id	sid	tid	token	lemma	pos
ejpam-3823	1	1	european	european	PROPN
ejpam-3823	1	2	journal	journal	PROPN
ejpam-3823	1	3	of	of	ADP
ejpam-3823	1	4	pure	pure	ADJ
ejpam-3823	1	5	and	and	CCONJ
ejpam-3823	1	6	applied	apply	VERB
ejpam-3823	1	7	mathematics	mathematic	NOUN
ejpam-3823	1	8	vol	vol	NOUN
ejpam-3823	1	9	.	.	PUNCT
ejpam-3823	2	1	14	14	NUM
ejpam-3823	2	2	,	,	PUNCT
ejpam-3823	2	3	no	no	INTJ
ejpam-3823	2	4	.	.	NOUN
ejpam-3823	2	5	4	4	NUM
ejpam-3823	2	6	,	,	PUNCT
ejpam-3823	2	7	2021	2021	NUM
ejpam-3823	2	8	,	,	PUNCT
ejpam-3823	2	9	1507	1507	NUM
ejpam-3823	2	10	-	-	SYM
ejpam-3823	2	11	1516	1516	NUM
ejpam-3823	2	12	issn	issn	PROPN
ejpam-3823	2	13	1307	1307	NUM
ejpam-3823	2	14	-	-	SYM
ejpam-3823	2	15	5543	5543	NUM
ejpam-3823	2	16	–	–	PUNCT
ejpam-3823	3	1	ejpam.com	ejpam.com	X
ejpam-3823	3	2	published	publish	VERB
ejpam-3823	3	3	by	by	ADP
ejpam-3823	3	4	new	new	PROPN
ejpam-3823	3	5	york	york	PROPN
ejpam-3823	3	6	business	business	PROPN
ejpam-3823	3	7	global	global	PROPN
ejpam-3823	3	8	on	on	ADP
ejpam-3823	3	9	micro	micro	ADJ
ejpam-3823	3	10	-	-	ADJ
ejpam-3823	3	11	generalized	generalize	VERB
ejpam-3823	3	12	closed	closed	ADJ
ejpam-3823	3	13	sets	set	NOUN
ejpam-3823	3	14	and	and	CCONJ
ejpam-3823	3	15	micro	micro	ADJ
ejpam-3823	3	16	-	-	ADJ
ejpam-3823	3	17	generalized	generalized	ADJ
ejpam-3823	3	18	continuity	continuity	NOUN
ejpam-3823	3	19	in	in	ADP
ejpam-3823	3	20	micro	micro	PROPN
ejpam-3823	3	21	topological	topological	PROPN
ejpam-3823	3	22	spaces	spaces	PROPN
ejpam-3823	3	23	taha	taha	PROPN
ejpam-3823	3	24	h.	h.	PROPN
ejpam-3823	3	25	jasim1	jasim1	PROPN
ejpam-3823	3	26	,	,	PUNCT
ejpam-3823	3	27	saja	saja	PROPN
ejpam-3823	3	28	s.	s.	PROPN
ejpam-3823	3	29	mohsen2,∗	mohsen2,∗	PROPN
ejpam-3823	3	30	,	,	PUNCT
ejpam-3823	3	31	kanayo	kanayo	PROPN
ejpam-3823	3	32	s.	s.	PROPN
ejpam-3823	3	33	eke3	eke3	PROPN
ejpam-3823	3	34	1	1	NUM
ejpam-3823	3	35	department	department	NOUN
ejpam-3823	3	36	of	of	ADP
ejpam-3823	3	37	mathematics	mathematic	NOUN
ejpam-3823	3	38	,	,	PUNCT
ejpam-3823	3	39	college	college	NOUN
ejpam-3823	3	40	of	of	ADP
ejpam-3823	3	41	computer	computer	NOUN
ejpam-3823	3	42	science	science	NOUN
ejpam-3823	3	43	and	and	CCONJ
ejpam-3823	3	44	mathematics	mathematic	NOUN
ejpam-3823	3	45	,	,	PUNCT
ejpam-3823	3	46	tikrit	tikrit	NOUN
ejpam-3823	3	47	university	university	NOUN
ejpam-3823	3	48	,	,	PUNCT
ejpam-3823	3	49	tikrit	tikrit	NOUN
ejpam-3823	3	50	,	,	PUNCT
ejpam-3823	3	51	iraq	iraq	PROPN
ejpam-3823	3	52	.	.	PUNCT
ejpam-3823	4	1	2	2	NUM
ejpam-3823	4	2	ministry	ministry	PROPN
ejpam-3823	4	3	of	of	ADP
ejpam-3823	4	4	education	education	PROPN
ejpam-3823	4	5	,	,	PUNCT
ejpam-3823	4	6	general	general	ADJ
ejpam-3823	4	7	directorate	directorate	NOUN
ejpam-3823	4	8	of	of	ADP
ejpam-3823	4	9	salah	salah	PROPN
ejpam-3823	4	10	alden	alden	PROPN
ejpam-3823	4	11	province	province	PROPN
ejpam-3823	4	12	education	education	PROPN
ejpam-3823	4	13	,	,	PUNCT
ejpam-3823	4	14	tikrit	tikrit	NOUN
ejpam-3823	4	15	,	,	PUNCT
ejpam-3823	4	16	iraq	iraq	PROPN
ejpam-3823	4	17	3	3	NUM
ejpam-3823	4	18	department	department	NOUN
ejpam-3823	4	19	of	of	ADP
ejpam-3823	4	20	mathematics	mathematic	NOUN
ejpam-3823	4	21	,	,	PUNCT
ejpam-3823	4	22	faculty	faculty	NOUN
ejpam-3823	4	23	of	of	ADP
ejpam-3823	4	24	science	science	NOUN
ejpam-3823	4	25	,	,	PUNCT
ejpam-3823	4	26	university	university	NOUN
ejpam-3823	4	27	of	of	ADP
ejpam-3823	4	28	lagos	lagos	PROPN
ejpam-3823	4	29	,	,	PUNCT
ejpam-3823	4	30	akoka	akoka	NOUN
ejpam-3823	4	31	,	,	PUNCT
ejpam-3823	4	32	lagos	lago	NOUN
ejpam-3823	4	33	,	,	PUNCT
ejpam-3823	4	34	nigeria	nigeria	PROPN
ejpam-3823	4	35	abstract	abstract	ADJ
ejpam-3823	4	36	.	.	PUNCT
ejpam-3823	5	1	the	the	DET
ejpam-3823	5	2	purpose	purpose	NOUN
ejpam-3823	5	3	of	of	ADP
ejpam-3823	5	4	this	this	DET
ejpam-3823	5	5	paper	paper	NOUN
ejpam-3823	5	6	is	be	AUX
ejpam-3823	5	7	to	to	PART
ejpam-3823	5	8	define	define	VERB
ejpam-3823	5	9	and	and	CCONJ
ejpam-3823	5	10	study	study	VERB
ejpam-3823	5	11	a	a	DET
ejpam-3823	5	12	new	new	ADJ
ejpam-3823	5	13	class	class	NOUN
ejpam-3823	5	14	of	of	ADP
ejpam-3823	5	15	sets	set	NOUN
ejpam-3823	5	16	called	call	VERB
ejpam-3823	5	17	microgeneralized	microgeneralize	VERB
ejpam-3823	5	18	closed	closed	ADJ
ejpam-3823	5	19	set	set	ADJ
ejpam-3823	5	20	and	and	CCONJ
ejpam-3823	5	21	define	define	VERB
ejpam-3823	5	22	micro	micro	ADJ
ejpam-3823	5	23	-	-	ADJ
ejpam-3823	5	24	generalized	generalized	ADJ
ejpam-3823	5	25	continuous	continuous	ADJ
ejpam-3823	5	26	function	function	NOUN
ejpam-3823	5	27	and	and	CCONJ
ejpam-3823	5	28	micro	micro	ADJ
ejpam-3823	5	29	-	-	ADJ
ejpam-3823	5	30	generalized	generalized	ADJ
ejpam-3823	5	31	irresolute	irresolute	ADJ
ejpam-3823	5	32	function	function	NOUN
ejpam-3823	5	33	in	in	ADP
ejpam-3823	5	34	micro	micro	ADJ
ejpam-3823	5	35	topological	topological	ADJ
ejpam-3823	5	36	spaces	space	NOUN
ejpam-3823	5	37	.	.	PUNCT
ejpam-3823	6	1	basic	basic	ADJ
ejpam-3823	6	2	properties	property	NOUN
ejpam-3823	6	3	of	of	ADP
ejpam-3823	6	4	micro	micro	ADJ
ejpam-3823	6	5	-	-	ADJ
ejpam-3823	6	6	generalized	generalize	VERB
ejpam-3823	6	7	closed	closed	ADJ
ejpam-3823	6	8	sets	set	NOUN
ejpam-3823	6	9	and	and	CCONJ
ejpam-3823	6	10	its	its	PRON
ejpam-3823	6	11	characterizations	characterization	NOUN
ejpam-3823	6	12	are	be	AUX
ejpam-3823	6	13	analyzed	analyze	VERB
ejpam-3823	6	14	.	.	PUNCT
ejpam-3823	7	1	2020	2020	NUM
ejpam-3823	7	2	mathematics	mathematics	PROPN
ejpam-3823	7	3	subject	subject	NOUN
ejpam-3823	7	4	classifications	classification	NOUN
ejpam-3823	7	5	:	:	PUNCT
ejpam-3823	7	6	54c10	54c10	NUM
ejpam-3823	7	7	,	,	PUNCT
ejpam-3823	7	8	18f60	18f60	NUM
ejpam-3823	7	9	key	key	ADJ
ejpam-3823	7	10	words	word	NOUN
ejpam-3823	7	11	and	and	CCONJ
ejpam-3823	7	12	phrases	phrase	NOUN
ejpam-3823	7	13	:	:	PUNCT
ejpam-3823	7	14	generalized	generalize	VERB
ejpam-3823	7	15	closed	close	VERB
ejpam-3823	7	16	,	,	PUNCT
ejpam-3823	7	17	nano	nano	NOUN
ejpam-3823	7	18	topology	topology	NOUN
ejpam-3823	7	19	,	,	PUNCT
ejpam-3823	7	20	nano	nano	NOUN
ejpam-3823	7	21	-	-	PUNCT
ejpam-3823	7	22	generalized	generalize	VERB
ejpam-3823	7	23	closed	close	VERB
ejpam-3823	7	24	,	,	PUNCT
ejpam-3823	7	25	micro	micro	ADJ
ejpam-3823	7	26	topology	topology	NOUN
ejpam-3823	7	27	,	,	PUNCT
ejpam-3823	7	28	micro	micro	ADJ
ejpam-3823	7	29	-	-	ADJ
ejpam-3823	7	30	generalized	generalized	ADJ
ejpam-3823	7	31	closed	closed	ADJ
ejpam-3823	7	32	,	,	PUNCT
ejpam-3823	7	33	micro	micro	ADJ
ejpam-3823	7	34	-	-	ADJ
ejpam-3823	7	35	generalized	generalized	ADJ
ejpam-3823	7	36	continuous	continuous	ADJ
ejpam-3823	7	37	function	function	NOUN
ejpam-3823	7	38	,	,	PUNCT
ejpam-3823	7	39	micro	micro	ADJ
ejpam-3823	7	40	-	-	ADJ
ejpam-3823	7	41	generalized	generalized	ADJ
ejpam-3823	7	42	irresolute	irresolute	ADJ
ejpam-3823	7	43	functions	function	NOUN
ejpam-3823	7	44	1	1	NUM
ejpam-3823	7	45	.	.	PUNCT
ejpam-3823	7	46	introduction	introduction	NOUN
ejpam-3823	7	47	the	the	DET
ejpam-3823	7	48	concept	concept	NOUN
ejpam-3823	7	49	of	of	ADP
ejpam-3823	7	50	closed	closed	ADJ
ejpam-3823	7	51	set	set	NOUN
ejpam-3823	7	52	plays	play	VERB
ejpam-3823	7	53	a	a	DET
ejpam-3823	7	54	fundamental	fundamental	ADJ
ejpam-3823	7	55	role	role	NOUN
ejpam-3823	7	56	in	in	ADP
ejpam-3823	7	57	general	general	ADJ
ejpam-3823	7	58	topology	topology	NOUN
ejpam-3823	7	59	and	and	CCONJ
ejpam-3823	7	60	real	real	ADJ
ejpam-3823	7	61	analysis	analysis	NOUN
ejpam-3823	7	62	.	.	PUNCT
ejpam-3823	8	1	in	in	ADP
ejpam-3823	8	2	1970	1970	NUM
ejpam-3823	8	3	,	,	PUNCT
ejpam-3823	8	4	levine	levine	PROPN
ejpam-3823	8	5	[	[	X
ejpam-3823	8	6	11	11	NUM
ejpam-3823	8	7	]	]	PUNCT
ejpam-3823	8	8	introduced	introduce	VERB
ejpam-3823	8	9	generalized	generalize	VERB
ejpam-3823	8	10	closed	close	VERB
ejpam-3823	8	11	sets	set	NOUN
ejpam-3823	8	12	in	in	ADP
ejpam-3823	8	13	topological	topological	ADJ
ejpam-3823	8	14	spaces	space	NOUN
ejpam-3823	8	15	.	.	PUNCT
ejpam-3823	9	1	the	the	DET
ejpam-3823	9	2	notion	notion	NOUN
ejpam-3823	9	3	of	of	ADP
ejpam-3823	9	4	nano	nano	NOUN
ejpam-3823	9	5	topology	topology	NOUN
ejpam-3823	9	6	is	be	AUX
ejpam-3823	9	7	introduced	introduce	VERB
ejpam-3823	9	8	by	by	ADP
ejpam-3823	9	9	thivagar	thivagar	NOUN
ejpam-3823	9	10	and	and	CCONJ
ejpam-3823	9	11	richard	richard	NOUN
ejpam-3823	10	1	[	[	X
ejpam-3823	10	2	13	13	NUM
ejpam-3823	10	3	]	]	PUNCT
ejpam-3823	10	4	whose	whose	DET
ejpam-3823	10	5	idea	idea	NOUN
ejpam-3823	10	6	of	of	ADP
ejpam-3823	10	7	nano	nano	NOUN
ejpam-3823	10	8	topological	topological	ADJ
ejpam-3823	10	9	structure	structure	NOUN
ejpam-3823	10	10	is	be	AUX
ejpam-3823	10	11	grounded	ground	VERB
ejpam-3823	10	12	on	on	ADP
ejpam-3823	10	13	lower	low	ADJ
ejpam-3823	10	14	,	,	PUNCT
ejpam-3823	10	15	upper	upper	ADJ
ejpam-3823	10	16	and	and	CCONJ
ejpam-3823	10	17	boundary	boundary	ADJ
ejpam-3823	10	18	approximations	approximation	NOUN
ejpam-3823	10	19	of	of	ADP
ejpam-3823	10	20	a	a	DET
ejpam-3823	10	21	subset	subset	NOUN
ejpam-3823	10	22	of	of	ADP
ejpam-3823	10	23	a	a	DET
ejpam-3823	10	24	universe	universe	NOUN
ejpam-3823	10	25	set	set	VERB
ejpam-3823	10	26	with	with	ADP
ejpam-3823	10	27	an	an	DET
ejpam-3823	10	28	equivalence	equivalence	NOUN
ejpam-3823	10	29	relation	relation	NOUN
ejpam-3823	10	30	on	on	ADP
ejpam-3823	10	31	it	it	PRON
ejpam-3823	10	32	.	.	PUNCT
ejpam-3823	11	1	they	they	PRON
ejpam-3823	11	2	went	go	VERB
ejpam-3823	11	3	further	far	ADV
ejpam-3823	11	4	in	in	ADP
ejpam-3823	11	5	the	the	DET
ejpam-3823	11	6	same	same	ADJ
ejpam-3823	11	7	reference	reference	NOUN
ejpam-3823	11	8	to	to	PART
ejpam-3823	11	9	introduce	introduce	VERB
ejpam-3823	11	10	the	the	DET
ejpam-3823	11	11	definition	definition	NOUN
ejpam-3823	11	12	of	of	ADP
ejpam-3823	11	13	closed	closed	ADJ
ejpam-3823	11	14	,	,	PUNCT
ejpam-3823	11	15	interior	interior	ADJ
ejpam-3823	11	16	and	and	CCONJ
ejpam-3823	11	17	closure	closure	NOUN
ejpam-3823	11	18	set	set	VERB
ejpam-3823	11	19	via	via	ADP
ejpam-3823	11	20	concept	concept	NOUN
ejpam-3823	11	21	of	of	ADP
ejpam-3823	11	22	nano	nano	NOUN
ejpam-3823	11	23	topology	topology	NOUN
ejpam-3823	11	24	.	.	PUNCT
ejpam-3823	12	1	in	in	ADP
ejpam-3823	12	2	2017	2017	NUM
ejpam-3823	12	3	,	,	PUNCT
ejpam-3823	12	4	bhuvaneswari	bhuvaneswari	ADJ
ejpam-3823	12	5	[	[	X
ejpam-3823	12	6	8	8	NUM
ejpam-3823	12	7	]	]	PUNCT
ejpam-3823	12	8	introduced	introduce	VERB
ejpam-3823	12	9	the	the	DET
ejpam-3823	12	10	notion	notion	NOUN
ejpam-3823	12	11	of	of	ADP
ejpam-3823	12	12	nano	nano	NOUN
ejpam-3823	12	13	topology	topology	NOUN
ejpam-3823	12	14	and	and	CCONJ
ejpam-3823	12	15	t.	t.	PROPN
ejpam-3823	12	16	m.	m.	PROPN
ejpam-3823	12	17	al	al	PROPN
ejpam-3823	12	18	-	-	PUNCT
ejpam-3823	12	19	shami	shami	PROPN
ejpam-3823	13	1	[	[	X
ejpam-3823	13	2	3	3	X
ejpam-3823	13	3	]	]	PUNCT
ejpam-3823	13	4	introduced	introduce	VERB
ejpam-3823	13	5	somewhere	somewhere	ADV
ejpam-3823	13	6	dense	dense	ADJ
ejpam-3823	13	7	sets	set	NOUN
ejpam-3823	13	8	and	and	CCONJ
ejpam-3823	13	9	st1	st1	PROPN
ejpam-3823	13	10	-	-	PUNCT
ejpam-3823	13	11	spaces	space	VERB
ejpam-3823	13	12	.	.	PUNCT
ejpam-3823	14	1	the	the	DET
ejpam-3823	14	2	significant	significant	ADJ
ejpam-3823	14	3	of	of	ADP
ejpam-3823	14	4	nano	nano	NOUN
ejpam-3823	14	5	topological	topological	ADJ
ejpam-3823	14	6	structure	structure	NOUN
ejpam-3823	14	7	is	be	AUX
ejpam-3823	14	8	that	that	SCONJ
ejpam-3823	14	9	it	it	PRON
ejpam-3823	14	10	is	be	AUX
ejpam-3823	14	11	needed	need	VERB
ejpam-3823	14	12	to	to	PART
ejpam-3823	14	13	sort	sort	VERB
ejpam-3823	14	14	approximation	approximation	NOUN
ejpam-3823	14	15	to	to	ADP
ejpam-3823	14	16	fit	fit	ADJ
ejpam-3823	14	17	mathematical	mathematical	ADJ
ejpam-3823	14	18	models	model	NOUN
ejpam-3823	14	19	of	of	ADP
ejpam-3823	14	20	real	real	ADJ
ejpam-3823	14	21	-	-	PUNCT
ejpam-3823	14	22	life	life	NOUN
ejpam-3823	14	23	problems	problem	NOUN
ejpam-3823	14	24	.	.	PUNCT
ejpam-3823	15	1	azzam	azzam	PROPN
ejpam-3823	16	1	[	[	X
ejpam-3823	16	2	7	7	NUM
ejpam-3823	16	3	]	]	PUNCT
ejpam-3823	16	4	expanded	expand	VERB
ejpam-3823	16	5	the	the	DET
ejpam-3823	16	6	nano	nano	NOUN
ejpam-3823	16	7	topological	topological	ADJ
ejpam-3823	16	8	structure	structure	NOUN
ejpam-3823	16	9	by	by	ADP
ejpam-3823	16	10	inserting	insert	VERB
ejpam-3823	16	11	grill	grill	NOUN
ejpam-3823	16	12	∗corresponding	∗corresponde	VERB
ejpam-3823	16	13	author	author	NOUN
ejpam-3823	16	14	.	.	PUNCT
ejpam-3823	17	1	doi	doi	NOUN
ejpam-3823	17	2	:	:	PUNCT
ejpam-3823	17	3	https://doi.org/10.29020/nybg.ejpam.v14i4.3823	https://doi.org/10.29020/nybg.ejpam.v14i4.3823	ADJ
ejpam-3823	17	4	email	email	NOUN
ejpam-3823	17	5	addresses	address	NOUN
ejpam-3823	17	6	:	:	PUNCT
ejpam-3823	17	7	tahahameed@tu.edu.iq	tahahameed@tu.edu.iq	ADJ
ejpam-3823	17	8	(	(	PUNCT
ejpam-3823	17	9	t.	t.	PROPN
ejpam-3823	17	10	h.	h.	PROPN
ejpam-3823	17	11	jasim	jasim	PROPN
ejpam-3823	17	12	)	)	PUNCT
ejpam-3823	17	13	,	,	PUNCT
ejpam-3823	17	14	saja.s.mohsen35504@st.tu.edu.iq	saja.s.mohsen35504@st.tu.edu.iq	PROPN
ejpam-3823	17	15	(	(	PUNCT
ejpam-3823	17	16	s.	s.	PROPN
ejpam-3823	17	17	s.	s.	PROPN
ejpam-3823	17	18	mohsen	mohsen	PROPN
ejpam-3823	17	19	)	)	PUNCT
ejpam-3823	17	20	,	,	PUNCT
ejpam-3823	17	21	skanayo@unilag.edu.ng	skanayo@unilag.edu.ng	PROPN
ejpam-3823	17	22	(	(	PUNCT
ejpam-3823	17	23	k.	k.	PROPN
ejpam-3823	17	24	s.	s.	PROPN
ejpam-3823	17	25	eke	eke	PROPN
ejpam-3823	17	26	)	)	PUNCT
ejpam-3823	17	27	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3823	17	28	1507	1507	NUM
ejpam-3823	17	29	©	©	PROPN
ejpam-3823	17	30	2021	2021	NUM
ejpam-3823	17	31	ejpam	ejpam	VERB
ejpam-3823	17	32	all	all	DET
ejpam-3823	17	33	rights	right	NOUN
ejpam-3823	17	34	reserved	reserve	VERB
ejpam-3823	17	35	.	.	PUNCT
ejpam-3823	18	1	t.	t.	PROPN
ejpam-3823	18	2	h.	h.	PROPN
ejpam-3823	18	3	jasim	jasim	PROPN
ejpam-3823	18	4	,	,	PUNCT
ejpam-3823	18	5	s.	s.	PROPN
ejpam-3823	18	6	s.	s.	PROPN
ejpam-3823	18	7	mohsen	mohsen	PROPN
ejpam-3823	18	8	,	,	PUNCT
ejpam-3823	18	9	k.	k.	PROPN
ejpam-3823	18	10	s.	s.	PROPN
ejpam-3823	18	11	eke	eke	PROPN
ejpam-3823	18	12	/	/	SYM
ejpam-3823	18	13	eur	eur	PROPN
ejpam-3823	18	14	.	.	PUNCT
ejpam-3823	19	1	j.	j.	PROPN
ejpam-3823	19	2	pure	pure	PROPN
ejpam-3823	19	3	appl	appl	PROPN
ejpam-3823	19	4	.	.	PROPN
ejpam-3823	19	5	math	math	PROPN
ejpam-3823	19	6	,	,	PUNCT
ejpam-3823	19	7	14	14	NUM
ejpam-3823	19	8	(	(	PUNCT
ejpam-3823	19	9	4	4	NUM
ejpam-3823	19	10	)	)	PUNCT
ejpam-3823	19	11	(	(	PUNCT
ejpam-3823	19	12	2021	2021	NUM
ejpam-3823	19	13	)	)	PUNCT
ejpam-3823	19	14	,	,	PUNCT
ejpam-3823	19	15	1507	1507	NUM
ejpam-3823	19	16	-	-	SYM
ejpam-3823	19	17	1516	1516	NUM
ejpam-3823	19	18	1508	1508	NUM
ejpam-3823	19	19	changes	change	NOUN
ejpam-3823	19	20	to	to	ADP
ejpam-3823	19	21	the	the	DET
ejpam-3823	19	22	lower	low	ADJ
ejpam-3823	19	23	approximation	approximation	NOUN
ejpam-3823	19	24	,	,	PUNCT
ejpam-3823	19	25	upper	upper	ADJ
ejpam-3823	19	26	approximation	approximation	NOUN
ejpam-3823	19	27	and	and	CCONJ
ejpam-3823	19	28	boundary	boundary	ADJ
ejpam-3823	19	29	regions	region	NOUN
ejpam-3823	19	30	that	that	PRON
ejpam-3823	19	31	resulted	result	VERB
ejpam-3823	19	32	in	in	ADP
ejpam-3823	19	33	grill	grill	NOUN
ejpam-3823	19	34	nano	nano	NOUN
ejpam-3823	19	35	topological	topological	ADJ
ejpam-3823	19	36	spaces	space	NOUN
ejpam-3823	19	37	.	.	PUNCT
ejpam-3823	20	1	the	the	DET
ejpam-3823	20	2	author	author	NOUN
ejpam-3823	20	3	equally	equally	ADV
ejpam-3823	20	4	defined	define	VERB
ejpam-3823	20	5	grill	grill	ADJ
ejpam-3823	20	6	nano	nano	NOUN
ejpam-3823	20	7	-	-	PUNCT
ejpam-3823	20	8	generalized	generalize	VERB
ejpam-3823	20	9	closed	close	VERB
ejpam-3823	20	10	sets	set	NOUN
ejpam-3823	20	11	which	which	PRON
ejpam-3823	20	12	is	be	AUX
ejpam-3823	20	13	an	an	DET
ejpam-3823	20	14	expansion	expansion	NOUN
ejpam-3823	20	15	of	of	ADP
ejpam-3823	20	16	nano	nano	NOUN
ejpam-3823	20	17	-	-	PUNCT
ejpam-3823	20	18	generalized	generalize	VERB
ejpam-3823	20	19	closed	closed	ADJ
ejpam-3823	20	20	sets	set	NOUN
ejpam-3823	20	21	in	in	ADP
ejpam-3823	20	22	grill	grill	ADJ
ejpam-3823	20	23	nano	nano	NOUN
ejpam-3823	20	24	topological	topological	ADJ
ejpam-3823	20	25	spaces	space	NOUN
ejpam-3823	20	26	.	.	PUNCT
ejpam-3823	21	1	in	in	ADP
ejpam-3823	21	2	2018	2018	NUM
ejpam-3823	21	3	,	,	PUNCT
ejpam-3823	21	4	t.	t.	PROPN
ejpam-3823	21	5	m.	m.	PROPN
ejpam-3823	21	6	al	al	PROPN
ejpam-3823	21	7	-	-	PUNCT
ejpam-3823	21	8	shami	shami	PROPN
ejpam-3823	22	1	[	[	X
ejpam-3823	22	2	4	4	NUM
ejpam-3823	22	3	]	]	PUNCT
ejpam-3823	22	4	given	give	VERB
ejpam-3823	22	5	that	that	DET
ejpam-3823	22	6	supra	supra	NOUN
ejpam-3823	22	7	semi	semi	NOUN
ejpam-3823	22	8	-	-	NOUN
ejpam-3823	22	9	compactness	compactness	NOUN
ejpam-3823	22	10	via	via	ADP
ejpam-3823	22	11	supra	supra	PROPN
ejpam-3823	22	12	topological	topological	ADJ
ejpam-3823	22	13	spaces	space	NOUN
ejpam-3823	22	14	.	.	PUNCT
ejpam-3823	23	1	in	in	ADP
ejpam-3823	23	2	2019	2019	NUM
ejpam-3823	23	3	,	,	PUNCT
ejpam-3823	23	4	chandrasekar	chandrasekar	X
ejpam-3823	23	5	[	[	X
ejpam-3823	23	6	9	9	NUM
ejpam-3823	23	7	]	]	PUNCT
ejpam-3823	23	8	introduced	introduce	VERB
ejpam-3823	23	9	the	the	DET
ejpam-3823	23	10	concept	concept	NOUN
ejpam-3823	23	11	of	of	ADP
ejpam-3823	23	12	micro	micro	ADJ
ejpam-3823	23	13	topology	topology	NOUN
ejpam-3823	23	14	which	which	PRON
ejpam-3823	23	15	is	be	AUX
ejpam-3823	23	16	simply	simply	ADV
ejpam-3823	23	17	an	an	DET
ejpam-3823	23	18	extension	extension	NOUN
ejpam-3823	23	19	of	of	ADP
ejpam-3823	23	20	nano	nano	NOUN
ejpam-3823	23	21	topology	topology	NOUN
ejpam-3823	23	22	and	and	CCONJ
ejpam-3823	23	23	t.	t.	PROPN
ejpam-3823	23	24	m.	m.	PROPN
ejpam-3823	23	25	al	al	PROPN
ejpam-3823	23	26	-	-	PUNCT
ejpam-3823	23	27	shami	shami	PROPN
ejpam-3823	23	28	and	and	CCONJ
ejpam-3823	23	29	t.	t.	PROPN
ejpam-3823	23	30	noiri	noiri	PROPN
ejpam-3823	24	1	[	[	X
ejpam-3823	24	2	6	6	NUM
ejpam-3823	24	3	]	]	PUNCT
ejpam-3823	24	4	provided	provide	VERB
ejpam-3823	24	5	more	more	ADJ
ejpam-3823	24	6	notions	notion	NOUN
ejpam-3823	24	7	and	and	CCONJ
ejpam-3823	24	8	mappings	mapping	NOUN
ejpam-3823	24	9	via	via	ADP
ejpam-3823	24	10	somewhere	somewhere	ADJ
ejpam-3823	24	11	dense	dense	ADJ
ejpam-3823	24	12	sets	set	NOUN
ejpam-3823	24	13	.	.	PUNCT
ejpam-3823	25	1	in	in	ADP
ejpam-3823	25	2	2020	2020	NUM
ejpam-3823	25	3	,	,	PUNCT
ejpam-3823	25	4	rasheed	rasheed	NOUN
ejpam-3823	25	5	and	and	CCONJ
ejpam-3823	25	6	jasim	jasim	NOUN
ejpam-3823	26	1	[	[	X
ejpam-3823	26	2	12	12	NUM
ejpam-3823	26	3	]	]	PUNCT
ejpam-3823	26	4	introduced	introduce	VERB
ejpam-3823	26	5	microα	microα	PROPN
ejpam-3823	26	6	-open	-open	PROPN
ejpam-3823	26	7	sets	set	NOUN
ejpam-3823	26	8	,	,	PUNCT
ejpam-3823	26	9	microα	microα	VERB
ejpam-3823	26	10	-continuous	-continuous	ADJ
ejpam-3823	26	11	functions	function	NOUN
ejpam-3823	26	12	and	and	CCONJ
ejpam-3823	26	13	some	some	PRON
ejpam-3823	26	14	of	of	ADP
ejpam-3823	26	15	their	their	PRON
ejpam-3823	26	16	properties	property	NOUN
ejpam-3823	26	17	are	be	AUX
ejpam-3823	26	18	investigated	investigate	VERB
ejpam-3823	26	19	and	and	CCONJ
ejpam-3823	26	20	t.m	t.m	PROPN
ejpam-3823	26	21	.	.	PROPN
ejpam-3823	26	22	al	al	PROPN
ejpam-3823	26	23	-	-	PUNCT
ejpam-3823	26	24	shami	shami	PROPN
ejpam-3823	27	1	[	[	X
ejpam-3823	27	2	10	10	NUM
ejpam-3823	27	3	]	]	PUNCT
ejpam-3823	27	4	,	,	PUNCT
ejpam-3823	27	5	[	[	X
ejpam-3823	27	6	2	2	NUM
ejpam-3823	27	7	]	]	PUNCT
ejpam-3823	27	8	,	,	PUNCT
ejpam-3823	28	1	[	[	X
ejpam-3823	28	2	1]and	1]and	NUM
ejpam-3823	28	3	[	[	X
ejpam-3823	28	4	5	5	NUM
ejpam-3823	28	5	]	]	PUNCT
ejpam-3823	28	6	studied	study	VERB
ejpam-3823	28	7	respectively	respectively	ADV
ejpam-3823	28	8	,	,	PUNCT
ejpam-3823	28	9	some	some	DET
ejpam-3823	28	10	applications	application	NOUN
ejpam-3823	28	11	of	of	ADP
ejpam-3823	28	12	supra	supra	ADJ
ejpam-3823	28	13	preopen	preopen	ADJ
ejpam-3823	28	14	sets	set	NOUN
ejpam-3823	28	15	,	,	PUNCT
ejpam-3823	28	16	limit	limit	VERB
ejpam-3823	28	17	points	point	NOUN
ejpam-3823	28	18	and	and	CCONJ
ejpam-3823	28	19	separation	separation	NOUN
ejpam-3823	28	20	axioms	axiom	NOUN
ejpam-3823	28	21	with	with	ADP
ejpam-3823	28	22	respect	respect	NOUN
ejpam-3823	28	23	to	to	ADP
ejpam-3823	28	24	supra	supra	PROPN
ejpam-3823	28	25	semi	semi	ADJ
ejpam-3823	28	26	-	-	ADJ
ejpam-3823	28	27	open	open	ADJ
ejpam-3823	28	28	sets	set	NOUN
ejpam-3823	28	29	,	,	PUNCT
ejpam-3823	28	30	para	para	ADJ
ejpam-3823	28	31	compactness	compactness	NOUN
ejpam-3823	28	32	on	on	ADP
ejpam-3823	28	33	supra	supra	PROPN
ejpam-3823	28	34	topological	topological	ADJ
ejpam-3823	28	35	spaces	space	NOUN
ejpam-3823	28	36	and	and	CCONJ
ejpam-3823	28	37	sum	sum	NOUN
ejpam-3823	28	38	of	of	ADP
ejpam-3823	28	39	the	the	DET
ejpam-3823	28	40	spaces	space	NOUN
ejpam-3823	28	41	on	on	ADP
ejpam-3823	28	42	ordered	order	VERB
ejpam-3823	28	43	setting	setting	NOUN
ejpam-3823	28	44	.	.	PUNCT
ejpam-3823	29	1	this	this	DET
ejpam-3823	29	2	research	research	NOUN
ejpam-3823	29	3	focus	focus	NOUN
ejpam-3823	29	4	on	on	ADP
ejpam-3823	29	5	the	the	DET
ejpam-3823	29	6	introduction	introduction	NOUN
ejpam-3823	29	7	of	of	ADP
ejpam-3823	29	8	a	a	DET
ejpam-3823	29	9	new	new	ADJ
ejpam-3823	29	10	class	class	NOUN
ejpam-3823	29	11	of	of	ADP
ejpam-3823	29	12	sets	set	NOUN
ejpam-3823	29	13	called	call	VERB
ejpam-3823	29	14	microgeneralized	microgeneralize	VERB
ejpam-3823	29	15	closed	closed	ADJ
ejpam-3823	29	16	set	set	ADJ
ejpam-3823	29	17	and	and	CCONJ
ejpam-3823	29	18	micro	micro	ADJ
ejpam-3823	29	19	-	-	ADJ
ejpam-3823	29	20	generalized	generalized	ADJ
ejpam-3823	29	21	continuous	continuous	ADJ
ejpam-3823	29	22	functions	function	NOUN
ejpam-3823	29	23	.	.	PUNCT
ejpam-3823	30	1	many	many	ADJ
ejpam-3823	30	2	characterizations	characterization	NOUN
ejpam-3823	30	3	and	and	CCONJ
ejpam-3823	30	4	theorems	theorem	NOUN
ejpam-3823	30	5	relating	relate	VERB
ejpam-3823	30	6	to	to	ADP
ejpam-3823	30	7	these	these	DET
ejpam-3823	30	8	sets	set	NOUN
ejpam-3823	30	9	are	be	AUX
ejpam-3823	30	10	proved	prove	VERB
ejpam-3823	30	11	.	.	PUNCT
ejpam-3823	31	1	2	2	X
ejpam-3823	31	2	.	.	X
ejpam-3823	31	3	preliminaries	preliminary	NOUN
ejpam-3823	31	4	in	in	ADP
ejpam-3823	31	5	this	this	DET
ejpam-3823	31	6	section	section	NOUN
ejpam-3823	31	7	,	,	PUNCT
ejpam-3823	31	8	we	we	PRON
ejpam-3823	31	9	recall	recall	VERB
ejpam-3823	31	10	some	some	DET
ejpam-3823	31	11	preliminary	preliminary	ADJ
ejpam-3823	31	12	definitions	definition	NOUN
ejpam-3823	31	13	that	that	PRON
ejpam-3823	31	14	led	lead	VERB
ejpam-3823	31	15	to	to	ADP
ejpam-3823	31	16	the	the	DET
ejpam-3823	31	17	development	development	NOUN
ejpam-3823	31	18	of	of	ADP
ejpam-3823	31	19	our	our	PRON
ejpam-3823	31	20	main	main	ADJ
ejpam-3823	31	21	results	result	NOUN
ejpam-3823	31	22	.	.	PUNCT
ejpam-3823	32	1	2.1	2.1	NUM
ejpam-3823	32	2	.	.	PUNCT
ejpam-3823	32	3	definition	definition	NOUN
ejpam-3823	32	4	[	[	X
ejpam-3823	32	5	11	11	NUM
ejpam-3823	32	6	]	]	PUNCT
ejpam-3823	32	7	a	a	DET
ejpam-3823	32	8	subset	subset	NOUN
ejpam-3823	32	9	b	b	NOUN
ejpam-3823	32	10	from	from	ADP
ejpam-3823	32	11	a	a	DET
ejpam-3823	32	12	topology	topology	NOUN
ejpam-3823	32	13	τ	τ	X
ejpam-3823	32	14	on	on	ADP
ejpam-3823	32	15	the	the	DET
ejpam-3823	32	16	space	space	NOUN
ejpam-3823	32	17	x	x	PRON
ejpam-3823	32	18	is	be	AUX
ejpam-3823	32	19	said	say	VERB
ejpam-3823	32	20	to	to	PART
ejpam-3823	32	21	be	be	AUX
ejpam-3823	32	22	generalized	generalize	VERB
ejpam-3823	32	23	closed	close	VERB
ejpam-3823	32	24	set	set	NOUN
ejpam-3823	32	25	(	(	PUNCT
ejpam-3823	32	26	shortly	shortly	ADV
ejpam-3823	32	27	g	g	NOUN
ejpam-3823	32	28	-	-	PUNCT
ejpam-3823	32	29	closed	closed	ADJ
ejpam-3823	32	30	)	)	PUNCT
ejpam-3823	32	31	if	if	SCONJ
ejpam-3823	32	32	cl.(b	cl.(b	NOUN
ejpam-3823	32	33	)	)	PUNCT
ejpam-3823	32	34	⊂	⊂	PROPN
ejpam-3823	32	35	u	u	PROPN
ejpam-3823	32	36	for	for	ADP
ejpam-3823	32	37	b	b	PROPN
ejpam-3823	32	38	⊂	⊂	PROPN
ejpam-3823	32	39	u	u	PROPN
ejpam-3823	32	40	and	and	CCONJ
ejpam-3823	32	41	u	u	NOUN
ejpam-3823	32	42	is	be	AUX
ejpam-3823	32	43	open	open	ADJ
ejpam-3823	32	44	in	in	ADP
ejpam-3823	32	45	(	(	PUNCT
ejpam-3823	32	46	x	x	NOUN
ejpam-3823	32	47	,	,	PUNCT
ejpam-3823	32	48	τ	τ	PROPN
ejpam-3823	32	49	)	)	PUNCT
ejpam-3823	32	50	.	.	PUNCT
ejpam-3823	33	1	a	a	DET
ejpam-3823	33	2	set	set	ADJ
ejpam-3823	33	3	b	b	PROPN
ejpam-3823	33	4	of	of	ADP
ejpam-3823	33	5	topological	topological	ADJ
ejpam-3823	33	6	space	space	NOUN
ejpam-3823	33	7	(	(	PUNCT
ejpam-3823	33	8	x	x	X
ejpam-3823	33	9	,	,	PUNCT
ejpam-3823	33	10	τ	τ	X
ejpam-3823	33	11	)	)	PUNCT
ejpam-3823	33	12	is	be	AUX
ejpam-3823	33	13	called	call	VERB
ejpam-3823	33	14	g	g	NOUN
ejpam-3823	33	15	-	-	PUNCT
ejpam-3823	33	16	open	open	ADJ
ejpam-3823	33	17	if	if	SCONJ
ejpam-3823	33	18	x	x	PRON
ejpam-3823	33	19	−b	−b	NOUN
ejpam-3823	33	20	is	be	AUX
ejpam-3823	33	21	g	g	NOUN
ejpam-3823	33	22	-	-	PUNCT
ejpam-3823	33	23	closed	closed	ADJ
ejpam-3823	33	24	.	.	PUNCT
ejpam-3823	34	1	2.2	2.2	NUM
ejpam-3823	34	2	.	.	PUNCT
ejpam-3823	34	3	definition	definition	NOUN
ejpam-3823	34	4	[	[	X
ejpam-3823	34	5	9	9	X
ejpam-3823	34	6	]	]	PUNCT
ejpam-3823	34	7	let	let	VERB
ejpam-3823	34	8	x	x	PRON
ejpam-3823	34	9	be	be	AUX
ejpam-3823	34	10	a	a	DET
ejpam-3823	34	11	non	non	ADJ
ejpam-3823	34	12	-	-	ADJ
ejpam-3823	34	13	empty	empty	ADJ
ejpam-3823	34	14	finite	finite	NOUN
ejpam-3823	34	15	set	set	NOUN
ejpam-3823	34	16	of	of	ADP
ejpam-3823	34	17	objects	object	NOUN
ejpam-3823	34	18	called	call	VERB
ejpam-3823	34	19	‘	'	PUNCT
ejpam-3823	34	20	universe	universe	NOUN
ejpam-3823	34	21	’	'	PUNCT
ejpam-3823	34	22	and	and	CCONJ
ejpam-3823	34	23	let	let	VERB
ejpam-3823	34	24	r	r	PRON
ejpam-3823	34	25	be	be	AUX
ejpam-3823	34	26	an	an	DET
ejpam-3823	34	27	‘	'	PUNCT
ejpam-3823	34	28	equivalence	equivalence	NOUN
ejpam-3823	34	29	relation	relation	NOUN
ejpam-3823	34	30	’	'	PUNCT
ejpam-3823	34	31	on	on	ADP
ejpam-3823	34	32	x	x	PUNCT
ejpam-3823	34	33	named	name	VERB
ejpam-3823	34	34	as	as	ADP
ejpam-3823	34	35	‘	'	PUNCT
ejpam-3823	34	36	the	the	DET
ejpam-3823	34	37	indiscernibility	indiscernibility	NOUN
ejpam-3823	34	38	relation	relation	NOUN
ejpam-3823	34	39	’	'	PUNCT
ejpam-3823	34	40	.	.	PUNCT
ejpam-3823	35	1	then	then	ADV
ejpam-3823	35	2	x	x	PUNCT
ejpam-3823	35	3	divided	divide	VERB
ejpam-3823	35	4	into	into	ADP
ejpam-3823	35	5	disjoint	disjoint	ADJ
ejpam-3823	35	6	equivalence	equivalence	NOUN
ejpam-3823	35	7	classes	class	NOUN
ejpam-3823	35	8	.	.	PUNCT
ejpam-3823	36	1	elements	element	NOUN
ejpam-3823	36	2	belonging	belong	VERB
ejpam-3823	36	3	to	to	ADP
ejpam-3823	36	4	the	the	DET
ejpam-3823	36	5	same	same	ADJ
ejpam-3823	36	6	equivalence	equivalence	NOUN
ejpam-3823	36	7	class	class	NOUN
ejpam-3823	36	8	are	be	AUX
ejpam-3823	36	9	said	say	VERB
ejpam-3823	36	10	to	to	PART
ejpam-3823	36	11	be	be	AUX
ejpam-3823	36	12	indiscernible	indiscernible	ADJ
ejpam-3823	36	13	with	with	ADP
ejpam-3823	36	14	one	one	NUM
ejpam-3823	36	15	another	another	DET
ejpam-3823	36	16	.	.	PUNCT
ejpam-3823	37	1	the	the	DET
ejpam-3823	37	2	pair	pair	NOUN
ejpam-3823	37	3	(	(	PUNCT
ejpam-3823	37	4	x	x	NOUN
ejpam-3823	37	5	,	,	PUNCT
ejpam-3823	37	6	r	r	NOUN
ejpam-3823	37	7	)	)	PUNCT
ejpam-3823	37	8	is	be	AUX
ejpam-3823	37	9	said	say	VERB
ejpam-3823	37	10	to	to	PART
ejpam-3823	37	11	be	be	AUX
ejpam-3823	37	12	‘	'	PUNCT
ejpam-3823	37	13	the	the	DET
ejpam-3823	37	14	approximation	approximation	NOUN
ejpam-3823	37	15	space	space	NOUN
ejpam-3823	37	16	’	'	PUNCT
ejpam-3823	37	17	.	.	PUNCT
ejpam-3823	38	1	let	let	VERB
ejpam-3823	38	2	a	a	DET
ejpam-3823	38	3	⊆	⊆	NUM
ejpam-3823	38	4	x	x	SYM
ejpam-3823	38	5	,	,	PUNCT
ejpam-3823	38	6	(	(	PUNCT
ejpam-3823	38	7	i	i	NOUN
ejpam-3823	38	8	)	)	PUNCT
ejpam-3823	38	9	the	the	DET
ejpam-3823	38	10	lower	low	ADJ
ejpam-3823	38	11	approximation	approximation	NOUN
ejpam-3823	38	12	of	of	ADP
ejpam-3823	38	13	a	a	DET
ejpam-3823	38	14	with	with	ADP
ejpam-3823	38	15	respect	respect	NOUN
ejpam-3823	38	16	to	to	ADP
ejpam-3823	38	17	r	r	NOUN
ejpam-3823	38	18	is	be	AUX
ejpam-3823	38	19	the	the	DET
ejpam-3823	38	20	set	set	NOUN
ejpam-3823	38	21	of	of	ADP
ejpam-3823	38	22	all	all	DET
ejpam-3823	38	23	objects	object	NOUN
ejpam-3823	38	24	,	,	PUNCT
ejpam-3823	38	25	which	which	PRON
ejpam-3823	38	26	can	can	AUX
ejpam-3823	38	27	be	be	AUX
ejpam-3823	38	28	for	for	ADP
ejpam-3823	38	29	certain	certain	ADJ
ejpam-3823	38	30	classified	classify	VERB
ejpam-3823	38	31	as	as	ADP
ejpam-3823	38	32	a	a	DET
ejpam-3823	38	33	with	with	ADP
ejpam-3823	38	34	respect	respect	NOUN
ejpam-3823	38	35	to	to	ADP
ejpam-3823	38	36	r	r	NOUN
ejpam-3823	38	37	and	and	CCONJ
ejpam-3823	38	38	it	it	PRON
ejpam-3823	38	39	is	be	AUX
ejpam-3823	38	40	denoted	denote	VERB
ejpam-3823	38	41	by	by	ADP
ejpam-3823	38	42	lr(a	lr(a	NOUN
ejpam-3823	38	43	)	)	PUNCT
ejpam-3823	38	44	.	.	PUNCT
ejpam-3823	39	1	that	that	PRON
ejpam-3823	39	2	is	be	AUX
ejpam-3823	39	3	lr(a	lr(a	PUNCT
ejpam-3823	39	4	)	)	PUNCT
ejpam-3823	39	5	=	=	PUNCT
ejpam-3823	39	6	∪(x	∪(x	PROPN
ejpam-3823	39	7	∈	∈	PROPN
ejpam-3823	39	8	x){r(x	x){r(x	NUM
ejpam-3823	39	9	)	)	PUNCT
ejpam-3823	39	10	:	:	PUNCT
ejpam-3823	40	1	r(x	r(x	X
ejpam-3823	40	2	)	)	PUNCT
ejpam-3823	40	3	⊆	⊆	NUM
ejpam-3823	40	4	a	a	DET
ejpam-3823	40	5	where	where	SCONJ
ejpam-3823	40	6	r(x	r(x	NOUN
ejpam-3823	40	7	)	)	PUNCT
ejpam-3823	40	8	}	}	PUNCT
ejpam-3823	40	9	denotes	denote	VERB
ejpam-3823	40	10	the	the	DET
ejpam-3823	40	11	equivalence	equivalence	NOUN
ejpam-3823	40	12	class	class	NOUN
ejpam-3823	40	13	determined	determine	VERB
ejpam-3823	40	14	by	by	ADP
ejpam-3823	40	15	x	x	SYM
ejpam-3823	40	16	∈	∈	PROPN
ejpam-3823	40	17	x.	x.	NOUN
ejpam-3823	40	18	(	(	PUNCT
ejpam-3823	40	19	ii	ii	PROPN
ejpam-3823	40	20	)	)	PUNCT
ejpam-3823	40	21	the	the	DET
ejpam-3823	40	22	upper	upper	ADJ
ejpam-3823	40	23	approximation	approximation	NOUN
ejpam-3823	40	24	of	of	ADP
ejpam-3823	40	25	a	a	DET
ejpam-3823	40	26	with	with	ADP
ejpam-3823	40	27	respect	respect	NOUN
ejpam-3823	40	28	to	to	ADP
ejpam-3823	40	29	r	r	NOUN
ejpam-3823	40	30	is	be	AUX
ejpam-3823	40	31	the	the	DET
ejpam-3823	40	32	set	set	NOUN
ejpam-3823	40	33	of	of	ADP
ejpam-3823	40	34	all	all	DET
ejpam-3823	40	35	objects	object	NOUN
ejpam-3823	40	36	,	,	PUNCT
ejpam-3823	40	37	which	which	PRON
ejpam-3823	40	38	can	can	AUX
ejpam-3823	40	39	be	be	AUX
ejpam-3823	40	40	possibly	possibly	ADV
ejpam-3823	40	41	classified	classify	VERB
ejpam-3823	40	42	as	as	ADP
ejpam-3823	40	43	a	a	DET
ejpam-3823	40	44	with	with	ADP
ejpam-3823	40	45	respect	respect	NOUN
ejpam-3823	40	46	to	to	ADP
ejpam-3823	40	47	r	r	NOUN
ejpam-3823	40	48	and	and	CCONJ
ejpam-3823	40	49	it	it	PRON
ejpam-3823	40	50	is	be	AUX
ejpam-3823	40	51	denoted	denote	VERB
ejpam-3823	40	52	by	by	ADP
ejpam-3823	40	53	ur(a	ur(a	PUNCT
ejpam-3823	40	54	)	)	PUNCT
ejpam-3823	40	55	.	.	PUNCT
ejpam-3823	41	1	that	that	PRON
ejpam-3823	41	2	is	be	AUX
ejpam-3823	41	3	,	,	PUNCT
ejpam-3823	41	4	ur(a	ur(a	PUNCT
ejpam-3823	41	5	)	)	PUNCT
ejpam-3823	41	6	=	=	PUNCT
ejpam-3823	41	7	∪(x	∪(x	PROPN
ejpam-3823	41	8	∈	∈	PROPN
ejpam-3823	41	9	x){r(x	x){r(x	NUM
ejpam-3823	41	10	)	)	PUNCT
ejpam-3823	41	11	:	:	PUNCT
ejpam-3823	42	1	r(x	r(x	X
ejpam-3823	42	2	)	)	PUNCT
ejpam-3823	42	3	∩a	∩a	PROPN
ejpam-3823	42	4	̸=	̸=	PROPN
ejpam-3823	42	5	ϕ	ϕ	NOUN
ejpam-3823	42	6	}	}	PUNCT
ejpam-3823	42	7	.	.	PUNCT
ejpam-3823	43	1	t.	t.	PROPN
ejpam-3823	43	2	h.	h.	PROPN
ejpam-3823	43	3	jasim	jasim	PROPN
ejpam-3823	43	4	,	,	PUNCT
ejpam-3823	43	5	s.	s.	PROPN
ejpam-3823	43	6	s.	s.	PROPN
ejpam-3823	43	7	mohsen	mohsen	PROPN
ejpam-3823	43	8	,	,	PUNCT
ejpam-3823	43	9	k.	k.	PROPN
ejpam-3823	43	10	s.	s.	PROPN
ejpam-3823	43	11	eke	eke	PROPN
ejpam-3823	43	12	/	/	SYM
ejpam-3823	43	13	eur	eur	PROPN
ejpam-3823	43	14	.	.	PUNCT
ejpam-3823	44	1	j.	j.	PROPN
ejpam-3823	44	2	pure	pure	PROPN
ejpam-3823	44	3	appl	appl	PROPN
ejpam-3823	44	4	.	.	PROPN
ejpam-3823	44	5	math	math	PROPN
ejpam-3823	44	6	,	,	PUNCT
ejpam-3823	44	7	14	14	NUM
ejpam-3823	44	8	(	(	PUNCT
ejpam-3823	44	9	4	4	NUM
ejpam-3823	44	10	)	)	PUNCT
ejpam-3823	44	11	(	(	PUNCT
ejpam-3823	44	12	2021	2021	NUM
ejpam-3823	44	13	)	)	PUNCT
ejpam-3823	44	14	,	,	PUNCT
ejpam-3823	44	15	1507	1507	NUM
ejpam-3823	44	16	-	-	SYM
ejpam-3823	44	17	1516	1516	NUM
ejpam-3823	44	18	1509	1509	NUM
ejpam-3823	44	19	(	(	PUNCT
ejpam-3823	44	20	iii	iii	NOUN
ejpam-3823	44	21	)	)	PUNCT
ejpam-3823	44	22	the	the	DET
ejpam-3823	44	23	boundary	boundary	ADJ
ejpam-3823	44	24	region	region	NOUN
ejpam-3823	44	25	of	of	ADP
ejpam-3823	44	26	a	a	PRON
ejpam-3823	44	27	with	with	ADP
ejpam-3823	44	28	respect	respect	NOUN
ejpam-3823	44	29	to	to	ADP
ejpam-3823	44	30	r	r	NOUN
ejpam-3823	44	31	is	be	AUX
ejpam-3823	44	32	the	the	DET
ejpam-3823	44	33	set	set	NOUN
ejpam-3823	44	34	of	of	ADP
ejpam-3823	44	35	all	all	DET
ejpam-3823	44	36	objects	object	NOUN
ejpam-3823	44	37	,	,	PUNCT
ejpam-3823	44	38	which	which	PRON
ejpam-3823	44	39	can	can	AUX
ejpam-3823	44	40	be	be	AUX
ejpam-3823	44	41	classified	classify	VERB
ejpam-3823	44	42	neither	neither	CCONJ
ejpam-3823	44	43	as	as	ADP
ejpam-3823	44	44	a	a	DET
ejpam-3823	44	45	nor	nor	CCONJ
ejpam-3823	44	46	as	as	ADP
ejpam-3823	44	47	not	not	PART
ejpam-3823	44	48	-	-	PUNCT
ejpam-3823	44	49	a	a	NOUN
ejpam-3823	44	50	with	with	ADP
ejpam-3823	44	51	respect	respect	NOUN
ejpam-3823	44	52	to	to	ADP
ejpam-3823	44	53	r	r	NOUN
ejpam-3823	44	54	and	and	CCONJ
ejpam-3823	44	55	it	it	PRON
ejpam-3823	44	56	is	be	AUX
ejpam-3823	44	57	denoted	denote	VERB
ejpam-3823	44	58	by	by	ADP
ejpam-3823	44	59	br(a	br(a	NOUN
ejpam-3823	44	60	)	)	PUNCT
ejpam-3823	44	61	.	.	PUNCT
ejpam-3823	45	1	that	that	PRON
ejpam-3823	45	2	is	be	AUX
ejpam-3823	45	3	,	,	PUNCT
ejpam-3823	45	4	br(a	br(a	X
ejpam-3823	45	5	)	)	PUNCT
ejpam-3823	46	1	=	=	SYM
ejpam-3823	46	2	ur(a)−	ur(a)−	NOUN
ejpam-3823	46	3	lr(a	lr(a	PUNCT
ejpam-3823	46	4	)	)	PUNCT
ejpam-3823	46	5	.	.	PUNCT
ejpam-3823	47	1	2.3	2.3	NUM
ejpam-3823	47	2	.	.	PUNCT
ejpam-3823	47	3	definition	definition	NOUN
ejpam-3823	47	4	[	[	X
ejpam-3823	47	5	13	13	NUM
ejpam-3823	47	6	]	]	PUNCT
ejpam-3823	47	7	let	let	VERB
ejpam-3823	47	8	x	x	PRON
ejpam-3823	47	9	be	be	AUX
ejpam-3823	47	10	the	the	DET
ejpam-3823	47	11	universe	universe	NOUN
ejpam-3823	47	12	,	,	PUNCT
ejpam-3823	47	13	r	r	NOUN
ejpam-3823	47	14	be	be	VERB
ejpam-3823	47	15	an	an	DET
ejpam-3823	47	16	equivalence	equivalence	NOUN
ejpam-3823	47	17	relation	relation	NOUN
ejpam-3823	47	18	on	on	ADP
ejpam-3823	47	19	x	x	PUNCT
ejpam-3823	47	20	and	and	CCONJ
ejpam-3823	47	21	τr(a	τr(a	NUM
ejpam-3823	47	22	)	)	PUNCT
ejpam-3823	48	1	=	=	PRON
ejpam-3823	48	2	{	{	PUNCT
ejpam-3823	48	3	ϕ,x	ϕ,x	NOUN
ejpam-3823	48	4	,	,	PUNCT
ejpam-3823	48	5	lr(a	lr(a	NOUN
ejpam-3823	48	6	)	)	PUNCT
ejpam-3823	48	7	,	,	PUNCT
ejpam-3823	48	8	ur(a	ur(a	PUNCT
ejpam-3823	48	9	)	)	PUNCT
ejpam-3823	48	10	,	,	PUNCT
ejpam-3823	48	11	br(a	br(a	NUM
ejpam-3823	48	12	)	)	PUNCT
ejpam-3823	48	13	}	}	PUNCT
ejpam-3823	48	14	where	where	SCONJ
ejpam-3823	48	15	a	a	DET
ejpam-3823	48	16	⊆	⊆	NUM
ejpam-3823	48	17	x.	x.	NOUN
ejpam-3823	48	18	then	then	ADV
ejpam-3823	48	19	τr(a	τr(a	NUM
ejpam-3823	48	20	)	)	PUNCT
ejpam-3823	48	21	satisfies	satisfy	VERB
ejpam-3823	48	22	the	the	DET
ejpam-3823	48	23	following	follow	VERB
ejpam-3823	48	24	axioms	axiom	NOUN
ejpam-3823	48	25	.	.	PUNCT
ejpam-3823	49	1	•	•	NUM
ejpam-3823	49	2	x	x	NOUN
ejpam-3823	49	3	and	and	CCONJ
ejpam-3823	49	4	ϕ	ϕ	PROPN
ejpam-3823	49	5	∈	∈	PROPN
ejpam-3823	49	6	τr(a	τr(a	NUM
ejpam-3823	49	7	)	)	PUNCT
ejpam-3823	49	8	.	.	PUNCT
ejpam-3823	50	1	•	•	NUM
ejpam-3823	50	2	the	the	DET
ejpam-3823	50	3	union	union	NOUN
ejpam-3823	50	4	of	of	ADP
ejpam-3823	50	5	the	the	DET
ejpam-3823	50	6	elements	element	NOUN
ejpam-3823	50	7	of	of	ADP
ejpam-3823	50	8	any	any	DET
ejpam-3823	50	9	sub	sub	NOUN
ejpam-3823	50	10	collection	collection	NOUN
ejpam-3823	50	11	of	of	ADP
ejpam-3823	50	12	τr(a	τr(a	NUM
ejpam-3823	50	13	)	)	PUNCT
ejpam-3823	50	14	is	be	AUX
ejpam-3823	50	15	in	in	ADP
ejpam-3823	50	16	τr(a	τr(a	NUM
ejpam-3823	50	17	)	)	PUNCT
ejpam-3823	50	18	.	.	PUNCT
ejpam-3823	51	1	•	•	NUM
ejpam-3823	51	2	the	the	DET
ejpam-3823	51	3	intersection	intersection	NOUN
ejpam-3823	51	4	of	of	ADP
ejpam-3823	51	5	the	the	DET
ejpam-3823	51	6	elements	element	NOUN
ejpam-3823	51	7	of	of	ADP
ejpam-3823	51	8	any	any	DET
ejpam-3823	51	9	finite	finite	ADJ
ejpam-3823	51	10	sub	sub	NOUN
ejpam-3823	51	11	collection	collection	NOUN
ejpam-3823	51	12	of	of	ADP
ejpam-3823	51	13	τr(a	τr(a	NUM
ejpam-3823	51	14	)	)	PUNCT
ejpam-3823	51	15	is	be	AUX
ejpam-3823	51	16	in	in	ADP
ejpam-3823	51	17	τr(a	τr(a	NUM
ejpam-3823	51	18	)	)	PUNCT
ejpam-3823	51	19	.	.	PUNCT
ejpam-3823	52	1	that	that	PRON
ejpam-3823	52	2	is	be	AUX
ejpam-3823	52	3	τr(a	τr(a	NUM
ejpam-3823	52	4	)	)	PUNCT
ejpam-3823	52	5	forms	form	VERB
ejpam-3823	52	6	a	a	DET
ejpam-3823	52	7	topology	topology	NOUN
ejpam-3823	52	8	on	on	ADP
ejpam-3823	52	9	x	x	PUNCT
ejpam-3823	52	10	called	call	VERB
ejpam-3823	52	11	the	the	DET
ejpam-3823	52	12	nano	nano	NOUN
ejpam-3823	52	13	topology	topology	NOUN
ejpam-3823	52	14	on	on	ADP
ejpam-3823	52	15	x	x	PUNCT
ejpam-3823	52	16	with	with	ADP
ejpam-3823	52	17	respect	respect	NOUN
ejpam-3823	52	18	to	to	ADP
ejpam-3823	52	19	a.	a.	NOUN
ejpam-3823	52	20	we	we	PRON
ejpam-3823	52	21	call	call	VERB
ejpam-3823	52	22	(	(	PUNCT
ejpam-3823	52	23	x	x	NOUN
ejpam-3823	52	24	,	,	PUNCT
ejpam-3823	52	25	τr(a	τr(a	NUM
ejpam-3823	52	26	)	)	PUNCT
ejpam-3823	52	27	)	)	PUNCT
ejpam-3823	53	1	the	the	DET
ejpam-3823	53	2	nano	nano	ADJ
ejpam-3823	53	3	topological	topological	ADJ
ejpam-3823	53	4	space	space	NOUN
ejpam-3823	53	5	.	.	PUNCT
ejpam-3823	54	1	the	the	DET
ejpam-3823	54	2	elements	element	NOUN
ejpam-3823	54	3	of	of	ADP
ejpam-3823	54	4	τr(a	τr(a	NUM
ejpam-3823	54	5	)	)	PUNCT
ejpam-3823	54	6	are	be	AUX
ejpam-3823	54	7	called	call	VERB
ejpam-3823	54	8	nano	nano	NOUN
ejpam-3823	54	9	open	open	ADJ
ejpam-3823	54	10	sets	set	NOUN
ejpam-3823	54	11	.	.	PUNCT
ejpam-3823	55	1	2.4	2.4	NUM
ejpam-3823	55	2	.	.	PUNCT
ejpam-3823	55	3	definition	definition	NOUN
ejpam-3823	55	4	[	[	X
ejpam-3823	55	5	13	13	NUM
ejpam-3823	55	6	]	]	X
ejpam-3823	55	7	if	if	SCONJ
ejpam-3823	55	8	(	(	PUNCT
ejpam-3823	55	9	x	x	X
ejpam-3823	55	10	,	,	PUNCT
ejpam-3823	55	11	τr(a	τr(a	NUM
ejpam-3823	55	12	)	)	PUNCT
ejpam-3823	55	13	)	)	PUNCT
ejpam-3823	55	14	is	be	AUX
ejpam-3823	55	15	nano	nano	ADJ
ejpam-3823	55	16	topological	topological	ADJ
ejpam-3823	55	17	space	space	NOUN
ejpam-3823	55	18	with	with	ADP
ejpam-3823	55	19	respect	respect	NOUN
ejpam-3823	55	20	to	to	ADP
ejpam-3823	55	21	a	a	DET
ejpam-3823	55	22	where	where	SCONJ
ejpam-3823	55	23	a	a	DET
ejpam-3823	55	24	⊆	⊆	NUM
ejpam-3823	55	25	x	x	SYM
ejpam-3823	55	26	,	,	PUNCT
ejpam-3823	55	27	if	if	SCONJ
ejpam-3823	55	28	b	b	PROPN
ejpam-3823	55	29	⊆	⊆	NUM
ejpam-3823	55	30	x	x	NUM
ejpam-3823	55	31	,	,	PUNCT
ejpam-3823	55	32	then	then	ADV
ejpam-3823	55	33	(	(	PUNCT
ejpam-3823	55	34	i	i	NOUN
ejpam-3823	55	35	)	)	PUNCT
ejpam-3823	55	36	the	the	DET
ejpam-3823	55	37	nano	nano	ADJ
ejpam-3823	55	38	interior	interior	NOUN
ejpam-3823	55	39	of	of	ADP
ejpam-3823	55	40	the	the	DET
ejpam-3823	55	41	setb	setb	NOUN
ejpam-3823	55	42	defined	define	VERB
ejpam-3823	55	43	as	as	ADP
ejpam-3823	55	44	the	the	DET
ejpam-3823	55	45	union	union	NOUN
ejpam-3823	55	46	of	of	ADP
ejpam-3823	55	47	all	all	DET
ejpam-3823	55	48	nano	nano	VERB
ejpam-3823	55	49	open	open	ADJ
ejpam-3823	55	50	subsets	subset	NOUN
ejpam-3823	55	51	contained	contain	VERB
ejpam-3823	55	52	in	in	ADP
ejpam-3823	55	53	b	b	PROPN
ejpam-3823	55	54	is	be	AUX
ejpam-3823	55	55	defined	define	VERB
ejpam-3823	55	56	by	by	ADP
ejpam-3823	55	57	n.int.(b	n.int.(b	NOUN
ejpam-3823	55	58	)	)	PUNCT
ejpam-3823	55	59	.	.	PUNCT
ejpam-3823	56	1	that	that	PRON
ejpam-3823	56	2	is	be	AUX
ejpam-3823	56	3	n.int.(b	n.int.(b	NOUN
ejpam-3823	56	4	)	)	PUNCT
ejpam-3823	57	1	is	be	AUX
ejpam-3823	57	2	the	the	DET
ejpam-3823	57	3	greatest	great	ADJ
ejpam-3823	57	4	nano	nano	NOUN
ejpam-3823	57	5	open	open	ADJ
ejpam-3823	57	6	subset	subset	NOUN
ejpam-3823	57	7	of	of	ADP
ejpam-3823	57	8	b.	b.	PROPN
ejpam-3823	57	9	(	(	PUNCT
ejpam-3823	57	10	ii	ii	PROPN
ejpam-3823	57	11	)	)	PUNCT
ejpam-3823	57	12	the	the	DET
ejpam-3823	57	13	nano	nano	NOUN
ejpam-3823	57	14	closure	closure	NOUN
ejpam-3823	57	15	of	of	ADP
ejpam-3823	57	16	the	the	DET
ejpam-3823	57	17	set	set	NOUN
ejpam-3823	57	18	b	b	NOUN
ejpam-3823	57	19	defined	define	VERB
ejpam-3823	57	20	as	as	ADP
ejpam-3823	57	21	the	the	DET
ejpam-3823	57	22	intersection	intersection	NOUN
ejpam-3823	57	23	of	of	ADP
ejpam-3823	57	24	all	all	DET
ejpam-3823	57	25	nano	nano	NOUN
ejpam-3823	57	26	closed	close	VERB
ejpam-3823	57	27	containing	contain	VERB
ejpam-3823	57	28	b	b	PROPN
ejpam-3823	57	29	is	be	AUX
ejpam-3823	57	30	denoted	denote	VERB
ejpam-3823	57	31	by	by	ADP
ejpam-3823	57	32	n.cl.(b	n.cl.(b	NOUN
ejpam-3823	57	33	)	)	PUNCT
ejpam-3823	57	34	.	.	PUNCT
ejpam-3823	58	1	that	that	PRON
ejpam-3823	58	2	is	be	AUX
ejpam-3823	58	3	n.cl.(b	n.cl.(b	NOUN
ejpam-3823	58	4	)	)	PUNCT
ejpam-3823	58	5	is	be	AUX
ejpam-3823	58	6	the	the	DET
ejpam-3823	58	7	smallest	small	ADJ
ejpam-3823	58	8	nano	nano	NOUN
ejpam-3823	58	9	closed	close	VERB
ejpam-3823	58	10	set	set	NOUN
ejpam-3823	58	11	containing	contain	VERB
ejpam-3823	58	12	b.	b.	PROPN
ejpam-3823	58	13	2.5	2.5	NUM
ejpam-3823	58	14	.	.	PUNCT
ejpam-3823	59	1	definition	definition	NOUN
ejpam-3823	60	1	[	[	X
ejpam-3823	60	2	7	7	X
ejpam-3823	60	3	]	]	X
ejpam-3823	60	4	a	a	DET
ejpam-3823	60	5	subset	subset	NOUN
ejpam-3823	60	6	b	b	PROPN
ejpam-3823	60	7	of	of	ADP
ejpam-3823	60	8	(	(	PUNCT
ejpam-3823	60	9	x	x	NOUN
ejpam-3823	60	10	,	,	PUNCT
ejpam-3823	60	11	τr(a))is	τr(a))is	PROPN
ejpam-3823	60	12	called	call	VERB
ejpam-3823	60	13	nano	nano	NOUN
ejpam-3823	60	14	-	-	PUNCT
ejpam-3823	60	15	generalized	generalize	VERB
ejpam-3823	60	16	closed	closed	ADJ
ejpam-3823	60	17	sets	set	NOUN
ejpam-3823	60	18	(	(	PUNCT
ejpam-3823	60	19	shortly	shortly	ADV
ejpam-3823	60	20	n.g	n.g	NOUN
ejpam-3823	60	21	-	-	PUNCT
ejpam-3823	60	22	closed	closed	ADJ
ejpam-3823	60	23	)	)	PUNCT
ejpam-3823	60	24	if	if	SCONJ
ejpam-3823	60	25	n.cl.(b	n.cl.(b	VERB
ejpam-3823	60	26	)	)	PUNCT
ejpam-3823	60	27	⊆	⊆	NUM
ejpam-3823	60	28	u	u	NOUN
ejpam-3823	60	29	for	for	ADP
ejpam-3823	60	30	b	b	NOUN
ejpam-3823	60	31	⊆	⊆	NUM
ejpam-3823	60	32	u	u	NOUN
ejpam-3823	60	33	and	and	CCONJ
ejpam-3823	60	34	u	u	NOUN
ejpam-3823	60	35	is	be	AUX
ejpam-3823	60	36	nano	nano	NOUN
ejpam-3823	60	37	open	open	ADJ
ejpam-3823	60	38	in	in	ADP
ejpam-3823	60	39	(	(	PUNCT
ejpam-3823	60	40	x	x	NOUN
ejpam-3823	60	41	,	,	PUNCT
ejpam-3823	60	42	τr(a	τr(a	NUM
ejpam-3823	60	43	)	)	PUNCT
ejpam-3823	60	44	)	)	PUNCT
ejpam-3823	60	45	.	.	PUNCT
ejpam-3823	61	1	a	a	DET
ejpam-3823	61	2	set	set	NOUN
ejpam-3823	61	3	b	b	PROPN
ejpam-3823	61	4	of	of	ADP
ejpam-3823	61	5	a	a	DET
ejpam-3823	61	6	nano	nano	ADJ
ejpam-3823	61	7	topological	topological	ADJ
ejpam-3823	61	8	space	space	NOUN
ejpam-3823	61	9	(	(	PUNCT
ejpam-3823	61	10	x	x	X
ejpam-3823	61	11	,	,	PUNCT
ejpam-3823	61	12	τr(a	τr(a	NUM
ejpam-3823	61	13	)	)	PUNCT
ejpam-3823	61	14	)	)	PUNCT
ejpam-3823	61	15	is	be	AUX
ejpam-3823	61	16	called	call	VERB
ejpam-3823	61	17	n.g	n.g	NOUN
ejpam-3823	61	18	-	-	PUNCT
ejpam-3823	61	19	open	open	ADJ
ejpam-3823	61	20	if	if	SCONJ
ejpam-3823	61	21	x	x	PRON
ejpam-3823	61	22	−b	−b	NOUN
ejpam-3823	61	23	is	be	AUX
ejpam-3823	61	24	n.g	n.g	NOUN
ejpam-3823	61	25	-	-	PUNCT
ejpam-3823	61	26	closed	closed	ADJ
ejpam-3823	61	27	.	.	PUNCT
ejpam-3823	62	1	3	3	X
ejpam-3823	62	2	.	.	X
ejpam-3823	62	3	micro	micro	ADJ
ejpam-3823	62	4	-	-	ADJ
ejpam-3823	62	5	generalized	generalize	VERB
ejpam-3823	62	6	closed	close	VERB
ejpam-3823	62	7	set	set	VERB
ejpam-3823	62	8	in	in	ADP
ejpam-3823	62	9	micro	micro	ADJ
ejpam-3823	62	10	topological	topological	ADJ
ejpam-3823	62	11	spaces	space	NOUN
ejpam-3823	62	12	in	in	ADP
ejpam-3823	62	13	this	this	DET
ejpam-3823	62	14	section	section	NOUN
ejpam-3823	62	15	,	,	PUNCT
ejpam-3823	62	16	the	the	DET
ejpam-3823	62	17	definition	definition	NOUN
ejpam-3823	62	18	of	of	ADP
ejpam-3823	62	19	micro	micro	ADJ
ejpam-3823	62	20	-	-	ADJ
ejpam-3823	62	21	generalized	generalize	VERB
ejpam-3823	62	22	closed	closed	ADJ
ejpam-3823	62	23	sets	set	NOUN
ejpam-3823	62	24	is	be	AUX
ejpam-3823	62	25	introduced	introduce	VERB
ejpam-3823	62	26	and	and	CCONJ
ejpam-3823	62	27	some	some	PRON
ejpam-3823	62	28	of	of	ADP
ejpam-3823	62	29	its	its	PRON
ejpam-3823	62	30	properties	property	NOUN
ejpam-3823	62	31	with	with	ADP
ejpam-3823	62	32	related	related	ADJ
ejpam-3823	62	33	theorems	theorem	NOUN
ejpam-3823	62	34	are	be	AUX
ejpam-3823	62	35	proved	prove	VERB
ejpam-3823	62	36	.	.	PUNCT
ejpam-3823	63	1	3.1	3.1	NUM
ejpam-3823	63	2	.	.	PUNCT
ejpam-3823	63	3	definition	definition	NOUN
ejpam-3823	63	4	[	[	X
ejpam-3823	63	5	9	9	X
ejpam-3823	63	6	]	]	X
ejpam-3823	63	7	if	if	SCONJ
ejpam-3823	63	8	(	(	PUNCT
ejpam-3823	63	9	x	x	X
ejpam-3823	63	10	,	,	PUNCT
ejpam-3823	63	11	τr(a	τr(a	NUM
ejpam-3823	63	12	)	)	PUNCT
ejpam-3823	63	13	)	)	PUNCT
ejpam-3823	63	14	is	be	AUX
ejpam-3823	63	15	a	a	DET
ejpam-3823	63	16	nano	nano	ADJ
ejpam-3823	63	17	topological	topological	ADJ
ejpam-3823	63	18	space	space	NOUN
ejpam-3823	63	19	then	then	ADV
ejpam-3823	63	20	µ(r)(a	µ(r)(a	NOUN
ejpam-3823	63	21	)	)	PUNCT
ejpam-3823	63	22	=	=	SYM
ejpam-3823	64	1	n	n	NOUN
ejpam-3823	64	2	∪	∪	NOUN
ejpam-3823	64	3	(	(	PUNCT
ejpam-3823	64	4	n	n	NOUN
ejpam-3823	64	5	′	′	NUM
ejpam-3823	64	6	∩	∩	NOUN
ejpam-3823	64	7	µ	µ	X
ejpam-3823	64	8	)	)	PUNCT
ejpam-3823	64	9	:	:	PUNCT
ejpam-3823	64	10	n	n	CCONJ
ejpam-3823	64	11	,	,	PUNCT
ejpam-3823	64	12	n	n	NOUN
ejpam-3823	64	13	′	′	NUM
ejpam-3823	64	14	∈	∈	NOUN
ejpam-3823	64	15	τr(a	τr(a	NUM
ejpam-3823	64	16	)	)	PUNCT
ejpam-3823	64	17	is	be	AUX
ejpam-3823	64	18	called	call	VERB
ejpam-3823	64	19	micro	micro	ADJ
ejpam-3823	64	20	topology	topology	NOUN
ejpam-3823	64	21	of	of	ADP
ejpam-3823	64	22	τr(a	τr(a	NUM
ejpam-3823	64	23	)	)	PUNCT
ejpam-3823	64	24	by	by	ADP
ejpam-3823	64	25	µ	µ	PRON
ejpam-3823	64	26	where	where	SCONJ
ejpam-3823	64	27	µ	µ	X
ejpam-3823	64	28	/∈	/∈	PUNCT
ejpam-3823	64	29	τr(a	τr(a	NUM
ejpam-3823	64	30	)	)	PUNCT
ejpam-3823	64	31	.	.	PUNCT
ejpam-3823	65	1	t.	t.	PROPN
ejpam-3823	65	2	h.	h.	PROPN
ejpam-3823	65	3	jasim	jasim	PROPN
ejpam-3823	65	4	,	,	PUNCT
ejpam-3823	65	5	s.	s.	PROPN
ejpam-3823	65	6	s.	s.	PROPN
ejpam-3823	65	7	mohsen	mohsen	PROPN
ejpam-3823	65	8	,	,	PUNCT
ejpam-3823	65	9	k.	k.	PROPN
ejpam-3823	65	10	s.	s.	PROPN
ejpam-3823	65	11	eke	eke	PROPN
ejpam-3823	65	12	/	/	SYM
ejpam-3823	65	13	eur	eur	PROPN
ejpam-3823	65	14	.	.	PUNCT
ejpam-3823	66	1	j.	j.	PROPN
ejpam-3823	66	2	pure	pure	PROPN
ejpam-3823	66	3	appl	appl	PROPN
ejpam-3823	66	4	.	.	PROPN
ejpam-3823	66	5	math	math	PROPN
ejpam-3823	66	6	,	,	PUNCT
ejpam-3823	66	7	14	14	NUM
ejpam-3823	66	8	(	(	PUNCT
ejpam-3823	66	9	4	4	NUM
ejpam-3823	66	10	)	)	PUNCT
ejpam-3823	66	11	(	(	PUNCT
ejpam-3823	66	12	2021	2021	NUM
ejpam-3823	66	13	)	)	PUNCT
ejpam-3823	66	14	,	,	PUNCT
ejpam-3823	66	15	1507	1507	NUM
ejpam-3823	66	16	-	-	SYM
ejpam-3823	66	17	1516	1516	NUM
ejpam-3823	66	18	1510	1510	NUM
ejpam-3823	66	19	3.2	3.2	NUM
ejpam-3823	66	20	.	.	PUNCT
ejpam-3823	67	1	definition	definition	NOUN
ejpam-3823	67	2	[	[	X
ejpam-3823	67	3	9	9	X
ejpam-3823	67	4	]	]	X
ejpam-3823	67	5	the	the	DET
ejpam-3823	67	6	micro	micro	ADJ
ejpam-3823	67	7	topology	topology	NOUN
ejpam-3823	67	8	µr(a	µr(a	PUNCT
ejpam-3823	67	9	)	)	PUNCT
ejpam-3823	67	10	satisfies	satisfy	VERB
ejpam-3823	67	11	the	the	DET
ejpam-3823	67	12	following	follow	VERB
ejpam-3823	67	13	axioms	axiom	NOUN
ejpam-3823	67	14	(	(	PUNCT
ejpam-3823	67	15	i	i	NOUN
ejpam-3823	67	16	)	)	PUNCT
ejpam-3823	67	17	x	x	PUNCT
ejpam-3823	67	18	and	and	CCONJ
ejpam-3823	67	19	∅	∅	NOUN
ejpam-3823	67	20	∈	∈	PROPN
ejpam-3823	67	21	µr(a	µr(a	NUM
ejpam-3823	67	22	)	)	PUNCT
ejpam-3823	67	23	.	.	PUNCT
ejpam-3823	68	1	(	(	PUNCT
ejpam-3823	68	2	ii	ii	X
ejpam-3823	68	3	)	)	PUNCT
ejpam-3823	68	4	the	the	DET
ejpam-3823	68	5	union	union	NOUN
ejpam-3823	68	6	of	of	ADP
ejpam-3823	68	7	the	the	DET
ejpam-3823	68	8	elements	element	NOUN
ejpam-3823	68	9	of	of	ADP
ejpam-3823	68	10	any	any	DET
ejpam-3823	68	11	subcollection	subcollection	NOUN
ejpam-3823	68	12	form	form	NOUN
ejpam-3823	68	13	µr(a	µr(a	PUNCT
ejpam-3823	68	14	)	)	PUNCT
ejpam-3823	68	15	is	be	AUX
ejpam-3823	68	16	in	in	ADP
ejpam-3823	68	17	µr(a	µr(a	PUNCT
ejpam-3823	68	18	)	)	PUNCT
ejpam-3823	68	19	.	.	PUNCT
ejpam-3823	69	1	(	(	PUNCT
ejpam-3823	69	2	iii	iii	X
ejpam-3823	69	3	)	)	PUNCT
ejpam-3823	69	4	the	the	DET
ejpam-3823	69	5	intersection	intersection	NOUN
ejpam-3823	69	6	of	of	ADP
ejpam-3823	69	7	the	the	DET
ejpam-3823	69	8	elements	element	NOUN
ejpam-3823	69	9	of	of	ADP
ejpam-3823	69	10	any	any	DET
ejpam-3823	69	11	finite	finite	ADJ
ejpam-3823	69	12	sub	sub	NOUN
ejpam-3823	69	13	collection	collection	NOUN
ejpam-3823	69	14	of	of	ADP
ejpam-3823	69	15	µr(a	µr(a	PUNCT
ejpam-3823	69	16	)	)	PUNCT
ejpam-3823	69	17	is	be	AUX
ejpam-3823	69	18	in	in	ADP
ejpam-3823	69	19	µr(a	µr(a	PUNCT
ejpam-3823	69	20	)	)	PUNCT
ejpam-3823	69	21	.	.	PUNCT
ejpam-3823	70	1	then	then	ADV
ejpam-3823	70	2	µr(a	µr(a	PUNCT
ejpam-3823	70	3	)	)	PUNCT
ejpam-3823	70	4	is	be	AUX
ejpam-3823	70	5	called	call	VERB
ejpam-3823	70	6	micro	micro	ADJ
ejpam-3823	70	7	topology	topology	PROPN
ejpam-3823	70	8	onx	onx	PROPN
ejpam-3823	70	9	with	with	ADP
ejpam-3823	70	10	respect	respect	NOUN
ejpam-3823	70	11	toa	toa	PROPN
ejpam-3823	70	12	.	.	PUNCT
ejpam-3823	71	1	the	the	DET
ejpam-3823	71	2	triplet	triplet	NOUN
ejpam-3823	71	3	(	(	PUNCT
ejpam-3823	71	4	x	x	NOUN
ejpam-3823	71	5	,	,	PUNCT
ejpam-3823	71	6	τr(a	τr(a	NUM
ejpam-3823	71	7	)	)	PUNCT
ejpam-3823	71	8	,	,	PUNCT
ejpam-3823	71	9	µr(a	µr(a	NUM
ejpam-3823	71	10	)	)	PUNCT
ejpam-3823	71	11	)	)	PUNCT
ejpam-3823	71	12	is	be	AUX
ejpam-3823	71	13	called	call	VERB
ejpam-3823	71	14	micro	micro	ADJ
ejpam-3823	71	15	topological	topological	ADJ
ejpam-3823	71	16	spaces	space	NOUN
ejpam-3823	71	17	and	and	CCONJ
ejpam-3823	71	18	the	the	DET
ejpam-3823	71	19	elements	element	NOUN
ejpam-3823	71	20	of	of	ADP
ejpam-3823	71	21	µr(a	µr(a	X
ejpam-3823	71	22	)	)	PUNCT
ejpam-3823	71	23	are	be	AUX
ejpam-3823	71	24	called	call	VERB
ejpam-3823	71	25	micro	micro	ADJ
ejpam-3823	71	26	open	open	ADJ
ejpam-3823	71	27	sets	set	NOUN
ejpam-3823	71	28	and	and	CCONJ
ejpam-3823	71	29	the	the	DET
ejpam-3823	71	30	complement	complement	NOUN
ejpam-3823	71	31	of	of	ADP
ejpam-3823	71	32	a	a	DET
ejpam-3823	71	33	micro	micro	ADJ
ejpam-3823	71	34	open	open	ADJ
ejpam-3823	71	35	set	set	NOUN
ejpam-3823	71	36	is	be	AUX
ejpam-3823	71	37	called	call	VERB
ejpam-3823	71	38	a	a	DET
ejpam-3823	71	39	micro	micro	NOUN
ejpam-3823	71	40	closed	close	VERB
ejpam-3823	71	41	set	set	NOUN
ejpam-3823	71	42	.	.	PUNCT
ejpam-3823	72	1	3.3	3.3	NUM
ejpam-3823	72	2	.	.	PUNCT
ejpam-3823	73	1	definition	definition	NOUN
ejpam-3823	73	2	[	[	X
ejpam-3823	73	3	12	12	NUM
ejpam-3823	73	4	]	]	PUNCT
ejpam-3823	73	5	the	the	DET
ejpam-3823	73	6	micro	micro	ADJ
ejpam-3823	73	7	closure	closure	NOUN
ejpam-3823	73	8	of	of	ADP
ejpam-3823	73	9	a	a	DET
ejpam-3823	73	10	setb	setb	NOUN
ejpam-3823	73	11	is	be	AUX
ejpam-3823	73	12	defined	define	VERB
ejpam-3823	73	13	bymic.cl.(b	bymic.cl.(b	NOUN
ejpam-3823	73	14	)	)	PUNCT
ejpam-3823	74	1	=	=	SYM
ejpam-3823	74	2	∩	∩	NOUN
ejpam-3823	74	3	{	{	PUNCT
ejpam-3823	74	4	f	f	NOUN
ejpam-3823	74	5	:	:	PUNCT
ejpam-3823	74	6	fismicroclosedset	fismicroclosedset	VERB
ejpam-3823	74	7	,	,	PUNCT
ejpam-3823	74	8	b	b	PROPN
ejpam-3823	74	9	⊆	⊆	NUM
ejpam-3823	74	10	f	f	NOUN
ejpam-3823	74	11	}	}	PUNCT
ejpam-3823	74	12	and	and	CCONJ
ejpam-3823	74	13	the	the	DET
ejpam-3823	74	14	micro	micro	ADJ
ejpam-3823	74	15	interior	interior	PROPN
ejpam-3823	74	16	of	of	ADP
ejpam-3823	74	17	a	a	DET
ejpam-3823	74	18	setb	setb	NOUN
ejpam-3823	74	19	is	be	AUX
ejpam-3823	74	20	defined	define	VERB
ejpam-3823	74	21	bymic.int.(b	bymic.int.(b	ADV
ejpam-3823	74	22	)	)	PUNCT
ejpam-3823	74	23	=	=	SYM
ejpam-3823	74	24	∪	∪	X
ejpam-3823	74	25	{	{	PUNCT
ejpam-3823	74	26	u	u	NOUN
ejpam-3823	74	27	:	:	PUNCT
ejpam-3823	74	28	uismicroopenset	uismicroopenset	ADJ
ejpam-3823	74	29	,	,	PUNCT
ejpam-3823	74	30	u	u	NOUN
ejpam-3823	74	31	⊆	⊆	NUM
ejpam-3823	74	32	b	b	PROPN
ejpam-3823	74	33	}	}	PUNCT
ejpam-3823	74	34	.	.	PUNCT
ejpam-3823	75	1	3.4	3.4	NUM
ejpam-3823	75	2	.	.	PUNCT
ejpam-3823	75	3	definition	definition	NOUN
ejpam-3823	75	4	a	a	DET
ejpam-3823	75	5	sub	sub	NOUN
ejpam-3823	75	6	set	set	NOUN
ejpam-3823	75	7	b	b	PROPN
ejpam-3823	75	8	of	of	ADP
ejpam-3823	75	9	(	(	PUNCT
ejpam-3823	75	10	x	x	NOUN
ejpam-3823	75	11	,	,	PUNCT
ejpam-3823	75	12	τr(a	τr(a	NUM
ejpam-3823	75	13	)	)	PUNCT
ejpam-3823	75	14	,	,	PUNCT
ejpam-3823	75	15	µr(a	µr(a	NUM
ejpam-3823	75	16	)	)	PUNCT
ejpam-3823	75	17	)	)	PUNCT
ejpam-3823	75	18	is	be	AUX
ejpam-3823	75	19	called	call	VERB
ejpam-3823	75	20	micro	micro	ADJ
ejpam-3823	75	21	-	-	ADJ
ejpam-3823	75	22	generalized	generalize	VERB
ejpam-3823	75	23	closed	close	VERB
ejpam-3823	75	24	set	set	NOUN
ejpam-3823	75	25	(	(	PUNCT
ejpam-3823	75	26	shortly	shortly	ADV
ejpam-3823	75	27	,	,	PUNCT
ejpam-3823	75	28	mic.g	mic.g	PROPN
ejpam-3823	75	29	-	-	PUNCT
ejpam-3823	75	30	closed	closed	ADJ
ejpam-3823	75	31	)	)	PUNCT
ejpam-3823	75	32	if	if	SCONJ
ejpam-3823	75	33	mic.cl.(b	mic.cl.(b	ADJ
ejpam-3823	75	34	)	)	PUNCT
ejpam-3823	75	35	⊆	⊆	NUM
ejpam-3823	75	36	uforb	uforb	NOUN
ejpam-3823	75	37	⊆	⊆	NUM
ejpam-3823	75	38	uandu	uandu	NOUN
ejpam-3823	75	39	is	be	AUX
ejpam-3823	75	40	microopensetin(x	microopensetin(x	NUM
ejpam-3823	75	41	,	,	PUNCT
ejpam-3823	75	42	τr(a	τr(a	NUM
ejpam-3823	75	43	)	)	PUNCT
ejpam-3823	75	44	,	,	PUNCT
ejpam-3823	75	45	µr(a	µr(a	NUM
ejpam-3823	75	46	)	)	PUNCT
ejpam-3823	75	47	)	)	PUNCT
ejpam-3823	75	48	.	.	PUNCT
ejpam-3823	76	1	a	a	DET
ejpam-3823	76	2	set	set	NOUN
ejpam-3823	76	3	b	b	PROPN
ejpam-3823	76	4	of	of	ADP
ejpam-3823	76	5	a	a	DET
ejpam-3823	76	6	micro	micro	ADJ
ejpam-3823	76	7	topological	topological	ADJ
ejpam-3823	76	8	space	space	NOUN
ejpam-3823	76	9	(	(	PUNCT
ejpam-3823	76	10	x	x	X
ejpam-3823	76	11	,	,	PUNCT
ejpam-3823	76	12	τr(a	τr(a	NUM
ejpam-3823	76	13	)	)	PUNCT
ejpam-3823	76	14	,	,	PUNCT
ejpam-3823	76	15	µr(a	µr(a	NUM
ejpam-3823	76	16	)	)	PUNCT
ejpam-3823	76	17	)	)	PUNCT
ejpam-3823	76	18	is	be	AUX
ejpam-3823	76	19	called	call	VERB
ejpam-3823	76	20	mic.g	mic.g	NOUN
ejpam-3823	76	21	-	-	PUNCT
ejpam-3823	76	22	open	open	ADJ
ejpam-3823	76	23	if	if	SCONJ
ejpam-3823	76	24	x	x	PROPN
ejpam-3823	76	25	b	b	PROPN
ejpam-3823	76	26	is	be	AUX
ejpam-3823	76	27	mic.g	mic.g	NOUN
ejpam-3823	76	28	-	-	PUNCT
ejpam-3823	76	29	closed	closed	ADJ
ejpam-3823	76	30	.	.	PUNCT
ejpam-3823	77	1	3.5	3.5	NUM
ejpam-3823	77	2	.	.	PUNCT
ejpam-3823	77	3	remark	remark	VERB
ejpam-3823	77	4	every	every	DET
ejpam-3823	77	5	micro	micro	NOUN
ejpam-3823	77	6	closed	close	VERB
ejpam-3823	77	7	set	set	NOUN
ejpam-3823	77	8	is	be	AUX
ejpam-3823	77	9	micro	micro	ADJ
ejpam-3823	77	10	-	-	ADJ
ejpam-3823	77	11	generalized	generalize	VERB
ejpam-3823	77	12	closed	closed	ADJ
ejpam-3823	77	13	set	set	NOUN
ejpam-3823	77	14	.	.	PUNCT
ejpam-3823	78	1	3.6	3.6	NUM
ejpam-3823	78	2	.	.	PUNCT
ejpam-3823	78	3	example	example	NOUN
ejpam-3823	78	4	let	let	VERB
ejpam-3823	78	5	x	x	PUNCT
ejpam-3823	78	6	=	=	NOUN
ejpam-3823	78	7	{	{	PUNCT
ejpam-3823	78	8	1	1	NUM
ejpam-3823	78	9	,	,	PUNCT
ejpam-3823	78	10	2	2	NUM
ejpam-3823	78	11	,	,	PUNCT
ejpam-3823	78	12	3	3	NUM
ejpam-3823	78	13	,	,	PUNCT
ejpam-3823	78	14	4	4	NUM
ejpam-3823	78	15	}	}	PUNCT
ejpam-3823	78	16	with	with	ADP
ejpam-3823	78	17	x	x	X
ejpam-3823	78	18	/	/	SYM
ejpam-3823	78	19	r	r	NOUN
ejpam-3823	78	20	=	=	PUNCT
ejpam-3823	78	21	{	{	PUNCT
ejpam-3823	78	22	{	{	PUNCT
ejpam-3823	78	23	1	1	NUM
ejpam-3823	78	24	}	}	PUNCT
ejpam-3823	78	25	,	,	PUNCT
ejpam-3823	78	26	{	{	PUNCT
ejpam-3823	78	27	3	3	NUM
ejpam-3823	78	28	}	}	PUNCT
ejpam-3823	78	29	,	,	PUNCT
ejpam-3823	78	30	{	{	PUNCT
ejpam-3823	78	31	2	2	NUM
ejpam-3823	78	32	,	,	PUNCT
ejpam-3823	78	33	4	4	NUM
ejpam-3823	78	34	}	}	PUNCT
ejpam-3823	78	35	}	}	PUNCT
ejpam-3823	78	36	and	and	CCONJ
ejpam-3823	78	37	a	a	DET
ejpam-3823	78	38	=	=	X
ejpam-3823	78	39	{	{	PUNCT
ejpam-3823	78	40	1	1	NUM
ejpam-3823	78	41	,	,	PUNCT
ejpam-3823	78	42	2	2	NUM
ejpam-3823	78	43	}	}	PUNCT
ejpam-3823	78	44	.	.	PUNCT
ejpam-3823	79	1	then	then	ADV
ejpam-3823	79	2	the	the	DET
ejpam-3823	79	3	nano	nano	NOUN
ejpam-3823	79	4	topology	topology	NOUN
ejpam-3823	79	5	τr(a	τr(a	NUM
ejpam-3823	79	6	)	)	PUNCT
ejpam-3823	79	7	=	=	SYM
ejpam-3823	79	8	{	{	PUNCT
ejpam-3823	79	9	∅	∅	NOUN
ejpam-3823	79	10	,	,	PUNCT
ejpam-3823	79	11	x	x	PRON
ejpam-3823	79	12	,	,	PUNCT
ejpam-3823	79	13	{	{	PUNCT
ejpam-3823	79	14	1	1	NUM
ejpam-3823	79	15	}	}	PUNCT
ejpam-3823	79	16	,	,	PUNCT
ejpam-3823	79	17	{	{	PUNCT
ejpam-3823	79	18	2	2	NUM
ejpam-3823	79	19	,	,	PUNCT
ejpam-3823	79	20	4	4	NUM
ejpam-3823	79	21	}	}	PUNCT
ejpam-3823	79	22	,	,	PUNCT
ejpam-3823	79	23	{	{	PUNCT
ejpam-3823	79	24	1	1	NUM
ejpam-3823	79	25	,	,	PUNCT
ejpam-3823	79	26	2	2	NUM
ejpam-3823	79	27	,	,	PUNCT
ejpam-3823	79	28	4	4	NUM
ejpam-3823	79	29	}	}	PUNCT
ejpam-3823	79	30	}	}	PUNCT
ejpam-3823	79	31	which	which	PRON
ejpam-3823	79	32	are	be	AUX
ejpam-3823	79	33	nano	nano	VERB
ejpam-3823	79	34	open	open	ADJ
ejpam-3823	79	35	sets	set	NOUN
ejpam-3823	79	36	,	,	PUNCT
ejpam-3823	79	37	and	and	CCONJ
ejpam-3823	79	38	the	the	DET
ejpam-3823	79	39	nano	nano	NOUN
ejpam-3823	79	40	closed	close	VERB
ejpam-3823	79	41	sets	set	NOUN
ejpam-3823	79	42	=	=	SYM
ejpam-3823	79	43	{	{	PUNCT
ejpam-3823	79	44	∅	∅	NOUN
ejpam-3823	79	45	,	,	PUNCT
ejpam-3823	79	46	x	x	PRON
ejpam-3823	79	47	,	,	PUNCT
ejpam-3823	79	48	{	{	PUNCT
ejpam-3823	79	49	3	3	NUM
ejpam-3823	79	50	}	}	PUNCT
ejpam-3823	79	51	,	,	PUNCT
ejpam-3823	79	52	{	{	PUNCT
ejpam-3823	79	53	1	1	NUM
ejpam-3823	79	54	,	,	PUNCT
ejpam-3823	79	55	}	}	PUNCT
ejpam-3823	79	56	,	,	PUNCT
ejpam-3823	79	57	{	{	PUNCT
ejpam-3823	79	58	2	2	NUM
ejpam-3823	79	59	,	,	PUNCT
ejpam-3823	79	60	3	3	NUM
ejpam-3823	79	61	,	,	PUNCT
ejpam-3823	79	62	4	4	NUM
ejpam-3823	79	63	}	}	PUNCT
ejpam-3823	79	64	}	}	PUNCT
ejpam-3823	79	65	.	.	PUNCT
ejpam-3823	80	1	let	let	VERB
ejpam-3823	80	2	µ	µ	X
ejpam-3823	80	3	=	=	PUNCT
ejpam-3823	80	4	{	{	PUNCT
ejpam-3823	80	5	3	3	NUM
ejpam-3823	80	6	}	}	PUNCT
ejpam-3823	80	7	then	then	ADV
ejpam-3823	80	8	the	the	DET
ejpam-3823	80	9	micro	micro	ADJ
ejpam-3823	80	10	topology	topology	NOUN
ejpam-3823	80	11	µr(a	µr(a	PUNCT
ejpam-3823	80	12	)	)	PUNCT
ejpam-3823	80	13	=	=	SYM
ejpam-3823	80	14	{	{	PUNCT
ejpam-3823	80	15	∅	∅	NOUN
ejpam-3823	80	16	,	,	PUNCT
ejpam-3823	80	17	x	x	PRON
ejpam-3823	80	18	,	,	PUNCT
ejpam-3823	80	19	{	{	PUNCT
ejpam-3823	80	20	1	1	NUM
ejpam-3823	80	21	}	}	PUNCT
ejpam-3823	80	22	,	,	PUNCT
ejpam-3823	80	23	{	{	PUNCT
ejpam-3823	80	24	3	3	NUM
ejpam-3823	80	25	}	}	PUNCT
ejpam-3823	80	26	,	,	PUNCT
ejpam-3823	80	27	{	{	PUNCT
ejpam-3823	80	28	1	1	NUM
ejpam-3823	80	29	,	,	PUNCT
ejpam-3823	80	30	3	3	NUM
ejpam-3823	80	31	}	}	PUNCT
ejpam-3823	80	32	,	,	PUNCT
ejpam-3823	80	33	{	{	PUNCT
ejpam-3823	80	34	2	2	NUM
ejpam-3823	80	35	,	,	PUNCT
ejpam-3823	80	36	4	4	NUM
ejpam-3823	80	37	}	}	PUNCT
ejpam-3823	80	38	,	,	PUNCT
ejpam-3823	80	39	{	{	PUNCT
ejpam-3823	80	40	2	2	NUM
ejpam-3823	80	41	,	,	PUNCT
ejpam-3823	80	42	3	3	NUM
ejpam-3823	80	43	,	,	PUNCT
ejpam-3823	80	44	4	4	NUM
ejpam-3823	80	45	}	}	PUNCT
ejpam-3823	80	46	,	,	PUNCT
ejpam-3823	80	47	{	{	PUNCT
ejpam-3823	80	48	1	1	NUM
ejpam-3823	80	49	,	,	PUNCT
ejpam-3823	80	50	2	2	NUM
ejpam-3823	80	51	,	,	PUNCT
ejpam-3823	80	52	4	4	NUM
ejpam-3823	80	53	}	}	PUNCT
ejpam-3823	80	54	}	}	PUNCT
ejpam-3823	80	55	and	and	CCONJ
ejpam-3823	80	56	the	the	DET
ejpam-3823	80	57	micro	micro	ADJ
ejpam-3823	80	58	closed	closed	ADJ
ejpam-3823	80	59	sets	set	NOUN
ejpam-3823	80	60	=	=	NOUN
ejpam-3823	80	61	{	{	PUNCT
ejpam-3823	80	62	∅	∅	NOUN
ejpam-3823	80	63	,	,	PUNCT
ejpam-3823	80	64	x	x	PRON
ejpam-3823	80	65	,	,	PUNCT
ejpam-3823	80	66	{	{	PUNCT
ejpam-3823	80	67	1	1	NUM
ejpam-3823	80	68	}	}	PUNCT
ejpam-3823	80	69	,	,	PUNCT
ejpam-3823	80	70	{	{	PUNCT
ejpam-3823	80	71	3	3	NUM
ejpam-3823	80	72	}	}	PUNCT
ejpam-3823	80	73	,	,	PUNCT
ejpam-3823	80	74	{	{	PUNCT
ejpam-3823	80	75	2	2	NUM
ejpam-3823	80	76	,	,	PUNCT
ejpam-3823	80	77	4	4	NUM
ejpam-3823	80	78	}	}	PUNCT
ejpam-3823	80	79	,	,	PUNCT
ejpam-3823	80	80	{	{	PUNCT
ejpam-3823	80	81	1	1	NUM
ejpam-3823	80	82	,	,	PUNCT
ejpam-3823	80	83	3	3	NUM
ejpam-3823	80	84	}	}	PUNCT
ejpam-3823	80	85	,	,	PUNCT
ejpam-3823	80	86	{	{	PUNCT
ejpam-3823	80	87	2	2	NUM
ejpam-3823	80	88	,	,	PUNCT
ejpam-3823	80	89	3	3	NUM
ejpam-3823	80	90	,	,	PUNCT
ejpam-3823	80	91	4	4	NUM
ejpam-3823	80	92	}	}	PUNCT
ejpam-3823	80	93	,	,	PUNCT
ejpam-3823	80	94	{	{	PUNCT
ejpam-3823	80	95	1	1	NUM
ejpam-3823	80	96	,	,	PUNCT
ejpam-3823	80	97	2	2	NUM
ejpam-3823	80	98	,	,	PUNCT
ejpam-3823	80	99	4	4	NUM
ejpam-3823	80	100	}	}	PUNCT
ejpam-3823	80	101	}	}	PUNCT
ejpam-3823	80	102	.	.	PUNCT
ejpam-3823	81	1	show	show	VERB
ejpam-3823	81	2	that	that	SCONJ
ejpam-3823	81	3	the	the	DET
ejpam-3823	81	4	set	set	NOUN
ejpam-3823	81	5	b	b	PROPN
ejpam-3823	81	6	=	=	X
ejpam-3823	81	7	{	{	PUNCT
ejpam-3823	81	8	1	1	NUM
ejpam-3823	81	9	,	,	PUNCT
ejpam-3823	81	10	2	2	NUM
ejpam-3823	81	11	,	,	PUNCT
ejpam-3823	81	12	3	3	NUM
ejpam-3823	81	13	}	}	PUNCT
ejpam-3823	81	14	⊆	⊆	NUM
ejpam-3823	81	15	x	x	PUNCT
ejpam-3823	81	16	is	be	AUX
ejpam-3823	81	17	mic.g	mic.g	NOUN
ejpam-3823	81	18	-	-	PUNCT
ejpam-3823	81	19	closed	closed	ADJ
ejpam-3823	81	20	but	but	CCONJ
ejpam-3823	81	21	not	not	PART
ejpam-3823	81	22	micro	micro	ADJ
ejpam-3823	81	23	-	-	ADJ
ejpam-3823	81	24	closed	closed	ADJ
ejpam-3823	81	25	set	set	NOUN
ejpam-3823	81	26	.	.	PUNCT
ejpam-3823	82	1	3.7	3.7	NUM
ejpam-3823	82	2	.	.	PUNCT
ejpam-3823	83	1	proposition	proposition	NOUN
ejpam-3823	83	2	every	every	DET
ejpam-3823	83	3	nano	nano	NOUN
ejpam-3823	83	4	open	open	ADJ
ejpam-3823	83	5	set	set	NOUN
ejpam-3823	83	6	is	be	AUX
ejpam-3823	83	7	micro	micro	ADJ
ejpam-3823	83	8	open	open	ADJ
ejpam-3823	83	9	set	set	NOUN
ejpam-3823	83	10	.	.	PUNCT
ejpam-3823	84	1	proof	proof	NOUN
ejpam-3823	84	2	:	:	PUNCT
ejpam-3823	84	3	let	let	VERB
ejpam-3823	84	4	b	b	X
ejpam-3823	84	5	∈	∈	PROPN
ejpam-3823	84	6	τr(a	τr(a	NUM
ejpam-3823	84	7	)	)	PUNCT
ejpam-3823	84	8	and	and	CCONJ
ejpam-3823	84	9	µ	µ	X
ejpam-3823	84	10	/∈	/∈	PUNCT
ejpam-3823	84	11	τr(a	τr(a	NUM
ejpam-3823	84	12	)	)	PUNCT
ejpam-3823	84	13	,	,	PUNCT
ejpam-3823	84	14	now	now	ADV
ejpam-3823	84	15	from	from	ADP
ejpam-3823	84	16	the	the	DET
ejpam-3823	84	17	definition	definition	NOUN
ejpam-3823	84	18	of	of	ADP
ejpam-3823	84	19	micro	micro	PROPN
ejpam-3823	84	20	topology	topology	NOUN
ejpam-3823	84	21	we	we	PRON
ejpam-3823	84	22	have	have	VERB
ejpam-3823	84	23	b	b	SYM
ejpam-3823	84	24	∪	∪	X
ejpam-3823	84	25	(	(	PUNCT
ejpam-3823	84	26	∅	∅	NOUN
ejpam-3823	84	27	∩	∩	NOUN
ejpam-3823	84	28	µ	µ	NOUN
ejpam-3823	84	29	)	)	PUNCT
ejpam-3823	84	30	=	=	SYM
ejpam-3823	85	1	b	b	PROPN
ejpam-3823	85	2	thus	thus	ADV
ejpam-3823	85	3	b	b	X
ejpam-3823	85	4	∈	∈	PROPN
ejpam-3823	85	5	µr(a	µr(a	NUM
ejpam-3823	85	6	)	)	PUNCT
ejpam-3823	85	7	.	.	PUNCT
ejpam-3823	86	1	hence	hence	ADV
ejpam-3823	86	2	b	b	X
ejpam-3823	86	3	is	be	AUX
ejpam-3823	86	4	micro	micro	X
ejpam-3823	86	5	open	open	ADJ
ejpam-3823	86	6	set	set	NOUN
ejpam-3823	86	7	.	.	PUNCT
ejpam-3823	87	1	t.	t.	PROPN
ejpam-3823	87	2	h.	h.	PROPN
ejpam-3823	87	3	jasim	jasim	PROPN
ejpam-3823	87	4	,	,	PUNCT
ejpam-3823	87	5	s.	s.	PROPN
ejpam-3823	87	6	s.	s.	PROPN
ejpam-3823	87	7	mohsen	mohsen	PROPN
ejpam-3823	87	8	,	,	PUNCT
ejpam-3823	87	9	k.	k.	PROPN
ejpam-3823	87	10	s.	s.	PROPN
ejpam-3823	87	11	eke	eke	PROPN
ejpam-3823	87	12	/	/	SYM
ejpam-3823	87	13	eur	eur	PROPN
ejpam-3823	87	14	.	.	PUNCT
ejpam-3823	88	1	j.	j.	PROPN
ejpam-3823	88	2	pure	pure	PROPN
ejpam-3823	88	3	appl	appl	PROPN
ejpam-3823	88	4	.	.	PROPN
ejpam-3823	88	5	math	math	PROPN
ejpam-3823	88	6	,	,	PUNCT
ejpam-3823	88	7	14	14	NUM
ejpam-3823	88	8	(	(	PUNCT
ejpam-3823	88	9	4	4	NUM
ejpam-3823	88	10	)	)	PUNCT
ejpam-3823	88	11	(	(	PUNCT
ejpam-3823	88	12	2021	2021	NUM
ejpam-3823	88	13	)	)	PUNCT
ejpam-3823	88	14	,	,	PUNCT
ejpam-3823	88	15	1507	1507	NUM
ejpam-3823	88	16	-	-	SYM
ejpam-3823	88	17	1516	1516	NUM
ejpam-3823	88	18	1511	1511	NUM
ejpam-3823	88	19	3.8	3.8	NUM
ejpam-3823	88	20	.	.	PUNCT
ejpam-3823	88	21	remark	remark	VERB
ejpam-3823	88	22	the	the	DET
ejpam-3823	88	23	nano	nano	NOUN
ejpam-3823	88	24	topology	topology	NOUN
ejpam-3823	88	25	and	and	CCONJ
ejpam-3823	88	26	micro	micro	PROPN
ejpam-3823	88	27	topology	topology	NOUN
ejpam-3823	88	28	are	be	AUX
ejpam-3823	88	29	equivalent	equivalent	ADJ
ejpam-3823	88	30	when	when	SCONJ
ejpam-3823	88	31	µ	µ	X
ejpam-3823	88	32	∈	∈	NOUN
ejpam-3823	88	33	τr(a	τr(a	NUM
ejpam-3823	88	34	)	)	PUNCT
ejpam-3823	88	35	and	and	CCONJ
ejpam-3823	88	36	this	this	PRON
ejpam-3823	88	37	clear	clear	ADJ
ejpam-3823	88	38	from	from	ADP
ejpam-3823	88	39	the	the	DET
ejpam-3823	88	40	definition	definition	NOUN
ejpam-3823	88	41	of	of	ADP
ejpam-3823	88	42	micro	micro	PROPN
ejpam-3823	88	43	topology	topology	NOUN
ejpam-3823	88	44	(	(	PUNCT
ejpam-3823	88	45	3.1	3.1	NUM
ejpam-3823	88	46	)	)	PUNCT
ejpam-3823	88	47	.	.	PUNCT
ejpam-3823	89	1	3.9	3.9	NUM
ejpam-3823	89	2	.	.	PUNCT
ejpam-3823	89	3	theorem	theorem	VERB
ejpam-3823	89	4	every	every	DET
ejpam-3823	89	5	nano	nano	NOUN
ejpam-3823	89	6	-	-	PUNCT
ejpam-3823	89	7	generalized	generalize	VERB
ejpam-3823	89	8	closed	close	VERB
ejpam-3823	89	9	set	set	NOUN
ejpam-3823	89	10	is	be	AUX
ejpam-3823	89	11	micro	micro	ADJ
ejpam-3823	89	12	-	-	ADJ
ejpam-3823	89	13	generalized	generalize	VERB
ejpam-3823	89	14	closed	closed	ADJ
ejpam-3823	89	15	set	set	NOUN
ejpam-3823	89	16	.	.	PUNCT
ejpam-3823	90	1	proof	proof	NOUN
ejpam-3823	90	2	:	:	PUNCT
ejpam-3823	90	3	suppose	suppose	VERB
ejpam-3823	90	4	that	that	SCONJ
ejpam-3823	90	5	b	b	PROPN
ejpam-3823	90	6	is	be	AUX
ejpam-3823	90	7	a	a	DET
ejpam-3823	90	8	ng	ng	PROPN
ejpam-3823	90	9	-	-	PUNCT
ejpam-3823	90	10	closed	closed	ADJ
ejpam-3823	90	11	set	set	NOUN
ejpam-3823	90	12	in	in	ADP
ejpam-3823	90	13	(	(	PUNCT
ejpam-3823	90	14	x	x	NOUN
ejpam-3823	90	15	,	,	PUNCT
ejpam-3823	90	16	τr(a	τr(a	NUM
ejpam-3823	90	17	)	)	PUNCT
ejpam-3823	90	18	)	)	PUNCT
ejpam-3823	90	19	then	then	ADV
ejpam-3823	90	20	mic.cl.(b	mic.cl.(b	X
ejpam-3823	90	21	)	)	PUNCT
ejpam-3823	90	22	⊆	⊆	NUM
ejpam-3823	90	23	u	u	NOUN
ejpam-3823	90	24	,	,	PUNCT
ejpam-3823	90	25	for	for	ADP
ejpam-3823	90	26	b	b	NOUN
ejpam-3823	91	1	⊆	⊆	NUM
ejpam-3823	91	2	u	u	NOUN
ejpam-3823	91	3	for	for	ADP
ejpam-3823	91	4	all	all	DET
ejpam-3823	91	5	u	u	NOUN
ejpam-3823	91	6	is	be	AUX
ejpam-3823	91	7	nano	nano	NOUN
ejpam-3823	91	8	open	open	ADJ
ejpam-3823	91	9	set	set	NOUN
ejpam-3823	91	10	.	.	PUNCT
ejpam-3823	92	1	since	since	SCONJ
ejpam-3823	92	2	every	every	DET
ejpam-3823	92	3	nano	nano	NOUN
ejpam-3823	92	4	open	open	ADJ
ejpam-3823	92	5	set	set	NOUN
ejpam-3823	92	6	is	be	AUX
ejpam-3823	92	7	micro	micro	ADJ
ejpam-3823	92	8	open	open	ADJ
ejpam-3823	92	9	set	set	NOUN
ejpam-3823	92	10	(	(	PUNCT
ejpam-3823	92	11	see	see	VERB
ejpam-3823	92	12	proposition	proposition	NOUN
ejpam-3823	92	13	(	(	PUNCT
ejpam-3823	92	14	3.7	3.7	NUM
ejpam-3823	92	15	)	)	PUNCT
ejpam-3823	92	16	)	)	PUNCT
ejpam-3823	92	17	.	.	PUNCT
ejpam-3823	93	1	then	then	ADV
ejpam-3823	93	2	we	we	PRON
ejpam-3823	93	3	get	get	VERB
ejpam-3823	93	4	,	,	PUNCT
ejpam-3823	93	5	mic.cl(b	mic.cl(b	NOUN
ejpam-3823	93	6	)	)	PUNCT
ejpam-3823	93	7	⊆	⊆	NUM
ejpam-3823	93	8	u	u	NOUN
ejpam-3823	93	9	,	,	PUNCT
ejpam-3823	93	10	for	for	ADP
ejpam-3823	93	11	b	b	NOUN
ejpam-3823	93	12	⊆	⊆	NUM
ejpam-3823	93	13	u	u	NOUN
ejpam-3823	93	14	for	for	ADP
ejpam-3823	93	15	all	all	DET
ejpam-3823	93	16	u	u	NOUN
ejpam-3823	93	17	is	be	AUX
ejpam-3823	93	18	micro	micro	ADV
ejpam-3823	93	19	open	open	ADJ
ejpam-3823	93	20	set	set	NOUN
ejpam-3823	93	21	.	.	PUNCT
ejpam-3823	94	1	thus	thus	ADV
ejpam-3823	94	2	,	,	PUNCT
ejpam-3823	94	3	the	the	DET
ejpam-3823	94	4	set	set	PROPN
ejpam-3823	94	5	b	b	PROPN
ejpam-3823	94	6	is	be	AUX
ejpam-3823	94	7	mic.g	mic.g	NOUN
ejpam-3823	94	8	-	-	PUNCT
ejpam-3823	94	9	closed	closed	ADJ
ejpam-3823	94	10	set	set	NOUN
ejpam-3823	94	11	.	.	PUNCT
ejpam-3823	95	1	3.10	3.10	NUM
ejpam-3823	95	2	.	.	PUNCT
ejpam-3823	95	3	example	example	NOUN
ejpam-3823	95	4	in	in	ADP
ejpam-3823	95	5	the	the	DET
ejpam-3823	95	6	same	same	ADJ
ejpam-3823	95	7	example	example	NOUN
ejpam-3823	95	8	(	(	PUNCT
ejpam-3823	95	9	3.6	3.6	NUM
ejpam-3823	95	10	)	)	PUNCT
ejpam-3823	95	11	above	above	ADP
ejpam-3823	95	12	let	let	VERB
ejpam-3823	95	13	b	b	NOUN
ejpam-3823	95	14	=	=	X
ejpam-3823	95	15	{	{	PUNCT
ejpam-3823	95	16	1	1	NUM
ejpam-3823	95	17	,	,	PUNCT
ejpam-3823	95	18	2	2	NUM
ejpam-3823	95	19	}	}	PUNCT
ejpam-3823	95	20	⊆	⊆	NUM
ejpam-3823	95	21	{	{	PUNCT
ejpam-3823	95	22	1	1	NUM
ejpam-3823	95	23	,	,	PUNCT
ejpam-3823	95	24	2	2	NUM
ejpam-3823	95	25	,	,	PUNCT
ejpam-3823	95	26	4	4	NUM
ejpam-3823	95	27	}	}	PUNCT
ejpam-3823	95	28	∈	∈	PROPN
ejpam-3823	95	29	τr(a	τr(a	NUM
ejpam-3823	95	30	)	)	PUNCT
ejpam-3823	95	31	and	and	CCONJ
ejpam-3823	95	32	n.cl	n.cl	PROPN
ejpam-3823	95	33	.	.	PROPN
ejpam-3823	95	34	{	{	PUNCT
ejpam-3823	96	1	1	1	NUM
ejpam-3823	96	2	,	,	PUNCT
ejpam-3823	96	3	2	2	NUM
ejpam-3823	96	4	}	}	PUNCT
ejpam-3823	96	5	=	=	SYM
ejpam-3823	96	6	x	x	SYM
ejpam-3823	96	7	̸⊆	̸⊆	NOUN
ejpam-3823	96	8	{	{	PUNCT
ejpam-3823	96	9	1	1	NUM
ejpam-3823	96	10	,	,	PUNCT
ejpam-3823	96	11	2	2	NUM
ejpam-3823	96	12	,	,	PUNCT
ejpam-3823	96	13	4	4	NUM
ejpam-3823	96	14	}	}	PUNCT
ejpam-3823	96	15	.then	.then	X
ejpam-3823	96	16	b	b	NOUN
ejpam-3823	96	17	is	be	AUX
ejpam-3823	96	18	not	not	PART
ejpam-3823	96	19	nano	nano	VERB
ejpam-3823	96	20	-	-	PUNCT
ejpam-3823	96	21	generalized	generalize	VERB
ejpam-3823	96	22	closed	close	VERB
ejpam-3823	96	23	set	set	VERB
ejpam-3823	96	24	.but	.but	PUNCT
ejpam-3823	97	1	b	b	X
ejpam-3823	97	2	=	=	NOUN
ejpam-3823	97	3	{	{	PUNCT
ejpam-3823	97	4	1	1	NUM
ejpam-3823	97	5	,	,	PUNCT
ejpam-3823	97	6	2	2	NUM
ejpam-3823	97	7	}	}	PUNCT
ejpam-3823	97	8	⊆	⊆	NUM
ejpam-3823	97	9	{	{	PUNCT
ejpam-3823	97	10	1	1	NUM
ejpam-3823	97	11	,	,	PUNCT
ejpam-3823	97	12	2	2	NUM
ejpam-3823	97	13	,	,	PUNCT
ejpam-3823	97	14	4	4	NUM
ejpam-3823	97	15	}	}	PUNCT
ejpam-3823	97	16	∈	∈	PROPN
ejpam-3823	97	17	µr(a	µr(a	NUM
ejpam-3823	97	18	)	)	PUNCT
ejpam-3823	97	19	such	such	ADJ
ejpam-3823	97	20	that	that	SCONJ
ejpam-3823	97	21	mic.cl	mic.cl	PROPN
ejpam-3823	97	22	.	.	PUNCT
ejpam-3823	97	23	{	{	PUNCT
ejpam-3823	98	1	1	1	NUM
ejpam-3823	98	2	,	,	PUNCT
ejpam-3823	98	3	2	2	NUM
ejpam-3823	98	4	}	}	PUNCT
ejpam-3823	98	5	=	=	SYM
ejpam-3823	98	6	{	{	PUNCT
ejpam-3823	98	7	1	1	NUM
ejpam-3823	98	8	,	,	PUNCT
ejpam-3823	98	9	2	2	NUM
ejpam-3823	98	10	,	,	PUNCT
ejpam-3823	98	11	4	4	NUM
ejpam-3823	98	12	}	}	PUNCT
ejpam-3823	98	13	thus	thus	ADV
ejpam-3823	98	14	b	b	NOUN
ejpam-3823	98	15	is	be	AUX
ejpam-3823	98	16	micro	micro	ADJ
ejpam-3823	98	17	-	-	ADJ
ejpam-3823	98	18	generalized	generalize	VERB
ejpam-3823	98	19	closed	closed	ADJ
ejpam-3823	98	20	set	set	NOUN
ejpam-3823	98	21	.	.	PUNCT
ejpam-3823	99	1	3.11	3.11	NUM
ejpam-3823	99	2	.	.	PUNCT
ejpam-3823	99	3	theorem	theorem	NOUN
ejpam-3823	99	4	let	let	VERB
ejpam-3823	99	5	(	(	PUNCT
ejpam-3823	99	6	x	x	NOUN
ejpam-3823	99	7	,	,	PUNCT
ejpam-3823	99	8	τr(a	τr(a	NUM
ejpam-3823	99	9	)	)	PUNCT
ejpam-3823	99	10	,	,	PUNCT
ejpam-3823	99	11	µr(a	µr(a	NUM
ejpam-3823	99	12	)	)	PUNCT
ejpam-3823	99	13	)	)	PUNCT
ejpam-3823	99	14	be	be	AUX
ejpam-3823	99	15	a	a	DET
ejpam-3823	99	16	micro	micro	ADJ
ejpam-3823	99	17	topological	topological	ADJ
ejpam-3823	99	18	space	space	NOUN
ejpam-3823	99	19	.	.	PUNCT
ejpam-3823	100	1	if	if	SCONJ
ejpam-3823	100	2	b	b	NOUN
ejpam-3823	100	3	and	and	CCONJ
ejpam-3823	100	4	c	c	PROPN
ejpam-3823	100	5	are	be	AUX
ejpam-3823	100	6	micro	micro	ADJ
ejpam-3823	100	7	-	-	ADJ
ejpam-3823	100	8	generalized	generalized	ADJ
ejpam-3823	100	9	closed	closed	ADJ
ejpam-3823	100	10	sets	set	NOUN
ejpam-3823	100	11	,	,	PUNCT
ejpam-3823	100	12	then	then	ADV
ejpam-3823	100	13	b	b	X
ejpam-3823	100	14	∪	∪	NOUN
ejpam-3823	100	15	c	c	PROPN
ejpam-3823	100	16	is	be	AUX
ejpam-3823	100	17	micro	micro	ADJ
ejpam-3823	100	18	-	-	ADJ
ejpam-3823	100	19	generalized	generalize	VERB
ejpam-3823	100	20	closed	closed	ADJ
ejpam-3823	100	21	set	set	NOUN
ejpam-3823	100	22	.	.	PUNCT
ejpam-3823	101	1	proof	proof	NOUN
ejpam-3823	101	2	:	:	PUNCT
ejpam-3823	101	3	let	let	VERB
ejpam-3823	101	4	b	b	NOUN
ejpam-3823	101	5	and	and	CCONJ
ejpam-3823	101	6	c	c	PROPN
ejpam-3823	101	7	are	be	AUX
ejpam-3823	101	8	mic.g	mic.g	NOUN
ejpam-3823	101	9	-	-	PUNCT
ejpam-3823	101	10	closed	closed	ADJ
ejpam-3823	101	11	sets	set	NOUN
ejpam-3823	101	12	.	.	PUNCT
ejpam-3823	102	1	then	then	ADV
ejpam-3823	102	2	mic.cl.(b	mic.cl.(b	ADJ
ejpam-3823	102	3	)	)	PUNCT
ejpam-3823	102	4	⊆	⊆	NUM
ejpam-3823	102	5	u	u	NOUN
ejpam-3823	102	6	when	when	SCONJ
ejpam-3823	102	7	every	every	DET
ejpam-3823	102	8	b	b	NOUN
ejpam-3823	102	9	⊆	⊆	NUM
ejpam-3823	102	10	u	u	NOUN
ejpam-3823	102	11	and	and	CCONJ
ejpam-3823	102	12	u	u	NOUN
ejpam-3823	102	13	is	be	AUX
ejpam-3823	102	14	micro	micro	X
ejpam-3823	102	15	open	open	ADJ
ejpam-3823	102	16	set	set	NOUN
ejpam-3823	102	17	and	and	CCONJ
ejpam-3823	102	18	mic.cl.(c	mic.cl.(c	NOUN
ejpam-3823	102	19	)	)	PUNCT
ejpam-3823	102	20	⊆	⊆	NUM
ejpam-3823	102	21	v	v	NOUN
ejpam-3823	102	22	for	for	ADP
ejpam-3823	102	23	c	c	PROPN
ejpam-3823	102	24	⊆	⊆	NUM
ejpam-3823	102	25	v	v	NOUN
ejpam-3823	102	26	and	and	CCONJ
ejpam-3823	102	27	v	v	NOUN
ejpam-3823	102	28	is	be	AUX
ejpam-3823	102	29	micro	micro	X
ejpam-3823	102	30	open	open	ADJ
ejpam-3823	102	31	set	set	NOUN
ejpam-3823	102	32	.	.	PUNCT
ejpam-3823	103	1	since	since	SCONJ
ejpam-3823	103	2	b	b	PROPN
ejpam-3823	103	3	is	be	AUX
ejpam-3823	103	4	subset	subset	VERB
ejpam-3823	103	5	of	of	ADP
ejpam-3823	103	6	u	u	PROPN
ejpam-3823	103	7	and	and	CCONJ
ejpam-3823	103	8	c	c	PROPN
ejpam-3823	103	9	is	be	AUX
ejpam-3823	103	10	subset	subset	VERB
ejpam-3823	103	11	of	of	ADP
ejpam-3823	103	12	v	v	NOUN
ejpam-3823	103	13	,	,	PUNCT
ejpam-3823	103	14	thus	thus	ADV
ejpam-3823	103	15	b	b	X
ejpam-3823	103	16	∪c	∪c	NUM
ejpam-3823	103	17	⊆	⊆	NUM
ejpam-3823	103	18	u	u	NOUN
ejpam-3823	103	19	∪	∪	NOUN
ejpam-3823	103	20	v	v	NOUN
ejpam-3823	103	21	and	and	CCONJ
ejpam-3823	103	22	u	u	NOUN
ejpam-3823	103	23	∪	∪	NOUN
ejpam-3823	103	24	v	v	NOUN
ejpam-3823	103	25	is	be	AUX
ejpam-3823	103	26	micro	micro	X
ejpam-3823	103	27	open	open	ADJ
ejpam-3823	103	28	set	set	NOUN
ejpam-3823	103	29	.	.	PUNCT
ejpam-3823	104	1	then	then	ADV
ejpam-3823	104	2	mic.cl(b)∪mic.cl(c	mic.cl(b)∪mic.cl(c	PROPN
ejpam-3823	104	3	)	)	PUNCT
ejpam-3823	105	1	⊆	⊆	NUM
ejpam-3823	105	2	u	u	NOUN
ejpam-3823	105	3	∪v	∪v	PUNCT
ejpam-3823	105	4	,	,	PUNCT
ejpam-3823	105	5	since	since	SCONJ
ejpam-3823	105	6	mic.cl(b	mic.cl(b	NOUN
ejpam-3823	105	7	∪c	∪c	NOUN
ejpam-3823	105	8	)	)	PUNCT
ejpam-3823	105	9	=	=	SYM
ejpam-3823	105	10	mic.cl(b)∪mic.cl(c	mic.cl(b)∪mic.cl(c	PROPN
ejpam-3823	105	11	)	)	PUNCT
ejpam-3823	105	12	then	then	ADV
ejpam-3823	105	13	mic.cl(b	mic.cl(b	VERB
ejpam-3823	105	14	∪	∪	PROPN
ejpam-3823	105	15	c	c	NOUN
ejpam-3823	105	16	)	)	PUNCT
ejpam-3823	105	17	⊆	⊆	NUM
ejpam-3823	105	18	u	u	NOUN
ejpam-3823	105	19	∪	∪	VERB
ejpam-3823	105	20	v	v	NOUN
ejpam-3823	105	21	for	for	ADP
ejpam-3823	105	22	b	b	NOUN
ejpam-3823	105	23	∪	∪	NOUN
ejpam-3823	105	24	c	c	NOUN
ejpam-3823	105	25	⊆	⊆	NUM
ejpam-3823	105	26	u	u	NOUN
ejpam-3823	105	27	∪	∪	ADJ
ejpam-3823	105	28	v	v	NOUN
ejpam-3823	105	29	and	and	CCONJ
ejpam-3823	105	30	u	u	NOUN
ejpam-3823	105	31	∪	∪	NOUN
ejpam-3823	105	32	v	v	NOUN
ejpam-3823	105	33	is	be	AUX
ejpam-3823	105	34	micro	micro	X
ejpam-3823	105	35	open	open	ADJ
ejpam-3823	105	36	set	set	NOUN
ejpam-3823	105	37	.	.	PUNCT
ejpam-3823	106	1	which	which	PRON
ejpam-3823	106	2	leads	lead	VERB
ejpam-3823	106	3	to	to	ADP
ejpam-3823	106	4	b	b	PROPN
ejpam-3823	106	5	∪	∪	NOUN
ejpam-3823	106	6	c	c	PROPN
ejpam-3823	106	7	is	be	AUX
ejpam-3823	106	8	micro	micro	ADJ
ejpam-3823	106	9	-	-	ADJ
ejpam-3823	106	10	generalized	generalize	VERB
ejpam-3823	106	11	closed	closed	ADJ
ejpam-3823	106	12	set	set	NOUN
ejpam-3823	106	13	.	.	PUNCT
ejpam-3823	107	1	3.12	3.12	NUM
ejpam-3823	107	2	.	.	X
ejpam-3823	107	3	proposition	proposition	NOUN
ejpam-3823	107	4	let	let	VERB
ejpam-3823	107	5	(	(	PUNCT
ejpam-3823	107	6	x	x	NOUN
ejpam-3823	107	7	,	,	PUNCT
ejpam-3823	107	8	τr(a	τr(a	NUM
ejpam-3823	107	9	)	)	PUNCT
ejpam-3823	107	10	,	,	PUNCT
ejpam-3823	107	11	µr(a	µr(a	NUM
ejpam-3823	107	12	)	)	PUNCT
ejpam-3823	107	13	)	)	PUNCT
ejpam-3823	107	14	be	be	AUX
ejpam-3823	107	15	a	a	DET
ejpam-3823	107	16	micro	micro	ADJ
ejpam-3823	107	17	topological	topological	ADJ
ejpam-3823	107	18	space	space	NOUN
ejpam-3823	107	19	and	and	CCONJ
ejpam-3823	107	20	bandc	bandc	NOUN
ejpam-3823	107	21	are	be	AUX
ejpam-3823	107	22	subset	subset	VERB
ejpam-3823	107	23	of	of	ADP
ejpam-3823	107	24	x	x	SYM
ejpam-3823	107	25	such	such	ADJ
ejpam-3823	107	26	that	that	DET
ejpam-3823	107	27	b	b	NOUN
ejpam-3823	107	28	⊆	⊆	NUM
ejpam-3823	107	29	c	c	NOUN
ejpam-3823	107	30	,	,	PUNCT
ejpam-3823	107	31	then	then	ADV
ejpam-3823	107	32	:	:	PUNCT
ejpam-3823	107	33	(	(	PUNCT
ejpam-3823	107	34	i	i	NOUN
ejpam-3823	107	35	)	)	PUNCT
ejpam-3823	107	36	if	if	SCONJ
ejpam-3823	107	37	b	b	PROPN
ejpam-3823	107	38	is	be	AUX
ejpam-3823	107	39	a	a	DET
ejpam-3823	107	40	micro	micro	ADJ
ejpam-3823	107	41	-	-	ADJ
ejpam-3823	107	42	generalized	generalize	VERB
ejpam-3823	107	43	closed	close	VERB
ejpam-3823	107	44	set	set	NOUN
ejpam-3823	107	45	then	then	ADV
ejpam-3823	107	46	it	it	PRON
ejpam-3823	107	47	is	be	AUX
ejpam-3823	107	48	not	not	PART
ejpam-3823	107	49	necessary	necessary	ADJ
ejpam-3823	107	50	that	that	SCONJ
ejpam-3823	107	51	c	c	PROPN
ejpam-3823	107	52	is	be	AUX
ejpam-3823	107	53	microgeneralized	microgeneralize	VERB
ejpam-3823	107	54	closed	closed	ADJ
ejpam-3823	107	55	set	set	NOUN
ejpam-3823	107	56	.	.	PUNCT
ejpam-3823	108	1	(	(	PUNCT
ejpam-3823	108	2	ii	ii	NOUN
ejpam-3823	108	3	)	)	PUNCT
ejpam-3823	108	4	if	if	SCONJ
ejpam-3823	108	5	c	c	PROPN
ejpam-3823	108	6	is	be	AUX
ejpam-3823	108	7	a	a	DET
ejpam-3823	108	8	micro	micro	ADJ
ejpam-3823	108	9	-	-	ADJ
ejpam-3823	108	10	generalized	generalize	VERB
ejpam-3823	108	11	closed	close	VERB
ejpam-3823	108	12	set	set	NOUN
ejpam-3823	108	13	then	then	ADV
ejpam-3823	108	14	it	it	PRON
ejpam-3823	108	15	is	be	AUX
ejpam-3823	108	16	not	not	PART
ejpam-3823	108	17	necessary	necessary	ADJ
ejpam-3823	108	18	that	that	SCONJ
ejpam-3823	108	19	b	b	NOUN
ejpam-3823	108	20	is	be	AUX
ejpam-3823	108	21	microgeneralized	microgeneralize	VERB
ejpam-3823	108	22	closed	closed	ADJ
ejpam-3823	108	23	set	set	NOUN
ejpam-3823	108	24	.	.	PUNCT
ejpam-3823	109	1	the	the	DET
ejpam-3823	109	2	proposition	proposition	NOUN
ejpam-3823	109	3	above	above	ADP
ejpam-3823	109	4	needs	need	VERB
ejpam-3823	109	5	the	the	DET
ejpam-3823	109	6	following	follow	VERB
ejpam-3823	109	7	example	example	NOUN
ejpam-3823	109	8	:	:	PUNCT
ejpam-3823	109	9	t.	t.	PROPN
ejpam-3823	109	10	h.	h.	PROPN
ejpam-3823	109	11	jasim	jasim	PROPN
ejpam-3823	109	12	,	,	PUNCT
ejpam-3823	109	13	s.	s.	PROPN
ejpam-3823	109	14	s.	s.	PROPN
ejpam-3823	109	15	mohsen	mohsen	PROPN
ejpam-3823	109	16	,	,	PUNCT
ejpam-3823	109	17	k.	k.	PROPN
ejpam-3823	109	18	s.	s.	PROPN
ejpam-3823	109	19	eke	eke	PROPN
ejpam-3823	109	20	/	/	SYM
ejpam-3823	109	21	eur	eur	PROPN
ejpam-3823	109	22	.	.	PUNCT
ejpam-3823	110	1	j.	j.	PROPN
ejpam-3823	110	2	pure	pure	PROPN
ejpam-3823	110	3	appl	appl	PROPN
ejpam-3823	110	4	.	.	PROPN
ejpam-3823	110	5	math	math	PROPN
ejpam-3823	110	6	,	,	PUNCT
ejpam-3823	110	7	14	14	NUM
ejpam-3823	110	8	(	(	PUNCT
ejpam-3823	110	9	4	4	NUM
ejpam-3823	110	10	)	)	PUNCT
ejpam-3823	110	11	(	(	PUNCT
ejpam-3823	110	12	2021	2021	NUM
ejpam-3823	110	13	)	)	PUNCT
ejpam-3823	110	14	,	,	PUNCT
ejpam-3823	110	15	1507	1507	NUM
ejpam-3823	110	16	-	-	SYM
ejpam-3823	110	17	1516	1516	NUM
ejpam-3823	110	18	1512	1512	NUM
ejpam-3823	110	19	3.13	3.13	NUM
ejpam-3823	110	20	.	.	PUNCT
ejpam-3823	111	1	example	example	NOUN
ejpam-3823	111	2	let	let	VERB
ejpam-3823	111	3	x	x	PUNCT
ejpam-3823	111	4	=	=	PRON
ejpam-3823	111	5	{	{	PUNCT
ejpam-3823	111	6	a	a	DET
ejpam-3823	111	7	,	,	PUNCT
ejpam-3823	111	8	b	b	NOUN
ejpam-3823	111	9	,	,	PUNCT
ejpam-3823	111	10	c	c	NOUN
ejpam-3823	111	11	,	,	PUNCT
ejpam-3823	111	12	d	d	NOUN
ejpam-3823	111	13	}	}	PUNCT
ejpam-3823	111	14	with	with	ADP
ejpam-3823	111	15	x	x	X
ejpam-3823	111	16	/	/	SYM
ejpam-3823	111	17	r	r	NOUN
ejpam-3823	111	18	=	=	PUNCT
ejpam-3823	111	19	{	{	PUNCT
ejpam-3823	111	20	{	{	PUNCT
ejpam-3823	111	21	a	a	NOUN
ejpam-3823	111	22	}	}	PUNCT
ejpam-3823	111	23	,	,	PUNCT
ejpam-3823	111	24	{	{	PUNCT
ejpam-3823	111	25	c	c	NOUN
ejpam-3823	111	26	}	}	PUNCT
ejpam-3823	111	27	,	,	PUNCT
ejpam-3823	111	28	{	{	PUNCT
ejpam-3823	111	29	b	b	X
ejpam-3823	111	30	,	,	PUNCT
ejpam-3823	111	31	d	d	NOUN
ejpam-3823	111	32	}	}	PUNCT
ejpam-3823	111	33	}	}	PUNCT
ejpam-3823	111	34	and	and	CCONJ
ejpam-3823	111	35	a	a	DET
ejpam-3823	111	36	=	=	X
ejpam-3823	111	37	{	{	PUNCT
ejpam-3823	111	38	b	b	NOUN
ejpam-3823	111	39	,	,	PUNCT
ejpam-3823	111	40	d	d	NOUN
ejpam-3823	111	41	}	}	PUNCT
ejpam-3823	111	42	.	.	PUNCT
ejpam-3823	112	1	then	then	ADV
ejpam-3823	112	2	τr(a	τr(a	NUM
ejpam-3823	112	3	)	)	PUNCT
ejpam-3823	113	1	=	=	NOUN
ejpam-3823	113	2	{	{	PUNCT
ejpam-3823	113	3	∅	∅	NOUN
ejpam-3823	113	4	,	,	PUNCT
ejpam-3823	113	5	x	x	PRON
ejpam-3823	113	6	,	,	PUNCT
ejpam-3823	113	7	{	{	PUNCT
ejpam-3823	113	8	b	b	X
ejpam-3823	113	9	,	,	PUNCT
ejpam-3823	113	10	d	d	NOUN
ejpam-3823	113	11	}	}	PUNCT
ejpam-3823	113	12	}	}	PUNCT
ejpam-3823	113	13	.	.	PUNCT
ejpam-3823	114	1	let	let	VERB
ejpam-3823	114	2	µ	µ	X
ejpam-3823	114	3	=	=	PUNCT
ejpam-3823	114	4	{	{	PUNCT
ejpam-3823	114	5	a	a	PROPN
ejpam-3823	114	6	,	,	PUNCT
ejpam-3823	114	7	b	b	NOUN
ejpam-3823	114	8	,	,	PUNCT
ejpam-3823	114	9	c	c	NOUN
ejpam-3823	114	10	}	}	PUNCT
ejpam-3823	114	11	,	,	PUNCT
ejpam-3823	114	12	then	then	ADV
ejpam-3823	114	13	µr(a	µr(a	PUNCT
ejpam-3823	114	14	)	)	PUNCT
ejpam-3823	114	15	=	=	SYM
ejpam-3823	114	16	{	{	PUNCT
ejpam-3823	114	17	∅	∅	NOUN
ejpam-3823	114	18	,	,	PUNCT
ejpam-3823	114	19	x	x	PRON
ejpam-3823	114	20	,	,	PUNCT
ejpam-3823	114	21	{	{	PUNCT
ejpam-3823	114	22	b	b	NOUN
ejpam-3823	114	23	}	}	PUNCT
ejpam-3823	114	24	,	,	PUNCT
ejpam-3823	114	25	{	{	PUNCT
ejpam-3823	114	26	b	b	X
ejpam-3823	114	27	,	,	PUNCT
ejpam-3823	114	28	d	d	NOUN
ejpam-3823	114	29	}	}	PUNCT
ejpam-3823	114	30	,	,	PUNCT
ejpam-3823	114	31	{	{	PUNCT
ejpam-3823	114	32	a	a	DET
ejpam-3823	114	33	,	,	PUNCT
ejpam-3823	114	34	b	b	NOUN
ejpam-3823	114	35	,	,	PUNCT
ejpam-3823	114	36	c	c	NOUN
ejpam-3823	114	37	}	}	PUNCT
ejpam-3823	114	38	}	}	PUNCT
ejpam-3823	114	39	.	.	PUNCT
ejpam-3823	115	1	we	we	PRON
ejpam-3823	115	2	have	have	VERB
ejpam-3823	115	3	:	:	PUNCT
ejpam-3823	115	4	(	(	PUNCT
ejpam-3823	115	5	i	i	NOUN
ejpam-3823	115	6	)	)	PUNCT
ejpam-3823	115	7	the	the	DET
ejpam-3823	115	8	set	set	NOUN
ejpam-3823	115	9	b	b	PROPN
ejpam-3823	115	10	=	=	INTJ
ejpam-3823	115	11	{	{	PUNCT
ejpam-3823	115	12	a	a	PROPN
ejpam-3823	115	13	,	,	PUNCT
ejpam-3823	115	14	c	c	NOUN
ejpam-3823	115	15	}	}	PUNCT
ejpam-3823	115	16	is	be	AUX
ejpam-3823	115	17	mic.g	mic.g	NOUN
ejpam-3823	115	18	-	-	PUNCT
ejpam-3823	115	19	closed	closed	ADJ
ejpam-3823	115	20	but	but	CCONJ
ejpam-3823	115	21	the	the	DET
ejpam-3823	115	22	set	set	NOUN
ejpam-3823	115	23	c	c	NOUN
ejpam-3823	115	24	=	=	PRON
ejpam-3823	115	25	{	{	PUNCT
ejpam-3823	115	26	a	a	DET
ejpam-3823	115	27	,	,	PUNCT
ejpam-3823	115	28	b	b	NOUN
ejpam-3823	115	29	,	,	PUNCT
ejpam-3823	115	30	c	c	NOUN
ejpam-3823	115	31	}	}	PUNCT
ejpam-3823	115	32	is	be	AUX
ejpam-3823	115	33	not	not	PART
ejpam-3823	115	34	mic.g	mic.g	PROPN
ejpam-3823	115	35	-	-	PUNCT
ejpam-3823	115	36	closed	closed	ADJ
ejpam-3823	115	37	.	.	PUNCT
ejpam-3823	116	1	(	(	PUNCT
ejpam-3823	116	2	ii	ii	X
ejpam-3823	116	3	)	)	PUNCT
ejpam-3823	116	4	the	the	DET
ejpam-3823	116	5	set	set	NOUN
ejpam-3823	116	6	c	c	NOUN
ejpam-3823	116	7	=	=	SYM
ejpam-3823	116	8	{	{	PUNCT
ejpam-3823	116	9	b	b	NOUN
ejpam-3823	116	10	,	,	PUNCT
ejpam-3823	116	11	c	c	NOUN
ejpam-3823	116	12	,	,	PUNCT
ejpam-3823	116	13	d	d	NOUN
ejpam-3823	116	14	}	}	PUNCT
ejpam-3823	116	15	is	be	AUX
ejpam-3823	116	16	mic.g	mic.g	NOUN
ejpam-3823	116	17	-	-	PUNCT
ejpam-3823	116	18	closed	closed	ADJ
ejpam-3823	116	19	but	but	CCONJ
ejpam-3823	116	20	the	the	DET
ejpam-3823	116	21	set	set	NOUN
ejpam-3823	116	22	b	b	PROPN
ejpam-3823	116	23	=	=	SYM
ejpam-3823	116	24	{	{	PUNCT
ejpam-3823	116	25	b	b	NOUN
ejpam-3823	116	26	,	,	PUNCT
ejpam-3823	116	27	c	c	NOUN
ejpam-3823	116	28	}	}	PUNCT
ejpam-3823	116	29	is	be	AUX
ejpam-3823	116	30	not	not	PART
ejpam-3823	116	31	mic.g	mic.g	PROPN
ejpam-3823	116	32	-	-	PUNCT
ejpam-3823	116	33	closed	closed	ADJ
ejpam-3823	116	34	.	.	PUNCT
ejpam-3823	117	1	3.14	3.14	NUM
ejpam-3823	117	2	.	.	PUNCT
ejpam-3823	117	3	remark	remark	PROPN
ejpam-3823	117	4	let	let	VERB
ejpam-3823	117	5	(	(	PUNCT
ejpam-3823	117	6	x	x	X
ejpam-3823	117	7	,	,	PUNCT
ejpam-3823	117	8	τr(a	τr(a	NUM
ejpam-3823	117	9	)	)	PUNCT
ejpam-3823	117	10	,	,	PUNCT
ejpam-3823	117	11	µr(a	µr(a	NUM
ejpam-3823	117	12	)	)	PUNCT
ejpam-3823	117	13	)	)	PUNCT
ejpam-3823	117	14	be	be	AUX
ejpam-3823	117	15	a	a	DET
ejpam-3823	117	16	micro	micro	ADJ
ejpam-3823	117	17	topological	topological	ADJ
ejpam-3823	117	18	space	space	NOUN
ejpam-3823	117	19	.	.	PUNCT
ejpam-3823	118	1	if	if	SCONJ
ejpam-3823	118	2	b	b	NOUN
ejpam-3823	118	3	and	and	CCONJ
ejpam-3823	118	4	c	c	PROPN
ejpam-3823	118	5	are	be	AUX
ejpam-3823	118	6	micro	micro	ADJ
ejpam-3823	118	7	-	-	ADJ
ejpam-3823	118	8	generalized	generalized	ADJ
ejpam-3823	118	9	closed	closed	ADJ
ejpam-3823	118	10	sets	set	NOUN
ejpam-3823	118	11	,	,	PUNCT
ejpam-3823	118	12	then	then	ADV
ejpam-3823	118	13	b	b	PROPN
ejpam-3823	118	14	∩	∩	NOUN
ejpam-3823	118	15	c	c	NOUN
ejpam-3823	118	16	need	need	AUX
ejpam-3823	118	17	not	not	PART
ejpam-3823	118	18	be	be	AUX
ejpam-3823	118	19	a	a	DET
ejpam-3823	118	20	micro	micro	ADJ
ejpam-3823	118	21	-	-	ADJ
ejpam-3823	118	22	generalized	generalize	VERB
ejpam-3823	118	23	closed	close	VERB
ejpam-3823	118	24	set	set	NOUN
ejpam-3823	118	25	,	,	PUNCT
ejpam-3823	118	26	we	we	PRON
ejpam-3823	118	27	can	can	AUX
ejpam-3823	118	28	consider	consider	VERB
ejpam-3823	118	29	the	the	DET
ejpam-3823	118	30	set	set	NOUN
ejpam-3823	118	31	b	b	PROPN
ejpam-3823	118	32	=	=	INTJ
ejpam-3823	118	33	{	{	PUNCT
ejpam-3823	118	34	a	a	PROPN
ejpam-3823	118	35	,	,	PUNCT
ejpam-3823	118	36	b	b	NOUN
ejpam-3823	118	37	,	,	PUNCT
ejpam-3823	118	38	d	d	NOUN
ejpam-3823	118	39	}	}	PUNCT
ejpam-3823	118	40	and	and	CCONJ
ejpam-3823	118	41	the	the	DET
ejpam-3823	118	42	set	set	NOUN
ejpam-3823	118	43	c	c	NOUN
ejpam-3823	118	44	=	=	SYM
ejpam-3823	118	45	{	{	PUNCT
ejpam-3823	118	46	b	b	NOUN
ejpam-3823	118	47	,	,	PUNCT
ejpam-3823	118	48	c	c	NOUN
ejpam-3823	118	49	,	,	PUNCT
ejpam-3823	118	50	d	d	NOUN
ejpam-3823	118	51	}	}	PUNCT
ejpam-3823	118	52	in	in	ADP
ejpam-3823	118	53	the	the	DET
ejpam-3823	118	54	example	example	NOUN
ejpam-3823	118	55	(	(	PUNCT
ejpam-3823	118	56	3.13	3.13	NUM
ejpam-3823	118	57	)	)	PUNCT
ejpam-3823	118	58	each	each	PRON
ejpam-3823	118	59	of	of	ADP
ejpam-3823	118	60	them	they	PRON
ejpam-3823	118	61	are	be	AUX
ejpam-3823	118	62	microgeneralized	microgeneralize	VERB
ejpam-3823	118	63	closed	closed	ADJ
ejpam-3823	118	64	set	set	ADJ
ejpam-3823	118	65	but	but	CCONJ
ejpam-3823	118	66	b	b	NOUN
ejpam-3823	118	67	∩	∩	NOUN
ejpam-3823	118	68	c	c	NOUN
ejpam-3823	118	69	=	=	SYM
ejpam-3823	118	70	{	{	PUNCT
ejpam-3823	118	71	b	b	NOUN
ejpam-3823	118	72	,	,	PUNCT
ejpam-3823	118	73	d	d	NOUN
ejpam-3823	118	74	}	}	PUNCT
ejpam-3823	118	75	is	be	AUX
ejpam-3823	118	76	not	not	PART
ejpam-3823	118	77	micro	micro	ADJ
ejpam-3823	118	78	-	-	ADJ
ejpam-3823	118	79	generalized	generalize	VERB
ejpam-3823	118	80	closed	closed	ADJ
ejpam-3823	118	81	set	set	NOUN
ejpam-3823	118	82	.	.	PUNCT
ejpam-3823	119	1	3.15	3.15	NUM
ejpam-3823	119	2	.	.	PUNCT
ejpam-3823	120	1	proposition	proposition	NOUN
ejpam-3823	120	2	let	let	VERB
ejpam-3823	120	3	(	(	PUNCT
ejpam-3823	120	4	x	x	NOUN
ejpam-3823	120	5	,	,	PUNCT
ejpam-3823	120	6	τr(a	τr(a	NUM
ejpam-3823	120	7	)	)	PUNCT
ejpam-3823	120	8	,	,	PUNCT
ejpam-3823	120	9	µr(a	µr(a	NUM
ejpam-3823	120	10	)	)	PUNCT
ejpam-3823	120	11	)	)	PUNCT
ejpam-3823	120	12	be	be	AUX
ejpam-3823	120	13	a	a	DET
ejpam-3823	120	14	micro	micro	ADJ
ejpam-3823	120	15	topological	topological	ADJ
ejpam-3823	120	16	space	space	NOUN
ejpam-3823	120	17	.	.	PUNCT
ejpam-3823	121	1	if	if	SCONJ
ejpam-3823	121	2	b	b	NOUN
ejpam-3823	121	3	is	be	AUX
ejpam-3823	121	4	not	not	PART
ejpam-3823	121	5	micro	micro	ADJ
ejpam-3823	121	6	open	open	ADJ
ejpam-3823	121	7	set	set	NOUN
ejpam-3823	121	8	and	and	CCONJ
ejpam-3823	121	9	not	not	PART
ejpam-3823	121	10	subset	subset	VERB
ejpam-3823	121	11	of	of	ADP
ejpam-3823	121	12	any	any	DET
ejpam-3823	121	13	micro	micro	ADJ
ejpam-3823	121	14	open	open	ADJ
ejpam-3823	121	15	set	set	VERB
ejpam-3823	121	16	in	in	ADP
ejpam-3823	121	17	x	x	PROPN
ejpam-3823	121	18	(	(	PUNCT
ejpam-3823	121	19	just	just	ADV
ejpam-3823	121	20	b	b	NOUN
ejpam-3823	121	21	⊆	⊆	NUM
ejpam-3823	121	22	x	x	SYM
ejpam-3823	121	23	)	)	PUNCT
ejpam-3823	121	24	then	then	ADV
ejpam-3823	121	25	b	b	X
ejpam-3823	121	26	is	be	AUX
ejpam-3823	121	27	micro	micro	ADJ
ejpam-3823	121	28	-	-	ADJ
ejpam-3823	121	29	generalized	generalize	VERB
ejpam-3823	121	30	closed	closed	ADJ
ejpam-3823	121	31	set	set	NOUN
ejpam-3823	121	32	.	.	PUNCT
ejpam-3823	122	1	proof	proof	NOUN
ejpam-3823	122	2	:	:	PUNCT
ejpam-3823	122	3	let	let	VERB
ejpam-3823	122	4	b	b	X
ejpam-3823	122	5	/∈	/∈	PUNCT
ejpam-3823	122	6	µr(a	µr(a	VERB
ejpam-3823	122	7	)	)	PUNCT
ejpam-3823	122	8	and	and	CCONJ
ejpam-3823	122	9	not	not	PART
ejpam-3823	122	10	subset	subset	VERB
ejpam-3823	122	11	of	of	ADP
ejpam-3823	122	12	any	any	DET
ejpam-3823	122	13	micro	micro	ADJ
ejpam-3823	122	14	open	open	ADJ
ejpam-3823	122	15	set	set	VERB
ejpam-3823	122	16	in	in	ADP
ejpam-3823	122	17	x	x	PROPN
ejpam-3823	122	18	(	(	PUNCT
ejpam-3823	122	19	just	just	ADV
ejpam-3823	122	20	b	b	NOUN
ejpam-3823	122	21	⊆	⊆	NUM
ejpam-3823	122	22	x	x	NOUN
ejpam-3823	122	23	)	)	PUNCT
ejpam-3823	122	24	.	.	PUNCT
ejpam-3823	123	1	then	then	ADV
ejpam-3823	123	2	mic.cl(b	mic.cl(b	VERB
ejpam-3823	123	3	)	)	PUNCT
ejpam-3823	123	4	⊆	⊆	NUM
ejpam-3823	123	5	c	c	NOUN
ejpam-3823	123	6	where	where	SCONJ
ejpam-3823	123	7	c	c	PROPN
ejpam-3823	123	8	is	be	AUX
ejpam-3823	123	9	micro	micro	ADV
ejpam-3823	123	10	closed	close	VERB
ejpam-3823	123	11	set	set	VERB
ejpam-3823	123	12	and	and	CCONJ
ejpam-3823	123	13	c	c	NOUN
ejpam-3823	123	14	⊆	⊆	NUM
ejpam-3823	123	15	x.	x.	NOUN
ejpam-3823	123	16	thus	thus	ADV
ejpam-3823	123	17	mic.cl(b	mic.cl(b	X
ejpam-3823	123	18	)	)	PUNCT
ejpam-3823	124	1	⊆	⊆	NUM
ejpam-3823	124	2	x.	x.	NOUN
ejpam-3823	124	3	that	that	PRON
ejpam-3823	124	4	is	be	AUX
ejpam-3823	124	5	,	,	PUNCT
ejpam-3823	124	6	b	b	PROPN
ejpam-3823	124	7	is	be	AUX
ejpam-3823	124	8	mic.g	mic.g	NOUN
ejpam-3823	124	9	-	-	PUNCT
ejpam-3823	124	10	closed	close	VERB
ejpam-3823	124	11	set	set	NOUN
ejpam-3823	124	12	in	in	ADP
ejpam-3823	124	13	x.	x.	PROPN
ejpam-3823	124	14	3.16	3.16	NUM
ejpam-3823	124	15	.	.	PUNCT
ejpam-3823	125	1	example	example	NOUN
ejpam-3823	125	2	in	in	ADP
ejpam-3823	125	3	the	the	DET
ejpam-3823	125	4	example	example	NOUN
ejpam-3823	125	5	(	(	PUNCT
ejpam-3823	125	6	3.13	3.13	NUM
ejpam-3823	125	7	)	)	PUNCT
ejpam-3823	125	8	,	,	PUNCT
ejpam-3823	125	9	let	let	VERB
ejpam-3823	125	10	µ	µ	X
ejpam-3823	125	11	=	=	PUNCT
ejpam-3823	125	12	{	{	PUNCT
ejpam-3823	125	13	a	a	NOUN
ejpam-3823	125	14	}	}	PUNCT
ejpam-3823	125	15	then	then	ADV
ejpam-3823	125	16	µr(a	µr(a	PUNCT
ejpam-3823	125	17	)	)	PUNCT
ejpam-3823	125	18	=	=	SYM
ejpam-3823	125	19	{	{	PUNCT
ejpam-3823	125	20	∅	∅	NOUN
ejpam-3823	125	21	,	,	PUNCT
ejpam-3823	125	22	x	x	PRON
ejpam-3823	125	23	,	,	PUNCT
ejpam-3823	125	24	{	{	PUNCT
ejpam-3823	125	25	a	a	PRON
ejpam-3823	125	26	}	}	PUNCT
ejpam-3823	125	27	,	,	PUNCT
ejpam-3823	125	28	{	{	PUNCT
ejpam-3823	125	29	b	b	X
ejpam-3823	125	30	,	,	PUNCT
ejpam-3823	125	31	d	d	NOUN
ejpam-3823	125	32	}	}	PUNCT
ejpam-3823	125	33	,	,	PUNCT
ejpam-3823	125	34	{	{	PUNCT
ejpam-3823	125	35	a	a	DET
ejpam-3823	125	36	,	,	PUNCT
ejpam-3823	125	37	b	b	NOUN
ejpam-3823	125	38	,	,	PUNCT
ejpam-3823	125	39	d	d	NOUN
ejpam-3823	125	40	}	}	PUNCT
ejpam-3823	125	41	}	}	PUNCT
ejpam-3823	125	42	.	.	PUNCT
ejpam-3823	126	1	the	the	DET
ejpam-3823	126	2	set	set	PROPN
ejpam-3823	126	3	b	b	PROPN
ejpam-3823	126	4	=	=	PRON
ejpam-3823	126	5	{	{	PUNCT
ejpam-3823	126	6	c	c	NOUN
ejpam-3823	126	7	}	}	PUNCT
ejpam-3823	126	8	is	be	AUX
ejpam-3823	126	9	not	not	PART
ejpam-3823	126	10	micro	micro	ADJ
ejpam-3823	126	11	open	open	ADJ
ejpam-3823	126	12	set	set	NOUN
ejpam-3823	126	13	and	and	CCONJ
ejpam-3823	126	14	not	not	PART
ejpam-3823	126	15	subset	subset	VERB
ejpam-3823	126	16	of	of	ADP
ejpam-3823	126	17	any	any	DET
ejpam-3823	126	18	micro	micro	ADJ
ejpam-3823	126	19	open	open	ADJ
ejpam-3823	126	20	set	set	VERB
ejpam-3823	126	21	in	in	ADP
ejpam-3823	126	22	x	x	PROPN
ejpam-3823	126	23	(	(	PUNCT
ejpam-3823	126	24	just	just	ADV
ejpam-3823	126	25	b	b	NOUN
ejpam-3823	126	26	⊆	⊆	NUM
ejpam-3823	126	27	x	x	SYM
ejpam-3823	126	28	)	)	PUNCT
ejpam-3823	126	29	.	.	PUNCT
ejpam-3823	127	1	then	then	ADV
ejpam-3823	127	2	mic.cl(b	mic.cl(b	VERB
ejpam-3823	127	3	)	)	PUNCT
ejpam-3823	128	1	=	=	PRON
ejpam-3823	128	2	{	{	PUNCT
ejpam-3823	128	3	c	c	NOUN
ejpam-3823	128	4	}	}	PUNCT
ejpam-3823	128	5	⊆	⊆	NUM
ejpam-3823	128	6	x	x	SYM
ejpam-3823	128	7	where	where	SCONJ
ejpam-3823	128	8	x	x	PRON
ejpam-3823	128	9	is	be	AUX
ejpam-3823	128	10	micro	micro	X
ejpam-3823	128	11	open	open	ADJ
ejpam-3823	128	12	set	set	NOUN
ejpam-3823	128	13	,	,	PUNCT
ejpam-3823	128	14	so	so	CCONJ
ejpam-3823	128	15	b	b	PROPN
ejpam-3823	128	16	is	be	AUX
ejpam-3823	128	17	mic.g	mic.g	NOUN
ejpam-3823	128	18	-	-	PUNCT
ejpam-3823	128	19	closed	close	VERB
ejpam-3823	128	20	set	set	NOUN
ejpam-3823	128	21	in	in	ADP
ejpam-3823	128	22	x.	x.	PROPN
ejpam-3823	128	23	3.17	3.17	NUM
ejpam-3823	128	24	.	.	PUNCT
ejpam-3823	128	25	remark	remark	NOUN
ejpam-3823	128	26	if	if	SCONJ
ejpam-3823	128	27	every	every	DET
ejpam-3823	128	28	set	set	NOUN
ejpam-3823	128	29	in	in	ADP
ejpam-3823	128	30	a	a	DET
ejpam-3823	128	31	micro	micro	ADJ
ejpam-3823	128	32	topology	topology	NOUN
ejpam-3823	128	33	is	be	AUX
ejpam-3823	128	34	micro	micro	ADV
ejpam-3823	128	35	open	open	ADJ
ejpam-3823	128	36	,	,	PUNCT
ejpam-3823	128	37	then	then	ADV
ejpam-3823	128	38	a	a	DET
ejpam-3823	128	39	micro	micro	ADJ
ejpam-3823	128	40	topology	topology	NOUN
ejpam-3823	128	41	is	be	AUX
ejpam-3823	128	42	the	the	DET
ejpam-3823	128	43	discrete	discrete	NOUN
ejpam-3823	128	44	.	.	PUNCT
ejpam-3823	129	1	hence	hence	ADV
ejpam-3823	129	2	,	,	PUNCT
ejpam-3823	129	3	every	every	DET
ejpam-3823	129	4	set	set	NOUN
ejpam-3823	129	5	is	be	AUX
ejpam-3823	129	6	both	both	PRON
ejpam-3823	129	7	micro	micro	ADJ
ejpam-3823	129	8	open	open	ADJ
ejpam-3823	129	9	and	and	CCONJ
ejpam-3823	129	10	micro	micro	ADJ
ejpam-3823	129	11	g	g	NOUN
ejpam-3823	129	12	-	-	PUNCT
ejpam-3823	129	13	closed	closed	ADJ
ejpam-3823	129	14	.	.	PUNCT
ejpam-3823	130	1	4	4	X
ejpam-3823	130	2	.	.	X
ejpam-3823	130	3	micro	micro	ADJ
ejpam-3823	130	4	-	-	ADJ
ejpam-3823	130	5	generalized	generalize	VERB
ejpam-3823	130	6	continuous	continuous	ADJ
ejpam-3823	130	7	function	function	NOUN
ejpam-3823	130	8	and	and	CCONJ
ejpam-3823	130	9	micro	micro	ADJ
ejpam-3823	130	10	-	-	ADJ
ejpam-3823	130	11	generalized	generalized	ADJ
ejpam-3823	130	12	irresolute	irresolute	ADJ
ejpam-3823	130	13	function	function	NOUN
ejpam-3823	130	14	in	in	ADP
ejpam-3823	130	15	this	this	DET
ejpam-3823	130	16	segment	segment	NOUN
ejpam-3823	130	17	we	we	PRON
ejpam-3823	130	18	present	present	VERB
ejpam-3823	130	19	the	the	DET
ejpam-3823	130	20	definition	definition	NOUN
ejpam-3823	130	21	of	of	ADP
ejpam-3823	130	22	micro	micro	ADJ
ejpam-3823	130	23	-	-	ADJ
ejpam-3823	130	24	generalized	generalized	ADJ
ejpam-3823	130	25	continuous	continuous	ADJ
ejpam-3823	130	26	function	function	NOUN
ejpam-3823	130	27	and	and	CCONJ
ejpam-3823	130	28	the	the	DET
ejpam-3823	130	29	micro	micro	ADJ
ejpam-3823	130	30	-	-	ADJ
ejpam-3823	130	31	generalized	generalized	ADJ
ejpam-3823	130	32	irresolute	irresolute	ADJ
ejpam-3823	130	33	function	function	NOUN
ejpam-3823	130	34	.	.	PUNCT
ejpam-3823	131	1	t.	t.	PROPN
ejpam-3823	131	2	h.	h.	PROPN
ejpam-3823	131	3	jasim	jasim	PROPN
ejpam-3823	131	4	,	,	PUNCT
ejpam-3823	131	5	s.	s.	PROPN
ejpam-3823	131	6	s.	s.	PROPN
ejpam-3823	131	7	mohsen	mohsen	PROPN
ejpam-3823	131	8	,	,	PUNCT
ejpam-3823	131	9	k.	k.	PROPN
ejpam-3823	131	10	s.	s.	PROPN
ejpam-3823	131	11	eke	eke	PROPN
ejpam-3823	131	12	/	/	SYM
ejpam-3823	131	13	eur	eur	PROPN
ejpam-3823	131	14	.	.	PUNCT
ejpam-3823	132	1	j.	j.	PROPN
ejpam-3823	132	2	pure	pure	PROPN
ejpam-3823	132	3	appl	appl	PROPN
ejpam-3823	132	4	.	.	PROPN
ejpam-3823	132	5	math	math	PROPN
ejpam-3823	132	6	,	,	PUNCT
ejpam-3823	132	7	14	14	NUM
ejpam-3823	132	8	(	(	PUNCT
ejpam-3823	132	9	4	4	NUM
ejpam-3823	132	10	)	)	PUNCT
ejpam-3823	132	11	(	(	PUNCT
ejpam-3823	132	12	2021	2021	NUM
ejpam-3823	132	13	)	)	PUNCT
ejpam-3823	132	14	,	,	PUNCT
ejpam-3823	132	15	1507	1507	NUM
ejpam-3823	132	16	-	-	SYM
ejpam-3823	132	17	1516	1516	NUM
ejpam-3823	132	18	1513	1513	NUM
ejpam-3823	132	19	4.1	4.1	NUM
ejpam-3823	132	20	.	.	PUNCT
ejpam-3823	133	1	definition	definition	NOUN
ejpam-3823	133	2	let	let	VERB
ejpam-3823	133	3	(	(	PUNCT
ejpam-3823	133	4	x	x	NOUN
ejpam-3823	133	5	,	,	PUNCT
ejpam-3823	133	6	τr(a	τr(a	NUM
ejpam-3823	133	7	)	)	PUNCT
ejpam-3823	133	8	,	,	PUNCT
ejpam-3823	133	9	µr(a	µr(a	NUM
ejpam-3823	133	10	)	)	PUNCT
ejpam-3823	133	11	)	)	PUNCT
ejpam-3823	134	1	and	and	CCONJ
ejpam-3823	134	2	(	(	PUNCT
ejpam-3823	134	3	y	y	PROPN
ejpam-3823	134	4	,	,	PUNCT
ejpam-3823	134	5	τ	τ	PROPN
ejpam-3823	134	6	′r(a	′r(a	PROPN
ejpam-3823	134	7	)	)	PUNCT
ejpam-3823	134	8	,	,	PUNCT
ejpam-3823	134	9	µ′	µ′	PROPN
ejpam-3823	134	10	r(a	r(a	PROPN
ejpam-3823	134	11	)	)	PUNCT
ejpam-3823	134	12	)	)	PUNCT
ejpam-3823	134	13	be	be	AUX
ejpam-3823	134	14	two	two	NUM
ejpam-3823	134	15	micro	micro	ADJ
ejpam-3823	134	16	topological	topological	ADJ
ejpam-3823	134	17	spaces	space	NOUN
ejpam-3823	134	18	.	.	PUNCT
ejpam-3823	135	1	a	a	DET
ejpam-3823	135	2	function	function	NOUN
ejpam-3823	135	3	f	f	NOUN
ejpam-3823	135	4	:	:	PUNCT
ejpam-3823	135	5	x	x	X
ejpam-3823	135	6	→	→	SYM
ejpam-3823	135	7	y	y	PROPN
ejpam-3823	135	8	is	be	AUX
ejpam-3823	135	9	called	call	VERB
ejpam-3823	135	10	micro	micro	ADJ
ejpam-3823	135	11	-	-	ADJ
ejpam-3823	135	12	generalized	generalized	ADJ
ejpam-3823	135	13	continuous	continuous	ADJ
ejpam-3823	135	14	function	function	NOUN
ejpam-3823	135	15	(	(	PUNCT
ejpam-3823	135	16	shortly	shortly	ADV
ejpam-3823	135	17	mic.g	mic.g	NOUN
ejpam-3823	135	18	-	-	PUNCT
ejpam-3823	135	19	continuous	continuous	ADJ
ejpam-3823	135	20	)	)	PUNCT
ejpam-3823	135	21	if	if	SCONJ
ejpam-3823	135	22	f−1(b	f−1(b	PROPN
ejpam-3823	135	23	)	)	PUNCT
ejpam-3823	135	24	is	be	AUX
ejpam-3823	135	25	mic.g	mic.g	NOUN
ejpam-3823	135	26	-	-	PUNCT
ejpam-3823	135	27	closed	closed	ADJ
ejpam-3823	135	28	set	set	NOUN
ejpam-3823	135	29	in	in	ADP
ejpam-3823	135	30	x	x	PUNCT
ejpam-3823	135	31	for	for	ADP
ejpam-3823	135	32	every	every	DET
ejpam-3823	135	33	micro	micro	ADJ
ejpam-3823	135	34	-	-	ADJ
ejpam-3823	135	35	closed	closed	ADJ
ejpam-3823	135	36	set	set	VERB
ejpam-3823	135	37	biny	biny	NOUN
ejpam-3823	135	38	.	.	PUNCT
ejpam-3823	136	1	4.2	4.2	NUM
ejpam-3823	136	2	.	.	PUNCT
ejpam-3823	136	3	example	example	NOUN
ejpam-3823	136	4	let	let	VERB
ejpam-3823	136	5	x	x	PUNCT
ejpam-3823	136	6	=	=	NOUN
ejpam-3823	136	7	{	{	PUNCT
ejpam-3823	136	8	1	1	NUM
ejpam-3823	136	9	,	,	PUNCT
ejpam-3823	136	10	2	2	NUM
ejpam-3823	136	11	,	,	PUNCT
ejpam-3823	136	12	3	3	NUM
ejpam-3823	136	13	,	,	PUNCT
ejpam-3823	136	14	4	4	NUM
ejpam-3823	136	15	,	,	PUNCT
ejpam-3823	136	16	5	5	NUM
ejpam-3823	136	17	}	}	PUNCT
ejpam-3823	136	18	,	,	PUNCT
ejpam-3823	136	19	with	with	ADP
ejpam-3823	136	20	x	x	X
ejpam-3823	136	21	/	/	SYM
ejpam-3823	136	22	r	r	NOUN
ejpam-3823	136	23	=	=	PUNCT
ejpam-3823	136	24	{	{	PUNCT
ejpam-3823	136	25	{	{	PUNCT
ejpam-3823	136	26	1	1	NUM
ejpam-3823	136	27	}	}	PUNCT
ejpam-3823	136	28	,	,	PUNCT
ejpam-3823	136	29	{	{	PUNCT
ejpam-3823	136	30	5	5	NUM
ejpam-3823	136	31	}	}	PUNCT
ejpam-3823	136	32	,	,	PUNCT
ejpam-3823	136	33	{	{	PUNCT
ejpam-3823	136	34	2	2	NUM
ejpam-3823	136	35	,	,	PUNCT
ejpam-3823	136	36	3	3	NUM
ejpam-3823	136	37	,	,	PUNCT
ejpam-3823	136	38	4	4	NUM
ejpam-3823	136	39	}	}	PUNCT
ejpam-3823	136	40	}	}	PUNCT
ejpam-3823	136	41	and	and	CCONJ
ejpam-3823	136	42	a	a	DET
ejpam-3823	136	43	=	=	X
ejpam-3823	136	44	{	{	PUNCT
ejpam-3823	136	45	1	1	NUM
ejpam-3823	136	46	,	,	PUNCT
ejpam-3823	136	47	2	2	NUM
ejpam-3823	136	48	}	}	PUNCT
ejpam-3823	136	49	⊆	⊆	NUM
ejpam-3823	136	50	x.	x.	NOUN
ejpam-3823	136	51	then	then	ADV
ejpam-3823	136	52	τr(a	τr(a	NUM
ejpam-3823	136	53	)	)	PUNCT
ejpam-3823	136	54	=	=	SYM
ejpam-3823	136	55	{	{	PUNCT
ejpam-3823	136	56	∅	∅	NOUN
ejpam-3823	136	57	,	,	PUNCT
ejpam-3823	136	58	x	x	PRON
ejpam-3823	136	59	,	,	PUNCT
ejpam-3823	136	60	{	{	PUNCT
ejpam-3823	136	61	1	1	NUM
ejpam-3823	136	62	}	}	PUNCT
ejpam-3823	136	63	,	,	PUNCT
ejpam-3823	136	64	{	{	PUNCT
ejpam-3823	136	65	2	2	NUM
ejpam-3823	136	66	,	,	PUNCT
ejpam-3823	136	67	3	3	NUM
ejpam-3823	136	68	,	,	PUNCT
ejpam-3823	136	69	4	4	NUM
ejpam-3823	136	70	}	}	PUNCT
ejpam-3823	136	71	,	,	PUNCT
ejpam-3823	136	72	{	{	PUNCT
ejpam-3823	136	73	1	1	NUM
ejpam-3823	136	74	,	,	PUNCT
ejpam-3823	136	75	2	2	NUM
ejpam-3823	136	76	,	,	PUNCT
ejpam-3823	136	77	3	3	NUM
ejpam-3823	136	78	,	,	PUNCT
ejpam-3823	136	79	4	4	NUM
ejpam-3823	136	80	}	}	PUNCT
ejpam-3823	136	81	}	}	PUNCT
ejpam-3823	136	82	.	.	PUNCT
ejpam-3823	137	1	letµ	letµ	NOUN
ejpam-3823	137	2	=	=	PUNCT
ejpam-3823	137	3	{	{	PUNCT
ejpam-3823	137	4	2	2	NUM
ejpam-3823	137	5	}	}	PUNCT
ejpam-3823	137	6	,	,	PUNCT
ejpam-3823	137	7	then	then	ADV
ejpam-3823	137	8	µr(a	µr(a	PUNCT
ejpam-3823	137	9	)	)	PUNCT
ejpam-3823	137	10	=	=	SYM
ejpam-3823	137	11	{	{	PUNCT
ejpam-3823	137	12	∅	∅	NOUN
ejpam-3823	137	13	,	,	PUNCT
ejpam-3823	137	14	x	x	PRON
ejpam-3823	137	15	,	,	PUNCT
ejpam-3823	137	16	{	{	PUNCT
ejpam-3823	137	17	1	1	NUM
ejpam-3823	137	18	}	}	PUNCT
ejpam-3823	137	19	,	,	PUNCT
ejpam-3823	137	20	{	{	PUNCT
ejpam-3823	137	21	2	2	NUM
ejpam-3823	137	22	}	}	PUNCT
ejpam-3823	137	23	,	,	PUNCT
ejpam-3823	137	24	{	{	PUNCT
ejpam-3823	137	25	1	1	NUM
ejpam-3823	137	26	,	,	PUNCT
ejpam-3823	137	27	2	2	NUM
ejpam-3823	137	28	}	}	PUNCT
ejpam-3823	137	29	,	,	PUNCT
ejpam-3823	137	30	{	{	PUNCT
ejpam-3823	137	31	2	2	NUM
ejpam-3823	137	32	,	,	PUNCT
ejpam-3823	137	33	3	3	NUM
ejpam-3823	137	34	,	,	PUNCT
ejpam-3823	137	35	4	4	NUM
ejpam-3823	137	36	}	}	PUNCT
ejpam-3823	137	37	,	,	PUNCT
ejpam-3823	137	38	{	{	PUNCT
ejpam-3823	137	39	1	1	NUM
ejpam-3823	137	40	,	,	PUNCT
ejpam-3823	137	41	2	2	NUM
ejpam-3823	137	42	,	,	PUNCT
ejpam-3823	137	43	3	3	NUM
ejpam-3823	137	44	,	,	PUNCT
ejpam-3823	137	45	4	4	NUM
ejpam-3823	137	46	}	}	PUNCT
ejpam-3823	137	47	}	}	PUNCT
ejpam-3823	137	48	and	and	CCONJ
ejpam-3823	137	49	the	the	DET
ejpam-3823	137	50	micro	micro	ADJ
ejpam-3823	137	51	closed	closed	ADJ
ejpam-3823	137	52	sets	set	NOUN
ejpam-3823	137	53	=	=	SYM
ejpam-3823	137	54	{	{	PUNCT
ejpam-3823	137	55	∅	∅	NOUN
ejpam-3823	137	56	,	,	PUNCT
ejpam-3823	137	57	x	x	PRON
ejpam-3823	137	58	,	,	PUNCT
ejpam-3823	137	59	{	{	PUNCT
ejpam-3823	137	60	5	5	NUM
ejpam-3823	137	61	}	}	PUNCT
ejpam-3823	137	62	,	,	PUNCT
ejpam-3823	137	63	{	{	PUNCT
ejpam-3823	137	64	1	1	NUM
ejpam-3823	137	65	,	,	PUNCT
ejpam-3823	137	66	5	5	NUM
ejpam-3823	137	67	}	}	PUNCT
ejpam-3823	137	68	,	,	PUNCT
ejpam-3823	137	69	{	{	PUNCT
ejpam-3823	137	70	3	3	NUM
ejpam-3823	137	71	,	,	PUNCT
ejpam-3823	137	72	4	4	NUM
ejpam-3823	137	73	,	,	PUNCT
ejpam-3823	137	74	5	5	NUM
ejpam-3823	137	75	}	}	PUNCT
ejpam-3823	137	76	{	{	PUNCT
ejpam-3823	137	77	1	1	NUM
ejpam-3823	137	78	,	,	PUNCT
ejpam-3823	137	79	3	3	NUM
ejpam-3823	137	80	,	,	PUNCT
ejpam-3823	137	81	4	4	NUM
ejpam-3823	137	82	,	,	PUNCT
ejpam-3823	137	83	5	5	NUM
ejpam-3823	137	84	}	}	PUNCT
ejpam-3823	137	85	,	,	PUNCT
ejpam-3823	137	86	{	{	PUNCT
ejpam-3823	137	87	2	2	NUM
ejpam-3823	137	88	,	,	PUNCT
ejpam-3823	137	89	3	3	NUM
ejpam-3823	137	90	,	,	PUNCT
ejpam-3823	137	91	4	4	NUM
ejpam-3823	137	92	,	,	PUNCT
ejpam-3823	137	93	5	5	NUM
ejpam-3823	137	94	}	}	PUNCT
ejpam-3823	137	95	}	}	PUNCT
ejpam-3823	137	96	.let	.let	PUNCT
ejpam-3823	138	1	y	y	PROPN
ejpam-3823	138	2	=	=	PUNCT
ejpam-3823	138	3	{	{	PUNCT
ejpam-3823	138	4	p	p	X
ejpam-3823	138	5	,	,	PUNCT
ejpam-3823	138	6	q	q	ADJ
ejpam-3823	138	7	,	,	PUNCT
ejpam-3823	138	8	r	r	NOUN
ejpam-3823	138	9	,	,	PUNCT
ejpam-3823	138	10	s	s	PROPN
ejpam-3823	138	11	,	,	PUNCT
ejpam-3823	138	12	t	t	PROPN
ejpam-3823	138	13	}	}	PUNCT
ejpam-3823	138	14	,	,	PUNCT
ejpam-3823	138	15	with	with	ADP
ejpam-3823	138	16	y	y	NOUN
ejpam-3823	138	17	/	/	SYM
ejpam-3823	138	18	r	r	NOUN
ejpam-3823	138	19	=	=	PUNCT
ejpam-3823	138	20	{	{	PUNCT
ejpam-3823	138	21	{	{	PUNCT
ejpam-3823	138	22	s	s	NOUN
ejpam-3823	138	23	}	}	PUNCT
ejpam-3823	138	24	,	,	PUNCT
ejpam-3823	138	25	{	{	PUNCT
ejpam-3823	138	26	t	t	NOUN
ejpam-3823	138	27	}	}	PUNCT
ejpam-3823	138	28	,	,	PUNCT
ejpam-3823	138	29	{	{	PUNCT
ejpam-3823	138	30	p	p	X
ejpam-3823	138	31	,	,	PUNCT
ejpam-3823	138	32	q	q	ADJ
ejpam-3823	138	33	,	,	PUNCT
ejpam-3823	138	34	r	r	NOUN
ejpam-3823	138	35	}	}	PUNCT
ejpam-3823	138	36	}	}	PUNCT
ejpam-3823	138	37	and	and	CCONJ
ejpam-3823	138	38	a	a	DET
ejpam-3823	138	39	=	=	X
ejpam-3823	138	40	{	{	PUNCT
ejpam-3823	138	41	p	p	X
ejpam-3823	138	42	,	,	PUNCT
ejpam-3823	138	43	q	q	NOUN
ejpam-3823	138	44	}	}	PUNCT
ejpam-3823	138	45	⊆	⊆	NUM
ejpam-3823	138	46	y	y	NOUN
ejpam-3823	138	47	.	.	PUNCT
ejpam-3823	139	1	then	then	ADV
ejpam-3823	139	2	τ	τ	PROPN
ejpam-3823	139	3	′r(a	′r(a	PROPN
ejpam-3823	139	4	)	)	PUNCT
ejpam-3823	139	5	=	=	PRON
ejpam-3823	139	6	{	{	PUNCT
ejpam-3823	139	7	∅	∅	NOUN
ejpam-3823	139	8	,	,	PUNCT
ejpam-3823	139	9	y	y	PROPN
ejpam-3823	139	10	,	,	PUNCT
ejpam-3823	139	11	{	{	PUNCT
ejpam-3823	140	1	p	p	X
ejpam-3823	140	2	,	,	PUNCT
ejpam-3823	140	3	q	q	ADJ
ejpam-3823	140	4	,	,	PUNCT
ejpam-3823	140	5	r	r	NOUN
ejpam-3823	140	6	}	}	PUNCT
ejpam-3823	140	7	}	}	PUNCT
ejpam-3823	140	8	.	.	PUNCT
ejpam-3823	141	1	let	let	VERB
ejpam-3823	141	2	τ	τ	X
ejpam-3823	141	3	′	′	NUM
ejpam-3823	142	1	=	=	PUNCT
ejpam-3823	142	2	{	{	PUNCT
ejpam-3823	142	3	s	s	NOUN
ejpam-3823	142	4	}	}	PUNCT
ejpam-3823	142	5	,	,	PUNCT
ejpam-3823	142	6	then	then	ADV
ejpam-3823	142	7	µ′	µ′	X
ejpam-3823	142	8	r(a	r(a	PROPN
ejpam-3823	142	9	)	)	PUNCT
ejpam-3823	142	10	=	=	SYM
ejpam-3823	142	11	{	{	PUNCT
ejpam-3823	142	12	∅	∅	NOUN
ejpam-3823	142	13	,	,	PUNCT
ejpam-3823	142	14	y	y	PROPN
ejpam-3823	142	15	,	,	PUNCT
ejpam-3823	142	16	{	{	PUNCT
ejpam-3823	142	17	s	s	NOUN
ejpam-3823	142	18	}	}	PUNCT
ejpam-3823	142	19	,	,	PUNCT
ejpam-3823	142	20	{	{	PUNCT
ejpam-3823	142	21	p	p	X
ejpam-3823	142	22	,	,	PUNCT
ejpam-3823	142	23	q	q	ADJ
ejpam-3823	142	24	,	,	PUNCT
ejpam-3823	142	25	r	r	NOUN
ejpam-3823	142	26	}	}	PUNCT
ejpam-3823	142	27	,	,	PUNCT
ejpam-3823	142	28	{	{	PUNCT
ejpam-3823	142	29	p	p	X
ejpam-3823	142	30	,	,	PUNCT
ejpam-3823	142	31	q	q	ADJ
ejpam-3823	142	32	,	,	PUNCT
ejpam-3823	142	33	r	r	NOUN
ejpam-3823	142	34	,	,	PUNCT
ejpam-3823	142	35	s	s	PART
ejpam-3823	142	36	}	}	PUNCT
ejpam-3823	142	37	}	}	PUNCT
ejpam-3823	142	38	and	and	CCONJ
ejpam-3823	142	39	the	the	DET
ejpam-3823	142	40	micro	micro	ADJ
ejpam-3823	142	41	closed	closed	ADJ
ejpam-3823	142	42	sets	set	NOUN
ejpam-3823	142	43	=	=	SYM
ejpam-3823	142	44	{	{	PUNCT
ejpam-3823	142	45	∅	∅	NOUN
ejpam-3823	142	46	,	,	PUNCT
ejpam-3823	142	47	y	y	PROPN
ejpam-3823	142	48	,	,	PUNCT
ejpam-3823	142	49	{	{	PUNCT
ejpam-3823	142	50	t	t	NOUN
ejpam-3823	142	51	}	}	PUNCT
ejpam-3823	142	52	,	,	PUNCT
ejpam-3823	142	53	{	{	PUNCT
ejpam-3823	142	54	s	s	PROPN
ejpam-3823	142	55	,	,	PUNCT
ejpam-3823	142	56	t	t	PROPN
ejpam-3823	142	57	}	}	PUNCT
ejpam-3823	142	58	,	,	PUNCT
ejpam-3823	142	59	{	{	PUNCT
ejpam-3823	142	60	p	p	X
ejpam-3823	142	61	,	,	PUNCT
ejpam-3823	142	62	q	q	ADJ
ejpam-3823	142	63	,	,	PUNCT
ejpam-3823	142	64	r	r	NOUN
ejpam-3823	142	65	,	,	PUNCT
ejpam-3823	142	66	t	t	NOUN
ejpam-3823	142	67	}	}	PUNCT
ejpam-3823	142	68	}	}	PUNCT
ejpam-3823	142	69	.	.	PUNCT
ejpam-3823	143	1	let	let	VERB
ejpam-3823	143	2	f	f	PRON
ejpam-3823	143	3	:	:	PUNCT
ejpam-3823	143	4	x	x	X
ejpam-3823	143	5	→	→	SYM
ejpam-3823	143	6	y	y	X
ejpam-3823	143	7	be	be	AUX
ejpam-3823	143	8	a	a	DET
ejpam-3823	143	9	function	function	NOUN
ejpam-3823	143	10	defined	define	VERB
ejpam-3823	143	11	as	as	ADP
ejpam-3823	143	12	f(1	f(1	PROPN
ejpam-3823	143	13	)	)	PUNCT
ejpam-3823	144	1	=	=	SYM
ejpam-3823	144	2	s	s	PROPN
ejpam-3823	144	3	,	,	PUNCT
ejpam-3823	144	4	f(2	f(2	PROPN
ejpam-3823	144	5	)	)	PUNCT
ejpam-3823	144	6	=	=	SYM
ejpam-3823	145	1	q	q	X
ejpam-3823	145	2	,	,	PUNCT
ejpam-3823	145	3	f(3	f(3	PROPN
ejpam-3823	145	4	)	)	PUNCT
ejpam-3823	145	5	=	=	SYM
ejpam-3823	146	1	r	r	NOUN
ejpam-3823	146	2	,	,	PUNCT
ejpam-3823	146	3	f(4	f(4	PROPN
ejpam-3823	146	4	)	)	PUNCT
ejpam-3823	146	5	=	=	SYM
ejpam-3823	147	1	p	p	NOUN
ejpam-3823	147	2	,	,	PUNCT
ejpam-3823	147	3	f(5	f(5	PROPN
ejpam-3823	147	4	)	)	PUNCT
ejpam-3823	148	1	=	=	SYM
ejpam-3823	148	2	t.	t.	PROPN
ejpam-3823	148	3	micro	micro	PROPN
ejpam-3823	148	4	closed	close	VERB
ejpam-3823	148	5	set	set	VERB
ejpam-3823	148	6	in	in	ADP
ejpam-3823	148	7	y	y	PROPN
ejpam-3823	148	8	are	be	AUX
ejpam-3823	148	9	{	{	PUNCT
ejpam-3823	148	10	t	t	NOUN
ejpam-3823	148	11	}	}	PUNCT
ejpam-3823	148	12	,	,	PUNCT
ejpam-3823	148	13	{	{	PUNCT
ejpam-3823	148	14	s	s	PROPN
ejpam-3823	148	15	,	,	PUNCT
ejpam-3823	148	16	t	t	PROPN
ejpam-3823	148	17	}	}	PUNCT
ejpam-3823	148	18	,	,	PUNCT
ejpam-3823	148	19	{	{	PUNCT
ejpam-3823	149	1	p	p	X
ejpam-3823	149	2	,	,	PUNCT
ejpam-3823	149	3	q	q	ADJ
ejpam-3823	149	4	,	,	PUNCT
ejpam-3823	149	5	r	r	NOUN
ejpam-3823	149	6	,	,	PUNCT
ejpam-3823	149	7	t	t	NOUN
ejpam-3823	149	8	}	}	PUNCT
ejpam-3823	149	9	and	and	CCONJ
ejpam-3823	149	10	the	the	DET
ejpam-3823	149	11	sets	set	NOUN
ejpam-3823	149	12	{	{	PUNCT
ejpam-3823	149	13	5	5	NUM
ejpam-3823	149	14	}	}	PUNCT
ejpam-3823	149	15	,	,	PUNCT
ejpam-3823	149	16	{	{	PUNCT
ejpam-3823	149	17	{	{	PUNCT
ejpam-3823	149	18	1	1	NUM
ejpam-3823	149	19	,	,	PUNCT
ejpam-3823	149	20	5	5	NUM
ejpam-3823	149	21	}	}	PUNCT
ejpam-3823	149	22	,	,	PUNCT
ejpam-3823	149	23	{	{	PUNCT
ejpam-3823	149	24	2	2	NUM
ejpam-3823	149	25	,	,	PUNCT
ejpam-3823	149	26	3	3	NUM
ejpam-3823	149	27	,	,	PUNCT
ejpam-3823	149	28	4	4	NUM
ejpam-3823	149	29	,	,	PUNCT
ejpam-3823	149	30	5	5	NUM
ejpam-3823	149	31	}	}	PUNCT
ejpam-3823	149	32	are	be	AUX
ejpam-3823	149	33	mic.g	mic.g	NOUN
ejpam-3823	149	34	-	-	PUNCT
ejpam-3823	149	35	closed	close	VERB
ejpam-3823	149	36	sets	set	NOUN
ejpam-3823	149	37	in	in	ADP
ejpam-3823	149	38	x.	x.	NOUN
ejpam-3823	149	39	thus	thus	ADV
ejpam-3823	149	40	f−1(b	f−1(b	PROPN
ejpam-3823	149	41	)	)	PUNCT
ejpam-3823	149	42	is	be	AUX
ejpam-3823	149	43	mic.g	mic.g	NOUN
ejpam-3823	149	44	-	-	PUNCT
ejpam-3823	149	45	closed	closed	ADJ
ejpam-3823	149	46	set	set	NOUN
ejpam-3823	149	47	in	in	ADP
ejpam-3823	149	48	x	x	PUNCT
ejpam-3823	149	49	for	for	ADP
ejpam-3823	149	50	every	every	DET
ejpam-3823	149	51	micro	micro	ADJ
ejpam-3823	149	52	-	-	ADJ
ejpam-3823	149	53	closed	closed	ADJ
ejpam-3823	149	54	set	set	VERB
ejpam-3823	149	55	biny	biny	NOUN
ejpam-3823	149	56	.	.	PUNCT
ejpam-3823	150	1	then	then	ADV
ejpam-3823	150	2	f	f	PROPN
ejpam-3823	150	3	is	be	AUX
ejpam-3823	150	4	micro	micro	ADJ
ejpam-3823	150	5	-	-	ADJ
ejpam-3823	150	6	generalized	generalized	ADJ
ejpam-3823	150	7	continuous	continuous	ADJ
ejpam-3823	150	8	function	function	NOUN
ejpam-3823	150	9	.	.	PUNCT
ejpam-3823	151	1	4.3	4.3	NUM
ejpam-3823	151	2	.	.	PUNCT
ejpam-3823	151	3	definition	definition	NOUN
ejpam-3823	151	4	let	let	VERB
ejpam-3823	151	5	(	(	PUNCT
ejpam-3823	151	6	x	x	NOUN
ejpam-3823	151	7	,	,	PUNCT
ejpam-3823	151	8	τr(a	τr(a	NUM
ejpam-3823	151	9	)	)	PUNCT
ejpam-3823	151	10	,	,	PUNCT
ejpam-3823	151	11	µr(a	µr(a	NUM
ejpam-3823	151	12	)	)	PUNCT
ejpam-3823	151	13	)	)	PUNCT
ejpam-3823	152	1	and	and	CCONJ
ejpam-3823	152	2	(	(	PUNCT
ejpam-3823	152	3	y	y	PROPN
ejpam-3823	152	4	,	,	PUNCT
ejpam-3823	152	5	τ	τ	PROPN
ejpam-3823	152	6	′r(a	′r(a	PROPN
ejpam-3823	152	7	)	)	PUNCT
ejpam-3823	152	8	,	,	PUNCT
ejpam-3823	152	9	µ′	µ′	PROPN
ejpam-3823	152	10	r(a	r(a	PROPN
ejpam-3823	152	11	)	)	PUNCT
ejpam-3823	152	12	)	)	PUNCT
ejpam-3823	152	13	be	be	AUX
ejpam-3823	152	14	two	two	NUM
ejpam-3823	152	15	micro	micro	ADJ
ejpam-3823	152	16	topological	topological	ADJ
ejpam-3823	152	17	spaces	space	NOUN
ejpam-3823	152	18	.	.	PUNCT
ejpam-3823	153	1	a	a	DET
ejpam-3823	153	2	function	function	NOUN
ejpam-3823	153	3	f	f	NOUN
ejpam-3823	153	4	:	:	PUNCT
ejpam-3823	153	5	x	x	X
ejpam-3823	153	6	→	→	SYM
ejpam-3823	153	7	y	y	PROPN
ejpam-3823	153	8	is	be	AUX
ejpam-3823	153	9	called	call	VERB
ejpam-3823	153	10	micro	micro	ADJ
ejpam-3823	153	11	-	-	ADJ
ejpam-3823	153	12	generalized	generalized	ADJ
ejpam-3823	153	13	irresolute	irresolute	ADJ
ejpam-3823	153	14	function	function	NOUN
ejpam-3823	153	15	if	if	SCONJ
ejpam-3823	153	16	f−1(b	f−1(b	PROPN
ejpam-3823	153	17	)	)	PUNCT
ejpam-3823	153	18	is	be	AUX
ejpam-3823	153	19	mic.g	mic.g	NOUN
ejpam-3823	153	20	-	-	PUNCT
ejpam-3823	153	21	closed	closed	ADJ
ejpam-3823	153	22	set	set	NOUN
ejpam-3823	153	23	in	in	ADP
ejpam-3823	153	24	x	x	PUNCT
ejpam-3823	153	25	for	for	ADP
ejpam-3823	153	26	every	every	DET
ejpam-3823	153	27	micro.g	micro.g	NOUN
ejpam-3823	153	28	-	-	PUNCT
ejpam-3823	153	29	closed	closed	ADJ
ejpam-3823	153	30	set	set	VERB
ejpam-3823	153	31	biny	biny	NOUN
ejpam-3823	153	32	.	.	PUNCT
ejpam-3823	154	1	4.4	4.4	NUM
ejpam-3823	154	2	.	.	PUNCT
ejpam-3823	154	3	example	example	NOUN
ejpam-3823	154	4	let	let	VERB
ejpam-3823	154	5	x	x	PUNCT
ejpam-3823	154	6	=	=	PRON
ejpam-3823	154	7	{	{	PUNCT
ejpam-3823	154	8	a	a	DET
ejpam-3823	154	9	,	,	PUNCT
ejpam-3823	154	10	b	b	NOUN
ejpam-3823	154	11	,	,	PUNCT
ejpam-3823	154	12	c	c	NOUN
ejpam-3823	154	13	}	}	PUNCT
ejpam-3823	154	14	with	with	ADP
ejpam-3823	154	15	x	x	X
ejpam-3823	154	16	/	/	SYM
ejpam-3823	154	17	r	r	NOUN
ejpam-3823	154	18	=	=	PUNCT
ejpam-3823	154	19	{	{	PUNCT
ejpam-3823	154	20	{	{	PUNCT
ejpam-3823	154	21	a	a	NOUN
ejpam-3823	154	22	}	}	PUNCT
ejpam-3823	154	23	,	,	PUNCT
ejpam-3823	154	24	{	{	PUNCT
ejpam-3823	154	25	b	b	X
ejpam-3823	154	26	,	,	PUNCT
ejpam-3823	154	27	c	c	NOUN
ejpam-3823	154	28	}	}	PUNCT
ejpam-3823	154	29	}	}	PUNCT
ejpam-3823	154	30	and	and	CCONJ
ejpam-3823	154	31	a	a	DET
ejpam-3823	154	32	=	=	X
ejpam-3823	154	33	{	{	PUNCT
ejpam-3823	154	34	b	b	NOUN
ejpam-3823	154	35	,	,	PUNCT
ejpam-3823	154	36	c	c	NOUN
ejpam-3823	154	37	}	}	PUNCT
ejpam-3823	154	38	⊆	⊆	NUM
ejpam-3823	154	39	x.	x.	NOUN
ejpam-3823	154	40	then	then	ADV
ejpam-3823	154	41	τr(a	τr(a	NUM
ejpam-3823	154	42	)	)	PUNCT
ejpam-3823	155	1	=	=	NOUN
ejpam-3823	155	2	{	{	PUNCT
ejpam-3823	155	3	∅	∅	NOUN
ejpam-3823	155	4	,	,	PUNCT
ejpam-3823	155	5	x	x	PRON
ejpam-3823	155	6	,	,	PUNCT
ejpam-3823	155	7	{	{	PUNCT
ejpam-3823	155	8	b	b	NOUN
ejpam-3823	155	9	,	,	PUNCT
ejpam-3823	155	10	c	c	NOUN
ejpam-3823	155	11	}	}	PUNCT
ejpam-3823	155	12	}	}	PUNCT
ejpam-3823	155	13	.	.	PUNCT
ejpam-3823	156	1	let	let	VERB
ejpam-3823	156	2	µ	µ	X
ejpam-3823	156	3	=	=	PUNCT
ejpam-3823	156	4	{	{	PUNCT
ejpam-3823	156	5	a	a	NOUN
ejpam-3823	156	6	}	}	PUNCT
ejpam-3823	156	7	,	,	PUNCT
ejpam-3823	156	8	then	then	ADV
ejpam-3823	156	9	µr(a	µr(a	PUNCT
ejpam-3823	156	10	)	)	PUNCT
ejpam-3823	156	11	=	=	SYM
ejpam-3823	156	12	{	{	PUNCT
ejpam-3823	156	13	∅	∅	NOUN
ejpam-3823	156	14	,	,	PUNCT
ejpam-3823	156	15	x	x	PRON
ejpam-3823	156	16	,	,	PUNCT
ejpam-3823	156	17	{	{	PUNCT
ejpam-3823	156	18	a	a	PRON
ejpam-3823	156	19	}	}	PUNCT
ejpam-3823	156	20	,	,	PUNCT
ejpam-3823	156	21	{	{	PUNCT
ejpam-3823	156	22	b	b	X
ejpam-3823	156	23	,	,	PUNCT
ejpam-3823	156	24	c	c	NOUN
ejpam-3823	156	25	}	}	PUNCT
ejpam-3823	156	26	.	.	PUNCT
ejpam-3823	157	1	let	let	VERB
ejpam-3823	157	2	y	y	PROPN
ejpam-3823	157	3	=	=	PUNCT
ejpam-3823	157	4	{	{	PUNCT
ejpam-3823	157	5	1	1	NUM
ejpam-3823	157	6	,	,	PUNCT
ejpam-3823	157	7	2	2	NUM
ejpam-3823	157	8	,	,	PUNCT
ejpam-3823	157	9	3	3	NUM
ejpam-3823	157	10	}	}	PUNCT
ejpam-3823	157	11	,	,	PUNCT
ejpam-3823	157	12	with	with	ADP
ejpam-3823	157	13	y	y	NOUN
ejpam-3823	157	14	/	/	SYM
ejpam-3823	157	15	r	r	NOUN
ejpam-3823	157	16	=	=	PUNCT
ejpam-3823	157	17	{	{	PUNCT
ejpam-3823	157	18	{	{	PUNCT
ejpam-3823	157	19	2	2	NUM
ejpam-3823	157	20	}	}	PUNCT
ejpam-3823	157	21	,	,	PUNCT
ejpam-3823	157	22	{	{	PUNCT
ejpam-3823	157	23	1	1	NUM
ejpam-3823	157	24	,	,	PUNCT
ejpam-3823	157	25	3	3	NUM
ejpam-3823	157	26	}	}	PUNCT
ejpam-3823	157	27	}	}	PUNCT
ejpam-3823	157	28	and	and	CCONJ
ejpam-3823	157	29	a	a	DET
ejpam-3823	157	30	=	=	X
ejpam-3823	157	31	{	{	PUNCT
ejpam-3823	157	32	1	1	NUM
ejpam-3823	157	33	,	,	PUNCT
ejpam-3823	157	34	3	3	NUM
ejpam-3823	157	35	}	}	SYM
ejpam-3823	157	36	⊆	⊆	NUM
ejpam-3823	157	37	y	y	PROPN
ejpam-3823	157	38	,	,	PUNCT
ejpam-3823	157	39	then	then	ADV
ejpam-3823	157	40	τr(a	τr(a	NUM
ejpam-3823	157	41	)	)	PUNCT
ejpam-3823	157	42	=	=	SYM
ejpam-3823	157	43	{	{	PUNCT
ejpam-3823	157	44	∅	∅	NOUN
ejpam-3823	157	45	,	,	PUNCT
ejpam-3823	157	46	y	y	PROPN
ejpam-3823	157	47	,	,	PUNCT
ejpam-3823	157	48	{	{	PUNCT
ejpam-3823	157	49	1	1	NUM
ejpam-3823	157	50	,	,	PUNCT
ejpam-3823	157	51	3	3	NUM
ejpam-3823	157	52	}	}	PUNCT
ejpam-3823	157	53	}	}	PUNCT
ejpam-3823	157	54	.	.	PUNCT
ejpam-3823	158	1	let	let	VERB
ejpam-3823	158	2	µ′	µ′	NOUN
ejpam-3823	158	3	=	=	SYM
ejpam-3823	158	4	{	{	PUNCT
ejpam-3823	158	5	2	2	NUM
ejpam-3823	158	6	}	}	PUNCT
ejpam-3823	158	7	,	,	PUNCT
ejpam-3823	158	8	then	then	ADV
ejpam-3823	158	9	µ′	µ′	X
ejpam-3823	158	10	r(a	r(a	PROPN
ejpam-3823	158	11	)	)	PUNCT
ejpam-3823	158	12	=	=	SYM
ejpam-3823	158	13	{	{	PUNCT
ejpam-3823	158	14	∅	∅	NOUN
ejpam-3823	158	15	,	,	PUNCT
ejpam-3823	158	16	y	y	PROPN
ejpam-3823	158	17	,	,	PUNCT
ejpam-3823	158	18	{	{	PUNCT
ejpam-3823	158	19	2	2	NUM
ejpam-3823	158	20	}	}	PUNCT
ejpam-3823	158	21	,	,	PUNCT
ejpam-3823	158	22	{	{	PUNCT
ejpam-3823	158	23	1	1	NUM
ejpam-3823	158	24	,	,	PUNCT
ejpam-3823	158	25	3	3	NUM
ejpam-3823	158	26	}	}	PUNCT
ejpam-3823	158	27	}	}	PUNCT
ejpam-3823	158	28	.	.	PUNCT
ejpam-3823	159	1	let	let	VERB
ejpam-3823	159	2	f	f	PRON
ejpam-3823	159	3	:	:	PUNCT
ejpam-3823	159	4	x	x	X
ejpam-3823	159	5	→	→	SYM
ejpam-3823	159	6	y	y	X
ejpam-3823	159	7	be	be	AUX
ejpam-3823	159	8	a	a	DET
ejpam-3823	159	9	function	function	NOUN
ejpam-3823	159	10	defined	define	VERB
ejpam-3823	159	11	as	as	ADP
ejpam-3823	159	12	f(a	f(a	NOUN
ejpam-3823	159	13	)	)	PUNCT
ejpam-3823	159	14	=	=	SYM
ejpam-3823	159	15	2	2	NUM
ejpam-3823	159	16	,	,	PUNCT
ejpam-3823	159	17	f(b	f(b	PROPN
ejpam-3823	159	18	)	)	PUNCT
ejpam-3823	159	19	=	=	SYM
ejpam-3823	159	20	1	1	NUM
ejpam-3823	159	21	,	,	PUNCT
ejpam-3823	159	22	f(c	f(c	PROPN
ejpam-3823	159	23	)	)	PUNCT
ejpam-3823	159	24	=	=	SYM
ejpam-3823	160	1	3	3	X
ejpam-3823	160	2	.	.	PUNCT
ejpam-3823	161	1	mic.g	mic.g	NOUN
ejpam-3823	161	2	-	-	PUNCT
ejpam-3823	161	3	closed	closed	ADJ
ejpam-3823	161	4	sets	set	NOUN
ejpam-3823	161	5	in	in	ADP
ejpam-3823	161	6	x	x	SYM
ejpam-3823	161	7	are	be	AUX
ejpam-3823	161	8	{	{	PUNCT
ejpam-3823	161	9	a	a	PRON
ejpam-3823	161	10	}	}	PUNCT
ejpam-3823	161	11	,	,	PUNCT
ejpam-3823	161	12	{	{	PUNCT
ejpam-3823	161	13	b	b	NOUN
ejpam-3823	161	14	}	}	PUNCT
ejpam-3823	161	15	,	,	PUNCT
ejpam-3823	161	16	{	{	PUNCT
ejpam-3823	161	17	c	c	NOUN
ejpam-3823	161	18	}	}	PUNCT
ejpam-3823	161	19	,	,	PUNCT
ejpam-3823	161	20	{	{	PUNCT
ejpam-3823	161	21	a	a	PRON
ejpam-3823	161	22	,	,	PUNCT
ejpam-3823	161	23	b	b	NOUN
ejpam-3823	161	24	}	}	PUNCT
ejpam-3823	161	25	,	,	PUNCT
ejpam-3823	161	26	{	{	PUNCT
ejpam-3823	161	27	a	a	X
ejpam-3823	161	28	,	,	PUNCT
ejpam-3823	161	29	c	c	NOUN
ejpam-3823	161	30	}	}	PUNCT
ejpam-3823	161	31	,	,	PUNCT
ejpam-3823	161	32	{	{	PUNCT
ejpam-3823	161	33	b	b	X
ejpam-3823	161	34	,	,	PUNCT
ejpam-3823	161	35	c	c	NOUN
ejpam-3823	161	36	}	}	PUNCT
ejpam-3823	161	37	and	and	CCONJ
ejpam-3823	161	38	mic.g	mic.g	NOUN
ejpam-3823	161	39	-	-	PUNCT
ejpam-3823	161	40	closed	closed	ADJ
ejpam-3823	161	41	sets	set	NOUN
ejpam-3823	161	42	in	in	ADP
ejpam-3823	161	43	y	y	PROPN
ejpam-3823	161	44	are	be	AUX
ejpam-3823	161	45	{	{	PUNCT
ejpam-3823	161	46	1	1	NUM
ejpam-3823	161	47	}	}	PUNCT
ejpam-3823	161	48	,	,	PUNCT
ejpam-3823	161	49	{	{	PUNCT
ejpam-3823	161	50	2	2	NUM
ejpam-3823	161	51	}	}	PUNCT
ejpam-3823	161	52	,	,	PUNCT
ejpam-3823	161	53	{	{	PUNCT
ejpam-3823	161	54	3	3	NUM
ejpam-3823	161	55	}	}	PUNCT
ejpam-3823	161	56	,	,	PUNCT
ejpam-3823	161	57	{	{	PUNCT
ejpam-3823	161	58	1	1	NUM
ejpam-3823	161	59	,	,	PUNCT
ejpam-3823	161	60	2	2	NUM
ejpam-3823	161	61	}	}	PUNCT
ejpam-3823	161	62	,	,	PUNCT
ejpam-3823	161	63	{	{	PUNCT
ejpam-3823	161	64	1	1	NUM
ejpam-3823	161	65	,	,	PUNCT
ejpam-3823	161	66	3	3	NUM
ejpam-3823	161	67	}	}	PUNCT
ejpam-3823	161	68	,	,	PUNCT
ejpam-3823	161	69	{	{	PUNCT
ejpam-3823	161	70	2	2	NUM
ejpam-3823	161	71	,	,	PUNCT
ejpam-3823	161	72	3	3	NUM
ejpam-3823	161	73	}	}	PUNCT
ejpam-3823	161	74	.	.	PUNCT
ejpam-3823	162	1	therefore	therefore	ADV
ejpam-3823	162	2	for	for	ADP
ejpam-3823	162	3	every	every	DET
ejpam-3823	162	4	mic.gclosed	mic.gclose	VERB
ejpam-3823	162	5	set	set	VERB
ejpam-3823	162	6	biny	biny	NOUN
ejpam-3823	162	7	,	,	PUNCT
ejpam-3823	162	8	f−1(b	f−1(b	PROPN
ejpam-3823	162	9	)	)	PUNCT
ejpam-3823	162	10	is	be	AUX
ejpam-3823	162	11	mic.g	mic.g	NOUN
ejpam-3823	162	12	-	-	PUNCT
ejpam-3823	162	13	closed	close	VERB
ejpam-3823	162	14	set	set	NOUN
ejpam-3823	162	15	in	in	ADP
ejpam-3823	162	16	x.	x.	NOUN
ejpam-3823	162	17	then	then	ADV
ejpam-3823	162	18	f	f	PROPN
ejpam-3823	162	19	is	be	AUX
ejpam-3823	162	20	micro	micro	ADJ
ejpam-3823	162	21	-	-	ADJ
ejpam-3823	162	22	generalized	generalized	ADJ
ejpam-3823	162	23	irresolute	irresolute	ADJ
ejpam-3823	162	24	function	function	NOUN
ejpam-3823	162	25	4.5	4.5	NUM
ejpam-3823	162	26	.	.	PUNCT
ejpam-3823	163	1	theorem	theorem	NOUN
ejpam-3823	163	2	let	let	VERB
ejpam-3823	163	3	f	f	NOUN
ejpam-3823	163	4	:	:	PUNCT
ejpam-3823	163	5	x	x	X
ejpam-3823	163	6	→	→	SYM
ejpam-3823	163	7	y	y	X
ejpam-3823	163	8	be	be	AUX
ejpam-3823	163	9	a	a	DET
ejpam-3823	163	10	function	function	NOUN
ejpam-3823	163	11	from	from	ADP
ejpam-3823	163	12	micro	micro	ADJ
ejpam-3823	163	13	topological	topological	ADJ
ejpam-3823	163	14	space	space	NOUN
ejpam-3823	163	15	(	(	PUNCT
ejpam-3823	163	16	x	x	X
ejpam-3823	163	17	,	,	PUNCT
ejpam-3823	163	18	τr(a	τr(a	NUM
ejpam-3823	163	19	)	)	PUNCT
ejpam-3823	163	20	,	,	PUNCT
ejpam-3823	163	21	µr(a	µr(a	NUM
ejpam-3823	163	22	)	)	PUNCT
ejpam-3823	163	23	)	)	PUNCT
ejpam-3823	163	24	to	to	ADP
ejpam-3823	163	25	micro	micro	VERB
ejpam-3823	163	26	topological	topological	ADJ
ejpam-3823	163	27	space	space	NOUN
ejpam-3823	163	28	(	(	PUNCT
ejpam-3823	163	29	y	y	PROPN
ejpam-3823	163	30	,	,	PUNCT
ejpam-3823	163	31	τ	τ	PROPN
ejpam-3823	163	32	′r(a	′r(a	PROPN
ejpam-3823	163	33	)	)	PUNCT
ejpam-3823	163	34	,	,	PUNCT
ejpam-3823	163	35	µ′	µ′	PROPN
ejpam-3823	163	36	r(a	r(a	PROPN
ejpam-3823	163	37	)	)	PUNCT
ejpam-3823	163	38	)	)	PUNCT
ejpam-3823	163	39	.	.	PUNCT
ejpam-3823	164	1	if	if	SCONJ
ejpam-3823	164	2	f	f	PROPN
ejpam-3823	164	3	:	:	PUNCT
ejpam-3823	164	4	x	x	X
ejpam-3823	164	5	→	→	SYM
ejpam-3823	164	6	y	y	PROPN
ejpam-3823	164	7	is	be	AUX
ejpam-3823	164	8	micro	micro	ADV
ejpam-3823	164	9	continuous	continuous	ADJ
ejpam-3823	164	10	function	function	NOUN
ejpam-3823	164	11	[	[	X
ejpam-3823	164	12	12	12	NUM
ejpam-3823	164	13	]	]	PUNCT
ejpam-3823	164	14	,	,	PUNCT
ejpam-3823	164	15	then	then	ADV
ejpam-3823	164	16	f	f	X
ejpam-3823	164	17	:	:	PUNCT
ejpam-3823	164	18	x	x	X
ejpam-3823	164	19	→	→	SYM
ejpam-3823	164	20	y	y	PROPN
ejpam-3823	164	21	is	be	AUX
ejpam-3823	164	22	micro	micro	ADJ
ejpam-3823	164	23	-	-	ADJ
ejpam-3823	164	24	generalized	generalized	ADJ
ejpam-3823	164	25	continuous	continuous	ADJ
ejpam-3823	164	26	function	function	NOUN
ejpam-3823	164	27	.	.	PUNCT
ejpam-3823	165	1	proof	proof	NOUN
ejpam-3823	165	2	:	:	PUNCT
ejpam-3823	165	3	suppose	suppose	VERB
ejpam-3823	165	4	that	that	SCONJ
ejpam-3823	165	5	the	the	DET
ejpam-3823	165	6	function	function	NOUN
ejpam-3823	165	7	f	f	NOUN
ejpam-3823	165	8	:	:	PUNCT
ejpam-3823	165	9	x	x	X
ejpam-3823	165	10	→	→	SYM
ejpam-3823	165	11	y	y	PROPN
ejpam-3823	165	12	is	be	AUX
ejpam-3823	165	13	micro	micro	ADV
ejpam-3823	165	14	continuous	continuous	ADJ
ejpam-3823	165	15	function	function	NOUN
ejpam-3823	165	16	from	from	ADP
ejpam-3823	165	17	micro	micro	ADJ
ejpam-3823	165	18	topological	topological	ADJ
ejpam-3823	165	19	space	space	NOUN
ejpam-3823	165	20	(	(	PUNCT
ejpam-3823	165	21	x	x	X
ejpam-3823	165	22	,	,	PUNCT
ejpam-3823	165	23	τr(a	τr(a	NUM
ejpam-3823	165	24	)	)	PUNCT
ejpam-3823	165	25	,	,	PUNCT
ejpam-3823	165	26	µr(a	µr(a	NUM
ejpam-3823	165	27	)	)	PUNCT
ejpam-3823	165	28	)	)	PUNCT
ejpam-3823	165	29	to	to	ADP
ejpam-3823	165	30	micro	micro	VERB
ejpam-3823	165	31	topological	topological	ADJ
ejpam-3823	165	32	space	space	NOUN
ejpam-3823	165	33	(	(	PUNCT
ejpam-3823	165	34	y	y	PROPN
ejpam-3823	165	35	,	,	PUNCT
ejpam-3823	165	36	τ	τ	PROPN
ejpam-3823	165	37	′r(a	′r(a	PROPN
ejpam-3823	165	38	)	)	PUNCT
ejpam-3823	165	39	,	,	PUNCT
ejpam-3823	165	40	µ′	µ′	PROPN
ejpam-3823	165	41	r(a	r(a	PROPN
ejpam-3823	165	42	)	)	PUNCT
ejpam-3823	165	43	)	)	PUNCT
ejpam-3823	165	44	.	.	PUNCT
ejpam-3823	166	1	that	that	PRON
ejpam-3823	166	2	is	be	AUX
ejpam-3823	166	3	the	the	DET
ejpam-3823	166	4	inverse	inverse	ADJ
ejpam-3823	166	5	image	image	NOUN
ejpam-3823	166	6	of	of	ADP
ejpam-3823	166	7	any	any	DET
ejpam-3823	166	8	micro	micro	NOUN
ejpam-3823	166	9	–	–	PUNCT
ejpam-3823	166	10	closed	closed	ADJ
ejpam-3823	166	11	set	set	VERB
ejpam-3823	166	12	in	in	ADP
ejpam-3823	166	13	(	(	PUNCT
ejpam-3823	166	14	y	y	PROPN
ejpam-3823	166	15	,	,	PUNCT
ejpam-3823	166	16	τ	τ	PROPN
ejpam-3823	166	17	′r(a	′r(a	PROPN
ejpam-3823	166	18	)	)	PUNCT
ejpam-3823	166	19	,	,	PUNCT
ejpam-3823	166	20	µ′	µ′	PROPN
ejpam-3823	166	21	r(a	r(a	PROPN
ejpam-3823	166	22	)	)	PUNCT
ejpam-3823	166	23	)	)	PUNCT
ejpam-3823	166	24	is	be	AUX
ejpam-3823	166	25	micro	micro	ADJ
ejpam-3823	166	26	-	-	ADJ
ejpam-3823	166	27	closed	closed	ADJ
ejpam-3823	166	28	set	set	ADJ
ejpam-3823	166	29	t.	t.	PROPN
ejpam-3823	166	30	h.	h.	PROPN
ejpam-3823	166	31	jasim	jasim	PROPN
ejpam-3823	166	32	,	,	PUNCT
ejpam-3823	166	33	s.	s.	PROPN
ejpam-3823	166	34	s.	s.	PROPN
ejpam-3823	166	35	mohsen	mohsen	PROPN
ejpam-3823	166	36	,	,	PUNCT
ejpam-3823	166	37	k.	k.	PROPN
ejpam-3823	166	38	s.	s.	PROPN
ejpam-3823	166	39	eke	eke	PROPN
ejpam-3823	166	40	/	/	SYM
ejpam-3823	166	41	eur	eur	PROPN
ejpam-3823	166	42	.	.	PUNCT
ejpam-3823	167	1	j.	j.	PROPN
ejpam-3823	167	2	pure	pure	PROPN
ejpam-3823	167	3	appl	appl	PROPN
ejpam-3823	167	4	.	.	PROPN
ejpam-3823	167	5	math	math	PROPN
ejpam-3823	167	6	,	,	PUNCT
ejpam-3823	167	7	14	14	NUM
ejpam-3823	167	8	(	(	PUNCT
ejpam-3823	167	9	4	4	NUM
ejpam-3823	167	10	)	)	PUNCT
ejpam-3823	167	11	(	(	PUNCT
ejpam-3823	167	12	2021	2021	NUM
ejpam-3823	167	13	)	)	PUNCT
ejpam-3823	167	14	,	,	PUNCT
ejpam-3823	167	15	1507	1507	NUM
ejpam-3823	167	16	-	-	SYM
ejpam-3823	167	17	1516	1516	NUM
ejpam-3823	167	18	1514	1514	NUM
ejpam-3823	167	19	in	in	ADP
ejpam-3823	167	20	(	(	PUNCT
ejpam-3823	167	21	x	x	NOUN
ejpam-3823	167	22	,	,	PUNCT
ejpam-3823	167	23	τr(a	τr(a	NUM
ejpam-3823	167	24	)	)	PUNCT
ejpam-3823	167	25	,	,	PUNCT
ejpam-3823	167	26	µr(a	µr(a	NUM
ejpam-3823	167	27	)	)	PUNCT
ejpam-3823	167	28	)	)	PUNCT
ejpam-3823	167	29	.	.	PUNCT
ejpam-3823	168	1	let	let	VERB
ejpam-3823	168	2	b	b	X
ejpam-3823	168	3	be	be	AUX
ejpam-3823	168	4	a	a	DET
ejpam-3823	168	5	micro	micro	ADJ
ejpam-3823	168	6	-	-	ADJ
ejpam-3823	168	7	closed	closed	ADJ
ejpam-3823	168	8	set	set	NOUN
ejpam-3823	168	9	in	in	ADP
ejpam-3823	168	10	(	(	PUNCT
ejpam-3823	168	11	y	y	PROPN
ejpam-3823	168	12	,	,	PUNCT
ejpam-3823	168	13	τ	τ	PROPN
ejpam-3823	168	14	′r(a	′r(a	PROPN
ejpam-3823	168	15	)	)	PUNCT
ejpam-3823	168	16	,	,	PUNCT
ejpam-3823	168	17	µ′	µ′	PROPN
ejpam-3823	168	18	r(a	r(a	PROPN
ejpam-3823	168	19	)	)	PUNCT
ejpam-3823	168	20	)	)	PUNCT
ejpam-3823	168	21	.	.	PUNCT
ejpam-3823	169	1	then	then	ADV
ejpam-3823	169	2	f−1(b	f−1(b	PROPN
ejpam-3823	169	3	)	)	PUNCT
ejpam-3823	169	4	is	be	AUX
ejpam-3823	169	5	micro	micro	ADJ
ejpam-3823	169	6	-	-	ADJ
ejpam-3823	169	7	closed	closed	ADJ
ejpam-3823	169	8	set	set	NOUN
ejpam-3823	169	9	in	in	ADP
ejpam-3823	169	10	(	(	PUNCT
ejpam-3823	169	11	x	x	NOUN
ejpam-3823	169	12	,	,	PUNCT
ejpam-3823	169	13	τr(a	τr(a	NUM
ejpam-3823	169	14	)	)	PUNCT
ejpam-3823	169	15	,	,	PUNCT
ejpam-3823	169	16	µr(a	µr(a	NUM
ejpam-3823	169	17	)	)	PUNCT
ejpam-3823	169	18	)	)	PUNCT
ejpam-3823	169	19	.	.	PUNCT
ejpam-3823	170	1	now	now	ADV
ejpam-3823	170	2	by	by	ADP
ejpam-3823	170	3	remark	remark	NOUN
ejpam-3823	170	4	3.5	3.5	NUM
ejpam-3823	170	5	(	(	PUNCT
ejpam-3823	170	6	every	every	DET
ejpam-3823	170	7	micro	micro	NOUN
ejpam-3823	170	8	closed	close	VERB
ejpam-3823	170	9	set	set	NOUN
ejpam-3823	170	10	is	be	AUX
ejpam-3823	170	11	micro	micro	ADJ
ejpam-3823	170	12	-	-	ADJ
ejpam-3823	170	13	generalized	generalized	ADJ
ejpam-3823	170	14	closed	close	VERB
ejpam-3823	170	15	set	set	NOUN
ejpam-3823	170	16	)	)	PUNCT
ejpam-3823	170	17	we	we	PRON
ejpam-3823	170	18	get	get	VERB
ejpam-3823	170	19	,	,	PUNCT
ejpam-3823	170	20	f−1(b	f−1(b	PROPN
ejpam-3823	170	21	)	)	PUNCT
ejpam-3823	170	22	is	be	AUX
ejpam-3823	170	23	micro	micro	ADJ
ejpam-3823	170	24	-	-	ADJ
ejpam-3823	170	25	generalized	generalize	VERB
ejpam-3823	170	26	closed	close	VERB
ejpam-3823	170	27	set	set	VERB
ejpam-3823	170	28	in	in	ADP
ejpam-3823	170	29	(	(	PUNCT
ejpam-3823	170	30	x	x	NOUN
ejpam-3823	170	31	,	,	PUNCT
ejpam-3823	170	32	τr(a	τr(a	NUM
ejpam-3823	170	33	)	)	PUNCT
ejpam-3823	170	34	,	,	PUNCT
ejpam-3823	170	35	µr(a	µr(a	NUM
ejpam-3823	170	36	)	)	PUNCT
ejpam-3823	170	37	)	)	PUNCT
ejpam-3823	170	38	.	.	PUNCT
ejpam-3823	171	1	thus	thus	ADV
ejpam-3823	171	2	f	f	X
ejpam-3823	171	3	:	:	PUNCT
ejpam-3823	171	4	x	x	X
ejpam-3823	171	5	→	→	SYM
ejpam-3823	171	6	y	y	PROPN
ejpam-3823	171	7	is	be	AUX
ejpam-3823	171	8	micro	micro	ADJ
ejpam-3823	171	9	-	-	ADJ
ejpam-3823	171	10	generalized	generalized	ADJ
ejpam-3823	171	11	continuous	continuous	ADJ
ejpam-3823	171	12	function	function	NOUN
ejpam-3823	171	13	.	.	PUNCT
ejpam-3823	172	1	4.6	4.6	NUM
ejpam-3823	172	2	.	.	PUNCT
ejpam-3823	172	3	theorem	theorem	VERB
ejpam-3823	172	4	every	every	DET
ejpam-3823	172	5	micro	micro	ADJ
ejpam-3823	172	6	-	-	ADJ
ejpam-3823	172	7	generalized	generalized	ADJ
ejpam-3823	172	8	irresolute	irresolute	ADJ
ejpam-3823	172	9	function	function	NOUN
ejpam-3823	172	10	is	be	AUX
ejpam-3823	172	11	micro	micro	ADJ
ejpam-3823	172	12	-	-	ADJ
ejpam-3823	172	13	generalized	generalized	ADJ
ejpam-3823	172	14	continuous	continuous	ADJ
ejpam-3823	172	15	function	function	NOUN
ejpam-3823	172	16	.	.	PUNCT
ejpam-3823	173	1	proof	proof	NOUN
ejpam-3823	173	2	:	:	PUNCT
ejpam-3823	173	3	suppose	suppose	VERB
ejpam-3823	173	4	that	that	SCONJ
ejpam-3823	173	5	the	the	DET
ejpam-3823	173	6	function	function	NOUN
ejpam-3823	173	7	f	f	NOUN
ejpam-3823	173	8	:	:	PUNCT
ejpam-3823	173	9	x	x	X
ejpam-3823	173	10	→	→	SYM
ejpam-3823	173	11	y	y	PROPN
ejpam-3823	173	12	is	be	AUX
ejpam-3823	173	13	micro	micro	ADJ
ejpam-3823	173	14	-	-	ADJ
ejpam-3823	173	15	generalized	generalized	ADJ
ejpam-3823	173	16	irresolute	irresolute	ADJ
ejpam-3823	173	17	function	function	NOUN
ejpam-3823	173	18	from	from	ADP
ejpam-3823	173	19	micro	micro	ADJ
ejpam-3823	173	20	topological	topological	ADJ
ejpam-3823	173	21	space	space	NOUN
ejpam-3823	173	22	(	(	PUNCT
ejpam-3823	173	23	x	x	X
ejpam-3823	173	24	,	,	PUNCT
ejpam-3823	173	25	τr(a	τr(a	NUM
ejpam-3823	173	26	)	)	PUNCT
ejpam-3823	173	27	,	,	PUNCT
ejpam-3823	173	28	µr(a	µr(a	NUM
ejpam-3823	173	29	)	)	PUNCT
ejpam-3823	173	30	)	)	PUNCT
ejpam-3823	173	31	to	to	ADP
ejpam-3823	173	32	micro	micro	VERB
ejpam-3823	173	33	topological	topological	ADJ
ejpam-3823	173	34	space	space	NOUN
ejpam-3823	173	35	(	(	PUNCT
ejpam-3823	173	36	y	y	PROPN
ejpam-3823	173	37	,	,	PUNCT
ejpam-3823	173	38	τ	τ	PROPN
ejpam-3823	173	39	′r(a	′r(a	PROPN
ejpam-3823	173	40	)	)	PUNCT
ejpam-3823	173	41	,	,	PUNCT
ejpam-3823	173	42	µ′	µ′	PROPN
ejpam-3823	173	43	r(a	r(a	PROPN
ejpam-3823	173	44	)	)	PUNCT
ejpam-3823	173	45	)	)	PUNCT
ejpam-3823	173	46	.	.	PUNCT
ejpam-3823	174	1	we	we	PRON
ejpam-3823	174	2	want	want	VERB
ejpam-3823	174	3	to	to	PART
ejpam-3823	174	4	prove	prove	VERB
ejpam-3823	174	5	that	that	PRON
ejpam-3823	174	6	f	f	X
ejpam-3823	174	7	:	:	PUNCT
ejpam-3823	174	8	x	x	X
ejpam-3823	174	9	→	→	SYM
ejpam-3823	174	10	y	y	PROPN
ejpam-3823	174	11	is	be	AUX
ejpam-3823	174	12	micro	micro	ADJ
ejpam-3823	174	13	-	-	ADJ
ejpam-3823	174	14	generalized	generalized	ADJ
ejpam-3823	174	15	continuous	continuous	ADJ
ejpam-3823	174	16	function	function	NOUN
ejpam-3823	174	17	.	.	PUNCT
ejpam-3823	175	1	let	let	VERB
ejpam-3823	175	2	b	b	X
ejpam-3823	175	3	be	be	AUX
ejpam-3823	175	4	microclosed	microclose	VERB
ejpam-3823	175	5	set	set	VERB
ejpam-3823	175	6	in	in	ADP
ejpam-3823	175	7	(	(	PUNCT
ejpam-3823	175	8	y	y	PROPN
ejpam-3823	175	9	,	,	PUNCT
ejpam-3823	175	10	τ	τ	PROPN
ejpam-3823	175	11	′r(a	′r(a	PROPN
ejpam-3823	175	12	)	)	PUNCT
ejpam-3823	175	13	,	,	PUNCT
ejpam-3823	175	14	µ′	µ′	PROPN
ejpam-3823	175	15	r(a	r(a	PROPN
ejpam-3823	175	16	)	)	PUNCT
ejpam-3823	175	17	)	)	PUNCT
ejpam-3823	175	18	then	then	ADV
ejpam-3823	175	19	f−1(b	f−1(b	PROPN
ejpam-3823	175	20	)	)	PUNCT
ejpam-3823	175	21	is	be	AUX
ejpam-3823	175	22	micro	micro	ADJ
ejpam-3823	175	23	-	-	ADJ
ejpam-3823	175	24	closed	closed	ADJ
ejpam-3823	175	25	set	set	NOUN
ejpam-3823	175	26	in	in	ADP
ejpam-3823	175	27	(	(	PUNCT
ejpam-3823	175	28	x	x	NOUN
ejpam-3823	175	29	,	,	PUNCT
ejpam-3823	175	30	τr(a	τr(a	NUM
ejpam-3823	175	31	)	)	PUNCT
ejpam-3823	175	32	,	,	PUNCT
ejpam-3823	175	33	µr(a	µr(a	NUM
ejpam-3823	175	34	)	)	PUNCT
ejpam-3823	175	35	)	)	PUNCT
ejpam-3823	175	36	and	and	CCONJ
ejpam-3823	175	37	by	by	ADP
ejpam-3823	175	38	remark	remark	NOUN
ejpam-3823	175	39	3.5	3.5	NUM
ejpam-3823	175	40	(	(	PUNCT
ejpam-3823	175	41	every	every	DET
ejpam-3823	175	42	micro	micro	NOUN
ejpam-3823	175	43	closed	close	VERB
ejpam-3823	175	44	set	set	NOUN
ejpam-3823	175	45	is	be	AUX
ejpam-3823	175	46	micro	micro	ADJ
ejpam-3823	175	47	-	-	ADJ
ejpam-3823	175	48	generalized	generalized	ADJ
ejpam-3823	175	49	closed	close	VERB
ejpam-3823	175	50	set	set	NOUN
ejpam-3823	175	51	)	)	PUNCT
ejpam-3823	175	52	we	we	PRON
ejpam-3823	175	53	get	get	VERB
ejpam-3823	175	54	,	,	PUNCT
ejpam-3823	175	55	f−1(b	f−1(b	PROPN
ejpam-3823	175	56	)	)	PUNCT
ejpam-3823	175	57	is	be	AUX
ejpam-3823	175	58	micro	micro	ADJ
ejpam-3823	175	59	-	-	ADJ
ejpam-3823	175	60	generalized	generalize	VERB
ejpam-3823	175	61	closed	close	VERB
ejpam-3823	175	62	set	set	VERB
ejpam-3823	175	63	in	in	ADP
ejpam-3823	175	64	(	(	PUNCT
ejpam-3823	175	65	x	x	NOUN
ejpam-3823	175	66	,	,	PUNCT
ejpam-3823	175	67	τr(a	τr(a	NUM
ejpam-3823	175	68	)	)	PUNCT
ejpam-3823	175	69	,	,	PUNCT
ejpam-3823	175	70	µr(a	µr(a	NUM
ejpam-3823	175	71	)	)	PUNCT
ejpam-3823	175	72	)	)	PUNCT
ejpam-3823	175	73	.	.	PUNCT
ejpam-3823	176	1	thus	thus	ADV
ejpam-3823	176	2	f	f	X
ejpam-3823	176	3	:	:	PUNCT
ejpam-3823	176	4	x	x	X
ejpam-3823	176	5	→	→	SYM
ejpam-3823	176	6	y	y	PROPN
ejpam-3823	176	7	is	be	AUX
ejpam-3823	176	8	micro	micro	ADJ
ejpam-3823	176	9	-	-	ADJ
ejpam-3823	176	10	generalized	generalized	ADJ
ejpam-3823	176	11	continuous	continuous	ADJ
ejpam-3823	176	12	function	function	NOUN
ejpam-3823	176	13	.	.	PUNCT
ejpam-3823	177	1	4.7	4.7	NUM
ejpam-3823	177	2	.	.	PUNCT
ejpam-3823	178	1	definition	definition	NOUN
ejpam-3823	178	2	let	let	VERB
ejpam-3823	178	3	(	(	PUNCT
ejpam-3823	178	4	x	x	NOUN
ejpam-3823	178	5	,	,	PUNCT
ejpam-3823	178	6	τr(a	τr(a	NUM
ejpam-3823	178	7	)	)	PUNCT
ejpam-3823	178	8	,	,	PUNCT
ejpam-3823	178	9	µr(a	µr(a	NUM
ejpam-3823	178	10	)	)	PUNCT
ejpam-3823	178	11	)	)	PUNCT
ejpam-3823	179	1	and	and	CCONJ
ejpam-3823	179	2	(	(	PUNCT
ejpam-3823	179	3	y	y	PROPN
ejpam-3823	179	4	,	,	PUNCT
ejpam-3823	179	5	τ	τ	PROPN
ejpam-3823	179	6	′r(a	′r(a	PROPN
ejpam-3823	179	7	)	)	PUNCT
ejpam-3823	179	8	,	,	PUNCT
ejpam-3823	179	9	µ′	µ′	PROPN
ejpam-3823	179	10	r(a	r(a	PROPN
ejpam-3823	179	11	)	)	PUNCT
ejpam-3823	179	12	)	)	PUNCT
ejpam-3823	179	13	be	be	AUX
ejpam-3823	179	14	two	two	NUM
ejpam-3823	179	15	micro	micro	ADJ
ejpam-3823	179	16	topological	topological	ADJ
ejpam-3823	179	17	spaces	space	NOUN
ejpam-3823	179	18	.	.	PUNCT
ejpam-3823	180	1	a	a	DET
ejpam-3823	180	2	function	function	NOUN
ejpam-3823	180	3	f	f	NOUN
ejpam-3823	180	4	:	:	PUNCT
ejpam-3823	180	5	x	x	X
ejpam-3823	180	6	→	→	SYM
ejpam-3823	180	7	y	y	PROPN
ejpam-3823	180	8	is	be	AUX
ejpam-3823	180	9	called	call	VERB
ejpam-3823	180	10	micro	micro	ADJ
ejpam-3823	180	11	-	-	ADJ
ejpam-3823	180	12	generalized	generalized	ADJ
ejpam-3823	180	13	continuous	continuous	ADJ
ejpam-3823	180	14	function	function	NOUN
ejpam-3823	180	15	at	at	ADP
ejpam-3823	180	16	a	a	DET
ejpam-3823	180	17	point	point	NOUN
ejpam-3823	180	18	c	c	NOUN
ejpam-3823	180	19	∈	∈	PROPN
ejpam-3823	180	20	x	x	INTJ
ejpam-3823	180	21	if	if	SCONJ
ejpam-3823	180	22	for	for	ADP
ejpam-3823	180	23	every	every	DET
ejpam-3823	180	24	micro	micro	ADJ
ejpam-3823	180	25	-	-	ADJ
ejpam-3823	180	26	closed	closed	ADJ
ejpam-3823	180	27	set	set	NOUN
ejpam-3823	180	28	g	g	NOUN
ejpam-3823	180	29	containing	contain	VERB
ejpam-3823	180	30	f(c)iny	f(c)iny	NOUN
ejpam-3823	180	31	,	,	PUNCT
ejpam-3823	180	32	there	there	PRON
ejpam-3823	180	33	are	be	VERB
ejpam-3823	180	34	exist	exist	VERB
ejpam-3823	180	35	a	a	DET
ejpam-3823	180	36	mic.g	mic.g	PROPN
ejpam-3823	180	37	-	-	PUNCT
ejpam-3823	180	38	closed	closed	ADJ
ejpam-3823	180	39	b	b	NOUN
ejpam-3823	180	40	containing	contain	VERB
ejpam-3823	180	41	cinx	cinx	ADP
ejpam-3823	180	42	such	such	ADJ
ejpam-3823	180	43	that	that	DET
ejpam-3823	180	44	f(b	f(b	PROPN
ejpam-3823	180	45	)	)	PUNCT
ejpam-3823	180	46	⊆	⊆	NUM
ejpam-3823	180	47	g.	g.	PROPN
ejpam-3823	180	48	4.8	4.8	NUM
ejpam-3823	180	49	.	.	PUNCT
ejpam-3823	181	1	theorem	theorem	VERB
ejpam-3823	181	2	let	let	VERB
ejpam-3823	181	3	(	(	PUNCT
ejpam-3823	181	4	x	x	NOUN
ejpam-3823	181	5	,	,	PUNCT
ejpam-3823	181	6	τr(a	τr(a	NUM
ejpam-3823	181	7	)	)	PUNCT
ejpam-3823	181	8	,	,	PUNCT
ejpam-3823	181	9	µr(a	µr(a	NUM
ejpam-3823	181	10	)	)	PUNCT
ejpam-3823	181	11	)	)	PUNCT
ejpam-3823	182	1	and	and	CCONJ
ejpam-3823	182	2	(	(	PUNCT
ejpam-3823	182	3	y	y	PROPN
ejpam-3823	182	4	,	,	PUNCT
ejpam-3823	182	5	τ	τ	PROPN
ejpam-3823	182	6	′r(a	′r(a	PROPN
ejpam-3823	182	7	)	)	PUNCT
ejpam-3823	182	8	,	,	PUNCT
ejpam-3823	182	9	µ′	µ′	PROPN
ejpam-3823	182	10	r(a	r(a	PROPN
ejpam-3823	182	11	)	)	PUNCT
ejpam-3823	182	12	)	)	PUNCT
ejpam-3823	182	13	be	be	AUX
ejpam-3823	182	14	two	two	NUM
ejpam-3823	182	15	micro	micro	ADJ
ejpam-3823	182	16	topological	topological	ADJ
ejpam-3823	182	17	spaces	space	NOUN
ejpam-3823	182	18	.	.	PUNCT
ejpam-3823	183	1	a	a	DET
ejpam-3823	183	2	function	function	NOUN
ejpam-3823	183	3	f	f	NOUN
ejpam-3823	183	4	:	:	PUNCT
ejpam-3823	183	5	x	x	X
ejpam-3823	183	6	→	→	SYM
ejpam-3823	183	7	y	y	PROPN
ejpam-3823	183	8	is	be	AUX
ejpam-3823	183	9	micro	micro	ADJ
ejpam-3823	183	10	-	-	ADJ
ejpam-3823	183	11	generalized	generalized	ADJ
ejpam-3823	183	12	continuous	continuous	ADJ
ejpam-3823	183	13	function	function	NOUN
ejpam-3823	183	14	if	if	SCONJ
ejpam-3823	183	15	and	and	CCONJ
ejpam-3823	183	16	only	only	ADV
ejpam-3823	183	17	if	if	SCONJ
ejpam-3823	183	18	f	f	PROPN
ejpam-3823	183	19	is	be	AUX
ejpam-3823	183	20	microgeneralized	microgeneralize	VERB
ejpam-3823	183	21	continuous	continuous	ADJ
ejpam-3823	183	22	function	function	NOUN
ejpam-3823	183	23	at	at	ADP
ejpam-3823	183	24	each	each	DET
ejpam-3823	183	25	point	point	NOUN
ejpam-3823	183	26	of	of	ADP
ejpam-3823	183	27	x.	x.	NOUN
ejpam-3823	183	28	proof	proof	NOUN
ejpam-3823	183	29	:	:	PUNCT
ejpam-3823	183	30	let	let	VERB
ejpam-3823	183	31	f	f	PRON
ejpam-3823	183	32	:	:	PUNCT
ejpam-3823	183	33	x	x	X
ejpam-3823	183	34	→	→	SYM
ejpam-3823	183	35	y	y	PROPN
ejpam-3823	183	36	be	be	AUX
ejpam-3823	183	37	mic.g	mic.g	NOUN
ejpam-3823	183	38	-	-	PUNCT
ejpam-3823	183	39	continuous	continuous	ADJ
ejpam-3823	183	40	.	.	PUNCT
ejpam-3823	184	1	let	let	VERB
ejpam-3823	184	2	c	c	NOUN
ejpam-3823	184	3	∈	∈	VERB
ejpam-3823	184	4	x	x	X
ejpam-3823	184	5	,	,	PUNCT
ejpam-3823	184	6	and	and	CCONJ
ejpam-3823	184	7	g	g	PROPN
ejpam-3823	184	8	be	be	AUX
ejpam-3823	184	9	a	a	DET
ejpam-3823	184	10	micro	micro	ADJ
ejpam-3823	184	11	-	-	ADJ
ejpam-3823	184	12	closed	closed	ADJ
ejpam-3823	184	13	set	set	NOUN
ejpam-3823	184	14	in	in	ADP
ejpam-3823	184	15	y	y	NOUN
ejpam-3823	184	16	containing	contain	VERB
ejpam-3823	184	17	f(c	f(c	PROPN
ejpam-3823	184	18	)	)	PUNCT
ejpam-3823	184	19	.	.	PUNCT
ejpam-3823	185	1	since	since	SCONJ
ejpam-3823	185	2	f	f	PROPN
ejpam-3823	185	3	is	be	AUX
ejpam-3823	185	4	mic.g	mic.g	NOUN
ejpam-3823	185	5	-	-	PUNCT
ejpam-3823	185	6	continuous	continuous	ADJ
ejpam-3823	185	7	,	,	PUNCT
ejpam-3823	185	8	f−1(g	f−1(g	PROPN
ejpam-3823	185	9	)	)	PUNCT
ejpam-3823	185	10	is	be	AUX
ejpam-3823	185	11	mic.g	mic.g	NOUN
ejpam-3823	185	12	-	-	PUNCT
ejpam-3823	185	13	closed	closed	ADJ
ejpam-3823	185	14	in	in	ADP
ejpam-3823	185	15	x	x	PUNCT
ejpam-3823	185	16	containing	contain	VERB
ejpam-3823	185	17	c.	c.	NOUN
ejpam-3823	185	18	let	let	VERB
ejpam-3823	185	19	b	b	PROPN
ejpam-3823	185	20	=	=	SYM
ejpam-3823	185	21	f−1(g	f−1(g	PROPN
ejpam-3823	185	22	)	)	PUNCT
ejpam-3823	185	23	,	,	PUNCT
ejpam-3823	185	24	then	then	ADV
ejpam-3823	185	25	f(g	f(g	NOUN
ejpam-3823	185	26	)	)	PUNCT
ejpam-3823	185	27	f(b	f(b	PROPN
ejpam-3823	185	28	)	)	PUNCT
ejpam-3823	185	29	⊆	⊆	NUM
ejpam-3823	185	30	g	g	NOUN
ejpam-3823	185	31	,	,	PUNCT
ejpam-3823	185	32	and	and	CCONJ
ejpam-3823	185	33	f(a	f(a	NOUN
ejpam-3823	185	34	)	)	PUNCT
ejpam-3823	185	35	∈	∈	PROPN
ejpam-3823	185	36	b.	b.	NOUN
ejpam-3823	186	1	hence	hence	ADV
ejpam-3823	186	2	f	f	PROPN
ejpam-3823	186	3	is	be	AUX
ejpam-3823	186	4	continuous	continuous	ADJ
ejpam-3823	186	5	at	at	ADP
ejpam-3823	186	6	c.	c.	NOUN
ejpam-3823	186	7	conversely	conversely	ADV
ejpam-3823	186	8	,	,	PUNCT
ejpam-3823	186	9	suppose	suppose	VERB
ejpam-3823	186	10	f	f	PROPN
ejpam-3823	186	11	is	be	AUX
ejpam-3823	186	12	mic.g	mic.g	NOUN
ejpam-3823	186	13	-	-	ADJ
ejpam-3823	186	14	continuous	continuous	ADJ
ejpam-3823	186	15	at	at	ADP
ejpam-3823	186	16	each	each	DET
ejpam-3823	186	17	point	point	NOUN
ejpam-3823	186	18	of	of	ADP
ejpam-3823	186	19	x.	x.	NOUN
ejpam-3823	186	20	let	let	VERB
ejpam-3823	186	21	g	g	NOUN
ejpam-3823	186	22	be	be	AUX
ejpam-3823	186	23	micro	micro	ADJ
ejpam-3823	186	24	-	-	ADJ
ejpam-3823	186	25	closed	closed	ADJ
ejpam-3823	186	26	set	set	NOUN
ejpam-3823	186	27	in	in	ADP
ejpam-3823	186	28	y	y	PROPN
ejpam-3823	186	29	.	.	PUNCT
ejpam-3823	187	1	if	if	SCONJ
ejpam-3823	187	2	f−1(g	f−1(g	NUM
ejpam-3823	187	3	)	)	PUNCT
ejpam-3823	188	1	=	=	PUNCT
ejpam-3823	188	2	∅	∅	NOUN
ejpam-3823	188	3	then	then	ADV
ejpam-3823	188	4	it	it	PRON
ejpam-3823	188	5	is	be	AUX
ejpam-3823	188	6	mic.g	mic.g	NOUN
ejpam-3823	188	7	-	-	PUNCT
ejpam-3823	188	8	closed	closed	ADJ
ejpam-3823	188	9	.	.	PUNCT
ejpam-3823	189	1	so	so	ADV
ejpam-3823	189	2	let	let	VERB
ejpam-3823	189	3	f−1(g	f−1(g	NUM
ejpam-3823	189	4	)	)	PUNCT
ejpam-3823	189	5	̸=	̸=	PROPN
ejpam-3823	189	6	∅.	∅.	ADV
ejpam-3823	189	7	take	take	VERB
ejpam-3823	189	8	any	any	DET
ejpam-3823	189	9	c	c	PROPN
ejpam-3823	189	10	∈	∈	PROPN
ejpam-3823	189	11	f−1(g	f−1(g	PROPN
ejpam-3823	189	12	)	)	PUNCT
ejpam-3823	189	13	,	,	PUNCT
ejpam-3823	189	14	then	then	ADV
ejpam-3823	189	15	f(c	f(c	PROPN
ejpam-3823	189	16	)	)	PUNCT
ejpam-3823	189	17	∈	∈	PROPN
ejpam-3823	189	18	g.	g.	NOUN
ejpam-3823	189	19	since	since	SCONJ
ejpam-3823	189	20	f	f	PROPN
ejpam-3823	189	21	is	be	AUX
ejpam-3823	189	22	mic.g	mic.g	NOUN
ejpam-3823	189	23	-	-	ADJ
ejpam-3823	189	24	continuous	continuous	ADJ
ejpam-3823	189	25	at	at	ADP
ejpam-3823	189	26	each	each	DET
ejpam-3823	189	27	point	point	NOUN
ejpam-3823	189	28	there	there	PRON
ejpam-3823	189	29	exist	exist	VERB
ejpam-3823	189	30	a	a	DET
ejpam-3823	189	31	mic.g	mic.g	PROPN
ejpam-3823	189	32	-	-	PUNCT
ejpam-3823	189	33	closed	close	VERB
ejpam-3823	189	34	set	set	VERB
ejpam-3823	189	35	bc	bc	NOUN
ejpam-3823	189	36	containing	contain	VERB
ejpam-3823	189	37	c	c	PROPN
ejpam-3823	189	38	such	such	ADJ
ejpam-3823	189	39	that	that	DET
ejpam-3823	189	40	f(bc	f(bc	NUM
ejpam-3823	189	41	)	)	PUNCT
ejpam-3823	189	42	⊆	⊆	NUM
ejpam-3823	189	43	g.	g.	NOUN
ejpam-3823	189	44	let	let	VERB
ejpam-3823	189	45	b	b	NOUN
ejpam-3823	189	46	=	=	SYM
ejpam-3823	189	47	(	(	PUNCT
ejpam-3823	189	48	bc|c	bc|c	NOUN
ejpam-3823	189	49	∈	∈	PROPN
ejpam-3823	189	50	f−1(g	f−1(g	PROPN
ejpam-3823	189	51	)	)	PUNCT
ejpam-3823	189	52	)	)	PUNCT
ejpam-3823	189	53	.	.	PUNCT
ejpam-3823	190	1	claim	claim	NOUN
ejpam-3823	190	2	:	:	PUNCT
ejpam-3823	190	3	b	b	X
ejpam-3823	190	4	=	=	SYM
ejpam-3823	190	5	f−1(g	f−1(g	PROPN
ejpam-3823	190	6	)	)	PUNCT
ejpam-3823	190	7	if	if	SCONJ
ejpam-3823	190	8	a	a	DET
ejpam-3823	190	9	∈	∈	PROPN
ejpam-3823	190	10	f−1(g	f−1(g	NOUN
ejpam-3823	190	11	)	)	PUNCT
ejpam-3823	190	12	then	then	ADV
ejpam-3823	190	13	a	a	DET
ejpam-3823	190	14	∈	∈	PROPN
ejpam-3823	190	15	ba	ba	PROPN
ejpam-3823	190	16	⊆	⊆	NUM
ejpam-3823	190	17	b.	b.	PROPN
ejpam-3823	190	18	hence	hence	ADV
ejpam-3823	190	19	f−1(g	f−1(g	PROPN
ejpam-3823	190	20	)	)	PUNCT
ejpam-3823	190	21	⊆	⊆	NUM
ejpam-3823	190	22	b.	b.	NOUN
ejpam-3823	190	23	on	on	ADP
ejpam-3823	190	24	the	the	DET
ejpam-3823	190	25	other	other	ADJ
ejpam-3823	190	26	hand	hand	NOUN
ejpam-3823	190	27	,	,	PUNCT
ejpam-3823	190	28	suppose	suppose	VERB
ejpam-3823	190	29	b	b	X
ejpam-3823	190	30	∈	∈	PROPN
ejpam-3823	190	31	b	b	PROPN
ejpam-3823	190	32	then	then	ADV
ejpam-3823	190	33	b	b	PROPN
ejpam-3823	190	34	∈	∈	PROPN
ejpam-3823	190	35	bc	bc	PROPN
ejpam-3823	190	36	for	for	ADP
ejpam-3823	190	37	some	some	DET
ejpam-3823	190	38	c	c	PROPN
ejpam-3823	190	39	and	and	CCONJ
ejpam-3823	190	40	b	b	PROPN
ejpam-3823	190	41	∈	∈	PROPN
ejpam-3823	190	42	f−1(g	f−1(g	PROPN
ejpam-3823	190	43	)	)	PUNCT
ejpam-3823	190	44	.	.	PUNCT
ejpam-3823	191	1	hence	hence	ADV
ejpam-3823	191	2	b	b	X
ejpam-3823	191	3	=	=	SYM
ejpam-3823	191	4	f−1(g	f−1(g	PROPN
ejpam-3823	191	5	)	)	PUNCT
ejpam-3823	191	6	.	.	PUNCT
ejpam-3823	192	1	since	since	SCONJ
ejpam-3823	192	2	bc	bc	PROPN
ejpam-3823	192	3	is	be	AUX
ejpam-3823	192	4	mic.g	mic.g	PROPN
ejpam-3823	192	5	-	-	PUNCT
ejpam-3823	192	6	closed	closed	ADJ
ejpam-3823	192	7	set	set	NOUN
ejpam-3823	192	8	,	,	PUNCT
ejpam-3823	192	9	by	by	ADP
ejpam-3823	192	10	dentition	dentition	NOUN
ejpam-3823	192	11	(	(	PUNCT
ejpam-3823	192	12	4.7	4.7	NUM
ejpam-3823	192	13	)	)	PUNCT
ejpam-3823	192	14	b	b	NOUN
ejpam-3823	192	15	is	be	AUX
ejpam-3823	192	16	mic.g	mic.g	NOUN
ejpam-3823	192	17	-	-	PUNCT
ejpam-3823	192	18	closed	closed	ADJ
ejpam-3823	192	19	and	and	CCONJ
ejpam-3823	192	20	hence	hence	ADV
ejpam-3823	192	21	b	b	X
ejpam-3823	192	22	=	=	SYM
ejpam-3823	192	23	f−1(g	f−1(g	PROPN
ejpam-3823	192	24	)	)	PUNCT
ejpam-3823	192	25	is	be	AUX
ejpam-3823	192	26	mic.g	mic.g	NOUN
ejpam-3823	192	27	-	-	PUNCT
ejpam-3823	192	28	closed	closed	ADJ
ejpam-3823	192	29	set	set	NOUN
ejpam-3823	192	30	for	for	ADP
ejpam-3823	192	31	every	every	DET
ejpam-3823	192	32	micro	micro	ADJ
ejpam-3823	192	33	-	-	ADJ
ejpam-3823	192	34	closed	closed	ADJ
ejpam-3823	192	35	set	set	VERB
ejpam-3823	192	36	g	g	NOUN
ejpam-3823	192	37	in	in	ADP
ejpam-3823	192	38	y	y	PROPN
ejpam-3823	192	39	.	.	PUNCT
ejpam-3823	193	1	hence	hence	ADV
ejpam-3823	193	2	f	f	PROPN
ejpam-3823	193	3	is	be	AUX
ejpam-3823	193	4	mic.g	mic.g	NOUN
ejpam-3823	193	5	-	-	PUNCT
ejpam-3823	193	6	continuous	continuous	ADJ
ejpam-3823	193	7	.	.	PUNCT
ejpam-3823	194	1	4.9	4.9	NUM
ejpam-3823	194	2	.	.	PUNCT
ejpam-3823	194	3	theorem	theorem	VERB
ejpam-3823	194	4	let	let	VERB
ejpam-3823	194	5	(	(	PUNCT
ejpam-3823	194	6	x	x	NOUN
ejpam-3823	194	7	,	,	PUNCT
ejpam-3823	194	8	τr(a	τr(a	NUM
ejpam-3823	194	9	)	)	PUNCT
ejpam-3823	194	10	,	,	PUNCT
ejpam-3823	194	11	µr(a	µr(a	NUM
ejpam-3823	194	12	)	)	PUNCT
ejpam-3823	194	13	)	)	PUNCT
ejpam-3823	195	1	and	and	CCONJ
ejpam-3823	195	2	(	(	PUNCT
ejpam-3823	195	3	y	y	PROPN
ejpam-3823	195	4	,	,	PUNCT
ejpam-3823	195	5	τ	τ	PROPN
ejpam-3823	195	6	′r(a	′r(a	PROPN
ejpam-3823	195	7	)	)	PUNCT
ejpam-3823	195	8	,	,	PUNCT
ejpam-3823	195	9	µ′	µ′	PROPN
ejpam-3823	195	10	r(a	r(a	PROPN
ejpam-3823	195	11	)	)	PUNCT
ejpam-3823	195	12	)	)	PUNCT
ejpam-3823	195	13	be	be	AUX
ejpam-3823	195	14	two	two	NUM
ejpam-3823	195	15	micro	micro	ADJ
ejpam-3823	195	16	topological	topological	ADJ
ejpam-3823	195	17	spaces	space	NOUN
ejpam-3823	195	18	.	.	PUNCT
ejpam-3823	196	1	then	then	ADV
ejpam-3823	196	2	f	f	X
ejpam-3823	196	3	:	:	PUNCT
ejpam-3823	196	4	x	x	X
ejpam-3823	196	5	→	→	SYM
ejpam-3823	196	6	y	y	PROPN
ejpam-3823	196	7	is	be	AUX
ejpam-3823	196	8	micro	micro	ADJ
ejpam-3823	196	9	-	-	ADJ
ejpam-3823	196	10	generalized	generalized	ADJ
ejpam-3823	196	11	continuous	continuous	ADJ
ejpam-3823	196	12	function	function	NOUN
ejpam-3823	196	13	if	if	SCONJ
ejpam-3823	196	14	and	and	CCONJ
ejpam-3823	196	15	only	only	ADV
ejpam-3823	196	16	if	if	SCONJ
ejpam-3823	196	17	f−1(b	f−1(b	PROPN
ejpam-3823	196	18	)	)	PUNCT
ejpam-3823	196	19	is	be	AUX
ejpam-3823	196	20	mic.g	mic.g	NOUN
ejpam-3823	196	21	-	-	PUNCT
ejpam-3823	196	22	open	open	ADJ
ejpam-3823	196	23	references	reference	NOUN
ejpam-3823	196	24	1515	1515	NUM
ejpam-3823	196	25	in	in	ADP
ejpam-3823	196	26	x	x	X
ejpam-3823	196	27	whenever	whenever	SCONJ
ejpam-3823	196	28	b	b	NOUN
ejpam-3823	196	29	is	be	AUX
ejpam-3823	196	30	microopen	microopen	ADJ
ejpam-3823	196	31	in	in	ADP
ejpam-3823	196	32	y	y	PROPN
ejpam-3823	196	33	.	.	PUNCT
ejpam-3823	197	1	proof	proof	NOUN
ejpam-3823	197	2	:	:	PUNCT
ejpam-3823	197	3	let	let	VERB
ejpam-3823	197	4	f	f	PRON
ejpam-3823	197	5	:	:	PUNCT
ejpam-3823	197	6	x	x	X
ejpam-3823	197	7	→	→	SYM
ejpam-3823	197	8	y	y	PROPN
ejpam-3823	197	9	is	be	AUX
ejpam-3823	197	10	micro	micro	ADJ
ejpam-3823	197	11	-	-	ADJ
ejpam-3823	197	12	generalized	generalized	ADJ
ejpam-3823	197	13	continuous	continuous	ADJ
ejpam-3823	197	14	function	function	NOUN
ejpam-3823	197	15	and	and	CCONJ
ejpam-3823	197	16	b	b	AUX
ejpam-3823	197	17	be	be	AUX
ejpam-3823	197	18	micro	micro	ADJ
ejpam-3823	197	19	-	-	ADJ
ejpam-3823	197	20	open	open	ADJ
ejpam-3823	197	21	in	in	ADP
ejpam-3823	197	22	y	y	PROPN
ejpam-3823	197	23	.	.	PUNCT
ejpam-3823	198	1	then	then	ADV
ejpam-3823	198	2	bc	bc	PROPN
ejpam-3823	198	3	is	be	AUX
ejpam-3823	198	4	micro	micro	ADJ
ejpam-3823	198	5	-	-	VERB
ejpam-3823	198	6	closed	closed	ADJ
ejpam-3823	198	7	in	in	ADP
ejpam-3823	198	8	y	y	PROPN
ejpam-3823	198	9	.	.	PUNCT
ejpam-3823	199	1	by	by	ADP
ejpam-3823	199	2	hypothesis	hypothesis	NOUN
ejpam-3823	199	3	f−1(bc	f−1(bc	VERB
ejpam-3823	199	4	)	)	PUNCT
ejpam-3823	199	5	is	be	AUX
ejpam-3823	199	6	mic.g	mic.g	NOUN
ejpam-3823	199	7	-	-	PUNCT
ejpam-3823	199	8	closed	closed	ADJ
ejpam-3823	199	9	in	in	ADP
ejpam-3823	199	10	x	x	PRON
ejpam-3823	199	11	,	,	PUNCT
ejpam-3823	199	12	i.e.	i.e.	X
ejpam-3823	199	13	,	,	PUNCT
ejpam-3823	199	14	[	[	X
ejpam-3823	199	15	f−1(b)]c	f−1(b)]c	PROPN
ejpam-3823	199	16	is	be	AUX
ejpam-3823	199	17	mic.g	mic.g	PROPN
ejpam-3823	199	18	-	-	PUNCT
ejpam-3823	199	19	closed	close	VERB
ejpam-3823	199	20	set	set	NOUN
ejpam-3823	199	21	in	in	ADP
ejpam-3823	199	22	x.	x.	NOUN
ejpam-3823	199	23	hence	hence	ADV
ejpam-3823	199	24	f−1(b	f−1(b	PROPN
ejpam-3823	199	25	)	)	PUNCT
ejpam-3823	199	26	is	be	AUX
ejpam-3823	199	27	mic.g	mic.g	NOUN
ejpam-3823	199	28	-	-	PUNCT
ejpam-3823	199	29	open	open	ADJ
ejpam-3823	199	30	in	in	ADP
ejpam-3823	199	31	x.	x.	NOUN
ejpam-3823	199	32	whenever	whenever	SCONJ
ejpam-3823	199	33	b	b	PROPN
ejpam-3823	199	34	is	be	AUX
ejpam-3823	199	35	micro	micro	ADJ
ejpam-3823	199	36	-	-	NOUN
ejpam-3823	199	37	open	open	ADJ
ejpam-3823	199	38	in	in	ADP
ejpam-3823	199	39	y	y	PROPN
ejpam-3823	199	40	.	.	PUNCT
ejpam-3823	200	1	conversely	conversely	ADV
ejpam-3823	200	2	,	,	PUNCT
ejpam-3823	200	3	suppose	suppose	VERB
ejpam-3823	200	4	f−1(b	f−1(b	PROPN
ejpam-3823	200	5	)	)	PUNCT
ejpam-3823	200	6	is	be	AUX
ejpam-3823	200	7	mic.g	mic.g	NOUN
ejpam-3823	200	8	-	-	PUNCT
ejpam-3823	200	9	open	open	NOUN
ejpam-3823	200	10	set	set	NOUN
ejpam-3823	200	11	in	in	ADP
ejpam-3823	200	12	x	x	PUNCT
ejpam-3823	200	13	whenever	whenever	SCONJ
ejpam-3823	200	14	b	b	NOUN
ejpam-3823	200	15	is	be	AUX
ejpam-3823	200	16	micro	micro	ADJ
ejpam-3823	200	17	-	-	NOUN
ejpam-3823	200	18	open	open	ADJ
ejpam-3823	200	19	in	in	ADP
ejpam-3823	200	20	y	y	PROPN
ejpam-3823	200	21	.	.	PUNCT
ejpam-3823	201	1	let	let	VERB
ejpam-3823	201	2	h	h	NOUN
ejpam-3823	201	3	is	be	AUX
ejpam-3823	201	4	micro	micro	ADJ
ejpam-3823	201	5	-	-	VERB
ejpam-3823	201	6	closed	closed	ADJ
ejpam-3823	201	7	in	in	ADP
ejpam-3823	201	8	y	y	PROPN
ejpam-3823	201	9	then	then	ADV
ejpam-3823	201	10	hc	hc	PROPN
ejpam-3823	201	11	is	be	AUX
ejpam-3823	201	12	micro	micro	ADJ
ejpam-3823	201	13	-	-	NOUN
ejpam-3823	201	14	open	open	ADJ
ejpam-3823	201	15	in	in	ADP
ejpam-3823	201	16	y	y	PROPN
ejpam-3823	201	17	.	.	PUNCT
ejpam-3823	202	1	by	by	ADP
ejpam-3823	202	2	assumption	assumption	NOUN
ejpam-3823	202	3	f−1(hc	f−1(hc	PROPN
ejpam-3823	202	4	)	)	PUNCT
ejpam-3823	202	5	is	be	AUX
ejpam-3823	202	6	mic.g	mic.g	NOUN
ejpam-3823	202	7	-	-	PUNCT
ejpam-3823	202	8	open	open	ADJ
ejpam-3823	202	9	in	in	ADP
ejpam-3823	202	10	x.i.e	x.i.e	NOUN
ejpam-3823	202	11	.	.	PUNCT
ejpam-3823	202	12	,	,	PUNCT
ejpam-3823	203	1	[	[	X
ejpam-3823	203	2	f−1(h)]c	f−1(h)]c	PROPN
ejpam-3823	203	3	is	be	AUX
ejpam-3823	203	4	mic.g	mic.g	NOUN
ejpam-3823	203	5	-	-	PUNCT
ejpam-3823	203	6	open	open	ADJ
ejpam-3823	203	7	in	in	ADP
ejpam-3823	203	8	x.	x.	PROPN
ejpam-3823	203	9	then	then	ADV
ejpam-3823	203	10	f−1(h	f−1(h	PROPN
ejpam-3823	203	11	)	)	PUNCT
ejpam-3823	203	12	is	be	AUX
ejpam-3823	203	13	mic.g	mic.g	NOUN
ejpam-3823	203	14	-	-	PUNCT
ejpam-3823	203	15	closed	closed	ADJ
ejpam-3823	203	16	in	in	ADP
ejpam-3823	203	17	x.	x.	NOUN
ejpam-3823	203	18	hence	hence	ADV
ejpam-3823	203	19	f	f	PROPN
ejpam-3823	203	20	is	be	AUX
ejpam-3823	203	21	mic.g	mic.g	NOUN
ejpam-3823	203	22	-	-	PUNCT
ejpam-3823	203	23	continuous	continuous	ADJ
ejpam-3823	203	24	function	function	NOUN
ejpam-3823	203	25	.	.	PUNCT
ejpam-3823	204	1	4.10	4.10	NUM
ejpam-3823	204	2	.	.	PUNCT
ejpam-3823	204	3	theorem	theorem	VERB
ejpam-3823	204	4	let	let	VERB
ejpam-3823	204	5	(	(	PUNCT
ejpam-3823	204	6	x	x	NOUN
ejpam-3823	204	7	,	,	PUNCT
ejpam-3823	204	8	τr(a	τr(a	NUM
ejpam-3823	204	9	)	)	PUNCT
ejpam-3823	204	10	,	,	PUNCT
ejpam-3823	204	11	µr(a)),(y	µr(a)),(y	PROPN
ejpam-3823	204	12	,	,	PUNCT
ejpam-3823	204	13	τ	τ	PROPN
ejpam-3823	204	14	′r(a	′r(a	PROPN
ejpam-3823	204	15	)	)	PUNCT
ejpam-3823	204	16	,	,	PUNCT
ejpam-3823	204	17	µ	µ	X
ejpam-3823	204	18	′	′	NUM
ejpam-3823	204	19	r(a	r(a	NUM
ejpam-3823	204	20	)	)	PUNCT
ejpam-3823	204	21	)	)	PUNCT
ejpam-3823	205	1	and	and	CCONJ
ejpam-3823	205	2	(	(	PUNCT
ejpam-3823	205	3	z	z	NOUN
ejpam-3823	205	4	,	,	PUNCT
ejpam-3823	205	5	τ	τ	PROPN
ejpam-3823	205	6	′′r(a	′′r(a	NOUN
ejpam-3823	205	7	)	)	PUNCT
ejpam-3823	205	8	,	,	PUNCT
ejpam-3823	205	9	µ′′	µ′′	PROPN
ejpam-3823	205	10	r(a	r(a	VERB
ejpam-3823	205	11	)	)	PUNCT
ejpam-3823	205	12	)	)	PUNCT
ejpam-3823	205	13	be	be	AUX
ejpam-3823	205	14	three	three	NUM
ejpam-3823	205	15	micro	micro	ADJ
ejpam-3823	205	16	-	-	ADJ
ejpam-3823	205	17	topological	topological	ADJ
ejpam-3823	205	18	spaces	space	NOUN
ejpam-3823	205	19	.	.	PUNCT
ejpam-3823	206	1	if	if	SCONJ
ejpam-3823	206	2	f	f	PROPN
ejpam-3823	206	3	:	:	PUNCT
ejpam-3823	206	4	x	x	X
ejpam-3823	206	5	→	→	SYM
ejpam-3823	206	6	y	y	PROPN
ejpam-3823	206	7	and	and	CCONJ
ejpam-3823	206	8	g	g	PROPN
ejpam-3823	206	9	:	:	PUNCT
ejpam-3823	206	10	y	y	PROPN
ejpam-3823	206	11	→	→	SYM
ejpam-3823	206	12	z	z	PROPN
ejpam-3823	206	13	are	be	AUX
ejpam-3823	206	14	micro	micro	ADJ
ejpam-3823	206	15	-	-	ADJ
ejpam-3823	206	16	generalized	generalized	ADJ
ejpam-3823	206	17	irresolute	irresolute	ADJ
ejpam-3823	206	18	functions	function	NOUN
ejpam-3823	206	19	then	then	ADV
ejpam-3823	206	20	g	g	PROPN
ejpam-3823	206	21	◦	◦	NOUN
ejpam-3823	207	1	f	f	X
ejpam-3823	207	2	:	:	PUNCT
ejpam-3823	207	3	x	x	X
ejpam-3823	207	4	→	→	SYM
ejpam-3823	207	5	z	z	NOUN
ejpam-3823	207	6	is	be	AUX
ejpam-3823	207	7	also	also	ADV
ejpam-3823	207	8	micro	micro	ADJ
ejpam-3823	207	9	-	-	ADJ
ejpam-3823	207	10	generalized	generalized	ADJ
ejpam-3823	207	11	irresolute	irresolute	ADJ
ejpam-3823	207	12	function	function	NOUN
ejpam-3823	207	13	.	.	PUNCT
ejpam-3823	208	1	proof	proof	NOUN
ejpam-3823	208	2	:	:	PUNCT
ejpam-3823	208	3	let	let	VERB
ejpam-3823	208	4	b	b	X
ejpam-3823	208	5	be	be	AUX
ejpam-3823	208	6	a	a	DET
ejpam-3823	208	7	mic.g	mic.g	PROPN
ejpam-3823	208	8	-	-	PUNCT
ejpam-3823	208	9	closed	close	VERB
ejpam-3823	208	10	set	set	NOUN
ejpam-3823	208	11	in	in	ADP
ejpam-3823	208	12	z.	z.	PROPN
ejpam-3823	208	13	since	since	SCONJ
ejpam-3823	208	14	by	by	ADP
ejpam-3823	208	15	g	g	PROPN
ejpam-3823	208	16	is	be	AUX
ejpam-3823	208	17	micro	micro	ADJ
ejpam-3823	208	18	-	-	ADJ
ejpam-3823	208	19	generalized	generalized	ADJ
ejpam-3823	208	20	irresolute	irresolute	ADJ
ejpam-3823	208	21	function	function	NOUN
ejpam-3823	208	22	,	,	PUNCT
ejpam-3823	208	23	then	then	ADV
ejpam-3823	208	24	g−1(b	g−1(b	PROPN
ejpam-3823	208	25	)	)	PUNCT
ejpam-3823	208	26	is	be	AUX
ejpam-3823	208	27	mic.g	mic.g	NOUN
ejpam-3823	208	28	-	-	PUNCT
ejpam-3823	208	29	closed	close	VERB
ejpam-3823	208	30	set	set	NOUN
ejpam-3823	208	31	in	in	ADP
ejpam-3823	208	32	y	y	PROPN
ejpam-3823	208	33	.	.	PUNCT
ejpam-3823	209	1	now	now	ADV
ejpam-3823	209	2	since	since	SCONJ
ejpam-3823	209	3	by	by	ADP
ejpam-3823	209	4	f	f	PROPN
ejpam-3823	209	5	is	be	AUX
ejpam-3823	209	6	micro	micro	ADJ
ejpam-3823	209	7	-	-	ADJ
ejpam-3823	209	8	generalized	generalized	ADJ
ejpam-3823	209	9	irresolute	irresolute	ADJ
ejpam-3823	209	10	function	function	NOUN
ejpam-3823	209	11	,	,	PUNCT
ejpam-3823	209	12	then	then	ADV
ejpam-3823	209	13	f−1(g−1(b	f−1(g−1(b	PROPN
ejpam-3823	209	14	)	)	PUNCT
ejpam-3823	209	15	)	)	PUNCT
ejpam-3823	210	1	is	be	AUX
ejpam-3823	210	2	mic.g	mic.g	NOUN
ejpam-3823	210	3	-	-	PUNCT
ejpam-3823	210	4	closed	closed	ADJ
ejpam-3823	210	5	set	set	NOUN
ejpam-3823	210	6	in	in	ADP
ejpam-3823	210	7	x	x	PUNCT
ejpam-3823	210	8	but	but	CCONJ
ejpam-3823	210	9	(	(	PUNCT
ejpam-3823	210	10	g	g	PROPN
ejpam-3823	210	11	◦	◦	NOUN
ejpam-3823	210	12	f)−1(b	f)−1(b	PROPN
ejpam-3823	210	13	)	)	PUNCT
ejpam-3823	211	1	=	=	PUNCT
ejpam-3823	211	2	(	(	PUNCT
ejpam-3823	211	3	f−1	f−1	PROPN
ejpam-3823	211	4	◦	◦	NOUN
ejpam-3823	211	5	g−1)(b	g−1)(b	PROPN
ejpam-3823	211	6	)	)	PUNCT
ejpam-3823	211	7	=	=	SYM
ejpam-3823	211	8	f−1(g−1(b	f−1(g−1(b	PROPN
ejpam-3823	211	9	)	)	PUNCT
ejpam-3823	211	10	)	)	PUNCT
ejpam-3823	211	11	.	.	PUNCT
ejpam-3823	212	1	thus	thus	ADV
ejpam-3823	212	2	(	(	PUNCT
ejpam-3823	212	3	g	g	PROPN
ejpam-3823	212	4	◦	◦	NOUN
ejpam-3823	212	5	f)−1(b	f)−1(b	NOUN
ejpam-3823	212	6	)	)	PUNCT
ejpam-3823	212	7	is	be	AUX
ejpam-3823	212	8	mic.g	mic.g	NOUN
ejpam-3823	212	9	-	-	PUNCT
ejpam-3823	212	10	closed	close	VERB
ejpam-3823	212	11	set	set	NOUN
ejpam-3823	212	12	in	in	ADP
ejpam-3823	212	13	x.	x.	NOUN
ejpam-3823	212	14	hence	hence	ADV
ejpam-3823	212	15	g	g	PROPN
ejpam-3823	212	16	◦	◦	NOUN
ejpam-3823	212	17	f	f	PROPN
ejpam-3823	212	18	is	be	AUX
ejpam-3823	212	19	micro	micro	ADJ
ejpam-3823	212	20	-	-	ADJ
ejpam-3823	212	21	generalized	generalized	ADJ
ejpam-3823	212	22	irresolute	irresolute	ADJ
ejpam-3823	212	23	function	function	NOUN
ejpam-3823	212	24	.	.	PUNCT
ejpam-3823	213	1	4.11	4.11	NUM
ejpam-3823	213	2	.	.	PUNCT
ejpam-3823	213	3	theorem	theorem	NOUN
ejpam-3823	213	4	let	let	VERB
ejpam-3823	213	5	(	(	PUNCT
ejpam-3823	213	6	x	x	NOUN
ejpam-3823	213	7	,	,	PUNCT
ejpam-3823	213	8	τr(a	τr(a	NUM
ejpam-3823	213	9	)	)	PUNCT
ejpam-3823	213	10	,	,	PUNCT
ejpam-3823	213	11	µr(a	µr(a	NUM
ejpam-3823	213	12	)	)	PUNCT
ejpam-3823	213	13	)	)	PUNCT
ejpam-3823	213	14	,	,	PUNCT
ejpam-3823	213	15	(	(	PUNCT
ejpam-3823	213	16	y	y	PROPN
ejpam-3823	213	17	,	,	PUNCT
ejpam-3823	213	18	τ	τ	PROPN
ejpam-3823	213	19	′r(a	′r(a	PROPN
ejpam-3823	213	20	)	)	PUNCT
ejpam-3823	213	21	,	,	PUNCT
ejpam-3823	213	22	µ′	µ′	PROPN
ejpam-3823	213	23	r(a	r(a	PROPN
ejpam-3823	213	24	)	)	PUNCT
ejpam-3823	213	25	)	)	PUNCT
ejpam-3823	214	1	and	and	CCONJ
ejpam-3823	214	2	(	(	PUNCT
ejpam-3823	214	3	z	z	NOUN
ejpam-3823	214	4	,	,	PUNCT
ejpam-3823	214	5	τ	τ	PROPN
ejpam-3823	214	6	′′r(a	′′r(a	NOUN
ejpam-3823	214	7	)	)	PUNCT
ejpam-3823	214	8	,	,	PUNCT
ejpam-3823	214	9	µ′′	µ′′	PROPN
ejpam-3823	214	10	r(a	r(a	VERB
ejpam-3823	214	11	)	)	PUNCT
ejpam-3823	214	12	)	)	PUNCT
ejpam-3823	214	13	be	be	AUX
ejpam-3823	214	14	three	three	NUM
ejpam-3823	214	15	micro	micro	ADJ
ejpam-3823	214	16	-	-	ADJ
ejpam-3823	214	17	topological	topological	ADJ
ejpam-3823	214	18	spaces	space	NOUN
ejpam-3823	214	19	.	.	PUNCT
ejpam-3823	215	1	if	if	SCONJ
ejpam-3823	215	2	f	f	PROPN
ejpam-3823	215	3	:	:	PUNCT
ejpam-3823	215	4	x	x	X
ejpam-3823	215	5	→	→	SYM
ejpam-3823	215	6	y	y	PROPN
ejpam-3823	215	7	is	be	AUX
ejpam-3823	215	8	a	a	DET
ejpam-3823	215	9	micro	micro	ADJ
ejpam-3823	215	10	-	-	ADJ
ejpam-3823	215	11	generalized	generalized	ADJ
ejpam-3823	215	12	continuous	continuous	ADJ
ejpam-3823	215	13	function	function	NOUN
ejpam-3823	215	14	and	and	CCONJ
ejpam-3823	215	15	g	g	NOUN
ejpam-3823	215	16	:	:	PUNCT
ejpam-3823	215	17	y	y	PROPN
ejpam-3823	215	18	→	→	SYM
ejpam-3823	215	19	z	z	AUX
ejpam-3823	215	20	be	be	AUX
ejpam-3823	215	21	a	a	DET
ejpam-3823	215	22	micro	micro	ADJ
ejpam-3823	215	23	-	-	ADJ
ejpam-3823	215	24	continuous	continuous	ADJ
ejpam-3823	215	25	function	function	NOUN
ejpam-3823	215	26	then	then	ADV
ejpam-3823	215	27	g	g	PROPN
ejpam-3823	215	28	◦	◦	NOUN
ejpam-3823	216	1	f	f	X
ejpam-3823	216	2	:	:	PUNCT
ejpam-3823	216	3	x	x	X
ejpam-3823	216	4	→	→	SYM
ejpam-3823	216	5	z	z	NOUN
ejpam-3823	216	6	is	be	AUX
ejpam-3823	216	7	micro	micro	ADJ
ejpam-3823	216	8	-	-	ADJ
ejpam-3823	216	9	generalized	generalized	ADJ
ejpam-3823	216	10	continuous	continuous	ADJ
ejpam-3823	216	11	function	function	NOUN
ejpam-3823	216	12	.	.	PUNCT
ejpam-3823	217	1	proof	proof	NOUN
ejpam-3823	217	2	:	:	PUNCT
ejpam-3823	217	3	let	let	VERB
ejpam-3823	217	4	b	b	X
ejpam-3823	217	5	be	be	AUX
ejpam-3823	217	6	a	a	DET
ejpam-3823	217	7	micro	micro	ADJ
ejpam-3823	217	8	-	-	ADJ
ejpam-3823	217	9	closed	closed	ADJ
ejpam-3823	217	10	set	set	NOUN
ejpam-3823	217	11	in	in	ADP
ejpam-3823	217	12	z.	z.	PROPN
ejpam-3823	217	13	since	since	SCONJ
ejpam-3823	217	14	by	by	ADP
ejpam-3823	217	15	g	g	PROPN
ejpam-3823	217	16	is	be	AUX
ejpam-3823	217	17	micro	micro	ADJ
ejpam-3823	217	18	-	-	ADJ
ejpam-3823	217	19	continuous	continuous	ADJ
ejpam-3823	217	20	function	function	NOUN
ejpam-3823	217	21	,	,	PUNCT
ejpam-3823	217	22	then	then	ADV
ejpam-3823	217	23	g−1(b	g−1(b	PROPN
ejpam-3823	217	24	)	)	PUNCT
ejpam-3823	217	25	is	be	AUX
ejpam-3823	217	26	micro	micro	ADJ
ejpam-3823	217	27	-	-	ADJ
ejpam-3823	217	28	closed	closed	ADJ
ejpam-3823	217	29	set	set	NOUN
ejpam-3823	217	30	in	in	ADP
ejpam-3823	217	31	y	y	PROPN
ejpam-3823	217	32	.	.	PUNCT
ejpam-3823	218	1	now	now	ADV
ejpam-3823	218	2	since	since	SCONJ
ejpam-3823	218	3	by	by	ADP
ejpam-3823	218	4	f	f	PROPN
ejpam-3823	218	5	is	be	AUX
ejpam-3823	218	6	micro	micro	ADJ
ejpam-3823	218	7	-	-	ADJ
ejpam-3823	218	8	generalized	generalized	ADJ
ejpam-3823	218	9	continuous	continuous	ADJ
ejpam-3823	218	10	function	function	NOUN
ejpam-3823	218	11	,	,	PUNCT
ejpam-3823	218	12	then	then	ADV
ejpam-3823	218	13	f−1(g−1(b	f−1(g−1(b	PROPN
ejpam-3823	218	14	)	)	PUNCT
ejpam-3823	218	15	)	)	PUNCT
ejpam-3823	219	1	is	be	AUX
ejpam-3823	219	2	micro	micro	ADJ
ejpam-3823	219	3	-	-	ADJ
ejpam-3823	219	4	generalized	generalize	VERB
ejpam-3823	219	5	closed	close	VERB
ejpam-3823	219	6	set	set	VERB
ejpam-3823	219	7	inx	inx	NOUN
ejpam-3823	219	8	but	but	CCONJ
ejpam-3823	219	9	(	(	PUNCT
ejpam-3823	219	10	g	g	PROPN
ejpam-3823	219	11	◦	◦	NOUN
ejpam-3823	219	12	f)−1(b	f)−1(b	NOUN
ejpam-3823	219	13	)	)	PUNCT
ejpam-3823	220	1	=	=	SYM
ejpam-3823	220	2	(	(	PUNCT
ejpam-3823	220	3	f−1	f−1	PROPN
ejpam-3823	220	4	◦	◦	NOUN
ejpam-3823	220	5	g−1)(b	g−1)(b	PROPN
ejpam-3823	220	6	)	)	PUNCT
ejpam-3823	220	7	=	=	SYM
ejpam-3823	220	8	f−1(g−1(b	f−1(g−1(b	PROPN
ejpam-3823	220	9	)	)	PUNCT
ejpam-3823	220	10	)	)	PUNCT
ejpam-3823	220	11	.	.	PUNCT
ejpam-3823	221	1	thus	thus	ADV
ejpam-3823	221	2	(	(	PUNCT
ejpam-3823	221	3	g	g	NOUN
ejpam-3823	221	4	◦	◦	NOUN
ejpam-3823	221	5	f)−1(b	f)−1(b	NOUN
ejpam-3823	221	6	)	)	PUNCT
ejpam-3823	221	7	is	be	AUX
ejpam-3823	221	8	micro	micro	ADJ
ejpam-3823	221	9	-	-	ADJ
ejpam-3823	221	10	generalized	generalize	VERB
ejpam-3823	221	11	closed	close	VERB
ejpam-3823	221	12	set	set	VERB
ejpam-3823	221	13	in	in	ADP
ejpam-3823	221	14	x.	x.	NOUN
ejpam-3823	221	15	hence	hence	ADV
ejpam-3823	221	16	g	g	PROPN
ejpam-3823	221	17	◦	◦	NOUN
ejpam-3823	221	18	f	f	PROPN
ejpam-3823	221	19	is	be	AUX
ejpam-3823	221	20	microgeneralized	microgeneralize	VERB
ejpam-3823	221	21	continuous	continuous	ADJ
ejpam-3823	221	22	function	function	NOUN
ejpam-3823	221	23	.	.	PUNCT
ejpam-3823	222	1	references	reference	NOUN
ejpam-3823	222	2	[	[	X
ejpam-3823	222	3	1	1	NUM
ejpam-3823	222	4	]	]	PUNCT
ejpam-3823	222	5	t	t	PROPN
ejpam-3823	222	6	al	al	PROPN
ejpam-3823	222	7	-	-	PUNCT
ejpam-3823	222	8	shami	shami	PROPN
ejpam-3823	222	9	.	.	PUNCT
ejpam-3823	223	1	paracompactness	paracompactness	NOUN
ejpam-3823	223	2	on	on	ADP
ejpam-3823	223	3	supra	supra	PROPN
ejpam-3823	223	4	topological	topological	ADJ
ejpam-3823	223	5	spaces	space	NOUN
ejpam-3823	223	6	.	.	PUNCT
ejpam-3823	224	1	journal	journal	NOUN
ejpam-3823	224	2	of	of	ADP
ejpam-3823	224	3	linear	linear	PROPN
ejpam-3823	224	4	and	and	CCONJ
ejpam-3823	224	5	topological	topological	ADJ
ejpam-3823	224	6	algebra	algebra	NOUN
ejpam-3823	224	7	(	(	PUNCT
ejpam-3823	224	8	jlta	jlta	PROPN
ejpam-3823	224	9	)	)	PUNCT
ejpam-3823	224	10	,	,	PUNCT
ejpam-3823	224	11	9(02):121–127	9(02):121–127	NUM
ejpam-3823	224	12	,	,	PUNCT
ejpam-3823	224	13	2020	2020	NUM
ejpam-3823	224	14	.	.	PUNCT
ejpam-3823	225	1	[	[	X
ejpam-3823	225	2	2	2	NUM
ejpam-3823	225	3	]	]	X
ejpam-3823	225	4	tareq	tareq	PROPN
ejpam-3823	225	5	m	m	PROPN
ejpam-3823	225	6	al	al	PROPN
ejpam-3823	225	7	-	-	PUNCT
ejpam-3823	225	8	shami	shami	PROPN
ejpam-3823	225	9	,	,	PUNCT
ejpam-3823	225	10	ea	ea	X
ejpam-3823	225	11	abo	abo	NOUN
ejpam-3823	225	12	-	-	PUNCT
ejpam-3823	225	13	tabl	tabl	NOUN
ejpam-3823	225	14	,	,	PUNCT
ejpam-3823	225	15	baravan	baravan	PROPN
ejpam-3823	225	16	assad	assad	PROPN
ejpam-3823	225	17	,	,	PUNCT
ejpam-3823	225	18	and	and	CCONJ
ejpam-3823	225	19	mohamed	mohamed	PROPN
ejpam-3823	225	20	arahet	arahet	PROPN
ejpam-3823	225	21	.	.	PUNCT
ejpam-3823	226	1	limit	limit	VERB
ejpam-3823	226	2	points	point	NOUN
ejpam-3823	226	3	and	and	CCONJ
ejpam-3823	226	4	separation	separation	NOUN
ejpam-3823	226	5	axioms	axiom	NOUN
ejpam-3823	226	6	with	with	ADP
ejpam-3823	226	7	respect	respect	NOUN
ejpam-3823	226	8	to	to	ADP
ejpam-3823	226	9	supra	supra	PROPN
ejpam-3823	226	10	semi	semi	ADJ
ejpam-3823	226	11	-	-	ADJ
ejpam-3823	226	12	open	open	ADJ
ejpam-3823	226	13	sets	set	NOUN
ejpam-3823	226	14	.	.	PUNCT
ejpam-3823	227	1	european	european	ADJ
ejpam-3823	227	2	journal	journal	PROPN
ejpam-3823	227	3	of	of	ADP
ejpam-3823	227	4	pure	pure	ADJ
ejpam-3823	227	5	and	and	CCONJ
ejpam-3823	227	6	applied	applied	ADJ
ejpam-3823	227	7	mathematics	mathematic	NOUN
ejpam-3823	227	8	,	,	PUNCT
ejpam-3823	227	9	13(3):427–443	13(3):427–443	PROPN
ejpam-3823	227	10	,	,	PUNCT
ejpam-3823	227	11	2020	2020	NUM
ejpam-3823	227	12	.	.	PUNCT
ejpam-3823	228	1	[	[	X
ejpam-3823	228	2	3	3	X
ejpam-3823	228	3	]	]	PUNCT
ejpam-3823	228	4	tm	tm	PROPN
ejpam-3823	228	5	al	al	PROPN
ejpam-3823	228	6	-	-	PUNCT
ejpam-3823	228	7	shami	shami	PROPN
ejpam-3823	228	8	.	.	PUNCT
ejpam-3823	229	1	somewhere	somewhere	ADV
ejpam-3823	229	2	dense	dense	ADJ
ejpam-3823	229	3	sets	set	NOUN
ejpam-3823	229	4	and	and	CCONJ
ejpam-3823	229	5	st1	st1	PROPN
ejpam-3823	229	6	-	-	PUNCT
ejpam-3823	229	7	spaces	spaces	PROPN
ejpam-3823	229	8	.	.	PUNCT
ejpam-3823	230	1	punjab	punjab	PROPN
ejpam-3823	230	2	university	university	PROPN
ejpam-3823	230	3	journal	journal	NOUN
ejpam-3823	230	4	of	of	ADP
ejpam-3823	230	5	mathematics	mathematic	NOUN
ejpam-3823	230	6	,	,	PUNCT
ejpam-3823	230	7	49(2):101–111	49(2):101–111	PROPN
ejpam-3823	230	8	,	,	PUNCT
ejpam-3823	230	9	2017	2017	NUM
ejpam-3823	230	10	.	.	PUNCT
ejpam-3823	231	1	[	[	X
ejpam-3823	231	2	4	4	X
ejpam-3823	231	3	]	]	PUNCT
ejpam-3823	231	4	tm	tm	PROPN
ejpam-3823	231	5	al	al	PROPN
ejpam-3823	231	6	-	-	PUNCT
ejpam-3823	231	7	shami	shami	PROPN
ejpam-3823	231	8	.	.	PUNCT
ejpam-3823	232	1	supra	supra	ADJ
ejpam-3823	232	2	semi	semi	NOUN
ejpam-3823	232	3	-	-	NOUN
ejpam-3823	232	4	compactness	compactness	NOUN
ejpam-3823	232	5	via	via	ADP
ejpam-3823	232	6	supra	supra	PROPN
ejpam-3823	232	7	topological	topological	PROPN
ejpam-3823	232	8	spaces	space	NOUN
ejpam-3823	232	9	.	.	PUNCT
ejpam-3823	233	1	journal	journal	PROPN
ejpam-3823	233	2	of	of	ADP
ejpam-3823	233	3	taibah	taibah	PROPN
ejpam-3823	233	4	university	university	PROPN
ejpam-3823	233	5	for	for	ADP
ejpam-3823	233	6	science	science	NOUN
ejpam-3823	233	7	,	,	PUNCT
ejpam-3823	233	8	12(3):338–343	12(3):338–343	PROPN
ejpam-3823	233	9	,	,	PUNCT
ejpam-3823	233	10	2018	2018	NUM
ejpam-3823	233	11	.	.	PUNCT
ejpam-3823	234	1	references	reference	NOUN
ejpam-3823	234	2	1516	1516	NUM
ejpam-3823	235	1	[	[	X
ejpam-3823	235	2	5	5	NUM
ejpam-3823	235	3	]	]	PUNCT
ejpam-3823	235	4	tm	tm	PROPN
ejpam-3823	235	5	al	al	PROPN
ejpam-3823	235	6	-	-	PUNCT
ejpam-3823	235	7	shami	shami	PROPN
ejpam-3823	235	8	.	.	PUNCT
ejpam-3823	236	1	sum	sum	NOUN
ejpam-3823	236	2	of	of	ADP
ejpam-3823	236	3	the	the	DET
ejpam-3823	236	4	spaces	space	NOUN
ejpam-3823	236	5	on	on	ADP
ejpam-3823	236	6	ordered	order	VERB
ejpam-3823	236	7	setting	setting	NOUN
ejpam-3823	236	8	.	.	PUNCT
ejpam-3823	237	1	moroccan	moroccan	PROPN
ejpam-3823	237	2	j.	j.	PROPN
ejpam-3823	237	3	of	of	ADP
ejpam-3823	237	4	pure	pure	ADJ
ejpam-3823	237	5	and	and	CCONJ
ejpam-3823	237	6	appl	appl	ADJ
ejpam-3823	237	7	.	.	PUNCT
ejpam-3823	238	1	anal	anal	ADJ
ejpam-3823	238	2	,	,	PUNCT
ejpam-3823	238	3	6(2):255–265	6(2):255–265	NOUN
ejpam-3823	238	4	,	,	PUNCT
ejpam-3823	238	5	2020	2020	NUM
ejpam-3823	238	6	.	.	PUNCT
ejpam-3823	239	1	[	[	X
ejpam-3823	239	2	6	6	NUM
ejpam-3823	239	3	]	]	PUNCT
ejpam-3823	239	4	tm	tm	PROPN
ejpam-3823	239	5	al	al	PROPN
ejpam-3823	239	6	-	-	PUNCT
ejpam-3823	239	7	shami	shami	PROPN
ejpam-3823	239	8	and	and	CCONJ
ejpam-3823	239	9	t	t	PROPN
ejpam-3823	239	10	noiri	noiri	PROPN
ejpam-3823	239	11	.	.	PUNCT
ejpam-3823	240	1	more	more	ADJ
ejpam-3823	240	2	notions	notion	NOUN
ejpam-3823	240	3	and	and	CCONJ
ejpam-3823	240	4	mappings	mapping	NOUN
ejpam-3823	240	5	via	via	ADP
ejpam-3823	240	6	somewhere	somewhere	ADJ
ejpam-3823	240	7	dense	dense	ADJ
ejpam-3823	240	8	sets	set	NOUN
ejpam-3823	240	9	.	.	PUNCT
ejpam-3823	241	1	afrika	afrika	ADJ
ejpam-3823	241	2	matematika	matematika	PROPN
ejpam-3823	241	3	,	,	PUNCT
ejpam-3823	241	4	30(7):1011–1024	30(7):1011–1024	PROPN
ejpam-3823	241	5	,	,	PUNCT
ejpam-3823	241	6	2019	2019	NUM
ejpam-3823	241	7	.	.	PUNCT
ejpam-3823	242	1	[	[	X
ejpam-3823	242	2	7	7	X
ejpam-3823	242	3	]	]	X
ejpam-3823	242	4	aa	aa	PROPN
ejpam-3823	242	5	azzam	azzam	PROPN
ejpam-3823	242	6	.	.	PUNCT
ejpam-3823	242	7	grill	grill	PROPN
ejpam-3823	242	8	nano	nano	NOUN
ejpam-3823	242	9	topological	topological	ADJ
ejpam-3823	242	10	spaces	space	NOUN
ejpam-3823	242	11	with	with	ADP
ejpam-3823	242	12	grill	grill	NOUN
ejpam-3823	242	13	nano	nano	NOUN
ejpam-3823	242	14	generalized	generalize	VERB
ejpam-3823	242	15	closed	closed	ADJ
ejpam-3823	242	16	sets	set	NOUN
ejpam-3823	242	17	.	.	PUNCT
ejpam-3823	243	1	journal	journal	NOUN
ejpam-3823	243	2	of	of	ADP
ejpam-3823	243	3	the	the	DET
ejpam-3823	243	4	egyptian	egyptian	PROPN
ejpam-3823	243	5	mathematical	mathematical	PROPN
ejpam-3823	243	6	society	society	NOUN
ejpam-3823	243	7	,	,	PUNCT
ejpam-3823	243	8	25(2):164–166	25(2):164–166	PROPN
ejpam-3823	243	9	,	,	PUNCT
ejpam-3823	243	10	2017	2017	NUM
ejpam-3823	243	11	.	.	PUNCT
ejpam-3823	244	1	[	[	X
ejpam-3823	244	2	8	8	NUM
ejpam-3823	244	3	]	]	SYM
ejpam-3823	244	4	m	m	NOUN
ejpam-3823	244	5	bhuvaneswari	bhuvaneswari	NOUN
ejpam-3823	244	6	.	.	PUNCT
ejpam-3823	245	1	a	a	DET
ejpam-3823	245	2	study	study	NOUN
ejpam-3823	245	3	on	on	ADP
ejpam-3823	245	4	nano	nano	NOUN
ejpam-3823	245	5	topology	topology	NOUN
ejpam-3823	245	6	.	.	PUNCT
ejpam-3823	246	1	a	a	DET
ejpam-3823	246	2	journal	journal	NOUN
ejpam-3823	246	3	of	of	ADP
ejpam-3823	246	4	nehru	nehru	PROPN
ejpam-3823	246	5	arts	arts	PROPN
ejpam-3823	246	6	and	and	CCONJ
ejpam-3823	246	7	science	science	PROPN
ejpam-3823	246	8	college	college	PROPN
ejpam-3823	246	9	,	,	PUNCT
ejpam-3823	246	10	5(1	5(1	NUM
ejpam-3823	246	11	)	)	PUNCT
ejpam-3823	246	12	,	,	PUNCT
ejpam-3823	246	13	2017	2017	NUM
ejpam-3823	246	14	.	.	PUNCT
ejpam-3823	247	1	[	[	X
ejpam-3823	247	2	9	9	NUM
ejpam-3823	247	3	]	]	PUNCT
ejpam-3823	247	4	sakkraiveeranan	sakkraiveeranan	NOUN
ejpam-3823	247	5	chandrasekar	chandrasekar	PROPN
ejpam-3823	247	6	.	.	PUNCT
ejpam-3823	248	1	on	on	ADP
ejpam-3823	248	2	micro	micro	PROPN
ejpam-3823	248	3	topological	topological	ADJ
ejpam-3823	248	4	spaces	space	NOUN
ejpam-3823	248	5	.	.	PUNCT
ejpam-3823	249	1	journal	journal	NOUN
ejpam-3823	249	2	of	of	ADP
ejpam-3823	249	3	new	new	ADJ
ejpam-3823	249	4	theory	theory	NOUN
ejpam-3823	249	5	,	,	PUNCT
ejpam-3823	249	6	(	(	PUNCT
ejpam-3823	249	7	26):23–31	26):23–31	NUM
ejpam-3823	249	8	,	,	PUNCT
ejpam-3823	249	9	2019	2019	NUM
ejpam-3823	249	10	.	.	PUNCT
ejpam-3823	250	1	[	[	X
ejpam-3823	250	2	10	10	NUM
ejpam-3823	250	3	]	]	X
ejpam-3823	250	4	me	i	PRON
ejpam-3823	250	5	el	el	PROPN
ejpam-3823	250	6	-	-	PUNCT
ejpam-3823	250	7	shafei	shafei	PROPN
ejpam-3823	250	8	,	,	PUNCT
ejpam-3823	250	9	ah	ah	INTJ
ejpam-3823	250	10	zakari	zakari	NOUN
ejpam-3823	250	11	,	,	PUNCT
ejpam-3823	250	12	and	and	CCONJ
ejpam-3823	250	13	tm	tm	PROPN
ejpam-3823	250	14	al	al	PROPN
ejpam-3823	250	15	-	-	PUNCT
ejpam-3823	250	16	shami	shami	PROPN
ejpam-3823	250	17	.	.	PUNCT
ejpam-3823	251	1	some	some	DET
ejpam-3823	251	2	applications	application	NOUN
ejpam-3823	251	3	of	of	ADP
ejpam-3823	251	4	supra	supra	ADJ
ejpam-3823	251	5	preopen	preopen	ADJ
ejpam-3823	251	6	sets	set	NOUN
ejpam-3823	251	7	.	.	PUNCT
ejpam-3823	252	1	journal	journal	NOUN
ejpam-3823	252	2	of	of	ADP
ejpam-3823	252	3	mathematics	mathematic	NOUN
ejpam-3823	252	4	,	,	PUNCT
ejpam-3823	252	5	2020	2020	NUM
ejpam-3823	252	6	,	,	PUNCT
ejpam-3823	252	7	2020	2020	NUM
ejpam-3823	252	8	.	.	PUNCT
ejpam-3823	253	1	[	[	X
ejpam-3823	253	2	11	11	NUM
ejpam-3823	253	3	]	]	PUNCT
ejpam-3823	253	4	norman	norman	PROPN
ejpam-3823	253	5	levine	levine	PROPN
ejpam-3823	253	6	.	.	PUNCT
ejpam-3823	254	1	generalized	generalize	VERB
ejpam-3823	254	2	closed	closed	ADJ
ejpam-3823	254	3	sets	set	NOUN
ejpam-3823	254	4	in	in	ADP
ejpam-3823	254	5	topology	topology	NOUN
ejpam-3823	254	6	.	.	PUNCT
ejpam-3823	255	1	rendiconti	rendiconti	VERB
ejpam-3823	255	2	del	del	PROPN
ejpam-3823	255	3	circolo	circolo	PROPN
ejpam-3823	255	4	matematico	matematico	NOUN
ejpam-3823	255	5	di	di	NOUN
ejpam-3823	255	6	palermo	palermo	NOUN
ejpam-3823	255	7	,	,	PUNCT
ejpam-3823	255	8	19(1):89–96	19(1):89–96	NUM
ejpam-3823	255	9	,	,	PUNCT
ejpam-3823	255	10	1970	1970	NUM
ejpam-3823	255	11	.	.	PUNCT
ejpam-3823	256	1	[	[	X
ejpam-3823	256	2	12	12	NUM
ejpam-3823	256	3	]	]	PUNCT
ejpam-3823	256	4	reem	reem	PROPN
ejpam-3823	256	5	o	o	X
ejpam-3823	256	6	rasheed	rasheed	NOUN
ejpam-3823	256	7	and	and	CCONJ
ejpam-3823	256	8	taha	taha	PROPN
ejpam-3823	256	9	h	h	PROPN
ejpam-3823	256	10	jasim	jasim	PROPN
ejpam-3823	256	11	.	.	PUNCT
ejpam-3823	257	1	on	on	ADP
ejpam-3823	257	2	micro	micro	PROPN
ejpam-3823	257	3	-	-	NOUN
ejpam-3823	257	4	α	α	ADJ
ejpam-3823	257	5	-	-	ADJ
ejpam-3823	257	6	open	open	ADJ
ejpam-3823	257	7	sets	set	NOUN
ejpam-3823	257	8	and	and	CCONJ
ejpam-3823	257	9	micro	micro	NOUN
ejpam-3823	257	10	-	-	NOUN
ejpam-3823	257	11	α	α	ADJ
ejpam-3823	257	12	-	-	ADJ
ejpam-3823	257	13	continuous	continuous	ADJ
ejpam-3823	257	14	functions	function	NOUN
ejpam-3823	257	15	in	in	ADP
ejpam-3823	257	16	micro	micro	ADJ
ejpam-3823	257	17	topological	topological	ADJ
ejpam-3823	257	18	spaces	space	NOUN
ejpam-3823	257	19	.	.	PUNCT
ejpam-3823	258	1	in	in	ADP
ejpam-3823	258	2	journal	journal	PROPN
ejpam-3823	258	3	of	of	ADP
ejpam-3823	258	4	physics	physics	PROPN
ejpam-3823	258	5	:	:	PUNCT
ejpam-3823	258	6	conference	conference	NOUN
ejpam-3823	258	7	series	series	NOUN
ejpam-3823	258	8	,	,	PUNCT
ejpam-3823	258	9	volume	volume	NOUN
ejpam-3823	258	10	1530	1530	NUM
ejpam-3823	258	11	,	,	PUNCT
ejpam-3823	258	12	page	page	NOUN
ejpam-3823	258	13	012061	012061	NUM
ejpam-3823	258	14	.	.	PUNCT
ejpam-3823	259	1	iop	iop	PROPN
ejpam-3823	259	2	publishing	publishing	NOUN
ejpam-3823	259	3	,	,	PUNCT
ejpam-3823	259	4	2020	2020	NUM
ejpam-3823	259	5	.	.	PUNCT
ejpam-3823	260	1	[	[	X
ejpam-3823	260	2	13	13	NUM
ejpam-3823	260	3	]	]	PUNCT
ejpam-3823	260	4	m	m	VERB
ejpam-3823	260	5	lellis	lellis	PROPN
ejpam-3823	260	6	thivagar	thivagar	NOUN
ejpam-3823	260	7	and	and	CCONJ
ejpam-3823	260	8	carmel	carmel	PROPN
ejpam-3823	260	9	richard	richard	PROPN
ejpam-3823	260	10	.	.	PUNCT
ejpam-3823	261	1	on	on	ADP
ejpam-3823	261	2	nano	nano	NOUN
ejpam-3823	261	3	forms	form	NOUN
ejpam-3823	261	4	of	of	ADP
ejpam-3823	261	5	weakly	weakly	ADJ
ejpam-3823	261	6	open	open	ADJ
ejpam-3823	261	7	sets	set	NOUN
ejpam-3823	261	8	.	.	PUNCT
ejpam-3823	262	1	international	international	ADJ
ejpam-3823	262	2	journal	journal	NOUN
ejpam-3823	262	3	of	of	ADP
ejpam-3823	262	4	mathematics	mathematics	PROPN
ejpam-3823	262	5	and	and	CCONJ
ejpam-3823	262	6	statistics	statistic	NOUN
ejpam-3823	262	7	invention	invention	NOUN
ejpam-3823	262	8	,	,	PUNCT
ejpam-3823	262	9	1(1):31–37	1(1):31–37	NUM
ejpam-3823	262	10	,	,	PUNCT
ejpam-3823	262	11	2013	2013	NUM
ejpam-3823	262	12	.	.	PUNCT