id	sid	tid	token	lemma	pos
ejpam-5453	1	1	european	european	PROPN
ejpam-5453	1	2	journal	journal	PROPN
ejpam-5453	1	3	of	of	ADP
ejpam-5453	1	4	pure	pure	ADJ
ejpam-5453	1	5	and	and	CCONJ
ejpam-5453	1	6	applied	apply	VERB
ejpam-5453	1	7	mathematics	mathematic	NOUN
ejpam-5453	1	8	vol	vol	NOUN
ejpam-5453	1	9	.	.	PROPN
ejpam-5453	2	1	17	17	NUM
ejpam-5453	2	2	,	,	PUNCT
ejpam-5453	2	3	no	no	INTJ
ejpam-5453	2	4	.	.	NOUN
ejpam-5453	2	5	4	4	NUM
ejpam-5453	2	6	,	,	PUNCT
ejpam-5453	2	7	2024	2024	NUM
ejpam-5453	2	8	,	,	PUNCT
ejpam-5453	2	9	2843	2843	NUM
ejpam-5453	2	10	-	-	SYM
ejpam-5453	2	11	2877	2877	NUM
ejpam-5453	2	12	issn	issn	PROPN
ejpam-5453	2	13	1307	1307	NUM
ejpam-5453	2	14	-	-	SYM
ejpam-5453	2	15	5543	5543	NUM
ejpam-5453	2	16	–	–	PUNCT
ejpam-5453	3	1	ejpam.com	ejpam.com	X
ejpam-5453	3	2	published	publish	VERB
ejpam-5453	3	3	by	by	ADP
ejpam-5453	3	4	new	new	PROPN
ejpam-5453	3	5	york	york	PROPN
ejpam-5453	3	6	business	business	PROPN
ejpam-5453	3	7	global	global	ADJ
ejpam-5453	3	8	extending	extend	VERB
ejpam-5453	3	9	approximations	approximation	NOUN
ejpam-5453	3	10	spaces	space	NOUN
ejpam-5453	3	11	using	use	VERB
ejpam-5453	3	12	nearly	nearly	ADV
ejpam-5453	3	13	open	open	ADJ
ejpam-5453	3	14	sets	set	NOUN
ejpam-5453	3	15	,	,	PUNCT
ejpam-5453	3	16	subset	subset	ADJ
ejpam-5453	3	17	neighborhoods	neighborhood	NOUN
ejpam-5453	3	18	,	,	PUNCT
ejpam-5453	3	19	and	and	CCONJ
ejpam-5453	3	20	ideals	ideal	NOUN
ejpam-5453	3	21	:	:	PUNCT
ejpam-5453	3	22	a	a	DET
ejpam-5453	3	23	medical	medical	ADJ
ejpam-5453	3	24	application	application	NOUN
ejpam-5453	3	25	mona	mona	PROPN
ejpam-5453	3	26	hosny1,2	hosny1,2	PROPN
ejpam-5453	3	27	1	1	NUM
ejpam-5453	3	28	department	department	NOUN
ejpam-5453	3	29	of	of	ADP
ejpam-5453	3	30	mathematics	mathematic	NOUN
ejpam-5453	3	31	,	,	PUNCT
ejpam-5453	3	32	college	college	NOUN
ejpam-5453	3	33	of	of	ADP
ejpam-5453	3	34	science	science	NOUN
ejpam-5453	3	35	,	,	PUNCT
ejpam-5453	3	36	king	king	PROPN
ejpam-5453	3	37	khalid	khalid	PROPN
ejpam-5453	3	38	university	university	PROPN
ejpam-5453	3	39	,	,	PUNCT
ejpam-5453	3	40	abha	abha	NOUN
ejpam-5453	3	41	,	,	PUNCT
ejpam-5453	3	42	61413	61413	NUM
ejpam-5453	3	43	,	,	PUNCT
ejpam-5453	3	44	saudi	saudi	PROPN
ejpam-5453	3	45	arabia	arabia	PROPN
ejpam-5453	3	46	2	2	NUM
ejpam-5453	3	47	department	department	NOUN
ejpam-5453	3	48	of	of	ADP
ejpam-5453	3	49	mathematics	mathematic	NOUN
ejpam-5453	3	50	,	,	PUNCT
ejpam-5453	3	51	faculty	faculty	NOUN
ejpam-5453	3	52	of	of	ADP
ejpam-5453	3	53	education	education	NOUN
ejpam-5453	3	54	,	,	PUNCT
ejpam-5453	3	55	ain	ain	PROPN
ejpam-5453	3	56	shams	shams	PROPN
ejpam-5453	3	57	university	university	PROPN
ejpam-5453	3	58	,	,	PUNCT
ejpam-5453	3	59	roxy	roxy	PROPN
ejpam-5453	3	60	,	,	PUNCT
ejpam-5453	3	61	11341	11341	NUM
ejpam-5453	3	62	,	,	PUNCT
ejpam-5453	3	63	cairo	cairo	PROPN
ejpam-5453	3	64	,	,	PUNCT
ejpam-5453	3	65	egypt	egypt	PROPN
ejpam-5453	3	66	abstract	abstract	PROPN
ejpam-5453	3	67	.	.	PUNCT
ejpam-5453	4	1	the	the	DET
ejpam-5453	4	2	close	close	ADJ
ejpam-5453	4	3	resemblance	resemblance	NOUN
ejpam-5453	4	4	between	between	ADP
ejpam-5453	4	5	rough	rough	ADJ
ejpam-5453	4	6	sets	set	NOUN
ejpam-5453	4	7	and	and	CCONJ
ejpam-5453	4	8	topology	topology	NOUN
ejpam-5453	4	9	arises	arise	VERB
ejpam-5453	4	10	from	from	ADP
ejpam-5453	4	11	the	the	DET
ejpam-5453	4	12	analogy	analogy	NOUN
ejpam-5453	4	13	between	between	ADP
ejpam-5453	4	14	topological	topological	ADJ
ejpam-5453	4	15	operators	operator	NOUN
ejpam-5453	4	16	and	and	CCONJ
ejpam-5453	4	17	rough	rough	ADJ
ejpam-5453	4	18	approximations	approximation	NOUN
ejpam-5453	4	19	.	.	PUNCT
ejpam-5453	5	1	this	this	DET
ejpam-5453	5	2	connection	connection	NOUN
ejpam-5453	5	3	fosters	foster	VERB
ejpam-5453	5	4	combined	combined	ADJ
ejpam-5453	5	5	studies	study	NOUN
ejpam-5453	5	6	between	between	ADP
ejpam-5453	5	7	them	they	PRON
ejpam-5453	5	8	.	.	PUNCT
ejpam-5453	6	1	therefore	therefore	ADV
ejpam-5453	6	2	,	,	PUNCT
ejpam-5453	6	3	this	this	DET
ejpam-5453	6	4	paper	paper	NOUN
ejpam-5453	6	5	is	be	AUX
ejpam-5453	6	6	created	create	VERB
ejpam-5453	6	7	new	new	ADJ
ejpam-5453	6	8	approximations	approximation	NOUN
ejpam-5453	6	9	by	by	ADP
ejpam-5453	6	10	leveraging	leverage	VERB
ejpam-5453	6	11	topological	topological	ADJ
ejpam-5453	6	12	concepts	concept	NOUN
ejpam-5453	6	13	.	.	PUNCT
ejpam-5453	7	1	additionally	additionally	ADV
ejpam-5453	7	2	,	,	PUNCT
ejpam-5453	7	3	it	it	PRON
ejpam-5453	7	4	is	be	AUX
ejpam-5453	7	5	depicted	depict	VERB
ejpam-5453	7	6	that	that	SCONJ
ejpam-5453	7	7	how	how	SCONJ
ejpam-5453	7	8	a	a	DET
ejpam-5453	7	9	specific	specific	ADJ
ejpam-5453	7	10	combination	combination	NOUN
ejpam-5453	7	11	of	of	ADP
ejpam-5453	7	12	ideals	ideal	NOUN
ejpam-5453	7	13	is	be	AUX
ejpam-5453	7	14	utilized	utilize	VERB
ejpam-5453	7	15	to	to	PART
ejpam-5453	7	16	approach	approach	VERB
ejpam-5453	7	17	rough	rough	ADV
ejpam-5453	7	18	from	from	ADP
ejpam-5453	7	19	a	a	DET
ejpam-5453	7	20	topological	topological	ADJ
ejpam-5453	7	21	perspective	perspective	NOUN
ejpam-5453	7	22	.	.	PUNCT
ejpam-5453	8	1	as	as	SCONJ
ejpam-5453	8	2	,	,	PUNCT
ejpam-5453	8	3	ideals	ideal	NOUN
ejpam-5453	8	4	are	be	AUX
ejpam-5453	8	5	valuable	valuable	ADJ
ejpam-5453	8	6	topological	topological	ADJ
ejpam-5453	8	7	tools	tool	NOUN
ejpam-5453	8	8	for	for	ADP
ejpam-5453	8	9	reducing	reduce	VERB
ejpam-5453	8	10	uncertainty	uncertainty	NOUN
ejpam-5453	8	11	.	.	PUNCT
ejpam-5453	9	1	so	so	ADV
ejpam-5453	9	2	,	,	PUNCT
ejpam-5453	9	3	ideal	ideal	ADJ
ejpam-5453	9	4	structures	structure	NOUN
ejpam-5453	9	5	are	be	AUX
ejpam-5453	9	6	used	use	VERB
ejpam-5453	9	7	to	to	PART
ejpam-5453	9	8	create	create	VERB
ejpam-5453	9	9	new	new	ADJ
ejpam-5453	9	10	generalized	generalized	ADJ
ejpam-5453	9	11	approximation	approximation	NOUN
ejpam-5453	9	12	spaces	space	NOUN
ejpam-5453	9	13	that	that	PRON
ejpam-5453	9	14	minimize	minimize	VERB
ejpam-5453	9	15	vagueness	vagueness	NOUN
ejpam-5453	9	16	.	.	PUNCT
ejpam-5453	10	1	initially	initially	ADV
ejpam-5453	10	2	,	,	PUNCT
ejpam-5453	10	3	new	new	ADJ
ejpam-5453	10	4	topologies	topology	NOUN
ejpam-5453	10	5	concepts	concept	NOUN
ejpam-5453	10	6	are	be	AUX
ejpam-5453	10	7	proposed	propose	VERB
ejpam-5453	10	8	relying	rely	VERB
ejpam-5453	10	9	on	on	ADP
ejpam-5453	10	10	various	various	ADJ
ejpam-5453	10	11	types	type	NOUN
ejpam-5453	10	12	of	of	ADP
ejpam-5453	10	13	the	the	DET
ejpam-5453	10	14	subset	subset	ADJ
ejpam-5453	10	15	neighborhoods	neighborhood	NOUN
ejpam-5453	10	16	via	via	ADP
ejpam-5453	10	17	ideals	ideal	NOUN
ejpam-5453	10	18	,	,	PUNCT
ejpam-5453	10	19	and	and	CCONJ
ejpam-5453	10	20	their	their	PRON
ejpam-5453	10	21	relationships	relationship	NOUN
ejpam-5453	10	22	are	be	AUX
ejpam-5453	10	23	analyzed	analyze	VERB
ejpam-5453	10	24	.	.	PUNCT
ejpam-5453	11	1	thereafter	thereafter	ADV
ejpam-5453	11	2	,	,	PUNCT
ejpam-5453	11	3	new	new	ADJ
ejpam-5453	11	4	approximations	approximation	NOUN
ejpam-5453	11	5	are	be	AUX
ejpam-5453	11	6	derived	derive	VERB
ejpam-5453	11	7	from	from	ADP
ejpam-5453	11	8	the	the	DET
ejpam-5453	11	9	proposed	propose	VERB
ejpam-5453	11	10	topological	topological	ADJ
ejpam-5453	11	11	concepts	concept	NOUN
ejpam-5453	11	12	.	.	PUNCT
ejpam-5453	12	1	moreover	moreover	ADV
ejpam-5453	12	2	,	,	PUNCT
ejpam-5453	12	3	all	all	DET
ejpam-5453	12	4	the	the	DET
ejpam-5453	12	5	present	present	ADJ
ejpam-5453	12	6	results	result	NOUN
ejpam-5453	12	7	are	be	AUX
ejpam-5453	12	8	compared	compare	VERB
ejpam-5453	12	9	with	with	ADP
ejpam-5453	12	10	earlier	early	ADJ
ejpam-5453	12	11	models	model	NOUN
ejpam-5453	12	12	to	to	PART
ejpam-5453	12	13	highlight	highlight	VERB
ejpam-5453	12	14	the	the	DET
ejpam-5453	12	15	advantages	advantage	NOUN
ejpam-5453	12	16	and	and	CCONJ
ejpam-5453	12	17	merits	merit	NOUN
ejpam-5453	12	18	of	of	ADP
ejpam-5453	12	19	the	the	DET
ejpam-5453	12	20	current	current	ADJ
ejpam-5453	12	21	technique	technique	NOUN
ejpam-5453	12	22	.	.	PUNCT
ejpam-5453	13	1	the	the	DET
ejpam-5453	13	2	present	present	ADJ
ejpam-5453	13	3	manners	manner	NOUN
ejpam-5453	13	4	are	be	AUX
ejpam-5453	13	5	more	more	ADV
ejpam-5453	13	6	precise	precise	ADJ
ejpam-5453	13	7	than	than	ADP
ejpam-5453	13	8	previous	previous	ADJ
ejpam-5453	13	9	approaches	approach	NOUN
ejpam-5453	13	10	as	as	SCONJ
ejpam-5453	13	11	they	they	PRON
ejpam-5453	13	12	are	be	AUX
ejpam-5453	13	13	particularly	particularly	ADV
ejpam-5453	13	14	valuable	valuable	ADJ
ejpam-5453	13	15	for	for	ADP
ejpam-5453	13	16	reducing	reduce	VERB
ejpam-5453	13	17	vagueness	vagueness	NOUN
ejpam-5453	13	18	.	.	PUNCT
ejpam-5453	14	1	more	more	ADV
ejpam-5453	14	2	importantly	importantly	ADV
ejpam-5453	14	3	,	,	PUNCT
ejpam-5453	14	4	three	three	NUM
ejpam-5453	14	5	distinct	distinct	ADJ
ejpam-5453	14	6	perspectives	perspective	NOUN
ejpam-5453	14	7	are	be	AUX
ejpam-5453	14	8	presented	present	VERB
ejpam-5453	14	9	to	to	PART
ejpam-5453	14	10	elicit	elicit	VERB
ejpam-5453	14	11	membership	membership	NOUN
ejpam-5453	14	12	functions	function	NOUN
ejpam-5453	14	13	.	.	PUNCT
ejpam-5453	15	1	to	to	PART
ejpam-5453	15	2	emphasize	emphasize	VERB
ejpam-5453	15	3	the	the	DET
ejpam-5453	15	4	importance	importance	NOUN
ejpam-5453	15	5	of	of	ADP
ejpam-5453	15	6	this	this	DET
ejpam-5453	15	7	paper	paper	NOUN
ejpam-5453	15	8	,	,	PUNCT
ejpam-5453	15	9	a	a	DET
ejpam-5453	15	10	numerical	numerical	ADJ
ejpam-5453	15	11	example	example	NOUN
ejpam-5453	15	12	related	relate	VERB
ejpam-5453	15	13	to	to	ADP
ejpam-5453	15	14	chikungunya	chikungunya	NOUN
ejpam-5453	15	15	disease	disease	NOUN
ejpam-5453	15	16	is	be	AUX
ejpam-5453	15	17	provided	provide	VERB
ejpam-5453	15	18	.	.	PUNCT
ejpam-5453	16	1	this	this	PRON
ejpam-5453	16	2	enables	enable	VERB
ejpam-5453	16	3	specialists	specialist	NOUN
ejpam-5453	16	4	to	to	PART
ejpam-5453	16	5	accurately	accurately	ADV
ejpam-5453	16	6	assess	assess	VERB
ejpam-5453	16	7	the	the	DET
ejpam-5453	16	8	factors	factor	NOUN
ejpam-5453	16	9	influencing	influence	VERB
ejpam-5453	16	10	chikungunya	chikungunya	NOUN
ejpam-5453	16	11	disease	disease	NOUN
ejpam-5453	16	12	.	.	PUNCT
ejpam-5453	17	1	so	so	ADV
ejpam-5453	17	2	,	,	PUNCT
ejpam-5453	17	3	specialists	specialist	NOUN
ejpam-5453	17	4	and	and	CCONJ
ejpam-5453	17	5	consultants	consultant	NOUN
ejpam-5453	17	6	can	can	AUX
ejpam-5453	17	7	handle	handle	VERB
ejpam-5453	17	8	insufficient	insufficient	ADJ
ejpam-5453	17	9	data	datum	NOUN
ejpam-5453	17	10	regarding	regard	VERB
ejpam-5453	17	11	disease	disease	NOUN
ejpam-5453	17	12	symptoms	symptom	NOUN
ejpam-5453	17	13	,	,	PUNCT
ejpam-5453	17	14	resulting	result	VERB
ejpam-5453	17	15	in	in	ADP
ejpam-5453	17	16	easier	easy	ADJ
ejpam-5453	17	17	and	and	CCONJ
ejpam-5453	17	18	more	more	ADV
ejpam-5453	17	19	accurate	accurate	ADJ
ejpam-5453	17	20	patient	patient	NOUN
ejpam-5453	17	21	diagnoses	diagnosis	NOUN
ejpam-5453	17	22	.	.	PUNCT
ejpam-5453	18	1	the	the	DET
ejpam-5453	18	2	study	study	NOUN
ejpam-5453	18	3	wraps	wrap	VERB
ejpam-5453	18	4	up	up	ADP
ejpam-5453	18	5	with	with	ADP
ejpam-5453	18	6	a	a	DET
ejpam-5453	18	7	summary	summary	NOUN
ejpam-5453	18	8	and	and	CCONJ
ejpam-5453	18	9	proposals	proposal	NOUN
ejpam-5453	18	10	for	for	ADP
ejpam-5453	18	11	future	future	ADJ
ejpam-5453	18	12	research	research	NOUN
ejpam-5453	18	13	.	.	PUNCT
ejpam-5453	19	1	2020	2020	NUM
ejpam-5453	19	2	mathematics	mathematic	NOUN
ejpam-5453	19	3	subject	subject	NOUN
ejpam-5453	19	4	classifications	classification	NOUN
ejpam-5453	19	5	:	:	PUNCT
ejpam-5453	19	6	03e99	03e99	NUM
ejpam-5453	19	7	,	,	PUNCT
ejpam-5453	19	8	54a05	54a05	NUM
ejpam-5453	19	9	,	,	PUNCT
ejpam-5453	19	10	54e99	54e99	DET
ejpam-5453	19	11	key	key	ADJ
ejpam-5453	19	12	words	word	NOUN
ejpam-5453	19	13	and	and	CCONJ
ejpam-5453	19	14	phrases	phrase	NOUN
ejpam-5453	19	15	:	:	PUNCT
ejpam-5453	19	16	rough	rough	ADJ
ejpam-5453	19	17	set	set	NOUN
ejpam-5453	19	18	,	,	PUNCT
ejpam-5453	19	19	topology	topology	NOUN
ejpam-5453	19	20	,	,	PUNCT
ejpam-5453	19	21	ideal	ideal	ADJ
ejpam-5453	19	22	,	,	PUNCT
ejpam-5453	19	23	subset	subset	VERB
ejpam-5453	19	24	neighborhood	neighborhood	NOUN
ejpam-5453	19	25	1	1	NUM
ejpam-5453	19	26	.	.	PUNCT
ejpam-5453	20	1	introduction	introduction	NOUN
ejpam-5453	20	2	the	the	DET
ejpam-5453	20	3	issues	issue	NOUN
ejpam-5453	20	4	of	of	ADP
ejpam-5453	20	5	imprecision	imprecision	NOUN
ejpam-5453	20	6	in	in	ADP
ejpam-5453	20	7	information	information	NOUN
ejpam-5453	20	8	systems	system	NOUN
ejpam-5453	20	9	used	use	VERB
ejpam-5453	20	10	for	for	ADP
ejpam-5453	20	11	data	datum	NOUN
ejpam-5453	20	12	analysis	analysis	NOUN
ejpam-5453	20	13	have	have	AUX
ejpam-5453	20	14	long	long	ADV
ejpam-5453	20	15	been	be	AUX
ejpam-5453	20	16	a	a	DET
ejpam-5453	20	17	concern	concern	NOUN
ejpam-5453	20	18	.	.	PUNCT
ejpam-5453	21	1	many	many	ADJ
ejpam-5453	21	2	researchers	researcher	NOUN
ejpam-5453	21	3	,	,	PUNCT
ejpam-5453	21	4	especially	especially	ADV
ejpam-5453	21	5	those	those	PRON
ejpam-5453	21	6	specializing	specialize	VERB
ejpam-5453	21	7	in	in	ADP
ejpam-5453	21	8	artificial	artificial	ADJ
ejpam-5453	21	9	intelligence	intelligence	NOUN
ejpam-5453	21	10	,	,	PUNCT
ejpam-5453	21	11	had	have	AUX
ejpam-5453	21	12	sought	seek	VERB
ejpam-5453	21	13	effective	effective	ADJ
ejpam-5453	21	14	tools	tool	NOUN
ejpam-5453	21	15	to	to	PART
ejpam-5453	21	16	address	address	VERB
ejpam-5453	21	17	these	these	DET
ejpam-5453	21	18	challenges	challenge	NOUN
ejpam-5453	21	19	.	.	PUNCT
ejpam-5453	22	1	one	one	NUM
ejpam-5453	22	2	such	such	ADJ
ejpam-5453	22	3	tool	tool	NOUN
ejpam-5453	22	4	that	that	PRON
ejpam-5453	22	5	have	have	AUX
ejpam-5453	22	6	been	be	AUX
ejpam-5453	22	7	proposed	propose	VERB
ejpam-5453	22	8	doi	doi	NOUN
ejpam-5453	22	9	:	:	PUNCT
ejpam-5453	22	10	https://doi.org/10.29020/nybg.ejpam.v17i4.5453	https://doi.org/10.29020/nybg.ejpam.v17i4.5453	NOUN
ejpam-5453	22	11	email	email	NOUN
ejpam-5453	22	12	address	address	NOUN
ejpam-5453	22	13	:	:	PUNCT
ejpam-5453	22	14	monahosny@edu.asu.edu.eg	monahosny@edu.asu.edu.eg	NOUN
ejpam-5453	22	15	(	(	PUNCT
ejpam-5453	22	16	m.	m.	PROPN
ejpam-5453	22	17	hosny	hosny	PROPN
ejpam-5453	22	18	)	)	PUNCT
ejpam-5453	22	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5453	22	20	2843	2843	NUM
ejpam-5453	23	1	copyright	copyright	NOUN
ejpam-5453	23	2	:	:	PUNCT
ejpam-5453	23	3	©	©	PROPN
ejpam-5453	23	4	2024	2024	NUM
ejpam-5453	23	5	the	the	DET
ejpam-5453	23	6	author(s	author(s	NOUN
ejpam-5453	23	7	)	)	PUNCT
ejpam-5453	23	8	.	.	PUNCT
ejpam-5453	24	1	(	(	PUNCT
ejpam-5453	24	2	cc	cc	NOUN
ejpam-5453	24	3	by	by	ADP
ejpam-5453	24	4	-	-	PUNCT
ejpam-5453	24	5	nc	nc	PROPN
ejpam-5453	24	6	4.0	4.0	NUM
ejpam-5453	24	7	)	)	PUNCT
ejpam-5453	24	8	m.	m.	NOUN
ejpam-5453	24	9	hosny	hosny	PROPN
ejpam-5453	24	10	/	/	SYM
ejpam-5453	24	11	eur	eur	PROPN
ejpam-5453	24	12	.	.	PUNCT
ejpam-5453	25	1	j.	j.	PROPN
ejpam-5453	25	2	pure	pure	PROPN
ejpam-5453	25	3	appl	appl	PROPN
ejpam-5453	25	4	.	.	PROPN
ejpam-5453	25	5	math	math	PROPN
ejpam-5453	25	6	,	,	PUNCT
ejpam-5453	25	7	17	17	NUM
ejpam-5453	25	8	(	(	PUNCT
ejpam-5453	25	9	4	4	NUM
ejpam-5453	25	10	)	)	PUNCT
ejpam-5453	25	11	(	(	PUNCT
ejpam-5453	25	12	2024	2024	NUM
ejpam-5453	25	13	)	)	PUNCT
ejpam-5453	25	14	,	,	PUNCT
ejpam-5453	25	15	2843	2843	NUM
ejpam-5453	25	16	-	-	SYM
ejpam-5453	25	17	2877	2877	NUM
ejpam-5453	25	18	2844	2844	NUM
ejpam-5453	25	19	is	be	AUX
ejpam-5453	25	20	rough	rough	ADJ
ejpam-5453	25	21	set	set	NOUN
ejpam-5453	25	22	theory	theory	NOUN
ejpam-5453	25	23	.	.	PUNCT
ejpam-5453	26	1	it	it	PRON
ejpam-5453	26	2	is	be	AUX
ejpam-5453	26	3	emerged	emerge	VERB
ejpam-5453	26	4	as	as	ADP
ejpam-5453	26	5	a	a	DET
ejpam-5453	26	6	non	non	ADJ
ejpam-5453	26	7	-	-	ADJ
ejpam-5453	26	8	statistical	statistical	ADJ
ejpam-5453	26	9	method	method	NOUN
ejpam-5453	26	10	for	for	ADP
ejpam-5453	26	11	analyzing	analyze	VERB
ejpam-5453	26	12	the	the	DET
ejpam-5453	26	13	data	datum	NOUN
ejpam-5453	26	14	[	[	X
ejpam-5453	26	15	37	37	NUM
ejpam-5453	26	16	,	,	PUNCT
ejpam-5453	26	17	38	38	NUM
ejpam-5453	26	18	]	]	PUNCT
ejpam-5453	26	19	.	.	PUNCT
ejpam-5453	27	1	this	this	DET
ejpam-5453	27	2	theory	theory	NOUN
ejpam-5453	27	3	addresses	address	VERB
ejpam-5453	27	4	complex	complex	ADJ
ejpam-5453	27	5	real	real	ADJ
ejpam-5453	27	6	-	-	PUNCT
ejpam-5453	27	7	life	life	NOUN
ejpam-5453	27	8	problems	problem	NOUN
ejpam-5453	27	9	by	by	ADP
ejpam-5453	27	10	partitioning	partition	VERB
ejpam-5453	27	11	a	a	DET
ejpam-5453	27	12	data	datum	NOUN
ejpam-5453	27	13	set	set	VERB
ejpam-5453	27	14	with	with	ADP
ejpam-5453	27	15	inherent	inherent	ADJ
ejpam-5453	27	16	uncertainty	uncertainty	NOUN
ejpam-5453	27	17	into	into	ADP
ejpam-5453	27	18	three	three	NUM
ejpam-5453	27	19	distinct	distinct	ADJ
ejpam-5453	27	20	regions	region	NOUN
ejpam-5453	27	21	:	:	PUNCT
ejpam-5453	27	22	the	the	DET
ejpam-5453	27	23	lower	low	ADJ
ejpam-5453	27	24	approximation	approximation	NOUN
ejpam-5453	27	25	,	,	PUNCT
ejpam-5453	27	26	which	which	PRON
ejpam-5453	27	27	encompasses	encompass	VERB
ejpam-5453	27	28	the	the	DET
ejpam-5453	27	29	confirmed	confirmed	ADJ
ejpam-5453	27	30	information	information	NOUN
ejpam-5453	27	31	;	;	PUNCT
ejpam-5453	27	32	the	the	DET
ejpam-5453	27	33	upper	upper	ADJ
ejpam-5453	27	34	approximation	approximation	NOUN
ejpam-5453	27	35	,	,	PUNCT
ejpam-5453	27	36	which	which	PRON
ejpam-5453	27	37	includes	include	VERB
ejpam-5453	27	38	information	information	NOUN
ejpam-5453	27	39	whose	whose	DET
ejpam-5453	27	40	membership	membership	NOUN
ejpam-5453	27	41	in	in	ADP
ejpam-5453	27	42	the	the	DET
ejpam-5453	27	43	set	set	NOUN
ejpam-5453	27	44	can	can	AUX
ejpam-5453	27	45	not	not	PART
ejpam-5453	27	46	be	be	AUX
ejpam-5453	27	47	definitively	definitively	ADV
ejpam-5453	27	48	determined	determine	VERB
ejpam-5453	27	49	;	;	PUNCT
ejpam-5453	27	50	and	and	CCONJ
ejpam-5453	27	51	the	the	DET
ejpam-5453	27	52	boundary	boundary	ADJ
ejpam-5453	27	53	area	area	NOUN
ejpam-5453	27	54	,	,	PUNCT
ejpam-5453	27	55	represented	represent	VERB
ejpam-5453	27	56	by	by	ADP
ejpam-5453	27	57	the	the	DET
ejpam-5453	27	58	gap	gap	NOUN
ejpam-5453	27	59	between	between	ADP
ejpam-5453	27	60	the	the	DET
ejpam-5453	27	61	upper	upper	ADJ
ejpam-5453	27	62	and	and	CCONJ
ejpam-5453	27	63	lower	low	ADJ
ejpam-5453	27	64	approximations	approximation	NOUN
ejpam-5453	27	65	.	.	PUNCT
ejpam-5453	28	1	vagueness	vagueness	NOUN
ejpam-5453	28	2	is	be	AUX
ejpam-5453	28	3	related	relate	VERB
ejpam-5453	28	4	to	to	ADP
ejpam-5453	28	5	the	the	DET
ejpam-5453	28	6	boundary	boundary	NOUN
ejpam-5453	28	7	,	,	PUNCT
ejpam-5453	28	8	where	where	SCONJ
ejpam-5453	28	9	objects	object	NOUN
ejpam-5453	28	10	can	can	AUX
ejpam-5453	28	11	not	not	PART
ejpam-5453	28	12	be	be	AUX
ejpam-5453	28	13	clearly	clearly	ADV
ejpam-5453	28	14	classified	classify	VERB
ejpam-5453	28	15	.	.	PUNCT
ejpam-5453	29	1	consequently	consequently	ADV
ejpam-5453	29	2	,	,	PUNCT
ejpam-5453	29	3	the	the	DET
ejpam-5453	29	4	level	level	NOUN
ejpam-5453	29	5	of	of	ADP
ejpam-5453	29	6	set	set	NOUN
ejpam-5453	29	7	’s	’s	PART
ejpam-5453	29	8	ambiguity	ambiguity	NOUN
ejpam-5453	29	9	,	,	PUNCT
ejpam-5453	29	10	depends	depend	VERB
ejpam-5453	29	11	on	on	ADP
ejpam-5453	29	12	the	the	DET
ejpam-5453	29	13	boundary	boundary	ADJ
ejpam-5453	29	14	contains	contain	VERB
ejpam-5453	29	15	element	element	NOUN
ejpam-5453	29	16	or	or	CCONJ
ejpam-5453	29	17	not	not	PART
ejpam-5453	29	18	.	.	PUNCT
ejpam-5453	30	1	a	a	DET
ejpam-5453	30	2	nonempty	nonempty	ADJ
ejpam-5453	30	3	boundary	boundary	NOUN
ejpam-5453	30	4	indicates	indicate	VERB
ejpam-5453	30	5	insufficient	insufficient	ADJ
ejpam-5453	30	6	knowledge	knowledge	NOUN
ejpam-5453	30	7	to	to	PART
ejpam-5453	30	8	precisely	precisely	ADV
ejpam-5453	30	9	define	define	VERB
ejpam-5453	30	10	the	the	DET
ejpam-5453	30	11	set	set	NOUN
ejpam-5453	30	12	.	.	PUNCT
ejpam-5453	31	1	therefore	therefore	ADV
ejpam-5453	31	2	,	,	PUNCT
ejpam-5453	31	3	a	a	DET
ejpam-5453	31	4	key	key	ADJ
ejpam-5453	31	5	goal	goal	NOUN
ejpam-5453	31	6	is	be	AUX
ejpam-5453	31	7	to	to	PART
ejpam-5453	31	8	minimize	minimize	VERB
ejpam-5453	31	9	the	the	DET
ejpam-5453	31	10	boundary	boundary	NOUN
ejpam-5453	31	11	and	and	CCONJ
ejpam-5453	31	12	enhance	enhance	VERB
ejpam-5453	31	13	the	the	DET
ejpam-5453	31	14	set	set	NOUN
ejpam-5453	31	15	’s	’s	PART
ejpam-5453	31	16	accuracy	accuracy	NOUN
ejpam-5453	31	17	.	.	PUNCT
ejpam-5453	32	1	in	in	ADP
ejpam-5453	32	2	standard	standard	ADJ
ejpam-5453	32	3	model	model	NOUN
ejpam-5453	32	4	,	,	PUNCT
ejpam-5453	32	5	approximations	approximation	NOUN
ejpam-5453	32	6	were	be	AUX
ejpam-5453	32	7	defined	define	VERB
ejpam-5453	32	8	in	in	ADP
ejpam-5453	32	9	terms	term	NOUN
ejpam-5453	32	10	of	of	ADP
ejpam-5453	32	11	equivalence	equivalence	NOUN
ejpam-5453	32	12	classes	class	NOUN
ejpam-5453	32	13	.	.	PUNCT
ejpam-5453	33	1	however	however	ADV
ejpam-5453	33	2	,	,	PUNCT
ejpam-5453	33	3	the	the	DET
ejpam-5453	33	4	equivalence	equivalence	NOUN
ejpam-5453	33	5	relations	relation	NOUN
ejpam-5453	33	6	were	be	AUX
ejpam-5453	33	7	overly	overly	ADV
ejpam-5453	33	8	constraining	constrain	VERB
ejpam-5453	33	9	for	for	ADP
ejpam-5453	33	10	applications	application	NOUN
ejpam-5453	33	11	.	.	PUNCT
ejpam-5453	34	1	to	to	PART
ejpam-5453	34	2	broaden	broaden	VERB
ejpam-5453	34	3	the	the	DET
ejpam-5453	34	4	aspects	aspect	NOUN
ejpam-5453	34	5	of	of	ADP
ejpam-5453	34	6	this	this	DET
ejpam-5453	34	7	theory	theory	NOUN
ejpam-5453	34	8	,	,	PUNCT
ejpam-5453	34	9	researchers	researcher	NOUN
ejpam-5453	34	10	have	have	AUX
ejpam-5453	34	11	suggested	suggest	VERB
ejpam-5453	34	12	various	various	ADJ
ejpam-5453	34	13	extensions	extension	NOUN
ejpam-5453	34	14	.	.	PUNCT
ejpam-5453	35	1	for	for	ADP
ejpam-5453	35	2	instance	instance	NOUN
ejpam-5453	35	3	,	,	PUNCT
ejpam-5453	35	4	equivalence	equivalence	NOUN
ejpam-5453	35	5	classes	class	NOUN
ejpam-5453	35	6	have	have	AUX
ejpam-5453	35	7	been	be	AUX
ejpam-5453	35	8	replaced	replace	VERB
ejpam-5453	35	9	with	with	ADP
ejpam-5453	35	10	other	other	ADJ
ejpam-5453	35	11	models	model	NOUN
ejpam-5453	35	12	in	in	ADP
ejpam-5453	35	13	several	several	ADJ
ejpam-5453	35	14	studies	study	NOUN
ejpam-5453	35	15	(	(	PUNCT
ejpam-5453	35	16	see	see	VERB
ejpam-5453	35	17	:	:	PUNCT
ejpam-5453	35	18	[	[	X
ejpam-5453	35	19	34	34	NUM
ejpam-5453	35	20	,	,	PUNCT
ejpam-5453	35	21	36	36	NUM
ejpam-5453	35	22	]	]	NUM
ejpam-5453	35	23	)	)	PUNCT
ejpam-5453	35	24	.	.	PUNCT
ejpam-5453	36	1	additionally	additionally	ADV
ejpam-5453	36	2	,	,	PUNCT
ejpam-5453	36	3	neighborhood	neighborhood	NOUN
ejpam-5453	36	4	systems	system	NOUN
ejpam-5453	36	5	extend	extend	VERB
ejpam-5453	36	6	rough	rough	ADJ
ejpam-5453	36	7	set	set	NOUN
ejpam-5453	36	8	theory	theory	NOUN
ejpam-5453	36	9	by	by	ADP
ejpam-5453	36	10	substituting	substitute	VERB
ejpam-5453	36	11	equivalence	equivalence	NOUN
ejpam-5453	36	12	classes	class	NOUN
ejpam-5453	36	13	with	with	ADP
ejpam-5453	36	14	neighborhoods	neighborhood	NOUN
ejpam-5453	36	15	in	in	ADP
ejpam-5453	36	16	the	the	DET
ejpam-5453	36	17	definition	definition	NOUN
ejpam-5453	36	18	of	of	ADP
ejpam-5453	36	19	approximations	approximation	NOUN
ejpam-5453	36	20	(	(	PUNCT
ejpam-5453	36	21	see	see	VERB
ejpam-5453	36	22	:	:	PUNCT
ejpam-5453	36	23	[	[	X
ejpam-5453	36	24	3	3	NUM
ejpam-5453	36	25	,	,	PUNCT
ejpam-5453	36	26	5–13	5–13	PROPN
ejpam-5453	36	27	,	,	PUNCT
ejpam-5453	36	28	16	16	NUM
ejpam-5453	36	29	,	,	PUNCT
ejpam-5453	36	30	25	25	NUM
ejpam-5453	36	31	,	,	PUNCT
ejpam-5453	36	32	42	42	NUM
ejpam-5453	36	33	]	]	PUNCT
ejpam-5453	36	34	)	)	PUNCT
ejpam-5453	36	35	.	.	PUNCT
ejpam-5453	37	1	topology	topology	NOUN
ejpam-5453	37	2	is	be	AUX
ejpam-5453	37	3	a	a	DET
ejpam-5453	37	4	prevalent	prevalent	NOUN
ejpam-5453	37	5	across	across	ADP
ejpam-5453	37	6	nearly	nearly	ADV
ejpam-5453	37	7	all	all	PRON
ejpam-5453	37	8	branches	branch	NOUN
ejpam-5453	37	9	of	of	ADP
ejpam-5453	37	10	mathematics	mathematic	NOUN
ejpam-5453	37	11	(	(	PUNCT
ejpam-5453	37	12	see	see	VERB
ejpam-5453	37	13	:	:	PUNCT
ejpam-5453	37	14	[	[	X
ejpam-5453	37	15	29	29	NUM
ejpam-5453	37	16	,	,	PUNCT
ejpam-5453	37	17	40	40	NUM
ejpam-5453	37	18	]	]	PUNCT
ejpam-5453	37	19	)	)	PUNCT
ejpam-5453	37	20	.	.	PUNCT
ejpam-5453	38	1	it	it	PRON
ejpam-5453	38	2	has	have	AUX
ejpam-5453	38	3	become	become	VERB
ejpam-5453	38	4	a	a	DET
ejpam-5453	38	5	significant	significant	ADJ
ejpam-5453	38	6	unifying	unifying	ADJ
ejpam-5453	38	7	idea	idea	NOUN
ejpam-5453	38	8	in	in	ADP
ejpam-5453	38	9	mathematics	mathematic	NOUN
ejpam-5453	38	10	.	.	PUNCT
ejpam-5453	39	1	the	the	DET
ejpam-5453	39	2	upper	upper	ADJ
ejpam-5453	39	3	and	and	CCONJ
ejpam-5453	39	4	lower	low	ADJ
ejpam-5453	39	5	approximations	approximation	NOUN
ejpam-5453	39	6	correspond	correspond	VERB
ejpam-5453	39	7	to	to	ADP
ejpam-5453	39	8	the	the	DET
ejpam-5453	39	9	closure	closure	NOUN
ejpam-5453	39	10	and	and	CCONJ
ejpam-5453	39	11	interior	interior	NOUN
ejpam-5453	39	12	of	of	ADP
ejpam-5453	39	13	a	a	DET
ejpam-5453	39	14	set	set	NOUN
ejpam-5453	39	15	.	.	PUNCT
ejpam-5453	40	1	therefore	therefore	ADV
ejpam-5453	40	2	,	,	PUNCT
ejpam-5453	40	3	different	different	ADJ
ejpam-5453	40	4	studies	study	NOUN
ejpam-5453	40	5	have	have	AUX
ejpam-5453	40	6	explored	explore	VERB
ejpam-5453	40	7	the	the	DET
ejpam-5453	40	8	intersection	intersection	NOUN
ejpam-5453	40	9	of	of	ADP
ejpam-5453	40	10	topological	topological	ADJ
ejpam-5453	40	11	space	space	NOUN
ejpam-5453	40	12	and	and	CCONJ
ejpam-5453	40	13	rough	rough	ADJ
ejpam-5453	40	14	set	set	NOUN
ejpam-5453	40	15	theory	theory	NOUN
ejpam-5453	40	16	(	(	PUNCT
ejpam-5453	40	17	see	see	VERB
ejpam-5453	40	18	:	:	PUNCT
ejpam-5453	40	19	[	[	X
ejpam-5453	40	20	22	22	NUM
ejpam-5453	40	21	,	,	PUNCT
ejpam-5453	40	22	33	33	NUM
ejpam-5453	40	23	,	,	PUNCT
ejpam-5453	40	24	39	39	NUM
ejpam-5453	40	25	,	,	PUNCT
ejpam-5453	40	26	44	44	NUM
ejpam-5453	40	27	]	]	PUNCT
ejpam-5453	40	28	)	)	PUNCT
ejpam-5453	40	29	.	.	PUNCT
ejpam-5453	41	1	many	many	ADJ
ejpam-5453	41	2	mathematicians	mathematician	NOUN
ejpam-5453	41	3	redirected	redirect	VERB
ejpam-5453	41	4	their	their	PRON
ejpam-5453	41	5	attention	attention	NOUN
ejpam-5453	41	6	to	to	ADP
ejpam-5453	41	7	the	the	DET
ejpam-5453	41	8	near	near	ADJ
ejpam-5453	41	9	(	(	PUNCT
ejpam-5453	41	10	or	or	CCONJ
ejpam-5453	41	11	nearly	nearly	ADV
ejpam-5453	41	12	)	)	PUNCT
ejpam-5453	41	13	open	open	ADJ
ejpam-5453	41	14	concept	concept	NOUN
ejpam-5453	41	15	as	as	ADP
ejpam-5453	41	16	an	an	DET
ejpam-5453	41	17	extension	extension	NOUN
ejpam-5453	41	18	of	of	ADP
ejpam-5453	41	19	open	open	ADJ
ejpam-5453	41	20	sets	set	NOUN
ejpam-5453	41	21	in	in	ADP
ejpam-5453	41	22	topology	topology	NOUN
ejpam-5453	41	23	[	[	X
ejpam-5453	41	24	4	4	NUM
ejpam-5453	41	25	,	,	PUNCT
ejpam-5453	41	26	20	20	NUM
ejpam-5453	41	27	]	]	PUNCT
ejpam-5453	41	28	.	.	PUNCT
ejpam-5453	42	1	hosny	hosny	PROPN
ejpam-5453	43	1	[	[	X
ejpam-5453	43	2	22	22	NUM
ejpam-5453	43	3	]	]	PUNCT
ejpam-5453	43	4	,	,	PUNCT
ejpam-5453	43	5	hosny	hosny	PROPN
ejpam-5453	43	6	and	and	CCONJ
ejpam-5453	43	7	al	al	PROPN
ejpam-5453	43	8	-	-	PUNCT
ejpam-5453	43	9	shami	shami	PROPN
ejpam-5453	43	10	[	[	X
ejpam-5453	43	11	26	26	NUM
ejpam-5453	43	12	]	]	PUNCT
ejpam-5453	43	13	presented	present	VERB
ejpam-5453	43	14	℘-nearly	℘-nearly	ADV
ejpam-5453	43	15	open	open	ADJ
ejpam-5453	43	16	and	and	CCONJ
ejpam-5453	43	17	℘-nearly	℘-nearly	ADJ
ejpam-5453	43	18	approximations	approximation	NOUN
ejpam-5453	43	19	via	via	ADP
ejpam-5453	43	20	ideals	ideal	NOUN
ejpam-5453	43	21	.	.	PUNCT
ejpam-5453	44	1	these	these	DET
ejpam-5453	44	2	manners	manner	NOUN
ejpam-5453	44	3	generalize	generalize	VERB
ejpam-5453	44	4	℘-nearly	℘-nearly	ADV
ejpam-5453	44	5	open	open	ADJ
ejpam-5453	44	6	and	and	CCONJ
ejpam-5453	44	7	℘-nearly	℘-nearly	ADJ
ejpam-5453	44	8	approximations	approximation	NOUN
ejpam-5453	44	9	.	.	PUNCT
ejpam-5453	45	1	meanwhile	meanwhile	ADV
ejpam-5453	45	2	,	,	PUNCT
ejpam-5453	45	3	various	various	ADJ
ejpam-5453	45	4	techniques	technique	NOUN
ejpam-5453	45	5	have	have	AUX
ejpam-5453	45	6	been	be	AUX
ejpam-5453	45	7	developed	develop	VERB
ejpam-5453	45	8	to	to	PART
ejpam-5453	45	9	construct	construct	VERB
ejpam-5453	45	10	topological	topological	ADJ
ejpam-5453	45	11	spaces	space	NOUN
ejpam-5453	45	12	using	use	VERB
ejpam-5453	45	13	neighborhood	neighborhood	NOUN
ejpam-5453	45	14	systems	system	NOUN
ejpam-5453	45	15	and	and	CCONJ
ejpam-5453	45	16	their	their	PRON
ejpam-5453	45	17	generalization	generalization	NOUN
ejpam-5453	45	18	.	.	PUNCT
ejpam-5453	46	1	in	in	ADP
ejpam-5453	46	2	this	this	DET
ejpam-5453	46	3	direction	direction	NOUN
ejpam-5453	46	4	,	,	PUNCT
ejpam-5453	46	5	initial	initial	ADJ
ejpam-5453	46	6	right	right	ADJ
ejpam-5453	46	7	neighborhoods	neighborhood	NOUN
ejpam-5453	46	8	were	be	AUX
ejpam-5453	46	9	presented	present	VERB
ejpam-5453	46	10	in	in	ADP
ejpam-5453	46	11	[	[	X
ejpam-5453	46	12	18	18	NUM
ejpam-5453	46	13	]	]	PUNCT
ejpam-5453	46	14	.	.	PUNCT
ejpam-5453	47	1	thereafter	thereafter	ADV
ejpam-5453	47	2	,	,	PUNCT
ejpam-5453	47	3	the	the	DET
ejpam-5453	47	4	remaining	remain	VERB
ejpam-5453	47	5	seven	seven	NUM
ejpam-5453	47	6	notions	notion	NOUN
ejpam-5453	47	7	of	of	ADP
ejpam-5453	47	8	initial	initial	ADJ
ejpam-5453	47	9	neighborhoods	neighborhood	NOUN
ejpam-5453	47	10	were	be	AUX
ejpam-5453	47	11	suggested	suggest	VERB
ejpam-5453	47	12	under	under	ADP
ejpam-5453	47	13	the	the	DET
ejpam-5453	47	14	name	name	NOUN
ejpam-5453	47	15	subset	subset	VERB
ejpam-5453	47	16	neighborhoods	neighborhood	NOUN
ejpam-5453	47	17	in	in	ADP
ejpam-5453	47	18	[	[	X
ejpam-5453	47	19	10	10	NUM
ejpam-5453	47	20	]	]	PUNCT
ejpam-5453	47	21	.	.	PUNCT
ejpam-5453	48	1	more	more	ADV
ejpam-5453	48	2	recently	recently	ADV
ejpam-5453	48	3	,	,	PUNCT
ejpam-5453	48	4	yildirim	yildirim	PROPN
ejpam-5453	49	1	[	[	X
ejpam-5453	49	2	43	43	NUM
ejpam-5453	49	3	]	]	PUNCT
ejpam-5453	49	4	formed	form	VERB
ejpam-5453	49	5	a	a	DET
ejpam-5453	49	6	topology	topology	NOUN
ejpam-5453	49	7	based	base	VERB
ejpam-5453	49	8	on	on	ADP
ejpam-5453	49	9	the	the	DET
ejpam-5453	49	10	subset	subset	ADJ
ejpam-5453	49	11	neighborhoods	neighborhood	NOUN
ejpam-5453	49	12	.	.	PUNCT
ejpam-5453	50	1	moreover	moreover	ADV
ejpam-5453	50	2	,	,	PUNCT
ejpam-5453	50	3	she	she	PRON
ejpam-5453	50	4	[	[	X
ejpam-5453	50	5	43	43	NUM
ejpam-5453	50	6	]	]	PUNCT
ejpam-5453	50	7	presented	present	VERB
ejpam-5453	50	8	near	near	ADP
ejpam-5453	50	9	open	open	ADJ
ejpam-5453	50	10	sets	set	NOUN
ejpam-5453	50	11	relying	rely	VERB
ejpam-5453	50	12	on	on	ADP
ejpam-5453	50	13	various	various	ADJ
ejpam-5453	50	14	types	type	NOUN
ejpam-5453	50	15	of	of	ADP
ejpam-5453	50	16	subset	subset	ADJ
ejpam-5453	50	17	neighborhoods	neighborhood	NOUN
ejpam-5453	50	18	,	,	PUNCT
ejpam-5453	50	19	namely	namely	ADV
ejpam-5453	50	20	s℘-near	s℘-near	ADJ
ejpam-5453	50	21	open	open	ADJ
ejpam-5453	50	22	sets	set	NOUN
ejpam-5453	50	23	.	.	PUNCT
ejpam-5453	51	1	in	in	ADP
ejpam-5453	51	2	[	[	X
ejpam-5453	51	3	43	43	NUM
ejpam-5453	51	4	]	]	PUNCT
ejpam-5453	51	5	,	,	PUNCT
ejpam-5453	51	6	approximations	approximation	NOUN
ejpam-5453	51	7	were	be	AUX
ejpam-5453	51	8	established	establish	VERB
ejpam-5453	51	9	and	and	CCONJ
ejpam-5453	51	10	evaluate	evaluate	VERB
ejpam-5453	51	11	related	relate	VERB
ejpam-5453	51	12	to	to	ADP
ejpam-5453	51	13	[	[	X
ejpam-5453	51	14	1	1	NUM
ejpam-5453	51	15	,	,	PUNCT
ejpam-5453	51	16	2	2	NUM
ejpam-5453	51	17	,	,	PUNCT
ejpam-5453	51	18	30	30	NUM
ejpam-5453	51	19	]	]	PUNCT
ejpam-5453	51	20	under	under	ADP
ejpam-5453	51	21	the	the	DET
ejpam-5453	51	22	restricted	restricted	ADJ
ejpam-5453	51	23	condition	condition	NOUN
ejpam-5453	51	24	of	of	ADP
ejpam-5453	51	25	similarity	similarity	NOUN
ejpam-5453	51	26	relations	relation	NOUN
ejpam-5453	51	27	.	.	PUNCT
ejpam-5453	52	1	a	a	DET
ejpam-5453	52	2	nonempty	nonempty	ADJ
ejpam-5453	52	3	collection	collection	NOUN
ejpam-5453	52	4	d	d	NOUN
ejpam-5453	52	5	of	of	ADP
ejpam-5453	52	6	subsets	subset	NOUN
ejpam-5453	52	7	of	of	ADP
ejpam-5453	52	8	a	a	DET
ejpam-5453	52	9	set	set	NOUN
ejpam-5453	52	10	v	v	NOUN
ejpam-5453	52	11	is	be	AUX
ejpam-5453	52	12	known	know	VERB
ejpam-5453	52	13	an	an	DET
ejpam-5453	52	14	ideal	ideal	NOUN
ejpam-5453	52	15	on	on	ADP
ejpam-5453	52	16	v	v	NUM
ejpam-5453	52	17	,	,	PUNCT
ejpam-5453	52	18	if	if	SCONJ
ejpam-5453	52	19	d	d	NOUN
ejpam-5453	52	20	is	be	AUX
ejpam-5453	52	21	closed	close	VERB
ejpam-5453	52	22	under	under	ADP
ejpam-5453	52	23	finite	finite	ADJ
ejpam-5453	52	24	unions	union	NOUN
ejpam-5453	52	25	and	and	CCONJ
ejpam-5453	52	26	subsets	subset	NOUN
ejpam-5453	52	27	[	[	X
ejpam-5453	52	28	28	28	NUM
ejpam-5453	52	29	]	]	PUNCT
ejpam-5453	52	30	.	.	PUNCT
ejpam-5453	53	1	ideal	ideal	PROPN
ejpam-5453	53	2	in	in	ADP
ejpam-5453	53	3	topological	topological	ADJ
ejpam-5453	53	4	spaces	space	NOUN
ejpam-5453	53	5	was	be	AUX
ejpam-5453	53	6	first	first	ADV
ejpam-5453	53	7	studied	study	VERB
ejpam-5453	53	8	in	in	ADP
ejpam-5453	53	9	(	(	PUNCT
ejpam-5453	53	10	see	see	VERB
ejpam-5453	53	11	:	:	PUNCT
ejpam-5453	53	12	[	[	X
ejpam-5453	53	13	32	32	NUM
ejpam-5453	53	14	,	,	PUNCT
ejpam-5453	53	15	41	41	NUM
ejpam-5453	53	16	]	]	PUNCT
ejpam-5453	53	17	)	)	PUNCT
ejpam-5453	53	18	.	.	PUNCT
ejpam-5453	54	1	thereafter	thereafter	ADV
ejpam-5453	54	2	,	,	PUNCT
ejpam-5453	54	3	high	high	ADJ
ejpam-5453	54	4	-	-	PUNCT
ejpam-5453	54	5	quality	quality	NOUN
ejpam-5453	54	6	papers	paper	NOUN
ejpam-5453	54	7	presented	present	VERB
ejpam-5453	54	8	(	(	PUNCT
ejpam-5453	54	9	see	see	VERB
ejpam-5453	54	10	:	:	PUNCT
ejpam-5453	54	11	[	[	X
ejpam-5453	54	12	17	17	NUM
ejpam-5453	54	13	,	,	PUNCT
ejpam-5453	54	14	19	19	NUM
ejpam-5453	54	15	,	,	PUNCT
ejpam-5453	54	16	28	28	NUM
ejpam-5453	54	17	]	]	PUNCT
ejpam-5453	54	18	)	)	PUNCT
ejpam-5453	54	19	.	.	PUNCT
ejpam-5453	55	1	the	the	DET
ejpam-5453	55	2	primary	primary	ADJ
ejpam-5453	55	3	advantage	advantage	NOUN
ejpam-5453	55	4	of	of	ADP
ejpam-5453	55	5	incorporating	incorporate	VERB
ejpam-5453	55	6	ideals	ideal	NOUN
ejpam-5453	55	7	into	into	ADP
ejpam-5453	55	8	this	this	DET
ejpam-5453	55	9	theory	theory	NOUN
ejpam-5453	55	10	was	be	AUX
ejpam-5453	55	11	their	their	PRON
ejpam-5453	55	12	ability	ability	NOUN
ejpam-5453	55	13	to	to	PART
ejpam-5453	55	14	reduce	reduce	VERB
ejpam-5453	55	15	vagueness	vagueness	NOUN
ejpam-5453	55	16	by	by	ADP
ejpam-5453	55	17	refining	refine	VERB
ejpam-5453	55	18	the	the	DET
ejpam-5453	55	19	boundaries	boundary	NOUN
ejpam-5453	55	20	of	of	ADP
ejpam-5453	55	21	concepts	concept	NOUN
ejpam-5453	55	22	.	.	PUNCT
ejpam-5453	56	1	so	so	ADV
ejpam-5453	56	2	,	,	PUNCT
ejpam-5453	56	3	it	it	PRON
ejpam-5453	56	4	increases	increase	VERB
ejpam-5453	56	5	the	the	DET
ejpam-5453	56	6	certain	certain	ADJ
ejpam-5453	56	7	knowledge	knowledge	NOUN
ejpam-5453	56	8	,	,	PUNCT
ejpam-5453	56	9	thereby	thereby	ADV
ejpam-5453	56	10	enhancing	enhance	VERB
ejpam-5453	56	11	the	the	DET
ejpam-5453	56	12	reliability	reliability	NOUN
ejpam-5453	56	13	of	of	ADP
ejpam-5453	56	14	decision	decision	NOUN
ejpam-5453	56	15	making	make	VERB
ejpam-5453	56	16	methods	method	NOUN
ejpam-5453	56	17	.	.	PUNCT
ejpam-5453	57	1	accordingly	accordingly	ADV
ejpam-5453	57	2	,	,	PUNCT
ejpam-5453	57	3	using	use	VERB
ejpam-5453	57	4	ideals	ideal	NOUN
ejpam-5453	57	5	is	be	AUX
ejpam-5453	57	6	a	a	DET
ejpam-5453	57	7	robust	robust	ADJ
ejpam-5453	57	8	technique	technique	NOUN
ejpam-5453	57	9	for	for	ADP
ejpam-5453	57	10	clarifying	clarify	VERB
ejpam-5453	57	11	and	and	CCONJ
ejpam-5453	57	12	precisely	precisely	ADV
ejpam-5453	57	13	defining	define	VERB
ejpam-5453	57	14	concepts	concept	NOUN
ejpam-5453	57	15	.	.	PUNCT
ejpam-5453	58	1	so	so	ADV
ejpam-5453	58	2	,	,	PUNCT
ejpam-5453	58	3	the	the	DET
ejpam-5453	58	4	exploration	exploration	NOUN
ejpam-5453	58	5	of	of	ADP
ejpam-5453	58	6	rough	rough	ADJ
ejpam-5453	58	7	set	set	NOUN
ejpam-5453	58	8	theory	theory	NOUN
ejpam-5453	58	9	with	with	ADP
ejpam-5453	58	10	ideals	ideal	NOUN
ejpam-5453	58	11	has	have	AUX
ejpam-5453	58	12	become	become	VERB
ejpam-5453	58	13	a	a	DET
ejpam-5453	58	14	prominent	prominent	ADJ
ejpam-5453	58	15	and	and	CCONJ
ejpam-5453	58	16	engaging	engaging	ADJ
ejpam-5453	58	17	research	research	NOUN
ejpam-5453	58	18	area	area	NOUN
ejpam-5453	58	19	,	,	PUNCT
ejpam-5453	58	20	attracting	attract	VERB
ejpam-5453	58	21	m.	m.	NOUN
ejpam-5453	58	22	hosny	hosny	PROPN
ejpam-5453	58	23	/	/	SYM
ejpam-5453	58	24	eur	eur	PROPN
ejpam-5453	58	25	.	.	PUNCT
ejpam-5453	59	1	j.	j.	PROPN
ejpam-5453	59	2	pure	pure	PROPN
ejpam-5453	59	3	appl	appl	PROPN
ejpam-5453	59	4	.	.	PROPN
ejpam-5453	59	5	math	math	PROPN
ejpam-5453	59	6	,	,	PUNCT
ejpam-5453	59	7	17	17	NUM
ejpam-5453	59	8	(	(	PUNCT
ejpam-5453	59	9	4	4	NUM
ejpam-5453	59	10	)	)	PUNCT
ejpam-5453	59	11	(	(	PUNCT
ejpam-5453	59	12	2024	2024	NUM
ejpam-5453	59	13	)	)	PUNCT
ejpam-5453	59	14	,	,	PUNCT
ejpam-5453	59	15	2843	2843	NUM
ejpam-5453	59	16	-	-	SYM
ejpam-5453	59	17	2877	2877	NUM
ejpam-5453	59	18	2845	2845	NUM
ejpam-5453	59	19	significant	significant	ADJ
ejpam-5453	59	20	attention	attention	NOUN
ejpam-5453	59	21	from	from	ADP
ejpam-5453	59	22	researchers	researcher	NOUN
ejpam-5453	59	23	(	(	PUNCT
ejpam-5453	59	24	see	see	VERB
ejpam-5453	59	25	[	[	X
ejpam-5453	59	26	20	20	NUM
ejpam-5453	59	27	,	,	PUNCT
ejpam-5453	59	28	21	21	NUM
ejpam-5453	59	29	,	,	PUNCT
ejpam-5453	59	30	23	23	NUM
ejpam-5453	59	31	,	,	PUNCT
ejpam-5453	59	32	24	24	NUM
ejpam-5453	59	33	,	,	PUNCT
ejpam-5453	59	34	27	27	NUM
ejpam-5453	59	35	,	,	PUNCT
ejpam-5453	59	36	35	35	NUM
ejpam-5453	59	37	]	]	PUNCT
ejpam-5453	59	38	)	)	PUNCT
ejpam-5453	59	39	.	.	PUNCT
ejpam-5453	60	1	hence	hence	ADV
ejpam-5453	60	2	,	,	PUNCT
ejpam-5453	60	3	ideals	ideal	NOUN
ejpam-5453	60	4	have	have	AUX
ejpam-5453	60	5	been	be	AUX
ejpam-5453	60	6	widely	widely	ADV
ejpam-5453	60	7	applied	apply	VERB
ejpam-5453	60	8	within	within	ADP
ejpam-5453	60	9	this	this	DET
ejpam-5453	60	10	theoretical	theoretical	ADJ
ejpam-5453	60	11	framework	framework	NOUN
ejpam-5453	60	12	.	.	PUNCT
ejpam-5453	61	1	the	the	DET
ejpam-5453	61	2	aim	aim	NOUN
ejpam-5453	61	3	of	of	ADP
ejpam-5453	61	4	this	this	DET
ejpam-5453	61	5	manuscript	manuscript	NOUN
ejpam-5453	61	6	is	be	AUX
ejpam-5453	61	7	to	to	PART
ejpam-5453	61	8	advance	advance	VERB
ejpam-5453	61	9	research	research	NOUN
ejpam-5453	61	10	in	in	ADP
ejpam-5453	61	11	these	these	DET
ejpam-5453	61	12	directions	direction	NOUN
ejpam-5453	61	13	.	.	PUNCT
ejpam-5453	62	1	it	it	PRON
ejpam-5453	62	2	highlights	highlight	VERB
ejpam-5453	62	3	that	that	SCONJ
ejpam-5453	62	4	ideals	ideal	NOUN
ejpam-5453	62	5	are	be	AUX
ejpam-5453	62	6	crucial	crucial	ADJ
ejpam-5453	62	7	in	in	ADP
ejpam-5453	62	8	this	this	DET
ejpam-5453	62	9	study	study	NOUN
ejpam-5453	62	10	.	.	PUNCT
ejpam-5453	63	1	this	this	DET
ejpam-5453	63	2	work	work	NOUN
ejpam-5453	63	3	comprises	comprise	VERB
ejpam-5453	63	4	seven	seven	NUM
ejpam-5453	63	5	sections	section	NOUN
ejpam-5453	63	6	.	.	PUNCT
ejpam-5453	64	1	the	the	DET
ejpam-5453	64	2	fundamental	fundamental	ADJ
ejpam-5453	64	3	definitions	definition	NOUN
ejpam-5453	64	4	and	and	CCONJ
ejpam-5453	64	5	properties	property	NOUN
ejpam-5453	64	6	are	be	AUX
ejpam-5453	64	7	given	give	VERB
ejpam-5453	64	8	in	in	ADP
ejpam-5453	64	9	section	section	NOUN
ejpam-5453	64	10	2	2	NUM
ejpam-5453	64	11	.	.	PUNCT
ejpam-5453	64	12	afterwards	afterwards	ADV
ejpam-5453	64	13	,	,	PUNCT
ejpam-5453	64	14	section	section	NOUN
ejpam-5453	64	15	3	3	NUM
ejpam-5453	64	16	introduces	introduce	NOUN
ejpam-5453	64	17	and	and	CCONJ
ejpam-5453	64	18	examines	examine	VERB
ejpam-5453	64	19	new	new	ADJ
ejpam-5453	64	20	s℘-nearly	s℘-nearly	ADV
ejpam-5453	64	21	open	open	ADJ
ejpam-5453	64	22	sets	set	NOUN
ejpam-5453	64	23	related	relate	VERB
ejpam-5453	64	24	to	to	ADP
ejpam-5453	64	25	an	an	DET
ejpam-5453	64	26	ideal	ideal	ADJ
ejpam-5453	64	27	d	d	NOUN
ejpam-5453	64	28	,	,	PUNCT
ejpam-5453	64	29	denoted	denote	VERB
ejpam-5453	64	30	by	by	ADP
ejpam-5453	64	31	d	d	PROPN
ejpam-5453	64	32	-	-	NOUN
ejpam-5453	64	33	αs℘-open	αs℘-open	ADJ
ejpam-5453	64	34	,	,	PUNCT
ejpam-5453	64	35	d	d	X
ejpam-5453	64	36	-	-	PUNCT
ejpam-5453	64	37	θβs℘open	θβs℘open	ADJ
ejpam-5453	64	38	,	,	PUNCT
ejpam-5453	64	39	d	d	NOUN
ejpam-5453	64	40	-	-	PUNCT
ejpam-5453	64	41	ps℘-open	ps℘-open	ADJ
ejpam-5453	64	42	,	,	PUNCT
ejpam-5453	64	43	d	d	NOUN
ejpam-5453	64	44	-	-	PUNCT
ejpam-5453	64	45	ss℘-open	ss℘-open	ADJ
ejpam-5453	64	46	,	,	PUNCT
ejpam-5453	64	47	d	d	NOUN
ejpam-5453	64	48	-	-	PUNCT
ejpam-5453	64	49	βs℘-open	βs℘-open	ADJ
ejpam-5453	64	50	and	and	CCONJ
ejpam-5453	64	51	d	d	ADJ
ejpam-5453	64	52	-	-	ADJ
ejpam-5453	64	53	θβs℘-open	θβs℘-open	ADJ
ejpam-5453	64	54	sets	set	NOUN
ejpam-5453	64	55	.	.	PUNCT
ejpam-5453	65	1	after	after	ADP
ejpam-5453	65	2	substituting	substitute	VERB
ejpam-5453	65	3	d	d	NOUN
ejpam-5453	65	4	=	=	PUNCT
ejpam-5453	65	5	{	{	PUNCT
ejpam-5453	65	6	∅	∅	NOUN
ejpam-5453	65	7	}	}	PUNCT
ejpam-5453	65	8	into	into	ADP
ejpam-5453	65	9	the	the	DET
ejpam-5453	65	10	current	current	ADJ
ejpam-5453	65	11	definitions	definition	NOUN
ejpam-5453	65	12	,	,	PUNCT
ejpam-5453	65	13	we	we	PRON
ejpam-5453	65	14	find	find	VERB
ejpam-5453	65	15	that	that	SCONJ
ejpam-5453	65	16	the	the	DET
ejpam-5453	65	17	resulting	result	VERB
ejpam-5453	65	18	definitions	definition	NOUN
ejpam-5453	65	19	are	be	AUX
ejpam-5453	65	20	equivalent	equivalent	ADJ
ejpam-5453	65	21	to	to	ADP
ejpam-5453	65	22	those	those	PRON
ejpam-5453	65	23	defined	define	VERB
ejpam-5453	65	24	by	by	ADP
ejpam-5453	65	25	yildirim	yildirim	PROPN
ejpam-5453	66	1	[	[	X
ejpam-5453	66	2	43	43	NUM
ejpam-5453	66	3	]	]	PUNCT
ejpam-5453	66	4	.	.	PUNCT
ejpam-5453	67	1	this	this	DET
ejpam-5453	67	2	equivalence	equivalence	NOUN
ejpam-5453	67	3	shows	show	VERB
ejpam-5453	67	4	that	that	SCONJ
ejpam-5453	67	5	the	the	DET
ejpam-5453	67	6	specific	specific	ADJ
ejpam-5453	67	7	case	case	NOUN
ejpam-5453	67	8	of	of	ADP
ejpam-5453	67	9	the	the	DET
ejpam-5453	67	10	current	current	ADJ
ejpam-5453	67	11	framework	framework	NOUN
ejpam-5453	67	12	are	be	AUX
ejpam-5453	67	13	coincided	coincide	VERB
ejpam-5453	67	14	with	with	ADP
ejpam-5453	67	15	yildirim	yildirim	PROPN
ejpam-5453	67	16	’s	’s	PART
ejpam-5453	67	17	definitions	definition	NOUN
ejpam-5453	67	18	.	.	PUNCT
ejpam-5453	68	1	so	so	ADV
ejpam-5453	68	2	,	,	PUNCT
ejpam-5453	68	3	the	the	DET
ejpam-5453	68	4	last	last	ADJ
ejpam-5453	68	5	definitions	definition	NOUN
ejpam-5453	68	6	[	[	X
ejpam-5453	68	7	43	43	NUM
ejpam-5453	68	8	]	]	PUNCT
ejpam-5453	68	9	are	be	AUX
ejpam-5453	68	10	considered	consider	VERB
ejpam-5453	68	11	as	as	ADP
ejpam-5453	68	12	a	a	DET
ejpam-5453	68	13	special	special	ADJ
ejpam-5453	68	14	case	case	NOUN
ejpam-5453	68	15	of	of	ADP
ejpam-5453	68	16	the	the	DET
ejpam-5453	68	17	current	current	ADJ
ejpam-5453	68	18	ones	one	NOUN
ejpam-5453	68	19	.	.	PUNCT
ejpam-5453	69	1	moreover	moreover	ADV
ejpam-5453	69	2	,	,	PUNCT
ejpam-5453	69	3	the	the	DET
ejpam-5453	69	4	essential	essential	ADJ
ejpam-5453	69	5	comparisons	comparison	NOUN
ejpam-5453	69	6	of	of	ADP
ejpam-5453	69	7	these	these	DET
ejpam-5453	69	8	manners	manner	NOUN
ejpam-5453	69	9	with	with	ADP
ejpam-5453	69	10	the	the	DET
ejpam-5453	69	11	prior	prior	ADJ
ejpam-5453	69	12	ones	one	NOUN
ejpam-5453	69	13	[	[	X
ejpam-5453	69	14	1	1	NUM
ejpam-5453	69	15	,	,	PUNCT
ejpam-5453	69	16	2	2	NUM
ejpam-5453	69	17	,	,	PUNCT
ejpam-5453	69	18	22	22	NUM
ejpam-5453	69	19	,	,	PUNCT
ejpam-5453	69	20	26	26	NUM
ejpam-5453	69	21	,	,	PUNCT
ejpam-5453	69	22	30	30	NUM
ejpam-5453	69	23	]	]	PUNCT
ejpam-5453	69	24	are	be	AUX
ejpam-5453	69	25	stated	state	VERB
ejpam-5453	69	26	.	.	PUNCT
ejpam-5453	70	1	furthermore	furthermore	ADV
ejpam-5453	70	2	,	,	PUNCT
ejpam-5453	70	3	it	it	PRON
ejpam-5453	70	4	is	be	AUX
ejpam-5453	70	5	demonstrated	demonstrate	VERB
ejpam-5453	70	6	that	that	SCONJ
ejpam-5453	70	7	d	d	NOUN
ejpam-5453	70	8	-	-	PUNCT
ejpam-5453	70	9	αs℘o(v	αs℘o(v	NUM
ejpam-5453	70	10	)	)	PUNCT
ejpam-5453	70	11	and	and	CCONJ
ejpam-5453	70	12	d	d	PROPN
ejpam-5453	70	13	-	-	PUNCT
ejpam-5453	70	14	ps℘o(v	ps℘o(v	NOUN
ejpam-5453	70	15	)	)	PUNCT
ejpam-5453	70	16	are	be	AUX
ejpam-5453	70	17	distinct	distinct	ADJ
ejpam-5453	70	18	(	(	PUNCT
ejpam-5453	70	19	see	see	VERB
ejpam-5453	70	20	example	example	NOUN
ejpam-5453	70	21	3.1	3.1	NUM
ejpam-5453	70	22	)	)	PUNCT
ejpam-5453	70	23	,	,	PUNCT
ejpam-5453	70	24	even	even	ADV
ejpam-5453	70	25	though	though	SCONJ
ejpam-5453	70	26	every	every	DET
ejpam-5453	70	27	element	element	NOUN
ejpam-5453	70	28	in	in	ADP
ejpam-5453	70	29	αs℘	αs℘	PROPN
ejpam-5453	70	30	is	be	AUX
ejpam-5453	70	31	in	in	ADP
ejpam-5453	70	32	ps℘o(v	ps℘o(v	PROPN
ejpam-5453	70	33	)	)	PUNCT
ejpam-5453	70	34	as	as	SCONJ
ejpam-5453	70	35	noted	note	VERB
ejpam-5453	70	36	in	in	ADP
ejpam-5453	70	37	[	[	X
ejpam-5453	70	38	43	43	NUM
ejpam-5453	70	39	]	]	PUNCT
ejpam-5453	70	40	.	.	PUNCT
ejpam-5453	71	1	section	section	NOUN
ejpam-5453	71	2	4	4	NUM
ejpam-5453	71	3	seeks	seek	VERB
ejpam-5453	71	4	to	to	PART
ejpam-5453	71	5	exhibit	exhibit	VERB
ejpam-5453	71	6	approximations	approximation	NOUN
ejpam-5453	71	7	derived	derive	VERB
ejpam-5453	71	8	from	from	ADP
ejpam-5453	71	9	s℘-nearly	s℘-nearly	ADV
ejpam-5453	71	10	open	open	ADJ
ejpam-5453	71	11	sets	set	NOUN
ejpam-5453	71	12	in	in	ADP
ejpam-5453	71	13	the	the	DET
ejpam-5453	71	14	context	context	NOUN
ejpam-5453	71	15	of	of	ADP
ejpam-5453	71	16	ideals	ideal	NOUN
ejpam-5453	71	17	.	.	PUNCT
ejpam-5453	72	1	the	the	DET
ejpam-5453	72	2	relationships	relationship	NOUN
ejpam-5453	72	3	between	between	ADP
ejpam-5453	72	4	these	these	DET
ejpam-5453	72	5	approximations	approximation	NOUN
ejpam-5453	72	6	and	and	CCONJ
ejpam-5453	72	7	those	those	PRON
ejpam-5453	72	8	proposed	propose	VERB
ejpam-5453	72	9	in	in	ADP
ejpam-5453	72	10	[	[	X
ejpam-5453	72	11	1	1	NUM
ejpam-5453	72	12	,	,	PUNCT
ejpam-5453	72	13	2	2	NUM
ejpam-5453	72	14	,	,	PUNCT
ejpam-5453	72	15	22	22	NUM
ejpam-5453	72	16	,	,	PUNCT
ejpam-5453	72	17	26	26	NUM
ejpam-5453	72	18	,	,	PUNCT
ejpam-5453	72	19	30	30	NUM
ejpam-5453	72	20	,	,	PUNCT
ejpam-5453	72	21	43	43	NUM
ejpam-5453	72	22	]	]	PUNCT
ejpam-5453	72	23	are	be	AUX
ejpam-5453	72	24	presented	present	VERB
ejpam-5453	72	25	in	in	ADP
ejpam-5453	72	26	theorems	theorem	NOUN
ejpam-5453	72	27	4.1	4.1	NUM
ejpam-5453	72	28	,	,	PUNCT
ejpam-5453	72	29	4.2	4.2	NUM
ejpam-5453	72	30	,	,	PUNCT
ejpam-5453	72	31	4.3	4.3	NUM
ejpam-5453	72	32	and	and	CCONJ
ejpam-5453	72	33	corollaries	corollary	NOUN
ejpam-5453	72	34	4.1	4.1	NUM
ejpam-5453	72	35	,	,	PUNCT
ejpam-5453	72	36	4.3	4.3	NUM
ejpam-5453	72	37	,	,	PUNCT
ejpam-5453	72	38	4.5	4.5	NUM
ejpam-5453	72	39	.	.	PUNCT
ejpam-5453	73	1	section	section	NOUN
ejpam-5453	73	2	5	5	NUM
ejpam-5453	73	3	focuses	focus	VERB
ejpam-5453	73	4	on	on	ADP
ejpam-5453	73	5	defining	define	VERB
ejpam-5453	73	6	three	three	NUM
ejpam-5453	73	7	types	type	NOUN
ejpam-5453	73	8	of	of	ADP
ejpam-5453	73	9	membership	membership	NOUN
ejpam-5453	73	10	functions	function	NOUN
ejpam-5453	73	11	.	.	PUNCT
ejpam-5453	74	1	thereafter	thereafter	ADV
ejpam-5453	74	2	,	,	PUNCT
ejpam-5453	74	3	the	the	DET
ejpam-5453	74	4	core	core	NOUN
ejpam-5453	74	5	features	feature	NOUN
ejpam-5453	74	6	and	and	CCONJ
ejpam-5453	74	7	relationships	relationship	NOUN
ejpam-5453	74	8	of	of	ADP
ejpam-5453	74	9	these	these	DET
ejpam-5453	74	10	functions	function	NOUN
ejpam-5453	74	11	are	be	AUX
ejpam-5453	74	12	derived	derive	VERB
ejpam-5453	74	13	and	and	CCONJ
ejpam-5453	74	14	compared	compare	VERB
ejpam-5453	74	15	to	to	ADP
ejpam-5453	74	16	the	the	DET
ejpam-5453	74	17	earlier	early	ADJ
ejpam-5453	74	18	ones	one	NOUN
ejpam-5453	74	19	in	in	ADP
ejpam-5453	74	20	[	[	X
ejpam-5453	74	21	1	1	NUM
ejpam-5453	74	22	,	,	PUNCT
ejpam-5453	74	23	22	22	NUM
ejpam-5453	74	24	,	,	PUNCT
ejpam-5453	74	25	26	26	NUM
ejpam-5453	74	26	]	]	PUNCT
ejpam-5453	74	27	.	.	PUNCT
ejpam-5453	75	1	in	in	ADP
ejpam-5453	75	2	section	section	NOUN
ejpam-5453	75	3	6	6	NUM
ejpam-5453	75	4	,	,	PUNCT
ejpam-5453	75	5	the	the	DET
ejpam-5453	75	6	paper	paper	NOUN
ejpam-5453	75	7	presents	present	VERB
ejpam-5453	75	8	a	a	DET
ejpam-5453	75	9	medical	medical	ADJ
ejpam-5453	75	10	application	application	NOUN
ejpam-5453	75	11	to	to	PART
ejpam-5453	75	12	show	show	VERB
ejpam-5453	75	13	the	the	DET
ejpam-5453	75	14	practical	practical	ADJ
ejpam-5453	75	15	applicability	applicability	NOUN
ejpam-5453	75	16	and	and	CCONJ
ejpam-5453	75	17	effectiveness	effectiveness	NOUN
ejpam-5453	75	18	of	of	ADP
ejpam-5453	75	19	the	the	DET
ejpam-5453	75	20	suggested	suggest	VERB
ejpam-5453	75	21	models	model	NOUN
ejpam-5453	75	22	and	and	CCONJ
ejpam-5453	75	23	exhibits	exhibit	VERB
ejpam-5453	75	24	how	how	SCONJ
ejpam-5453	75	25	ideals	ideal	NOUN
ejpam-5453	75	26	play	play	VERB
ejpam-5453	75	27	a	a	DET
ejpam-5453	75	28	crucial	crucial	ADJ
ejpam-5453	75	29	role	role	NOUN
ejpam-5453	75	30	in	in	ADP
ejpam-5453	75	31	decision	decision	NOUN
ejpam-5453	75	32	-	-	PUNCT
ejpam-5453	75	33	making	making	NOUN
ejpam-5453	75	34	.	.	PUNCT
ejpam-5453	76	1	accordingly	accordingly	ADV
ejpam-5453	76	2	,	,	PUNCT
ejpam-5453	76	3	the	the	DET
ejpam-5453	76	4	current	current	ADJ
ejpam-5453	76	5	manners	manner	NOUN
ejpam-5453	76	6	allow	allow	VERB
ejpam-5453	76	7	specialists	specialist	NOUN
ejpam-5453	76	8	to	to	PART
ejpam-5453	76	9	classify	classify	VERB
ejpam-5453	76	10	people	people	NOUN
ejpam-5453	76	11	with	with	ADP
ejpam-5453	76	12	chikungunya	chikungunya	NOUN
ejpam-5453	76	13	disease	disease	NOUN
ejpam-5453	76	14	easily	easily	ADV
ejpam-5453	76	15	and	and	CCONJ
ejpam-5453	76	16	with	with	ADP
ejpam-5453	76	17	high	high	ADJ
ejpam-5453	76	18	accuracy	accuracy	NOUN
ejpam-5453	76	19	.	.	PUNCT
ejpam-5453	77	1	eventually	eventually	ADV
ejpam-5453	77	2	,	,	PUNCT
ejpam-5453	77	3	a	a	DET
ejpam-5453	77	4	summary	summary	NOUN
ejpam-5453	77	5	of	of	ADP
ejpam-5453	77	6	the	the	DET
ejpam-5453	77	7	work	work	NOUN
ejpam-5453	77	8	’s	’s	PART
ejpam-5453	77	9	contributions	contribution	NOUN
ejpam-5453	77	10	and	and	CCONJ
ejpam-5453	77	11	recommendations	recommendation	NOUN
ejpam-5453	77	12	directions	direction	NOUN
ejpam-5453	77	13	are	be	AUX
ejpam-5453	77	14	given	give	VERB
ejpam-5453	77	15	.	.	PUNCT
ejpam-5453	78	1	2	2	X
ejpam-5453	78	2	.	.	X
ejpam-5453	78	3	preliminaries	preliminary	NOUN
ejpam-5453	78	4	definition	definition	NOUN
ejpam-5453	78	5	2.1	2.1	NUM
ejpam-5453	78	6	.	.	PUNCT
ejpam-5453	79	1	[	[	X
ejpam-5453	79	2	1	1	NUM
ejpam-5453	79	3	,	,	PUNCT
ejpam-5453	79	4	14	14	NUM
ejpam-5453	79	5	,	,	PUNCT
ejpam-5453	79	6	15	15	NUM
ejpam-5453	79	7	,	,	PUNCT
ejpam-5453	79	8	31	31	NUM
ejpam-5453	79	9	]	]	PUNCT
ejpam-5453	79	10	let	let	VERB
ejpam-5453	79	11	υ	υ	PRON
ejpam-5453	79	12	be	be	AUX
ejpam-5453	79	13	an	an	DET
ejpam-5453	79	14	arbitrary	arbitrary	ADJ
ejpam-5453	79	15	binary	binary	ADJ
ejpam-5453	79	16	relation	relation	NOUN
ejpam-5453	79	17	on	on	ADP
ejpam-5453	79	18	a	a	DET
ejpam-5453	79	19	finite	finite	NOUN
ejpam-5453	79	20	set	set	VERB
ejpam-5453	79	21	v	v	ADP
ejpam-5453	79	22	̸=	̸=	PROPN
ejpam-5453	79	23	∅	∅	NOUN
ejpam-5453	79	24	and	and	CCONJ
ejpam-5453	79	25	t	t	NOUN
ejpam-5453	79	26	∈	∈	PROPN
ejpam-5453	80	1	v.	v.	CCONJ
ejpam-5453	80	2	then	then	ADV
ejpam-5453	80	3	,	,	PUNCT
ejpam-5453	80	4	the	the	DET
ejpam-5453	80	5	℘-neighborhood	℘-neighborhood	NOUN
ejpam-5453	80	6	of	of	ADP
ejpam-5453	80	7	t	t	PROPN
ejpam-5453	80	8	∈	∈	PROPN
ejpam-5453	80	9	v	v	NOUN
ejpam-5453	80	10	(	(	PUNCT
ejpam-5453	80	11	in	in	ADP
ejpam-5453	80	12	brief	brief	ADJ
ejpam-5453	80	13	,	,	PUNCT
ejpam-5453	80	14	ℵ℘(t	ℵ℘(t	NOUN
ejpam-5453	80	15	)	)	PUNCT
ejpam-5453	80	16	)	)	PUNCT
ejpam-5453	80	17	,	,	PUNCT
ejpam-5453	80	18	∀℘	∀℘	PROPN
ejpam-5453	80	19	∈	∈	PROPN
ejpam-5453	80	20	{	{	PUNCT
ejpam-5453	80	21	r	r	NOUN
ejpam-5453	80	22	,	,	PUNCT
ejpam-5453	80	23	l	l	NOUN
ejpam-5453	80	24	,	,	PUNCT
ejpam-5453	80	25	i	i	PRON
ejpam-5453	80	26	,	,	PUNCT
ejpam-5453	80	27	u	u	PROPN
ejpam-5453	80	28	,	,	PUNCT
ejpam-5453	80	29	⟨r⟩	⟨r⟩	PROPN
ejpam-5453	80	30	,	,	PUNCT
ejpam-5453	80	31	⟨l⟩	⟨l⟩	PROPN
ejpam-5453	80	32	,	,	PUNCT
ejpam-5453	80	33	⟨i⟩	⟨i⟩	PROPN
ejpam-5453	80	34	,	,	PUNCT
ejpam-5453	80	35	⟨u⟩	⟨u⟩	AUX
ejpam-5453	80	36	}	}	PUNCT
ejpam-5453	80	37	is	be	AUX
ejpam-5453	80	38	introduced	introduce	VERB
ejpam-5453	80	39	by	by	ADP
ejpam-5453	80	40	:	:	PUNCT
ejpam-5453	80	41	(	(	PUNCT
ejpam-5453	80	42	i	i	NOUN
ejpam-5453	80	43	)	)	PUNCT
ejpam-5453	80	44	r	r	NOUN
ejpam-5453	80	45	-	-	PUNCT
ejpam-5453	80	46	neighborhood	neighborhood	NOUN
ejpam-5453	80	47	:	:	PUNCT
ejpam-5453	80	48	ℵr(t	ℵr(t	NUM
ejpam-5453	80	49	)	)	PUNCT
ejpam-5453	80	50	=	=	PRON
ejpam-5453	81	1	{	{	PUNCT
ejpam-5453	81	2	s	s	NOUN
ejpam-5453	81	3	∈	∈	NOUN
ejpam-5453	81	4	v	v	NOUN
ejpam-5453	81	5	:	:	PUNCT
ejpam-5453	81	6	(	(	PUNCT
ejpam-5453	81	7	t	t	PROPN
ejpam-5453	81	8	,	,	PUNCT
ejpam-5453	81	9	s	s	PART
ejpam-5453	81	10	)	)	PUNCT
ejpam-5453	81	11	∈	∈	PROPN
ejpam-5453	81	12	υ	υ	NOUN
ejpam-5453	81	13	}	}	PUNCT
ejpam-5453	81	14	.	.	PUNCT
ejpam-5453	82	1	(	(	PUNCT
ejpam-5453	82	2	ii	ii	NOUN
ejpam-5453	82	3	)	)	PUNCT
ejpam-5453	82	4	l	l	NOUN
ejpam-5453	82	5	-	-	ADJ
ejpam-5453	82	6	left	leave	VERB
ejpam-5453	82	7	neighborhood	neighborhood	NOUN
ejpam-5453	82	8	:	:	PUNCT
ejpam-5453	82	9	ℵl(t	ℵl(t	X
ejpam-5453	82	10	)	)	PUNCT
ejpam-5453	82	11	=	=	PRON
ejpam-5453	82	12	{	{	PUNCT
ejpam-5453	82	13	a	a	DET
ejpam-5453	82	14	∈	∈	NOUN
ejpam-5453	82	15	v	v	NOUN
ejpam-5453	82	16	:	:	PUNCT
ejpam-5453	82	17	(	(	PUNCT
ejpam-5453	82	18	s	s	X
ejpam-5453	82	19	,	,	PUNCT
ejpam-5453	82	20	t	t	PROPN
ejpam-5453	82	21	)	)	PUNCT
ejpam-5453	82	22	∈	∈	PROPN
ejpam-5453	82	23	υ	υ	NOUN
ejpam-5453	82	24	}	}	PUNCT
ejpam-5453	82	25	.	.	PUNCT
ejpam-5453	83	1	(	(	PUNCT
ejpam-5453	83	2	iii	iii	NOUN
ejpam-5453	83	3	)	)	PUNCT
ejpam-5453	83	4	ℵi(t	ℵi(t	NOUN
ejpam-5453	83	5	)	)	PUNCT
ejpam-5453	83	6	=	=	SYM
ejpam-5453	83	7	ℵr(t	ℵr(t	X
ejpam-5453	83	8	)	)	PUNCT
ejpam-5453	83	9	∩	∩	NOUN
ejpam-5453	83	10	ℵl(t	ℵl(t	NOUN
ejpam-5453	83	11	)	)	PUNCT
ejpam-5453	83	12	.	.	PUNCT
ejpam-5453	84	1	(	(	PUNCT
ejpam-5453	84	2	iv	iv	X
ejpam-5453	84	3	)	)	PUNCT
ejpam-5453	84	4	ℵu	ℵu	NOUN
ejpam-5453	84	5	(	(	PUNCT
ejpam-5453	84	6	t	t	PROPN
ejpam-5453	84	7	)	)	PUNCT
ejpam-5453	84	8	=	=	SYM
ejpam-5453	84	9	ℵr(t	ℵr(t	X
ejpam-5453	84	10	)	)	PUNCT
ejpam-5453	84	11	∪	∪	ADP
ejpam-5453	84	12	ℵl(t	ℵl(t	NOUN
ejpam-5453	84	13	)	)	PUNCT
ejpam-5453	84	14	.	.	PUNCT
ejpam-5453	85	1	(	(	PUNCT
ejpam-5453	85	2	v	v	NOUN
ejpam-5453	85	3	)	)	PUNCT
ejpam-5453	85	4	ℵ⟨r⟩(t	ℵ⟨r⟩(t	NUM
ejpam-5453	85	5	)	)	PUNCT
ejpam-5453	86	1	=	=	SYM
ejpam-5453	86	2	⋂	⋂	PROPN
ejpam-5453	86	3	t∈ℵr(s	t∈ℵr(s	PROPN
ejpam-5453	86	4	)	)	PUNCT
ejpam-5453	86	5	ℵr(s	ℵr(s	NUM
ejpam-5453	86	6	)	)	PUNCT
ejpam-5453	86	7	.	.	PUNCT
ejpam-5453	87	1	(	(	PUNCT
ejpam-5453	87	2	vi	vi	NOUN
ejpam-5453	87	3	)	)	PUNCT
ejpam-5453	87	4	ℵ⟨l⟩(t	ℵ⟨l⟩(t	NUM
ejpam-5453	87	5	)	)	PUNCT
ejpam-5453	88	1	=	=	SYM
ejpam-5453	88	2	⋂	⋂	PROPN
ejpam-5453	88	3	t∈ℵl(s	t∈ℵl(s	PROPN
ejpam-5453	88	4	)	)	PUNCT
ejpam-5453	88	5	ℵl(s	ℵl(s	NUM
ejpam-5453	88	6	)	)	PUNCT
ejpam-5453	88	7	.	.	PUNCT
ejpam-5453	89	1	(	(	PUNCT
ejpam-5453	89	2	vii	vii	PROPN
ejpam-5453	89	3	)	)	PUNCT
ejpam-5453	89	4	ℵ⟨i⟩(t	ℵ⟨i⟩(t	NUM
ejpam-5453	89	5	)	)	PUNCT
ejpam-5453	89	6	=	=	SYM
ejpam-5453	89	7	ℵ⟨r⟩(t	ℵ⟨r⟩(t	X
ejpam-5453	89	8	)	)	PUNCT
ejpam-5453	89	9	∩	∩	NOUN
ejpam-5453	89	10	ℵ⟨l⟩(t	ℵ⟨l⟩(t	NUM
ejpam-5453	89	11	)	)	PUNCT
ejpam-5453	89	12	.	.	PUNCT
ejpam-5453	90	1	m.	m.	PROPN
ejpam-5453	90	2	hosny	hosny	PROPN
ejpam-5453	90	3	/	/	SYM
ejpam-5453	90	4	eur	eur	PROPN
ejpam-5453	90	5	.	.	PUNCT
ejpam-5453	91	1	j.	j.	PROPN
ejpam-5453	91	2	pure	pure	PROPN
ejpam-5453	91	3	appl	appl	PROPN
ejpam-5453	91	4	.	.	PROPN
ejpam-5453	91	5	math	math	PROPN
ejpam-5453	91	6	,	,	PUNCT
ejpam-5453	91	7	17	17	NUM
ejpam-5453	91	8	(	(	PUNCT
ejpam-5453	91	9	4	4	NUM
ejpam-5453	91	10	)	)	PUNCT
ejpam-5453	91	11	(	(	PUNCT
ejpam-5453	91	12	2024	2024	NUM
ejpam-5453	91	13	)	)	PUNCT
ejpam-5453	91	14	,	,	PUNCT
ejpam-5453	91	15	2843	2843	NUM
ejpam-5453	91	16	-	-	SYM
ejpam-5453	91	17	2877	2877	NUM
ejpam-5453	91	18	2846	2846	NUM
ejpam-5453	91	19	(	(	PUNCT
ejpam-5453	91	20	viii	viii	NOUN
ejpam-5453	91	21	)	)	PUNCT
ejpam-5453	91	22	ℵ⟨u⟩(t	ℵ⟨u⟩(t	NUM
ejpam-5453	91	23	)	)	PUNCT
ejpam-5453	92	1	=	=	SYM
ejpam-5453	92	2	ℵ⟨r⟩(t	ℵ⟨r⟩(t	X
ejpam-5453	92	3	)	)	PUNCT
ejpam-5453	92	4	∪	∪	ADP
ejpam-5453	92	5	ℵ⟨l⟩(t	ℵ⟨l⟩(t	NUM
ejpam-5453	92	6	)	)	PUNCT
ejpam-5453	92	7	.	.	PUNCT
ejpam-5453	93	1	(	(	PUNCT
ejpam-5453	93	2	ix	ix	ADP
ejpam-5453	93	3	)	)	PUNCT
ejpam-5453	93	4	the	the	DET
ejpam-5453	93	5	triple	triple	ADJ
ejpam-5453	93	6	(	(	PUNCT
ejpam-5453	93	7	v	v	NOUN
ejpam-5453	93	8	,	,	PUNCT
ejpam-5453	93	9	υ	υ	NOUN
ejpam-5453	93	10	,	,	PUNCT
ejpam-5453	93	11	π℘	π℘	NUM
ejpam-5453	93	12	)	)	PUNCT
ejpam-5453	93	13	is	be	AUX
ejpam-5453	93	14	known	know	VERB
ejpam-5453	93	15	as	as	ADP
ejpam-5453	93	16	a	a	DET
ejpam-5453	93	17	℘-neighborhood	℘-neighborhood	NOUN
ejpam-5453	93	18	space	space	NOUN
ejpam-5453	93	19	(	(	PUNCT
ejpam-5453	93	20	or	or	CCONJ
ejpam-5453	93	21	℘-ns	℘-ns	ADV
ejpam-5453	93	22	for	for	ADP
ejpam-5453	93	23	short	short	ADJ
ejpam-5453	93	24	)	)	PUNCT
ejpam-5453	93	25	,	,	PUNCT
ejpam-5453	93	26	with	with	ADP
ejpam-5453	93	27	π℘	π℘	NOUN
ejpam-5453	93	28	being	be	AUX
ejpam-5453	93	29	a	a	DET
ejpam-5453	93	30	mapping	mapping	NOUN
ejpam-5453	93	31	from	from	ADP
ejpam-5453	93	32	v	v	NUM
ejpam-5453	93	33	to	to	ADP
ejpam-5453	93	34	p	p	NOUN
ejpam-5453	93	35	(	(	PUNCT
ejpam-5453	93	36	v	v	NOUN
ejpam-5453	93	37	)	)	PUNCT
ejpam-5453	93	38	that	that	PRON
ejpam-5453	93	39	assigns	assign	VERB
ejpam-5453	93	40	each	each	DET
ejpam-5453	93	41	t	t	NOUN
ejpam-5453	93	42	∈	∈	PROPN
ejpam-5453	93	43	v	v	NOUN
ejpam-5453	93	44	with	with	ADP
ejpam-5453	93	45	a	a	DET
ejpam-5453	93	46	℘-neighborhood	℘-neighborhood	NOUN
ejpam-5453	93	47	.	.	PUNCT
ejpam-5453	94	1	theorem	theorem	VERB
ejpam-5453	94	2	2.1	2.1	NUM
ejpam-5453	94	3	.	.	PUNCT
ejpam-5453	95	1	[	[	X
ejpam-5453	95	2	1	1	NUM
ejpam-5453	95	3	,	,	PUNCT
ejpam-5453	95	4	2	2	NUM
ejpam-5453	95	5	,	,	PUNCT
ejpam-5453	95	6	30	30	NUM
ejpam-5453	95	7	]	]	PUNCT
ejpam-5453	95	8	the	the	DET
ejpam-5453	95	9	topology	topology	NOUN
ejpam-5453	95	10	on	on	ADP
ejpam-5453	95	11	v	v	NUM
ejpam-5453	95	12	derived	derive	VERB
ejpam-5453	95	13	from	from	ADP
ejpam-5453	95	14	an	an	DET
ejpam-5453	95	15	approximation	approximation	NOUN
ejpam-5453	95	16	space	space	NOUN
ejpam-5453	95	17	(	(	PUNCT
ejpam-5453	95	18	v	v	NOUN
ejpam-5453	95	19	,	,	PUNCT
ejpam-5453	95	20	υ	υ	NOUN
ejpam-5453	95	21	)	)	PUNCT
ejpam-5453	95	22	given	give	VERB
ejpam-5453	95	23	by	by	ADP
ejpam-5453	95	24	τ℘	τ℘	NOUN
ejpam-5453	95	25	=	=	SYM
ejpam-5453	95	26	{	{	PUNCT
ejpam-5453	95	27	m	m	PROPN
ejpam-5453	95	28	⊆	⊆	NUM
ejpam-5453	95	29	v	v	NOUN
ejpam-5453	95	30	:	:	PUNCT
ejpam-5453	95	31	ℵ℘(t	ℵ℘(t	X
ejpam-5453	95	32	)	)	PUNCT
ejpam-5453	96	1	⊆	⊆	NUM
ejpam-5453	96	2	m,∀t	m,∀t	ADJ
ejpam-5453	96	3	∈	∈	PROPN
ejpam-5453	96	4	m	m	PRON
ejpam-5453	96	5	}	}	PUNCT
ejpam-5453	96	6	,	,	PUNCT
ejpam-5453	96	7	∀℘.	∀℘.	PROPN
ejpam-5453	96	8	sets	set	NOUN
ejpam-5453	96	9	in	in	ADP
ejpam-5453	96	10	τ℘	τ℘	NUM
ejpam-5453	96	11	are	be	AUX
ejpam-5453	96	12	termed	term	VERB
ejpam-5453	96	13	℘-open	℘-open	ADJ
ejpam-5453	96	14	,	,	PUNCT
ejpam-5453	96	15	their	their	PRON
ejpam-5453	96	16	complements	complement	NOUN
ejpam-5453	96	17	are	be	AUX
ejpam-5453	96	18	℘-closed	℘-close	VERB
ejpam-5453	96	19	set	set	VERB
ejpam-5453	96	20	and	and	CCONJ
ejpam-5453	96	21	all	all	DET
ejpam-5453	96	22	℘-closed	℘-close	VERB
ejpam-5453	96	23	set	set	NOUN
ejpam-5453	96	24	is	be	AUX
ejpam-5453	96	25	denoted	denote	VERB
ejpam-5453	96	26	by	by	ADP
ejpam-5453	96	27	ℸ℘.	ℸ℘.	NOUN
ejpam-5453	96	28	definition	definition	NOUN
ejpam-5453	96	29	2.2	2.2	NUM
ejpam-5453	96	30	.	.	PUNCT
ejpam-5453	97	1	[	[	X
ejpam-5453	97	2	1	1	NUM
ejpam-5453	97	3	,	,	PUNCT
ejpam-5453	97	4	2	2	NUM
ejpam-5453	97	5	,	,	PUNCT
ejpam-5453	97	6	30	30	NUM
ejpam-5453	97	7	]	]	PUNCT
ejpam-5453	97	8	the	the	DET
ejpam-5453	97	9	℘-lower	℘-lower	NOUN
ejpam-5453	97	10	and	and	CCONJ
ejpam-5453	97	11	℘-upper	℘-upper	ADJ
ejpam-5453	97	12	approximations	approximation	NOUN
ejpam-5453	97	13	,	,	PUNCT
ejpam-5453	97	14	boundary	boundary	ADJ
ejpam-5453	97	15	region	region	NOUN
ejpam-5453	97	16	and	and	CCONJ
ejpam-5453	97	17	accuracy	accuracy	NOUN
ejpam-5453	97	18	of	of	ADP
ejpam-5453	97	19	a	a	DET
ejpam-5453	97	20	set	set	NOUN
ejpam-5453	97	21	m	m	NOUN
ejpam-5453	97	22	are	be	AUX
ejpam-5453	97	23	n℘(m	n℘(m	ADJ
ejpam-5453	97	24	)	)	PUNCT
ejpam-5453	98	1	=	=	SYM
ejpam-5453	98	2	∪{n	∪{n	PROPN
ejpam-5453	98	3	∈	∈	NOUN
ejpam-5453	98	4	τ℘	τ℘	NUM
ejpam-5453	98	5	:	:	PUNCT
ejpam-5453	98	6	n	n	PROPN
ejpam-5453	98	7	⊆	⊆	NUM
ejpam-5453	98	8	m	m	NOUN
ejpam-5453	98	9	}	}	PUNCT
ejpam-5453	98	10	=	=	SYM
ejpam-5453	98	11	int℘(m	int℘(m	X
ejpam-5453	98	12	)	)	PUNCT
ejpam-5453	98	13	(	(	PUNCT
ejpam-5453	98	14	represents	represent	VERB
ejpam-5453	98	15	the	the	DET
ejpam-5453	98	16	topological	topological	ADJ
ejpam-5453	98	17	℘-interior	℘-interior	ADJ
ejpam-5453	98	18	operator	operator	NOUN
ejpam-5453	98	19	)	)	PUNCT
ejpam-5453	98	20	,	,	PUNCT
ejpam-5453	98	21	n℘(m	n℘(m	ADJ
ejpam-5453	98	22	)	)	PUNCT
ejpam-5453	98	23	=	=	SYM
ejpam-5453	99	1	∩{q	∩{q	PROPN
ejpam-5453	99	2	:	:	PUNCT
ejpam-5453	99	3	q	q	NOUN
ejpam-5453	99	4	′	′	NUM
ejpam-5453	99	5	∈	∈	NOUN
ejpam-5453	99	6	τ℘	τ℘	NOUN
ejpam-5453	99	7	and	and	CCONJ
ejpam-5453	99	8	m	m	PROPN
ejpam-5453	99	9	⊆	⊆	NUM
ejpam-5453	99	10	q	q	NOUN
ejpam-5453	99	11	}	}	PUNCT
ejpam-5453	99	12	=	=	SYM
ejpam-5453	99	13	cl℘(m	cl℘(m	NOUN
ejpam-5453	99	14	)	)	PUNCT
ejpam-5453	99	15	(	(	PUNCT
ejpam-5453	99	16	represents	represent	VERB
ejpam-5453	99	17	the	the	DET
ejpam-5453	99	18	topological	topological	ADJ
ejpam-5453	99	19	℘-closure	℘-closure	NOUN
ejpam-5453	99	20	operator	operator	NOUN
ejpam-5453	99	21	)	)	PUNCT
ejpam-5453	99	22	,	,	PUNCT
ejpam-5453	99	23	b℘(m	b℘(m	PROPN
ejpam-5453	99	24	)	)	PUNCT
ejpam-5453	99	25	=	=	SYM
ejpam-5453	99	26	n℘(m)−n℘(m	n℘(m)−n℘(m	ADJ
ejpam-5453	99	27	)	)	PUNCT
ejpam-5453	99	28	,	,	PUNCT
ejpam-5453	99	29	a℘(m	a℘(m	NOUN
ejpam-5453	99	30	)	)	PUNCT
ejpam-5453	100	1	=	=	SYM
ejpam-5453	100	2	|n℘(m)|	|n℘(m)|	PUNCT
ejpam-5453	101	1	|n℘(m)|	|n℘(m)|	INTJ
ejpam-5453	101	2	,	,	PUNCT
ejpam-5453	101	3	where	where	SCONJ
ejpam-5453	101	4	m	m	NOUN
ejpam-5453	101	5	is	be	AUX
ejpam-5453	101	6	nonempty	nonempty	ADJ
ejpam-5453	101	7	.	.	PUNCT
ejpam-5453	102	1	definition	definition	NOUN
ejpam-5453	102	2	2.3	2.3	NUM
ejpam-5453	102	3	.	.	PUNCT
ejpam-5453	103	1	[	[	X
ejpam-5453	103	2	1	1	NUM
ejpam-5453	103	3	,	,	PUNCT
ejpam-5453	103	4	2	2	NUM
ejpam-5453	103	5	,	,	PUNCT
ejpam-5453	103	6	30	30	NUM
ejpam-5453	103	7	]	]	PUNCT
ejpam-5453	103	8	let	let	VERB
ejpam-5453	103	9	(	(	PUNCT
ejpam-5453	103	10	v	v	NOUN
ejpam-5453	103	11	,	,	PUNCT
ejpam-5453	103	12	υ	υ	NOUN
ejpam-5453	103	13	,	,	PUNCT
ejpam-5453	103	14	π℘	π℘	NUM
ejpam-5453	103	15	)	)	PUNCT
ejpam-5453	103	16	be	be	AUX
ejpam-5453	103	17	a	a	DET
ejpam-5453	103	18	℘-nbds	℘-nbds	NOUN
ejpam-5453	103	19	.	.	PUNCT
ejpam-5453	104	1	m	m	PROPN
ejpam-5453	105	1	⊆	⊆	NUM
ejpam-5453	105	2	v	v	NOUN
ejpam-5453	105	3	is	be	AUX
ejpam-5453	105	4	termed	term	VERB
ejpam-5453	105	5	a	a	DET
ejpam-5453	105	6	℘-exact	℘-exact	NOUN
ejpam-5453	105	7	set	set	VERB
ejpam-5453	105	8	if	if	SCONJ
ejpam-5453	105	9	n℘(m	n℘(m	VERB
ejpam-5453	105	10	)	)	PUNCT
ejpam-5453	105	11	=	=	SYM
ejpam-5453	105	12	n℘(m	n℘(m	NOUN
ejpam-5453	105	13	)	)	PUNCT
ejpam-5453	105	14	.	.	PUNCT
ejpam-5453	106	1	otherwise	otherwise	ADV
ejpam-5453	106	2	,	,	PUNCT
ejpam-5453	106	3	m	m	VERB
ejpam-5453	106	4	is	be	AUX
ejpam-5453	106	5	known	know	VERB
ejpam-5453	106	6	as	as	ADP
ejpam-5453	106	7	a	a	DET
ejpam-5453	106	8	℘-rough	℘-rough	NOUN
ejpam-5453	106	9	set	set	NOUN
ejpam-5453	106	10	.	.	PUNCT
ejpam-5453	107	1	definition	definition	NOUN
ejpam-5453	107	2	2.4	2.4	NUM
ejpam-5453	107	3	.	.	PUNCT
ejpam-5453	108	1	[	[	X
ejpam-5453	108	2	22	22	NUM
ejpam-5453	108	3	,	,	PUNCT
ejpam-5453	108	4	26	26	NUM
ejpam-5453	108	5	]	]	X
ejpam-5453	108	6	let	let	VERB
ejpam-5453	108	7	(	(	PUNCT
ejpam-5453	108	8	v	v	NOUN
ejpam-5453	108	9	,	,	PUNCT
ejpam-5453	108	10	υ	υ	NOUN
ejpam-5453	108	11	,	,	PUNCT
ejpam-5453	108	12	π℘	π℘	NUM
ejpam-5453	108	13	)	)	PUNCT
ejpam-5453	108	14	be	be	VERB
ejpam-5453	108	15	a	a	DET
ejpam-5453	108	16	℘-nbds	℘-nbds	NOUN
ejpam-5453	108	17	and	and	CCONJ
ejpam-5453	108	18	d	d	NOUN
ejpam-5453	108	19	be	be	AUX
ejpam-5453	108	20	an	an	DET
ejpam-5453	108	21	ideal	ideal	NOUN
ejpam-5453	108	22	on	on	ADP
ejpam-5453	108	23	v	v	NUM
ejpam-5453	108	24	.	.	PUNCT
ejpam-5453	109	1	m	m	VERB
ejpam-5453	109	2	⊆	⊆	NUM
ejpam-5453	109	3	v	v	NOUN
ejpam-5453	109	4	is	be	AUX
ejpam-5453	109	5	called	call	VERB
ejpam-5453	109	6	(	(	PUNCT
ejpam-5453	109	7	i	i	NOUN
ejpam-5453	109	8	)	)	PUNCT
ejpam-5453	109	9	d	d	X
ejpam-5453	109	10	-	-	PUNCT
ejpam-5453	109	11	p℘-open	p℘-open	ADJ
ejpam-5453	109	12	,	,	PUNCT
ejpam-5453	109	13	if	if	SCONJ
ejpam-5453	109	14	∃g	∃g	PROPN
ejpam-5453	109	15	∈	∈	NOUN
ejpam-5453	109	16	τ℘	τ℘	X
ejpam-5453	109	17	·	·	PUNCT
ejpam-5453	109	18	∋	∋	NOUN
ejpam-5453	109	19	·	·	PUNCT
ejpam-5453	109	20	(	(	PUNCT
ejpam-5453	109	21	m	m	VERB
ejpam-5453	109	22	−	−	NOUN
ejpam-5453	109	23	g	g	NOUN
ejpam-5453	109	24	)	)	PUNCT
ejpam-5453	109	25	∈	∈	PROPN
ejpam-5453	109	26	d	d	NOUN
ejpam-5453	109	27	and	and	CCONJ
ejpam-5453	109	28	(	(	PUNCT
ejpam-5453	109	29	g	g	PROPN
ejpam-5453	109	30	−	−	PROPN
ejpam-5453	109	31	cl℘(m	cl℘(m	PROPN
ejpam-5453	109	32	)	)	PUNCT
ejpam-5453	109	33	)	)	PUNCT
ejpam-5453	110	1	∈	∈	PROPN
ejpam-5453	110	2	d.	d.	PROPN
ejpam-5453	110	3	(	(	PUNCT
ejpam-5453	110	4	ii	ii	PROPN
ejpam-5453	110	5	)	)	PUNCT
ejpam-5453	110	6	d	d	X
ejpam-5453	110	7	-	-	PUNCT
ejpam-5453	110	8	s℘-open	s℘-open	ADJ
ejpam-5453	110	9	)	)	PUNCT
ejpam-5453	110	10	,	,	PUNCT
ejpam-5453	110	11	if	if	SCONJ
ejpam-5453	110	12	∃g	∃g	PROPN
ejpam-5453	110	13	∈	∈	NOUN
ejpam-5453	110	14	τ℘	τ℘	X
ejpam-5453	110	15	·	·	PUNCT
ejpam-5453	110	16	∋	∋	NOUN
ejpam-5453	110	17	·	·	PUNCT
ejpam-5453	110	18	(	(	PUNCT
ejpam-5453	110	19	m	m	NOUN
ejpam-5453	110	20	−	−	PROPN
ejpam-5453	110	21	cl℘(g	cl℘(g	NOUN
ejpam-5453	110	22	)	)	PUNCT
ejpam-5453	110	23	)	)	PUNCT
ejpam-5453	110	24	∈	∈	PROPN
ejpam-5453	111	1	d	d	NOUN
ejpam-5453	111	2	and	and	CCONJ
ejpam-5453	111	3	(	(	PUNCT
ejpam-5453	111	4	g	g	PROPN
ejpam-5453	111	5	−m	−m	NOUN
ejpam-5453	111	6	)	)	PUNCT
ejpam-5453	111	7	∈	∈	PROPN
ejpam-5453	111	8	d.	d.	PROPN
ejpam-5453	111	9	(	(	PUNCT
ejpam-5453	111	10	iii	iii	NOUN
ejpam-5453	111	11	)	)	PUNCT
ejpam-5453	111	12	d	d	NOUN
ejpam-5453	111	13	-	-	PUNCT
ejpam-5453	111	14	β℘-open	β℘-open	ADJ
ejpam-5453	111	15	,	,	PUNCT
ejpam-5453	111	16	if	if	SCONJ
ejpam-5453	111	17	∃g	∃g	PROPN
ejpam-5453	111	18	∈	∈	NOUN
ejpam-5453	111	19	τ℘	τ℘	X
ejpam-5453	111	20	·	·	PUNCT
ejpam-5453	111	21	∋	∋	NOUN
ejpam-5453	111	22	·	·	PUNCT
ejpam-5453	111	23	(	(	PUNCT
ejpam-5453	111	24	m	m	NOUN
ejpam-5453	111	25	−	−	PROPN
ejpam-5453	111	26	cl℘(g	cl℘(g	NOUN
ejpam-5453	111	27	)	)	PUNCT
ejpam-5453	111	28	)	)	PUNCT
ejpam-5453	111	29	∈	∈	PROPN
ejpam-5453	112	1	d	d	NOUN
ejpam-5453	112	2	and	and	CCONJ
ejpam-5453	112	3	(	(	PUNCT
ejpam-5453	112	4	g	g	PROPN
ejpam-5453	112	5	−	−	PROPN
ejpam-5453	112	6	cl℘(m	cl℘(m	PROPN
ejpam-5453	112	7	)	)	PUNCT
ejpam-5453	112	8	)	)	PUNCT
ejpam-5453	113	1	∈	∈	PROPN
ejpam-5453	113	2	d.	d.	PROPN
ejpam-5453	113	3	(	(	PUNCT
ejpam-5453	113	4	iv	iv	X
ejpam-5453	113	5	)	)	PUNCT
ejpam-5453	113	6	d	d	NOUN
ejpam-5453	113	7	-	-	PUNCT
ejpam-5453	113	8	θβ℘-open	θβ℘-open	NOUN
ejpam-5453	113	9	if	if	SCONJ
ejpam-5453	113	10	∃	∃	PROPN
ejpam-5453	113	11	g	g	PROPN
ejpam-5453	113	12	∈	∈	PROPN
ejpam-5453	113	13	τ℘	τ℘	X
ejpam-5453	113	14	·	·	PUNCT
ejpam-5453	113	15	∋	∋	NOUN
ejpam-5453	113	16	·	·	PUNCT
ejpam-5453	113	17	(	(	PUNCT
ejpam-5453	113	18	m	m	NOUN
ejpam-5453	113	19	−	−	NOUN
ejpam-5453	113	20	cls℘(g	cls℘(g	NUM
ejpam-5453	113	21	)	)	PUNCT
ejpam-5453	113	22	)	)	PUNCT
ejpam-5453	113	23	∈	∈	PROPN
ejpam-5453	114	1	d	d	NOUN
ejpam-5453	114	2	and	and	CCONJ
ejpam-5453	114	3	(	(	PUNCT
ejpam-5453	114	4	g	g	PROPN
ejpam-5453	114	5	−	−	PROPN
ejpam-5453	114	6	clθ℘(m	clθ℘(m	NOUN
ejpam-5453	114	7	)	)	PUNCT
ejpam-5453	114	8	)	)	PUNCT
ejpam-5453	115	1	∈	∈	PROPN
ejpam-5453	115	2	d	d	NOUN
ejpam-5453	115	3	,	,	PUNCT
ejpam-5453	115	4	clθ℘(m	clθ℘(m	NUM
ejpam-5453	115	5	)	)	PUNCT
ejpam-5453	115	6	=	=	PRON
ejpam-5453	116	1	{	{	PUNCT
ejpam-5453	116	2	t	t	PROPN
ejpam-5453	116	3	∈	∈	PROPN
ejpam-5453	116	4	v	v	NOUN
ejpam-5453	116	5	:	:	PUNCT
ejpam-5453	116	6	m	m	PROPN
ejpam-5453	116	7	∩	∩	ADJ
ejpam-5453	116	8	cl℘(g	cl℘(g	NOUN
ejpam-5453	116	9	)	)	PUNCT
ejpam-5453	116	10	̸=	̸=	PROPN
ejpam-5453	116	11	∅,g	∅,g	CCONJ
ejpam-5453	116	12	∈	∈	NOUN
ejpam-5453	116	13	τ℘	τ℘	NOUN
ejpam-5453	116	14	and	and	CCONJ
ejpam-5453	116	15	t	t	NOUN
ejpam-5453	116	16	∈	∈	PROPN
ejpam-5453	116	17	g	g	PROPN
ejpam-5453	116	18	}	}	PUNCT
ejpam-5453	116	19	.	.	PUNCT
ejpam-5453	117	1	these	these	PRON
ejpam-5453	117	2	are	be	AUX
ejpam-5453	117	3	named	name	VERB
ejpam-5453	117	4	d-℘-nearly	d-℘-nearly	ADV
ejpam-5453	117	5	open	open	ADJ
ejpam-5453	117	6	,	,	PUNCT
ejpam-5453	117	7	their	their	PRON
ejpam-5453	117	8	complements	complement	NOUN
ejpam-5453	117	9	are	be	AUX
ejpam-5453	117	10	named	name	VERB
ejpam-5453	117	11	d-℘-nearly	d-℘-nearly	ADV
ejpam-5453	117	12	closed	close	VERB
ejpam-5453	117	13	,	,	PUNCT
ejpam-5453	117	14	all	all	PRON
ejpam-5453	117	15	d-℘-nearly	d-℘-nearly	ADV
ejpam-5453	117	16	open	open	ADJ
ejpam-5453	117	17	of	of	ADP
ejpam-5453	117	18	v	v	NUM
ejpam-5453	117	19	indicated	indicate	VERB
ejpam-5453	117	20	by	by	ADP
ejpam-5453	117	21	d	d	PROPN
ejpam-5453	117	22	-	-	PUNCT
ejpam-5453	117	23	ξ℘o(v	ξ℘o(v	NUM
ejpam-5453	117	24	)	)	PUNCT
ejpam-5453	117	25	and	and	CCONJ
ejpam-5453	117	26	all	all	PRON
ejpam-5453	117	27	d-℘-nearly	d-℘-nearly	ADV
ejpam-5453	117	28	closed	close	VERB
ejpam-5453	117	29	of	of	ADP
ejpam-5453	117	30	v	v	NOUN
ejpam-5453	117	31	indicated	indicate	VERB
ejpam-5453	117	32	by	by	ADP
ejpam-5453	117	33	d	d	NOUN
ejpam-5453	117	34	-	-	NOUN
ejpam-5453	117	35	ξ℘c(v	ξ℘c(v	NOUN
ejpam-5453	117	36	)	)	PUNCT
ejpam-5453	117	37	,	,	PUNCT
ejpam-5453	117	38	∀ξ	∀ξ	X
ejpam-5453	117	39	∈	∈	NOUN
ejpam-5453	117	40	{	{	PUNCT
ejpam-5453	117	41	p	p	X
ejpam-5453	117	42	,	,	PUNCT
ejpam-5453	117	43	s	s	PROPN
ejpam-5453	117	44	,	,	PUNCT
ejpam-5453	117	45	α	α	PROPN
ejpam-5453	117	46	,	,	PUNCT
ejpam-5453	117	47	β	β	X
ejpam-5453	117	48	,	,	PUNCT
ejpam-5453	117	49	θβ	θβ	ADP
ejpam-5453	117	50	}	}	PUNCT
ejpam-5453	117	51	.	.	PUNCT
ejpam-5453	118	1	definition	definition	NOUN
ejpam-5453	118	2	2.5	2.5	NUM
ejpam-5453	118	3	.	.	PUNCT
ejpam-5453	119	1	[	[	X
ejpam-5453	119	2	22	22	NUM
ejpam-5453	119	3	,	,	PUNCT
ejpam-5453	119	4	26	26	NUM
ejpam-5453	119	5	]	]	SYM
ejpam-5453	119	6	let(v	let(v	PROPN
ejpam-5453	119	7	,	,	PUNCT
ejpam-5453	119	8	υ	υ	NOUN
ejpam-5453	119	9	,	,	PUNCT
ejpam-5453	119	10	π℘	π℘	NUM
ejpam-5453	119	11	)	)	PUNCT
ejpam-5453	119	12	be	be	AUX
ejpam-5453	119	13	a	a	DET
ejpam-5453	119	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	119	15	,	,	PUNCT
ejpam-5453	119	16	d	d	PRON
ejpam-5453	119	17	be	be	AUX
ejpam-5453	119	18	an	an	DET
ejpam-5453	119	19	ideal	ideal	NOUN
ejpam-5453	119	20	on	on	ADP
ejpam-5453	119	21	v	v	NUM
ejpam-5453	119	22	and	and	CCONJ
ejpam-5453	119	23	m	m	PROPN
ejpam-5453	119	24	⊆	⊆	NUM
ejpam-5453	119	25	v.	v.	ADP
ejpam-5453	119	26	the	the	DET
ejpam-5453	119	27	d-℘-nearly	d-℘-nearly	ADV
ejpam-5453	119	28	lower	low	ADJ
ejpam-5453	119	29	,	,	PUNCT
ejpam-5453	119	30	d-℘-nearly	d-℘-nearly	ADV
ejpam-5453	119	31	upper	upper	ADJ
ejpam-5453	119	32	approximations	approximation	NOUN
ejpam-5453	119	33	,	,	PUNCT
ejpam-5453	119	34	d-℘-nearly	d-℘-nearly	ADV
ejpam-5453	119	35	boundary	boundary	ADJ
ejpam-5453	119	36	regions	region	NOUN
ejpam-5453	119	37	and	and	CCONJ
ejpam-5453	119	38	d℘-nearly	d℘-nearly	ADV
ejpam-5453	119	39	accuracy	accuracy	NOUN
ejpam-5453	119	40	of	of	ADP
ejpam-5453	119	41	m	m	PROPN
ejpam-5453	119	42	are	be	AUX
ejpam-5453	119	43	:	:	PUNCT
ejpam-5453	119	44	nd−ξ	nd−ξ	ADJ
ejpam-5453	119	45	℘	℘	PROPN
ejpam-5453	119	46	(	(	PUNCT
ejpam-5453	119	47	m	m	NOUN
ejpam-5453	119	48	)	)	PUNCT
ejpam-5453	120	1	=	=	PUNCT
ejpam-5453	120	2	∪{g	∪{g	PROPN
ejpam-5453	120	3	∈	∈	PROPN
ejpam-5453	121	1	d	d	X
ejpam-5453	121	2	-	-	PUNCT
ejpam-5453	121	3	ξ℘o(v	ξ℘o(v	NUM
ejpam-5453	121	4	)	)	PUNCT
ejpam-5453	121	5	:	:	PUNCT
ejpam-5453	121	6	g	g	PROPN
ejpam-5453	121	7	⊆	⊆	NUM
ejpam-5453	121	8	m	m	NOUN
ejpam-5453	121	9	}	}	PUNCT
ejpam-5453	121	10	,	,	PUNCT
ejpam-5453	121	11	n	n	CCONJ
ejpam-5453	121	12	d−ξ	d−ξ	NOUN
ejpam-5453	121	13	℘	℘	PROPN
ejpam-5453	121	14	(	(	PUNCT
ejpam-5453	121	15	m	m	NOUN
ejpam-5453	121	16	)	)	PUNCT
ejpam-5453	121	17	=	=	VERB
ejpam-5453	122	1	∩{h	∩{h	PUNCT
ejpam-5453	122	2	∈	∈	PROPN
ejpam-5453	122	3	d	d	NOUN
ejpam-5453	122	4	-	-	PUNCT
ejpam-5453	122	5	ξ℘c(v	ξ℘c(v	NOUN
ejpam-5453	122	6	)	)	PUNCT
ejpam-5453	122	7	:	:	PUNCT
ejpam-5453	123	1	m	m	VERB
ejpam-5453	123	2	⊆	⊆	NUM
ejpam-5453	123	3	h	h	NOUN
ejpam-5453	123	4	}	}	PUNCT
ejpam-5453	123	5	,	,	PUNCT
ejpam-5453	123	6	bd−ξ	bd−ξ	PROPN
ejpam-5453	123	7	℘	℘	PROPN
ejpam-5453	123	8	(	(	PUNCT
ejpam-5453	123	9	m	m	NOUN
ejpam-5453	123	10	)	)	PUNCT
ejpam-5453	123	11	=	=	SYM
ejpam-5453	123	12	n	n	NOUN
ejpam-5453	123	13	d−ξ	d−ξ	NOUN
ejpam-5453	123	14	℘	℘	PROPN
ejpam-5453	123	15	(	(	PUNCT
ejpam-5453	123	16	m)−nd−ξ	m)−nd−ξ	NOUN
ejpam-5453	123	17	℘	℘	PROPN
ejpam-5453	123	18	(	(	PUNCT
ejpam-5453	123	19	m	m	NOUN
ejpam-5453	123	20	)	)	PUNCT
ejpam-5453	123	21	.	.	PUNCT
ejpam-5453	124	1	ad−ξ	ad−ξ	PROPN
ejpam-5453	124	2	℘	℘	PROPN
ejpam-5453	124	3	(	(	PUNCT
ejpam-5453	124	4	m	m	NOUN
ejpam-5453	124	5	)	)	PUNCT
ejpam-5453	124	6	=	=	PUNCT
ejpam-5453	124	7	|nd−ξ	|nd−ξ	ADP
ejpam-5453	124	8	℘	℘	PROPN
ejpam-5453	124	9	(	(	PUNCT
ejpam-5453	124	10	m)|	m)|	ADJ
ejpam-5453	124	11	|nd−ξ	|nd−ξ	ADP
ejpam-5453	124	12	℘	℘	PROPN
ejpam-5453	124	13	(	(	PUNCT
ejpam-5453	124	14	m)|	m)|	INTJ
ejpam-5453	124	15	,	,	PUNCT
ejpam-5453	124	16	where	where	SCONJ
ejpam-5453	124	17	|nd−ξ	|nd−ξ	ADP
ejpam-5453	124	18	℘	℘	PROPN
ejpam-5453	124	19	(	(	PUNCT
ejpam-5453	124	20	m)|	m)|	NOUN
ejpam-5453	124	21	=	=	NOUN
ejpam-5453	124	22	̸	̸	NUM
ejpam-5453	124	23	0	0	NUM
ejpam-5453	124	24	.	.	PUNCT
ejpam-5453	125	1	m.	m.	PROPN
ejpam-5453	125	2	hosny	hosny	PROPN
ejpam-5453	125	3	/	/	SYM
ejpam-5453	125	4	eur	eur	PROPN
ejpam-5453	125	5	.	.	PUNCT
ejpam-5453	126	1	j.	j.	PROPN
ejpam-5453	126	2	pure	pure	PROPN
ejpam-5453	126	3	appl	appl	PROPN
ejpam-5453	126	4	.	.	PROPN
ejpam-5453	126	5	math	math	PROPN
ejpam-5453	126	6	,	,	PUNCT
ejpam-5453	126	7	17	17	NUM
ejpam-5453	126	8	(	(	PUNCT
ejpam-5453	126	9	4	4	NUM
ejpam-5453	126	10	)	)	PUNCT
ejpam-5453	126	11	(	(	PUNCT
ejpam-5453	126	12	2024	2024	NUM
ejpam-5453	126	13	)	)	PUNCT
ejpam-5453	126	14	,	,	PUNCT
ejpam-5453	126	15	2843	2843	NUM
ejpam-5453	126	16	-	-	SYM
ejpam-5453	126	17	2877	2877	NUM
ejpam-5453	126	18	2847	2847	NUM
ejpam-5453	126	19	definition	definition	NOUN
ejpam-5453	126	20	2.6	2.6	NUM
ejpam-5453	126	21	.	.	PUNCT
ejpam-5453	127	1	[	[	X
ejpam-5453	127	2	22	22	NUM
ejpam-5453	127	3	,	,	PUNCT
ejpam-5453	127	4	26	26	NUM
ejpam-5453	127	5	]	]	X
ejpam-5453	127	6	let	let	VERB
ejpam-5453	127	7	(	(	PUNCT
ejpam-5453	127	8	v	v	NOUN
ejpam-5453	127	9	,	,	PUNCT
ejpam-5453	127	10	υ	υ	NOUN
ejpam-5453	127	11	,	,	PUNCT
ejpam-5453	127	12	π℘	π℘	NUM
ejpam-5453	127	13	)	)	PUNCT
ejpam-5453	127	14	be	be	VERB
ejpam-5453	127	15	a	a	DET
ejpam-5453	127	16	℘-nbds	℘-nbds	NOUN
ejpam-5453	127	17	and	and	CCONJ
ejpam-5453	127	18	d	d	NOUN
ejpam-5453	127	19	be	be	AUX
ejpam-5453	127	20	an	an	DET
ejpam-5453	127	21	ideal	ideal	NOUN
ejpam-5453	127	22	on	on	ADP
ejpam-5453	127	23	v	v	NUM
ejpam-5453	127	24	.	.	PUNCT
ejpam-5453	128	1	a	a	DET
ejpam-5453	128	2	subset	subset	NOUN
ejpam-5453	128	3	m	m	NOUN
ejpam-5453	128	4	⊆	⊆	NUM
ejpam-5453	128	5	v	v	NOUN
ejpam-5453	128	6	is	be	AUX
ejpam-5453	128	7	termed	term	VERB
ejpam-5453	128	8	a	a	DET
ejpam-5453	128	9	d	d	ADJ
ejpam-5453	128	10	-	-	ADJ
ejpam-5453	128	11	ξ℘-exact	ξ℘-exact	ADJ
ejpam-5453	128	12	set	set	NOUN
ejpam-5453	128	13	if	if	SCONJ
ejpam-5453	128	14	n	n	PRON
ejpam-5453	128	15	d−ξ	d−ξ	NOUN
ejpam-5453	129	1	℘	℘	PROPN
ejpam-5453	129	2	(	(	PUNCT
ejpam-5453	129	3	m	m	NOUN
ejpam-5453	129	4	)	)	PUNCT
ejpam-5453	129	5	=	=	SYM
ejpam-5453	129	6	nd−ξ	nd−ξ	ADJ
ejpam-5453	129	7	℘	℘	PROPN
ejpam-5453	129	8	(	(	PUNCT
ejpam-5453	129	9	m	m	NOUN
ejpam-5453	129	10	)	)	PUNCT
ejpam-5453	129	11	.	.	PUNCT
ejpam-5453	130	1	otherwise	otherwise	ADV
ejpam-5453	130	2	,	,	PUNCT
ejpam-5453	130	3	m	m	VERB
ejpam-5453	130	4	is	be	AUX
ejpam-5453	130	5	known	know	VERB
ejpam-5453	130	6	as	as	ADP
ejpam-5453	130	7	a	a	DET
ejpam-5453	130	8	d	d	NOUN
ejpam-5453	130	9	-	-	PUNCT
ejpam-5453	130	10	ξ℘-rough	ξ℘-rough	NOUN
ejpam-5453	130	11	set	set	NOUN
ejpam-5453	130	12	.	.	PUNCT
ejpam-5453	131	1	definition	definition	NOUN
ejpam-5453	131	2	2.7	2.7	NUM
ejpam-5453	131	3	.	.	PUNCT
ejpam-5453	132	1	[	[	X
ejpam-5453	132	2	10	10	NUM
ejpam-5453	132	3	]	]	PUNCT
ejpam-5453	132	4	take	take	VERB
ejpam-5453	132	5	υ	υ	NOUN
ejpam-5453	132	6	as	as	ADP
ejpam-5453	132	7	an	an	DET
ejpam-5453	132	8	arbitrary	arbitrary	ADJ
ejpam-5453	132	9	binary	binary	ADJ
ejpam-5453	132	10	relation	relation	NOUN
ejpam-5453	132	11	on	on	ADP
ejpam-5453	132	12	a	a	DET
ejpam-5453	132	13	finite	finite	NOUN
ejpam-5453	132	14	set	set	VERB
ejpam-5453	132	15	v	v	ADP
ejpam-5453	132	16	̸=	̸=	PROPN
ejpam-5453	132	17	∅	∅	NOUN
ejpam-5453	132	18	and	and	CCONJ
ejpam-5453	132	19	t	t	NOUN
ejpam-5453	132	20	∈	∈	PROPN
ejpam-5453	133	1	v.	v.	CCONJ
ejpam-5453	133	2	then	then	ADV
ejpam-5453	133	3	the	the	DET
ejpam-5453	133	4	subset	subset	ADJ
ejpam-5453	133	5	neighborhood	neighborhood	NOUN
ejpam-5453	133	6	of	of	ADP
ejpam-5453	133	7	t	t	PROPN
ejpam-5453	133	8	∈	∈	PROPN
ejpam-5453	133	9	v	v	NOUN
ejpam-5453	133	10	(	(	PUNCT
ejpam-5453	133	11	briefly	briefly	ADV
ejpam-5453	133	12	,	,	PUNCT
ejpam-5453	133	13	s℘(t)),∀℘	s℘(t)),∀℘	PRON
ejpam-5453	133	14	is	be	AUX
ejpam-5453	133	15	defined	define	VERB
ejpam-5453	133	16	by	by	ADP
ejpam-5453	133	17	follows	follow	VERB
ejpam-5453	133	18	,	,	PUNCT
ejpam-5453	133	19	(	(	PUNCT
ejpam-5453	133	20	i	i	NOUN
ejpam-5453	133	21	)	)	PUNCT
ejpam-5453	133	22	sr(t	sr(t	PUNCT
ejpam-5453	133	23	)	)	PUNCT
ejpam-5453	134	1	=	=	PRON
ejpam-5453	134	2	{	{	PUNCT
ejpam-5453	134	3	s	s	NOUN
ejpam-5453	134	4	∈	∈	X
ejpam-5453	134	5	v	v	NOUN
ejpam-5453	134	6	:	:	PUNCT
ejpam-5453	134	7	ℵr(t	ℵr(t	NUM
ejpam-5453	134	8	)	)	PUNCT
ejpam-5453	134	9	⊆	⊆	NUM
ejpam-5453	134	10	ℵr(s)}[18	ℵr(s)}[18	NOUN
ejpam-5453	134	11	]	]	PUNCT
ejpam-5453	134	12	.	.	PUNCT
ejpam-5453	134	13	(	(	PUNCT
ejpam-5453	134	14	ii	ii	NOUN
ejpam-5453	134	15	)	)	PUNCT
ejpam-5453	134	16	sl(t	sl(t	NOUN
ejpam-5453	134	17	)	)	PUNCT
ejpam-5453	134	18	=	=	PUNCT
ejpam-5453	134	19	{	{	PUNCT
ejpam-5453	134	20	s	s	NOUN
ejpam-5453	134	21	∈	∈	X
ejpam-5453	134	22	v	v	NOUN
ejpam-5453	134	23	:	:	PUNCT
ejpam-5453	134	24	ℵl(t	ℵl(t	NOUN
ejpam-5453	134	25	)	)	PUNCT
ejpam-5453	134	26	⊆	⊆	NUM
ejpam-5453	134	27	ℵl(s)}[10	ℵl(s)}[10	NUM
ejpam-5453	134	28	]	]	PUNCT
ejpam-5453	134	29	.	.	PUNCT
ejpam-5453	135	1	(	(	PUNCT
ejpam-5453	135	2	iii	iii	NOUN
ejpam-5453	135	3	)	)	PUNCT
ejpam-5453	135	4	si(t	si(t	X
ejpam-5453	135	5	)	)	PUNCT
ejpam-5453	135	6	=	=	SYM
ejpam-5453	135	7	sr(t	sr(t	NOUN
ejpam-5453	135	8	)	)	PUNCT
ejpam-5453	135	9	∩	∩	NOUN
ejpam-5453	135	10	sl(t)[10	sl(t)[10	NUM
ejpam-5453	135	11	]	]	PUNCT
ejpam-5453	135	12	.	.	PUNCT
ejpam-5453	136	1	(	(	PUNCT
ejpam-5453	136	2	iv	iv	X
ejpam-5453	136	3	)	)	PUNCT
ejpam-5453	136	4	su	su	PROPN
ejpam-5453	136	5	(	(	PUNCT
ejpam-5453	136	6	t	t	PROPN
ejpam-5453	136	7	)	)	PUNCT
ejpam-5453	136	8	=	=	PUNCT
ejpam-5453	136	9	sr(t	sr(t	NOUN
ejpam-5453	136	10	)	)	PUNCT
ejpam-5453	136	11	∪	∪	ADP
ejpam-5453	136	12	sl(t)[10	sl(t)[10	ADV
ejpam-5453	136	13	]	]	PUNCT
ejpam-5453	136	14	.	.	PUNCT
ejpam-5453	137	1	(	(	PUNCT
ejpam-5453	137	2	v	v	NOUN
ejpam-5453	137	3	)	)	PUNCT
ejpam-5453	137	4	s⟨r⟩(t	s⟨r⟩(t	NOUN
ejpam-5453	137	5	)	)	PUNCT
ejpam-5453	137	6	=	=	PRON
ejpam-5453	137	7	{	{	PUNCT
ejpam-5453	137	8	s	s	NOUN
ejpam-5453	137	9	∈	∈	NOUN
ejpam-5453	137	10	v	v	NOUN
ejpam-5453	137	11	:	:	PUNCT
ejpam-5453	137	12	ℵ⟨r⟩(t	ℵ⟨r⟩(t	NUM
ejpam-5453	137	13	)	)	PUNCT
ejpam-5453	137	14	⊆	⊆	NUM
ejpam-5453	137	15	ℵ⟨r⟩(t)}[10	ℵ⟨r⟩(t)}[10	NOUN
ejpam-5453	137	16	]	]	PUNCT
ejpam-5453	137	17	.	.	PUNCT
ejpam-5453	138	1	(	(	PUNCT
ejpam-5453	138	2	vi	vi	NOUN
ejpam-5453	138	3	)	)	PUNCT
ejpam-5453	138	4	s⟨l⟩(t	s⟨l⟩(t	NOUN
ejpam-5453	138	5	)	)	PUNCT
ejpam-5453	139	1	=	=	PRON
ejpam-5453	139	2	{	{	PUNCT
ejpam-5453	139	3	s	s	NOUN
ejpam-5453	139	4	∈	∈	NOUN
ejpam-5453	139	5	v	v	NOUN
ejpam-5453	139	6	:	:	PUNCT
ejpam-5453	139	7	ℵ⟨l⟩(t	ℵ⟨l⟩(t	NUM
ejpam-5453	139	8	)	)	PUNCT
ejpam-5453	139	9	⊆	⊆	NUM
ejpam-5453	139	10	ℵ⟨l⟩(t)}[10	ℵ⟨l⟩(t)}[10	X
ejpam-5453	139	11	]	]	PUNCT
ejpam-5453	139	12	.	.	PUNCT
ejpam-5453	140	1	(	(	PUNCT
ejpam-5453	140	2	vii	vii	PROPN
ejpam-5453	140	3	)	)	PUNCT
ejpam-5453	140	4	s⟨i⟩(t	s⟨i⟩(t	NOUN
ejpam-5453	140	5	)	)	PUNCT
ejpam-5453	140	6	=	=	SYM
ejpam-5453	140	7	s⟨r⟩(t	s⟨r⟩(t	NOUN
ejpam-5453	140	8	)	)	PUNCT
ejpam-5453	140	9	∩	∩	NOUN
ejpam-5453	140	10	s⟨l⟩(t)[10	s⟨l⟩(t)[10	NUM
ejpam-5453	140	11	]	]	PUNCT
ejpam-5453	140	12	.	.	PUNCT
ejpam-5453	141	1	(	(	PUNCT
ejpam-5453	141	2	viii	viii	NOUN
ejpam-5453	141	3	)	)	PUNCT
ejpam-5453	141	4	s⟨u⟩(t	s⟨u⟩(t	PROPN
ejpam-5453	141	5	)	)	PUNCT
ejpam-5453	141	6	=	=	SYM
ejpam-5453	141	7	s⟨r⟩(t	s⟨r⟩(t	X
ejpam-5453	141	8	)	)	PUNCT
ejpam-5453	141	9	∪	∪	ADP
ejpam-5453	141	10	s⟨l⟩(t)[10	s⟨l⟩(t)[10	NOUN
ejpam-5453	141	11	]	]	PUNCT
ejpam-5453	141	12	.	.	PUNCT
ejpam-5453	142	1	theorem	theorem	VERB
ejpam-5453	142	2	2.2	2.2	NUM
ejpam-5453	142	3	.	.	PUNCT
ejpam-5453	143	1	[	[	X
ejpam-5453	143	2	43	43	NUM
ejpam-5453	143	3	]	]	X
ejpam-5453	143	4	let	let	ADJ
ejpam-5453	143	5	(	(	PUNCT
ejpam-5453	143	6	v	v	NOUN
ejpam-5453	143	7	,	,	PUNCT
ejpam-5453	143	8	υ	υ	NOUN
ejpam-5453	143	9	,	,	PUNCT
ejpam-5453	143	10	π℘	π℘	NUM
ejpam-5453	143	11	)	)	PUNCT
ejpam-5453	143	12	be	be	AUX
ejpam-5453	143	13	a	a	DET
ejpam-5453	143	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	143	15	.	.	PUNCT
ejpam-5453	144	1	then	then	ADV
ejpam-5453	144	2	τs℘	τs℘	NOUN
ejpam-5453	144	3	=	=	PUNCT
ejpam-5453	144	4	{	{	PUNCT
ejpam-5453	144	5	m	m	PROPN
ejpam-5453	144	6	⊆	⊆	NUM
ejpam-5453	144	7	v	v	NOUN
ejpam-5453	144	8	:	:	PUNCT
ejpam-5453	144	9	s℘(t	s℘(t	NOUN
ejpam-5453	144	10	)	)	PUNCT
ejpam-5453	144	11	⊆	⊆	NUM
ejpam-5453	144	12	m,∀t	m,∀t	ADJ
ejpam-5453	144	13	∈	∈	PROPN
ejpam-5453	144	14	m	m	NOUN
ejpam-5453	144	15	}	}	PUNCT
ejpam-5453	144	16	,	,	PUNCT
ejpam-5453	144	17	∀s℘	∀s℘	NOUN
ejpam-5453	144	18	constitutes	constitute	VERB
ejpam-5453	144	19	a	a	DET
ejpam-5453	144	20	topology	topology	NOUN
ejpam-5453	144	21	on	on	ADP
ejpam-5453	144	22	v.	v.	ADP
ejpam-5453	144	23	sets	set	NOUN
ejpam-5453	144	24	in	in	ADP
ejpam-5453	144	25	τs℘	τs℘	PROPN
ejpam-5453	144	26	are	be	AUX
ejpam-5453	144	27	termed	term	VERB
ejpam-5453	144	28	s℘-open	s℘-open	ADJ
ejpam-5453	144	29	,	,	PUNCT
ejpam-5453	144	30	their	their	PRON
ejpam-5453	144	31	complements	complement	NOUN
ejpam-5453	144	32	are	be	AUX
ejpam-5453	144	33	s℘-closed	s℘-close	VERB
ejpam-5453	144	34	set	set	VERB
ejpam-5453	144	35	and	and	CCONJ
ejpam-5453	144	36	all	all	DET
ejpam-5453	144	37	s℘-closed	s℘-close	VERB
ejpam-5453	144	38	set	set	NOUN
ejpam-5453	144	39	is	be	AUX
ejpam-5453	144	40	indicated	indicate	VERB
ejpam-5453	144	41	by	by	ADP
ejpam-5453	144	42	ℸs℘	ℸs℘	PROPN
ejpam-5453	144	43	.	.	PUNCT
ejpam-5453	145	1	definition	definition	NOUN
ejpam-5453	145	2	2.8	2.8	NUM
ejpam-5453	145	3	.	.	PUNCT
ejpam-5453	146	1	[	[	X
ejpam-5453	146	2	43	43	NUM
ejpam-5453	146	3	]	]	X
ejpam-5453	146	4	let	let	ADJ
ejpam-5453	146	5	(	(	PUNCT
ejpam-5453	146	6	v	v	NOUN
ejpam-5453	146	7	,	,	PUNCT
ejpam-5453	146	8	υ	υ	NOUN
ejpam-5453	146	9	,	,	PUNCT
ejpam-5453	146	10	π℘	π℘	NUM
ejpam-5453	146	11	)	)	PUNCT
ejpam-5453	146	12	be	be	AUX
ejpam-5453	146	13	a	a	DET
ejpam-5453	146	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	146	15	.	.	PUNCT
ejpam-5453	147	1	then	then	ADV
ejpam-5453	147	2	s℘-lower	s℘-lower	NOUN
ejpam-5453	147	3	and	and	CCONJ
ejpam-5453	147	4	s℘-upper	s℘-upper	PRON
ejpam-5453	147	5	approximations	approximation	NOUN
ejpam-5453	147	6	,	,	PUNCT
ejpam-5453	147	7	boundary	boundary	ADJ
ejpam-5453	147	8	region	region	NOUN
ejpam-5453	147	9	and	and	CCONJ
ejpam-5453	147	10	accuracy	accuracy	NOUN
ejpam-5453	147	11	of	of	ADP
ejpam-5453	147	12	a	a	DET
ejpam-5453	147	13	set	set	NOUN
ejpam-5453	147	14	m	m	AUX
ejpam-5453	147	15	derived	derive	VERB
ejpam-5453	147	16	from	from	ADP
ejpam-5453	147	17	a	a	DET
ejpam-5453	147	18	topological	topological	ADJ
ejpam-5453	147	19	space	space	NOUN
ejpam-5453	147	20	(	(	PUNCT
ejpam-5453	147	21	v	v	NOUN
ejpam-5453	147	22	,	,	PUNCT
ejpam-5453	147	23	τs℘	τs℘	NOUN
ejpam-5453	147	24	)	)	PUNCT
ejpam-5453	147	25	are	be	AUX
ejpam-5453	147	26	respectively	respectively	ADV
ejpam-5453	147	27	determined	determine	VERB
ejpam-5453	147	28	by	by	ADP
ejpam-5453	147	29	ns℘(m	ns℘(m	NOUN
ejpam-5453	147	30	)	)	PUNCT
ejpam-5453	148	1	=	=	PUNCT
ejpam-5453	148	2	∪{n	∪{n	NOUN
ejpam-5453	148	3	∈	∈	PROPN
ejpam-5453	149	1	τs℘	τs℘	NOUN
ejpam-5453	149	2	:	:	PUNCT
ejpam-5453	149	3	n	n	PROPN
ejpam-5453	149	4	⊆	⊆	NUM
ejpam-5453	149	5	m	m	NOUN
ejpam-5453	149	6	}	}	PUNCT
ejpam-5453	149	7	=	=	SYM
ejpam-5453	149	8	ints℘(m	ints℘(m	PROPN
ejpam-5453	149	9	)	)	PUNCT
ejpam-5453	149	10	(	(	PUNCT
ejpam-5453	149	11	represents	represent	VERB
ejpam-5453	149	12	the	the	DET
ejpam-5453	149	13	topological	topological	ADJ
ejpam-5453	149	14	s℘-interior	s℘-interior	ADJ
ejpam-5453	149	15	operator	operator	NOUN
ejpam-5453	149	16	)	)	PUNCT
ejpam-5453	149	17	,	,	PUNCT
ejpam-5453	149	18	ns℘(m	ns℘(m	NOUN
ejpam-5453	149	19	)	)	PUNCT
ejpam-5453	149	20	=	=	SYM
ejpam-5453	150	1	∩{q	∩{q	PROPN
ejpam-5453	150	2	:	:	PUNCT
ejpam-5453	150	3	q	q	NOUN
ejpam-5453	151	1	′	′	NUM
ejpam-5453	151	2	∈	∈	PROPN
ejpam-5453	151	3	τs℘	τs℘	NOUN
ejpam-5453	151	4	and	and	CCONJ
ejpam-5453	151	5	m	m	PROPN
ejpam-5453	151	6	⊆	⊆	NUM
ejpam-5453	151	7	q	q	NOUN
ejpam-5453	151	8	}	}	PUNCT
ejpam-5453	151	9	=	=	SYM
ejpam-5453	151	10	cls℘(m	cls℘(m	NUM
ejpam-5453	151	11	)	)	PUNCT
ejpam-5453	151	12	(	(	PUNCT
ejpam-5453	151	13	represents	represent	VERB
ejpam-5453	151	14	the	the	DET
ejpam-5453	151	15	topological	topological	ADJ
ejpam-5453	151	16	s℘-closure	s℘-closure	NOUN
ejpam-5453	151	17	operator	operator	NOUN
ejpam-5453	151	18	)	)	PUNCT
ejpam-5453	151	19	,	,	PUNCT
ejpam-5453	151	20	bs℘(m	bs℘(m	PROPN
ejpam-5453	151	21	)	)	PUNCT
ejpam-5453	151	22	=	=	SYM
ejpam-5453	151	23	ns℘(m)−ns℘(m	ns℘(m)−ns℘(m	PROPN
ejpam-5453	151	24	)	)	PUNCT
ejpam-5453	151	25	,	,	PUNCT
ejpam-5453	151	26	as℘(m	as℘(m	PROPN
ejpam-5453	151	27	)	)	PUNCT
ejpam-5453	151	28	=	=	SYM
ejpam-5453	152	1	|ns℘	|ns℘	PROPN
ejpam-5453	152	2	(	(	PUNCT
ejpam-5453	152	3	m)|	m)|	PROPN
ejpam-5453	152	4	|ns℘	|ns℘	PROPN
ejpam-5453	152	5	(	(	PUNCT
ejpam-5453	152	6	m)|	m)|	INTJ
ejpam-5453	152	7	,	,	PUNCT
ejpam-5453	152	8	where	where	SCONJ
ejpam-5453	152	9	m	m	NOUN
ejpam-5453	152	10	is	be	AUX
ejpam-5453	152	11	nonempty	nonempty	ADJ
ejpam-5453	152	12	.	.	PUNCT
ejpam-5453	153	1	definition	definition	NOUN
ejpam-5453	153	2	2.9	2.9	NUM
ejpam-5453	153	3	.	.	PUNCT
ejpam-5453	154	1	[	[	X
ejpam-5453	154	2	43	43	NUM
ejpam-5453	154	3	]	]	X
ejpam-5453	154	4	let	let	ADJ
ejpam-5453	154	5	(	(	PUNCT
ejpam-5453	154	6	v	v	NOUN
ejpam-5453	154	7	,	,	PUNCT
ejpam-5453	154	8	υ	υ	NOUN
ejpam-5453	154	9	,	,	PUNCT
ejpam-5453	154	10	π℘	π℘	NUM
ejpam-5453	154	11	)	)	PUNCT
ejpam-5453	154	12	be	be	AUX
ejpam-5453	154	13	a	a	DET
ejpam-5453	154	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	154	15	.	.	PUNCT
ejpam-5453	155	1	a	a	DET
ejpam-5453	155	2	subset	subset	NOUN
ejpam-5453	155	3	m	m	NOUN
ejpam-5453	155	4	⊆	⊆	NUM
ejpam-5453	155	5	v	v	NOUN
ejpam-5453	155	6	is	be	AUX
ejpam-5453	155	7	termed	term	VERB
ejpam-5453	155	8	a	a	DET
ejpam-5453	155	9	s℘-exact	s℘-exact	PROPN
ejpam-5453	155	10	set	set	NOUN
ejpam-5453	155	11	if	if	SCONJ
ejpam-5453	155	12	ns℘(m	ns℘(m	NOUN
ejpam-5453	155	13	)	)	PUNCT
ejpam-5453	155	14	)	)	PUNCT
ejpam-5453	156	1	=	=	SYM
ejpam-5453	156	2	ns℘(m	ns℘(m	NOUN
ejpam-5453	156	3	)	)	PUNCT
ejpam-5453	156	4	.	.	PUNCT
ejpam-5453	157	1	otherwise	otherwise	ADV
ejpam-5453	157	2	,	,	PUNCT
ejpam-5453	157	3	m	m	VERB
ejpam-5453	157	4	is	be	AUX
ejpam-5453	157	5	known	know	VERB
ejpam-5453	157	6	as	as	ADP
ejpam-5453	157	7	a	a	DET
ejpam-5453	157	8	s℘-rough	s℘-rough	ADJ
ejpam-5453	157	9	set	set	NOUN
ejpam-5453	157	10	.	.	PUNCT
ejpam-5453	158	1	proposition	proposition	NOUN
ejpam-5453	158	2	2.1	2.1	NUM
ejpam-5453	158	3	.	.	PUNCT
ejpam-5453	159	1	[	[	X
ejpam-5453	159	2	43	43	NUM
ejpam-5453	159	3	]	]	X
ejpam-5453	159	4	let	let	ADJ
ejpam-5453	159	5	(	(	PUNCT
ejpam-5453	159	6	v	v	NOUN
ejpam-5453	159	7	,	,	PUNCT
ejpam-5453	159	8	υ	υ	NOUN
ejpam-5453	159	9	,	,	PUNCT
ejpam-5453	159	10	πs℘	πs℘	ADV
ejpam-5453	159	11	)	)	PUNCT
ejpam-5453	159	12	be	be	VERB
ejpam-5453	159	13	a	a	DET
ejpam-5453	159	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	159	15	,	,	PUNCT
ejpam-5453	159	16	υ	υ	PROPN
ejpam-5453	159	17	be	be	VERB
ejpam-5453	159	18	a	a	DET
ejpam-5453	159	19	similarity	similarity	NOUN
ejpam-5453	159	20	relation	relation	NOUN
ejpam-5453	159	21	,	,	PUNCT
ejpam-5453	159	22	℘	℘	PROPN
ejpam-5453	159	23	∈	∈	PROPN
ejpam-5453	159	24	{	{	PUNCT
ejpam-5453	159	25	r	r	NOUN
ejpam-5453	159	26	,	,	PUNCT
ejpam-5453	159	27	l	l	NOUN
ejpam-5453	159	28	,	,	PUNCT
ejpam-5453	159	29	i	i	PRON
ejpam-5453	159	30	,	,	PUNCT
ejpam-5453	159	31	u	u	NOUN
ejpam-5453	159	32	}	}	PUNCT
ejpam-5453	159	33	and	and	CCONJ
ejpam-5453	159	34	m	m	PROPN
ejpam-5453	159	35	⊆	⊆	NUM
ejpam-5453	159	36	v.	v.	ADP
ejpam-5453	159	37	then	then	ADV
ejpam-5453	159	38	,	,	PUNCT
ejpam-5453	159	39	τ℘	τ℘	VERB
ejpam-5453	159	40	⊆	⊆	NUM
ejpam-5453	159	41	τs℘	τs℘	NOUN
ejpam-5453	159	42	.	.	PUNCT
ejpam-5453	160	1	m.	m.	PROPN
ejpam-5453	160	2	hosny	hosny	PROPN
ejpam-5453	160	3	/	/	SYM
ejpam-5453	160	4	eur	eur	PROPN
ejpam-5453	160	5	.	.	PUNCT
ejpam-5453	161	1	j.	j.	PROPN
ejpam-5453	161	2	pure	pure	PROPN
ejpam-5453	161	3	appl	appl	PROPN
ejpam-5453	161	4	.	.	PROPN
ejpam-5453	161	5	math	math	PROPN
ejpam-5453	161	6	,	,	PUNCT
ejpam-5453	161	7	17	17	NUM
ejpam-5453	161	8	(	(	PUNCT
ejpam-5453	161	9	4	4	NUM
ejpam-5453	161	10	)	)	PUNCT
ejpam-5453	161	11	(	(	PUNCT
ejpam-5453	161	12	2024	2024	NUM
ejpam-5453	161	13	)	)	PUNCT
ejpam-5453	161	14	,	,	PUNCT
ejpam-5453	161	15	2843	2843	NUM
ejpam-5453	161	16	-	-	SYM
ejpam-5453	161	17	2877	2877	NUM
ejpam-5453	161	18	2848	2848	NUM
ejpam-5453	161	19	theorem	theorem	VERB
ejpam-5453	161	20	2.3	2.3	NUM
ejpam-5453	161	21	.	.	PUNCT
ejpam-5453	162	1	[	[	X
ejpam-5453	162	2	43	43	NUM
ejpam-5453	162	3	]	]	X
ejpam-5453	162	4	let	let	ADJ
ejpam-5453	162	5	(	(	PUNCT
ejpam-5453	162	6	v	v	NOUN
ejpam-5453	162	7	,	,	PUNCT
ejpam-5453	162	8	υ	υ	NOUN
ejpam-5453	162	9	,	,	PUNCT
ejpam-5453	162	10	πs℘	πs℘	ADV
ejpam-5453	162	11	)	)	PUNCT
ejpam-5453	162	12	be	be	VERB
ejpam-5453	162	13	a	a	DET
ejpam-5453	162	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	162	15	,	,	PUNCT
ejpam-5453	162	16	υ	υ	PROPN
ejpam-5453	162	17	be	be	VERB
ejpam-5453	162	18	a	a	DET
ejpam-5453	162	19	similarity	similarity	NOUN
ejpam-5453	162	20	relation	relation	NOUN
ejpam-5453	162	21	,	,	PUNCT
ejpam-5453	162	22	℘	℘	PROPN
ejpam-5453	162	23	∈	∈	PROPN
ejpam-5453	162	24	{	{	PUNCT
ejpam-5453	162	25	r	r	NOUN
ejpam-5453	162	26	,	,	PUNCT
ejpam-5453	162	27	l	l	NOUN
ejpam-5453	162	28	,	,	PUNCT
ejpam-5453	162	29	i	i	PRON
ejpam-5453	162	30	,	,	PUNCT
ejpam-5453	162	31	u	u	NOUN
ejpam-5453	162	32	}	}	PUNCT
ejpam-5453	162	33	and	and	CCONJ
ejpam-5453	162	34	m	m	PROPN
ejpam-5453	162	35	⊆	⊆	NUM
ejpam-5453	162	36	v.	v.	ADP
ejpam-5453	162	37	then	then	ADV
ejpam-5453	162	38	,	,	PUNCT
ejpam-5453	162	39	(	(	PUNCT
ejpam-5453	162	40	i	i	NOUN
ejpam-5453	162	41	)	)	PUNCT
ejpam-5453	162	42	τ℘	τ℘	VERB
ejpam-5453	162	43	⊆	⊆	NUM
ejpam-5453	162	44	τs℘	τs℘	NOUN
ejpam-5453	162	45	.	.	PUNCT
ejpam-5453	163	1	(	(	PUNCT
ejpam-5453	163	2	ii	ii	NOUN
ejpam-5453	163	3	)	)	PUNCT
ejpam-5453	163	4	n℘(m	n℘(m	NOUN
ejpam-5453	163	5	)	)	PUNCT
ejpam-5453	163	6	⊆	⊆	NUM
ejpam-5453	163	7	ns℘(m	ns℘(m	NOUN
ejpam-5453	163	8	)	)	PUNCT
ejpam-5453	163	9	.	.	PUNCT
ejpam-5453	164	1	(	(	PUNCT
ejpam-5453	164	2	iii	iii	X
ejpam-5453	164	3	)	)	PUNCT
ejpam-5453	164	4	ns℘(m	ns℘(m	NOUN
ejpam-5453	164	5	)	)	PUNCT
ejpam-5453	164	6	⊆	⊆	NUM
ejpam-5453	164	7	n℘(m	n℘(m	NOUN
ejpam-5453	164	8	)	)	PUNCT
ejpam-5453	164	9	.	.	PUNCT
ejpam-5453	165	1	(	(	PUNCT
ejpam-5453	165	2	iv	iv	X
ejpam-5453	165	3	)	)	PUNCT
ejpam-5453	165	4	bs℘(m	bs℘(m	PROPN
ejpam-5453	165	5	)	)	PUNCT
ejpam-5453	165	6	⊆	⊆	NUM
ejpam-5453	165	7	b℘(m	b℘(m	NOUN
ejpam-5453	165	8	)	)	PUNCT
ejpam-5453	165	9	.	.	PUNCT
ejpam-5453	166	1	(	(	PUNCT
ejpam-5453	166	2	v	v	NOUN
ejpam-5453	166	3	)	)	PUNCT
ejpam-5453	166	4	a℘(m	a℘(m	NOUN
ejpam-5453	166	5	)	)	PUNCT
ejpam-5453	166	6	≤	≤	NUM
ejpam-5453	166	7	as℘(m	as℘(m	NOUN
ejpam-5453	166	8	)	)	PUNCT
ejpam-5453	166	9	.	.	PUNCT
ejpam-5453	167	1	definition	definition	NOUN
ejpam-5453	167	2	2.10	2.10	NUM
ejpam-5453	167	3	.	.	PUNCT
ejpam-5453	168	1	[	[	X
ejpam-5453	168	2	43	43	NUM
ejpam-5453	168	3	]	]	X
ejpam-5453	168	4	let	let	ADJ
ejpam-5453	168	5	(	(	PUNCT
ejpam-5453	168	6	v	v	NOUN
ejpam-5453	168	7	,	,	PUNCT
ejpam-5453	168	8	υ	υ	NOUN
ejpam-5453	168	9	,	,	PUNCT
ejpam-5453	168	10	π℘	π℘	NUM
ejpam-5453	168	11	)	)	PUNCT
ejpam-5453	168	12	be	be	AUX
ejpam-5453	168	13	a	a	DET
ejpam-5453	168	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	168	15	.	.	PUNCT
ejpam-5453	169	1	m	m	PROPN
ejpam-5453	170	1	⊆	⊆	NUM
ejpam-5453	170	2	v	v	NOUN
ejpam-5453	170	3	is	be	AUX
ejpam-5453	170	4	(	(	PUNCT
ejpam-5453	170	5	i	i	NOUN
ejpam-5453	170	6	)	)	PUNCT
ejpam-5453	170	7	s℘-preopen	s℘-preopen	PROPN
ejpam-5453	170	8	(	(	PUNCT
ejpam-5453	170	9	ps℘-open	ps℘-open	NOUN
ejpam-5453	170	10	)	)	PUNCT
ejpam-5453	170	11	,	,	PUNCT
ejpam-5453	170	12	if	if	SCONJ
ejpam-5453	170	13	ints℘(cls℘(m	ints℘(cls℘(m	NOUN
ejpam-5453	170	14	)	)	PUNCT
ejpam-5453	170	15	)	)	PUNCT
ejpam-5453	170	16	⊇	⊇	PROPN
ejpam-5453	170	17	m.	m.	NOUN
ejpam-5453	170	18	(	(	PUNCT
ejpam-5453	170	19	ii	ii	PROPN
ejpam-5453	170	20	)	)	PUNCT
ejpam-5453	170	21	s℘-semiopen	s℘-semiopen	PROPN
ejpam-5453	170	22	(	(	PUNCT
ejpam-5453	170	23	ss℘-open	ss℘-open	NOUN
ejpam-5453	170	24	)	)	PUNCT
ejpam-5453	170	25	,	,	PUNCT
ejpam-5453	170	26	if	if	SCONJ
ejpam-5453	170	27	cls℘(ints℘(m	cls℘(ints℘(m	NOUN
ejpam-5453	170	28	)	)	PUNCT
ejpam-5453	170	29	)	)	PUNCT
ejpam-5453	170	30	⊇	⊇	PROPN
ejpam-5453	170	31	m.	m.	NOUN
ejpam-5453	170	32	(	(	PUNCT
ejpam-5453	170	33	iii	iii	NOUN
ejpam-5453	170	34	)	)	PUNCT
ejpam-5453	170	35	αs℘-open	αs℘-open	NOUN
ejpam-5453	170	36	,	,	PUNCT
ejpam-5453	170	37	if	if	SCONJ
ejpam-5453	170	38	m	m	PROPN
ejpam-5453	170	39	⊆	⊆	NUM
ejpam-5453	170	40	ints℘	ints℘	PROPN
ejpam-5453	170	41	[	[	X
ejpam-5453	170	42	cls℘(ints℘(m	cls℘(ints℘(m	NOUN
ejpam-5453	170	43	)	)	PUNCT
ejpam-5453	170	44	)	)	PUNCT
ejpam-5453	170	45	]	]	PUNCT
ejpam-5453	170	46	.	.	PUNCT
ejpam-5453	171	1	(	(	PUNCT
ejpam-5453	171	2	iv	iv	X
ejpam-5453	171	3	)	)	PUNCT
ejpam-5453	171	4	βs℘-open	βs℘-open	NOUN
ejpam-5453	171	5	(	(	PUNCT
ejpam-5453	171	6	semi	semi	ADV
ejpam-5453	171	7	preopen	preopen	ADJ
ejpam-5453	171	8	)	)	PUNCT
ejpam-5453	171	9	,	,	PUNCT
ejpam-5453	171	10	if	if	SCONJ
ejpam-5453	171	11	m	m	PROPN
ejpam-5453	171	12	⊆	⊆	NUM
ejpam-5453	171	13	cls℘	cls℘	NOUN
ejpam-5453	171	14	[	[	X
ejpam-5453	171	15	ints℘(cls℘(m	ints℘(cls℘(m	NOUN
ejpam-5453	171	16	)	)	PUNCT
ejpam-5453	171	17	)	)	PUNCT
ejpam-5453	172	1	]	]	PUNCT
ejpam-5453	172	2	.	.	PUNCT
ejpam-5453	173	1	(	(	PUNCT
ejpam-5453	173	2	v	v	NOUN
ejpam-5453	173	3	)	)	PUNCT
ejpam-5453	173	4	θβs℘-open	θβs℘-open	NOUN
ejpam-5453	173	5	,	,	PUNCT
ejpam-5453	173	6	if	if	SCONJ
ejpam-5453	173	7	m	m	PROPN
ejpam-5453	173	8	⊆	⊆	NUM
ejpam-5453	173	9	cls℘	cls℘	ADJ
ejpam-5453	174	1	[	[	X
ejpam-5453	174	2	ints℘(cl	ints℘(cl	NOUN
ejpam-5453	174	3	θ	θ	PROPN
ejpam-5453	174	4	s℘(m	s℘(m	PROPN
ejpam-5453	174	5	)	)	PUNCT
ejpam-5453	174	6	)	)	PUNCT
ejpam-5453	174	7	]	]	PUNCT
ejpam-5453	174	8	,	,	PUNCT
ejpam-5453	174	9	where	where	SCONJ
ejpam-5453	174	10	clθs℘(m	clθs℘(m	NOUN
ejpam-5453	174	11	)	)	PUNCT
ejpam-5453	175	1	=	=	PRON
ejpam-5453	175	2	{	{	PUNCT
ejpam-5453	175	3	t	t	PROPN
ejpam-5453	175	4	∈	∈	PROPN
ejpam-5453	175	5	v	v	NOUN
ejpam-5453	175	6	:	:	PUNCT
ejpam-5453	175	7	m	m	PROPN
ejpam-5453	175	8	∩	∩	ADJ
ejpam-5453	175	9	cls℘(g	cls℘(g	PUNCT
ejpam-5453	175	10	)	)	PUNCT
ejpam-5453	175	11	̸=	̸=	PROPN
ejpam-5453	175	12	∅,g	∅,g	NOUN
ejpam-5453	175	13	∈	∈	PROPN
ejpam-5453	175	14	τs℘	τs℘	NOUN
ejpam-5453	175	15	and	and	CCONJ
ejpam-5453	175	16	t	t	NOUN
ejpam-5453	175	17	∈	∈	PROPN
ejpam-5453	175	18	g	g	PROPN
ejpam-5453	175	19	}	}	PUNCT
ejpam-5453	175	20	.	.	PUNCT
ejpam-5453	176	1	these	these	PRON
ejpam-5453	176	2	are	be	AUX
ejpam-5453	176	3	named	name	VERB
ejpam-5453	176	4	s℘-nearly	s℘-nearly	ADV
ejpam-5453	176	5	open	open	ADJ
ejpam-5453	176	6	,	,	PUNCT
ejpam-5453	176	7	all	all	PRON
ejpam-5453	176	8	s℘-nearly	s℘-nearly	ADV
ejpam-5453	176	9	open	open	ADJ
ejpam-5453	176	10	of	of	ADP
ejpam-5453	176	11	v	v	NUM
ejpam-5453	176	12	indicated	indicate	VERB
ejpam-5453	176	13	by	by	ADP
ejpam-5453	176	14	ξs℘o(v	ξs℘o(v	NOUN
ejpam-5453	176	15	)	)	PUNCT
ejpam-5453	176	16	,	,	PUNCT
ejpam-5453	176	17	their	their	PRON
ejpam-5453	176	18	complements	complement	NOUN
ejpam-5453	176	19	are	be	AUX
ejpam-5453	176	20	named	name	VERB
ejpam-5453	176	21	s℘-nearly	s℘-nearly	ADV
ejpam-5453	176	22	closed	close	VERB
ejpam-5453	176	23	and	and	CCONJ
ejpam-5453	176	24	all	all	PRON
ejpam-5453	176	25	s℘-nearly	s℘-nearly	ADV
ejpam-5453	176	26	closed	close	VERB
ejpam-5453	176	27	of	of	ADP
ejpam-5453	176	28	v	v	NOUN
ejpam-5453	176	29	indicated	indicate	VERB
ejpam-5453	176	30	by	by	ADP
ejpam-5453	176	31	ξs℘c(v	ξs℘c(v	NOUN
ejpam-5453	176	32	)	)	PUNCT
ejpam-5453	176	33	,	,	PUNCT
ejpam-5453	176	34	∀ξ	∀ξ	X
ejpam-5453	176	35	∈	∈	NOUN
ejpam-5453	176	36	{	{	PUNCT
ejpam-5453	176	37	p	p	X
ejpam-5453	176	38	,	,	PUNCT
ejpam-5453	176	39	s	s	PROPN
ejpam-5453	176	40	,	,	PUNCT
ejpam-5453	176	41	α	α	PROPN
ejpam-5453	176	42	,	,	PUNCT
ejpam-5453	176	43	β	β	X
ejpam-5453	176	44	,	,	PUNCT
ejpam-5453	176	45	θβ	θβ	ADP
ejpam-5453	176	46	}	}	PUNCT
ejpam-5453	176	47	.	.	PUNCT
ejpam-5453	177	1	proposition	proposition	NOUN
ejpam-5453	177	2	2.2	2.2	NUM
ejpam-5453	177	3	.	.	PUNCT
ejpam-5453	178	1	[	[	X
ejpam-5453	178	2	43	43	NUM
ejpam-5453	178	3	]	]	X
ejpam-5453	178	4	let	let	ADJ
ejpam-5453	178	5	(	(	PUNCT
ejpam-5453	178	6	v	v	NOUN
ejpam-5453	178	7	,	,	PUNCT
ejpam-5453	178	8	υ	υ	NOUN
ejpam-5453	178	9	,	,	PUNCT
ejpam-5453	178	10	π℘	π℘	NUM
ejpam-5453	178	11	)	)	PUNCT
ejpam-5453	178	12	be	be	AUX
ejpam-5453	178	13	a	a	DET
ejpam-5453	178	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	178	15	.	.	PUNCT
ejpam-5453	179	1	then	then	ADV
ejpam-5453	179	2	,	,	PUNCT
ejpam-5453	179	3	the	the	DET
ejpam-5453	179	4	implications	implication	NOUN
ejpam-5453	179	5	between	between	ADP
ejpam-5453	179	6	τs℘	τs℘	PROPN
ejpam-5453	179	7	,	,	PUNCT
ejpam-5453	179	8	ℸs℘	ℸs℘	PROPN
ejpam-5453	179	9	,	,	PUNCT
ejpam-5453	179	10	ξs℘o(v	ξs℘o(v	PROPN
ejpam-5453	179	11	)	)	PUNCT
ejpam-5453	179	12	and	and	CCONJ
ejpam-5453	179	13	ξs℘c(v	ξs℘c(v	NOUN
ejpam-5453	179	14	)	)	PUNCT
ejpam-5453	179	15	are	be	AUX
ejpam-5453	179	16	τs℘(ℸs℘	τs℘(ℸs℘	NOUN
ejpam-5453	179	17	)	)	PUNCT
ejpam-5453	179	18	⇒	⇒	PROPN
ejpam-5453	179	19	αs℘o(αs℘c	αs℘o(αs℘c	PROPN
ejpam-5453	179	20	)	)	PUNCT
ejpam-5453	179	21	⇒	⇒	PROPN
ejpam-5453	179	22	ps℘o(ps℘c	ps℘o(ps℘c	PROPN
ejpam-5453	179	23	)	)	PUNCT
ejpam-5453	179	24	⇓	⇓	PROPN
ejpam-5453	179	25	⇓	⇓	PROPN
ejpam-5453	179	26	ss℘o(ss℘c	ss℘o(ss℘c	NOUN
ejpam-5453	179	27	)	)	PUNCT
ejpam-5453	179	28	⇒	⇒	PROPN
ejpam-5453	179	29	βs℘o(βs℘c	βs℘o(βs℘c	PROPN
ejpam-5453	179	30	)	)	PUNCT
ejpam-5453	179	31	⇒	⇒	PROPN
ejpam-5453	179	32	θβs℘o(θβs℘c	θβs℘o(θβs℘c	PROPN
ejpam-5453	179	33	)	)	PUNCT
ejpam-5453	179	34	.	.	PUNCT
ejpam-5453	180	1	definition	definition	NOUN
ejpam-5453	180	2	2.11	2.11	NUM
ejpam-5453	180	3	.	.	PUNCT
ejpam-5453	181	1	[	[	X
ejpam-5453	181	2	43	43	NUM
ejpam-5453	181	3	]	]	X
ejpam-5453	181	4	let	let	ADJ
ejpam-5453	181	5	(	(	PUNCT
ejpam-5453	181	6	v	v	NOUN
ejpam-5453	181	7	,	,	PUNCT
ejpam-5453	181	8	υ	υ	NOUN
ejpam-5453	181	9	,	,	PUNCT
ejpam-5453	181	10	π℘	π℘	NUM
ejpam-5453	181	11	)	)	PUNCT
ejpam-5453	181	12	be	be	AUX
ejpam-5453	181	13	a	a	DET
ejpam-5453	181	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	181	15	,	,	PUNCT
ejpam-5453	181	16	m	m	VERB
ejpam-5453	181	17	⊆	⊆	NUM
ejpam-5453	181	18	v.	v.	ADP
ejpam-5453	181	19	the	the	DET
ejpam-5453	181	20	s℘-nearly	s℘-nearly	ADV
ejpam-5453	181	21	lower	low	ADJ
ejpam-5453	181	22	,	,	PUNCT
ejpam-5453	181	23	s℘-nearly	s℘-nearly	ADV
ejpam-5453	181	24	upper	upper	ADJ
ejpam-5453	181	25	approximations	approximation	NOUN
ejpam-5453	181	26	,	,	PUNCT
ejpam-5453	181	27	s℘-nearly	s℘-nearly	ADV
ejpam-5453	181	28	boundary	boundary	ADJ
ejpam-5453	181	29	regions	region	NOUN
ejpam-5453	181	30	and	and	CCONJ
ejpam-5453	181	31	s℘-nearly	s℘-nearly	ADV
ejpam-5453	181	32	accuracy	accuracy	NOUN
ejpam-5453	181	33	of	of	ADP
ejpam-5453	181	34	m	m	NOUN
ejpam-5453	181	35	are	be	AUX
ejpam-5453	181	36	:	:	PUNCT
ejpam-5453	181	37	nξ	nξ	PROPN
ejpam-5453	181	38	s℘(m	s℘(m	PROPN
ejpam-5453	181	39	)	)	PUNCT
ejpam-5453	181	40	is	be	AUX
ejpam-5453	181	41	the	the	DET
ejpam-5453	181	42	union	union	NOUN
ejpam-5453	181	43	of	of	ADP
ejpam-5453	181	44	all	all	DET
ejpam-5453	181	45	s℘-nearly	s℘-nearly	ADV
ejpam-5453	181	46	open	open	ADJ
ejpam-5453	181	47	sets	set	NOUN
ejpam-5453	181	48	which	which	PRON
ejpam-5453	181	49	are	be	AUX
ejpam-5453	181	50	subset	subset	VERB
ejpam-5453	181	51	of	of	ADP
ejpam-5453	181	52	m	m	NOUN
ejpam-5453	181	53	=	=	PUNCT
ejpam-5453	181	54	s℘-nearly	s℘-nearly	ADV
ejpam-5453	181	55	interior	interior	ADJ
ejpam-5453	181	56	of	of	ADP
ejpam-5453	181	57	m	m	PROPN
ejpam-5453	181	58	.	.	PUNCT
ejpam-5453	182	1	n	n	X
ejpam-5453	182	2	ξ	ξ	X
ejpam-5453	182	3	s℘(m	s℘(m	PROPN
ejpam-5453	182	4	)	)	PUNCT
ejpam-5453	182	5	is	be	AUX
ejpam-5453	182	6	the	the	DET
ejpam-5453	182	7	intersection	intersection	NOUN
ejpam-5453	182	8	of	of	ADP
ejpam-5453	182	9	all	all	DET
ejpam-5453	182	10	s℘-nearly	s℘-nearly	ADV
ejpam-5453	182	11	closed	close	VERB
ejpam-5453	182	12	sets	set	NOUN
ejpam-5453	182	13	which	which	PRON
ejpam-5453	182	14	are	be	AUX
ejpam-5453	182	15	superset	superset	NOUN
ejpam-5453	182	16	of	of	ADP
ejpam-5453	182	17	m	m	NOUN
ejpam-5453	182	18	=	=	PUNCT
ejpam-5453	182	19	s℘-nearly	s℘-nearly	ADV
ejpam-5453	182	20	closure	closure	NOUN
ejpam-5453	182	21	of	of	ADP
ejpam-5453	182	22	a.	a.	NOUN
ejpam-5453	182	23	bξ	bξ	PROPN
ejpam-5453	182	24	s℘(m	s℘(m	PROPN
ejpam-5453	182	25	)	)	PUNCT
ejpam-5453	182	26	=	=	SYM
ejpam-5453	183	1	n	n	SYM
ejpam-5453	183	2	ξ	ξ	PROPN
ejpam-5453	183	3	s℘(m)−nξ	s℘(m)−nξ	PROPN
ejpam-5453	183	4	s℘(m	s℘(m	PROPN
ejpam-5453	183	5	)	)	PUNCT
ejpam-5453	183	6	.	.	PUNCT
ejpam-5453	184	1	aξ	aξ	PROPN
ejpam-5453	184	2	s℘(m	s℘(m	PROPN
ejpam-5453	184	3	)	)	PUNCT
ejpam-5453	185	1	=	=	SYM
ejpam-5453	185	2	|nξ	|nξ	NUM
ejpam-5453	185	3	s℘	s℘	NOUN
ejpam-5453	185	4	(	(	PUNCT
ejpam-5453	185	5	m)|	m)|	NOUN
ejpam-5453	185	6	|nξ	|nξ	NUM
ejpam-5453	185	7	s℘	s℘	NOUN
ejpam-5453	185	8	(	(	PUNCT
ejpam-5453	185	9	m)|	m)|	INTJ
ejpam-5453	185	10	,	,	PUNCT
ejpam-5453	185	11	where	where	SCONJ
ejpam-5453	185	12	|nξ	|nξ	X
ejpam-5453	185	13	s℘(m)|	s℘(m)|	ADJ
ejpam-5453	185	14	=	=	NOUN
ejpam-5453	185	15	̸	̸	NUM
ejpam-5453	185	16	0	0	NUM
ejpam-5453	185	17	.	.	PUNCT
ejpam-5453	186	1	definition	definition	NOUN
ejpam-5453	186	2	2.12	2.12	NUM
ejpam-5453	186	3	.	.	PUNCT
ejpam-5453	187	1	[	[	X
ejpam-5453	187	2	43	43	NUM
ejpam-5453	187	3	]	]	X
ejpam-5453	187	4	let	let	ADJ
ejpam-5453	187	5	(	(	PUNCT
ejpam-5453	187	6	v	v	NOUN
ejpam-5453	187	7	,	,	PUNCT
ejpam-5453	187	8	υ	υ	NOUN
ejpam-5453	187	9	,	,	PUNCT
ejpam-5453	187	10	π℘	π℘	NUM
ejpam-5453	187	11	)	)	PUNCT
ejpam-5453	187	12	be	be	AUX
ejpam-5453	187	13	a	a	DET
ejpam-5453	187	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	187	15	.	.	PUNCT
ejpam-5453	188	1	m	m	PROPN
ejpam-5453	189	1	⊆	⊆	NUM
ejpam-5453	189	2	v	v	NOUN
ejpam-5453	189	3	is	be	AUX
ejpam-5453	189	4	s℘-nearly	s℘-nearly	ADV
ejpam-5453	189	5	exact	exact	ADJ
ejpam-5453	189	6	if	if	SCONJ
ejpam-5453	189	7	n	n	PRON
ejpam-5453	189	8	ξ	ξ	PROPN
ejpam-5453	189	9	s℘(m	s℘(m	PROPN
ejpam-5453	189	10	)	)	PUNCT
ejpam-5453	189	11	=	=	PUNCT
ejpam-5453	189	12	nξ	nξ	PROPN
ejpam-5453	189	13	s℘(m	s℘(m	PROPN
ejpam-5453	189	14	)	)	PUNCT
ejpam-5453	189	15	.	.	PUNCT
ejpam-5453	190	1	otherwise	otherwise	ADV
ejpam-5453	190	2	,	,	PUNCT
ejpam-5453	190	3	m	m	VERB
ejpam-5453	190	4	is	be	AUX
ejpam-5453	190	5	s℘-nearly	s℘-nearly	ADV
ejpam-5453	190	6	rough	rough	ADJ
ejpam-5453	190	7	.	.	PUNCT
ejpam-5453	191	1	m.	m.	PROPN
ejpam-5453	191	2	hosny	hosny	PROPN
ejpam-5453	191	3	/	/	SYM
ejpam-5453	191	4	eur	eur	PROPN
ejpam-5453	191	5	.	.	PUNCT
ejpam-5453	192	1	j.	j.	PROPN
ejpam-5453	192	2	pure	pure	PROPN
ejpam-5453	192	3	appl	appl	PROPN
ejpam-5453	192	4	.	.	PROPN
ejpam-5453	192	5	math	math	PROPN
ejpam-5453	192	6	,	,	PUNCT
ejpam-5453	192	7	17	17	NUM
ejpam-5453	192	8	(	(	PUNCT
ejpam-5453	192	9	4	4	NUM
ejpam-5453	192	10	)	)	PUNCT
ejpam-5453	192	11	(	(	PUNCT
ejpam-5453	192	12	2024	2024	NUM
ejpam-5453	192	13	)	)	PUNCT
ejpam-5453	192	14	,	,	PUNCT
ejpam-5453	192	15	2843	2843	NUM
ejpam-5453	192	16	-	-	SYM
ejpam-5453	192	17	2877	2877	NUM
ejpam-5453	192	18	2849	2849	NUM
ejpam-5453	192	19	theorem	theorem	VERB
ejpam-5453	192	20	2.4	2.4	NUM
ejpam-5453	192	21	.	.	PUNCT
ejpam-5453	193	1	[	[	X
ejpam-5453	193	2	43	43	NUM
ejpam-5453	193	3	]	]	X
ejpam-5453	193	4	let	let	ADJ
ejpam-5453	193	5	(	(	PUNCT
ejpam-5453	193	6	v	v	NOUN
ejpam-5453	193	7	,	,	PUNCT
ejpam-5453	193	8	υ	υ	NOUN
ejpam-5453	193	9	,	,	PUNCT
ejpam-5453	193	10	π℘	π℘	NUM
ejpam-5453	193	11	)	)	PUNCT
ejpam-5453	193	12	be	be	VERB
ejpam-5453	193	13	a	a	DET
ejpam-5453	193	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	193	15	and	and	CCONJ
ejpam-5453	193	16	m	m	PROPN
ejpam-5453	193	17	⊆	⊆	NUM
ejpam-5453	193	18	v.	v.	ADP
ejpam-5453	193	19	then	then	ADV
ejpam-5453	193	20	,	,	PUNCT
ejpam-5453	193	21	ns℘(m	ns℘(m	PROPN
ejpam-5453	193	22	)	)	PUNCT
ejpam-5453	193	23	⊆	⊆	NUM
ejpam-5453	193	24	nξ	nξ	ADP
ejpam-5453	193	25	s℘(m	s℘(m	PROPN
ejpam-5453	193	26	)	)	PUNCT
ejpam-5453	193	27	⊆	⊆	NUM
ejpam-5453	193	28	m	m	NUM
ejpam-5453	193	29	⊆	⊆	NUM
ejpam-5453	193	30	n	n	SYM
ejpam-5453	193	31	ξ	ξ	PROPN
ejpam-5453	193	32	s℘(m	s℘(m	PROPN
ejpam-5453	193	33	)	)	PUNCT
ejpam-5453	193	34	⊆	⊆	NUM
ejpam-5453	193	35	ns℘(m	ns℘(m	NOUN
ejpam-5453	193	36	)	)	PUNCT
ejpam-5453	193	37	.	.	PUNCT
ejpam-5453	194	1	definition	definition	NOUN
ejpam-5453	194	2	2.13	2.13	NUM
ejpam-5453	194	3	.	.	PUNCT
ejpam-5453	195	1	[	[	X
ejpam-5453	195	2	1	1	X
ejpam-5453	195	3	]	]	X
ejpam-5453	195	4	let	let	VERB
ejpam-5453	195	5	(	(	PUNCT
ejpam-5453	195	6	v	v	NOUN
ejpam-5453	195	7	,	,	PUNCT
ejpam-5453	195	8	υ	υ	NOUN
ejpam-5453	195	9	,	,	PUNCT
ejpam-5453	195	10	π℘	π℘	NUM
ejpam-5453	195	11	)	)	PUNCT
ejpam-5453	195	12	be	be	AUX
ejpam-5453	195	13	a	a	DET
ejpam-5453	195	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	195	15	,	,	PUNCT
ejpam-5453	195	16	t	t	PROPN
ejpam-5453	195	17	∈	∈	PROPN
ejpam-5453	195	18	v	v	NOUN
ejpam-5453	195	19	and	and	CCONJ
ejpam-5453	195	20	m	m	PROPN
ejpam-5453	195	21	⊆	⊆	NUM
ejpam-5453	195	22	v	v	NOUN
ejpam-5453	195	23	(	(	PUNCT
ejpam-5453	195	24	i	i	NOUN
ejpam-5453	195	25	)	)	PUNCT
ejpam-5453	195	26	if	if	SCONJ
ejpam-5453	195	27	t	t	PROPN
ejpam-5453	195	28	∈	∈	PROPN
ejpam-5453	195	29	n℘(m	n℘(m	NOUN
ejpam-5453	195	30	)	)	PUNCT
ejpam-5453	195	31	,	,	PUNCT
ejpam-5453	195	32	then	then	ADV
ejpam-5453	195	33	t	t	PROPN
ejpam-5453	195	34	is	be	AUX
ejpam-5453	195	35	℘-surely	℘-surely	ADV
ejpam-5453	195	36	belongs	belong	VERB
ejpam-5453	195	37	to	to	ADP
ejpam-5453	195	38	m	m	PROPN
ejpam-5453	195	39	,	,	PUNCT
ejpam-5453	195	40	denoted	denote	VERB
ejpam-5453	195	41	by	by	ADP
ejpam-5453	195	42	t	t	PROPN
ejpam-5453	195	43	∈℘m	∈℘m	PROPN
ejpam-5453	195	44	(	(	PUNCT
ejpam-5453	195	45	ii	ii	NOUN
ejpam-5453	195	46	)	)	PUNCT
ejpam-5453	195	47	if	if	SCONJ
ejpam-5453	195	48	t	t	PROPN
ejpam-5453	195	49	∈	∈	PROPN
ejpam-5453	195	50	n℘(m	n℘(m	NOUN
ejpam-5453	195	51	)	)	PUNCT
ejpam-5453	195	52	,	,	PUNCT
ejpam-5453	195	53	then	then	ADV
ejpam-5453	195	54	t	t	PROPN
ejpam-5453	195	55	is	be	AUX
ejpam-5453	195	56	℘-possibly	℘-possibly	ADV
ejpam-5453	195	57	belongs	belong	VERB
ejpam-5453	195	58	to	to	ADP
ejpam-5453	195	59	m	m	PROPN
ejpam-5453	195	60	,	,	PUNCT
ejpam-5453	195	61	denoted	denote	VERB
ejpam-5453	195	62	by	by	ADP
ejpam-5453	195	63	t	t	PROPN
ejpam-5453	195	64	∈℘m	∈℘m	PROPN
ejpam-5453	195	65	definition	definition	NOUN
ejpam-5453	195	66	2.14	2.14	NUM
ejpam-5453	195	67	.	.	PUNCT
ejpam-5453	196	1	[	[	X
ejpam-5453	196	2	1	1	X
ejpam-5453	196	3	]	]	X
ejpam-5453	196	4	let	let	VERB
ejpam-5453	196	5	(	(	PUNCT
ejpam-5453	196	6	v	v	NOUN
ejpam-5453	196	7	,	,	PUNCT
ejpam-5453	196	8	υ	υ	NOUN
ejpam-5453	196	9	,	,	PUNCT
ejpam-5453	196	10	π℘	π℘	NUM
ejpam-5453	196	11	)	)	PUNCT
ejpam-5453	196	12	be	be	VERB
ejpam-5453	196	13	a	a	DET
ejpam-5453	196	14	℘-nbds	℘-nbds	NOUN
ejpam-5453	196	15	and	and	CCONJ
ejpam-5453	196	16	m	m	PROPN
ejpam-5453	196	17	⊆	⊆	NUM
ejpam-5453	196	18	v	v	NOUN
ejpam-5453	196	19	and	and	CCONJ
ejpam-5453	196	20	t	t	NOUN
ejpam-5453	196	21	∈	∈	PROPN
ejpam-5453	196	22	v.	v.	ADP
ejpam-5453	196	23	the	the	DET
ejpam-5453	196	24	℘-rough	℘-rough	NOUN
ejpam-5453	196	25	membership	membership	NOUN
ejpam-5453	196	26	functions	function	NOUN
ejpam-5453	196	27	of	of	ADP
ejpam-5453	196	28	m	m	NOUN
ejpam-5453	196	29	are	be	AUX
ejpam-5453	196	30	presented	present	VERB
ejpam-5453	196	31	by	by	ADP
ejpam-5453	196	32	ω℘	ω℘	NOUN
ejpam-5453	196	33	m	m	VERB
ejpam-5453	196	34	:	:	PUNCT
ejpam-5453	196	35	v	v	X
ejpam-5453	196	36	→	→	SYM
ejpam-5453	196	37	[	[	X
ejpam-5453	196	38	0	0	NUM
ejpam-5453	196	39	,	,	PUNCT
ejpam-5453	196	40	1	1	NUM
ejpam-5453	196	41	]	]	PUNCT
ejpam-5453	196	42	,	,	PUNCT
ejpam-5453	196	43	with	with	ADP
ejpam-5453	196	44	ω℘	ω℘	NOUN
ejpam-5453	196	45	m	m	VERB
ejpam-5453	196	46	(	(	PUNCT
ejpam-5453	196	47	t	t	PROPN
ejpam-5453	196	48	)	)	PUNCT
ejpam-5453	196	49	=	=	SYM
ejpam-5453	197	1	|∩ℵ℘(t)∩m	|∩ℵ℘(t)∩m	NOUN
ejpam-5453	197	2	|	|	ADV
ejpam-5453	197	3	|∩ℵ℘(t)|	|∩ℵ℘(t)|	VERB
ejpam-5453	197	4	,	,	PUNCT
ejpam-5453	197	5	∩ℵ℘(t	∩ℵ℘(t	PRON
ejpam-5453	197	6	)	)	PUNCT
ejpam-5453	197	7	̸=	̸=	PROPN
ejpam-5453	197	8	∅	∅	NOUN
ejpam-5453	197	9	and	and	CCONJ
ejpam-5453	197	10	|m	|m	NOUN
ejpam-5453	197	11	|	|	ADV
ejpam-5453	197	12	is	be	AUX
ejpam-5453	197	13	cardinality	cardinality	NOUN
ejpam-5453	197	14	of	of	ADP
ejpam-5453	197	15	m.	m.	NOUN
ejpam-5453	197	16	definition	definition	NOUN
ejpam-5453	197	17	2.15	2.15	NUM
ejpam-5453	197	18	.	.	PUNCT
ejpam-5453	198	1	[	[	X
ejpam-5453	198	2	22	22	NUM
ejpam-5453	198	3	,	,	PUNCT
ejpam-5453	198	4	26	26	NUM
ejpam-5453	198	5	]	]	PUNCT
ejpam-5453	198	6	the	the	DET
ejpam-5453	198	7	subsequent	subsequent	ADJ
ejpam-5453	198	8	features	feature	VERB
ejpam-5453	198	9	valid	valid	ADJ
ejpam-5453	198	10	for	for	ADP
ejpam-5453	198	11	each	each	DET
ejpam-5453	198	12	subset	subset	NOUN
ejpam-5453	198	13	m	m	VERB
ejpam-5453	198	14	.	.	PUNCT
ejpam-5453	199	1	(	(	PUNCT
ejpam-5453	199	2	i	i	NOUN
ejpam-5453	199	3	)	)	PUNCT
ejpam-5453	199	4	if	if	SCONJ
ejpam-5453	199	5	t	t	PROPN
ejpam-5453	199	6	∈	∈	PROPN
ejpam-5453	199	7	rd−ξ	rd−ξ	NOUN
ejpam-5453	199	8	℘	℘	PROPN
ejpam-5453	199	9	(	(	PUNCT
ejpam-5453	199	10	m	m	NOUN
ejpam-5453	199	11	)	)	PUNCT
ejpam-5453	199	12	,	,	PUNCT
ejpam-5453	199	13	then	then	ADV
ejpam-5453	199	14	t	t	PROPN
ejpam-5453	199	15	is	be	AUX
ejpam-5453	199	16	d−	d−	PROPN
ejpam-5453	199	17	ξ℘-certainly	ξ℘-certainly	ADJ
ejpam-5453	199	18	belongs	belong	VERB
ejpam-5453	199	19	to	to	ADP
ejpam-5453	199	20	m	m	PROPN
ejpam-5453	199	21	,	,	PUNCT
ejpam-5453	199	22	symbolized	symbolize	VERB
ejpam-5453	199	23	by	by	ADP
ejpam-5453	199	24	t	t	PROPN
ejpam-5453	199	25	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	199	26	℘	℘	PROPN
ejpam-5453	199	27	m	m	PRON
ejpam-5453	199	28	.	.	PUNCT
ejpam-5453	200	1	(	(	PUNCT
ejpam-5453	200	2	ii	ii	NOUN
ejpam-5453	200	3	)	)	PUNCT
ejpam-5453	200	4	if	if	SCONJ
ejpam-5453	200	5	t	t	PROPN
ejpam-5453	200	6	∈	∈	PROPN
ejpam-5453	200	7	rd−ξ	rd−ξ	NOUN
ejpam-5453	200	8	℘	℘	PROPN
ejpam-5453	200	9	(	(	PUNCT
ejpam-5453	200	10	m	m	NOUN
ejpam-5453	200	11	)	)	PUNCT
ejpam-5453	200	12	,	,	PUNCT
ejpam-5453	200	13	then	then	ADV
ejpam-5453	200	14	t	t	PROPN
ejpam-5453	200	15	is	be	AUX
ejpam-5453	200	16	d−	d−	PROPN
ejpam-5453	200	17	ξ℘-probably	ξ℘-probably	ADV
ejpam-5453	200	18	belongs	belong	VERB
ejpam-5453	200	19	to	to	ADP
ejpam-5453	200	20	m	m	PROPN
ejpam-5453	200	21	,	,	PUNCT
ejpam-5453	200	22	symbolized	symbolize	VERB
ejpam-5453	200	23	by	by	ADP
ejpam-5453	200	24	t	t	PROPN
ejpam-5453	200	25	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	200	26	℘	℘	PROPN
ejpam-5453	200	27	m	m	VERB
ejpam-5453	200	28	.	.	PUNCT
ejpam-5453	201	1	definition	definition	NOUN
ejpam-5453	201	2	2.16	2.16	NUM
ejpam-5453	201	3	.	.	PUNCT
ejpam-5453	202	1	[	[	X
ejpam-5453	202	2	22	22	NUM
ejpam-5453	202	3	,	,	PUNCT
ejpam-5453	202	4	26	26	NUM
ejpam-5453	202	5	]	]	X
ejpam-5453	202	6	let	let	VERB
ejpam-5453	202	7	(	(	PUNCT
ejpam-5453	202	8	v	v	NOUN
ejpam-5453	202	9	,	,	PUNCT
ejpam-5453	202	10	υ	υ	NOUN
ejpam-5453	202	11	,	,	PUNCT
ejpam-5453	202	12	π℘	π℘	NUM
ejpam-5453	202	13	)	)	PUNCT
ejpam-5453	202	14	be	be	AUX
ejpam-5453	202	15	a	a	DET
ejpam-5453	202	16	℘-nbds	℘-nbds	NOUN
ejpam-5453	202	17	,	,	PUNCT
ejpam-5453	202	18	d	d	PRON
ejpam-5453	202	19	be	be	AUX
ejpam-5453	202	20	an	an	DET
ejpam-5453	202	21	ideal	ideal	NOUN
ejpam-5453	202	22	on	on	ADP
ejpam-5453	202	23	v	v	NOUN
ejpam-5453	202	24	,	,	PUNCT
ejpam-5453	202	25	m	m	PROPN
ejpam-5453	202	26	⊆	⊆	NUM
ejpam-5453	202	27	v	v	NOUN
ejpam-5453	202	28	and	and	CCONJ
ejpam-5453	202	29	t	t	NOUN
ejpam-5453	202	30	∈	∈	PROPN
ejpam-5453	202	31	v.	v.	ADP
ejpam-5453	202	32	the	the	DET
ejpam-5453	202	33	d	d	NOUN
ejpam-5453	202	34	-	-	PUNCT
ejpam-5453	202	35	s℘-nearly	s℘-nearly	ADV
ejpam-5453	202	36	rough	rough	ADJ
ejpam-5453	202	37	membership	membership	NOUN
ejpam-5453	202	38	functions	function	NOUN
ejpam-5453	202	39	of	of	ADP
ejpam-5453	202	40	a	a	DET
ejpam-5453	202	41	℘-nbds	℘-nbds	NOUN
ejpam-5453	202	42	on	on	ADP
ejpam-5453	202	43	v	v	NOUN
ejpam-5453	202	44	for	for	ADP
ejpam-5453	202	45	a	a	DET
ejpam-5453	202	46	m	m	NOUN
ejpam-5453	202	47	are	be	AUX
ejpam-5453	202	48	defines	define	NOUN
ejpam-5453	202	49	by	by	ADP
ejpam-5453	202	50	ω	ω	NUM
ejpam-5453	202	51	d−ξ℘	d−ξ℘	NOUN
ejpam-5453	202	52	m	m	VERB
ejpam-5453	202	53	:	:	PUNCT
ejpam-5453	202	54	v	v	X
ejpam-5453	202	55	→	→	SYM
ejpam-5453	202	56	[	[	X
ejpam-5453	202	57	0	0	NUM
ejpam-5453	202	58	,	,	PUNCT
ejpam-5453	202	59	1	1	NUM
ejpam-5453	202	60	]	]	PUNCT
ejpam-5453	202	61	,	,	PUNCT
ejpam-5453	202	62	where	where	SCONJ
ejpam-5453	202	63	ω	ω	NUM
ejpam-5453	202	64	d−ξ℘	d−ξ℘	NOUN
ejpam-5453	202	65	m	m	VERB
ejpam-5453	202	66	(	(	PUNCT
ejpam-5453	202	67	t	t	NOUN
ejpam-5453	202	68	)	)	PUNCT
ejpam-5453	202	69	=	=	PRON
ejpam-5453	202	70	{	{	PUNCT
ejpam-5453	202	71	1	1	NUM
ejpam-5453	202	72	if	if	SCONJ
ejpam-5453	202	73	1∈χd−ξ℘	1∈χd−ξ℘	NUM
ejpam-5453	202	74	m	m	PROPN
ejpam-5453	202	75	(	(	PUNCT
ejpam-5453	202	76	t	t	PROPN
ejpam-5453	202	77	)	)	PUNCT
ejpam-5453	202	78	.	.	PUNCT
ejpam-5453	203	1	min(χ	min(χ	PROPN
ejpam-5453	203	2	d−ξ℘	d−ξ℘	NOUN
ejpam-5453	203	3	m	m	VERB
ejpam-5453	203	4	(	(	PUNCT
ejpam-5453	203	5	t	t	PROPN
ejpam-5453	203	6	)	)	PUNCT
ejpam-5453	203	7	)	)	PUNCT
ejpam-5453	203	8	otherwise	otherwise	ADV
ejpam-5453	203	9	.	.	PUNCT
ejpam-5453	203	10	}	}	PUNCT
ejpam-5453	203	11	.	.	PUNCT
ejpam-5453	204	1	and	and	CCONJ
ejpam-5453	204	2	χ	χ	DET
ejpam-5453	204	3	d−ξ℘	d−ξ℘	NOUN
ejpam-5453	204	4	m	m	VERB
ejpam-5453	204	5	(	(	PUNCT
ejpam-5453	204	6	t	t	NOUN
ejpam-5453	204	7	)	)	PUNCT
ejpam-5453	204	8	=	=	PUNCT
ejpam-5453	205	1	|d−ξ℘(t)∩m	|d−ξ℘(t)∩m	NOUN
ejpam-5453	205	2	|	|	INTJ
ejpam-5453	205	3	|d−ξ℘(t)|	|d−ξ℘(t)|	ADJ
ejpam-5453	205	4	,	,	PUNCT
ejpam-5453	205	5	t	t	PROPN
ejpam-5453	205	6	∈	∈	PROPN
ejpam-5453	205	7	d−	d−	PROPN
ejpam-5453	205	8	ξ℘(t	ξ℘(t	PROPN
ejpam-5453	205	9	)	)	PUNCT
ejpam-5453	205	10	,	,	PUNCT
ejpam-5453	205	11	d−	d−	PROPN
ejpam-5453	205	12	ξ℘(t	ξ℘(t	PROPN
ejpam-5453	205	13	)	)	PUNCT
ejpam-5453	205	14	∈	∈	PROPN
ejpam-5453	205	15	d	d	X
ejpam-5453	205	16	-	-	PUNCT
ejpam-5453	205	17	ξ℘o(v	ξ℘o(v	NUM
ejpam-5453	205	18	)	)	PUNCT
ejpam-5453	205	19	.	.	PUNCT
ejpam-5453	206	1	3	3	X
ejpam-5453	206	2	.	.	X
ejpam-5453	206	3	s℘-nearly	s℘-nearly	ADV
ejpam-5453	206	4	open	open	ADJ
ejpam-5453	206	5	sets	set	NOUN
ejpam-5453	206	6	via	via	ADP
ejpam-5453	206	7	ideals	ideal	NOUN
ejpam-5453	206	8	and	and	CCONJ
ejpam-5453	206	9	comparisons	comparison	NOUN
ejpam-5453	206	10	with	with	ADP
ejpam-5453	206	11	the	the	DET
ejpam-5453	206	12	prior	prior	ADJ
ejpam-5453	206	13	studies	study	NOUN
ejpam-5453	206	14	this	this	DET
ejpam-5453	206	15	section	section	NOUN
ejpam-5453	206	16	introduces	introduce	VERB
ejpam-5453	206	17	a	a	DET
ejpam-5453	206	18	new	new	ADJ
ejpam-5453	206	19	nearly	nearly	ADV
ejpam-5453	206	20	open	open	ADJ
ejpam-5453	206	21	sets	set	NOUN
ejpam-5453	206	22	,	,	PUNCT
ejpam-5453	206	23	namely	namely	ADV
ejpam-5453	206	24	d	d	ADJ
ejpam-5453	206	25	-	-	PUNCT
ejpam-5453	206	26	αs℘-open	αs℘-open	ADJ
ejpam-5453	206	27	sets	set	NOUN
ejpam-5453	206	28	.	.	PUNCT
ejpam-5453	207	1	these	these	DET
ejpam-5453	207	2	sets	set	NOUN
ejpam-5453	207	3	are	be	AUX
ejpam-5453	207	4	defined	define	VERB
ejpam-5453	207	5	using	use	VERB
ejpam-5453	207	6	subset	subset	ADJ
ejpam-5453	207	7	neighbourhood	neighbourhood	NOUN
ejpam-5453	207	8	and	and	CCONJ
ejpam-5453	207	9	ideal	ideal	ADJ
ejpam-5453	207	10	to	to	PART
ejpam-5453	207	11	be	be	AUX
ejpam-5453	207	12	a	a	DET
ejpam-5453	207	13	preliminary	preliminary	ADJ
ejpam-5453	207	14	step	step	NOUN
ejpam-5453	207	15	toward	toward	ADP
ejpam-5453	207	16	developing	develop	VERB
ejpam-5453	207	17	rough	rough	ADJ
ejpam-5453	207	18	set	set	NOUN
ejpam-5453	207	19	paradigms	paradigm	NOUN
ejpam-5453	207	20	.	.	PUNCT
ejpam-5453	208	1	moreover	moreover	ADV
ejpam-5453	208	2	,	,	PUNCT
ejpam-5453	208	3	the	the	DET
ejpam-5453	208	4	key	key	ADJ
ejpam-5453	208	5	characteristics	characteristic	NOUN
ejpam-5453	208	6	of	of	ADP
ejpam-5453	208	7	these	these	DET
ejpam-5453	208	8	classes	class	NOUN
ejpam-5453	208	9	are	be	AUX
ejpam-5453	208	10	outlined	outline	VERB
ejpam-5453	208	11	and	and	CCONJ
ejpam-5453	208	12	clarified	clarify	VERB
ejpam-5453	208	13	how	how	SCONJ
ejpam-5453	208	14	it	it	PRON
ejpam-5453	208	15	relates	relate	VERB
ejpam-5453	208	16	to	to	ADP
ejpam-5453	208	17	the	the	DET
ejpam-5453	208	18	previously	previously	ADV
ejpam-5453	208	19	discussed	discuss	VERB
ejpam-5453	208	20	classes	class	NOUN
ejpam-5453	208	21	.	.	PUNCT
ejpam-5453	209	1	3.1	3.1	NUM
ejpam-5453	209	2	.	.	PUNCT
ejpam-5453	210	1	s℘-nearly	s℘-nearly	ADV
ejpam-5453	210	2	open	open	ADJ
ejpam-5453	210	3	sets	set	NOUN
ejpam-5453	210	4	via	via	ADP
ejpam-5453	210	5	ideals	ideal	NOUN
ejpam-5453	210	6	definition	definition	NOUN
ejpam-5453	210	7	3.1	3.1	NUM
ejpam-5453	210	8	.	.	PUNCT
ejpam-5453	211	1	let	let	AUX
ejpam-5453	211	2	(	(	PUNCT
ejpam-5453	211	3	v	v	NOUN
ejpam-5453	211	4	,	,	PUNCT
ejpam-5453	211	5	υ	υ	NOUN
ejpam-5453	211	6	,	,	PUNCT
ejpam-5453	211	7	π℘	π℘	NUM
ejpam-5453	211	8	)	)	PUNCT
ejpam-5453	211	9	be	be	VERB
ejpam-5453	211	10	a	a	DET
ejpam-5453	211	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	211	12	and	and	CCONJ
ejpam-5453	211	13	d	d	NOUN
ejpam-5453	211	14	be	be	AUX
ejpam-5453	211	15	an	an	DET
ejpam-5453	211	16	ideal	ideal	NOUN
ejpam-5453	211	17	on	on	ADP
ejpam-5453	211	18	v	v	NUM
ejpam-5453	211	19	.	.	PUNCT
ejpam-5453	212	1	m	m	VERB
ejpam-5453	212	2	⊆	⊆	NUM
ejpam-5453	212	3	v	v	NOUN
ejpam-5453	212	4	is	be	AUX
ejpam-5453	212	5	called	call	VERB
ejpam-5453	212	6	(	(	PUNCT
ejpam-5453	212	7	i	i	NOUN
ejpam-5453	212	8	)	)	PUNCT
ejpam-5453	212	9	d	d	X
ejpam-5453	212	10	-	-	PUNCT
ejpam-5453	212	11	αs℘-open	αs℘-open	ADJ
ejpam-5453	212	12	,	,	PUNCT
ejpam-5453	212	13	if	if	SCONJ
ejpam-5453	212	14	∃g	∃g	PROPN
ejpam-5453	212	15	∈	∈	PROPN
ejpam-5453	212	16	τs℘	τs℘	NOUN
ejpam-5453	212	17	·	·	PUNCT
ejpam-5453	212	18	∋	∋	NOUN
ejpam-5453	212	19	·	·	PUNCT
ejpam-5453	212	20	(	(	PUNCT
ejpam-5453	212	21	m	m	PROPN
ejpam-5453	212	22	−	−	NOUN
ejpam-5453	212	23	ints℘(cls℘((g	ints℘(cls℘((g	NOUN
ejpam-5453	212	24	)	)	PUNCT
ejpam-5453	212	25	)	)	PUNCT
ejpam-5453	213	1	∈	∈	PROPN
ejpam-5453	213	2	d	d	NOUN
ejpam-5453	213	3	and	and	CCONJ
ejpam-5453	213	4	(	(	PUNCT
ejpam-5453	213	5	g	g	PROPN
ejpam-5453	213	6	−m	−m	NOUN
ejpam-5453	213	7	)	)	PUNCT
ejpam-5453	213	8	∈	∈	PROPN
ejpam-5453	213	9	d.	d.	PROPN
ejpam-5453	213	10	(	(	PUNCT
ejpam-5453	213	11	ii	ii	PROPN
ejpam-5453	213	12	)	)	PUNCT
ejpam-5453	213	13	d	d	X
ejpam-5453	213	14	-	-	PUNCT
ejpam-5453	213	15	s℘-preopen	s℘-preopen	ADJ
ejpam-5453	213	16	(	(	PUNCT
ejpam-5453	213	17	shortly	shortly	ADV
ejpam-5453	213	18	d	d	NOUN
ejpam-5453	213	19	-	-	NOUN
ejpam-5453	213	20	ps℘-open	ps℘-open	NOUN
ejpam-5453	213	21	)	)	PUNCT
ejpam-5453	213	22	,	,	PUNCT
ejpam-5453	213	23	if	if	SCONJ
ejpam-5453	213	24	∃g	∃g	PROPN
ejpam-5453	213	25	∈	∈	PROPN
ejpam-5453	213	26	τs℘	τs℘	NOUN
ejpam-5453	213	27	·	·	PUNCT
ejpam-5453	213	28	∋	∋	NOUN
ejpam-5453	213	29	·	·	PUNCT
ejpam-5453	213	30	(	(	PUNCT
ejpam-5453	213	31	m	m	VERB
ejpam-5453	213	32	−	−	NOUN
ejpam-5453	213	33	g	g	NOUN
ejpam-5453	213	34	)	)	PUNCT
ejpam-5453	213	35	∈	∈	PROPN
ejpam-5453	213	36	d	d	NOUN
ejpam-5453	213	37	and	and	CCONJ
ejpam-5453	213	38	(	(	PUNCT
ejpam-5453	213	39	g	g	PROPN
ejpam-5453	213	40	−	−	PROPN
ejpam-5453	213	41	cls℘(m	cls℘(m	NUM
ejpam-5453	213	42	)	)	PUNCT
ejpam-5453	213	43	)	)	PUNCT
ejpam-5453	214	1	∈	∈	PROPN
ejpam-5453	214	2	d.	d.	PROPN
ejpam-5453	214	3	(	(	PUNCT
ejpam-5453	214	4	iii	iii	NOUN
ejpam-5453	214	5	)	)	PUNCT
ejpam-5453	214	6	d	d	PROPN
ejpam-5453	214	7	-	-	PUNCT
ejpam-5453	214	8	s℘-semi	s℘-semi	X
ejpam-5453	214	9	open	open	ADJ
ejpam-5453	214	10	(	(	PUNCT
ejpam-5453	214	11	shortly	shortly	ADV
ejpam-5453	214	12	d	d	X
ejpam-5453	214	13	-	-	PUNCT
ejpam-5453	214	14	ss℘-open	ss℘-open	ADJ
ejpam-5453	214	15	)	)	PUNCT
ejpam-5453	214	16	,	,	PUNCT
ejpam-5453	214	17	if	if	SCONJ
ejpam-5453	214	18	∃g	∃g	PROPN
ejpam-5453	214	19	∈	∈	PROPN
ejpam-5453	214	20	τs℘	τs℘	NOUN
ejpam-5453	214	21	·	·	PUNCT
ejpam-5453	214	22	∋	∋	NOUN
ejpam-5453	214	23	·	·	PUNCT
ejpam-5453	214	24	(	(	PUNCT
ejpam-5453	214	25	m	m	NOUN
ejpam-5453	214	26	−	−	NOUN
ejpam-5453	214	27	cls℘(g	cls℘(g	NUM
ejpam-5453	214	28	)	)	PUNCT
ejpam-5453	214	29	)	)	PUNCT
ejpam-5453	215	1	∈	∈	PROPN
ejpam-5453	215	2	d	d	NOUN
ejpam-5453	215	3	and	and	CCONJ
ejpam-5453	215	4	(	(	PUNCT
ejpam-5453	215	5	g	g	PROPN
ejpam-5453	215	6	−m	−m	NOUN
ejpam-5453	215	7	)	)	PUNCT
ejpam-5453	215	8	∈	∈	PROPN
ejpam-5453	215	9	d.	d.	PROPN
ejpam-5453	215	10	(	(	PUNCT
ejpam-5453	215	11	iv	iv	X
ejpam-5453	215	12	)	)	PUNCT
ejpam-5453	215	13	d	d	X
ejpam-5453	215	14	-	-	PUNCT
ejpam-5453	215	15	βs℘-open	βs℘-open	ADJ
ejpam-5453	215	16	,	,	PUNCT
ejpam-5453	215	17	if	if	SCONJ
ejpam-5453	215	18	∃g	∃g	PROPN
ejpam-5453	215	19	∈	∈	PROPN
ejpam-5453	215	20	τs℘	τs℘	NOUN
ejpam-5453	215	21	·	·	PUNCT
ejpam-5453	215	22	∋	∋	NOUN
ejpam-5453	215	23	·	·	PUNCT
ejpam-5453	215	24	(	(	PUNCT
ejpam-5453	215	25	m	m	NOUN
ejpam-5453	215	26	−	−	NOUN
ejpam-5453	215	27	cls℘(g	cls℘(g	NUM
ejpam-5453	215	28	)	)	PUNCT
ejpam-5453	215	29	)	)	PUNCT
ejpam-5453	216	1	∈	∈	PROPN
ejpam-5453	216	2	d	d	NOUN
ejpam-5453	216	3	and	and	CCONJ
ejpam-5453	216	4	(	(	PUNCT
ejpam-5453	216	5	g	g	PROPN
ejpam-5453	216	6	−	−	PROPN
ejpam-5453	216	7	cls℘(m	cls℘(m	NUM
ejpam-5453	216	8	)	)	PUNCT
ejpam-5453	216	9	)	)	PUNCT
ejpam-5453	217	1	∈	∈	PROPN
ejpam-5453	217	2	d.	d.	PROPN
ejpam-5453	217	3	m.	m.	PROPN
ejpam-5453	217	4	hosny	hosny	PROPN
ejpam-5453	217	5	/	/	SYM
ejpam-5453	217	6	eur	eur	PROPN
ejpam-5453	217	7	.	.	PUNCT
ejpam-5453	218	1	j.	j.	PROPN
ejpam-5453	218	2	pure	pure	PROPN
ejpam-5453	218	3	appl	appl	PROPN
ejpam-5453	218	4	.	.	PROPN
ejpam-5453	218	5	math	math	PROPN
ejpam-5453	218	6	,	,	PUNCT
ejpam-5453	218	7	17	17	NUM
ejpam-5453	218	8	(	(	PUNCT
ejpam-5453	218	9	4	4	NUM
ejpam-5453	218	10	)	)	PUNCT
ejpam-5453	218	11	(	(	PUNCT
ejpam-5453	218	12	2024	2024	NUM
ejpam-5453	218	13	)	)	PUNCT
ejpam-5453	218	14	,	,	PUNCT
ejpam-5453	218	15	2843	2843	NUM
ejpam-5453	218	16	-	-	SYM
ejpam-5453	218	17	2877	2877	NUM
ejpam-5453	218	18	2850	2850	NUM
ejpam-5453	218	19	(	(	PUNCT
ejpam-5453	218	20	v	v	NOUN
ejpam-5453	218	21	)	)	PUNCT
ejpam-5453	218	22	d	d	NOUN
ejpam-5453	218	23	-	-	NOUN
ejpam-5453	218	24	θβs℘-open	θβs℘-open	ADJ
ejpam-5453	219	1	if	if	SCONJ
ejpam-5453	219	2	∃	∃	PROPN
ejpam-5453	219	3	g	g	PROPN
ejpam-5453	219	4	∈	∈	PROPN
ejpam-5453	219	5	τs℘	τs℘	PROPN
ejpam-5453	219	6	·	·	PUNCT
ejpam-5453	219	7	∋	∋	NOUN
ejpam-5453	219	8	·	·	PUNCT
ejpam-5453	219	9	(	(	PUNCT
ejpam-5453	219	10	m	m	NOUN
ejpam-5453	219	11	−	−	NOUN
ejpam-5453	219	12	cls℘(g	cls℘(g	NUM
ejpam-5453	219	13	)	)	PUNCT
ejpam-5453	219	14	)	)	PUNCT
ejpam-5453	219	15	∈	∈	PROPN
ejpam-5453	219	16	d	d	NOUN
ejpam-5453	219	17	and	and	CCONJ
ejpam-5453	219	18	(	(	PUNCT
ejpam-5453	219	19	g	g	NOUN
ejpam-5453	219	20	−	−	PROPN
ejpam-5453	219	21	clθs℘(m	clθs℘(m	NOUN
ejpam-5453	219	22	)	)	PUNCT
ejpam-5453	219	23	)	)	PUNCT
ejpam-5453	220	1	∈	∈	PROPN
ejpam-5453	220	2	d.	d.	NOUN
ejpam-5453	220	3	these	these	PRON
ejpam-5453	220	4	are	be	AUX
ejpam-5453	220	5	named	name	VERB
ejpam-5453	220	6	d	d	ADJ
ejpam-5453	220	7	-	-	PUNCT
ejpam-5453	220	8	s℘-nearly	s℘-nearly	ADV
ejpam-5453	220	9	open	open	ADJ
ejpam-5453	220	10	,	,	PUNCT
ejpam-5453	220	11	their	their	PRON
ejpam-5453	220	12	complements	complement	NOUN
ejpam-5453	220	13	are	be	AUX
ejpam-5453	220	14	named	name	VERB
ejpam-5453	220	15	d	d	AUX
ejpam-5453	220	16	-	-	PUNCT
ejpam-5453	220	17	s℘-nearly	s℘-nearly	ADV
ejpam-5453	220	18	closed	closed	ADJ
ejpam-5453	220	19	,	,	PUNCT
ejpam-5453	220	20	all	all	PRON
ejpam-5453	220	21	d	d	ADJ
ejpam-5453	220	22	-	-	PUNCT
ejpam-5453	220	23	s℘-nearly	s℘-nearly	ADV
ejpam-5453	220	24	open	open	ADJ
ejpam-5453	220	25	of	of	ADP
ejpam-5453	220	26	v	v	NUM
ejpam-5453	220	27	indicated	indicate	VERB
ejpam-5453	220	28	by	by	ADP
ejpam-5453	220	29	d	d	PROPN
ejpam-5453	220	30	-	-	PUNCT
ejpam-5453	220	31	ξs℘o(v	ξs℘o(v	NOUN
ejpam-5453	220	32	)	)	PUNCT
ejpam-5453	220	33	and	and	CCONJ
ejpam-5453	220	34	all	all	PRON
ejpam-5453	220	35	d	d	ADJ
ejpam-5453	220	36	-	-	PUNCT
ejpam-5453	220	37	s℘-nearly	s℘-nearly	ADV
ejpam-5453	220	38	closed	close	VERB
ejpam-5453	220	39	of	of	ADP
ejpam-5453	220	40	v	v	NOUN
ejpam-5453	220	41	indicated	indicate	VERB
ejpam-5453	220	42	by	by	ADP
ejpam-5453	220	43	d	d	PROPN
ejpam-5453	220	44	-	-	PUNCT
ejpam-5453	220	45	ξs℘c(v	ξs℘c(v	NOUN
ejpam-5453	220	46	)	)	PUNCT
ejpam-5453	220	47	,	,	PUNCT
ejpam-5453	220	48	∀ξ	∀ξ	X
ejpam-5453	220	49	∈	∈	NOUN
ejpam-5453	220	50	{	{	PUNCT
ejpam-5453	220	51	p	p	X
ejpam-5453	220	52	,	,	PUNCT
ejpam-5453	220	53	s	s	PROPN
ejpam-5453	220	54	,	,	PUNCT
ejpam-5453	220	55	α	α	PROPN
ejpam-5453	220	56	,	,	PUNCT
ejpam-5453	220	57	β	β	X
ejpam-5453	220	58	,	,	PUNCT
ejpam-5453	220	59	θβ	θβ	ADP
ejpam-5453	220	60	}	}	PUNCT
ejpam-5453	220	61	.	.	PUNCT
ejpam-5453	221	1	example	example	NOUN
ejpam-5453	221	2	3.1	3.1	NUM
ejpam-5453	221	3	.	.	PUNCT
ejpam-5453	222	1	let	let	VERB
ejpam-5453	222	2	v	v	VERB
ejpam-5453	222	3	=	=	SYM
ejpam-5453	222	4	{	{	PUNCT
ejpam-5453	222	5	l1	l1	PROPN
ejpam-5453	222	6	,	,	PUNCT
ejpam-5453	222	7	l2	l2	NOUN
ejpam-5453	222	8	,	,	PUNCT
ejpam-5453	222	9	l3	l3	PROPN
ejpam-5453	222	10	,	,	PUNCT
ejpam-5453	222	11	l4	l4	PROPN
ejpam-5453	222	12	}	}	PUNCT
ejpam-5453	222	13	,	,	PUNCT
ejpam-5453	222	14	υ	υ	NOUN
ejpam-5453	222	15	=	=	PRON
ejpam-5453	222	16	{	{	PUNCT
ejpam-5453	222	17	(	(	PUNCT
ejpam-5453	222	18	l1	l1	PROPN
ejpam-5453	222	19	,	,	PUNCT
ejpam-5453	222	20	l1	l1	PROPN
ejpam-5453	222	21	)	)	PUNCT
ejpam-5453	222	22	,	,	PUNCT
ejpam-5453	222	23	(	(	PUNCT
ejpam-5453	222	24	l2	l2	NOUN
ejpam-5453	222	25	,	,	PUNCT
ejpam-5453	222	26	l1	l1	PROPN
ejpam-5453	222	27	)	)	PUNCT
ejpam-5453	222	28	,	,	PUNCT
ejpam-5453	222	29	(	(	PUNCT
ejpam-5453	222	30	l2	l2	NOUN
ejpam-5453	222	31	,	,	PUNCT
ejpam-5453	222	32	l4	l4	PROPN
ejpam-5453	222	33	)	)	PUNCT
ejpam-5453	222	34	,	,	PUNCT
ejpam-5453	222	35	(	(	PUNCT
ejpam-5453	222	36	l3	l3	PROPN
ejpam-5453	222	37	,	,	PUNCT
ejpam-5453	222	38	l1	l1	PROPN
ejpam-5453	222	39	)	)	PUNCT
ejpam-5453	222	40	,	,	PUNCT
ejpam-5453	222	41	(	(	PUNCT
ejpam-5453	222	42	l3	l3	PROPN
ejpam-5453	222	43	,	,	PUNCT
ejpam-5453	222	44	l3	l3	PROPN
ejpam-5453	222	45	)	)	PUNCT
ejpam-5453	222	46	,	,	PUNCT
ejpam-5453	222	47	(	(	PUNCT
ejpam-5453	222	48	l4	l4	PROPN
ejpam-5453	222	49	,	,	PUNCT
ejpam-5453	222	50	l1	l1	PROPN
ejpam-5453	222	51	)	)	PUNCT
ejpam-5453	222	52	,	,	PUNCT
ejpam-5453	222	53	(	(	PUNCT
ejpam-5453	222	54	l4	l4	PROPN
ejpam-5453	222	55	,	,	PUNCT
ejpam-5453	222	56	l3	l3	PROPN
ejpam-5453	222	57	)	)	PUNCT
ejpam-5453	222	58	}	}	PUNCT
ejpam-5453	222	59	,	,	PUNCT
ejpam-5453	222	60	and	and	CCONJ
ejpam-5453	222	61	d	d	X
ejpam-5453	222	62	=	=	SYM
ejpam-5453	222	63	{	{	PUNCT
ejpam-5453	222	64	∅	∅	NOUN
ejpam-5453	222	65	,	,	PUNCT
ejpam-5453	222	66	{	{	PUNCT
ejpam-5453	222	67	l1	l1	PROPN
ejpam-5453	222	68	}	}	PUNCT
ejpam-5453	222	69	,	,	PUNCT
ejpam-5453	222	70	{	{	PUNCT
ejpam-5453	222	71	l2	l2	NOUN
ejpam-5453	222	72	}	}	PUNCT
ejpam-5453	222	73	,	,	PUNCT
ejpam-5453	222	74	{	{	PUNCT
ejpam-5453	222	75	l1	l1	PROPN
ejpam-5453	222	76	,	,	PUNCT
ejpam-5453	222	77	l2	l2	NOUN
ejpam-5453	222	78	}	}	PUNCT
ejpam-5453	222	79	}	}	PUNCT
ejpam-5453	222	80	.	.	PUNCT
ejpam-5453	223	1	then	then	ADV
ejpam-5453	223	2	,	,	PUNCT
ejpam-5453	223	3	τsr	τsr	X
ejpam-5453	223	4	=	=	SYM
ejpam-5453	223	5	{	{	PUNCT
ejpam-5453	223	6	v	v	NOUN
ejpam-5453	223	7	,	,	PUNCT
ejpam-5453	223	8	ϕ	ϕ	NOUN
ejpam-5453	223	9	,	,	PUNCT
ejpam-5453	223	10	{	{	PUNCT
ejpam-5453	223	11	l2	l2	NOUN
ejpam-5453	223	12	}	}	PUNCT
ejpam-5453	223	13	,	,	PUNCT
ejpam-5453	223	14	{	{	PUNCT
ejpam-5453	223	15	l3	l3	PROPN
ejpam-5453	223	16	,	,	PUNCT
ejpam-5453	223	17	l4	l4	PROPN
ejpam-5453	223	18	}	}	PUNCT
ejpam-5453	223	19	,	,	PUNCT
ejpam-5453	223	20	{	{	PUNCT
ejpam-5453	223	21	l2	l2	NOUN
ejpam-5453	223	22	,	,	PUNCT
ejpam-5453	223	23	l3	l3	PROPN
ejpam-5453	223	24	,	,	PUNCT
ejpam-5453	223	25	l4	l4	PROPN
ejpam-5453	223	26	}	}	PUNCT
ejpam-5453	223	27	}	}	PUNCT
ejpam-5453	223	28	,	,	PUNCT
ejpam-5453	223	29	and	and	CCONJ
ejpam-5453	223	30	m	m	AUX
ejpam-5453	223	31	=	=	SYM
ejpam-5453	223	32	{	{	PUNCT
ejpam-5453	223	33	l1	l1	PROPN
ejpam-5453	223	34	}	}	PUNCT
ejpam-5453	223	35	∈	∈	PROPN
ejpam-5453	223	36	d	d	NOUN
ejpam-5453	223	37	-	-	PUNCT
ejpam-5453	223	38	βsro(v	βsro(v	NOUN
ejpam-5453	223	39	)	)	PUNCT
ejpam-5453	223	40	(	(	PUNCT
ejpam-5453	223	41	respectively	respectively	ADV
ejpam-5453	223	42	,	,	PUNCT
ejpam-5453	223	43	d	d	X
ejpam-5453	223	44	-	-	PUNCT
ejpam-5453	223	45	ssro(v	ssro(v	NOUN
ejpam-5453	223	46	)	)	PUNCT
ejpam-5453	223	47	,	,	PUNCT
ejpam-5453	223	48	d	d	X
ejpam-5453	223	49	-	-	PUNCT
ejpam-5453	223	50	psro(v	psro(v	NOUN
ejpam-5453	223	51	)	)	PUNCT
ejpam-5453	223	52	,	,	PUNCT
ejpam-5453	223	53	d	d	X
ejpam-5453	223	54	-	-	PUNCT
ejpam-5453	223	55	αsro(v	αsro(v	NOUN
ejpam-5453	223	56	)	)	PUNCT
ejpam-5453	223	57	)	)	PUNCT
ejpam-5453	223	58	,	,	PUNCT
ejpam-5453	223	59	butm=	butm=	X
ejpam-5453	223	60	{	{	PUNCT
ejpam-5453	223	61	l1	l1	PROPN
ejpam-5453	223	62	}	}	PUNCT
ejpam-5453	223	63	̸∈	̸∈	PROPN
ejpam-5453	223	64	βsro(v	βsro(v	NOUN
ejpam-5453	223	65	)	)	PUNCT
ejpam-5453	223	66	(	(	PUNCT
ejpam-5453	223	67	respectively	respectively	ADV
ejpam-5453	223	68	,	,	PUNCT
ejpam-5453	223	69	ssro(v	ssro(v	NOUN
ejpam-5453	223	70	)	)	PUNCT
ejpam-5453	223	71	,	,	PUNCT
ejpam-5453	223	72	psro(v	psro(v	NOUN
ejpam-5453	223	73	)	)	PUNCT
ejpam-5453	223	74	,	,	PUNCT
ejpam-5453	223	75	αsro(v	αsro(v	NOUN
ejpam-5453	223	76	)	)	PUNCT
ejpam-5453	223	77	)	)	PUNCT
ejpam-5453	223	78	.	.	PUNCT
ejpam-5453	224	1	the	the	DET
ejpam-5453	224	2	following	follow	VERB
ejpam-5453	224	3	finding	find	VERB
ejpam-5453	224	4	highlights	highlight	NOUN
ejpam-5453	224	5	the	the	DET
ejpam-5453	224	6	rapports	rapport	NOUN
ejpam-5453	224	7	among	among	ADP
ejpam-5453	224	8	the	the	DET
ejpam-5453	224	9	d	d	NOUN
ejpam-5453	224	10	-	-	PUNCT
ejpam-5453	224	11	s℘-nearly	s℘-nearly	ADV
ejpam-5453	224	12	open	open	ADJ
ejpam-5453	224	13	sets	set	NOUN
ejpam-5453	224	14	.	.	PUNCT
ejpam-5453	225	1	proposition	proposition	NOUN
ejpam-5453	225	2	3.1	3.1	NUM
ejpam-5453	225	3	.	.	PUNCT
ejpam-5453	226	1	let	let	AUX
ejpam-5453	226	2	(	(	PUNCT
ejpam-5453	226	3	v	v	NOUN
ejpam-5453	226	4	,	,	PUNCT
ejpam-5453	226	5	υ	υ	NOUN
ejpam-5453	226	6	,	,	PUNCT
ejpam-5453	226	7	π℘	π℘	NUM
ejpam-5453	226	8	)	)	PUNCT
ejpam-5453	226	9	be	be	VERB
ejpam-5453	226	10	a	a	DET
ejpam-5453	226	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	226	12	and	and	CCONJ
ejpam-5453	226	13	d	d	NOUN
ejpam-5453	226	14	be	be	AUX
ejpam-5453	226	15	an	an	DET
ejpam-5453	226	16	ideal	ideal	NOUN
ejpam-5453	226	17	on	on	ADP
ejpam-5453	226	18	v.	v.	ADP
ejpam-5453	226	19	then	then	ADV
ejpam-5453	226	20	d	d	X
ejpam-5453	226	21	-	-	PUNCT
ejpam-5453	226	22	αs℘-open	αs℘-open	ADJ
ejpam-5453	226	23	d	d	X
ejpam-5453	226	24	-	-	PUNCT
ejpam-5453	226	25	ps℘-open	ps℘-open	ADJ
ejpam-5453	226	26	⇓	⇓	PROPN
ejpam-5453	226	27	⇓	⇓	PROPN
ejpam-5453	226	28	d	d	PROPN
ejpam-5453	226	29	-	-	PUNCT
ejpam-5453	226	30	ss℘-open	ss℘-open	ADJ
ejpam-5453	226	31	⇒	⇒	NOUN
ejpam-5453	226	32	d	d	NOUN
ejpam-5453	226	33	-	-	PUNCT
ejpam-5453	226	34	βs℘-open	βs℘-open	ADJ
ejpam-5453	226	35	⇒	⇒	NOUN
ejpam-5453	226	36	d	d	NOUN
ejpam-5453	226	37	-	-	PUNCT
ejpam-5453	226	38	θβs℘-open	θβs℘-open	ADJ
ejpam-5453	226	39	.	.	PUNCT
ejpam-5453	227	1	proof	proof	NOUN
ejpam-5453	227	2	.	.	PUNCT
ejpam-5453	228	1	straightforward	straightforward	ADJ
ejpam-5453	228	2	by	by	ADP
ejpam-5453	228	3	definition	definition	NOUN
ejpam-5453	228	4	3.1	3.1	NUM
ejpam-5453	228	5	.	.	PUNCT
ejpam-5453	229	1	remark	remark	PROPN
ejpam-5453	229	2	3.1	3.1	NUM
ejpam-5453	229	3	.	.	PUNCT
ejpam-5453	230	1	in	in	ADP
ejpam-5453	230	2	example	example	NOUN
ejpam-5453	230	3	3.1	3.1	NUM
ejpam-5453	230	4	(	(	PUNCT
ejpam-5453	230	5	i	i	NOUN
ejpam-5453	230	6	)	)	PUNCT
ejpam-5453	230	7	{	{	PUNCT
ejpam-5453	230	8	l3	l3	NOUN
ejpam-5453	230	9	}	}	PUNCT
ejpam-5453	230	10	∈	∈	PROPN
ejpam-5453	230	11	d	d	NOUN
ejpam-5453	230	12	-	-	PUNCT
ejpam-5453	230	13	βsro(v	βsro(v	NOUN
ejpam-5453	230	14	)	)	PUNCT
ejpam-5453	230	15	,	,	PUNCT
ejpam-5453	230	16	̸∈	̸∈	PROPN
ejpam-5453	230	17	d	d	PROPN
ejpam-5453	230	18	-	-	PUNCT
ejpam-5453	230	19	αsro(v	αsro(v	NOUN
ejpam-5453	230	20	)	)	PUNCT
ejpam-5453	230	21	,	,	PUNCT
ejpam-5453	230	22	̸∈	̸∈	PROPN
ejpam-5453	230	23	d	d	PROPN
ejpam-5453	230	24	-	-	PUNCT
ejpam-5453	230	25	ssro(v	ssro(v	VERB
ejpam-5453	230	26	)	)	PUNCT
ejpam-5453	230	27	.	.	PUNCT
ejpam-5453	231	1	(	(	PUNCT
ejpam-5453	231	2	ii	ii	NOUN
ejpam-5453	231	3	)	)	PUNCT
ejpam-5453	231	4	{	{	PUNCT
ejpam-5453	231	5	l3	l3	PROPN
ejpam-5453	231	6	}	}	PUNCT
ejpam-5453	231	7	∈	∈	PROPN
ejpam-5453	231	8	d	d	NOUN
ejpam-5453	231	9	-	-	PUNCT
ejpam-5453	231	10	psro(v	psro(v	NOUN
ejpam-5453	231	11	)	)	PUNCT
ejpam-5453	231	12	,	,	PUNCT
ejpam-5453	231	13	̸∈	̸∈	PROPN
ejpam-5453	231	14	d	d	PROPN
ejpam-5453	231	15	-	-	PUNCT
ejpam-5453	231	16	αsro(v	αsro(v	NOUN
ejpam-5453	231	17	)	)	PUNCT
ejpam-5453	231	18	.	.	PUNCT
ejpam-5453	232	1	(	(	PUNCT
ejpam-5453	232	2	iii	iii	X
ejpam-5453	232	3	)	)	PUNCT
ejpam-5453	232	4	if	if	SCONJ
ejpam-5453	232	5	d	d	NOUN
ejpam-5453	232	6	=	=	SYM
ejpam-5453	232	7	{	{	PUNCT
ejpam-5453	232	8	∅	∅	NOUN
ejpam-5453	232	9	,	,	PUNCT
ejpam-5453	232	10	{	{	PUNCT
ejpam-5453	232	11	l2	l2	NOUN
ejpam-5453	232	12	}	}	PUNCT
ejpam-5453	232	13	}	}	PUNCT
ejpam-5453	232	14	,	,	PUNCT
ejpam-5453	232	15	then	then	ADV
ejpam-5453	232	16	(	(	PUNCT
ejpam-5453	232	17	a	a	X
ejpam-5453	232	18	)	)	PUNCT
ejpam-5453	232	19	{	{	PUNCT
ejpam-5453	232	20	l1	l1	PROPN
ejpam-5453	232	21	,	,	PUNCT
ejpam-5453	232	22	l2	l2	NOUN
ejpam-5453	232	23	}	}	PUNCT
ejpam-5453	232	24	∈	∈	PROPN
ejpam-5453	232	25	d	d	NOUN
ejpam-5453	232	26	-	-	PUNCT
ejpam-5453	232	27	ssro(v	ssro(v	NOUN
ejpam-5453	232	28	)	)	PUNCT
ejpam-5453	232	29	̸∈	̸∈	PROPN
ejpam-5453	232	30	d	d	PROPN
ejpam-5453	232	31	-	-	PUNCT
ejpam-5453	232	32	αsro(v	αsro(v	NOUN
ejpam-5453	232	33	)	)	PUNCT
ejpam-5453	232	34	.	.	PUNCT
ejpam-5453	233	1	(	(	PUNCT
ejpam-5453	233	2	b	b	X
ejpam-5453	233	3	)	)	PUNCT
ejpam-5453	233	4	{	{	PUNCT
ejpam-5453	233	5	l1	l1	PROPN
ejpam-5453	233	6	,	,	PUNCT
ejpam-5453	233	7	l2	l2	NOUN
ejpam-5453	233	8	}	}	PUNCT
ejpam-5453	233	9	∈	∈	PROPN
ejpam-5453	233	10	d	d	NOUN
ejpam-5453	233	11	-	-	PUNCT
ejpam-5453	233	12	βsro(v	βsro(v	NOUN
ejpam-5453	233	13	)	)	PUNCT
ejpam-5453	233	14	,	,	PUNCT
ejpam-5453	233	15	but	but	CCONJ
ejpam-5453	233	16	it	it	PRON
ejpam-5453	233	17	is	be	AUX
ejpam-5453	233	18	not	not	PART
ejpam-5453	233	19	d	d	NOUN
ejpam-5453	233	20	-	-	PUNCT
ejpam-5453	233	21	psro(v	psro(v	NOUN
ejpam-5453	233	22	)	)	PUNCT
ejpam-5453	233	23	.	.	PUNCT
ejpam-5453	234	1	(	(	PUNCT
ejpam-5453	234	2	c	c	X
ejpam-5453	234	3	)	)	PUNCT
ejpam-5453	234	4	{	{	PUNCT
ejpam-5453	234	5	l1	l1	PROPN
ejpam-5453	234	6	,	,	PUNCT
ejpam-5453	234	7	l3	l3	PROPN
ejpam-5453	234	8	,	,	PUNCT
ejpam-5453	234	9	l4	l4	PROPN
ejpam-5453	234	10	}	}	PUNCT
ejpam-5453	234	11	∈	∈	PROPN
ejpam-5453	235	1	d	d	NOUN
ejpam-5453	235	2	-	-	PUNCT
ejpam-5453	235	3	ssro(v	ssro(v	NOUN
ejpam-5453	235	4	)	)	PUNCT
ejpam-5453	235	5	̸∈	̸∈	PROPN
ejpam-5453	235	6	d	d	PROPN
ejpam-5453	235	7	-	-	PUNCT
ejpam-5453	235	8	psro(v	psro(v	NOUN
ejpam-5453	235	9	)	)	PUNCT
ejpam-5453	235	10	.	.	PUNCT
ejpam-5453	236	1	(	(	PUNCT
ejpam-5453	236	2	d	d	X
ejpam-5453	236	3	)	)	PUNCT
ejpam-5453	236	4	{	{	PUNCT
ejpam-5453	236	5	l4	l4	PROPN
ejpam-5453	236	6	}	}	PUNCT
ejpam-5453	236	7	∈	∈	PROPN
ejpam-5453	236	8	d	d	NOUN
ejpam-5453	236	9	-	-	PUNCT
ejpam-5453	236	10	psro(v	psro(v	NOUN
ejpam-5453	236	11	)	)	PUNCT
ejpam-5453	236	12	̸∈	̸∈	PROPN
ejpam-5453	236	13	d	d	PROPN
ejpam-5453	236	14	-	-	PUNCT
ejpam-5453	236	15	psro(v	psro(v	NOUN
ejpam-5453	236	16	)	)	PUNCT
ejpam-5453	236	17	.	.	PUNCT
ejpam-5453	237	1	(	(	PUNCT
ejpam-5453	237	2	e	e	X
ejpam-5453	237	3	)	)	PUNCT
ejpam-5453	237	4	{	{	PUNCT
ejpam-5453	237	5	l1	l1	PROPN
ejpam-5453	237	6	}	}	PUNCT
ejpam-5453	237	7	∈	∈	PROPN
ejpam-5453	237	8	d	d	X
ejpam-5453	237	9	-	-	PUNCT
ejpam-5453	237	10	αsro(v	αsro(v	NOUN
ejpam-5453	237	11	)	)	PUNCT
ejpam-5453	237	12	̸∈	̸∈	PROPN
ejpam-5453	237	13	d	d	PROPN
ejpam-5453	237	14	-	-	PUNCT
ejpam-5453	237	15	psro(v	psro(v	NOUN
ejpam-5453	237	16	)	)	PUNCT
ejpam-5453	237	17	.	.	PUNCT
ejpam-5453	238	1	(	(	PUNCT
ejpam-5453	238	2	f	f	X
ejpam-5453	238	3	)	)	PUNCT
ejpam-5453	238	4	{	{	PUNCT
ejpam-5453	238	5	l3	l3	NOUN
ejpam-5453	238	6	}	}	PUNCT
ejpam-5453	238	7	∈	∈	PROPN
ejpam-5453	238	8	d	d	NOUN
ejpam-5453	238	9	-	-	PUNCT
ejpam-5453	238	10	psro(v	psro(v	NOUN
ejpam-5453	238	11	)	)	PUNCT
ejpam-5453	238	12	̸∈	̸∈	PROPN
ejpam-5453	238	13	d	d	PROPN
ejpam-5453	238	14	-	-	PUNCT
ejpam-5453	238	15	αsro(v	αsro(v	NOUN
ejpam-5453	238	16	)	)	PUNCT
ejpam-5453	238	17	.	.	PUNCT
ejpam-5453	239	1	(	(	PUNCT
ejpam-5453	239	2	g	g	NOUN
ejpam-5453	239	3	)	)	PUNCT
ejpam-5453	239	4	{	{	PUNCT
ejpam-5453	239	5	l1	l1	PROPN
ejpam-5453	239	6	}	}	PUNCT
ejpam-5453	239	7	∈	∈	PROPN
ejpam-5453	239	8	d	d	X
ejpam-5453	239	9	-	-	PUNCT
ejpam-5453	239	10	θβsro(v	θβsro(v	NOUN
ejpam-5453	239	11	)	)	PUNCT
ejpam-5453	239	12	̸∈	̸∈	PROPN
ejpam-5453	239	13	d	d	PROPN
ejpam-5453	239	14	-	-	PUNCT
ejpam-5453	239	15	βsro(v	βsro(v	NOUN
ejpam-5453	239	16	)	)	PUNCT
ejpam-5453	239	17	.	.	PUNCT
ejpam-5453	240	1	accordingly	accordingly	ADV
ejpam-5453	240	2	,	,	PUNCT
ejpam-5453	240	3	it	it	PRON
ejpam-5453	240	4	is	be	AUX
ejpam-5453	240	5	not	not	PART
ejpam-5453	240	6	sro(v	sro(v	NOUN
ejpam-5453	240	7	)	)	PUNCT
ejpam-5453	240	8	,	,	PUNCT
ejpam-5453	240	9	d	d	X
ejpam-5453	240	10	-	-	PUNCT
ejpam-5453	240	11	αsro(v	αsro(v	NOUN
ejpam-5453	240	12	)	)	PUNCT
ejpam-5453	240	13	,	,	PUNCT
ejpam-5453	240	14	d	d	X
ejpam-5453	240	15	-	-	PUNCT
ejpam-5453	240	16	ssro(v	ssro(v	NOUN
ejpam-5453	240	17	)	)	PUNCT
ejpam-5453	240	18	and	and	CCONJ
ejpam-5453	240	19	d	d	X
ejpam-5453	240	20	-	-	PUNCT
ejpam-5453	240	21	psro(v	psro(v	NOUN
ejpam-5453	240	22	)	)	PUNCT
ejpam-5453	240	23	.	.	PUNCT
ejpam-5453	241	1	remark	remark	PROPN
ejpam-5453	241	2	3.2	3.2	NUM
ejpam-5453	241	3	.	.	PUNCT
ejpam-5453	241	4	example	example	NOUN
ejpam-5453	241	5	3.1	3.1	NUM
ejpam-5453	241	6	clarifies	clarifie	NOUN
ejpam-5453	241	7	that	that	SCONJ
ejpam-5453	241	8	(	(	PUNCT
ejpam-5453	241	9	i	i	NOUN
ejpam-5453	241	10	)	)	PUNCT
ejpam-5453	241	11	d	d	PROPN
ejpam-5453	241	12	-	-	PUNCT
ejpam-5453	241	13	αs℘o(v	αs℘o(v	NUM
ejpam-5453	241	14	)	)	PUNCT
ejpam-5453	241	15	and	and	CCONJ
ejpam-5453	241	16	d	d	PROPN
ejpam-5453	241	17	-	-	PUNCT
ejpam-5453	241	18	ps℘o(v	ps℘o(v	NOUN
ejpam-5453	241	19	)	)	PUNCT
ejpam-5453	241	20	are	be	AUX
ejpam-5453	241	21	distinct	distinct	ADJ
ejpam-5453	241	22	even	even	ADV
ejpam-5453	241	23	though	though	SCONJ
ejpam-5453	241	24	every	every	DET
ejpam-5453	241	25	element	element	NOUN
ejpam-5453	241	26	in	in	ADP
ejpam-5453	241	27	αs℘o(v	αs℘o(v	NUM
ejpam-5453	241	28	)	)	PUNCT
ejpam-5453	241	29	is	be	AUX
ejpam-5453	241	30	in	in	ADP
ejpam-5453	241	31	ps℘o(v	ps℘o(v	PROPN
ejpam-5453	241	32	)	)	PUNCT
ejpam-5453	242	1	[	[	X
ejpam-5453	242	2	43	43	NUM
ejpam-5453	242	3	]	]	PUNCT
ejpam-5453	242	4	.	.	PUNCT
ejpam-5453	243	1	(	(	PUNCT
ejpam-5453	243	2	ii	ii	NOUN
ejpam-5453	243	3	)	)	PUNCT
ejpam-5453	243	4	d	d	X
ejpam-5453	243	5	-	-	PUNCT
ejpam-5453	243	6	ss℘-open	ss℘-open	ADJ
ejpam-5453	243	7	sets	set	NOUN
ejpam-5453	243	8	and	and	CCONJ
ejpam-5453	243	9	d	d	NOUN
ejpam-5453	243	10	-	-	PUNCT
ejpam-5453	243	11	ps℘-open	ps℘-open	ADJ
ejpam-5453	243	12	sets	set	NOUN
ejpam-5453	243	13	are	be	AUX
ejpam-5453	243	14	incomparable	incomparable	ADJ
ejpam-5453	243	15	.	.	PUNCT
ejpam-5453	244	1	proposition	proposition	NOUN
ejpam-5453	244	2	3.2	3.2	NUM
ejpam-5453	244	3	.	.	PUNCT
ejpam-5453	245	1	let	let	AUX
ejpam-5453	245	2	(	(	PUNCT
ejpam-5453	245	3	v	v	NOUN
ejpam-5453	245	4	,	,	PUNCT
ejpam-5453	245	5	υ	υ	NOUN
ejpam-5453	245	6	,	,	PUNCT
ejpam-5453	245	7	π℘	π℘	NUM
ejpam-5453	245	8	)	)	PUNCT
ejpam-5453	245	9	be	be	AUX
ejpam-5453	245	10	a	a	DET
ejpam-5453	245	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	245	12	and	and	CCONJ
ejpam-5453	245	13	let	let	VERB
ejpam-5453	245	14	d	d	PRON
ejpam-5453	245	15	be	be	AUX
ejpam-5453	245	16	an	an	DET
ejpam-5453	245	17	ideal	ideal	NOUN
ejpam-5453	245	18	on	on	ADP
ejpam-5453	245	19	v	v	NOUN
ejpam-5453	245	20	.	.	PUNCT
ejpam-5453	246	1	then	then	ADV
ejpam-5453	246	2	m.	m.	PROPN
ejpam-5453	246	3	hosny	hosny	PROPN
ejpam-5453	246	4	/	/	SYM
ejpam-5453	246	5	eur	eur	PROPN
ejpam-5453	246	6	.	.	PUNCT
ejpam-5453	247	1	j.	j.	PROPN
ejpam-5453	247	2	pure	pure	PROPN
ejpam-5453	247	3	appl	appl	PROPN
ejpam-5453	247	4	.	.	PROPN
ejpam-5453	247	5	math	math	PROPN
ejpam-5453	247	6	,	,	PUNCT
ejpam-5453	247	7	17	17	NUM
ejpam-5453	247	8	(	(	PUNCT
ejpam-5453	247	9	4	4	NUM
ejpam-5453	247	10	)	)	PUNCT
ejpam-5453	247	11	(	(	PUNCT
ejpam-5453	247	12	2024	2024	NUM
ejpam-5453	247	13	)	)	PUNCT
ejpam-5453	247	14	,	,	PUNCT
ejpam-5453	247	15	2843	2843	NUM
ejpam-5453	247	16	-	-	SYM
ejpam-5453	247	17	2877	2877	NUM
ejpam-5453	247	18	2851	2851	NUM
ejpam-5453	247	19	τs℘(γs℘	τs℘(γs℘	NOUN
ejpam-5453	247	20	)	)	PUNCT
ejpam-5453	247	21	⇒	⇒	NOUN
ejpam-5453	247	22	d	d	X
ejpam-5453	247	23	-	-	PUNCT
ejpam-5453	247	24	αs℘o(d	αs℘o(d	NOUN
ejpam-5453	247	25	-	-	PUNCT
ejpam-5453	247	26	αs℘c	αs℘c	NOUN
ejpam-5453	247	27	)	)	PUNCT
ejpam-5453	247	28	d	d	NOUN
ejpam-5453	247	29	-	-	PUNCT
ejpam-5453	247	30	ps℘o(d	ps℘o(d	NOUN
ejpam-5453	247	31	-	-	NOUN
ejpam-5453	247	32	ps℘c	ps℘c	NOUN
ejpam-5453	247	33	)	)	PUNCT
ejpam-5453	247	34	⇓	⇓	PROPN
ejpam-5453	247	35	⇓	⇓	PROPN
ejpam-5453	247	36	d	d	PROPN
ejpam-5453	247	37	-	-	PUNCT
ejpam-5453	247	38	ss℘o(d	ss℘o(d	NOUN
ejpam-5453	247	39	-	-	PUNCT
ejpam-5453	247	40	ss℘c	ss℘c	NOUN
ejpam-5453	247	41	)	)	PUNCT
ejpam-5453	247	42	⇒	⇒	NOUN
ejpam-5453	247	43	d	d	X
ejpam-5453	247	44	-	-	ADJ
ejpam-5453	247	45	βs℘o(d	βs℘o(d	ADV
ejpam-5453	247	46	-	-	PUNCT
ejpam-5453	247	47	βs℘c	βs℘c	NOUN
ejpam-5453	247	48	)	)	PUNCT
ejpam-5453	247	49	⇒	⇒	NOUN
ejpam-5453	247	50	d	d	PROPN
ejpam-5453	247	51	-	-	PUNCT
ejpam-5453	247	52	θβs℘o(dθβs℘c	θβs℘o(dθβs℘c	NOUN
ejpam-5453	247	53	)	)	PUNCT
ejpam-5453	247	54	.	.	PUNCT
ejpam-5453	248	1	proof	proof	NOUN
ejpam-5453	248	2	.	.	PUNCT
ejpam-5453	249	1	by	by	ADP
ejpam-5453	249	2	proposition	proposition	NOUN
ejpam-5453	249	3	2.2	2.2	NUM
ejpam-5453	249	4	[	[	X
ejpam-5453	249	5	43	43	NUM
ejpam-5453	249	6	]	]	PUNCT
ejpam-5453	249	7	,	,	PUNCT
ejpam-5453	249	8	and	and	CCONJ
ejpam-5453	249	9	propositions	proposition	NOUN
ejpam-5453	249	10	3.4,3.1	3.4,3.1	NUM
ejpam-5453	249	11	,	,	PUNCT
ejpam-5453	249	12	the	the	DET
ejpam-5453	249	13	proof	proof	NOUN
ejpam-5453	249	14	is	be	AUX
ejpam-5453	249	15	evident	evident	ADJ
ejpam-5453	249	16	.	.	PUNCT
ejpam-5453	250	1	remark	remark	NOUN
ejpam-5453	250	2	3.3	3.3	NUM
ejpam-5453	250	3	.	.	PUNCT
ejpam-5453	251	1	“	"	PUNCT
ejpam-5453	251	2	τs℘(γs℘	τs℘(γs℘	NOUN
ejpam-5453	251	3	)	)	PUNCT
ejpam-5453	251	4	⇐	⇐	ADJ
ejpam-5453	251	5	d	d	NOUN
ejpam-5453	251	6	-	-	PUNCT
ejpam-5453	251	7	αs℘o(d	αs℘o(d	NOUN
ejpam-5453	251	8	-	-	PUNCT
ejpam-5453	251	9	αs℘c	αs℘c	NOUN
ejpam-5453	251	10	)	)	PUNCT
ejpam-5453	251	11	”	"	PUNCT
ejpam-5453	251	12	is	be	AUX
ejpam-5453	251	13	false	false	ADJ
ejpam-5453	251	14	.	.	PUNCT
ejpam-5453	252	1	in	in	ADP
ejpam-5453	252	2	example	example	NOUN
ejpam-5453	252	3	3.1	3.1	NUM
ejpam-5453	252	4	,	,	PUNCT
ejpam-5453	252	5	m	m	PRON
ejpam-5453	252	6	=	=	PUNCT
ejpam-5453	252	7	{	{	PUNCT
ejpam-5453	252	8	l1	l1	PROPN
ejpam-5453	252	9	}	}	PUNCT
ejpam-5453	252	10	∈	∈	PROPN
ejpam-5453	252	11	dαsro(v	dαsro(v	NOUN
ejpam-5453	252	12	)	)	PUNCT
ejpam-5453	252	13	,	,	PUNCT
ejpam-5453	252	14	̸∈	̸∈	PROPN
ejpam-5453	252	15	τsr	τsr	VERB
ejpam-5453	252	16	.	.	PUNCT
ejpam-5453	253	1	proposition	proposition	NOUN
ejpam-5453	253	2	3.3	3.3	NUM
ejpam-5453	253	3	.	.	PUNCT
ejpam-5453	254	1	let	let	AUX
ejpam-5453	254	2	(	(	PUNCT
ejpam-5453	254	3	v	v	NOUN
ejpam-5453	254	4	,	,	PUNCT
ejpam-5453	254	5	υ	υ	NOUN
ejpam-5453	254	6	,	,	PUNCT
ejpam-5453	254	7	π℘	π℘	NUM
ejpam-5453	254	8	)	)	PUNCT
ejpam-5453	254	9	be	be	AUX
ejpam-5453	254	10	a	a	DET
ejpam-5453	254	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	254	12	,	,	PUNCT
ejpam-5453	254	13	d	d	PRON
ejpam-5453	254	14	be	be	AUX
ejpam-5453	254	15	an	an	DET
ejpam-5453	254	16	ideal	ideal	NOUN
ejpam-5453	254	17	on	on	ADP
ejpam-5453	254	18	v	v	NOUN
ejpam-5453	254	19	,	,	PUNCT
ejpam-5453	254	20	υ	υ	PROPN
ejpam-5453	254	21	be	be	AUX
ejpam-5453	254	22	a	a	DET
ejpam-5453	254	23	similarity	similarity	NOUN
ejpam-5453	254	24	relation	relation	NOUN
ejpam-5453	254	25	,	,	PUNCT
ejpam-5453	254	26	℘	℘	PROPN
ejpam-5453	254	27	∈	∈	PROPN
ejpam-5453	254	28	{	{	PUNCT
ejpam-5453	254	29	r	r	NOUN
ejpam-5453	254	30	,	,	PUNCT
ejpam-5453	254	31	l	l	NOUN
ejpam-5453	254	32	,	,	PUNCT
ejpam-5453	254	33	i	i	PRON
ejpam-5453	254	34	,	,	PUNCT
ejpam-5453	254	35	u	u	NOUN
ejpam-5453	254	36	}	}	PUNCT
ejpam-5453	254	37	and	and	CCONJ
ejpam-5453	254	38	m	m	PROPN
ejpam-5453	254	39	⊆	⊆	NUM
ejpam-5453	254	40	v.	v.	ADP
ejpam-5453	254	41	then	then	ADV
ejpam-5453	254	42	τ℘(γ℘	τ℘(γ℘	X
ejpam-5453	254	43	)	)	PUNCT
ejpam-5453	254	44	⇒	⇒	NOUN
ejpam-5453	254	45	τs℘(γs℘	τs℘(γs℘	NOUN
ejpam-5453	254	46	)	)	PUNCT
ejpam-5453	254	47	⇒	⇒	NOUN
ejpam-5453	254	48	d	d	X
ejpam-5453	254	49	-	-	PUNCT
ejpam-5453	254	50	αs℘o(d	αs℘o(d	NOUN
ejpam-5453	254	51	-	-	PUNCT
ejpam-5453	254	52	αs℘c	αs℘c	NOUN
ejpam-5453	254	53	)	)	PUNCT
ejpam-5453	254	54	d	d	NOUN
ejpam-5453	254	55	-	-	PUNCT
ejpam-5453	254	56	ps℘o(d	ps℘o(d	NOUN
ejpam-5453	254	57	-	-	NOUN
ejpam-5453	254	58	ps℘c	ps℘c	NOUN
ejpam-5453	254	59	)	)	PUNCT
ejpam-5453	254	60	⇓	⇓	PROPN
ejpam-5453	254	61	⇓	⇓	PROPN
ejpam-5453	254	62	d	d	PROPN
ejpam-5453	254	63	-	-	PUNCT
ejpam-5453	254	64	ss℘o(d	ss℘o(d	NOUN
ejpam-5453	254	65	-	-	PUNCT
ejpam-5453	254	66	ss℘c	ss℘c	NOUN
ejpam-5453	254	67	)	)	PUNCT
ejpam-5453	254	68	⇒	⇒	NOUN
ejpam-5453	254	69	d	d	X
ejpam-5453	254	70	-	-	ADJ
ejpam-5453	254	71	βs℘o(d	βs℘o(d	ADV
ejpam-5453	254	72	-	-	PUNCT
ejpam-5453	254	73	βs℘c	βs℘c	NOUN
ejpam-5453	254	74	)	)	PUNCT
ejpam-5453	254	75	⇒	⇒	NOUN
ejpam-5453	254	76	d	d	PROPN
ejpam-5453	254	77	-	-	PUNCT
ejpam-5453	254	78	θβs℘o(dθβs℘c	θβs℘o(dθβs℘c	NOUN
ejpam-5453	254	79	)	)	PUNCT
ejpam-5453	254	80	.	.	PUNCT
ejpam-5453	255	1	proof	proof	NOUN
ejpam-5453	255	2	.	.	PUNCT
ejpam-5453	256	1	by	by	ADP
ejpam-5453	256	2	theorem	theorem	ADJ
ejpam-5453	256	3	2.3	2.3	NUM
ejpam-5453	256	4	and	and	CCONJ
ejpam-5453	256	5	proposition	proposition	NOUN
ejpam-5453	256	6	3.2	3.2	NUM
ejpam-5453	256	7	the	the	DET
ejpam-5453	256	8	proof	proof	NOUN
ejpam-5453	256	9	is	be	AUX
ejpam-5453	256	10	uncomplicated	uncomplicated	ADJ
ejpam-5453	256	11	.	.	PUNCT
ejpam-5453	257	1	remark	remark	VERB
ejpam-5453	257	2	3.4	3.4	NUM
ejpam-5453	257	3	.	.	PUNCT
ejpam-5453	258	1	it	it	PRON
ejpam-5453	258	2	should	should	AUX
ejpam-5453	258	3	be	be	AUX
ejpam-5453	258	4	noted	note	VERB
ejpam-5453	258	5	that	that	SCONJ
ejpam-5453	258	6	(	(	PUNCT
ejpam-5453	258	7	i	i	NOUN
ejpam-5453	258	8	)	)	PUNCT
ejpam-5453	258	9	the	the	DET
ejpam-5453	258	10	similarity	similarity	NOUN
ejpam-5453	258	11	relation	relation	NOUN
ejpam-5453	258	12	in	in	ADP
ejpam-5453	258	13	proposition	proposition	NOUN
ejpam-5453	258	14	3.3	3.3	NUM
ejpam-5453	258	15	is	be	AUX
ejpam-5453	258	16	indispensable	indispensable	ADJ
ejpam-5453	258	17	as	as	ADP
ejpam-5453	258	18	example	example	NOUN
ejpam-5453	258	19	3.2	3.2	NUM
ejpam-5453	258	20	.	.	PUNCT
ejpam-5453	259	1	let	let	VERB
ejpam-5453	259	2	v	v	VERB
ejpam-5453	259	3	=	=	SYM
ejpam-5453	259	4	{	{	PUNCT
ejpam-5453	259	5	l1	l1	PROPN
ejpam-5453	259	6	,	,	PUNCT
ejpam-5453	259	7	l2	l2	NOUN
ejpam-5453	259	8	,	,	PUNCT
ejpam-5453	259	9	l3	l3	PROPN
ejpam-5453	259	10	,	,	PUNCT
ejpam-5453	259	11	l4	l4	PROPN
ejpam-5453	259	12	}	}	PUNCT
ejpam-5453	259	13	and	and	CCONJ
ejpam-5453	259	14	υ	υ	NOUN
ejpam-5453	259	15	=	=	PRON
ejpam-5453	259	16	{	{	PUNCT
ejpam-5453	259	17	(	(	PUNCT
ejpam-5453	259	18	l1	l1	PROPN
ejpam-5453	259	19	,	,	PUNCT
ejpam-5453	259	20	l1	l1	PROPN
ejpam-5453	259	21	)	)	PUNCT
ejpam-5453	259	22	,	,	PUNCT
ejpam-5453	259	23	(	(	PUNCT
ejpam-5453	259	24	l2	l2	NOUN
ejpam-5453	259	25	,	,	PUNCT
ejpam-5453	259	26	l2	l2	NOUN
ejpam-5453	259	27	)	)	PUNCT
ejpam-5453	259	28	,	,	PUNCT
ejpam-5453	259	29	(	(	PUNCT
ejpam-5453	259	30	l1	l1	PROPN
ejpam-5453	259	31	,	,	PUNCT
ejpam-5453	259	32	l3	l3	PROPN
ejpam-5453	259	33	)	)	PUNCT
ejpam-5453	259	34	,	,	PUNCT
ejpam-5453	259	35	(	(	PUNCT
ejpam-5453	259	36	l2	l2	NOUN
ejpam-5453	259	37	,	,	PUNCT
ejpam-5453	259	38	l3	l3	PROPN
ejpam-5453	259	39	)	)	PUNCT
ejpam-5453	259	40	,	,	PUNCT
ejpam-5453	259	41	(	(	PUNCT
ejpam-5453	259	42	l2	l2	NOUN
ejpam-5453	259	43	,	,	PUNCT
ejpam-5453	259	44	l4	l4	PROPN
ejpam-5453	259	45	)	)	PUNCT
ejpam-5453	259	46	}	}	PUNCT
ejpam-5453	259	47	.	.	PUNCT
ejpam-5453	260	1	then	then	ADV
ejpam-5453	260	2	,	,	PUNCT
ejpam-5453	260	3	τr	τr	PUNCT
ejpam-5453	260	4	=	=	PRON
ejpam-5453	260	5	{	{	PUNCT
ejpam-5453	260	6	v	v	NOUN
ejpam-5453	260	7	,	,	PUNCT
ejpam-5453	260	8	∅	∅	NOUN
ejpam-5453	260	9	,	,	PUNCT
ejpam-5453	260	10	{	{	PUNCT
ejpam-5453	260	11	l3	l3	X
ejpam-5453	260	12	}	}	PUNCT
ejpam-5453	260	13	,	,	PUNCT
ejpam-5453	260	14	{	{	PUNCT
ejpam-5453	260	15	l4	l4	PROPN
ejpam-5453	260	16	}	}	PUNCT
ejpam-5453	260	17	,	,	PUNCT
ejpam-5453	260	18	{	{	PUNCT
ejpam-5453	260	19	l3	l3	PROPN
ejpam-5453	260	20	,	,	PUNCT
ejpam-5453	260	21	l4	l4	PROPN
ejpam-5453	260	22	}	}	PUNCT
ejpam-5453	260	23	,	,	PUNCT
ejpam-5453	260	24	{	{	PUNCT
ejpam-5453	260	25	l2	l2	NOUN
ejpam-5453	260	26	,	,	PUNCT
ejpam-5453	260	27	l3	l3	PROPN
ejpam-5453	260	28	,	,	PUNCT
ejpam-5453	260	29	l4	l4	PROPN
ejpam-5453	260	30	}	}	PUNCT
ejpam-5453	260	31	}	}	PUNCT
ejpam-5453	260	32	and	and	CCONJ
ejpam-5453	260	33	τsr	τsr	X
ejpam-5453	260	34	=	=	PUNCT
ejpam-5453	260	35	{	{	PUNCT
ejpam-5453	260	36	v	v	NOUN
ejpam-5453	260	37	,	,	PUNCT
ejpam-5453	260	38	∅	∅	NOUN
ejpam-5453	260	39	,	,	PUNCT
ejpam-5453	260	40	{	{	PUNCT
ejpam-5453	260	41	l1	l1	PROPN
ejpam-5453	260	42	}	}	PUNCT
ejpam-5453	260	43	,	,	PUNCT
ejpam-5453	260	44	{	{	PUNCT
ejpam-5453	260	45	l2	l2	NOUN
ejpam-5453	260	46	}	}	PUNCT
ejpam-5453	260	47	,	,	PUNCT
ejpam-5453	260	48	{	{	PUNCT
ejpam-5453	260	49	l1	l1	PROPN
ejpam-5453	260	50	,	,	PUNCT
ejpam-5453	260	51	l2	l2	NOUN
ejpam-5453	260	52	}	}	PUNCT
ejpam-5453	260	53	}	}	PUNCT
ejpam-5453	260	54	are	be	AUX
ejpam-5453	260	55	incomparable	incomparable	ADJ
ejpam-5453	260	56	.	.	PUNCT
ejpam-5453	261	1	(	(	PUNCT
ejpam-5453	261	2	ii	ii	NOUN
ejpam-5453	261	3	)	)	PUNCT
ejpam-5453	261	4	“	"	PUNCT
ejpam-5453	261	5	τ℘(γ℘	τ℘(γ℘	X
ejpam-5453	261	6	)	)	PUNCT
ejpam-5453	261	7	⇐	⇐	ADJ
ejpam-5453	261	8	d	d	NOUN
ejpam-5453	261	9	-	-	PUNCT
ejpam-5453	261	10	αs℘o(d	αs℘o(d	NOUN
ejpam-5453	261	11	-	-	PUNCT
ejpam-5453	261	12	αs℘c	αs℘c	NOUN
ejpam-5453	261	13	)	)	PUNCT
ejpam-5453	261	14	”	"	PUNCT
ejpam-5453	261	15	is	be	AUX
ejpam-5453	261	16	incorrect	incorrect	ADJ
ejpam-5453	261	17	as	as	ADP
ejpam-5453	261	18	:	:	PUNCT
ejpam-5453	261	19	example	example	NOUN
ejpam-5453	261	20	3.3	3.3	NUM
ejpam-5453	261	21	.	.	PUNCT
ejpam-5453	262	1	let	let	VERB
ejpam-5453	262	2	v	v	VERB
ejpam-5453	262	3	=	=	SYM
ejpam-5453	262	4	{	{	PUNCT
ejpam-5453	262	5	l1	l1	PROPN
ejpam-5453	262	6	,	,	PUNCT
ejpam-5453	262	7	l2	l2	NOUN
ejpam-5453	262	8	,	,	PUNCT
ejpam-5453	262	9	l3	l3	PROPN
ejpam-5453	262	10	,	,	PUNCT
ejpam-5453	262	11	l4	l4	PROPN
ejpam-5453	262	12	}	}	PUNCT
ejpam-5453	262	13	,	,	PUNCT
ejpam-5453	262	14	υ	υ	NOUN
ejpam-5453	262	15	=	=	PRON
ejpam-5453	262	16	{	{	PUNCT
ejpam-5453	262	17	(	(	PUNCT
ejpam-5453	262	18	l1	l1	PROPN
ejpam-5453	262	19	,	,	PUNCT
ejpam-5453	262	20	l1	l1	PROPN
ejpam-5453	262	21	)	)	PUNCT
ejpam-5453	262	22	,	,	PUNCT
ejpam-5453	262	23	(	(	PUNCT
ejpam-5453	262	24	l2	l2	NOUN
ejpam-5453	262	25	,	,	PUNCT
ejpam-5453	262	26	l2	l2	NOUN
ejpam-5453	262	27	)	)	PUNCT
ejpam-5453	262	28	,	,	PUNCT
ejpam-5453	262	29	(	(	PUNCT
ejpam-5453	262	30	l3	l3	PROPN
ejpam-5453	262	31	,	,	PUNCT
ejpam-5453	262	32	l3	l3	PROPN
ejpam-5453	262	33	)	)	PUNCT
ejpam-5453	262	34	,	,	PUNCT
ejpam-5453	262	35	(	(	PUNCT
ejpam-5453	262	36	l4	l4	PROPN
ejpam-5453	262	37	,	,	PUNCT
ejpam-5453	262	38	l4	l4	PROPN
ejpam-5453	262	39	)	)	PUNCT
ejpam-5453	262	40	,	,	PUNCT
ejpam-5453	262	41	(	(	PUNCT
ejpam-5453	262	42	l1	l1	PROPN
ejpam-5453	262	43	,	,	PUNCT
ejpam-5453	262	44	l2	l2	NOUN
ejpam-5453	262	45	)	)	PUNCT
ejpam-5453	262	46	,	,	PUNCT
ejpam-5453	262	47	(	(	PUNCT
ejpam-5453	262	48	l2	l2	NOUN
ejpam-5453	262	49	,	,	PUNCT
ejpam-5453	262	50	l1	l1	PROPN
ejpam-5453	262	51	)	)	PUNCT
ejpam-5453	262	52	,	,	PUNCT
ejpam-5453	262	53	(	(	PUNCT
ejpam-5453	262	54	l2	l2	NOUN
ejpam-5453	262	55	,	,	PUNCT
ejpam-5453	262	56	l4	l4	PROPN
ejpam-5453	262	57	)	)	PUNCT
ejpam-5453	262	58	,	,	PUNCT
ejpam-5453	262	59	(	(	PUNCT
ejpam-5453	262	60	l4	l4	PROPN
ejpam-5453	262	61	,	,	PUNCT
ejpam-5453	262	62	l2	l2	NOUN
ejpam-5453	262	63	)	)	PUNCT
ejpam-5453	262	64	,	,	PUNCT
ejpam-5453	262	65	(	(	PUNCT
ejpam-5453	262	66	l3	l3	PROPN
ejpam-5453	262	67	,	,	PUNCT
ejpam-5453	262	68	l4	l4	PROPN
ejpam-5453	262	69	)	)	PUNCT
ejpam-5453	262	70	,	,	PUNCT
ejpam-5453	262	71	(	(	PUNCT
ejpam-5453	262	72	l4	l4	PROPN
ejpam-5453	262	73	,	,	PUNCT
ejpam-5453	262	74	l3	l3	PROPN
ejpam-5453	262	75	)	)	PUNCT
ejpam-5453	262	76	}	}	PUNCT
ejpam-5453	262	77	,	,	PUNCT
ejpam-5453	262	78	and	and	CCONJ
ejpam-5453	263	1	d	d	X
ejpam-5453	263	2	=	=	SYM
ejpam-5453	263	3	{	{	PUNCT
ejpam-5453	263	4	∅	∅	NOUN
ejpam-5453	263	5	,	,	PUNCT
ejpam-5453	263	6	{	{	PUNCT
ejpam-5453	263	7	l3	l3	NOUN
ejpam-5453	263	8	}	}	PUNCT
ejpam-5453	263	9	}	}	PUNCT
ejpam-5453	263	10	.	.	PUNCT
ejpam-5453	264	1	then	then	ADV
ejpam-5453	264	2	it	it	PRON
ejpam-5453	264	3	is	be	AUX
ejpam-5453	264	4	clear	clear	ADJ
ejpam-5453	264	5	that	that	SCONJ
ejpam-5453	264	6	,	,	PUNCT
ejpam-5453	264	7	{	{	PUNCT
ejpam-5453	264	8	l2	l2	NOUN
ejpam-5453	264	9	}	}	PUNCT
ejpam-5453	264	10	∈	∈	PROPN
ejpam-5453	265	1	d	d	X
ejpam-5453	265	2	-	-	PUNCT
ejpam-5453	265	3	αsr	αsr	PRON
ejpam-5453	265	4	,	,	PUNCT
ejpam-5453	265	5	̸∈	̸∈	PROPN
ejpam-5453	265	6	τr	τr	PROPN
ejpam-5453	265	7	(	(	PUNCT
ejpam-5453	265	8	iii	iii	NOUN
ejpam-5453	265	9	)	)	PUNCT
ejpam-5453	265	10	example	example	NOUN
ejpam-5453	265	11	3.3	3.3	NUM
ejpam-5453	265	12	shows	show	NOUN
ejpam-5453	265	13	also	also	ADV
ejpam-5453	265	14	that	that	SCONJ
ejpam-5453	265	15	τs℘	τs℘	NOUN
ejpam-5453	265	16	,	,	PUNCT
ejpam-5453	265	17	τ℘	τ℘	NUM
ejpam-5453	265	18	are	be	AUX
ejpam-5453	265	19	not	not	PART
ejpam-5453	265	20	comparable	comparable	ADJ
ejpam-5453	265	21	if	if	SCONJ
ejpam-5453	265	22	℘	℘	NUM
ejpam-5453	265	23	∈	∈	PROPN
ejpam-5453	265	24	{	{	PUNCT
ejpam-5453	265	25	<	<	X
ejpam-5453	265	26	r	r	X
ejpam-5453	265	27	>	>	PUNCT
ejpam-5453	265	28	,	,	PUNCT
ejpam-5453	265	29	<	<	X
ejpam-5453	265	30	l	l	X
ejpam-5453	265	31	>	>	PUNCT
ejpam-5453	265	32	,	,	PUNCT
ejpam-5453	265	33	<	<	X
ejpam-5453	265	34	i	i	X
ejpam-5453	265	35	>	>	X
ejpam-5453	265	36	,	,	PUNCT
ejpam-5453	265	37	<	<	X
ejpam-5453	265	38	u	u	X
ejpam-5453	265	39	>	>	X
ejpam-5453	265	40	}	}	PUNCT
ejpam-5453	265	41	.	.	PUNCT
ejpam-5453	266	1	then	then	ADV
ejpam-5453	266	2	,	,	PUNCT
ejpam-5453	266	3	τs	τs	ADP
ejpam-5453	266	4	<	<	X
ejpam-5453	266	5	r	r	X
ejpam-5453	266	6	>	>	X
ejpam-5453	266	7	=	=	PUNCT
ejpam-5453	266	8	{	{	PUNCT
ejpam-5453	266	9	v	v	NOUN
ejpam-5453	266	10	,	,	PUNCT
ejpam-5453	266	11	∅	∅	NOUN
ejpam-5453	266	12	,	,	PUNCT
ejpam-5453	266	13	{	{	PUNCT
ejpam-5453	266	14	l1	l1	PROPN
ejpam-5453	266	15	}	}	PUNCT
ejpam-5453	266	16	,	,	PUNCT
ejpam-5453	266	17	{	{	PUNCT
ejpam-5453	266	18	l3	l3	X
ejpam-5453	266	19	}	}	PUNCT
ejpam-5453	266	20	,	,	PUNCT
ejpam-5453	266	21	{	{	PUNCT
ejpam-5453	266	22	l1	l1	PROPN
ejpam-5453	266	23	,	,	PUNCT
ejpam-5453	266	24	l2	l2	NOUN
ejpam-5453	266	25	}	}	PUNCT
ejpam-5453	266	26	,	,	PUNCT
ejpam-5453	266	27	{	{	PUNCT
ejpam-5453	266	28	l1	l1	PROPN
ejpam-5453	266	29	,	,	PUNCT
ejpam-5453	266	30	l3	l3	PROPN
ejpam-5453	266	31	}	}	PUNCT
ejpam-5453	266	32	,	,	PUNCT
ejpam-5453	266	33	{	{	PUNCT
ejpam-5453	266	34	l3	l3	PROPN
ejpam-5453	266	35	,	,	PUNCT
ejpam-5453	266	36	l4	l4	PROPN
ejpam-5453	266	37	}	}	PUNCT
ejpam-5453	266	38	,	,	PUNCT
ejpam-5453	266	39	{	{	PUNCT
ejpam-5453	266	40	l1	l1	PROPN
ejpam-5453	266	41	,	,	PUNCT
ejpam-5453	266	42	l2	l2	NOUN
ejpam-5453	266	43	,	,	PUNCT
ejpam-5453	266	44	l3	l3	PROPN
ejpam-5453	266	45	}	}	PUNCT
ejpam-5453	266	46	,	,	PUNCT
ejpam-5453	266	47	{	{	PUNCT
ejpam-5453	266	48	l1	l1	PROPN
ejpam-5453	266	49	,	,	PUNCT
ejpam-5453	266	50	l3	l3	PROPN
ejpam-5453	266	51	,	,	PUNCT
ejpam-5453	266	52	l4	l4	PROPN
ejpam-5453	266	53	}	}	PUNCT
ejpam-5453	266	54	}	}	PUNCT
ejpam-5453	266	55	and	and	CCONJ
ejpam-5453	266	56	τ	τ	X
ejpam-5453	266	57	<	<	X
ejpam-5453	266	58	r	r	X
ejpam-5453	266	59	>	>	X
ejpam-5453	266	60	=	=	PUNCT
ejpam-5453	266	61	{	{	PUNCT
ejpam-5453	266	62	v	v	NOUN
ejpam-5453	266	63	,	,	PUNCT
ejpam-5453	266	64	∅	∅	NOUN
ejpam-5453	266	65	,	,	PUNCT
ejpam-5453	266	66	{	{	PUNCT
ejpam-5453	266	67	l2	l2	NOUN
ejpam-5453	266	68	}	}	PUNCT
ejpam-5453	266	69	,	,	PUNCT
ejpam-5453	266	70	{	{	PUNCT
ejpam-5453	266	71	l4	l4	PROPN
ejpam-5453	266	72	}	}	PUNCT
ejpam-5453	266	73	,	,	PUNCT
ejpam-5453	266	74	{	{	PUNCT
ejpam-5453	266	75	l1	l1	PROPN
ejpam-5453	266	76	,	,	PUNCT
ejpam-5453	266	77	l2	l2	NOUN
ejpam-5453	266	78	}	}	PUNCT
ejpam-5453	266	79	,	,	PUNCT
ejpam-5453	266	80	{	{	PUNCT
ejpam-5453	266	81	l2	l2	NOUN
ejpam-5453	266	82	,	,	PUNCT
ejpam-5453	266	83	l4	l4	PROPN
ejpam-5453	266	84	}	}	PUNCT
ejpam-5453	266	85	,	,	PUNCT
ejpam-5453	266	86	{	{	PUNCT
ejpam-5453	266	87	l3	l3	PROPN
ejpam-5453	266	88	,	,	PUNCT
ejpam-5453	266	89	l4	l4	PROPN
ejpam-5453	266	90	}	}	PUNCT
ejpam-5453	266	91	,	,	PUNCT
ejpam-5453	266	92	{	{	PUNCT
ejpam-5453	266	93	l1	l1	PROPN
ejpam-5453	266	94	,	,	PUNCT
ejpam-5453	266	95	l2	l2	NOUN
ejpam-5453	266	96	,	,	PUNCT
ejpam-5453	266	97	l4	l4	PROPN
ejpam-5453	266	98	}	}	PUNCT
ejpam-5453	266	99	,	,	PUNCT
ejpam-5453	266	100	{	{	PUNCT
ejpam-5453	266	101	l2	l2	NOUN
ejpam-5453	266	102	,	,	PUNCT
ejpam-5453	266	103	l3	l3	PROPN
ejpam-5453	266	104	,	,	PUNCT
ejpam-5453	266	105	l4	l4	PROPN
ejpam-5453	266	106	}	}	PUNCT
ejpam-5453	266	107	}	}	PUNCT
ejpam-5453	266	108	.	.	PUNCT
ejpam-5453	267	1	so	so	ADV
ejpam-5453	267	2	,	,	PUNCT
ejpam-5453	267	3	proposition	proposition	NOUN
ejpam-5453	267	4	3.3	3.3	NUM
ejpam-5453	267	5	applies	apply	VERB
ejpam-5453	267	6	only	only	ADV
ejpam-5453	267	7	for	for	ADP
ejpam-5453	267	8	℘	℘	PROPN
ejpam-5453	267	9	∈	∈	PROPN
ejpam-5453	267	10	{	{	PUNCT
ejpam-5453	267	11	r	r	NOUN
ejpam-5453	267	12	,	,	PUNCT
ejpam-5453	267	13	l	l	NOUN
ejpam-5453	267	14	,	,	PUNCT
ejpam-5453	267	15	i	i	PRON
ejpam-5453	267	16	,	,	PUNCT
ejpam-5453	267	17	u	u	NOUN
ejpam-5453	267	18	}	}	PUNCT
ejpam-5453	267	19	.	.	PUNCT
ejpam-5453	268	1	theorem	theorem	VERB
ejpam-5453	268	2	3.1	3.1	NUM
ejpam-5453	268	3	.	.	PUNCT
ejpam-5453	269	1	let	let	AUX
ejpam-5453	269	2	(	(	PUNCT
ejpam-5453	269	3	v	v	NOUN
ejpam-5453	269	4	,	,	PUNCT
ejpam-5453	269	5	υ	υ	NOUN
ejpam-5453	269	6	,	,	PUNCT
ejpam-5453	269	7	π℘	π℘	NUM
ejpam-5453	269	8	)	)	PUNCT
ejpam-5453	269	9	be	be	VERB
ejpam-5453	269	10	a	a	DET
ejpam-5453	269	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	269	12	and	and	CCONJ
ejpam-5453	269	13	d	d	NOUN
ejpam-5453	269	14	be	be	AUX
ejpam-5453	269	15	an	an	DET
ejpam-5453	269	16	ideal	ideal	NOUN
ejpam-5453	269	17	on	on	ADP
ejpam-5453	269	18	v.	v.	ADV
ejpam-5453	269	19	then	then	ADV
ejpam-5453	269	20	,	,	PUNCT
ejpam-5453	269	21	the	the	DET
ejpam-5453	269	22	union	union	NOUN
ejpam-5453	269	23	of	of	ADP
ejpam-5453	269	24	two	two	NUM
ejpam-5453	269	25	d	d	NOUN
ejpam-5453	269	26	-	-	NOUN
ejpam-5453	269	27	αs℘-open	αs℘-open	ADJ
ejpam-5453	269	28	(	(	PUNCT
ejpam-5453	269	29	respectively	respectively	ADV
ejpam-5453	269	30	,	,	PUNCT
ejpam-5453	269	31	d	d	NOUN
ejpam-5453	269	32	-	-	PUNCT
ejpam-5453	269	33	ss℘-open	ss℘-open	ADJ
ejpam-5453	269	34	,	,	PUNCT
ejpam-5453	269	35	d	d	NOUN
ejpam-5453	269	36	-	-	PUNCT
ejpam-5453	269	37	ps℘-open	ps℘-open	ADJ
ejpam-5453	269	38	,	,	PUNCT
ejpam-5453	269	39	d	d	NOUN
ejpam-5453	269	40	-	-	PUNCT
ejpam-5453	269	41	βs℘-open	βs℘-open	ADJ
ejpam-5453	269	42	)	)	PUNCT
ejpam-5453	269	43	sets	set	NOUN
ejpam-5453	269	44	is	be	AUX
ejpam-5453	269	45	also	also	ADV
ejpam-5453	269	46	d	d	ADJ
ejpam-5453	269	47	-	-	PUNCT
ejpam-5453	269	48	αs℘-open	αs℘-open	ADJ
ejpam-5453	269	49	(	(	PUNCT
ejpam-5453	269	50	respectively	respectively	ADV
ejpam-5453	269	51	,	,	PUNCT
ejpam-5453	269	52	d	d	NOUN
ejpam-5453	269	53	-	-	PUNCT
ejpam-5453	269	54	ss℘-open	ss℘-open	ADJ
ejpam-5453	269	55	,	,	PUNCT
ejpam-5453	269	56	d	d	NOUN
ejpam-5453	269	57	-	-	PUNCT
ejpam-5453	269	58	ps℘-open	ps℘-open	ADJ
ejpam-5453	269	59	,	,	PUNCT
ejpam-5453	269	60	d	d	PROPN
ejpam-5453	269	61	-	-	PUNCT
ejpam-5453	269	62	βj	βj	NOUN
ejpam-5453	269	63	-open	-open	NOUN
ejpam-5453	269	64	)	)	PUNCT
ejpam-5453	269	65	set	set	NOUN
ejpam-5453	269	66	.	.	PUNCT
ejpam-5453	270	1	proof	proof	NOUN
ejpam-5453	270	2	.	.	PUNCT
ejpam-5453	271	1	we	we	PRON
ejpam-5453	271	2	prove	prove	VERB
ejpam-5453	271	3	in	in	ADP
ejpam-5453	271	4	the	the	DET
ejpam-5453	271	5	case	case	NOUN
ejpam-5453	271	6	of	of	ADP
ejpam-5453	271	7	d	d	PROPN
ejpam-5453	271	8	-	-	PUNCT
ejpam-5453	271	9	αs℘-open	αs℘-open	ADJ
ejpam-5453	271	10	sets	set	NOUN
ejpam-5453	271	11	and	and	CCONJ
ejpam-5453	271	12	the	the	DET
ejpam-5453	271	13	others	other	NOUN
ejpam-5453	271	14	cases	case	NOUN
ejpam-5453	271	15	are	be	AUX
ejpam-5453	271	16	similarly	similarly	ADV
ejpam-5453	271	17	.	.	PUNCT
ejpam-5453	272	1	let	let	VERB
ejpam-5453	272	2	m	m	PRON
ejpam-5453	272	3	,	,	PUNCT
ejpam-5453	272	4	n	n	PROPN
ejpam-5453	272	5	∈	∈	PROPN
ejpam-5453	272	6	d	d	PROPN
ejpam-5453	272	7	-	-	PUNCT
ejpam-5453	272	8	αs℘o(v	αs℘o(v	NUM
ejpam-5453	272	9	)	)	PUNCT
ejpam-5453	272	10	.	.	PUNCT
ejpam-5453	273	1	then	then	ADV
ejpam-5453	273	2	,	,	PUNCT
ejpam-5453	273	3	∃g	∃g	PROPN
ejpam-5453	273	4	,	,	PUNCT
ejpam-5453	273	5	h	h	NOUN
ejpam-5453	273	6	∈	∈	PROPN
ejpam-5453	274	1	τs℘	τs℘	NOUN
ejpam-5453	274	2	such	such	ADJ
ejpam-5453	274	3	that	that	SCONJ
ejpam-5453	274	4	(	(	PUNCT
ejpam-5453	274	5	m	m	NOUN
ejpam-5453	274	6	−	−	PROPN
ejpam-5453	274	7	ints℘cls℘(g	ints℘cls℘(g	NOUN
ejpam-5453	274	8	)	)	PUNCT
ejpam-5453	274	9	)	)	PUNCT
ejpam-5453	275	1	∈	∈	PROPN
ejpam-5453	275	2	d	d	NOUN
ejpam-5453	275	3	,	,	PUNCT
ejpam-5453	275	4	(	(	PUNCT
ejpam-5453	275	5	g−m	g−m	PROPN
ejpam-5453	275	6	)	)	PUNCT
ejpam-5453	275	7	∈	∈	PROPN
ejpam-5453	276	1	d	d	PROPN
ejpam-5453	276	2	,	,	PUNCT
ejpam-5453	276	3	(	(	PUNCT
ejpam-5453	276	4	n	n	CCONJ
ejpam-5453	276	5	−	−	PROPN
ejpam-5453	276	6	ints℘cls℘(h	ints℘cls℘(h	ADJ
ejpam-5453	276	7	)	)	PUNCT
ejpam-5453	276	8	)	)	PUNCT
ejpam-5453	277	1	∈	∈	PROPN
ejpam-5453	277	2	d	d	NOUN
ejpam-5453	277	3	and	and	CCONJ
ejpam-5453	277	4	(	(	PUNCT
ejpam-5453	277	5	h	h	NOUN
ejpam-5453	277	6	−	−	PROPN
ejpam-5453	277	7	n	n	CCONJ
ejpam-5453	277	8	)	)	PUNCT
ejpam-5453	277	9	∈	∈	PROPN
ejpam-5453	277	10	d.	d.	PROPN
ejpam-5453	277	11	since	since	SCONJ
ejpam-5453	277	12	,	,	PUNCT
ejpam-5453	277	13	(	(	PUNCT
ejpam-5453	277	14	g	g	PROPN
ejpam-5453	277	15	−	−	PROPN
ejpam-5453	277	16	(	(	PUNCT
ejpam-5453	277	17	m	m	PROPN
ejpam-5453	277	18	∪	∪	ADJ
ejpam-5453	277	19	n	n	CCONJ
ejpam-5453	277	20	)	)	PUNCT
ejpam-5453	277	21	)	)	PUNCT
ejpam-5453	278	1	⊆	⊆	X
ejpam-5453	278	2	(	(	PUNCT
ejpam-5453	278	3	g	g	PROPN
ejpam-5453	278	4	−	−	PROPN
ejpam-5453	278	5	m	m	PROPN
ejpam-5453	278	6	)	)	PUNCT
ejpam-5453	278	7	and	and	CCONJ
ejpam-5453	278	8	m.	m.	PROPN
ejpam-5453	278	9	hosny	hosny	PROPN
ejpam-5453	278	10	/	/	SYM
ejpam-5453	278	11	eur	eur	PROPN
ejpam-5453	278	12	.	.	PUNCT
ejpam-5453	279	1	j.	j.	PROPN
ejpam-5453	279	2	pure	pure	PROPN
ejpam-5453	279	3	appl	appl	PROPN
ejpam-5453	279	4	.	.	PROPN
ejpam-5453	279	5	math	math	PROPN
ejpam-5453	279	6	,	,	PUNCT
ejpam-5453	279	7	17	17	NUM
ejpam-5453	279	8	(	(	PUNCT
ejpam-5453	279	9	4	4	NUM
ejpam-5453	279	10	)	)	PUNCT
ejpam-5453	279	11	(	(	PUNCT
ejpam-5453	279	12	2024	2024	NUM
ejpam-5453	279	13	)	)	PUNCT
ejpam-5453	279	14	,	,	PUNCT
ejpam-5453	279	15	2843	2843	NUM
ejpam-5453	279	16	-	-	SYM
ejpam-5453	279	17	2877	2877	NUM
ejpam-5453	279	18	2852	2852	NUM
ejpam-5453	279	19	(	(	PUNCT
ejpam-5453	279	20	g	g	PROPN
ejpam-5453	279	21	−	−	PROPN
ejpam-5453	279	22	m	m	NOUN
ejpam-5453	279	23	)	)	PUNCT
ejpam-5453	279	24	∈	∈	PROPN
ejpam-5453	280	1	d	d	NOUN
ejpam-5453	280	2	,	,	PUNCT
ejpam-5453	280	3	so	so	CCONJ
ejpam-5453	280	4	(	(	PUNCT
ejpam-5453	280	5	g	g	PROPN
ejpam-5453	280	6	−	−	PROPN
ejpam-5453	280	7	(	(	PUNCT
ejpam-5453	280	8	m	m	PROPN
ejpam-5453	280	9	∪	∪	ADJ
ejpam-5453	280	10	n	n	CCONJ
ejpam-5453	280	11	)	)	PUNCT
ejpam-5453	280	12	)	)	PUNCT
ejpam-5453	281	1	∈	∈	PROPN
ejpam-5453	281	2	d.	d.	PROPN
ejpam-5453	281	3	similarly	similarly	ADV
ejpam-5453	281	4	,	,	PUNCT
ejpam-5453	281	5	(	(	PUNCT
ejpam-5453	281	6	h	h	NOUN
ejpam-5453	281	7	−	−	PROPN
ejpam-5453	281	8	(	(	PUNCT
ejpam-5453	281	9	m	m	PROPN
ejpam-5453	281	10	∪	∪	ADJ
ejpam-5453	281	11	n	n	CCONJ
ejpam-5453	281	12	)	)	PUNCT
ejpam-5453	281	13	)	)	PUNCT
ejpam-5453	282	1	∈	∈	PROPN
ejpam-5453	282	2	d	d	NOUN
ejpam-5453	282	3	,	,	PUNCT
ejpam-5453	282	4	and	and	CCONJ
ejpam-5453	282	5	hence	hence	ADV
ejpam-5453	282	6	(	(	PUNCT
ejpam-5453	282	7	g	g	PROPN
ejpam-5453	282	8	−	−	PROPN
ejpam-5453	282	9	(	(	PUNCT
ejpam-5453	282	10	m	m	PROPN
ejpam-5453	282	11	∪	∪	ADJ
ejpam-5453	282	12	n	n	CCONJ
ejpam-5453	282	13	)	)	PUNCT
ejpam-5453	282	14	)	)	PUNCT
ejpam-5453	282	15	∪	∪	ADV
ejpam-5453	282	16	(	(	PUNCT
ejpam-5453	282	17	h	h	NOUN
ejpam-5453	282	18	−	−	PROPN
ejpam-5453	282	19	(	(	PUNCT
ejpam-5453	282	20	m	m	PROPN
ejpam-5453	282	21	∪	∪	ADJ
ejpam-5453	282	22	n	n	CCONJ
ejpam-5453	282	23	)	)	PUNCT
ejpam-5453	282	24	)	)	PUNCT
ejpam-5453	283	1	∈	∈	PROPN
ejpam-5453	283	2	d.	d.	PROPN
ejpam-5453	283	3	let	let	VERB
ejpam-5453	283	4	w	w	NOUN
ejpam-5453	283	5	=	=	PUNCT
ejpam-5453	283	6	g	g	PROPN
ejpam-5453	283	7	∪	∪	ADJ
ejpam-5453	283	8	h	h	NOUN
ejpam-5453	283	9	,	,	PUNCT
ejpam-5453	283	10	then	then	ADV
ejpam-5453	283	11	(	(	PUNCT
ejpam-5453	283	12	w	w	PROPN
ejpam-5453	283	13	−	−	PROPN
ejpam-5453	283	14	(	(	PUNCT
ejpam-5453	283	15	m	m	NOUN
ejpam-5453	283	16	∪	∪	ADJ
ejpam-5453	283	17	n	n	CCONJ
ejpam-5453	283	18	)	)	PUNCT
ejpam-5453	283	19	)	)	PUNCT
ejpam-5453	284	1	∈	∈	PROPN
ejpam-5453	284	2	d.	d.	PROPN
ejpam-5453	284	3	also	also	ADV
ejpam-5453	284	4	,	,	PUNCT
ejpam-5453	284	5	(	(	PUNCT
ejpam-5453	284	6	m	m	VERB
ejpam-5453	284	7	−	−	NOUN
ejpam-5453	284	8	ints℘cls℘(w	ints℘cls℘(w	NOUN
ejpam-5453	284	9	)	)	PUNCT
ejpam-5453	284	10	)	)	PUNCT
ejpam-5453	285	1	⊆	⊆	NUM
ejpam-5453	285	2	(	(	PUNCT
ejpam-5453	285	3	m	m	NOUN
ejpam-5453	285	4	−	−	PROPN
ejpam-5453	285	5	ints℘cls℘(g	ints℘cls℘(g	NOUN
ejpam-5453	285	6	)	)	PUNCT
ejpam-5453	285	7	)	)	PUNCT
ejpam-5453	286	1	∈	∈	PROPN
ejpam-5453	286	2	d	d	NOUN
ejpam-5453	286	3	and	and	CCONJ
ejpam-5453	286	4	(	(	PUNCT
ejpam-5453	286	5	n	n	CCONJ
ejpam-5453	286	6	−	−	PROPN
ejpam-5453	286	7	ints℘cls℘(w	ints℘cls℘(w	NOUN
ejpam-5453	286	8	)	)	PUNCT
ejpam-5453	286	9	)	)	PUNCT
ejpam-5453	287	1	⊆	⊆	NUM
ejpam-5453	287	2	(	(	PUNCT
ejpam-5453	287	3	n	n	CCONJ
ejpam-5453	287	4	−	−	PROPN
ejpam-5453	287	5	ints℘cls℘(h	ints℘cls℘(h	ADJ
ejpam-5453	287	6	)	)	PUNCT
ejpam-5453	287	7	)	)	PUNCT
ejpam-5453	288	1	∈	∈	PROPN
ejpam-5453	288	2	d.	d.	NOUN
ejpam-5453	288	3	then	then	ADV
ejpam-5453	288	4	,	,	PUNCT
ejpam-5453	288	5	(	(	PUNCT
ejpam-5453	288	6	m	m	VERB
ejpam-5453	288	7	−	−	NOUN
ejpam-5453	288	8	ints℘cls℘(w	ints℘cls℘(w	NOUN
ejpam-5453	288	9	)	)	PUNCT
ejpam-5453	288	10	)	)	PUNCT
ejpam-5453	288	11	∪	∪	NOUN
ejpam-5453	288	12	(	(	PUNCT
ejpam-5453	288	13	n	n	CCONJ
ejpam-5453	288	14	−	−	PROPN
ejpam-5453	288	15	ints℘cls℘(w	ints℘cls℘(w	NOUN
ejpam-5453	288	16	)	)	PUNCT
ejpam-5453	288	17	)	)	PUNCT
ejpam-5453	289	1	∈	∈	PROPN
ejpam-5453	289	2	d	d	NOUN
ejpam-5453	289	3	and	and	CCONJ
ejpam-5453	289	4	so	so	ADV
ejpam-5453	289	5	(	(	PUNCT
ejpam-5453	289	6	(	(	PUNCT
ejpam-5453	289	7	m	m	NOUN
ejpam-5453	289	8	∪	∪	NOUN
ejpam-5453	289	9	n	n	CCONJ
ejpam-5453	289	10	)	)	PUNCT
ejpam-5453	289	11	−	−	PROPN
ejpam-5453	289	12	ints℘cls℘(w	ints℘cls℘(w	NOUN
ejpam-5453	289	13	)	)	PUNCT
ejpam-5453	289	14	)	)	PUNCT
ejpam-5453	290	1	⊆	⊆	NUM
ejpam-5453	290	2	(	(	PUNCT
ejpam-5453	290	3	m	m	NOUN
ejpam-5453	290	4	−	−	PROPN
ejpam-5453	290	5	ints℘cls℘(g	ints℘cls℘(g	NOUN
ejpam-5453	290	6	)	)	PUNCT
ejpam-5453	290	7	)	)	PUNCT
ejpam-5453	290	8	∪	∪	NOUN
ejpam-5453	290	9	(	(	PUNCT
ejpam-5453	290	10	n	n	CCONJ
ejpam-5453	290	11	−	−	PROPN
ejpam-5453	290	12	ints℘cls℘(h	ints℘cls℘(h	ADJ
ejpam-5453	290	13	)	)	PUNCT
ejpam-5453	290	14	)	)	PUNCT
ejpam-5453	291	1	∈	∈	PROPN
ejpam-5453	291	2	d.	d.	PROPN
ejpam-5453	291	3	thus	thus	ADV
ejpam-5453	291	4	,	,	PUNCT
ejpam-5453	291	5	m	m	VERB
ejpam-5453	291	6	∪n	∪n	PROPN
ejpam-5453	291	7	∈	∈	PROPN
ejpam-5453	291	8	d	d	NOUN
ejpam-5453	291	9	-	-	PUNCT
ejpam-5453	291	10	αs℘o(v	αs℘o(v	NUM
ejpam-5453	291	11	)	)	PUNCT
ejpam-5453	291	12	.	.	PUNCT
ejpam-5453	292	1	remark	remark	PROPN
ejpam-5453	292	2	3.5	3.5	NUM
ejpam-5453	292	3	.	.	PUNCT
ejpam-5453	293	1	d	d	X
ejpam-5453	293	2	-	-	PUNCT
ejpam-5453	293	3	ξs℘o(v	ξs℘o(v	NOUN
ejpam-5453	293	4	)	)	PUNCT
ejpam-5453	293	5	do	do	AUX
ejpam-5453	293	6	not	not	PART
ejpam-5453	293	7	generate	generate	VERB
ejpam-5453	293	8	a	a	DET
ejpam-5453	293	9	topology	topology	NOUN
ejpam-5453	293	10	as	as	ADP
ejpam-5453	293	11	in	in	ADP
ejpam-5453	293	12	example	example	NOUN
ejpam-5453	293	13	3.1	3.1	NUM
ejpam-5453	293	14	,	,	PUNCT
ejpam-5453	293	15	take	take	VERB
ejpam-5453	293	16	d	d	NOUN
ejpam-5453	293	17	=	=	PUNCT
ejpam-5453	293	18	{	{	PUNCT
ejpam-5453	293	19	∅	∅	NOUN
ejpam-5453	293	20	,	,	PUNCT
ejpam-5453	293	21	{	{	PUNCT
ejpam-5453	293	22	l1	l1	PROPN
ejpam-5453	293	23	}	}	PUNCT
ejpam-5453	293	24	,	,	PUNCT
ejpam-5453	293	25	{	{	PUNCT
ejpam-5453	293	26	l4	l4	PROPN
ejpam-5453	293	27	}	}	PUNCT
ejpam-5453	293	28	,	,	PUNCT
ejpam-5453	293	29	{	{	PUNCT
ejpam-5453	293	30	l1	l1	PROPN
ejpam-5453	293	31	,	,	PUNCT
ejpam-5453	293	32	l4	l4	PROPN
ejpam-5453	293	33	}	}	PUNCT
ejpam-5453	293	34	}	}	PUNCT
ejpam-5453	293	35	,	,	PUNCT
ejpam-5453	293	36	then	then	ADV
ejpam-5453	293	37	m	m	VERB
ejpam-5453	293	38	=	=	SYM
ejpam-5453	293	39	{	{	PUNCT
ejpam-5453	293	40	l1	l1	PROPN
ejpam-5453	293	41	,	,	PUNCT
ejpam-5453	293	42	l2	l2	NOUN
ejpam-5453	293	43	}	}	PUNCT
ejpam-5453	293	44	,	,	PUNCT
ejpam-5453	293	45	n	n	NOUN
ejpam-5453	293	46	=	=	SYM
ejpam-5453	293	47	{	{	PUNCT
ejpam-5453	293	48	l1	l1	PROPN
ejpam-5453	293	49	,	,	PUNCT
ejpam-5453	293	50	l4	l4	PROPN
ejpam-5453	293	51	}	}	PUNCT
ejpam-5453	293	52	∈	∈	PROPN
ejpam-5453	294	1	d	d	X
ejpam-5453	294	2	-	-	PUNCT
ejpam-5453	294	3	αsro(v	αsro(v	NOUN
ejpam-5453	294	4	)	)	PUNCT
ejpam-5453	294	5	,	,	PUNCT
ejpam-5453	294	6	but	but	CCONJ
ejpam-5453	294	7	m	m	PROPN
ejpam-5453	294	8	∩n	∩n	NOUN
ejpam-5453	294	9	=	=	PRON
ejpam-5453	294	10	{	{	PUNCT
ejpam-5453	294	11	l1	l1	PROPN
ejpam-5453	294	12	}	}	PUNCT
ejpam-5453	294	13	̸∈	̸∈	PROPN
ejpam-5453	294	14	d	d	PROPN
ejpam-5453	294	15	-	-	PUNCT
ejpam-5453	294	16	αsro(v	αsro(v	NOUN
ejpam-5453	294	17	)	)	PUNCT
ejpam-5453	294	18	.	.	PUNCT
ejpam-5453	295	1	additionally	additionally	ADV
ejpam-5453	295	2	,	,	PUNCT
ejpam-5453	295	3	if	if	SCONJ
ejpam-5453	295	4	d	d	PROPN
ejpam-5453	295	5	=	=	PUNCT
ejpam-5453	295	6	{	{	PUNCT
ejpam-5453	295	7	∅	∅	NOUN
ejpam-5453	295	8	,	,	PUNCT
ejpam-5453	295	9	{	{	PUNCT
ejpam-5453	295	10	l2	l2	NOUN
ejpam-5453	295	11	}	}	PUNCT
ejpam-5453	295	12	}	}	PUNCT
ejpam-5453	295	13	,	,	PUNCT
ejpam-5453	295	14	then	then	ADV
ejpam-5453	295	15	(	(	PUNCT
ejpam-5453	295	16	i	i	NOUN
ejpam-5453	295	17	)	)	PUNCT
ejpam-5453	295	18	m	m	VERB
ejpam-5453	295	19	=	=	PUNCT
ejpam-5453	295	20	{	{	PUNCT
ejpam-5453	295	21	l1	l1	PROPN
ejpam-5453	295	22	,	,	PUNCT
ejpam-5453	295	23	l2	l2	NOUN
ejpam-5453	295	24	,	,	PUNCT
ejpam-5453	295	25	l3	l3	PROPN
ejpam-5453	295	26	}	}	PUNCT
ejpam-5453	295	27	,	,	PUNCT
ejpam-5453	295	28	n	n	NOUN
ejpam-5453	295	29	=	=	SYM
ejpam-5453	295	30	{	{	PUNCT
ejpam-5453	295	31	l1	l1	PROPN
ejpam-5453	295	32	,	,	PUNCT
ejpam-5453	295	33	l2	l2	NOUN
ejpam-5453	295	34	,	,	PUNCT
ejpam-5453	295	35	l4	l4	PROPN
ejpam-5453	295	36	}	}	PUNCT
ejpam-5453	295	37	∈	∈	PROPN
ejpam-5453	295	38	d	d	NOUN
ejpam-5453	295	39	-	-	PUNCT
ejpam-5453	295	40	psro(v	psro(v	NOUN
ejpam-5453	295	41	)	)	PUNCT
ejpam-5453	295	42	,	,	PUNCT
ejpam-5453	295	43	but	but	CCONJ
ejpam-5453	295	44	m	m	PROPN
ejpam-5453	295	45	∩n	∩n	NOUN
ejpam-5453	295	46	=	=	PRON
ejpam-5453	295	47	{	{	PUNCT
ejpam-5453	295	48	l1	l1	PROPN
ejpam-5453	295	49	,	,	PUNCT
ejpam-5453	295	50	l2	l2	PROPN
ejpam-5453	295	51	}	}	PUNCT
ejpam-5453	295	52	̸∈	̸∈	PROPN
ejpam-5453	295	53	d	d	PROPN
ejpam-5453	295	54	-	-	PUNCT
ejpam-5453	295	55	psro(v	psro(v	NOUN
ejpam-5453	295	56	)	)	PUNCT
ejpam-5453	295	57	.	.	PUNCT
ejpam-5453	296	1	(	(	PUNCT
ejpam-5453	296	2	ii	ii	X
ejpam-5453	296	3	)	)	PUNCT
ejpam-5453	296	4	m	m	PROPN
ejpam-5453	296	5	=	=	SYM
ejpam-5453	296	6	{	{	PUNCT
ejpam-5453	296	7	l1	l1	PROPN
ejpam-5453	296	8	,	,	PUNCT
ejpam-5453	296	9	l2	l2	NOUN
ejpam-5453	296	10	}	}	PUNCT
ejpam-5453	296	11	,	,	PUNCT
ejpam-5453	296	12	n	n	NOUN
ejpam-5453	296	13	=	=	SYM
ejpam-5453	296	14	{	{	PUNCT
ejpam-5453	296	15	l1	l1	PROPN
ejpam-5453	296	16	,	,	PUNCT
ejpam-5453	296	17	l3	l3	PROPN
ejpam-5453	296	18	,	,	PUNCT
ejpam-5453	296	19	l4	l4	PROPN
ejpam-5453	296	20	}	}	PUNCT
ejpam-5453	296	21	∈	∈	PROPN
ejpam-5453	296	22	d	d	NOUN
ejpam-5453	296	23	-	-	PUNCT
ejpam-5453	296	24	ssro(v	ssro(v	NOUN
ejpam-5453	296	25	)	)	PUNCT
ejpam-5453	296	26	,	,	PUNCT
ejpam-5453	296	27	but	but	CCONJ
ejpam-5453	296	28	m	m	PROPN
ejpam-5453	296	29	∩n	∩n	NOUN
ejpam-5453	296	30	=	=	PRON
ejpam-5453	296	31	{	{	PUNCT
ejpam-5453	296	32	l1	l1	PROPN
ejpam-5453	296	33	}	}	PUNCT
ejpam-5453	296	34	̸∈	̸∈	PROPN
ejpam-5453	296	35	d	d	PROPN
ejpam-5453	296	36	-	-	PUNCT
ejpam-5453	296	37	ssro(v	ssro(v	VERB
ejpam-5453	296	38	)	)	PUNCT
ejpam-5453	296	39	.	.	PUNCT
ejpam-5453	297	1	(	(	PUNCT
ejpam-5453	297	2	iii	iii	X
ejpam-5453	297	3	)	)	PUNCT
ejpam-5453	297	4	m	m	PROPN
ejpam-5453	297	5	=	=	PUNCT
ejpam-5453	297	6	{	{	PUNCT
ejpam-5453	297	7	l1	l1	PROPN
ejpam-5453	297	8	,	,	PUNCT
ejpam-5453	297	9	l2	l2	NOUN
ejpam-5453	297	10	}	}	PUNCT
ejpam-5453	297	11	,	,	PUNCT
ejpam-5453	297	12	n	n	NOUN
ejpam-5453	297	13	=	=	SYM
ejpam-5453	297	14	{	{	PUNCT
ejpam-5453	297	15	l1	l1	PROPN
ejpam-5453	297	16	,	,	PUNCT
ejpam-5453	297	17	l3	l3	PROPN
ejpam-5453	297	18	}	}	PUNCT
ejpam-5453	297	19	∈	∈	PROPN
ejpam-5453	297	20	d	d	X
ejpam-5453	297	21	-	-	PUNCT
ejpam-5453	297	22	βsro(x	βsro(x	NOUN
ejpam-5453	297	23	)	)	PUNCT
ejpam-5453	297	24	,	,	PUNCT
ejpam-5453	297	25	but	but	CCONJ
ejpam-5453	297	26	m	m	PROPN
ejpam-5453	297	27	∩n	∩n	NOUN
ejpam-5453	297	28	=	=	PRON
ejpam-5453	297	29	{	{	PUNCT
ejpam-5453	297	30	l1	l1	PROPN
ejpam-5453	297	31	}	}	PUNCT
ejpam-5453	297	32	̸∈	̸∈	PROPN
ejpam-5453	297	33	d	d	PROPN
ejpam-5453	297	34	-	-	PUNCT
ejpam-5453	297	35	βsro(v	βsro(v	NOUN
ejpam-5453	297	36	)	)	PUNCT
ejpam-5453	297	37	.	.	PUNCT
ejpam-5453	298	1	remark	remark	PROPN
ejpam-5453	298	2	3.6	3.6	NUM
ejpam-5453	298	3	.	.	PUNCT
ejpam-5453	299	1	let	let	AUX
ejpam-5453	299	2	(	(	PUNCT
ejpam-5453	299	3	v	v	NOUN
ejpam-5453	299	4	,	,	PUNCT
ejpam-5453	299	5	υ	υ	NOUN
ejpam-5453	299	6	,	,	PUNCT
ejpam-5453	299	7	π℘	π℘	NUM
ejpam-5453	299	8	)	)	PUNCT
ejpam-5453	299	9	be	be	VERB
ejpam-5453	299	10	a	a	DET
ejpam-5453	299	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	299	12	and	and	CCONJ
ejpam-5453	299	13	d	d	NOUN
ejpam-5453	299	14	be	be	AUX
ejpam-5453	299	15	an	an	DET
ejpam-5453	299	16	ideal	ideal	NOUN
ejpam-5453	299	17	on	on	ADP
ejpam-5453	299	18	v.	v.	ADP
ejpam-5453	299	19	hence	hence	ADV
ejpam-5453	299	20	,	,	PUNCT
ejpam-5453	299	21	the	the	DET
ejpam-5453	299	22	statements	statement	NOUN
ejpam-5453	299	23	below	below	ADV
ejpam-5453	299	24	are	be	AUX
ejpam-5453	299	25	not	not	PART
ejpam-5453	299	26	true	true	ADJ
ejpam-5453	299	27	in	in	ADP
ejpam-5453	299	28	most	most	ADJ
ejpam-5453	299	29	cases	case	NOUN
ejpam-5453	299	30	:	:	PUNCT
ejpam-5453	299	31	(	(	PUNCT
ejpam-5453	299	32	i	i	NOUN
ejpam-5453	299	33	)	)	PUNCT
ejpam-5453	299	34	d	d	X
ejpam-5453	299	35	-	-	PUNCT
ejpam-5453	299	36	ξuo(v	ξuo(v	X
ejpam-5453	299	37	)	)	PUNCT
ejpam-5453	300	1	⊆	⊆	NUM
ejpam-5453	300	2	d	d	X
ejpam-5453	300	3	-	-	PUNCT
ejpam-5453	300	4	ξro(v	ξro(v	NOUN
ejpam-5453	300	5	)	)	PUNCT
ejpam-5453	300	6	⊆	⊆	NUM
ejpam-5453	300	7	d	d	X
ejpam-5453	300	8	-	-	PUNCT
ejpam-5453	300	9	ξio(v	ξio(v	NOUN
ejpam-5453	300	10	)	)	PUNCT
ejpam-5453	300	11	.	.	PUNCT
ejpam-5453	301	1	(	(	PUNCT
ejpam-5453	301	2	ii	ii	NOUN
ejpam-5453	301	3	)	)	PUNCT
ejpam-5453	301	4	d	d	X
ejpam-5453	301	5	-	-	PUNCT
ejpam-5453	301	6	ξuo(v	ξuo(v	X
ejpam-5453	301	7	)	)	PUNCT
ejpam-5453	301	8	⊆	⊆	NUM
ejpam-5453	301	9	d	d	X
ejpam-5453	301	10	-	-	PUNCT
ejpam-5453	301	11	ξlo(v	ξlo(v	ADJ
ejpam-5453	301	12	)	)	PUNCT
ejpam-5453	301	13	⊆	⊆	NUM
ejpam-5453	301	14	d	d	X
ejpam-5453	301	15	-	-	PUNCT
ejpam-5453	301	16	ξio(v	ξio(v	NOUN
ejpam-5453	301	17	)	)	PUNCT
ejpam-5453	301	18	.	.	PUNCT
ejpam-5453	302	1	(	(	PUNCT
ejpam-5453	302	2	iii	iii	X
ejpam-5453	302	3	)	)	PUNCT
ejpam-5453	302	4	d	d	NOUN
ejpam-5453	302	5	-	-	PUNCT
ejpam-5453	302	6	ξ	ξ	X
ejpam-5453	302	7	<	<	X
ejpam-5453	302	8	u	u	X
ejpam-5453	302	9	>	>	X
ejpam-5453	302	10	o(v	o(v	NOUN
ejpam-5453	302	11	)	)	PUNCT
ejpam-5453	302	12	⊆	⊆	NUM
ejpam-5453	302	13	d	d	X
ejpam-5453	302	14	-	-	PUNCT
ejpam-5453	302	15	ξ	ξ	NOUN
ejpam-5453	302	16	<	<	X
ejpam-5453	302	17	r	r	X
ejpam-5453	302	18	>	>	X
ejpam-5453	302	19	o(v	o(v	NOUN
ejpam-5453	302	20	)	)	PUNCT
ejpam-5453	302	21	⊆	⊆	NUM
ejpam-5453	302	22	d	d	X
ejpam-5453	302	23	-	-	PUNCT
ejpam-5453	302	24	ξ	ξ	X
ejpam-5453	302	25	<	<	X
ejpam-5453	302	26	i	i	X
ejpam-5453	302	27	>	>	X
ejpam-5453	302	28	o(v	o(v	PROPN
ejpam-5453	302	29	)	)	PUNCT
ejpam-5453	302	30	.	.	PUNCT
ejpam-5453	303	1	(	(	PUNCT
ejpam-5453	303	2	iv	iv	X
ejpam-5453	303	3	)	)	PUNCT
ejpam-5453	303	4	d	d	X
ejpam-5453	303	5	-	-	PUNCT
ejpam-5453	303	6	ξ	ξ	X
ejpam-5453	303	7	<	<	X
ejpam-5453	303	8	u	u	X
ejpam-5453	303	9	>	>	X
ejpam-5453	303	10	o(v	o(v	NOUN
ejpam-5453	303	11	)	)	PUNCT
ejpam-5453	303	12	⊆	⊆	NUM
ejpam-5453	303	13	d	d	X
ejpam-5453	303	14	-	-	SYM
ejpam-5453	303	15	ξ	ξ	X
ejpam-5453	303	16	<	<	X
ejpam-5453	303	17	l	l	X
ejpam-5453	303	18	>	>	X
ejpam-5453	303	19	o(v	o(v	NOUN
ejpam-5453	303	20	)	)	PUNCT
ejpam-5453	303	21	⊆	⊆	NUM
ejpam-5453	303	22	d	d	X
ejpam-5453	303	23	-	-	PUNCT
ejpam-5453	303	24	ξ	ξ	X
ejpam-5453	303	25	<	<	X
ejpam-5453	303	26	i	i	X
ejpam-5453	303	27	>	>	X
ejpam-5453	303	28	o(v	o(v	PROPN
ejpam-5453	303	29	)	)	PUNCT
ejpam-5453	303	30	.	.	PUNCT
ejpam-5453	304	1	(	(	PUNCT
ejpam-5453	304	2	v	v	NOUN
ejpam-5453	304	3	)	)	PUNCT
ejpam-5453	304	4	d	d	NOUN
ejpam-5453	304	5	-	-	PUNCT
ejpam-5453	304	6	ξro(v	ξro(v	NOUN
ejpam-5453	304	7	)	)	PUNCT
ejpam-5453	304	8	is	be	AUX
ejpam-5453	304	9	the	the	DET
ejpam-5453	304	10	dual	dual	ADJ
ejpam-5453	304	11	of	of	ADP
ejpam-5453	304	12	d	d	NOUN
ejpam-5453	304	13	-	-	PUNCT
ejpam-5453	304	14	ξlo(v	ξlo(v	ADJ
ejpam-5453	304	15	)	)	PUNCT
ejpam-5453	304	16	.	.	PUNCT
ejpam-5453	305	1	(	(	PUNCT
ejpam-5453	305	2	vi	vi	NOUN
ejpam-5453	305	3	)	)	PUNCT
ejpam-5453	305	4	d	d	NOUN
ejpam-5453	305	5	-	-	PUNCT
ejpam-5453	305	6	ξ	ξ	X
ejpam-5453	305	7	<	<	X
ejpam-5453	305	8	r	r	X
ejpam-5453	305	9	>	>	X
ejpam-5453	305	10	o(v	o(v	NOUN
ejpam-5453	305	11	)	)	PUNCT
ejpam-5453	305	12	is	be	AUX
ejpam-5453	305	13	the	the	DET
ejpam-5453	305	14	dual	dual	ADJ
ejpam-5453	305	15	of	of	ADP
ejpam-5453	305	16	d	d	PROPN
ejpam-5453	305	17	-	-	PUNCT
ejpam-5453	305	18	ξ	ξ	X
ejpam-5453	305	19	<	<	X
ejpam-5453	305	20	l	l	X
ejpam-5453	305	21	>	>	X
ejpam-5453	305	22	o(v	o(v	NOUN
ejpam-5453	305	23	)	)	PUNCT
ejpam-5453	305	24	.	.	PUNCT
ejpam-5453	306	1	example	example	NOUN
ejpam-5453	306	2	3.4	3.4	NUM
ejpam-5453	306	3	.	.	PUNCT
ejpam-5453	307	1	let	let	VERB
ejpam-5453	307	2	v	v	VERB
ejpam-5453	307	3	=	=	SYM
ejpam-5453	307	4	{	{	PUNCT
ejpam-5453	307	5	l1	l1	PROPN
ejpam-5453	307	6	,	,	PUNCT
ejpam-5453	307	7	l2	l2	NOUN
ejpam-5453	307	8	,	,	PUNCT
ejpam-5453	307	9	l3	l3	PROPN
ejpam-5453	307	10	,	,	PUNCT
ejpam-5453	307	11	l4	l4	PROPN
ejpam-5453	307	12	}	}	PUNCT
ejpam-5453	307	13	,	,	PUNCT
ejpam-5453	307	14	υ	υ	NOUN
ejpam-5453	307	15	=	=	PRON
ejpam-5453	307	16	{	{	PUNCT
ejpam-5453	307	17	(	(	PUNCT
ejpam-5453	307	18	l1	l1	PROPN
ejpam-5453	307	19	,	,	PUNCT
ejpam-5453	307	20	l1	l1	PROPN
ejpam-5453	307	21	)	)	PUNCT
ejpam-5453	307	22	,	,	PUNCT
ejpam-5453	307	23	(	(	PUNCT
ejpam-5453	307	24	l1	l1	PROPN
ejpam-5453	307	25	,	,	PUNCT
ejpam-5453	307	26	l2	l2	NOUN
ejpam-5453	307	27	)	)	PUNCT
ejpam-5453	307	28	,	,	PUNCT
ejpam-5453	307	29	(	(	PUNCT
ejpam-5453	307	30	l1	l1	PROPN
ejpam-5453	307	31	,	,	PUNCT
ejpam-5453	307	32	l3	l3	PROPN
ejpam-5453	307	33	)	)	PUNCT
ejpam-5453	307	34	,	,	PUNCT
ejpam-5453	307	35	(	(	PUNCT
ejpam-5453	307	36	l2	l2	NOUN
ejpam-5453	307	37	,	,	PUNCT
ejpam-5453	307	38	l4	l4	PROPN
ejpam-5453	307	39	)	)	PUNCT
ejpam-5453	307	40	,	,	PUNCT
ejpam-5453	307	41	(	(	PUNCT
ejpam-5453	307	42	l2	l2	NOUN
ejpam-5453	307	43	,	,	PUNCT
ejpam-5453	307	44	l3	l3	PROPN
ejpam-5453	307	45	)	)	PUNCT
ejpam-5453	307	46	}	}	PUNCT
ejpam-5453	307	47	,	,	PUNCT
ejpam-5453	307	48	and	and	CCONJ
ejpam-5453	307	49	if	if	SCONJ
ejpam-5453	307	50	d	d	PROPN
ejpam-5453	307	51	=	=	SYM
ejpam-5453	307	52	{	{	PUNCT
ejpam-5453	307	53	∅	∅	NOUN
ejpam-5453	307	54	,	,	PUNCT
ejpam-5453	307	55	{	{	PUNCT
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ejpam-5453	309	5	)	)	PUNCT
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ejpam-5453	310	2	,	,	PUNCT
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ejpam-5453	310	5	βsuo(v	βsuo(v	NOUN
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ejpam-5453	312	5	)	)	PUNCT
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ejpam-5453	316	3	(	(	PUNCT
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ejpam-5453	317	3	)	)	PUNCT
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ejpam-5453	320	8	r	r	X
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ejpam-5453	328	7	o(v	o(v	NOUN
ejpam-5453	328	8	)	)	PUNCT
ejpam-5453	328	9	⊈	⊈	PROPN
ejpam-5453	329	1	d	d	X
ejpam-5453	329	2	-	-	PUNCT
ejpam-5453	329	3	βs	βs	X
ejpam-5453	329	4	<	<	X
ejpam-5453	329	5	r	r	X
ejpam-5453	329	6	>	>	X
ejpam-5453	329	7	o(v	o(v	NOUN
ejpam-5453	329	8	)	)	PUNCT
ejpam-5453	329	9	⊈	⊈	PROPN
ejpam-5453	330	1	d	d	X
ejpam-5453	330	2	-	-	PUNCT
ejpam-5453	330	3	βs	βs	SYM
ejpam-5453	330	4	<	<	X
ejpam-5453	330	5	i	i	X
ejpam-5453	330	6	>	>	X
ejpam-5453	330	7	o(v	o(v	PROPN
ejpam-5453	330	8	)	)	PUNCT
ejpam-5453	330	9	,	,	PUNCT
ejpam-5453	330	10	d	d	X
ejpam-5453	330	11	-	-	PUNCT
ejpam-5453	330	12	βs	βs	X
ejpam-5453	330	13	<	<	X
ejpam-5453	330	14	l	l	X
ejpam-5453	330	15	>	>	X
ejpam-5453	330	16	o(v	o(v	PROPN
ejpam-5453	330	17	)	)	PUNCT
ejpam-5453	330	18	⊈	⊈	PROPN
ejpam-5453	331	1	d	d	X
ejpam-5453	331	2	-	-	PUNCT
ejpam-5453	331	3	βs	βs	SYM
ejpam-5453	331	4	<	<	X
ejpam-5453	331	5	i	i	X
ejpam-5453	331	6	>	>	X
ejpam-5453	331	7	o(v	o(v	PROPN
ejpam-5453	331	8	)	)	PUNCT
ejpam-5453	331	9	,	,	PUNCT
ejpam-5453	331	10	d	d	X
ejpam-5453	331	11	-	-	PUNCT
ejpam-5453	331	12	βsro(v	βsro(v	NOUN
ejpam-5453	331	13	)	)	PUNCT
ejpam-5453	331	14	is	be	AUX
ejpam-5453	331	15	not	not	PART
ejpam-5453	331	16	the	the	DET
ejpam-5453	331	17	dual	dual	ADJ
ejpam-5453	331	18	of	of	ADP
ejpam-5453	331	19	d	d	NOUN
ejpam-5453	331	20	-	-	PUNCT
ejpam-5453	331	21	βsro(v	βsro(v	NOUN
ejpam-5453	331	22	)	)	PUNCT
ejpam-5453	331	23	and	and	CCONJ
ejpam-5453	331	24	d	d	X
ejpam-5453	331	25	-	-	PUNCT
ejpam-5453	331	26	βs	βs	X
ejpam-5453	331	27	<	<	X
ejpam-5453	331	28	r	r	X
ejpam-5453	331	29	>	>	X
ejpam-5453	331	30	o(v	o(v	NOUN
ejpam-5453	331	31	)	)	PUNCT
ejpam-5453	331	32	is	be	AUX
ejpam-5453	331	33	not	not	PART
ejpam-5453	331	34	the	the	DET
ejpam-5453	331	35	dual	dual	ADJ
ejpam-5453	331	36	of	of	ADP
ejpam-5453	331	37	d	d	NOUN
ejpam-5453	331	38	-	-	PUNCT
ejpam-5453	331	39	βs	βs	X
ejpam-5453	331	40	<	<	X
ejpam-5453	331	41	l	l	X
ejpam-5453	331	42	>	>	X
ejpam-5453	331	43	o(v	o(v	PROPN
ejpam-5453	331	44	)	)	PUNCT
ejpam-5453	331	45	.	.	PUNCT
ejpam-5453	332	1	m.	m.	PROPN
ejpam-5453	332	2	hosny	hosny	PROPN
ejpam-5453	332	3	/	/	SYM
ejpam-5453	332	4	eur	eur	PROPN
ejpam-5453	332	5	.	.	PUNCT
ejpam-5453	333	1	j.	j.	PROPN
ejpam-5453	333	2	pure	pure	PROPN
ejpam-5453	333	3	appl	appl	PROPN
ejpam-5453	333	4	.	.	PROPN
ejpam-5453	333	5	math	math	PROPN
ejpam-5453	333	6	,	,	PUNCT
ejpam-5453	333	7	17	17	NUM
ejpam-5453	333	8	(	(	PUNCT
ejpam-5453	333	9	4	4	NUM
ejpam-5453	333	10	)	)	PUNCT
ejpam-5453	333	11	(	(	PUNCT
ejpam-5453	333	12	2024	2024	NUM
ejpam-5453	333	13	)	)	PUNCT
ejpam-5453	333	14	,	,	PUNCT
ejpam-5453	333	15	2843	2843	NUM
ejpam-5453	333	16	-	-	SYM
ejpam-5453	333	17	2877	2877	NUM
ejpam-5453	333	18	2853	2853	NUM
ejpam-5453	333	19	3.2	3.2	NUM
ejpam-5453	333	20	.	.	PUNCT
ejpam-5453	334	1	comparisons	comparison	NOUN
ejpam-5453	334	2	with	with	ADP
ejpam-5453	334	3	the	the	DET
ejpam-5453	334	4	prior	prior	ADJ
ejpam-5453	334	5	studies	study	NOUN
ejpam-5453	334	6	the	the	DET
ejpam-5453	334	7	following	follow	VERB
ejpam-5453	334	8	findings	finding	NOUN
ejpam-5453	334	9	confirm	confirm	VERB
ejpam-5453	334	10	that	that	SCONJ
ejpam-5453	334	11	the	the	DET
ejpam-5453	334	12	suggested	suggest	VERB
ejpam-5453	334	13	definition	definition	NOUN
ejpam-5453	334	14	3.1	3.1	NUM
ejpam-5453	334	15	is	be	AUX
ejpam-5453	334	16	superior	superior	ADJ
ejpam-5453	334	17	than	than	ADP
ejpam-5453	334	18	yildirim	yildirim	PROPN
ejpam-5453	334	19	’s	’s	PART
ejpam-5453	334	20	definition	definition	NOUN
ejpam-5453	334	21	2.10	2.10	NUM
ejpam-5453	334	22	[	[	X
ejpam-5453	334	23	43	43	NUM
ejpam-5453	334	24	]	]	PUNCT
ejpam-5453	334	25	.	.	PUNCT
ejpam-5453	335	1	proposition	proposition	NOUN
ejpam-5453	335	2	3.4	3.4	NUM
ejpam-5453	335	3	.	.	PUNCT
ejpam-5453	336	1	let	let	AUX
ejpam-5453	336	2	(	(	PUNCT
ejpam-5453	336	3	v	v	NOUN
ejpam-5453	336	4	,	,	PUNCT
ejpam-5453	336	5	υ	υ	NOUN
ejpam-5453	336	6	,	,	PUNCT
ejpam-5453	336	7	π℘	π℘	NUM
ejpam-5453	336	8	)	)	PUNCT
ejpam-5453	336	9	be	be	VERB
ejpam-5453	336	10	a	a	DET
ejpam-5453	336	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	336	12	and	and	CCONJ
ejpam-5453	336	13	d	d	NOUN
ejpam-5453	336	14	be	be	AUX
ejpam-5453	336	15	an	an	DET
ejpam-5453	336	16	ideal	ideal	NOUN
ejpam-5453	336	17	on	on	ADP
ejpam-5453	336	18	v	v	NOUN
ejpam-5453	336	19	.	.	PUNCT
ejpam-5453	337	1	then	then	ADV
ejpam-5453	337	2	αs℘-open	αs℘-open	VERB
ejpam-5453	337	3	⇒	⇒	NOUN
ejpam-5453	337	4	d	d	X
ejpam-5453	337	5	-	-	PUNCT
ejpam-5453	337	6	αs℘-open	αs℘-open	ADJ
ejpam-5453	337	7	.	.	PUNCT
ejpam-5453	338	1	ps℘-open	ps℘-open	NOUN
ejpam-5453	338	2	⇒	⇒	NOUN
ejpam-5453	339	1	d	d	NOUN
ejpam-5453	339	2	-	-	PUNCT
ejpam-5453	339	3	ps℘-open	ps℘-open	NOUN
ejpam-5453	339	4	.	.	PUNCT
ejpam-5453	340	1	ss℘-open	ss℘-open	ADJ
ejpam-5453	340	2	⇒	⇒	NOUN
ejpam-5453	341	1	d	d	NOUN
ejpam-5453	341	2	-	-	PUNCT
ejpam-5453	341	3	ss℘-open	ss℘-open	ADJ
ejpam-5453	341	4	.	.	PUNCT
ejpam-5453	342	1	βs℘-open	βs℘-open	ADJ
ejpam-5453	342	2	⇒	⇒	NOUN
ejpam-5453	343	1	d	d	X
ejpam-5453	343	2	-	-	PUNCT
ejpam-5453	343	3	βs℘-open	βs℘-open	ADJ
ejpam-5453	343	4	.	.	PUNCT
ejpam-5453	343	5	θβs℘-open	θβs℘-open	PROPN
ejpam-5453	343	6	⇒	⇒	PROPN
ejpam-5453	344	1	d	d	PROPN
ejpam-5453	344	2	-	-	PUNCT
ejpam-5453	344	3	θβs℘-open	θβs℘-open	ADJ
ejpam-5453	344	4	.	.	PUNCT
ejpam-5453	345	1	proof	proof	NOUN
ejpam-5453	345	2	.	.	PUNCT
ejpam-5453	346	1	by	by	ADP
ejpam-5453	346	2	applying	apply	VERB
ejpam-5453	346	3	definitions	definition	NOUN
ejpam-5453	346	4	2.10	2.10	NUM
ejpam-5453	346	5	and	and	CCONJ
ejpam-5453	346	6	3.1	3.1	NUM
ejpam-5453	346	7	.	.	PUNCT
ejpam-5453	346	8	example	example	NOUN
ejpam-5453	346	9	3.1	3.1	NUM
ejpam-5453	346	10	confirms	confirm	VERB
ejpam-5453	346	11	that	that	SCONJ
ejpam-5453	346	12	the	the	DET
ejpam-5453	346	13	reverse	reverse	ADJ
ejpam-5453	346	14	implications	implication	NOUN
ejpam-5453	346	15	of	of	ADP
ejpam-5453	346	16	proposition	proposition	NOUN
ejpam-5453	346	17	3.4	3.4	NUM
ejpam-5453	346	18	is	be	AUX
ejpam-5453	346	19	not	not	PART
ejpam-5453	346	20	guaranteed	guarantee	VERB
ejpam-5453	346	21	to	to	PART
ejpam-5453	346	22	be	be	AUX
ejpam-5453	346	23	true	true	ADJ
ejpam-5453	346	24	as	as	ADP
ejpam-5453	346	25	m	m	PROPN
ejpam-5453	346	26	=	=	SYM
ejpam-5453	346	27	{	{	PUNCT
ejpam-5453	346	28	l1	l1	PROPN
ejpam-5453	346	29	}	}	PUNCT
ejpam-5453	346	30	∈	∈	PROPN
ejpam-5453	346	31	d	d	NOUN
ejpam-5453	346	32	-	-	PUNCT
ejpam-5453	346	33	βsro(v	βsro(v	NOUN
ejpam-5453	346	34	)	)	PUNCT
ejpam-5453	346	35	(	(	PUNCT
ejpam-5453	346	36	respectively	respectively	ADV
ejpam-5453	346	37	,	,	PUNCT
ejpam-5453	346	38	d	d	X
ejpam-5453	346	39	-	-	PUNCT
ejpam-5453	346	40	ssro(v	ssro(v	NOUN
ejpam-5453	346	41	)	)	PUNCT
ejpam-5453	346	42	,	,	PUNCT
ejpam-5453	346	43	d	d	X
ejpam-5453	346	44	-	-	PUNCT
ejpam-5453	346	45	psro(v	psro(v	NOUN
ejpam-5453	346	46	)	)	PUNCT
ejpam-5453	346	47	,	,	PUNCT
ejpam-5453	346	48	d	d	X
ejpam-5453	346	49	-	-	PUNCT
ejpam-5453	346	50	αsro(v	αsro(v	NOUN
ejpam-5453	346	51	)	)	PUNCT
ejpam-5453	346	52	)	)	PUNCT
ejpam-5453	346	53	,	,	PUNCT
ejpam-5453	346	54	but	but	CCONJ
ejpam-5453	346	55	m	m	PROPN
ejpam-5453	346	56	=	=	SYM
ejpam-5453	346	57	{	{	PUNCT
ejpam-5453	346	58	l1	l1	PROPN
ejpam-5453	346	59	}	}	PUNCT
ejpam-5453	346	60	̸∈	̸∈	PROPN
ejpam-5453	346	61	βsro(v	βsro(v	NOUN
ejpam-5453	346	62	)	)	PUNCT
ejpam-5453	346	63	(	(	PUNCT
ejpam-5453	346	64	respectively	respectively	ADV
ejpam-5453	346	65	,	,	PUNCT
ejpam-5453	346	66	ssro(v	ssro(v	NOUN
ejpam-5453	346	67	)	)	PUNCT
ejpam-5453	346	68	,	,	PUNCT
ejpam-5453	346	69	psro(v	psro(v	NOUN
ejpam-5453	346	70	)	)	PUNCT
ejpam-5453	346	71	,	,	PUNCT
ejpam-5453	346	72	αsro(v	αsro(v	NOUN
ejpam-5453	346	73	)	)	PUNCT
ejpam-5453	346	74	)	)	PUNCT
ejpam-5453	346	75	.	.	PUNCT
ejpam-5453	347	1	theorem	theorem	ADJ
ejpam-5453	347	2	3.2	3.2	NUM
ejpam-5453	347	3	.	.	PUNCT
ejpam-5453	348	1	let	let	AUX
ejpam-5453	348	2	(	(	PUNCT
ejpam-5453	348	3	v	v	NOUN
ejpam-5453	348	4	,	,	PUNCT
ejpam-5453	348	5	υ	υ	NOUN
ejpam-5453	348	6	,	,	PUNCT
ejpam-5453	348	7	π℘	π℘	NUM
ejpam-5453	348	8	)	)	PUNCT
ejpam-5453	348	9	be	be	VERB
ejpam-5453	348	10	a	a	DET
ejpam-5453	348	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	348	12	and	and	CCONJ
ejpam-5453	348	13	d	d	NOUN
ejpam-5453	348	14	be	be	AUX
ejpam-5453	348	15	an	an	DET
ejpam-5453	348	16	ideal	ideal	NOUN
ejpam-5453	348	17	on	on	ADP
ejpam-5453	348	18	v	v	NOUN
ejpam-5453	348	19	.	.	PUNCT
ejpam-5453	349	1	if	if	SCONJ
ejpam-5453	349	2	d	d	NOUN
ejpam-5453	349	3	=	=	SYM
ejpam-5453	349	4	{	{	PUNCT
ejpam-5453	349	5	∅	∅	NOUN
ejpam-5453	349	6	}	}	PUNCT
ejpam-5453	349	7	in	in	ADP
ejpam-5453	349	8	the	the	DET
ejpam-5453	349	9	present	present	ADJ
ejpam-5453	349	10	manner	manner	NOUN
ejpam-5453	349	11	3.1	3.1	NUM
ejpam-5453	349	12	,	,	PUNCT
ejpam-5453	349	13	then	then	ADV
ejpam-5453	349	14	yildirim	yildirim	PROPN
ejpam-5453	349	15	’s	’s	PART
ejpam-5453	349	16	definition	definition	NOUN
ejpam-5453	349	17	is	be	AUX
ejpam-5453	349	18	obtained	obtain	VERB
ejpam-5453	349	19	2.10	2.10	NUM
ejpam-5453	349	20	[	[	X
ejpam-5453	349	21	43	43	NUM
ejpam-5453	349	22	]	]	PUNCT
ejpam-5453	349	23	.	.	PUNCT
ejpam-5453	350	1	proof	proof	NOUN
ejpam-5453	350	2	.	.	PUNCT
ejpam-5453	351	1	straightforward	straightforward	ADJ
ejpam-5453	351	2	.	.	PUNCT
ejpam-5453	352	1	theorem	theorem	ADJ
ejpam-5453	352	2	3.2	3.2	NUM
ejpam-5453	352	3	emphasizes	emphasize	VERB
ejpam-5453	352	4	that	that	SCONJ
ejpam-5453	352	5	yildirim	yildirim	PROPN
ejpam-5453	352	6	’s	’s	PART
ejpam-5453	352	7	definitions	definition	NOUN
ejpam-5453	352	8	[	[	X
ejpam-5453	352	9	43	43	NUM
ejpam-5453	352	10	]	]	PUNCT
ejpam-5453	352	11	can	can	AUX
ejpam-5453	352	12	be	be	AUX
ejpam-5453	352	13	interpreted	interpret	VERB
ejpam-5453	352	14	as	as	ADP
ejpam-5453	352	15	a	a	DET
ejpam-5453	352	16	special	special	ADJ
ejpam-5453	352	17	case	case	NOUN
ejpam-5453	352	18	of	of	ADP
ejpam-5453	352	19	the	the	DET
ejpam-5453	352	20	current	current	ADJ
ejpam-5453	352	21	ones	one	NOUN
ejpam-5453	352	22	.	.	PUNCT
ejpam-5453	353	1	as	as	ADP
ejpam-5453	353	2	,	,	PUNCT
ejpam-5453	353	3	when	when	SCONJ
ejpam-5453	353	4	d	d	NOUN
ejpam-5453	353	5	=	=	SYM
ejpam-5453	353	6	{	{	PUNCT
ejpam-5453	353	7	∅	∅	NOUN
ejpam-5453	353	8	}	}	PUNCT
ejpam-5453	353	9	in	in	ADP
ejpam-5453	353	10	the	the	DET
ejpam-5453	353	11	current	current	ADJ
ejpam-5453	353	12	definitions	definition	NOUN
ejpam-5453	353	13	,	,	PUNCT
ejpam-5453	353	14	we	we	PRON
ejpam-5453	353	15	see	see	VERB
ejpam-5453	353	16	that	that	SCONJ
ejpam-5453	353	17	the	the	DET
ejpam-5453	353	18	resulting	result	VERB
ejpam-5453	353	19	definitions	definition	NOUN
ejpam-5453	353	20	equivalent	equivalent	ADJ
ejpam-5453	353	21	to	to	ADP
ejpam-5453	353	22	those	those	PRON
ejpam-5453	353	23	put	put	VERB
ejpam-5453	353	24	forth	forth	ADP
ejpam-5453	353	25	by	by	ADP
ejpam-5453	353	26	yildirim	yildirim	PROPN
ejpam-5453	353	27	[	[	X
ejpam-5453	353	28	43	43	NUM
ejpam-5453	353	29	]	]	PUNCT
ejpam-5453	353	30	.	.	PUNCT
ejpam-5453	354	1	this	this	DET
ejpam-5453	354	2	equivalence	equivalence	NOUN
ejpam-5453	354	3	suggests	suggest	VERB
ejpam-5453	354	4	that	that	SCONJ
ejpam-5453	354	5	the	the	DET
ejpam-5453	354	6	specific	specific	ADJ
ejpam-5453	354	7	case	case	NOUN
ejpam-5453	354	8	in	in	ADP
ejpam-5453	354	9	the	the	DET
ejpam-5453	354	10	current	current	ADJ
ejpam-5453	354	11	framework	framework	NOUN
ejpam-5453	354	12	aligns	align	VERB
ejpam-5453	354	13	with	with	ADP
ejpam-5453	354	14	yildirim	yildirim	PROPN
ejpam-5453	354	15	’s	’s	PART
ejpam-5453	354	16	definitions	definition	NOUN
ejpam-5453	354	17	.	.	PUNCT
ejpam-5453	355	1	proposition	proposition	NOUN
ejpam-5453	355	2	3.5	3.5	NUM
ejpam-5453	355	3	.	.	PUNCT
ejpam-5453	356	1	let	let	AUX
ejpam-5453	356	2	(	(	PUNCT
ejpam-5453	356	3	v	v	NOUN
ejpam-5453	356	4	,	,	PUNCT
ejpam-5453	356	5	υ	υ	NOUN
ejpam-5453	356	6	,	,	PUNCT
ejpam-5453	356	7	π℘	π℘	NUM
ejpam-5453	356	8	)	)	PUNCT
ejpam-5453	356	9	be	be	AUX
ejpam-5453	356	10	a	a	DET
ejpam-5453	356	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	356	12	,	,	PUNCT
ejpam-5453	356	13	d	d	PRON
ejpam-5453	356	14	be	be	AUX
ejpam-5453	356	15	an	an	DET
ejpam-5453	356	16	ideal	ideal	NOUN
ejpam-5453	356	17	on	on	ADP
ejpam-5453	356	18	v	v	NOUN
ejpam-5453	356	19	,	,	PUNCT
ejpam-5453	356	20	υ	υ	PROPN
ejpam-5453	356	21	be	be	AUX
ejpam-5453	356	22	a	a	DET
ejpam-5453	356	23	similarity	similarity	NOUN
ejpam-5453	356	24	relation	relation	NOUN
ejpam-5453	356	25	,	,	PUNCT
ejpam-5453	356	26	℘	℘	PROPN
ejpam-5453	356	27	∈	∈	PROPN
ejpam-5453	356	28	{	{	PUNCT
ejpam-5453	356	29	r	r	NOUN
ejpam-5453	356	30	,	,	PUNCT
ejpam-5453	356	31	l	l	NOUN
ejpam-5453	356	32	,	,	PUNCT
ejpam-5453	356	33	i	i	PRON
ejpam-5453	356	34	,	,	PUNCT
ejpam-5453	356	35	u	u	NOUN
ejpam-5453	356	36	}	}	PUNCT
ejpam-5453	356	37	and	and	CCONJ
ejpam-5453	356	38	m	m	PROPN
ejpam-5453	356	39	⊆	⊆	NUM
ejpam-5453	356	40	v.	v.	ADP
ejpam-5453	356	41	then	then	ADV
ejpam-5453	356	42	d	d	X
ejpam-5453	356	43	-	-	PUNCT
ejpam-5453	356	44	ps℘-open	ps℘-open	ADJ
ejpam-5453	356	45	⇒	⇒	NOUN
ejpam-5453	356	46	d	d	X
ejpam-5453	356	47	-	-	PUNCT
ejpam-5453	356	48	p℘-open	p℘-open	ADJ
ejpam-5453	356	49	.	.	PUNCT
ejpam-5453	357	1	d	d	X
ejpam-5453	357	2	-	-	PUNCT
ejpam-5453	357	3	ss℘-open	ss℘-open	ADJ
ejpam-5453	357	4	⇒	⇒	NOUN
ejpam-5453	357	5	d	d	NOUN
ejpam-5453	357	6	-	-	PUNCT
ejpam-5453	357	7	s℘-open	s℘-open	ADJ
ejpam-5453	357	8	.	.	PUNCT
ejpam-5453	358	1	d	d	X
ejpam-5453	358	2	-	-	PUNCT
ejpam-5453	358	3	βs℘-open	βs℘-open	ADJ
ejpam-5453	358	4	⇒	⇒	NOUN
ejpam-5453	358	5	d	d	NOUN
ejpam-5453	358	6	-	-	PUNCT
ejpam-5453	358	7	β℘-open	β℘-open	ADJ
ejpam-5453	358	8	.	.	PUNCT
ejpam-5453	359	1	d	d	X
ejpam-5453	359	2	-	-	PUNCT
ejpam-5453	359	3	θβs℘-open	θβs℘-open	ADJ
ejpam-5453	359	4	⇒	⇒	NOUN
ejpam-5453	359	5	d	d	NOUN
ejpam-5453	359	6	-	-	PUNCT
ejpam-5453	359	7	θβ℘-open	θβ℘-open	NOUN
ejpam-5453	359	8	.	.	PUNCT
ejpam-5453	360	1	proof	proof	NOUN
ejpam-5453	360	2	.	.	PUNCT
ejpam-5453	361	1	by	by	ADP
ejpam-5453	361	2	applying	apply	VERB
ejpam-5453	361	3	definitions	definition	NOUN
ejpam-5453	361	4	2.4	2.4	NUM
ejpam-5453	361	5	and	and	CCONJ
ejpam-5453	361	6	3.1	3.1	NUM
ejpam-5453	361	7	.	.	PUNCT
ejpam-5453	361	8	example	example	NOUN
ejpam-5453	361	9	3.3	3.3	NUM
ejpam-5453	361	10	clarifies	clarifie	NOUN
ejpam-5453	361	11	that	that	SCONJ
ejpam-5453	361	12	the	the	DET
ejpam-5453	361	13	converse	converse	NOUN
ejpam-5453	361	14	of	of	ADP
ejpam-5453	361	15	proposition	proposition	NOUN
ejpam-5453	361	16	3.5	3.5	NUM
ejpam-5453	361	17	does	do	AUX
ejpam-5453	361	18	not	not	PART
ejpam-5453	361	19	always	always	ADV
ejpam-5453	361	20	apply	apply	VERB
ejpam-5453	361	21	,	,	PUNCT
ejpam-5453	361	22	consequently	consequently	ADV
ejpam-5453	361	23	the	the	DET
ejpam-5453	361	24	prior	prior	ADJ
ejpam-5453	361	25	manners	manner	NOUN
ejpam-5453	361	26	in	in	ADP
ejpam-5453	361	27	[	[	X
ejpam-5453	361	28	22	22	NUM
ejpam-5453	361	29	,	,	PUNCT
ejpam-5453	361	30	26	26	NUM
ejpam-5453	361	31	]	]	PUNCT
ejpam-5453	361	32	are	be	AUX
ejpam-5453	361	33	preferable	preferable	ADJ
ejpam-5453	361	34	than	than	ADP
ejpam-5453	361	35	the	the	DET
ejpam-5453	361	36	present	present	ADJ
ejpam-5453	361	37	one	one	NUM
ejpam-5453	361	38	in	in	ADP
ejpam-5453	361	39	the	the	DET
ejpam-5453	361	40	case	case	NOUN
ejpam-5453	361	41	of	of	ADP
ejpam-5453	361	42	similarity	similarity	NOUN
ejpam-5453	361	43	relation	relation	NOUN
ejpam-5453	361	44	.	.	PUNCT
ejpam-5453	362	1	m.	m.	PROPN
ejpam-5453	362	2	hosny	hosny	PROPN
ejpam-5453	362	3	/	/	SYM
ejpam-5453	362	4	eur	eur	PROPN
ejpam-5453	362	5	.	.	PUNCT
ejpam-5453	363	1	j.	j.	PROPN
ejpam-5453	363	2	pure	pure	PROPN
ejpam-5453	363	3	appl	appl	PROPN
ejpam-5453	363	4	.	.	PROPN
ejpam-5453	363	5	math	math	PROPN
ejpam-5453	363	6	,	,	PUNCT
ejpam-5453	363	7	17	17	NUM
ejpam-5453	363	8	(	(	PUNCT
ejpam-5453	363	9	4	4	NUM
ejpam-5453	363	10	)	)	PUNCT
ejpam-5453	363	11	(	(	PUNCT
ejpam-5453	363	12	2024	2024	NUM
ejpam-5453	363	13	)	)	PUNCT
ejpam-5453	363	14	,	,	PUNCT
ejpam-5453	363	15	2843	2843	NUM
ejpam-5453	363	16	-	-	SYM
ejpam-5453	363	17	2877	2877	NUM
ejpam-5453	363	18	2854	2854	NUM
ejpam-5453	363	19	4	4	NUM
ejpam-5453	363	20	.	.	PUNCT
ejpam-5453	363	21	approximations	approximation	NOUN
ejpam-5453	363	22	by	by	ADP
ejpam-5453	363	23	using	use	VERB
ejpam-5453	363	24	d	d	NOUN
ejpam-5453	363	25	-	-	PUNCT
ejpam-5453	363	26	s℘-nearly	s℘-nearly	ADV
ejpam-5453	363	27	open	open	ADJ
ejpam-5453	363	28	sets	set	NOUN
ejpam-5453	363	29	and	and	CCONJ
ejpam-5453	363	30	comparisons	comparison	NOUN
ejpam-5453	363	31	to	to	ADP
ejpam-5453	363	32	the	the	DET
ejpam-5453	363	33	prior	prior	ADJ
ejpam-5453	363	34	ones	one	NOUN
ejpam-5453	363	35	in	in	ADP
ejpam-5453	363	36	this	this	DET
ejpam-5453	363	37	section	section	NOUN
ejpam-5453	363	38	,	,	PUNCT
ejpam-5453	363	39	new	new	ADJ
ejpam-5453	363	40	rough	rough	ADJ
ejpam-5453	363	41	paradigms	paradigm	NOUN
ejpam-5453	363	42	inspired	inspire	VERB
ejpam-5453	363	43	by	by	ADP
ejpam-5453	363	44	the	the	DET
ejpam-5453	363	45	family	family	NOUN
ejpam-5453	364	1	d	d	NOUN
ejpam-5453	364	2	-	-	PUNCT
ejpam-5453	364	3	s℘-nearly	s℘-nearly	ADV
ejpam-5453	364	4	open	open	ADJ
ejpam-5453	364	5	sets	set	NOUN
ejpam-5453	364	6	are	be	AUX
ejpam-5453	364	7	introduced	introduce	VERB
ejpam-5453	364	8	.	.	PUNCT
ejpam-5453	365	1	additionally	additionally	ADV
ejpam-5453	365	2	,	,	PUNCT
ejpam-5453	365	3	the	the	DET
ejpam-5453	365	4	proposed	propose	VERB
ejpam-5453	365	5	models	model	NOUN
ejpam-5453	365	6	for	for	ADP
ejpam-5453	365	7	all	all	DET
ejpam-5453	365	8	cases	case	NOUN
ejpam-5453	365	9	of	of	ADP
ejpam-5453	365	10	d	d	NOUN
ejpam-5453	365	11	-	-	PUNCT
ejpam-5453	365	12	s℘-nearly	s℘-nearly	ADV
ejpam-5453	365	13	open	open	ADJ
ejpam-5453	365	14	sets	set	NOUN
ejpam-5453	365	15	are	be	AUX
ejpam-5453	365	16	compared	compare	VERB
ejpam-5453	365	17	using	use	VERB
ejpam-5453	365	18	counterexamples	counterexample	NOUN
ejpam-5453	365	19	to	to	PART
ejpam-5453	365	20	illustrate	illustrate	VERB
ejpam-5453	365	21	their	their	PRON
ejpam-5453	365	22	distinctions	distinction	NOUN
ejpam-5453	365	23	.	.	PUNCT
ejpam-5453	366	1	more	more	ADV
ejpam-5453	366	2	importantly	importantly	ADV
ejpam-5453	366	3	,	,	PUNCT
ejpam-5453	366	4	it	it	PRON
ejpam-5453	366	5	is	be	AUX
ejpam-5453	366	6	showed	show	VERB
ejpam-5453	366	7	that	that	SCONJ
ejpam-5453	366	8	how	how	SCONJ
ejpam-5453	366	9	these	these	DET
ejpam-5453	366	10	novel	novel	ADJ
ejpam-5453	366	11	paradigms	paradigm	NOUN
ejpam-5453	366	12	contribute	contribute	VERB
ejpam-5453	366	13	to	to	ADP
ejpam-5453	366	14	decision	decision	NOUN
ejpam-5453	366	15	-	-	PUNCT
ejpam-5453	366	16	making	making	NOUN
ejpam-5453	366	17	.	.	PUNCT
ejpam-5453	367	1	as	as	SCONJ
ejpam-5453	367	2	,	,	PUNCT
ejpam-5453	367	3	it	it	PRON
ejpam-5453	367	4	improves	improve	VERB
ejpam-5453	367	5	the	the	DET
ejpam-5453	367	6	accuracy	accuracy	NOUN
ejpam-5453	367	7	of	of	ADP
ejpam-5453	367	8	the	the	DET
ejpam-5453	367	9	knowledge	knowledge	NOUN
ejpam-5453	367	10	extracted	extract	VERB
ejpam-5453	367	11	,	,	PUNCT
ejpam-5453	367	12	compared	compare	VERB
ejpam-5453	367	13	to	to	ADP
ejpam-5453	367	14	existing	exist	VERB
ejpam-5453	367	15	ones	one	NOUN
ejpam-5453	367	16	.	.	PUNCT
ejpam-5453	368	1	4.1	4.1	NUM
ejpam-5453	368	2	.	.	PUNCT
ejpam-5453	368	3	approximations	approximation	NOUN
ejpam-5453	368	4	by	by	ADP
ejpam-5453	368	5	using	use	VERB
ejpam-5453	368	6	d	d	NOUN
ejpam-5453	368	7	-	-	PUNCT
ejpam-5453	368	8	s℘-nearly	s℘-nearly	ADV
ejpam-5453	368	9	open	open	ADJ
ejpam-5453	368	10	sets	set	NOUN
ejpam-5453	368	11	definition	definition	NOUN
ejpam-5453	368	12	4.1	4.1	NUM
ejpam-5453	368	13	.	.	PUNCT
ejpam-5453	369	1	let(v	let(v	PROPN
ejpam-5453	369	2	,	,	PUNCT
ejpam-5453	369	3	υ	υ	NOUN
ejpam-5453	369	4	,	,	PUNCT
ejpam-5453	369	5	π℘	π℘	NUM
ejpam-5453	369	6	)	)	PUNCT
ejpam-5453	369	7	be	be	AUX
ejpam-5453	369	8	a	a	DET
ejpam-5453	369	9	℘-nbds	℘-nbds	NOUN
ejpam-5453	369	10	,	,	PUNCT
ejpam-5453	369	11	d	d	PRON
ejpam-5453	369	12	be	be	AUX
ejpam-5453	369	13	an	an	DET
ejpam-5453	369	14	ideal	ideal	NOUN
ejpam-5453	369	15	on	on	ADP
ejpam-5453	369	16	v	v	NUM
ejpam-5453	369	17	and	and	CCONJ
ejpam-5453	369	18	m	m	PROPN
ejpam-5453	369	19	⊆	⊆	NUM
ejpam-5453	369	20	v.	v.	ADP
ejpam-5453	369	21	the	the	DET
ejpam-5453	369	22	ds℘-nearly	ds℘-nearly	ADV
ejpam-5453	369	23	lower	low	ADJ
ejpam-5453	369	24	,	,	PUNCT
ejpam-5453	369	25	d	d	X
ejpam-5453	369	26	-	-	PUNCT
ejpam-5453	369	27	s℘-nearly	s℘-nearly	ADV
ejpam-5453	369	28	upper	upper	ADJ
ejpam-5453	369	29	approximations	approximation	NOUN
ejpam-5453	369	30	,	,	PUNCT
ejpam-5453	369	31	d	d	X
ejpam-5453	369	32	-	-	PUNCT
ejpam-5453	369	33	s℘-nearly	s℘-nearly	ADV
ejpam-5453	369	34	boundary	boundary	ADJ
ejpam-5453	369	35	regions	region	NOUN
ejpam-5453	369	36	and	and	CCONJ
ejpam-5453	369	37	d	d	NOUN
ejpam-5453	369	38	-	-	PUNCT
ejpam-5453	369	39	s℘-nearly	s℘-nearly	ADV
ejpam-5453	369	40	accuracy	accuracy	NOUN
ejpam-5453	369	41	of	of	ADP
ejpam-5453	369	42	m	m	PROPN
ejpam-5453	369	43	are	be	AUX
ejpam-5453	369	44	:	:	PUNCT
ejpam-5453	369	45	nd−ξ	nd−ξ	ADJ
ejpam-5453	369	46	s℘	s℘	PROPN
ejpam-5453	369	47	(	(	PUNCT
ejpam-5453	369	48	m	m	NOUN
ejpam-5453	369	49	)	)	PUNCT
ejpam-5453	369	50	=	=	PUNCT
ejpam-5453	370	1	∪{g	∪{g	PROPN
ejpam-5453	370	2	∈	∈	PROPN
ejpam-5453	370	3	d	d	X
ejpam-5453	370	4	-	-	PUNCT
ejpam-5453	370	5	ξs℘o(v	ξs℘o(v	PROPN
ejpam-5453	370	6	)	)	PUNCT
ejpam-5453	370	7	:	:	PUNCT
ejpam-5453	370	8	g	g	PROPN
ejpam-5453	370	9	⊆	⊆	NUM
ejpam-5453	370	10	m	m	NOUN
ejpam-5453	370	11	}	}	PUNCT
ejpam-5453	370	12	=	=	SYM
ejpam-5453	370	13	d	d	X
ejpam-5453	370	14	-	-	PUNCT
ejpam-5453	370	15	s℘-nearly	s℘-nearly	ADV
ejpam-5453	370	16	interior	interior	ADJ
ejpam-5453	370	17	of	of	ADP
ejpam-5453	370	18	m	m	PROPN
ejpam-5453	370	19	.	.	PUNCT
ejpam-5453	371	1	n	n	CCONJ
ejpam-5453	371	2	d−ξ	d−ξ	NOUN
ejpam-5453	371	3	s℘	s℘	NOUN
ejpam-5453	371	4	(	(	PUNCT
ejpam-5453	371	5	m	m	NOUN
ejpam-5453	371	6	)	)	PUNCT
ejpam-5453	371	7	=	=	VERB
ejpam-5453	372	1	∩{h	∩{h	PUNCT
ejpam-5453	372	2	∈	∈	PROPN
ejpam-5453	372	3	d	d	X
ejpam-5453	372	4	-	-	PUNCT
ejpam-5453	372	5	ξs℘c(v	ξs℘c(v	NOUN
ejpam-5453	372	6	)	)	PUNCT
ejpam-5453	372	7	:	:	PUNCT
ejpam-5453	372	8	m	m	VERB
ejpam-5453	372	9	⊆	⊆	NUM
ejpam-5453	372	10	h	h	NOUN
ejpam-5453	372	11	}	}	PUNCT
ejpam-5453	372	12	=	=	SYM
ejpam-5453	372	13	d	d	X
ejpam-5453	372	14	-	-	PUNCT
ejpam-5453	372	15	s℘-nearly	s℘-nearly	ADV
ejpam-5453	372	16	closure	closure	NOUN
ejpam-5453	372	17	of	of	ADP
ejpam-5453	372	18	m	m	PROPN
ejpam-5453	372	19	.	.	PUNCT
ejpam-5453	373	1	bd−ξ	bd−ξ	PROPN
ejpam-5453	373	2	s℘	s℘	PROPN
ejpam-5453	373	3	(	(	PUNCT
ejpam-5453	373	4	m	m	NOUN
ejpam-5453	373	5	)	)	PUNCT
ejpam-5453	373	6	=	=	SYM
ejpam-5453	373	7	n	n	NUM
ejpam-5453	373	8	d−ξ	d−ξ	NOUN
ejpam-5453	373	9	s℘	s℘	NOUN
ejpam-5453	373	10	(	(	PUNCT
ejpam-5453	373	11	m)−nd−ξ	m)−nd−ξ	NOUN
ejpam-5453	373	12	s℘	s℘	NOUN
ejpam-5453	373	13	(	(	PUNCT
ejpam-5453	373	14	m	m	NOUN
ejpam-5453	373	15	)	)	PUNCT
ejpam-5453	373	16	.	.	PUNCT
ejpam-5453	374	1	ad−ξ	ad−ξ	PROPN
ejpam-5453	374	2	s℘	s℘	PROPN
ejpam-5453	374	3	(	(	PUNCT
ejpam-5453	374	4	m	m	NOUN
ejpam-5453	374	5	)	)	PUNCT
ejpam-5453	374	6	=	=	SYM
ejpam-5453	375	1	|nd−ξ	|nd−ξ	ADP
ejpam-5453	375	2	s℘	s℘	NOUN
ejpam-5453	375	3	(	(	PUNCT
ejpam-5453	375	4	m)|	m)|	ADJ
ejpam-5453	375	5	|nd−ξ	|nd−ξ	ADP
ejpam-5453	375	6	s℘	s℘	NOUN
ejpam-5453	375	7	(	(	PUNCT
ejpam-5453	375	8	m)|	m)|	INTJ
ejpam-5453	375	9	,	,	PUNCT
ejpam-5453	375	10	where	where	SCONJ
ejpam-5453	375	11	|nd−ξ	|nd−ξ	ADP
ejpam-5453	375	12	s℘	s℘	NOUN
ejpam-5453	375	13	(	(	PUNCT
ejpam-5453	375	14	m)|	m)|	NOUN
ejpam-5453	375	15	=	=	NOUN
ejpam-5453	375	16	̸	̸	NUM
ejpam-5453	375	17	0	0	NUM
ejpam-5453	375	18	.	.	PUNCT
ejpam-5453	376	1	proposition	proposition	NOUN
ejpam-5453	376	2	4.1	4.1	NUM
ejpam-5453	376	3	.	.	PUNCT
ejpam-5453	377	1	let	let	AUX
ejpam-5453	377	2	(	(	PUNCT
ejpam-5453	377	3	v	v	NOUN
ejpam-5453	377	4	,	,	PUNCT
ejpam-5453	377	5	υ	υ	NOUN
ejpam-5453	377	6	,	,	PUNCT
ejpam-5453	377	7	π℘	π℘	NUM
ejpam-5453	377	8	)	)	PUNCT
ejpam-5453	377	9	be	be	AUX
ejpam-5453	377	10	a	a	DET
ejpam-5453	377	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	377	12	,	,	PUNCT
ejpam-5453	377	13	d	d	PRON
ejpam-5453	377	14	be	be	AUX
ejpam-5453	377	15	an	an	DET
ejpam-5453	377	16	ideal	ideal	NOUN
ejpam-5453	377	17	on	on	ADP
ejpam-5453	377	18	v	v	NUM
ejpam-5453	377	19	and	and	CCONJ
ejpam-5453	377	20	m	m	PROPN
ejpam-5453	377	21	,	,	PUNCT
ejpam-5453	377	22	n	n	PROPN
ejpam-5453	377	23	⊆	⊆	NUM
ejpam-5453	377	24	v.	v.	ADP
ejpam-5453	377	25	then	then	ADV
ejpam-5453	377	26	,	,	PUNCT
ejpam-5453	377	27	(	(	PUNCT
ejpam-5453	377	28	i	i	NOUN
ejpam-5453	377	29	)	)	PUNCT
ejpam-5453	377	30	nd−ξ	nd−ξ	PROPN
ejpam-5453	377	31	s℘	s℘	PROPN
ejpam-5453	377	32	(	(	PUNCT
ejpam-5453	377	33	m	m	NOUN
ejpam-5453	377	34	)	)	PUNCT
ejpam-5453	378	1	⊆	⊆	NUM
ejpam-5453	378	2	m	m	NUM
ejpam-5453	378	3	⊆	⊆	NUM
ejpam-5453	378	4	n	n	PRON
ejpam-5453	378	5	d−ξ	d−ξ	NOUN
ejpam-5453	378	6	s℘	s℘	NOUN
ejpam-5453	378	7	(	(	PUNCT
ejpam-5453	378	8	m	m	NOUN
ejpam-5453	378	9	)	)	PUNCT
ejpam-5453	378	10	equality	equality	NOUN
ejpam-5453	378	11	hold	hold	VERB
ejpam-5453	378	12	if	if	SCONJ
ejpam-5453	378	13	m	m	NOUN
ejpam-5453	378	14	=	=	NOUN
ejpam-5453	378	15	∅	∅	NOUN
ejpam-5453	378	16	or	or	CCONJ
ejpam-5453	378	17	v.	v.	ADJ
ejpam-5453	378	18	(	(	PUNCT
ejpam-5453	378	19	ii	ii	NOUN
ejpam-5453	378	20	)	)	PUNCT
ejpam-5453	378	21	m	m	PROPN
ejpam-5453	378	22	⊆	⊆	NUM
ejpam-5453	378	23	n	n	PRON
ejpam-5453	378	24	⇒	⇒	NOUN
ejpam-5453	378	25	n	n	PRON
ejpam-5453	378	26	d−ξ	d−ξ	NOUN
ejpam-5453	378	27	s℘	s℘	NOUN
ejpam-5453	378	28	(	(	PUNCT
ejpam-5453	378	29	m	m	NOUN
ejpam-5453	378	30	)	)	PUNCT
ejpam-5453	378	31	⊆	⊆	NUM
ejpam-5453	378	32	n	n	PRON
ejpam-5453	378	33	d−ξ	d−ξ	NOUN
ejpam-5453	378	34	s℘	s℘	NOUN
ejpam-5453	378	35	(	(	PUNCT
ejpam-5453	378	36	n	n	CCONJ
ejpam-5453	378	37	)	)	PUNCT
ejpam-5453	378	38	.	.	PUNCT
ejpam-5453	379	1	(	(	PUNCT
ejpam-5453	379	2	iii	iii	X
ejpam-5453	379	3	)	)	PUNCT
ejpam-5453	379	4	m	m	PROPN
ejpam-5453	379	5	⊆	⊆	NUM
ejpam-5453	379	6	n	n	ADP
ejpam-5453	379	7	⇒	⇒	VERB
ejpam-5453	379	8	nd−ξ	nd−ξ	PROPN
ejpam-5453	379	9	s℘	s℘	PROPN
ejpam-5453	379	10	(	(	PUNCT
ejpam-5453	379	11	m	m	NOUN
ejpam-5453	379	12	)	)	PUNCT
ejpam-5453	380	1	⊆	⊆	NUM
ejpam-5453	380	2	nd−ξ	nd−ξ	ADJ
ejpam-5453	380	3	s℘	s℘	NOUN
ejpam-5453	380	4	(	(	PUNCT
ejpam-5453	380	5	n	n	CCONJ
ejpam-5453	380	6	)	)	PUNCT
ejpam-5453	380	7	.	.	PUNCT
ejpam-5453	381	1	(	(	PUNCT
ejpam-5453	381	2	iv	iv	X
ejpam-5453	381	3	)	)	PUNCT
ejpam-5453	381	4	n	n	NOUN
ejpam-5453	381	5	d−ξ	d−ξ	NOUN
ejpam-5453	381	6	s℘	s℘	NOUN
ejpam-5453	381	7	(	(	PUNCT
ejpam-5453	381	8	m	m	NOUN
ejpam-5453	381	9	∩n	∩n	NOUN
ejpam-5453	381	10	)	)	PUNCT
ejpam-5453	381	11	⊆	⊆	NUM
ejpam-5453	381	12	n	n	PRON
ejpam-5453	381	13	d−ξ	d−ξ	NOUN
ejpam-5453	381	14	s℘	s℘	NOUN
ejpam-5453	381	15	(	(	PUNCT
ejpam-5453	381	16	m	m	NOUN
ejpam-5453	381	17	)	)	PUNCT
ejpam-5453	381	18	∩n	∩n	NOUN
ejpam-5453	381	19	d−ξ	d−ξ	NOUN
ejpam-5453	381	20	s℘	s℘	PROPN
ejpam-5453	381	21	(	(	PUNCT
ejpam-5453	381	22	n	n	CCONJ
ejpam-5453	381	23	)	)	PUNCT
ejpam-5453	381	24	.	.	PUNCT
ejpam-5453	382	1	(	(	PUNCT
ejpam-5453	382	2	v	v	NOUN
ejpam-5453	382	3	)	)	PUNCT
ejpam-5453	382	4	nd−ξ	nd−ξ	NOUN
ejpam-5453	382	5	s℘	s℘	NOUN
ejpam-5453	382	6	(	(	PUNCT
ejpam-5453	382	7	m	m	NOUN
ejpam-5453	382	8	∪n	∪n	NUM
ejpam-5453	382	9	)	)	PUNCT
ejpam-5453	382	10	⊇	⊇	PROPN
ejpam-5453	382	11	nd−ξ	nd−ξ	PROPN
ejpam-5453	382	12	s℘	s℘	PROPN
ejpam-5453	382	13	(	(	PUNCT
ejpam-5453	382	14	m	m	NOUN
ejpam-5453	382	15	)	)	PUNCT
ejpam-5453	383	1	∪nd−ξ	∪nd−ξ	ADJ
ejpam-5453	383	2	s℘	s℘	NOUN
ejpam-5453	383	3	(	(	PUNCT
ejpam-5453	383	4	n	n	CCONJ
ejpam-5453	383	5	)	)	PUNCT
ejpam-5453	383	6	.	.	PUNCT
ejpam-5453	384	1	(	(	PUNCT
ejpam-5453	384	2	vi	vi	NOUN
ejpam-5453	384	3	)	)	PUNCT
ejpam-5453	384	4	n	n	NOUN
ejpam-5453	384	5	d−ξ	d−ξ	NOUN
ejpam-5453	384	6	s℘	s℘	NOUN
ejpam-5453	384	7	(	(	PUNCT
ejpam-5453	384	8	m	m	NOUN
ejpam-5453	384	9	∪n	∪n	NUM
ejpam-5453	384	10	)	)	PUNCT
ejpam-5453	384	11	⊇	⊇	NOUN
ejpam-5453	384	12	n	n	CCONJ
ejpam-5453	384	13	d−ξ	d−ξ	NOUN
ejpam-5453	384	14	s℘	s℘	NOUN
ejpam-5453	384	15	(	(	PUNCT
ejpam-5453	384	16	m	m	NOUN
ejpam-5453	384	17	)	)	PUNCT
ejpam-5453	384	18	∪n	∪n	NUM
ejpam-5453	384	19	d−ξ	d−ξ	NOUN
ejpam-5453	384	20	s℘	s℘	NOUN
ejpam-5453	384	21	(	(	PUNCT
ejpam-5453	384	22	n	n	CCONJ
ejpam-5453	384	23	)	)	PUNCT
ejpam-5453	384	24	.	.	PUNCT
ejpam-5453	385	1	(	(	PUNCT
ejpam-5453	385	2	vii	vii	PROPN
ejpam-5453	385	3	)	)	PUNCT
ejpam-5453	385	4	nd−ξ	nd−ξ	PROPN
ejpam-5453	385	5	s℘	s℘	PROPN
ejpam-5453	385	6	(	(	PUNCT
ejpam-5453	385	7	m	m	NOUN
ejpam-5453	385	8	∩n	∩n	NOUN
ejpam-5453	385	9	)	)	PUNCT
ejpam-5453	385	10	⊆	⊆	NUM
ejpam-5453	385	11	nd−ξ	nd−ξ	PROPN
ejpam-5453	385	12	s℘	s℘	NOUN
ejpam-5453	385	13	(	(	PUNCT
ejpam-5453	385	14	m	m	NOUN
ejpam-5453	385	15	)	)	PUNCT
ejpam-5453	386	1	∩nd−ξ	∩nd−ξ	PROPN
ejpam-5453	386	2	s℘	s℘	PROPN
ejpam-5453	386	3	(	(	PUNCT
ejpam-5453	386	4	n	n	CCONJ
ejpam-5453	386	5	)	)	PUNCT
ejpam-5453	386	6	.	.	PUNCT
ejpam-5453	387	1	(	(	PUNCT
ejpam-5453	387	2	viii	viii	NOUN
ejpam-5453	387	3	)	)	PUNCT
ejpam-5453	387	4	nd−ξ	nd−ξ	NOUN
ejpam-5453	387	5	s℘	s℘	PROPN
ejpam-5453	387	6	(	(	PUNCT
ejpam-5453	387	7	m	m	NOUN
ejpam-5453	387	8	)	)	PUNCT
ejpam-5453	387	9	=	=	SYM
ejpam-5453	387	10	(	(	PUNCT
ejpam-5453	387	11	n	n	CCONJ
ejpam-5453	387	12	d−ξ	d−ξ	NOUN
ejpam-5453	387	13	s℘	s℘	NOUN
ejpam-5453	387	14	(	(	PUNCT
ejpam-5453	387	15	m	m	NOUN
ejpam-5453	387	16	′	′	NUM
ejpam-5453	387	17	)	)	PUNCT
ejpam-5453	387	18	)	)	PUNCT
ejpam-5453	388	1	′	′	NUM
ejpam-5453	388	2	,	,	PUNCT
ejpam-5453	388	3	n	n	CCONJ
ejpam-5453	388	4	d−ξ	d−ξ	NOUN
ejpam-5453	388	5	s℘	s℘	NOUN
ejpam-5453	388	6	(	(	PUNCT
ejpam-5453	388	7	m	m	NOUN
ejpam-5453	388	8	)	)	PUNCT
ejpam-5453	388	9	=	=	SYM
ejpam-5453	388	10	(	(	PUNCT
ejpam-5453	388	11	nd−ξ	nd−ξ	ADJ
ejpam-5453	388	12	s℘	s℘	NOUN
ejpam-5453	388	13	(	(	PUNCT
ejpam-5453	388	14	m	m	NOUN
ejpam-5453	388	15	′	′	NUM
ejpam-5453	388	16	)	)	PUNCT
ejpam-5453	388	17	)	)	PUNCT
ejpam-5453	389	1	′	′	X
ejpam-5453	389	2	.	.	PUNCT
ejpam-5453	390	1	(	(	PUNCT
ejpam-5453	390	2	ix	ix	NOUN
ejpam-5453	390	3	)	)	PUNCT
ejpam-5453	390	4	n	n	NOUN
ejpam-5453	390	5	d−ξ	d−ξ	NOUN
ejpam-5453	390	6	s℘	s℘	NOUN
ejpam-5453	390	7	(	(	PUNCT
ejpam-5453	390	8	n	n	CCONJ
ejpam-5453	390	9	d−ξ	d−ξ	NOUN
ejpam-5453	390	10	s℘	s℘	NOUN
ejpam-5453	390	11	(	(	PUNCT
ejpam-5453	390	12	m	m	NOUN
ejpam-5453	390	13	)	)	PUNCT
ejpam-5453	390	14	)	)	PUNCT
ejpam-5453	390	15	=	=	SYM
ejpam-5453	391	1	n	n	NUM
ejpam-5453	391	2	d−ξ	d−ξ	NOUN
ejpam-5453	391	3	s℘	s℘	NOUN
ejpam-5453	391	4	(	(	PUNCT
ejpam-5453	391	5	m	m	NOUN
ejpam-5453	391	6	)	)	PUNCT
ejpam-5453	391	7	.	.	PUNCT
ejpam-5453	392	1	(	(	PUNCT
ejpam-5453	392	2	x	x	X
ejpam-5453	392	3	)	)	PUNCT
ejpam-5453	392	4	nd−ξ	nd−ξ	ADJ
ejpam-5453	392	5	s℘	s℘	NOUN
ejpam-5453	392	6	(	(	PUNCT
ejpam-5453	392	7	nd−ξ	nd−ξ	NOUN
ejpam-5453	392	8	s℘	s℘	PROPN
ejpam-5453	392	9	(	(	PUNCT
ejpam-5453	392	10	m	m	NOUN
ejpam-5453	392	11	)	)	PUNCT
ejpam-5453	392	12	)	)	PUNCT
ejpam-5453	393	1	=	=	SYM
ejpam-5453	393	2	nd−ξ	nd−ξ	PROPN
ejpam-5453	393	3	s℘	s℘	PROPN
ejpam-5453	393	4	(	(	PUNCT
ejpam-5453	393	5	m	m	NOUN
ejpam-5453	393	6	)	)	PUNCT
ejpam-5453	393	7	.	.	PUNCT
ejpam-5453	394	1	(	(	PUNCT
ejpam-5453	394	2	xi	xi	NOUN
ejpam-5453	394	3	)	)	PUNCT
ejpam-5453	394	4	nd−ξ	nd−ξ	PROPN
ejpam-5453	394	5	s℘	s℘	NOUN
ejpam-5453	394	6	(	(	PUNCT
ejpam-5453	394	7	nd−ξ	nd−ξ	NOUN
ejpam-5453	394	8	s℘	s℘	PROPN
ejpam-5453	394	9	(	(	PUNCT
ejpam-5453	394	10	m	m	NOUN
ejpam-5453	394	11	)	)	PUNCT
ejpam-5453	394	12	)	)	PUNCT
ejpam-5453	395	1	⊆	⊆	NUM
ejpam-5453	395	2	n	n	PRON
ejpam-5453	395	3	d−ξ	d−ξ	NOUN
ejpam-5453	395	4	s℘	s℘	NOUN
ejpam-5453	395	5	(	(	PUNCT
ejpam-5453	395	6	nd−ξ	nd−ξ	NOUN
ejpam-5453	395	7	s℘	s℘	NOUN
ejpam-5453	395	8	(	(	PUNCT
ejpam-5453	395	9	m	m	NOUN
ejpam-5453	395	10	)	)	PUNCT
ejpam-5453	395	11	)	)	PUNCT
ejpam-5453	395	12	.	.	PUNCT
ejpam-5453	396	1	m.	m.	PROPN
ejpam-5453	396	2	hosny	hosny	PROPN
ejpam-5453	396	3	/	/	SYM
ejpam-5453	396	4	eur	eur	PROPN
ejpam-5453	396	5	.	.	PUNCT
ejpam-5453	397	1	j.	j.	PROPN
ejpam-5453	397	2	pure	pure	PROPN
ejpam-5453	397	3	appl	appl	PROPN
ejpam-5453	397	4	.	.	PROPN
ejpam-5453	397	5	math	math	PROPN
ejpam-5453	397	6	,	,	PUNCT
ejpam-5453	397	7	17	17	NUM
ejpam-5453	397	8	(	(	PUNCT
ejpam-5453	397	9	4	4	NUM
ejpam-5453	397	10	)	)	PUNCT
ejpam-5453	397	11	(	(	PUNCT
ejpam-5453	397	12	2024	2024	NUM
ejpam-5453	397	13	)	)	PUNCT
ejpam-5453	397	14	,	,	PUNCT
ejpam-5453	397	15	2843	2843	NUM
ejpam-5453	397	16	-	-	SYM
ejpam-5453	397	17	2877	2877	NUM
ejpam-5453	397	18	2855	2855	NUM
ejpam-5453	397	19	(	(	PUNCT
ejpam-5453	397	20	xii	xii	NOUN
ejpam-5453	397	21	)	)	PUNCT
ejpam-5453	397	22	nd−ξ	nd−ξ	NOUN
ejpam-5453	398	1	s℘	s℘	NOUN
ejpam-5453	398	2	(	(	PUNCT
ejpam-5453	398	3	n	n	CCONJ
ejpam-5453	398	4	d−ξ	d−ξ	NOUN
ejpam-5453	398	5	s℘	s℘	NOUN
ejpam-5453	398	6	(	(	PUNCT
ejpam-5453	398	7	m	m	NOUN
ejpam-5453	398	8	)	)	PUNCT
ejpam-5453	398	9	)	)	PUNCT
ejpam-5453	399	1	⊆	⊆	NUM
ejpam-5453	399	2	n	n	PRON
ejpam-5453	399	3	d−ξ	d−ξ	NOUN
ejpam-5453	399	4	s℘	s℘	NOUN
ejpam-5453	399	5	(	(	PUNCT
ejpam-5453	399	6	n	n	CCONJ
ejpam-5453	399	7	d−ξ	d−ξ	NOUN
ejpam-5453	399	8	s℘	s℘	NOUN
ejpam-5453	399	9	(	(	PUNCT
ejpam-5453	399	10	m	m	NOUN
ejpam-5453	399	11	)	)	PUNCT
ejpam-5453	399	12	)	)	PUNCT
ejpam-5453	399	13	.	.	PUNCT
ejpam-5453	400	1	straightforward	straightforward	ADJ
ejpam-5453	400	2	using	use	VERB
ejpam-5453	400	3	d	d	NOUN
ejpam-5453	400	4	-	-	PUNCT
ejpam-5453	400	5	s℘-nearly	s℘-nearly	ADV
ejpam-5453	400	6	interior	interior	ADJ
ejpam-5453	400	7	and	and	CCONJ
ejpam-5453	400	8	d	d	NOUN
ejpam-5453	400	9	-	-	PUNCT
ejpam-5453	400	10	s℘-nearly	s℘-nearly	ADV
ejpam-5453	400	11	closure	closure	NOUN
ejpam-5453	400	12	,	,	PUNCT
ejpam-5453	400	13	so	so	CCONJ
ejpam-5453	400	14	it	it	PRON
ejpam-5453	400	15	is	be	AUX
ejpam-5453	400	16	not	not	PART
ejpam-5453	400	17	be	be	AUX
ejpam-5453	400	18	detailed	detail	VERB
ejpam-5453	400	19	here	here	ADV
ejpam-5453	400	20	.	.	PUNCT
ejpam-5453	401	1	remark	remark	VERB
ejpam-5453	401	2	4.1	4.1	NUM
ejpam-5453	401	3	.	.	PUNCT
ejpam-5453	402	1	in	in	ADP
ejpam-5453	402	2	example	example	NOUN
ejpam-5453	402	3	3.1	3.1	NUM
ejpam-5453	402	4	,	,	PUNCT
ejpam-5453	402	5	take	take	VERB
ejpam-5453	402	6	d	d	NOUN
ejpam-5453	402	7	=	=	PUNCT
ejpam-5453	402	8	{	{	PUNCT
ejpam-5453	402	9	∅	∅	NOUN
ejpam-5453	402	10	,	,	PUNCT
ejpam-5453	402	11	{	{	PUNCT
ejpam-5453	402	12	l2	l2	NOUN
ejpam-5453	402	13	}	}	PUNCT
ejpam-5453	402	14	}	}	PUNCT
ejpam-5453	402	15	.	.	PUNCT
ejpam-5453	403	1	it	it	PRON
ejpam-5453	403	2	shows	show	VERB
ejpam-5453	403	3	that	that	SCONJ
ejpam-5453	403	4	(	(	PUNCT
ejpam-5453	403	5	i	i	NOUN
ejpam-5453	403	6	)	)	PUNCT
ejpam-5453	403	7	if	if	SCONJ
ejpam-5453	403	8	m	m	ADV
ejpam-5453	403	9	=	=	SYM
ejpam-5453	403	10	{	{	PUNCT
ejpam-5453	403	11	l1	l1	PROPN
ejpam-5453	403	12	}	}	PUNCT
ejpam-5453	403	13	,	,	PUNCT
ejpam-5453	403	14	then	then	ADV
ejpam-5453	403	15	nd−β	nd−β	PROPN
ejpam-5453	403	16	sr	sr	PROPN
ejpam-5453	403	17	(	(	PUNCT
ejpam-5453	403	18	m	m	NOUN
ejpam-5453	403	19	)	)	PUNCT
ejpam-5453	403	20	=	=	SYM
ejpam-5453	403	21	ϕ	ϕ	NOUN
ejpam-5453	403	22	,	,	PUNCT
ejpam-5453	403	23	so	so	ADV
ejpam-5453	403	24	,	,	PUNCT
ejpam-5453	403	25	a	a	DET
ejpam-5453	403	26	⊈	⊈	PROPN
ejpam-5453	403	27	nd−β	nd−β	NOUN
ejpam-5453	403	28	sr	sr	PROPN
ejpam-5453	403	29	(	(	PUNCT
ejpam-5453	403	30	m	m	PROPN
ejpam-5453	403	31	)	)	PUNCT
ejpam-5453	403	32	.	.	PUNCT
ejpam-5453	404	1	additionally	additionally	ADV
ejpam-5453	404	2	,	,	PUNCT
ejpam-5453	404	3	take	take	VERB
ejpam-5453	404	4	m	m	NOUN
ejpam-5453	404	5	=	=	PUNCT
ejpam-5453	404	6	{	{	PUNCT
ejpam-5453	404	7	l2	l2	PROPN
ejpam-5453	404	8	,	,	PUNCT
ejpam-5453	404	9	l3	l3	PROPN
ejpam-5453	404	10	,	,	PUNCT
ejpam-5453	404	11	l4},n	l4},n	PROPN
ejpam-5453	404	12	d−β	d−β	PRON
ejpam-5453	404	13	sr	sr	PROPN
ejpam-5453	404	14	(	(	PUNCT
ejpam-5453	404	15	m	m	PROPN
ejpam-5453	404	16	)	)	PUNCT
ejpam-5453	404	17	=	=	SYM
ejpam-5453	404	18	v	v	NOUN
ejpam-5453	404	19	,	,	PUNCT
ejpam-5453	404	20	then	then	ADV
ejpam-5453	404	21	n	n	PROPN
ejpam-5453	404	22	d−β	d−β	NOUN
ejpam-5453	404	23	sr	sr	PROPN
ejpam-5453	404	24	(	(	PUNCT
ejpam-5453	404	25	m	m	PROPN
ejpam-5453	404	26	)	)	PUNCT
ejpam-5453	404	27	⊈	⊈	PROPN
ejpam-5453	404	28	m	m	NOUN
ejpam-5453	404	29	.	.	PUNCT
ejpam-5453	405	1	(	(	PUNCT
ejpam-5453	405	2	ii	ii	NOUN
ejpam-5453	405	3	)	)	PUNCT
ejpam-5453	405	4	if	if	SCONJ
ejpam-5453	405	5	m	m	ADV
ejpam-5453	405	6	=	=	SYM
ejpam-5453	405	7	{	{	PUNCT
ejpam-5453	405	8	l1	l1	PROPN
ejpam-5453	405	9	,	,	PUNCT
ejpam-5453	405	10	l2	l2	NOUN
ejpam-5453	405	11	}	}	PUNCT
ejpam-5453	405	12	,	,	PUNCT
ejpam-5453	405	13	n	n	NOUN
ejpam-5453	405	14	=	=	NOUN
ejpam-5453	405	15	{	{	PUNCT
ejpam-5453	405	16	l2	l2	NOUN
ejpam-5453	405	17	,	,	PUNCT
ejpam-5453	405	18	l3},m	l3},m	PROPN
ejpam-5453	405	19	∩n	∩n	NOUN
ejpam-5453	405	20	=	=	PRON
ejpam-5453	405	21	{	{	PUNCT
ejpam-5453	405	22	l2},n	l2},n	PROPN
ejpam-5453	405	23	d−s	d−s	PROPN
ejpam-5453	405	24	sr	sr	PROPN
ejpam-5453	405	25	(	(	PUNCT
ejpam-5453	405	26	m	m	PROPN
ejpam-5453	405	27	)	)	PUNCT
ejpam-5453	405	28	=	=	SYM
ejpam-5453	405	29	m	m	PROPN
ejpam-5453	405	30	,	,	PUNCT
ejpam-5453	405	31	n	n	PROPN
ejpam-5453	405	32	d−s	d−s	PROPN
ejpam-5453	405	33	sr	sr	PROPN
ejpam-5453	405	34	(	(	PUNCT
ejpam-5453	405	35	n	n	CCONJ
ejpam-5453	405	36	)	)	PUNCT
ejpam-5453	405	37	=	=	SYM
ejpam-5453	405	38	v	v	NOUN
ejpam-5453	405	39	,	,	PUNCT
ejpam-5453	405	40	n	n	PROPN
ejpam-5453	405	41	d−s	d−s	PROPN
ejpam-5453	405	42	sr	sr	PROPN
ejpam-5453	405	43	(	(	PUNCT
ejpam-5453	405	44	m	m	PROPN
ejpam-5453	405	45	∩	∩	NOUN
ejpam-5453	405	46	n	n	CCONJ
ejpam-5453	405	47	)	)	PUNCT
ejpam-5453	405	48	=	=	SYM
ejpam-5453	405	49	{	{	PUNCT
ejpam-5453	405	50	l2	l2	NOUN
ejpam-5453	405	51	}	}	PUNCT
ejpam-5453	405	52	,	,	PUNCT
ejpam-5453	405	53	then	then	ADV
ejpam-5453	405	54	n	n	PROPN
ejpam-5453	405	55	d−s	d−s	PROPN
ejpam-5453	405	56	sr	sr	PROPN
ejpam-5453	405	57	(	(	PUNCT
ejpam-5453	405	58	m	m	NOUN
ejpam-5453	405	59	)	)	PUNCT
ejpam-5453	405	60	∩	∩	NOUN
ejpam-5453	405	61	n	n	PROPN
ejpam-5453	405	62	d−s	d−s	PROPN
ejpam-5453	405	63	sr	sr	PROPN
ejpam-5453	405	64	(	(	PUNCT
ejpam-5453	405	65	n	n	CCONJ
ejpam-5453	405	66	)	)	PUNCT
ejpam-5453	405	67	=	=	PRON
ejpam-5453	405	68	{	{	PUNCT
ejpam-5453	405	69	l1	l1	PROPN
ejpam-5453	405	70	,	,	PUNCT
ejpam-5453	405	71	l2	l2	NOUN
ejpam-5453	405	72	}	}	PUNCT
ejpam-5453	405	73	⊈	⊈	PROPN
ejpam-5453	405	74	{	{	PUNCT
ejpam-5453	405	75	l2	l2	NOUN
ejpam-5453	405	76	}	}	PUNCT
ejpam-5453	405	77	=	=	SYM
ejpam-5453	405	78	n	n	PROPN
ejpam-5453	405	79	d−s	d−s	PROPN
ejpam-5453	405	80	sr	sr	PROPN
ejpam-5453	405	81	(	(	PUNCT
ejpam-5453	405	82	m	m	PROPN
ejpam-5453	405	83	∩n	∩n	NOUN
ejpam-5453	405	84	)	)	PUNCT
ejpam-5453	405	85	.	.	PUNCT
ejpam-5453	406	1	(	(	PUNCT
ejpam-5453	406	2	iii	iii	X
ejpam-5453	406	3	)	)	PUNCT
ejpam-5453	406	4	if	if	SCONJ
ejpam-5453	406	5	m	m	ADV
ejpam-5453	406	6	=	=	SYM
ejpam-5453	406	7	{	{	PUNCT
ejpam-5453	406	8	l1	l1	PROPN
ejpam-5453	406	9	,	,	PUNCT
ejpam-5453	406	10	l4	l4	PROPN
ejpam-5453	406	11	}	}	PUNCT
ejpam-5453	406	12	,	,	PUNCT
ejpam-5453	406	13	n	n	NOUN
ejpam-5453	406	14	=	=	SYM
ejpam-5453	406	15	{	{	PUNCT
ejpam-5453	406	16	l3	l3	PROPN
ejpam-5453	406	17	,	,	PUNCT
ejpam-5453	406	18	l4},m	l4},m	PROPN
ejpam-5453	406	19	∪	∪	NOUN
ejpam-5453	406	20	n	n	X
ejpam-5453	406	21	=	=	SYM
ejpam-5453	406	22	{	{	PUNCT
ejpam-5453	406	23	l1	l1	PROPN
ejpam-5453	406	24	,	,	PUNCT
ejpam-5453	406	25	l3	l3	PROPN
ejpam-5453	406	26	,	,	PUNCT
ejpam-5453	406	27	l4},nd−s	l4},nd−s	PROPN
ejpam-5453	406	28	sr	sr	PROPN
ejpam-5453	406	29	(	(	PUNCT
ejpam-5453	406	30	m	m	NOUN
ejpam-5453	406	31	)	)	PUNCT
ejpam-5453	406	32	=	=	SYM
ejpam-5453	406	33	∅,nd−s	∅,nd−s	PROPN
ejpam-5453	406	34	sr	sr	PROPN
ejpam-5453	406	35	(	(	PUNCT
ejpam-5453	406	36	n	n	CCONJ
ejpam-5453	406	37	)	)	PUNCT
ejpam-5453	406	38	=	=	SYM
ejpam-5453	406	39	{	{	PUNCT
ejpam-5453	406	40	l3	l3	PROPN
ejpam-5453	406	41	,	,	PUNCT
ejpam-5453	406	42	l4},nd−s	l4},nd−s	PROPN
ejpam-5453	406	43	sr	sr	PROPN
ejpam-5453	406	44	(	(	PUNCT
ejpam-5453	406	45	m	m	PROPN
ejpam-5453	406	46	∪	∪	NOUN
ejpam-5453	406	47	n	n	CCONJ
ejpam-5453	406	48	)	)	PUNCT
ejpam-5453	406	49	=	=	PRON
ejpam-5453	406	50	{	{	PUNCT
ejpam-5453	406	51	l1	l1	PROPN
ejpam-5453	406	52	,	,	PUNCT
ejpam-5453	406	53	l3	l3	PROPN
ejpam-5453	406	54	,	,	PUNCT
ejpam-5453	406	55	l4	l4	PROPN
ejpam-5453	406	56	}	}	PUNCT
ejpam-5453	406	57	,	,	PUNCT
ejpam-5453	406	58	then	then	ADV
ejpam-5453	406	59	nd−s	nd−s	PROPN
ejpam-5453	406	60	sr	sr	PROPN
ejpam-5453	406	61	(	(	PUNCT
ejpam-5453	406	62	m	m	PROPN
ejpam-5453	406	63	∪	∪	NOUN
ejpam-5453	406	64	n	n	CCONJ
ejpam-5453	406	65	)	)	PUNCT
ejpam-5453	406	66	=	=	PRON
ejpam-5453	406	67	{	{	PUNCT
ejpam-5453	406	68	l1	l1	PROPN
ejpam-5453	406	69	,	,	PUNCT
ejpam-5453	406	70	l3	l3	PROPN
ejpam-5453	406	71	,	,	PUNCT
ejpam-5453	406	72	l4	l4	PROPN
ejpam-5453	406	73	}	}	PUNCT
ejpam-5453	406	74	⊈	⊈	PROPN
ejpam-5453	406	75	{	{	PUNCT
ejpam-5453	406	76	l3	l3	PROPN
ejpam-5453	406	77	,	,	PUNCT
ejpam-5453	406	78	l4	l4	PROPN
ejpam-5453	406	79	}	}	PUNCT
ejpam-5453	406	80	=	=	SYM
ejpam-5453	406	81	nd−s	nd−s	PROPN
ejpam-5453	406	82	sr	sr	PROPN
ejpam-5453	406	83	(	(	PUNCT
ejpam-5453	406	84	m	m	PROPN
ejpam-5453	406	85	)	)	PUNCT
ejpam-5453	406	86	∪nd−s	∪nd−s	PROPN
ejpam-5453	406	87	sr	sr	PROPN
ejpam-5453	406	88	(	(	PUNCT
ejpam-5453	406	89	n	n	CCONJ
ejpam-5453	406	90	)	)	PUNCT
ejpam-5453	406	91	.	.	PUNCT
ejpam-5453	407	1	(	(	PUNCT
ejpam-5453	407	2	iv	iv	X
ejpam-5453	407	3	)	)	PUNCT
ejpam-5453	407	4	if	if	SCONJ
ejpam-5453	407	5	m	m	ADV
ejpam-5453	407	6	=	=	SYM
ejpam-5453	407	7	{	{	PUNCT
ejpam-5453	407	8	l2	l2	NOUN
ejpam-5453	407	9	,	,	PUNCT
ejpam-5453	407	10	l3	l3	PROPN
ejpam-5453	407	11	}	}	PUNCT
ejpam-5453	407	12	,	,	PUNCT
ejpam-5453	407	13	n	n	NOUN
ejpam-5453	407	14	=	=	NOUN
ejpam-5453	407	15	{	{	PUNCT
ejpam-5453	407	16	l2	l2	NOUN
ejpam-5453	407	17	,	,	PUNCT
ejpam-5453	407	18	l4},m	l4},m	PROPN
ejpam-5453	407	19	∪	∪	NOUN
ejpam-5453	407	20	n	n	NOUN
ejpam-5453	407	21	=	=	SYM
ejpam-5453	407	22	{	{	PUNCT
ejpam-5453	407	23	l2	l2	PROPN
ejpam-5453	407	24	,	,	PUNCT
ejpam-5453	407	25	l3	l3	PROPN
ejpam-5453	407	26	,	,	PUNCT
ejpam-5453	407	27	l4},n	l4},n	PROPN
ejpam-5453	407	28	d−β	d−β	PRON
ejpam-5453	407	29	sr	sr	PROPN
ejpam-5453	407	30	(	(	PUNCT
ejpam-5453	407	31	m	m	PROPN
ejpam-5453	407	32	)	)	PUNCT
ejpam-5453	407	33	=	=	PRON
ejpam-5453	407	34	{	{	PUNCT
ejpam-5453	407	35	l2	l2	NOUN
ejpam-5453	407	36	,	,	PUNCT
ejpam-5453	407	37	l3},n	l3},n	PROPN
ejpam-5453	407	38	d−β	d−β	PRON
ejpam-5453	407	39	sr	sr	PROPN
ejpam-5453	407	40	(	(	PUNCT
ejpam-5453	407	41	n	n	CCONJ
ejpam-5453	407	42	)	)	PUNCT
ejpam-5453	407	43	=	=	NOUN
ejpam-5453	407	44	{	{	PUNCT
ejpam-5453	407	45	l2	l2	NOUN
ejpam-5453	407	46	,	,	PUNCT
ejpam-5453	407	47	l4},n	l4},n	PROPN
ejpam-5453	407	48	d−β	d−β	PRON
ejpam-5453	407	49	sr	sr	PROPN
ejpam-5453	407	50	(	(	PUNCT
ejpam-5453	407	51	m	m	PROPN
ejpam-5453	407	52	∪	∪	NOUN
ejpam-5453	407	53	n	n	CCONJ
ejpam-5453	407	54	)	)	PUNCT
ejpam-5453	407	55	=	=	SYM
ejpam-5453	407	56	v	v	NOUN
ejpam-5453	407	57	,	,	PUNCT
ejpam-5453	407	58	then	then	ADV
ejpam-5453	407	59	n	n	PROPN
ejpam-5453	407	60	d−β	d−β	NOUN
ejpam-5453	407	61	sr	sr	PROPN
ejpam-5453	407	62	(	(	PUNCT
ejpam-5453	407	63	m	m	PROPN
ejpam-5453	407	64	∪	∪	NOUN
ejpam-5453	407	65	n	n	CCONJ
ejpam-5453	407	66	)	)	PUNCT
ejpam-5453	407	67	=	=	SYM
ejpam-5453	407	68	v	v	ADP
ejpam-5453	407	69	⊈	⊈	PROPN
ejpam-5453	407	70	{	{	PUNCT
ejpam-5453	407	71	l2	l2	NOUN
ejpam-5453	407	72	,	,	PUNCT
ejpam-5453	407	73	l3	l3	PROPN
ejpam-5453	407	74	,	,	PUNCT
ejpam-5453	407	75	l4	l4	PROPN
ejpam-5453	407	76	}	}	PUNCT
ejpam-5453	407	77	=	=	SYM
ejpam-5453	407	78	n	n	PROPN
ejpam-5453	407	79	d−β	d−β	NOUN
ejpam-5453	407	80	sr	sr	PROPN
ejpam-5453	407	81	(	(	PUNCT
ejpam-5453	407	82	m	m	NOUN
ejpam-5453	407	83	)	)	PUNCT
ejpam-5453	407	84	∪	∪	ADP
ejpam-5453	407	85	n	n	NUM
ejpam-5453	407	86	d−β	d−β	NOUN
ejpam-5453	407	87	sr	sr	PROPN
ejpam-5453	407	88	(	(	PUNCT
ejpam-5453	407	89	n	n	CCONJ
ejpam-5453	407	90	)	)	PUNCT
ejpam-5453	407	91	.	.	PUNCT
ejpam-5453	408	1	(	(	PUNCT
ejpam-5453	408	2	v	v	NOUN
ejpam-5453	408	3	)	)	PUNCT
ejpam-5453	408	4	if	if	SCONJ
ejpam-5453	408	5	m	m	ADV
ejpam-5453	408	6	=	=	SYM
ejpam-5453	408	7	{	{	PUNCT
ejpam-5453	408	8	l1	l1	PROPN
ejpam-5453	408	9	,	,	PUNCT
ejpam-5453	408	10	l3	l3	PROPN
ejpam-5453	408	11	}	}	PUNCT
ejpam-5453	408	12	,	,	PUNCT
ejpam-5453	408	13	n	n	NOUN
ejpam-5453	408	14	=	=	SYM
ejpam-5453	408	15	{	{	PUNCT
ejpam-5453	408	16	l1	l1	PROPN
ejpam-5453	408	17	,	,	PUNCT
ejpam-5453	408	18	l4},m∩n	l4},m∩n	NOUN
ejpam-5453	408	19	=	=	PRON
ejpam-5453	408	20	{	{	PUNCT
ejpam-5453	408	21	l1},nd−β	l1},nd−β	PROPN
ejpam-5453	408	22	sr	sr	PROPN
ejpam-5453	408	23	(	(	PUNCT
ejpam-5453	408	24	m	m	NOUN
ejpam-5453	408	25	)	)	PUNCT
ejpam-5453	408	26	=	=	PRON
ejpam-5453	408	27	{	{	PUNCT
ejpam-5453	408	28	l1	l1	PROPN
ejpam-5453	408	29	,	,	PUNCT
ejpam-5453	408	30	l3},nd−β	l3},nd−β	PROPN
ejpam-5453	408	31	sr	sr	PROPN
ejpam-5453	408	32	(	(	PUNCT
ejpam-5453	408	33	n	n	CCONJ
ejpam-5453	408	34	)	)	PUNCT
ejpam-5453	408	35	=	=	PRON
ejpam-5453	408	36	{	{	PUNCT
ejpam-5453	408	37	l1	l1	PROPN
ejpam-5453	408	38	,	,	PUNCT
ejpam-5453	408	39	l4},nd−β	l4},nd−β	PROPN
ejpam-5453	408	40	sr	sr	X
ejpam-5453	408	41	(	(	PUNCT
ejpam-5453	408	42	m∩	m∩	PROPN
ejpam-5453	408	43	n	n	CCONJ
ejpam-5453	408	44	)	)	PUNCT
ejpam-5453	408	45	=	=	NOUN
ejpam-5453	408	46	∅	∅	NOUN
ejpam-5453	408	47	,	,	PUNCT
ejpam-5453	408	48	then	then	ADV
ejpam-5453	408	49	nd−β	nd−β	PROPN
ejpam-5453	408	50	sr	sr	PROPN
ejpam-5453	408	51	(	(	PUNCT
ejpam-5453	408	52	m	m	NOUN
ejpam-5453	408	53	)	)	PUNCT
ejpam-5453	409	1	∩nd−β	∩nd−β	PROPN
ejpam-5453	409	2	sr	sr	PROPN
ejpam-5453	409	3	(	(	PUNCT
ejpam-5453	409	4	n	n	CCONJ
ejpam-5453	409	5	)	)	PUNCT
ejpam-5453	409	6	=	=	PRON
ejpam-5453	409	7	{	{	PUNCT
ejpam-5453	409	8	l1	l1	PROPN
ejpam-5453	409	9	}	}	PUNCT
ejpam-5453	409	10	⊈	⊈	PROPN
ejpam-5453	409	11	∅	∅	NOUN
ejpam-5453	409	12	=	=	SYM
ejpam-5453	409	13	nd−β	nd−β	NOUN
ejpam-5453	409	14	sr	sr	PROPN
ejpam-5453	409	15	(	(	PUNCT
ejpam-5453	409	16	m	m	PROPN
ejpam-5453	409	17	∩n	∩n	NOUN
ejpam-5453	409	18	)	)	PUNCT
ejpam-5453	409	19	.	.	PUNCT
ejpam-5453	410	1	(	(	PUNCT
ejpam-5453	410	2	vi	vi	X
ejpam-5453	410	3	)	)	PUNCT
ejpam-5453	410	4	if	if	SCONJ
ejpam-5453	410	5	m	m	ADV
ejpam-5453	410	6	=	=	SYM
ejpam-5453	410	7	{	{	PUNCT
ejpam-5453	410	8	l2	l2	PROPN
ejpam-5453	410	9	,	,	PUNCT
ejpam-5453	410	10	l3	l3	PROPN
ejpam-5453	410	11	,	,	PUNCT
ejpam-5453	410	12	l4},nd−β	l4},nd−β	PROPN
ejpam-5453	410	13	sr	sr	PROPN
ejpam-5453	410	14	(	(	PUNCT
ejpam-5453	410	15	nd−β	nd−β	PROPN
ejpam-5453	410	16	sr	sr	PROPN
ejpam-5453	410	17	(	(	PUNCT
ejpam-5453	410	18	m	m	NOUN
ejpam-5453	410	19	)	)	PUNCT
ejpam-5453	410	20	)	)	PUNCT
ejpam-5453	411	1	=	=	PUNCT
ejpam-5453	411	2	m	m	PROPN
ejpam-5453	411	3	,	,	PUNCT
ejpam-5453	411	4	n	n	PROPN
ejpam-5453	411	5	d−β	d−β	NOUN
ejpam-5453	411	6	sr	sr	PROPN
ejpam-5453	411	7	(	(	PUNCT
ejpam-5453	411	8	nd−β	nd−β	PROPN
ejpam-5453	411	9	sr	sr	PROPN
ejpam-5453	411	10	(	(	PUNCT
ejpam-5453	411	11	m	m	NOUN
ejpam-5453	411	12	)	)	PUNCT
ejpam-5453	411	13	)	)	PUNCT
ejpam-5453	412	1	=	=	SYM
ejpam-5453	412	2	v	v	X
ejpam-5453	412	3	,	,	PUNCT
ejpam-5453	412	4	then	then	ADV
ejpam-5453	412	5	n	n	PROPN
ejpam-5453	412	6	d−β	d−β	NOUN
ejpam-5453	412	7	sr	sr	PROPN
ejpam-5453	412	8	(	(	PUNCT
ejpam-5453	412	9	nd−β	nd−β	PROPN
ejpam-5453	412	10	sr	sr	PROPN
ejpam-5453	412	11	(	(	PUNCT
ejpam-5453	412	12	m	m	NOUN
ejpam-5453	412	13	)	)	PUNCT
ejpam-5453	412	14	)	)	PUNCT
ejpam-5453	413	1	⊈	⊈	PROPN
ejpam-5453	413	2	nd−β	nd−β	PROPN
ejpam-5453	413	3	sr	sr	PROPN
ejpam-5453	413	4	(	(	PUNCT
ejpam-5453	413	5	nd−β	nd−β	PROPN
ejpam-5453	413	6	sr	sr	PROPN
ejpam-5453	413	7	(	(	PUNCT
ejpam-5453	413	8	m	m	NOUN
ejpam-5453	413	9	)	)	PUNCT
ejpam-5453	413	10	)	)	PUNCT
ejpam-5453	413	11	.	.	PUNCT
ejpam-5453	414	1	(	(	PUNCT
ejpam-5453	414	2	vii	vii	PROPN
ejpam-5453	414	3	)	)	PUNCT
ejpam-5453	414	4	for	for	ADP
ejpam-5453	414	5	part	part	NOUN
ejpam-5453	414	6	12	12	NUM
ejpam-5453	414	7	,	,	PUNCT
ejpam-5453	414	8	if	if	SCONJ
ejpam-5453	414	9	m	m	ADV
ejpam-5453	414	10	=	=	SYM
ejpam-5453	414	11	{	{	PUNCT
ejpam-5453	414	12	l1},n	l1},n	NOUN
ejpam-5453	414	13	d−β	d−β	X
ejpam-5453	414	14	sr	sr	PROPN
ejpam-5453	414	15	(	(	PUNCT
ejpam-5453	414	16	n	n	PROPN
ejpam-5453	414	17	d−β	d−β	PRON
ejpam-5453	414	18	sr	sr	PROPN
ejpam-5453	414	19	(	(	PUNCT
ejpam-5453	414	20	m	m	NOUN
ejpam-5453	414	21	)	)	PUNCT
ejpam-5453	414	22	)	)	PUNCT
ejpam-5453	415	1	=	=	SYM
ejpam-5453	415	2	m	m	PROPN
ejpam-5453	415	3	,	,	PUNCT
ejpam-5453	415	4	nd−β	nd−β	PROPN
ejpam-5453	415	5	sr	sr	PROPN
ejpam-5453	415	6	(	(	PUNCT
ejpam-5453	415	7	n	n	PROPN
ejpam-5453	415	8	d−β	d−β	PRON
ejpam-5453	415	9	sr	sr	PROPN
ejpam-5453	415	10	(	(	PUNCT
ejpam-5453	415	11	m	m	NOUN
ejpam-5453	415	12	)	)	PUNCT
ejpam-5453	415	13	)	)	PUNCT
ejpam-5453	416	1	=	=	NOUN
ejpam-5453	416	2	∅	∅	NOUN
ejpam-5453	416	3	,	,	PUNCT
ejpam-5453	416	4	then	then	ADV
ejpam-5453	416	5	n	n	PROPN
ejpam-5453	416	6	d−β	d−β	NOUN
ejpam-5453	416	7	sr	sr	PROPN
ejpam-5453	416	8	(	(	PUNCT
ejpam-5453	416	9	n	n	PROPN
ejpam-5453	416	10	d−β	d−β	PRON
ejpam-5453	416	11	sr	sr	PROPN
ejpam-5453	416	12	(	(	PUNCT
ejpam-5453	416	13	m	m	NOUN
ejpam-5453	416	14	)	)	PUNCT
ejpam-5453	416	15	)	)	PUNCT
ejpam-5453	416	16	⊈	⊈	PROPN
ejpam-5453	416	17	nd−β	nd−β	PROPN
ejpam-5453	416	18	sr	sr	PROPN
ejpam-5453	416	19	(	(	PUNCT
ejpam-5453	416	20	n	n	PROPN
ejpam-5453	416	21	d−β	d−β	PRON
ejpam-5453	416	22	sr	sr	PROPN
ejpam-5453	416	23	(	(	PUNCT
ejpam-5453	416	24	m	m	NOUN
ejpam-5453	416	25	)	)	PUNCT
ejpam-5453	416	26	)	)	PUNCT
ejpam-5453	416	27	.	.	PUNCT
ejpam-5453	417	1	(	(	PUNCT
ejpam-5453	417	2	viii	viii	NOUN
ejpam-5453	417	3	)	)	PUNCT
ejpam-5453	417	4	if	if	SCONJ
ejpam-5453	417	5	m	m	ADV
ejpam-5453	417	6	=	=	SYM
ejpam-5453	417	7	{	{	PUNCT
ejpam-5453	417	8	l1	l1	PROPN
ejpam-5453	417	9	}	}	PUNCT
ejpam-5453	417	10	,	,	PUNCT
ejpam-5453	417	11	n	n	NOUN
ejpam-5453	417	12	=	=	NOUN
ejpam-5453	417	13	{	{	PUNCT
ejpam-5453	417	14	l2	l2	PROPN
ejpam-5453	417	15	,	,	PUNCT
ejpam-5453	417	16	l3	l3	PROPN
ejpam-5453	417	17	,	,	PUNCT
ejpam-5453	417	18	l4	l4	PROPN
ejpam-5453	417	19	}	}	PUNCT
ejpam-5453	417	20	,	,	PUNCT
ejpam-5453	417	21	then	then	ADV
ejpam-5453	417	22	n	n	PROPN
ejpam-5453	417	23	d−β	d−β	NOUN
ejpam-5453	417	24	sr	sr	PROPN
ejpam-5453	417	25	(	(	PUNCT
ejpam-5453	417	26	m	m	PROPN
ejpam-5453	417	27	)	)	PUNCT
ejpam-5453	417	28	=	=	PRON
ejpam-5453	417	29	{	{	PUNCT
ejpam-5453	417	30	l1},n	l1},n	NOUN
ejpam-5453	417	31	d−β	d−β	X
ejpam-5453	417	32	sr	sr	PROPN
ejpam-5453	417	33	(	(	PUNCT
ejpam-5453	417	34	n	n	CCONJ
ejpam-5453	417	35	)	)	PUNCT
ejpam-5453	417	36	)	)	PUNCT
ejpam-5453	418	1	=	=	SYM
ejpam-5453	418	2	v	v	X
ejpam-5453	418	3	.	.	PUNCT
ejpam-5453	419	1	therefore	therefore	ADV
ejpam-5453	419	2	,	,	PUNCT
ejpam-5453	419	3	n	n	PROPN
ejpam-5453	419	4	d−β	d−β	NOUN
ejpam-5453	419	5	sr	sr	PROPN
ejpam-5453	419	6	(	(	PUNCT
ejpam-5453	419	7	m	m	PROPN
ejpam-5453	419	8	)	)	PUNCT
ejpam-5453	419	9	⊆	⊆	NUM
ejpam-5453	419	10	n	n	NUM
ejpam-5453	419	11	d−β	d−β	NOUN
ejpam-5453	419	12	sr	sr	PROPN
ejpam-5453	419	13	(	(	PUNCT
ejpam-5453	419	14	n	n	CCONJ
ejpam-5453	419	15	)	)	PUNCT
ejpam-5453	419	16	,	,	PUNCT
ejpam-5453	419	17	but	but	CCONJ
ejpam-5453	419	18	m	m	VERB
ejpam-5453	419	19	⊈	⊈	PROPN
ejpam-5453	419	20	n.	n.	NOUN
ejpam-5453	419	21	(	(	PUNCT
ejpam-5453	419	22	ix	ix	PROPN
ejpam-5453	419	23	)	)	PUNCT
ejpam-5453	419	24	if	if	SCONJ
ejpam-5453	419	25	m	m	ADV
ejpam-5453	419	26	=	=	SYM
ejpam-5453	419	27	{	{	PUNCT
ejpam-5453	419	28	l1	l1	PROPN
ejpam-5453	419	29	}	}	PUNCT
ejpam-5453	419	30	,	,	PUNCT
ejpam-5453	419	31	n	n	NOUN
ejpam-5453	419	32	=	=	SYM
ejpam-5453	419	33	{	{	PUNCT
ejpam-5453	419	34	l3	l3	PROPN
ejpam-5453	419	35	}	}	PUNCT
ejpam-5453	419	36	,	,	PUNCT
ejpam-5453	419	37	then	then	ADV
ejpam-5453	419	38	nd−β	nd−β	PROPN
ejpam-5453	419	39	sr	sr	PROPN
ejpam-5453	419	40	(	(	PUNCT
ejpam-5453	419	41	m	m	NOUN
ejpam-5453	419	42	)	)	PUNCT
ejpam-5453	419	43	=	=	SYM
ejpam-5453	419	44	∅,nd−β	∅,nd−β	PROPN
ejpam-5453	419	45	sr	sr	PROPN
ejpam-5453	419	46	(	(	PUNCT
ejpam-5453	419	47	n	n	CCONJ
ejpam-5453	419	48	)	)	PUNCT
ejpam-5453	419	49	=	=	SYM
ejpam-5453	419	50	{	{	PUNCT
ejpam-5453	419	51	l3	l3	NOUN
ejpam-5453	419	52	}	}	PUNCT
ejpam-5453	419	53	.	.	PUNCT
ejpam-5453	420	1	therefore	therefore	ADV
ejpam-5453	420	2	,	,	PUNCT
ejpam-5453	420	3	nd−β	nd−β	PROPN
ejpam-5453	420	4	sr	sr	PROPN
ejpam-5453	420	5	(	(	PUNCT
ejpam-5453	420	6	m	m	PROPN
ejpam-5453	420	7	)	)	PUNCT
ejpam-5453	420	8	⊆	⊆	NUM
ejpam-5453	420	9	nd−β	nd−β	PROPN
ejpam-5453	420	10	sr	sr	PROPN
ejpam-5453	420	11	(	(	PUNCT
ejpam-5453	420	12	n	n	CCONJ
ejpam-5453	420	13	)	)	PUNCT
ejpam-5453	420	14	,	,	PUNCT
ejpam-5453	420	15	but	but	CCONJ
ejpam-5453	420	16	m	m	PRON
ejpam-5453	420	17	⊈	⊈	PROPN
ejpam-5453	420	18	n.	n.	NOUN
ejpam-5453	420	19	definition	definition	NOUN
ejpam-5453	420	20	4.2	4.2	NUM
ejpam-5453	420	21	.	.	PUNCT
ejpam-5453	420	22	let	let	AUX
ejpam-5453	420	23	(	(	PUNCT
ejpam-5453	420	24	v	v	NOUN
ejpam-5453	420	25	,	,	PUNCT
ejpam-5453	420	26	υ	υ	NOUN
ejpam-5453	420	27	,	,	PUNCT
ejpam-5453	420	28	π℘	π℘	NUM
ejpam-5453	420	29	)	)	PUNCT
ejpam-5453	420	30	be	be	AUX
ejpam-5453	420	31	a	a	DET
ejpam-5453	420	32	℘-nbds	℘-nbds	NOUN
ejpam-5453	420	33	,	,	PUNCT
ejpam-5453	420	34	d	d	PRON
ejpam-5453	420	35	be	be	AUX
ejpam-5453	420	36	an	an	DET
ejpam-5453	420	37	ideal	ideal	NOUN
ejpam-5453	420	38	on	on	ADP
ejpam-5453	420	39	v	v	NOUN
ejpam-5453	420	40	,	,	PUNCT
ejpam-5453	420	41	and	and	CCONJ
ejpam-5453	420	42	m	m	PROPN
ejpam-5453	420	43	⊆	⊆	NUM
ejpam-5453	420	44	v.	v.	ADP
ejpam-5453	420	45	m	m	PROPN
ejpam-5453	420	46	is	be	AUX
ejpam-5453	420	47	dξs℘-nearly	dξs℘-nearly	ADV
ejpam-5453	420	48	definable	definable	ADJ
ejpam-5453	420	49	(	(	PUNCT
ejpam-5453	420	50	d	d	ADJ
ejpam-5453	420	51	-	-	PUNCT
ejpam-5453	420	52	ξs℘-nearly	ξs℘-nearly	ADV
ejpam-5453	420	53	exact	exact	ADJ
ejpam-5453	420	54	)	)	PUNCT
ejpam-5453	420	55	set	set	VERB
ejpam-5453	420	56	if	if	SCONJ
ejpam-5453	420	57	n	n	PRON
ejpam-5453	420	58	d−ξ	d−ξ	NOUN
ejpam-5453	420	59	s℘	s℘	NOUN
ejpam-5453	420	60	(	(	PUNCT
ejpam-5453	420	61	m	m	NOUN
ejpam-5453	420	62	)	)	PUNCT
ejpam-5453	421	1	=	=	SYM
ejpam-5453	421	2	nd−ξ	nd−ξ	ADJ
ejpam-5453	421	3	s℘	s℘	PROPN
ejpam-5453	421	4	(	(	PUNCT
ejpam-5453	421	5	m	m	NOUN
ejpam-5453	421	6	)	)	PUNCT
ejpam-5453	421	7	.	.	PUNCT
ejpam-5453	422	1	otherwise	otherwise	ADV
ejpam-5453	422	2	,	,	PUNCT
ejpam-5453	422	3	m	m	VERB
ejpam-5453	422	4	is	be	AUX
ejpam-5453	422	5	d	d	ADJ
ejpam-5453	422	6	-	-	PUNCT
ejpam-5453	422	7	ξs℘-nearly	ξs℘-nearly	ADV
ejpam-5453	422	8	rough	rough	ADJ
ejpam-5453	422	9	set	set	NOUN
ejpam-5453	422	10	.	.	PUNCT
ejpam-5453	423	1	m.	m.	PROPN
ejpam-5453	423	2	hosny	hosny	PROPN
ejpam-5453	423	3	/	/	SYM
ejpam-5453	423	4	eur	eur	PROPN
ejpam-5453	423	5	.	.	PUNCT
ejpam-5453	424	1	j.	j.	PROPN
ejpam-5453	424	2	pure	pure	PROPN
ejpam-5453	424	3	appl	appl	PROPN
ejpam-5453	424	4	.	.	PROPN
ejpam-5453	424	5	math	math	PROPN
ejpam-5453	424	6	,	,	PUNCT
ejpam-5453	424	7	17	17	NUM
ejpam-5453	424	8	(	(	PUNCT
ejpam-5453	424	9	4	4	NUM
ejpam-5453	424	10	)	)	PUNCT
ejpam-5453	424	11	(	(	PUNCT
ejpam-5453	424	12	2024	2024	NUM
ejpam-5453	424	13	)	)	PUNCT
ejpam-5453	424	14	,	,	PUNCT
ejpam-5453	424	15	2843	2843	NUM
ejpam-5453	424	16	-	-	SYM
ejpam-5453	424	17	2877	2877	NUM
ejpam-5453	424	18	2856	2856	NUM
ejpam-5453	424	19	in	in	ADP
ejpam-5453	424	20	example	example	NOUN
ejpam-5453	424	21	3.1	3.1	NUM
ejpam-5453	424	22	,	,	PUNCT
ejpam-5453	424	23	take	take	VERB
ejpam-5453	424	24	d	d	NOUN
ejpam-5453	424	25	=	=	PUNCT
ejpam-5453	424	26	{	{	PUNCT
ejpam-5453	424	27	∅	∅	NOUN
ejpam-5453	424	28	,	,	PUNCT
ejpam-5453	424	29	{	{	PUNCT
ejpam-5453	424	30	l2	l2	NOUN
ejpam-5453	424	31	}	}	PUNCT
ejpam-5453	424	32	}	}	PUNCT
ejpam-5453	424	33	and	and	CCONJ
ejpam-5453	424	34	m	m	PROPN
ejpam-5453	424	35	=	=	NOUN
ejpam-5453	424	36	{	{	PUNCT
ejpam-5453	424	37	l2	l2	NOUN
ejpam-5453	424	38	}	}	PUNCT
ejpam-5453	424	39	is	be	AUX
ejpam-5453	424	40	d	d	NOUN
ejpam-5453	424	41	-	-	PUNCT
ejpam-5453	424	42	βsr	βsr	NOUN
ejpam-5453	424	43	-	-	PUNCT
ejpam-5453	424	44	exact	exact	ADJ
ejpam-5453	424	45	,	,	PUNCT
ejpam-5453	424	46	while	while	SCONJ
ejpam-5453	424	47	n	n	PROPN
ejpam-5453	424	48	=	=	SYM
ejpam-5453	424	49	{	{	PUNCT
ejpam-5453	424	50	l1	l1	PROPN
ejpam-5453	424	51	}	}	PUNCT
ejpam-5453	424	52	is	be	AUX
ejpam-5453	424	53	d	d	NOUN
ejpam-5453	424	54	-	-	PUNCT
ejpam-5453	424	55	βsr	βsr	NOUN
ejpam-5453	424	56	-	-	PUNCT
ejpam-5453	424	57	rough	rough	ADJ
ejpam-5453	424	58	.	.	PUNCT
ejpam-5453	425	1	remark	remark	PROPN
ejpam-5453	425	2	4.2	4.2	NUM
ejpam-5453	425	3	.	.	PUNCT
ejpam-5453	426	1	let	let	AUX
ejpam-5453	426	2	(	(	PUNCT
ejpam-5453	426	3	v	v	NOUN
ejpam-5453	426	4	,	,	PUNCT
ejpam-5453	426	5	υ	υ	NOUN
ejpam-5453	426	6	,	,	PUNCT
ejpam-5453	426	7	π℘	π℘	NUM
ejpam-5453	426	8	)	)	PUNCT
ejpam-5453	426	9	be	be	AUX
ejpam-5453	426	10	a	a	DET
ejpam-5453	426	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	426	12	,	,	PUNCT
ejpam-5453	426	13	d	d	PRON
ejpam-5453	426	14	be	be	AUX
ejpam-5453	426	15	an	an	DET
ejpam-5453	426	16	ideal	ideal	NOUN
ejpam-5453	426	17	on	on	ADP
ejpam-5453	426	18	v.	v.	ADP
ejpam-5453	426	19	then	then	ADV
ejpam-5453	426	20	the	the	DET
ejpam-5453	426	21	intersection	intersection	NOUN
ejpam-5453	426	22	of	of	ADP
ejpam-5453	426	23	two	two	NUM
ejpam-5453	426	24	d	d	ADJ
ejpam-5453	426	25	-	-	PUNCT
ejpam-5453	426	26	ξs℘-rough	ξs℘-rough	NOUN
ejpam-5453	426	27	sets	set	NOUN
ejpam-5453	426	28	need	need	VERB
ejpam-5453	426	29	not	not	PART
ejpam-5453	426	30	to	to	PART
ejpam-5453	426	31	be	be	AUX
ejpam-5453	426	32	d	d	NOUN
ejpam-5453	426	33	-	-	PUNCT
ejpam-5453	426	34	ξs℘-rough	ξs℘-rough	NOUN
ejpam-5453	426	35	set	set	VERB
ejpam-5453	426	36	as	as	ADP
ejpam-5453	426	37	in	in	ADP
ejpam-5453	426	38	example	example	NOUN
ejpam-5453	426	39	3.1	3.1	NUM
ejpam-5453	426	40	{	{	PUNCT
ejpam-5453	426	41	l1	l1	PROPN
ejpam-5453	426	42	,	,	PUNCT
ejpam-5453	426	43	l3	l3	PROPN
ejpam-5453	426	44	}	}	PUNCT
ejpam-5453	426	45	and	and	CCONJ
ejpam-5453	426	46	{	{	PUNCT
ejpam-5453	426	47	l1	l1	PROPN
ejpam-5453	426	48	,	,	PUNCT
ejpam-5453	426	49	l4	l4	PROPN
ejpam-5453	426	50	}	}	PUNCT
ejpam-5453	426	51	,	,	PUNCT
ejpam-5453	426	52	are	be	AUX
ejpam-5453	426	53	d	d	ADJ
ejpam-5453	426	54	-	-	PUNCT
ejpam-5453	426	55	ssr	ssr	ADJ
ejpam-5453	426	56	-	-	PUNCT
ejpam-5453	426	57	rough	rough	ADJ
ejpam-5453	426	58	sets	set	NOUN
ejpam-5453	426	59	,	,	PUNCT
ejpam-5453	426	60	{	{	PUNCT
ejpam-5453	426	61	l1	l1	PROPN
ejpam-5453	426	62	,	,	PUNCT
ejpam-5453	426	63	l3	l3	PROPN
ejpam-5453	426	64	}	}	PUNCT
ejpam-5453	426	65	∩	∩	NOUN
ejpam-5453	426	66	{	{	PUNCT
ejpam-5453	426	67	l1	l1	PROPN
ejpam-5453	426	68	,	,	PUNCT
ejpam-5453	426	69	l4	l4	PROPN
ejpam-5453	426	70	}	}	PUNCT
ejpam-5453	426	71	=	=	SYM
ejpam-5453	426	72	{	{	PUNCT
ejpam-5453	426	73	l1	l1	PROPN
ejpam-5453	426	74	}	}	PUNCT
ejpam-5453	426	75	is	be	AUX
ejpam-5453	426	76	not	not	PART
ejpam-5453	426	77	d	d	ADJ
ejpam-5453	426	78	-	-	PUNCT
ejpam-5453	426	79	ssr	ssr	ADJ
ejpam-5453	426	80	-	-	PUNCT
ejpam-5453	426	81	rough	rough	ADJ
ejpam-5453	426	82	set	set	NOUN
ejpam-5453	426	83	.	.	PUNCT
ejpam-5453	427	1	4.2	4.2	NUM
ejpam-5453	427	2	.	.	PUNCT
ejpam-5453	427	3	relationships	relationship	NOUN
ejpam-5453	427	4	among	among	ADP
ejpam-5453	427	5	the	the	DET
ejpam-5453	427	6	proposed	propose	VERB
ejpam-5453	427	7	approximations	approximation	NOUN
ejpam-5453	427	8	and	and	CCONJ
ejpam-5453	427	9	comparisons	comparison	NOUN
ejpam-5453	427	10	to	to	ADP
ejpam-5453	427	11	the	the	DET
ejpam-5453	427	12	prior	prior	ADJ
ejpam-5453	427	13	ones	one	NOUN
ejpam-5453	427	14	the	the	DET
ejpam-5453	427	15	following	follow	VERB
ejpam-5453	427	16	results	result	NOUN
ejpam-5453	427	17	underscore	underscore	VERB
ejpam-5453	427	18	the	the	DET
ejpam-5453	427	19	advantages	advantage	NOUN
ejpam-5453	427	20	of	of	ADP
ejpam-5453	427	21	the	the	DET
ejpam-5453	427	22	present	present	ADJ
ejpam-5453	427	23	manner	manner	NOUN
ejpam-5453	427	24	4.1	4.1	NUM
ejpam-5453	427	25	with	with	ADP
ejpam-5453	427	26	the	the	DET
ejpam-5453	427	27	comparison	comparison	NOUN
ejpam-5453	427	28	of	of	ADP
ejpam-5453	427	29	the	the	DET
ejpam-5453	427	30	prior	prior	ADJ
ejpam-5453	427	31	one	one	NUM
ejpam-5453	427	32	in	in	ADP
ejpam-5453	427	33	definitions	definition	NOUN
ejpam-5453	427	34	2.8	2.8	NUM
ejpam-5453	427	35	and	and	CCONJ
ejpam-5453	427	36	2.11	2.11	NUM
ejpam-5453	427	37	[	[	X
ejpam-5453	427	38	43	43	NUM
ejpam-5453	427	39	]	]	PUNCT
ejpam-5453	427	40	.	.	PUNCT
ejpam-5453	428	1	theorem	theorem	VERB
ejpam-5453	428	2	4.1	4.1	NUM
ejpam-5453	428	3	.	.	PUNCT
ejpam-5453	429	1	let	let	AUX
ejpam-5453	429	2	(	(	PUNCT
ejpam-5453	429	3	v	v	NOUN
ejpam-5453	429	4	,	,	PUNCT
ejpam-5453	429	5	υ	υ	NOUN
ejpam-5453	429	6	,	,	PUNCT
ejpam-5453	429	7	π℘	π℘	NUM
ejpam-5453	429	8	)	)	PUNCT
ejpam-5453	429	9	be	be	AUX
ejpam-5453	429	10	a	a	DET
ejpam-5453	429	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	429	12	,	,	PUNCT
ejpam-5453	429	13	d	d	PRON
ejpam-5453	429	14	be	be	AUX
ejpam-5453	429	15	an	an	DET
ejpam-5453	429	16	ideal	ideal	NOUN
ejpam-5453	429	17	on	on	ADP
ejpam-5453	429	18	v	v	NUM
ejpam-5453	429	19	and	and	CCONJ
ejpam-5453	429	20	m	m	PROPN
ejpam-5453	429	21	⊆	⊆	NUM
ejpam-5453	429	22	v.	v.	ADP
ejpam-5453	429	23	then	then	ADV
ejpam-5453	429	24	(	(	PUNCT
ejpam-5453	429	25	i	i	NOUN
ejpam-5453	429	26	)	)	PUNCT
ejpam-5453	429	27	nξ	nξ	ADP
ejpam-5453	429	28	s℘(m	s℘(m	PROPN
ejpam-5453	429	29	)	)	PUNCT
ejpam-5453	430	1	⊆	⊆	NUM
ejpam-5453	430	2	nd−ξ	nd−ξ	ADJ
ejpam-5453	430	3	s℘	s℘	NOUN
ejpam-5453	430	4	(	(	PUNCT
ejpam-5453	430	5	m	m	NOUN
ejpam-5453	430	6	)	)	PUNCT
ejpam-5453	430	7	.	.	PUNCT
ejpam-5453	431	1	(	(	PUNCT
ejpam-5453	431	2	ii	ii	X
ejpam-5453	431	3	)	)	PUNCT
ejpam-5453	431	4	ns℘(m	ns℘(m	PROPN
ejpam-5453	431	5	)	)	PUNCT
ejpam-5453	431	6	⊆	⊆	NUM
ejpam-5453	431	7	nd−ξ	nd−ξ	ADJ
ejpam-5453	431	8	s℘	s℘	NOUN
ejpam-5453	431	9	(	(	PUNCT
ejpam-5453	431	10	m	m	NOUN
ejpam-5453	431	11	)	)	PUNCT
ejpam-5453	431	12	.	.	PUNCT
ejpam-5453	432	1	(	(	PUNCT
ejpam-5453	432	2	iii	iii	X
ejpam-5453	432	3	)	)	PUNCT
ejpam-5453	432	4	n	n	NOUN
ejpam-5453	432	5	d−ξ	d−ξ	NOUN
ejpam-5453	432	6	s℘	s℘	NOUN
ejpam-5453	432	7	(	(	PUNCT
ejpam-5453	432	8	m	m	NOUN
ejpam-5453	432	9	)	)	PUNCT
ejpam-5453	432	10	⊆	⊆	NUM
ejpam-5453	432	11	n	n	SYM
ejpam-5453	432	12	ξ	ξ	PROPN
ejpam-5453	432	13	s℘(m	s℘(m	PROPN
ejpam-5453	432	14	)	)	PUNCT
ejpam-5453	432	15	.	.	PUNCT
ejpam-5453	433	1	(	(	PUNCT
ejpam-5453	433	2	iv	iv	X
ejpam-5453	433	3	)	)	PUNCT
ejpam-5453	433	4	n	n	NOUN
ejpam-5453	433	5	d−ξ	d−ξ	NOUN
ejpam-5453	433	6	s℘	s℘	NOUN
ejpam-5453	433	7	(	(	PUNCT
ejpam-5453	433	8	m	m	NOUN
ejpam-5453	433	9	)	)	PUNCT
ejpam-5453	433	10	⊆	⊆	NUM
ejpam-5453	433	11	ns℘(m	ns℘(m	NOUN
ejpam-5453	433	12	)	)	PUNCT
ejpam-5453	433	13	.	.	PUNCT
ejpam-5453	434	1	proof	proof	NOUN
ejpam-5453	434	2	.	.	PUNCT
ejpam-5453	435	1	(	(	PUNCT
ejpam-5453	435	2	1	1	X
ejpam-5453	435	3	)	)	PUNCT
ejpam-5453	435	4	nξ	nξ	ADP
ejpam-5453	435	5	s℘(m	s℘(m	PROPN
ejpam-5453	435	6	)	)	PUNCT
ejpam-5453	435	7	=	=	PUNCT
ejpam-5453	435	8	∪{g	∪{g	PROPN
ejpam-5453	435	9	∈	∈	PROPN
ejpam-5453	435	10	ξs℘o(v	ξs℘o(v	PROPN
ejpam-5453	435	11	)	)	PUNCT
ejpam-5453	435	12	:	:	PUNCT
ejpam-5453	436	1	g	g	PROPN
ejpam-5453	436	2	⊆	⊆	NUM
ejpam-5453	436	3	m	m	NOUN
ejpam-5453	436	4	}	}	PUNCT
ejpam-5453	436	5	⊆	⊆	NUM
ejpam-5453	436	6	∪{g	∪{g	PROPN
ejpam-5453	436	7	∈	∈	PROPN
ejpam-5453	436	8	d	d	X
ejpam-5453	436	9	-	-	PUNCT
ejpam-5453	436	10	ξs℘o(v	ξs℘o(v	PROPN
ejpam-5453	436	11	)	)	PUNCT
ejpam-5453	436	12	:	:	PUNCT
ejpam-5453	436	13	g	g	PROPN
ejpam-5453	436	14	⊆	⊆	NUM
ejpam-5453	436	15	m	m	PRON
ejpam-5453	436	16	}	}	PUNCT
ejpam-5453	436	17	=	=	SYM
ejpam-5453	436	18	nd−ξ	nd−ξ	ADJ
ejpam-5453	436	19	s℘	s℘	NOUN
ejpam-5453	436	20	(	(	PUNCT
ejpam-5453	436	21	m	m	NOUN
ejpam-5453	436	22	)	)	PUNCT
ejpam-5453	436	23	(	(	PUNCT
ejpam-5453	436	24	by	by	ADP
ejpam-5453	436	25	proposition	proposition	NOUN
ejpam-5453	436	26	3.1	3.1	NUM
ejpam-5453	436	27	)	)	PUNCT
ejpam-5453	436	28	.	.	PUNCT
ejpam-5453	437	1	(	(	PUNCT
ejpam-5453	437	2	2	2	X
ejpam-5453	437	3	)	)	PUNCT
ejpam-5453	437	4	by	by	ADP
ejpam-5453	437	5	theorem	theorem	ADJ
ejpam-5453	437	6	2.4	2.4	NUM
ejpam-5453	437	7	,	,	PUNCT
ejpam-5453	437	8	ns℘(m	ns℘(m	NOUN
ejpam-5453	437	9	)	)	PUNCT
ejpam-5453	437	10	⊆	⊆	NUM
ejpam-5453	437	11	nξ	nξ	ADP
ejpam-5453	437	12	s℘(m	s℘(m	PROPN
ejpam-5453	437	13	)	)	PUNCT
ejpam-5453	437	14	,	,	PUNCT
ejpam-5453	437	15	and	and	CCONJ
ejpam-5453	437	16	by	by	ADP
ejpam-5453	437	17	(	(	PUNCT
ejpam-5453	437	18	1	1	X
ejpam-5453	437	19	)	)	PUNCT
ejpam-5453	437	20	nξ	nξ	ADP
ejpam-5453	437	21	s℘(m	s℘(m	PROPN
ejpam-5453	437	22	)	)	PUNCT
ejpam-5453	438	1	⊆	⊆	NUM
ejpam-5453	438	2	nd−ξ	nd−ξ	ADJ
ejpam-5453	438	3	s℘	s℘	NOUN
ejpam-5453	438	4	(	(	PUNCT
ejpam-5453	438	5	m	m	NOUN
ejpam-5453	438	6	)	)	PUNCT
ejpam-5453	438	7	.	.	PUNCT
ejpam-5453	439	1	hence	hence	ADV
ejpam-5453	439	2	,	,	PUNCT
ejpam-5453	439	3	ns℘(m	ns℘(m	PROPN
ejpam-5453	439	4	)	)	PUNCT
ejpam-5453	439	5	⊆	⊆	NUM
ejpam-5453	439	6	nd−ξ	nd−ξ	ADJ
ejpam-5453	439	7	s℘	s℘	NOUN
ejpam-5453	439	8	(	(	PUNCT
ejpam-5453	439	9	m	m	NOUN
ejpam-5453	439	10	)	)	PUNCT
ejpam-5453	439	11	.	.	PUNCT
ejpam-5453	440	1	(	(	PUNCT
ejpam-5453	440	2	3	3	X
ejpam-5453	440	3	)	)	PUNCT
ejpam-5453	440	4	and	and	CCONJ
ejpam-5453	440	5	(	(	PUNCT
ejpam-5453	440	6	4	4	X
ejpam-5453	440	7	)	)	PUNCT
ejpam-5453	440	8	similar	similar	ADJ
ejpam-5453	440	9	to	to	ADP
ejpam-5453	440	10	(	(	PUNCT
ejpam-5453	440	11	1	1	NUM
ejpam-5453	440	12	)	)	PUNCT
ejpam-5453	440	13	and	and	CCONJ
ejpam-5453	440	14	(	(	PUNCT
ejpam-5453	440	15	2	2	NUM
ejpam-5453	440	16	)	)	PUNCT
ejpam-5453	440	17	.	.	PUNCT
ejpam-5453	441	1	corollary	corollary	ADJ
ejpam-5453	441	2	4.1	4.1	NUM
ejpam-5453	441	3	.	.	PUNCT
ejpam-5453	442	1	let	let	AUX
ejpam-5453	442	2	(	(	PUNCT
ejpam-5453	442	3	v	v	NOUN
ejpam-5453	442	4	,	,	PUNCT
ejpam-5453	442	5	υ	υ	NOUN
ejpam-5453	442	6	,	,	PUNCT
ejpam-5453	442	7	π℘	π℘	NUM
ejpam-5453	442	8	)	)	PUNCT
ejpam-5453	442	9	be	be	AUX
ejpam-5453	442	10	a	a	DET
ejpam-5453	442	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	442	12	,	,	PUNCT
ejpam-5453	442	13	d	d	PRON
ejpam-5453	442	14	be	be	AUX
ejpam-5453	442	15	an	an	DET
ejpam-5453	442	16	ideal	ideal	NOUN
ejpam-5453	442	17	on	on	ADP
ejpam-5453	442	18	v	v	NUM
ejpam-5453	442	19	and	and	CCONJ
ejpam-5453	442	20	m	m	PROPN
ejpam-5453	442	21	⊆	⊆	NUM
ejpam-5453	442	22	v.	v.	ADP
ejpam-5453	442	23	then	then	ADV
ejpam-5453	442	24	(	(	PUNCT
ejpam-5453	442	25	i	i	NOUN
ejpam-5453	442	26	)	)	PUNCT
ejpam-5453	442	27	bd−ξ	bd−ξ	PROPN
ejpam-5453	442	28	s℘	s℘	NOUN
ejpam-5453	442	29	(	(	PUNCT
ejpam-5453	442	30	m	m	NOUN
ejpam-5453	442	31	)	)	PUNCT
ejpam-5453	442	32	⊆	⊆	NUM
ejpam-5453	442	33	bξ	bξ	PROPN
ejpam-5453	442	34	s℘(m	s℘(m	PROPN
ejpam-5453	442	35	)	)	PUNCT
ejpam-5453	442	36	.	.	PUNCT
ejpam-5453	443	1	(	(	PUNCT
ejpam-5453	443	2	ii	ii	X
ejpam-5453	443	3	)	)	PUNCT
ejpam-5453	443	4	bd−ξ	bd−ξ	PROPN
ejpam-5453	443	5	s℘	s℘	NOUN
ejpam-5453	443	6	(	(	PUNCT
ejpam-5453	443	7	m	m	NOUN
ejpam-5453	443	8	)	)	PUNCT
ejpam-5453	443	9	⊆	⊆	NUM
ejpam-5453	443	10	bs℘(m	bs℘(m	NOUN
ejpam-5453	443	11	)	)	PUNCT
ejpam-5453	443	12	.	.	PUNCT
ejpam-5453	444	1	(	(	PUNCT
ejpam-5453	444	2	iii	iii	X
ejpam-5453	444	3	)	)	PUNCT
ejpam-5453	444	4	aξ	aξ	PROPN
ejpam-5453	444	5	s℘(m	s℘(m	PROPN
ejpam-5453	444	6	)	)	PUNCT
ejpam-5453	444	7	⩽	⩽	PROPN
ejpam-5453	444	8	ad−ξ	ad−ξ	PROPN
ejpam-5453	444	9	s℘	s℘	PROPN
ejpam-5453	444	10	(	(	PUNCT
ejpam-5453	444	11	m	m	NOUN
ejpam-5453	444	12	)	)	PUNCT
ejpam-5453	444	13	.	.	PUNCT
ejpam-5453	445	1	(	(	PUNCT
ejpam-5453	445	2	iv	iv	X
ejpam-5453	445	3	)	)	PUNCT
ejpam-5453	445	4	as℘(m	as℘(m	PROPN
ejpam-5453	445	5	)	)	PUNCT
ejpam-5453	445	6	⩽	⩽	PROPN
ejpam-5453	446	1	ad−ξ	ad−ξ	PROPN
ejpam-5453	446	2	s℘	s℘	PROPN
ejpam-5453	446	3	(	(	PUNCT
ejpam-5453	446	4	m	m	NOUN
ejpam-5453	446	5	)	)	PUNCT
ejpam-5453	446	6	.	.	PUNCT
ejpam-5453	447	1	corollary	corollary	ADJ
ejpam-5453	447	2	4.2	4.2	NUM
ejpam-5453	447	3	.	.	PUNCT
ejpam-5453	448	1	let	let	AUX
ejpam-5453	448	2	(	(	PUNCT
ejpam-5453	448	3	v	v	NOUN
ejpam-5453	448	4	,	,	PUNCT
ejpam-5453	448	5	υ	υ	NOUN
ejpam-5453	448	6	,	,	PUNCT
ejpam-5453	448	7	π℘	π℘	NUM
ejpam-5453	448	8	)	)	PUNCT
ejpam-5453	448	9	be	be	AUX
ejpam-5453	448	10	a	a	DET
ejpam-5453	448	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	448	12	,	,	PUNCT
ejpam-5453	448	13	d	d	PRON
ejpam-5453	448	14	be	be	AUX
ejpam-5453	448	15	an	an	DET
ejpam-5453	448	16	ideal	ideal	NOUN
ejpam-5453	448	17	on	on	ADP
ejpam-5453	448	18	v.	v.	INTJ
ejpam-5453	448	19	then	then	ADV
ejpam-5453	448	20	(	(	PUNCT
ejpam-5453	448	21	i	i	NOUN
ejpam-5453	448	22	)	)	PUNCT
ejpam-5453	448	23	every	every	DET
ejpam-5453	448	24	ξs℘-nearly	ξs℘-nearly	ADV
ejpam-5453	448	25	exact	exact	NOUN
ejpam-5453	448	26	subset	subset	NOUN
ejpam-5453	448	27	in	in	ADP
ejpam-5453	448	28	v	v	NOUN
ejpam-5453	448	29	is	be	AUX
ejpam-5453	448	30	d	d	NOUN
ejpam-5453	448	31	-	-	PUNCT
ejpam-5453	448	32	ξs℘-nearly	ξs℘-nearly	ADV
ejpam-5453	448	33	exact	exact	ADJ
ejpam-5453	448	34	.	.	PUNCT
ejpam-5453	449	1	(	(	PUNCT
ejpam-5453	449	2	ii	ii	NOUN
ejpam-5453	449	3	)	)	PUNCT
ejpam-5453	449	4	every	every	DET
ejpam-5453	449	5	s℘-exact	s℘-exact	PROPN
ejpam-5453	449	6	subset	subset	VERB
ejpam-5453	449	7	in	in	ADP
ejpam-5453	449	8	v	v	NUM
ejpam-5453	449	9	is	be	AUX
ejpam-5453	449	10	d	d	NOUN
ejpam-5453	449	11	-	-	PUNCT
ejpam-5453	449	12	ξs℘-nearly	ξs℘-nearly	ADV
ejpam-5453	449	13	exact	exact	ADJ
ejpam-5453	449	14	.	.	PUNCT
ejpam-5453	450	1	(	(	PUNCT
ejpam-5453	450	2	iii	iii	X
ejpam-5453	450	3	)	)	PUNCT
ejpam-5453	450	4	every	every	DET
ejpam-5453	450	5	d	d	PROPN
ejpam-5453	450	6	-	-	PUNCT
ejpam-5453	450	7	ξs℘-nearly	ξs℘-nearly	ADV
ejpam-5453	450	8	rough	rough	ADJ
ejpam-5453	450	9	subset	subset	NOUN
ejpam-5453	450	10	in	in	ADP
ejpam-5453	450	11	v	v	NOUN
ejpam-5453	450	12	is	be	AUX
ejpam-5453	450	13	ξs℘-nearly	ξs℘-nearly	ADV
ejpam-5453	450	14	rough	rough	ADJ
ejpam-5453	450	15	.	.	PUNCT
ejpam-5453	451	1	(	(	PUNCT
ejpam-5453	451	2	iv	iv	X
ejpam-5453	451	3	)	)	PUNCT
ejpam-5453	451	4	every	every	DET
ejpam-5453	451	5	d	d	PROPN
ejpam-5453	451	6	-	-	PUNCT
ejpam-5453	451	7	ξs℘-nearly	ξs℘-nearly	ADV
ejpam-5453	451	8	rough	rough	ADJ
ejpam-5453	451	9	subset	subset	NOUN
ejpam-5453	451	10	in	in	ADP
ejpam-5453	451	11	v	v	NOUN
ejpam-5453	451	12	is	be	AUX
ejpam-5453	451	13	s℘-rough	s℘-rough	ADJ
ejpam-5453	451	14	.	.	PUNCT
ejpam-5453	452	1	m.	m.	PROPN
ejpam-5453	452	2	hosny	hosny	PROPN
ejpam-5453	452	3	/	/	SYM
ejpam-5453	452	4	eur	eur	PROPN
ejpam-5453	452	5	.	.	PUNCT
ejpam-5453	453	1	j.	j.	PROPN
ejpam-5453	453	2	pure	pure	PROPN
ejpam-5453	453	3	appl	appl	PROPN
ejpam-5453	453	4	.	.	PROPN
ejpam-5453	453	5	math	math	PROPN
ejpam-5453	453	6	,	,	PUNCT
ejpam-5453	453	7	17	17	NUM
ejpam-5453	453	8	(	(	PUNCT
ejpam-5453	453	9	4	4	NUM
ejpam-5453	453	10	)	)	PUNCT
ejpam-5453	453	11	(	(	PUNCT
ejpam-5453	453	12	2024	2024	NUM
ejpam-5453	453	13	)	)	PUNCT
ejpam-5453	453	14	,	,	PUNCT
ejpam-5453	453	15	2843	2843	NUM
ejpam-5453	453	16	-	-	SYM
ejpam-5453	453	17	2877	2877	NUM
ejpam-5453	453	18	2857	2857	NUM
ejpam-5453	453	19	t	t	PROPN
ejpam-5453	453	20	ab	ab	PROPN
ejpam-5453	453	21	le	le	PROPN
ejpam-5453	453	22	1	1	NUM
ejpam-5453	453	23	:	:	PUNCT
ejpam-5453	453	24	t	t	NOUN
ejpam-5453	453	25	h	h	NOUN
ejpam-5453	454	1	e	e	PROPN
ejpam-5453	454	2	b	b	X
ejpam-5453	454	3	o	o	X
ejpam-5453	454	4	u	u	NOUN
ejpam-5453	454	5	n	n	PROPN
ejpam-5453	454	6	d	d	PROPN
ejpam-5453	454	7	ar	ar	PROPN
ejpam-5453	454	8	y	y	PROPN
ejpam-5453	454	9	re	re	PROPN
ejpam-5453	454	10	g	g	PROPN
ejpam-5453	454	11	io	io	PROPN
ejpam-5453	454	12	n	n	PROPN
ejpam-5453	454	13	s	s	PROPN
ejpam-5453	454	14	an	an	DET
ejpam-5453	454	15	d	d	X
ejpam-5453	454	16	ac	ac	PROPN
ejpam-5453	454	17	cu	cu	PROPN
ejpam-5453	454	18	ra	ra	PROPN
ejpam-5453	454	19	cy	cy	VERB
ejpam-5453	454	20	by	by	ADV
ejpam-5453	454	21	th	th	ADP
ejpam-5453	454	22	e	e	NOUN
ejpam-5453	454	23	pr	pr	X
ejpam-5453	454	24	io	io	PROPN
ejpam-5453	454	25	r	r	NOUN
ejpam-5453	454	26	m	m	PROPN
ejpam-5453	454	27	an	an	DET
ejpam-5453	454	28	n	n	ADV
ejpam-5453	454	29	er	er	INTJ
ejpam-5453	454	30	in	in	ADP
ejpam-5453	454	31	2	2	NUM
ejpam-5453	454	32	.8	.8	PROPN
ejpam-5453	455	1	[	[	X
ejpam-5453	455	2	4	4	NUM
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ejpam-5453	459	8	=	=	SYM
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ejpam-5453	472	1	a	a	DET
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ejpam-5453	472	4	β	β	X
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ejpam-5453	472	10	b	b	PROPN
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ejpam-5453	473	13	θ	θ	PROPN
ejpam-5453	473	14	β	β	X
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ejpam-5453	473	49	∅	∅	NOUN
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ejpam-5453	473	583	}	}	SYM
ejpam-5453	473	584	3	3	NUM
ejpam-5453	473	585	4	4	NUM
ejpam-5453	473	586	{	{	PUNCT
ejpam-5453	473	587	l	l	NOUN
ejpam-5453	473	588	1	1	NUM
ejpam-5453	473	589	}	}	SYM
ejpam-5453	473	590	3	3	NUM
ejpam-5453	473	591	4	4	NUM
ejpam-5453	473	592	∅	∅	NOUN
ejpam-5453	473	593	1	1	NUM
ejpam-5453	473	594	m.	m.	NOUN
ejpam-5453	473	595	hosny	hosny	PROPN
ejpam-5453	473	596	/	/	SYM
ejpam-5453	473	597	eur	eur	PROPN
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ejpam-5453	474	2	pure	pure	PROPN
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ejpam-5453	474	4	.	.	PROPN
ejpam-5453	474	5	math	math	PROPN
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ejpam-5453	474	7	17	17	NUM
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ejpam-5453	474	9	4	4	NUM
ejpam-5453	474	10	)	)	PUNCT
ejpam-5453	474	11	(	(	PUNCT
ejpam-5453	474	12	2024	2024	NUM
ejpam-5453	474	13	)	)	PUNCT
ejpam-5453	474	14	,	,	PUNCT
ejpam-5453	474	15	2843	2843	NUM
ejpam-5453	474	16	-	-	SYM
ejpam-5453	474	17	2877	2877	NUM
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ejpam-5453	474	19	t	t	PROPN
ejpam-5453	474	20	ab	ab	PROPN
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ejpam-5453	474	22	2	2	NUM
ejpam-5453	474	23	:	:	PUNCT
ejpam-5453	474	24	t	t	NOUN
ejpam-5453	474	25	h	h	NOUN
ejpam-5453	474	26	e	e	PROPN
ejpam-5453	474	27	b	b	X
ejpam-5453	474	28	o	o	X
ejpam-5453	474	29	u	u	NOUN
ejpam-5453	474	30	n	n	PROPN
ejpam-5453	474	31	d	d	PROPN
ejpam-5453	474	32	ar	ar	PROPN
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ejpam-5453	474	35	g	g	PROPN
ejpam-5453	474	36	io	io	PROPN
ejpam-5453	474	37	n	n	PROPN
ejpam-5453	474	38	s	s	PROPN
ejpam-5453	474	39	an	an	DET
ejpam-5453	474	40	d	d	X
ejpam-5453	474	41	ac	ac	PROPN
ejpam-5453	474	42	cu	cu	PROPN
ejpam-5453	474	43	ra	ra	PROPN
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ejpam-5453	475	4	e	e	NOUN
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ejpam-5453	475	7	r	r	NOUN
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ejpam-5453	475	10	n	n	ADV
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ejpam-5453	475	13	2	2	NUM
ejpam-5453	475	14	.1	.1	NUM
ejpam-5453	475	15	1	1	NUM
ejpam-5453	476	1	[	[	SYM
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ejpam-5453	476	5	an	an	DET
ejpam-5453	476	6	d	d	X
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ejpam-5453	476	8	e	e	NOUN
ejpam-5453	476	9	pr	pr	NOUN
ejpam-5453	476	10	es	es	VERB
ejpam-5453	476	11	en	en	ADP
ejpam-5453	476	12	t	t	PROPN
ejpam-5453	476	13	m	m	PROPN
ejpam-5453	476	14	an	an	DET
ejpam-5453	476	15	n	n	ADV
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ejpam-5453	476	18	4	4	NUM
ejpam-5453	476	19	.1	.1	NUM
ejpam-5453	476	20	fo	fo	ADP
ejpam-5453	476	21	r	r	NOUN
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ejpam-5453	476	23	=	=	SYM
ejpam-5453	476	24	{	{	PUNCT
ejpam-5453	476	25	α	α	NOUN
ejpam-5453	476	26	,	,	PUNCT
ejpam-5453	476	27	p	p	NOUN
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ejpam-5453	476	29	,	,	PUNCT
ejpam-5453	476	30	℘	℘	PROPN
ejpam-5453	476	31	=	=	SYM
ejpam-5453	476	32	r	r	NOUN
ejpam-5453	476	33	.	.	PUNCT
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ejpam-5453	477	3	h	h	NOUN
ejpam-5453	478	1	e	e	PROPN
ejpam-5453	478	2	p	p	PROPN
ejpam-5453	478	3	ri	ri	PROPN
ejpam-5453	478	4	or	or	CCONJ
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ejpam-5453	478	6	an	an	DET
ejpam-5453	478	7	n	n	ADV
ejpam-5453	478	8	er	er	INTJ
ejpam-5453	478	9	in	in	ADP
ejpam-5453	478	10	2	2	NUM
ejpam-5453	478	11	.	.	NOUN
ejpam-5453	478	12	11	11	NUM
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ejpam-5453	479	4	]	]	PUNCT
ejpam-5453	479	5	fo	fo	ADP
ejpam-5453	479	6	r	r	NOUN
ejpam-5453	479	7	ξ	ξ	X
ejpam-5453	479	8	=	=	SYM
ejpam-5453	479	9	α	α	PROPN
ejpam-5453	479	10	,	,	PUNCT
ejpam-5453	479	11	℘	℘	X
ejpam-5453	479	12	=	=	SYM
ejpam-5453	479	13	r	r	NOUN
ejpam-5453	479	14	t	t	NOUN
ejpam-5453	479	15	h	h	NOUN
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ejpam-5453	479	19	se	se	X
ejpam-5453	479	20	n	n	PROPN
ejpam-5453	479	21	t	t	PROPN
ejpam-5453	479	22	m	m	VERB
ejpam-5453	479	23	a	a	DET
ejpam-5453	479	24	n	n	CCONJ
ejpam-5453	479	25	n	n	ADV
ejpam-5453	479	26	er	er	INTJ
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ejpam-5453	479	28	4	4	NUM
ejpam-5453	479	29	.1	.1	NUM
ejpam-5453	479	30	fo	fo	ADP
ejpam-5453	479	31	r	r	NOUN
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ejpam-5453	479	33	=	=	SYM
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ejpam-5453	479	36	℘	℘	X
ejpam-5453	479	37	=	=	SYM
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ejpam-5453	479	39	t	t	NOUN
ejpam-5453	479	40	h	h	NOUN
ejpam-5453	480	1	e	e	NOUN
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ejpam-5453	481	4	a	a	DET
ejpam-5453	481	5	n	n	CCONJ
ejpam-5453	481	6	n	n	ADV
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ejpam-5453	481	9	2	2	NUM
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ejpam-5453	481	11	1	1	NUM
ejpam-5453	482	1	[	[	SYM
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ejpam-5453	482	5	fo	fo	ADP
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ejpam-5453	482	8	=	=	SYM
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ejpam-5453	482	10	,	,	PUNCT
ejpam-5453	482	11	℘	℘	X
ejpam-5453	482	12	=	=	SYM
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ejpam-5453	482	20	n	n	PROPN
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ejpam-5453	482	23	an	an	DET
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ejpam-5453	482	29	fo	fo	ADP
ejpam-5453	482	30	r	r	NOUN
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ejpam-5453	482	35	℘	℘	X
ejpam-5453	482	36	=	=	SYM
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ejpam-5453	482	44	)	)	PUNCT
ejpam-5453	482	45	a	a	DET
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ejpam-5453	482	48	r	r	NOUN
ejpam-5453	482	49	(	(	PUNCT
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ejpam-5453	482	51	)	)	PUNCT
ejpam-5453	483	1	b	b	PROPN
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ejpam-5453	484	2	−	−	PROPN
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ejpam-5453	485	1	a	a	PRON
ejpam-5453	486	1	d	d	NOUN
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ejpam-5453	486	3	α	α	PROPN
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ejpam-5453	486	9	b	b	PROPN
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ejpam-5453	487	3	r	r	NOUN
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ejpam-5453	487	5	m	m	PROPN
ejpam-5453	487	6	)	)	PUNCT
ejpam-5453	487	7	a	a	DET
ejpam-5453	487	8	p	p	NOUN
ejpam-5453	487	9	s	s	X
ejpam-5453	487	10	r	r	NOUN
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ejpam-5453	487	12	m	m	PROPN
ejpam-5453	487	13	)	)	PUNCT
ejpam-5453	487	14	b	b	PROPN
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ejpam-5453	488	2	−	−	PROPN
ejpam-5453	489	1	p	p	X
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ejpam-5453	489	3	r	r	NOUN
ejpam-5453	489	4	(	(	PUNCT
ejpam-5453	489	5	m	m	PROPN
ejpam-5453	489	6	)	)	PUNCT
ejpam-5453	489	7	a	a	PRON
ejpam-5453	490	1	d	d	NOUN
ejpam-5453	490	2	−	−	PROPN
ejpam-5453	491	1	p	p	X
ejpam-5453	491	2	s	s	X
ejpam-5453	491	3	r	r	NOUN
ejpam-5453	491	4	(	(	PUNCT
ejpam-5453	491	5	m	m	NOUN
ejpam-5453	491	6	)	)	PUNCT
ejpam-5453	491	7	{	{	PUNCT
ejpam-5453	491	8	l	l	NOUN
ejpam-5453	491	9	1	1	NUM
ejpam-5453	491	10	}	}	PUNCT
ejpam-5453	491	11	{	{	PUNCT
ejpam-5453	491	12	l	l	NOUN
ejpam-5453	491	13	1	1	NUM
ejpam-5453	491	14	}	}	SYM
ejpam-5453	491	15	0	0	NUM
ejpam-5453	491	16	∅	∅	NOUN
ejpam-5453	491	17	1	1	NUM
ejpam-5453	491	18	{	{	PUNCT
ejpam-5453	491	19	l	l	NOUN
ejpam-5453	491	20	1	1	NUM
ejpam-5453	491	21	}	}	SYM
ejpam-5453	491	22	0	0	NUM
ejpam-5453	491	23	∅	∅	NOUN
ejpam-5453	491	24	1	1	NUM
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ejpam-5453	491	26	l	l	NOUN
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ejpam-5453	491	30	l	l	NOUN
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ejpam-5453	491	33	1	1	NUM
ejpam-5453	491	34	2	2	NUM
ejpam-5453	491	35	∅	∅	NOUN
ejpam-5453	491	36	1	1	NUM
ejpam-5453	491	37	{	{	PUNCT
ejpam-5453	491	38	l	l	NOUN
ejpam-5453	491	39	1	1	NUM
ejpam-5453	491	40	}	}	SYM
ejpam-5453	491	41	1	1	NUM
ejpam-5453	491	42	2	2	NUM
ejpam-5453	491	43	∅	∅	NOUN
ejpam-5453	491	44	1	1	NUM
ejpam-5453	491	45	{	{	PUNCT
ejpam-5453	491	46	l	l	NOUN
ejpam-5453	491	47	3	3	NUM
ejpam-5453	491	48	}	}	PUNCT
ejpam-5453	491	49	{	{	PUNCT
ejpam-5453	491	50	l	l	NOUN
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ejpam-5453	491	61	l	l	NOUN
ejpam-5453	491	62	3	3	NUM
ejpam-5453	491	63	l	l	NOUN
ejpam-5453	491	64	4	4	NUM
ejpam-5453	491	65	}	}	SYM
ejpam-5453	491	66	0	0	NUM
ejpam-5453	491	67	∅	∅	NOUN
ejpam-5453	491	68	1	1	NUM
ejpam-5453	491	69	∅	∅	NOUN
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ejpam-5453	491	72	l	l	NOUN
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ejpam-5453	491	76	l	l	NOUN
ejpam-5453	491	77	1	1	NUM
ejpam-5453	491	78	,	,	PUNCT
ejpam-5453	491	79	l	l	NOUN
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ejpam-5453	491	81	,	,	PUNCT
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ejpam-5453	491	87	l	l	NOUN
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ejpam-5453	491	93	0	0	NUM
ejpam-5453	491	94	∅	∅	NOUN
ejpam-5453	491	95	1	1	NUM
ejpam-5453	491	96	∅	∅	NOUN
ejpam-5453	491	97	1	1	NUM
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ejpam-5453	491	99	l	l	NOUN
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ejpam-5453	491	106	l	l	NOUN
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ejpam-5453	491	111	∅	∅	NOUN
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ejpam-5453	491	119	∅	∅	NOUN
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ejpam-5453	491	122	l	l	NOUN
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ejpam-5453	491	129	l	l	NOUN
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ejpam-5453	491	131	,	,	PUNCT
ejpam-5453	491	132	l	l	NOUN
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ejpam-5453	491	140	l	l	NOUN
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ejpam-5453	491	142	,	,	PUNCT
ejpam-5453	491	143	l	l	NOUN
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ejpam-5453	491	148	{	{	PUNCT
ejpam-5453	491	149	l	l	NOUN
ejpam-5453	491	150	1	1	NUM
ejpam-5453	491	151	}	}	SYM
ejpam-5453	491	152	1	1	NUM
ejpam-5453	491	153	2	2	NUM
ejpam-5453	491	154	∅	∅	NOUN
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ejpam-5453	491	156	{	{	PUNCT
ejpam-5453	491	157	l	l	NOUN
ejpam-5453	491	158	1	1	NUM
ejpam-5453	491	159	,	,	PUNCT
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ejpam-5453	491	162	}	}	PUNCT
ejpam-5453	491	163	{	{	PUNCT
ejpam-5453	491	164	l	l	NOUN
ejpam-5453	491	165	1	1	NUM
ejpam-5453	491	166	,	,	PUNCT
ejpam-5453	491	167	l	l	NOUN
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ejpam-5453	491	169	,	,	PUNCT
ejpam-5453	491	170	l	l	NOUN
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ejpam-5453	491	172	}	}	PUNCT
ejpam-5453	491	173	0	0	NUM
ejpam-5453	491	174	{	{	PUNCT
ejpam-5453	491	175	l	l	NOUN
ejpam-5453	491	176	3	3	NUM
ejpam-5453	491	177	,	,	PUNCT
ejpam-5453	491	178	l	l	NOUN
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ejpam-5453	491	180	}	}	SYM
ejpam-5453	491	181	1	1	NUM
ejpam-5453	491	182	3	3	NUM
ejpam-5453	491	183	{	{	PUNCT
ejpam-5453	491	184	l	l	NOUN
ejpam-5453	491	185	1	1	NUM
ejpam-5453	491	186	}	}	SYM
ejpam-5453	491	187	1	1	NUM
ejpam-5453	491	188	2	2	NUM
ejpam-5453	491	189	∅	∅	NOUN
ejpam-5453	491	190	1	1	NUM
ejpam-5453	491	191	{	{	PUNCT
ejpam-5453	491	192	l	l	NOUN
ejpam-5453	491	193	2	2	NUM
ejpam-5453	491	194	,	,	PUNCT
ejpam-5453	491	195	l	l	NOUN
ejpam-5453	491	196	3	3	NUM
ejpam-5453	491	197	}	}	PUNCT
ejpam-5453	491	198	{	{	PUNCT
ejpam-5453	491	199	l	l	NOUN
ejpam-5453	491	200	1	1	NUM
ejpam-5453	491	201	,	,	PUNCT
ejpam-5453	491	202	l	l	NOUN
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ejpam-5453	491	204	,	,	PUNCT
ejpam-5453	491	205	l	l	NOUN
ejpam-5453	491	206	4	4	NUM
ejpam-5453	491	207	}	}	SYM
ejpam-5453	491	208	1	1	NUM
ejpam-5453	491	209	4	4	NUM
ejpam-5453	491	210	{	{	PUNCT
ejpam-5453	491	211	l	l	NOUN
ejpam-5453	491	212	3	3	NUM
ejpam-5453	491	213	,	,	PUNCT
ejpam-5453	491	214	l	l	NOUN
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ejpam-5453	491	216	}	}	SYM
ejpam-5453	491	217	1	1	NUM
ejpam-5453	491	218	3	3	NUM
ejpam-5453	491	219	{	{	PUNCT
ejpam-5453	491	220	l	l	NOUN
ejpam-5453	491	221	1	1	NUM
ejpam-5453	491	222	}	}	SYM
ejpam-5453	491	223	2	2	NUM
ejpam-5453	491	224	3	3	NUM
ejpam-5453	491	225	∅	∅	NOUN
ejpam-5453	491	226	1	1	NUM
ejpam-5453	491	227	{	{	PUNCT
ejpam-5453	491	228	l	l	NOUN
ejpam-5453	491	229	2	2	NUM
ejpam-5453	491	230	,	,	PUNCT
ejpam-5453	491	231	l	l	NOUN
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ejpam-5453	491	233	}	}	PUNCT
ejpam-5453	491	234	{	{	PUNCT
ejpam-5453	491	235	l	l	NOUN
ejpam-5453	491	236	1	1	NUM
ejpam-5453	491	237	,	,	PUNCT
ejpam-5453	491	238	l	l	NOUN
ejpam-5453	491	239	3	3	NUM
ejpam-5453	491	240	,	,	PUNCT
ejpam-5453	491	241	l	l	NOUN
ejpam-5453	491	242	4	4	NUM
ejpam-5453	491	243	}	}	SYM
ejpam-5453	491	244	1	1	NUM
ejpam-5453	491	245	4	4	NUM
ejpam-5453	491	246	{	{	PUNCT
ejpam-5453	491	247	l	l	NOUN
ejpam-5453	491	248	3	3	NUM
ejpam-5453	491	249	,	,	PUNCT
ejpam-5453	491	250	l	l	NOUN
ejpam-5453	491	251	4	4	NUM
ejpam-5453	491	252	}	}	SYM
ejpam-5453	491	253	1	1	NUM
ejpam-5453	491	254	3	3	NUM
ejpam-5453	491	255	{	{	PUNCT
ejpam-5453	491	256	l	l	NOUN
ejpam-5453	491	257	1	1	NUM
ejpam-5453	491	258	}	}	SYM
ejpam-5453	491	259	2	2	NUM
ejpam-5453	491	260	3	3	NUM
ejpam-5453	491	261	∅	∅	NOUN
ejpam-5453	491	262	1	1	NUM
ejpam-5453	491	263	{	{	PUNCT
ejpam-5453	491	264	l	l	NOUN
ejpam-5453	491	265	3	3	NUM
ejpam-5453	491	266	,	,	PUNCT
ejpam-5453	491	267	l	l	NOUN
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ejpam-5453	491	269	}	}	PUNCT
ejpam-5453	491	270	{	{	PUNCT
ejpam-5453	491	271	l	l	NOUN
ejpam-5453	491	272	1	1	NUM
ejpam-5453	491	273	}	}	SYM
ejpam-5453	491	274	2	2	NUM
ejpam-5453	491	275	3	3	NUM
ejpam-5453	491	276	∅	∅	NOUN
ejpam-5453	491	277	1	1	NUM
ejpam-5453	491	278	{	{	PUNCT
ejpam-5453	491	279	l	l	NOUN
ejpam-5453	491	280	1	1	NUM
ejpam-5453	491	281	}	}	SYM
ejpam-5453	491	282	2	2	NUM
ejpam-5453	491	283	3	3	NUM
ejpam-5453	491	284	∅	∅	NOUN
ejpam-5453	491	285	1	1	NUM
ejpam-5453	491	286	{	{	PUNCT
ejpam-5453	491	287	l	l	NOUN
ejpam-5453	491	288	1	1	NUM
ejpam-5453	491	289	,	,	PUNCT
ejpam-5453	491	290	l	l	NOUN
ejpam-5453	491	291	2	2	NUM
ejpam-5453	491	292	,	,	PUNCT
ejpam-5453	491	293	l	l	NOUN
ejpam-5453	491	294	3	3	NUM
ejpam-5453	491	295	}	}	PUNCT
ejpam-5453	491	296	{	{	PUNCT
ejpam-5453	491	297	l	l	NOUN
ejpam-5453	491	298	1	1	NUM
ejpam-5453	491	299	,	,	PUNCT
ejpam-5453	491	300	l	l	NOUN
ejpam-5453	491	301	3	3	NUM
ejpam-5453	491	302	,	,	PUNCT
ejpam-5453	491	303	l	l	NOUN
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ejpam-5453	491	305	}	}	SYM
ejpam-5453	491	306	1	1	NUM
ejpam-5453	491	307	4	4	NUM
ejpam-5453	491	308	{	{	PUNCT
ejpam-5453	491	309	l	l	NOUN
ejpam-5453	491	310	3	3	NUM
ejpam-5453	491	311	,	,	PUNCT
ejpam-5453	491	312	l	l	NOUN
ejpam-5453	491	313	4	4	NUM
ejpam-5453	491	314	}	}	SYM
ejpam-5453	491	315	1	1	NUM
ejpam-5453	491	316	2	2	NUM
ejpam-5453	491	317	∅	∅	NOUN
ejpam-5453	491	318	1	1	NUM
ejpam-5453	491	319	∅	∅	NOUN
ejpam-5453	491	320	1	1	NUM
ejpam-5453	491	321	{	{	PUNCT
ejpam-5453	491	322	l	l	NOUN
ejpam-5453	491	323	1	1	NUM
ejpam-5453	491	324	,	,	PUNCT
ejpam-5453	491	325	l	l	NOUN
ejpam-5453	491	326	2	2	NUM
ejpam-5453	491	327	,	,	PUNCT
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ejpam-5453	491	331	{	{	PUNCT
ejpam-5453	491	332	l	l	NOUN
ejpam-5453	491	333	1	1	NUM
ejpam-5453	491	334	,	,	PUNCT
ejpam-5453	491	335	l	l	NOUN
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ejpam-5453	491	341	1	1	NUM
ejpam-5453	491	342	4	4	NUM
ejpam-5453	491	343	{	{	PUNCT
ejpam-5453	491	344	l	l	NOUN
ejpam-5453	491	345	3	3	NUM
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ejpam-5453	491	347	l	l	NOUN
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ejpam-5453	491	350	1	1	NUM
ejpam-5453	491	351	2	2	NUM
ejpam-5453	491	352	∅	∅	NOUN
ejpam-5453	491	353	1	1	NUM
ejpam-5453	491	354	∅	∅	NOUN
ejpam-5453	491	355	1	1	NUM
ejpam-5453	491	356	{	{	PUNCT
ejpam-5453	491	357	a	a	DET
ejpam-5453	491	358	l	l	NOUN
ejpam-5453	491	359	1	1	NUM
ejpam-5453	491	360	,	,	PUNCT
ejpam-5453	491	361	l	l	NOUN
ejpam-5453	491	362	3	3	NUM
ejpam-5453	491	363	,	,	PUNCT
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ejpam-5453	491	368	l	l	NOUN
ejpam-5453	491	369	1	1	NUM
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ejpam-5453	491	371	2	2	NUM
ejpam-5453	491	372	3	3	NUM
ejpam-5453	491	373	∅	∅	NOUN
ejpam-5453	491	374	1	1	NUM
ejpam-5453	491	375	{	{	PUNCT
ejpam-5453	491	376	l	l	NOUN
ejpam-5453	491	377	1	1	NUM
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ejpam-5453	491	379	2	2	NUM
ejpam-5453	491	380	3	3	NUM
ejpam-5453	491	381	∅	∅	NOUN
ejpam-5453	491	382	1	1	NUM
ejpam-5453	491	383	{	{	PUNCT
ejpam-5453	491	384	l	l	NOUN
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ejpam-5453	491	386	,	,	PUNCT
ejpam-5453	491	387	l	l	NOUN
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ejpam-5453	491	389	,	,	PUNCT
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ejpam-5453	491	397	3	3	NUM
ejpam-5453	491	398	4	4	NUM
ejpam-5453	491	399	∅	∅	NOUN
ejpam-5453	491	400	1	1	NUM
ejpam-5453	491	401	{	{	PUNCT
ejpam-5453	491	402	l	l	NOUN
ejpam-5453	491	403	1	1	NUM
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ejpam-5453	491	405	3	3	NUM
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ejpam-5453	491	407	∅	∅	NOUN
ejpam-5453	491	408	1	1	NUM
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ejpam-5453	491	412	eur	eur	PROPN
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ejpam-5453	492	1	j.	j.	PROPN
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ejpam-5453	492	9	4	4	NUM
ejpam-5453	492	10	)	)	PUNCT
ejpam-5453	492	11	(	(	PUNCT
ejpam-5453	492	12	2024	2024	NUM
ejpam-5453	492	13	)	)	PUNCT
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ejpam-5453	492	16	-	-	SYM
ejpam-5453	492	17	2877	2877	NUM
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ejpam-5453	492	19	t	t	PROPN
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ejpam-5453	492	23	:	:	PUNCT
ejpam-5453	492	24	t	t	NOUN
ejpam-5453	492	25	h	h	NOUN
ejpam-5453	493	1	e	e	PROPN
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ejpam-5453	493	3	o	o	X
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ejpam-5453	493	13	s	s	PROPN
ejpam-5453	493	14	an	an	DET
ejpam-5453	493	15	d	d	X
ejpam-5453	493	16	ac	ac	PROPN
ejpam-5453	493	17	cu	cu	PROPN
ejpam-5453	493	18	ra	ra	PROPN
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ejpam-5453	493	22	e	e	NOUN
ejpam-5453	493	23	pr	pr	X
ejpam-5453	493	24	io	io	PROPN
ejpam-5453	493	25	r	r	NOUN
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ejpam-5453	493	31	2	2	NUM
ejpam-5453	493	32	.1	.1	NUM
ejpam-5453	493	33	1	1	NUM
ejpam-5453	494	1	[	[	SYM
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ejpam-5453	494	3	3	3	NUM
ejpam-5453	494	4	]	]	PUNCT
ejpam-5453	494	5	an	an	DET
ejpam-5453	494	6	d	d	X
ejpam-5453	494	7	th	th	X
ejpam-5453	494	8	e	e	NOUN
ejpam-5453	494	9	pr	pr	NOUN
ejpam-5453	494	10	es	es	VERB
ejpam-5453	494	11	en	en	ADP
ejpam-5453	494	12	t	t	PROPN
ejpam-5453	494	13	m	m	PROPN
ejpam-5453	494	14	an	an	DET
ejpam-5453	494	15	n	n	ADV
ejpam-5453	494	16	er	er	INTJ
ejpam-5453	494	17	in	in	ADP
ejpam-5453	494	18	4	4	NUM
ejpam-5453	494	19	.1	.1	NUM
ejpam-5453	494	20	fo	fo	ADP
ejpam-5453	494	21	r	r	NOUN
ejpam-5453	494	22	ξ	ξ	X
ejpam-5453	494	23	=	=	PUNCT
ejpam-5453	494	24	{	{	PUNCT
ejpam-5453	494	25	s	s	X
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ejpam-5453	494	27	β	β	X
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ejpam-5453	494	29	,	,	PUNCT
ejpam-5453	494	30	℘	℘	PROPN
ejpam-5453	494	31	=	=	SYM
ejpam-5453	494	32	r	r	NOUN
ejpam-5453	494	33	.	.	PUNCT
ejpam-5453	495	1	m	m	VERB
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ejpam-5453	495	3	h	h	NOUN
ejpam-5453	496	1	e	e	PROPN
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ejpam-5453	496	4	or	or	CCONJ
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ejpam-5453	496	6	an	an	DET
ejpam-5453	496	7	n	n	ADV
ejpam-5453	496	8	er	er	INTJ
ejpam-5453	496	9	in	in	ADP
ejpam-5453	496	10	2	2	NUM
ejpam-5453	496	11	.	.	NOUN
ejpam-5453	496	12	11	11	NUM
ejpam-5453	497	1	[	[	SYM
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ejpam-5453	497	4	]	]	PUNCT
ejpam-5453	497	5	fo	fo	ADP
ejpam-5453	497	6	r	r	NOUN
ejpam-5453	497	7	ξ	ξ	X
ejpam-5453	497	8	=	=	SYM
ejpam-5453	497	9	s	s	NOUN
ejpam-5453	497	10	,	,	PUNCT
ejpam-5453	497	11	℘	℘	X
ejpam-5453	497	12	=	=	SYM
ejpam-5453	497	13	r	r	NOUN
ejpam-5453	497	14	t	t	NOUN
ejpam-5453	497	15	h	h	NOUN
ejpam-5453	497	16	e	e	X
ejpam-5453	497	17	p	p	X
ejpam-5453	497	18	re	re	X
ejpam-5453	497	19	se	se	X
ejpam-5453	497	20	n	n	PROPN
ejpam-5453	497	21	t	t	PROPN
ejpam-5453	497	22	m	m	VERB
ejpam-5453	497	23	an	an	DET
ejpam-5453	497	24	n	n	ADV
ejpam-5453	497	25	er	er	INTJ
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ejpam-5453	497	28	.1	.1	NUM
ejpam-5453	497	29	fo	fo	ADP
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ejpam-5453	497	32	=	=	SYM
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ejpam-5453	497	35	℘	℘	X
ejpam-5453	497	36	=	=	SYM
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ejpam-5453	497	38	t	t	NOUN
ejpam-5453	497	39	h	h	NOUN
ejpam-5453	498	1	e	e	NOUN
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ejpam-5453	499	4	a	a	DET
ejpam-5453	499	5	n	n	CCONJ
ejpam-5453	499	6	n	n	ADV
ejpam-5453	499	7	er	er	INTJ
ejpam-5453	499	8	in	in	ADP
ejpam-5453	499	9	2	2	NUM
ejpam-5453	499	10	.1	.1	NUM
ejpam-5453	499	11	1	1	NUM
ejpam-5453	500	1	[	[	SYM
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ejpam-5453	500	5	fo	fo	ADP
ejpam-5453	500	6	r	r	NOUN
ejpam-5453	500	7	ξ	ξ	X
ejpam-5453	500	8	=	=	SYM
ejpam-5453	500	9	β	β	X
ejpam-5453	500	10	,	,	PUNCT
ejpam-5453	500	11	℘	℘	X
ejpam-5453	500	12	=	=	SYM
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ejpam-5453	505	348	}	}	SYM
ejpam-5453	505	349	3	3	NUM
ejpam-5453	505	350	4	4	NUM
ejpam-5453	505	351	∅	∅	NOUN
ejpam-5453	505	352	1	1	NUM
ejpam-5453	505	353	m.	m.	NOUN
ejpam-5453	505	354	hosny	hosny	PROPN
ejpam-5453	505	355	/	/	SYM
ejpam-5453	505	356	eur	eur	PROPN
ejpam-5453	505	357	.	.	PUNCT
ejpam-5453	506	1	j.	j.	PROPN
ejpam-5453	506	2	pure	pure	PROPN
ejpam-5453	506	3	appl	appl	PROPN
ejpam-5453	506	4	.	.	PROPN
ejpam-5453	506	5	math	math	PROPN
ejpam-5453	506	6	,	,	PUNCT
ejpam-5453	506	7	17	17	NUM
ejpam-5453	506	8	(	(	PUNCT
ejpam-5453	506	9	4	4	NUM
ejpam-5453	506	10	)	)	PUNCT
ejpam-5453	506	11	(	(	PUNCT
ejpam-5453	506	12	2024	2024	NUM
ejpam-5453	506	13	)	)	PUNCT
ejpam-5453	506	14	,	,	PUNCT
ejpam-5453	506	15	2843	2843	NUM
ejpam-5453	506	16	-	-	SYM
ejpam-5453	506	17	2877	2877	NUM
ejpam-5453	506	18	2860	2860	NUM
ejpam-5453	506	19	the	the	DET
ejpam-5453	506	20	boundary	boundary	ADJ
ejpam-5453	506	21	regions	region	NOUN
ejpam-5453	506	22	and	and	CCONJ
ejpam-5453	506	23	accuracy	accuracy	NOUN
ejpam-5453	506	24	by	by	ADP
ejpam-5453	506	25	the	the	DET
ejpam-5453	506	26	prior	prior	ADJ
ejpam-5453	506	27	manner	manner	NOUN
ejpam-5453	506	28	in	in	ADP
ejpam-5453	506	29	2.8	2.8	NUM
ejpam-5453	506	30	[	[	SYM
ejpam-5453	506	31	43	43	NUM
ejpam-5453	506	32	]	]	PUNCT
ejpam-5453	506	33	and	and	CCONJ
ejpam-5453	506	34	the	the	DET
ejpam-5453	506	35	present	present	ADJ
ejpam-5453	506	36	manner	manner	NOUN
ejpam-5453	506	37	in	in	ADP
ejpam-5453	506	38	4.1	4.1	NUM
ejpam-5453	506	39	are	be	AUX
ejpam-5453	506	40	calculated	calculate	VERB
ejpam-5453	506	41	in	in	ADP
ejpam-5453	506	42	table	table	NOUN
ejpam-5453	506	43	1	1	NUM
ejpam-5453	506	44	by	by	ADP
ejpam-5453	506	45	using	use	VERB
ejpam-5453	506	46	example	example	NOUN
ejpam-5453	506	47	3.1	3.1	NUM
ejpam-5453	506	48	when	when	SCONJ
ejpam-5453	506	49	d	d	PROPN
ejpam-5453	506	50	=	=	SYM
ejpam-5453	506	51	{	{	PUNCT
ejpam-5453	506	52	∅	∅	NOUN
ejpam-5453	506	53	,	,	PUNCT
ejpam-5453	506	54	{	{	PUNCT
ejpam-5453	506	55	l2	l2	NOUN
ejpam-5453	506	56	}	}	PUNCT
ejpam-5453	506	57	}	}	PUNCT
ejpam-5453	506	58	.	.	PUNCT
ejpam-5453	507	1	whereas	whereas	SCONJ
ejpam-5453	507	2	,	,	PUNCT
ejpam-5453	507	3	the	the	DET
ejpam-5453	507	4	boundary	boundary	ADJ
ejpam-5453	507	5	regions	region	NOUN
ejpam-5453	507	6	and	and	CCONJ
ejpam-5453	507	7	accuracy	accuracy	NOUN
ejpam-5453	507	8	by	by	ADP
ejpam-5453	507	9	the	the	DET
ejpam-5453	507	10	prior	prior	ADJ
ejpam-5453	507	11	manner	manner	NOUN
ejpam-5453	507	12	in	in	ADP
ejpam-5453	507	13	2.11	2.11	NUM
ejpam-5453	507	14	[	[	X
ejpam-5453	507	15	43	43	NUM
ejpam-5453	507	16	]	]	PUNCT
ejpam-5453	507	17	and	and	CCONJ
ejpam-5453	507	18	the	the	DET
ejpam-5453	507	19	present	present	ADJ
ejpam-5453	507	20	manner	manner	NOUN
ejpam-5453	507	21	in	in	ADP
ejpam-5453	507	22	4.1	4.1	NUM
ejpam-5453	507	23	are	be	AUX
ejpam-5453	507	24	computed	compute	VERB
ejpam-5453	507	25	in	in	ADP
ejpam-5453	507	26	tables	table	NOUN
ejpam-5453	507	27	2	2	NUM
ejpam-5453	507	28	,	,	PUNCT
ejpam-5453	507	29	3	3	NUM
ejpam-5453	507	30	by	by	ADP
ejpam-5453	507	31	using	use	VERB
ejpam-5453	507	32	example	example	NOUN
ejpam-5453	507	33	3.1	3.1	NUM
ejpam-5453	507	34	.	.	PUNCT
ejpam-5453	508	1	definition	definition	NOUN
ejpam-5453	508	2	4.1	4.1	NUM
ejpam-5453	508	3	is	be	AUX
ejpam-5453	508	4	superior	superior	ADJ
ejpam-5453	508	5	to	to	PART
ejpam-5453	508	6	definition	definition	NOUN
ejpam-5453	508	7	2.2	2.2	NUM
ejpam-5453	508	8	[	[	SYM
ejpam-5453	508	9	1	1	NUM
ejpam-5453	508	10	,	,	PUNCT
ejpam-5453	508	11	2	2	NUM
ejpam-5453	508	12	,	,	PUNCT
ejpam-5453	508	13	30	30	NUM
ejpam-5453	508	14	]	]	PUNCT
ejpam-5453	508	15	,	,	PUNCT
ejpam-5453	508	16	as	as	SCONJ
ejpam-5453	508	17	exhibited	exhibit	VERB
ejpam-5453	508	18	by	by	ADP
ejpam-5453	508	19	the	the	DET
ejpam-5453	508	20	subsequent	subsequent	ADJ
ejpam-5453	508	21	findings	finding	NOUN
ejpam-5453	508	22	.	.	PUNCT
ejpam-5453	509	1	theorem	theorem	VERB
ejpam-5453	509	2	4.2	4.2	NUM
ejpam-5453	509	3	.	.	PUNCT
ejpam-5453	510	1	let	let	AUX
ejpam-5453	510	2	(	(	PUNCT
ejpam-5453	510	3	v	v	NOUN
ejpam-5453	510	4	,	,	PUNCT
ejpam-5453	510	5	υ	υ	NOUN
ejpam-5453	510	6	,	,	PUNCT
ejpam-5453	510	7	π℘	π℘	NUM
ejpam-5453	510	8	)	)	PUNCT
ejpam-5453	510	9	be	be	AUX
ejpam-5453	510	10	a	a	DET
ejpam-5453	510	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	510	12	,	,	PUNCT
ejpam-5453	510	13	d	d	PRON
ejpam-5453	510	14	be	be	AUX
ejpam-5453	510	15	an	an	DET
ejpam-5453	510	16	ideal	ideal	NOUN
ejpam-5453	510	17	on	on	ADP
ejpam-5453	510	18	v	v	NOUN
ejpam-5453	510	19	,	,	PUNCT
ejpam-5453	510	20	υ	υ	PROPN
ejpam-5453	510	21	be	be	AUX
ejpam-5453	510	22	a	a	DET
ejpam-5453	510	23	similarity	similarity	NOUN
ejpam-5453	510	24	relation	relation	NOUN
ejpam-5453	510	25	,	,	PUNCT
ejpam-5453	510	26	℘	℘	PROPN
ejpam-5453	510	27	∈	∈	PROPN
ejpam-5453	510	28	{	{	PUNCT
ejpam-5453	510	29	r	r	NOUN
ejpam-5453	510	30	,	,	PUNCT
ejpam-5453	510	31	l	l	NOUN
ejpam-5453	510	32	,	,	PUNCT
ejpam-5453	510	33	i	i	PRON
ejpam-5453	510	34	,	,	PUNCT
ejpam-5453	510	35	u	u	NOUN
ejpam-5453	510	36	}	}	PUNCT
ejpam-5453	510	37	and	and	CCONJ
ejpam-5453	510	38	m	m	PROPN
ejpam-5453	510	39	⊆	⊆	NUM
ejpam-5453	510	40	v.	v.	ADP
ejpam-5453	510	41	then	then	ADV
ejpam-5453	510	42	(	(	PUNCT
ejpam-5453	510	43	i	i	NOUN
ejpam-5453	510	44	)	)	PUNCT
ejpam-5453	510	45	n℘(m	n℘(m	NOUN
ejpam-5453	510	46	)	)	PUNCT
ejpam-5453	510	47	⊆	⊆	NUM
ejpam-5453	510	48	nd−ξ	nd−ξ	ADJ
ejpam-5453	510	49	s℘	s℘	NOUN
ejpam-5453	510	50	(	(	PUNCT
ejpam-5453	510	51	m	m	NOUN
ejpam-5453	510	52	)	)	PUNCT
ejpam-5453	510	53	.	.	PUNCT
ejpam-5453	511	1	(	(	PUNCT
ejpam-5453	511	2	ii	ii	NOUN
ejpam-5453	511	3	)	)	PUNCT
ejpam-5453	511	4	n	n	PROPN
ejpam-5453	511	5	d−ξ	d−ξ	NOUN
ejpam-5453	511	6	s℘	s℘	NOUN
ejpam-5453	511	7	(	(	PUNCT
ejpam-5453	511	8	m	m	NOUN
ejpam-5453	511	9	)	)	PUNCT
ejpam-5453	511	10	⊆	⊆	NUM
ejpam-5453	511	11	n℘(m	n℘(m	NOUN
ejpam-5453	511	12	)	)	PUNCT
ejpam-5453	511	13	.	.	PUNCT
ejpam-5453	512	1	proof	proof	NOUN
ejpam-5453	512	2	.	.	PUNCT
ejpam-5453	513	1	(	(	PUNCT
ejpam-5453	513	2	1	1	X
ejpam-5453	513	3	)	)	PUNCT
ejpam-5453	513	4	by	by	ADP
ejpam-5453	513	5	theorem	theorem	ADJ
ejpam-5453	513	6	2.3	2.3	NUM
ejpam-5453	513	7	,	,	PUNCT
ejpam-5453	513	8	n℘(m	n℘(m	NOUN
ejpam-5453	513	9	)	)	PUNCT
ejpam-5453	513	10	⊆	⊆	NUM
ejpam-5453	513	11	ns℘(m	ns℘(m	NOUN
ejpam-5453	513	12	)	)	PUNCT
ejpam-5453	513	13	,	,	PUNCT
ejpam-5453	513	14	and	and	CCONJ
ejpam-5453	513	15	by	by	ADP
ejpam-5453	513	16	(	(	PUNCT
ejpam-5453	513	17	2	2	X
ejpam-5453	513	18	)	)	PUNCT
ejpam-5453	513	19	in	in	ADP
ejpam-5453	513	20	theorem	theorem	ADJ
ejpam-5453	513	21	4.1ns℘(m	4.1ns℘(m	NUM
ejpam-5453	513	22	)	)	PUNCT
ejpam-5453	513	23	⊆	⊆	NUM
ejpam-5453	513	24	nd−ξ	nd−ξ	ADJ
ejpam-5453	513	25	s℘	s℘	NOUN
ejpam-5453	513	26	(	(	PUNCT
ejpam-5453	513	27	m	m	NOUN
ejpam-5453	513	28	)	)	PUNCT
ejpam-5453	513	29	.	.	PUNCT
ejpam-5453	514	1	so	so	ADV
ejpam-5453	514	2	,	,	PUNCT
ejpam-5453	514	3	n℘(m	n℘(m	NOUN
ejpam-5453	514	4	)	)	PUNCT
ejpam-5453	514	5	⊆	⊆	NUM
ejpam-5453	514	6	nd−ξ	nd−ξ	ADJ
ejpam-5453	514	7	s℘	s℘	NOUN
ejpam-5453	514	8	(	(	PUNCT
ejpam-5453	514	9	m	m	NOUN
ejpam-5453	514	10	)	)	PUNCT
ejpam-5453	514	11	.	.	PUNCT
ejpam-5453	515	1	(	(	PUNCT
ejpam-5453	515	2	2	2	X
ejpam-5453	515	3	)	)	PUNCT
ejpam-5453	515	4	similar	similar	ADJ
ejpam-5453	515	5	to	to	ADP
ejpam-5453	515	6	(	(	PUNCT
ejpam-5453	515	7	1	1	NUM
ejpam-5453	515	8	)	)	PUNCT
ejpam-5453	515	9	.	.	PUNCT
ejpam-5453	516	1	corollary	corollary	NOUN
ejpam-5453	516	2	4.3	4.3	NUM
ejpam-5453	516	3	.	.	PUNCT
ejpam-5453	517	1	let	let	AUX
ejpam-5453	517	2	(	(	PUNCT
ejpam-5453	517	3	v	v	NOUN
ejpam-5453	517	4	,	,	PUNCT
ejpam-5453	517	5	υ	υ	NOUN
ejpam-5453	517	6	,	,	PUNCT
ejpam-5453	517	7	π℘	π℘	NUM
ejpam-5453	517	8	)	)	PUNCT
ejpam-5453	517	9	be	be	AUX
ejpam-5453	517	10	a	a	DET
ejpam-5453	517	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	517	12	,	,	PUNCT
ejpam-5453	517	13	d	d	PRON
ejpam-5453	517	14	be	be	AUX
ejpam-5453	517	15	an	an	DET
ejpam-5453	517	16	ideal	ideal	NOUN
ejpam-5453	517	17	on	on	ADP
ejpam-5453	517	18	v	v	NOUN
ejpam-5453	517	19	,	,	PUNCT
ejpam-5453	517	20	υ	υ	PROPN
ejpam-5453	517	21	be	be	AUX
ejpam-5453	517	22	a	a	DET
ejpam-5453	517	23	similarity	similarity	NOUN
ejpam-5453	517	24	relation	relation	NOUN
ejpam-5453	517	25	℘	℘	PROPN
ejpam-5453	517	26	∈	∈	PROPN
ejpam-5453	517	27	{	{	PUNCT
ejpam-5453	517	28	r	r	NOUN
ejpam-5453	517	29	,	,	PUNCT
ejpam-5453	517	30	l	l	NOUN
ejpam-5453	517	31	,	,	PUNCT
ejpam-5453	517	32	i	i	PRON
ejpam-5453	517	33	,	,	PUNCT
ejpam-5453	517	34	u	u	NOUN
ejpam-5453	517	35	}	}	PUNCT
ejpam-5453	517	36	and	and	CCONJ
ejpam-5453	517	37	m	m	PROPN
ejpam-5453	517	38	⊆	⊆	NUM
ejpam-5453	517	39	v.	v.	ADP
ejpam-5453	517	40	then	then	ADV
ejpam-5453	517	41	(	(	PUNCT
ejpam-5453	517	42	i	i	NOUN
ejpam-5453	517	43	)	)	PUNCT
ejpam-5453	517	44	bd−ξ	bd−ξ	PROPN
ejpam-5453	517	45	s℘	s℘	NOUN
ejpam-5453	517	46	(	(	PUNCT
ejpam-5453	517	47	m	m	NOUN
ejpam-5453	517	48	)	)	PUNCT
ejpam-5453	517	49	⊆	⊆	NUM
ejpam-5453	517	50	b℘(m	b℘(m	NOUN
ejpam-5453	517	51	)	)	PUNCT
ejpam-5453	517	52	.	.	PUNCT
ejpam-5453	518	1	(	(	PUNCT
ejpam-5453	518	2	ii	ii	NOUN
ejpam-5453	518	3	)	)	PUNCT
ejpam-5453	518	4	a℘(m	a℘(m	NOUN
ejpam-5453	518	5	)	)	PUNCT
ejpam-5453	518	6	⩽	⩽	PROPN
ejpam-5453	519	1	ad−ξ	ad−ξ	PROPN
ejpam-5453	519	2	s℘	s℘	PROPN
ejpam-5453	519	3	(	(	PUNCT
ejpam-5453	519	4	m	m	NOUN
ejpam-5453	519	5	)	)	PUNCT
ejpam-5453	519	6	.	.	PUNCT
ejpam-5453	520	1	corollary	corollary	NOUN
ejpam-5453	520	2	4.4	4.4	NUM
ejpam-5453	520	3	.	.	PUNCT
ejpam-5453	521	1	let	let	AUX
ejpam-5453	521	2	(	(	PUNCT
ejpam-5453	521	3	v	v	NOUN
ejpam-5453	521	4	,	,	PUNCT
ejpam-5453	521	5	υ	υ	NOUN
ejpam-5453	521	6	,	,	PUNCT
ejpam-5453	521	7	π℘	π℘	NUM
ejpam-5453	521	8	)	)	PUNCT
ejpam-5453	521	9	be	be	AUX
ejpam-5453	521	10	a	a	DET
ejpam-5453	521	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	521	12	,	,	PUNCT
ejpam-5453	521	13	d	d	PRON
ejpam-5453	521	14	be	be	AUX
ejpam-5453	521	15	an	an	DET
ejpam-5453	521	16	ideal	ideal	NOUN
ejpam-5453	521	17	on	on	ADP
ejpam-5453	521	18	v	v	NOUN
ejpam-5453	521	19	,	,	PUNCT
ejpam-5453	521	20	υ	υ	PROPN
ejpam-5453	521	21	be	be	AUX
ejpam-5453	521	22	a	a	DET
ejpam-5453	521	23	similarity	similarity	NOUN
ejpam-5453	521	24	relation	relation	NOUN
ejpam-5453	521	25	,	,	PUNCT
ejpam-5453	521	26	℘	℘	PROPN
ejpam-5453	521	27	∈	∈	PROPN
ejpam-5453	521	28	{	{	PUNCT
ejpam-5453	521	29	r	r	NOUN
ejpam-5453	521	30	,	,	PUNCT
ejpam-5453	521	31	l	l	NOUN
ejpam-5453	521	32	,	,	PUNCT
ejpam-5453	521	33	i	i	PRON
ejpam-5453	521	34	,	,	PUNCT
ejpam-5453	521	35	u	u	NOUN
ejpam-5453	521	36	}	}	PUNCT
ejpam-5453	521	37	and	and	CCONJ
ejpam-5453	521	38	m	m	PROPN
ejpam-5453	521	39	⊆	⊆	NUM
ejpam-5453	521	40	v.	v.	ADP
ejpam-5453	521	41	then	then	ADV
ejpam-5453	521	42	(	(	PUNCT
ejpam-5453	521	43	i	i	NOUN
ejpam-5453	521	44	)	)	PUNCT
ejpam-5453	521	45	every	every	DET
ejpam-5453	521	46	℘-exact	℘-exact	NOUN
ejpam-5453	521	47	subset	subset	VERB
ejpam-5453	521	48	in	in	ADP
ejpam-5453	521	49	v	v	PROPN
ejpam-5453	521	50	is	be	AUX
ejpam-5453	521	51	d	d	NOUN
ejpam-5453	521	52	-	-	PUNCT
ejpam-5453	521	53	ξs℘-nearly	ξs℘-nearly	ADV
ejpam-5453	521	54	exact	exact	ADJ
ejpam-5453	521	55	.	.	PUNCT
ejpam-5453	522	1	(	(	PUNCT
ejpam-5453	522	2	ii	ii	NOUN
ejpam-5453	522	3	)	)	PUNCT
ejpam-5453	522	4	every	every	DET
ejpam-5453	522	5	d	d	PROPN
ejpam-5453	522	6	-	-	PUNCT
ejpam-5453	522	7	ξs℘-nearly	ξs℘-nearly	ADV
ejpam-5453	522	8	rough	rough	ADJ
ejpam-5453	522	9	subset	subset	NOUN
ejpam-5453	522	10	in	in	ADP
ejpam-5453	522	11	v	v	NOUN
ejpam-5453	522	12	is	be	AUX
ejpam-5453	522	13	℘-rough	℘-rough	NOUN
ejpam-5453	522	14	.	.	PUNCT
ejpam-5453	523	1	the	the	DET
ejpam-5453	523	2	prior	prior	ADJ
ejpam-5453	523	3	approximations	approximation	NOUN
ejpam-5453	523	4	in	in	ADP
ejpam-5453	523	5	definition	definition	NOUN
ejpam-5453	523	6	2.5	2.5	NUM
ejpam-5453	523	7	[	[	X
ejpam-5453	523	8	22	22	NUM
ejpam-5453	523	9	,	,	PUNCT
ejpam-5453	523	10	26	26	NUM
ejpam-5453	523	11	]	]	PUNCT
ejpam-5453	523	12	are	be	AUX
ejpam-5453	523	13	outperform	outperform	ADJ
ejpam-5453	523	14	those	those	PRON
ejpam-5453	523	15	in	in	ADP
ejpam-5453	523	16	definition	definition	NOUN
ejpam-5453	523	17	4.1	4.1	NUM
ejpam-5453	523	18	in	in	ADP
ejpam-5453	523	19	the	the	DET
ejpam-5453	523	20	case	case	NOUN
ejpam-5453	523	21	of	of	ADP
ejpam-5453	523	22	similarity	similarity	NOUN
ejpam-5453	523	23	relation	relation	NOUN
ejpam-5453	523	24	,	,	PUNCT
ejpam-5453	523	25	as	as	SCONJ
ejpam-5453	523	26	displayed	display	VERB
ejpam-5453	523	27	in	in	ADP
ejpam-5453	523	28	the	the	DET
ejpam-5453	523	29	subsequent	subsequent	ADJ
ejpam-5453	523	30	results	result	NOUN
ejpam-5453	523	31	.	.	PUNCT
ejpam-5453	524	1	theorem	theorem	VERB
ejpam-5453	524	2	4.3	4.3	NUM
ejpam-5453	524	3	.	.	PUNCT
ejpam-5453	525	1	let	let	AUX
ejpam-5453	525	2	(	(	PUNCT
ejpam-5453	525	3	v	v	NOUN
ejpam-5453	525	4	,	,	PUNCT
ejpam-5453	525	5	υ	υ	NOUN
ejpam-5453	525	6	,	,	PUNCT
ejpam-5453	525	7	π℘	π℘	NUM
ejpam-5453	525	8	)	)	PUNCT
ejpam-5453	525	9	be	be	AUX
ejpam-5453	525	10	a	a	DET
ejpam-5453	525	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	525	12	,	,	PUNCT
ejpam-5453	525	13	d	d	PRON
ejpam-5453	525	14	be	be	AUX
ejpam-5453	525	15	an	an	DET
ejpam-5453	525	16	ideal	ideal	NOUN
ejpam-5453	525	17	on	on	ADP
ejpam-5453	525	18	v	v	NOUN
ejpam-5453	525	19	,	,	PUNCT
ejpam-5453	525	20	υ	υ	PROPN
ejpam-5453	525	21	be	be	AUX
ejpam-5453	525	22	a	a	DET
ejpam-5453	525	23	similarity	similarity	NOUN
ejpam-5453	525	24	relation	relation	NOUN
ejpam-5453	525	25	,	,	PUNCT
ejpam-5453	525	26	℘	℘	PROPN
ejpam-5453	525	27	∈	∈	PROPN
ejpam-5453	525	28	{	{	PUNCT
ejpam-5453	525	29	r	r	NOUN
ejpam-5453	525	30	,	,	PUNCT
ejpam-5453	525	31	l	l	NOUN
ejpam-5453	525	32	,	,	PUNCT
ejpam-5453	525	33	i	i	PRON
ejpam-5453	525	34	,	,	PUNCT
ejpam-5453	525	35	u	u	NOUN
ejpam-5453	525	36	}	}	PUNCT
ejpam-5453	525	37	and	and	CCONJ
ejpam-5453	525	38	m	m	PROPN
ejpam-5453	525	39	⊆	⊆	NUM
ejpam-5453	525	40	v.	v.	ADP
ejpam-5453	525	41	then	then	ADV
ejpam-5453	525	42	(	(	PUNCT
ejpam-5453	525	43	i	i	NOUN
ejpam-5453	525	44	)	)	PUNCT
ejpam-5453	525	45	nd−ξ	nd−ξ	PROPN
ejpam-5453	525	46	s℘	s℘	PROPN
ejpam-5453	525	47	(	(	PUNCT
ejpam-5453	525	48	m	m	NOUN
ejpam-5453	525	49	)	)	PUNCT
ejpam-5453	526	1	⊆	⊆	NUM
ejpam-5453	526	2	nd−ξ	nd−ξ	ADJ
ejpam-5453	526	3	℘	℘	PROPN
ejpam-5453	526	4	(	(	PUNCT
ejpam-5453	526	5	m	m	NOUN
ejpam-5453	526	6	)	)	PUNCT
ejpam-5453	526	7	.	.	PUNCT
ejpam-5453	527	1	(	(	PUNCT
ejpam-5453	527	2	ii	ii	NOUN
ejpam-5453	527	3	)	)	PUNCT
ejpam-5453	527	4	n	n	PROPN
ejpam-5453	527	5	d−ξ	d−ξ	NOUN
ejpam-5453	527	6	℘	℘	PROPN
ejpam-5453	527	7	(	(	PUNCT
ejpam-5453	527	8	m	m	NOUN
ejpam-5453	527	9	)	)	PUNCT
ejpam-5453	527	10	⊆	⊆	NUM
ejpam-5453	527	11	n	n	PRON
ejpam-5453	527	12	d−ξ	d−ξ	NOUN
ejpam-5453	527	13	s℘	s℘	NOUN
ejpam-5453	527	14	(	(	PUNCT
ejpam-5453	527	15	m	m	NOUN
ejpam-5453	527	16	)	)	PUNCT
ejpam-5453	527	17	.	.	PUNCT
ejpam-5453	528	1	proof	proof	NOUN
ejpam-5453	528	2	.	.	PUNCT
ejpam-5453	529	1	by	by	ADP
ejpam-5453	529	2	proposition	proposition	NOUN
ejpam-5453	529	3	3.5	3.5	NUM
ejpam-5453	529	4	,	,	PUNCT
ejpam-5453	529	5	the	the	DET
ejpam-5453	529	6	proof	proof	NOUN
ejpam-5453	529	7	is	be	AUX
ejpam-5453	529	8	evident	evident	ADJ
ejpam-5453	529	9	.	.	PUNCT
ejpam-5453	530	1	m.	m.	PROPN
ejpam-5453	530	2	hosny	hosny	PROPN
ejpam-5453	530	3	/	/	SYM
ejpam-5453	530	4	eur	eur	PROPN
ejpam-5453	530	5	.	.	PUNCT
ejpam-5453	531	1	j.	j.	PROPN
ejpam-5453	531	2	pure	pure	PROPN
ejpam-5453	531	3	appl	appl	PROPN
ejpam-5453	531	4	.	.	PROPN
ejpam-5453	531	5	math	math	PROPN
ejpam-5453	531	6	,	,	PUNCT
ejpam-5453	531	7	17	17	NUM
ejpam-5453	531	8	(	(	PUNCT
ejpam-5453	531	9	4	4	NUM
ejpam-5453	531	10	)	)	PUNCT
ejpam-5453	531	11	(	(	PUNCT
ejpam-5453	531	12	2024	2024	NUM
ejpam-5453	531	13	)	)	PUNCT
ejpam-5453	531	14	,	,	PUNCT
ejpam-5453	531	15	2843	2843	NUM
ejpam-5453	531	16	-	-	SYM
ejpam-5453	531	17	2877	2877	NUM
ejpam-5453	531	18	2861	2861	NUM
ejpam-5453	531	19	corollary	corollary	ADJ
ejpam-5453	531	20	4.5	4.5	NUM
ejpam-5453	531	21	.	.	PUNCT
ejpam-5453	532	1	let	let	AUX
ejpam-5453	532	2	(	(	PUNCT
ejpam-5453	532	3	v	v	NOUN
ejpam-5453	532	4	,	,	PUNCT
ejpam-5453	532	5	υ	υ	NOUN
ejpam-5453	532	6	,	,	PUNCT
ejpam-5453	532	7	π℘	π℘	NUM
ejpam-5453	532	8	)	)	PUNCT
ejpam-5453	532	9	be	be	AUX
ejpam-5453	532	10	a	a	DET
ejpam-5453	532	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	532	12	,	,	PUNCT
ejpam-5453	532	13	d	d	PRON
ejpam-5453	532	14	be	be	AUX
ejpam-5453	532	15	an	an	DET
ejpam-5453	532	16	ideal	ideal	NOUN
ejpam-5453	532	17	on	on	ADP
ejpam-5453	532	18	v	v	NOUN
ejpam-5453	532	19	,	,	PUNCT
ejpam-5453	532	20	υ	υ	PROPN
ejpam-5453	532	21	be	be	AUX
ejpam-5453	532	22	a	a	DET
ejpam-5453	532	23	similarity	similarity	NOUN
ejpam-5453	532	24	relation	relation	NOUN
ejpam-5453	532	25	℘	℘	PROPN
ejpam-5453	532	26	∈	∈	PROPN
ejpam-5453	532	27	{	{	PUNCT
ejpam-5453	532	28	r	r	NOUN
ejpam-5453	532	29	,	,	PUNCT
ejpam-5453	532	30	l	l	NOUN
ejpam-5453	532	31	,	,	PUNCT
ejpam-5453	532	32	i	i	PRON
ejpam-5453	532	33	,	,	PUNCT
ejpam-5453	532	34	u	u	NOUN
ejpam-5453	532	35	}	}	PUNCT
ejpam-5453	532	36	and	and	CCONJ
ejpam-5453	532	37	m	m	PROPN
ejpam-5453	532	38	⊆	⊆	NUM
ejpam-5453	532	39	v.	v.	ADP
ejpam-5453	532	40	then	then	ADV
ejpam-5453	532	41	(	(	PUNCT
ejpam-5453	532	42	i	i	NOUN
ejpam-5453	532	43	)	)	PUNCT
ejpam-5453	532	44	bd−ξ	bd−ξ	PROPN
ejpam-5453	532	45	℘	℘	PROPN
ejpam-5453	532	46	(	(	PUNCT
ejpam-5453	532	47	m	m	NOUN
ejpam-5453	532	48	)	)	PUNCT
ejpam-5453	533	1	⊆	⊆	NUM
ejpam-5453	533	2	bd−ξ	bd−ξ	PROPN
ejpam-5453	533	3	s℘	s℘	NOUN
ejpam-5453	533	4	(	(	PUNCT
ejpam-5453	533	5	m	m	NOUN
ejpam-5453	533	6	)	)	PUNCT
ejpam-5453	533	7	.	.	PUNCT
ejpam-5453	534	1	(	(	PUNCT
ejpam-5453	534	2	ii	ii	X
ejpam-5453	534	3	)	)	PUNCT
ejpam-5453	534	4	ad−ξ	ad−ξ	PROPN
ejpam-5453	534	5	s℘	s℘	PROPN
ejpam-5453	534	6	(	(	PUNCT
ejpam-5453	534	7	m	m	NOUN
ejpam-5453	534	8	)	)	PUNCT
ejpam-5453	534	9	⩽	⩽	ADJ
ejpam-5453	534	10	ad−ξ	ad−ξ	PROPN
ejpam-5453	534	11	℘	℘	PROPN
ejpam-5453	534	12	(	(	PUNCT
ejpam-5453	534	13	m	m	NOUN
ejpam-5453	534	14	)	)	PUNCT
ejpam-5453	534	15	.	.	PUNCT
ejpam-5453	535	1	corollary	corollary	ADJ
ejpam-5453	535	2	4.6	4.6	NUM
ejpam-5453	535	3	.	.	PUNCT
ejpam-5453	536	1	let	let	AUX
ejpam-5453	536	2	(	(	PUNCT
ejpam-5453	536	3	v	v	NOUN
ejpam-5453	536	4	,	,	PUNCT
ejpam-5453	536	5	υ	υ	NOUN
ejpam-5453	536	6	,	,	PUNCT
ejpam-5453	536	7	π℘	π℘	NUM
ejpam-5453	536	8	)	)	PUNCT
ejpam-5453	536	9	be	be	AUX
ejpam-5453	536	10	a	a	DET
ejpam-5453	536	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	536	12	,	,	PUNCT
ejpam-5453	536	13	d	d	PRON
ejpam-5453	536	14	be	be	AUX
ejpam-5453	536	15	an	an	DET
ejpam-5453	536	16	ideal	ideal	NOUN
ejpam-5453	536	17	on	on	ADP
ejpam-5453	536	18	v	v	NOUN
ejpam-5453	536	19	,	,	PUNCT
ejpam-5453	536	20	υ	υ	PROPN
ejpam-5453	536	21	be	be	AUX
ejpam-5453	536	22	a	a	DET
ejpam-5453	536	23	similarity	similarity	NOUN
ejpam-5453	536	24	relation	relation	NOUN
ejpam-5453	536	25	,	,	PUNCT
ejpam-5453	536	26	℘	℘	PROPN
ejpam-5453	536	27	∈	∈	PROPN
ejpam-5453	536	28	{	{	PUNCT
ejpam-5453	536	29	r	r	NOUN
ejpam-5453	536	30	,	,	PUNCT
ejpam-5453	536	31	l	l	NOUN
ejpam-5453	536	32	,	,	PUNCT
ejpam-5453	536	33	i	i	PRON
ejpam-5453	536	34	,	,	PUNCT
ejpam-5453	536	35	u	u	NOUN
ejpam-5453	536	36	}	}	PUNCT
ejpam-5453	536	37	and	and	CCONJ
ejpam-5453	536	38	m	m	PROPN
ejpam-5453	536	39	⊆	⊆	NUM
ejpam-5453	536	40	v.	v.	ADP
ejpam-5453	536	41	then	then	ADV
ejpam-5453	536	42	(	(	PUNCT
ejpam-5453	536	43	i	i	NOUN
ejpam-5453	536	44	)	)	PUNCT
ejpam-5453	536	45	every	every	DET
ejpam-5453	536	46	d	d	PROPN
ejpam-5453	536	47	-	-	PUNCT
ejpam-5453	536	48	ξs℘-nearly	ξs℘-nearly	ADV
ejpam-5453	536	49	exact	exact	ADJ
ejpam-5453	536	50	in	in	ADP
ejpam-5453	536	51	v	v	NUM
ejpam-5453	536	52	is	be	AUX
ejpam-5453	536	53	d	d	NOUN
ejpam-5453	536	54	-	-	PUNCT
ejpam-5453	536	55	ξ℘-nearly	ξ℘-nearly	ADV
ejpam-5453	536	56	exact	exact	ADJ
ejpam-5453	536	57	.	.	PUNCT
ejpam-5453	537	1	(	(	PUNCT
ejpam-5453	537	2	ii	ii	NOUN
ejpam-5453	537	3	)	)	PUNCT
ejpam-5453	537	4	every	every	DET
ejpam-5453	537	5	d	d	PROPN
ejpam-5453	537	6	-	-	PUNCT
ejpam-5453	537	7	ξ℘-nearly	ξ℘-nearly	ADV
ejpam-5453	537	8	rough	rough	ADJ
ejpam-5453	537	9	in	in	ADP
ejpam-5453	537	10	v	v	NUM
ejpam-5453	537	11	is	be	AUX
ejpam-5453	537	12	d	d	NOUN
ejpam-5453	537	13	-	-	PUNCT
ejpam-5453	537	14	ξs℘-nearly	ξs℘-nearly	ADV
ejpam-5453	537	15	rough	rough	ADJ
ejpam-5453	537	16	.	.	PUNCT
ejpam-5453	538	1	remark	remark	PROPN
ejpam-5453	538	2	4.3	4.3	NUM
ejpam-5453	538	3	.	.	PUNCT
ejpam-5453	539	1	it	it	PRON
ejpam-5453	539	2	should	should	AUX
ejpam-5453	539	3	be	be	AUX
ejpam-5453	539	4	noted	note	VERB
ejpam-5453	539	5	that	that	SCONJ
ejpam-5453	539	6	(	(	PUNCT
ejpam-5453	539	7	i	i	NOUN
ejpam-5453	539	8	)	)	PUNCT
ejpam-5453	539	9	the	the	DET
ejpam-5453	539	10	similarity	similarity	NOUN
ejpam-5453	539	11	relation	relation	NOUN
ejpam-5453	539	12	in	in	ADP
ejpam-5453	539	13	theorems	theorems	PROPN
ejpam-5453	539	14	4.2,4.3	4.2,4.3	PROPN
ejpam-5453	539	15	,	,	PUNCT
ejpam-5453	539	16	corollaries	corollary	NOUN
ejpam-5453	539	17	4.3	4.3	NUM
ejpam-5453	539	18	,	,	PUNCT
ejpam-5453	539	19	4.44.5	4.44.5	NUM
ejpam-5453	539	20	,	,	PUNCT
ejpam-5453	539	21	4.6	4.6	NUM
ejpam-5453	539	22	is	be	AUX
ejpam-5453	539	23	not	not	PART
ejpam-5453	539	24	dispensable	dispensable	ADJ
ejpam-5453	539	25	as	as	SCONJ
ejpam-5453	539	26	shown	show	VERB
ejpam-5453	539	27	in	in	ADP
ejpam-5453	539	28	example	example	NOUN
ejpam-5453	539	29	3.2	3.2	NUM
ejpam-5453	539	30	that	that	PRON
ejpam-5453	539	31	τ℘	τ℘	NUM
ejpam-5453	539	32	and	and	CCONJ
ejpam-5453	539	33	τs℘	τs℘	NOUN
ejpam-5453	539	34	are	be	AUX
ejpam-5453	539	35	not	not	PART
ejpam-5453	539	36	comparable	comparable	ADJ
ejpam-5453	539	37	.	.	PUNCT
ejpam-5453	540	1	consequently	consequently	ADV
ejpam-5453	540	2	,	,	PUNCT
ejpam-5453	540	3	it	it	PRON
ejpam-5453	540	4	is	be	AUX
ejpam-5453	540	5	meant	mean	VERB
ejpam-5453	540	6	that	that	SCONJ
ejpam-5453	540	7	we	we	PRON
ejpam-5453	540	8	can	can	AUX
ejpam-5453	540	9	not	not	PART
ejpam-5453	540	10	apply	apply	VERB
ejpam-5453	540	11	theorems	theorem	NOUN
ejpam-5453	540	12	4.2,4.3	4.2,4.3	PROPN
ejpam-5453	540	13	,	,	PUNCT
ejpam-5453	540	14	corollaries	corollary	NOUN
ejpam-5453	540	15	4.3	4.3	NUM
ejpam-5453	540	16	,	,	PUNCT
ejpam-5453	540	17	4.44.5	4.44.5	NUM
ejpam-5453	540	18	,	,	PUNCT
ejpam-5453	540	19	4.6	4.6	NUM
ejpam-5453	540	20	.	.	PUNCT
ejpam-5453	541	1	(	(	PUNCT
ejpam-5453	541	2	ii	ii	NOUN
ejpam-5453	541	3	)	)	PUNCT
ejpam-5453	541	4	the	the	DET
ejpam-5453	541	5	boundary	boundary	ADJ
ejpam-5453	541	6	regions	region	NOUN
ejpam-5453	541	7	and	and	CCONJ
ejpam-5453	541	8	accuracy	accuracy	NOUN
ejpam-5453	541	9	by	by	ADP
ejpam-5453	541	10	the	the	DET
ejpam-5453	541	11	prior	prior	ADJ
ejpam-5453	541	12	manner	manner	NOUN
ejpam-5453	541	13	in	in	ADP
ejpam-5453	541	14	2.2	2.2	NUM
ejpam-5453	541	15	[	[	SYM
ejpam-5453	541	16	1	1	NUM
ejpam-5453	541	17	,	,	PUNCT
ejpam-5453	541	18	2	2	NUM
ejpam-5453	541	19	,	,	PUNCT
ejpam-5453	541	20	30	30	NUM
ejpam-5453	541	21	]	]	PUNCT
ejpam-5453	541	22	,	,	PUNCT
ejpam-5453	541	23	2.5	2.5	NUM
ejpam-5453	542	1	[	[	X
ejpam-5453	542	2	22	22	NUM
ejpam-5453	542	3	,	,	PUNCT
ejpam-5453	542	4	26	26	NUM
ejpam-5453	542	5	]	]	PUNCT
ejpam-5453	542	6	and	and	CCONJ
ejpam-5453	542	7	the	the	DET
ejpam-5453	542	8	present	present	ADJ
ejpam-5453	542	9	manner	manner	NOUN
ejpam-5453	542	10	in	in	ADP
ejpam-5453	542	11	4.1	4.1	NUM
ejpam-5453	542	12	are	be	AUX
ejpam-5453	542	13	calculated	calculate	VERB
ejpam-5453	542	14	in	in	ADP
ejpam-5453	542	15	tables	table	NOUN
ejpam-5453	542	16	4	4	NUM
ejpam-5453	542	17	,	,	PUNCT
ejpam-5453	542	18	5	5	NUM
ejpam-5453	542	19	by	by	ADP
ejpam-5453	542	20	using	use	VERB
ejpam-5453	542	21	example	example	NOUN
ejpam-5453	542	22	3.3	3.3	NUM
ejpam-5453	542	23	.	.	PUNCT
ejpam-5453	543	1	the	the	DET
ejpam-5453	543	2	results	result	NOUN
ejpam-5453	543	3	underscore	underscore	VERB
ejpam-5453	543	4	the	the	DET
ejpam-5453	543	5	advantages	advantage	NOUN
ejpam-5453	543	6	of	of	ADP
ejpam-5453	543	7	the	the	DET
ejpam-5453	543	8	present	present	ADJ
ejpam-5453	543	9	manner	manner	NOUN
ejpam-5453	543	10	compared	compare	VERB
ejpam-5453	543	11	to	to	ADP
ejpam-5453	543	12	2.2	2.2	NUM
ejpam-5453	543	13	[	[	SYM
ejpam-5453	543	14	1	1	NUM
ejpam-5453	543	15	,	,	PUNCT
ejpam-5453	543	16	2	2	NUM
ejpam-5453	543	17	,	,	PUNCT
ejpam-5453	543	18	30	30	NUM
ejpam-5453	543	19	]	]	PUNCT
ejpam-5453	543	20	and	and	CCONJ
ejpam-5453	543	21	the	the	DET
ejpam-5453	543	22	superiority	superiority	NOUN
ejpam-5453	543	23	of	of	ADP
ejpam-5453	543	24	the	the	DET
ejpam-5453	543	25	old	old	ADJ
ejpam-5453	543	26	ones	one	NOUN
ejpam-5453	543	27	2.5	2.5	NUM
ejpam-5453	543	28	[	[	X
ejpam-5453	543	29	22	22	NUM
ejpam-5453	543	30	,	,	PUNCT
ejpam-5453	543	31	26	26	NUM
ejpam-5453	543	32	]	]	PUNCT
ejpam-5453	543	33	compared	compare	VERB
ejpam-5453	543	34	to	to	ADP
ejpam-5453	543	35	the	the	DET
ejpam-5453	543	36	current	current	ADJ
ejpam-5453	543	37	ones	one	NOUN
ejpam-5453	543	38	in	in	ADP
ejpam-5453	543	39	the	the	DET
ejpam-5453	543	40	presence	presence	NOUN
ejpam-5453	543	41	of	of	ADP
ejpam-5453	543	42	the	the	DET
ejpam-5453	543	43	similarity	similarity	NOUN
ejpam-5453	543	44	relation	relation	NOUN
ejpam-5453	543	45	.	.	PUNCT
ejpam-5453	544	1	(	(	PUNCT
ejpam-5453	544	2	iii	iii	X
ejpam-5453	544	3	)	)	PUNCT
ejpam-5453	544	4	example	example	NOUN
ejpam-5453	544	5	3.3	3.3	NUM
ejpam-5453	544	6	shows	show	NOUN
ejpam-5453	544	7	also	also	ADV
ejpam-5453	544	8	that	that	SCONJ
ejpam-5453	544	9	τs℘	τs℘	NOUN
ejpam-5453	544	10	,	,	PUNCT
ejpam-5453	544	11	τ℘	τ℘	NUM
ejpam-5453	544	12	are	be	AUX
ejpam-5453	544	13	not	not	PART
ejpam-5453	544	14	comparable	comparable	ADJ
ejpam-5453	544	15	if	if	SCONJ
ejpam-5453	544	16	℘	℘	NUM
ejpam-5453	544	17	∈	∈	PROPN
ejpam-5453	544	18	{	{	PUNCT
ejpam-5453	544	19	<	<	X
ejpam-5453	544	20	r	r	X
ejpam-5453	544	21	>	>	PUNCT
ejpam-5453	544	22	,	,	PUNCT
ejpam-5453	544	23	<	<	X
ejpam-5453	544	24	l	l	X
ejpam-5453	544	25	>	>	X
ejpam-5453	544	26	,	,	PUNCT
ejpam-5453	544	27	<	<	X
ejpam-5453	544	28	i	i	X
ejpam-5453	544	29	>	>	X
ejpam-5453	544	30	,	,	PUNCT
ejpam-5453	544	31	<	<	X
ejpam-5453	544	32	u	u	X
ejpam-5453	544	33	>	>	X
ejpam-5453	544	34	}	}	PUNCT
ejpam-5453	544	35	.	.	PUNCT
ejpam-5453	545	1	so	so	ADV
ejpam-5453	545	2	,	,	PUNCT
ejpam-5453	545	3	theorems	theorems	PROPN
ejpam-5453	545	4	4.2,4.3	4.2,4.3	PROPN
ejpam-5453	545	5	,	,	PUNCT
ejpam-5453	545	6	corollaries	corollary	NOUN
ejpam-5453	545	7	4.3	4.3	NUM
ejpam-5453	545	8	,	,	PUNCT
ejpam-5453	545	9	4.44.5	4.44.5	NUM
ejpam-5453	545	10	,	,	PUNCT
ejpam-5453	545	11	4.6	4.6	NUM
ejpam-5453	545	12	apply	apply	VERB
ejpam-5453	545	13	only	only	ADV
ejpam-5453	545	14	for	for	ADP
ejpam-5453	545	15	℘	℘	PROPN
ejpam-5453	545	16	∈	∈	PROPN
ejpam-5453	545	17	{	{	PUNCT
ejpam-5453	545	18	r	r	NOUN
ejpam-5453	545	19	,	,	PUNCT
ejpam-5453	545	20	l	l	NOUN
ejpam-5453	545	21	,	,	PUNCT
ejpam-5453	545	22	i	i	PRON
ejpam-5453	545	23	,	,	PUNCT
ejpam-5453	545	24	u	u	NOUN
ejpam-5453	545	25	}	}	PUNCT
ejpam-5453	545	26	.	.	PUNCT
ejpam-5453	546	1	m.	m.	PROPN
ejpam-5453	546	2	hosny	hosny	PROPN
ejpam-5453	546	3	/	/	SYM
ejpam-5453	546	4	eur	eur	PROPN
ejpam-5453	546	5	.	.	PUNCT
ejpam-5453	547	1	j.	j.	PROPN
ejpam-5453	547	2	pure	pure	PROPN
ejpam-5453	547	3	appl	appl	PROPN
ejpam-5453	547	4	.	.	PROPN
ejpam-5453	547	5	math	math	PROPN
ejpam-5453	547	6	,	,	PUNCT
ejpam-5453	547	7	17	17	NUM
ejpam-5453	547	8	(	(	PUNCT
ejpam-5453	547	9	4	4	NUM
ejpam-5453	547	10	)	)	PUNCT
ejpam-5453	547	11	(	(	PUNCT
ejpam-5453	547	12	2024	2024	NUM
ejpam-5453	547	13	)	)	PUNCT
ejpam-5453	547	14	,	,	PUNCT
ejpam-5453	547	15	2843	2843	NUM
ejpam-5453	547	16	-	-	SYM
ejpam-5453	547	17	2877	2877	NUM
ejpam-5453	547	18	2862	2862	NUM
ejpam-5453	547	19	t	t	NOUN
ejpam-5453	547	20	ab	ab	PROPN
ejpam-5453	547	21	le	le	PROPN
ejpam-5453	547	22	4	4	NUM
ejpam-5453	547	23	:	:	PUNCT
ejpam-5453	547	24	t	t	NOUN
ejpam-5453	547	25	h	h	NOUN
ejpam-5453	547	26	e	e	PROPN
ejpam-5453	547	27	b	b	X
ejpam-5453	547	28	o	o	X
ejpam-5453	547	29	u	u	NOUN
ejpam-5453	547	30	n	n	PROPN
ejpam-5453	547	31	d	d	PROPN
ejpam-5453	547	32	ar	ar	PROPN
ejpam-5453	547	33	y	y	PROPN
ejpam-5453	547	34	re	re	PROPN
ejpam-5453	547	35	g	g	PROPN
ejpam-5453	547	36	io	io	PROPN
ejpam-5453	547	37	n	n	PROPN
ejpam-5453	547	38	s	s	PROPN
ejpam-5453	547	39	an	an	DET
ejpam-5453	547	40	d	d	X
ejpam-5453	547	41	ac	ac	PROPN
ejpam-5453	547	42	cu	cu	PROPN
ejpam-5453	547	43	ra	ra	PROPN
ejpam-5453	548	1	cy	cy	VERB
ejpam-5453	548	2	by	by	ADV
ejpam-5453	548	3	th	th	ADP
ejpam-5453	548	4	e	e	NOUN
ejpam-5453	548	5	pr	pr	X
ejpam-5453	548	6	io	io	PROPN
ejpam-5453	548	7	r	r	NOUN
ejpam-5453	548	8	m	m	PROPN
ejpam-5453	548	9	an	an	DET
ejpam-5453	548	10	n	n	ADV
ejpam-5453	548	11	er	er	INTJ
ejpam-5453	548	12	in	in	ADP
ejpam-5453	548	13	2	2	NUM
ejpam-5453	548	14	.2	.2	NUM
ejpam-5453	549	1	[	[	X
ejpam-5453	549	2	1	1	NUM
ejpam-5453	549	3	,	,	PUNCT
ejpam-5453	549	4	2	2	NUM
ejpam-5453	549	5	,	,	PUNCT
ejpam-5453	549	6	3	3	NUM
ejpam-5453	549	7	0	0	NUM
ejpam-5453	549	8	]	]	PUNCT
ejpam-5453	549	9	fo	fo	ADP
ejpam-5453	549	10	r	r	NOUN
ejpam-5453	549	11	℘	℘	NOUN
ejpam-5453	549	12	=	=	PUNCT
ejpam-5453	549	13	r	r	NOUN
ejpam-5453	549	14	an	an	PROPN
ejpam-5453	549	15	d	d	X
ejpam-5453	549	16	th	th	X
ejpam-5453	549	17	e	e	NOUN
ejpam-5453	549	18	pr	pr	NOUN
ejpam-5453	549	19	es	es	VERB
ejpam-5453	549	20	en	en	ADP
ejpam-5453	549	21	t	t	PROPN
ejpam-5453	549	22	m	m	PROPN
ejpam-5453	549	23	an	an	DET
ejpam-5453	549	24	n	n	ADV
ejpam-5453	549	25	er	er	INTJ
ejpam-5453	549	26	in	in	ADP
ejpam-5453	549	27	4	4	NUM
ejpam-5453	549	28	.1	.1	NUM
ejpam-5453	549	29	fo	fo	ADP
ejpam-5453	549	30	r	r	NOUN
ejpam-5453	549	31	ξ	ξ	X
ejpam-5453	549	32	=	=	SYM
ejpam-5453	549	33	{	{	PUNCT
ejpam-5453	549	34	α	α	NOUN
ejpam-5453	549	35	,	,	PUNCT
ejpam-5453	549	36	p	p	X
ejpam-5453	549	37	,	,	PUNCT
ejpam-5453	549	38	s	s	PART
ejpam-5453	549	39	,	,	PUNCT
ejpam-5453	549	40	β	β	X
ejpam-5453	549	41	,	,	PUNCT
ejpam-5453	549	42	θ	θ	PROPN
ejpam-5453	549	43	β	β	X
ejpam-5453	549	44	}	}	PUNCT
ejpam-5453	549	45	,	,	PUNCT
ejpam-5453	549	46	℘	℘	PROPN
ejpam-5453	549	47	=	=	SYM
ejpam-5453	550	1	r	r	NOUN
ejpam-5453	550	2	.	.	PUNCT
ejpam-5453	551	1	m	m	VERB
ejpam-5453	552	1	d	d	NOUN
ejpam-5453	552	2	efi	efi	PROPN
ejpam-5453	552	3	n	n	ADV
ejpam-5453	552	4	it	it	PRON
ejpam-5453	552	5	io	io	PROPN
ejpam-5453	552	6	n	n	ADV
ejpam-5453	552	7	2	2	NUM
ejpam-5453	552	8	.	.	NOUN
ejpam-5453	552	9	2	2	NUM
ejpam-5453	553	1	[	[	SYM
ejpam-5453	553	2	1	1	NUM
ejpam-5453	553	3	,	,	PUNCT
ejpam-5453	553	4	2	2	NUM
ejpam-5453	553	5	,	,	PUNCT
ejpam-5453	553	6	30	30	NUM
ejpam-5453	553	7	]	]	PUNCT
ejpam-5453	553	8	fo	fo	ADP
ejpam-5453	553	9	r	r	NOUN
ejpam-5453	553	10	℘	℘	NOUN
ejpam-5453	553	11	=	=	SYM
ejpam-5453	553	12	r	r	NOUN
ejpam-5453	553	13	d	d	PROPN
ejpam-5453	553	14	efi	efi	NOUN
ejpam-5453	553	15	n	n	ADV
ejpam-5453	553	16	it	it	PRON
ejpam-5453	553	17	io	io	PROPN
ejpam-5453	553	18	n	n	PROPN
ejpam-5453	553	19	s	s	PROPN
ejpam-5453	553	20	4	4	NUM
ejpam-5453	553	21	.	.	NOUN
ejpam-5453	553	22	1	1	NUM
ejpam-5453	553	23	fo	fo	ADP
ejpam-5453	553	24	r	r	NOUN
ejpam-5453	553	25	ξ	ξ	X
ejpam-5453	553	26	=	=	SYM
ejpam-5453	553	27	α	α	PROPN
ejpam-5453	553	28	,	,	PUNCT
ejpam-5453	553	29	℘	℘	X
ejpam-5453	553	30	=	=	SYM
ejpam-5453	553	31	r	r	NOUN
ejpam-5453	553	32	d	d	PROPN
ejpam-5453	553	33	efi	efi	NOUN
ejpam-5453	553	34	n	n	ADV
ejpam-5453	553	35	it	it	PRON
ejpam-5453	553	36	io	io	PROPN
ejpam-5453	553	37	n	n	PROPN
ejpam-5453	553	38	s	s	PROPN
ejpam-5453	553	39	4	4	NUM
ejpam-5453	553	40	.	.	NOUN
ejpam-5453	553	41	1	1	NUM
ejpam-5453	553	42	fo	fo	ADP
ejpam-5453	553	43	r	r	NOUN
ejpam-5453	553	44	ξ	ξ	X
ejpam-5453	553	45	=	=	SYM
ejpam-5453	553	46	p	p	NOUN
ejpam-5453	553	47	,	,	PUNCT
ejpam-5453	553	48	℘	℘	X
ejpam-5453	553	49	=	=	SYM
ejpam-5453	553	50	r	r	NOUN
ejpam-5453	553	51	d	d	PROPN
ejpam-5453	553	52	efi	efi	NOUN
ejpam-5453	554	1	n	n	ADV
ejpam-5453	554	2	it	it	PRON
ejpam-5453	554	3	io	io	VERB
ejpam-5453	554	4	n	n	PROPN
ejpam-5453	554	5	s	s	PART
ejpam-5453	554	6	4	4	NUM
ejpam-5453	554	7	.1	.1	NUM
ejpam-5453	554	8	fo	fo	ADP
ejpam-5453	554	9	r	r	NOUN
ejpam-5453	554	10	ξ	ξ	X
ejpam-5453	554	11	=	=	SYM
ejpam-5453	554	12	s	s	NOUN
ejpam-5453	554	13	,	,	PUNCT
ejpam-5453	554	14	℘	℘	X
ejpam-5453	554	15	=	=	SYM
ejpam-5453	554	16	r	r	NOUN
ejpam-5453	554	17	d	d	PROPN
ejpam-5453	554	18	efi	efi	NOUN
ejpam-5453	554	19	n	n	ADV
ejpam-5453	554	20	it	it	PRON
ejpam-5453	554	21	io	io	PROPN
ejpam-5453	554	22	n	n	PROPN
ejpam-5453	554	23	s	s	PROPN
ejpam-5453	554	24	4	4	NUM
ejpam-5453	554	25	.	.	NOUN
ejpam-5453	554	26	1	1	NUM
ejpam-5453	554	27	fo	fo	ADP
ejpam-5453	554	28	r	r	NOUN
ejpam-5453	554	29	ξ	ξ	X
ejpam-5453	554	30	=	=	SYM
ejpam-5453	554	31	β	β	X
ejpam-5453	554	32	,	,	PUNCT
ejpam-5453	554	33	℘	℘	X
ejpam-5453	554	34	=	=	SYM
ejpam-5453	554	35	r	r	NOUN
ejpam-5453	554	36	d	d	PROPN
ejpam-5453	554	37	efi	efi	NOUN
ejpam-5453	554	38	n	n	ADV
ejpam-5453	554	39	it	it	PRON
ejpam-5453	554	40	io	io	PROPN
ejpam-5453	554	41	n	n	PROPN
ejpam-5453	554	42	s	s	PROPN
ejpam-5453	554	43	4	4	NUM
ejpam-5453	554	44	.	.	NOUN
ejpam-5453	554	45	1	1	NUM
ejpam-5453	554	46	fo	fo	ADP
ejpam-5453	554	47	r	r	NOUN
ejpam-5453	554	48	ξ	ξ	X
ejpam-5453	554	49	=	=	SYM
ejpam-5453	554	50	θβ	θβ	NOUN
ejpam-5453	554	51	,	,	PUNCT
ejpam-5453	554	52	℘	℘	X
ejpam-5453	554	53	=	=	SYM
ejpam-5453	554	54	r	r	NOUN
ejpam-5453	554	55	b	b	NOUN
ejpam-5453	554	56	r	r	NOUN
ejpam-5453	554	57	(	(	PUNCT
ejpam-5453	554	58	m	m	PROPN
ejpam-5453	554	59	)	)	PUNCT
ejpam-5453	554	60	a	a	DET
ejpam-5453	554	61	r	r	NOUN
ejpam-5453	554	62	(	(	PUNCT
ejpam-5453	554	63	m	m	PROPN
ejpam-5453	554	64	)	)	PUNCT
ejpam-5453	554	65	b	b	PROPN
ejpam-5453	555	1	d	d	NOUN
ejpam-5453	555	2	−	−	PROPN
ejpam-5453	555	3	α	α	PROPN
ejpam-5453	555	4	s	s	NOUN
ejpam-5453	555	5	r	r	NOUN
ejpam-5453	555	6	(	(	PUNCT
ejpam-5453	555	7	m	m	PROPN
ejpam-5453	555	8	)	)	PUNCT
ejpam-5453	556	1	a	a	PRON
ejpam-5453	557	1	d	d	NOUN
ejpam-5453	557	2	−	−	X
ejpam-5453	557	3	α	α	PROPN
ejpam-5453	557	4	s	s	NOUN
ejpam-5453	557	5	r	r	NOUN
ejpam-5453	557	6	(	(	PUNCT
ejpam-5453	557	7	m	m	PROPN
ejpam-5453	557	8	)	)	PUNCT
ejpam-5453	557	9	b	b	PROPN
ejpam-5453	558	1	d	d	NOUN
ejpam-5453	558	2	−	−	PROPN
ejpam-5453	559	1	p	p	X
ejpam-5453	559	2	s	s	X
ejpam-5453	559	3	r	r	NOUN
ejpam-5453	559	4	(	(	PUNCT
ejpam-5453	559	5	m	m	PROPN
ejpam-5453	559	6	)	)	PUNCT
ejpam-5453	559	7	a	a	PRON
ejpam-5453	560	1	d	d	NOUN
ejpam-5453	560	2	−	−	PROPN
ejpam-5453	561	1	p	p	X
ejpam-5453	561	2	s	s	X
ejpam-5453	561	3	r	r	NOUN
ejpam-5453	561	4	(	(	PUNCT
ejpam-5453	561	5	m	m	PROPN
ejpam-5453	561	6	)	)	PUNCT
ejpam-5453	561	7	b	b	PROPN
ejpam-5453	562	1	d	d	NOUN
ejpam-5453	562	2	−	−	PROPN
ejpam-5453	562	3	s	s	NOUN
ejpam-5453	562	4	s	s	X
ejpam-5453	562	5	r	r	NOUN
ejpam-5453	562	6	(	(	PUNCT
ejpam-5453	562	7	m	m	PROPN
ejpam-5453	562	8	)	)	PUNCT
ejpam-5453	562	9	a	a	PRON
ejpam-5453	563	1	d	d	NOUN
ejpam-5453	563	2	−	−	X
ejpam-5453	563	3	s	s	NOUN
ejpam-5453	563	4	s	s	X
ejpam-5453	563	5	r	r	NOUN
ejpam-5453	563	6	(	(	PUNCT
ejpam-5453	563	7	m	m	PROPN
ejpam-5453	563	8	)	)	PUNCT
ejpam-5453	563	9	b	b	PROPN
ejpam-5453	564	1	d	d	NOUN
ejpam-5453	564	2	−	−	X
ejpam-5453	564	3	β	β	X
ejpam-5453	564	4	s	s	NOUN
ejpam-5453	564	5	r	r	NOUN
ejpam-5453	564	6	(	(	PUNCT
ejpam-5453	564	7	m	m	PROPN
ejpam-5453	564	8	)	)	PUNCT
ejpam-5453	565	1	a	a	DET
ejpam-5453	565	2	d	d	NOUN
ejpam-5453	565	3	−	−	X
ejpam-5453	565	4	β	β	X
ejpam-5453	565	5	s	s	NOUN
ejpam-5453	565	6	r	r	NOUN
ejpam-5453	565	7	(	(	PUNCT
ejpam-5453	565	8	m	m	PROPN
ejpam-5453	565	9	)	)	PUNCT
ejpam-5453	565	10	b	b	PROPN
ejpam-5453	566	1	d	d	NOUN
ejpam-5453	566	2	−	−	PROPN
ejpam-5453	566	3	θ	θ	X
ejpam-5453	566	4	β	β	X
ejpam-5453	566	5	s	s	X
ejpam-5453	566	6	r	r	NOUN
ejpam-5453	566	7	(	(	PUNCT
ejpam-5453	566	8	m	m	PROPN
ejpam-5453	566	9	)	)	PUNCT
ejpam-5453	566	10	a	a	DET
ejpam-5453	566	11	d	d	NOUN
ejpam-5453	566	12	−	−	PROPN
ejpam-5453	566	13	θ	θ	PROPN
ejpam-5453	566	14	β	β	X
ejpam-5453	566	15	s	s	X
ejpam-5453	566	16	r	r	NOUN
ejpam-5453	566	17	(	(	PUNCT
ejpam-5453	566	18	m	m	PROPN
ejpam-5453	566	19	)	)	PUNCT
ejpam-5453	566	20	{	{	PUNCT
ejpam-5453	566	21	l	l	NOUN
ejpam-5453	566	22	1	1	NUM
ejpam-5453	566	23	}	}	PUNCT
ejpam-5453	566	24	v	v	NOUN
ejpam-5453	566	25	0	0	NUM
ejpam-5453	566	26	{	{	PUNCT
ejpam-5453	566	27	l	l	NOUN
ejpam-5453	566	28	1	1	NUM
ejpam-5453	566	29	}	}	PUNCT
ejpam-5453	566	30	0	0	NUM
ejpam-5453	566	31	{	{	PUNCT
ejpam-5453	566	32	l	l	NOUN
ejpam-5453	566	33	1	1	NUM
ejpam-5453	566	34	}	}	PUNCT
ejpam-5453	566	35	0	0	NUM
ejpam-5453	566	36	{	{	PUNCT
ejpam-5453	566	37	l	l	NOUN
ejpam-5453	566	38	1	1	NUM
ejpam-5453	566	39	}	}	PUNCT
ejpam-5453	566	40	0	0	NUM
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ejpam-5453	566	42	l	l	NOUN
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ejpam-5453	566	451	4	4	NUM
ejpam-5453	566	452	∅	∅	NOUN
ejpam-5453	566	453	1	1	NUM
ejpam-5453	566	454	{	{	PUNCT
ejpam-5453	566	455	a	a	DET
ejpam-5453	566	456	l	l	NOUN
ejpam-5453	566	457	1	1	NUM
ejpam-5453	566	458	,	,	PUNCT
ejpam-5453	566	459	l	l	NOUN
ejpam-5453	566	460	3	3	NUM
ejpam-5453	566	461	,	,	PUNCT
ejpam-5453	566	462	l	l	NOUN
ejpam-5453	566	463	4	4	NUM
ejpam-5453	566	464	}	}	PUNCT
ejpam-5453	566	465	v	v	NOUN
ejpam-5453	566	466	0	0	NUM
ejpam-5453	566	467	{	{	PUNCT
ejpam-5453	566	468	l	l	NOUN
ejpam-5453	566	469	1	1	NUM
ejpam-5453	566	470	}	}	SYM
ejpam-5453	566	471	2	2	NUM
ejpam-5453	566	472	3	3	NUM
ejpam-5453	566	473	{	{	PUNCT
ejpam-5453	566	474	l	l	NOUN
ejpam-5453	566	475	1	1	NUM
ejpam-5453	566	476	}	}	SYM
ejpam-5453	566	477	2	2	NUM
ejpam-5453	566	478	3	3	NUM
ejpam-5453	566	479	{	{	PUNCT
ejpam-5453	566	480	l	l	NOUN
ejpam-5453	566	481	1	1	NUM
ejpam-5453	566	482	}	}	SYM
ejpam-5453	566	483	2	2	NUM
ejpam-5453	566	484	3	3	NUM
ejpam-5453	566	485	{	{	PUNCT
ejpam-5453	566	486	l	l	NOUN
ejpam-5453	566	487	1	1	NUM
ejpam-5453	566	488	}	}	SYM
ejpam-5453	566	489	2	2	NUM
ejpam-5453	566	490	3	3	NUM
ejpam-5453	566	491	∅	∅	NOUN
ejpam-5453	566	492	1	1	NUM
ejpam-5453	566	493	{	{	PUNCT
ejpam-5453	566	494	l	l	NOUN
ejpam-5453	566	495	2	2	NUM
ejpam-5453	566	496	,	,	PUNCT
ejpam-5453	566	497	l	l	NOUN
ejpam-5453	566	498	3	3	NUM
ejpam-5453	566	499	,	,	PUNCT
ejpam-5453	566	500	l	l	NOUN
ejpam-5453	566	501	4	4	NUM
ejpam-5453	566	502	}	}	PUNCT
ejpam-5453	566	503	v	v	NOUN
ejpam-5453	566	504	0	0	NUM
ejpam-5453	566	505	{	{	PUNCT
ejpam-5453	566	506	l	l	NOUN
ejpam-5453	566	507	1	1	NUM
ejpam-5453	566	508	}	}	SYM
ejpam-5453	566	509	1	1	NUM
ejpam-5453	566	510	2	2	NUM
ejpam-5453	566	511	{	{	PUNCT
ejpam-5453	566	512	l	l	NOUN
ejpam-5453	566	513	1	1	NUM
ejpam-5453	566	514	}	}	SYM
ejpam-5453	566	515	1	1	NUM
ejpam-5453	566	516	2	2	NUM
ejpam-5453	566	517	{	{	PUNCT
ejpam-5453	566	518	l	l	NOUN
ejpam-5453	566	519	1	1	NUM
ejpam-5453	566	520	}	}	SYM
ejpam-5453	566	521	1	1	NUM
ejpam-5453	566	522	2	2	NUM
ejpam-5453	566	523	{	{	PUNCT
ejpam-5453	566	524	l	l	NOUN
ejpam-5453	566	525	1	1	NUM
ejpam-5453	566	526	}	}	SYM
ejpam-5453	566	527	1	1	NUM
ejpam-5453	566	528	2	2	NUM
ejpam-5453	566	529	∅	∅	NOUN
ejpam-5453	566	530	1	1	NUM
ejpam-5453	566	531	m.	m.	NOUN
ejpam-5453	566	532	hosny	hosny	PROPN
ejpam-5453	566	533	/	/	SYM
ejpam-5453	566	534	eur	eur	PROPN
ejpam-5453	566	535	.	.	PUNCT
ejpam-5453	567	1	j.	j.	PROPN
ejpam-5453	567	2	pure	pure	PROPN
ejpam-5453	567	3	appl	appl	PROPN
ejpam-5453	567	4	.	.	PROPN
ejpam-5453	567	5	math	math	PROPN
ejpam-5453	567	6	,	,	PUNCT
ejpam-5453	567	7	17	17	NUM
ejpam-5453	567	8	(	(	PUNCT
ejpam-5453	567	9	4	4	NUM
ejpam-5453	567	10	)	)	PUNCT
ejpam-5453	567	11	(	(	PUNCT
ejpam-5453	567	12	2024	2024	NUM
ejpam-5453	567	13	)	)	PUNCT
ejpam-5453	567	14	,	,	PUNCT
ejpam-5453	567	15	2843	2843	NUM
ejpam-5453	567	16	-	-	SYM
ejpam-5453	567	17	2877	2877	NUM
ejpam-5453	567	18	2863	2863	NUM
ejpam-5453	567	19	t	t	PROPN
ejpam-5453	567	20	ab	ab	PROPN
ejpam-5453	567	21	le	le	X
ejpam-5453	567	22	5	5	NUM
ejpam-5453	567	23	:	:	PUNCT
ejpam-5453	567	24	t	t	NOUN
ejpam-5453	567	25	h	h	NOUN
ejpam-5453	568	1	e	e	PROPN
ejpam-5453	568	2	b	b	X
ejpam-5453	568	3	o	o	X
ejpam-5453	568	4	u	u	NOUN
ejpam-5453	568	5	n	n	PROPN
ejpam-5453	568	6	d	d	PROPN
ejpam-5453	568	7	ar	ar	PROPN
ejpam-5453	568	8	y	y	PROPN
ejpam-5453	568	9	re	re	PROPN
ejpam-5453	568	10	g	g	PROPN
ejpam-5453	568	11	io	io	PROPN
ejpam-5453	568	12	n	n	PROPN
ejpam-5453	568	13	s	s	PROPN
ejpam-5453	568	14	an	an	DET
ejpam-5453	568	15	d	d	X
ejpam-5453	568	16	ac	ac	PROPN
ejpam-5453	568	17	cu	cu	PROPN
ejpam-5453	568	18	ra	ra	PROPN
ejpam-5453	568	19	cy	cy	VERB
ejpam-5453	568	20	by	by	ADV
ejpam-5453	568	21	th	th	ADP
ejpam-5453	568	22	e	e	NOUN
ejpam-5453	568	23	pr	pr	X
ejpam-5453	568	24	io	io	PROPN
ejpam-5453	568	25	r	r	NOUN
ejpam-5453	568	26	m	m	PROPN
ejpam-5453	568	27	an	an	DET
ejpam-5453	568	28	n	n	ADV
ejpam-5453	568	29	er	er	INTJ
ejpam-5453	568	30	in	in	ADP
ejpam-5453	568	31	2	2	NUM
ejpam-5453	568	32	.5	.5	NUM
ejpam-5453	569	1	[	[	PUNCT
ejpam-5453	569	2	2	2	NUM
ejpam-5453	569	3	2	2	NUM
ejpam-5453	569	4	,	,	PUNCT
ejpam-5453	569	5	2	2	NUM
ejpam-5453	569	6	6	6	NUM
ejpam-5453	569	7	]	]	PUNCT
ejpam-5453	570	1	an	an	DET
ejpam-5453	570	2	d	d	X
ejpam-5453	570	3	th	th	X
ejpam-5453	570	4	e	e	NOUN
ejpam-5453	570	5	pr	pr	NOUN
ejpam-5453	570	6	es	es	VERB
ejpam-5453	570	7	en	en	ADP
ejpam-5453	570	8	t	t	PROPN
ejpam-5453	570	9	m	m	PROPN
ejpam-5453	570	10	an	an	DET
ejpam-5453	570	11	n	n	ADV
ejpam-5453	570	12	er	er	INTJ
ejpam-5453	570	13	in	in	ADP
ejpam-5453	570	14	4	4	NUM
ejpam-5453	570	15	.1	.1	NUM
ejpam-5453	570	16	fo	fo	ADP
ejpam-5453	570	17	r	r	NOUN
ejpam-5453	570	18	ξ	ξ	X
ejpam-5453	570	19	=	=	PUNCT
ejpam-5453	570	20	{	{	PUNCT
ejpam-5453	570	21	p	p	X
ejpam-5453	570	22	,	,	PUNCT
ejpam-5453	570	23	s	s	PART
ejpam-5453	570	24	,	,	PUNCT
ejpam-5453	570	25	β	β	X
ejpam-5453	570	26	}	}	PUNCT
ejpam-5453	570	27	,	,	PUNCT
ejpam-5453	570	28	℘	℘	PROPN
ejpam-5453	570	29	=	=	SYM
ejpam-5453	570	30	r	r	NOUN
ejpam-5453	570	31	.	.	PUNCT
ejpam-5453	571	1	m	m	VERB
ejpam-5453	572	1	d	d	NOUN
ejpam-5453	572	2	efi	efi	PROPN
ejpam-5453	572	3	n	n	ADV
ejpam-5453	572	4	it	it	PRON
ejpam-5453	572	5	io	io	PROPN
ejpam-5453	572	6	n	n	ADV
ejpam-5453	572	7	2	2	NUM
ejpam-5453	572	8	.	.	NOUN
ejpam-5453	572	9	5	5	NUM
ejpam-5453	573	1	[	[	SYM
ejpam-5453	573	2	2	2	NUM
ejpam-5453	573	3	2	2	NUM
ejpam-5453	573	4	,	,	PUNCT
ejpam-5453	573	5	26	26	NUM
ejpam-5453	573	6	]	]	PUNCT
ejpam-5453	573	7	fo	fo	ADP
ejpam-5453	573	8	r	r	NOUN
ejpam-5453	574	1	ξ	ξ	X
ejpam-5453	574	2	=	=	SYM
ejpam-5453	574	3	p	p	NOUN
ejpam-5453	574	4	,	,	PUNCT
ejpam-5453	574	5	℘	℘	X
ejpam-5453	574	6	=	=	SYM
ejpam-5453	574	7	r	r	NOUN
ejpam-5453	574	8	d	d	PROPN
ejpam-5453	574	9	efi	efi	NOUN
ejpam-5453	575	1	n	n	ADV
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ejpam-5453	575	9	fo	fo	ADP
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ejpam-5453	575	12	=	=	SYM
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ejpam-5453	575	14	,	,	PUNCT
ejpam-5453	575	15	℘	℘	X
ejpam-5453	575	16	=	=	SYM
ejpam-5453	575	17	r	r	NOUN
ejpam-5453	575	18	d	d	PROPN
ejpam-5453	575	19	efi	efi	NOUN
ejpam-5453	575	20	n	n	ADV
ejpam-5453	575	21	it	it	PRON
ejpam-5453	575	22	io	io	PROPN
ejpam-5453	575	23	n	n	ADV
ejpam-5453	575	24	2	2	NUM
ejpam-5453	575	25	.	.	NOUN
ejpam-5453	575	26	5	5	NUM
ejpam-5453	576	1	[	[	SYM
ejpam-5453	576	2	2	2	NUM
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ejpam-5453	576	4	,	,	PUNCT
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ejpam-5453	576	7	fo	fo	ADP
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ejpam-5453	576	9	ξ	ξ	X
ejpam-5453	576	10	=	=	SYM
ejpam-5453	576	11	s	s	NOUN
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ejpam-5453	576	13	℘	℘	X
ejpam-5453	576	14	=	=	SYM
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ejpam-5453	576	16	d	d	PROPN
ejpam-5453	576	17	efi	efi	NOUN
ejpam-5453	577	1	n	n	ADV
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ejpam-5453	577	5	s	s	PART
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ejpam-5453	577	8	fo	fo	ADP
ejpam-5453	577	9	r	r	NOUN
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ejpam-5453	577	11	=	=	SYM
ejpam-5453	577	12	s	s	NOUN
ejpam-5453	577	13	,	,	PUNCT
ejpam-5453	577	14	℘	℘	X
ejpam-5453	577	15	=	=	SYM
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ejpam-5453	577	17	d	d	PROPN
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ejpam-5453	577	22	n	n	ADV
ejpam-5453	577	23	2	2	NUM
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ejpam-5453	578	1	[	[	PUNCT
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ejpam-5453	579	1	fo	fo	ADP
ejpam-5453	579	2	r	r	NOUN
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ejpam-5453	579	4	=	=	SYM
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ejpam-5453	579	6	,	,	PUNCT
ejpam-5453	579	7	℘	℘	X
ejpam-5453	579	8	=	=	SYM
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ejpam-5453	579	10	d	d	PROPN
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ejpam-5453	580	1	n	n	ADV
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ejpam-5453	580	9	fo	fo	ADP
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ejpam-5453	580	12	=	=	SYM
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ejpam-5453	580	14	,	,	PUNCT
ejpam-5453	580	15	℘	℘	X
ejpam-5453	580	16	=	=	SYM
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ejpam-5453	580	19	d	d	NOUN
ejpam-5453	580	20	−	−	PROPN
ejpam-5453	580	21	p	p	NOUN
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ejpam-5453	580	23	(	(	PUNCT
ejpam-5453	580	24	m	m	PROPN
ejpam-5453	580	25	)	)	PUNCT
ejpam-5453	580	26	a	a	PRON
ejpam-5453	581	1	d	d	NOUN
ejpam-5453	581	2	−	−	PROPN
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ejpam-5453	581	8	b	b	PROPN
ejpam-5453	582	1	d	d	NOUN
ejpam-5453	582	2	−	−	PROPN
ejpam-5453	583	1	p	p	X
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ejpam-5453	583	3	r	r	NOUN
ejpam-5453	583	4	(	(	PUNCT
ejpam-5453	583	5	m	m	PROPN
ejpam-5453	583	6	)	)	PUNCT
ejpam-5453	583	7	a	a	PRON
ejpam-5453	584	1	d	d	NOUN
ejpam-5453	584	2	−	−	PROPN
ejpam-5453	585	1	p	p	X
ejpam-5453	585	2	s	s	X
ejpam-5453	585	3	r	r	NOUN
ejpam-5453	585	4	(	(	PUNCT
ejpam-5453	585	5	m	m	PROPN
ejpam-5453	585	6	)	)	PUNCT
ejpam-5453	585	7	b	b	PROPN
ejpam-5453	586	1	d	d	NOUN
ejpam-5453	586	2	−	−	PROPN
ejpam-5453	586	3	s	s	PART
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ejpam-5453	586	5	(	(	PUNCT
ejpam-5453	586	6	m	m	PROPN
ejpam-5453	586	7	)	)	PUNCT
ejpam-5453	586	8	a	a	PRON
ejpam-5453	587	1	d	d	NOUN
ejpam-5453	587	2	−	−	PROPN
ejpam-5453	587	3	s	s	PART
ejpam-5453	587	4	r	r	NOUN
ejpam-5453	587	5	(	(	PUNCT
ejpam-5453	587	6	m	m	PROPN
ejpam-5453	587	7	)	)	PUNCT
ejpam-5453	587	8	b	b	PROPN
ejpam-5453	588	1	d	d	NOUN
ejpam-5453	588	2	−	−	PROPN
ejpam-5453	588	3	s	s	NOUN
ejpam-5453	588	4	s	s	X
ejpam-5453	588	5	r	r	NOUN
ejpam-5453	588	6	(	(	PUNCT
ejpam-5453	588	7	m	m	PROPN
ejpam-5453	588	8	)	)	PUNCT
ejpam-5453	588	9	a	a	PRON
ejpam-5453	589	1	d	d	NOUN
ejpam-5453	589	2	−	−	X
ejpam-5453	589	3	s	s	NOUN
ejpam-5453	589	4	s	s	X
ejpam-5453	589	5	r	r	NOUN
ejpam-5453	589	6	(	(	PUNCT
ejpam-5453	589	7	m	m	PROPN
ejpam-5453	589	8	)	)	PUNCT
ejpam-5453	589	9	b	b	PROPN
ejpam-5453	590	1	d	d	NOUN
ejpam-5453	590	2	−	−	X
ejpam-5453	590	3	β	β	NOUN
ejpam-5453	590	4	r	r	NOUN
ejpam-5453	590	5	(	(	PUNCT
ejpam-5453	590	6	m	m	PROPN
ejpam-5453	590	7	)	)	PUNCT
ejpam-5453	590	8	a	a	PRON
ejpam-5453	591	1	d	d	NOUN
ejpam-5453	591	2	−	−	X
ejpam-5453	591	3	β	β	NOUN
ejpam-5453	591	4	r	r	NOUN
ejpam-5453	591	5	(	(	PUNCT
ejpam-5453	591	6	m	m	PROPN
ejpam-5453	591	7	)	)	PUNCT
ejpam-5453	591	8	b	b	PROPN
ejpam-5453	592	1	d	d	NOUN
ejpam-5453	592	2	−	−	X
ejpam-5453	592	3	β	β	X
ejpam-5453	592	4	s	s	NOUN
ejpam-5453	592	5	r	r	NOUN
ejpam-5453	592	6	(	(	PUNCT
ejpam-5453	592	7	m	m	PROPN
ejpam-5453	592	8	)	)	PUNCT
ejpam-5453	593	1	a	a	DET
ejpam-5453	593	2	d	d	NOUN
ejpam-5453	593	3	−	−	X
ejpam-5453	593	4	β	β	X
ejpam-5453	593	5	s	s	NOUN
ejpam-5453	593	6	r	r	NOUN
ejpam-5453	593	7	(	(	PUNCT
ejpam-5453	593	8	m	m	PROPN
ejpam-5453	593	9	)	)	PUNCT
ejpam-5453	593	10	{	{	PUNCT
ejpam-5453	593	11	l	l	NOUN
ejpam-5453	593	12	1	1	NUM
ejpam-5453	593	13	}	}	PUNCT
ejpam-5453	593	14	∅	∅	NOUN
ejpam-5453	593	15	1	1	NUM
ejpam-5453	593	16	{	{	PUNCT
ejpam-5453	593	17	l	l	NOUN
ejpam-5453	593	18	1	1	NUM
ejpam-5453	593	19	}	}	PUNCT
ejpam-5453	593	20	0	0	NUM
ejpam-5453	593	21	{	{	PUNCT
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ejpam-5453	593	452	l	l	NOUN
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ejpam-5453	593	454	}	}	PUNCT
ejpam-5453	593	455	∅	∅	NOUN
ejpam-5453	593	456	1	1	NUM
ejpam-5453	593	457	{	{	PUNCT
ejpam-5453	593	458	l	l	NOUN
ejpam-5453	593	459	1	1	NUM
ejpam-5453	593	460	}	}	SYM
ejpam-5453	593	461	2	2	NUM
ejpam-5453	593	462	3	3	NUM
ejpam-5453	593	463	{	{	PUNCT
ejpam-5453	593	464	l	l	NOUN
ejpam-5453	593	465	1	1	NUM
ejpam-5453	593	466	}	}	SYM
ejpam-5453	593	467	2	2	NUM
ejpam-5453	593	468	3	3	NUM
ejpam-5453	593	469	{	{	PUNCT
ejpam-5453	593	470	l	l	NOUN
ejpam-5453	593	471	1	1	NUM
ejpam-5453	593	472	}	}	SYM
ejpam-5453	593	473	2	2	NUM
ejpam-5453	593	474	3	3	NUM
ejpam-5453	593	475	∅	∅	NOUN
ejpam-5453	593	476	1	1	NUM
ejpam-5453	593	477	{	{	PUNCT
ejpam-5453	593	478	l	l	NOUN
ejpam-5453	593	479	1	1	NUM
ejpam-5453	593	480	}	}	SYM
ejpam-5453	593	481	2	2	NUM
ejpam-5453	593	482	3	3	NUM
ejpam-5453	593	483	{	{	PUNCT
ejpam-5453	593	484	l	l	NOUN
ejpam-5453	593	485	2	2	NUM
ejpam-5453	593	486	,	,	PUNCT
ejpam-5453	593	487	l	l	NOUN
ejpam-5453	593	488	3	3	NUM
ejpam-5453	593	489	,	,	PUNCT
ejpam-5453	593	490	l	l	NOUN
ejpam-5453	593	491	4	4	NUM
ejpam-5453	593	492	}	}	PUNCT
ejpam-5453	593	493	∅	∅	NOUN
ejpam-5453	593	494	1	1	NUM
ejpam-5453	593	495	{	{	PUNCT
ejpam-5453	593	496	l	l	NOUN
ejpam-5453	593	497	1	1	NUM
ejpam-5453	593	498	}	}	SYM
ejpam-5453	593	499	1	1	NUM
ejpam-5453	593	500	2	2	NUM
ejpam-5453	593	501	{	{	PUNCT
ejpam-5453	593	502	l	l	NOUN
ejpam-5453	593	503	1	1	NUM
ejpam-5453	593	504	}	}	SYM
ejpam-5453	593	505	1	1	NUM
ejpam-5453	593	506	2	2	NUM
ejpam-5453	593	507	{	{	PUNCT
ejpam-5453	593	508	l	l	NOUN
ejpam-5453	593	509	1	1	NUM
ejpam-5453	593	510	}	}	SYM
ejpam-5453	593	511	1	1	NUM
ejpam-5453	593	512	2	2	NUM
ejpam-5453	593	513	∅	∅	NOUN
ejpam-5453	593	514	1	1	NUM
ejpam-5453	593	515	{	{	PUNCT
ejpam-5453	593	516	l	l	NOUN
ejpam-5453	593	517	1	1	NUM
ejpam-5453	593	518	}	}	SYM
ejpam-5453	593	519	1	1	NUM
ejpam-5453	593	520	2	2	NUM
ejpam-5453	593	521	m.	m.	NOUN
ejpam-5453	593	522	hosny	hosny	PROPN
ejpam-5453	593	523	/	/	SYM
ejpam-5453	593	524	eur	eur	PROPN
ejpam-5453	593	525	.	.	PUNCT
ejpam-5453	594	1	j.	j.	PROPN
ejpam-5453	594	2	pure	pure	PROPN
ejpam-5453	594	3	appl	appl	PROPN
ejpam-5453	594	4	.	.	PROPN
ejpam-5453	594	5	math	math	PROPN
ejpam-5453	594	6	,	,	PUNCT
ejpam-5453	594	7	17	17	NUM
ejpam-5453	594	8	(	(	PUNCT
ejpam-5453	594	9	4	4	NUM
ejpam-5453	594	10	)	)	PUNCT
ejpam-5453	594	11	(	(	PUNCT
ejpam-5453	594	12	2024	2024	NUM
ejpam-5453	594	13	)	)	PUNCT
ejpam-5453	594	14	,	,	PUNCT
ejpam-5453	594	15	2843	2843	NUM
ejpam-5453	594	16	-	-	SYM
ejpam-5453	594	17	2877	2877	NUM
ejpam-5453	594	18	2864	2864	NUM
ejpam-5453	594	19	the	the	DET
ejpam-5453	594	20	connections	connection	NOUN
ejpam-5453	594	21	among	among	ADP
ejpam-5453	594	22	the	the	DET
ejpam-5453	594	23	d	d	NOUN
ejpam-5453	594	24	-	-	PUNCT
ejpam-5453	594	25	s℘-nearly	s℘-nearly	ADV
ejpam-5453	594	26	lower	low	ADJ
ejpam-5453	594	27	(	(	PUNCT
ejpam-5453	594	28	upper	upper	ADJ
ejpam-5453	594	29	)	)	PUNCT
ejpam-5453	594	30	approximations	approximation	NOUN
ejpam-5453	594	31	,	,	PUNCT
ejpam-5453	594	32	d	d	ADJ
ejpam-5453	594	33	-	-	PUNCT
ejpam-5453	594	34	s℘-nearly	s℘-nearly	ADV
ejpam-5453	594	35	boundary	boundary	ADJ
ejpam-5453	594	36	regions	region	NOUN
ejpam-5453	594	37	and	and	CCONJ
ejpam-5453	594	38	d	d	NOUN
ejpam-5453	594	39	-	-	PUNCT
ejpam-5453	594	40	s℘-nearly	s℘-nearly	ADV
ejpam-5453	594	41	accuracy	accuracy	NOUN
ejpam-5453	594	42	are	be	AUX
ejpam-5453	594	43	introduced	introduce	VERB
ejpam-5453	594	44	in	in	ADP
ejpam-5453	594	45	the	the	DET
ejpam-5453	594	46	following	follow	VERB
ejpam-5453	594	47	results	result	NOUN
ejpam-5453	594	48	.	.	PUNCT
ejpam-5453	595	1	proposition	proposition	NOUN
ejpam-5453	595	2	4.2	4.2	NUM
ejpam-5453	595	3	.	.	PUNCT
ejpam-5453	596	1	let	let	AUX
ejpam-5453	596	2	(	(	PUNCT
ejpam-5453	596	3	v	v	NOUN
ejpam-5453	596	4	,	,	PUNCT
ejpam-5453	596	5	υ	υ	NOUN
ejpam-5453	596	6	,	,	PUNCT
ejpam-5453	596	7	π℘	π℘	NUM
ejpam-5453	596	8	)	)	PUNCT
ejpam-5453	596	9	be	be	AUX
ejpam-5453	596	10	a	a	DET
ejpam-5453	596	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	596	12	,	,	PUNCT
ejpam-5453	596	13	d	d	PRON
ejpam-5453	596	14	be	be	AUX
ejpam-5453	596	15	an	an	DET
ejpam-5453	596	16	ideal	ideal	NOUN
ejpam-5453	596	17	on	on	ADP
ejpam-5453	596	18	v	v	NUM
ejpam-5453	596	19	and	and	CCONJ
ejpam-5453	596	20	m	m	PROPN
ejpam-5453	596	21	⊆	⊆	NUM
ejpam-5453	596	22	v.	v.	ADP
ejpam-5453	596	23	then	then	ADV
ejpam-5453	596	24	(	(	PUNCT
ejpam-5453	596	25	i	i	NOUN
ejpam-5453	596	26	)	)	PUNCT
ejpam-5453	596	27	nd−p	nd−p	PROPN
ejpam-5453	596	28	s℘	s℘	NOUN
ejpam-5453	596	29	(	(	PUNCT
ejpam-5453	596	30	m	m	NOUN
ejpam-5453	596	31	)	)	PUNCT
ejpam-5453	597	1	⊆	⊆	NUM
ejpam-5453	597	2	nd−β	nd−β	PROPN
ejpam-5453	597	3	s℘	s℘	NOUN
ejpam-5453	597	4	(	(	PUNCT
ejpam-5453	597	5	m	m	NOUN
ejpam-5453	597	6	)	)	PUNCT
ejpam-5453	597	7	⊆	⊆	NUM
ejpam-5453	597	8	nd−θβ	nd−θβ	PROPN
ejpam-5453	597	9	s℘	s℘	NOUN
ejpam-5453	597	10	(	(	PUNCT
ejpam-5453	597	11	m	m	NOUN
ejpam-5453	597	12	)	)	PUNCT
ejpam-5453	597	13	.	.	PUNCT
ejpam-5453	598	1	(	(	PUNCT
ejpam-5453	598	2	ii	ii	X
ejpam-5453	598	3	)	)	PUNCT
ejpam-5453	598	4	nd−α	nd−α	PROPN
ejpam-5453	598	5	s℘	s℘	PROPN
ejpam-5453	598	6	(	(	PUNCT
ejpam-5453	598	7	m	m	NOUN
ejpam-5453	598	8	)	)	PUNCT
ejpam-5453	598	9	⊆	⊆	NUM
ejpam-5453	598	10	nd−s	nd−s	ADJ
ejpam-5453	598	11	s℘	s℘	NOUN
ejpam-5453	598	12	(	(	PUNCT
ejpam-5453	598	13	m	m	NOUN
ejpam-5453	598	14	)	)	PUNCT
ejpam-5453	598	15	⊆	⊆	NUM
ejpam-5453	598	16	nd−β	nd−β	PROPN
ejpam-5453	598	17	s℘	s℘	NOUN
ejpam-5453	598	18	(	(	PUNCT
ejpam-5453	598	19	m	m	NOUN
ejpam-5453	598	20	)	)	PUNCT
ejpam-5453	598	21	⊆	⊆	NUM
ejpam-5453	598	22	nd−θβ	nd−θβ	PROPN
ejpam-5453	598	23	s℘	s℘	NOUN
ejpam-5453	598	24	(	(	PUNCT
ejpam-5453	598	25	m	m	NOUN
ejpam-5453	598	26	)	)	PUNCT
ejpam-5453	598	27	.	.	PUNCT
ejpam-5453	599	1	(	(	PUNCT
ejpam-5453	599	2	iii	iii	X
ejpam-5453	599	3	)	)	PUNCT
ejpam-5453	599	4	n	n	CCONJ
ejpam-5453	599	5	d−θβ	d−θβ	PROPN
ejpam-5453	599	6	s℘	s℘	NOUN
ejpam-5453	599	7	(	(	PUNCT
ejpam-5453	599	8	m	m	NOUN
ejpam-5453	599	9	)	)	PUNCT
ejpam-5453	600	1	⊆	⊆	NUM
ejpam-5453	600	2	n	n	NUM
ejpam-5453	600	3	d−β	d−β	NOUN
ejpam-5453	600	4	s℘	s℘	NOUN
ejpam-5453	600	5	(	(	PUNCT
ejpam-5453	600	6	m	m	NOUN
ejpam-5453	600	7	)	)	PUNCT
ejpam-5453	600	8	⊆	⊆	NUM
ejpam-5453	600	9	n	n	NUM
ejpam-5453	600	10	d−p	d−p	PROPN
ejpam-5453	600	11	s℘	s℘	NOUN
ejpam-5453	600	12	(	(	PUNCT
ejpam-5453	600	13	m	m	NOUN
ejpam-5453	600	14	)	)	PUNCT
ejpam-5453	600	15	.	.	PUNCT
ejpam-5453	601	1	(	(	PUNCT
ejpam-5453	601	2	iv	iv	X
ejpam-5453	601	3	)	)	PUNCT
ejpam-5453	601	4	n	n	CCONJ
ejpam-5453	601	5	d−θβ	d−θβ	PROPN
ejpam-5453	601	6	s℘	s℘	NOUN
ejpam-5453	601	7	(	(	PUNCT
ejpam-5453	601	8	m	m	NOUN
ejpam-5453	601	9	)	)	PUNCT
ejpam-5453	602	1	⊆	⊆	NUM
ejpam-5453	602	2	n	n	NUM
ejpam-5453	602	3	d−β	d−β	NOUN
ejpam-5453	602	4	s℘	s℘	NOUN
ejpam-5453	602	5	(	(	PUNCT
ejpam-5453	602	6	m	m	NOUN
ejpam-5453	602	7	)	)	PUNCT
ejpam-5453	602	8	⊆	⊆	NUM
ejpam-5453	602	9	n	n	NOUN
ejpam-5453	602	10	d−s	d−s	NOUN
ejpam-5453	602	11	s℘	s℘	PROPN
ejpam-5453	602	12	(	(	PUNCT
ejpam-5453	602	13	m	m	NOUN
ejpam-5453	602	14	)	)	PUNCT
ejpam-5453	602	15	⊆	⊆	NUM
ejpam-5453	602	16	n	n	NUM
ejpam-5453	602	17	d−α	d−α	NOUN
ejpam-5453	602	18	s℘	s℘	NOUN
ejpam-5453	602	19	(	(	PUNCT
ejpam-5453	602	20	m	m	NOUN
ejpam-5453	602	21	)	)	PUNCT
ejpam-5453	602	22	.	.	PUNCT
ejpam-5453	603	1	proof	proof	NOUN
ejpam-5453	603	2	.	.	PUNCT
ejpam-5453	604	1	proposition	proposition	NOUN
ejpam-5453	604	2	3.1	3.1	NUM
ejpam-5453	604	3	renders	render	VERB
ejpam-5453	604	4	the	the	DET
ejpam-5453	604	5	proof	proof	NOUN
ejpam-5453	604	6	clear	clear	ADJ
ejpam-5453	604	7	.	.	PUNCT
ejpam-5453	605	1	corollary	corollary	ADJ
ejpam-5453	605	2	4.7	4.7	NUM
ejpam-5453	605	3	.	.	PUNCT
ejpam-5453	606	1	let	let	AUX
ejpam-5453	606	2	(	(	PUNCT
ejpam-5453	606	3	v	v	NOUN
ejpam-5453	606	4	,	,	PUNCT
ejpam-5453	606	5	υ	υ	NOUN
ejpam-5453	606	6	,	,	PUNCT
ejpam-5453	606	7	π℘	π℘	NUM
ejpam-5453	606	8	)	)	PUNCT
ejpam-5453	606	9	be	be	AUX
ejpam-5453	606	10	a	a	DET
ejpam-5453	606	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	606	12	,	,	PUNCT
ejpam-5453	606	13	d	d	PRON
ejpam-5453	606	14	be	be	AUX
ejpam-5453	606	15	an	an	DET
ejpam-5453	606	16	ideal	ideal	NOUN
ejpam-5453	606	17	on	on	ADP
ejpam-5453	606	18	v	v	NUM
ejpam-5453	606	19	and	and	CCONJ
ejpam-5453	606	20	m	m	PROPN
ejpam-5453	606	21	⊆	⊆	NUM
ejpam-5453	606	22	v.	v.	ADP
ejpam-5453	606	23	then	then	ADV
ejpam-5453	606	24	(	(	PUNCT
ejpam-5453	606	25	i	i	NOUN
ejpam-5453	606	26	)	)	PUNCT
ejpam-5453	606	27	bd−θβ	bd−θβ	NOUN
ejpam-5453	607	1	s℘	s℘	NOUN
ejpam-5453	607	2	(	(	PUNCT
ejpam-5453	607	3	m	m	NOUN
ejpam-5453	607	4	)	)	PUNCT
ejpam-5453	607	5	⊆	⊆	NUM
ejpam-5453	607	6	bd−β	bd−β	PROPN
ejpam-5453	607	7	s℘	s℘	NOUN
ejpam-5453	607	8	(	(	PUNCT
ejpam-5453	607	9	m	m	NOUN
ejpam-5453	607	10	)	)	PUNCT
ejpam-5453	607	11	⊆	⊆	NUM
ejpam-5453	607	12	bd−p	bd−p	PROPN
ejpam-5453	607	13	s℘	s℘	NOUN
ejpam-5453	607	14	(	(	PUNCT
ejpam-5453	607	15	m	m	NOUN
ejpam-5453	607	16	)	)	PUNCT
ejpam-5453	607	17	.	.	PUNCT
ejpam-5453	608	1	(	(	PUNCT
ejpam-5453	608	2	ii	ii	NOUN
ejpam-5453	608	3	)	)	PUNCT
ejpam-5453	608	4	bd−θβ	bd−θβ	NOUN
ejpam-5453	608	5	s℘	s℘	PROPN
ejpam-5453	608	6	(	(	PUNCT
ejpam-5453	608	7	m	m	NOUN
ejpam-5453	608	8	)	)	PUNCT
ejpam-5453	608	9	⊆	⊆	NUM
ejpam-5453	608	10	bd−β	bd−β	PROPN
ejpam-5453	608	11	s℘	s℘	NOUN
ejpam-5453	608	12	(	(	PUNCT
ejpam-5453	608	13	m	m	NOUN
ejpam-5453	608	14	)	)	PUNCT
ejpam-5453	609	1	⊆	⊆	NUM
ejpam-5453	609	2	bd−s	bd−s	NOUN
ejpam-5453	609	3	s℘	s℘	NOUN
ejpam-5453	609	4	(	(	PUNCT
ejpam-5453	609	5	m	m	NOUN
ejpam-5453	609	6	)	)	PUNCT
ejpam-5453	609	7	⊆	⊆	NUM
ejpam-5453	609	8	bd−α	bd−α	NOUN
ejpam-5453	609	9	s℘	s℘	NOUN
ejpam-5453	609	10	(	(	PUNCT
ejpam-5453	609	11	m	m	NOUN
ejpam-5453	609	12	)	)	PUNCT
ejpam-5453	609	13	.	.	PUNCT
ejpam-5453	610	1	(	(	PUNCT
ejpam-5453	610	2	iii	iii	X
ejpam-5453	610	3	)	)	PUNCT
ejpam-5453	610	4	ad−p	ad−p	PROPN
ejpam-5453	610	5	s℘	s℘	PROPN
ejpam-5453	610	6	(	(	PUNCT
ejpam-5453	610	7	m	m	NOUN
ejpam-5453	610	8	)	)	PUNCT
ejpam-5453	610	9	⩽	⩽	ADJ
ejpam-5453	610	10	ad−β	ad−β	ADJ
ejpam-5453	610	11	s℘	s℘	NOUN
ejpam-5453	610	12	(	(	PUNCT
ejpam-5453	610	13	m	m	NOUN
ejpam-5453	610	14	)	)	PUNCT
ejpam-5453	610	15	⩽	⩽	ADJ
ejpam-5453	611	1	ad−θβ	ad−θβ	PROPN
ejpam-5453	611	2	s℘	s℘	PROPN
ejpam-5453	611	3	(	(	PUNCT
ejpam-5453	611	4	m	m	NOUN
ejpam-5453	611	5	)	)	PUNCT
ejpam-5453	611	6	.	.	PUNCT
ejpam-5453	612	1	(	(	PUNCT
ejpam-5453	612	2	iv	iv	X
ejpam-5453	612	3	)	)	PUNCT
ejpam-5453	612	4	ad−α	ad−α	NOUN
ejpam-5453	612	5	s℘	s℘	NOUN
ejpam-5453	612	6	(	(	PUNCT
ejpam-5453	612	7	m	m	NOUN
ejpam-5453	612	8	)	)	PUNCT
ejpam-5453	612	9	⩽	⩽	ADJ
ejpam-5453	612	10	ad−s	ad−s	PROPN
ejpam-5453	612	11	s℘	s℘	PROPN
ejpam-5453	612	12	(	(	PUNCT
ejpam-5453	612	13	m	m	NOUN
ejpam-5453	612	14	)	)	PUNCT
ejpam-5453	612	15	⩽	⩽	ADJ
ejpam-5453	612	16	ad−β	ad−β	ADJ
ejpam-5453	612	17	s℘	s℘	NOUN
ejpam-5453	612	18	(	(	PUNCT
ejpam-5453	612	19	m	m	NOUN
ejpam-5453	612	20	)	)	PUNCT
ejpam-5453	612	21	⩽	⩽	ADJ
ejpam-5453	612	22	ad−θβ	ad−θβ	PROPN
ejpam-5453	612	23	s℘	s℘	PROPN
ejpam-5453	612	24	(	(	PUNCT
ejpam-5453	612	25	m	m	NOUN
ejpam-5453	612	26	)	)	PUNCT
ejpam-5453	612	27	.	.	PUNCT
ejpam-5453	613	1	corollary	corollary	ADJ
ejpam-5453	613	2	4.8	4.8	NUM
ejpam-5453	613	3	.	.	PUNCT
ejpam-5453	614	1	let	let	AUX
ejpam-5453	614	2	(	(	PUNCT
ejpam-5453	614	3	v	v	NOUN
ejpam-5453	614	4	,	,	PUNCT
ejpam-5453	614	5	υ	υ	NOUN
ejpam-5453	614	6	,	,	PUNCT
ejpam-5453	614	7	π℘	π℘	NUM
ejpam-5453	614	8	)	)	PUNCT
ejpam-5453	614	9	be	be	AUX
ejpam-5453	614	10	a	a	DET
ejpam-5453	614	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	614	12	,	,	PUNCT
ejpam-5453	614	13	d	d	PRON
ejpam-5453	614	14	be	be	AUX
ejpam-5453	614	15	an	an	DET
ejpam-5453	614	16	ideal	ideal	NOUN
ejpam-5453	614	17	on	on	ADP
ejpam-5453	614	18	v	v	NUM
ejpam-5453	614	19	and	and	CCONJ
ejpam-5453	614	20	m	m	PROPN
ejpam-5453	614	21	⊆	⊆	NUM
ejpam-5453	614	22	v.	v.	ADP
ejpam-5453	614	23	then	then	ADV
ejpam-5453	614	24	(	(	PUNCT
ejpam-5453	614	25	i	i	NOUN
ejpam-5453	614	26	)	)	PUNCT
ejpam-5453	614	27	m	m	VERB
ejpam-5453	614	28	is	be	AUX
ejpam-5453	614	29	s℘-exact	s℘-exact	ADJ
ejpam-5453	614	30	⇒	⇒	NOUN
ejpam-5453	614	31	m	m	VERB
ejpam-5453	614	32	is	be	AUX
ejpam-5453	614	33	d	d	ADJ
ejpam-5453	614	34	-	-	PUNCT
ejpam-5453	614	35	αs℘-exact	αs℘-exact	ADJ
ejpam-5453	614	36	⇒	⇒	NOUN
ejpam-5453	614	37	m	m	VERB
ejpam-5453	614	38	d	d	ADJ
ejpam-5453	614	39	-	-	PUNCT
ejpam-5453	614	40	ss℘-exact	ss℘-exact	NOUN
ejpam-5453	614	41	⇒	⇒	NOUN
ejpam-5453	614	42	m	m	VERB
ejpam-5453	614	43	d	d	ADJ
ejpam-5453	614	44	-	-	PUNCT
ejpam-5453	614	45	βs℘-exact	βs℘-exact	ADJ
ejpam-5453	614	46	⇒	⇒	NOUN
ejpam-5453	614	47	m	m	VERB
ejpam-5453	614	48	d	d	NOUN
ejpam-5453	614	49	-	-	NOUN
ejpam-5453	614	50	θβs℘-exact	θβs℘-exact	NOUN
ejpam-5453	614	51	.	.	PUNCT
ejpam-5453	615	1	(	(	PUNCT
ejpam-5453	615	2	ii	ii	X
ejpam-5453	615	3	)	)	PUNCT
ejpam-5453	615	4	m	m	VERB
ejpam-5453	615	5	is	be	AUX
ejpam-5453	615	6	d	d	ADJ
ejpam-5453	615	7	-	-	ADJ
ejpam-5453	615	8	ps℘-exact	ps℘-exact	ADJ
ejpam-5453	615	9	⇒	⇒	NOUN
ejpam-5453	615	10	m	m	VERB
ejpam-5453	615	11	d	d	ADJ
ejpam-5453	615	12	-	-	PUNCT
ejpam-5453	615	13	βs℘-exact	βs℘-exact	ADJ
ejpam-5453	615	14	⇒	⇒	NOUN
ejpam-5453	615	15	m	m	VERB
ejpam-5453	615	16	d	d	NOUN
ejpam-5453	615	17	-	-	ADJ
ejpam-5453	615	18	θβs℘-exact	θβs℘-exact	NOUN
ejpam-5453	615	19	.	.	PUNCT
ejpam-5453	616	1	table	table	NOUN
ejpam-5453	616	2	1	1	NUM
ejpam-5453	616	3	illustrates	illustrate	VERB
ejpam-5453	616	4	that	that	SCONJ
ejpam-5453	616	5	,	,	PUNCT
ejpam-5453	616	6	in	in	ADP
ejpam-5453	616	7	general	general	ADJ
ejpam-5453	616	8	,	,	PUNCT
ejpam-5453	616	9	the	the	DET
ejpam-5453	616	10	opposite	opposite	NOUN
ejpam-5453	616	11	of	of	ADP
ejpam-5453	616	12	corollaries	corollary	NOUN
ejpam-5453	616	13	4.7	4.7	NUM
ejpam-5453	616	14	,	,	PUNCT
ejpam-5453	616	15	4.8	4.8	NUM
ejpam-5453	616	16	,	,	PUNCT
ejpam-5453	616	17	as	as	ADV
ejpam-5453	616	18	well	well	ADV
ejpam-5453	616	19	as	as	ADP
ejpam-5453	616	20	proposition	proposition	NOUN
ejpam-5453	616	21	4.2	4.2	NUM
ejpam-5453	616	22	,	,	PUNCT
ejpam-5453	616	23	does	do	AUX
ejpam-5453	616	24	not	not	PART
ejpam-5453	616	25	hold	hold	VERB
ejpam-5453	616	26	.	.	PUNCT
ejpam-5453	617	1	remark	remark	PROPN
ejpam-5453	617	2	4.4	4.4	NUM
ejpam-5453	617	3	.	.	PUNCT
ejpam-5453	618	1	it	it	PRON
ejpam-5453	618	2	is	be	AUX
ejpam-5453	618	3	evident	evident	ADJ
ejpam-5453	618	4	that	that	SCONJ
ejpam-5453	618	5	various	various	ADJ
ejpam-5453	618	6	methods	method	NOUN
ejpam-5453	618	7	exist	exist	VERB
ejpam-5453	618	8	for	for	ADP
ejpam-5453	618	9	approximating	approximate	VERB
ejpam-5453	618	10	.	.	PUNCT
ejpam-5453	619	1	among	among	ADP
ejpam-5453	619	2	these	these	PRON
ejpam-5453	619	3	,	,	PUNCT
ejpam-5453	619	4	the	the	DET
ejpam-5453	619	5	most	most	ADV
ejpam-5453	619	6	effective	effective	ADJ
ejpam-5453	619	7	approach	approach	NOUN
ejpam-5453	619	8	involves	involve	VERB
ejpam-5453	619	9	using	use	VERB
ejpam-5453	619	10	d	d	NOUN
ejpam-5453	619	11	-	-	PUNCT
ejpam-5453	619	12	θβs℘	θβs℘	ADJ
ejpam-5453	619	13	for	for	ADP
ejpam-5453	619	14	constructing	construct	VERB
ejpam-5453	619	15	set	set	ADJ
ejpam-5453	619	16	approximations	approximation	NOUN
ejpam-5453	619	17	.	.	PUNCT
ejpam-5453	620	1	this	this	DET
ejpam-5453	620	2	family	family	NOUN
ejpam-5453	620	3	reduces	reduce	VERB
ejpam-5453	620	4	or	or	CCONJ
ejpam-5453	620	5	eliminates	eliminate	VERB
ejpam-5453	620	6	boundary	boundary	ADJ
ejpam-5453	620	7	regions	region	NOUN
ejpam-5453	620	8	.	.	PUNCT
ejpam-5453	621	1	d	d	X
ejpam-5453	621	2	-	-	PUNCT
ejpam-5453	621	3	θβs℘-accuracy	θβs℘-accuracy	NOUN
ejpam-5453	621	4	shows	show	NOUN
ejpam-5453	621	5	to	to	PART
ejpam-5453	621	6	be	be	AUX
ejpam-5453	621	7	more	more	ADV
ejpam-5453	621	8	precise	precise	ADJ
ejpam-5453	621	9	compared	compare	VERB
ejpam-5453	621	10	to	to	ADP
ejpam-5453	621	11	other	other	ADJ
ejpam-5453	621	12	families	family	NOUN
ejpam-5453	621	13	.	.	PUNCT
ejpam-5453	622	1	5	5	X
ejpam-5453	622	2	.	.	PUNCT
ejpam-5453	622	3	s℘-rough	s℘-rough	ADJ
ejpam-5453	622	4	,	,	PUNCT
ejpam-5453	622	5	s℘-nearly	s℘-nearly	ADV
ejpam-5453	622	6	rough	rough	ADJ
ejpam-5453	622	7	membership	membership	NOUN
ejpam-5453	622	8	functions	function	NOUN
ejpam-5453	622	9	and	and	CCONJ
ejpam-5453	622	10	generalization	generalization	NOUN
ejpam-5453	622	11	via	via	ADP
ejpam-5453	622	12	ideals	ideal	NOUN
ejpam-5453	622	13	various	various	ADJ
ejpam-5453	622	14	types	type	NOUN
ejpam-5453	622	15	of	of	ADP
ejpam-5453	622	16	rough	rough	ADJ
ejpam-5453	622	17	membership	membership	NOUN
ejpam-5453	622	18	functions	function	NOUN
ejpam-5453	622	19	are	be	AUX
ejpam-5453	622	20	defined	define	VERB
ejpam-5453	622	21	to	to	PART
ejpam-5453	622	22	characterize	characterize	VERB
ejpam-5453	622	23	the	the	DET
ejpam-5453	622	24	approximation	approximation	NOUN
ejpam-5453	622	25	operators	operator	NOUN
ejpam-5453	622	26	.	.	PUNCT
ejpam-5453	623	1	their	their	PRON
ejpam-5453	623	2	core	core	NOUN
ejpam-5453	623	3	properties	property	NOUN
ejpam-5453	623	4	are	be	AUX
ejpam-5453	623	5	studied	study	VERB
ejpam-5453	623	6	and	and	CCONJ
ejpam-5453	623	7	the	the	DET
ejpam-5453	623	8	relationships	relationship	NOUN
ejpam-5453	623	9	among	among	ADP
ejpam-5453	623	10	them	they	PRON
ejpam-5453	623	11	are	be	AUX
ejpam-5453	623	12	given	give	VERB
ejpam-5453	623	13	.	.	PUNCT
ejpam-5453	624	1	additionally	additionally	ADV
ejpam-5453	624	2	,	,	PUNCT
ejpam-5453	624	3	it	it	PRON
ejpam-5453	624	4	is	be	AUX
ejpam-5453	624	5	proved	prove	VERB
ejpam-5453	624	6	that	that	SCONJ
ejpam-5453	624	7	they	they	PRON
ejpam-5453	624	8	extended	extend	VERB
ejpam-5453	624	9	the	the	DET
ejpam-5453	624	10	traditional	traditional	ADJ
ejpam-5453	624	11	rough	rough	ADJ
ejpam-5453	624	12	membership	membership	NOUN
ejpam-5453	624	13	functions	function	NOUN
ejpam-5453	624	14	.	.	PUNCT
ejpam-5453	625	1	m.	m.	PROPN
ejpam-5453	625	2	hosny	hosny	PROPN
ejpam-5453	625	3	/	/	SYM
ejpam-5453	625	4	eur	eur	PROPN
ejpam-5453	625	5	.	.	PUNCT
ejpam-5453	626	1	j.	j.	PROPN
ejpam-5453	626	2	pure	pure	PROPN
ejpam-5453	626	3	appl	appl	PROPN
ejpam-5453	626	4	.	.	PROPN
ejpam-5453	626	5	math	math	PROPN
ejpam-5453	626	6	,	,	PUNCT
ejpam-5453	626	7	17	17	NUM
ejpam-5453	626	8	(	(	PUNCT
ejpam-5453	626	9	4	4	NUM
ejpam-5453	626	10	)	)	PUNCT
ejpam-5453	626	11	(	(	PUNCT
ejpam-5453	626	12	2024	2024	NUM
ejpam-5453	626	13	)	)	PUNCT
ejpam-5453	626	14	,	,	PUNCT
ejpam-5453	626	15	2843	2843	NUM
ejpam-5453	626	16	-	-	SYM
ejpam-5453	626	17	2877	2877	NUM
ejpam-5453	626	18	2865	2865	NUM
ejpam-5453	626	19	5.1	5.1	NUM
ejpam-5453	626	20	.	.	PUNCT
ejpam-5453	627	1	s℘-rough	s℘-rough	ADJ
ejpam-5453	627	2	membership	membership	NOUN
ejpam-5453	627	3	functions	function	NOUN
ejpam-5453	627	4	definition	definition	NOUN
ejpam-5453	627	5	5.1	5.1	NUM
ejpam-5453	627	6	.	.	PUNCT
ejpam-5453	628	1	let	let	AUX
ejpam-5453	628	2	(	(	PUNCT
ejpam-5453	628	3	v	v	NOUN
ejpam-5453	628	4	,	,	PUNCT
ejpam-5453	628	5	υ	υ	NOUN
ejpam-5453	628	6	,	,	PUNCT
ejpam-5453	628	7	π℘	π℘	NUM
ejpam-5453	628	8	)	)	PUNCT
ejpam-5453	628	9	be	be	AUX
ejpam-5453	628	10	a	a	DET
ejpam-5453	628	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	628	12	,	,	PUNCT
ejpam-5453	628	13	t	t	PROPN
ejpam-5453	628	14	∈	∈	PROPN
ejpam-5453	628	15	v	v	NOUN
ejpam-5453	628	16	and	and	CCONJ
ejpam-5453	628	17	m	m	PROPN
ejpam-5453	628	18	⊆	⊆	NUM
ejpam-5453	628	19	v.	v.	ADP
ejpam-5453	628	20	(	(	PUNCT
ejpam-5453	628	21	i	i	NOUN
ejpam-5453	628	22	)	)	PUNCT
ejpam-5453	628	23	if	if	SCONJ
ejpam-5453	628	24	t	t	PROPN
ejpam-5453	628	25	∈	∈	PROPN
ejpam-5453	628	26	ns℘(m	ns℘(m	PROPN
ejpam-5453	628	27	)	)	PUNCT
ejpam-5453	628	28	,	,	PUNCT
ejpam-5453	628	29	then	then	ADV
ejpam-5453	628	30	t	t	PROPN
ejpam-5453	628	31	is	be	AUX
ejpam-5453	628	32	s℘-nearly	s℘-nearly	ADV
ejpam-5453	628	33	surely	surely	ADV
ejpam-5453	628	34	(	(	PUNCT
ejpam-5453	628	35	s℘-surely	s℘-surely	ADV
ejpam-5453	628	36	)	)	PUNCT
ejpam-5453	628	37	belongs	belong	VERB
ejpam-5453	628	38	to	to	ADP
ejpam-5453	628	39	m	m	PRON
ejpam-5453	628	40	,	,	PUNCT
ejpam-5453	628	41	denoted	denote	VERB
ejpam-5453	628	42	by	by	ADP
ejpam-5453	628	43	t	t	PROPN
ejpam-5453	628	44	∈s℘m	∈s℘m	PUNCT
ejpam-5453	628	45	(	(	PUNCT
ejpam-5453	628	46	ii	ii	NOUN
ejpam-5453	628	47	)	)	PUNCT
ejpam-5453	628	48	if	if	SCONJ
ejpam-5453	628	49	t	t	PROPN
ejpam-5453	628	50	∈	∈	PROPN
ejpam-5453	628	51	ns℘(m	ns℘(m	PROPN
ejpam-5453	628	52	)	)	PUNCT
ejpam-5453	628	53	,	,	PUNCT
ejpam-5453	628	54	then	then	ADV
ejpam-5453	628	55	t	t	PROPN
ejpam-5453	628	56	is	be	AUX
ejpam-5453	628	57	s℘-nearly	s℘-nearly	ADV
ejpam-5453	628	58	possibly	possibly	ADV
ejpam-5453	628	59	(	(	PUNCT
ejpam-5453	628	60	s℘-possibly	s℘-possibly	ADV
ejpam-5453	628	61	)	)	PUNCT
ejpam-5453	628	62	belongs	belong	VERB
ejpam-5453	628	63	to	to	ADP
ejpam-5453	628	64	m	m	PRON
ejpam-5453	628	65	,	,	PUNCT
ejpam-5453	628	66	denoted	denote	VERB
ejpam-5453	628	67	by	by	ADP
ejpam-5453	628	68	t	t	PROPN
ejpam-5453	628	69	∈s℘m	∈s℘m	AUX
ejpam-5453	628	70	it	it	PRON
ejpam-5453	628	71	is	be	AUX
ejpam-5453	628	72	known	know	VERB
ejpam-5453	628	73	as	as	ADP
ejpam-5453	628	74	s℘-strong	s℘-strong	NOUN
ejpam-5453	628	75	and	and	CCONJ
ejpam-5453	628	76	s℘-weak	s℘-weak	PROPN
ejpam-5453	628	77	membership	membership	NOUN
ejpam-5453	628	78	relations	relation	NOUN
ejpam-5453	628	79	.	.	PUNCT
ejpam-5453	629	1	remark	remark	VERB
ejpam-5453	629	2	5.1	5.1	NUM
ejpam-5453	629	3	.	.	PUNCT
ejpam-5453	630	1	the	the	DET
ejpam-5453	630	2	s℘-approximations	s℘-approximation	NOUN
ejpam-5453	630	3	2.8	2.8	NUM
ejpam-5453	630	4	[	[	SYM
ejpam-5453	630	5	43	43	NUM
ejpam-5453	630	6	]	]	PUNCT
ejpam-5453	630	7	are	be	AUX
ejpam-5453	630	8	redefined	redefine	VERB
ejpam-5453	630	9	for	for	ADP
ejpam-5453	630	10	any	any	DET
ejpam-5453	630	11	m	m	ADJ
ejpam-5453	630	12	⊆	⊆	NUM
ejpam-5453	630	13	v	v	NOUN
ejpam-5453	630	14	by	by	ADP
ejpam-5453	630	15	using	use	VERB
ejpam-5453	630	16	∈s℘	∈s℘	X
ejpam-5453	630	17	and	and	CCONJ
ejpam-5453	630	18	∈s℘	∈s℘	NUM
ejpam-5453	630	19	as	as	SCONJ
ejpam-5453	630	20	follows	follow	VERB
ejpam-5453	630	21	:	:	PUNCT
ejpam-5453	630	22	(	(	PUNCT
ejpam-5453	630	23	i	i	NOUN
ejpam-5453	630	24	)	)	PUNCT
ejpam-5453	630	25	ns℘(m	ns℘(m	PROPN
ejpam-5453	630	26	)	)	PUNCT
ejpam-5453	630	27	=	=	PRON
ejpam-5453	630	28	{	{	PUNCT
ejpam-5453	630	29	t	t	PROPN
ejpam-5453	630	30	∈	∈	PROPN
ejpam-5453	630	31	v	v	NOUN
ejpam-5453	630	32	:	:	PUNCT
ejpam-5453	630	33	t	t	NOUN
ejpam-5453	630	34	∈s℘m	∈s℘m	PROPN
ejpam-5453	630	35	}	}	PUNCT
ejpam-5453	630	36	.	.	PUNCT
ejpam-5453	631	1	(	(	PUNCT
ejpam-5453	631	2	ii	ii	NOUN
ejpam-5453	631	3	)	)	PUNCT
ejpam-5453	631	4	ns℘(m	ns℘(m	PROPN
ejpam-5453	631	5	)	)	PUNCT
ejpam-5453	631	6	=	=	PRON
ejpam-5453	632	1	{	{	PUNCT
ejpam-5453	632	2	t	t	PROPN
ejpam-5453	632	3	∈	∈	PROPN
ejpam-5453	632	4	v	v	NOUN
ejpam-5453	632	5	:	:	PUNCT
ejpam-5453	632	6	t	t	NOUN
ejpam-5453	632	7	∈s℘m	∈s℘m	PROPN
ejpam-5453	632	8	}	}	PUNCT
ejpam-5453	632	9	.	.	PUNCT
ejpam-5453	633	1	lemma	lemma	PROPN
ejpam-5453	633	2	5.1	5.1	NUM
ejpam-5453	633	3	.	.	PUNCT
ejpam-5453	634	1	let	let	AUX
ejpam-5453	634	2	(	(	PUNCT
ejpam-5453	634	3	v	v	NOUN
ejpam-5453	634	4	,	,	PUNCT
ejpam-5453	634	5	υ	υ	NOUN
ejpam-5453	634	6	,	,	PUNCT
ejpam-5453	634	7	π℘	π℘	NUM
ejpam-5453	634	8	)	)	PUNCT
ejpam-5453	634	9	be	be	VERB
ejpam-5453	634	10	a	a	DET
ejpam-5453	634	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	634	12	and	and	CCONJ
ejpam-5453	634	13	m	m	PROPN
ejpam-5453	634	14	⊆	⊆	NUM
ejpam-5453	634	15	v.	v.	ADP
ejpam-5453	634	16	then	then	ADV
ejpam-5453	634	17	(	(	PUNCT
ejpam-5453	634	18	i	i	NOUN
ejpam-5453	634	19	)	)	PUNCT
ejpam-5453	634	20	if	if	SCONJ
ejpam-5453	634	21	t	t	PROPN
ejpam-5453	634	22	∈s℘m	∈s℘m	PROPN
ejpam-5453	634	23	,	,	PUNCT
ejpam-5453	634	24	then	then	ADV
ejpam-5453	634	25	t	t	PROPN
ejpam-5453	634	26	∈	∈	PROPN
ejpam-5453	634	27	m.	m.	NOUN
ejpam-5453	634	28	(	(	PUNCT
ejpam-5453	634	29	ii	ii	NOUN
ejpam-5453	634	30	)	)	PUNCT
ejpam-5453	634	31	if	if	SCONJ
ejpam-5453	634	32	t	t	PROPN
ejpam-5453	634	33	∈	∈	PROPN
ejpam-5453	634	34	m	m	PROPN
ejpam-5453	634	35	,	,	PUNCT
ejpam-5453	634	36	then	then	ADV
ejpam-5453	634	37	t	t	PROPN
ejpam-5453	634	38	∈s℘m	∈s℘m	AUX
ejpam-5453	634	39	.	.	PUNCT
ejpam-5453	635	1	proof	proof	NOUN
ejpam-5453	635	2	.	.	PUNCT
ejpam-5453	636	1	straightforward	straightforward	ADJ
ejpam-5453	636	2	.	.	PUNCT
ejpam-5453	637	1	remark	remark	VERB
ejpam-5453	637	2	5.2	5.2	NUM
ejpam-5453	637	3	.	.	PUNCT
ejpam-5453	638	1	in	in	ADP
ejpam-5453	638	2	example	example	NOUN
ejpam-5453	638	3	3.3	3.3	NUM
ejpam-5453	638	4	(	(	PUNCT
ejpam-5453	638	5	i	i	NOUN
ejpam-5453	638	6	)	)	PUNCT
ejpam-5453	638	7	if	if	SCONJ
ejpam-5453	638	8	m	m	ADV
ejpam-5453	638	9	=	=	SYM
ejpam-5453	638	10	{	{	PUNCT
ejpam-5453	638	11	l3	l3	PROPN
ejpam-5453	638	12	}	}	PUNCT
ejpam-5453	638	13	,	,	PUNCT
ejpam-5453	638	14	then	then	ADV
ejpam-5453	638	15	l3	l3	PROPN
ejpam-5453	638	16	∈	∈	PROPN
ejpam-5453	638	17	m	m	PROPN
ejpam-5453	638	18	,	,	PUNCT
ejpam-5453	638	19	but	but	CCONJ
ejpam-5453	638	20	l3	l3	PROPN
ejpam-5453	638	21	̸∈sr	̸∈sr	PROPN
ejpam-5453	638	22	m.	m.	PROPN
ejpam-5453	638	23	(	(	PUNCT
ejpam-5453	638	24	ii	ii	NOUN
ejpam-5453	638	25	)	)	PUNCT
ejpam-5453	638	26	if	if	SCONJ
ejpam-5453	638	27	m	m	ADV
ejpam-5453	638	28	=	=	SYM
ejpam-5453	638	29	{	{	PUNCT
ejpam-5453	638	30	l2	l2	NOUN
ejpam-5453	638	31	}	}	PUNCT
ejpam-5453	638	32	,	,	PUNCT
ejpam-5453	638	33	then	then	ADV
ejpam-5453	638	34	l1	l1	PROPN
ejpam-5453	638	35	∈sra	∈sra	PROPN
ejpam-5453	638	36	,	,	PUNCT
ejpam-5453	638	37	but	but	CCONJ
ejpam-5453	638	38	l1	l1	PROPN
ejpam-5453	638	39	̸∈	̸∈	PROPN
ejpam-5453	638	40	m.	m.	PROPN
ejpam-5453	638	41	definition	definition	NOUN
ejpam-5453	638	42	5.2	5.2	NUM
ejpam-5453	638	43	.	.	PUNCT
ejpam-5453	639	1	let	let	AUX
ejpam-5453	639	2	(	(	PUNCT
ejpam-5453	639	3	v	v	NOUN
ejpam-5453	639	4	,	,	PUNCT
ejpam-5453	639	5	υ	υ	NOUN
ejpam-5453	639	6	,	,	PUNCT
ejpam-5453	639	7	π℘	π℘	NUM
ejpam-5453	639	8	)	)	PUNCT
ejpam-5453	639	9	be	be	AUX
ejpam-5453	639	10	a	a	DET
ejpam-5453	639	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	639	12	,	,	PUNCT
ejpam-5453	639	13	m	m	VERB
ejpam-5453	639	14	⊆	⊆	NUM
ejpam-5453	639	15	v	v	NOUN
ejpam-5453	639	16	and	and	CCONJ
ejpam-5453	639	17	t	t	NOUN
ejpam-5453	639	18	∈	∈	PROPN
ejpam-5453	639	19	v.	v.	ADP
ejpam-5453	639	20	the	the	DET
ejpam-5453	639	21	s℘-rough	s℘-rough	ADJ
ejpam-5453	639	22	membership	membership	NOUN
ejpam-5453	639	23	functions	function	NOUN
ejpam-5453	639	24	of	of	ADP
ejpam-5453	639	25	m	m	NOUN
ejpam-5453	639	26	are	be	AUX
ejpam-5453	639	27	symbolized	symbolize	VERB
ejpam-5453	639	28	by	by	ADP
ejpam-5453	639	29	ω	ω	PROPN
ejpam-5453	639	30	s℘	s℘	NOUN
ejpam-5453	639	31	m	m	NOUN
ejpam-5453	639	32	:	:	PUNCT
ejpam-5453	640	1	v	v	X
ejpam-5453	640	2	→	→	SYM
ejpam-5453	640	3	[	[	X
ejpam-5453	640	4	0	0	NUM
ejpam-5453	640	5	,	,	PUNCT
ejpam-5453	640	6	1	1	NUM
ejpam-5453	640	7	]	]	PUNCT
ejpam-5453	640	8	,	,	PUNCT
ejpam-5453	640	9	with	with	ADP
ejpam-5453	640	10	ω	ω	NUM
ejpam-5453	640	11	s℘	s℘	NOUN
ejpam-5453	640	12	m	m	PROPN
ejpam-5453	640	13	(	(	PUNCT
ejpam-5453	640	14	t	t	PROPN
ejpam-5453	640	15	)	)	PUNCT
ejpam-5453	640	16	=	=	PRON
ejpam-5453	640	17	{	{	PUNCT
ejpam-5453	640	18	1	1	NUM
ejpam-5453	640	19	if	if	SCONJ
ejpam-5453	640	20	1∈	1∈	PROPN
ejpam-5453	640	21	χ	χ	PROPN
ejpam-5453	640	22	s℘	s℘	NOUN
ejpam-5453	640	23	m	m	VERB
ejpam-5453	640	24	(	(	PUNCT
ejpam-5453	640	25	t	t	PROPN
ejpam-5453	640	26	)	)	PUNCT
ejpam-5453	640	27	.	.	PUNCT
ejpam-5453	641	1	min(χ	min(χ	PROPN
ejpam-5453	641	2	s℘	s℘	NOUN
ejpam-5453	641	3	m	m	VERB
ejpam-5453	641	4	(	(	PUNCT
ejpam-5453	641	5	t	t	PROPN
ejpam-5453	641	6	)	)	PUNCT
ejpam-5453	641	7	)	)	PUNCT
ejpam-5453	641	8	otherwise	otherwise	ADV
ejpam-5453	641	9	.	.	PUNCT
ejpam-5453	642	1	}	}	PUNCT
ejpam-5453	642	2	,	,	PUNCT
ejpam-5453	642	3	and	and	CCONJ
ejpam-5453	642	4	χ	χ	PRON
ejpam-5453	642	5	s℘	s℘	NOUN
ejpam-5453	642	6	m	m	VERB
ejpam-5453	642	7	(	(	PUNCT
ejpam-5453	642	8	t	t	PROPN
ejpam-5453	642	9	)	)	PUNCT
ejpam-5453	642	10	=	=	PUNCT
ejpam-5453	642	11	|∩s℘(t)∩m	|∩s℘(t)∩m	NOUN
ejpam-5453	642	12	|	|	ADV
ejpam-5453	642	13	|∩s℘(t)|	|∩s℘(t)|	ADJ
ejpam-5453	642	14	,	,	PUNCT
ejpam-5453	642	15	∩s℘(t	∩s℘(t	NOUN
ejpam-5453	642	16	)	)	PUNCT
ejpam-5453	642	17	̸=	̸=	PROPN
ejpam-5453	642	18	∅.	∅.	ADV
ejpam-5453	642	19	remark	remark	NOUN
ejpam-5453	642	20	5.3	5.3	NUM
ejpam-5453	642	21	.	.	PUNCT
ejpam-5453	643	1	the	the	DET
ejpam-5453	643	2	s℘-rough	s℘-rough	ADJ
ejpam-5453	643	3	membership	membership	NOUN
ejpam-5453	643	4	functions	function	NOUN
ejpam-5453	643	5	serve	serve	VERB
ejpam-5453	643	6	to	to	PART
ejpam-5453	643	7	establish	establish	VERB
ejpam-5453	643	8	the	the	DET
ejpam-5453	643	9	s℘-lower	s℘-lower	NOUN
ejpam-5453	643	10	(	(	PUNCT
ejpam-5453	643	11	upper	upper	ADJ
ejpam-5453	643	12	)	)	PUNCT
ejpam-5453	643	13	approximations	approximation	NOUN
ejpam-5453	643	14	in	in	ADP
ejpam-5453	643	15	the	the	DET
ejpam-5453	643	16	following	follow	VERB
ejpam-5453	643	17	manner	manner	NOUN
ejpam-5453	643	18	:	:	PUNCT
ejpam-5453	643	19	(	(	PUNCT
ejpam-5453	643	20	i	i	NOUN
ejpam-5453	643	21	)	)	PUNCT
ejpam-5453	643	22	ns℘(m	ns℘(m	PROPN
ejpam-5453	643	23	)	)	PUNCT
ejpam-5453	643	24	=	=	PRON
ejpam-5453	644	1	{	{	PUNCT
ejpam-5453	644	2	t	t	PROPN
ejpam-5453	644	3	∈	∈	PROPN
ejpam-5453	644	4	v	v	NOUN
ejpam-5453	644	5	:	:	PUNCT
ejpam-5453	644	6	ω	ω	NUM
ejpam-5453	644	7	s℘	s℘	NOUN
ejpam-5453	644	8	m	m	PROPN
ejpam-5453	644	9	(	(	PUNCT
ejpam-5453	644	10	t	t	PROPN
ejpam-5453	644	11	)	)	PUNCT
ejpam-5453	644	12	=	=	PUNCT
ejpam-5453	645	1	1	1	NUM
ejpam-5453	645	2	}	}	PUNCT
ejpam-5453	645	3	.	.	PUNCT
ejpam-5453	646	1	(	(	PUNCT
ejpam-5453	646	2	ii	ii	NOUN
ejpam-5453	646	3	)	)	PUNCT
ejpam-5453	646	4	ns℘(m	ns℘(m	PROPN
ejpam-5453	646	5	)	)	PUNCT
ejpam-5453	646	6	=	=	PRON
ejpam-5453	647	1	{	{	PUNCT
ejpam-5453	647	2	t	t	PROPN
ejpam-5453	647	3	∈	∈	PROPN
ejpam-5453	647	4	v	v	NOUN
ejpam-5453	647	5	:	:	PUNCT
ejpam-5453	647	6	ω	ω	NUM
ejpam-5453	647	7	s℘	s℘	NOUN
ejpam-5453	647	8	m	m	PROPN
ejpam-5453	647	9	(	(	PUNCT
ejpam-5453	647	10	t	t	PROPN
ejpam-5453	647	11	)	)	PUNCT
ejpam-5453	647	12	>	>	X
ejpam-5453	647	13	0	0	NUM
ejpam-5453	647	14	}	}	PUNCT
ejpam-5453	647	15	.	.	PUNCT
ejpam-5453	648	1	(	(	PUNCT
ejpam-5453	648	2	iii	iii	X
ejpam-5453	648	3	)	)	PUNCT
ejpam-5453	648	4	bs℘(m	bs℘(m	PROPN
ejpam-5453	648	5	)	)	PUNCT
ejpam-5453	648	6	=	=	PRON
ejpam-5453	648	7	{	{	PUNCT
ejpam-5453	648	8	t	t	PROPN
ejpam-5453	648	9	∈	∈	PROPN
ejpam-5453	648	10	v	v	NOUN
ejpam-5453	648	11	:	:	PUNCT
ejpam-5453	648	12	0	0	NUM
ejpam-5453	648	13	<	<	X
ejpam-5453	648	14	ω	ω	NUM
ejpam-5453	648	15	s℘	s℘	NOUN
ejpam-5453	648	16	m	m	PROPN
ejpam-5453	648	17	(	(	PUNCT
ejpam-5453	648	18	t	t	PROPN
ejpam-5453	648	19	)	)	PUNCT
ejpam-5453	648	20	<	<	X
ejpam-5453	648	21	1	1	NUM
ejpam-5453	648	22	}	}	PUNCT
ejpam-5453	648	23	.	.	PUNCT
ejpam-5453	649	1	proposition	proposition	NOUN
ejpam-5453	649	2	5.1	5.1	NUM
ejpam-5453	649	3	.	.	PUNCT
ejpam-5453	650	1	let	let	AUX
ejpam-5453	650	2	(	(	PUNCT
ejpam-5453	650	3	v	v	NOUN
ejpam-5453	650	4	,	,	PUNCT
ejpam-5453	650	5	υ	υ	NOUN
ejpam-5453	650	6	,	,	PUNCT
ejpam-5453	650	7	π℘	π℘	NUM
ejpam-5453	650	8	)	)	PUNCT
ejpam-5453	650	9	be	be	VERB
ejpam-5453	650	10	a	a	DET
ejpam-5453	650	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	650	12	and	and	CCONJ
ejpam-5453	650	13	m	m	PROPN
ejpam-5453	650	14	,	,	PUNCT
ejpam-5453	650	15	n	n	PROPN
ejpam-5453	650	16	⊆	⊆	NUM
ejpam-5453	650	17	v.	v.	ADP
ejpam-5453	650	18	then	then	ADV
ejpam-5453	650	19	,	,	PUNCT
ejpam-5453	650	20	m.	m.	PROPN
ejpam-5453	650	21	hosny	hosny	PROPN
ejpam-5453	650	22	/	/	SYM
ejpam-5453	650	23	eur	eur	PROPN
ejpam-5453	650	24	.	.	PUNCT
ejpam-5453	651	1	j.	j.	PROPN
ejpam-5453	651	2	pure	pure	PROPN
ejpam-5453	651	3	appl	appl	PROPN
ejpam-5453	651	4	.	.	PROPN
ejpam-5453	651	5	math	math	PROPN
ejpam-5453	651	6	,	,	PUNCT
ejpam-5453	651	7	17	17	NUM
ejpam-5453	651	8	(	(	PUNCT
ejpam-5453	651	9	4	4	NUM
ejpam-5453	651	10	)	)	PUNCT
ejpam-5453	651	11	(	(	PUNCT
ejpam-5453	651	12	2024	2024	NUM
ejpam-5453	651	13	)	)	PUNCT
ejpam-5453	651	14	,	,	PUNCT
ejpam-5453	651	15	2843	2843	NUM
ejpam-5453	651	16	-	-	SYM
ejpam-5453	651	17	2877	2877	NUM
ejpam-5453	651	18	2866	2866	NUM
ejpam-5453	651	19	(	(	PUNCT
ejpam-5453	651	20	i	i	NOUN
ejpam-5453	651	21	)	)	PUNCT
ejpam-5453	651	22	if	if	SCONJ
ejpam-5453	651	23	ω	ω	NUM
ejpam-5453	651	24	s℘	s℘	NOUN
ejpam-5453	651	25	m	m	PROPN
ejpam-5453	651	26	(	(	PUNCT
ejpam-5453	651	27	t	t	PROPN
ejpam-5453	651	28	)	)	PUNCT
ejpam-5453	651	29	=	=	SYM
ejpam-5453	651	30	1	1	NUM
ejpam-5453	651	31	⇔	⇔	X
ejpam-5453	651	32	t∈s℘m	t∈s℘m	NOUN
ejpam-5453	651	33	.	.	PUNCT
ejpam-5453	651	34	(	(	PUNCT
ejpam-5453	651	35	ii	ii	NOUN
ejpam-5453	651	36	)	)	PUNCT
ejpam-5453	651	37	if	if	SCONJ
ejpam-5453	651	38	ω	ω	NUM
ejpam-5453	651	39	s℘	s℘	NOUN
ejpam-5453	651	40	m	m	PROPN
ejpam-5453	651	41	(	(	PUNCT
ejpam-5453	651	42	t	t	PROPN
ejpam-5453	651	43	)	)	PUNCT
ejpam-5453	651	44	=	=	SYM
ejpam-5453	651	45	0	0	NUM
ejpam-5453	651	46	⇔	⇔	PROPN
ejpam-5453	651	47	t	t	PROPN
ejpam-5453	651	48	∈	∈	PROPN
ejpam-5453	651	49	v	v	ADP
ejpam-5453	651	50	−ns℘(m	−ns℘(m	PROPN
ejpam-5453	651	51	)	)	PUNCT
ejpam-5453	651	52	.	.	PUNCT
ejpam-5453	652	1	(	(	PUNCT
ejpam-5453	652	2	iii	iii	X
ejpam-5453	652	3	)	)	PUNCT
ejpam-5453	652	4	if	if	SCONJ
ejpam-5453	652	5	0	0	NUM
ejpam-5453	652	6	<	<	X
ejpam-5453	652	7	ω	ω	NUM
ejpam-5453	652	8	s℘	s℘	NOUN
ejpam-5453	652	9	m	m	PROPN
ejpam-5453	652	10	(	(	PUNCT
ejpam-5453	652	11	t	t	PROPN
ejpam-5453	652	12	)	)	PUNCT
ejpam-5453	652	13	<	<	X
ejpam-5453	652	14	1	1	NUM
ejpam-5453	652	15	⇔	⇔	PROPN
ejpam-5453	652	16	t	t	PROPN
ejpam-5453	652	17	∈	∈	PROPN
ejpam-5453	652	18	bs℘(m	bs℘(m	PROPN
ejpam-5453	652	19	)	)	PUNCT
ejpam-5453	652	20	.	.	PUNCT
ejpam-5453	653	1	(	(	PUNCT
ejpam-5453	653	2	iv	iv	X
ejpam-5453	653	3	)	)	PUNCT
ejpam-5453	653	4	if	if	SCONJ
ejpam-5453	653	5	ω	ω	NUM
ejpam-5453	653	6	s℘	s℘	NOUN
ejpam-5453	653	7	m	m	VERB
ejpam-5453	653	8	′	′	NUM
ejpam-5453	653	9	(	(	PUNCT
ejpam-5453	653	10	t	t	NOUN
ejpam-5453	653	11	)	)	PUNCT
ejpam-5453	653	12	=	=	SYM
ejpam-5453	653	13	1−	1−	NUM
ejpam-5453	653	14	ω	ω	NUM
ejpam-5453	653	15	s℘	s℘	NOUN
ejpam-5453	653	16	m	m	PROPN
ejpam-5453	653	17	(	(	PUNCT
ejpam-5453	653	18	t	t	PROPN
ejpam-5453	653	19	)	)	PUNCT
ejpam-5453	653	20	,	,	PUNCT
ejpam-5453	653	21	∀	∀	X
ejpam-5453	653	22	t	t	NOUN
ejpam-5453	653	23	∈	∈	PROPN
ejpam-5453	653	24	v.	v.	PROPN
ejpam-5453	653	25	(	(	PUNCT
ejpam-5453	653	26	v	v	NOUN
ejpam-5453	653	27	)	)	PUNCT
ejpam-5453	653	28	if	if	SCONJ
ejpam-5453	653	29	ω	ω	NUM
ejpam-5453	653	30	s℘	s℘	NOUN
ejpam-5453	653	31	m∪n	m∪n	NOUN
ejpam-5453	653	32	(	(	PUNCT
ejpam-5453	653	33	t	t	NOUN
ejpam-5453	653	34	)	)	PUNCT
ejpam-5453	653	35	≥	≥	NOUN
ejpam-5453	653	36	max(ω	max(ω	PROPN
ejpam-5453	653	37	s℘	s℘	NOUN
ejpam-5453	653	38	m	m	VERB
ejpam-5453	653	39	(	(	PUNCT
ejpam-5453	653	40	t	t	PROPN
ejpam-5453	653	41	)	)	PUNCT
ejpam-5453	653	42	,	,	PUNCT
ejpam-5453	653	43	ω	ω	NUM
ejpam-5453	653	44	s℘	s℘	NOUN
ejpam-5453	653	45	n	n	CCONJ
ejpam-5453	653	46	(	(	PUNCT
ejpam-5453	653	47	t	t	PROPN
ejpam-5453	653	48	)	)	PUNCT
ejpam-5453	653	49	)	)	PUNCT
ejpam-5453	653	50	,	,	PUNCT
ejpam-5453	653	51	∀	∀	X
ejpam-5453	653	52	t	t	NOUN
ejpam-5453	653	53	∈	∈	PROPN
ejpam-5453	653	54	v.	v.	PROPN
ejpam-5453	653	55	(	(	PUNCT
ejpam-5453	653	56	vi	vi	PROPN
ejpam-5453	653	57	)	)	PUNCT
ejpam-5453	654	1	if	if	SCONJ
ejpam-5453	654	2	ω	ω	NUM
ejpam-5453	654	3	s℘	s℘	PROPN
ejpam-5453	654	4	m∩n	m∩n	PROPN
ejpam-5453	654	5	(	(	PUNCT
ejpam-5453	654	6	t	t	PROPN
ejpam-5453	654	7	)	)	PUNCT
ejpam-5453	654	8	≤	≤	NOUN
ejpam-5453	654	9	min(ω	min(ω	NUM
ejpam-5453	654	10	s℘	s℘	NOUN
ejpam-5453	654	11	m	m	PROPN
ejpam-5453	654	12	(	(	PUNCT
ejpam-5453	654	13	t	t	PROPN
ejpam-5453	654	14	)	)	PUNCT
ejpam-5453	654	15	,	,	PUNCT
ejpam-5453	654	16	ω	ω	NUM
ejpam-5453	654	17	s℘	s℘	NOUN
ejpam-5453	654	18	n	n	CCONJ
ejpam-5453	654	19	(	(	PUNCT
ejpam-5453	654	20	t	t	PROPN
ejpam-5453	654	21	)	)	PUNCT
ejpam-5453	654	22	)	)	PUNCT
ejpam-5453	654	23	,	,	PUNCT
ejpam-5453	654	24	∀	∀	X
ejpam-5453	654	25	t	t	NOUN
ejpam-5453	654	26	∈	∈	PROPN
ejpam-5453	654	27	v.	v.	ADP
ejpam-5453	654	28	proof	proof	NOUN
ejpam-5453	654	29	.	.	PUNCT
ejpam-5453	655	1	we	we	PRON
ejpam-5453	655	2	prove	prove	VERB
ejpam-5453	655	3	(	(	PUNCT
ejpam-5453	655	4	1	1	NUM
ejpam-5453	655	5	)	)	PUNCT
ejpam-5453	655	6	and	and	CCONJ
ejpam-5453	655	7	handle	handle	VERB
ejpam-5453	655	8	the	the	DET
ejpam-5453	655	9	others	other	NOUN
ejpam-5453	655	10	in	in	ADP
ejpam-5453	655	11	a	a	DET
ejpam-5453	655	12	similar	similar	ADJ
ejpam-5453	655	13	manner	manner	NOUN
ejpam-5453	655	14	.	.	PUNCT
ejpam-5453	655	15	t∈s℘m	t∈s℘m	X
ejpam-5453	655	16	⇔	⇔	PROPN
ejpam-5453	655	17	t	t	PROPN
ejpam-5453	655	18	∈	∈	PROPN
ejpam-5453	655	19	ns℘(m	ns℘(m	PROPN
ejpam-5453	655	20	)	)	PUNCT
ejpam-5453	655	21	.	.	PUNCT
ejpam-5453	656	1	since	since	SCONJ
ejpam-5453	656	2	ns℘(m	ns℘(m	NOUN
ejpam-5453	656	3	)	)	PUNCT
ejpam-5453	656	4	is	be	AUX
ejpam-5453	656	5	s℘-open	s℘-open	ADJ
ejpam-5453	656	6	contained	contain	VERB
ejpam-5453	656	7	in	in	ADP
ejpam-5453	656	8	m	m	PROPN
ejpam-5453	656	9	,	,	PUNCT
ejpam-5453	656	10	thus	thus	ADV
ejpam-5453	656	11	|ns℘	|ns℘	PROPN
ejpam-5453	656	12	(	(	PUNCT
ejpam-5453	656	13	m)∩a|	m)∩a|	NOUN
ejpam-5453	656	14	|ns℘	|ns℘	PROPN
ejpam-5453	656	15	(	(	PUNCT
ejpam-5453	656	16	m)|	m)|	ADJ
ejpam-5453	656	17	=	=	SYM
ejpam-5453	656	18	|ns℘	|ns℘	PROPN
ejpam-5453	656	19	(	(	PUNCT
ejpam-5453	656	20	m)|	m)|	PROPN
ejpam-5453	656	21	|ns℘	|ns℘	PROPN
ejpam-5453	656	22	(	(	PUNCT
ejpam-5453	656	23	m)|	m)|	NOUN
ejpam-5453	656	24	=	=	ADJ
ejpam-5453	656	25	1	1	NUM
ejpam-5453	656	26	.	.	PUNCT
ejpam-5453	657	1	then	then	ADV
ejpam-5453	657	2	,	,	PUNCT
ejpam-5453	657	3	1	1	NUM
ejpam-5453	657	4	∈	∈	NOUN
ejpam-5453	657	5	χ	χ	PRON
ejpam-5453	657	6	s℘	s℘	NOUN
ejpam-5453	657	7	m	m	VERB
ejpam-5453	657	8	(	(	PUNCT
ejpam-5453	657	9	t	t	PROPN
ejpam-5453	657	10	)	)	PUNCT
ejpam-5453	658	1	so	so	ADV
ejpam-5453	658	2	ω	ω	NUM
ejpam-5453	658	3	s℘	s℘	NOUN
ejpam-5453	658	4	m	m	PROPN
ejpam-5453	658	5	(	(	PUNCT
ejpam-5453	658	6	t	t	PROPN
ejpam-5453	658	7	)	)	PUNCT
ejpam-5453	658	8	=	=	NOUN
ejpam-5453	658	9	1	1	NUM
ejpam-5453	658	10	.	.	X
ejpam-5453	658	11	5.2	5.2	NUM
ejpam-5453	658	12	.	.	PUNCT
ejpam-5453	659	1	s℘-nearly	s℘-nearly	ADV
ejpam-5453	659	2	rough	rough	ADJ
ejpam-5453	659	3	membership	membership	NOUN
ejpam-5453	659	4	functions	function	NOUN
ejpam-5453	659	5	definition	definition	NOUN
ejpam-5453	659	6	5.3	5.3	NUM
ejpam-5453	659	7	.	.	PUNCT
ejpam-5453	660	1	let	let	AUX
ejpam-5453	660	2	(	(	PUNCT
ejpam-5453	660	3	v	v	NOUN
ejpam-5453	660	4	,	,	PUNCT
ejpam-5453	660	5	υ	υ	NOUN
ejpam-5453	660	6	,	,	PUNCT
ejpam-5453	660	7	π℘	π℘	NUM
ejpam-5453	660	8	)	)	PUNCT
ejpam-5453	660	9	be	be	AUX
ejpam-5453	660	10	a	a	DET
ejpam-5453	660	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	660	12	,	,	PUNCT
ejpam-5453	660	13	t	t	PROPN
ejpam-5453	660	14	∈	∈	PROPN
ejpam-5453	660	15	v	v	NOUN
ejpam-5453	660	16	and	and	CCONJ
ejpam-5453	660	17	m	m	PROPN
ejpam-5453	660	18	⊆	⊆	NUM
ejpam-5453	660	19	v.	v.	ADP
ejpam-5453	660	20	(	(	PUNCT
ejpam-5453	660	21	i	i	NOUN
ejpam-5453	660	22	)	)	PUNCT
ejpam-5453	660	23	if	if	SCONJ
ejpam-5453	660	24	t	t	PROPN
ejpam-5453	660	25	∈	∈	PROPN
ejpam-5453	660	26	nξ	nξ	ADP
ejpam-5453	660	27	s℘(m	s℘(m	PROPN
ejpam-5453	660	28	)	)	PUNCT
ejpam-5453	660	29	,	,	PUNCT
ejpam-5453	660	30	then	then	ADV
ejpam-5453	660	31	t	t	PROPN
ejpam-5453	660	32	is	be	AUX
ejpam-5453	660	33	s℘-nearly	s℘-nearly	ADV
ejpam-5453	660	34	surely	surely	ADV
ejpam-5453	660	35	(	(	PUNCT
ejpam-5453	660	36	ξs℘-surely	ξs℘-surely	ADV
ejpam-5453	660	37	)	)	PUNCT
ejpam-5453	660	38	belongs	belong	VERB
ejpam-5453	660	39	to	to	ADP
ejpam-5453	660	40	m	m	PRON
ejpam-5453	660	41	,	,	PUNCT
ejpam-5453	660	42	denoted	denote	VERB
ejpam-5453	660	43	by	by	ADP
ejpam-5453	660	44	t	t	PROPN
ejpam-5453	660	45	∈ξ	∈ξ	PROPN
ejpam-5453	660	46	s℘m	s℘m	NOUN
ejpam-5453	660	47	(	(	PUNCT
ejpam-5453	660	48	ii	ii	NOUN
ejpam-5453	660	49	)	)	PUNCT
ejpam-5453	660	50	if	if	SCONJ
ejpam-5453	660	51	t	t	PROPN
ejpam-5453	660	52	∈	∈	PROPN
ejpam-5453	660	53	n	n	X
ejpam-5453	660	54	ξ	ξ	PROPN
ejpam-5453	660	55	s℘(m	s℘(m	PROPN
ejpam-5453	660	56	)	)	PUNCT
ejpam-5453	660	57	,	,	PUNCT
ejpam-5453	660	58	then	then	ADV
ejpam-5453	660	59	t	t	PROPN
ejpam-5453	660	60	is	be	AUX
ejpam-5453	660	61	s℘-nearly	s℘-nearly	ADV
ejpam-5453	660	62	possibly	possibly	ADV
ejpam-5453	660	63	(	(	PUNCT
ejpam-5453	660	64	ξs℘-possibly	ξs℘-possibly	ADV
ejpam-5453	660	65	)	)	PUNCT
ejpam-5453	660	66	belongs	belong	VERB
ejpam-5453	660	67	to	to	ADP
ejpam-5453	660	68	m	m	PRON
ejpam-5453	660	69	,	,	PUNCT
ejpam-5453	660	70	denoted	denote	VERB
ejpam-5453	660	71	by	by	ADP
ejpam-5453	660	72	t	t	PROPN
ejpam-5453	660	73	∈ξ	∈ξ	PROPN
ejpam-5453	660	74	s℘m	s℘m	NOUN
ejpam-5453	660	75	it	it	PRON
ejpam-5453	660	76	is	be	AUX
ejpam-5453	660	77	known	know	VERB
ejpam-5453	660	78	as	as	ADP
ejpam-5453	660	79	s℘-nearly	s℘-nearly	ADV
ejpam-5453	660	80	strong	strong	ADJ
ejpam-5453	660	81	and	and	CCONJ
ejpam-5453	660	82	s℘-nearly	s℘-nearly	ADV
ejpam-5453	660	83	weak	weak	ADJ
ejpam-5453	660	84	membership	membership	NOUN
ejpam-5453	660	85	relations	relation	NOUN
ejpam-5453	660	86	.	.	PUNCT
ejpam-5453	661	1	remark	remark	PROPN
ejpam-5453	661	2	5.4	5.4	NUM
ejpam-5453	661	3	.	.	PUNCT
ejpam-5453	662	1	the	the	DET
ejpam-5453	662	2	s℘-nearly	s℘-nearly	ADJ
ejpam-5453	662	3	approximations	approximation	NOUN
ejpam-5453	662	4	are	be	AUX
ejpam-5453	662	5	redefined	redefine	VERB
ejpam-5453	662	6	for	for	ADP
ejpam-5453	662	7	any	any	DET
ejpam-5453	662	8	m	m	ADJ
ejpam-5453	662	9	⊆	⊆	NUM
ejpam-5453	662	10	v	v	NOUN
ejpam-5453	662	11	by	by	ADP
ejpam-5453	662	12	using	use	VERB
ejpam-5453	662	13	∈ξ	∈ξ	NUM
ejpam-5453	662	14	s℘	s℘	NOUN
ejpam-5453	662	15	and	and	CCONJ
ejpam-5453	662	16	∈ξ	∈ξ	VERB
ejpam-5453	662	17	s℘	s℘	NOUN
ejpam-5453	662	18	as	as	SCONJ
ejpam-5453	662	19	follows	follow	VERB
ejpam-5453	662	20	:	:	PUNCT
ejpam-5453	662	21	(	(	PUNCT
ejpam-5453	662	22	i	i	NOUN
ejpam-5453	662	23	)	)	PUNCT
ejpam-5453	662	24	nξ	nξ	ADP
ejpam-5453	662	25	s℘(m	s℘(m	PROPN
ejpam-5453	662	26	)	)	PUNCT
ejpam-5453	662	27	=	=	PRON
ejpam-5453	663	1	{	{	PUNCT
ejpam-5453	663	2	t	t	PROPN
ejpam-5453	663	3	∈	∈	PROPN
ejpam-5453	663	4	v	v	NOUN
ejpam-5453	663	5	:	:	PUNCT
ejpam-5453	663	6	t	t	PROPN
ejpam-5453	663	7	∈ξ	∈ξ	PROPN
ejpam-5453	663	8	s℘m	s℘m	NOUN
ejpam-5453	663	9	}	}	PUNCT
ejpam-5453	663	10	.	.	PUNCT
ejpam-5453	664	1	(	(	PUNCT
ejpam-5453	664	2	ii	ii	NOUN
ejpam-5453	664	3	)	)	PUNCT
ejpam-5453	664	4	n	n	PRON
ejpam-5453	664	5	ξ	ξ	PROPN
ejpam-5453	664	6	s℘(m	s℘(m	PROPN
ejpam-5453	664	7	)	)	PUNCT
ejpam-5453	664	8	=	=	SYM
ejpam-5453	664	9	{	{	PUNCT
ejpam-5453	664	10	t	t	PROPN
ejpam-5453	664	11	∈	∈	PROPN
ejpam-5453	664	12	v	v	NOUN
ejpam-5453	664	13	:	:	PUNCT
ejpam-5453	664	14	t	t	PROPN
ejpam-5453	664	15	∈ξ	∈ξ	PROPN
ejpam-5453	664	16	s℘m	s℘m	NOUN
ejpam-5453	664	17	}	}	PUNCT
ejpam-5453	664	18	.	.	PUNCT
ejpam-5453	665	1	lemma	lemma	PROPN
ejpam-5453	665	2	5.2	5.2	NUM
ejpam-5453	665	3	.	.	PUNCT
ejpam-5453	666	1	let	let	AUX
ejpam-5453	666	2	(	(	PUNCT
ejpam-5453	666	3	v	v	NOUN
ejpam-5453	666	4	,	,	PUNCT
ejpam-5453	666	5	υ	υ	NOUN
ejpam-5453	666	6	,	,	PUNCT
ejpam-5453	666	7	π℘	π℘	NUM
ejpam-5453	666	8	)	)	PUNCT
ejpam-5453	666	9	be	be	VERB
ejpam-5453	666	10	a	a	DET
ejpam-5453	666	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	666	12	and	and	CCONJ
ejpam-5453	666	13	m	m	PROPN
ejpam-5453	666	14	⊆	⊆	NUM
ejpam-5453	666	15	v.	v.	ADP
ejpam-5453	666	16	then	then	ADV
ejpam-5453	666	17	(	(	PUNCT
ejpam-5453	666	18	i	i	NOUN
ejpam-5453	666	19	)	)	PUNCT
ejpam-5453	666	20	if	if	SCONJ
ejpam-5453	666	21	t	t	PROPN
ejpam-5453	666	22	∈ξ	∈ξ	PROPN
ejpam-5453	666	23	s℘m	s℘m	NOUN
ejpam-5453	666	24	,	,	PUNCT
ejpam-5453	666	25	then	then	ADV
ejpam-5453	666	26	t	t	PROPN
ejpam-5453	666	27	∈	∈	PROPN
ejpam-5453	666	28	m.	m.	NOUN
ejpam-5453	666	29	(	(	PUNCT
ejpam-5453	666	30	ii	ii	NOUN
ejpam-5453	666	31	)	)	PUNCT
ejpam-5453	666	32	if	if	SCONJ
ejpam-5453	666	33	t	t	PROPN
ejpam-5453	666	34	∈	∈	PROPN
ejpam-5453	666	35	m	m	PROPN
ejpam-5453	666	36	,	,	PUNCT
ejpam-5453	666	37	then	then	ADV
ejpam-5453	666	38	t	t	PROPN
ejpam-5453	666	39	∈ξ	∈ξ	PROPN
ejpam-5453	666	40	s℘m	s℘m	NOUN
ejpam-5453	666	41	.	.	PUNCT
ejpam-5453	666	42	proof	proof	NOUN
ejpam-5453	666	43	.	.	PUNCT
ejpam-5453	667	1	straightforward	straightforward	ADJ
ejpam-5453	667	2	.	.	PUNCT
ejpam-5453	668	1	remark	remark	VERB
ejpam-5453	668	2	5.5	5.5	NUM
ejpam-5453	668	3	.	.	PUNCT
ejpam-5453	669	1	in	in	ADP
ejpam-5453	669	2	example	example	NOUN
ejpam-5453	669	3	3.1	3.1	NUM
ejpam-5453	669	4	m.	m.	NOUN
ejpam-5453	669	5	hosny	hosny	PROPN
ejpam-5453	669	6	/	/	SYM
ejpam-5453	669	7	eur	eur	PROPN
ejpam-5453	669	8	.	.	PUNCT
ejpam-5453	670	1	j.	j.	PROPN
ejpam-5453	670	2	pure	pure	PROPN
ejpam-5453	670	3	appl	appl	PROPN
ejpam-5453	670	4	.	.	PROPN
ejpam-5453	670	5	math	math	PROPN
ejpam-5453	670	6	,	,	PUNCT
ejpam-5453	670	7	17	17	NUM
ejpam-5453	670	8	(	(	PUNCT
ejpam-5453	670	9	4	4	NUM
ejpam-5453	670	10	)	)	PUNCT
ejpam-5453	670	11	(	(	PUNCT
ejpam-5453	670	12	2024	2024	NUM
ejpam-5453	670	13	)	)	PUNCT
ejpam-5453	670	14	,	,	PUNCT
ejpam-5453	670	15	2843	2843	NUM
ejpam-5453	670	16	-	-	SYM
ejpam-5453	670	17	2877	2877	NUM
ejpam-5453	670	18	2867	2867	NUM
ejpam-5453	670	19	(	(	PUNCT
ejpam-5453	670	20	i	i	NOUN
ejpam-5453	670	21	)	)	PUNCT
ejpam-5453	670	22	if	if	SCONJ
ejpam-5453	670	23	m	m	ADV
ejpam-5453	670	24	=	=	SYM
ejpam-5453	670	25	{	{	PUNCT
ejpam-5453	670	26	l1	l1	PROPN
ejpam-5453	670	27	}	}	PUNCT
ejpam-5453	670	28	,	,	PUNCT
ejpam-5453	670	29	then	then	ADV
ejpam-5453	670	30	l1	l1	PROPN
ejpam-5453	670	31	∈	∈	PROPN
ejpam-5453	670	32	m	m	PROPN
ejpam-5453	670	33	,	,	PUNCT
ejpam-5453	670	34	but	but	CCONJ
ejpam-5453	670	35	l1	l1	PROPN
ejpam-5453	670	36	̸∈β	̸∈β	PROPN
ejpam-5453	670	37	sr	sr	PROPN
ejpam-5453	670	38	m.	m.	PROPN
ejpam-5453	670	39	(	(	PUNCT
ejpam-5453	670	40	ii	ii	PROPN
ejpam-5453	670	41	)	)	PUNCT
ejpam-5453	670	42	if	if	SCONJ
ejpam-5453	670	43	m	m	ADV
ejpam-5453	670	44	=	=	SYM
ejpam-5453	670	45	{	{	PUNCT
ejpam-5453	670	46	l2	l2	PROPN
ejpam-5453	670	47	,	,	PUNCT
ejpam-5453	670	48	l3	l3	PROPN
ejpam-5453	670	49	,	,	PUNCT
ejpam-5453	670	50	l4	l4	PROPN
ejpam-5453	670	51	}	}	PUNCT
ejpam-5453	670	52	,	,	PUNCT
ejpam-5453	670	53	then	then	ADV
ejpam-5453	670	54	l1	l1	PROPN
ejpam-5453	670	55	∈β	∈β	PROPN
ejpam-5453	670	56	srm	srm	PROPN
ejpam-5453	670	57	,	,	PUNCT
ejpam-5453	670	58	but	but	CCONJ
ejpam-5453	670	59	l1	l1	PROPN
ejpam-5453	670	60	̸∈	̸∈	PROPN
ejpam-5453	670	61	m.	m.	PROPN
ejpam-5453	670	62	definition	definition	NOUN
ejpam-5453	670	63	5.4	5.4	NUM
ejpam-5453	670	64	.	.	PUNCT
ejpam-5453	671	1	let	let	AUX
ejpam-5453	671	2	(	(	PUNCT
ejpam-5453	671	3	v	v	NOUN
ejpam-5453	671	4	,	,	PUNCT
ejpam-5453	671	5	υ	υ	NOUN
ejpam-5453	671	6	,	,	PUNCT
ejpam-5453	671	7	π℘	π℘	NUM
ejpam-5453	671	8	)	)	PUNCT
ejpam-5453	671	9	be	be	AUX
ejpam-5453	671	10	a	a	DET
ejpam-5453	671	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	671	12	,	,	PUNCT
ejpam-5453	671	13	m	m	VERB
ejpam-5453	671	14	⊆	⊆	NUM
ejpam-5453	671	15	v	v	NOUN
ejpam-5453	671	16	and	and	CCONJ
ejpam-5453	671	17	t	t	NOUN
ejpam-5453	671	18	∈	∈	PROPN
ejpam-5453	671	19	v.	v.	ADP
ejpam-5453	671	20	the	the	DET
ejpam-5453	671	21	s℘-rough	s℘-rough	ADJ
ejpam-5453	671	22	nearly	nearly	ADV
ejpam-5453	671	23	membership	membership	NOUN
ejpam-5453	671	24	functions	function	NOUN
ejpam-5453	671	25	of	of	ADP
ejpam-5453	671	26	m	m	NOUN
ejpam-5453	671	27	are	be	AUX
ejpam-5453	671	28	defined	define	VERB
ejpam-5453	671	29	by	by	ADP
ejpam-5453	671	30	ω	ω	PROPN
ejpam-5453	671	31	ξs℘	ξs℘	PROPN
ejpam-5453	671	32	m	m	PRON
ejpam-5453	671	33	:	:	PUNCT
ejpam-5453	671	34	v	v	X
ejpam-5453	671	35	→	→	SYM
ejpam-5453	671	36	[	[	X
ejpam-5453	671	37	0	0	NUM
ejpam-5453	671	38	,	,	PUNCT
ejpam-5453	671	39	1	1	NUM
ejpam-5453	671	40	]	]	PUNCT
ejpam-5453	671	41	,	,	PUNCT
ejpam-5453	671	42	where	where	SCONJ
ejpam-5453	671	43	ω	ω	PROPN
ejpam-5453	671	44	ξs℘	ξs℘	PROPN
ejpam-5453	671	45	m	m	PROPN
ejpam-5453	671	46	(	(	PUNCT
ejpam-5453	671	47	t	t	PROPN
ejpam-5453	671	48	)	)	PUNCT
ejpam-5453	671	49	=	=	PRON
ejpam-5453	672	1	{	{	PUNCT
ejpam-5453	672	2	1	1	NUM
ejpam-5453	672	3	if	if	SCONJ
ejpam-5453	672	4	1∈	1∈	PROPN
ejpam-5453	672	5	χ	χ	PROPN
ejpam-5453	672	6	ξs℘	ξs℘	PROPN
ejpam-5453	672	7	m	m	PROPN
ejpam-5453	672	8	(	(	PUNCT
ejpam-5453	672	9	t	t	PROPN
ejpam-5453	672	10	)	)	PUNCT
ejpam-5453	672	11	.	.	PUNCT
ejpam-5453	673	1	min(χ	min(χ	PROPN
ejpam-5453	673	2	ξs℘	ξs℘	PROPN
ejpam-5453	673	3	m	m	PROPN
ejpam-5453	673	4	(	(	PUNCT
ejpam-5453	673	5	t	t	PROPN
ejpam-5453	673	6	)	)	PUNCT
ejpam-5453	673	7	)	)	PUNCT
ejpam-5453	673	8	otherwise	otherwise	ADV
ejpam-5453	673	9	.	.	PUNCT
ejpam-5453	673	10	}	}	PUNCT
ejpam-5453	673	11	.	.	PUNCT
ejpam-5453	674	1	and	and	CCONJ
ejpam-5453	674	2	χ	χ	PRON
ejpam-5453	674	3	ξs℘	ξs℘	PROPN
ejpam-5453	674	4	m	m	PROPN
ejpam-5453	674	5	(	(	PUNCT
ejpam-5453	674	6	t	t	PROPN
ejpam-5453	674	7	)	)	PUNCT
ejpam-5453	674	8	=	=	SYM
ejpam-5453	674	9	|ξs℘	|ξs℘	NOUN
ejpam-5453	674	10	(	(	PUNCT
ejpam-5453	674	11	t)∩m	t)∩m	NOUN
ejpam-5453	674	12	|	|	NOUN
ejpam-5453	674	13	|ξs℘	|ξs℘	NOUN
ejpam-5453	674	14	(	(	PUNCT
ejpam-5453	674	15	t)|	t)|	INTJ
ejpam-5453	674	16	,	,	PUNCT
ejpam-5453	674	17	t	t	PROPN
ejpam-5453	674	18	∈	∈	PROPN
ejpam-5453	674	19	ξs℘(t	ξs℘(t	NOUN
ejpam-5453	674	20	)	)	PUNCT
ejpam-5453	674	21	,	,	PUNCT
ejpam-5453	674	22	ξs℘(t	ξs℘(t	NOUN
ejpam-5453	674	23	)	)	PUNCT
ejpam-5453	674	24	∈	∈	PROPN
ejpam-5453	674	25	ξs℘o(v	ξs℘o(v	PROPN
ejpam-5453	674	26	)	)	PUNCT
ejpam-5453	674	27	.	.	PUNCT
ejpam-5453	675	1	remark	remark	PROPN
ejpam-5453	675	2	5.6	5.6	NUM
ejpam-5453	675	3	.	.	PUNCT
ejpam-5453	676	1	the	the	DET
ejpam-5453	676	2	s℘-rough	s℘-rough	ADJ
ejpam-5453	676	3	nearly	nearly	ADV
ejpam-5453	676	4	membership	membership	NOUN
ejpam-5453	676	5	functions	function	NOUN
ejpam-5453	676	6	are	be	AUX
ejpam-5453	676	7	employed	employ	VERB
ejpam-5453	676	8	to	to	PART
ejpam-5453	676	9	define	define	VERB
ejpam-5453	676	10	the	the	DET
ejpam-5453	676	11	s℘nearly	s℘nearly	ADV
ejpam-5453	676	12	lower	low	ADJ
ejpam-5453	676	13	(	(	PUNCT
ejpam-5453	676	14	upper	upper	ADJ
ejpam-5453	676	15	)	)	PUNCT
ejpam-5453	676	16	approximations	approximation	NOUN
ejpam-5453	676	17	as	as	SCONJ
ejpam-5453	676	18	outlined	outline	VERB
ejpam-5453	676	19	below	below	ADV
ejpam-5453	676	20	:	:	PUNCT
ejpam-5453	676	21	(	(	PUNCT
ejpam-5453	676	22	i	i	NOUN
ejpam-5453	676	23	)	)	PUNCT
ejpam-5453	676	24	nξ	nξ	ADP
ejpam-5453	676	25	s℘(m	s℘(m	PROPN
ejpam-5453	676	26	)	)	PUNCT
ejpam-5453	676	27	=	=	PRON
ejpam-5453	677	1	{	{	PUNCT
ejpam-5453	677	2	t	t	PROPN
ejpam-5453	677	3	∈	∈	PROPN
ejpam-5453	677	4	v	v	NOUN
ejpam-5453	677	5	:	:	PUNCT
ejpam-5453	677	6	ω	ω	PROPN
ejpam-5453	677	7	ξs℘	ξs℘	PROPN
ejpam-5453	677	8	m	m	PROPN
ejpam-5453	677	9	(	(	PUNCT
ejpam-5453	677	10	t	t	PROPN
ejpam-5453	677	11	)	)	PUNCT
ejpam-5453	677	12	=	=	PUNCT
ejpam-5453	678	1	1	1	NUM
ejpam-5453	678	2	}	}	PUNCT
ejpam-5453	678	3	.	.	PUNCT
ejpam-5453	679	1	(	(	PUNCT
ejpam-5453	679	2	ii	ii	NOUN
ejpam-5453	679	3	)	)	PUNCT
ejpam-5453	679	4	n	n	PRON
ejpam-5453	679	5	ξ	ξ	PROPN
ejpam-5453	679	6	s℘(m	s℘(m	PROPN
ejpam-5453	679	7	)	)	PUNCT
ejpam-5453	679	8	=	=	SYM
ejpam-5453	679	9	{	{	PUNCT
ejpam-5453	679	10	t	t	PROPN
ejpam-5453	679	11	∈	∈	PROPN
ejpam-5453	679	12	v	v	NOUN
ejpam-5453	679	13	:	:	PUNCT
ejpam-5453	679	14	ω	ω	PROPN
ejpam-5453	679	15	ξs℘	ξs℘	PROPN
ejpam-5453	679	16	m	m	PROPN
ejpam-5453	679	17	(	(	PUNCT
ejpam-5453	679	18	t	t	PROPN
ejpam-5453	679	19	)	)	PUNCT
ejpam-5453	679	20	>	>	X
ejpam-5453	679	21	0	0	NUM
ejpam-5453	679	22	}	}	PUNCT
ejpam-5453	679	23	.	.	PUNCT
ejpam-5453	680	1	(	(	PUNCT
ejpam-5453	680	2	iii	iii	NOUN
ejpam-5453	680	3	)	)	PUNCT
ejpam-5453	680	4	bξ	bξ	PROPN
ejpam-5453	680	5	s℘(m	s℘(m	PROPN
ejpam-5453	680	6	)	)	PUNCT
ejpam-5453	680	7	=	=	PRON
ejpam-5453	680	8	{	{	PUNCT
ejpam-5453	680	9	t	t	PROPN
ejpam-5453	680	10	∈	∈	PROPN
ejpam-5453	680	11	v	v	NOUN
ejpam-5453	680	12	:	:	PUNCT
ejpam-5453	680	13	0	0	NUM
ejpam-5453	680	14	<	<	X
ejpam-5453	680	15	ω	ω	NUM
ejpam-5453	680	16	ξs℘	ξs℘	PROPN
ejpam-5453	680	17	m	m	PROPN
ejpam-5453	680	18	(	(	PUNCT
ejpam-5453	680	19	t	t	PROPN
ejpam-5453	680	20	)	)	PUNCT
ejpam-5453	680	21	<	<	X
ejpam-5453	680	22	1	1	NUM
ejpam-5453	680	23	}	}	PUNCT
ejpam-5453	680	24	.	.	PUNCT
ejpam-5453	681	1	lemma	lemma	PROPN
ejpam-5453	681	2	5.3	5.3	NUM
ejpam-5453	681	3	.	.	PUNCT
ejpam-5453	682	1	let	let	AUX
ejpam-5453	682	2	(	(	PUNCT
ejpam-5453	682	3	v	v	NOUN
ejpam-5453	682	4	,	,	PUNCT
ejpam-5453	682	5	υ	υ	NOUN
ejpam-5453	682	6	,	,	PUNCT
ejpam-5453	682	7	π℘	π℘	NUM
ejpam-5453	682	8	)	)	PUNCT
ejpam-5453	682	9	be	be	VERB
ejpam-5453	682	10	a	a	DET
ejpam-5453	682	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	682	12	and	and	CCONJ
ejpam-5453	682	13	m	m	PROPN
ejpam-5453	682	14	⊆	⊆	NUM
ejpam-5453	682	15	v.	v.	ADP
ejpam-5453	682	16	then	then	ADV
ejpam-5453	682	17	,	,	PUNCT
ejpam-5453	682	18	(	(	PUNCT
ejpam-5453	682	19	i	i	NOUN
ejpam-5453	682	20	)	)	PUNCT
ejpam-5453	682	21	ω	ω	PROPN
ejpam-5453	682	22	s℘	s℘	NOUN
ejpam-5453	682	23	m	m	PROPN
ejpam-5453	682	24	(	(	PUNCT
ejpam-5453	682	25	t	t	PROPN
ejpam-5453	682	26	)	)	PUNCT
ejpam-5453	682	27	=	=	SYM
ejpam-5453	682	28	1	1	NUM
ejpam-5453	682	29	⇒	⇒	NOUN
ejpam-5453	682	30	ω	ω	NOUN
ejpam-5453	682	31	ξs℘	ξs℘	PROPN
ejpam-5453	682	32	m	m	PROPN
ejpam-5453	682	33	(	(	PUNCT
ejpam-5453	682	34	t	t	PROPN
ejpam-5453	682	35	)	)	PUNCT
ejpam-5453	683	1	=	=	NOUN
ejpam-5453	683	2	1,∀	1,∀	NUM
ejpam-5453	683	3	t	t	NOUN
ejpam-5453	683	4	∈	∈	PROPN
ejpam-5453	683	5	v.	v.	PROPN
ejpam-5453	683	6	(	(	PUNCT
ejpam-5453	683	7	ii	ii	PROPN
ejpam-5453	683	8	)	)	PUNCT
ejpam-5453	683	9	ω	ω	PROPN
ejpam-5453	683	10	s℘	s℘	NOUN
ejpam-5453	683	11	m	m	PROPN
ejpam-5453	683	12	(	(	PUNCT
ejpam-5453	683	13	t	t	PROPN
ejpam-5453	683	14	)	)	PUNCT
ejpam-5453	683	15	=	=	SYM
ejpam-5453	683	16	0	0	NUM
ejpam-5453	683	17	⇒	⇒	PROPN
ejpam-5453	683	18	ω	ω	NUM
ejpam-5453	683	19	ξs℘	ξs℘	PROPN
ejpam-5453	683	20	m	m	PROPN
ejpam-5453	683	21	(	(	PUNCT
ejpam-5453	683	22	t	t	PROPN
ejpam-5453	683	23	)	)	PUNCT
ejpam-5453	683	24	=	=	SYM
ejpam-5453	684	1	0,∀	0,∀	NUM
ejpam-5453	684	2	t	t	NOUN
ejpam-5453	684	3	∈	∈	NOUN
ejpam-5453	684	4	v.	v.	ADP
ejpam-5453	684	5	proposition	proposition	NOUN
ejpam-5453	684	6	5.2	5.2	NUM
ejpam-5453	684	7	.	.	PUNCT
ejpam-5453	685	1	let	let	AUX
ejpam-5453	685	2	(	(	PUNCT
ejpam-5453	685	3	v	v	NOUN
ejpam-5453	685	4	,	,	PUNCT
ejpam-5453	685	5	υ	υ	NOUN
ejpam-5453	685	6	,	,	PUNCT
ejpam-5453	685	7	π℘	π℘	NUM
ejpam-5453	685	8	)	)	PUNCT
ejpam-5453	685	9	be	be	VERB
ejpam-5453	685	10	a	a	DET
ejpam-5453	685	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	685	12	and	and	CCONJ
ejpam-5453	685	13	m	m	PROPN
ejpam-5453	685	14	,	,	PUNCT
ejpam-5453	685	15	n	n	PROPN
ejpam-5453	685	16	⊆	⊆	NUM
ejpam-5453	685	17	v.	v.	ADP
ejpam-5453	685	18	then	then	ADV
ejpam-5453	685	19	,	,	PUNCT
ejpam-5453	685	20	(	(	PUNCT
ejpam-5453	685	21	i	i	NOUN
ejpam-5453	685	22	)	)	PUNCT
ejpam-5453	686	1	if	if	SCONJ
ejpam-5453	686	2	ω	ω	PROPN
ejpam-5453	686	3	ξs℘	ξs℘	PROPN
ejpam-5453	686	4	m	m	PROPN
ejpam-5453	686	5	(	(	PUNCT
ejpam-5453	686	6	t	t	PROPN
ejpam-5453	686	7	)	)	PUNCT
ejpam-5453	686	8	=	=	SYM
ejpam-5453	686	9	1	1	NUM
ejpam-5453	686	10	⇔	⇔	PROPN
ejpam-5453	686	11	t	t	PROPN
ejpam-5453	686	12	∈	∈	PROPN
ejpam-5453	686	13	∈ξs℘	∈ξs℘	PROPN
ejpam-5453	686	14	s℘	s℘	NOUN
ejpam-5453	686	15	m.	m.	NOUN
ejpam-5453	686	16	(	(	PUNCT
ejpam-5453	686	17	ii	ii	NOUN
ejpam-5453	686	18	)	)	PUNCT
ejpam-5453	686	19	if	if	SCONJ
ejpam-5453	686	20	ω	ω	PROPN
ejpam-5453	686	21	ξs℘	ξs℘	PROPN
ejpam-5453	686	22	m	m	PROPN
ejpam-5453	686	23	(	(	PUNCT
ejpam-5453	686	24	t	t	PROPN
ejpam-5453	686	25	)	)	PUNCT
ejpam-5453	686	26	=	=	SYM
ejpam-5453	686	27	0	0	NUM
ejpam-5453	686	28	⇔	⇔	PROPN
ejpam-5453	686	29	t	t	PROPN
ejpam-5453	686	30	∈	∈	PROPN
ejpam-5453	686	31	v	v	ADP
ejpam-5453	686	32	−n	−n	PROPN
ejpam-5453	686	33	ξ	ξ	PROPN
ejpam-5453	686	34	s℘(m	s℘(m	PROPN
ejpam-5453	686	35	)	)	PUNCT
ejpam-5453	686	36	.	.	PUNCT
ejpam-5453	687	1	(	(	PUNCT
ejpam-5453	687	2	iii	iii	X
ejpam-5453	687	3	)	)	PUNCT
ejpam-5453	687	4	if	if	SCONJ
ejpam-5453	687	5	0	0	NUM
ejpam-5453	687	6	<	<	X
ejpam-5453	687	7	ω	ω	NUM
ejpam-5453	687	8	ξs℘	ξs℘	PROPN
ejpam-5453	687	9	m	m	PROPN
ejpam-5453	687	10	(	(	PUNCT
ejpam-5453	687	11	t	t	PROPN
ejpam-5453	687	12	)	)	PUNCT
ejpam-5453	687	13	<	<	X
ejpam-5453	687	14	1	1	NUM
ejpam-5453	687	15	⇔	⇔	X
ejpam-5453	687	16	x	x	SYM
ejpam-5453	687	17	∈	∈	PROPN
ejpam-5453	687	18	bξ	bξ	NOUN
ejpam-5453	687	19	s℘(m	s℘(m	PROPN
ejpam-5453	687	20	)	)	PUNCT
ejpam-5453	687	21	.	.	PUNCT
ejpam-5453	688	1	(	(	PUNCT
ejpam-5453	688	2	iv	iv	X
ejpam-5453	688	3	)	)	PUNCT
ejpam-5453	688	4	if	if	SCONJ
ejpam-5453	688	5	ω	ω	PROPN
ejpam-5453	688	6	ξs℘	ξs℘	PROPN
ejpam-5453	688	7	m	m	ADJ
ejpam-5453	688	8	′	′	NUM
ejpam-5453	688	9	(	(	PUNCT
ejpam-5453	688	10	t	t	NOUN
ejpam-5453	688	11	)	)	PUNCT
ejpam-5453	688	12	=	=	SYM
ejpam-5453	689	1	1−	1−	NUM
ejpam-5453	689	2	ω	ω	NUM
ejpam-5453	689	3	ξs℘	ξs℘	PROPN
ejpam-5453	689	4	m	m	PROPN
ejpam-5453	689	5	(	(	PUNCT
ejpam-5453	689	6	x),∀	x),∀	PROPN
ejpam-5453	689	7	t	t	PROPN
ejpam-5453	689	8	∈	∈	PROPN
ejpam-5453	689	9	v.	v.	PROPN
ejpam-5453	689	10	(	(	PUNCT
ejpam-5453	689	11	v	v	NOUN
ejpam-5453	689	12	)	)	PUNCT
ejpam-5453	689	13	if	if	SCONJ
ejpam-5453	689	14	ω	ω	VERB
ejpam-5453	689	15	ξs℘	ξs℘	PROPN
ejpam-5453	689	16	m∪n	m∪n	NOUN
ejpam-5453	689	17	(	(	PUNCT
ejpam-5453	689	18	t	t	PROPN
ejpam-5453	689	19	)	)	PUNCT
ejpam-5453	689	20	≥	≥	NOUN
ejpam-5453	689	21	max(ω	max(ω	PROPN
ejpam-5453	689	22	ξs℘	ξs℘	PROPN
ejpam-5453	689	23	m	m	PROPN
ejpam-5453	689	24	(	(	PUNCT
ejpam-5453	689	25	t	t	PROPN
ejpam-5453	689	26	)	)	PUNCT
ejpam-5453	689	27	,	,	PUNCT
ejpam-5453	689	28	ω	ω	NUM
ejpam-5453	689	29	ξs℘	ξs℘	PROPN
ejpam-5453	689	30	n	n	CCONJ
ejpam-5453	689	31	(	(	PUNCT
ejpam-5453	689	32	t)),∀	t)),∀	PROPN
ejpam-5453	689	33	t	t	PROPN
ejpam-5453	689	34	∈	∈	PROPN
ejpam-5453	689	35	v.	v.	PROPN
ejpam-5453	689	36	(	(	PUNCT
ejpam-5453	689	37	vi	vi	PROPN
ejpam-5453	689	38	)	)	PUNCT
ejpam-5453	689	39	if	if	SCONJ
ejpam-5453	689	40	ω	ω	NUM
ejpam-5453	689	41	ξs℘	ξs℘	PROPN
ejpam-5453	689	42	m∩n	m∩n	PROPN
ejpam-5453	689	43	(	(	PUNCT
ejpam-5453	689	44	t	t	PROPN
ejpam-5453	689	45	)	)	PUNCT
ejpam-5453	689	46	≤	≤	NOUN
ejpam-5453	689	47	min(ω	min(ω	VERB
ejpam-5453	689	48	ξs℘	ξs℘	PROPN
ejpam-5453	689	49	m	m	ADJ
ejpam-5453	689	50	(	(	PUNCT
ejpam-5453	689	51	t	t	PROPN
ejpam-5453	689	52	)	)	PUNCT
ejpam-5453	689	53	,	,	PUNCT
ejpam-5453	689	54	ω	ω	NUM
ejpam-5453	689	55	ξs℘	ξs℘	PROPN
ejpam-5453	689	56	n	n	CCONJ
ejpam-5453	689	57	(	(	PUNCT
ejpam-5453	689	58	t)),∀	t)),∀	PROPN
ejpam-5453	689	59	t	t	NOUN
ejpam-5453	689	60	∈	∈	PROPN
ejpam-5453	689	61	v.	v.	ADP
ejpam-5453	689	62	proof	proof	NOUN
ejpam-5453	689	63	.	.	PUNCT
ejpam-5453	690	1	it	it	PRON
ejpam-5453	690	2	resembles	resemble	VERB
ejpam-5453	690	3	proposition	proposition	NOUN
ejpam-5453	690	4	5.1	5.1	NUM
ejpam-5453	690	5	.	.	PUNCT
ejpam-5453	691	1	m.	m.	PROPN
ejpam-5453	691	2	hosny	hosny	PROPN
ejpam-5453	691	3	/	/	SYM
ejpam-5453	691	4	eur	eur	PROPN
ejpam-5453	691	5	.	.	PUNCT
ejpam-5453	692	1	j.	j.	PROPN
ejpam-5453	692	2	pure	pure	PROPN
ejpam-5453	692	3	appl	appl	PROPN
ejpam-5453	692	4	.	.	PROPN
ejpam-5453	692	5	math	math	PROPN
ejpam-5453	692	6	,	,	PUNCT
ejpam-5453	692	7	17	17	NUM
ejpam-5453	692	8	(	(	PUNCT
ejpam-5453	692	9	4	4	NUM
ejpam-5453	692	10	)	)	PUNCT
ejpam-5453	692	11	(	(	PUNCT
ejpam-5453	692	12	2024	2024	NUM
ejpam-5453	692	13	)	)	PUNCT
ejpam-5453	692	14	,	,	PUNCT
ejpam-5453	692	15	2843	2843	NUM
ejpam-5453	692	16	-	-	SYM
ejpam-5453	692	17	2877	2877	NUM
ejpam-5453	692	18	2868	2868	NUM
ejpam-5453	692	19	5.3	5.3	NUM
ejpam-5453	692	20	.	.	PUNCT
ejpam-5453	693	1	s℘-nearly	s℘-nearly	ADV
ejpam-5453	693	2	rough	rough	ADJ
ejpam-5453	693	3	membership	membership	NOUN
ejpam-5453	693	4	functions	function	NOUN
ejpam-5453	693	5	via	via	ADP
ejpam-5453	693	6	ideals	ideal	NOUN
ejpam-5453	693	7	definition	definition	NOUN
ejpam-5453	693	8	5.5	5.5	NUM
ejpam-5453	693	9	.	.	PUNCT
ejpam-5453	694	1	let	let	AUX
ejpam-5453	694	2	(	(	PUNCT
ejpam-5453	694	3	v	v	NOUN
ejpam-5453	694	4	,	,	PUNCT
ejpam-5453	694	5	υ	υ	NOUN
ejpam-5453	694	6	,	,	PUNCT
ejpam-5453	694	7	π℘	π℘	NUM
ejpam-5453	694	8	)	)	PUNCT
ejpam-5453	694	9	be	be	AUX
ejpam-5453	694	10	a	a	DET
ejpam-5453	694	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	694	12	,	,	PUNCT
ejpam-5453	694	13	d	d	PRON
ejpam-5453	694	14	be	be	AUX
ejpam-5453	694	15	an	an	DET
ejpam-5453	694	16	ideal	ideal	NOUN
ejpam-5453	694	17	on	on	ADP
ejpam-5453	694	18	v	v	NOUN
ejpam-5453	694	19	and	and	CCONJ
ejpam-5453	694	20	t	t	NOUN
ejpam-5453	694	21	∈	∈	PROPN
ejpam-5453	694	22	v	v	NOUN
ejpam-5453	694	23	.	.	PUNCT
ejpam-5453	695	1	(	(	PUNCT
ejpam-5453	695	2	i	i	NOUN
ejpam-5453	695	3	)	)	PUNCT
ejpam-5453	695	4	if	if	SCONJ
ejpam-5453	695	5	t	t	PROPN
ejpam-5453	695	6	∈	∈	PROPN
ejpam-5453	695	7	nd−ξ	nd−ξ	PROPN
ejpam-5453	695	8	s℘	s℘	PROPN
ejpam-5453	695	9	(	(	PUNCT
ejpam-5453	695	10	m	m	NOUN
ejpam-5453	695	11	)	)	PUNCT
ejpam-5453	695	12	,	,	PUNCT
ejpam-5453	695	13	then	then	ADV
ejpam-5453	695	14	t	t	PROPN
ejpam-5453	695	15	is	be	AUX
ejpam-5453	695	16	s℘-nearly	s℘-nearly	ADV
ejpam-5453	695	17	surely	surely	ADV
ejpam-5453	695	18	with	with	ADP
ejpam-5453	695	19	respect	respect	NOUN
ejpam-5453	695	20	to	to	ADP
ejpam-5453	695	21	d	d	PROPN
ejpam-5453	695	22	(	(	PUNCT
ejpam-5453	695	23	d−ξs℘-surely	d−ξs℘-surely	ADV
ejpam-5453	695	24	)	)	PUNCT
ejpam-5453	695	25	belongs	belong	VERB
ejpam-5453	695	26	to	to	ADP
ejpam-5453	695	27	m	m	PROPN
ejpam-5453	695	28	,	,	PUNCT
ejpam-5453	695	29	denoted	denote	VERB
ejpam-5453	695	30	by	by	ADP
ejpam-5453	695	31	t	t	PROPN
ejpam-5453	695	32	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	695	33	s℘	s℘	PROPN
ejpam-5453	695	34	m.	m.	NOUN
ejpam-5453	695	35	(	(	PUNCT
ejpam-5453	695	36	ii	ii	NOUN
ejpam-5453	695	37	)	)	PUNCT
ejpam-5453	695	38	if	if	SCONJ
ejpam-5453	695	39	t	t	PROPN
ejpam-5453	695	40	∈	∈	PROPN
ejpam-5453	695	41	n	n	CCONJ
ejpam-5453	695	42	d−ξ	d−ξ	NOUN
ejpam-5453	695	43	s℘	s℘	NOUN
ejpam-5453	695	44	(	(	PUNCT
ejpam-5453	695	45	m	m	NOUN
ejpam-5453	695	46	)	)	PUNCT
ejpam-5453	695	47	,	,	PUNCT
ejpam-5453	695	48	then	then	ADV
ejpam-5453	695	49	t	t	PROPN
ejpam-5453	695	50	is	be	AUX
ejpam-5453	695	51	s℘-nearly	s℘-nearly	ADV
ejpam-5453	695	52	possibly	possibly	ADV
ejpam-5453	695	53	with	with	ADP
ejpam-5453	695	54	respect	respect	NOUN
ejpam-5453	695	55	to	to	ADP
ejpam-5453	695	56	d	d	PROPN
ejpam-5453	695	57	(	(	PUNCT
ejpam-5453	695	58	d	d	NOUN
ejpam-5453	695	59	−	−	PROPN
ejpam-5453	695	60	ξs℘-possibly	ξs℘-possibly	ADV
ejpam-5453	695	61	)	)	PUNCT
ejpam-5453	695	62	belongs	belong	VERB
ejpam-5453	695	63	to	to	ADP
ejpam-5453	695	64	m	m	PROPN
ejpam-5453	695	65	,	,	PUNCT
ejpam-5453	695	66	denoted	denote	VERB
ejpam-5453	695	67	by	by	ADP
ejpam-5453	695	68	t	t	PROPN
ejpam-5453	695	69	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	695	70	s℘	s℘	PROPN
ejpam-5453	695	71	m.	m.	NOUN
ejpam-5453	695	72	it	it	PRON
ejpam-5453	695	73	is	be	AUX
ejpam-5453	695	74	known	know	VERB
ejpam-5453	695	75	as	as	ADP
ejpam-5453	695	76	s℘-nearly	s℘-nearly	ADV
ejpam-5453	695	77	strong	strong	ADJ
ejpam-5453	695	78	and	and	CCONJ
ejpam-5453	695	79	s℘-nearly	s℘-nearly	ADV
ejpam-5453	695	80	weak	weak	ADJ
ejpam-5453	695	81	membership	membership	NOUN
ejpam-5453	695	82	relations	relation	NOUN
ejpam-5453	695	83	with	with	ADP
ejpam-5453	695	84	respect	respect	NOUN
ejpam-5453	695	85	to	to	ADP
ejpam-5453	695	86	d	d	NOUN
ejpam-5453	695	87	respectively	respectively	ADV
ejpam-5453	695	88	.	.	PUNCT
ejpam-5453	696	1	remark	remark	PROPN
ejpam-5453	696	2	5.7	5.7	NUM
ejpam-5453	696	3	.	.	PUNCT
ejpam-5453	697	1	based	base	VERB
ejpam-5453	697	2	on	on	ADP
ejpam-5453	697	3	definition	definition	NOUN
ejpam-5453	697	4	5.5	5.5	NUM
ejpam-5453	697	5	the	the	DET
ejpam-5453	697	6	s℘-nearly	s℘-nearly	ADV
ejpam-5453	697	7	approximations	approximation	NOUN
ejpam-5453	697	8	via	via	ADP
ejpam-5453	697	9	ideal	ideal	NOUN
ejpam-5453	697	10	for	for	ADP
ejpam-5453	697	11	any	any	DET
ejpam-5453	697	12	m	m	NOUN
ejpam-5453	697	13	⊆	⊆	NUM
ejpam-5453	697	14	v	v	NOUN
ejpam-5453	697	15	can	can	AUX
ejpam-5453	697	16	be	be	AUX
ejpam-5453	697	17	expressed	express	VERB
ejpam-5453	697	18	as	as	ADP
ejpam-5453	697	19	:	:	PUNCT
ejpam-5453	697	20	(	(	PUNCT
ejpam-5453	697	21	i	i	NOUN
ejpam-5453	697	22	)	)	PUNCT
ejpam-5453	697	23	nd−ξ	nd−ξ	PROPN
ejpam-5453	697	24	s℘	s℘	PROPN
ejpam-5453	697	25	(	(	PUNCT
ejpam-5453	697	26	m	m	NOUN
ejpam-5453	697	27	)	)	PUNCT
ejpam-5453	697	28	=	=	PRON
ejpam-5453	697	29	{	{	PUNCT
ejpam-5453	697	30	t	t	PROPN
ejpam-5453	697	31	∈	∈	PROPN
ejpam-5453	697	32	v	v	NOUN
ejpam-5453	697	33	:	:	PUNCT
ejpam-5453	697	34	t	t	PROPN
ejpam-5453	697	35	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	697	36	s℘	s℘	PROPN
ejpam-5453	697	37	m	m	PRON
ejpam-5453	697	38	}	}	PUNCT
ejpam-5453	697	39	.	.	PUNCT
ejpam-5453	698	1	(	(	PUNCT
ejpam-5453	698	2	ii	ii	NOUN
ejpam-5453	698	3	)	)	PUNCT
ejpam-5453	698	4	n	n	PROPN
ejpam-5453	698	5	d−ξ	d−ξ	NOUN
ejpam-5453	698	6	s℘	s℘	NOUN
ejpam-5453	698	7	(	(	PUNCT
ejpam-5453	698	8	m	m	NOUN
ejpam-5453	698	9	)	)	PUNCT
ejpam-5453	698	10	=	=	PRON
ejpam-5453	698	11	{	{	PUNCT
ejpam-5453	698	12	t	t	PROPN
ejpam-5453	698	13	∈	∈	PROPN
ejpam-5453	698	14	v	v	NOUN
ejpam-5453	698	15	:	:	PUNCT
ejpam-5453	698	16	t	t	PROPN
ejpam-5453	698	17	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	698	18	s℘	s℘	PROPN
ejpam-5453	698	19	m	m	PRON
ejpam-5453	698	20	}	}	PUNCT
ejpam-5453	698	21	.	.	PUNCT
ejpam-5453	699	1	lemma	lemma	PROPN
ejpam-5453	699	2	5.4	5.4	NUM
ejpam-5453	699	3	.	.	PUNCT
ejpam-5453	700	1	let	let	AUX
ejpam-5453	700	2	(	(	PUNCT
ejpam-5453	700	3	v	v	NOUN
ejpam-5453	700	4	,	,	PUNCT
ejpam-5453	700	5	υ	υ	NOUN
ejpam-5453	700	6	,	,	PUNCT
ejpam-5453	700	7	π℘	π℘	NUM
ejpam-5453	700	8	)	)	PUNCT
ejpam-5453	700	9	be	be	AUX
ejpam-5453	700	10	a	a	DET
ejpam-5453	700	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	700	12	,	,	PUNCT
ejpam-5453	700	13	d	d	PRON
ejpam-5453	700	14	be	be	AUX
ejpam-5453	700	15	an	an	DET
ejpam-5453	700	16	ideal	ideal	NOUN
ejpam-5453	700	17	on	on	ADP
ejpam-5453	700	18	v	v	NUM
ejpam-5453	700	19	and	and	CCONJ
ejpam-5453	700	20	m	m	PROPN
ejpam-5453	700	21	⊆	⊆	NUM
ejpam-5453	700	22	v.	v.	ADP
ejpam-5453	700	23	then	then	ADV
ejpam-5453	700	24	(	(	PUNCT
ejpam-5453	700	25	i	i	NOUN
ejpam-5453	700	26	)	)	PUNCT
ejpam-5453	700	27	if	if	SCONJ
ejpam-5453	700	28	t	t	PROPN
ejpam-5453	700	29	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	700	30	s℘	s℘	PROPN
ejpam-5453	700	31	m	m	PROPN
ejpam-5453	700	32	,	,	PUNCT
ejpam-5453	700	33	then	then	ADV
ejpam-5453	700	34	t	t	PROPN
ejpam-5453	700	35	∈	∈	PROPN
ejpam-5453	700	36	m.	m.	NOUN
ejpam-5453	700	37	(	(	PUNCT
ejpam-5453	700	38	ii	ii	NOUN
ejpam-5453	700	39	)	)	PUNCT
ejpam-5453	700	40	if	if	SCONJ
ejpam-5453	700	41	t	t	PROPN
ejpam-5453	700	42	∈	∈	PROPN
ejpam-5453	700	43	m	m	PROPN
ejpam-5453	700	44	,	,	PUNCT
ejpam-5453	700	45	then	then	ADV
ejpam-5453	700	46	t	t	PROPN
ejpam-5453	700	47	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	700	48	s℘	s℘	PROPN
ejpam-5453	700	49	m.	m.	NOUN
ejpam-5453	700	50	proof	proof	NOUN
ejpam-5453	700	51	.	.	PUNCT
ejpam-5453	701	1	straightforward	straightforward	ADJ
ejpam-5453	701	2	.	.	PUNCT
ejpam-5453	702	1	remark	remark	VERB
ejpam-5453	702	2	5.8	5.8	NUM
ejpam-5453	702	3	.	.	PUNCT
ejpam-5453	703	1	in	in	ADP
ejpam-5453	703	2	example	example	NOUN
ejpam-5453	703	3	3.1	3.1	NUM
ejpam-5453	703	4	,	,	PUNCT
ejpam-5453	703	5	if	if	SCONJ
ejpam-5453	703	6	d	d	PROPN
ejpam-5453	703	7	=	=	PUNCT
ejpam-5453	703	8	{	{	PUNCT
ejpam-5453	703	9	∅	∅	NOUN
ejpam-5453	703	10	,	,	PUNCT
ejpam-5453	703	11	l2	l2	NOUN
ejpam-5453	703	12	}	}	PUNCT
ejpam-5453	703	13	,	,	PUNCT
ejpam-5453	703	14	then	then	ADV
ejpam-5453	703	15	(	(	PUNCT
ejpam-5453	703	16	i	i	NOUN
ejpam-5453	703	17	)	)	PUNCT
ejpam-5453	703	18	l1	l1	PROPN
ejpam-5453	703	19	∈	∈	PROPN
ejpam-5453	703	20	{	{	PUNCT
ejpam-5453	703	21	l1	l1	PROPN
ejpam-5453	703	22	}	}	PUNCT
ejpam-5453	703	23	,	,	PUNCT
ejpam-5453	703	24	but	but	CCONJ
ejpam-5453	703	25	l1	l1	PROPN
ejpam-5453	703	26	̸∈d−β	̸∈d−β	PROPN
ejpam-5453	704	1	sr	sr	PROPN
ejpam-5453	704	2	m.	m.	NOUN
ejpam-5453	704	3	(	(	PUNCT
ejpam-5453	704	4	ii	ii	NOUN
ejpam-5453	704	5	)	)	PUNCT
ejpam-5453	704	6	l1	l1	PROPN
ejpam-5453	704	7	∈d−β	∈d−β	PROPN
ejpam-5453	704	8	r	r	NOUN
ejpam-5453	704	9	m	m	PROPN
ejpam-5453	704	10	,	,	PUNCT
ejpam-5453	704	11	but	but	CCONJ
ejpam-5453	704	12	l1	l1	PROPN
ejpam-5453	704	13	̸∈	̸∈	PROPN
ejpam-5453	704	14	{	{	PUNCT
ejpam-5453	704	15	l2	l2	PROPN
ejpam-5453	704	16	,	,	PUNCT
ejpam-5453	704	17	l3	l3	PROPN
ejpam-5453	704	18	,	,	PUNCT
ejpam-5453	704	19	l4	l4	PROPN
ejpam-5453	704	20	}	}	PUNCT
ejpam-5453	704	21	.	.	PUNCT
ejpam-5453	705	1	proposition	proposition	NOUN
ejpam-5453	705	2	5.3	5.3	NUM
ejpam-5453	705	3	.	.	PUNCT
ejpam-5453	706	1	let	let	AUX
ejpam-5453	706	2	(	(	PUNCT
ejpam-5453	706	3	v	v	NOUN
ejpam-5453	706	4	,	,	PUNCT
ejpam-5453	706	5	υ	υ	NOUN
ejpam-5453	706	6	,	,	PUNCT
ejpam-5453	706	7	π℘	π℘	NUM
ejpam-5453	706	8	)	)	PUNCT
ejpam-5453	706	9	be	be	AUX
ejpam-5453	706	10	a	a	DET
ejpam-5453	706	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	706	12	,	,	PUNCT
ejpam-5453	706	13	d	d	PRON
ejpam-5453	706	14	be	be	AUX
ejpam-5453	706	15	an	an	DET
ejpam-5453	706	16	ideal	ideal	NOUN
ejpam-5453	706	17	on	on	ADP
ejpam-5453	706	18	v	v	NUM
ejpam-5453	706	19	and	and	CCONJ
ejpam-5453	706	20	m	m	PROPN
ejpam-5453	706	21	⊆	⊆	NUM
ejpam-5453	706	22	v.	v.	ADP
ejpam-5453	706	23	then	then	ADV
ejpam-5453	706	24	(	(	PUNCT
ejpam-5453	706	25	i	i	NOUN
ejpam-5453	706	26	)	)	PUNCT
ejpam-5453	706	27	if	if	SCONJ
ejpam-5453	706	28	t	t	NOUN
ejpam-5453	706	29	∈s℘m	∈s℘m	PUNCT
ejpam-5453	706	30	⇒	⇒	VERB
ejpam-5453	706	31	t	t	PROPN
ejpam-5453	706	32	∈ξ	∈ξ	PROPN
ejpam-5453	706	33	s℘m	s℘m	NOUN
ejpam-5453	706	34	⇒	⇒	PROPN
ejpam-5453	706	35	t	t	PROPN
ejpam-5453	706	36	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	706	37	s℘	s℘	PROPN
ejpam-5453	706	38	m.	m.	NOUN
ejpam-5453	706	39	(	(	PUNCT
ejpam-5453	706	40	ii	ii	NOUN
ejpam-5453	706	41	)	)	PUNCT
ejpam-5453	706	42	if	if	SCONJ
ejpam-5453	706	43	t	t	PROPN
ejpam-5453	706	44	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	706	45	s℘	s℘	PROPN
ejpam-5453	706	46	m	m	PROPN
ejpam-5453	706	47	⇒	⇒	PROPN
ejpam-5453	706	48	t	t	PROPN
ejpam-5453	706	49	∈ξ	∈ξ	PROPN
ejpam-5453	706	50	s℘m	s℘m	NOUN
ejpam-5453	706	51	⇒	⇒	NOUN
ejpam-5453	706	52	t	t	PROPN
ejpam-5453	706	53	∈s℘m	∈s℘m	PROPN
ejpam-5453	706	54	.	.	PUNCT
ejpam-5453	707	1	proof	proof	NOUN
ejpam-5453	707	2	.	.	PUNCT
ejpam-5453	708	1	we	we	PRON
ejpam-5453	708	2	demonstrate	demonstrate	VERB
ejpam-5453	708	3	(	(	PUNCT
ejpam-5453	708	4	1	1	NUM
ejpam-5453	708	5	)	)	PUNCT
ejpam-5453	708	6	and	and	CCONJ
ejpam-5453	708	7	address	address	VERB
ejpam-5453	708	8	the	the	DET
ejpam-5453	708	9	others	other	NOUN
ejpam-5453	708	10	similarly	similarly	ADV
ejpam-5453	708	11	.	.	PUNCT
ejpam-5453	709	1	t	t	NOUN
ejpam-5453	709	2	∈s℘m	∈s℘m	PUNCT
ejpam-5453	709	3	⇒	⇒	VERB
ejpam-5453	709	4	t	t	PROPN
ejpam-5453	709	5	∈	∈	PROPN
ejpam-5453	709	6	ns℘(m	ns℘(m	PROPN
ejpam-5453	709	7	)	)	PUNCT
ejpam-5453	709	8	⇒	⇒	NOUN
ejpam-5453	709	9	t	t	PROPN
ejpam-5453	709	10	∈	∈	PROPN
ejpam-5453	709	11	nξ	nξ	ADP
ejpam-5453	709	12	s℘(m	s℘(m	PROPN
ejpam-5453	709	13	)	)	PUNCT
ejpam-5453	709	14	by	by	ADP
ejpam-5453	709	15	theorem	theorem	VERB
ejpam-5453	709	16	2.3	2.3	NUM
ejpam-5453	710	1	[	[	X
ejpam-5453	710	2	43	43	NUM
ejpam-5453	710	3	]	]	PUNCT
ejpam-5453	710	4	.	.	PUNCT
ejpam-5453	711	1	hence	hence	ADV
ejpam-5453	711	2	,	,	PUNCT
ejpam-5453	711	3	t	t	PROPN
ejpam-5453	711	4	∈ξ	∈ξ	PROPN
ejpam-5453	711	5	s℘m	s℘m	NOUN
ejpam-5453	711	6	,	,	PUNCT
ejpam-5453	711	7	so	so	ADV
ejpam-5453	711	8	,	,	PUNCT
ejpam-5453	711	9	t	t	PROPN
ejpam-5453	711	10	∈	∈	PROPN
ejpam-5453	711	11	nξ	nξ	ADP
ejpam-5453	711	12	s℘(m	s℘(m	PROPN
ejpam-5453	711	13	)	)	PUNCT
ejpam-5453	711	14	⇒	⇒	PROPN
ejpam-5453	711	15	t	t	PROPN
ejpam-5453	711	16	∈	∈	PROPN
ejpam-5453	711	17	nd−ξ	nd−ξ	PROPN
ejpam-5453	711	18	s℘	s℘	PROPN
ejpam-5453	711	19	(	(	PUNCT
ejpam-5453	711	20	m	m	NOUN
ejpam-5453	711	21	)	)	PUNCT
ejpam-5453	711	22	by	by	ADP
ejpam-5453	711	23	theorem	theorem	NOUN
ejpam-5453	711	24	4.1	4.1	NUM
ejpam-5453	711	25	.	.	PUNCT
ejpam-5453	712	1	therefore	therefore	ADV
ejpam-5453	712	2	,	,	PUNCT
ejpam-5453	712	3	t	t	PROPN
ejpam-5453	712	4	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	712	5	s℘	s℘	PROPN
ejpam-5453	712	6	m.	m.	NOUN
ejpam-5453	712	7	remark	remark	VERB
ejpam-5453	712	8	5.9	5.9	NUM
ejpam-5453	712	9	.	.	PUNCT
ejpam-5453	713	1	in	in	ADP
ejpam-5453	713	2	example	example	NOUN
ejpam-5453	713	3	3.1	3.1	NUM
ejpam-5453	713	4	(	(	PUNCT
ejpam-5453	713	5	i	i	NOUN
ejpam-5453	713	6	)	)	PUNCT
ejpam-5453	713	7	if	if	SCONJ
ejpam-5453	713	8	m	m	ADV
ejpam-5453	713	9	=	=	SYM
ejpam-5453	713	10	{	{	PUNCT
ejpam-5453	713	11	l1	l1	PROPN
ejpam-5453	713	12	}	}	PUNCT
ejpam-5453	713	13	,	,	PUNCT
ejpam-5453	713	14	then	then	ADV
ejpam-5453	713	15	l1	l1	PROPN
ejpam-5453	713	16	∈d−β	∈d−β	PROPN
ejpam-5453	713	17	sr	sr	PROPN
ejpam-5453	713	18	m	m	PROPN
ejpam-5453	713	19	,	,	PUNCT
ejpam-5453	713	20	but	but	CCONJ
ejpam-5453	713	21	l1	l1	PROPN
ejpam-5453	713	22	̸∈β	̸∈β	PROPN
ejpam-5453	713	23	sr	sr	PROPN
ejpam-5453	713	24	m	m	PROPN
ejpam-5453	713	25	and	and	CCONJ
ejpam-5453	713	26	l1	l1	PROPN
ejpam-5453	713	27	̸∈r	̸∈r	PROPN
ejpam-5453	713	28	m.	m.	NOUN
ejpam-5453	713	29	(	(	PUNCT
ejpam-5453	713	30	ii	ii	NOUN
ejpam-5453	713	31	)	)	PUNCT
ejpam-5453	713	32	if	if	SCONJ
ejpam-5453	713	33	m	m	ADV
ejpam-5453	713	34	=	=	SYM
ejpam-5453	713	35	{	{	PUNCT
ejpam-5453	713	36	l2	l2	NOUN
ejpam-5453	713	37	}	}	PUNCT
ejpam-5453	713	38	,	,	PUNCT
ejpam-5453	713	39	then	then	ADV
ejpam-5453	713	40	l1	l1	PROPN
ejpam-5453	713	41	∈rm	∈rm	PROPN
ejpam-5453	713	42	,	,	PUNCT
ejpam-5453	713	43	but	but	CCONJ
ejpam-5453	713	44	l1	l1	PROPN
ejpam-5453	713	45	̸∈	̸∈	PROPN
ejpam-5453	713	46	β	β	PROPN
ejpam-5453	713	47	srm	srm	PROPN
ejpam-5453	713	48	and	and	CCONJ
ejpam-5453	713	49	l1	l1	PROPN
ejpam-5453	713	50	̸∈	̸∈	PROPN
ejpam-5453	713	51	d−β	d−β	PROPN
ejpam-5453	713	52	sr	sr	PROPN
ejpam-5453	713	53	m.	m.	PROPN
ejpam-5453	713	54	m.	m.	PROPN
ejpam-5453	713	55	hosny	hosny	PROPN
ejpam-5453	713	56	/	/	SYM
ejpam-5453	713	57	eur	eur	PROPN
ejpam-5453	713	58	.	.	PUNCT
ejpam-5453	714	1	j.	j.	PROPN
ejpam-5453	714	2	pure	pure	PROPN
ejpam-5453	714	3	appl	appl	PROPN
ejpam-5453	714	4	.	.	PROPN
ejpam-5453	714	5	math	math	PROPN
ejpam-5453	714	6	,	,	PUNCT
ejpam-5453	714	7	17	17	NUM
ejpam-5453	714	8	(	(	PUNCT
ejpam-5453	714	9	4	4	NUM
ejpam-5453	714	10	)	)	PUNCT
ejpam-5453	714	11	(	(	PUNCT
ejpam-5453	714	12	2024	2024	NUM
ejpam-5453	714	13	)	)	PUNCT
ejpam-5453	714	14	,	,	PUNCT
ejpam-5453	714	15	2843	2843	NUM
ejpam-5453	714	16	-	-	SYM
ejpam-5453	714	17	2877	2877	NUM
ejpam-5453	714	18	2869	2869	NUM
ejpam-5453	714	19	the	the	DET
ejpam-5453	714	20	present	present	ADJ
ejpam-5453	714	21	membership	membership	NOUN
ejpam-5453	714	22	relations	relation	NOUN
ejpam-5453	714	23	is	be	AUX
ejpam-5453	714	24	more	more	ADV
ejpam-5453	714	25	accurate	accurate	ADJ
ejpam-5453	714	26	than	than	ADP
ejpam-5453	714	27	the	the	DET
ejpam-5453	714	28	previous	previous	ADJ
ejpam-5453	714	29	ones	one	NOUN
ejpam-5453	714	30	in	in	ADP
ejpam-5453	714	31	[	[	X
ejpam-5453	714	32	1	1	NUM
ejpam-5453	714	33	,	,	PUNCT
ejpam-5453	714	34	22	22	NUM
ejpam-5453	714	35	,	,	PUNCT
ejpam-5453	714	36	26	26	NUM
ejpam-5453	714	37	]	]	PUNCT
ejpam-5453	714	38	as	as	SCONJ
ejpam-5453	714	39	it	it	PRON
ejpam-5453	714	40	illustrated	illustrate	VERB
ejpam-5453	714	41	in	in	ADP
ejpam-5453	714	42	the	the	DET
ejpam-5453	714	43	following	follow	VERB
ejpam-5453	714	44	consequences	consequence	NOUN
ejpam-5453	714	45	.	.	PUNCT
ejpam-5453	715	1	proposition	proposition	NOUN
ejpam-5453	715	2	5.4	5.4	NUM
ejpam-5453	715	3	.	.	PUNCT
ejpam-5453	716	1	let	let	AUX
ejpam-5453	716	2	(	(	PUNCT
ejpam-5453	716	3	v	v	NOUN
ejpam-5453	716	4	,	,	PUNCT
ejpam-5453	716	5	υ	υ	NOUN
ejpam-5453	716	6	,	,	PUNCT
ejpam-5453	716	7	π℘	π℘	NUM
ejpam-5453	716	8	)	)	PUNCT
ejpam-5453	716	9	be	be	AUX
ejpam-5453	716	10	a	a	DET
ejpam-5453	716	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	716	12	,	,	PUNCT
ejpam-5453	716	13	d	d	PRON
ejpam-5453	716	14	be	be	AUX
ejpam-5453	716	15	an	an	DET
ejpam-5453	716	16	ideal	ideal	NOUN
ejpam-5453	716	17	on	on	ADP
ejpam-5453	716	18	v	v	NOUN
ejpam-5453	716	19	,	,	PUNCT
ejpam-5453	716	20	υ	υ	PROPN
ejpam-5453	716	21	be	be	AUX
ejpam-5453	716	22	a	a	DET
ejpam-5453	716	23	similarity	similarity	NOUN
ejpam-5453	716	24	relation	relation	NOUN
ejpam-5453	716	25	,	,	PUNCT
ejpam-5453	716	26	℘	℘	PROPN
ejpam-5453	716	27	∈	∈	PROPN
ejpam-5453	716	28	{	{	PUNCT
ejpam-5453	716	29	r	r	NOUN
ejpam-5453	716	30	,	,	PUNCT
ejpam-5453	716	31	l	l	NOUN
ejpam-5453	716	32	,	,	PUNCT
ejpam-5453	716	33	i	i	PRON
ejpam-5453	716	34	,	,	PUNCT
ejpam-5453	716	35	u	u	NOUN
ejpam-5453	716	36	}	}	PUNCT
ejpam-5453	716	37	and	and	CCONJ
ejpam-5453	716	38	m	m	PROPN
ejpam-5453	716	39	⊆	⊆	NUM
ejpam-5453	716	40	v.	v.	ADP
ejpam-5453	716	41	then	then	ADV
ejpam-5453	716	42	(	(	PUNCT
ejpam-5453	716	43	i	i	NOUN
ejpam-5453	716	44	)	)	PUNCT
ejpam-5453	716	45	if	if	SCONJ
ejpam-5453	716	46	t	t	PROPN
ejpam-5453	716	47	∈℘m	∈℘m	PROPN
ejpam-5453	716	48	⇒	⇒	VERB
ejpam-5453	716	49	t	t	PROPN
ejpam-5453	716	50	∈s℘m	∈s℘m	PUNCT
ejpam-5453	716	51	⇒	⇒	VERB
ejpam-5453	716	52	t	t	PROPN
ejpam-5453	716	53	∈ξ	∈ξ	PROPN
ejpam-5453	716	54	s℘m	s℘m	NOUN
ejpam-5453	716	55	⇒	⇒	PROPN
ejpam-5453	716	56	t	t	PROPN
ejpam-5453	716	57	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	716	58	s℘	s℘	PROPN
ejpam-5453	716	59	m.	m.	NOUN
ejpam-5453	716	60	(	(	PUNCT
ejpam-5453	716	61	ii	ii	NOUN
ejpam-5453	716	62	)	)	PUNCT
ejpam-5453	716	63	if	if	SCONJ
ejpam-5453	716	64	t	t	PROPN
ejpam-5453	716	65	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	716	66	s℘	s℘	PROPN
ejpam-5453	716	67	m	m	PROPN
ejpam-5453	716	68	⇒	⇒	PROPN
ejpam-5453	716	69	t	t	PROPN
ejpam-5453	716	70	∈ξ	∈ξ	PROPN
ejpam-5453	716	71	s℘m	s℘m	NOUN
ejpam-5453	716	72	⇒	⇒	NOUN
ejpam-5453	716	73	t	t	PROPN
ejpam-5453	716	74	∈s℘m	∈s℘m	PUNCT
ejpam-5453	716	75	⇒	⇒	PROPN
ejpam-5453	716	76	t	t	PROPN
ejpam-5453	716	77	∈℘m	∈℘m	PROPN
ejpam-5453	716	78	.	.	PUNCT
ejpam-5453	717	1	proof	proof	NOUN
ejpam-5453	717	2	.	.	PUNCT
ejpam-5453	718	1	(	(	PUNCT
ejpam-5453	718	2	i	i	NOUN
ejpam-5453	718	3	)	)	PUNCT
ejpam-5453	718	4	we	we	PRON
ejpam-5453	718	5	only	only	ADV
ejpam-5453	718	6	prove	prove	VERB
ejpam-5453	718	7	t	t	PROPN
ejpam-5453	718	8	∈℘m	∈℘m	PROPN
ejpam-5453	718	9	⇒	⇒	PROPN
ejpam-5453	718	10	t	t	PROPN
ejpam-5453	718	11	∈s℘m	∈s℘m	PUNCT
ejpam-5453	718	12	and	and	CCONJ
ejpam-5453	718	13	the	the	DET
ejpam-5453	718	14	other	other	ADJ
ejpam-5453	718	15	cases	case	NOUN
ejpam-5453	718	16	directly	directly	ADV
ejpam-5453	718	17	by	by	ADP
ejpam-5453	718	18	proposition	proposition	NOUN
ejpam-5453	718	19	5.3	5.3	NUM
ejpam-5453	718	20	.	.	PUNCT
ejpam-5453	719	1	let	let	VERB
ejpam-5453	719	2	t	t	PROPN
ejpam-5453	719	3	∈℘m	∈℘m	PROPN
ejpam-5453	719	4	⇒	⇒	NOUN
ejpam-5453	719	5	t	t	PROPN
ejpam-5453	719	6	∈	∈	PROPN
ejpam-5453	719	7	n℘(m	n℘(m	NOUN
ejpam-5453	719	8	)	)	PUNCT
ejpam-5453	719	9	⇒	⇒	NOUN
ejpam-5453	719	10	t	t	PROPN
ejpam-5453	719	11	∈	∈	PROPN
ejpam-5453	719	12	ns℘(m	ns℘(m	PROPN
ejpam-5453	719	13	)	)	PUNCT
ejpam-5453	719	14	by	by	ADP
ejpam-5453	719	15	theorem	theorem	NOUN
ejpam-5453	719	16	2.3	2.3	NUM
ejpam-5453	719	17	.	.	PUNCT
ejpam-5453	720	1	therefore	therefore	ADV
ejpam-5453	720	2	,	,	PUNCT
ejpam-5453	720	3	t	t	PROPN
ejpam-5453	720	4	∈s℘m	∈s℘m	PROPN
ejpam-5453	720	5	.	.	PUNCT
ejpam-5453	720	6	(	(	PUNCT
ejpam-5453	720	7	ii	ii	NOUN
ejpam-5453	720	8	)	)	PUNCT
ejpam-5453	720	9	similar	similar	ADJ
ejpam-5453	720	10	to	to	ADP
ejpam-5453	720	11	(	(	PUNCT
ejpam-5453	720	12	1	1	NUM
ejpam-5453	720	13	)	)	PUNCT
ejpam-5453	720	14	.	.	PUNCT
ejpam-5453	721	1	proposition	proposition	NOUN
ejpam-5453	721	2	5.5	5.5	NUM
ejpam-5453	721	3	.	.	PUNCT
ejpam-5453	722	1	let	let	AUX
ejpam-5453	722	2	(	(	PUNCT
ejpam-5453	722	3	v	v	NOUN
ejpam-5453	722	4	,	,	PUNCT
ejpam-5453	722	5	υ	υ	NOUN
ejpam-5453	722	6	,	,	PUNCT
ejpam-5453	722	7	π℘	π℘	NUM
ejpam-5453	722	8	)	)	PUNCT
ejpam-5453	722	9	be	be	AUX
ejpam-5453	722	10	a	a	DET
ejpam-5453	722	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	722	12	,	,	PUNCT
ejpam-5453	722	13	d	d	PRON
ejpam-5453	722	14	be	be	AUX
ejpam-5453	722	15	an	an	DET
ejpam-5453	722	16	ideal	ideal	NOUN
ejpam-5453	722	17	on	on	ADP
ejpam-5453	722	18	v	v	NOUN
ejpam-5453	722	19	,	,	PUNCT
ejpam-5453	722	20	υ	υ	PROPN
ejpam-5453	722	21	be	be	AUX
ejpam-5453	722	22	a	a	DET
ejpam-5453	722	23	similarity	similarity	NOUN
ejpam-5453	722	24	relation	relation	NOUN
ejpam-5453	722	25	,	,	PUNCT
ejpam-5453	722	26	℘	℘	PROPN
ejpam-5453	722	27	∈	∈	PROPN
ejpam-5453	722	28	{	{	PUNCT
ejpam-5453	722	29	r	r	NOUN
ejpam-5453	722	30	,	,	PUNCT
ejpam-5453	722	31	l	l	NOUN
ejpam-5453	722	32	,	,	PUNCT
ejpam-5453	722	33	i	i	PRON
ejpam-5453	722	34	,	,	PUNCT
ejpam-5453	722	35	u	u	NOUN
ejpam-5453	722	36	}	}	PUNCT
ejpam-5453	722	37	and	and	CCONJ
ejpam-5453	722	38	m	m	PROPN
ejpam-5453	722	39	⊆	⊆	NUM
ejpam-5453	722	40	v.	v.	ADP
ejpam-5453	722	41	then	then	ADV
ejpam-5453	722	42	(	(	PUNCT
ejpam-5453	722	43	i	i	NOUN
ejpam-5453	722	44	)	)	PUNCT
ejpam-5453	722	45	if	if	SCONJ
ejpam-5453	722	46	t	t	PROPN
ejpam-5453	722	47	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	722	48	s℘	s℘	PROPN
ejpam-5453	722	49	m	m	PROPN
ejpam-5453	722	50	⇒	⇒	PROPN
ejpam-5453	722	51	t	t	PROPN
ejpam-5453	722	52	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	722	53	℘	℘	PROPN
ejpam-5453	722	54	m.	m.	NOUN
ejpam-5453	722	55	(	(	PUNCT
ejpam-5453	722	56	ii	ii	NOUN
ejpam-5453	722	57	)	)	PUNCT
ejpam-5453	722	58	if	if	SCONJ
ejpam-5453	722	59	t	t	PROPN
ejpam-5453	722	60	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	722	61	℘	℘	PROPN
ejpam-5453	722	62	m	m	VERB
ejpam-5453	722	63	⇒	⇒	PROPN
ejpam-5453	722	64	t	t	PROPN
ejpam-5453	722	65	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	722	66	s℘	s℘	PROPN
ejpam-5453	722	67	m.	m.	NOUN
ejpam-5453	722	68	proof	proof	NOUN
ejpam-5453	722	69	.	.	PUNCT
ejpam-5453	723	1	(	(	PUNCT
ejpam-5453	723	2	i	i	NOUN
ejpam-5453	723	3	)	)	PUNCT
ejpam-5453	723	4	let	let	VERB
ejpam-5453	723	5	t	t	PROPN
ejpam-5453	723	6	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	723	7	s℘	s℘	PROPN
ejpam-5453	723	8	m	m	PROPN
ejpam-5453	723	9	⇒	⇒	PROPN
ejpam-5453	723	10	t	t	PROPN
ejpam-5453	723	11	∈	∈	PROPN
ejpam-5453	723	12	nd−ξ	nd−ξ	PROPN
ejpam-5453	723	13	s℘	s℘	PROPN
ejpam-5453	723	14	(	(	PUNCT
ejpam-5453	723	15	m	m	NOUN
ejpam-5453	723	16	)	)	PUNCT
ejpam-5453	723	17	⇒	⇒	NOUN
ejpam-5453	723	18	t	t	PROPN
ejpam-5453	723	19	∈	∈	PROPN
ejpam-5453	723	20	nd−ξ	nd−ξ	PROPN
ejpam-5453	723	21	℘	℘	PROPN
ejpam-5453	723	22	(	(	PUNCT
ejpam-5453	723	23	m	m	NOUN
ejpam-5453	723	24	)	)	PUNCT
ejpam-5453	723	25	by	by	ADP
ejpam-5453	723	26	theorem	theorem	NOUN
ejpam-5453	723	27	4.3	4.3	NUM
ejpam-5453	723	28	.	.	PUNCT
ejpam-5453	724	1	therefore	therefore	ADV
ejpam-5453	724	2	,	,	PUNCT
ejpam-5453	724	3	t	t	PROPN
ejpam-5453	724	4	∈d−ξ	∈d−ξ	PROPN
ejpam-5453	724	5	℘	℘	PROPN
ejpam-5453	724	6	m.	m.	NOUN
ejpam-5453	724	7	(	(	PUNCT
ejpam-5453	724	8	ii	ii	NOUN
ejpam-5453	724	9	)	)	PUNCT
ejpam-5453	724	10	similar	similar	ADJ
ejpam-5453	724	11	to	to	ADP
ejpam-5453	724	12	(	(	PUNCT
ejpam-5453	724	13	1	1	NUM
ejpam-5453	724	14	)	)	PUNCT
ejpam-5453	724	15	.	.	PUNCT
ejpam-5453	725	1	definition	definition	NOUN
ejpam-5453	725	2	5.6	5.6	NUM
ejpam-5453	725	3	.	.	PUNCT
ejpam-5453	726	1	let	let	AUX
ejpam-5453	726	2	(	(	PUNCT
ejpam-5453	726	3	v	v	NOUN
ejpam-5453	726	4	,	,	PUNCT
ejpam-5453	726	5	υ	υ	NOUN
ejpam-5453	726	6	,	,	PUNCT
ejpam-5453	726	7	π℘	π℘	NUM
ejpam-5453	726	8	)	)	PUNCT
ejpam-5453	726	9	be	be	AUX
ejpam-5453	726	10	a	a	DET
ejpam-5453	726	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	726	12	,	,	PUNCT
ejpam-5453	726	13	d	d	PRON
ejpam-5453	726	14	be	be	AUX
ejpam-5453	726	15	an	an	DET
ejpam-5453	726	16	ideal	ideal	NOUN
ejpam-5453	726	17	on	on	ADP
ejpam-5453	726	18	v	v	NOUN
ejpam-5453	726	19	,	,	PUNCT
ejpam-5453	726	20	m	m	PROPN
ejpam-5453	726	21	⊆	⊆	NUM
ejpam-5453	726	22	v	v	NOUN
ejpam-5453	726	23	and	and	CCONJ
ejpam-5453	726	24	t	t	NOUN
ejpam-5453	726	25	∈	∈	PROPN
ejpam-5453	726	26	v.	v.	ADP
ejpam-5453	726	27	the	the	DET
ejpam-5453	726	28	d	d	NOUN
ejpam-5453	726	29	-	-	PUNCT
ejpam-5453	726	30	s℘-nearly	s℘-nearly	ADV
ejpam-5453	726	31	rough	rough	ADJ
ejpam-5453	726	32	membership	membership	NOUN
ejpam-5453	726	33	functions	function	NOUN
ejpam-5453	726	34	of	of	ADP
ejpam-5453	726	35	a	a	DET
ejpam-5453	726	36	℘-nbds	℘-nbds	NOUN
ejpam-5453	726	37	on	on	ADP
ejpam-5453	726	38	v	v	NOUN
ejpam-5453	726	39	for	for	ADP
ejpam-5453	726	40	a	a	DET
ejpam-5453	726	41	m	m	NOUN
ejpam-5453	726	42	are	be	AUX
ejpam-5453	726	43	symbolized	symbolize	VERB
ejpam-5453	726	44	by	by	ADP
ejpam-5453	726	45	ω	ω	NUM
ejpam-5453	726	46	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	726	47	m	m	PROPN
ejpam-5453	726	48	:	:	PUNCT
ejpam-5453	726	49	v	v	X
ejpam-5453	726	50	→	→	SYM
ejpam-5453	726	51	[	[	X
ejpam-5453	726	52	0	0	NUM
ejpam-5453	726	53	,	,	PUNCT
ejpam-5453	726	54	1	1	NUM
ejpam-5453	726	55	]	]	PUNCT
ejpam-5453	726	56	,	,	PUNCT
ejpam-5453	726	57	where	where	SCONJ
ejpam-5453	726	58	ω	ω	X
ejpam-5453	726	59	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	726	60	m	m	PROPN
ejpam-5453	726	61	(	(	PUNCT
ejpam-5453	726	62	t	t	PROPN
ejpam-5453	726	63	)	)	PUNCT
ejpam-5453	726	64	=	=	PRON
ejpam-5453	726	65	{	{	PUNCT
ejpam-5453	726	66	1	1	NUM
ejpam-5453	726	67	if	if	SCONJ
ejpam-5453	726	68	1∈χ	1∈χ	NUM
ejpam-5453	726	69	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	726	70	m	m	PROPN
ejpam-5453	726	71	(	(	PUNCT
ejpam-5453	726	72	t	t	PROPN
ejpam-5453	726	73	)	)	PUNCT
ejpam-5453	726	74	.	.	PUNCT
ejpam-5453	727	1	min(χ	min(χ	PROPN
ejpam-5453	727	2	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	727	3	m	m	PROPN
ejpam-5453	727	4	(	(	PUNCT
ejpam-5453	727	5	t	t	PROPN
ejpam-5453	727	6	)	)	PUNCT
ejpam-5453	727	7	)	)	PUNCT
ejpam-5453	727	8	otherwise	otherwise	ADV
ejpam-5453	727	9	.	.	PUNCT
ejpam-5453	727	10	}	}	PUNCT
ejpam-5453	727	11	.	.	PUNCT
ejpam-5453	728	1	and	and	CCONJ
ejpam-5453	728	2	χ	χ	DET
ejpam-5453	728	3	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	728	4	m	m	PROPN
ejpam-5453	728	5	(	(	PUNCT
ejpam-5453	728	6	t	t	PROPN
ejpam-5453	728	7	)	)	PUNCT
ejpam-5453	728	8	=	=	SYM
ejpam-5453	728	9	|d−ξs℘	|d−ξs℘	PROPN
ejpam-5453	728	10	(	(	PUNCT
ejpam-5453	728	11	t)∩m	t)∩m	NOUN
ejpam-5453	728	12	|	|	ADV
ejpam-5453	728	13	|d−ξs℘	|d−ξs℘	PROPN
ejpam-5453	729	1	(	(	PUNCT
ejpam-5453	729	2	t)|	t)|	INTJ
ejpam-5453	729	3	,	,	PUNCT
ejpam-5453	729	4	t	t	PROPN
ejpam-5453	729	5	∈	∈	PROPN
ejpam-5453	729	6	d−	d−	PROPN
ejpam-5453	729	7	ξs℘(t	ξs℘(t	NOUN
ejpam-5453	729	8	)	)	PUNCT
ejpam-5453	729	9	,	,	PUNCT
ejpam-5453	729	10	d−	d−	PROPN
ejpam-5453	729	11	ξs℘(t	ξs℘(t	NOUN
ejpam-5453	729	12	)	)	PUNCT
ejpam-5453	729	13	∈	∈	PROPN
ejpam-5453	729	14	d	d	PROPN
ejpam-5453	729	15	-	-	PUNCT
ejpam-5453	729	16	ξs℘o(v	ξs℘o(v	PROPN
ejpam-5453	729	17	)	)	PUNCT
ejpam-5453	729	18	.	.	PUNCT
ejpam-5453	730	1	remark	remark	VERB
ejpam-5453	730	2	5.10	5.10	NUM
ejpam-5453	730	3	.	.	PUNCT
ejpam-5453	731	1	the	the	PRON
ejpam-5453	731	2	d	d	NOUN
ejpam-5453	731	3	-	-	PUNCT
ejpam-5453	731	4	s℘-nearly	s℘-nearly	ADV
ejpam-5453	731	5	rough	rough	ADJ
ejpam-5453	731	6	membership	membership	NOUN
ejpam-5453	731	7	functions	function	NOUN
ejpam-5453	731	8	are	be	AUX
ejpam-5453	731	9	utilized	utilize	VERB
ejpam-5453	731	10	to	to	PART
ejpam-5453	731	11	present	present	VERB
ejpam-5453	731	12	the	the	DET
ejpam-5453	731	13	d	d	NOUN
ejpam-5453	731	14	-	-	PUNCT
ejpam-5453	731	15	s℘-nearly	s℘-nearly	ADV
ejpam-5453	731	16	lower	low	ADJ
ejpam-5453	731	17	(	(	PUNCT
ejpam-5453	731	18	upper	upper	ADJ
ejpam-5453	731	19	)	)	PUNCT
ejpam-5453	731	20	approximations	approximation	NOUN
ejpam-5453	731	21	as	as	ADP
ejpam-5453	731	22	:	:	PUNCT
ejpam-5453	731	23	(	(	PUNCT
ejpam-5453	731	24	i	i	NOUN
ejpam-5453	731	25	)	)	PUNCT
ejpam-5453	731	26	nd−ξ	nd−ξ	PROPN
ejpam-5453	731	27	s℘	s℘	PROPN
ejpam-5453	731	28	(	(	PUNCT
ejpam-5453	731	29	m	m	NOUN
ejpam-5453	731	30	)	)	PUNCT
ejpam-5453	731	31	=	=	PRON
ejpam-5453	731	32	{	{	PUNCT
ejpam-5453	731	33	t	t	PROPN
ejpam-5453	731	34	∈	∈	PROPN
ejpam-5453	731	35	v	v	NOUN
ejpam-5453	731	36	:	:	PUNCT
ejpam-5453	731	37	ω	ω	NUM
ejpam-5453	731	38	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	731	39	m	m	PROPN
ejpam-5453	731	40	(	(	PUNCT
ejpam-5453	731	41	t	t	PROPN
ejpam-5453	731	42	)	)	PUNCT
ejpam-5453	731	43	=	=	PUNCT
ejpam-5453	732	1	1	1	NUM
ejpam-5453	732	2	}	}	PUNCT
ejpam-5453	732	3	.	.	PUNCT
ejpam-5453	733	1	(	(	PUNCT
ejpam-5453	733	2	ii	ii	NOUN
ejpam-5453	733	3	)	)	PUNCT
ejpam-5453	733	4	n	n	PROPN
ejpam-5453	733	5	d−ξ	d−ξ	NOUN
ejpam-5453	733	6	s℘	s℘	NOUN
ejpam-5453	733	7	(	(	PUNCT
ejpam-5453	733	8	m	m	NOUN
ejpam-5453	733	9	)	)	PUNCT
ejpam-5453	733	10	=	=	PRON
ejpam-5453	733	11	{	{	PUNCT
ejpam-5453	733	12	t	t	PROPN
ejpam-5453	733	13	∈	∈	PROPN
ejpam-5453	733	14	v	v	NOUN
ejpam-5453	733	15	:	:	PUNCT
ejpam-5453	733	16	ω	ω	NUM
ejpam-5453	733	17	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	733	18	m	m	PROPN
ejpam-5453	733	19	(	(	PUNCT
ejpam-5453	733	20	t	t	PROPN
ejpam-5453	733	21	)	)	PUNCT
ejpam-5453	733	22	>	>	X
ejpam-5453	733	23	0	0	NUM
ejpam-5453	733	24	}	}	PUNCT
ejpam-5453	733	25	.	.	PUNCT
ejpam-5453	734	1	(	(	PUNCT
ejpam-5453	734	2	iii	iii	X
ejpam-5453	734	3	)	)	PUNCT
ejpam-5453	734	4	bd−ξ	bd−ξ	PROPN
ejpam-5453	734	5	s℘	s℘	NOUN
ejpam-5453	734	6	(	(	PUNCT
ejpam-5453	734	7	m	m	NOUN
ejpam-5453	734	8	)	)	PUNCT
ejpam-5453	734	9	=	=	PRON
ejpam-5453	734	10	{	{	PUNCT
ejpam-5453	734	11	t	t	PROPN
ejpam-5453	734	12	∈	∈	PROPN
ejpam-5453	734	13	v	v	NOUN
ejpam-5453	734	14	:	:	PUNCT
ejpam-5453	734	15	0	0	NUM
ejpam-5453	734	16	<	<	X
ejpam-5453	734	17	ω	ω	NUM
ejpam-5453	734	18	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	734	19	m	m	PROPN
ejpam-5453	734	20	(	(	PUNCT
ejpam-5453	734	21	t	t	PROPN
ejpam-5453	734	22	)	)	PUNCT
ejpam-5453	734	23	<	<	X
ejpam-5453	734	24	1	1	NUM
ejpam-5453	734	25	}	}	PUNCT
ejpam-5453	734	26	.	.	PUNCT
ejpam-5453	735	1	m.	m.	PROPN
ejpam-5453	735	2	hosny	hosny	PROPN
ejpam-5453	735	3	/	/	SYM
ejpam-5453	735	4	eur	eur	PROPN
ejpam-5453	735	5	.	.	PUNCT
ejpam-5453	736	1	j.	j.	PROPN
ejpam-5453	736	2	pure	pure	PROPN
ejpam-5453	736	3	appl	appl	PROPN
ejpam-5453	736	4	.	.	PROPN
ejpam-5453	736	5	math	math	PROPN
ejpam-5453	736	6	,	,	PUNCT
ejpam-5453	736	7	17	17	NUM
ejpam-5453	736	8	(	(	PUNCT
ejpam-5453	736	9	4	4	NUM
ejpam-5453	736	10	)	)	PUNCT
ejpam-5453	736	11	(	(	PUNCT
ejpam-5453	736	12	2024	2024	NUM
ejpam-5453	736	13	)	)	PUNCT
ejpam-5453	736	14	,	,	PUNCT
ejpam-5453	736	15	2843	2843	NUM
ejpam-5453	736	16	-	-	SYM
ejpam-5453	736	17	2877	2877	NUM
ejpam-5453	736	18	2870	2870	NUM
ejpam-5453	736	19	proposition	proposition	NOUN
ejpam-5453	736	20	5.6	5.6	NUM
ejpam-5453	736	21	.	.	PUNCT
ejpam-5453	737	1	let	let	AUX
ejpam-5453	737	2	(	(	PUNCT
ejpam-5453	737	3	v	v	NOUN
ejpam-5453	737	4	,	,	PUNCT
ejpam-5453	737	5	υ	υ	NOUN
ejpam-5453	737	6	,	,	PUNCT
ejpam-5453	737	7	π℘	π℘	NUM
ejpam-5453	737	8	)	)	PUNCT
ejpam-5453	737	9	be	be	AUX
ejpam-5453	737	10	a	a	DET
ejpam-5453	737	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	737	12	,	,	PUNCT
ejpam-5453	737	13	d	d	PRON
ejpam-5453	737	14	be	be	AUX
ejpam-5453	737	15	an	an	DET
ejpam-5453	737	16	ideal	ideal	NOUN
ejpam-5453	737	17	on	on	ADP
ejpam-5453	737	18	v	v	NUM
ejpam-5453	737	19	and	and	CCONJ
ejpam-5453	737	20	m	m	PROPN
ejpam-5453	737	21	,	,	PUNCT
ejpam-5453	737	22	n	n	PROPN
ejpam-5453	737	23	⊆	⊆	NUM
ejpam-5453	737	24	v.	v.	ADP
ejpam-5453	737	25	then	then	ADV
ejpam-5453	737	26	(	(	PUNCT
ejpam-5453	737	27	i	i	NOUN
ejpam-5453	737	28	)	)	PUNCT
ejpam-5453	737	29	if	if	SCONJ
ejpam-5453	737	30	ω	ω	PROPN
ejpam-5453	737	31	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	737	32	m	m	PROPN
ejpam-5453	737	33	(	(	PUNCT
ejpam-5453	737	34	t	t	PROPN
ejpam-5453	737	35	)	)	PUNCT
ejpam-5453	737	36	=	=	SYM
ejpam-5453	737	37	1	1	NUM
ejpam-5453	737	38	⇔	⇔	PROPN
ejpam-5453	737	39	t	t	PROPN
ejpam-5453	737	40	∈	∈	PROPN
ejpam-5453	737	41	∈d−ξs℘	∈d−ξs℘	NOUN
ejpam-5453	737	42	s℘	s℘	NOUN
ejpam-5453	737	43	m.	m.	NOUN
ejpam-5453	737	44	(	(	PUNCT
ejpam-5453	737	45	ii	ii	NOUN
ejpam-5453	737	46	)	)	PUNCT
ejpam-5453	738	1	if	if	SCONJ
ejpam-5453	738	2	ω	ω	PROPN
ejpam-5453	738	3	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	738	4	m	m	PROPN
ejpam-5453	738	5	(	(	PUNCT
ejpam-5453	738	6	x	x	NOUN
ejpam-5453	738	7	)	)	PUNCT
ejpam-5453	738	8	=	=	SYM
ejpam-5453	738	9	0	0	NUM
ejpam-5453	738	10	⇔	⇔	PROPN
ejpam-5453	738	11	t	t	PROPN
ejpam-5453	738	12	∈	∈	PROPN
ejpam-5453	738	13	v	v	ADP
ejpam-5453	738	14	−n	−n	ADJ
ejpam-5453	738	15	d−ξ	d−ξ	NOUN
ejpam-5453	738	16	s℘	s℘	NOUN
ejpam-5453	738	17	(	(	PUNCT
ejpam-5453	738	18	m	m	NOUN
ejpam-5453	738	19	)	)	PUNCT
ejpam-5453	738	20	.	.	PUNCT
ejpam-5453	739	1	(	(	PUNCT
ejpam-5453	739	2	iii	iii	X
ejpam-5453	739	3	)	)	PUNCT
ejpam-5453	739	4	if	if	SCONJ
ejpam-5453	739	5	0	0	NUM
ejpam-5453	739	6	<	<	X
ejpam-5453	739	7	ω	ω	NUM
ejpam-5453	739	8	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	739	9	m	m	PROPN
ejpam-5453	739	10	(	(	PUNCT
ejpam-5453	739	11	t	t	PROPN
ejpam-5453	739	12	)	)	PUNCT
ejpam-5453	739	13	<	<	X
ejpam-5453	739	14	1	1	NUM
ejpam-5453	739	15	⇔	⇔	PROPN
ejpam-5453	739	16	t	t	PROPN
ejpam-5453	739	17	∈	∈	PROPN
ejpam-5453	739	18	bd−ξ	bd−ξ	PROPN
ejpam-5453	739	19	s℘	s℘	PROPN
ejpam-5453	739	20	(	(	PUNCT
ejpam-5453	739	21	m	m	NOUN
ejpam-5453	739	22	)	)	PUNCT
ejpam-5453	739	23	.	.	PUNCT
ejpam-5453	740	1	(	(	PUNCT
ejpam-5453	740	2	iv	iv	X
ejpam-5453	740	3	)	)	PUNCT
ejpam-5453	740	4	if	if	SCONJ
ejpam-5453	740	5	ω	ω	PROPN
ejpam-5453	740	6	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	740	7	m	m	VERB
ejpam-5453	740	8	′	′	NUM
ejpam-5453	740	9	(	(	PUNCT
ejpam-5453	740	10	t	t	NOUN
ejpam-5453	740	11	)	)	PUNCT
ejpam-5453	740	12	=	=	SYM
ejpam-5453	741	1	1−	1−	NUM
ejpam-5453	741	2	ω	ω	NUM
ejpam-5453	741	3	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	741	4	m	m	PROPN
ejpam-5453	741	5	(	(	PUNCT
ejpam-5453	741	6	t),∀	t),∀	PROPN
ejpam-5453	741	7	t	t	PROPN
ejpam-5453	741	8	∈	∈	PROPN
ejpam-5453	741	9	v.	v.	PROPN
ejpam-5453	741	10	(	(	PUNCT
ejpam-5453	741	11	v	v	NOUN
ejpam-5453	741	12	)	)	PUNCT
ejpam-5453	742	1	if	if	SCONJ
ejpam-5453	742	2	ω	ω	NUM
ejpam-5453	742	3	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	742	4	m∪n	m∪n	NOUN
ejpam-5453	742	5	(	(	PUNCT
ejpam-5453	742	6	t	t	PROPN
ejpam-5453	742	7	)	)	PUNCT
ejpam-5453	742	8	≥	≥	NOUN
ejpam-5453	742	9	max(ω	max(ω	PROPN
ejpam-5453	742	10	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	742	11	m	m	PROPN
ejpam-5453	742	12	(	(	PUNCT
ejpam-5453	742	13	t	t	PROPN
ejpam-5453	742	14	)	)	PUNCT
ejpam-5453	742	15	,	,	PUNCT
ejpam-5453	742	16	ω	ω	NUM
ejpam-5453	742	17	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	742	18	n	n	PROPN
ejpam-5453	742	19	(	(	PUNCT
ejpam-5453	742	20	t	t	PROPN
ejpam-5453	742	21	)	)	PUNCT
ejpam-5453	742	22	)	)	PUNCT
ejpam-5453	742	23	,	,	PUNCT
ejpam-5453	742	24	∀	∀	X
ejpam-5453	742	25	t	t	NOUN
ejpam-5453	742	26	∈	∈	PROPN
ejpam-5453	742	27	v.	v.	PROPN
ejpam-5453	742	28	(	(	PUNCT
ejpam-5453	742	29	vi	vi	PROPN
ejpam-5453	742	30	)	)	PUNCT
ejpam-5453	742	31	if	if	SCONJ
ejpam-5453	742	32	ω	ω	PROPN
ejpam-5453	742	33	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	742	34	m∩n	m∩n	PROPN
ejpam-5453	742	35	(	(	PUNCT
ejpam-5453	742	36	t	t	PROPN
ejpam-5453	742	37	)	)	PUNCT
ejpam-5453	742	38	≤	≤	NOUN
ejpam-5453	742	39	min(ω	min(ω	PRON
ejpam-5453	742	40	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	742	41	m	m	PROPN
ejpam-5453	742	42	(	(	PUNCT
ejpam-5453	742	43	t	t	PROPN
ejpam-5453	742	44	)	)	PUNCT
ejpam-5453	742	45	,	,	PUNCT
ejpam-5453	742	46	ω	ω	NUM
ejpam-5453	742	47	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	742	48	n	n	PROPN
ejpam-5453	742	49	(	(	PUNCT
ejpam-5453	742	50	t	t	PROPN
ejpam-5453	742	51	)	)	PUNCT
ejpam-5453	742	52	)	)	PUNCT
ejpam-5453	742	53	,	,	PUNCT
ejpam-5453	742	54	∀	∀	X
ejpam-5453	742	55	t	t	NOUN
ejpam-5453	742	56	∈	∈	PROPN
ejpam-5453	742	57	v.	v.	ADP
ejpam-5453	742	58	proof	proof	NOUN
ejpam-5453	742	59	.	.	PUNCT
ejpam-5453	743	1	it	it	PRON
ejpam-5453	743	2	is	be	AUX
ejpam-5453	743	3	similar	similar	ADJ
ejpam-5453	743	4	to	to	PART
ejpam-5453	743	5	proposition	proposition	VERB
ejpam-5453	743	6	5.1	5.1	NUM
ejpam-5453	743	7	.	.	PUNCT
ejpam-5453	744	1	lemma	lemma	PROPN
ejpam-5453	744	2	5.5	5.5	NUM
ejpam-5453	744	3	.	.	PUNCT
ejpam-5453	745	1	let	let	AUX
ejpam-5453	745	2	(	(	PUNCT
ejpam-5453	745	3	v	v	NOUN
ejpam-5453	745	4	,	,	PUNCT
ejpam-5453	745	5	υ	υ	NOUN
ejpam-5453	745	6	,	,	PUNCT
ejpam-5453	745	7	π℘	π℘	NUM
ejpam-5453	745	8	)	)	PUNCT
ejpam-5453	745	9	be	be	AUX
ejpam-5453	745	10	a	a	DET
ejpam-5453	745	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	745	12	,	,	PUNCT
ejpam-5453	745	13	d	d	PRON
ejpam-5453	745	14	be	be	AUX
ejpam-5453	745	15	an	an	DET
ejpam-5453	745	16	ideal	ideal	NOUN
ejpam-5453	745	17	on	on	ADP
ejpam-5453	745	18	v	v	NUM
ejpam-5453	745	19	and	and	CCONJ
ejpam-5453	745	20	m	m	PROPN
ejpam-5453	745	21	⊆	⊆	NUM
ejpam-5453	745	22	v.	v.	ADP
ejpam-5453	745	23	then	then	ADV
ejpam-5453	745	24	(	(	PUNCT
ejpam-5453	745	25	i	i	NOUN
ejpam-5453	745	26	)	)	PUNCT
ejpam-5453	745	27	ω	ω	PROPN
ejpam-5453	745	28	s℘	s℘	NOUN
ejpam-5453	745	29	m	m	PROPN
ejpam-5453	745	30	(	(	PUNCT
ejpam-5453	745	31	t	t	PROPN
ejpam-5453	745	32	)	)	PUNCT
ejpam-5453	745	33	=	=	SYM
ejpam-5453	745	34	1	1	NUM
ejpam-5453	745	35	⇒	⇒	NOUN
ejpam-5453	745	36	ω	ω	NOUN
ejpam-5453	746	1	ξs℘	ξs℘	PROPN
ejpam-5453	746	2	m	m	PROPN
ejpam-5453	746	3	(	(	PUNCT
ejpam-5453	746	4	t	t	PROPN
ejpam-5453	746	5	)	)	PUNCT
ejpam-5453	746	6	=	=	SYM
ejpam-5453	746	7	1	1	NUM
ejpam-5453	746	8	⇒	⇒	NOUN
ejpam-5453	746	9	ω	ω	NOUN
ejpam-5453	746	10	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	746	11	m	m	PROPN
ejpam-5453	746	12	(	(	PUNCT
ejpam-5453	746	13	t	t	PROPN
ejpam-5453	746	14	)	)	PUNCT
ejpam-5453	746	15	=	=	SYM
ejpam-5453	746	16	1	1	NUM
ejpam-5453	746	17	,	,	PUNCT
ejpam-5453	746	18	∀	∀	X
ejpam-5453	746	19	t	t	NOUN
ejpam-5453	746	20	∈	∈	PROPN
ejpam-5453	746	21	v.	v.	PROPN
ejpam-5453	746	22	(	(	PUNCT
ejpam-5453	746	23	ii	ii	PROPN
ejpam-5453	746	24	)	)	PUNCT
ejpam-5453	746	25	ω	ω	PROPN
ejpam-5453	746	26	s℘	s℘	NOUN
ejpam-5453	746	27	m	m	PROPN
ejpam-5453	746	28	(	(	PUNCT
ejpam-5453	746	29	t	t	PROPN
ejpam-5453	746	30	)	)	PUNCT
ejpam-5453	746	31	=	=	SYM
ejpam-5453	746	32	0	0	NUM
ejpam-5453	746	33	⇒	⇒	PROPN
ejpam-5453	746	34	ω	ω	NUM
ejpam-5453	746	35	ξs℘	ξs℘	PROPN
ejpam-5453	746	36	m	m	PROPN
ejpam-5453	746	37	(	(	PUNCT
ejpam-5453	746	38	t	t	PROPN
ejpam-5453	746	39	)	)	PUNCT
ejpam-5453	746	40	=	=	SYM
ejpam-5453	746	41	0	0	NUM
ejpam-5453	746	42	⇒	⇒	PROPN
ejpam-5453	746	43	ω	ω	X
ejpam-5453	746	44	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	746	45	m	m	PROPN
ejpam-5453	746	46	(	(	PUNCT
ejpam-5453	746	47	t	t	PROPN
ejpam-5453	746	48	)	)	PUNCT
ejpam-5453	746	49	=	=	SYM
ejpam-5453	747	1	0,∀	0,∀	NUM
ejpam-5453	747	2	t	t	NOUN
ejpam-5453	747	3	∈	∈	NOUN
ejpam-5453	747	4	v.	v.	ADP
ejpam-5453	747	5	proof	proof	NOUN
ejpam-5453	747	6	.	.	PUNCT
ejpam-5453	748	1	(	(	PUNCT
ejpam-5453	748	2	i	i	NOUN
ejpam-5453	748	3	)	)	PUNCT
ejpam-5453	748	4	ω	ω	PROPN
ejpam-5453	748	5	s℘	s℘	NOUN
ejpam-5453	748	6	m	m	PROPN
ejpam-5453	748	7	(	(	PUNCT
ejpam-5453	748	8	t	t	PROPN
ejpam-5453	748	9	)	)	PUNCT
ejpam-5453	748	10	=	=	SYM
ejpam-5453	748	11	1	1	NUM
ejpam-5453	748	12	⇒	⇒	NOUN
ejpam-5453	748	13	t	t	PROPN
ejpam-5453	748	14	∈	∈	PROPN
ejpam-5453	748	15	ns℘(m	ns℘(m	PROPN
ejpam-5453	748	16	)	)	PUNCT
ejpam-5453	748	17	⇒	⇒	NOUN
ejpam-5453	748	18	t	t	PROPN
ejpam-5453	748	19	∈	∈	PROPN
ejpam-5453	748	20	nξ	nξ	ADP
ejpam-5453	748	21	s℘(m	s℘(m	PROPN
ejpam-5453	748	22	)	)	PUNCT
ejpam-5453	748	23	by	by	ADP
ejpam-5453	748	24	theorem	theorem	ADJ
ejpam-5453	748	25	2.4	2.4	NUM
ejpam-5453	748	26	[	[	SYM
ejpam-5453	748	27	43	43	NUM
ejpam-5453	748	28	]	]	PUNCT
ejpam-5453	748	29	.	.	PUNCT
ejpam-5453	749	1	therefore	therefore	ADV
ejpam-5453	749	2	,	,	PUNCT
ejpam-5453	749	3	ω	ω	PROPN
ejpam-5453	749	4	ξs℘	ξs℘	PROPN
ejpam-5453	749	5	m	m	PROPN
ejpam-5453	749	6	(	(	PUNCT
ejpam-5453	749	7	t	t	PROPN
ejpam-5453	749	8	)	)	PUNCT
ejpam-5453	749	9	=	=	SYM
ejpam-5453	750	1	1	1	X
ejpam-5453	750	2	.	.	PUNCT
ejpam-5453	750	3	let	let	VERB
ejpam-5453	750	4	ω	ω	PUNCT
ejpam-5453	750	5	ξs℘	ξs℘	PROPN
ejpam-5453	750	6	m	m	ADJ
ejpam-5453	750	7	(	(	PUNCT
ejpam-5453	750	8	x	x	NOUN
ejpam-5453	750	9	)	)	PUNCT
ejpam-5453	750	10	=	=	SYM
ejpam-5453	750	11	1	1	NUM
ejpam-5453	750	12	,	,	PUNCT
ejpam-5453	750	13	then	then	ADV
ejpam-5453	750	14	t	t	PROPN
ejpam-5453	750	15	∈	∈	PROPN
ejpam-5453	750	16	nξ	nξ	ADP
ejpam-5453	750	17	s℘(m	s℘(m	PROPN
ejpam-5453	750	18	)	)	PUNCT
ejpam-5453	750	19	⇒	⇒	PROPN
ejpam-5453	750	20	t	t	PROPN
ejpam-5453	750	21	∈	∈	PROPN
ejpam-5453	750	22	nd−ξ	nd−ξ	PROPN
ejpam-5453	750	23	s℘	s℘	PROPN
ejpam-5453	750	24	(	(	PUNCT
ejpam-5453	750	25	m	m	NOUN
ejpam-5453	750	26	)	)	PUNCT
ejpam-5453	750	27	by	by	ADP
ejpam-5453	750	28	theorem	theorem	NOUN
ejpam-5453	750	29	4.1	4.1	NUM
ejpam-5453	750	30	.	.	PUNCT
ejpam-5453	751	1	hence	hence	ADV
ejpam-5453	751	2	,	,	PUNCT
ejpam-5453	751	3	ω	ω	PROPN
ejpam-5453	751	4	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	751	5	m	m	PROPN
ejpam-5453	751	6	(	(	PUNCT
ejpam-5453	751	7	t	t	PROPN
ejpam-5453	751	8	)	)	PUNCT
ejpam-5453	751	9	=	=	NOUN
ejpam-5453	751	10	1,∀	1,∀	NUM
ejpam-5453	751	11	t	t	NOUN
ejpam-5453	751	12	∈	∈	PROPN
ejpam-5453	751	13	v.	v.	PROPN
ejpam-5453	751	14	(	(	PUNCT
ejpam-5453	751	15	ii	ii	PROPN
ejpam-5453	751	16	)	)	PUNCT
ejpam-5453	751	17	ω	ω	PROPN
ejpam-5453	751	18	s℘	s℘	NOUN
ejpam-5453	751	19	m	m	PROPN
ejpam-5453	751	20	(	(	PUNCT
ejpam-5453	751	21	t	t	PROPN
ejpam-5453	751	22	)	)	PUNCT
ejpam-5453	751	23	=	=	SYM
ejpam-5453	751	24	0	0	NUM
ejpam-5453	751	25	⇒	⇒	NOUN
ejpam-5453	751	26	t	t	PROPN
ejpam-5453	751	27	∈	∈	PROPN
ejpam-5453	751	28	v	v	ADP
ejpam-5453	751	29	−	−	PROPN
ejpam-5453	751	30	ns℘(m	ns℘(m	NOUN
ejpam-5453	751	31	)	)	PUNCT
ejpam-5453	751	32	⇒	⇒	NOUN
ejpam-5453	751	33	t	t	PROPN
ejpam-5453	751	34	∈	∈	PROPN
ejpam-5453	751	35	v	v	ADP
ejpam-5453	751	36	−	−	PROPN
ejpam-5453	751	37	n	n	CCONJ
ejpam-5453	751	38	ξ	ξ	X
ejpam-5453	751	39	s℘(m	s℘(m	PROPN
ejpam-5453	751	40	)	)	PUNCT
ejpam-5453	751	41	by	by	ADP
ejpam-5453	751	42	theorem	theorem	ADJ
ejpam-5453	751	43	2.4	2.4	NUM
ejpam-5453	751	44	[	[	SYM
ejpam-5453	751	45	43	43	NUM
ejpam-5453	751	46	]	]	PUNCT
ejpam-5453	751	47	.	.	PUNCT
ejpam-5453	752	1	hence	hence	ADV
ejpam-5453	752	2	,	,	PUNCT
ejpam-5453	752	3	ω	ω	PROPN
ejpam-5453	752	4	ξs℘	ξs℘	PROPN
ejpam-5453	752	5	m	m	PROPN
ejpam-5453	752	6	(	(	PUNCT
ejpam-5453	752	7	t	t	PROPN
ejpam-5453	752	8	)	)	PUNCT
ejpam-5453	752	9	=	=	NOUN
ejpam-5453	753	1	0	0	X
ejpam-5453	753	2	.	.	PUNCT
ejpam-5453	754	1	let	let	VERB
ejpam-5453	754	2	ω	ω	PUNCT
ejpam-5453	754	3	ξs℘	ξs℘	PROPN
ejpam-5453	754	4	m	m	PROPN
ejpam-5453	754	5	(	(	PUNCT
ejpam-5453	754	6	t	t	PROPN
ejpam-5453	754	7	)	)	PUNCT
ejpam-5453	754	8	=	=	SYM
ejpam-5453	754	9	0	0	NUM
ejpam-5453	754	10	,	,	PUNCT
ejpam-5453	754	11	then	then	ADV
ejpam-5453	754	12	t	t	PROPN
ejpam-5453	754	13	∈	∈	PROPN
ejpam-5453	754	14	v	v	ADP
ejpam-5453	754	15	−n	−n	PROPN
ejpam-5453	754	16	ξ	ξ	PROPN
ejpam-5453	754	17	s℘(m	s℘(m	PROPN
ejpam-5453	754	18	)	)	PUNCT
ejpam-5453	754	19	⇒	⇒	NOUN
ejpam-5453	754	20	t	t	PROPN
ejpam-5453	754	21	∈	∈	PROPN
ejpam-5453	754	22	v	v	ADP
ejpam-5453	754	23	−n	−n	ADJ
ejpam-5453	754	24	d−ξ	d−ξ	NOUN
ejpam-5453	754	25	s℘	s℘	NOUN
ejpam-5453	754	26	(	(	PUNCT
ejpam-5453	754	27	m	m	NOUN
ejpam-5453	754	28	)	)	PUNCT
ejpam-5453	754	29	by	by	ADP
ejpam-5453	754	30	theorem	theorem	NOUN
ejpam-5453	754	31	4.1	4.1	NUM
ejpam-5453	754	32	.	.	PUNCT
ejpam-5453	755	1	hence	hence	ADV
ejpam-5453	755	2	,	,	PUNCT
ejpam-5453	755	3	ω	ω	PROPN
ejpam-5453	755	4	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	755	5	m	m	PROPN
ejpam-5453	755	6	(	(	PUNCT
ejpam-5453	755	7	t	t	PROPN
ejpam-5453	755	8	)	)	PUNCT
ejpam-5453	755	9	=	=	SYM
ejpam-5453	756	1	0,∀	0,∀	NUM
ejpam-5453	756	2	t	t	NOUN
ejpam-5453	756	3	∈	∈	NOUN
ejpam-5453	756	4	v.	v.	ADP
ejpam-5453	756	5	remark	remark	NOUN
ejpam-5453	756	6	5.11	5.11	NUM
ejpam-5453	756	7	.	.	PUNCT
ejpam-5453	757	1	the	the	DET
ejpam-5453	757	2	opposite	opposite	NOUN
ejpam-5453	757	3	of	of	ADP
ejpam-5453	757	4	lemma	lemma	PROPN
ejpam-5453	757	5	5.5	5.5	NUM
ejpam-5453	757	6	is	be	AUX
ejpam-5453	757	7	incorrect	incorrect	ADJ
ejpam-5453	757	8	,	,	PUNCT
ejpam-5453	757	9	as	as	SCONJ
ejpam-5453	757	10	shown	show	VERB
ejpam-5453	757	11	in	in	ADP
ejpam-5453	757	12	example	example	NOUN
ejpam-5453	757	13	3.1	3.1	NUM
ejpam-5453	757	14	.	.	PUNCT
ejpam-5453	758	1	the	the	DET
ejpam-5453	758	2	different	different	ADJ
ejpam-5453	758	3	types	type	NOUN
ejpam-5453	758	4	of	of	ADP
ejpam-5453	758	5	membership	membership	NOUN
ejpam-5453	758	6	functions	function	NOUN
ejpam-5453	758	7	defined	define	VERB
ejpam-5453	758	8	in	in	ADP
ejpam-5453	758	9	this	this	DET
ejpam-5453	758	10	manuscript	manuscript	NOUN
ejpam-5453	758	11	are	be	AUX
ejpam-5453	758	12	more	more	ADV
ejpam-5453	758	13	precise	precise	ADJ
ejpam-5453	758	14	and	and	CCONJ
ejpam-5453	758	15	general	general	ADJ
ejpam-5453	758	16	than	than	ADP
ejpam-5453	758	17	the	the	DET
ejpam-5453	758	18	last	last	ADJ
ejpam-5453	758	19	ones	one	NOUN
ejpam-5453	758	20	in	in	ADP
ejpam-5453	758	21	[	[	X
ejpam-5453	758	22	1	1	NUM
ejpam-5453	758	23	]	]	PUNCT
ejpam-5453	758	24	as	as	SCONJ
ejpam-5453	758	25	it	it	PRON
ejpam-5453	758	26	is	be	AUX
ejpam-5453	758	27	presented	present	VERB
ejpam-5453	758	28	in	in	ADP
ejpam-5453	758	29	the	the	DET
ejpam-5453	758	30	following	follow	VERB
ejpam-5453	758	31	consequences	consequence	NOUN
ejpam-5453	758	32	.	.	PUNCT
ejpam-5453	759	1	lemma	lemma	PROPN
ejpam-5453	759	2	5.6	5.6	NUM
ejpam-5453	759	3	.	.	PUNCT
ejpam-5453	760	1	let	let	AUX
ejpam-5453	760	2	(	(	PUNCT
ejpam-5453	760	3	v	v	NOUN
ejpam-5453	760	4	,	,	PUNCT
ejpam-5453	760	5	υ	υ	NOUN
ejpam-5453	760	6	,	,	PUNCT
ejpam-5453	760	7	π℘	π℘	NUM
ejpam-5453	760	8	)	)	PUNCT
ejpam-5453	760	9	be	be	AUX
ejpam-5453	760	10	a	a	DET
ejpam-5453	760	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	760	12	,	,	PUNCT
ejpam-5453	760	13	d	d	PRON
ejpam-5453	760	14	be	be	AUX
ejpam-5453	760	15	an	an	DET
ejpam-5453	760	16	ideal	ideal	NOUN
ejpam-5453	760	17	on	on	ADP
ejpam-5453	760	18	v	v	NOUN
ejpam-5453	760	19	,	,	PUNCT
ejpam-5453	760	20	υ	υ	PROPN
ejpam-5453	760	21	be	be	AUX
ejpam-5453	760	22	a	a	DET
ejpam-5453	760	23	similarity	similarity	NOUN
ejpam-5453	760	24	relation	relation	NOUN
ejpam-5453	760	25	,	,	PUNCT
ejpam-5453	760	26	℘	℘	PROPN
ejpam-5453	760	27	∈	∈	PROPN
ejpam-5453	760	28	{	{	PUNCT
ejpam-5453	760	29	r	r	NOUN
ejpam-5453	760	30	,	,	PUNCT
ejpam-5453	760	31	l	l	NOUN
ejpam-5453	760	32	,	,	PUNCT
ejpam-5453	760	33	i	i	PRON
ejpam-5453	760	34	,	,	PUNCT
ejpam-5453	760	35	u	u	NOUN
ejpam-5453	760	36	}	}	PUNCT
ejpam-5453	760	37	and	and	CCONJ
ejpam-5453	760	38	m	m	PROPN
ejpam-5453	760	39	⊆	⊆	NUM
ejpam-5453	760	40	v.	v.	ADP
ejpam-5453	760	41	then	then	ADV
ejpam-5453	760	42	(	(	PUNCT
ejpam-5453	760	43	i	i	NOUN
ejpam-5453	760	44	)	)	PUNCT
ejpam-5453	760	45	ω℘	ω℘	NOUN
ejpam-5453	760	46	m	m	VERB
ejpam-5453	760	47	(	(	PUNCT
ejpam-5453	760	48	t	t	PROPN
ejpam-5453	760	49	)	)	PUNCT
ejpam-5453	760	50	=	=	SYM
ejpam-5453	760	51	1	1	NUM
ejpam-5453	760	52	⇒	⇒	NOUN
ejpam-5453	760	53	ω	ω	NUM
ejpam-5453	760	54	s℘	s℘	NOUN
ejpam-5453	760	55	m	m	PROPN
ejpam-5453	760	56	(	(	PUNCT
ejpam-5453	760	57	t	t	PROPN
ejpam-5453	760	58	)	)	PUNCT
ejpam-5453	760	59	=	=	SYM
ejpam-5453	760	60	1	1	NUM
ejpam-5453	760	61	⇒	⇒	NOUN
ejpam-5453	760	62	ω	ω	NOUN
ejpam-5453	760	63	ξs℘	ξs℘	PROPN
ejpam-5453	760	64	m	m	PROPN
ejpam-5453	760	65	(	(	PUNCT
ejpam-5453	760	66	t	t	PROPN
ejpam-5453	760	67	)	)	PUNCT
ejpam-5453	760	68	=	=	SYM
ejpam-5453	760	69	1	1	NUM
ejpam-5453	760	70	⇒	⇒	NOUN
ejpam-5453	760	71	ω	ω	NOUN
ejpam-5453	760	72	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	760	73	m	m	PROPN
ejpam-5453	760	74	(	(	PUNCT
ejpam-5453	760	75	t	t	PROPN
ejpam-5453	760	76	)	)	PUNCT
ejpam-5453	760	77	=	=	SYM
ejpam-5453	760	78	1	1	NUM
ejpam-5453	760	79	,	,	PUNCT
ejpam-5453	760	80	∀	∀	X
ejpam-5453	760	81	t	t	NOUN
ejpam-5453	760	82	∈	∈	PROPN
ejpam-5453	760	83	v.	v.	PROPN
ejpam-5453	760	84	(	(	PUNCT
ejpam-5453	760	85	ii	ii	NOUN
ejpam-5453	760	86	)	)	PUNCT
ejpam-5453	760	87	ω℘	ω℘	NOUN
ejpam-5453	760	88	m	m	PROPN
ejpam-5453	760	89	(	(	PUNCT
ejpam-5453	760	90	t	t	PROPN
ejpam-5453	760	91	)	)	PUNCT
ejpam-5453	760	92	=	=	SYM
ejpam-5453	760	93	0	0	NUM
ejpam-5453	760	94	⇒	⇒	PROPN
ejpam-5453	760	95	ω	ω	NUM
ejpam-5453	760	96	s℘	s℘	NOUN
ejpam-5453	760	97	m	m	PROPN
ejpam-5453	760	98	(	(	PUNCT
ejpam-5453	760	99	t	t	PROPN
ejpam-5453	760	100	)	)	PUNCT
ejpam-5453	760	101	=	=	SYM
ejpam-5453	760	102	0	0	NUM
ejpam-5453	760	103	⇒	⇒	PROPN
ejpam-5453	760	104	ω	ω	NUM
ejpam-5453	760	105	ξs℘	ξs℘	PROPN
ejpam-5453	760	106	m	m	PROPN
ejpam-5453	760	107	(	(	PUNCT
ejpam-5453	760	108	t	t	PROPN
ejpam-5453	760	109	)	)	PUNCT
ejpam-5453	760	110	=	=	SYM
ejpam-5453	760	111	0	0	NUM
ejpam-5453	760	112	⇒	⇒	PROPN
ejpam-5453	760	113	ω	ω	X
ejpam-5453	760	114	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	760	115	m	m	PROPN
ejpam-5453	760	116	(	(	PUNCT
ejpam-5453	760	117	t	t	PROPN
ejpam-5453	760	118	)	)	PUNCT
ejpam-5453	760	119	=	=	SYM
ejpam-5453	760	120	0	0	NUM
ejpam-5453	760	121	,	,	PUNCT
ejpam-5453	760	122	∀	∀	X
ejpam-5453	760	123	t	t	NOUN
ejpam-5453	760	124	∈	∈	PROPN
ejpam-5453	760	125	v.	v.	ADP
ejpam-5453	760	126	proof	proof	NOUN
ejpam-5453	760	127	.	.	PUNCT
ejpam-5453	761	1	m.	m.	PROPN
ejpam-5453	761	2	hosny	hosny	PROPN
ejpam-5453	761	3	/	/	SYM
ejpam-5453	761	4	eur	eur	PROPN
ejpam-5453	761	5	.	.	PUNCT
ejpam-5453	762	1	j.	j.	PROPN
ejpam-5453	762	2	pure	pure	PROPN
ejpam-5453	762	3	appl	appl	PROPN
ejpam-5453	762	4	.	.	PROPN
ejpam-5453	762	5	math	math	PROPN
ejpam-5453	762	6	,	,	PUNCT
ejpam-5453	762	7	17	17	NUM
ejpam-5453	762	8	(	(	PUNCT
ejpam-5453	762	9	4	4	NUM
ejpam-5453	762	10	)	)	PUNCT
ejpam-5453	762	11	(	(	PUNCT
ejpam-5453	762	12	2024	2024	NUM
ejpam-5453	762	13	)	)	PUNCT
ejpam-5453	762	14	,	,	PUNCT
ejpam-5453	762	15	2843	2843	NUM
ejpam-5453	762	16	-	-	SYM
ejpam-5453	762	17	2877	2877	NUM
ejpam-5453	762	18	2871	2871	NUM
ejpam-5453	762	19	(	(	PUNCT
ejpam-5453	762	20	i	i	NOUN
ejpam-5453	762	21	)	)	PUNCT
ejpam-5453	762	22	ω℘	ω℘	NOUN
ejpam-5453	762	23	m	m	VERB
ejpam-5453	762	24	(	(	PUNCT
ejpam-5453	762	25	t	t	PROPN
ejpam-5453	762	26	)	)	PUNCT
ejpam-5453	762	27	=	=	SYM
ejpam-5453	762	28	1	1	NUM
ejpam-5453	762	29	⇒	⇒	NOUN
ejpam-5453	762	30	t	t	X
ejpam-5453	762	31	∈	∈	PROPN
ejpam-5453	762	32	n℘(m	n℘(m	NOUN
ejpam-5453	762	33	)	)	PUNCT
ejpam-5453	762	34	⇒	⇒	NOUN
ejpam-5453	762	35	t	t	PROPN
ejpam-5453	762	36	∈	∈	PROPN
ejpam-5453	762	37	ns℘(m	ns℘(m	PROPN
ejpam-5453	762	38	)	)	PUNCT
ejpam-5453	762	39	by	by	ADP
ejpam-5453	762	40	theorem	theorem	NOUN
ejpam-5453	762	41	2.3	2.3	NUM
ejpam-5453	762	42	.	.	PUNCT
ejpam-5453	763	1	therefore	therefore	ADV
ejpam-5453	763	2	,	,	PUNCT
ejpam-5453	763	3	ω	ω	NUM
ejpam-5453	763	4	s℘	s℘	NOUN
ejpam-5453	763	5	m	m	PROPN
ejpam-5453	763	6	(	(	PUNCT
ejpam-5453	763	7	t	t	PROPN
ejpam-5453	763	8	)	)	PUNCT
ejpam-5453	763	9	=	=	SYM
ejpam-5453	764	1	1	1	X
ejpam-5453	764	2	.	.	PUNCT
ejpam-5453	764	3	(	(	PUNCT
ejpam-5453	764	4	ii	ii	NOUN
ejpam-5453	764	5	)	)	PUNCT
ejpam-5453	764	6	ω℘	ω℘	NOUN
ejpam-5453	764	7	m	m	PROPN
ejpam-5453	764	8	(	(	PUNCT
ejpam-5453	764	9	t	t	PROPN
ejpam-5453	764	10	)	)	PUNCT
ejpam-5453	764	11	=	=	SYM
ejpam-5453	764	12	0	0	NUM
ejpam-5453	764	13	⇒	⇒	NOUN
ejpam-5453	764	14	t	t	PROPN
ejpam-5453	764	15	∈	∈	PROPN
ejpam-5453	764	16	v	v	ADP
ejpam-5453	764	17	−n℘(m	−n℘(m	ADJ
ejpam-5453	764	18	)	)	PUNCT
ejpam-5453	764	19	⇒	⇒	NOUN
ejpam-5453	764	20	t	t	PROPN
ejpam-5453	764	21	∈	∈	PROPN
ejpam-5453	764	22	v	v	ADP
ejpam-5453	764	23	−ns℘(m	−ns℘(m	NOUN
ejpam-5453	764	24	)	)	PUNCT
ejpam-5453	764	25	by	by	ADP
ejpam-5453	764	26	theorem	theorem	ADJ
ejpam-5453	764	27	2.3	2.3	NUM
ejpam-5453	764	28	.	.	PUNCT
ejpam-5453	765	1	hence	hence	ADV
ejpam-5453	765	2	,	,	PUNCT
ejpam-5453	765	3	ω	ω	NUM
ejpam-5453	765	4	s℘	s℘	NOUN
ejpam-5453	765	5	m	m	PROPN
ejpam-5453	765	6	(	(	PUNCT
ejpam-5453	765	7	t	t	PROPN
ejpam-5453	765	8	)	)	PUNCT
ejpam-5453	765	9	=	=	NOUN
ejpam-5453	766	1	0	0	X
ejpam-5453	766	2	.	.	PUNCT
ejpam-5453	767	1	the	the	DET
ejpam-5453	767	2	other	other	ADJ
ejpam-5453	767	3	cases	case	NOUN
ejpam-5453	767	4	directly	directly	ADV
ejpam-5453	767	5	by	by	ADP
ejpam-5453	767	6	lemma	lemma	PROPN
ejpam-5453	767	7	5.5	5.5	NUM
ejpam-5453	767	8	.	.	PUNCT
ejpam-5453	768	1	lemma	lemma	PROPN
ejpam-5453	768	2	5.7	5.7	NUM
ejpam-5453	768	3	.	.	PUNCT
ejpam-5453	769	1	let	let	AUX
ejpam-5453	769	2	(	(	PUNCT
ejpam-5453	769	3	v	v	NOUN
ejpam-5453	769	4	,	,	PUNCT
ejpam-5453	769	5	υ	υ	NOUN
ejpam-5453	769	6	,	,	PUNCT
ejpam-5453	769	7	π℘	π℘	NUM
ejpam-5453	769	8	)	)	PUNCT
ejpam-5453	769	9	be	be	AUX
ejpam-5453	769	10	a	a	DET
ejpam-5453	769	11	℘-nbds	℘-nbds	NOUN
ejpam-5453	769	12	,	,	PUNCT
ejpam-5453	769	13	d	d	PRON
ejpam-5453	769	14	be	be	AUX
ejpam-5453	769	15	an	an	DET
ejpam-5453	769	16	ideal	ideal	NOUN
ejpam-5453	769	17	on	on	ADP
ejpam-5453	769	18	v	v	NOUN
ejpam-5453	769	19	,	,	PUNCT
ejpam-5453	769	20	υ	υ	PROPN
ejpam-5453	769	21	be	be	AUX
ejpam-5453	769	22	a	a	DET
ejpam-5453	769	23	similarity	similarity	NOUN
ejpam-5453	769	24	relation	relation	NOUN
ejpam-5453	769	25	,	,	PUNCT
ejpam-5453	769	26	℘	℘	PROPN
ejpam-5453	769	27	∈	∈	PROPN
ejpam-5453	769	28	{	{	PUNCT
ejpam-5453	769	29	r	r	NOUN
ejpam-5453	769	30	,	,	PUNCT
ejpam-5453	769	31	l	l	NOUN
ejpam-5453	769	32	,	,	PUNCT
ejpam-5453	769	33	i	i	PRON
ejpam-5453	769	34	,	,	PUNCT
ejpam-5453	769	35	u	u	NOUN
ejpam-5453	769	36	}	}	PUNCT
ejpam-5453	769	37	and	and	CCONJ
ejpam-5453	769	38	m	m	PROPN
ejpam-5453	769	39	⊆	⊆	NUM
ejpam-5453	769	40	v.	v.	ADP
ejpam-5453	769	41	then	then	ADV
ejpam-5453	769	42	(	(	PUNCT
ejpam-5453	769	43	i	i	NOUN
ejpam-5453	769	44	)	)	PUNCT
ejpam-5453	769	45	ω	ω	PROPN
ejpam-5453	769	46	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	769	47	m	m	PROPN
ejpam-5453	769	48	(	(	PUNCT
ejpam-5453	769	49	t	t	PROPN
ejpam-5453	769	50	)	)	PUNCT
ejpam-5453	769	51	=	=	SYM
ejpam-5453	769	52	1	1	NUM
ejpam-5453	769	53	⇒	⇒	NOUN
ejpam-5453	769	54	ω	ω	NUM
ejpam-5453	769	55	d−ξ℘	d−ξ℘	NOUN
ejpam-5453	769	56	m	m	PROPN
ejpam-5453	769	57	(	(	PUNCT
ejpam-5453	769	58	t	t	NOUN
ejpam-5453	769	59	)	)	PUNCT
ejpam-5453	769	60	=	=	SYM
ejpam-5453	769	61	1	1	NUM
ejpam-5453	769	62	,	,	PUNCT
ejpam-5453	769	63	∀	∀	X
ejpam-5453	769	64	t	t	NOUN
ejpam-5453	769	65	∈	∈	PROPN
ejpam-5453	769	66	v.	v.	PROPN
ejpam-5453	769	67	(	(	PUNCT
ejpam-5453	769	68	ii	ii	PROPN
ejpam-5453	769	69	)	)	PUNCT
ejpam-5453	769	70	ω	ω	PROPN
ejpam-5453	769	71	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	769	72	m	m	PROPN
ejpam-5453	769	73	(	(	PUNCT
ejpam-5453	769	74	t	t	PROPN
ejpam-5453	769	75	)	)	PUNCT
ejpam-5453	769	76	=	=	SYM
ejpam-5453	769	77	0	0	NUM
ejpam-5453	769	78	⇒	⇒	PROPN
ejpam-5453	769	79	ω	ω	NUM
ejpam-5453	769	80	d−ξ℘	d−ξ℘	NOUN
ejpam-5453	769	81	m	m	PROPN
ejpam-5453	769	82	(	(	PUNCT
ejpam-5453	769	83	t	t	NOUN
ejpam-5453	769	84	)	)	PUNCT
ejpam-5453	769	85	=	=	SYM
ejpam-5453	769	86	0	0	NUM
ejpam-5453	769	87	,	,	PUNCT
ejpam-5453	769	88	∀	∀	X
ejpam-5453	769	89	t	t	NOUN
ejpam-5453	769	90	∈	∈	PROPN
ejpam-5453	769	91	v.	v.	ADP
ejpam-5453	769	92	proof	proof	NOUN
ejpam-5453	769	93	.	.	PUNCT
ejpam-5453	770	1	(	(	PUNCT
ejpam-5453	770	2	i	i	NOUN
ejpam-5453	770	3	)	)	PUNCT
ejpam-5453	770	4	ω	ω	PROPN
ejpam-5453	770	5	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	770	6	m	m	PROPN
ejpam-5453	770	7	(	(	PUNCT
ejpam-5453	770	8	t	t	PROPN
ejpam-5453	770	9	)	)	PUNCT
ejpam-5453	770	10	=	=	SYM
ejpam-5453	770	11	1	1	NUM
ejpam-5453	770	12	⇒	⇒	NOUN
ejpam-5453	770	13	t	t	PROPN
ejpam-5453	770	14	∈	∈	PROPN
ejpam-5453	770	15	nd−ξ	nd−ξ	PROPN
ejpam-5453	770	16	s℘	s℘	PROPN
ejpam-5453	770	17	(	(	PUNCT
ejpam-5453	770	18	m	m	NOUN
ejpam-5453	770	19	)	)	PUNCT
ejpam-5453	770	20	⇒	⇒	NOUN
ejpam-5453	770	21	t	t	PROPN
ejpam-5453	770	22	∈	∈	PROPN
ejpam-5453	770	23	nd−ξ	nd−ξ	PROPN
ejpam-5453	770	24	℘	℘	PROPN
ejpam-5453	770	25	(	(	PUNCT
ejpam-5453	770	26	m	m	NOUN
ejpam-5453	770	27	)	)	PUNCT
ejpam-5453	770	28	.	.	PUNCT
ejpam-5453	771	1	by	by	ADP
ejpam-5453	771	2	theorem	theorem	NOUN
ejpam-5453	771	3	4.3	4.3	NUM
ejpam-5453	771	4	.	.	PUNCT
ejpam-5453	772	1	therefore	therefore	ADV
ejpam-5453	772	2	,	,	PUNCT
ejpam-5453	772	3	ω	ω	NUM
ejpam-5453	772	4	d−ξ℘	d−ξ℘	NOUN
ejpam-5453	772	5	m	m	PROPN
ejpam-5453	772	6	(	(	PUNCT
ejpam-5453	772	7	t	t	NOUN
ejpam-5453	772	8	)	)	PUNCT
ejpam-5453	772	9	=	=	SYM
ejpam-5453	773	1	1	1	X
ejpam-5453	773	2	.	.	PUNCT
ejpam-5453	773	3	(	(	PUNCT
ejpam-5453	773	4	ii	ii	NOUN
ejpam-5453	773	5	)	)	PUNCT
ejpam-5453	773	6	ω	ω	PROPN
ejpam-5453	773	7	d−ξs℘	d−ξs℘	PROPN
ejpam-5453	773	8	m	m	PROPN
ejpam-5453	773	9	(	(	PUNCT
ejpam-5453	773	10	t	t	PROPN
ejpam-5453	773	11	)	)	PUNCT
ejpam-5453	773	12	=	=	SYM
ejpam-5453	773	13	0	0	NUM
ejpam-5453	773	14	⇒	⇒	NOUN
ejpam-5453	773	15	t	t	PROPN
ejpam-5453	773	16	∈	∈	PROPN
ejpam-5453	773	17	v	v	NOUN
ejpam-5453	773	18	−n	−n	ADJ
ejpam-5453	773	19	d−ξ	d−ξ	NOUN
ejpam-5453	773	20	s℘	s℘	NOUN
ejpam-5453	773	21	(	(	PUNCT
ejpam-5453	773	22	m	m	NOUN
ejpam-5453	773	23	)	)	PUNCT
ejpam-5453	773	24	⇒	⇒	NOUN
ejpam-5453	773	25	t	t	PROPN
ejpam-5453	773	26	∈	∈	PROPN
ejpam-5453	773	27	v	v	NOUN
ejpam-5453	773	28	−n	−n	ADJ
ejpam-5453	773	29	d−ξ	d−ξ	NOUN
ejpam-5453	773	30	℘	℘	PROPN
ejpam-5453	773	31	(	(	PUNCT
ejpam-5453	773	32	m	m	NOUN
ejpam-5453	773	33	)	)	PUNCT
ejpam-5453	773	34	by	by	ADP
ejpam-5453	773	35	theorem	theorem	NOUN
ejpam-5453	773	36	4.3	4.3	NUM
ejpam-5453	773	37	.	.	PUNCT
ejpam-5453	774	1	hence	hence	ADV
ejpam-5453	774	2	,	,	PUNCT
ejpam-5453	774	3	ω	ω	NUM
ejpam-5453	774	4	d−ξ℘	d−ξ℘	NOUN
ejpam-5453	774	5	m	m	PROPN
ejpam-5453	774	6	(	(	PUNCT
ejpam-5453	774	7	t	t	NOUN
ejpam-5453	774	8	)	)	PUNCT
ejpam-5453	774	9	=	=	NOUN
ejpam-5453	774	10	0	0	X
ejpam-5453	774	11	.	.	PUNCT
ejpam-5453	774	12	example	example	NOUN
ejpam-5453	774	13	3.2	3.2	NUM
ejpam-5453	774	14	confirms	confirm	VERB
ejpam-5453	774	15	that	that	SCONJ
ejpam-5453	774	16	the	the	DET
ejpam-5453	774	17	similarity	similarity	NOUN
ejpam-5453	774	18	relation	relation	NOUN
ejpam-5453	774	19	in	in	ADP
ejpam-5453	774	20	propositions	proposition	NOUN
ejpam-5453	774	21	5.4	5.4	NUM
ejpam-5453	774	22	,	,	PUNCT
ejpam-5453	774	23	5.5	5.5	NUM
ejpam-5453	774	24	and	and	CCONJ
ejpam-5453	774	25	lemma	lemma	PROPN
ejpam-5453	774	26	5.6	5.6	NUM
ejpam-5453	774	27	is	be	AUX
ejpam-5453	774	28	not	not	PART
ejpam-5453	774	29	dispensable	dispensable	ADJ
ejpam-5453	774	30	.	.	PUNCT
ejpam-5453	775	1	additionally	additionally	ADV
ejpam-5453	775	2	,	,	PUNCT
ejpam-5453	775	3	example	example	NOUN
ejpam-5453	775	4	3.3	3.3	NUM
ejpam-5453	775	5	illustrates	illustrate	VERB
ejpam-5453	775	6	that	that	SCONJ
ejpam-5453	775	7	,	,	PUNCT
ejpam-5453	775	8	in	in	ADP
ejpam-5453	775	9	general	general	ADJ
ejpam-5453	775	10	,	,	PUNCT
ejpam-5453	775	11	the	the	DET
ejpam-5453	775	12	opposite	opposite	NOUN
ejpam-5453	775	13	of	of	ADP
ejpam-5453	775	14	propositions	proposition	NOUN
ejpam-5453	775	15	5.4	5.4	NUM
ejpam-5453	775	16	,	,	PUNCT
ejpam-5453	775	17	5.5	5.5	NUM
ejpam-5453	775	18	and	and	CCONJ
ejpam-5453	775	19	lemma	lemma	PROPN
ejpam-5453	775	20	5.6	5.6	NUM
ejpam-5453	775	21	dose	dose	NOUN
ejpam-5453	775	22	not	not	PART
ejpam-5453	775	23	hold	hold	VERB
ejpam-5453	775	24	and	and	CCONJ
ejpam-5453	775	25	τs℘	τs℘	NOUN
ejpam-5453	775	26	,	,	PUNCT
ejpam-5453	775	27	τ℘	τ℘	NUM
ejpam-5453	775	28	are	be	AUX
ejpam-5453	775	29	incomparable	incomparable	ADJ
ejpam-5453	775	30	if	if	SCONJ
ejpam-5453	775	31	℘	℘	NUM
ejpam-5453	775	32	∈	∈	PROPN
ejpam-5453	775	33	{	{	PUNCT
ejpam-5453	775	34	<	<	X
ejpam-5453	775	35	r	r	X
ejpam-5453	775	36	>	>	PUNCT
ejpam-5453	775	37	,	,	PUNCT
ejpam-5453	775	38	<	<	X
ejpam-5453	775	39	l	l	X
ejpam-5453	775	40	>	>	PUNCT
ejpam-5453	775	41	,	,	PUNCT
ejpam-5453	775	42	<	<	X
ejpam-5453	775	43	i	i	X
ejpam-5453	775	44	>	>	X
ejpam-5453	775	45	,	,	PUNCT
ejpam-5453	775	46	<	<	X
ejpam-5453	775	47	u	u	X
ejpam-5453	775	48	>	>	X
ejpam-5453	775	49	}	}	PUNCT
ejpam-5453	775	50	.	.	PUNCT
ejpam-5453	776	1	so	so	ADV
ejpam-5453	776	2	,	,	PUNCT
ejpam-5453	776	3	propositions	proposition	NOUN
ejpam-5453	776	4	5.4	5.4	NUM
ejpam-5453	776	5	,	,	PUNCT
ejpam-5453	776	6	5.5	5.5	NUM
ejpam-5453	776	7	and	and	CCONJ
ejpam-5453	776	8	lemma	lemma	PROPN
ejpam-5453	776	9	5.6	5.6	NUM
ejpam-5453	776	10	apply	apply	VERB
ejpam-5453	776	11	only	only	ADV
ejpam-5453	776	12	for	for	ADP
ejpam-5453	776	13	℘	℘	PROPN
ejpam-5453	776	14	∈	∈	PROPN
ejpam-5453	776	15	{	{	PUNCT
ejpam-5453	776	16	r	r	NOUN
ejpam-5453	776	17	,	,	PUNCT
ejpam-5453	776	18	l	l	NOUN
ejpam-5453	776	19	,	,	PUNCT
ejpam-5453	776	20	i	i	PRON
ejpam-5453	776	21	,	,	PUNCT
ejpam-5453	776	22	u	u	NOUN
ejpam-5453	776	23	}	}	PUNCT
ejpam-5453	776	24	.	.	PUNCT
ejpam-5453	777	1	6	6	X
ejpam-5453	777	2	.	.	X
ejpam-5453	777	3	medical	medical	ADJ
ejpam-5453	777	4	example	example	NOUN
ejpam-5453	777	5	:	:	PUNCT
ejpam-5453	777	6	chikungunya	chikungunya	ADJ
ejpam-5453	777	7	disease	disease	NOUN
ejpam-5453	777	8	this	this	DET
ejpam-5453	777	9	section	section	NOUN
ejpam-5453	777	10	primarily	primarily	ADV
ejpam-5453	777	11	seeks	seek	VERB
ejpam-5453	777	12	to	to	PART
ejpam-5453	777	13	evaluate	evaluate	VERB
ejpam-5453	777	14	the	the	DET
ejpam-5453	777	15	suggested	suggest	VERB
ejpam-5453	777	16	technique	technique	NOUN
ejpam-5453	777	17	by	by	ADP
ejpam-5453	777	18	comparing	compare	VERB
ejpam-5453	777	19	it	it	PRON
ejpam-5453	777	20	with	with	ADP
ejpam-5453	777	21	the	the	DET
ejpam-5453	777	22	prior	prior	ADJ
ejpam-5453	777	23	approach	approach	NOUN
ejpam-5453	777	24	in	in	ADP
ejpam-5453	777	25	[	[	X
ejpam-5453	777	26	1	1	NUM
ejpam-5453	777	27	,	,	PUNCT
ejpam-5453	777	28	2	2	NUM
ejpam-5453	777	29	,	,	PUNCT
ejpam-5453	777	30	30	30	NUM
ejpam-5453	777	31	,	,	PUNCT
ejpam-5453	777	32	43	43	NUM
ejpam-5453	777	33	]	]	PUNCT
ejpam-5453	777	34	,	,	PUNCT
ejpam-5453	777	35	using	use	VERB
ejpam-5453	777	36	the	the	DET
ejpam-5453	777	37	chikungunya	chikungunya	NOUN
ejpam-5453	777	38	disease	disease	NOUN
ejpam-5453	777	39	information	information	NOUN
ejpam-5453	777	40	system	system	NOUN
ejpam-5453	777	41	.	.	PUNCT
ejpam-5453	778	1	common	common	ADJ
ejpam-5453	778	2	symptoms	symptom	NOUN
ejpam-5453	778	3	include	include	VERB
ejpam-5453	778	4	joint	joint	ADJ
ejpam-5453	778	5	pain	pain	NOUN
ejpam-5453	778	6	,	,	PUNCT
ejpam-5453	778	7	fever	fever	NOUN
ejpam-5453	778	8	,	,	PUNCT
ejpam-5453	778	9	while	while	SCONJ
ejpam-5453	778	10	joint	joint	ADJ
ejpam-5453	778	11	swelling	swelling	NOUN
ejpam-5453	778	12	,	,	PUNCT
ejpam-5453	778	13	headache	headache	NOUN
ejpam-5453	778	14	,	,	PUNCT
ejpam-5453	778	15	and	and	CCONJ
ejpam-5453	778	16	rash	rash	NOUN
ejpam-5453	778	17	may	may	AUX
ejpam-5453	778	18	also	also	ADV
ejpam-5453	778	19	occur	occur	VERB
ejpam-5453	778	20	but	but	CCONJ
ejpam-5453	778	21	vary	vary	VERB
ejpam-5453	778	22	among	among	ADP
ejpam-5453	778	23	individuals	individual	NOUN
ejpam-5453	778	24	.	.	PUNCT
ejpam-5453	779	1	until	until	ADP
ejpam-5453	779	2	now	now	ADV
ejpam-5453	779	3	,	,	PUNCT
ejpam-5453	779	4	there	there	PRON
ejpam-5453	779	5	is	be	VERB
ejpam-5453	779	6	no	no	DET
ejpam-5453	779	7	specific	specific	ADJ
ejpam-5453	779	8	treatment	treatment	NOUN
ejpam-5453	779	9	or	or	CCONJ
ejpam-5453	779	10	vaccine	vaccine	NOUN
ejpam-5453	779	11	for	for	ADP
ejpam-5453	779	12	chikungunya	chikungunya	NOUN
ejpam-5453	779	13	.	.	PUNCT
ejpam-5453	780	1	however	however	ADV
ejpam-5453	780	2	,	,	PUNCT
ejpam-5453	780	3	some	some	DET
ejpam-5453	780	4	symptoms	symptom	NOUN
ejpam-5453	780	5	relief	relief	NOUN
ejpam-5453	780	6	can	can	AUX
ejpam-5453	780	7	be	be	AUX
ejpam-5453	780	8	obtained	obtain	VERB
ejpam-5453	780	9	through	through	ADP
ejpam-5453	780	10	fluids	fluid	NOUN
ejpam-5453	780	11	,	,	PUNCT
ejpam-5453	780	12	rest	rest	NOUN
ejpam-5453	780	13	,	,	PUNCT
ejpam-5453	780	14	and	and	CCONJ
ejpam-5453	780	15	over	over	ADP
ejpam-5453	780	16	-	-	PUNCT
ejpam-5453	780	17	the	the	DET
ejpam-5453	780	18	-	-	PUNCT
ejpam-5453	780	19	counter	counter	NOUN
ejpam-5453	780	20	pain	pain	NOUN
ejpam-5453	780	21	relievers	reliever	NOUN
ejpam-5453	780	22	.	.	PUNCT
ejpam-5453	781	1	although	although	SCONJ
ejpam-5453	781	2	most	most	ADJ
ejpam-5453	781	3	patients	patient	NOUN
ejpam-5453	781	4	recover	recover	VERB
ejpam-5453	781	5	within	within	ADP
ejpam-5453	781	6	a	a	DET
ejpam-5453	781	7	week	week	NOUN
ejpam-5453	781	8	,	,	PUNCT
ejpam-5453	781	9	the	the	DET
ejpam-5453	781	10	riskiness	riskiness	NOUN
ejpam-5453	781	11	of	of	ADP
ejpam-5453	781	12	this	this	DET
ejpam-5453	781	13	sickness	sickness	NOUN
ejpam-5453	781	14	is	be	AUX
ejpam-5453	781	15	that	that	SCONJ
ejpam-5453	781	16	joint	joint	ADJ
ejpam-5453	781	17	pain	pain	NOUN
ejpam-5453	781	18	can	can	AUX
ejpam-5453	781	19	be	be	AUX
ejpam-5453	781	20	intense	intense	ADJ
ejpam-5453	781	21	and	and	CCONJ
ejpam-5453	781	22	long	long	ADV
ejpam-5453	781	23	-	-	PUNCT
ejpam-5453	781	24	lasting	last	VERB
ejpam-5453	781	25	,	,	PUNCT
ejpam-5453	781	26	potentially	potentially	ADV
ejpam-5453	781	27	persisting	persist	VERB
ejpam-5453	781	28	for	for	ADP
ejpam-5453	781	29	months	month	NOUN
ejpam-5453	781	30	.	.	PUNCT
ejpam-5453	782	1	chikungunya	chikungunya	NOUN
ejpam-5453	782	2	poses	pose	VERB
ejpam-5453	782	3	a	a	DET
ejpam-5453	782	4	significant	significant	ADJ
ejpam-5453	782	5	medical	medical	ADJ
ejpam-5453	782	6	challenge	challenge	NOUN
ejpam-5453	782	7	in	in	ADP
ejpam-5453	782	8	many	many	ADJ
ejpam-5453	782	9	regions	region	NOUN
ejpam-5453	782	10	in	in	ADP
ejpam-5453	782	11	the	the	DET
ejpam-5453	782	12	following	follow	VERB
ejpam-5453	782	13	analysis	analysis	NOUN
ejpam-5453	782	14	assist	assist	VERB
ejpam-5453	782	15	the	the	DET
ejpam-5453	782	16	decision	decision	NOUN
ejpam-5453	782	17	-	-	PUNCT
ejpam-5453	782	18	makers	maker	NOUN
ejpam-5453	782	19	in	in	ADP
ejpam-5453	782	20	making	make	VERB
ejpam-5453	782	21	a	a	DET
ejpam-5453	782	22	precise	precise	ADJ
ejpam-5453	782	23	decision	decision	NOUN
ejpam-5453	782	24	for	for	ADP
ejpam-5453	782	25	the	the	DET
ejpam-5453	782	26	specific	specific	ADJ
ejpam-5453	782	27	subset	subset	NOUN
ejpam-5453	782	28	of	of	ADP
ejpam-5453	782	29	patients	patient	NOUN
ejpam-5453	782	30	which	which	PRON
ejpam-5453	782	31	are	be	AUX
ejpam-5453	782	32	considered	consider	VERB
ejpam-5453	782	33	.	.	PUNCT
ejpam-5453	783	1	table	table	NOUN
ejpam-5453	783	2	6	6	NUM
ejpam-5453	783	3	lists	list	NOUN
ejpam-5453	783	4	patients	patient	NOUN
ejpam-5453	783	5	v	v	ADP
ejpam-5453	783	6	=	=	SYM
ejpam-5453	783	7	{	{	PUNCT
ejpam-5453	783	8	l1	l1	PROPN
ejpam-5453	783	9	,	,	PUNCT
ejpam-5453	783	10	l2	l2	NOUN
ejpam-5453	783	11	,	,	PUNCT
ejpam-5453	783	12	l3	l3	PROPN
ejpam-5453	783	13	,	,	PUNCT
ejpam-5453	783	14	l4	l4	PROPN
ejpam-5453	783	15	,	,	PUNCT
ejpam-5453	783	16	l5	l5	PROPN
ejpam-5453	783	17	,	,	PUNCT
ejpam-5453	783	18	l6	l6	PROPN
ejpam-5453	783	19	,	,	PUNCT
ejpam-5453	783	20	l7	l7	PROPN
ejpam-5453	783	21	}	}	PUNCT
ejpam-5453	783	22	in	in	ADP
ejpam-5453	783	23	rows	row	NOUN
ejpam-5453	783	24	,	,	PUNCT
ejpam-5453	783	25	and	and	CCONJ
ejpam-5453	783	26	the	the	DET
ejpam-5453	783	27	details	detail	NOUN
ejpam-5453	783	28	of	of	ADP
ejpam-5453	783	29	symptoms	symptom	NOUN
ejpam-5453	783	30	(	(	PUNCT
ejpam-5453	783	31	attributes)in	attributes)in	NOUN
ejpam-5453	783	32	columns	column	NOUN
ejpam-5453	783	33	:	:	PUNCT
ejpam-5453	783	34	⊺1	⊺1	NOUN
ejpam-5453	783	35	represents	represent	VERB
ejpam-5453	783	36	a	a	DET
ejpam-5453	783	37	fever	fever	NOUN
ejpam-5453	783	38	,	,	PUNCT
ejpam-5453	783	39	⊺2	⊺2	PROPN
ejpam-5453	783	40	represents	represent	VERB
ejpam-5453	783	41	joint	joint	ADJ
ejpam-5453	783	42	pains	pain	NOUN
ejpam-5453	783	43	,	,	PUNCT
ejpam-5453	783	44	⊺3	⊺3	PROPN
ejpam-5453	783	45	represents	represent	VERB
ejpam-5453	783	46	joint	joint	ADJ
ejpam-5453	783	47	swelling	swelling	NOUN
ejpam-5453	783	48	,	,	PUNCT
ejpam-5453	783	49	and	and	CCONJ
ejpam-5453	783	50	⊺4	⊺4	PROPN
ejpam-5453	783	51	represents	represent	VERB
ejpam-5453	783	52	a	a	DET
ejpam-5453	783	53	headache	headache	NOUN
ejpam-5453	783	54	,	,	PUNCT
ejpam-5453	783	55	⊺5	⊺5	PROPN
ejpam-5453	783	56	is	be	AUX
ejpam-5453	783	57	rash	rash	ADJ
ejpam-5453	783	58	,	,	PUNCT
ejpam-5453	783	59	where	where	SCONJ
ejpam-5453	783	60	⊺1,⊺2	⊺1,⊺2	PROPN
ejpam-5453	783	61	,	,	PUNCT
ejpam-5453	783	62	⊺3,⊺4	⊺3,⊺4	PROPN
ejpam-5453	783	63	represented	represent	VERB
ejpam-5453	783	64	by	by	ADP
ejpam-5453	783	65	two	two	NUM
ejpam-5453	783	66	values	value	NOUN
ejpam-5453	783	67	:	:	PUNCT
ejpam-5453	783	68	“	"	PUNCT
ejpam-5453	783	69	⊤•	⊤•	X
ejpam-5453	783	70	”	"	PUNCT
ejpam-5453	783	71	and	and	CCONJ
ejpam-5453	783	72	“	"	PUNCT
ejpam-5453	783	73	⊤	⊤	PROPN
ejpam-5453	783	74	◦	◦	NOUN
ejpam-5453	783	75	”	"	PUNCT
ejpam-5453	783	76	which	which	PRON
ejpam-5453	783	77	respectively	respectively	ADV
ejpam-5453	783	78	show	show	VERB
ejpam-5453	783	79	m.	m.	NOUN
ejpam-5453	783	80	hosny	hosny	PROPN
ejpam-5453	783	81	/	/	SYM
ejpam-5453	783	82	eur	eur	PROPN
ejpam-5453	783	83	.	.	PUNCT
ejpam-5453	784	1	j.	j.	PROPN
ejpam-5453	784	2	pure	pure	PROPN
ejpam-5453	784	3	appl	appl	PROPN
ejpam-5453	784	4	.	.	PROPN
ejpam-5453	784	5	math	math	PROPN
ejpam-5453	784	6	,	,	PUNCT
ejpam-5453	784	7	17	17	NUM
ejpam-5453	784	8	(	(	PUNCT
ejpam-5453	784	9	4	4	NUM
ejpam-5453	784	10	)	)	PUNCT
ejpam-5453	784	11	(	(	PUNCT
ejpam-5453	784	12	2024	2024	NUM
ejpam-5453	784	13	)	)	PUNCT
ejpam-5453	784	14	,	,	PUNCT
ejpam-5453	784	15	2843	2843	NUM
ejpam-5453	784	16	-	-	SYM
ejpam-5453	784	17	2877	2877	NUM
ejpam-5453	784	18	2872	2872	NUM
ejpam-5453	784	19	whether	whether	SCONJ
ejpam-5453	784	20	each	each	DET
ejpam-5453	784	21	symptom	symptom	NOUN
ejpam-5453	784	22	is	be	AUX
ejpam-5453	784	23	present	present	ADJ
ejpam-5453	784	24	or	or	CCONJ
ejpam-5453	784	25	absent	absent	ADJ
ejpam-5453	784	26	for	for	ADP
ejpam-5453	784	27	the	the	DET
ejpam-5453	784	28	patients	patient	NOUN
ejpam-5453	784	29	.	.	PUNCT
ejpam-5453	785	1	while	while	SCONJ
ejpam-5453	785	2	,	,	PUNCT
ejpam-5453	785	3	⊺5	⊺5	NOUN
ejpam-5453	785	4	represented	represent	VERB
ejpam-5453	785	5	by	by	ADP
ejpam-5453	785	6	three	three	NUM
ejpam-5453	785	7	values	value	NOUN
ejpam-5453	785	8	:	:	PUNCT
ejpam-5453	785	9	(	(	PUNCT
ejpam-5453	785	10	f1	f1	NOUN
ejpam-5453	785	11	)	)	PUNCT
ejpam-5453	785	12	,	,	PUNCT
ejpam-5453	785	13	(	(	PUNCT
ejpam-5453	785	14	f2	f2	PROPN
ejpam-5453	785	15	)	)	PUNCT
ejpam-5453	785	16	and	and	CCONJ
ejpam-5453	785	17	(	(	PUNCT
ejpam-5453	785	18	f3	f3	ADJ
ejpam-5453	785	19	)	)	PUNCT
ejpam-5453	785	20	.	.	PUNCT
ejpam-5453	786	1	the	the	DET
ejpam-5453	786	2	disease	disease	NOUN
ejpam-5453	786	3	decision	decision	NOUN
ejpam-5453	786	4	d	d	NOUN
ejpam-5453	786	5	is	be	AUX
ejpam-5453	786	6	displayed	display	VERB
ejpam-5453	786	7	in	in	ADP
ejpam-5453	786	8	the	the	DET
ejpam-5453	786	9	seventh	seventh	ADJ
ejpam-5453	786	10	column	column	NOUN
ejpam-5453	786	11	by	by	ADP
ejpam-5453	786	12	two	two	NUM
ejpam-5453	786	13	possible	possible	ADJ
ejpam-5453	786	14	values	value	NOUN
ejpam-5453	786	15	“	"	PUNCT
ejpam-5453	786	16	yes	yes	INTJ
ejpam-5453	786	17	”	"	PUNCT
ejpam-5453	786	18	or	or	CCONJ
ejpam-5453	786	19	“	"	PUNCT
ejpam-5453	786	20	no	no	INTJ
ejpam-5453	786	21	”	"	PUNCT
ejpam-5453	786	22	.	.	PUNCT
ejpam-5453	787	1	v	v	X
ejpam-5453	787	2	⊺1	⊺1	VERB
ejpam-5453	787	3	⊺2	⊺2	VERB
ejpam-5453	787	4	⊺3	⊺3	PROPN
ejpam-5453	787	5	⊺4	⊺4	PROPN
ejpam-5453	787	6	⊺5	⊺5	NOUN
ejpam-5453	787	7	chikungunya	chikungunya	NOUN
ejpam-5453	787	8	disease	disease	NOUN
ejpam-5453	787	9	l1	l1	PROPN
ejpam-5453	787	10	⊤•	⊤•	PROPN
ejpam-5453	787	11	⊤	⊤	PROPN
ejpam-5453	787	12	◦	◦	NOUN
ejpam-5453	787	13	⊤	⊤	NUM
ejpam-5453	787	14	◦	◦	NOUN
ejpam-5453	787	15	⊤	⊤	NUM
ejpam-5453	787	16	◦	◦	NOUN
ejpam-5453	787	17	(	(	PUNCT
ejpam-5453	787	18	f1	f1	NOUN
ejpam-5453	787	19	)	)	PUNCT
ejpam-5453	787	20	no	no	DET
ejpam-5453	787	21	l2	l2	NOUN
ejpam-5453	787	22	⊤•	⊤•	PROPN
ejpam-5453	787	23	⊤•	⊤•	PROPN
ejpam-5453	787	24	⊤	⊤	PROPN
ejpam-5453	787	25	◦	◦	NOUN
ejpam-5453	787	26	⊤	⊤	NUM
ejpam-5453	787	27	◦	◦	NOUN
ejpam-5453	787	28	(	(	PUNCT
ejpam-5453	787	29	f3	f3	ADJ
ejpam-5453	787	30	)	)	PUNCT
ejpam-5453	787	31	yes	yes	NUM
ejpam-5453	787	32	l3	l3	PROPN
ejpam-5453	787	33	⊤	⊤	PROPN
ejpam-5453	787	34	◦	◦	PROPN
ejpam-5453	787	35	⊤	⊤	NOUN
ejpam-5453	787	36	◦	◦	NOUN
ejpam-5453	787	37	⊤•	⊤•	PROPN
ejpam-5453	787	38	⊤•	⊤•	PROPN
ejpam-5453	787	39	(	(	PUNCT
ejpam-5453	787	40	f1	f1	PROPN
ejpam-5453	787	41	)	)	PUNCT
ejpam-5453	787	42	no	no	DET
ejpam-5453	787	43	l4	l4	PROPN
ejpam-5453	788	1	⊤•	⊤•	PROPN
ejpam-5453	788	2	⊤•	⊤•	PROPN
ejpam-5453	788	3	⊤•	⊤•	PROPN
ejpam-5453	788	4	⊤	⊤	PROPN
ejpam-5453	788	5	◦	◦	NOUN
ejpam-5453	788	6	(	(	PUNCT
ejpam-5453	788	7	f3	f3	ADJ
ejpam-5453	788	8	)	)	PUNCT
ejpam-5453	788	9	yes	yes	INTJ
ejpam-5453	789	1	l5	l5	PROPN
ejpam-5453	789	2	⊤	⊤	PROPN
ejpam-5453	789	3	◦	◦	NOUN
ejpam-5453	789	4	⊤	⊤	NOUN
ejpam-5453	789	5	◦	◦	NOUN
ejpam-5453	789	6	⊤•	⊤•	PROPN
ejpam-5453	789	7	⊤•	⊤•	PROPN
ejpam-5453	789	8	(	(	PUNCT
ejpam-5453	789	9	f1	f1	PROPN
ejpam-5453	789	10	)	)	PUNCT
ejpam-5453	789	11	no	no	DET
ejpam-5453	789	12	l6	l6	PROPN
ejpam-5453	789	13	⊤	⊤	PROPN
ejpam-5453	789	14	◦	◦	NOUN
ejpam-5453	789	15	⊤•	⊤•	NOUN
ejpam-5453	789	16	⊤	⊤	PROPN
ejpam-5453	789	17	◦	◦	NOUN
ejpam-5453	789	18	⊤•	⊤•	PROPN
ejpam-5453	789	19	(	(	PUNCT
ejpam-5453	789	20	f2	f2	PROPN
ejpam-5453	789	21	)	)	PUNCT
ejpam-5453	789	22	no	no	PROPN
ejpam-5453	789	23	l7	l7	PROPN
ejpam-5453	789	24	⊤•	⊤•	PROPN
ejpam-5453	789	25	⊤	⊤	PROPN
ejpam-5453	789	26	◦	◦	PROPN
ejpam-5453	789	27	⊤•	⊤•	PROPN
ejpam-5453	789	28	⊤•	⊤•	PROPN
ejpam-5453	789	29	(	(	PUNCT
ejpam-5453	789	30	f2	f2	PROPN
ejpam-5453	789	31	)	)	PUNCT
ejpam-5453	789	32	yes	yes	INTJ
ejpam-5453	789	33	table	table	NOUN
ejpam-5453	789	34	6	6	NUM
ejpam-5453	789	35	:	:	PUNCT
ejpam-5453	789	36	information	information	NOUN
ejpam-5453	789	37	system	system	NOUN
ejpam-5453	789	38	of	of	ADP
ejpam-5453	789	39	chikungunya	chikungunya	NOUN
ejpam-5453	789	40	disease	disease	NOUN
ejpam-5453	789	41	ϖ(li	ϖ(li	PROPN
ejpam-5453	789	42	,	,	PUNCT
ejpam-5453	789	43	lj	lj	PROPN
ejpam-5453	789	44	)	)	PUNCT
ejpam-5453	789	45	represents	represent	VERB
ejpam-5453	789	46	the	the	DET
ejpam-5453	789	47	similarity	similarity	NOUN
ejpam-5453	789	48	between	between	ADP
ejpam-5453	789	49	two	two	NUM
ejpam-5453	789	50	patients	patient	NOUN
ejpam-5453	789	51	li	li	PROPN
ejpam-5453	789	52	,	,	PUNCT
ejpam-5453	789	53	lj	lj	INTJ
ejpam-5453	789	54	.	.	PUNCT
ejpam-5453	790	1	it	it	PRON
ejpam-5453	790	2	is	be	AUX
ejpam-5453	790	3	computed	compute	VERB
ejpam-5453	790	4	in	in	ADP
ejpam-5453	790	5	table	table	NOUN
ejpam-5453	790	6	7	7	NUM
ejpam-5453	790	7	by	by	ADP
ejpam-5453	790	8	ϖ(li	ϖ(li	PROPN
ejpam-5453	790	9	,	,	PUNCT
ejpam-5453	790	10	lj	lj	PROPN
ejpam-5453	790	11	)	)	PUNCT
ejpam-5453	790	12	=	=	SYM
ejpam-5453	791	1	∑n	∑n	PROPN
ejpam-5453	791	2	k=1(⊺k(li	k=1(⊺k(li	NOUN
ejpam-5453	791	3	)	)	PUNCT
ejpam-5453	791	4	=	=	SYM
ejpam-5453	791	5	⊺k(lj	⊺k(lj	PROPN
ejpam-5453	791	6	)	)	PUNCT
ejpam-5453	791	7	)	)	PUNCT
ejpam-5453	792	1	n	n	CCONJ
ejpam-5453	792	2	(	(	PUNCT
ejpam-5453	792	3	1	1	NUM
ejpam-5453	792	4	)	)	PUNCT
ejpam-5453	792	5	where	where	SCONJ
ejpam-5453	792	6	,	,	PUNCT
ejpam-5453	792	7	n	n	CCONJ
ejpam-5453	792	8	the	the	DET
ejpam-5453	792	9	number	number	NOUN
ejpam-5453	792	10	of	of	ADP
ejpam-5453	792	11	symptoms	symptom	NOUN
ejpam-5453	792	12	.	.	PUNCT
ejpam-5453	793	1	l1	l1	PROPN
ejpam-5453	793	2	l2	l2	PROPN
ejpam-5453	793	3	l3	l3	PROPN
ejpam-5453	793	4	l4	l4	PROPN
ejpam-5453	793	5	l5	l5	PROPN
ejpam-5453	793	6	l6	l6	PROPN
ejpam-5453	793	7	l7	l7	PROPN
ejpam-5453	793	8	l1	l1	PROPN
ejpam-5453	793	9	1	1	NUM
ejpam-5453	793	10	0.6	0.6	NUM
ejpam-5453	793	11	0.4	0.4	NUM
ejpam-5453	793	12	0.4	0.4	NUM
ejpam-5453	793	13	0.4	0.4	NUM
ejpam-5453	793	14	0.2	0.2	NUM
ejpam-5453	793	15	0.4	0.4	NUM
ejpam-5453	793	16	l2	l2	NOUN
ejpam-5453	793	17	0.6	0.6	NUM
ejpam-5453	793	18	1	1	NUM
ejpam-5453	793	19	0	0	NUM
ejpam-5453	793	20	0.8	0.8	NUM
ejpam-5453	793	21	0	0	NUM
ejpam-5453	793	22	0.4	0.4	NUM
ejpam-5453	793	23	0.2	0.2	NUM
ejpam-5453	793	24	l3	l3	NOUN
ejpam-5453	793	25	0.4	0.4	NUM
ejpam-5453	793	26	0	0	NUM
ejpam-5453	793	27	1	1	NUM
ejpam-5453	793	28	0.2	0.2	NUM
ejpam-5453	793	29	1	1	NUM
ejpam-5453	793	30	0.4	0.4	NUM
ejpam-5453	793	31	0.6	0.6	NUM
ejpam-5453	793	32	l4	l4	PROPN
ejpam-5453	793	33	0.4	0.4	NUM
ejpam-5453	793	34	0.8	0.8	NUM
ejpam-5453	793	35	0.2	0.2	NUM
ejpam-5453	793	36	1	1	NUM
ejpam-5453	793	37	0.2	0.2	NUM
ejpam-5453	793	38	0.2	0.2	NUM
ejpam-5453	793	39	0.6	0.6	NUM
ejpam-5453	793	40	l5	l5	PROPN
ejpam-5453	793	41	0.4	0.4	NUM
ejpam-5453	793	42	0	0	NUM
ejpam-5453	793	43	1	1	NUM
ejpam-5453	793	44	0.2	0.2	NUM
ejpam-5453	793	45	1	1	NUM
ejpam-5453	793	46	0.4	0.4	NUM
ejpam-5453	793	47	0.6	0.6	NUM
ejpam-5453	793	48	l6	l6	PROPN
ejpam-5453	793	49	0.2	0.2	NUM
ejpam-5453	793	50	0.4	0.4	NUM
ejpam-5453	793	51	0.4	0.4	NUM
ejpam-5453	793	52	0.2	0.2	NUM
ejpam-5453	793	53	0.4	0.4	NUM
ejpam-5453	793	54	1	1	NUM
ejpam-5453	793	55	0.4	0.4	NUM
ejpam-5453	793	56	l7	l7	NOUN
ejpam-5453	793	57	0.4	0.4	NUM
ejpam-5453	793	58	0.2	0.2	NUM
ejpam-5453	793	59	0.6	0.6	NUM
ejpam-5453	793	60	0.4	0.4	NUM
ejpam-5453	793	61	0.6	0.6	NUM
ejpam-5453	793	62	0.4	0.4	NUM
ejpam-5453	793	63	1	1	NUM
ejpam-5453	793	64	table	table	NOUN
ejpam-5453	793	65	7	7	NUM
ejpam-5453	793	66	:	:	PUNCT
ejpam-5453	793	67	similarities	similarity	NOUN
ejpam-5453	793	68	of	of	ADP
ejpam-5453	793	69	the	the	DET
ejpam-5453	793	70	patients	patient	NOUN
ejpam-5453	793	71	’	'	PUNCT
ejpam-5453	793	72	symptoms	symptom	VERB
ejpam-5453	793	73	the	the	DET
ejpam-5453	793	74	relation	relation	NOUN
ejpam-5453	793	75	between	between	ADP
ejpam-5453	793	76	patients	patient	NOUN
ejpam-5453	793	77	are	be	AUX
ejpam-5453	793	78	based	base	VERB
ejpam-5453	793	79	on	on	ADP
ejpam-5453	793	80	their	their	PRON
ejpam-5453	793	81	shared	share	VERB
ejpam-5453	793	82	symptoms	symptom	NOUN
ejpam-5453	793	83	and	and	CCONJ
ejpam-5453	793	84	represented	represent	VERB
ejpam-5453	793	85	by	by	ADP
ejpam-5453	793	86	liυlj	liυlj	ADJ
ejpam-5453	793	87	⇐	⇐	PROPN
ejpam-5453	793	88	⇒	⇒	PROPN
ejpam-5453	793	89	ϖ(li	ϖ(li	PROPN
ejpam-5453	793	90	,	,	PUNCT
ejpam-5453	793	91	lj	lj	PROPN
ejpam-5453	793	92	)	)	PUNCT
ejpam-5453	793	93	≥	≥	NOUN
ejpam-5453	793	94	0.6	0.6	NUM
ejpam-5453	793	95	.	.	PUNCT
ejpam-5453	794	1	relation	relation	NOUN
ejpam-5453	794	2	is	be	AUX
ejpam-5453	794	3	introduced	introduce	VERB
ejpam-5453	794	4	by	by	ADP
ejpam-5453	794	5	the	the	DET
ejpam-5453	794	6	system	system	NOUN
ejpam-5453	794	7	’s	’s	PART
ejpam-5453	794	8	experts	expert	NOUN
ejpam-5453	794	9	,	,	PUNCT
ejpam-5453	794	10	therefore	therefore	ADV
ejpam-5453	794	11	it	it	PRON
ejpam-5453	794	12	may	may	AUX
ejpam-5453	794	13	be	be	AUX
ejpam-5453	794	14	changed	change	VERB
ejpam-5453	794	15	under	under	ADP
ejpam-5453	794	16	their	their	PRON
ejpam-5453	794	17	considerations	consideration	NOUN
ejpam-5453	794	18	.	.	PUNCT
ejpam-5453	795	1	hence	hence	ADV
ejpam-5453	795	2	,	,	PUNCT
ejpam-5453	795	3	υ	υ	PROPN
ejpam-5453	795	4	=	=	PRON
ejpam-5453	795	5	{	{	PUNCT
ejpam-5453	795	6	(	(	PUNCT
ejpam-5453	795	7	l1	l1	PROPN
ejpam-5453	795	8	,	,	PUNCT
ejpam-5453	795	9	l1	l1	PROPN
ejpam-5453	795	10	)	)	PUNCT
ejpam-5453	795	11	,	,	PUNCT
ejpam-5453	795	12	(	(	PUNCT
ejpam-5453	795	13	l2	l2	NOUN
ejpam-5453	795	14	,	,	PUNCT
ejpam-5453	795	15	l2	l2	NOUN
ejpam-5453	795	16	)	)	PUNCT
ejpam-5453	795	17	,	,	PUNCT
ejpam-5453	795	18	(	(	PUNCT
ejpam-5453	795	19	l3	l3	PROPN
ejpam-5453	795	20	,	,	PUNCT
ejpam-5453	795	21	l3	l3	PROPN
ejpam-5453	795	22	)	)	PUNCT
ejpam-5453	795	23	,	,	PUNCT
ejpam-5453	795	24	(	(	PUNCT
ejpam-5453	795	25	l4	l4	PROPN
ejpam-5453	795	26	,	,	PUNCT
ejpam-5453	795	27	l4	l4	PROPN
ejpam-5453	795	28	)	)	PUNCT
ejpam-5453	795	29	,	,	PUNCT
ejpam-5453	795	30	(	(	PUNCT
ejpam-5453	795	31	l5	l5	ADJ
ejpam-5453	795	32	,	,	PUNCT
ejpam-5453	795	33	l5	l5	PROPN
ejpam-5453	795	34	)	)	PUNCT
ejpam-5453	795	35	,	,	PUNCT
ejpam-5453	795	36	(	(	PUNCT
ejpam-5453	795	37	l6	l6	PROPN
ejpam-5453	795	38	,	,	PUNCT
ejpam-5453	795	39	l6	l6	NOUN
ejpam-5453	795	40	)	)	PUNCT
ejpam-5453	795	41	,	,	PUNCT
ejpam-5453	795	42	(	(	PUNCT
ejpam-5453	795	43	l7	l7	PROPN
ejpam-5453	795	44	,	,	PUNCT
ejpam-5453	795	45	l7	l7	PROPN
ejpam-5453	795	46	)	)	PUNCT
ejpam-5453	795	47	,	,	PUNCT
ejpam-5453	795	48	(	(	PUNCT
ejpam-5453	795	49	l1	l1	PROPN
ejpam-5453	795	50	,	,	PUNCT
ejpam-5453	795	51	l2	l2	NOUN
ejpam-5453	795	52	)	)	PUNCT
ejpam-5453	795	53	,	,	PUNCT
ejpam-5453	795	54	(	(	PUNCT
ejpam-5453	795	55	l2	l2	NOUN
ejpam-5453	795	56	,	,	PUNCT
ejpam-5453	795	57	l1	l1	PROPN
ejpam-5453	795	58	)	)	PUNCT
ejpam-5453	795	59	,	,	PUNCT
ejpam-5453	795	60	(	(	PUNCT
ejpam-5453	795	61	l2	l2	NOUN
ejpam-5453	795	62	,	,	PUNCT
ejpam-5453	795	63	l4	l4	PROPN
ejpam-5453	795	64	)	)	PUNCT
ejpam-5453	795	65	,	,	PUNCT
ejpam-5453	795	66	(	(	PUNCT
ejpam-5453	795	67	l3	l3	PROPN
ejpam-5453	795	68	,	,	PUNCT
ejpam-5453	795	69	l7	l7	PROPN
ejpam-5453	795	70	)	)	PUNCT
ejpam-5453	795	71	,	,	PUNCT
ejpam-5453	795	72	(	(	PUNCT
ejpam-5453	795	73	l4	l4	PROPN
ejpam-5453	795	74	,	,	PUNCT
ejpam-5453	795	75	l2	l2	NOUN
ejpam-5453	795	76	)	)	PUNCT
ejpam-5453	795	77	,	,	PUNCT
ejpam-5453	795	78	(	(	PUNCT
ejpam-5453	795	79	l4	l4	PROPN
ejpam-5453	795	80	,	,	PUNCT
ejpam-5453	795	81	l7	l7	PROPN
ejpam-5453	795	82	)	)	PUNCT
ejpam-5453	795	83	,	,	PUNCT
ejpam-5453	795	84	(	(	PUNCT
ejpam-5453	795	85	l5	l5	PROPN
ejpam-5453	795	86	,	,	PUNCT
ejpam-5453	795	87	l7	l7	PROPN
ejpam-5453	795	88	)	)	PUNCT
ejpam-5453	795	89	,	,	PUNCT
ejpam-5453	795	90	(	(	PUNCT
ejpam-5453	795	91	l7	l7	PROPN
ejpam-5453	795	92	,	,	PUNCT
ejpam-5453	795	93	l3	l3	PROPN
ejpam-5453	795	94	)	)	PUNCT
ejpam-5453	795	95	,	,	PUNCT
ejpam-5453	795	96	(	(	PUNCT
ejpam-5453	795	97	l7	l7	PROPN
ejpam-5453	795	98	,	,	PUNCT
ejpam-5453	795	99	l5	l5	PROPN
ejpam-5453	795	100	)	)	PUNCT
ejpam-5453	795	101	}	}	PUNCT
ejpam-5453	795	102	and	and	CCONJ
ejpam-5453	795	103	letd	letd	NOUN
ejpam-5453	795	104	=	=	SYM
ejpam-5453	795	105	{	{	PUNCT
ejpam-5453	795	106	∅	∅	NOUN
ejpam-5453	795	107	,	,	PUNCT
ejpam-5453	795	108	{	{	PUNCT
ejpam-5453	795	109	l7	l7	NOUN
ejpam-5453	795	110	}	}	PUNCT
ejpam-5453	795	111	}	}	PUNCT
ejpam-5453	795	112	.	.	PUNCT
ejpam-5453	796	1	the	the	DET
ejpam-5453	796	2	uninfected	uninfected	ADJ
ejpam-5453	796	3	patients	patient	NOUN
ejpam-5453	796	4	with	with	ADP
ejpam-5453	796	5	chikungunya	chikungunya	NOUN
ejpam-5453	796	6	are	be	AUX
ejpam-5453	796	7	represented	represent	VERB
ejpam-5453	796	8	by	by	ADP
ejpam-5453	796	9	the	the	DET
ejpam-5453	796	10	set	set	NOUN
ejpam-5453	796	11	m	m	PROPN
ejpam-5453	796	12	=	=	SYM
ejpam-5453	796	13	{	{	PUNCT
ejpam-5453	796	14	l1	l1	PROPN
ejpam-5453	796	15	,	,	PUNCT
ejpam-5453	796	16	l3	l3	PROPN
ejpam-5453	796	17	,	,	PUNCT
ejpam-5453	796	18	l5	l5	PROPN
ejpam-5453	796	19	,	,	PUNCT
ejpam-5453	796	20	l6	l6	NOUN
ejpam-5453	796	21	}	}	PUNCT
ejpam-5453	796	22	while	while	SCONJ
ejpam-5453	796	23	the	the	DET
ejpam-5453	796	24	infected	infected	ADJ
ejpam-5453	796	25	n	n	NOUN
ejpam-5453	796	26	=	=	CCONJ
ejpam-5453	796	27	{	{	PUNCT
ejpam-5453	796	28	l2	l2	PROPN
ejpam-5453	796	29	,	,	PUNCT
ejpam-5453	796	30	l4	l4	PROPN
ejpam-5453	796	31	,	,	PUNCT
ejpam-5453	796	32	l7	l7	PROPN
ejpam-5453	796	33	}	}	PUNCT
ejpam-5453	796	34	.	.	PUNCT
ejpam-5453	797	1	their	their	PRON
ejpam-5453	797	2	approximation	approximation	NOUN
ejpam-5453	797	3	,	,	PUNCT
ejpam-5453	797	4	boundary	boundary	ADJ
ejpam-5453	797	5	regions	region	NOUN
ejpam-5453	797	6	and	and	CCONJ
ejpam-5453	797	7	accuracy	accuracy	NOUN
ejpam-5453	797	8	by	by	ADP
ejpam-5453	797	9	the	the	DET
ejpam-5453	797	10	prior	prior	ADJ
ejpam-5453	797	11	manner	manner	NOUN
ejpam-5453	797	12	in	in	ADP
ejpam-5453	797	13	[	[	X
ejpam-5453	797	14	1	1	NUM
ejpam-5453	797	15	,	,	PUNCT
ejpam-5453	797	16	43	43	NUM
ejpam-5453	797	17	]	]	PUNCT
ejpam-5453	797	18	and	and	CCONJ
ejpam-5453	797	19	the	the	DET
ejpam-5453	797	20	present	present	ADJ
ejpam-5453	797	21	manner	manner	NOUN
ejpam-5453	797	22	are	be	AUX
ejpam-5453	797	23	calculated	calculate	VERB
ejpam-5453	797	24	as	as	SCONJ
ejpam-5453	797	25	follows	follow	VERB
ejpam-5453	797	26	.	.	PUNCT
ejpam-5453	798	1	(	(	PUNCT
ejpam-5453	798	2	i	i	NOUN
ejpam-5453	798	3	)	)	PUNCT
ejpam-5453	798	4	the	the	DET
ejpam-5453	798	5	uninfected	uninfected	ADJ
ejpam-5453	798	6	patients	patient	NOUN
ejpam-5453	798	7	m	m	VERB
ejpam-5453	798	8	=	=	PUNCT
ejpam-5453	798	9	{	{	PUNCT
ejpam-5453	798	10	l1	l1	PROPN
ejpam-5453	798	11	,	,	PUNCT
ejpam-5453	798	12	l3	l3	PROPN
ejpam-5453	798	13	,	,	PUNCT
ejpam-5453	798	14	l5	l5	PROPN
ejpam-5453	798	15	,	,	PUNCT
ejpam-5453	798	16	l6	l6	PROPN
ejpam-5453	798	17	}	}	PUNCT
ejpam-5453	798	18	(	(	PUNCT
ejpam-5453	798	19	i	i	NOUN
ejpam-5453	798	20	)	)	PUNCT
ejpam-5453	798	21	the	the	DET
ejpam-5453	798	22	prior	prior	ADJ
ejpam-5453	798	23	manner	manner	NOUN
ejpam-5453	798	24	in	in	ADP
ejpam-5453	798	25	2.2	2.2	NUM
ejpam-5453	798	26	[	[	SYM
ejpam-5453	798	27	1	1	NUM
ejpam-5453	798	28	,	,	PUNCT
ejpam-5453	798	29	2	2	NUM
ejpam-5453	798	30	,	,	PUNCT
ejpam-5453	798	31	30	30	NUM
ejpam-5453	798	32	]	]	NUM
ejpam-5453	798	33	:	:	PUNCT
ejpam-5453	798	34	m.	m.	PROPN
ejpam-5453	798	35	hosny	hosny	PROPN
ejpam-5453	798	36	/	/	SYM
ejpam-5453	798	37	eur	eur	PROPN
ejpam-5453	798	38	.	.	PUNCT
ejpam-5453	799	1	j.	j.	PROPN
ejpam-5453	799	2	pure	pure	PROPN
ejpam-5453	799	3	appl	appl	PROPN
ejpam-5453	799	4	.	.	PROPN
ejpam-5453	799	5	math	math	PROPN
ejpam-5453	799	6	,	,	PUNCT
ejpam-5453	799	7	17	17	NUM
ejpam-5453	799	8	(	(	PUNCT
ejpam-5453	799	9	4	4	NUM
ejpam-5453	799	10	)	)	PUNCT
ejpam-5453	799	11	(	(	PUNCT
ejpam-5453	799	12	2024	2024	NUM
ejpam-5453	799	13	)	)	PUNCT
ejpam-5453	799	14	,	,	PUNCT
ejpam-5453	799	15	2843	2843	NUM
ejpam-5453	799	16	-	-	SYM
ejpam-5453	799	17	2877	2877	NUM
ejpam-5453	799	18	2873	2873	NUM
ejpam-5453	799	19	•	•	NOUN
ejpam-5453	799	20	nr(m	nr(m	NOUN
ejpam-5453	799	21	)	)	PUNCT
ejpam-5453	799	22	=	=	PRON
ejpam-5453	799	23	{	{	PUNCT
ejpam-5453	799	24	l6	l6	PROPN
ejpam-5453	799	25	}	}	PUNCT
ejpam-5453	799	26	;	;	PUNCT
ejpam-5453	799	27	•	•	NUM
ejpam-5453	799	28	nr(m	nr(m	NOUN
ejpam-5453	799	29	)	)	PUNCT
ejpam-5453	799	30	=	=	SYM
ejpam-5453	799	31	v	v	NOUN
ejpam-5453	799	32	;	;	PUNCT
ejpam-5453	799	33	•	•	NUM
ejpam-5453	799	34	br(m	br(m	NUM
ejpam-5453	799	35	)	)	PUNCT
ejpam-5453	799	36	=	=	SYM
ejpam-5453	800	1	v	v	ADP
ejpam-5453	800	2	\	\	PROPN
ejpam-5453	800	3	{	{	PUNCT
ejpam-5453	800	4	l6	l6	PROPN
ejpam-5453	800	5	}	}	PUNCT
ejpam-5453	800	6	;	;	PUNCT
ejpam-5453	800	7	•	•	X
ejpam-5453	800	8	ar(m	ar(m	NUM
ejpam-5453	800	9	)	)	PUNCT
ejpam-5453	800	10	=	=	SYM
ejpam-5453	800	11	1	1	NUM
ejpam-5453	800	12	7	7	NUM
ejpam-5453	800	13	.	.	PUNCT
ejpam-5453	801	1	(	(	PUNCT
ejpam-5453	801	2	ii	ii	X
ejpam-5453	801	3	)	)	PUNCT
ejpam-5453	801	4	yildirim	yildirim	PROPN
ejpam-5453	801	5	’s	’s	PART
ejpam-5453	801	6	manner	manner	NOUN
ejpam-5453	801	7	in	in	ADP
ejpam-5453	801	8	definition	definition	NOUN
ejpam-5453	801	9	2.8	2.8	NUM
ejpam-5453	802	1	[	[	X
ejpam-5453	802	2	43	43	NUM
ejpam-5453	802	3	]	]	X
ejpam-5453	802	4	:	:	PUNCT
ejpam-5453	802	5	•	•	NUM
ejpam-5453	802	6	nsr(m	nsr(m	PROPN
ejpam-5453	802	7	)	)	PUNCT
ejpam-5453	802	8	=	=	PRON
ejpam-5453	802	9	{	{	PUNCT
ejpam-5453	802	10	l6	l6	PROPN
ejpam-5453	802	11	}	}	PUNCT
ejpam-5453	802	12	;	;	PUNCT
ejpam-5453	803	1	•	•	NUM
ejpam-5453	803	2	nsr(m	nsr(m	NUM
ejpam-5453	803	3	)	)	PUNCT
ejpam-5453	803	4	=	=	SYM
ejpam-5453	803	5	{	{	PUNCT
ejpam-5453	803	6	l1	l1	PROPN
ejpam-5453	803	7	,	,	PUNCT
ejpam-5453	803	8	l3	l3	PROPN
ejpam-5453	803	9	,	,	PUNCT
ejpam-5453	803	10	l5	l5	PROPN
ejpam-5453	803	11	,	,	PUNCT
ejpam-5453	803	12	l6	l6	PROPN
ejpam-5453	803	13	}	}	PUNCT
ejpam-5453	803	14	;	;	PUNCT
ejpam-5453	803	15	•	•	NUM
ejpam-5453	803	16	bsr(m	bsr(m	PROPN
ejpam-5453	803	17	)	)	PUNCT
ejpam-5453	803	18	=	=	PRON
ejpam-5453	803	19	{	{	PUNCT
ejpam-5453	803	20	l1	l1	PROPN
ejpam-5453	803	21	,	,	PUNCT
ejpam-5453	803	22	l3	l3	PROPN
ejpam-5453	803	23	,	,	PUNCT
ejpam-5453	803	24	l5	l5	PROPN
ejpam-5453	803	25	}	}	PUNCT
ejpam-5453	803	26	;	;	PUNCT
ejpam-5453	803	27	•	•	ADV
ejpam-5453	803	28	asr(m	asr(m	ADV
ejpam-5453	803	29	)	)	PUNCT
ejpam-5453	803	30	=	=	SYM
ejpam-5453	803	31	1	1	NUM
ejpam-5453	803	32	4	4	NUM
ejpam-5453	803	33	.	.	PUNCT
ejpam-5453	804	1	(	(	PUNCT
ejpam-5453	804	2	iii	iii	X
ejpam-5453	804	3	)	)	PUNCT
ejpam-5453	804	4	yildirim	yildirim	PROPN
ejpam-5453	804	5	’s	’s	PART
ejpam-5453	804	6	manner	manner	NOUN
ejpam-5453	804	7	in	in	ADP
ejpam-5453	804	8	definition	definition	NOUN
ejpam-5453	805	1	2.11	2.11	NUM
ejpam-5453	805	2	[	[	X
ejpam-5453	805	3	43	43	NUM
ejpam-5453	805	4	]	]	X
ejpam-5453	805	5	:	:	PUNCT
ejpam-5453	805	6	•	•	INTJ
ejpam-5453	805	7	nβ	nβ	ADJ
ejpam-5453	805	8	sr(m	sr(m	NOUN
ejpam-5453	805	9	)	)	PUNCT
ejpam-5453	805	10	=	=	PRON
ejpam-5453	805	11	{	{	PUNCT
ejpam-5453	805	12	l6	l6	PROPN
ejpam-5453	805	13	}	}	PUNCT
ejpam-5453	805	14	;	;	PUNCT
ejpam-5453	805	15	•	•	ADP
ejpam-5453	805	16	n	n	X
ejpam-5453	805	17	β	β	X
ejpam-5453	805	18	sr(m	sr(m	X
ejpam-5453	805	19	)	)	PUNCT
ejpam-5453	805	20	=	=	PRON
ejpam-5453	805	21	{	{	PUNCT
ejpam-5453	805	22	l1	l1	PROPN
ejpam-5453	805	23	,	,	PUNCT
ejpam-5453	805	24	l3	l3	PROPN
ejpam-5453	805	25	,	,	PUNCT
ejpam-5453	805	26	l5	l5	PROPN
ejpam-5453	805	27	,	,	PUNCT
ejpam-5453	805	28	l6	l6	PROPN
ejpam-5453	805	29	}	}	PUNCT
ejpam-5453	805	30	;	;	PUNCT
ejpam-5453	805	31	•	•	NUM
ejpam-5453	805	32	bβ	bβ	NOUN
ejpam-5453	805	33	sr(m	sr(m	NOUN
ejpam-5453	805	34	)	)	PUNCT
ejpam-5453	805	35	=	=	PRON
ejpam-5453	805	36	{	{	PUNCT
ejpam-5453	805	37	l1	l1	PROPN
ejpam-5453	805	38	,	,	PUNCT
ejpam-5453	805	39	l3	l3	PROPN
ejpam-5453	805	40	,	,	PUNCT
ejpam-5453	805	41	l5	l5	PROPN
ejpam-5453	805	42	}	}	PUNCT
ejpam-5453	805	43	;	;	PUNCT
ejpam-5453	805	44	•	•	X
ejpam-5453	805	45	aβ	aβ	NOUN
ejpam-5453	805	46	sr(m	sr(m	NOUN
ejpam-5453	805	47	)	)	PUNCT
ejpam-5453	805	48	=	=	SYM
ejpam-5453	805	49	1	1	NUM
ejpam-5453	805	50	4	4	NUM
ejpam-5453	805	51	.	.	PUNCT
ejpam-5453	806	1	(	(	PUNCT
ejpam-5453	806	2	iv	iv	X
ejpam-5453	806	3	)	)	PUNCT
ejpam-5453	806	4	the	the	DET
ejpam-5453	806	5	present	present	ADJ
ejpam-5453	806	6	manner	manner	NOUN
ejpam-5453	806	7	in	in	ADP
ejpam-5453	806	8	definition	definition	NOUN
ejpam-5453	806	9	4.1	4.1	NUM
ejpam-5453	806	10	•	•	NOUN
ejpam-5453	806	11	nd−β	nd−β	PROPN
ejpam-5453	806	12	sr	sr	PROPN
ejpam-5453	806	13	(	(	PUNCT
ejpam-5453	806	14	m	m	NOUN
ejpam-5453	806	15	)	)	PUNCT
ejpam-5453	806	16	=	=	PRON
ejpam-5453	806	17	{	{	PUNCT
ejpam-5453	806	18	l1	l1	PROPN
ejpam-5453	806	19	,	,	PUNCT
ejpam-5453	806	20	l3	l3	PROPN
ejpam-5453	806	21	,	,	PUNCT
ejpam-5453	806	22	l5	l5	PROPN
ejpam-5453	806	23	,	,	PUNCT
ejpam-5453	806	24	l6	l6	PROPN
ejpam-5453	806	25	}	}	PUNCT
ejpam-5453	806	26	;	;	PUNCT
ejpam-5453	806	27	•	•	NUM
ejpam-5453	806	28	n	n	PRON
ejpam-5453	806	29	d−β	d−β	NOUN
ejpam-5453	806	30	sr	sr	PROPN
ejpam-5453	806	31	(	(	PUNCT
ejpam-5453	806	32	m	m	PROPN
ejpam-5453	806	33	)	)	PUNCT
ejpam-5453	806	34	=	=	PRON
ejpam-5453	806	35	{	{	PUNCT
ejpam-5453	806	36	l1	l1	PROPN
ejpam-5453	806	37	,	,	PUNCT
ejpam-5453	806	38	l3	l3	PROPN
ejpam-5453	806	39	,	,	PUNCT
ejpam-5453	806	40	l5	l5	PROPN
ejpam-5453	806	41	,	,	PUNCT
ejpam-5453	806	42	l6	l6	PROPN
ejpam-5453	806	43	}	}	PUNCT
ejpam-5453	806	44	;	;	PUNCT
ejpam-5453	807	1	•	•	NUM
ejpam-5453	807	2	bd−β	bd−β	PROPN
ejpam-5453	807	3	sr	sr	PROPN
ejpam-5453	807	4	(	(	PUNCT
ejpam-5453	807	5	m	m	NOUN
ejpam-5453	807	6	)	)	PUNCT
ejpam-5453	807	7	=	=	SYM
ejpam-5453	807	8	∅	∅	NOUN
ejpam-5453	807	9	;	;	PUNCT
ejpam-5453	807	10	•	•	NUM
ejpam-5453	807	11	ad−β	ad−β	PROPN
ejpam-5453	807	12	sr	sr	PROPN
ejpam-5453	807	13	(	(	PUNCT
ejpam-5453	807	14	m	m	NOUN
ejpam-5453	807	15	)	)	PUNCT
ejpam-5453	807	16	=	=	SYM
ejpam-5453	807	17	1	1	X
ejpam-5453	807	18	.	.	PUNCT
ejpam-5453	807	19	(	(	PUNCT
ejpam-5453	807	20	ii	ii	NOUN
ejpam-5453	807	21	)	)	PUNCT
ejpam-5453	807	22	the	the	DET
ejpam-5453	807	23	infection	infection	NOUN
ejpam-5453	807	24	patients	patient	NOUN
ejpam-5453	807	25	n	n	NOUN
ejpam-5453	807	26	=	=	CCONJ
ejpam-5453	807	27	{	{	PUNCT
ejpam-5453	807	28	l2	l2	PROPN
ejpam-5453	807	29	,	,	PUNCT
ejpam-5453	807	30	l4	l4	PROPN
ejpam-5453	807	31	,	,	PUNCT
ejpam-5453	807	32	l7	l7	PROPN
ejpam-5453	807	33	}	}	PUNCT
ejpam-5453	807	34	(	(	PUNCT
ejpam-5453	807	35	i	i	NOUN
ejpam-5453	807	36	)	)	PUNCT
ejpam-5453	807	37	the	the	DET
ejpam-5453	807	38	prior	prior	ADJ
ejpam-5453	807	39	manner	manner	NOUN
ejpam-5453	807	40	2.2	2.2	NUM
ejpam-5453	807	41	[	[	SYM
ejpam-5453	807	42	1	1	NUM
ejpam-5453	807	43	,	,	PUNCT
ejpam-5453	807	44	2	2	NUM
ejpam-5453	807	45	,	,	PUNCT
ejpam-5453	807	46	30	30	NUM
ejpam-5453	807	47	]	]	NUM
ejpam-5453	807	48	:	:	PUNCT
ejpam-5453	807	49	•	•	NUM
ejpam-5453	807	50	nr(m	nr(m	NOUN
ejpam-5453	807	51	)	)	PUNCT
ejpam-5453	807	52	=	=	SYM
ejpam-5453	807	53	∅	∅	NOUN
ejpam-5453	807	54	;	;	PUNCT
ejpam-5453	807	55	•	•	NUM
ejpam-5453	807	56	nr(m	nr(m	NOUN
ejpam-5453	807	57	)	)	PUNCT
ejpam-5453	807	58	=	=	SYM
ejpam-5453	807	59	v	v	NOUN
ejpam-5453	807	60	;	;	PUNCT
ejpam-5453	807	61	•	•	NUM
ejpam-5453	807	62	br(m	br(m	NUM
ejpam-5453	807	63	)	)	PUNCT
ejpam-5453	807	64	=	=	SYM
ejpam-5453	807	65	v	v	NOUN
ejpam-5453	807	66	;	;	PUNCT
ejpam-5453	807	67	•	•	NUM
ejpam-5453	807	68	ar(m	ar(m	NUM
ejpam-5453	807	69	)	)	PUNCT
ejpam-5453	807	70	=	=	SYM
ejpam-5453	807	71	0	0	X
ejpam-5453	807	72	.	.	PUNCT
ejpam-5453	807	73	(	(	PUNCT
ejpam-5453	807	74	ii	ii	X
ejpam-5453	807	75	)	)	PUNCT
ejpam-5453	807	76	yildirim	yildirim	PROPN
ejpam-5453	807	77	’s	’s	PART
ejpam-5453	807	78	manner	manner	NOUN
ejpam-5453	807	79	in	in	ADP
ejpam-5453	807	80	definition	definition	NOUN
ejpam-5453	807	81	2.8	2.8	NUM
ejpam-5453	807	82	[	[	X
ejpam-5453	807	83	43	43	NUM
ejpam-5453	807	84	]	]	X
ejpam-5453	807	85	:	:	PUNCT
ejpam-5453	807	86	•	•	NUM
ejpam-5453	807	87	nsr(n	nsr(n	PROPN
ejpam-5453	807	88	)	)	PUNCT
ejpam-5453	807	89	=	=	PRON
ejpam-5453	807	90	{	{	PUNCT
ejpam-5453	807	91	l2	l2	PROPN
ejpam-5453	807	92	,	,	PUNCT
ejpam-5453	807	93	l4	l4	PROPN
ejpam-5453	807	94	,	,	PUNCT
ejpam-5453	807	95	l7	l7	PROPN
ejpam-5453	807	96	}	}	PUNCT
ejpam-5453	807	97	;	;	PUNCT
ejpam-5453	807	98	•	•	NUM
ejpam-5453	807	99	nsr(n	nsr(n	X
ejpam-5453	807	100	)	)	PUNCT
ejpam-5453	807	101	=	=	SYM
ejpam-5453	807	102	{	{	PUNCT
ejpam-5453	807	103	l1	l1	PROPN
ejpam-5453	807	104	,	,	PUNCT
ejpam-5453	807	105	l2	l2	NOUN
ejpam-5453	807	106	,	,	PUNCT
ejpam-5453	807	107	l3	l3	PROPN
ejpam-5453	807	108	,	,	PUNCT
ejpam-5453	807	109	l4	l4	PROPN
ejpam-5453	807	110	,	,	PUNCT
ejpam-5453	807	111	l5	l5	PROPN
ejpam-5453	807	112	,	,	PUNCT
ejpam-5453	807	113	l7	l7	PROPN
ejpam-5453	807	114	}	}	PUNCT
ejpam-5453	807	115	;	;	PUNCT
ejpam-5453	807	116	•	•	NUM
ejpam-5453	807	117	bsr(n	bsr(n	PROPN
ejpam-5453	807	118	)	)	PUNCT
ejpam-5453	807	119	=	=	PRON
ejpam-5453	807	120	{	{	PUNCT
ejpam-5453	807	121	l1	l1	PROPN
ejpam-5453	807	122	,	,	PUNCT
ejpam-5453	807	123	l3	l3	PROPN
ejpam-5453	807	124	,	,	PUNCT
ejpam-5453	807	125	l5	l5	PROPN
ejpam-5453	807	126	}	}	PUNCT
ejpam-5453	807	127	;	;	PUNCT
ejpam-5453	807	128	•	•	NUM
ejpam-5453	807	129	asr(n	asr(n	X
ejpam-5453	807	130	)	)	PUNCT
ejpam-5453	807	131	=	=	SYM
ejpam-5453	807	132	1	1	NUM
ejpam-5453	807	133	2	2	NUM
ejpam-5453	807	134	.	.	PUNCT
ejpam-5453	807	135	(	(	PUNCT
ejpam-5453	807	136	iii	iii	X
ejpam-5453	807	137	)	)	PUNCT
ejpam-5453	807	138	yildirim	yildirim	PROPN
ejpam-5453	807	139	’s	’s	PART
ejpam-5453	807	140	manner	manner	NOUN
ejpam-5453	807	141	in	in	ADP
ejpam-5453	807	142	definition	definition	NOUN
ejpam-5453	807	143	2.11	2.11	NUM
ejpam-5453	807	144	[	[	X
ejpam-5453	807	145	43	43	NUM
ejpam-5453	807	146	]	]	X
ejpam-5453	807	147	:	:	PUNCT
ejpam-5453	807	148	•	•	NUM
ejpam-5453	807	149	nβ	nβ	INTJ
ejpam-5453	807	150	sr(n	sr(n	NOUN
ejpam-5453	807	151	)	)	PUNCT
ejpam-5453	807	152	=	=	PRON
ejpam-5453	807	153	{	{	PUNCT
ejpam-5453	807	154	l2	l2	PROPN
ejpam-5453	807	155	,	,	PUNCT
ejpam-5453	807	156	l4	l4	PROPN
ejpam-5453	807	157	,	,	PUNCT
ejpam-5453	807	158	l7	l7	PROPN
ejpam-5453	807	159	}	}	PUNCT
ejpam-5453	807	160	;	;	PUNCT
ejpam-5453	807	161	•	•	ADP
ejpam-5453	807	162	n	n	X
ejpam-5453	807	163	β	β	X
ejpam-5453	807	164	sr(n	sr(n	NOUN
ejpam-5453	807	165	)	)	PUNCT
ejpam-5453	807	166	=	=	PRON
ejpam-5453	807	167	{	{	PUNCT
ejpam-5453	807	168	l1	l1	PROPN
ejpam-5453	807	169	,	,	PUNCT
ejpam-5453	807	170	l2	l2	NOUN
ejpam-5453	807	171	,	,	PUNCT
ejpam-5453	807	172	l4	l4	PROPN
ejpam-5453	807	173	,	,	PUNCT
ejpam-5453	807	174	l7	l7	PROPN
ejpam-5453	807	175	}	}	PUNCT
ejpam-5453	807	176	;	;	PUNCT
ejpam-5453	807	177	m.	m.	PROPN
ejpam-5453	807	178	hosny	hosny	PROPN
ejpam-5453	807	179	/	/	SYM
ejpam-5453	807	180	eur	eur	PROPN
ejpam-5453	807	181	.	.	PUNCT
ejpam-5453	808	1	j.	j.	PROPN
ejpam-5453	808	2	pure	pure	PROPN
ejpam-5453	808	3	appl	appl	PROPN
ejpam-5453	808	4	.	.	PROPN
ejpam-5453	808	5	math	math	PROPN
ejpam-5453	808	6	,	,	PUNCT
ejpam-5453	808	7	17	17	NUM
ejpam-5453	808	8	(	(	PUNCT
ejpam-5453	808	9	4	4	NUM
ejpam-5453	808	10	)	)	PUNCT
ejpam-5453	808	11	(	(	PUNCT
ejpam-5453	808	12	2024	2024	NUM
ejpam-5453	808	13	)	)	PUNCT
ejpam-5453	808	14	,	,	PUNCT
ejpam-5453	808	15	2843	2843	NUM
ejpam-5453	808	16	-	-	SYM
ejpam-5453	808	17	2877	2877	NUM
ejpam-5453	808	18	2874	2874	NUM
ejpam-5453	808	19	•	•	NOUN
ejpam-5453	808	20	bβ	bβ	NOUN
ejpam-5453	808	21	sr(n	sr(n	NOUN
ejpam-5453	808	22	)	)	PUNCT
ejpam-5453	808	23	=	=	PRON
ejpam-5453	808	24	{	{	PUNCT
ejpam-5453	808	25	l1	l1	PROPN
ejpam-5453	808	26	}	}	PUNCT
ejpam-5453	808	27	;	;	PUNCT
ejpam-5453	808	28	•	•	X
ejpam-5453	808	29	aβ	aβ	NOUN
ejpam-5453	808	30	sr(n	sr(n	NOUN
ejpam-5453	808	31	)	)	PUNCT
ejpam-5453	808	32	=	=	SYM
ejpam-5453	808	33	3	3	NUM
ejpam-5453	808	34	4	4	NUM
ejpam-5453	808	35	.	.	PUNCT
ejpam-5453	809	1	(	(	PUNCT
ejpam-5453	809	2	iv	iv	X
ejpam-5453	809	3	)	)	PUNCT
ejpam-5453	809	4	the	the	DET
ejpam-5453	809	5	present	present	ADJ
ejpam-5453	809	6	manner	manner	NOUN
ejpam-5453	809	7	in	in	ADP
ejpam-5453	809	8	definition	definition	NOUN
ejpam-5453	809	9	4.1	4.1	NUM
ejpam-5453	809	10	•	•	NOUN
ejpam-5453	809	11	nd−β	nd−β	PROPN
ejpam-5453	809	12	sr	sr	PROPN
ejpam-5453	809	13	(	(	PUNCT
ejpam-5453	809	14	n	n	CCONJ
ejpam-5453	809	15	)	)	PUNCT
ejpam-5453	809	16	=	=	NOUN
ejpam-5453	809	17	{	{	PUNCT
ejpam-5453	809	18	l2	l2	PROPN
ejpam-5453	809	19	,	,	PUNCT
ejpam-5453	809	20	l4	l4	PROPN
ejpam-5453	809	21	,	,	PUNCT
ejpam-5453	809	22	l7	l7	PROPN
ejpam-5453	809	23	}	}	PUNCT
ejpam-5453	809	24	;	;	PUNCT
ejpam-5453	810	1	•	•	NUM
ejpam-5453	810	2	n	n	PRON
ejpam-5453	810	3	d−β	d−β	NOUN
ejpam-5453	810	4	sr	sr	PROPN
ejpam-5453	810	5	(	(	PUNCT
ejpam-5453	810	6	n	n	CCONJ
ejpam-5453	810	7	)	)	PUNCT
ejpam-5453	810	8	=	=	NOUN
ejpam-5453	810	9	{	{	PUNCT
ejpam-5453	810	10	l2	l2	PROPN
ejpam-5453	810	11	,	,	PUNCT
ejpam-5453	810	12	l4	l4	PROPN
ejpam-5453	810	13	,	,	PUNCT
ejpam-5453	810	14	l7	l7	PROPN
ejpam-5453	810	15	}	}	PUNCT
ejpam-5453	810	16	;	;	PUNCT
ejpam-5453	810	17	•	•	NUM
ejpam-5453	810	18	bd−β	bd−β	PROPN
ejpam-5453	810	19	sr	sr	PROPN
ejpam-5453	810	20	(	(	PUNCT
ejpam-5453	810	21	n	n	CCONJ
ejpam-5453	810	22	)	)	PUNCT
ejpam-5453	810	23	=	=	NOUN
ejpam-5453	810	24	∅	∅	NOUN
ejpam-5453	810	25	;	;	PUNCT
ejpam-5453	810	26	•	•	NUM
ejpam-5453	810	27	ad−β	ad−β	PROPN
ejpam-5453	810	28	sr	sr	PROPN
ejpam-5453	810	29	(	(	PUNCT
ejpam-5453	810	30	n	n	CCONJ
ejpam-5453	810	31	)	)	PUNCT
ejpam-5453	810	32	=	=	SYM
ejpam-5453	810	33	1	1	X
ejpam-5453	810	34	.	.	PUNCT
ejpam-5453	810	35	based	base	VERB
ejpam-5453	810	36	on	on	ADP
ejpam-5453	810	37	this	this	DET
ejpam-5453	810	38	calculations	calculation	NOUN
ejpam-5453	810	39	,	,	PUNCT
ejpam-5453	810	40	the	the	DET
ejpam-5453	810	41	boundary	boundary	ADJ
ejpam-5453	810	42	regions	region	NOUN
ejpam-5453	810	43	for	for	ADP
ejpam-5453	810	44	the	the	DET
ejpam-5453	810	45	uninfected	uninfected	ADJ
ejpam-5453	810	46	and	and	CCONJ
ejpam-5453	810	47	infected	infected	ADJ
ejpam-5453	810	48	sets	set	NOUN
ejpam-5453	810	49	according	accord	VERB
ejpam-5453	810	50	to	to	ADP
ejpam-5453	810	51	the	the	DET
ejpam-5453	810	52	manners	manner	NOUN
ejpam-5453	810	53	in	in	ADP
ejpam-5453	810	54	[	[	X
ejpam-5453	810	55	1	1	NUM
ejpam-5453	810	56	,	,	PUNCT
ejpam-5453	810	57	2	2	NUM
ejpam-5453	810	58	,	,	PUNCT
ejpam-5453	810	59	30	30	NUM
ejpam-5453	810	60	,	,	PUNCT
ejpam-5453	810	61	43	43	NUM
ejpam-5453	810	62	]	]	PUNCT
ejpam-5453	810	63	are	be	AUX
ejpam-5453	810	64	v	v	ADJ
ejpam-5453	810	65	,	,	PUNCT
ejpam-5453	810	66	{	{	PUNCT
ejpam-5453	810	67	l1	l1	PROPN
ejpam-5453	810	68	,	,	PUNCT
ejpam-5453	810	69	l2	l2	NOUN
ejpam-5453	810	70	,	,	PUNCT
ejpam-5453	810	71	l3	l3	PROPN
ejpam-5453	810	72	,	,	PUNCT
ejpam-5453	810	73	l4	l4	PROPN
ejpam-5453	810	74	,	,	PUNCT
ejpam-5453	810	75	l5	l5	PROPN
ejpam-5453	810	76	,	,	PUNCT
ejpam-5453	810	77	l7	l7	PROPN
ejpam-5453	810	78	}	}	PUNCT
ejpam-5453	810	79	,	,	PUNCT
ejpam-5453	810	80	{	{	PUNCT
ejpam-5453	810	81	l1	l1	PROPN
ejpam-5453	810	82	,	,	PUNCT
ejpam-5453	810	83	l2	l2	NOUN
ejpam-5453	810	84	,	,	PUNCT
ejpam-5453	810	85	l4	l4	PROPN
ejpam-5453	810	86	,	,	PUNCT
ejpam-5453	810	87	l7	l7	PROPN
ejpam-5453	810	88	}	}	PUNCT
ejpam-5453	810	89	,	,	PUNCT
ejpam-5453	810	90	respectively	respectively	ADV
ejpam-5453	810	91	.	.	PUNCT
ejpam-5453	811	1	this	this	PRON
ejpam-5453	811	2	indicates	indicate	VERB
ejpam-5453	811	3	that	that	SCONJ
ejpam-5453	811	4	,	,	PUNCT
ejpam-5453	811	5	in	in	ADP
ejpam-5453	811	6	this	this	DET
ejpam-5453	811	7	case	case	NOUN
ejpam-5453	811	8	,	,	PUNCT
ejpam-5453	811	9	it	it	PRON
ejpam-5453	811	10	is	be	AUX
ejpam-5453	811	11	difficult	difficult	ADJ
ejpam-5453	811	12	to	to	PART
ejpam-5453	811	13	determine	determine	VERB
ejpam-5453	811	14	whether	whether	SCONJ
ejpam-5453	811	15	individuals	individual	NOUN
ejpam-5453	811	16	are	be	AUX
ejpam-5453	811	17	infected	infect	VERB
ejpam-5453	811	18	or	or	CCONJ
ejpam-5453	811	19	not	not	PART
ejpam-5453	811	20	.	.	PUNCT
ejpam-5453	812	1	therefore	therefore	ADV
ejpam-5453	812	2	,	,	PUNCT
ejpam-5453	812	3	the	the	DET
ejpam-5453	812	4	vagueness	vagueness	NOUN
ejpam-5453	812	5	is	be	AUX
ejpam-5453	812	6	increased	increase	VERB
ejpam-5453	812	7	and	and	CCONJ
ejpam-5453	812	8	accordingly	accordingly	ADV
ejpam-5453	812	9	the	the	DET
ejpam-5453	812	10	accuracy	accuracy	NOUN
ejpam-5453	812	11	of	of	ADP
ejpam-5453	812	12	madedecision	madedecision	NOUN
ejpam-5453	812	13	loses	lose	VERB
ejpam-5453	812	14	.	.	PUNCT
ejpam-5453	813	1	the	the	DET
ejpam-5453	813	2	boundary	boundary	NOUN
ejpam-5453	813	3	relied	rely	VERB
ejpam-5453	813	4	on	on	ADP
ejpam-5453	813	5	the	the	DET
ejpam-5453	813	6	present	present	ADJ
ejpam-5453	813	7	manner	manner	NOUN
ejpam-5453	813	8	is	be	AUX
ejpam-5453	813	9	∅.	∅.	NOUN
ejpam-5453	813	10	it	it	PRON
ejpam-5453	813	11	is	be	AUX
ejpam-5453	813	12	indicated	indicate	VERB
ejpam-5453	813	13	to	to	ADP
ejpam-5453	813	14	a	a	DET
ejpam-5453	813	15	successful	successful	ADJ
ejpam-5453	813	16	reduction	reduction	NOUN
ejpam-5453	813	17	in	in	ADP
ejpam-5453	813	18	vagueness	vagueness	NOUN
ejpam-5453	813	19	for	for	ADP
ejpam-5453	813	20	the	the	DET
ejpam-5453	813	21	two	two	NUM
ejpam-5453	813	22	sets	set	NOUN
ejpam-5453	813	23	which	which	PRON
ejpam-5453	813	24	achieved	achieve	VERB
ejpam-5453	813	25	an	an	DET
ejpam-5453	813	26	enhanced	enhanced	ADJ
ejpam-5453	813	27	accuracy	accuracy	NOUN
ejpam-5453	813	28	.	.	PUNCT
ejpam-5453	814	1	7	7	X
ejpam-5453	814	2	.	.	X
ejpam-5453	814	3	conclusions	conclusion	NOUN
ejpam-5453	814	4	the	the	DET
ejpam-5453	814	5	primary	primary	ADJ
ejpam-5453	814	6	goal	goal	NOUN
ejpam-5453	814	7	of	of	ADP
ejpam-5453	814	8	this	this	DET
ejpam-5453	814	9	theory	theory	NOUN
ejpam-5453	814	10	is	be	AUX
ejpam-5453	814	11	to	to	PART
ejpam-5453	814	12	minimize	minimize	VERB
ejpam-5453	814	13	the	the	DET
ejpam-5453	814	14	boundary	boundary	NOUN
ejpam-5453	814	15	by	by	ADP
ejpam-5453	814	16	reducing	reduce	VERB
ejpam-5453	814	17	upper	upper	ADJ
ejpam-5453	814	18	and	and	CCONJ
ejpam-5453	814	19	increasing	increase	VERB
ejpam-5453	814	20	lower	lower	ADV
ejpam-5453	814	21	,	,	PUNCT
ejpam-5453	814	22	thereby	thereby	ADV
ejpam-5453	814	23	maximizing	maximize	VERB
ejpam-5453	814	24	the	the	DET
ejpam-5453	814	25	accuracy	accuracy	NOUN
ejpam-5453	814	26	measure	measure	NOUN
ejpam-5453	814	27	.	.	PUNCT
ejpam-5453	815	1	rough	rough	ADJ
ejpam-5453	815	2	set	set	NOUN
ejpam-5453	815	3	theory	theory	NOUN
ejpam-5453	815	4	is	be	AUX
ejpam-5453	815	5	a	a	DET
ejpam-5453	815	6	vast	vast	ADJ
ejpam-5453	815	7	domain	domain	NOUN
ejpam-5453	815	8	with	with	ADP
ejpam-5453	815	9	numerous	numerous	ADJ
ejpam-5453	815	10	innovations	innovation	NOUN
ejpam-5453	815	11	with	with	ADP
ejpam-5453	815	12	various	various	ADJ
ejpam-5453	815	13	branches	branch	NOUN
ejpam-5453	815	14	.	.	PUNCT
ejpam-5453	816	1	one	one	NUM
ejpam-5453	816	2	of	of	ADP
ejpam-5453	816	3	these	these	DET
ejpam-5453	816	4	branches	branch	NOUN
ejpam-5453	816	5	is	be	AUX
ejpam-5453	816	6	the	the	DET
ejpam-5453	816	7	derivation	derivation	NOUN
ejpam-5453	816	8	of	of	ADP
ejpam-5453	816	9	rough	rough	ADJ
ejpam-5453	816	10	sets	set	NOUN
ejpam-5453	816	11	from	from	ADP
ejpam-5453	816	12	topology	topology	NOUN
ejpam-5453	816	13	,	,	PUNCT
ejpam-5453	816	14	highlighting	highlight	VERB
ejpam-5453	816	15	a	a	DET
ejpam-5453	816	16	strong	strong	ADJ
ejpam-5453	816	17	homogeneity	homogeneity	NOUN
ejpam-5453	816	18	between	between	ADP
ejpam-5453	816	19	rough	rough	ADJ
ejpam-5453	816	20	set	set	NOUN
ejpam-5453	816	21	theory	theory	NOUN
ejpam-5453	816	22	and	and	CCONJ
ejpam-5453	816	23	topology	topology	NOUN
ejpam-5453	816	24	.	.	PUNCT
ejpam-5453	817	1	topological	topological	ADJ
ejpam-5453	817	2	concepts	concept	NOUN
ejpam-5453	817	3	are	be	AUX
ejpam-5453	817	4	widely	widely	ADV
ejpam-5453	817	5	recognized	recognize	VERB
ejpam-5453	817	6	as	as	ADP
ejpam-5453	817	7	essential	essential	ADJ
ejpam-5453	817	8	for	for	ADP
ejpam-5453	817	9	understanding	understand	VERB
ejpam-5453	817	10	rough	rough	ADJ
ejpam-5453	817	11	set	set	NOUN
ejpam-5453	817	12	theory	theory	NOUN
ejpam-5453	817	13	,	,	PUNCT
ejpam-5453	817	14	with	with	ADP
ejpam-5453	817	15	ideals	ideal	NOUN
ejpam-5453	817	16	being	be	AUX
ejpam-5453	817	17	particularly	particularly	ADV
ejpam-5453	817	18	important	important	ADJ
ejpam-5453	817	19	.	.	PUNCT
ejpam-5453	818	1	ideals	ideal	NOUN
ejpam-5453	818	2	have	have	AUX
ejpam-5453	818	3	significantly	significantly	ADV
ejpam-5453	818	4	contributed	contribute	VERB
ejpam-5453	818	5	to	to	ADP
ejpam-5453	818	6	the	the	DET
ejpam-5453	818	7	generalization	generalization	NOUN
ejpam-5453	818	8	of	of	ADP
ejpam-5453	818	9	rough	rough	ADJ
ejpam-5453	818	10	sets	set	NOUN
ejpam-5453	818	11	.	.	PUNCT
ejpam-5453	819	1	specifically	specifically	ADV
ejpam-5453	819	2	,	,	PUNCT
ejpam-5453	819	3	ideals	ideal	NOUN
ejpam-5453	819	4	had	have	AUX
ejpam-5453	819	5	proven	prove	VERB
ejpam-5453	819	6	effective	effective	ADJ
ejpam-5453	819	7	in	in	ADP
ejpam-5453	819	8	enhancing	enhance	VERB
ejpam-5453	819	9	lower	low	ADJ
ejpam-5453	819	10	approximations	approximation	NOUN
ejpam-5453	819	11	and	and	CCONJ
ejpam-5453	819	12	reducing	reduce	VERB
ejpam-5453	819	13	upper	upper	ADJ
ejpam-5453	819	14	approximations	approximation	NOUN
ejpam-5453	819	15	,	,	PUNCT
ejpam-5453	819	16	thereby	thereby	ADV
ejpam-5453	819	17	narrowing	narrow	VERB
ejpam-5453	819	18	the	the	DET
ejpam-5453	819	19	boundary	boundary	ADJ
ejpam-5453	819	20	region	region	NOUN
ejpam-5453	819	21	and	and	CCONJ
ejpam-5453	819	22	improving	improve	VERB
ejpam-5453	819	23	accuracy	accuracy	NOUN
ejpam-5453	819	24	.	.	PUNCT
ejpam-5453	820	1	this	this	DET
ejpam-5453	820	2	process	process	NOUN
ejpam-5453	820	3	effectively	effectively	ADV
ejpam-5453	820	4	addressed	address	VERB
ejpam-5453	820	5	vagueness	vagueness	NOUN
ejpam-5453	820	6	which	which	PRON
ejpam-5453	820	7	is	be	AUX
ejpam-5453	820	8	a	a	DET
ejpam-5453	820	9	crucial	crucial	ADJ
ejpam-5453	820	10	objective	objective	NOUN
ejpam-5453	820	11	in	in	ADP
ejpam-5453	820	12	rough	rough	ADJ
ejpam-5453	820	13	set	set	NOUN
ejpam-5453	820	14	theory	theory	NOUN
ejpam-5453	820	15	.	.	PUNCT
ejpam-5453	821	1	in	in	ADP
ejpam-5453	821	2	the	the	DET
ejpam-5453	821	3	present	present	ADJ
ejpam-5453	821	4	results	result	NOUN
ejpam-5453	821	5	,	,	PUNCT
ejpam-5453	821	6	new	new	ADJ
ejpam-5453	821	7	topological	topological	ADJ
ejpam-5453	821	8	concepts	concept	NOUN
ejpam-5453	821	9	utilizing	utilize	VERB
ejpam-5453	821	10	ideals	ideal	NOUN
ejpam-5453	821	11	were	be	AUX
ejpam-5453	821	12	explored	explore	VERB
ejpam-5453	821	13	.	.	PUNCT
ejpam-5453	822	1	moreover	moreover	ADV
ejpam-5453	822	2	,	,	PUNCT
ejpam-5453	822	3	the	the	DET
ejpam-5453	822	4	characteristics	characteristic	NOUN
ejpam-5453	822	5	of	of	ADP
ejpam-5453	822	6	the	the	DET
ejpam-5453	822	7	proposed	propose	VERB
ejpam-5453	822	8	concepts	concept	NOUN
ejpam-5453	822	9	were	be	AUX
ejpam-5453	822	10	analyzed	analyze	VERB
ejpam-5453	822	11	,	,	PUNCT
ejpam-5453	822	12	and	and	CCONJ
ejpam-5453	822	13	their	their	PRON
ejpam-5453	822	14	features	feature	NOUN
ejpam-5453	822	15	were	be	AUX
ejpam-5453	822	16	discussed	discuss	VERB
ejpam-5453	822	17	.	.	PUNCT
ejpam-5453	823	1	relationships	relationship	NOUN
ejpam-5453	823	2	among	among	ADP
ejpam-5453	823	3	different	different	ADJ
ejpam-5453	823	4	types	type	NOUN
ejpam-5453	823	5	of	of	ADP
ejpam-5453	823	6	these	these	DET
ejpam-5453	823	7	notions	notion	NOUN
ejpam-5453	823	8	were	be	AUX
ejpam-5453	823	9	conducted	conduct	VERB
ejpam-5453	823	10	.	.	PUNCT
ejpam-5453	824	1	after	after	ADP
ejpam-5453	824	2	that	that	PRON
ejpam-5453	824	3	,	,	PUNCT
ejpam-5453	824	4	new	new	ADJ
ejpam-5453	824	5	operators	operator	NOUN
ejpam-5453	824	6	were	be	AUX
ejpam-5453	824	7	presented	present	VERB
ejpam-5453	824	8	relying	rely	VERB
ejpam-5453	824	9	on	on	ADP
ejpam-5453	824	10	ideals	ideal	NOUN
ejpam-5453	824	11	.	.	PUNCT
ejpam-5453	825	1	ideal	ideal	PROPN
ejpam-5453	825	2	increased	increase	VERB
ejpam-5453	825	3	the	the	DET
ejpam-5453	825	4	data	datum	NOUN
ejpam-5453	825	5	which	which	PRON
ejpam-5453	825	6	derived	derive	VERB
ejpam-5453	825	7	from	from	ADP
ejpam-5453	825	8	the	the	DET
ejpam-5453	825	9	information	information	NOUN
ejpam-5453	825	10	systems	system	NOUN
ejpam-5453	825	11	by	by	ADP
ejpam-5453	825	12	using	use	VERB
ejpam-5453	825	13	rough	rough	ADJ
ejpam-5453	825	14	set	set	NOUN
ejpam-5453	825	15	.	.	PUNCT
ejpam-5453	826	1	comparisons	comparison	NOUN
ejpam-5453	826	2	between	between	ADP
ejpam-5453	826	3	the	the	DET
ejpam-5453	826	4	current	current	ADJ
ejpam-5453	826	5	and	and	CCONJ
ejpam-5453	826	6	previous	previous	ADJ
ejpam-5453	826	7	versions	version	NOUN
ejpam-5453	826	8	were	be	AUX
ejpam-5453	826	9	provided	provide	VERB
ejpam-5453	826	10	,	,	PUNCT
ejpam-5453	826	11	demonstrating	demonstrate	VERB
ejpam-5453	826	12	that	that	SCONJ
ejpam-5453	826	13	the	the	DET
ejpam-5453	826	14	current	current	ADJ
ejpam-5453	826	15	approach	approach	NOUN
ejpam-5453	826	16	was	be	AUX
ejpam-5453	826	17	both	both	CCONJ
ejpam-5453	826	18	more	more	ADV
ejpam-5453	826	19	accurate	accurate	ADJ
ejpam-5453	826	20	and	and	CCONJ
ejpam-5453	826	21	more	more	ADV
ejpam-5453	826	22	general	general	ADJ
ejpam-5453	826	23	.	.	PUNCT
ejpam-5453	827	1	as	as	SCONJ
ejpam-5453	827	2	,	,	PUNCT
ejpam-5453	827	3	the	the	DET
ejpam-5453	827	4	current	current	ADJ
ejpam-5453	827	5	approach	approach	NOUN
ejpam-5453	827	6	helped	help	VERB
ejpam-5453	827	7	in	in	ADP
ejpam-5453	827	8	reducing	reduce	VERB
ejpam-5453	827	9	vagueness	vagueness	NOUN
ejpam-5453	827	10	and	and	CCONJ
ejpam-5453	827	11	,	,	PUNCT
ejpam-5453	827	12	as	as	ADP
ejpam-5453	827	13	a	a	DET
ejpam-5453	827	14	result	result	NOUN
ejpam-5453	827	15	,	,	PUNCT
ejpam-5453	827	16	improved	improved	ADJ
ejpam-5453	827	17	accuracy	accuracy	NOUN
ejpam-5453	827	18	.	.	PUNCT
ejpam-5453	828	1	additionally	additionally	ADV
ejpam-5453	828	2	,	,	PUNCT
ejpam-5453	828	3	three	three	NUM
ejpam-5453	828	4	types	type	NOUN
ejpam-5453	828	5	of	of	ADP
ejpam-5453	828	6	rough	rough	ADJ
ejpam-5453	828	7	membership	membership	NOUN
ejpam-5453	828	8	functions	function	NOUN
ejpam-5453	828	9	were	be	AUX
ejpam-5453	828	10	introduced	introduce	VERB
ejpam-5453	828	11	.	.	PUNCT
ejpam-5453	829	1	relationships	relationship	NOUN
ejpam-5453	829	2	among	among	ADP
ejpam-5453	829	3	them	they	PRON
ejpam-5453	829	4	were	be	AUX
ejpam-5453	829	5	also	also	ADV
ejpam-5453	829	6	highlighted	highlight	VERB
ejpam-5453	829	7	.	.	PUNCT
ejpam-5453	830	1	furthermore	furthermore	ADV
ejpam-5453	830	2	,	,	PUNCT
ejpam-5453	830	3	an	an	DET
ejpam-5453	830	4	example	example	NOUN
ejpam-5453	830	5	from	from	ADP
ejpam-5453	830	6	the	the	DET
ejpam-5453	830	7	medical	medical	ADJ
ejpam-5453	830	8	field	field	NOUN
ejpam-5453	830	9	was	be	AUX
ejpam-5453	830	10	given	give	VERB
ejpam-5453	830	11	to	to	PART
ejpam-5453	830	12	prove	prove	VERB
ejpam-5453	830	13	the	the	DET
ejpam-5453	830	14	utility	utility	NOUN
ejpam-5453	830	15	of	of	ADP
ejpam-5453	830	16	the	the	DET
ejpam-5453	830	17	present	present	ADJ
ejpam-5453	830	18	concepts	concept	NOUN
ejpam-5453	830	19	in	in	ADP
ejpam-5453	830	20	a	a	DET
ejpam-5453	830	21	practical	practical	ADJ
ejpam-5453	830	22	context	context	NOUN
ejpam-5453	830	23	.	.	PUNCT
ejpam-5453	831	1	the	the	DET
ejpam-5453	831	2	proposed	propose	VERB
ejpam-5453	831	3	manners	manner	NOUN
ejpam-5453	831	4	through	through	ADP
ejpam-5453	831	5	this	this	DET
ejpam-5453	831	6	medical	medical	ADJ
ejpam-5453	831	7	example	example	NOUN
ejpam-5453	831	8	had	have	AUX
ejpam-5453	831	9	proven	prove	VERB
ejpam-5453	831	10	to	to	PART
ejpam-5453	831	11	be	be	AUX
ejpam-5453	831	12	effective	effective	ADJ
ejpam-5453	831	13	and	and	CCONJ
ejpam-5453	831	14	robust	robust	ADJ
ejpam-5453	831	15	in	in	ADP
ejpam-5453	831	16	reducing	reduce	VERB
ejpam-5453	831	17	the	the	DET
ejpam-5453	831	18	boundary	boundary	NOUN
ejpam-5453	831	19	and	and	CCONJ
ejpam-5453	831	20	enhancing	enhance	VERB
ejpam-5453	831	21	the	the	DET
ejpam-5453	831	22	accuracy	accuracy	NOUN
ejpam-5453	831	23	.	.	PUNCT
ejpam-5453	832	1	references	reference	NOUN
ejpam-5453	832	2	2875	2875	NUM
ejpam-5453	832	3	a	a	DET
ejpam-5453	832	4	promising	promising	ADJ
ejpam-5453	832	5	direction	direction	NOUN
ejpam-5453	832	6	for	for	ADP
ejpam-5453	832	7	future	future	ADJ
ejpam-5453	832	8	work	work	NOUN
ejpam-5453	832	9	will	will	AUX
ejpam-5453	832	10	focus	focus	VERB
ejpam-5453	832	11	on	on	ADP
ejpam-5453	832	12	investigating	investigate	VERB
ejpam-5453	832	13	new	new	ADJ
ejpam-5453	832	14	approximations	approximation	NOUN
ejpam-5453	832	15	using	use	VERB
ejpam-5453	832	16	distinct	distinct	ADJ
ejpam-5453	832	17	and	and	CCONJ
ejpam-5453	832	18	innovative	innovative	ADJ
ejpam-5453	832	19	neighborhoods	neighborhood	NOUN
ejpam-5453	832	20	via	via	ADP
ejpam-5453	832	21	two	two	NUM
ejpam-5453	832	22	ideals	ideal	NOUN
ejpam-5453	832	23	and	and	CCONJ
ejpam-5453	832	24	expanding	expand	VERB
ejpam-5453	832	25	the	the	DET
ejpam-5453	832	26	current	current	ADJ
ejpam-5453	832	27	rough	rough	ADJ
ejpam-5453	832	28	set	set	NOUN
ejpam-5453	832	29	paradigms	paradigm	NOUN
ejpam-5453	832	30	to	to	ADP
ejpam-5453	832	31	rough	rough	ADJ
ejpam-5453	832	32	multiset	multiset	NOUN
ejpam-5453	832	33	with	with	ADP
ejpam-5453	832	34	multiset	multiset	ADJ
ejpam-5453	832	35	ideals	ideal	NOUN
ejpam-5453	832	36	.	.	PUNCT
ejpam-5453	833	1	references	reference	NOUN
ejpam-5453	833	2	[	[	X
ejpam-5453	833	3	1	1	NUM
ejpam-5453	833	4	]	]	PUNCT
ejpam-5453	833	5	m.	m.	PROPN
ejpam-5453	833	6	e.	e.	PROPN
ejpam-5453	833	7	abd	abd	PROPN
ejpam-5453	833	8	-	-	PROPN
ejpam-5453	833	9	el	el	PROPN
ejpam-5453	833	10	-	-	PUNCT
ejpam-5453	833	11	monsef	monsef	ADJ
ejpam-5453	833	12	,	,	PUNCT
ejpam-5453	833	13	a.	a.	NOUN
ejpam-5453	833	14	m.	m.	NOUN
ejpam-5453	833	15	kozae	kozae	PROPN
ejpam-5453	833	16	,	,	PUNCT
ejpam-5453	833	17	and	and	CCONJ
ejpam-5453	833	18	m.	m.	PROPN
ejpam-5453	833	19	k.	k.	PROPN
ejpam-5453	834	1	el	el	PROPN
ejpam-5453	834	2	-	-	PROPN
ejpam-5453	834	3	bably	bably	ADV
ejpam-5453	834	4	.	.	PUNCT
ejpam-5453	835	1	new	new	ADJ
ejpam-5453	835	2	generalized	generalized	ADJ
ejpam-5453	835	3	definitions	definition	NOUN
ejpam-5453	835	4	of	of	ADP
ejpam-5453	835	5	rough	rough	ADJ
ejpam-5453	835	6	membership	membership	NOUN
ejpam-5453	835	7	relations	relation	NOUN
ejpam-5453	835	8	and	and	CCONJ
ejpam-5453	835	9	functions	function	NOUN
ejpam-5453	835	10	from	from	ADP
ejpam-5453	835	11	topological	topological	ADJ
ejpam-5453	835	12	point	point	NOUN
ejpam-5453	835	13	of	of	ADP
ejpam-5453	835	14	view	view	NOUN
ejpam-5453	835	15	.	.	PUNCT
ejpam-5453	836	1	journal	journal	NOUN
ejpam-5453	836	2	of	of	ADP
ejpam-5453	836	3	advances	advance	NOUN
ejpam-5453	836	4	in	in	ADP
ejpam-5453	836	5	mathematics	mathematic	NOUN
ejpam-5453	836	6	,	,	PUNCT
ejpam-5453	836	7	8:1635–1652	8:1635–1652	NUM
ejpam-5453	836	8	,	,	PUNCT
ejpam-5453	836	9	2014	2014	NUM
ejpam-5453	836	10	.	.	PUNCT
ejpam-5453	837	1	[	[	X
ejpam-5453	837	2	2	2	NUM
ejpam-5453	837	3	]	]	PUNCT
ejpam-5453	837	4	a.	a.	NOUN
ejpam-5453	837	5	a.	a.	NOUN
ejpam-5453	837	6	abo	abo	PROPN
ejpam-5453	837	7	-	-	PUNCT
ejpam-5453	837	8	khadra	khadra	PROPN
ejpam-5453	837	9	,	,	PUNCT
ejpam-5453	837	10	b.	b.	PROPN
ejpam-5453	837	11	m.	m.	PROPN
ejpam-5453	837	12	taher	taher	PROPN
ejpam-5453	837	13	,	,	PUNCT
ejpam-5453	837	14	and	and	CCONJ
ejpam-5453	837	15	m.	m.	PROPN
ejpam-5453	837	16	k.	k.	PROPN
ejpam-5453	838	1	el	el	PROPN
ejpam-5453	838	2	-	-	PROPN
ejpam-5453	838	3	bably	bably	ADV
ejpam-5453	838	4	.	.	PUNCT
ejpam-5453	839	1	generalization	generalization	NOUN
ejpam-5453	839	2	of	of	ADP
ejpam-5453	839	3	pawlak	pawlak	ADJ
ejpam-5453	839	4	approximation	approximation	NOUN
ejpam-5453	839	5	space	space	NOUN
ejpam-5453	839	6	.	.	PUNCT
ejpam-5453	840	1	the	the	DET
ejpam-5453	840	2	egyptian	egyptian	PROPN
ejpam-5453	840	3	mathematical	mathematical	PROPN
ejpam-5453	840	4	society	society	NOUN
ejpam-5453	840	5	,	,	PUNCT
ejpam-5453	840	6	cairo	cairo	PROPN
ejpam-5453	840	7	,	,	PUNCT
ejpam-5453	840	8	3	3	NUM
ejpam-5453	840	9	top	top	NOUN
ejpam-5453	840	10	.	.	PUNCT
ejpam-5453	840	11	,	,	PUNCT
ejpam-5453	840	12	geom	geom	PROPN
ejpam-5453	840	13	.	.	PROPN
ejpam-5453	840	14	,	,	PUNCT
ejpam-5453	840	15	pages	page	NOUN
ejpam-5453	840	16	335–346	335–346	NUM
ejpam-5453	840	17	,	,	PUNCT
ejpam-5453	840	18	2007	2007	NUM
ejpam-5453	840	19	.	.	PUNCT
ejpam-5453	841	1	[	[	X
ejpam-5453	841	2	3	3	X
ejpam-5453	841	3	]	]	X
ejpam-5453	841	4	e.	e.	PROPN
ejpam-5453	841	5	a.	a.	PROPN
ejpam-5453	841	6	abo	abo	PROPN
ejpam-5453	841	7	-	-	PUNCT
ejpam-5453	841	8	tabl	tabl	NOUN
ejpam-5453	841	9	.	.	PUNCT
ejpam-5453	842	1	a	a	DET
ejpam-5453	842	2	comparison	comparison	NOUN
ejpam-5453	842	3	of	of	ADP
ejpam-5453	842	4	two	two	NUM
ejpam-5453	842	5	kinds	kind	NOUN
ejpam-5453	842	6	of	of	ADP
ejpam-5453	842	7	definitions	definition	NOUN
ejpam-5453	842	8	of	of	ADP
ejpam-5453	842	9	rough	rough	ADJ
ejpam-5453	842	10	approximations	approximation	NOUN
ejpam-5453	842	11	based	base	VERB
ejpam-5453	842	12	on	on	ADP
ejpam-5453	842	13	a	a	DET
ejpam-5453	842	14	similarity	similarity	NOUN
ejpam-5453	842	15	relation	relation	NOUN
ejpam-5453	842	16	.	.	PUNCT
ejpam-5453	843	1	inform	inform	NOUN
ejpam-5453	843	2	.	.	PUNCT
ejpam-5453	844	1	sci	sci	PROPN
ejpam-5453	844	2	.	.	PROPN
ejpam-5453	844	3	,	,	PUNCT
ejpam-5453	844	4	181:2587–2596	181:2587–2596	NUM
ejpam-5453	844	5	,	,	PUNCT
ejpam-5453	844	6	2011	2011	NUM
ejpam-5453	844	7	.	.	PUNCT
ejpam-5453	845	1	[	[	X
ejpam-5453	845	2	4	4	X
ejpam-5453	845	3	]	]	X
ejpam-5453	845	4	h.	h.	PROPN
ejpam-5453	845	5	m.	m.	PROPN
ejpam-5453	845	6	abu	abu	PROPN
ejpam-5453	845	7	-	-	PUNCT
ejpam-5453	845	8	doniaa	doniaa	PROPN
ejpam-5453	845	9	and	and	CCONJ
ejpam-5453	845	10	a.	a.	NOUN
ejpam-5453	845	11	s.	s.	PROPN
ejpam-5453	845	12	salama	salama	PROPN
ejpam-5453	845	13	.	.	PUNCT
ejpam-5453	846	1	generalization	generalization	NOUN
ejpam-5453	846	2	of	of	ADP
ejpam-5453	846	3	pawlak	pawlak	ADJ
ejpam-5453	846	4	’s	’s	PART
ejpam-5453	846	5	rough	rough	ADJ
ejpam-5453	846	6	approximation	approximation	NOUN
ejpam-5453	846	7	spaces	space	NOUN
ejpam-5453	846	8	by	by	ADP
ejpam-5453	846	9	using	use	VERB
ejpam-5453	846	10	αβ	αβ	ADJ
ejpam-5453	846	11	-	-	PUNCT
ejpam-5453	846	12	open	open	ADJ
ejpam-5453	846	13	sets	set	NOUN
ejpam-5453	846	14	.	.	PUNCT
ejpam-5453	847	1	int	int	NOUN
ejpam-5453	847	2	.	.	PUNCT
ejpam-5453	848	1	j.	j.	PROPN
ejpam-5453	848	2	approx	approx	PROPN
ejpam-5453	848	3	.	.	PUNCT
ejpam-5453	849	1	reason	reason	NOUN
ejpam-5453	849	2	.	.	PUNCT
ejpam-5453	849	3	,	,	PUNCT
ejpam-5453	849	4	53:1094–1105	53:1094–1105	NUM
ejpam-5453	849	5	,	,	PUNCT
ejpam-5453	849	6	2012	2012	NUM
ejpam-5453	849	7	.	.	PUNCT
ejpam-5453	850	1	[	[	X
ejpam-5453	850	2	5	5	X
ejpam-5453	850	3	]	]	PUNCT
ejpam-5453	850	4	t.	t.	PROPN
ejpam-5453	850	5	m.	m.	PROPN
ejpam-5453	850	6	al	al	PROPN
ejpam-5453	850	7	-	-	PUNCT
ejpam-5453	850	8	shami	shami	PROPN
ejpam-5453	850	9	.	.	PUNCT
ejpam-5453	851	1	an	an	DET
ejpam-5453	851	2	improvement	improvement	NOUN
ejpam-5453	851	3	of	of	ADP
ejpam-5453	851	4	rough	rough	ADJ
ejpam-5453	851	5	sets	set	NOUN
ejpam-5453	851	6	’	'	PUNCT
ejpam-5453	851	7	accuracy	accuracy	NOUN
ejpam-5453	851	8	measure	measure	NOUN
ejpam-5453	851	9	using	use	VERB
ejpam-5453	851	10	containment	containment	NOUN
ejpam-5453	851	11	neighborhoods	neighborhood	NOUN
ejpam-5453	851	12	with	with	ADP
ejpam-5453	851	13	a	a	DET
ejpam-5453	851	14	medical	medical	ADJ
ejpam-5453	851	15	application	application	NOUN
ejpam-5453	851	16	.	.	PUNCT
ejpam-5453	852	1	inform	inform	NOUN
ejpam-5453	852	2	.	.	PUNCT
ejpam-5453	853	1	sci	sci	PROPN
ejpam-5453	853	2	.	.	PROPN
ejpam-5453	853	3	,	,	PUNCT
ejpam-5453	853	4	569:110–124	569:110–124	NUM
ejpam-5453	853	5	,	,	PUNCT
ejpam-5453	853	6	2021	2021	NUM
ejpam-5453	853	7	.	.	PUNCT
ejpam-5453	854	1	[	[	X
ejpam-5453	854	2	6	6	NUM
ejpam-5453	854	3	]	]	PUNCT
ejpam-5453	854	4	t.	t.	PROPN
ejpam-5453	854	5	m.	m.	PROPN
ejpam-5453	854	6	al	al	PROPN
ejpam-5453	854	7	-	-	PUNCT
ejpam-5453	854	8	shami	shami	PROPN
ejpam-5453	854	9	.	.	PUNCT
ejpam-5453	855	1	improvement	improvement	NOUN
ejpam-5453	855	2	of	of	ADP
ejpam-5453	855	3	the	the	DET
ejpam-5453	855	4	approximations	approximation	NOUN
ejpam-5453	855	5	and	and	CCONJ
ejpam-5453	855	6	accuracy	accuracy	NOUN
ejpam-5453	855	7	measure	measure	NOUN
ejpam-5453	855	8	of	of	ADP
ejpam-5453	855	9	a	a	DET
ejpam-5453	855	10	rough	rough	ADJ
ejpam-5453	855	11	set	set	NOUN
ejpam-5453	855	12	using	use	VERB
ejpam-5453	855	13	somewhere	somewhere	ADV
ejpam-5453	855	14	dense	dense	ADJ
ejpam-5453	855	15	sets	set	NOUN
ejpam-5453	855	16	.	.	PUNCT
ejpam-5453	856	1	soft	soft	ADJ
ejpam-5453	856	2	computing	computing	NOUN
ejpam-5453	856	3	,	,	PUNCT
ejpam-5453	856	4	25(23):14449–14460	25(23):14449–14460	NUM
ejpam-5453	856	5	,	,	PUNCT
ejpam-5453	856	6	2021	2021	NUM
ejpam-5453	856	7	.	.	PUNCT
ejpam-5453	857	1	[	[	X
ejpam-5453	857	2	7	7	X
ejpam-5453	857	3	]	]	PUNCT
ejpam-5453	857	4	t.	t.	PROPN
ejpam-5453	857	5	m.	m.	PROPN
ejpam-5453	857	6	al	al	PROPN
ejpam-5453	857	7	-	-	PUNCT
ejpam-5453	857	8	shami	shami	PROPN
ejpam-5453	857	9	.	.	PUNCT
ejpam-5453	858	1	maximal	maximal	ADJ
ejpam-5453	858	2	rough	rough	ADJ
ejpam-5453	858	3	neighborhoods	neighborhood	NOUN
ejpam-5453	858	4	with	with	ADP
ejpam-5453	858	5	a	a	DET
ejpam-5453	858	6	medical	medical	ADJ
ejpam-5453	858	7	application	application	NOUN
ejpam-5453	858	8	.	.	PUNCT
ejpam-5453	859	1	journal	journal	PROPN
ejpam-5453	859	2	of	of	ADP
ejpam-5453	859	3	ambient	ambient	ADJ
ejpam-5453	859	4	intelligence	intelligence	NOUN
ejpam-5453	859	5	and	and	CCONJ
ejpam-5453	859	6	humanized	humanize	VERB
ejpam-5453	859	7	computing	computing	NOUN
ejpam-5453	859	8	,	,	PUNCT
ejpam-5453	859	9	2022	2022	NUM
ejpam-5453	859	10	.	.	PUNCT
ejpam-5453	860	1	[	[	X
ejpam-5453	860	2	8	8	X
ejpam-5453	860	3	]	]	PUNCT
ejpam-5453	860	4	t.	t.	PROPN
ejpam-5453	860	5	m.	m.	PROPN
ejpam-5453	860	6	al	al	PROPN
ejpam-5453	860	7	-	-	PUNCT
ejpam-5453	860	8	shami	shami	PROPN
ejpam-5453	860	9	.	.	PUNCT
ejpam-5453	861	1	topological	topological	ADJ
ejpam-5453	861	2	approach	approach	NOUN
ejpam-5453	861	3	to	to	PART
ejpam-5453	861	4	generate	generate	VERB
ejpam-5453	861	5	new	new	ADJ
ejpam-5453	861	6	rough	rough	ADJ
ejpam-5453	861	7	set	set	NOUN
ejpam-5453	861	8	models	model	NOUN
ejpam-5453	861	9	.	.	PUNCT
ejpam-5453	862	1	complex	complex	ADJ
ejpam-5453	862	2	&	&	CCONJ
ejpam-5453	862	3	intelligent	intelligent	ADJ
ejpam-5453	862	4	systems	system	NOUN
ejpam-5453	862	5	,	,	PUNCT
ejpam-5453	862	6	2022	2022	NUM
ejpam-5453	862	7	.	.	PUNCT
ejpam-5453	863	1	[	[	X
ejpam-5453	863	2	9	9	NUM
ejpam-5453	863	3	]	]	PUNCT
ejpam-5453	863	4	t.	t.	PROPN
ejpam-5453	863	5	m.	m.	PROPN
ejpam-5453	863	6	al	al	PROPN
ejpam-5453	863	7	-	-	PUNCT
ejpam-5453	863	8	shami	shami	PROPN
ejpam-5453	863	9	,	,	PUNCT
ejpam-5453	863	10	i.	i.	PROPN
ejpam-5453	863	11	alshammari	alshammari	PROPN
ejpam-5453	863	12	,	,	PUNCT
ejpam-5453	863	13	and	and	CCONJ
ejpam-5453	864	1	m.	m.	PROPN
ejpam-5453	864	2	e.	e.	PROPN
ejpam-5453	864	3	el	el	PROPN
ejpam-5453	864	4	-	-	PROPN
ejpam-5453	864	5	shafei	shafei	PROPN
ejpam-5453	864	6	.	.	PUNCT
ejpam-5453	865	1	a	a	DET
ejpam-5453	865	2	comparison	comparison	NOUN
ejpam-5453	865	3	of	of	ADP
ejpam-5453	865	4	two	two	NUM
ejpam-5453	865	5	types	type	NOUN
ejpam-5453	865	6	of	of	ADP
ejpam-5453	865	7	rough	rough	ADJ
ejpam-5453	865	8	approximations	approximation	NOUN
ejpam-5453	865	9	based	base	VERB
ejpam-5453	865	10	on	on	ADP
ejpam-5453	865	11	nk	nk	PROPN
ejpam-5453	865	12	-	-	PUNCT
ejpam-5453	865	13	neighborhoods	neighborhood	NOUN
ejpam-5453	865	14	.	.	PUNCT
ejpam-5453	866	1	journal	journal	NOUN
ejpam-5453	866	2	of	of	ADP
ejpam-5453	866	3	intelligent	intelligent	ADJ
ejpam-5453	866	4	&	&	CCONJ
ejpam-5453	866	5	fuzzy	fuzzy	ADJ
ejpam-5453	866	6	systems	system	NOUN
ejpam-5453	866	7	,	,	PUNCT
ejpam-5453	866	8	41(1):1393–1406	41(1):1393–1406	NUM
ejpam-5453	866	9	,	,	PUNCT
ejpam-5453	866	10	2021	2021	NUM
ejpam-5453	866	11	.	.	PUNCT
ejpam-5453	867	1	[	[	X
ejpam-5453	867	2	10	10	NUM
ejpam-5453	867	3	]	]	PUNCT
ejpam-5453	867	4	t.	t.	PROPN
ejpam-5453	867	5	m.	m.	PROPN
ejpam-5453	867	6	al	al	PROPN
ejpam-5453	867	7	-	-	PUNCT
ejpam-5453	867	8	shami	shami	PROPN
ejpam-5453	867	9	and	and	CCONJ
ejpam-5453	867	10	d.	d.	PROPN
ejpam-5453	867	11	ciucci	ciucci	PROPN
ejpam-5453	867	12	.	.	PUNCT
ejpam-5453	868	1	subset	subset	ADJ
ejpam-5453	868	2	neighborhood	neighborhood	NOUN
ejpam-5453	868	3	rough	rough	ADJ
ejpam-5453	868	4	sets	set	NOUN
ejpam-5453	868	5	.	.	PUNCT
ejpam-5453	869	1	knowledge	knowledge	NOUN
ejpam-5453	869	2	-	-	PUNCT
ejpam-5453	869	3	based	base	VERB
ejpam-5453	869	4	systems	system	NOUN
ejpam-5453	869	5	,	,	PUNCT
ejpam-5453	869	6	237	237	NUM
ejpam-5453	869	7	,	,	PUNCT
ejpam-5453	869	8	2022	2022	NUM
ejpam-5453	869	9	.	.	PUNCT
ejpam-5453	870	1	[	[	X
ejpam-5453	870	2	11	11	NUM
ejpam-5453	870	3	]	]	PUNCT
ejpam-5453	870	4	t.	t.	PROPN
ejpam-5453	870	5	m.	m.	PROPN
ejpam-5453	870	6	al	al	PROPN
ejpam-5453	870	7	-	-	PUNCT
ejpam-5453	870	8	shami	shami	PROPN
ejpam-5453	870	9	,	,	PUNCT
ejpam-5453	870	10	w.	w.	PROPN
ejpam-5453	870	11	q.	q.	PROPN
ejpam-5453	870	12	fu	fu	PROPN
ejpam-5453	870	13	,	,	PUNCT
ejpam-5453	870	14	and	and	CCONJ
ejpam-5453	870	15	e.	e.	PROPN
ejpam-5453	870	16	a.	a.	PROPN
ejpam-5453	870	17	abo	abo	PROPN
ejpam-5453	870	18	-	-	PUNCT
ejpam-5453	870	19	tabl	tabl	NOUN
ejpam-5453	870	20	.	.	PUNCT
ejpam-5453	871	1	new	new	ADJ
ejpam-5453	871	2	rough	rough	ADJ
ejpam-5453	871	3	approximations	approximation	NOUN
ejpam-5453	871	4	based	base	VERB
ejpam-5453	871	5	on	on	ADP
ejpam-5453	871	6	e	e	NOUN
ejpam-5453	871	7	-	-	NOUN
ejpam-5453	871	8	neighborhoods	neighborhood	NOUN
ejpam-5453	871	9	.	.	PUNCT
ejpam-5453	872	1	complexity	complexity	NOUN
ejpam-5453	872	2	,	,	PUNCT
ejpam-5453	872	3	2021	2021	NUM
ejpam-5453	872	4	.	.	PUNCT
ejpam-5453	873	1	[	[	X
ejpam-5453	873	2	12	12	NUM
ejpam-5453	873	3	]	]	PUNCT
ejpam-5453	873	4	t.	t.	PROPN
ejpam-5453	873	5	m.	m.	PROPN
ejpam-5453	873	6	al	al	PROPN
ejpam-5453	873	7	-	-	PUNCT
ejpam-5453	873	8	shami	shami	PROPN
ejpam-5453	873	9	and	and	CCONJ
ejpam-5453	873	10	m.	m.	PROPN
ejpam-5453	873	11	hosny	hosny	PROPN
ejpam-5453	873	12	.	.	PUNCT
ejpam-5453	874	1	generalized	generalized	ADJ
ejpam-5453	874	2	approximation	approximation	NOUN
ejpam-5453	874	3	spaces	space	NOUN
ejpam-5453	874	4	generation	generation	NOUN
ejpam-5453	874	5	from	from	ADP
ejpam-5453	874	6	ℶj	ℶj	ADJ
ejpam-5453	874	7	-	-	PUNCT
ejpam-5453	874	8	neighborhoods	neighborhood	NOUN
ejpam-5453	874	9	and	and	CCONJ
ejpam-5453	874	10	ideals	ideal	NOUN
ejpam-5453	874	11	with	with	ADP
ejpam-5453	874	12	application	application	NOUN
ejpam-5453	874	13	to	to	ADP
ejpam-5453	874	14	chikungunya	chikungunya	NOUN
ejpam-5453	874	15	disease	disease	NOUN
ejpam-5453	874	16	.	.	PUNCT
ejpam-5453	875	1	aims	aim	VERB
ejpam-5453	875	2	mathematics	mathematic	NOUN
ejpam-5453	875	3	,	,	PUNCT
ejpam-5453	875	4	9(4):10050–10077	9(4):10050–10077	NUM
ejpam-5453	875	5	,	,	PUNCT
ejpam-5453	875	6	2024	2024	NUM
ejpam-5453	875	7	.	.	PUNCT
ejpam-5453	876	1	[	[	X
ejpam-5453	876	2	13	13	NUM
ejpam-5453	876	3	]	]	PUNCT
ejpam-5453	876	4	t.	t.	PROPN
ejpam-5453	876	5	m.	m.	PROPN
ejpam-5453	876	6	al	al	PROPN
ejpam-5453	876	7	-	-	PUNCT
ejpam-5453	876	8	shami	shami	PROPN
ejpam-5453	876	9	and	and	CCONJ
ejpam-5453	876	10	a.	a.	PROPN
ejpam-5453	876	11	mhemdi	mhemdi	PROPN
ejpam-5453	876	12	.	.	PUNCT
ejpam-5453	877	1	approximation	approximation	NOUN
ejpam-5453	877	2	spaces	space	NOUN
ejpam-5453	877	3	inspired	inspire	VERB
ejpam-5453	877	4	by	by	ADP
ejpam-5453	877	5	subset	subset	VERB
ejpam-5453	877	6	rough	rough	ADJ
ejpam-5453	877	7	neighborhoods	neighborhood	NOUN
ejpam-5453	877	8	with	with	ADP
ejpam-5453	877	9	applications	application	NOUN
ejpam-5453	877	10	.	.	PUNCT
ejpam-5453	878	1	demonstratio	demonstratio	PROPN
ejpam-5453	878	2	mathematica	mathematica	PROPN
ejpam-5453	878	3	,	,	PUNCT
ejpam-5453	878	4	56(1	56(1	NUM
ejpam-5453	878	5	)	)	PUNCT
ejpam-5453	878	6	,	,	PUNCT
ejpam-5453	878	7	2023	2023	NUM
ejpam-5453	878	8	.	.	PUNCT
ejpam-5453	879	1	references	reference	NOUN
ejpam-5453	879	2	2876	2876	NUM
ejpam-5453	879	3	[	[	X
ejpam-5453	879	4	14	14	NUM
ejpam-5453	879	5	]	]	PUNCT
ejpam-5453	879	6	a.	a.	NOUN
ejpam-5453	879	7	a.	a.	PROPN
ejpam-5453	879	8	allam	allam	PROPN
ejpam-5453	879	9	,	,	PUNCT
ejpam-5453	879	10	m.	m.	PROPN
ejpam-5453	879	11	y.	y.	PROPN
ejpam-5453	879	12	bakeir	bakeir	PROPN
ejpam-5453	879	13	,	,	PUNCT
ejpam-5453	879	14	and	and	CCONJ
ejpam-5453	879	15	e.	e.	PROPN
ejpam-5453	879	16	a.	a.	PROPN
ejpam-5453	879	17	abo	abo	PROPN
ejpam-5453	879	18	-	-	PUNCT
ejpam-5453	879	19	tabl	tabl	NOUN
ejpam-5453	879	20	.	.	PUNCT
ejpam-5453	880	1	new	new	ADJ
ejpam-5453	880	2	approach	approach	NOUN
ejpam-5453	880	3	for	for	ADP
ejpam-5453	880	4	closure	closure	NOUN
ejpam-5453	880	5	spaces	space	NOUN
ejpam-5453	880	6	by	by	ADP
ejpam-5453	880	7	relations	relation	NOUN
ejpam-5453	880	8	.	.	PUNCT
ejpam-5453	881	1	acta	acta	PROPN
ejpam-5453	881	2	mathematica	mathematica	PROPN
ejpam-5453	881	3	academiae	academiae	PROPN
ejpam-5453	881	4	paedagogicae	paedagogicae	VERB
ejpam-5453	881	5	nyiregyháziensis	nyiregyháziensis	NOUN
ejpam-5453	881	6	,	,	PUNCT
ejpam-5453	881	7	22:285–304	22:285–304	PROPN
ejpam-5453	881	8	,	,	PUNCT
ejpam-5453	881	9	2006	2006	NUM
ejpam-5453	881	10	.	.	PUNCT
ejpam-5453	882	1	[	[	X
ejpam-5453	882	2	15	15	NUM
ejpam-5453	882	3	]	]	X
ejpam-5453	882	4	b.	b.	PROPN
ejpam-5453	882	5	de	de	X
ejpam-5453	882	6	baets	baet	NOUN
ejpam-5453	882	7	and	and	CCONJ
ejpam-5453	882	8	e.	e.	PROPN
ejpam-5453	882	9	kerre	kerre	PROPN
ejpam-5453	882	10	.	.	PUNCT
ejpam-5453	883	1	a	a	DET
ejpam-5453	883	2	revision	revision	NOUN
ejpam-5453	883	3	of	of	ADP
ejpam-5453	883	4	bandler	bandler	NOUN
ejpam-5453	883	5	-	-	PUNCT
ejpam-5453	883	6	kohout	kohout	NOUN
ejpam-5453	883	7	compositions	composition	NOUN
ejpam-5453	883	8	of	of	ADP
ejpam-5453	883	9	relations	relation	NOUN
ejpam-5453	883	10	.	.	PUNCT
ejpam-5453	884	1	math	math	PROPN
ejpam-5453	884	2	.	.	PUNCT
ejpam-5453	885	1	pannon	pannon	PROPN
ejpam-5453	885	2	.	.	PROPN
ejpam-5453	885	3	,	,	PUNCT
ejpam-5453	885	4	4(1):59–78	4(1):59–78	NUM
ejpam-5453	885	5	,	,	PUNCT
ejpam-5453	885	6	1993	1993	NUM
ejpam-5453	885	7	.	.	PUNCT
ejpam-5453	886	1	[	[	X
ejpam-5453	886	2	16	16	NUM
ejpam-5453	886	3	]	]	PUNCT
ejpam-5453	886	4	j.	j.	PROPN
ejpam-5453	886	5	dai	dai	PROPN
ejpam-5453	886	6	,	,	PUNCT
ejpam-5453	886	7	s.	s.	PROPN
ejpam-5453	886	8	gao	gao	PROPN
ejpam-5453	886	9	,	,	PUNCT
ejpam-5453	886	10	and	and	CCONJ
ejpam-5453	886	11	g.	g.	PROPN
ejpam-5453	886	12	zheng	zheng	PROPN
ejpam-5453	886	13	.	.	PUNCT
ejpam-5453	887	1	generalized	generalize	VERB
ejpam-5453	887	2	rough	rough	ADJ
ejpam-5453	887	3	set	set	NOUN
ejpam-5453	887	4	models	model	NOUN
ejpam-5453	887	5	determined	determine	VERB
ejpam-5453	887	6	by	by	ADP
ejpam-5453	887	7	multiple	multiple	ADJ
ejpam-5453	887	8	neighborhoods	neighborhood	NOUN
ejpam-5453	887	9	generated	generate	VERB
ejpam-5453	887	10	from	from	ADP
ejpam-5453	887	11	a	a	DET
ejpam-5453	887	12	similarity	similarity	NOUN
ejpam-5453	887	13	relation	relation	NOUN
ejpam-5453	887	14	.	.	PUNCT
ejpam-5453	888	1	soft	soft	ADJ
ejpam-5453	888	2	computing	computing	NOUN
ejpam-5453	888	3	,	,	PUNCT
ejpam-5453	888	4	22:2081–2094	22:2081–2094	NUM
ejpam-5453	888	5	,	,	PUNCT
ejpam-5453	888	6	2018	2018	NUM
ejpam-5453	888	7	.	.	PUNCT
ejpam-5453	889	1	[	[	X
ejpam-5453	889	2	17	17	NUM
ejpam-5453	889	3	]	]	X
ejpam-5453	889	4	e.	e.	PROPN
ejpam-5453	889	5	ekici	ekici	PROPN
ejpam-5453	889	6	and	and	CCONJ
ejpam-5453	889	7	t.	t.	PROPN
ejpam-5453	889	8	noiri	noiri	PROPN
ejpam-5453	889	9	.	.	PUNCT
ejpam-5453	890	1	∗-extremally	∗-extremally	ADV
ejpam-5453	890	2	disconnected	disconnect	VERB
ejpam-5453	890	3	ideal	ideal	ADJ
ejpam-5453	890	4	topological	topological	ADJ
ejpam-5453	890	5	spaces	space	NOUN
ejpam-5453	890	6	.	.	PUNCT
ejpam-5453	891	1	acta	acta	PROPN
ejpam-5453	891	2	math	math	PROPN
ejpam-5453	891	3	.	.	PUNCT
ejpam-5453	892	1	hungar	hungar	PROPN
ejpam-5453	892	2	.	.	PUNCT
ejpam-5453	892	3	,	,	PUNCT
ejpam-5453	892	4	122:81–90	122:81–90	NUM
ejpam-5453	892	5	,	,	PUNCT
ejpam-5453	892	6	2009	2009	NUM
ejpam-5453	892	7	.	.	PUNCT
ejpam-5453	893	1	[	[	X
ejpam-5453	893	2	18	18	NUM
ejpam-5453	893	3	]	]	PUNCT
ejpam-5453	893	4	m.	m.	NOUN
ejpam-5453	893	5	el	el	PROPN
ejpam-5453	893	6	-	-	PUNCT
ejpam-5453	893	7	sayed	say	VERB
ejpam-5453	893	8	,	,	PUNCT
ejpam-5453	893	9	m.	m.	NOUN
ejpam-5453	893	10	a.	a.	PROPN
ejpam-5453	893	11	el	el	PROPN
ejpam-5453	893	12	safty	safty	PROPN
ejpam-5453	893	13	,	,	PUNCT
ejpam-5453	893	14	and	and	CCONJ
ejpam-5453	893	15	m.	m.	PROPN
ejpam-5453	893	16	k.	k.	PROPN
ejpam-5453	894	1	el	el	PROPN
ejpam-5453	894	2	-	-	PROPN
ejpam-5453	894	3	bably	bably	ADV
ejpam-5453	894	4	.	.	PUNCT
ejpam-5453	895	1	topological	topological	ADJ
ejpam-5453	895	2	approach	approach	NOUN
ejpam-5453	895	3	for	for	ADP
ejpam-5453	895	4	decisionmaking	decisionmake	VERB
ejpam-5453	895	5	of	of	ADP
ejpam-5453	895	6	covid-19	covid-19	PROPN
ejpam-5453	895	7	infection	infection	NOUN
ejpam-5453	895	8	via	via	ADP
ejpam-5453	895	9	a	a	DET
ejpam-5453	895	10	nano	nano	NOUN
ejpam-5453	895	11	-	-	PUNCT
ejpam-5453	895	12	topology	topology	NOUN
ejpam-5453	895	13	model	model	NOUN
ejpam-5453	895	14	.	.	PUNCT
ejpam-5453	896	1	aims	aim	VERB
ejpam-5453	896	2	mathematics	mathematic	NOUN
ejpam-5453	896	3	,	,	PUNCT
ejpam-5453	896	4	6:7872	6:7872	NUM
ejpam-5453	896	5	–	–	PUNCT
ejpam-5453	896	6	7894	7894	NUM
ejpam-5453	896	7	,	,	PUNCT
ejpam-5453	896	8	2021	2021	NUM
ejpam-5453	896	9	.	.	PUNCT
ejpam-5453	897	1	[	[	X
ejpam-5453	897	2	19	19	NUM
ejpam-5453	897	3	]	]	X
ejpam-5453	897	4	e.	e.	PROPN
ejpam-5453	897	5	hatir	hatir	PROPN
ejpam-5453	897	6	and	and	CCONJ
ejpam-5453	897	7	t.	t.	PROPN
ejpam-5453	897	8	noiri	noiri	PROPN
ejpam-5453	897	9	.	.	PUNCT
ejpam-5453	898	1	on	on	ADP
ejpam-5453	898	2	semi	semi	ADJ
ejpam-5453	898	3	-	-	ADJ
ejpam-5453	898	4	i	i	PRON
ejpam-5453	898	5	-	-	PUNCT
ejpam-5453	898	6	open	open	ADJ
ejpam-5453	898	7	set	set	NOUN
ejpam-5453	898	8	and	and	CCONJ
ejpam-5453	898	9	semi	semi	ADJ
ejpam-5453	898	10	-	-	ADJ
ejpam-5453	898	11	i	i	ADV
ejpam-5453	898	12	-	-	PUNCT
ejpam-5453	898	13	continuous	continuous	ADJ
ejpam-5453	898	14	functions	function	NOUN
ejpam-5453	898	15	.	.	PUNCT
ejpam-5453	899	1	acta	acta	PROPN
ejpam-5453	899	2	math	math	PROPN
ejpam-5453	899	3	.	.	PUNCT
ejpam-5453	900	1	hungar	hungar	PROPN
ejpam-5453	900	2	.	.	PUNCT
ejpam-5453	900	3	,	,	PUNCT
ejpam-5453	900	4	107:345–353	107:345–353	NUM
ejpam-5453	900	5	,	,	PUNCT
ejpam-5453	900	6	2005	2005	NUM
ejpam-5453	900	7	.	.	PUNCT
ejpam-5453	901	1	[	[	X
ejpam-5453	901	2	20	20	NUM
ejpam-5453	901	3	]	]	PUNCT
ejpam-5453	901	4	m.	m.	PROPN
ejpam-5453	901	5	hosny	hosny	PROPN
ejpam-5453	901	6	.	.	PUNCT
ejpam-5453	902	1	on	on	ADP
ejpam-5453	902	2	generalization	generalization	NOUN
ejpam-5453	902	3	of	of	ADP
ejpam-5453	902	4	rough	rough	ADJ
ejpam-5453	902	5	sets	set	NOUN
ejpam-5453	902	6	by	by	ADP
ejpam-5453	902	7	using	use	VERB
ejpam-5453	902	8	two	two	NUM
ejpam-5453	902	9	different	different	ADJ
ejpam-5453	902	10	methods	method	NOUN
ejpam-5453	902	11	.	.	PUNCT
ejpam-5453	903	1	journal	journal	NOUN
ejpam-5453	903	2	of	of	ADP
ejpam-5453	903	3	intelligent	intelligent	ADJ
ejpam-5453	903	4	&	&	CCONJ
ejpam-5453	903	5	fuzzy	fuzzy	ADJ
ejpam-5453	903	6	systems	system	NOUN
ejpam-5453	903	7	,	,	PUNCT
ejpam-5453	903	8	35(1):979–993	35(1):979–993	PROPN
ejpam-5453	903	9	,	,	PUNCT
ejpam-5453	903	10	2018	2018	NUM
ejpam-5453	903	11	.	.	PUNCT
ejpam-5453	904	1	[	[	X
ejpam-5453	904	2	21	21	NUM
ejpam-5453	904	3	]	]	X
ejpam-5453	904	4	m.	m.	PROPN
ejpam-5453	904	5	hosny	hosny	PROPN
ejpam-5453	904	6	.	.	PUNCT
ejpam-5453	905	1	idealization	idealization	NOUN
ejpam-5453	905	2	of	of	ADP
ejpam-5453	905	3	j	j	NOUN
ejpam-5453	905	4	-	-	PUNCT
ejpam-5453	905	5	approximation	approximation	NOUN
ejpam-5453	905	6	spaces	space	NOUN
ejpam-5453	905	7	.	.	PUNCT
ejpam-5453	906	1	filomat	filomat	PROPN
ejpam-5453	906	2	,	,	PUNCT
ejpam-5453	906	3	34(2):287–301	34(2):287–301	PROPN
ejpam-5453	906	4	,	,	PUNCT
ejpam-5453	906	5	2020	2020	NUM
ejpam-5453	906	6	.	.	PUNCT
ejpam-5453	907	1	[	[	X
ejpam-5453	907	2	22	22	NUM
ejpam-5453	907	3	]	]	PUNCT
ejpam-5453	907	4	m.	m.	PROPN
ejpam-5453	907	5	hosny	hosny	PROPN
ejpam-5453	907	6	.	.	PUNCT
ejpam-5453	908	1	topological	topological	ADJ
ejpam-5453	908	2	approach	approach	NOUN
ejpam-5453	908	3	for	for	ADP
ejpam-5453	908	4	rough	rough	ADJ
ejpam-5453	908	5	sets	set	NOUN
ejpam-5453	908	6	by	by	ADP
ejpam-5453	908	7	using	use	VERB
ejpam-5453	908	8	j	j	NOUN
ejpam-5453	908	9	-	-	PUNCT
ejpam-5453	908	10	nearly	nearly	ADV
ejpam-5453	908	11	concepts	concept	NOUN
ejpam-5453	908	12	via	via	ADP
ejpam-5453	908	13	ideals	ideal	NOUN
ejpam-5453	908	14	.	.	PUNCT
ejpam-5453	909	1	filomat	filomat	NOUN
ejpam-5453	909	2	,	,	PUNCT
ejpam-5453	909	3	34(2):273–286	34(2):273–286	NUM
ejpam-5453	909	4	,	,	PUNCT
ejpam-5453	909	5	2020	2020	NUM
ejpam-5453	909	6	.	.	PUNCT
ejpam-5453	910	1	[	[	X
ejpam-5453	910	2	23	23	NUM
ejpam-5453	910	3	]	]	PUNCT
ejpam-5453	910	4	m.	m.	PROPN
ejpam-5453	910	5	hosny	hosny	PROPN
ejpam-5453	910	6	.	.	PUNCT
ejpam-5453	911	1	rough	rough	ADJ
ejpam-5453	911	2	sets	set	NOUN
ejpam-5453	911	3	theory	theory	NOUN
ejpam-5453	911	4	via	via	ADP
ejpam-5453	911	5	new	new	ADJ
ejpam-5453	911	6	topological	topological	ADJ
ejpam-5453	911	7	notions	notion	NOUN
ejpam-5453	911	8	based	base	VERB
ejpam-5453	911	9	on	on	ADP
ejpam-5453	911	10	ideals	ideal	NOUN
ejpam-5453	911	11	and	and	CCONJ
ejpam-5453	911	12	applications	application	NOUN
ejpam-5453	911	13	.	.	PUNCT
ejpam-5453	912	1	aims	aim	VERB
ejpam-5453	912	2	mathematics	mathematic	NOUN
ejpam-5453	912	3	,	,	PUNCT
ejpam-5453	912	4	7:869–902	7:869–902	NUM
ejpam-5453	912	5	,	,	PUNCT
ejpam-5453	912	6	2021	2021	NUM
ejpam-5453	912	7	.	.	PUNCT
ejpam-5453	913	1	[	[	X
ejpam-5453	913	2	24	24	NUM
ejpam-5453	913	3	]	]	PUNCT
ejpam-5453	913	4	m.	m.	NOUN
ejpam-5453	913	5	hosny	hosny	PROPN
ejpam-5453	913	6	.	.	PUNCT
ejpam-5453	914	1	topologies	topology	NOUN
ejpam-5453	914	2	generated	generate	VERB
ejpam-5453	914	3	by	by	ADP
ejpam-5453	914	4	two	two	NUM
ejpam-5453	914	5	ideals	ideal	NOUN
ejpam-5453	914	6	and	and	CCONJ
ejpam-5453	914	7	the	the	DET
ejpam-5453	914	8	corresponding	correspond	VERB
ejpam-5453	914	9	j	j	NOUN
ejpam-5453	914	10	-	-	PUNCT
ejpam-5453	914	11	approximations	approximation	NOUN
ejpam-5453	914	12	spaces	space	VERB
ejpam-5453	914	13	with	with	ADP
ejpam-5453	914	14	applications	application	NOUN
ejpam-5453	914	15	.	.	PUNCT
ejpam-5453	915	1	journal	journal	NOUN
ejpam-5453	915	2	of	of	ADP
ejpam-5453	915	3	mathematics	mathematic	NOUN
ejpam-5453	915	4	,	,	PUNCT
ejpam-5453	915	5	2021	2021	NUM
ejpam-5453	915	6	.	.	PUNCT
ejpam-5453	916	1	[	[	X
ejpam-5453	916	2	25	25	NUM
ejpam-5453	916	3	]	]	PUNCT
ejpam-5453	916	4	m.	m.	PROPN
ejpam-5453	916	5	hosny	hosny	PROPN
ejpam-5453	916	6	.	.	PUNCT
ejpam-5453	917	1	generalization	generalization	NOUN
ejpam-5453	917	2	of	of	ADP
ejpam-5453	917	3	rough	rough	ADJ
ejpam-5453	917	4	sets	set	NOUN
ejpam-5453	917	5	using	use	VERB
ejpam-5453	917	6	maximal	maximal	ADJ
ejpam-5453	917	7	right	right	ADJ
ejpam-5453	917	8	neighborhood	neighborhood	NOUN
ejpam-5453	917	9	systems	system	NOUN
ejpam-5453	917	10	and	and	CCONJ
ejpam-5453	917	11	ideals	ideal	NOUN
ejpam-5453	917	12	with	with	ADP
ejpam-5453	917	13	medical	medical	ADJ
ejpam-5453	917	14	applications	application	NOUN
ejpam-5453	917	15	.	.	PUNCT
ejpam-5453	918	1	aims	aim	VERB
ejpam-5453	918	2	mathematics	mathematic	NOUN
ejpam-5453	918	3	,	,	PUNCT
ejpam-5453	918	4	7(7):13104–13138	7(7):13104–13138	NUM
ejpam-5453	918	5	,	,	PUNCT
ejpam-5453	918	6	2022	2022	NUM
ejpam-5453	918	7	.	.	PUNCT
ejpam-5453	919	1	[	[	X
ejpam-5453	919	2	26	26	NUM
ejpam-5453	919	3	]	]	PUNCT
ejpam-5453	919	4	m.	m.	NOUN
ejpam-5453	919	5	hosny	hosny	PROPN
ejpam-5453	919	6	and	and	CCONJ
ejpam-5453	919	7	t.	t.	PROPN
ejpam-5453	919	8	m.	m.	PROPN
ejpam-5453	919	9	al	al	PROPN
ejpam-5453	919	10	-	-	PUNCT
ejpam-5453	919	11	shami	shami	PROPN
ejpam-5453	919	12	.	.	PUNCT
ejpam-5453	920	1	employing	employ	VERB
ejpam-5453	920	2	a	a	DET
ejpam-5453	920	3	generalization	generalization	NOUN
ejpam-5453	920	4	of	of	ADP
ejpam-5453	920	5	open	open	ADJ
ejpam-5453	920	6	sets	set	NOUN
ejpam-5453	920	7	defined	define	VERB
ejpam-5453	920	8	by	by	ADP
ejpam-5453	920	9	ideals	ideal	NOUN
ejpam-5453	920	10	to	to	PART
ejpam-5453	920	11	initiate	initiate	VERB
ejpam-5453	920	12	novel	novel	ADJ
ejpam-5453	920	13	rough	rough	ADJ
ejpam-5453	920	14	approximation	approximation	NOUN
ejpam-5453	920	15	spaces	space	NOUN
ejpam-5453	920	16	with	with	ADP
ejpam-5453	920	17	a	a	DET
ejpam-5453	920	18	chemical	chemical	NOUN
ejpam-5453	920	19	application	application	NOUN
ejpam-5453	920	20	.	.	PUNCT
ejpam-5453	921	1	european	european	ADJ
ejpam-5453	921	2	journal	journal	PROPN
ejpam-5453	921	3	of	of	ADP
ejpam-5453	921	4	pure	pure	ADJ
ejpam-5453	921	5	and	and	CCONJ
ejpam-5453	921	6	applied	applied	ADJ
ejpam-5453	921	7	mathematics	mathematic	NOUN
ejpam-5453	921	8	,	,	PUNCT
ejpam-5453	921	9	2024	2024	NUM
ejpam-5453	921	10	.	.	PUNCT
ejpam-5453	922	1	[	[	X
ejpam-5453	922	2	27	27	NUM
ejpam-5453	922	3	]	]	PUNCT
ejpam-5453	922	4	m.	m.	NOUN
ejpam-5453	922	5	hosny	hosny	PROPN
ejpam-5453	922	6	and	and	CCONJ
ejpam-5453	922	7	m.	m.	NOUN
ejpam-5453	922	8	raafat	raafat	NOUN
ejpam-5453	922	9	.	.	PUNCT
ejpam-5453	923	1	on	on	ADP
ejpam-5453	923	2	generalization	generalization	NOUN
ejpam-5453	923	3	of	of	ADP
ejpam-5453	923	4	rough	rough	ADJ
ejpam-5453	923	5	multiset	multiset	NOUN
ejpam-5453	923	6	via	via	ADP
ejpam-5453	923	7	multiset	multiset	ADJ
ejpam-5453	923	8	ideals	ideal	NOUN
ejpam-5453	923	9	.	.	PUNCT
ejpam-5453	924	1	journal	journal	NOUN
ejpam-5453	924	2	of	of	ADP
ejpam-5453	924	3	intelligent	intelligent	ADJ
ejpam-5453	924	4	fuzzy	fuzzy	ADJ
ejpam-5453	924	5	systems	system	NOUN
ejpam-5453	924	6	,	,	PUNCT
ejpam-5453	924	7	33:1249–1261	33:1249–1261	NUM
ejpam-5453	924	8	,	,	PUNCT
ejpam-5453	924	9	2017	2017	NUM
ejpam-5453	924	10	.	.	PUNCT
ejpam-5453	925	1	[	[	X
ejpam-5453	925	2	28	28	NUM
ejpam-5453	925	3	]	]	X
ejpam-5453	925	4	d.	d.	PROPN
ejpam-5453	925	5	jankovic	jankovic	PROPN
ejpam-5453	925	6	and	and	CCONJ
ejpam-5453	925	7	t.	t.	PROPN
ejpam-5453	925	8	r.	r.	PROPN
ejpam-5453	925	9	hamlet	hamlet	PROPN
ejpam-5453	925	10	.	.	PUNCT
ejpam-5453	926	1	new	new	ADJ
ejpam-5453	926	2	topologies	topology	NOUN
ejpam-5453	926	3	from	from	ADP
ejpam-5453	926	4	old	old	ADJ
ejpam-5453	926	5	via	via	ADP
ejpam-5453	926	6	ideals	ideal	NOUN
ejpam-5453	926	7	.	.	PUNCT
ejpam-5453	927	1	amer	amer	PROPN
ejpam-5453	927	2	.	.	PUNCT
ejpam-5453	927	3	math	math	PROPN
ejpam-5453	927	4	.	.	PUNCT
ejpam-5453	928	1	monthly	monthly	ADJ
ejpam-5453	928	2	,	,	PUNCT
ejpam-5453	928	3	97:295–310	97:295–310	PROPN
ejpam-5453	928	4	,	,	PUNCT
ejpam-5453	928	5	1990	1990	NUM
ejpam-5453	928	6	.	.	PUNCT
ejpam-5453	929	1	references	reference	NOUN
ejpam-5453	929	2	2877	2877	NUM
ejpam-5453	930	1	[	[	X
ejpam-5453	930	2	29	29	NUM
ejpam-5453	930	3	]	]	PUNCT
ejpam-5453	930	4	j.	j.	PROPN
ejpam-5453	930	5	jarvinen	jarvinen	PROPN
ejpam-5453	930	6	and	and	CCONJ
ejpam-5453	930	7	j.	j.	PROPN
ejpam-5453	930	8	kortelainen	kortelainen	PROPN
ejpam-5453	930	9	.	.	PUNCT
ejpam-5453	931	1	a	a	DET
ejpam-5453	931	2	unifying	unifying	ADJ
ejpam-5453	931	3	study	study	NOUN
ejpam-5453	931	4	between	between	ADP
ejpam-5453	931	5	model	model	NOUN
ejpam-5453	931	6	-	-	PUNCT
ejpam-5453	931	7	like	like	ADJ
ejpam-5453	931	8	operators	operator	NOUN
ejpam-5453	931	9	,	,	PUNCT
ejpam-5453	931	10	topologies	topology	NOUN
ejpam-5453	931	11	,	,	PUNCT
ejpam-5453	931	12	and	and	CCONJ
ejpam-5453	931	13	fuzzy	fuzzy	ADJ
ejpam-5453	931	14	sets	set	NOUN
ejpam-5453	931	15	.	.	PUNCT
ejpam-5453	932	1	fuzzy	fuzzy	ADJ
ejpam-5453	932	2	sets	set	NOUN
ejpam-5453	932	3	and	and	CCONJ
ejpam-5453	932	4	systems	system	NOUN
ejpam-5453	932	5	,	,	PUNCT
ejpam-5453	932	6	158:1217–1225	158:1217–1225	PROPN
ejpam-5453	932	7	,	,	PUNCT
ejpam-5453	932	8	2007	2007	NUM
ejpam-5453	932	9	.	.	PUNCT
ejpam-5453	933	1	[	[	X
ejpam-5453	933	2	30	30	NUM
ejpam-5453	933	3	]	]	PUNCT
ejpam-5453	933	4	a.	a.	NOUN
ejpam-5453	933	5	m.	m.	NOUN
ejpam-5453	933	6	kozae	kozae	PROPN
ejpam-5453	933	7	,	,	PUNCT
ejpam-5453	933	8	s.	s.	PROPN
ejpam-5453	933	9	a.	a.	PROPN
ejpam-5453	933	10	el	el	PROPN
ejpam-5453	933	11	-	-	PUNCT
ejpam-5453	933	12	sheikh	sheikh	PROPN
ejpam-5453	933	13	,	,	PUNCT
ejpam-5453	933	14	e.	e.	PROPN
ejpam-5453	933	15	h.	h.	PROPN
ejpam-5453	933	16	aly	aly	PROPN
ejpam-5453	933	17	,	,	PUNCT
ejpam-5453	933	18	and	and	CCONJ
ejpam-5453	933	19	m.	m.	PROPN
ejpam-5453	933	20	hosny	hosny	PROPN
ejpam-5453	933	21	.	.	PUNCT
ejpam-5453	934	1	rough	rough	ADJ
ejpam-5453	934	2	sets	set	NOUN
ejpam-5453	934	3	and	and	CCONJ
ejpam-5453	934	4	its	its	PRON
ejpam-5453	934	5	applications	application	NOUN
ejpam-5453	934	6	in	in	ADP
ejpam-5453	934	7	a	a	DET
ejpam-5453	934	8	computer	computer	NOUN
ejpam-5453	934	9	network	network	NOUN
ejpam-5453	934	10	.	.	PUNCT
ejpam-5453	935	1	annals	annal	NOUN
ejpam-5453	935	2	of	of	ADP
ejpam-5453	935	3	fuzzy	fuzzy	ADJ
ejpam-5453	935	4	mathematics	mathematic	NOUN
ejpam-5453	935	5	and	and	CCONJ
ejpam-5453	935	6	informatics	informatic	NOUN
ejpam-5453	935	7	,	,	PUNCT
ejpam-5453	935	8	6(3):605–624	6(3):605–624	PRON
ejpam-5453	935	9	,	,	PUNCT
ejpam-5453	935	10	2013	2013	NUM
ejpam-5453	935	11	.	.	PUNCT
ejpam-5453	936	1	[	[	X
ejpam-5453	936	2	31	31	NUM
ejpam-5453	936	3	]	]	PUNCT
ejpam-5453	936	4	a.	a.	NOUN
ejpam-5453	936	5	m.	m.	NOUN
ejpam-5453	936	6	kozae	kozae	PROPN
ejpam-5453	936	7	,	,	PUNCT
ejpam-5453	936	8	s.	s.	PROPN
ejpam-5453	936	9	a.	a.	PROPN
ejpam-5453	936	10	el	el	PROPN
ejpam-5453	936	11	-	-	PUNCT
ejpam-5453	936	12	sheikh	sheikh	NOUN
ejpam-5453	936	13	,	,	PUNCT
ejpam-5453	936	14	and	and	CCONJ
ejpam-5453	936	15	m.	m.	PROPN
ejpam-5453	936	16	hosny	hosny	PROPN
ejpam-5453	936	17	.	.	PUNCT
ejpam-5453	937	1	on	on	ADP
ejpam-5453	937	2	generalized	generalize	VERB
ejpam-5453	937	3	rough	rough	ADJ
ejpam-5453	937	4	sets	set	NOUN
ejpam-5453	937	5	and	and	CCONJ
ejpam-5453	937	6	closure	closure	NOUN
ejpam-5453	937	7	spaces	space	NOUN
ejpam-5453	937	8	.	.	PUNCT
ejpam-5453	938	1	int	int	PROPN
ejpam-5453	938	2	j	j	PROPN
ejpam-5453	938	3	appl	appl	PROPN
ejpam-5453	938	4	math	math	PROPN
ejpam-5453	938	5	,	,	PUNCT
ejpam-5453	938	6	23:997–1023	23:997–1023	NUM
ejpam-5453	938	7	,	,	PUNCT
ejpam-5453	938	8	2010	2010	NUM
ejpam-5453	938	9	.	.	PUNCT
ejpam-5453	939	1	[	[	X
ejpam-5453	939	2	32	32	NUM
ejpam-5453	939	3	]	]	PUNCT
ejpam-5453	939	4	k.	k.	PROPN
ejpam-5453	939	5	kuratowski	kuratowski	PROPN
ejpam-5453	939	6	.	.	PUNCT
ejpam-5453	940	1	topology	topology	NOUN
ejpam-5453	940	2	vol	vol	NOUN
ejpam-5453	940	3	.	.	PUNCT
ejpam-5453	940	4	i.	i.	PROPN
ejpam-5453	940	5	academic	academic	PROPN
ejpam-5453	940	6	press	press	PROPN
ejpam-5453	940	7	,	,	PUNCT
ejpam-5453	940	8	new	new	PROPN
ejpam-5453	940	9	york	york	PROPN
ejpam-5453	940	10	,	,	PUNCT
ejpam-5453	940	11	1966	1966	NUM
ejpam-5453	940	12	.	.	PUNCT
ejpam-5453	941	1	[	[	X
ejpam-5453	941	2	33	33	NUM
ejpam-5453	941	3	]	]	PUNCT
ejpam-5453	941	4	z.	z.	PROPN
ejpam-5453	941	5	li	li	PROPN
ejpam-5453	941	6	,	,	PUNCT
ejpam-5453	941	7	t.	t.	PROPN
ejpam-5453	941	8	xie	xie	PROPN
ejpam-5453	941	9	,	,	PUNCT
ejpam-5453	941	10	and	and	CCONJ
ejpam-5453	941	11	q.	q.	PROPN
ejpam-5453	941	12	li	li	PROPN
ejpam-5453	941	13	.	.	PUNCT
ejpam-5453	941	14	topological	topological	ADJ
ejpam-5453	941	15	structure	structure	NOUN
ejpam-5453	941	16	of	of	ADP
ejpam-5453	941	17	generalized	generalized	ADJ
ejpam-5453	941	18	rough	rough	ADJ
ejpam-5453	941	19	sets	set	NOUN
ejpam-5453	941	20	.	.	PUNCT
ejpam-5453	942	1	computers	computer	NOUN
ejpam-5453	942	2	&	&	CCONJ
ejpam-5453	942	3	mathematics	mathematics	PROPN
ejpam-5453	942	4	with	with	ADP
ejpam-5453	942	5	applications	application	NOUN
ejpam-5453	942	6	,	,	PUNCT
ejpam-5453	942	7	63:1066–1071	63:1066–1071	PROPN
ejpam-5453	942	8	,	,	PUNCT
ejpam-5453	942	9	2012	2012	NUM
ejpam-5453	942	10	.	.	PUNCT
ejpam-5453	943	1	[	[	X
ejpam-5453	943	2	34	34	NUM
ejpam-5453	943	3	]	]	PUNCT
ejpam-5453	943	4	x.	x.	NOUN
ejpam-5453	943	5	ma	ma	PROPN
ejpam-5453	943	6	,	,	PUNCT
ejpam-5453	943	7	qi	qi	PROPN
ejpam-5453	943	8	liu	liu	PROPN
ejpam-5453	943	9	,	,	PUNCT
ejpam-5453	943	10	and	and	CCONJ
ejpam-5453	943	11	j.	j.	PROPN
ejpam-5453	943	12	zhan	zhan	PROPN
ejpam-5453	943	13	.	.	PUNCT
ejpam-5453	944	1	a	a	DET
ejpam-5453	944	2	survey	survey	NOUN
ejpam-5453	944	3	of	of	ADP
ejpam-5453	944	4	decision	decision	NOUN
ejpam-5453	944	5	making	make	VERB
ejpam-5453	944	6	methods	method	NOUN
ejpam-5453	944	7	based	base	VERB
ejpam-5453	944	8	on	on	ADP
ejpam-5453	944	9	certain	certain	ADJ
ejpam-5453	944	10	hybrid	hybrid	ADJ
ejpam-5453	944	11	soft	soft	ADJ
ejpam-5453	944	12	set	set	NOUN
ejpam-5453	944	13	models	model	NOUN
ejpam-5453	944	14	.	.	PUNCT
ejpam-5453	945	1	artificial	artificial	ADJ
ejpam-5453	945	2	intelligence	intelligence	NOUN
ejpam-5453	945	3	review	review	NOUN
ejpam-5453	945	4	,	,	PUNCT
ejpam-5453	945	5	47:507–530	47:507–530	PROPN
ejpam-5453	945	6	,	,	PUNCT
ejpam-5453	945	7	2017	2017	NUM
ejpam-5453	945	8	.	.	PUNCT
ejpam-5453	946	1	[	[	X
ejpam-5453	946	2	35	35	NUM
ejpam-5453	946	3	]	]	X
ejpam-5453	946	4	h.	h.	PROPN
ejpam-5453	946	5	mustafa	mustafa	PROPN
ejpam-5453	946	6	,	,	PUNCT
ejpam-5453	946	7	t.	t.	PROPN
ejpam-5453	946	8	m.	m.	PROPN
ejpam-5453	946	9	al	al	PROPN
ejpam-5453	946	10	-	-	PUNCT
ejpam-5453	946	11	shami	shami	PROPN
ejpam-5453	946	12	,	,	PUNCT
ejpam-5453	946	13	and	and	CCONJ
ejpam-5453	946	14	r.	r.	PROPN
ejpam-5453	946	15	wassef	wassef	PROPN
ejpam-5453	946	16	.	.	PUNCT
ejpam-5453	947	1	rough	rough	ADJ
ejpam-5453	947	2	set	set	NOUN
ejpam-5453	947	3	paradigms	paradigm	NOUN
ejpam-5453	947	4	via	via	ADP
ejpam-5453	947	5	containment	containment	NOUN
ejpam-5453	947	6	neighborhoods	neighborhood	NOUN
ejpam-5453	947	7	and	and	CCONJ
ejpam-5453	947	8	ideals	ideal	NOUN
ejpam-5453	947	9	.	.	PUNCT
ejpam-5453	948	1	filomat	filomat	NOUN
ejpam-5453	948	2	,	,	PUNCT
ejpam-5453	948	3	37(14):4683–4702	37(14):4683–4702	NOUN
ejpam-5453	948	4	,	,	PUNCT
ejpam-5453	948	5	2023	2023	NUM
ejpam-5453	948	6	.	.	PUNCT
ejpam-5453	949	1	[	[	X
ejpam-5453	949	2	36	36	NUM
ejpam-5453	949	3	]	]	X
ejpam-5453	949	4	s.	s.	PROPN
ejpam-5453	949	5	pal	pal	PROPN
ejpam-5453	949	6	and	and	CCONJ
ejpam-5453	949	7	p.	p.	PROPN
ejpam-5453	949	8	mitra	mitra	PROPN
ejpam-5453	949	9	.	.	PUNCT
ejpam-5453	950	1	case	case	NOUN
ejpam-5453	950	2	generation	generation	NOUN
ejpam-5453	950	3	using	use	VERB
ejpam-5453	950	4	rough	rough	ADJ
ejpam-5453	950	5	sets	set	NOUN
ejpam-5453	950	6	with	with	ADP
ejpam-5453	950	7	fuzzy	fuzzy	ADJ
ejpam-5453	950	8	representation	representation	NOUN
ejpam-5453	950	9	.	.	PUNCT
ejpam-5453	951	1	ieee	ieee	NOUN
ejpam-5453	951	2	transactions	transaction	NOUN
ejpam-5453	951	3	on	on	ADP
ejpam-5453	951	4	knowledge	knowledge	NOUN
ejpam-5453	951	5	and	and	CCONJ
ejpam-5453	951	6	data	datum	NOUN
ejpam-5453	951	7	engineering	engineering	NOUN
ejpam-5453	951	8	,	,	PUNCT
ejpam-5453	951	9	16:293–300	16:293–300	NUM
ejpam-5453	951	10	,	,	PUNCT
ejpam-5453	951	11	2004	2004	NUM
ejpam-5453	951	12	.	.	PUNCT
ejpam-5453	952	1	[	[	X
ejpam-5453	952	2	37	37	NUM
ejpam-5453	952	3	]	]	PUNCT
ejpam-5453	952	4	z.	z.	PROPN
ejpam-5453	952	5	pawlak	pawlak	PROPN
ejpam-5453	952	6	.	.	PUNCT
ejpam-5453	953	1	rough	rough	ADJ
ejpam-5453	953	2	sets	set	NOUN
ejpam-5453	953	3	.	.	PUNCT
ejpam-5453	954	1	international	international	ADJ
ejpam-5453	954	2	journal	journal	NOUN
ejpam-5453	954	3	of	of	ADP
ejpam-5453	954	4	computer	computer	NOUN
ejpam-5453	954	5	and	and	CCONJ
ejpam-5453	954	6	information	information	NOUN
ejpam-5453	954	7	sciences	science	NOUN
ejpam-5453	954	8	,	,	PUNCT
ejpam-5453	954	9	11(5):341–356	11(5):341–356	NUM
ejpam-5453	954	10	,	,	PUNCT
ejpam-5453	954	11	1982	1982	NUM
ejpam-5453	954	12	.	.	PUNCT
ejpam-5453	955	1	[	[	X
ejpam-5453	955	2	38	38	NUM
ejpam-5453	955	3	]	]	PUNCT
ejpam-5453	955	4	z.	z.	PROPN
ejpam-5453	955	5	pawlak	pawlak	PROPN
ejpam-5453	955	6	.	.	PUNCT
ejpam-5453	956	1	rough	rough	ADJ
ejpam-5453	956	2	concept	concept	NOUN
ejpam-5453	956	3	analysis	analysis	NOUN
ejpam-5453	956	4	.	.	PUNCT
ejpam-5453	957	1	bull	bull	NOUN
ejpam-5453	957	2	.	.	PUNCT
ejpam-5453	958	1	pol	pol	PROPN
ejpam-5453	958	2	.	.	PUNCT
ejpam-5453	959	1	acad	acad	PROPN
ejpam-5453	959	2	.	.	PUNCT
ejpam-5453	960	1	sci	sci	PROPN
ejpam-5453	960	2	.	.	PUNCT
ejpam-5453	960	3	math	math	PROPN
ejpam-5453	960	4	.	.	PUNCT
ejpam-5453	960	5	,	,	PUNCT
ejpam-5453	961	1	33:495–498	33:495–498	PROPN
ejpam-5453	961	2	,	,	PUNCT
ejpam-5453	961	3	1985	1985	NUM
ejpam-5453	961	4	.	.	PUNCT
ejpam-5453	962	1	[	[	X
ejpam-5453	962	2	39	39	NUM
ejpam-5453	962	3	]	]	PUNCT
ejpam-5453	962	4	z.	z.	PROPN
ejpam-5453	962	5	pei	pei	PROPN
ejpam-5453	962	6	,	,	PUNCT
ejpam-5453	962	7	d.	d.	PROPN
ejpam-5453	962	8	pei	pei	PROPN
ejpam-5453	962	9	,	,	PUNCT
ejpam-5453	962	10	and	and	CCONJ
ejpam-5453	962	11	l.	l.	PROPN
ejpam-5453	962	12	zheng	zheng	PROPN
ejpam-5453	962	13	.	.	PUNCT
ejpam-5453	963	1	topology	topology	NOUN
ejpam-5453	963	2	vs	vs	ADP
ejpam-5453	963	3	generalized	generalize	VERB
ejpam-5453	963	4	rough	rough	ADJ
ejpam-5453	963	5	sets	set	NOUN
ejpam-5453	963	6	.	.	PUNCT
ejpam-5453	964	1	int	int	NOUN
ejpam-5453	964	2	.	.	PUNCT
ejpam-5453	965	1	j.	j.	PROPN
ejpam-5453	965	2	approx	approx	PROPN
ejpam-5453	965	3	.	.	PUNCT
ejpam-5453	966	1	reason	reason	NOUN
ejpam-5453	966	2	.	.	PUNCT
ejpam-5453	966	3	,	,	PUNCT
ejpam-5453	966	4	52:231–239	52:231–239	PROPN
ejpam-5453	966	5	,	,	PUNCT
ejpam-5453	966	6	2011	2011	NUM
ejpam-5453	966	7	.	.	PUNCT
ejpam-5453	967	1	[	[	X
ejpam-5453	967	2	40	40	NUM
ejpam-5453	967	3	]	]	PUNCT
ejpam-5453	967	4	l.	l.	PROPN
ejpam-5453	967	5	polkowski	polkowski	PROPN
ejpam-5453	967	6	.	.	PUNCT
ejpam-5453	968	1	rough	rough	ADJ
ejpam-5453	968	2	sets	set	NOUN
ejpam-5453	968	3	:	:	PUNCT
ejpam-5453	968	4	mathematical	mathematical	ADJ
ejpam-5453	968	5	foundations	foundation	NOUN
ejpam-5453	968	6	.	.	PUNCT
ejpam-5453	969	1	physica	physica	NOUN
ejpam-5453	969	2	-	-	PUNCT
ejpam-5453	969	3	verlag	verlag	PROPN
ejpam-5453	969	4	,	,	PUNCT
ejpam-5453	969	5	heidelberg	heidelberg	PROPN
ejpam-5453	969	6	,	,	PUNCT
ejpam-5453	969	7	2002	2002	NUM
ejpam-5453	969	8	.	.	PUNCT
ejpam-5453	970	1	[	[	X
ejpam-5453	970	2	41	41	NUM
ejpam-5453	970	3	]	]	PUNCT
ejpam-5453	970	4	r.	r.	PROPN
ejpam-5453	970	5	vaidynathaswamy	vaidynathaswamy	PROPN
ejpam-5453	970	6	.	.	PUNCT
ejpam-5453	971	1	the	the	DET
ejpam-5453	971	2	localization	localization	NOUN
ejpam-5453	971	3	theory	theory	NOUN
ejpam-5453	971	4	in	in	ADP
ejpam-5453	971	5	set	set	NOUN
ejpam-5453	971	6	topology	topology	NOUN
ejpam-5453	971	7	.	.	PUNCT
ejpam-5453	972	1	proc	proc	NOUN
ejpam-5453	972	2	.	.	PUNCT
ejpam-5453	973	1	ind	ind	NOUN
ejpam-5453	973	2	.	.	PUNCT
ejpam-5453	974	1	acad	acad	PROPN
ejpam-5453	974	2	.	.	PROPN
ejpam-5453	974	3	of	of	ADP
ejpam-5453	974	4	sci	sci	PROPN
ejpam-5453	974	5	.	.	PROPN
ejpam-5453	974	6	,	,	PUNCT
ejpam-5453	974	7	20:515–561	20:515–561	PROPN
ejpam-5453	974	8	,	,	PUNCT
ejpam-5453	974	9	1945	1945	NUM
ejpam-5453	974	10	.	.	PUNCT
ejpam-5453	975	1	[	[	X
ejpam-5453	975	2	42	42	NUM
ejpam-5453	975	3	]	]	X
ejpam-5453	975	4	y.	y.	PROPN
ejpam-5453	975	5	y.	y.	PROPN
ejpam-5453	975	6	yao	yao	PROPN
ejpam-5453	975	7	.	.	PUNCT
ejpam-5453	976	1	relational	relational	ADJ
ejpam-5453	976	2	interpretations	interpretation	NOUN
ejpam-5453	976	3	of	of	ADP
ejpam-5453	976	4	neighborhood	neighborhood	NOUN
ejpam-5453	976	5	operators	operator	NOUN
ejpam-5453	976	6	and	and	CCONJ
ejpam-5453	976	7	rough	rough	ADJ
ejpam-5453	976	8	set	set	NOUN
ejpam-5453	976	9	approximation	approximation	NOUN
ejpam-5453	976	10	operators	operator	NOUN
ejpam-5453	976	11	.	.	PUNCT
ejpam-5453	977	1	inform	inform	NOUN
ejpam-5453	977	2	.	.	PUNCT
ejpam-5453	978	1	sci	sci	PROPN
ejpam-5453	978	2	.	.	PROPN
ejpam-5453	978	3	,	,	PUNCT
ejpam-5453	978	4	111:239–259	111:239–259	NUM
ejpam-5453	978	5	,	,	PUNCT
ejpam-5453	978	6	1998	1998	NUM
ejpam-5453	978	7	.	.	PUNCT
ejpam-5453	979	1	[	[	X
ejpam-5453	979	2	43	43	NUM
ejpam-5453	979	3	]	]	X
ejpam-5453	979	4	e.	e.	PROPN
ejpam-5453	979	5	d.	d.	PROPN
ejpam-5453	979	6	yildirim	yildirim	PROPN
ejpam-5453	979	7	.	.	PUNCT
ejpam-5453	980	1	new	new	ADJ
ejpam-5453	980	2	topological	topological	ADJ
ejpam-5453	980	3	approaches	approach	NOUN
ejpam-5453	980	4	to	to	ADP
ejpam-5453	980	5	rough	rough	ADJ
ejpam-5453	980	6	sets	set	NOUN
ejpam-5453	980	7	via	via	ADP
ejpam-5453	980	8	subset	subset	ADJ
ejpam-5453	980	9	neighborhoods	neighborhood	NOUN
ejpam-5453	980	10	.	.	PUNCT
ejpam-5453	981	1	journal	journal	NOUN
ejpam-5453	981	2	of	of	ADP
ejpam-5453	981	3	mathematics	mathematic	NOUN
ejpam-5453	981	4	,	,	PUNCT
ejpam-5453	981	5	2022	2022	NUM
ejpam-5453	981	6	.	.	PUNCT
ejpam-5453	982	1	[	[	X
ejpam-5453	982	2	44	44	NUM
ejpam-5453	982	3	]	]	PUNCT
ejpam-5453	982	4	w.	w.	PROPN
ejpam-5453	982	5	zhu	zhu	PROPN
ejpam-5453	982	6	.	.	PUNCT
ejpam-5453	983	1	topological	topological	ADJ
ejpam-5453	983	2	approaches	approach	NOUN
ejpam-5453	983	3	to	to	ADP
ejpam-5453	983	4	covering	cover	VERB
ejpam-5453	983	5	rough	rough	ADJ
ejpam-5453	983	6	sets	set	NOUN
ejpam-5453	983	7	.	.	PUNCT
ejpam-5453	984	1	inform	inform	NOUN
ejpam-5453	984	2	.	.	PUNCT
ejpam-5453	985	1	sci	sci	PROPN
ejpam-5453	985	2	.	.	PROPN
ejpam-5453	985	3	,	,	PUNCT
ejpam-5453	985	4	177(6):1499	177(6):1499	NUM
ejpam-5453	985	5	–	–	PUNCT
ejpam-5453	985	6	1508	1508	NUM
ejpam-5453	985	7	,	,	PUNCT
ejpam-5453	985	8	2007	2007	NUM
ejpam-5453	985	9	.	.	PUNCT