejpam-7160	171	6	mnl∗	mnl∗	PROPN
ejpam-7160	171	7	ι	ι	X
ejpam-7160	171	8	-up	-up	PUNCT
ejpam-7160	171	9	app	app	NOUN
ejpam-7160	171	10	of	of	ADP
ejpam-7160	171	11	c	c	PROPN
ejpam-7160	171	12	are	be	AUX
ejpam-7160	171	13	defined	define	VERB
ejpam-7160	171	14	by	by	ADP
ejpam-7160	171	15	×l∗	×l∗	PROPN
ejpam-7160	171	16	mn	mn	PROPN
ejpam-7160	171	17	ι	ι	PROPN
ejpam-7160	171	18	(	(	PUNCT
ejpam-7160	171	19	c	c	NOUN
ejpam-7160	171	20	)	)	PUNCT
ejpam-7160	171	21	=	=	PRON
ejpam-7160	171	22	{	{	PUNCT
ejpam-7160	171	23	π1	π1	NOUN
ejpam-7160	171	24	∈	∈	PROPN
ejpam-7160	171	25	π	π	NOUN
ejpam-7160	171	26	:	:	PUNCT
ejpam-7160	171	27	mn	mn	PROPN
ejpam-7160	171	28	ι(π1	ι(π1	PROPN
ejpam-7160	171	29	)	)	PUNCT
ejpam-7160	172	1	⊓	⊓	PROPN
ejpam-7160	172	2	cc	cc	NOUN
ejpam-7160	172	3	/∈	/∈	PUNCT
ejpam-7160	172	4	l	l	NOUN
ejpam-7160	172	5	}	}	PUNCT
ejpam-7160	172	6	.	.	PUNCT
ejpam-7160	173	1	×l∗	×l∗	PROPN
ejpam-7160	173	2	mn	mn	PROPN
ejpam-7160	173	3	ι	ι	PROPN
ejpam-7160	173	4	(	(	PUNCT
ejpam-7160	173	5	c	c	NOUN
ejpam-7160	173	6	)	)	PUNCT
ejpam-7160	173	7	=	=	PRON
ejpam-7160	173	8	{	{	PUNCT
ejpam-7160	173	9	π1	π1	NOUN
ejpam-7160	173	10	∈	∈	PROPN
ejpam-7160	173	11	π	π	NOUN
ejpam-7160	173	12	:	:	PUNCT
ejpam-7160	173	13	mn	mn	PROPN
ejpam-7160	173	14	ι(π1	ι(π1	PROPN
ejpam-7160	173	15	)	)	PUNCT
ejpam-7160	174	1	⊓	⊓	PROPN
ejpam-7160	174	2	c	c	NOUN
ejpam-7160	174	3	∈	∈	PROPN
ejpam-7160	174	4	l	l	NOUN
ejpam-7160	174	5	}	}	PUNCT
ejpam-7160	174	6	.	.	PUNCT
ejpam-7160	175	1	al∗	al∗	PROPN
ejpam-7160	175	2	mn	mn	PROPN
ejpam-7160	175	3	ι	ι	PROPN
ejpam-7160	175	4	(	(	PUNCT
ejpam-7160	175	5	c	c	NOUN
ejpam-7160	175	6	)	)	PUNCT
ejpam-7160	175	7	=	=	SYM
ejpam-7160	176	1	|×l∗	|×l∗	PROPN
ejpam-7160	176	2	mn	mn	PROPN
ejpam-7160	176	3	ι	ι	PROPN
ejpam-7160	176	4	(	(	PUNCT
ejpam-7160	176	5	c)|	c)|	PROPN
ejpam-7160	176	6	|×l∗	|×l∗	PROPN
ejpam-7160	176	7	mn	mn	PROPN
ejpam-7160	176	8	ι	ι	PROPN
ejpam-7160	176	9	(	(	PUNCT
ejpam-7160	176	10	c)|	c)|	PROPN
ejpam-7160	176	11	,	,	PUNCT
ejpam-7160	176	12	where	where	SCONJ
ejpam-7160	176	13	×l∗	×l∗	PROPN
ejpam-7160	176	14	mn	mn	PROPN
ejpam-7160	176	15	ι	ι	X
ejpam-7160	176	16	(	(	PUNCT
ejpam-7160	176	17	c	c	NOUN
ejpam-7160	176	18	)	)	PUNCT
ejpam-7160	176	19	̸=	̸=	PROPN
ejpam-7160	176	20	ϕ	ϕ	NOUN
ejpam-7160	176	21	,	,	PUNCT
ejpam-7160	176	22	.	.	PUNCT
ejpam-7160	177	1	bl∗	bl∗	PROPN
ejpam-7160	177	2	mn	mn	PROPN
ejpam-7160	177	3	ι	ι	PROPN
ejpam-7160	177	4	(	(	PUNCT
ejpam-7160	177	5	c	c	NOUN
ejpam-7160	177	6	)	)	PUNCT
ejpam-7160	177	7	=	=	VERB
ejpam-7160	177	8	×l∗	×l∗	VERB
ejpam-7160	177	9	mn	mn	PROPN
ejpam-7160	177	10	ι	ι	PROPN
ejpam-7160	177	11	(	(	PUNCT
ejpam-7160	177	12	c)\×l∗	c)\×l∗	PROPN
ejpam-7160	177	13	mn	mn	PROPN
ejpam-7160	177	14	ι	ι	PROPN
ejpam-7160	177	15	(	(	PUNCT
ejpam-7160	177	16	c	c	NOUN
ejpam-7160	177	17	)	)	PUNCT
ejpam-7160	177	18	.	.	PUNCT
ejpam-7160	178	1	definition	definition	NOUN
ejpam-7160	178	2	13	13	NUM
ejpam-7160	178	3	.	.	PUNCT
ejpam-7160	179	1	let	let	AUX
ejpam-7160	179	2	(	(	PUNCT
ejpam-7160	179	3	π,×,mn	π,×,mn	ADV
ejpam-7160	179	4	ι	ι	AUX
ejpam-7160	179	5	)	)	PUNCT
ejpam-7160	179	6	be	be	VERB
ejpam-7160	179	7	a	a	DET
ejpam-7160	179	8	mn	mn	PROPN
ejpam-7160	179	9	ι	ι	PROPN
ejpam-7160	179	10	-	-	PUNCT
ejpam-7160	179	11	app	app	NOUN
ejpam-7160	179	12	space	space	NOUN
ejpam-7160	179	13	and	and	CCONJ
ejpam-7160	179	14	l	l	NOUN
ejpam-7160	179	15	be	be	AUX
ejpam-7160	179	16	a	a	DET
ejpam-7160	179	17	grill	grill	NOUN
ejpam-7160	179	18	on	on	ADP
ejpam-7160	179	19	π	π	PROPN
ejpam-7160	179	20	.	.	PUNCT
ejpam-7160	180	1	the	the	DET
ejpam-7160	180	2	mnl∗∗	mnl∗∗	PROPN
ejpam-7160	180	3	ι	ι	PROPN
ejpam-7160	180	4	lw	lw	PROPN
ejpam-7160	180	5	and	and	CCONJ
ejpam-7160	180	6	mnl∗∗	mnl∗∗	PROPN
ejpam-7160	180	7	ι	ι	PROPN
ejpam-7160	180	8	-up	-up	NOUN
ejpam-7160	180	9	-	-	NOUN
ejpam-7160	180	10	apps	app	NOUN
ejpam-7160	180	11	of	of	ADP
ejpam-7160	180	12	c	c	NOUN
ejpam-7160	180	13	are	be	AUX
ejpam-7160	180	14	defined	define	VERB
ejpam-7160	180	15	by	by	ADP
ejpam-7160	180	16	×l∗∗	×l∗∗	X
ejpam-7160	180	17	mn	mn	PROPN
ejpam-7160	180	18	ι	ι	PROPN
ejpam-7160	180	19	(	(	PUNCT
ejpam-7160	180	20	c	c	NOUN
ejpam-7160	180	21	)	)	PUNCT
ejpam-7160	180	22	=	=	PRON
ejpam-7160	181	1	{	{	PUNCT
ejpam-7160	181	2	π1	π1	NOUN
ejpam-7160	181	3	∈	∈	PROPN
ejpam-7160	181	4	c	c	NOUN
ejpam-7160	181	5	:	:	PUNCT
ejpam-7160	181	6	mn	mn	PROPN
ejpam-7160	181	7	ι(π1	ι(π1	PROPN
ejpam-7160	181	8	)	)	PUNCT
ejpam-7160	182	1	⊓	⊓	PROPN
ejpam-7160	182	2	cc	cc	NOUN
ejpam-7160	182	3	/∈	/∈	PUNCT
ejpam-7160	182	4	l	l	NOUN
ejpam-7160	182	5	}	}	PUNCT
ejpam-7160	182	6	.	.	PUNCT
ejpam-7160	182	7	a.	a.	NOUN
ejpam-7160	182	8	a.	a.	PROPN
ejpam-7160	182	9	azzam	azzam	PROPN
ejpam-7160	182	10	et	et	PROPN
ejpam-7160	182	11	al	al	PROPN
ejpam-7160	182	12	.	.	PUNCT
ejpam-7160	182	13	/	/	SYM
ejpam-7160	182	14	eur	eur	PROPN
ejpam-7160	182	15	.	.	PUNCT
ejpam-7160	183	1	j.	j.	PROPN
ejpam-7160	183	2	pure	pure	PROPN
ejpam-7160	183	3	appl	appl	PROPN
ejpam-7160	183	4	.	.	PROPN
ejpam-7160	183	5	math	math	PROPN
ejpam-7160	183	6	,	,	PUNCT
ejpam-7160	183	7	18	18	NUM
ejpam-7160	183	8	(	(	PUNCT
ejpam-7160	183	9	4	4	NUM
ejpam-7160	183	10	)	)	PUNCT
ejpam-7160	183	11	(	(	PUNCT
ejpam-7160	183	12	2025	2025	NUM
ejpam-7160	183	13	)	)	PUNCT
ejpam-7160	183	14	,	,	PUNCT
ejpam-7160	183	15	7160	7160	NUM
ejpam-7160	183	16	7	7	NUM
ejpam-7160	183	17	of	of	ADP
ejpam-7160	183	18	22	22	NUM
ejpam-7160	183	19	×l∗∗	×l∗∗	NOUN
ejpam-7160	183	20	mn	mn	PROPN
ejpam-7160	183	21	ι	ι	PROPN
ejpam-7160	183	22	(	(	PUNCT
ejpam-7160	183	23	c	c	NOUN
ejpam-7160	183	24	)	)	PUNCT
ejpam-7160	183	25	=	=	PUNCT
ejpam-7160	184	1	c	c	PROPN
ejpam-7160	184	2	⊔	⊔	PROPN
ejpam-7160	184	3	×l∗	×l∗	VERB
ejpam-7160	184	4	mn	mn	PROPN
ejpam-7160	184	5	ι	ι	PROPN
ejpam-7160	184	6	(	(	PUNCT
ejpam-7160	184	7	c	c	NOUN
ejpam-7160	184	8	)	)	PUNCT
ejpam-7160	184	9	.	.	PUNCT
ejpam-7160	185	1	al∗∗	al∗∗	PROPN
ejpam-7160	186	1	mn	mn	PROPN
ejpam-7160	186	2	ι	ι	PROPN
ejpam-7160	186	3	(	(	PUNCT
ejpam-7160	186	4	c	c	NOUN
ejpam-7160	186	5	)	)	PUNCT
ejpam-7160	186	6	=	=	SYM
ejpam-7160	186	7	|×l∗∗	|×l∗∗	PROPN
ejpam-7160	186	8	mn	mn	PROPN
ejpam-7160	186	9	ι	ι	PROPN
ejpam-7160	187	1	(	(	PUNCT
ejpam-7160	187	2	c)|	c)|	PROPN
ejpam-7160	187	3	|×l∗∗	|×l∗∗	PROPN
ejpam-7160	187	4	mn	mn	PROPN
ejpam-7160	187	5	ι	ι	PROPN
ejpam-7160	187	6	(	(	PUNCT
ejpam-7160	187	7	c)|	c)|	NOUN
ejpam-7160	187	8	,	,	PUNCT
ejpam-7160	187	9	where	where	SCONJ
ejpam-7160	187	10	×l∗∗	×l∗∗	X
ejpam-7160	187	11	mn	mn	PROPN
ejpam-7160	187	12	ι	ι	PROPN
ejpam-7160	187	13	(	(	PUNCT
ejpam-7160	187	14	c	c	NOUN
ejpam-7160	187	15	)	)	PUNCT
ejpam-7160	187	16	̸=	̸=	PROPN
ejpam-7160	187	17	ϕ	ϕ	NOUN
ejpam-7160	187	18	,	,	PUNCT
ejpam-7160	187	19	.	.	PUNCT
ejpam-7160	188	1	bl∗∗	bl∗∗	PROPN
ejpam-7160	188	2	mn	mn	PROPN
ejpam-7160	188	3	ι	ι	PROPN
ejpam-7160	188	4	(	(	PUNCT
ejpam-7160	188	5	c	c	NOUN
ejpam-7160	188	6	)	)	PUNCT
ejpam-7160	188	7	=	=	SYM
ejpam-7160	188	8	×l∗∗	×l∗∗	X
ejpam-7160	188	9	mn	mn	PROPN
ejpam-7160	188	10	ι	ι	PROPN
ejpam-7160	188	11	(	(	PUNCT
ejpam-7160	188	12	c)\×l∗∗	c)\×l∗∗	PROPN
ejpam-7160	188	13	mn	mn	PROPN
ejpam-7160	188	14	ι	ι	PROPN
ejpam-7160	188	15	(	(	PUNCT
ejpam-7160	188	16	c	c	NOUN
ejpam-7160	188	17	)	)	PUNCT
ejpam-7160	188	18	.	.	PUNCT
ejpam-7160	189	1	definition	definition	NOUN
ejpam-7160	189	2	14	14	NUM
ejpam-7160	189	3	.	.	PUNCT
ejpam-7160	190	1	let	let	VERB
ejpam-7160	190	2	(	(	PUNCT
ejpam-7160	190	3	π,×,mn	π,×,mn	ADV
ejpam-7160	190	4	ι	ι	AUX
ejpam-7160	190	5	)	)	PUNCT
ejpam-7160	190	6	be	be	VERB
ejpam-7160	190	7	a	a	DET
ejpam-7160	190	8	mn	mn	PROPN
ejpam-7160	190	9	ι	ι	PROPN
ejpam-7160	190	10	-	-	PUNCT
ejpam-7160	190	11	app	app	NOUN
ejpam-7160	190	12	space	space	NOUN
ejpam-7160	190	13	and	and	CCONJ
ejpam-7160	190	14	l	l	NOUN
ejpam-7160	190	15	be	be	AUX
ejpam-7160	190	16	a	a	DET
ejpam-7160	190	17	grill	grill	NOUN
ejpam-7160	190	18	on	on	ADP
ejpam-7160	190	19	π	π	PROPN
ejpam-7160	190	20	.	.	PUNCT
ejpam-7160	191	1	the	the	DET
ejpam-7160	191	2	mnl∗∗∗	mnl∗∗∗	PROPN
ejpam-7160	191	3	ι	ι	PROPN
ejpam-7160	191	4	-up	-up	X
ejpam-7160	191	5	and	and	CCONJ
ejpam-7160	191	6	mnl∗∗∗	mnl∗∗∗	ADJ
ejpam-7160	191	7	ι	ι	PROPN
ejpam-7160	191	8	-lw	-lw	NOUN
ejpam-7160	191	9	-	-	PUNCT
ejpam-7160	191	10	apps	app	NOUN
ejpam-7160	191	11	of	of	ADP
ejpam-7160	191	12	c	c	NOUN
ejpam-7160	191	13	are	be	AUX
ejpam-7160	191	14	defined	define	VERB
ejpam-7160	191	15	by	by	ADP
ejpam-7160	191	16	×l∗∗∗	×l∗∗∗	PROPN
ejpam-7160	191	17	mn	mn	PROPN
ejpam-7160	191	18	ι	ι	PROPN
ejpam-7160	191	19	(	(	PUNCT
ejpam-7160	191	20	c	c	NOUN
ejpam-7160	191	21	)	)	PUNCT
ejpam-7160	191	22	=	=	SYM
ejpam-7160	192	1	⊔{mn	⊔{mn	NOUN
ejpam-7160	192	2	ι(π1	ι(π1	NUM
ejpam-7160	192	3	)	)	PUNCT
ejpam-7160	192	4	:	:	PUNCT
ejpam-7160	193	1	mn	mn	PROPN
ejpam-7160	193	2	ι(π1	ι(π1	PROPN
ejpam-7160	193	3	)	)	PUNCT
ejpam-7160	194	1	⊓	⊓	PROPN
ejpam-7160	194	2	cc	cc	ADP
ejpam-7160	194	3	∈	∈	PROPN
ejpam-7160	194	4	l	l	NOUN
ejpam-7160	194	5	}	}	PUNCT
ejpam-7160	194	6	.	.	PUNCT
ejpam-7160	195	1	×l∗∗∗	×l∗∗∗	PROPN
ejpam-7160	195	2	mn	mn	PROPN
ejpam-7160	195	3	ι	ι	PROPN
ejpam-7160	195	4	(	(	PUNCT
ejpam-7160	195	5	c	c	NOUN
ejpam-7160	195	6	)	)	PUNCT
ejpam-7160	195	7	=	=	NOUN
ejpam-7160	196	1	[	[	X
ejpam-7160	196	2	×l∗∗∗	×l∗∗∗	PROPN
ejpam-7160	196	3	mn	mn	PROPN
ejpam-7160	196	4	ι	ι	PROPN
ejpam-7160	196	5	(	(	PUNCT
ejpam-7160	196	6	cc)]c	cc)]c	PROPN
ejpam-7160	196	7	.	.	PUNCT
ejpam-7160	197	1	al∗∗∗	al∗∗∗	PROPN
ejpam-7160	197	2	mn	mn	PROPN
ejpam-7160	197	3	ι	ι	PROPN
ejpam-7160	197	4	(	(	PUNCT
ejpam-7160	197	5	c	c	NOUN
ejpam-7160	197	6	)	)	PUNCT
ejpam-7160	197	7	=	=	PUNCT
ejpam-7160	198	1	|×l∗∗∗	|×l∗∗∗	PROPN
ejpam-7160	198	2	mn	mn	PROPN
ejpam-7160	198	3	ι	ι	PROPN
ejpam-7160	198	4	(	(	PUNCT
ejpam-7160	198	5	c)|	c)|	PROPN
ejpam-7160	198	6	|×l∗∗∗	|×l∗∗∗	PROPN
ejpam-7160	198	7	mn	mn	PROPN
ejpam-7160	198	8	ι	ι	PROPN
ejpam-7160	198	9	(	(	PUNCT
ejpam-7160	198	10	c)|	c)|	NOUN
ejpam-7160	198	11	,	,	PUNCT
ejpam-7160	198	12	where	where	SCONJ
ejpam-7160	198	13	×l∗∗∗	×l∗∗∗	PROPN
ejpam-7160	198	14	mn	mn	PROPN
ejpam-7160	198	15	ι	ι	PROPN
ejpam-7160	198	16	(	(	PUNCT
ejpam-7160	198	17	c	c	NOUN
ejpam-7160	198	18	)	)	PUNCT
ejpam-7160	198	19	̸=	̸=	PROPN
ejpam-7160	198	20	ϕ	ϕ	NOUN
ejpam-7160	198	21	,	,	PUNCT
ejpam-7160	198	22	.	.	PUNCT
ejpam-7160	199	1	bl∗∗∗	bl∗∗∗	PROPN
ejpam-7160	199	2	mn	mn	PROPN
ejpam-7160	200	1	ι	ι	PROPN
ejpam-7160	200	2	(	(	PUNCT
ejpam-7160	200	3	c	c	NOUN
ejpam-7160	200	4	)	)	PUNCT
ejpam-7160	200	5	=	=	NOUN
ejpam-7160	201	1	×l∗∗∗	×l∗∗∗	PROPN
ejpam-7160	201	2	mn	mn	PROPN
ejpam-7160	201	3	ι	ι	PROPN
ejpam-7160	201	4	(	(	PUNCT
ejpam-7160	201	5	c)\×l∗∗∗	c)\×l∗∗∗	PROPN
ejpam-7160	201	6	mn	mn	PROPN
ejpam-7160	201	7	ι	ι	PROPN
ejpam-7160	201	8	(	(	PUNCT
ejpam-7160	201	9	c	c	NOUN
ejpam-7160	201	10	)	)	PUNCT
ejpam-7160	201	11	.	.	PUNCT
ejpam-7160	202	1	theorem	theorem	NOUN
ejpam-7160	202	2	3	3	NUM
ejpam-7160	202	3	.	.	PUNCT
ejpam-7160	203	1	[	[	X
ejpam-7160	203	2	52	52	NUM
ejpam-7160	203	3	]	]	PUNCT
ejpam-7160	203	4	let	let	NOUN
ejpam-7160	203	5	(	(	PUNCT
ejpam-7160	203	6	π,×	π,×	PROPN
ejpam-7160	203	7	,	,	PUNCT
ejpam-7160	203	8	ζι	ζι	X
ejpam-7160	203	9	)	)	PUNCT
ejpam-7160	203	10	be	be	AUX
ejpam-7160	203	11	a	a	DET
ejpam-7160	203	12	ι	ι	ADV
ejpam-7160	203	13	-	-	PUNCT
ejpam-7160	203	14	ns	ns	ADJ
ejpam-7160	203	15	and	and	CCONJ
ejpam-7160	203	16	π1	π1	ADJ
ejpam-7160	203	17	∈	∈	PROPN
ejpam-7160	203	18	π	π	PROPN
ejpam-7160	203	19	.	.	PUNCT
ejpam-7160	204	1	then	then	ADV
ejpam-7160	204	2	the	the	DET
ejpam-7160	204	3	following	follow	VERB
ejpam-7160	204	4	statement	statement	NOUN
ejpam-7160	204	5	are	be	AUX
ejpam-7160	204	6	true	true	ADJ
ejpam-7160	204	7	:	:	PUNCT
ejpam-7160	204	8	(	(	PUNCT
ejpam-7160	204	9	1	1	X
ejpam-7160	204	10	)	)	PUNCT
ejpam-7160	204	11	mn	mn	PROPN
ejpam-7160	204	12	⟨ι⟩(π1	⟨ι⟩(π1	NUM
ejpam-7160	204	13	)	)	PUNCT
ejpam-7160	204	14	⊑	⊑	PROPN
ejpam-7160	204	15	mn	mn	PROPN
ejpam-7160	204	16	ι(π1	ι(π1	PROPN
ejpam-7160	204	17	)	)	PUNCT
ejpam-7160	204	18	,	,	PUNCT
ejpam-7160	205	1	ι	ι	PROPN
ejpam-7160	205	2	∈	∈	PROPN
ejpam-7160	205	3	{	{	PUNCT
ejpam-7160	205	4	r	r	NOUN
ejpam-7160	205	5	,	,	PUNCT
ejpam-7160	205	6	l	l	NOUN
ejpam-7160	205	7	,	,	PUNCT
ejpam-7160	205	8	i	i	PRON
ejpam-7160	205	9	,	,	PUNCT
ejpam-7160	205	10	u	u	NOUN
ejpam-7160	205	11	}	}	PUNCT
ejpam-7160	205	12	;	;	PUNCT
ejpam-7160	205	13	(	(	PUNCT
ejpam-7160	205	14	2	2	X
ejpam-7160	205	15	)	)	PUNCT
ejpam-7160	205	16	mn	mn	PROPN
ejpam-7160	205	17	r(π1	r(π1	PROPN
ejpam-7160	205	18	)	)	PUNCT
ejpam-7160	205	19	=	=	SYM
ejpam-7160	205	20	mn	mn	PROPN
ejpam-7160	205	21	l(π1	l(π1	PROPN
ejpam-7160	205	22	)	)	PUNCT
ejpam-7160	206	1	=	=	SYM
ejpam-7160	206	2	mn	mn	PROPN
ejpam-7160	206	3	i(π1	i(π1	PROPN
ejpam-7160	206	4	)	)	PUNCT
ejpam-7160	207	1	=	=	SYM
ejpam-7160	207	2	mn	mn	PROPN
ejpam-7160	207	3	u(π1	u(π1	PROPN
ejpam-7160	207	4	)	)	PUNCT
ejpam-7160	207	5	,	,	PUNCT
ejpam-7160	207	6	and	and	CCONJ
ejpam-7160	207	7	mn	mn	PROPN
ejpam-7160	207	8	⟨r⟩(π1),mn	⟨r⟩(π1),mn	PROPN
ejpam-7160	207	9	⟨l⟩(π1	⟨l⟩(π1	NUM
ejpam-7160	207	10	)	)	PUNCT
ejpam-7160	208	1	=	=	SYM
ejpam-7160	208	2	mn	mn	PROPN
ejpam-7160	208	3	⟨i⟩(π1	⟨i⟩(π1	PRON
ejpam-7160	208	4	)	)	PUNCT
ejpam-7160	209	1	=	=	SYM
ejpam-7160	209	2	mn	mn	PROPN
ejpam-7160	209	3	⟨u⟩(π1	⟨u⟩(π1	NUM
ejpam-7160	209	4	)	)	PUNCT
ejpam-7160	209	5	when	when	SCONJ
ejpam-7160	209	6	×	×	NOUN
ejpam-7160	209	7	is	be	AUX
ejpam-7160	209	8	symmetric	symmetric	ADJ
ejpam-7160	209	9	;	;	PUNCT
ejpam-7160	209	10	(	(	PUNCT
ejpam-7160	209	11	3	3	X
ejpam-7160	209	12	)	)	PUNCT
ejpam-7160	209	13	mn	mn	NOUN
ejpam-7160	209	14	⟨ι⟩(π1	⟨ι⟩(π1	NUM
ejpam-7160	209	15	)	)	PUNCT
ejpam-7160	210	1	=	=	SYM
ejpam-7160	210	2	mn	mn	PROPN
ejpam-7160	210	3	ι(π1	ι(π1	PROPN
ejpam-7160	210	4	)	)	PUNCT
ejpam-7160	210	5	∀ι	∀ι	ADP
ejpam-7160	210	6	∈	∈	PROPN
ejpam-7160	210	7	{	{	PUNCT
ejpam-7160	210	8	r	r	NOUN
ejpam-7160	210	9	,	,	PUNCT
ejpam-7160	210	10	l	l	NOUN
ejpam-7160	210	11	,	,	PUNCT
ejpam-7160	210	12	i	i	PRON
ejpam-7160	210	13	,	,	PUNCT
ejpam-7160	210	14	u	u	NOUN
ejpam-7160	210	15	}	}	PUNCT
ejpam-7160	210	16	at	at	ADP
ejpam-7160	210	17	what	what	DET
ejpam-7160	210	18	time	time	NOUN
ejpam-7160	210	19	×	×	NOUN
ejpam-7160	210	20	exhibits	exhibit	VERB
ejpam-7160	210	21	symmetry	symmetry	NOUN
ejpam-7160	210	22	and	and	CCONJ
ejpam-7160	210	23	transitivity	transitivity	NOUN
ejpam-7160	210	24	.	.	PUNCT
ejpam-7160	210	25	;	;	PUNCT
ejpam-7160	210	26	(	(	PUNCT
ejpam-7160	210	27	4	4	X
ejpam-7160	210	28	)	)	PUNCT
ejpam-7160	210	29	al	al	PROPN
ejpam-7160	210	30	types	type	NOUN
ejpam-7160	210	31	of	of	ADP
ejpam-7160	210	32	mn	mn	PROPN
ejpam-7160	210	33	⟨ι⟩(π1	⟨ι⟩(π1	NUM
ejpam-7160	210	34	)	)	PUNCT
ejpam-7160	210	35	are	be	AUX
ejpam-7160	210	36	equal	equal	ADJ
ejpam-7160	210	37	when	when	SCONJ
ejpam-7160	210	38	×	×	NOUN
ejpam-7160	210	39	is	be	AUX
ejpam-7160	210	40	equivalence	equivalence	NOUN
ejpam-7160	210	41	.	.	PUNCT
ejpam-7160	211	1	theorem	theorem	ADJ
ejpam-7160	211	2	4	4	NUM
ejpam-7160	211	3	.	.	PUNCT
ejpam-7160	212	1	if	if	SCONJ
ejpam-7160	212	2	(	(	PUNCT
ejpam-7160	212	3	π,×,mn	π,×,mn	NOUN
ejpam-7160	212	4	ι	ι	PROPN
ejpam-7160	212	5	)	)	PUNCT
ejpam-7160	212	6	is	be	AUX
ejpam-7160	212	7	a	a	DET
ejpam-7160	212	8	mn	mn	PROPN
ejpam-7160	212	9	ι	ι	PROPN
ejpam-7160	212	10	-	-	PUNCT
ejpam-7160	212	11	ns	ns	ADJ
ejpam-7160	212	12	,	,	PUNCT
ejpam-7160	212	13	l	l	NOUN
ejpam-7160	212	14	is	be	AUX
ejpam-7160	212	15	a	a	DET
ejpam-7160	212	16	grill	grill	NOUN
ejpam-7160	212	17	on	on	ADP
ejpam-7160	212	18	π	π	PROPN
ejpam-7160	212	19	,	,	PUNCT
ejpam-7160	212	20	and	and	CCONJ
ejpam-7160	212	21	×	×	NOUN
ejpam-7160	212	22	is	be	AUX
ejpam-7160	212	23	a	a	DET
ejpam-7160	212	24	br	br	NOUN
ejpam-7160	212	25	,	,	PUNCT
ejpam-7160	212	26	the	the	DET
ejpam-7160	212	27	families	family	NOUN
ejpam-7160	212	28	τlmn	τlmn	NOUN
ejpam-7160	212	29	ι	ι	X
ejpam-7160	213	1	=	=	X
ejpam-7160	213	2	{	{	PUNCT
ejpam-7160	213	3	c	c	NOUN
ejpam-7160	213	4	⊑	⊑	X
ejpam-7160	213	5	π	π	X
ejpam-7160	213	6	:	:	PUNCT
ejpam-7160	213	7	mn	mn	PROPN
ejpam-7160	213	8	ι(π1	ι(π1	PROPN
ejpam-7160	213	9	)	)	PUNCT
ejpam-7160	213	10	⊓cc	⊓cc	NUM
ejpam-7160	213	11	/∈	/∈	PUNCT
ejpam-7160	213	12	l,∀π1	l,∀π1	ADJ
ejpam-7160	213	13	∈	∈	PROPN
ejpam-7160	213	14	c	c	AUX
ejpam-7160	213	15	}	}	PUNCT
ejpam-7160	213	16	represents	represent	VERB
ejpam-7160	213	17	as	as	ADP
ejpam-7160	213	18	mnl	mnl	NOUN
ejpam-7160	213	19	ι	ι	DET
ejpam-7160	213	20	-topology	-topology	NOUN
ejpam-7160	213	21	on	on	ADP
ejpam-7160	213	22	π	π	PROPN
ejpam-7160	213	23	about	about	ADP
ejpam-7160	213	24	the	the	DET
ejpam-7160	213	25	grill	grill	NOUN
ejpam-7160	213	26	l	l	NOUN
ejpam-7160	213	27	,	,	PUNCT
ejpam-7160	213	28	∀ι	∀ι	ADP
ejpam-7160	213	29	∈	∈	PROPN
ejpam-7160	213	30	{	{	PUNCT
ejpam-7160	213	31	r	r	NOUN
ejpam-7160	213	32	,	,	PUNCT
ejpam-7160	213	33	l	l	NOUN
ejpam-7160	213	34	,	,	PUNCT
ejpam-7160	213	35	u	u	NOUN
ejpam-7160	213	36	,	,	PUNCT
ejpam-7160	213	37	i	i	NOUN
ejpam-7160	213	38	}	}	PUNCT
ejpam-7160	213	39	.	.	PUNCT
ejpam-7160	214	1	proof	proof	NOUN
ejpam-7160	214	2	.	.	PUNCT
ejpam-7160	215	1	(	(	PUNCT
ejpam-7160	215	2	1	1	X
ejpam-7160	215	3	)	)	PUNCT
ejpam-7160	215	4	π	π	PROPN
ejpam-7160	215	5	,	,	PUNCT
ejpam-7160	215	6	ϕ	ϕ	PROPN
ejpam-7160	215	7	clearly	clearly	ADV
ejpam-7160	215	8	belongs	belong	VERB
ejpam-7160	215	9	to	to	ADP
ejpam-7160	215	10	τlmn	τlmn	NOUN
ejpam-7160	215	11	ι	ι	X
ejpam-7160	215	12	.	.	PUNCT
ejpam-7160	216	1	(	(	PUNCT
ejpam-7160	216	2	2	2	X
ejpam-7160	216	3	)	)	PUNCT
ejpam-7160	216	4	let	let	VERB
ejpam-7160	216	5	c1	c1	PROPN
ejpam-7160	216	6	,	,	PUNCT
ejpam-7160	216	7	c2	c2	PROPN
ejpam-7160	216	8	∈	∈	PROPN
ejpam-7160	216	9	τlmn	τlmn	NOUN
ejpam-7160	216	10	ι	ι	PROPN
ejpam-7160	216	11	,	,	PUNCT
ejpam-7160	216	12	π1	π1	PROPN
ejpam-7160	216	13	∈	∈	PROPN
ejpam-7160	216	14	c1	c1	NOUN
ejpam-7160	216	15	⊓	⊓	PROPN
ejpam-7160	216	16	c2	c2	PROPN
ejpam-7160	216	17	.	.	PUNCT
ejpam-7160	217	1	then	then	ADV
ejpam-7160	217	2	mn	mn	PROPN
ejpam-7160	217	3	ι(π1	ι(π1	PROPN
ejpam-7160	217	4	)	)	PUNCT
ejpam-7160	218	1	⊓	⊓	PROPN
ejpam-7160	218	2	cc	cc	VERB
ejpam-7160	218	3	1	1	NUM
ejpam-7160	218	4	/∈	/∈	PUNCT
ejpam-7160	218	5	l	l	NOUN
ejpam-7160	218	6	,	,	PUNCT
ejpam-7160	218	7	and	and	CCONJ
ejpam-7160	218	8	mn	mn	PROPN
ejpam-7160	218	9	ι(π1	ι(π1	PROPN
ejpam-7160	218	10	)	)	PUNCT
ejpam-7160	219	1	⊓	⊓	PROPN
ejpam-7160	219	2	cc	cc	VERB
ejpam-7160	219	3	2	2	NUM
ejpam-7160	219	4	/∈	/∈	PUNCT
ejpam-7160	219	5	l	l	NOUN
ejpam-7160	219	6	⇒	⇒	NOUN
ejpam-7160	219	7	(	(	PUNCT
ejpam-7160	219	8	mn	mn	PROPN
ejpam-7160	219	9	ι(π1	ι(π1	PROPN
ejpam-7160	219	10	)	)	PUNCT
ejpam-7160	220	1	⊓	⊓	PROPN
ejpam-7160	220	2	cc	cc	ADP
ejpam-7160	220	3	1	1	NUM
ejpam-7160	220	4	)	)	PUNCT
ejpam-7160	220	5	⊔	⊔	PROPN
ejpam-7160	220	6	(	(	PUNCT
ejpam-7160	220	7	mn	mn	PROPN
ejpam-7160	220	8	ι(π1	ι(π1	PROPN
ejpam-7160	220	9	)	)	PUNCT
ejpam-7160	221	1	⊓	⊓	PROPN
ejpam-7160	221	2	cc	cc	ADP
ejpam-7160	221	3	2	2	NUM
ejpam-7160	221	4	)	)	PUNCT
ejpam-7160	221	5	/∈	/∈	PUNCT
ejpam-7160	222	1	l	l	NOUN
ejpam-7160	222	2	a.	a.	NOUN
ejpam-7160	222	3	a.	a.	NOUN
ejpam-7160	222	4	azzam	azzam	PROPN
ejpam-7160	222	5	et	et	PROPN
ejpam-7160	222	6	al	al	PROPN
ejpam-7160	222	7	.	.	PUNCT
ejpam-7160	222	8	/	/	SYM
ejpam-7160	222	9	eur	eur	PROPN
ejpam-7160	222	10	.	.	PUNCT
ejpam-7160	223	1	j.	j.	PROPN
ejpam-7160	223	2	pure	pure	PROPN
ejpam-7160	223	3	appl	appl	PROPN
ejpam-7160	223	4	.	.	PROPN
ejpam-7160	223	5	math	math	PROPN
ejpam-7160	223	6	,	,	PUNCT
ejpam-7160	223	7	18	18	NUM
ejpam-7160	223	8	(	(	PUNCT
ejpam-7160	223	9	4	4	NUM
ejpam-7160	223	10	)	)	PUNCT
ejpam-7160	223	11	(	(	PUNCT
ejpam-7160	223	12	2025	2025	NUM
ejpam-7160	223	13	)	)	PUNCT
ejpam-7160	223	14	,	,	PUNCT
ejpam-7160	223	15	7160	7160	NUM
ejpam-7160	223	16	8	8	NUM
ejpam-7160	223	17	of	of	ADP
ejpam-7160	223	18	22	22	NUM
ejpam-7160	223	19	⇒	⇒	PROPN
ejpam-7160	223	20	mn	mn	PROPN
ejpam-7160	223	21	ι(π1	ι(π1	PROPN
ejpam-7160	223	22	)	)	PUNCT
ejpam-7160	224	1	⊓	⊓	NOUN
ejpam-7160	224	2	(	(	PUNCT
ejpam-7160	224	3	cc	cc	NOUN
ejpam-7160	224	4	1	1	NUM
ejpam-7160	224	5	⊔	⊔	PROPN
ejpam-7160	224	6	cc	cc	PROPN
ejpam-7160	224	7	2	2	NUM
ejpam-7160	224	8	)	)	PUNCT
ejpam-7160	224	9	/∈	/∈	PUNCT
ejpam-7160	225	1	l	l	NOUN
ejpam-7160	225	2	⇒	⇒	PROPN
ejpam-7160	225	3	mn	mn	PROPN
ejpam-7160	225	4	ι(π1	ι(π1	PROPN
ejpam-7160	225	5	)	)	PUNCT
ejpam-7160	226	1	⊓	⊓	NOUN
ejpam-7160	226	2	(	(	PUNCT
ejpam-7160	226	3	c1	c1	NOUN
ejpam-7160	226	4	⊓	⊓	PROPN
ejpam-7160	226	5	c2	c2	PROPN
ejpam-7160	226	6	)	)	PUNCT
ejpam-7160	226	7	c	c	PROPN
ejpam-7160	226	8	/∈	/∈	PUNCT
ejpam-7160	226	9	l	l	NOUN
ejpam-7160	226	10	⇒	⇒	NOUN
ejpam-7160	226	11	c1	c1	PROPN
ejpam-7160	226	12	⊓	⊓	PROPN
ejpam-7160	226	13	c2	c2	PROPN
ejpam-7160	226	14	∈	∈	PROPN
ejpam-7160	226	15	l.	l.	PROPN
ejpam-7160	226	16	(	(	PUNCT
ejpam-7160	226	17	3	3	X
ejpam-7160	226	18	)	)	PUNCT
ejpam-7160	226	19	let	let	VERB
ejpam-7160	226	20	ci	ci	PROPN
ejpam-7160	226	21	∈	∈	PROPN
ejpam-7160	226	22	τlmn	τlmn	NOUN
ejpam-7160	226	23	ι	ι	ADP
ejpam-7160	226	24	∀i	∀i	NOUN
ejpam-7160	226	25	∈	∈	PROPN
ejpam-7160	226	26	i	i	PRON
ejpam-7160	226	27	,	,	PUNCT
ejpam-7160	226	28	and	and	CCONJ
ejpam-7160	226	29	π1	π1	PROPN
ejpam-7160	226	30	∈	∈	PROPN
ejpam-7160	226	31	⊔i∈ici	⊔i∈ici	NOUN
ejpam-7160	226	32	.	.	PUNCT
ejpam-7160	227	1	then	then	ADV
ejpam-7160	227	2	,	,	PUNCT
ejpam-7160	227	3	exist	exist	VERB
ejpam-7160	227	4	i0	i0	PROPN
ejpam-7160	227	5	∈	∈	PROPN
ejpam-7160	228	1	i	i	PRON
ejpam-7160	228	2	such	such	VERB
ejpam-7160	228	3	that	that	DET
ejpam-7160	228	4	π1	π1	ADJ
ejpam-7160	228	5	∈	∈	PROPN
ejpam-7160	228	6	ci0	ci0	ADV
ejpam-7160	228	7	,	,	PUNCT
ejpam-7160	228	8	i.e.	i.e.	X
ejpam-7160	228	9	,	,	PUNCT
ejpam-7160	228	10	mn	mn	PROPN
ejpam-7160	228	11	ι	ι	X
ejpam-7160	228	12	⊓	⊓	PROPN
ejpam-7160	228	13	(	(	PUNCT
ejpam-7160	228	14	ci0	ci0	PROPN
ejpam-7160	228	15	)	)	PUNCT
ejpam-7160	228	16	c	c	NOUN
ejpam-7160	228	17	/∈	/∈	PUNCT
ejpam-7160	228	18	l.	l.	PROPN
ejpam-7160	228	19	⇒	⇒	PROPN
ejpam-7160	229	1	mn	mn	PROPN
ejpam-7160	229	2	ι	ι	PRON
ejpam-7160	229	3	⊓	⊓	PROPN
ejpam-7160	229	4	(	(	PUNCT
ejpam-7160	229	5	⊔i∈ici	⊔i∈ici	PROPN
ejpam-7160	229	6	)	)	PUNCT
ejpam-7160	229	7	/∈	/∈	PUNCT
ejpam-7160	230	1	l	l	NOUN
ejpam-7160	230	2	⇒	⇒	NOUN
ejpam-7160	230	3	c1	c1	PROPN
ejpam-7160	230	4	⊓	⊓	PROPN
ejpam-7160	230	5	c2	c2	PROPN
ejpam-7160	230	6	∈	∈	PROPN
ejpam-7160	230	7	τlmn	τlmn	NOUN
ejpam-7160	230	8	ι	ι	X
ejpam-7160	230	9	.	.	PUNCT
ejpam-7160	231	1	τlmn	τlmn	PROPN
ejpam-7160	231	2	ι	ι	PROPN
ejpam-7160	231	3	indicates	indicate	VERB
ejpam-7160	231	4	a	a	DET
ejpam-7160	231	5	mnl	mnl	NOUN
ejpam-7160	231	6	ι	ι	DET
ejpam-7160	231	7	-topology	-topology	NOUN
ejpam-7160	231	8	on	on	ADP
ejpam-7160	231	9	π	π	PROPN
ejpam-7160	231	10	with	with	ADP
ejpam-7160	231	11	respect	respect	NOUN
ejpam-7160	231	12	to	to	ADP
ejpam-7160	231	13	the	the	DET
ejpam-7160	231	14	grill	grill	NOUN
ejpam-7160	231	15	l.	l.	PROPN
ejpam-7160	231	16	definition	definition	NOUN
ejpam-7160	231	17	15	15	NUM
ejpam-7160	231	18	.	.	PUNCT
ejpam-7160	232	1	let	let	AUX
ejpam-7160	232	2	(	(	PUNCT
ejpam-7160	232	3	π,×,mn	π,×,mn	ADV
ejpam-7160	232	4	ι	ι	AUX
ejpam-7160	232	5	)	)	PUNCT
ejpam-7160	232	6	be	be	VERB
ejpam-7160	232	7	a	a	DET
ejpam-7160	232	8	mn	mn	PROPN
ejpam-7160	232	9	ι	ι	PROPN
ejpam-7160	232	10	-	-	PUNCT
ejpam-7160	232	11	app	app	NOUN
ejpam-7160	232	12	space	space	NOUN
ejpam-7160	232	13	,	,	PUNCT
ejpam-7160	232	14	l	l	NOUN
ejpam-7160	232	15	be	be	VERB
ejpam-7160	232	16	a	a	DET
ejpam-7160	232	17	grill	grill	NOUN
ejpam-7160	232	18	on	on	ADP
ejpam-7160	232	19	π	π	PROPN
ejpam-7160	232	20	,	,	PUNCT
ejpam-7160	232	21	and	and	CCONJ
ejpam-7160	232	22	c	c	ADP
ejpam-7160	232	23	⊑	⊑	X
ejpam-7160	232	24	π	π	X
ejpam-7160	232	25	.	.	PUNCT
ejpam-7160	233	1	if	if	SCONJ
ejpam-7160	233	2	c	c	PROPN
ejpam-7160	233	3	∈	∈	PROPN
ejpam-7160	233	4	τlmn	τlmn	NOUN
ejpam-7160	233	5	ι	ι	PROPN
ejpam-7160	233	6	,	,	PUNCT
ejpam-7160	233	7	then	then	ADV
ejpam-7160	233	8	it	it	PRON
ejpam-7160	233	9	is	be	AUX
ejpam-7160	233	10	known	know	VERB
ejpam-7160	233	11	as	as	ADP
ejpam-7160	233	12	lmn	lmn	PROPN
ejpam-7160	233	13	ι	ι	X
ejpam-7160	233	14	-	-	PUNCT
ejpam-7160	233	15	open	open	ADJ
ejpam-7160	233	16	,	,	PUNCT
ejpam-7160	233	17	and	and	CCONJ
ejpam-7160	233	18	if	if	SCONJ
ejpam-7160	233	19	cc	cc	PROPN
ejpam-7160	233	20	∈	∈	PROPN
ejpam-7160	233	21	τlmn	τlmn	NOUN
ejpam-7160	233	22	ι	ι	PROPN
ejpam-7160	233	23	,	,	PUNCT
ejpam-7160	233	24	that	that	PRON
ejpam-7160	233	25	is	be	AUX
ejpam-7160	233	26	closed	close	VERB
ejpam-7160	233	27	lmn	lmn	PROPN
ejpam-7160	233	28	ι	ι	X
ejpam-7160	233	29	-	-	PUNCT
ejpam-7160	233	30	closed	closed	ADJ
ejpam-7160	233	31	.	.	PUNCT
ejpam-7160	234	1	all	all	DET
ejpam-7160	234	2	lmn	lmn	PROPN
ejpam-7160	234	3	ι	ι	NOUN
ejpam-7160	234	4	-	-	PUNCT
ejpam-7160	234	5	closed	closed	ADJ
ejpam-7160	234	6	subset	subset	NOUN
ejpam-7160	234	7	of	of	ADP
ejpam-7160	234	8	π	π	PROPN
ejpam-7160	234	9	are	be	AUX
ejpam-7160	234	10	revered	revere	VERB
ejpam-7160	234	11	by	by	ADP
ejpam-7160	234	12	τlmn	τlmn	NOUN
ejpam-7160	234	13	ι	ι	PROPN
ejpam-7160	234	14	.	.	PUNCT
ejpam-7160	235	1	definition	definition	NOUN
ejpam-7160	235	2	16	16	NUM
ejpam-7160	235	3	.	.	PUNCT
ejpam-7160	236	1	let	let	VERB
ejpam-7160	236	2	(	(	PUNCT
ejpam-7160	236	3	π,×,mn	π,×,mn	ADV
ejpam-7160	236	4	ι	ι	AUX
ejpam-7160	236	5	)	)	PUNCT
ejpam-7160	236	6	be	be	VERB
ejpam-7160	236	7	a	a	DET
ejpam-7160	236	8	mn	mn	PROPN
ejpam-7160	236	9	ι	ι	PROPN
ejpam-7160	236	10	-	-	PUNCT
ejpam-7160	236	11	app	app	NOUN
ejpam-7160	236	12	space	space	NOUN
ejpam-7160	236	13	,	,	PUNCT
ejpam-7160	236	14	and	and	CCONJ
ejpam-7160	236	15	l	l	NOUN
ejpam-7160	236	16	be	be	AUX
ejpam-7160	236	17	a	a	DET
ejpam-7160	236	18	grill	grill	NOUN
ejpam-7160	236	19	on	on	ADP
ejpam-7160	236	20	π	π	PROPN
ejpam-7160	236	21	.	.	PUNCT
ejpam-7160	237	1	the	the	DET
ejpam-7160	237	2	lmn	lmn	PROPN
ejpam-7160	237	3	ι	ι	PROPN
ejpam-7160	237	4	-	-	ADJ
ejpam-7160	237	5	interior	interior	ADJ
ejpam-7160	237	6	and	and	CCONJ
ejpam-7160	237	7	lmn	lmn	PROPN
ejpam-7160	237	8	ι	ι	NOUN
ejpam-7160	237	9	-	-	PUNCT
ejpam-7160	237	10	closure	closure	NOUN
ejpam-7160	237	11	of	of	ADP
ejpam-7160	237	12	c	c	NOUN
ejpam-7160	237	13	⊑	⊑	X
ejpam-7160	237	14	π	π	NOUN
ejpam-7160	237	15	are	be	AUX
ejpam-7160	237	16	intlmn	intlmn	ADJ
ejpam-7160	237	17	ι	ι	X
ejpam-7160	237	18	(	(	PUNCT
ejpam-7160	237	19	c	c	NOUN
ejpam-7160	237	20	)	)	PUNCT
ejpam-7160	237	21	=	=	SYM
ejpam-7160	237	22	⊔{g	⊔{g	PROPN
ejpam-7160	237	23	∈	∈	PROPN
ejpam-7160	237	24	τlmn	τlmn	NOUN
ejpam-7160	237	25	ι	ι	X
ejpam-7160	237	26	:	:	PUNCT
ejpam-7160	237	27	g	g	X
ejpam-7160	237	28	⊑	⊑	X
ejpam-7160	237	29	c	c	NOUN
ejpam-7160	237	30	}	}	PUNCT
ejpam-7160	237	31	,	,	PUNCT
ejpam-7160	237	32	and	and	CCONJ
ejpam-7160	237	33	cllmn	cllmn	VERB
ejpam-7160	237	34	ι	ι	X
ejpam-7160	237	35	(	(	PUNCT
ejpam-7160	237	36	c	c	NOUN
ejpam-7160	237	37	)	)	PUNCT
ejpam-7160	238	1	=	=	SYM
ejpam-7160	238	2	⊓{y	⊓{y	ADJ
ejpam-7160	238	3	:	:	PUNCT
ejpam-7160	238	4	y	y	PROPN
ejpam-7160	238	5	c	c	PROPN
ejpam-7160	238	6	∈	∈	PROPN
ejpam-7160	238	7	τlmn	τlmn	NOUN
ejpam-7160	238	8	ι	ι	X
ejpam-7160	238	9	:	:	PUNCT
ejpam-7160	238	10	c	c	X
ejpam-7160	238	11	⊑	⊑	X
ejpam-7160	238	12	y	y	PROPN
ejpam-7160	238	13	}	}	PUNCT
ejpam-7160	238	14	.	.	PUNCT
ejpam-7160	239	1	the	the	DET
ejpam-7160	239	2	prior	prior	ADJ
ejpam-7160	239	3	topologies	topology	NOUN
ejpam-7160	239	4	in	in	ADP
ejpam-7160	239	5	[	[	X
ejpam-7160	239	6	34	34	NUM
ejpam-7160	239	7	,	,	PUNCT
ejpam-7160	239	8	56	56	NUM
ejpam-7160	239	9	]	]	PUNCT
ejpam-7160	239	10	are	be	AUX
ejpam-7160	239	11	weaker	weak	ADJ
ejpam-7160	239	12	than	than	ADP
ejpam-7160	239	13	the	the	DET
ejpam-7160	239	14	present	present	ADJ
ejpam-7160	239	15	ones	one	NOUN
ejpam-7160	239	16	,	,	PUNCT
ejpam-7160	239	17	as	as	SCONJ
ejpam-7160	239	18	shown	show	VERB
ejpam-7160	239	19	by	by	ADP
ejpam-7160	239	20	theorem	theorem	ADJ
ejpam-7160	239	21	3.4	3.4	NUM
ejpam-7160	239	22	.	.	PUNCT
ejpam-7160	240	1	theorem	theorem	NOUN
ejpam-7160	240	2	5	5	NUM
ejpam-7160	240	3	.	.	PUNCT
ejpam-7160	241	1	if	if	SCONJ
ejpam-7160	241	2	(	(	PUNCT
ejpam-7160	241	3	π,×,mn	π,×,mn	NOUN
ejpam-7160	241	4	ι	ι	PROPN
ejpam-7160	241	5	)	)	PUNCT
ejpam-7160	241	6	is	be	AUX
ejpam-7160	241	7	a	a	DET
ejpam-7160	241	8	mn	mn	PROPN
ejpam-7160	241	9	ι	ι	PROPN
ejpam-7160	241	10	-	-	PUNCT
ejpam-7160	241	11	ns	ns	ADJ
ejpam-7160	241	12	,	,	PUNCT
ejpam-7160	241	13	and	and	CCONJ
ejpam-7160	241	14	l	l	NOUN
ejpam-7160	241	15	is	be	AUX
ejpam-7160	241	16	a	a	DET
ejpam-7160	241	17	grill	grill	NOUN
ejpam-7160	241	18	on	on	ADP
ejpam-7160	241	19	π	π	PROPN
ejpam-7160	241	20	.	.	PUNCT
ejpam-7160	242	1	then	then	ADV
ejpam-7160	242	2	,	,	PUNCT
ejpam-7160	242	3	τmn	τmn	PROPN
ejpam-7160	242	4	ι	ι	X
ejpam-7160	242	5	⊑	⊑	DET
ejpam-7160	242	6	τlmn	τlmn	PROPN
ejpam-7160	242	7	ι	ι	X
ejpam-7160	242	8	.	.	PUNCT
ejpam-7160	243	1	proof	proof	NOUN
ejpam-7160	243	2	.	.	PUNCT
ejpam-7160	244	1	consider	consider	VERB
ejpam-7160	244	2	c	c	NOUN
ejpam-7160	244	3	∈	∈	PROPN
ejpam-7160	244	4	τmn	τmn	PROPN
ejpam-7160	244	5	ι	ι	X
ejpam-7160	244	6	.	.	PUNCT
ejpam-7160	245	1	thus	thus	ADV
ejpam-7160	245	2	,	,	PUNCT
ejpam-7160	245	3	mn	mn	PROPN
ejpam-7160	245	4	ι(π1	ι(π1	PROPN
ejpam-7160	245	5	)	)	PUNCT
ejpam-7160	246	1	⊑	⊑	PROPN
ejpam-7160	246	2	c	c	PROPN
ejpam-7160	246	3	∀π1	∀π1	PROPN
ejpam-7160	246	4	∈	∈	PROPN
ejpam-7160	246	5	c.	c.	NOUN
ejpam-7160	246	6	therefore	therefore	ADV
ejpam-7160	246	7	,	,	PUNCT
ejpam-7160	246	8	mn	mn	PROPN
ejpam-7160	246	9	ι(π1	ι(π1	PROPN
ejpam-7160	246	10	)	)	PUNCT
ejpam-7160	247	1	⊓	⊓	PROPN
ejpam-7160	247	2	cc	cc	PROPN
ejpam-7160	247	3	/∈	/∈	PROPN
ejpam-7160	247	4	l.	l.	PROPN
ejpam-7160	248	1	so	so	ADV
ejpam-7160	248	2	,	,	PUNCT
ejpam-7160	248	3	c	c	PROPN
ejpam-7160	248	4	∈	∈	PROPN
ejpam-7160	248	5	τlmn	τlmn	NOUN
ejpam-7160	248	6	ι	ι	X
ejpam-7160	248	7	.	.	PUNCT
ejpam-7160	249	1	therefore	therefore	ADV
ejpam-7160	249	2	,	,	PUNCT
ejpam-7160	249	3	τmn	τmn	ADJ
ejpam-7160	249	4	ι	ι	X
ejpam-7160	250	1	⊑	⊑	DET
ejpam-7160	250	2	τlmn	τlmn	PROPN
ejpam-7160	250	3	ι	ι	X
ejpam-7160	250	4	.	.	PUNCT
ejpam-7160	250	5	remark	remark	PROPN
ejpam-7160	250	6	1	1	NUM
ejpam-7160	250	7	.	.	PUNCT
ejpam-7160	251	1	the	the	DET
ejpam-7160	251	2	following	follow	VERB
ejpam-7160	251	3	should	should	AUX
ejpam-7160	251	4	be	be	AUX
ejpam-7160	251	5	understood	understand	VERB
ejpam-7160	251	6	:	:	PUNCT
ejpam-7160	251	7	(	(	PUNCT
ejpam-7160	251	8	1	1	X
ejpam-7160	251	9	)	)	PUNCT
ejpam-7160	251	10	at	at	ADP
ejpam-7160	251	11	l	l	NOUN
ejpam-7160	251	12	=	=	SYM
ejpam-7160	251	13	{	{	PUNCT
ejpam-7160	251	14	π	π	NOUN
ejpam-7160	251	15	}	}	PUNCT
ejpam-7160	251	16	in	in	ADP
ejpam-7160	251	17	an	an	DET
ejpam-7160	251	18	τmn	τmn	ADJ
ejpam-7160	251	19	ι	ι	NOUN
ejpam-7160	251	20	-	-	PUNCT
ejpam-7160	251	21	topology	topology	NOUN
ejpam-7160	251	22	,	,	PUNCT
ejpam-7160	251	23	then	then	ADV
ejpam-7160	251	24	τmn	τmn	VERB
ejpam-7160	251	25	ι	ι	X
ejpam-7160	251	26	=	=	SYM
ejpam-7160	251	27	τlmn	τlmn	NOUN
ejpam-7160	251	28	ι	ι	X
ejpam-7160	251	29	.	.	PUNCT
ejpam-7160	252	1	(	(	PUNCT
ejpam-7160	252	2	2	2	X
ejpam-7160	252	3	)	)	PUNCT
ejpam-7160	252	4	τmn	τmn	NOUN
ejpam-7160	253	1	ι	ι	X
ejpam-7160	253	2	⊑	⊑	DET
ejpam-7160	253	3	τlmn	τlmn	PROPN
ejpam-7160	253	4	ι	ι	X
ejpam-7160	253	5	,	,	PUNCT
ejpam-7160	253	6	as	as	SCONJ
ejpam-7160	253	7	observed	observe	VERB
ejpam-7160	253	8	in	in	ADP
ejpam-7160	253	9	example	example	NOUN
ejpam-7160	253	10	3.9	3.9	NUM
ejpam-7160	253	11	.	.	PUNCT
ejpam-7160	253	12	example	example	NOUN
ejpam-7160	254	1	1	1	NUM
ejpam-7160	254	2	.	.	PUNCT
ejpam-7160	255	1	let	let	VERB
ejpam-7160	255	2	×	×	NOUN
ejpam-7160	255	3	=	=	SYM
ejpam-7160	255	4	{	{	PUNCT
ejpam-7160	255	5	{	{	PUNCT
ejpam-7160	255	6	π1	π1	NOUN
ejpam-7160	255	7	,	,	PUNCT
ejpam-7160	255	8	π1	π1	NOUN
ejpam-7160	255	9	}	}	PUNCT
ejpam-7160	255	10	,	,	PUNCT
ejpam-7160	255	11	{	{	PUNCT
ejpam-7160	255	12	π1	π1	NOUN
ejpam-7160	255	13	,	,	PUNCT
ejpam-7160	255	14	π2	π2	PROPN
ejpam-7160	255	15	}	}	PUNCT
ejpam-7160	255	16	,	,	PUNCT
ejpam-7160	255	17	{	{	PUNCT
ejpam-7160	255	18	π2	π2	ADV
ejpam-7160	255	19	,	,	PUNCT
ejpam-7160	255	20	π2	π2	PROPN
ejpam-7160	255	21	}	}	PUNCT
ejpam-7160	255	22	,	,	PUNCT
ejpam-7160	255	23	{	{	PUNCT
ejpam-7160	255	24	π3	π3	NOUN
ejpam-7160	255	25	,	,	PUNCT
ejpam-7160	255	26	π3	π3	NOUN
ejpam-7160	255	27	}	}	PUNCT
ejpam-7160	255	28	,	,	PUNCT
ejpam-7160	255	29	{	{	PUNCT
ejpam-7160	255	30	π2	π2	ADV
ejpam-7160	255	31	,	,	PUNCT
ejpam-7160	255	32	π3	π3	NOUN
ejpam-7160	255	33	}	}	PUNCT
ejpam-7160	255	34	,	,	PUNCT
ejpam-7160	255	35	{	{	PUNCT
ejpam-7160	255	36	π3	π3	NOUN
ejpam-7160	255	37	,	,	PUNCT
ejpam-7160	255	38	π2	π2	ADV
ejpam-7160	255	39	}	}	PUNCT
ejpam-7160	255	40	}	}	PUNCT
ejpam-7160	255	41	be	be	AUX
ejpam-7160	255	42	a	a	DET
ejpam-7160	255	43	br	br	NOUN
ejpam-7160	255	44	on	on	ADP
ejpam-7160	255	45	π	π	PROPN
ejpam-7160	255	46	=	=	SYM
ejpam-7160	255	47	{	{	PUNCT
ejpam-7160	255	48	π1	π1	NOUN
ejpam-7160	255	49	,	,	PUNCT
ejpam-7160	255	50	π2	π2	PROPN
ejpam-7160	255	51	,	,	PUNCT
ejpam-7160	255	52	π3	π3	NOUN
ejpam-7160	255	53	,	,	PUNCT
ejpam-7160	255	54	π4	π4	PROPN
ejpam-7160	255	55	}	}	PUNCT
ejpam-7160	255	56	.	.	PUNCT
ejpam-7160	256	1	table	table	NOUN
ejpam-7160	256	2	1	1	NUM
ejpam-7160	256	3	contains	contain	VERB
ejpam-7160	256	4	all	all	DET
ejpam-7160	256	5	mn	mn	PROPN
ejpam-7160	256	6	ι	ι	X
ejpam-7160	256	7	nbds	nbds	NOUN
ejpam-7160	256	8	.	.	PUNCT
ejpam-7160	257	1	a.	a.	PROPN
ejpam-7160	257	2	a.	a.	PROPN
ejpam-7160	257	3	azzam	azzam	PROPN
ejpam-7160	257	4	et	et	PROPN
ejpam-7160	257	5	al	al	PROPN
ejpam-7160	257	6	.	.	PUNCT
ejpam-7160	257	7	/	/	SYM
ejpam-7160	257	8	eur	eur	PROPN
ejpam-7160	257	9	.	.	PUNCT
ejpam-7160	258	1	j.	j.	PROPN
ejpam-7160	258	2	pure	pure	PROPN
ejpam-7160	258	3	appl	appl	PROPN
ejpam-7160	258	4	.	.	PROPN
ejpam-7160	258	5	math	math	PROPN
ejpam-7160	258	6	,	,	PUNCT
ejpam-7160	258	7	18	18	NUM
ejpam-7160	258	8	(	(	PUNCT
ejpam-7160	258	9	4	4	NUM
ejpam-7160	258	10	)	)	PUNCT
ejpam-7160	258	11	(	(	PUNCT
ejpam-7160	258	12	2025	2025	NUM
ejpam-7160	258	13	)	)	PUNCT
ejpam-7160	258	14	,	,	PUNCT
ejpam-7160	258	15	7160	7160	NUM
ejpam-7160	258	16	9	9	NUM
ejpam-7160	258	17	of	of	ADP
ejpam-7160	258	18	22	22	NUM
ejpam-7160	258	19	table	table	NOUN
ejpam-7160	258	20	1	1	NUM
ejpam-7160	258	21	:	:	PUNCT
ejpam-7160	258	22	mn	mn	PROPN
ejpam-7160	258	23	ι	ι	PROPN
ejpam-7160	258	24	nbds	nbds	PROPN
ejpam-7160	258	25	π1	π1	ADJ
ejpam-7160	258	26	π2	π2	ADJ
ejpam-7160	258	27	π3	π3	NOUN
ejpam-7160	258	28	π4	π4	NOUN
ejpam-7160	258	29	.	.	PUNCT
ejpam-7160	259	1	nr	nr	PRON
ejpam-7160	259	2	{	{	PUNCT
ejpam-7160	259	3	π1	π1	PROPN
ejpam-7160	259	4	,	,	PUNCT
ejpam-7160	259	5	π2	π2	PROPN
ejpam-7160	259	6	}	}	PUNCT
ejpam-7160	259	7	{	{	PUNCT
ejpam-7160	259	8	π2	π2	ADV
ejpam-7160	259	9	,	,	PUNCT
ejpam-7160	259	10	π3	π3	NOUN
ejpam-7160	259	11	}	}	PUNCT
ejpam-7160	259	12	{	{	PUNCT
ejpam-7160	259	13	π2	π2	ADV
ejpam-7160	259	14	,	,	PUNCT
ejpam-7160	259	15	π3	π3	NOUN
ejpam-7160	259	16	}	}	PUNCT
ejpam-7160	259	17	ϕ	ϕ	PROPN
ejpam-7160	259	18	nl	nl	PROPN
ejpam-7160	259	19	{	{	PUNCT
ejpam-7160	259	20	π1	π1	NOUN
ejpam-7160	259	21	}	}	PUNCT
ejpam-7160	259	22	{	{	PUNCT
ejpam-7160	259	23	π1	π1	NOUN
ejpam-7160	259	24	,	,	PUNCT
ejpam-7160	259	25	π2	π2	ADJ
ejpam-7160	259	26	,	,	PUNCT
ejpam-7160	259	27	π3	π3	NOUN
ejpam-7160	259	28	}	}	PUNCT
ejpam-7160	259	29	{	{	PUNCT
ejpam-7160	259	30	π2	π2	ADV
ejpam-7160	259	31	,	,	PUNCT
ejpam-7160	259	32	π3	π3	NOUN
ejpam-7160	259	33	}	}	PUNCT
ejpam-7160	259	34	ϕ	ϕ	PROPN
ejpam-7160	259	35	nu	nu	INTJ
ejpam-7160	259	36	{	{	PUNCT
ejpam-7160	259	37	π1	π1	NOUN
ejpam-7160	259	38	,	,	PUNCT
ejpam-7160	259	39	π2	π2	ADJ
ejpam-7160	259	40	}	}	PUNCT
ejpam-7160	259	41	{	{	PUNCT
ejpam-7160	259	42	π1	π1	NOUN
ejpam-7160	259	43	,	,	PUNCT
ejpam-7160	259	44	π2	π2	ADJ
ejpam-7160	259	45	,	,	PUNCT
ejpam-7160	259	46	π3	π3	NOUN
ejpam-7160	259	47	}	}	PUNCT
ejpam-7160	259	48	{	{	PUNCT
ejpam-7160	259	49	π2	π2	ADV
ejpam-7160	259	50	,	,	PUNCT
ejpam-7160	259	51	π3	π3	NOUN
ejpam-7160	259	52	}	}	PUNCT
ejpam-7160	259	53	ϕ	ϕ	PROPN
ejpam-7160	259	54	ni	ni	PROPN
ejpam-7160	259	55	{	{	PUNCT
ejpam-7160	259	56	π1	π1	NOUN
ejpam-7160	259	57	}	}	PUNCT
ejpam-7160	259	58	{	{	PUNCT
ejpam-7160	259	59	π2	π2	ADJ
ejpam-7160	259	60	,	,	PUNCT
ejpam-7160	259	61	π3	π3	NOUN
ejpam-7160	259	62	}	}	PUNCT
ejpam-7160	259	63	{	{	PUNCT
ejpam-7160	259	64	π2	π2	ADV
ejpam-7160	259	65	,	,	PUNCT
ejpam-7160	259	66	π3	π3	NOUN
ejpam-7160	259	67	}	}	PUNCT
ejpam-7160	259	68	ϕ	ϕ	NOUN
ejpam-7160	259	69	mn	mn	PROPN
ejpam-7160	259	70	r	r	NOUN
ejpam-7160	259	71	{	{	PUNCT
ejpam-7160	259	72	π1	π1	NOUN
ejpam-7160	259	73	,	,	PUNCT
ejpam-7160	259	74	π2	π2	PROPN
ejpam-7160	259	75	}	}	PUNCT
ejpam-7160	259	76	{	{	PUNCT
ejpam-7160	259	77	π2	π2	ADV
ejpam-7160	259	78	}	}	PUNCT
ejpam-7160	259	79	{	{	PUNCT
ejpam-7160	259	80	π2	π2	ADV
ejpam-7160	259	81	,	,	PUNCT
ejpam-7160	259	82	π3	π3	NOUN
ejpam-7160	259	83	}	}	PUNCT
ejpam-7160	259	84	ϕ	ϕ	PROPN
ejpam-7160	259	85	mn	mn	PROPN
ejpam-7160	259	86	l	l	PROPN
ejpam-7160	259	87	{	{	PUNCT
ejpam-7160	259	88	π1	π1	NOUN
ejpam-7160	259	89	}	}	PUNCT
ejpam-7160	259	90	{	{	PUNCT
ejpam-7160	259	91	π2	π2	ADJ
ejpam-7160	259	92	,	,	PUNCT
ejpam-7160	259	93	π3	π3	NOUN
ejpam-7160	259	94	}	}	PUNCT
ejpam-7160	259	95	{	{	PUNCT
ejpam-7160	259	96	π2	π2	ADV
ejpam-7160	259	97	,	,	PUNCT
ejpam-7160	259	98	π3	π3	NOUN
ejpam-7160	259	99	}	}	PUNCT
ejpam-7160	259	100	ϕ	ϕ	PROPN
ejpam-7160	259	101	mn	mn	PROPN
ejpam-7160	259	102	u	u	PROPN
ejpam-7160	259	103	{	{	PUNCT
ejpam-7160	259	104	π1	π1	NOUN
ejpam-7160	259	105	,	,	PUNCT
ejpam-7160	259	106	π2	π2	PROPN
ejpam-7160	259	107	}	}	PUNCT
ejpam-7160	259	108	{	{	PUNCT
ejpam-7160	259	109	π2	π2	ADV
ejpam-7160	259	110	,	,	PUNCT
ejpam-7160	259	111	π3	π3	NOUN
ejpam-7160	259	112	}	}	PUNCT
ejpam-7160	259	113	{	{	PUNCT
ejpam-7160	259	114	π2	π2	ADV
ejpam-7160	259	115	,	,	PUNCT
ejpam-7160	259	116	π3	π3	NOUN
ejpam-7160	259	117	}	}	PUNCT
ejpam-7160	259	118	ϕ	ϕ	PROPN
ejpam-7160	259	119	mn	mn	PROPN
ejpam-7160	260	1	i	i	PRON
ejpam-7160	260	2	{	{	PUNCT
ejpam-7160	260	3	π1	π1	PROPN
ejpam-7160	260	4	}	}	PUNCT
ejpam-7160	260	5	{	{	PUNCT
ejpam-7160	260	6	π2	π2	ADJ
ejpam-7160	260	7	,	,	PUNCT
ejpam-7160	260	8	π3	π3	NOUN
ejpam-7160	260	9	}	}	PUNCT
ejpam-7160	260	10	{	{	PUNCT
ejpam-7160	260	11	π2	π2	ADV
ejpam-7160	260	12	,	,	PUNCT
ejpam-7160	260	13	π3	π3	NOUN
ejpam-7160	260	14	}	}	PUNCT
ejpam-7160	260	15	ϕ	ϕ	NOUN
ejpam-7160	260	16	mn	mn	PROPN
ejpam-7160	260	17	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	260	18	{	{	PUNCT
ejpam-7160	260	19	π1	π1	NOUN
ejpam-7160	260	20	,	,	PUNCT
ejpam-7160	260	21	π2	π2	PROPN
ejpam-7160	260	22	}	}	PUNCT
ejpam-7160	260	23	{	{	PUNCT
ejpam-7160	260	24	π2	π2	ADV
ejpam-7160	260	25	}	}	PUNCT
ejpam-7160	260	26	{	{	PUNCT
ejpam-7160	260	27	π2	π2	ADV
ejpam-7160	260	28	,	,	PUNCT
ejpam-7160	260	29	π3	π3	NOUN
ejpam-7160	260	30	}	}	PUNCT
ejpam-7160	260	31	ϕ	ϕ	PROPN
ejpam-7160	260	32	mn	mn	PROPN
ejpam-7160	260	33	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	260	34	{	{	PUNCT
ejpam-7160	260	35	π1	π1	NOUN
ejpam-7160	260	36	}	}	PUNCT
ejpam-7160	260	37	{	{	PUNCT
ejpam-7160	260	38	π2	π2	ADJ
ejpam-7160	260	39	,	,	PUNCT
ejpam-7160	260	40	π3	π3	NOUN
ejpam-7160	260	41	}	}	PUNCT
ejpam-7160	260	42	{	{	PUNCT
ejpam-7160	260	43	π2	π2	ADV
ejpam-7160	260	44	,	,	PUNCT
ejpam-7160	260	45	π3	π3	NOUN
ejpam-7160	260	46	}	}	PUNCT
ejpam-7160	260	47	ϕ	ϕ	PROPN
ejpam-7160	260	48	mn	mn	PROPN
ejpam-7160	260	49	⟨u⟩	⟨u⟩	PROPN
ejpam-7160	260	50	{	{	PUNCT
ejpam-7160	260	51	π1	π1	NOUN
ejpam-7160	260	52	,	,	PUNCT
ejpam-7160	260	53	π2	π2	PROPN
ejpam-7160	260	54	}	}	PUNCT
ejpam-7160	260	55	{	{	PUNCT
ejpam-7160	260	56	π2	π2	ADV
ejpam-7160	260	57	,	,	PUNCT
ejpam-7160	260	58	π3	π3	NOUN
ejpam-7160	260	59	}	}	PUNCT
ejpam-7160	260	60	{	{	PUNCT
ejpam-7160	260	61	π2	π2	ADV
ejpam-7160	260	62	,	,	PUNCT
ejpam-7160	260	63	π3	π3	NOUN
ejpam-7160	260	64	}	}	PUNCT
ejpam-7160	260	65	ϕ	ϕ	PROPN
ejpam-7160	260	66	mn	mn	PROPN
ejpam-7160	260	67	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	260	68	{	{	PUNCT
ejpam-7160	260	69	π1	π1	NOUN
ejpam-7160	260	70	}	}	PUNCT
ejpam-7160	260	71	{	{	PUNCT
ejpam-7160	260	72	π2	π2	ADV
ejpam-7160	260	73	}	}	PUNCT
ejpam-7160	260	74	{	{	PUNCT
ejpam-7160	260	75	π2	π2	ADV
ejpam-7160	260	76	,	,	PUNCT
ejpam-7160	260	77	π3	π3	NOUN
ejpam-7160	260	78	}	}	PUNCT
ejpam-7160	260	79	ϕ	ϕ	NOUN
ejpam-7160	260	80	let	let	VERB
ejpam-7160	260	81	l	l	NOUN
ejpam-7160	260	82	=	=	PRON
ejpam-7160	260	83	{	{	PUNCT
ejpam-7160	260	84	{	{	PUNCT
ejpam-7160	260	85	π2	π2	ADV
ejpam-7160	260	86	}	}	PUNCT
ejpam-7160	260	87	,	,	PUNCT
ejpam-7160	260	88	{	{	PUNCT
ejpam-7160	260	89	π1	π1	NOUN
ejpam-7160	260	90	,	,	PUNCT
ejpam-7160	260	91	π2	π2	PROPN
ejpam-7160	260	92	}	}	PUNCT
ejpam-7160	260	93	,	,	PUNCT
ejpam-7160	260	94	{	{	PUNCT
ejpam-7160	260	95	π2	π2	ADV
ejpam-7160	260	96	,	,	PUNCT
ejpam-7160	260	97	π3	π3	NOUN
ejpam-7160	260	98	}	}	PUNCT
ejpam-7160	260	99	,	,	PUNCT
ejpam-7160	260	100	{	{	PUNCT
ejpam-7160	260	101	π2	π2	ADV
ejpam-7160	260	102	,	,	PUNCT
ejpam-7160	260	103	π4	π4	NOUN
ejpam-7160	260	104	}	}	PUNCT
ejpam-7160	260	105	,	,	PUNCT
ejpam-7160	260	106	{	{	PUNCT
ejpam-7160	260	107	π1	π1	NOUN
ejpam-7160	260	108	,	,	PUNCT
ejpam-7160	260	109	π2	π2	ADJ
ejpam-7160	260	110	,	,	PUNCT
ejpam-7160	260	111	π3	π3	NOUN
ejpam-7160	260	112	}	}	PUNCT
ejpam-7160	260	113	,	,	PUNCT
ejpam-7160	260	114	{	{	PUNCT
ejpam-7160	260	115	π1	π1	NOUN
ejpam-7160	260	116	,	,	PUNCT
ejpam-7160	260	117	π2	π2	PROPN
ejpam-7160	260	118	,	,	PUNCT
ejpam-7160	260	119	π4	π4	NOUN
ejpam-7160	260	120	}	}	PUNCT
ejpam-7160	260	121	,	,	PUNCT
ejpam-7160	260	122	{	{	PUNCT
ejpam-7160	260	123	π2	π2	ADV
ejpam-7160	260	124	,	,	PUNCT
ejpam-7160	260	125	π3	π3	NOUN
ejpam-7160	260	126	,	,	PUNCT
ejpam-7160	260	127	π4},π	π4},π	NOUN
ejpam-7160	260	128	}	}	PUNCT
ejpam-7160	260	129	.	.	PUNCT
ejpam-7160	261	1	as	as	ADP
ejpam-7160	261	2	a	a	DET
ejpam-7160	261	3	result	result	NOUN
ejpam-7160	261	4	,	,	PUNCT
ejpam-7160	261	5	the	the	DET
ejpam-7160	261	6	following	follow	VERB
ejpam-7160	261	7	claims	claim	NOUN
ejpam-7160	261	8	are	be	AUX
ejpam-7160	261	9	accurate	accurate	ADJ
ejpam-7160	261	10	:	:	PUNCT
ejpam-7160	261	11	(	(	PUNCT
ejpam-7160	261	12	1	1	X
ejpam-7160	261	13	)	)	PUNCT
ejpam-7160	261	14	τmn	τmn	NOUN
ejpam-7160	262	1	r	r	NOUN
ejpam-7160	262	2	=	=	SYM
ejpam-7160	262	3	{	{	PUNCT
ejpam-7160	262	4	π	π	PROPN
ejpam-7160	262	5	,	,	PUNCT
ejpam-7160	262	6	ϕ	ϕ	NOUN
ejpam-7160	262	7	,	,	PUNCT
ejpam-7160	262	8	{	{	PUNCT
ejpam-7160	262	9	π2	π2	ADV
ejpam-7160	262	10	}	}	PUNCT
ejpam-7160	262	11	,	,	PUNCT
ejpam-7160	262	12	{	{	PUNCT
ejpam-7160	262	13	π4	π4	PROPN
ejpam-7160	262	14	}	}	PUNCT
ejpam-7160	262	15	,	,	PUNCT
ejpam-7160	262	16	{	{	PUNCT
ejpam-7160	262	17	π1	π1	NOUN
ejpam-7160	262	18	,	,	PUNCT
ejpam-7160	262	19	π2	π2	PROPN
ejpam-7160	262	20	}	}	PUNCT
ejpam-7160	262	21	,	,	PUNCT
ejpam-7160	262	22	{	{	PUNCT
ejpam-7160	262	23	π2	π2	ADV
ejpam-7160	262	24	,	,	PUNCT
ejpam-7160	262	25	π3	π3	NOUN
ejpam-7160	262	26	}	}	PUNCT
ejpam-7160	262	27	,	,	PUNCT
ejpam-7160	262	28	{	{	PUNCT
ejpam-7160	262	29	π2	π2	ADV
ejpam-7160	262	30	,	,	PUNCT
ejpam-7160	262	31	π4	π4	NOUN
ejpam-7160	262	32	}	}	PUNCT
ejpam-7160	262	33	,	,	PUNCT
ejpam-7160	262	34	{	{	PUNCT
ejpam-7160	262	35	π1	π1	NOUN
ejpam-7160	262	36	,	,	PUNCT
ejpam-7160	262	37	π2	π2	ADJ
ejpam-7160	262	38	,	,	PUNCT
ejpam-7160	262	39	π3	π3	NOUN
ejpam-7160	262	40	}	}	PUNCT
ejpam-7160	262	41	,	,	PUNCT
ejpam-7160	262	42	{	{	PUNCT
ejpam-7160	262	43	π1	π1	NOUN
ejpam-7160	262	44	,	,	PUNCT
ejpam-7160	262	45	π2	π2	PROPN
ejpam-7160	262	46	,	,	PUNCT
ejpam-7160	262	47	π4	π4	NOUN
ejpam-7160	262	48	}	}	PUNCT
ejpam-7160	262	49	,	,	PUNCT
ejpam-7160	262	50	{	{	PUNCT
ejpam-7160	262	51	π2	π2	ADV
ejpam-7160	262	52	,	,	PUNCT
ejpam-7160	262	53	π3	π3	NOUN
ejpam-7160	262	54	,	,	PUNCT
ejpam-7160	262	55	π4	π4	PROPN
ejpam-7160	262	56	}	}	PUNCT
ejpam-7160	262	57	}	}	PUNCT
ejpam-7160	262	58	,	,	PUNCT
ejpam-7160	262	59	and	and	CCONJ
ejpam-7160	262	60	τlmn	τlmn	NOUN
ejpam-7160	262	61	r	r	NOUN
ejpam-7160	262	62	=	=	PUNCT
ejpam-7160	262	63	{	{	PUNCT
ejpam-7160	262	64	{	{	PUNCT
ejpam-7160	262	65	π2	π2	ADV
ejpam-7160	262	66	}	}	PUNCT
ejpam-7160	262	67	,	,	PUNCT
ejpam-7160	262	68	{	{	PUNCT
ejpam-7160	262	69	π4	π4	PROPN
ejpam-7160	262	70	}	}	PUNCT
ejpam-7160	262	71	,	,	PUNCT
ejpam-7160	262	72	{	{	PUNCT
ejpam-7160	262	73	π1	π1	NOUN
ejpam-7160	262	74	,	,	PUNCT
ejpam-7160	262	75	π2	π2	PROPN
ejpam-7160	262	76	}	}	PUNCT
ejpam-7160	262	77	,	,	PUNCT
ejpam-7160	262	78	{	{	PUNCT
ejpam-7160	262	79	π2	π2	ADV
ejpam-7160	262	80	,	,	PUNCT
ejpam-7160	262	81	π3	π3	NOUN
ejpam-7160	262	82	}	}	PUNCT
ejpam-7160	262	83	,	,	PUNCT
ejpam-7160	262	84	{	{	PUNCT
ejpam-7160	262	85	π2	π2	ADV
ejpam-7160	262	86	,	,	PUNCT
ejpam-7160	262	87	π4	π4	NOUN
ejpam-7160	262	88	}	}	PUNCT
ejpam-7160	262	89	,	,	PUNCT
ejpam-7160	262	90	{	{	PUNCT
ejpam-7160	262	91	π1	π1	NOUN
ejpam-7160	262	92	,	,	PUNCT
ejpam-7160	262	93	π2	π2	ADJ
ejpam-7160	262	94	,	,	PUNCT
ejpam-7160	262	95	π3	π3	NOUN
ejpam-7160	262	96	}	}	PUNCT
ejpam-7160	262	97	,	,	PUNCT
ejpam-7160	262	98	{	{	PUNCT
ejpam-7160	262	99	π1	π1	NOUN
ejpam-7160	262	100	,	,	PUNCT
ejpam-7160	262	101	π2	π2	PROPN
ejpam-7160	262	102	,	,	PUNCT
ejpam-7160	262	103	π4	π4	NOUN
ejpam-7160	262	104	}	}	PUNCT
ejpam-7160	262	105	,	,	PUNCT
ejpam-7160	262	106	{	{	PUNCT
ejpam-7160	262	107	π2	π2	ADV
ejpam-7160	262	108	,	,	PUNCT
ejpam-7160	262	109	π3	π3	NOUN
ejpam-7160	262	110	,	,	PUNCT
ejpam-7160	262	111	π4	π4	PROPN
ejpam-7160	262	112	}	}	PUNCT
ejpam-7160	262	113	,	,	PUNCT
ejpam-7160	262	114	π	π	PROPN
ejpam-7160	262	115	,	,	PUNCT
ejpam-7160	262	116	ϕ	ϕ	NOUN
ejpam-7160	262	117	}	}	PUNCT
ejpam-7160	262	118	.	.	PUNCT
ejpam-7160	263	1	(	(	PUNCT
ejpam-7160	263	2	2	2	X
ejpam-7160	263	3	)	)	PUNCT
ejpam-7160	263	4	τmn	τmn	NOUN
ejpam-7160	263	5	l	l	NOUN
ejpam-7160	263	6	=	=	SYM
ejpam-7160	263	7	{	{	PUNCT
ejpam-7160	263	8	π	π	PROPN
ejpam-7160	263	9	,	,	PUNCT
ejpam-7160	263	10	ϕ	ϕ	NOUN
ejpam-7160	263	11	,	,	PUNCT
ejpam-7160	263	12	{	{	PUNCT
ejpam-7160	263	13	π1	π1	NOUN
ejpam-7160	263	14	}	}	PUNCT
ejpam-7160	263	15	,	,	PUNCT
ejpam-7160	263	16	{	{	PUNCT
ejpam-7160	263	17	π4	π4	PROPN
ejpam-7160	263	18	}	}	PUNCT
ejpam-7160	263	19	,	,	PUNCT
ejpam-7160	263	20	{	{	PUNCT
ejpam-7160	263	21	π1	π1	NOUN
ejpam-7160	263	22	,	,	PUNCT
ejpam-7160	263	23	π4	π4	PROPN
ejpam-7160	263	24	}	}	PUNCT
ejpam-7160	263	25	,	,	PUNCT
ejpam-7160	263	26	{	{	PUNCT
ejpam-7160	263	27	π2	π2	ADV
ejpam-7160	263	28	,	,	PUNCT
ejpam-7160	263	29	π3	π3	NOUN
ejpam-7160	263	30	}	}	PUNCT
ejpam-7160	263	31	,	,	PUNCT
ejpam-7160	263	32	{	{	PUNCT
ejpam-7160	263	33	π1	π1	NOUN
ejpam-7160	263	34	,	,	PUNCT
ejpam-7160	263	35	π2	π2	ADJ
ejpam-7160	263	36	,	,	PUNCT
ejpam-7160	263	37	π3	π3	NOUN
ejpam-7160	263	38	}	}	PUNCT
ejpam-7160	263	39	,	,	PUNCT
ejpam-7160	263	40	{	{	PUNCT
ejpam-7160	263	41	π2	π2	ADV
ejpam-7160	263	42	,	,	PUNCT
ejpam-7160	263	43	π3	π3	NOUN
ejpam-7160	263	44	,	,	PUNCT
ejpam-7160	263	45	π4	π4	PROPN
ejpam-7160	263	46	}	}	PUNCT
ejpam-7160	263	47	}	}	PUNCT
ejpam-7160	263	48	,	,	PUNCT
ejpam-7160	263	49	and	and	CCONJ
ejpam-7160	263	50	τlmn	τlmn	NOUN
ejpam-7160	263	51	l	l	NOUN
ejpam-7160	263	52	=	=	SYM
ejpam-7160	263	53	{	{	PUNCT
ejpam-7160	263	54	{	{	PUNCT
ejpam-7160	263	55	π1	π1	NOUN
ejpam-7160	263	56	}	}	PUNCT
ejpam-7160	263	57	,	,	PUNCT
ejpam-7160	263	58	{	{	PUNCT
ejpam-7160	263	59	π2	π2	ADV
ejpam-7160	263	60	}	}	PUNCT
ejpam-7160	263	61	,	,	PUNCT
ejpam-7160	263	62	{	{	PUNCT
ejpam-7160	263	63	π4	π4	PROPN
ejpam-7160	263	64	}	}	PUNCT
ejpam-7160	263	65	,	,	PUNCT
ejpam-7160	263	66	{	{	PUNCT
ejpam-7160	263	67	π1	π1	NOUN
ejpam-7160	263	68	,	,	PUNCT
ejpam-7160	263	69	π2	π2	PROPN
ejpam-7160	263	70	}	}	PUNCT
ejpam-7160	263	71	,	,	PUNCT
ejpam-7160	263	72	{	{	PUNCT
ejpam-7160	263	73	π1	π1	NOUN
ejpam-7160	263	74	,	,	PUNCT
ejpam-7160	263	75	π4	π4	PROPN
ejpam-7160	263	76	}	}	PUNCT
ejpam-7160	263	77	,	,	PUNCT
ejpam-7160	263	78	{	{	PUNCT
ejpam-7160	263	79	π2	π2	ADV
ejpam-7160	263	80	,	,	PUNCT
ejpam-7160	263	81	π3	π3	NOUN
ejpam-7160	263	82	}	}	PUNCT
ejpam-7160	263	83	,	,	PUNCT
ejpam-7160	263	84	{	{	PUNCT
ejpam-7160	263	85	π2	π2	ADV
ejpam-7160	263	86	,	,	PUNCT
ejpam-7160	263	87	π4	π4	NOUN
ejpam-7160	263	88	}	}	PUNCT
ejpam-7160	263	89	,	,	PUNCT
ejpam-7160	263	90	{	{	PUNCT
ejpam-7160	263	91	π1	π1	NOUN
ejpam-7160	263	92	,	,	PUNCT
ejpam-7160	263	93	π2	π2	ADJ
ejpam-7160	263	94	,	,	PUNCT
ejpam-7160	263	95	π3	π3	NOUN
ejpam-7160	263	96	}	}	PUNCT
ejpam-7160	263	97	,	,	PUNCT
ejpam-7160	263	98	{	{	PUNCT
ejpam-7160	263	99	π1	π1	NOUN
ejpam-7160	263	100	,	,	PUNCT
ejpam-7160	263	101	π2	π2	PROPN
ejpam-7160	263	102	,	,	PUNCT
ejpam-7160	263	103	π4	π4	NOUN
ejpam-7160	263	104	}	}	PUNCT
ejpam-7160	263	105	,	,	PUNCT
ejpam-7160	263	106	{	{	PUNCT
ejpam-7160	263	107	π2	π2	ADV
ejpam-7160	263	108	,	,	PUNCT
ejpam-7160	263	109	π3	π3	NOUN
ejpam-7160	263	110	,	,	PUNCT
ejpam-7160	263	111	π4},π	π4},π	NOUN
ejpam-7160	263	112	,	,	PUNCT
ejpam-7160	263	113	ϕ	ϕ	NOUN
ejpam-7160	263	114	}	}	PUNCT
ejpam-7160	263	115	.	.	PUNCT
ejpam-7160	264	1	(	(	PUNCT
ejpam-7160	264	2	3	3	X
ejpam-7160	264	3	)	)	PUNCT
ejpam-7160	264	4	τmnu	τmnu	NOUN
ejpam-7160	264	5	=	=	SYM
ejpam-7160	264	6	{	{	PUNCT
ejpam-7160	264	7	π	π	PROPN
ejpam-7160	264	8	,	,	PUNCT
ejpam-7160	264	9	ϕ	ϕ	NOUN
ejpam-7160	264	10	,	,	PUNCT
ejpam-7160	264	11	{	{	PUNCT
ejpam-7160	264	12	π4	π4	PROPN
ejpam-7160	264	13	}	}	PUNCT
ejpam-7160	264	14	,	,	PUNCT
ejpam-7160	264	15	{	{	PUNCT
ejpam-7160	264	16	π2	π2	ADV
ejpam-7160	264	17	,	,	PUNCT
ejpam-7160	264	18	π3	π3	NOUN
ejpam-7160	264	19	}	}	PUNCT
ejpam-7160	264	20	,	,	PUNCT
ejpam-7160	264	21	{	{	PUNCT
ejpam-7160	264	22	π1	π1	NOUN
ejpam-7160	264	23	,	,	PUNCT
ejpam-7160	264	24	π2	π2	ADJ
ejpam-7160	264	25	,	,	PUNCT
ejpam-7160	264	26	π3	π3	NOUN
ejpam-7160	264	27	}	}	PUNCT
ejpam-7160	264	28	,	,	PUNCT
ejpam-7160	264	29	{	{	PUNCT
ejpam-7160	264	30	π2	π2	ADV
ejpam-7160	264	31	,	,	PUNCT
ejpam-7160	264	32	π3	π3	NOUN
ejpam-7160	264	33	,	,	PUNCT
ejpam-7160	264	34	π4	π4	PROPN
ejpam-7160	264	35	}	}	PUNCT
ejpam-7160	264	36	}	}	PUNCT
ejpam-7160	264	37	,	,	PUNCT
ejpam-7160	264	38	and	and	CCONJ
ejpam-7160	264	39	τlmnu	τlmnu	NOUN
ejpam-7160	264	40	=	=	SYM
ejpam-7160	264	41	{	{	PUNCT
ejpam-7160	264	42	{	{	PUNCT
ejpam-7160	264	43	π2	π2	ADV
ejpam-7160	264	44	}	}	PUNCT
ejpam-7160	264	45	,	,	PUNCT
ejpam-7160	264	46	{	{	PUNCT
ejpam-7160	264	47	π4	π4	PROPN
ejpam-7160	264	48	}	}	PUNCT
ejpam-7160	264	49	,	,	PUNCT
ejpam-7160	264	50	{	{	PUNCT
ejpam-7160	264	51	π1	π1	NOUN
ejpam-7160	264	52	,	,	PUNCT
ejpam-7160	264	53	π2	π2	PROPN
ejpam-7160	264	54	}	}	PUNCT
ejpam-7160	264	55	,	,	PUNCT
ejpam-7160	264	56	{	{	PUNCT
ejpam-7160	264	57	π2	π2	ADV
ejpam-7160	264	58	,	,	PUNCT
ejpam-7160	264	59	π3	π3	NOUN
ejpam-7160	264	60	}	}	PUNCT
ejpam-7160	264	61	,	,	PUNCT
ejpam-7160	264	62	{	{	PUNCT
ejpam-7160	264	63	π2	π2	ADV
ejpam-7160	264	64	,	,	PUNCT
ejpam-7160	264	65	π4	π4	NOUN
ejpam-7160	264	66	}	}	PUNCT
ejpam-7160	264	67	,	,	PUNCT
ejpam-7160	264	68	{	{	PUNCT
ejpam-7160	264	69	π1	π1	NOUN
ejpam-7160	264	70	,	,	PUNCT
ejpam-7160	264	71	π2	π2	ADJ
ejpam-7160	264	72	,	,	PUNCT
ejpam-7160	264	73	π3	π3	NOUN
ejpam-7160	264	74	}	}	PUNCT
ejpam-7160	264	75	,	,	PUNCT
ejpam-7160	264	76	{	{	PUNCT
ejpam-7160	264	77	π1	π1	NOUN
ejpam-7160	264	78	,	,	PUNCT
ejpam-7160	264	79	π2	π2	PROPN
ejpam-7160	264	80	,	,	PUNCT
ejpam-7160	264	81	π4	π4	NOUN
ejpam-7160	264	82	}	}	PUNCT
ejpam-7160	264	83	,	,	PUNCT
ejpam-7160	264	84	{	{	PUNCT
ejpam-7160	264	85	π2	π2	ADV
ejpam-7160	264	86	,	,	PUNCT
ejpam-7160	264	87	π3	π3	NOUN
ejpam-7160	264	88	,	,	PUNCT
ejpam-7160	264	89	π4	π4	PROPN
ejpam-7160	264	90	}	}	PUNCT
ejpam-7160	264	91	,	,	PUNCT
ejpam-7160	264	92	π	π	PROPN
ejpam-7160	264	93	,	,	PUNCT
ejpam-7160	264	94	ϕ	ϕ	NOUN
ejpam-7160	264	95	}	}	PUNCT
ejpam-7160	264	96	.	.	PUNCT
ejpam-7160	265	1	(	(	PUNCT
ejpam-7160	265	2	4	4	X
ejpam-7160	265	3	)	)	PUNCT
ejpam-7160	265	4	τmn	τmn	NOUN
ejpam-7160	266	1	i	i	NOUN
ejpam-7160	266	2	=	=	PUNCT
ejpam-7160	266	3	{	{	PUNCT
ejpam-7160	266	4	π	π	PROPN
ejpam-7160	266	5	,	,	PUNCT
ejpam-7160	266	6	ϕ	ϕ	NOUN
ejpam-7160	266	7	,	,	PUNCT
ejpam-7160	266	8	{	{	PUNCT
ejpam-7160	266	9	π1	π1	NOUN
ejpam-7160	266	10	}	}	PUNCT
ejpam-7160	266	11	,	,	PUNCT
ejpam-7160	266	12	{	{	PUNCT
ejpam-7160	266	13	π2	π2	ADV
ejpam-7160	266	14	}	}	PUNCT
ejpam-7160	266	15	,	,	PUNCT
ejpam-7160	266	16	{	{	PUNCT
ejpam-7160	266	17	π4	π4	PROPN
ejpam-7160	266	18	}	}	PUNCT
ejpam-7160	266	19	,	,	PUNCT
ejpam-7160	266	20	{	{	PUNCT
ejpam-7160	266	21	π1	π1	NOUN
ejpam-7160	266	22	,	,	PUNCT
ejpam-7160	266	23	π2	π2	PROPN
ejpam-7160	266	24	}	}	PUNCT
ejpam-7160	266	25	,	,	PUNCT
ejpam-7160	266	26	{	{	PUNCT
ejpam-7160	266	27	π1	π1	NOUN
ejpam-7160	266	28	,	,	PUNCT
ejpam-7160	266	29	π4	π4	PROPN
ejpam-7160	266	30	}	}	PUNCT
ejpam-7160	266	31	,	,	PUNCT
ejpam-7160	266	32	{	{	PUNCT
ejpam-7160	266	33	π2	π2	ADV
ejpam-7160	266	34	,	,	PUNCT
ejpam-7160	266	35	π3	π3	NOUN
ejpam-7160	266	36	}	}	PUNCT
ejpam-7160	266	37	,	,	PUNCT
ejpam-7160	266	38	{	{	PUNCT
ejpam-7160	266	39	π2	π2	ADV
ejpam-7160	266	40	,	,	PUNCT
ejpam-7160	266	41	π4	π4	NOUN
ejpam-7160	266	42	}	}	PUNCT
ejpam-7160	266	43	,	,	PUNCT
ejpam-7160	266	44	{	{	PUNCT
ejpam-7160	266	45	π1	π1	NOUN
ejpam-7160	266	46	,	,	PUNCT
ejpam-7160	266	47	π2	π2	ADJ
ejpam-7160	266	48	,	,	PUNCT
ejpam-7160	266	49	π3	π3	NOUN
ejpam-7160	266	50	}	}	PUNCT
ejpam-7160	266	51	,	,	PUNCT
ejpam-7160	266	52	{	{	PUNCT
ejpam-7160	266	53	π1	π1	NOUN
ejpam-7160	266	54	,	,	PUNCT
ejpam-7160	266	55	π2	π2	PROPN
ejpam-7160	266	56	,	,	PUNCT
ejpam-7160	266	57	π4	π4	NOUN
ejpam-7160	266	58	}	}	PUNCT
ejpam-7160	266	59	,	,	PUNCT
ejpam-7160	266	60	{	{	PUNCT
ejpam-7160	266	61	π2	π2	ADV
ejpam-7160	266	62	,	,	PUNCT
ejpam-7160	266	63	π3	π3	NOUN
ejpam-7160	266	64	,	,	PUNCT
ejpam-7160	266	65	π4	π4	PROPN
ejpam-7160	266	66	}	}	PUNCT
ejpam-7160	266	67	}	}	PUNCT
ejpam-7160	266	68	,	,	PUNCT
ejpam-7160	266	69	and	and	CCONJ
ejpam-7160	266	70	a.	a.	NOUN
ejpam-7160	266	71	a.	a.	PROPN
ejpam-7160	267	1	azzam	azzam	PROPN
ejpam-7160	267	2	et	et	PROPN
ejpam-7160	267	3	al	al	PROPN
ejpam-7160	267	4	.	.	PUNCT
ejpam-7160	267	5	/	/	SYM
ejpam-7160	267	6	eur	eur	PROPN
ejpam-7160	267	7	.	.	PUNCT
ejpam-7160	268	1	j.	j.	PROPN
ejpam-7160	268	2	pure	pure	PROPN
ejpam-7160	268	3	appl	appl	PROPN
ejpam-7160	268	4	.	.	PROPN
ejpam-7160	268	5	math	math	PROPN
ejpam-7160	268	6	,	,	PUNCT
ejpam-7160	268	7	18	18	NUM
ejpam-7160	268	8	(	(	PUNCT
ejpam-7160	268	9	4	4	NUM
ejpam-7160	268	10	)	)	PUNCT
ejpam-7160	268	11	(	(	PUNCT
ejpam-7160	268	12	2025	2025	NUM
ejpam-7160	268	13	)	)	PUNCT
ejpam-7160	268	14	,	,	PUNCT
ejpam-7160	268	15	7160	7160	NUM
ejpam-7160	268	16	10	10	NUM
ejpam-7160	268	17	of	of	ADP
ejpam-7160	268	18	22	22	NUM
ejpam-7160	268	19	τlmn	τlmn	NOUN
ejpam-7160	269	1	i	i	PRON
ejpam-7160	269	2	=	=	SYM
ejpam-7160	269	3	{	{	PUNCT
ejpam-7160	269	4	{	{	PUNCT
ejpam-7160	269	5	π1	π1	NOUN
ejpam-7160	269	6	}	}	PUNCT
ejpam-7160	269	7	,	,	PUNCT
ejpam-7160	269	8	{	{	PUNCT
ejpam-7160	269	9	π2	π2	ADV
ejpam-7160	269	10	}	}	PUNCT
ejpam-7160	269	11	,	,	PUNCT
ejpam-7160	269	12	{	{	PUNCT
ejpam-7160	269	13	π4	π4	PROPN
ejpam-7160	269	14	}	}	PUNCT
ejpam-7160	269	15	,	,	PUNCT
ejpam-7160	269	16	{	{	PUNCT
ejpam-7160	269	17	π1	π1	NOUN
ejpam-7160	269	18	,	,	PUNCT
ejpam-7160	269	19	π2	π2	PROPN
ejpam-7160	269	20	}	}	PUNCT
ejpam-7160	269	21	,	,	PUNCT
ejpam-7160	269	22	{	{	PUNCT
ejpam-7160	269	23	π1	π1	NOUN
ejpam-7160	269	24	,	,	PUNCT
ejpam-7160	269	25	π4	π4	PROPN
ejpam-7160	269	26	}	}	PUNCT
ejpam-7160	269	27	,	,	PUNCT
ejpam-7160	269	28	{	{	PUNCT
ejpam-7160	269	29	π2	π2	ADV
ejpam-7160	269	30	,	,	PUNCT
ejpam-7160	269	31	π3	π3	NOUN
ejpam-7160	269	32	}	}	PUNCT
ejpam-7160	269	33	,	,	PUNCT
ejpam-7160	269	34	{	{	PUNCT
ejpam-7160	269	35	π2	π2	ADV
ejpam-7160	269	36	,	,	PUNCT
ejpam-7160	269	37	π4	π4	NOUN
ejpam-7160	269	38	}	}	PUNCT
ejpam-7160	269	39	,	,	PUNCT
ejpam-7160	269	40	{	{	PUNCT
ejpam-7160	269	41	π1	π1	NOUN
ejpam-7160	269	42	,	,	PUNCT
ejpam-7160	269	43	π2	π2	ADJ
ejpam-7160	269	44	,	,	PUNCT
ejpam-7160	269	45	π3	π3	NOUN
ejpam-7160	269	46	}	}	PUNCT
ejpam-7160	269	47	,	,	PUNCT
ejpam-7160	269	48	{	{	PUNCT
ejpam-7160	269	49	π1	π1	NOUN
ejpam-7160	269	50	,	,	PUNCT
ejpam-7160	269	51	π2	π2	PROPN
ejpam-7160	269	52	,	,	PUNCT
ejpam-7160	269	53	π4	π4	NOUN
ejpam-7160	269	54	}	}	PUNCT
ejpam-7160	269	55	,	,	PUNCT
ejpam-7160	269	56	{	{	PUNCT
ejpam-7160	269	57	π2	π2	ADV
ejpam-7160	269	58	,	,	PUNCT
ejpam-7160	269	59	π3	π3	NOUN
ejpam-7160	269	60	,	,	PUNCT
ejpam-7160	269	61	π4},π	π4},π	NOUN
ejpam-7160	269	62	,	,	PUNCT
ejpam-7160	269	63	ϕ	ϕ	NOUN
ejpam-7160	269	64	}	}	PUNCT
ejpam-7160	269	65	.	.	PUNCT
ejpam-7160	270	1	(	(	PUNCT
ejpam-7160	270	2	5	5	X
ejpam-7160	270	3	)	)	PUNCT
ejpam-7160	270	4	τmn	τmn	NOUN
ejpam-7160	271	1	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	271	2	=	=	PRON
ejpam-7160	271	3	{	{	PUNCT
ejpam-7160	271	4	π	π	PROPN
ejpam-7160	271	5	,	,	PUNCT
ejpam-7160	271	6	ϕ	ϕ	NOUN
ejpam-7160	271	7	,	,	PUNCT
ejpam-7160	271	8	{	{	PUNCT
ejpam-7160	271	9	π2	π2	ADV
ejpam-7160	271	10	}	}	PUNCT
ejpam-7160	271	11	,	,	PUNCT
ejpam-7160	271	12	{	{	PUNCT
ejpam-7160	271	13	π4	π4	PROPN
ejpam-7160	271	14	}	}	PUNCT
ejpam-7160	271	15	,	,	PUNCT
ejpam-7160	271	16	{	{	PUNCT
ejpam-7160	271	17	π1	π1	NOUN
ejpam-7160	271	18	,	,	PUNCT
ejpam-7160	271	19	π2	π2	PROPN
ejpam-7160	271	20	}	}	PUNCT
ejpam-7160	271	21	,	,	PUNCT
ejpam-7160	271	22	{	{	PUNCT
ejpam-7160	271	23	π2	π2	ADV
ejpam-7160	271	24	,	,	PUNCT
ejpam-7160	271	25	π3	π3	NOUN
ejpam-7160	271	26	}	}	PUNCT
ejpam-7160	271	27	,	,	PUNCT
ejpam-7160	271	28	{	{	PUNCT
ejpam-7160	271	29	π2	π2	ADV
ejpam-7160	271	30	,	,	PUNCT
ejpam-7160	271	31	π4	π4	NOUN
ejpam-7160	271	32	}	}	PUNCT
ejpam-7160	271	33	,	,	PUNCT
ejpam-7160	271	34	{	{	PUNCT
ejpam-7160	271	35	π1	π1	NOUN
ejpam-7160	271	36	,	,	PUNCT
ejpam-7160	271	37	π2	π2	ADJ
ejpam-7160	271	38	,	,	PUNCT
ejpam-7160	271	39	π3	π3	NOUN
ejpam-7160	271	40	}	}	PUNCT
ejpam-7160	271	41	,	,	PUNCT
ejpam-7160	271	42	{	{	PUNCT
ejpam-7160	271	43	π1	π1	NOUN
ejpam-7160	271	44	,	,	PUNCT
ejpam-7160	271	45	π2	π2	PROPN
ejpam-7160	271	46	,	,	PUNCT
ejpam-7160	271	47	π4	π4	NOUN
ejpam-7160	271	48	}	}	PUNCT
ejpam-7160	271	49	,	,	PUNCT
ejpam-7160	271	50	{	{	PUNCT
ejpam-7160	271	51	π2	π2	ADV
ejpam-7160	271	52	,	,	PUNCT
ejpam-7160	271	53	π3	π3	NOUN
ejpam-7160	271	54	,	,	PUNCT
ejpam-7160	271	55	π4	π4	PROPN
ejpam-7160	271	56	}	}	PUNCT
ejpam-7160	271	57	}	}	PUNCT
ejpam-7160	271	58	,	,	PUNCT
ejpam-7160	271	59	and	and	CCONJ
ejpam-7160	271	60	τlmn	τlmn	NOUN
ejpam-7160	271	61	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	271	62	=	=	PRON
ejpam-7160	271	63	{	{	PUNCT
ejpam-7160	271	64	{	{	PUNCT
ejpam-7160	271	65	π2	π2	ADV
ejpam-7160	271	66	}	}	PUNCT
ejpam-7160	271	67	,	,	PUNCT
ejpam-7160	271	68	{	{	PUNCT
ejpam-7160	271	69	π4	π4	PROPN
ejpam-7160	271	70	}	}	PUNCT
ejpam-7160	271	71	,	,	PUNCT
ejpam-7160	271	72	{	{	PUNCT
ejpam-7160	271	73	π1	π1	NOUN
ejpam-7160	271	74	,	,	PUNCT
ejpam-7160	271	75	π2	π2	PROPN
ejpam-7160	271	76	}	}	PUNCT
ejpam-7160	271	77	,	,	PUNCT
ejpam-7160	271	78	{	{	PUNCT
ejpam-7160	271	79	π2	π2	ADV
ejpam-7160	271	80	,	,	PUNCT
ejpam-7160	271	81	π3	π3	NOUN
ejpam-7160	271	82	}	}	PUNCT
ejpam-7160	271	83	,	,	PUNCT
ejpam-7160	271	84	{	{	PUNCT
ejpam-7160	271	85	π2	π2	ADV
ejpam-7160	271	86	,	,	PUNCT
ejpam-7160	271	87	π4	π4	NOUN
ejpam-7160	271	88	}	}	PUNCT
ejpam-7160	271	89	,	,	PUNCT
ejpam-7160	271	90	{	{	PUNCT
ejpam-7160	271	91	π1	π1	NOUN
ejpam-7160	271	92	,	,	PUNCT
ejpam-7160	271	93	π2	π2	ADJ
ejpam-7160	271	94	,	,	PUNCT
ejpam-7160	271	95	π3	π3	NOUN
ejpam-7160	271	96	}	}	PUNCT
ejpam-7160	271	97	,	,	PUNCT
ejpam-7160	271	98	{	{	PUNCT
ejpam-7160	271	99	π1	π1	NOUN
ejpam-7160	271	100	,	,	PUNCT
ejpam-7160	271	101	π2	π2	PROPN
ejpam-7160	271	102	,	,	PUNCT
ejpam-7160	271	103	π4	π4	NOUN
ejpam-7160	271	104	}	}	PUNCT
ejpam-7160	271	105	,	,	PUNCT
ejpam-7160	271	106	{	{	PUNCT
ejpam-7160	271	107	π2	π2	ADV
ejpam-7160	271	108	,	,	PUNCT
ejpam-7160	271	109	π3	π3	NOUN
ejpam-7160	271	110	,	,	PUNCT
ejpam-7160	271	111	π4	π4	PROPN
ejpam-7160	271	112	}	}	PUNCT
ejpam-7160	271	113	,	,	PUNCT
ejpam-7160	271	114	π	π	PROPN
ejpam-7160	271	115	,	,	PUNCT
ejpam-7160	271	116	ϕ	ϕ	NOUN
ejpam-7160	271	117	}	}	PUNCT
ejpam-7160	271	118	.	.	PUNCT
ejpam-7160	272	1	(	(	PUNCT
ejpam-7160	272	2	6	6	NUM
ejpam-7160	272	3	)	)	PUNCT
ejpam-7160	272	4	τmn	τmn	NOUN
ejpam-7160	272	5	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	272	6	=	=	PUNCT
ejpam-7160	272	7	{	{	PUNCT
ejpam-7160	272	8	π	π	PROPN
ejpam-7160	272	9	,	,	PUNCT
ejpam-7160	272	10	ϕ	ϕ	NOUN
ejpam-7160	272	11	,	,	PUNCT
ejpam-7160	272	12	{	{	PUNCT
ejpam-7160	272	13	π1	π1	NOUN
ejpam-7160	272	14	}	}	PUNCT
ejpam-7160	272	15	,	,	PUNCT
ejpam-7160	272	16	{	{	PUNCT
ejpam-7160	272	17	π4	π4	PROPN
ejpam-7160	272	18	}	}	PUNCT
ejpam-7160	272	19	,	,	PUNCT
ejpam-7160	272	20	{	{	PUNCT
ejpam-7160	272	21	π1	π1	NOUN
ejpam-7160	272	22	,	,	PUNCT
ejpam-7160	272	23	π4	π4	PROPN
ejpam-7160	272	24	}	}	PUNCT
ejpam-7160	272	25	,	,	PUNCT
ejpam-7160	272	26	{	{	PUNCT
ejpam-7160	272	27	π2	π2	ADV
ejpam-7160	272	28	,	,	PUNCT
ejpam-7160	272	29	π3	π3	NOUN
ejpam-7160	272	30	}	}	PUNCT
ejpam-7160	272	31	,	,	PUNCT
ejpam-7160	272	32	{	{	PUNCT
ejpam-7160	272	33	π1	π1	NOUN
ejpam-7160	272	34	,	,	PUNCT
ejpam-7160	272	35	π2	π2	ADJ
ejpam-7160	272	36	,	,	PUNCT
ejpam-7160	272	37	π3	π3	NOUN
ejpam-7160	272	38	}	}	PUNCT
ejpam-7160	272	39	,	,	PUNCT
ejpam-7160	272	40	{	{	PUNCT
ejpam-7160	272	41	π2	π2	ADV
ejpam-7160	272	42	,	,	PUNCT
ejpam-7160	272	43	π3	π3	NOUN
ejpam-7160	272	44	,	,	PUNCT
ejpam-7160	272	45	π4	π4	PROPN
ejpam-7160	272	46	}	}	PUNCT
ejpam-7160	272	47	}	}	PUNCT
ejpam-7160	272	48	,	,	PUNCT
ejpam-7160	272	49	and	and	CCONJ
ejpam-7160	272	50	τlmn	τlmn	NOUN
ejpam-7160	272	51	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	272	52	=	=	SYM
ejpam-7160	272	53	{	{	PUNCT
ejpam-7160	272	54	{	{	PUNCT
ejpam-7160	272	55	π1	π1	NOUN
ejpam-7160	272	56	}	}	PUNCT
ejpam-7160	272	57	,	,	PUNCT
ejpam-7160	272	58	{	{	PUNCT
ejpam-7160	272	59	π2	π2	ADV
ejpam-7160	272	60	}	}	PUNCT
ejpam-7160	272	61	,	,	PUNCT
ejpam-7160	272	62	{	{	PUNCT
ejpam-7160	272	63	π4	π4	PROPN
ejpam-7160	272	64	}	}	PUNCT
ejpam-7160	272	65	,	,	PUNCT
ejpam-7160	272	66	{	{	PUNCT
ejpam-7160	272	67	π1	π1	NOUN
ejpam-7160	272	68	,	,	PUNCT
ejpam-7160	272	69	π2	π2	PROPN
ejpam-7160	272	70	}	}	PUNCT
ejpam-7160	272	71	,	,	PUNCT
ejpam-7160	272	72	{	{	PUNCT
ejpam-7160	272	73	π1	π1	NOUN
ejpam-7160	272	74	,	,	PUNCT
ejpam-7160	272	75	π4	π4	PROPN
ejpam-7160	272	76	}	}	PUNCT
ejpam-7160	272	77	,	,	PUNCT
ejpam-7160	272	78	{	{	PUNCT
ejpam-7160	272	79	π2	π2	ADV
ejpam-7160	272	80	,	,	PUNCT
ejpam-7160	272	81	π3	π3	NOUN
ejpam-7160	272	82	}	}	PUNCT
ejpam-7160	272	83	,	,	PUNCT
ejpam-7160	272	84	{	{	PUNCT
ejpam-7160	272	85	π2	π2	ADV
ejpam-7160	272	86	,	,	PUNCT
ejpam-7160	272	87	π4	π4	NOUN
ejpam-7160	272	88	}	}	PUNCT
ejpam-7160	272	89	,	,	PUNCT
ejpam-7160	272	90	{	{	PUNCT
ejpam-7160	272	91	π1	π1	NOUN
ejpam-7160	272	92	,	,	PUNCT
ejpam-7160	272	93	π2	π2	ADJ
ejpam-7160	272	94	,	,	PUNCT
ejpam-7160	272	95	π3	π3	NOUN
ejpam-7160	272	96	}	}	PUNCT
ejpam-7160	272	97	,	,	PUNCT
ejpam-7160	272	98	{	{	PUNCT
ejpam-7160	272	99	π1	π1	NOUN
ejpam-7160	272	100	,	,	PUNCT
ejpam-7160	272	101	π2	π2	PROPN
ejpam-7160	272	102	,	,	PUNCT
ejpam-7160	272	103	π4	π4	NOUN
ejpam-7160	272	104	}	}	PUNCT
ejpam-7160	272	105	,	,	PUNCT
ejpam-7160	272	106	{	{	PUNCT
ejpam-7160	272	107	π2	π2	ADV
ejpam-7160	272	108	,	,	PUNCT
ejpam-7160	272	109	π3	π3	NOUN
ejpam-7160	272	110	,	,	PUNCT
ejpam-7160	272	111	π4},π	π4},π	NOUN
ejpam-7160	272	112	,	,	PUNCT
ejpam-7160	272	113	ϕ	ϕ	NOUN
ejpam-7160	272	114	}	}	PUNCT
ejpam-7160	272	115	.	.	PUNCT
ejpam-7160	273	1	(	(	PUNCT
ejpam-7160	273	2	7	7	X
ejpam-7160	273	3	)	)	PUNCT
ejpam-7160	273	4	τmn	τmn	ADJ
ejpam-7160	273	5	⟨u⟩	⟨u⟩	PROPN
ejpam-7160	273	6	=	=	SYM
ejpam-7160	273	7	{	{	PUNCT
ejpam-7160	273	8	π	π	PROPN
ejpam-7160	273	9	,	,	PUNCT
ejpam-7160	273	10	ϕ	ϕ	NOUN
ejpam-7160	273	11	,	,	PUNCT
ejpam-7160	273	12	{	{	PUNCT
ejpam-7160	273	13	π4	π4	PROPN
ejpam-7160	273	14	}	}	PUNCT
ejpam-7160	273	15	,	,	PUNCT
ejpam-7160	273	16	{	{	PUNCT
ejpam-7160	273	17	π2	π2	ADV
ejpam-7160	273	18	,	,	PUNCT
ejpam-7160	273	19	π3	π3	NOUN
ejpam-7160	273	20	}	}	PUNCT
ejpam-7160	273	21	,	,	PUNCT
ejpam-7160	273	22	{	{	PUNCT
ejpam-7160	273	23	π1	π1	NOUN
ejpam-7160	273	24	,	,	PUNCT
ejpam-7160	273	25	π2	π2	ADJ
ejpam-7160	273	26	,	,	PUNCT
ejpam-7160	273	27	π3	π3	NOUN
ejpam-7160	273	28	}	}	PUNCT
ejpam-7160	273	29	,	,	PUNCT
ejpam-7160	273	30	{	{	PUNCT
ejpam-7160	273	31	π2	π2	ADV
ejpam-7160	273	32	,	,	PUNCT
ejpam-7160	273	33	π3	π3	NOUN
ejpam-7160	273	34	,	,	PUNCT
ejpam-7160	273	35	π4	π4	PROPN
ejpam-7160	273	36	}	}	PUNCT
ejpam-7160	273	37	}	}	PUNCT
ejpam-7160	273	38	,	,	PUNCT
ejpam-7160	273	39	and	and	CCONJ
ejpam-7160	273	40	τlmn	τlmn	NOUN
ejpam-7160	273	41	⟨u⟩	⟨u⟩	PROPN
ejpam-7160	273	42	=	=	SYM
ejpam-7160	273	43	{	{	PUNCT
ejpam-7160	273	44	{	{	PUNCT
ejpam-7160	273	45	π2	π2	ADV
ejpam-7160	273	46	}	}	PUNCT
ejpam-7160	273	47	,	,	PUNCT
ejpam-7160	273	48	{	{	PUNCT
ejpam-7160	273	49	π4	π4	PROPN
ejpam-7160	273	50	}	}	PUNCT
ejpam-7160	273	51	,	,	PUNCT
ejpam-7160	273	52	{	{	PUNCT
ejpam-7160	273	53	π1	π1	NOUN
ejpam-7160	273	54	,	,	PUNCT
ejpam-7160	273	55	π2	π2	PROPN
ejpam-7160	273	56	}	}	PUNCT
ejpam-7160	273	57	,	,	PUNCT
ejpam-7160	273	58	{	{	PUNCT
ejpam-7160	273	59	π2	π2	ADV
ejpam-7160	273	60	,	,	PUNCT
ejpam-7160	273	61	π3	π3	NOUN
ejpam-7160	273	62	}	}	PUNCT
ejpam-7160	273	63	,	,	PUNCT
ejpam-7160	273	64	{	{	PUNCT
ejpam-7160	273	65	π2	π2	ADV
ejpam-7160	273	66	,	,	PUNCT
ejpam-7160	273	67	π4	π4	NOUN
ejpam-7160	273	68	}	}	PUNCT
ejpam-7160	273	69	,	,	PUNCT
ejpam-7160	273	70	{	{	PUNCT
ejpam-7160	273	71	π1	π1	NOUN
ejpam-7160	273	72	,	,	PUNCT
ejpam-7160	273	73	π2	π2	ADJ
ejpam-7160	273	74	,	,	PUNCT
ejpam-7160	273	75	π3	π3	NOUN
ejpam-7160	273	76	}	}	PUNCT
ejpam-7160	273	77	,	,	PUNCT
ejpam-7160	273	78	{	{	PUNCT
ejpam-7160	273	79	π1	π1	NOUN
ejpam-7160	273	80	,	,	PUNCT
ejpam-7160	273	81	π2	π2	PROPN
ejpam-7160	273	82	,	,	PUNCT
ejpam-7160	273	83	π4	π4	NOUN
ejpam-7160	273	84	}	}	PUNCT
ejpam-7160	273	85	,	,	PUNCT
ejpam-7160	273	86	{	{	PUNCT
ejpam-7160	273	87	π2	π2	ADV
ejpam-7160	273	88	,	,	PUNCT
ejpam-7160	273	89	π3	π3	NOUN
ejpam-7160	273	90	,	,	PUNCT
ejpam-7160	273	91	π4	π4	PROPN
ejpam-7160	273	92	}	}	PUNCT
ejpam-7160	273	93	,	,	PUNCT
ejpam-7160	273	94	π	π	PROPN
ejpam-7160	273	95	,	,	PUNCT
ejpam-7160	273	96	ϕ	ϕ	NOUN
ejpam-7160	273	97	}	}	PUNCT
ejpam-7160	273	98	.	.	PUNCT
ejpam-7160	274	1	(	(	PUNCT
ejpam-7160	274	2	8)	8)	NUM
ejpam-7160	274	3	τmn	τmn	NOUN
ejpam-7160	274	4	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	274	5	=	=	PUNCT
ejpam-7160	274	6	{	{	PUNCT
ejpam-7160	274	7	π	π	PROPN
ejpam-7160	274	8	,	,	PUNCT
ejpam-7160	274	9	ϕ	ϕ	NOUN
ejpam-7160	274	10	,	,	PUNCT
ejpam-7160	274	11	{	{	PUNCT
ejpam-7160	274	12	π1	π1	NOUN
ejpam-7160	274	13	}	}	PUNCT
ejpam-7160	274	14	,	,	PUNCT
ejpam-7160	274	15	{	{	PUNCT
ejpam-7160	274	16	π2	π2	ADV
ejpam-7160	274	17	}	}	PUNCT
ejpam-7160	274	18	,	,	PUNCT
ejpam-7160	274	19	{	{	PUNCT
ejpam-7160	274	20	π4	π4	PROPN
ejpam-7160	274	21	}	}	PUNCT
ejpam-7160	274	22	,	,	PUNCT
ejpam-7160	274	23	{	{	PUNCT
ejpam-7160	274	24	π1	π1	NOUN
ejpam-7160	274	25	,	,	PUNCT
ejpam-7160	274	26	π2	π2	PROPN
ejpam-7160	274	27	}	}	PUNCT
ejpam-7160	274	28	,	,	PUNCT
ejpam-7160	274	29	{	{	PUNCT
ejpam-7160	274	30	π1	π1	NOUN
ejpam-7160	274	31	,	,	PUNCT
ejpam-7160	274	32	π4	π4	PROPN
ejpam-7160	274	33	}	}	PUNCT
ejpam-7160	274	34	,	,	PUNCT
ejpam-7160	274	35	{	{	PUNCT
ejpam-7160	274	36	π2	π2	ADV
ejpam-7160	274	37	,	,	PUNCT
ejpam-7160	274	38	π3	π3	NOUN
ejpam-7160	274	39	}	}	PUNCT
ejpam-7160	274	40	,	,	PUNCT
ejpam-7160	274	41	{	{	PUNCT
ejpam-7160	274	42	π2	π2	ADV
ejpam-7160	274	43	,	,	PUNCT
ejpam-7160	274	44	π4	π4	NOUN
ejpam-7160	274	45	}	}	PUNCT
ejpam-7160	274	46	,	,	PUNCT
ejpam-7160	274	47	{	{	PUNCT
ejpam-7160	274	48	π1	π1	NOUN
ejpam-7160	274	49	,	,	PUNCT
ejpam-7160	274	50	π2	π2	ADJ
ejpam-7160	274	51	,	,	PUNCT
ejpam-7160	274	52	π3	π3	NOUN
ejpam-7160	274	53	}	}	PUNCT
ejpam-7160	274	54	,	,	PUNCT
ejpam-7160	274	55	{	{	PUNCT
ejpam-7160	274	56	π1	π1	NOUN
ejpam-7160	274	57	,	,	PUNCT
ejpam-7160	274	58	π2	π2	PROPN
ejpam-7160	274	59	,	,	PUNCT
ejpam-7160	274	60	π4	π4	NOUN
ejpam-7160	274	61	}	}	PUNCT
ejpam-7160	274	62	,	,	PUNCT
ejpam-7160	274	63	{	{	PUNCT
ejpam-7160	274	64	π2	π2	ADV
ejpam-7160	274	65	,	,	PUNCT
ejpam-7160	274	66	π3	π3	NOUN
ejpam-7160	274	67	,	,	PUNCT
ejpam-7160	274	68	π4	π4	PROPN
ejpam-7160	274	69	}	}	PUNCT
ejpam-7160	274	70	}	}	PUNCT
ejpam-7160	274	71	,	,	PUNCT
ejpam-7160	274	72	and	and	CCONJ
ejpam-7160	274	73	τlmn	τlmn	NOUN
ejpam-7160	274	74	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	274	75	=	=	SYM
ejpam-7160	274	76	{	{	PUNCT
ejpam-7160	274	77	{	{	PUNCT
ejpam-7160	274	78	π1	π1	NOUN
ejpam-7160	274	79	}	}	PUNCT
ejpam-7160	274	80	,	,	PUNCT
ejpam-7160	274	81	{	{	PUNCT
ejpam-7160	274	82	π2	π2	ADV
ejpam-7160	274	83	}	}	PUNCT
ejpam-7160	274	84	,	,	PUNCT
ejpam-7160	274	85	{	{	PUNCT
ejpam-7160	274	86	π4	π4	PROPN
ejpam-7160	274	87	}	}	PUNCT
ejpam-7160	274	88	,	,	PUNCT
ejpam-7160	274	89	{	{	PUNCT
ejpam-7160	274	90	π1	π1	NOUN
ejpam-7160	274	91	,	,	PUNCT
ejpam-7160	274	92	π2	π2	PROPN
ejpam-7160	274	93	}	}	PUNCT
ejpam-7160	274	94	,	,	PUNCT
ejpam-7160	274	95	{	{	PUNCT
ejpam-7160	274	96	π1	π1	NOUN
ejpam-7160	274	97	,	,	PUNCT
ejpam-7160	274	98	π4	π4	PROPN
ejpam-7160	274	99	}	}	PUNCT
ejpam-7160	274	100	,	,	PUNCT
ejpam-7160	274	101	{	{	PUNCT
ejpam-7160	274	102	π2	π2	ADV
ejpam-7160	274	103	,	,	PUNCT
ejpam-7160	274	104	π3	π3	NOUN
ejpam-7160	274	105	}	}	PUNCT
ejpam-7160	274	106	,	,	PUNCT
ejpam-7160	274	107	{	{	PUNCT
ejpam-7160	274	108	π2	π2	ADV
ejpam-7160	274	109	,	,	PUNCT
ejpam-7160	274	110	π4	π4	NOUN
ejpam-7160	274	111	}	}	PUNCT
ejpam-7160	274	112	,	,	PUNCT
ejpam-7160	274	113	{	{	PUNCT
ejpam-7160	274	114	π1	π1	NOUN
ejpam-7160	274	115	,	,	PUNCT
ejpam-7160	274	116	π2	π2	ADJ
ejpam-7160	274	117	,	,	PUNCT
ejpam-7160	274	118	π3	π3	NOUN
ejpam-7160	274	119	}	}	PUNCT
ejpam-7160	274	120	,	,	PUNCT
ejpam-7160	274	121	{	{	PUNCT
ejpam-7160	274	122	π1	π1	NOUN
ejpam-7160	274	123	,	,	PUNCT
ejpam-7160	274	124	π2	π2	PROPN
ejpam-7160	274	125	,	,	PUNCT
ejpam-7160	274	126	π4	π4	NOUN
ejpam-7160	274	127	}	}	PUNCT
ejpam-7160	274	128	,	,	PUNCT
ejpam-7160	274	129	{	{	PUNCT
ejpam-7160	274	130	π2	π2	ADV
ejpam-7160	274	131	,	,	PUNCT
ejpam-7160	274	132	π3	π3	NOUN
ejpam-7160	274	133	,	,	PUNCT
ejpam-7160	274	134	π4},π	π4},π	NOUN
ejpam-7160	274	135	,	,	PUNCT
ejpam-7160	274	136	ϕ	ϕ	NOUN
ejpam-7160	274	137	}	}	PUNCT
ejpam-7160	274	138	.	.	PUNCT
ejpam-7160	275	1	remark	remark	PROPN
ejpam-7160	275	2	2	2	NUM
ejpam-7160	275	3	.	.	NOUN
ejpam-7160	275	4	example	example	NOUN
ejpam-7160	275	5	3.9	3.9	NUM
ejpam-7160	275	6	indicates	indicate	VERB
ejpam-7160	275	7	that	that	SCONJ
ejpam-7160	275	8	the	the	DET
ejpam-7160	275	9	method	method	NOUN
ejpam-7160	275	10	described	describe	VERB
ejpam-7160	275	11	in	in	ADP
ejpam-7160	275	12	this	this	DET
ejpam-7160	275	13	section	section	NOUN
ejpam-7160	275	14	in	in	ADP
ejpam-7160	275	15	distinct	distinct	NOUN
ejpam-7160	275	16	from	from	ADP
ejpam-7160	275	17	those	those	PRON
ejpam-7160	275	18	in	in	ADP
ejpam-7160	275	19	[	[	X
ejpam-7160	275	20	16	16	NUM
ejpam-7160	275	21	,	,	PUNCT
ejpam-7160	275	22	19	19	NUM
ejpam-7160	275	23	,	,	PUNCT
ejpam-7160	275	24	52	52	NUM
ejpam-7160	275	25	]	]	PUNCT
ejpam-7160	275	26	.	.	PUNCT
ejpam-7160	276	1	proposition	proposition	NOUN
ejpam-7160	276	2	2	2	NUM
ejpam-7160	276	3	.	.	PUNCT
ejpam-7160	276	4	while	while	SCONJ
ejpam-7160	276	5	l	l	NOUN
ejpam-7160	276	6	is	be	AUX
ejpam-7160	276	7	a	a	DET
ejpam-7160	276	8	grill	grill	NOUN
ejpam-7160	276	9	on	on	ADP
ejpam-7160	276	10	π	π	PROPN
ejpam-7160	276	11	,	,	PUNCT
ejpam-7160	276	12	(	(	PUNCT
ejpam-7160	276	13	π,×,mn	π,×,mn	ADV
ejpam-7160	276	14	ι	ι	PROPN
ejpam-7160	276	15	)	)	PUNCT
ejpam-7160	276	16	is	be	AUX
ejpam-7160	276	17	a	a	DET
ejpam-7160	276	18	mn	mn	PROPN
ejpam-7160	276	19	ι	ι	AUX
ejpam-7160	276	20	-	-	PUNCT
ejpam-7160	276	21	ns	ns	NOUN
ejpam-7160	276	22	.	.	PUNCT
ejpam-7160	277	1	consequently	consequently	ADV
ejpam-7160	277	2	,	,	PUNCT
ejpam-7160	277	3	the	the	DET
ejpam-7160	277	4	following	follow	VERB
ejpam-7160	277	5	claims	claim	NOUN
ejpam-7160	277	6	are	be	AUX
ejpam-7160	277	7	accurate	accurate	ADJ
ejpam-7160	277	8	:	:	PUNCT
ejpam-7160	277	9	(	(	PUNCT
ejpam-7160	277	10	1	1	X
ejpam-7160	277	11	)	)	PUNCT
ejpam-7160	277	12	τlmnu	τlmnu	NOUN
ejpam-7160	277	13	⊑	⊑	DET
ejpam-7160	277	14	τlmn	τlmn	NOUN
ejpam-7160	277	15	r	r	NOUN
ejpam-7160	277	16	;	;	PUNCT
ejpam-7160	277	17	(	(	PUNCT
ejpam-7160	277	18	2	2	X
ejpam-7160	277	19	)	)	PUNCT
ejpam-7160	277	20	τlmnu	τlmnu	NOUN
ejpam-7160	277	21	⊑	⊑	DET
ejpam-7160	277	22	τlmn	τlmn	NOUN
ejpam-7160	277	23	l	l	NOUN
ejpam-7160	277	24	;	;	PUNCT
ejpam-7160	277	25	(	(	PUNCT
ejpam-7160	277	26	3	3	X
ejpam-7160	277	27	)	)	PUNCT
ejpam-7160	277	28	τlmn	τlmn	NOUN
ejpam-7160	277	29	r	r	NOUN
ejpam-7160	277	30	⊑	⊑	X
ejpam-7160	277	31	τlmn	τlmn	NOUN
ejpam-7160	278	1	i	i	PRON
ejpam-7160	278	2	;	;	PUNCT
ejpam-7160	279	1	a.	a.	NOUN
ejpam-7160	279	2	a.	a.	PROPN
ejpam-7160	279	3	azzam	azzam	PROPN
ejpam-7160	279	4	et	et	PROPN
ejpam-7160	279	5	al	al	PROPN
ejpam-7160	279	6	.	.	PUNCT
ejpam-7160	279	7	/	/	SYM
ejpam-7160	279	8	eur	eur	PROPN
ejpam-7160	279	9	.	.	PUNCT
ejpam-7160	280	1	j.	j.	PROPN
ejpam-7160	280	2	pure	pure	PROPN
ejpam-7160	280	3	appl	appl	PROPN
ejpam-7160	280	4	.	.	PROPN
ejpam-7160	280	5	math	math	PROPN
ejpam-7160	280	6	,	,	PUNCT
ejpam-7160	280	7	18	18	NUM
ejpam-7160	280	8	(	(	PUNCT
ejpam-7160	280	9	4	4	NUM
ejpam-7160	280	10	)	)	PUNCT
ejpam-7160	280	11	(	(	PUNCT
ejpam-7160	280	12	2025	2025	NUM
ejpam-7160	280	13	)	)	PUNCT
ejpam-7160	280	14	,	,	PUNCT
ejpam-7160	280	15	7160	7160	NUM
ejpam-7160	280	16	11	11	NUM
ejpam-7160	280	17	of	of	ADP
ejpam-7160	280	18	22	22	NUM
ejpam-7160	280	19	(	(	PUNCT
ejpam-7160	280	20	4	4	NUM
ejpam-7160	280	21	)	)	PUNCT
ejpam-7160	280	22	τlmn	τlmn	NOUN
ejpam-7160	280	23	l	l	NOUN
ejpam-7160	280	24	⊑	⊑	X
ejpam-7160	280	25	τlmn	τlmn	NOUN
ejpam-7160	281	1	i	i	PRON
ejpam-7160	281	2	;	;	PUNCT
ejpam-7160	281	3	(	(	PUNCT
ejpam-7160	281	4	5	5	X
ejpam-7160	281	5	)	)	PUNCT
ejpam-7160	281	6	τlmn	τlmn	NOUN
ejpam-7160	281	7	⟨u⟩	⟨u⟩	PROPN
ejpam-7160	281	8	⊑	⊑	DET
ejpam-7160	281	9	τlmn	τlmn	NOUN
ejpam-7160	282	1	⟨r⟩	⟨r⟩	X
ejpam-7160	282	2	;	;	PUNCT
ejpam-7160	282	3	(	(	PUNCT
ejpam-7160	282	4	6	6	NUM
ejpam-7160	282	5	)	)	PUNCT
ejpam-7160	282	6	τlmn	τlmn	NOUN
ejpam-7160	282	7	⟨u⟩	⟨u⟩	PROPN
ejpam-7160	282	8	⊑	⊑	PRON
ejpam-7160	282	9	τlmn	τlmn	NOUN
ejpam-7160	282	10	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	282	11	;	;	PUNCT
ejpam-7160	282	12	(	(	PUNCT
ejpam-7160	282	13	7	7	X
ejpam-7160	282	14	)	)	PUNCT
ejpam-7160	282	15	τlmn	τlmn	NOUN
ejpam-7160	283	1	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	283	2	⊑	⊑	DET
ejpam-7160	283	3	τlmn	τlmn	PROPN
ejpam-7160	283	4	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	283	5	;	;	PUNCT
ejpam-7160	283	6	(	(	PUNCT
ejpam-7160	283	7	8)	8)	NUM
ejpam-7160	283	8	τlmn	τlmn	NOUN
ejpam-7160	283	9	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	283	10	⊑	⊑	PRON
ejpam-7160	283	11	τlmn	τlmn	PROPN
ejpam-7160	283	12	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	283	13	.	.	PUNCT
ejpam-7160	284	1	proof	proof	NOUN
ejpam-7160	284	2	.	.	PUNCT
ejpam-7160	285	1	let	let	VERB
ejpam-7160	285	2	c	c	NOUN
ejpam-7160	285	3	∈	∈	NOUN
ejpam-7160	285	4	τlmnu	τlmnu	NOUN
ejpam-7160	285	5	.	.	PUNCT
ejpam-7160	286	1	consequently	consequently	ADV
ejpam-7160	286	2	,	,	PUNCT
ejpam-7160	286	3	mn	mn	PROPN
ejpam-7160	286	4	u(π1	u(π1	NOUN
ejpam-7160	286	5	)	)	PUNCT
ejpam-7160	286	6	⊓	⊓	PROPN
ejpam-7160	286	7	cc	cc	PROPN
ejpam-7160	286	8	/∈	/∈	PROPN
ejpam-7160	286	9	l	l	NOUN
ejpam-7160	286	10	for	for	ADP
ejpam-7160	286	11	every	every	DET
ejpam-7160	286	12	π1	π1	PROPN
ejpam-7160	286	13	∈	∈	PROPN
ejpam-7160	286	14	c.	c.	NOUN
ejpam-7160	286	15	consequently	consequently	ADV
ejpam-7160	286	16	,	,	PUNCT
ejpam-7160	286	17	(	(	PUNCT
ejpam-7160	286	18	mn	mn	PROPN
ejpam-7160	286	19	r(π1)⊔mn	r(π1)⊔mn	PROPN
ejpam-7160	286	20	l(π1))⊓cc	l(π1))⊓cc	NOUN
ejpam-7160	286	21	/∈	/∈	PUNCT
ejpam-7160	286	22	l,∀π1	l,∀π1	PROPN
ejpam-7160	286	23	∈	∈	PROPN
ejpam-7160	286	24	c.	c.	PROPN
ejpam-7160	286	25	therefore	therefore	ADV
ejpam-7160	286	26	,	,	PUNCT
ejpam-7160	286	27	for	for	ADP
ejpam-7160	286	28	every	every	DET
ejpam-7160	286	29	π1	π1	ADJ
ejpam-7160	286	30	∈	∈	PROPN
ejpam-7160	286	31	c	c	X
ejpam-7160	286	32	,	,	PUNCT
ejpam-7160	286	33	mn	mn	PROPN
ejpam-7160	286	34	r(π1)⊓cc	r(π1)⊓cc	PROPN
ejpam-7160	286	35	/∈	/∈	PUNCT
ejpam-7160	287	1	l	l	NOUN
ejpam-7160	287	2	,	,	PUNCT
ejpam-7160	287	3	and	and	CCONJ
ejpam-7160	287	4	mn	mn	PROPN
ejpam-7160	287	5	l(π1	l(π1	PROPN
ejpam-7160	287	6	)	)	PUNCT
ejpam-7160	288	1	⊓	⊓	PROPN
ejpam-7160	288	2	cc	cc	PROPN
ejpam-7160	288	3	/∈	/∈	PROPN
ejpam-7160	288	4	l.	l.	PROPN
ejpam-7160	288	5	consequently	consequently	ADV
ejpam-7160	288	6	,	,	PUNCT
ejpam-7160	288	7	c	c	PROPN
ejpam-7160	288	8	∈	∈	PROPN
ejpam-7160	288	9	mn	mn	PROPN
ejpam-7160	288	10	r	r	NOUN
ejpam-7160	288	11	for	for	ADP
ejpam-7160	288	12	all	all	DET
ejpam-7160	288	13	π1	π1	ADJ
ejpam-7160	288	14	∈	∈	PROPN
ejpam-7160	288	15	c	c	NOUN
ejpam-7160	288	16	,	,	PUNCT
ejpam-7160	288	17	and	and	CCONJ
ejpam-7160	288	18	c	c	PROPN
ejpam-7160	288	19	∈	∈	PROPN
ejpam-7160	288	20	mn	mn	PROPN
ejpam-7160	288	21	l	l	PROPN
ejpam-7160	288	22	for	for	ADP
ejpam-7160	288	23	all	all	DET
ejpam-7160	288	24	π1	π1	PROPN
ejpam-7160	288	25	∈	∈	PROPN
ejpam-7160	288	26	c.	c.	NOUN
ejpam-7160	288	27	therefore	therefore	ADV
ejpam-7160	288	28	,	,	PUNCT
ejpam-7160	288	29	τlmnu	τlmnu	ADP
ejpam-7160	288	30	⊑	⊑	DET
ejpam-7160	288	31	τlmn	τlmn	ADJ
ejpam-7160	288	32	r	r	NOUN
ejpam-7160	288	33	and	and	CCONJ
ejpam-7160	288	34	this	this	PRON
ejpam-7160	288	35	demonstrates	demonstrate	VERB
ejpam-7160	288	36	(	(	PUNCT
ejpam-7160	288	37	1	1	NUM
ejpam-7160	288	38	)	)	PUNCT
ejpam-7160	288	39	,	,	PUNCT
ejpam-7160	288	40	(	(	PUNCT
ejpam-7160	288	41	2	2	NUM
ejpam-7160	288	42	)	)	PUNCT
ejpam-7160	288	43	,	,	PUNCT
ejpam-7160	288	44	(	(	PUNCT
ejpam-7160	288	45	3	3	X
ejpam-7160	288	46	)	)	PUNCT
ejpam-7160	288	47	and	and	CCONJ
ejpam-7160	288	48	(	(	PUNCT
ejpam-7160	288	49	4	4	NUM
ejpam-7160	288	50	)	)	PUNCT
ejpam-7160	288	51	.	.	PUNCT
ejpam-7160	289	1	similar	similar	ADJ
ejpam-7160	289	2	evidence	evidence	NOUN
ejpam-7160	289	3	can	can	AUX
ejpam-7160	289	4	be	be	AUX
ejpam-7160	289	5	used	use	VERB
ejpam-7160	289	6	to	to	PART
ejpam-7160	289	7	support	support	VERB
ejpam-7160	289	8	statements	statement	NOUN
ejpam-7160	289	9	(	(	PUNCT
ejpam-7160	289	10	5	5	NUM
ejpam-7160	289	11	)	)	PUNCT
ejpam-7160	289	12	,	,	PUNCT
ejpam-7160	289	13	(	(	PUNCT
ejpam-7160	289	14	6	6	NUM
ejpam-7160	289	15	)	)	PUNCT
ejpam-7160	289	16	,	,	PUNCT
ejpam-7160	289	17	(	(	PUNCT
ejpam-7160	289	18	7	7	NUM
ejpam-7160	289	19	)	)	PUNCT
ejpam-7160	289	20	,	,	PUNCT
ejpam-7160	289	21	and	and	CCONJ
ejpam-7160	289	22	(	(	PUNCT
ejpam-7160	289	23	8)	8)	NUM
ejpam-7160	289	24	.	.	PUNCT
ejpam-7160	289	25	corollary	corollary	ADJ
ejpam-7160	289	26	1	1	NUM
ejpam-7160	289	27	.	.	PUNCT
ejpam-7160	290	1	let	let	AUX
ejpam-7160	290	2	(	(	PUNCT
ejpam-7160	290	3	π,×	π,×	PROPN
ejpam-7160	290	4	,	,	PUNCT
ejpam-7160	290	5	ζι	ζι	NOUN
ejpam-7160	290	6	)	)	PUNCT
ejpam-7160	290	7	denote	denote	VERB
ejpam-7160	290	8	a	a	DET
ejpam-7160	290	9	ι	ι	NOUN
ejpam-7160	290	10	-	-	PUNCT
ejpam-7160	290	11	ns	ns	ADJ
ejpam-7160	290	12	,	,	PUNCT
ejpam-7160	290	13	and	and	CCONJ
ejpam-7160	290	14	let	let	VERB
ejpam-7160	290	15	l	l	NOUN
ejpam-7160	290	16	represent	represent	VERB
ejpam-7160	290	17	a	a	DET
ejpam-7160	290	18	grill	grill	NOUN
ejpam-7160	290	19	on	on	ADP
ejpam-7160	290	20	π	π	PROPN
ejpam-7160	290	21	.	.	PUNCT
ejpam-7160	291	1	subsequently	subsequently	ADV
ejpam-7160	291	2	,	,	PUNCT
ejpam-7160	291	3	the	the	DET
ejpam-7160	291	4	ensuing	ensue	VERB
ejpam-7160	291	5	statements	statement	NOUN
ejpam-7160	291	6	are	be	AUX
ejpam-7160	291	7	accurate	accurate	ADJ
ejpam-7160	291	8	:	:	PUNCT
ejpam-7160	291	9	(	(	PUNCT
ejpam-7160	291	10	1	1	X
ejpam-7160	291	11	)	)	PUNCT
ejpam-7160	291	12	τlmnu	τlmnu	NOUN
ejpam-7160	291	13	⊑	⊑	DET
ejpam-7160	291	14	τlmn	τlmn	NOUN
ejpam-7160	291	15	r	r	NOUN
ejpam-7160	291	16	⊑	⊑	X
ejpam-7160	291	17	τlmn	τlmn	NOUN
ejpam-7160	291	18	i	i	PRON
ejpam-7160	291	19	;	;	PUNCT
ejpam-7160	291	20	(	(	PUNCT
ejpam-7160	291	21	2	2	X
ejpam-7160	291	22	)	)	PUNCT
ejpam-7160	291	23	τlmnu	τlmnu	NOUN
ejpam-7160	291	24	⊑	⊑	DET
ejpam-7160	291	25	τlmn	τlmn	NOUN
ejpam-7160	291	26	l	l	NOUN
ejpam-7160	291	27	⊑	⊑	DET
ejpam-7160	291	28	τlmn	τlmn	NOUN
ejpam-7160	291	29	i	i	PRON
ejpam-7160	291	30	;	;	PUNCT
ejpam-7160	291	31	(	(	PUNCT
ejpam-7160	291	32	3	3	X
ejpam-7160	291	33	)	)	PUNCT
ejpam-7160	291	34	τlmn	τlmn	NOUN
ejpam-7160	291	35	⟨u⟩	⟨u⟩	PROPN
ejpam-7160	291	36	⊑	⊑	PRON
ejpam-7160	291	37	τlmn	τlmn	NOUN
ejpam-7160	292	1	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	292	2	⊑	⊑	X
ejpam-7160	292	3	τ	τ	PROPN
ejpam-7160	292	4	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	292	5	mn	mn	PROPN
ejpam-7160	292	6	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	292	7	;	;	PUNCT
ejpam-7160	292	8	(	(	PUNCT
ejpam-7160	292	9	4	4	X
ejpam-7160	292	10	)	)	PUNCT
ejpam-7160	292	11	τlmn	τlmn	NOUN
ejpam-7160	292	12	⟨u⟩	⟨u⟩	PROPN
ejpam-7160	292	13	⊑	⊑	PRON
ejpam-7160	292	14	τlmn	τlmn	NOUN
ejpam-7160	292	15	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	292	16	⊑	⊑	PRON
ejpam-7160	292	17	τlmn	τlmn	PROPN
ejpam-7160	292	18	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	292	19	.	.	PUNCT
ejpam-7160	293	1	theorem	theorem	VERB
ejpam-7160	293	2	3.13	3.13	NUM
ejpam-7160	293	3	offers	offer	VERB
ejpam-7160	293	4	a	a	DET
ejpam-7160	293	5	distinctive	distinctive	ADJ
ejpam-7160	293	6	characterisation	characterisation	NOUN
ejpam-7160	293	7	of	of	ADP
ejpam-7160	293	8	the	the	DET
ejpam-7160	293	9	suggested	suggest	VERB
ejpam-7160	293	10	topologies	topology	NOUN
ejpam-7160	293	11	by	by	ADP
ejpam-7160	293	12	contrasting	contrast	VERB
ejpam-7160	293	13	τlmn	τlmn	NOUN
ejpam-7160	293	14	ι	ι	PROPN
ejpam-7160	293	15	and	and	CCONJ
ejpam-7160	293	16	τlmn	τlmn	NOUN
ejpam-7160	293	17	⟨ι⟩	⟨ι⟩	PROPN
ejpam-7160	293	18	.	.	PUNCT
ejpam-7160	294	1	thus	thus	ADV
ejpam-7160	294	2	,	,	PUNCT
ejpam-7160	294	3	corollary	corollary	ADJ
ejpam-7160	294	4	3.14	3.14	NUM
ejpam-7160	294	5	delineates	delineate	VERB
ejpam-7160	294	6	both	both	CCONJ
ejpam-7160	294	7	the	the	DET
ejpam-7160	294	8	smallest	small	ADJ
ejpam-7160	294	9	τlmn	τlmn	NOUN
ejpam-7160	294	10	r	r	NOUN
ejpam-7160	294	11	and	and	CCONJ
ejpam-7160	294	12	the	the	DET
ejpam-7160	294	13	greatest	great	ADJ
ejpam-7160	294	14	τlmn	τlmn	NOUN
ejpam-7160	294	15	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	294	16	.	.	PUNCT
ejpam-7160	295	1	theorem	theorem	VERB
ejpam-7160	295	2	6	6	NUM
ejpam-7160	295	3	.	.	PUNCT
ejpam-7160	296	1	if	if	SCONJ
ejpam-7160	296	2	(	(	PUNCT
ejpam-7160	296	3	π,×	π,×	PROPN
ejpam-7160	296	4	,	,	PUNCT
ejpam-7160	296	5	ζι	ζι	NOUN
ejpam-7160	296	6	)	)	PUNCT
ejpam-7160	296	7	constitutes	constitute	VERB
ejpam-7160	296	8	a	a	DET
ejpam-7160	296	9	ι	ι	ADV
ejpam-7160	296	10	-	-	PUNCT
ejpam-7160	296	11	ns	ns	ADJ
ejpam-7160	296	12	,	,	PUNCT
ejpam-7160	296	13	and	and	CCONJ
ejpam-7160	296	14	l	l	NOUN
ejpam-7160	296	15	represents	represent	VERB
ejpam-7160	296	16	a	a	DET
ejpam-7160	296	17	grill	grill	NOUN
ejpam-7160	296	18	on	on	ADP
ejpam-7160	296	19	π	π	PROPN
ejpam-7160	296	20	.	.	PUNCT
ejpam-7160	297	1	consequently	consequently	ADV
ejpam-7160	297	2	,	,	PUNCT
ejpam-7160	297	3	τlmn	τlmn	NOUN
ejpam-7160	297	4	ι	ι	ADP
ejpam-7160	297	5	⊑	⊑	DET
ejpam-7160	297	6	τlmn	τlmn	NOUN
ejpam-7160	298	1	⟨ι⟩	⟨ι⟩	PROPN
ejpam-7160	298	2	,	,	PUNCT
ejpam-7160	298	3	where	where	SCONJ
ejpam-7160	298	4	ι	ι	PRON
ejpam-7160	298	5	∈	∈	PROPN
ejpam-7160	298	6	{	{	PUNCT
ejpam-7160	298	7	r	r	NOUN
ejpam-7160	298	8	,	,	PUNCT
ejpam-7160	298	9	l	l	NOUN
ejpam-7160	298	10	,	,	PUNCT
ejpam-7160	298	11	i	i	PRON
ejpam-7160	298	12	,	,	PUNCT
ejpam-7160	298	13	u	u	NOUN
ejpam-7160	298	14	}	}	PUNCT
ejpam-7160	298	15	.	.	PUNCT
ejpam-7160	299	1	proof	proof	NOUN
ejpam-7160	299	2	.	.	PUNCT
ejpam-7160	300	1	let	let	VERB
ejpam-7160	300	2	c	c	NOUN
ejpam-7160	300	3	∈	∈	PROPN
ejpam-7160	300	4	τlmn	τlmn	NOUN
ejpam-7160	300	5	r	r	NOUN
ejpam-7160	300	6	.	.	PUNCT
ejpam-7160	301	1	then	then	ADV
ejpam-7160	301	2	,	,	PUNCT
ejpam-7160	301	3	for	for	ADP
ejpam-7160	301	4	every	every	DET
ejpam-7160	301	5	π1	π1	ADJ
ejpam-7160	301	6	∈	∈	PROPN
ejpam-7160	301	7	c	c	X
ejpam-7160	301	8	,	,	PUNCT
ejpam-7160	301	9	it	it	PRON
ejpam-7160	301	10	holds	hold	VERB
ejpam-7160	301	11	that	that	SCONJ
ejpam-7160	301	12	mn	mn	PROPN
ejpam-7160	301	13	r(π1	r(π1	PROPN
ejpam-7160	301	14	)	)	PUNCT
ejpam-7160	302	1	⊓	⊓	PROPN
ejpam-7160	302	2	cc	cc	NOUN
ejpam-7160	302	3	/∈	/∈	PROPN
ejpam-7160	302	4	l	l	NOUN
ejpam-7160	302	5	,	,	PUNCT
ejpam-7160	302	6	and	and	CCONJ
ejpam-7160	302	7	consequently	consequently	ADV
ejpam-7160	302	8	,	,	PUNCT
ejpam-7160	302	9	mn	mn	PROPN
ejpam-7160	302	10	⟨r⟩(π1	⟨r⟩(π1	NUM
ejpam-7160	302	11	)	)	PUNCT
ejpam-7160	303	1	⊓	⊓	PROPN
ejpam-7160	303	2	cc	cc	PROPN
ejpam-7160	303	3	/∈	/∈	PROPN
ejpam-7160	303	4	l	l	NOUN
ejpam-7160	303	5	for	for	ADP
ejpam-7160	303	6	all	all	DET
ejpam-7160	303	7	π1	π1	PROPN
ejpam-7160	303	8	∈	∈	PROPN
ejpam-7160	303	9	c.	c.	NOUN
ejpam-7160	303	10	consequently	consequently	ADV
ejpam-7160	303	11	,	,	PUNCT
ejpam-7160	303	12	c	c	PROPN
ejpam-7160	303	13	∈	∈	PROPN
ejpam-7160	303	14	τlmn	τlmn	NOUN
ejpam-7160	303	15	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	303	16	.	.	PUNCT
ejpam-7160	304	1	therefore	therefore	ADV
ejpam-7160	304	2	,	,	PUNCT
ejpam-7160	304	3	τlmn	τlmn	NOUN
ejpam-7160	304	4	r	r	NOUN
ejpam-7160	304	5	⊑	⊑	DET
ejpam-7160	304	6	τlmn	τlmn	NOUN
ejpam-7160	304	7	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	304	8	the	the	DET
ejpam-7160	304	9	remaining	remain	VERB
ejpam-7160	304	10	assertions	assertion	NOUN
ejpam-7160	304	11	can	can	AUX
ejpam-7160	304	12	be	be	AUX
ejpam-7160	304	13	substantiated	substantiate	VERB
ejpam-7160	304	14	in	in	ADP
ejpam-7160	304	15	a	a	DET
ejpam-7160	304	16	same	same	ADJ
ejpam-7160	304	17	way	way	NOUN
ejpam-7160	304	18	.	.	PUNCT
ejpam-7160	305	1	corollary	corollary	ADJ
ejpam-7160	305	2	2	2	NUM
ejpam-7160	305	3	.	.	PUNCT
ejpam-7160	306	1	if	if	SCONJ
ejpam-7160	306	2	(	(	PUNCT
ejpam-7160	306	3	π,×	π,×	PROPN
ejpam-7160	306	4	,	,	PUNCT
ejpam-7160	306	5	ζι	ζι	NOUN
ejpam-7160	306	6	)	)	PUNCT
ejpam-7160	306	7	constitutes	constitute	VERB
ejpam-7160	306	8	a	a	DET
ejpam-7160	306	9	ι	ι	ADV
ejpam-7160	306	10	-	-	PUNCT
ejpam-7160	306	11	ns	ns	ADJ
ejpam-7160	306	12	,	,	PUNCT
ejpam-7160	306	13	and	and	CCONJ
ejpam-7160	306	14	l	l	NOUN
ejpam-7160	306	15	represents	represent	VERB
ejpam-7160	306	16	a	a	DET
ejpam-7160	306	17	grill	grill	NOUN
ejpam-7160	306	18	on	on	ADP
ejpam-7160	306	19	π	π	PROPN
ejpam-7160	306	20	.	.	PUNCT
ejpam-7160	307	1	consequently	consequently	ADV
ejpam-7160	307	2	,	,	PUNCT
ejpam-7160	307	3	τlmnu	τlmnu	NOUN
ejpam-7160	307	4	⊑	⊑	DET
ejpam-7160	307	5	τlmn	τlmn	NOUN
ejpam-7160	307	6	ι	ι	ADP
ejpam-7160	307	7	⊑	⊑	DET
ejpam-7160	307	8	τlmn	τlmn	PROPN
ejpam-7160	307	9	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	307	10	,	,	PUNCT
ejpam-7160	307	11	where	where	SCONJ
ejpam-7160	307	12	ι	ι	PRON
ejpam-7160	307	13	∈	∈	PROPN
ejpam-7160	307	14	{	{	PUNCT
ejpam-7160	307	15	r	r	NOUN
ejpam-7160	307	16	,	,	PUNCT
ejpam-7160	307	17	l	l	NOUN
ejpam-7160	307	18	,	,	PUNCT
ejpam-7160	307	19	i	i	PRON
ejpam-7160	307	20	,	,	PUNCT
ejpam-7160	307	21	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	307	22	,	,	PUNCT
ejpam-7160	307	23	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	307	24	,	,	PUNCT
ejpam-7160	307	25	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	307	26	}	}	PUNCT
ejpam-7160	307	27	.	.	PUNCT
ejpam-7160	308	1	a.	a.	NOUN
ejpam-7160	308	2	a.	a.	PROPN
ejpam-7160	308	3	azzam	azzam	PROPN
ejpam-7160	308	4	et	et	PROPN
ejpam-7160	308	5	al	al	PROPN
ejpam-7160	308	6	.	.	PUNCT
ejpam-7160	308	7	/	/	SYM
ejpam-7160	308	8	eur	eur	PROPN
ejpam-7160	308	9	.	.	PUNCT
ejpam-7160	309	1	j.	j.	PROPN
ejpam-7160	309	2	pure	pure	PROPN
ejpam-7160	309	3	appl	appl	PROPN
ejpam-7160	309	4	.	.	PROPN
ejpam-7160	309	5	math	math	PROPN
ejpam-7160	309	6	,	,	PUNCT
ejpam-7160	309	7	18	18	NUM
ejpam-7160	309	8	(	(	PUNCT
ejpam-7160	309	9	4	4	NUM
ejpam-7160	309	10	)	)	PUNCT
ejpam-7160	309	11	(	(	PUNCT
ejpam-7160	309	12	2025	2025	NUM
ejpam-7160	309	13	)	)	PUNCT
ejpam-7160	309	14	,	,	PUNCT
ejpam-7160	309	15	7160	7160	NUM
ejpam-7160	309	16	12	12	NUM
ejpam-7160	309	17	of	of	ADP
ejpam-7160	309	18	22	22	NUM
ejpam-7160	309	19	remark	remark	NOUN
ejpam-7160	309	20	3	3	NUM
ejpam-7160	309	21	.	.	NOUN
ejpam-7160	309	22	example	example	NOUN
ejpam-7160	309	23	3.9	3.9	NUM
ejpam-7160	309	24	illustrates	illustrate	VERB
ejpam-7160	309	25	that	that	SCONJ
ejpam-7160	309	26	the	the	DET
ejpam-7160	309	27	notable	notable	ADJ
ejpam-7160	309	28	differences	difference	NOUN
ejpam-7160	309	29	between	between	ADP
ejpam-7160	309	30	the	the	DET
ejpam-7160	309	31	current	current	ADJ
ejpam-7160	309	32	methodology	methodology	NOUN
ejpam-7160	309	33	and	and	CCONJ
ejpam-7160	309	34	those	those	PRON
ejpam-7160	309	35	presented	present	VERB
ejpam-7160	309	36	in	in	ADP
ejpam-7160	309	37	[	[	X
ejpam-7160	309	38	16	16	NUM
ejpam-7160	309	39	,	,	PUNCT
ejpam-7160	309	40	18	18	NUM
ejpam-7160	309	41	]	]	PUNCT
ejpam-7160	309	42	are	be	AUX
ejpam-7160	309	43	that	that	DET
ejpam-7160	309	44	τlmn	τlmn	NOUN
ejpam-7160	309	45	ι	ι	ADP
ejpam-7160	309	46	⊑	⊑	DET
ejpam-7160	309	47	τlmn	τlmn	NOUN
ejpam-7160	309	48	⟨ι⟩	⟨ι⟩	PROPN
ejpam-7160	309	49	,	,	PUNCT
ejpam-7160	309	50	where	where	SCONJ
ejpam-7160	309	51	ι	ι	PRON
ejpam-7160	309	52	∈	∈	PROPN
ejpam-7160	309	53	{	{	PUNCT
ejpam-7160	309	54	r	r	NOUN
ejpam-7160	309	55	,	,	PUNCT
ejpam-7160	309	56	l	l	NOUN
ejpam-7160	309	57	,	,	PUNCT
ejpam-7160	309	58	i	i	PRON
ejpam-7160	309	59	,	,	PUNCT
ejpam-7160	309	60	u	u	NOUN
ejpam-7160	309	61	}	}	PUNCT
ejpam-7160	309	62	,	,	PUNCT
ejpam-7160	309	63	despite	despite	SCONJ
ejpam-7160	309	64	the	the	DET
ejpam-7160	309	65	fact	fact	NOUN
ejpam-7160	309	66	that	that	SCONJ
ejpam-7160	309	67	τlnι	τlnι	PROPN
ejpam-7160	309	68	and	and	CCONJ
ejpam-7160	309	69	τln⟨ι⟩	τln⟨ι⟩	NOUN
ejpam-7160	309	70	are	be	AUX
ejpam-7160	309	71	not	not	PART
ejpam-7160	309	72	comparable	comparable	ADJ
ejpam-7160	309	73	.	.	PUNCT
ejpam-7160	310	1	moreover	moreover	ADV
ejpam-7160	310	2	,	,	PUNCT
ejpam-7160	310	3	it	it	PRON
ejpam-7160	310	4	confirms	confirm	VERB
ejpam-7160	310	5	that	that	SCONJ
ejpam-7160	310	6	the	the	DET
ejpam-7160	310	7	converses	converse	NOUN
ejpam-7160	310	8	of	of	ADP
ejpam-7160	310	9	proposition	proposition	NOUN
ejpam-7160	310	10	3.11	3.11	NUM
ejpam-7160	310	11	and	and	CCONJ
ejpam-7160	310	12	corollary	corollary	ADJ
ejpam-7160	310	13	3.12	3.12	NUM
ejpam-7160	310	14	are	be	AUX
ejpam-7160	310	15	not	not	PART
ejpam-7160	310	16	universally	universally	ADV
ejpam-7160	310	17	valid	valid	ADJ
ejpam-7160	310	18	.	.	PUNCT
ejpam-7160	311	1	(	(	PUNCT
ejpam-7160	311	2	1	1	NUM
ejpam-7160	311	3	)	)	PUNCT
ejpam-7160	311	4	τlmn	τlmn	NOUN
ejpam-7160	312	1	i	i	PRON
ejpam-7160	312	2	⊈	⊈	VERB
ejpam-7160	312	3	τlmn	τlmn	NOUN
ejpam-7160	312	4	r	r	NOUN
ejpam-7160	312	5	;	;	PUNCT
ejpam-7160	312	6	(	(	PUNCT
ejpam-7160	312	7	2	2	X
ejpam-7160	312	8	)	)	PUNCT
ejpam-7160	312	9	τlmn	τlmn	NOUN
ejpam-7160	312	10	i	i	PRON
ejpam-7160	312	11	⊈	⊈	VERB
ejpam-7160	312	12	τlmnu	τlmnu	NOUN
ejpam-7160	312	13	;	;	PUNCT
ejpam-7160	312	14	(	(	PUNCT
ejpam-7160	312	15	3	3	X
ejpam-7160	312	16	)	)	PUNCT
ejpam-7160	312	17	τlmn	τlmn	NOUN
ejpam-7160	312	18	l	l	NOUN
ejpam-7160	312	19	⊈	⊈	NOUN
ejpam-7160	312	20	τlmnu	τlmnu	NOUN
ejpam-7160	312	21	;	;	PUNCT
ejpam-7160	312	22	(	(	PUNCT
ejpam-7160	312	23	4	4	X
ejpam-7160	312	24	)	)	PUNCT
ejpam-7160	312	25	τlmn	τlmn	NOUN
ejpam-7160	312	26	l	l	NOUN
ejpam-7160	312	27	⊈	⊈	PROPN
ejpam-7160	312	28	τlmn	τlmn	NOUN
ejpam-7160	312	29	r	r	NOUN
ejpam-7160	312	30	;	;	PUNCT
ejpam-7160	313	1	(	(	PUNCT
ejpam-7160	313	2	5	5	NUM
ejpam-7160	313	3	)	)	PUNCT
ejpam-7160	313	4	τlmn	τlmn	NOUN
ejpam-7160	313	5	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	313	6	⊈	⊈	X
ejpam-7160	313	7	τlmn	τlmn	NOUN
ejpam-7160	313	8	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	313	9	;	;	PUNCT
ejpam-7160	313	10	(	(	PUNCT
ejpam-7160	313	11	6	6	NUM
ejpam-7160	313	12	)	)	PUNCT
ejpam-7160	313	13	τlmn	τlmn	NOUN
ejpam-7160	313	14	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	314	1	⊈	⊈	PROPN
ejpam-7160	314	2	τlmn	τlmn	NOUN
ejpam-7160	314	3	⟨u⟩	⟨u⟩	PROPN
ejpam-7160	314	4	;	;	PUNCT
ejpam-7160	314	5	(	(	PUNCT
ejpam-7160	314	6	7	7	X
ejpam-7160	314	7	)	)	PUNCT
ejpam-7160	314	8	τlmn	τlmn	NOUN
ejpam-7160	314	9	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	314	10	⊈	⊈	PROPN
ejpam-7160	314	11	τlmn	τlmn	NOUN
ejpam-7160	314	12	⟨u⟩	⟨u⟩	PROPN
ejpam-7160	314	13	;	;	PUNCT
ejpam-7160	314	14	(	(	PUNCT
ejpam-7160	314	15	8)	8)	NUM
ejpam-7160	314	16	τlmn	τlmn	NOUN
ejpam-7160	314	17	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	314	18	⊈	⊈	X
ejpam-7160	315	1	τlmn	τlmn	NOUN
ejpam-7160	315	2	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	315	3	.	.	PUNCT
ejpam-7160	316	1	theorem	theorem	VERB
ejpam-7160	316	2	3.17	3.17	NUM
ejpam-7160	316	3	specifies	specifie	NOUN
ejpam-7160	316	4	the	the	DET
ejpam-7160	316	5	necessary	necessary	ADJ
ejpam-7160	316	6	criteria	criterion	NOUN
ejpam-7160	316	7	to	to	PART
ejpam-7160	316	8	determine	determine	VERB
ejpam-7160	316	9	equivalents	equivalent	NOUN
ejpam-7160	316	10	among	among	ADP
ejpam-7160	316	11	the	the	DET
ejpam-7160	316	12	suggested	suggest	VERB
ejpam-7160	316	13	topologies	topology	NOUN
ejpam-7160	316	14	.	.	PUNCT
ejpam-7160	317	1	theorem	theorem	VERB
ejpam-7160	317	2	7	7	NUM
ejpam-7160	317	3	.	.	PUNCT
ejpam-7160	318	1	if	if	SCONJ
ejpam-7160	318	2	(	(	PUNCT
ejpam-7160	318	3	π,×	π,×	PROPN
ejpam-7160	318	4	,	,	PUNCT
ejpam-7160	318	5	ζι	ζι	NOUN
ejpam-7160	318	6	)	)	PUNCT
ejpam-7160	318	7	constitutes	constitute	VERB
ejpam-7160	318	8	a	a	DET
ejpam-7160	318	9	ι	ι	ADV
ejpam-7160	318	10	-	-	PUNCT
ejpam-7160	318	11	ns	ns	ADJ
ejpam-7160	318	12	,	,	PUNCT
ejpam-7160	318	13	and	and	CCONJ
ejpam-7160	318	14	l	l	NOUN
ejpam-7160	318	15	represents	represent	VERB
ejpam-7160	318	16	a	a	DET
ejpam-7160	318	17	grill	grill	NOUN
ejpam-7160	318	18	on	on	ADP
ejpam-7160	318	19	π	π	PROPN
ejpam-7160	318	20	.	.	PUNCT
ejpam-7160	319	1	then	then	ADV
ejpam-7160	319	2	,	,	PUNCT
ejpam-7160	319	3	(	(	PUNCT
ejpam-7160	319	4	1	1	X
ejpam-7160	319	5	)	)	PUNCT
ejpam-7160	319	6	τlmn	τlmn	NOUN
ejpam-7160	319	7	r	r	NOUN
ejpam-7160	319	8	=	=	SYM
ejpam-7160	319	9	τlmn	τlmn	NOUN
ejpam-7160	320	1	i	i	NOUN
ejpam-7160	320	2	=	=	NOUN
ejpam-7160	320	3	τlmn	τlmn	NOUN
ejpam-7160	320	4	l	l	NOUN
ejpam-7160	320	5	=	=	SYM
ejpam-7160	320	6	τlmnu	τlmnu	NOUN
ejpam-7160	320	7	and	and	CCONJ
ejpam-7160	320	8	τlmn	τlmn	NOUN
ejpam-7160	320	9	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	320	10	=	=	SYM
ejpam-7160	320	11	τlmn	τlmn	NOUN
ejpam-7160	321	1	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	321	2	=	=	PUNCT
ejpam-7160	321	3	τlmn	τlmn	NOUN
ejpam-7160	321	4	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	321	5	=	=	SYM
ejpam-7160	321	6	τlmn	τlmn	NOUN
ejpam-7160	321	7	⟨u⟩	⟨u⟩	NOUN
ejpam-7160	321	8	at	at	ADP
ejpam-7160	321	9	×	×	PROPN
ejpam-7160	321	10	is	be	AUX
ejpam-7160	321	11	symmetric	symmetric	ADJ
ejpam-7160	321	12	;	;	PUNCT
ejpam-7160	321	13	(	(	PUNCT
ejpam-7160	321	14	2	2	X
ejpam-7160	321	15	)	)	PUNCT
ejpam-7160	321	16	τlmn	τlmn	NOUN
ejpam-7160	321	17	r	r	NOUN
ejpam-7160	321	18	=	=	SYM
ejpam-7160	321	19	τlmn	τlmn	NOUN
ejpam-7160	322	1	i	i	NOUN
ejpam-7160	322	2	=	=	NOUN
ejpam-7160	322	3	τlmn	τlmn	NOUN
ejpam-7160	322	4	l	l	NOUN
ejpam-7160	322	5	=	=	SYM
ejpam-7160	322	6	τlmnu	τlmnu	NOUN
ejpam-7160	322	7	=	=	SYM
ejpam-7160	322	8	τlmn	τlmn	NOUN
ejpam-7160	322	9	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	322	10	=	=	SYM
ejpam-7160	322	11	τlmn	τlmn	NOUN
ejpam-7160	322	12	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	322	13	=	=	PUNCT
ejpam-7160	322	14	τlmn	τlmn	NOUN
ejpam-7160	322	15	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	322	16	=	=	SYM
ejpam-7160	322	17	τlmn	τlmn	NOUN
ejpam-7160	322	18	⟨u⟩	⟨u⟩	NOUN
ejpam-7160	322	19	at	at	ADP
ejpam-7160	322	20	×	×	PROPN
ejpam-7160	322	21	is	be	AUX
ejpam-7160	322	22	equivalence	equivalence	NOUN
ejpam-7160	322	23	.	.	PUNCT
ejpam-7160	323	1	proof	proof	NOUN
ejpam-7160	323	2	.	.	PUNCT
ejpam-7160	324	1	(	(	PUNCT
ejpam-7160	324	2	1	1	X
ejpam-7160	324	3	)	)	PUNCT
ejpam-7160	324	4	let	let	VERB
ejpam-7160	324	5	c	c	NOUN
ejpam-7160	324	6	∈	∈	PROPN
ejpam-7160	324	7	τlmn	τlmn	NOUN
ejpam-7160	324	8	r	r	NOUN
ejpam-7160	324	9	.	.	PUNCT
ejpam-7160	325	1	consequently	consequently	ADV
ejpam-7160	325	2	,	,	PUNCT
ejpam-7160	325	3	mn	mn	PROPN
ejpam-7160	325	4	r(π1	r(π1	PROPN
ejpam-7160	325	5	)	)	PUNCT
ejpam-7160	326	1	⊑	⊑	PROPN
ejpam-7160	326	2	c	c	X
ejpam-7160	326	3	,	,	PUNCT
ejpam-7160	326	4	∀π1	∀π1	ADJ
ejpam-7160	326	5	∈	∈	PROPN
ejpam-7160	326	6	c.	c.	NOUN
ejpam-7160	326	7	⇔mn	⇔mn	PROPN
ejpam-7160	326	8	i(π1	i(π1	NOUN
ejpam-7160	326	9	)	)	PUNCT
ejpam-7160	326	10	⊑	⊑	PROPN
ejpam-7160	326	11	c	c	PROPN
ejpam-7160	326	12	,	,	PUNCT
ejpam-7160	326	13	mn	mn	PROPN
ejpam-7160	326	14	l(π1	l(π1	PROPN
ejpam-7160	326	15	)	)	PUNCT
ejpam-7160	326	16	⊑	⊑	PROPN
ejpam-7160	327	1	c	c	PROPN
ejpam-7160	327	2	,	,	PUNCT
ejpam-7160	327	3	mn	mn	PROPN
ejpam-7160	327	4	u(π1	u(π1	PROPN
ejpam-7160	327	5	)	)	PUNCT
ejpam-7160	327	6	⊑	⊑	PROPN
ejpam-7160	328	1	c	c	PROPN
ejpam-7160	328	2	,	,	PUNCT
ejpam-7160	328	3	∀π1	∀π1	ADJ
ejpam-7160	328	4	∈	∈	PROPN
ejpam-7160	328	5	c	c	NOUN
ejpam-7160	328	6	(	(	PUNCT
ejpam-7160	328	7	from	from	ADP
ejpam-7160	328	8	theorem	theorem	ADJ
ejpam-7160	328	9	3.4	3.4	NUM
ejpam-7160	328	10	)	)	PUNCT
ejpam-7160	328	11	.	.	PUNCT
ejpam-7160	329	1	consequently	consequently	ADV
ejpam-7160	329	2	τlmn	τlmn	ADJ
ejpam-7160	329	3	r	r	NOUN
ejpam-7160	329	4	=	=	SYM
ejpam-7160	329	5	τlmn	τlmn	NOUN
ejpam-7160	329	6	l	l	NOUN
ejpam-7160	329	7	=	=	SYM
ejpam-7160	329	8	τlmn	τlmn	NOUN
ejpam-7160	330	1	i	i	NOUN
ejpam-7160	330	2	=	=	SYM
ejpam-7160	330	3	τlmnu	τlmnu	NOUN
ejpam-7160	330	4	,	,	PUNCT
ejpam-7160	330	5	and	and	CCONJ
ejpam-7160	330	6	τlmn	τlmn	NOUN
ejpam-7160	330	7	⟨r⟩	⟨r⟩	PROPN
ejpam-7160	330	8	=	=	SYM
ejpam-7160	330	9	τlmn	τlmn	NOUN
ejpam-7160	330	10	⟨l⟩	⟨l⟩	PROPN
ejpam-7160	330	11	=	=	SYM
ejpam-7160	330	12	τlmn	τlmn	NOUN
ejpam-7160	330	13	⟨i⟩	⟨i⟩	PROPN
ejpam-7160	330	14	=	=	SYM
ejpam-7160	330	15	τlmn	τlmn	PROPN
ejpam-7160	330	16	⟨u⟩	⟨u⟩	PROPN
ejpam-7160	330	17	.	.	PUNCT
ejpam-7160	331	1	(	(	PUNCT
ejpam-7160	331	2	2	2	X
ejpam-7160	331	3	)	)	PUNCT
ejpam-7160	331	4	the	the	DET
ejpam-7160	331	5	evidence	evidence	NOUN
ejpam-7160	331	6	is	be	AUX
ejpam-7160	331	7	simple	simple	ADJ
ejpam-7160	331	8	.	.	PUNCT
ejpam-7160	332	1	to	to	PART
ejpam-7160	332	2	investigate	investigate	VERB
ejpam-7160	332	3	the	the	DET
ejpam-7160	332	4	characteristic	characteristic	NOUN
ejpam-7160	332	5	of	of	ADP
ejpam-7160	332	6	monotonicity	monotonicity	NOUN
ejpam-7160	332	7	in	in	ADP
ejpam-7160	332	8	the	the	DET
ejpam-7160	332	9	fourth	fourth	ADJ
ejpam-7160	332	10	section	section	NOUN
ejpam-7160	332	11	,	,	PUNCT
ejpam-7160	332	12	which	which	PRON
ejpam-7160	332	13	is	be	AUX
ejpam-7160	332	14	essential	essential	ADJ
ejpam-7160	332	15	,	,	PUNCT
ejpam-7160	332	16	we	we	PRON
ejpam-7160	332	17	must	must	AUX
ejpam-7160	332	18	initially	initially	ADV
ejpam-7160	332	19	analyze	analyze	VERB
ejpam-7160	332	20	the	the	DET
ejpam-7160	332	21	relationship	relationship	NOUN
ejpam-7160	332	22	between	between	ADP
ejpam-7160	332	23	the	the	DET
ejpam-7160	332	24	two	two	NUM
ejpam-7160	332	25	topologies	topology	NOUN
ejpam-7160	332	26	produced	produce	VERB
ejpam-7160	332	27	by	by	ADP
ejpam-7160	332	28	the	the	DET
ejpam-7160	332	29	two	two	NUM
ejpam-7160	332	30	subset	subset	NOUN
ejpam-7160	332	31	relations	relation	NOUN
ejpam-7160	332	32	.	.	PUNCT
ejpam-7160	333	1	this	this	PRON
ejpam-7160	333	2	is	be	AUX
ejpam-7160	333	3	discussed	discuss	VERB
ejpam-7160	333	4	in	in	ADP
ejpam-7160	333	5	the	the	DET
ejpam-7160	333	6	following	follow	VERB
ejpam-7160	333	7	major	major	ADJ
ejpam-7160	333	8	proposition	proposition	NOUN
ejpam-7160	333	9	.	.	PUNCT
ejpam-7160	334	1	proposition	proposition	NOUN
ejpam-7160	334	2	3	3	X
ejpam-7160	334	3	.	.	PUNCT
ejpam-7160	335	1	let	let	VERB
ejpam-7160	335	2	(	(	PUNCT
ejpam-7160	335	3	π,×.	π,×.	ADV
ejpam-7160	335	4	,	,	PUNCT
ejpam-7160	335	5	ζ1ι	ζ1ι	NOUN
ejpam-7160	335	6	)	)	PUNCT
ejpam-7160	335	7	,	,	PUNCT
ejpam-7160	335	8	and	and	CCONJ
ejpam-7160	335	9	(	(	PUNCT
ejpam-7160	335	10	π,×	π,×	PROPN
ejpam-7160	335	11	..	..	PROPN
ejpam-7160	335	12	,	,	PUNCT
ejpam-7160	335	13	ζ2ι	ζ2ι	NOUN
ejpam-7160	335	14	)	)	PUNCT
ejpam-7160	335	15	be	be	VERB
ejpam-7160	335	16	two	two	NUM
ejpam-7160	335	17	ι	ι	ADV
ejpam-7160	335	18	-	-	PUNCT
ejpam-7160	335	19	ns	ns	ADJ
ejpam-7160	335	20	,	,	PUNCT
ejpam-7160	336	1	l	l	NOUN
ejpam-7160	336	2	be	be	VERB
ejpam-7160	336	3	a	a	DET
ejpam-7160	336	4	grill	grill	NOUN
ejpam-7160	336	5	on	on	ADP
ejpam-7160	336	6	π	π	PROPN
ejpam-7160	336	7	,	,	PUNCT
ejpam-7160	336	8	and	and	CCONJ
ejpam-7160	336	9	×.	×.	PROPN
ejpam-7160	336	10	⊑	⊑	PRON
ejpam-7160	336	11	×	×	NOUN
ejpam-7160	336	12	...	...	PUNCT
ejpam-7160	336	13	then	then	ADV
ejpam-7160	336	14	,	,	PUNCT
ejpam-7160	336	15	τmn	τmn	ADJ
ejpam-7160	336	16	2ι	2ι	NUM
ejpam-7160	336	17	⊑	⊑	X
ejpam-7160	336	18	τmn	τmn	ADJ
ejpam-7160	336	19	1ι	1ι	NOUN
ejpam-7160	336	20	,	,	PUNCT
ejpam-7160	336	21	ι	ι	PROPN
ejpam-7160	336	22	∈	∈	PROPN
ejpam-7160	336	23	{	{	PUNCT
ejpam-7160	336	24	r	r	NOUN
ejpam-7160	336	25	,	,	PUNCT
ejpam-7160	336	26	l	l	NOUN
ejpam-7160	336	27	,	,	PUNCT
ejpam-7160	336	28	i	i	PRON
ejpam-7160	336	29	,	,	PUNCT
ejpam-7160	336	30	u	u	NOUN
ejpam-7160	336	31	}	}	PUNCT
ejpam-7160	336	32	.	.	PUNCT
ejpam-7160	337	1	a.	a.	PROPN
ejpam-7160	337	2	a.	a.	PROPN
ejpam-7160	337	3	azzam	azzam	PROPN
ejpam-7160	337	4	et	et	PROPN
ejpam-7160	337	5	al	al	PROPN
ejpam-7160	337	6	.	.	PUNCT
ejpam-7160	337	7	/	/	SYM
ejpam-7160	337	8	eur	eur	PROPN
ejpam-7160	337	9	.	.	PUNCT
ejpam-7160	338	1	j.	j.	PROPN
ejpam-7160	338	2	pure	pure	PROPN
ejpam-7160	338	3	appl	appl	PROPN
ejpam-7160	338	4	.	.	PROPN
ejpam-7160	338	5	math	math	PROPN
ejpam-7160	338	6	,	,	PUNCT
ejpam-7160	338	7	18	18	NUM
ejpam-7160	338	8	(	(	PUNCT
ejpam-7160	338	9	4	4	NUM
ejpam-7160	338	10	)	)	PUNCT
ejpam-7160	338	11	(	(	PUNCT
ejpam-7160	338	12	2025	2025	NUM
ejpam-7160	338	13	)	)	PUNCT
ejpam-7160	338	14	,	,	PUNCT
ejpam-7160	338	15	7160	7160	NUM
ejpam-7160	338	16	13	13	NUM
ejpam-7160	338	17	of	of	ADP
ejpam-7160	338	18	22	22	NUM
ejpam-7160	338	19	proof	proof	NOUN
ejpam-7160	338	20	.	.	PUNCT
ejpam-7160	339	1	let	let	VERB
ejpam-7160	339	2	c	c	NOUN
ejpam-7160	339	3	∈	∈	VERB
ejpam-7160	339	4	τmn	τmn	PROPN
ejpam-7160	340	1	2r	2r	NUM
ejpam-7160	340	2	.	.	PUNCT
ejpam-7160	341	1	then	then	ADV
ejpam-7160	341	2	,	,	PUNCT
ejpam-7160	341	3	mn	mn	PROPN
ejpam-7160	341	4	2r(π1	2r(π1	NUM
ejpam-7160	341	5	)	)	PUNCT
ejpam-7160	342	1	⊓	⊓	PROPN
ejpam-7160	342	2	cc	cc	PART
ejpam-7160	342	3	/∈	/∈	PROPN
ejpam-7160	342	4	l	l	NOUN
ejpam-7160	342	5	,	,	PUNCT
ejpam-7160	342	6	∀π1	∀π1	ADJ
ejpam-7160	342	7	∈	∈	PROPN
ejpam-7160	342	8	c.	c.	NOUN
ejpam-7160	343	1	thus	thus	ADV
ejpam-7160	343	2	,	,	PUNCT
ejpam-7160	343	3	mn	mn	PROPN
ejpam-7160	343	4	1r(π1	1r(π1	NUM
ejpam-7160	343	5	)	)	PUNCT
ejpam-7160	343	6	⊓	⊓	PROPN
ejpam-7160	343	7	cc	cc	PART
ejpam-7160	343	8	/∈	/∈	PROPN
ejpam-7160	343	9	l	l	NOUN
ejpam-7160	343	10	,	,	PUNCT
ejpam-7160	343	11	∀π1	∀π1	ADJ
ejpam-7160	343	12	∈	∈	PROPN
ejpam-7160	343	13	c.	c.	NOUN
ejpam-7160	343	14	consequently	consequently	ADV
ejpam-7160	343	15	,	,	PUNCT
ejpam-7160	343	16	c	c	PROPN
ejpam-7160	343	17	∈	∈	PROPN
ejpam-7160	343	18	mn	mn	PROPN
ejpam-7160	343	19	1r	1r	NUM
ejpam-7160	343	20	,	,	PUNCT
ejpam-7160	343	21	and	and	CCONJ
ejpam-7160	343	22	hence	hence	ADV
ejpam-7160	343	23	,	,	PUNCT
ejpam-7160	343	24	τmn	τmn	ADJ
ejpam-7160	343	25	2r	2r	NUM
ejpam-7160	343	26	(	(	PUNCT
ejpam-7160	343	27	π1	π1	NOUN
ejpam-7160	343	28	)	)	PUNCT
ejpam-7160	343	29	⊑	⊑	X
ejpam-7160	343	30	τmn	τmn	PROPN
ejpam-7160	343	31	1r	1r	NUM
ejpam-7160	343	32	(	(	PUNCT
ejpam-7160	343	33	π1	π1	NOUN
ejpam-7160	343	34	)	)	PUNCT
ejpam-7160	343	35	;	;	PUNCT
ejpam-7160	343	36	the	the	DET
ejpam-7160	343	37	remaining	remain	VERB
ejpam-7160	343	38	cases	case	NOUN
ejpam-7160	343	39	can	can	AUX
ejpam-7160	343	40	be	be	AUX
ejpam-7160	343	41	demonstrated	demonstrate	VERB
ejpam-7160	343	42	in	in	ADP
ejpam-7160	343	43	a	a	DET
ejpam-7160	343	44	comparable	comparable	ADJ
ejpam-7160	343	45	way	way	NOUN
ejpam-7160	343	46	.	.	PUNCT
ejpam-7160	344	1	4	4	X
ejpam-7160	344	2	.	.	NOUN
ejpam-7160	344	3	approximate	approximate	ADJ
ejpam-7160	344	4	models	model	NOUN
ejpam-7160	344	5	grill	grill	VERB
ejpam-7160	344	6	this	this	DET
ejpam-7160	344	7	part	part	NOUN
ejpam-7160	344	8	presents	present	VERB
ejpam-7160	344	9	preliminary	preliminary	ADJ
ejpam-7160	344	10	models	model	NOUN
ejpam-7160	344	11	employing	employ	VERB
ejpam-7160	344	12	τlmn	τlmn	NOUN
ejpam-7160	344	13	ι	ι	DET
ejpam-7160	344	14	-topologies	-topologie	NOUN
ejpam-7160	344	15	and	and	CCONJ
ejpam-7160	344	16	elucidates	elucidate	VERB
ejpam-7160	344	17	their	their	PRON
ejpam-7160	344	18	principal	principal	ADJ
ejpam-7160	344	19	characteristics	characteristic	NOUN
ejpam-7160	344	20	.	.	PUNCT
ejpam-7160	345	1	these	these	DET
ejpam-7160	345	2	mathematical	mathematical	ADJ
ejpam-7160	345	3	representations	representation	NOUN
ejpam-7160	345	4	preserve	preserve	VERB
ejpam-7160	345	5	the	the	DET
ejpam-7160	345	6	characteristic	characteristic	NOUN
ejpam-7160	345	7	of	of	ADP
ejpam-7160	345	8	monotonicity	monotonicity	NOUN
ejpam-7160	345	9	unencumbered	unencumbered	ADJ
ejpam-7160	345	10	by	by	ADP
ejpam-7160	345	11	limitations	limitation	NOUN
ejpam-7160	345	12	.	.	PUNCT
ejpam-7160	346	1	conversely	conversely	ADV
ejpam-7160	346	2	,	,	PUNCT
ejpam-7160	346	3	it	it	PRON
ejpam-7160	346	4	may	may	AUX
ejpam-7160	346	5	be	be	AUX
ejpam-7160	346	6	either	either	CCONJ
ejpam-7160	346	7	forfeited	forfeit	VERB
ejpam-7160	346	8	or	or	CCONJ
ejpam-7160	346	9	maintained	maintain	VERB
ejpam-7160	346	10	under	under	ADP
ejpam-7160	346	11	stringent	stringent	ADJ
ejpam-7160	346	12	terms	term	NOUN
ejpam-7160	346	13	in	in	ADP
ejpam-7160	346	14	certain	certain	ADJ
ejpam-7160	346	15	prior	prior	ADJ
ejpam-7160	346	16	methodologies	methodology	NOUN
ejpam-7160	346	17	[	[	X
ejpam-7160	346	18	16	16	NUM
ejpam-7160	346	19	,	,	PUNCT
ejpam-7160	346	20	52	52	NUM
ejpam-7160	346	21	]	]	PUNCT
ejpam-7160	346	22	.	.	PUNCT
ejpam-7160	347	1	definition	definition	NOUN
ejpam-7160	347	2	4.1	4.1	NUM
ejpam-7160	347	3	employs	employ	VERB
ejpam-7160	347	4	the	the	DET
ejpam-7160	347	5	topologies	topology	NOUN
ejpam-7160	347	6	established	establish	VERB
ejpam-7160	347	7	in	in	ADP
ejpam-7160	347	8	section	section	NOUN
ejpam-7160	347	9	3	3	NUM
ejpam-7160	347	10	to	to	PART
ejpam-7160	347	11	furnish	furnish	VERB
ejpam-7160	347	12	apps	app	NOUN
ejpam-7160	347	13	.	.	PUNCT
ejpam-7160	348	1	definition	definition	NOUN
ejpam-7160	348	2	17	17	NUM
ejpam-7160	348	3	.	.	PUNCT
ejpam-7160	349	1	if	if	SCONJ
ejpam-7160	349	2	(	(	PUNCT
ejpam-7160	349	3	π,×	π,×	PROPN
ejpam-7160	349	4	,	,	PUNCT
ejpam-7160	349	5	ζι	ζι	NOUN
ejpam-7160	349	6	)	)	PUNCT
ejpam-7160	349	7	constitutes	constitute	VERB
ejpam-7160	349	8	a	a	DET
ejpam-7160	349	9	ι	ι	ADV
ejpam-7160	349	10	-	-	PUNCT
ejpam-7160	349	11	ns	ns	ADJ
ejpam-7160	349	12	,	,	PUNCT
ejpam-7160	349	13	and	and	CCONJ
ejpam-7160	349	14	l	l	NOUN
ejpam-7160	349	15	represents	represent	VERB
ejpam-7160	349	16	a	a	DET
ejpam-7160	349	17	grill	grill	NOUN
ejpam-7160	349	18	on	on	ADP
ejpam-7160	349	19	π	π	PROPN
ejpam-7160	349	20	.	.	PUNCT
ejpam-7160	350	1	the	the	DET
ejpam-7160	350	2	lmn	lmn	PROPN
ejpam-7160	350	3	ι	ι	PROPN
ejpam-7160	350	4	-	-	PUNCT
ejpam-7160	350	5	lw	lw	NOUN
ejpam-7160	350	6	-	-	PUNCT
ejpam-7160	350	7	app	app	NOUN
ejpam-7160	350	8	×l	×l	PROPN
ejpam-7160	350	9	mn	mn	PROPN
ejpam-7160	350	10	ι	ι	PROPN
ejpam-7160	350	11	,	,	PUNCT
ejpam-7160	350	12	and	and	CCONJ
ejpam-7160	350	13	l	l	PROPN
ejpam-7160	350	14	-	-	PROPN
ejpam-7160	350	15	mn	mn	PROPN
ejpam-7160	350	16	ι	ι	PROPN
ejpam-7160	350	17	-	-	PUNCT
ejpam-7160	350	18	up	up	ADP
ejpam-7160	350	19	-	-	PUNCT
ejpam-7160	350	20	app	app	NOUN
ejpam-7160	350	21	×l	×l	PROPN
ejpam-7160	350	22	mn	mn	PROPN
ejpam-7160	350	23	ι	ι	PROPN
ejpam-7160	350	24	of	of	ADP
ejpam-7160	350	25	c	c	NOUN
ejpam-7160	350	26	⊑	⊑	X
ejpam-7160	351	1	π	π	PROPN
ejpam-7160	351	2	are	be	AUX
ejpam-7160	351	3	×l	×l	PROPN
ejpam-7160	351	4	mn	mn	PROPN
ejpam-7160	351	5	ι	ι	PROPN
ejpam-7160	351	6	(	(	PUNCT
ejpam-7160	351	7	c	c	NOUN
ejpam-7160	351	8	)	)	PUNCT
ejpam-7160	351	9	=	=	SYM
ejpam-7160	351	10	⊔{g	⊔{g	PROPN
ejpam-7160	351	11	∈	∈	PROPN
ejpam-7160	351	12	τlmn	τlmn	NOUN
ejpam-7160	351	13	ι	ι	X
ejpam-7160	351	14	:	:	PUNCT
ejpam-7160	351	15	g	g	X
ejpam-7160	351	16	⊑	⊑	X
ejpam-7160	351	17	c	c	X
ejpam-7160	351	18	}	}	PUNCT
ejpam-7160	351	19	=	=	SYM
ejpam-7160	351	20	intlmn	intlmn	NOUN
ejpam-7160	351	21	ι	ι	PROPN
ejpam-7160	351	22	,	,	PUNCT
ejpam-7160	351	23	×l	×l	PUNCT
ejpam-7160	351	24	mn	mn	PROPN
ejpam-7160	351	25	ι	ι	PROPN
ejpam-7160	351	26	(	(	PUNCT
ejpam-7160	351	27	c	c	NOUN
ejpam-7160	351	28	)	)	PUNCT
ejpam-7160	351	29	=	=	SYM
ejpam-7160	351	30	⊓{y	⊓{y	PUNCT
ejpam-7160	351	31	∈	∈	ADJ
ejpam-7160	351	32	τlmn	τlmn	NOUN
ejpam-7160	351	33	ι	ι	X
ejpam-7160	351	34	:	:	PUNCT
ejpam-7160	351	35	c	c	X
ejpam-7160	351	36	⊑	⊑	X
ejpam-7160	351	37	y	y	PROPN
ejpam-7160	351	38	}	}	PUNCT
ejpam-7160	352	1	=	=	PUNCT
ejpam-7160	352	2	cllmn	cllmn	NOUN
ejpam-7160	352	3	ι	ι	X
ejpam-7160	352	4	.	.	PUNCT
ejpam-7160	353	1	the	the	DET
ejpam-7160	353	2	principal	principal	ADJ
ejpam-7160	353	3	characteristics	characteristic	NOUN
ejpam-7160	353	4	of	of	ADP
ejpam-7160	353	5	the	the	DET
ejpam-7160	353	6	proposed	propose	VERB
ejpam-7160	353	7	apps	app	NOUN
ejpam-7160	353	8	are	be	AUX
ejpam-7160	353	9	addressed	address	VERB
ejpam-7160	353	10	in	in	ADP
ejpam-7160	353	11	the	the	DET
ejpam-7160	353	12	exposition	exposition	NOUN
ejpam-7160	353	13	of	of	ADP
ejpam-7160	353	14	the	the	DET
ejpam-7160	353	15	ensuing	ensue	VERB
ejpam-7160	353	16	outcomes	outcome	NOUN
ejpam-7160	353	17	.	.	PUNCT
ejpam-7160	354	1	proposition	proposition	NOUN
ejpam-7160	354	2	4	4	NUM
ejpam-7160	354	3	.	.	PUNCT
ejpam-7160	355	1	if	if	SCONJ
ejpam-7160	355	2	(	(	PUNCT
ejpam-7160	355	3	π,×	π,×	PROPN
ejpam-7160	355	4	,	,	PUNCT
ejpam-7160	355	5	ζι	ζι	NOUN
ejpam-7160	355	6	)	)	PUNCT
ejpam-7160	355	7	forms	form	VERB
ejpam-7160	355	8	a	a	DET
ejpam-7160	355	9	ι	ι	ADV
ejpam-7160	355	10	-	-	PUNCT
ejpam-7160	355	11	ns	ns	ADJ
ejpam-7160	355	12	,	,	PUNCT
ejpam-7160	355	13	l	l	NOUN
ejpam-7160	355	14	denotes	denote	VERB
ejpam-7160	355	15	a	a	DET
ejpam-7160	355	16	grill	grill	NOUN
ejpam-7160	355	17	on	on	ADP
ejpam-7160	355	18	π	π	PROPN
ejpam-7160	355	19	,	,	PUNCT
ejpam-7160	355	20	and	and	CCONJ
ejpam-7160	356	1	c	c	X
ejpam-7160	356	2	,	,	PUNCT
ejpam-7160	356	3	g	g	PROPN
ejpam-7160	356	4	∈	∈	PROPN
ejpam-7160	356	5	π	π	PROPN
ejpam-7160	356	6	.	.	PUNCT
ejpam-7160	356	7	subsequently	subsequently	ADV
ejpam-7160	356	8	,	,	PUNCT
ejpam-7160	356	9	the	the	DET
ejpam-7160	356	10	ensuing	ensue	VERB
ejpam-7160	356	11	assertions	assertion	NOUN
ejpam-7160	356	12	are	be	AUX
ejpam-7160	356	13	accurate	accurate	ADJ
ejpam-7160	356	14	:	:	PUNCT
ejpam-7160	356	15	(	(	PUNCT
ejpam-7160	356	16	1	1	X
ejpam-7160	356	17	)	)	PUNCT
ejpam-7160	356	18	×l	×l	PROPN
ejpam-7160	356	19	mn	mn	PROPN
ejpam-7160	356	20	ι	ι	PROPN
ejpam-7160	356	21	(	(	PUNCT
ejpam-7160	356	22	c	c	NOUN
ejpam-7160	356	23	)	)	PUNCT
ejpam-7160	356	24	⊑	⊑	PROPN
ejpam-7160	356	25	c	c	X
ejpam-7160	356	26	;	;	PUNCT
ejpam-7160	356	27	(	(	PUNCT
ejpam-7160	356	28	2	2	X
ejpam-7160	356	29	)	)	PUNCT
ejpam-7160	357	1	×l	×l	PROPN
ejpam-7160	357	2	mn	mn	PROPN
ejpam-7160	357	3	ι	ι	PROPN
ejpam-7160	357	4	(	(	PUNCT
ejpam-7160	357	5	ϕ	ϕ	NOUN
ejpam-7160	357	6	)	)	PUNCT
ejpam-7160	357	7	=	=	SYM
ejpam-7160	357	8	ϕ	ϕ	NOUN
ejpam-7160	357	9	;	;	PUNCT
ejpam-7160	357	10	(	(	PUNCT
ejpam-7160	357	11	3	3	X
ejpam-7160	357	12	)	)	PUNCT
ejpam-7160	357	13	×l	×l	PROPN
ejpam-7160	357	14	mn	mn	PROPN
ejpam-7160	357	15	ι	ι	PROPN
ejpam-7160	357	16	(	(	PUNCT
ejpam-7160	357	17	π	π	NOUN
ejpam-7160	357	18	)	)	PUNCT
ejpam-7160	357	19	=	=	SYM
ejpam-7160	357	20	π	π	PROPN
ejpam-7160	357	21	;	;	PUNCT
ejpam-7160	357	22	(	(	PUNCT
ejpam-7160	357	23	4	4	X
ejpam-7160	357	24	)	)	PUNCT
ejpam-7160	357	25	if	if	SCONJ
ejpam-7160	357	26	c	c	PROPN
ejpam-7160	357	27	⊑	⊑	PRON
ejpam-7160	357	28	g	g	PROPN
ejpam-7160	357	29	,	,	PUNCT
ejpam-7160	357	30	then	then	ADV
ejpam-7160	357	31	×l	×l	PUNCT
ejpam-7160	357	32	mn	mn	PROPN
ejpam-7160	357	33	ι	ι	PROPN
ejpam-7160	357	34	(	(	PUNCT
ejpam-7160	357	35	c	c	NOUN
ejpam-7160	357	36	)	)	PUNCT
ejpam-7160	357	37	⊑	⊑	PRON
ejpam-7160	357	38	×l	×l	PROPN
ejpam-7160	357	39	mn	mn	PROPN
ejpam-7160	357	40	ι	ι	PROPN
ejpam-7160	357	41	(	(	PUNCT
ejpam-7160	357	42	g	g	NOUN
ejpam-7160	357	43	)	)	PUNCT
ejpam-7160	357	44	;	;	PUNCT
ejpam-7160	357	45	(	(	PUNCT
ejpam-7160	357	46	5	5	X
ejpam-7160	357	47	)	)	PUNCT
ejpam-7160	357	48	×l	×l	PROPN
ejpam-7160	357	49	mn	mn	PROPN
ejpam-7160	357	50	ι	ι	PROPN
ejpam-7160	357	51	(	(	PUNCT
ejpam-7160	357	52	c	c	NOUN
ejpam-7160	357	53	⊓g	⊓g	NOUN
ejpam-7160	357	54	)	)	PUNCT
ejpam-7160	357	55	=	=	SYM
ejpam-7160	357	56	×l	×l	PROPN
ejpam-7160	357	57	mn	mn	PROPN
ejpam-7160	357	58	ι	ι	PROPN
ejpam-7160	357	59	(	(	PUNCT
ejpam-7160	357	60	c	c	NOUN
ejpam-7160	357	61	)	)	PUNCT
ejpam-7160	357	62	⊓	⊓	PROPN
ejpam-7160	357	63	×l	×l	PROPN
ejpam-7160	357	64	mn	mn	PROPN
ejpam-7160	357	65	ι	ι	PROPN
ejpam-7160	357	66	(	(	PUNCT
ejpam-7160	357	67	g	g	NOUN
ejpam-7160	357	68	)	)	PUNCT
ejpam-7160	357	69	;	;	PUNCT
ejpam-7160	357	70	(	(	PUNCT
ejpam-7160	357	71	6	6	NUM
ejpam-7160	357	72	)	)	PUNCT
ejpam-7160	357	73	×l	×l	PROPN
ejpam-7160	357	74	mn	mn	PROPN
ejpam-7160	357	75	ι	ι	PROPN
ejpam-7160	357	76	(	(	PUNCT
ejpam-7160	357	77	cc	cc	NOUN
ejpam-7160	357	78	)	)	PUNCT
ejpam-7160	357	79	=	=	SYM
ejpam-7160	357	80	(	(	PUNCT
ejpam-7160	357	81	×l	×l	PUNCT
ejpam-7160	357	82	mn	mn	PROPN
ejpam-7160	357	83	ι	ι	PROPN
ejpam-7160	357	84	(	(	PUNCT
ejpam-7160	357	85	c))c	c))c	PROPN
ejpam-7160	357	86	;	;	PUNCT
ejpam-7160	357	87	(	(	PUNCT
ejpam-7160	357	88	7	7	X
ejpam-7160	357	89	)	)	PUNCT
ejpam-7160	357	90	×l	×l	PROPN
ejpam-7160	357	91	mn	mn	PROPN
ejpam-7160	357	92	ι	ι	PROPN
ejpam-7160	357	93	(	(	PUNCT
ejpam-7160	357	94	×l	×l	PUNCT
ejpam-7160	357	95	mn	mn	PROPN
ejpam-7160	357	96	ι	ι	PROPN
ejpam-7160	357	97	(	(	PUNCT
ejpam-7160	357	98	c	c	NOUN
ejpam-7160	357	99	)	)	PUNCT
ejpam-7160	357	100	)	)	PUNCT
ejpam-7160	357	101	=	=	PUNCT
ejpam-7160	358	1	×l	×l	PROPN
ejpam-7160	358	2	mn	mn	PROPN
ejpam-7160	358	3	ι	ι	PROPN
ejpam-7160	358	4	(	(	PUNCT
ejpam-7160	358	5	c	c	NOUN
ejpam-7160	358	6	)	)	PUNCT
ejpam-7160	358	7	.	.	PUNCT
ejpam-7160	359	1	proof	proof	NOUN
ejpam-7160	359	2	.	.	PUNCT
ejpam-7160	360	1	given	give	VERB
ejpam-7160	360	2	that	that	DET
ejpam-7160	360	3	1	1	NUM
ejpam-7160	360	4	,	,	PUNCT
ejpam-7160	360	5	2	2	NUM
ejpam-7160	360	6	,	,	PUNCT
ejpam-7160	360	7	and	and	CCONJ
ejpam-7160	360	8	3	3	NUM
ejpam-7160	360	9	are	be	AUX
ejpam-7160	360	10	readily	readily	ADV
ejpam-7160	360	11	demonstrable	demonstrable	ADJ
ejpam-7160	360	12	,	,	PUNCT
ejpam-7160	360	13	we	we	PRON
ejpam-7160	360	14	shall	shall	AUX
ejpam-7160	360	15	commence	commence	VERB
ejpam-7160	360	16	with	with	ADP
ejpam-7160	360	17	the	the	DET
ejpam-7160	360	18	proof	proof	NOUN
ejpam-7160	360	19	of	of	ADP
ejpam-7160	360	20	4	4	NUM
ejpam-7160	360	21	.	.	PUNCT
ejpam-7160	360	22	a.	a.	NOUN
ejpam-7160	360	23	a.	a.	PROPN
ejpam-7160	360	24	azzam	azzam	PROPN
ejpam-7160	360	25	et	et	PROPN
ejpam-7160	360	26	al	al	PROPN
ejpam-7160	360	27	.	.	PUNCT
ejpam-7160	360	28	/	/	SYM
ejpam-7160	360	29	eur	eur	PROPN
ejpam-7160	360	30	.	.	PUNCT
ejpam-7160	361	1	j.	j.	PROPN
ejpam-7160	361	2	pure	pure	PROPN
ejpam-7160	361	3	appl	appl	PROPN
ejpam-7160	361	4	.	.	PROPN
ejpam-7160	361	5	math	math	PROPN
ejpam-7160	361	6	,	,	PUNCT
ejpam-7160	361	7	18	18	NUM
ejpam-7160	361	8	(	(	PUNCT
ejpam-7160	361	9	4	4	NUM
ejpam-7160	361	10	)	)	PUNCT
ejpam-7160	361	11	(	(	PUNCT
ejpam-7160	361	12	2025	2025	NUM
ejpam-7160	361	13	)	)	PUNCT
ejpam-7160	361	14	,	,	PUNCT
ejpam-7160	361	15	7160	7160	NUM
ejpam-7160	361	16	14	14	NUM
ejpam-7160	361	17	of	of	ADP
ejpam-7160	361	18	22	22	NUM
ejpam-7160	361	19	(	(	PUNCT
ejpam-7160	361	20	4	4	NUM
ejpam-7160	361	21	)	)	PUNCT
ejpam-7160	361	22	let	let	VERB
ejpam-7160	361	23	c	c	PROPN
ejpam-7160	361	24	⊑	⊑	DET
ejpam-7160	361	25	g.	g.	PROPN
ejpam-7160	361	26	then	then	ADV
ejpam-7160	361	27	,	,	PUNCT
ejpam-7160	361	28	⊔{g	⊔{g	PROPN
ejpam-7160	361	29	∈	∈	PROPN
ejpam-7160	361	30	τlmn	τlmn	NOUN
ejpam-7160	362	1	ι	ι	X
ejpam-7160	362	2	:	:	PUNCT
ejpam-7160	362	3	g	g	X
ejpam-7160	362	4	⊑	⊑	X
ejpam-7160	362	5	c	c	AUX
ejpam-7160	362	6	}	}	PUNCT
ejpam-7160	362	7	⊑	⊑	DET
ejpam-7160	362	8	⊔{g	⊔{g	PROPN
ejpam-7160	362	9	∈	∈	PROPN
ejpam-7160	362	10	τlmn	τlmn	NOUN
ejpam-7160	362	11	ι	ι	X
ejpam-7160	362	12	:	:	PUNCT
ejpam-7160	362	13	g	g	PROPN
ejpam-7160	362	14	⊑	⊑	X
ejpam-7160	362	15	g	g	NOUN
ejpam-7160	362	16	}	}	PUNCT
ejpam-7160	362	17	,	,	PUNCT
ejpam-7160	362	18	and	and	CCONJ
ejpam-7160	362	19	so	so	ADV
ejpam-7160	362	20	×l	×l	PUNCT
ejpam-7160	362	21	mn	mn	PROPN
ejpam-7160	362	22	ι	ι	PROPN
ejpam-7160	362	23	(	(	PUNCT
ejpam-7160	362	24	c	c	NOUN
ejpam-7160	362	25	)	)	PUNCT
ejpam-7160	362	26	⊑	⊑	PRON
ejpam-7160	362	27	×l	×l	PROPN
ejpam-7160	362	28	mn	mn	PROPN
ejpam-7160	362	29	ι	ι	PROPN
ejpam-7160	362	30	(	(	PUNCT
ejpam-7160	362	31	g	g	NOUN
ejpam-7160	362	32	)	)	PUNCT
ejpam-7160	362	33	.	.	PUNCT
ejpam-7160	363	1	(	(	PUNCT
ejpam-7160	363	2	5	5	NUM
ejpam-7160	363	3	)	)	PUNCT
ejpam-7160	363	4	from	from	ADP
ejpam-7160	363	5	(	(	PUNCT
ejpam-7160	363	6	4	4	NUM
ejpam-7160	363	7	)	)	PUNCT
ejpam-7160	363	8	,	,	PUNCT
ejpam-7160	363	9	×l	×l	PUNCT
ejpam-7160	363	10	mn	mn	PROPN
ejpam-7160	363	11	ι	ι	X
ejpam-7160	363	12	(	(	PUNCT
ejpam-7160	363	13	c	c	NOUN
ejpam-7160	363	14	⊓	⊓	PROPN
ejpam-7160	363	15	g	g	NOUN
ejpam-7160	363	16	)	)	PUNCT
ejpam-7160	363	17	⊑	⊑	PRON
ejpam-7160	363	18	×l	×l	PROPN
ejpam-7160	364	1	mn	mn	PROPN
ejpam-7160	364	2	ι	ι	PROPN
ejpam-7160	364	3	(	(	PUNCT
ejpam-7160	364	4	c	c	NOUN
ejpam-7160	364	5	)	)	PUNCT
ejpam-7160	364	6	⊓	⊓	PROPN
ejpam-7160	364	7	×l	×l	PROPN
ejpam-7160	364	8	mn	mn	PROPN
ejpam-7160	364	9	ι	ι	PROPN
ejpam-7160	364	10	(	(	PUNCT
ejpam-7160	364	11	g	g	NOUN
ejpam-7160	364	12	)	)	PUNCT
ejpam-7160	365	1	.	.	PUNCT
ejpam-7160	366	1	since	since	SCONJ
ejpam-7160	366	2	×l	×l	PROPN
ejpam-7160	366	3	mn	mn	PROPN
ejpam-7160	366	4	ι	ι	PROPN
ejpam-7160	366	5	(	(	PUNCT
ejpam-7160	366	6	c	c	NOUN
ejpam-7160	366	7	)	)	PUNCT
ejpam-7160	366	8	⊑	⊑	PROPN
ejpam-7160	366	9	c	c	NOUN
ejpam-7160	366	10	,	,	PUNCT
ejpam-7160	366	11	and	and	CCONJ
ejpam-7160	366	12	×l	×l	PUNCT
ejpam-7160	366	13	mn	mn	PROPN
ejpam-7160	366	14	ι	ι	PROPN
ejpam-7160	366	15	(	(	PUNCT
ejpam-7160	366	16	g	g	NOUN
ejpam-7160	366	17	)	)	PUNCT
ejpam-7160	366	18	⊑	⊑	PROPN
ejpam-7160	366	19	g	g	PROPN
ejpam-7160	366	20	,	,	PUNCT
ejpam-7160	366	21	it	it	PRON
ejpam-7160	366	22	follows	follow	VERB
ejpam-7160	366	23	that	that	SCONJ
ejpam-7160	366	24	×l	×l	PUNCT
ejpam-7160	366	25	mn	mn	PROPN
ejpam-7160	366	26	ι	ι	PROPN
ejpam-7160	366	27	(	(	PUNCT
ejpam-7160	366	28	c	c	NOUN
ejpam-7160	366	29	)	)	PUNCT
ejpam-7160	366	30	⊓	⊓	PROPN
ejpam-7160	366	31	×l	×l	PROPN
ejpam-7160	366	32	mn	mn	PROPN
ejpam-7160	366	33	ι	ι	PROPN
ejpam-7160	366	34	(	(	PUNCT
ejpam-7160	366	35	g	g	NOUN
ejpam-7160	366	36	)	)	PUNCT
ejpam-7160	366	37	⊑	⊑	PROPN
ejpam-7160	367	1	c	c	X
ejpam-7160	367	2	⊓g	⊓g	PROPN
ejpam-7160	367	3	.	.	PUNCT
ejpam-7160	368	1	consequently	consequently	ADV
ejpam-7160	368	2	,	,	PUNCT
ejpam-7160	368	3	×l	×l	PUNCT
ejpam-7160	368	4	mn	mn	PROPN
ejpam-7160	368	5	ι	ι	PROPN
ejpam-7160	368	6	(	(	PUNCT
ejpam-7160	368	7	×l	×l	PUNCT
ejpam-7160	368	8	mn	mn	PROPN
ejpam-7160	368	9	ι	ι	PROPN
ejpam-7160	368	10	(	(	PUNCT
ejpam-7160	368	11	c)⊓×l	c)⊓×l	PROPN
ejpam-7160	368	12	mn	mn	PROPN
ejpam-7160	368	13	ι	ι	PROPN
ejpam-7160	368	14	(	(	PUNCT
ejpam-7160	368	15	g	g	NOUN
ejpam-7160	368	16	)	)	PUNCT
ejpam-7160	368	17	)	)	PUNCT
ejpam-7160	368	18	⊑	⊑	PRON
ejpam-7160	368	19	×l	×l	PROPN
ejpam-7160	368	20	mn	mn	PROPN
ejpam-7160	368	21	ι	ι	PROPN
ejpam-7160	368	22	(	(	PUNCT
ejpam-7160	368	23	c⊓g	c⊓g	NOUN
ejpam-7160	368	24	)	)	PUNCT
ejpam-7160	368	25	.	.	PUNCT
ejpam-7160	369	1	then	then	ADV
ejpam-7160	369	2	,	,	PUNCT
ejpam-7160	369	3	×l	×l	PUNCT
ejpam-7160	369	4	mn	mn	PROPN
ejpam-7160	369	5	ι	ι	PROPN
ejpam-7160	369	6	(	(	PUNCT
ejpam-7160	369	7	c)⊓×l	c)⊓×l	PROPN
ejpam-7160	369	8	mn	mn	PROPN
ejpam-7160	369	9	ι	ι	PROPN
ejpam-7160	369	10	(	(	PUNCT
ejpam-7160	369	11	g	g	NOUN
ejpam-7160	369	12	)	)	PUNCT
ejpam-7160	369	13	⊑	⊑	PRON
ejpam-7160	369	14	×l	×l	PROPN
ejpam-7160	369	15	mn	mn	PROPN
ejpam-7160	369	16	ι	ι	PROPN
ejpam-7160	369	17	(	(	PUNCT
ejpam-7160	369	18	c⊓	c⊓	NUM
ejpam-7160	369	19	g	g	NOUN
ejpam-7160	369	20	)	)	PUNCT
ejpam-7160	369	21	.	.	PUNCT
ejpam-7160	370	1	thus	thus	ADV
ejpam-7160	370	2	,	,	PUNCT
ejpam-7160	370	3	×l	×l	PROPN
ejpam-7160	370	4	mn	mn	PROPN
ejpam-7160	370	5	ι	ι	PROPN
ejpam-7160	370	6	(	(	PUNCT
ejpam-7160	370	7	c	c	NOUN
ejpam-7160	370	8	⊓g	⊓g	NOUN
ejpam-7160	370	9	)	)	PUNCT
ejpam-7160	370	10	=	=	SYM
ejpam-7160	370	11	×l	×l	PROPN
ejpam-7160	370	12	mn	mn	PROPN
ejpam-7160	370	13	ι	ι	PROPN
ejpam-7160	370	14	(	(	PUNCT
ejpam-7160	370	15	c	c	NOUN
ejpam-7160	370	16	)	)	PUNCT
ejpam-7160	370	17	⊓	⊓	PROPN
ejpam-7160	370	18	×l	×l	PROPN
ejpam-7160	370	19	mn	mn	PROPN
ejpam-7160	370	20	ι	ι	PROPN
ejpam-7160	370	21	(	(	PUNCT
ejpam-7160	370	22	g	g	NOUN
ejpam-7160	370	23	)	)	PUNCT
ejpam-7160	370	24	.	.	PUNCT
ejpam-7160	371	1	(	(	PUNCT
ejpam-7160	371	2	6	6	X
ejpam-7160	371	3	)	)	PUNCT
ejpam-7160	371	4	let	let	VERB
ejpam-7160	371	5	π1	π1	PROPN
ejpam-7160	371	6	∈	∈	PROPN
ejpam-7160	371	7	×l	×l	PROPN
ejpam-7160	371	8	mn	mn	PROPN
ejpam-7160	371	9	ι	ι	PROPN
ejpam-7160	371	10	(	(	PUNCT
ejpam-7160	371	11	cc	cc	NOUN
ejpam-7160	371	12	)	)	PUNCT
ejpam-7160	371	13	.	.	PUNCT
ejpam-7160	372	1	at	at	ADP
ejpam-7160	372	2	hence	hence	ADV
ejpam-7160	372	3	,	,	PUNCT
ejpam-7160	372	4	∃	∃	PROPN
ejpam-7160	372	5	g	g	PROPN
ejpam-7160	372	6	∈	∈	PROPN
ejpam-7160	372	7	τlmn	τlmn	NOUN
ejpam-7160	372	8	ι	ι	ADP
ejpam-7160	372	9	such	such	ADJ
ejpam-7160	372	10	that	that	DET
ejpam-7160	372	11	π1	π1	NOUN
ejpam-7160	372	12	∈	∈	PROPN
ejpam-7160	372	13	g	g	PROPN
ejpam-7160	372	14	⊑	⊑	X
ejpam-7160	372	15	cc	cc	PROPN
ejpam-7160	372	16	,	,	PUNCT
ejpam-7160	372	17	and	and	CCONJ
ejpam-7160	372	18	so	so	ADV
ejpam-7160	372	19	g	g	PROPN
ejpam-7160	372	20	⊓	⊓	PROPN
ejpam-7160	372	21	c	c	NOUN
ejpam-7160	372	22	=	=	SYM
ejpam-7160	372	23	ϕ.	ϕ.	PROPN
ejpam-7160	372	24	therefore	therefore	ADV
ejpam-7160	372	25	,	,	PUNCT
ejpam-7160	372	26	π1	π1	PROPN
ejpam-7160	372	27	/∈	/∈	PUNCT
ejpam-7160	373	1	×l	×l	PROPN
ejpam-7160	373	2	mn	mn	PROPN
ejpam-7160	373	3	ι	ι	PROPN
ejpam-7160	373	4	(	(	PUNCT
ejpam-7160	373	5	c	c	NOUN
ejpam-7160	373	6	)	)	PUNCT
ejpam-7160	373	7	.	.	PUNCT
ejpam-7160	374	1	thus	thus	ADV
ejpam-7160	374	2	,	,	PUNCT
ejpam-7160	374	3	π1	π1	ADJ
ejpam-7160	374	4	∈	∈	PROPN
ejpam-7160	374	5	(	(	PUNCT
ejpam-7160	374	6	×l	×l	PUNCT
ejpam-7160	374	7	mn	mn	PROPN
ejpam-7160	374	8	ι	ι	PROPN
ejpam-7160	374	9	(	(	PUNCT
ejpam-7160	374	10	c))c	c))c	NOUN
ejpam-7160	374	11	.	.	PUNCT
ejpam-7160	375	1	conversely	conversely	ADV
ejpam-7160	375	2	,	,	PUNCT
ejpam-7160	375	3	let	let	VERB
ejpam-7160	375	4	π1	π1	PROPN
ejpam-7160	375	5	∈	∈	PROPN
ejpam-7160	375	6	(	(	PUNCT
ejpam-7160	375	7	×l	×l	PUNCT
ejpam-7160	375	8	mn	mn	PROPN
ejpam-7160	375	9	ι	ι	PROPN
ejpam-7160	375	10	(	(	PUNCT
ejpam-7160	375	11	c))c	c))c	PROPN
ejpam-7160	375	12	.	.	PUNCT
ejpam-7160	376	1	then	then	ADV
ejpam-7160	376	2	,	,	PUNCT
ejpam-7160	376	3	π1	π1	PROPN
ejpam-7160	376	4	/∈	/∈	PUNCT
ejpam-7160	376	5	×l	×l	PROPN
ejpam-7160	376	6	mn	mn	PROPN
ejpam-7160	376	7	ι	ι	PROPN
ejpam-7160	376	8	(	(	PUNCT
ejpam-7160	376	9	c	c	NOUN
ejpam-7160	376	10	)	)	PUNCT
ejpam-7160	376	11	,	,	PUNCT
ejpam-7160	376	12	and	and	CCONJ
ejpam-7160	376	13	so	so	ADV
ejpam-7160	376	14	∃o	∃o	PROPN
ejpam-7160	376	15	∈	∈	PROPN
ejpam-7160	376	16	τlmn	τlmn	NOUN
ejpam-7160	377	1	ι	ι	ADP
ejpam-7160	377	2	that	that	DET
ejpam-7160	377	3	π1	π1	NOUN
ejpam-7160	377	4	∈	∈	PROPN
ejpam-7160	377	5	g	g	NOUN
ejpam-7160	377	6	,	,	PUNCT
ejpam-7160	377	7	and	and	CCONJ
ejpam-7160	377	8	c	c	X
ejpam-7160	377	9	⊓g	⊓g	PROPN
ejpam-7160	378	1	=	=	PUNCT
ejpam-7160	378	2	ϕ.	ϕ.	PROPN
ejpam-7160	379	1	so	so	ADV
ejpam-7160	379	2	,	,	PUNCT
ejpam-7160	379	3	π1	π1	PROPN
ejpam-7160	379	4	∈	∈	PROPN
ejpam-7160	379	5	g	g	PROPN
ejpam-7160	379	6	⊑	⊑	X
ejpam-7160	379	7	cc	cc	PROPN
ejpam-7160	379	8	.	.	PROPN
ejpam-7160	379	9	hence	hence	ADV
ejpam-7160	379	10	,	,	PUNCT
ejpam-7160	379	11	π1	π1	PROPN
ejpam-7160	379	12	∈	∈	PROPN
ejpam-7160	379	13	×l	×l	PROPN
ejpam-7160	379	14	mn	mn	PROPN
ejpam-7160	379	15	ι	ι	PROPN
ejpam-7160	379	16	(	(	PUNCT
ejpam-7160	379	17	cc	cc	NOUN
ejpam-7160	379	18	)	)	PUNCT
ejpam-7160	379	19	.	.	PUNCT
ejpam-7160	380	1	(	(	PUNCT
ejpam-7160	380	2	7	7	X
ejpam-7160	380	3	)	)	PUNCT
ejpam-7160	380	4	×l	×l	PROPN
ejpam-7160	380	5	mn	mn	PROPN
ejpam-7160	380	6	ι	ι	PROPN
ejpam-7160	380	7	(	(	PUNCT
ejpam-7160	380	8	×l	×l	PUNCT
ejpam-7160	380	9	mn	mn	PROPN
ejpam-7160	380	10	ι	ι	PROPN
ejpam-7160	380	11	(	(	PUNCT
ejpam-7160	380	12	c	c	NOUN
ejpam-7160	380	13	)	)	PUNCT
ejpam-7160	380	14	)	)	PUNCT
ejpam-7160	381	1	⊑	⊑	PRON
ejpam-7160	382	1	×l	×l	PROPN
ejpam-7160	382	2	mn	mn	PROPN
ejpam-7160	382	3	ι	ι	PROPN
ejpam-7160	382	4	(	(	PUNCT
ejpam-7160	382	5	c	c	NOUN
ejpam-7160	382	6	)	)	PUNCT
ejpam-7160	382	7	by	by	ADP
ejpam-7160	382	8	(	(	PUNCT
ejpam-7160	382	9	1	1	NUM
ejpam-7160	382	10	)	)	PUNCT
ejpam-7160	382	11	.	.	PUNCT
ejpam-7160	383	1	on	on	ADP
ejpam-7160	383	2	the	the	DET
ejpam-7160	383	3	other	other	ADJ
ejpam-7160	383	4	hand	hand	NOUN
ejpam-7160	383	5	,	,	PUNCT
ejpam-7160	383	6	let	let	VERB
ejpam-7160	383	7	π1	π1	PROPN
ejpam-7160	383	8	∈	∈	PROPN
ejpam-7160	383	9	×l	×l	PROPN
ejpam-7160	383	10	mn	mn	PROPN
ejpam-7160	383	11	ι	ι	PROPN
ejpam-7160	383	12	(	(	PUNCT
ejpam-7160	383	13	c	c	NOUN
ejpam-7160	383	14	)	)	PUNCT
ejpam-7160	383	15	.	.	PUNCT
ejpam-7160	384	1	then	then	ADV
ejpam-7160	384	2	,	,	PUNCT
ejpam-7160	384	3	∃g	∃g	PROPN
ejpam-7160	384	4	∈	∈	PROPN
ejpam-7160	384	5	τlmn	τlmn	NOUN
ejpam-7160	384	6	ι	ι	ADP
ejpam-7160	384	7	that	that	DET
ejpam-7160	384	8	π1	π1	NOUN
ejpam-7160	384	9	∈	∈	PROPN
ejpam-7160	384	10	g	g	PROPN
ejpam-7160	384	11	⊑	⊑	PROPN
ejpam-7160	384	12	c	c	X
ejpam-7160	384	13	,	,	PUNCT
ejpam-7160	384	14	×l	×l	PUNCT
ejpam-7160	384	15	mn	mn	PROPN
ejpam-7160	384	16	ι	ι	PROPN
ejpam-7160	384	17	(	(	PUNCT
ejpam-7160	384	18	g	g	NOUN
ejpam-7160	384	19	)	)	PUNCT
ejpam-7160	384	20	⊑	⊑	PRON
ejpam-7160	384	21	×l	×l	PROPN
ejpam-7160	384	22	mn	mn	PROPN
ejpam-7160	384	23	ι	ι	PROPN
ejpam-7160	384	24	(	(	PUNCT
ejpam-7160	384	25	c	c	NOUN
ejpam-7160	384	26	)	)	PUNCT
ejpam-7160	384	27	(	(	PUNCT
ejpam-7160	384	28	from(4	from(4	PROPN
ejpam-7160	384	29	)	)	PUNCT
ejpam-7160	384	30	)	)	PUNCT
ejpam-7160	384	31	.	.	PUNCT
ejpam-7160	385	1	it	it	PRON
ejpam-7160	385	2	is	be	AUX
ejpam-7160	385	3	observed	observe	VERB
ejpam-7160	385	4	that	that	SCONJ
ejpam-7160	385	5	g	g	NOUN
ejpam-7160	385	6	=	=	PUNCT
ejpam-7160	385	7	×l	×l	PROPN
ejpam-7160	385	8	mn	mn	PROPN
ejpam-7160	385	9	ι	ι	PROPN
ejpam-7160	385	10	(	(	PUNCT
ejpam-7160	385	11	g	g	NOUN
ejpam-7160	385	12	)	)	PUNCT
ejpam-7160	385	13	from	from	ADP
ejpam-7160	385	14	definition	definition	NOUN
ejpam-7160	385	15	4.1	4.1	NUM
ejpam-7160	385	16	.	.	PUNCT
ejpam-7160	386	1	so	so	ADV
ejpam-7160	386	2	{	{	PUNCT
ejpam-7160	386	3	π1	π1	ADJ
ejpam-7160	386	4	}	}	PUNCT
ejpam-7160	386	5	∈	∈	PROPN
ejpam-7160	386	6	×l	×l	PROPN
ejpam-7160	386	7	mn	mn	PROPN
ejpam-7160	386	8	ι	ι	PROPN
ejpam-7160	386	9	(	(	PUNCT
ejpam-7160	386	10	g	g	NOUN
ejpam-7160	386	11	)	)	PUNCT
ejpam-7160	386	12	⊑	⊑	PRON
ejpam-7160	386	13	×l	×l	PROPN
ejpam-7160	386	14	mn	mn	PROPN
ejpam-7160	386	15	ι	ι	X
ejpam-7160	386	16	(	(	PUNCT
ejpam-7160	386	17	×l	×l	PUNCT
ejpam-7160	386	18	mn	mn	PROPN
ejpam-7160	386	19	ι	ι	PROPN
ejpam-7160	386	20	(	(	PUNCT
ejpam-7160	386	21	c	c	NOUN
ejpam-7160	386	22	)	)	PUNCT
ejpam-7160	386	23	)	)	PUNCT
ejpam-7160	386	24	.	.	PUNCT
ejpam-7160	387	1	consequently	consequently	ADV
ejpam-7160	387	2	,	,	PUNCT
ejpam-7160	387	3	×l	×l	PROPN
ejpam-7160	387	4	mn	mn	PROPN
ejpam-7160	387	5	ι	ι	PROPN
ejpam-7160	387	6	(	(	PUNCT
ejpam-7160	387	7	×l	×l	PUNCT
ejpam-7160	387	8	mn	mn	PROPN
ejpam-7160	387	9	ι	ι	PROPN
ejpam-7160	387	10	(	(	PUNCT
ejpam-7160	387	11	c	c	NOUN
ejpam-7160	387	12	)	)	PUNCT
ejpam-7160	387	13	)	)	PUNCT
ejpam-7160	387	14	⊒	⊒	PUNCT
ejpam-7160	388	1	×l	×l	PROPN
ejpam-7160	388	2	mn	mn	PROPN
ejpam-7160	388	3	ι	ι	PROPN
ejpam-7160	388	4	(	(	PUNCT
ejpam-7160	388	5	c	c	NOUN
ejpam-7160	388	6	)	)	PUNCT
ejpam-7160	388	7	.	.	PUNCT
ejpam-7160	389	1	corollary	corollary	ADJ
ejpam-7160	389	2	3	3	X
ejpam-7160	389	3	.	.	PUNCT
ejpam-7160	390	1	if	if	SCONJ
ejpam-7160	390	2	(	(	PUNCT
ejpam-7160	390	3	π,×	π,×	PROPN
ejpam-7160	390	4	,	,	PUNCT
ejpam-7160	390	5	ζι	ζι	NOUN
ejpam-7160	390	6	)	)	PUNCT
ejpam-7160	390	7	forms	form	VERB
ejpam-7160	390	8	a	a	DET
ejpam-7160	390	9	ι	ι	ADV
ejpam-7160	390	10	-	-	PUNCT
ejpam-7160	390	11	ns	ns	ADJ
ejpam-7160	390	12	,	,	PUNCT
ejpam-7160	390	13	l	l	NOUN
ejpam-7160	390	14	denotes	denote	VERB
ejpam-7160	390	15	a	a	DET
ejpam-7160	390	16	grill	grill	NOUN
ejpam-7160	390	17	on	on	ADP
ejpam-7160	390	18	π	π	PROPN
ejpam-7160	390	19	,	,	PUNCT
ejpam-7160	390	20	and	and	CCONJ
ejpam-7160	391	1	c	c	X
ejpam-7160	391	2	,	,	PUNCT
ejpam-7160	391	3	g	g	PROPN
ejpam-7160	391	4	∈	∈	PROPN
ejpam-7160	391	5	π	π	X
ejpam-7160	391	6	.	.	PUNCT
ejpam-7160	392	1	then	then	ADV
ejpam-7160	392	2	,	,	PUNCT
ejpam-7160	392	3	×l	×l	PUNCT
ejpam-7160	392	4	mn	mn	PROPN
ejpam-7160	392	5	ι	ι	PROPN
ejpam-7160	392	6	(	(	PUNCT
ejpam-7160	392	7	c	c	NOUN
ejpam-7160	392	8	)	)	PUNCT
ejpam-7160	392	9	⊔	⊔	PROPN
ejpam-7160	392	10	×l	×l	PROPN
ejpam-7160	392	11	mn	mn	PROPN
ejpam-7160	392	12	ι	ι	PROPN
ejpam-7160	392	13	(	(	PUNCT
ejpam-7160	392	14	g	g	NOUN
ejpam-7160	392	15	)	)	PUNCT
ejpam-7160	392	16	⊑	⊑	PRON
ejpam-7160	393	1	×l	×l	PROPN
ejpam-7160	393	2	mn	mn	PROPN
ejpam-7160	393	3	ι	ι	PROPN
ejpam-7160	393	4	(	(	PUNCT
ejpam-7160	393	5	c	c	NOUN
ejpam-7160	393	6	⊔g	⊔g	PROPN
ejpam-7160	393	7	)	)	PUNCT
ejpam-7160	393	8	.	.	PUNCT
ejpam-7160	394	1	proof	proof	NOUN
ejpam-7160	394	2	.	.	PUNCT
ejpam-7160	395	1	this	this	PRON
ejpam-7160	395	2	can	can	AUX
ejpam-7160	395	3	be	be	AUX
ejpam-7160	395	4	directly	directly	ADV
ejpam-7160	395	5	deduced	deduce	VERB
ejpam-7160	395	6	from	from	ADP
ejpam-7160	395	7	(	(	PUNCT
ejpam-7160	395	8	5	5	NUM
ejpam-7160	395	9	)	)	PUNCT
ejpam-7160	395	10	of	of	ADP
ejpam-7160	395	11	proposition	proposition	NOUN
ejpam-7160	395	12	4.2	4.2	NUM
ejpam-7160	395	13	.	.	PUNCT
ejpam-7160	396	1	remark	remark	VERB
ejpam-7160	396	2	4	4	NUM
ejpam-7160	396	3	.	.	PUNCT
ejpam-7160	397	1	in	in	ADP
ejpam-7160	397	2	example	example	NOUN
ejpam-7160	397	3	3.10	3.10	NUM
ejpam-7160	397	4	,	,	PUNCT
ejpam-7160	397	5	the	the	DET
ejpam-7160	397	6	subsequent	subsequent	ADJ
ejpam-7160	397	7	propositions	proposition	NOUN
ejpam-7160	397	8	are	be	AUX
ejpam-7160	397	9	accurate	accurate	ADJ
ejpam-7160	397	10	:	:	PUNCT
ejpam-7160	397	11	(	(	PUNCT
ejpam-7160	397	12	1	1	X
ejpam-7160	397	13	)	)	PUNCT
ejpam-7160	397	14	×l	×l	NOUN
ejpam-7160	397	15	mn	mn	PROPN
ejpam-7160	397	16	r	r	NOUN
ejpam-7160	397	17	(	(	PUNCT
ejpam-7160	397	18	{	{	PUNCT
ejpam-7160	397	19	π3	π3	NOUN
ejpam-7160	397	20	}	}	PUNCT
ejpam-7160	397	21	)	)	PUNCT
ejpam-7160	397	22	=	=	PUNCT
ejpam-7160	398	1	ϕ	ϕ	X
ejpam-7160	398	2	⊑	⊑	PRON
ejpam-7160	398	3	{	{	PUNCT
ejpam-7160	398	4	π3	π3	NOUN
ejpam-7160	398	5	}	}	PUNCT
ejpam-7160	398	6	;	;	PUNCT
ejpam-7160	398	7	(	(	PUNCT
ejpam-7160	398	8	2	2	X
ejpam-7160	398	9	)	)	PUNCT
ejpam-7160	398	10	×l	×l	NOUN
ejpam-7160	398	11	mn	mn	PROPN
ejpam-7160	398	12	r	r	NOUN
ejpam-7160	398	13	(	(	PUNCT
ejpam-7160	398	14	{	{	PUNCT
ejpam-7160	398	15	π3	π3	NOUN
ejpam-7160	398	16	}	}	PUNCT
ejpam-7160	398	17	)	)	PUNCT
ejpam-7160	399	1	=	=	PUNCT
ejpam-7160	399	2	ϕ	ϕ	X
ejpam-7160	399	3	⊑	⊑	PRON
ejpam-7160	399	4	{	{	PUNCT
ejpam-7160	399	5	π4	π4	PROPN
ejpam-7160	399	6	}	}	PUNCT
ejpam-7160	399	7	=	=	PUNCT
ejpam-7160	399	8	×l	×l	NOUN
ejpam-7160	399	9	mn	mn	PROPN
ejpam-7160	399	10	r	r	NOUN
ejpam-7160	399	11	(	(	PUNCT
ejpam-7160	399	12	{	{	PUNCT
ejpam-7160	399	13	π4	π4	NOUN
ejpam-7160	399	14	}	}	PUNCT
ejpam-7160	399	15	)	)	PUNCT
ejpam-7160	399	16	but	but	CCONJ
ejpam-7160	399	17	{	{	PUNCT
ejpam-7160	399	18	π3	π3	NOUN
ejpam-7160	399	19	}	}	PUNCT
ejpam-7160	399	20	⊈	⊈	PROPN
ejpam-7160	399	21	{	{	PUNCT
ejpam-7160	399	22	π4	π4	PROPN
ejpam-7160	399	23	}	}	PUNCT
ejpam-7160	399	24	;	;	PUNCT
ejpam-7160	399	25	(	(	PUNCT
ejpam-7160	399	26	3	3	X
ejpam-7160	399	27	)	)	PUNCT
ejpam-7160	399	28	×l	×l	NOUN
ejpam-7160	399	29	mn	mn	PROPN
ejpam-7160	399	30	r	r	NOUN
ejpam-7160	399	31	(	(	PUNCT
ejpam-7160	399	32	{	{	PUNCT
ejpam-7160	399	33	π2})⊔×l	π2})⊔×l	PROPN
ejpam-7160	399	34	mn	mn	PROPN
ejpam-7160	399	35	r	r	NOUN
ejpam-7160	399	36	(	(	PUNCT
ejpam-7160	399	37	{	{	PUNCT
ejpam-7160	399	38	π1	π1	NOUN
ejpam-7160	399	39	,	,	PUNCT
ejpam-7160	399	40	π2	π2	ADJ
ejpam-7160	399	41	,	,	PUNCT
ejpam-7160	399	42	π3	π3	NOUN
ejpam-7160	399	43	}	}	PUNCT
ejpam-7160	399	44	)	)	PUNCT
ejpam-7160	399	45	=	=	SYM
ejpam-7160	399	46	{	{	PUNCT
ejpam-7160	399	47	π1	π1	NOUN
ejpam-7160	399	48	,	,	PUNCT
ejpam-7160	399	49	π2	π2	ADJ
ejpam-7160	399	50	,	,	PUNCT
ejpam-7160	399	51	π3	π3	NOUN
ejpam-7160	399	52	}	}	PUNCT
ejpam-7160	399	53	)	)	PUNCT
ejpam-7160	399	54	=	=	PUNCT
ejpam-7160	399	55	×l	×l	PROPN
ejpam-7160	399	56	mn	mn	PROPN
ejpam-7160	399	57	r	r	NOUN
ejpam-7160	399	58	(	(	PUNCT
ejpam-7160	399	59	{	{	PUNCT
ejpam-7160	399	60	π2}⊔×l	π2}⊔×l	NOUN
ejpam-7160	399	61	mn	mn	PROPN
ejpam-7160	399	62	r	r	NOUN
ejpam-7160	399	63	{	{	PUNCT
ejpam-7160	399	64	π1	π1	NOUN
ejpam-7160	399	65	,	,	PUNCT
ejpam-7160	399	66	π2	π2	ADJ
ejpam-7160	399	67	,	,	PUNCT
ejpam-7160	399	68	π3	π3	NOUN
ejpam-7160	399	69	}	}	PUNCT
ejpam-7160	399	70	)	)	PUNCT
ejpam-7160	399	71	proposition	proposition	NOUN
ejpam-7160	399	72	5	5	NUM
ejpam-7160	399	73	.	.	PUNCT
ejpam-7160	400	1	if	if	SCONJ
ejpam-7160	400	2	(	(	PUNCT
ejpam-7160	400	3	π,×	π,×	PROPN
ejpam-7160	400	4	,	,	PUNCT
ejpam-7160	400	5	ζι	ζι	NOUN
ejpam-7160	400	6	)	)	PUNCT
ejpam-7160	400	7	forms	form	VERB
ejpam-7160	400	8	a	a	DET
ejpam-7160	400	9	ι	ι	ADV
ejpam-7160	400	10	-	-	PUNCT
ejpam-7160	400	11	ns	ns	ADJ
ejpam-7160	400	12	,	,	PUNCT
ejpam-7160	400	13	l	l	NOUN
ejpam-7160	400	14	denotes	denote	VERB
ejpam-7160	400	15	a	a	DET
ejpam-7160	400	16	grill	grill	NOUN
ejpam-7160	400	17	on	on	ADP
ejpam-7160	400	18	π	π	PROPN
ejpam-7160	400	19	,	,	PUNCT
ejpam-7160	400	20	and	and	CCONJ
ejpam-7160	401	1	c	c	X
ejpam-7160	401	2	,	,	PUNCT
ejpam-7160	401	3	g	g	PROPN
ejpam-7160	401	4	∈	∈	PROPN
ejpam-7160	401	5	π	π	PROPN
ejpam-7160	401	6	.	.	PUNCT
ejpam-7160	401	7	subsequently	subsequently	ADV
ejpam-7160	401	8	,	,	PUNCT
ejpam-7160	401	9	the	the	DET
ejpam-7160	401	10	ensuing	ensue	VERB
ejpam-7160	401	11	assertions	assertion	NOUN
ejpam-7160	401	12	are	be	AUX
ejpam-7160	401	13	accurate	accurate	ADJ
ejpam-7160	401	14	:	:	PUNCT
ejpam-7160	401	15	(	(	PUNCT
ejpam-7160	401	16	1	1	X
ejpam-7160	401	17	)	)	PUNCT
ejpam-7160	401	18	c	c	NOUN
ejpam-7160	401	19	⊑	⊑	PRON
ejpam-7160	401	20	×l	×l	PROPN
ejpam-7160	401	21	mn	mn	PROPN
ejpam-7160	401	22	ι	ι	PROPN
ejpam-7160	401	23	(	(	PUNCT
ejpam-7160	401	24	c	c	NOUN
ejpam-7160	401	25	)	)	PUNCT
ejpam-7160	401	26	;	;	PUNCT
ejpam-7160	402	1	(	(	PUNCT
ejpam-7160	402	2	2	2	X
ejpam-7160	402	3	)	)	PUNCT
ejpam-7160	402	4	×l	×l	PROPN
ejpam-7160	402	5	mn	mn	PROPN
ejpam-7160	402	6	ι	ι	PROPN
ejpam-7160	402	7	(	(	PUNCT
ejpam-7160	402	8	ϕ	ϕ	NOUN
ejpam-7160	402	9	)	)	PUNCT
ejpam-7160	402	10	=	=	SYM
ejpam-7160	402	11	ϕ	ϕ	NOUN
ejpam-7160	402	12	;	;	PUNCT
ejpam-7160	402	13	(	(	PUNCT
ejpam-7160	402	14	3	3	X
ejpam-7160	402	15	)	)	PUNCT
ejpam-7160	402	16	×l	×l	PROPN
ejpam-7160	402	17	mn	mn	PROPN
ejpam-7160	402	18	ι	ι	PROPN
ejpam-7160	402	19	(	(	PUNCT
ejpam-7160	402	20	c	c	NOUN
ejpam-7160	402	21	)	)	PUNCT
ejpam-7160	402	22	=	=	SYM
ejpam-7160	403	1	c	c	NOUN
ejpam-7160	403	2	;	;	PUNCT
ejpam-7160	403	3	(	(	PUNCT
ejpam-7160	403	4	4	4	X
ejpam-7160	403	5	)	)	PUNCT
ejpam-7160	403	6	if	if	SCONJ
ejpam-7160	403	7	c	c	PROPN
ejpam-7160	403	8	⊑	⊑	PRON
ejpam-7160	403	9	g	g	PROPN
ejpam-7160	403	10	,	,	PUNCT
ejpam-7160	403	11	then	then	ADV
ejpam-7160	403	12	×l	×l	PUNCT
ejpam-7160	403	13	mn	mn	PROPN
ejpam-7160	403	14	ι	ι	PROPN
ejpam-7160	403	15	(	(	PUNCT
ejpam-7160	403	16	c	c	NOUN
ejpam-7160	403	17	)	)	PUNCT
ejpam-7160	403	18	⊑	⊑	PRON
ejpam-7160	403	19	×l	×l	PROPN
ejpam-7160	403	20	mn	mn	PROPN
ejpam-7160	403	21	ι	ι	PROPN
ejpam-7160	403	22	(	(	PUNCT
ejpam-7160	403	23	g	g	NOUN
ejpam-7160	403	24	)	)	PUNCT
ejpam-7160	403	25	;	;	PUNCT
ejpam-7160	403	26	(	(	PUNCT
ejpam-7160	403	27	5	5	X
ejpam-7160	403	28	)	)	PUNCT
ejpam-7160	403	29	×l	×l	PROPN
ejpam-7160	403	30	mn	mn	PROPN
ejpam-7160	403	31	ι	ι	PROPN
ejpam-7160	403	32	(	(	PUNCT
ejpam-7160	403	33	c	c	NOUN
ejpam-7160	403	34	⊔g	⊔g	PROPN
ejpam-7160	403	35	)	)	PUNCT
ejpam-7160	403	36	=	=	PUNCT
ejpam-7160	404	1	×l	×l	PROPN
ejpam-7160	404	2	mn	mn	PROPN
ejpam-7160	404	3	ι	ι	PROPN
ejpam-7160	404	4	(	(	PUNCT
ejpam-7160	404	5	c	c	NOUN
ejpam-7160	404	6	)	)	PUNCT
ejpam-7160	404	7	⊔	⊔	PROPN
ejpam-7160	404	8	×l	×l	PROPN
ejpam-7160	404	9	mn	mn	PROPN
ejpam-7160	404	10	ι	ι	PROPN
ejpam-7160	404	11	(	(	PUNCT
ejpam-7160	404	12	g	g	NOUN
ejpam-7160	404	13	)	)	PUNCT
ejpam-7160	404	14	;	;	PUNCT
ejpam-7160	404	15	a.	a.	NOUN
ejpam-7160	404	16	a.	a.	PROPN
ejpam-7160	404	17	azzam	azzam	PROPN
ejpam-7160	404	18	et	et	PROPN
ejpam-7160	404	19	al	al	PROPN
ejpam-7160	404	20	.	.	PUNCT
ejpam-7160	404	21	/	/	SYM
ejpam-7160	404	22	eur	eur	PROPN
ejpam-7160	404	23	.	.	PUNCT
ejpam-7160	405	1	j.	j.	PROPN
ejpam-7160	405	2	pure	pure	PROPN
ejpam-7160	405	3	appl	appl	PROPN
ejpam-7160	405	4	.	.	PROPN
ejpam-7160	405	5	math	math	PROPN
ejpam-7160	405	6	,	,	PUNCT
ejpam-7160	405	7	18	18	NUM
ejpam-7160	405	8	(	(	PUNCT
ejpam-7160	405	9	4	4	NUM
ejpam-7160	405	10	)	)	PUNCT
ejpam-7160	405	11	(	(	PUNCT
ejpam-7160	405	12	2025	2025	NUM
ejpam-7160	405	13	)	)	PUNCT
ejpam-7160	405	14	,	,	PUNCT
ejpam-7160	405	15	7160	7160	NUM
ejpam-7160	405	16	15	15	NUM
ejpam-7160	405	17	of	of	ADP
ejpam-7160	405	18	22	22	NUM
ejpam-7160	405	19	(	(	PUNCT
ejpam-7160	405	20	6	6	NUM
ejpam-7160	405	21	)	)	PUNCT
ejpam-7160	405	22	×l	×l	PROPN
ejpam-7160	405	23	mn	mn	PROPN
ejpam-7160	405	24	ι	ι	PROPN
ejpam-7160	405	25	(	(	PUNCT
ejpam-7160	405	26	cc	cc	NOUN
ejpam-7160	405	27	)	)	PUNCT
ejpam-7160	405	28	=	=	SYM
ejpam-7160	405	29	(	(	PUNCT
ejpam-7160	405	30	×l	×l	PUNCT
ejpam-7160	405	31	mn	mn	PROPN
ejpam-7160	405	32	ι	ι	PROPN
ejpam-7160	405	33	(	(	PUNCT
ejpam-7160	405	34	c))c	c))c	PROPN
ejpam-7160	405	35	;	;	PUNCT
ejpam-7160	405	36	(	(	PUNCT
ejpam-7160	405	37	7	7	X
ejpam-7160	405	38	)	)	PUNCT
ejpam-7160	405	39	×l	×l	PROPN
ejpam-7160	405	40	mn	mn	PROPN
ejpam-7160	405	41	ι	ι	PROPN
ejpam-7160	405	42	(	(	PUNCT
ejpam-7160	405	43	×l	×l	PUNCT
ejpam-7160	405	44	mn	mn	PROPN
ejpam-7160	405	45	ι	ι	PROPN
ejpam-7160	405	46	(	(	PUNCT
ejpam-7160	405	47	c	c	NOUN
ejpam-7160	405	48	)	)	PUNCT
ejpam-7160	405	49	)	)	PUNCT
ejpam-7160	406	1	=	=	PUNCT
ejpam-7160	406	2	×l	×l	PROPN
ejpam-7160	406	3	mn	mn	PROPN
ejpam-7160	406	4	ι	ι	PROPN
ejpam-7160	406	5	(	(	PUNCT
ejpam-7160	406	6	c	c	NOUN
ejpam-7160	406	7	)	)	PUNCT
ejpam-7160	406	8	.	.	PUNCT
ejpam-7160	407	1	proof	proof	NOUN
ejpam-7160	407	2	.	.	PUNCT
ejpam-7160	408	1	the	the	DET
ejpam-7160	408	2	demonstration	demonstration	NOUN
ejpam-7160	408	3	parallels	parallel	VERB
ejpam-7160	408	4	that	that	SCONJ
ejpam-7160	408	5	of	of	ADP
ejpam-7160	408	6	proposition	proposition	NOUN
ejpam-7160	408	7	4.2	4.2	NUM
ejpam-7160	408	8	.	.	PUNCT
ejpam-7160	409	1	corollary	corollary	ADJ
ejpam-7160	409	2	4	4	NUM
ejpam-7160	409	3	.	.	PUNCT
ejpam-7160	410	1	if	if	SCONJ
ejpam-7160	410	2	(	(	PUNCT
ejpam-7160	410	3	π,×	π,×	PROPN
ejpam-7160	410	4	,	,	PUNCT
ejpam-7160	410	5	ζι	ζι	NOUN
ejpam-7160	410	6	)	)	PUNCT
ejpam-7160	410	7	forms	form	VERB
ejpam-7160	410	8	a	a	DET
ejpam-7160	410	9	ι	ι	ADV
ejpam-7160	410	10	-	-	PUNCT
ejpam-7160	410	11	ns	ns	ADJ
ejpam-7160	410	12	,	,	PUNCT
ejpam-7160	410	13	l	l	NOUN
ejpam-7160	410	14	denotes	denote	VERB
ejpam-7160	410	15	a	a	DET
ejpam-7160	410	16	grill	grill	NOUN
ejpam-7160	410	17	on	on	ADP
ejpam-7160	410	18	π	π	PROPN
ejpam-7160	410	19	,	,	PUNCT
ejpam-7160	410	20	and	and	CCONJ
ejpam-7160	411	1	c	c	X
ejpam-7160	411	2	,	,	PUNCT
ejpam-7160	411	3	g	g	PROPN
ejpam-7160	411	4	∈	∈	PROPN
ejpam-7160	411	5	π	π	X
ejpam-7160	411	6	.	.	PUNCT
ejpam-7160	412	1	then	then	ADV
ejpam-7160	412	2	,	,	PUNCT
ejpam-7160	412	3	×l	×l	PUNCT
ejpam-7160	412	4	mn	mn	PROPN
ejpam-7160	412	5	ι	ι	PROPN
ejpam-7160	412	6	(	(	PUNCT
ejpam-7160	412	7	c	c	NOUN
ejpam-7160	412	8	⊓g	⊓g	PROPN
ejpam-7160	412	9	)	)	PUNCT
ejpam-7160	412	10	⊑	⊑	PRON
ejpam-7160	412	11	×l	×l	PROPN
ejpam-7160	412	12	mn	mn	PROPN
ejpam-7160	412	13	ι	ι	PROPN
ejpam-7160	412	14	(	(	PUNCT
ejpam-7160	412	15	c	c	NOUN
ejpam-7160	412	16	)	)	PUNCT
ejpam-7160	412	17	⊓	⊓	PROPN
ejpam-7160	412	18	×l	×l	PROPN
ejpam-7160	412	19	mn	mn	PROPN
ejpam-7160	412	20	ι	ι	PROPN
ejpam-7160	412	21	(	(	PUNCT
ejpam-7160	412	22	g	g	NOUN
ejpam-7160	412	23	)	)	PUNCT
ejpam-7160	412	24	proof	proof	NOUN
ejpam-7160	412	25	.	.	PUNCT
ejpam-7160	413	1	it	it	PRON
ejpam-7160	413	2	is	be	AUX
ejpam-7160	413	3	directly	directly	ADV
ejpam-7160	413	4	deducible	deducible	ADJ
ejpam-7160	413	5	from	from	ADP
ejpam-7160	413	6	proposition	proposition	NOUN
ejpam-7160	413	7	4.2	4.2	NUM
ejpam-7160	413	8	(	(	PUNCT
ejpam-7160	413	9	4	4	NUM
ejpam-7160	413	10	)	)	PUNCT
ejpam-7160	413	11	.	.	PUNCT
ejpam-7160	414	1	remark	remark	NOUN
ejpam-7160	414	2	5	5	NUM
ejpam-7160	414	3	.	.	PUNCT
ejpam-7160	415	1	in	in	ADP
ejpam-7160	415	2	example	example	NOUN
ejpam-7160	415	3	3.10	3.10	NUM
ejpam-7160	415	4	,	,	PUNCT
ejpam-7160	415	5	the	the	DET
ejpam-7160	415	6	subsequent	subsequent	ADJ
ejpam-7160	415	7	propositions	proposition	NOUN
ejpam-7160	415	8	are	be	AUX
ejpam-7160	415	9	accurate	accurate	ADJ
ejpam-7160	415	10	:	:	PUNCT
ejpam-7160	415	11	(	(	PUNCT
ejpam-7160	415	12	1	1	X
ejpam-7160	415	13	)	)	PUNCT
ejpam-7160	415	14	×l	×l	NOUN
ejpam-7160	415	15	mn	mn	PROPN
ejpam-7160	415	16	r	r	NOUN
ejpam-7160	415	17	(	(	PUNCT
ejpam-7160	415	18	{	{	PUNCT
ejpam-7160	415	19	π1	π1	ADJ
ejpam-7160	415	20	⊓	⊓	PROPN
ejpam-7160	415	21	π2	π2	ADV
ejpam-7160	415	22	}	}	PUNCT
ejpam-7160	415	23	)	)	PUNCT
ejpam-7160	415	24	=	=	PUNCT
ejpam-7160	416	1	ϕ	ϕ	X
ejpam-7160	416	2	⊑	⊑	X
ejpam-7160	416	3	{	{	PUNCT
ejpam-7160	416	4	π2	π2	ADJ
ejpam-7160	416	5	}	}	PUNCT
ejpam-7160	416	6	=	=	NOUN
ejpam-7160	416	7	×l	×l	NOUN
ejpam-7160	416	8	mn	mn	PROPN
ejpam-7160	416	9	r	r	NOUN
ejpam-7160	416	10	(	(	PUNCT
ejpam-7160	416	11	{	{	PUNCT
ejpam-7160	416	12	π1	π1	NOUN
ejpam-7160	416	13	}	}	PUNCT
ejpam-7160	416	14	)	)	PUNCT
ejpam-7160	417	1	⊓	⊓	PROPN
ejpam-7160	417	2	×l	×l	NOUN
ejpam-7160	417	3	mn	mn	NOUN
ejpam-7160	417	4	r	r	NOUN
ejpam-7160	417	5	(	(	PUNCT
ejpam-7160	417	6	{	{	PUNCT
ejpam-7160	417	7	π2	π2	NOUN
ejpam-7160	417	8	)	)	PUNCT
ejpam-7160	417	9	}	}	PUNCT
ejpam-7160	417	10	)	)	PUNCT
ejpam-7160	417	11	;	;	PUNCT
ejpam-7160	417	12	(	(	PUNCT
ejpam-7160	417	13	2	2	X
ejpam-7160	417	14	)	)	PUNCT
ejpam-7160	417	15	×l	×l	NOUN
ejpam-7160	417	16	mn	mn	PROPN
ejpam-7160	417	17	r	r	NOUN
ejpam-7160	417	18	(	(	PUNCT
ejpam-7160	417	19	{	{	PUNCT
ejpam-7160	417	20	π2	π2	ADV
ejpam-7160	417	21	}	}	PUNCT
ejpam-7160	417	22	)	)	PUNCT
ejpam-7160	417	23	=	=	SYM
ejpam-7160	417	24	{	{	PUNCT
ejpam-7160	417	25	π2	π2	X
ejpam-7160	417	26	}	}	PUNCT
ejpam-7160	417	27	⊑	⊑	X
ejpam-7160	417	28	{	{	PUNCT
ejpam-7160	417	29	π2	π2	ADJ
ejpam-7160	417	30	,	,	PUNCT
ejpam-7160	417	31	π4	π4	NOUN
ejpam-7160	417	32	}	}	PUNCT
ejpam-7160	417	33	=	=	PUNCT
ejpam-7160	417	34	×l	×l	NOUN
ejpam-7160	417	35	mn	mn	PROPN
ejpam-7160	417	36	r	r	NOUN
ejpam-7160	417	37	(	(	PUNCT
ejpam-7160	417	38	{	{	PUNCT
ejpam-7160	417	39	π2	π2	ADJ
ejpam-7160	417	40	,	,	PUNCT
ejpam-7160	417	41	π4	π4	NOUN
ejpam-7160	417	42	}	}	PUNCT
ejpam-7160	417	43	)	)	PUNCT
ejpam-7160	417	44	;	;	PUNCT
ejpam-7160	417	45	(	(	PUNCT
ejpam-7160	417	46	3	3	X
ejpam-7160	417	47	)	)	PUNCT
ejpam-7160	417	48	{	{	PUNCT
ejpam-7160	417	49	π1	π1	NOUN
ejpam-7160	417	50	,	,	PUNCT
ejpam-7160	417	51	π3	π3	PROPN
ejpam-7160	417	52	}	}	PUNCT
ejpam-7160	417	53	⊑	⊑	X
ejpam-7160	417	54	×l	×l	PROPN
ejpam-7160	417	55	mn	mn	PROPN
ejpam-7160	417	56	r	r	NOUN
ejpam-7160	417	57	(	(	PUNCT
ejpam-7160	417	58	{	{	PUNCT
ejpam-7160	417	59	π1	π1	NOUN
ejpam-7160	417	60	,	,	PUNCT
ejpam-7160	417	61	π3	π3	NOUN
ejpam-7160	417	62	}	}	PUNCT
ejpam-7160	417	63	)	)	PUNCT
ejpam-7160	417	64	=	=	SYM
ejpam-7160	417	65	{	{	PUNCT
ejpam-7160	417	66	π1	π1	NOUN
ejpam-7160	417	67	,	,	PUNCT
ejpam-7160	417	68	π2	π2	ADJ
ejpam-7160	417	69	,	,	PUNCT
ejpam-7160	417	70	π3	π3	NOUN
ejpam-7160	417	71	}	}	PUNCT
ejpam-7160	417	72	.	.	PUNCT
ejpam-7160	418	1	definition	definition	NOUN
ejpam-7160	418	2	18	18	NUM
ejpam-7160	418	3	.	.	PUNCT
ejpam-7160	419	1	if	if	SCONJ
ejpam-7160	419	2	(	(	PUNCT
ejpam-7160	419	3	π,×	π,×	PROPN
ejpam-7160	419	4	,	,	PUNCT
ejpam-7160	419	5	ζι	ζι	NOUN
ejpam-7160	419	6	)	)	PUNCT
ejpam-7160	419	7	forms	form	VERB
ejpam-7160	419	8	a	a	DET
ejpam-7160	419	9	ι	ι	ADV
ejpam-7160	419	10	-	-	PUNCT
ejpam-7160	419	11	ns	ns	ADJ
ejpam-7160	419	12	,	,	PUNCT
ejpam-7160	419	13	l	l	NOUN
ejpam-7160	419	14	denotes	denote	VERB
ejpam-7160	419	15	a	a	DET
ejpam-7160	419	16	grill	grill	NOUN
ejpam-7160	419	17	on	on	ADP
ejpam-7160	419	18	π	π	PROPN
ejpam-7160	419	19	.	.	PUNCT
ejpam-7160	420	1	the	the	DET
ejpam-7160	420	2	l	l	PROPN
ejpam-7160	420	3	-	-	PROPN
ejpam-7160	420	4	mn	mn	ADJ
ejpam-7160	420	5	ι	ι	NOUN
ejpam-7160	420	6	-	-	PUNCT
ejpam-7160	420	7	accuracy	accuracy	NOUN
ejpam-7160	420	8	is	be	AUX
ejpam-7160	420	9	al	al	PROPN
ejpam-7160	420	10	mn	mn	PROPN
ejpam-7160	420	11	ι	ι	PROPN
ejpam-7160	420	12	(	(	PUNCT
ejpam-7160	420	13	c	c	NOUN
ejpam-7160	420	14	)	)	PUNCT
ejpam-7160	420	15	=	=	SYM
ejpam-7160	420	16	|×l	|×l	PROPN
ejpam-7160	420	17	mn	mn	PROPN
ejpam-7160	420	18	ι	ι	PROPN
ejpam-7160	421	1	(	(	PUNCT
ejpam-7160	421	2	c)|	c)|	PROPN
ejpam-7160	421	3	|×l	|×l	NOUN
ejpam-7160	421	4	mn	mn	PROPN
ejpam-7160	421	5	ι	ι	PROPN
ejpam-7160	421	6	(	(	PUNCT
ejpam-7160	421	7	c)|	c)|	PROPN
ejpam-7160	421	8	,	,	PUNCT
ejpam-7160	421	9	where	where	SCONJ
ejpam-7160	421	10	c	c	X
ejpam-7160	421	11	̸=	̸=	PROPN
ejpam-7160	421	12	ϕ	ϕ	NOUN
ejpam-7160	421	13	,	,	PUNCT
ejpam-7160	421	14	proposition	proposition	NOUN
ejpam-7160	421	15	4.9	4.9	NUM
ejpam-7160	421	16	ensures	ensure	VERB
ejpam-7160	421	17	that	that	SCONJ
ejpam-7160	421	18	when	when	SCONJ
ejpam-7160	421	19	more	more	ADJ
ejpam-7160	421	20	data	datum	NOUN
ejpam-7160	421	21	is	be	AUX
ejpam-7160	421	22	added	add	VERB
ejpam-7160	421	23	,	,	PUNCT
ejpam-7160	421	24	the	the	DET
ejpam-7160	421	25	lo	lo	PROPN
ejpam-7160	421	26	-	-	PUNCT
ejpam-7160	421	27	app	app	NOUN
ejpam-7160	421	28	wo	will	AUX
ejpam-7160	421	29	n’t	not	PART
ejpam-7160	421	30	get	get	VERB
ejpam-7160	421	31	smaller	small	ADJ
ejpam-7160	421	32	.	.	PUNCT
ejpam-7160	422	1	similarly	similarly	ADV
ejpam-7160	422	2	,	,	PUNCT
ejpam-7160	422	3	there	there	PRON
ejpam-7160	422	4	is	be	VERB
ejpam-7160	422	5	no	no	DET
ejpam-7160	422	6	drop	drop	NOUN
ejpam-7160	422	7	in	in	ADP
ejpam-7160	422	8	the	the	DET
ejpam-7160	422	9	up	up	ADV
ejpam-7160	422	10	-	-	PUNCT
ejpam-7160	422	11	app	app	NOUN
ejpam-7160	422	12	.	.	PUNCT
ejpam-7160	423	1	thus	thus	ADV
ejpam-7160	423	2	,	,	PUNCT
ejpam-7160	423	3	monotonicity	monotonicity	NOUN
ejpam-7160	423	4	is	be	AUX
ejpam-7160	423	5	a	a	DET
ejpam-7160	423	6	characteristic	characteristic	NOUN
ejpam-7160	423	7	of	of	ADP
ejpam-7160	423	8	the	the	DET
ejpam-7160	423	9	suggested	suggest	VERB
ejpam-7160	423	10	model	model	NOUN
ejpam-7160	423	11	.	.	PUNCT
ejpam-7160	424	1	this	this	DET
ejpam-7160	424	2	characteristic	characteristic	ADJ
ejpam-7160	424	3	guarantees	guarantee	VERB
ejpam-7160	424	4	that	that	SCONJ
ejpam-7160	424	5	when	when	SCONJ
ejpam-7160	424	6	additional	additional	ADJ
ejpam-7160	424	7	information	information	NOUN
ejpam-7160	424	8	becomes	become	VERB
ejpam-7160	424	9	available	available	ADJ
ejpam-7160	424	10	,	,	PUNCT
ejpam-7160	424	11	the	the	DET
ejpam-7160	424	12	apps	app	NOUN
ejpam-7160	424	13	either	either	CCONJ
ejpam-7160	424	14	increase	increase	VERB
ejpam-7160	424	15	in	in	ADP
ejpam-7160	424	16	accuracy	accuracy	NOUN
ejpam-7160	424	17	or	or	CCONJ
ejpam-7160	424	18	remain	remain	VERB
ejpam-7160	424	19	constant	constant	ADJ
ejpam-7160	424	20	,	,	PUNCT
ejpam-7160	424	21	never	never	ADV
ejpam-7160	424	22	declining	decline	VERB
ejpam-7160	424	23	.	.	PUNCT
ejpam-7160	425	1	proposition	proposition	NOUN
ejpam-7160	425	2	6	6	NUM
ejpam-7160	425	3	.	.	PUNCT
ejpam-7160	426	1	let	let	VERB
ejpam-7160	426	2	(	(	PUNCT
ejpam-7160	426	3	π,×1	π,×1	NUM
ejpam-7160	426	4	,	,	PUNCT
ejpam-7160	426	5	ζ1ι	ζ1ι	PROPN
ejpam-7160	426	6	)	)	PUNCT
ejpam-7160	426	7	and	and	CCONJ
ejpam-7160	426	8	(	(	PUNCT
ejpam-7160	426	9	π,×2	π,×2	NOUN
ejpam-7160	426	10	,	,	PUNCT
ejpam-7160	426	11	ζ2ι	ζ2ι	NOUN
ejpam-7160	426	12	)	)	PUNCT
ejpam-7160	426	13	be	be	AUX
ejpam-7160	426	14	two	two	NUM
ejpam-7160	426	15	ι	ι	ADV
ejpam-7160	426	16	-	-	PUNCT
ejpam-7160	426	17	ns	ns	ADJ
ejpam-7160	426	18	,	,	PUNCT
ejpam-7160	426	19	l	l	NOUN
ejpam-7160	426	20	represent	represent	VERB
ejpam-7160	426	21	a	a	DET
ejpam-7160	426	22	grill	grill	NOUN
ejpam-7160	426	23	on	on	ADP
ejpam-7160	426	24	π	π	PROPN
ejpam-7160	426	25	,	,	PUNCT
ejpam-7160	426	26	and	and	CCONJ
ejpam-7160	426	27	×.	×.	PROPN
ejpam-7160	426	28	⊑	⊑	PRON
ejpam-7160	426	29	×	×	NOUN
ejpam-7160	426	30	...	...	PUNCT
ejpam-7160	426	31	for	for	ADP
ejpam-7160	426	32	all	all	PRON
ejpam-7160	426	33	ι	ι	PRON
ejpam-7160	426	34	∈	∈	NOUN
ejpam-7160	426	35	{	{	PUNCT
ejpam-7160	426	36	r	r	NOUN
ejpam-7160	426	37	,	,	PUNCT
ejpam-7160	426	38	l	l	NOUN
ejpam-7160	426	39	,	,	PUNCT
ejpam-7160	426	40	i	i	PRON
ejpam-7160	426	41	,	,	PUNCT
ejpam-7160	426	42	u	u	NOUN
ejpam-7160	426	43	}	}	PUNCT
ejpam-7160	426	44	,	,	PUNCT
ejpam-7160	426	45	c	c	PROPN
ejpam-7160	426	46	is	be	AUX
ejpam-7160	426	47	a	a	DET
ejpam-7160	426	48	subclass	subclass	NOUN
ejpam-7160	426	49	of	of	ADP
ejpam-7160	426	50	π	π	PROPN
ejpam-7160	426	51	,	,	PUNCT
ejpam-7160	426	52	and	and	CCONJ
ejpam-7160	426	53	the	the	DET
ejpam-7160	426	54	subsequent	subsequent	ADJ
ejpam-7160	426	55	propositions	proposition	NOUN
ejpam-7160	426	56	are	be	AUX
ejpam-7160	426	57	accurate	accurate	ADJ
ejpam-7160	426	58	:	:	PUNCT
ejpam-7160	426	59	(	(	PUNCT
ejpam-7160	426	60	1	1	X
ejpam-7160	426	61	)	)	PUNCT
ejpam-7160	426	62	×l	×l	NOUN
ejpam-7160	426	63	mn	mn	NOUN
ejpam-7160	426	64	1ι	1ι	NUM
ejpam-7160	426	65	(	(	PUNCT
ejpam-7160	426	66	c	c	X
ejpam-7160	426	67	)	)	PUNCT
ejpam-7160	426	68	⊑	⊑	PRON
ejpam-7160	426	69	×l	×l	PROPN
ejpam-7160	426	70	mn	mn	PROPN
ejpam-7160	426	71	2ι	2ι	NUM
ejpam-7160	426	72	(	(	PUNCT
ejpam-7160	426	73	c	c	NOUN
ejpam-7160	426	74	)	)	PUNCT
ejpam-7160	426	75	;	;	PUNCT
ejpam-7160	426	76	(	(	PUNCT
ejpam-7160	426	77	2	2	X
ejpam-7160	426	78	)	)	PUNCT
ejpam-7160	426	79	×l	×l	PROPN
ejpam-7160	426	80	mn	mn	PROPN
ejpam-7160	426	81	2ι	2ι	NUM
ejpam-7160	426	82	(	(	PUNCT
ejpam-7160	426	83	c	c	X
ejpam-7160	426	84	)	)	PUNCT
ejpam-7160	426	85	⊑	⊑	PRON
ejpam-7160	426	86	×l	×l	PROPN
ejpam-7160	426	87	mn	mn	PROPN
ejpam-7160	426	88	1ι	1ι	NUM
ejpam-7160	426	89	(	(	PUNCT
ejpam-7160	426	90	c	c	NOUN
ejpam-7160	426	91	)	)	PUNCT
ejpam-7160	426	92	;	;	PUNCT
ejpam-7160	426	93	(	(	PUNCT
ejpam-7160	426	94	3	3	X
ejpam-7160	426	95	)	)	PUNCT
ejpam-7160	426	96	al	al	PROPN
ejpam-7160	426	97	mn	mn	PROPN
ejpam-7160	426	98	2ι	2ι	PROPN
ejpam-7160	426	99	(	(	PUNCT
ejpam-7160	426	100	c	c	NOUN
ejpam-7160	426	101	)	)	PUNCT
ejpam-7160	426	102	≤	≤	NOUN
ejpam-7160	426	103	al	al	PROPN
ejpam-7160	426	104	mn	mn	PROPN
ejpam-7160	426	105	1ι	1ι	NUM
ejpam-7160	426	106	(	(	PUNCT
ejpam-7160	426	107	c	c	NOUN
ejpam-7160	426	108	)	)	PUNCT
ejpam-7160	426	109	.	.	PUNCT
ejpam-7160	427	1	proof	proof	NOUN
ejpam-7160	427	2	.	.	PUNCT
ejpam-7160	428	1	(	(	PUNCT
ejpam-7160	428	2	1	1	X
ejpam-7160	428	3	)	)	PUNCT
ejpam-7160	428	4	×l	×l	NOUN
ejpam-7160	428	5	mn	mn	NOUN
ejpam-7160	428	6	1ι	1ι	NUM
ejpam-7160	428	7	(	(	PUNCT
ejpam-7160	428	8	c	c	X
ejpam-7160	428	9	)	)	PUNCT
ejpam-7160	428	10	=	=	SYM
ejpam-7160	428	11	⊓{y	⊓{y	PUNCT
ejpam-7160	428	12	∈	∈	ADJ
ejpam-7160	428	13	τlmn	τlmn	NOUN
ejpam-7160	428	14	1ι	1ι	NOUN
ejpam-7160	428	15	:	:	PUNCT
ejpam-7160	428	16	c	c	NOUN
ejpam-7160	428	17	⊑	⊑	X
ejpam-7160	428	18	y	y	PROPN
ejpam-7160	428	19	}	}	PUNCT
ejpam-7160	428	20	⊑	⊑	PRON
ejpam-7160	428	21	⊓{y	⊓{y	PROPN
ejpam-7160	428	22	∈	∈	PROPN
ejpam-7160	428	23	τlmn	τlmn	NOUN
ejpam-7160	428	24	2ι	2ι	NUM
ejpam-7160	428	25	:	:	PUNCT
ejpam-7160	428	26	c	c	X
ejpam-7160	428	27	⊑	⊑	X
ejpam-7160	428	28	y	y	PROPN
ejpam-7160	428	29	}	}	PUNCT
ejpam-7160	428	30	=	=	PUNCT
ejpam-7160	428	31	×l	×l	PROPN
ejpam-7160	428	32	mn	mn	PROPN
ejpam-7160	428	33	2ι	2ι	NUM
ejpam-7160	428	34	(	(	PUNCT
ejpam-7160	428	35	c	c	NOUN
ejpam-7160	428	36	)	)	PUNCT
ejpam-7160	428	37	(	(	PUNCT
ejpam-7160	428	38	from	from	ADP
ejpam-7160	428	39	proposition	proposition	NOUN
ejpam-7160	428	40	3.18	3.18	NUM
ejpam-7160	428	41	)	)	PUNCT
ejpam-7160	428	42	.	.	PUNCT
ejpam-7160	429	1	so	so	ADV
ejpam-7160	429	2	,	,	PUNCT
ejpam-7160	429	3	×l	×l	PUNCT
ejpam-7160	429	4	mn	mn	PROPN
ejpam-7160	429	5	1ι	1ι	NUM
ejpam-7160	429	6	(	(	PUNCT
ejpam-7160	429	7	c	c	X
ejpam-7160	429	8	)	)	PUNCT
ejpam-7160	429	9	⊑	⊑	PRON
ejpam-7160	429	10	×l	×l	PROPN
ejpam-7160	429	11	mn	mn	PROPN
ejpam-7160	429	12	2ι	2ι	NUM
ejpam-7160	429	13	(	(	PUNCT
ejpam-7160	429	14	c	c	NOUN
ejpam-7160	429	15	)	)	PUNCT
ejpam-7160	429	16	.	.	PUNCT
ejpam-7160	430	1	(	(	PUNCT
ejpam-7160	430	2	2	2	X
ejpam-7160	430	3	)	)	PUNCT
ejpam-7160	430	4	let	let	VERB
ejpam-7160	430	5	×l	×l	PROPN
ejpam-7160	430	6	mn	mn	PROPN
ejpam-7160	430	7	2ι	2ι	PROPN
ejpam-7160	430	8	(	(	PUNCT
ejpam-7160	430	9	c	c	NOUN
ejpam-7160	430	10	)	)	PUNCT
ejpam-7160	430	11	=	=	SYM
ejpam-7160	430	12	⊔{g	⊔{g	PROPN
ejpam-7160	430	13	∈	∈	PROPN
ejpam-7160	430	14	τlmn	τlmn	NOUN
ejpam-7160	430	15	2ι	2ι	NUM
ejpam-7160	430	16	:	:	PUNCT
ejpam-7160	430	17	g	g	X
ejpam-7160	430	18	⊑	⊑	X
ejpam-7160	430	19	c	c	AUX
ejpam-7160	430	20	}	}	PUNCT
ejpam-7160	430	21	⊑	⊑	DET
ejpam-7160	430	22	⊔{g	⊔{g	PROPN
ejpam-7160	430	23	∈	∈	PROPN
ejpam-7160	430	24	τlmn	τlmn	NOUN
ejpam-7160	430	25	1ι	1ι	NOUN
ejpam-7160	430	26	:	:	PUNCT
ejpam-7160	431	1	g	g	X
ejpam-7160	431	2	⊑	⊑	X
ejpam-7160	431	3	c	c	X
ejpam-7160	431	4	}	}	PUNCT
ejpam-7160	431	5	=	=	NOUN
ejpam-7160	431	6	×l	×l	NOUN
ejpam-7160	431	7	mn	mn	NOUN
ejpam-7160	431	8	1ι	1ι	NUM
ejpam-7160	431	9	(	(	PUNCT
ejpam-7160	431	10	c	c	NOUN
ejpam-7160	431	11	)	)	PUNCT
ejpam-7160	431	12	(	(	PUNCT
ejpam-7160	431	13	from	from	ADP
ejpam-7160	431	14	proposition	proposition	NOUN
ejpam-7160	431	15	3.18	3.18	NUM
ejpam-7160	431	16	)	)	PUNCT
ejpam-7160	431	17	.	.	PUNCT
ejpam-7160	432	1	so	so	ADV
ejpam-7160	432	2	,	,	PUNCT
ejpam-7160	432	3	×l	×l	PUNCT
ejpam-7160	432	4	mn	mn	PROPN
ejpam-7160	432	5	2ι	2ι	NUM
ejpam-7160	432	6	(	(	PUNCT
ejpam-7160	432	7	c	c	X
ejpam-7160	432	8	)	)	PUNCT
ejpam-7160	432	9	⊑	⊑	PRON
ejpam-7160	432	10	×l	×l	PROPN
ejpam-7160	432	11	mn	mn	PROPN
ejpam-7160	432	12	1ι	1ι	NUM
ejpam-7160	432	13	(	(	PUNCT
ejpam-7160	432	14	c	c	NOUN
ejpam-7160	432	15	)	)	PUNCT
ejpam-7160	432	16	.	.	PUNCT
ejpam-7160	433	1	a.	a.	PROPN
ejpam-7160	433	2	a.	a.	PROPN
ejpam-7160	433	3	azzam	azzam	PROPN
ejpam-7160	433	4	et	et	PROPN
ejpam-7160	433	5	al	al	PROPN
ejpam-7160	433	6	.	.	PUNCT
ejpam-7160	433	7	/	/	SYM
ejpam-7160	433	8	eur	eur	PROPN
ejpam-7160	433	9	.	.	PUNCT
ejpam-7160	434	1	j.	j.	PROPN
ejpam-7160	434	2	pure	pure	PROPN
ejpam-7160	434	3	appl	appl	PROPN
ejpam-7160	434	4	.	.	PROPN
ejpam-7160	434	5	math	math	PROPN
ejpam-7160	434	6	,	,	PUNCT
ejpam-7160	434	7	18	18	NUM
ejpam-7160	434	8	(	(	PUNCT
ejpam-7160	434	9	4	4	NUM
ejpam-7160	434	10	)	)	PUNCT
ejpam-7160	434	11	(	(	PUNCT
ejpam-7160	434	12	2025	2025	NUM
ejpam-7160	434	13	)	)	PUNCT
ejpam-7160	434	14	,	,	PUNCT
ejpam-7160	434	15	7160	7160	NUM
ejpam-7160	434	16	16	16	NUM
ejpam-7160	434	17	of	of	ADP
ejpam-7160	434	18	22	22	NUM
ejpam-7160	434	19	(	(	PUNCT
ejpam-7160	434	20	3	3	NUM
ejpam-7160	434	21	)	)	PUNCT
ejpam-7160	434	22	al	al	PROPN
ejpam-7160	434	23	mn	mn	PROPN
ejpam-7160	434	24	1ι	1ι	NUM
ejpam-7160	434	25	(	(	PUNCT
ejpam-7160	434	26	c	c	NOUN
ejpam-7160	434	27	)	)	PUNCT
ejpam-7160	434	28	=	=	SYM
ejpam-7160	434	29	|×l	|×l	NOUN
ejpam-7160	434	30	mn1ι	mn1ι	NOUN
ejpam-7160	434	31	(	(	PUNCT
ejpam-7160	434	32	c)|	c)|	PROPN
ejpam-7160	434	33	|×l	|×l	NOUN
ejpam-7160	434	34	mn1ι	mn1ι	PROPN
ejpam-7160	434	35	(	(	PUNCT
ejpam-7160	434	36	c)|	c)|	PROPN
ejpam-7160	434	37	≤	≤	NOUN
ejpam-7160	434	38	|×l	|×l	NOUN
ejpam-7160	434	39	mn2ι	mn2ι	PROPN
ejpam-7160	434	40	(	(	PUNCT
ejpam-7160	434	41	c)|	c)|	PROPN
ejpam-7160	434	42	|×l	|×l	NOUN
ejpam-7160	434	43	mn2ι	mn2ι	PROPN
ejpam-7160	434	44	(	(	PUNCT
ejpam-7160	434	45	c)|	c)|	PROPN
ejpam-7160	434	46	=	=	PUNCT
ejpam-7160	434	47	al	al	PROPN
ejpam-7160	434	48	mn	mn	PROPN
ejpam-7160	434	49	2ι	2ι	PROPN
ejpam-7160	434	50	(	(	PUNCT
ejpam-7160	434	51	c	c	NOUN
ejpam-7160	434	52	)	)	PUNCT
ejpam-7160	434	53	definition	definition	NOUN
ejpam-7160	434	54	19	19	NUM
ejpam-7160	434	55	.	.	PUNCT
ejpam-7160	435	1	if	if	SCONJ
ejpam-7160	435	2	(	(	PUNCT
ejpam-7160	435	3	π,×	π,×	PROPN
ejpam-7160	435	4	,	,	PUNCT
ejpam-7160	435	5	ζι	ζι	NOUN
ejpam-7160	435	6	)	)	PUNCT
ejpam-7160	435	7	forms	form	VERB
ejpam-7160	435	8	a	a	DET
ejpam-7160	435	9	ι	ι	ADV
ejpam-7160	435	10	-	-	PUNCT
ejpam-7160	435	11	ns	ns	ADJ
ejpam-7160	435	12	,	,	PUNCT
ejpam-7160	435	13	l	l	NOUN
ejpam-7160	435	14	denotes	denote	VERB
ejpam-7160	435	15	a	a	DET
ejpam-7160	435	16	grill	grill	NOUN
ejpam-7160	435	17	on	on	ADP
ejpam-7160	435	18	π	π	PROPN
ejpam-7160	435	19	.	.	PUNCT
ejpam-7160	436	1	the	the	DET
ejpam-7160	436	2	l	l	PROPN
ejpam-7160	436	3	-	-	PROPN
ejpam-7160	436	4	mn	mn	ADJ
ejpam-7160	436	5	ι	ι	NOUN
ejpam-7160	436	6	-	-	PUNCT
ejpam-7160	436	7	positive	positive	ADJ
ejpam-7160	436	8	,	,	PUNCT
ejpam-7160	436	9	l	l	PROPN
ejpam-7160	436	10	-	-	NOUN
ejpam-7160	436	11	mn	mn	ADJ
ejpam-7160	436	12	ι	ι	NOUN
ejpam-7160	436	13	-	-	PUNCT
ejpam-7160	436	14	boundary	boundary	ADJ
ejpam-7160	436	15	,	,	PUNCT
ejpam-7160	436	16	and	and	CCONJ
ejpam-7160	436	17	l	l	PROPN
ejpam-7160	436	18	-	-	PROPN
ejpam-7160	436	19	mn	mn	ADJ
ejpam-7160	436	20	ι	ι	PROPN
ejpam-7160	436	21	-	-	PUNCT
ejpam-7160	436	22	negative	negative	ADJ
ejpam-7160	436	23	regions	region	NOUN
ejpam-7160	436	24	of	of	ADP
ejpam-7160	436	25	c	c	NOUN
ejpam-7160	436	26	⊑	⊑	X
ejpam-7160	436	27	π	π	PROPN
ejpam-7160	436	28	are	be	AUX
ejpam-7160	436	29	×l+	×l+	PROPN
ejpam-7160	436	30	mn	mn	PROPN
ejpam-7160	436	31	ι	ι	PROPN
ejpam-7160	436	32	(	(	PUNCT
ejpam-7160	436	33	c	c	NOUN
ejpam-7160	436	34	)	)	PUNCT
ejpam-7160	436	35	=	=	SYM
ejpam-7160	436	36	×l	×l	PROPN
ejpam-7160	436	37	mn	mn	PROPN
ejpam-7160	436	38	ι	ι	X
ejpam-7160	436	39	(	(	PUNCT
ejpam-7160	436	40	c	c	NOUN
ejpam-7160	436	41	)	)	PUNCT
ejpam-7160	436	42	,	,	PUNCT
ejpam-7160	436	43	×l−	×l−	VERB
ejpam-7160	436	44	mn	mn	PROPN
ejpam-7160	436	45	ι	ι	PROPN
ejpam-7160	436	46	(	(	PUNCT
ejpam-7160	436	47	c	c	NOUN
ejpam-7160	436	48	)	)	PUNCT
ejpam-7160	437	1	=	=	PUNCT
ejpam-7160	437	2	π\×l	π\×l	PROPN
ejpam-7160	437	3	mn	mn	PROPN
ejpam-7160	437	4	ι	ι	X
ejpam-7160	437	5	(	(	PUNCT
ejpam-7160	437	6	c	c	NOUN
ejpam-7160	437	7	)	)	PUNCT
ejpam-7160	437	8	,	,	PUNCT
ejpam-7160	437	9	bl	bl	PROPN
ejpam-7160	437	10	mn	mn	PROPN
ejpam-7160	438	1	ι	ι	PROPN
ejpam-7160	438	2	(	(	PUNCT
ejpam-7160	438	3	c	c	NOUN
ejpam-7160	438	4	)	)	PUNCT
ejpam-7160	438	5	=	=	SYM
ejpam-7160	439	1	×l	×l	PROPN
ejpam-7160	439	2	mn	mn	PROPN
ejpam-7160	439	3	ι	ι	PROPN
ejpam-7160	439	4	(	(	PUNCT
ejpam-7160	439	5	c)\×l	c)\×l	PROPN
ejpam-7160	439	6	mn	mn	PROPN
ejpam-7160	439	7	ι	ι	PROPN
ejpam-7160	439	8	(	(	PUNCT
ejpam-7160	439	9	c	c	NOUN
ejpam-7160	439	10	)	)	PUNCT
ejpam-7160	439	11	.	.	PUNCT
ejpam-7160	440	1	proposition	proposition	NOUN
ejpam-7160	440	2	7	7	NUM
ejpam-7160	440	3	.	.	PUNCT
ejpam-7160	441	1	let	let	VERB
ejpam-7160	441	2	(	(	PUNCT
ejpam-7160	441	3	π,×1	π,×1	NUM
ejpam-7160	441	4	,	,	PUNCT
ejpam-7160	441	5	ζ1ι	ζ1ι	PROPN
ejpam-7160	441	6	)	)	PUNCT
ejpam-7160	441	7	and	and	CCONJ
ejpam-7160	441	8	(	(	PUNCT
ejpam-7160	441	9	π,×2	π,×2	NOUN
ejpam-7160	441	10	,	,	PUNCT
ejpam-7160	441	11	ζ2ι	ζ2ι	NOUN
ejpam-7160	441	12	)	)	PUNCT
ejpam-7160	441	13	be	be	AUX
ejpam-7160	441	14	two	two	NUM
ejpam-7160	441	15	ι	ι	ADV
ejpam-7160	441	16	-	-	PUNCT
ejpam-7160	441	17	ns	ns	ADJ
ejpam-7160	441	18	,	,	PUNCT
ejpam-7160	441	19	l	l	NOUN
ejpam-7160	441	20	represent	represent	VERB
ejpam-7160	441	21	a	a	DET
ejpam-7160	441	22	grill	grill	NOUN
ejpam-7160	441	23	on	on	ADP
ejpam-7160	441	24	π	π	PROPN
ejpam-7160	441	25	,	,	PUNCT
ejpam-7160	441	26	and	and	CCONJ
ejpam-7160	441	27	×.	×.	PROPN
ejpam-7160	441	28	⊑	⊑	PRON
ejpam-7160	441	29	×	×	NOUN
ejpam-7160	441	30	...	...	PUNCT
ejpam-7160	441	31	for	for	ADP
ejpam-7160	441	32	all	all	PRON
ejpam-7160	441	33	ι	ι	PRON
ejpam-7160	441	34	∈	∈	NOUN
ejpam-7160	441	35	{	{	PUNCT
ejpam-7160	441	36	r	r	NOUN
ejpam-7160	441	37	,	,	PUNCT
ejpam-7160	441	38	l	l	NOUN
ejpam-7160	441	39	,	,	PUNCT
ejpam-7160	441	40	i	i	PRON
ejpam-7160	441	41	,	,	PUNCT
ejpam-7160	441	42	u	u	NOUN
ejpam-7160	441	43	}	}	PUNCT
ejpam-7160	441	44	,	,	PUNCT
ejpam-7160	441	45	c	c	PROPN
ejpam-7160	441	46	is	be	AUX
ejpam-7160	441	47	a	a	DET
ejpam-7160	441	48	subclass	subclass	NOUN
ejpam-7160	441	49	of	of	ADP
ejpam-7160	441	50	π	π	PROPN
ejpam-7160	441	51	,	,	PUNCT
ejpam-7160	441	52	and	and	CCONJ
ejpam-7160	441	53	the	the	DET
ejpam-7160	441	54	subsequent	subsequent	ADJ
ejpam-7160	441	55	propositions	proposition	NOUN
ejpam-7160	441	56	are	be	AUX
ejpam-7160	441	57	accurate	accurate	ADJ
ejpam-7160	441	58	:	:	PUNCT
ejpam-7160	441	59	(	(	PUNCT
ejpam-7160	441	60	1	1	X
ejpam-7160	441	61	)	)	PUNCT
ejpam-7160	441	62	bl	bl	NOUN
ejpam-7160	441	63	mn	mn	PROPN
ejpam-7160	441	64	1ι	1ι	NUM
ejpam-7160	441	65	(	(	PUNCT
ejpam-7160	441	66	c	c	X
ejpam-7160	441	67	)	)	PUNCT
ejpam-7160	441	68	⊑	⊑	PROPN
ejpam-7160	442	1	bl	bl	PROPN
ejpam-7160	442	2	mn	mn	PROPN
ejpam-7160	442	3	2ι	2ι	PROPN
ejpam-7160	442	4	(	(	PUNCT
ejpam-7160	442	5	c	c	NOUN
ejpam-7160	442	6	)	)	PUNCT
ejpam-7160	442	7	;	;	PUNCT
ejpam-7160	442	8	(	(	PUNCT
ejpam-7160	442	9	2	2	X
ejpam-7160	442	10	)	)	PUNCT
ejpam-7160	442	11	×l−	×l−	NOUN
ejpam-7160	442	12	mn	mn	PROPN
ejpam-7160	442	13	2ι	2ι	PROPN
ejpam-7160	442	14	(	(	PUNCT
ejpam-7160	442	15	c	c	X
ejpam-7160	442	16	)	)	PUNCT
ejpam-7160	442	17	⊑	⊑	PART
ejpam-7160	442	18	×l−	×l−	VERB
ejpam-7160	442	19	mn	mn	NOUN
ejpam-7160	442	20	1ι	1ι	NOUN
ejpam-7160	442	21	(	(	PUNCT
ejpam-7160	442	22	c	c	NOUN
ejpam-7160	442	23	)	)	PUNCT
ejpam-7160	442	24	.	.	PUNCT
ejpam-7160	443	1	proof	proof	NOUN
ejpam-7160	443	2	.	.	PUNCT
ejpam-7160	444	1	(	(	PUNCT
ejpam-7160	444	2	1	1	X
ejpam-7160	444	3	)	)	PUNCT
ejpam-7160	444	4	let	let	VERB
ejpam-7160	444	5	π1	π1	PROPN
ejpam-7160	444	6	∈	∈	PROPN
ejpam-7160	444	7	bl	bl	PROPN
ejpam-7160	444	8	mn	mn	PROPN
ejpam-7160	444	9	1ι	1ι	NUM
ejpam-7160	444	10	(	(	PUNCT
ejpam-7160	444	11	c	c	NOUN
ejpam-7160	444	12	)	)	PUNCT
ejpam-7160	444	13	.	.	PUNCT
ejpam-7160	445	1	then	then	ADV
ejpam-7160	445	2	,	,	PUNCT
ejpam-7160	445	3	π1	π1	PROPN
ejpam-7160	445	4	∈	∈	PROPN
ejpam-7160	445	5	×l	×l	PROPN
ejpam-7160	445	6	mn	mn	PROPN
ejpam-7160	445	7	1ι	1ι	NUM
ejpam-7160	445	8	(	(	PUNCT
ejpam-7160	445	9	c)\×l	c)\×l	NOUN
ejpam-7160	445	10	mn	mn	PROPN
ejpam-7160	445	11	1ι	1ι	NUM
ejpam-7160	445	12	(	(	PUNCT
ejpam-7160	445	13	c	c	NOUN
ejpam-7160	445	14	)	)	PUNCT
ejpam-7160	445	15	.	.	PUNCT
ejpam-7160	446	1	therefore	therefore	ADV
ejpam-7160	446	2	,	,	PUNCT
ejpam-7160	446	3	π1	π1	PROPN
ejpam-7160	446	4	∈	∈	PROPN
ejpam-7160	446	5	×l	×l	NOUN
ejpam-7160	446	6	mn	mn	NOUN
ejpam-7160	446	7	1ι	1ι	NUM
ejpam-7160	446	8	(	(	PUNCT
ejpam-7160	446	9	c	c	NOUN
ejpam-7160	446	10	)	)	PUNCT
ejpam-7160	446	11	,	,	PUNCT
ejpam-7160	446	12	and	and	CCONJ
ejpam-7160	446	13	π1	π1	ADJ
ejpam-7160	446	14	∈	∈	PROPN
ejpam-7160	446	15	(	(	PUNCT
ejpam-7160	446	16	×l	×l	PUNCT
ejpam-7160	446	17	mn	mn	PROPN
ejpam-7160	446	18	1ι	1ι	NUM
ejpam-7160	446	19	(	(	PUNCT
ejpam-7160	446	20	c))c	c))c	NOUN
ejpam-7160	446	21	.	.	PUNCT
ejpam-7160	447	1	so	so	ADV
ejpam-7160	447	2	,	,	PUNCT
ejpam-7160	447	3	π1	π1	ADJ
ejpam-7160	447	4	∈	∈	PROPN
ejpam-7160	447	5	×l	×l	PROPN
ejpam-7160	447	6	mn	mn	PROPN
ejpam-7160	447	7	2ι	2ι	PROPN
ejpam-7160	447	8	(	(	PUNCT
ejpam-7160	447	9	c	c	NOUN
ejpam-7160	447	10	)	)	PUNCT
ejpam-7160	447	11	,	,	PUNCT
ejpam-7160	447	12	and	and	CCONJ
ejpam-7160	447	13	π1	π1	ADJ
ejpam-7160	447	14	∈	∈	PROPN
ejpam-7160	447	15	(	(	PUNCT
ejpam-7160	447	16	×l	×l	PUNCT
ejpam-7160	447	17	mn	mn	PROPN
ejpam-7160	447	18	2ι	2ι	PROPN
ejpam-7160	447	19	(	(	PUNCT
ejpam-7160	447	20	c))c	c))c	PROPN
ejpam-7160	447	21	.	.	PUNCT
ejpam-7160	448	1	therefore	therefore	ADV
ejpam-7160	448	2	,	,	PUNCT
ejpam-7160	448	3	π1	π1	PROPN
ejpam-7160	448	4	∈	∈	PROPN
ejpam-7160	448	5	bl	bl	PROPN
ejpam-7160	448	6	mn	mn	PROPN
ejpam-7160	448	7	2ι	2ι	PROPN
ejpam-7160	448	8	(	(	PUNCT
ejpam-7160	448	9	c	c	NOUN
ejpam-7160	448	10	)	)	PUNCT
ejpam-7160	448	11	,	,	PUNCT
ejpam-7160	448	12	bl	bl	PROPN
ejpam-7160	448	13	mn	mn	PROPN
ejpam-7160	448	14	1ι	1ι	NUM
ejpam-7160	448	15	(	(	PUNCT
ejpam-7160	448	16	c	c	X
ejpam-7160	448	17	)	)	PUNCT
ejpam-7160	448	18	⊑	⊑	PROPN
ejpam-7160	448	19	bl	bl	PROPN
ejpam-7160	448	20	mn	mn	PROPN
ejpam-7160	448	21	2ι	2ι	PROPN
ejpam-7160	448	22	(	(	PUNCT
ejpam-7160	448	23	c	c	NOUN
ejpam-7160	448	24	)	)	PUNCT
ejpam-7160	448	25	.	.	PUNCT
ejpam-7160	449	1	(	(	PUNCT
ejpam-7160	449	2	2	2	X
ejpam-7160	449	3	)	)	PUNCT
ejpam-7160	449	4	this	this	PRON
ejpam-7160	449	5	is	be	AUX
ejpam-7160	449	6	derived	derive	VERB
ejpam-7160	449	7	from	from	ADP
ejpam-7160	449	8	proposition	proposition	NOUN
ejpam-7160	449	9	4.9	4.9	NUM
ejpam-7160	449	10	.	.	PUNCT
ejpam-7160	450	1	definition	definition	NOUN
ejpam-7160	450	2	20	20	NUM
ejpam-7160	450	3	.	.	PUNCT
ejpam-7160	451	1	if	if	SCONJ
ejpam-7160	451	2	(	(	PUNCT
ejpam-7160	451	3	π,×	π,×	PROPN
ejpam-7160	451	4	,	,	PUNCT
ejpam-7160	451	5	ζι	ζι	NOUN
ejpam-7160	451	6	)	)	PUNCT
ejpam-7160	451	7	forms	form	VERB
ejpam-7160	451	8	a	a	DET
ejpam-7160	451	9	ι	ι	ADV
ejpam-7160	451	10	-	-	PUNCT
ejpam-7160	451	11	ns	ns	ADJ
ejpam-7160	451	12	,	,	PUNCT
ejpam-7160	451	13	l	l	NOUN
ejpam-7160	451	14	denotes	denote	VERB
ejpam-7160	451	15	a	a	DET
ejpam-7160	451	16	grill	grill	NOUN
ejpam-7160	451	17	on	on	ADP
ejpam-7160	451	18	π	π	PROPN
ejpam-7160	451	19	.	.	PUNCT
ejpam-7160	452	1	c	c	PROPN
ejpam-7160	452	2	⊑	⊑	X
ejpam-7160	452	3	π	π	PROPN
ejpam-7160	452	4	is	be	AUX
ejpam-7160	452	5	l	l	NOUN
ejpam-7160	452	6	-	-	NOUN
ejpam-7160	452	7	mn	mn	ADJ
ejpam-7160	452	8	ι	ι	NOUN
ejpam-7160	452	9	-	-	PUNCT
ejpam-7160	452	10	exact	exact	ADJ
ejpam-7160	452	11	if	if	SCONJ
ejpam-7160	452	12	×l	×l	PUNCT
ejpam-7160	452	13	mn	mn	PROPN
ejpam-7160	452	14	ι	ι	X
ejpam-7160	452	15	(	(	PUNCT
ejpam-7160	452	16	c	c	NOUN
ejpam-7160	452	17	)	)	PUNCT
ejpam-7160	452	18	)	)	PUNCT
ejpam-7160	453	1	=	=	PUNCT
ejpam-7160	454	1	×l	×l	PROPN
ejpam-7160	454	2	mn	mn	PROPN
ejpam-7160	454	3	ι	ι	PROPN
ejpam-7160	454	4	(	(	PUNCT
ejpam-7160	454	5	c	c	NOUN
ejpam-7160	454	6	)	)	PUNCT
ejpam-7160	454	7	)	)	PUNCT
ejpam-7160	455	1	=	=	SYM
ejpam-7160	455	2	c	c	X
ejpam-7160	455	3	;	;	PUNCT
ejpam-7160	455	4	otherwise	otherwise	ADV
ejpam-7160	455	5	,	,	PUNCT
ejpam-7160	455	6	it	it	PRON
ejpam-7160	455	7	is	be	AUX
ejpam-7160	455	8	l	l	NOUN
ejpam-7160	455	9	-	-	PROPN
ejpam-7160	455	10	mn	mn	ADJ
ejpam-7160	455	11	ι	ι	PROPN
ejpam-7160	455	12	-	-	PUNCT
ejpam-7160	455	13	rough	rough	ADJ
ejpam-7160	455	14	.	.	PUNCT
ejpam-7160	456	1	proposition	proposition	NOUN
ejpam-7160	456	2	8	8	NUM
ejpam-7160	456	3	.	.	PUNCT
ejpam-7160	457	1	if	if	SCONJ
ejpam-7160	457	2	(	(	PUNCT
ejpam-7160	457	3	π,×	π,×	PROPN
ejpam-7160	457	4	,	,	PUNCT
ejpam-7160	457	5	ζι	ζι	NOUN
ejpam-7160	457	6	)	)	PUNCT
ejpam-7160	457	7	forms	form	VERB
ejpam-7160	457	8	a	a	DET
ejpam-7160	457	9	ι	ι	ADV
ejpam-7160	457	10	-	-	PUNCT
ejpam-7160	457	11	ns	ns	ADJ
ejpam-7160	457	12	,	,	PUNCT
ejpam-7160	457	13	l	l	NOUN
ejpam-7160	457	14	denotes	denote	VERB
ejpam-7160	457	15	a	a	DET
ejpam-7160	457	16	grill	grill	NOUN
ejpam-7160	457	17	on	on	ADP
ejpam-7160	457	18	π	π	PROPN
ejpam-7160	457	19	.	.	PUNCT
ejpam-7160	458	1	c	c	PROPN
ejpam-7160	458	2	⊑	⊑	X
ejpam-7160	458	3	π	π	PROPN
ejpam-7160	458	4	is	be	AUX
ejpam-7160	458	5	l	l	NOUN
ejpam-7160	458	6	-	-	NOUN
ejpam-7160	458	7	mn	mn	ADJ
ejpam-7160	458	8	ι	ι	NOUN
ejpam-7160	458	9	-	-	PUNCT
ejpam-7160	458	10	exact	exact	ADJ
ejpam-7160	458	11	if	if	SCONJ
ejpam-7160	458	12	and	and	CCONJ
ejpam-7160	458	13	only	only	ADV
ejpam-7160	458	14	if	if	SCONJ
ejpam-7160	458	15	bl	bl	PROPN
ejpam-7160	458	16	mn	mn	PROPN
ejpam-7160	458	17	ι	ι	PROPN
ejpam-7160	458	18	(	(	PUNCT
ejpam-7160	458	19	c	c	NOUN
ejpam-7160	458	20	)	)	PUNCT
ejpam-7160	458	21	=	=	SYM
ejpam-7160	458	22	ϕ	ϕ	NOUN
ejpam-7160	458	23	.	.	PUNCT
ejpam-7160	459	1	proof	proof	NOUN
ejpam-7160	459	2	.	.	PUNCT
ejpam-7160	460	1	let	let	VERB
ejpam-7160	460	2	c	c	PRON
ejpam-7160	460	3	be	be	AUX
ejpam-7160	460	4	any	any	DET
ejpam-7160	460	5	l	l	NOUN
ejpam-7160	460	6	-	-	PROPN
ejpam-7160	460	7	mn	mn	ADJ
ejpam-7160	460	8	ι	ι	NOUN
ejpam-7160	460	9	-	-	PUNCT
ejpam-7160	460	10	exact	exact	ADJ
ejpam-7160	460	11	.	.	PUNCT
ejpam-7160	461	1	then	then	ADV
ejpam-7160	461	2	,	,	PUNCT
ejpam-7160	461	3	bl	bl	PROPN
ejpam-7160	461	4	mn	mn	PROPN
ejpam-7160	461	5	ι	ι	PROPN
ejpam-7160	461	6	(	(	PUNCT
ejpam-7160	461	7	c	c	NOUN
ejpam-7160	461	8	)	)	PUNCT
ejpam-7160	461	9	=	=	SYM
ejpam-7160	462	1	×l	×l	PROPN
ejpam-7160	462	2	mn	mn	PROPN
ejpam-7160	462	3	ι	ι	PROPN
ejpam-7160	462	4	(	(	PUNCT
ejpam-7160	462	5	c)\×l	c)\×l	PROPN
ejpam-7160	462	6	mn	mn	PROPN
ejpam-7160	462	7	ι	ι	PROPN
ejpam-7160	462	8	(	(	PUNCT
ejpam-7160	462	9	c	c	NOUN
ejpam-7160	462	10	)	)	PUNCT
ejpam-7160	463	1	=	=	NOUN
ejpam-7160	463	2	ϕ.	ϕ.	NOUN
ejpam-7160	463	3	conversely	conversely	ADV
ejpam-7160	463	4	,	,	PUNCT
ejpam-7160	463	5	bl	bl	PROPN
ejpam-7160	463	6	mn	mn	PROPN
ejpam-7160	463	7	ι	ι	PROPN
ejpam-7160	463	8	(	(	PUNCT
ejpam-7160	463	9	c	c	NOUN
ejpam-7160	463	10	)	)	PUNCT
ejpam-7160	463	11	=	=	SYM
ejpam-7160	463	12	ϕ	ϕ	NOUN
ejpam-7160	463	13	;	;	PUNCT
ejpam-7160	463	14	hence	hence	ADV
ejpam-7160	463	15	,	,	PUNCT
ejpam-7160	463	16	×l	×l	PROPN
ejpam-7160	463	17	mn	mn	PROPN
ejpam-7160	463	18	ι	ι	PROPN
ejpam-7160	463	19	(	(	PUNCT
ejpam-7160	463	20	c)\×l	c)\×l	PROPN
ejpam-7160	463	21	mn	mn	PROPN
ejpam-7160	463	22	ι	ι	PROPN
ejpam-7160	463	23	(	(	PUNCT
ejpam-7160	463	24	c	c	NOUN
ejpam-7160	463	25	)	)	PUNCT
ejpam-7160	463	26	=	=	SYM
ejpam-7160	463	27	ϕ	ϕ	NOUN
ejpam-7160	463	28	,	,	PUNCT
ejpam-7160	463	29	and	and	CCONJ
ejpam-7160	463	30	so×l	so×l	PROPN
ejpam-7160	463	31	mn	mn	PROPN
ejpam-7160	463	32	ι	ι	X
ejpam-7160	464	1	(	(	PUNCT
ejpam-7160	464	2	c	c	NOUN
ejpam-7160	464	3	)	)	PUNCT
ejpam-7160	464	4	⊑	⊑	PRON
ejpam-7160	464	5	×l	×l	PROPN
ejpam-7160	464	6	mn	mn	PROPN
ejpam-7160	464	7	ι	ι	PROPN
ejpam-7160	464	8	(	(	PUNCT
ejpam-7160	464	9	c	c	NOUN
ejpam-7160	464	10	)	)	PUNCT
ejpam-7160	464	11	.	.	PUNCT
ejpam-7160	465	1	however	however	ADV
ejpam-7160	465	2	,	,	PUNCT
ejpam-7160	465	3	×l	×l	PROPN
ejpam-7160	465	4	mn	mn	PROPN
ejpam-7160	465	5	ι	ι	PROPN
ejpam-7160	465	6	(	(	PUNCT
ejpam-7160	465	7	c	c	NOUN
ejpam-7160	465	8	)	)	PUNCT
ejpam-7160	465	9	⊑	⊑	PRON
ejpam-7160	465	10	×l	×l	PROPN
ejpam-7160	465	11	mn	mn	PROPN
ejpam-7160	465	12	ι	ι	PROPN
ejpam-7160	465	13	(	(	PUNCT
ejpam-7160	465	14	c	c	NOUN
ejpam-7160	465	15	)	)	PUNCT
ejpam-7160	465	16	.	.	PUNCT
ejpam-7160	466	1	thus	thus	ADV
ejpam-7160	466	2	,	,	PUNCT
ejpam-7160	466	3	×l	×l	PROPN
ejpam-7160	466	4	mn	mn	PROPN
ejpam-7160	466	5	ι	ι	PROPN
ejpam-7160	466	6	(	(	PUNCT
ejpam-7160	466	7	c	c	NOUN
ejpam-7160	466	8	)	)	PUNCT
ejpam-7160	466	9	=	=	SYM
ejpam-7160	467	1	×l	×l	PROPN
ejpam-7160	467	2	mn	mn	PROPN
ejpam-7160	467	3	ι	ι	X
ejpam-7160	467	4	(	(	PUNCT
ejpam-7160	467	5	c	c	NOUN
ejpam-7160	467	6	)	)	PUNCT
ejpam-7160	467	7	,	,	PUNCT
ejpam-7160	467	8	and	and	CCONJ
ejpam-7160	467	9	c	c	PROPN
ejpam-7160	467	10	is	be	AUX
ejpam-7160	467	11	l	l	NOUN
ejpam-7160	467	12	-	-	PROPN
ejpam-7160	467	13	mn	mn	ADJ
ejpam-7160	467	14	ι	ι	NOUN
ejpam-7160	467	15	-	-	PUNCT
ejpam-7160	467	16	exact	exact	ADJ
ejpam-7160	467	17	.	.	PUNCT
ejpam-7160	468	1	a.	a.	NOUN
ejpam-7160	468	2	a.	a.	PROPN
ejpam-7160	468	3	azzam	azzam	PROPN
ejpam-7160	468	4	et	et	PROPN
ejpam-7160	468	5	al	al	PROPN
ejpam-7160	468	6	.	.	PUNCT
ejpam-7160	468	7	/	/	SYM
ejpam-7160	468	8	eur	eur	PROPN
ejpam-7160	468	9	.	.	PUNCT
ejpam-7160	469	1	j.	j.	PROPN
ejpam-7160	469	2	pure	pure	PROPN
ejpam-7160	469	3	appl	appl	PROPN
ejpam-7160	469	4	.	.	PROPN
ejpam-7160	469	5	math	math	PROPN
ejpam-7160	469	6	,	,	PUNCT
ejpam-7160	469	7	18	18	NUM
ejpam-7160	469	8	(	(	PUNCT
ejpam-7160	469	9	4	4	NUM
ejpam-7160	469	10	)	)	PUNCT
ejpam-7160	469	11	(	(	PUNCT
ejpam-7160	469	12	2025	2025	NUM
ejpam-7160	469	13	)	)	PUNCT
ejpam-7160	469	14	,	,	PUNCT
ejpam-7160	469	15	7160	7160	NUM
ejpam-7160	469	16	17	17	NUM
ejpam-7160	469	17	of	of	ADP
ejpam-7160	469	18	22	22	NUM
ejpam-7160	469	19	5	5	NUM
ejpam-7160	469	20	.	.	PUNCT
ejpam-7160	470	1	an	an	DET
ejpam-7160	470	2	application	application	NOUN
ejpam-7160	470	3	of	of	ADP
ejpam-7160	470	4	the	the	DET
ejpam-7160	470	5	suggested	suggest	VERB
ejpam-7160	470	6	approach	approach	NOUN
ejpam-7160	470	7	for	for	ADP
ejpam-7160	470	8	heart	heart	NOUN
ejpam-7160	470	9	failure	failure	NOUN
ejpam-7160	470	10	this	this	DET
ejpam-7160	470	11	paragraph	paragraph	NOUN
ejpam-7160	470	12	presents	present	VERB
ejpam-7160	470	13	the	the	DET
ejpam-7160	470	14	experimental	experimental	ADJ
ejpam-7160	470	15	results	result	NOUN
ejpam-7160	470	16	of	of	ADP
ejpam-7160	470	17	a	a	DET
ejpam-7160	470	18	preparation	preparation	NOUN
ejpam-7160	470	19	study	study	NOUN
ejpam-7160	470	20	conducted	conduct	VERB
ejpam-7160	470	21	on	on	ADP
ejpam-7160	470	22	five	five	NUM
ejpam-7160	470	23	symptoms	symptom	NOUN
ejpam-7160	470	24	of	of	ADP
ejpam-7160	470	25	heart	heart	NOUN
ejpam-7160	470	26	disease	disease	NOUN
ejpam-7160	470	27	,	,	PUNCT
ejpam-7160	470	28	as	as	SCONJ
ejpam-7160	470	29	outlined	outline	VERB
ejpam-7160	470	30	by	by	ADP
ejpam-7160	470	31	dickstein	dickstein	ADV
ejpam-7160	470	32	et	et	PROPN
ejpam-7160	470	33	al	al	PROPN
ejpam-7160	470	34	.	.	PUNCT
ejpam-7160	471	1	[	[	X
ejpam-7160	471	2	57	57	NUM
ejpam-7160	471	3	]	]	PUNCT
ejpam-7160	471	4	,	,	PUNCT
ejpam-7160	471	5	including	include	VERB
ejpam-7160	471	6	seven	seven	NUM
ejpam-7160	471	7	patients	patient	NOUN
ejpam-7160	471	8	.	.	PUNCT
ejpam-7160	472	1	the	the	DET
ejpam-7160	472	2	research	research	NOUN
ejpam-7160	472	3	was	be	AUX
ejpam-7160	472	4	carried	carry	VERB
ejpam-7160	472	5	out	out	ADP
ejpam-7160	472	6	in	in	ADP
ejpam-7160	472	7	the	the	DET
ejpam-7160	472	8	cardiology	cardiology	NOUN
ejpam-7160	472	9	department	department	PROPN
ejpam-7160	472	10	of	of	ADP
ejpam-7160	472	11	al	al	PROPN
ejpam-7160	472	12	-	-	PUNCT
ejpam-7160	472	13	azhar	azhar	PROPN
ejpam-7160	472	14	university	university	PROPN
ejpam-7160	472	15	[	[	X
ejpam-7160	472	16	58	58	NUM
ejpam-7160	472	17	]	]	PUNCT
ejpam-7160	472	18	.	.	PUNCT
ejpam-7160	473	1	the	the	DET
ejpam-7160	473	2	quantity	quantity	NOUN
ejpam-7160	473	3	of	of	ADP
ejpam-7160	473	4	training	training	NOUN
ejpam-7160	473	5	data	datum	NOUN
ejpam-7160	473	6	utilized	utilize	VERB
ejpam-7160	473	7	twenty	twenty	NUM
ejpam-7160	473	8	-	-	PUNCT
ejpam-7160	473	9	five	five	NUM
ejpam-7160	473	10	records	record	NOUN
ejpam-7160	473	11	were	be	AUX
ejpam-7160	473	12	analyzed	analyze	VERB
ejpam-7160	473	13	,	,	PUNCT
ejpam-7160	473	14	while	while	SCONJ
ejpam-7160	473	15	the	the	DET
ejpam-7160	473	16	other	other	ADJ
ejpam-7160	473	17	data	datum	NOUN
ejpam-7160	473	18	were	be	AUX
ejpam-7160	473	19	forwarded	forward	VERB
ejpam-7160	473	20	to	to	ADP
ejpam-7160	473	21	this	this	DET
ejpam-7160	473	22	institution	institution	NOUN
ejpam-7160	473	23	displaying	display	VERB
ejpam-7160	473	24	similar	similar	ADJ
ejpam-7160	473	25	presented	present	VERB
ejpam-7160	473	26	symptoms	symptom	NOUN
ejpam-7160	473	27	,	,	PUNCT
ejpam-7160	473	28	comprehensive	comprehensive	ADJ
ejpam-7160	473	29	history	history	NOUN
ejpam-7160	473	30	,	,	PUNCT
ejpam-7160	473	31	physical	physical	ADJ
ejpam-7160	473	32	examination	examination	NOUN
ejpam-7160	473	33	,	,	PUNCT
ejpam-7160	473	34	complete	complete	ADJ
ejpam-7160	473	35	laboratory	laboratory	NOUN
ejpam-7160	473	36	tests	test	NOUN
ejpam-7160	473	37	,	,	PUNCT
ejpam-7160	473	38	resting	rest	VERB
ejpam-7160	473	39	electrocardiogram	electrocardiogram	NOUN
ejpam-7160	473	40	,	,	PUNCT
ejpam-7160	473	41	and	and	CCONJ
ejpam-7160	473	42	conventional	conventional	ADJ
ejpam-7160	473	43	echocardiographic	echocardiographic	ADJ
ejpam-7160	473	44	assessment	assessment	NOUN
ejpam-7160	473	45	were	be	AUX
ejpam-7160	473	46	conducted	conduct	VERB
ejpam-7160	473	47	.	.	PUNCT
ejpam-7160	474	1	the	the	DET
ejpam-7160	474	2	information	information	NOUN
ejpam-7160	474	3	system	system	NOUN
ejpam-7160	474	4	contains	contain	VERB
ejpam-7160	474	5	data	datum	NOUN
ejpam-7160	474	6	for	for	ADP
ejpam-7160	474	7	just	just	ADV
ejpam-7160	474	8	seven	seven	NUM
ejpam-7160	474	9	patients	patient	NOUN
ejpam-7160	474	10	with	with	ADP
ejpam-7160	474	11	similar	similar	ADJ
ejpam-7160	474	12	characteristics	characteristic	NOUN
ejpam-7160	474	13	,	,	PUNCT
ejpam-7160	474	14	as	as	SCONJ
ejpam-7160	474	15	discussed	discuss	VERB
ejpam-7160	474	16	in	in	ADP
ejpam-7160	474	17	table	table	NOUN
ejpam-7160	474	18	2	2	NUM
ejpam-7160	474	19	,	,	PUNCT
ejpam-7160	474	20	regarding	regard	VERB
ejpam-7160	474	21	the	the	DET
ejpam-7160	474	22	heart	heart	NOUN
ejpam-7160	474	23	failure	failure	NOUN
ejpam-7160	474	24	issue	issue	NOUN
ejpam-7160	474	25	.	.	PUNCT
ejpam-7160	475	1	the	the	DET
ejpam-7160	475	2	columns	column	NOUN
ejpam-7160	475	3	denote	denote	VERB
ejpam-7160	475	4	the	the	DET
ejpam-7160	475	5	symptoms	symptom	NOUN
ejpam-7160	475	6	,	,	PUNCT
ejpam-7160	475	7	where	where	SCONJ
ejpam-7160	475	8	’	'	PUNCT
ejpam-7160	475	9	e	e	X
ejpam-7160	475	10	’	'	PUNCT
ejpam-7160	475	11	indicates	indicate	VERB
ejpam-7160	475	12	the	the	DET
ejpam-7160	475	13	presence	presence	NOUN
ejpam-7160	475	14	of	of	ADP
ejpam-7160	475	15	symptoms	symptom	NOUN
ejpam-7160	475	16	and	and	CCONJ
ejpam-7160	475	17	’	'	PUNCT
ejpam-7160	475	18	ne	ne	NOUN
ejpam-7160	475	19	’	'	PUNCT
ejpam-7160	475	20	signifies	signify	VERB
ejpam-7160	475	21	their	their	PRON
ejpam-7160	475	22	absence	absence	NOUN
ejpam-7160	475	23	,	,	PUNCT
ejpam-7160	475	24	pertaining	pertain	VERB
ejpam-7160	475	25	to	to	ADP
ejpam-7160	475	26	the	the	DET
ejpam-7160	475	27	diagnosis	diagnosis	NOUN
ejpam-7160	475	28	of	of	ADP
ejpam-7160	475	29	heart	heart	NOUN
ejpam-7160	475	30	failure	failure	NOUN
ejpam-7160	475	31	[	[	X
ejpam-7160	475	32	57	57	NUM
ejpam-7160	475	33	]	]	PUNCT
ejpam-7160	475	34	(	(	PUNCT
ejpam-7160	475	35	condition	condition	NOUN
ejpam-7160	475	36	characteristics	characteristic	NOUN
ejpam-7160	475	37	)	)	PUNCT
ejpam-7160	475	38	.	.	PUNCT
ejpam-7160	476	1	where	where	SCONJ
ejpam-7160	476	2	bs	bs	PROPN
ejpam-7160	476	3	is	be	AUX
ejpam-7160	476	4	the	the	DET
ejpam-7160	476	5	breathlessness	breathlessness	NOUN
ejpam-7160	476	6	,	,	PUNCT
ejpam-7160	476	7	oa	oa	PROPN
ejpam-7160	476	8	is	be	AUX
ejpam-7160	476	9	the	the	DET
ejpam-7160	476	10	orthopnea	orthopnea	NOUN
ejpam-7160	476	11	,	,	PUNCT
ejpam-7160	476	12	pa	pa	PROPN
ejpam-7160	476	13	is	be	AUX
ejpam-7160	476	14	the	the	DET
ejpam-7160	476	15	paroxysmal	paroxysmal	ADJ
ejpam-7160	476	16	nocturnal	nocturnal	ADJ
ejpam-7160	476	17	dyspnea	dyspnea	NOUN
ejpam-7160	476	18	,	,	PUNCT
ejpam-7160	476	19	re	re	VERB
ejpam-7160	476	20	reduced	reduce	VERB
ejpam-7160	476	21	exercise	exercise	NOUN
ejpam-7160	476	22	tolerance	tolerance	NOUN
ejpam-7160	476	23	,	,	PUNCT
ejpam-7160	476	24	ag	ag	PROPN
ejpam-7160	476	25	is	be	AUX
ejpam-7160	476	26	the	the	DET
ejpam-7160	476	27	ankle	ankle	NOUN
ejpam-7160	476	28	swelling	swelling	NOUN
ejpam-7160	476	29	.	.	PUNCT
ejpam-7160	477	1	the	the	DET
ejpam-7160	477	2	attribute	attribute	NOUN
ejpam-7160	477	3	d	d	NOUN
ejpam-7160	477	4	represents	represent	VERB
ejpam-7160	477	5	the	the	DET
ejpam-7160	477	6	determination	determination	NOUN
ejpam-7160	477	7	of	of	ADP
ejpam-7160	477	8	heart	heart	NOUN
ejpam-7160	477	9	failure	failure	NOUN
ejpam-7160	477	10	.	.	PUNCT
ejpam-7160	478	1	the	the	DET
ejpam-7160	478	2	rows	row	NOUN
ejpam-7160	478	3	in	in	ADP
ejpam-7160	478	4	table	table	NOUN
ejpam-7160	478	5	2	2	NUM
ejpam-7160	478	6	,	,	PUNCT
ejpam-7160	478	7	π	π	X
ejpam-7160	478	8	=	=	PUNCT
ejpam-7160	478	9	{	{	PUNCT
ejpam-7160	478	10	π1	π1	NOUN
ejpam-7160	478	11	,	,	PUNCT
ejpam-7160	478	12	π2	π2	PROPN
ejpam-7160	478	13	,	,	PUNCT
ejpam-7160	478	14	π3	π3	NOUN
ejpam-7160	478	15	,	,	PUNCT
ejpam-7160	478	16	π4	π4	NOUN
ejpam-7160	478	17	,	,	PUNCT
ejpam-7160	478	18	π5	π5	PROPN
ejpam-7160	478	19	,	,	PUNCT
ejpam-7160	478	20	π8	π8	PROPN
ejpam-7160	478	21	,	,	PUNCT
ejpam-7160	478	22	π9	π9	PROPN
ejpam-7160	478	23	}	}	PUNCT
ejpam-7160	478	24	represents	represent	VERB
ejpam-7160	478	25	the	the	DET
ejpam-7160	478	26	patients	patient	NOUN
ejpam-7160	478	27	.	.	PUNCT
ejpam-7160	479	1	let	let	VERB
ejpam-7160	479	2	us	we	PRON
ejpam-7160	479	3	consider	consider	VERB
ejpam-7160	479	4	the	the	DET
ejpam-7160	479	5	expert	expert	NOUN
ejpam-7160	479	6	of	of	ADP
ejpam-7160	479	7	the	the	DET
ejpam-7160	479	8	system	system	NOUN
ejpam-7160	479	9	who	who	PRON
ejpam-7160	479	10	has	have	AUX
ejpam-7160	479	11	offered	offer	VERB
ejpam-7160	479	12	the	the	DET
ejpam-7160	479	13	subsequent	subsequent	ADJ
ejpam-7160	479	14	relation	relation	NOUN
ejpam-7160	479	15	×	×	NOUN
ejpam-7160	479	16	on	on	ADP
ejpam-7160	479	17	the	the	DET
ejpam-7160	479	18	set	set	NOUN
ejpam-7160	479	19	of	of	ADP
ejpam-7160	479	20	patients	patient	NOUN
ejpam-7160	479	21	π	π	VERB
ejpam-7160	479	22	to	to	PART
ejpam-7160	479	23	delineate	delineate	VERB
ejpam-7160	479	24	the	the	DET
ejpam-7160	479	25	connections	connection	NOUN
ejpam-7160	479	26	among	among	ADP
ejpam-7160	479	27	them	they	PRON
ejpam-7160	479	28	based	base	VERB
ejpam-7160	479	29	on	on	ADP
ejpam-7160	479	30	their	their	PRON
ejpam-7160	479	31	symptoms	symptom	NOUN
ejpam-7160	479	32	:	:	PUNCT
ejpam-7160	479	33	πi×πj	πi×πj	PROPN
ejpam-7160	479	34	⇔f(πi	⇔f(πi	ADV
ejpam-7160	479	35	)	)	PUNCT
ejpam-7160	479	36	⊑	⊑	PRON
ejpam-7160	479	37	f(πj	f(πj	PROPN
ejpam-7160	479	38	)	)	PUNCT
ejpam-7160	479	39	,	,	PUNCT
ejpam-7160	479	40	where	where	SCONJ
ejpam-7160	479	41	the	the	DET
ejpam-7160	479	42	function	function	NOUN
ejpam-7160	479	43	is	be	AUX
ejpam-7160	479	44	defined	define	VERB
ejpam-7160	479	45	by	by	ADP
ejpam-7160	479	46	f(π1	f(π1	NOUN
ejpam-7160	479	47	)	)	PUNCT
ejpam-7160	480	1	=	=	SYM
ejpam-7160	480	2	{	{	PUNCT
ejpam-7160	480	3	bs	bs	PROPN
ejpam-7160	480	4	,	,	PUNCT
ejpam-7160	480	5	oa	oa	PROPN
ejpam-7160	480	6	,	,	PUNCT
ejpam-7160	480	7	pa	pa	PROPN
ejpam-7160	480	8	,	,	PUNCT
ejpam-7160	480	9	re	re	ADJ
ejpam-7160	480	10	}	}	PUNCT
ejpam-7160	480	11	,	,	PUNCT
ejpam-7160	480	12	f(π2	f(π2	NOUN
ejpam-7160	480	13	)	)	PUNCT
ejpam-7160	480	14	=	=	PRON
ejpam-7160	480	15	{	{	PUNCT
ejpam-7160	480	16	re	re	PROPN
ejpam-7160	480	17	,	,	PUNCT
ejpam-7160	480	18	ag	ag	PROPN
ejpam-7160	480	19	}	}	PUNCT
ejpam-7160	480	20	,	,	PUNCT
ejpam-7160	480	21	f(π3	f(π3	ADJ
ejpam-7160	480	22	)	)	PUNCT
ejpam-7160	480	23	=	=	SYM
ejpam-7160	480	24	{	{	PUNCT
ejpam-7160	480	25	bs	bs	PROPN
ejpam-7160	480	26	,	,	PUNCT
ejpam-7160	480	27	oa	oa	PROPN
ejpam-7160	480	28	,	,	PUNCT
ejpam-7160	480	29	pa	pa	PROPN
ejpam-7160	480	30	,	,	PUNCT
ejpam-7160	480	31	re	re	PROPN
ejpam-7160	480	32	,	,	PUNCT
ejpam-7160	480	33	ag	ag	PROPN
ejpam-7160	480	34	}	}	PUNCT
ejpam-7160	480	35	,	,	PUNCT
ejpam-7160	480	36	f(π4	f(π4	NOUN
ejpam-7160	480	37	)	)	PUNCT
ejpam-7160	480	38	=	=	PRON
ejpam-7160	480	39	{	{	PUNCT
ejpam-7160	480	40	re	re	NOUN
ejpam-7160	480	41	}	}	PUNCT
ejpam-7160	480	42	,	,	PUNCT
ejpam-7160	480	43	f(π5	f(π5	NUM
ejpam-7160	480	44	)	)	PUNCT
ejpam-7160	481	1	=	=	PRON
ejpam-7160	481	2	{	{	PUNCT
ejpam-7160	481	3	bs	bs	NOUN
ejpam-7160	481	4	,	,	PUNCT
ejpam-7160	481	5	re	re	NOUN
ejpam-7160	481	6	,	,	PUNCT
ejpam-7160	481	7	ag	ag	PROPN
ejpam-7160	481	8	}	}	PUNCT
ejpam-7160	481	9	,	,	PUNCT
ejpam-7160	481	10	f(π8	f(π8	PROPN
ejpam-7160	481	11	)	)	PUNCT
ejpam-7160	481	12	=	=	PRON
ejpam-7160	482	1	{	{	PUNCT
ejpam-7160	482	2	bs	bs	PROPN
ejpam-7160	482	3	,	,	PUNCT
ejpam-7160	482	4	oa	oa	PROPN
ejpam-7160	482	5	,	,	PUNCT
ejpam-7160	482	6	re	re	PROPN
ejpam-7160	482	7	,	,	PUNCT
ejpam-7160	482	8	ag	ag	PROPN
ejpam-7160	482	9	}	}	PUNCT
ejpam-7160	482	10	,	,	PUNCT
ejpam-7160	482	11	f(π9	f(π9	NOUN
ejpam-7160	482	12	)	)	PUNCT
ejpam-7160	482	13	=	=	PRON
ejpam-7160	482	14	{	{	PUNCT
ejpam-7160	482	15	bs	bs	PROPN
ejpam-7160	482	16	,	,	PUNCT
ejpam-7160	482	17	pa	pa	PROPN
ejpam-7160	482	18	,	,	PUNCT
ejpam-7160	482	19	re	re	ADP
ejpam-7160	482	20	}	}	PUNCT
ejpam-7160	482	21	.	.	PUNCT
ejpam-7160	483	1	then	then	ADV
ejpam-7160	483	2	,	,	PUNCT
ejpam-7160	483	3	×	×	NOUN
ejpam-7160	483	4	=	=	SYM
ejpam-7160	483	5	{	{	PUNCT
ejpam-7160	483	6	(	(	PUNCT
ejpam-7160	483	7	π1	π1	NOUN
ejpam-7160	483	8	,	,	PUNCT
ejpam-7160	483	9	π1	π1	NOUN
ejpam-7160	483	10	)	)	PUNCT
ejpam-7160	483	11	,	,	PUNCT
ejpam-7160	483	12	(	(	PUNCT
ejpam-7160	483	13	π1	π1	NOUN
ejpam-7160	483	14	,	,	PUNCT
ejpam-7160	483	15	π3	π3	NOUN
ejpam-7160	483	16	)	)	PUNCT
ejpam-7160	483	17	,	,	PUNCT
ejpam-7160	483	18	(	(	PUNCT
ejpam-7160	483	19	π2	π2	X
ejpam-7160	483	20	,	,	PUNCT
ejpam-7160	483	21	π2	π2	NOUN
ejpam-7160	483	22	)	)	PUNCT
ejpam-7160	483	23	,	,	PUNCT
ejpam-7160	483	24	(	(	PUNCT
ejpam-7160	483	25	π2	π2	X
ejpam-7160	483	26	,	,	PUNCT
ejpam-7160	483	27	π3	π3	NOUN
ejpam-7160	483	28	)	)	PUNCT
ejpam-7160	483	29	,	,	PUNCT
ejpam-7160	483	30	(	(	PUNCT
ejpam-7160	483	31	π2	π2	X
ejpam-7160	483	32	,	,	PUNCT
ejpam-7160	483	33	π5	π5	PROPN
ejpam-7160	483	34	)	)	PUNCT
ejpam-7160	483	35	,	,	PUNCT
ejpam-7160	483	36	(	(	PUNCT
ejpam-7160	483	37	π2	π2	X
ejpam-7160	483	38	,	,	PUNCT
ejpam-7160	483	39	π8	π8	PROPN
ejpam-7160	483	40	)	)	PUNCT
ejpam-7160	483	41	,	,	PUNCT
ejpam-7160	483	42	(	(	PUNCT
ejpam-7160	483	43	π3	π3	NOUN
ejpam-7160	483	44	,	,	PUNCT
ejpam-7160	483	45	π3	π3	NOUN
ejpam-7160	483	46	)	)	PUNCT
ejpam-7160	483	47	,	,	PUNCT
ejpam-7160	483	48	(	(	PUNCT
ejpam-7160	483	49	π4	π4	PROPN
ejpam-7160	483	50	,	,	PUNCT
ejpam-7160	483	51	π1	π1	NOUN
ejpam-7160	483	52	)	)	PUNCT
ejpam-7160	483	53	(	(	PUNCT
ejpam-7160	483	54	π4	π4	NOUN
ejpam-7160	483	55	,	,	PUNCT
ejpam-7160	483	56	π2	π2	NOUN
ejpam-7160	483	57	)	)	PUNCT
ejpam-7160	483	58	,	,	PUNCT
ejpam-7160	483	59	(	(	PUNCT
ejpam-7160	483	60	π4	π4	INTJ
ejpam-7160	483	61	,	,	PUNCT
ejpam-7160	483	62	π3	π3	PROPN
ejpam-7160	483	63	)	)	PUNCT
ejpam-7160	483	64	,	,	PUNCT
ejpam-7160	483	65	(	(	PUNCT
ejpam-7160	483	66	π4	π4	NOUN
ejpam-7160	483	67	,	,	PUNCT
ejpam-7160	483	68	π4	π4	PROPN
ejpam-7160	483	69	)	)	PUNCT
ejpam-7160	483	70	,	,	PUNCT
ejpam-7160	483	71	(	(	PUNCT
ejpam-7160	483	72	π4	π4	NOUN
ejpam-7160	483	73	,	,	PUNCT
ejpam-7160	483	74	π5	π5	PROPN
ejpam-7160	483	75	)	)	PUNCT
ejpam-7160	483	76	,	,	PUNCT
ejpam-7160	483	77	(	(	PUNCT
ejpam-7160	483	78	π4	π4	PROPN
ejpam-7160	483	79	,	,	PUNCT
ejpam-7160	483	80	π8	π8	PROPN
ejpam-7160	483	81	)	)	PUNCT
ejpam-7160	483	82	,	,	PUNCT
ejpam-7160	483	83	(	(	PUNCT
ejpam-7160	483	84	π4	π4	NOUN
ejpam-7160	483	85	,	,	PUNCT
ejpam-7160	483	86	π9	π9	NOUN
ejpam-7160	483	87	)	)	PUNCT
ejpam-7160	483	88	,	,	PUNCT
ejpam-7160	483	89	(	(	PUNCT
ejpam-7160	483	90	π5	π5	X
ejpam-7160	483	91	,	,	PUNCT
ejpam-7160	483	92	π3	π3	PROPN
ejpam-7160	483	93	)	)	PUNCT
ejpam-7160	483	94	,	,	PUNCT
ejpam-7160	483	95	(	(	PUNCT
ejpam-7160	483	96	π5	π5	X
ejpam-7160	483	97	,	,	PUNCT
ejpam-7160	483	98	π5	π5	PROPN
ejpam-7160	483	99	)	)	PUNCT
ejpam-7160	483	100	,	,	PUNCT
ejpam-7160	483	101	(	(	PUNCT
ejpam-7160	483	102	π5	π5	X
ejpam-7160	483	103	,	,	PUNCT
ejpam-7160	483	104	π8	π8	PROPN
ejpam-7160	483	105	)	)	PUNCT
ejpam-7160	483	106	(	(	PUNCT
ejpam-7160	483	107	π8	π8	NOUN
ejpam-7160	483	108	,	,	PUNCT
ejpam-7160	483	109	π3	π3	PROPN
ejpam-7160	483	110	)	)	PUNCT
ejpam-7160	483	111	,	,	PUNCT
ejpam-7160	483	112	(	(	PUNCT
ejpam-7160	483	113	π8	π8	PROPN
ejpam-7160	483	114	,	,	PUNCT
ejpam-7160	483	115	π8	π8	PROPN
ejpam-7160	483	116	)	)	PUNCT
ejpam-7160	483	117	,	,	PUNCT
ejpam-7160	483	118	(	(	PUNCT
ejpam-7160	483	119	π9	π9	NOUN
ejpam-7160	483	120	,	,	PUNCT
ejpam-7160	483	121	π1	π1	NOUN
ejpam-7160	483	122	)	)	PUNCT
ejpam-7160	483	123	,	,	PUNCT
ejpam-7160	483	124	(	(	PUNCT
ejpam-7160	483	125	π9	π9	NOUN
ejpam-7160	483	126	,	,	PUNCT
ejpam-7160	483	127	π3	π3	NOUN
ejpam-7160	483	128	)	)	PUNCT
ejpam-7160	483	129	,	,	PUNCT
ejpam-7160	483	130	(	(	PUNCT
ejpam-7160	483	131	π9	π9	NOUN
ejpam-7160	483	132	,	,	PUNCT
ejpam-7160	483	133	π9	π9	NOUN
ejpam-7160	483	134	)	)	PUNCT
ejpam-7160	483	135	}	}	PUNCT
ejpam-7160	483	136	.	.	PUNCT
ejpam-7160	484	1	hence	hence	ADV
ejpam-7160	484	2	,	,	PUNCT
ejpam-7160	484	3	mn	mn	PROPN
ejpam-7160	484	4	r(π1	r(π1	PROPN
ejpam-7160	484	5	)	)	PUNCT
ejpam-7160	485	1	=	=	PRON
ejpam-7160	485	2	{	{	PUNCT
ejpam-7160	485	3	π1	π1	NOUN
ejpam-7160	485	4	,	,	PUNCT
ejpam-7160	485	5	π3	π3	PROPN
ejpam-7160	485	6	}	}	PUNCT
ejpam-7160	485	7	,	,	PUNCT
ejpam-7160	485	8	mn	mn	PROPN
ejpam-7160	485	9	r(π2	r(π2	NOUN
ejpam-7160	485	10	)	)	PUNCT
ejpam-7160	485	11	=	=	PRON
ejpam-7160	485	12	{	{	PUNCT
ejpam-7160	485	13	π2	π2	ADV
ejpam-7160	485	14	,	,	PUNCT
ejpam-7160	485	15	π3	π3	NOUN
ejpam-7160	485	16	,	,	PUNCT
ejpam-7160	485	17	π5	π5	PROPN
ejpam-7160	485	18	,	,	PUNCT
ejpam-7160	485	19	π8	π8	PROPN
ejpam-7160	485	20	}	}	PUNCT
ejpam-7160	485	21	,	,	PUNCT
ejpam-7160	485	22	mn	mn	PROPN
ejpam-7160	485	23	r(π3	r(π3	PROPN
ejpam-7160	485	24	)	)	PUNCT
ejpam-7160	486	1	=	=	PRON
ejpam-7160	486	2	{	{	PUNCT
ejpam-7160	486	3	π3	π3	NOUN
ejpam-7160	486	4	}	}	PUNCT
ejpam-7160	486	5	,	,	PUNCT
ejpam-7160	486	6	mn	mn	PROPN
ejpam-7160	486	7	r(π4	r(π4	X
ejpam-7160	486	8	)	)	PUNCT
ejpam-7160	487	1	=	=	SYM
ejpam-7160	487	2	π	π	PROPN
ejpam-7160	487	3	,	,	PUNCT
ejpam-7160	487	4	mn	mn	PROPN
ejpam-7160	487	5	r(π5	r(π5	PROPN
ejpam-7160	487	6	)	)	PUNCT
ejpam-7160	488	1	=	=	PRON
ejpam-7160	488	2	{	{	PUNCT
ejpam-7160	488	3	π3	π3	NOUN
ejpam-7160	488	4	,	,	PUNCT
ejpam-7160	488	5	π5	π5	PROPN
ejpam-7160	488	6	,	,	PUNCT
ejpam-7160	488	7	π8	π8	PROPN
ejpam-7160	488	8	}	}	PUNCT
ejpam-7160	488	9	,	,	PUNCT
ejpam-7160	488	10	mn	mn	PROPN
ejpam-7160	488	11	r(π8	r(π8	PROPN
ejpam-7160	488	12	)	)	PUNCT
ejpam-7160	488	13	=	=	PRON
ejpam-7160	488	14	{	{	PUNCT
ejpam-7160	488	15	π3	π3	NOUN
ejpam-7160	488	16	,	,	PUNCT
ejpam-7160	488	17	π8	π8	PROPN
ejpam-7160	488	18	}	}	PUNCT
ejpam-7160	488	19	,	,	PUNCT
ejpam-7160	488	20	and	and	CCONJ
ejpam-7160	488	21	mn	mn	PROPN
ejpam-7160	488	22	r(π9	r(π9	NOUN
ejpam-7160	488	23	)	)	PUNCT
ejpam-7160	489	1	=	=	SYM
ejpam-7160	489	2	{	{	PUNCT
ejpam-7160	489	3	π1	π1	NOUN
ejpam-7160	489	4	,	,	PUNCT
ejpam-7160	489	5	π3	π3	NOUN
ejpam-7160	489	6	,	,	PUNCT
ejpam-7160	489	7	π9	π9	NOUN
ejpam-7160	489	8	}	}	PUNCT
ejpam-7160	489	9	.	.	PUNCT
ejpam-7160	490	1	let	let	VERB
ejpam-7160	490	2	l	l	NOUN
ejpam-7160	490	3	=	=	PUNCT
ejpam-7160	490	4	{	{	PUNCT
ejpam-7160	490	5	π	π	NOUN
ejpam-7160	490	6	}	}	PUNCT
ejpam-7160	490	7	,	,	PUNCT
ejpam-7160	490	8	then	then	ADV
ejpam-7160	490	9	τlmn	τlmn	NOUN
ejpam-7160	490	10	r	r	NOUN
ejpam-7160	490	11	=	=	SYM
ejpam-7160	490	12	2π(the	2π(the	PROPN
ejpam-7160	490	13	set	set	NOUN
ejpam-7160	490	14	of	of	ADP
ejpam-7160	490	15	all	all	DET
ejpam-7160	490	16	subsets	subset	NOUN
ejpam-7160	490	17	of	of	ADP
ejpam-7160	490	18	π	π	PROPN
ejpam-7160	490	19	)	)	PUNCT
ejpam-7160	490	20	.	.	PUNCT
ejpam-7160	491	1	i1	i1	PROPN
ejpam-7160	491	2	=	=	PUNCT
ejpam-7160	491	3	{	{	PUNCT
ejpam-7160	491	4	π1	π1	PROPN
ejpam-7160	491	5	,	,	PUNCT
ejpam-7160	491	6	π3	π3	NOUN
ejpam-7160	491	7	,	,	PUNCT
ejpam-7160	491	8	π8	π8	NOUN
ejpam-7160	491	9	,	,	PUNCT
ejpam-7160	491	10	π9	π9	NOUN
ejpam-7160	491	11	}	}	PUNCT
ejpam-7160	491	12	are	be	AUX
ejpam-7160	491	13	the	the	DET
ejpam-7160	491	14	afflicted	afflict	VERB
ejpam-7160	491	15	patients	patient	NOUN
ejpam-7160	491	16	,	,	PUNCT
ejpam-7160	491	17	in	in	ADP
ejpam-7160	491	18	contrast	contrast	NOUN
ejpam-7160	491	19	,	,	PUNCT
ejpam-7160	491	20	the	the	DET
ejpam-7160	491	21	uninfected	uninfected	ADJ
ejpam-7160	491	22	patients	patient	NOUN
ejpam-7160	491	23	are	be	AUX
ejpam-7160	491	24	represented	represent	VERB
ejpam-7160	491	25	by	by	ADP
ejpam-7160	491	26	i2	i2	PROPN
ejpam-7160	491	27	=	=	PUNCT
ejpam-7160	491	28	{	{	PUNCT
ejpam-7160	491	29	π2	π2	PROPN
ejpam-7160	491	30	,	,	PUNCT
ejpam-7160	491	31	π4	π4	NOUN
ejpam-7160	491	32	,	,	PUNCT
ejpam-7160	491	33	π5	π5	PROPN
ejpam-7160	491	34	}	}	PUNCT
ejpam-7160	491	35	.	.	PUNCT
ejpam-7160	492	1	consequently	consequently	ADV
ejpam-7160	492	2	,	,	PUNCT
ejpam-7160	492	3	the	the	DET
ejpam-7160	492	4	lw	lw	NOUN
ejpam-7160	492	5	-	-	PUNCT
ejpam-7160	492	6	app	app	NOUN
ejpam-7160	492	7	,	,	PUNCT
ejpam-7160	492	8	the	the	DET
ejpam-7160	492	9	up	up	ADV
ejpam-7160	492	10	-	-	PUNCT
ejpam-7160	492	11	app	app	NOUN
ejpam-7160	492	12	,	,	PUNCT
ejpam-7160	492	13	and	and	CCONJ
ejpam-7160	492	14	the	the	DET
ejpam-7160	492	15	accuracy	accuracy	NOUN
ejpam-7160	492	16	of	of	ADP
ejpam-7160	492	17	i1	i1	PROPN
ejpam-7160	492	18	are	be	AUX
ejpam-7160	492	19	computed	compute	VERB
ejpam-7160	492	20	as	as	ADP
ejpam-7160	492	21	case(i	case(i	PROPN
ejpam-7160	492	22	)	)	PUNCT
ejpam-7160	492	23	the	the	DET
ejpam-7160	492	24	the	the	DET
ejpam-7160	492	25	afflicted	afflict	VERB
ejpam-7160	492	26	patients	patient	NOUN
ejpam-7160	492	27	i1	i1	PROPN
ejpam-7160	493	1	=	=	PUNCT
ejpam-7160	493	2	{	{	PUNCT
ejpam-7160	493	3	π1	π1	NOUN
ejpam-7160	493	4	,	,	PUNCT
ejpam-7160	493	5	π3	π3	NOUN
ejpam-7160	493	6	,	,	PUNCT
ejpam-7160	493	7	π8	π8	NOUN
ejpam-7160	493	8	,	,	PUNCT
ejpam-7160	493	9	π9	π9	PROPN
ejpam-7160	493	10	}	}	PUNCT
ejpam-7160	493	11	(	(	PUNCT
ejpam-7160	493	12	1	1	X
ejpam-7160	493	13	)	)	PUNCT
ejpam-7160	493	14	ismail	ismail	NOUN
ejpam-7160	493	15	’s	’s	PART
ejpam-7160	493	16	method	method	NOUN
ejpam-7160	493	17	[	[	X
ejpam-7160	493	18	52	52	NUM
ejpam-7160	493	19	]	]	PUNCT
ejpam-7160	493	20	in	in	ADP
ejpam-7160	493	21	definition	definition	NOUN
ejpam-7160	493	22	17	17	NUM
ejpam-7160	493	23	:	:	PUNCT
ejpam-7160	493	24	×mn	×mn	ADJ
ejpam-7160	493	25	r	r	NOUN
ejpam-7160	493	26	(	(	PUNCT
ejpam-7160	493	27	i1	i1	PROPN
ejpam-7160	493	28	)	)	PUNCT
ejpam-7160	493	29	=	=	PROPN
ejpam-7160	493	30	i1	i1	PROPN
ejpam-7160	493	31	;	;	PUNCT
ejpam-7160	493	32	×mn	×mn	PROPN
ejpam-7160	493	33	r(i1	r(i1	NOUN
ejpam-7160	493	34	)	)	PUNCT
ejpam-7160	493	35	=	=	SYM
ejpam-7160	493	36	π	π	PROPN
ejpam-7160	493	37	;	;	PUNCT
ejpam-7160	493	38	amn	amn	PROPN
ejpam-7160	493	39	r(i1	r(i1	NOUN
ejpam-7160	493	40	)	)	PUNCT
ejpam-7160	493	41	=	=	PUNCT
ejpam-7160	493	42	4	4	NUM
ejpam-7160	493	43	7	7	NUM
ejpam-7160	493	44	;	;	PUNCT
ejpam-7160	493	45	bl	bl	PROPN
ejpam-7160	493	46	mn	mn	PROPN
ejpam-7160	493	47	r	r	PROPN
ejpam-7160	493	48	(	(	PUNCT
ejpam-7160	493	49	i1	i1	PROPN
ejpam-7160	493	50	)	)	PUNCT
ejpam-7160	493	51	=	=	PRON
ejpam-7160	493	52	{	{	PUNCT
ejpam-7160	493	53	π2	π2	PROPN
ejpam-7160	493	54	,	,	PUNCT
ejpam-7160	493	55	π4	π4	NOUN
ejpam-7160	493	56	,	,	PUNCT
ejpam-7160	493	57	π5	π5	PROPN
ejpam-7160	493	58	}	}	PUNCT
ejpam-7160	493	59	a.	a.	NOUN
ejpam-7160	493	60	a.	a.	NOUN
ejpam-7160	493	61	azzam	azzam	PROPN
ejpam-7160	493	62	et	et	PROPN
ejpam-7160	493	63	al	al	PROPN
ejpam-7160	493	64	.	.	PUNCT
ejpam-7160	493	65	/	/	SYM
ejpam-7160	493	66	eur	eur	PROPN
ejpam-7160	493	67	.	.	PUNCT
ejpam-7160	494	1	j.	j.	PROPN
ejpam-7160	494	2	pure	pure	PROPN
ejpam-7160	494	3	appl	appl	PROPN
ejpam-7160	494	4	.	.	PROPN
ejpam-7160	494	5	math	math	PROPN
ejpam-7160	494	6	,	,	PUNCT
ejpam-7160	494	7	18	18	NUM
ejpam-7160	494	8	(	(	PUNCT
ejpam-7160	494	9	4	4	NUM
ejpam-7160	494	10	)	)	PUNCT
ejpam-7160	494	11	(	(	PUNCT
ejpam-7160	494	12	2025	2025	NUM
ejpam-7160	494	13	)	)	PUNCT
ejpam-7160	494	14	,	,	PUNCT
ejpam-7160	494	15	7160	7160	NUM
ejpam-7160	494	16	18	18	NUM
ejpam-7160	494	17	of	of	ADP
ejpam-7160	494	18	22	22	NUM
ejpam-7160	494	19	(	(	PUNCT
ejpam-7160	494	20	2	2	NUM
ejpam-7160	494	21	)	)	PUNCT
ejpam-7160	494	22	the	the	DET
ejpam-7160	494	23	proposed	propose	VERB
ejpam-7160	494	24	definitions	definition	NOUN
ejpam-7160	494	25	4.1	4.1	NUM
ejpam-7160	494	26	,	,	PUNCT
ejpam-7160	494	27	4.8	4.8	NUM
ejpam-7160	494	28	,	,	PUNCT
ejpam-7160	494	29	and	and	CCONJ
ejpam-7160	494	30	4.10	4.10	NUM
ejpam-7160	494	31	.	.	PUNCT
ejpam-7160	495	1	×l	×l	PROPN
ejpam-7160	495	2	mn	mn	PROPN
ejpam-7160	495	3	r	r	PROPN
ejpam-7160	495	4	(	(	PUNCT
ejpam-7160	495	5	i1	i1	PROPN
ejpam-7160	495	6	)	)	PUNCT
ejpam-7160	495	7	=	=	PROPN
ejpam-7160	495	8	i1	i1	PROPN
ejpam-7160	495	9	;	;	PUNCT
ejpam-7160	495	10	×l	×l	PUNCT
ejpam-7160	495	11	mn	mn	PROPN
ejpam-7160	495	12	r	r	PROPN
ejpam-7160	495	13	(	(	PUNCT
ejpam-7160	495	14	i1	i1	PROPN
ejpam-7160	495	15	)	)	PUNCT
ejpam-7160	495	16	=	=	PROPN
ejpam-7160	495	17	i1	i1	PROPN
ejpam-7160	495	18	;	;	PUNCT
ejpam-7160	495	19	al	al	PROPN
ejpam-7160	495	20	mn	mn	PROPN
ejpam-7160	495	21	r	r	PROPN
ejpam-7160	495	22	(	(	PUNCT
ejpam-7160	495	23	i1	i1	PROPN
ejpam-7160	495	24	)	)	PUNCT
ejpam-7160	495	25	=	=	PUNCT
ejpam-7160	496	1	1	1	NUM
ejpam-7160	496	2	;	;	PUNCT
ejpam-7160	496	3	bl	bl	PROPN
ejpam-7160	496	4	mn	mn	PROPN
ejpam-7160	496	5	r	r	PROPN
ejpam-7160	496	6	(	(	PUNCT
ejpam-7160	496	7	i2	i2	PROPN
ejpam-7160	496	8	)	)	PUNCT
ejpam-7160	496	9	=	=	PUNCT
ejpam-7160	496	10	ϕ	ϕ	NOUN
ejpam-7160	496	11	case	case	NOUN
ejpam-7160	496	12	(	(	PUNCT
ejpam-7160	496	13	ii	ii	NOUN
ejpam-7160	496	14	)	)	PUNCT
ejpam-7160	496	15	the	the	DET
ejpam-7160	496	16	uninfected	uninfected	ADJ
ejpam-7160	496	17	patients	patient	NOUN
ejpam-7160	496	18	i2	i2	PROPN
ejpam-7160	496	19	=	=	PUNCT
ejpam-7160	496	20	{	{	PUNCT
ejpam-7160	496	21	π2	π2	PROPN
ejpam-7160	496	22	,	,	PUNCT
ejpam-7160	496	23	π4	π4	NOUN
ejpam-7160	496	24	,	,	PUNCT
ejpam-7160	496	25	π5}.(1	π5}.(1	PROPN
ejpam-7160	496	26	)	)	PUNCT
ejpam-7160	496	27	ismail	ismail	PROPN
ejpam-7160	496	28	’s	’s	PART
ejpam-7160	496	29	method	method	NOUN
ejpam-7160	497	1	[	[	X
ejpam-7160	497	2	52	52	NUM
ejpam-7160	497	3	]	]	PUNCT
ejpam-7160	497	4	in	in	ADP
ejpam-7160	497	5	definition	definition	NOUN
ejpam-7160	497	6	17	17	NUM
ejpam-7160	497	7	:	:	PUNCT
ejpam-7160	497	8	×mn	×mn	ADJ
ejpam-7160	497	9	r	r	NOUN
ejpam-7160	497	10	(	(	PUNCT
ejpam-7160	497	11	i2	i2	PROPN
ejpam-7160	497	12	)	)	PUNCT
ejpam-7160	497	13	=	=	SYM
ejpam-7160	497	14	ϕ	ϕ	PROPN
ejpam-7160	497	15	;	;	PUNCT
ejpam-7160	497	16	×mn	×mn	ADJ
ejpam-7160	497	17	r(i2	r(i2	NOUN
ejpam-7160	497	18	)	)	PUNCT
ejpam-7160	497	19	=	=	SYM
ejpam-7160	497	20	{	{	PUNCT
ejpam-7160	497	21	π2	π2	PROPN
ejpam-7160	497	22	,	,	PUNCT
ejpam-7160	497	23	π4	π4	NOUN
ejpam-7160	497	24	,	,	PUNCT
ejpam-7160	497	25	π5	π5	PROPN
ejpam-7160	497	26	}	}	PUNCT
ejpam-7160	497	27	;	;	PUNCT
ejpam-7160	497	28	amn	amn	PROPN
ejpam-7160	497	29	r(i1	r(i1	NOUN
ejpam-7160	497	30	)	)	PUNCT
ejpam-7160	497	31	=	=	SYM
ejpam-7160	497	32	0	0	NUM
ejpam-7160	497	33	;	;	PUNCT
ejpam-7160	497	34	bl	bl	PROPN
ejpam-7160	497	35	mn	mn	PROPN
ejpam-7160	497	36	r	r	PROPN
ejpam-7160	497	37	(	(	PUNCT
ejpam-7160	497	38	i2	i2	PROPN
ejpam-7160	497	39	)	)	PUNCT
ejpam-7160	497	40	=	=	SYM
ejpam-7160	497	41	{	{	PUNCT
ejpam-7160	497	42	π2	π2	PROPN
ejpam-7160	497	43	,	,	PUNCT
ejpam-7160	497	44	π4	π4	NOUN
ejpam-7160	497	45	,	,	PUNCT
ejpam-7160	497	46	π5	π5	PROPN
ejpam-7160	497	47	}	}	PUNCT
ejpam-7160	497	48	(	(	PUNCT
ejpam-7160	497	49	2	2	X
ejpam-7160	497	50	)	)	PUNCT
ejpam-7160	497	51	the	the	DET
ejpam-7160	497	52	proposed	propose	VERB
ejpam-7160	497	53	definitions	definition	NOUN
ejpam-7160	497	54	4.1	4.1	NUM
ejpam-7160	497	55	,	,	PUNCT
ejpam-7160	497	56	4.8	4.8	NUM
ejpam-7160	497	57	,	,	PUNCT
ejpam-7160	497	58	and	and	CCONJ
ejpam-7160	497	59	4.10	4.10	NUM
ejpam-7160	497	60	.	.	PUNCT
ejpam-7160	498	1	×l	×l	PROPN
ejpam-7160	498	2	mn	mn	PROPN
ejpam-7160	498	3	r	r	NOUN
ejpam-7160	498	4	(	(	PUNCT
ejpam-7160	498	5	i2	i2	PROPN
ejpam-7160	498	6	)	)	PUNCT
ejpam-7160	498	7	=	=	SYM
ejpam-7160	498	8	i2	i2	PROPN
ejpam-7160	498	9	;	;	PUNCT
ejpam-7160	498	10	×l	×l	PUNCT
ejpam-7160	498	11	mn	mn	PROPN
ejpam-7160	498	12	r	r	PROPN
ejpam-7160	498	13	(	(	PUNCT
ejpam-7160	498	14	i2	i2	PROPN
ejpam-7160	498	15	)	)	PUNCT
ejpam-7160	498	16	=	=	SYM
ejpam-7160	498	17	i2	i2	PROPN
ejpam-7160	498	18	;	;	PUNCT
ejpam-7160	498	19	al	al	PROPN
ejpam-7160	498	20	mn	mn	PROPN
ejpam-7160	498	21	r	r	PROPN
ejpam-7160	498	22	(	(	PUNCT
ejpam-7160	498	23	i2	i2	PROPN
ejpam-7160	498	24	)	)	PUNCT
ejpam-7160	498	25	=	=	SYM
ejpam-7160	498	26	1	1	NUM
ejpam-7160	498	27	;	;	PUNCT
ejpam-7160	498	28	bl	bl	PROPN
ejpam-7160	498	29	mn	mn	PROPN
ejpam-7160	498	30	r	r	PROPN
ejpam-7160	498	31	(	(	PUNCT
ejpam-7160	498	32	i2	i2	PROPN
ejpam-7160	498	33	)	)	PUNCT
ejpam-7160	498	34	=	=	SYM
ejpam-7160	499	1	ϕ.	ϕ.	PROPN
ejpam-7160	499	2	consequently	consequently	ADV
ejpam-7160	499	3	,	,	PUNCT
ejpam-7160	499	4	ismail	ismail	PROPN
ejpam-7160	499	5	’s	’s	PART
ejpam-7160	499	6	boundaries	boundary	NOUN
ejpam-7160	499	7	[	[	X
ejpam-7160	499	8	52	52	NUM
ejpam-7160	499	9	]	]	PUNCT
ejpam-7160	499	10	for	for	ADP
ejpam-7160	499	11	infected	infected	ADJ
ejpam-7160	499	12	and	and	CCONJ
ejpam-7160	499	13	uninfected	uninfected	ADJ
ejpam-7160	499	14	persons	person	NOUN
ejpam-7160	499	15	are	be	AUX
ejpam-7160	499	16	{	{	PUNCT
ejpam-7160	499	17	π2	π2	ADV
ejpam-7160	499	18	,	,	PUNCT
ejpam-7160	499	19	π4	π4	NOUN
ejpam-7160	499	20	,	,	PUNCT
ejpam-7160	499	21	π5	π5	PROPN
ejpam-7160	499	22	}	}	PUNCT
ejpam-7160	499	23	,	,	PUNCT
ejpam-7160	499	24	resulting	result	VERB
ejpam-7160	499	25	in	in	ADP
ejpam-7160	499	26	ambiguity	ambiguity	NOUN
ejpam-7160	499	27	and	and	CCONJ
ejpam-7160	499	28	diminished	diminish	VERB
ejpam-7160	499	29	decision	decision	NOUN
ejpam-7160	499	30	precision	precision	NOUN
ejpam-7160	499	31	.	.	PUNCT
ejpam-7160	500	1	conversely	conversely	ADV
ejpam-7160	500	2	,	,	PUNCT
ejpam-7160	500	3	the	the	DET
ejpam-7160	500	4	current	current	ADJ
ejpam-7160	500	5	methodology	methodology	NOUN
ejpam-7160	500	6	produces	produce	VERB
ejpam-7160	500	7	a	a	DET
ejpam-7160	500	8	null	null	ADJ
ejpam-7160	500	9	border	border	NOUN
ejpam-7160	500	10	,	,	PUNCT
ejpam-7160	500	11	so	so	ADV
ejpam-7160	500	12	diminishing	diminishing	NOUN
ejpam-7160	500	13	ambiguity	ambiguity	NOUN
ejpam-7160	500	14	and	and	CCONJ
ejpam-7160	500	15	improving	improve	VERB
ejpam-7160	500	16	precision	precision	NOUN
ejpam-7160	500	17	.	.	PUNCT
ejpam-7160	501	1	6	6	X
ejpam-7160	501	2	.	.	X
ejpam-7160	501	3	conclusion	conclusion	NOUN
ejpam-7160	501	4	rough	rough	ADJ
ejpam-7160	501	5	set	set	NOUN
ejpam-7160	501	6	theory	theory	NOUN
ejpam-7160	501	7	is	be	AUX
ejpam-7160	501	8	a	a	DET
ejpam-7160	501	9	mathematical	mathematical	ADJ
ejpam-7160	501	10	framework	framework	NOUN
ejpam-7160	501	11	designed	design	VERB
ejpam-7160	501	12	to	to	PART
ejpam-7160	501	13	address	address	VERB
ejpam-7160	501	14	uncertainty	uncertainty	NOUN
ejpam-7160	501	15	.	.	PUNCT
ejpam-7160	502	1	grills	grill	NOUN
ejpam-7160	502	2	can	can	AUX
ejpam-7160	502	3	enhance	enhance	VERB
ejpam-7160	502	4	this	this	DET
ejpam-7160	502	5	idea	idea	NOUN
ejpam-7160	502	6	,	,	PUNCT
ejpam-7160	502	7	serving	serve	VERB
ejpam-7160	502	8	as	as	ADP
ejpam-7160	502	9	an	an	DET
ejpam-7160	502	10	effective	effective	ADJ
ejpam-7160	502	11	instrument	instrument	NOUN
ejpam-7160	502	12	for	for	ADP
ejpam-7160	502	13	diminishing	diminish	VERB
ejpam-7160	502	14	ambiguity	ambiguity	NOUN
ejpam-7160	502	15	by	by	ADP
ejpam-7160	502	16	enabling	enable	VERB
ejpam-7160	502	17	a	a	DET
ejpam-7160	502	18	wider	wide	ADJ
ejpam-7160	502	19	approximation	approximation	NOUN
ejpam-7160	502	20	.	.	PUNCT
ejpam-7160	503	1	a	a	DET
ejpam-7160	503	2	primary	primary	ADJ
ejpam-7160	503	3	emphasis	emphasis	NOUN
ejpam-7160	503	4	in	in	ADP
ejpam-7160	503	5	the	the	DET
ejpam-7160	503	6	study	study	NOUN
ejpam-7160	503	7	of	of	ADP
ejpam-7160	503	8	rough	rough	ADJ
ejpam-7160	503	9	sets	set	NOUN
ejpam-7160	503	10	is	be	AUX
ejpam-7160	503	11	the	the	DET
ejpam-7160	503	12	minimization	minimization	NOUN
ejpam-7160	503	13	of	of	ADP
ejpam-7160	503	14	boundaries	boundary	NOUN
ejpam-7160	503	15	to	to	PART
ejpam-7160	503	16	improve	improve	VERB
ejpam-7160	503	17	precision	precision	NOUN
ejpam-7160	503	18	.	.	PUNCT
ejpam-7160	504	1	grills	grill	NOUN
ejpam-7160	504	2	is	be	AUX
ejpam-7160	504	3	one	one	NUM
ejpam-7160	504	4	of	of	ADP
ejpam-7160	504	5	the	the	DET
ejpam-7160	504	6	most	most	ADV
ejpam-7160	504	7	efficient	efficient	ADJ
ejpam-7160	504	8	methods	method	NOUN
ejpam-7160	504	9	for	for	ADP
ejpam-7160	504	10	accomplishing	accomplish	VERB
ejpam-7160	504	11	this	this	PRON
ejpam-7160	504	12	.	.	PUNCT
ejpam-7160	505	1	consequently	consequently	ADV
ejpam-7160	505	2	,	,	PUNCT
ejpam-7160	505	3	numerous	numerous	ADJ
ejpam-7160	505	4	techniques	technique	NOUN
ejpam-7160	505	5	employing	employ	VERB
ejpam-7160	505	6	grills	grill	NOUN
ejpam-7160	505	7	for	for	ADP
ejpam-7160	505	8	the	the	DET
ejpam-7160	505	9	construction	construction	NOUN
ejpam-7160	505	10	of	of	ADP
ejpam-7160	505	11	diverse	diverse	ADJ
ejpam-7160	505	12	topologies	topology	NOUN
ejpam-7160	505	13	have	have	AUX
ejpam-7160	505	14	been	be	AUX
ejpam-7160	505	15	suggested	suggest	VERB
ejpam-7160	505	16	.	.	PUNCT
ejpam-7160	506	1	the	the	DET
ejpam-7160	506	2	previous	previous	ADJ
ejpam-7160	506	3	topologies	topology	NOUN
ejpam-7160	506	4	utilizing	utilize	VERB
ejpam-7160	506	5	a.	a.	NOUN
ejpam-7160	506	6	a.	a.	NOUN
ejpam-7160	506	7	azzam	azzam	PROPN
ejpam-7160	506	8	et	et	PROPN
ejpam-7160	506	9	al	al	PROPN
ejpam-7160	506	10	.	.	PUNCT
ejpam-7160	506	11	/	/	SYM
ejpam-7160	506	12	eur	eur	PROPN
ejpam-7160	506	13	.	.	PUNCT
ejpam-7160	507	1	j.	j.	PROPN
ejpam-7160	507	2	pure	pure	PROPN
ejpam-7160	507	3	appl	appl	PROPN
ejpam-7160	507	4	.	.	PROPN
ejpam-7160	507	5	math	math	PROPN
ejpam-7160	507	6	,	,	PUNCT
ejpam-7160	507	7	18	18	NUM
ejpam-7160	507	8	(	(	PUNCT
ejpam-7160	507	9	4	4	NUM
ejpam-7160	507	10	)	)	PUNCT
ejpam-7160	507	11	(	(	PUNCT
ejpam-7160	507	12	2025	2025	NUM
ejpam-7160	507	13	)	)	PUNCT
ejpam-7160	507	14	,	,	PUNCT
ejpam-7160	507	15	7160	7160	NUM
ejpam-7160	507	16	19	19	NUM
ejpam-7160	507	17	of	of	ADP
ejpam-7160	507	18	22	22	NUM
ejpam-7160	507	19	table	table	NOUN
ejpam-7160	507	20	2	2	NUM
ejpam-7160	507	21	:	:	PUNCT
ejpam-7160	507	22	information	information	NOUN
ejpam-7160	507	23	system	system	NOUN
ejpam-7160	507	24	for	for	ADP
ejpam-7160	507	25	heart	heart	NOUN
ejpam-7160	507	26	failure	failure	NOUN
ejpam-7160	507	27	patients	patient	NOUN
ejpam-7160	507	28	bs	bs	INTJ
ejpam-7160	507	29	oa	oa	PROPN
ejpam-7160	507	30	pa	pa	PROPN
ejpam-7160	507	31	re	re	PROPN
ejpam-7160	507	32	ag	ag	PROPN
ejpam-7160	507	33	d.	d.	PROPN
ejpam-7160	507	34	π1	π1	PROPN
ejpam-7160	507	35	e	e	PROPN
ejpam-7160	507	36	e	e	X
ejpam-7160	507	37	e	e	X
ejpam-7160	507	38	e	e	X
ejpam-7160	507	39	ne	ne	X
ejpam-7160	507	40	e	e	PROPN
ejpam-7160	507	41	π2	π2	X
ejpam-7160	507	42	ne	ne	PROPN
ejpam-7160	507	43	ne	ne	X
ejpam-7160	507	44	ne	ne	X
ejpam-7160	507	45	e	e	X
ejpam-7160	507	46	e	e	X
ejpam-7160	507	47	ne	ne	X
ejpam-7160	507	48	π3	π3	PROPN
ejpam-7160	507	49	e	e	X
ejpam-7160	507	50	e	e	X
ejpam-7160	507	51	e	e	X
ejpam-7160	507	52	e	e	X
ejpam-7160	507	53	e	e	X
ejpam-7160	507	54	e	e	X
ejpam-7160	507	55	π4	π4	ADP
ejpam-7160	507	56	ne	ne	PROPN
ejpam-7160	507	57	ne	ne	X
ejpam-7160	507	58	ne	ne	X
ejpam-7160	507	59	e	e	PROPN
ejpam-7160	507	60	ne	ne	X
ejpam-7160	507	61	ne	ne	X
ejpam-7160	507	62	π5	π5	PROPN
ejpam-7160	507	63	e	e	X
ejpam-7160	507	64	ne	ne	X
ejpam-7160	507	65	ne	ne	X
ejpam-7160	507	66	e	e	PROPN
ejpam-7160	507	67	e	e	PROPN
ejpam-7160	507	68	ne	ne	X
ejpam-7160	507	69	π8	π8	PROPN
ejpam-7160	507	70	e	e	X
ejpam-7160	507	71	e	e	X
ejpam-7160	507	72	ne	ne	X
ejpam-7160	507	73	e	e	X
ejpam-7160	507	74	e	e	X
ejpam-7160	507	75	e	e	X
ejpam-7160	507	76	π9	π9	PROPN
ejpam-7160	507	77	e	e	PROPN
ejpam-7160	507	78	ne	ne	X
ejpam-7160	507	79	e	e	X
ejpam-7160	507	80	e	e	X
ejpam-7160	507	81	ne	ne	X
ejpam-7160	507	82	e	e	X
ejpam-7160	507	83	π10	π10	X
ejpam-7160	507	84	ne	ne	PROPN
ejpam-7160	507	85	ne	ne	X
ejpam-7160	507	86	ne	ne	X
ejpam-7160	507	87	e	e	PROPN
ejpam-7160	507	88	e	e	PROPN
ejpam-7160	507	89	ne	ne	PROPN
ejpam-7160	507	90	grills	grill	NOUN
ejpam-7160	507	91	were	be	AUX
ejpam-7160	507	92	less	less	ADV
ejpam-7160	507	93	refined	refined	ADJ
ejpam-7160	507	94	than	than	ADP
ejpam-7160	507	95	the	the	DET
ejpam-7160	507	96	current	current	ADJ
ejpam-7160	507	97	ones	one	NOUN
ejpam-7160	507	98	.	.	PUNCT
ejpam-7160	508	1	the	the	DET
ejpam-7160	508	2	existing	exist	VERB
ejpam-7160	508	3	topologies	topology	NOUN
ejpam-7160	508	4	are	be	AUX
ejpam-7160	508	5	more	more	ADV
ejpam-7160	508	6	extensive	extensive	ADJ
ejpam-7160	508	7	and	and	CCONJ
ejpam-7160	508	8	provide	provide	VERB
ejpam-7160	508	9	a	a	DET
ejpam-7160	508	10	significant	significant	ADJ
ejpam-7160	508	11	amount	amount	NOUN
ejpam-7160	508	12	of	of	ADP
ejpam-7160	508	13	information	information	NOUN
ejpam-7160	508	14	that	that	PRON
ejpam-7160	508	15	is	be	AUX
ejpam-7160	508	16	beneficial	beneficial	ADJ
ejpam-7160	508	17	for	for	ADP
ejpam-7160	508	18	the	the	DET
ejpam-7160	508	19	analysis	analysis	NOUN
ejpam-7160	508	20	of	of	ADP
ejpam-7160	508	21	rough	rough	ADJ
ejpam-7160	508	22	sets	set	NOUN
ejpam-7160	508	23	.	.	PUNCT
ejpam-7160	509	1	we	we	PRON
ejpam-7160	509	2	utilized	utilize	VERB
ejpam-7160	509	3	the	the	DET
ejpam-7160	509	4	neighborhood	neighborhood	NOUN
ejpam-7160	509	5	relation	relation	NOUN
ejpam-7160	509	6	with	with	ADP
ejpam-7160	509	7	the	the	DET
ejpam-7160	509	8	grill	grill	NOUN
ejpam-7160	509	9	,	,	PUNCT
ejpam-7160	509	10	which	which	PRON
ejpam-7160	509	11	is	be	AUX
ejpam-7160	509	12	among	among	ADP
ejpam-7160	509	13	the	the	DET
ejpam-7160	509	14	most	most	ADV
ejpam-7160	509	15	effective	effective	ADJ
ejpam-7160	509	16	relations	relation	NOUN
ejpam-7160	509	17	and	and	CCONJ
ejpam-7160	509	18	has	have	AUX
ejpam-7160	509	19	broadened	broaden	VERB
ejpam-7160	509	20	the	the	DET
ejpam-7160	509	21	topological	topological	ADJ
ejpam-7160	509	22	structures	structure	NOUN
ejpam-7160	509	23	.	.	PUNCT
ejpam-7160	510	1	this	this	PRON
ejpam-7160	510	2	increases	increase	VERB
ejpam-7160	510	3	its	its	PRON
ejpam-7160	510	4	relevance	relevance	NOUN
ejpam-7160	510	5	in	in	ADP
ejpam-7160	510	6	domains	domain	NOUN
ejpam-7160	510	7	necessitating	necessitate	VERB
ejpam-7160	510	8	extensive	extensive	ADJ
ejpam-7160	510	9	samples	sample	NOUN
ejpam-7160	510	10	,	,	PUNCT
ejpam-7160	510	11	such	such	ADJ
ejpam-7160	510	12	as	as	ADP
ejpam-7160	510	13	worldwide	worldwide	ADJ
ejpam-7160	510	14	epidemics	epidemic	NOUN
ejpam-7160	510	15	.	.	PUNCT
ejpam-7160	511	1	the	the	DET
ejpam-7160	511	2	characteristics	characteristic	NOUN
ejpam-7160	511	3	of	of	ADP
ejpam-7160	511	4	these	these	DET
ejpam-7160	511	5	topologies	topology	NOUN
ejpam-7160	511	6	were	be	AUX
ejpam-7160	511	7	examined	examine	VERB
ejpam-7160	511	8	,	,	PUNCT
ejpam-7160	511	9	including	include	VERB
ejpam-7160	511	10	comparative	comparative	ADJ
ejpam-7160	511	11	analyses	analysis	NOUN
ejpam-7160	511	12	among	among	ADP
ejpam-7160	511	13	them	they	PRON
ejpam-7160	511	14	.	.	PUNCT
ejpam-7160	512	1	the	the	DET
ejpam-7160	512	2	smallest	small	ADJ
ejpam-7160	512	3	and	and	CCONJ
ejpam-7160	512	4	largest	large	ADJ
ejpam-7160	512	5	topologies	topology	NOUN
ejpam-7160	512	6	were	be	AUX
ejpam-7160	512	7	determined	determine	VERB
ejpam-7160	512	8	,	,	PUNCT
ejpam-7160	512	9	a	a	DET
ejpam-7160	512	10	task	task	NOUN
ejpam-7160	512	11	not	not	PART
ejpam-7160	512	12	accomplished	accomplish	VERB
ejpam-7160	512	13	in	in	ADP
ejpam-7160	512	14	prior	prior	ADJ
ejpam-7160	512	15	studies	study	NOUN
ejpam-7160	512	16	.	.	PUNCT
ejpam-7160	513	1	furthermore	furthermore	ADV
ejpam-7160	513	2	,	,	PUNCT
ejpam-7160	513	3	novel	novel	ADJ
ejpam-7160	513	4	approximations	approximation	NOUN
ejpam-7160	513	5	were	be	AUX
ejpam-7160	513	6	proposed	propose	VERB
ejpam-7160	513	7	,	,	PUNCT
ejpam-7160	513	8	employing	employ	VERB
ejpam-7160	513	9	these	these	DET
ejpam-7160	513	10	suggested	suggest	VERB
ejpam-7160	513	11	topologies	topology	NOUN
ejpam-7160	513	12	as	as	ADP
ejpam-7160	513	13	an	an	DET
ejpam-7160	513	14	extension	extension	NOUN
ejpam-7160	513	15	of	of	ADP
ejpam-7160	513	16	the	the	DET
ejpam-7160	513	17	previous	previous	ADJ
ejpam-7160	513	18	model	model	NOUN
ejpam-7160	513	19	.	.	PUNCT
ejpam-7160	514	1	this	this	PRON
ejpam-7160	514	2	increases	increase	VERB
ejpam-7160	514	3	its	its	PRON
ejpam-7160	514	4	relevance	relevance	NOUN
ejpam-7160	514	5	in	in	ADP
ejpam-7160	514	6	domains	domain	NOUN
ejpam-7160	514	7	necessitating	necessitate	VERB
ejpam-7160	514	8	extensive	extensive	ADJ
ejpam-7160	514	9	samples	sample	NOUN
ejpam-7160	514	10	,	,	PUNCT
ejpam-7160	514	11	such	such	ADJ
ejpam-7160	514	12	as	as	ADP
ejpam-7160	514	13	worldwide	worldwide	ADJ
ejpam-7160	514	14	epidemics	epidemic	NOUN
ejpam-7160	514	15	.	.	PUNCT
ejpam-7160	515	1	a	a	DET
ejpam-7160	515	2	promising	promising	ADJ
ejpam-7160	515	3	avenue	avenue	NOUN
ejpam-7160	515	4	for	for	ADP
ejpam-7160	515	5	future	future	ADJ
ejpam-7160	515	6	study	study	NOUN
ejpam-7160	515	7	will	will	AUX
ejpam-7160	515	8	include	include	VERB
ejpam-7160	515	9	the	the	DET
ejpam-7160	515	10	following	following	NOUN
ejpam-7160	515	11	:	:	PUNCT
ejpam-7160	515	12	(	(	PUNCT
ejpam-7160	515	13	1	1	X
ejpam-7160	515	14	)	)	PUNCT
ejpam-7160	515	15	introducing	introduce	VERB
ejpam-7160	515	16	two	two	NUM
ejpam-7160	515	17	grills	grill	NOUN
ejpam-7160	515	18	instead	instead	ADV
ejpam-7160	515	19	of	of	ADP
ejpam-7160	515	20	one	one	NUM
ejpam-7160	515	21	to	to	PART
ejpam-7160	515	22	generalize	generalize	VERB
ejpam-7160	515	23	the	the	DET
ejpam-7160	515	24	current	current	ADJ
ejpam-7160	515	25	method	method	NOUN
ejpam-7160	515	26	;	;	PUNCT
ejpam-7160	515	27	(	(	PUNCT
ejpam-7160	515	28	2	2	X
ejpam-7160	515	29	)	)	PUNCT
ejpam-7160	515	30	developing	develop	VERB
ejpam-7160	515	31	a	a	DET
ejpam-7160	515	32	soft	soft	ADJ
ejpam-7160	515	33	-	-	PUNCT
ejpam-7160	515	34	topology	topology	NOUN
ejpam-7160	515	35	to	to	PART
ejpam-7160	515	36	enhance	enhance	VERB
ejpam-7160	515	37	the	the	DET
ejpam-7160	515	38	existing	exist	VERB
ejpam-7160	515	39	work	work	NOUN
ejpam-7160	515	40	;	;	PUNCT
ejpam-7160	515	41	(	(	PUNCT
ejpam-7160	515	42	3	3	X
ejpam-7160	515	43	)	)	PUNCT
ejpam-7160	515	44	extending	extend	VERB
ejpam-7160	515	45	the	the	DET
ejpam-7160	515	46	present	present	ADJ
ejpam-7160	515	47	paper	paper	NOUN
ejpam-7160	515	48	to	to	PART
ejpam-7160	515	49	encompass	encompass	VERB
ejpam-7160	515	50	fuzzy	fuzzy	ADJ
ejpam-7160	515	51	and	and	CCONJ
ejpam-7160	515	52	picture	picture	NOUN
ejpam-7160	515	53	sets	set	NOUN
ejpam-7160	515	54	;	;	PUNCT
ejpam-7160	515	55	(	(	PUNCT
ejpam-7160	515	56	4	4	X
ejpam-7160	515	57	)	)	PUNCT
ejpam-7160	515	58	comparison	comparison	NOUN
ejpam-7160	515	59	between	between	ADP
ejpam-7160	515	60	grills	grill	NOUN
ejpam-7160	515	61	and	and	CCONJ
ejpam-7160	515	62	ideals	ideal	NOUN
ejpam-7160	515	63	to	to	PART
ejpam-7160	515	64	generalize	generalize	VERB
ejpam-7160	515	65	the	the	DET
ejpam-7160	515	66	prevailing	prevail	VERB
ejpam-7160	515	67	methodology	methodology	NOUN
ejpam-7160	515	68	.	.	PUNCT
ejpam-7160	516	1	conflict	conflict	NOUN
ejpam-7160	516	2	of	of	ADP
ejpam-7160	516	3	interest	interest	NOUN
ejpam-7160	516	4	there	there	PRON
ejpam-7160	516	5	are	be	VERB
ejpam-7160	516	6	no	no	DET
ejpam-7160	516	7	conflicting	conflict	VERB
ejpam-7160	516	8	interests	interest	NOUN
ejpam-7160	516	9	,	,	PUNCT
ejpam-7160	516	10	according	accord	VERB
ejpam-7160	516	11	to	to	ADP
ejpam-7160	516	12	the	the	DET
ejpam-7160	516	13	authors	author	NOUN
ejpam-7160	516	14	.	.	PUNCT
ejpam-7160	517	1	acknowledgements	acknowledgement	NOUN
ejpam-7160	517	2	the	the	DET
ejpam-7160	517	3	authors	author	NOUN
ejpam-7160	517	4	extend	extend	VERB
ejpam-7160	517	5	their	their	PRON
ejpam-7160	517	6	appreciation	appreciation	NOUN
ejpam-7160	517	7	to	to	ADP
ejpam-7160	517	8	prince	prince	PROPN
ejpam-7160	517	9	sattam	sattam	PROPN
ejpam-7160	517	10	bin	bin	PROPN
ejpam-7160	517	11	abdulaziz	abdulaziz	PROPN
ejpam-7160	517	12	university	university	PROPN
ejpam-7160	517	13	for	for	ADP
ejpam-7160	517	14	funding	fund	VERB
ejpam-7160	517	15	this	this	DET
ejpam-7160	517	16	research	research	NOUN
ejpam-7160	517	17	work	work	NOUN
ejpam-7160	517	18	through	through	ADP
ejpam-7160	517	19	the	the	DET
ejpam-7160	517	20	project	project	NOUN
ejpam-7160	517	21	number	number	NOUN
ejpam-7160	517	22	(	(	PUNCT
ejpam-7160	517	23	psau/2025/01/34111	psau/2025/01/34111	PROPN
ejpam-7160	517	24	)	)	PUNCT
ejpam-7160	517	25	.	.	PUNCT
ejpam-7160	518	1	references	reference	NOUN
ejpam-7160	518	2	[	[	X
ejpam-7160	518	3	1	1	NUM
ejpam-7160	518	4	]	]	PUNCT
ejpam-7160	518	5	pawlak	pawlak	ADJ
ejpam-7160	518	6	v.	v.	ADP
ejpam-7160	518	7	,	,	PUNCT
ejpam-7160	518	8	rough	rough	ADJ
ejpam-7160	518	9	sets	set	NOUN
ejpam-7160	518	10	.	.	PUNCT
ejpam-7160	519	1	int	int	NOUN
ejpam-7160	519	2	.	.	PUNCT
ejpam-7160	520	1	j.	j.	PROPN
ejpam-7160	520	2	comput	comput	PROPN
ejpam-7160	520	3	.	.	PUNCT
ejpam-7160	521	1	inf	inf	PROPN
ejpam-7160	521	2	.	.	PUNCT
ejpam-7160	522	1	sci	sci	PROPN
ejpam-7160	522	2	.	.	PROPN
ejpam-7160	522	3	1982	1982	NUM
ejpam-7160	522	4	,	,	PUNCT
ejpam-7160	522	5	11	11	NUM
ejpam-7160	522	6	,	,	PUNCT
ejpam-7160	522	7	341–356	341–356	NUM
ejpam-7160	522	8	.	.	PUNCT
ejpam-7160	523	1	[	[	X
ejpam-7160	523	2	2	2	NUM
ejpam-7160	523	3	]	]	PUNCT
ejpam-7160	523	4	pawlak	pawlak	NOUN
ejpam-7160	523	5	v.	v.	ADP
ejpam-7160	523	6	,	,	PUNCT
ejpam-7160	523	7	rough	rough	ADJ
ejpam-7160	523	8	concept	concept	NOUN
ejpam-7160	523	9	analysis	analysis	NOUN
ejpam-7160	523	10	.	.	PUNCT
ejpam-7160	524	1	bull	bull	NOUN
ejpam-7160	524	2	.	.	PUNCT
ejpam-7160	525	1	pol	pol	PROPN
ejpam-7160	525	2	.	.	PUNCT
ejpam-7160	526	1	acad	acad	PROPN
ejpam-7160	526	2	.	.	PUNCT
ejpam-7160	527	1	sci	sci	PROPN
ejpam-7160	527	2	.	.	PUNCT
ejpam-7160	527	3	math	math	PROPN
ejpam-7160	527	4	.	.	PUNCT
ejpam-7160	528	1	1985	1985	NUM
ejpam-7160	528	2	,	,	PUNCT
ejpam-7160	528	3	33	33	NUM
ejpam-7160	528	4	,	,	PUNCT
ejpam-7160	528	5	495–498	495–498	NUM
ejpam-7160	528	6	.	.	PUNCT
ejpam-7160	529	1	[	[	X
ejpam-7160	529	2	3	3	X
ejpam-7160	529	3	]	]	X
ejpam-7160	529	4	ma	ma	PROPN
ejpam-7160	529	5	x.	x.	PROPN
ejpam-7160	529	6	,	,	PUNCT
ejpam-7160	529	7	liu	liu	PROPN
ejpam-7160	529	8	q.	q.	PROPN
ejpam-7160	529	9	,	,	PUNCT
ejpam-7160	529	10	zhan	zhan	PROPN
ejpam-7160	529	11	j.	j.	PROPN
ejpam-7160	529	12	,	,	PUNCT
ejpam-7160	529	13	a	a	DET
ejpam-7160	529	14	survey	survey	NOUN
ejpam-7160	529	15	of	of	ADP
ejpam-7160	529	16	decision	decision	NOUN
ejpam-7160	529	17	-	-	PUNCT
ejpam-7160	529	18	making	make	VERB
ejpam-7160	529	19	methods	method	NOUN
ejpam-7160	529	20	based	base	VERB
ejpam-7160	529	21	on	on	ADP
ejpam-7160	529	22	certain	certain	ADJ
ejpam-7160	529	23	hybrid	hybrid	ADJ
ejpam-7160	529	24	soft	soft	ADJ
ejpam-7160	529	25	set	set	NOUN
ejpam-7160	529	26	models	model	NOUN
ejpam-7160	529	27	.	.	PUNCT
ejpam-7160	530	1	artif	artif	INTJ
ejpam-7160	530	2	.	.	PUNCT
ejpam-7160	531	1	intell	intell	PROPN
ejpam-7160	531	2	.	.	PUNCT
ejpam-7160	532	1	rev	rev	PROPN
ejpam-7160	532	2	.	.	PROPN
ejpam-7160	532	3	2017	2017	NUM
ejpam-7160	532	4	,	,	PUNCT
ejpam-7160	532	5	47	47	NUM
ejpam-7160	532	6	,	,	PUNCT
ejpam-7160	532	7	507–530	507–530	NUM
ejpam-7160	532	8	.	.	PUNCT
ejpam-7160	533	1	a.	a.	PROPN
ejpam-7160	533	2	a.	a.	PROPN
ejpam-7160	533	3	azzam	azzam	PROPN
ejpam-7160	533	4	et	et	PROPN
ejpam-7160	533	5	al	al	PROPN
ejpam-7160	533	6	.	.	PUNCT
ejpam-7160	533	7	/	/	SYM
ejpam-7160	533	8	eur	eur	PROPN
ejpam-7160	533	9	.	.	PUNCT
ejpam-7160	534	1	j.	j.	PROPN
ejpam-7160	534	2	pure	pure	PROPN
ejpam-7160	534	3	appl	appl	PROPN
ejpam-7160	534	4	.	.	PROPN
ejpam-7160	534	5	math	math	PROPN
ejpam-7160	534	6	,	,	PUNCT
ejpam-7160	534	7	18	18	NUM
ejpam-7160	534	8	(	(	PUNCT
ejpam-7160	534	9	4	4	NUM
ejpam-7160	534	10	)	)	PUNCT
ejpam-7160	534	11	(	(	PUNCT
ejpam-7160	534	12	2025	2025	NUM
ejpam-7160	534	13	)	)	PUNCT
ejpam-7160	534	14	,	,	PUNCT
ejpam-7160	534	15	7160	7160	NUM
ejpam-7160	534	16	20	20	NUM
ejpam-7160	534	17	of	of	ADP
ejpam-7160	534	18	22	22	NUM
ejpam-7160	535	1	[	[	X
ejpam-7160	535	2	4	4	NUM
ejpam-7160	535	3	]	]	X
ejpam-7160	535	4	pal	pal	ADJ
ejpam-7160	535	5	s.	s.	PROPN
ejpam-7160	535	6	,	,	PUNCT
ejpam-7160	535	7	mitra	mitra	PROPN
ejpam-7160	535	8	p.	p.	PROPN
ejpam-7160	535	9	,	,	PUNCT
ejpam-7160	535	10	case	case	NOUN
ejpam-7160	535	11	generation	generation	NOUN
ejpam-7160	535	12	using	use	VERB
ejpam-7160	535	13	rough	rough	ADJ
ejpam-7160	535	14	sets	set	NOUN
ejpam-7160	535	15	with	with	ADP
ejpam-7160	535	16	fuzzy	fuzzy	ADJ
ejpam-7160	535	17	representation	representation	NOUN
ejpam-7160	535	18	.	.	PUNCT
ejpam-7160	536	1	ieee	ieee	PROPN
ejpam-7160	536	2	trans	trans	PROPN
ejpam-7160	536	3	.	.	PROPN
ejpam-7160	537	1	knowl	knowl	PROPN
ejpam-7160	537	2	.	.	PUNCT
ejpam-7160	538	1	data	data	PROPN
ejpam-7160	538	2	eng	eng	PROPN
ejpam-7160	538	3	.	.	PROPN
ejpam-7160	538	4	2004	2004	NUM
ejpam-7160	538	5	,	,	PUNCT
ejpam-7160	538	6	16	16	NUM
ejpam-7160	538	7	,	,	PUNCT
ejpam-7160	538	8	293–300	293–300	NUM
ejpam-7160	538	9	.	.	PUNCT
ejpam-7160	539	1	[	[	X
ejpam-7160	539	2	5	5	NUM
ejpam-7160	539	3	]	]	PUNCT
ejpam-7160	539	4	zhan	zhan	PROPN
ejpam-7160	539	5	j.	j.	PROPN
ejpam-7160	539	6	,	,	PUNCT
ejpam-7160	539	7	davvaz	davvaz	PROPN
ejpam-7160	539	8	b.	b.	PROPN
ejpam-7160	539	9	,	,	PUNCT
ejpam-7160	539	10	characterizations	characterization	NOUN
ejpam-7160	539	11	of	of	ADP
ejpam-7160	539	12	two	two	NUM
ejpam-7160	539	13	kinds	kind	NOUN
ejpam-7160	539	14	of	of	ADP
ejpam-7160	539	15	hemirings	hemiring	NOUN
ejpam-7160	539	16	based	base	VERB
ejpam-7160	539	17	on	on	ADP
ejpam-7160	539	18	probability	probability	NOUN
ejpam-7160	539	19	spaces	space	NOUN
ejpam-7160	539	20	.	.	PUNCT
ejpam-7160	539	21	soft	soft	ADJ
ejpam-7160	539	22	comput	comput	NOUN
ejpam-7160	539	23	.	.	PUNCT
ejpam-7160	540	1	2016	2016	NUM
ejpam-7160	540	2	,	,	PUNCT
ejpam-7160	540	3	20	20	NUM
ejpam-7160	540	4	,	,	PUNCT
ejpam-7160	540	5	637–648	637–648	NUM
ejpam-7160	540	6	.	.	PUNCT
ejpam-7160	541	1	[	[	X
ejpam-7160	541	2	6	6	NUM
ejpam-7160	541	3	]	]	X
ejpam-7160	541	4	zhu	zhu	PROPN
ejpam-7160	541	5	w.	w.	PROPN
ejpam-7160	541	6	,	,	PUNCT
ejpam-7160	541	7	wang	wang	PROPN
ejpam-7160	541	8	f.	f.	PROPN
ejpam-7160	541	9	,	,	PUNCT
ejpam-7160	541	10	reduction	reduction	NOUN
ejpam-7160	541	11	and	and	CCONJ
ejpam-7160	541	12	axiomization	axiomization	NOUN
ejpam-7160	541	13	of	of	ADP
ejpam-7160	541	14	covering	cover	VERB
ejpam-7160	541	15	generalized	generalized	ADJ
ejpam-7160	541	16	rough	rough	ADJ
ejpam-7160	541	17	sets	set	NOUN
ejpam-7160	541	18	.	.	PUNCT
ejpam-7160	542	1	inf	inf	PROPN
ejpam-7160	542	2	.	.	PUNCT
ejpam-7160	543	1	sci	sci	PROPN
ejpam-7160	543	2	.	.	PROPN
ejpam-7160	543	3	2003	2003	NUM
ejpam-7160	543	4	,	,	PUNCT
ejpam-7160	543	5	152	152	NUM
ejpam-7160	543	6	,	,	PUNCT
ejpam-7160	543	7	217–230	217–230	NUM
ejpam-7160	543	8	.	.	PUNCT
ejpam-7160	544	1	[	[	X
ejpam-7160	544	2	7	7	X
ejpam-7160	544	3	]	]	X
ejpam-7160	544	4	skowron	skowron	ADJ
ejpam-7160	544	5	a.	a.	NOUN
ejpam-7160	544	6	,	,	PUNCT
ejpam-7160	544	7	on	on	ADP
ejpam-7160	544	8	topology	topology	NOUN
ejpam-7160	544	9	in	in	ADP
ejpam-7160	544	10	information	information	NOUN
ejpam-7160	544	11	system	system	NOUN
ejpam-7160	544	12	.	.	PUNCT
ejpam-7160	545	1	bull	bull	NOUN
ejpam-7160	545	2	.	.	PUNCT
ejpam-7160	546	1	pol	pol	PROPN
ejpam-7160	546	2	.	.	PUNCT
ejpam-7160	547	1	acad	acad	PROPN
ejpam-7160	547	2	.	.	PUNCT
ejpam-7160	548	1	sci	sci	PROPN
ejpam-7160	548	2	.	.	PUNCT
ejpam-7160	548	3	math	math	PROPN
ejpam-7160	548	4	.	.	PUNCT
ejpam-7160	549	1	1988	1988	NUM
ejpam-7160	549	2	,	,	PUNCT
ejpam-7160	549	3	36	36	NUM
ejpam-7160	549	4	,	,	PUNCT
ejpam-7160	549	5	477–480	477–480	NUM
ejpam-7160	549	6	.	.	PUNCT
ejpam-7160	550	1	[	[	X
ejpam-7160	550	2	8	8	NUM
ejpam-7160	550	3	]	]	SYM
ejpam-7160	550	4	wiweger	wiweger	ADJ
ejpam-7160	550	5	a.	a.	NOUN
ejpam-7160	550	6	,	,	PUNCT
ejpam-7160	550	7	on	on	ADP
ejpam-7160	550	8	topological	topological	ADJ
ejpam-7160	550	9	rough	rough	ADJ
ejpam-7160	550	10	sets	set	NOUN
ejpam-7160	550	11	.	.	PUNCT
ejpam-7160	551	1	bull	bull	NOUN
ejpam-7160	551	2	.	.	PUNCT
ejpam-7160	552	1	pol	pol	PROPN
ejpam-7160	552	2	.	.	PUNCT
ejpam-7160	553	1	acad	acad	PROPN
ejpam-7160	553	2	.	.	PUNCT
ejpam-7160	554	1	sci	sci	PROPN
ejpam-7160	554	2	.	.	PUNCT
ejpam-7160	554	3	math	math	PROPN
ejpam-7160	554	4	.	.	PUNCT
ejpam-7160	555	1	1989	1989	NUM
ejpam-7160	555	2	,	,	PUNCT
ejpam-7160	555	3	37	37	NUM
ejpam-7160	555	4	,	,	PUNCT
ejpam-7160	555	5	89–93	89–93	NUM
ejpam-7160	555	6	.	.	PUNCT
ejpam-7160	556	1	[	[	X
ejpam-7160	556	2	9	9	NUM
ejpam-7160	556	3	]	]	SYM
ejpam-7160	556	4	li	li	PROPN
ejpam-7160	556	5	x.	x.	PROPN
ejpam-7160	556	6	,	,	PUNCT
ejpam-7160	556	7	liu	liu	PROPN
ejpam-7160	556	8	s.	s.	PROPN
ejpam-7160	556	9	,	,	PUNCT
ejpam-7160	556	10	matroidal	matroidal	NOUN
ejpam-7160	556	11	approaches	approach	NOUN
ejpam-7160	556	12	to	to	ADP
ejpam-7160	556	13	rough	rough	ADJ
ejpam-7160	556	14	sets	set	NOUN
ejpam-7160	556	15	via	via	ADP
ejpam-7160	556	16	closure	closure	NOUN
ejpam-7160	556	17	operators	operator	NOUN
ejpam-7160	556	18	.	.	PUNCT
ejpam-7160	557	1	int	int	NOUN
ejpam-7160	557	2	.	.	PUNCT
ejpam-7160	558	1	j.	j.	PROPN
ejpam-7160	558	2	approx	approx	PROPN
ejpam-7160	558	3	.	.	PUNCT
ejpam-7160	559	1	reason	reason	NOUN
ejpam-7160	559	2	.	.	PUNCT
ejpam-7160	560	1	2012	2012	NUM
ejpam-7160	560	2	,	,	PUNCT
ejpam-7160	560	3	53	53	NUM
ejpam-7160	560	4	,	,	PUNCT
ejpam-7160	560	5	513–527	513–527	NUM
ejpam-7160	560	6	.	.	PUNCT
ejpam-7160	561	1	[	[	X
ejpam-7160	561	2	10	10	NUM
ejpam-7160	561	3	]	]	X
ejpam-7160	561	4	pei	pei	PROPN
ejpam-7160	561	5	v.	v.	PROPN
ejpam-7160	561	6	,	,	PUNCT
ejpam-7160	561	7	pei	pei	PROPN
ejpam-7160	561	8	d.	d.	PROPN
ejpam-7160	561	9	,	,	PUNCT
ejpam-7160	561	10	zheng	zheng	PROPN
ejpam-7160	561	11	,	,	PUNCT
ejpam-7160	561	12	l.	l.	PROPN
ejpam-7160	561	13	topology	topology	PROPN
ejpam-7160	561	14	vs	vs	ADP
ejpam-7160	561	15	generalized	generalize	VERB
ejpam-7160	561	16	rough	rough	ADJ
ejpam-7160	561	17	sets	set	NOUN
ejpam-7160	561	18	.	.	PUNCT
ejpam-7160	562	1	int	int	NOUN
ejpam-7160	562	2	.	.	PUNCT
ejpam-7160	563	1	j.	j.	PROPN
ejpam-7160	563	2	approx	approx	PROPN
ejpam-7160	563	3	.	.	PUNCT
ejpam-7160	564	1	reason	reason	NOUN
ejpam-7160	564	2	.	.	PUNCT
ejpam-7160	565	1	2011	2011	NUM
ejpam-7160	565	2	,	,	PUNCT
ejpam-7160	565	3	52	52	NUM
ejpam-7160	565	4	,	,	PUNCT
ejpam-7160	565	5	231–239	231–239	NUM
ejpam-7160	565	6	.	.	PUNCT
ejpam-7160	566	1	[	[	X
ejpam-7160	566	2	11	11	NUM
ejpam-7160	566	3	]	]	X
ejpam-7160	566	4	rady	rady	PROPN
ejpam-7160	566	5	e.a	e.a	PROPN
ejpam-7160	566	6	.	.	PROPN
ejpam-7160	566	7	,	,	PUNCT
ejpam-7160	566	8	kozae	kozae	PROPN
ejpam-7160	566	9	a.m.	a.m.	PROPN
ejpam-7160	566	10	,	,	PUNCT
ejpam-7160	566	11	abd	abd	PROPN
ejpam-7160	566	12	el	el	PROPN
ejpam-7160	566	13	-	-	PUNCT
ejpam-7160	566	14	monsef	monsef	PROPN
ejpam-7160	566	15	m.m.e	m.m.e	PROPN
ejpam-7160	566	16	.	.	PROPN
ejpam-7160	566	17	,	,	PUNCT
ejpam-7160	566	18	generalized	generalize	VERB
ejpam-7160	566	19	rough	rough	ADJ
ejpam-7160	566	20	sets	set	NOUN
ejpam-7160	566	21	.	.	PUNCT
ejpam-7160	567	1	chaos	chaos	NOUN
ejpam-7160	567	2	solitons	soliton	NOUN
ejpam-7160	567	3	fractals	fractal	NOUN
ejpam-7160	567	4	2004	2004	NUM
ejpam-7160	567	5	,	,	PUNCT
ejpam-7160	567	6	21	21	NUM
ejpam-7160	567	7	,	,	PUNCT
ejpam-7160	567	8	49–53	49–53	NUM
ejpam-7160	567	9	.	.	PUNCT
ejpam-7160	568	1	[	[	X
ejpam-7160	568	2	12	12	NUM
ejpam-7160	568	3	]	]	X
ejpam-7160	568	4	li	li	PROPN
ejpam-7160	568	5	v.	v.	PROPN
ejpam-7160	568	6	,	,	PUNCT
ejpam-7160	568	7	xie	xie	PROPN
ejpam-7160	568	8	t.	t.	PROPN
ejpam-7160	568	9	,	,	PUNCT
ejpam-7160	568	10	li	li	PROPN
ejpam-7160	568	11	q.	q.	PROPN
ejpam-7160	568	12	,	,	PUNCT
ejpam-7160	568	13	topological	topological	ADJ
ejpam-7160	568	14	structure	structure	NOUN
ejpam-7160	568	15	of	of	ADP
ejpam-7160	568	16	generalized	generalized	ADJ
ejpam-7160	568	17	rough	rough	ADJ
ejpam-7160	568	18	sets	set	NOUN
ejpam-7160	568	19	.	.	PUNCT
ejpam-7160	569	1	comput	comput	NOUN
ejpam-7160	569	2	.	.	PUNCT
ejpam-7160	570	1	math	math	NOUN
ejpam-7160	570	2	.	.	PUNCT
ejpam-7160	571	1	appl	appl	PROPN
ejpam-7160	571	2	.	.	PROPN
ejpam-7160	571	3	2012	2012	NUM
ejpam-7160	571	4	,	,	PUNCT
ejpam-7160	571	5	63	63	NUM
ejpam-7160	571	6	,	,	PUNCT
ejpam-7160	571	7	1066–1071	1066–1071	NUM
ejpam-7160	571	8	.	.	PUNCT
ejpam-7160	572	1	[	[	X
ejpam-7160	572	2	13	13	NUM
ejpam-7160	572	3	]	]	PUNCT
ejpam-7160	572	4	salama	salama	PROPN
ejpam-7160	572	5	a.s	a.s	PROPN
ejpam-7160	572	6	.	.	PROPN
ejpam-7160	572	7	,	,	PUNCT
ejpam-7160	572	8	some	some	DET
ejpam-7160	572	9	topological	topological	ADJ
ejpam-7160	572	10	properties	property	NOUN
ejpam-7160	572	11	of	of	ADP
ejpam-7160	572	12	rough	rough	ADJ
ejpam-7160	572	13	sets	set	NOUN
ejpam-7160	572	14	with	with	ADP
ejpam-7160	572	15	tools	tool	NOUN
ejpam-7160	572	16	for	for	ADP
ejpam-7160	572	17	data	datum	NOUN
ejpam-7160	572	18	mining	mining	NOUN
ejpam-7160	572	19	.	.	PUNCT
ejpam-7160	573	1	int	int	NOUN
ejpam-7160	573	2	.	.	PUNCT
ejpam-7160	574	1	j.	j.	PROPN
ejpam-7160	574	2	comput	comput	PROPN
ejpam-7160	574	3	.	.	PUNCT
ejpam-7160	575	1	sci	sci	PROPN
ejpam-7160	575	2	.	.	PROPN
ejpam-7160	575	3	2011	2011	NUM
ejpam-7160	575	4	,	,	PUNCT
ejpam-7160	575	5	8	8	NUM
ejpam-7160	575	6	,	,	PUNCT
ejpam-7160	575	7	588–595	588–595	NUM
ejpam-7160	575	8	.	.	PUNCT
ejpam-7160	576	1	[	[	X
ejpam-7160	576	2	14	14	NUM
ejpam-7160	576	3	]	]	X
ejpam-7160	576	4	zhu	zhu	PROPN
ejpam-7160	576	5	w.	w.	PROPN
ejpam-7160	576	6	,	,	PUNCT
ejpam-7160	576	7	topological	topological	ADJ
ejpam-7160	576	8	approaches	approach	NOUN
ejpam-7160	576	9	to	to	ADP
ejpam-7160	576	10	covering	cover	VERB
ejpam-7160	576	11	rough	rough	ADJ
ejpam-7160	576	12	sets	set	NOUN
ejpam-7160	576	13	.	.	PUNCT
ejpam-7160	577	1	inf	inf	PROPN
ejpam-7160	577	2	.	.	PUNCT
ejpam-7160	578	1	sci	sci	PROPN
ejpam-7160	578	2	.	.	PROPN
ejpam-7160	578	3	2007	2007	NUM
ejpam-7160	578	4	,	,	PUNCT
ejpam-7160	578	5	177	177	NUM
ejpam-7160	578	6	,	,	PUNCT
ejpam-7160	578	7	1499–1508	1499–1508	NUM
ejpam-7160	578	8	.	.	PUNCT
ejpam-7160	579	1	[	[	X
ejpam-7160	579	2	15	15	NUM
ejpam-7160	579	3	]	]	X
ejpam-7160	579	4	choquet	choquet	NOUN
ejpam-7160	579	5	,	,	PUNCT
ejpam-7160	579	6	sur	sur	PROPN
ejpam-7160	579	7	les	les	X
ejpam-7160	579	8	notions	notion	NOUN
ejpam-7160	579	9	de	de	ADP
ejpam-7160	579	10	filter	filter	NOUN
ejpam-7160	579	11	et	et	PROPN
ejpam-7160	579	12	.	.	PUNCT
ejpam-7160	579	13	grill	grill	NOUN
ejpam-7160	579	14	,	,	PUNCT
ejpam-7160	579	15	completes	complete	VERB
ejpam-7160	579	16	rendus	rendus	PROPN
ejpam-7160	579	17	acad	acad	PROPN
ejpam-7160	579	18	.	.	PUNCT
ejpam-7160	580	1	sci	sci	PROPN
ejpam-7160	580	2	.	.	PROPN
ejpam-7160	580	3	paris	paris	PROPN
ejpam-7160	580	4	,	,	PUNCT
ejpam-7160	580	5	1947	1947	NUM
ejpam-7160	580	6	,	,	PUNCT
ejpam-7160	580	7	224	224	NUM
ejpam-7160	580	8	,	,	PUNCT
ejpam-7160	580	9	171173	171173	NUM
ejpam-7160	580	10	.	.	PUNCT
ejpam-7160	581	1	[	[	X
ejpam-7160	581	2	16	16	NUM
ejpam-7160	581	3	]	]	PUNCT
ejpam-7160	581	4	azzam	azzam	PROPN
ejpam-7160	581	5	a.	a.	PROPN
ejpam-7160	581	6	a.	a.	PROPN
ejpam-7160	581	7	,	,	PUNCT
ejpam-7160	581	8	comparison	comparison	NOUN
ejpam-7160	581	9	of	of	ADP
ejpam-7160	581	10	two	two	NUM
ejpam-7160	581	11	types	type	NOUN
ejpam-7160	581	12	of	of	ADP
ejpam-7160	581	13	rough	rough	ADJ
ejpam-7160	581	14	approximation	approximation	NOUN
ejpam-7160	581	15	via	via	ADP
ejpam-7160	581	16	grill	grill	NOUN
ejpam-7160	581	17	,	,	PUNCT
ejpam-7160	581	18	italian	italian	ADJ
ejpam-7160	581	19	journal	journal	NOUN
ejpam-7160	581	20	of	of	ADP
ejpam-7160	581	21	pure	pure	ADJ
ejpam-7160	581	22	and	and	CCONJ
ejpam-7160	581	23	applied	applied	ADJ
ejpam-7160	581	24	mathematics	mathematic	NOUN
ejpam-7160	581	25	,	,	PUNCT
ejpam-7160	581	26	2022	2022	NUM
ejpam-7160	581	27	,	,	PUNCT
ejpam-7160	581	28	47	47	NUM
ejpam-7160	581	29	,	,	PUNCT
ejpam-7160	581	30	258–270	258–270	NUM
ejpam-7160	581	31	.	.	PUNCT
ejpam-7160	582	1	[	[	X
ejpam-7160	582	2	17	17	NUM
ejpam-7160	582	3	]	]	PUNCT
ejpam-7160	582	4	azzam	azzam	PROPN
ejpam-7160	582	5	a.	a.	PROPN
ejpam-7160	582	6	a.	a.	PROPN
ejpam-7160	582	7	,	,	PUNCT
ejpam-7160	582	8	grill	grill	ADJ
ejpam-7160	582	9	nano	nano	NOUN
ejpam-7160	582	10	topological	topological	ADJ
ejpam-7160	582	11	spaces	space	NOUN
ejpam-7160	582	12	with	with	ADP
ejpam-7160	582	13	grill	grill	NOUN
ejpam-7160	582	14	nano	nano	NOUN
ejpam-7160	582	15	generalized	generalize	VERB
ejpam-7160	582	16	closed	closed	ADJ
ejpam-7160	582	17	sets	set	NOUN
ejpam-7160	582	18	,	,	PUNCT
ejpam-7160	582	19	j.	j.	PROPN
ejpam-7160	582	20	of	of	ADP
ejpam-7160	582	21	the	the	DET
ejpam-7160	582	22	egyptian	egyptian	PROPN
ejpam-7160	582	23	mathematical	mathematical	ADJ
ejpam-7160	582	24	society,2017	society,2017	NOUN
ejpam-7160	582	25	,	,	PUNCT
ejpam-7160	582	26	25	25	NUM
ejpam-7160	582	27	,	,	PUNCT
ejpam-7160	582	28	164	164	NUM
ejpam-7160	582	29	-	-	SYM
ejpam-7160	582	30	166	166	NUM
ejpam-7160	582	31	.	.	PUNCT
ejpam-7160	583	1	[	[	X
ejpam-7160	583	2	18	18	NUM
ejpam-7160	583	3	]	]	X
ejpam-7160	583	4	aldawood	aldawood	NOUN
ejpam-7160	583	5	m.	m.	NOUN
ejpam-7160	583	6	,	,	PUNCT
ejpam-7160	583	7	azzam	azzam	PROPN
ejpam-7160	583	8	a.a	a.a	PROPN
ejpam-7160	583	9	.	.	PROPN
ejpam-7160	583	10	,	,	PUNCT
ejpam-7160	583	11	expanded	expand	VERB
ejpam-7160	583	12	rough	rough	ADJ
ejpam-7160	583	13	approximation	approximation	NOUN
ejpam-7160	583	14	spaces	space	NOUN
ejpam-7160	583	15	using	use	VERB
ejpam-7160	583	16	grill	grill	NOUN
ejpam-7160	583	17	and	and	CCONJ
ejpam-7160	583	18	maximal	maximal	ADJ
ejpam-7160	583	19	rough	rough	ADJ
ejpam-7160	583	20	neighborhoods	neighborhood	NOUN
ejpam-7160	583	21	for	for	ADP
ejpam-7160	583	22	medical	medical	ADJ
ejpam-7160	583	23	applications	application	NOUN
ejpam-7160	583	24	.	.	PUNCT
ejpam-7160	584	1	axioms	axiom	VERB
ejpam-7160	584	2	2025	2025	NUM
ejpam-7160	584	3	.	.	PUNCT
ejpam-7160	585	1	[	[	X
ejpam-7160	585	2	19	19	NUM
ejpam-7160	585	3	]	]	X
ejpam-7160	585	4	nasef	nasef	PROPN
ejpam-7160	585	5	a.	a.	PROPN
ejpam-7160	585	6	a.	a.	PROPN
ejpam-7160	585	7	,	,	PUNCT
ejpam-7160	585	8	azzam	azzam	PROPN
ejpam-7160	585	9	a.	a.	PROPN
ejpam-7160	585	10	a.	a.	PROPN
ejpam-7160	585	11	,	,	PUNCT
ejpam-7160	585	12	some	some	DET
ejpam-7160	585	13	topological	topological	ADJ
ejpam-7160	585	14	operators	operator	NOUN
ejpam-7160	585	15	via	via	ADP
ejpam-7160	585	16	grills	grill	NOUN
ejpam-7160	585	17	,	,	PUNCT
ejpam-7160	585	18	journal	journal	NOUN
ejpam-7160	585	19	of	of	ADP
ejpam-7160	585	20	linear	linear	PROPN
ejpam-7160	585	21	and	and	CCONJ
ejpam-7160	585	22	topological	topological	ADJ
ejpam-7160	585	23	algebra	algebra	NOUN
ejpam-7160	585	24	,	,	PUNCT
ejpam-7160	585	25	2016	2016	NUM
ejpam-7160	585	26	,	,	PUNCT
ejpam-7160	585	27	5	5	NUM
ejpam-7160	585	28	,	,	PUNCT
ejpam-7160	585	29	199	199	NUM
ejpam-7160	585	30	-	-	SYM
ejpam-7160	585	31	204	204	NUM
ejpam-7160	585	32	.	.	PUNCT
ejpam-7160	586	1	[	[	X
ejpam-7160	586	2	20	20	NUM
ejpam-7160	586	3	]	]	X
ejpam-7160	586	4	roy	roy	PROPN
ejpam-7160	586	5	b	b	PROPN
ejpam-7160	586	6	,	,	PUNCT
ejpam-7160	586	7	mukherjee	mukherjee	PROPN
ejpam-7160	586	8	m.	m.	PROPN
ejpam-7160	586	9	n	n	CCONJ
ejpam-7160	586	10	,	,	PUNCT
ejpam-7160	586	11	on	on	ADP
ejpam-7160	586	12	a	a	DET
ejpam-7160	586	13	typical	typical	ADJ
ejpam-7160	586	14	topology	topology	NOUN
ejpam-7160	586	15	induced	induce	VERB
ejpam-7160	586	16	by	by	ADP
ejpam-7160	586	17	a	a	DET
ejpam-7160	586	18	grill	grill	NOUN
ejpam-7160	586	19	,	,	PUNCT
ejpam-7160	586	20	soochow	soochow	PROPN
ejpam-7160	586	21	journal	journal	NOUN
ejpam-7160	586	22	of	of	ADP
ejpam-7160	586	23	math	math	NOUN
ejpam-7160	586	24	.	.	PUNCT
ejpam-7160	586	25	,	,	PUNCT
ejpam-7160	586	26	2007	2007	NUM
ejpam-7160	586	27	,	,	PUNCT
ejpam-7160	586	28	33	33	NUM
ejpam-7160	586	29	,	,	PUNCT
ejpam-7160	586	30	771	771	NUM
ejpam-7160	586	31	-	-	SYM
ejpam-7160	586	32	786	786	NUM
ejpam-7160	586	33	.	.	PUNCT
ejpam-7160	587	1	[	[	X
ejpam-7160	587	2	21	21	NUM
ejpam-7160	587	3	]	]	X
ejpam-7160	587	4	azzam	azzam	PROPN
ejpam-7160	587	5	a.	a.	PROPN
ejpam-7160	587	6	a.	a.	PROPN
ejpam-7160	587	7	,	,	PUNCT
ejpam-7160	587	8	hussein	hussein	PROPN
ejpam-7160	587	9	s.	s.	PROPN
ejpam-7160	587	10	s.	s.	PROPN
ejpam-7160	587	11	,	,	PUNCT
ejpam-7160	587	12	and	and	CCONJ
ejpam-7160	587	13	osman	osman	PROPN
ejpam-7160	587	14	h.	h.	PROPN
ejpam-7160	587	15	s.	s.	PROPN
ejpam-7160	587	16	,	,	PUNCT
ejpam-7160	587	17	compactness	compactness	NOUN
ejpam-7160	587	18	of	of	ADP
ejpam-7160	587	19	topological	topological	ADJ
ejpam-7160	587	20	spaces	space	NOUN
ejpam-7160	587	21	with	with	ADP
ejpam-7160	587	22	grill	grill	NOUN
ejpam-7160	587	23	,	,	PUNCT
ejpam-7160	587	24	italian	italian	ADJ
ejpam-7160	587	25	journal	journal	NOUN
ejpam-7160	587	26	of	of	ADP
ejpam-7160	587	27	pure	pure	ADJ
ejpam-7160	587	28	and	and	CCONJ
ejpam-7160	587	29	applied	apply	VERB
ejpam-7160	587	30	,	,	PUNCT
ejpam-7160	587	31	2020	2020	NUM
ejpam-7160	587	32	,	,	PUNCT
ejpam-7160	587	33	44	44	NUM
ejpam-7160	587	34	,	,	PUNCT
ejpam-7160	587	35	198	198	NUM
ejpam-7160	587	36	-	-	SYM
ejpam-7160	587	37	207	207	NUM
ejpam-7160	587	38	.	.	PUNCT
ejpam-7160	588	1	[	[	X
ejpam-7160	588	2	22	22	NUM
ejpam-7160	588	3	]	]	SYM
ejpam-7160	588	4	yao	yao	PROPN
ejpam-7160	588	5	,	,	PUNCT
ejpam-7160	588	6	y.y	y.y	PROPN
ejpam-7160	588	7	.	.	PROPN
ejpam-7160	588	8	two	two	NUM
ejpam-7160	588	9	views	view	NOUN
ejpam-7160	588	10	of	of	ADP
ejpam-7160	588	11	the	the	DET
ejpam-7160	588	12	theory	theory	NOUN
ejpam-7160	588	13	of	of	ADP
ejpam-7160	588	14	rough	rough	ADJ
ejpam-7160	588	15	sets	set	NOUN
ejpam-7160	588	16	in	in	ADP
ejpam-7160	588	17	finite	finite	ADJ
ejpam-7160	588	18	universes	universe	NOUN
ejpam-7160	588	19	.	.	PUNCT
ejpam-7160	589	1	int	int	NOUN
ejpam-7160	589	2	.	.	PUNCT
ejpam-7160	590	1	j.	j.	PROPN
ejpam-7160	590	2	approx	approx	PROPN
ejpam-7160	590	3	.	.	PUNCT
ejpam-7160	591	1	reason	reason	NOUN
ejpam-7160	591	2	.	.	PUNCT
ejpam-7160	592	1	1996	1996	NUM
ejpam-7160	592	2	,	,	PUNCT
ejpam-7160	592	3	15	15	NUM
ejpam-7160	592	4	,	,	PUNCT
ejpam-7160	592	5	291–317	291–317	NUM
ejpam-7160	592	6	.	.	PUNCT
ejpam-7160	593	1	[	[	X
ejpam-7160	593	2	23	23	NUM
ejpam-7160	593	3	]	]	X
ejpam-7160	593	4	yao	yao	PROPN
ejpam-7160	593	5	,	,	PUNCT
ejpam-7160	593	6	y.y	y.y	PROPN
ejpam-7160	593	7	.	.	PROPN
ejpam-7160	593	8	relational	relational	ADJ
ejpam-7160	593	9	interpretations	interpretation	NOUN
ejpam-7160	593	10	of	of	ADP
ejpam-7160	593	11	neighborhood	neighborhood	NOUN
ejpam-7160	593	12	operators	operator	NOUN
ejpam-7160	593	13	and	and	CCONJ
ejpam-7160	593	14	rough	rough	ADJ
ejpam-7160	593	15	set	set	NOUN
ejpam-7160	593	16	approximation	approximation	NOUN
ejpam-7160	593	17	operators	operator	NOUN
ejpam-7160	593	18	.	.	PUNCT
ejpam-7160	594	1	inform	inform	NOUN
ejpam-7160	594	2	.	.	PUNCT
ejpam-7160	595	1	sci	sci	PROPN
ejpam-7160	595	2	.	.	PROPN
ejpam-7160	595	3	1998	1998	NUM
ejpam-7160	595	4	,	,	PUNCT
ejpam-7160	595	5	111	111	NUM
ejpam-7160	595	6	,	,	PUNCT
ejpam-7160	595	7	239–259	239–259	NUM
ejpam-7160	595	8	.	.	PUNCT
ejpam-7160	596	1	[	[	X
ejpam-7160	596	2	24	24	NUM
ejpam-7160	596	3	]	]	X
ejpam-7160	596	4	allam	allam	PROPN
ejpam-7160	596	5	,	,	PUNCT
ejpam-7160	596	6	a.	a.	PROPN
ejpam-7160	596	7	a.	a.	PROPN
ejpam-7160	596	8	,	,	PUNCT
ejpam-7160	596	9	bakeir	bakeir	PRON
ejpam-7160	596	10	m.	m.	NOUN
ejpam-7160	596	11	y.	y.	PROPN
ejpam-7160	596	12	y	y	PROPN
ejpam-7160	596	13	,	,	PUNCT
ejpam-7160	596	14	abo	abo	ADJ
ejpam-7160	596	15	-	-	PUNCT
ejpam-7160	596	16	tabl	tabl	NOUN
ejpam-7160	596	17	e.	e.	PROPN
ejpam-7160	596	18	a.	a.	PROPN
ejpam-7160	596	19	,	,	PUNCT
ejpam-7160	596	20	new	new	ADJ
ejpam-7160	596	21	approach	approach	NOUN
ejpam-7160	596	22	for	for	ADP
ejpam-7160	596	23	basic	basic	ADJ
ejpam-7160	596	24	rough	rough	ADJ
ejpam-7160	596	25	set	set	NOUN
ejpam-7160	596	26	concepts	concept	NOUN
ejpam-7160	596	27	.	.	PUNCT
ejpam-7160	597	1	in	in	ADP
ejpam-7160	597	2	:	:	PUNCT
ejpam-7160	597	3	international	international	ADJ
ejpam-7160	597	4	workshop	workshop	NOUN
ejpam-7160	597	5	on	on	ADP
ejpam-7160	597	6	rough	rough	ADJ
ejpam-7160	597	7	sets	set	NOUN
ejpam-7160	597	8	,	,	PUNCT
ejpam-7160	597	9	fuzzy	fuzzy	ADJ
ejpam-7160	597	10	sets	set	NOUN
ejpam-7160	597	11	,	,	PUNCT
ejpam-7160	597	12	data	datum	NOUN
ejpam-7160	597	13	mining	mining	NOUN
ejpam-7160	597	14	,	,	PUNCT
ejpam-7160	597	15	and	and	CCONJ
ejpam-7160	597	16	granular	granular	ADJ
ejpam-7160	597	17	computing	computing	NOUN
ejpam-7160	597	18	.	.	PUNCT
ejpam-7160	598	1	lecture	lecture	NOUN
ejpam-7160	598	2	notes	note	NOUN
ejpam-7160	598	3	in	in	ADP
ejpam-7160	598	4	artificial	artificial	ADJ
ejpam-7160	598	5	intelligence	intelligence	NOUN
ejpam-7160	598	6	,	,	PUNCT
ejpam-7160	598	7	3641	3641	NUM
ejpam-7160	598	8	,	,	PUNCT
ejpam-7160	598	9	springer	springer	NOUN
ejpam-7160	598	10	,	,	PUNCT
ejpam-7160	598	11	regina	regina	PROPN
ejpam-7160	598	12	,	,	PUNCT
ejpam-7160	598	13	2005	2005	NUM
ejpam-7160	598	14	,	,	PUNCT
ejpam-7160	598	15	64–73	64–73	NUM
ejpam-7160	598	16	.	.	PUNCT
ejpam-7160	599	1	[	[	X
ejpam-7160	599	2	25	25	NUM
ejpam-7160	599	3	]	]	X
ejpam-7160	599	4	allam	allam	PROPN
ejpam-7160	599	5	,	,	PUNCT
ejpam-7160	599	6	a.	a.	PROPN
ejpam-7160	599	7	a.	a.	PROPN
ejpam-7160	599	8	,	,	PUNCT
ejpam-7160	599	9	bakeir	bakeir	PRON
ejpam-7160	599	10	m.	m.	NOUN
ejpam-7160	599	11	y.	y.	PROPN
ejpam-7160	599	12	y	y	PROPN
ejpam-7160	599	13	,	,	PUNCT
ejpam-7160	599	14	abo	abo	ADJ
ejpam-7160	599	15	-	-	PUNCT
ejpam-7160	599	16	tabl	tabl	NOUN
ejpam-7160	599	17	e.	e.	PROPN
ejpam-7160	599	18	a.	a.	PROPN
ejpam-7160	599	19	,	,	PUNCT
ejpam-7160	599	20	new	new	ADJ
ejpam-7160	599	21	approach	approach	NOUN
ejpam-7160	599	22	for	for	ADP
ejpam-7160	599	23	closure	closure	NOUN
ejpam-7160	599	24	spaces	space	NOUN
ejpam-7160	599	25	by	by	ADP
ejpam-7160	599	26	relations	relation	NOUN
ejpam-7160	599	27	,	,	PUNCT
ejpam-7160	599	28	acta	acta	PROPN
ejpam-7160	599	29	math	math	PROPN
ejpam-7160	599	30	.	.	PUNCT
ejpam-7160	600	1	acad	acad	PROPN
ejpam-7160	600	2	.	.	PUNCT
ejpam-7160	601	1	paedagog	paedagog	PROPN
ejpam-7160	601	2	.	.	PUNCT
ejpam-7160	602	1	nyregyhziensis	nyregyhziensis	NOUN
ejpam-7160	602	2	,	,	PUNCT
ejpam-7160	602	3	2006	2006	NUM
ejpam-7160	602	4	,	,	PUNCT
ejpam-7160	602	5	22	22	NUM
ejpam-7160	602	6	,	,	PUNCT
ejpam-7160	602	7	285–304	285–304	NUM
ejpam-7160	602	8	.	.	PUNCT
ejpam-7160	602	9	a.	a.	NOUN
ejpam-7160	602	10	a.	a.	PROPN
ejpam-7160	602	11	azzam	azzam	PROPN
ejpam-7160	602	12	et	et	PROPN
ejpam-7160	602	13	al	al	PROPN
ejpam-7160	602	14	.	.	PUNCT
ejpam-7160	602	15	/	/	SYM
ejpam-7160	602	16	eur	eur	PROPN
ejpam-7160	602	17	.	.	PUNCT
ejpam-7160	603	1	j.	j.	PROPN
ejpam-7160	603	2	pure	pure	PROPN
ejpam-7160	603	3	appl	appl	PROPN
ejpam-7160	603	4	.	.	PROPN
ejpam-7160	603	5	math	math	PROPN
ejpam-7160	603	6	,	,	PUNCT
ejpam-7160	603	7	18	18	NUM
ejpam-7160	603	8	(	(	PUNCT
ejpam-7160	603	9	4	4	NUM
ejpam-7160	603	10	)	)	PUNCT
ejpam-7160	603	11	(	(	PUNCT
ejpam-7160	603	12	2025	2025	NUM
ejpam-7160	603	13	)	)	PUNCT
ejpam-7160	603	14	,	,	PUNCT
ejpam-7160	603	15	7160	7160	NUM
ejpam-7160	603	16	21	21	NUM
ejpam-7160	603	17	of	of	ADP
ejpam-7160	603	18	22	22	NUM
ejpam-7160	604	1	[	[	X
ejpam-7160	604	2	26	26	NUM
ejpam-7160	604	3	]	]	X
ejpam-7160	604	4	atef	atef	PROPN
ejpam-7160	604	5	m.	m.	PROPN
ejpam-7160	604	6	,	,	PUNCT
ejpam-7160	604	7	khalil	khalil	PROPN
ejpam-7160	604	8	a.	a.	PROPN
ejpam-7160	604	9	m.	m.	PROPN
ejpam-7160	604	10	,	,	PUNCT
ejpam-7160	604	11	li	li	PROPN
ejpam-7160	604	12	s.	s.	PROPN
ejpam-7160	604	13	g.	g.	PROPN
ejpam-7160	604	14	,	,	PUNCT
ejpam-7160	604	15	azzam	azzam	PROPN
ejpam-7160	604	16	a.	a.	PROPN
ejpam-7160	604	17	a.	a.	PROPN
ejpam-7160	604	18	,	,	PUNCT
ejpam-7160	604	19	el	el	PROPN
ejpam-7160	604	20	atik	atik	PROPN
ejpam-7160	604	21	a.	a.	PROPN
ejpam-7160	604	22	a.	a.	PROPN
ejpam-7160	604	23	,	,	PUNCT
ejpam-7160	604	24	comparison	comparison	NOUN
ejpam-7160	604	25	of	of	ADP
ejpam-7160	604	26	six	six	NUM
ejpam-7160	604	27	types	type	NOUN
ejpam-7160	604	28	of	of	ADP
ejpam-7160	604	29	rough	rough	ADJ
ejpam-7160	604	30	approximations	approximation	NOUN
ejpam-7160	604	31	based	base	VERB
ejpam-7160	604	32	on	on	ADP
ejpam-7160	604	33	j	j	PROPN
ejpam-7160	604	34	-	-	PUNCT
ejpam-7160	604	35	neighborhood	neighborhood	NOUN
ejpam-7160	604	36	space	space	NOUN
ejpam-7160	604	37	and	and	CCONJ
ejpam-7160	604	38	j	j	NOUN
ejpam-7160	604	39	-	-	PUNCT
ejpam-7160	604	40	adhesion	adhesion	NOUN
ejpam-7160	604	41	neighborhood	neighborhood	NOUN
ejpam-7160	604	42	space	space	NOUN
ejpam-7160	604	43	.	.	PUNCT
ejpam-7160	605	1	j	j	PROPN
ejpam-7160	605	2	intell	intell	PROPN
ejpam-7160	605	3	fuzzy	fuzzy	ADJ
ejpam-7160	605	4	syst	syst	NOUN
ejpam-7160	605	5	,	,	PUNCT
ejpam-7160	605	6	2020	2020	NUM
ejpam-7160	605	7	,	,	PUNCT
ejpam-7160	605	8	39	39	NUM
ejpam-7160	605	9	,	,	PUNCT
ejpam-7160	605	10	4515–4531	4515–4531	NUM
ejpam-7160	605	11	.	.	PUNCT
ejpam-7160	606	1	[	[	X
ejpam-7160	606	2	27	27	NUM
ejpam-7160	606	3	]	]	SYM
ejpam-7160	606	4	27	27	NUM
ejpam-7160	606	5	.	.	PUNCT
ejpam-7160	607	1	mareay	mareay	PROPN
ejpam-7160	607	2	r.	r.	PROPN
ejpam-7160	607	3	,	,	PUNCT
ejpam-7160	607	4	generalized	generalize	VERB
ejpam-7160	607	5	rough	rough	ADJ
ejpam-7160	607	6	sets	set	NOUN
ejpam-7160	607	7	based	base	VERB
ejpam-7160	607	8	on	on	ADP
ejpam-7160	607	9	neighborhood	neighborhood	NOUN
ejpam-7160	607	10	systems	system	NOUN
ejpam-7160	607	11	and	and	CCONJ
ejpam-7160	607	12	topological	topological	ADJ
ejpam-7160	607	13	spaces	space	NOUN
ejpam-7160	607	14	.	.	PUNCT
ejpam-7160	608	1	j	j	PROPN
ejpam-7160	608	2	egypt	egypt	PROPN
ejpam-7160	608	3	math	math	PROPN
ejpam-7160	608	4	soc	soc	PROPN
ejpam-7160	608	5	.	.	PUNCT
ejpam-7160	608	6	,	,	PUNCT
ejpam-7160	608	7	2016	2016	NUM
ejpam-7160	608	8	,	,	PUNCT
ejpam-7160	608	9	24	24	NUM
ejpam-7160	608	10	,	,	PUNCT
ejpam-7160	608	11	603–608	603–608	NUM
ejpam-7160	608	12	.	.	PUNCT
ejpam-7160	609	1	[	[	X
ejpam-7160	609	2	28	28	NUM
ejpam-7160	609	3	]	]	X
ejpam-7160	609	4	al	al	PROPN
ejpam-7160	609	5	-	-	PUNCT
ejpam-7160	609	6	shami	shami	PROPN
ejpam-7160	609	7	t.	t.	PROPN
ejpam-7160	609	8	m.	m.	NOUN
ejpam-7160	609	9	,	,	PUNCT
ejpam-7160	609	10	maximal	maximal	ADJ
ejpam-7160	609	11	rough	rough	ADJ
ejpam-7160	609	12	neighborhoods	neighborhood	NOUN
ejpam-7160	609	13	with	with	ADP
ejpam-7160	609	14	a	a	DET
ejpam-7160	609	15	medical	medical	ADJ
ejpam-7160	609	16	application	application	NOUN
ejpam-7160	609	17	.	.	PUNCT
ejpam-7160	610	1	j	j	PROPN
ejpam-7160	610	2	am	be	AUX
ejpam-7160	610	3	bient	bient	ADJ
ejpam-7160	610	4	intell	intell	PROPN
ejpam-7160	610	5	humaniz	humaniz	VERB
ejpam-7160	610	6	comput	comput	NOUN
ejpam-7160	610	7	.	.	PUNCT
ejpam-7160	610	8	,	,	PUNCT
ejpam-7160	610	9	2023	2023	NUM
ejpam-7160	610	10	,	,	PUNCT
ejpam-7160	610	11	14	14	NUM
ejpam-7160	610	12	,	,	PUNCT
ejpam-7160	610	13	16373–16384	16373–16384	NUM
ejpam-7160	610	14	.	.	PUNCT
ejpam-7160	611	1	[	[	X
ejpam-7160	611	2	29	29	NUM
ejpam-7160	611	3	]	]	X
ejpam-7160	611	4	dai	dai	PROPN
ejpam-7160	611	5	j.	j.	PROPN
ejpam-7160	611	6	,	,	PUNCT
ejpam-7160	611	7	xu	xu	PROPN
ejpam-7160	611	8	q.	q.	PROPN
ejpam-7160	611	9	,	,	PUNCT
ejpam-7160	611	10	approximations	approximation	NOUN
ejpam-7160	611	11	and	and	CCONJ
ejpam-7160	611	12	uncertainty	uncertainty	NOUN
ejpam-7160	611	13	measures	measure	NOUN
ejpam-7160	611	14	in	in	ADP
ejpam-7160	611	15	incomplete	incomplete	ADJ
ejpam-7160	611	16	information	information	NOUN
ejpam-7160	611	17	systems	system	NOUN
ejpam-7160	611	18	,	,	PUNCT
ejpam-7160	611	19	inform	inform	NOUN
ejpam-7160	611	20	.	.	PUNCT
ejpam-7160	612	1	sci	sci	PROPN
ejpam-7160	612	2	.	.	PROPN
ejpam-7160	612	3	,	,	PUNCT
ejpam-7160	612	4	2012	2012	NUM
ejpam-7160	612	5	,	,	PUNCT
ejpam-7160	612	6	198	198	NUM
ejpam-7160	612	7	,	,	PUNCT
ejpam-7160	612	8	62–80	62–80	NUM
ejpam-7160	612	9	.	.	PUNCT
ejpam-7160	613	1	https://doi.org/10.1016/j.ins.2012.02.032	https://doi.org/10.1016/j.ins.2012.02.032	NOUN
ejpam-7160	613	2	.	.	PUNCT
ejpam-7160	614	1	[	[	X
ejpam-7160	614	2	30	30	NUM
ejpam-7160	614	3	]	]	X
ejpam-7160	614	4	al	al	PROPN
ejpam-7160	614	5	-	-	PUNCT
ejpam-7160	614	6	shami	shami	PROPN
ejpam-7160	614	7	t.	t.	PROPN
ejpam-7160	614	8	,	,	PUNCT
ejpam-7160	614	9	hosny	hosny	PROPN
ejpam-7160	614	10	m.	m.	PROPN
ejpam-7160	614	11	,	,	PUNCT
ejpam-7160	614	12	m.	m.	NOUN
ejpam-7160	614	13	,	,	PUNCT
ejpam-7160	614	14	ara	ara	PROPN
ejpam-7160	614	15	m.	m.	PROPN
ejpam-7160	614	16	r	r	PROPN
ejpam-7160	614	17	,	,	PUNCT
ejpam-7160	614	18	hosny	hosny	PROPN
ejpam-7160	614	19	r.	r.	PROPN
ejpam-7160	614	20	a.	a.	PROPN
ejpam-7160	614	21	,	,	PUNCT
ejpam-7160	614	22	generalized	generalize	VERB
ejpam-7160	614	23	rough	rough	ADJ
ejpam-7160	614	24	approximation	approximation	NOUN
ejpam-7160	614	25	spaces	space	NOUN
ejpam-7160	614	26	inspired	inspire	VERB
ejpam-7160	614	27	by	by	ADP
ejpam-7160	614	28	cardinality	cardinality	NOUN
ejpam-7160	614	29	neighborhoods	neighborhood	NOUN
ejpam-7160	614	30	and	and	CCONJ
ejpam-7160	614	31	ideals	ideal	NOUN
ejpam-7160	614	32	with	with	ADP
ejpam-7160	614	33	application	application	NOUN
ejpam-7160	614	34	to	to	ADP
ejpam-7160	614	35	dengue	dengue	NOUN
ejpam-7160	614	36	disease	disease	NOUN
ejpam-7160	614	37	.	.	PUNCT
ejpam-7160	615	1	j	j	PROPN
ejpam-7160	615	2	appl	appl	PROPN
ejpam-7160	615	3	math	math	PROPN
ejpam-7160	615	4	comput	comput	PROPN
ejpam-7160	615	5	,	,	PUNCT
ejpam-7160	615	6	2024	2024	NUM
ejpam-7160	615	7	.	.	PUNCT
ejpam-7160	616	1	https://	https://	PROPN
ejpam-7160	616	2	doi.org/10.1007/s12190-024	doi.org/10.1007/s12190-024	ADJ
ejpam-7160	616	3	02235	02235	NUM
ejpam-7160	616	4	-	-	SYM
ejpam-7160	616	5	9	9	NUM
ejpam-7160	616	6	.	.	PUNCT
ejpam-7160	617	1	[	[	X
ejpam-7160	617	2	31	31	NUM
ejpam-7160	617	3	]	]	SYM
ejpam-7160	617	4	31	31	NUM
ejpam-7160	617	5	.	.	PUNCT
ejpam-7160	618	1	al	al	PROPN
ejpam-7160	618	2	-	-	PUNCT
ejpam-7160	618	3	shami	shami	PROPN
ejpam-7160	618	4	t.	t.	PROPN
ejpam-7160	618	5	m.	m.	PROPN
ejpam-7160	618	6	,	,	PUNCT
ejpam-7160	618	7	hosny	hosny	PROPN
ejpam-7160	618	8	r.	r.	PROPN
ejpam-7160	618	9	a.	a.	PROPN
ejpam-7160	618	10	,	,	PUNCT
ejpam-7160	618	11	mhemdi	mhemdi	PROPN
ejpam-7160	618	12	a.	a.	PROPN
ejpam-7160	618	13	,	,	PUNCT
ejpam-7160	618	14	hosny	hosny	PROPN
ejpam-7160	618	15	m.	m.	PROPN
ejpam-7160	618	16	,	,	PUNCT
ejpam-7160	618	17	cardinality	cardinality	NOUN
ejpam-7160	618	18	rough	rough	ADJ
ejpam-7160	618	19	neighbor	neighbor	NOUN
ejpam-7160	618	20	hoods	hood	NOUN
ejpam-7160	618	21	with	with	ADP
ejpam-7160	618	22	applications	application	NOUN
ejpam-7160	618	23	.	.	PUNCT
ejpam-7160	619	1	aims	aim	VERB
ejpam-7160	619	2	math	math	NOUN
ejpam-7160	619	3	,	,	PUNCT
ejpam-7160	619	4	2024	2024	NUM
ejpam-7160	619	5	,	,	PUNCT
ejpam-7160	619	6	9	9	NUM
ejpam-7160	619	7	,	,	PUNCT
ejpam-7160	619	8	31366–31392	31366–31392	NUM
ejpam-7160	619	9	.	.	PUNCT
ejpam-7160	620	1	[	[	X
ejpam-7160	620	2	32	32	NUM
ejpam-7160	620	3	]	]	PUNCT
ejpam-7160	620	4	a.	a.	NOUN
ejpam-7160	620	5	a.	a.	PROPN
ejpam-7160	620	6	azzam	azzam	PROPN
ejpam-7160	620	7	,	,	PUNCT
ejpam-7160	620	8	rough	rough	ADJ
ejpam-7160	620	9	neighborhood	neighborhood	NOUN
ejpam-7160	620	10	ideal	ideal	NOUN
ejpam-7160	620	11	and	and	CCONJ
ejpam-7160	620	12	its	its	PRON
ejpam-7160	620	13	applications	application	NOUN
ejpam-7160	620	14	,	,	PUNCT
ejpam-7160	620	15	ijfis	ijfis	NOUN
ejpam-7160	620	16	,	,	PUNCT
ejpam-7160	620	17	2024	2024	NUM
ejpam-7160	620	18	,	,	PUNCT
ejpam-7160	620	19	24	24	NUM
ejpam-7160	620	20	,	,	PUNCT
ejpam-7160	620	21	1	1	NUM
ejpam-7160	620	22	-	-	SYM
ejpam-7160	620	23	7	7	NUM
ejpam-7160	620	24	.	.	PUNCT
ejpam-7160	620	25	http://doi.org/10.5391/ijfis.2024.24.1.1	http://doi.org/10.5391/ijfis.2024.24.1.1	NOUN
ejpam-7160	620	26	.	.	PUNCT
ejpam-7160	621	1	[	[	X
ejpam-7160	621	2	33	33	NUM
ejpam-7160	621	3	]	]	PUNCT
ejpam-7160	621	4	m.	m.	PROPN
ejpam-7160	621	5	hosny	hosny	PROPN
ejpam-7160	621	6	,	,	PUNCT
ejpam-7160	621	7	generalization	generalization	NOUN
ejpam-7160	621	8	of	of	ADP
ejpam-7160	621	9	rough	rough	ADJ
ejpam-7160	621	10	sets	set	NOUN
ejpam-7160	621	11	using	use	VERB
ejpam-7160	621	12	maximal	maximal	ADJ
ejpam-7160	621	13	right	right	ADJ
ejpam-7160	621	14	neighborhood	neighborhood	NOUN
ejpam-7160	621	15	systems	system	NOUN
ejpam-7160	621	16	and	and	CCONJ
ejpam-7160	621	17	ideals	ideal	NOUN
ejpam-7160	621	18	with	with	ADP
ejpam-7160	621	19	medical	medical	ADJ
ejpam-7160	621	20	applications	application	NOUN
ejpam-7160	621	21	.	.	PUNCT
ejpam-7160	621	22	aims	aim	VERB
ejpam-7160	621	23	math	math	NOUN
ejpam-7160	621	24	.	.	PUNCT
ejpam-7160	622	1	2022	2022	NUM
ejpam-7160	622	2	,	,	PUNCT
ejpam-7160	622	3	7	7	NUM
ejpam-7160	622	4	,	,	PUNCT
ejpam-7160	622	5	13104–13138	13104–13138	NUM
ejpam-7160	622	6	.	.	PUNCT
ejpam-7160	623	1	[	[	X
ejpam-7160	623	2	34	34	NUM
ejpam-7160	623	3	]	]	X
ejpam-7160	623	4	d.i	d.i	PROPN
ejpam-7160	623	5	.	.	PROPN
ejpam-7160	623	6	taher	taher	PROPN
ejpam-7160	623	7	,	,	PUNCT
ejpam-7160	623	8	r.	r.	PROPN
ejpam-7160	623	9	abu	abu	PROPN
ejpam-7160	623	10	-	-	PUNCT
ejpam-7160	623	11	gdairi	gdairi	PROPN
ejpam-7160	623	12	,	,	PUNCT
ejpam-7160	623	13	m.k	m.k	PROPN
ejpam-7160	623	14	,	,	PUNCT
ejpam-7160	623	15	el	el	PROPN
ejpam-7160	623	16	-	-	ADJ
ejpam-7160	623	17	bably	bably	ADV
ejpam-7160	623	18	,	,	PUNCT
ejpam-7160	623	19	m.a	m.a	PROPN
ejpam-7160	623	20	.	.	PROPN
ejpam-7160	623	21	el	el	PROPN
ejpam-7160	623	22	-	-	PUNCT
ejpam-7160	623	23	gayar	gayar	NOUN
ejpam-7160	623	24	,	,	PUNCT
ejpam-7160	623	25	decision	decision	NOUN
ejpam-7160	623	26	-	-	PUNCT
ejpam-7160	623	27	making	making	NOUN
ejpam-7160	623	28	in	in	ADP
ejpam-7160	623	29	diagnosing	diagnose	VERB
ejpam-7160	623	30	heart	heart	NOUN
ejpam-7160	623	31	failure	failure	NOUN
ejpam-7160	623	32	problems	problem	NOUN
ejpam-7160	623	33	using	use	VERB
ejpam-7160	623	34	basic	basic	ADJ
ejpam-7160	623	35	rough	rough	ADJ
ejpam-7160	623	36	sets	set	NOUN
ejpam-7160	623	37	.	.	PUNCT
ejpam-7160	624	1	aims	aim	VERB
ejpam-7160	624	2	math	math	NOUN
ejpam-7160	624	3	.	.	PUNCT
ejpam-7160	625	1	2024	2024	NUM
ejpam-7160	625	2	,	,	PUNCT
ejpam-7160	625	3	9	9	NUM
ejpam-7160	625	4	,	,	PUNCT
ejpam-7160	625	5	21816–21847	21816–21847	NOUN
ejpam-7160	625	6	.	.	PUNCT
ejpam-7160	626	1	[	[	X
ejpam-7160	626	2	35	35	NUM
ejpam-7160	626	3	]	]	SYM
ejpam-7160	626	4	abo	abo	NOUN
ejpam-7160	626	5	-	-	PUNCT
ejpam-7160	626	6	tabl	tabl	NOUN
ejpam-7160	626	7	e.	e.	PROPN
ejpam-7160	626	8	a.	a.	PROPN
ejpam-7160	626	9	,	,	PUNCT
ejpam-7160	626	10	a	a	DET
ejpam-7160	626	11	comparison	comparison	NOUN
ejpam-7160	626	12	of	of	ADP
ejpam-7160	626	13	two	two	NUM
ejpam-7160	626	14	kinds	kind	NOUN
ejpam-7160	626	15	of	of	ADP
ejpam-7160	626	16	definitions	definition	NOUN
ejpam-7160	626	17	of	of	ADP
ejpam-7160	626	18	rough	rough	ADJ
ejpam-7160	626	19	approximations	approximation	NOUN
ejpam-7160	626	20	based	base	VERB
ejpam-7160	626	21	on	on	ADP
ejpam-7160	626	22	a	a	DET
ejpam-7160	626	23	similarity	similarity	NOUN
ejpam-7160	626	24	relation	relation	NOUN
ejpam-7160	626	25	,	,	PUNCT
ejpam-7160	626	26	inform	inform	NOUN
ejpam-7160	626	27	.	.	PUNCT
ejpam-7160	627	1	sci	sci	PROPN
ejpam-7160	627	2	.	.	PROPN
ejpam-7160	627	3	,	,	PUNCT
ejpam-7160	627	4	2011	2011	NUM
ejpam-7160	627	5	,	,	PUNCT
ejpam-7160	627	6	181	181	NUM
ejpam-7160	627	7	,	,	PUNCT
ejpam-7160	627	8	2587–2596	2587–2596	NUM
ejpam-7160	627	9	.	.	PUNCT
ejpam-7160	628	1	https://doi.org/10.1016/j.ins.2011.01.007	https://doi.org/10.1016/j.ins.2011.01.007	NOUN
ejpam-7160	628	2	.	.	PUNCT
ejpam-7160	629	1	[	[	X
ejpam-7160	629	2	36	36	NUM
ejpam-7160	629	3	]	]	X
ejpam-7160	629	4	dai	dai	PROPN
ejpam-7160	629	5	j.	j.	PROPN
ejpam-7160	629	6	,	,	PUNCT
ejpam-7160	629	7	gao	gao	PROPN
ejpam-7160	629	8	s.	s.	PROPN
ejpam-7160	629	9	,	,	PUNCT
ejpam-7160	629	10	zheng	zheng	PROPN
ejpam-7160	629	11	g.	g.	PROPN
ejpam-7160	629	12	,	,	PUNCT
ejpam-7160	629	13	generalized	generalize	VERB
ejpam-7160	629	14	rough	rough	ADJ
ejpam-7160	629	15	set	set	NOUN
ejpam-7160	629	16	models	model	NOUN
ejpam-7160	629	17	determined	determine	VERB
ejpam-7160	629	18	by	by	ADP
ejpam-7160	629	19	multi	multi	PROPN
ejpam-7160	629	20	ple	ple	PROPN
ejpam-7160	629	21	neighborhoods	neighborhood	NOUN
ejpam-7160	629	22	generated	generate	VERB
ejpam-7160	629	23	from	from	ADP
ejpam-7160	629	24	a	a	DET
ejpam-7160	629	25	similarity	similarity	NOUN
ejpam-7160	629	26	relation	relation	NOUN
ejpam-7160	629	27	,	,	PUNCT
ejpam-7160	629	28	soft	soft	ADJ
ejpam-7160	629	29	comput	comput	NOUN
ejpam-7160	629	30	.	.	PUNCT
ejpam-7160	630	1	,	,	PUNCT
ejpam-7160	630	2	2018	2018	NUM
ejpam-7160	630	3	,	,	PUNCT
ejpam-7160	630	4	13	13	NUM
ejpam-7160	630	5	,	,	PUNCT
ejpam-7160	630	6	2081–2094	2081–2094	NUM
ejpam-7160	630	7	.	.	PUNCT
ejpam-7160	631	1	https://doi.org/10.1007/s00500-017-2672-x	https://doi.org/10.1007/s00500-017-2672-x	PROPN
ejpam-7160	631	2	.	.	PUNCT
ejpam-7160	632	1	[	[	X
ejpam-7160	632	2	37	37	NUM
ejpam-7160	632	3	]	]	X
ejpam-7160	632	4	abdelaziz	abdelaziz	PROPN
ejpam-7160	632	5	m	m	PROPN
ejpam-7160	632	6	,	,	PUNCT
ejpam-7160	632	7	abu	abu	PROPN
ejpam-7160	632	8	-	-	PUNCT
ejpam-7160	632	9	donia	donia	PROPN
ejpam-7160	632	10	h.	h.	PROPN
ejpam-7160	632	11	m	m	PROPN
ejpam-7160	632	12	,	,	PUNCT
ejpam-7160	632	13	hosny	hosny	PROPN
ejpam-7160	632	14	r	r	PROPN
ejpam-7160	632	15	a	a	PROPN
ejpam-7160	632	16	,	,	PUNCT
ejpam-7160	632	17	hazae	hazae	X
ejpam-7160	632	18	sl	sl	NOUN
ejpam-7160	632	19	,	,	PUNCT
ejpam-7160	632	20	ibrahim	ibrahim	PROPN
ejpam-7160	632	21	r	r	PROPN
ejpam-7160	632	22	a	a	PRON
ejpam-7160	632	23	,	,	PUNCT
ejpam-7160	632	24	improve	improve	VERB
ejpam-7160	632	25	devolutionary	devolutionary	NOUN
ejpam-7160	632	26	based	base	VERB
ejpam-7160	632	27	feature	feature	NOUN
ejpam-7160	632	28	selection	selection	NOUN
ejpam-7160	632	29	technique	technique	NOUN
ejpam-7160	632	30	using	use	VERB
ejpam-7160	632	31	extension	extension	NOUN
ejpam-7160	632	32	of	of	ADP
ejpam-7160	632	33	knowledge	knowledge	NOUN
ejpam-7160	632	34	based	base	VERB
ejpam-7160	632	35	on	on	ADP
ejpam-7160	632	36	the	the	DET
ejpam-7160	632	37	rough	rough	ADJ
ejpam-7160	632	38	approximations	approximation	NOUN
ejpam-7160	632	39	.	.	PUNCT
ejpam-7160	633	1	inf	inf	PROPN
ejpam-7160	633	2	sci	sci	PROPN
ejpam-7160	633	3	,	,	PUNCT
ejpam-7160	633	4	2022	2022	NUM
ejpam-7160	633	5	,	,	PUNCT
ejpam-7160	633	6	594	594	NUM
ejpam-7160	633	7	,	,	PUNCT
ejpam-7160	633	8	76–94	76–94	NUM
ejpam-7160	633	9	.	.	PUNCT
ejpam-7160	634	1	[	[	X
ejpam-7160	634	2	38	38	NUM
ejpam-7160	634	3	]	]	PUNCT
ejpam-7160	634	4	akama	akama	PROPN
ejpam-7160	634	5	s	s	PROPN
ejpam-7160	634	6	,	,	PUNCT
ejpam-7160	634	7	murai	murai	PROPN
ejpam-7160	634	8	t	t	PROPN
ejpam-7160	634	9	,	,	PUNCT
ejpam-7160	634	10	kudo	kudo	PROPN
ejpam-7160	634	11	y	y	PROPN
ejpam-7160	634	12	(	(	PUNCT
ejpam-7160	634	13	2018	2018	NUM
ejpam-7160	634	14	)	)	PUNCT
ejpam-7160	634	15	,	,	PUNCT
ejpam-7160	634	16	reasoning	reason	VERB
ejpam-7160	634	17	with	with	ADP
ejpam-7160	634	18	rough	rough	ADJ
ejpam-7160	634	19	sets	set	NOUN
ejpam-7160	634	20	,	,	PUNCT
ejpam-7160	634	21	vol	vol	NOUN
ejpam-7160	634	22	142	142	NUM
ejpam-7160	634	23	.	.	PUNCT
ejpam-7160	635	1	springer	springer	NOUN
ejpam-7160	635	2	,	,	PUNCT
ejpam-7160	635	3	new	new	PROPN
ejpam-7160	635	4	york	york	PROPN
ejpam-7160	636	1	[	[	X
ejpam-7160	636	2	39	39	NUM
ejpam-7160	636	3	]	]	PUNCT
ejpam-7160	636	4	kryszkiewicz	kryszkiewicz	NOUN
ejpam-7160	636	5	m	m	PROPN
ejpam-7160	636	6	rough	rough	ADJ
ejpam-7160	636	7	,	,	PUNCT
ejpam-7160	636	8	set	set	VERB
ejpam-7160	636	9	approach	approach	NOUN
ejpam-7160	636	10	to	to	ADP
ejpam-7160	636	11	incomplete	incomplete	ADJ
ejpam-7160	636	12	information	information	NOUN
ejpam-7160	636	13	systems	system	NOUN
ejpam-7160	636	14	.	.	PUNCT
ejpam-7160	637	1	inf	inf	PROPN
ejpam-7160	637	2	sci	sci	PROPN
ejpam-7160	637	3	,	,	PUNCT
ejpam-7160	637	4	1998	1998	NUM
ejpam-7160	637	5	,	,	PUNCT
ejpam-7160	637	6	112:39–49	112:39–49	X
ejpam-7160	637	7	.	.	PUNCT
ejpam-7160	638	1	[	[	X
ejpam-7160	638	2	40	40	NUM
ejpam-7160	638	3	]	]	PUNCT
ejpam-7160	638	4	mareay	mareay	ADJ
ejpam-7160	638	5	r	r	NOUN
ejpam-7160	638	6	,	,	PUNCT
ejpam-7160	638	7	soft	soft	ADJ
ejpam-7160	638	8	rough	rough	ADJ
ejpam-7160	638	9	sets	set	NOUN
ejpam-7160	638	10	based	base	VERB
ejpam-7160	638	11	on	on	ADP
ejpam-7160	638	12	covering	covering	NOUN
ejpam-7160	638	13	and	and	CCONJ
ejpam-7160	638	14	their	their	PRON
ejpam-7160	638	15	applications	application	NOUN
ejpam-7160	638	16	.	.	PUNCT
ejpam-7160	639	1	j	j	PROPN
ejpam-7160	639	2	math	math	PROPN
ejpam-7160	639	3	ind	ind	PROPN
ejpam-7160	639	4	,	,	PUNCT
ejpam-7160	639	5	2024	2024	NUM
ejpam-7160	639	6	,	,	PUNCT
ejpam-7160	639	7	14	14	NUM
ejpam-7160	639	8	,	,	PUNCT
ejpam-7160	639	9	1–11	1–11	PROPN
ejpam-7160	639	10	.	.	PUNCT
ejpam-7160	640	1	[	[	X
ejpam-7160	640	2	41	41	NUM
ejpam-7160	640	3	]	]	X
ejpam-7160	640	4	hosny	hosny	PROPN
ejpam-7160	640	5	m	m	PROPN
ejpam-7160	640	6	,	,	PUNCT
ejpam-7160	640	7	al	al	PROPN
ejpam-7160	640	8	-	-	PUNCT
ejpam-7160	640	9	shami	shami	PROPN
ejpam-7160	640	10	tm	tm	PROPN
ejpam-7160	640	11	,	,	PUNCT
ejpam-7160	640	12	rough	rough	ADJ
ejpam-7160	640	13	set	set	NOUN
ejpam-7160	640	14	models	model	NOUN
ejpam-7160	640	15	in	in	ADP
ejpam-7160	640	16	a	a	DET
ejpam-7160	640	17	more	more	ADV
ejpam-7160	640	18	general	general	ADJ
ejpam-7160	640	19	manner	manner	NOUN
ejpam-7160	640	20	with	with	ADP
ejpam-7160	640	21	applications	application	NOUN
ejpam-7160	640	22	.	.	PUNCT
ejpam-7160	641	1	aims	aim	VERB
ejpam-7160	641	2	math	math	NOUN
ejpam-7160	641	3	,	,	PUNCT
ejpam-7160	641	4	2022	2022	NUM
ejpam-7160	641	5	,	,	PUNCT
ejpam-7160	641	6	7	7	NUM
ejpam-7160	641	7	,	,	PUNCT
ejpam-7160	641	8	18971–19017	18971–19017	NUM
ejpam-7160	641	9	.	.	PUNCT
ejpam-7160	642	1	[	[	X
ejpam-7160	642	2	42	42	NUM
ejpam-7160	642	3	]	]	PUNCT
ejpam-7160	642	4	wiweger	wiweger	NOUN
ejpam-7160	642	5	a	a	X
ejpam-7160	642	6	,	,	PUNCT
ejpam-7160	642	7	on	on	ADP
ejpam-7160	642	8	topological	topological	ADJ
ejpam-7160	642	9	rough	rough	ADJ
ejpam-7160	642	10	sets	set	NOUN
ejpam-7160	642	11	.	.	PUNCT
ejpam-7160	643	1	bull	bull	NOUN
ejpam-7160	643	2	polish	polish	ADJ
ejpam-7160	643	3	acad	acad	PROPN
ejpam-7160	643	4	sci	sci	PROPN
ejpam-7160	643	5	math	math	PROPN
ejpam-7160	643	6	,	,	PUNCT
ejpam-7160	643	7	1989	1989	NUM
ejpam-7160	643	8	,	,	PUNCT
ejpam-7160	643	9	37	37	NUM
ejpam-7160	643	10	,	,	PUNCT
ejpam-7160	643	11	89–93	89–93	NUM
ejpam-7160	643	12	.	.	PUNCT
ejpam-7160	644	1	[	[	X
ejpam-7160	644	2	43	43	NUM
ejpam-7160	644	3	]	]	SYM
ejpam-7160	644	4	abo	abo	NOUN
ejpam-7160	644	5	-	-	PUNCT
ejpam-7160	644	6	tabl	tabl	NOUN
ejpam-7160	644	7	e	e	PROPN
ejpam-7160	644	8	a	a	NOUN
ejpam-7160	644	9	,	,	PUNCT
ejpam-7160	644	10	rough	rough	ADJ
ejpam-7160	644	11	sets	set	NOUN
ejpam-7160	644	12	and	and	CCONJ
ejpam-7160	644	13	topological	topological	ADJ
ejpam-7160	644	14	spaces	space	NOUN
ejpam-7160	644	15	based	base	VERB
ejpam-7160	644	16	on	on	ADP
ejpam-7160	644	17	similarity	similarity	NOUN
ejpam-7160	644	18	.	.	PUNCT
ejpam-7160	645	1	int	int	PROPN
ejpam-7160	645	2	j	j	PROPN
ejpam-7160	645	3	mach	mach	NOUN
ejpam-7160	645	4	learn	learn	VERB
ejpam-7160	645	5	cybern	cybern	NOUN
ejpam-7160	645	6	,	,	PUNCT
ejpam-7160	645	7	2013	2013	NUM
ejpam-7160	645	8	,	,	PUNCT
ejpam-7160	645	9	4	4	NUM
ejpam-7160	645	10	,	,	PUNCT
ejpam-7160	645	11	451	451	NUM
ejpam-7160	645	12	458	458	NUM
ejpam-7160	645	13	.	.	PUNCT
ejpam-7160	646	1	[	[	X
ejpam-7160	646	2	44	44	NUM
ejpam-7160	646	3	]	]	X
ejpam-7160	646	4	al	al	PROPN
ejpam-7160	646	5	-	-	PUNCT
ejpam-7160	646	6	shami	shami	PROPN
ejpam-7160	646	7	t	t	PROPN
ejpam-7160	646	8	m	m	PROPN
ejpam-7160	646	9	,	,	PUNCT
ejpam-7160	646	10	improvement	improvement	NOUN
ejpam-7160	646	11	of	of	ADP
ejpam-7160	646	12	the	the	DET
ejpam-7160	646	13	approximations	approximation	NOUN
ejpam-7160	646	14	and	and	CCONJ
ejpam-7160	646	15	accuracy	accuracy	NOUN
ejpam-7160	646	16	measure	measure	NOUN
ejpam-7160	646	17	of	of	ADP
ejpam-7160	646	18	a	a	DET
ejpam-7160	646	19	rough	rough	ADJ
ejpam-7160	646	20	se	se	NOUN
ejpam-7160	646	21	tusing	tuse	VERB
ejpam-7160	646	22	somewhere	somewhere	ADV
ejpam-7160	646	23	dense	dense	ADJ
ejpam-7160	646	24	sets	set	NOUN
ejpam-7160	646	25	.	.	PUNCT
ejpam-7160	646	26	soft	soft	ADJ
ejpam-7160	646	27	comput	comput	NOUN
ejpam-7160	646	28	,	,	PUNCT
ejpam-7160	646	29	2021	2021	NUM
ejpam-7160	646	30	,	,	PUNCT
ejpam-7160	646	31	25	25	NUM
ejpam-7160	646	32	,	,	PUNCT
ejpam-7160	646	33	14449–14460	14449–14460	NUM
ejpam-7160	646	34	.	.	PUNCT
ejpam-7160	647	1	[	[	X
ejpam-7160	647	2	45	45	NUM
ejpam-7160	647	3	]	]	X
ejpam-7160	647	4	al	al	PROPN
ejpam-7160	647	5	-	-	PUNCT
ejpam-7160	647	6	shami	shami	PROPN
ejpam-7160	647	7	t	t	PROPN
ejpam-7160	647	8	m	m	PROPN
ejpam-7160	647	9	,	,	PUNCT
ejpam-7160	647	10	topological	topological	ADJ
ejpam-7160	647	11	approach	approach	NOUN
ejpam-7160	647	12	to	to	PART
ejpam-7160	647	13	generate	generate	VERB
ejpam-7160	647	14	new	new	ADJ
ejpam-7160	647	15	rough	rough	ADJ
ejpam-7160	647	16	set	set	NOUN
ejpam-7160	647	17	models	model	NOUN
ejpam-7160	647	18	.	.	PUNCT
ejpam-7160	648	1	complex	complex	ADJ
ejpam-7160	648	2	intell	intell	PROPN
ejpam-7160	648	3	syst	syst	NOUN
ejpam-7160	648	4	,	,	PUNCT
ejpam-7160	648	5	2022	2022	NUM
ejpam-7160	648	6	,	,	PUNCT
ejpam-7160	648	7	8	8	NUM
ejpam-7160	648	8	,	,	PUNCT
ejpam-7160	648	9	4101	4101	NUM
ejpam-7160	648	10	4113	4113	NUM
ejpam-7160	648	11	.	.	PUNCT
ejpam-7160	649	1	a.	a.	NOUN
ejpam-7160	649	2	a.	a.	PROPN
ejpam-7160	649	3	azzam	azzam	PROPN
ejpam-7160	649	4	et	et	PROPN
ejpam-7160	649	5	al	al	PROPN
ejpam-7160	649	6	.	.	PUNCT
ejpam-7160	649	7	/	/	SYM
ejpam-7160	649	8	eur	eur	PROPN
ejpam-7160	649	9	.	.	PUNCT
ejpam-7160	650	1	j.	j.	PROPN
ejpam-7160	650	2	pure	pure	PROPN
ejpam-7160	650	3	appl	appl	PROPN
ejpam-7160	650	4	.	.	PROPN
ejpam-7160	650	5	math	math	PROPN
ejpam-7160	650	6	,	,	PUNCT
ejpam-7160	650	7	18	18	NUM
ejpam-7160	650	8	(	(	PUNCT
ejpam-7160	650	9	4	4	NUM
ejpam-7160	650	10	)	)	PUNCT
ejpam-7160	650	11	(	(	PUNCT
ejpam-7160	650	12	2025	2025	NUM
ejpam-7160	650	13	)	)	PUNCT
ejpam-7160	650	14	,	,	PUNCT
ejpam-7160	650	15	7160	7160	NUM
ejpam-7160	650	16	22	22	NUM
ejpam-7160	650	17	of	of	ADP
ejpam-7160	650	18	22	22	NUM
ejpam-7160	651	1	[	[	X
ejpam-7160	651	2	46	46	NUM
ejpam-7160	651	3	]	]	PUNCT
ejpam-7160	651	4	salama	salama	NOUN
ejpam-7160	651	5	a	a	DET
ejpam-7160	651	6	s	s	PROPN
ejpam-7160	651	7	,	,	PUNCT
ejpam-7160	651	8	topological	topological	ADJ
ejpam-7160	651	9	solution	solution	NOUN
ejpam-7160	651	10	for	for	ADP
ejpam-7160	651	11	missing	miss	VERB
ejpam-7160	651	12	attribute	attribute	NOUN
ejpam-7160	651	13	values	value	NOUN
ejpam-7160	651	14	in	in	ADP
ejpam-7160	651	15	incomplete	incomplete	ADJ
ejpam-7160	651	16	information	information	NOUN
ejpam-7160	651	17	tables	table	NOUN
ejpam-7160	651	18	.	.	PUNCT
ejpam-7160	652	1	inf	inf	PROPN
ejpam-7160	652	2	sci	sci	PROPN
ejpam-7160	652	3	,	,	PUNCT
ejpam-7160	652	4	2010	2010	NUM
ejpam-7160	652	5	,	,	PUNCT
ejpam-7160	652	6	180	180	NUM
ejpam-7160	652	7	,	,	PUNCT
ejpam-7160	652	8	631–639	631–639	NUM
ejpam-7160	652	9	.	.	PUNCT
ejpam-7160	653	1	[	[	X
ejpam-7160	653	2	47	47	NUM
ejpam-7160	653	3	]	]	X
ejpam-7160	653	4	wu	wu	PROPN
ejpam-7160	653	5	h	h	PROPN
ejpam-7160	653	6	,	,	PUNCT
ejpam-7160	653	7	liu	liu	PROPN
ejpam-7160	653	8	g	g	PROPN
ejpam-7160	653	9	,	,	PUNCT
ejpam-7160	653	10	the	the	DET
ejpam-7160	653	11	relationships	relationship	NOUN
ejpam-7160	653	12	between	between	ADP
ejpam-7160	653	13	topologies	topology	NOUN
ejpam-7160	653	14	and	and	CCONJ
ejpam-7160	653	15	generalized	generalize	VERB
ejpam-7160	653	16	rough	rough	ADJ
ejpam-7160	653	17	sets	set	NOUN
ejpam-7160	653	18	.	.	PUNCT
ejpam-7160	654	1	int	int	NOUN
ejpam-7160	654	2	j	j	PROPN
ejpam-7160	654	3	approx	approx	PROPN
ejpam-7160	654	4	reason	reason	NOUN
ejpam-7160	654	5	,	,	PUNCT
ejpam-7160	654	6	2020	2020	NUM
ejpam-7160	654	7	,	,	PUNCT
ejpam-7160	654	8	119	119	NUM
ejpam-7160	654	9	,	,	PUNCT
ejpam-7160	654	10	313–324	313–324	NUM
ejpam-7160	654	11	.	.	PUNCT
ejpam-7160	655	1	[	[	X
ejpam-7160	655	2	48	48	NUM
ejpam-7160	655	3	]	]	X
ejpam-7160	655	4	el	el	PROPN
ejpam-7160	655	5	-	-	PROPN
ejpam-7160	655	6	sharkasy	sharkasy	VERB
ejpam-7160	655	7	m	m	PROPN
ejpam-7160	655	8	m	m	NOUN
ejpam-7160	655	9	,	,	PUNCT
ejpam-7160	655	10	minimal	minimal	ADJ
ejpam-7160	655	11	structure	structure	NOUN
ejpam-7160	655	12	approximation	approximation	NOUN
ejpam-7160	655	13	space	space	NOUN
ejpam-7160	655	14	and	and	CCONJ
ejpam-7160	655	15	some	some	PRON
ejpam-7160	655	16	of	of	ADP
ejpam-7160	655	17	its	its	PRON
ejpam-7160	655	18	application	application	NOUN
ejpam-7160	655	19	.	.	PUNCT
ejpam-7160	656	1	j	j	PROPN
ejpam-7160	656	2	intell	intell	PROPN
ejpam-7160	656	3	fuzzy	fuzzy	ADJ
ejpam-7160	656	4	syst	syst	NOUN
ejpam-7160	656	5	,	,	PUNCT
ejpam-7160	656	6	2021	2021	NUM
ejpam-7160	656	7	,	,	PUNCT
ejpam-7160	656	8	40	40	NUM
ejpam-7160	656	9	,	,	PUNCT
ejpam-7160	656	10	973–982	973–982	NUM
ejpam-7160	656	11	.	.	PUNCT
ejpam-7160	657	1	[	[	X
ejpam-7160	657	2	49	49	NUM
ejpam-7160	657	3	]	]	X
ejpam-7160	657	4	al	al	PROPN
ejpam-7160	657	5	-	-	PUNCT
ejpam-7160	657	6	shami	shami	PROPN
ejpam-7160	657	7	tm	tm	PROPN
ejpam-7160	657	8	,	,	PUNCT
ejpam-7160	657	9	alshammari	alshammari	PROPN
ejpam-7160	657	10	i	i	PROPN
ejpam-7160	657	11	,	,	PUNCT
ejpam-7160	657	12	roughsets	roughset	NOUN
ejpam-7160	657	13	models	model	NOUN
ejpam-7160	657	14	inspired	inspire	VERB
ejpam-7160	657	15	by	by	ADP
ejpam-7160	657	16	supra	supra	ADJ
ejpam-7160	657	17	-	-	PUNCT
ejpam-7160	657	18	topology	topology	NOUN
ejpam-7160	657	19	structures	structure	NOUN
ejpam-7160	657	20	.	.	PUNCT
ejpam-7160	658	1	artif	artif	PROPN
ejpam-7160	658	2	intell	intell	PROPN
ejpam-7160	658	3	rev	rev	PROPN
ejpam-7160	658	4	,	,	PUNCT
ejpam-7160	658	5	2023	2023	NUM
ejpam-7160	658	6	,	,	PUNCT
ejpam-7160	658	7	56	56	NUM
ejpam-7160	658	8	,	,	PUNCT
ejpam-7160	658	9	6855–6883	6855–6883	NUM
ejpam-7160	658	10	.	.	PUNCT
ejpam-7160	659	1	[	[	X
ejpam-7160	659	2	50	50	NUM
ejpam-7160	659	3	]	]	X
ejpam-7160	659	4	al	al	PROPN
ejpam-7160	659	5	-	-	PUNCT
ejpam-7160	659	6	shami	shami	PROPN
ejpam-7160	659	7	tm	tm	PROPN
ejpam-7160	659	8	,	,	PUNCT
ejpam-7160	659	9	mhemdi	mhemdi	PROPN
ejpam-7160	659	10	a	a	PRON
ejpam-7160	659	11	,	,	PUNCT
ejpam-7160	659	12	approximation	approximation	NOUN
ejpam-7160	659	13	operators	operator	NOUN
ejpam-7160	659	14	and	and	CCONJ
ejpam-7160	659	15	accuracy	accuracy	NOUN
ejpam-7160	659	16	measures	measure	NOUN
ejpam-7160	659	17	of	of	ADP
ejpam-7160	659	18	rough	rough	ADJ
ejpam-7160	659	19	sets	set	NOUN
ejpam-7160	659	20	from	from	ADP
ejpam-7160	659	21	an	an	DET
ejpam-7160	659	22	infra	infra	NOUN
ejpam-7160	659	23	-	-	PUNCT
ejpam-7160	659	24	topology	topology	NOUN
ejpam-7160	659	25	view	view	NOUN
ejpam-7160	659	26	.	.	PUNCT
ejpam-7160	660	1	soft	soft	ADJ
ejpam-7160	660	2	comput	comput	NOUN
ejpam-7160	660	3	,	,	PUNCT
ejpam-7160	660	4	2023	2023	NUM
ejpam-7160	660	5	,	,	PUNCT
ejpam-7160	660	6	27	27	NUM
ejpam-7160	660	7	,	,	PUNCT
ejpam-7160	660	8	1317–1330	1317–1330	NUM
ejpam-7160	660	9	.	.	PUNCT
ejpam-7160	661	1	[	[	X
ejpam-7160	661	2	51	51	NUM
ejpam-7160	661	3	]	]	PUNCT
ejpam-7160	661	4	salama	salama	NOUN
ejpam-7160	661	5	a	a	DET
ejpam-7160	661	6	s	s	PROPN
ejpam-7160	661	7	,	,	PUNCT
ejpam-7160	661	8	bitopological	bitopological	ADJ
ejpam-7160	661	9	approximation	approximation	NOUN
ejpam-7160	661	10	apace	apace	NOUN
ejpam-7160	661	11	with	with	ADP
ejpam-7160	661	12	application	application	NOUN
ejpam-7160	661	13	to	to	ADP
ejpam-7160	661	14	data	data	NOUN
ejpam-7160	661	15	reduction	reduction	NOUN
ejpam-7160	661	16	in	in	ADP
ejpam-7160	661	17	multi	multi	ADJ
ejpam-7160	661	18	-	-	ADJ
ejpam-7160	661	19	valued	value	VERB
ejpam-7160	661	20	information	information	NOUN
ejpam-7160	661	21	systems	system	NOUN
ejpam-7160	661	22	.	.	PUNCT
ejpam-7160	662	1	filomat	filomat	PROPN
ejpam-7160	662	2	,	,	PUNCT
ejpam-7160	662	3	2020	2020	NUM
ejpam-7160	662	4	,	,	PUNCT
ejpam-7160	662	5	34	34	NUM
ejpam-7160	662	6	,	,	PUNCT
ejpam-7160	662	7	99–110	99–110	PROPN
ejpam-7160	662	8	.	.	PUNCT
ejpam-7160	663	1	[	[	X
ejpam-7160	663	2	52	52	NUM
ejpam-7160	663	3	]	]	PUNCT
ejpam-7160	663	4	shbair	shbair	NOUN
ejpam-7160	663	5	t	t	PROPN
ejpam-7160	663	6	,	,	PUNCT
ejpam-7160	663	7	salama	salama	PROPN
ejpam-7160	663	8	a.	a.	PROPN
ejpam-7160	663	9	,	,	PUNCT
ejpam-7160	663	10	embaby	embaby	NOUN
ejpam-7160	663	11	a.	a.	NOUN
ejpam-7160	663	12	,	,	PUNCT
ejpam-7160	663	13	and	and	CCONJ
ejpam-7160	663	14	el	el	PROPN
ejpam-7160	663	15	-	-	PUNCT
ejpam-7160	663	16	atik	atik	PROPN
ejpam-7160	663	17	a.	a.	PROPN
ejpam-7160	663	18	,	,	PUNCT
ejpam-7160	663	19	some	some	DET
ejpam-7160	663	20	topological	topological	ADJ
ejpam-7160	663	21	approaches	approach	NOUN
ejpam-7160	663	22	of	of	ADP
ejpam-7160	663	23	rough	rough	ADJ
ejpam-7160	663	24	sets	set	NOUN
ejpam-7160	663	25	through	through	ADP
ejpam-7160	663	26	minimal	minimal	ADJ
ejpam-7160	663	27	neighborhoods	neighborhood	NOUN
ejpam-7160	663	28	and	and	CCONJ
ejpam-7160	663	29	decision	decision	NOUN
ejpam-7160	663	30	making	making	NOUN
ejpam-7160	663	31	.	.	PUNCT
ejpam-7160	664	1	journal	journal	NOUN
ejpam-7160	664	2	of	of	ADP
ejpam-7160	664	3	mathematics	mathematics	PROPN
ejpam-7160	664	4	2024	2024	NUM
ejpam-7160	664	5	,	,	PUNCT
ejpam-7160	664	6	2024	2024	NUM
ejpam-7160	664	7	,	,	PUNCT
ejpam-7160	664	8	2214422	2214422	NUM
ejpam-7160	664	9	.	.	PUNCT
ejpam-7160	665	1	[	[	X
ejpam-7160	665	2	53	53	NUM
ejpam-7160	665	3	]	]	X
ejpam-7160	665	4	al	al	PROPN
ejpam-7160	665	5	-	-	PUNCT
ejpam-7160	665	6	shami	shami	PROPN
ejpam-7160	665	7	t.m	t.m	PROPN
ejpam-7160	665	8	.	.	PROPN
ejpam-7160	665	9	;	;	PUNCT
ejpam-7160	665	10	alshammari	alshammari	PROPN
ejpam-7160	665	11	,	,	PUNCT
ejpam-7160	665	12	i.	i.	NOUN
ejpam-7160	665	13	approximation	approximation	NOUN
ejpam-7160	665	14	spaces	space	NOUN
ejpam-7160	665	15	inspired	inspire	VERB
ejpam-7160	665	16	by	by	ADP
ejpam-7160	665	17	subset	subset	VERB
ejpam-7160	665	18	rough	rough	ADJ
ejpam-7160	665	19	neighborhoods	neighborhood	NOUN
ejpam-7160	665	20	with	with	ADP
ejpam-7160	665	21	applications	application	NOUN
ejpam-7160	665	22	.	.	PUNCT
ejpam-7160	666	1	demonstr	demonstr	PROPN
ejpam-7160	666	2	.	.	PUNCT
ejpam-7160	667	1	math	math	NOUN
ejpam-7160	667	2	.	.	PUNCT
ejpam-7160	668	1	2023	2023	NUM
ejpam-7160	668	2	,	,	PUNCT
ejpam-7160	668	3	56	56	NUM
ejpam-7160	668	4	,	,	PUNCT
ejpam-7160	668	5	1–24	1–24	PROPN
ejpam-7160	668	6	.	.	PUNCT
ejpam-7160	669	1	[	[	X
ejpam-7160	669	2	54	54	NUM
ejpam-7160	669	3	]	]	X
ejpam-7160	669	4	hosny	hosny	PROPN
ejpam-7160	669	5	r.a	r.a	PROPN
ejpam-7160	669	6	.	.	PROPN
ejpam-7160	669	7	;	;	PUNCT
ejpam-7160	669	8	asaad	asaad	PROPN
ejpam-7160	669	9	,	,	PUNCT
ejpam-7160	669	10	b.a	b.a	PROPN
ejpam-7160	669	11	.	.	PROPN
ejpam-7160	669	12	;	;	PUNCT
ejpam-7160	669	13	azzam	azzam	PROPN
ejpam-7160	669	14	,	,	PUNCT
ejpam-7160	669	15	a.a	a.a	PROPN
ejpam-7160	669	16	.	.	PROPN
ejpam-7160	669	17	;	;	PUNCT
ejpam-7160	669	18	al	al	PROPN
ejpam-7160	669	19	-	-	PUNCT
ejpam-7160	669	20	shami	shami	PROPN
ejpam-7160	669	21	,	,	PUNCT
ejpam-7160	669	22	t.m	t.m	PROPN
ejpam-7160	669	23	.	.	PROPN
ejpam-7160	669	24	various	various	ADJ
ejpam-7160	669	25	topologies	topology	NOUN
ejpam-7160	669	26	generated	generate	VERB
ejpam-7160	669	27	from	from	ADP
ejpam-7160	669	28	ej	ej	NOUN
ejpam-7160	669	29	-	-	PUNCT
ejpam-7160	669	30	neighbourhoods	neighbourhood	NOUN
ejpam-7160	669	31	via	via	ADP
ejpam-7160	669	32	ideals	ideal	NOUN
ejpam-7160	669	33	.	.	PUNCT
ejpam-7160	670	1	complexity	complexity	NOUN
ejpam-7160	670	2	2021	2021	NUM
ejpam-7160	670	3	,	,	PUNCT
ejpam-7160	670	4	2021	2021	NUM
ejpam-7160	670	5	,	,	PUNCT
ejpam-7160	670	6	4149368	4149368	NUM
ejpam-7160	670	7	.	.	PUNCT
ejpam-7160	671	1	[	[	X
ejpam-7160	671	2	55	55	NUM
ejpam-7160	671	3	]	]	PUNCT
ejpam-7160	671	4	azzam	azzam	PROPN
ejpam-7160	671	5	a.	a.	PROPN
ejpam-7160	671	6	a.	a.	PROPN
ejpam-7160	671	7	,	,	PUNCT
ejpam-7160	671	8	aldawood	aldawood	NOUN
ejpam-7160	671	9	m.	m.	NOUN
ejpam-7160	671	10	,	,	PUNCT
ejpam-7160	671	11	and	and	CCONJ
ejpam-7160	671	12	alreshidi	alreshidi	PROPN
ejpam-7160	671	13	b.	b.	PROPN
ejpam-7160	671	14	,	,	PUNCT
ejpam-7160	671	15	improving	improve	VERB
ejpam-7160	671	16	cardinality	cardinality	NOUN
ejpam-7160	671	17	rough	rough	ADJ
ejpam-7160	671	18	neighborhoods	neighborhood	NOUN
ejpam-7160	671	19	via	via	ADP
ejpam-7160	671	20	grills	grill	NOUN
ejpam-7160	671	21	and	and	CCONJ
ejpam-7160	671	22	their	their	PRON
ejpam-7160	671	23	applications	application	NOUN
ejpam-7160	671	24	,	,	PUNCT
ejpam-7160	671	25	ejpam	ejpam	NOUN
ejpam-7160	671	26	(	(	PUNCT
ejpam-7160	671	27	acceptence	acceptence	NOUN
ejpam-7160	671	28	)	)	PUNCT
ejpam-7160	671	29	.	.	PUNCT
ejpam-7160	672	1	[	[	X
ejpam-7160	672	2	56	56	NUM
ejpam-7160	672	3	]	]	X
ejpam-7160	672	4	azzam	azzam	PROPN
ejpam-7160	672	5	a.a	a.a	PROPN
ejpam-7160	672	6	.	.	PROPN
ejpam-7160	672	7	;	;	PUNCT
ejpam-7160	672	8	al	al	PROPN
ejpam-7160	672	9	-	-	PUNCT
ejpam-7160	672	10	shami	shami	PROPN
ejpam-7160	672	11	,	,	PUNCT
ejpam-7160	672	12	t.m	t.m	PROPN
ejpam-7160	672	13	.	.	PROPN
ejpam-7160	672	14	five	five	NUM
ejpam-7160	672	15	generalized	generalized	ADJ
ejpam-7160	672	16	rough	rough	ADJ
ejpam-7160	672	17	approximation	approximation	NOUN
ejpam-7160	672	18	spaces	space	NOUN
ejpam-7160	672	19	produced	produce	VERB
ejpam-7160	672	20	by	by	ADP
ejpam-7160	672	21	maximal	maximal	ADJ
ejpam-7160	672	22	rough	rough	ADJ
ejpam-7160	672	23	neighborhoods	neighborhood	NOUN
ejpam-7160	672	24	.	.	PUNCT
ejpam-7160	673	1	symmetry	symmetry	NOUN
ejpam-7160	673	2	2023	2023	NUM
ejpam-7160	673	3	,	,	PUNCT
ejpam-7160	673	4	15	15	NUM
ejpam-7160	673	5	,	,	PUNCT
ejpam-7160	673	6	751	751	NUM
ejpam-7160	673	7	.	.	PUNCT
ejpam-7160	674	1	[	[	X
ejpam-7160	674	2	57	57	NUM
ejpam-7160	674	3	]	]	X
ejpam-7160	674	4	dickstein	dickstein	PROPN
ejpam-7160	674	5	k.	k.	PROPN
ejpam-7160	674	6	,	,	PUNCT
ejpam-7160	674	7	et	et	PROPN
ejpam-7160	674	8	al	al	PROPN
ejpam-7160	674	9	.	.	PROPN
ejpam-7160	674	10	,	,	PUNCT
ejpam-7160	674	11	developed	develop	VERB
ejpam-7160	674	12	in	in	ADP
ejpam-7160	674	13	collaboration	collaboration	NOUN
ejpam-7160	674	14	with	with	ADP
ejpam-7160	674	15	the	the	DET
ejpam-7160	674	16	heart	heart	NOUN
ejpam-7160	674	17	failure	failure	NOUN
ejpam-7160	674	18	association	association	NOUN
ejpam-7160	674	19	of	of	ADP
ejpam-7160	674	20	the	the	DET
ejpam-7160	674	21	esc	esc	NOUN
ejpam-7160	674	22	(	(	PUNCT
ejpam-7160	674	23	hfa	hfa	PROPN
ejpam-7160	674	24	)	)	PUNCT
ejpam-7160	674	25	and	and	CCONJ
ejpam-7160	674	26	endorsed	endorse	VERB
ejpam-7160	674	27	by	by	ADP
ejpam-7160	674	28	the	the	DET
ejpam-7160	674	29	european	european	PROPN
ejpam-7160	674	30	society	society	NOUN
ejpam-7160	674	31	of	of	ADP
ejpam-7160	674	32	intensive	intensive	ADJ
ejpam-7160	674	33	care	care	NOUN
ejpam-7160	674	34	medicine	medicine	NOUN
ejpam-7160	674	35	(	(	PUNCT
ejpam-7160	674	36	esicm	esicm	NOUN
ejpam-7160	674	37	)	)	PUNCT
ejpam-7160	674	38	,	,	PUNCT
ejpam-7160	674	39	european	european	PROPN
ejpam-7160	674	40	journal	journal	PROPN
ejpam-7160	674	41	of	of	ADP
ejpam-7160	674	42	heart	heart	NOUN
ejpam-7160	674	43	failure	failure	NOUN
ejpam-7160	674	44	,	,	PUNCT
ejpam-7160	674	45	10(10	10(10	NUM
ejpam-7160	674	46	)	)	PUNCT
ejpam-7160	674	47	(	(	PUNCT
ejpam-7160	674	48	2008	2008	NUM
ejpam-7160	674	49	)	)	PUNCT
ejpam-7160	674	50	,	,	PUNCT
ejpam-7160	674	51	933–989	933–989	NUM
ejpam-7160	674	52	.	.	PUNCT
ejpam-7160	675	1	[	[	X
ejpam-7160	675	2	58	58	NUM
ejpam-7160	675	3	]	]	PUNCT
ejpam-7160	675	4	azzam	azzam	PROPN
ejpam-7160	675	5	a.	a.	PROPN
ejpam-7160	675	6	a.	a.	PROPN
ejpam-7160	675	7	,	,	PUNCT
ejpam-7160	675	8	ahmed	ahmed	PROPN
ejpam-7160	675	9	mostafa	mostafa	PROPN
ejpam-7160	675	10	khalil	khalil	PROPN
ejpam-7160	675	11	,	,	PUNCT
ejpam-7160	675	12	and	and	CCONJ
ejpam-7160	675	13	sheng	sheng	NOUN
ejpam-7160	675	14	-	-	PUNCT
ejpam-7160	675	15	gang	gang	NOUN
ejpam-7160	675	16	li	li	PROPN
ejpam-7160	675	17	,	,	PUNCT
ejpam-7160	675	18	medical	medical	ADJ
ejpam-7160	675	19	applications	application	NOUN
ejpam-7160	675	20	via	via	ADP
ejpam-7160	675	21	minimal	minimal	ADJ
ejpam-7160	675	22	topological	topological	ADJ
ejpam-7160	675	23	structure	structure	NOUN
ejpam-7160	675	24	,	,	PUNCT
ejpam-7160	675	25	journal	journal	NOUN
ejpam-7160	675	26	of	of	ADP
ejpam-7160	675	27	intelligent	intelligent	ADJ
ejpam-7160	675	28	and	and	CCONJ
ejpam-7160	675	29	fuzzy	fuzzy	ADJ
ejpam-7160	675	30	systems	system	NOUN
ejpam-7160	675	31	39(3	39(3	NUM
ejpam-7160	675	32	)	)	PUNCT
ejpam-7160	675	33	(	(	PUNCT
ejpam-7160	675	34	2020	2020	NUM
ejpam-7160	675	35	)	)	PUNCT
ejpam-7160	675	36	,	,	PUNCT
ejpam-7160	675	37	4723	4723	NUM
ejpam-7160	675	38	-	-	SYM
ejpam-7160	675	39	4730	4730	NUM
ejpam-7160	675	40	.	.	PUNCT