id	sid	tid	token	lemma	pos
ejpam-5831	1	1	european	european	PROPN
ejpam-5831	1	2	journal	journal	PROPN
ejpam-5831	1	3	of	of	ADP
ejpam-5831	1	4	pure	pure	ADJ
ejpam-5831	1	5	and	and	CCONJ
ejpam-5831	1	6	applied	applied	ADJ
ejpam-5831	1	7	mathematics	mathematic	NOUN
ejpam-5831	1	8	2025	2025	NUM
ejpam-5831	1	9	,	,	PUNCT
ejpam-5831	1	10	vol	vol	NOUN
ejpam-5831	1	11	.	.	PROPN
ejpam-5831	1	12	18	18	NUM
ejpam-5831	1	13	,	,	PUNCT
ejpam-5831	1	14	issue	issue	NOUN
ejpam-5831	1	15	2	2	NUM
ejpam-5831	1	16	,	,	PUNCT
ejpam-5831	1	17	article	article	NOUN
ejpam-5831	1	18	number	number	NOUN
ejpam-5831	1	19	5831	5831	NUM
ejpam-5831	1	20	issn	issn	VERB
ejpam-5831	1	21	1307	1307	NUM
ejpam-5831	1	22	-	-	SYM
ejpam-5831	1	23	5543	5543	NUM
ejpam-5831	1	24	–	–	PUNCT
ejpam-5831	1	25	ejpam.com	ejpam.com	X
ejpam-5831	1	26	published	publish	VERB
ejpam-5831	1	27	by	by	ADP
ejpam-5831	1	28	new	new	PROPN
ejpam-5831	1	29	york	york	PROPN
ejpam-5831	1	30	business	business	PROPN
ejpam-5831	1	31	global	global	ADJ
ejpam-5831	1	32	pretopological	pretopological	ADJ
ejpam-5831	1	33	spaces	space	NOUN
ejpam-5831	1	34	induced	induce	VERB
ejpam-5831	1	35	by	by	ADP
ejpam-5831	1	36	rough	rough	ADJ
ejpam-5831	1	37	sets	set	NOUN
ejpam-5831	1	38	and	and	CCONJ
ejpam-5831	1	39	their	their	PRON
ejpam-5831	1	40	applications	application	NOUN
ejpam-5831	1	41	a.	a.	NOUN
ejpam-5831	1	42	a.	a.	PROPN
ejpam-5831	1	43	azzam1,2,∗	azzam1,2,∗	PROPN
ejpam-5831	1	44	,	,	PUNCT
ejpam-5831	1	45	r.	r.	PROPN
ejpam-5831	1	46	mareay3	mareay3	PROPN
ejpam-5831	1	47	,	,	PUNCT
ejpam-5831	1	48	gehad	gehad	PROPN
ejpam-5831	1	49	m.	m.	PROPN
ejpam-5831	1	50	abd	abd	PROPN
ejpam-5831	1	51	-	-	PUNCT
ejpam-5831	1	52	elhamed1,4	elhamed1,4	PROPN
ejpam-5831	1	53	,	,	PUNCT
ejpam-5831	1	54	m.	m.	NOUN
ejpam-5831	1	55	aldawood1	aldawood1	PROPN
ejpam-5831	1	56	,	,	PUNCT
ejpam-5831	1	57	manal	manal	PROPN
ejpam-5831	1	58	e.	e.	PROPN
ejpam-5831	1	59	ali5	ali5	PROPN
ejpam-5831	1	60	1	1	NUM
ejpam-5831	1	61	department	department	NOUN
ejpam-5831	1	62	of	of	ADP
ejpam-5831	1	63	mathematics	mathematic	NOUN
ejpam-5831	1	64	,	,	PUNCT
ejpam-5831	1	65	faculty	faculty	NOUN
ejpam-5831	1	66	of	of	ADP
ejpam-5831	1	67	science	science	NOUN
ejpam-5831	1	68	and	and	CCONJ
ejpam-5831	1	69	humanities	humanity	NOUN
ejpam-5831	1	70	,	,	PUNCT
ejpam-5831	1	71	prince	prince	PROPN
ejpam-5831	1	72	sattam	sattam	PROPN
ejpam-5831	1	73	bin	bin	PROPN
ejpam-5831	1	74	abdulaziz	abdulaziz	PROPN
ejpam-5831	1	75	university	university	PROPN
ejpam-5831	1	76	,	,	PUNCT
ejpam-5831	1	77	alkharj	alkharj	VERB
ejpam-5831	1	78	11942	11942	NUM
ejpam-5831	1	79	,	,	PUNCT
ejpam-5831	1	80	saudi	saudi	PROPN
ejpam-5831	1	81	arabia	arabia	PROPN
ejpam-5831	1	82	2	2	NUM
ejpam-5831	1	83	department	department	NOUN
ejpam-5831	1	84	of	of	ADP
ejpam-5831	1	85	mathematics	mathematic	NOUN
ejpam-5831	1	86	,	,	PUNCT
ejpam-5831	1	87	faculty	faculty	NOUN
ejpam-5831	1	88	of	of	ADP
ejpam-5831	1	89	science	science	NOUN
ejpam-5831	1	90	,	,	PUNCT
ejpam-5831	1	91	new	new	ADJ
ejpam-5831	1	92	valley	valley	NOUN
ejpam-5831	1	93	university	university	NOUN
ejpam-5831	1	94	,	,	PUNCT
ejpam-5831	1	95	elkharga	elkharga	NOUN
ejpam-5831	1	96	72511	72511	NUM
ejpam-5831	1	97	,	,	PUNCT
ejpam-5831	1	98	egypt	egypt	PROPN
ejpam-5831	1	99	3	3	NUM
ejpam-5831	1	100	department	department	NOUN
ejpam-5831	1	101	of	of	ADP
ejpam-5831	1	102	mathematics	mathematic	NOUN
ejpam-5831	1	103	,	,	PUNCT
ejpam-5831	1	104	faculty	faculty	NOUN
ejpam-5831	1	105	of	of	ADP
ejpam-5831	1	106	science	science	NOUN
ejpam-5831	1	107	,	,	PUNCT
ejpam-5831	1	108	kafrelsheikh	kafrelsheikh	PROPN
ejpam-5831	1	109	university	university	PROPN
ejpam-5831	1	110	,	,	PUNCT
ejpam-5831	1	111	kafrelsheikh	kafrelsheikh	PROPN
ejpam-5831	1	112	33516	33516	NUM
ejpam-5831	1	113	,	,	PUNCT
ejpam-5831	1	114	egypt	egypt	PROPN
ejpam-5831	1	115	4	4	NUM
ejpam-5831	1	116	department	department	NOUN
ejpam-5831	1	117	of	of	ADP
ejpam-5831	1	118	mathematics	mathematic	NOUN
ejpam-5831	1	119	,	,	PUNCT
ejpam-5831	1	120	college	college	NOUN
ejpam-5831	1	121	of	of	ADP
ejpam-5831	1	122	girls	girl	NOUN
ejpam-5831	1	123	,	,	PUNCT
ejpam-5831	1	124	ain	ain	PROPN
ejpam-5831	1	125	shams	shams	PROPN
ejpam-5831	1	126	university	university	PROPN
ejpam-5831	1	127	,	,	PUNCT
ejpam-5831	1	128	egypt	egypt	PROPN
ejpam-5831	1	129	5	5	NUM
ejpam-5831	1	130	department	department	PROPN
ejpam-5831	1	131	of	of	ADP
ejpam-5831	1	132	physics	physics	PROPN
ejpam-5831	1	133	and	and	CCONJ
ejpam-5831	1	134	engineering	engineering	NOUN
ejpam-5831	1	135	mathematics	mathematic	NOUN
ejpam-5831	1	136	,	,	PUNCT
ejpam-5831	1	137	faculty	faculty	NOUN
ejpam-5831	1	138	of	of	ADP
ejpam-5831	1	139	engineering	engineering	PROPN
ejpam-5831	1	140	,	,	PUNCT
ejpam-5831	1	141	kafrelsheikh	kafrelsheikh	PROPN
ejpam-5831	1	142	university	university	PROPN
ejpam-5831	1	143	,	,	PUNCT
ejpam-5831	1	144	kafrelsheikh	kafrelsheikh	NOUN
ejpam-5831	1	145	,	,	PUNCT
ejpam-5831	1	146	33516	33516	NUM
ejpam-5831	1	147	,	,	PUNCT
ejpam-5831	1	148	egypt	egypt	PROPN
ejpam-5831	1	149	abstract	abstract	NOUN
ejpam-5831	1	150	.	.	PUNCT
ejpam-5831	2	1	in	in	ADP
ejpam-5831	2	2	this	this	DET
ejpam-5831	2	3	paper	paper	NOUN
ejpam-5831	2	4	,	,	PUNCT
ejpam-5831	2	5	we	we	PRON
ejpam-5831	2	6	generate	generate	VERB
ejpam-5831	2	7	pretopological	pretopological	ADJ
ejpam-5831	2	8	spaces	space	NOUN
ejpam-5831	2	9	from	from	ADP
ejpam-5831	2	10	a	a	DET
ejpam-5831	2	11	binary	binary	ADJ
ejpam-5831	2	12	relation	relation	NOUN
ejpam-5831	2	13	.	.	PUNCT
ejpam-5831	3	1	we	we	PRON
ejpam-5831	3	2	introduce	introduce	VERB
ejpam-5831	3	3	a	a	DET
ejpam-5831	3	4	new	new	ADJ
ejpam-5831	3	5	approximation	approximation	NOUN
ejpam-5831	3	6	space	space	NOUN
ejpam-5831	3	7	by	by	ADP
ejpam-5831	3	8	using	use	VERB
ejpam-5831	3	9	pretopological	pretopological	ADJ
ejpam-5831	3	10	concepts	concept	NOUN
ejpam-5831	3	11	.	.	PUNCT
ejpam-5831	4	1	some	some	DET
ejpam-5831	4	2	properties	property	NOUN
ejpam-5831	4	3	and	and	CCONJ
ejpam-5831	4	4	the	the	DET
ejpam-5831	4	5	comparison	comparison	NOUN
ejpam-5831	4	6	among	among	ADP
ejpam-5831	4	7	different	different	ADJ
ejpam-5831	4	8	types	type	NOUN
ejpam-5831	4	9	of	of	ADP
ejpam-5831	4	10	lower	low	ADJ
ejpam-5831	4	11	approximation	approximation	NOUN
ejpam-5831	4	12	and	and	CCONJ
ejpam-5831	4	13	the	the	DET
ejpam-5831	4	14	upper	upper	ADJ
ejpam-5831	4	15	approximation	approximation	NOUN
ejpam-5831	4	16	are	be	AUX
ejpam-5831	4	17	studied	study	VERB
ejpam-5831	4	18	.	.	PUNCT
ejpam-5831	5	1	we	we	PRON
ejpam-5831	5	2	introduce	introduce	VERB
ejpam-5831	5	3	an	an	DET
ejpam-5831	5	4	application	application	NOUN
ejpam-5831	5	5	of	of	ADP
ejpam-5831	5	6	pretopological	pretopological	ADJ
ejpam-5831	5	7	spaces	space	NOUN
ejpam-5831	5	8	in	in	ADP
ejpam-5831	5	9	rough	rough	ADJ
ejpam-5831	5	10	approximation	approximation	NOUN
ejpam-5831	5	11	.	.	PUNCT
ejpam-5831	6	1	some	some	DET
ejpam-5831	6	2	generalizations	generalization	NOUN
ejpam-5831	6	3	of	of	ADP
ejpam-5831	6	4	rough	rough	ADJ
ejpam-5831	6	5	sets	set	NOUN
ejpam-5831	6	6	concepts	concept	NOUN
ejpam-5831	6	7	based	base	VERB
ejpam-5831	6	8	on	on	ADP
ejpam-5831	6	9	pretopological	pretopological	ADJ
ejpam-5831	6	10	space	space	NOUN
ejpam-5831	6	11	are	be	AUX
ejpam-5831	6	12	introduced	introduce	VERB
ejpam-5831	6	13	.	.	PUNCT
ejpam-5831	7	1	2020	2020	NUM
ejpam-5831	7	2	mathematics	mathematics	PROPN
ejpam-5831	7	3	subject	subject	NOUN
ejpam-5831	7	4	classifications	classification	NOUN
ejpam-5831	7	5	:	:	PUNCT
ejpam-5831	7	6	4a40	4a40	NUM
ejpam-5831	7	7	,	,	PUNCT
ejpam-5831	7	8	03e72	03e72	NUM
ejpam-5831	7	9	,	,	PUNCT
ejpam-5831	7	10	54c08	54c08	NUM
ejpam-5831	7	11	.	.	PUNCT
ejpam-5831	8	1	key	key	ADJ
ejpam-5831	8	2	words	word	NOUN
ejpam-5831	8	3	and	and	CCONJ
ejpam-5831	8	4	phrases	phrase	NOUN
ejpam-5831	8	5	:	:	PUNCT
ejpam-5831	8	6	topological	topological	ADJ
ejpam-5831	8	7	space	space	NOUN
ejpam-5831	8	8	,	,	PUNCT
ejpam-5831	8	9	pretopological	pretopological	ADJ
ejpam-5831	8	10	spaces	space	NOUN
ejpam-5831	8	11	,	,	PUNCT
ejpam-5831	8	12	rough	rough	ADJ
ejpam-5831	8	13	sets	set	NOUN
ejpam-5831	8	14	.	.	PUNCT
ejpam-5831	9	1	1	1	X
ejpam-5831	9	2	.	.	X
ejpam-5831	9	3	introduction	introduction	NOUN
ejpam-5831	9	4	there	there	PRON
ejpam-5831	9	5	are	be	VERB
ejpam-5831	9	6	a	a	DET
ejpam-5831	9	7	huge	huge	ADJ
ejpam-5831	9	8	amount	amount	NOUN
ejpam-5831	9	9	of	of	ADP
ejpam-5831	9	10	information	information	NOUN
ejpam-5831	9	11	based	base	VERB
ejpam-5831	9	12	on	on	ADP
ejpam-5831	9	13	technology	technology	NOUN
ejpam-5831	9	14	and	and	CCONJ
ejpam-5831	9	15	there	there	PRON
ejpam-5831	9	16	is	be	VERB
ejpam-5831	9	17	a	a	DET
ejpam-5831	9	18	need	need	ADJ
ejpam-5831	9	19	high	high	ADJ
ejpam-5831	9	20	accurate	accurate	ADJ
ejpam-5831	9	21	tools	tool	NOUN
ejpam-5831	9	22	for	for	ADP
ejpam-5831	9	23	discovering	discover	VERB
ejpam-5831	9	24	their	their	PRON
ejpam-5831	9	25	valuable	valuable	ADJ
ejpam-5831	9	26	knowledge	knowledge	NOUN
ejpam-5831	9	27	.	.	PUNCT
ejpam-5831	10	1	the	the	DET
ejpam-5831	10	2	field	field	NOUN
ejpam-5831	10	3	of	of	ADP
ejpam-5831	10	4	information	information	NOUN
ejpam-5831	10	5	technology	technology	NOUN
ejpam-5831	10	6	is	be	AUX
ejpam-5831	10	7	an	an	DET
ejpam-5831	10	8	important	important	ADJ
ejpam-5831	10	9	filed	file	VERB
ejpam-5831	10	10	and	and	CCONJ
ejpam-5831	10	11	has	have	AUX
ejpam-5831	10	12	attracted	attract	VERB
ejpam-5831	10	13	the	the	DET
ejpam-5831	10	14	researchers	researcher	NOUN
ejpam-5831	10	15	in	in	ADP
ejpam-5831	10	16	many	many	ADJ
ejpam-5831	10	17	fields	field	NOUN
ejpam-5831	10	18	.	.	PUNCT
ejpam-5831	11	1	the	the	DET
ejpam-5831	11	2	topological	topological	ADJ
ejpam-5831	11	3	generalizations	generalization	NOUN
ejpam-5831	11	4	of	of	ADP
ejpam-5831	11	5	rough	rough	ADJ
ejpam-5831	11	6	set	set	NOUN
ejpam-5831	11	7	theory	theory	NOUN
ejpam-5831	11	8	based	base	VERB
ejpam-5831	11	9	on	on	ADP
ejpam-5831	11	10	concepts	concept	NOUN
ejpam-5831	11	11	of	of	ADP
ejpam-5831	11	12	near	near	ADP
ejpam-5831	11	13	open	open	ADJ
ejpam-5831	11	14	sets	set	NOUN
ejpam-5831	11	15	are	be	AUX
ejpam-5831	11	16	presented	present	VERB
ejpam-5831	11	17	in	in	ADP
ejpam-5831	11	18	many	many	ADJ
ejpam-5831	11	19	researches	research	NOUN
ejpam-5831	11	20	.	.	PUNCT
ejpam-5831	12	1	abu	abu	PROPN
ejpam-5831	12	2	-	-	PUNCT
ejpam-5831	12	3	donia	donia	PROPN
ejpam-5831	13	1	[	[	X
ejpam-5831	13	2	1	1	NUM
ejpam-5831	13	3	]	]	PUNCT
ejpam-5831	13	4	introduced	introduce	VERB
ejpam-5831	13	5	new	new	ADJ
ejpam-5831	13	6	kinds	kind	NOUN
ejpam-5831	13	7	of	of	ADP
ejpam-5831	13	8	rough	rough	ADJ
ejpam-5831	13	9	set	set	VERB
ejpam-5831	13	10	approximations	approximation	NOUN
ejpam-5831	13	11	via	via	ADP
ejpam-5831	13	12	multi	multi	ADJ
ejpam-5831	13	13	knowledge	knowledge	NOUN
ejpam-5831	13	14	base	base	NOUN
ejpam-5831	13	15	,	,	PUNCT
ejpam-5831	13	16	this	this	PRON
ejpam-5831	13	17	means	mean	VERB
ejpam-5831	13	18	family	family	NOUN
ejpam-5831	13	19	of	of	ADP
ejpam-5831	13	20	finite	finite	ADJ
ejpam-5831	13	21	number	number	NOUN
ejpam-5831	13	22	of	of	ADP
ejpam-5831	13	23	(	(	PUNCT
ejpam-5831	13	24	reflexive	reflexive	ADJ
ejpam-5831	13	25	,	,	PUNCT
ejpam-5831	13	26	tolerance	tolerance	NOUN
ejpam-5831	13	27	,	,	PUNCT
ejpam-5831	13	28	dominance	dominance	NOUN
ejpam-5831	13	29	,	,	PUNCT
ejpam-5831	13	30	equivalence	equivalence	NOUN
ejpam-5831	13	31	)	)	PUNCT
ejpam-5831	13	32	relations	relation	NOUN
ejpam-5831	13	33	by	by	ADP
ejpam-5831	13	34	two	two	NUM
ejpam-5831	13	35	techniques.abu	techniques.abu	NOUN
ejpam-5831	13	36	-	-	PUNCT
ejpam-5831	13	37	donia	donia	PROPN
ejpam-5831	13	38	,	,	PUNCT
ejpam-5831	13	39	a.s	a.s	PROPN
ejpam-5831	13	40	.	.	PROPN
ejpam-5831	13	41	salama	salama	NOUN
ejpam-5831	14	1	[	[	X
ejpam-5831	14	2	2	2	NUM
ejpam-5831	14	3	]	]	PUNCT
ejpam-5831	14	4	extended	extended	ADJ
ejpam-5831	14	5	∗corresponding	∗corresponding	NOUN
ejpam-5831	14	6	author	author	NOUN
ejpam-5831	14	7	.	.	PUNCT
ejpam-5831	15	1	doi	doi	NOUN
ejpam-5831	15	2	:	:	PUNCT
ejpam-5831	15	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5831	https://doi.org/10.29020/nybg.ejpam.v18i2.5831	NUM
ejpam-5831	15	4	email	email	NOUN
ejpam-5831	15	5	addresses	address	VERB
ejpam-5831	15	6	:	:	PUNCT
ejpam-5831	15	7	azzam0911@yahoo.com	azzam0911@yahoo.com	X
ejpam-5831	15	8	(	(	PUNCT
ejpam-5831	15	9	a.	a.	NOUN
ejpam-5831	15	10	a.	a.	PROPN
ejpam-5831	15	11	azzam	azzam	PROPN
ejpam-5831	15	12	)	)	PUNCT
ejpam-5831	15	13	,	,	PUNCT
ejpam-5831	15	14	roshdeymareay@sci.kfs.edu.eg	roshdeymareay@sci.kfs.edu.eg	X
ejpam-5831	15	15	(	(	PUNCT
ejpam-5831	15	16	r.	r.	PROPN
ejpam-5831	15	17	mareay	mareay	NOUN
ejpam-5831	15	18	)	)	PUNCT
ejpam-5831	15	19	,	,	PUNCT
ejpam-5831	15	20	gehadmahfood@gmail.com	gehadmahfood@gmail.com	X
ejpam-5831	15	21	(	(	PUNCT
ejpam-5831	15	22	g.	g.	PROPN
ejpam-5831	15	23	m.	m.	PROPN
ejpam-5831	15	24	abd	abd	PROPN
ejpam-5831	15	25	-	-	PUNCT
ejpam-5831	15	26	elhamed	elhame	VERB
ejpam-5831	15	27	)	)	PUNCT
ejpam-5831	15	28	,	,	PUNCT
ejpam-5831	15	29	m.aldawood@psau.edu.sa	m.aldawood@psau.edu.sa	PROPN
ejpam-5831	15	30	(	(	PUNCT
ejpam-5831	15	31	m.	m.	NOUN
ejpam-5831	15	32	aldawood	aldawood	PROPN
ejpam-5831	15	33	)	)	PUNCT
ejpam-5831	15	34	,	,	PUNCT
ejpam-5831	15	35	manal.ali@eng.kfs.edu.eg	manal.ali@eng.kfs.edu.eg	PROPN
ejpam-5831	15	36	(	(	PUNCT
ejpam-5831	15	37	m.	m.	PROPN
ejpam-5831	15	38	e.	e.	PROPN
ejpam-5831	15	39	ali	ali	PROPN
ejpam-5831	15	40	)	)	PUNCT
ejpam-5831	15	41	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5831	16	1	1	1	NUM
ejpam-5831	16	2	copyright	copyright	NOUN
ejpam-5831	16	3	:	:	PUNCT
ejpam-5831	16	4	©	©	PROPN
ejpam-5831	16	5	2025	2025	NUM
ejpam-5831	16	6	the	the	DET
ejpam-5831	16	7	author(s	author(s	NOUN
ejpam-5831	16	8	)	)	PUNCT
ejpam-5831	16	9	.	.	PUNCT
ejpam-5831	17	1	(	(	PUNCT
ejpam-5831	17	2	cc	cc	NOUN
ejpam-5831	17	3	by	by	ADP
ejpam-5831	17	4	-	-	PUNCT
ejpam-5831	17	5	nc	nc	PROPN
ejpam-5831	17	6	4.0	4.0	NUM
ejpam-5831	17	7	)	)	PUNCT
ejpam-5831	17	8	a.	a.	NOUN
ejpam-5831	17	9	a.	a.	NOUN
ejpam-5831	17	10	azza	azza	NOUN
ejpam-5831	17	11	et	et	PROPN
ejpam-5831	17	12	al	al	PROPN
ejpam-5831	17	13	.	.	PUNCT
ejpam-5831	17	14	/	/	SYM
ejpam-5831	17	15	eur	eur	PROPN
ejpam-5831	17	16	.	.	PUNCT
ejpam-5831	18	1	j.	j.	PROPN
ejpam-5831	18	2	pure	pure	PROPN
ejpam-5831	18	3	appl	appl	PROPN
ejpam-5831	18	4	.	.	PROPN
ejpam-5831	18	5	math	math	PROPN
ejpam-5831	18	6	,	,	PUNCT
ejpam-5831	18	7	18	18	NUM
ejpam-5831	18	8	(	(	PUNCT
ejpam-5831	18	9	2	2	NUM
ejpam-5831	18	10	)	)	PUNCT
ejpam-5831	18	11	(	(	PUNCT
ejpam-5831	18	12	2025	2025	NUM
ejpam-5831	18	13	)	)	PUNCT
ejpam-5831	18	14	,	,	PUNCT
ejpam-5831	18	15	5831	5831	NUM
ejpam-5831	18	16	2	2	NUM
ejpam-5831	18	17	of	of	ADP
ejpam-5831	18	18	11	11	NUM
ejpam-5831	18	19	pawlak	pawlak	ADJ
ejpam-5831	18	20	’s	’s	PART
ejpam-5831	18	21	rough	rough	ADJ
ejpam-5831	18	22	set	set	NOUN
ejpam-5831	18	23	model	model	NOUN
ejpam-5831	18	24	to	to	ADP
ejpam-5831	18	25	a	a	DET
ejpam-5831	18	26	topological	topological	ADJ
ejpam-5831	18	27	structure	structure	NOUN
ejpam-5831	18	28	,	,	PUNCT
ejpam-5831	18	29	where	where	SCONJ
ejpam-5831	18	30	the	the	DET
ejpam-5831	18	31	set	set	NOUN
ejpam-5831	18	32	approximations	approximation	NOUN
ejpam-5831	18	33	are	be	AUX
ejpam-5831	18	34	defined	define	VERB
ejpam-5831	18	35	by	by	ADP
ejpam-5831	18	36	the	the	DET
ejpam-5831	18	37	topological	topological	ADJ
ejpam-5831	18	38	concept	concept	NOUN
ejpam-5831	18	39	δβ	δβ	NOUN
ejpam-5831	18	40	-	-	PUNCT
ejpam-5831	18	41	open	open	ADJ
ejpam-5831	18	42	sets	set	NOUN
ejpam-5831	18	43	.	.	PUNCT
ejpam-5831	19	1	in	in	ADP
ejpam-5831	19	2	[	[	X
ejpam-5831	19	3	3	3	NUM
ejpam-5831	19	4	]	]	PUNCT
ejpam-5831	19	5	,	,	PUNCT
ejpam-5831	19	6	al	al	PROPN
ejpam-5831	19	7	-	-	PUNCT
ejpam-5831	19	8	shami	shami	PROPN
ejpam-5831	19	9	and	and	CCONJ
ejpam-5831	19	10	mhemdi	mhemdi	PROPN
ejpam-5831	19	11	introduced	introduce	VERB
ejpam-5831	19	12	the	the	DET
ejpam-5831	19	13	concept	concept	NOUN
ejpam-5831	19	14	of	of	ADP
ejpam-5831	19	15	overlapping	overlap	VERB
ejpam-5831	19	16	containment	containment	NOUN
ejpam-5831	19	17	rough	rough	ADJ
ejpam-5831	19	18	neighborhoods	neighborhood	NOUN
ejpam-5831	19	19	and	and	CCONJ
ejpam-5831	19	20	their	their	PRON
ejpam-5831	19	21	corresponding	corresponding	ADJ
ejpam-5831	19	22	generalized	generalized	ADJ
ejpam-5831	19	23	approximation	approximation	NOUN
ejpam-5831	19	24	spaces	space	NOUN
ejpam-5831	19	25	,	,	PUNCT
ejpam-5831	19	26	which	which	PRON
ejpam-5831	19	27	were	be	AUX
ejpam-5831	19	28	then	then	ADV
ejpam-5831	19	29	applied	apply	VERB
ejpam-5831	19	30	to	to	ADP
ejpam-5831	19	31	computational	computational	ADJ
ejpam-5831	19	32	problems	problem	NOUN
ejpam-5831	19	33	.	.	PUNCT
ejpam-5831	20	1	finally	finally	ADV
ejpam-5831	20	2	,	,	PUNCT
ejpam-5831	20	3	kaur	kaur	PROPN
ejpam-5831	20	4	et	et	PROPN
ejpam-5831	20	5	.	.	PUNCT
ejpam-5831	21	1	al	al	PROPN
ejpam-5831	21	2	.	.	PUNCT
ejpam-5831	22	1	[	[	X
ejpam-5831	22	2	4	4	X
ejpam-5831	22	3	]	]	PUNCT
ejpam-5831	22	4	presented	present	VERB
ejpam-5831	22	5	a	a	DET
ejpam-5831	22	6	novel	novel	ADJ
ejpam-5831	22	7	multi	multi	ADJ
ejpam-5831	22	8	-	-	ADJ
ejpam-5831	22	9	ideal	ideal	ADJ
ejpam-5831	22	10	nano	nano	NOUN
ejpam-5831	22	11	-	-	PUNCT
ejpam-5831	22	12	topological	topological	ADJ
ejpam-5831	22	13	model	model	NOUN
ejpam-5831	22	14	aimed	aim	VERB
ejpam-5831	22	15	at	at	ADP
ejpam-5831	22	16	improving	improve	VERB
ejpam-5831	22	17	the	the	DET
ejpam-5831	22	18	diagnosis	diagnosis	NOUN
ejpam-5831	22	19	and	and	CCONJ
ejpam-5831	22	20	treatment	treatment	NOUN
ejpam-5831	22	21	of	of	ADP
ejpam-5831	22	22	dengue	dengue	NOUN
ejpam-5831	22	23	.	.	PUNCT
ejpam-5831	23	1	collectively	collectively	ADV
ejpam-5831	23	2	,	,	PUNCT
ejpam-5831	23	3	these	these	DET
ejpam-5831	23	4	manuscripts	manuscript	NOUN
ejpam-5831	23	5	contribute	contribute	VERB
ejpam-5831	23	6	significantly	significantly	ADV
ejpam-5831	23	7	to	to	ADP
ejpam-5831	23	8	the	the	DET
ejpam-5831	23	9	theoretical	theoretical	ADJ
ejpam-5831	23	10	foundations	foundation	NOUN
ejpam-5831	23	11	and	and	CCONJ
ejpam-5831	23	12	practical	practical	ADJ
ejpam-5831	23	13	implementations	implementation	NOUN
ejpam-5831	23	14	of	of	ADP
ejpam-5831	23	15	rough	rough	ADJ
ejpam-5831	23	16	set	set	NOUN
ejpam-5831	23	17	theory	theory	NOUN
ejpam-5831	23	18	,	,	PUNCT
ejpam-5831	23	19	particularly	particularly	ADV
ejpam-5831	23	20	in	in	ADP
ejpam-5831	23	21	the	the	DET
ejpam-5831	23	22	medical	medical	ADJ
ejpam-5831	23	23	domain	domain	NOUN
ejpam-5831	23	24	.	.	PUNCT
ejpam-5831	24	1	a.	a.	PROPN
ejpam-5831	24	2	galton	galton	PROPN
ejpam-5831	25	1	[	[	X
ejpam-5831	25	2	5	5	NUM
ejpam-5831	25	3	]	]	PUNCT
ejpam-5831	25	4	applied	apply	VERB
ejpam-5831	25	5	topological	topological	ADJ
ejpam-5831	25	6	concepts	concept	NOUN
ejpam-5831	25	7	to	to	ADP
ejpam-5831	25	8	the	the	DET
ejpam-5831	25	9	problem	problem	NOUN
ejpam-5831	25	10	of	of	ADP
ejpam-5831	25	11	describing	describe	VERB
ejpam-5831	25	12	motion	motion	NOUN
ejpam-5831	25	13	in	in	ADP
ejpam-5831	25	14	discrete	discrete	ADJ
ejpam-5831	25	15	space	space	NOUN
ejpam-5831	25	16	space	space	NOUN
ejpam-5831	25	17	.	.	PUNCT
ejpam-5831	26	1	tareq	tareq	PROPN
ejpam-5831	26	2	m.	m.	PROPN
ejpam-5831	26	3	al	al	PROPN
ejpam-5831	26	4	-	-	PUNCT
ejpam-5831	26	5	shami	shami	PROPN
ejpam-5831	26	6	and	and	CCONJ
ejpam-5831	26	7	et	et	PROPN
ejpam-5831	26	8	al	al	PROPN
ejpam-5831	26	9	.	.	PUNCT
ejpam-5831	27	1	[	[	X
ejpam-5831	27	2	6	6	NUM
ejpam-5831	27	3	]	]	PUNCT
ejpam-5831	27	4	studied	study	VERB
ejpam-5831	27	5	the	the	DET
ejpam-5831	27	6	concept	concept	NOUN
ejpam-5831	27	7	of	of	ADP
ejpam-5831	27	8	primal	primal	ADJ
ejpam-5831	27	9	soft	soft	ADJ
ejpam-5831	27	10	topology	topology	NOUN
ejpam-5831	27	11	based	base	VERB
ejpam-5831	27	12	on	on	ADP
ejpam-5831	27	13	the	the	DET
ejpam-5831	27	14	soft	soft	ADJ
ejpam-5831	27	15	primal	primal	NOUN
ejpam-5831	27	16	,	,	PUNCT
ejpam-5831	27	17	which	which	PRON
ejpam-5831	27	18	is	be	AUX
ejpam-5831	27	19	a	a	DET
ejpam-5831	27	20	complementary	complementary	ADJ
ejpam-5831	27	21	concept	concept	NOUN
ejpam-5831	27	22	of	of	ADP
ejpam-5831	27	23	a	a	DET
ejpam-5831	27	24	soft	soft	ADJ
ejpam-5831	27	25	grill	grill	NOUN
ejpam-5831	27	26	.	.	PUNCT
ejpam-5831	28	1	r.	r.	PROPN
ejpam-5831	28	2	mareay	mareay	PROPN
ejpam-5831	28	3	and	and	CCONJ
ejpam-5831	28	4	et	et	NOUN
ejpam-5831	28	5	al.[7	al.[7	PROPN
ejpam-5831	28	6	]	]	X
ejpam-5831	28	7	putted	putt	VERB
ejpam-5831	28	8	fourth	fourth	ADV
ejpam-5831	28	9	some	some	DET
ejpam-5831	28	10	concepts	concept	NOUN
ejpam-5831	28	11	of	of	ADP
ejpam-5831	28	12	topological	topological	ADJ
ejpam-5831	28	13	near	near	ADP
ejpam-5831	28	14	open	open	ADJ
ejpam-5831	28	15	sets	set	NOUN
ejpam-5831	28	16	and	and	CCONJ
ejpam-5831	28	17	a	a	DET
ejpam-5831	28	18	new	new	ADJ
ejpam-5831	28	19	approximation	approximation	NOUN
ejpam-5831	28	20	structure	structure	NOUN
ejpam-5831	28	21	based	base	VERB
ejpam-5831	28	22	on	on	ADP
ejpam-5831	28	23	the	the	DET
ejpam-5831	28	24	topological	topological	ADJ
ejpam-5831	28	25	near	near	ADP
ejpam-5831	28	26	open	open	ADJ
ejpam-5831	28	27	sets	set	NOUN
ejpam-5831	28	28	is	be	AUX
ejpam-5831	28	29	introduced	introduce	VERB
ejpam-5831	28	30	.	.	PUNCT
ejpam-5831	29	1	new	new	ADJ
ejpam-5831	29	2	models	model	NOUN
ejpam-5831	29	3	of	of	ADP
ejpam-5831	29	4	intuitionistic	intuitionistic	ADJ
ejpam-5831	29	5	fuzzy	fuzzy	ADJ
ejpam-5831	29	6	set	set	VERB
ejpam-5831	29	7	approximation	approximation	NOUN
ejpam-5831	29	8	space	space	NOUN
ejpam-5831	29	9	depending	depend	VERB
ejpam-5831	29	10	on	on	ADP
ejpam-5831	29	11	covering	covering	NOUN
ejpam-5831	29	12	are	be	AUX
ejpam-5831	29	13	defined	define	VERB
ejpam-5831	29	14	via	via	ADP
ejpam-5831	29	15	neighborhood	neighborhood	NOUN
ejpam-5831	29	16	concept	concept	NOUN
ejpam-5831	29	17	[	[	X
ejpam-5831	29	18	8	8	NUM
ejpam-5831	29	19	]	]	PUNCT
ejpam-5831	29	20	.	.	PUNCT
ejpam-5831	30	1	an	an	DET
ejpam-5831	30	2	attributes	attribute	NOUN
ejpam-5831	30	3	reduction	reduction	NOUN
ejpam-5831	30	4	method	method	NOUN
ejpam-5831	30	5	is	be	AUX
ejpam-5831	30	6	introduced	introduce	VERB
ejpam-5831	30	7	[	[	PUNCT
ejpam-5831	30	8	9	9	NUM
ejpam-5831	30	9	]	]	PUNCT
ejpam-5831	30	10	based	base	VERB
ejpam-5831	30	11	on	on	ADP
ejpam-5831	30	12	constructing	construct	VERB
ejpam-5831	30	13	a	a	DET
ejpam-5831	30	14	weighted	weighted	ADJ
ejpam-5831	30	15	pre	pre	NOUN
ejpam-5831	30	16	-	-	NOUN
ejpam-5831	30	17	topology	topology	NOUN
ejpam-5831	30	18	that	that	PRON
ejpam-5831	30	19	represents	represent	VERB
ejpam-5831	30	20	the	the	DET
ejpam-5831	30	21	information	information	NOUN
ejpam-5831	30	22	system	system	NOUN
ejpam-5831	30	23	under	under	ADP
ejpam-5831	30	24	consideration	consideration	NOUN
ejpam-5831	30	25	.	.	PUNCT
ejpam-5831	31	1	k.	k.	PROPN
ejpam-5831	31	2	y.	y.	PROPN
ejpam-5831	31	3	qin	qin	PROPN
ejpam-5831	31	4	,	,	PUNCT
ejpam-5831	31	5	z.	z.	PROPN
ejpam-5831	31	6	pei	pei	PROPN
ejpam-5831	32	1	[	[	X
ejpam-5831	32	2	10	10	NUM
ejpam-5831	32	3	]	]	PUNCT
ejpam-5831	32	4	introduced	introduce	VERB
ejpam-5831	32	5	the	the	DET
ejpam-5831	32	6	discussion	discussion	NOUN
ejpam-5831	32	7	of	of	ADP
ejpam-5831	32	8	the	the	DET
ejpam-5831	32	9	relationship	relationship	NOUN
ejpam-5831	32	10	between	between	ADP
ejpam-5831	32	11	fuzzy	fuzzy	ADJ
ejpam-5831	32	12	topologies	topology	NOUN
ejpam-5831	32	13	and	and	CCONJ
ejpam-5831	32	14	fuzzy	fuzzy	ADJ
ejpam-5831	32	15	rough	rough	ADJ
ejpam-5831	32	16	set	set	NOUN
ejpam-5831	32	17	models	model	NOUN
ejpam-5831	32	18	and	and	CCONJ
ejpam-5831	32	19	the	the	DET
ejpam-5831	32	20	axiom	axiom	NOUN
ejpam-5831	32	21	of	of	ADP
ejpam-5831	32	22	fuzzy	fuzzy	ADJ
ejpam-5831	32	23	topology	topology	NOUN
ejpam-5831	32	24	.	.	PUNCT
ejpam-5831	33	1	k.	k.	PROPN
ejpam-5831	34	1	y.	y.	PROPN
ejpam-5831	34	2	qin	qin	PROPN
ejpam-5831	35	1	[	[	X
ejpam-5831	35	2	11	11	NUM
ejpam-5831	35	3	]	]	PUNCT
ejpam-5831	35	4	discussed	discuss	VERB
ejpam-5831	35	5	the	the	DET
ejpam-5831	35	6	relationship	relationship	NOUN
ejpam-5831	35	7	between	between	ADP
ejpam-5831	35	8	generalized	generalize	VERB
ejpam-5831	35	9	rough	rough	ADJ
ejpam-5831	35	10	sets	set	NOUN
ejpam-5831	35	11	based	base	VERB
ejpam-5831	35	12	on	on	ADP
ejpam-5831	35	13	reflexive	reflexive	ADJ
ejpam-5831	35	14	and	and	CCONJ
ejpam-5831	35	15	transitive	transitive	ADJ
ejpam-5831	35	16	relations	relation	NOUN
ejpam-5831	35	17	and	and	CCONJ
ejpam-5831	35	18	the	the	DET
ejpam-5831	35	19	topologies	topology	NOUN
ejpam-5831	35	20	on	on	ADP
ejpam-5831	35	21	the	the	DET
ejpam-5831	35	22	universe	universe	NOUN
ejpam-5831	35	23	which	which	PRON
ejpam-5831	35	24	is	be	AUX
ejpam-5831	35	25	not	not	PART
ejpam-5831	35	26	limited	limit	VERB
ejpam-5831	35	27	to	to	PART
ejpam-5831	35	28	be	be	AUX
ejpam-5831	35	29	finite	finite	VERB
ejpam-5831	35	30	.	.	PUNCT
ejpam-5831	35	31	a.	a.	PROPN
ejpam-5831	35	32	s.	s.	PROPN
ejpam-5831	35	33	salama	salama	PROPN
ejpam-5831	36	1	[	[	X
ejpam-5831	36	2	12	12	NUM
ejpam-5831	36	3	]	]	PUNCT
ejpam-5831	36	4	introduced	introduce	VERB
ejpam-5831	36	5	new	new	ADJ
ejpam-5831	36	6	pre	pre	ADJ
ejpam-5831	36	7	-	-	ADJ
ejpam-5831	36	8	topological	topological	ADJ
ejpam-5831	36	9	approximations	approximation	NOUN
ejpam-5831	36	10	,	,	PUNCT
ejpam-5831	36	11	pre	pre	ADJ
ejpam-5831	36	12	-	-	ADJ
ejpam-5831	36	13	topological	topological	ADJ
ejpam-5831	36	14	measures	measure	NOUN
ejpam-5831	36	15	and	and	CCONJ
ejpam-5831	36	16	a	a	DET
ejpam-5831	36	17	new	new	ADJ
ejpam-5831	36	18	method	method	NOUN
ejpam-5831	36	19	of	of	ADP
ejpam-5831	36	20	data	datum	NOUN
ejpam-5831	36	21	decomposition	decomposition	NOUN
ejpam-5831	36	22	to	to	PART
ejpam-5831	36	23	avoid	avoid	VERB
ejpam-5831	36	24	the	the	DET
ejpam-5831	36	25	necessity	necessity	NOUN
ejpam-5831	36	26	of	of	ADP
ejpam-5831	36	27	reasoning	reasoning	NOUN
ejpam-5831	36	28	from	from	ADP
ejpam-5831	36	29	data	datum	NOUN
ejpam-5831	36	30	with	with	ADP
ejpam-5831	36	31	missing	miss	VERB
ejpam-5831	36	32	attribute	attribute	NOUN
ejpam-5831	36	33	values	value	NOUN
ejpam-5831	36	34	.	.	PUNCT
ejpam-5831	37	1	the	the	DET
ejpam-5831	37	2	concept	concept	NOUN
ejpam-5831	37	3	of	of	ADP
ejpam-5831	37	4	near	near	ADP
ejpam-5831	37	5	open	open	ADJ
ejpam-5831	37	6	sets	set	NOUN
ejpam-5831	37	7	is	be	AUX
ejpam-5831	37	8	an	an	DET
ejpam-5831	37	9	accurate	accurate	ADJ
ejpam-5831	37	10	and	and	CCONJ
ejpam-5831	37	11	applicable	applicable	ADJ
ejpam-5831	37	12	tool	tool	NOUN
ejpam-5831	37	13	for	for	ADP
ejpam-5831	37	14	dealing	deal	VERB
ejpam-5831	37	15	with	with	ADP
ejpam-5831	37	16	data	datum	NOUN
ejpam-5831	37	17	.	.	PUNCT
ejpam-5831	38	1	in	in	ADP
ejpam-5831	38	2	1989	1989	NUM
ejpam-5831	38	3	,	,	PUNCT
ejpam-5831	38	4	wiweger	wiweger	X
ejpam-5831	38	5	[	[	X
ejpam-5831	38	6	13	13	NUM
ejpam-5831	38	7	]	]	PUNCT
ejpam-5831	38	8	introduced	introduce	VERB
ejpam-5831	38	9	the	the	DET
ejpam-5831	38	10	concept	concept	NOUN
ejpam-5831	38	11	of	of	ADP
ejpam-5831	38	12	topological	topological	ADJ
ejpam-5831	38	13	rough	rough	ADJ
ejpam-5831	38	14	set	set	NOUN
ejpam-5831	38	15	.	.	PUNCT
ejpam-5831	39	1	this	this	DET
ejpam-5831	39	2	concept	concept	NOUN
ejpam-5831	39	3	was	be	AUX
ejpam-5831	39	4	the	the	DET
ejpam-5831	39	5	basic	basic	ADJ
ejpam-5831	39	6	start	start	NOUN
ejpam-5831	39	7	point	point	NOUN
ejpam-5831	39	8	for	for	ADP
ejpam-5831	39	9	many	many	ADJ
ejpam-5831	39	10	researchers	researcher	NOUN
ejpam-5831	39	11	in	in	ADP
ejpam-5831	39	12	generalization	generalization	NOUN
ejpam-5831	39	13	of	of	ADP
ejpam-5831	39	14	rough	rough	ADJ
ejpam-5831	39	15	set	set	NOUN
ejpam-5831	39	16	.	.	PUNCT
ejpam-5831	40	1	wiweger	wiweger	PROPN
ejpam-5831	40	2	’s	’s	PART
ejpam-5831	40	3	generalization	generalization	NOUN
ejpam-5831	40	4	defined	define	VERB
ejpam-5831	40	5	approximation	approximation	NOUN
ejpam-5831	40	6	space	space	NOUN
ejpam-5831	40	7	by	by	ADP
ejpam-5831	40	8	using	use	VERB
ejpam-5831	40	9	the	the	DET
ejpam-5831	40	10	interior	interior	ADJ
ejpam-5831	40	11	and	and	CCONJ
ejpam-5831	40	12	closure	closure	NOUN
ejpam-5831	40	13	operators	operator	NOUN
ejpam-5831	40	14	which	which	PRON
ejpam-5831	40	15	are	be	AUX
ejpam-5831	40	16	define	define	ADJ
ejpam-5831	40	17	on	on	ADP
ejpam-5831	40	18	the	the	DET
ejpam-5831	40	19	the	the	DET
ejpam-5831	40	20	topological	topological	ADJ
ejpam-5831	40	21	spaces	space	NOUN
ejpam-5831	40	22	.	.	PUNCT
ejpam-5831	41	1	m.	m.	NOUN
ejpam-5831	41	2	e.	e.	PROPN
ejpam-5831	41	3	abd	abd	PROPN
ejpam-5831	42	1	el	el	PROPN
ejpam-5831	42	2	-	-	PROPN
ejpam-5831	42	3	monsef	monsef	PROPN
ejpam-5831	42	4	et	et	PROPN
ejpam-5831	42	5	.	.	PUNCT
ejpam-5831	43	1	al	al	PROPN
ejpam-5831	43	2	.	.	PUNCT
ejpam-5831	44	1	[	[	X
ejpam-5831	44	2	14	14	NUM
ejpam-5831	44	3	]	]	PUNCT
ejpam-5831	44	4	introduced	introduce	VERB
ejpam-5831	44	5	β	β	VERB
ejpam-5831	44	6	-	-	ADJ
ejpam-5831	44	7	open	open	ADJ
ejpam-5831	44	8	set	set	VERB
ejpam-5831	44	9	concept	concept	NOUN
ejpam-5831	44	10	.	.	PUNCT
ejpam-5831	45	1	this	this	DET
ejpam-5831	45	2	concept	concept	NOUN
ejpam-5831	45	3	has	have	AUX
ejpam-5831	45	4	been	be	AUX
ejpam-5831	45	5	used	use	VERB
ejpam-5831	45	6	by	by	ADP
ejpam-5831	45	7	many	many	ADJ
ejpam-5831	45	8	researchers	researcher	NOUN
ejpam-5831	45	9	in	in	ADP
ejpam-5831	45	10	generalization	generalization	NOUN
ejpam-5831	45	11	of	of	ADP
ejpam-5831	45	12	rough	rough	ADJ
ejpam-5831	45	13	set	set	NOUN
ejpam-5831	45	14	.	.	PUNCT
ejpam-5831	46	1	since	since	SCONJ
ejpam-5831	46	2	the	the	DET
ejpam-5831	46	3	closure	closure	NOUN
ejpam-5831	46	4	function	function	NOUN
ejpam-5831	46	5	has	have	VERB
ejpam-5831	46	6	an	an	DET
ejpam-5831	46	7	idempotent	idempotent	ADJ
ejpam-5831	46	8	property	property	NOUN
ejpam-5831	46	9	in	in	ADP
ejpam-5831	46	10	topology	topology	NOUN
ejpam-5831	46	11	,	,	PUNCT
ejpam-5831	46	12	so	so	ADV
ejpam-5831	46	13	the	the	DET
ejpam-5831	46	14	the	the	DET
ejpam-5831	46	15	classical	classical	ADJ
ejpam-5831	46	16	topology	topology	NOUN
ejpam-5831	46	17	is	be	AUX
ejpam-5831	46	18	not	not	PART
ejpam-5831	46	19	more	more	ADV
ejpam-5831	46	20	adequate	adequate	ADJ
ejpam-5831	46	21	.	.	PUNCT
ejpam-5831	47	1	the	the	DET
ejpam-5831	47	2	formalism	formalism	NOUN
ejpam-5831	47	3	of	of	ADP
ejpam-5831	47	4	pretopology	pretopology	NOUN
ejpam-5831	47	5	comes	come	VERB
ejpam-5831	47	6	from	from	ADP
ejpam-5831	47	7	usual	usual	ADJ
ejpam-5831	47	8	topology	topology	NOUN
ejpam-5831	47	9	with	with	ADP
ejpam-5831	47	10	weaker	weak	ADJ
ejpam-5831	47	11	axioms	axiom	NOUN
ejpam-5831	47	12	.	.	PUNCT
ejpam-5831	48	1	the	the	DET
ejpam-5831	48	2	applications	application	NOUN
ejpam-5831	48	3	of	of	ADP
ejpam-5831	48	4	pretopology	pretopology	NOUN
ejpam-5831	48	5	in	in	ADP
ejpam-5831	48	6	the	the	DET
ejpam-5831	48	7	problems	problem	NOUN
ejpam-5831	48	8	of	of	ADP
ejpam-5831	48	9	social	social	ADJ
ejpam-5831	48	10	sciences	science	NOUN
ejpam-5831	48	11	find	find	VERB
ejpam-5831	48	12	their	their	PRON
ejpam-5831	48	13	foundations	foundation	NOUN
ejpam-5831	48	14	[	[	X
ejpam-5831	48	15	15	15	NUM
ejpam-5831	48	16	,	,	PUNCT
ejpam-5831	48	17	16	16	NUM
ejpam-5831	48	18	]	]	PUNCT
ejpam-5831	48	19	.	.	PUNCT
ejpam-5831	49	1	in	in	ADP
ejpam-5831	49	2	1975	1975	NUM
ejpam-5831	49	3	,	,	PUNCT
ejpam-5831	49	4	the	the	DET
ejpam-5831	49	5	first	first	ADJ
ejpam-5831	49	6	definition	definition	NOUN
ejpam-5831	49	7	of	of	ADP
ejpam-5831	49	8	pretopology	pretopology	NOUN
ejpam-5831	49	9	space	space	NOUN
ejpam-5831	49	10	[	[	X
ejpam-5831	49	11	17	17	NUM
ejpam-5831	49	12	]	]	PUNCT
ejpam-5831	49	13	was	be	AUX
ejpam-5831	49	14	given	give	VERB
ejpam-5831	49	15	by	by	ADP
ejpam-5831	49	16	marcel	marcel	PROPN
ejpam-5831	49	17	brissaud	brissaud	NOUN
ejpam-5831	49	18	.	.	PUNCT
ejpam-5831	50	1	this	this	DET
ejpam-5831	50	2	definition	definition	NOUN
ejpam-5831	50	3	of	of	ADP
ejpam-5831	50	4	marcel	marcel	PROPN
ejpam-5831	50	5	brissaud	brissaud	PROPN
ejpam-5831	50	6	,	,	PUNCT
ejpam-5831	50	7	who	who	PRON
ejpam-5831	50	8	is	be	AUX
ejpam-5831	50	9	known	know	VERB
ejpam-5831	50	10	as	as	ADP
ejpam-5831	50	11	”	"	PUNCT
ejpam-5831	50	12	pretopology	pretopology	NOUN
ejpam-5831	50	13	’s	’s	PART
ejpam-5831	50	14	father	father	NOUN
ejpam-5831	50	15	”	"	PUNCT
ejpam-5831	50	16	,	,	PUNCT
ejpam-5831	50	17	is	be	AUX
ejpam-5831	50	18	based	base	VERB
ejpam-5831	50	19	on	on	ADP
ejpam-5831	50	20	čech	čech	PUNCT
ejpam-5831	50	21	closure	closure	NOUN
ejpam-5831	50	22	operator	operator	NOUN
ejpam-5831	50	23	[	[	X
ejpam-5831	50	24	18	18	NUM
ejpam-5831	50	25	]	]	PUNCT
ejpam-5831	50	26	,	,	PUNCT
ejpam-5831	50	27	works	work	NOUN
ejpam-5831	50	28	of	of	ADP
ejpam-5831	50	29	frochet	frochet	NOUN
ejpam-5831	50	30	spaces	space	NOUN
ejpam-5831	50	31	[	[	X
ejpam-5831	50	32	19	19	NUM
ejpam-5831	50	33	]	]	PUNCT
ejpam-5831	50	34	,	,	PUNCT
ejpam-5831	50	35	and	and	CCONJ
ejpam-5831	50	36	closure	closure	NOUN
ejpam-5831	50	37	axioms	axiom	NOUN
ejpam-5831	50	38	of	of	ADP
ejpam-5831	50	39	kuratowski	kuratowski	NOUN
ejpam-5831	50	40	[	[	X
ejpam-5831	50	41	20	20	NUM
ejpam-5831	50	42	]	]	PUNCT
ejpam-5831	50	43	.	.	PUNCT
ejpam-5831	51	1	based	base	VERB
ejpam-5831	51	2	on	on	ADP
ejpam-5831	51	3	these	these	DET
ejpam-5831	51	4	works	work	NOUN
ejpam-5831	51	5	,	,	PUNCT
ejpam-5831	51	6	many	many	ADJ
ejpam-5831	51	7	of	of	ADP
ejpam-5831	51	8	important	important	ADJ
ejpam-5831	51	9	theories	theory	NOUN
ejpam-5831	51	10	in	in	ADP
ejpam-5831	51	11	pretopology	pretopology	NOUN
ejpam-5831	51	12	have	have	AUX
ejpam-5831	51	13	been	be	AUX
ejpam-5831	51	14	developed	develop	VERB
ejpam-5831	51	15	during	during	ADP
ejpam-5831	51	16	the	the	DET
ejpam-5831	51	17	1970	1970	NUM
ejpam-5831	51	18	’s	’s	NOUN
ejpam-5831	51	19	and	and	CCONJ
ejpam-5831	51	20	1980	1980	NUM
ejpam-5831	51	21	’s	’s	NOUN
ejpam-5831	51	22	such	such	ADJ
ejpam-5831	51	23	as	as	ADP
ejpam-5831	51	24	marcel	marcel	PROPN
ejpam-5831	51	25	brissaud	brissaud	VERB
ejpam-5831	52	1	[	[	X
ejpam-5831	52	2	21–24	21–24	NUM
ejpam-5831	52	3	]	]	PUNCT
ejpam-5831	52	4	,	,	PUNCT
ejpam-5831	52	5	jean	jean	PROPN
ejpam-5831	52	6	-	-	PUNCT
ejpam-5831	52	7	paul	paul	PROPN
ejpam-5831	52	8	auray	auray	PROPN
ejpam-5831	52	9	[	[	X
ejpam-5831	52	10	25	25	NUM
ejpam-5831	52	11	,	,	PUNCT
ejpam-5831	52	12	26	26	NUM
ejpam-5831	52	13	]	]	PUNCT
ejpam-5831	52	14	,	,	PUNCT
ejpam-5831	52	15	nicolas	nicolas	PROPN
ejpam-5831	52	16	nicoloyannis	nicoloyannis	PROPN
ejpam-5831	53	1	[	[	X
ejpam-5831	53	2	27	27	NUM
ejpam-5831	53	3	]	]	PUNCT
ejpam-5831	53	4	,	,	PUNCT
ejpam-5831	53	5	gerard	gerard	PROPN
ejpam-5831	53	6	duru	duru	PROPN
ejpam-5831	54	1	[	[	X
ejpam-5831	54	2	28	28	NUM
ejpam-5831	54	3	,	,	PUNCT
ejpam-5831	54	4	29	29	NUM
ejpam-5831	54	5	]	]	PUNCT
ejpam-5831	54	6	,	,	PUNCT
ejpam-5831	54	7	michel	michel	PROPN
ejpam-5831	54	8	lamure	lamure	NOUN
ejpam-5831	54	9	[	[	X
ejpam-5831	54	10	30	30	NUM
ejpam-5831	54	11	]	]	PUNCT
ejpam-5831	54	12	,	,	PUNCT
ejpam-5831	54	13	and	and	CCONJ
ejpam-5831	54	14	hubert	hubert	PROPN
ejpam-5831	54	15	emptoz	emptoz	PROPN
ejpam-5831	55	1	[	[	X
ejpam-5831	55	2	31	31	NUM
ejpam-5831	55	3	]	]	PUNCT
ejpam-5831	55	4	,	,	PUNCT
ejpam-5831	55	5	and	and	CCONJ
ejpam-5831	55	6	et	et	NOUN
ejpam-5831	55	7	.	.	PUNCT
ejpam-5831	56	1	al	al	PROPN
ejpam-5831	56	2	.	.	PUNCT
ejpam-5831	57	1	[	[	X
ejpam-5831	57	2	32–34	32–34	NUM
ejpam-5831	57	3	]	]	PUNCT
ejpam-5831	57	4	.	.	PUNCT
ejpam-5831	58	1	some	some	DET
ejpam-5831	58	2	concepts	concept	NOUN
ejpam-5831	58	3	of	of	ADP
ejpam-5831	58	4	pretopological	pretopological	ADJ
ejpam-5831	58	5	spaces	space	NOUN
ejpam-5831	58	6	are	be	AUX
ejpam-5831	58	7	investigated	investigate	VERB
ejpam-5831	58	8	during	during	ADP
ejpam-5831	58	9	this	this	DET
ejpam-5831	58	10	paper	paper	NOUN
ejpam-5831	58	11	.	.	PUNCT
ejpam-5831	59	1	different	different	ADJ
ejpam-5831	59	2	kinds	kind	NOUN
ejpam-5831	59	3	of	of	ADP
ejpam-5831	59	4	pretopological	pretopological	ADJ
ejpam-5831	59	5	lapprs	lapprs	NOUN
ejpam-5831	59	6	and	and	CCONJ
ejpam-5831	59	7	uapprs	uapprs	NOUN
ejpam-5831	59	8	are	be	AUX
ejpam-5831	59	9	introduced	introduce	VERB
ejpam-5831	59	10	.	.	PUNCT
ejpam-5831	60	1	in	in	ADP
ejpam-5831	60	2	this	this	DET
ejpam-5831	60	3	paper	paper	NOUN
ejpam-5831	60	4	,	,	PUNCT
ejpam-5831	60	5	we	we	PRON
ejpam-5831	60	6	give	give	VERB
ejpam-5831	60	7	and	and	CCONJ
ejpam-5831	60	8	investigate	investigate	VERB
ejpam-5831	60	9	some	some	DET
ejpam-5831	60	10	concepts	concept	NOUN
ejpam-5831	60	11	of	of	ADP
ejpam-5831	60	12	pretopological	pretopological	ADJ
ejpam-5831	60	13	spaces	space	NOUN
ejpam-5831	60	14	.	.	PUNCT
ejpam-5831	61	1	different	different	ADJ
ejpam-5831	61	2	types	type	NOUN
ejpam-5831	61	3	of	of	ADP
ejpam-5831	61	4	pretopological	pretopological	ADJ
ejpam-5831	61	5	lower	low	ADJ
ejpam-5831	61	6	and	and	CCONJ
ejpam-5831	61	7	upper	upper	ADJ
ejpam-5831	61	8	approximations	approximation	NOUN
ejpam-5831	61	9	are	be	AUX
ejpam-5831	61	10	introduced	introduce	VERB
ejpam-5831	61	11	.	.	PUNCT
ejpam-5831	62	1	this	this	DET
ejpam-5831	62	2	paper	paper	NOUN
ejpam-5831	62	3	give	give	VERB
ejpam-5831	62	4	a.	a.	NOUN
ejpam-5831	62	5	a.	a.	NOUN
ejpam-5831	62	6	azza	azza	NOUN
ejpam-5831	62	7	et	et	PROPN
ejpam-5831	62	8	al	al	PROPN
ejpam-5831	62	9	.	.	PUNCT
ejpam-5831	62	10	/	/	SYM
ejpam-5831	62	11	eur	eur	PROPN
ejpam-5831	62	12	.	.	PUNCT
ejpam-5831	63	1	j.	j.	PROPN
ejpam-5831	63	2	pure	pure	PROPN
ejpam-5831	63	3	appl	appl	PROPN
ejpam-5831	63	4	.	.	PROPN
ejpam-5831	63	5	math	math	PROPN
ejpam-5831	63	6	,	,	PUNCT
ejpam-5831	63	7	18	18	NUM
ejpam-5831	63	8	(	(	PUNCT
ejpam-5831	63	9	2	2	NUM
ejpam-5831	63	10	)	)	PUNCT
ejpam-5831	63	11	(	(	PUNCT
ejpam-5831	63	12	2025	2025	NUM
ejpam-5831	63	13	)	)	PUNCT
ejpam-5831	63	14	,	,	PUNCT
ejpam-5831	63	15	5831	5831	NUM
ejpam-5831	63	16	3	3	NUM
ejpam-5831	63	17	of	of	ADP
ejpam-5831	63	18	11	11	NUM
ejpam-5831	63	19	the	the	DET
ejpam-5831	63	20	relationship	relationship	NOUN
ejpam-5831	63	21	within	within	ADP
ejpam-5831	63	22	distinct	distinct	ADJ
ejpam-5831	63	23	types	type	NOUN
ejpam-5831	63	24	of	of	ADP
ejpam-5831	63	25	pretopological	pretopological	ADJ
ejpam-5831	63	26	lapprs	lapprs	NOUN
ejpam-5831	63	27	and	and	CCONJ
ejpam-5831	63	28	uapprs	uapprs	ADJ
ejpam-5831	63	29	.	.	PUNCT
ejpam-5831	64	1	some	some	DET
ejpam-5831	64	2	generalizations	generalization	NOUN
ejpam-5831	64	3	of	of	ADP
ejpam-5831	64	4	rough	rough	ADJ
ejpam-5831	64	5	theory	theory	NOUN
ejpam-5831	64	6	concepts	concept	NOUN
ejpam-5831	64	7	depending	depend	VERB
ejpam-5831	64	8	on	on	ADP
ejpam-5831	64	9	pretopological	pretopological	ADJ
ejpam-5831	64	10	space	space	NOUN
ejpam-5831	64	11	are	be	AUX
ejpam-5831	64	12	introduced	introduce	VERB
ejpam-5831	64	13	.	.	PUNCT
ejpam-5831	65	1	2	2	X
ejpam-5831	65	2	.	.	X
ejpam-5831	65	3	preliminary	preliminary	ADJ
ejpam-5831	65	4	of	of	ADP
ejpam-5831	65	5	pretopological	pretopological	ADJ
ejpam-5831	65	6	concepts	concept	NOUN
ejpam-5831	65	7	and	and	CCONJ
ejpam-5831	65	8	rough	rough	ADJ
ejpam-5831	65	9	theory	theory	NOUN
ejpam-5831	65	10	in	in	ADP
ejpam-5831	65	11	this	this	DET
ejpam-5831	65	12	part	part	NOUN
ejpam-5831	65	13	,	,	PUNCT
ejpam-5831	65	14	we	we	PRON
ejpam-5831	65	15	give	give	VERB
ejpam-5831	65	16	some	some	DET
ejpam-5831	65	17	primary	primary	ADJ
ejpam-5831	65	18	concepts	concept	NOUN
ejpam-5831	65	19	of	of	ADP
ejpam-5831	65	20	pretopological	pretopological	ADJ
ejpam-5831	65	21	spaces	space	NOUN
ejpam-5831	65	22	and	and	CCONJ
ejpam-5831	65	23	rough	rough	ADJ
ejpam-5831	65	24	theory	theory	NOUN
ejpam-5831	65	25	.	.	PUNCT
ejpam-5831	66	1	definition	definition	NOUN
ejpam-5831	66	2	2.1	2.1	NUM
ejpam-5831	66	3	.	.	PUNCT
ejpam-5831	67	1	[	[	X
ejpam-5831	67	2	20	20	NUM
ejpam-5831	67	3	]	]	PUNCT
ejpam-5831	67	4	assume	assume	VERB
ejpam-5831	67	5	that	that	SCONJ
ejpam-5831	67	6	x	x	PUNCT
ejpam-5831	67	7	̸=	̸=	PROPN
ejpam-5831	67	8	∅	∅	NOUN
ejpam-5831	67	9	.	.	PUNCT
ejpam-5831	68	1	then	then	ADV
ejpam-5831	68	2	the	the	DET
ejpam-5831	68	3	operator	operator	NOUN
ejpam-5831	68	4	cl	cl	NOUN
ejpam-5831	68	5	:	:	PUNCT
ejpam-5831	68	6	p	p	X
ejpam-5831	68	7	(	(	PUNCT
ejpam-5831	68	8	x	x	NOUN
ejpam-5831	68	9	)	)	PUNCT
ejpam-5831	68	10	→	→	SYM
ejpam-5831	68	11	p	p	X
ejpam-5831	68	12	(	(	PUNCT
ejpam-5831	68	13	x	x	X
ejpam-5831	68	14	)	)	PUNCT
ejpam-5831	68	15	is	be	AUX
ejpam-5831	68	16	called	call	VERB
ejpam-5831	68	17	kuratowski	kuratowski	ADJ
ejpam-5831	68	18	closure	closure	NOUN
ejpam-5831	68	19	if	if	SCONJ
ejpam-5831	68	20	the	the	DET
ejpam-5831	68	21	following	follow	VERB
ejpam-5831	68	22	properties	property	NOUN
ejpam-5831	68	23	are	be	AUX
ejpam-5831	68	24	hold	hold	NOUN
ejpam-5831	68	25	:	:	PUNCT
ejpam-5831	68	26	i.	i.	NOUN
ejpam-5831	68	27	cl(∅	cl(∅	PROPN
ejpam-5831	68	28	)	)	PUNCT
ejpam-5831	69	1	=	=	SYM
ejpam-5831	69	2	∅	∅	NOUN
ejpam-5831	69	3	,	,	PUNCT
ejpam-5831	69	4	ii	ii	PROPN
ejpam-5831	69	5	.	.	PUNCT
ejpam-5831	70	1	if	if	SCONJ
ejpam-5831	70	2	a1	a1	VERB
ejpam-5831	70	3	⊆	⊆	NUM
ejpam-5831	70	4	x	x	NOUN
ejpam-5831	70	5	,	,	PUNCT
ejpam-5831	70	6	then	then	ADV
ejpam-5831	70	7	a1	a1	VERB
ejpam-5831	70	8	⊆	⊆	NUM
ejpam-5831	70	9	cl(a1	cl(a1	NOUN
ejpam-5831	70	10	)	)	PUNCT
ejpam-5831	70	11	,	,	PUNCT
ejpam-5831	70	12	iii	iii	PROPN
ejpam-5831	70	13	.	.	PROPN
ejpam-5831	70	14	∀a1	∀a1	PROPN
ejpam-5831	70	15	,	,	PUNCT
ejpam-5831	70	16	a2	a2	PROPN
ejpam-5831	70	17	⊆	⊆	NUM
ejpam-5831	70	18	x	x	NOUN
ejpam-5831	70	19	,	,	PUNCT
ejpam-5831	70	20	cl(a1	cl(a1	NOUN
ejpam-5831	70	21	∪a2	∪a2	NOUN
ejpam-5831	70	22	)	)	PUNCT
ejpam-5831	70	23	=	=	SYM
ejpam-5831	70	24	cl(a1	cl(a1	NOUN
ejpam-5831	70	25	)	)	PUNCT
ejpam-5831	70	26	∪	∪	ADP
ejpam-5831	70	27	cl(a2	cl(a2	PROPN
ejpam-5831	70	28	)	)	PUNCT
ejpam-5831	70	29	,	,	PUNCT
ejpam-5831	70	30	iv	iv	X
ejpam-5831	70	31	.	.	PUNCT
ejpam-5831	70	32	∀a1	∀a1	PROPN
ejpam-5831	70	33	⊆	⊆	NUM
ejpam-5831	70	34	x	x	NOUN
ejpam-5831	70	35	,	,	PUNCT
ejpam-5831	70	36	cl(cl(a1	cl(cl(a1	NOUN
ejpam-5831	70	37	)	)	PUNCT
ejpam-5831	70	38	)	)	PUNCT
ejpam-5831	71	1	=	=	SYM
ejpam-5831	71	2	cl(a1	cl(a1	NOUN
ejpam-5831	71	3	)	)	PUNCT
ejpam-5831	71	4	,	,	PUNCT
ejpam-5831	71	5	.	.	PUNCT
ejpam-5831	72	1	definition	definition	NOUN
ejpam-5831	72	2	2.2	2.2	NUM
ejpam-5831	72	3	.	.	PUNCT
ejpam-5831	73	1	[	[	X
ejpam-5831	73	2	17	17	NUM
ejpam-5831	73	3	]	]	PUNCT
ejpam-5831	73	4	for	for	ADP
ejpam-5831	73	5	any	any	DET
ejpam-5831	73	6	a	a	DET
ejpam-5831	73	7	nonempty	nonempty	ADV
ejpam-5831	73	8	set	set	VERB
ejpam-5831	73	9	x	x	NOUN
ejpam-5831	73	10	,	,	PUNCT
ejpam-5831	73	11	the	the	DET
ejpam-5831	73	12	operator	operator	NOUN
ejpam-5831	73	13	l	l	NOUN
ejpam-5831	73	14	:	:	PUNCT
ejpam-5831	74	1	p	p	X
ejpam-5831	74	2	(	(	PUNCT
ejpam-5831	74	3	x	x	NOUN
ejpam-5831	74	4	)	)	PUNCT
ejpam-5831	74	5	→	→	SYM
ejpam-5831	74	6	p	p	X
ejpam-5831	74	7	(	(	PUNCT
ejpam-5831	74	8	x	x	X
ejpam-5831	74	9	)	)	PUNCT
ejpam-5831	74	10	is	be	AUX
ejpam-5831	74	11	called	call	VERB
ejpam-5831	74	12	pseudo	pseudo	NOUN
ejpam-5831	74	13	closure	closure	NOUN
ejpam-5831	74	14	if	if	SCONJ
ejpam-5831	74	15	the	the	DET
ejpam-5831	74	16	following	follow	VERB
ejpam-5831	74	17	properties	property	NOUN
ejpam-5831	74	18	are	be	AUX
ejpam-5831	74	19	hold	hold	NOUN
ejpam-5831	74	20	:	:	PUNCT
ejpam-5831	74	21	i.	i.	PROPN
ejpam-5831	74	22	l(∅	l(∅	PROPN
ejpam-5831	74	23	)	)	PUNCT
ejpam-5831	75	1	=	=	SYM
ejpam-5831	75	2	∅	∅	NOUN
ejpam-5831	75	3	,	,	PUNCT
ejpam-5831	75	4	ii	ii	PROPN
ejpam-5831	75	5	.	.	PUNCT
ejpam-5831	75	6	∀a1	∀a1	PROPN
ejpam-5831	75	7	⊆	⊆	NUM
ejpam-5831	75	8	x	x	NOUN
ejpam-5831	75	9	,	,	PUNCT
ejpam-5831	75	10	a1	a1	VERB
ejpam-5831	75	11	⊆	⊆	NUM
ejpam-5831	75	12	l(a1	l(a1	NOUN
ejpam-5831	75	13	)	)	PUNCT
ejpam-5831	75	14	,	,	PUNCT
ejpam-5831	75	15	definition	definition	NOUN
ejpam-5831	75	16	2.3	2.3	NUM
ejpam-5831	75	17	.	.	PUNCT
ejpam-5831	76	1	[	[	X
ejpam-5831	76	2	17	17	NUM
ejpam-5831	76	3	]	]	PUNCT
ejpam-5831	76	4	if	if	SCONJ
ejpam-5831	76	5	a	a	DET
ejpam-5831	76	6	mapping	mapping	NOUN
ejpam-5831	76	7	l	l	NOUN
ejpam-5831	76	8	:	:	PUNCT
ejpam-5831	77	1	p	p	X
ejpam-5831	77	2	(	(	PUNCT
ejpam-5831	77	3	x	x	NOUN
ejpam-5831	77	4	)	)	PUNCT
ejpam-5831	77	5	→	→	SYM
ejpam-5831	77	6	p	p	X
ejpam-5831	77	7	(	(	PUNCT
ejpam-5831	77	8	x	x	X
ejpam-5831	77	9	)	)	PUNCT
ejpam-5831	77	10	is	be	AUX
ejpam-5831	77	11	pseudo	pseudo	NOUN
ejpam-5831	77	12	closure	closure	NOUN
ejpam-5831	77	13	and	and	CCONJ
ejpam-5831	77	14	x	x	X
ejpam-5831	77	15	is	be	AUX
ejpam-5831	77	16	any	any	DET
ejpam-5831	77	17	set	set	NOUN
ejpam-5831	77	18	.	.	PUNCT
ejpam-5831	78	1	then	then	ADV
ejpam-5831	78	2	,	,	PUNCT
ejpam-5831	78	3	(	(	PUNCT
ejpam-5831	78	4	x	x	NOUN
ejpam-5831	78	5	,	,	PUNCT
ejpam-5831	78	6	l	l	NOUN
ejpam-5831	78	7	)	)	PUNCT
ejpam-5831	78	8	is	be	AUX
ejpam-5831	78	9	called	call	VERB
ejpam-5831	78	10	a	a	DET
ejpam-5831	78	11	pretopological	pretopological	ADJ
ejpam-5831	78	12	space	space	NOUN
ejpam-5831	78	13	.	.	PUNCT
ejpam-5831	79	1	definition	definition	NOUN
ejpam-5831	79	2	2.4	2.4	NUM
ejpam-5831	79	3	.	.	PUNCT
ejpam-5831	80	1	[	[	X
ejpam-5831	80	2	17	17	NUM
ejpam-5831	80	3	]	]	X
ejpam-5831	80	4	let	let	AUX
ejpam-5831	80	5	(	(	PUNCT
ejpam-5831	80	6	x	x	NOUN
ejpam-5831	80	7	,	,	PUNCT
ejpam-5831	80	8	l	l	NOUN
ejpam-5831	80	9	)	)	PUNCT
ejpam-5831	80	10	be	be	AUX
ejpam-5831	80	11	pretopological	pretopological	ADJ
ejpam-5831	80	12	space	space	NOUN
ejpam-5831	80	13	and	and	CCONJ
ejpam-5831	80	14	interior	interior	ADJ
ejpam-5831	80	15	function	function	NOUN
ejpam-5831	80	16	.	.	PUNCT
ejpam-5831	81	1	then	then	ADV
ejpam-5831	81	2	,	,	PUNCT
ejpam-5831	81	3	i(a	i(a	PROPN
ejpam-5831	81	4	)	)	PUNCT
ejpam-5831	81	5	=	=	PUNCT
ejpam-5831	82	1	(	(	PUNCT
ejpam-5831	82	2	a(l(ac)))c	a(l(ac)))c	VERB
ejpam-5831	82	3	definition	definition	NOUN
ejpam-5831	82	4	2.5	2.5	NUM
ejpam-5831	82	5	.	.	PUNCT
ejpam-5831	83	1	[	[	X
ejpam-5831	83	2	17	17	NUM
ejpam-5831	83	3	]	]	PUNCT
ejpam-5831	83	4	assume	assume	VERB
ejpam-5831	83	5	that	that	SCONJ
ejpam-5831	83	6	(	(	PUNCT
ejpam-5831	83	7	x	x	X
ejpam-5831	83	8	,	,	PUNCT
ejpam-5831	83	9	l	l	NOUN
ejpam-5831	83	10	)	)	PUNCT
ejpam-5831	83	11	is	be	AUX
ejpam-5831	83	12	pretopological	pretopological	ADJ
ejpam-5831	83	13	space	space	NOUN
ejpam-5831	83	14	and	and	CCONJ
ejpam-5831	83	15	i	i	PRON
ejpam-5831	83	16	:	:	PUNCT
ejpam-5831	83	17	p	p	X
ejpam-5831	83	18	(	(	PUNCT
ejpam-5831	83	19	x	x	NOUN
ejpam-5831	83	20	)	)	PUNCT
ejpam-5831	83	21	→	→	SYM
ejpam-5831	83	22	p	p	X
ejpam-5831	83	23	(	(	PUNCT
ejpam-5831	83	24	x	x	X
ejpam-5831	83	25	)	)	PUNCT
ejpam-5831	83	26	is	be	AUX
ejpam-5831	83	27	a	a	DET
ejpam-5831	83	28	mapping	mapping	NOUN
ejpam-5831	83	29	.	.	PUNCT
ejpam-5831	84	1	then	then	ADV
ejpam-5831	84	2	,	,	PUNCT
ejpam-5831	84	3	i	i	PRON
ejpam-5831	84	4	is	be	AUX
ejpam-5831	84	5	called	call	VERB
ejpam-5831	84	6	interior	interior	ADJ
ejpam-5831	84	7	mapping	mapping	NOUN
ejpam-5831	84	8	if	if	SCONJ
ejpam-5831	84	9	the	the	DET
ejpam-5831	84	10	following	following	NOUN
ejpam-5831	84	11	are	be	AUX
ejpam-5831	84	12	satisfied	satisfied	ADJ
ejpam-5831	84	13	:	:	PUNCT
ejpam-5831	84	14	i.	i.	NOUN
ejpam-5831	84	15	i(x	i(x	PROPN
ejpam-5831	84	16	)	)	PUNCT
ejpam-5831	85	1	=	=	SYM
ejpam-5831	85	2	x	x	PROPN
ejpam-5831	85	3	,	,	PUNCT
ejpam-5831	85	4	ii	ii	PROPN
ejpam-5831	85	5	.	.	PUNCT
ejpam-5831	86	1	if	if	SCONJ
ejpam-5831	86	2	a1	a1	NOUN
ejpam-5831	86	3	⊆	⊆	NUM
ejpam-5831	86	4	x.	x.	NOUN
ejpam-5831	86	5	then	then	ADV
ejpam-5831	86	6	,	,	PUNCT
ejpam-5831	86	7	i(a1	i(a1	NOUN
ejpam-5831	86	8	)	)	PUNCT
ejpam-5831	87	1	⊂	⊂	PROPN
ejpam-5831	87	2	a1	a1	PROPN
ejpam-5831	87	3	.	.	PUNCT
ejpam-5831	88	1	definition	definition	NOUN
ejpam-5831	88	2	2.6	2.6	NUM
ejpam-5831	88	3	.	.	PUNCT
ejpam-5831	89	1	[	[	X
ejpam-5831	89	2	17	17	NUM
ejpam-5831	89	3	]	]	X
ejpam-5831	89	4	if	if	SCONJ
ejpam-5831	89	5	a1	a1	VERB
ejpam-5831	89	6	⊆	⊆	NUM
ejpam-5831	89	7	x	x	PUNCT
ejpam-5831	89	8	and	and	CCONJ
ejpam-5831	89	9	(	(	PUNCT
ejpam-5831	89	10	x	x	NOUN
ejpam-5831	89	11	,	,	PUNCT
ejpam-5831	89	12	l	l	NOUN
ejpam-5831	89	13	)	)	PUNCT
ejpam-5831	89	14	is	be	AUX
ejpam-5831	89	15	pretopological	pretopological	ADJ
ejpam-5831	89	16	space	space	NOUN
ejpam-5831	89	17	.	.	PUNCT
ejpam-5831	90	1	then	then	ADV
ejpam-5831	90	2	,	,	PUNCT
ejpam-5831	90	3	a1	a1	NOUN
ejpam-5831	90	4	is	be	AUX
ejpam-5831	90	5	said	say	VERB
ejpam-5831	90	6	to	to	PART
ejpam-5831	90	7	be	be	AUX
ejpam-5831	90	8	closed	close	VERB
ejpam-5831	90	9	if	if	SCONJ
ejpam-5831	90	10	and	and	CCONJ
ejpam-5831	90	11	only	only	ADV
ejpam-5831	90	12	if	if	SCONJ
ejpam-5831	90	13	l(a1	l(a1	NOUN
ejpam-5831	90	14	)	)	PUNCT
ejpam-5831	90	15	=	=	SYM
ejpam-5831	90	16	a1	a1	NOUN
ejpam-5831	90	17	.	.	NOUN
ejpam-5831	90	18	definition	definition	NOUN
ejpam-5831	90	19	2.7	2.7	NUM
ejpam-5831	90	20	.	.	PUNCT
ejpam-5831	91	1	[	[	X
ejpam-5831	91	2	17	17	NUM
ejpam-5831	91	3	]	]	PUNCT
ejpam-5831	91	4	assume	assume	VERB
ejpam-5831	91	5	that	that	SCONJ
ejpam-5831	91	6	(	(	PUNCT
ejpam-5831	91	7	x	x	X
ejpam-5831	91	8	,	,	PUNCT
ejpam-5831	91	9	l	l	NOUN
ejpam-5831	91	10	)	)	PUNCT
ejpam-5831	91	11	be	be	AUX
ejpam-5831	91	12	pretopological	pretopological	ADJ
ejpam-5831	91	13	space	space	NOUN
ejpam-5831	91	14	,	,	PUNCT
ejpam-5831	91	15	a1	a1	NOUN
ejpam-5831	91	16	⊆	⊆	NUM
ejpam-5831	91	17	x.	x.	NOUN
ejpam-5831	91	18	then	then	ADV
ejpam-5831	91	19	,	,	PUNCT
ejpam-5831	91	20	a1	a1	PROPN
ejpam-5831	91	21	is	be	AUX
ejpam-5831	91	22	said	say	VERB
ejpam-5831	91	23	to	to	PART
ejpam-5831	91	24	be	be	AUX
ejpam-5831	91	25	open	open	ADJ
ejpam-5831	91	26	if	if	SCONJ
ejpam-5831	91	27	and	and	CCONJ
ejpam-5831	91	28	only	only	ADV
ejpam-5831	91	29	if	if	SCONJ
ejpam-5831	91	30	i(a1	i(a1	NOUN
ejpam-5831	92	1	)	)	PUNCT
ejpam-5831	92	2	=	=	SYM
ejpam-5831	92	3	a1	a1	PROPN
ejpam-5831	92	4	.	.	PUNCT
ejpam-5831	92	5	a.	a.	PROPN
ejpam-5831	92	6	a.	a.	PROPN
ejpam-5831	92	7	azza	azza	PROPN
ejpam-5831	92	8	et	et	PROPN
ejpam-5831	92	9	al	al	PROPN
ejpam-5831	92	10	.	.	PUNCT
ejpam-5831	92	11	/	/	SYM
ejpam-5831	92	12	eur	eur	PROPN
ejpam-5831	92	13	.	.	PUNCT
ejpam-5831	93	1	j.	j.	PROPN
ejpam-5831	93	2	pure	pure	PROPN
ejpam-5831	93	3	appl	appl	PROPN
ejpam-5831	93	4	.	.	PROPN
ejpam-5831	93	5	math	math	PROPN
ejpam-5831	93	6	,	,	PUNCT
ejpam-5831	93	7	18	18	NUM
ejpam-5831	93	8	(	(	PUNCT
ejpam-5831	93	9	2	2	NUM
ejpam-5831	93	10	)	)	PUNCT
ejpam-5831	93	11	(	(	PUNCT
ejpam-5831	93	12	2025	2025	NUM
ejpam-5831	93	13	)	)	PUNCT
ejpam-5831	93	14	,	,	PUNCT
ejpam-5831	93	15	5831	5831	NUM
ejpam-5831	93	16	4	4	NUM
ejpam-5831	93	17	of	of	ADP
ejpam-5831	93	18	11	11	NUM
ejpam-5831	93	19	2.1	2.1	NUM
ejpam-5831	93	20	.	.	PUNCT
ejpam-5831	94	1	basic	basic	ADJ
ejpam-5831	94	2	concepts	concept	NOUN
ejpam-5831	94	3	of	of	ADP
ejpam-5831	94	4	the	the	DET
ejpam-5831	94	5	pawlakś	pawlakś	NOUN
ejpam-5831	94	6	rough	rough	ADJ
ejpam-5831	94	7	theory	theory	NOUN
ejpam-5831	94	8	assume	assume	VERB
ejpam-5831	94	9	that	that	SCONJ
ejpam-5831	94	10	r	r	NOUN
ejpam-5831	94	11	is	be	AUX
ejpam-5831	94	12	an	an	DET
ejpam-5831	94	13	equivalence	equivalence	NOUN
ejpam-5831	94	14	relation	relation	NOUN
ejpam-5831	94	15	on	on	ADP
ejpam-5831	94	16	a	a	DET
ejpam-5831	94	17	nonempty	nonempty	ADV
ejpam-5831	94	18	set	set	VERB
ejpam-5831	94	19	x.	x.	NOUN
ejpam-5831	94	20	then	then	ADV
ejpam-5831	94	21	,	,	PUNCT
ejpam-5831	94	22	x	x	X
ejpam-5831	94	23	/	/	SYM
ejpam-5831	94	24	r	r	NOUN
ejpam-5831	94	25	=	=	SYM
ejpam-5831	94	26	{	{	PUNCT
ejpam-5831	94	27	y1	y1	NOUN
ejpam-5831	94	28	,	,	PUNCT
ejpam-5831	94	29	y2	y2	PROPN
ejpam-5831	94	30	,	,	PUNCT
ejpam-5831	94	31	y3	y3	PROPN
ejpam-5831	94	32	,	,	PUNCT
ejpam-5831	94	33	...	...	PUNCT
ejpam-5831	94	34	,	,	PUNCT
ejpam-5831	94	35	ym	ym	PRON
ejpam-5831	94	36	}	}	PUNCT
ejpam-5831	94	37	is	be	AUX
ejpam-5831	94	38	a	a	DET
ejpam-5831	94	39	partition	partition	NOUN
ejpam-5831	94	40	on	on	ADP
ejpam-5831	94	41	x	x	NOUN
ejpam-5831	94	42	,	,	PUNCT
ejpam-5831	94	43	where	where	SCONJ
ejpam-5831	94	44	r	r	NOUN
ejpam-5831	94	45	is	be	AUX
ejpam-5831	94	46	an	an	DET
ejpam-5831	94	47	equivalence	equivalence	NOUN
ejpam-5831	94	48	which	which	PRON
ejpam-5831	94	49	generate	generate	VERB
ejpam-5831	94	50	the	the	DET
ejpam-5831	94	51	equivalence	equivalence	NOUN
ejpam-5831	94	52	classes	class	NOUN
ejpam-5831	94	53	y1	y1	PROPN
ejpam-5831	94	54	,	,	PUNCT
ejpam-5831	94	55	y2	y2	PROPN
ejpam-5831	94	56	,	,	PUNCT
ejpam-5831	94	57	y3	y3	PROPN
ejpam-5831	94	58	,	,	PUNCT
ejpam-5831	94	59	...	...	PUNCT
ejpam-5831	94	60	,	,	PUNCT
ejpam-5831	95	1	ym	ym	PROPN
ejpam-5831	95	2	.	.	PUNCT
ejpam-5831	95	3	.	.	PUNCT
ejpam-5831	96	1	definition	definition	NOUN
ejpam-5831	96	2	2.8	2.8	NUM
ejpam-5831	96	3	.	.	PUNCT
ejpam-5831	97	1	[	[	X
ejpam-5831	97	2	35	35	NUM
ejpam-5831	97	3	]	]	PUNCT
ejpam-5831	97	4	assume	assume	VERB
ejpam-5831	97	5	that	that	SCONJ
ejpam-5831	97	6	r	r	NOUN
ejpam-5831	97	7	is	be	AUX
ejpam-5831	97	8	an	an	DET
ejpam-5831	97	9	equivalence	equivalence	NOUN
ejpam-5831	97	10	relation	relation	NOUN
ejpam-5831	97	11	on	on	ADP
ejpam-5831	97	12	a	a	DET
ejpam-5831	97	13	nonempty	nonempty	ADV
ejpam-5831	97	14	set	set	VERB
ejpam-5831	97	15	x.	x.	NOUN
ejpam-5831	97	16	for	for	ADP
ejpam-5831	97	17	any	any	DET
ejpam-5831	97	18	a1	a1	NOUN
ejpam-5831	97	19	⊆	⊆	NUM
ejpam-5831	97	20	x	x	NOUN
ejpam-5831	97	21	,	,	PUNCT
ejpam-5831	97	22	the	the	DET
ejpam-5831	97	23	set	set	NOUN
ejpam-5831	97	24	r(a1	r(a1	NOUN
ejpam-5831	97	25	)	)	PUNCT
ejpam-5831	97	26	=	=	PUNCT
ejpam-5831	97	27	∪{yi	∪{yi	NUM
ejpam-5831	97	28	∈	∈	PROPN
ejpam-5831	97	29	x	x	X
ejpam-5831	97	30	/	/	SYM
ejpam-5831	97	31	r	r	NOUN
ejpam-5831	97	32	:	:	PUNCT
ejpam-5831	97	33	yi	yi	PROPN
ejpam-5831	97	34	⊆	⊆	NUM
ejpam-5831	97	35	a1	a1	NOUN
ejpam-5831	97	36	}	}	PUNCT
ejpam-5831	97	37	is	be	AUX
ejpam-5831	97	38	called	call	VERB
ejpam-5831	97	39	lappros	lappro	NOUN
ejpam-5831	97	40	of	of	ADP
ejpam-5831	97	41	a1	a1	NOUN
ejpam-5831	97	42	and	and	CCONJ
ejpam-5831	97	43	the	the	DET
ejpam-5831	97	44	set	set	NOUN
ejpam-5831	97	45	r(a1	r(a1	NOUN
ejpam-5831	97	46	)	)	PUNCT
ejpam-5831	97	47	=	=	PUNCT
ejpam-5831	98	1	∪{yi	∪{yi	NUM
ejpam-5831	98	2	∈	∈	PROPN
ejpam-5831	98	3	x	x	X
ejpam-5831	98	4	/	/	SYM
ejpam-5831	98	5	r	r	NOUN
ejpam-5831	98	6	:	:	PUNCT
ejpam-5831	98	7	yi	yi	PROPN
ejpam-5831	98	8	∩a1	∩a1	PUNCT
ejpam-5831	99	1	̸=	̸=	PROPN
ejpam-5831	99	2	∅	∅	NOUN
ejpam-5831	99	3	}	}	PUNCT
ejpam-5831	99	4	is	be	AUX
ejpam-5831	99	5	called	call	VERB
ejpam-5831	99	6	uappros	uappro	NOUN
ejpam-5831	99	7	of	of	ADP
ejpam-5831	99	8	a1	a1	PROPN
ejpam-5831	99	9	.	.	PUNCT
ejpam-5831	100	1	proposition	proposition	NOUN
ejpam-5831	100	2	2.1	2.1	NUM
ejpam-5831	100	3	.	.	PUNCT
ejpam-5831	101	1	[	[	X
ejpam-5831	101	2	35	35	NUM
ejpam-5831	101	3	]	]	PUNCT
ejpam-5831	101	4	assume	assume	VERB
ejpam-5831	101	5	that	that	SCONJ
ejpam-5831	101	6	k	k	PROPN
ejpam-5831	101	7	=	=	PRON
ejpam-5831	101	8	(	(	PUNCT
ejpam-5831	101	9	x	x	X
ejpam-5831	101	10	,	,	PUNCT
ejpam-5831	101	11	r	r	NOUN
ejpam-5831	101	12	)	)	PUNCT
ejpam-5831	101	13	is	be	AUX
ejpam-5831	101	14	an	an	DET
ejpam-5831	101	15	approximation	approximation	NOUN
ejpam-5831	101	16	structure	structure	NOUN
ejpam-5831	101	17	.	.	PUNCT
ejpam-5831	102	1	then	then	ADV
ejpam-5831	102	2	,	,	PUNCT
ejpam-5831	102	3	the	the	DET
ejpam-5831	102	4	following	follow	VERB
ejpam-5831	102	5	properties	property	NOUN
ejpam-5831	102	6	are	be	AUX
ejpam-5831	102	7	hold	hold	ADJ
ejpam-5831	102	8	,	,	PUNCT
ejpam-5831	102	9	for	for	ADP
ejpam-5831	102	10	x1	x1	PROPN
ejpam-5831	102	11	,	,	PUNCT
ejpam-5831	102	12	x2	x2	PROPN
ejpam-5831	102	13	⊆	⊆	NUM
ejpam-5831	102	14	x	x	SYM
ejpam-5831	102	15	:	:	PUNCT
ejpam-5831	102	16	(	(	PUNCT
ejpam-5831	102	17	il	il	PROPN
ejpam-5831	102	18	)	)	PUNCT
ejpam-5831	102	19	r(x	r(x	PROPN
ejpam-5831	102	20	)	)	PUNCT
ejpam-5831	102	21	=	=	SYM
ejpam-5831	103	1	x	x	X
ejpam-5831	103	2	;	;	PUNCT
ejpam-5831	103	3	(	(	PUNCT
ejpam-5831	103	4	ih	ih	X
ejpam-5831	103	5	)	)	PUNCT
ejpam-5831	103	6	r(x	r(x	PROPN
ejpam-5831	103	7	)	)	PUNCT
ejpam-5831	104	1	=	=	SYM
ejpam-5831	105	1	x	x	X
ejpam-5831	105	2	;	;	PUNCT
ejpam-5831	105	3	(	(	PUNCT
ejpam-5831	105	4	iil	iil	NOUN
ejpam-5831	105	5	)	)	PUNCT
ejpam-5831	105	6	r(∅	r(∅	PROPN
ejpam-5831	105	7	)	)	PUNCT
ejpam-5831	105	8	=	=	SYM
ejpam-5831	105	9	∅	∅	NOUN
ejpam-5831	105	10	;	;	PUNCT
ejpam-5831	105	11	(	(	PUNCT
ejpam-5831	105	12	iih	iih	ADJ
ejpam-5831	105	13	)	)	PUNCT
ejpam-5831	105	14	r(∅	r(∅	NOUN
ejpam-5831	105	15	)	)	PUNCT
ejpam-5831	105	16	=	=	SYM
ejpam-5831	105	17	∅	∅	NOUN
ejpam-5831	105	18	;	;	PUNCT
ejpam-5831	105	19	(	(	PUNCT
ejpam-5831	105	20	iiil	iiil	ADJ
ejpam-5831	105	21	)	)	PUNCT
ejpam-5831	105	22	r(x1	r(x1	NOUN
ejpam-5831	105	23	)	)	PUNCT
ejpam-5831	105	24	⊆	⊆	NUM
ejpam-5831	105	25	x1	x1	NUM
ejpam-5831	105	26	;	;	PUNCT
ejpam-5831	105	27	.	.	PUNCT
ejpam-5831	106	1	(	(	PUNCT
ejpam-5831	106	2	iiih	iiih	NOUN
ejpam-5831	106	3	)	)	PUNCT
ejpam-5831	106	4	x1	x1	PROPN
ejpam-5831	107	1	⊆	⊆	NUM
ejpam-5831	107	2	r(x1	r(x1	NOUN
ejpam-5831	107	3	)	)	PUNCT
ejpam-5831	107	4	.	.	PUNCT
ejpam-5831	108	1	(	(	PUNCT
ejpam-5831	108	2	ivl	ivl	NOUN
ejpam-5831	108	3	)	)	PUNCT
ejpam-5831	108	4	r(x1	r(x1	PROPN
ejpam-5831	108	5	∩x2	∩x2	X
ejpam-5831	108	6	)	)	PUNCT
ejpam-5831	108	7	=	=	SYM
ejpam-5831	108	8	r(x1	r(x1	ADJ
ejpam-5831	108	9	)	)	PUNCT
ejpam-5831	108	10	∩r(x2	∩r(x2	NOUN
ejpam-5831	108	11	)	)	PUNCT
ejpam-5831	108	12	;	;	PUNCT
ejpam-5831	108	13	(	(	PUNCT
ejpam-5831	108	14	ivh	ivh	X
ejpam-5831	108	15	)	)	PUNCT
ejpam-5831	108	16	r(x1	r(x1	ADJ
ejpam-5831	108	17	∪x2	∪x2	X
ejpam-5831	108	18	)	)	PUNCT
ejpam-5831	108	19	=	=	SYM
ejpam-5831	108	20	r(x1	r(x1	ADJ
ejpam-5831	108	21	)	)	PUNCT
ejpam-5831	108	22	∪r(x2	∪r(x2	NOUN
ejpam-5831	108	23	)	)	PUNCT
ejpam-5831	108	24	;	;	PUNCT
ejpam-5831	108	25	(	(	PUNCT
ejpam-5831	108	26	v	v	NOUN
ejpam-5831	108	27	)	)	PUNCT
ejpam-5831	108	28	r(xc	r(xc	VERB
ejpam-5831	108	29	1	1	NUM
ejpam-5831	108	30	)	)	PUNCT
ejpam-5831	108	31	=	=	NOUN
ejpam-5831	109	1	[	[	X
ejpam-5831	109	2	r(x1	r(x1	NOUN
ejpam-5831	109	3	)	)	PUNCT
ejpam-5831	109	4	]	]	PUNCT
ejpam-5831	110	1	c	c	X
ejpam-5831	110	2	,	,	PUNCT
ejpam-5831	110	3	where	where	SCONJ
ejpam-5831	110	4	(	(	PUNCT
ejpam-5831	110	5	xc	xc	NOUN
ejpam-5831	110	6	1	1	NUM
ejpam-5831	110	7	)	)	PUNCT
ejpam-5831	110	8	is	be	AUX
ejpam-5831	110	9	the	the	DET
ejpam-5831	110	10	complement	complement	NOUN
ejpam-5831	110	11	of	of	ADP
ejpam-5831	110	12	x1	x1	PROPN
ejpam-5831	110	13	;	;	PUNCT
ejpam-5831	110	14	(	(	PUNCT
ejpam-5831	110	15	vil	vil	ADJ
ejpam-5831	110	16	)	)	PUNCT
ejpam-5831	110	17	r(r(x1	r(r(x1	NOUN
ejpam-5831	110	18	)	)	PUNCT
ejpam-5831	110	19	)	)	PUNCT
ejpam-5831	111	1	=	=	SYM
ejpam-5831	111	2	r(x1	r(x1	PROPN
ejpam-5831	111	3	)	)	PUNCT
ejpam-5831	111	4	;	;	PUNCT
ejpam-5831	111	5	(	(	PUNCT
ejpam-5831	111	6	vih	vih	NOUN
ejpam-5831	111	7	)	)	PUNCT
ejpam-5831	111	8	r(r(x1	r(r(x1	NOUN
ejpam-5831	111	9	)	)	PUNCT
ejpam-5831	111	10	)	)	PUNCT
ejpam-5831	112	1	=	=	SYM
ejpam-5831	112	2	r(x1	r(x1	PROPN
ejpam-5831	112	3	)	)	PUNCT
ejpam-5831	112	4	;	;	PUNCT
ejpam-5831	112	5	(	(	PUNCT
ejpam-5831	112	6	viil	viil	NOUN
ejpam-5831	112	7	)	)	PUNCT
ejpam-5831	112	8	x1	x1	PROPN
ejpam-5831	112	9	⊆	⊆	NUM
ejpam-5831	112	10	x2	x2	PROPN
ejpam-5831	112	11	⇒	⇒	PROPN
ejpam-5831	112	12	r(x1	r(x1	PROPN
ejpam-5831	112	13	)	)	PUNCT
ejpam-5831	112	14	⊆	⊆	NUM
ejpam-5831	112	15	r(x2	r(x2	NOUN
ejpam-5831	112	16	)	)	PUNCT
ejpam-5831	112	17	;	;	PUNCT
ejpam-5831	112	18	(	(	PUNCT
ejpam-5831	112	19	viih	viih	ADJ
ejpam-5831	112	20	)	)	PUNCT
ejpam-5831	112	21	x1	x1	PROPN
ejpam-5831	113	1	⊆	⊆	NUM
ejpam-5831	113	2	x2	x2	PROPN
ejpam-5831	113	3	⇒	⇒	PROPN
ejpam-5831	113	4	r(x1	r(x1	PROPN
ejpam-5831	113	5	)	)	PUNCT
ejpam-5831	113	6	⊆	⊆	NUM
ejpam-5831	113	7	r(x2	r(x2	NOUN
ejpam-5831	113	8	)	)	PUNCT
ejpam-5831	113	9	;	;	PUNCT
ejpam-5831	113	10	(	(	PUNCT
ejpam-5831	113	11	viiil	viiil	NOUN
ejpam-5831	113	12	)	)	PUNCT
ejpam-5831	113	13	r(r(x1	r(r(x1	NOUN
ejpam-5831	113	14	)	)	PUNCT
ejpam-5831	113	15	)	)	PUNCT
ejpam-5831	114	1	c	c	NOUN
ejpam-5831	114	2	=	=	SYM
ejpam-5831	114	3	(	(	PUNCT
ejpam-5831	114	4	r(x1	r(x1	NOUN
ejpam-5831	114	5	)	)	PUNCT
ejpam-5831	114	6	)	)	PUNCT
ejpam-5831	115	1	c	c	NOUN
ejpam-5831	115	2	;	;	PUNCT
ejpam-5831	115	3	(	(	PUNCT
ejpam-5831	115	4	viiih	viiih	ADJ
ejpam-5831	115	5	)	)	PUNCT
ejpam-5831	115	6	r(r(x1	r(r(x1	NOUN
ejpam-5831	115	7	)	)	PUNCT
ejpam-5831	115	8	)	)	PUNCT
ejpam-5831	116	1	c	c	NOUN
ejpam-5831	116	2	=	=	SYM
ejpam-5831	116	3	(	(	PUNCT
ejpam-5831	116	4	r(x1	r(x1	NOUN
ejpam-5831	116	5	)	)	PUNCT
ejpam-5831	116	6	)	)	PUNCT
ejpam-5831	117	1	c	c	X
ejpam-5831	117	2	;	;	PUNCT
ejpam-5831	117	3	(	(	PUNCT
ejpam-5831	117	4	ixl	ixl	ADJ
ejpam-5831	117	5	)	)	PUNCT
ejpam-5831	117	6	r(x1	r(x1	ADJ
ejpam-5831	117	7	)	)	PUNCT
ejpam-5831	117	8	∪r(x2	∪r(x2	NOUN
ejpam-5831	117	9	)	)	PUNCT
ejpam-5831	117	10	⊆	⊆	NUM
ejpam-5831	117	11	r(x1	r(x1	NOUN
ejpam-5831	117	12	∪x2	∪x2	X
ejpam-5831	117	13	)	)	PUNCT
ejpam-5831	117	14	;	;	PUNCT
ejpam-5831	117	15	(	(	PUNCT
ejpam-5831	117	16	ixh	ixh	PROPN
ejpam-5831	117	17	)	)	PUNCT
ejpam-5831	117	18	r(x1	r(x1	PROPN
ejpam-5831	117	19	∩x2	∩x2	X
ejpam-5831	117	20	)	)	PUNCT
ejpam-5831	117	21	⊆	⊆	NUM
ejpam-5831	117	22	r(x	r(x	PROPN
ejpam-5831	117	23	)	)	PUNCT
ejpam-5831	117	24	∩r(x2	∩r(x2	NOUN
ejpam-5831	117	25	)	)	PUNCT
ejpam-5831	117	26	;	;	PUNCT
ejpam-5831	118	1	a.	a.	PROPN
ejpam-5831	118	2	a.	a.	NOUN
ejpam-5831	118	3	azza	azza	PROPN
ejpam-5831	118	4	et	et	PROPN
ejpam-5831	118	5	al	al	PROPN
ejpam-5831	118	6	.	.	PUNCT
ejpam-5831	118	7	/	/	SYM
ejpam-5831	118	8	eur	eur	PROPN
ejpam-5831	118	9	.	.	PUNCT
ejpam-5831	119	1	j.	j.	PROPN
ejpam-5831	119	2	pure	pure	PROPN
ejpam-5831	119	3	appl	appl	PROPN
ejpam-5831	119	4	.	.	PROPN
ejpam-5831	119	5	math	math	PROPN
ejpam-5831	119	6	,	,	PUNCT
ejpam-5831	119	7	18	18	NUM
ejpam-5831	119	8	(	(	PUNCT
ejpam-5831	119	9	2	2	NUM
ejpam-5831	119	10	)	)	PUNCT
ejpam-5831	119	11	(	(	PUNCT
ejpam-5831	119	12	2025	2025	NUM
ejpam-5831	119	13	)	)	PUNCT
ejpam-5831	119	14	,	,	PUNCT
ejpam-5831	119	15	5831	5831	NUM
ejpam-5831	119	16	5	5	NUM
ejpam-5831	119	17	of	of	ADP
ejpam-5831	119	18	11	11	NUM
ejpam-5831	119	19	3	3	NUM
ejpam-5831	119	20	.	.	PUNCT
ejpam-5831	120	1	rough	rough	ADJ
ejpam-5831	120	2	pretopological	pretopological	ADJ
ejpam-5831	120	3	approximation	approximation	NOUN
ejpam-5831	120	4	space	space	NOUN
ejpam-5831	120	5	this	this	DET
ejpam-5831	120	6	section	section	NOUN
ejpam-5831	120	7	introduces	introduce	VERB
ejpam-5831	120	8	the	the	DET
ejpam-5831	120	9	application	application	NOUN
ejpam-5831	120	10	of	of	ADP
ejpam-5831	120	11	pretopological	pretopological	ADJ
ejpam-5831	120	12	space	space	NOUN
ejpam-5831	120	13	in	in	ADP
ejpam-5831	120	14	rough	rough	ADJ
ejpam-5831	120	15	approximation	approximation	NOUN
ejpam-5831	120	16	space	space	NOUN
ejpam-5831	120	17	.	.	PUNCT
ejpam-5831	121	1	let	let	VERB
ejpam-5831	121	2	r	r	PRON
ejpam-5831	121	3	be	be	AUX
ejpam-5831	121	4	a	a	DET
ejpam-5831	121	5	binary	binary	ADJ
ejpam-5831	121	6	relation	relation	NOUN
ejpam-5831	121	7	which	which	PRON
ejpam-5831	121	8	defined	define	VERB
ejpam-5831	121	9	on	on	ADP
ejpam-5831	121	10	a	a	DET
ejpam-5831	121	11	finite	finite	NOUN
ejpam-5831	121	12	set	set	NOUN
ejpam-5831	121	13	x.	x.	NOUN
ejpam-5831	121	14	suppose	suppose	VERB
ejpam-5831	121	15	that	that	SCONJ
ejpam-5831	121	16	r(x	r(x	PROPN
ejpam-5831	121	17	)	)	PUNCT
ejpam-5831	121	18	is	be	AUX
ejpam-5831	121	19	a	a	DET
ejpam-5831	121	20	neighborhood	neighborhood	NOUN
ejpam-5831	121	21	of	of	ADP
ejpam-5831	121	22	x	x	PUNCT
ejpam-5831	121	23	which	which	PRON
ejpam-5831	121	24	is	be	AUX
ejpam-5831	121	25	defined	define	VERB
ejpam-5831	121	26	by	by	ADP
ejpam-5831	121	27	r(x	r(x	PROPN
ejpam-5831	121	28	)	)	PUNCT
ejpam-5831	122	1	=	=	PRON
ejpam-5831	122	2	{	{	PUNCT
ejpam-5831	122	3	y	y	PROPN
ejpam-5831	122	4	∈	∈	PROPN
ejpam-5831	122	5	:	:	PUNCT
ejpam-5831	122	6	(	(	PUNCT
ejpam-5831	122	7	x	x	X
ejpam-5831	122	8	,	,	PUNCT
ejpam-5831	122	9	y	y	NOUN
ejpam-5831	122	10	)	)	PUNCT
ejpam-5831	122	11	∈	∈	NOUN
ejpam-5831	122	12	r	r	NOUN
ejpam-5831	122	13	}	}	PUNCT
ejpam-5831	122	14	and	and	CCONJ
ejpam-5831	122	15	r−1(x	r−1(x	NOUN
ejpam-5831	122	16	)	)	PUNCT
ejpam-5831	122	17	=	=	PRON
ejpam-5831	123	1	{	{	PUNCT
ejpam-5831	123	2	y	y	PROPN
ejpam-5831	123	3	∈	∈	PROPN
ejpam-5831	123	4	x	x	X
ejpam-5831	123	5	:	:	PUNCT
ejpam-5831	123	6	(	(	PUNCT
ejpam-5831	123	7	y	y	NOUN
ejpam-5831	123	8	,	,	PUNCT
ejpam-5831	123	9	x	x	NOUN
ejpam-5831	123	10	)	)	PUNCT
ejpam-5831	123	11	∈	∈	PROPN
ejpam-5831	123	12	r	r	NOUN
ejpam-5831	123	13	}	}	PUNCT
ejpam-5831	123	14	.	.	PUNCT
ejpam-5831	124	1	hence	hence	ADV
ejpam-5831	124	2	,	,	PUNCT
ejpam-5831	124	3	we	we	PRON
ejpam-5831	124	4	will	will	AUX
ejpam-5831	124	5	define	define	VERB
ejpam-5831	124	6	the	the	DET
ejpam-5831	124	7	pseudo	pseudo	NOUN
ejpam-5831	124	8	-	-	NOUN
ejpam-5831	124	9	closure	closure	NOUN
ejpam-5831	124	10	γd	γd	NOUN
ejpam-5831	124	11	(	(	PUNCT
ejpam-5831	124	12	.	.	PUNCT
ejpam-5831	124	13	)	)	PUNCT
ejpam-5831	125	1	and	and	CCONJ
ejpam-5831	125	2	the	the	DET
ejpam-5831	125	3	interior	interior	ADJ
ejpam-5831	125	4	function	function	NOUN
ejpam-5831	125	5	i	i	PROPN
ejpam-5831	125	6	d	d	PROPN
ejpam-5831	125	7	(	(	PUNCT
ejpam-5831	125	8	.	.	PUNCT
ejpam-5831	125	9	)	)	PUNCT
ejpam-5831	125	10	as	as	SCONJ
ejpam-5831	125	11	follow	follow	VERB
ejpam-5831	125	12	:	:	PUNCT
ejpam-5831	125	13	definition	definition	NOUN
ejpam-5831	125	14	3.1	3.1	NUM
ejpam-5831	125	15	.	.	PUNCT
ejpam-5831	126	1	for	for	ADP
ejpam-5831	126	2	any	any	DET
ejpam-5831	126	3	a	a	DET
ejpam-5831	126	4	nonempty	nonempty	ADV
ejpam-5831	126	5	set	set	VERB
ejpam-5831	126	6	x	x	NOUN
ejpam-5831	126	7	,	,	PUNCT
ejpam-5831	126	8	and	and	CCONJ
ejpam-5831	126	9	r	r	NOUN
ejpam-5831	126	10	is	be	AUX
ejpam-5831	126	11	a	a	DET
ejpam-5831	126	12	binary	binary	ADJ
ejpam-5831	126	13	relation	relation	NOUN
ejpam-5831	126	14	defined	define	VERB
ejpam-5831	126	15	on	on	ADP
ejpam-5831	126	16	r.	r.	PROPN
ejpam-5831	126	17	suppose	suppose	VERB
ejpam-5831	126	18	γd	γd	ADP
ejpam-5831	126	19	(	(	PUNCT
ejpam-5831	126	20	.	.	PUNCT
ejpam-5831	126	21	)	)	PUNCT
ejpam-5831	127	1	:	:	PUNCT
ejpam-5831	127	2	p	p	X
ejpam-5831	127	3	(	(	PUNCT
ejpam-5831	127	4	x	x	NOUN
ejpam-5831	127	5	)	)	PUNCT
ejpam-5831	127	6	→	→	SYM
ejpam-5831	127	7	p	p	X
ejpam-5831	127	8	(	(	PUNCT
ejpam-5831	127	9	x	x	NOUN
ejpam-5831	127	10	)	)	PUNCT
ejpam-5831	127	11	defined	define	VERB
ejpam-5831	127	12	by	by	ADP
ejpam-5831	127	13	γd(a1	γd(a1	PRON
ejpam-5831	127	14	)	)	PUNCT
ejpam-5831	127	15	=	=	PRON
ejpam-5831	127	16	{	{	PUNCT
ejpam-5831	127	17	x	x	PUNCT
ejpam-5831	127	18	∈	∈	NOUN
ejpam-5831	127	19	x	x	X
ejpam-5831	127	20	:	:	PUNCT
ejpam-5831	127	21	r(x	r(x	NOUN
ejpam-5831	127	22	)	)	PUNCT
ejpam-5831	127	23	∩	∩	NOUN
ejpam-5831	127	24	a1	a1	NOUN
ejpam-5831	127	25	̸=	̸=	PROPN
ejpam-5831	127	26	∅	∅	NOUN
ejpam-5831	127	27	}	}	PUNCT
ejpam-5831	127	28	∪	∪	ADJ
ejpam-5831	127	29	a1	a1	NOUN
ejpam-5831	127	30	,	,	PUNCT
ejpam-5831	127	31	∀a1	∀a1	X
ejpam-5831	127	32	⊆	⊆	NUM
ejpam-5831	127	33	x.	x.	NOUN
ejpam-5831	127	34	then	then	ADV
ejpam-5831	127	35	γd	γd	ADP
ejpam-5831	127	36	(	(	PUNCT
ejpam-5831	127	37	.	.	PUNCT
ejpam-5831	127	38	)	)	PUNCT
ejpam-5831	127	39	is	be	AUX
ejpam-5831	127	40	called	call	VERB
ejpam-5831	127	41	pseudo	pseudo	NOUN
ejpam-5831	127	42	closure	closure	NOUN
ejpam-5831	127	43	if	if	SCONJ
ejpam-5831	127	44	the	the	DET
ejpam-5831	127	45	following	follow	VERB
ejpam-5831	127	46	properties	property	NOUN
ejpam-5831	127	47	are	be	AUX
ejpam-5831	127	48	hold	hold	ADJ
ejpam-5831	127	49	:	:	PUNCT
ejpam-5831	127	50	i.	i.	NOUN
ejpam-5831	127	51	γd(∅	γd(∅	PROPN
ejpam-5831	127	52	)	)	PUNCT
ejpam-5831	127	53	=	=	NOUN
ejpam-5831	127	54	∅	∅	NOUN
ejpam-5831	127	55	,	,	PUNCT
ejpam-5831	127	56	ii	ii	PROPN
ejpam-5831	127	57	.	.	PUNCT
ejpam-5831	127	58	∀a1	∀a1	PROPN
ejpam-5831	127	59	⊆	⊆	NUM
ejpam-5831	127	60	x	x	NOUN
ejpam-5831	127	61	,	,	PUNCT
ejpam-5831	127	62	a1	a1	VERB
ejpam-5831	127	63	⊆	⊆	NUM
ejpam-5831	127	64	γd(a1	γd(a1	NOUN
ejpam-5831	127	65	)	)	PUNCT
ejpam-5831	127	66	,	,	PUNCT
ejpam-5831	127	67	hence	hence	ADV
ejpam-5831	127	68	(	(	PUNCT
ejpam-5831	127	69	x	x	X
ejpam-5831	127	70	,	,	PUNCT
ejpam-5831	127	71	γd	γd	NOUN
ejpam-5831	127	72	)	)	PUNCT
ejpam-5831	127	73	is	be	AUX
ejpam-5831	127	74	called	call	VERB
ejpam-5831	127	75	pretopological	pretopological	ADJ
ejpam-5831	127	76	space	space	NOUN
ejpam-5831	127	77	definition	definition	NOUN
ejpam-5831	127	78	3.2	3.2	NUM
ejpam-5831	127	79	.	.	PUNCT
ejpam-5831	128	1	consider	consider	VERB
ejpam-5831	128	2	(	(	PUNCT
ejpam-5831	128	3	x	x	NOUN
ejpam-5831	128	4	,	,	PUNCT
ejpam-5831	128	5	γd	γd	NOUN
ejpam-5831	128	6	)	)	PUNCT
ejpam-5831	128	7	is	be	AUX
ejpam-5831	128	8	pretopological	pretopological	ADJ
ejpam-5831	128	9	space	space	NOUN
ejpam-5831	128	10	.	.	PUNCT
ejpam-5831	129	1	suppose	suppose	VERB
ejpam-5831	129	2	that	that	SCONJ
ejpam-5831	129	3	i	i	PROPN
ejpam-5831	129	4	d	d	PROPN
ejpam-5831	129	5	(	(	PUNCT
ejpam-5831	129	6	.	.	PUNCT
ejpam-5831	129	7	)	)	PUNCT
ejpam-5831	129	8	:	:	PUNCT
ejpam-5831	130	1	p	p	X
ejpam-5831	130	2	(	(	PUNCT
ejpam-5831	130	3	x	x	NOUN
ejpam-5831	130	4	)	)	PUNCT
ejpam-5831	130	5	→	→	SYM
ejpam-5831	130	6	p	p	X
ejpam-5831	130	7	(	(	PUNCT
ejpam-5831	130	8	x	x	NOUN
ejpam-5831	130	9	)	)	PUNCT
ejpam-5831	130	10	defined	define	VERB
ejpam-5831	130	11	by	by	ADP
ejpam-5831	130	12	id(a1	id(a1	NOUN
ejpam-5831	130	13	)	)	PUNCT
ejpam-5831	130	14	=	=	PRON
ejpam-5831	130	15	{	{	PUNCT
ejpam-5831	130	16	x	x	PUNCT
ejpam-5831	130	17	∈	∈	PROPN
ejpam-5831	130	18	x	x	X
ejpam-5831	130	19	:	:	PUNCT
ejpam-5831	130	20	r(x)∩a1	r(x)∩a1	PROPN
ejpam-5831	130	21	̸=	̸=	PROPN
ejpam-5831	130	22	∅	∅	NOUN
ejpam-5831	130	23	}	}	PUNCT
ejpam-5831	130	24	,	,	PUNCT
ejpam-5831	130	25	∀a1	∀a1	PROPN
ejpam-5831	130	26	⊆	⊆	NUM
ejpam-5831	130	27	x.	x.	NOUN
ejpam-5831	130	28	then	then	ADV
ejpam-5831	130	29	i	i	PROPN
ejpam-5831	130	30	d	d	PROPN
ejpam-5831	130	31	(	(	PUNCT
ejpam-5831	130	32	.	.	PUNCT
ejpam-5831	130	33	)	)	PUNCT
ejpam-5831	130	34	is	be	AUX
ejpam-5831	130	35	called	call	VERB
ejpam-5831	130	36	interior	interior	ADJ
ejpam-5831	130	37	function	function	NOUN
ejpam-5831	130	38	if	if	SCONJ
ejpam-5831	130	39	the	the	DET
ejpam-5831	130	40	following	follow	VERB
ejpam-5831	130	41	properties	property	NOUN
ejpam-5831	130	42	are	be	AUX
ejpam-5831	130	43	hold	hold	ADJ
ejpam-5831	130	44	:	:	PUNCT
ejpam-5831	130	45	i.	i.	NOUN
ejpam-5831	130	46	id(∅	id(∅	ADV
ejpam-5831	130	47	)	)	PUNCT
ejpam-5831	130	48	=	=	SYM
ejpam-5831	130	49	∅	∅	NOUN
ejpam-5831	130	50	,	,	PUNCT
ejpam-5831	130	51	ii	ii	PROPN
ejpam-5831	130	52	.	.	PUNCT
ejpam-5831	130	53	∀a1	∀a1	PROPN
ejpam-5831	130	54	⊆	⊆	NUM
ejpam-5831	130	55	x	x	NOUN
ejpam-5831	130	56	,	,	PUNCT
ejpam-5831	130	57	id(a1	id(a1	NOUN
ejpam-5831	130	58	)	)	PUNCT
ejpam-5831	130	59	⊆	⊆	NUM
ejpam-5831	130	60	a1	a1	NOUN
ejpam-5831	130	61	,	,	PUNCT
ejpam-5831	130	62	the	the	DET
ejpam-5831	130	63	pretopological	pretopological	ADJ
ejpam-5831	130	64	space	space	NOUN
ejpam-5831	130	65	,	,	PUNCT
ejpam-5831	130	66	represented	represent	VERB
ejpam-5831	130	67	by	by	ADP
ejpam-5831	130	68	γd	γd	ADP
ejpam-5831	130	69	;	;	PUNCT
ejpam-5831	130	70	i	i	PROPN
ejpam-5831	130	71	d	d	PROPN
ejpam-5831	130	72	,	,	PUNCT
ejpam-5831	130	73	is	be	AUX
ejpam-5831	130	74	created	create	VERB
ejpam-5831	130	75	from	from	ADP
ejpam-5831	130	76	the	the	DET
ejpam-5831	130	77	pseudo	pseudo	NOUN
ejpam-5831	130	78	-	-	NOUN
ejpam-5831	130	79	closure	closure	NOUN
ejpam-5831	130	80	function	function	NOUN
ejpam-5831	130	81	that	that	PRON
ejpam-5831	130	82	depends	depend	VERB
ejpam-5831	130	83	on	on	ADP
ejpam-5831	130	84	r(x	r(x	PROPN
ejpam-5831	130	85	)	)	PUNCT
ejpam-5831	130	86	and	and	CCONJ
ejpam-5831	130	87	is	be	AUX
ejpam-5831	130	88	called	call	VERB
ejpam-5831	130	89	the	the	DET
ejpam-5831	130	90	pseudo	pseudo	NOUN
ejpam-5831	130	91	-	-	NOUN
ejpam-5831	130	92	closure	closure	NOUN
ejpam-5831	130	93	of	of	ADP
ejpam-5831	130	94	descendants	descendant	NOUN
ejpam-5831	130	95	.	.	PUNCT
ejpam-5831	131	1	likewise	likewise	ADV
ejpam-5831	131	2	,	,	PUNCT
ejpam-5831	131	3	we	we	PRON
ejpam-5831	131	4	refer	refer	VERB
ejpam-5831	131	5	to	to	ADP
ejpam-5831	131	6	the	the	DET
ejpam-5831	131	7	pretopological	pretopological	ADJ
ejpam-5831	131	8	space	space	NOUN
ejpam-5831	131	9	,	,	PUNCT
ejpam-5831	131	10	represented	represent	VERB
ejpam-5831	131	11	by	by	ADP
ejpam-5831	131	12	γa	γa	PROPN
ejpam-5831	131	13	;	;	PUNCT
ejpam-5831	131	14	ia	ia	PROPN
ejpam-5831	131	15	,	,	PUNCT
ejpam-5831	131	16	that	that	PRON
ejpam-5831	131	17	is	be	AUX
ejpam-5831	131	18	produced	produce	VERB
ejpam-5831	131	19	by	by	ADP
ejpam-5831	131	20	the	the	DET
ejpam-5831	131	21	pseudoclosure	pseudoclosure	ADJ
ejpam-5831	131	22	function	function	NOUN
ejpam-5831	131	23	based	base	VERB
ejpam-5831	131	24	on	on	ADP
ejpam-5831	131	25	r−1(x	r−1(x	NOUN
ejpam-5831	131	26	)	)	PUNCT
ejpam-5831	131	27	by	by	ADP
ejpam-5831	131	28	pseudo	pseudo	NOUN
ejpam-5831	131	29	-	-	NOUN
ejpam-5831	131	30	closure	closure	NOUN
ejpam-5831	131	31	of	of	ADP
ejpam-5831	131	32	ascendants	ascendant	NOUN
ejpam-5831	131	33	.	.	PUNCT
ejpam-5831	132	1	definition	definition	NOUN
ejpam-5831	132	2	3.3	3.3	NUM
ejpam-5831	132	3	.	.	PUNCT
ejpam-5831	132	4	suppose	suppose	VERB
ejpam-5831	132	5	that	that	SCONJ
ejpam-5831	132	6	(	(	PUNCT
ejpam-5831	132	7	x	x	NOUN
ejpam-5831	132	8	,	,	PUNCT
ejpam-5831	132	9	γd	γd	NOUN
ejpam-5831	132	10	)	)	PUNCT
ejpam-5831	132	11	is	be	AUX
ejpam-5831	132	12	pretopological	pretopological	ADJ
ejpam-5831	132	13	space	space	NOUN
ejpam-5831	132	14	.	.	PUNCT
ejpam-5831	133	1	then	then	ADV
ejpam-5831	133	2	,	,	PUNCT
ejpam-5831	133	3	we	we	PRON
ejpam-5831	133	4	define	define	VERB
ejpam-5831	133	5	the	the	DET
ejpam-5831	133	6	pretopological	pretopological	ADJ
ejpam-5831	133	7	lapprs	lapprs	ADJ
ejpam-5831	133	8	and	and	CCONJ
ejpam-5831	133	9	pretopological	pretopological	ADJ
ejpam-5831	133	10	uapprs	uapprs	NOUN
ejpam-5831	133	11	of	of	ADP
ejpam-5831	133	12	a	a	DET
ejpam-5831	133	13	subset	subset	NOUN
ejpam-5831	133	14	a	a	DET
ejpam-5831	133	15	⊆	⊆	NUM
ejpam-5831	133	16	x	x	SYM
ejpam-5831	133	17	as	as	ADP
ejpam-5831	133	18	the	the	DET
ejpam-5831	133	19	following	following	NOUN
ejpam-5831	133	20	:	:	PUNCT
ejpam-5831	133	21	id(a	id(a	NOUN
ejpam-5831	133	22	)	)	PUNCT
ejpam-5831	133	23	=	=	SYM
ejpam-5831	133	24	{	{	PUNCT
ejpam-5831	133	25	x	x	PUNCT
ejpam-5831	133	26	∈	∈	NOUN
ejpam-5831	133	27	x	x	X
ejpam-5831	133	28	:	:	PUNCT
ejpam-5831	133	29	r(x	r(x	NOUN
ejpam-5831	133	30	)	)	PUNCT
ejpam-5831	134	1	⊆	⊆	NUM
ejpam-5831	134	2	a	a	PRON
ejpam-5831	134	3	}	}	PUNCT
ejpam-5831	134	4	,	,	PUNCT
ejpam-5831	134	5	∀a	∀a	VERB
ejpam-5831	134	6	⊆	⊆	NUM
ejpam-5831	134	7	x	x	SYM
ejpam-5831	134	8	γd(a	γd(a	X
ejpam-5831	134	9	)	)	PUNCT
ejpam-5831	134	10	=	=	PRON
ejpam-5831	134	11	{	{	PUNCT
ejpam-5831	134	12	x	x	PUNCT
ejpam-5831	134	13	∈	∈	NOUN
ejpam-5831	134	14	x	x	X
ejpam-5831	134	15	:	:	PUNCT
ejpam-5831	134	16	r(x	r(x	NOUN
ejpam-5831	134	17	)	)	PUNCT
ejpam-5831	134	18	∩a	∩a	PROPN
ejpam-5831	134	19	̸=	̸=	PROPN
ejpam-5831	134	20	∅	∅	NOUN
ejpam-5831	134	21	}	}	PUNCT
ejpam-5831	134	22	∪a	∪a	NUM
ejpam-5831	134	23	,	,	PUNCT
ejpam-5831	134	24	∀a	∀a	VERB
ejpam-5831	134	25	⊆	⊆	NUM
ejpam-5831	134	26	x	x	X
ejpam-5831	134	27	ia(a	ia(a	NOUN
ejpam-5831	134	28	)	)	PUNCT
ejpam-5831	134	29	=	=	PRON
ejpam-5831	134	30	{	{	PUNCT
ejpam-5831	134	31	x	x	PUNCT
ejpam-5831	134	32	∈	∈	NOUN
ejpam-5831	134	33	x	x	X
ejpam-5831	134	34	:	:	PUNCT
ejpam-5831	134	35	r−1(x	r−1(x	NOUN
ejpam-5831	134	36	)	)	PUNCT
ejpam-5831	134	37	⊆	⊆	X
ejpam-5831	134	38	a	a	PRON
ejpam-5831	134	39	}	}	PUNCT
ejpam-5831	134	40	,	,	PUNCT
ejpam-5831	134	41	∀a	∀a	VERB
ejpam-5831	134	42	⊆	⊆	NUM
ejpam-5831	134	43	x	x	X
ejpam-5831	134	44	γa(a	γa(a	NUM
ejpam-5831	134	45	)	)	PUNCT
ejpam-5831	134	46	=	=	PRON
ejpam-5831	135	1	{	{	PUNCT
ejpam-5831	135	2	x	x	PUNCT
ejpam-5831	135	3	∈	∈	NOUN
ejpam-5831	135	4	x	x	X
ejpam-5831	135	5	:	:	PUNCT
ejpam-5831	135	6	r−1(x	r−1(x	ADJ
ejpam-5831	135	7	)	)	PUNCT
ejpam-5831	135	8	∩a	∩a	PROPN
ejpam-5831	135	9	̸=	̸=	PROPN
ejpam-5831	135	10	∅	∅	NOUN
ejpam-5831	135	11	}	}	PUNCT
ejpam-5831	135	12	∪a	∪a	NUM
ejpam-5831	135	13	,	,	PUNCT
ejpam-5831	135	14	∀a	∀a	VERB
ejpam-5831	135	15	⊆	⊆	NUM
ejpam-5831	135	16	x.	x.	NOUN
ejpam-5831	135	17	the	the	DET
ejpam-5831	135	18	approximation	approximation	NOUN
ejpam-5831	135	19	structure	structure	NOUN
ejpam-5831	135	20	(	(	PUNCT
ejpam-5831	135	21	x	x	NOUN
ejpam-5831	135	22	,	,	PUNCT
ejpam-5831	135	23	r	r	NOUN
ejpam-5831	135	24	)	)	PUNCT
ejpam-5831	135	25	is	be	AUX
ejpam-5831	135	26	called	call	VERB
ejpam-5831	135	27	pretopological	pretopological	ADJ
ejpam-5831	135	28	approximation	approximation	NOUN
ejpam-5831	135	29	space	space	NOUN
ejpam-5831	135	30	.	.	PUNCT
ejpam-5831	136	1	definition	definition	NOUN
ejpam-5831	136	2	3.4	3.4	NUM
ejpam-5831	136	3	.	.	PUNCT
ejpam-5831	136	4	assume	assume	VERB
ejpam-5831	136	5	that	that	SCONJ
ejpam-5831	136	6	(	(	PUNCT
ejpam-5831	136	7	x	x	X
ejpam-5831	136	8	,	,	PUNCT
ejpam-5831	136	9	r	r	NOUN
ejpam-5831	136	10	)	)	PUNCT
ejpam-5831	136	11	is	be	AUX
ejpam-5831	136	12	a	a	DET
ejpam-5831	136	13	pretopological	pretopological	ADJ
ejpam-5831	136	14	approximation	approximation	NOUN
ejpam-5831	136	15	structure	structure	NOUN
ejpam-5831	136	16	.	.	PUNCT
ejpam-5831	137	1	then	then	ADV
ejpam-5831	137	2	∀a	∀a	VERB
ejpam-5831	137	3	⊆	⊆	NUM
ejpam-5831	137	4	x	x	SYM
ejpam-5831	137	5	:	:	PUNCT
ejpam-5831	137	6	i.	i.	NOUN
ejpam-5831	137	7	if	if	SCONJ
ejpam-5831	137	8	a	a	DET
ejpam-5831	137	9	⊆	⊆	NUM
ejpam-5831	137	10	γa(id(a	γa(id(a	X
ejpam-5831	137	11	)	)	PUNCT
ejpam-5831	137	12	)	)	PUNCT
ejpam-5831	137	13	,	,	PUNCT
ejpam-5831	137	14	then	then	ADV
ejpam-5831	137	15	a	a	PRON
ejpam-5831	137	16	is	be	AUX
ejpam-5831	137	17	semi	semi	ADV
ejpam-5831	137	18	rough	rough	ADJ
ejpam-5831	137	19	(	(	PUNCT
ejpam-5831	137	20	sad	sad	ADJ
ejpam-5831	137	21	-	-	PUNCT
ejpam-5831	137	22	rough	rough	ADJ
ejpam-5831	137	23	)	)	PUNCT
ejpam-5831	137	24	,	,	PUNCT
ejpam-5831	137	25	ii	ii	PROPN
ejpam-5831	137	26	.	.	PUNCT
ejpam-5831	138	1	if	if	SCONJ
ejpam-5831	138	2	a	a	DET
ejpam-5831	138	3	⊆	⊆	NUM
ejpam-5831	138	4	γd(ia(a	γd(ia(a	NUM
ejpam-5831	138	5	)	)	PUNCT
ejpam-5831	138	6	)	)	PUNCT
ejpam-5831	138	7	,	,	PUNCT
ejpam-5831	138	8	then	then	ADV
ejpam-5831	138	9	a	a	PRON
ejpam-5831	138	10	is	be	AUX
ejpam-5831	138	11	prerough	prerough	NOUN
ejpam-5831	138	12	(	(	PUNCT
ejpam-5831	138	13	pad	pad	NOUN
ejpam-5831	138	14	-	-	PUNCT
ejpam-5831	138	15	rough	rough	NOUN
ejpam-5831	138	16	)	)	PUNCT
ejpam-5831	138	17	,	,	PUNCT
ejpam-5831	138	18	iii	iii	X
ejpam-5831	138	19	.	.	PUNCT
ejpam-5831	139	1	if	if	SCONJ
ejpam-5831	139	2	a	a	DET
ejpam-5831	139	3	⊆	⊆	NUM
ejpam-5831	139	4	γa(id(γa(a	γa(id(γa(a	PROPN
ejpam-5831	139	5	)	)	PUNCT
ejpam-5831	139	6	)	)	PUNCT
ejpam-5831	139	7	)	)	PUNCT
ejpam-5831	139	8	,	,	PUNCT
ejpam-5831	139	9	then	then	ADV
ejpam-5831	139	10	a	a	PRON
ejpam-5831	139	11	is	be	AUX
ejpam-5831	139	12	semi	semi	ADJ
ejpam-5831	139	13	-	-	ADJ
ejpam-5831	139	14	prerough	prerough	ADJ
ejpam-5831	139	15	(	(	PUNCT
ejpam-5831	139	16	βad	βad	NOUN
ejpam-5831	139	17	-	-	PUNCT
ejpam-5831	139	18	rough	rough	NOUN
ejpam-5831	139	19	)	)	PUNCT
ejpam-5831	139	20	,	,	PUNCT
ejpam-5831	140	1	a.	a.	NOUN
ejpam-5831	140	2	a.	a.	NOUN
ejpam-5831	140	3	azza	azza	PROPN
ejpam-5831	140	4	et	et	PROPN
ejpam-5831	140	5	al	al	PROPN
ejpam-5831	140	6	.	.	PUNCT
ejpam-5831	140	7	/	/	SYM
ejpam-5831	140	8	eur	eur	PROPN
ejpam-5831	140	9	.	.	PUNCT
ejpam-5831	141	1	j.	j.	PROPN
ejpam-5831	141	2	pure	pure	PROPN
ejpam-5831	141	3	appl	appl	PROPN
ejpam-5831	141	4	.	.	PROPN
ejpam-5831	141	5	math	math	PROPN
ejpam-5831	141	6	,	,	PUNCT
ejpam-5831	141	7	18	18	NUM
ejpam-5831	141	8	(	(	PUNCT
ejpam-5831	141	9	2	2	NUM
ejpam-5831	141	10	)	)	PUNCT
ejpam-5831	141	11	(	(	PUNCT
ejpam-5831	141	12	2025	2025	NUM
ejpam-5831	141	13	)	)	PUNCT
ejpam-5831	141	14	,	,	PUNCT
ejpam-5831	141	15	5831	5831	NUM
ejpam-5831	141	16	6	6	NUM
ejpam-5831	141	17	of	of	ADP
ejpam-5831	141	18	11	11	NUM
ejpam-5831	141	19	iv	iv	NUM
ejpam-5831	141	20	.	.	PUNCT
ejpam-5831	142	1	if	if	SCONJ
ejpam-5831	142	2	a	a	DET
ejpam-5831	142	3	⊆	⊆	NUM
ejpam-5831	142	4	id(γa(id(a	id(γa(id(a	NOUN
ejpam-5831	142	5	)	)	PUNCT
ejpam-5831	142	6	)	)	PUNCT
ejpam-5831	142	7	)	)	PUNCT
ejpam-5831	142	8	,	,	PUNCT
ejpam-5831	142	9	then	then	ADV
ejpam-5831	142	10	a	a	PRON
ejpam-5831	142	11	is	be	AUX
ejpam-5831	142	12	α	α	NOUN
ejpam-5831	142	13	-	-	ADJ
ejpam-5831	142	14	rough	rough	ADJ
ejpam-5831	142	15	(	(	PUNCT
ejpam-5831	142	16	αad	αad	NOUN
ejpam-5831	142	17	-	-	ADJ
ejpam-5831	142	18	rough	rough	ADJ
ejpam-5831	142	19	)	)	PUNCT
ejpam-5831	142	20	,	,	PUNCT
ejpam-5831	143	1	v.	v.	CCONJ
ejpam-5831	143	2	if	if	SCONJ
ejpam-5831	143	3	a	a	DET
ejpam-5831	143	4	⊆	⊆	NUM
ejpam-5831	143	5	γa(id(a	γa(id(a	X
ejpam-5831	143	6	)	)	PUNCT
ejpam-5831	143	7	)	)	PUNCT
ejpam-5831	144	1	∪	∪	ADP
ejpam-5831	144	2	id(γa(a	id(γa(a	NOUN
ejpam-5831	144	3	)	)	PUNCT
ejpam-5831	144	4	)	)	PUNCT
ejpam-5831	144	5	,	,	PUNCT
ejpam-5831	144	6	then	then	ADV
ejpam-5831	144	7	a	a	PRON
ejpam-5831	144	8	is	be	AUX
ejpam-5831	144	9	γ	γ	X
ejpam-5831	144	10	-	-	ADJ
ejpam-5831	144	11	rough	rough	ADJ
ejpam-5831	144	12	(	(	PUNCT
ejpam-5831	144	13	γad	γad	NOUN
ejpam-5831	144	14	-	-	PUNCT
ejpam-5831	144	15	rough	rough	ADJ
ejpam-5831	144	16	)	)	PUNCT
ejpam-5831	144	17	.	.	PUNCT
ejpam-5831	145	1	in	in	ADP
ejpam-5831	145	2	the	the	DET
ejpam-5831	145	3	pretopological	pretopological	ADJ
ejpam-5831	145	4	approximation	approximation	NOUN
ejpam-5831	145	5	space	space	NOUN
ejpam-5831	145	6	(	(	PUNCT
ejpam-5831	145	7	x	x	X
ejpam-5831	145	8	,	,	PUNCT
ejpam-5831	145	9	r	r	NOUN
ejpam-5831	145	10	)	)	PUNCT
ejpam-5831	145	11	,	,	PUNCT
ejpam-5831	145	12	the	the	DET
ejpam-5831	145	13	set	set	ADJ
ejpam-5831	145	14	family	family	NOUN
ejpam-5831	145	15	of	of	ADP
ejpam-5831	145	16	all	all	DET
ejpam-5831	145	17	sad	sad	ADJ
ejpam-5831	145	18	-	-	ADJ
ejpam-5831	145	19	rough	rough	ADJ
ejpam-5831	145	20	(	(	PUNCT
ejpam-5831	145	21	resp	resp	NOUN
ejpam-5831	145	22	.	.	PUNCT
ejpam-5831	146	1	pad	pad	NOUN
ejpam-5831	146	2	-	-	PUNCT
ejpam-5831	146	3	rough	rough	ADJ
ejpam-5831	146	4	,	,	PUNCT
ejpam-5831	146	5	βad	βad	NOUN
ejpam-5831	146	6	-	-	PUNCT
ejpam-5831	146	7	rough	rough	ADJ
ejpam-5831	146	8	,	,	PUNCT
ejpam-5831	146	9	αad	αad	NOUN
ejpam-5831	146	10	-	-	ADJ
ejpam-5831	146	11	rough	rough	ADJ
ejpam-5831	146	12	and	and	CCONJ
ejpam-5831	146	13	γad	γad	NOUN
ejpam-5831	146	14	-	-	PUNCT
ejpam-5831	146	15	rough	rough	ADJ
ejpam-5831	146	16	)	)	PUNCT
ejpam-5831	146	17	is	be	AUX
ejpam-5831	146	18	denoted	denote	VERB
ejpam-5831	146	19	by	by	ADP
ejpam-5831	146	20	fsad(x)(resp	fsad(x)(resp	PROPN
ejpam-5831	146	21	.	.	PUNCT
ejpam-5831	147	1	fpad(x	fpad(x	VERB
ejpam-5831	147	2	)	)	PUNCT
ejpam-5831	147	3	,	,	PUNCT
ejpam-5831	147	4	fβad(x	fβad(x	NOUN
ejpam-5831	147	5	)	)	PUNCT
ejpam-5831	147	6	,	,	PUNCT
ejpam-5831	147	7	fαad(x	fαad(x	NOUN
ejpam-5831	147	8	)	)	PUNCT
ejpam-5831	147	9	,	,	PUNCT
ejpam-5831	147	10	and	and	CCONJ
ejpam-5831	147	11	fγad(x	fγad(x	NOUN
ejpam-5831	147	12	)	)	PUNCT
ejpam-5831	147	13	)	)	PUNCT
ejpam-5831	147	14	.	.	PUNCT
ejpam-5831	148	1	the	the	DET
ejpam-5831	148	2	complement	complement	NOUN
ejpam-5831	148	3	of	of	ADP
ejpam-5831	148	4	the	the	DET
ejpam-5831	148	5	sets	set	NOUN
ejpam-5831	148	6	sad(x)(resp	sad(x)(resp	PROPN
ejpam-5831	148	7	.	.	PUNCT
ejpam-5831	148	8	pad(x	pad(x	PROPN
ejpam-5831	148	9	)	)	PUNCT
ejpam-5831	148	10	,	,	PUNCT
ejpam-5831	148	11	βad(x	βad(x	PUNCT
ejpam-5831	148	12	)	)	PUNCT
ejpam-5831	148	13	,	,	PUNCT
ejpam-5831	148	14	αad(x	αad(x	NOUN
ejpam-5831	148	15	)	)	PUNCT
ejpam-5831	148	16	,	,	PUNCT
ejpam-5831	148	17	and	and	CCONJ
ejpam-5831	148	18	γad(x	γad(x	NOUN
ejpam-5831	148	19	)	)	PUNCT
ejpam-5831	148	20	)	)	PUNCT
ejpam-5831	148	21	in	in	ADP
ejpam-5831	148	22	(	(	PUNCT
ejpam-5831	148	23	x	x	NOUN
ejpam-5831	148	24	,	,	PUNCT
ejpam-5831	148	25	r	r	NOUN
ejpam-5831	148	26	)	)	PUNCT
ejpam-5831	148	27	is	be	AUX
ejpam-5831	148	28	called	call	VERB
ejpam-5831	148	29	sc	sc	PROPN
ejpam-5831	148	30	ad	ad	NOUN
ejpam-5831	148	31	-	-	PUNCT
ejpam-5831	148	32	rough	rough	ADJ
ejpam-5831	148	33	(	(	PUNCT
ejpam-5831	148	34	resp	resp	NOUN
ejpam-5831	148	35	.	.	PUNCT
ejpam-5831	149	1	p	p	NOUN
ejpam-5831	149	2	c	c	NOUN
ejpam-5831	149	3	ad	ad	NOUN
ejpam-5831	149	4	-	-	PUNCT
ejpam-5831	149	5	rough	rough	ADJ
ejpam-5831	149	6	,	,	PUNCT
ejpam-5831	149	7	βc	βc	INTJ
ejpam-5831	149	8	ad	ad	NOUN
ejpam-5831	149	9	-	-	PUNCT
ejpam-5831	149	10	rough	rough	ADJ
ejpam-5831	149	11	,	,	PUNCT
ejpam-5831	149	12	αc	αc	NOUN
ejpam-5831	149	13	ad	ad	NOUN
ejpam-5831	149	14	-	-	PUNCT
ejpam-5831	149	15	rough	rough	ADJ
ejpam-5831	149	16	and	and	CCONJ
ejpam-5831	149	17	γcad	γcad	NOUN
ejpam-5831	149	18	-	-	PUNCT
ejpam-5831	149	19	rough	rough	NOUN
ejpam-5831	149	20	)	)	PUNCT
ejpam-5831	149	21	and	and	CCONJ
ejpam-5831	149	22	is	be	AUX
ejpam-5831	149	23	denoted	denote	VERB
ejpam-5831	149	24	by	by	ADP
ejpam-5831	149	25	fsc	fsc	PROPN
ejpam-5831	149	26	ad	ad	NOUN
ejpam-5831	149	27	-	-	PUNCT
ejpam-5831	149	28	rough	rough	ADJ
ejpam-5831	149	29	(	(	PUNCT
ejpam-5831	149	30	resp	resp	NOUN
ejpam-5831	149	31	.	.	PUNCT
ejpam-5831	150	1	fp	fp	PROPN
ejpam-5831	150	2	c	c	NOUN
ejpam-5831	150	3	ad	ad	NOUN
ejpam-5831	150	4	-	-	PUNCT
ejpam-5831	150	5	rough	rough	ADJ
ejpam-5831	150	6	,	,	PUNCT
ejpam-5831	150	7	fβc	fβc	ADJ
ejpam-5831	150	8	ad	ad	NOUN
ejpam-5831	150	9	-	-	PUNCT
ejpam-5831	150	10	rough	rough	ADJ
ejpam-5831	150	11	,	,	PUNCT
ejpam-5831	150	12	fαc	fαc	X
ejpam-5831	150	13	ad	ad	NOUN
ejpam-5831	150	14	-	-	PUNCT
ejpam-5831	150	15	rough	rough	ADJ
ejpam-5831	150	16	and	and	CCONJ
ejpam-5831	150	17	fγcad	fγcad	NOUN
ejpam-5831	150	18	-	-	PUNCT
ejpam-5831	150	19	rough	rough	ADJ
ejpam-5831	150	20	)	)	PUNCT
ejpam-5831	150	21	.	.	PUNCT
ejpam-5831	151	1	proposition	proposition	NOUN
ejpam-5831	151	2	3.1	3.1	NUM
ejpam-5831	151	3	.	.	PUNCT
ejpam-5831	152	1	if	if	SCONJ
ejpam-5831	152	2	(	(	PUNCT
ejpam-5831	152	3	x	x	NOUN
ejpam-5831	152	4	,	,	PUNCT
ejpam-5831	152	5	r	r	NOUN
ejpam-5831	152	6	)	)	PUNCT
ejpam-5831	152	7	is	be	AUX
ejpam-5831	152	8	a	a	DET
ejpam-5831	152	9	pretopological	pretopological	ADJ
ejpam-5831	152	10	approximation	approximation	NOUN
ejpam-5831	152	11	structure	structure	NOUN
ejpam-5831	152	12	.	.	PUNCT
ejpam-5831	153	1	then	then	ADV
ejpam-5831	153	2	,	,	PUNCT
ejpam-5831	153	3	the	the	DET
ejpam-5831	153	4	following	follow	VERB
ejpam-5831	153	5	properties	property	NOUN
ejpam-5831	153	6	are	be	AUX
ejpam-5831	153	7	satisfied	satisfied	ADJ
ejpam-5831	153	8	:	:	PUNCT
ejpam-5831	153	9	i.	i.	PROPN
ejpam-5831	153	10	fαad(x	fαad(x	PROPN
ejpam-5831	153	11	)	)	PUNCT
ejpam-5831	153	12	⊆	⊆	NUM
ejpam-5831	153	13	fsad(x	fsad(x	NOUN
ejpam-5831	153	14	)	)	PUNCT
ejpam-5831	153	15	⊆	⊆	NUM
ejpam-5831	153	16	fγad(x	fγad(x	NOUN
ejpam-5831	153	17	)	)	PUNCT
ejpam-5831	153	18	⊆	⊆	NUM
ejpam-5831	153	19	fβad(x	fβad(x	NOUN
ejpam-5831	153	20	)	)	PUNCT
ejpam-5831	153	21	,	,	PUNCT
ejpam-5831	153	22	ii	ii	PROPN
ejpam-5831	153	23	.	.	PUNCT
ejpam-5831	154	1	fαad(x	fαad(x	NOUN
ejpam-5831	154	2	)	)	PUNCT
ejpam-5831	154	3	⊆	⊆	NUM
ejpam-5831	154	4	fpad(x	fpad(x	NOUN
ejpam-5831	154	5	)	)	PUNCT
ejpam-5831	154	6	⊆	⊆	NUM
ejpam-5831	154	7	fγad(x	fγad(x	NOUN
ejpam-5831	154	8	)	)	PUNCT
ejpam-5831	154	9	⊆	⊆	NUM
ejpam-5831	154	10	fβad(x	fβad(x	NOUN
ejpam-5831	154	11	)	)	PUNCT
ejpam-5831	154	12	,	,	PUNCT
ejpam-5831	154	13	proof	proof	NOUN
ejpam-5831	154	14	it	it	PRON
ejpam-5831	154	15	’s	’	VERB
ejpam-5831	154	16	clear	clear	ADJ
ejpam-5831	154	17	from	from	ADP
ejpam-5831	154	18	the	the	DET
ejpam-5831	154	19	above	above	ADJ
ejpam-5831	154	20	definition	definition	NOUN
ejpam-5831	154	21	.	.	PUNCT
ejpam-5831	155	1	□	□	PUNCT
ejpam-5831	155	2	example	example	NOUN
ejpam-5831	155	3	3.1	3.1	NUM
ejpam-5831	155	4	.	.	PUNCT
ejpam-5831	156	1	consider	consider	VERB
ejpam-5831	156	2	x	x	PUNCT
ejpam-5831	156	3	=	=	PRON
ejpam-5831	156	4	{	{	PUNCT
ejpam-5831	156	5	a	a	DET
ejpam-5831	156	6	,	,	PUNCT
ejpam-5831	156	7	b	b	NOUN
ejpam-5831	156	8	,	,	PUNCT
ejpam-5831	156	9	c	c	NOUN
ejpam-5831	156	10	,	,	PUNCT
ejpam-5831	156	11	d	d	NOUN
ejpam-5831	156	12	}	}	PUNCT
ejpam-5831	156	13	is	be	AUX
ejpam-5831	156	14	the	the	DET
ejpam-5831	156	15	universe	universe	NOUN
ejpam-5831	156	16	set	set	NOUN
ejpam-5831	156	17	.	.	PUNCT
ejpam-5831	157	1	suppose	suppose	VERB
ejpam-5831	157	2	that	that	SCONJ
ejpam-5831	157	3	r	r	NOUN
ejpam-5831	157	4	is	be	AUX
ejpam-5831	157	5	a	a	DET
ejpam-5831	157	6	binary	binary	ADJ
ejpam-5831	157	7	relation	relation	NOUN
ejpam-5831	157	8	defined	define	VERB
ejpam-5831	157	9	on	on	ADP
ejpam-5831	157	10	x	x	PUNCT
ejpam-5831	157	11	by	by	ADP
ejpam-5831	157	12	r	r	NOUN
ejpam-5831	157	13	=	=	SYM
ejpam-5831	157	14	{	{	PUNCT
ejpam-5831	157	15	(	(	PUNCT
ejpam-5831	157	16	a	a	PRON
ejpam-5831	157	17	,	,	PUNCT
ejpam-5831	157	18	a	a	NOUN
ejpam-5831	157	19	)	)	PUNCT
ejpam-5831	157	20	,	,	PUNCT
ejpam-5831	157	21	(	(	PUNCT
ejpam-5831	157	22	a	a	DET
ejpam-5831	157	23	,	,	PUNCT
ejpam-5831	157	24	d	d	NOUN
ejpam-5831	157	25	)	)	PUNCT
ejpam-5831	157	26	,	,	PUNCT
ejpam-5831	157	27	(	(	PUNCT
ejpam-5831	157	28	a	a	DET
ejpam-5831	157	29	,	,	PUNCT
ejpam-5831	157	30	c	c	NOUN
ejpam-5831	157	31	)	)	PUNCT
ejpam-5831	157	32	,	,	PUNCT
ejpam-5831	157	33	(	(	PUNCT
ejpam-5831	157	34	b	b	X
ejpam-5831	157	35	,	,	PUNCT
ejpam-5831	157	36	b	b	NOUN
ejpam-5831	157	37	)	)	PUNCT
ejpam-5831	157	38	,	,	PUNCT
ejpam-5831	157	39	(	(	PUNCT
ejpam-5831	157	40	b	b	X
ejpam-5831	157	41	,	,	PUNCT
ejpam-5831	157	42	d	d	NOUN
ejpam-5831	157	43	)	)	PUNCT
ejpam-5831	157	44	,	,	PUNCT
ejpam-5831	157	45	(	(	PUNCT
ejpam-5831	157	46	c	c	X
ejpam-5831	157	47	,	,	PUNCT
ejpam-5831	157	48	d	d	NOUN
ejpam-5831	157	49	)	)	PUNCT
ejpam-5831	157	50	,	,	PUNCT
ejpam-5831	157	51	(	(	PUNCT
ejpam-5831	157	52	c	c	X
ejpam-5831	157	53	,	,	PUNCT
ejpam-5831	157	54	a	a	NOUN
ejpam-5831	157	55	)	)	PUNCT
ejpam-5831	157	56	,	,	PUNCT
ejpam-5831	157	57	(	(	PUNCT
ejpam-5831	157	58	c	c	X
ejpam-5831	157	59	,	,	PUNCT
ejpam-5831	157	60	b	b	NOUN
ejpam-5831	157	61	)	)	PUNCT
ejpam-5831	157	62	,	,	PUNCT
ejpam-5831	157	63	(	(	PUNCT
ejpam-5831	157	64	d	d	X
ejpam-5831	157	65	,	,	PUNCT
ejpam-5831	157	66	a	a	NOUN
ejpam-5831	157	67	)	)	PUNCT
ejpam-5831	157	68	}	}	PUNCT
ejpam-5831	157	69	.	.	PUNCT
ejpam-5831	158	1	hence	hence	ADV
ejpam-5831	158	2	r(a	r(a	X
ejpam-5831	158	3	)	)	PUNCT
ejpam-5831	159	1	=	=	PRON
ejpam-5831	159	2	{	{	PUNCT
ejpam-5831	159	3	a	a	X
ejpam-5831	159	4	,	,	PUNCT
ejpam-5831	159	5	c	c	NOUN
ejpam-5831	159	6	,	,	PUNCT
ejpam-5831	159	7	d	d	NOUN
ejpam-5831	159	8	}	}	PUNCT
ejpam-5831	159	9	,	,	PUNCT
ejpam-5831	159	10	r(b	r(b	PROPN
ejpam-5831	159	11	)	)	PUNCT
ejpam-5831	159	12	=	=	PUNCT
ejpam-5831	159	13	{	{	PUNCT
ejpam-5831	159	14	b	b	NOUN
ejpam-5831	159	15	,	,	PUNCT
ejpam-5831	159	16	d	d	NOUN
ejpam-5831	159	17	}	}	PUNCT
ejpam-5831	159	18	,	,	PUNCT
ejpam-5831	159	19	r(c	r(c	NUM
ejpam-5831	159	20	)	)	PUNCT
ejpam-5831	159	21	=	=	PRON
ejpam-5831	159	22	{	{	PUNCT
ejpam-5831	159	23	a	a	PRON
ejpam-5831	159	24	,	,	PUNCT
ejpam-5831	159	25	b	b	NOUN
ejpam-5831	159	26	,	,	PUNCT
ejpam-5831	159	27	d	d	NOUN
ejpam-5831	159	28	}	}	PUNCT
ejpam-5831	159	29	,	,	PUNCT
ejpam-5831	159	30	r(d	r(d	NOUN
ejpam-5831	159	31	)	)	PUNCT
ejpam-5831	159	32	=	=	PUNCT
ejpam-5831	159	33	{	{	PUNCT
ejpam-5831	159	34	a	a	NOUN
ejpam-5831	159	35	}	}	PUNCT
ejpam-5831	159	36	and	and	CCONJ
ejpam-5831	159	37	r−1(a	r−1(a	PROPN
ejpam-5831	159	38	)	)	PUNCT
ejpam-5831	160	1	=	=	PRON
ejpam-5831	160	2	{	{	PUNCT
ejpam-5831	160	3	a	a	X
ejpam-5831	160	4	,	,	PUNCT
ejpam-5831	160	5	c	c	NOUN
ejpam-5831	160	6	,	,	PUNCT
ejpam-5831	160	7	d	d	NOUN
ejpam-5831	160	8	}	}	PUNCT
ejpam-5831	160	9	,	,	PUNCT
ejpam-5831	160	10	r−1(b	r−1(b	PROPN
ejpam-5831	160	11	)	)	PUNCT
ejpam-5831	160	12	=	=	PUNCT
ejpam-5831	160	13	{	{	PUNCT
ejpam-5831	160	14	b	b	NOUN
ejpam-5831	160	15	,	,	PUNCT
ejpam-5831	160	16	c	c	NOUN
ejpam-5831	160	17	}	}	PUNCT
ejpam-5831	160	18	,	,	PUNCT
ejpam-5831	160	19	r−1(c	r−1(c	PROPN
ejpam-5831	160	20	)	)	PUNCT
ejpam-5831	160	21	=	=	PRON
ejpam-5831	161	1	{	{	PUNCT
ejpam-5831	161	2	a	a	NOUN
ejpam-5831	161	3	}	}	PUNCT
ejpam-5831	161	4	,	,	PUNCT
ejpam-5831	161	5	r−1(d	r−1(d	PROPN
ejpam-5831	161	6	)	)	PUNCT
ejpam-5831	162	1	=	=	PRON
ejpam-5831	162	2	{	{	PUNCT
ejpam-5831	162	3	a	a	DET
ejpam-5831	162	4	,	,	PUNCT
ejpam-5831	162	5	b	b	NOUN
ejpam-5831	162	6	,	,	PUNCT
ejpam-5831	162	7	c	c	NOUN
ejpam-5831	162	8	}	}	PUNCT
ejpam-5831	162	9	.	.	PUNCT
ejpam-5831	163	1	therefore	therefore	ADV
ejpam-5831	163	2	,	,	PUNCT
ejpam-5831	163	3	fsad(x	fsad(x	NOUN
ejpam-5831	163	4	)	)	PUNCT
ejpam-5831	163	5	=	=	SYM
ejpam-5831	163	6	fαad(x	fαad(x	NOUN
ejpam-5831	163	7	)	)	PUNCT
ejpam-5831	163	8	=	=	SYM
ejpam-5831	163	9	{	{	PUNCT
ejpam-5831	163	10	x	x	NOUN
ejpam-5831	163	11	,	,	PUNCT
ejpam-5831	163	12	∅	∅	NOUN
ejpam-5831	163	13	,	,	PUNCT
ejpam-5831	163	14	{	{	PUNCT
ejpam-5831	163	15	a	a	PRON
ejpam-5831	163	16	,	,	PUNCT
ejpam-5831	163	17	d	d	NOUN
ejpam-5831	163	18	}	}	PUNCT
ejpam-5831	163	19	,	,	PUNCT
ejpam-5831	163	20	{	{	PUNCT
ejpam-5831	163	21	d	d	X
ejpam-5831	163	22	}	}	PUNCT
ejpam-5831	163	23	,	,	PUNCT
ejpam-5831	163	24	{	{	PUNCT
ejpam-5831	163	25	a	a	X
ejpam-5831	163	26	}	}	PUNCT
ejpam-5831	163	27	,	,	PUNCT
ejpam-5831	163	28	{	{	PUNCT
ejpam-5831	163	29	b	b	X
ejpam-5831	163	30	,	,	PUNCT
ejpam-5831	163	31	d	d	NOUN
ejpam-5831	163	32	}	}	PUNCT
ejpam-5831	163	33	,	,	PUNCT
ejpam-5831	163	34	{	{	PUNCT
ejpam-5831	163	35	a	a	PRON
ejpam-5831	163	36	,	,	PUNCT
ejpam-5831	163	37	c	c	NOUN
ejpam-5831	163	38	,	,	PUNCT
ejpam-5831	163	39	d	d	NOUN
ejpam-5831	163	40	}	}	PUNCT
ejpam-5831	163	41	,	,	PUNCT
ejpam-5831	163	42	{	{	PUNCT
ejpam-5831	163	43	a	a	DET
ejpam-5831	163	44	,	,	PUNCT
ejpam-5831	163	45	b	b	NOUN
ejpam-5831	163	46	,	,	PUNCT
ejpam-5831	163	47	d	d	NOUN
ejpam-5831	163	48	}	}	PUNCT
ejpam-5831	163	49	}	}	PUNCT
ejpam-5831	163	50	,	,	PUNCT
ejpam-5831	163	51	fpad(x	fpad(x	NOUN
ejpam-5831	163	52	)	)	PUNCT
ejpam-5831	163	53	=	=	SYM
ejpam-5831	163	54	fβad(x	fβad(x	NOUN
ejpam-5831	163	55	)	)	PUNCT
ejpam-5831	163	56	=	=	SYM
ejpam-5831	163	57	fγad(x	fγad(x	NOUN
ejpam-5831	163	58	)	)	PUNCT
ejpam-5831	163	59	=	=	PRON
ejpam-5831	163	60	{	{	PUNCT
ejpam-5831	163	61	x	x	NOUN
ejpam-5831	163	62	,	,	PUNCT
ejpam-5831	163	63	∅	∅	NOUN
ejpam-5831	163	64	,	,	PUNCT
ejpam-5831	163	65	{	{	PUNCT
ejpam-5831	163	66	a	a	PRON
ejpam-5831	163	67	,	,	PUNCT
ejpam-5831	163	68	b	b	NOUN
ejpam-5831	163	69	,	,	PUNCT
ejpam-5831	163	70	d	d	NOUN
ejpam-5831	163	71	}	}	PUNCT
ejpam-5831	163	72	,	,	PUNCT
ejpam-5831	163	73	{	{	PUNCT
ejpam-5831	163	74	a	a	PRON
ejpam-5831	163	75	,	,	PUNCT
ejpam-5831	163	76	c	c	NOUN
ejpam-5831	163	77	,	,	PUNCT
ejpam-5831	163	78	d	d	NOUN
ejpam-5831	163	79	}	}	PUNCT
ejpam-5831	163	80	,	,	PUNCT
ejpam-5831	163	81	{	{	PUNCT
ejpam-5831	163	82	a	a	DET
ejpam-5831	163	83	,	,	PUNCT
ejpam-5831	163	84	b	b	NOUN
ejpam-5831	163	85	,	,	PUNCT
ejpam-5831	163	86	c	c	NOUN
ejpam-5831	163	87	}	}	PUNCT
ejpam-5831	163	88	,	,	PUNCT
ejpam-5831	163	89	{	{	PUNCT
ejpam-5831	163	90	a	a	X
ejpam-5831	163	91	,	,	PUNCT
ejpam-5831	163	92	c	c	NOUN
ejpam-5831	163	93	}	}	PUNCT
ejpam-5831	163	94	,	,	PUNCT
ejpam-5831	163	95	{	{	PUNCT
ejpam-5831	163	96	a	a	PRON
ejpam-5831	163	97	,	,	PUNCT
ejpam-5831	163	98	d	d	NOUN
ejpam-5831	163	99	}	}	PUNCT
ejpam-5831	163	100	,	,	PUNCT
ejpam-5831	163	101	{	{	PUNCT
ejpam-5831	163	102	a	a	DET
ejpam-5831	163	103	,	,	PUNCT
ejpam-5831	163	104	b	b	NOUN
ejpam-5831	163	105	}	}	PUNCT
ejpam-5831	163	106	,	,	PUNCT
ejpam-5831	163	107	{	{	PUNCT
ejpam-5831	163	108	b	b	X
ejpam-5831	163	109	,	,	PUNCT
ejpam-5831	163	110	d	d	NOUN
ejpam-5831	163	111	}	}	PUNCT
ejpam-5831	163	112	,	,	PUNCT
ejpam-5831	163	113	{	{	PUNCT
ejpam-5831	163	114	a	a	X
ejpam-5831	163	115	}	}	PUNCT
ejpam-5831	163	116	,	,	PUNCT
ejpam-5831	163	117	{	{	PUNCT
ejpam-5831	163	118	d	d	NOUN
ejpam-5831	163	119	}	}	PUNCT
ejpam-5831	163	120	}	}	PUNCT
ejpam-5831	163	121	.	.	PUNCT
ejpam-5831	164	1	definition	definition	NOUN
ejpam-5831	164	2	3.5	3.5	NUM
ejpam-5831	164	3	.	.	PUNCT
ejpam-5831	165	1	assume	assume	VERB
ejpam-5831	165	2	that	that	SCONJ
ejpam-5831	165	3	(	(	PUNCT
ejpam-5831	165	4	x	x	X
ejpam-5831	165	5	,	,	PUNCT
ejpam-5831	165	6	r	r	NOUN
ejpam-5831	165	7	)	)	PUNCT
ejpam-5831	165	8	is	be	AUX
ejpam-5831	165	9	a	a	DET
ejpam-5831	165	10	pretopological	pretopological	ADJ
ejpam-5831	165	11	approximation	approximation	NOUN
ejpam-5831	165	12	structure	structure	NOUN
ejpam-5831	165	13	,	,	PUNCT
ejpam-5831	165	14	a	a	DET
ejpam-5831	165	15	⊆	⊆	NUM
ejpam-5831	165	16	x.	x.	NOUN
ejpam-5831	165	17	then	then	ADV
ejpam-5831	165	18	,	,	PUNCT
ejpam-5831	165	19	we	we	PRON
ejpam-5831	165	20	denote	denote	VERB
ejpam-5831	165	21	the	the	DET
ejpam-5831	165	22	general	general	ADJ
ejpam-5831	165	23	lower	low	ADJ
ejpam-5831	165	24	of	of	ADP
ejpam-5831	165	25	a	a	PRON
ejpam-5831	165	26	by	by	ADP
ejpam-5831	165	27	µ	µ	X
ejpam-5831	165	28	ad	ad	NOUN
ejpam-5831	165	29	(	(	PUNCT
ejpam-5831	165	30	a	a	NOUN
ejpam-5831	165	31	)	)	PUNCT
ejpam-5831	165	32	for	for	ADP
ejpam-5831	165	33	all	all	DET
ejpam-5831	165	34	µad	µad	PRON
ejpam-5831	165	35	∈	∈	PROPN
ejpam-5831	165	36	{	{	PUNCT
ejpam-5831	165	37	sad	sad	ADJ
ejpam-5831	165	38	,	,	PUNCT
ejpam-5831	165	39	pad	pad	NOUN
ejpam-5831	165	40	,	,	PUNCT
ejpam-5831	165	41	βad	βad	PROPN
ejpam-5831	165	42	,	,	PUNCT
ejpam-5831	165	43	αad	αad	PROPN
ejpam-5831	165	44	,	,	PUNCT
ejpam-5831	165	45	γad	γad	X
ejpam-5831	165	46	}	}	PUNCT
ejpam-5831	165	47	and	and	CCONJ
ejpam-5831	165	48	is	be	AUX
ejpam-5831	165	49	defined	define	VERB
ejpam-5831	165	50	by	by	ADP
ejpam-5831	165	51	µ	µ	X
ejpam-5831	165	52	ad	ad	NOUN
ejpam-5831	165	53	(	(	PUNCT
ejpam-5831	165	54	a	a	NOUN
ejpam-5831	165	55	)	)	PUNCT
ejpam-5831	165	56	=	=	PUNCT
ejpam-5831	165	57	∪{g	∪{g	PROPN
ejpam-5831	165	58	∈	∈	PROPN
ejpam-5831	165	59	fµad	fµad	NOUN
ejpam-5831	165	60	:	:	PUNCT
ejpam-5831	165	61	g	g	PROPN
ejpam-5831	165	62	⊆	⊆	NUM
ejpam-5831	165	63	a	a	PRON
ejpam-5831	165	64	}	}	PUNCT
ejpam-5831	165	65	.	.	PUNCT
ejpam-5831	166	1	definition	definition	NOUN
ejpam-5831	166	2	3.6	3.6	NUM
ejpam-5831	166	3	.	.	PUNCT
ejpam-5831	167	1	assume	assume	VERB
ejpam-5831	167	2	that	that	SCONJ
ejpam-5831	167	3	(	(	PUNCT
ejpam-5831	167	4	x	x	X
ejpam-5831	167	5	,	,	PUNCT
ejpam-5831	167	6	r	r	NOUN
ejpam-5831	167	7	)	)	PUNCT
ejpam-5831	167	8	is	be	AUX
ejpam-5831	167	9	a	a	DET
ejpam-5831	167	10	pretopological	pretopological	ADJ
ejpam-5831	167	11	approximation	approximation	NOUN
ejpam-5831	167	12	structure	structure	NOUN
ejpam-5831	167	13	,	,	PUNCT
ejpam-5831	167	14	a	a	DET
ejpam-5831	167	15	⊆	⊆	NUM
ejpam-5831	167	16	x.	x.	NOUN
ejpam-5831	167	17	then	then	ADV
ejpam-5831	167	18	,	,	PUNCT
ejpam-5831	167	19	we	we	PRON
ejpam-5831	167	20	denote	denote	VERB
ejpam-5831	167	21	the	the	DET
ejpam-5831	167	22	general	general	ADJ
ejpam-5831	167	23	upper	upper	NOUN
ejpam-5831	167	24	of	of	ADP
ejpam-5831	167	25	a	a	PRON
ejpam-5831	167	26	by	by	ADP
ejpam-5831	167	27	µad(a	µad(a	NOUN
ejpam-5831	167	28	)	)	PUNCT
ejpam-5831	167	29	for	for	ADP
ejpam-5831	167	30	all	all	DET
ejpam-5831	167	31	µad	µad	PRON
ejpam-5831	167	32	∈	∈	PROPN
ejpam-5831	167	33	{	{	PUNCT
ejpam-5831	167	34	sad	sad	ADJ
ejpam-5831	167	35	,	,	PUNCT
ejpam-5831	167	36	pad	pad	NOUN
ejpam-5831	167	37	,	,	PUNCT
ejpam-5831	167	38	βad	βad	PROPN
ejpam-5831	167	39	,	,	PUNCT
ejpam-5831	167	40	αad	αad	PROPN
ejpam-5831	167	41	,	,	PUNCT
ejpam-5831	167	42	γad	γad	X
ejpam-5831	167	43	}	}	PUNCT
ejpam-5831	167	44	and	and	CCONJ
ejpam-5831	167	45	is	be	AUX
ejpam-5831	167	46	defined	define	VERB
ejpam-5831	167	47	by	by	ADP
ejpam-5831	167	48	µad(a	µad(a	NOUN
ejpam-5831	167	49	)	)	PUNCT
ejpam-5831	168	1	=	=	SYM
ejpam-5831	168	2	∩{h	∩{h	PUNCT
ejpam-5831	168	3	∈	∈	PROPN
ejpam-5831	168	4	fµc	fµc	VERB
ejpam-5831	168	5	ad	ad	NOUN
ejpam-5831	168	6	:	:	PUNCT
ejpam-5831	168	7	a	a	DET
ejpam-5831	168	8	⊆	⊆	NUM
ejpam-5831	168	9	h	h	NOUN
ejpam-5831	168	10	}	}	PUNCT
ejpam-5831	168	11	.	.	PUNCT
ejpam-5831	169	1	definition	definition	NOUN
ejpam-5831	169	2	3.7	3.7	NUM
ejpam-5831	169	3	.	.	PUNCT
ejpam-5831	169	4	suppose	suppose	VERB
ejpam-5831	169	5	that	that	SCONJ
ejpam-5831	169	6	(	(	PUNCT
ejpam-5831	169	7	x	x	X
ejpam-5831	169	8	,	,	PUNCT
ejpam-5831	169	9	r	r	NOUN
ejpam-5831	169	10	)	)	PUNCT
ejpam-5831	169	11	is	be	AUX
ejpam-5831	169	12	a	a	DET
ejpam-5831	169	13	pretopological	pretopological	ADJ
ejpam-5831	169	14	approximation	approximation	NOUN
ejpam-5831	169	15	structure	structure	NOUN
ejpam-5831	169	16	and	and	CCONJ
ejpam-5831	169	17	a	a	DET
ejpam-5831	169	18	⊆	⊆	NUM
ejpam-5831	169	19	x.	x.	NOUN
ejpam-5831	169	20	hence	hence	ADV
ejpam-5831	169	21	,	,	PUNCT
ejpam-5831	169	22	∀µad	∀µad	PROPN
ejpam-5831	169	23	∈	∈	PROPN
ejpam-5831	169	24	{	{	PUNCT
ejpam-5831	169	25	sad	sad	ADJ
ejpam-5831	169	26	,	,	PUNCT
ejpam-5831	169	27	pad	pad	NOUN
ejpam-5831	169	28	,	,	PUNCT
ejpam-5831	169	29	βad	βad	PROPN
ejpam-5831	169	30	,	,	PUNCT
ejpam-5831	169	31	αad	αad	PROPN
ejpam-5831	169	32	,	,	PUNCT
ejpam-5831	169	33	γad	γad	PROPN
ejpam-5831	169	34	}	}	PUNCT
ejpam-5831	169	35	the	the	DET
ejpam-5831	169	36	pretopological	pretopological	ADJ
ejpam-5831	169	37	general	general	ADJ
ejpam-5831	169	38	lower	low	ADJ
ejpam-5831	169	39	and	and	CCONJ
ejpam-5831	169	40	the	the	DET
ejpam-5831	169	41	pretopological	pretopological	ADJ
ejpam-5831	169	42	general	general	ADJ
ejpam-5831	169	43	upper	upper	ADJ
ejpam-5831	169	44	approximations	approximation	NOUN
ejpam-5831	169	45	are	be	AUX
ejpam-5831	169	46	defined	define	VERB
ejpam-5831	169	47	as	as	ADP
ejpam-5831	169	48	iµad(a	iµad(a	PROPN
ejpam-5831	169	49	)	)	PUNCT
ejpam-5831	169	50	=	=	SYM
ejpam-5831	169	51	µ	µ	PRON
ejpam-5831	169	52	ad	ad	NOUN
ejpam-5831	169	53	(	(	PUNCT
ejpam-5831	169	54	a	a	NOUN
ejpam-5831	169	55	)	)	PUNCT
ejpam-5831	169	56	,	,	PUNCT
ejpam-5831	169	57	γµad(a	γµad(a	PROPN
ejpam-5831	169	58	)	)	PUNCT
ejpam-5831	169	59	=	=	SYM
ejpam-5831	169	60	µad(a	µad(a	PROPN
ejpam-5831	169	61	)	)	PUNCT
ejpam-5831	169	62	.	.	PUNCT
ejpam-5831	170	1	proposition	proposition	NOUN
ejpam-5831	170	2	3.2	3.2	NUM
ejpam-5831	170	3	.	.	PUNCT
ejpam-5831	171	1	assume	assume	VERB
ejpam-5831	171	2	that	that	SCONJ
ejpam-5831	171	3	(	(	PUNCT
ejpam-5831	171	4	x	x	X
ejpam-5831	171	5	,	,	PUNCT
ejpam-5831	171	6	r	r	NOUN
ejpam-5831	171	7	)	)	PUNCT
ejpam-5831	171	8	is	be	AUX
ejpam-5831	171	9	a	a	DET
ejpam-5831	171	10	pretopological	pretopological	ADJ
ejpam-5831	171	11	approximation	approximation	NOUN
ejpam-5831	171	12	space	space	NOUN
ejpam-5831	171	13	,	,	PUNCT
ejpam-5831	171	14	r	r	NOUN
ejpam-5831	171	15	is	be	AUX
ejpam-5831	171	16	a	a	DET
ejpam-5831	171	17	binary	binary	ADJ
ejpam-5831	171	18	relation	relation	NOUN
ejpam-5831	171	19	on	on	ADP
ejpam-5831	171	20	x.	x.	NOUN
ejpam-5831	171	21	then	then	ADV
ejpam-5831	171	22	,	,	PUNCT
ejpam-5831	171	23	for	for	ADP
ejpam-5831	171	24	any	any	DET
ejpam-5831	171	25	a	a	DET
ejpam-5831	171	26	⊆	⊆	NUM
ejpam-5831	171	27	x	x	SYM
ejpam-5831	171	28	the	the	DET
ejpam-5831	171	29	following	follow	VERB
ejpam-5831	171	30	properties	property	NOUN
ejpam-5831	171	31	are	be	AUX
ejpam-5831	171	32	satisfied	satisfied	ADJ
ejpam-5831	171	33	:	:	PUNCT
ejpam-5831	171	34	i.	i.	PROPN
ejpam-5831	171	35	id(a	id(a	PROPN
ejpam-5831	171	36	)	)	PUNCT
ejpam-5831	172	1	⊆	⊆	NUM
ejpam-5831	172	2	iαad	iαad	NOUN
ejpam-5831	172	3	⊆	⊆	NUM
ejpam-5831	172	4	isad	isad	ADJ
ejpam-5831	172	5	⊆	⊆	NUM
ejpam-5831	172	6	iγad	iγad	NOUN
ejpam-5831	172	7	⊆	⊆	NUM
ejpam-5831	172	8	iβad	iβad	NOUN
ejpam-5831	172	9	⊆	⊆	X
ejpam-5831	172	10	a	a	DET
ejpam-5831	172	11	⊆	⊆	NUM
ejpam-5831	172	12	γβad	γβad	NOUN
ejpam-5831	172	13	⊆	⊆	NUM
ejpam-5831	172	14	γγad(a	γγad(a	PROPN
ejpam-5831	172	15	)	)	PUNCT
ejpam-5831	172	16	⊆	⊆	NUM
ejpam-5831	172	17	γsad(a	γsad(a	NUM
ejpam-5831	172	18	)	)	PUNCT
ejpam-5831	172	19	⊆	⊆	NUM
ejpam-5831	172	20	γαad	γαad	NOUN
ejpam-5831	172	21	⊆	⊆	NUM
ejpam-5831	172	22	γd(a	γd(a	NUM
ejpam-5831	172	23	)	)	PUNCT
ejpam-5831	172	24	,	,	PUNCT
ejpam-5831	172	25	ii	ii	PROPN
ejpam-5831	172	26	.	.	PROPN
ejpam-5831	172	27	ia(a	ia(a	PUNCT
ejpam-5831	172	28	)	)	PUNCT
ejpam-5831	172	29	⊆	⊆	NUM
ejpam-5831	172	30	iαad	iαad	NOUN
ejpam-5831	172	31	⊆	⊆	NUM
ejpam-5831	172	32	ipad	ipad	NOUN
ejpam-5831	172	33	⊆	⊆	NUM
ejpam-5831	172	34	iγad	iγad	NOUN
ejpam-5831	172	35	⊆	⊆	NUM
ejpam-5831	172	36	iβad	iβad	NOUN
ejpam-5831	172	37	⊆	⊆	X
ejpam-5831	172	38	a	a	DET
ejpam-5831	172	39	⊆	⊆	NUM
ejpam-5831	172	40	γβad	γβad	NOUN
ejpam-5831	172	41	⊆	⊆	NUM
ejpam-5831	172	42	γγad(a	γγad(a	PROPN
ejpam-5831	172	43	)	)	PUNCT
ejpam-5831	172	44	⊆	⊆	NUM
ejpam-5831	172	45	γpad(a	γpad(a	PROPN
ejpam-5831	172	46	)	)	PUNCT
ejpam-5831	172	47	⊆	⊆	NUM
ejpam-5831	172	48	γαad	γαad	NOUN
ejpam-5831	172	49	⊆	⊆	NUM
ejpam-5831	172	50	γd(a	γd(a	PROPN
ejpam-5831	172	51	)	)	PUNCT
ejpam-5831	172	52	,	,	PUNCT
ejpam-5831	172	53	a.	a.	PROPN
ejpam-5831	172	54	a.	a.	PROPN
ejpam-5831	172	55	azza	azza	PROPN
ejpam-5831	172	56	et	et	PROPN
ejpam-5831	172	57	al	al	PROPN
ejpam-5831	172	58	.	.	PUNCT
ejpam-5831	172	59	/	/	SYM
ejpam-5831	172	60	eur	eur	PROPN
ejpam-5831	172	61	.	.	PUNCT
ejpam-5831	173	1	j.	j.	PROPN
ejpam-5831	173	2	pure	pure	PROPN
ejpam-5831	173	3	appl	appl	PROPN
ejpam-5831	173	4	.	.	PROPN
ejpam-5831	173	5	math	math	PROPN
ejpam-5831	173	6	,	,	PUNCT
ejpam-5831	173	7	18	18	NUM
ejpam-5831	173	8	(	(	PUNCT
ejpam-5831	173	9	2	2	NUM
ejpam-5831	173	10	)	)	PUNCT
ejpam-5831	173	11	(	(	PUNCT
ejpam-5831	173	12	2025	2025	NUM
ejpam-5831	173	13	)	)	PUNCT
ejpam-5831	173	14	,	,	PUNCT
ejpam-5831	173	15	5831	5831	NUM
ejpam-5831	173	16	7	7	NUM
ejpam-5831	173	17	of	of	ADP
ejpam-5831	173	18	11	11	NUM
ejpam-5831	173	19	proof	proof	NOUN
ejpam-5831	173	20	:	:	PUNCT
ejpam-5831	173	21	we	we	PRON
ejpam-5831	173	22	will	will	AUX
ejpam-5831	173	23	prove	prove	VERB
ejpam-5831	173	24	the	the	DET
ejpam-5831	173	25	part	part	NOUN
ejpam-5831	173	26	(	(	PUNCT
ejpam-5831	173	27	i	i	NOUN
ejpam-5831	173	28	)	)	PUNCT
ejpam-5831	173	29	and	and	CCONJ
ejpam-5831	173	30	we	we	PRON
ejpam-5831	173	31	can	can	AUX
ejpam-5831	173	32	prove	prove	VERB
ejpam-5831	173	33	(	(	PUNCT
ejpam-5831	173	34	ii	ii	NOUN
ejpam-5831	173	35	)	)	PUNCT
ejpam-5831	173	36	in	in	ADP
ejpam-5831	173	37	the	the	DET
ejpam-5831	173	38	same	same	ADJ
ejpam-5831	173	39	way	way	NOUN
ejpam-5831	173	40	.	.	PUNCT
ejpam-5831	174	1	i.	i.	PROPN
ejpam-5831	174	2	since	since	SCONJ
ejpam-5831	174	3	id(a	id(a	NOUN
ejpam-5831	174	4	)	)	PUNCT
ejpam-5831	174	5	=	=	SYM
ejpam-5831	174	6	{	{	PUNCT
ejpam-5831	174	7	x	x	PUNCT
ejpam-5831	174	8	∈	∈	NOUN
ejpam-5831	174	9	x	x	X
ejpam-5831	174	10	:	:	PUNCT
ejpam-5831	174	11	r(x	r(x	NOUN
ejpam-5831	174	12	)	)	PUNCT
ejpam-5831	174	13	⊆	⊆	NUM
ejpam-5831	174	14	a	a	DET
ejpam-5831	174	15	}	}	PUNCT
ejpam-5831	174	16	⊆	⊆	NUM
ejpam-5831	174	17	∪{g1	∪{g1	NUM
ejpam-5831	174	18	∈	∈	PROPN
ejpam-5831	174	19	fαad(x	fαad(x	NOUN
ejpam-5831	174	20	)	)	PUNCT
ejpam-5831	174	21	:	:	PUNCT
ejpam-5831	174	22	g1	g1	VERB
ejpam-5831	174	23	⊆	⊆	X
ejpam-5831	174	24	a	a	DET
ejpam-5831	174	25	}	}	PUNCT
ejpam-5831	174	26	⊆	⊆	NUM
ejpam-5831	174	27	∪{g1	∪{g1	NUM
ejpam-5831	174	28	∈	∈	NOUN
ejpam-5831	174	29	fsad(x	fsad(x	NOUN
ejpam-5831	174	30	)	)	PUNCT
ejpam-5831	174	31	:	:	PUNCT
ejpam-5831	174	32	g1	g1	VERB
ejpam-5831	174	33	⊆	⊆	X
ejpam-5831	174	34	a	a	DET
ejpam-5831	174	35	}	}	PUNCT
ejpam-5831	174	36	⊆	⊆	NUM
ejpam-5831	174	37	∪{g1	∪{g1	ADJ
ejpam-5831	174	38	∈	∈	PROPN
ejpam-5831	174	39	fγad(x	fγad(x	NOUN
ejpam-5831	174	40	)	)	PUNCT
ejpam-5831	174	41	:	:	PUNCT
ejpam-5831	174	42	g1	g1	VERB
ejpam-5831	174	43	⊆	⊆	X
ejpam-5831	174	44	a	a	DET
ejpam-5831	174	45	}	}	PUNCT
ejpam-5831	174	46	⊆	⊆	NUM
ejpam-5831	174	47	∪{g1	∪{g1	ADJ
ejpam-5831	174	48	∈	∈	NOUN
ejpam-5831	174	49	fβad(x	fβad(x	NOUN
ejpam-5831	174	50	)	)	PUNCT
ejpam-5831	174	51	:	:	PUNCT
ejpam-5831	174	52	g1	g1	VERB
ejpam-5831	174	53	⊆	⊆	X
ejpam-5831	174	54	a	a	DET
ejpam-5831	174	55	}	}	PUNCT
ejpam-5831	174	56	⊆	⊆	NUM
ejpam-5831	174	57	a	a	DET
ejpam-5831	174	58	⊆	⊆	NUM
ejpam-5831	174	59	∩{g2	∩{g2	PROPN
ejpam-5831	174	60	∈	∈	PROPN
ejpam-5831	174	61	fβc	fβc	NOUN
ejpam-5831	174	62	ad(x	ad(x	PUNCT
ejpam-5831	174	63	)	)	PUNCT
ejpam-5831	174	64	:	:	PUNCT
ejpam-5831	174	65	a	a	DET
ejpam-5831	174	66	⊆	⊆	NUM
ejpam-5831	174	67	h	h	NOUN
ejpam-5831	174	68	}	}	PUNCT
ejpam-5831	174	69	⊆	⊆	NUM
ejpam-5831	174	70	∩{g2	∩{g2	PROPN
ejpam-5831	174	71	∈	∈	PROPN
ejpam-5831	174	72	fγcad(x	fγcad(x	NOUN
ejpam-5831	174	73	)	)	PUNCT
ejpam-5831	174	74	:	:	PUNCT
ejpam-5831	174	75	a	a	DET
ejpam-5831	174	76	⊆	⊆	NUM
ejpam-5831	174	77	g2	g2	NOUN
ejpam-5831	174	78	}	}	PUNCT
ejpam-5831	174	79	⊆	⊆	NUM
ejpam-5831	174	80	∩{g2	∩{g2	PROPN
ejpam-5831	174	81	∈	∈	PROPN
ejpam-5831	174	82	fsc	fsc	PROPN
ejpam-5831	174	83	ad(x	ad(x	ADV
ejpam-5831	174	84	)	)	PUNCT
ejpam-5831	174	85	:	:	PUNCT
ejpam-5831	174	86	a	a	DET
ejpam-5831	174	87	⊆	⊆	NUM
ejpam-5831	174	88	g2	g2	NOUN
ejpam-5831	174	89	}	}	PUNCT
ejpam-5831	174	90	⊆	⊆	NUM
ejpam-5831	174	91	∩{g2	∩{g2	PROPN
ejpam-5831	174	92	∈	∈	PROPN
ejpam-5831	174	93	fαc	fαc	NOUN
ejpam-5831	174	94	ad(x	ad(x	PUNCT
ejpam-5831	174	95	)	)	PUNCT
ejpam-5831	174	96	:	:	PUNCT
ejpam-5831	174	97	a	a	DET
ejpam-5831	174	98	⊆	⊆	NUM
ejpam-5831	174	99	g2	g2	NOUN
ejpam-5831	174	100	}	}	PUNCT
ejpam-5831	174	101	⊆	⊆	NUM
ejpam-5831	174	102	{	{	PUNCT
ejpam-5831	174	103	x	x	SYM
ejpam-5831	174	104	∈	∈	PROPN
ejpam-5831	174	105	x	x	X
ejpam-5831	174	106	:	:	PUNCT
ejpam-5831	174	107	r(x	r(x	NOUN
ejpam-5831	174	108	)	)	PUNCT
ejpam-5831	174	109	∩	∩	NOUN
ejpam-5831	174	110	a	a	DET
ejpam-5831	174	111	̸=	̸=	PROPN
ejpam-5831	174	112	∅	∅	NOUN
ejpam-5831	174	113	}	}	PUNCT
ejpam-5831	174	114	.	.	PUNCT
ejpam-5831	175	1	therefore	therefore	ADV
ejpam-5831	175	2	,	,	PUNCT
ejpam-5831	175	3	id(a	id(a	ADJ
ejpam-5831	175	4	)	)	PUNCT
ejpam-5831	175	5	⊆	⊆	NUM
ejpam-5831	175	6	iαad	iαad	NOUN
ejpam-5831	175	7	⊆	⊆	NUM
ejpam-5831	175	8	isad	isad	ADJ
ejpam-5831	175	9	⊆	⊆	NUM
ejpam-5831	175	10	iγad	iγad	NOUN
ejpam-5831	175	11	⊆	⊆	NUM
ejpam-5831	175	12	iβad	iβad	NOUN
ejpam-5831	175	13	⊆	⊆	X
ejpam-5831	175	14	a	a	DET
ejpam-5831	175	15	⊆	⊆	NUM
ejpam-5831	175	16	γβad	γβad	NOUN
ejpam-5831	175	17	⊆	⊆	NUM
ejpam-5831	175	18	γγad(a	γγad(a	PROPN
ejpam-5831	175	19	)	)	PUNCT
ejpam-5831	175	20	⊆	⊆	NUM
ejpam-5831	175	21	γsad(a	γsad(a	NUM
ejpam-5831	175	22	)	)	PUNCT
ejpam-5831	175	23	⊆	⊆	NUM
ejpam-5831	175	24	γαad	γαad	NOUN
ejpam-5831	175	25	⊆	⊆	NUM
ejpam-5831	175	26	γd(a	γd(a	NUM
ejpam-5831	175	27	)	)	PUNCT
ejpam-5831	175	28	.	.	PUNCT
ejpam-5831	176	1	□	□	PUNCT
ejpam-5831	176	2	example	example	NOUN
ejpam-5831	176	3	3.2	3.2	NUM
ejpam-5831	176	4	.	.	PUNCT
ejpam-5831	176	5	suppose	suppose	VERB
ejpam-5831	176	6	that	that	SCONJ
ejpam-5831	176	7	a1	a1	NOUN
ejpam-5831	176	8	=	=	PUNCT
ejpam-5831	176	9	{	{	PUNCT
ejpam-5831	176	10	a	a	X
ejpam-5831	176	11	,	,	PUNCT
ejpam-5831	176	12	c	c	NOUN
ejpam-5831	176	13	}	}	PUNCT
ejpam-5831	176	14	,	,	PUNCT
ejpam-5831	176	15	a2	a2	PROPN
ejpam-5831	176	16	=	=	PUNCT
ejpam-5831	176	17	{	{	PUNCT
ejpam-5831	176	18	c	c	NOUN
ejpam-5831	176	19	,	,	PUNCT
ejpam-5831	176	20	d	d	NOUN
ejpam-5831	176	21	}	}	PUNCT
ejpam-5831	176	22	.	.	PUNCT
ejpam-5831	177	1	then	then	ADV
ejpam-5831	177	2	by	by	ADP
ejpam-5831	177	3	using	use	VERB
ejpam-5831	177	4	example	example	NOUN
ejpam-5831	177	5	3.1	3.1	NUM
ejpam-5831	177	6	,	,	PUNCT
ejpam-5831	177	7	iαad(a1	iαad(a1	NOUN
ejpam-5831	177	8	)	)	PUNCT
ejpam-5831	178	1	=	=	PUNCT
ejpam-5831	178	2	{	{	PUNCT
ejpam-5831	178	3	a	a	NOUN
ejpam-5831	178	4	}	}	PUNCT
ejpam-5831	178	5	,	,	PUNCT
ejpam-5831	178	6	ipad(a	ipad(a	PROPN
ejpam-5831	178	7	)	)	PUNCT
ejpam-5831	178	8	=	=	PRON
ejpam-5831	178	9	{	{	PUNCT
ejpam-5831	178	10	a	a	X
ejpam-5831	178	11	,	,	PUNCT
ejpam-5831	178	12	c	c	NOUN
ejpam-5831	178	13	}	}	PUNCT
ejpam-5831	178	14	,	,	PUNCT
ejpam-5831	178	15	γpad(a2	γpad(a2	PROPN
ejpam-5831	178	16	)	)	PUNCT
ejpam-5831	178	17	=	=	PRON
ejpam-5831	179	1	{	{	PUNCT
ejpam-5831	179	2	c	c	NOUN
ejpam-5831	179	3	,	,	PUNCT
ejpam-5831	179	4	d	d	NOUN
ejpam-5831	179	5	}	}	PUNCT
ejpam-5831	179	6	,	,	PUNCT
ejpam-5831	179	7	γαad(a2	γαad(a2	ADV
ejpam-5831	179	8	)	)	PUNCT
ejpam-5831	179	9	=	=	PRON
ejpam-5831	179	10	{	{	PUNCT
ejpam-5831	179	11	b	b	PROPN
ejpam-5831	179	12	,	,	PUNCT
ejpam-5831	179	13	c	c	NOUN
ejpam-5831	179	14	,	,	PUNCT
ejpam-5831	179	15	d	d	NOUN
ejpam-5831	179	16	}	}	PUNCT
ejpam-5831	179	17	.	.	PUNCT
ejpam-5831	180	1	therefore	therefore	ADV
ejpam-5831	180	2	,	,	PUNCT
ejpam-5831	180	3	iαad(a1	iαad(a1	NOUN
ejpam-5831	180	4	)	)	PUNCT
ejpam-5831	180	5	⊆	⊆	NUM
ejpam-5831	180	6	ipad(a1	ipad(a1	NOUN
ejpam-5831	180	7	)	)	PUNCT
ejpam-5831	180	8	,	,	PUNCT
ejpam-5831	180	9	γpad(a2	γpad(a2	PROPN
ejpam-5831	180	10	)	)	PUNCT
ejpam-5831	180	11	⊆	⊆	NUM
ejpam-5831	180	12	γαad(a2	γαad(a2	NUM
ejpam-5831	180	13	)	)	PUNCT
ejpam-5831	180	14	.	.	PUNCT
ejpam-5831	181	1	proposition	proposition	NOUN
ejpam-5831	181	2	3.3	3.3	NUM
ejpam-5831	181	3	.	.	PUNCT
ejpam-5831	182	1	assume	assume	VERB
ejpam-5831	182	2	that	that	SCONJ
ejpam-5831	182	3	(	(	PUNCT
ejpam-5831	182	4	x	x	X
ejpam-5831	182	5	,	,	PUNCT
ejpam-5831	182	6	r	r	NOUN
ejpam-5831	182	7	)	)	PUNCT
ejpam-5831	182	8	is	be	AUX
ejpam-5831	182	9	a	a	DET
ejpam-5831	182	10	pretopological	pretopological	ADJ
ejpam-5831	182	11	approximation	approximation	NOUN
ejpam-5831	182	12	structure	structure	NOUN
ejpam-5831	182	13	and	and	CCONJ
ejpam-5831	182	14	a1	a1	NOUN
ejpam-5831	182	15	,	,	PUNCT
ejpam-5831	182	16	a2	a2	PROPN
ejpam-5831	182	17	⊆	⊆	NUM
ejpam-5831	182	18	x.	x.	NOUN
ejpam-5831	182	19	hence	hence	ADV
ejpam-5831	182	20	,	,	PUNCT
ejpam-5831	182	21	∀µad	∀µad	PROPN
ejpam-5831	182	22	∈	∈	PROPN
ejpam-5831	182	23	{	{	PUNCT
ejpam-5831	182	24	sad	sad	ADJ
ejpam-5831	182	25	,	,	PUNCT
ejpam-5831	182	26	pad	pad	NOUN
ejpam-5831	182	27	,	,	PUNCT
ejpam-5831	182	28	βad	βad	PROPN
ejpam-5831	182	29	,	,	PUNCT
ejpam-5831	182	30	αad	αad	PROPN
ejpam-5831	182	31	,	,	PUNCT
ejpam-5831	182	32	γad	γad	PROPN
ejpam-5831	182	33	}	}	PUNCT
ejpam-5831	182	34	the	the	DET
ejpam-5831	182	35	following	follow	VERB
ejpam-5831	182	36	axioms	axiom	NOUN
ejpam-5831	182	37	are	be	AUX
ejpam-5831	182	38	satisfied	satisfied	ADJ
ejpam-5831	182	39	:	:	PUNCT
ejpam-5831	182	40	i.	i.	NOUN
ejpam-5831	182	41	iµad(x	iµad(x	PROPN
ejpam-5831	182	42	)	)	PUNCT
ejpam-5831	182	43	=	=	SYM
ejpam-5831	183	1	γµad(x	γµad(x	NOUN
ejpam-5831	183	2	)	)	PUNCT
ejpam-5831	183	3	=	=	SYM
ejpam-5831	183	4	x	x	PROPN
ejpam-5831	183	5	,	,	PUNCT
ejpam-5831	183	6	ii	ii	PROPN
ejpam-5831	183	7	.	.	PUNCT
ejpam-5831	184	1	iµad(∅	iµad(∅	CCONJ
ejpam-5831	185	1	)	)	PUNCT
ejpam-5831	185	2	=	=	PUNCT
ejpam-5831	185	3	γµad(∅	γµad(∅	ADJ
ejpam-5831	185	4	)	)	PUNCT
ejpam-5831	185	5	=	=	NOUN
ejpam-5831	185	6	∅	∅	NOUN
ejpam-5831	185	7	,	,	PUNCT
ejpam-5831	185	8	iii	iii	NOUN
ejpam-5831	185	9	.	.	PUNCT
ejpam-5831	186	1	if	if	SCONJ
ejpam-5831	186	2	a1	a1	NOUN
ejpam-5831	186	3	⊆	⊆	NUM
ejpam-5831	186	4	a2	a2	PROPN
ejpam-5831	186	5	,	,	PUNCT
ejpam-5831	186	6	then	then	ADV
ejpam-5831	186	7	iµad(a1	iµad(a1	VERB
ejpam-5831	186	8	)	)	PUNCT
ejpam-5831	186	9	⊆	⊆	NUM
ejpam-5831	186	10	iµad(a2	iµad(a2	NOUN
ejpam-5831	186	11	)	)	PUNCT
ejpam-5831	186	12	,	,	PUNCT
ejpam-5831	186	13	γµad(a1	γµad(a1	NOUN
ejpam-5831	186	14	)	)	PUNCT
ejpam-5831	186	15	⊆	⊆	NUM
ejpam-5831	186	16	γµad(a2	γµad(a2	NOUN
ejpam-5831	186	17	)	)	PUNCT
ejpam-5831	186	18	,	,	PUNCT
ejpam-5831	186	19	iv	iv	X
ejpam-5831	186	20	.	.	PUNCT
ejpam-5831	186	21	iµad(a1	iµad(a1	NOUN
ejpam-5831	186	22	)	)	PUNCT
ejpam-5831	186	23	∪	∪	ADP
ejpam-5831	186	24	iµad(a2	iµad(a2	PROPN
ejpam-5831	186	25	)	)	PUNCT
ejpam-5831	186	26	⊆	⊆	NUM
ejpam-5831	186	27	iµad(a1	iµad(a1	NOUN
ejpam-5831	186	28	∪a2	∪a2	NOUN
ejpam-5831	186	29	)	)	PUNCT
ejpam-5831	186	30	,	,	PUNCT
ejpam-5831	186	31	v.	v.	ADP
ejpam-5831	186	32	γµad(a1	γµad(a1	NOUN
ejpam-5831	186	33	∩a2	∩a2	NUM
ejpam-5831	186	34	)	)	PUNCT
ejpam-5831	186	35	⊆	⊆	NUM
ejpam-5831	186	36	γµad(a1	γµad(a1	NOUN
ejpam-5831	186	37	)	)	PUNCT
ejpam-5831	186	38	∩	∩	NOUN
ejpam-5831	186	39	γµad(a2	γµad(a2	NOUN
ejpam-5831	186	40	)	)	PUNCT
ejpam-5831	186	41	,	,	PUNCT
ejpam-5831	186	42	vi	vi	PROPN
ejpam-5831	186	43	.	.	X
ejpam-5831	186	44	γµad(a1	γµad(a1	NOUN
ejpam-5831	186	45	)	)	PUNCT
ejpam-5831	186	46	∪	∪	X
ejpam-5831	186	47	γµad(a2	γµad(a2	NOUN
ejpam-5831	186	48	)	)	PUNCT
ejpam-5831	186	49	⊆	⊆	NUM
ejpam-5831	186	50	γµad(a1	γµad(a1	NOUN
ejpam-5831	186	51	∪a2	∪a2	PRON
ejpam-5831	186	52	)	)	PUNCT
ejpam-5831	186	53	,	,	PUNCT
ejpam-5831	186	54	vii	vii	PROPN
ejpam-5831	186	55	.	.	PROPN
ejpam-5831	186	56	iµad(a1	iµad(a1	NOUN
ejpam-5831	186	57	∩a2	∩a2	PROPN
ejpam-5831	186	58	)	)	PUNCT
ejpam-5831	186	59	⊆	⊆	NUM
ejpam-5831	186	60	iµad(a1	iµad(a1	NOUN
ejpam-5831	186	61	)	)	PUNCT
ejpam-5831	186	62	∩	∩	NOUN
ejpam-5831	186	63	iµad(a2	iµad(a2	NOUN
ejpam-5831	186	64	)	)	PUNCT
ejpam-5831	186	65	,	,	PUNCT
ejpam-5831	186	66	viii	viii	PROPN
ejpam-5831	186	67	.	.	PUNCT
ejpam-5831	187	1	iµad(ac	iµad(ac	ADJ
ejpam-5831	187	2	1	1	NUM
ejpam-5831	187	3	)	)	PUNCT
ejpam-5831	187	4	=	=	SYM
ejpam-5831	187	5	(	(	PUNCT
ejpam-5831	187	6	γµad(a1	γµad(a1	NOUN
ejpam-5831	187	7	)	)	PUNCT
ejpam-5831	187	8	)	)	PUNCT
ejpam-5831	188	1	c	c	X
ejpam-5831	188	2	,	,	PUNCT
ejpam-5831	188	3	ix	ix	ADJ
ejpam-5831	188	4	.	.	PUNCT
ejpam-5831	189	1	γµad(ac	γµad(ac	PRON
ejpam-5831	189	2	1	1	NUM
ejpam-5831	189	3	)	)	PUNCT
ejpam-5831	189	4	=	=	SYM
ejpam-5831	189	5	(	(	PUNCT
ejpam-5831	189	6	iµad(a1	iµad(a1	NOUN
ejpam-5831	189	7	)	)	PUNCT
ejpam-5831	189	8	)	)	PUNCT
ejpam-5831	190	1	c.	c.	NOUN
ejpam-5831	190	2	proof	proof	NOUN
ejpam-5831	190	3	since	since	SCONJ
ejpam-5831	190	4	µad	µad	PROPN
ejpam-5831	190	5	∈	∈	PROPN
ejpam-5831	190	6	{	{	PUNCT
ejpam-5831	190	7	sad	sad	ADJ
ejpam-5831	190	8	,	,	PUNCT
ejpam-5831	190	9	pad	pad	NOUN
ejpam-5831	190	10	,	,	PUNCT
ejpam-5831	190	11	βad	βad	PROPN
ejpam-5831	190	12	,	,	PUNCT
ejpam-5831	190	13	αad	αad	PROPN
ejpam-5831	190	14	,	,	PUNCT
ejpam-5831	190	15	γad	γad	PROPN
ejpam-5831	190	16	}	}	PUNCT
ejpam-5831	190	17	,	,	PUNCT
ejpam-5831	190	18	then	then	ADV
ejpam-5831	190	19	by	by	ADP
ejpam-5831	190	20	the	the	DET
ejpam-5831	190	21	properties	property	NOUN
ejpam-5831	190	22	of	of	ADP
ejpam-5831	190	23	iµad	iµad	NOUN
ejpam-5831	190	24	and	and	CCONJ
ejpam-5831	190	25	γµad	γµad	NOUN
ejpam-5831	190	26	,	,	PUNCT
ejpam-5831	190	27	the	the	DET
ejpam-5831	190	28	proof	proof	NOUN
ejpam-5831	190	29	is	be	AUX
ejpam-5831	190	30	complete	complete	ADJ
ejpam-5831	190	31	.	.	PUNCT
ejpam-5831	191	1	the	the	DET
ejpam-5831	191	2	converse	converse	NOUN
ejpam-5831	191	3	of	of	ADP
ejpam-5831	191	4	axioms	axiom	NOUN
ejpam-5831	191	5	iv	iv	X
ejpam-5831	191	6	and	and	CCONJ
ejpam-5831	191	7	v	v	NOUN
ejpam-5831	191	8	in	in	ADP
ejpam-5831	191	9	proposition	proposition	NOUN
ejpam-5831	191	10	3.3	3.3	NUM
ejpam-5831	191	11	do	do	AUX
ejpam-5831	191	12	not	not	PART
ejpam-5831	191	13	hold	hold	VERB
ejpam-5831	191	14	in	in	ADP
ejpam-5831	191	15	general	general	ADJ
ejpam-5831	191	16	.	.	PUNCT
ejpam-5831	192	1	this	this	PRON
ejpam-5831	192	2	will	will	AUX
ejpam-5831	192	3	be	be	AUX
ejpam-5831	192	4	shown	show	VERB
ejpam-5831	192	5	in	in	ADP
ejpam-5831	192	6	the	the	DET
ejpam-5831	192	7	next	next	ADJ
ejpam-5831	192	8	example	example	NOUN
ejpam-5831	192	9	,	,	PUNCT
ejpam-5831	192	10	so	so	ADV
ejpam-5831	192	11	take	take	VERB
ejpam-5831	192	12	µad	µad	ADV
ejpam-5831	192	13	=	=	SYM
ejpam-5831	192	14	sad	sad	ADJ
ejpam-5831	192	15	.	.	PUNCT
ejpam-5831	192	16	example	example	NOUN
ejpam-5831	193	1	3.3	3.3	NUM
ejpam-5831	193	2	.	.	PUNCT
ejpam-5831	194	1	if	if	SCONJ
ejpam-5831	194	2	a1	a1	NOUN
ejpam-5831	194	3	=	=	SYM
ejpam-5831	194	4	{	{	PUNCT
ejpam-5831	194	5	d	d	NOUN
ejpam-5831	194	6	}	}	PUNCT
ejpam-5831	194	7	,	,	PUNCT
ejpam-5831	194	8	a2	a2	PROPN
ejpam-5831	194	9	=	=	PUNCT
ejpam-5831	194	10	{	{	PUNCT
ejpam-5831	194	11	a	a	X
ejpam-5831	194	12	,	,	PUNCT
ejpam-5831	194	13	c	c	NOUN
ejpam-5831	194	14	}	}	PUNCT
ejpam-5831	194	15	and	and	CCONJ
ejpam-5831	194	16	by	by	ADP
ejpam-5831	194	17	using	use	VERB
ejpam-5831	194	18	example	example	NOUN
ejpam-5831	194	19	3.1	3.1	NUM
ejpam-5831	194	20	.	.	PUNCT
ejpam-5831	195	1	then	then	ADV
ejpam-5831	195	2	,	,	PUNCT
ejpam-5831	195	3	isad(a1	isad(a1	VERB
ejpam-5831	195	4	)	)	PUNCT
ejpam-5831	195	5	=	=	PUNCT
ejpam-5831	195	6	{	{	PUNCT
ejpam-5831	195	7	d	d	NOUN
ejpam-5831	195	8	}	}	PUNCT
ejpam-5831	195	9	,	,	PUNCT
ejpam-5831	195	10	isad(a2	isad(a2	ADJ
ejpam-5831	195	11	)	)	PUNCT
ejpam-5831	195	12	=	=	PRON
ejpam-5831	196	1	{	{	PUNCT
ejpam-5831	196	2	a	a	X
ejpam-5831	196	3	}	}	PUNCT
ejpam-5831	196	4	,	,	PUNCT
ejpam-5831	196	5	isad(a1	isad(a1	VERB
ejpam-5831	196	6	∪a2	∪a2	PRON
ejpam-5831	196	7	)	)	PUNCT
ejpam-5831	197	1	=	=	PRON
ejpam-5831	197	2	{	{	PUNCT
ejpam-5831	197	3	a	a	X
ejpam-5831	197	4	,	,	PUNCT
ejpam-5831	197	5	c	c	NOUN
ejpam-5831	197	6	,	,	PUNCT
ejpam-5831	197	7	d	d	NOUN
ejpam-5831	197	8	}	}	PUNCT
ejpam-5831	197	9	.	.	PUNCT
ejpam-5831	198	1	therefore	therefore	ADV
ejpam-5831	198	2	isad(a1)∪	isad(a1)∪	ADJ
ejpam-5831	198	3	isad(a2	isad(a2	ADV
ejpam-5831	198	4	)	)	PUNCT
ejpam-5831	199	1	̸=	̸=	PROPN
ejpam-5831	199	2	isad(a1	isad(a1	VERB
ejpam-5831	199	3	∪a2	∪a2	NOUN
ejpam-5831	199	4	)	)	PUNCT
ejpam-5831	199	5	.	.	PUNCT
ejpam-5831	200	1	also	also	ADV
ejpam-5831	200	2	,	,	PUNCT
ejpam-5831	200	3	γsad(a1	γsad(a1	ADV
ejpam-5831	200	4	)	)	PUNCT
ejpam-5831	200	5	=	=	PUNCT
ejpam-5831	200	6	{	{	PUNCT
ejpam-5831	200	7	b	b	PROPN
ejpam-5831	200	8	,	,	PUNCT
ejpam-5831	200	9	c	c	NOUN
ejpam-5831	200	10	,	,	PUNCT
ejpam-5831	200	11	d	d	NOUN
ejpam-5831	200	12	}	}	PUNCT
ejpam-5831	200	13	,	,	PUNCT
ejpam-5831	200	14	γsad(a2	γsad(a2	NOUN
ejpam-5831	200	15	)	)	PUNCT
ejpam-5831	201	1	=	=	PRON
ejpam-5831	201	2	{	{	PUNCT
ejpam-5831	201	3	a	a	NOUN
ejpam-5831	201	4	,	,	PUNCT
ejpam-5831	201	5	c},γsad(a1	c},γsad(a1	NOUN
ejpam-5831	201	6	∩	∩	ADJ
ejpam-5831	201	7	a2	a2	NOUN
ejpam-5831	201	8	)	)	PUNCT
ejpam-5831	201	9	=	=	NOUN
ejpam-5831	202	1	∅	∅	NOUN
ejpam-5831	202	2	,	,	PUNCT
ejpam-5831	202	3	hence	hence	ADV
ejpam-5831	202	4	γµad(a1	γµad(a1	VERB
ejpam-5831	202	5	∩	∩	ADJ
ejpam-5831	202	6	a2	a2	PROPN
ejpam-5831	202	7	)	)	PUNCT
ejpam-5831	202	8	̸=	̸=	PROPN
ejpam-5831	202	9	γµad(a1	γµad(a1	NOUN
ejpam-5831	202	10	)	)	PUNCT
ejpam-5831	202	11	∩	∩	NOUN
ejpam-5831	202	12	γµad(a2	γµad(a2	NOUN
ejpam-5831	202	13	)	)	PUNCT
ejpam-5831	202	14	proposition	proposition	NOUN
ejpam-5831	202	15	3.4	3.4	NUM
ejpam-5831	202	16	.	.	PUNCT
ejpam-5831	203	1	if	if	SCONJ
ejpam-5831	203	2	a	a	DET
ejpam-5831	203	3	⊆	⊆	NUM
ejpam-5831	203	4	x	x	SYM
ejpam-5831	203	5	and	and	CCONJ
ejpam-5831	203	6	(	(	PUNCT
ejpam-5831	203	7	x	x	NOUN
ejpam-5831	203	8	,	,	PUNCT
ejpam-5831	203	9	r	r	NOUN
ejpam-5831	203	10	)	)	PUNCT
ejpam-5831	203	11	is	be	AUX
ejpam-5831	203	12	a	a	DET
ejpam-5831	203	13	pretopological	pretopological	ADJ
ejpam-5831	203	14	approximation	approximation	NOUN
ejpam-5831	203	15	space	space	NOUN
ejpam-5831	203	16	.	.	PUNCT
ejpam-5831	204	1	then	then	ADV
ejpam-5831	204	2	,	,	PUNCT
ejpam-5831	204	3	∀µad	∀µad	PROPN
ejpam-5831	204	4	∈	∈	PROPN
ejpam-5831	204	5	{	{	PUNCT
ejpam-5831	204	6	sad	sad	ADJ
ejpam-5831	204	7	,	,	PUNCT
ejpam-5831	204	8	pad	pad	NOUN
ejpam-5831	204	9	,	,	PUNCT
ejpam-5831	204	10	βad	βad	PROPN
ejpam-5831	204	11	,	,	PUNCT
ejpam-5831	204	12	αad	αad	PROPN
ejpam-5831	204	13	,	,	PUNCT
ejpam-5831	204	14	γad	γad	PROPN
ejpam-5831	204	15	}	}	PUNCT
ejpam-5831	204	16	the	the	DET
ejpam-5831	204	17	following	follow	VERB
ejpam-5831	204	18	axioms	axiom	NOUN
ejpam-5831	204	19	do	do	AUX
ejpam-5831	204	20	not	not	PART
ejpam-5831	204	21	satisfied	satisfied	ADJ
ejpam-5831	204	22	:	:	PUNCT
ejpam-5831	204	23	i.	i.	PROPN
ejpam-5831	204	24	iµad(iµad(a	iµad(iµad(a	PROPN
ejpam-5831	204	25	)	)	PUNCT
ejpam-5831	204	26	)	)	PUNCT
ejpam-5831	205	1	=	=	PUNCT
ejpam-5831	205	2	iµad(a	iµad(a	PROPN
ejpam-5831	205	3	)	)	PUNCT
ejpam-5831	205	4	̸=	̸=	PROPN
ejpam-5831	205	5	γµad(iµad(a	γµad(iµad(a	NUM
ejpam-5831	205	6	)	)	PUNCT
ejpam-5831	205	7	)	)	PUNCT
ejpam-5831	205	8	,	,	PUNCT
ejpam-5831	205	9	a.	a.	NOUN
ejpam-5831	205	10	a.	a.	PROPN
ejpam-5831	205	11	azza	azza	PROPN
ejpam-5831	205	12	et	et	PROPN
ejpam-5831	205	13	al	al	PROPN
ejpam-5831	205	14	.	.	PUNCT
ejpam-5831	205	15	/	/	SYM
ejpam-5831	205	16	eur	eur	PROPN
ejpam-5831	205	17	.	.	PUNCT
ejpam-5831	206	1	j.	j.	PROPN
ejpam-5831	206	2	pure	pure	PROPN
ejpam-5831	206	3	appl	appl	PROPN
ejpam-5831	206	4	.	.	PROPN
ejpam-5831	206	5	math	math	PROPN
ejpam-5831	206	6	,	,	PUNCT
ejpam-5831	206	7	18	18	NUM
ejpam-5831	206	8	(	(	PUNCT
ejpam-5831	206	9	2	2	NUM
ejpam-5831	206	10	)	)	PUNCT
ejpam-5831	206	11	(	(	PUNCT
ejpam-5831	206	12	2025	2025	NUM
ejpam-5831	206	13	)	)	PUNCT
ejpam-5831	206	14	,	,	PUNCT
ejpam-5831	206	15	5831	5831	NUM
ejpam-5831	206	16	8	8	NUM
ejpam-5831	206	17	of	of	ADP
ejpam-5831	206	18	11	11	NUM
ejpam-5831	206	19	ii	ii	NOUN
ejpam-5831	206	20	.	.	PUNCT
ejpam-5831	207	1	γµad(γµad(a	γµad(γµad(a	PROPN
ejpam-5831	207	2	)	)	PUNCT
ejpam-5831	207	3	)	)	PUNCT
ejpam-5831	208	1	=	=	SYM
ejpam-5831	208	2	γµad(a	γµad(a	PROPN
ejpam-5831	208	3	)	)	PUNCT
ejpam-5831	208	4	̸=	̸=	PROPN
ejpam-5831	208	5	iµad(γµad(a	iµad(γµad(a	NUM
ejpam-5831	208	6	)	)	PUNCT
ejpam-5831	208	7	)	)	PUNCT
ejpam-5831	208	8	,	,	PUNCT
ejpam-5831	208	9	the	the	DET
ejpam-5831	208	10	following	follow	VERB
ejpam-5831	208	11	is	be	AUX
ejpam-5831	208	12	an	an	DET
ejpam-5831	208	13	counter	counter	ADJ
ejpam-5831	208	14	example	example	NOUN
ejpam-5831	208	15	for	for	ADP
ejpam-5831	208	16	the	the	DET
ejpam-5831	208	17	above	above	ADJ
ejpam-5831	208	18	proposition	proposition	NOUN
ejpam-5831	208	19	by	by	ADP
ejpam-5831	208	20	taking	take	VERB
ejpam-5831	208	21	µad	µad	ADV
ejpam-5831	208	22	=	=	SYM
ejpam-5831	208	23	sad	sad	ADJ
ejpam-5831	208	24	,	,	PUNCT
ejpam-5831	208	25	pad	pad	PROPN
ejpam-5831	208	26	.	.	PUNCT
ejpam-5831	208	27	example	example	NOUN
ejpam-5831	209	1	3.4	3.4	NUM
ejpam-5831	209	2	.	.	PUNCT
ejpam-5831	210	1	let	let	VERB
ejpam-5831	210	2	a1	a1	NOUN
ejpam-5831	210	3	=	=	SYM
ejpam-5831	210	4	{	{	PUNCT
ejpam-5831	210	5	b	b	PROPN
ejpam-5831	210	6	,	,	PUNCT
ejpam-5831	210	7	c	c	NOUN
ejpam-5831	210	8	,	,	PUNCT
ejpam-5831	210	9	d	d	NOUN
ejpam-5831	210	10	}	}	PUNCT
ejpam-5831	210	11	and	and	CCONJ
ejpam-5831	210	12	by	by	ADP
ejpam-5831	210	13	using	use	VERB
ejpam-5831	210	14	example	example	NOUN
ejpam-5831	210	15	3.1	3.1	NUM
ejpam-5831	210	16	.	.	NUM
ejpam-5831	210	17	,	,	PUNCT
ejpam-5831	210	18	isad(a1	isad(a1	VERB
ejpam-5831	210	19	)	)	PUNCT
ejpam-5831	210	20	=	=	PUNCT
ejpam-5831	210	21	{	{	PUNCT
ejpam-5831	210	22	b	b	NOUN
ejpam-5831	210	23	,	,	PUNCT
ejpam-5831	210	24	d	d	NOUN
ejpam-5831	210	25	}	}	PUNCT
ejpam-5831	210	26	,	,	PUNCT
ejpam-5831	210	27	isad(isad(a1	isad(isad(a1	NOUN
ejpam-5831	210	28	)	)	PUNCT
ejpam-5831	210	29	)	)	PUNCT
ejpam-5831	211	1	=	=	PRON
ejpam-5831	211	2	{	{	PUNCT
ejpam-5831	211	3	b	b	NOUN
ejpam-5831	211	4	,	,	PUNCT
ejpam-5831	211	5	d	d	NOUN
ejpam-5831	211	6	}	}	PUNCT
ejpam-5831	211	7	,	,	PUNCT
ejpam-5831	211	8	then	then	ADV
ejpam-5831	211	9	γsad(isad(a1	γsad(isad(a1	NOUN
ejpam-5831	211	10	)	)	PUNCT
ejpam-5831	211	11	)	)	PUNCT
ejpam-5831	212	1	=	=	SYM
ejpam-5831	212	2	isad{b	isad{b	PROPN
ejpam-5831	212	3	,	,	PUNCT
ejpam-5831	212	4	d	d	NOUN
ejpam-5831	212	5	}	}	PUNCT
ejpam-5831	212	6	=	=	SYM
ejpam-5831	212	7	{	{	PUNCT
ejpam-5831	212	8	b	b	PROPN
ejpam-5831	212	9	,	,	PUNCT
ejpam-5831	212	10	c	c	NOUN
ejpam-5831	212	11	,	,	PUNCT
ejpam-5831	212	12	d	d	NOUN
ejpam-5831	212	13	}	}	PUNCT
ejpam-5831	212	14	̸=	̸=	PROPN
ejpam-5831	212	15	isad(isad(a1	isad(isad(a1	NOUN
ejpam-5831	212	16	)	)	PUNCT
ejpam-5831	212	17	)	)	PUNCT
ejpam-5831	212	18	.	.	PUNCT
ejpam-5831	213	1	let	let	VERB
ejpam-5831	213	2	a2	a2	PROPN
ejpam-5831	213	3	=	=	PUNCT
ejpam-5831	213	4	{	{	PUNCT
ejpam-5831	213	5	c	c	NOUN
ejpam-5831	213	6	}	}	PUNCT
ejpam-5831	213	7	,	,	PUNCT
ejpam-5831	213	8	γpad(a2	γpad(a2	PROPN
ejpam-5831	213	9	)	)	PUNCT
ejpam-5831	213	10	=	=	PRON
ejpam-5831	214	1	{	{	PUNCT
ejpam-5831	214	2	c},γpad(γpad(a2	c},γpad(γpad(a2	NOUN
ejpam-5831	214	3	)	)	PUNCT
ejpam-5831	214	4	)	)	PUNCT
ejpam-5831	215	1	=	=	NOUN
ejpam-5831	215	2	∅	∅	NOUN
ejpam-5831	215	3	,	,	PUNCT
ejpam-5831	215	4	then	then	ADV
ejpam-5831	215	5	ipad(γpad(a2	ipad(γpad(a2	ADJ
ejpam-5831	215	6	)	)	PUNCT
ejpam-5831	215	7	)	)	PUNCT
ejpam-5831	216	1	=	=	SYM
ejpam-5831	216	2	γµad(γµad(a2	γµad(γµad(a2	ADJ
ejpam-5831	216	3	)	)	PUNCT
ejpam-5831	216	4	)	)	PUNCT
ejpam-5831	217	1	=	=	PUNCT
ejpam-5831	217	2	∅	∅	NOUN
ejpam-5831	217	3	=	=	NOUN
ejpam-5831	217	4	̸	̸	X
ejpam-5831	217	5	γµad(a2	γµad(a2	NOUN
ejpam-5831	217	6	)	)	PUNCT
ejpam-5831	217	7	.	.	PUNCT
ejpam-5831	218	1	4	4	X
ejpam-5831	218	2	.	.	NOUN
ejpam-5831	218	3	pretopological	pretopological	ADJ
ejpam-5831	218	4	generalizations	generalization	NOUN
ejpam-5831	218	5	of	of	ADP
ejpam-5831	218	6	rough	rough	ADJ
ejpam-5831	218	7	theory	theory	NOUN
ejpam-5831	218	8	sets	set	VERB
ejpam-5831	218	9	concepts	concept	NOUN
ejpam-5831	218	10	through	through	ADP
ejpam-5831	218	11	this	this	DET
ejpam-5831	218	12	section	section	NOUN
ejpam-5831	218	13	,	,	PUNCT
ejpam-5831	218	14	some	some	DET
ejpam-5831	218	15	generalizations	generalization	NOUN
ejpam-5831	218	16	of	of	ADP
ejpam-5831	218	17	rough	rough	ADJ
ejpam-5831	218	18	theory	theory	NOUN
ejpam-5831	218	19	concepts	concept	NOUN
ejpam-5831	218	20	based	base	VERB
ejpam-5831	218	21	on	on	ADP
ejpam-5831	218	22	pretopological	pretopological	ADJ
ejpam-5831	218	23	space	space	NOUN
ejpam-5831	218	24	are	be	AUX
ejpam-5831	218	25	introduced	introduce	VERB
ejpam-5831	218	26	by	by	ADP
ejpam-5831	218	27	using	use	VERB
ejpam-5831	218	28	iµad	iµad	NOUN
ejpam-5831	218	29	and	and	CCONJ
ejpam-5831	218	30	γµad	γµad	PROPN
ejpam-5831	218	31	approximation	approximation	NOUN
ejpam-5831	218	32	operators	operator	NOUN
ejpam-5831	218	33	.	.	PUNCT
ejpam-5831	219	1	definition	definition	NOUN
ejpam-5831	219	2	4.1	4.1	NUM
ejpam-5831	219	3	.	.	PUNCT
ejpam-5831	220	1	assume	assume	VERB
ejpam-5831	220	2	that	that	SCONJ
ejpam-5831	220	3	(	(	PUNCT
ejpam-5831	220	4	x	x	X
ejpam-5831	220	5	,	,	PUNCT
ejpam-5831	220	6	r	r	NOUN
ejpam-5831	220	7	)	)	PUNCT
ejpam-5831	220	8	is	be	AUX
ejpam-5831	220	9	a	a	DET
ejpam-5831	220	10	pretopological	pretopological	ADJ
ejpam-5831	220	11	approximation	approximation	NOUN
ejpam-5831	220	12	structure	structure	NOUN
ejpam-5831	220	13	and	and	CCONJ
ejpam-5831	220	14	a	a	DET
ejpam-5831	220	15	⊆	⊆	NUM
ejpam-5831	220	16	x.	x.	NOUN
ejpam-5831	220	17	hence	hence	ADV
ejpam-5831	220	18	,	,	PUNCT
ejpam-5831	220	19	∀µad	∀µad	PROPN
ejpam-5831	220	20	∈	∈	PROPN
ejpam-5831	220	21	{	{	PUNCT
ejpam-5831	220	22	sad	sad	ADJ
ejpam-5831	220	23	,	,	PUNCT
ejpam-5831	220	24	pad	pad	NOUN
ejpam-5831	220	25	,	,	PUNCT
ejpam-5831	220	26	βad	βad	PROPN
ejpam-5831	220	27	,	,	PUNCT
ejpam-5831	220	28	αad	αad	PROPN
ejpam-5831	220	29	,	,	PUNCT
ejpam-5831	220	30	γad	γad	PROPN
ejpam-5831	220	31	}	}	PUNCT
ejpam-5831	220	32	we	we	PRON
ejpam-5831	220	33	define	define	VERB
ejpam-5831	220	34	the	the	DET
ejpam-5831	220	35	following	following	NOUN
ejpam-5831	220	36	:	:	PUNCT
ejpam-5831	220	37	i.	i.	PROPN
ejpam-5831	220	38	a	a	PROPN
ejpam-5831	220	39	is	be	AUX
ejpam-5831	220	40	totally	totally	ADV
ejpam-5831	220	41	pretopoligical	pretopoligical	ADJ
ejpam-5831	220	42	µad	µad	ADJ
ejpam-5831	220	43	-	-	PUNCT
ejpam-5831	220	44	definable	definable	ADJ
ejpam-5831	220	45	(	(	PUNCT
ejpam-5831	220	46	µad	µad	ADJ
ejpam-5831	220	47	-	-	PUNCT
ejpam-5831	220	48	exact	exact	ADJ
ejpam-5831	220	49	)	)	PUNCT
ejpam-5831	220	50	set	set	VERB
ejpam-5831	220	51	if	if	SCONJ
ejpam-5831	220	52	iµad(a	iµad(a	PROPN
ejpam-5831	220	53	)	)	PUNCT
ejpam-5831	220	54	=	=	SYM
ejpam-5831	220	55	γµad(a	γµad(a	PROPN
ejpam-5831	220	56	)	)	PUNCT
ejpam-5831	220	57	=	=	SYM
ejpam-5831	220	58	a	a	PROPN
ejpam-5831	220	59	,	,	PUNCT
ejpam-5831	220	60	ii	ii	NOUN
ejpam-5831	220	61	.	.	PUNCT
ejpam-5831	221	1	a	a	PRON
ejpam-5831	221	2	is	be	AUX
ejpam-5831	221	3	internally	internally	ADV
ejpam-5831	221	4	pretopoligical	pretopoligical	ADJ
ejpam-5831	221	5	µad	µad	ADJ
ejpam-5831	221	6	-	-	PUNCT
ejpam-5831	221	7	definable	definable	ADJ
ejpam-5831	221	8	set	set	NOUN
ejpam-5831	221	9	if	if	SCONJ
ejpam-5831	221	10	iµad(a	iµad(a	PROPN
ejpam-5831	221	11	)	)	PUNCT
ejpam-5831	221	12	=	=	SYM
ejpam-5831	221	13	a	a	PRON
ejpam-5831	221	14	and	and	CCONJ
ejpam-5831	221	15	γµad(a	γµad(a	PROPN
ejpam-5831	221	16	)	)	PUNCT
ejpam-5831	221	17	̸=	̸=	PROPN
ejpam-5831	221	18	a	a	DET
ejpam-5831	221	19	,	,	PUNCT
ejpam-5831	221	20	iii	iii	NOUN
ejpam-5831	221	21	.	.	PUNCT
ejpam-5831	222	1	a	a	PRON
ejpam-5831	222	2	is	be	AUX
ejpam-5831	222	3	externally	externally	ADV
ejpam-5831	222	4	pretopoligical	pretopoligical	ADJ
ejpam-5831	222	5	µad	µad	ADJ
ejpam-5831	222	6	-	-	PUNCT
ejpam-5831	222	7	definable	definable	ADJ
ejpam-5831	222	8	set	set	NOUN
ejpam-5831	222	9	if	if	SCONJ
ejpam-5831	222	10	iµad(a	iµad(a	PROPN
ejpam-5831	222	11	)	)	PUNCT
ejpam-5831	222	12	̸=	̸=	PROPN
ejpam-5831	222	13	a	a	PRON
ejpam-5831	222	14	and	and	CCONJ
ejpam-5831	222	15	γµad(a	γµad(a	PROPN
ejpam-5831	222	16	)	)	PUNCT
ejpam-5831	222	17	=	=	SYM
ejpam-5831	223	1	a	a	DET
ejpam-5831	223	2	,	,	PUNCT
ejpam-5831	223	3	iv	iv	X
ejpam-5831	223	4	.	.	PUNCT
ejpam-5831	224	1	a	a	PRON
ejpam-5831	224	2	is	be	AUX
ejpam-5831	224	3	topologically	topologically	ADV
ejpam-5831	224	4	µad	µad	ADJ
ejpam-5831	224	5	-	-	ADJ
ejpam-5831	224	6	indefinable	indefinable	ADJ
ejpam-5831	224	7	(	(	PUNCT
ejpam-5831	224	8	µad	µad	ADJ
ejpam-5831	224	9	-	-	PUNCT
ejpam-5831	224	10	rough	rough	ADJ
ejpam-5831	224	11	)	)	PUNCT
ejpam-5831	224	12	set	set	VERB
ejpam-5831	224	13	if	if	SCONJ
ejpam-5831	224	14	iµad(a	iµad(a	PROPN
ejpam-5831	224	15	)	)	PUNCT
ejpam-5831	224	16	̸=	̸=	PROPN
ejpam-5831	224	17	a	a	PRON
ejpam-5831	224	18	and	and	CCONJ
ejpam-5831	224	19	γµad(a	γµad(a	PROPN
ejpam-5831	224	20	)	)	PUNCT
ejpam-5831	224	21	̸=	̸=	PROPN
ejpam-5831	224	22	a.	a.	NOUN
ejpam-5831	224	23	example	example	NOUN
ejpam-5831	224	24	4.1	4.1	NUM
ejpam-5831	224	25	.	.	PUNCT
ejpam-5831	225	1	by	by	ADP
ejpam-5831	225	2	using	use	VERB
ejpam-5831	225	3	example	example	NOUN
ejpam-5831	225	4	3.1	3.1	NUM
ejpam-5831	225	5	,	,	PUNCT
ejpam-5831	225	6	the	the	DET
ejpam-5831	225	7	set	set	NOUN
ejpam-5831	225	8	a	a	X
ejpam-5831	225	9	=	=	X
ejpam-5831	225	10	{	{	PUNCT
ejpam-5831	225	11	a	a	PRON
ejpam-5831	225	12	}	}	PUNCT
ejpam-5831	225	13	is	be	AUX
ejpam-5831	225	14	topologically	topologically	ADV
ejpam-5831	225	15	αad	αad	ADJ
ejpam-5831	225	16	-	-	ADJ
ejpam-5831	225	17	indefinable	indefinable	ADJ
ejpam-5831	225	18	(	(	PUNCT
ejpam-5831	225	19	αad	αad	NOUN
ejpam-5831	225	20	-	-	ADJ
ejpam-5831	225	21	rough	rough	ADJ
ejpam-5831	225	22	)	)	PUNCT
ejpam-5831	225	23	set	set	NOUN
ejpam-5831	225	24	,	,	PUNCT
ejpam-5831	225	25	the	the	DET
ejpam-5831	225	26	set	set	NOUN
ejpam-5831	225	27	b	b	PROPN
ejpam-5831	225	28	=	=	X
ejpam-5831	225	29	{	{	PUNCT
ejpam-5831	225	30	a	a	X
ejpam-5831	225	31	,	,	PUNCT
ejpam-5831	225	32	c	c	NOUN
ejpam-5831	225	33	}	}	PUNCT
ejpam-5831	225	34	is	be	AUX
ejpam-5831	225	35	totally	totally	ADV
ejpam-5831	225	36	pretopoligical	pretopoligical	ADJ
ejpam-5831	225	37	pad	pad	NOUN
ejpam-5831	225	38	-	-	PUNCT
ejpam-5831	225	39	definable	definable	ADJ
ejpam-5831	225	40	(	(	PUNCT
ejpam-5831	225	41	pad	pad	NOUN
ejpam-5831	225	42	-	-	PUNCT
ejpam-5831	225	43	exact	exact	NOUN
ejpam-5831	225	44	)	)	PUNCT
ejpam-5831	225	45	set	set	NOUN
ejpam-5831	225	46	.	.	PUNCT
ejpam-5831	226	1	definition	definition	NOUN
ejpam-5831	226	2	4.2	4.2	NUM
ejpam-5831	226	3	.	.	PUNCT
ejpam-5831	226	4	suppose	suppose	VERB
ejpam-5831	226	5	that	that	SCONJ
ejpam-5831	226	6	(	(	PUNCT
ejpam-5831	226	7	x	x	X
ejpam-5831	226	8	,	,	PUNCT
ejpam-5831	226	9	r	r	NOUN
ejpam-5831	226	10	)	)	PUNCT
ejpam-5831	226	11	is	be	AUX
ejpam-5831	226	12	a	a	DET
ejpam-5831	226	13	pretopological	pretopological	ADJ
ejpam-5831	226	14	approximation	approximation	NOUN
ejpam-5831	226	15	structure	structure	NOUN
ejpam-5831	226	16	and	and	CCONJ
ejpam-5831	226	17	a	a	DET
ejpam-5831	226	18	⊆	⊆	NUM
ejpam-5831	226	19	x.	x.	NOUN
ejpam-5831	226	20	then	then	ADV
ejpam-5831	226	21	,	,	PUNCT
ejpam-5831	226	22	we	we	PRON
ejpam-5831	226	23	define	define	VERB
ejpam-5831	226	24	the	the	DET
ejpam-5831	226	25	accuracy	accuracy	NOUN
ejpam-5831	226	26	measure	measure	NOUN
ejpam-5831	226	27	of	of	ADP
ejpam-5831	226	28	any	any	DET
ejpam-5831	226	29	set	set	NOUN
ejpam-5831	226	30	a	a	DET
ejpam-5831	226	31	as	as	ADP
ejpam-5831	226	32	:	:	PUNCT
ejpam-5831	226	33	accµad	accµad	NOUN
ejpam-5831	226	34	(	(	PUNCT
ejpam-5831	226	35	a	a	X
ejpam-5831	226	36	)	)	PUNCT
ejpam-5831	226	37	=	=	SYM
ejpam-5831	227	1	|iµad(a)|	|iµad(a)|	PROPN
ejpam-5831	227	2	|γµad(a)|	|γµad(a)|	PROPN
ejpam-5831	227	3	,	,	PUNCT
ejpam-5831	227	4	γµad(a	γµad(a	PROPN
ejpam-5831	227	5	)	)	PUNCT
ejpam-5831	227	6	̸=	̸=	PROPN
ejpam-5831	227	7	∅	∅	NOUN
ejpam-5831	227	8	,	,	PUNCT
ejpam-5831	227	9	where	where	SCONJ
ejpam-5831	227	10	µad	µad	DET
ejpam-5831	227	11	∈	∈	PROPN
ejpam-5831	227	12	{	{	PUNCT
ejpam-5831	227	13	sad	sad	ADJ
ejpam-5831	227	14	,	,	PUNCT
ejpam-5831	227	15	pad	pad	NOUN
ejpam-5831	227	16	,	,	PUNCT
ejpam-5831	227	17	βad	βad	PROPN
ejpam-5831	227	18	,	,	PUNCT
ejpam-5831	227	19	αad	αad	PROPN
ejpam-5831	227	20	,	,	PUNCT
ejpam-5831	227	21	γad	γad	X
ejpam-5831	227	22	}	}	PUNCT
ejpam-5831	227	23	and	and	CCONJ
ejpam-5831	227	24	where	where	SCONJ
ejpam-5831	227	25	|	|	ADV
ejpam-5831	227	26	a	a	DET
ejpam-5831	227	27	|	|	NOUN
ejpam-5831	227	28	is	be	AUX
ejpam-5831	227	29	cardinality	cardinality	NOUN
ejpam-5831	227	30	of	of	ADP
ejpam-5831	227	31	a.	a.	NOUN
ejpam-5831	227	32	by	by	ADP
ejpam-5831	227	33	the	the	DET
ejpam-5831	227	34	accuracy	accuracy	NOUN
ejpam-5831	227	35	measure	measure	NOUN
ejpam-5831	227	36	,	,	PUNCT
ejpam-5831	227	37	we	we	PRON
ejpam-5831	227	38	can	can	AUX
ejpam-5831	227	39	determine	determine	VERB
ejpam-5831	227	40	the	the	DET
ejpam-5831	227	41	exactness	exactness	NOUN
ejpam-5831	227	42	of	of	ADP
ejpam-5831	227	43	any	any	DET
ejpam-5831	227	44	subset	subset	NOUN
ejpam-5831	227	45	a	a	DET
ejpam-5831	227	46	⊆	⊆	NUM
ejpam-5831	227	47	x.	x.	NOUN
ejpam-5831	227	48	the	the	DET
ejpam-5831	227	49	relationship	relationship	NOUN
ejpam-5831	227	50	among	among	ADP
ejpam-5831	227	51	the	the	DET
ejpam-5831	227	52	four	four	NUM
ejpam-5831	227	53	types	type	NOUN
ejpam-5831	227	54	of	of	ADP
ejpam-5831	227	55	accuracy	accuracy	NOUN
ejpam-5831	227	56	measure	measure	NOUN
ejpam-5831	227	57	is	be	AUX
ejpam-5831	227	58	given	give	VERB
ejpam-5831	227	59	as	as	ADP
ejpam-5831	227	60	the	the	DET
ejpam-5831	227	61	following	following	NOUN
ejpam-5831	227	62	:	:	PUNCT
ejpam-5831	227	63	i.	i.	NOUN
ejpam-5831	227	64	0	0	PUNCT
ejpam-5831	227	65	≤	≤	NUM
ejpam-5831	228	1	accd(a	accd(a	ADP
ejpam-5831	228	2	)	)	PUNCT
ejpam-5831	228	3	≤	≤	NUM
ejpam-5831	228	4	accαad	accαad	NOUN
ejpam-5831	228	5	≤	≤	X
ejpam-5831	228	6	accsad	accsad	ADJ
ejpam-5831	228	7	≤	≤	PROPN
ejpam-5831	228	8	accγad	accγad	PROPN
ejpam-5831	228	9	≤	≤	NOUN
ejpam-5831	228	10	accβad	accβad	NOUN
ejpam-5831	228	11	≤	≤	NUM
ejpam-5831	228	12	1	1	NUM
ejpam-5831	228	13	,	,	PUNCT
ejpam-5831	228	14	ii	ii	NOUN
ejpam-5831	228	15	.	.	NOUN
ejpam-5831	228	16	0	0	NUM
ejpam-5831	229	1	≤	≤	NUM
ejpam-5831	230	1	accd(a	accd(a	ADP
ejpam-5831	230	2	)	)	PUNCT
ejpam-5831	230	3	≤	≤	NUM
ejpam-5831	230	4	accαad	accαad	NOUN
ejpam-5831	230	5	≤	≤	PROPN
ejpam-5831	230	6	accpad	accpad	PROPN
ejpam-5831	230	7	≤	≤	PROPN
ejpam-5831	230	8	accγad	accγad	PROPN
ejpam-5831	230	9	≤	≤	NOUN
ejpam-5831	230	10	accβad	accβad	NOUN
ejpam-5831	230	11	≤	≤	NUM
ejpam-5831	230	12	1	1	NUM
ejpam-5831	230	13	.	.	PUNCT
ejpam-5831	231	1	hence	hence	ADV
ejpam-5831	231	2	,	,	PUNCT
ejpam-5831	231	3	the	the	DET
ejpam-5831	231	4	best	good	ADJ
ejpam-5831	231	5	the	the	DET
ejpam-5831	231	6	accuracy	accuracy	NOUN
ejpam-5831	231	7	for	for	ADP
ejpam-5831	231	8	approximation	approximation	NOUN
ejpam-5831	231	9	is	be	AUX
ejpam-5831	231	10	µad	µad	ADJ
ejpam-5831	231	11	=	=	NOUN
ejpam-5831	231	12	βad	βad	NOUN
ejpam-5831	231	13	as	as	ADP
ejpam-5831	231	14	in	in	ADP
ejpam-5831	231	15	the	the	DET
ejpam-5831	231	16	next	next	ADJ
ejpam-5831	231	17	example	example	NOUN
ejpam-5831	231	18	:	:	PUNCT
ejpam-5831	231	19	example	example	NOUN
ejpam-5831	231	20	4.2	4.2	NUM
ejpam-5831	231	21	.	.	PUNCT
ejpam-5831	232	1	continued	continue	VERB
ejpam-5831	232	2	from	from	ADP
ejpam-5831	232	3	example	example	NOUN
ejpam-5831	232	4	3.1	3.1	NUM
ejpam-5831	232	5	.	.	NUM
ejpam-5831	232	6	,	,	PUNCT
ejpam-5831	232	7	the	the	DET
ejpam-5831	232	8	compression	compression	NOUN
ejpam-5831	232	9	between	between	ADP
ejpam-5831	232	10	some	some	DET
ejpam-5831	232	11	types	type	NOUN
ejpam-5831	232	12	of	of	ADP
ejpam-5831	232	13	accuracy	accuracy	NOUN
ejpam-5831	232	14	measure	measure	NOUN
ejpam-5831	232	15	are	be	AUX
ejpam-5831	232	16	listed	list	VERB
ejpam-5831	232	17	in	in	ADP
ejpam-5831	232	18	table	table	NOUN
ejpam-5831	232	19	1	1	NUM
ejpam-5831	232	20	definition	definition	NOUN
ejpam-5831	232	21	4.3	4.3	NUM
ejpam-5831	232	22	.	.	PUNCT
ejpam-5831	233	1	suppose	suppose	VERB
ejpam-5831	233	2	that	that	SCONJ
ejpam-5831	233	3	(	(	PUNCT
ejpam-5831	233	4	x	x	X
ejpam-5831	233	5	,	,	PUNCT
ejpam-5831	233	6	r	r	NOUN
ejpam-5831	233	7	)	)	PUNCT
ejpam-5831	233	8	is	be	AUX
ejpam-5831	233	9	a	a	DET
ejpam-5831	233	10	pretopological	pretopological	ADJ
ejpam-5831	233	11	approximation	approximation	NOUN
ejpam-5831	233	12	structure	structure	NOUN
ejpam-5831	233	13	and	and	CCONJ
ejpam-5831	233	14	a1	a1	NOUN
ejpam-5831	233	15	,	,	PUNCT
ejpam-5831	233	16	a2	a2	PROPN
ejpam-5831	233	17	⊆	⊆	NUM
ejpam-5831	233	18	x.	x.	NOUN
ejpam-5831	233	19	then	then	ADV
ejpam-5831	233	20	,	,	PUNCT
ejpam-5831	233	21	∀µad	∀µad	PROPN
ejpam-5831	233	22	∈	∈	PROPN
ejpam-5831	233	23	{	{	PUNCT
ejpam-5831	233	24	sad	sad	ADJ
ejpam-5831	233	25	,	,	PUNCT
ejpam-5831	233	26	pad	pad	NOUN
ejpam-5831	233	27	,	,	PUNCT
ejpam-5831	233	28	βad	βad	PROPN
ejpam-5831	233	29	,	,	PUNCT
ejpam-5831	233	30	αad	αad	PROPN
ejpam-5831	233	31	,	,	PUNCT
ejpam-5831	233	32	γad	γad	PROPN
ejpam-5831	233	33	}	}	PUNCT
ejpam-5831	233	34	the	the	DET
ejpam-5831	233	35	following	follow	VERB
ejpam-5831	233	36	are	be	AUX
ejpam-5831	233	37	defined	define	VERB
ejpam-5831	233	38	:	:	PUNCT
ejpam-5831	233	39	i.	i.	PROPN
ejpam-5831	233	40	a1⊆̃µada2	a1⊆̃µada2	PROPN
ejpam-5831	233	41	if	if	SCONJ
ejpam-5831	233	42	iµad(a1	iµad(a1	NOUN
ejpam-5831	233	43	)	)	PUNCT
ejpam-5831	233	44	⊆	⊆	NUM
ejpam-5831	233	45	iµad(a2	iµad(a2	NOUN
ejpam-5831	233	46	)	)	PUNCT
ejpam-5831	233	47	,	,	PUNCT
ejpam-5831	234	1	a.	a.	PROPN
ejpam-5831	234	2	a.	a.	PROPN
ejpam-5831	234	3	azza	azza	PROPN
ejpam-5831	234	4	et	et	PROPN
ejpam-5831	234	5	al	al	PROPN
ejpam-5831	234	6	.	.	PUNCT
ejpam-5831	234	7	/	/	SYM
ejpam-5831	234	8	eur	eur	PROPN
ejpam-5831	234	9	.	.	PUNCT
ejpam-5831	235	1	j.	j.	PROPN
ejpam-5831	235	2	pure	pure	PROPN
ejpam-5831	235	3	appl	appl	PROPN
ejpam-5831	235	4	.	.	PROPN
ejpam-5831	235	5	math	math	PROPN
ejpam-5831	235	6	,	,	PUNCT
ejpam-5831	235	7	18	18	NUM
ejpam-5831	235	8	(	(	PUNCT
ejpam-5831	235	9	2	2	NUM
ejpam-5831	235	10	)	)	PUNCT
ejpam-5831	235	11	(	(	PUNCT
ejpam-5831	235	12	2025	2025	NUM
ejpam-5831	235	13	)	)	PUNCT
ejpam-5831	235	14	,	,	PUNCT
ejpam-5831	235	15	5831	5831	NUM
ejpam-5831	235	16	9	9	NUM
ejpam-5831	235	17	of	of	ADP
ejpam-5831	235	18	11	11	NUM
ejpam-5831	235	19	table	table	NOUN
ejpam-5831	235	20	1	1	NUM
ejpam-5831	235	21	:	:	PUNCT
ejpam-5831	235	22	the	the	DET
ejpam-5831	235	23	compression	compression	NOUN
ejpam-5831	235	24	between	between	ADP
ejpam-5831	235	25	some	some	DET
ejpam-5831	235	26	types	type	NOUN
ejpam-5831	235	27	of	of	ADP
ejpam-5831	235	28	accuracy	accuracy	NOUN
ejpam-5831	235	29	measure	measure	NOUN
ejpam-5831	235	30	seta	seta	PROPN
ejpam-5831	235	31	accsad	accsad	PROPN
ejpam-5831	235	32	accβad	accβad	PROPN
ejpam-5831	235	33	{	{	PUNCT
ejpam-5831	235	34	a	a	PROPN
ejpam-5831	235	35	,	,	PUNCT
ejpam-5831	235	36	b	b	NOUN
ejpam-5831	235	37	}	}	SYM
ejpam-5831	235	38	1	1	NUM
ejpam-5831	235	39	3	3	NUM
ejpam-5831	235	40	2	2	NUM
ejpam-5831	235	41	3	3	NUM
ejpam-5831	235	42	{	{	PUNCT
ejpam-5831	235	43	a	a	PRON
ejpam-5831	235	44	,	,	PUNCT
ejpam-5831	235	45	c	c	NOUN
ejpam-5831	235	46	}	}	SYM
ejpam-5831	236	1	1	1	NUM
ejpam-5831	236	2	2	2	NUM
ejpam-5831	236	3	1	1	NUM
ejpam-5831	236	4	{	{	PUNCT
ejpam-5831	236	5	b	b	NOUN
ejpam-5831	236	6	,	,	PUNCT
ejpam-5831	236	7	d	d	NOUN
ejpam-5831	236	8	}	}	SYM
ejpam-5831	236	9	2	2	NUM
ejpam-5831	236	10	3	3	NUM
ejpam-5831	236	11	1	1	NUM
ejpam-5831	236	12	{	{	PUNCT
ejpam-5831	236	13	a	a	PRON
ejpam-5831	236	14	,	,	PUNCT
ejpam-5831	236	15	b	b	NOUN
ejpam-5831	236	16	,	,	PUNCT
ejpam-5831	236	17	c	c	NOUN
ejpam-5831	236	18	}	}	SYM
ejpam-5831	236	19	1	1	NUM
ejpam-5831	236	20	3	3	NUM
ejpam-5831	236	21	1	1	NUM
ejpam-5831	236	22	ii	ii	NOUN
ejpam-5831	236	23	.	.	PUNCT
ejpam-5831	237	1	a1⊆̃	a1⊆̃	PROPN
ejpam-5831	237	2	µad	µad	PROPN
ejpam-5831	237	3	a2	a2	PROPN
ejpam-5831	237	4	if	if	SCONJ
ejpam-5831	237	5	γµad(a1	γµad(a1	NOUN
ejpam-5831	237	6	)	)	PUNCT
ejpam-5831	237	7	⊆	⊆	NUM
ejpam-5831	237	8	γµad(a2	γµad(a2	NOUN
ejpam-5831	237	9	)	)	PUNCT
ejpam-5831	237	10	.	.	PUNCT
ejpam-5831	237	11	example	example	NOUN
ejpam-5831	238	1	4.3	4.3	NUM
ejpam-5831	238	2	.	.	PUNCT
ejpam-5831	239	1	by	by	ADP
ejpam-5831	239	2	using	use	VERB
ejpam-5831	239	3	example	example	NOUN
ejpam-5831	239	4	3.1	3.1	NUM
ejpam-5831	239	5	,	,	PUNCT
ejpam-5831	239	6	consider	consider	VERB
ejpam-5831	239	7	a1	a1	NOUN
ejpam-5831	239	8	=	=	SYM
ejpam-5831	239	9	{	{	PUNCT
ejpam-5831	239	10	d	d	NOUN
ejpam-5831	239	11	}	}	PUNCT
ejpam-5831	239	12	,	,	PUNCT
ejpam-5831	239	13	a2	a2	PROPN
ejpam-5831	239	14	=	=	PUNCT
ejpam-5831	239	15	{	{	PUNCT
ejpam-5831	239	16	a	a	X
ejpam-5831	239	17	,	,	PUNCT
ejpam-5831	239	18	c	c	NOUN
ejpam-5831	239	19	}	}	PUNCT
ejpam-5831	239	20	,	,	PUNCT
ejpam-5831	239	21	a3	a3	NOUN
ejpam-5831	239	22	=	=	SYM
ejpam-5831	239	23	{	{	PUNCT
ejpam-5831	239	24	b	b	PROPN
ejpam-5831	239	25	,	,	PUNCT
ejpam-5831	239	26	d	d	NOUN
ejpam-5831	239	27	}	}	PUNCT
ejpam-5831	239	28	and	and	CCONJ
ejpam-5831	239	29	a4	a4	NOUN
ejpam-5831	239	30	=	=	SYM
ejpam-5831	239	31	{	{	PUNCT
ejpam-5831	239	32	c	c	NOUN
ejpam-5831	239	33	,	,	PUNCT
ejpam-5831	239	34	d	d	NOUN
ejpam-5831	239	35	}	}	PUNCT
ejpam-5831	239	36	.	.	PUNCT
ejpam-5831	240	1	hence	hence	ADV
ejpam-5831	240	2	,	,	PUNCT
ejpam-5831	240	3	we	we	PRON
ejpam-5831	240	4	have	have	VERB
ejpam-5831	240	5	:	:	PUNCT
ejpam-5831	240	6	a1⊆̃	a1⊆̃	ADP
ejpam-5831	240	7	sad	sad	PROPN
ejpam-5831	240	8	a2	a2	PROPN
ejpam-5831	240	9	and	and	CCONJ
ejpam-5831	240	10	a3⊆̃βada4	a3⊆̃βada4	PROPN
ejpam-5831	240	11	.	.	PUNCT
ejpam-5831	241	1	proposition	proposition	NOUN
ejpam-5831	241	2	4.1	4.1	NUM
ejpam-5831	241	3	.	.	PUNCT
ejpam-5831	242	1	assume	assume	VERB
ejpam-5831	242	2	that	that	SCONJ
ejpam-5831	242	3	(	(	PUNCT
ejpam-5831	242	4	x	x	X
ejpam-5831	242	5	,	,	PUNCT
ejpam-5831	242	6	r	r	NOUN
ejpam-5831	242	7	)	)	PUNCT
ejpam-5831	242	8	be	be	AUX
ejpam-5831	242	9	a	a	DET
ejpam-5831	242	10	pretopological	pretopological	ADJ
ejpam-5831	242	11	approximation	approximation	NOUN
ejpam-5831	242	12	structure	structure	NOUN
ejpam-5831	242	13	and	and	CCONJ
ejpam-5831	242	14	a	a	DET
ejpam-5831	242	15	⊆	⊆	NUM
ejpam-5831	242	16	x.	x.	NOUN
ejpam-5831	242	17	then	then	ADV
ejpam-5831	242	18	,	,	PUNCT
ejpam-5831	242	19	∀µad	∀µad	PROPN
ejpam-5831	242	20	∈	∈	PROPN
ejpam-5831	242	21	{	{	PUNCT
ejpam-5831	242	22	sad	sad	ADJ
ejpam-5831	242	23	,	,	PUNCT
ejpam-5831	242	24	pad	pad	NOUN
ejpam-5831	242	25	,	,	PUNCT
ejpam-5831	242	26	βad	βad	PROPN
ejpam-5831	242	27	,	,	PUNCT
ejpam-5831	242	28	αad	αad	PROPN
ejpam-5831	242	29	,	,	PUNCT
ejpam-5831	242	30	γad	γad	PROPN
ejpam-5831	242	31	}	}	PUNCT
ejpam-5831	242	32	,	,	PUNCT
ejpam-5831	243	1	x	x	PUNCT
ejpam-5831	243	2	∈	∈	NOUN
ejpam-5831	243	3	x	x	PUNCT
ejpam-5831	243	4	the	the	DET
ejpam-5831	243	5	following	follow	VERB
ejpam-5831	243	6	are	be	AUX
ejpam-5831	243	7	defined	define	VERB
ejpam-5831	243	8	:	:	PUNCT
ejpam-5831	243	9	i.	i.	NOUN
ejpam-5831	243	10	if	if	SCONJ
ejpam-5831	243	11	x∈̃µada	x∈̃µada	PROPN
ejpam-5831	243	12	,	,	PUNCT
ejpam-5831	243	13	hence	hence	ADV
ejpam-5831	243	14	x	x	ADP
ejpam-5831	243	15	∈	∈	PROPN
ejpam-5831	243	16	a	a	DET
ejpam-5831	243	17	,	,	PUNCT
ejpam-5831	243	18	ii	ii	NOUN
ejpam-5831	243	19	.	.	PUNCT
ejpam-5831	244	1	if	if	SCONJ
ejpam-5831	244	2	x/̃∈µada	x/̃∈µada	PROPN
ejpam-5831	244	3	,	,	PUNCT
ejpam-5831	244	4	hence	hence	ADV
ejpam-5831	244	5	x	x	NOUN
ejpam-5831	244	6	/∈	/∈	PUNCT
ejpam-5831	244	7	a.	a.	NOUN
ejpam-5831	244	8	proof	proof	NOUN
ejpam-5831	244	9	it	it	PRON
ejpam-5831	244	10	’s	’	VERB
ejpam-5831	244	11	clear	clear	ADJ
ejpam-5831	244	12	from	from	ADP
ejpam-5831	244	13	the	the	DET
ejpam-5831	244	14	above	above	ADJ
ejpam-5831	244	15	definition	definition	NOUN
ejpam-5831	244	16	.	.	PUNCT
ejpam-5831	245	1	□	□	PUNCT
ejpam-5831	245	2	the	the	DET
ejpam-5831	245	3	next	next	ADJ
ejpam-5831	245	4	example	example	NOUN
ejpam-5831	245	5	shows	show	VERB
ejpam-5831	245	6	that	that	SCONJ
ejpam-5831	245	7	the	the	DET
ejpam-5831	245	8	converse	converse	NOUN
ejpam-5831	245	9	of	of	ADP
ejpam-5831	245	10	proposition	proposition	NOUN
ejpam-5831	245	11	4.1	4.1	NUM
ejpam-5831	245	12	does	do	AUX
ejpam-5831	245	13	n’t	not	PART
ejpam-5831	245	14	hold	hold	VERB
ejpam-5831	245	15	in	in	ADP
ejpam-5831	245	16	general	general	ADJ
ejpam-5831	245	17	:	:	PUNCT
ejpam-5831	245	18	the	the	DET
ejpam-5831	245	19	converse	converse	NOUN
ejpam-5831	245	20	of	of	ADP
ejpam-5831	245	21	the	the	DET
ejpam-5831	245	22	proposition	proposition	NOUN
ejpam-5831	245	23	4.4	4.4	NUM
ejpam-5831	245	24	is	be	AUX
ejpam-5831	245	25	not	not	PART
ejpam-5831	245	26	true	true	ADJ
ejpam-5831	245	27	as	as	ADP
ejpam-5831	245	28	in	in	ADP
ejpam-5831	245	29	the	the	DET
ejpam-5831	245	30	following	follow	VERB
ejpam-5831	245	31	example	example	NOUN
ejpam-5831	245	32	:	:	PUNCT
ejpam-5831	245	33	example	example	NOUN
ejpam-5831	245	34	4.4	4.4	NUM
ejpam-5831	245	35	.	.	PUNCT
ejpam-5831	246	1	continued	continue	VERB
ejpam-5831	246	2	from	from	ADP
ejpam-5831	246	3	example	example	NOUN
ejpam-5831	246	4	3.1	3.1	NUM
ejpam-5831	246	5	,	,	PUNCT
ejpam-5831	246	6	let	let	VERB
ejpam-5831	246	7	a1	a1	NOUN
ejpam-5831	246	8	=	=	PUNCT
ejpam-5831	246	9	{	{	PUNCT
ejpam-5831	246	10	a	a	PRON
ejpam-5831	246	11	,	,	PUNCT
ejpam-5831	246	12	b.c	b.c	NOUN
ejpam-5831	246	13	}	}	PUNCT
ejpam-5831	246	14	and	and	CCONJ
ejpam-5831	246	15	a2	a2	PROPN
ejpam-5831	246	16	=	=	PUNCT
ejpam-5831	246	17	{	{	PUNCT
ejpam-5831	246	18	a	a	X
ejpam-5831	246	19	,	,	PUNCT
ejpam-5831	246	20	d	d	NOUN
ejpam-5831	246	21	}	}	PUNCT
ejpam-5831	246	22	,	,	PUNCT
ejpam-5831	246	23	then	then	ADV
ejpam-5831	246	24	we	we	PRON
ejpam-5831	246	25	get	get	VERB
ejpam-5831	246	26	b	b	PROPN
ejpam-5831	246	27	∈	∈	PROPN
ejpam-5831	246	28	a1	a1	NOUN
ejpam-5831	246	29	,	,	PUNCT
ejpam-5831	246	30	but	but	CCONJ
ejpam-5831	246	31	b	b	X
ejpam-5831	246	32	/̃∈µada1	/̃∈µada1	PROPN
ejpam-5831	246	33	.	.	PUNCT
ejpam-5831	247	1	also	also	ADV
ejpam-5831	247	2	,	,	PUNCT
ejpam-5831	247	3	b	b	PROPN
ejpam-5831	247	4	/∈	/∈	PUNCT
ejpam-5831	247	5	a2	a2	PROPN
ejpam-5831	247	6	,	,	PUNCT
ejpam-5831	247	7	but	but	CCONJ
ejpam-5831	247	8	b∈̃sada2	b∈̃sada2	NOUN
ejpam-5831	247	9	and	and	CCONJ
ejpam-5831	247	10	b∈̃γada2	b∈̃γada2	NOUN
ejpam-5831	247	11	.	.	PUNCT
ejpam-5831	248	1	5	5	X
ejpam-5831	248	2	.	.	X
ejpam-5831	248	3	conclusion	conclusion	NOUN
ejpam-5831	248	4	this	this	DET
ejpam-5831	248	5	paper	paper	NOUN
ejpam-5831	248	6	used	use	VERB
ejpam-5831	248	7	the	the	DET
ejpam-5831	248	8	pretopological	pretopological	ADJ
ejpam-5831	248	9	concepts	concept	NOUN
ejpam-5831	248	10	to	to	PART
ejpam-5831	248	11	generate	generate	VERB
ejpam-5831	248	12	rough	rough	ADJ
ejpam-5831	248	13	approximation	approximation	NOUN
ejpam-5831	248	14	space	space	NOUN
ejpam-5831	248	15	.	.	PUNCT
ejpam-5831	249	1	different	different	ADJ
ejpam-5831	249	2	types	type	NOUN
ejpam-5831	249	3	of	of	ADP
ejpam-5831	249	4	lower	low	ADJ
ejpam-5831	249	5	and	and	CCONJ
ejpam-5831	249	6	upper	upper	ADJ
ejpam-5831	249	7	approximation	approximation	NOUN
ejpam-5831	249	8	are	be	AUX
ejpam-5831	249	9	generated	generate	VERB
ejpam-5831	249	10	based	base	VERB
ejpam-5831	249	11	on	on	ADP
ejpam-5831	249	12	pretopological	pretopological	ADJ
ejpam-5831	249	13	space	space	NOUN
ejpam-5831	249	14	.	.	PUNCT
ejpam-5831	250	1	we	we	PRON
ejpam-5831	250	2	have	have	AUX
ejpam-5831	250	3	got	get	VERB
ejpam-5831	250	4	the	the	DET
ejpam-5831	250	5	best	good	ADJ
ejpam-5831	250	6	the	the	DET
ejpam-5831	250	7	accuracy	accuracy	NOUN
ejpam-5831	250	8	for	for	ADP
ejpam-5831	250	9	approximation	approximation	NOUN
ejpam-5831	250	10	using	use	VERB
ejpam-5831	250	11	our	our	PRON
ejpam-5831	250	12	approach	approach	NOUN
ejpam-5831	250	13	.	.	PUNCT
ejpam-5831	251	1	our	our	PRON
ejpam-5831	251	2	approach	approach	NOUN
ejpam-5831	251	3	will	will	AUX
ejpam-5831	251	4	be	be	AUX
ejpam-5831	251	5	useful	useful	ADJ
ejpam-5831	251	6	in	in	ADP
ejpam-5831	251	7	knowledge	knowledge	NOUN
ejpam-5831	251	8	discovery	discovery	NOUN
ejpam-5831	251	9	.	.	PUNCT
ejpam-5831	252	1	in	in	ADP
ejpam-5831	252	2	the	the	DET
ejpam-5831	252	3	future	future	ADJ
ejpam-5831	252	4	work	work	NOUN
ejpam-5831	252	5	,	,	PUNCT
ejpam-5831	252	6	we	we	PRON
ejpam-5831	252	7	will	will	AUX
ejpam-5831	252	8	study	study	VERB
ejpam-5831	252	9	more	more	ADJ
ejpam-5831	252	10	applications	application	NOUN
ejpam-5831	252	11	of	of	ADP
ejpam-5831	252	12	these	these	DET
ejpam-5831	252	13	tools	tool	NOUN
ejpam-5831	252	14	based	base	VERB
ejpam-5831	252	15	on	on	ADP
ejpam-5831	252	16	generalizations	generalization	NOUN
ejpam-5831	252	17	of	of	ADP
ejpam-5831	252	18	pretopological	pretopological	ADJ
ejpam-5831	252	19	concepts	concept	NOUN
ejpam-5831	252	20	.	.	PUNCT
ejpam-5831	253	1	moreover	moreover	ADV
ejpam-5831	253	2	,	,	PUNCT
ejpam-5831	253	3	we	we	PRON
ejpam-5831	253	4	will	will	AUX
ejpam-5831	253	5	study	study	VERB
ejpam-5831	253	6	the	the	DET
ejpam-5831	253	7	connection	connection	NOUN
ejpam-5831	253	8	between	between	ADP
ejpam-5831	253	9	pretopological	pretopological	ADJ
ejpam-5831	253	10	spaces	space	NOUN
ejpam-5831	253	11	and	and	CCONJ
ejpam-5831	253	12	soft	soft	ADJ
ejpam-5831	253	13	set	set	NOUN
ejpam-5831	253	14	theory	theory	NOUN
ejpam-5831	253	15	.	.	PUNCT
ejpam-5831	254	1	acknowledgements	acknowledgement	NOUN
ejpam-5831	254	2	this	this	DET
ejpam-5831	254	3	study	study	NOUN
ejpam-5831	254	4	is	be	AUX
ejpam-5831	254	5	supported	support	VERB
ejpam-5831	254	6	via	via	ADP
ejpam-5831	254	7	funding	funding	NOUN
ejpam-5831	254	8	from	from	ADP
ejpam-5831	254	9	prince	prince	PROPN
ejpam-5831	254	10	sattam	sattam	PROPN
ejpam-5831	254	11	bin	bin	PROPN
ejpam-5831	254	12	abdulaziz	abdulaziz	PROPN
ejpam-5831	254	13	university	university	PROPN
ejpam-5831	254	14	project	project	NOUN
ejpam-5831	254	15	number	number	NOUN
ejpam-5831	254	16	(	(	PUNCT
ejpam-5831	254	17	psau/2025	psau/2025	NOUN
ejpam-5831	254	18	/	/	SYM
ejpam-5831	254	19	r/1446	r/1446	PROPN
ejpam-5831	254	20	)	)	PUNCT
ejpam-5831	254	21	.	.	PUNCT
ejpam-5831	255	1	a.	a.	PROPN
ejpam-5831	255	2	a.	a.	PROPN
ejpam-5831	255	3	azza	azza	PROPN
ejpam-5831	255	4	et	et	PROPN
ejpam-5831	255	5	al	al	PROPN
ejpam-5831	255	6	.	.	PUNCT
ejpam-5831	255	7	/	/	SYM
ejpam-5831	255	8	eur	eur	PROPN
ejpam-5831	255	9	.	.	PUNCT
ejpam-5831	256	1	j.	j.	PROPN
ejpam-5831	256	2	pure	pure	PROPN
ejpam-5831	256	3	appl	appl	PROPN
ejpam-5831	256	4	.	.	PROPN
ejpam-5831	256	5	math	math	PROPN
ejpam-5831	256	6	,	,	PUNCT
ejpam-5831	256	7	18	18	NUM
ejpam-5831	256	8	(	(	PUNCT
ejpam-5831	256	9	2	2	NUM
ejpam-5831	256	10	)	)	PUNCT
ejpam-5831	256	11	(	(	PUNCT
ejpam-5831	256	12	2025	2025	NUM
ejpam-5831	256	13	)	)	PUNCT
ejpam-5831	256	14	,	,	PUNCT
ejpam-5831	256	15	5831	5831	NUM
ejpam-5831	256	16	10	10	NUM
ejpam-5831	256	17	of	of	ADP
ejpam-5831	256	18	11	11	NUM
ejpam-5831	256	19	references	reference	NOUN
ejpam-5831	256	20	[	[	X
ejpam-5831	256	21	1	1	NUM
ejpam-5831	256	22	]	]	PUNCT
ejpam-5831	256	23	h.	h.	PROPN
ejpam-5831	256	24	m.	m.	PROPN
ejpam-5831	256	25	abu	abu	PROPN
ejpam-5831	256	26	-	-	PUNCT
ejpam-5831	256	27	donia	donia	PROPN
ejpam-5831	256	28	.	.	PUNCT
ejpam-5831	257	1	multi	multi	PROPN
ejpam-5831	257	2	knowledge	knowledge	NOUN
ejpam-5831	257	3	based	base	VERB
ejpam-5831	257	4	rough	rough	ADJ
ejpam-5831	257	5	approximations	approximation	NOUN
ejpam-5831	257	6	and	and	CCONJ
ejpam-5831	257	7	applications	application	NOUN
ejpam-5831	257	8	.	.	PUNCT
ejpam-5831	258	1	knowledge	knowledge	NOUN
ejpam-5831	258	2	-	-	PUNCT
ejpam-5831	258	3	based	base	VERB
ejpam-5831	258	4	systems	system	NOUN
ejpam-5831	258	5	,	,	PUNCT
ejpam-5831	258	6	26:20–29	26:20–29	NUM
ejpam-5831	258	7	,	,	PUNCT
ejpam-5831	258	8	2012	2012	NUM
ejpam-5831	258	9	.	.	PUNCT
ejpam-5831	259	1	[	[	X
ejpam-5831	259	2	2	2	X
ejpam-5831	259	3	]	]	PUNCT
ejpam-5831	259	4	h.	h.	PROPN
ejpam-5831	259	5	m.	m.	PROPN
ejpam-5831	259	6	abu	abu	PROPN
ejpam-5831	259	7	-	-	PUNCT
ejpam-5831	259	8	donia	donia	PROPN
ejpam-5831	259	9	and	and	CCONJ
ejpam-5831	259	10	a.	a.	NOUN
ejpam-5831	259	11	s.	s.	PROPN
ejpam-5831	259	12	salama	salama	PROPN
ejpam-5831	259	13	.	.	PUNCT
ejpam-5831	260	1	generalization	generalization	NOUN
ejpam-5831	260	2	of	of	ADP
ejpam-5831	260	3	pawlak	pawlak	ADJ
ejpam-5831	260	4	’s	’s	PART
ejpam-5831	260	5	rough	rough	ADJ
ejpam-5831	260	6	approximation	approximation	NOUN
ejpam-5831	260	7	spaces	space	NOUN
ejpam-5831	260	8	by	by	ADP
ejpam-5831	260	9	using	use	VERB
ejpam-5831	260	10	δ	δ	PROPN
ejpam-5831	260	11	-	-	PUNCT
ejpam-5831	260	12	open	open	ADJ
ejpam-5831	260	13	sets	set	NOUN
ejpam-5831	260	14	.	.	PUNCT
ejpam-5831	261	1	international	international	ADJ
ejpam-5831	261	2	journal	journal	PROPN
ejpam-5831	261	3	of	of	ADP
ejpam-5831	261	4	approximate	approximate	ADJ
ejpam-5831	261	5	reasoning	reasoning	NOUN
ejpam-5831	261	6	,	,	PUNCT
ejpam-5831	261	7	53:1094–1105	53:1094–1105	NUM
ejpam-5831	261	8	,	,	PUNCT
ejpam-5831	261	9	2012	2012	NUM
ejpam-5831	261	10	.	.	PUNCT
ejpam-5831	262	1	[	[	X
ejpam-5831	262	2	3	3	X
ejpam-5831	262	3	]	]	PUNCT
ejpam-5831	262	4	t.	t.	PROPN
ejpam-5831	262	5	m.	m.	PROPN
ejpam-5831	262	6	al	al	PROPN
ejpam-5831	262	7	-	-	PUNCT
ejpam-5831	262	8	shami	shami	PROPN
ejpam-5831	262	9	and	and	CCONJ
ejpam-5831	262	10	a.	a.	NOUN
ejpam-5831	262	11	mhemdi	mhemdi	PROPN
ejpam-5831	262	12	.	.	PUNCT
ejpam-5831	263	1	overlapping	overlap	VERB
ejpam-5831	263	2	containment	containment	NOUN
ejpam-5831	263	3	rough	rough	ADJ
ejpam-5831	263	4	neighborhoods	neighborhood	NOUN
ejpam-5831	263	5	and	and	CCONJ
ejpam-5831	263	6	their	their	PRON
ejpam-5831	263	7	generalized	generalized	ADJ
ejpam-5831	263	8	approximation	approximation	NOUN
ejpam-5831	263	9	spaces	space	NOUN
ejpam-5831	263	10	with	with	ADP
ejpam-5831	263	11	applications	application	NOUN
ejpam-5831	263	12	.	.	PUNCT
ejpam-5831	264	1	journal	journal	NOUN
ejpam-5831	264	2	of	of	ADP
ejpam-5831	264	3	applied	apply	VERB
ejpam-5831	264	4	mathematics	mathematic	NOUN
ejpam-5831	264	5	and	and	CCONJ
ejpam-5831	264	6	computing	computing	NOUN
ejpam-5831	264	7	,	,	PUNCT
ejpam-5831	264	8	71(1):869–900	71(1):869–900	NUM
ejpam-5831	264	9	,	,	PUNCT
ejpam-5831	264	10	2024	2024	NUM
ejpam-5831	264	11	.	.	PUNCT
ejpam-5831	265	1	[	[	X
ejpam-5831	265	2	4	4	X
ejpam-5831	265	3	]	]	PUNCT
ejpam-5831	265	4	k.	k.	PROPN
ejpam-5831	265	5	kaur	kaur	PROPN
ejpam-5831	265	6	,	,	PUNCT
ejpam-5831	265	7	a.	a.	PROPN
ejpam-5831	265	8	gupta	gupta	PROPN
ejpam-5831	265	9	,	,	PUNCT
ejpam-5831	265	10	t.	t.	PROPN
ejpam-5831	265	11	m.	m.	PROPN
ejpam-5831	265	12	al	al	PROPN
ejpam-5831	265	13	-	-	PUNCT
ejpam-5831	265	14	shami	shami	PROPN
ejpam-5831	265	15	,	,	PUNCT
ejpam-5831	265	16	and	and	CCONJ
ejpam-5831	265	17	m.	m.	PROPN
ejpam-5831	265	18	hosny	hosny	PROPN
ejpam-5831	265	19	.	.	PUNCT
ejpam-5831	266	1	a	a	DET
ejpam-5831	266	2	new	new	ADJ
ejpam-5831	266	3	multi	multi	ADJ
ejpam-5831	266	4	-	-	ADJ
ejpam-5831	266	5	ideal	ideal	ADJ
ejpam-5831	266	6	nanotopological	nanotopological	ADJ
ejpam-5831	266	7	model	model	NOUN
ejpam-5831	266	8	via	via	ADP
ejpam-5831	266	9	neighborhoods	neighborhood	NOUN
ejpam-5831	266	10	for	for	ADP
ejpam-5831	266	11	diagnosis	diagnosis	NOUN
ejpam-5831	266	12	and	and	CCONJ
ejpam-5831	266	13	cure	cure	NOUN
ejpam-5831	266	14	of	of	ADP
ejpam-5831	266	15	dengue	dengue	NOUN
ejpam-5831	266	16	.	.	PUNCT
ejpam-5831	267	1	computational	computational	ADJ
ejpam-5831	267	2	and	and	CCONJ
ejpam-5831	267	3	applied	applied	ADJ
ejpam-5831	267	4	mathematics	mathematic	NOUN
ejpam-5831	267	5	,	,	PUNCT
ejpam-5831	267	6	43:400	43:400	NUM
ejpam-5831	267	7	,	,	PUNCT
ejpam-5831	267	8	2024	2024	NUM
ejpam-5831	267	9	.	.	PUNCT
ejpam-5831	268	1	[	[	X
ejpam-5831	268	2	5	5	NUM
ejpam-5831	268	3	]	]	PUNCT
ejpam-5831	268	4	a.	a.	PROPN
ejpam-5831	268	5	galton	galton	PROPN
ejpam-5831	268	6	.	.	PUNCT
ejpam-5831	269	1	a	a	DET
ejpam-5831	269	2	generalized	generalized	ADJ
ejpam-5831	269	3	topological	topological	ADJ
ejpam-5831	269	4	view	view	NOUN
ejpam-5831	269	5	of	of	ADP
ejpam-5831	269	6	motion	motion	NOUN
ejpam-5831	269	7	in	in	ADP
ejpam-5831	269	8	discrete	discrete	ADJ
ejpam-5831	269	9	space	space	NOUN
ejpam-5831	269	10	.	.	PUNCT
ejpam-5831	270	1	theoretical	theoretical	ADJ
ejpam-5831	270	2	computer	computer	NOUN
ejpam-5831	270	3	science	science	NOUN
ejpam-5831	270	4	,	,	PUNCT
ejpam-5831	270	5	305(1–3):111–134	305(1–3):111–134	NUM
ejpam-5831	270	6	,	,	PUNCT
ejpam-5831	270	7	2003	2003	NUM
ejpam-5831	270	8	.	.	PUNCT
ejpam-5831	271	1	[	[	X
ejpam-5831	271	2	6	6	NUM
ejpam-5831	271	3	]	]	PUNCT
ejpam-5831	271	4	tareq	tareq	PROPN
ejpam-5831	271	5	m.	m.	PROPN
ejpam-5831	271	6	al	al	PROPN
ejpam-5831	271	7	-	-	PUNCT
ejpam-5831	271	8	shami	shami	PROPN
ejpam-5831	271	9	,	,	PUNCT
ejpam-5831	271	10	zanyar	zanyar	PROPN
ejpam-5831	271	11	a.	a.	NOUN
ejpam-5831	271	12	ameen	ameen	PROPN
ejpam-5831	271	13	,	,	PUNCT
ejpam-5831	271	14	radwan	radwan	VERB
ejpam-5831	271	15	abu	abu	PROPN
ejpam-5831	271	16	-	-	PUNCT
ejpam-5831	271	17	gdairi	gdairi	PROPN
ejpam-5831	271	18	,	,	PUNCT
ejpam-5831	271	19	and	and	CCONJ
ejpam-5831	271	20	abdelwaheb	abdelwaheb	PROPN
ejpam-5831	271	21	mhemdi	mhemdi	PROPN
ejpam-5831	271	22	.	.	PUNCT
ejpam-5831	272	1	on	on	ADP
ejpam-5831	272	2	primal	primal	ADJ
ejpam-5831	272	3	soft	soft	ADJ
ejpam-5831	272	4	topology	topology	NOUN
ejpam-5831	272	5	.	.	PUNCT
ejpam-5831	273	1	mathematics	mathematic	NOUN
ejpam-5831	273	2	,	,	PUNCT
ejpam-5831	273	3	11(10):23–29	11(10):23–29	NUM
ejpam-5831	273	4	,	,	PUNCT
ejpam-5831	273	5	2023	2023	NUM
ejpam-5831	273	6	.	.	PUNCT
ejpam-5831	274	1	[	[	X
ejpam-5831	274	2	7	7	X
ejpam-5831	274	3	]	]	X
ejpam-5831	274	4	r.	r.	PROPN
ejpam-5831	274	5	mareay	mareay	PROPN
ejpam-5831	274	6	,	,	PUNCT
ejpam-5831	274	7	r.	r.	PROPN
ejpam-5831	274	8	abu	abu	PROPN
ejpam-5831	274	9	-	-	PUNCT
ejpam-5831	274	10	gdairi	gdairi	PROPN
ejpam-5831	274	11	,	,	PUNCT
ejpam-5831	274	12	and	and	CCONJ
ejpam-5831	274	13	m.	m.	PROPN
ejpam-5831	274	14	badr	badr	PROPN
ejpam-5831	274	15	.	.	PUNCT
ejpam-5831	275	1	modeling	modeling	NOUN
ejpam-5831	275	2	of	of	ADP
ejpam-5831	275	3	covid-19	covid-19	PROPN
ejpam-5831	275	4	in	in	ADP
ejpam-5831	275	5	view	view	NOUN
ejpam-5831	275	6	of	of	ADP
ejpam-5831	275	7	rough	rough	ADJ
ejpam-5831	275	8	topology	topology	NOUN
ejpam-5831	275	9	.	.	PUNCT
ejpam-5831	276	1	axioms	axiom	NOUN
ejpam-5831	276	2	,	,	PUNCT
ejpam-5831	276	3	12:663	12:663	NUM
ejpam-5831	276	4	,	,	PUNCT
ejpam-5831	276	5	2023	2023	NUM
ejpam-5831	276	6	.	.	PUNCT
ejpam-5831	277	1	[	[	X
ejpam-5831	277	2	8	8	NUM
ejpam-5831	277	3	]	]	X
ejpam-5831	277	4	r.	r.	PROPN
ejpam-5831	277	5	mareay	mareay	PROPN
ejpam-5831	277	6	,	,	PUNCT
ejpam-5831	277	7	i.	i.	PROPN
ejpam-5831	277	8	noaman	noaman	PROPN
ejpam-5831	277	9	,	,	PUNCT
ejpam-5831	277	10	r.	r.	PROPN
ejpam-5831	277	11	abu	abu	PROPN
ejpam-5831	277	12	-	-	PUNCT
ejpam-5831	277	13	gdairi	gdairi	PROPN
ejpam-5831	277	14	,	,	PUNCT
ejpam-5831	277	15	and	and	CCONJ
ejpam-5831	277	16	m.	m.	PROPN
ejpam-5831	277	17	badr	badr	PROPN
ejpam-5831	277	18	.	.	PUNCT
ejpam-5831	278	1	on	on	ADP
ejpam-5831	278	2	covering	covering	NOUN
ejpam-5831	278	3	-	-	PUNCT
ejpam-5831	278	4	based	base	VERB
ejpam-5831	278	5	rough	rough	ADJ
ejpam-5831	278	6	intuitionistic	intuitionistic	ADJ
ejpam-5831	278	7	fuzzy	fuzzy	ADJ
ejpam-5831	278	8	sets	set	NOUN
ejpam-5831	278	9	.	.	PUNCT
ejpam-5831	279	1	mathematics	mathematic	NOUN
ejpam-5831	279	2	,	,	PUNCT
ejpam-5831	279	3	10:4079	10:4079	NUM
ejpam-5831	279	4	,	,	PUNCT
ejpam-5831	279	5	2022	2022	NUM
ejpam-5831	279	6	.	.	PUNCT
ejpam-5831	280	1	[	[	X
ejpam-5831	280	2	9	9	NUM
ejpam-5831	280	3	]	]	SYM
ejpam-5831	280	4	asmaa	asmaa	PROPN
ejpam-5831	280	5	m.	m.	PROPN
ejpam-5831	280	6	nasr	nasr	PROPN
ejpam-5831	280	7	,	,	PUNCT
ejpam-5831	280	8	hewayda	hewayda	NOUN
ejpam-5831	280	9	elghawalby	elghawalby	PROPN
ejpam-5831	280	10	,	,	PUNCT
ejpam-5831	280	11	and	and	CCONJ
ejpam-5831	280	12	r.	r.	PROPN
ejpam-5831	280	13	mareay	mareay	PROPN
ejpam-5831	280	14	.	.	PUNCT
ejpam-5831	280	15	weighted	weight	VERB
ejpam-5831	280	16	pretopology	pretopology	NOUN
ejpam-5831	280	17	and	and	CCONJ
ejpam-5831	280	18	reduction	reduction	NOUN
ejpam-5831	280	19	of	of	ADP
ejpam-5831	280	20	information	information	NOUN
ejpam-5831	280	21	system	system	NOUN
ejpam-5831	280	22	.	.	PUNCT
ejpam-5831	281	1	journal	journal	NOUN
ejpam-5831	281	2	of	of	ADP
ejpam-5831	281	3	intelligent	intelligent	ADJ
ejpam-5831	281	4	and	and	CCONJ
ejpam-5831	281	5	fuzzy	fuzzy	ADJ
ejpam-5831	281	6	systems	system	NOUN
ejpam-5831	281	7	,	,	PUNCT
ejpam-5831	281	8	44:4975	44:4975	NUM
ejpam-5831	281	9	–	–	PUNCT
ejpam-5831	281	10	4985	4985	NUM
ejpam-5831	281	11	,	,	PUNCT
ejpam-5831	281	12	2023	2023	NUM
ejpam-5831	281	13	.	.	PUNCT
ejpam-5831	282	1	[	[	X
ejpam-5831	282	2	10	10	NUM
ejpam-5831	282	3	]	]	PUNCT
ejpam-5831	282	4	k.	k.	PROPN
ejpam-5831	282	5	y.	y.	PROPN
ejpam-5831	282	6	qin	qin	PROPN
ejpam-5831	282	7	and	and	CCONJ
ejpam-5831	282	8	z.	z.	PROPN
ejpam-5831	282	9	pei	pei	PROPN
ejpam-5831	282	10	.	.	PUNCT
ejpam-5831	283	1	on	on	ADP
ejpam-5831	283	2	the	the	DET
ejpam-5831	283	3	topological	topological	ADJ
ejpam-5831	283	4	properties	property	NOUN
ejpam-5831	283	5	of	of	ADP
ejpam-5831	283	6	fuzzy	fuzzy	ADJ
ejpam-5831	283	7	rough	rough	ADJ
ejpam-5831	283	8	sets	set	NOUN
ejpam-5831	283	9	.	.	PUNCT
ejpam-5831	284	1	fuzzy	fuzzy	ADJ
ejpam-5831	284	2	sets	set	NOUN
ejpam-5831	284	3	and	and	CCONJ
ejpam-5831	284	4	systems	system	NOUN
ejpam-5831	284	5	,	,	PUNCT
ejpam-5831	284	6	151(3):601–613	151(3):601–613	NUM
ejpam-5831	284	7	,	,	PUNCT
ejpam-5831	284	8	2005	2005	NUM
ejpam-5831	284	9	.	.	PUNCT
ejpam-5831	285	1	[	[	X
ejpam-5831	285	2	11	11	NUM
ejpam-5831	285	3	]	]	PUNCT
ejpam-5831	285	4	k.	k.	PROPN
ejpam-5831	285	5	y.	y.	PROPN
ejpam-5831	285	6	qin	qin	PROPN
ejpam-5831	285	7	,	,	PUNCT
ejpam-5831	285	8	j.	j.	PROPN
ejpam-5831	285	9	l.	l.	PROPN
ejpam-5831	285	10	yang	yang	PROPN
ejpam-5831	285	11	,	,	PUNCT
ejpam-5831	285	12	and	and	CCONJ
ejpam-5831	285	13	z.	z.	PROPN
ejpam-5831	285	14	pei	pei	PROPN
ejpam-5831	285	15	.	.	PROPN
ejpam-5831	286	1	generalized	generalize	VERB
ejpam-5831	286	2	rough	rough	ADJ
ejpam-5831	286	3	sets	set	NOUN
ejpam-5831	286	4	based	base	VERB
ejpam-5831	286	5	on	on	ADP
ejpam-5831	286	6	reflexive	reflexive	ADJ
ejpam-5831	286	7	and	and	CCONJ
ejpam-5831	286	8	transitive	transitive	ADJ
ejpam-5831	286	9	relations	relation	NOUN
ejpam-5831	286	10	.	.	PUNCT
ejpam-5831	287	1	information	information	NOUN
ejpam-5831	287	2	sciences	sciences	PROPN
ejpam-5831	287	3	,	,	PUNCT
ejpam-5831	287	4	178:4138–4141	178:4138–4141	NUM
ejpam-5831	287	5	,	,	PUNCT
ejpam-5831	287	6	2008	2008	NUM
ejpam-5831	287	7	.	.	PUNCT
ejpam-5831	288	1	[	[	X
ejpam-5831	288	2	12	12	NUM
ejpam-5831	288	3	]	]	PUNCT
ejpam-5831	288	4	a.	a.	NOUN
ejpam-5831	288	5	s.	s.	PROPN
ejpam-5831	288	6	salama	salama	PROPN
ejpam-5831	288	7	.	.	PUNCT
ejpam-5831	289	1	topological	topological	ADJ
ejpam-5831	289	2	solution	solution	NOUN
ejpam-5831	289	3	of	of	ADP
ejpam-5831	289	4	missing	miss	VERB
ejpam-5831	289	5	attribute	attribute	NOUN
ejpam-5831	289	6	values	value	NOUN
ejpam-5831	289	7	problem	problem	NOUN
ejpam-5831	289	8	in	in	ADP
ejpam-5831	289	9	incomplete	incomplete	ADJ
ejpam-5831	289	10	information	information	NOUN
ejpam-5831	289	11	tables	table	NOUN
ejpam-5831	289	12	.	.	PUNCT
ejpam-5831	290	1	information	information	NOUN
ejpam-5831	290	2	sciences	sciences	PROPN
ejpam-5831	290	3	,	,	PUNCT
ejpam-5831	290	4	180:631–639	180:631–639	NUM
ejpam-5831	290	5	,	,	PUNCT
ejpam-5831	290	6	2010	2010	NUM
ejpam-5831	290	7	.	.	PUNCT
ejpam-5831	291	1	[	[	X
ejpam-5831	291	2	13	13	NUM
ejpam-5831	291	3	]	]	PUNCT
ejpam-5831	291	4	z.	z.	PROPN
ejpam-5831	291	5	pawlak	pawlak	PROPN
ejpam-5831	291	6	.	.	PUNCT
ejpam-5831	292	1	rough	rough	ADJ
ejpam-5831	292	2	sets	set	NOUN
ejpam-5831	292	3	.	.	PUNCT
ejpam-5831	293	1	international	international	ADJ
ejpam-5831	293	2	journal	journal	NOUN
ejpam-5831	293	3	of	of	ADP
ejpam-5831	293	4	computer	computer	NOUN
ejpam-5831	293	5	and	and	CCONJ
ejpam-5831	293	6	information	information	NOUN
ejpam-5831	293	7	sciences	science	NOUN
ejpam-5831	293	8	,	,	PUNCT
ejpam-5831	293	9	11(5):341–356	11(5):341–356	NUM
ejpam-5831	293	10	,	,	PUNCT
ejpam-5831	293	11	1982	1982	NUM
ejpam-5831	293	12	.	.	PUNCT
ejpam-5831	294	1	[	[	X
ejpam-5831	294	2	14	14	NUM
ejpam-5831	294	3	]	]	X
ejpam-5831	294	4	d.	d.	PROPN
ejpam-5831	294	5	g.	g.	PROPN
ejpam-5831	294	6	chen	chen	PROPN
ejpam-5831	294	7	and	and	CCONJ
ejpam-5831	294	8	w.	w.	PROPN
ejpam-5831	294	9	x.	x.	PROPN
ejpam-5831	294	10	zhang	zhang	PROPN
ejpam-5831	294	11	.	.	PUNCT
ejpam-5831	295	1	rough	rough	ADJ
ejpam-5831	295	2	sets	set	NOUN
ejpam-5831	295	3	and	and	CCONJ
ejpam-5831	295	4	topological	topological	ADJ
ejpam-5831	295	5	spaces	space	NOUN
ejpam-5831	295	6	.	.	PUNCT
ejpam-5831	296	1	journal	journal	PROPN
ejpam-5831	296	2	of	of	ADP
ejpam-5831	296	3	xi’an	xi’an	PROPN
ejpam-5831	296	4	jiaotong	jiaotong	PROPN
ejpam-5831	296	5	university	university	PROPN
ejpam-5831	296	6	,	,	PUNCT
ejpam-5831	296	7	35:1313–1315	35:1313–1315	PROPN
ejpam-5831	296	8	,	,	PUNCT
ejpam-5831	296	9	2001	2001	NUM
ejpam-5831	296	10	.	.	PUNCT
ejpam-5831	297	1	[	[	X
ejpam-5831	297	2	15	15	NUM
ejpam-5831	297	3	]	]	PUNCT
ejpam-5831	297	4	z.	z.	PROPN
ejpam-5831	297	5	belmandt	belmandt	PROPN
ejpam-5831	297	6	.	.	PUNCT
ejpam-5831	298	1	manuel	manuel	PROPN
ejpam-5831	298	2	de	de	X
ejpam-5831	298	3	prétopologie	prétopologie	ADP
ejpam-5831	298	4	et	et	NOUN
ejpam-5831	298	5	ses	se	NOUN
ejpam-5831	298	6	applications	application	NOUN
ejpam-5831	298	7	.	.	PUNCT
ejpam-5831	299	1	hermès	hermès	PROPN
ejpam-5831	299	2	,	,	PUNCT
ejpam-5831	299	3	1993	1993	NUM
ejpam-5831	299	4	.	.	PUNCT
ejpam-5831	300	1	[	[	X
ejpam-5831	300	2	16	16	NUM
ejpam-5831	300	3	]	]	PUNCT
ejpam-5831	300	4	z.	z.	PROPN
ejpam-5831	300	5	belmandt	belmandt	PROPN
ejpam-5831	300	6	.	.	PUNCT
ejpam-5831	301	1	basics	basic	NOUN
ejpam-5831	301	2	of	of	ADP
ejpam-5831	301	3	pretopology	pretopology	NOUN
ejpam-5831	301	4	.	.	PUNCT
ejpam-5831	302	1	hermann	hermann	PROPN
ejpam-5831	302	2	,	,	PUNCT
ejpam-5831	302	3	2011	2011	NUM
ejpam-5831	302	4	.	.	PUNCT
ejpam-5831	303	1	[	[	X
ejpam-5831	303	2	17	17	NUM
ejpam-5831	303	3	]	]	PUNCT
ejpam-5831	303	4	m.	m.	NOUN
ejpam-5831	303	5	brissaud	brissaud	NOUN
ejpam-5831	303	6	.	.	PUNCT
ejpam-5831	304	1	les	les	PROPN
ejpam-5831	304	2	espaces	espace	NOUN
ejpam-5831	304	3	prétopologiques	prétopologique	NOUN
ejpam-5831	304	4	.	.	PUNCT
ejpam-5831	305	1	compte	compte	PROPN
ejpam-5831	305	2	-	-	PUNCT
ejpam-5831	305	3	rendu	rendu	NOUN
ejpam-5831	305	4	de	de	PROPN
ejpam-5831	305	5	l’académie	l’académie	PROPN
ejpam-5831	305	6	des	des	X
ejpam-5831	305	7	sciences	sciences	PROPN
ejpam-5831	305	8	,	,	PUNCT
ejpam-5831	305	9	280(a):705–708	280(a):705–708	NUM
ejpam-5831	305	10	,	,	PUNCT
ejpam-5831	305	11	1975	1975	NUM
ejpam-5831	305	12	.	.	PUNCT
ejpam-5831	306	1	[	[	X
ejpam-5831	306	2	18	18	NUM
ejpam-5831	306	3	]	]	X
ejpam-5831	306	4	e.	e.	PROPN
ejpam-5831	306	5	čech	čech	PROPN
ejpam-5831	306	6	.	.	PUNCT
ejpam-5831	307	1	topological	topological	ADJ
ejpam-5831	307	2	spaces	space	NOUN
ejpam-5831	307	3	.	.	PUNCT
ejpam-5831	308	1	john	john	PROPN
ejpam-5831	308	2	wiley	wiley	PROPN
ejpam-5831	308	3	and	and	CCONJ
ejpam-5831	308	4	sons	son	NOUN
ejpam-5831	308	5	,	,	PUNCT
ejpam-5831	308	6	new	new	PROPN
ejpam-5831	308	7	york	york	PROPN
ejpam-5831	308	8	,	,	PUNCT
ejpam-5831	308	9	ny	ny	PROPN
ejpam-5831	308	10	,	,	PUNCT
ejpam-5831	308	11	usa	usa	PROPN
ejpam-5831	308	12	,	,	PUNCT
ejpam-5831	308	13	1966	1966	NUM
ejpam-5831	308	14	.	.	PUNCT
ejpam-5831	309	1	[	[	X
ejpam-5831	309	2	19	19	NUM
ejpam-5831	309	3	]	]	PUNCT
ejpam-5831	309	4	m.	m.	NOUN
ejpam-5831	309	5	fréchet	fréchet	PROPN
ejpam-5831	309	6	.	.	PUNCT
ejpam-5831	309	7	espaces	espace	VERB
ejpam-5831	309	8	abstraits	abstrait	NOUN
ejpam-5831	309	9	.	.	PUNCT
ejpam-5831	310	1	hermann	hermann	PROPN
ejpam-5831	310	2	,	,	PUNCT
ejpam-5831	310	3	1928	1928	NUM
ejpam-5831	310	4	.	.	PUNCT
ejpam-5831	311	1	[	[	X
ejpam-5831	311	2	20	20	NUM
ejpam-5831	311	3	]	]	PUNCT
ejpam-5831	311	4	k.	k.	PROPN
ejpam-5831	311	5	kuratowski	kuratowski	PROPN
ejpam-5831	311	6	.	.	PUNCT
ejpam-5831	312	1	topologie	topologie	PROPN
ejpam-5831	312	2	.	.	PUNCT
ejpam-5831	313	1	nak	nak	PROPN
ejpam-5831	313	2	lad	lad	PROPN
ejpam-5831	313	3	polskiego	polskiego	PROPN
ejpam-5831	313	4	towarzystwa	towarzystwa	PROPN
ejpam-5831	313	5	matematycznego	matematycznego	PROPN
ejpam-5831	313	6	,	,	PUNCT
ejpam-5831	313	7	warszawa	warszawa	X
ejpam-5831	313	8	,	,	PUNCT
ejpam-5831	313	9	1952	1952	NUM
ejpam-5831	313	10	.	.	PUNCT
ejpam-5831	314	1	oclc	oclc	PROPN
ejpam-5831	314	2	:	:	PUNCT
ejpam-5831	314	3	3014396	3014396	NUM
ejpam-5831	314	4	.	.	PUNCT
ejpam-5831	315	1	[	[	X
ejpam-5831	315	2	21	21	NUM
ejpam-5831	315	3	]	]	PUNCT
ejpam-5831	315	4	j.-p	j.-p	PROPN
ejpam-5831	315	5	.	.	PUNCT
ejpam-5831	316	1	auray	auray	NOUN
ejpam-5831	316	2	,	,	PUNCT
ejpam-5831	316	3	m.	m.	NOUN
ejpam-5831	316	4	brissaud	brissaud	NOUN
ejpam-5831	316	5	,	,	PUNCT
ejpam-5831	316	6	and	and	CCONJ
ejpam-5831	316	7	g.	g.	PROPN
ejpam-5831	316	8	duru	duru	PROPN
ejpam-5831	316	9	.	.	PUNCT
ejpam-5831	317	1	les	les	PROPN
ejpam-5831	317	2	apports	apport	NOUN
ejpam-5831	317	3	de	de	X
ejpam-5831	317	4	la	la	X
ejpam-5831	317	5	prétopologie	prétopologie	PROPN
ejpam-5831	317	6	.	.	PUNCT
ejpam-5831	318	1	in	in	ADP
ejpam-5831	318	2	112e	112e	NUM
ejpam-5831	318	3	a.	a.	NOUN
ejpam-5831	318	4	a.	a.	NOUN
ejpam-5831	318	5	azza	azza	NOUN
ejpam-5831	318	6	et	et	PROPN
ejpam-5831	318	7	al	al	PROPN
ejpam-5831	318	8	.	.	PUNCT
ejpam-5831	318	9	/	/	SYM
ejpam-5831	318	10	eur	eur	PROPN
ejpam-5831	318	11	.	.	PUNCT
ejpam-5831	319	1	j.	j.	PROPN
ejpam-5831	319	2	pure	pure	PROPN
ejpam-5831	319	3	appl	appl	PROPN
ejpam-5831	319	4	.	.	PROPN
ejpam-5831	319	5	math	math	PROPN
ejpam-5831	319	6	,	,	PUNCT
ejpam-5831	319	7	18	18	NUM
ejpam-5831	319	8	(	(	PUNCT
ejpam-5831	319	9	2	2	NUM
ejpam-5831	319	10	)	)	PUNCT
ejpam-5831	319	11	(	(	PUNCT
ejpam-5831	319	12	2025	2025	NUM
ejpam-5831	319	13	)	)	PUNCT
ejpam-5831	319	14	,	,	PUNCT
ejpam-5831	319	15	5831	5831	NUM
ejpam-5831	319	16	11	11	NUM
ejpam-5831	319	17	of	of	ADP
ejpam-5831	319	18	11	11	NUM
ejpam-5831	319	19	congrès	congrès	PROPN
ejpam-5831	319	20	national	national	PROPN
ejpam-5831	319	21	des	des	PROPN
ejpam-5831	319	22	sociétés	sociétés	PROPN
ejpam-5831	319	23	savantes	savante	NOUN
ejpam-5831	319	24	,	,	PUNCT
ejpam-5831	319	25	volume	volume	NOUN
ejpam-5831	319	26	iv	iv	NUM
ejpam-5831	319	27	,	,	PUNCT
ejpam-5831	319	28	pages	page	NOUN
ejpam-5831	319	29	15–29	15–29	NUM
ejpam-5831	319	30	.	.	PUNCT
ejpam-5831	320	1	sciences	sciences	PROPN
ejpam-5831	320	2	fasc	fasc	PROPN
ejpam-5831	320	3	,	,	PUNCT
ejpam-5831	320	4	1987	1987	NUM
ejpam-5831	320	5	.	.	PUNCT
ejpam-5831	321	1	[	[	X
ejpam-5831	321	2	22	22	NUM
ejpam-5831	321	3	]	]	PUNCT
ejpam-5831	321	4	m.	m.	NOUN
ejpam-5831	321	5	brissaud	brissaud	NOUN
ejpam-5831	321	6	.	.	PUNCT
ejpam-5831	322	1	espaces	espace	VERB
ejpam-5831	322	2	prétopologiques	prétopologique	NOUN
ejpam-5831	322	3	généralisés	généralisés	PROPN
ejpam-5831	322	4	et	et	NOUN
ejpam-5831	322	5	application	application	NOUN
ejpam-5831	322	6	:	:	PUNCT
ejpam-5831	322	7	connexités	connexité	NOUN
ejpam-5831	322	8	,	,	PUNCT
ejpam-5831	322	9	compacité	compacité	ADV
ejpam-5831	322	10	,	,	PUNCT
ejpam-5831	322	11	espaces	espace	NOUN
ejpam-5831	322	12	préférencés	préférencé	VERB
ejpam-5831	322	13	généraux	généraux	PROPN
ejpam-5831	322	14	.	.	PUNCT
ejpam-5831	323	1	technical	technical	ADJ
ejpam-5831	323	2	report	report	NOUN
ejpam-5831	323	3	,	,	PUNCT
ejpam-5831	323	4	ura	ura	PROPN
ejpam-5831	323	5	394	394	NUM
ejpam-5831	323	6	,	,	PUNCT
ejpam-5831	323	7	lyon	lyon	NOUN
ejpam-5831	323	8	,	,	PUNCT
ejpam-5831	323	9	1986	1986	NUM
ejpam-5831	323	10	.	.	PUNCT
ejpam-5831	324	1	[	[	X
ejpam-5831	324	2	23	23	NUM
ejpam-5831	324	3	]	]	X
ejpam-5831	324	4	m.	m.	NOUN
ejpam-5831	324	5	brissaud	brissaud	NOUN
ejpam-5831	324	6	.	.	PUNCT
ejpam-5831	325	1	analyse	analyse	NOUN
ejpam-5831	325	2	prétopologique	prétopologique	PROPN
ejpam-5831	325	3	du	du	PROPN
ejpam-5831	325	4	recouvrement	recouvrement	NOUN
ejpam-5831	325	5	d’un	d’un	PROPN
ejpam-5831	325	6	référentiel	référentiel	PROPN
ejpam-5831	325	7	.	.	PUNCT
ejpam-5831	326	1	connexités	connexités	PROPN
ejpam-5831	326	2	et	et	NOUN
ejpam-5831	326	3	point	point	NOUN
ejpam-5831	326	4	fixe	fixe	PROPN
ejpam-5831	326	5	.	.	PUNCT
ejpam-5831	327	1	in	in	ADP
ejpam-5831	327	2	xxiiie	xxiiie	NOUN
ejpam-5831	327	3	colloque	colloque	NOUN
ejpam-5831	327	4	structures	structure	NOUN
ejpam-5831	327	5	économiques	économiques	PROPN
ejpam-5831	327	6	et	et	NOUN
ejpam-5831	327	7	économétrie	économétrie	PROPN
ejpam-5831	327	8	,	,	PUNCT
ejpam-5831	327	9	lyon	lyon	NOUN
ejpam-5831	327	10	,	,	PUNCT
ejpam-5831	327	11	1991	1991	NUM
ejpam-5831	327	12	.	.	PUNCT
ejpam-5831	328	1	[	[	X
ejpam-5831	328	2	24	24	NUM
ejpam-5831	328	3	]	]	PUNCT
ejpam-5831	328	4	m.	m.	NOUN
ejpam-5831	328	5	brissaud	brissaud	NOUN
ejpam-5831	328	6	.	.	PUNCT
ejpam-5831	329	1	adhérence	adhérence	ADP
ejpam-5831	329	2	et	et	PROPN
ejpam-5831	329	3	acceptabilité	acceptabilité	NOUN
ejpam-5831	329	4	multicritères	multicritères	PROPN
ejpam-5831	329	5	.	.	PUNCT
ejpam-5831	330	1	analyse	analyse	PROPN
ejpam-5831	330	2	prétopologique	prétopologique	PROPN
ejpam-5831	330	3	.	.	PUNCT
ejpam-5831	331	1	in	in	ADP
ejpam-5831	331	2	xxivme	xxivme	PROPN
ejpam-5831	331	3	colloque	colloque	PROPN
ejpam-5831	331	4	structures	structures	PROPN
ejpam-5831	331	5	économiques	économiques	PROPN
ejpam-5831	331	6	et	et	NOUN
ejpam-5831	331	7	économétrie	économétrie	PROPN
ejpam-5831	331	8	,	,	PUNCT
ejpam-5831	331	9	lyon	lyon	NOUN
ejpam-5831	331	10	,	,	PUNCT
ejpam-5831	331	11	1992	1992	NUM
ejpam-5831	331	12	.	.	PUNCT
ejpam-5831	332	1	[	[	X
ejpam-5831	332	2	25	25	NUM
ejpam-5831	332	3	]	]	PUNCT
ejpam-5831	332	4	j.-p	j.-p	PROPN
ejpam-5831	332	5	.	.	PUNCT
ejpam-5831	332	6	auray	auray	NOUN
ejpam-5831	332	7	.	.	PUNCT
ejpam-5831	333	1	contribution	contribution	NOUN
ejpam-5831	333	2	à	à	PROPN
ejpam-5831	333	3	l’étude	l’étude	PROPN
ejpam-5831	333	4	des	des	PROPN
ejpam-5831	333	5	structures	structure	NOUN
ejpam-5831	333	6	pauvres	pauvre	NOUN
ejpam-5831	333	7	.	.	PUNCT
ejpam-5831	334	1	phd	phd	NOUN
ejpam-5831	334	2	thesis	thesis	PROPN
ejpam-5831	334	3	,	,	PUNCT
ejpam-5831	334	4	université	université	ADJ
ejpam-5831	334	5	lyon	lyon	PROPN
ejpam-5831	334	6	1	1	NUM
ejpam-5831	334	7	,	,	PUNCT
ejpam-5831	334	8	1982	1982	NUM
ejpam-5831	334	9	.	.	PUNCT
ejpam-5831	335	1	[	[	X
ejpam-5831	335	2	26	26	NUM
ejpam-5831	335	3	]	]	PUNCT
ejpam-5831	335	4	j.-p	j.-p	PROPN
ejpam-5831	335	5	.	.	PUNCT
ejpam-5831	336	1	auray	auray	PROPN
ejpam-5831	336	2	,	,	PUNCT
ejpam-5831	336	3	g.	g.	PROPN
ejpam-5831	336	4	duru	duru	PROPN
ejpam-5831	336	5	,	,	PUNCT
ejpam-5831	336	6	and	and	CCONJ
ejpam-5831	336	7	m.	m.	NOUN
ejpam-5831	336	8	mougeot	mougeot	PROPN
ejpam-5831	336	9	.	.	PUNCT
ejpam-5831	337	1	a	a	DET
ejpam-5831	337	2	pretopological	pretopological	ADJ
ejpam-5831	337	3	analysis	analysis	NOUN
ejpam-5831	337	4	of	of	ADP
ejpam-5831	337	5	input	input	NOUN
ejpam-5831	337	6	-	-	PUNCT
ejpam-5831	337	7	output	output	NOUN
ejpam-5831	337	8	model	model	NOUN
ejpam-5831	337	9	.	.	PUNCT
ejpam-5831	338	1	economics	economic	NOUN
ejpam-5831	338	2	letters	letter	NOUN
ejpam-5831	338	3	,	,	PUNCT
ejpam-5831	338	4	2(4	2(4	NUM
ejpam-5831	338	5	)	)	PUNCT
ejpam-5831	338	6	,	,	PUNCT
ejpam-5831	338	7	1979	1979	NUM
ejpam-5831	338	8	.	.	PUNCT
ejpam-5831	339	1	[	[	X
ejpam-5831	339	2	27	27	NUM
ejpam-5831	339	3	]	]	X
ejpam-5831	339	4	n.	n.	NOUN
ejpam-5831	339	5	nicoloyannis	nicoloyannis	PROPN
ejpam-5831	339	6	.	.	PUNCT
ejpam-5831	340	1	structures	structure	NOUN
ejpam-5831	340	2	prétopologiques	prétopologique	VERB
ejpam-5831	340	3	et	et	NOUN
ejpam-5831	340	4	classification	classification	NOUN
ejpam-5831	340	5	automatique	automatique	NOUN
ejpam-5831	340	6	.	.	PUNCT
ejpam-5831	341	1	le	le	PROPN
ejpam-5831	341	2	logiciel	logiciel	PROPN
ejpam-5831	341	3	demon	demon	PROPN
ejpam-5831	341	4	.	.	PUNCT
ejpam-5831	342	1	phd	phd	NOUN
ejpam-5831	342	2	thesis	thesis	PROPN
ejpam-5831	342	3	,	,	PUNCT
ejpam-5831	342	4	université	université	ADJ
ejpam-5831	342	5	lyon	lyon	PROPN
ejpam-5831	342	6	1	1	NUM
ejpam-5831	342	7	,	,	PUNCT
ejpam-5831	342	8	1988	1988	NUM
ejpam-5831	342	9	.	.	PUNCT
ejpam-5831	343	1	[	[	X
ejpam-5831	343	2	28	28	NUM
ejpam-5831	343	3	]	]	X
ejpam-5831	343	4	g.	g.	PROPN
ejpam-5831	343	5	duru	duru	PROPN
ejpam-5831	343	6	.	.	PUNCT
ejpam-5831	344	1	nouveaux	nouveaux	PROPN
ejpam-5831	344	2	éléments	éléments	PROPN
ejpam-5831	344	3	de	de	PROPN
ejpam-5831	344	4	prétopologie	prétopologie	PROPN
ejpam-5831	344	5	.	.	PUNCT
ejpam-5831	345	1	technical	technical	ADJ
ejpam-5831	345	2	report	report	PROPN
ejpam-5831	345	3	,	,	PUNCT
ejpam-5831	345	4	faculté	faculté	PROPN
ejpam-5831	345	5	de	de	PROPN
ejpam-5831	345	6	droit	droit	PROPN
ejpam-5831	345	7	et	et	PROPN
ejpam-5831	345	8	des	des	PROPN
ejpam-5831	345	9	sciences	sciences	PROPN
ejpam-5831	345	10	économiques	économiques	PROPN
ejpam-5831	345	11	de	de	PROPN
ejpam-5831	345	12	besançon	besançon	PROPN
ejpam-5831	345	13	,	,	PUNCT
ejpam-5831	345	14	1977	1977	NUM
ejpam-5831	345	15	.	.	PUNCT
ejpam-5831	346	1	[	[	X
ejpam-5831	346	2	29	29	NUM
ejpam-5831	346	3	]	]	X
ejpam-5831	346	4	g.	g.	PROPN
ejpam-5831	346	5	duru	duru	PROPN
ejpam-5831	346	6	.	.	PUNCT
ejpam-5831	347	1	contribution	contribution	NOUN
ejpam-5831	347	2	à	à	PROPN
ejpam-5831	347	3	l’étude	l’étude	PROPN
ejpam-5831	347	4	des	des	PROPN
ejpam-5831	347	5	structures	structure	NOUN
ejpam-5831	347	6	des	des	PROPN
ejpam-5831	347	7	systèmes	systèmes	PROPN
ejpam-5831	347	8	complexes	complexe	VERB
ejpam-5831	347	9	dans	dan	NOUN
ejpam-5831	347	10	les	les	PROPN
ejpam-5831	347	11	sciences	sciences	PROPN
ejpam-5831	347	12	humaines	humaine	NOUN
ejpam-5831	347	13	.	.	PUNCT
ejpam-5831	348	1	phd	phd	NOUN
ejpam-5831	348	2	thesis	thesis	NOUN
ejpam-5831	348	3	,	,	PUNCT
ejpam-5831	348	4	université	université	ADJ
ejpam-5831	348	5	lyon	lyon	PROPN
ejpam-5831	348	6	1	1	NUM
ejpam-5831	348	7	,	,	PUNCT
ejpam-5831	348	8	1980	1980	NUM
ejpam-5831	348	9	.	.	PUNCT
ejpam-5831	349	1	[	[	X
ejpam-5831	349	2	30	30	NUM
ejpam-5831	349	3	]	]	PUNCT
ejpam-5831	349	4	m.	m.	NOUN
ejpam-5831	349	5	lamure	lamure	NOUN
ejpam-5831	349	6	.	.	PUNCT
ejpam-5831	350	1	espaces	espace	VERB
ejpam-5831	350	2	abstraits	abstrait	NOUN
ejpam-5831	350	3	et	et	NOUN
ejpam-5831	350	4	reconnaissance	reconnaissance	NOUN
ejpam-5831	350	5	des	des	X
ejpam-5831	350	6	formes	forme	NOUN
ejpam-5831	350	7	.	.	PUNCT
ejpam-5831	351	1	application	application	NOUN
ejpam-5831	351	2	au	au	PROPN
ejpam-5831	351	3	traitement	traitement	PROPN
ejpam-5831	351	4	des	des	PROPN
ejpam-5831	351	5	images	image	NOUN
ejpam-5831	351	6	digitales	digitale	NOUN
ejpam-5831	351	7	.	.	PUNCT
ejpam-5831	352	1	phd	phd	NOUN
ejpam-5831	352	2	thesis	thesis	NOUN
ejpam-5831	352	3	,	,	PUNCT
ejpam-5831	352	4	université	université	ADJ
ejpam-5831	352	5	lyon	lyon	PROPN
ejpam-5831	352	6	1	1	NUM
ejpam-5831	352	7	,	,	PUNCT
ejpam-5831	352	8	1987	1987	NUM
ejpam-5831	352	9	.	.	PUNCT
ejpam-5831	353	1	[	[	X
ejpam-5831	353	2	31	31	NUM
ejpam-5831	353	3	]	]	PUNCT
ejpam-5831	353	4	h.	h.	PROPN
ejpam-5831	353	5	emptoz	emptoz	PROPN
ejpam-5831	353	6	.	.	PUNCT
ejpam-5831	354	1	modèles	modèle	VERB
ejpam-5831	354	2	prétopologiques	prétopologique	NOUN
ejpam-5831	354	3	pour	pour	VERB
ejpam-5831	354	4	la	la	PRON
ejpam-5831	354	5	reconnaissance	reconnaissance	NOUN
ejpam-5831	354	6	des	des	X
ejpam-5831	354	7	formes	forme	NOUN
ejpam-5831	354	8	.	.	PUNCT
ejpam-5831	355	1	application	application	NOUN
ejpam-5831	355	2	en	en	X
ejpam-5831	355	3	neurophysiologie	neurophysiologie	PROPN
ejpam-5831	355	4	.	.	PUNCT
ejpam-5831	356	1	phd	phd	NOUN
ejpam-5831	356	2	thesis	thesis	PROPN
ejpam-5831	356	3	,	,	PUNCT
ejpam-5831	356	4	université	université	ADJ
ejpam-5831	356	5	lyon	lyon	PROPN
ejpam-5831	356	6	1	1	NUM
ejpam-5831	356	7	,	,	PUNCT
ejpam-5831	356	8	1983	1983	NUM
ejpam-5831	356	9	.	.	PUNCT
ejpam-5831	357	1	[	[	X
ejpam-5831	357	2	32	32	NUM
ejpam-5831	357	3	]	]	PUNCT
ejpam-5831	357	4	v.	v.	ADP
ejpam-5831	357	5	levorato	levorato	PROPN
ejpam-5831	357	6	and	and	CCONJ
ejpam-5831	357	7	m.	m.	NOUN
ejpam-5831	357	8	bui	bui	PROPN
ejpam-5831	357	9	.	.	PUNCT
ejpam-5831	358	1	data	datum	NOUN
ejpam-5831	358	2	structures	structure	NOUN
ejpam-5831	358	3	and	and	CCONJ
ejpam-5831	358	4	algorithms	algorithm	NOUN
ejpam-5831	358	5	for	for	ADP
ejpam-5831	358	6	pretopology	pretopology	NOUN
ejpam-5831	358	7	:	:	PUNCT
ejpam-5831	358	8	the	the	DET
ejpam-5831	358	9	java	java	PROPN
ejpam-5831	358	10	based	base	VERB
ejpam-5831	358	11	software	software	NOUN
ejpam-5831	358	12	library	library	PROPN
ejpam-5831	358	13	pretopolib	pretopolib	PROPN
ejpam-5831	358	14	.	.	PUNCT
ejpam-5831	359	1	in	in	ADP
ejpam-5831	359	2	innovative	innovative	ADJ
ejpam-5831	359	3	internet	internet	NOUN
ejpam-5831	359	4	community	community	NOUN
ejpam-5831	359	5	systems	system	NOUN
ejpam-5831	359	6	(	(	PUNCT
ejpam-5831	359	7	i2cs	i2cs	PROPN
ejpam-5831	359	8	)	)	PUNCT
ejpam-5831	359	9	,	,	PUNCT
ejpam-5831	359	10	pages	page	VERB
ejpam-5831	359	11	122–134	122–134	NUM
ejpam-5831	359	12	,	,	PUNCT
ejpam-5831	359	13	fort	fort	PROPN
ejpam-5831	359	14	de	de	PROPN
ejpam-5831	359	15	france	france	PROPN
ejpam-5831	359	16	,	,	PUNCT
ejpam-5831	359	17	martinique	martinique	PROPN
ejpam-5831	359	18	,	,	PUNCT
ejpam-5831	359	19	june	june	PROPN
ejpam-5831	359	20	2008	2008	NUM
ejpam-5831	359	21	.	.	PUNCT
ejpam-5831	360	1	ieee	ieee	NOUN
ejpam-5831	360	2	.	.	PUNCT
ejpam-5831	361	1	[	[	X
ejpam-5831	361	2	33	33	NUM
ejpam-5831	361	3	]	]	PUNCT
ejpam-5831	361	4	z.	z.	PROPN
ejpam-5831	361	5	belmandt	belmandt	PROPN
ejpam-5831	361	6	.	.	PUNCT
ejpam-5831	362	1	basics	basic	NOUN
ejpam-5831	362	2	of	of	ADP
ejpam-5831	362	3	pretopology	pretopology	NOUN
ejpam-5831	362	4	.	.	PUNCT
ejpam-5831	363	1	hermann	hermann	PROPN
ejpam-5831	363	2	,	,	PUNCT
ejpam-5831	363	3	2011	2011	NUM
ejpam-5831	363	4	.	.	PUNCT
ejpam-5831	364	1	[	[	X
ejpam-5831	364	2	34	34	NUM
ejpam-5831	364	3	]	]	PUNCT
ejpam-5831	364	4	z.	z.	PROPN
ejpam-5831	364	5	belmandt	belmandt	PROPN
ejpam-5831	364	6	.	.	PUNCT
ejpam-5831	365	1	manuel	manuel	PROPN
ejpam-5831	365	2	de	de	X
ejpam-5831	365	3	prétopologie	prétopologie	ADP
ejpam-5831	365	4	et	et	NOUN
ejpam-5831	365	5	ses	se	NOUN
ejpam-5831	365	6	applications	application	NOUN
ejpam-5831	365	7	.	.	PUNCT
ejpam-5831	366	1	hermès	hermès	PROPN
ejpam-5831	366	2	,	,	PUNCT
ejpam-5831	366	3	1993	1993	NUM
ejpam-5831	366	4	.	.	PUNCT
ejpam-5831	367	1	[	[	X
ejpam-5831	367	2	35	35	NUM
ejpam-5831	367	3	]	]	PUNCT
ejpam-5831	367	4	z.	z.	PROPN
ejpam-5831	367	5	pawlak	pawlak	PROPN
ejpam-5831	367	6	.	.	PUNCT
ejpam-5831	368	1	rough	rough	ADJ
ejpam-5831	368	2	sets	set	NOUN
ejpam-5831	368	3	:	:	PUNCT
ejpam-5831	368	4	theoretical	theoretical	ADJ
ejpam-5831	368	5	aspects	aspect	NOUN
ejpam-5831	368	6	of	of	ADP
ejpam-5831	368	7	reasoning	reasoning	NOUN
ejpam-5831	368	8	about	about	ADP
ejpam-5831	368	9	data	datum	NOUN
ejpam-5831	368	10	.	.	PUNCT
ejpam-5831	369	1	kluwer	kluwer	NOUN
ejpam-5831	369	2	academic	academic	ADJ
ejpam-5831	369	3	publishers	publisher	NOUN
ejpam-5831	369	4	,	,	PUNCT
ejpam-5831	369	5	boston	boston	PROPN
ejpam-5831	369	6	,	,	PUNCT
ejpam-5831	369	7	1991	1991	NUM
ejpam-5831	369	8	.	.	PUNCT