id	sid	tid	token	lemma	pos
ejpam-5347	1	1	european	european	PROPN
ejpam-5347	1	2	journal	journal	PROPN
ejpam-5347	1	3	of	of	ADP
ejpam-5347	1	4	pure	pure	ADJ
ejpam-5347	1	5	and	and	CCONJ
ejpam-5347	1	6	applied	apply	VERB
ejpam-5347	1	7	mathematics	mathematic	NOUN
ejpam-5347	1	8	vol	vol	NOUN
ejpam-5347	1	9	.	.	PROPN
ejpam-5347	2	1	17	17	NUM
ejpam-5347	2	2	,	,	PUNCT
ejpam-5347	2	3	no	no	INTJ
ejpam-5347	2	4	.	.	NOUN
ejpam-5347	2	5	4	4	NUM
ejpam-5347	2	6	,	,	PUNCT
ejpam-5347	2	7	2024	2024	NUM
ejpam-5347	2	8	,	,	PUNCT
ejpam-5347	2	9	2574	2574	NUM
ejpam-5347	2	10	-	-	SYM
ejpam-5347	2	11	2585	2585	NUM
ejpam-5347	2	12	issn	issn	PROPN
ejpam-5347	2	13	1307	1307	NUM
ejpam-5347	2	14	-	-	SYM
ejpam-5347	2	15	5543	5543	NUM
ejpam-5347	2	16	–	–	PUNCT
ejpam-5347	3	1	ejpam.com	ejpam.com	X
ejpam-5347	3	2	published	publish	VERB
ejpam-5347	3	3	by	by	ADP
ejpam-5347	3	4	new	new	PROPN
ejpam-5347	3	5	york	york	PROPN
ejpam-5347	3	6	business	business	PROPN
ejpam-5347	3	7	global	global	PROPN
ejpam-5347	3	8	a	a	DET
ejpam-5347	3	9	new	new	ADJ
ejpam-5347	3	10	outlook	outlook	NOUN
ejpam-5347	3	11	on	on	ADP
ejpam-5347	3	12	omega	omega	NOUN
ejpam-5347	3	13	closed	close	VERB
ejpam-5347	3	14	functions	function	NOUN
ejpam-5347	3	15	in	in	ADP
ejpam-5347	3	16	bitopological	bitopological	ADJ
ejpam-5347	3	17	spaces	space	NOUN
ejpam-5347	3	18	and	and	CCONJ
ejpam-5347	3	19	related	related	ADJ
ejpam-5347	3	20	aspects	aspect	NOUN
ejpam-5347	3	21	ali	ali	PROPN
ejpam-5347	3	22	a.	a.	PROPN
ejpam-5347	3	23	atoom1,∗	atoom1,∗	PROPN
ejpam-5347	3	24	,	,	PUNCT
ejpam-5347	3	25	hamza	hamza	PROPN
ejpam-5347	3	26	qoqazeh2	qoqazeh2	PROPN
ejpam-5347	3	27	,	,	PUNCT
ejpam-5347	3	28	maryam	maryam	PROPN
ejpam-5347	3	29	m	m	PROPN
ejpam-5347	3	30	alholi3	alholi3	PROPN
ejpam-5347	3	31	,	,	PUNCT
ejpam-5347	3	32	eman	eman	PROPN
ejpam-5347	3	33	almuhur4	almuhur4	PROPN
ejpam-5347	3	34	,	,	PUNCT
ejpam-5347	3	35	eman	eman	PROPN
ejpam-5347	3	36	hussein5	hussein5	PROPN
ejpam-5347	3	37	,	,	PUNCT
ejpam-5347	3	38	anas	anas	PROPN
ejpam-5347	3	39	a.	a.	PROPN
ejpam-5347	3	40	owledat6	owledat6	PROPN
ejpam-5347	3	41	,	,	PUNCT
ejpam-5347	3	42	abeer	abeer	PROPN
ejpam-5347	3	43	a.	a.	PROPN
ejpam-5347	3	44	al	al	PROPN
ejpam-5347	3	45	-	-	PUNCT
ejpam-5347	3	46	nana7	nana7	PROPN
ejpam-5347	3	47	1	1	NUM
ejpam-5347	3	48	mathematics	mathematic	NOUN
ejpam-5347	3	49	,	,	PUNCT
ejpam-5347	3	50	science	science	NOUN
ejpam-5347	3	51	,	,	PUNCT
ejpam-5347	3	52	ajloun	ajloun	ADJ
ejpam-5347	3	53	national	national	ADJ
ejpam-5347	3	54	university	university	PROPN
ejpam-5347	3	55	,	,	PUNCT
ejpam-5347	3	56	ajloun	ajloun	PROPN
ejpam-5347	3	57	,	,	PUNCT
ejpam-5347	3	58	jordan	jordan	PROPN
ejpam-5347	3	59	2	2	NUM
ejpam-5347	3	60	mathematics	mathematic	NOUN
ejpam-5347	3	61	,	,	PUNCT
ejpam-5347	3	62	science	science	NOUN
ejpam-5347	3	63	and	and	CCONJ
ejpam-5347	3	64	information	information	NOUN
ejpam-5347	3	65	technology	technology	NOUN
ejpam-5347	3	66	,	,	PUNCT
ejpam-5347	3	67	irbid	irbid	VERB
ejpam-5347	3	68	national	national	ADJ
ejpam-5347	3	69	university	university	NOUN
ejpam-5347	3	70	,	,	PUNCT
ejpam-5347	3	71	irbid	irbid	PROPN
ejpam-5347	3	72	,	,	PUNCT
ejpam-5347	3	73	jordan	jordan	PROPN
ejpam-5347	3	74	3	3	NUM
ejpam-5347	3	75	applied	apply	VERB
ejpam-5347	3	76	,	,	PUNCT
ejpam-5347	3	77	taibah	taibah	PROPN
ejpam-5347	3	78	university	university	PROPN
ejpam-5347	3	79	,	,	PUNCT
ejpam-5347	3	80	al	al	PROPN
ejpam-5347	3	81	ula	ula	PROPN
ejpam-5347	3	82	,	,	PUNCT
ejpam-5347	3	83	saudi	saudi	PROPN
ejpam-5347	3	84	arabia	arabia	PROPN
ejpam-5347	3	85	4	4	NUM
ejpam-5347	3	86	mathematics	mathematic	NOUN
ejpam-5347	3	87	,	,	PUNCT
ejpam-5347	3	88	arts	art	NOUN
ejpam-5347	3	89	and	and	CCONJ
ejpam-5347	3	90	science	science	NOUN
ejpam-5347	3	91	,	,	PUNCT
ejpam-5347	3	92	applied	apply	VERB
ejpam-5347	3	93	science	science	NOUN
ejpam-5347	3	94	private	private	ADJ
ejpam-5347	3	95	university	university	NOUN
ejpam-5347	3	96	,	,	PUNCT
ejpam-5347	3	97	amman	amman	PROPN
ejpam-5347	3	98	,	,	PUNCT
ejpam-5347	3	99	jordan	jordan	PROPN
ejpam-5347	3	100	5	5	NUM
ejpam-5347	3	101	mathematics	mathematic	NOUN
ejpam-5347	3	102	,	,	PUNCT
ejpam-5347	3	103	arts	art	NOUN
ejpam-5347	3	104	and	and	CCONJ
ejpam-5347	3	105	science	science	NOUN
ejpam-5347	3	106	,	,	PUNCT
ejpam-5347	3	107	amman	amman	PROPN
ejpam-5347	3	108	arab	arab	PROPN
ejpam-5347	3	109	university	university	PROPN
ejpam-5347	3	110	,	,	PUNCT
ejpam-5347	3	111	amman	amman	PROPN
ejpam-5347	3	112	,	,	PUNCT
ejpam-5347	3	113	jordan	jordan	PROPN
ejpam-5347	3	114	6	6	NUM
ejpam-5347	3	115	ministry	ministry	PROPN
ejpam-5347	3	116	of	of	ADP
ejpam-5347	3	117	education	education	PROPN
ejpam-5347	3	118	,	,	PUNCT
ejpam-5347	3	119	amman	amman	PROPN
ejpam-5347	3	120	,	,	PUNCT
ejpam-5347	3	121	jordan	jordan	PROPN
ejpam-5347	3	122	7	7	NUM
ejpam-5347	3	123	mathematics	mathematic	NOUN
ejpam-5347	3	124	,	,	PUNCT
ejpam-5347	3	125	science	science	NOUN
ejpam-5347	3	126	,	,	PUNCT
ejpam-5347	3	127	prince	prince	PROPN
ejpam-5347	3	128	sattam	sattam	PROPN
ejpam-5347	3	129	bin	bin	PROPN
ejpam-5347	3	130	abdulaziz	abdulaziz	PROPN
ejpam-5347	3	131	university	university	PROPN
ejpam-5347	3	132	,	,	PUNCT
ejpam-5347	3	133	alkharj	alkharj	VERB
ejpam-5347	3	134	,	,	PUNCT
ejpam-5347	3	135	saudi	saudi	PROPN
ejpam-5347	3	136	arabia	arabia	PROPN
ejpam-5347	3	137	abstract	abstract	NOUN
ejpam-5347	3	138	.	.	PUNCT
ejpam-5347	4	1	many	many	ADJ
ejpam-5347	4	2	studies	study	NOUN
ejpam-5347	4	3	have	have	AUX
ejpam-5347	4	4	employed	employ	VERB
ejpam-5347	4	5	a	a	DET
ejpam-5347	4	6	variety	variety	NOUN
ejpam-5347	4	7	of	of	ADP
ejpam-5347	4	8	techniques	technique	NOUN
ejpam-5347	4	9	to	to	PART
ejpam-5347	4	10	further	far	ADV
ejpam-5347	4	11	investigate	investigate	VERB
ejpam-5347	4	12	topological	topological	ADJ
ejpam-5347	4	13	space	space	NOUN
ejpam-5347	4	14	,	,	PUNCT
ejpam-5347	4	15	particularly	particularly	ADV
ejpam-5347	4	16	the	the	DET
ejpam-5347	4	17	notion	notion	NOUN
ejpam-5347	4	18	of	of	ADP
ejpam-5347	4	19	bitopological	bitopological	ADJ
ejpam-5347	4	20	spaces	space	NOUN
ejpam-5347	4	21	,	,	PUNCT
ejpam-5347	4	22	due	due	ADP
ejpam-5347	4	23	to	to	ADP
ejpam-5347	4	24	the	the	DET
ejpam-5347	4	25	significance	significance	NOUN
ejpam-5347	4	26	of	of	ADP
ejpam-5347	4	27	topological	topological	ADJ
ejpam-5347	4	28	space	space	NOUN
ejpam-5347	4	29	in	in	ADP
ejpam-5347	4	30	data	datum	NOUN
ejpam-5347	4	31	processing	processing	NOUN
ejpam-5347	4	32	as	as	ADV
ejpam-5347	4	33	well	well	ADV
ejpam-5347	4	34	as	as	ADP
ejpam-5347	4	35	certain	certain	ADJ
ejpam-5347	4	36	implementations	implementation	NOUN
ejpam-5347	4	37	.	.	PUNCT
ejpam-5347	5	1	numerous	numerous	ADJ
ejpam-5347	5	2	extended	extended	ADJ
ejpam-5347	5	3	topological	topological	ADJ
ejpam-5347	5	4	structures	structure	NOUN
ejpam-5347	5	5	have	have	AUX
ejpam-5347	5	6	been	be	AUX
ejpam-5347	5	7	laid	lay	VERB
ejpam-5347	5	8	out	out	ADP
ejpam-5347	5	9	subsequently	subsequently	ADV
ejpam-5347	5	10	.	.	PUNCT
ejpam-5347	6	1	of	of	ADP
ejpam-5347	6	2	those	those	DET
ejpam-5347	6	3	abstractions	abstraction	NOUN
ejpam-5347	6	4	,	,	PUNCT
ejpam-5347	6	5	functions	function	NOUN
ejpam-5347	6	6	in	in	ADP
ejpam-5347	6	7	topology	topology	NOUN
ejpam-5347	6	8	was	be	AUX
ejpam-5347	6	9	one	one	NUM
ejpam-5347	6	10	of	of	ADP
ejpam-5347	6	11	which	which	PRON
ejpam-5347	6	12	was	be	AUX
ejpam-5347	6	13	most	most	ADV
ejpam-5347	6	14	noteworthy	noteworthy	ADJ
ejpam-5347	6	15	.	.	PUNCT
ejpam-5347	7	1	in	in	ADP
ejpam-5347	7	2	order	order	NOUN
ejpam-5347	7	3	to	to	PART
ejpam-5347	7	4	assist	assist	VERB
ejpam-5347	7	5	in	in	ADP
ejpam-5347	7	6	this	this	DET
ejpam-5347	7	7	trend	trend	NOUN
ejpam-5347	7	8	,	,	PUNCT
ejpam-5347	7	9	we	we	PRON
ejpam-5347	7	10	focused	focus	VERB
ejpam-5347	7	11	our	our	PRON
ejpam-5347	7	12	research	research	NOUN
ejpam-5347	7	13	on	on	ADP
ejpam-5347	7	14	the	the	DET
ejpam-5347	7	15	idea	idea	NOUN
ejpam-5347	7	16	of	of	ADP
ejpam-5347	7	17	open	open	ADJ
ejpam-5347	7	18	and	and	CCONJ
ejpam-5347	7	19	closed	closed	ADJ
ejpam-5347	7	20	sets	set	NOUN
ejpam-5347	7	21	,	,	PUNCT
ejpam-5347	7	22	which	which	PRON
ejpam-5347	7	23	is	be	AUX
ejpam-5347	7	24	one	one	NUM
ejpam-5347	7	25	of	of	ADP
ejpam-5347	7	26	the	the	DET
ejpam-5347	7	27	strongest	strong	ADJ
ejpam-5347	7	28	techniques	technique	NOUN
ejpam-5347	7	29	available	available	ADJ
ejpam-5347	7	30	to	to	PART
ejpam-5347	7	31	present	present	VERB
ejpam-5347	7	32	scientists	scientist	NOUN
ejpam-5347	7	33	for	for	ADP
ejpam-5347	7	34	the	the	DET
ejpam-5347	7	35	study	study	NOUN
ejpam-5347	7	36	of	of	ADP
ejpam-5347	7	37	computer	computer	NOUN
ejpam-5347	7	38	graphics	graphic	NOUN
ejpam-5347	7	39	and	and	CCONJ
ejpam-5347	7	40	digital	digital	ADJ
ejpam-5347	7	41	topology.new	topology.new	NOUN
ejpam-5347	7	42	functions	function	NOUN
ejpam-5347	7	43	,	,	PUNCT
ejpam-5347	7	44	pairwise	pairwise	NOUN
ejpam-5347	7	45	ω−closed	ω−close	VERB
ejpam-5347	7	46	functions	function	NOUN
ejpam-5347	7	47	,	,	PUNCT
ejpam-5347	7	48	which	which	PRON
ejpam-5347	7	49	are	be	AUX
ejpam-5347	7	50	strictly	strictly	ADV
ejpam-5347	7	51	weaker	weak	ADJ
ejpam-5347	7	52	than	than	ADP
ejpam-5347	7	53	pairwise	pairwise	NOUN
ejpam-5347	7	54	closed	closed	ADJ
ejpam-5347	7	55	functions	function	NOUN
ejpam-5347	7	56	,	,	PUNCT
ejpam-5347	7	57	will	will	AUX
ejpam-5347	7	58	be	be	AUX
ejpam-5347	7	59	introduced	introduce	VERB
ejpam-5347	7	60	in	in	ADP
ejpam-5347	7	61	this	this	DET
ejpam-5347	7	62	study	study	NOUN
ejpam-5347	7	63	.	.	PUNCT
ejpam-5347	8	1	by	by	ADP
ejpam-5347	8	2	applying	apply	VERB
ejpam-5347	8	3	the	the	DET
ejpam-5347	8	4	p̋−space	p̋−space	NOUN
ejpam-5347	8	5	definition	definition	NOUN
ejpam-5347	8	6	,	,	PUNCT
ejpam-5347	8	7	whose	whose	DET
ejpam-5347	8	8	is	be	AUX
ejpam-5347	8	9	a	a	DET
ejpam-5347	8	10	p−space	p−space	NOUN
ejpam-5347	8	11	modification	modification	NOUN
ejpam-5347	8	12	.	.	PUNCT
ejpam-5347	9	1	additionally	additionally	ADV
ejpam-5347	9	2	,	,	PUNCT
ejpam-5347	9	3	we	we	PRON
ejpam-5347	9	4	establish	establish	VERB
ejpam-5347	9	5	different	different	ADJ
ejpam-5347	9	6	projection	projection	NOUN
ejpam-5347	9	7	and	and	CCONJ
ejpam-5347	9	8	product	product	NOUN
ejpam-5347	9	9	theories	theory	NOUN
ejpam-5347	9	10	pertaining	pertain	VERB
ejpam-5347	9	11	to	to	ADP
ejpam-5347	9	12	pairwise	pairwise	NOUN
ejpam-5347	9	13	lindel	lindel	NOUN
ejpam-5347	9	14	..	..	PUNCT
ejpam-5347	9	15	of	of	ADP
ejpam-5347	9	16	and	and	CCONJ
ejpam-5347	9	17	pairwise	pairwise	NOUN
ejpam-5347	9	18	paracompact	paracompact	NOUN
ejpam-5347	9	19	spaces	space	NOUN
ejpam-5347	9	20	utilizing	utilize	VERB
ejpam-5347	9	21	p̋−spaces	p̋−space	NOUN
ejpam-5347	9	22	.	.	PUNCT
ejpam-5347	10	1	we	we	PRON
ejpam-5347	10	2	analyze	analyze	VERB
ejpam-5347	10	3	images	image	NOUN
ejpam-5347	10	4	and	and	CCONJ
ejpam-5347	10	5	inverse	inverse	NOUN
ejpam-5347	10	6	images	image	NOUN
ejpam-5347	10	7	that	that	PRON
ejpam-5347	10	8	have	have	AUX
ejpam-5347	10	9	been	be	AUX
ejpam-5347	10	10	chosen	choose	VERB
ejpam-5347	10	11	topological	topological	ADJ
ejpam-5347	10	12	attributes	attribute	NOUN
ejpam-5347	10	13	for	for	ADP
ejpam-5347	10	14	every	every	DET
ejpam-5347	10	15	one	one	NUM
ejpam-5347	10	16	of	of	ADP
ejpam-5347	10	17	these	these	DET
ejpam-5347	10	18	functions	function	NOUN
ejpam-5347	10	19	.	.	PUNCT
ejpam-5347	11	1	in	in	ADP
ejpam-5347	11	2	the	the	DET
ejpam-5347	11	3	final	final	ADJ
ejpam-5347	11	4	analysis	analysis	NOUN
ejpam-5347	11	5	,	,	PUNCT
ejpam-5347	11	6	we	we	PRON
ejpam-5347	11	7	explore	explore	VERB
ejpam-5347	11	8	several	several	ADJ
ejpam-5347	11	9	counterexamples	counterexample	NOUN
ejpam-5347	11	10	that	that	PRON
ejpam-5347	11	11	correspond	correspond	VERB
ejpam-5347	11	12	to	to	ADP
ejpam-5347	11	13	the	the	DET
ejpam-5347	11	14	offered	offer	VERB
ejpam-5347	11	15	definitions	definition	NOUN
ejpam-5347	11	16	and	and	CCONJ
ejpam-5347	11	17	theorems	theorem	NOUN
ejpam-5347	11	18	.	.	PROPN
ejpam-5347	12	1	2020	2020	NUM
ejpam-5347	12	2	mathematics	mathematic	NOUN
ejpam-5347	12	3	subject	subject	NOUN
ejpam-5347	12	4	classifications	classification	NOUN
ejpam-5347	12	5	:	:	PUNCT
ejpam-5347	12	6	54e55,54b10,54d30	54e55,54b10,54d30	NUM
ejpam-5347	12	7	key	key	ADJ
ejpam-5347	12	8	words	word	NOUN
ejpam-5347	12	9	and	and	CCONJ
ejpam-5347	12	10	phrases	phrase	NOUN
ejpam-5347	12	11	:	:	PUNCT
ejpam-5347	12	12	bitopological	bitopological	ADJ
ejpam-5347	12	13	spaces	space	NOUN
ejpam-5347	12	14	,	,	PUNCT
ejpam-5347	12	15	p̋−space	p̋−space	NOUN
ejpam-5347	12	16	,	,	PUNCT
ejpam-5347	12	17	pair−lindel	pair−lindel	NOUN
ejpam-5347	12	18	..	..	PUNCT
ejpam-5347	12	19	of	of	ADP
ejpam-5347	12	20	,	,	PUNCT
ejpam-5347	12	21	pair−ω−closed	pair−ω−closed	ADJ
ejpam-5347	12	22	functions	function	NOUN
ejpam-5347	12	23	,	,	PUNCT
ejpam-5347	12	24	perfect	perfect	ADJ
ejpam-5347	12	25	function	function	NOUN
ejpam-5347	12	26	,	,	PUNCT
ejpam-5347	12	27	pair−ω−continuous	pair−ω−continuous	ADJ
ejpam-5347	12	28	functions	function	NOUN
ejpam-5347	12	29	,	,	PUNCT
ejpam-5347	12	30	pairparacompact	pairparacompact	NOUN
ejpam-5347	12	31	∗corresponding	∗corresponde	VERB
ejpam-5347	12	32	author	author	NOUN
ejpam-5347	12	33	.	.	PUNCT
ejpam-5347	13	1	doi	doi	NOUN
ejpam-5347	13	2	:	:	PUNCT
ejpam-5347	13	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5347	https://doi.org/10.29020/nybg.ejpam.v17i4.5347	ADJ
ejpam-5347	13	4	email	email	NOUN
ejpam-5347	13	5	addresses	address	NOUN
ejpam-5347	13	6	:	:	PUNCT
ejpam-5347	13	7	aliatoom@anu.edu.jo	aliatoom@anu.edu.jo	NOUN
ejpam-5347	13	8	(	(	PUNCT
ejpam-5347	13	9	a.	a.	NOUN
ejpam-5347	13	10	atoom	atoom	PROPN
ejpam-5347	13	11	)	)	PUNCT
ejpam-5347	13	12	,	,	PUNCT
ejpam-5347	13	13	hhaaqq983@gmail.com	hhaaqq983@gmail.com	X
ejpam-5347	13	14	(	(	PUNCT
ejpam-5347	13	15	h.	h.	PROPN
ejpam-5347	13	16	qoqazeh	qoqazeh	PROPN
ejpam-5347	13	17	)	)	PUNCT
ejpam-5347	13	18	,	,	PUNCT
ejpam-5347	13	19	mholi@taibahu.edu.sa	mholi@taibahu.edu.sa	NOUN
ejpam-5347	13	20	(	(	PUNCT
ejpam-5347	13	21	m.	m.	NOUN
ejpam-5347	13	22	alholi	alholi	PROPN
ejpam-5347	13	23	)	)	PUNCT
ejpam-5347	13	24	,	,	PUNCT
ejpam-5347	13	25	e	e	PROPN
ejpam-5347	13	26	almuhur@asu.edu.jo	almuhur@asu.edu.jo	NOUN
ejpam-5347	13	27	(	(	PUNCT
ejpam-5347	13	28	e.	e.	PROPN
ejpam-5347	13	29	almuhur	almuhur	PROPN
ejpam-5347	13	30	)	)	PUNCT
ejpam-5347	13	31	,	,	PUNCT
ejpam-5347	13	32	e.hussein@aau.edu.jo	e.hussein@aau.edu.jo	PROPN
ejpam-5347	13	33	(	(	PUNCT
ejpam-5347	13	34	e.	e.	PROPN
ejpam-5347	13	35	hussein	hussein	PROPN
ejpam-5347	13	36	)	)	PUNCT
ejpam-5347	13	37	,	,	PUNCT
ejpam-5347	13	38	emanbasssam@gmail.com	emanbasssam@gmail.com	X
ejpam-5347	13	39	(	(	PUNCT
ejpam-5347	13	40	a.	a.	NOUN
ejpam-5347	13	41	owledat	owledat	NOUN
ejpam-5347	13	42	)	)	PUNCT
ejpam-5347	13	43	,	,	PUNCT
ejpam-5347	13	44	a.alnana@psau.edu.sa	a.alnana@psau.edu.sa	PROPN
ejpam-5347	13	45	(	(	PUNCT
ejpam-5347	13	46	a.	a.	PROPN
ejpam-5347	13	47	al	al	PROPN
ejpam-5347	13	48	-	-	PUNCT
ejpam-5347	13	49	nana	nana	PROPN
ejpam-5347	13	50	)	)	PUNCT
ejpam-5347	13	51	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5347	14	1	2574	2574	NUM
ejpam-5347	14	2	copyright	copyright	NOUN
ejpam-5347	14	3	:	:	PUNCT
ejpam-5347	14	4	©	©	PROPN
ejpam-5347	14	5	2024	2024	NUM
ejpam-5347	14	6	the	the	DET
ejpam-5347	14	7	author(s	author(s	NOUN
ejpam-5347	14	8	)	)	PUNCT
ejpam-5347	14	9	.	.	PUNCT
ejpam-5347	15	1	(	(	PUNCT
ejpam-5347	15	2	cc	cc	NOUN
ejpam-5347	15	3	by	by	ADP
ejpam-5347	15	4	-	-	PUNCT
ejpam-5347	15	5	nc	nc	PROPN
ejpam-5347	15	6	4.0	4.0	NUM
ejpam-5347	15	7	)	)	PUNCT
ejpam-5347	15	8	a.	a.	NOUN
ejpam-5347	15	9	atoom	atoom	NOUN
ejpam-5347	15	10	et	et	PROPN
ejpam-5347	15	11	al	al	PROPN
ejpam-5347	15	12	.	.	PUNCT
ejpam-5347	15	13	/	/	SYM
ejpam-5347	15	14	eur	eur	PROPN
ejpam-5347	15	15	.	.	PUNCT
ejpam-5347	16	1	j.	j.	PROPN
ejpam-5347	16	2	pure	pure	PROPN
ejpam-5347	16	3	appl	appl	PROPN
ejpam-5347	16	4	.	.	PROPN
ejpam-5347	16	5	math	math	PROPN
ejpam-5347	16	6	,	,	PUNCT
ejpam-5347	16	7	17	17	NUM
ejpam-5347	16	8	(	(	PUNCT
ejpam-5347	16	9	4	4	NUM
ejpam-5347	16	10	)	)	PUNCT
ejpam-5347	16	11	(	(	PUNCT
ejpam-5347	16	12	2024	2024	NUM
ejpam-5347	16	13	)	)	PUNCT
ejpam-5347	16	14	,	,	PUNCT
ejpam-5347	16	15	2574	2574	NUM
ejpam-5347	16	16	-	-	SYM
ejpam-5347	16	17	2585	2585	NUM
ejpam-5347	16	18	2575	2575	NUM
ejpam-5347	16	19	1	1	NUM
ejpam-5347	16	20	.	.	PUNCT
ejpam-5347	17	1	introduction	introduction	NOUN
ejpam-5347	17	2	several	several	ADJ
ejpam-5347	17	3	broad	broad	ADJ
ejpam-5347	17	4	topological	topological	ADJ
ejpam-5347	17	5	configurations	configuration	NOUN
ejpam-5347	17	6	have	have	AUX
ejpam-5347	17	7	been	be	AUX
ejpam-5347	17	8	explored	explore	VERB
ejpam-5347	17	9	subsequently	subsequently	ADV
ejpam-5347	17	10	.	.	PUNCT
ejpam-5347	18	1	in	in	ADP
ejpam-5347	18	2	light	light	NOUN
ejpam-5347	18	3	of	of	ADP
ejpam-5347	18	4	the	the	DET
ejpam-5347	18	5	topological	topological	ADJ
ejpam-5347	18	6	space	space	NOUN
ejpam-5347	18	7	’s	’s	PART
ejpam-5347	18	8	significance	significance	NOUN
ejpam-5347	18	9	in	in	ADP
ejpam-5347	18	10	analysis	analysis	NOUN
ejpam-5347	18	11	and	and	CCONJ
ejpam-5347	18	12	various	various	ADJ
ejpam-5347	18	13	other	other	ADJ
ejpam-5347	18	14	uses	use	NOUN
ejpam-5347	18	15	,	,	PUNCT
ejpam-5347	18	16	see	see	VERB
ejpam-5347	18	17	[	[	X
ejpam-5347	18	18	2	2	NUM
ejpam-5347	18	19	,	,	PUNCT
ejpam-5347	18	20	3	3	NUM
ejpam-5347	18	21	,	,	PUNCT
ejpam-5347	18	22	5	5	NUM
ejpam-5347	18	23	]	]	PUNCT
ejpam-5347	18	24	.	.	PUNCT
ejpam-5347	19	1	one	one	NUM
ejpam-5347	19	2	of	of	ADP
ejpam-5347	19	3	the	the	DET
ejpam-5347	19	4	most	most	ADV
ejpam-5347	19	5	fundamental	fundamental	ADJ
ejpam-5347	19	6	topological	topological	ADJ
ejpam-5347	19	7	space	space	NOUN
ejpam-5347	19	8	improvements	improvement	NOUN
ejpam-5347	19	9	is	be	AUX
ejpam-5347	19	10	represented	represent	VERB
ejpam-5347	19	11	by	by	ADP
ejpam-5347	19	12	the	the	DET
ejpam-5347	19	13	closed	close	VERB
ejpam-5347	19	14	functions	function	NOUN
ejpam-5347	19	15	.	.	PUNCT
ejpam-5347	20	1	general	general	ADJ
ejpam-5347	20	2	topology	topology	PROPN
ejpam-5347	20	3	informs	inform	VERB
ejpam-5347	20	4	us	we	PRON
ejpam-5347	20	5	that	that	SCONJ
ejpam-5347	20	6	closed	closed	ADJ
ejpam-5347	20	7	sets	set	NOUN
ejpam-5347	20	8	are	be	AUX
ejpam-5347	20	9	crucial	crucial	ADJ
ejpam-5347	20	10	for	for	ADP
ejpam-5347	20	11	the	the	DET
ejpam-5347	20	12	creation	creation	NOUN
ejpam-5347	20	13	of	of	ADP
ejpam-5347	20	14	new	new	ADJ
ejpam-5347	20	15	set	set	NOUN
ejpam-5347	20	16	forms	form	NOUN
ejpam-5347	20	17	and	and	CCONJ
ejpam-5347	20	18	have	have	VERB
ejpam-5347	20	19	vital	vital	ADJ
ejpam-5347	20	20	topological	topological	ADJ
ejpam-5347	20	21	traits	trait	NOUN
ejpam-5347	20	22	.	.	PUNCT
ejpam-5347	21	1	to	to	PART
ejpam-5347	21	2	expand	expand	VERB
ejpam-5347	21	3	on	on	ADP
ejpam-5347	21	4	multiple	multiple	ADJ
ejpam-5347	21	5	features	feature	NOUN
ejpam-5347	21	6	of	of	ADP
ejpam-5347	21	7	closed	closed	ADJ
ejpam-5347	21	8	functions	function	NOUN
ejpam-5347	21	9	,	,	PUNCT
ejpam-5347	21	10	ω−closed	ω−close	VERB
ejpam-5347	21	11	functions	function	NOUN
ejpam-5347	21	12	are	be	AUX
ejpam-5347	21	13	primarily	primarily	ADV
ejpam-5347	21	14	included	include	VERB
ejpam-5347	21	15	in	in	ADP
ejpam-5347	21	16	the	the	DET
ejpam-5347	21	17	topology	topology	NOUN
ejpam-5347	21	18	.	.	PUNCT
ejpam-5347	22	1	compactness	compactness	NOUN
ejpam-5347	22	2	and	and	CCONJ
ejpam-5347	22	3	lindel	lindel	NOUN
ejpam-5347	22	4	..	..	PUNCT
ejpam-5347	23	1	of	of	ADP
ejpam-5347	23	2	are	be	AUX
ejpam-5347	23	3	the	the	DET
ejpam-5347	23	4	fundamental	fundamental	ADJ
ejpam-5347	23	5	elements	element	NOUN
ejpam-5347	23	6	in	in	ADP
ejpam-5347	23	7	standardized	standardized	ADJ
ejpam-5347	23	8	topology	topology	NOUN
ejpam-5347	23	9	.	.	PUNCT
ejpam-5347	24	1	additionally	additionally	ADV
ejpam-5347	24	2	,	,	PUNCT
ejpam-5347	24	3	topology	topology	NOUN
ejpam-5347	24	4	and	and	CCONJ
ejpam-5347	24	5	closed	close	VERB
ejpam-5347	24	6	function	function	NOUN
ejpam-5347	24	7	theories	theory	NOUN
ejpam-5347	24	8	have	have	VERB
ejpam-5347	24	9	a	a	DET
ejpam-5347	24	10	frequent	frequent	ADJ
ejpam-5347	24	11	application	application	NOUN
ejpam-5347	24	12	in	in	ADP
ejpam-5347	24	13	mathematical	mathematical	ADJ
ejpam-5347	24	14	evaluation	evaluation	NOUN
ejpam-5347	24	15	and	and	CCONJ
ejpam-5347	24	16	logical	logical	ADJ
ejpam-5347	24	17	arithmetic	arithmetic	ADJ
ejpam-5347	24	18	correspondingly	correspondingly	ADV
ejpam-5347	24	19	.	.	PUNCT
ejpam-5347	25	1	both	both	PRON
ejpam-5347	25	2	of	of	ADP
ejpam-5347	25	3	these	these	DET
ejpam-5347	25	4	notions	notion	NOUN
ejpam-5347	25	5	are	be	AUX
ejpam-5347	25	6	also	also	ADV
ejpam-5347	25	7	very	very	ADV
ejpam-5347	25	8	useful	useful	ADJ
ejpam-5347	25	9	in	in	ADP
ejpam-5347	25	10	real	real	ADJ
ejpam-5347	25	11	-	-	PUNCT
ejpam-5347	25	12	world	world	NOUN
ejpam-5347	25	13	applications	application	NOUN
ejpam-5347	25	14	.	.	PUNCT
ejpam-5347	26	1	a	a	DET
ejpam-5347	26	2	novel	novel	ADJ
ejpam-5347	26	3	kind	kind	NOUN
ejpam-5347	26	4	of	of	ADP
ejpam-5347	26	5	mappings	mapping	NOUN
ejpam-5347	26	6	known	know	VERB
ejpam-5347	26	7	as	as	ADP
ejpam-5347	26	8	ω−closed	ω−close	VERB
ejpam-5347	26	9	mappings	mapping	NOUN
ejpam-5347	26	10	,	,	PUNCT
ejpam-5347	26	11	which	which	PRON
ejpam-5347	26	12	are	be	AUX
ejpam-5347	26	13	precisely	precisely	ADV
ejpam-5347	26	14	weaker	weak	ADJ
ejpam-5347	26	15	than	than	ADP
ejpam-5347	26	16	closed	closed	ADJ
ejpam-5347	26	17	mappings	mapping	NOUN
ejpam-5347	26	18	,	,	PUNCT
ejpam-5347	26	19	was	be	AUX
ejpam-5347	26	20	created	create	VERB
ejpam-5347	26	21	by	by	ADP
ejpam-5347	26	22	[	[	X
ejpam-5347	26	23	11	11	NUM
ejpam-5347	26	24	]	]	PUNCT
ejpam-5347	26	25	in	in	ADP
ejpam-5347	26	26	1982	1982	NUM
ejpam-5347	26	27	.	.	PUNCT
ejpam-5347	27	1	he	he	PRON
ejpam-5347	27	2	then	then	ADV
ejpam-5347	27	3	goes	go	VERB
ejpam-5347	27	4	over	over	ADP
ejpam-5347	27	5	a	a	DET
ejpam-5347	27	6	few	few	ADJ
ejpam-5347	27	7	more	more	ADJ
ejpam-5347	27	8	situations	situation	NOUN
ejpam-5347	27	9	that	that	PRON
ejpam-5347	27	10	have	have	VERB
ejpam-5347	27	11	relevance	relevance	NOUN
ejpam-5347	27	12	to	to	ADP
ejpam-5347	27	13	the	the	DET
ejpam-5347	27	14	definitions	definition	NOUN
ejpam-5347	27	15	and	and	CCONJ
ejpam-5347	27	16	theorems	theorem	NOUN
ejpam-5347	27	17	which	which	PRON
ejpam-5347	27	18	are	be	AUX
ejpam-5347	27	19	presented	present	VERB
ejpam-5347	27	20	,	,	PUNCT
ejpam-5347	27	21	as	as	SCONJ
ejpam-5347	27	22	he	he	PRON
ejpam-5347	27	23	proposed	propose	VERB
ejpam-5347	27	24	the	the	DET
ejpam-5347	27	25	subsequent	subsequent	ADJ
ejpam-5347	27	26	definitions	definition	NOUN
ejpam-5347	27	27	of	of	ADP
ejpam-5347	27	28	ω−open	ω−open	ADJ
ejpam-5347	27	29	and	and	CCONJ
ejpam-5347	27	30	ω−closed	ω−close	VERB
ejpam-5347	27	31	sets	set	NOUN
ejpam-5347	27	32	.	.	PUNCT
ejpam-5347	28	1	if	if	SCONJ
ejpam-5347	28	2	j	j	PROPN
ejpam-5347	28	3	has	have	VERB
ejpam-5347	28	4	all	all	PRON
ejpam-5347	28	5	of	of	ADP
ejpam-5347	28	6	its	its	PRON
ejpam-5347	28	7	condensation	condensation	NOUN
ejpam-5347	28	8	points	point	NOUN
ejpam-5347	28	9	,	,	PUNCT
ejpam-5347	28	10	then	then	ADV
ejpam-5347	28	11	it	it	PRON
ejpam-5347	28	12	is	be	AUX
ejpam-5347	28	13	commonly	commonly	ADV
ejpam-5347	28	14	referred	refer	VERB
ejpam-5347	28	15	to	to	ADP
ejpam-5347	28	16	as	as	ADP
ejpam-5347	28	17	being	be	AUX
ejpam-5347	28	18	ω−closed	ω−close	VERB
ejpam-5347	28	19	.	.	PUNCT
ejpam-5347	28	20	ω−open	ω−open	PROPN
ejpam-5347	28	21	is	be	AUX
ejpam-5347	28	22	the	the	DET
ejpam-5347	28	23	complement	complement	NOUN
ejpam-5347	28	24	of	of	ADP
ejpam-5347	28	25	an	an	DET
ejpam-5347	28	26	ω−closed	ω−close	VERB
ejpam-5347	28	27	set	set	NOUN
ejpam-5347	28	28	.	.	PUNCT
ejpam-5347	29	1	likewise	likewise	ADV
ejpam-5347	29	2	the	the	DET
ejpam-5347	29	3	intersection	intersection	NOUN
ejpam-5347	29	4	of	of	ADP
ejpam-5347	29	5	all	all	DET
ejpam-5347	29	6	ω−closed	ω−close	VERB
ejpam-5347	29	7	sets	set	NOUN
ejpam-5347	29	8	that	that	PRON
ejpam-5347	29	9	contain	contain	VERB
ejpam-5347	29	10	j	j	PROPN
ejpam-5347	29	11	will	will	AUX
ejpam-5347	29	12	be	be	AUX
ejpam-5347	29	13	indicated	indicate	VERB
ejpam-5347	29	14	by	by	ADP
ejpam-5347	29	15	clω	clω	PROPN
ejpam-5347	29	16	j	j	PROPN
ejpam-5347	29	17	.	.	PUNCT
ejpam-5347	30	1	the	the	DET
ejpam-5347	30	2	idea	idea	NOUN
ejpam-5347	30	3	of	of	ADP
ejpam-5347	30	4	the	the	DET
ejpam-5347	30	5	existence	existence	NOUN
ejpam-5347	30	6	of	of	ADP
ejpam-5347	30	7	a	a	DET
ejpam-5347	30	8	bitopological	bitopological	ADJ
ejpam-5347	30	9	space	space	NOUN
ejpam-5347	30	10	was	be	AUX
ejpam-5347	30	11	initially	initially	ADV
ejpam-5347	30	12	introduced	introduce	VERB
ejpam-5347	30	13	by	by	ADP
ejpam-5347	30	14	[	[	X
ejpam-5347	30	15	13	13	NUM
ejpam-5347	30	16	]	]	PUNCT
ejpam-5347	30	17	in	in	ADP
ejpam-5347	30	18	1963	1963	NUM
ejpam-5347	30	19	.	.	PUNCT
ejpam-5347	31	1	since	since	SCONJ
ejpam-5347	31	2	then	then	ADV
ejpam-5347	31	3	,	,	PUNCT
ejpam-5347	31	4	other	other	ADJ
ejpam-5347	31	5	single	single	ADJ
ejpam-5347	31	6	topological	topological	ADJ
ejpam-5347	31	7	qualities	quality	NOUN
ejpam-5347	31	8	,	,	PUNCT
ejpam-5347	31	9	including	include	VERB
ejpam-5347	31	10	lindel	lindel	NOUN
ejpam-5347	31	11	..	..	PUNCT
ejpam-5347	31	12	ofness	ofness	NOUN
ejpam-5347	31	13	,	,	PUNCT
ejpam-5347	31	14	mapping	mapping	NOUN
ejpam-5347	31	15	types	type	NOUN
ejpam-5347	31	16	,	,	PUNCT
ejpam-5347	31	17	separation	separation	NOUN
ejpam-5347	31	18	axioms	axiom	NOUN
ejpam-5347	31	19	,	,	PUNCT
ejpam-5347	31	20	compactness	compactness	NOUN
ejpam-5347	31	21	and	and	CCONJ
ejpam-5347	31	22	metacompactness	metacompactness	NOUN
ejpam-5347	31	23	,	,	PUNCT
ejpam-5347	31	24	have	have	AUX
ejpam-5347	31	25	also	also	ADV
ejpam-5347	31	26	been	be	AUX
ejpam-5347	31	27	stretched	stretch	VERB
ejpam-5347	31	28	to	to	ADP
ejpam-5347	31	29	bitopological	bitopological	ADJ
ejpam-5347	31	30	spaces.we	spaces.we	PRON
ejpam-5347	31	31	are	be	AUX
ejpam-5347	31	32	going	go	VERB
ejpam-5347	31	33	to	to	PART
ejpam-5347	31	34	utilize	utilize	VERB
ejpam-5347	31	35	pairwise	pairwise	NOUN
ejpam-5347	31	36	lindel	lindel	NOUN
ejpam-5347	31	37	..	..	PUNCT
ejpam-5347	31	38	of	of	ADP
ejpam-5347	31	39	as	as	ADP
ejpam-5347	31	40	pair	pair	NOUN
ejpam-5347	31	41	-	-	PUNCT
ejpam-5347	31	42	lindel	lindel	NOUN
ejpam-5347	31	43	..	..	PUNCT
ejpam-5347	31	44	of	of	ADP
ejpam-5347	31	45	during	during	ADP
ejpam-5347	31	46	the	the	DET
ejpam-5347	31	47	course	course	NOUN
ejpam-5347	31	48	of	of	ADP
ejpam-5347	31	49	this	this	DET
ejpam-5347	31	50	investigation	investigation	NOUN
ejpam-5347	31	51	,	,	PUNCT
ejpam-5347	31	52	and	and	CCONJ
ejpam-5347	31	53	pairsignifies	pairsignifie	NOUN
ejpam-5347	31	54	pairwise	pairwise	VERB
ejpam-5347	31	55	.	.	PUNCT
ejpam-5347	32	1	the	the	DET
ejpam-5347	32	2	fundamental	fundamental	ADJ
ejpam-5347	32	3	definitions	definition	NOUN
ejpam-5347	32	4	employed	employ	VERB
ejpam-5347	32	5	in	in	ADP
ejpam-5347	32	6	this	this	DET
ejpam-5347	32	7	investigation	investigation	NOUN
ejpam-5347	32	8	are	be	AUX
ejpam-5347	32	9	presented	present	VERB
ejpam-5347	32	10	in	in	ADP
ejpam-5347	32	11	section	section	NOUN
ejpam-5347	32	12	2	2	NUM
ejpam-5347	32	13	.	.	PUNCT
ejpam-5347	33	1	we	we	PRON
ejpam-5347	33	2	demonstrate	demonstrate	VERB
ejpam-5347	33	3	some	some	DET
ejpam-5347	33	4	properties	property	NOUN
ejpam-5347	33	5	of	of	ADP
ejpam-5347	33	6	pair−ω−closed	pair−ω−closed	ADJ
ejpam-5347	33	7	functions	function	NOUN
ejpam-5347	33	8	in	in	ADP
ejpam-5347	33	9	section	section	NOUN
ejpam-5347	33	10	3	3	NUM
ejpam-5347	33	11	.	.	PUNCT
ejpam-5347	34	1	the	the	DET
ejpam-5347	34	2	association	association	NOUN
ejpam-5347	34	3	between	between	ADP
ejpam-5347	34	4	particular	particular	ADJ
ejpam-5347	34	5	weakened	weaken	VERB
ejpam-5347	34	6	versions	version	NOUN
ejpam-5347	34	7	of	of	ADP
ejpam-5347	34	8	pairwise	pairwise	NOUN
ejpam-5347	34	9	closed	close	VERB
ejpam-5347	34	10	functions	function	NOUN
ejpam-5347	34	11	and	and	CCONJ
ejpam-5347	34	12	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	34	13	functions	function	NOUN
ejpam-5347	34	14	is	be	AUX
ejpam-5347	34	15	illustrated	illustrate	VERB
ejpam-5347	34	16	with	with	ADP
ejpam-5347	34	17	several	several	ADJ
ejpam-5347	34	18	instances	instance	NOUN
ejpam-5347	34	19	in	in	ADP
ejpam-5347	34	20	.	.	PUNCT
ejpam-5347	35	1	subsequently	subsequently	ADV
ejpam-5347	35	2	,	,	PUNCT
ejpam-5347	35	3	the	the	DET
ejpam-5347	35	4	more	more	ADV
ejpam-5347	35	5	complex	complex	ADJ
ejpam-5347	35	6	characteristics	characteristic	NOUN
ejpam-5347	35	7	of	of	ADP
ejpam-5347	35	8	the	the	DET
ejpam-5347	35	9	pair−ω−closed	pair−ω−closed	PROPN
ejpam-5347	35	10	functions	function	NOUN
ejpam-5347	35	11	,	,	PUNCT
ejpam-5347	35	12	notably	notably	ADV
ejpam-5347	35	13	their	their	PRON
ejpam-5347	35	14	product	product	NOUN
ejpam-5347	35	15	and	and	CCONJ
ejpam-5347	35	16	projection	projection	NOUN
ejpam-5347	35	17	,	,	PUNCT
ejpam-5347	35	18	are	be	AUX
ejpam-5347	35	19	covered	cover	VERB
ejpam-5347	35	20	in	in	ADP
ejpam-5347	35	21	section	section	NOUN
ejpam-5347	35	22	4	4	NUM
ejpam-5347	35	23	.	.	PUNCT
ejpam-5347	36	1	in	in	ADP
ejpam-5347	36	2	the	the	DET
ejpam-5347	36	3	end	end	NOUN
ejpam-5347	36	4	,	,	PUNCT
ejpam-5347	36	5	in	in	ADP
ejpam-5347	36	6	section	section	NOUN
ejpam-5347	36	7	5	5	NUM
ejpam-5347	36	8	,	,	PUNCT
ejpam-5347	36	9	we	we	PRON
ejpam-5347	36	10	go	go	VERB
ejpam-5347	36	11	through	through	ADP
ejpam-5347	36	12	a	a	DET
ejpam-5347	36	13	variety	variety	NOUN
ejpam-5347	36	14	of	of	ADP
ejpam-5347	36	15	counterexamples	counterexample	NOUN
ejpam-5347	36	16	that	that	PRON
ejpam-5347	36	17	are	be	AUX
ejpam-5347	36	18	pertinent	pertinent	ADJ
ejpam-5347	36	19	to	to	ADP
ejpam-5347	36	20	the	the	DET
ejpam-5347	36	21	definitions	definition	NOUN
ejpam-5347	36	22	and	and	CCONJ
ejpam-5347	36	23	theorems	theorem	NOUN
ejpam-5347	36	24	offered	offer	VERB
ejpam-5347	36	25	in	in	ADP
ejpam-5347	36	26	the	the	DET
ejpam-5347	36	27	earlier	early	ADJ
ejpam-5347	36	28	sections	section	NOUN
ejpam-5347	36	29	.	.	PUNCT
ejpam-5347	37	1	2	2	X
ejpam-5347	37	2	.	.	X
ejpam-5347	37	3	basic	basic	ADJ
ejpam-5347	37	4	definitions	definition	NOUN
ejpam-5347	37	5	and	and	CCONJ
ejpam-5347	37	6	preliminary	preliminary	ADJ
ejpam-5347	37	7	remarks	remark	NOUN
ejpam-5347	37	8	some	some	DET
ejpam-5347	37	9	key	key	ADJ
ejpam-5347	37	10	ideas	idea	NOUN
ejpam-5347	37	11	and	and	CCONJ
ejpam-5347	37	12	details	detail	NOUN
ejpam-5347	37	13	that	that	PRON
ejpam-5347	37	14	were	be	AUX
ejpam-5347	37	15	employed	employ	VERB
ejpam-5347	37	16	in	in	ADP
ejpam-5347	37	17	the	the	DET
ejpam-5347	37	18	research	research	NOUN
ejpam-5347	37	19	are	be	AUX
ejpam-5347	37	20	presented	present	VERB
ejpam-5347	37	21	in	in	ADP
ejpam-5347	37	22	this	this	DET
ejpam-5347	37	23	part	part	NOUN
ejpam-5347	37	24	.	.	PUNCT
ejpam-5347	38	1	definition	definition	NOUN
ejpam-5347	38	2	1	1	NUM
ejpam-5347	38	3	.	.	PUNCT
ejpam-5347	39	1	[	[	X
ejpam-5347	39	2	4	4	X
ejpam-5347	39	3	]	]	X
ejpam-5347	39	4	a	a	DET
ejpam-5347	39	5	function	function	NOUN
ejpam-5347	39	6	υ	υ	NOUN
ejpam-5347	39	7	:	:	PUNCT
ejpam-5347	39	8	(	(	PUNCT
ejpam-5347	39	9	d	d	NOUN
ejpam-5347	39	10	,	,	PUNCT
ejpam-5347	39	11	κ1	κ1	NOUN
ejpam-5347	39	12	,	,	PUNCT
ejpam-5347	39	13	κ2	κ2	PROPN
ejpam-5347	39	14	)	)	PUNCT
ejpam-5347	39	15	→	→	SYM
ejpam-5347	39	16	(	(	PUNCT
ejpam-5347	39	17	g	g	NOUN
ejpam-5347	39	18	,	,	PUNCT
ejpam-5347	39	19	υ1	υ1	NOUN
ejpam-5347	39	20	,	,	PUNCT
ejpam-5347	39	21	υ2	υ2	PROPN
ejpam-5347	39	22	)	)	PUNCT
ejpam-5347	39	23	is	be	AUX
ejpam-5347	39	24	referred	refer	VERB
ejpam-5347	39	25	to	to	ADP
ejpam-5347	39	26	as	as	ADV
ejpam-5347	39	27	pair−continuous	pair−continuous	ADJ
ejpam-5347	39	28	,	,	PUNCT
ejpam-5347	39	29	whether	whether	SCONJ
ejpam-5347	39	30	υ1	υ1	PROPN
ejpam-5347	39	31	:	:	PUNCT
ejpam-5347	39	32	(	(	PUNCT
ejpam-5347	39	33	d	d	NOUN
ejpam-5347	39	34	,	,	PUNCT
ejpam-5347	39	35	κ1	κ1	NOUN
ejpam-5347	39	36	)	)	PUNCT
ejpam-5347	39	37	→	→	SYM
ejpam-5347	39	38	(	(	PUNCT
ejpam-5347	39	39	g	g	NOUN
ejpam-5347	39	40	,	,	PUNCT
ejpam-5347	39	41	υ1	υ1	ADJ
ejpam-5347	39	42	)	)	PUNCT
ejpam-5347	39	43	and	and	CCONJ
ejpam-5347	39	44	υ2	υ2	NOUN
ejpam-5347	39	45	:	:	PUNCT
ejpam-5347	39	46	(	(	PUNCT
ejpam-5347	39	47	d	d	NOUN
ejpam-5347	39	48	,	,	PUNCT
ejpam-5347	39	49	κ2	κ2	NOUN
ejpam-5347	39	50	)	)	PUNCT
ejpam-5347	39	51	→	→	SYM
ejpam-5347	39	52	(	(	PUNCT
ejpam-5347	39	53	g	g	NOUN
ejpam-5347	39	54	,	,	PUNCT
ejpam-5347	39	55	υ2	υ2	NOUN
ejpam-5347	39	56	)	)	PUNCT
ejpam-5347	39	57	are	be	AUX
ejpam-5347	39	58	continuous	continuous	ADJ
ejpam-5347	39	59	functions	function	NOUN
ejpam-5347	39	60	.	.	PUNCT
ejpam-5347	40	1	definition	definition	NOUN
ejpam-5347	40	2	2	2	NUM
ejpam-5347	40	3	.	.	PUNCT
ejpam-5347	41	1	[	[	X
ejpam-5347	41	2	8	8	NUM
ejpam-5347	41	3	]	]	X
ejpam-5347	41	4	a	a	DET
ejpam-5347	41	5	function	function	NOUN
ejpam-5347	41	6	υ	υ	NOUN
ejpam-5347	41	7	:	:	PUNCT
ejpam-5347	41	8	(	(	PUNCT
ejpam-5347	41	9	d	d	NOUN
ejpam-5347	41	10	,	,	PUNCT
ejpam-5347	41	11	κ1	κ1	NOUN
ejpam-5347	41	12	,	,	PUNCT
ejpam-5347	41	13	κ2	κ2	PROPN
ejpam-5347	41	14	)	)	PUNCT
ejpam-5347	41	15	→	→	SYM
ejpam-5347	41	16	(	(	PUNCT
ejpam-5347	41	17	g	g	NOUN
ejpam-5347	41	18	,	,	PUNCT
ejpam-5347	41	19	υ1	υ1	NOUN
ejpam-5347	41	20	,	,	PUNCT
ejpam-5347	41	21	υ2	υ2	PROPN
ejpam-5347	41	22	)	)	PUNCT
ejpam-5347	41	23	is	be	AUX
ejpam-5347	41	24	referred	refer	VERB
ejpam-5347	41	25	to	to	ADP
ejpam-5347	41	26	as	as	SCONJ
ejpam-5347	41	27	pair−closed	pair−close	VERB
ejpam-5347	41	28	,	,	PUNCT
ejpam-5347	41	29	if	if	SCONJ
ejpam-5347	41	30	υ1	υ1	PROPN
ejpam-5347	41	31	:	:	PUNCT
ejpam-5347	41	32	(	(	PUNCT
ejpam-5347	41	33	d	d	NOUN
ejpam-5347	41	34	,	,	PUNCT
ejpam-5347	41	35	κ1	κ1	NOUN
ejpam-5347	41	36	)	)	PUNCT
ejpam-5347	41	37	→	→	SYM
ejpam-5347	41	38	(	(	PUNCT
ejpam-5347	41	39	g	g	NOUN
ejpam-5347	41	40	,	,	PUNCT
ejpam-5347	41	41	υ1	υ1	ADJ
ejpam-5347	41	42	)	)	PUNCT
ejpam-5347	41	43	and	and	CCONJ
ejpam-5347	41	44	υ2	υ2	NOUN
ejpam-5347	41	45	:	:	PUNCT
ejpam-5347	41	46	(	(	PUNCT
ejpam-5347	41	47	d	d	NOUN
ejpam-5347	41	48	,	,	PUNCT
ejpam-5347	41	49	κ2	κ2	NOUN
ejpam-5347	41	50	)	)	PUNCT
ejpam-5347	41	51	→	→	SYM
ejpam-5347	41	52	(	(	PUNCT
ejpam-5347	41	53	g	g	NOUN
ejpam-5347	41	54	,	,	PUNCT
ejpam-5347	41	55	υ2	υ2	NOUN
ejpam-5347	41	56	)	)	PUNCT
ejpam-5347	41	57	are	be	AUX
ejpam-5347	41	58	closed	closed	ADJ
ejpam-5347	41	59	functions	function	NOUN
ejpam-5347	41	60	.	.	PUNCT
ejpam-5347	42	1	that	that	PRON
ejpam-5347	42	2	is	be	AUX
ejpam-5347	42	3	cruel	cruel	ADJ
ejpam-5347	42	4	h1is	h1is	NOUN
ejpam-5347	42	5	closed	close	VERB
ejpam-5347	42	6	in	in	ADP
ejpam-5347	42	7	κ1	κ1	NOUN
ejpam-5347	42	8	,	,	PUNCT
ejpam-5347	42	9	then	then	ADV
ejpam-5347	42	10	υ(h1	υ(h1	PROPN
ejpam-5347	42	11	)	)	PUNCT
ejpam-5347	42	12	is	be	AUX
ejpam-5347	42	13	closed	close	VERB
ejpam-5347	42	14	in	in	ADP
ejpam-5347	42	15	υ1	υ1	PROPN
ejpam-5347	42	16	,	,	PUNCT
ejpam-5347	42	17	and	and	CCONJ
ejpam-5347	42	18	if	if	SCONJ
ejpam-5347	42	19	h2	h2	NOUN
ejpam-5347	42	20	is	be	AUX
ejpam-5347	42	21	closed	close	VERB
ejpam-5347	42	22	in	in	ADP
ejpam-5347	42	23	κ2	κ2	NOUN
ejpam-5347	42	24	,	,	PUNCT
ejpam-5347	42	25	then	then	ADV
ejpam-5347	42	26	υ(h2	υ(h2	NOUN
ejpam-5347	42	27	)	)	PUNCT
ejpam-5347	42	28	is	be	AUX
ejpam-5347	42	29	closed	close	VERB
ejpam-5347	42	30	in	in	ADP
ejpam-5347	42	31	υ2	υ2	PROPN
ejpam-5347	42	32	.	.	PUNCT
ejpam-5347	43	1	a.	a.	NOUN
ejpam-5347	43	2	atoom	atoom	PROPN
ejpam-5347	43	3	et	et	PROPN
ejpam-5347	43	4	al	al	PROPN
ejpam-5347	43	5	.	.	PUNCT
ejpam-5347	43	6	/	/	SYM
ejpam-5347	43	7	eur	eur	PROPN
ejpam-5347	43	8	.	.	PUNCT
ejpam-5347	44	1	j.	j.	PROPN
ejpam-5347	44	2	pure	pure	PROPN
ejpam-5347	44	3	appl	appl	PROPN
ejpam-5347	44	4	.	.	PROPN
ejpam-5347	44	5	math	math	PROPN
ejpam-5347	44	6	,	,	PUNCT
ejpam-5347	44	7	17	17	NUM
ejpam-5347	44	8	(	(	PUNCT
ejpam-5347	44	9	4	4	NUM
ejpam-5347	44	10	)	)	PUNCT
ejpam-5347	44	11	(	(	PUNCT
ejpam-5347	44	12	2024	2024	NUM
ejpam-5347	44	13	)	)	PUNCT
ejpam-5347	44	14	,	,	PUNCT
ejpam-5347	44	15	2574	2574	NUM
ejpam-5347	44	16	-	-	SYM
ejpam-5347	44	17	2585	2585	NUM
ejpam-5347	44	18	2576	2576	NUM
ejpam-5347	44	19	definition	definition	NOUN
ejpam-5347	44	20	3	3	NUM
ejpam-5347	44	21	.	.	PUNCT
ejpam-5347	45	1	[	[	X
ejpam-5347	45	2	15	15	NUM
ejpam-5347	45	3	]	]	X
ejpam-5347	45	4	a	a	DET
ejpam-5347	45	5	cover	cover	NOUN
ejpam-5347	45	6	t	t	NOUN
ejpam-5347	45	7	of	of	ADP
ejpam-5347	45	8	the	the	DET
ejpam-5347	45	9	bitopological	bitopological	ADJ
ejpam-5347	45	10	space	space	NOUN
ejpam-5347	45	11	(	(	PUNCT
ejpam-5347	45	12	d	d	NOUN
ejpam-5347	45	13	,	,	PUNCT
ejpam-5347	45	14	κ1	κ1	NOUN
ejpam-5347	45	15	,	,	PUNCT
ejpam-5347	45	16	κ2	κ2	PROPN
ejpam-5347	45	17	)	)	PUNCT
ejpam-5347	45	18	has	have	AUX
ejpam-5347	45	19	been	be	AUX
ejpam-5347	45	20	referred	refer	VERB
ejpam-5347	45	21	to	to	PART
ejpam-5347	45	22	κ1κ2−	κ1κ2−	VERB
ejpam-5347	45	23	open	open	ADJ
ejpam-5347	45	24	if	if	SCONJ
ejpam-5347	45	25	t	t	PROPN
ejpam-5347	45	26	⊂	⊂	PROPN
ejpam-5347	45	27	κ1	κ1	PROPN
ejpam-5347	45	28	∪	∪	PROPN
ejpam-5347	45	29	κ2	κ2	PROPN
ejpam-5347	45	30	.	.	PUNCT
ejpam-5347	46	1	additionally	additionally	ADV
ejpam-5347	46	2	,	,	PUNCT
ejpam-5347	46	3	t	t	PROPN
ejpam-5347	46	4	contains	contain	VERB
ejpam-5347	46	5	at	at	ADP
ejpam-5347	46	6	least	least	ADJ
ejpam-5347	46	7	one−nonempty	one−nonempty	ADJ
ejpam-5347	46	8	member	member	NOUN
ejpam-5347	46	9	of	of	ADP
ejpam-5347	46	10	κ2	κ2	NOUN
ejpam-5347	46	11	,	,	PUNCT
ejpam-5347	46	12	it	it	PRON
ejpam-5347	46	13	is	be	AUX
ejpam-5347	46	14	regarded	regard	VERB
ejpam-5347	46	15	as	as	ADP
ejpam-5347	46	16	pair−open	pair−open	ADJ
ejpam-5347	46	17	.	.	PUNCT
ejpam-5347	47	1	definition	definition	NOUN
ejpam-5347	47	2	4	4	NUM
ejpam-5347	47	3	.	.	PUNCT
ejpam-5347	48	1	[	[	X
ejpam-5347	48	2	12	12	NUM
ejpam-5347	48	3	]	]	X
ejpam-5347	48	4	if	if	SCONJ
ejpam-5347	48	5	any	any	DET
ejpam-5347	48	6	pair−open	pair−open	ADJ
ejpam-5347	48	7	cover	cover	NOUN
ejpam-5347	48	8	of	of	ADP
ejpam-5347	48	9	a	a	DET
ejpam-5347	48	10	bitopological	bitopological	ADJ
ejpam-5347	48	11	space	space	NOUN
ejpam-5347	48	12	has	have	VERB
ejpam-5347	48	13	a	a	DET
ejpam-5347	48	14	countable	countable	ADJ
ejpam-5347	48	15	subcover	subcover	NOUN
ejpam-5347	48	16	,	,	PUNCT
ejpam-5347	48	17	the	the	DET
ejpam-5347	48	18	space	space	NOUN
ejpam-5347	48	19	is	be	AUX
ejpam-5347	48	20	commonly	commonly	ADV
ejpam-5347	48	21	referred	refer	VERB
ejpam-5347	48	22	to	to	ADP
ejpam-5347	48	23	as	as	ADP
ejpam-5347	48	24	a	a	DET
ejpam-5347	48	25	pair−lindel	pair−lindel	NOUN
ejpam-5347	48	26	..	..	PUNCT
ejpam-5347	48	27	of	of	ADP
ejpam-5347	48	28	.	.	PUNCT
ejpam-5347	49	1	definition	definition	NOUN
ejpam-5347	49	2	5	5	NUM
ejpam-5347	49	3	.	.	PUNCT
ejpam-5347	50	1	[	[	X
ejpam-5347	50	2	13	13	NUM
ejpam-5347	50	3	]	]	X
ejpam-5347	50	4	if	if	SCONJ
ejpam-5347	50	5	any	any	DET
ejpam-5347	50	6	κ1κ2−open	κ1κ2−open	ADJ
ejpam-5347	50	7	cover	cover	NOUN
ejpam-5347	50	8	of	of	ADP
ejpam-5347	50	9	a	a	DET
ejpam-5347	50	10	bitopological	bitopological	ADJ
ejpam-5347	50	11	space	space	NOUN
ejpam-5347	50	12	has	have	VERB
ejpam-5347	50	13	a	a	DET
ejpam-5347	50	14	countable	countable	ADJ
ejpam-5347	50	15	subcover	subcover	NOUN
ejpam-5347	50	16	,	,	PUNCT
ejpam-5347	50	17	the	the	DET
ejpam-5347	50	18	space	space	NOUN
ejpam-5347	50	19	is	be	AUX
ejpam-5347	50	20	commonly	commonly	ADV
ejpam-5347	50	21	referred	refer	VERB
ejpam-5347	50	22	to	to	ADP
ejpam-5347	50	23	as	as	ADP
ejpam-5347	50	24	a	a	DET
ejpam-5347	50	25	s−lindel	s−lindel	PROPN
ejpam-5347	50	26	..	..	PUNCT
ejpam-5347	50	27	of	of	ADP
ejpam-5347	50	28	.	.	PUNCT
ejpam-5347	51	1	definition	definition	NOUN
ejpam-5347	51	2	6	6	NUM
ejpam-5347	51	3	.	.	PUNCT
ejpam-5347	52	1	[	[	X
ejpam-5347	52	2	17	17	NUM
ejpam-5347	52	3	]	]	PUNCT
ejpam-5347	52	4	whether	whether	SCONJ
ejpam-5347	52	5	t	t	X
ejpam-5347	52	6	˜	˜	PROPN
ejpam-5347	52	7	,	,	PUNCT
ejpam-5347	52	8	p	p	PROPN
ejpam-5347	52	9	˜	˜	PROPN
ejpam-5347	52	10	are	be	AUX
ejpam-5347	52	11	pair−open	pair−open	ADJ
ejpam-5347	52	12	covers	cover	NOUN
ejpam-5347	52	13	,	,	PUNCT
ejpam-5347	52	14	we	we	PRON
ejpam-5347	52	15	say	say	VERB
ejpam-5347	52	16	that	that	SCONJ
ejpam-5347	52	17	p	p	PROPN
ejpam-5347	52	18	˜	˜	PROPN
ejpam-5347	52	19	is	be	AUX
ejpam-5347	52	20	a	a	DET
ejpam-5347	52	21	parallel	parallel	ADJ
ejpam-5347	52	22	refinement	refinement	NOUN
ejpam-5347	52	23	of	of	ADP
ejpam-5347	52	24	t	t	PROPN
ejpam-5347	52	25	˜	˜	PROPN
ejpam-5347	52	26	,	,	PUNCT
ejpam-5347	52	27	solely	solely	ADV
ejpam-5347	52	28	in	in	ADP
ejpam-5347	52	29	the	the	DET
ejpam-5347	52	30	event	event	NOUN
ejpam-5347	52	31	that	that	PRON
ejpam-5347	52	32	any	any	DET
ejpam-5347	52	33	p1	p1	PROPN
ejpam-5347	52	34	∈	∈	PROPN
ejpam-5347	52	35	p	p	PROPN
ejpam-5347	52	36	˜	˜	PROPN
ejpam-5347	52	37	,	,	PUNCT
ejpam-5347	52	38	in	in	ADP
ejpam-5347	52	39	a	a	DET
ejpam-5347	52	40	way	way	NOUN
ejpam-5347	52	41	that	that	PRON
ejpam-5347	52	42	p	p	PROPN
ejpam-5347	52	43	∈	∈	PROPN
ejpam-5347	52	44	κ1is	κ1i	NOUN
ejpam-5347	52	45	included	include	VERB
ejpam-5347	52	46	in	in	ADP
ejpam-5347	52	47	t1	t1	PROPN
ejpam-5347	52	48	∈	∈	PROPN
ejpam-5347	52	49	t	t	NOUN
ejpam-5347	52	50	˜	˜	PROPN
ejpam-5347	52	51	and	and	CCONJ
ejpam-5347	52	52	t1	t1	NOUN
ejpam-5347	52	53	∈	∈	PROPN
ejpam-5347	52	54	κ1	κ1	NOUN
ejpam-5347	52	55	,	,	PUNCT
ejpam-5347	52	56	and	and	CCONJ
ejpam-5347	52	57	p2	p2	PROPN
ejpam-5347	52	58	∈	∈	PROPN
ejpam-5347	52	59	v	v	ADP
ejpam-5347	52	60	˜	˜	PROPN
ejpam-5347	52	61	,	,	PUNCT
ejpam-5347	52	62	such	such	ADJ
ejpam-5347	52	63	that	that	SCONJ
ejpam-5347	52	64	p	p	PROPN
ejpam-5347	52	65	∈	∈	PROPN
ejpam-5347	52	66	κ2	κ2	NOUN
ejpam-5347	52	67	is	be	AUX
ejpam-5347	52	68	included	include	VERB
ejpam-5347	52	69	in	in	ADP
ejpam-5347	52	70	t2	t2	PROPN
ejpam-5347	52	71	∈	∈	PROPN
ejpam-5347	52	72	t	t	NOUN
ejpam-5347	52	73	˜	˜	PROPN
ejpam-5347	52	74	and	and	CCONJ
ejpam-5347	52	75	t2	t2	PROPN
ejpam-5347	52	76	∈	∈	PROPN
ejpam-5347	52	77	κ2	κ2	NOUN
ejpam-5347	52	78	.	.	PUNCT
ejpam-5347	53	1	definition	definition	NOUN
ejpam-5347	53	2	7	7	NUM
ejpam-5347	53	3	.	.	PUNCT
ejpam-5347	54	1	[	[	X
ejpam-5347	54	2	4	4	X
ejpam-5347	54	3	]	]	X
ejpam-5347	54	4	a	a	DET
ejpam-5347	54	5	pair−open	pair−open	ADJ
ejpam-5347	54	6	cover	cover	NOUN
ejpam-5347	54	7	p	p	PROPN
ejpam-5347	54	8	˜	˜	PROPN
ejpam-5347	54	9	is	be	AUX
ejpam-5347	54	10	known	know	VERB
ejpam-5347	54	11	as	as	ADP
ejpam-5347	54	12	locally	locally	ADV
ejpam-5347	54	13	finite	finite	NOUN
ejpam-5347	54	14	particularly	particularly	ADV
ejpam-5347	54	15	in	in	ADP
ejpam-5347	54	16	the	the	DET
ejpam-5347	54	17	event	event	NOUN
ejpam-5347	54	18	that	that	PRON
ejpam-5347	54	19	∀d	∀d	PUNCT
ejpam-5347	54	20	∈	∈	PROPN
ejpam-5347	54	21	d	d	NOUN
ejpam-5347	54	22	,	,	PUNCT
ejpam-5347	54	23	there	there	PRON
ejpam-5347	54	24	’s	’	VERB
ejpam-5347	54	25	an	an	DET
ejpam-5347	54	26	open	open	ADJ
ejpam-5347	54	27	set	set	VERB
ejpam-5347	54	28	t1	t1	PROPN
ejpam-5347	54	29	∈	∈	PROPN
ejpam-5347	54	30	κ1	κ1	NOUN
ejpam-5347	54	31	,	,	PUNCT
ejpam-5347	54	32	to	to	ADP
ejpam-5347	54	33	the	the	DET
ejpam-5347	54	34	extent	extent	NOUN
ejpam-5347	54	35	that	that	PRON
ejpam-5347	54	36	t1	t1	PROPN
ejpam-5347	54	37	intersects	intersect	VERB
ejpam-5347	54	38	numerous	numerous	ADJ
ejpam-5347	54	39	individuals	individual	NOUN
ejpam-5347	54	40	of	of	ADP
ejpam-5347	54	41	p	p	PROPN
ejpam-5347	54	42	⋂	⋂	PROPN
ejpam-5347	54	43	κ1	κ1	NOUN
ejpam-5347	54	44	,	,	PUNCT
ejpam-5347	54	45	or	or	CCONJ
ejpam-5347	54	46	to	to	ADP
ejpam-5347	54	47	the	the	DET
ejpam-5347	54	48	extent	extent	NOUN
ejpam-5347	54	49	that	that	SCONJ
ejpam-5347	54	50	an	an	DET
ejpam-5347	54	51	open	open	ADJ
ejpam-5347	54	52	set	set	VERB
ejpam-5347	54	53	t2	t2	PROPN
ejpam-5347	54	54	∈	∈	PROPN
ejpam-5347	54	55	κ2	κ2	NOUN
ejpam-5347	54	56	,	,	PUNCT
ejpam-5347	54	57	to	to	ADP
ejpam-5347	54	58	the	the	DET
ejpam-5347	54	59	extent	extent	NOUN
ejpam-5347	54	60	that	that	PRON
ejpam-5347	54	61	t1	t1	PROPN
ejpam-5347	54	62	intersects	intersect	VERB
ejpam-5347	54	63	numerous	numerous	ADJ
ejpam-5347	54	64	individuals	individual	NOUN
ejpam-5347	54	65	of	of	ADP
ejpam-5347	54	66	p	p	PROPN
ejpam-5347	54	67	⋂	⋂	PROPN
ejpam-5347	54	68	κ2	κ2	PROPN
ejpam-5347	54	69	.	.	PUNCT
ejpam-5347	55	1	definition	definition	NOUN
ejpam-5347	55	2	8	8	NUM
ejpam-5347	55	3	.	.	PUNCT
ejpam-5347	56	1	[	[	X
ejpam-5347	56	2	13	13	NUM
ejpam-5347	56	3	]	]	PUNCT
ejpam-5347	56	4	a	a	DET
ejpam-5347	56	5	space	space	NOUN
ejpam-5347	56	6	(	(	PUNCT
ejpam-5347	56	7	d	d	NOUN
ejpam-5347	56	8	,	,	PUNCT
ejpam-5347	56	9	κ1	κ1	NOUN
ejpam-5347	56	10	,	,	PUNCT
ejpam-5347	56	11	κ2	κ2	PROPN
ejpam-5347	56	12	)	)	PUNCT
ejpam-5347	56	13	is	be	AUX
ejpam-5347	56	14	defined	define	VERB
ejpam-5347	56	15	as	as	ADP
ejpam-5347	56	16	pair−paracompact	pair−paracompact	NOUN
ejpam-5347	56	17	,	,	PUNCT
ejpam-5347	56	18	whether	whether	SCONJ
ejpam-5347	56	19	and	and	CCONJ
ejpam-5347	56	20	only	only	ADV
ejpam-5347	56	21	whether	whether	SCONJ
ejpam-5347	56	22	any	any	DET
ejpam-5347	56	23	pair−open	pair−open	ADJ
ejpam-5347	56	24	cover	cover	NOUN
ejpam-5347	56	25	has	have	VERB
ejpam-5347	56	26	a	a	DET
ejpam-5347	56	27	pair−open	pair−open	ADJ
ejpam-5347	56	28	locally	locally	ADV
ejpam-5347	56	29	finite	finite	ADJ
ejpam-5347	56	30	parallel	parallel	NOUN
ejpam-5347	56	31	refinement	refinement	NOUN
ejpam-5347	56	32	.	.	PUNCT
ejpam-5347	57	1	definition	definition	NOUN
ejpam-5347	57	2	9	9	NUM
ejpam-5347	57	3	.	.	PUNCT
ejpam-5347	58	1	[	[	X
ejpam-5347	58	2	7	7	X
ejpam-5347	58	3	]	]	X
ejpam-5347	58	4	a	a	DET
ejpam-5347	58	5	point	point	NOUN
ejpam-5347	58	6	d	d	NOUN
ejpam-5347	58	7	of	of	ADP
ejpam-5347	58	8	a	a	DET
ejpam-5347	58	9	space	space	NOUN
ejpam-5347	58	10	d	d	NOUN
ejpam-5347	58	11	is	be	AUX
ejpam-5347	58	12	known	know	VERB
ejpam-5347	58	13	as	as	ADP
ejpam-5347	58	14	a	a	DET
ejpam-5347	58	15	condensation	condensation	NOUN
ejpam-5347	58	16	point	point	NOUN
ejpam-5347	58	17	of	of	ADP
ejpam-5347	58	18	the	the	DET
ejpam-5347	58	19	set	set	NOUN
ejpam-5347	58	20	m	m	PROPN
ejpam-5347	58	21	⊂	⊂	PROPN
ejpam-5347	59	1	d	d	X
ejpam-5347	59	2	,	,	PUNCT
ejpam-5347	59	3	if	if	SCONJ
ejpam-5347	59	4	an	an	DET
ejpam-5347	59	5	arbitrary	arbitrary	ADJ
ejpam-5347	59	6	neigborhood	neigborhood	NOUN
ejpam-5347	59	7	(	(	PUNCT
ejpam-5347	59	8	briefly	briefly	ADV
ejpam-5347	59	9	,	,	PUNCT
ejpam-5347	59	10	nbd	nbd	PROPN
ejpam-5347	59	11	)	)	PUNCT
ejpam-5347	59	12	of	of	ADP
ejpam-5347	59	13	the	the	DET
ejpam-5347	59	14	point	point	NOUN
ejpam-5347	59	15	d	d	NOUN
ejpam-5347	59	16	contains	contain	VERB
ejpam-5347	59	17	an	an	DET
ejpam-5347	59	18	uncountable	uncountable	ADJ
ejpam-5347	59	19	subset	subset	NOUN
ejpam-5347	59	20	of	of	ADP
ejpam-5347	59	21	this	this	DET
ejpam-5347	59	22	set	set	NOUN
ejpam-5347	59	23	.	.	PUNCT
ejpam-5347	60	1	definition	definition	NOUN
ejpam-5347	60	2	10	10	NUM
ejpam-5347	60	3	.	.	PUNCT
ejpam-5347	61	1	[	[	X
ejpam-5347	61	2	6	6	NUM
ejpam-5347	61	3	]	]	PUNCT
ejpam-5347	61	4	the	the	DET
ejpam-5347	61	5	intersection	intersection	NOUN
ejpam-5347	61	6	of	of	ADP
ejpam-5347	61	7	countably	countably	ADV
ejpam-5347	61	8	several	several	ADJ
ejpam-5347	61	9	open	open	ADJ
ejpam-5347	61	10	sets	set	NOUN
ejpam-5347	61	11	is	be	AUX
ejpam-5347	61	12	an	an	DET
ejpam-5347	61	13	open	open	ADJ
ejpam-5347	61	14	set	set	NOUN
ejpam-5347	61	15	when	when	SCONJ
ejpam-5347	61	16	it	it	PRON
ejpam-5347	61	17	is	be	AUX
ejpam-5347	61	18	the	the	DET
ejpam-5347	61	19	case	case	NOUN
ejpam-5347	61	20	unless	unless	SCONJ
ejpam-5347	61	21	space	space	NOUN
ejpam-5347	61	22	d	d	NOUN
ejpam-5347	61	23	is	be	AUX
ejpam-5347	61	24	referred	refer	VERB
ejpam-5347	61	25	to	to	ADP
ejpam-5347	61	26	by	by	ADP
ejpam-5347	61	27	the	the	DET
ejpam-5347	61	28	term	term	NOUN
ejpam-5347	61	29	pair−space	pair−space	NOUN
ejpam-5347	61	30	.	.	PUNCT
ejpam-5347	62	1	definition	definition	NOUN
ejpam-5347	62	2	11	11	NUM
ejpam-5347	62	3	.	.	PUNCT
ejpam-5347	63	1	[	[	X
ejpam-5347	63	2	9	9	X
ejpam-5347	63	3	]	]	X
ejpam-5347	63	4	whenever	whenever	SCONJ
ejpam-5347	63	5	each	each	DET
ejpam-5347	63	6	countably	countably	ADV
ejpam-5347	63	7	pair−open	pair−open	ADJ
ejpam-5347	63	8	cover	cover	NOUN
ejpam-5347	63	9	of	of	ADP
ejpam-5347	63	10	a	a	DET
ejpam-5347	63	11	bitopological	bitopological	ADJ
ejpam-5347	63	12	space	space	NOUN
ejpam-5347	63	13	(	(	PUNCT
ejpam-5347	63	14	d	d	NOUN
ejpam-5347	63	15	,	,	PUNCT
ejpam-5347	63	16	κ1	κ1	NOUN
ejpam-5347	63	17	,	,	PUNCT
ejpam-5347	63	18	κ2	κ2	PROPN
ejpam-5347	63	19	)	)	PUNCT
ejpam-5347	63	20	has	have	VERB
ejpam-5347	63	21	a	a	DET
ejpam-5347	63	22	finite	finite	ADJ
ejpam-5347	63	23	subcover	subcover	NOUN
ejpam-5347	63	24	,	,	PUNCT
ejpam-5347	63	25	therefore	therefore	ADV
ejpam-5347	63	26	the	the	DET
ejpam-5347	63	27	space	space	NOUN
ejpam-5347	63	28	is	be	AUX
ejpam-5347	63	29	referred	refer	VERB
ejpam-5347	63	30	to	to	PART
ejpam-5347	63	31	be	be	AUX
ejpam-5347	63	32	pair−countably	pair−countably	ADV
ejpam-5347	63	33	compact	compact	ADJ
ejpam-5347	63	34	.	.	PUNCT
ejpam-5347	64	1	definition	definition	NOUN
ejpam-5347	64	2	12	12	NUM
ejpam-5347	64	3	.	.	PUNCT
ejpam-5347	65	1	[	[	X
ejpam-5347	65	2	9	9	NUM
ejpam-5347	65	3	]	]	PUNCT
ejpam-5347	65	4	when	when	SCONJ
ejpam-5347	65	5	there	there	PRON
ejpam-5347	65	6	is	be	VERB
ejpam-5347	65	7	a	a	DET
ejpam-5347	65	8	finite	finite	ADJ
ejpam-5347	65	9	subcover	subcover	NOUN
ejpam-5347	65	10	for	for	ADP
ejpam-5347	65	11	each	each	DET
ejpam-5347	65	12	countably	countably	ADV
ejpam-5347	65	13	κ1κ2−open	κ1κ2−open	ADJ
ejpam-5347	65	14	cover	cover	NOUN
ejpam-5347	65	15	of	of	ADP
ejpam-5347	65	16	a	a	DET
ejpam-5347	65	17	bitopological	bitopological	ADJ
ejpam-5347	65	18	space(d	space(d	PROPN
ejpam-5347	65	19	,	,	PUNCT
ejpam-5347	65	20	κ1	κ1	NOUN
ejpam-5347	65	21	,	,	PUNCT
ejpam-5347	65	22	κ2	κ2	PROPN
ejpam-5347	65	23	)	)	PUNCT
ejpam-5347	65	24	,	,	PUNCT
ejpam-5347	65	25	subsequently	subsequently	ADV
ejpam-5347	65	26	the	the	DET
ejpam-5347	65	27	space	space	NOUN
ejpam-5347	65	28	has	have	AUX
ejpam-5347	65	29	been	be	AUX
ejpam-5347	65	30	referred	refer	VERB
ejpam-5347	65	31	to	to	ADP
ejpam-5347	65	32	as	as	ADP
ejpam-5347	65	33	s−countably	s−countably	ADV
ejpam-5347	65	34	compact	compact	ADJ
ejpam-5347	65	35	.	.	PUNCT
ejpam-5347	66	1	definition	definition	NOUN
ejpam-5347	66	2	13	13	NUM
ejpam-5347	66	3	.	.	PUNCT
ejpam-5347	67	1	[	[	X
ejpam-5347	67	2	18	18	NUM
ejpam-5347	67	3	]	]	X
ejpam-5347	67	4	whenever	whenever	SCONJ
ejpam-5347	67	5	a	a	DET
ejpam-5347	67	6	function	function	NOUN
ejpam-5347	67	7	υ	υ	NOUN
ejpam-5347	67	8	:	:	PUNCT
ejpam-5347	67	9	(	(	PUNCT
ejpam-5347	67	10	d	d	NOUN
ejpam-5347	67	11	,	,	PUNCT
ejpam-5347	67	12	κ1	κ1	NOUN
ejpam-5347	67	13	,	,	PUNCT
ejpam-5347	67	14	κ2	κ2	PROPN
ejpam-5347	67	15	)	)	PUNCT
ejpam-5347	67	16	→	→	SYM
ejpam-5347	67	17	(	(	PUNCT
ejpam-5347	67	18	g	g	NOUN
ejpam-5347	67	19	,	,	PUNCT
ejpam-5347	67	20	υ1	υ1	NOUN
ejpam-5347	67	21	,	,	PUNCT
ejpam-5347	67	22	υ2	υ2	PROPN
ejpam-5347	67	23	)	)	PUNCT
ejpam-5347	67	24	is	be	AUX
ejpam-5347	67	25	referred	refer	VERB
ejpam-5347	67	26	to	to	ADP
ejpam-5347	67	27	as	as	ADP
ejpam-5347	67	28	pair−weakly	pair−weakly	ADV
ejpam-5347	67	29	continuous	continuous	ADJ
ejpam-5347	67	30	,	,	PUNCT
ejpam-5347	67	31	it	it	PRON
ejpam-5347	67	32	means	mean	VERB
ejpam-5347	67	33	that	that	SCONJ
ejpam-5347	67	34	υ−1(t	υ−1(t	PROPN
ejpam-5347	67	35	)	)	PUNCT
ejpam-5347	67	36	is	be	AUX
ejpam-5347	67	37	pair−ω−open	pair−ω−open	VERB
ejpam-5347	67	38	for	for	ADP
ejpam-5347	67	39	each	each	DET
ejpam-5347	67	40	pair−open	pair−open	NOUN
ejpam-5347	67	41	set	set	VERB
ejpam-5347	67	42	t	t	PROPN
ejpam-5347	67	43	⊂	⊂	PROPN
ejpam-5347	67	44	g.	g.	PROPN
ejpam-5347	67	45	definition	definition	NOUN
ejpam-5347	67	46	14	14	NUM
ejpam-5347	67	47	.	.	PUNCT
ejpam-5347	68	1	[	[	X
ejpam-5347	68	2	14	14	NUM
ejpam-5347	68	3	]	]	PUNCT
ejpam-5347	68	4	assuming	assume	VERB
ejpam-5347	68	5	a	a	DET
ejpam-5347	68	6	bitopological	bitopological	ADJ
ejpam-5347	68	7	space	space	NOUN
ejpam-5347	68	8	(	(	PUNCT
ejpam-5347	68	9	d	d	NOUN
ejpam-5347	68	10	,	,	PUNCT
ejpam-5347	68	11	κ1	κ1	NOUN
ejpam-5347	68	12	,	,	PUNCT
ejpam-5347	68	13	κ2	κ2	PROPN
ejpam-5347	68	14	)	)	PUNCT
ejpam-5347	68	15	,	,	PUNCT
ejpam-5347	68	16	we	we	PRON
ejpam-5347	68	17	declare	declare	VERB
ejpam-5347	68	18	that	that	SCONJ
ejpam-5347	68	19	κ1is	κ1i	VERB
ejpam-5347	68	20	locally	locally	ADV
ejpam-5347	68	21	lindel	lindel	NOUN
ejpam-5347	68	22	..	..	PUNCT
ejpam-5347	68	23	of	of	ADP
ejpam-5347	68	24	with	with	ADP
ejpam-5347	68	25	respect	respect	NOUN
ejpam-5347	68	26	to	to	ADP
ejpam-5347	68	27	κ2.when	κ2.when	PROPN
ejpam-5347	68	28	there	there	PRON
ejpam-5347	68	29	is	be	VERB
ejpam-5347	68	30	a	a	DET
ejpam-5347	68	31	κ1	κ1	NOUN
ejpam-5347	68	32	nbd	nbd	PROPN
ejpam-5347	68	33	td	td	NOUN
ejpam-5347	68	34	of	of	ADP
ejpam-5347	68	35	d.	d.	PROPN
ejpam-5347	68	36	in	in	ADP
ejpam-5347	68	37	a	a	DET
ejpam-5347	68	38	way	way	NOUN
ejpam-5347	68	39	that	that	PRON
ejpam-5347	68	40	td	td	NOUN
ejpam-5347	68	41	κ2	κ2	PROPN
ejpam-5347	68	42	is	be	AUX
ejpam-5347	68	43	pair−lindel	pair−lindel	NOUN
ejpam-5347	68	44	..	..	PUNCT
ejpam-5347	68	45	of	of	ADP
ejpam-5347	68	46	all	all	PRON
ejpam-5347	68	47	of	of	ADP
ejpam-5347	68	48	them	they	PRON
ejpam-5347	68	49	d	d	X
ejpam-5347	68	50	∈	∈	PROPN
ejpam-5347	68	51	(	(	PUNCT
ejpam-5347	68	52	d	d	NOUN
ejpam-5347	68	53	,	,	PUNCT
ejpam-5347	68	54	κ1	κ1	NOUN
ejpam-5347	68	55	,	,	PUNCT
ejpam-5347	68	56	κ2	κ2	PROPN
ejpam-5347	68	57	)	)	PUNCT
ejpam-5347	68	58	.	.	PUNCT
ejpam-5347	69	1	a.	a.	NOUN
ejpam-5347	69	2	atoom	atoom	PROPN
ejpam-5347	69	3	et	et	PROPN
ejpam-5347	69	4	al	al	PROPN
ejpam-5347	69	5	.	.	PUNCT
ejpam-5347	69	6	/	/	SYM
ejpam-5347	69	7	eur	eur	PROPN
ejpam-5347	69	8	.	.	PUNCT
ejpam-5347	70	1	j.	j.	PROPN
ejpam-5347	70	2	pure	pure	PROPN
ejpam-5347	70	3	appl	appl	PROPN
ejpam-5347	70	4	.	.	PROPN
ejpam-5347	70	5	math	math	PROPN
ejpam-5347	70	6	,	,	PUNCT
ejpam-5347	70	7	17	17	NUM
ejpam-5347	70	8	(	(	PUNCT
ejpam-5347	70	9	4	4	NUM
ejpam-5347	70	10	)	)	PUNCT
ejpam-5347	70	11	(	(	PUNCT
ejpam-5347	70	12	2024	2024	NUM
ejpam-5347	70	13	)	)	PUNCT
ejpam-5347	70	14	,	,	PUNCT
ejpam-5347	70	15	2574	2574	NUM
ejpam-5347	70	16	-	-	SYM
ejpam-5347	70	17	2585	2585	NUM
ejpam-5347	70	18	2577	2577	NUM
ejpam-5347	70	19	3	3	NUM
ejpam-5347	70	20	.	.	PUNCT
ejpam-5347	71	1	a	a	DET
ejpam-5347	71	2	novel	novel	ADJ
ejpam-5347	71	3	categorization	categorization	NOUN
ejpam-5347	71	4	of	of	ADP
ejpam-5347	71	5	closed	closed	ADJ
ejpam-5347	71	6	functions	function	NOUN
ejpam-5347	71	7	the	the	DET
ejpam-5347	71	8	notion	notion	NOUN
ejpam-5347	71	9	of	of	ADP
ejpam-5347	71	10	ω−closed	ω−close	VERB
ejpam-5347	71	11	functions	function	NOUN
ejpam-5347	71	12	in	in	ADP
ejpam-5347	71	13	bitopological	bitopological	ADJ
ejpam-5347	71	14	spaces	space	NOUN
ejpam-5347	71	15	is	be	AUX
ejpam-5347	71	16	introduced	introduce	VERB
ejpam-5347	71	17	and	and	CCONJ
ejpam-5347	71	18	their	their	PRON
ejpam-5347	71	19	relation	relation	NOUN
ejpam-5347	71	20	to	to	ADP
ejpam-5347	71	21	other	other	ADJ
ejpam-5347	71	22	spaces	space	NOUN
ejpam-5347	71	23	is	be	AUX
ejpam-5347	71	24	illustrated	illustrate	VERB
ejpam-5347	71	25	in	in	ADP
ejpam-5347	71	26	this	this	DET
ejpam-5347	71	27	section	section	NOUN
ejpam-5347	71	28	.	.	PUNCT
ejpam-5347	72	1	definition	definition	NOUN
ejpam-5347	72	2	15	15	NUM
ejpam-5347	72	3	.	.	PUNCT
ejpam-5347	73	1	a	a	DET
ejpam-5347	73	2	pair−ω−closed	pair−ω−closed	ADJ
ejpam-5347	73	3	function	function	NOUN
ejpam-5347	73	4	can	can	AUX
ejpam-5347	73	5	be	be	AUX
ejpam-5347	73	6	expressed	express	VERB
ejpam-5347	73	7	as	as	ADP
ejpam-5347	73	8	υ	υ	NOUN
ejpam-5347	73	9	:	:	PUNCT
ejpam-5347	73	10	(	(	PUNCT
ejpam-5347	73	11	d	d	NOUN
ejpam-5347	73	12	,	,	PUNCT
ejpam-5347	73	13	κ1	κ1	NOUN
ejpam-5347	73	14	,	,	PUNCT
ejpam-5347	73	15	κ2	κ2	PROPN
ejpam-5347	73	16	)	)	PUNCT
ejpam-5347	73	17	→	→	SYM
ejpam-5347	73	18	(	(	PUNCT
ejpam-5347	73	19	g	g	NOUN
ejpam-5347	73	20	,	,	PUNCT
ejpam-5347	73	21	υ1	υ1	NOUN
ejpam-5347	73	22	,	,	PUNCT
ejpam-5347	73	23	υ2	υ2	PROPN
ejpam-5347	73	24	)	)	PUNCT
ejpam-5347	73	25	when	when	SCONJ
ejpam-5347	73	26	it	it	PRON
ejpam-5347	73	27	mappings	mapping	VERB
ejpam-5347	73	28	pair−closed	pair−close	VERB
ejpam-5347	73	29	sets	set	NOUN
ejpam-5347	73	30	onto	onto	ADP
ejpam-5347	73	31	pair−ω−closed	pair−ω−closed	ADJ
ejpam-5347	73	32	sets	set	NOUN
ejpam-5347	73	33	.	.	PUNCT
ejpam-5347	74	1	definition	definition	NOUN
ejpam-5347	74	2	16	16	NUM
ejpam-5347	74	3	.	.	PUNCT
ejpam-5347	75	1	a	a	DET
ejpam-5347	75	2	pair−	pair−	NOUN
ejpam-5347	75	3	semi−ω−closed	semi−ω−close	VERB
ejpam-5347	75	4	function	function	NOUN
ejpam-5347	75	5	can	can	AUX
ejpam-5347	75	6	be	be	AUX
ejpam-5347	75	7	expressed	express	VERB
ejpam-5347	75	8	as	as	ADP
ejpam-5347	75	9	υ	υ	NOUN
ejpam-5347	75	10	:	:	PUNCT
ejpam-5347	75	11	(	(	PUNCT
ejpam-5347	75	12	d	d	NOUN
ejpam-5347	75	13	,	,	PUNCT
ejpam-5347	75	14	κ1	κ1	NOUN
ejpam-5347	75	15	,	,	PUNCT
ejpam-5347	75	16	κ2	κ2	PROPN
ejpam-5347	75	17	)	)	PUNCT
ejpam-5347	75	18	→	→	SYM
ejpam-5347	75	19	(	(	PUNCT
ejpam-5347	75	20	g	g	NOUN
ejpam-5347	75	21	,	,	PUNCT
ejpam-5347	75	22	υ1	υ1	NOUN
ejpam-5347	75	23	,	,	PUNCT
ejpam-5347	75	24	υ2	υ2	PROPN
ejpam-5347	75	25	)	)	PUNCT
ejpam-5347	75	26	when	when	SCONJ
ejpam-5347	75	27	it	it	PRON
ejpam-5347	75	28	mappings	mapping	VERB
ejpam-5347	75	29	pair−	pair−	NOUN
ejpam-5347	75	30	semi	semi	ADV
ejpam-5347	75	31	closed	closed	ADJ
ejpam-5347	75	32	sets	set	NOUN
ejpam-5347	75	33	onto	onto	ADP
ejpam-5347	75	34	pair−semi−ω−closed	pair−semi−ω−close	VERB
ejpam-5347	75	35	sets	set	NOUN
ejpam-5347	75	36	.	.	PUNCT
ejpam-5347	76	1	definition	definition	NOUN
ejpam-5347	76	2	17	17	NUM
ejpam-5347	76	3	.	.	PUNCT
ejpam-5347	77	1	whenever	whenever	SCONJ
ejpam-5347	77	2	υ−1(l	υ−1(l	NOUN
ejpam-5347	77	3	)	)	PUNCT
ejpam-5347	77	4	is	be	AUX
ejpam-5347	77	5	pair−	pair−	NOUN
ejpam-5347	77	6	lindel	lindel	NOUN
ejpam-5347	77	7	..	..	PUNCT
ejpam-5347	77	8	of	of	ADP
ejpam-5347	77	9	every	every	DET
ejpam-5347	77	10	individual	individual	ADJ
ejpam-5347	77	11	pair−	pair−	NOUN
ejpam-5347	77	12	lindel	lindel	PROPN
ejpam-5347	77	13	..	..	PUNCT
ejpam-5347	77	14	of	of	ADP
ejpam-5347	77	15	closed	closed	ADJ
ejpam-5347	77	16	subset	subset	NOUN
ejpam-5347	77	17	l	l	NOUN
ejpam-5347	77	18	of	of	ADP
ejpam-5347	77	19	(	(	PUNCT
ejpam-5347	77	20	g	g	PROPN
ejpam-5347	77	21	,	,	PUNCT
ejpam-5347	77	22	υ1	υ1	NOUN
ejpam-5347	77	23	,	,	PUNCT
ejpam-5347	77	24	υ2	υ2	NOUN
ejpam-5347	77	25	)	)	PUNCT
ejpam-5347	77	26	,	,	PUNCT
ejpam-5347	77	27	subsequently	subsequently	ADV
ejpam-5347	77	28	υ	υ	X
ejpam-5347	77	29	:	:	PUNCT
ejpam-5347	77	30	(	(	PUNCT
ejpam-5347	77	31	d	d	NOUN
ejpam-5347	77	32	,	,	PUNCT
ejpam-5347	77	33	κ1	κ1	NOUN
ejpam-5347	77	34	,	,	PUNCT
ejpam-5347	77	35	κ2	κ2	PROPN
ejpam-5347	77	36	)	)	PUNCT
ejpam-5347	77	37	→	→	SYM
ejpam-5347	77	38	(	(	PUNCT
ejpam-5347	77	39	g	g	NOUN
ejpam-5347	77	40	,	,	PUNCT
ejpam-5347	77	41	υ1	υ1	NOUN
ejpam-5347	77	42	,	,	PUNCT
ejpam-5347	77	43	υ2	υ2	PROPN
ejpam-5347	77	44	)	)	PUNCT
ejpam-5347	77	45	is	be	AUX
ejpam-5347	77	46	a	a	DET
ejpam-5347	77	47	pair−	pair−	NOUN
ejpam-5347	77	48	lindel	lindel	NOUN
ejpam-5347	77	49	..	..	PUNCT
ejpam-5347	77	50	of	of	ADP
ejpam-5347	77	51	function	function	NOUN
ejpam-5347	77	52	.	.	PUNCT
ejpam-5347	78	1	definition	definition	NOUN
ejpam-5347	78	2	18	18	NUM
ejpam-5347	78	3	.	.	PUNCT
ejpam-5347	79	1	whenever	whenever	SCONJ
ejpam-5347	79	2	υ−1(l	υ−1(l	NOUN
ejpam-5347	79	3	)	)	PUNCT
ejpam-5347	79	4	is	be	AUX
ejpam-5347	79	5	pair−semi	pair−semi	X
ejpam-5347	79	6	lindel	lindel	NOUN
ejpam-5347	79	7	..	..	PUNCT
ejpam-5347	79	8	of	of	ADP
ejpam-5347	79	9	every	every	DET
ejpam-5347	79	10	individual	individual	ADJ
ejpam-5347	79	11	pair−	pair−	NOUN
ejpam-5347	79	12	semi	semi	ADJ
ejpam-5347	79	13	lindel	lindel	PROPN
ejpam-5347	79	14	..	..	PUNCT
ejpam-5347	79	15	of	of	ADP
ejpam-5347	79	16	closed	closed	ADJ
ejpam-5347	79	17	subset	subset	NOUN
ejpam-5347	79	18	l	l	NOUN
ejpam-5347	79	19	of	of	ADP
ejpam-5347	79	20	(	(	PUNCT
ejpam-5347	79	21	g	g	PROPN
ejpam-5347	79	22	,	,	PUNCT
ejpam-5347	79	23	υ1	υ1	NOUN
ejpam-5347	79	24	,	,	PUNCT
ejpam-5347	79	25	υ2	υ2	NOUN
ejpam-5347	79	26	)	)	PUNCT
ejpam-5347	79	27	,	,	PUNCT
ejpam-5347	79	28	subsequently	subsequently	ADV
ejpam-5347	79	29	υ	υ	X
ejpam-5347	79	30	:	:	PUNCT
ejpam-5347	79	31	(	(	PUNCT
ejpam-5347	79	32	d	d	NOUN
ejpam-5347	79	33	,	,	PUNCT
ejpam-5347	79	34	κ1	κ1	NOUN
ejpam-5347	79	35	,	,	PUNCT
ejpam-5347	79	36	κ2	κ2	PROPN
ejpam-5347	79	37	)	)	PUNCT
ejpam-5347	79	38	→	→	SYM
ejpam-5347	79	39	(	(	PUNCT
ejpam-5347	79	40	g	g	NOUN
ejpam-5347	79	41	,	,	PUNCT
ejpam-5347	79	42	υ1	υ1	NOUN
ejpam-5347	79	43	,	,	PUNCT
ejpam-5347	79	44	υ2	υ2	PROPN
ejpam-5347	79	45	)	)	PUNCT
ejpam-5347	79	46	is	be	AUX
ejpam-5347	79	47	a	a	DET
ejpam-5347	79	48	pair−semi	pair−semi	NOUN
ejpam-5347	79	49	lindel	lindel	NOUN
ejpam-5347	79	50	..	..	PUNCT
ejpam-5347	79	51	of	of	ADP
ejpam-5347	79	52	function	function	NOUN
ejpam-5347	79	53	.	.	PUNCT
ejpam-5347	80	1	definition	definition	NOUN
ejpam-5347	80	2	19	19	NUM
ejpam-5347	80	3	.	.	PUNCT
ejpam-5347	81	1	if	if	SCONJ
ejpam-5347	81	2	the	the	DET
ejpam-5347	81	3	intersection	intersection	NOUN
ejpam-5347	81	4	of	of	ADP
ejpam-5347	81	5	a	a	DET
ejpam-5347	81	6	countably	countably	ADV
ejpam-5347	81	7	many	many	ADJ
ejpam-5347	81	8	open	open	ADJ
ejpam-5347	81	9	sets	set	NOUN
ejpam-5347	81	10	is	be	AUX
ejpam-5347	81	11	an	an	DET
ejpam-5347	81	12	ω−open	ω−open	NOUN
ejpam-5347	81	13	set	set	NOUN
ejpam-5347	81	14	,	,	PUNCT
ejpam-5347	81	15	therefore	therefore	ADV
ejpam-5347	81	16	space	space	NOUN
ejpam-5347	81	17	d	d	NOUN
ejpam-5347	81	18	is	be	AUX
ejpam-5347	81	19	known	know	VERB
ejpam-5347	81	20	to	to	ADP
ejpam-5347	81	21	as	as	ADP
ejpam-5347	81	22	a	a	DET
ejpam-5347	81	23	p̋−space	p̋−space	NOUN
ejpam-5347	81	24	.	.	PUNCT
ejpam-5347	82	1	definition	definition	NOUN
ejpam-5347	82	2	20	20	NUM
ejpam-5347	82	3	.	.	PUNCT
ejpam-5347	83	1	when	when	SCONJ
ejpam-5347	83	2	there	there	PRON
ejpam-5347	83	3	is	be	VERB
ejpam-5347	83	4	a	a	DET
ejpam-5347	83	5	pair−open	pair−open	ADJ
ejpam-5347	83	6	subset	subset	NOUN
ejpam-5347	83	7	td	td	NOUN
ejpam-5347	83	8	including	include	VERB
ejpam-5347	83	9	d	d	PROPN
ejpam-5347	83	10	that	that	PRON
ejpam-5347	83	11	means	mean	VERB
ejpam-5347	83	12	td	td	PROPN
ejpam-5347	83	13	−	−	PROPN
ejpam-5347	83	14	j	j	PROPN
ejpam-5347	83	15	is	be	AUX
ejpam-5347	83	16	a	a	DET
ejpam-5347	83	17	countable	countable	ADJ
ejpam-5347	83	18	set	set	NOUN
ejpam-5347	83	19	,	,	PUNCT
ejpam-5347	83	20	therefore	therefore	ADV
ejpam-5347	83	21	a	a	DET
ejpam-5347	83	22	subset	subset	NOUN
ejpam-5347	83	23	j	j	PROPN
ejpam-5347	83	24	of	of	ADP
ejpam-5347	83	25	a	a	DET
ejpam-5347	83	26	bitopological	bitopological	ADJ
ejpam-5347	83	27	space	space	NOUN
ejpam-5347	83	28	(	(	PUNCT
ejpam-5347	83	29	d	d	NOUN
ejpam-5347	83	30	,	,	PUNCT
ejpam-5347	83	31	κ1	κ1	NOUN
ejpam-5347	83	32	,	,	PUNCT
ejpam-5347	83	33	κ2	κ2	PROPN
ejpam-5347	83	34	)	)	PUNCT
ejpam-5347	83	35	is	be	AUX
ejpam-5347	83	36	pair−	pair−	NOUN
ejpam-5347	83	37	ω−open	ω−open	PROPN
ejpam-5347	83	38	.	.	PUNCT
ejpam-5347	84	1	pair−	pair−	PROPN
ejpam-5347	84	2	ω−closed	ω−closed	PROPN
ejpam-5347	84	3	sets	set	NOUN
ejpam-5347	84	4	have	have	AUX
ejpam-5347	84	5	been	be	AUX
ejpam-5347	84	6	defined	define	VERB
ejpam-5347	84	7	to	to	PART
ejpam-5347	84	8	be	be	AUX
ejpam-5347	84	9	the	the	DET
ejpam-5347	84	10	complement	complement	NOUN
ejpam-5347	84	11	of	of	ADP
ejpam-5347	84	12	pair−	pair−	NOUN
ejpam-5347	84	13	ω−open	ω−open	PROPN
ejpam-5347	84	14	sets	set	VERB
ejpam-5347	84	15	.	.	PUNCT
ejpam-5347	85	1	definition	definition	NOUN
ejpam-5347	85	2	21	21	NUM
ejpam-5347	85	3	.	.	PUNCT
ejpam-5347	85	4	pair−ω	pair−ω	VERB
ejpam-5347	85	5	−	−	PROPN
ejpam-5347	85	6	bo(j	bo(j	NOUN
ejpam-5347	85	7	)	)	PUNCT
ejpam-5347	85	8	as	as	ADV
ejpam-5347	85	9	well	well	ADV
ejpam-5347	85	10	as	as	ADP
ejpam-5347	85	11	pair−	pair−	NOUN
ejpam-5347	85	12	ω	ω	NUM
ejpam-5347	85	13	−	−	PROPN
ejpam-5347	85	14	bc(j	bc(j	PUNCT
ejpam-5347	85	15	)	)	PUNCT
ejpam-5347	85	16	is	be	AUX
ejpam-5347	85	17	the	the	DET
ejpam-5347	85	18	family	family	NOUN
ejpam-5347	85	19	of	of	ADP
ejpam-5347	85	20	all	all	DET
ejpam-5347	85	21	pair−	pair−	NOUN
ejpam-5347	85	22	ω−open	ω−open	PROPN
ejpam-5347	85	23	as	as	ADV
ejpam-5347	85	24	well	well	ADV
ejpam-5347	85	25	as	as	ADP
ejpam-5347	85	26	pair−	pair−	NOUN
ejpam-5347	85	27	ω−closed	ω−close	VERB
ejpam-5347	85	28	subsets	subset	NOUN
ejpam-5347	85	29	of	of	ADP
ejpam-5347	85	30	a	a	DET
ejpam-5347	85	31	space	space	NOUN
ejpam-5347	85	32	(	(	PUNCT
ejpam-5347	85	33	d	d	NOUN
ejpam-5347	85	34	,	,	PUNCT
ejpam-5347	85	35	κ1	κ1	NOUN
ejpam-5347	85	36	,	,	PUNCT
ejpam-5347	85	37	κ2	κ2	PROPN
ejpam-5347	85	38	)	)	PUNCT
ejpam-5347	85	39	.	.	PUNCT
ejpam-5347	86	1	moreover	moreover	ADV
ejpam-5347	86	2	,	,	PUNCT
ejpam-5347	86	3	pair−ω	pair−ω	VERB
ejpam-5347	86	4	−	−	NOUN
ejpam-5347	86	5	bo(d	bo(d	PUNCT
ejpam-5347	86	6	;	;	PUNCT
ejpam-5347	86	7	d	d	X
ejpam-5347	86	8	)	)	PUNCT
ejpam-5347	86	9	represents	represent	VERB
ejpam-5347	86	10	the	the	DET
ejpam-5347	86	11	family	family	NOUN
ejpam-5347	86	12	of	of	ADP
ejpam-5347	86	13	all	all	DET
ejpam-5347	86	14	pair−ω−open	pair−ω−open	ADJ
ejpam-5347	86	15	sets	set	NOUN
ejpam-5347	86	16	of	of	ADP
ejpam-5347	86	17	(	(	PUNCT
ejpam-5347	86	18	d	d	PROPN
ejpam-5347	86	19	,	,	PUNCT
ejpam-5347	86	20	κ1	κ1	NOUN
ejpam-5347	86	21	,	,	PUNCT
ejpam-5347	86	22	κ2	κ2	PROPN
ejpam-5347	86	23	)	)	PUNCT
ejpam-5347	86	24	including	include	VERB
ejpam-5347	86	25	d.	d.	PROPN
ejpam-5347	86	26	definition	definition	NOUN
ejpam-5347	86	27	22	22	NUM
ejpam-5347	86	28	.	.	PUNCT
ejpam-5347	87	1	whether	whether	SCONJ
ejpam-5347	87	2	there	there	PRON
ejpam-5347	87	3	’s	’	VERB
ejpam-5347	87	4	a	a	DET
ejpam-5347	87	5	κ1κ2−open	κ1κ2−open	NOUN
ejpam-5347	87	6	subset	subset	NOUN
ejpam-5347	87	7	td	td	NOUN
ejpam-5347	87	8	comprising	comprise	VERB
ejpam-5347	87	9	d	d	NOUN
ejpam-5347	87	10	that	that	PRON
ejpam-5347	87	11	implies	imply	VERB
ejpam-5347	87	12	td−j	td−j	NOUN
ejpam-5347	87	13	is	be	AUX
ejpam-5347	87	14	a	a	DET
ejpam-5347	87	15	countable	countable	ADJ
ejpam-5347	87	16	set	set	NOUN
ejpam-5347	87	17	.	.	PUNCT
ejpam-5347	88	1	consequently	consequently	ADV
ejpam-5347	88	2	a	a	DET
ejpam-5347	88	3	subset	subset	NOUN
ejpam-5347	88	4	j	j	PROPN
ejpam-5347	88	5	of	of	ADP
ejpam-5347	88	6	a	a	DET
ejpam-5347	88	7	bitopological	bitopological	ADJ
ejpam-5347	88	8	space	space	NOUN
ejpam-5347	88	9	(	(	PUNCT
ejpam-5347	88	10	d	d	NOUN
ejpam-5347	88	11	,	,	PUNCT
ejpam-5347	88	12	κ1	κ1	NOUN
ejpam-5347	88	13	,	,	PUNCT
ejpam-5347	88	14	κ2	κ2	PROPN
ejpam-5347	88	15	)	)	PUNCT
ejpam-5347	88	16	is	be	AUX
ejpam-5347	88	17	pair−semi−	pair−semi−	ADJ
ejpam-5347	88	18	ω−open	ω−open	NOUN
ejpam-5347	88	19	.	.	PUNCT
ejpam-5347	89	1	pair−semi-−ω−closed	pair−semi-−ω−close	VERB
ejpam-5347	89	2	sets	set	NOUN
ejpam-5347	89	3	deemed	deem	VERB
ejpam-5347	89	4	to	to	PART
ejpam-5347	89	5	be	be	AUX
ejpam-5347	89	6	the	the	DET
ejpam-5347	89	7	complement	complement	NOUN
ejpam-5347	89	8	of	of	ADP
ejpam-5347	89	9	pair−semi−	pair−semi−	ADJ
ejpam-5347	89	10	ω−open	ω−open	NOUN
ejpam-5347	89	11	sets	set	NOUN
ejpam-5347	89	12	.	.	PUNCT
ejpam-5347	90	1	definition	definition	NOUN
ejpam-5347	90	2	23	23	NUM
ejpam-5347	90	3	.	.	PUNCT
ejpam-5347	91	1	pair−semi−ω−bo(j	pair−semi−ω−bo(j	ADJ
ejpam-5347	91	2	)	)	PUNCT
ejpam-5347	91	3	as	as	ADV
ejpam-5347	91	4	well	well	ADV
ejpam-5347	91	5	as	as	ADP
ejpam-5347	91	6	pair−semi−	pair−semi−	ADJ
ejpam-5347	91	7	ω−bc(j	ω−bc(j	NUM
ejpam-5347	91	8	)	)	PUNCT
ejpam-5347	91	9	is	be	AUX
ejpam-5347	91	10	the	the	DET
ejpam-5347	91	11	family	family	NOUN
ejpam-5347	91	12	of	of	ADP
ejpam-5347	91	13	all	all	DET
ejpam-5347	91	14	pair−semi−	pair−semi−	ADJ
ejpam-5347	91	15	ω−open	ω−open	NOUN
ejpam-5347	91	16	.	.	PUNCT
ejpam-5347	92	1	additionally	additionally	ADV
ejpam-5347	92	2	pair−semi−	pair−semi−	ADJ
ejpam-5347	92	3	ω−closed	ω−close	VERB
ejpam-5347	92	4	subsets	subset	NOUN
ejpam-5347	92	5	of	of	ADP
ejpam-5347	92	6	a	a	DET
ejpam-5347	92	7	space	space	NOUN
ejpam-5347	92	8	(	(	PUNCT
ejpam-5347	92	9	d	d	NOUN
ejpam-5347	92	10	,	,	PUNCT
ejpam-5347	92	11	κ1	κ1	NOUN
ejpam-5347	92	12	,	,	PUNCT
ejpam-5347	92	13	κ2	κ2	PROPN
ejpam-5347	92	14	)	)	PUNCT
ejpam-5347	92	15	.	.	PUNCT
ejpam-5347	93	1	furthermore	furthermore	ADV
ejpam-5347	93	2	,	,	PUNCT
ejpam-5347	93	3	pair−semi−ω	pair−semi−ω	ADJ
ejpam-5347	93	4	−	−	NOUN
ejpam-5347	93	5	bo(d	bo(d	PUNCT
ejpam-5347	93	6	;	;	PUNCT
ejpam-5347	93	7	d	d	X
ejpam-5347	93	8	)	)	PUNCT
ejpam-5347	93	9	represents	represent	VERB
ejpam-5347	93	10	the	the	DET
ejpam-5347	93	11	family	family	NOUN
ejpam-5347	93	12	of	of	ADP
ejpam-5347	93	13	all	all	DET
ejpam-5347	93	14	pair−semi−ω−open	pair−semi−ω−open	NOUN
ejpam-5347	93	15	sets	set	NOUN
ejpam-5347	93	16	of	of	ADP
ejpam-5347	93	17	(	(	PUNCT
ejpam-5347	93	18	d	d	PROPN
ejpam-5347	93	19	,	,	PUNCT
ejpam-5347	93	20	κ1	κ1	NOUN
ejpam-5347	93	21	,	,	PUNCT
ejpam-5347	93	22	κ2	κ2	PROPN
ejpam-5347	93	23	)	)	PUNCT
ejpam-5347	93	24	encompassing	encompass	VERB
ejpam-5347	93	25	d.	d.	PROPN
ejpam-5347	93	26	a.	a.	PROPN
ejpam-5347	93	27	atoom	atoom	PROPN
ejpam-5347	93	28	et	et	PROPN
ejpam-5347	93	29	al	al	PROPN
ejpam-5347	93	30	.	.	PUNCT
ejpam-5347	93	31	/	/	SYM
ejpam-5347	93	32	eur	eur	PROPN
ejpam-5347	93	33	.	.	PUNCT
ejpam-5347	94	1	j.	j.	PROPN
ejpam-5347	94	2	pure	pure	PROPN
ejpam-5347	94	3	appl	appl	PROPN
ejpam-5347	94	4	.	.	PROPN
ejpam-5347	94	5	math	math	PROPN
ejpam-5347	94	6	,	,	PUNCT
ejpam-5347	94	7	17	17	NUM
ejpam-5347	94	8	(	(	PUNCT
ejpam-5347	94	9	4	4	NUM
ejpam-5347	94	10	)	)	PUNCT
ejpam-5347	94	11	(	(	PUNCT
ejpam-5347	94	12	2024	2024	NUM
ejpam-5347	94	13	)	)	PUNCT
ejpam-5347	94	14	,	,	PUNCT
ejpam-5347	94	15	2574	2574	NUM
ejpam-5347	94	16	-	-	SYM
ejpam-5347	94	17	2585	2585	NUM
ejpam-5347	94	18	2578	2578	NUM
ejpam-5347	94	19	theorem	theorem	VERB
ejpam-5347	94	20	1	1	NUM
ejpam-5347	94	21	.	.	PUNCT
ejpam-5347	95	1	in	in	ADP
ejpam-5347	95	2	a	a	DET
ejpam-5347	95	3	space	space	NOUN
ejpam-5347	95	4	(	(	PUNCT
ejpam-5347	95	5	d	d	NOUN
ejpam-5347	95	6	,	,	PUNCT
ejpam-5347	95	7	κ1	κ1	NOUN
ejpam-5347	95	8	,	,	PUNCT
ejpam-5347	95	9	κ2	κ2	PROPN
ejpam-5347	95	10	)	)	PUNCT
ejpam-5347	95	11	,	,	PUNCT
ejpam-5347	95	12	any	any	DET
ejpam-5347	95	13	pair−	pair−	NOUN
ejpam-5347	95	14	lindel	lindel	NOUN
ejpam-5347	95	15	..	..	PUNCT
ejpam-5347	95	16	of	of	ADP
ejpam-5347	95	17	,	,	PUNCT
ejpam-5347	95	18	pair−ω−open	pair−ω−open	PROPN
ejpam-5347	95	19	subset	subset	NOUN
ejpam-5347	95	20	j	j	PROPN
ejpam-5347	95	21	has	have	VERB
ejpam-5347	95	22	the	the	DET
ejpam-5347	95	23	form	form	NOUN
ejpam-5347	95	24	l\n	l\n	PROPN
ejpam-5347	95	25	,	,	PUNCT
ejpam-5347	95	26	where	where	SCONJ
ejpam-5347	95	27	l	l	NOUN
ejpam-5347	95	28	is	be	AUX
ejpam-5347	95	29	a	a	DET
ejpam-5347	95	30	pair−open	pair−open	ADJ
ejpam-5347	95	31	and	and	CCONJ
ejpam-5347	95	32	n	n	PRON
ejpam-5347	95	33	is	be	AUX
ejpam-5347	95	34	a	a	DET
ejpam-5347	95	35	countable	countable	ADJ
ejpam-5347	95	36	set	set	NOUN
ejpam-5347	95	37	;	;	PUNCT
ejpam-5347	95	38	specifically	specifically	ADV
ejpam-5347	95	39	,	,	PUNCT
ejpam-5347	95	40	j	j	PROPN
ejpam-5347	95	41	is	be	AUX
ejpam-5347	95	42	a	a	DET
ejpam-5347	95	43	gδ−set	gδ−set	NOUN
ejpam-5347	95	44	.	.	PUNCT
ejpam-5347	96	1	proof	proof	NOUN
ejpam-5347	96	2	.	.	PUNCT
ejpam-5347	97	1	for	for	ADP
ejpam-5347	97	2	any	any	DET
ejpam-5347	97	3	value	value	NOUN
ejpam-5347	97	4	of	of	ADP
ejpam-5347	97	5	d	d	PROPN
ejpam-5347	97	6	in	in	ADP
ejpam-5347	97	7	j	j	PROPN
ejpam-5347	97	8	,	,	PUNCT
ejpam-5347	97	9	there	there	PRON
ejpam-5347	97	10	’s	’	VERB
ejpam-5347	97	11	is	be	AUX
ejpam-5347	97	12	a	a	DET
ejpam-5347	97	13	pair−open	pair−open	NOUN
ejpam-5347	97	14	subset	subset	NOUN
ejpam-5347	97	15	td	td	NOUN
ejpam-5347	97	16	which	which	PRON
ejpam-5347	97	17	includes	include	VERB
ejpam-5347	97	18	d	d	NOUN
ejpam-5347	97	19	and	and	CCONJ
ejpam-5347	97	20	is	be	AUX
ejpam-5347	97	21	countable	countable	ADJ
ejpam-5347	97	22	set	set	VERB
ejpam-5347	97	23	td	td	NOUN
ejpam-5347	97	24	−	−	PROPN
ejpam-5347	97	25	j	j	PROPN
ejpam-5347	97	26	.	.	PUNCT
ejpam-5347	98	1	a	a	DET
ejpam-5347	98	2	countable	countable	ADJ
ejpam-5347	98	3	set	set	NOUN
ejpam-5347	98	4	is	be	AUX
ejpam-5347	98	5	created	create	VERB
ejpam-5347	98	6	when	when	SCONJ
ejpam-5347	98	7	there	there	PRON
ejpam-5347	98	8	is	be	VERB
ejpam-5347	98	9	a	a	DET
ejpam-5347	98	10	pair−open	pair−open	NOUN
ejpam-5347	98	11	subset	subset	NOUN
ejpam-5347	98	12	td	td	NOUN
ejpam-5347	98	13	−	−	PROPN
ejpam-5347	98	14	j	j	PROPN
ejpam-5347	98	15	containing	contain	VERB
ejpam-5347	98	16	d	d	NOUN
ejpam-5347	98	17	for	for	ADP
ejpam-5347	98	18	every	every	DET
ejpam-5347	98	19	d	d	NOUN
ejpam-5347	98	20	that	that	PRON
ejpam-5347	98	21	is	be	AUX
ejpam-5347	98	22	in	in	ADP
ejpam-5347	98	23	j	j	PROPN
ejpam-5347	98	24	.	.	PUNCT
ejpam-5347	99	1	claim	claim	NOUN
ejpam-5347	99	2	t1	t1	NOUN
ejpam-5347	99	3	,	,	PUNCT
ejpam-5347	99	4	t2	t2	NOUN
ejpam-5347	99	5	,	,	PUNCT
ejpam-5347	99	6	...	...	PUNCT
ejpam-5347	100	1	∈	∈	PROPN
ejpam-5347	100	2	κ1	κ1	NOUN
ejpam-5347	100	3	,	,	PUNCT
ejpam-5347	100	4	t	t	PROPN
ejpam-5347	100	5	∗	∗	NOUN
ejpam-5347	100	6	1	1	NUM
ejpam-5347	100	7	,	,	PUNCT
ejpam-5347	100	8	t	t	PROPN
ejpam-5347	100	9	∗	∗	X
ejpam-5347	100	10	2	2	NUM
ejpam-5347	100	11	,	,	PUNCT
ejpam-5347	100	12	...	...	PUNCT
ejpam-5347	101	1	∈	∈	PROPN
ejpam-5347	101	2	κ2	κ2	NOUN
ejpam-5347	101	3	,	,	PUNCT
ejpam-5347	101	4	thus	thus	ADV
ejpam-5347	101	5	j	j	PROPN
ejpam-5347	101	6	⊂	⊂	PROPN
ejpam-5347	101	7	∞⋃	∞⋃	PROPN
ejpam-5347	101	8	i=1	i=1	PROPN
ejpam-5347	102	1	ti	ti	PROPN
ejpam-5347	102	2	∪	∪	ADP
ejpam-5347	102	3	∞⋃	∞⋃	PROPN
ejpam-5347	102	4	j=1	j=1	PROPN
ejpam-5347	102	5	t	t	PROPN
ejpam-5347	102	6	∗	∗	PROPN
ejpam-5347	102	7	j	j	PROPN
ejpam-5347	102	8	,	,	PUNCT
ejpam-5347	102	9	during	during	ADP
ejpam-5347	102	10	which	which	PRON
ejpam-5347	102	11	ti	ti	NOUN
ejpam-5347	102	12	∩	∩	NOUN
ejpam-5347	102	13	(	(	PUNCT
ejpam-5347	102	14	j	j	PROPN
ejpam-5347	102	15	−d	−d	PROPN
ejpam-5347	102	16	)	)	PUNCT
ejpam-5347	102	17	is	be	AUX
ejpam-5347	102	18	κ1	κ1	NOUN
ejpam-5347	102	19	countable	countable	ADJ
ejpam-5347	102	20	,	,	PUNCT
ejpam-5347	102	21	t	t	PROPN
ejpam-5347	102	22	∗	∗	NOUN
ejpam-5347	102	23	j	j	PROPN
ejpam-5347	102	24	∩	∩	PROPN
ejpam-5347	102	25	(	(	PUNCT
ejpam-5347	102	26	j	j	PROPN
ejpam-5347	102	27	−d	−d	PROPN
ejpam-5347	102	28	)	)	PUNCT
ejpam-5347	102	29	is	be	AUX
ejpam-5347	102	30	κ2−countable	κ2−countable	ADJ
ejpam-5347	102	31	.	.	PUNCT
ejpam-5347	103	1	presently	presently	ADV
ejpam-5347	103	2	,	,	PUNCT
ejpam-5347	103	3	ti	ti	X
ejpam-5347	103	4	∩	∩	NOUN
ejpam-5347	103	5	(	(	PUNCT
ejpam-5347	103	6	j	j	PROPN
ejpam-5347	103	7	−d	−d	PROPN
ejpam-5347	103	8	)	)	PUNCT
ejpam-5347	103	9	=	=	NOUN
ejpam-5347	103	10	∞⋃	∞⋃	PROPN
ejpam-5347	103	11	n=1	n=1	PROPN
ejpam-5347	103	12	di	di	PROPN
ejpam-5347	103	13	,	,	PUNCT
ejpam-5347	103	14	n	n	CCONJ
ejpam-5347	103	15	,	,	PUNCT
ejpam-5347	103	16	i	i	PRON
ejpam-5347	103	17	=	=	NOUN
ejpam-5347	103	18	1	1	NUM
ejpam-5347	103	19	,	,	PUNCT
ejpam-5347	103	20	2	2	NUM
ejpam-5347	103	21	,	,	PUNCT
ejpam-5347	103	22	...	...	PUNCT
ejpam-5347	103	23	,	,	PUNCT
ejpam-5347	103	24	t	t	PROPN
ejpam-5347	103	25	∗	∗	NOUN
ejpam-5347	103	26	j	j	PROPN
ejpam-5347	103	27	∩	∩	PROPN
ejpam-5347	103	28	(	(	PUNCT
ejpam-5347	103	29	j	j	PROPN
ejpam-5347	103	30	−d	−d	PROPN
ejpam-5347	103	31	)	)	PUNCT
ejpam-5347	104	1	=	=	PROPN
ejpam-5347	104	2	∞⋃	∞⋃	PROPN
ejpam-5347	104	3	m=1	m=1	PROPN
ejpam-5347	104	4	dh	dh	PROPN
ejpam-5347	104	5	,	,	PUNCT
ejpam-5347	104	6	m	m	PROPN
ejpam-5347	104	7	,	,	PUNCT
ejpam-5347	104	8	h	h	NOUN
ejpam-5347	104	9	=	=	SYM
ejpam-5347	104	10	1	1	NUM
ejpam-5347	104	11	,	,	PUNCT
ejpam-5347	104	12	2	2	NUM
ejpam-5347	104	13	...	...	PUNCT
ejpam-5347	104	14	right	right	ADV
ejpam-5347	104	15	now	now	ADV
ejpam-5347	104	16	,	,	PUNCT
ejpam-5347	104	17	j	j	PROPN
ejpam-5347	105	1	=	=	SYM
ejpam-5347	105	2	∪(ti\	∪(ti\	PROPN
ejpam-5347	105	3	∞⋃	∞⋃	PROPN
ejpam-5347	105	4	n=1	n=1	PROPN
ejpam-5347	105	5	di	di	PROPN
ejpam-5347	105	6	,	,	PUNCT
ejpam-5347	105	7	n	n	CCONJ
ejpam-5347	105	8	)	)	PUNCT
ejpam-5347	105	9	∪	∪	NOUN
ejpam-5347	105	10	(	(	PUNCT
ejpam-5347	105	11	t	t	PROPN
ejpam-5347	105	12	∗	∗	NOUN
ejpam-5347	105	13	h\	h\	PROPN
ejpam-5347	106	1	∞⋃	∞⋃	PROPN
ejpam-5347	106	2	m=1	m=1	PROPN
ejpam-5347	106	3	dh	dh	PROPN
ejpam-5347	106	4	,	,	PUNCT
ejpam-5347	106	5	m	m	NOUN
ejpam-5347	106	6	)	)	PUNCT
ejpam-5347	107	1	=	=	SYM
ejpam-5347	107	2	∪	∪	ADP
ejpam-5347	107	3	∞⋃	∞⋃	PROPN
ejpam-5347	107	4	i=1	i=1	PROPN
ejpam-5347	107	5	(	(	PUNCT
ejpam-5347	107	6	ti\l1	ti\l1	NUM
ejpam-5347	107	7	)	)	PUNCT
ejpam-5347	107	8	∪	∪	ADP
ejpam-5347	107	9	∞⋃	∞⋃	NOUN
ejpam-5347	107	10	j=1	j=1	NOUN
ejpam-5347	107	11	(	(	PUNCT
ejpam-5347	107	12	t	t	NOUN
ejpam-5347	107	13	∗	∗	X
ejpam-5347	107	14	h\l2	h\l2	PROPN
ejpam-5347	107	15	)	)	PUNCT
ejpam-5347	107	16	.	.	PUNCT
ejpam-5347	108	1	enable	enable	VERB
ejpam-5347	108	2	l	l	NOUN
ejpam-5347	108	3	=	=	SYM
ejpam-5347	108	4	l1	l1	PROPN
ejpam-5347	108	5	∪	∪	PROPN
ejpam-5347	108	6	l2	l2	PROPN
ejpam-5347	108	7	,	,	PUNCT
ejpam-5347	108	8	and	and	CCONJ
ejpam-5347	108	9	l	l	PROPN
ejpam-5347	108	10	⊂	⊂	PROPN
ejpam-5347	108	11	∞⋃	∞⋃	PROPN
ejpam-5347	108	12	n=1	n=1	PROPN
ejpam-5347	108	13	di	di	PROPN
ejpam-5347	108	14	,	,	PUNCT
ejpam-5347	108	15	n	n	PROPN
ejpam-5347	108	16	∪	∪	VERB
ejpam-5347	108	17	∞⋃	∞⋃	PROPN
ejpam-5347	108	18	m=1	m=1	PROPN
ejpam-5347	108	19	dh	dh	PROPN
ejpam-5347	108	20	,	,	PUNCT
ejpam-5347	108	21	m.	m.	NOUN
ejpam-5347	108	22	corollary	corollary	NOUN
ejpam-5347	108	23	1	1	NUM
ejpam-5347	108	24	.	.	PUNCT
ejpam-5347	109	1	let	let	VERB
ejpam-5347	109	2	’s	’s	NOUN
ejpam-5347	109	3	consider	consider	VERB
ejpam-5347	109	4	the	the	DET
ejpam-5347	109	5	hereditary	hereditary	ADJ
ejpam-5347	109	6	lindel	lindel	NOUN
ejpam-5347	109	7	..	..	PUNCT
ejpam-5347	109	8	of	of	ADP
ejpam-5347	109	9	space	space	NOUN
ejpam-5347	109	10	(	(	PUNCT
ejpam-5347	109	11	d	d	NOUN
ejpam-5347	109	12	,	,	PUNCT
ejpam-5347	109	13	κ1	κ1	NOUN
ejpam-5347	109	14	,	,	PUNCT
ejpam-5347	109	15	κ2	κ2	PROPN
ejpam-5347	109	16	)	)	PUNCT
ejpam-5347	109	17	.	.	PUNCT
ejpam-5347	110	1	following	follow	VERB
ejpam-5347	110	2	this	this	PRON
ejpam-5347	110	3	,	,	PUNCT
ejpam-5347	110	4	a	a	DET
ejpam-5347	110	5	gδ−set	gδ−set	NOUN
ejpam-5347	110	6	is	be	AUX
ejpam-5347	110	7	any	any	DET
ejpam-5347	110	8	pair−ω−open	pair−ω−open	ADJ
ejpam-5347	110	9	subset	subset	NOUN
ejpam-5347	110	10	of	of	ADP
ejpam-5347	110	11	a	a	DET
ejpam-5347	110	12	space	space	NOUN
ejpam-5347	110	13	(	(	PUNCT
ejpam-5347	110	14	d	d	NOUN
ejpam-5347	110	15	,	,	PUNCT
ejpam-5347	110	16	κ1	κ1	NOUN
ejpam-5347	110	17	,	,	PUNCT
ejpam-5347	110	18	κ2	κ2	PROPN
ejpam-5347	110	19	)	)	PUNCT
ejpam-5347	110	20	.	.	PUNCT
ejpam-5347	111	1	theorem	theorem	NOUN
ejpam-5347	111	2	2	2	NUM
ejpam-5347	111	3	.	.	PUNCT
ejpam-5347	112	1	in	in	ADP
ejpam-5347	112	2	a	a	DET
ejpam-5347	112	3	space	space	NOUN
ejpam-5347	112	4	(	(	PUNCT
ejpam-5347	112	5	d	d	NOUN
ejpam-5347	112	6	,	,	PUNCT
ejpam-5347	112	7	κ1	κ1	NOUN
ejpam-5347	112	8	,	,	PUNCT
ejpam-5347	112	9	κ2	κ2	PROPN
ejpam-5347	112	10	)	)	PUNCT
ejpam-5347	112	11	,	,	PUNCT
ejpam-5347	112	12	any	any	DET
ejpam-5347	112	13	s−	s−	PROPN
ejpam-5347	112	14	lindel	lindel	NOUN
ejpam-5347	112	15	..	..	PUNCT
ejpam-5347	112	16	of	of	ADP
ejpam-5347	112	17	,	,	PUNCT
ejpam-5347	112	18	s−ω−open	s−ω−open	PROPN
ejpam-5347	112	19	subset	subset	VERB
ejpam-5347	112	20	j	j	PROPN
ejpam-5347	112	21	has	have	VERB
ejpam-5347	112	22	the	the	DET
ejpam-5347	112	23	form	form	NOUN
ejpam-5347	112	24	l\n	l\n	PROPN
ejpam-5347	112	25	,	,	PUNCT
ejpam-5347	112	26	where	where	SCONJ
ejpam-5347	112	27	l	l	NOUN
ejpam-5347	112	28	is	be	AUX
ejpam-5347	112	29	a	a	DET
ejpam-5347	112	30	κ1κ2−open	κ1κ2−open	NOUN
ejpam-5347	112	31	and	and	CCONJ
ejpam-5347	112	32	n	n	PRON
ejpam-5347	112	33	is	be	AUX
ejpam-5347	112	34	a	a	DET
ejpam-5347	112	35	countable	countable	ADJ
ejpam-5347	112	36	set	set	NOUN
ejpam-5347	112	37	;	;	PUNCT
ejpam-5347	112	38	specifically	specifically	ADV
ejpam-5347	112	39	,	,	PUNCT
ejpam-5347	112	40	j	j	PROPN
ejpam-5347	112	41	is	be	AUX
ejpam-5347	112	42	a	a	DET
ejpam-5347	112	43	gδ−set	gδ−set	NOUN
ejpam-5347	112	44	.	.	PUNCT
ejpam-5347	113	1	proof	proof	NOUN
ejpam-5347	113	2	.	.	PUNCT
ejpam-5347	114	1	the	the	DET
ejpam-5347	114	2	proof	proof	NOUN
ejpam-5347	114	3	use	use	VERB
ejpam-5347	114	4	the	the	DET
ejpam-5347	114	5	same	same	ADJ
ejpam-5347	114	6	methodology	methodology	NOUN
ejpam-5347	114	7	as	as	ADP
ejpam-5347	114	8	theorem	theorem	ADJ
ejpam-5347	114	9	1	1	NUM
ejpam-5347	114	10	.	.	PUNCT
ejpam-5347	114	11	corollary	corollary	ADJ
ejpam-5347	114	12	2	2	NUM
ejpam-5347	114	13	.	.	PUNCT
ejpam-5347	115	1	let	let	VERB
ejpam-5347	115	2	’s	’s	NOUN
ejpam-5347	115	3	consider	consider	VERB
ejpam-5347	115	4	the	the	DET
ejpam-5347	115	5	hereditary	hereditary	ADJ
ejpam-5347	115	6	lindel	lindel	NOUN
ejpam-5347	115	7	..	..	PUNCT
ejpam-5347	115	8	of	of	ADP
ejpam-5347	115	9	space	space	NOUN
ejpam-5347	115	10	(	(	PUNCT
ejpam-5347	115	11	d	d	NOUN
ejpam-5347	115	12	,	,	PUNCT
ejpam-5347	115	13	κ1	κ1	NOUN
ejpam-5347	115	14	,	,	PUNCT
ejpam-5347	115	15	κ2	κ2	PROPN
ejpam-5347	115	16	)	)	PUNCT
ejpam-5347	115	17	.	.	PUNCT
ejpam-5347	116	1	following	follow	VERB
ejpam-5347	116	2	this	this	PRON
ejpam-5347	116	3	,	,	PUNCT
ejpam-5347	116	4	a	a	DET
ejpam-5347	116	5	gδ−set	gδ−set	NOUN
ejpam-5347	116	6	is	be	AUX
ejpam-5347	116	7	any	any	DET
ejpam-5347	116	8	s−ω−open	s−ω−open	ADJ
ejpam-5347	116	9	subset	subset	NOUN
ejpam-5347	116	10	of	of	ADP
ejpam-5347	116	11	a	a	DET
ejpam-5347	116	12	space	space	NOUN
ejpam-5347	116	13	(	(	PUNCT
ejpam-5347	116	14	d	d	NOUN
ejpam-5347	116	15	,	,	PUNCT
ejpam-5347	116	16	κ1	κ1	NOUN
ejpam-5347	116	17	,	,	PUNCT
ejpam-5347	116	18	κ2	κ2	PROPN
ejpam-5347	116	19	)	)	PUNCT
ejpam-5347	116	20	.	.	PUNCT
ejpam-5347	117	1	it	it	PRON
ejpam-5347	117	2	is	be	AUX
ejpam-5347	117	3	incorrect	incorrect	ADJ
ejpam-5347	117	4	to	to	PART
ejpam-5347	117	5	assert	assert	VERB
ejpam-5347	117	6	that	that	SCONJ
ejpam-5347	117	7	theorem	theorem	NOUN
ejpam-5347	117	8	3.1	3.1	NUM
ejpam-5347	117	9	is	be	AUX
ejpam-5347	117	10	contradictory	contradictory	ADJ
ejpam-5347	117	11	.	.	PUNCT
ejpam-5347	118	1	considering	consider	VERB
ejpam-5347	118	2	a	a	DET
ejpam-5347	118	3	specific	specific	ADJ
ejpam-5347	118	4	illustration	illustration	NOUN
ejpam-5347	118	5	:	:	PUNCT
ejpam-5347	118	6	example	example	NOUN
ejpam-5347	118	7	1	1	X
ejpam-5347	118	8	.	.	X
ejpam-5347	118	9	consider	consider	VERB
ejpam-5347	118	10	two	two	NUM
ejpam-5347	118	11	topologies	topology	NOUN
ejpam-5347	118	12	κ1	κ1	NOUN
ejpam-5347	118	13	,	,	PUNCT
ejpam-5347	118	14	κ2	κ2	NOUN
ejpam-5347	118	15	on	on	ADP
ejpam-5347	118	16	r	r	NOUN
ejpam-5347	118	17	by	by	ADP
ejpam-5347	118	18	the	the	DET
ejpam-5347	118	19	basis	basis	NOUN
ejpam-5347	118	20	h1	h1	NOUN
ejpam-5347	118	21	=	=	SYM
ejpam-5347	118	22	{	{	PUNCT
ejpam-5347	118	23	(	(	PUNCT
ejpam-5347	118	24	−∞	−∞	NOUN
ejpam-5347	118	25	,	,	PUNCT
ejpam-5347	118	26	j	j	PROPN
ejpam-5347	118	27	)	)	PUNCT
ejpam-5347	118	28	:	:	PUNCT
ejpam-5347	119	1	j	j	PROPN
ejpam-5347	119	2	>	>	X
ejpam-5347	119	3	0	0	NUM
ejpam-5347	119	4	}	}	PUNCT
ejpam-5347	119	5	∪	∪	X
ejpam-5347	119	6	{	{	PUNCT
ejpam-5347	119	7	{	{	PUNCT
ejpam-5347	119	8	d	d	NOUN
ejpam-5347	119	9	}	}	PUNCT
ejpam-5347	119	10	:	:	PUNCT
ejpam-5347	119	11	d	d	X
ejpam-5347	119	12	>	>	X
ejpam-5347	119	13	0	0	NUM
ejpam-5347	119	14	}	}	PUNCT
ejpam-5347	119	15	,	,	PUNCT
ejpam-5347	119	16	h2	h2	NOUN
ejpam-5347	119	17	=	=	SYM
ejpam-5347	119	18	{	{	PUNCT
ejpam-5347	119	19	(	(	PUNCT
ejpam-5347	119	20	d,∞	d,∞	PROPN
ejpam-5347	119	21	)	)	PUNCT
ejpam-5347	119	22	:	:	PUNCT
ejpam-5347	120	1	d	d	X
ejpam-5347	120	2	<	<	X
ejpam-5347	120	3	0	0	NUM
ejpam-5347	120	4	}	}	PUNCT
ejpam-5347	120	5	∪	∪	X
ejpam-5347	120	6	{	{	PUNCT
ejpam-5347	120	7	{	{	PUNCT
ejpam-5347	120	8	d	d	NOUN
ejpam-5347	120	9	}	}	PUNCT
ejpam-5347	120	10	:	:	PUNCT
ejpam-5347	121	1	d	d	X
ejpam-5347	121	2	<	<	X
ejpam-5347	121	3	0	0	NUM
ejpam-5347	121	4	}	}	PUNCT
ejpam-5347	121	5	,	,	PUNCT
ejpam-5347	121	6	then	then	ADV
ejpam-5347	121	7	(	(	PUNCT
ejpam-5347	121	8	r	r	NOUN
ejpam-5347	121	9	,	,	PUNCT
ejpam-5347	121	10	κ1	κ1	NOUN
ejpam-5347	121	11	,	,	PUNCT
ejpam-5347	121	12	κ2	κ2	PROPN
ejpam-5347	121	13	)	)	PUNCT
ejpam-5347	121	14	is	be	AUX
ejpam-5347	121	15	pair−lindel	pair−lindel	NOUN
ejpam-5347	121	16	..	..	PUNCT
ejpam-5347	121	17	of	of	ADP
ejpam-5347	121	18	.	.	PUNCT
ejpam-5347	122	1	the	the	DET
ejpam-5347	122	2	ensuing	ensue	VERB
ejpam-5347	122	3	theorem	theorem	NOUN
ejpam-5347	122	4	extends	extend	VERB
ejpam-5347	122	5	the	the	DET
ejpam-5347	122	6	widely	widely	ADV
ejpam-5347	122	7	recognized	recognize	VERB
ejpam-5347	122	8	theorem	theorem	VERB
ejpam-5347	122	9	,	,	PUNCT
ejpam-5347	122	10	which	which	PRON
ejpam-5347	122	11	states	state	VERB
ejpam-5347	122	12	that	that	PRON
ejpam-5347	122	13	closed	close	VERB
ejpam-5347	122	14	continuous	continuous	ADJ
ejpam-5347	122	15	functionings	functioning	NOUN
ejpam-5347	122	16	with	with	ADP
ejpam-5347	122	17	pair−lindel	pair−lindel	NOUN
ejpam-5347	122	18	..	..	PUNCT
ejpam-5347	122	19	of	of	ADP
ejpam-5347	122	20	counter	counter	ADJ
ejpam-5347	122	21	images	image	NOUN
ejpam-5347	122	22	maintain	maintain	VERB
ejpam-5347	122	23	the	the	DET
ejpam-5347	122	24	pair−lindel	pair−lindel	NOUN
ejpam-5347	122	25	..	..	PUNCT
ejpam-5347	122	26	of	of	ADP
ejpam-5347	122	27	property	property	NOUN
ejpam-5347	122	28	under	under	ADP
ejpam-5347	122	29	taking	take	VERB
ejpam-5347	122	30	counter	counter	ADJ
ejpam-5347	122	31	images	image	NOUN
ejpam-5347	122	32	.	.	PUNCT
ejpam-5347	123	1	theorem	theorem	NOUN
ejpam-5347	123	2	3	3	NUM
ejpam-5347	123	3	.	.	X
ejpam-5347	123	4	letting	let	VERB
ejpam-5347	123	5	υ	υ	PRON
ejpam-5347	123	6	represent	represent	VERB
ejpam-5347	123	7	a	a	DET
ejpam-5347	123	8	pair−continuous	pair−continuous	ADJ
ejpam-5347	123	9	pair−ω−closed	pair−ω−closed	ADJ
ejpam-5347	123	10	functioning	functioning	NOUN
ejpam-5347	123	11	of	of	ADP
ejpam-5347	123	12	a	a	DET
ejpam-5347	123	13	space	space	NOUN
ejpam-5347	123	14	onto	onto	ADP
ejpam-5347	123	15	(	(	PUNCT
ejpam-5347	123	16	g	g	PROPN
ejpam-5347	123	17	,	,	PUNCT
ejpam-5347	123	18	υ1	υ1	NOUN
ejpam-5347	123	19	,	,	PUNCT
ejpam-5347	123	20	υ2	υ2	PROPN
ejpam-5347	123	21	)	)	PUNCT
ejpam-5347	123	22	from	from	ADP
ejpam-5347	123	23	(	(	PUNCT
ejpam-5347	123	24	d	d	NOUN
ejpam-5347	123	25	,	,	PUNCT
ejpam-5347	123	26	κ1	κ1	NOUN
ejpam-5347	123	27	,	,	PUNCT
ejpam-5347	123	28	κ2	κ2	PROPN
ejpam-5347	123	29	)	)	PUNCT
ejpam-5347	123	30	.	.	PUNCT
ejpam-5347	124	1	which	which	PRON
ejpam-5347	124	2	means	mean	VERB
ejpam-5347	124	3	that	that	SCONJ
ejpam-5347	124	4	for	for	ADP
ejpam-5347	124	5	every	every	DET
ejpam-5347	124	6	g	g	PROPN
ejpam-5347	124	7	∈	∈	PROPN
ejpam-5347	124	8	(	(	PUNCT
ejpam-5347	124	9	g	g	NOUN
ejpam-5347	124	10	,	,	PUNCT
ejpam-5347	124	11	υ1	υ1	NOUN
ejpam-5347	124	12	,	,	PUNCT
ejpam-5347	124	13	υ2	υ2	PROPN
ejpam-5347	124	14	)	)	PUNCT
ejpam-5347	124	15	,	,	PUNCT
ejpam-5347	124	16	υ	υ	PRON
ejpam-5347	124	17	−1(g	−1(g	NOUN
ejpam-5347	124	18	)	)	PUNCT
ejpam-5347	124	19	is	be	AUX
ejpam-5347	124	20	pair−lindel	pair−lindel	NOUN
ejpam-5347	124	21	..	..	PUNCT
ejpam-5347	124	22	of	of	ADP
ejpam-5347	124	23	.	.	PUNCT
ejpam-5347	125	1	while	while	SCONJ
ejpam-5347	125	2	(	(	PUNCT
ejpam-5347	125	3	g	g	NOUN
ejpam-5347	125	4	,	,	PUNCT
ejpam-5347	125	5	υ1	υ1	NOUN
ejpam-5347	125	6	,	,	PUNCT
ejpam-5347	125	7	υ2	υ2	PROPN
ejpam-5347	125	8	)	)	PUNCT
ejpam-5347	125	9	is	be	AUX
ejpam-5347	125	10	such	such	DET
ejpam-5347	125	11	a	a	DET
ejpam-5347	125	12	case	case	NOUN
ejpam-5347	125	13	,	,	PUNCT
ejpam-5347	125	14	therefore	therefore	ADV
ejpam-5347	125	15	(	(	PUNCT
ejpam-5347	125	16	d	d	NOUN
ejpam-5347	125	17	,	,	PUNCT
ejpam-5347	125	18	κ1	κ1	NOUN
ejpam-5347	125	19	,	,	PUNCT
ejpam-5347	125	20	κ2	κ2	PROPN
ejpam-5347	125	21	)	)	PUNCT
ejpam-5347	125	22	is	be	AUX
ejpam-5347	125	23	pair−lindel	pair−lindel	NOUN
ejpam-5347	125	24	..	..	PUNCT
ejpam-5347	125	25	of	of	ADP
ejpam-5347	125	26	.	.	PUNCT
ejpam-5347	126	1	proof	proof	NOUN
ejpam-5347	126	2	.	.	PUNCT
ejpam-5347	127	1	let	let	VERB
ejpam-5347	127	2	us	we	PRON
ejpam-5347	127	3	know	know	VERB
ejpam-5347	127	4	t	t	NOUN
ejpam-5347	127	5	˜	˜	PROPN
ejpam-5347	127	6	=	=	PRON
ejpam-5347	127	7	{	{	PUNCT
ejpam-5347	127	8	tδ	tδ	NOUN
ejpam-5347	127	9	:	:	PUNCT
ejpam-5347	127	10	δ	δ	PROPN
ejpam-5347	127	11	∈	∈	PROPN
ejpam-5347	127	12	ξ	ξ	PROPN
ejpam-5347	127	13	}	}	PUNCT
ejpam-5347	127	14	is	be	AUX
ejpam-5347	127	15	a	a	DET
ejpam-5347	127	16	pair−open	pair−open	ADJ
ejpam-5347	127	17	cover	cover	NOUN
ejpam-5347	127	18	of	of	ADP
ejpam-5347	127	19	(	(	PUNCT
ejpam-5347	127	20	d	d	PROPN
ejpam-5347	127	21	,	,	PUNCT
ejpam-5347	127	22	κ1	κ1	NOUN
ejpam-5347	127	23	,	,	PUNCT
ejpam-5347	127	24	κ2	κ2	PROPN
ejpam-5347	127	25	)	)	PUNCT
ejpam-5347	127	26	.	.	PUNCT
ejpam-5347	128	1	in	in	ADP
ejpam-5347	128	2	the	the	DET
ejpam-5347	128	3	meantime	meantime	NOUN
ejpam-5347	128	4	late	late	ADJ
ejpam-5347	128	5	∀g	∀g	X
ejpam-5347	128	6	∈	∈	NOUN
ejpam-5347	128	7	(	(	PUNCT
ejpam-5347	128	8	g	g	NOUN
ejpam-5347	128	9	,	,	PUNCT
ejpam-5347	128	10	υ1	υ1	NOUN
ejpam-5347	128	11	,	,	PUNCT
ejpam-5347	128	12	υ2	υ2	PROPN
ejpam-5347	128	13	)	)	PUNCT
ejpam-5347	128	14	,	,	PUNCT
ejpam-5347	128	15	υ−1(g	υ−1(g	PROPN
ejpam-5347	128	16	)	)	PUNCT
ejpam-5347	128	17	is	be	AUX
ejpam-5347	128	18	pair−lindel	pair−lindel	NOUN
ejpam-5347	128	19	..	..	PUNCT
ejpam-5347	129	1	of	of	ADP
ejpam-5347	129	2	,	,	PUNCT
ejpam-5347	129	3	the	the	DET
ejpam-5347	129	4	situation	situation	NOUN
ejpam-5347	129	5	exists	exist	VERB
ejpam-5347	129	6	a	a	DET
ejpam-5347	129	7	countable	countable	ADJ
ejpam-5347	129	8	a.	a.	NOUN
ejpam-5347	129	9	atoom	atoom	NOUN
ejpam-5347	129	10	et	et	PROPN
ejpam-5347	129	11	al	al	PROPN
ejpam-5347	129	12	.	.	PUNCT
ejpam-5347	129	13	/	/	SYM
ejpam-5347	129	14	eur	eur	PROPN
ejpam-5347	129	15	.	.	PUNCT
ejpam-5347	130	1	j.	j.	PROPN
ejpam-5347	130	2	pure	pure	PROPN
ejpam-5347	130	3	appl	appl	PROPN
ejpam-5347	130	4	.	.	PROPN
ejpam-5347	130	5	math	math	PROPN
ejpam-5347	130	6	,	,	PUNCT
ejpam-5347	130	7	17	17	NUM
ejpam-5347	130	8	(	(	PUNCT
ejpam-5347	130	9	4	4	NUM
ejpam-5347	130	10	)	)	PUNCT
ejpam-5347	130	11	(	(	PUNCT
ejpam-5347	130	12	2024	2024	NUM
ejpam-5347	130	13	)	)	PUNCT
ejpam-5347	130	14	,	,	PUNCT
ejpam-5347	130	15	2574	2574	NUM
ejpam-5347	130	16	-	-	SYM
ejpam-5347	130	17	2585	2585	NUM
ejpam-5347	130	18	2579	2579	NUM
ejpam-5347	130	19	subsets	subset	NOUN
ejpam-5347	130	20	ξy	ξy	PROPN
ejpam-5347	130	21	,	,	PUNCT
ejpam-5347	130	22	ξ	ξ	PROPN
ejpam-5347	130	23	∗	∗	X
ejpam-5347	130	24	y	y	PROPN
ejpam-5347	130	25	of	of	ADP
ejpam-5347	130	26	ξ	ξ	PROPN
ejpam-5347	130	27	,	,	PUNCT
ejpam-5347	130	28	which	which	PRON
ejpam-5347	130	29	means	mean	VERB
ejpam-5347	130	30	υ−1(g	υ−1(g	PROPN
ejpam-5347	130	31	)	)	PUNCT
ejpam-5347	131	1	⊆	⊆	NUM
ejpam-5347	131	2	⋃	⋃	NOUN
ejpam-5347	131	3	δ∈ξg	δ∈ξg	NOUN
ejpam-5347	131	4	{	{	PUNCT
ejpam-5347	131	5	nδ	nδ	ADP
ejpam-5347	131	6	:	:	PUNCT
ejpam-5347	131	7	δ	δ	PROPN
ejpam-5347	131	8	∈	∈	PROPN
ejpam-5347	131	9	ξg	ξg	PROPN
ejpam-5347	131	10	}	}	PUNCT
ejpam-5347	131	11	⋃	⋃	X
ejpam-5347	131	12	⋃	⋃	PUNCT
ejpam-5347	131	13	α∈	α∈	PROPN
ejpam-5347	131	14	λ∗	λ∗	NOUN
ejpam-5347	131	15	y	y	INTJ
ejpam-5347	131	16	{	{	PUNCT
ejpam-5347	131	17	mδ	mδ	PROPN
ejpam-5347	131	18	:	:	PUNCT
ejpam-5347	131	19	δ	δ	PROPN
ejpam-5347	131	20	∈	∈	PROPN
ejpam-5347	131	21	ξ∗	ξ∗	NOUN
ejpam-5347	131	22	g	g	PROPN
ejpam-5347	131	23	}	}	PUNCT
ejpam-5347	131	24	,	,	PUNCT
ejpam-5347	131	25	at	at	ADP
ejpam-5347	131	26	which	which	PRON
ejpam-5347	131	27	{	{	PUNCT
ejpam-5347	131	28	nδ	nδ	ADP
ejpam-5347	131	29	:	:	PUNCT
ejpam-5347	131	30	δ	δ	PROPN
ejpam-5347	131	31	∈	∈	PROPN
ejpam-5347	131	32	ξg	ξg	PROPN
ejpam-5347	131	33	}	}	PUNCT
ejpam-5347	131	34	is	be	AUX
ejpam-5347	131	35	κ1−open	κ1−open	ADJ
ejpam-5347	131	36	,	,	PUNCT
ejpam-5347	131	37	{	{	PUNCT
ejpam-5347	131	38	mδ	mδ	NOUN
ejpam-5347	131	39	:	:	PUNCT
ejpam-5347	131	40	δ	δ	PROPN
ejpam-5347	131	41	∈	∈	PROPN
ejpam-5347	131	42	ξ∗	ξ∗	PROPN
ejpam-5347	131	43	g	g	NOUN
ejpam-5347	131	44	}	}	PUNCT
ejpam-5347	131	45	is	be	AUX
ejpam-5347	131	46	κ2−open	κ2−open	ADJ
ejpam-5347	131	47	.	.	PUNCT
ejpam-5347	132	1	assume	assume	VERB
ejpam-5347	132	2	hg	hg	X
ejpam-5347	133	1	=	=	SYM
ejpam-5347	133	2	(	(	PUNCT
ejpam-5347	133	3	g	g	PROPN
ejpam-5347	133	4	,	,	PUNCT
ejpam-5347	133	5	υ1	υ1	PROPN
ejpam-5347	133	6	,	,	PUNCT
ejpam-5347	133	7	υ2)−υ((d	υ2)−υ((d	NOUN
ejpam-5347	133	8	,	,	PUNCT
ejpam-5347	133	9	κ1	κ1	NOUN
ejpam-5347	133	10	,	,	PUNCT
ejpam-5347	133	11	κ2)−	κ2)−	ADJ
ejpam-5347	133	12	⋃	⋃	NOUN
ejpam-5347	133	13	δ∈ξg	δ∈ξg	NOUN
ejpam-5347	133	14	nδ	nδ	NOUN
ejpam-5347	133	15	)	)	PUNCT
ejpam-5347	133	16	is	be	AUX
ejpam-5347	133	17	a	a	DET
ejpam-5347	133	18	ρ1	ρ1	NOUN
ejpam-5347	133	19	-	-	PUNCT
ejpam-5347	133	20	open	open	ADJ
ejpam-5347	133	21	set	set	NOUN
ejpam-5347	133	22	comprising	comprising	NOUN
ejpam-5347	133	23	g	g	NOUN
ejpam-5347	133	24	,	,	PUNCT
ejpam-5347	133	25	and	and	CCONJ
ejpam-5347	133	26	h∗	h∗	PROPN
ejpam-5347	133	27	g	g	PROPN
ejpam-5347	133	28	=	=	SYM
ejpam-5347	133	29	(	(	PUNCT
ejpam-5347	133	30	g	g	PROPN
ejpam-5347	133	31	,	,	PUNCT
ejpam-5347	133	32	υ1	υ1	PROPN
ejpam-5347	133	33	,	,	PUNCT
ejpam-5347	133	34	υ2)−υ((d	υ2)−υ((d	NOUN
ejpam-5347	133	35	,	,	PUNCT
ejpam-5347	133	36	κ1	κ1	NOUN
ejpam-5347	133	37	,	,	PUNCT
ejpam-5347	133	38	κ2)−	κ2)−	PROPN
ejpam-5347	133	39	⋃	⋃	PUNCT
ejpam-5347	133	40	δ∈ξ∗	δ∈ξ∗	NOUN
ejpam-5347	133	41	g	g	PROPN
ejpam-5347	133	42	mδ	mδ	NOUN
ejpam-5347	133	43	)	)	PUNCT
ejpam-5347	133	44	is	be	AUX
ejpam-5347	133	45	a	a	DET
ejpam-5347	133	46	ρ2	ρ2	NOUN
ejpam-5347	133	47	-	-	PUNCT
ejpam-5347	133	48	open	open	ADJ
ejpam-5347	133	49	set	set	NOUN
ejpam-5347	133	50	comprising	comprising	NOUN
ejpam-5347	133	51	g	g	NOUN
ejpam-5347	133	52	,	,	PUNCT
ejpam-5347	133	53	where	where	SCONJ
ejpam-5347	133	54	υ−1	υ−1	PROPN
ejpam-5347	133	55	(	(	PUNCT
ejpam-5347	133	56	hg	hg	NOUN
ejpam-5347	133	57	)	)	PUNCT
ejpam-5347	133	58	⊆	⊆	NUM
ejpam-5347	133	59	⋃	⋃	NOUN
ejpam-5347	133	60	δ∈ξg	δ∈ξg	ADJ
ejpam-5347	133	61	vα	vα	PROPN
ejpam-5347	133	62	,	,	PUNCT
ejpam-5347	133	63	υ−1	υ−1	PROPN
ejpam-5347	133	64	(	(	PUNCT
ejpam-5347	133	65	h∗	h∗	PROPN
ejpam-5347	133	66	g	g	PROPN
ejpam-5347	133	67	)	)	PUNCT
ejpam-5347	133	68	⊆	⊆	NUM
ejpam-5347	133	69	⋃	⋃	NOUN
ejpam-5347	133	70	δ∈ξ∗	δ∈ξ∗	NOUN
ejpam-5347	133	71	g	g	PROPN
ejpam-5347	133	72	mδ	mδ	NOUN
ejpam-5347	133	73	.	.	PROPN
ejpam-5347	134	1	assume	assume	VERB
ejpam-5347	135	1	h	h	NOUN
ejpam-5347	135	2	˜	˜	PROPN
ejpam-5347	135	3	g	g	PROPN
ejpam-5347	135	4	=	=	PUNCT
ejpam-5347	135	5	{	{	PUNCT
ejpam-5347	135	6	hg	hg	NOUN
ejpam-5347	135	7	:	:	PUNCT
ejpam-5347	135	8	g	g	PROPN
ejpam-5347	135	9	∈	∈	PROPN
ejpam-5347	135	10	(	(	PUNCT
ejpam-5347	135	11	g	g	NOUN
ejpam-5347	135	12	,	,	PUNCT
ejpam-5347	135	13	υ1	υ1	NOUN
ejpam-5347	135	14	,	,	PUNCT
ejpam-5347	135	15	υ2	υ2	NOUN
ejpam-5347	135	16	)	)	PUNCT
ejpam-5347	135	17	}	}	PUNCT
ejpam-5347	135	18	⋃	⋃	ADP
ejpam-5347	136	1	{	{	PUNCT
ejpam-5347	136	2	h∗	h∗	PROPN
ejpam-5347	136	3	g	g	NOUN
ejpam-5347	136	4	:	:	PUNCT
ejpam-5347	136	5	g	g	PROPN
ejpam-5347	136	6	∈	∈	PROPN
ejpam-5347	136	7	(	(	PUNCT
ejpam-5347	136	8	g	g	NOUN
ejpam-5347	136	9	,	,	PUNCT
ejpam-5347	136	10	υ1	υ1	NOUN
ejpam-5347	136	11	,	,	PUNCT
ejpam-5347	136	12	υ2	υ2	NOUN
ejpam-5347	136	13	)	)	PUNCT
ejpam-5347	136	14	}	}	PUNCT
ejpam-5347	136	15	is	be	AUX
ejpam-5347	136	16	a	a	DET
ejpam-5347	136	17	pair−open	pair−open	ADJ
ejpam-5347	136	18	cover	cover	NOUN
ejpam-5347	136	19	of	of	ADP
ejpam-5347	136	20	(	(	PUNCT
ejpam-5347	136	21	g	g	PROPN
ejpam-5347	136	22	,	,	PUNCT
ejpam-5347	136	23	υ1	υ1	NOUN
ejpam-5347	136	24	,	,	PUNCT
ejpam-5347	136	25	υ2	υ2	PROPN
ejpam-5347	136	26	)	)	PUNCT
ejpam-5347	136	27	.	.	PUNCT
ejpam-5347	137	1	considering	consider	VERB
ejpam-5347	137	2	υ	υ	PROPN
ejpam-5347	137	3	is	be	AUX
ejpam-5347	137	4	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	137	5	,	,	PUNCT
ejpam-5347	137	6	h	h	NOUN
ejpam-5347	137	7	˜	˜	PROPN
ejpam-5347	137	8	g	g	PROPN
ejpam-5347	137	9	is	be	AUX
ejpam-5347	137	10	pair−ω−open	pair−ω−open	ADJ
ejpam-5347	137	11	for	for	ADP
ejpam-5347	137	12	each	each	DET
ejpam-5347	137	13	g	g	PROPN
ejpam-5347	137	14	∈	∈	PROPN
ejpam-5347	137	15	(	(	PUNCT
ejpam-5347	137	16	g	g	NOUN
ejpam-5347	137	17	,	,	PUNCT
ejpam-5347	137	18	υ1	υ1	NOUN
ejpam-5347	137	19	,	,	PUNCT
ejpam-5347	137	20	υ2	υ2	PROPN
ejpam-5347	137	21	)	)	PUNCT
ejpam-5347	137	22	.	.	PUNCT
ejpam-5347	138	1	thus	thus	ADV
ejpam-5347	138	2	,	,	PUNCT
ejpam-5347	138	3	there	there	PRON
ejpam-5347	138	4	is	be	VERB
ejpam-5347	138	5	an	an	DET
ejpam-5347	138	6	open	open	ADJ
ejpam-5347	138	7	pair−nbd	pair−nbd	PROPN
ejpam-5347	138	8	h	h	NOUN
ejpam-5347	138	9	\	\	PROPN
ejpam-5347	138	10	g	g	PROPN
ejpam-5347	138	11	.in	.in	PUNCT
ejpam-5347	138	12	a	a	DET
ejpam-5347	138	13	manner	manner	NOUN
ejpam-5347	138	14	that	that	PRON
ejpam-5347	138	15	h	h	NOUN
ejpam-5347	138	16	\	\	NOUN
ejpam-5347	138	17	g	g	PROPN
ejpam-5347	138	18	∩	∩	X
ejpam-5347	138	19	(	(	PUNCT
ejpam-5347	138	20	(	(	PUNCT
ejpam-5347	138	21	d	d	NOUN
ejpam-5347	138	22	,	,	PUNCT
ejpam-5347	138	23	κ1	κ1	NOUN
ejpam-5347	138	24	,	,	PUNCT
ejpam-5347	138	25	κ2)−h	κ2)−h	PROPN
ejpam-5347	138	26	\	\	PROPN
ejpam-5347	138	27	g	g	NOUN
ejpam-5347	138	28	)	)	PUNCT
ejpam-5347	138	29	is	be	AUX
ejpam-5347	138	30	countable	countable	ADJ
ejpam-5347	138	31	.	.	PUNCT
ejpam-5347	139	1	now	now	ADV
ejpam-5347	139	2	h	h	VERB
ejpam-5347	139	3	\	\	NOUN
ejpam-5347	139	4	g	g	PROPN
ejpam-5347	139	5	=	=	PUNCT
ejpam-5347	139	6	(	(	PUNCT
ejpam-5347	139	7	h	h	NOUN
ejpam-5347	139	8	˜	˜	PROPN
ejpam-5347	139	9	g	g	PROPN
ejpam-5347	139	10	∩hg)∪	∩hg)∪	NOUN
ejpam-5347	139	11	h	h	NOUN
ejpam-5347	139	12	\	\	NOUN
ejpam-5347	140	1	g	g	PROPN
ejpam-5347	140	2	∩	∩	X
ejpam-5347	140	3	(	(	PUNCT
ejpam-5347	140	4	(	(	PUNCT
ejpam-5347	140	5	d	d	NOUN
ejpam-5347	140	6	,	,	PUNCT
ejpam-5347	140	7	κ1	κ1	NOUN
ejpam-5347	140	8	,	,	PUNCT
ejpam-5347	140	9	κ2)−hg	κ2)−hg	NOUN
ejpam-5347	140	10	)	)	PUNCT
ejpam-5347	140	11	.consequently	.consequently	ADV
ejpam-5347	140	12	,	,	PUNCT
ejpam-5347	140	13	υ−1	υ−1	PROPN
ejpam-5347	140	14	(	(	PUNCT
ejpam-5347	140	15	h	h	NOUN
ejpam-5347	140	16	\	\	PROPN
ejpam-5347	140	17	g	g	PROPN
ejpam-5347	140	18	)	)	PUNCT
ejpam-5347	140	19	is	be	AUX
ejpam-5347	140	20	enclosed	enclose	VERB
ejpam-5347	140	21	in	in	ADP
ejpam-5347	140	22	a	a	DET
ejpam-5347	140	23	union	union	NOUN
ejpam-5347	140	24	of	of	ADP
ejpam-5347	140	25	countably	countably	ADV
ejpam-5347	140	26	large	large	ADJ
ejpam-5347	140	27	number	number	NOUN
ejpam-5347	140	28	of	of	ADP
ejpam-5347	140	29	members	member	NOUN
ejpam-5347	140	30	of	of	ADP
ejpam-5347	140	31	t	t	NOUN
ejpam-5347	140	32	˜	˜	PROPN
ejpam-5347	140	33	.	.	PUNCT
ejpam-5347	141	1	because	because	SCONJ
ejpam-5347	141	2	of	of	ADP
ejpam-5347	141	3	this	this	PRON
ejpam-5347	141	4	{	{	PUNCT
ejpam-5347	141	5	h	h	NOUN
ejpam-5347	141	6	\	\	PROPN
ejpam-5347	141	7	g	g	PROPN
ejpam-5347	141	8	,	,	PUNCT
ejpam-5347	141	9	g	g	PROPN
ejpam-5347	141	10	∈	∈	PROPN
ejpam-5347	141	11	(	(	PUNCT
ejpam-5347	141	12	g	g	NOUN
ejpam-5347	141	13	,	,	PUNCT
ejpam-5347	141	14	υ1	υ1	NOUN
ejpam-5347	141	15	,	,	PUNCT
ejpam-5347	141	16	υ2	υ2	PROPN
ejpam-5347	141	17	)	)	PUNCT
ejpam-5347	141	18	}	}	PUNCT
ejpam-5347	141	19	is	be	AUX
ejpam-5347	141	20	a	a	DET
ejpam-5347	141	21	pair−open	pair−open	ADJ
ejpam-5347	141	22	cover	cover	NOUN
ejpam-5347	141	23	of	of	ADP
ejpam-5347	141	24	(	(	PUNCT
ejpam-5347	141	25	g	g	PROPN
ejpam-5347	141	26	,	,	PUNCT
ejpam-5347	141	27	υ1	υ1	NOUN
ejpam-5347	141	28	,	,	PUNCT
ejpam-5347	141	29	υ2	υ2	PROPN
ejpam-5347	141	30	)	)	PUNCT
ejpam-5347	141	31	and	and	CCONJ
ejpam-5347	141	32	it	it	PRON
ejpam-5347	141	33	is	be	AUX
ejpam-5347	141	34	pair−lindel	pair−lindel	NOUN
ejpam-5347	141	35	..	..	PUNCT
ejpam-5347	141	36	of	of	ADP
ejpam-5347	141	37	,	,	PUNCT
ejpam-5347	141	38	{	{	PUNCT
ejpam-5347	141	39	h	h	NOUN
ejpam-5347	141	40	\	\	PROPN
ejpam-5347	141	41	g	g	PROPN
ejpam-5347	141	42	,	,	PUNCT
ejpam-5347	141	43	g	g	PROPN
ejpam-5347	141	44	∈	∈	PROPN
ejpam-5347	141	45	(	(	PUNCT
ejpam-5347	141	46	g	g	NOUN
ejpam-5347	141	47	,	,	PUNCT
ejpam-5347	141	48	υ1	υ1	NOUN
ejpam-5347	141	49	,	,	PUNCT
ejpam-5347	141	50	υ2	υ2	PROPN
ejpam-5347	141	51	)	)	PUNCT
ejpam-5347	141	52	}	}	PUNCT
ejpam-5347	141	53	has	have	VERB
ejpam-5347	141	54	a	a	DET
ejpam-5347	141	55	countable	countable	ADJ
ejpam-5347	141	56	subcover	subcover	NOUN
ejpam-5347	141	57	.	.	PUNCT
ejpam-5347	142	1	therefore	therefore	ADV
ejpam-5347	142	2	(	(	PUNCT
ejpam-5347	142	3	d	d	NOUN
ejpam-5347	142	4	,	,	PUNCT
ejpam-5347	142	5	κ1	κ1	NOUN
ejpam-5347	142	6	,	,	PUNCT
ejpam-5347	142	7	κ2	κ2	PROPN
ejpam-5347	142	8	)	)	PUNCT
ejpam-5347	142	9	is	be	AUX
ejpam-5347	142	10	the	the	DET
ejpam-5347	142	11	union	union	NOUN
ejpam-5347	142	12	of	of	ADP
ejpam-5347	142	13	countably	countably	ADV
ejpam-5347	142	14	large	large	ADJ
ejpam-5347	142	15	number	number	NOUN
ejpam-5347	142	16	of	of	ADP
ejpam-5347	142	17	members	member	NOUN
ejpam-5347	142	18	of	of	ADP
ejpam-5347	142	19	{	{	PUNCT
ejpam-5347	142	20	υ−1	υ−1	PROPN
ejpam-5347	142	21	(	(	PUNCT
ejpam-5347	142	22	h	h	NOUN
ejpam-5347	142	23	\	\	PROPN
ejpam-5347	142	24	g	g	PROPN
ejpam-5347	142	25	)	)	PUNCT
ejpam-5347	142	26	,	,	PUNCT
ejpam-5347	142	27	g	g	PROPN
ejpam-5347	142	28	∈	∈	PROPN
ejpam-5347	142	29	(	(	PUNCT
ejpam-5347	142	30	g	g	NOUN
ejpam-5347	142	31	,	,	PUNCT
ejpam-5347	142	32	υ1	υ1	NOUN
ejpam-5347	142	33	,	,	PUNCT
ejpam-5347	142	34	υ2	υ2	NOUN
ejpam-5347	142	35	)	)	PUNCT
ejpam-5347	142	36	}	}	PUNCT
ejpam-5347	142	37	,	,	PUNCT
ejpam-5347	142	38	since	since	SCONJ
ejpam-5347	142	39	each	each	DET
ejpam-5347	142	40	υ−1	υ−1	PROPN
ejpam-5347	142	41	(	(	PUNCT
ejpam-5347	142	42	h	h	NOUN
ejpam-5347	142	43	\	\	PROPN
ejpam-5347	142	44	g	g	PROPN
ejpam-5347	142	45	)	)	PUNCT
ejpam-5347	142	46	is	be	AUX
ejpam-5347	142	47	contained	contain	VERB
ejpam-5347	142	48	in	in	ADP
ejpam-5347	142	49	the	the	DET
ejpam-5347	142	50	union	union	NOUN
ejpam-5347	142	51	of	of	ADP
ejpam-5347	142	52	countably	countably	ADV
ejpam-5347	142	53	large	large	ADJ
ejpam-5347	142	54	number	number	NOUN
ejpam-5347	142	55	of	of	ADP
ejpam-5347	142	56	members	member	NOUN
ejpam-5347	142	57	of	of	ADP
ejpam-5347	142	58	t	t	NOUN
ejpam-5347	142	59	˜	˜	PROPN
ejpam-5347	142	60	.consequently	.consequently	ADV
ejpam-5347	142	61	,	,	PUNCT
ejpam-5347	142	62	(	(	PUNCT
ejpam-5347	142	63	d	d	X
ejpam-5347	142	64	,	,	PUNCT
ejpam-5347	142	65	κ1	κ1	NOUN
ejpam-5347	142	66	,	,	PUNCT
ejpam-5347	142	67	κ2	κ2	PROPN
ejpam-5347	142	68	)	)	PUNCT
ejpam-5347	142	69	is	be	AUX
ejpam-5347	142	70	the	the	DET
ejpam-5347	142	71	union	union	NOUN
ejpam-5347	142	72	of	of	ADP
ejpam-5347	142	73	countably	countably	ADV
ejpam-5347	142	74	large	large	ADJ
ejpam-5347	142	75	number	number	NOUN
ejpam-5347	142	76	of	of	ADP
ejpam-5347	142	77	members	member	NOUN
ejpam-5347	142	78	of	of	ADP
ejpam-5347	142	79	t	t	NOUN
ejpam-5347	142	80	˜	˜	PROPN
ejpam-5347	142	81	.hence	.hence	ADP
ejpam-5347	142	82	,	,	PUNCT
ejpam-5347	142	83	(	(	PUNCT
ejpam-5347	142	84	d	d	NOUN
ejpam-5347	142	85	,	,	PUNCT
ejpam-5347	142	86	κ1	κ1	NOUN
ejpam-5347	142	87	,	,	PUNCT
ejpam-5347	142	88	κ2	κ2	PROPN
ejpam-5347	142	89	)	)	PUNCT
ejpam-5347	142	90	is	be	AUX
ejpam-5347	142	91	pair−lindel	pair−lindel	NOUN
ejpam-5347	142	92	..	..	PUNCT
ejpam-5347	142	93	of	of	ADP
ejpam-5347	142	94	.	.	PUNCT
ejpam-5347	143	1	corollary	corollary	ADJ
ejpam-5347	143	2	3	3	NUM
ejpam-5347	143	3	.	.	PUNCT
ejpam-5347	144	1	(	(	PUNCT
ejpam-5347	144	2	i	i	NOUN
ejpam-5347	144	3	)	)	PUNCT
ejpam-5347	144	4	a	a	DET
ejpam-5347	144	5	pair−	pair−	NOUN
ejpam-5347	144	6	ω−subset	ω−subset	PUNCT
ejpam-5347	144	7	of	of	ADP
ejpam-5347	144	8	a	a	DET
ejpam-5347	144	9	pair−	pair−	NOUN
ejpam-5347	144	10	lindel	lindel	NOUN
ejpam-5347	144	11	..	..	PUNCT
ejpam-5347	144	12	of	of	ADP
ejpam-5347	144	13	space	space	NOUN
ejpam-5347	144	14	is	be	AUX
ejpam-5347	144	15	pair−lindel	pair−lindel	NOUN
ejpam-5347	144	16	..	..	PUNCT
ejpam-5347	144	17	of	of	ADP
ejpam-5347	144	18	(	(	PUNCT
ejpam-5347	144	19	ii	ii	NOUN
ejpam-5347	144	20	)	)	PUNCT
ejpam-5347	144	21	if	if	SCONJ
ejpam-5347	144	22	υ	υ	X
ejpam-5347	144	23	:	:	PUNCT
ejpam-5347	144	24	(	(	PUNCT
ejpam-5347	144	25	d	d	NOUN
ejpam-5347	144	26	,	,	PUNCT
ejpam-5347	144	27	κ1	κ1	NOUN
ejpam-5347	144	28	,	,	PUNCT
ejpam-5347	144	29	κ2	κ2	PROPN
ejpam-5347	144	30	)	)	PUNCT
ejpam-5347	144	31	→	→	SYM
ejpam-5347	144	32	(	(	PUNCT
ejpam-5347	144	33	g	g	NOUN
ejpam-5347	144	34	,	,	PUNCT
ejpam-5347	144	35	υ1	υ1	NOUN
ejpam-5347	144	36	,	,	PUNCT
ejpam-5347	144	37	υ2	υ2	PROPN
ejpam-5347	144	38	)	)	PUNCT
ejpam-5347	144	39	is	be	AUX
ejpam-5347	144	40	pair−continuous	pair−continuous	ADJ
ejpam-5347	144	41	function	function	NOUN
ejpam-5347	144	42	from	from	ADP
ejpam-5347	144	43	(	(	PUNCT
ejpam-5347	144	44	d	d	NOUN
ejpam-5347	144	45	,	,	PUNCT
ejpam-5347	144	46	κ1	κ1	NOUN
ejpam-5347	144	47	,	,	PUNCT
ejpam-5347	144	48	κ2	κ2	PROPN
ejpam-5347	144	49	)	)	PUNCT
ejpam-5347	144	50	to	to	ADP
ejpam-5347	144	51	(	(	PUNCT
ejpam-5347	144	52	g	g	PROPN
ejpam-5347	144	53	,	,	PUNCT
ejpam-5347	144	54	υ1	υ1	NOUN
ejpam-5347	144	55	,	,	PUNCT
ejpam-5347	144	56	υ2	υ2	NOUN
ejpam-5347	144	57	)	)	PUNCT
ejpam-5347	144	58	,	,	PUNCT
ejpam-5347	144	59	so	so	CCONJ
ejpam-5347	144	60	the	the	DET
ejpam-5347	144	61	subsequent	subsequent	ADJ
ejpam-5347	144	62	ones	one	NOUN
ejpam-5347	144	63	are	be	AUX
ejpam-5347	144	64	comparable	comparable	ADJ
ejpam-5347	144	65	:	:	PUNCT
ejpam-5347	144	66	(	(	PUNCT
ejpam-5347	144	67	a	a	X
ejpam-5347	144	68	)	)	PUNCT
ejpam-5347	144	69	υ	υ	NOUN
ejpam-5347	144	70	is	be	AUX
ejpam-5347	144	71	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	144	72	;	;	PUNCT
ejpam-5347	144	73	(	(	PUNCT
ejpam-5347	144	74	b	b	X
ejpam-5347	144	75	)	)	PUNCT
ejpam-5347	144	76	for	for	ADP
ejpam-5347	144	77	each	each	DET
ejpam-5347	144	78	g	g	PROPN
ejpam-5347	144	79	∈	∈	PROPN
ejpam-5347	144	80	(	(	PUNCT
ejpam-5347	144	81	g	g	NOUN
ejpam-5347	144	82	,	,	PUNCT
ejpam-5347	144	83	υ1	υ1	NOUN
ejpam-5347	144	84	,	,	PUNCT
ejpam-5347	144	85	υ2	υ2	PROPN
ejpam-5347	144	86	)	)	PUNCT
ejpam-5347	144	87	and	and	CCONJ
ejpam-5347	144	88	any	any	DET
ejpam-5347	144	89	pair−open	pair−open	NOUN
ejpam-5347	144	90	set	set	VERB
ejpam-5347	144	91	t	t	PROPN
ejpam-5347	144	92	,	,	PUNCT
ejpam-5347	144	93	that	that	PRON
ejpam-5347	144	94	is	be	AUX
ejpam-5347	144	95	to	to	PART
ejpam-5347	144	96	say	say	VERB
ejpam-5347	144	97	υ−1(g	υ−1(g	PROPN
ejpam-5347	144	98	)	)	PUNCT
ejpam-5347	145	1	⊂	⊂	PROPN
ejpam-5347	145	2	t	t	PROPN
ejpam-5347	145	3	,	,	PUNCT
ejpam-5347	145	4	it	it	PRON
ejpam-5347	145	5	actually	actually	ADV
ejpam-5347	145	6	exists	exist	VERB
ejpam-5347	145	7	a	a	DET
ejpam-5347	145	8	pair−ω−open	pair−ω−open	NOUN
ejpam-5347	145	9	set	set	NOUN
ejpam-5347	145	10	qg	qg	PROPN
ejpam-5347	146	1	such	such	ADJ
ejpam-5347	146	2	that	that	SCONJ
ejpam-5347	146	3	g	g	PROPN
ejpam-5347	146	4	∈	∈	PROPN
ejpam-5347	146	5	qg	qg	PROPN
ejpam-5347	146	6	and	and	CCONJ
ejpam-5347	146	7	υ−1(qg	υ−1(qg	PROPN
ejpam-5347	146	8	)	)	PUNCT
ejpam-5347	146	9	⊂	⊂	PROPN
ejpam-5347	146	10	u.	u.	PROPN
ejpam-5347	146	11	corollary	corollary	PROPN
ejpam-5347	146	12	4	4	NUM
ejpam-5347	146	13	.	.	PUNCT
ejpam-5347	147	1	(	(	PUNCT
ejpam-5347	147	2	i	i	NOUN
ejpam-5347	147	3	)	)	PUNCT
ejpam-5347	147	4	a	a	DET
ejpam-5347	147	5	s−	s−	PROPN
ejpam-5347	147	6	ω−subset	ω−subset	PUNCT
ejpam-5347	147	7	of	of	ADP
ejpam-5347	147	8	a	a	DET
ejpam-5347	147	9	s−	s−	PROPN
ejpam-5347	147	10	lindel	lindel	NOUN
ejpam-5347	147	11	..	..	PUNCT
ejpam-5347	147	12	of	of	ADP
ejpam-5347	147	13	space	space	NOUN
ejpam-5347	147	14	is	be	AUX
ejpam-5347	147	15	s−lindel	s−lindel	PROPN
ejpam-5347	147	16	..	..	PUNCT
ejpam-5347	147	17	of	of	ADP
ejpam-5347	147	18	(	(	PUNCT
ejpam-5347	147	19	ii	ii	NOUN
ejpam-5347	147	20	)	)	PUNCT
ejpam-5347	147	21	if	if	SCONJ
ejpam-5347	147	22	υ	υ	X
ejpam-5347	147	23	:	:	PUNCT
ejpam-5347	147	24	(	(	PUNCT
ejpam-5347	147	25	d	d	NOUN
ejpam-5347	147	26	,	,	PUNCT
ejpam-5347	147	27	κ1	κ1	NOUN
ejpam-5347	147	28	,	,	PUNCT
ejpam-5347	147	29	κ2	κ2	PROPN
ejpam-5347	147	30	)	)	PUNCT
ejpam-5347	147	31	→	→	SYM
ejpam-5347	147	32	(	(	PUNCT
ejpam-5347	147	33	g	g	NOUN
ejpam-5347	147	34	,	,	PUNCT
ejpam-5347	147	35	υ1	υ1	NOUN
ejpam-5347	147	36	,	,	PUNCT
ejpam-5347	147	37	υ2	υ2	PROPN
ejpam-5347	147	38	)	)	PUNCT
ejpam-5347	147	39	is	be	AUX
ejpam-5347	147	40	s−continuous	s−continuous	ADJ
ejpam-5347	147	41	function	function	NOUN
ejpam-5347	147	42	from	from	ADP
ejpam-5347	147	43	(	(	PUNCT
ejpam-5347	147	44	d	d	NOUN
ejpam-5347	147	45	,	,	PUNCT
ejpam-5347	147	46	κ1	κ1	NOUN
ejpam-5347	147	47	,	,	PUNCT
ejpam-5347	147	48	κ2	κ2	PROPN
ejpam-5347	147	49	)	)	PUNCT
ejpam-5347	147	50	to	to	ADP
ejpam-5347	147	51	(	(	PUNCT
ejpam-5347	147	52	g	g	PROPN
ejpam-5347	147	53	,	,	PUNCT
ejpam-5347	147	54	υ1	υ1	NOUN
ejpam-5347	147	55	,	,	PUNCT
ejpam-5347	147	56	υ2	υ2	NOUN
ejpam-5347	147	57	)	)	PUNCT
ejpam-5347	147	58	,	,	PUNCT
ejpam-5347	147	59	so	so	CCONJ
ejpam-5347	147	60	the	the	DET
ejpam-5347	147	61	subsequent	subsequent	ADJ
ejpam-5347	147	62	ones	one	NOUN
ejpam-5347	147	63	are	be	AUX
ejpam-5347	147	64	comparable	comparable	ADJ
ejpam-5347	147	65	:(	:(	PUNCT
ejpam-5347	147	66	a	a	X
ejpam-5347	147	67	)	)	PUNCT
ejpam-5347	147	68	υ	υ	NOUN
ejpam-5347	147	69	is	be	AUX
ejpam-5347	147	70	s−ω−closed	s−ω−close	VERB
ejpam-5347	147	71	;	;	PUNCT
ejpam-5347	147	72	(	(	PUNCT
ejpam-5347	147	73	b	b	X
ejpam-5347	147	74	)	)	PUNCT
ejpam-5347	147	75	for	for	ADP
ejpam-5347	147	76	each	each	DET
ejpam-5347	147	77	g	g	PROPN
ejpam-5347	147	78	∈	∈	PROPN
ejpam-5347	147	79	(	(	PUNCT
ejpam-5347	147	80	g	g	NOUN
ejpam-5347	147	81	,	,	PUNCT
ejpam-5347	147	82	υ1	υ1	NOUN
ejpam-5347	147	83	,	,	PUNCT
ejpam-5347	147	84	υ2	υ2	PROPN
ejpam-5347	147	85	)	)	PUNCT
ejpam-5347	147	86	and	and	CCONJ
ejpam-5347	147	87	any	any	DET
ejpam-5347	147	88	s−open	s−open	NOUN
ejpam-5347	147	89	set	set	VERB
ejpam-5347	147	90	t	t	PROPN
ejpam-5347	147	91	,	,	PUNCT
ejpam-5347	147	92	that	that	PRON
ejpam-5347	147	93	is	be	AUX
ejpam-5347	147	94	to	to	PART
ejpam-5347	147	95	say	say	VERB
ejpam-5347	147	96	υ−1(g	υ−1(g	PROPN
ejpam-5347	147	97	)	)	PUNCT
ejpam-5347	148	1	⊂	⊂	PROPN
ejpam-5347	148	2	t	t	PROPN
ejpam-5347	148	3	,	,	PUNCT
ejpam-5347	148	4	it	it	PRON
ejpam-5347	148	5	actually	actually	ADV
ejpam-5347	148	6	exists	exist	VERB
ejpam-5347	148	7	a	a	DET
ejpam-5347	148	8	s−ω−open	s−ω−open	NOUN
ejpam-5347	148	9	set	set	VERB
ejpam-5347	148	10	qg	qg	PROPN
ejpam-5347	148	11	such	such	ADJ
ejpam-5347	148	12	that	that	SCONJ
ejpam-5347	148	13	g	g	PROPN
ejpam-5347	148	14	∈	∈	PROPN
ejpam-5347	148	15	qg	qg	PROPN
ejpam-5347	148	16	and	and	CCONJ
ejpam-5347	148	17	υ−1(qg	υ−1(qg	PROPN
ejpam-5347	148	18	)	)	PUNCT
ejpam-5347	148	19	⊂	⊂	PROPN
ejpam-5347	148	20	u.	u.	PROPN
ejpam-5347	148	21	theorem	theorem	ADJ
ejpam-5347	148	22	4	4	NUM
ejpam-5347	148	23	.	.	PUNCT
ejpam-5347	148	24	assume	assume	VERB
ejpam-5347	148	25	υ	υ	PRON
ejpam-5347	148	26	be	be	AUX
ejpam-5347	148	27	pair−continuous	pair−continuous	ADJ
ejpam-5347	148	28	s	s	NOUN
ejpam-5347	148	29	-	-	PUNCT
ejpam-5347	148	30	ω−closed	ω−close	VERB
ejpam-5347	148	31	functioning	functioning	NOUN
ejpam-5347	148	32	of	of	ADP
ejpam-5347	148	33	a	a	DET
ejpam-5347	148	34	space	space	NOUN
ejpam-5347	148	35	(	(	PUNCT
ejpam-5347	148	36	d	d	NOUN
ejpam-5347	148	37	,	,	PUNCT
ejpam-5347	148	38	κ1	κ1	NOUN
ejpam-5347	148	39	,	,	PUNCT
ejpam-5347	148	40	κ2	κ2	PROPN
ejpam-5347	148	41	)	)	PUNCT
ejpam-5347	148	42	onto	onto	ADP
ejpam-5347	148	43	(	(	PUNCT
ejpam-5347	148	44	g	g	PROPN
ejpam-5347	148	45	,	,	PUNCT
ejpam-5347	148	46	υ1	υ1	PROPN
ejpam-5347	148	47	,	,	PUNCT
ejpam-5347	148	48	υ2),so	υ2),so	PROPN
ejpam-5347	148	49	that	that	SCONJ
ejpam-5347	148	50	υ−1(g	υ−1(g	PROPN
ejpam-5347	148	51	)	)	PUNCT
ejpam-5347	148	52	is	be	AUX
ejpam-5347	148	53	s	s	NOUN
ejpam-5347	148	54	-	-	NOUN
ejpam-5347	148	55	lindel	lindel	NOUN
ejpam-5347	148	56	..	..	PUNCT
ejpam-5347	148	57	of	of	ADP
ejpam-5347	148	58	,	,	PUNCT
ejpam-5347	148	59	for	for	ADP
ejpam-5347	148	60	every	every	DET
ejpam-5347	148	61	g	g	PROPN
ejpam-5347	148	62	∈	∈	PROPN
ejpam-5347	148	63	(	(	PUNCT
ejpam-5347	148	64	g	g	NOUN
ejpam-5347	148	65	,	,	PUNCT
ejpam-5347	148	66	υ1	υ1	NOUN
ejpam-5347	148	67	,	,	PUNCT
ejpam-5347	148	68	υ2	υ2	NOUN
ejpam-5347	148	69	)	)	PUNCT
ejpam-5347	148	70	,	,	PUNCT
ejpam-5347	148	71	subsequently	subsequently	ADV
ejpam-5347	148	72	(	(	PUNCT
ejpam-5347	148	73	d	d	NOUN
ejpam-5347	148	74	,	,	PUNCT
ejpam-5347	148	75	κ1	κ1	NOUN
ejpam-5347	148	76	,	,	PUNCT
ejpam-5347	148	77	κ2	κ2	PROPN
ejpam-5347	148	78	)	)	PUNCT
ejpam-5347	148	79	is	be	AUX
ejpam-5347	148	80	s	s	NOUN
ejpam-5347	148	81	-	-	NOUN
ejpam-5347	148	82	lindel	lindel	NOUN
ejpam-5347	148	83	..	..	PUNCT
ejpam-5347	148	84	of	of	ADP
ejpam-5347	148	85	,	,	PUNCT
ejpam-5347	148	86	whether	whether	SCONJ
ejpam-5347	148	87	(	(	PUNCT
ejpam-5347	148	88	g	g	NOUN
ejpam-5347	148	89	,	,	PUNCT
ejpam-5347	148	90	υ1	υ1	NOUN
ejpam-5347	148	91	,	,	PUNCT
ejpam-5347	148	92	υ2	υ2	PROPN
ejpam-5347	148	93	)	)	PUNCT
ejpam-5347	148	94	is	be	AUX
ejpam-5347	148	95	indeed	indeed	ADV
ejpam-5347	148	96	.	.	PUNCT
ejpam-5347	149	1	proof	proof	NOUN
ejpam-5347	149	2	.	.	PUNCT
ejpam-5347	150	1	using	use	VERB
ejpam-5347	150	2	the	the	DET
ejpam-5347	150	3	identical	identical	ADJ
ejpam-5347	150	4	method	method	NOUN
ejpam-5347	150	5	as	as	SCONJ
ejpam-5347	150	6	the	the	DET
ejpam-5347	150	7	theorem	theorem	NOUN
ejpam-5347	150	8	previously	previously	ADV
ejpam-5347	150	9	mentioned	mention	VERB
ejpam-5347	150	10	,	,	PUNCT
ejpam-5347	150	11	the	the	DET
ejpam-5347	150	12	proof	proof	NOUN
ejpam-5347	150	13	is	be	AUX
ejpam-5347	150	14	produced	produce	VERB
ejpam-5347	150	15	.	.	PUNCT
ejpam-5347	151	1	theorem	theorem	NOUN
ejpam-5347	151	2	5	5	NUM
ejpam-5347	151	3	.	.	PUNCT
ejpam-5347	151	4	suppose	suppose	VERB
ejpam-5347	151	5	that	that	SCONJ
ejpam-5347	151	6	υ	υ	PROPN
ejpam-5347	151	7	is	be	AUX
ejpam-5347	151	8	a	a	DET
ejpam-5347	151	9	ω−closed	ω−close	VERB
ejpam-5347	151	10	pair−continuous	pair−continuous	ADJ
ejpam-5347	151	11	function	function	NOUN
ejpam-5347	151	12	of	of	ADP
ejpam-5347	151	13	a	a	DET
ejpam-5347	151	14	a.	a.	NOUN
ejpam-5347	151	15	atoom	atoom	NOUN
ejpam-5347	151	16	et	et	PROPN
ejpam-5347	151	17	al	al	PROPN
ejpam-5347	151	18	.	.	PUNCT
ejpam-5347	151	19	/	/	SYM
ejpam-5347	151	20	eur	eur	PROPN
ejpam-5347	151	21	.	.	PUNCT
ejpam-5347	152	1	j.	j.	PROPN
ejpam-5347	152	2	pure	pure	PROPN
ejpam-5347	152	3	appl	appl	PROPN
ejpam-5347	152	4	.	.	PROPN
ejpam-5347	152	5	math	math	PROPN
ejpam-5347	152	6	,	,	PUNCT
ejpam-5347	152	7	17	17	NUM
ejpam-5347	152	8	(	(	PUNCT
ejpam-5347	152	9	4	4	NUM
ejpam-5347	152	10	)	)	PUNCT
ejpam-5347	152	11	(	(	PUNCT
ejpam-5347	152	12	2024	2024	NUM
ejpam-5347	152	13	)	)	PUNCT
ejpam-5347	152	14	,	,	PUNCT
ejpam-5347	152	15	2574	2574	NUM
ejpam-5347	152	16	-	-	SYM
ejpam-5347	152	17	2585	2585	NUM
ejpam-5347	152	18	2580	2580	NUM
ejpam-5347	152	19	regular	regular	ADJ
ejpam-5347	152	20	space	space	NOUN
ejpam-5347	152	21	(	(	PUNCT
ejpam-5347	152	22	d	d	NOUN
ejpam-5347	152	23	,	,	PUNCT
ejpam-5347	152	24	κ1	κ1	NOUN
ejpam-5347	152	25	,	,	PUNCT
ejpam-5347	152	26	κ2	κ2	PROPN
ejpam-5347	152	27	)	)	PUNCT
ejpam-5347	152	28	onto	onto	ADP
ejpam-5347	152	29	(	(	PUNCT
ejpam-5347	152	30	g	g	PROPN
ejpam-5347	152	31	,	,	PUNCT
ejpam-5347	152	32	υ1	υ1	PROPN
ejpam-5347	152	33	,	,	PUNCT
ejpam-5347	152	34	υ2).when	υ2).when	ADJ
ejpam-5347	152	35	(	(	PUNCT
ejpam-5347	152	36	g	g	NOUN
ejpam-5347	152	37	,	,	PUNCT
ejpam-5347	152	38	υ1	υ1	NOUN
ejpam-5347	152	39	,	,	PUNCT
ejpam-5347	152	40	υ2	υ2	PROPN
ejpam-5347	152	41	)	)	PUNCT
ejpam-5347	152	42	is	be	AUX
ejpam-5347	152	43	pair−paracompact	pair−paracompact	ADJ
ejpam-5347	152	44	and	and	CCONJ
ejpam-5347	152	45	υ−1(g	υ−1(g	PROPN
ejpam-5347	152	46	)	)	PUNCT
ejpam-5347	152	47	is	be	AUX
ejpam-5347	152	48	pair−paracompact	pair−paracompact	NOUN
ejpam-5347	152	49	relative	relative	ADJ
ejpam-5347	152	50	to	to	ADP
ejpam-5347	152	51	(	(	PUNCT
ejpam-5347	152	52	d	d	NOUN
ejpam-5347	152	53	,	,	PUNCT
ejpam-5347	152	54	κ1	κ1	NOUN
ejpam-5347	152	55	,	,	PUNCT
ejpam-5347	152	56	κ2	κ2	PROPN
ejpam-5347	152	57	)	)	PUNCT
ejpam-5347	152	58	.	.	PUNCT
ejpam-5347	153	1	for	for	ADP
ejpam-5347	153	2	every	every	DET
ejpam-5347	153	3	g	g	NOUN
ejpam-5347	153	4	in	in	ADP
ejpam-5347	153	5	(	(	PUNCT
ejpam-5347	153	6	g	g	NOUN
ejpam-5347	153	7	,	,	PUNCT
ejpam-5347	153	8	υ1	υ1	NOUN
ejpam-5347	153	9	,	,	PUNCT
ejpam-5347	153	10	υ2	υ2	PROPN
ejpam-5347	153	11	)	)	PUNCT
ejpam-5347	153	12	,	,	PUNCT
ejpam-5347	153	13	then	then	ADV
ejpam-5347	153	14	(	(	PUNCT
ejpam-5347	153	15	d	d	NOUN
ejpam-5347	153	16	,	,	PUNCT
ejpam-5347	153	17	κ1	κ1	NOUN
ejpam-5347	153	18	,	,	PUNCT
ejpam-5347	153	19	κ2	κ2	PROPN
ejpam-5347	153	20	)	)	PUNCT
ejpam-5347	153	21	is	be	AUX
ejpam-5347	153	22	pair−paracompact	pair−paracompact	NOUN
ejpam-5347	153	23	.	.	PUNCT
ejpam-5347	154	1	proof	proof	NOUN
ejpam-5347	154	2	.	.	PUNCT
ejpam-5347	155	1	present	present	ADJ
ejpam-5347	155	2	alongside	alongside	ADP
ejpam-5347	155	3	t	t	NOUN
ejpam-5347	155	4	˜	˜	PROPN
ejpam-5347	155	5	=	=	PRON
ejpam-5347	156	1	{	{	PUNCT
ejpam-5347	156	2	tδ	tδ	NOUN
ejpam-5347	156	3	:	:	PUNCT
ejpam-5347	156	4	δ	δ	PROPN
ejpam-5347	156	5	∈	∈	PROPN
ejpam-5347	156	6	ξ	ξ	PROPN
ejpam-5347	156	7	}	}	PUNCT
ejpam-5347	156	8	is	be	AUX
ejpam-5347	156	9	a	a	DET
ejpam-5347	156	10	pair−open	pair−open	ADJ
ejpam-5347	156	11	cover	cover	NOUN
ejpam-5347	156	12	of	of	ADP
ejpam-5347	156	13	(	(	PUNCT
ejpam-5347	156	14	d	d	PROPN
ejpam-5347	156	15	,	,	PUNCT
ejpam-5347	156	16	κ1	κ1	NOUN
ejpam-5347	156	17	,	,	PUNCT
ejpam-5347	156	18	κ2	κ2	PROPN
ejpam-5347	156	19	)	)	PUNCT
ejpam-5347	156	20	.	.	PUNCT
ejpam-5347	157	1	meanwhile	meanwhile	ADV
ejpam-5347	157	2	,	,	PUNCT
ejpam-5347	157	3	early	early	ADJ
ejpam-5347	157	4	∀g	∀g	X
ejpam-5347	157	5	∈	∈	NOUN
ejpam-5347	157	6	(	(	PUNCT
ejpam-5347	157	7	g	g	NOUN
ejpam-5347	157	8	,	,	PUNCT
ejpam-5347	157	9	υ1	υ1	NOUN
ejpam-5347	157	10	,	,	PUNCT
ejpam-5347	157	11	υ2	υ2	PROPN
ejpam-5347	157	12	)	)	PUNCT
ejpam-5347	157	13	,	,	PUNCT
ejpam-5347	157	14	υ−1(g	υ−1(g	PROPN
ejpam-5347	157	15	)	)	PUNCT
ejpam-5347	157	16	is	be	AUX
ejpam-5347	157	17	pair−paracompact	pair−paracompact	NOUN
ejpam-5347	157	18	,	,	PUNCT
ejpam-5347	157	19	t	t	PROPN
ejpam-5347	157	20	˜	˜	PROPN
ejpam-5347	157	21	has	have	VERB
ejpam-5347	157	22	a	a	DET
ejpam-5347	157	23	pair−open	pair−open	ADJ
ejpam-5347	157	24	locally	locally	ADV
ejpam-5347	157	25	finite	finite	ADJ
ejpam-5347	157	26	refinement	refinement	NOUN
ejpam-5347	157	27	in(d	in(d	NOUN
ejpam-5347	157	28	,	,	PUNCT
ejpam-5347	157	29	κ1	κ1	NOUN
ejpam-5347	157	30	,	,	PUNCT
ejpam-5347	157	31	κ2	κ2	PROPN
ejpam-5347	157	32	)	)	PUNCT
ejpam-5347	157	33	which	which	PRON
ejpam-5347	157	34	at	at	ADP
ejpam-5347	157	35	first	first	ADJ
ejpam-5347	157	36	cover	cover	NOUN
ejpam-5347	157	37	υ−1(g),it	υ−1(g),it	ADJ
ejpam-5347	157	38	is	be	AUX
ejpam-5347	157	39	a	a	DET
ejpam-5347	157	40	real	real	ADJ
ejpam-5347	157	41	issue	issue	NOUN
ejpam-5347	157	42	a	a	DET
ejpam-5347	157	43	countable	countable	ADJ
ejpam-5347	157	44	subsets	subset	NOUN
ejpam-5347	157	45	ξg	ξg	NOUN
ejpam-5347	157	46	,	,	PUNCT
ejpam-5347	157	47	ξ	ξ	PROPN
ejpam-5347	157	48	∗	∗	NOUN
ejpam-5347	157	49	g	g	NOUN
ejpam-5347	157	50	of	of	ADP
ejpam-5347	157	51	ξ	ξ	PROPN
ejpam-5347	157	52	,	,	PUNCT
ejpam-5347	157	53	this	this	PRON
ejpam-5347	157	54	implies	imply	VERB
ejpam-5347	157	55	υ−1(g	υ−1(g	PROPN
ejpam-5347	157	56	)	)	PUNCT
ejpam-5347	157	57	⊆	⊆	NUM
ejpam-5347	157	58	⋃	⋃	NOUN
ejpam-5347	157	59	δ∈ξg	δ∈ξg	NOUN
ejpam-5347	157	60	{	{	PUNCT
ejpam-5347	157	61	nδ	nδ	ADP
ejpam-5347	157	62	:	:	PUNCT
ejpam-5347	157	63	δ	δ	PROPN
ejpam-5347	157	64	∈	∈	PROPN
ejpam-5347	157	65	ξg	ξg	PROPN
ejpam-5347	157	66	}	}	PUNCT
ejpam-5347	157	67	⋃	⋃	X
ejpam-5347	157	68	⋃	⋃	PUNCT
ejpam-5347	157	69	α∈	α∈	PROPN
ejpam-5347	157	70	λ∗	λ∗	NOUN
ejpam-5347	157	71	y	y	INTJ
ejpam-5347	157	72	{	{	PUNCT
ejpam-5347	157	73	mδ	mδ	PROPN
ejpam-5347	157	74	:	:	PUNCT
ejpam-5347	157	75	δ	δ	PROPN
ejpam-5347	157	76	∈	∈	PROPN
ejpam-5347	157	77	ξ∗	ξ∗	NOUN
ejpam-5347	157	78	g	g	PROPN
ejpam-5347	157	79	}	}	PUNCT
ejpam-5347	157	80	,	,	PUNCT
ejpam-5347	157	81	at	at	ADP
ejpam-5347	157	82	which	which	PRON
ejpam-5347	157	83	{	{	PUNCT
ejpam-5347	157	84	nδ	nδ	ADP
ejpam-5347	157	85	:	:	PUNCT
ejpam-5347	157	86	δ	δ	PROPN
ejpam-5347	157	87	∈	∈	PROPN
ejpam-5347	157	88	ξg	ξg	PROPN
ejpam-5347	157	89	}	}	PUNCT
ejpam-5347	157	90	is	be	AUX
ejpam-5347	157	91	κ1−open	κ1−open	ADJ
ejpam-5347	157	92	,	,	PUNCT
ejpam-5347	157	93	{	{	PUNCT
ejpam-5347	157	94	mδ	mδ	NOUN
ejpam-5347	157	95	:	:	PUNCT
ejpam-5347	157	96	δ	δ	PROPN
ejpam-5347	157	97	∈	∈	PROPN
ejpam-5347	157	98	ξ∗	ξ∗	PROPN
ejpam-5347	157	99	g	g	NOUN
ejpam-5347	157	100	}	}	PUNCT
ejpam-5347	157	101	is	be	AUX
ejpam-5347	157	102	κ2−open	κ2−open	ADJ
ejpam-5347	157	103	.	.	PUNCT
ejpam-5347	158	1	consider	consider	VERB
ejpam-5347	158	2	hg	hg	NOUN
ejpam-5347	158	3	=	=	SYM
ejpam-5347	158	4	(	(	PUNCT
ejpam-5347	158	5	g	g	PROPN
ejpam-5347	158	6	,	,	PUNCT
ejpam-5347	158	7	υ1	υ1	PROPN
ejpam-5347	158	8	,	,	PUNCT
ejpam-5347	158	9	υ2)−υ((d	υ2)−υ((d	NOUN
ejpam-5347	158	10	,	,	PUNCT
ejpam-5347	158	11	κ1	κ1	NOUN
ejpam-5347	158	12	,	,	PUNCT
ejpam-5347	158	13	κ2)−	κ2)−	ADJ
ejpam-5347	158	14	⋃	⋃	NOUN
ejpam-5347	158	15	δ∈ξg	δ∈ξg	NOUN
ejpam-5347	158	16	nδ	nδ	NOUN
ejpam-5347	158	17	)	)	PUNCT
ejpam-5347	158	18	is	be	AUX
ejpam-5347	158	19	a	a	DET
ejpam-5347	158	20	ρ1	ρ1	NOUN
ejpam-5347	158	21	-	-	PUNCT
ejpam-5347	158	22	open	open	ADJ
ejpam-5347	158	23	set	set	NOUN
ejpam-5347	158	24	comprising	comprising	NOUN
ejpam-5347	158	25	g	g	NOUN
ejpam-5347	158	26	,	,	PUNCT
ejpam-5347	158	27	and	and	CCONJ
ejpam-5347	158	28	h∗	h∗	PROPN
ejpam-5347	158	29	g	g	PROPN
ejpam-5347	158	30	=	=	SYM
ejpam-5347	158	31	(	(	PUNCT
ejpam-5347	158	32	g	g	PROPN
ejpam-5347	158	33	,	,	PUNCT
ejpam-5347	158	34	υ1	υ1	PROPN
ejpam-5347	158	35	,	,	PUNCT
ejpam-5347	158	36	υ2)−υ((d	υ2)−υ((d	NOUN
ejpam-5347	158	37	,	,	PUNCT
ejpam-5347	158	38	κ1	κ1	NOUN
ejpam-5347	158	39	,	,	PUNCT
ejpam-5347	158	40	κ2)−	κ2)−	PROPN
ejpam-5347	158	41	⋃	⋃	PUNCT
ejpam-5347	158	42	δ∈ξ∗	δ∈ξ∗	NOUN
ejpam-5347	158	43	g	g	PROPN
ejpam-5347	158	44	mδ	mδ	NOUN
ejpam-5347	158	45	)	)	PUNCT
ejpam-5347	158	46	is	be	AUX
ejpam-5347	158	47	a	a	DET
ejpam-5347	158	48	ρ2	ρ2	NOUN
ejpam-5347	158	49	-	-	PUNCT
ejpam-5347	158	50	open	open	ADJ
ejpam-5347	158	51	set	set	NOUN
ejpam-5347	158	52	comprising	comprising	NOUN
ejpam-5347	158	53	g	g	NOUN
ejpam-5347	158	54	,	,	PUNCT
ejpam-5347	158	55	where	where	SCONJ
ejpam-5347	158	56	υ−1	υ−1	PROPN
ejpam-5347	158	57	(	(	PUNCT
ejpam-5347	158	58	hg	hg	NOUN
ejpam-5347	158	59	)	)	PUNCT
ejpam-5347	158	60	⊆	⊆	NUM
ejpam-5347	158	61	⋃	⋃	NOUN
ejpam-5347	158	62	δ∈ξg	δ∈ξg	ADJ
ejpam-5347	158	63	vα	vα	PROPN
ejpam-5347	158	64	,	,	PUNCT
ejpam-5347	158	65	υ−1	υ−1	PROPN
ejpam-5347	158	66	(	(	PUNCT
ejpam-5347	158	67	h∗	h∗	PROPN
ejpam-5347	158	68	g	g	PROPN
ejpam-5347	158	69	)	)	PUNCT
ejpam-5347	158	70	⊆	⊆	NUM
ejpam-5347	158	71	⋃	⋃	NOUN
ejpam-5347	158	72	δ∈ξ∗	δ∈ξ∗	NOUN
ejpam-5347	158	73	g	g	PROPN
ejpam-5347	158	74	mδ	mδ	NOUN
ejpam-5347	158	75	.	.	PROPN
ejpam-5347	159	1	assume	assume	VERB
ejpam-5347	159	2	h	h	NOUN
ejpam-5347	160	1	˜	˜	PROPN
ejpam-5347	160	2	g	g	PROPN
ejpam-5347	160	3	=	=	PUNCT
ejpam-5347	160	4	{	{	PUNCT
ejpam-5347	160	5	hg	hg	NOUN
ejpam-5347	160	6	:	:	PUNCT
ejpam-5347	160	7	g	g	PROPN
ejpam-5347	160	8	∈	∈	PROPN
ejpam-5347	160	9	(	(	PUNCT
ejpam-5347	160	10	g	g	NOUN
ejpam-5347	160	11	,	,	PUNCT
ejpam-5347	160	12	υ1	υ1	PROPN
ejpam-5347	160	13	,	,	PUNCT
ejpam-5347	160	14	υ2)}⋃	υ2)}⋃	NUM
ejpam-5347	160	15	{	{	PUNCT
ejpam-5347	160	16	h∗	h∗	NOUN
ejpam-5347	160	17	g	g	NOUN
ejpam-5347	160	18	:	:	PUNCT
ejpam-5347	161	1	g	g	PROPN
ejpam-5347	161	2	∈	∈	PROPN
ejpam-5347	161	3	(	(	PUNCT
ejpam-5347	161	4	g	g	NOUN
ejpam-5347	161	5	,	,	PUNCT
ejpam-5347	161	6	υ1	υ1	NOUN
ejpam-5347	161	7	,	,	PUNCT
ejpam-5347	161	8	υ2	υ2	NOUN
ejpam-5347	161	9	)	)	PUNCT
ejpam-5347	161	10	}	}	PUNCT
ejpam-5347	161	11	is	be	AUX
ejpam-5347	161	12	a	a	DET
ejpam-5347	161	13	pair−open	pair−open	ADJ
ejpam-5347	161	14	cover	cover	NOUN
ejpam-5347	161	15	of	of	ADP
ejpam-5347	161	16	(	(	PUNCT
ejpam-5347	161	17	g	g	PROPN
ejpam-5347	161	18	,	,	PUNCT
ejpam-5347	161	19	υ1	υ1	NOUN
ejpam-5347	161	20	,	,	PUNCT
ejpam-5347	161	21	υ2	υ2	PROPN
ejpam-5347	161	22	)	)	PUNCT
ejpam-5347	161	23	.	.	PUNCT
ejpam-5347	162	1	taking	take	VERB
ejpam-5347	162	2	into	into	ADP
ejpam-5347	162	3	account	account	NOUN
ejpam-5347	162	4	υ	υ	PROPN
ejpam-5347	162	5	is	be	AUX
ejpam-5347	162	6	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	162	7	,	,	PUNCT
ejpam-5347	162	8	h	h	NOUN
ejpam-5347	162	9	˜	˜	PROPN
ejpam-5347	162	10	g	g	PROPN
ejpam-5347	162	11	is	be	AUX
ejpam-5347	162	12	pair−ω−open	pair−ω−open	ADJ
ejpam-5347	162	13	for	for	ADP
ejpam-5347	162	14	each	each	DET
ejpam-5347	162	15	g	g	PROPN
ejpam-5347	162	16	∈	∈	PROPN
ejpam-5347	162	17	(	(	PUNCT
ejpam-5347	162	18	g	g	NOUN
ejpam-5347	162	19	,	,	PUNCT
ejpam-5347	162	20	υ1	υ1	NOUN
ejpam-5347	162	21	,	,	PUNCT
ejpam-5347	162	22	υ2	υ2	PROPN
ejpam-5347	162	23	)	)	PUNCT
ejpam-5347	162	24	.	.	PUNCT
ejpam-5347	163	1	thus	thus	ADV
ejpam-5347	163	2	,	,	PUNCT
ejpam-5347	163	3	there	there	PRON
ejpam-5347	163	4	is	be	VERB
ejpam-5347	163	5	an	an	DET
ejpam-5347	163	6	open	open	ADJ
ejpam-5347	163	7	pair−neibourhood	pair−neibourhood	NOUN
ejpam-5347	163	8	h	h	NOUN
ejpam-5347	163	9	\	\	PROPN
ejpam-5347	163	10	g	g	PROPN
ejpam-5347	163	11	.in	.in	PUNCT
ejpam-5347	163	12	away	away	ADV
ejpam-5347	163	13	that	that	SCONJ
ejpam-5347	163	14	h	h	NOUN
ejpam-5347	163	15	\	\	NOUN
ejpam-5347	163	16	g	g	PROPN
ejpam-5347	163	17	∩	∩	X
ejpam-5347	163	18	(	(	PUNCT
ejpam-5347	163	19	(	(	PUNCT
ejpam-5347	163	20	d	d	NOUN
ejpam-5347	163	21	,	,	PUNCT
ejpam-5347	163	22	κ1	κ1	NOUN
ejpam-5347	163	23	,	,	PUNCT
ejpam-5347	163	24	κ2	κ2	NOUN
ejpam-5347	163	25	)	)	PUNCT
ejpam-5347	163	26	−h	−h	VERB
ejpam-5347	163	27	\	\	PROPN
ejpam-5347	163	28	g	g	NOUN
ejpam-5347	163	29	)	)	PUNCT
ejpam-5347	163	30	is	be	AUX
ejpam-5347	163	31	countable	countable	ADJ
ejpam-5347	163	32	.	.	PUNCT
ejpam-5347	164	1	considering	consider	VERB
ejpam-5347	164	2	(	(	PUNCT
ejpam-5347	164	3	g	g	NOUN
ejpam-5347	164	4	,	,	PUNCT
ejpam-5347	164	5	υ1	υ1	NOUN
ejpam-5347	164	6	,	,	PUNCT
ejpam-5347	164	7	υ2	υ2	PROPN
ejpam-5347	164	8	)	)	PUNCT
ejpam-5347	164	9	is	be	AUX
ejpam-5347	164	10	pair−paracompact	pair−paracompact	NOUN
ejpam-5347	165	1	h	h	NOUN
ejpam-5347	165	2	˜	˜	PROPN
ejpam-5347	165	3	has	have	AUX
ejpam-5347	165	4	pair−open	pair−open	VERB
ejpam-5347	165	5	locally	locally	ADV
ejpam-5347	165	6	finite	finite	ADJ
ejpam-5347	165	7	parallel	parallel	ADJ
ejpam-5347	165	8	refinement	refinement	NOUN
ejpam-5347	165	9	declare	declare	VERB
ejpam-5347	165	10	that	that	SCONJ
ejpam-5347	165	11	:	:	PUNCT
ejpam-5347	165	12	q	q	PROPN
ejpam-5347	165	13	˜	˜	PROPN
ejpam-5347	165	14	=	=	PUNCT
ejpam-5347	165	15	{	{	PUNCT
ejpam-5347	165	16	qd	qd	NOUN
ejpam-5347	165	17	:	:	PUNCT
ejpam-5347	165	18	d	d	X
ejpam-5347	165	19	∈	∈	PROPN
ejpam-5347	165	20	ω1	ω1	PROPN
ejpam-5347	165	21	}	}	PUNCT
ejpam-5347	165	22	⋃	⋃	NOUN
ejpam-5347	165	23	{	{	PUNCT
ejpam-5347	165	24	q∗	q∗	NOUN
ejpam-5347	165	25	d	d	NOUN
ejpam-5347	165	26	:	:	PUNCT
ejpam-5347	165	27	d	d	X
ejpam-5347	165	28	∈	∈	PROPN
ejpam-5347	165	29	ω2	ω2	PROPN
ejpam-5347	165	30	}	}	PUNCT
ejpam-5347	165	31	,	,	PUNCT
ejpam-5347	165	32	where	where	SCONJ
ejpam-5347	165	33	{	{	PUNCT
ejpam-5347	165	34	qd	qd	NOUN
ejpam-5347	165	35	:	:	PUNCT
ejpam-5347	165	36	d	d	PROPN
ejpam-5347	165	37	∈	∈	PROPN
ejpam-5347	165	38	ω1	ω1	PROPN
ejpam-5347	165	39	}	}	PUNCT
ejpam-5347	165	40	is	be	AUX
ejpam-5347	165	41	υ1	υ1	ADJ
ejpam-5347	165	42	-	-	PUNCT
ejpam-5347	165	43	locally	locally	ADV
ejpam-5347	165	44	finite	finite	ADJ
ejpam-5347	165	45	paracompact	paracompact	NOUN
ejpam-5347	165	46	of	of	ADP
ejpam-5347	165	47	hg	hg	NOUN
ejpam-5347	165	48	,	,	PUNCT
ejpam-5347	165	49	and	and	CCONJ
ejpam-5347	165	50	{	{	PUNCT
ejpam-5347	165	51	q∗	q∗	NOUN
ejpam-5347	165	52	d	d	NOUN
ejpam-5347	165	53	:	:	PUNCT
ejpam-5347	165	54	d	d	X
ejpam-5347	165	55	∈	∈	PROPN
ejpam-5347	165	56	ω2	ω2	ADJ
ejpam-5347	165	57	}	}	PUNCT
ejpam-5347	165	58	is	be	AUX
ejpam-5347	165	59	υ2	υ2	NOUN
ejpam-5347	165	60	-	-	PUNCT
ejpam-5347	165	61	locally	locally	ADV
ejpam-5347	165	62	finite	finite	ADJ
ejpam-5347	165	63	paracompact	paracompact	NOUN
ejpam-5347	165	64	of	of	ADP
ejpam-5347	165	65	h	h	NOUN
ejpam-5347	165	66	\	\	PROPN
ejpam-5347	165	67	g	g	PROPN
ejpam-5347	165	68	,	,	PUNCT
ejpam-5347	165	69	ω	ω	PROPN
ejpam-5347	165	70	=	=	SYM
ejpam-5347	165	71	ω1	ω1	PROPN
ejpam-5347	165	72	⋃	⋃	PROPN
ejpam-5347	165	73	ω2.let	ω2.let	NOUN
ejpam-5347	165	74	l1	l1	PROPN
ejpam-5347	165	75	=	=	PROPN
ejpam-5347	165	76	{	{	PUNCT
ejpam-5347	165	77	υ−1(qd	υ−1(qd	PROPN
ejpam-5347	165	78	)	)	PUNCT
ejpam-5347	165	79	⋂	⋂	PROPN
ejpam-5347	165	80	δi	δi	NOUN
ejpam-5347	165	81	nδ	nδ	NOUN
ejpam-5347	165	82	,	,	PUNCT
ejpam-5347	165	83	i	i	PRON
ejpam-5347	165	84	=	=	NOUN
ejpam-5347	165	85	1	1	NUM
ejpam-5347	165	86	,	,	PUNCT
ejpam-5347	165	87	2	2	NUM
ejpam-5347	165	88	,	,	PUNCT
ejpam-5347	165	89	...	...	PUNCT
ejpam-5347	165	90	,	,	PUNCT
ejpam-5347	165	91	n	n	CCONJ
ejpam-5347	165	92	,	,	PUNCT
ejpam-5347	165	93	d	d	PROPN
ejpam-5347	165	94	∈	∈	PROPN
ejpam-5347	165	95	ω1	ω1	PROPN
ejpam-5347	165	96	,	,	PUNCT
ejpam-5347	165	97	δ	δ	PROPN
ejpam-5347	165	98	∈	∈	PROPN
ejpam-5347	165	99	ξg	ξg	PROPN
ejpam-5347	165	100	}	}	PUNCT
ejpam-5347	165	101	is	be	AUX
ejpam-5347	165	102	κ1−	κ1−	NOUN
ejpam-5347	165	103	open	open	ADJ
ejpam-5347	165	104	locally	locally	ADV
ejpam-5347	165	105	finite	finite	ADJ
ejpam-5347	165	106	parallel	parallel	ADJ
ejpam-5347	165	107	refinement	refinement	NOUN
ejpam-5347	165	108	of	of	ADP
ejpam-5347	165	109	{	{	PUNCT
ejpam-5347	165	110	nδ	nδ	PROPN
ejpam-5347	165	111	:	:	PUNCT
ejpam-5347	165	112	δ	δ	PROPN
ejpam-5347	165	113	∈	∈	PROPN
ejpam-5347	165	114	ξg},and	ξg},and	ADV
ejpam-5347	165	115	let	let	VERB
ejpam-5347	165	116	l2	l2	NOUN
ejpam-5347	165	117	=	=	SYM
ejpam-5347	165	118	{	{	PUNCT
ejpam-5347	165	119	υ−1(q∗	υ−1(q∗	PROPN
ejpam-5347	165	120	d	d	NOUN
ejpam-5347	165	121	)	)	PUNCT
ejpam-5347	165	122	⋂	⋂	PROPN
ejpam-5347	165	123	mδi	mδi	NOUN
ejpam-5347	165	124	,	,	PUNCT
ejpam-5347	165	125	i	i	PRON
ejpam-5347	165	126	=	=	NOUN
ejpam-5347	165	127	1	1	NUM
ejpam-5347	165	128	,	,	PUNCT
ejpam-5347	165	129	2	2	NUM
ejpam-5347	165	130	,	,	PUNCT
ejpam-5347	165	131	...	...	PUNCT
ejpam-5347	165	132	,	,	PUNCT
ejpam-5347	165	133	n	n	CCONJ
ejpam-5347	165	134	,	,	PUNCT
ejpam-5347	165	135	d	d	PROPN
ejpam-5347	165	136	∈	∈	PROPN
ejpam-5347	165	137	ω2	ω2	PROPN
ejpam-5347	165	138	,	,	PUNCT
ejpam-5347	165	139	δ	δ	PROPN
ejpam-5347	165	140	∈	∈	PROPN
ejpam-5347	165	141	ξ∗	ξ∗	PROPN
ejpam-5347	165	142	g	g	NOUN
ejpam-5347	165	143	}	}	PUNCT
ejpam-5347	165	144	is	be	AUX
ejpam-5347	165	145	κ2−	κ2−	NOUN
ejpam-5347	165	146	open	open	ADJ
ejpam-5347	165	147	locally	locally	ADV
ejpam-5347	165	148	finite	finite	ADJ
ejpam-5347	165	149	parallel	parallel	ADJ
ejpam-5347	165	150	refinement	refinement	NOUN
ejpam-5347	165	151	of	of	ADP
ejpam-5347	165	152	{	{	PUNCT
ejpam-5347	165	153	mδ	mδ	NOUN
ejpam-5347	165	154	:	:	PUNCT
ejpam-5347	165	155	δ	δ	PROPN
ejpam-5347	165	156	∈	∈	PROPN
ejpam-5347	165	157	ξ∗	ξ∗	NOUN
ejpam-5347	165	158	g	g	PROPN
ejpam-5347	165	159	}	}	PUNCT
ejpam-5347	165	160	.	.	PUNCT
ejpam-5347	166	1	let	let	VERB
ejpam-5347	167	1	l	l	NOUN
ejpam-5347	167	2	˜	˜	PROPN
ejpam-5347	167	3	=	=	PUNCT
ejpam-5347	167	4	{	{	PUNCT
ejpam-5347	167	5	l1	l1	PROPN
ejpam-5347	167	6	⋃	⋃	NOUN
ejpam-5347	167	7	l2	l2	NOUN
ejpam-5347	167	8	}	}	PUNCT
ejpam-5347	167	9	,	,	PUNCT
ejpam-5347	167	10	then	then	ADV
ejpam-5347	167	11	l	l	PROPN
ejpam-5347	167	12	˜	˜	PROPN
ejpam-5347	167	13	is	be	AUX
ejpam-5347	167	14	pair−open	pair−open	ADJ
ejpam-5347	167	15	locally	locally	ADV
ejpam-5347	167	16	finite	finite	ADJ
ejpam-5347	167	17	parallel	parallel	ADJ
ejpam-5347	167	18	refinement	refinement	NOUN
ejpam-5347	167	19	of	of	ADP
ejpam-5347	167	20	t	t	PROPN
ejpam-5347	167	21	˜	˜	PROPN
ejpam-5347	167	22	,	,	PUNCT
ejpam-5347	167	23	so	so	CCONJ
ejpam-5347	167	24	(	(	PUNCT
ejpam-5347	167	25	d	d	NOUN
ejpam-5347	167	26	,	,	PUNCT
ejpam-5347	167	27	κ1	κ1	NOUN
ejpam-5347	167	28	,	,	PUNCT
ejpam-5347	167	29	κ2	κ2	PROPN
ejpam-5347	167	30	)	)	PUNCT
ejpam-5347	167	31	is	be	AUX
ejpam-5347	167	32	pair−paracompact	pair−paracompact	ADJ
ejpam-5347	167	33	space	space	NOUN
ejpam-5347	167	34	.	.	PUNCT
ejpam-5347	168	1	theorem	theorem	NOUN
ejpam-5347	168	2	6	6	NUM
ejpam-5347	168	3	.	.	PUNCT
ejpam-5347	169	1	allow	allow	VERB
ejpam-5347	169	2	υ	υ	NOUN
ejpam-5347	169	3	:	:	PUNCT
ejpam-5347	169	4	(	(	PUNCT
ejpam-5347	169	5	d	d	NOUN
ejpam-5347	169	6	,	,	PUNCT
ejpam-5347	169	7	κ1	κ1	NOUN
ejpam-5347	169	8	,	,	PUNCT
ejpam-5347	169	9	κ2	κ2	PROPN
ejpam-5347	169	10	)	)	PUNCT
ejpam-5347	169	11	→	→	SYM
ejpam-5347	169	12	(	(	PUNCT
ejpam-5347	169	13	g	g	NOUN
ejpam-5347	169	14	,	,	PUNCT
ejpam-5347	169	15	υ1	υ1	NOUN
ejpam-5347	169	16	,	,	PUNCT
ejpam-5347	169	17	υ2	υ2	PROPN
ejpam-5347	169	18	)	)	PUNCT
ejpam-5347	169	19	is	be	AUX
ejpam-5347	169	20	pair−continuous	pair−continuous	ADJ
ejpam-5347	169	21	function	function	NOUN
ejpam-5347	169	22	from	from	ADP
ejpam-5347	169	23	(	(	PUNCT
ejpam-5347	169	24	d	d	NOUN
ejpam-5347	169	25	,	,	PUNCT
ejpam-5347	169	26	κ1	κ1	NOUN
ejpam-5347	169	27	,	,	PUNCT
ejpam-5347	169	28	κ2)onto	κ2)onto	NOUN
ejpam-5347	169	29	(	(	PUNCT
ejpam-5347	169	30	g	g	NOUN
ejpam-5347	169	31	,	,	PUNCT
ejpam-5347	169	32	υ1	υ1	NOUN
ejpam-5347	169	33	,	,	PUNCT
ejpam-5347	169	34	υ2	υ2	PROPN
ejpam-5347	169	35	)	)	PUNCT
ejpam-5347	169	36	,	,	PUNCT
ejpam-5347	169	37	where	where	SCONJ
ejpam-5347	169	38	(	(	PUNCT
ejpam-5347	169	39	g	g	NOUN
ejpam-5347	169	40	,	,	PUNCT
ejpam-5347	169	41	υ1	υ1	PROPN
ejpam-5347	169	42	,	,	PUNCT
ejpam-5347	169	43	υ2)is	υ2)is	PROPN
ejpam-5347	169	44	pair−locally	pair−locally	NOUN
ejpam-5347	169	45	lindel	lindel	NOUN
ejpam-5347	169	46	..	..	PUNCT
ejpam-5347	169	47	of	of	ADP
ejpam-5347	169	48	pair−hausdorff	pair−hausdorff	NOUN
ejpam-5347	169	49	p̋−space	p̋−space	NOUN
ejpam-5347	169	50	.	.	PUNCT
ejpam-5347	170	1	therefore	therefore	ADV
ejpam-5347	170	2	the	the	DET
ejpam-5347	170	3	subsequent	subsequent	ADJ
ejpam-5347	170	4	statements	statement	NOUN
ejpam-5347	170	5	are	be	AUX
ejpam-5347	170	6	comparable	comparable	ADJ
ejpam-5347	170	7	:	:	PUNCT
ejpam-5347	170	8	(	(	PUNCT
ejpam-5347	170	9	a	a	X
ejpam-5347	170	10	)	)	PUNCT
ejpam-5347	170	11	υ	υ	NOUN
ejpam-5347	170	12	is	be	AUX
ejpam-5347	170	13	a	a	DET
ejpam-5347	170	14	pair−ω−closed	pair−ω−closed	ADJ
ejpam-5347	170	15	function	function	NOUN
ejpam-5347	170	16	and	and	CCONJ
ejpam-5347	170	17	for	for	ADP
ejpam-5347	170	18	each	each	DET
ejpam-5347	170	19	g	g	PROPN
ejpam-5347	170	20	∈	∈	PROPN
ejpam-5347	170	21	(	(	PUNCT
ejpam-5347	170	22	g	g	NOUN
ejpam-5347	170	23	,	,	PUNCT
ejpam-5347	170	24	υ1	υ1	PROPN
ejpam-5347	170	25	,	,	PUNCT
ejpam-5347	170	26	υ2),υ	υ2),υ	PROPN
ejpam-5347	170	27	−1(g	−1(g	NOUN
ejpam-5347	170	28	)	)	PUNCT
ejpam-5347	170	29	is	be	AUX
ejpam-5347	170	30	pair−lindel	pair−lindel	NOUN
ejpam-5347	170	31	..	..	PUNCT
ejpam-5347	170	32	of	of	ADP
ejpam-5347	170	33	.	.	PUNCT
ejpam-5347	171	1	(	(	PUNCT
ejpam-5347	171	2	b	b	X
ejpam-5347	171	3	)	)	PUNCT
ejpam-5347	171	4	υ	υ	NOUN
ejpam-5347	171	5	is	be	AUX
ejpam-5347	171	6	a	a	DET
ejpam-5347	171	7	pair−	pair−	NOUN
ejpam-5347	171	8	lindel	lindel	NOUN
ejpam-5347	171	9	..	..	PUNCT
ejpam-5347	171	10	of	of	ADP
ejpam-5347	171	11	function	function	NOUN
ejpam-5347	171	12	.	.	PUNCT
ejpam-5347	172	1	proof	proof	NOUN
ejpam-5347	172	2	.	.	PUNCT
ejpam-5347	173	1	(	(	PUNCT
ejpam-5347	173	2	a	a	X
ejpam-5347	173	3	)	)	PUNCT
ejpam-5347	173	4	→	→	SYM
ejpam-5347	173	5	(	(	PUNCT
ejpam-5347	173	6	b	b	X
ejpam-5347	173	7	)	)	PUNCT
ejpam-5347	173	8	originates	originate	NOUN
ejpam-5347	173	9	using	use	VERB
ejpam-5347	173	10	the	the	DET
ejpam-5347	173	11	identical	identical	ADJ
ejpam-5347	173	12	method	method	NOUN
ejpam-5347	173	13	as	as	ADP
ejpam-5347	173	14	in	in	ADP
ejpam-5347	173	15	theorem	theorem	NOUN
ejpam-5347	173	16	3	3	NUM
ejpam-5347	173	17	.	.	PUNCT
ejpam-5347	173	18	(	(	PUNCT
ejpam-5347	173	19	b	b	NOUN
ejpam-5347	173	20	)	)	PUNCT
ejpam-5347	173	21	→	→	PUNCT
ejpam-5347	173	22	(	(	PUNCT
ejpam-5347	173	23	a	a	X
ejpam-5347	173	24	)	)	PUNCT
ejpam-5347	173	25	:	:	PUNCT
ejpam-5347	173	26	let	let	VERB
ejpam-5347	173	27	υ	υ	PRON
ejpam-5347	173	28	:	:	PUNCT
ejpam-5347	173	29	(	(	PUNCT
ejpam-5347	173	30	d	d	NOUN
ejpam-5347	173	31	,	,	PUNCT
ejpam-5347	173	32	κ1	κ1	NOUN
ejpam-5347	173	33	,	,	PUNCT
ejpam-5347	173	34	κ2	κ2	PROPN
ejpam-5347	173	35	)	)	PUNCT
ejpam-5347	173	36	→	→	SYM
ejpam-5347	173	37	(	(	PUNCT
ejpam-5347	173	38	g	g	NOUN
ejpam-5347	173	39	,	,	PUNCT
ejpam-5347	173	40	υ1	υ1	NOUN
ejpam-5347	173	41	,	,	PUNCT
ejpam-5347	173	42	υ2	υ2	PROPN
ejpam-5347	173	43	)	)	PUNCT
ejpam-5347	173	44	be	be	VERB
ejpam-5347	173	45	pair−continuous	pair−continuous	ADJ
ejpam-5347	173	46	function	function	NOUN
ejpam-5347	173	47	pair−lindel	pair−lindel	NOUN
ejpam-5347	173	48	..	..	PUNCT
ejpam-5347	174	1	of	of	ADP
ejpam-5347	174	2	,	,	PUNCT
ejpam-5347	174	3	where	where	SCONJ
ejpam-5347	174	4	(	(	PUNCT
ejpam-5347	174	5	g	g	NOUN
ejpam-5347	174	6	,	,	PUNCT
ejpam-5347	174	7	υ1	υ1	NOUN
ejpam-5347	174	8	,	,	PUNCT
ejpam-5347	174	9	υ2	υ2	PROPN
ejpam-5347	174	10	)	)	PUNCT
ejpam-5347	174	11	is	be	AUX
ejpam-5347	174	12	pair−locally	pair−locally	ADV
ejpam-5347	174	13	lindel	lindel	NOUN
ejpam-5347	174	14	..	..	PUNCT
ejpam-5347	174	15	of	of	ADP
ejpam-5347	174	16	pair−hausdorff	pair−hausdorff	NOUN
ejpam-5347	174	17	p̋−space	p̋−space	NOUN
ejpam-5347	174	18	.	.	PUNCT
ejpam-5347	175	1	demonstrating	demonstrate	VERB
ejpam-5347	175	2	that	that	SCONJ
ejpam-5347	175	3	υ	υ	PROPN
ejpam-5347	175	4	is	be	AUX
ejpam-5347	175	5	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	175	6	function	function	NOUN
ejpam-5347	175	7	is	be	AUX
ejpam-5347	175	8	adequate	adequate	ADJ
ejpam-5347	175	9	.	.	PUNCT
ejpam-5347	176	1	let	let	VERB
ejpam-5347	176	2	s1is	s1is	PUNCT
ejpam-5347	176	3	closed	close	VERB
ejpam-5347	176	4	in	in	ADP
ejpam-5347	176	5	κ1	κ1	PROPN
ejpam-5347	176	6	.assume	.assume	SYM
ejpam-5347	176	7	υ(s1	υ(s1	PROPN
ejpam-5347	176	8	)	)	PUNCT
ejpam-5347	176	9	is	be	AUX
ejpam-5347	176	10	not	not	PART
ejpam-5347	176	11	ω−	ω−	ADV
ejpam-5347	176	12	closed	close	VERB
ejpam-5347	176	13	in	in	ADP
ejpam-5347	176	14	υ1	υ1	PROPN
ejpam-5347	176	15	,	,	PUNCT
ejpam-5347	176	16	therefor	therefor	ADP
ejpam-5347	176	17	a	a	DET
ejpam-5347	176	18	point	point	NOUN
ejpam-5347	176	19	is	be	AUX
ejpam-5347	176	20	present	present	ADJ
ejpam-5347	176	21	g0	g0	ADJ
ejpam-5347	176	22	∈	∈	PROPN
ejpam-5347	176	23	(	(	PUNCT
ejpam-5347	176	24	g	g	NOUN
ejpam-5347	176	25	,	,	PUNCT
ejpam-5347	176	26	υ1	υ1	NOUN
ejpam-5347	176	27	,	,	PUNCT
ejpam-5347	176	28	υ2	υ2	PROPN
ejpam-5347	176	29	)	)	PUNCT
ejpam-5347	176	30	−	−	PROPN
ejpam-5347	176	31	υ(s1	υ(s1	NOUN
ejpam-5347	176	32	)	)	PUNCT
ejpam-5347	176	33	.	.	PUNCT
ejpam-5347	177	1	in	in	ADP
ejpam-5347	177	2	this	this	DET
ejpam-5347	177	3	way	way	NOUN
ejpam-5347	177	4	in	in	ADP
ejpam-5347	177	5	order	order	NOUN
ejpam-5347	177	6	for	for	ADP
ejpam-5347	177	7	every	every	DET
ejpam-5347	177	8	neighborhood	neighborhood	NOUN
ejpam-5347	177	9	n	n	PRON
ejpam-5347	177	10	of	of	ADP
ejpam-5347	177	11	g0	g0	PROPN
ejpam-5347	177	12	,	,	PUNCT
ejpam-5347	177	13	n	n	PRON
ejpam-5347	177	14	∩	∩	ADJ
ejpam-5347	177	15	υ(s1	υ(s1	NOUN
ejpam-5347	177	16	)	)	PUNCT
ejpam-5347	177	17	is	be	AUX
ejpam-5347	177	18	uncountable	uncountable	ADJ
ejpam-5347	177	19	.	.	PUNCT
ejpam-5347	178	1	because	because	SCONJ
ejpam-5347	178	2	of	of	ADP
ejpam-5347	178	3	(	(	PUNCT
ejpam-5347	178	4	g	g	PROPN
ejpam-5347	178	5	,	,	PUNCT
ejpam-5347	178	6	υ1	υ1	NOUN
ejpam-5347	178	7	,	,	PUNCT
ejpam-5347	178	8	υ2	υ2	PROPN
ejpam-5347	178	9	)	)	PUNCT
ejpam-5347	178	10	is	be	AUX
ejpam-5347	178	11	pair−locally	pair−locally	ADV
ejpam-5347	178	12	lindel	lindel	NOUN
ejpam-5347	178	13	..	..	PUNCT
ejpam-5347	178	14	of	of	ADP
ejpam-5347	178	15	,	,	PUNCT
ejpam-5347	178	16	there	there	PRON
ejpam-5347	178	17	exists	exist	VERB
ejpam-5347	178	18	υ1−neighborhoodm	υ1−neighborhoodm	PROPN
ejpam-5347	178	19	of	of	ADP
ejpam-5347	178	20	g0	g0	PROPN
ejpam-5347	178	21	,	,	PUNCT
ejpam-5347	178	22	so	so	ADV
ejpam-5347	178	23	thatm	thatm	NOUN
ejpam-5347	178	24	υ2	υ2	PROPN
ejpam-5347	178	25	is	be	AUX
ejpam-5347	178	26	pair−lindel	pair−lindel	NOUN
ejpam-5347	178	27	..	..	PUNCT
ejpam-5347	178	28	of	of	ADP
ejpam-5347	178	29	.	.	PUNCT
ejpam-5347	179	1	check	check	VERB
ejpam-5347	179	2	now	now	ADV
ejpam-5347	179	3	υ(s1)∩m	υ(s1)∩m	PROPN
ejpam-5347	179	4	υ2	υ2	NOUN
ejpam-5347	179	5	is	be	AUX
ejpam-5347	179	6	not	not	PART
ejpam-5347	179	7	pair−	pair−	NOUN
ejpam-5347	179	8	lindel	lindel	NOUN
ejpam-5347	179	9	..	..	PUNCT
ejpam-5347	180	1	of	of	ADP
ejpam-5347	180	2	.	.	PUNCT
ejpam-5347	181	1	while	while	SCONJ
ejpam-5347	181	2	such	such	ADJ
ejpam-5347	181	3	is	be	AUX
ejpam-5347	181	4	the	the	DET
ejpam-5347	181	5	case	case	NOUN
ejpam-5347	181	6	,	,	PUNCT
ejpam-5347	181	7	it	it	PRON
ejpam-5347	181	8	is	be	AUX
ejpam-5347	181	9	evident	evident	ADJ
ejpam-5347	181	10	that	that	SCONJ
ejpam-5347	181	11	it	it	PRON
ejpam-5347	181	12	is	be	AUX
ejpam-5347	181	13	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	181	14	,	,	PUNCT
ejpam-5347	181	15	therefore	therefore	ADV
ejpam-5347	181	16	there	there	PRON
ejpam-5347	181	17	is	be	VERB
ejpam-5347	181	18	a	a	DET
ejpam-5347	181	19	υ1−	υ1−	NOUN
ejpam-5347	181	20	neighborhood	neighborhood	NOUN
ejpam-5347	181	21	k	k	NOUN
ejpam-5347	181	22	of	of	ADP
ejpam-5347	181	23	g0	g0	PROPN
ejpam-5347	181	24	.	.	PUNCT
ejpam-5347	182	1	in	in	ADP
ejpam-5347	182	2	a	a	DET
ejpam-5347	182	3	way	way	NOUN
ejpam-5347	182	4	that	that	PRON
ejpam-5347	182	5	υ(s1)∩k	υ(s1)∩k	PROPN
ejpam-5347	182	6	is	be	AUX
ejpam-5347	182	7	a.	a.	NOUN
ejpam-5347	182	8	atoom	atoom	NOUN
ejpam-5347	182	9	et	et	PROPN
ejpam-5347	182	10	al	al	PROPN
ejpam-5347	182	11	.	.	PUNCT
ejpam-5347	182	12	/	/	SYM
ejpam-5347	182	13	eur	eur	PROPN
ejpam-5347	182	14	.	.	PUNCT
ejpam-5347	183	1	j.	j.	PROPN
ejpam-5347	183	2	pure	pure	PROPN
ejpam-5347	183	3	appl	appl	PROPN
ejpam-5347	183	4	.	.	PROPN
ejpam-5347	183	5	math	math	PROPN
ejpam-5347	183	6	,	,	PUNCT
ejpam-5347	183	7	17	17	NUM
ejpam-5347	183	8	(	(	PUNCT
ejpam-5347	183	9	4	4	NUM
ejpam-5347	183	10	)	)	PUNCT
ejpam-5347	183	11	(	(	PUNCT
ejpam-5347	183	12	2024	2024	NUM
ejpam-5347	183	13	)	)	PUNCT
ejpam-5347	183	14	,	,	PUNCT
ejpam-5347	183	15	2574	2574	NUM
ejpam-5347	183	16	-	-	SYM
ejpam-5347	183	17	2585	2585	NUM
ejpam-5347	183	18	2581	2581	NUM
ejpam-5347	183	19	countable	countable	ADJ
ejpam-5347	183	20	,	,	PUNCT
ejpam-5347	183	21	and	and	CCONJ
ejpam-5347	183	22	these	these	PRON
ejpam-5347	183	23	is	be	AUX
ejpam-5347	183	24	not	not	PART
ejpam-5347	183	25	feasible	feasible	ADJ
ejpam-5347	183	26	.	.	PUNCT
ejpam-5347	184	1	presently	presently	ADV
ejpam-5347	184	2	m	m	PROPN
ejpam-5347	184	3	υ2	υ2	PROPN
ejpam-5347	184	4	is	be	AUX
ejpam-5347	184	5	pair−	pair−	NOUN
ejpam-5347	184	6	lindel	lindel	NOUN
ejpam-5347	184	7	..	..	PUNCT
ejpam-5347	185	1	of	of	ADP
ejpam-5347	185	2	,	,	PUNCT
ejpam-5347	185	3	so	so	ADV
ejpam-5347	185	4	υ−1(m	υ−1(m	PROPN
ejpam-5347	185	5	υ2	υ2	PROPN
ejpam-5347	185	6	)	)	PUNCT
ejpam-5347	185	7	is	be	AUX
ejpam-5347	185	8	pair−lindel	pair−lindel	NOUN
ejpam-5347	185	9	..	..	PUNCT
ejpam-5347	185	10	of	of	ADP
ejpam-5347	185	11	and	and	CCONJ
ejpam-5347	185	12	s1	s1	PROPN
ejpam-5347	185	13	∩	∩	NOUN
ejpam-5347	185	14	υ−1(m	υ−1(m	PROPN
ejpam-5347	185	15	υ2	υ2	PROPN
ejpam-5347	185	16	)	)	PUNCT
ejpam-5347	185	17	is	be	AUX
ejpam-5347	185	18	pair−lindel	pair−lindel	NOUN
ejpam-5347	185	19	..	..	PUNCT
ejpam-5347	185	20	of	of	ADP
ejpam-5347	185	21	subset	subset	NOUN
ejpam-5347	185	22	of	of	ADP
ejpam-5347	185	23	(	(	PUNCT
ejpam-5347	185	24	d	d	PROPN
ejpam-5347	185	25	,	,	PUNCT
ejpam-5347	185	26	κ1	κ1	NOUN
ejpam-5347	185	27	,	,	PUNCT
ejpam-5347	185	28	κ2).consequently	κ2).consequently	ADV
ejpam-5347	185	29	υ(s1	υ(s1	ADJ
ejpam-5347	185	30	∩	∩	NOUN
ejpam-5347	185	31	υ−1(m	υ−1(m	PROPN
ejpam-5347	185	32	υ2	υ2	NOUN
ejpam-5347	185	33	)	)	PUNCT
ejpam-5347	185	34	)	)	PUNCT
ejpam-5347	186	1	=	=	SYM
ejpam-5347	186	2	υ(s1	υ(s1	X
ejpam-5347	186	3	)	)	PUNCT
ejpam-5347	187	1	∩m	∩m	PROPN
ejpam-5347	187	2	υ2	υ2	PROPN
ejpam-5347	187	3	is	be	AUX
ejpam-5347	187	4	pair−lindel	pair−lindel	NOUN
ejpam-5347	187	5	..	..	PUNCT
ejpam-5347	188	1	of	of	ADP
ejpam-5347	188	2	,	,	PUNCT
ejpam-5347	188	3	it	it	PRON
ejpam-5347	188	4	is	be	AUX
ejpam-5347	188	5	paradoxical.therefore	paradoxical.therefore	NOUN
ejpam-5347	188	6	υ(s1	υ(s1	NOUN
ejpam-5347	188	7	)	)	PUNCT
ejpam-5347	188	8	is	be	AUX
ejpam-5347	188	9	not	not	PART
ejpam-5347	188	10	ω−	ω−	ADV
ejpam-5347	188	11	closed	close	VERB
ejpam-5347	188	12	in	in	ADP
ejpam-5347	188	13	υ1	υ1	PROPN
ejpam-5347	188	14	.	.	PUNCT
ejpam-5347	189	1	comparative	comparative	ADJ
ejpam-5347	189	2	to	to	PART
ejpam-5347	189	3	s2	s2	VERB
ejpam-5347	189	4	is	be	AUX
ejpam-5347	189	5	closed	close	VERB
ejpam-5347	189	6	in	in	ADP
ejpam-5347	189	7	κ2	κ2	NOUN
ejpam-5347	189	8	,	,	PUNCT
ejpam-5347	189	9	υ(s2	υ(s2	VERB
ejpam-5347	189	10	)	)	PUNCT
ejpam-5347	189	11	is	be	AUX
ejpam-5347	189	12	not	not	PART
ejpam-5347	189	13	ω−	ω−	ADV
ejpam-5347	189	14	closed	close	VERB
ejpam-5347	189	15	in	in	ADP
ejpam-5347	189	16	υ2	υ2	NOUN
ejpam-5347	189	17	.	.	PUNCT
ejpam-5347	190	1	hence	hence	ADV
ejpam-5347	190	2	υ(s	υ(s	PROPN
ejpam-5347	190	3	)	)	PUNCT
ejpam-5347	190	4	is	be	AUX
ejpam-5347	190	5	pair−	pair−	NOUN
ejpam-5347	190	6	ω−	ω−	INTJ
ejpam-5347	190	7	closed	close	VERB
ejpam-5347	190	8	.	.	PUNCT
ejpam-5347	191	1	4	4	X
ejpam-5347	191	2	.	.	X
ejpam-5347	191	3	a	a	DET
ejpam-5347	191	4	novel	novel	ADJ
ejpam-5347	191	5	applications	application	NOUN
ejpam-5347	191	6	of	of	ADP
ejpam-5347	191	7	projection	projection	NOUN
ejpam-5347	191	8	and	and	CCONJ
ejpam-5347	191	9	product	product	NOUN
ejpam-5347	191	10	theorems	theorem	NOUN
ejpam-5347	191	11	here	here	ADV
ejpam-5347	191	12	,	,	PUNCT
ejpam-5347	191	13	we	we	PRON
ejpam-5347	191	14	derive	derive	VERB
ejpam-5347	191	15	various	various	ADJ
ejpam-5347	191	16	applications	application	NOUN
ejpam-5347	191	17	of	of	ADP
ejpam-5347	191	18	projection	projection	NOUN
ejpam-5347	191	19	and	and	CCONJ
ejpam-5347	191	20	product	product	NOUN
ejpam-5347	191	21	theorems	theorem	NOUN
ejpam-5347	191	22	for	for	ADP
ejpam-5347	191	23	pair−lindel	pair−lindel	NOUN
ejpam-5347	191	24	..	..	PUNCT
ejpam-5347	191	25	of	of	ADP
ejpam-5347	191	26	,	,	PUNCT
ejpam-5347	191	27	pair−paracompact	pair−paracompact	NOUN
ejpam-5347	191	28	spaces	space	NOUN
ejpam-5347	191	29	using	use	VERB
ejpam-5347	191	30	the	the	DET
ejpam-5347	191	31	findings	finding	NOUN
ejpam-5347	191	32	from	from	ADP
ejpam-5347	191	33	the	the	DET
ejpam-5347	191	34	preceding	precede	VERB
ejpam-5347	191	35	sections	section	NOUN
ejpam-5347	191	36	.	.	PUNCT
ejpam-5347	192	1	theorem	theorem	VERB
ejpam-5347	192	2	7	7	NUM
ejpam-5347	192	3	.	.	X
ejpam-5347	193	1	assume	assume	VERB
ejpam-5347	193	2	(	(	PUNCT
ejpam-5347	193	3	d	d	NOUN
ejpam-5347	193	4	,	,	PUNCT
ejpam-5347	193	5	κ1	κ1	NOUN
ejpam-5347	193	6	,	,	PUNCT
ejpam-5347	193	7	κ2	κ2	PROPN
ejpam-5347	193	8	)	)	PUNCT
ejpam-5347	193	9	is	be	AUX
ejpam-5347	193	10	a	a	DET
ejpam-5347	193	11	pair−lindel	pair−lindel	NOUN
ejpam-5347	193	12	..	..	PUNCT
ejpam-5347	193	13	of	of	ADP
ejpam-5347	193	14	space	space	NOUN
ejpam-5347	193	15	and	and	CCONJ
ejpam-5347	193	16	(	(	PUNCT
ejpam-5347	193	17	g	g	NOUN
ejpam-5347	193	18	,	,	PUNCT
ejpam-5347	193	19	υ1	υ1	NOUN
ejpam-5347	193	20	,	,	PUNCT
ejpam-5347	193	21	υ2	υ2	PROPN
ejpam-5347	193	22	)	)	PUNCT
ejpam-5347	193	23	be	be	VERB
ejpam-5347	193	24	a	a	DET
ejpam-5347	193	25	p̋−space	p̋−space	NOUN
ejpam-5347	193	26	,	,	PUNCT
ejpam-5347	193	27	subsequent	subsequent	VERB
ejpam-5347	193	28	the	the	DET
ejpam-5347	193	29	projection	projection	NOUN
ejpam-5347	193	30	p	p	NOUN
ejpam-5347	193	31	:	:	PUNCT
ejpam-5347	193	32	(	(	PUNCT
ejpam-5347	193	33	d	d	X
ejpam-5347	193	34	×	×	NOUN
ejpam-5347	193	35	g	g	NOUN
ejpam-5347	193	36	,	,	PUNCT
ejpam-5347	193	37	κ1	κ1	NOUN
ejpam-5347	193	38	×	×	PROPN
ejpam-5347	193	39	υ1	υ1	PROPN
ejpam-5347	193	40	,	,	PUNCT
ejpam-5347	193	41	κ2	κ2	PROPN
ejpam-5347	193	42	×	×	NOUN
ejpam-5347	193	43	υ2	υ2	NOUN
ejpam-5347	193	44	)	)	PUNCT
ejpam-5347	193	45	→	→	SYM
ejpam-5347	193	46	(	(	PUNCT
ejpam-5347	193	47	g	g	NOUN
ejpam-5347	193	48	,	,	PUNCT
ejpam-5347	193	49	υ1	υ1	NOUN
ejpam-5347	193	50	,	,	PUNCT
ejpam-5347	193	51	υ2	υ2	PROPN
ejpam-5347	193	52	)	)	PUNCT
ejpam-5347	193	53	is	be	AUX
ejpam-5347	193	54	pair−	pair−	NOUN
ejpam-5347	193	55	ω−	ω−	ADP
ejpam-5347	193	56	closed	close	VERB
ejpam-5347	193	57	functions	function	NOUN
ejpam-5347	193	58	.	.	PUNCT
ejpam-5347	194	1	proof	proof	NOUN
ejpam-5347	194	2	.	.	PUNCT
ejpam-5347	195	1	let	let	VERB
ejpam-5347	195	2	g	g	PROPN
ejpam-5347	195	3	∈	∈	PROPN
ejpam-5347	195	4	(	(	PUNCT
ejpam-5347	195	5	g	g	NOUN
ejpam-5347	195	6	,	,	PUNCT
ejpam-5347	195	7	υ1	υ1	NOUN
ejpam-5347	195	8	,	,	PUNCT
ejpam-5347	195	9	υ2	υ2	PROPN
ejpam-5347	195	10	)	)	PUNCT
ejpam-5347	195	11	and	and	CCONJ
ejpam-5347	195	12	n̋=	n̋=	ADV
ejpam-5347	195	13	{	{	PUNCT
ejpam-5347	195	14	kδ	kδ	NOUN
ejpam-5347	195	15	:	:	PUNCT
ejpam-5347	195	16	δ	δ	PROPN
ejpam-5347	195	17	∈	∈	PROPN
ejpam-5347	195	18	ξ	ξ	PROPN
ejpam-5347	195	19	}	}	PUNCT
ejpam-5347	195	20	×	×	NOUN
ejpam-5347	195	21	{	{	PUNCT
ejpam-5347	195	22	lδ	lδ	NOUN
ejpam-5347	195	23	:	:	PUNCT
ejpam-5347	195	24	δ	δ	PROPN
ejpam-5347	195	25	∈	∈	PROPN
ejpam-5347	195	26	ξ	ξ	PROPN
ejpam-5347	195	27	}	}	PUNCT
ejpam-5347	195	28	be	be	VERB
ejpam-5347	195	29	a	a	DET
ejpam-5347	195	30	(	(	PUNCT
ejpam-5347	195	31	κ1	κ1	PROPN
ejpam-5347	195	32	×	×	PROPN
ejpam-5347	195	33	υ1	υ1	PROPN
ejpam-5347	195	34	)	)	PUNCT
ejpam-5347	195	35	,	,	PUNCT
ejpam-5347	195	36	(	(	PUNCT
ejpam-5347	195	37	κ2	κ2	NOUN
ejpam-5347	195	38	×	×	NOUN
ejpam-5347	195	39	υ2	υ2	NOUN
ejpam-5347	195	40	)	)	PUNCT
ejpam-5347	195	41	open	open	ADJ
ejpam-5347	195	42	cover	cover	NOUN
ejpam-5347	195	43	ofd	ofd	NOUN
ejpam-5347	195	44	×g	×g	NOUN
ejpam-5347	195	45	,	,	PUNCT
ejpam-5347	195	46	where	where	SCONJ
ejpam-5347	195	47	{	{	PUNCT
ejpam-5347	195	48	kδ	kδ	NOUN
ejpam-5347	195	49	:	:	PUNCT
ejpam-5347	196	1	δ	δ	PROPN
ejpam-5347	196	2	∈	∈	PROPN
ejpam-5347	196	3	ξ	ξ	X
ejpam-5347	196	4	}	}	PUNCT
ejpam-5347	196	5	is	be	AUX
ejpam-5347	196	6	pair−open	pair−open	ADJ
ejpam-5347	196	7	cover	cover	NOUN
ejpam-5347	196	8	of	of	ADP
ejpam-5347	196	9	(	(	PUNCT
ejpam-5347	196	10	d	d	PROPN
ejpam-5347	196	11	,	,	PUNCT
ejpam-5347	196	12	κ1	κ1	NOUN
ejpam-5347	196	13	,	,	PUNCT
ejpam-5347	196	14	κ2	κ2	PROPN
ejpam-5347	196	15	)	)	PUNCT
ejpam-5347	196	16	and	and	CCONJ
ejpam-5347	196	17	{	{	PUNCT
ejpam-5347	196	18	lδ	lδ	X
ejpam-5347	196	19	:	:	PUNCT
ejpam-5347	196	20	δ	δ	PROPN
ejpam-5347	196	21	∈	∈	PROPN
ejpam-5347	196	22	ξ	ξ	X
ejpam-5347	196	23	}	}	PUNCT
ejpam-5347	196	24	is	be	AUX
ejpam-5347	196	25	pair−open	pair−open	ADJ
ejpam-5347	196	26	cover	cover	NOUN
ejpam-5347	196	27	of	of	ADP
ejpam-5347	196	28	(	(	PUNCT
ejpam-5347	196	29	g	g	PROPN
ejpam-5347	196	30	,	,	PUNCT
ejpam-5347	196	31	υ1	υ1	NOUN
ejpam-5347	196	32	,	,	PUNCT
ejpam-5347	196	33	υ2	υ2	PROPN
ejpam-5347	196	34	)	)	PUNCT
ejpam-5347	196	35	.	.	PUNCT
ejpam-5347	197	1	in	in	ADP
ejpam-5347	197	2	a	a	DET
ejpam-5347	197	3	way	way	NOUN
ejpam-5347	197	4	that	that	PRON
ejpam-5347	197	5	p−1(g	p−1(g	NOUN
ejpam-5347	197	6	)	)	PUNCT
ejpam-5347	197	7	=	=	SYM
ejpam-5347	197	8	dg	dg	NOUN
ejpam-5347	198	1	=	=	SYM
ejpam-5347	198	2	d	d	X
ejpam-5347	198	3	×	×	PROPN
ejpam-5347	198	4	{	{	PUNCT
ejpam-5347	198	5	g	g	NOUN
ejpam-5347	198	6	}	}	PUNCT
ejpam-5347	198	7	⊂	⊂	PROPN
ejpam-5347	198	8	n.	n.	NOUN
ejpam-5347	198	9	for	for	ADP
ejpam-5347	198	10	every	every	DET
ejpam-5347	198	11	(	(	PUNCT
ejpam-5347	198	12	d	d	NOUN
ejpam-5347	198	13	,	,	PUNCT
ejpam-5347	198	14	g	g	NOUN
ejpam-5347	198	15	)	)	PUNCT
ejpam-5347	198	16	∈	∈	PROPN
ejpam-5347	199	1	d	d	X
ejpam-5347	199	2	×	×	NOUN
ejpam-5347	199	3	{	{	PUNCT
ejpam-5347	199	4	g	g	NOUN
ejpam-5347	199	5	}	}	PUNCT
ejpam-5347	199	6	.	.	PUNCT
ejpam-5347	200	1	let	let	VERB
ejpam-5347	200	2	jd	jd	PROPN
ejpam-5347	200	3	and	and	CCONJ
ejpam-5347	200	4	jg(d	jg(d	PROPN
ejpam-5347	200	5	)	)	PUNCT
ejpam-5347	200	6	be	be	AUX
ejpam-5347	200	7	a	a	DET
ejpam-5347	200	8	pair−open	pair−open	ADJ
ejpam-5347	200	9	neighborhood	neighborhood	NOUN
ejpam-5347	200	10	of	of	ADP
ejpam-5347	200	11	(	(	PUNCT
ejpam-5347	200	12	d	d	PROPN
ejpam-5347	200	13	,	,	PUNCT
ejpam-5347	200	14	κ1	κ1	NOUN
ejpam-5347	200	15	,	,	PUNCT
ejpam-5347	200	16	κ2	κ2	PROPN
ejpam-5347	200	17	)	)	PUNCT
ejpam-5347	200	18	and	and	CCONJ
ejpam-5347	200	19	(	(	PUNCT
ejpam-5347	200	20	g	g	NOUN
ejpam-5347	200	21	,	,	PUNCT
ejpam-5347	200	22	υ1	υ1	NOUN
ejpam-5347	200	23	,	,	PUNCT
ejpam-5347	200	24	υ2	υ2	PROPN
ejpam-5347	200	25	)	)	PUNCT
ejpam-5347	200	26	,	,	PUNCT
ejpam-5347	200	27	such	such	ADJ
ejpam-5347	200	28	that	that	SCONJ
ejpam-5347	200	29	(	(	PUNCT
ejpam-5347	200	30	d	d	NOUN
ejpam-5347	200	31	,	,	PUNCT
ejpam-5347	200	32	g	g	NOUN
ejpam-5347	200	33	)	)	PUNCT
ejpam-5347	200	34	∈	∈	PROPN
ejpam-5347	200	35	jd	jd	PROPN
ejpam-5347	200	36	×	×	PROPN
ejpam-5347	200	37	jg(d	jg(d	NOUN
ejpam-5347	200	38	)	)	PUNCT
ejpam-5347	201	1	⊂	⊂	PROPN
ejpam-5347	202	1	u.	u.	PROPN
ejpam-5347	202	2	now	now	ADV
ejpam-5347	202	3	{	{	PUNCT
ejpam-5347	202	4	jd	jd	PROPN
ejpam-5347	202	5	:	:	PUNCT
ejpam-5347	202	6	d	d	X
ejpam-5347	202	7	∈	∈	PROPN
ejpam-5347	202	8	d	d	X
ejpam-5347	202	9	}	}	PUNCT
ejpam-5347	202	10	is	be	AUX
ejpam-5347	202	11	pair−open	pair−open	ADJ
ejpam-5347	202	12	cover	cover	NOUN
ejpam-5347	202	13	of	of	ADP
ejpam-5347	202	14	(	(	PUNCT
ejpam-5347	202	15	d	d	PROPN
ejpam-5347	202	16	,	,	PUNCT
ejpam-5347	202	17	κ1	κ1	NOUN
ejpam-5347	202	18	,	,	PUNCT
ejpam-5347	202	19	κ2	κ2	PROPN
ejpam-5347	202	20	)	)	PUNCT
ejpam-5347	202	21	.	.	PUNCT
ejpam-5347	203	1	consequently	consequently	ADV
ejpam-5347	203	2	it	it	PRON
ejpam-5347	203	3	has	have	VERB
ejpam-5347	203	4	a	a	DET
ejpam-5347	203	5	countable	countable	ADJ
ejpam-5347	203	6	subcover	subcover	NOUN
ejpam-5347	203	7	{	{	PUNCT
ejpam-5347	203	8	jdi	jdi	PROPN
ejpam-5347	203	9	}	}	PUNCT
ejpam-5347	203	10	∞	∞	PROPN
ejpam-5347	203	11	i=1	i=1	PROPN
ejpam-5347	203	12	.thus	.thus	ADV
ejpam-5347	203	13	,	,	PUNCT
ejpam-5347	203	14	d×{g	d×{g	ADP
ejpam-5347	203	15	}	}	PUNCT
ejpam-5347	203	16	⊂	⊂	PROPN
ejpam-5347	203	17	∞⋃	∞⋃	PROPN
ejpam-5347	203	18	i=1	i=1	PROPN
ejpam-5347	204	1	jdi	jdi	PROPN
ejpam-5347	204	2	×	×	PROPN
ejpam-5347	204	3	jg(di	jg(di	PROPN
ejpam-5347	204	4	)	)	PUNCT
ejpam-5347	205	1	⊂	⊂	PROPN
ejpam-5347	205	2	n̋.	n̋.	NOUN
ejpam-5347	205	3	let	let	VERB
ejpam-5347	205	4	wg	wg	VERB
ejpam-5347	205	5	=	=	PUNCT
ejpam-5347	205	6	∞⋂	∞⋂	PROPN
ejpam-5347	205	7	i=1	i=1	PROPN
ejpam-5347	205	8	jg(di	jg(di	PROPN
ejpam-5347	205	9	)	)	PUNCT
ejpam-5347	205	10	and	and	CCONJ
ejpam-5347	205	11	w	w	X
ejpam-5347	205	12	=	=	PUNCT
ejpam-5347	205	13	{	{	PUNCT
ejpam-5347	205	14	wg	wg	NOUN
ejpam-5347	205	15	:	:	PUNCT
ejpam-5347	205	16	g	g	PROPN
ejpam-5347	205	17	∈	∈	PROPN
ejpam-5347	205	18	g	g	PROPN
ejpam-5347	205	19	}	}	PUNCT
ejpam-5347	205	20	,	,	PUNCT
ejpam-5347	205	21	then	then	ADV
ejpam-5347	205	22	d	d	X
ejpam-5347	205	23	×	×	PROPN
ejpam-5347	205	24	{	{	PUNCT
ejpam-5347	205	25	g	g	NOUN
ejpam-5347	205	26	}	}	PUNCT
ejpam-5347	205	27	⊂	⊂	PROPN
ejpam-5347	205	28	∞⋃	∞⋃	PROPN
ejpam-5347	205	29	i=1	i=1	PROPN
ejpam-5347	206	1	jdi	jdi	PROPN
ejpam-5347	206	2	×	×	PROPN
ejpam-5347	206	3	gy	gy	PROPN
ejpam-5347	206	4	⊂n̋	⊂n̋	PROPN
ejpam-5347	206	5	and	and	CCONJ
ejpam-5347	206	6	wg	wg	PROPN
ejpam-5347	206	7	is	be	AUX
ejpam-5347	206	8	pair−ω−	pair−ω−	PROPN
ejpam-5347	206	9	open	open	ADJ
ejpam-5347	206	10	set	set	NOUN
ejpam-5347	206	11	,	,	PUNCT
ejpam-5347	206	12	as	as	ADP
ejpam-5347	206	13	of	of	ADP
ejpam-5347	206	14	late	late	ADJ
ejpam-5347	206	15	(	(	PUNCT
ejpam-5347	206	16	g	g	NOUN
ejpam-5347	206	17	,	,	PUNCT
ejpam-5347	206	18	υ1	υ1	NOUN
ejpam-5347	206	19	,	,	PUNCT
ejpam-5347	206	20	υ2	υ2	PROPN
ejpam-5347	206	21	)	)	PUNCT
ejpam-5347	206	22	is	be	AUX
ejpam-5347	206	23	a	a	DET
ejpam-5347	206	24	p̋−space	p̋−space	NOUN
ejpam-5347	206	25	.	.	PUNCT
ejpam-5347	207	1	consequently	consequently	ADV
ejpam-5347	207	2	,	,	PUNCT
ejpam-5347	207	3	for	for	ADP
ejpam-5347	207	4	every	every	DET
ejpam-5347	207	5	g	g	PROPN
ejpam-5347	207	6	∈	∈	PROPN
ejpam-5347	207	7	(	(	PUNCT
ejpam-5347	207	8	g	g	NOUN
ejpam-5347	207	9	,	,	PUNCT
ejpam-5347	207	10	υ1	υ1	NOUN
ejpam-5347	207	11	,	,	PUNCT
ejpam-5347	207	12	υ2	υ2	PROPN
ejpam-5347	207	13	)	)	PUNCT
ejpam-5347	207	14	,	,	PUNCT
ejpam-5347	207	15	there	there	PRON
ejpam-5347	207	16	is	be	VERB
ejpam-5347	207	17	pair−ω−	pair−ω−	PROPN
ejpam-5347	207	18	open	open	ADJ
ejpam-5347	207	19	setwg	setwg	VERB
ejpam-5347	207	20	such	such	ADJ
ejpam-5347	207	21	that	that	SCONJ
ejpam-5347	207	22	g	g	PROPN
ejpam-5347	207	23	∈	∈	PROPN
ejpam-5347	207	24	wg	wg	PROPN
ejpam-5347	207	25	and	and	CCONJ
ejpam-5347	207	26	p−1(g	p−1(g	PROPN
ejpam-5347	207	27	)	)	PUNCT
ejpam-5347	207	28	⊂n̋.	⊂n̋.	PROPN
ejpam-5347	207	29	thus	thus	ADV
ejpam-5347	207	30	,	,	PUNCT
ejpam-5347	207	31	according	accord	VERB
ejpam-5347	207	32	to	to	ADP
ejpam-5347	207	33	theorem	theorem	NOUN
ejpam-5347	207	34	1	1	NUM
ejpam-5347	207	35	,	,	PUNCT
ejpam-5347	207	36	the	the	DET
ejpam-5347	207	37	projection	projection	NOUN
ejpam-5347	207	38	p	p	NOUN
ejpam-5347	207	39	is	be	AUX
ejpam-5347	207	40	a	a	DET
ejpam-5347	207	41	pair−	pair−	NOUN
ejpam-5347	207	42	ω−	ω−	ADP
ejpam-5347	207	43	closed	close	VERB
ejpam-5347	207	44	functions	function	NOUN
ejpam-5347	207	45	.	.	PUNCT
ejpam-5347	208	1	theorem	theorem	ADJ
ejpam-5347	208	2	8	8	NUM
ejpam-5347	208	3	.	.	PUNCT
ejpam-5347	209	1	assume	assume	VERB
ejpam-5347	209	2	(	(	PUNCT
ejpam-5347	209	3	d	d	NOUN
ejpam-5347	209	4	,	,	PUNCT
ejpam-5347	209	5	κ1	κ1	NOUN
ejpam-5347	209	6	,	,	PUNCT
ejpam-5347	209	7	κ2	κ2	PROPN
ejpam-5347	209	8	)	)	PUNCT
ejpam-5347	209	9	is	be	AUX
ejpam-5347	209	10	a	a	DET
ejpam-5347	209	11	s−lindel	s−lindel	PROPN
ejpam-5347	209	12	..	..	PUNCT
ejpam-5347	209	13	of	of	ADP
ejpam-5347	209	14	space	space	NOUN
ejpam-5347	209	15	and	and	CCONJ
ejpam-5347	209	16	(	(	PUNCT
ejpam-5347	209	17	g	g	NOUN
ejpam-5347	209	18	,	,	PUNCT
ejpam-5347	209	19	υ1	υ1	NOUN
ejpam-5347	209	20	,	,	PUNCT
ejpam-5347	209	21	υ2	υ2	PROPN
ejpam-5347	209	22	)	)	PUNCT
ejpam-5347	209	23	be	be	VERB
ejpam-5347	209	24	a	a	DET
ejpam-5347	209	25	p̋−space	p̋−space	NOUN
ejpam-5347	209	26	,	,	PUNCT
ejpam-5347	209	27	subsequent	subsequent	VERB
ejpam-5347	209	28	the	the	DET
ejpam-5347	209	29	projection	projection	NOUN
ejpam-5347	209	30	p	p	NOUN
ejpam-5347	209	31	:	:	PUNCT
ejpam-5347	209	32	(	(	PUNCT
ejpam-5347	209	33	d	d	X
ejpam-5347	209	34	×	×	NOUN
ejpam-5347	209	35	g	g	NOUN
ejpam-5347	209	36	,	,	PUNCT
ejpam-5347	209	37	κ1	κ1	NOUN
ejpam-5347	209	38	×	×	PROPN
ejpam-5347	209	39	υ1	υ1	PROPN
ejpam-5347	209	40	,	,	PUNCT
ejpam-5347	209	41	κ2	κ2	PROPN
ejpam-5347	209	42	×	×	NOUN
ejpam-5347	209	43	υ2	υ2	NOUN
ejpam-5347	209	44	)	)	PUNCT
ejpam-5347	209	45	→	→	SYM
ejpam-5347	209	46	(	(	PUNCT
ejpam-5347	209	47	g	g	NOUN
ejpam-5347	209	48	,	,	PUNCT
ejpam-5347	209	49	υ1	υ1	NOUN
ejpam-5347	209	50	,	,	PUNCT
ejpam-5347	209	51	υ2	υ2	PROPN
ejpam-5347	209	52	)	)	PUNCT
ejpam-5347	209	53	is	be	AUX
ejpam-5347	209	54	s−	s−	PROPN
ejpam-5347	209	55	ω−	ω−	ADP
ejpam-5347	209	56	closed	closed	ADJ
ejpam-5347	209	57	functions	function	NOUN
ejpam-5347	209	58	.	.	PUNCT
ejpam-5347	210	1	proof	proof	NOUN
ejpam-5347	210	2	.	.	PUNCT
ejpam-5347	211	1	the	the	DET
ejpam-5347	211	2	proof	proof	NOUN
ejpam-5347	211	3	use	use	VERB
ejpam-5347	211	4	the	the	DET
ejpam-5347	211	5	same	same	ADJ
ejpam-5347	211	6	methodology	methodology	NOUN
ejpam-5347	211	7	as	as	ADP
ejpam-5347	211	8	theorem	theorem	ADJ
ejpam-5347	211	9	7	7	NUM
ejpam-5347	211	10	.	.	PUNCT
ejpam-5347	211	11	theorem	theorem	NOUN
ejpam-5347	211	12	9	9	NUM
ejpam-5347	211	13	.	.	PUNCT
ejpam-5347	212	1	let	let	VERB
ejpam-5347	212	2	(	(	PUNCT
ejpam-5347	212	3	d	d	NOUN
ejpam-5347	212	4	,	,	PUNCT
ejpam-5347	212	5	κ1	κ1	NOUN
ejpam-5347	212	6	,	,	PUNCT
ejpam-5347	212	7	κ2	κ2	PROPN
ejpam-5347	212	8	)	)	PUNCT
ejpam-5347	212	9	,	,	PUNCT
ejpam-5347	212	10	(	(	PUNCT
ejpam-5347	212	11	g	g	NOUN
ejpam-5347	212	12	,	,	PUNCT
ejpam-5347	212	13	υ1	υ1	PROPN
ejpam-5347	212	14	,	,	PUNCT
ejpam-5347	212	15	υ2	υ2	PROPN
ejpam-5347	212	16	)	)	PUNCT
ejpam-5347	212	17	be	be	VERB
ejpam-5347	212	18	any	any	DET
ejpam-5347	212	19	bitopological	bitopological	ADJ
ejpam-5347	212	20	spaces,(d	spaces,(d	PROPN
ejpam-5347	212	21	,	,	PUNCT
ejpam-5347	212	22	κ1	κ1	NOUN
ejpam-5347	212	23	,	,	PUNCT
ejpam-5347	212	24	κ2	κ2	PROPN
ejpam-5347	212	25	)	)	PUNCT
ejpam-5347	212	26	be	be	AUX
ejpam-5347	212	27	a	a	DET
ejpam-5347	212	28	pair−lindel	pair−lindel	NOUN
ejpam-5347	212	29	..	..	PUNCT
ejpam-5347	212	30	of	of	ADP
ejpam-5347	212	31	space	space	NOUN
ejpam-5347	212	32	and	and	CCONJ
ejpam-5347	212	33	(	(	PUNCT
ejpam-5347	212	34	g	g	NOUN
ejpam-5347	212	35	,	,	PUNCT
ejpam-5347	212	36	υ1	υ1	NOUN
ejpam-5347	212	37	,	,	PUNCT
ejpam-5347	212	38	υ2	υ2	PROPN
ejpam-5347	212	39	)	)	PUNCT
ejpam-5347	212	40	be	be	AUX
ejpam-5347	212	41	a	a	DET
ejpam-5347	212	42	p̋−space	p̋−space	NOUN
ejpam-5347	213	1	then	then	ADV
ejpam-5347	213	2	the	the	DET
ejpam-5347	213	3	projection	projection	NOUN
ejpam-5347	213	4	function	function	NOUN
ejpam-5347	213	5	π	π	NOUN
ejpam-5347	213	6	:	:	PUNCT
ejpam-5347	213	7	(	(	PUNCT
ejpam-5347	213	8	d	d	NOUN
ejpam-5347	213	9	×g	×g	NOUN
ejpam-5347	213	10	,	,	PUNCT
ejpam-5347	213	11	κ1	κ1	NOUN
ejpam-5347	213	12	×	×	PROPN
ejpam-5347	213	13	υ1	υ1	PROPN
ejpam-5347	213	14	,	,	PUNCT
ejpam-5347	213	15	κ2	κ2	PROPN
ejpam-5347	213	16	×	×	NOUN
ejpam-5347	213	17	υ2	υ2	NOUN
ejpam-5347	213	18	)	)	PUNCT
ejpam-5347	213	19	→	→	SYM
ejpam-5347	213	20	(	(	PUNCT
ejpam-5347	213	21	g	g	NOUN
ejpam-5347	213	22	,	,	PUNCT
ejpam-5347	213	23	υ1	υ1	NOUN
ejpam-5347	213	24	,	,	PUNCT
ejpam-5347	213	25	υ2	υ2	PROPN
ejpam-5347	213	26	)	)	PUNCT
ejpam-5347	213	27	is	be	AUX
ejpam-5347	213	28	pair−	pair−	NOUN
ejpam-5347	213	29	ω−closed	ω−close	VERB
ejpam-5347	213	30	.	.	PUNCT
ejpam-5347	214	1	proof	proof	NOUN
ejpam-5347	214	2	.	.	PUNCT
ejpam-5347	215	1	if	if	SCONJ
ejpam-5347	215	2	(	(	PUNCT
ejpam-5347	215	3	d	d	NOUN
ejpam-5347	215	4	,	,	PUNCT
ejpam-5347	215	5	κ1	κ1	NOUN
ejpam-5347	215	6	,	,	PUNCT
ejpam-5347	215	7	κ2	κ2	PROPN
ejpam-5347	215	8	)	)	PUNCT
ejpam-5347	215	9	is	be	AUX
ejpam-5347	215	10	pair−lindel	pair−lindel	NOUN
ejpam-5347	215	11	..	..	PUNCT
ejpam-5347	215	12	of	of	ADP
ejpam-5347	215	13	,	,	PUNCT
ejpam-5347	215	14	then	then	ADV
ejpam-5347	215	15	(	(	PUNCT
ejpam-5347	215	16	d	d	NOUN
ejpam-5347	215	17	,	,	PUNCT
ejpam-5347	215	18	κ1	κ1	NOUN
ejpam-5347	215	19	)	)	PUNCT
ejpam-5347	215	20	is	be	AUX
ejpam-5347	215	21	lindel	lindel	NOUN
ejpam-5347	215	22	..	..	PUNCT
ejpam-5347	215	23	of	of	ADP
ejpam-5347	215	24	and	and	CCONJ
ejpam-5347	215	25	(	(	PUNCT
ejpam-5347	215	26	d	d	PROPN
ejpam-5347	215	27	,	,	PUNCT
ejpam-5347	215	28	κ2	κ2	NOUN
ejpam-5347	215	29	)	)	PUNCT
ejpam-5347	215	30	is	be	AUX
ejpam-5347	215	31	lindel	lindel	NOUN
ejpam-5347	215	32	..	..	PUNCT
ejpam-5347	215	33	of	of	ADP
ejpam-5347	215	34	.	.	PUNCT
ejpam-5347	216	1	consequently	consequently	ADV
ejpam-5347	216	2	,	,	PUNCT
ejpam-5347	216	3	the	the	DET
ejpam-5347	216	4	projection	projection	NOUN
ejpam-5347	216	5	functions	function	NOUN
ejpam-5347	216	6	:	:	PUNCT
ejpam-5347	216	7	π1	π1	NOUN
ejpam-5347	216	8	:	:	PUNCT
ejpam-5347	216	9	(	(	PUNCT
ejpam-5347	216	10	d	d	NOUN
ejpam-5347	216	11	×g	×g	NOUN
ejpam-5347	216	12	,	,	PUNCT
ejpam-5347	216	13	κ1	κ1	NOUN
ejpam-5347	216	14	×υ1	×υ1	PROPN
ejpam-5347	216	15	)	)	PUNCT
ejpam-5347	216	16	→	→	SYM
ejpam-5347	216	17	(	(	PUNCT
ejpam-5347	216	18	g	g	NOUN
ejpam-5347	216	19	,	,	PUNCT
ejpam-5347	216	20	υ1	υ1	PROPN
ejpam-5347	216	21	)	)	PUNCT
ejpam-5347	216	22	,	,	PUNCT
ejpam-5347	216	23	π2	π2	X
ejpam-5347	216	24	:	:	PUNCT
ejpam-5347	216	25	(	(	PUNCT
ejpam-5347	216	26	d	d	NOUN
ejpam-5347	216	27	×g	×g	NOUN
ejpam-5347	216	28	,	,	PUNCT
ejpam-5347	216	29	κ2	κ2	PROPN
ejpam-5347	216	30	×	×	NOUN
ejpam-5347	216	31	υ2	υ2	NOUN
ejpam-5347	216	32	)	)	PUNCT
ejpam-5347	216	33	→	→	SYM
ejpam-5347	216	34	(	(	PUNCT
ejpam-5347	216	35	g	g	NOUN
ejpam-5347	216	36	,	,	PUNCT
ejpam-5347	216	37	υ2	υ2	NOUN
ejpam-5347	216	38	)	)	PUNCT
ejpam-5347	216	39	are	be	AUX
ejpam-5347	216	40	ω−	ω−	ADV
ejpam-5347	216	41	closed	closed	ADJ
ejpam-5347	216	42	.	.	PUNCT
ejpam-5347	217	1	thus	thus	ADV
ejpam-5347	217	2	π	π	X
ejpam-5347	217	3	is	be	AUX
ejpam-5347	217	4	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	217	5	.	.	PUNCT
ejpam-5347	217	6	a.	a.	PROPN
ejpam-5347	217	7	atoom	atoom	PROPN
ejpam-5347	217	8	et	et	PROPN
ejpam-5347	217	9	al	al	PROPN
ejpam-5347	217	10	.	.	PUNCT
ejpam-5347	217	11	/	/	SYM
ejpam-5347	217	12	eur	eur	PROPN
ejpam-5347	217	13	.	.	PUNCT
ejpam-5347	218	1	j.	j.	PROPN
ejpam-5347	218	2	pure	pure	PROPN
ejpam-5347	218	3	appl	appl	PROPN
ejpam-5347	218	4	.	.	PROPN
ejpam-5347	218	5	math	math	PROPN
ejpam-5347	218	6	,	,	PUNCT
ejpam-5347	218	7	17	17	NUM
ejpam-5347	218	8	(	(	PUNCT
ejpam-5347	218	9	4	4	NUM
ejpam-5347	218	10	)	)	PUNCT
ejpam-5347	218	11	(	(	PUNCT
ejpam-5347	218	12	2024	2024	NUM
ejpam-5347	218	13	)	)	PUNCT
ejpam-5347	218	14	,	,	PUNCT
ejpam-5347	218	15	2574	2574	NUM
ejpam-5347	218	16	-	-	SYM
ejpam-5347	218	17	2585	2585	NUM
ejpam-5347	218	18	2582	2582	NUM
ejpam-5347	218	19	theorem	theorem	VERB
ejpam-5347	218	20	10	10	NUM
ejpam-5347	218	21	.	.	PUNCT
ejpam-5347	219	1	let	let	AUX
ejpam-5347	219	2	(	(	PUNCT
ejpam-5347	219	3	d	d	NOUN
ejpam-5347	219	4	,	,	PUNCT
ejpam-5347	219	5	κ1	κ1	NOUN
ejpam-5347	219	6	,	,	PUNCT
ejpam-5347	219	7	κ2	κ2	PROPN
ejpam-5347	219	8	)	)	PUNCT
ejpam-5347	219	9	,	,	PUNCT
ejpam-5347	219	10	(	(	PUNCT
ejpam-5347	219	11	g	g	NOUN
ejpam-5347	219	12	,	,	PUNCT
ejpam-5347	219	13	υ1	υ1	PROPN
ejpam-5347	219	14	,	,	PUNCT
ejpam-5347	219	15	υ2	υ2	PROPN
ejpam-5347	219	16	)	)	PUNCT
ejpam-5347	219	17	be	be	VERB
ejpam-5347	219	18	any	any	DET
ejpam-5347	219	19	bitopological	bitopological	ADJ
ejpam-5347	219	20	spaces	space	NOUN
ejpam-5347	219	21	,	,	PUNCT
ejpam-5347	219	22	(	(	PUNCT
ejpam-5347	219	23	d	d	NOUN
ejpam-5347	219	24	,	,	PUNCT
ejpam-5347	219	25	κ1	κ1	NOUN
ejpam-5347	219	26	,	,	PUNCT
ejpam-5347	219	27	κ2	κ2	PROPN
ejpam-5347	219	28	)	)	PUNCT
ejpam-5347	219	29	be	be	AUX
ejpam-5347	219	30	a	a	DET
ejpam-5347	219	31	s−lindel	s−lindel	PROPN
ejpam-5347	219	32	..	..	PUNCT
ejpam-5347	219	33	of	of	ADP
ejpam-5347	219	34	space	space	NOUN
ejpam-5347	219	35	and	and	CCONJ
ejpam-5347	219	36	(	(	PUNCT
ejpam-5347	219	37	g	g	NOUN
ejpam-5347	219	38	,	,	PUNCT
ejpam-5347	219	39	υ1	υ1	NOUN
ejpam-5347	219	40	,	,	PUNCT
ejpam-5347	219	41	υ2	υ2	PROPN
ejpam-5347	219	42	)	)	PUNCT
ejpam-5347	219	43	be	be	VERB
ejpam-5347	219	44	a	a	DET
ejpam-5347	219	45	p̋−space	p̋−space	NOUN
ejpam-5347	220	1	then	then	ADV
ejpam-5347	220	2	the	the	DET
ejpam-5347	220	3	projection	projection	NOUN
ejpam-5347	220	4	function	function	NOUN
ejpam-5347	220	5	π	π	NOUN
ejpam-5347	220	6	:	:	PUNCT
ejpam-5347	220	7	(	(	PUNCT
ejpam-5347	220	8	d	d	NOUN
ejpam-5347	220	9	×g	×g	NOUN
ejpam-5347	220	10	,	,	PUNCT
ejpam-5347	220	11	κ1	κ1	NOUN
ejpam-5347	220	12	×	×	PROPN
ejpam-5347	220	13	υ1	υ1	PROPN
ejpam-5347	220	14	,	,	PUNCT
ejpam-5347	220	15	κ2	κ2	PROPN
ejpam-5347	220	16	×	×	NOUN
ejpam-5347	220	17	υ2	υ2	NOUN
ejpam-5347	220	18	)	)	PUNCT
ejpam-5347	220	19	→	→	SYM
ejpam-5347	220	20	(	(	PUNCT
ejpam-5347	220	21	g	g	NOUN
ejpam-5347	220	22	,	,	PUNCT
ejpam-5347	220	23	υ1	υ1	NOUN
ejpam-5347	220	24	,	,	PUNCT
ejpam-5347	220	25	υ2	υ2	PROPN
ejpam-5347	220	26	)	)	PUNCT
ejpam-5347	220	27	is	be	AUX
ejpam-5347	220	28	s−	s−	PROPN
ejpam-5347	220	29	ω−closed	ω−close	VERB
ejpam-5347	220	30	.	.	PUNCT
ejpam-5347	221	1	proof	proof	NOUN
ejpam-5347	221	2	.	.	PUNCT
ejpam-5347	222	1	if	if	SCONJ
ejpam-5347	222	2	(	(	PUNCT
ejpam-5347	222	3	g	g	NOUN
ejpam-5347	222	4	,	,	PUNCT
ejpam-5347	222	5	υ1	υ1	NOUN
ejpam-5347	222	6	,	,	PUNCT
ejpam-5347	222	7	υ2	υ2	PROPN
ejpam-5347	222	8	)	)	PUNCT
ejpam-5347	222	9	is	be	AUX
ejpam-5347	222	10	s−lindel	s−lindel	PROPN
ejpam-5347	222	11	..	..	PUNCT
ejpam-5347	222	12	of	of	ADP
ejpam-5347	222	13	,	,	PUNCT
ejpam-5347	222	14	then	then	ADV
ejpam-5347	222	15	(	(	PUNCT
ejpam-5347	222	16	d	d	NOUN
ejpam-5347	222	17	,	,	PUNCT
ejpam-5347	222	18	κ1	κ1	NOUN
ejpam-5347	222	19	)	)	PUNCT
ejpam-5347	222	20	is	be	AUX
ejpam-5347	222	21	lindel	lindel	NOUN
ejpam-5347	222	22	..	..	PUNCT
ejpam-5347	222	23	of	of	ADP
ejpam-5347	222	24	and	and	CCONJ
ejpam-5347	222	25	(	(	PUNCT
ejpam-5347	222	26	d	d	PROPN
ejpam-5347	222	27	,	,	PUNCT
ejpam-5347	222	28	κ2	κ2	NOUN
ejpam-5347	222	29	)	)	PUNCT
ejpam-5347	222	30	is	be	AUX
ejpam-5347	222	31	lindel	lindel	NOUN
ejpam-5347	222	32	..	..	PUNCT
ejpam-5347	222	33	of	of	ADP
ejpam-5347	222	34	.	.	PUNCT
ejpam-5347	223	1	consequently	consequently	ADV
ejpam-5347	223	2	,	,	PUNCT
ejpam-5347	223	3	the	the	DET
ejpam-5347	223	4	projection	projection	NOUN
ejpam-5347	223	5	functions	function	NOUN
ejpam-5347	223	6	:	:	PUNCT
ejpam-5347	223	7	π1	π1	NOUN
ejpam-5347	223	8	:	:	PUNCT
ejpam-5347	223	9	(	(	PUNCT
ejpam-5347	223	10	d	d	NOUN
ejpam-5347	223	11	×g	×g	NOUN
ejpam-5347	223	12	,	,	PUNCT
ejpam-5347	223	13	κ1	κ1	NOUN
ejpam-5347	223	14	×υ1	×υ1	PROPN
ejpam-5347	223	15	)	)	PUNCT
ejpam-5347	223	16	→	→	SYM
ejpam-5347	223	17	(	(	PUNCT
ejpam-5347	223	18	g	g	NOUN
ejpam-5347	223	19	,	,	PUNCT
ejpam-5347	223	20	υ1	υ1	PROPN
ejpam-5347	223	21	)	)	PUNCT
ejpam-5347	223	22	,	,	PUNCT
ejpam-5347	223	23	π2	π2	X
ejpam-5347	223	24	:	:	PUNCT
ejpam-5347	223	25	(	(	PUNCT
ejpam-5347	223	26	d	d	NOUN
ejpam-5347	223	27	×g	×g	NOUN
ejpam-5347	223	28	,	,	PUNCT
ejpam-5347	223	29	κ2	κ2	PROPN
ejpam-5347	223	30	×	×	NOUN
ejpam-5347	223	31	υ2	υ2	NOUN
ejpam-5347	223	32	)	)	PUNCT
ejpam-5347	223	33	→	→	SYM
ejpam-5347	223	34	(	(	PUNCT
ejpam-5347	223	35	g	g	NOUN
ejpam-5347	223	36	,	,	PUNCT
ejpam-5347	223	37	υ2	υ2	NOUN
ejpam-5347	223	38	)	)	PUNCT
ejpam-5347	223	39	are	be	AUX
ejpam-5347	223	40	ω−	ω−	ADV
ejpam-5347	223	41	closed	closed	ADJ
ejpam-5347	223	42	.	.	PUNCT
ejpam-5347	224	1	thus	thus	ADV
ejpam-5347	224	2	π	π	PROPN
ejpam-5347	224	3	is	be	AUX
ejpam-5347	224	4	s−ω−closed	s−ω−close	VERB
ejpam-5347	224	5	.	.	PUNCT
ejpam-5347	225	1	theorem	theorem	VERB
ejpam-5347	225	2	11	11	NUM
ejpam-5347	225	3	.	.	PUNCT
ejpam-5347	226	1	assume	assume	VERB
ejpam-5347	226	2	(	(	PUNCT
ejpam-5347	226	3	g	g	NOUN
ejpam-5347	226	4	,	,	PUNCT
ejpam-5347	226	5	υ1	υ1	PROPN
ejpam-5347	226	6	,	,	PUNCT
ejpam-5347	226	7	υ2	υ2	PROPN
ejpam-5347	226	8	)	)	PUNCT
ejpam-5347	226	9	be	be	VERB
ejpam-5347	226	10	a	a	DET
ejpam-5347	226	11	topological	topological	ADJ
ejpam-5347	226	12	space	space	NOUN
ejpam-5347	226	13	in	in	ADP
ejpam-5347	226	14	which	which	PRON
ejpam-5347	226	15	a	a	DET
ejpam-5347	226	16	fσ−set	fσ−set	NOUN
ejpam-5347	226	17	which	which	PRON
ejpam-5347	226	18	is	be	AUX
ejpam-5347	226	19	not	not	PART
ejpam-5347	226	20	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	226	21	,	,	PUNCT
ejpam-5347	226	22	and	and	CCONJ
ejpam-5347	226	23	(	(	PUNCT
ejpam-5347	226	24	d	d	NOUN
ejpam-5347	226	25	,	,	PUNCT
ejpam-5347	226	26	κ1	κ1	NOUN
ejpam-5347	226	27	,	,	PUNCT
ejpam-5347	226	28	κ2	κ2	PROPN
ejpam-5347	226	29	)	)	PUNCT
ejpam-5347	226	30	be	be	VERB
ejpam-5347	226	31	any	any	DET
ejpam-5347	226	32	bitopological	bitopological	ADJ
ejpam-5347	226	33	space	space	NOUN
ejpam-5347	226	34	.	.	PUNCT
ejpam-5347	227	1	if	if	SCONJ
ejpam-5347	227	2	the	the	DET
ejpam-5347	227	3	projection	projection	NOUN
ejpam-5347	227	4	(	(	PUNCT
ejpam-5347	227	5	d	d	NOUN
ejpam-5347	227	6	×g	×g	NOUN
ejpam-5347	227	7	,	,	PUNCT
ejpam-5347	227	8	κ1	κ1	NOUN
ejpam-5347	227	9	×	×	PROPN
ejpam-5347	227	10	υ1	υ1	PROPN
ejpam-5347	227	11	,	,	PUNCT
ejpam-5347	227	12	κ2	κ2	PROPN
ejpam-5347	227	13	×	×	NOUN
ejpam-5347	227	14	υ2	υ2	NOUN
ejpam-5347	227	15	)	)	PUNCT
ejpam-5347	227	16	→	→	SYM
ejpam-5347	227	17	(	(	PUNCT
ejpam-5347	227	18	g	g	NOUN
ejpam-5347	227	19	,	,	PUNCT
ejpam-5347	227	20	υ1	υ1	NOUN
ejpam-5347	227	21	,	,	PUNCT
ejpam-5347	227	22	υ2	υ2	PROPN
ejpam-5347	227	23	)	)	PUNCT
ejpam-5347	227	24	is	be	AUX
ejpam-5347	227	25	pair−	pair−	NOUN
ejpam-5347	227	26	ω−closed	ω−closed	NUM
ejpam-5347	227	27	,	,	PUNCT
ejpam-5347	227	28	then	then	ADV
ejpam-5347	227	29	(	(	PUNCT
ejpam-5347	227	30	d	d	NOUN
ejpam-5347	227	31	,	,	PUNCT
ejpam-5347	227	32	κ1	κ1	NOUN
ejpam-5347	227	33	,	,	PUNCT
ejpam-5347	227	34	κ2	κ2	PROPN
ejpam-5347	227	35	)	)	PUNCT
ejpam-5347	227	36	is	be	AUX
ejpam-5347	227	37	pair−countably	pair−countably	ADV
ejpam-5347	227	38	compact	compact	ADJ
ejpam-5347	227	39	.	.	PUNCT
ejpam-5347	228	1	proof	proof	NOUN
ejpam-5347	228	2	.	.	PUNCT
ejpam-5347	229	1	assume	assume	VERB
ejpam-5347	229	2	∞⋃	∞⋃	PROPN
ejpam-5347	230	1	i=1	i=1	PROPN
ejpam-5347	231	1	ji	ji	PROPN
ejpam-5347	231	2	is	be	AUX
ejpam-5347	231	3	a	a	DET
ejpam-5347	231	4	pair−f−subset	pair−f−subset	NOUN
ejpam-5347	231	5	of	of	ADP
ejpam-5347	231	6	(	(	PUNCT
ejpam-5347	231	7	g	g	PROPN
ejpam-5347	231	8	,	,	PUNCT
ejpam-5347	231	9	υ1	υ1	NOUN
ejpam-5347	231	10	,	,	PUNCT
ejpam-5347	231	11	υ2	υ2	PROPN
ejpam-5347	231	12	)	)	PUNCT
ejpam-5347	231	13	which	which	PRON
ejpam-5347	231	14	is	be	AUX
ejpam-5347	231	15	not	not	PART
ejpam-5347	231	16	pair−	pair−	NOUN
ejpam-5347	231	17	ω−closed	ω−close	VERB
ejpam-5347	231	18	,	,	PUNCT
ejpam-5347	231	19	and	and	CCONJ
ejpam-5347	231	20	(	(	PUNCT
ejpam-5347	231	21	d	d	NOUN
ejpam-5347	231	22	,	,	PUNCT
ejpam-5347	231	23	κ1	κ1	NOUN
ejpam-5347	231	24	,	,	PUNCT
ejpam-5347	231	25	κ2	κ2	PROPN
ejpam-5347	231	26	)	)	PUNCT
ejpam-5347	231	27	is	be	AUX
ejpam-5347	231	28	not	not	PART
ejpam-5347	231	29	pair−countably	pair−countably	ADV
ejpam-5347	231	30	compact	compact	ADJ
ejpam-5347	231	31	.	.	PUNCT
ejpam-5347	232	1	subsequently	subsequently	ADV
ejpam-5347	232	2	,	,	PUNCT
ejpam-5347	232	3	there	there	ADV
ejpam-5347	232	4	a	a	DET
ejpam-5347	232	5	decreasing	decrease	VERB
ejpam-5347	232	6	pairwise	pairwise	NOUN
ejpam-5347	232	7	sequence	sequence	NOUN
ejpam-5347	232	8	{	{	PUNCT
ejpam-5347	232	9	ki}∞i=1of	ki}∞i=1of	NOUN
ejpam-5347	232	10	pair−closed	pair−close	VERB
ejpam-5347	232	11	subsets	subset	NOUN
ejpam-5347	232	12	of	of	ADP
ejpam-5347	232	13	(	(	PUNCT
ejpam-5347	232	14	d	d	PROPN
ejpam-5347	232	15	,	,	PUNCT
ejpam-5347	232	16	κ1	κ1	NOUN
ejpam-5347	232	17	,	,	PUNCT
ejpam-5347	232	18	κ2	κ2	PROPN
ejpam-5347	232	19	)	)	PUNCT
ejpam-5347	232	20	,	,	PUNCT
ejpam-5347	232	21	in	in	ADP
ejpam-5347	232	22	a	a	DET
ejpam-5347	232	23	manner	manner	NOUN
ejpam-5347	232	24	that	that	PRON
ejpam-5347	232	25	∞⋂	∞⋂	PROPN
ejpam-5347	232	26	i=1	i=1	PROPN
ejpam-5347	232	27	ki	ki	PROPN
ejpam-5347	233	1	=	=	PROPN
ejpam-5347	233	2	ϕ.	ϕ.	PROPN
ejpam-5347	233	3	let	let	VERB
ejpam-5347	233	4	f	f	NOUN
ejpam-5347	233	5	=	=	PUNCT
ejpam-5347	233	6	∞⋃	∞⋃	PROPN
ejpam-5347	233	7	i=1	i=1	X
ejpam-5347	234	1	(	(	PUNCT
ejpam-5347	234	2	ji×ki	ji×ki	PROPN
ejpam-5347	234	3	,	,	PUNCT
ejpam-5347	234	4	κ1	κ1	NOUN
ejpam-5347	234	5	×υ1	×υ1	PROPN
ejpam-5347	234	6	,	,	PUNCT
ejpam-5347	234	7	κ2	κ2	PROPN
ejpam-5347	234	8	×υ2	×υ2	PROPN
ejpam-5347	234	9	)	)	PUNCT
ejpam-5347	234	10	,	,	PUNCT
ejpam-5347	234	11	afterwards	afterwards	ADV
ejpam-5347	234	12	it	it	PRON
ejpam-5347	234	13	is	be	AUX
ejpam-5347	234	14	evident	evident	ADJ
ejpam-5347	234	15	to	to	ADP
ejpam-5347	234	16	us	we	PRON
ejpam-5347	234	17	that	that	SCONJ
ejpam-5347	234	18	f	f	PROPN
ejpam-5347	234	19	is	be	AUX
ejpam-5347	234	20	a	a	DET
ejpam-5347	234	21	pair−closed	pair−close	VERB
ejpam-5347	234	22	subset	subset	NOUN
ejpam-5347	234	23	of	of	ADP
ejpam-5347	234	24	(	(	PUNCT
ejpam-5347	234	25	j	j	PROPN
ejpam-5347	234	26	×k	×k	PROPN
ejpam-5347	234	27	,	,	PUNCT
ejpam-5347	234	28	κ1	κ1	NOUN
ejpam-5347	234	29	×	×	PROPN
ejpam-5347	234	30	υ1	υ1	PROPN
ejpam-5347	234	31	,	,	PUNCT
ejpam-5347	234	32	κ2	κ2	PROPN
ejpam-5347	234	33	×	×	NOUN
ejpam-5347	234	34	υ2	υ2	NOUN
ejpam-5347	234	35	)	)	PUNCT
ejpam-5347	234	36	.	.	PUNCT
ejpam-5347	235	1	likewise	likewise	ADV
ejpam-5347	235	2	for	for	ADP
ejpam-5347	235	3	each	each	PRON
ejpam-5347	235	4	of	of	ADP
ejpam-5347	235	5	the	the	DET
ejpam-5347	235	6	points	point	NOUN
ejpam-5347	235	7	(	(	PUNCT
ejpam-5347	235	8	d	d	NOUN
ejpam-5347	235	9	,	,	PUNCT
ejpam-5347	235	10	g	g	NOUN
ejpam-5347	235	11	)	)	PUNCT
ejpam-5347	235	12	∈	∈	PROPN
ejpam-5347	235	13	(	(	PUNCT
ejpam-5347	235	14	j	j	PROPN
ejpam-5347	235	15	×k	×k	PROPN
ejpam-5347	235	16	,	,	PUNCT
ejpam-5347	235	17	κ1	κ1	NOUN
ejpam-5347	235	18	×	×	PROPN
ejpam-5347	235	19	υ1	υ1	PROPN
ejpam-5347	235	20	,	,	PUNCT
ejpam-5347	235	21	κ2	κ2	PROPN
ejpam-5347	235	22	×	×	NOUN
ejpam-5347	235	23	υ2	υ2	NOUN
ejpam-5347	235	24	)	)	PUNCT
ejpam-5347	235	25	,	,	PUNCT
ejpam-5347	235	26	p(d	p(d	PROPN
ejpam-5347	235	27	,	,	PUNCT
ejpam-5347	235	28	g	g	NOUN
ejpam-5347	235	29	)	)	PUNCT
ejpam-5347	235	30	=	=	PUNCT
ejpam-5347	236	1	g.	g.	PROPN
ejpam-5347	236	2	next	next	ADP
ejpam-5347	236	3	p(f	p(f	PROPN
ejpam-5347	236	4	)	)	PUNCT
ejpam-5347	237	1	=	=	SYM
ejpam-5347	237	2	∞⋃	∞⋃	PROPN
ejpam-5347	237	3	i=1	i=1	PROPN
ejpam-5347	238	1	ji	ji	PROPN
ejpam-5347	238	2	is	be	AUX
ejpam-5347	238	3	not	not	PART
ejpam-5347	238	4	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	238	5	,	,	PUNCT
ejpam-5347	238	6	consequently	consequently	ADV
ejpam-5347	238	7	the	the	DET
ejpam-5347	238	8	projection	projection	NOUN
ejpam-5347	238	9	is	be	AUX
ejpam-5347	238	10	not	not	PART
ejpam-5347	238	11	pair−	pair−	NOUN
ejpam-5347	238	12	ω−closed.thus	ω−closed.thus	NOUN
ejpam-5347	238	13	,	,	PUNCT
ejpam-5347	238	14	the	the	DET
ejpam-5347	238	15	outcome	outcome	NOUN
ejpam-5347	238	16	.	.	PUNCT
ejpam-5347	239	1	corollary	corollary	ADJ
ejpam-5347	239	2	5	5	NUM
ejpam-5347	239	3	.	.	PUNCT
ejpam-5347	240	1	assume	assume	VERB
ejpam-5347	240	2	(	(	PUNCT
ejpam-5347	240	3	g	g	NOUN
ejpam-5347	240	4	,	,	PUNCT
ejpam-5347	240	5	υ1	υ1	PROPN
ejpam-5347	240	6	,	,	PUNCT
ejpam-5347	240	7	υ2	υ2	PROPN
ejpam-5347	240	8	)	)	PUNCT
ejpam-5347	240	9	be	be	VERB
ejpam-5347	240	10	a	a	DET
ejpam-5347	240	11	topological	topological	ADJ
ejpam-5347	240	12	space	space	NOUN
ejpam-5347	240	13	in	in	ADP
ejpam-5347	240	14	which	which	PRON
ejpam-5347	240	15	a	a	DET
ejpam-5347	240	16	fσ−set	fσ−set	NOUN
ejpam-5347	240	17	which	which	PRON
ejpam-5347	240	18	is	be	AUX
ejpam-5347	240	19	not	not	PART
ejpam-5347	240	20	s−ω−closed	s−ω−close	VERB
ejpam-5347	240	21	,	,	PUNCT
ejpam-5347	240	22	and	and	CCONJ
ejpam-5347	240	23	(	(	PUNCT
ejpam-5347	240	24	d	d	NOUN
ejpam-5347	240	25	,	,	PUNCT
ejpam-5347	240	26	κ1	κ1	NOUN
ejpam-5347	240	27	,	,	PUNCT
ejpam-5347	240	28	κ2	κ2	PROPN
ejpam-5347	240	29	)	)	PUNCT
ejpam-5347	240	30	be	be	VERB
ejpam-5347	240	31	any	any	DET
ejpam-5347	240	32	bitopological	bitopological	ADJ
ejpam-5347	240	33	space	space	NOUN
ejpam-5347	240	34	.	.	PUNCT
ejpam-5347	241	1	if	if	SCONJ
ejpam-5347	241	2	the	the	DET
ejpam-5347	241	3	projection	projection	NOUN
ejpam-5347	241	4	(	(	PUNCT
ejpam-5347	241	5	d	d	NOUN
ejpam-5347	241	6	×g	×g	NOUN
ejpam-5347	241	7	,	,	PUNCT
ejpam-5347	241	8	κ1	κ1	NOUN
ejpam-5347	241	9	×	×	PROPN
ejpam-5347	241	10	υ1	υ1	PROPN
ejpam-5347	241	11	,	,	PUNCT
ejpam-5347	241	12	κ2	κ2	PROPN
ejpam-5347	241	13	×	×	NOUN
ejpam-5347	241	14	υ2	υ2	NOUN
ejpam-5347	241	15	)	)	PUNCT
ejpam-5347	241	16	→	→	SYM
ejpam-5347	241	17	(	(	PUNCT
ejpam-5347	241	18	g	g	NOUN
ejpam-5347	241	19	,	,	PUNCT
ejpam-5347	241	20	υ1	υ1	NOUN
ejpam-5347	241	21	,	,	PUNCT
ejpam-5347	241	22	υ2	υ2	PROPN
ejpam-5347	241	23	)	)	PUNCT
ejpam-5347	241	24	is	be	AUX
ejpam-5347	241	25	s−	s−	PROPN
ejpam-5347	241	26	ω−closed	ω−close	VERB
ejpam-5347	241	27	,	,	PUNCT
ejpam-5347	241	28	then	then	ADV
ejpam-5347	241	29	(	(	PUNCT
ejpam-5347	241	30	d	d	NOUN
ejpam-5347	241	31	,	,	PUNCT
ejpam-5347	241	32	κ1	κ1	NOUN
ejpam-5347	241	33	,	,	PUNCT
ejpam-5347	241	34	κ2	κ2	PROPN
ejpam-5347	241	35	)	)	PUNCT
ejpam-5347	241	36	is	be	AUX
ejpam-5347	241	37	s−countably	s−countably	ADV
ejpam-5347	241	38	compact	compact	ADJ
ejpam-5347	241	39	.	.	PUNCT
ejpam-5347	242	1	theorem	theorem	NOUN
ejpam-5347	242	2	12	12	NUM
ejpam-5347	242	3	.	.	PUNCT
ejpam-5347	243	1	a	a	DET
ejpam-5347	243	2	space	space	NOUN
ejpam-5347	243	3	(	(	PUNCT
ejpam-5347	243	4	g	g	NOUN
ejpam-5347	243	5	,	,	PUNCT
ejpam-5347	243	6	υ1	υ1	NOUN
ejpam-5347	243	7	,	,	PUNCT
ejpam-5347	243	8	υ2	υ2	PROPN
ejpam-5347	243	9	)	)	PUNCT
ejpam-5347	243	10	is	be	AUX
ejpam-5347	243	11	p̋−space	p̋−space	NOUN
ejpam-5347	244	1	if	if	SCONJ
ejpam-5347	245	1	and	and	CCONJ
ejpam-5347	245	2	only	only	ADV
ejpam-5347	245	3	if	if	SCONJ
ejpam-5347	245	4	for	for	ADP
ejpam-5347	245	5	pair−lindel	pair−lindel	NOUN
ejpam-5347	245	6	..	..	PUNCT
ejpam-5347	245	7	of	of	ADP
ejpam-5347	245	8	space	space	NOUN
ejpam-5347	245	9	(	(	PUNCT
ejpam-5347	245	10	d	d	NOUN
ejpam-5347	245	11	,	,	PUNCT
ejpam-5347	245	12	κ1	κ1	NOUN
ejpam-5347	245	13	,	,	PUNCT
ejpam-5347	245	14	κ2	κ2	PROPN
ejpam-5347	245	15	)	)	PUNCT
ejpam-5347	245	16	,	,	PUNCT
ejpam-5347	245	17	then	then	ADV
ejpam-5347	245	18	the	the	DET
ejpam-5347	245	19	projection	projection	NOUN
ejpam-5347	245	20	(	(	PUNCT
ejpam-5347	245	21	d	d	NOUN
ejpam-5347	245	22	×g	×g	NOUN
ejpam-5347	245	23	,	,	PUNCT
ejpam-5347	245	24	κ1	κ1	NOUN
ejpam-5347	245	25	×υ1	×υ1	PROPN
ejpam-5347	245	26	,	,	PUNCT
ejpam-5347	245	27	κ2	κ2	PROPN
ejpam-5347	245	28	×υ2	×υ2	PROPN
ejpam-5347	245	29	)	)	PUNCT
ejpam-5347	245	30	→	→	SYM
ejpam-5347	245	31	(	(	PUNCT
ejpam-5347	245	32	g	g	NOUN
ejpam-5347	245	33	,	,	PUNCT
ejpam-5347	245	34	υ1	υ1	NOUN
ejpam-5347	245	35	,	,	PUNCT
ejpam-5347	245	36	υ2	υ2	PROPN
ejpam-5347	245	37	)	)	PUNCT
ejpam-5347	245	38	is	be	AUX
ejpam-5347	245	39	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	245	40	.	.	PUNCT
ejpam-5347	246	1	proof	proof	NOUN
ejpam-5347	246	2	.	.	PUNCT
ejpam-5347	247	1	the	the	DET
ejpam-5347	247	2	requirement	requirement	NOUN
ejpam-5347	247	3	portion	portion	NOUN
ejpam-5347	247	4	is	be	AUX
ejpam-5347	247	5	derived	derive	VERB
ejpam-5347	247	6	from	from	ADP
ejpam-5347	247	7	theorem	theorem	ADJ
ejpam-5347	247	8	7	7	NUM
ejpam-5347	247	9	,	,	PUNCT
ejpam-5347	247	10	as	as	SCONJ
ejpam-5347	247	11	the	the	DET
ejpam-5347	247	12	condition	condition	NOUN
ejpam-5347	247	13	must	must	AUX
ejpam-5347	247	14	be	be	AUX
ejpam-5347	247	15	sufficient	sufficient	ADJ
ejpam-5347	247	16	.	.	PUNCT
ejpam-5347	248	1	presume	presume	VERB
ejpam-5347	248	2	(	(	PUNCT
ejpam-5347	248	3	g	g	NOUN
ejpam-5347	248	4	,	,	PUNCT
ejpam-5347	248	5	υ1	υ1	NOUN
ejpam-5347	248	6	,	,	PUNCT
ejpam-5347	248	7	υ2	υ2	PROPN
ejpam-5347	248	8	)	)	PUNCT
ejpam-5347	248	9	is	be	AUX
ejpam-5347	248	10	not	not	PART
ejpam-5347	248	11	p̋−space	p̋−space	NOUN
ejpam-5347	248	12	.	.	PUNCT
ejpam-5347	249	1	for	for	ADP
ejpam-5347	249	2	any	any	DET
ejpam-5347	249	3	pair−lindel	pair−lindel	NOUN
ejpam-5347	249	4	..	..	PUNCT
ejpam-5347	249	5	of	of	ADP
ejpam-5347	249	6	space	space	NOUN
ejpam-5347	249	7	(	(	PUNCT
ejpam-5347	249	8	d	d	NOUN
ejpam-5347	249	9	,	,	PUNCT
ejpam-5347	249	10	κ1	κ1	NOUN
ejpam-5347	249	11	,	,	PUNCT
ejpam-5347	249	12	κ2	κ2	PROPN
ejpam-5347	249	13	)	)	PUNCT
ejpam-5347	249	14	then	then	ADV
ejpam-5347	249	15	the	the	DET
ejpam-5347	249	16	projection	projection	NOUN
ejpam-5347	249	17	(	(	PUNCT
ejpam-5347	249	18	d	d	NOUN
ejpam-5347	249	19	×	×	NOUN
ejpam-5347	249	20	g	g	NOUN
ejpam-5347	249	21	,	,	PUNCT
ejpam-5347	249	22	κ1	κ1	NOUN
ejpam-5347	249	23	×	×	PROPN
ejpam-5347	249	24	υ1	υ1	PROPN
ejpam-5347	249	25	,	,	PUNCT
ejpam-5347	249	26	κ2	κ2	PROPN
ejpam-5347	249	27	×	×	NOUN
ejpam-5347	249	28	υ2	υ2	NOUN
ejpam-5347	249	29	)	)	PUNCT
ejpam-5347	249	30	→	→	SYM
ejpam-5347	249	31	(	(	PUNCT
ejpam-5347	249	32	g	g	NOUN
ejpam-5347	249	33	,	,	PUNCT
ejpam-5347	249	34	υ1	υ1	NOUN
ejpam-5347	249	35	,	,	PUNCT
ejpam-5347	249	36	υ2	υ2	PROPN
ejpam-5347	249	37	)	)	PUNCT
ejpam-5347	249	38	is	be	AUX
ejpam-5347	249	39	pair−	pair−	NOUN
ejpam-5347	249	40	ω−closed	ω−close	VERB
ejpam-5347	249	41	.	.	PUNCT
ejpam-5347	250	1	let	let	VERB
ejpam-5347	250	2	d	d	NOUN
ejpam-5347	250	3	=	=	SYM
ejpam-5347	250	4	r	r	NOUN
ejpam-5347	250	5	is	be	AUX
ejpam-5347	250	6	the	the	DET
ejpam-5347	250	7	set	set	NOUN
ejpam-5347	250	8	of	of	ADP
ejpam-5347	250	9	real	real	ADJ
ejpam-5347	250	10	numbers	number	NOUN
ejpam-5347	250	11	with	with	ADP
ejpam-5347	250	12	usual	usual	ADJ
ejpam-5347	250	13	topology	topology	NOUN
ejpam-5347	250	14	(	(	PUNCT
ejpam-5347	250	15	r	r	NOUN
ejpam-5347	250	16	,	,	PUNCT
ejpam-5347	250	17	κu	κu	NOUN
ejpam-5347	250	18	,	,	PUNCT
ejpam-5347	250	19	κu	κu	NOUN
ejpam-5347	250	20	)	)	PUNCT
ejpam-5347	250	21	.	.	PUNCT
ejpam-5347	251	1	hence	hence	ADV
ejpam-5347	251	2	by	by	ADP
ejpam-5347	251	3	the	the	DET
ejpam-5347	251	4	earlier	early	ADJ
ejpam-5347	251	5	theorem	theorem	ADJ
ejpam-5347	251	6	,	,	PUNCT
ejpam-5347	251	7	(	(	PUNCT
ejpam-5347	251	8	d	d	NOUN
ejpam-5347	251	9	,	,	PUNCT
ejpam-5347	251	10	κ1	κ1	NOUN
ejpam-5347	251	11	,	,	PUNCT
ejpam-5347	251	12	κ2	κ2	PROPN
ejpam-5347	251	13	)	)	PUNCT
ejpam-5347	251	14	is	be	AUX
ejpam-5347	251	15	pair−coutably	pair−coutably	ADV
ejpam-5347	251	16	compact	compact	ADJ
ejpam-5347	251	17	,	,	PUNCT
ejpam-5347	251	18	it	it	PRON
ejpam-5347	251	19	is	be	AUX
ejpam-5347	251	20	paradoxical	paradoxical	ADJ
ejpam-5347	251	21	.	.	PUNCT
ejpam-5347	252	1	a.	a.	NOUN
ejpam-5347	252	2	atoom	atoom	PROPN
ejpam-5347	252	3	et	et	PROPN
ejpam-5347	252	4	al	al	PROPN
ejpam-5347	252	5	.	.	PUNCT
ejpam-5347	252	6	/	/	SYM
ejpam-5347	252	7	eur	eur	PROPN
ejpam-5347	252	8	.	.	PUNCT
ejpam-5347	253	1	j.	j.	PROPN
ejpam-5347	253	2	pure	pure	PROPN
ejpam-5347	253	3	appl	appl	PROPN
ejpam-5347	253	4	.	.	PROPN
ejpam-5347	253	5	math	math	PROPN
ejpam-5347	253	6	,	,	PUNCT
ejpam-5347	253	7	17	17	NUM
ejpam-5347	253	8	(	(	PUNCT
ejpam-5347	253	9	4	4	NUM
ejpam-5347	253	10	)	)	PUNCT
ejpam-5347	253	11	(	(	PUNCT
ejpam-5347	253	12	2024	2024	NUM
ejpam-5347	253	13	)	)	PUNCT
ejpam-5347	253	14	,	,	PUNCT
ejpam-5347	253	15	2574	2574	NUM
ejpam-5347	253	16	-	-	SYM
ejpam-5347	253	17	2585	2585	NUM
ejpam-5347	253	18	2583	2583	NUM
ejpam-5347	253	19	theorem	theorem	VERB
ejpam-5347	253	20	13	13	NUM
ejpam-5347	253	21	.	.	PUNCT
ejpam-5347	254	1	assume	assume	VERB
ejpam-5347	254	2	(	(	PUNCT
ejpam-5347	254	3	d	d	NOUN
ejpam-5347	254	4	,	,	PUNCT
ejpam-5347	254	5	κ1	κ1	NOUN
ejpam-5347	254	6	,	,	PUNCT
ejpam-5347	254	7	κ2	κ2	PROPN
ejpam-5347	254	8	)	)	PUNCT
ejpam-5347	254	9	,	,	PUNCT
ejpam-5347	254	10	(	(	PUNCT
ejpam-5347	254	11	g	g	NOUN
ejpam-5347	254	12	,	,	PUNCT
ejpam-5347	254	13	υ1	υ1	NOUN
ejpam-5347	254	14	,	,	PUNCT
ejpam-5347	254	15	υ2	υ2	PROPN
ejpam-5347	254	16	)	)	PUNCT
ejpam-5347	254	17	is	be	AUX
ejpam-5347	254	18	any	any	DET
ejpam-5347	254	19	bitopological	bitopological	ADJ
ejpam-5347	254	20	spaces	space	NOUN
ejpam-5347	254	21	with	with	ADP
ejpam-5347	254	22	the	the	DET
ejpam-5347	254	23	property	property	NOUN
ejpam-5347	254	24	that	that	PRON
ejpam-5347	254	25	every	every	DET
ejpam-5347	254	26	pair−lindel	pair−lindel	NOUN
ejpam-5347	254	27	..	..	PUNCT
ejpam-5347	254	28	of	of	ADP
ejpam-5347	254	29	subset	subset	NOUN
ejpam-5347	254	30	is	be	AUX
ejpam-5347	254	31	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	254	32	.	.	PUNCT
ejpam-5347	255	1	when	when	SCONJ
ejpam-5347	255	2	υ	υ	X
ejpam-5347	255	3	:	:	PUNCT
ejpam-5347	255	4	(	(	PUNCT
ejpam-5347	255	5	d	d	NOUN
ejpam-5347	255	6	,	,	PUNCT
ejpam-5347	255	7	κ1	κ1	NOUN
ejpam-5347	255	8	,	,	PUNCT
ejpam-5347	255	9	κ2	κ2	PROPN
ejpam-5347	255	10	)	)	PUNCT
ejpam-5347	255	11	→	→	SYM
ejpam-5347	255	12	(	(	PUNCT
ejpam-5347	255	13	g	g	NOUN
ejpam-5347	255	14	,	,	PUNCT
ejpam-5347	255	15	υ1	υ1	NOUN
ejpam-5347	255	16	,	,	PUNCT
ejpam-5347	255	17	υ2	υ2	PROPN
ejpam-5347	255	18	)	)	PUNCT
ejpam-5347	255	19	is	be	AUX
ejpam-5347	255	20	pair−lindel	pair−lindel	NOUN
ejpam-5347	255	21	..	..	PUNCT
ejpam-5347	256	1	of	of	ADP
ejpam-5347	256	2	,	,	PUNCT
ejpam-5347	256	3	then	then	ADV
ejpam-5347	256	4	υ	υ	PROPN
ejpam-5347	256	5	is	be	AUX
ejpam-5347	256	6	pair−weakly	pair−weakly	ADV
ejpam-5347	256	7	continuous	continuous	ADJ
ejpam-5347	256	8	.	.	PUNCT
ejpam-5347	257	1	proof	proof	NOUN
ejpam-5347	257	2	.	.	PUNCT
ejpam-5347	258	1	let	let	VERB
ejpam-5347	258	2	p1	p1	PROPN
ejpam-5347	258	3	:	:	PUNCT
ejpam-5347	258	4	(	(	PUNCT
ejpam-5347	258	5	d	d	NOUN
ejpam-5347	258	6	×g	×g	NOUN
ejpam-5347	258	7	,	,	PUNCT
ejpam-5347	258	8	κ1	κ1	NOUN
ejpam-5347	258	9	×υ1	×υ1	PROPN
ejpam-5347	258	10	,	,	PUNCT
ejpam-5347	258	11	κ2	κ2	PROPN
ejpam-5347	258	12	×υ2	×υ2	PROPN
ejpam-5347	258	13	)	)	PUNCT
ejpam-5347	258	14	→	→	SYM
ejpam-5347	258	15	(	(	PUNCT
ejpam-5347	258	16	d	d	NOUN
ejpam-5347	258	17	,	,	PUNCT
ejpam-5347	258	18	κ1	κ1	NOUN
ejpam-5347	258	19	,	,	PUNCT
ejpam-5347	258	20	κ2	κ2	PROPN
ejpam-5347	258	21	)	)	PUNCT
ejpam-5347	258	22	,	,	PUNCT
ejpam-5347	258	23	p2	p2	PROPN
ejpam-5347	258	24	:	:	PUNCT
ejpam-5347	258	25	(	(	PUNCT
ejpam-5347	258	26	d	d	NOUN
ejpam-5347	258	27	×g	×g	NOUN
ejpam-5347	258	28	,	,	PUNCT
ejpam-5347	258	29	κ1	κ1	NOUN
ejpam-5347	258	30	×υ1	×υ1	PROPN
ejpam-5347	258	31	,	,	PUNCT
ejpam-5347	258	32	κ2	κ2	PROPN
ejpam-5347	258	33	×υ2	×υ2	PROPN
ejpam-5347	258	34	)	)	PUNCT
ejpam-5347	258	35	→	→	SYM
ejpam-5347	258	36	(	(	PUNCT
ejpam-5347	258	37	g	g	NOUN
ejpam-5347	258	38	,	,	PUNCT
ejpam-5347	258	39	υ1	υ1	NOUN
ejpam-5347	258	40	,	,	PUNCT
ejpam-5347	258	41	υ2	υ2	PROPN
ejpam-5347	258	42	)	)	PUNCT
ejpam-5347	258	43	be	be	VERB
ejpam-5347	258	44	the	the	DET
ejpam-5347	258	45	projections	projection	NOUN
ejpam-5347	258	46	,	,	PUNCT
ejpam-5347	258	47	then	then	ADV
ejpam-5347	258	48	(	(	PUNCT
ejpam-5347	258	49	d	d	NOUN
ejpam-5347	258	50	,	,	PUNCT
ejpam-5347	258	51	κ1	κ1	NOUN
ejpam-5347	258	52	,	,	PUNCT
ejpam-5347	258	53	κ2	κ2	PROPN
ejpam-5347	258	54	)	)	PUNCT
ejpam-5347	258	55	and	and	CCONJ
ejpam-5347	258	56	range	range	VERB
ejpam-5347	258	57	υ	υ	NOUN
ejpam-5347	258	58	of	of	ADP
ejpam-5347	258	59	a	a	DET
ejpam-5347	258	60	pair−lindel	pair−lindel	NOUN
ejpam-5347	258	61	..	..	PUNCT
ejpam-5347	258	62	of	of	ADP
ejpam-5347	258	63	set	set	NOUN
ejpam-5347	258	64	as	as	ADP
ejpam-5347	258	65	images	image	NOUN
ejpam-5347	258	66	of	of	ADP
ejpam-5347	258	67	pair−lindel	pair−lindel	NOUN
ejpam-5347	258	68	..	..	PUNCT
ejpam-5347	258	69	of	of	ADP
ejpam-5347	258	70	sets	set	NOUN
ejpam-5347	258	71	under	under	ADP
ejpam-5347	258	72	p1and	p1and	NUM
ejpam-5347	259	1	p2.let	p2.let	PROPN
ejpam-5347	259	2	z∗	z∗	NOUN
ejpam-5347	259	3	1	1	NUM
ejpam-5347	259	4	=	=	PUNCT
ejpam-5347	259	5	p1\υ	p1\υ	NOUN
ejpam-5347	259	6	.	.	PUNCT
ejpam-5347	260	1	ensure	ensure	VERB
ejpam-5347	260	2	that	that	SCONJ
ejpam-5347	260	3	z∗	z∗	NOUN
ejpam-5347	260	4	1	1	NUM
ejpam-5347	260	5	is	be	AUX
ejpam-5347	260	6	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	260	7	.	.	PUNCT
ejpam-5347	261	1	actually	actually	ADV
ejpam-5347	261	2	,	,	PUNCT
ejpam-5347	261	3	if	if	SCONJ
ejpam-5347	261	4	t	t	PROPN
ejpam-5347	261	5	is	be	AUX
ejpam-5347	261	6	pair−closed	pair−close	VERB
ejpam-5347	261	7	,	,	PUNCT
ejpam-5347	261	8	then	then	ADV
ejpam-5347	261	9	t	t	PROPN
ejpam-5347	261	10	is	be	AUX
ejpam-5347	261	11	pair−lindel	pair−lindel	NOUN
ejpam-5347	261	12	..	..	PUNCT
ejpam-5347	261	13	of	of	ADP
ejpam-5347	261	14	,	,	PUNCT
ejpam-5347	261	15	z∗	z∗	PROPN
ejpam-5347	261	16	1	1	NUM
ejpam-5347	261	17	(	(	PUNCT
ejpam-5347	261	18	t	t	PROPN
ejpam-5347	261	19	)	)	PUNCT
ejpam-5347	261	20	is	be	AUX
ejpam-5347	261	21	pair−lindel	pair−lindel	NOUN
ejpam-5347	261	22	..	..	PUNCT
ejpam-5347	262	1	of	of	ADP
ejpam-5347	262	2	.	.	PUNCT
ejpam-5347	263	1	therefore	therefore	ADV
ejpam-5347	263	2	,	,	PUNCT
ejpam-5347	263	3	it	it	PRON
ejpam-5347	263	4	is	be	AUX
ejpam-5347	263	5	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	263	6	.	.	PUNCT
ejpam-5347	264	1	since	since	SCONJ
ejpam-5347	264	2	υ	υ	PROPN
ejpam-5347	264	3	is	be	AUX
ejpam-5347	264	4	a	a	DET
ejpam-5347	264	5	function	function	NOUN
ejpam-5347	264	6	defined	define	VERB
ejpam-5347	264	7	on	on	ADP
ejpam-5347	264	8	(	(	PUNCT
ejpam-5347	264	9	d	d	NOUN
ejpam-5347	264	10	,	,	PUNCT
ejpam-5347	264	11	κ1	κ1	NOUN
ejpam-5347	264	12	,	,	PUNCT
ejpam-5347	264	13	κ2	κ2	PROPN
ejpam-5347	264	14	)	)	PUNCT
ejpam-5347	264	15	,	,	PUNCT
ejpam-5347	264	16	z∗	z∗	NOUN
ejpam-5347	264	17	1	1	NUM
ejpam-5347	264	18	is	be	AUX
ejpam-5347	264	19	a	a	DET
ejpam-5347	264	20	bijection	bijection	NOUN
ejpam-5347	264	21	onto	onto	ADP
ejpam-5347	264	22	(	(	PUNCT
ejpam-5347	264	23	d	d	NOUN
ejpam-5347	264	24	,	,	PUNCT
ejpam-5347	264	25	κ1	κ1	NOUN
ejpam-5347	264	26	,	,	PUNCT
ejpam-5347	264	27	κ2).this	κ2).this	PRON
ejpam-5347	264	28	combined	combine	VERB
ejpam-5347	264	29	with	with	ADP
ejpam-5347	264	30	reality	reality	NOUN
ejpam-5347	264	31	that	that	SCONJ
ejpam-5347	264	32	z∗	z∗	NOUN
ejpam-5347	264	33	1	1	NUM
ejpam-5347	264	34	is	be	AUX
ejpam-5347	264	35	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	264	36	,	,	PUNCT
ejpam-5347	264	37	means	mean	VERB
ejpam-5347	264	38	that	that	SCONJ
ejpam-5347	264	39	for	for	SCONJ
ejpam-5347	264	40	each	each	DET
ejpam-5347	264	41	pair−open	pair−open	NOUN
ejpam-5347	264	42	set	set	VERB
ejpam-5347	264	43	v	v	ADP
ejpam-5347	264	44	,	,	PUNCT
ejpam-5347	264	45	z∗	z∗	NOUN
ejpam-5347	264	46	1	1	NUM
ejpam-5347	264	47	(	(	PUNCT
ejpam-5347	264	48	v	v	NOUN
ejpam-5347	264	49	)	)	PUNCT
ejpam-5347	264	50	is	be	AUX
ejpam-5347	264	51	pair−ω−open	pair−ω−open	VERB
ejpam-5347	264	52	in	in	ADP
ejpam-5347	264	53	(	(	PUNCT
ejpam-5347	264	54	d	d	NOUN
ejpam-5347	264	55	,	,	PUNCT
ejpam-5347	264	56	κ1	κ1	NOUN
ejpam-5347	264	57	,	,	PUNCT
ejpam-5347	264	58	κ2	κ2	PROPN
ejpam-5347	264	59	)	)	PUNCT
ejpam-5347	264	60	.	.	PUNCT
ejpam-5347	265	1	presently	presently	ADV
ejpam-5347	265	2	υ	υ	NOUN
ejpam-5347	265	3	=	=	NOUN
ejpam-5347	265	4	p2	p2	PROPN
ejpam-5347	265	5	◦	◦	NOUN
ejpam-5347	265	6	z∗−1	z∗−1	PROPN
ejpam-5347	265	7	1	1	NUM
ejpam-5347	265	8	.υ	.υ	NOUN
ejpam-5347	265	9	thus	thus	ADV
ejpam-5347	265	10	possesses	possess	VERB
ejpam-5347	265	11	the	the	DET
ejpam-5347	265	12	necessary	necessary	ADJ
ejpam-5347	265	13	attribute	attribute	NOUN
ejpam-5347	265	14	.	.	PUNCT
ejpam-5347	266	1	corollary	corollary	ADJ
ejpam-5347	266	2	6	6	NUM
ejpam-5347	266	3	.	.	PUNCT
ejpam-5347	267	1	let	let	AUX
ejpam-5347	267	2	(	(	PUNCT
ejpam-5347	267	3	d	d	NOUN
ejpam-5347	267	4	,	,	PUNCT
ejpam-5347	267	5	κ1	κ1	NOUN
ejpam-5347	267	6	,	,	PUNCT
ejpam-5347	267	7	κ2	κ2	PROPN
ejpam-5347	267	8	)	)	PUNCT
ejpam-5347	267	9	be	be	AUX
ejpam-5347	267	10	a	a	DET
ejpam-5347	267	11	pair−lindel	pair−lindel	NOUN
ejpam-5347	267	12	..	..	PUNCT
ejpam-5347	267	13	of	of	ADP
ejpam-5347	267	14	space	space	NOUN
ejpam-5347	267	15	and	and	CCONJ
ejpam-5347	267	16	(	(	PUNCT
ejpam-5347	267	17	g	g	NOUN
ejpam-5347	267	18	,	,	PUNCT
ejpam-5347	267	19	υ1	υ1	NOUN
ejpam-5347	267	20	,	,	PUNCT
ejpam-5347	267	21	υ2	υ2	PROPN
ejpam-5347	267	22	)	)	PUNCT
ejpam-5347	267	23	be	be	VERB
ejpam-5347	267	24	a	a	DET
ejpam-5347	267	25	p̋−space	p̋−space	NOUN
ejpam-5347	267	26	.	.	PUNCT
ejpam-5347	268	1	therefore	therefore	ADV
ejpam-5347	268	2	the	the	DET
ejpam-5347	268	3	subsequent	subsequent	ADJ
ejpam-5347	268	4	statement	statement	NOUN
ejpam-5347	268	5	is	be	AUX
ejpam-5347	268	6	true	true	ADJ
ejpam-5347	268	7	:	:	PUNCT
ejpam-5347	268	8	(	(	PUNCT
ejpam-5347	268	9	i	i	NOUN
ejpam-5347	268	10	)	)	PUNCT
ejpam-5347	268	11	(	(	PUNCT
ejpam-5347	268	12	d	d	NOUN
ejpam-5347	268	13	×g	×g	NOUN
ejpam-5347	268	14	,	,	PUNCT
ejpam-5347	268	15	κ1	κ1	NOUN
ejpam-5347	268	16	×	×	PROPN
ejpam-5347	268	17	υ1	υ1	PROPN
ejpam-5347	268	18	,	,	PUNCT
ejpam-5347	268	19	κ2	κ2	PROPN
ejpam-5347	268	20	×	×	NOUN
ejpam-5347	268	21	υ2	υ2	NOUN
ejpam-5347	268	22	)	)	PUNCT
ejpam-5347	268	23	is	be	AUX
ejpam-5347	268	24	pair−lindel	pair−lindel	NOUN
ejpam-5347	268	25	..	..	PUNCT
ejpam-5347	268	26	of	of	ADP
ejpam-5347	268	27	if	if	SCONJ
ejpam-5347	268	28	and	and	CCONJ
ejpam-5347	268	29	only	only	ADV
ejpam-5347	268	30	if	if	SCONJ
ejpam-5347	268	31	(	(	PUNCT
ejpam-5347	268	32	g	g	NOUN
ejpam-5347	268	33	,	,	PUNCT
ejpam-5347	268	34	υ1	υ1	NOUN
ejpam-5347	268	35	,	,	PUNCT
ejpam-5347	268	36	υ2	υ2	PROPN
ejpam-5347	268	37	)	)	PUNCT
ejpam-5347	268	38	is	be	AUX
ejpam-5347	268	39	indeed	indeed	ADV
ejpam-5347	268	40	,	,	PUNCT
ejpam-5347	268	41	(	(	PUNCT
ejpam-5347	268	42	ii	ii	NOUN
ejpam-5347	268	43	)	)	PUNCT
ejpam-5347	268	44	(	(	PUNCT
ejpam-5347	268	45	d	d	NOUN
ejpam-5347	268	46	×g	×g	NOUN
ejpam-5347	268	47	,	,	PUNCT
ejpam-5347	268	48	κ1	κ1	NOUN
ejpam-5347	268	49	×	×	PROPN
ejpam-5347	268	50	υ1	υ1	PROPN
ejpam-5347	268	51	,	,	PUNCT
ejpam-5347	268	52	κ2	κ2	PROPN
ejpam-5347	268	53	×	×	NOUN
ejpam-5347	268	54	υ2	υ2	NOUN
ejpam-5347	268	55	)	)	PUNCT
ejpam-5347	268	56	is	be	AUX
ejpam-5347	268	57	pair−paracompact	pair−paracompact	NOUN
ejpam-5347	268	58	if	if	SCONJ
ejpam-5347	268	59	and	and	CCONJ
ejpam-5347	268	60	only	only	ADV
ejpam-5347	268	61	if	if	SCONJ
ejpam-5347	268	62	(	(	PUNCT
ejpam-5347	268	63	g	g	NOUN
ejpam-5347	268	64	,	,	PUNCT
ejpam-5347	268	65	υ1	υ1	NOUN
ejpam-5347	268	66	,	,	PUNCT
ejpam-5347	268	67	υ2	υ2	PROPN
ejpam-5347	268	68	)	)	PUNCT
ejpam-5347	268	69	is	be	AUX
ejpam-5347	268	70	so	so	ADV
ejpam-5347	268	71	.	.	PUNCT
ejpam-5347	269	1	5	5	X
ejpam-5347	269	2	.	.	X
ejpam-5347	269	3	some	some	DET
ejpam-5347	269	4	counter	counter	ADJ
ejpam-5347	269	5	examples	example	NOUN
ejpam-5347	269	6	we	we	PRON
ejpam-5347	269	7	go	go	VERB
ejpam-5347	269	8	over	over	ADP
ejpam-5347	269	9	a	a	DET
ejpam-5347	269	10	number	number	NOUN
ejpam-5347	269	11	of	of	ADP
ejpam-5347	269	12	counterexamples	counterexample	NOUN
ejpam-5347	269	13	in	in	ADP
ejpam-5347	269	14	this	this	DET
ejpam-5347	269	15	section	section	NOUN
ejpam-5347	269	16	that	that	PRON
ejpam-5347	269	17	are	be	AUX
ejpam-5347	269	18	pertinent	pertinent	ADJ
ejpam-5347	269	19	to	to	ADP
ejpam-5347	269	20	the	the	DET
ejpam-5347	269	21	definitions	definition	NOUN
ejpam-5347	269	22	and	and	CCONJ
ejpam-5347	269	23	theorems	theorem	NOUN
ejpam-5347	269	24	in	in	ADP
ejpam-5347	269	25	the	the	DET
ejpam-5347	269	26	preceding	precede	VERB
ejpam-5347	269	27	sections	section	NOUN
ejpam-5347	269	28	.	.	PUNCT
ejpam-5347	270	1	we	we	PRON
ejpam-5347	270	2	will	will	AUX
ejpam-5347	270	3	begin	begin	VERB
ejpam-5347	270	4	with	with	ADP
ejpam-5347	270	5	some	some	DET
ejpam-5347	270	6	instances	instance	NOUN
ejpam-5347	270	7	pertaining	pertain	VERB
ejpam-5347	270	8	to	to	ADP
ejpam-5347	270	9	the	the	DET
ejpam-5347	270	10	pair−ω−	pair−ω−	PROPN
ejpam-5347	270	11	closed	close	VERB
ejpam-5347	270	12	functions	function	NOUN
ejpam-5347	270	13	.	.	PUNCT
ejpam-5347	271	1	example	example	NOUN
ejpam-5347	271	2	2	2	NUM
ejpam-5347	271	3	.	.	PUNCT
ejpam-5347	272	1	let	let	VERB
ejpam-5347	272	2	υbe	υbe	NOUN
ejpam-5347	272	3	functioning	function	VERB
ejpam-5347	272	4	from	from	ADP
ejpam-5347	272	5	a	a	DET
ejpam-5347	272	6	discrete	discrete	ADJ
ejpam-5347	272	7	countable	countable	ADJ
ejpam-5347	272	8	space	space	NOUN
ejpam-5347	272	9	(	(	PUNCT
ejpam-5347	272	10	d	d	NOUN
ejpam-5347	272	11	,	,	PUNCT
ejpam-5347	272	12	κ1	κ1	NOUN
ejpam-5347	272	13	,	,	PUNCT
ejpam-5347	272	14	κ2	κ2	PROPN
ejpam-5347	272	15	)	)	PUNCT
ejpam-5347	272	16	onto	onto	ADP
ejpam-5347	272	17	the	the	DET
ejpam-5347	272	18	space	space	NOUN
ejpam-5347	272	19	of	of	ADP
ejpam-5347	272	20	rationals	rational	NOUN
ejpam-5347	272	21	(	(	PUNCT
ejpam-5347	272	22	g	g	NOUN
ejpam-5347	272	23	,	,	PUNCT
ejpam-5347	272	24	υ1	υ1	PROPN
ejpam-5347	272	25	,	,	PUNCT
ejpam-5347	272	26	υ2).next	υ2).next	PROPN
ejpam-5347	272	27	,	,	PUNCT
ejpam-5347	272	28	υis	υis	X
ejpam-5347	272	29	a	a	DET
ejpam-5347	272	30	pair−continuous	pair−continuous	ADJ
ejpam-5347	272	31	pair−ω−closed	pair−ω−closed	PROPN
ejpam-5347	272	32	function	function	NOUN
ejpam-5347	272	33	.	.	PUNCT
ejpam-5347	273	1	but	but	CCONJ
ejpam-5347	273	2	still	still	ADV
ejpam-5347	273	3	υ	υ	PROPN
ejpam-5347	273	4	is	be	AUX
ejpam-5347	273	5	not	not	PART
ejpam-5347	273	6	pair−closed	pair−close	VERB
ejpam-5347	273	7	.	.	PUNCT
ejpam-5347	274	1	additionally	additionally	ADV
ejpam-5347	274	2	,	,	PUNCT
ejpam-5347	274	3	for	for	ADP
ejpam-5347	274	4	every	every	DET
ejpam-5347	274	5	g	g	NOUN
ejpam-5347	274	6	in	in	ADP
ejpam-5347	274	7	(	(	PUNCT
ejpam-5347	274	8	g	g	NOUN
ejpam-5347	274	9	,	,	PUNCT
ejpam-5347	274	10	υ1	υ1	PROPN
ejpam-5347	274	11	,	,	PUNCT
ejpam-5347	274	12	υ2),υ	υ2),υ	PROPN
ejpam-5347	274	13	−1(g	−1(g	NOUN
ejpam-5347	274	14	)	)	PUNCT
ejpam-5347	274	15	is	be	AUX
ejpam-5347	274	16	pair−lindel	pair−lindel	NOUN
ejpam-5347	274	17	..	..	PUNCT
ejpam-5347	274	18	of	of	ADP
ejpam-5347	274	19	.	.	PUNCT
ejpam-5347	275	1	additionally	additionally	ADV
ejpam-5347	275	2	(	(	PUNCT
ejpam-5347	275	3	d	d	NOUN
ejpam-5347	275	4	,	,	PUNCT
ejpam-5347	275	5	κ1	κ1	NOUN
ejpam-5347	275	6	,	,	PUNCT
ejpam-5347	275	7	κ2	κ2	PROPN
ejpam-5347	275	8	)	)	PUNCT
ejpam-5347	275	9	,	,	PUNCT
ejpam-5347	275	10	(	(	PUNCT
ejpam-5347	275	11	g	g	NOUN
ejpam-5347	275	12	,	,	PUNCT
ejpam-5347	275	13	υ1	υ1	NOUN
ejpam-5347	275	14	,	,	PUNCT
ejpam-5347	275	15	υ2	υ2	PROPN
ejpam-5347	275	16	)	)	PUNCT
ejpam-5347	275	17	are	be	AUX
ejpam-5347	275	18	a	a	DET
ejpam-5347	275	19	pair−lindel	pair−lindel	NOUN
ejpam-5347	275	20	..	..	PUNCT
ejpam-5347	275	21	of	of	ADP
ejpam-5347	275	22	spaces	space	NOUN
ejpam-5347	275	23	,	,	PUNCT
ejpam-5347	275	24	therefore	therefore	ADV
ejpam-5347	275	25	pair−paracompact	pair−paracompact	NOUN
ejpam-5347	275	26	spaces	space	NOUN
ejpam-5347	275	27	.	.	PUNCT
ejpam-5347	276	1	theorem	theorem	NOUN
ejpam-5347	276	2	3	3	NUM
ejpam-5347	276	3	is	be	AUX
ejpam-5347	276	4	therefore	therefore	ADV
ejpam-5347	276	5	more	more	ADV
ejpam-5347	276	6	generic	generic	ADJ
ejpam-5347	276	7	than	than	ADP
ejpam-5347	276	8	the	the	DET
ejpam-5347	276	9	one	one	NOUN
ejpam-5347	276	10	that	that	PRON
ejpam-5347	276	11	presumes	presume	VERB
ejpam-5347	276	12	the	the	DET
ejpam-5347	276	13	function	function	NOUN
ejpam-5347	276	14	to	to	PART
ejpam-5347	276	15	be	be	AUX
ejpam-5347	276	16	pair−closed	pair−close	VERB
ejpam-5347	276	17	.	.	PUNCT
ejpam-5347	277	1	in	in	ADP
ejpam-5347	277	2	connection	connection	NOUN
ejpam-5347	277	3	theorem	theorem	VERB
ejpam-5347	277	4	13	13	NUM
ejpam-5347	277	5	,	,	PUNCT
ejpam-5347	277	6	the	the	DET
ejpam-5347	277	7	example	example	NOUN
ejpam-5347	277	8	that	that	PRON
ejpam-5347	277	9	follows	follow	VERB
ejpam-5347	277	10	is	be	AUX
ejpam-5347	277	11	examined	examine	VERB
ejpam-5347	277	12	.	.	PUNCT
ejpam-5347	278	1	example	example	NOUN
ejpam-5347	279	1	3	3	X
ejpam-5347	279	2	.	.	X
ejpam-5347	280	1	assume	assume	VERB
ejpam-5347	280	2	s	s	PRON
ejpam-5347	280	3	be	be	AUX
ejpam-5347	280	4	the	the	DET
ejpam-5347	280	5	sorgenfry	sorgenfry	ADJ
ejpam-5347	280	6	line	line	NOUN
ejpam-5347	280	7	and	and	CCONJ
ejpam-5347	280	8	the	the	DET
ejpam-5347	280	9	sorgenfry	sorgenfry	ADJ
ejpam-5347	280	10	plane	plane	NOUN
ejpam-5347	280	11	s	s	PART
ejpam-5347	280	12	×	×	PROPN
ejpam-5347	280	13	s.	s.	PROPN
ejpam-5347	280	14	it	it	PRON
ejpam-5347	280	15	is	be	AUX
ejpam-5347	280	16	aware	aware	ADJ
ejpam-5347	280	17	of	of	ADP
ejpam-5347	280	18	this	this	PRON
ejpam-5347	280	19	(	(	PUNCT
ejpam-5347	280	20	r	r	NOUN
ejpam-5347	280	21	,	,	PUNCT
ejpam-5347	280	22	κs	κs	NOUN
ejpam-5347	280	23	,	,	PUNCT
ejpam-5347	280	24	κs	κs	NOUN
ejpam-5347	280	25	)	)	PUNCT
ejpam-5347	281	1	is	be	AUX
ejpam-5347	281	2	pair−lindel	pair−lindel	NOUN
ejpam-5347	281	3	..	..	PUNCT
ejpam-5347	281	4	of	of	ADP
ejpam-5347	281	5	spaces	space	NOUN
ejpam-5347	281	6	,	,	PUNCT
ejpam-5347	281	7	therefore	therefore	ADV
ejpam-5347	281	8	pair−paracompact	pair−paracompact	NOUN
ejpam-5347	281	9	spaces	space	NOUN
ejpam-5347	281	10	.	.	PUNCT
ejpam-5347	282	1	however	however	ADV
ejpam-5347	282	2	s	s	AUX
ejpam-5347	282	3	×	×	PROPN
ejpam-5347	282	4	s	s	VERB
ejpam-5347	282	5	is	be	AUX
ejpam-5347	282	6	not	not	PART
ejpam-5347	282	7	pair−normal	pair−normal	ADJ
ejpam-5347	282	8	so	so	ADV
ejpam-5347	282	9	it	it	PRON
ejpam-5347	282	10	is	be	AUX
ejpam-5347	282	11	not	not	PART
ejpam-5347	282	12	pair−paracompact	pair−paracompact	ADJ
ejpam-5347	282	13	.	.	PUNCT
ejpam-5347	283	1	example	example	NOUN
ejpam-5347	284	1	4	4	NUM
ejpam-5347	284	2	.	.	PUNCT
ejpam-5347	285	1	we	we	PRON
ejpam-5347	285	2	are	be	AUX
ejpam-5347	285	3	going	go	VERB
ejpam-5347	285	4	to	to	PART
ejpam-5347	285	5	concentrate	concentrate	VERB
ejpam-5347	285	6	on	on	ADP
ejpam-5347	285	7	p̋−space	p̋−space	NOUN
ejpam-5347	285	8	.	.	PUNCT
ejpam-5347	286	1	pay	pay	VERB
ejpam-5347	286	2	attention	attention	NOUN
ejpam-5347	286	3	to	to	ADP
ejpam-5347	286	4	any	any	DET
ejpam-5347	286	5	space	space	NOUN
ejpam-5347	286	6	lacking	lack	VERB
ejpam-5347	286	7	a	a	DET
ejpam-5347	286	8	condensation	condensation	NOUN
ejpam-5347	286	9	point	point	NOUN
ejpam-5347	286	10	is	be	AUX
ejpam-5347	286	11	a	a	DET
ejpam-5347	286	12	p̋−space	p̋−space	NOUN
ejpam-5347	286	13	,	,	PUNCT
ejpam-5347	286	14	but	but	CCONJ
ejpam-5347	286	15	not	not	PART
ejpam-5347	286	16	a	a	DET
ejpam-5347	286	17	pair−space	pair−space	NOUN
ejpam-5347	286	18	.	.	PUNCT
ejpam-5347	287	1	considering	consider	VERB
ejpam-5347	287	2	the	the	DET
ejpam-5347	287	3	foregoing	foregoing	NOUN
ejpam-5347	287	4	,	,	PUNCT
ejpam-5347	287	5	any	any	DET
ejpam-5347	287	6	countable	countable	ADJ
ejpam-5347	287	7	space	space	NOUN
ejpam-5347	287	8	is	be	AUX
ejpam-5347	287	9	a	a	DET
ejpam-5347	287	10	p̋−space	p̋−space	NOUN
ejpam-5347	287	11	.	.	PUNCT
ejpam-5347	288	1	as	as	ADP
ejpam-5347	288	2	an	an	DET
ejpam-5347	288	3	illustration	illustration	NOUN
ejpam-5347	288	4	of	of	ADP
ejpam-5347	288	5	uncountable	uncountable	ADJ
ejpam-5347	288	6	p̋−space	p̋−space	NOUN
ejpam-5347	288	7	n	n	ADP
ejpam-5347	288	8	∪	∪	NOUN
ejpam-5347	288	9	r	r	NOUN
ejpam-5347	288	10	,	,	PUNCT
ejpam-5347	288	11	that	that	PRON
ejpam-5347	288	12	is	be	AUX
ejpam-5347	288	13	first	first	ADV
ejpam-5347	288	14	countable	countable	ADJ
ejpam-5347	288	15	,	,	PUNCT
ejpam-5347	288	16	locally	locally	ADV
ejpam-5347	288	17	compact	compact	ADJ
ejpam-5347	288	18	and	and	CCONJ
ejpam-5347	288	19	0−dimensional	0−dimensional	ADJ
ejpam-5347	288	20	,	,	PUNCT
ejpam-5347	288	21	however	however	ADV
ejpam-5347	288	22	,	,	PUNCT
ejpam-5347	288	23	it	it	PRON
ejpam-5347	288	24	lacks	lack	VERB
ejpam-5347	288	25	condensation	condensation	NOUN
ejpam-5347	288	26	point	point	NOUN
ejpam-5347	288	27	.	.	PUNCT
ejpam-5347	289	1	consequently	consequently	ADV
ejpam-5347	289	2	it	it	PRON
ejpam-5347	289	3	is	be	AUX
ejpam-5347	289	4	p̋−space	p̋−space	NOUN
ejpam-5347	289	5	though	though	SCONJ
ejpam-5347	289	6	not	not	PART
ejpam-5347	289	7	a	a	DET
ejpam-5347	289	8	pair−space	pair−space	NOUN
ejpam-5347	289	9	.	.	PUNCT
ejpam-5347	290	1	references	reference	NOUN
ejpam-5347	290	2	2584	2584	NUM
ejpam-5347	290	3	6	6	NUM
ejpam-5347	290	4	.	.	PUNCT
ejpam-5347	291	1	conclusions	conclusion	NOUN
ejpam-5347	291	2	this	this	DET
ejpam-5347	291	3	study	study	NOUN
ejpam-5347	291	4	has	have	AUX
ejpam-5347	291	5	shown	show	VERB
ejpam-5347	291	6	us	we	PRON
ejpam-5347	291	7	that	that	SCONJ
ejpam-5347	291	8	the	the	DET
ejpam-5347	291	9	pair	pair	NOUN
ejpam-5347	291	10	−ω−closed	−ω−close	VERB
ejpam-5347	291	11	functions	function	NOUN
ejpam-5347	291	12	are	be	AUX
ejpam-5347	291	13	an	an	DET
ejpam-5347	291	14	extension	extension	NOUN
ejpam-5347	291	15	of	of	ADP
ejpam-5347	291	16	pair−closed	pair−close	VERB
ejpam-5347	291	17	functions	function	NOUN
ejpam-5347	291	18	.	.	PUNCT
ejpam-5347	292	1	they	they	PRON
ejpam-5347	292	2	are	be	AUX
ejpam-5347	292	3	specified	specify	VERB
ejpam-5347	292	4	on	on	ADP
ejpam-5347	292	5	topological	topological	ADJ
ejpam-5347	292	6	spaces	space	NOUN
ejpam-5347	292	7	and	and	CCONJ
ejpam-5347	292	8	have	have	VERB
ejpam-5347	292	9	an	an	DET
ejpam-5347	292	10	effective	effective	ADJ
ejpam-5347	292	11	method	method	NOUN
ejpam-5347	292	12	of	of	ADP
ejpam-5347	292	13	holding	hold	VERB
ejpam-5347	292	14	onto	onto	ADP
ejpam-5347	292	15	sequence	sequence	NOUN
ejpam-5347	292	16	bounds	bound	NOUN
ejpam-5347	292	17	.	.	PUNCT
ejpam-5347	293	1	this	this	PRON
ejpam-5347	293	2	suggests	suggest	VERB
ejpam-5347	293	3	that	that	SCONJ
ejpam-5347	293	4	if	if	SCONJ
ejpam-5347	293	5	a	a	DET
ejpam-5347	293	6	series	series	NOUN
ejpam-5347	293	7	has	have	VERB
ejpam-5347	293	8	a	a	DET
ejpam-5347	293	9	sequence	sequence	NOUN
ejpam-5347	293	10	of	of	ADP
ejpam-5347	293	11	points	point	NOUN
ejpam-5347	293	12	in	in	ADP
ejpam-5347	293	13	the	the	DET
ejpam-5347	293	14	function	function	NOUN
ejpam-5347	293	15	’s	’s	PART
ejpam-5347	293	16	domain	domain	NOUN
ejpam-5347	293	17	that	that	PRON
ejpam-5347	293	18	converge	converge	VERB
ejpam-5347	293	19	to	to	ADP
ejpam-5347	293	20	a	a	DET
ejpam-5347	293	21	point	point	NOUN
ejpam-5347	293	22	,	,	PUNCT
ejpam-5347	293	23	then	then	ADV
ejpam-5347	293	24	the	the	DET
ejpam-5347	293	25	image	image	NOUN
ejpam-5347	293	26	of	of	ADP
ejpam-5347	293	27	the	the	DET
ejpam-5347	293	28	series	series	NOUN
ejpam-5347	293	29	under	under	ADP
ejpam-5347	293	30	the	the	DET
ejpam-5347	293	31	function	function	NOUN
ejpam-5347	293	32	will	will	AUX
ejpam-5347	293	33	also	also	ADV
ejpam-5347	293	34	converge	converge	VERB
ejpam-5347	293	35	to	to	ADP
ejpam-5347	293	36	the	the	DET
ejpam-5347	293	37	image	image	NOUN
ejpam-5347	293	38	of	of	ADP
ejpam-5347	293	39	the	the	DET
ejpam-5347	293	40	point	point	NOUN
ejpam-5347	293	41	.	.	PUNCT
ejpam-5347	294	1	it	it	PRON
ejpam-5347	294	2	’s	’	VERB
ejpam-5347	294	3	a	a	DET
ejpam-5347	294	4	way	way	NOUN
ejpam-5347	294	5	to	to	PART
ejpam-5347	294	6	extend	extend	VERB
ejpam-5347	294	7	the	the	DET
ejpam-5347	294	8	notion	notion	NOUN
ejpam-5347	294	9	of	of	ADP
ejpam-5347	294	10	closest	close	ADJ
ejpam-5347	294	11	to	to	ADP
ejpam-5347	294	12	more	more	ADV
ejpam-5347	294	13	complicated	complicated	ADJ
ejpam-5347	294	14	situations	situation	NOUN
ejpam-5347	294	15	,	,	PUNCT
ejpam-5347	294	16	such	such	ADJ
ejpam-5347	294	17	weakening	weaken	VERB
ejpam-5347	294	18	these	these	DET
ejpam-5347	294	19	functions	function	NOUN
ejpam-5347	294	20	,	,	PUNCT
ejpam-5347	294	21	therefore	therefore	ADV
ejpam-5347	294	22	we	we	PRON
ejpam-5347	294	23	obtain	obtain	VERB
ejpam-5347	294	24	and	and	CCONJ
ejpam-5347	294	25	investigate	investigate	VERB
ejpam-5347	294	26	their	their	PRON
ejpam-5347	294	27	key	key	ADJ
ejpam-5347	294	28	characteristics	characteristic	NOUN
ejpam-5347	294	29	in	in	ADP
ejpam-5347	294	30	this	this	DET
ejpam-5347	294	31	study	study	NOUN
ejpam-5347	294	32	,	,	PUNCT
ejpam-5347	294	33	to	to	PART
ejpam-5347	294	34	ensure	ensure	VERB
ejpam-5347	294	35	the	the	DET
ejpam-5347	294	36	concepts	concept	NOUN
ejpam-5347	294	37	of	of	ADP
ejpam-5347	294	38	pairwise	pairwise	PROPN
ejpam-5347	294	39	pair−ω−closed	pair−ω−close	VERB
ejpam-5347	294	40	are	be	AUX
ejpam-5347	294	41	understood	understand	VERB
ejpam-5347	294	42	.	.	PUNCT
ejpam-5347	295	1	we	we	PRON
ejpam-5347	295	2	have	have	AUX
ejpam-5347	295	3	examined	examine	VERB
ejpam-5347	295	4	the	the	DET
ejpam-5347	295	5	salient	salient	NOUN
ejpam-5347	295	6	features	feature	NOUN
ejpam-5347	295	7	of	of	ADP
ejpam-5347	295	8	these	these	DET
ejpam-5347	295	9	concepts	concept	NOUN
ejpam-5347	295	10	and	and	CCONJ
ejpam-5347	295	11	shown	show	VERB
ejpam-5347	295	12	how	how	SCONJ
ejpam-5347	295	13	they	they	PRON
ejpam-5347	295	14	apply	apply	VERB
ejpam-5347	295	15	to	to	ADP
ejpam-5347	295	16	different	different	ADJ
ejpam-5347	295	17	situations	situation	NOUN
ejpam-5347	295	18	.	.	PUNCT
ejpam-5347	296	1	we	we	PRON
ejpam-5347	296	2	determined	determine	VERB
ejpam-5347	296	3	their	their	PRON
ejpam-5347	296	4	overall	overall	ADJ
ejpam-5347	296	5	fundamental	fundamental	ADJ
ejpam-5347	296	6	features	feature	NOUN
ejpam-5347	296	7	and	and	CCONJ
ejpam-5347	296	8	the	the	DET
ejpam-5347	296	9	prerequisites	prerequisite	NOUN
ejpam-5347	296	10	that	that	PRON
ejpam-5347	296	11	need	need	VERB
ejpam-5347	296	12	to	to	PART
ejpam-5347	296	13	be	be	AUX
ejpam-5347	296	14	satisfied	satisfied	ADJ
ejpam-5347	296	15	for	for	ADP
ejpam-5347	296	16	similar	similar	ADJ
ejpam-5347	296	17	linkages	linkage	NOUN
ejpam-5347	296	18	to	to	PART
ejpam-5347	296	19	be	be	AUX
ejpam-5347	296	20	made	make	VERB
ejpam-5347	296	21	between	between	ADP
ejpam-5347	296	22	them	they	PRON
ejpam-5347	296	23	.	.	PUNCT
ejpam-5347	297	1	we	we	PRON
ejpam-5347	297	2	discussed	discuss	VERB
ejpam-5347	297	3	their	their	PRON
ejpam-5347	297	4	key	key	ADJ
ejpam-5347	297	5	characteristics	characteristic	NOUN
ejpam-5347	297	6	and	and	CCONJ
ejpam-5347	297	7	gave	give	VERB
ejpam-5347	297	8	examples	example	NOUN
ejpam-5347	297	9	of	of	ADP
ejpam-5347	297	10	how	how	SCONJ
ejpam-5347	297	11	they	they	PRON
ejpam-5347	297	12	complement	complement	VERB
ejpam-5347	297	13	one	one	NUM
ejpam-5347	297	14	another	another	DET
ejpam-5347	297	15	.	.	PUNCT
ejpam-5347	298	1	the	the	DET
ejpam-5347	298	2	study	study	NOUN
ejpam-5347	298	3	provided	provide	VERB
ejpam-5347	298	4	multiple	multiple	ADJ
ejpam-5347	298	5	examples	example	NOUN
ejpam-5347	298	6	of	of	ADP
ejpam-5347	298	7	various	various	ADJ
ejpam-5347	298	8	functions	function	NOUN
ejpam-5347	298	9	along	along	ADV
ejpam-5347	298	10	with	with	ADP
ejpam-5347	298	11	highlighting	highlight	VERB
ejpam-5347	298	12	their	their	PRON
ejpam-5347	298	13	properties.these	properties.these	ADJ
ejpam-5347	298	14	functions	function	NOUN
ejpam-5347	298	15	will	will	AUX
ejpam-5347	298	16	act	act	VERB
ejpam-5347	298	17	as	as	ADP
ejpam-5347	298	18	a	a	DET
ejpam-5347	298	19	basis	basis	NOUN
ejpam-5347	298	20	for	for	ADP
ejpam-5347	298	21	additional	additional	ADJ
ejpam-5347	298	22	studies	study	NOUN
ejpam-5347	298	23	into	into	ADP
ejpam-5347	298	24	the	the	DET
ejpam-5347	298	25	potential	potential	ADJ
ejpam-5347	298	26	applications	application	NOUN
ejpam-5347	298	27	of	of	ADP
ejpam-5347	298	28	each	each	PRON
ejpam-5347	298	29	of	of	ADP
ejpam-5347	298	30	these	these	DET
ejpam-5347	298	31	functions	function	NOUN
ejpam-5347	298	32	.	.	PUNCT
ejpam-5347	299	1	other	other	ADJ
ejpam-5347	299	2	versions	version	NOUN
ejpam-5347	299	3	of	of	ADP
ejpam-5347	299	4	these	these	DET
ejpam-5347	299	5	duties	duty	NOUN
ejpam-5347	299	6	including	include	VERB
ejpam-5347	299	7	fuzzy	fuzzy	ADJ
ejpam-5347	299	8	,	,	PUNCT
ejpam-5347	299	9	soft	soft	ADJ
ejpam-5347	299	10	,	,	PUNCT
ejpam-5347	299	11	and	and	CCONJ
ejpam-5347	299	12	group	group	NOUN
ejpam-5347	299	13	,	,	PUNCT
ejpam-5347	299	14	[	[	X
ejpam-5347	299	15	1],[10],[12],[16],[18	1],[10],[12],[16],[18	NUM
ejpam-5347	299	16	]	]	PUNCT
ejpam-5347	299	17	and	and	CCONJ
ejpam-5347	299	18	[	[	X
ejpam-5347	299	19	19	19	NUM
ejpam-5347	299	20	]	]	PUNCT
ejpam-5347	299	21	.	.	PUNCT
ejpam-5347	300	1	,	,	PUNCT
ejpam-5347	300	2	might	might	AUX
ejpam-5347	300	3	be	be	AUX
ejpam-5347	300	4	the	the	DET
ejpam-5347	300	5	subject	subject	NOUN
ejpam-5347	300	6	of	of	ADP
ejpam-5347	300	7	future	future	ADJ
ejpam-5347	300	8	investigation	investigation	NOUN
ejpam-5347	300	9	.	.	PUNCT
ejpam-5347	301	1	acknowledgements	acknowledgement	NOUN
ejpam-5347	301	2	we	we	PRON
ejpam-5347	301	3	sincerely	sincerely	ADV
ejpam-5347	301	4	thank	thank	VERB
ejpam-5347	301	5	everyone	everyone	PRON
ejpam-5347	301	6	who	who	PRON
ejpam-5347	301	7	made	make	VERB
ejpam-5347	301	8	a	a	DET
ejpam-5347	301	9	contribution	contribution	NOUN
ejpam-5347	301	10	to	to	ADP
ejpam-5347	301	11	this	this	DET
ejpam-5347	301	12	research	research	NOUN
ejpam-5347	301	13	.	.	PUNCT
ejpam-5347	302	1	their	their	PRON
ejpam-5347	302	2	cooperation	cooperation	NOUN
ejpam-5347	302	3	,	,	PUNCT
ejpam-5347	302	4	guidance	guidance	NOUN
ejpam-5347	302	5	,	,	PUNCT
ejpam-5347	302	6	and	and	CCONJ
ejpam-5347	302	7	support	support	NOUN
ejpam-5347	302	8	have	have	AUX
ejpam-5347	302	9	been	be	AUX
ejpam-5347	302	10	crucial	crucial	ADJ
ejpam-5347	302	11	to	to	ADP
ejpam-5347	302	12	completing	complete	VERB
ejpam-5347	302	13	the	the	DET
ejpam-5347	302	14	work	work	NOUN
ejpam-5347	302	15	.	.	PUNCT
ejpam-5347	303	1	references	reference	NOUN
ejpam-5347	303	2	[	[	X
ejpam-5347	303	3	1	1	NUM
ejpam-5347	303	4	]	]	PUNCT
ejpam-5347	303	5	m	m	VERB
ejpam-5347	303	6	massa’deh	massa’deh	NOUN
ejpam-5347	303	7	a	a	DET
ejpam-5347	303	8	fallatah	fallatah	NOUN
ejpam-5347	303	9	and	and	CCONJ
ejpam-5347	303	10	a	a	DET
ejpam-5347	303	11	alkouri	alkouri	NOUN
ejpam-5347	303	12	.	.	PUNCT
ejpam-5347	304	1	homomorphism	homomorphism	NOUN
ejpam-5347	304	2	of	of	ADP
ejpam-5347	304	3	tripolar	tripolar	ADJ
ejpam-5347	304	4	fuzzy	fuzzy	ADJ
ejpam-5347	304	5	soft	soft	ADJ
ejpam-5347	304	6	γsemiring	γsemiring	NOUN
ejpam-5347	304	7	.	.	PUNCT
ejpam-5347	305	1	wseas	wseas	NOUN
ejpam-5347	305	2	transactions	transaction	NOUN
ejpam-5347	305	3	on	on	ADP
ejpam-5347	305	4	mathematics	mathematic	NOUN
ejpam-5347	305	5	,	,	PUNCT
ejpam-5347	305	6	19(10):37394/23206	19(10):37394/23206	NUM
ejpam-5347	305	7	,	,	PUNCT
ejpam-5347	305	8	2020	2020	NUM
ejpam-5347	305	9	.	.	PUNCT
ejpam-5347	306	1	[	[	X
ejpam-5347	306	2	2	2	NUM
ejpam-5347	306	3	]	]	X
ejpam-5347	306	4	s	s	PART
ejpam-5347	306	5	al	al	PROPN
ejpam-5347	306	6	-	-	PUNCT
ejpam-5347	306	7	ghour	ghour	PROPN
ejpam-5347	306	8	.	.	PUNCT
ejpam-5347	307	1	on	on	ADP
ejpam-5347	307	2	soft	soft	ADJ
ejpam-5347	307	3	generalized	generalized	ADJ
ejpam-5347	307	4	ω	ω	ADJ
ejpam-5347	307	5	-	-	ADJ
ejpam-5347	307	6	closed	closed	ADJ
ejpam-5347	307	7	sets	set	NOUN
ejpam-5347	307	8	and	and	CCONJ
ejpam-5347	307	9	soft	soft	ADJ
ejpam-5347	307	10	t1/2	t1/2	ADJ
ejpam-5347	307	11	spaces	space	NOUN
ejpam-5347	307	12	in	in	ADP
ejpam-5347	307	13	soft	soft	ADJ
ejpam-5347	307	14	topological	topological	ADJ
ejpam-5347	307	15	spaces	space	NOUN
ejpam-5347	307	16	.	.	PUNCT
ejpam-5347	308	1	axioms	axiom	NOUN
ejpam-5347	308	2	,	,	PUNCT
ejpam-5347	308	3	194	194	NUM
ejpam-5347	308	4	,	,	PUNCT
ejpam-5347	308	5	11.5:79–85	11.5:79–85	NUM
ejpam-5347	308	6	,	,	PUNCT
ejpam-5347	308	7	2022	2022	NUM
ejpam-5347	308	8	.	.	PUNCT
ejpam-5347	309	1	[	[	X
ejpam-5347	309	2	3	3	NUM
ejpam-5347	309	3	]	]	X
ejpam-5347	309	4	w	w	PROPN
ejpam-5347	309	5	al	al	PROPN
ejpam-5347	309	6	-	-	PUNCT
ejpam-5347	309	7	luwaici	luwaici	PROPN
ejpam-5347	309	8	and	and	CCONJ
ejpam-5347	309	9	a	a	DET
ejpam-5347	309	10	al	al	PROPN
ejpam-5347	309	11	-	-	PUNCT
ejpam-5347	309	12	omari	omari	PROPN
ejpam-5347	309	13	.	.	PUNCT
ejpam-5347	310	1	some	some	DET
ejpam-5347	310	2	characteristics	characteristic	NOUN
ejpam-5347	310	3	of	of	ADP
ejpam-5347	310	4	rare	rare	ADJ
ejpam-5347	310	5	ωcontinuous	ωcontinuous	ADJ
ejpam-5347	310	6	functions	function	NOUN
ejpam-5347	310	7	.	.	PUNCT
ejpam-5347	311	1	italian	italian	ADJ
ejpam-5347	311	2	journal	journal	NOUN
ejpam-5347	311	3	of	of	ADP
ejpam-5347	311	4	pure	pure	ADJ
ejpam-5347	311	5	and	and	CCONJ
ejpam-5347	311	6	applied	applied	ADJ
ejpam-5347	311	7	mathematics	mathematic	NOUN
ejpam-5347	311	8	,	,	PUNCT
ejpam-5347	311	9	2:751–759	2:751–759	NUM
ejpam-5347	311	10	,	,	PUNCT
ejpam-5347	311	11	2022	2022	NUM
ejpam-5347	311	12	.	.	PUNCT
ejpam-5347	312	1	[	[	X
ejpam-5347	312	2	4	4	X
ejpam-5347	312	3	]	]	X
ejpam-5347	312	4	a	a	DET
ejpam-5347	312	5	ali	ali	PROPN
ejpam-5347	312	6	and	and	CCONJ
ejpam-5347	312	7	h	h	PROPN
ejpam-5347	312	8	hdeib	hdeib	PROPN
ejpam-5347	312	9	.	.	PUNCT
ejpam-5347	313	1	on	on	ADP
ejpam-5347	313	2	pairwise	pairwise	PROPN
ejpam-5347	313	3	lindelöf	lindelöf	NOUN
ejpam-5347	313	4	spaces	space	VERB
ejpam-5347	313	5	.	.	PUNCT
ejpam-5347	314	1	revista	revista	PROPN
ejpam-5347	314	2	colombiana	colombiana	PROPN
ejpam-5347	314	3	de	de	PROPN
ejpam-5347	314	4	matematicas	matematicas	PROPN
ejpam-5347	314	5	,	,	PUNCT
ejpam-5347	314	6	17:37–58	17:37–58	NUM
ejpam-5347	314	7	,	,	PUNCT
ejpam-5347	314	8	1983	1983	NUM
ejpam-5347	314	9	.	.	PUNCT
ejpam-5347	315	1	[	[	X
ejpam-5347	315	2	5	5	X
ejpam-5347	315	3	]	]	PUNCT
ejpam-5347	315	4	j	j	PROPN
ejpam-5347	315	5	argyros	argyros	PROPN
ejpam-5347	315	6	and	and	CCONJ
ejpam-5347	315	7	s	s	PROPN
ejpam-5347	315	8	george	george	NOUN
ejpam-5347	315	9	.	.	PUNCT
ejpam-5347	316	1	extending	extend	VERB
ejpam-5347	316	2	the	the	DET
ejpam-5347	316	3	pplicability	pplicability	NOUN
ejpam-5347	316	4	of	of	ADP
ejpam-5347	316	5	the	the	DET
ejpam-5347	316	6	super	super	ADJ
ejpam-5347	316	7	-	-	ADJ
ejpam-5347	316	8	halley	halley	ADJ
ejpam-5347	316	9	-	-	PUNCT
ejpam-5347	316	10	like	like	ADJ
ejpam-5347	316	11	method	method	NOUN
ejpam-5347	316	12	using	use	VERB
ejpam-5347	316	13	ω	ω	NUM
ejpam-5347	316	14	-continuous	-continuous	ADJ
ejpam-5347	316	15	derivatives	derivative	NOUN
ejpam-5347	316	16	and	and	CCONJ
ejpam-5347	316	17	restricted	restrict	VERB
ejpam-5347	316	18	convergence	convergence	NOUN
ejpam-5347	316	19	domains	domain	NOUN
ejpam-5347	316	20	.	.	PUNCT
ejpam-5347	317	1	in	in	ADP
ejpam-5347	317	2	annales	annales	PROPN
ejpam-5347	317	3	mathematicae	mathematicae	PROPN
ejpam-5347	317	4	silesianae	silesianae	PROPN
ejpam-5347	317	5	,	,	PUNCT
ejpam-5347	317	6	33:21–40	33:21–40	PROPN
ejpam-5347	317	7	,	,	PUNCT
ejpam-5347	317	8	2019	2019	NUM
ejpam-5347	317	9	.	.	PUNCT
ejpam-5347	318	1	[	[	X
ejpam-5347	318	2	6	6	NUM
ejpam-5347	318	3	]	]	PUNCT
ejpam-5347	318	4	a	a	DET
ejpam-5347	318	5	atoom	atoom	NOUN
ejpam-5347	318	6	.	.	PUNCT
ejpam-5347	319	1	study	study	NOUN
ejpam-5347	319	2	of	of	ADP
ejpam-5347	319	3	pairwise	pairwise	PROPN
ejpam-5347	319	4	−ω−compact	−ω−compact	PROPN
ejpam-5347	319	5	spaces	space	NOUN
ejpam-5347	319	6	.	.	PUNCT
ejpam-5347	320	1	global	global	ADJ
ejpam-5347	320	2	journal	journal	PROPN
ejpam-5347	320	3	of	of	ADP
ejpam-5347	320	4	pure	pure	ADJ
ejpam-5347	320	5	and	and	CCONJ
ejpam-5347	320	6	applied	applied	ADJ
ejpam-5347	320	7	mathematics	mathematic	NOUN
ejpam-5347	320	8	,	,	PUNCT
ejpam-5347	320	9	14.11:1453–1459	14.11:1453–1459	NUM
ejpam-5347	320	10	,	,	PUNCT
ejpam-5347	320	11	2018	2018	NUM
ejpam-5347	320	12	.	.	PUNCT
ejpam-5347	321	1	references	reference	NOUN
ejpam-5347	321	2	2585	2585	NUM
ejpam-5347	321	3	[	[	X
ejpam-5347	321	4	7	7	X
ejpam-5347	321	5	]	]	X
ejpam-5347	321	6	a	a	DET
ejpam-5347	321	7	atoom	atoom	NOUN
ejpam-5347	321	8	.	.	PUNCT
ejpam-5347	322	1	on	on	ADP
ejpam-5347	322	2	pairwise−ω−perfect	pairwise−ω−perfect	PROPN
ejpam-5347	322	3	functions	function	NOUN
ejpam-5347	322	4	.	.	PUNCT
ejpam-5347	323	1	j.	j.	PROPN
ejpam-5347	323	2	math	math	PROPN
ejpam-5347	323	3	.	.	PUNCT
ejpam-5347	324	1	comput	comput	NOUN
ejpam-5347	324	2	,	,	PUNCT
ejpam-5347	324	3	,	,	PUNCT
ejpam-5347	324	4	12	12	NUM
ejpam-5347	324	5	:	:	PUNCT
ejpam-5347	324	6	article	article	NOUN
ejpam-5347	324	7	i	i	PROPN
ejpam-5347	324	8	d	d	PROPN
ejpam-5347	324	9	33	33	NUM
ejpam-5347	324	10	,	,	PUNCT
ejpam-5347	324	11	2021	2021	NUM
ejpam-5347	324	12	.	.	PUNCT
ejpam-5347	325	1	[	[	X
ejpam-5347	325	2	8	8	NUM
ejpam-5347	325	3	]	]	X
ejpam-5347	325	4	m	m	VERB
ejpam-5347	325	5	datta	datta	PROPN
ejpam-5347	325	6	.	.	PUNCT
ejpam-5347	325	7	projection	projection	ADJ
ejpam-5347	325	8	bitopological	bitopological	ADJ
ejpam-5347	325	9	spaces	space	NOUN
ejpam-5347	325	10	.	.	PUNCT
ejpam-5347	326	1	austral	austral	ADJ
ejpam-5347	326	2	.	.	PUNCT
ejpam-5347	326	3	math	math	NOUN
ejpam-5347	326	4	.	.	PUNCT
ejpam-5347	327	1	soc	soc	PROPN
ejpam-5347	327	2	.	.	PUNCT
ejpam-5347	327	3	,	,	PUNCT
ejpam-5347	327	4	13:327–334	13:327–334	PROPN
ejpam-5347	327	5	,	,	PUNCT
ejpam-5347	327	6	1976	1976	NUM
ejpam-5347	327	7	.	.	PUNCT
ejpam-5347	328	1	[	[	X
ejpam-5347	328	2	9	9	NUM
ejpam-5347	328	3	]	]	X
ejpam-5347	328	4	a	a	DET
ejpam-5347	328	5	atoom	atoom	NOUN
ejpam-5347	328	6	et.al	et.al	PROPN
ejpam-5347	328	7	.	.	PUNCT
ejpam-5347	329	1	significant	significant	ADJ
ejpam-5347	329	2	modification	modification	NOUN
ejpam-5347	329	3	of	of	ADP
ejpam-5347	329	4	pairwise−ω−continuous	pairwise−ω−continuous	ADJ
ejpam-5347	329	5	functions	function	NOUN
ejpam-5347	329	6	with	with	ADP
ejpam-5347	329	7	associated	associated	ADJ
ejpam-5347	329	8	concepts	concept	NOUN
ejpam-5347	329	9	.	.	PUNCT
ejpam-5347	330	1	wseas	wseas	PROPN
ejpam-5347	330	2	transactions	transaction	NOUN
ejpam-5347	330	3	on	on	ADP
ejpam-5347	330	4	mathematics	mathematic	NOUN
ejpam-5347	330	5	,	,	PUNCT
ejpam-5347	330	6	,	,	PUNCT
ejpam-5347	330	7	22:961–970	22:961–970	NUM
ejpam-5347	330	8	,	,	PUNCT
ejpam-5347	330	9	2023	2023	NUM
ejpam-5347	330	10	.	.	PUNCT
ejpam-5347	331	1	[	[	X
ejpam-5347	331	2	10	10	NUM
ejpam-5347	331	3	]	]	X
ejpam-5347	331	4	o	o	NOUN
ejpam-5347	331	5	gutik	gutik	NOUN
ejpam-5347	331	6	and	and	CCONJ
ejpam-5347	331	7	i	i	PRON
ejpam-5347	331	8	pozdniakova	pozdniakova	VERB
ejpam-5347	331	9	.	.	PUNCT
ejpam-5347	332	1	on	on	ADP
ejpam-5347	332	2	a	a	DET
ejpam-5347	332	3	semigroup	semigroup	NOUN
ejpam-5347	332	4	generated	generate	VERB
ejpam-5347	332	5	by	by	ADP
ejpam-5347	332	6	the	the	DET
ejpam-5347	332	7	extended	extended	ADJ
ejpam-5347	332	8	bicyclic	bicyclic	NOUN
ejpam-5347	332	9	semigroup	semigroup	NOUN
ejpam-5347	332	10	and	and	CCONJ
ejpam-5347	332	11	the	the	DET
ejpam-5347	332	12	ω−closed	ω−close	VERB
ejpam-5347	332	13	family	family	NOUN
ejpam-5347	332	14	.	.	PUNCT
ejpam-5347	333	1	journal	journal	PROPN
ejpam-5347	333	2	of	of	ADP
ejpam-5347	333	3	mathematical	mathematical	ADJ
ejpam-5347	333	4	sciences	science	NOUN
ejpam-5347	333	5	,	,	PUNCT
ejpam-5347	333	6	274.5:602	274.5:602	NUM
ejpam-5347	333	7	–	–	PUNCT
ejpam-5347	333	8	617	617	NUM
ejpam-5347	333	9	,	,	PUNCT
ejpam-5347	333	10	2023	2023	NUM
ejpam-5347	333	11	.	.	PUNCT
ejpam-5347	334	1	[	[	X
ejpam-5347	334	2	11	11	NUM
ejpam-5347	334	3	]	]	X
ejpam-5347	334	4	h	h	PROPN
ejpam-5347	334	5	hdeib	hdeib	PROPN
ejpam-5347	334	6	.	.	PUNCT
ejpam-5347	335	1	ω	ω	VERB
ejpam-5347	335	2	-	-	PUNCT
ejpam-5347	335	3	closed	close	VERB
ejpam-5347	335	4	mappings	mapping	NOUN
ejpam-5347	335	5	.	.	PUNCT
ejpam-5347	336	1	r.c.d.matematics	r.c.d.matematic	NOUN
ejpam-5347	336	2	,	,	PUNCT
ejpam-5347	336	3	pages	page	NOUN
ejpam-5347	336	4	65–78	65–78	NUM
ejpam-5347	336	5	,	,	PUNCT
ejpam-5347	336	6	1982	1982	NUM
ejpam-5347	336	7	.	.	PUNCT
ejpam-5347	337	1	[	[	X
ejpam-5347	337	2	12	12	NUM
ejpam-5347	337	3	]	]	X
ejpam-5347	337	4	q	q	X
ejpam-5347	337	5	imran	imran	PROPN
ejpam-5347	337	6	.	.	PUNCT
ejpam-5347	338	1	alpha	alpha	PROPN
ejpam-5347	338	2	star	star	PROPN
ejpam-5347	338	3	generalized	generalize	VERB
ejpam-5347	338	4	ω−closed	ω−close	VERB
ejpam-5347	338	5	sets	set	NOUN
ejpam-5347	338	6	in	in	ADP
ejpam-5347	338	7	bitopological	bitopological	ADJ
ejpam-5347	338	8	spaces	space	NOUN
ejpam-5347	338	9	.	.	PUNCT
ejpam-5347	339	1	journal	journal	PROPN
ejpam-5347	339	2	of	of	ADP
ejpam-5347	339	3	kufa	kufa	PROPN
ejpam-5347	339	4	for	for	ADP
ejpam-5347	339	5	mathematics	mathematic	NOUN
ejpam-5347	339	6	and	and	CCONJ
ejpam-5347	339	7	computer	computer	NOUN
ejpam-5347	339	8	,	,	PUNCT
ejpam-5347	339	9	2.1:95–102	2.1:95–102	NUM
ejpam-5347	339	10	,	,	PUNCT
ejpam-5347	339	11	2014	2014	NUM
ejpam-5347	339	12	.	.	PUNCT
ejpam-5347	340	1	[	[	X
ejpam-5347	340	2	13	13	NUM
ejpam-5347	340	3	]	]	X
ejpam-5347	340	4	j	j	PROPN
ejpam-5347	340	5	kelly	kelly	PROPN
ejpam-5347	340	6	.	.	PUNCT
ejpam-5347	341	1	bitopological	bitopological	ADJ
ejpam-5347	341	2	spaces	space	NOUN
ejpam-5347	341	3	.	.	PUNCT
ejpam-5347	342	1	proc.londan	proc.londan	PROPN
ejpam-5347	342	2	math.soc	math.soc	X
ejpam-5347	342	3	,	,	PUNCT
ejpam-5347	342	4	,	,	PUNCT
ejpam-5347	342	5	13:71–89	13:71–89	NUM
ejpam-5347	342	6	,	,	PUNCT
ejpam-5347	342	7	1963	1963	NUM
ejpam-5347	342	8	.	.	PUNCT
ejpam-5347	343	1	[	[	X
ejpam-5347	343	2	14	14	NUM
ejpam-5347	343	3	]	]	PUNCT
ejpam-5347	343	4	a	a	DET
ejpam-5347	343	5	killiman	killiman	NOUN
ejpam-5347	343	6	and	and	CCONJ
ejpam-5347	343	7	z	z	NOUN
ejpam-5347	343	8	salleh	salleh	PROPN
ejpam-5347	343	9	.	.	PUNCT
ejpam-5347	344	1	product	product	NOUN
ejpam-5347	344	2	properties	property	NOUN
ejpam-5347	344	3	for	for	ADP
ejpam-5347	344	4	pairwise	pairwise	NOUN
ejpam-5347	344	5	lindel	lindel	NOUN
ejpam-5347	344	6	..	..	PUNCT
ejpam-5347	344	7	of	of	ADP
ejpam-5347	344	8	spaces	space	NOUN
ejpam-5347	344	9	.	.	PUNCT
ejpam-5347	345	1	bull.malays.math.sci.soc	bull.malays.math.sci.soc	PROPN
ejpam-5347	345	2	,	,	PUNCT
ejpam-5347	345	3	,	,	PUNCT
ejpam-5347	345	4	34(2):231	34(2):231	NUM
ejpam-5347	345	5	–	–	PUNCT
ejpam-5347	345	6	246	246	NUM
ejpam-5347	345	7	,	,	PUNCT
ejpam-5347	345	8	2011	2011	NUM
ejpam-5347	345	9	.	.	PUNCT
ejpam-5347	346	1	[	[	X
ejpam-5347	346	2	15	15	NUM
ejpam-5347	346	3	]	]	X
ejpam-5347	346	4	h	h	NOUN
ejpam-5347	346	5	hoyle	hoyle	PROPN
ejpam-5347	346	6	iii	iii	PROPN
ejpam-5347	346	7	p	p	X
ejpam-5347	346	8	fletcher	fletcher	PROPN
ejpam-5347	346	9	,	,	PUNCT
ejpam-5347	346	10	b	b	NOUN
ejpam-5347	346	11	hughes	hughe	NOUN
ejpam-5347	346	12	and	and	CCONJ
ejpam-5347	346	13	c	c	PROPN
ejpam-5347	346	14	patty	patty	PROPN
ejpam-5347	346	15	.	.	PUNCT
ejpam-5347	347	1	the	the	DET
ejpam-5347	347	2	comparison	comparison	NOUN
ejpam-5347	347	3	of	of	ADP
ejpam-5347	347	4	topologies	topology	NOUN
ejpam-5347	347	5	.	.	PUNCT
ejpam-5347	348	1	duke	duke	PROPN
ejpam-5347	348	2	math	math	PROPN
ejpam-5347	348	3	.	.	PUNCT
ejpam-5347	348	4	,	,	PUNCT
ejpam-5347	348	5	36:325–331	36:325–331	PROPN
ejpam-5347	348	6	,	,	PUNCT
ejpam-5347	348	7	1969	1969	NUM
ejpam-5347	348	8	.	.	PUNCT
ejpam-5347	349	1	[	[	X
ejpam-5347	349	2	16	16	NUM
ejpam-5347	349	3	]	]	PUNCT
ejpam-5347	349	4	n	n	PRON
ejpam-5347	349	5	paul	paul	PROPN
ejpam-5347	349	6	.	.	PUNCT
ejpam-5347	350	1	remarks	remark	NOUN
ejpam-5347	350	2	on	on	ADP
ejpam-5347	350	3	soft	soft	ADJ
ejpam-5347	350	4	omega	omega	NOUN
ejpam-5347	350	5	-	-	PUNCT
ejpam-5347	350	6	closed	close	VERB
ejpam-5347	350	7	sets	set	NOUN
ejpam-5347	350	8	in	in	ADP
ejpam-5347	350	9	soft	soft	ADJ
ejpam-5347	350	10	topological	topological	ADJ
ejpam-5347	350	11	spaces	space	NOUN
ejpam-5347	350	12	.	.	PUNCT
ejpam-5347	351	1	boletim	boletim	PROPN
ejpam-5347	351	2	da	da	PROPN
ejpam-5347	351	3	sociedade	sociedade	PROPN
ejpam-5347	351	4	paranaense	paranaense	PROPN
ejpam-5347	351	5	de	de	PROPN
ejpam-5347	351	6	matemetica	matemetica	PROPN
ejpam-5347	351	7	,	,	PUNCT
ejpam-5347	351	8	33.1:183–192	33.1:183–192	NUM
ejpam-5347	351	9	,	,	PUNCT
ejpam-5347	351	10	2015	2015	NUM
ejpam-5347	351	11	.	.	PUNCT
ejpam-5347	352	1	[	[	X
ejpam-5347	352	2	17	17	NUM
ejpam-5347	352	3	]	]	X
ejpam-5347	352	4	e	e	NOUN
ejpam-5347	352	5	ryszard	ryszard	NOUN
ejpam-5347	352	6	.	.	PUNCT
ejpam-5347	353	1	general	general	ADJ
ejpam-5347	353	2	topology	topology	PROPN
ejpam-5347	353	3	.	.	PUNCT
ejpam-5347	354	1	second	second	PROPN
ejpam-5347	354	2	edition	edition	PROPN
ejpam-5347	354	3	,	,	PUNCT
ejpam-5347	354	4	berlin	berlin	PROPN
ejpam-5347	354	5	,	,	PUNCT
ejpam-5347	354	6	heldermann	heldermann	NOUN
ejpam-5347	354	7	,	,	PUNCT
ejpam-5347	354	8	1989	1989	NUM
ejpam-5347	354	9	.	.	PUNCT
ejpam-5347	355	1	[	[	X
ejpam-5347	355	2	18	18	NUM
ejpam-5347	355	3	]	]	PUNCT
ejpam-5347	355	4	m	m	NOUN
ejpam-5347	355	5	thivagar	thivagar	NOUN
ejpam-5347	355	6	and	and	CCONJ
ejpam-5347	355	7	m	m	NOUN
ejpam-5347	355	8	anbuchelvi	anbuchelvi	NOUN
ejpam-5347	355	9	.	.	PUNCT
ejpam-5347	356	1	new	new	ADJ
ejpam-5347	356	2	spaces	space	NOUN
ejpam-5347	356	3	and	and	CCONJ
ejpam-5347	356	4	continuity	continuity	NOUN
ejpam-5347	356	5	via	via	ADP
ejpam-5347	356	6	ω	ω	VERB
ejpam-5347	356	7	-	-	PUNCT
ejpam-5347	356	8	closed	close	VERB
ejpam-5347	356	9	sets	set	NOUN
ejpam-5347	356	10	.	.	PUNCT
ejpam-5347	357	1	boletim	boletim	PROPN
ejpam-5347	357	2	da	da	PROPN
ejpam-5347	357	3	sociedade	sociedade	PROPN
ejpam-5347	357	4	paranaense	paranaense	PROPN
ejpam-5347	357	5	de	de	PROPN
ejpam-5347	357	6	matemtica	matemtica	PROPN
ejpam-5347	357	7	,	,	PUNCT
ejpam-5347	357	8	20:143–161	20:143–161	NUM
ejpam-5347	357	9	,	,	PUNCT
ejpam-5347	357	10	2014	2014	NUM
ejpam-5347	357	11	.	.	PUNCT
ejpam-5347	358	1	[	[	X
ejpam-5347	358	2	19	19	NUM
ejpam-5347	358	3	]	]	X
ejpam-5347	358	4	i	i	PRON
ejpam-5347	358	5	vainstin	vainstin	VERB
ejpam-5347	358	6	.	.	PUNCT
ejpam-5347	359	1	on	on	ADP
ejpam-5347	359	2	closed	closed	ADJ
ejpam-5347	359	3	mappings	mapping	NOUN
ejpam-5347	359	4	.	.	PUNCT
ejpam-5347	360	1	zanhekii	zanhekii	PROPN
ejpam-5347	361	1	mock.vhnb	mock.vhnb	PROPN
ejpam-5347	361	2	.	.	PROPN
ejpam-5347	361	3	,	,	PUNCT
ejpam-5347	361	4	155:3–53	155:3–53	NUM
ejpam-5347	361	5	,	,	PUNCT
ejpam-5347	361	6	1952	1952	NUM
ejpam-5347	361	7	.	.	PUNCT