id	sid	tid	token	lemma	pos
ejpam-5962	1	1	european	european	PROPN
ejpam-5962	1	2	journal	journal	PROPN
ejpam-5962	1	3	of	of	ADP
ejpam-5962	1	4	pure	pure	ADJ
ejpam-5962	1	5	and	and	CCONJ
ejpam-5962	1	6	applied	applied	ADJ
ejpam-5962	1	7	mathematics	mathematic	NOUN
ejpam-5962	1	8	2025	2025	NUM
ejpam-5962	1	9	,	,	PUNCT
ejpam-5962	1	10	vol	vol	NOUN
ejpam-5962	1	11	.	.	PROPN
ejpam-5962	1	12	18	18	NUM
ejpam-5962	1	13	,	,	PUNCT
ejpam-5962	1	14	issue	issue	NOUN
ejpam-5962	1	15	2	2	NUM
ejpam-5962	1	16	,	,	PUNCT
ejpam-5962	1	17	article	article	NOUN
ejpam-5962	1	18	number	number	NOUN
ejpam-5962	1	19	5962	5962	NUM
ejpam-5962	1	20	issn	issn	VERB
ejpam-5962	1	21	1307	1307	NUM
ejpam-5962	1	22	-	-	SYM
ejpam-5962	1	23	5543	5543	NUM
ejpam-5962	1	24	–	–	PUNCT
ejpam-5962	1	25	ejpam.com	ejpam.com	X
ejpam-5962	1	26	published	publish	VERB
ejpam-5962	1	27	by	by	ADP
ejpam-5962	1	28	new	new	PROPN
ejpam-5962	1	29	york	york	PROPN
ejpam-5962	1	30	business	business	PROPN
ejpam-5962	1	31	global	global	PROPN
ejpam-5962	1	32	on	on	ADP
ejpam-5962	1	33	the	the	DET
ejpam-5962	1	34	distinctive	distinctive	ADJ
ejpam-5962	1	35	bi	bi	NOUN
ejpam-5962	1	36	-	-	NOUN
ejpam-5962	1	37	generations	generation	NOUN
ejpam-5962	1	38	that	that	PRON
ejpam-5962	1	39	are	be	AUX
ejpam-5962	1	40	arising	arise	VERB
ejpam-5962	1	41	three	three	NUM
ejpam-5962	1	42	frameworks	framework	NOUN
ejpam-5962	1	43	for	for	ADP
ejpam-5962	1	44	maximal	maximal	ADJ
ejpam-5962	1	45	and	and	CCONJ
ejpam-5962	1	46	minimal	minimal	ADJ
ejpam-5962	1	47	bitopologies	bitopologie	NOUN
ejpam-5962	1	48	spaces	space	NOUN
ejpam-5962	1	49	,	,	PUNCT
ejpam-5962	1	50	their	their	PRON
ejpam-5962	1	51	relationship	relationship	NOUN
ejpam-5962	1	52	to	to	ADP
ejpam-5962	1	53	bitopological	bitopological	ADJ
ejpam-5962	1	54	spaces	space	NOUN
ejpam-5962	1	55	,	,	PUNCT
ejpam-5962	1	56	and	and	CCONJ
ejpam-5962	1	57	their	their	PRON
ejpam-5962	1	58	respective	respective	ADJ
ejpam-5962	1	59	applications	application	NOUN
ejpam-5962	1	60	ali	ali	PROPN
ejpam-5962	1	61	a.	a.	PROPN
ejpam-5962	1	62	atoom1,∗	atoom1,∗	PROPN
ejpam-5962	1	63	,	,	PUNCT
ejpam-5962	1	64	mutaib	mutaib	PROPN
ejpam-5962	1	65	al	al	PROPN
ejpam-5962	1	66	-	-	PUNCT
ejpam-5962	1	67	otaibi2	otaibi2	PROPN
ejpam-5962	1	68	,	,	PUNCT
ejpam-5962	1	69	hamza	hamza	PROPN
ejpam-5962	1	70	qoqazeh3	qoqazeh3	PROPN
ejpam-5962	1	71	,	,	PUNCT
ejpam-5962	1	72	al	al	PROPN
ejpam-5962	1	73	-	-	PUNCT
ejpam-5962	1	74	faroq	faroq	PROPN
ejpam-5962	1	75	omar	omar	PROPN
ejpam-5962	1	76	alkhawaldeh4	alkhawaldeh4	PROPN
ejpam-5962	1	77	1	1	NUM
ejpam-5962	1	78	department	department	NOUN
ejpam-5962	1	79	of	of	ADP
ejpam-5962	1	80	mathematics	mathematic	NOUN
ejpam-5962	1	81	,	,	PUNCT
ejpam-5962	1	82	faculty	faculty	NOUN
ejpam-5962	1	83	of	of	ADP
ejpam-5962	1	84	science	science	NOUN
ejpam-5962	1	85	,	,	PUNCT
ejpam-5962	1	86	ajloun	ajloun	ADJ
ejpam-5962	1	87	national	national	ADJ
ejpam-5962	1	88	university	university	PROPN
ejpam-5962	1	89	,	,	PUNCT
ejpam-5962	1	90	p.o	p.o	PROPN
ejpam-5962	1	91	.	.	PROPN
ejpam-5962	1	92	box	box	PROPN
ejpam-5962	1	93	43	43	NUM
ejpam-5962	1	94	,	,	PUNCT
ejpam-5962	1	95	ajloun	ajloun	ADJ
ejpam-5962	1	96	26810	26810	NUM
ejpam-5962	1	97	,	,	PUNCT
ejpam-5962	1	98	jordan	jordan	PROPN
ejpam-5962	1	99	2	2	NUM
ejpam-5962	1	100	faculty	faculty	NOUN
ejpam-5962	1	101	of	of	ADP
ejpam-5962	1	102	arts	art	NOUN
ejpam-5962	1	103	and	and	CCONJ
ejpam-5962	1	104	science	science	NOUN
ejpam-5962	1	105	,	,	PUNCT
ejpam-5962	1	106	amman	amman	PROPN
ejpam-5962	1	107	arab	arab	PROPN
ejpam-5962	1	108	university	university	PROPN
ejpam-5962	1	109	,	,	PUNCT
ejpam-5962	1	110	amman	amman	PROPN
ejpam-5962	1	111	,	,	PUNCT
ejpam-5962	1	112	p.o.box	p.o.box	PROPN
ejpam-5962	1	113	24	24	NUM
ejpam-5962	1	114	,	,	PUNCT
ejpam-5962	1	115	amman	amman	PROPN
ejpam-5962	1	116	,	,	PUNCT
ejpam-5962	1	117	jordan	jordan	PROPN
ejpam-5962	1	118	3	3	NUM
ejpam-5962	1	119	department	department	PROPN
ejpam-5962	1	120	of	of	ADP
ejpam-5962	1	121	mathematics	mathematic	NOUN
ejpam-5962	1	122	,	,	PUNCT
ejpam-5962	1	123	irbid	irbid	ADJ
ejpam-5962	1	124	national	national	ADJ
ejpam-5962	1	125	university	university	NOUN
ejpam-5962	1	126	,	,	PUNCT
ejpam-5962	1	127	irbid	irbid	PROPN
ejpam-5962	1	128	,	,	PUNCT
ejpam-5962	1	129	jordan	jordan	PROPN
ejpam-5962	1	130	4	4	NUM
ejpam-5962	1	131	amman	amman	PROPN
ejpam-5962	1	132	arab	arab	PROPN
ejpam-5962	1	133	university	university	PROPN
ejpam-5962	1	134	,	,	PUNCT
ejpam-5962	1	135	amman	amman	PROPN
ejpam-5962	1	136	,	,	PUNCT
ejpam-5962	1	137	p.o.box	p.o.box	PROPN
ejpam-5962	1	138	24	24	NUM
ejpam-5962	1	139	,	,	PUNCT
ejpam-5962	1	140	amman	amman	PROPN
ejpam-5962	1	141	,	,	PUNCT
ejpam-5962	1	142	jordan	jordan	PROPN
ejpam-5962	1	143	abstract	abstract	PROPN
ejpam-5962	1	144	.	.	PUNCT
ejpam-5962	2	1	due	due	ADP
ejpam-5962	2	2	to	to	ADP
ejpam-5962	2	3	the	the	DET
ejpam-5962	2	4	widespread	widespread	ADJ
ejpam-5962	2	5	use	use	NOUN
ejpam-5962	2	6	of	of	ADP
ejpam-5962	2	7	various	various	ADJ
ejpam-5962	2	8	mathematical	mathematical	ADJ
ejpam-5962	2	9	concepts	concept	NOUN
ejpam-5962	2	10	,	,	PUNCT
ejpam-5962	2	11	operations	operation	NOUN
ejpam-5962	2	12	,	,	PUNCT
ejpam-5962	2	13	relations	relation	NOUN
ejpam-5962	2	14	,	,	PUNCT
ejpam-5962	2	15	findings	finding	NOUN
ejpam-5962	2	16	,	,	PUNCT
ejpam-5962	2	17	numerous	numerous	ADJ
ejpam-5962	2	18	writers	writer	NOUN
ejpam-5962	2	19	have	have	AUX
ejpam-5962	2	20	established	establish	VERB
ejpam-5962	2	21	these	these	DET
ejpam-5962	2	22	concepts	concept	NOUN
ejpam-5962	2	23	in	in	ADP
ejpam-5962	2	24	minimal	minimal	ADJ
ejpam-5962	2	25	spaces	space	NOUN
ejpam-5962	2	26	.	.	PUNCT
ejpam-5962	3	1	determining	determine	VERB
ejpam-5962	3	2	how	how	SCONJ
ejpam-5962	3	3	to	to	PART
ejpam-5962	3	4	create	create	VERB
ejpam-5962	3	5	pairwise	pairwise	NOUN
ejpam-5962	3	6	minimal	minimal	ADJ
ejpam-5962	3	7	spaces	space	NOUN
ejpam-5962	3	8	by	by	ADP
ejpam-5962	3	9	utilizing	utilize	VERB
ejpam-5962	3	10	a	a	DET
ejpam-5962	3	11	variety	variety	NOUN
ejpam-5962	3	12	of	of	ADP
ejpam-5962	3	13	set	set	NOUN
ejpam-5962	3	14	operators	operator	NOUN
ejpam-5962	3	15	is	be	AUX
ejpam-5962	3	16	what	what	PRON
ejpam-5962	3	17	this	this	DET
ejpam-5962	3	18	article	article	NOUN
ejpam-5962	3	19	is	be	AUX
ejpam-5962	3	20	about	about	ADP
ejpam-5962	3	21	.	.	PUNCT
ejpam-5962	4	1	specific	specific	ADJ
ejpam-5962	4	2	kinds	kind	NOUN
ejpam-5962	4	3	of	of	ADP
ejpam-5962	4	4	minimal	minimal	ADJ
ejpam-5962	4	5	spaces	space	NOUN
ejpam-5962	4	6	and	and	CCONJ
ejpam-5962	4	7	their	their	PRON
ejpam-5962	4	8	classical	classical	ADJ
ejpam-5962	4	9	bitopologies	bitopologie	NOUN
ejpam-5962	4	10	interact	interact	VERB
ejpam-5962	4	11	with	with	ADP
ejpam-5962	4	12	one	one	NUM
ejpam-5962	4	13	another	another	DET
ejpam-5962	4	14	to	to	PART
ejpam-5962	4	15	form	form	VERB
ejpam-5962	4	16	symmetry	symmetry	NOUN
ejpam-5962	4	17	.	.	PUNCT
ejpam-5962	5	1	through	through	ADP
ejpam-5962	5	2	the	the	DET
ejpam-5962	5	3	study	study	NOUN
ejpam-5962	5	4	of	of	ADP
ejpam-5962	5	5	sets	set	NOUN
ejpam-5962	5	6	,	,	PUNCT
ejpam-5962	5	7	we	we	PRON
ejpam-5962	5	8	can	can	AUX
ejpam-5962	5	9	investigate	investigate	VERB
ejpam-5962	5	10	the	the	DET
ejpam-5962	5	11	characteristics	characteristic	NOUN
ejpam-5962	5	12	and	and	CCONJ
ejpam-5962	5	13	behaviors	behavior	NOUN
ejpam-5962	5	14	of	of	ADP
ejpam-5962	5	15	traditional	traditional	ADJ
ejpam-5962	5	16	bitopological	bitopological	ADJ
ejpam-5962	5	17	ideas	idea	NOUN
ejpam-5962	5	18	.	.	PUNCT
ejpam-5962	6	1	closed	close	VERB
ejpam-5962	6	2	spaces	space	NOUN
ejpam-5962	6	3	are	be	AUX
ejpam-5962	6	4	a	a	DET
ejpam-5962	6	5	new	new	ADJ
ejpam-5962	6	6	class	class	NOUN
ejpam-5962	6	7	of	of	ADP
ejpam-5962	6	8	bitopological	bitopological	ADJ
ejpam-5962	6	9	spaces	space	NOUN
ejpam-5962	6	10	that	that	PRON
ejpam-5962	6	11	we	we	PRON
ejpam-5962	6	12	characterize	characterize	VERB
ejpam-5962	6	13	and	and	CCONJ
ejpam-5962	6	14	assess	assess	VERB
ejpam-5962	6	15	in	in	ADP
ejpam-5962	6	16	this	this	DET
ejpam-5962	6	17	study	study	NOUN
ejpam-5962	6	18	.	.	PUNCT
ejpam-5962	7	1	we	we	PRON
ejpam-5962	7	2	also	also	ADV
ejpam-5962	7	3	establish	establish	VERB
ejpam-5962	7	4	links	link	NOUN
ejpam-5962	7	5	among	among	ADP
ejpam-5962	7	6	this	this	DET
ejpam-5962	7	7	novel	novel	ADJ
ejpam-5962	7	8	category	category	NOUN
ejpam-5962	7	9	of	of	ADP
ejpam-5962	7	10	minimal	minimal	ADJ
ejpam-5962	7	11	spaces	space	NOUN
ejpam-5962	7	12	and	and	CCONJ
ejpam-5962	7	13	other	other	ADJ
ejpam-5962	7	14	classes	class	NOUN
ejpam-5962	7	15	of	of	ADP
ejpam-5962	7	16	generalized	generalized	ADJ
ejpam-5962	7	17	spaces	space	NOUN
ejpam-5962	7	18	.	.	PUNCT
ejpam-5962	8	1	furthermore	furthermore	ADV
ejpam-5962	8	2	,	,	PUNCT
ejpam-5962	8	3	we	we	PRON
ejpam-5962	8	4	introduce	introduce	VERB
ejpam-5962	8	5	and	and	CCONJ
ejpam-5962	8	6	analyze	analyze	VERB
ejpam-5962	8	7	the	the	DET
ejpam-5962	8	8	closed	close	VERB
ejpam-5962	8	9	spaces	space	NOUN
ejpam-5962	8	10	that	that	PRON
ejpam-5962	8	11	were	be	AUX
ejpam-5962	8	12	originally	originally	ADV
ejpam-5962	8	13	suggested	suggest	VERB
ejpam-5962	8	14	here	here	ADV
ejpam-5962	8	15	,	,	PUNCT
ejpam-5962	8	16	illustrate	illustrate	VERB
ejpam-5962	8	17	this	this	DET
ejpam-5962	8	18	innovative	innovative	ADJ
ejpam-5962	8	19	idea	idea	NOUN
ejpam-5962	8	20	,	,	PUNCT
ejpam-5962	8	21	make	make	VERB
ejpam-5962	8	22	clear	clear	ADJ
ejpam-5962	8	23	the	the	DET
ejpam-5962	8	24	interactions	interaction	NOUN
ejpam-5962	8	25	that	that	PRON
ejpam-5962	8	26	go	go	VERB
ejpam-5962	8	27	along	along	ADP
ejpam-5962	8	28	with	with	ADP
ejpam-5962	8	29	it	it	PRON
ejpam-5962	8	30	,	,	PUNCT
ejpam-5962	8	31	pinpoint	pinpoint	VERB
ejpam-5962	8	32	the	the	DET
ejpam-5962	8	33	requirements	requirement	NOUN
ejpam-5962	8	34	for	for	ADP
ejpam-5962	8	35	its	its	PRON
ejpam-5962	8	36	successful	successful	ADJ
ejpam-5962	8	37	application	application	NOUN
ejpam-5962	8	38	,	,	PUNCT
ejpam-5962	8	39	and	and	CCONJ
ejpam-5962	8	40	offer	offer	VERB
ejpam-5962	8	41	applications	application	NOUN
ejpam-5962	8	42	and	and	CCONJ
ejpam-5962	8	43	counter	counter	NOUN
ejpam-5962	8	44	-	-	NOUN
ejpam-5962	8	45	examples	example	NOUN
ejpam-5962	8	46	.	.	PUNCT
ejpam-5962	9	1	additional	additional	ADJ
ejpam-5962	9	2	explanations	explanation	NOUN
ejpam-5962	9	3	are	be	AUX
ejpam-5962	9	4	provided	provide	VERB
ejpam-5962	9	5	for	for	ADP
ejpam-5962	9	6	the	the	DET
ejpam-5962	9	7	pairwise	pairwise	NOUN
ejpam-5962	9	8	minimal	minimal	ADJ
ejpam-5962	9	9	hausdorff	hausdorff	NOUN
ejpam-5962	9	10	spaces	space	NOUN
ejpam-5962	9	11	,	,	PUNCT
ejpam-5962	9	12	pairwise	pairwise	PROPN
ejpam-5962	9	13	minimal	minimal	ADJ
ejpam-5962	9	14	lindelöf	lindelöf	NOUN
ejpam-5962	9	15	closed	close	VERB
ejpam-5962	9	16	spaces	space	NOUN
ejpam-5962	9	17	,	,	PUNCT
ejpam-5962	9	18	pairwise	pairwise	NOUN
ejpam-5962	9	19	minimal	minimal	ADJ
ejpam-5962	9	20	compact	compact	ADJ
ejpam-5962	9	21	closed	closed	ADJ
ejpam-5962	9	22	spaces	space	NOUN
ejpam-5962	9	23	,	,	PUNCT
ejpam-5962	9	24	and	and	CCONJ
ejpam-5962	9	25	maximal	maximal	ADJ
ejpam-5962	9	26	and	and	CCONJ
ejpam-5962	9	27	minimal	minimal	ADJ
ejpam-5962	9	28	bitopologies	bitopologie	NOUN
ejpam-5962	9	29	.	.	PUNCT
ejpam-5962	10	1	with	with	ADP
ejpam-5962	10	2	of	of	ADP
ejpam-5962	10	3	revenue	revenue	NOUN
ejpam-5962	10	4	of	of	ADP
ejpam-5962	10	5	these	these	DET
ejpam-5962	10	6	spaces	space	NOUN
ejpam-5962	10	7	,	,	PUNCT
ejpam-5962	10	8	we	we	PRON
ejpam-5962	10	9	look	look	VERB
ejpam-5962	10	10	at	at	ADP
ejpam-5962	10	11	inverse	inverse	NOUN
ejpam-5962	10	12	images	image	NOUN
ejpam-5962	10	13	having	have	VERB
ejpam-5962	10	14	particular	particular	ADJ
ejpam-5962	10	15	bitopological	bitopological	ADJ
ejpam-5962	10	16	characteristics	characteristic	NOUN
ejpam-5962	10	17	.	.	PUNCT
ejpam-5962	11	1	the	the	DET
ejpam-5962	11	2	discussion	discussion	NOUN
ejpam-5962	11	3	concludes	conclude	VERB
ejpam-5962	11	4	with	with	ADP
ejpam-5962	11	5	the	the	DET
ejpam-5962	11	6	identification	identification	NOUN
ejpam-5962	11	7	of	of	ADP
ejpam-5962	11	8	related	related	ADJ
ejpam-5962	11	9	product	product	NOUN
ejpam-5962	11	10	conclusions	conclusion	NOUN
ejpam-5962	11	11	for	for	ADP
ejpam-5962	11	12	these	these	DET
ejpam-5962	11	13	ideas	idea	NOUN
ejpam-5962	11	14	.	.	PUNCT
ejpam-5962	12	1	key	key	ADJ
ejpam-5962	12	2	words	word	NOUN
ejpam-5962	12	3	and	and	CCONJ
ejpam-5962	12	4	phrases	phrase	NOUN
ejpam-5962	12	5	:	:	PUNCT
ejpam-5962	12	6	maximal	maximal	ADJ
ejpam-5962	12	7	and	and	CCONJ
ejpam-5962	12	8	minimal	minimal	ADJ
ejpam-5962	12	9	bitopologies	bitopologie	NOUN
ejpam-5962	12	10	,	,	PUNCT
ejpam-5962	12	11	pairwise	pairwise	NOUN
ejpam-5962	12	12	minimal	minimal	ADJ
ejpam-5962	12	13	compact	compact	ADJ
ejpam-5962	12	14	closed	closed	ADJ
ejpam-5962	12	15	spaces	space	NOUN
ejpam-5962	12	16	,	,	PUNCT
ejpam-5962	12	17	pairwise	pairwise	PROPN
ejpam-5962	12	18	minimal	minimal	ADJ
ejpam-5962	12	19	lindelöf	lindelöf	NOUN
ejpam-5962	12	20	closed	close	VERB
ejpam-5962	12	21	spaces	space	NOUN
ejpam-5962	12	22	,	,	PUNCT
ejpam-5962	12	23	pairwise	pairwise	NOUN
ejpam-5962	12	24	minimal	minimal	ADJ
ejpam-5962	12	25	hausdorff	hausdorff	NOUN
ejpam-5962	12	26	spaces	space	NOUN
ejpam-5962	12	27	.	.	PUNCT
ejpam-5962	13	1	∗corresponding	∗corresponde	VERB
ejpam-5962	13	2	author	author	NOUN
ejpam-5962	13	3	.	.	PUNCT
ejpam-5962	14	1	doi	doi	NOUN
ejpam-5962	14	2	:	:	PUNCT
ejpam-5962	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5962	https://doi.org/10.29020/nybg.ejpam.v18i2.5962	PROPN
ejpam-5962	14	4	email	email	NOUN
ejpam-5962	14	5	addresses	address	NOUN
ejpam-5962	14	6	:	:	PUNCT
ejpam-5962	14	7	aliatoom@anu.edu.jo	aliatoom@anu.edu.jo	NOUN
ejpam-5962	14	8	(	(	PUNCT
ejpam-5962	14	9	a.a	a.a	PROPN
ejpam-5962	14	10	.	.	PROPN
ejpam-5962	14	11	atoom	atoom	PROPN
ejpam-5962	14	12	)	)	PUNCT
ejpam-5962	14	13	,	,	PUNCT
ejpam-5962	14	14	dr.mutaib68@aau.edu.jo	dr.mutaib68@aau.edu.jo	NOUN
ejpam-5962	14	15	(	(	PUNCT
ejpam-5962	14	16	m.	m.	NOUN
ejpam-5962	14	17	al	al	PROPN
ejpam-5962	14	18	-	-	PUNCT
ejpam-5962	14	19	otaibi	otaibi	NOUN
ejpam-5962	14	20	)	)	PUNCT
ejpam-5962	14	21	,	,	PUNCT
ejpam-5962	14	22	hhaaqq983@gmail.com	hhaaqq983@gmail.com	X
ejpam-5962	14	23	(	(	PUNCT
ejpam-5962	14	24	h.	h.	PROPN
ejpam-5962	14	25	qoqazeh	qoqazeh	PROPN
ejpam-5962	14	26	)	)	PUNCT
ejpam-5962	14	27	,	,	PUNCT
ejpam-5962	14	28	alfaroqoomar@gmail.com	alfaroqoomar@gmail.com	PROPN
ejpam-5962	14	29	(	(	PUNCT
ejpam-5962	14	30	f.o	f.o	PROPN
ejpam-5962	14	31	.	.	PROPN
ejpam-5962	14	32	alkhawaldeh	alkhawaldeh	PROPN
ejpam-5962	14	33	)	)	PUNCT
ejpam-5962	14	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5962	15	1	1	1	NUM
ejpam-5962	15	2	copyright	copyright	NOUN
ejpam-5962	15	3	:	:	PUNCT
ejpam-5962	15	4	©	©	PROPN
ejpam-5962	15	5	2025	2025	NUM
ejpam-5962	15	6	the	the	DET
ejpam-5962	15	7	author(s	author(s	NOUN
ejpam-5962	15	8	)	)	PUNCT
ejpam-5962	15	9	.	.	PUNCT
ejpam-5962	16	1	(	(	PUNCT
ejpam-5962	16	2	cc	cc	NOUN
ejpam-5962	16	3	by	by	ADP
ejpam-5962	16	4	-	-	PUNCT
ejpam-5962	16	5	nc	nc	PROPN
ejpam-5962	16	6	4.0	4.0	NUM
ejpam-5962	16	7	)	)	PUNCT
ejpam-5962	16	8	a.	a.	NOUN
ejpam-5962	16	9	a.	a.	NOUN
ejpam-5962	16	10	atoom	atoom	PROPN
ejpam-5962	16	11	et	et	PROPN
ejpam-5962	16	12	al	al	PROPN
ejpam-5962	16	13	.	.	PUNCT
ejpam-5962	16	14	/	/	SYM
ejpam-5962	16	15	eur	eur	PROPN
ejpam-5962	16	16	.	.	PUNCT
ejpam-5962	17	1	j.	j.	PROPN
ejpam-5962	17	2	pure	pure	PROPN
ejpam-5962	17	3	appl	appl	PROPN
ejpam-5962	17	4	.	.	PROPN
ejpam-5962	17	5	math	math	PROPN
ejpam-5962	17	6	,	,	PUNCT
ejpam-5962	17	7	18	18	NUM
ejpam-5962	17	8	(	(	PUNCT
ejpam-5962	17	9	2	2	NUM
ejpam-5962	17	10	)	)	PUNCT
ejpam-5962	17	11	(	(	PUNCT
ejpam-5962	17	12	2025	2025	NUM
ejpam-5962	17	13	)	)	PUNCT
ejpam-5962	17	14	,	,	PUNCT
ejpam-5962	17	15	5962	5962	NUM
ejpam-5962	17	16	2	2	NUM
ejpam-5962	17	17	of	of	ADP
ejpam-5962	17	18	17	17	NUM
ejpam-5962	17	19	1	1	NUM
ejpam-5962	17	20	.	.	PUNCT
ejpam-5962	18	1	introduction	introduction	NOUN
ejpam-5962	18	2	recognizing	recognize	VERB
ejpam-5962	18	3	the	the	DET
ejpam-5962	18	4	significance	significance	NOUN
ejpam-5962	18	5	of	of	ADP
ejpam-5962	18	6	topological	topological	ADJ
ejpam-5962	18	7	space	space	NOUN
ejpam-5962	18	8	in	in	ADP
ejpam-5962	18	9	data	data	NOUN
ejpam-5962	18	10	analysis	analysis	NOUN
ejpam-5962	18	11	and	and	CCONJ
ejpam-5962	18	12	some	some	DET
ejpam-5962	18	13	applications	application	NOUN
ejpam-5962	18	14	,	,	PUNCT
ejpam-5962	18	15	numerous	numerous	ADJ
ejpam-5962	18	16	studies	study	NOUN
ejpam-5962	18	17	have	have	AUX
ejpam-5962	18	18	employed	employ	VERB
ejpam-5962	18	19	a	a	DET
ejpam-5962	18	20	variety	variety	NOUN
ejpam-5962	18	21	of	of	ADP
ejpam-5962	18	22	techniques	technique	NOUN
ejpam-5962	18	23	to	to	PART
ejpam-5962	18	24	increase	increase	VERB
ejpam-5962	18	25	that	that	DET
ejpam-5962	18	26	space	space	NOUN
ejpam-5962	18	27	,	,	PUNCT
ejpam-5962	18	28	including	include	VERB
ejpam-5962	18	29	the	the	DET
ejpam-5962	18	30	idea	idea	NOUN
ejpam-5962	18	31	of	of	ADP
ejpam-5962	18	32	minimal	minimal	ADJ
ejpam-5962	18	33	spaces	space	NOUN
ejpam-5962	18	34	.	.	PUNCT
ejpam-5962	19	1	many	many	ADJ
ejpam-5962	19	2	research	research	NOUN
ejpam-5962	19	3	have	have	AUX
ejpam-5962	19	4	used	use	VERB
ejpam-5962	19	5	a	a	DET
ejpam-5962	19	6	range	range	NOUN
ejpam-5962	19	7	of	of	ADP
ejpam-5962	19	8	methods	method	NOUN
ejpam-5962	19	9	to	to	PART
ejpam-5962	19	10	expand	expand	VERB
ejpam-5962	19	11	topological	topological	ADJ
ejpam-5962	19	12	space	space	NOUN
ejpam-5962	19	13	,	,	PUNCT
ejpam-5962	19	14	including	include	VERB
ejpam-5962	19	15	the	the	DET
ejpam-5962	19	16	concept	concept	NOUN
ejpam-5962	19	17	of	of	ADP
ejpam-5962	19	18	minimum	minimum	ADJ
ejpam-5962	19	19	spaces	space	NOUN
ejpam-5962	19	20	,	,	PUNCT
ejpam-5962	19	21	because	because	SCONJ
ejpam-5962	19	22	of	of	ADP
ejpam-5962	19	23	its	its	PRON
ejpam-5962	19	24	importance	importance	NOUN
ejpam-5962	19	25	in	in	ADP
ejpam-5962	19	26	data	data	NOUN
ejpam-5962	19	27	processing	processing	NOUN
ejpam-5962	19	28	and	and	CCONJ
ejpam-5962	19	29	some	some	DET
ejpam-5962	19	30	applications	application	NOUN
ejpam-5962	19	31	.	.	PUNCT
ejpam-5962	20	1	numerous	numerous	ADJ
ejpam-5962	20	2	authors	author	NOUN
ejpam-5962	20	3	have	have	AUX
ejpam-5962	20	4	established	establish	VERB
ejpam-5962	20	5	these	these	DET
ejpam-5962	20	6	notions	notion	NOUN
ejpam-5962	20	7	in	in	ADP
ejpam-5962	20	8	minimal	minimal	ADJ
ejpam-5962	20	9	spaces	space	NOUN
ejpam-5962	20	10	due	due	ADP
ejpam-5962	20	11	to	to	ADP
ejpam-5962	20	12	the	the	DET
ejpam-5962	20	13	widespread	widespread	ADJ
ejpam-5962	20	14	use	use	NOUN
ejpam-5962	20	15	of	of	ADP
ejpam-5962	20	16	various	various	ADJ
ejpam-5962	20	17	operations	operation	NOUN
ejpam-5962	20	18	,	,	PUNCT
ejpam-5962	20	19	relations	relation	NOUN
ejpam-5962	20	20	,	,	PUNCT
ejpam-5962	20	21	results	result	NOUN
ejpam-5962	20	22	,	,	PUNCT
ejpam-5962	20	23	and	and	CCONJ
ejpam-5962	20	24	other	other	ADJ
ejpam-5962	20	25	aspects	aspect	NOUN
ejpam-5962	20	26	in	in	ADP
ejpam-5962	20	27	mathematics	mathematic	NOUN
ejpam-5962	20	28	and	and	CCONJ
ejpam-5962	20	29	related	related	ADJ
ejpam-5962	20	30	subjects	subject	NOUN
ejpam-5962	20	31	.	.	PUNCT
ejpam-5962	21	1	this	this	DET
ejpam-5962	21	2	article	article	NOUN
ejpam-5962	21	3	focuses	focus	VERB
ejpam-5962	21	4	on	on	ADP
ejpam-5962	21	5	figuring	figure	VERB
ejpam-5962	21	6	out	out	ADP
ejpam-5962	21	7	how	how	SCONJ
ejpam-5962	21	8	to	to	PART
ejpam-5962	21	9	construct	construct	VERB
ejpam-5962	21	10	pairwise	pairwise	NOUN
ejpam-5962	21	11	minimum	minimum	NOUN
ejpam-5962	21	12	spaces	space	NOUN
ejpam-5962	21	13	using	use	VERB
ejpam-5962	21	14	various	various	ADJ
ejpam-5962	21	15	set	set	NOUN
ejpam-5962	21	16	operators	operator	NOUN
ejpam-5962	21	17	.	.	PUNCT
ejpam-5962	22	1	symmetry	symmetry	NOUN
ejpam-5962	22	2	is	be	AUX
ejpam-5962	22	3	the	the	DET
ejpam-5962	22	4	result	result	NOUN
ejpam-5962	22	5	of	of	ADP
ejpam-5962	22	6	interactions	interaction	NOUN
ejpam-5962	22	7	between	between	ADP
ejpam-5962	22	8	certain	certain	ADJ
ejpam-5962	22	9	types	type	NOUN
ejpam-5962	22	10	of	of	ADP
ejpam-5962	22	11	minimum	minimum	ADJ
ejpam-5962	22	12	spaces	space	NOUN
ejpam-5962	22	13	and	and	CCONJ
ejpam-5962	22	14	their	their	PRON
ejpam-5962	22	15	classical	classical	ADJ
ejpam-5962	22	16	topologies	topology	NOUN
ejpam-5962	22	17	.	.	PUNCT
ejpam-5962	23	1	a.	a.	PROPN
ejpam-5962	23	2	s.	s.	PROPN
ejpam-5962	23	3	parhomenko	parhomenko	PROPN
ejpam-5962	24	1	[	[	X
ejpam-5962	24	2	1	1	NUM
ejpam-5962	24	3	]	]	PUNCT
ejpam-5962	24	4	established	establish	VERB
ejpam-5962	24	5	that	that	SCONJ
ejpam-5962	24	6	compact	compact	ADJ
ejpam-5962	24	7	hausdorff	hausdorff	NOUN
ejpam-5962	24	8	spaces	space	NOUN
ejpam-5962	24	9	are	be	AUX
ejpam-5962	24	10	minimal	minimal	ADJ
ejpam-5962	24	11	hausdorff	hausdorff	NOUN
ejpam-5962	24	12	in	in	ADP
ejpam-5962	24	13	1939	1939	NUM
ejpam-5962	24	14	,	,	PUNCT
ejpam-5962	24	15	which	which	PRON
ejpam-5962	24	16	is	be	AUX
ejpam-5962	24	17	when	when	SCONJ
ejpam-5962	24	18	the	the	DET
ejpam-5962	24	19	idea	idea	NOUN
ejpam-5962	24	20	of	of	ADP
ejpam-5962	24	21	minimal	minimal	ADJ
ejpam-5962	24	22	topologies	topology	NOUN
ejpam-5962	24	23	was	be	AUX
ejpam-5962	24	24	first	first	ADV
ejpam-5962	24	25	proposed	propose	VERB
ejpam-5962	24	26	.	.	PUNCT
ejpam-5962	25	1	compact	compact	ADJ
ejpam-5962	25	2	hausdorff	hausdorff	NOUN
ejpam-5962	25	3	spaces	space	NOUN
ejpam-5962	25	4	are	be	AUX
ejpam-5962	25	5	maximally	maximally	ADV
ejpam-5962	25	6	compact	compact	ADJ
ejpam-5962	25	7	in	in	ADP
ejpam-5962	25	8	addition	addition	NOUN
ejpam-5962	25	9	to	to	ADP
ejpam-5962	25	10	being	be	AUX
ejpam-5962	25	11	minimal	minimal	ADJ
ejpam-5962	25	12	hausdorff	hausdorff	NOUN
ejpam-5962	25	13	,	,	PUNCT
ejpam-5962	25	14	as	as	SCONJ
ejpam-5962	25	15	e.	e.	PROPN
ejpam-5962	25	16	hewitt	hewitt	PROPN
ejpam-5962	26	1	[	[	X
ejpam-5962	26	2	2	2	X
ejpam-5962	26	3	]	]	PUNCT
ejpam-5962	26	4	demonstrated	demonstrate	VERB
ejpam-5962	26	5	four	four	NUM
ejpam-5962	26	6	years	year	NOUN
ejpam-5962	26	7	later	later	ADV
ejpam-5962	26	8	.	.	PUNCT
ejpam-5962	27	1	if	if	SCONJ
ejpam-5962	27	2	non	non	ADJ
ejpam-5962	27	3	-	-	ADJ
ejpam-5962	27	4	hausdorff	hausdorff	ADJ
ejpam-5962	27	5	maximal	maximal	ADJ
ejpam-5962	27	6	compact	compact	ADJ
ejpam-5962	27	7	spaces	space	NOUN
ejpam-5962	27	8	or	or	CCONJ
ejpam-5962	27	9	non	non	ADJ
ejpam-5962	27	10	-	-	ADJ
ejpam-5962	27	11	hausdorff	hausdorff	ADJ
ejpam-5962	27	12	minimal	minimal	ADJ
ejpam-5962	27	13	compact	compact	ADJ
ejpam-5962	27	14	spaces	space	NOUN
ejpam-5962	27	15	exist	exist	VERB
ejpam-5962	27	16	,	,	PUNCT
ejpam-5962	27	17	r.	r.	PROPN
ejpam-5962	27	18	vaidyanathaswamy	vaidyanathaswamy	NOUN
ejpam-5962	28	1	[	[	X
ejpam-5962	28	2	3	3	X
ejpam-5962	28	3	]	]	PUNCT
ejpam-5962	28	4	questioned	question	VERB
ejpam-5962	28	5	this	this	PRON
ejpam-5962	28	6	in	in	ADP
ejpam-5962	28	7	1947	1947	NUM
ejpam-5962	28	8	.	.	PUNCT
ejpam-5962	29	1	the	the	DET
ejpam-5962	29	2	existence	existence	NOUN
ejpam-5962	29	3	of	of	ADP
ejpam-5962	29	4	these	these	DET
ejpam-5962	29	5	minimal	minimal	ADJ
ejpam-5962	29	6	hausdorff	hausdorff	NOUN
ejpam-5962	29	7	spaces	space	NOUN
ejpam-5962	29	8	was	be	AUX
ejpam-5962	29	9	demonstrated	demonstrate	VERB
ejpam-5962	29	10	and	and	CCONJ
ejpam-5962	29	11	all	all	DET
ejpam-5962	29	12	minimal	minimal	ADJ
ejpam-5962	29	13	hausdorff	hausdorff	NOUN
ejpam-5962	29	14	spaces	space	NOUN
ejpam-5962	29	15	were	be	AUX
ejpam-5962	29	16	described	describe	VERB
ejpam-5962	29	17	by	by	ADP
ejpam-5962	29	18	a.	a.	NOUN
ejpam-5962	29	19	ramanathan	ramanathan	PROPN
ejpam-5962	30	1	[	[	X
ejpam-5962	30	2	4	4	NUM
ejpam-5962	30	3	]	]	PUNCT
ejpam-5962	30	4	,	,	PUNCT
ejpam-5962	30	5	[	[	X
ejpam-5962	30	6	5	5	NUM
ejpam-5962	30	7	]	]	PUNCT
ejpam-5962	30	8	in	in	ADP
ejpam-5962	30	9	the	the	DET
ejpam-5962	30	10	same	same	ADJ
ejpam-5962	30	11	year	year	NOUN
ejpam-5962	30	12	.	.	PUNCT
ejpam-5962	31	1	the	the	DET
ejpam-5962	31	2	other	other	ADJ
ejpam-5962	31	3	portion	portion	NOUN
ejpam-5962	31	4	of	of	ADP
ejpam-5962	31	5	vaidyanathaswamy	vaidyanathaswamy	NOUN
ejpam-5962	31	6	’s	’s	PART
ejpam-5962	31	7	query	query	NOUN
ejpam-5962	31	8	was	be	AUX
ejpam-5962	31	9	addressed	address	VERB
ejpam-5962	31	10	by	by	ADP
ejpam-5962	31	11	hing	he	VERB
ejpam-5962	31	12	tong	tong	PROPN
ejpam-5962	32	1	[	[	X
ejpam-5962	32	2	6	6	NUM
ejpam-5962	32	3	]	]	PUNCT
ejpam-5962	32	4	in	in	ADP
ejpam-5962	32	5	1948	1948	NUM
ejpam-5962	32	6	when	when	SCONJ
ejpam-5962	32	7	he	he	PRON
ejpam-5962	32	8	created	create	VERB
ejpam-5962	32	9	an	an	DET
ejpam-5962	32	10	illustration	illustration	NOUN
ejpam-5962	32	11	of	of	ADP
ejpam-5962	32	12	a	a	DET
ejpam-5962	32	13	maximal	maximal	ADJ
ejpam-5962	32	14	compact	compact	ADJ
ejpam-5962	32	15	space	space	NOUN
ejpam-5962	32	16	that	that	PRON
ejpam-5962	32	17	was	be	AUX
ejpam-5962	32	18	n’t	not	PART
ejpam-5962	32	19	hausdorff	hausdorff	NOUN
ejpam-5962	32	20	.	.	PUNCT
ejpam-5962	33	1	a.	a.	NOUN
ejpam-5962	33	2	ramanathan	ramanathan	PROPN
ejpam-5962	34	1	[	[	X
ejpam-5962	34	2	7	7	X
ejpam-5962	34	3	]	]	PUNCT
ejpam-5962	34	4	established	establish	VERB
ejpam-5962	34	5	the	the	DET
ejpam-5962	34	6	maximal	maximal	ADJ
ejpam-5962	34	7	compactness	compactness	NOUN
ejpam-5962	34	8	of	of	ADP
ejpam-5962	34	9	a	a	DET
ejpam-5962	34	10	topological	topological	ADJ
ejpam-5962	34	11	space	space	NOUN
ejpam-5962	34	12	in	in	ADP
ejpam-5962	34	13	1948	1948	NUM
ejpam-5962	34	14	.	.	PUNCT
ejpam-5962	35	1	when	when	SCONJ
ejpam-5962	35	2	and	and	CCONJ
ejpam-5962	35	3	only	only	ADV
ejpam-5962	35	4	when	when	SCONJ
ejpam-5962	35	5	its	its	PRON
ejpam-5962	35	6	compact	compact	ADJ
ejpam-5962	35	7	subsets	subset	NOUN
ejpam-5962	35	8	exactly	exactly	ADV
ejpam-5962	35	9	match	match	VERB
ejpam-5962	35	10	the	the	DET
ejpam-5962	35	11	closed	closed	ADJ
ejpam-5962	35	12	sets	set	NOUN
ejpam-5962	35	13	.	.	PUNCT
ejpam-5962	36	1	in	in	ADP
ejpam-5962	36	2	1963	1963	NUM
ejpam-5962	36	3	,	,	PUNCT
ejpam-5962	36	4	n.	n.	PROPN
ejpam-5962	36	5	smythe	smythe	PROPN
ejpam-5962	36	6	and	and	CCONJ
ejpam-5962	36	7	c.	c.	PROPN
ejpam-5962	36	8	a.	a.	PROPN
ejpam-5962	36	9	wilkins	wilkins	PROPN
ejpam-5962	36	10	[	[	X
ejpam-5962	36	11	8	8	NUM
ejpam-5962	36	12	]	]	PUNCT
ejpam-5962	36	13	created	create	VERB
ejpam-5962	36	14	an	an	DET
ejpam-5962	36	15	example	example	NOUN
ejpam-5962	36	16	of	of	ADP
ejpam-5962	36	17	a	a	DET
ejpam-5962	36	18	maximal	maximal	ADJ
ejpam-5962	36	19	compact	compact	ADJ
ejpam-5962	36	20	space	space	NOUN
ejpam-5962	36	21	without	without	ADP
ejpam-5962	36	22	isolated	isolated	ADJ
ejpam-5962	36	23	points	point	NOUN
ejpam-5962	36	24	that	that	PRON
ejpam-5962	36	25	are	be	AUX
ejpam-5962	36	26	strictly	strictly	ADV
ejpam-5962	36	27	weaker	weak	ADJ
ejpam-5962	36	28	than	than	ADP
ejpam-5962	36	29	a	a	DET
ejpam-5962	36	30	minimal	minimal	ADJ
ejpam-5962	36	31	hausdorff	hausdorff	NOUN
ejpam-5962	36	32	topology	topology	NOUN
ejpam-5962	36	33	,	,	PUNCT
ejpam-5962	36	34	which	which	PRON
ejpam-5962	36	35	was	be	AUX
ejpam-5962	36	36	the	the	DET
ejpam-5962	36	37	first	first	ADJ
ejpam-5962	36	38	significant	significant	ADJ
ejpam-5962	36	39	work	work	NOUN
ejpam-5962	36	40	on	on	ADP
ejpam-5962	36	41	maximal	maximal	ADJ
ejpam-5962	36	42	characteristics	characteristic	NOUN
ejpam-5962	36	43	.	.	PUNCT
ejpam-5962	37	1	every	every	DET
ejpam-5962	37	2	compact	compact	ADJ
ejpam-5962	37	3	set	set	NOUN
ejpam-5962	37	4	must	must	AUX
ejpam-5962	37	5	be	be	AUX
ejpam-5962	37	6	closed	close	VERB
ejpam-5962	37	7	for	for	ADP
ejpam-5962	37	8	a	a	DET
ejpam-5962	37	9	topological	topological	ADJ
ejpam-5962	37	10	space	space	NOUN
ejpam-5962	37	11	to	to	PART
ejpam-5962	37	12	be	be	AUX
ejpam-5962	37	13	referred	refer	VERB
ejpam-5962	37	14	to	to	ADP
ejpam-5962	37	15	as	as	ADP
ejpam-5962	37	16	a	a	DET
ejpam-5962	37	17	compact	compact	ADJ
ejpam-5962	37	18	closed	closed	ADJ
ejpam-5962	37	19	space	space	NOUN
ejpam-5962	37	20	.	.	PUNCT
ejpam-5962	38	1	because	because	SCONJ
ejpam-5962	38	2	every	every	DET
ejpam-5962	38	3	compact	compact	ADJ
ejpam-5962	38	4	closed	closed	ADJ
ejpam-5962	38	5	space	space	NOUN
ejpam-5962	38	6	is	be	AUX
ejpam-5962	38	7	a	a	DET
ejpam-5962	38	8	t1−space	t1−space	NOUN
ejpam-5962	38	9	and	and	CCONJ
ejpam-5962	38	10	every	every	DET
ejpam-5962	38	11	compact	compact	ADJ
ejpam-5962	38	12	closed	closed	ADJ
ejpam-5962	38	13	space	space	NOUN
ejpam-5962	38	14	is	be	AUX
ejpam-5962	38	15	a	a	DET
ejpam-5962	38	16	t2−space	t2−space	NOUN
ejpam-5962	38	17	,	,	PUNCT
ejpam-5962	38	18	the	the	DET
ejpam-5962	38	19	compact	compact	ADJ
ejpam-5962	38	20	closed	close	VERB
ejpam-5962	38	21	property	property	NOUN
ejpam-5962	38	22	can	can	AUX
ejpam-5962	38	23	be	be	AUX
ejpam-5962	38	24	viewed	view	VERB
ejpam-5962	38	25	as	as	ADP
ejpam-5962	38	26	a	a	DET
ejpam-5962	38	27	separation	separation	NOUN
ejpam-5962	38	28	axiom	axiom	NOUN
ejpam-5962	38	29	between	between	ADP
ejpam-5962	38	30	t1	t1	NOUN
ejpam-5962	38	31	and	and	CCONJ
ejpam-5962	38	32	t2	t2	PROPN
ejpam-5962	38	33	.	.	PUNCT
ejpam-5962	39	1	e.	e.	PROPN
ejpam-5962	39	2	hewitt	hewitt	PROPN
ejpam-5962	40	1	[	[	X
ejpam-5962	40	2	2	2	X
ejpam-5962	40	3	]	]	PUNCT
ejpam-5962	40	4	demonstrated	demonstrate	VERB
ejpam-5962	40	5	in	in	ADP
ejpam-5962	40	6	1943	1943	NUM
ejpam-5962	40	7	that	that	PRON
ejpam-5962	40	8	a	a	DET
ejpam-5962	40	9	compact	compact	ADJ
ejpam-5962	40	10	t2	t2	NOUN
ejpam-5962	40	11	space	space	NOUN
ejpam-5962	40	12	is	be	AUX
ejpam-5962	40	13	both	both	PRON
ejpam-5962	40	14	minimally	minimally	ADV
ejpam-5962	40	15	and	and	CCONJ
ejpam-5962	40	16	maximally	maximally	ADV
ejpam-5962	40	17	compact	compact	ADJ
ejpam-5962	40	18	;	;	PUNCT
ejpam-5962	40	19	for	for	ADP
ejpam-5962	40	20	related	related	ADJ
ejpam-5962	40	21	work	work	NOUN
ejpam-5962	40	22	,	,	PUNCT
ejpam-5962	40	23	see	see	VERB
ejpam-5962	40	24	[	[	X
ejpam-5962	40	25	7	7	NUM
ejpam-5962	40	26	]	]	PUNCT
ejpam-5962	40	27	,	,	PUNCT
ejpam-5962	41	1	[	[	X
ejpam-5962	41	2	8	8	NUM
ejpam-5962	41	3	]	]	PUNCT
ejpam-5962	41	4	.	.	PUNCT
ejpam-5962	42	1	if	if	SCONJ
ejpam-5962	42	2	a	a	DET
ejpam-5962	42	3	space	space	NOUN
ejpam-5962	42	4	is	be	AUX
ejpam-5962	42	5	minimally	minimally	ADV
ejpam-5962	42	6	compact	compact	ADJ
ejpam-5962	42	7	closed	closed	ADJ
ejpam-5962	42	8	,	,	PUNCT
ejpam-5962	42	9	is	be	AUX
ejpam-5962	42	10	it	it	PRON
ejpam-5962	42	11	maximally	maximally	ADV
ejpam-5962	42	12	compact	compact	ADJ
ejpam-5962	42	13	?	?	PUNCT
ejpam-5962	43	1	questioned	question	VERB
ejpam-5962	43	2	r.	r.	PROPN
ejpam-5962	43	3	larson	larson	PROPN
ejpam-5962	43	4	k,[9	k,[9	PROPN
ejpam-5962	43	5	]	]	PUNCT
ejpam-5962	43	6	.	.	PUNCT
ejpam-5962	44	1	is	be	AUX
ejpam-5962	44	2	there	there	PRON
ejpam-5962	44	3	a	a	DET
ejpam-5962	44	4	minimal	minimal	ADJ
ejpam-5962	44	5	compact	compact	ADJ
ejpam-5962	44	6	closed	close	VERB
ejpam-5962	44	7	topology	topology	NOUN
ejpam-5962	44	8	in	in	ADP
ejpam-5962	44	9	every	every	DET
ejpam-5962	44	10	compact	compact	ADJ
ejpam-5962	44	11	closed	close	VERB
ejpam-5962	44	12	topology	topology	NOUN
ejpam-5962	44	13	?	?	PUNCT
ejpam-5962	45	1	this	this	PRON
ejpam-5962	45	2	is	be	AUX
ejpam-5962	45	3	a	a	DET
ejpam-5962	45	4	similar	similar	ADJ
ejpam-5962	45	5	query	query	NOUN
ejpam-5962	45	6	.	.	PUNCT
ejpam-5962	46	1	this	this	PRON
ejpam-5962	46	2	is	be	AUX
ejpam-5962	46	3	n’t	not	PART
ejpam-5962	46	4	always	always	ADV
ejpam-5962	46	5	the	the	DET
ejpam-5962	46	6	case	case	NOUN
ejpam-5962	46	7	,	,	PUNCT
ejpam-5962	46	8	as	as	SCONJ
ejpam-5962	46	9	w.	w.	NOUN
ejpam-5962	46	10	fleissner	fleissner	PROPN
ejpam-5962	46	11	demonstrated	demonstrate	VERB
ejpam-5962	46	12	.	.	PUNCT
ejpam-5962	47	1	he	he	PRON
ejpam-5962	47	2	created	create	VERB
ejpam-5962	47	3	a	a	DET
ejpam-5962	47	4	compact	compact	ADJ
ejpam-5962	47	5	closed	close	VERB
ejpam-5962	47	6	topology	topology	NOUN
ejpam-5962	47	7	in	in	ADP
ejpam-5962	47	8	[	[	X
ejpam-5962	47	9	10	10	NUM
ejpam-5962	47	10	]	]	PUNCT
ejpam-5962	47	11	that	that	PRON
ejpam-5962	47	12	is	be	AUX
ejpam-5962	47	13	not	not	PART
ejpam-5962	47	14	a	a	DET
ejpam-5962	47	15	minimal	minimal	ADJ
ejpam-5962	47	16	compact	compact	ADJ
ejpam-5962	47	17	closed	close	VERB
ejpam-5962	47	18	topology	topology	NOUN
ejpam-5962	47	19	.	.	PUNCT
ejpam-5962	48	1	every	every	DET
ejpam-5962	48	2	hausdorff	hausdorff	ADJ
ejpam-5962	48	3	compact	compact	ADJ
ejpam-5962	48	4	space	space	NOUN
ejpam-5962	48	5	is	be	AUX
ejpam-5962	48	6	maximally	maximally	ADV
ejpam-5962	48	7	compact	compact	ADJ
ejpam-5962	48	8	and	and	CCONJ
ejpam-5962	48	9	minimally	minimally	ADV
ejpam-5962	48	10	compact	compact	ADJ
ejpam-5962	48	11	,	,	PUNCT
ejpam-5962	48	12	as	as	SCONJ
ejpam-5962	48	13	is	be	AUX
ejpam-5962	48	14	well	well	ADV
ejpam-5962	48	15	known	know	VERB
ejpam-5962	48	16	.	.	PUNCT
ejpam-5962	49	1	however	however	ADV
ejpam-5962	49	2	,	,	PUNCT
ejpam-5962	49	3	the	the	DET
ejpam-5962	49	4	author	author	NOUN
ejpam-5962	49	5	in	in	ADP
ejpam-5962	49	6	[	[	X
ejpam-5962	49	7	8	8	NUM
ejpam-5962	49	8	]	]	PUNCT
ejpam-5962	49	9	has	have	AUX
ejpam-5962	49	10	demonstrated	demonstrate	VERB
ejpam-5962	49	11	that	that	SCONJ
ejpam-5962	49	12	there	there	PRON
ejpam-5962	49	13	are	be	VERB
ejpam-5962	49	14	minimal	minimal	ADJ
ejpam-5962	49	15	hausdorff	hausdorff	NOUN
ejpam-5962	49	16	spaces	space	NOUN
ejpam-5962	49	17	that	that	PRON
ejpam-5962	49	18	are	be	AUX
ejpam-5962	49	19	neither	neither	CCONJ
ejpam-5962	49	20	maximally	maximally	ADV
ejpam-5962	49	21	compact	compact	ADJ
ejpam-5962	49	22	nor	nor	CCONJ
ejpam-5962	49	23	minimally	minimally	ADV
ejpam-5962	49	24	compact	compact	ADJ
ejpam-5962	49	25	,	,	PUNCT
ejpam-5962	49	26	and	and	CCONJ
ejpam-5962	49	27	there	there	PRON
ejpam-5962	49	28	are	be	VERB
ejpam-5962	49	29	hausdorff	hausdorff	NOUN
ejpam-5962	49	30	spaces	space	NOUN
ejpam-5962	49	31	that	that	PRON
ejpam-5962	49	32	are	be	AUX
ejpam-5962	49	33	neither	neither	CCONJ
ejpam-5962	49	34	minimally	minimally	ADV
ejpam-5962	49	35	compact	compact	ADJ
ejpam-5962	49	36	nor	nor	CCONJ
ejpam-5962	49	37	maximally	maximally	ADV
ejpam-5962	49	38	compact	compact	ADJ
ejpam-5962	49	39	.	.	PUNCT
ejpam-5962	50	1	although	although	SCONJ
ejpam-5962	50	2	the	the	DET
ejpam-5962	50	3	notion	notion	NOUN
ejpam-5962	50	4	of	of	ADP
ejpam-5962	50	5	a	a	DET
ejpam-5962	50	6	compact	compact	ADJ
ejpam-5962	50	7	closed	closed	ADJ
ejpam-5962	50	8	space	space	NOUN
ejpam-5962	50	9	is	be	AUX
ejpam-5962	50	10	not	not	PART
ejpam-5962	50	11	mentioned	mention	VERB
ejpam-5962	50	12	,	,	PUNCT
ejpam-5962	50	13	it	it	PRON
ejpam-5962	50	14	was	be	AUX
ejpam-5962	50	15	demonstrated	demonstrate	VERB
ejpam-5962	50	16	in	in	ADP
ejpam-5962	50	17	the	the	DET
ejpam-5962	50	18	same	same	ADJ
ejpam-5962	50	19	work	work	NOUN
ejpam-5962	50	20	that	that	PRON
ejpam-5962	50	21	maximal	maximal	ADJ
ejpam-5962	50	22	compact	compact	ADJ
ejpam-5962	50	23	spaces	space	NOUN
ejpam-5962	50	24	are	be	AUX
ejpam-5962	50	25	compact	compact	ADV
ejpam-5962	50	26	closed	closed	ADJ
ejpam-5962	50	27	.	.	PUNCT
ejpam-5962	51	1	any	any	DET
ejpam-5962	51	2	t2	t2	NOUN
ejpam-5962	51	3	-	-	PUNCT
ejpam-5962	51	4	space	space	NOUN
ejpam-5962	51	5	is	be	AUX
ejpam-5962	51	6	closed	close	VERB
ejpam-5962	51	7	compact	compact	ADJ
ejpam-5962	51	8	;	;	PUNCT
ejpam-5962	51	9	nonetheless	nonetheless	ADV
ejpam-5962	51	10	,	,	PUNCT
ejpam-5962	51	11	if	if	SCONJ
ejpam-5962	51	12	a	a	DET
ejpam-5962	51	13	space	space	NOUN
ejpam-5962	51	14	is	be	AUX
ejpam-5962	51	15	closed	close	VERB
ejpam-5962	51	16	compact	compact	ADJ
ejpam-5962	51	17	,	,	PUNCT
ejpam-5962	51	18	it	it	PRON
ejpam-5962	51	19	means	mean	VERB
ejpam-5962	51	20	that	that	SCONJ
ejpam-5962	51	21	its	its	PRON
ejpam-5962	51	22	singletons	singleton	NOUN
ejpam-5962	51	23	are	be	AUX
ejpam-5962	51	24	closed	close	VERB
ejpam-5962	51	25	,	,	PUNCT
ejpam-5962	51	26	which	which	PRON
ejpam-5962	51	27	indicates	indicate	VERB
ejpam-5962	51	28	that	that	SCONJ
ejpam-5962	51	29	the	the	DET
ejpam-5962	51	30	space	space	NOUN
ejpam-5962	51	31	is	be	AUX
ejpam-5962	51	32	t1	t1	NOUN
ejpam-5962	51	33	.	.	PUNCT
ejpam-5962	52	1	this	this	DET
ejpam-5962	52	2	viewpoint	viewpoint	NOUN
ejpam-5962	52	3	suggests	suggest	VERB
ejpam-5962	52	4	that	that	SCONJ
ejpam-5962	52	5	the	the	DET
ejpam-5962	52	6	closed	closed	ADJ
ejpam-5962	52	7	compact	compact	ADJ
ejpam-5962	52	8	quality	quality	NOUN
ejpam-5962	52	9	might	might	AUX
ejpam-5962	52	10	be	be	AUX
ejpam-5962	52	11	thought	think	VERB
ejpam-5962	52	12	of	of	ADP
ejpam-5962	52	13	as	as	ADP
ejpam-5962	52	14	a	a	DET
ejpam-5962	52	15	sort	sort	NOUN
ejpam-5962	52	16	of	of	ADP
ejpam-5962	52	17	separation	separation	NOUN
ejpam-5962	52	18	axiom	axiom	NOUN
ejpam-5962	52	19	between	between	ADP
ejpam-5962	52	20	t1	t1	NOUN
ejpam-5962	52	21	and	and	CCONJ
ejpam-5962	52	22	t2	t2	NOUN
ejpam-5962	52	23	.	.	PUNCT
ejpam-5962	53	1	a.	a.	NOUN
ejpam-5962	53	2	a.	a.	PROPN
ejpam-5962	53	3	atoom	atoom	PROPN
ejpam-5962	53	4	et	et	PROPN
ejpam-5962	53	5	al	al	PROPN
ejpam-5962	53	6	.	.	PUNCT
ejpam-5962	53	7	/	/	SYM
ejpam-5962	53	8	eur	eur	PROPN
ejpam-5962	53	9	.	.	PUNCT
ejpam-5962	54	1	j.	j.	PROPN
ejpam-5962	54	2	pure	pure	PROPN
ejpam-5962	54	3	appl	appl	PROPN
ejpam-5962	54	4	.	.	PROPN
ejpam-5962	54	5	math	math	PROPN
ejpam-5962	54	6	,	,	PUNCT
ejpam-5962	54	7	18	18	NUM
ejpam-5962	54	8	(	(	PUNCT
ejpam-5962	54	9	2	2	NUM
ejpam-5962	54	10	)	)	PUNCT
ejpam-5962	54	11	(	(	PUNCT
ejpam-5962	54	12	2025	2025	NUM
ejpam-5962	54	13	)	)	PUNCT
ejpam-5962	54	14	,	,	PUNCT
ejpam-5962	54	15	5962	5962	NUM
ejpam-5962	54	16	3	3	NUM
ejpam-5962	54	17	of	of	ADP
ejpam-5962	54	18	17	17	NUM
ejpam-5962	54	19	in	in	ADP
ejpam-5962	54	20	[	[	PUNCT
ejpam-5962	54	21	9	9	NUM
ejpam-5962	54	22	]	]	PUNCT
ejpam-5962	54	23	,	,	PUNCT
ejpam-5962	54	24	questioned	question	VERB
ejpam-5962	54	25	the	the	DET
ejpam-5962	54	26	assumption	assumption	NOUN
ejpam-5962	54	27	that	that	SCONJ
ejpam-5962	54	28	all	all	DET
ejpam-5962	54	29	closed	closed	ADJ
ejpam-5962	54	30	compact	compact	ADJ
ejpam-5962	54	31	spaces	space	NOUN
ejpam-5962	54	32	that	that	PRON
ejpam-5962	54	33	do	do	AUX
ejpam-5962	54	34	not	not	PART
ejpam-5962	54	35	accept	accept	VERB
ejpam-5962	54	36	any	any	DET
ejpam-5962	54	37	strictly	strictly	ADV
ejpam-5962	54	38	coarser	coarse	ADJ
ejpam-5962	54	39	closed	closed	ADJ
ejpam-5962	54	40	compact	compact	ADJ
ejpam-5962	54	41	topology	topology	NOUN
ejpam-5962	54	42	must	must	AUX
ejpam-5962	54	43	be	be	AUX
ejpam-5962	54	44	compact	compact	ADJ
ejpam-5962	54	45	.	.	PUNCT
ejpam-5962	55	1	such	such	DET
ejpam-5962	55	2	a	a	DET
ejpam-5962	55	3	question	question	NOUN
ejpam-5962	55	4	,	,	PUNCT
ejpam-5962	55	5	which	which	PRON
ejpam-5962	55	6	is	be	AUX
ejpam-5962	55	7	also	also	ADV
ejpam-5962	55	8	taken	take	VERB
ejpam-5962	55	9	into	into	ADP
ejpam-5962	55	10	account	account	NOUN
ejpam-5962	55	11	in	in	ADP
ejpam-5962	55	12	[	[	X
ejpam-5962	55	13	11	11	NUM
ejpam-5962	55	14	]	]	PUNCT
ejpam-5962	55	15	,	,	PUNCT
ejpam-5962	55	16	naturally	naturally	ADV
ejpam-5962	55	17	fits	fit	VERB
ejpam-5962	55	18	into	into	ADP
ejpam-5962	55	19	inquiries	inquiry	NOUN
ejpam-5962	55	20	into	into	ADP
ejpam-5962	55	21	topologies	topology	NOUN
ejpam-5962	55	22	that	that	PRON
ejpam-5962	55	23	are	be	AUX
ejpam-5962	55	24	(	(	PUNCT
ejpam-5962	55	25	or	or	CCONJ
ejpam-5962	55	26	are	be	AUX
ejpam-5962	55	27	not	not	PART
ejpam-5962	55	28	)	)	PUNCT
ejpam-5962	55	29	minimal	minimal	ADJ
ejpam-5962	55	30	or	or	CCONJ
ejpam-5962	55	31	maximal	maximal	ADJ
ejpam-5962	55	32	among	among	ADP
ejpam-5962	55	33	those	those	PRON
ejpam-5962	55	34	enjoying	enjoy	VERB
ejpam-5962	55	35	a	a	DET
ejpam-5962	55	36	particular	particular	ADJ
ejpam-5962	55	37	attribute	attribute	NOUN
ejpam-5962	55	38	.	.	PUNCT
ejpam-5962	56	1	the	the	DET
ejpam-5962	56	2	growth	growth	NOUN
ejpam-5962	56	3	of	of	ADP
ejpam-5962	56	4	general	general	ADJ
ejpam-5962	56	5	topology	topology	NOUN
ejpam-5962	56	6	has	have	AUX
ejpam-5962	56	7	been	be	AUX
ejpam-5962	56	8	greatly	greatly	ADV
ejpam-5962	56	9	influenced	influence	VERB
ejpam-5962	56	10	by	by	ADP
ejpam-5962	56	11	the	the	DET
ejpam-5962	56	12	traditional	traditional	ADJ
ejpam-5962	56	13	generalizations	generalization	NOUN
ejpam-5962	56	14	of	of	ADP
ejpam-5962	56	15	lindelöf	lindelöf	PROPN
ejpam-5962	56	16	spaces	space	VERB
ejpam-5962	56	17	,	,	PUNCT
ejpam-5962	56	18	such	such	ADJ
ejpam-5962	56	19	as	as	SCONJ
ejpam-5962	56	20	hereditarily	hereditarily	ADJ
ejpam-5962	56	21	and	and	CCONJ
ejpam-5962	56	22	maximally	maximally	ADV
ejpam-5962	56	23	lindelöf	lindelöf	NOUN
ejpam-5962	56	24	spaces	space	VERB
ejpam-5962	56	25	.	.	PUNCT
ejpam-5962	57	1	the	the	DET
ejpam-5962	57	2	class	class	NOUN
ejpam-5962	57	3	of	of	ADP
ejpam-5962	57	4	lindelöf	lindelöf	NOUN
ejpam-5962	57	5	closed	close	VERB
ejpam-5962	57	6	spaces	space	NOUN
ejpam-5962	57	7	is	be	AUX
ejpam-5962	57	8	one	one	NUM
ejpam-5962	57	9	particular	particular	ADJ
ejpam-5962	57	10	class	class	NOUN
ejpam-5962	57	11	of	of	ADP
ejpam-5962	57	12	spaces	space	NOUN
ejpam-5962	57	13	that	that	PRON
ejpam-5962	57	14	is	be	AUX
ejpam-5962	57	15	relatively	relatively	ADV
ejpam-5962	57	16	new	new	ADJ
ejpam-5962	57	17	as	as	ADP
ejpam-5962	57	18	a	a	DET
ejpam-5962	57	19	notion	notion	NOUN
ejpam-5962	57	20	but	but	CCONJ
ejpam-5962	57	21	has	have	AUX
ejpam-5962	57	22	been	be	AUX
ejpam-5962	57	23	thoroughly	thoroughly	ADV
ejpam-5962	57	24	researched	research	VERB
ejpam-5962	57	25	in	in	ADP
ejpam-5962	57	26	recent	recent	ADJ
ejpam-5962	57	27	years	year	NOUN
ejpam-5962	57	28	.	.	PUNCT
ejpam-5962	58	1	in	in	ADP
ejpam-5962	58	2	[	[	X
ejpam-5962	58	3	12	12	NUM
ejpam-5962	58	4	]	]	PUNCT
ejpam-5962	58	5	and	and	CCONJ
ejpam-5962	58	6	[	[	X
ejpam-5962	58	7	13	13	NUM
ejpam-5962	58	8	]	]	PUNCT
ejpam-5962	58	9	,	,	PUNCT
ejpam-5962	58	10	a	a	DET
ejpam-5962	58	11	topological	topological	ADJ
ejpam-5962	58	12	space	space	NOUN
ejpam-5962	58	13	is	be	AUX
ejpam-5962	58	14	referred	refer	VERB
ejpam-5962	58	15	to	to	ADP
ejpam-5962	58	16	as	as	SCONJ
ejpam-5962	58	17	a	a	DET
ejpam-5962	58	18	lindelöf	lindelöf	NOUN
ejpam-5962	58	19	closed	close	VERB
ejpam-5962	58	20	space	space	NOUN
ejpam-5962	58	21	if	if	SCONJ
ejpam-5962	58	22	all	all	PRON
ejpam-5962	58	23	of	of	ADP
ejpam-5962	58	24	its	its	PRON
ejpam-5962	58	25	lindelöf	lindelöf	NOUN
ejpam-5962	58	26	subsets	subset	NOUN
ejpam-5962	58	27	are	be	AUX
ejpam-5962	58	28	closed	closed	ADJ
ejpam-5962	58	29	.	.	PUNCT
ejpam-5962	59	1	this	this	DET
ejpam-5962	59	2	idea	idea	NOUN
ejpam-5962	59	3	,	,	PUNCT
ejpam-5962	59	4	which	which	PRON
ejpam-5962	59	5	has	have	VERB
ejpam-5962	59	6	a	a	DET
ejpam-5962	59	7	tight	tight	ADJ
ejpam-5962	59	8	connection	connection	NOUN
ejpam-5962	59	9	to	to	ADP
ejpam-5962	59	10	p	p	NOUN
ejpam-5962	59	11	-	-	PUNCT
ejpam-5962	59	12	spaces	space	NOUN
ejpam-5962	59	13	,	,	PUNCT
ejpam-5962	59	14	came	come	VERB
ejpam-5962	59	15	forth	forth	ADV
ejpam-5962	59	16	as	as	ADP
ejpam-5962	59	17	a	a	DET
ejpam-5962	59	18	result	result	NOUN
ejpam-5962	59	19	of	of	ADP
ejpam-5962	59	20	research	research	NOUN
ejpam-5962	59	21	on	on	ADP
ejpam-5962	59	22	maximal	maximal	ADJ
ejpam-5962	59	23	lindelöf	lindelöf	NOUN
ejpam-5962	59	24	spaces	space	VERB
ejpam-5962	59	25	[	[	X
ejpam-5962	59	26	14	14	NUM
ejpam-5962	59	27	]	]	PUNCT
ejpam-5962	59	28	.	.	PUNCT
ejpam-5962	60	1	bitopological	bitopological	ADJ
ejpam-5962	60	2	spaces	space	NOUN
ejpam-5962	60	3	were	be	AUX
ejpam-5962	60	4	first	first	ADV
ejpam-5962	60	5	discussed	discuss	VERB
ejpam-5962	60	6	and	and	CCONJ
ejpam-5962	60	7	introduced	introduce	VERB
ejpam-5962	60	8	in	in	ADP
ejpam-5962	60	9	[	[	X
ejpam-5962	60	10	14	14	NUM
ejpam-5962	60	11	]	]	PUNCT
ejpam-5962	60	12	.	.	PUNCT
ejpam-5962	61	1	numerous	numerous	ADJ
ejpam-5962	61	2	mathematicians	mathematician	NOUN
ejpam-5962	61	3	investigated	investigate	VERB
ejpam-5962	61	4	a	a	DET
ejpam-5962	61	5	variety	variety	NOUN
ejpam-5962	61	6	of	of	ADP
ejpam-5962	61	7	ideas	idea	NOUN
ejpam-5962	61	8	in	in	ADP
ejpam-5962	61	9	bitopological	bitopological	ADJ
ejpam-5962	61	10	spaces	space	NOUN
ejpam-5962	61	11	,	,	PUNCT
ejpam-5962	61	12	which	which	PRON
ejpam-5962	61	13	has	have	AUX
ejpam-5962	61	14	now	now	ADV
ejpam-5962	61	15	developed	develop	VERB
ejpam-5962	61	16	into	into	ADP
ejpam-5962	61	17	a	a	DET
ejpam-5962	61	18	significant	significant	ADJ
ejpam-5962	61	19	area	area	NOUN
ejpam-5962	61	20	of	of	ADP
ejpam-5962	61	21	study	study	NOUN
ejpam-5962	61	22	in	in	ADP
ejpam-5962	61	23	general	general	ADJ
ejpam-5962	61	24	topology	topology	NOUN
ejpam-5962	61	25	.	.	PUNCT
ejpam-5962	62	1	there	there	PRON
ejpam-5962	62	2	have	have	AUX
ejpam-5962	62	3	been	be	AUX
ejpam-5962	62	4	a	a	DET
ejpam-5962	62	5	few	few	ADJ
ejpam-5962	62	6	generalized	generalized	ADJ
ejpam-5962	62	7	topological	topological	ADJ
ejpam-5962	62	8	structures	structure	NOUN
ejpam-5962	62	9	put	put	VERB
ejpam-5962	62	10	forth	forth	ADP
ejpam-5962	62	11	recently	recently	ADV
ejpam-5962	62	12	.	.	PUNCT
ejpam-5962	63	1	topological	topological	ADJ
ejpam-5962	63	2	space	space	NOUN
ejpam-5962	63	3	is	be	AUX
ejpam-5962	63	4	crucial	crucial	ADJ
ejpam-5962	63	5	for	for	ADP
ejpam-5962	63	6	analysis	analysis	NOUN
ejpam-5962	63	7	and	and	CCONJ
ejpam-5962	63	8	a	a	DET
ejpam-5962	63	9	wide	wide	ADJ
ejpam-5962	63	10	range	range	NOUN
ejpam-5962	63	11	of	of	ADP
ejpam-5962	63	12	applications	application	NOUN
ejpam-5962	63	13	;	;	PUNCT
ejpam-5962	63	14	for	for	ADP
ejpam-5962	63	15	further	further	ADJ
ejpam-5962	63	16	information	information	NOUN
ejpam-5962	63	17	,	,	PUNCT
ejpam-5962	63	18	see	see	VERB
ejpam-5962	63	19	one	one	NUM
ejpam-5962	63	20	of	of	ADP
ejpam-5962	63	21	the	the	DET
ejpam-5962	63	22	key	key	ADJ
ejpam-5962	63	23	generalizations	generalization	NOUN
ejpam-5962	63	24	of	of	ADP
ejpam-5962	63	25	the	the	DET
ejpam-5962	63	26	topological	topological	ADJ
ejpam-5962	63	27	space	space	NOUN
ejpam-5962	63	28	represented	represent	VERB
ejpam-5962	63	29	by	by	ADP
ejpam-5962	63	30	the	the	DET
ejpam-5962	63	31	compact	compact	ADJ
ejpam-5962	63	32	closed	close	VERB
ejpam-5962	63	33	and	and	CCONJ
ejpam-5962	63	34	lindelöf	lindelöf	NOUN
ejpam-5962	63	35	closed	close	VERB
ejpam-5962	63	36	spaces	space	NOUN
ejpam-5962	63	37	.	.	PUNCT
ejpam-5962	64	1	in	in	ADP
ejpam-5962	64	2	this	this	DET
ejpam-5962	64	3	article	article	NOUN
ejpam-5962	64	4	,	,	PUNCT
ejpam-5962	64	5	we	we	PRON
ejpam-5962	64	6	explore	explore	VERB
ejpam-5962	64	7	the	the	DET
ejpam-5962	64	8	idea	idea	NOUN
ejpam-5962	64	9	of	of	ADP
ejpam-5962	64	10	bitopological	bitopological	ADJ
ejpam-5962	64	11	spaces	space	NOUN
ejpam-5962	64	12	,	,	PUNCT
ejpam-5962	64	13	maximal	maximal	ADJ
ejpam-5962	64	14	and	and	CCONJ
ejpam-5962	64	15	minimal	minimal	ADJ
ejpam-5962	64	16	bitopologies	bitopologie	NOUN
ejpam-5962	64	17	,	,	PUNCT
ejpam-5962	64	18	pairwise	pairwise	NOUN
ejpam-5962	64	19	minimal	minimal	ADJ
ejpam-5962	64	20	compact	compact	ADJ
ejpam-5962	64	21	closed	closed	ADJ
ejpam-5962	64	22	spaces	space	NOUN
ejpam-5962	64	23	,	,	PUNCT
ejpam-5962	64	24	pairwise	pairwise	PROPN
ejpam-5962	64	25	minimal	minimal	ADJ
ejpam-5962	64	26	lindelöf	lindelöf	NOUN
ejpam-5962	64	27	closed	close	VERB
ejpam-5962	64	28	spaces	space	NOUN
ejpam-5962	64	29	,	,	PUNCT
ejpam-5962	64	30	pairwise	pairwise	NOUN
ejpam-5962	64	31	minimal	minimal	ADJ
ejpam-5962	64	32	hausdorff	hausdorff	NOUN
ejpam-5962	64	33	spaces	space	NOUN
ejpam-5962	64	34	,	,	PUNCT
ejpam-5962	64	35	as	as	ADV
ejpam-5962	64	36	well	well	ADV
ejpam-5962	64	37	as	as	ADP
ejpam-5962	64	38	their	their	PRON
ejpam-5962	64	39	connections	connection	NOUN
ejpam-5962	64	40	to	to	ADP
ejpam-5962	64	41	other	other	ADJ
ejpam-5962	64	42	bitopological	bitopological	ADJ
ejpam-5962	64	43	ideas	idea	NOUN
ejpam-5962	64	44	.	.	PUNCT
ejpam-5962	65	1	o(z	o(z	NOUN
ejpam-5962	65	2	)	)	PUNCT
ejpam-5962	65	3	stands	stand	VERB
ejpam-5962	65	4	for	for	ADP
ejpam-5962	65	5	the	the	DET
ejpam-5962	65	6	set	set	NOUN
ejpam-5962	65	7	of	of	ADP
ejpam-5962	65	8	all	all	DET
ejpam-5962	65	9	topologies	topology	NOUN
ejpam-5962	65	10	on	on	ADP
ejpam-5962	65	11	z	z	NOUN
ejpam-5962	65	12	that	that	PRON
ejpam-5962	65	13	have	have	VERB
ejpam-5962	65	14	the	the	DET
ejpam-5962	65	15	property	property	NOUN
ejpam-5962	65	16	o	o	NOUN
ejpam-5962	65	17	,	,	PUNCT
ejpam-5962	65	18	where	where	SCONJ
ejpam-5962	65	19	o	o	NOUN
ejpam-5962	65	20	is	be	AUX
ejpam-5962	65	21	a	a	DET
ejpam-5962	65	22	topological	topological	ADJ
ejpam-5962	65	23	property	property	NOUN
ejpam-5962	65	24	,	,	PUNCT
ejpam-5962	65	25	z	z	PROPN
ejpam-5962	65	26	is	be	AUX
ejpam-5962	65	27	a	a	DET
ejpam-5962	65	28	nonempty	nonempty	ADJ
ejpam-5962	65	29	set	set	NOUN
ejpam-5962	65	30	,	,	PUNCT
ejpam-5962	65	31	and	and	CCONJ
ejpam-5962	65	32	o	o	NOUN
ejpam-5962	65	33	is	be	AUX
ejpam-5962	65	34	the	the	DET
ejpam-5962	65	35	property	property	NOUN
ejpam-5962	65	36	.	.	PUNCT
ejpam-5962	66	1	by	by	ADP
ejpam-5962	66	2	including	include	VERB
ejpam-5962	66	3	sets	set	NOUN
ejpam-5962	66	4	,	,	PUNCT
ejpam-5962	66	5	o(z	o(z	NOUN
ejpam-5962	66	6	)	)	PUNCT
ejpam-5962	66	7	is	be	AUX
ejpam-5962	66	8	partially	partially	ADV
ejpam-5962	66	9	sorted	sort	VERB
ejpam-5962	66	10	.	.	PUNCT
ejpam-5962	67	1	the	the	DET
ejpam-5962	67	2	patial	patial	ADJ
ejpam-5962	67	3	ordering	order	VERB
ejpam-5962	67	4	≤	≤	NOUN
ejpam-5962	67	5	means	mean	VERB
ejpam-5962	67	6	that	that	SCONJ
ejpam-5962	67	7	such	such	ADJ
ejpam-5962	67	8	that	that	SCONJ
ejpam-5962	67	9	(	(	PUNCT
ejpam-5962	67	10	z	z	NOUN
ejpam-5962	67	11	,	,	PUNCT
ejpam-5962	67	12	ϑ	ϑ	X
ejpam-5962	67	13	\	\	PROPN
ejpam-5962	67	14	1	1	NUM
ejpam-5962	67	15	,	,	PUNCT
ejpam-5962	67	16	ϑ	ϑ	X
ejpam-5962	67	17	\	\	PROPN
ejpam-5962	67	18	2	2	NUM
ejpam-5962	67	19	)	)	PUNCT
ejpam-5962	67	20	≤	≤	NOUN
ejpam-5962	67	21	(	(	PUNCT
ejpam-5962	67	22	z	z	NOUN
ejpam-5962	67	23	,	,	PUNCT
ejpam-5962	67	24	ϑ1	ϑ1	NOUN
ejpam-5962	67	25	,	,	PUNCT
ejpam-5962	67	26	ϑ2	ϑ2	PROPN
ejpam-5962	67	27	)	)	PUNCT
ejpam-5962	67	28	iff	iff	PROPN
ejpam-5962	67	29	ϑ	ϑ	X
ejpam-5962	67	30	\	\	PROPN
ejpam-5962	67	31	1	1	NUM
ejpam-5962	67	32	≤	≤	NUM
ejpam-5962	67	33	ϑ1	ϑ1	NOUN
ejpam-5962	67	34	and	and	CCONJ
ejpam-5962	67	35	ϑ	ϑ	X
ejpam-5962	67	36	\	\	PROPN
ejpam-5962	67	37	2	2	NUM
ejpam-5962	67	38	≤	≤	NUM
ejpam-5962	67	39	ϑ2	ϑ2	NOUN
ejpam-5962	67	40	.	.	PUNCT
ejpam-5962	68	1	the	the	DET
ejpam-5962	68	2	paper	paper	NOUN
ejpam-5962	68	3	is	be	AUX
ejpam-5962	68	4	organized	organize	VERB
ejpam-5962	68	5	as	as	SCONJ
ejpam-5962	68	6	follows	follow	VERB
ejpam-5962	68	7	:	:	PUNCT
ejpam-5962	68	8	section	section	NOUN
ejpam-5962	68	9	2	2	NUM
ejpam-5962	68	10	provides	provide	VERB
ejpam-5962	68	11	fundamental	fundamental	ADJ
ejpam-5962	68	12	definitions	definition	NOUN
ejpam-5962	68	13	and	and	CCONJ
ejpam-5962	68	14	theorems	theorem	NOUN
ejpam-5962	68	15	for	for	ADP
ejpam-5962	68	16	bitopological	bitopological	ADJ
ejpam-5962	68	17	spaces	space	NOUN
ejpam-5962	68	18	,	,	PUNCT
ejpam-5962	68	19	including	include	VERB
ejpam-5962	68	20	crucial	crucial	ADJ
ejpam-5962	68	21	terminologies	terminology	NOUN
ejpam-5962	68	22	relevant	relevant	ADJ
ejpam-5962	68	23	to	to	ADP
ejpam-5962	68	24	our	our	PRON
ejpam-5962	68	25	research	research	NOUN
ejpam-5962	68	26	.	.	PUNCT
ejpam-5962	69	1	building	build	VERB
ejpam-5962	69	2	on	on	ADP
ejpam-5962	69	3	these	these	DET
ejpam-5962	69	4	foundations	foundation	NOUN
ejpam-5962	69	5	,	,	PUNCT
ejpam-5962	69	6	section	section	NOUN
ejpam-5962	69	7	3	3	NUM
ejpam-5962	69	8	introduces	introduce	VERB
ejpam-5962	69	9	new	new	ADJ
ejpam-5962	69	10	generations	generation	NOUN
ejpam-5962	69	11	of	of	ADP
ejpam-5962	69	12	pairwise	pairwise	NOUN
ejpam-5962	69	13	compact	compact	ADJ
ejpam-5962	69	14	closed	close	VERB
ejpam-5962	69	15	spaces	space	NOUN
ejpam-5962	69	16	and	and	CCONJ
ejpam-5962	69	17	explores	explore	VERB
ejpam-5962	69	18	their	their	PRON
ejpam-5962	69	19	relationships	relationship	NOUN
ejpam-5962	69	20	to	to	ADP
ejpam-5962	69	21	other	other	ADJ
ejpam-5962	69	22	types	type	NOUN
ejpam-5962	69	23	of	of	ADP
ejpam-5962	69	24	spaces	space	NOUN
ejpam-5962	69	25	.	.	PUNCT
ejpam-5962	70	1	section	section	NOUN
ejpam-5962	70	2	4	4	NUM
ejpam-5962	70	3	expands	expand	VERB
ejpam-5962	70	4	on	on	ADP
ejpam-5962	70	5	this	this	DET
ejpam-5962	70	6	approach	approach	NOUN
ejpam-5962	70	7	by	by	ADP
ejpam-5962	70	8	introducing	introduce	VERB
ejpam-5962	70	9	additional	additional	ADJ
ejpam-5962	70	10	properties	property	NOUN
ejpam-5962	70	11	and	and	CCONJ
ejpam-5962	70	12	novel	novel	ADJ
ejpam-5962	70	13	definitions	definition	NOUN
ejpam-5962	70	14	for	for	ADP
ejpam-5962	70	15	pairwise	pairwise	NOUN
ejpam-5962	70	16	compact	compact	ADJ
ejpam-5962	70	17	closed	closed	ADJ
ejpam-5962	70	18	spaces	space	NOUN
ejpam-5962	70	19	.	.	PUNCT
ejpam-5962	71	1	in	in	ADP
ejpam-5962	71	2	section	section	NOUN
ejpam-5962	71	3	5	5	NUM
ejpam-5962	71	4	,	,	PUNCT
ejpam-5962	71	5	we	we	PRON
ejpam-5962	71	6	additionally	additionally	ADV
ejpam-5962	71	7	discuss	discuss	VERB
ejpam-5962	71	8	the	the	DET
ejpam-5962	71	9	topological	topological	ADJ
ejpam-5962	71	10	characterizations	characterization	NOUN
ejpam-5962	71	11	of	of	ADP
ejpam-5962	71	12	pairwise	pairwise	NOUN
ejpam-5962	71	13	minimal	minimal	ADJ
ejpam-5962	71	14	compact	compact	ADJ
ejpam-5962	71	15	closed	closed	ADJ
ejpam-5962	71	16	spaces	space	NOUN
ejpam-5962	71	17	,	,	PUNCT
ejpam-5962	71	18	supported	support	VERB
ejpam-5962	71	19	by	by	ADP
ejpam-5962	71	20	a	a	DET
ejpam-5962	71	21	diagram	diagram	NOUN
ejpam-5962	71	22	illustrating	illustrate	VERB
ejpam-5962	71	23	their	their	PRON
ejpam-5962	71	24	interconnections	interconnection	NOUN
ejpam-5962	71	25	.	.	PUNCT
ejpam-5962	72	1	section	section	NOUN
ejpam-5962	72	2	6	6	NUM
ejpam-5962	72	3	focuses	focus	VERB
ejpam-5962	72	4	on	on	ADP
ejpam-5962	72	5	pairwise	pairwise	NOUN
ejpam-5962	72	6	lindel	lindel	NOUN
ejpam-5962	72	7	of	of	ADP
ejpam-5962	72	8	closed	closed	ADJ
ejpam-5962	72	9	spaces	space	NOUN
ejpam-5962	72	10	,	,	PUNCT
ejpam-5962	72	11	demonstrating	demonstrate	VERB
ejpam-5962	72	12	advanced	advanced	ADJ
ejpam-5962	72	13	characteristics	characteristic	NOUN
ejpam-5962	72	14	and	and	CCONJ
ejpam-5962	72	15	oddities	oddity	NOUN
ejpam-5962	72	16	in	in	ADP
ejpam-5962	72	17	cartesian	cartesian	ADJ
ejpam-5962	72	18	multiplication	multiplication	NOUN
ejpam-5962	72	19	under	under	ADP
ejpam-5962	72	20	specified	specified	ADJ
ejpam-5962	72	21	conditions	condition	NOUN
ejpam-5962	72	22	.	.	PUNCT
ejpam-5962	73	1	section	section	NOUN
ejpam-5962	73	2	7	7	NUM
ejpam-5962	73	3	expands	expand	VERB
ejpam-5962	73	4	on	on	ADP
ejpam-5962	73	5	this	this	DET
ejpam-5962	73	6	analysis	analysis	NOUN
ejpam-5962	73	7	by	by	ADP
ejpam-5962	73	8	defining	define	VERB
ejpam-5962	73	9	paired	pair	VERB
ejpam-5962	73	10	minimal	minimal	ADJ
ejpam-5962	73	11	lindelö	lindelö	NOUN
ejpam-5962	73	12	of	of	ADP
ejpam-5962	73	13	closed	closed	ADJ
ejpam-5962	73	14	spaces	space	NOUN
ejpam-5962	73	15	,	,	PUNCT
ejpam-5962	73	16	together	together	ADV
ejpam-5962	73	17	with	with	ADP
ejpam-5962	73	18	a	a	DET
ejpam-5962	73	19	diagrammatic	diagrammatic	ADJ
ejpam-5962	73	20	description	description	NOUN
ejpam-5962	73	21	of	of	ADP
ejpam-5962	73	22	their	their	PRON
ejpam-5962	73	23	structural	structural	ADJ
ejpam-5962	73	24	relationships	relationship	NOUN
ejpam-5962	73	25	.	.	PUNCT
ejpam-5962	74	1	section	section	NOUN
ejpam-5962	74	2	8	8	NUM
ejpam-5962	74	3	introduces	introduce	VERB
ejpam-5962	74	4	a	a	DET
ejpam-5962	74	5	novel	novel	ADJ
ejpam-5962	74	6	notion	notion	NOUN
ejpam-5962	74	7	of	of	ADP
ejpam-5962	74	8	pairwise	pairwise	PROPN
ejpam-5962	74	9	minimal	minimal	ADJ
ejpam-5962	74	10	hausdorff	hausdorff	NOUN
ejpam-5962	74	11	spaces	space	NOUN
ejpam-5962	74	12	and	and	CCONJ
ejpam-5962	74	13	analyzes	analyze	VERB
ejpam-5962	74	14	their	their	PRON
ejpam-5962	74	15	properties	property	NOUN
ejpam-5962	74	16	.	.	PUNCT
ejpam-5962	75	1	finally	finally	ADV
ejpam-5962	75	2	,	,	PUNCT
ejpam-5962	75	3	section	section	NOUN
ejpam-5962	75	4	9	9	NUM
ejpam-5962	75	5	finishes	finish	VERB
ejpam-5962	75	6	the	the	DET
ejpam-5962	75	7	paper	paper	NOUN
ejpam-5962	75	8	by	by	ADP
ejpam-5962	75	9	describing	describe	VERB
ejpam-5962	75	10	applications	application	NOUN
ejpam-5962	75	11	of	of	ADP
ejpam-5962	75	12	minimal	minimal	ADJ
ejpam-5962	75	13	spaces	space	NOUN
ejpam-5962	75	14	in	in	ADP
ejpam-5962	75	15	bitopological	bitopological	ADJ
ejpam-5962	75	16	settings	setting	NOUN
ejpam-5962	75	17	and	and	CCONJ
ejpam-5962	75	18	highlighting	highlight	VERB
ejpam-5962	75	19	intriguing	intriguing	ADJ
ejpam-5962	75	20	prospects	prospect	NOUN
ejpam-5962	75	21	for	for	ADP
ejpam-5962	75	22	future	future	ADJ
ejpam-5962	75	23	research	research	NOUN
ejpam-5962	75	24	.	.	PUNCT
ejpam-5962	76	1	2	2	X
ejpam-5962	76	2	.	.	NUM
ejpam-5962	76	3	preliminaries	preliminary	NOUN
ejpam-5962	76	4	and	and	CCONJ
ejpam-5962	76	5	basic	basic	ADJ
ejpam-5962	76	6	definitions	definition	NOUN
ejpam-5962	76	7	we	we	PRON
ejpam-5962	76	8	provide	provide	VERB
ejpam-5962	76	9	the	the	DET
ejpam-5962	76	10	fundamental	fundamental	ADJ
ejpam-5962	76	11	definitions	definition	NOUN
ejpam-5962	76	12	and	and	CCONJ
ejpam-5962	76	13	theorems	theorem	NOUN
ejpam-5962	76	14	that	that	SCONJ
ejpam-5962	76	15	we	we	PRON
ejpam-5962	76	16	will	will	AUX
ejpam-5962	76	17	use	use	VERB
ejpam-5962	76	18	to	to	PART
ejpam-5962	76	19	support	support	VERB
ejpam-5962	76	20	our	our	PRON
ejpam-5962	76	21	primary	primary	ADJ
ejpam-5962	76	22	findings	finding	NOUN
ejpam-5962	76	23	in	in	ADP
ejpam-5962	76	24	the	the	DET
ejpam-5962	76	25	following	follow	VERB
ejpam-5962	76	26	sections	section	NOUN
ejpam-5962	76	27	.	.	PUNCT
ejpam-5962	77	1	throughout	throughout	ADP
ejpam-5962	77	2	this	this	DET
ejpam-5962	77	3	publication	publication	NOUN
ejpam-5962	77	4	,	,	PUNCT
ejpam-5962	77	5	we	we	PRON
ejpam-5962	77	6	will	will	AUX
ejpam-5962	77	7	refer	refer	VERB
ejpam-5962	77	8	to	to	ADP
ejpam-5962	77	9	a.	a.	NOUN
ejpam-5962	77	10	a.	a.	PROPN
ejpam-5962	77	11	atoom	atoom	PROPN
ejpam-5962	77	12	et	et	PROPN
ejpam-5962	77	13	al	al	PROPN
ejpam-5962	77	14	.	.	PUNCT
ejpam-5962	77	15	/	/	SYM
ejpam-5962	77	16	eur	eur	PROPN
ejpam-5962	77	17	.	.	PUNCT
ejpam-5962	78	1	j.	j.	PROPN
ejpam-5962	78	2	pure	pure	PROPN
ejpam-5962	78	3	appl	appl	PROPN
ejpam-5962	78	4	.	.	PROPN
ejpam-5962	78	5	math	math	PROPN
ejpam-5962	78	6	,	,	PUNCT
ejpam-5962	78	7	18	18	NUM
ejpam-5962	78	8	(	(	PUNCT
ejpam-5962	78	9	2	2	NUM
ejpam-5962	78	10	)	)	PUNCT
ejpam-5962	78	11	(	(	PUNCT
ejpam-5962	78	12	2025	2025	NUM
ejpam-5962	78	13	)	)	PUNCT
ejpam-5962	78	14	,	,	PUNCT
ejpam-5962	78	15	5962	5962	NUM
ejpam-5962	78	16	4	4	NUM
ejpam-5962	78	17	of	of	ADP
ejpam-5962	78	18	17	17	NUM
ejpam-5962	78	19	bitopological	bitopological	ADJ
ejpam-5962	78	20	spaces	space	NOUN
ejpam-5962	78	21	as	as	ADP
ejpam-5962	78	22	”	"	PUNCT
ejpam-5962	78	23	spaces	space	NOUN
ejpam-5962	78	24	”	"	PUNCT
ejpam-5962	78	25	to	to	PART
ejpam-5962	78	26	set	set	VERB
ejpam-5962	78	27	the	the	DET
ejpam-5962	78	28	scene	scene	NOUN
ejpam-5962	78	29	for	for	ADP
ejpam-5962	78	30	our	our	PRON
ejpam-5962	78	31	inquiry	inquiry	NOUN
ejpam-5962	78	32	.	.	PUNCT
ejpam-5962	79	1	we	we	PRON
ejpam-5962	79	2	’ll	’ll	AUX
ejpam-5962	79	3	start	start	VERB
ejpam-5962	79	4	by	by	ADP
ejpam-5962	79	5	going	go	VERB
ejpam-5962	79	6	through	through	ADP
ejpam-5962	79	7	the	the	DET
ejpam-5962	79	8	key	key	ADJ
ejpam-5962	79	9	terminologies	terminology	NOUN
ejpam-5962	79	10	and	and	CCONJ
ejpam-5962	79	11	findings	finding	NOUN
ejpam-5962	79	12	that	that	PRON
ejpam-5962	79	13	will	will	AUX
ejpam-5962	79	14	be	be	AUX
ejpam-5962	79	15	used	use	VERB
ejpam-5962	79	16	to	to	ADP
ejpam-5962	79	17	this	this	DET
ejpam-5962	79	18	project	project	NOUN
ejpam-5962	79	19	as	as	ADP
ejpam-5962	79	20	a	a	DET
ejpam-5962	79	21	whole	whole	NOUN
ejpam-5962	79	22	.	.	PUNCT
ejpam-5962	80	1	definition	definition	NOUN
ejpam-5962	80	2	2.1	2.1	NUM
ejpam-5962	80	3	.	.	PUNCT
ejpam-5962	81	1	[	[	X
ejpam-5962	81	2	10	10	NUM
ejpam-5962	81	3	]	]	PUNCT
ejpam-5962	81	4	in	in	ADP
ejpam-5962	81	5	(	(	PUNCT
ejpam-5962	81	6	z	z	NOUN
ejpam-5962	81	7	,	,	PUNCT
ejpam-5962	81	8	ϑ1	ϑ1	NOUN
ejpam-5962	81	9	,	,	PUNCT
ejpam-5962	81	10	ϑ2	ϑ2	PROPN
ejpam-5962	81	11	)	)	PUNCT
ejpam-5962	81	12	,	,	PUNCT
ejpam-5962	81	13	z	z	PROPN
ejpam-5962	81	14	⊂	⊂	PROPN
ejpam-5962	82	1	a	a	PRON
ejpam-5962	82	2	is	be	AUX
ejpam-5962	82	3	bicompact	bicompact	ADJ
ejpam-5962	82	4	if	if	SCONJ
ejpam-5962	82	5	and	and	CCONJ
ejpam-5962	82	6	only	only	ADV
ejpam-5962	82	7	if	if	SCONJ
ejpam-5962	82	8	a	a	PRON
ejpam-5962	82	9	is	be	AUX
ejpam-5962	82	10	both	both	PRON
ejpam-5962	82	11	ϑ1	ϑ1	NOUN
ejpam-5962	82	12	-	-	PUNCT
ejpam-5962	82	13	compact	compact	ADJ
ejpam-5962	82	14	and	and	CCONJ
ejpam-5962	82	15	ϑ2	ϑ2	NOUN
ejpam-5962	82	16	-	-	PUNCT
ejpam-5962	82	17	compact	compact	ADJ
ejpam-5962	82	18	.	.	PUNCT
ejpam-5962	83	1	definition	definition	NOUN
ejpam-5962	83	2	2.2	2.2	NUM
ejpam-5962	83	3	.	.	PUNCT
ejpam-5962	84	1	[	[	X
ejpam-5962	84	2	10	10	NUM
ejpam-5962	84	3	]	]	X
ejpam-5962	84	4	a	a	DET
ejpam-5962	84	5	cover	cover	NOUN
ejpam-5962	84	6	b̂	b̂	NOUN
ejpam-5962	84	7	of	of	ADP
ejpam-5962	84	8	(	(	PUNCT
ejpam-5962	84	9	z	z	NOUN
ejpam-5962	84	10	,	,	PUNCT
ejpam-5962	84	11	ϑ1	ϑ1	NOUN
ejpam-5962	84	12	,	,	PUNCT
ejpam-5962	84	13	ϑ2	ϑ2	PROPN
ejpam-5962	84	14	)	)	PUNCT
ejpam-5962	84	15	is	be	AUX
ejpam-5962	84	16	called	call	VERB
ejpam-5962	84	17	pairwise	pairwise	NOUN
ejpam-5962	84	18	open	open	ADJ
ejpam-5962	84	19	if	if	SCONJ
ejpam-5962	84	20	b̂	b̂	NOUN
ejpam-5962	84	21	⊂	⊂	PROPN
ejpam-5962	84	22	ϑ1	ϑ1	PROPN
ejpam-5962	84	23	∪	∪	ADJ
ejpam-5962	84	24	ϑ2	ϑ2	NOUN
ejpam-5962	84	25	,	,	PUNCT
ejpam-5962	84	26	b̂	b̂	NOUN
ejpam-5962	84	27	∩ϑi	∩ϑi	PROPN
ejpam-5962	84	28	⊂	⊂	PROPN
ejpam-5962	84	29	{	{	PUNCT
ejpam-5962	84	30	a	a	DET
ejpam-5962	84	31	̸=	̸=	PROPN
ejpam-5962	84	32	ϕ	ϕ	NOUN
ejpam-5962	84	33	}	}	PUNCT
ejpam-5962	84	34	.	.	PUNCT
ejpam-5962	85	1	if	if	SCONJ
ejpam-5962	85	2	every	every	DET
ejpam-5962	85	3	pairwise	pairwise	NOUN
ejpam-5962	85	4	open	open	ADJ
ejpam-5962	85	5	cover	cover	NOUN
ejpam-5962	85	6	of	of	ADP
ejpam-5962	85	7	(	(	PUNCT
ejpam-5962	85	8	z	z	NOUN
ejpam-5962	85	9	,	,	PUNCT
ejpam-5962	85	10	ϑ1	ϑ1	NOUN
ejpam-5962	85	11	,	,	PUNCT
ejpam-5962	85	12	ϑ2	ϑ2	PROPN
ejpam-5962	85	13	)	)	PUNCT
ejpam-5962	85	14	has	have	VERB
ejpam-5962	85	15	a	a	DET
ejpam-5962	85	16	finite	finite	ADJ
ejpam-5962	85	17	subcover	subcover	NOUN
ejpam-5962	85	18	,	,	PUNCT
ejpam-5962	85	19	then	then	ADV
ejpam-5962	85	20	the	the	DET
ejpam-5962	85	21	space	space	NOUN
ejpam-5962	85	22	is	be	AUX
ejpam-5962	85	23	called	call	VERB
ejpam-5962	85	24	pairwise	pairwise	NOUN
ejpam-5962	85	25	compact	compact	ADJ
ejpam-5962	85	26	.	.	PUNCT
ejpam-5962	86	1	definition	definition	NOUN
ejpam-5962	86	2	2.3	2.3	NUM
ejpam-5962	86	3	.	.	PUNCT
ejpam-5962	87	1	[	[	X
ejpam-5962	87	2	15	15	NUM
ejpam-5962	87	3	]	]	X
ejpam-5962	87	4	a	a	DET
ejpam-5962	87	5	space	space	NOUN
ejpam-5962	87	6	(	(	PUNCT
ejpam-5962	87	7	z	z	NOUN
ejpam-5962	87	8	,	,	PUNCT
ejpam-5962	87	9	ϑ1	ϑ1	NOUN
ejpam-5962	87	10	,	,	PUNCT
ejpam-5962	87	11	ϑ2	ϑ2	PROPN
ejpam-5962	87	12	)	)	PUNCT
ejpam-5962	87	13	is	be	AUX
ejpam-5962	87	14	called	call	VERB
ejpam-5962	87	15	pairwise	pairwise	NOUN
ejpam-5962	87	16	t1	t1	NOUN
ejpam-5962	87	17	if	if	SCONJ
ejpam-5962	87	18	for	for	ADP
ejpam-5962	87	19	each	each	DET
ejpam-5962	87	20	two	two	NUM
ejpam-5962	87	21	distinct	distinct	ADJ
ejpam-5962	87	22	points	point	NOUN
ejpam-5962	87	23	z	z	NOUN
ejpam-5962	87	24	and	and	CCONJ
ejpam-5962	87	25	n	n	CCONJ
ejpam-5962	87	26	,	,	PUNCT
ejpam-5962	87	27	there	there	PRON
ejpam-5962	87	28	are	be	VERB
ejpam-5962	87	29	a	a	DET
ejpam-5962	87	30	ϑ1	ϑ1	NOUN
ejpam-5962	87	31	-	-	PUNCT
ejpam-5962	87	32	open	open	NOUN
ejpam-5962	87	33	set	set	NOUN
ejpam-5962	87	34	d	d	NOUN
ejpam-5962	87	35	and	and	CCONJ
ejpam-5962	87	36	a	a	DET
ejpam-5962	87	37	ϑ2	ϑ2	NOUN
ejpam-5962	87	38	-	-	PUNCT
ejpam-5962	87	39	open	open	NOUN
ejpam-5962	87	40	set	set	NOUN
ejpam-5962	87	41	f	f	PROPN
ejpam-5962	88	1	such	such	ADJ
ejpam-5962	88	2	that	that	SCONJ
ejpam-5962	88	3	z	z	PROPN
ejpam-5962	88	4	∈	∈	PROPN
ejpam-5962	88	5	d	d	PROPN
ejpam-5962	88	6	,	,	PUNCT
ejpam-5962	88	7	n	n	PROPN
ejpam-5962	88	8	/∈	/∈	PUNCT
ejpam-5962	88	9	f	f	NOUN
ejpam-5962	88	10	,	,	PUNCT
ejpam-5962	88	11	and	and	CCONJ
ejpam-5962	88	12	n	n	CCONJ
ejpam-5962	88	13	∈	∈	PROPN
ejpam-5962	88	14	f	f	X
ejpam-5962	88	15	,	,	PUNCT
ejpam-5962	88	16	z	z	NOUN
ejpam-5962	88	17	/∈	/∈	PUNCT
ejpam-5962	89	1	d	d	INTJ
ejpam-5962	89	2	.	.	PUNCT
ejpam-5962	90	1	definition	definition	NOUN
ejpam-5962	90	2	2.4	2.4	NUM
ejpam-5962	90	3	.	.	PUNCT
ejpam-5962	91	1	[	[	X
ejpam-5962	91	2	15	15	NUM
ejpam-5962	91	3	]	]	X
ejpam-5962	91	4	a	a	DET
ejpam-5962	91	5	space	space	NOUN
ejpam-5962	91	6	(	(	PUNCT
ejpam-5962	91	7	z	z	NOUN
ejpam-5962	91	8	,	,	PUNCT
ejpam-5962	91	9	ϑ1	ϑ1	NOUN
ejpam-5962	91	10	,	,	PUNCT
ejpam-5962	91	11	ϑ2	ϑ2	PROPN
ejpam-5962	91	12	)	)	PUNCT
ejpam-5962	91	13	is	be	AUX
ejpam-5962	91	14	called	call	VERB
ejpam-5962	91	15	pairwise	pairwise	NOUN
ejpam-5962	91	16	hausdroff	hausdroff	NOUN
ejpam-5962	91	17	(	(	PUNCT
ejpam-5962	91	18	pairwise	pairwise	NOUN
ejpam-5962	91	19	t2	t2	NOUN
ejpam-5962	91	20	)	)	PUNCT
ejpam-5962	91	21	if	if	SCONJ
ejpam-5962	91	22	for	for	ADP
ejpam-5962	91	23	each	each	DET
ejpam-5962	91	24	two	two	NUM
ejpam-5962	91	25	distinct	distinct	ADJ
ejpam-5962	91	26	points	point	NOUN
ejpam-5962	91	27	z	z	NOUN
ejpam-5962	91	28	and	and	CCONJ
ejpam-5962	91	29	n	n	CCONJ
ejpam-5962	91	30	,	,	PUNCT
ejpam-5962	91	31	there	there	PRON
ejpam-5962	91	32	are	be	VERB
ejpam-5962	91	33	a	a	DET
ejpam-5962	91	34	ϑ1	ϑ1	NOUN
ejpam-5962	91	35	-	-	PUNCT
ejpam-5962	91	36	open	open	NOUN
ejpam-5962	91	37	set	set	NOUN
ejpam-5962	91	38	q	q	PROPN
ejpam-5962	91	39	and	and	CCONJ
ejpam-5962	91	40	a	a	DET
ejpam-5962	91	41	ϑ2	ϑ2	NOUN
ejpam-5962	91	42	-	-	PUNCT
ejpam-5962	91	43	open	open	NOUN
ejpam-5962	91	44	set	set	NOUN
ejpam-5962	91	45	w	w	ADP
ejpam-5962	91	46	such	such	ADJ
ejpam-5962	91	47	that	that	SCONJ
ejpam-5962	91	48	z	z	PROPN
ejpam-5962	91	49	∈	∈	PROPN
ejpam-5962	91	50	d	d	PROPN
ejpam-5962	91	51	,	,	PUNCT
ejpam-5962	91	52	n	n	PROPN
ejpam-5962	91	53	∈	∈	PROPN
ejpam-5962	91	54	f	f	X
ejpam-5962	91	55	,	,	PUNCT
ejpam-5962	91	56	and	and	CCONJ
ejpam-5962	91	57	d	d	X
ejpam-5962	91	58	∩	∩	ADJ
ejpam-5962	91	59	f	f	PROPN
ejpam-5962	91	60	=	=	PUNCT
ejpam-5962	91	61	ϕ.	ϕ.	PROPN
ejpam-5962	91	62	definition	definition	NOUN
ejpam-5962	91	63	2.5	2.5	NUM
ejpam-5962	91	64	.	.	PUNCT
ejpam-5962	92	1	[	[	X
ejpam-5962	92	2	10	10	NUM
ejpam-5962	92	3	]	]	X
ejpam-5962	92	4	a	a	DET
ejpam-5962	92	5	function	function	NOUN
ejpam-5962	92	6	φ	φ	NOUN
ejpam-5962	92	7	:	:	PUNCT
ejpam-5962	92	8	(	(	PUNCT
ejpam-5962	92	9	z	z	NOUN
ejpam-5962	92	10	,	,	PUNCT
ejpam-5962	92	11	ϑ1	ϑ1	NOUN
ejpam-5962	92	12	,	,	PUNCT
ejpam-5962	92	13	ϑ2	ϑ2	PROPN
ejpam-5962	92	14	)	)	PUNCT
ejpam-5962	92	15	→	→	SYM
ejpam-5962	92	16	(	(	PUNCT
ejpam-5962	92	17	n	n	CCONJ
ejpam-5962	92	18	,	,	PUNCT
ejpam-5962	92	19	β1	β1	PROPN
ejpam-5962	92	20	,	,	PUNCT
ejpam-5962	92	21	β2	β2	NOUN
ejpam-5962	92	22	)	)	PUNCT
ejpam-5962	92	23	is	be	AUX
ejpam-5962	92	24	called	call	VERB
ejpam-5962	92	25	pairwise	pairwise	NOUN
ejpam-5962	92	26	continuous	continuous	ADJ
ejpam-5962	92	27	,	,	PUNCT
ejpam-5962	92	28	if	if	SCONJ
ejpam-5962	92	29	φ1	φ1	NOUN
ejpam-5962	92	30	:	:	PUNCT
ejpam-5962	92	31	(	(	PUNCT
ejpam-5962	92	32	z	z	NOUN
ejpam-5962	92	33	,	,	PUNCT
ejpam-5962	92	34	ϑ1	ϑ1	PROPN
ejpam-5962	92	35	)	)	PUNCT
ejpam-5962	92	36	→	→	SYM
ejpam-5962	92	37	(	(	PUNCT
ejpam-5962	92	38	n	n	CCONJ
ejpam-5962	92	39	,	,	PUNCT
ejpam-5962	92	40	β1	β1	PROPN
ejpam-5962	92	41	)	)	PUNCT
ejpam-5962	92	42	and	and	CCONJ
ejpam-5962	92	43	φ2	φ2	PROPN
ejpam-5962	92	44	:	:	PUNCT
ejpam-5962	92	45	(	(	PUNCT
ejpam-5962	92	46	z	z	NOUN
ejpam-5962	92	47	,	,	PUNCT
ejpam-5962	92	48	ϑ2	ϑ2	PROPN
ejpam-5962	92	49	)	)	PUNCT
ejpam-5962	92	50	→	→	SYM
ejpam-5962	92	51	(	(	PUNCT
ejpam-5962	92	52	n	n	CCONJ
ejpam-5962	92	53	,	,	PUNCT
ejpam-5962	92	54	β2	β2	NOUN
ejpam-5962	92	55	)	)	PUNCT
ejpam-5962	92	56	are	be	AUX
ejpam-5962	92	57	continuous	continuous	ADJ
ejpam-5962	92	58	functions	function	NOUN
ejpam-5962	92	59	.	.	PUNCT
ejpam-5962	93	1	definition	definition	NOUN
ejpam-5962	93	2	2.6	2.6	NUM
ejpam-5962	93	3	.	.	PUNCT
ejpam-5962	94	1	[	[	X
ejpam-5962	94	2	10	10	NUM
ejpam-5962	94	3	]	]	X
ejpam-5962	94	4	:	:	PUNCT
ejpam-5962	94	5	a	a	DET
ejpam-5962	94	6	function	function	NOUN
ejpam-5962	94	7	φ	φ	NOUN
ejpam-5962	94	8	:	:	PUNCT
ejpam-5962	94	9	(	(	PUNCT
ejpam-5962	94	10	z	z	NOUN
ejpam-5962	94	11	,	,	PUNCT
ejpam-5962	94	12	ϑ1	ϑ1	NOUN
ejpam-5962	94	13	,	,	PUNCT
ejpam-5962	94	14	ϑ2	ϑ2	PROPN
ejpam-5962	94	15	)	)	PUNCT
ejpam-5962	94	16	→	→	SYM
ejpam-5962	94	17	(	(	PUNCT
ejpam-5962	94	18	n	n	CCONJ
ejpam-5962	94	19	,	,	PUNCT
ejpam-5962	94	20	β1	β1	PROPN
ejpam-5962	94	21	,	,	PUNCT
ejpam-5962	94	22	β2	β2	NOUN
ejpam-5962	94	23	)	)	PUNCT
ejpam-5962	94	24	is	be	AUX
ejpam-5962	94	25	called	call	VERB
ejpam-5962	94	26	pairwise	pairwise	NOUN
ejpam-5962	94	27	closed	close	VERB
ejpam-5962	94	28	,	,	PUNCT
ejpam-5962	94	29	if	if	SCONJ
ejpam-5962	94	30	φ1	φ1	NOUN
ejpam-5962	94	31	:	:	PUNCT
ejpam-5962	94	32	(	(	PUNCT
ejpam-5962	94	33	z	z	NOUN
ejpam-5962	94	34	,	,	PUNCT
ejpam-5962	94	35	ϑ1	ϑ1	PROPN
ejpam-5962	94	36	)	)	PUNCT
ejpam-5962	94	37	→	→	SYM
ejpam-5962	94	38	(	(	PUNCT
ejpam-5962	94	39	n	n	CCONJ
ejpam-5962	94	40	,	,	PUNCT
ejpam-5962	94	41	β1	β1	PROPN
ejpam-5962	94	42	)	)	PUNCT
ejpam-5962	94	43	and	and	CCONJ
ejpam-5962	94	44	φ2	φ2	PROPN
ejpam-5962	94	45	:	:	PUNCT
ejpam-5962	94	46	(	(	PUNCT
ejpam-5962	94	47	z	z	NOUN
ejpam-5962	94	48	,	,	PUNCT
ejpam-5962	94	49	ϑ2	ϑ2	PROPN
ejpam-5962	94	50	)	)	PUNCT
ejpam-5962	94	51	→	→	SYM
ejpam-5962	94	52	(	(	PUNCT
ejpam-5962	94	53	n	n	CCONJ
ejpam-5962	94	54	,	,	PUNCT
ejpam-5962	94	55	β2	β2	NOUN
ejpam-5962	94	56	)	)	PUNCT
ejpam-5962	94	57	are	be	AUX
ejpam-5962	94	58	closed	closed	ADJ
ejpam-5962	94	59	functions	function	NOUN
ejpam-5962	94	60	.	.	PUNCT
ejpam-5962	95	1	as	as	ADP
ejpam-5962	95	2	a	a	DET
ejpam-5962	95	3	result	result	NOUN
ejpam-5962	95	4	,	,	PUNCT
ejpam-5962	95	5	if	if	SCONJ
ejpam-5962	95	6	a1is	a1is	PUNCT
ejpam-5962	95	7	closed	close	VERB
ejpam-5962	95	8	in	in	ADP
ejpam-5962	95	9	ϑ1	ϑ1	PROPN
ejpam-5962	95	10	,	,	PUNCT
ejpam-5962	95	11	then	then	ADV
ejpam-5962	95	12	φ1(a1	φ1(a1	NUM
ejpam-5962	95	13	)	)	PUNCT
ejpam-5962	95	14	is	be	AUX
ejpam-5962	95	15	closed	close	VERB
ejpam-5962	95	16	in	in	ADP
ejpam-5962	95	17	β1	β1	PROPN
ejpam-5962	95	18	,	,	PUNCT
ejpam-5962	95	19	and	and	CCONJ
ejpam-5962	95	20	if	if	SCONJ
ejpam-5962	95	21	a2	a2	PROPN
ejpam-5962	95	22	is	be	AUX
ejpam-5962	95	23	closed	close	VERB
ejpam-5962	95	24	in	in	ADP
ejpam-5962	95	25	ϑ2	ϑ2	NOUN
ejpam-5962	95	26	,	,	PUNCT
ejpam-5962	95	27	then	then	ADV
ejpam-5962	95	28	φ2(a2	φ2(a2	ADJ
ejpam-5962	95	29	)	)	PUNCT
ejpam-5962	95	30	is	be	AUX
ejpam-5962	95	31	closed	close	VERB
ejpam-5962	95	32	in	in	ADP
ejpam-5962	95	33	β2	β2	PROPN
ejpam-5962	95	34	.	.	PUNCT
ejpam-5962	96	1	definition	definition	NOUN
ejpam-5962	96	2	2.7	2.7	NUM
ejpam-5962	96	3	.	.	PUNCT
ejpam-5962	97	1	[	[	X
ejpam-5962	97	2	15	15	NUM
ejpam-5962	97	3	]	]	X
ejpam-5962	97	4	a	a	DET
ejpam-5962	97	5	bitopological	bitopological	ADJ
ejpam-5962	97	6	space	space	NOUN
ejpam-5962	97	7	(	(	PUNCT
ejpam-5962	97	8	z	z	NOUN
ejpam-5962	97	9	,	,	PUNCT
ejpam-5962	97	10	ϑ1	ϑ1	NOUN
ejpam-5962	97	11	,	,	PUNCT
ejpam-5962	97	12	ϑ2	ϑ2	PROPN
ejpam-5962	97	13	)	)	PUNCT
ejpam-5962	97	14	is	be	AUX
ejpam-5962	97	15	said	say	VERB
ejpam-5962	97	16	to	to	PART
ejpam-5962	97	17	be	be	AUX
ejpam-5962	97	18	pairwise	pairwise	NOUN
ejpam-5962	97	19	locally	locally	ADV
ejpam-5962	97	20	compact	compact	ADJ
ejpam-5962	97	21	if	if	SCONJ
ejpam-5962	97	22	each	each	PRON
ejpam-5962	97	23	z	z	NOUN
ejpam-5962	97	24	∈	∈	PROPN
ejpam-5962	98	1	z	z	NOUN
ejpam-5962	98	2	,	,	PUNCT
ejpam-5962	98	3	there	there	PRON
ejpam-5962	98	4	exist	exist	VERB
ejpam-5962	98	5	ϑ1−open	ϑ1−open	ADJ
ejpam-5962	98	6	nieghbourhood	nieghbourhood	NOUN
ejpam-5962	98	7	of	of	ADP
ejpam-5962	98	8	z	z	NOUN
ejpam-5962	98	9	,	,	PUNCT
ejpam-5962	98	10	whose	whose	DET
ejpam-5962	98	11	ϑ1−closure	ϑ1−closure	ADP
ejpam-5962	98	12	is	be	AUX
ejpam-5962	98	13	pairwise	pairwise	NOUN
ejpam-5962	98	14	compact	compact	ADJ
ejpam-5962	98	15	or	or	CCONJ
ejpam-5962	98	16	a	a	DET
ejpam-5962	98	17	ϑ2−open	ϑ2−open	ADJ
ejpam-5962	98	18	nieghbourhood	nieghbourhood	NOUN
ejpam-5962	98	19	of	of	ADP
ejpam-5962	98	20	z	z	NOUN
ejpam-5962	98	21	,	,	PUNCT
ejpam-5962	98	22	whose	whose	DET
ejpam-5962	98	23	ϑ2−closure	ϑ2−closure	NOUN
ejpam-5962	98	24	is	be	AUX
ejpam-5962	98	25	pairwise	pairwise	NOUN
ejpam-5962	98	26	compact	compact	ADJ
ejpam-5962	98	27	.	.	PUNCT
ejpam-5962	99	1	definition	definition	NOUN
ejpam-5962	99	2	2.8	2.8	NUM
ejpam-5962	99	3	.	.	PUNCT
ejpam-5962	100	1	[	[	X
ejpam-5962	100	2	16	16	NUM
ejpam-5962	100	3	]	]	PUNCT
ejpam-5962	100	4	a	a	DET
ejpam-5962	100	5	function	function	NOUN
ejpam-5962	100	6	φ	φ	NOUN
ejpam-5962	100	7	:	:	PUNCT
ejpam-5962	100	8	(	(	PUNCT
ejpam-5962	100	9	z	z	NOUN
ejpam-5962	100	10	,	,	PUNCT
ejpam-5962	100	11	ϑ1	ϑ1	NOUN
ejpam-5962	100	12	,	,	PUNCT
ejpam-5962	100	13	ϑ2	ϑ2	PROPN
ejpam-5962	100	14	)	)	PUNCT
ejpam-5962	100	15	→	→	SYM
ejpam-5962	100	16	(	(	PUNCT
ejpam-5962	100	17	n	n	CCONJ
ejpam-5962	100	18	,	,	PUNCT
ejpam-5962	100	19	β1	β1	PROPN
ejpam-5962	100	20	,	,	PUNCT
ejpam-5962	100	21	β2	β2	NOUN
ejpam-5962	100	22	)	)	PUNCT
ejpam-5962	100	23	is	be	AUX
ejpam-5962	100	24	called	call	VERB
ejpam-5962	100	25	pairwise	pairwise	PROPN
ejpam-5962	100	26	homomorphism	homomorphism	NOUN
ejpam-5962	100	27	,	,	PUNCT
ejpam-5962	100	28	iff	iff	PROPN
ejpam-5962	100	29	φ1	φ1	PROPN
ejpam-5962	100	30	:	:	PUNCT
ejpam-5962	100	31	(	(	PUNCT
ejpam-5962	100	32	z	z	X
ejpam-5962	100	33	,	,	PUNCT
ejpam-5962	100	34	ϑ1	ϑ1	PROPN
ejpam-5962	100	35	)	)	PUNCT
ejpam-5962	100	36	→	→	SYM
ejpam-5962	100	37	(	(	PUNCT
ejpam-5962	100	38	n	n	CCONJ
ejpam-5962	100	39	,	,	PUNCT
ejpam-5962	100	40	β1	β1	PROPN
ejpam-5962	100	41	)	)	PUNCT
ejpam-5962	100	42	and	and	CCONJ
ejpam-5962	100	43	φ2	φ2	PROPN
ejpam-5962	100	44	:	:	PUNCT
ejpam-5962	100	45	(	(	PUNCT
ejpam-5962	100	46	z	z	NOUN
ejpam-5962	100	47	,	,	PUNCT
ejpam-5962	100	48	ϑ2	ϑ2	PROPN
ejpam-5962	100	49	)	)	PUNCT
ejpam-5962	100	50	→	→	SYM
ejpam-5962	100	51	(	(	PUNCT
ejpam-5962	100	52	n	n	CCONJ
ejpam-5962	100	53	,	,	PUNCT
ejpam-5962	100	54	β2	β2	PROPN
ejpam-5962	100	55	)	)	PUNCT
ejpam-5962	100	56	are	be	AUX
ejpam-5962	100	57	homomorphism	homomorphism	NOUN
ejpam-5962	100	58	.	.	PUNCT
ejpam-5962	101	1	definition	definition	NOUN
ejpam-5962	101	2	2.9	2.9	NUM
ejpam-5962	101	3	.	.	PUNCT
ejpam-5962	102	1	[	[	X
ejpam-5962	102	2	16	16	NUM
ejpam-5962	102	3	]	]	PUNCT
ejpam-5962	102	4	a	a	DET
ejpam-5962	102	5	space	space	NOUN
ejpam-5962	102	6	(	(	PUNCT
ejpam-5962	102	7	z	z	NOUN
ejpam-5962	102	8	,	,	PUNCT
ejpam-5962	102	9	ϑ	ϑ	NOUN
ejpam-5962	102	10	)	)	PUNCT
ejpam-5962	102	11	is	be	AUX
ejpam-5962	102	12	called	call	VERB
ejpam-5962	102	13	a	a	DET
ejpam-5962	102	14	p	p	NOUN
ejpam-5962	102	15	-	-	PUNCT
ejpam-5962	102	16	space	space	NOUN
ejpam-5962	102	17	if	if	SCONJ
ejpam-5962	102	18	every	every	DET
ejpam-5962	102	19	countable	countable	ADJ
ejpam-5962	102	20	intersection	intersection	NOUN
ejpam-5962	102	21	of	of	ADP
ejpam-5962	102	22	open	open	ADJ
ejpam-5962	102	23	sets	set	NOUN
ejpam-5962	102	24	in	in	ADP
ejpam-5962	102	25	ϑ	ϑ	PROPN
ejpam-5962	102	26	is	be	AUX
ejpam-5962	102	27	itself	itself	PRON
ejpam-5962	102	28	an	an	DET
ejpam-5962	102	29	open	open	ADJ
ejpam-5962	102	30	set	set	NOUN
ejpam-5962	102	31	.	.	PUNCT
ejpam-5962	103	1	3	3	X
ejpam-5962	103	2	.	.	X
ejpam-5962	103	3	new	new	ADJ
ejpam-5962	103	4	generations	generation	NOUN
ejpam-5962	103	5	of	of	ADP
ejpam-5962	103	6	pairwise	pairwise	NOUN
ejpam-5962	103	7	compact	compact	ADJ
ejpam-5962	103	8	closed	close	VERB
ejpam-5962	103	9	spaces	space	NOUN
ejpam-5962	103	10	we	we	PRON
ejpam-5962	103	11	describe	describe	VERB
ejpam-5962	103	12	pairwise	pairwise	NOUN
ejpam-5962	103	13	compact	compact	ADJ
ejpam-5962	103	14	closed	close	VERB
ejpam-5962	103	15	spaces	space	NOUN
ejpam-5962	103	16	in	in	ADP
ejpam-5962	103	17	bitopological	bitopological	ADJ
ejpam-5962	103	18	spaces	space	NOUN
ejpam-5962	103	19	in	in	ADP
ejpam-5962	103	20	this	this	DET
ejpam-5962	103	21	section	section	NOUN
ejpam-5962	103	22	and	and	CCONJ
ejpam-5962	103	23	demonstrate	demonstrate	VERB
ejpam-5962	103	24	how	how	SCONJ
ejpam-5962	103	25	they	they	PRON
ejpam-5962	103	26	relate	relate	VERB
ejpam-5962	103	27	to	to	ADP
ejpam-5962	103	28	other	other	ADJ
ejpam-5962	103	29	spaces	space	NOUN
ejpam-5962	103	30	.	.	PUNCT
ejpam-5962	104	1	definition	definition	NOUN
ejpam-5962	104	2	3.1	3.1	NUM
ejpam-5962	104	3	.	.	PUNCT
ejpam-5962	105	1	a	a	DET
ejpam-5962	105	2	bitopological	bitopological	ADJ
ejpam-5962	105	3	space	space	NOUN
ejpam-5962	105	4	(	(	PUNCT
ejpam-5962	105	5	z	z	NOUN
ejpam-5962	105	6	,	,	PUNCT
ejpam-5962	105	7	ϑ1	ϑ1	NOUN
ejpam-5962	105	8	,	,	PUNCT
ejpam-5962	105	9	ϑ2	ϑ2	PROPN
ejpam-5962	105	10	)	)	PUNCT
ejpam-5962	105	11	is	be	AUX
ejpam-5962	105	12	called	call	VERB
ejpam-5962	105	13	a	a	DET
ejpam-5962	105	14	pairwise	pairwise	NOUN
ejpam-5962	105	15	compact	compact	ADJ
ejpam-5962	105	16	closed	close	VERB
ejpam-5962	105	17	space	space	NOUN
ejpam-5962	105	18	if	if	SCONJ
ejpam-5962	105	19	:	:	PUNCT
ejpam-5962	105	20	every	every	DET
ejpam-5962	105	21	ϑ1	ϑ1	NOUN
ejpam-5962	105	22	-	-	PUNCT
ejpam-5962	105	23	compact	compact	ADJ
ejpam-5962	105	24	subset	subset	NOUN
ejpam-5962	105	25	of	of	ADP
ejpam-5962	105	26	z	z	PROPN
ejpam-5962	105	27	is	be	AUX
ejpam-5962	105	28	ϑ2	ϑ2	NOUN
ejpam-5962	105	29	-	-	PUNCT
ejpam-5962	105	30	closed	closed	ADJ
ejpam-5962	105	31	,	,	PUNCT
ejpam-5962	105	32	every	every	DET
ejpam-5962	105	33	ϑ2	ϑ2	NOUN
ejpam-5962	105	34	-	-	ADJ
ejpam-5962	105	35	compact	compact	ADJ
ejpam-5962	105	36	subset	subset	NOUN
ejpam-5962	105	37	of	of	ADP
ejpam-5962	105	38	z	z	PROPN
ejpam-5962	105	39	is	be	AUX
ejpam-5962	105	40	ϑ1	ϑ1	NOUN
ejpam-5962	105	41	-	-	PUNCT
ejpam-5962	105	42	closed	closed	ADJ
ejpam-5962	105	43	.	.	PUNCT
ejpam-5962	106	1	because	because	SCONJ
ejpam-5962	106	2	each	each	DET
ejpam-5962	106	3	singleton	singleton	NOUN
ejpam-5962	106	4	is	be	AUX
ejpam-5962	106	5	compact	compact	ADJ
ejpam-5962	106	6	,	,	PUNCT
ejpam-5962	106	7	it	it	PRON
ejpam-5962	106	8	is	be	AUX
ejpam-5962	106	9	simple	simple	ADJ
ejpam-5962	106	10	to	to	PART
ejpam-5962	106	11	demonstrate	demonstrate	VERB
ejpam-5962	106	12	that	that	SCONJ
ejpam-5962	106	13	every	every	DET
ejpam-5962	106	14	pairwise	pairwise	NOUN
ejpam-5962	106	15	hausdorff	hausdorff	NOUN
ejpam-5962	106	16	space	space	NOUN
ejpam-5962	106	17	is	be	AUX
ejpam-5962	106	18	also	also	ADV
ejpam-5962	106	19	a	a	DET
ejpam-5962	106	20	pairwise	pairwise	NOUN
ejpam-5962	106	21	compact	compact	ADJ
ejpam-5962	106	22	closed	close	VERB
ejpam-5962	106	23	space	space	NOUN
ejpam-5962	106	24	and	and	CCONJ
ejpam-5962	106	25	every	every	DET
ejpam-5962	106	26	pairwise	pairwise	NOUN
ejpam-5962	106	27	compact	compact	ADJ
ejpam-5962	106	28	closed	close	VERB
ejpam-5962	106	29	space	space	NOUN
ejpam-5962	106	30	is	be	AUX
ejpam-5962	106	31	also	also	ADV
ejpam-5962	106	32	a	a	DET
ejpam-5962	106	33	pairwise	pairwise	NOUN
ejpam-5962	106	34	t1−space	t1−space	NOUN
ejpam-5962	106	35	.	.	PUNCT
ejpam-5962	107	1	the	the	DET
ejpam-5962	107	2	instances	instance	NOUN
ejpam-5962	107	3	that	that	PRON
ejpam-5962	107	4	follow	follow	VERB
ejpam-5962	107	5	demonstrate	demonstrate	NOUN
ejpam-5962	107	6	that	that	SCONJ
ejpam-5962	107	7	the	the	DET
ejpam-5962	107	8	opposite	opposite	ADJ
ejpam-5962	107	9	need	need	AUX
ejpam-5962	107	10	not	not	PART
ejpam-5962	107	11	be	be	AUX
ejpam-5962	107	12	true	true	ADJ
ejpam-5962	107	13	.	.	PUNCT
ejpam-5962	108	1	a.	a.	NOUN
ejpam-5962	108	2	a.	a.	PROPN
ejpam-5962	108	3	atoom	atoom	PROPN
ejpam-5962	108	4	et	et	PROPN
ejpam-5962	108	5	al	al	PROPN
ejpam-5962	108	6	.	.	PUNCT
ejpam-5962	108	7	/	/	SYM
ejpam-5962	108	8	eur	eur	PROPN
ejpam-5962	108	9	.	.	PUNCT
ejpam-5962	109	1	j.	j.	PROPN
ejpam-5962	109	2	pure	pure	PROPN
ejpam-5962	109	3	appl	appl	PROPN
ejpam-5962	109	4	.	.	PROPN
ejpam-5962	109	5	math	math	PROPN
ejpam-5962	109	6	,	,	PUNCT
ejpam-5962	109	7	18	18	NUM
ejpam-5962	109	8	(	(	PUNCT
ejpam-5962	109	9	2	2	NUM
ejpam-5962	109	10	)	)	PUNCT
ejpam-5962	109	11	(	(	PUNCT
ejpam-5962	109	12	2025	2025	NUM
ejpam-5962	109	13	)	)	PUNCT
ejpam-5962	109	14	,	,	PUNCT
ejpam-5962	109	15	5962	5962	NUM
ejpam-5962	109	16	5	5	NUM
ejpam-5962	109	17	of	of	ADP
ejpam-5962	109	18	17	17	NUM
ejpam-5962	109	19	example	example	NOUN
ejpam-5962	109	20	3.1	3.1	NUM
ejpam-5962	109	21	.	.	PUNCT
ejpam-5962	110	1	let	let	VERB
ejpam-5962	110	2	ϑcc	ϑcc	NOUN
ejpam-5962	110	3	be	be	AUX
ejpam-5962	110	4	cocountable	cocountable	ADJ
ejpam-5962	110	5	topology	topology	NOUN
ejpam-5962	110	6	,	,	PUNCT
ejpam-5962	110	7	then	then	ADV
ejpam-5962	110	8	(	(	PUNCT
ejpam-5962	110	9	r,ϑcc	r,ϑcc	NOUN
ejpam-5962	110	10	,	,	PUNCT
ejpam-5962	110	11	ϑcc	ϑcc	NOUN
ejpam-5962	110	12	)	)	PUNCT
ejpam-5962	110	13	is	be	AUX
ejpam-5962	110	14	pairwise	pairwise	NOUN
ejpam-5962	110	15	compact	compact	ADJ
ejpam-5962	110	16	closed	close	VERB
ejpam-5962	110	17	space	space	NOUN
ejpam-5962	110	18	but	but	CCONJ
ejpam-5962	110	19	not	not	PART
ejpam-5962	110	20	pairwise	pairwise	NOUN
ejpam-5962	110	21	hausdorff	hausdorff	NOUN
ejpam-5962	110	22	space	space	NOUN
ejpam-5962	110	23	.	.	PUNCT
ejpam-5962	111	1	example	example	NOUN
ejpam-5962	111	2	3.2	3.2	NUM
ejpam-5962	111	3	.	.	PUNCT
ejpam-5962	112	1	let	let	VERB
ejpam-5962	112	2	ϑcof	ϑcof	NOUN
ejpam-5962	112	3	be	be	AUX
ejpam-5962	112	4	cofinite	cofinite	NOUN
ejpam-5962	112	5	topology	topology	NOUN
ejpam-5962	112	6	,	,	PUNCT
ejpam-5962	112	7	then	then	ADV
ejpam-5962	112	8	(	(	PUNCT
ejpam-5962	112	9	r,ϑcof	r,ϑcof	PROPN
ejpam-5962	112	10	,	,	PUNCT
ejpam-5962	112	11	ϑcof	ϑcof	PROPN
ejpam-5962	112	12	)	)	PUNCT
ejpam-5962	112	13	is	be	AUX
ejpam-5962	112	14	pairwise	pairwise	NOUN
ejpam-5962	112	15	t1−spaces	t1−space	NOUN
ejpam-5962	112	16	,	,	PUNCT
ejpam-5962	112	17	where	where	SCONJ
ejpam-5962	112	18	is	be	AUX
ejpam-5962	112	19	not	not	PART
ejpam-5962	112	20	pairwise	pairwise	NOUN
ejpam-5962	112	21	compact	compact	ADJ
ejpam-5962	112	22	closed	close	VERB
ejpam-5962	112	23	space	space	NOUN
ejpam-5962	112	24	.	.	PUNCT
ejpam-5962	113	1	proposition	proposition	NOUN
ejpam-5962	113	2	3.1	3.1	NUM
ejpam-5962	113	3	.	.	PUNCT
ejpam-5962	114	1	let	let	AUX
ejpam-5962	114	2	(	(	PUNCT
ejpam-5962	114	3	z	z	NOUN
ejpam-5962	114	4	,	,	PUNCT
ejpam-5962	114	5	ϑ1	ϑ1	NOUN
ejpam-5962	114	6	,	,	PUNCT
ejpam-5962	114	7	ϑ2	ϑ2	PROPN
ejpam-5962	114	8	)	)	PUNCT
ejpam-5962	114	9	be	be	VERB
ejpam-5962	114	10	a	a	DET
ejpam-5962	114	11	pairwise	pairwise	NOUN
ejpam-5962	114	12	locally	locally	ADV
ejpam-5962	114	13	compact	compact	ADJ
ejpam-5962	114	14	space	space	NOUN
ejpam-5962	114	15	.	.	PUNCT
ejpam-5962	115	1	if	if	SCONJ
ejpam-5962	115	2	(	(	PUNCT
ejpam-5962	115	3	z	z	NOUN
ejpam-5962	115	4	,	,	PUNCT
ejpam-5962	115	5	ϑ1	ϑ1	NOUN
ejpam-5962	115	6	,	,	PUNCT
ejpam-5962	115	7	ϑ2	ϑ2	PROPN
ejpam-5962	115	8	)	)	PUNCT
ejpam-5962	115	9	is	be	AUX
ejpam-5962	115	10	a	a	DET
ejpam-5962	115	11	pairwise	pairwise	NOUN
ejpam-5962	115	12	compact	compact	ADJ
ejpam-5962	115	13	closed	close	VERB
ejpam-5962	115	14	space	space	NOUN
ejpam-5962	115	15	,	,	PUNCT
ejpam-5962	115	16	then	then	ADV
ejpam-5962	115	17	it	it	PRON
ejpam-5962	115	18	is	be	AUX
ejpam-5962	115	19	a	a	DET
ejpam-5962	115	20	pairwise	pairwise	NOUN
ejpam-5962	115	21	t3	t3	NOUN
ejpam-5962	115	22	-	-	PUNCT
ejpam-5962	115	23	space	space	NOUN
ejpam-5962	115	24	.	.	PUNCT
ejpam-5962	116	1	proof	proof	NOUN
ejpam-5962	116	2	.	.	PUNCT
ejpam-5962	117	1	consider	consider	VERB
ejpam-5962	117	2	this	this	PRON
ejpam-5962	117	3	(	(	PUNCT
ejpam-5962	117	4	z	z	NOUN
ejpam-5962	117	5	,	,	PUNCT
ejpam-5962	117	6	ϑ1	ϑ1	NOUN
ejpam-5962	117	7	,	,	PUNCT
ejpam-5962	117	8	ϑ2	ϑ2	PROPN
ejpam-5962	117	9	)	)	PUNCT
ejpam-5962	117	10	is	be	AUX
ejpam-5962	117	11	pairwise	pairwise	NOUN
ejpam-5962	117	12	compact	compact	ADJ
ejpam-5962	117	13	closed	close	VERB
ejpam-5962	117	14	space	space	NOUN
ejpam-5962	117	15	.	.	PUNCT
ejpam-5962	118	1	on	on	ADP
ejpam-5962	118	2	account	account	NOUN
ejpam-5962	118	3	of	of	ADP
ejpam-5962	118	4	(	(	PUNCT
ejpam-5962	118	5	z	z	NOUN
ejpam-5962	118	6	,	,	PUNCT
ejpam-5962	118	7	ϑ1	ϑ1	NOUN
ejpam-5962	118	8	,	,	PUNCT
ejpam-5962	118	9	ϑ2	ϑ2	PROPN
ejpam-5962	118	10	)	)	PUNCT
ejpam-5962	118	11	is	be	AUX
ejpam-5962	118	12	a	a	DET
ejpam-5962	118	13	pairwise	pairwise	NOUN
ejpam-5962	118	14	locally	locally	ADV
ejpam-5962	118	15	compact	compact	ADJ
ejpam-5962	118	16	,	,	PUNCT
ejpam-5962	118	17	there	there	PRON
ejpam-5962	118	18	exist	exist	VERB
ejpam-5962	118	19	ϑ1−open	ϑ1−open	ADJ
ejpam-5962	118	20	nieghbourhood	nieghbourhood	NOUN
ejpam-5962	118	21	of	of	ADP
ejpam-5962	118	22	(	(	PUNCT
ejpam-5962	118	23	z	z	NOUN
ejpam-5962	118	24	,	,	PUNCT
ejpam-5962	118	25	ϑ1	ϑ1	NOUN
ejpam-5962	118	26	,	,	PUNCT
ejpam-5962	118	27	ϑ2	ϑ2	PROPN
ejpam-5962	118	28	)	)	PUNCT
ejpam-5962	118	29	,	,	PUNCT
ejpam-5962	118	30	whose	whose	DET
ejpam-5962	118	31	ϑ1−closure	ϑ1−closure	NOUN
ejpam-5962	118	32	is	be	AUX
ejpam-5962	118	33	pairwise	pairwise	NOUN
ejpam-5962	118	34	compact	compact	ADJ
ejpam-5962	118	35	.	.	PUNCT
ejpam-5962	119	1	consequently	consequently	ADV
ejpam-5962	119	2	,	,	PUNCT
ejpam-5962	119	3	the	the	DET
ejpam-5962	119	4	set	set	NOUN
ejpam-5962	119	5	of	of	ADP
ejpam-5962	119	6	pairwise	pairwise	NOUN
ejpam-5962	119	7	compact	compact	ADJ
ejpam-5962	119	8	of	of	ADP
ejpam-5962	119	9	nieghbourhood	nieghbourhood	PROPN
ejpam-5962	119	10	z	z	NOUN
ejpam-5962	119	11	∈	∈	PROPN
ejpam-5962	119	12	(	(	PUNCT
ejpam-5962	119	13	z	z	NOUN
ejpam-5962	119	14	,	,	PUNCT
ejpam-5962	119	15	ϑ1	ϑ1	NOUN
ejpam-5962	119	16	,	,	PUNCT
ejpam-5962	119	17	ϑ2	ϑ2	PROPN
ejpam-5962	119	18	)	)	PUNCT
ejpam-5962	119	19	shall	shall	AUX
ejpam-5962	119	20	be	be	AUX
ejpam-5962	119	21	a	a	DET
ejpam-5962	119	22	local	local	ADJ
ejpam-5962	119	23	base	base	NOUN
ejpam-5962	119	24	of	of	ADP
ejpam-5962	119	25	z	z	PROPN
ejpam-5962	119	26	∈	∈	PROPN
ejpam-5962	119	27	(	(	PUNCT
ejpam-5962	119	28	z	z	NOUN
ejpam-5962	119	29	,	,	PUNCT
ejpam-5962	119	30	ϑ1	ϑ1	PROPN
ejpam-5962	119	31	,	,	PUNCT
ejpam-5962	119	32	ϑ2).because	ϑ2).because	NOUN
ejpam-5962	119	33	(	(	PUNCT
ejpam-5962	119	34	z	z	NOUN
ejpam-5962	119	35	,	,	PUNCT
ejpam-5962	119	36	ϑ1	ϑ1	NOUN
ejpam-5962	119	37	,	,	PUNCT
ejpam-5962	119	38	ϑ2	ϑ2	PROPN
ejpam-5962	119	39	)	)	PUNCT
ejpam-5962	119	40	is	be	AUX
ejpam-5962	119	41	pairwise	pairwise	NOUN
ejpam-5962	119	42	compact	compact	ADJ
ejpam-5962	119	43	closed	close	VERB
ejpam-5962	119	44	space	space	NOUN
ejpam-5962	119	45	,	,	PUNCT
ejpam-5962	119	46	the	the	DET
ejpam-5962	119	47	like	like	ADJ
ejpam-5962	119	48	set	set	NOUN
ejpam-5962	119	49	is	be	AUX
ejpam-5962	119	50	ϑ2−closed	ϑ2−close	VERB
ejpam-5962	119	51	nieghbourhood	nieghbourhood	NOUN
ejpam-5962	119	52	of	of	ADP
ejpam-5962	119	53	z	z	NOUN
ejpam-5962	119	54	∈	∈	PROPN
ejpam-5962	119	55	(	(	PUNCT
ejpam-5962	119	56	z	z	NOUN
ejpam-5962	119	57	,	,	PUNCT
ejpam-5962	119	58	ϑ1	ϑ1	NOUN
ejpam-5962	119	59	,	,	PUNCT
ejpam-5962	119	60	ϑ2	ϑ2	PROPN
ejpam-5962	119	61	)	)	PUNCT
ejpam-5962	119	62	and	and	CCONJ
ejpam-5962	119	63	retain	retain	VERB
ejpam-5962	119	64	a	a	DET
ejpam-5962	119	65	local	local	ADJ
ejpam-5962	119	66	foundation	foundation	NOUN
ejpam-5962	119	67	of	of	ADP
ejpam-5962	119	68	z	z	PROPN
ejpam-5962	119	69	∈	∈	PROPN
ejpam-5962	119	70	(	(	PUNCT
ejpam-5962	119	71	z	z	NOUN
ejpam-5962	119	72	,	,	PUNCT
ejpam-5962	119	73	ϑ1	ϑ1	NOUN
ejpam-5962	119	74	,	,	PUNCT
ejpam-5962	119	75	ϑ2	ϑ2	PROPN
ejpam-5962	119	76	)	)	PUNCT
ejpam-5962	119	77	.	.	PUNCT
ejpam-5962	120	1	subsequently	subsequently	ADV
ejpam-5962	120	2	(	(	PUNCT
ejpam-5962	120	3	z	z	NOUN
ejpam-5962	120	4	,	,	PUNCT
ejpam-5962	120	5	ϑ1	ϑ1	NOUN
ejpam-5962	120	6	,	,	PUNCT
ejpam-5962	120	7	ϑ2	ϑ2	PROPN
ejpam-5962	120	8	)	)	PUNCT
ejpam-5962	120	9	is	be	AUX
ejpam-5962	120	10	pairwise	pairwise	NOUN
ejpam-5962	120	11	regular	regular	ADJ
ejpam-5962	120	12	and	and	CCONJ
ejpam-5962	120	13	pairwise	pairwise	NOUN
ejpam-5962	120	14	t1−space	t1−space	NOUN
ejpam-5962	120	15	,	,	PUNCT
ejpam-5962	120	16	then	then	ADV
ejpam-5962	120	17	(	(	PUNCT
ejpam-5962	120	18	z	z	NOUN
ejpam-5962	120	19	,	,	PUNCT
ejpam-5962	120	20	ϑ1	ϑ1	NOUN
ejpam-5962	120	21	,	,	PUNCT
ejpam-5962	120	22	ϑ2	ϑ2	PROPN
ejpam-5962	120	23	)	)	PUNCT
ejpam-5962	120	24	is	be	AUX
ejpam-5962	120	25	pairwise	pairwise	PROPN
ejpam-5962	120	26	t3−space	t3−space	NOUN
ejpam-5962	120	27	,	,	PUNCT
ejpam-5962	120	28	which	which	PRON
ejpam-5962	120	29	is	be	AUX
ejpam-5962	120	30	t2−space	t2−space	NOUN
ejpam-5962	120	31	.	.	PUNCT
ejpam-5962	121	1	the	the	DET
ejpam-5962	121	2	continuous	continuous	ADJ
ejpam-5962	121	3	image	image	NOUN
ejpam-5962	121	4	of	of	ADP
ejpam-5962	121	5	a	a	DET
ejpam-5962	121	6	pairwise	pairwise	NOUN
ejpam-5962	121	7	compact	compact	ADJ
ejpam-5962	121	8	closed	close	VERB
ejpam-5962	121	9	space	space	NOUN
ejpam-5962	121	10	is	be	AUX
ejpam-5962	121	11	not	not	PART
ejpam-5962	121	12	necessarily	necessarily	ADV
ejpam-5962	121	13	pairwise	pairwise	NOUN
ejpam-5962	121	14	compact	compact	ADV
ejpam-5962	121	15	closed	close	VERB
ejpam-5962	121	16	,	,	PUNCT
ejpam-5962	121	17	as	as	SCONJ
ejpam-5962	121	18	illustrated	illustrate	VERB
ejpam-5962	121	19	in	in	ADP
ejpam-5962	121	20	the	the	DET
ejpam-5962	121	21	following	follow	VERB
ejpam-5962	121	22	example	example	NOUN
ejpam-5962	121	23	.	.	PUNCT
ejpam-5962	122	1	example	example	NOUN
ejpam-5962	122	2	3.3	3.3	NUM
ejpam-5962	122	3	.	.	PUNCT
ejpam-5962	123	1	suppose	suppose	VERB
ejpam-5962	123	2	φ	φ	PROPN
ejpam-5962	123	3	:	:	PUNCT
ejpam-5962	123	4	(	(	PUNCT
ejpam-5962	123	5	r,ϑu	r,ϑu	NUM
ejpam-5962	123	6	,	,	PUNCT
ejpam-5962	123	7	ϑu	ϑu	NOUN
ejpam-5962	123	8	)	)	PUNCT
ejpam-5962	123	9	→	→	SYM
ejpam-5962	123	10	(	(	PUNCT
ejpam-5962	123	11	r	r	NOUN
ejpam-5962	123	12	,	,	PUNCT
ejpam-5962	123	13	βind	βind	ADJ
ejpam-5962	123	14	,	,	PUNCT
ejpam-5962	123	15	βind	βind	NOUN
ejpam-5962	123	16	)	)	PUNCT
ejpam-5962	123	17	.	.	PUNCT
ejpam-5962	124	1	it	it	PRON
ejpam-5962	124	2	is	be	AUX
ejpam-5962	124	3	obvious	obvious	ADJ
ejpam-5962	124	4	that	that	SCONJ
ejpam-5962	124	5	(	(	PUNCT
ejpam-5962	124	6	r,ϑu	r,ϑu	NUM
ejpam-5962	124	7	,	,	PUNCT
ejpam-5962	124	8	ϑu	ϑu	NOUN
ejpam-5962	124	9	)	)	PUNCT
ejpam-5962	124	10	is	be	AUX
ejpam-5962	124	11	pairwise	pairwise	NOUN
ejpam-5962	124	12	compact	compact	ADJ
ejpam-5962	124	13	closed	close	VERB
ejpam-5962	124	14	space	space	NOUN
ejpam-5962	124	15	,	,	PUNCT
ejpam-5962	124	16	nevertheless	nevertheless	ADV
ejpam-5962	124	17	,	,	PUNCT
ejpam-5962	124	18	(	(	PUNCT
ejpam-5962	124	19	r	r	NOUN
ejpam-5962	124	20	,	,	PUNCT
ejpam-5962	124	21	βind	βind	ADJ
ejpam-5962	124	22	,	,	PUNCT
ejpam-5962	124	23	βind	βind	NOUN
ejpam-5962	124	24	)	)	PUNCT
ejpam-5962	124	25	is	be	AUX
ejpam-5962	124	26	not	not	PART
ejpam-5962	124	27	pairwise	pairwise	NOUN
ejpam-5962	124	28	compact	compact	ADJ
ejpam-5962	124	29	closed	close	VERB
ejpam-5962	124	30	space	space	NOUN
ejpam-5962	124	31	,	,	PUNCT
ejpam-5962	124	32	but	but	CCONJ
ejpam-5962	124	33	whatever	whatever	DET
ejpam-5962	124	34	βind−compact	βind−compact	NOUN
ejpam-5962	124	35	subset	subset	NOUN
ejpam-5962	124	36	is	be	AUX
ejpam-5962	124	37	not	not	PART
ejpam-5962	124	38	βind−closed	βind−close	VERB
ejpam-5962	124	39	.	.	PUNCT
ejpam-5962	125	1	theorem	theorem	VERB
ejpam-5962	125	2	3.1	3.1	NUM
ejpam-5962	125	3	.	.	PUNCT
ejpam-5962	126	1	let	let	VERB
ejpam-5962	126	2	φ	φ	PROPN
ejpam-5962	126	3	:	:	PUNCT
ejpam-5962	126	4	(	(	PUNCT
ejpam-5962	126	5	z	z	NOUN
ejpam-5962	126	6	,	,	PUNCT
ejpam-5962	126	7	ϑ1	ϑ1	NOUN
ejpam-5962	126	8	,	,	PUNCT
ejpam-5962	126	9	ϑ2	ϑ2	PROPN
ejpam-5962	126	10	)	)	PUNCT
ejpam-5962	126	11	−−−−−−−→	−−−−−−−→	NOUN
ejpam-5962	126	12	injection(n	injection(n	PROPN
ejpam-5962	126	13	,	,	PUNCT
ejpam-5962	126	14	β1	β1	PROPN
ejpam-5962	126	15	,	,	PUNCT
ejpam-5962	126	16	β2	β2	PROPN
ejpam-5962	126	17	)	)	PUNCT
ejpam-5962	126	18	be	be	VERB
ejpam-5962	126	19	a	a	DET
ejpam-5962	126	20	pairwise	pairwise	NOUN
ejpam-5962	126	21	continuous	continuous	ADJ
ejpam-5962	126	22	function	function	NOUN
ejpam-5962	126	23	.	.	PUNCT
ejpam-5962	127	1	if	if	SCONJ
ejpam-5962	127	2	(	(	PUNCT
ejpam-5962	127	3	n	n	X
ejpam-5962	127	4	,	,	PUNCT
ejpam-5962	127	5	β1	β1	PROPN
ejpam-5962	127	6	,	,	PUNCT
ejpam-5962	127	7	β2	β2	NOUN
ejpam-5962	127	8	)	)	PUNCT
ejpam-5962	127	9	is	be	AUX
ejpam-5962	127	10	a	a	DET
ejpam-5962	127	11	pairwise	pairwise	NOUN
ejpam-5962	127	12	compact	compact	ADJ
ejpam-5962	127	13	closed	close	VERB
ejpam-5962	127	14	space	space	NOUN
ejpam-5962	127	15	,	,	PUNCT
ejpam-5962	127	16	then	then	ADV
ejpam-5962	127	17	(	(	PUNCT
ejpam-5962	127	18	z	z	NOUN
ejpam-5962	127	19	,	,	PUNCT
ejpam-5962	127	20	ϑ1	ϑ1	NOUN
ejpam-5962	127	21	,	,	PUNCT
ejpam-5962	127	22	ϑ2	ϑ2	PROPN
ejpam-5962	127	23	)	)	PUNCT
ejpam-5962	127	24	inherits	inherit	VERB
ejpam-5962	127	25	the	the	DET
ejpam-5962	127	26	pairwise	pairwise	NOUN
ejpam-5962	127	27	compact	compact	ADJ
ejpam-5962	127	28	closed	close	VERB
ejpam-5962	127	29	property	property	NOUN
ejpam-5962	127	30	.	.	PUNCT
ejpam-5962	128	1	proof	proof	NOUN
ejpam-5962	128	2	.	.	PUNCT
ejpam-5962	129	1	make	make	VERB
ejpam-5962	129	2	u	u	PRON
ejpam-5962	129	3	any	any	DET
ejpam-5962	129	4	ϑ1−compact	ϑ1−compact	NOUN
ejpam-5962	129	5	subset	subset	NOUN
ejpam-5962	129	6	of	of	ADP
ejpam-5962	129	7	(	(	PUNCT
ejpam-5962	129	8	z	z	NOUN
ejpam-5962	129	9	,	,	PUNCT
ejpam-5962	129	10	ϑ1	ϑ1	NOUN
ejpam-5962	129	11	,	,	PUNCT
ejpam-5962	129	12	ϑ2	ϑ2	PROPN
ejpam-5962	129	13	)	)	PUNCT
ejpam-5962	129	14	,	,	PUNCT
ejpam-5962	129	15	then	then	ADV
ejpam-5962	129	16	φ(u	φ(u	NOUN
ejpam-5962	129	17	)	)	PUNCT
ejpam-5962	129	18	is	be	AUX
ejpam-5962	129	19	β1−compact	β1−compact	NOUN
ejpam-5962	129	20	subset	subset	VERB
ejpam-5962	129	21	in	in	ADP
ejpam-5962	129	22	(	(	PUNCT
ejpam-5962	129	23	n	n	CCONJ
ejpam-5962	129	24	,	,	PUNCT
ejpam-5962	129	25	β1	β1	NOUN
ejpam-5962	129	26	,	,	PUNCT
ejpam-5962	129	27	β2	β2	PROPN
ejpam-5962	129	28	)	)	PUNCT
ejpam-5962	129	29	.	.	PUNCT
ejpam-5962	130	1	due	due	ADP
ejpam-5962	130	2	to	to	ADP
ejpam-5962	130	3	the	the	DET
ejpam-5962	130	4	fact	fact	NOUN
ejpam-5962	130	5	that	that	SCONJ
ejpam-5962	130	6	(	(	PUNCT
ejpam-5962	130	7	n	n	X
ejpam-5962	130	8	,	,	PUNCT
ejpam-5962	130	9	β1	β1	PROPN
ejpam-5962	130	10	,	,	PUNCT
ejpam-5962	130	11	β2	β2	NOUN
ejpam-5962	130	12	)	)	PUNCT
ejpam-5962	130	13	is	be	AUX
ejpam-5962	130	14	pairwise	pairwise	NOUN
ejpam-5962	130	15	compact	compact	ADJ
ejpam-5962	130	16	closed	close	VERB
ejpam-5962	130	17	space	space	NOUN
ejpam-5962	130	18	,	,	PUNCT
ejpam-5962	130	19	φ(u	φ(u	NOUN
ejpam-5962	130	20	)	)	PUNCT
ejpam-5962	130	21	is	be	AUX
ejpam-5962	130	22	β2−closed	β2−close	VERB
ejpam-5962	130	23	subset	subset	NOUN
ejpam-5962	130	24	of	of	ADP
ejpam-5962	130	25	(	(	PUNCT
ejpam-5962	130	26	n	n	X
ejpam-5962	130	27	,	,	PUNCT
ejpam-5962	130	28	β1	β1	PROPN
ejpam-5962	130	29	,	,	PUNCT
ejpam-5962	130	30	β2	β2	NOUN
ejpam-5962	130	31	)	)	PUNCT
ejpam-5962	130	32	,	,	PUNCT
ejpam-5962	130	33	and	and	CCONJ
ejpam-5962	130	34	φ	φ	PROPN
ejpam-5962	130	35	is	be	AUX
ejpam-5962	130	36	injection	injection	NOUN
ejpam-5962	130	37	,	,	PUNCT
ejpam-5962	130	38	consequently	consequently	ADV
ejpam-5962	130	39	φ−1(φ(u	φ−1(φ(u	NOUN
ejpam-5962	130	40	)	)	PUNCT
ejpam-5962	130	41	)	)	PUNCT
ejpam-5962	131	1	=	=	SYM
ejpam-5962	131	2	u	u	NOUN
ejpam-5962	131	3	is	be	AUX
ejpam-5962	131	4	ϑ2−closed	ϑ2−close	VERB
ejpam-5962	131	5	subset	subset	NOUN
ejpam-5962	131	6	of	of	ADP
ejpam-5962	131	7	(	(	PUNCT
ejpam-5962	131	8	z	z	NOUN
ejpam-5962	131	9	,	,	PUNCT
ejpam-5962	131	10	ϑ1	ϑ1	NOUN
ejpam-5962	131	11	,	,	PUNCT
ejpam-5962	131	12	ϑ2	ϑ2	PROPN
ejpam-5962	131	13	)	)	PUNCT
ejpam-5962	131	14	.	.	PUNCT
ejpam-5962	132	1	comparably	comparably	ADV
ejpam-5962	132	2	,	,	PUNCT
ejpam-5962	132	3	for	for	ADP
ejpam-5962	132	4	v	v	NOUN
ejpam-5962	132	5	is	be	AUX
ejpam-5962	132	6	ϑ2−compact	ϑ2−compact	NOUN
ejpam-5962	132	7	subset	subset	VERB
ejpam-5962	132	8	of	of	ADP
ejpam-5962	132	9	(	(	PUNCT
ejpam-5962	132	10	z	z	NOUN
ejpam-5962	132	11	,	,	PUNCT
ejpam-5962	132	12	ϑ1	ϑ1	NOUN
ejpam-5962	132	13	,	,	PUNCT
ejpam-5962	132	14	ϑ2	ϑ2	PROPN
ejpam-5962	132	15	)	)	PUNCT
ejpam-5962	132	16	.	.	PUNCT
ejpam-5962	133	1	it	it	PRON
ejpam-5962	133	2	follows	follow	VERB
ejpam-5962	133	3	that	that	SCONJ
ejpam-5962	133	4	,	,	PUNCT
ejpam-5962	133	5	(	(	PUNCT
ejpam-5962	133	6	z	z	NOUN
ejpam-5962	133	7	,	,	PUNCT
ejpam-5962	133	8	ϑ1	ϑ1	NOUN
ejpam-5962	133	9	,	,	PUNCT
ejpam-5962	133	10	ϑ2	ϑ2	PROPN
ejpam-5962	133	11	)	)	PUNCT
ejpam-5962	133	12	is	be	AUX
ejpam-5962	133	13	pairwise	pairwise	NOUN
ejpam-5962	133	14	compact	compact	ADJ
ejpam-5962	133	15	closed	close	VERB
ejpam-5962	133	16	space	space	NOUN
ejpam-5962	133	17	.	.	PUNCT
ejpam-5962	134	1	theorem	theorem	ADJ
ejpam-5962	134	2	3.2	3.2	NUM
ejpam-5962	134	3	.	.	PUNCT
ejpam-5962	135	1	the	the	DET
ejpam-5962	135	2	property	property	NOUN
ejpam-5962	135	3	of	of	ADP
ejpam-5962	135	4	being	be	AUX
ejpam-5962	135	5	a	a	DET
ejpam-5962	135	6	pairwise	pairwise	NOUN
ejpam-5962	135	7	compact	compact	ADJ
ejpam-5962	135	8	closed	close	VERB
ejpam-5962	135	9	space	space	NOUN
ejpam-5962	135	10	is	be	AUX
ejpam-5962	135	11	a	a	DET
ejpam-5962	135	12	bitopological	bitopological	ADJ
ejpam-5962	135	13	invariant	invariant	NOUN
ejpam-5962	135	14	;	;	PUNCT
ejpam-5962	135	15	that	that	ADV
ejpam-5962	135	16	is	is	ADV
ejpam-5962	135	17	,	,	PUNCT
ejpam-5962	135	18	it	it	PRON
ejpam-5962	135	19	is	be	AUX
ejpam-5962	135	20	preserved	preserve	VERB
ejpam-5962	135	21	under	under	ADP
ejpam-5962	135	22	pairwise	pairwise	NOUN
ejpam-5962	135	23	homeomorphisms	homeomorphism	NOUN
ejpam-5962	135	24	.	.	PUNCT
ejpam-5962	136	1	proof	proof	NOUN
ejpam-5962	136	2	.	.	PUNCT
ejpam-5962	137	1	assuming	assume	VERB
ejpam-5962	137	2	that	that	SCONJ
ejpam-5962	137	3	(	(	PUNCT
ejpam-5962	137	4	z	z	NOUN
ejpam-5962	137	5	,	,	PUNCT
ejpam-5962	137	6	ϑ1	ϑ1	NOUN
ejpam-5962	137	7	,	,	PUNCT
ejpam-5962	137	8	ϑ2	ϑ2	PROPN
ejpam-5962	137	9	)	)	PUNCT
ejpam-5962	137	10	is	be	AUX
ejpam-5962	137	11	a	a	DET
ejpam-5962	137	12	pairwise	pairwise	NOUN
ejpam-5962	137	13	compact	compact	ADJ
ejpam-5962	137	14	closed	close	VERB
ejpam-5962	137	15	space	space	NOUN
ejpam-5962	137	16	and	and	CCONJ
ejpam-5962	137	17	φ	φ	NOUN
ejpam-5962	137	18	:	:	PUNCT
ejpam-5962	137	19	(	(	PUNCT
ejpam-5962	137	20	z	z	NOUN
ejpam-5962	137	21	,	,	PUNCT
ejpam-5962	137	22	ϑ1	ϑ1	NOUN
ejpam-5962	137	23	,	,	PUNCT
ejpam-5962	137	24	ϑ2	ϑ2	PROPN
ejpam-5962	137	25	)	)	PUNCT
ejpam-5962	137	26	→	→	SYM
ejpam-5962	137	27	(	(	PUNCT
ejpam-5962	137	28	n	n	CCONJ
ejpam-5962	137	29	,	,	PUNCT
ejpam-5962	137	30	β1	β1	PROPN
ejpam-5962	137	31	,	,	PUNCT
ejpam-5962	137	32	β2	β2	PROPN
ejpam-5962	137	33	)	)	PUNCT
ejpam-5962	137	34	be	be	VERB
ejpam-5962	137	35	a	a	DET
ejpam-5962	137	36	pairwise	pairwise	NOUN
ejpam-5962	137	37	homeomorphism	homeomorphism	NOUN
ejpam-5962	137	38	and	and	CCONJ
ejpam-5962	137	39	u	u	NOUN
ejpam-5962	137	40	be	be	VERB
ejpam-5962	137	41	any	any	DET
ejpam-5962	137	42	β1−compact	β1−compact	NOUN
ejpam-5962	137	43	subset	subset	NOUN
ejpam-5962	137	44	of	of	ADP
ejpam-5962	137	45	(	(	PUNCT
ejpam-5962	137	46	n	n	X
ejpam-5962	137	47	,	,	PUNCT
ejpam-5962	137	48	β1	β1	PROPN
ejpam-5962	137	49	,	,	PUNCT
ejpam-5962	137	50	β2	β2	PROPN
ejpam-5962	137	51	)	)	PUNCT
ejpam-5962	137	52	,	,	PUNCT
ejpam-5962	137	53	then	then	ADV
ejpam-5962	137	54	φ−1(u	φ−1(u	PROPN
ejpam-5962	137	55	)	)	PUNCT
ejpam-5962	137	56	is	be	AUX
ejpam-5962	137	57	ϑ1−compact	ϑ1−compact	NOUN
ejpam-5962	137	58	in	in	ADP
ejpam-5962	137	59	(	(	PUNCT
ejpam-5962	137	60	z	z	NOUN
ejpam-5962	137	61	,	,	PUNCT
ejpam-5962	137	62	ϑ1	ϑ1	NOUN
ejpam-5962	137	63	,	,	PUNCT
ejpam-5962	137	64	ϑ2	ϑ2	PROPN
ejpam-5962	137	65	)	)	PUNCT
ejpam-5962	137	66	,	,	PUNCT
ejpam-5962	137	67	but	but	CCONJ
ejpam-5962	137	68	(	(	PUNCT
ejpam-5962	137	69	z	z	NOUN
ejpam-5962	137	70	,	,	PUNCT
ejpam-5962	137	71	ϑ1	ϑ1	NOUN
ejpam-5962	137	72	,	,	PUNCT
ejpam-5962	137	73	ϑ2	ϑ2	PROPN
ejpam-5962	137	74	)	)	PUNCT
ejpam-5962	137	75	is	be	AUX
ejpam-5962	137	76	pairwise	pairwise	NOUN
ejpam-5962	137	77	compact	compact	ADJ
ejpam-5962	137	78	closed	close	VERB
ejpam-5962	137	79	space	space	NOUN
ejpam-5962	137	80	,	,	PUNCT
ejpam-5962	137	81	so	so	ADV
ejpam-5962	137	82	φ−1(u	φ−1(u	PROPN
ejpam-5962	137	83	)	)	PUNCT
ejpam-5962	137	84	is	be	AUX
ejpam-5962	137	85	ϑ2−closed	ϑ2−close	VERB
ejpam-5962	137	86	in	in	ADP
ejpam-5962	137	87	(	(	PUNCT
ejpam-5962	137	88	z	z	NOUN
ejpam-5962	137	89	,	,	PUNCT
ejpam-5962	137	90	ϑ1	ϑ1	NOUN
ejpam-5962	137	91	,	,	PUNCT
ejpam-5962	137	92	ϑ2	ϑ2	PROPN
ejpam-5962	137	93	)	)	PUNCT
ejpam-5962	137	94	,	,	PUNCT
ejpam-5962	137	95	then	then	ADV
ejpam-5962	137	96	φ−1(φ(u	φ−1(φ(u	NOUN
ejpam-5962	137	97	)	)	PUNCT
ejpam-5962	137	98	)	)	PUNCT
ejpam-5962	138	1	=	=	SYM
ejpam-5962	138	2	u	u	NOUN
ejpam-5962	138	3	is	be	AUX
ejpam-5962	138	4	β2−closed	β2−close	VERB
ejpam-5962	138	5	in	in	ADP
ejpam-5962	138	6	(	(	PUNCT
ejpam-5962	138	7	n	n	CCONJ
ejpam-5962	138	8	,	,	PUNCT
ejpam-5962	138	9	β1	β1	NOUN
ejpam-5962	138	10	,	,	PUNCT
ejpam-5962	138	11	β2	β2	PROPN
ejpam-5962	138	12	)	)	PUNCT
ejpam-5962	138	13	.	.	PUNCT
ejpam-5962	139	1	the	the	DET
ejpam-5962	139	2	β2−compact	β2−compact	PROPN
ejpam-5962	139	3	subset	subset	NOUN
ejpam-5962	139	4	of	of	ADP
ejpam-5962	139	5	(	(	PUNCT
ejpam-5962	139	6	n	n	X
ejpam-5962	139	7	,	,	PUNCT
ejpam-5962	139	8	β1	β1	PROPN
ejpam-5962	139	9	,	,	PUNCT
ejpam-5962	139	10	β2	β2	NOUN
ejpam-5962	139	11	)	)	PUNCT
ejpam-5962	139	12	is	be	AUX
ejpam-5962	139	13	analogous	analogous	ADJ
ejpam-5962	139	14	for	for	ADP
ejpam-5962	139	15	v	v	NOUN
ejpam-5962	139	16	.	.	PUNCT
ejpam-5962	140	1	thus	thus	ADV
ejpam-5962	140	2	,	,	PUNCT
ejpam-5962	140	3	pairwise	pairwise	NOUN
ejpam-5962	140	4	compact	compact	ADJ
ejpam-5962	140	5	closed	close	VERB
ejpam-5962	140	6	space	space	NOUN
ejpam-5962	140	7	(	(	PUNCT
ejpam-5962	140	8	n	n	X
ejpam-5962	140	9	,	,	PUNCT
ejpam-5962	140	10	β1	β1	PROPN
ejpam-5962	140	11	,	,	PUNCT
ejpam-5962	140	12	β2	β2	NOUN
ejpam-5962	140	13	)	)	PUNCT
ejpam-5962	140	14	is	be	AUX
ejpam-5962	140	15	defined	define	VERB
ejpam-5962	140	16	.	.	PUNCT
ejpam-5962	141	1	theorem	theorem	VERB
ejpam-5962	141	2	3.3	3.3	NUM
ejpam-5962	141	3	.	.	PUNCT
ejpam-5962	142	1	being	be	AUX
ejpam-5962	142	2	pairwise	pairwise	NOUN
ejpam-5962	142	3	compact	compact	ADJ
ejpam-5962	142	4	in	in	ADP
ejpam-5962	142	5	a	a	DET
ejpam-5962	142	6	closed	closed	ADJ
ejpam-5962	142	7	space	space	NOUN
ejpam-5962	142	8	is	be	AUX
ejpam-5962	142	9	a	a	DET
ejpam-5962	142	10	heritable	heritable	ADJ
ejpam-5962	142	11	trait	trait	NOUN
ejpam-5962	142	12	.	.	PUNCT
ejpam-5962	143	1	a.	a.	NOUN
ejpam-5962	143	2	a.	a.	PROPN
ejpam-5962	143	3	atoom	atoom	PROPN
ejpam-5962	143	4	et	et	PROPN
ejpam-5962	143	5	al	al	PROPN
ejpam-5962	143	6	.	.	PUNCT
ejpam-5962	143	7	/	/	SYM
ejpam-5962	143	8	eur	eur	PROPN
ejpam-5962	143	9	.	.	PUNCT
ejpam-5962	144	1	j.	j.	PROPN
ejpam-5962	144	2	pure	pure	PROPN
ejpam-5962	144	3	appl	appl	PROPN
ejpam-5962	144	4	.	.	PROPN
ejpam-5962	144	5	math	math	PROPN
ejpam-5962	144	6	,	,	PUNCT
ejpam-5962	144	7	18	18	NUM
ejpam-5962	144	8	(	(	PUNCT
ejpam-5962	144	9	2	2	NUM
ejpam-5962	144	10	)	)	PUNCT
ejpam-5962	144	11	(	(	PUNCT
ejpam-5962	144	12	2025	2025	NUM
ejpam-5962	144	13	)	)	PUNCT
ejpam-5962	144	14	,	,	PUNCT
ejpam-5962	144	15	5962	5962	NUM
ejpam-5962	144	16	6	6	NUM
ejpam-5962	144	17	of	of	ADP
ejpam-5962	144	18	17	17	NUM
ejpam-5962	144	19	proof	proof	NOUN
ejpam-5962	144	20	.	.	PUNCT
ejpam-5962	145	1	assume	assume	VERB
ejpam-5962	145	2	that	that	SCONJ
ejpam-5962	145	3	(	(	PUNCT
ejpam-5962	145	4	z	z	X
ejpam-5962	145	5	,	,	PUNCT
ejpam-5962	145	6	ϑ1z	ϑ1z	VERB
ejpam-5962	145	7	,	,	PUNCT
ejpam-5962	145	8	ϑ2z	ϑ2z	NOUN
ejpam-5962	145	9	)	)	PUNCT
ejpam-5962	145	10	is	be	AUX
ejpam-5962	145	11	pairwise	pairwise	NOUN
ejpam-5962	145	12	compact	compact	ADJ
ejpam-5962	145	13	closed	close	VERB
ejpam-5962	145	14	space	space	NOUN
ejpam-5962	145	15	and	and	CCONJ
ejpam-5962	145	16	(	(	PUNCT
ejpam-5962	145	17	n,ϑ1n	n,ϑ1n	X
ejpam-5962	145	18	,	,	PUNCT
ejpam-5962	145	19	ϑ2n	ϑ2n	PROPN
ejpam-5962	145	20	)	)	PUNCT
ejpam-5962	145	21	is	be	AUX
ejpam-5962	145	22	subspace	subspace	NOUN
ejpam-5962	145	23	of	of	ADP
ejpam-5962	145	24	(	(	PUNCT
ejpam-5962	145	25	z	z	PROPN
ejpam-5962	145	26	,	,	PUNCT
ejpam-5962	145	27	ϑ1z	ϑ1z	VERB
ejpam-5962	145	28	,	,	PUNCT
ejpam-5962	145	29	ϑ2z	ϑ2z	NOUN
ejpam-5962	145	30	)	)	PUNCT
ejpam-5962	145	31	.	.	PUNCT
ejpam-5962	146	1	let	let	VERB
ejpam-5962	146	2	’s	’s	PRON
ejpam-5962	146	3	assume	assume	VERB
ejpam-5962	146	4	that	that	SCONJ
ejpam-5962	146	5	u	u	PROPN
ejpam-5962	146	6	is	be	AUX
ejpam-5962	146	7	ϑ1n−compact	ϑ1n−compact	ADV
ejpam-5962	146	8	subset	subset	VERB
ejpam-5962	146	9	in	in	ADP
ejpam-5962	146	10	(	(	PUNCT
ejpam-5962	146	11	n,ϑ1n	n,ϑ1n	NOUN
ejpam-5962	146	12	,	,	PUNCT
ejpam-5962	146	13	ϑ2n).due	ϑ2n).due	NUM
ejpam-5962	146	14	to	to	ADP
ejpam-5962	146	15	the	the	DET
ejpam-5962	146	16	fact	fact	NOUN
ejpam-5962	146	17	that	that	SCONJ
ejpam-5962	146	18	(	(	PUNCT
ejpam-5962	146	19	n,ϑ1n	n,ϑ1n	X
ejpam-5962	146	20	,	,	PUNCT
ejpam-5962	146	21	ϑ2n	ϑ2n	PROPN
ejpam-5962	146	22	)	)	PUNCT
ejpam-5962	146	23	⊆	⊆	NUM
ejpam-5962	146	24	(	(	PUNCT
ejpam-5962	146	25	z	z	NOUN
ejpam-5962	146	26	,	,	PUNCT
ejpam-5962	146	27	ϑ1z	ϑ1z	VERB
ejpam-5962	146	28	,	,	PUNCT
ejpam-5962	146	29	ϑ2z	ϑ2z	NOUN
ejpam-5962	146	30	)	)	PUNCT
ejpam-5962	146	31	,	,	PUNCT
ejpam-5962	146	32	u	u	NOUN
ejpam-5962	146	33	is	be	AUX
ejpam-5962	146	34	ϑ1z−compact	ϑ1z−compact	PRON
ejpam-5962	146	35	subset	subset	VERB
ejpam-5962	146	36	in	in	ADP
ejpam-5962	146	37	(	(	PUNCT
ejpam-5962	146	38	z	z	PROPN
ejpam-5962	146	39	,	,	PUNCT
ejpam-5962	146	40	ϑ1z	ϑ1z	VERB
ejpam-5962	146	41	,	,	PUNCT
ejpam-5962	146	42	ϑ2z	ϑ2z	NOUN
ejpam-5962	146	43	)	)	PUNCT
ejpam-5962	146	44	,	,	PUNCT
ejpam-5962	146	45	but	but	CCONJ
ejpam-5962	146	46	(	(	PUNCT
ejpam-5962	146	47	z	z	X
ejpam-5962	146	48	,	,	PUNCT
ejpam-5962	146	49	ϑ1z	ϑ1z	VERB
ejpam-5962	146	50	,	,	PUNCT
ejpam-5962	146	51	ϑ2z	ϑ2z	NOUN
ejpam-5962	146	52	)	)	PUNCT
ejpam-5962	146	53	is	be	AUX
ejpam-5962	146	54	pairwise	pairwise	NOUN
ejpam-5962	146	55	compact	compact	ADJ
ejpam-5962	146	56	closed	close	VERB
ejpam-5962	146	57	space	space	NOUN
ejpam-5962	146	58	,	,	PUNCT
ejpam-5962	146	59	so	so	CCONJ
ejpam-5962	146	60	u	u	NOUN
ejpam-5962	146	61	is	be	AUX
ejpam-5962	146	62	ϑ1z−closed	ϑ1z−close	VERB
ejpam-5962	146	63	subset	subset	VERB
ejpam-5962	146	64	in	in	ADP
ejpam-5962	146	65	(	(	PUNCT
ejpam-5962	146	66	z	z	PROPN
ejpam-5962	146	67	,	,	PUNCT
ejpam-5962	146	68	ϑ1z	ϑ1z	VERB
ejpam-5962	146	69	,	,	PUNCT
ejpam-5962	146	70	ϑ2z	ϑ2z	NOUN
ejpam-5962	146	71	)	)	PUNCT
ejpam-5962	146	72	,	,	PUNCT
ejpam-5962	146	73	thus	thus	ADV
ejpam-5962	146	74	u	u	NOUN
ejpam-5962	146	75	is	be	AUX
ejpam-5962	146	76	ϑ1n−closed	ϑ1n−close	VERB
ejpam-5962	146	77	subset	subset	VERB
ejpam-5962	146	78	in	in	ADP
ejpam-5962	146	79	(	(	PUNCT
ejpam-5962	146	80	n,ϑ1n	n,ϑ1n	INTJ
ejpam-5962	146	81	,	,	PUNCT
ejpam-5962	146	82	ϑ2n	ϑ2n	PROPN
ejpam-5962	146	83	)	)	PUNCT
ejpam-5962	146	84	,	,	PUNCT
ejpam-5962	146	85	because	because	SCONJ
ejpam-5962	146	86	u	u	NOUN
ejpam-5962	146	87	∩	∩	NOUN
ejpam-5962	146	88	n	n	NOUN
ejpam-5962	146	89	=	=	PUNCT
ejpam-5962	146	90	u.	u.	NOUN
ejpam-5962	146	91	equivalently	equivalently	ADV
ejpam-5962	146	92	for	for	ADP
ejpam-5962	146	93	v	v	PROPN
ejpam-5962	146	94	is	be	AUX
ejpam-5962	146	95	ϑ2n−compact	ϑ2n−compact	NOUN
ejpam-5962	146	96	subset	subset	VERB
ejpam-5962	146	97	in	in	ADP
ejpam-5962	146	98	(	(	PUNCT
ejpam-5962	146	99	n,ϑ1n	n,ϑ1n	INTJ
ejpam-5962	146	100	,	,	PUNCT
ejpam-5962	146	101	ϑ2n	ϑ2n	PROPN
ejpam-5962	146	102	)	)	PUNCT
ejpam-5962	146	103	.	.	PUNCT
ejpam-5962	147	1	as	as	ADP
ejpam-5962	147	2	a	a	DET
ejpam-5962	147	3	result	result	NOUN
ejpam-5962	147	4	(	(	PUNCT
ejpam-5962	147	5	n,ϑ1n	n,ϑ1n	X
ejpam-5962	147	6	,	,	PUNCT
ejpam-5962	147	7	ϑ2n	ϑ2n	PROPN
ejpam-5962	147	8	)	)	PUNCT
ejpam-5962	147	9	is	be	AUX
ejpam-5962	147	10	pairwise	pairwise	NOUN
ejpam-5962	147	11	compact	compact	ADJ
ejpam-5962	147	12	closed	close	VERB
ejpam-5962	147	13	space	space	NOUN
ejpam-5962	147	14	.	.	PUNCT
ejpam-5962	148	1	theorem	theorem	VERB
ejpam-5962	148	2	3.4	3.4	NUM
ejpam-5962	148	3	.	.	PUNCT
ejpam-5962	149	1	whenever	whenever	SCONJ
ejpam-5962	149	2	(	(	PUNCT
ejpam-5962	149	3	z	z	NOUN
ejpam-5962	149	4	,	,	PUNCT
ejpam-5962	149	5	ϑ1	ϑ1	NOUN
ejpam-5962	149	6	,	,	PUNCT
ejpam-5962	149	7	ϑ2	ϑ2	PROPN
ejpam-5962	149	8	)	)	PUNCT
ejpam-5962	149	9	be	be	VERB
ejpam-5962	149	10	pairwise	pairwise	NOUN
ejpam-5962	149	11	compact	compact	ADJ
ejpam-5962	149	12	compact	compact	ADJ
ejpam-5962	149	13	closed	close	VERB
ejpam-5962	149	14	space	space	NOUN
ejpam-5962	149	15	and	and	CCONJ
ejpam-5962	149	16	(	(	PUNCT
ejpam-5962	149	17	n,ϑ1	n,ϑ1	PROPN
ejpam-5962	149	18	,	,	PUNCT
ejpam-5962	149	19	ϑ2	ϑ2	PROPN
ejpam-5962	149	20	)	)	PUNCT
ejpam-5962	150	1	⊂	⊂	PROPN
ejpam-5962	150	2	(	(	PUNCT
ejpam-5962	150	3	z	z	NOUN
ejpam-5962	150	4	,	,	PUNCT
ejpam-5962	150	5	ϑ1	ϑ1	NOUN
ejpam-5962	150	6	,	,	PUNCT
ejpam-5962	150	7	ϑ2	ϑ2	PROPN
ejpam-5962	150	8	)	)	PUNCT
ejpam-5962	150	9	,	,	PUNCT
ejpam-5962	150	10	then	then	ADV
ejpam-5962	150	11	(	(	PUNCT
ejpam-5962	150	12	n,ϑ1	n,ϑ1	NOUN
ejpam-5962	150	13	,	,	PUNCT
ejpam-5962	150	14	ϑ2	ϑ2	PROPN
ejpam-5962	150	15	)	)	PUNCT
ejpam-5962	150	16	is	be	AUX
ejpam-5962	150	17	pairwise	pairwise	NOUN
ejpam-5962	150	18	compact	compact	ADJ
ejpam-5962	150	19	when	when	SCONJ
ejpam-5962	150	20	and	and	CCONJ
ejpam-5962	150	21	only	only	ADV
ejpam-5962	150	22	when	when	SCONJ
ejpam-5962	150	23	(	(	PUNCT
ejpam-5962	150	24	n,ϑ1	n,ϑ1	NOUN
ejpam-5962	150	25	,	,	PUNCT
ejpam-5962	150	26	ϑ2	ϑ2	PROPN
ejpam-5962	150	27	)	)	PUNCT
ejpam-5962	150	28	is	be	AUX
ejpam-5962	150	29	pairwise	pairwise	NOUN
ejpam-5962	150	30	closed	close	VERB
ejpam-5962	150	31	in	in	ADP
ejpam-5962	150	32	(	(	PUNCT
ejpam-5962	150	33	z	z	NOUN
ejpam-5962	150	34	,	,	PUNCT
ejpam-5962	150	35	ϑ1	ϑ1	NOUN
ejpam-5962	150	36	,	,	PUNCT
ejpam-5962	150	37	ϑ2	ϑ2	PROPN
ejpam-5962	150	38	)	)	PUNCT
ejpam-5962	150	39	.	.	PUNCT
ejpam-5962	151	1	proof	proof	NOUN
ejpam-5962	151	2	.	.	PUNCT
ejpam-5962	152	1	consider	consider	VERB
ejpam-5962	152	2	the	the	DET
ejpam-5962	152	3	idea	idea	NOUN
ejpam-5962	152	4	that	that	SCONJ
ejpam-5962	152	5	(	(	PUNCT
ejpam-5962	152	6	n,ϑ1	n,ϑ1	NOUN
ejpam-5962	152	7	,	,	PUNCT
ejpam-5962	152	8	ϑ2	ϑ2	PROPN
ejpam-5962	152	9	)	)	PUNCT
ejpam-5962	152	10	is	be	AUX
ejpam-5962	152	11	pairwise	pairwise	NOUN
ejpam-5962	152	12	compact	compact	ADJ
ejpam-5962	152	13	.	.	PUNCT
ejpam-5962	153	1	the	the	DET
ejpam-5962	153	2	pairwise	pairwise	NOUN
ejpam-5962	153	3	closed	close	VERB
ejpam-5962	153	4	space	space	NOUN
ejpam-5962	153	5	(	(	PUNCT
ejpam-5962	153	6	n,ϑ1	n,ϑ1	NOUN
ejpam-5962	153	7	,	,	PUNCT
ejpam-5962	153	8	ϑ2	ϑ2	PROPN
ejpam-5962	153	9	)	)	PUNCT
ejpam-5962	153	10	follows	follow	VERB
ejpam-5962	153	11	from	from	ADP
ejpam-5962	153	12	the	the	DET
ejpam-5962	153	13	fact	fact	NOUN
ejpam-5962	153	14	that	that	SCONJ
ejpam-5962	153	15	(	(	PUNCT
ejpam-5962	153	16	z	z	X
ejpam-5962	153	17	,	,	PUNCT
ejpam-5962	153	18	ϑ1	ϑ1	NOUN
ejpam-5962	153	19	,	,	PUNCT
ejpam-5962	153	20	ϑ2	ϑ2	PROPN
ejpam-5962	153	21	)	)	PUNCT
ejpam-5962	153	22	is	be	AUX
ejpam-5962	153	23	a	a	DET
ejpam-5962	153	24	pairwise	pairwise	NOUN
ejpam-5962	153	25	compact	compact	ADJ
ejpam-5962	153	26	closed	close	VERB
ejpam-5962	153	27	space	space	NOUN
ejpam-5962	153	28	.	.	PUNCT
ejpam-5962	154	1	in	in	ADP
ejpam-5962	154	2	the	the	DET
ejpam-5962	154	3	opposite	opposite	ADJ
ejpam-5962	154	4	scenario	scenario	NOUN
ejpam-5962	154	5	,	,	PUNCT
ejpam-5962	154	6	if	if	SCONJ
ejpam-5962	154	7	(	(	PUNCT
ejpam-5962	154	8	n,ϑ1	n,ϑ1	NOUN
ejpam-5962	154	9	,	,	PUNCT
ejpam-5962	154	10	ϑ2	ϑ2	PROPN
ejpam-5962	154	11	)	)	PUNCT
ejpam-5962	154	12	is	be	AUX
ejpam-5962	154	13	pairwise	pairwise	NOUN
ejpam-5962	154	14	closed	close	VERB
ejpam-5962	154	15	in	in	ADP
ejpam-5962	154	16	(	(	PUNCT
ejpam-5962	154	17	z	z	NOUN
ejpam-5962	154	18	,	,	PUNCT
ejpam-5962	154	19	ϑ1	ϑ1	NOUN
ejpam-5962	154	20	,	,	PUNCT
ejpam-5962	154	21	ϑ2	ϑ2	PROPN
ejpam-5962	154	22	)	)	PUNCT
ejpam-5962	154	23	,	,	PUNCT
ejpam-5962	154	24	then	then	ADV
ejpam-5962	154	25	(	(	PUNCT
ejpam-5962	154	26	n,ϑ1	n,ϑ1	NOUN
ejpam-5962	154	27	,	,	PUNCT
ejpam-5962	154	28	ϑ2	ϑ2	PROPN
ejpam-5962	154	29	)	)	PUNCT
ejpam-5962	154	30	is	be	AUX
ejpam-5962	154	31	pairwise	pairwise	NOUN
ejpam-5962	154	32	compact	compact	ADJ
ejpam-5962	154	33	since	since	SCONJ
ejpam-5962	154	34	(	(	PUNCT
ejpam-5962	154	35	z	z	NOUN
ejpam-5962	154	36	,	,	PUNCT
ejpam-5962	154	37	ϑ1	ϑ1	NOUN
ejpam-5962	154	38	,	,	PUNCT
ejpam-5962	154	39	ϑ2	ϑ2	PROPN
ejpam-5962	154	40	)	)	PUNCT
ejpam-5962	154	41	is	be	AUX
ejpam-5962	154	42	pairwise	pairwise	NOUN
ejpam-5962	154	43	compact	compact	ADJ
ejpam-5962	154	44	.	.	PUNCT
ejpam-5962	155	1	4	4	X
ejpam-5962	155	2	.	.	X
ejpam-5962	155	3	further	further	ADJ
ejpam-5962	155	4	properties	property	NOUN
ejpam-5962	155	5	of	of	ADP
ejpam-5962	155	6	pairwise	pairwise	NOUN
ejpam-5962	155	7	compact	compact	ADJ
ejpam-5962	155	8	closed	close	VERB
ejpam-5962	155	9	spaces	space	NOUN
ejpam-5962	155	10	in	in	ADP
ejpam-5962	155	11	this	this	DET
ejpam-5962	155	12	section	section	NOUN
ejpam-5962	155	13	,	,	PUNCT
ejpam-5962	155	14	we	we	PRON
ejpam-5962	155	15	provide	provide	VERB
ejpam-5962	155	16	new	new	ADJ
ejpam-5962	155	17	definitions	definition	NOUN
ejpam-5962	155	18	as	as	ADV
ejpam-5962	155	19	well	well	ADV
ejpam-5962	155	20	as	as	ADP
ejpam-5962	155	21	additional	additional	ADJ
ejpam-5962	155	22	pairwise	pairwise	NOUN
ejpam-5962	155	23	compact	compact	ADJ
ejpam-5962	155	24	closed	close	VERB
ejpam-5962	155	25	space	space	NOUN
ejpam-5962	155	26	qualities	quality	NOUN
ejpam-5962	155	27	.	.	PUNCT
ejpam-5962	156	1	definition	definition	NOUN
ejpam-5962	156	2	4.1	4.1	NUM
ejpam-5962	156	3	.	.	PUNCT
ejpam-5962	157	1	a	a	DET
ejpam-5962	157	2	function	function	NOUN
ejpam-5962	157	3	φ	φ	NOUN
ejpam-5962	157	4	:	:	PUNCT
ejpam-5962	157	5	(	(	PUNCT
ejpam-5962	157	6	z	z	NOUN
ejpam-5962	157	7	,	,	PUNCT
ejpam-5962	157	8	ϑ1	ϑ1	NOUN
ejpam-5962	157	9	,	,	PUNCT
ejpam-5962	157	10	ϑ2	ϑ2	PROPN
ejpam-5962	157	11	)	)	PUNCT
ejpam-5962	157	12	→	→	SYM
ejpam-5962	157	13	(	(	PUNCT
ejpam-5962	157	14	n	n	CCONJ
ejpam-5962	157	15	,	,	PUNCT
ejpam-5962	157	16	β1	β1	PROPN
ejpam-5962	157	17	,	,	PUNCT
ejpam-5962	157	18	β2	β2	NOUN
ejpam-5962	157	19	)	)	PUNCT
ejpam-5962	157	20	is	be	AUX
ejpam-5962	157	21	called	call	VERB
ejpam-5962	157	22	a	a	DET
ejpam-5962	157	23	pairwise	pairwise	NOUN
ejpam-5962	157	24	compactpreserving	compactpreserving	NOUN
ejpam-5962	157	25	function	function	NOUN
ejpam-5962	157	26	if	if	SCONJ
ejpam-5962	157	27	the	the	DET
ejpam-5962	157	28	inverse	inverse	ADJ
ejpam-5962	157	29	image	image	NOUN
ejpam-5962	157	30	of	of	ADP
ejpam-5962	157	31	every	every	DET
ejpam-5962	157	32	pairwise	pairwise	NOUN
ejpam-5962	157	33	compact	compact	ADJ
ejpam-5962	157	34	subset	subset	NOUN
ejpam-5962	157	35	of	of	ADP
ejpam-5962	157	36	(	(	PUNCT
ejpam-5962	157	37	n	n	X
ejpam-5962	157	38	,	,	PUNCT
ejpam-5962	157	39	β1	β1	PROPN
ejpam-5962	157	40	,	,	PUNCT
ejpam-5962	157	41	β2	β2	NOUN
ejpam-5962	157	42	)	)	PUNCT
ejpam-5962	157	43	is	be	AUX
ejpam-5962	157	44	pairwise	pairwise	NOUN
ejpam-5962	157	45	compact	compact	ADJ
ejpam-5962	157	46	in	in	ADP
ejpam-5962	157	47	(	(	PUNCT
ejpam-5962	157	48	z	z	NOUN
ejpam-5962	157	49	,	,	PUNCT
ejpam-5962	157	50	ϑ1	ϑ1	NOUN
ejpam-5962	157	51	,	,	PUNCT
ejpam-5962	157	52	ϑ2	ϑ2	PROPN
ejpam-5962	157	53	)	)	PUNCT
ejpam-5962	157	54	.	.	PUNCT
ejpam-5962	158	1	definition	definition	NOUN
ejpam-5962	158	2	4.2	4.2	NUM
ejpam-5962	158	3	.	.	PUNCT
ejpam-5962	159	1	a	a	DET
ejpam-5962	159	2	bitopological	bitopological	ADJ
ejpam-5962	159	3	compact	compact	ADJ
ejpam-5962	159	4	space	space	NOUN
ejpam-5962	159	5	(	(	PUNCT
ejpam-5962	159	6	z	z	NOUN
ejpam-5962	159	7	,	,	PUNCT
ejpam-5962	159	8	ϑ1	ϑ1	NOUN
ejpam-5962	159	9	,	,	PUNCT
ejpam-5962	159	10	ϑ2	ϑ2	PROPN
ejpam-5962	159	11	)	)	PUNCT
ejpam-5962	159	12	is	be	AUX
ejpam-5962	159	13	allegedly	allegedly	ADV
ejpam-5962	159	14	pairwise	pairwise	VERB
ejpam-5962	159	15	maximal	maximal	ADJ
ejpam-5962	159	16	compact	compact	ADJ
ejpam-5962	159	17	topology	topology	NOUN
ejpam-5962	159	18	if	if	SCONJ
ejpam-5962	159	19	(	(	PUNCT
ejpam-5962	159	20	z	z	NOUN
ejpam-5962	159	21	,	,	PUNCT
ejpam-5962	159	22	ϑ1	ϑ1	NOUN
ejpam-5962	159	23	,	,	PUNCT
ejpam-5962	159	24	ϑ2	ϑ2	NOUN
ejpam-5962	159	25	)	)	PUNCT
ejpam-5962	159	26	≤	≤	NOUN
ejpam-5962	159	27	(	(	PUNCT
ejpam-5962	159	28	z	z	NOUN
ejpam-5962	159	29	,	,	PUNCT
ejpam-5962	159	30	ϑ	ϑ	X
ejpam-5962	159	31	/	/	SYM
ejpam-5962	159	32	1	1	NUM
ejpam-5962	159	33	,	,	PUNCT
ejpam-5962	159	34	ϑ	ϑ	X
ejpam-5962	159	35	/	/	SYM
ejpam-5962	159	36	2	2	NUM
ejpam-5962	159	37	)	)	PUNCT
ejpam-5962	159	38	like	like	ADP
ejpam-5962	159	39	that	that	DET
ejpam-5962	159	40	ϑ1	ϑ1	NOUN
ejpam-5962	159	41	≤	≤	PROPN
ejpam-5962	159	42	ϑ	ϑ	X
ejpam-5962	159	43	/	/	SYM
ejpam-5962	159	44	1	1	NUM
ejpam-5962	159	45	and	and	CCONJ
ejpam-5962	159	46	ϑ2	ϑ2	PROPN
ejpam-5962	159	47	≤	≤	PROPN
ejpam-5962	159	48	ϑ	ϑ	X
ejpam-5962	159	49	/	/	SYM
ejpam-5962	159	50	2	2	NUM
ejpam-5962	159	51	indicates	indicate	VERB
ejpam-5962	159	52	(	(	PUNCT
ejpam-5962	159	53	z	z	NOUN
ejpam-5962	159	54	,	,	PUNCT
ejpam-5962	159	55	ϑ	ϑ	X
ejpam-5962	159	56	/	/	SYM
ejpam-5962	159	57	1	1	NUM
ejpam-5962	159	58	,	,	PUNCT
ejpam-5962	159	59	ϑ	ϑ	X
ejpam-5962	159	60	/	/	SYM
ejpam-5962	159	61	2	2	NUM
ejpam-5962	159	62	)	)	PUNCT
ejpam-5962	159	63	is	be	AUX
ejpam-5962	159	64	not	not	PART
ejpam-5962	159	65	pairwise	pairwise	NOUN
ejpam-5962	159	66	compact	compact	ADJ
ejpam-5962	159	67	.	.	PUNCT
ejpam-5962	160	1	definition	definition	NOUN
ejpam-5962	160	2	4.3	4.3	NUM
ejpam-5962	160	3	.	.	PUNCT
ejpam-5962	161	1	a	a	DET
ejpam-5962	161	2	function	function	NOUN
ejpam-5962	161	3	φ	φ	NOUN
ejpam-5962	161	4	:	:	PUNCT
ejpam-5962	161	5	(	(	PUNCT
ejpam-5962	161	6	z	z	NOUN
ejpam-5962	161	7	,	,	PUNCT
ejpam-5962	161	8	ϑ1	ϑ1	NOUN
ejpam-5962	161	9	,	,	PUNCT
ejpam-5962	161	10	ϑ2	ϑ2	PROPN
ejpam-5962	161	11	)	)	PUNCT
ejpam-5962	161	12	→	→	SYM
ejpam-5962	161	13	(	(	PUNCT
ejpam-5962	161	14	n	n	CCONJ
ejpam-5962	161	15	,	,	PUNCT
ejpam-5962	161	16	β1	β1	PROPN
ejpam-5962	161	17	,	,	PUNCT
ejpam-5962	161	18	β2	β2	NOUN
ejpam-5962	161	19	)	)	PUNCT
ejpam-5962	161	20	is	be	AUX
ejpam-5962	161	21	allegedly	allegedly	ADV
ejpam-5962	161	22	pairwise	pairwise	VERB
ejpam-5962	161	23	k−function	k−function	NOUN
ejpam-5962	161	24	whenever	whenever	SCONJ
ejpam-5962	161	25	the	the	DET
ejpam-5962	161	26	inverse	inverse	NOUN
ejpam-5962	161	27	of	of	ADP
ejpam-5962	161	28	any	any	DET
ejpam-5962	161	29	pairwise	pairwise	NOUN
ejpam-5962	161	30	compact	compact	ADJ
ejpam-5962	161	31	subset	subset	NOUN
ejpam-5962	161	32	of	of	ADP
ejpam-5962	161	33	(	(	PUNCT
ejpam-5962	161	34	n	n	X
ejpam-5962	161	35	,	,	PUNCT
ejpam-5962	161	36	β1	β1	PROPN
ejpam-5962	161	37	,	,	PUNCT
ejpam-5962	161	38	β2	β2	NOUN
ejpam-5962	161	39	)	)	PUNCT
ejpam-5962	161	40	is	be	AUX
ejpam-5962	161	41	pairwise	pairwise	NOUN
ejpam-5962	161	42	compact	compact	ADJ
ejpam-5962	161	43	in	in	ADP
ejpam-5962	161	44	(	(	PUNCT
ejpam-5962	161	45	z	z	NOUN
ejpam-5962	161	46	,	,	PUNCT
ejpam-5962	161	47	ϑ1	ϑ1	NOUN
ejpam-5962	161	48	,	,	PUNCT
ejpam-5962	161	49	ϑ2	ϑ2	PROPN
ejpam-5962	161	50	)	)	PUNCT
ejpam-5962	161	51	and	and	CCONJ
ejpam-5962	161	52	any	any	DET
ejpam-5962	161	53	pairwise	pairwise	NOUN
ejpam-5962	161	54	compact	compact	NOUN
ejpam-5962	161	55	subset	subset	NOUN
ejpam-5962	161	56	’s	’s	PART
ejpam-5962	161	57	image	image	NOUN
ejpam-5962	161	58	(	(	PUNCT
ejpam-5962	161	59	z	z	NOUN
ejpam-5962	161	60	,	,	PUNCT
ejpam-5962	161	61	ϑ1	ϑ1	NOUN
ejpam-5962	161	62	,	,	PUNCT
ejpam-5962	161	63	ϑ2	ϑ2	PROPN
ejpam-5962	161	64	)	)	PUNCT
ejpam-5962	161	65	is	be	AUX
ejpam-5962	161	66	pairwise	pairwise	NOUN
ejpam-5962	161	67	compact	compact	NOUN
ejpam-5962	161	68	subset	subset	NOUN
ejpam-5962	161	69	in	in	ADP
ejpam-5962	161	70	(	(	PUNCT
ejpam-5962	161	71	n	n	CCONJ
ejpam-5962	161	72	,	,	PUNCT
ejpam-5962	161	73	β1	β1	NOUN
ejpam-5962	161	74	,	,	PUNCT
ejpam-5962	161	75	β2	β2	PROPN
ejpam-5962	161	76	)	)	PUNCT
ejpam-5962	161	77	.	.	PUNCT
ejpam-5962	162	1	theorem	theorem	VERB
ejpam-5962	162	2	4.1	4.1	NUM
ejpam-5962	162	3	.	.	PUNCT
ejpam-5962	163	1	allow	allow	VERB
ejpam-5962	163	2	φ	φ	PROPN
ejpam-5962	163	3	:	:	PUNCT
ejpam-5962	163	4	(	(	PUNCT
ejpam-5962	163	5	z	z	NOUN
ejpam-5962	163	6	,	,	PUNCT
ejpam-5962	163	7	ϑ1	ϑ1	NOUN
ejpam-5962	163	8	,	,	PUNCT
ejpam-5962	163	9	ϑ2)onto	ϑ2)onto	PROPN
ejpam-5962	163	10	closed−−−−−−−−→	closed−−−−−−−−→	NOUN
ejpam-5962	163	11	(	(	PUNCT
ejpam-5962	163	12	n	n	CCONJ
ejpam-5962	163	13	,	,	PUNCT
ejpam-5962	163	14	β1	β1	PROPN
ejpam-5962	163	15	,	,	PUNCT
ejpam-5962	163	16	β2	β2	PROPN
ejpam-5962	163	17	)	)	PUNCT
ejpam-5962	163	18	be	be	AUX
ejpam-5962	163	19	pairwise	pairwise	NOUN
ejpam-5962	163	20	k−function	k−function	NOUN
ejpam-5962	163	21	.	.	PUNCT
ejpam-5962	164	1	when	when	SCONJ
ejpam-5962	164	2	(	(	PUNCT
ejpam-5962	164	3	z	z	NOUN
ejpam-5962	164	4	,	,	PUNCT
ejpam-5962	164	5	ϑ1	ϑ1	NOUN
ejpam-5962	164	6	,	,	PUNCT
ejpam-5962	164	7	ϑ2	ϑ2	PROPN
ejpam-5962	164	8	)	)	PUNCT
ejpam-5962	164	9	is	be	AUX
ejpam-5962	164	10	pairwise	pairwise	NOUN
ejpam-5962	164	11	compact	compact	ADJ
ejpam-5962	164	12	closed	close	VERB
ejpam-5962	164	13	space	space	NOUN
ejpam-5962	164	14	,	,	PUNCT
ejpam-5962	164	15	then	then	ADV
ejpam-5962	164	16	(	(	PUNCT
ejpam-5962	164	17	n	n	X
ejpam-5962	164	18	,	,	PUNCT
ejpam-5962	164	19	β1	β1	PROPN
ejpam-5962	164	20	,	,	PUNCT
ejpam-5962	164	21	β2	β2	NOUN
ejpam-5962	164	22	)	)	PUNCT
ejpam-5962	164	23	follows	follow	VERB
ejpam-5962	164	24	.	.	PUNCT
ejpam-5962	165	1	proof	proof	NOUN
ejpam-5962	165	2	.	.	PUNCT
ejpam-5962	166	1	suppose	suppose	VERB
ejpam-5962	166	2	u	u	PRON
ejpam-5962	166	3	be	be	AUX
ejpam-5962	166	4	β1−compact	β1−compact	NOUN
ejpam-5962	166	5	set	set	VERB
ejpam-5962	166	6	in	in	ADP
ejpam-5962	166	7	(	(	PUNCT
ejpam-5962	166	8	n	n	CCONJ
ejpam-5962	166	9	,	,	PUNCT
ejpam-5962	166	10	β1	β1	NOUN
ejpam-5962	166	11	,	,	PUNCT
ejpam-5962	166	12	β2	β2	PROPN
ejpam-5962	166	13	)	)	PUNCT
ejpam-5962	166	14	.	.	PUNCT
ejpam-5962	167	1	to	to	PART
ejpam-5962	167	2	demonstrate	demonstrate	VERB
ejpam-5962	167	3	that	that	SCONJ
ejpam-5962	167	4	u	u	NOUN
ejpam-5962	167	5	is	be	AUX
ejpam-5962	167	6	β2−closed	β2−close	VERB
ejpam-5962	167	7	in	in	ADP
ejpam-5962	167	8	(	(	PUNCT
ejpam-5962	167	9	n	n	CCONJ
ejpam-5962	167	10	,	,	PUNCT
ejpam-5962	167	11	β1	β1	PROPN
ejpam-5962	167	12	,	,	PUNCT
ejpam-5962	167	13	β2).while	β2).while	PRON
ejpam-5962	167	14	φ	φ	PROPN
ejpam-5962	167	15	is	be	AUX
ejpam-5962	167	16	pairwise	pairwise	PROPN
ejpam-5962	167	17	k−function	k−function	NOUN
ejpam-5962	167	18	,	,	PUNCT
ejpam-5962	167	19	consequently	consequently	ADV
ejpam-5962	167	20	φ−1(z	φ−1(z	NOUN
ejpam-5962	167	21	)	)	PUNCT
ejpam-5962	167	22	is	be	AUX
ejpam-5962	167	23	ϑ1−compact	ϑ1−compact	NOUN
ejpam-5962	167	24	in	in	ADP
ejpam-5962	167	25	(	(	PUNCT
ejpam-5962	167	26	z	z	NOUN
ejpam-5962	167	27	,	,	PUNCT
ejpam-5962	167	28	ϑ1	ϑ1	NOUN
ejpam-5962	167	29	,	,	PUNCT
ejpam-5962	167	30	ϑ2	ϑ2	PROPN
ejpam-5962	167	31	)	)	PUNCT
ejpam-5962	167	32	,	,	PUNCT
ejpam-5962	167	33	whereas	whereas	SCONJ
ejpam-5962	167	34	(	(	PUNCT
ejpam-5962	167	35	z	z	NOUN
ejpam-5962	167	36	,	,	PUNCT
ejpam-5962	167	37	ϑ1	ϑ1	NOUN
ejpam-5962	167	38	,	,	PUNCT
ejpam-5962	167	39	ϑ2	ϑ2	PROPN
ejpam-5962	167	40	)	)	PUNCT
ejpam-5962	167	41	is	be	AUX
ejpam-5962	167	42	pairwise	pairwise	NOUN
ejpam-5962	167	43	compact	compact	ADJ
ejpam-5962	167	44	closed	close	VERB
ejpam-5962	167	45	space	space	NOUN
ejpam-5962	167	46	,	,	PUNCT
ejpam-5962	167	47	φ−1(z	φ−1(z	PROPN
ejpam-5962	167	48	)	)	PUNCT
ejpam-5962	167	49	is	be	AUX
ejpam-5962	167	50	ϑ2−closed	ϑ2−close	VERB
ejpam-5962	167	51	in	in	ADP
ejpam-5962	167	52	(	(	PUNCT
ejpam-5962	167	53	z	z	NOUN
ejpam-5962	167	54	,	,	PUNCT
ejpam-5962	167	55	ϑ1	ϑ1	NOUN
ejpam-5962	167	56	,	,	PUNCT
ejpam-5962	167	57	ϑ2	ϑ2	PROPN
ejpam-5962	167	58	)	)	PUNCT
ejpam-5962	167	59	otherwise	otherwise	ADV
ejpam-5962	167	60	.	.	PUNCT
ejpam-5962	168	1	due	due	ADP
ejpam-5962	168	2	to	to	ADP
ejpam-5962	168	3	the	the	DET
ejpam-5962	168	4	fact	fact	NOUN
ejpam-5962	168	5	that	that	SCONJ
ejpam-5962	168	6	φ	φ	PROPN
ejpam-5962	168	7	is	be	AUX
ejpam-5962	168	8	pairwise	pairwise	NOUN
ejpam-5962	168	9	closed	closed	ADJ
ejpam-5962	168	10	and	and	CCONJ
ejpam-5962	168	11	onto	onto	ADP
ejpam-5962	168	12	,	,	PUNCT
ejpam-5962	168	13	φ(φ−1(u	φ(φ−1(u	PROPN
ejpam-5962	168	14	)	)	PUNCT
ejpam-5962	168	15	=	=	SYM
ejpam-5962	168	16	u	u	NOUN
ejpam-5962	168	17	is	be	AUX
ejpam-5962	168	18	β2	β2	VERB
ejpam-5962	168	19	−closed	−close	VERB
ejpam-5962	168	20	in	in	ADP
ejpam-5962	168	21	(	(	PUNCT
ejpam-5962	168	22	n	n	CCONJ
ejpam-5962	168	23	,	,	PUNCT
ejpam-5962	168	24	β1	β1	NOUN
ejpam-5962	168	25	,	,	PUNCT
ejpam-5962	168	26	β2	β2	PROPN
ejpam-5962	168	27	)	)	PUNCT
ejpam-5962	168	28	.	.	PUNCT
ejpam-5962	169	1	a	a	DET
ejpam-5962	169	2	β2	β2	ADJ
ejpam-5962	169	3	-	-	PUNCT
ejpam-5962	169	4	compact	compact	ADJ
ejpam-5962	169	5	set	set	NOUN
ejpam-5962	169	6	in	in	ADP
ejpam-5962	169	7	(	(	PUNCT
ejpam-5962	169	8	n	n	CCONJ
ejpam-5962	169	9	,	,	PUNCT
ejpam-5962	169	10	β1	β1	NOUN
ejpam-5962	169	11	,	,	PUNCT
ejpam-5962	169	12	β2	β2	NOUN
ejpam-5962	169	13	)	)	PUNCT
ejpam-5962	169	14	is	be	AUX
ejpam-5962	169	15	analogous	analogous	ADJ
ejpam-5962	169	16	for	for	ADP
ejpam-5962	169	17	v	v	NOUN
ejpam-5962	169	18	.	.	PUNCT
ejpam-5962	170	1	(	(	PUNCT
ejpam-5962	170	2	n	n	CCONJ
ejpam-5962	170	3	,	,	PUNCT
ejpam-5962	170	4	β1	β1	PROPN
ejpam-5962	170	5	,	,	PUNCT
ejpam-5962	170	6	β2	β2	NOUN
ejpam-5962	170	7	)	)	PUNCT
ejpam-5962	170	8	is	be	AUX
ejpam-5962	170	9	a	a	DET
ejpam-5962	170	10	pairwise	pairwise	NOUN
ejpam-5962	170	11	compact	compact	ADJ
ejpam-5962	170	12	closed	close	VERB
ejpam-5962	170	13	space	space	NOUN
ejpam-5962	170	14	as	as	ADP
ejpam-5962	170	15	a	a	DET
ejpam-5962	170	16	result	result	NOUN
ejpam-5962	170	17	.	.	PUNCT
ejpam-5962	171	1	a.	a.	NOUN
ejpam-5962	171	2	a.	a.	PROPN
ejpam-5962	171	3	atoom	atoom	PROPN
ejpam-5962	171	4	et	et	PROPN
ejpam-5962	171	5	al	al	PROPN
ejpam-5962	171	6	.	.	PUNCT
ejpam-5962	171	7	/	/	SYM
ejpam-5962	171	8	eur	eur	PROPN
ejpam-5962	171	9	.	.	PUNCT
ejpam-5962	172	1	j.	j.	PROPN
ejpam-5962	172	2	pure	pure	PROPN
ejpam-5962	172	3	appl	appl	PROPN
ejpam-5962	172	4	.	.	PROPN
ejpam-5962	172	5	math	math	PROPN
ejpam-5962	172	6	,	,	PUNCT
ejpam-5962	172	7	18	18	NUM
ejpam-5962	172	8	(	(	PUNCT
ejpam-5962	172	9	2	2	NUM
ejpam-5962	172	10	)	)	PUNCT
ejpam-5962	172	11	(	(	PUNCT
ejpam-5962	172	12	2025	2025	NUM
ejpam-5962	172	13	)	)	PUNCT
ejpam-5962	172	14	,	,	PUNCT
ejpam-5962	172	15	5962	5962	NUM
ejpam-5962	172	16	7	7	NUM
ejpam-5962	172	17	of	of	ADP
ejpam-5962	172	18	17	17	NUM
ejpam-5962	172	19	theorem	theorem	VERB
ejpam-5962	172	20	4.2	4.2	NUM
ejpam-5962	172	21	.	.	PUNCT
ejpam-5962	173	1	allow	allow	VERB
ejpam-5962	173	2	φ	φ	PROPN
ejpam-5962	173	3	:	:	PUNCT
ejpam-5962	173	4	(	(	PUNCT
ejpam-5962	173	5	z	z	NOUN
ejpam-5962	173	6	,	,	PUNCT
ejpam-5962	173	7	ϑ1	ϑ1	NOUN
ejpam-5962	173	8	,	,	PUNCT
ejpam-5962	173	9	ϑ2	ϑ2	PROPN
ejpam-5962	173	10	)	)	PUNCT
ejpam-5962	173	11	→	→	SYM
ejpam-5962	173	12	(	(	PUNCT
ejpam-5962	173	13	n	n	CCONJ
ejpam-5962	173	14	,	,	PUNCT
ejpam-5962	173	15	β1	β1	PROPN
ejpam-5962	173	16	,	,	PUNCT
ejpam-5962	173	17	β2	β2	PROPN
ejpam-5962	173	18	)	)	PUNCT
ejpam-5962	173	19	be	be	VERB
ejpam-5962	173	20	pairwise	pairwise	NOUN
ejpam-5962	173	21	continuous	continuous	ADJ
ejpam-5962	173	22	function	function	NOUN
ejpam-5962	173	23	.	.	PUNCT
ejpam-5962	174	1	when	when	SCONJ
ejpam-5962	174	2	(	(	PUNCT
ejpam-5962	174	3	n	n	X
ejpam-5962	174	4	,	,	PUNCT
ejpam-5962	174	5	β1	β1	PROPN
ejpam-5962	174	6	,	,	PUNCT
ejpam-5962	174	7	β2	β2	NOUN
ejpam-5962	174	8	)	)	PUNCT
ejpam-5962	174	9	is	be	AUX
ejpam-5962	174	10	pairwise	pairwise	NOUN
ejpam-5962	174	11	compact	compact	ADJ
ejpam-5962	174	12	closed	close	VERB
ejpam-5962	174	13	space	space	NOUN
ejpam-5962	174	14	and	and	CCONJ
ejpam-5962	174	15	(	(	PUNCT
ejpam-5962	174	16	z	z	NOUN
ejpam-5962	174	17	,	,	PUNCT
ejpam-5962	174	18	ϑ1	ϑ1	NOUN
ejpam-5962	174	19	,	,	PUNCT
ejpam-5962	174	20	ϑ2	ϑ2	PROPN
ejpam-5962	174	21	)	)	PUNCT
ejpam-5962	174	22	is	be	AUX
ejpam-5962	174	23	pairwise	pairwise	NOUN
ejpam-5962	174	24	compact	compact	ADJ
ejpam-5962	174	25	,	,	PUNCT
ejpam-5962	174	26	subsequently	subsequently	ADV
ejpam-5962	174	27	,	,	PUNCT
ejpam-5962	174	28	φ	φ	PROPN
ejpam-5962	174	29	is	be	AUX
ejpam-5962	174	30	pairwise	pairwise	NOUN
ejpam-5962	174	31	closed	close	VERB
ejpam-5962	174	32	function	function	NOUN
ejpam-5962	174	33	.	.	PUNCT
ejpam-5962	175	1	proof	proof	NOUN
ejpam-5962	175	2	.	.	PUNCT
ejpam-5962	176	1	if	if	SCONJ
ejpam-5962	176	2	u	u	PRON
ejpam-5962	176	3	be	be	AUX
ejpam-5962	176	4	ϑ1−closed	ϑ1−close	VERB
ejpam-5962	176	5	set	set	VERB
ejpam-5962	176	6	in	in	ADP
ejpam-5962	176	7	(	(	PUNCT
ejpam-5962	176	8	z	z	NOUN
ejpam-5962	176	9	,	,	PUNCT
ejpam-5962	176	10	ϑ1	ϑ1	NOUN
ejpam-5962	176	11	,	,	PUNCT
ejpam-5962	176	12	ϑ2	ϑ2	PROPN
ejpam-5962	176	13	)	)	PUNCT
ejpam-5962	176	14	,	,	PUNCT
ejpam-5962	176	15	yet	yet	CCONJ
ejpam-5962	176	16	(	(	PUNCT
ejpam-5962	176	17	z	z	NOUN
ejpam-5962	176	18	,	,	PUNCT
ejpam-5962	176	19	ϑ1	ϑ1	NOUN
ejpam-5962	176	20	,	,	PUNCT
ejpam-5962	176	21	ϑ2	ϑ2	PROPN
ejpam-5962	176	22	)	)	PUNCT
ejpam-5962	176	23	is	be	AUX
ejpam-5962	176	24	pairwise	pairwise	NOUN
ejpam-5962	176	25	compact	compact	ADJ
ejpam-5962	176	26	,	,	PUNCT
ejpam-5962	176	27	then	then	ADV
ejpam-5962	176	28	u	u	NOUN
ejpam-5962	176	29	is	be	AUX
ejpam-5962	176	30	ϑ1−compact	ϑ1−compact	NOUN
ejpam-5962	176	31	in	in	ADP
ejpam-5962	176	32	(	(	PUNCT
ejpam-5962	176	33	z	z	NOUN
ejpam-5962	176	34	,	,	PUNCT
ejpam-5962	176	35	ϑ1	ϑ1	NOUN
ejpam-5962	176	36	,	,	PUNCT
ejpam-5962	176	37	ϑ2	ϑ2	PROPN
ejpam-5962	176	38	)	)	PUNCT
ejpam-5962	176	39	.	.	PUNCT
ejpam-5962	177	1	considering	consider	VERB
ejpam-5962	177	2	that	that	SCONJ
ejpam-5962	177	3	φ	φ	PROPN
ejpam-5962	177	4	is	be	AUX
ejpam-5962	177	5	pairwise	pairwise	NOUN
ejpam-5962	177	6	continuous	continuous	ADJ
ejpam-5962	177	7	function	function	NOUN
ejpam-5962	177	8	,	,	PUNCT
ejpam-5962	177	9	then	then	ADV
ejpam-5962	177	10	φ(u	φ(u	NOUN
ejpam-5962	177	11	)	)	PUNCT
ejpam-5962	177	12	is	be	AUX
ejpam-5962	177	13	β1−compact	β1−compact	ADJ
ejpam-5962	177	14	in	in	ADP
ejpam-5962	177	15	(	(	PUNCT
ejpam-5962	177	16	n	n	CCONJ
ejpam-5962	177	17	,	,	PUNCT
ejpam-5962	177	18	β1	β1	NOUN
ejpam-5962	177	19	,	,	PUNCT
ejpam-5962	177	20	β2	β2	PROPN
ejpam-5962	177	21	)	)	PUNCT
ejpam-5962	177	22	.	.	PUNCT
ejpam-5962	178	1	due	due	ADP
ejpam-5962	178	2	to	to	ADP
ejpam-5962	178	3	the	the	DET
ejpam-5962	178	4	fact	fact	NOUN
ejpam-5962	178	5	that	that	SCONJ
ejpam-5962	178	6	(	(	PUNCT
ejpam-5962	178	7	n	n	X
ejpam-5962	178	8	,	,	PUNCT
ejpam-5962	178	9	β1	β1	PROPN
ejpam-5962	178	10	,	,	PUNCT
ejpam-5962	178	11	β2	β2	NOUN
ejpam-5962	178	12	)	)	PUNCT
ejpam-5962	178	13	is	be	AUX
ejpam-5962	178	14	pairwise	pairwise	NOUN
ejpam-5962	178	15	compact	compact	ADJ
ejpam-5962	178	16	closed	close	VERB
ejpam-5962	178	17	space	space	NOUN
ejpam-5962	178	18	,	,	PUNCT
ejpam-5962	178	19	so	so	SCONJ
ejpam-5962	178	20	φ(u	φ(u	NOUN
ejpam-5962	178	21	)	)	PUNCT
ejpam-5962	178	22	is	be	AUX
ejpam-5962	178	23	β1−closed	β1−close	VERB
ejpam-5962	178	24	in	in	ADP
ejpam-5962	178	25	(	(	PUNCT
ejpam-5962	178	26	n	n	CCONJ
ejpam-5962	178	27	,	,	PUNCT
ejpam-5962	178	28	β1	β1	NOUN
ejpam-5962	178	29	,	,	PUNCT
ejpam-5962	178	30	β2	β2	PROPN
ejpam-5962	178	31	)	)	PUNCT
ejpam-5962	178	32	.	.	PUNCT
ejpam-5962	179	1	comparable	comparable	ADJ
ejpam-5962	179	2	tov	tov	INTJ
ejpam-5962	179	3	is	be	AUX
ejpam-5962	179	4	β2−closed	β2−close	VERB
ejpam-5962	179	5	set	set	VERB
ejpam-5962	179	6	in	in	ADP
ejpam-5962	179	7	(	(	PUNCT
ejpam-5962	179	8	n	n	CCONJ
ejpam-5962	179	9	,	,	PUNCT
ejpam-5962	179	10	β1	β1	PROPN
ejpam-5962	179	11	,	,	PUNCT
ejpam-5962	179	12	β2).as	β2).as	PRON
ejpam-5962	179	13	a	a	DET
ejpam-5962	179	14	result	result	NOUN
ejpam-5962	179	15	,	,	PUNCT
ejpam-5962	179	16	φ	φ	PROPN
ejpam-5962	179	17	is	be	AUX
ejpam-5962	179	18	pairwise	pairwise	NOUN
ejpam-5962	179	19	closed	close	VERB
ejpam-5962	179	20	function	function	NOUN
ejpam-5962	179	21	.	.	PUNCT
ejpam-5962	180	1	5	5	X
ejpam-5962	180	2	.	.	X
ejpam-5962	180	3	several	several	ADJ
ejpam-5962	180	4	pairwise	pairwise	NOUN
ejpam-5962	180	5	minimal	minimal	ADJ
ejpam-5962	180	6	compact	compact	ADJ
ejpam-5962	180	7	closed	close	VERB
ejpam-5962	180	8	space	space	NOUN
ejpam-5962	180	9	theorems	theorem	VERB
ejpam-5962	180	10	more	more	ADJ
ejpam-5962	180	11	information	information	NOUN
ejpam-5962	180	12	about	about	ADP
ejpam-5962	180	13	the	the	DET
ejpam-5962	180	14	pairwise	pairwise	NOUN
ejpam-5962	180	15	minimal	minimal	ADJ
ejpam-5962	180	16	compact	compact	ADJ
ejpam-5962	180	17	closed	closed	ADJ
ejpam-5962	180	18	spaces	space	NOUN
ejpam-5962	180	19	’	'	PUNCT
ejpam-5962	180	20	topological	topological	ADJ
ejpam-5962	180	21	characteristics	characteristic	NOUN
ejpam-5962	180	22	is	be	AUX
ejpam-5962	180	23	included	include	VERB
ejpam-5962	180	24	in	in	ADP
ejpam-5962	180	25	this	this	DET
ejpam-5962	180	26	section	section	NOUN
ejpam-5962	180	27	,	,	PUNCT
ejpam-5962	180	28	along	along	ADP
ejpam-5962	180	29	with	with	ADP
ejpam-5962	180	30	a	a	DET
ejpam-5962	180	31	diagram	diagram	NOUN
ejpam-5962	180	32	illustrating	illustrate	VERB
ejpam-5962	180	33	how	how	SCONJ
ejpam-5962	180	34	these	these	DET
ejpam-5962	180	35	spaces	space	NOUN
ejpam-5962	180	36	are	be	AUX
ejpam-5962	180	37	connected	connect	VERB
ejpam-5962	180	38	in	in	ADP
ejpam-5962	180	39	general	general	ADJ
ejpam-5962	180	40	.	.	PUNCT
ejpam-5962	181	1	definition	definition	NOUN
ejpam-5962	181	2	5.1	5.1	NUM
ejpam-5962	181	3	.	.	PUNCT
ejpam-5962	182	1	it	it	PRON
ejpam-5962	182	2	is	be	AUX
ejpam-5962	182	3	argued	argue	VERB
ejpam-5962	182	4	that	that	SCONJ
ejpam-5962	182	5	a	a	DET
ejpam-5962	182	6	bitopological	bitopological	ADJ
ejpam-5962	182	7	space	space	NOUN
ejpam-5962	182	8	(	(	PUNCT
ejpam-5962	182	9	z	z	NOUN
ejpam-5962	182	10	,	,	PUNCT
ejpam-5962	182	11	ϑ1	ϑ1	NOUN
ejpam-5962	182	12	,	,	PUNCT
ejpam-5962	182	13	ϑ2	ϑ2	PROPN
ejpam-5962	182	14	)	)	PUNCT
ejpam-5962	182	15	is	be	AUX
ejpam-5962	182	16	pairwise	pairwise	NOUN
ejpam-5962	182	17	minimal	minimal	ADJ
ejpam-5962	182	18	compact	compact	ADJ
ejpam-5962	182	19	closed	close	VERB
ejpam-5962	182	20	space	space	NOUN
ejpam-5962	182	21	,	,	PUNCT
ejpam-5962	182	22	(	(	PUNCT
ejpam-5962	182	23	z	z	NOUN
ejpam-5962	182	24	,	,	PUNCT
ejpam-5962	182	25	ϑ1	ϑ1	NOUN
ejpam-5962	182	26	,	,	PUNCT
ejpam-5962	182	27	ϑ2	ϑ2	NOUN
ejpam-5962	182	28	)	)	PUNCT
ejpam-5962	182	29	≤	≤	NOUN
ejpam-5962	182	30	(	(	PUNCT
ejpam-5962	182	31	z	z	NOUN
ejpam-5962	182	32	,	,	PUNCT
ejpam-5962	182	33	ϑ	ϑ	X
ejpam-5962	182	34	/	/	SYM
ejpam-5962	182	35	1	1	NUM
ejpam-5962	182	36	,	,	PUNCT
ejpam-5962	182	37	ϑ	ϑ	X
ejpam-5962	182	38	/	/	SYM
ejpam-5962	182	39	2	2	NUM
ejpam-5962	182	40	)	)	PUNCT
ejpam-5962	182	41	like	like	ADP
ejpam-5962	182	42	that	that	DET
ejpam-5962	182	43	ϑ	ϑ	PROPN
ejpam-5962	182	44	/	/	SYM
ejpam-5962	182	45	1	1	NUM
ejpam-5962	182	46	≤	≤	NOUN
ejpam-5962	182	47	ϑ1	ϑ1	NOUN
ejpam-5962	182	48	and	and	CCONJ
ejpam-5962	182	49	ϑ	ϑ	PROPN
ejpam-5962	182	50	/	/	SYM
ejpam-5962	182	51	2	2	NUM
ejpam-5962	182	52	≤	≤	NOUN
ejpam-5962	182	53	ϑ2	ϑ2	NOUN
ejpam-5962	182	54	indicates	indicate	VERB
ejpam-5962	182	55	(	(	PUNCT
ejpam-5962	182	56	z	z	NOUN
ejpam-5962	182	57	,	,	PUNCT
ejpam-5962	182	58	ϑ	ϑ	X
ejpam-5962	182	59	/	/	SYM
ejpam-5962	182	60	1	1	NUM
ejpam-5962	182	61	,	,	PUNCT
ejpam-5962	182	62	ϑ	ϑ	X
ejpam-5962	182	63	/	/	SYM
ejpam-5962	182	64	2	2	NUM
ejpam-5962	182	65	)	)	PUNCT
ejpam-5962	182	66	is	be	AUX
ejpam-5962	182	67	not	not	PART
ejpam-5962	182	68	pairwise	pairwise	NOUN
ejpam-5962	182	69	compact	compact	ADJ
ejpam-5962	182	70	closed	close	VERB
ejpam-5962	182	71	compact	compact	ADJ
ejpam-5962	182	72	.	.	PUNCT
ejpam-5962	183	1	theorem	theorem	VERB
ejpam-5962	183	2	5.1	5.1	NUM
ejpam-5962	183	3	.	.	PUNCT
ejpam-5962	184	1	a	a	DET
ejpam-5962	184	2	pairwise	pairwise	NOUN
ejpam-5962	184	3	compact	compact	ADJ
ejpam-5962	184	4	closed	close	VERB
ejpam-5962	184	5	spaces	space	NOUN
ejpam-5962	184	6	is	be	AUX
ejpam-5962	184	7	one	one	NUM
ejpam-5962	184	8	that	that	PRON
ejpam-5962	184	9	is	be	AUX
ejpam-5962	184	10	a	a	DET
ejpam-5962	184	11	pairwise	pairwise	NOUN
ejpam-5962	184	12	minimal	minimal	ADJ
ejpam-5962	184	13	compact	compact	ADJ
ejpam-5962	184	14	closed	closed	ADJ
ejpam-5962	184	15	space	space	NOUN
ejpam-5962	184	16	.	.	PUNCT
ejpam-5962	185	1	proof	proof	NOUN
ejpam-5962	185	2	.	.	PUNCT
ejpam-5962	186	1	assume	assume	VERB
ejpam-5962	186	2	that	that	SCONJ
ejpam-5962	186	3	(	(	PUNCT
ejpam-5962	186	4	z	z	NOUN
ejpam-5962	186	5	,	,	PUNCT
ejpam-5962	186	6	ϑ1	ϑ1	NOUN
ejpam-5962	186	7	,	,	PUNCT
ejpam-5962	186	8	ϑ2	ϑ2	PROPN
ejpam-5962	186	9	)	)	PUNCT
ejpam-5962	186	10	is	be	AUX
ejpam-5962	186	11	pairwise	pairwise	NOUN
ejpam-5962	186	12	compact	compact	ADJ
ejpam-5962	186	13	closed	close	VERB
ejpam-5962	186	14	spaces	space	NOUN
ejpam-5962	186	15	and	and	CCONJ
ejpam-5962	186	16	not	not	PART
ejpam-5962	186	17	pairwise	pairwise	VERB
ejpam-5962	186	18	minimal	minimal	ADJ
ejpam-5962	186	19	compact	compact	ADJ
ejpam-5962	186	20	closed	closed	ADJ
ejpam-5962	186	21	space	space	NOUN
ejpam-5962	186	22	,	,	PUNCT
ejpam-5962	186	23	then	then	ADV
ejpam-5962	186	24	there	there	PRON
ejpam-5962	186	25	is	be	VERB
ejpam-5962	186	26	ϑ	ϑ	ADJ
ejpam-5962	186	27	/	/	SYM
ejpam-5962	186	28	1	1	NUM
ejpam-5962	186	29	≤	≤	NOUN
ejpam-5962	186	30	ϑ1	ϑ1	NOUN
ejpam-5962	186	31	and	and	CCONJ
ejpam-5962	186	32	ϑ	ϑ	PROPN
ejpam-5962	186	33	/	/	SYM
ejpam-5962	186	34	2	2	NUM
ejpam-5962	186	35	≤	≤	NOUN
ejpam-5962	186	36	ϑ2	ϑ2	NOUN
ejpam-5962	186	37	and	and	CCONJ
ejpam-5962	186	38	(	(	PUNCT
ejpam-5962	186	39	z	z	NOUN
ejpam-5962	186	40	,	,	PUNCT
ejpam-5962	186	41	ϑ	ϑ	X
ejpam-5962	186	42	/	/	SYM
ejpam-5962	186	43	1	1	NUM
ejpam-5962	186	44	,	,	PUNCT
ejpam-5962	186	45	ϑ	ϑ	X
ejpam-5962	186	46	/	/	SYM
ejpam-5962	186	47	2	2	NUM
ejpam-5962	186	48	)	)	PUNCT
ejpam-5962	186	49	is	be	AUX
ejpam-5962	186	50	pairwise	pairwise	NOUN
ejpam-5962	186	51	compact	compact	ADJ
ejpam-5962	186	52	closed	close	VERB
ejpam-5962	186	53	space	space	NOUN
ejpam-5962	186	54	.	.	PUNCT
ejpam-5962	187	1	now	now	ADV
ejpam-5962	187	2	that	that	SCONJ
ejpam-5962	187	3	we	we	PRON
ejpam-5962	187	4	’ve	’ve	AUX
ejpam-5962	187	5	established	establish	VERB
ejpam-5962	187	6	that	that	SCONJ
ejpam-5962	187	7	θz	θz	NOUN
ejpam-5962	187	8	:	:	PUNCT
ejpam-5962	187	9	(	(	PUNCT
ejpam-5962	187	10	z	z	NOUN
ejpam-5962	187	11	,	,	PUNCT
ejpam-5962	187	12	ϑ1	ϑ1	NOUN
ejpam-5962	187	13	,	,	PUNCT
ejpam-5962	187	14	ϑ2	ϑ2	PROPN
ejpam-5962	187	15	)	)	PUNCT
ejpam-5962	187	16	→	→	SYM
ejpam-5962	187	17	(	(	PUNCT
ejpam-5962	187	18	z	z	NOUN
ejpam-5962	187	19	,	,	PUNCT
ejpam-5962	187	20	ϑ	ϑ	X
ejpam-5962	187	21	/	/	SYM
ejpam-5962	187	22	1	1	NUM
ejpam-5962	187	23	,	,	PUNCT
ejpam-5962	187	24	ϑ	ϑ	X
ejpam-5962	187	25	/	/	SYM
ejpam-5962	187	26	2	2	NUM
ejpam-5962	187	27	)	)	PUNCT
ejpam-5962	187	28	be	be	AUX
ejpam-5962	187	29	an	an	DET
ejpam-5962	187	30	identity	identity	NOUN
ejpam-5962	187	31	function	function	NOUN
ejpam-5962	187	32	,	,	PUNCT
ejpam-5962	187	33	then	then	ADV
ejpam-5962	187	34	θz	θz	PROPN
ejpam-5962	187	35	is	be	AUX
ejpam-5962	187	36	pairwise	pairwise	NOUN
ejpam-5962	187	37	continuous	continuous	ADJ
ejpam-5962	187	38	and	and	CCONJ
ejpam-5962	187	39	pairwise	pairwise	NOUN
ejpam-5962	187	40	closed	close	VERB
ejpam-5962	187	41	and	and	CCONJ
ejpam-5962	187	42	so	so	ADV
ejpam-5962	187	43	pairwise	pairwise	PROPN
ejpam-5962	187	44	homomorphism	homomorphism	NOUN
ejpam-5962	187	45	.	.	PUNCT
ejpam-5962	188	1	therefor	therefor	ADP
ejpam-5962	188	2	ϑ	ϑ	PROPN
ejpam-5962	188	3	/	/	SYM
ejpam-5962	188	4	1	1	NUM
ejpam-5962	188	5	=	=	SYM
ejpam-5962	188	6	ϑ1	ϑ1	NOUN
ejpam-5962	188	7	,	,	PUNCT
ejpam-5962	188	8	ϑ2	ϑ2	PROPN
ejpam-5962	188	9	=	=	SYM
ejpam-5962	188	10	ϑ	ϑ	PROPN
ejpam-5962	188	11	/	/	SYM
ejpam-5962	188	12	2	2	NUM
ejpam-5962	188	13	,	,	PUNCT
ejpam-5962	188	14	we	we	PRON
ejpam-5962	188	15	obtain	obtain	VERB
ejpam-5962	188	16	contradiction	contradiction	NOUN
ejpam-5962	188	17	.	.	PUNCT
ejpam-5962	189	1	as	as	ADP
ejpam-5962	189	2	a	a	DET
ejpam-5962	189	3	result	result	NOUN
ejpam-5962	189	4	,	,	PUNCT
ejpam-5962	189	5	(	(	PUNCT
ejpam-5962	189	6	z	z	NOUN
ejpam-5962	189	7	,	,	PUNCT
ejpam-5962	189	8	ϑ1	ϑ1	NOUN
ejpam-5962	189	9	,	,	PUNCT
ejpam-5962	189	10	ϑ2	ϑ2	PROPN
ejpam-5962	189	11	)	)	PUNCT
ejpam-5962	189	12	is	be	AUX
ejpam-5962	189	13	pairwise	pairwise	NOUN
ejpam-5962	189	14	minimal	minimal	ADJ
ejpam-5962	189	15	compact	compact	ADJ
ejpam-5962	189	16	closed	closed	ADJ
ejpam-5962	189	17	space	space	NOUN
ejpam-5962	189	18	.	.	PUNCT
ejpam-5962	190	1	example	example	NOUN
ejpam-5962	190	2	5.1	5.1	NUM
ejpam-5962	190	3	.	.	PUNCT
ejpam-5962	191	1	assuming	assume	VERB
ejpam-5962	191	2	z	z	PROPN
ejpam-5962	191	3	̸=	̸=	PROPN
ejpam-5962	191	4	ϕ	ϕ	NOUN
ejpam-5962	191	5	be	be	VERB
ejpam-5962	191	6	any	any	DET
ejpam-5962	191	7	finite	finite	NOUN
ejpam-5962	191	8	set	set	NOUN
ejpam-5962	191	9	and	and	CCONJ
ejpam-5962	191	10	ϑdis	ϑdi	NOUN
ejpam-5962	191	11	is	be	AUX
ejpam-5962	191	12	discrete	discrete	ADJ
ejpam-5962	191	13	topology	topology	NOUN
ejpam-5962	191	14	,	,	PUNCT
ejpam-5962	191	15	correspondingly	correspondingly	ADV
ejpam-5962	191	16	,	,	PUNCT
ejpam-5962	191	17	(	(	PUNCT
ejpam-5962	191	18	z	z	NOUN
ejpam-5962	191	19	,	,	PUNCT
ejpam-5962	191	20	ϑdis	ϑdi	NOUN
ejpam-5962	191	21	,	,	PUNCT
ejpam-5962	191	22	ϑdis	ϑdi	NOUN
ejpam-5962	191	23	)	)	PUNCT
ejpam-5962	191	24	is	be	AUX
ejpam-5962	191	25	pairwise	pairwise	NOUN
ejpam-5962	191	26	minimal	minimal	ADJ
ejpam-5962	191	27	compact	compact	ADJ
ejpam-5962	191	28	closed	closed	ADJ
ejpam-5962	191	29	space	space	NOUN
ejpam-5962	191	30	.	.	PUNCT
ejpam-5962	192	1	the	the	DET
ejpam-5962	192	2	example	example	NOUN
ejpam-5962	192	3	that	that	PRON
ejpam-5962	192	4	follows	follow	VERB
ejpam-5962	192	5	demonstrates	demonstrate	VERB
ejpam-5962	192	6	that	that	SCONJ
ejpam-5962	192	7	pairwise	pairwise	NOUN
ejpam-5962	192	8	minimal	minimal	ADJ
ejpam-5962	192	9	compact	compact	ADJ
ejpam-5962	192	10	closed	close	VERB
ejpam-5962	192	11	space	space	NOUN
ejpam-5962	192	12	is	be	AUX
ejpam-5962	192	13	not	not	PART
ejpam-5962	192	14	always	always	ADV
ejpam-5962	192	15	represented	represent	VERB
ejpam-5962	192	16	by	by	ADP
ejpam-5962	192	17	its	its	PRON
ejpam-5962	192	18	continuous	continuous	ADJ
ejpam-5962	192	19	image	image	NOUN
ejpam-5962	192	20	.	.	PUNCT
ejpam-5962	193	1	example	example	NOUN
ejpam-5962	194	1	5.2	5.2	NUM
ejpam-5962	194	2	.	.	PUNCT
ejpam-5962	195	1	let	let	VERB
ejpam-5962	195	2	ϑdis	ϑdi	NOUN
ejpam-5962	195	3	,	,	PUNCT
ejpam-5962	195	4	ϑind	ϑind	NOUN
ejpam-5962	195	5	is	be	AUX
ejpam-5962	195	6	discrete	discrete	ADJ
ejpam-5962	195	7	topology	topology	NOUN
ejpam-5962	195	8	and	and	CCONJ
ejpam-5962	195	9	indiscrete	indiscrete	ADJ
ejpam-5962	195	10	topology	topology	NOUN
ejpam-5962	195	11	respectivly	respectivly	ADJ
ejpam-5962	195	12	.	.	PUNCT
ejpam-5962	196	1	consider	consider	VERB
ejpam-5962	196	2	the	the	DET
ejpam-5962	196	3	following	following	NOUN
ejpam-5962	196	4	:	:	PUNCT
ejpam-5962	196	5	θz	θz	NOUN
ejpam-5962	196	6	:	:	PUNCT
ejpam-5962	196	7	(	(	PUNCT
ejpam-5962	196	8	z	z	NOUN
ejpam-5962	196	9	,	,	PUNCT
ejpam-5962	196	10	ϑdis	ϑdi	NOUN
ejpam-5962	196	11	,	,	PUNCT
ejpam-5962	196	12	ϑdis	ϑdi	NOUN
ejpam-5962	196	13	)	)	PUNCT
ejpam-5962	196	14	→	→	SYM
ejpam-5962	196	15	(	(	PUNCT
ejpam-5962	196	16	z	z	NOUN
ejpam-5962	196	17	,	,	PUNCT
ejpam-5962	196	18	ϑind	ϑind	ADJ
ejpam-5962	196	19	,	,	PUNCT
ejpam-5962	196	20	ϑind	ϑind	NOUN
ejpam-5962	196	21	)	)	PUNCT
ejpam-5962	196	22	be	be	VERB
ejpam-5962	196	23	an	an	DET
ejpam-5962	196	24	identity	identity	NOUN
ejpam-5962	196	25	function	function	NOUN
ejpam-5962	196	26	.	.	PUNCT
ejpam-5962	197	1	it	it	PRON
ejpam-5962	197	2	is	be	AUX
ejpam-5962	197	3	demonstrated	demonstrate	VERB
ejpam-5962	197	4	example	example	NOUN
ejpam-5962	197	5	3.3	3.3	NUM
ejpam-5962	197	6	shows	show	VERB
ejpam-5962	197	7	that	that	SCONJ
ejpam-5962	197	8	(	(	PUNCT
ejpam-5962	197	9	z	z	NOUN
ejpam-5962	197	10	,	,	PUNCT
ejpam-5962	197	11	ϑdis	ϑdi	NOUN
ejpam-5962	197	12	,	,	PUNCT
ejpam-5962	197	13	ϑdis	ϑdi	NOUN
ejpam-5962	197	14	)	)	PUNCT
ejpam-5962	197	15	is	be	AUX
ejpam-5962	197	16	pairwise	pairwise	NOUN
ejpam-5962	197	17	minimal	minimal	ADJ
ejpam-5962	197	18	compact	compact	ADJ
ejpam-5962	197	19	closed	closed	ADJ
ejpam-5962	197	20	space	space	NOUN
ejpam-5962	197	21	,	,	PUNCT
ejpam-5962	197	22	and	and	CCONJ
ejpam-5962	197	23	demonstrated	demonstrate	VERB
ejpam-5962	197	24	example	example	NOUN
ejpam-5962	197	25	5.1	5.1	NUM
ejpam-5962	197	26	shows	show	VERB
ejpam-5962	197	27	that	that	SCONJ
ejpam-5962	197	28	(	(	PUNCT
ejpam-5962	197	29	z	z	NOUN
ejpam-5962	197	30	,	,	PUNCT
ejpam-5962	197	31	ϑind	ϑind	ADJ
ejpam-5962	197	32	,	,	PUNCT
ejpam-5962	197	33	ϑind	ϑind	NOUN
ejpam-5962	197	34	)	)	PUNCT
ejpam-5962	197	35	is	be	AUX
ejpam-5962	197	36	not	not	PART
ejpam-5962	197	37	pairwise	pairwise	NOUN
ejpam-5962	197	38	minimal	minimal	ADJ
ejpam-5962	197	39	compact	compact	ADJ
ejpam-5962	197	40	closed	closed	ADJ
ejpam-5962	197	41	space	space	NOUN
ejpam-5962	197	42	.	.	PUNCT
ejpam-5962	198	1	theorem	theorem	VERB
ejpam-5962	198	2	5.2	5.2	NUM
ejpam-5962	198	3	.	.	PUNCT
ejpam-5962	199	1	being	be	AUX
ejpam-5962	199	2	pairwise	pairwise	NOUN
ejpam-5962	199	3	minimal	minimal	ADJ
ejpam-5962	199	4	compact	compact	ADJ
ejpam-5962	199	5	closed	close	VERB
ejpam-5962	199	6	space	space	NOUN
ejpam-5962	199	7	is	be	AUX
ejpam-5962	199	8	a	a	DET
ejpam-5962	199	9	bitopological	bitopological	ADJ
ejpam-5962	199	10	property	property	NOUN
ejpam-5962	199	11	.	.	PUNCT
ejpam-5962	200	1	a.	a.	NOUN
ejpam-5962	200	2	a.	a.	PROPN
ejpam-5962	200	3	atoom	atoom	PROPN
ejpam-5962	200	4	et	et	PROPN
ejpam-5962	200	5	al	al	PROPN
ejpam-5962	200	6	.	.	PUNCT
ejpam-5962	200	7	/	/	SYM
ejpam-5962	200	8	eur	eur	PROPN
ejpam-5962	200	9	.	.	PUNCT
ejpam-5962	201	1	j.	j.	PROPN
ejpam-5962	201	2	pure	pure	PROPN
ejpam-5962	201	3	appl	appl	PROPN
ejpam-5962	201	4	.	.	PROPN
ejpam-5962	201	5	math	math	PROPN
ejpam-5962	201	6	,	,	PUNCT
ejpam-5962	201	7	18	18	NUM
ejpam-5962	201	8	(	(	PUNCT
ejpam-5962	201	9	2	2	NUM
ejpam-5962	201	10	)	)	PUNCT
ejpam-5962	201	11	(	(	PUNCT
ejpam-5962	201	12	2025	2025	NUM
ejpam-5962	201	13	)	)	PUNCT
ejpam-5962	201	14	,	,	PUNCT
ejpam-5962	201	15	5962	5962	NUM
ejpam-5962	201	16	8	8	NUM
ejpam-5962	201	17	of	of	ADP
ejpam-5962	201	18	17	17	NUM
ejpam-5962	201	19	proof	proof	NOUN
ejpam-5962	201	20	.	.	PUNCT
ejpam-5962	202	1	assume	assume	VERB
ejpam-5962	202	2	that	that	SCONJ
ejpam-5962	202	3	(	(	PUNCT
ejpam-5962	202	4	z	z	NOUN
ejpam-5962	202	5	,	,	PUNCT
ejpam-5962	202	6	ϑ1	ϑ1	NOUN
ejpam-5962	202	7	,	,	PUNCT
ejpam-5962	202	8	ϑ2	ϑ2	PROPN
ejpam-5962	202	9	)	)	PUNCT
ejpam-5962	202	10	is	be	AUX
ejpam-5962	202	11	a	a	DET
ejpam-5962	202	12	pairwise	pairwise	NOUN
ejpam-5962	202	13	minimal	minimal	ADJ
ejpam-5962	202	14	compact	compact	ADJ
ejpam-5962	202	15	closed	close	VERB
ejpam-5962	202	16	space	space	NOUN
ejpam-5962	202	17	and	and	CCONJ
ejpam-5962	202	18	φ	φ	NOUN
ejpam-5962	202	19	:	:	PUNCT
ejpam-5962	202	20	(	(	PUNCT
ejpam-5962	202	21	z	z	NOUN
ejpam-5962	202	22	,	,	PUNCT
ejpam-5962	202	23	ϑ1	ϑ1	NOUN
ejpam-5962	202	24	,	,	PUNCT
ejpam-5962	202	25	ϑ2	ϑ2	PROPN
ejpam-5962	202	26	)	)	PUNCT
ejpam-5962	202	27	→	→	SYM
ejpam-5962	202	28	(	(	PUNCT
ejpam-5962	202	29	n	n	CCONJ
ejpam-5962	202	30	,	,	PUNCT
ejpam-5962	202	31	β1	β1	PROPN
ejpam-5962	202	32	,	,	PUNCT
ejpam-5962	202	33	β2	β2	PROPN
ejpam-5962	202	34	)	)	PUNCT
ejpam-5962	202	35	be	be	VERB
ejpam-5962	202	36	a	a	DET
ejpam-5962	202	37	pairwise	pairwise	NOUN
ejpam-5962	202	38	homeomorphism	homeomorphism	NOUN
ejpam-5962	202	39	and	and	CCONJ
ejpam-5962	202	40	(	(	PUNCT
ejpam-5962	202	41	n	n	CCONJ
ejpam-5962	202	42	,	,	PUNCT
ejpam-5962	202	43	β1	β1	PROPN
ejpam-5962	202	44	,	,	PUNCT
ejpam-5962	202	45	β2	β2	NOUN
ejpam-5962	202	46	)	)	PUNCT
ejpam-5962	202	47	is	be	AUX
ejpam-5962	202	48	not	not	PART
ejpam-5962	202	49	pairwise	pairwise	NOUN
ejpam-5962	202	50	minimal	minimal	ADJ
ejpam-5962	202	51	compact	compact	ADJ
ejpam-5962	202	52	closed	closed	ADJ
ejpam-5962	202	53	space	space	NOUN
ejpam-5962	202	54	,	,	PUNCT
ejpam-5962	202	55	there	there	PRON
ejpam-5962	202	56	existsβ	existsβ	NOUN
ejpam-5962	202	57	/	/	SYM
ejpam-5962	202	58	1	1	NUM
ejpam-5962	202	59	≤	≤	NOUN
ejpam-5962	202	60	β1	β1	NOUN
ejpam-5962	202	61	,	,	PUNCT
ejpam-5962	202	62	β	β	X
ejpam-5962	202	63	/	/	SYM
ejpam-5962	202	64	2	2	NUM
ejpam-5962	202	65	≤	≤	NOUN
ejpam-5962	202	66	β2	β2	NOUN
ejpam-5962	202	67	,	,	PUNCT
ejpam-5962	202	68	such	such	ADJ
ejpam-5962	202	69	that	that	SCONJ
ejpam-5962	202	70	(	(	PUNCT
ejpam-5962	202	71	n	n	X
ejpam-5962	202	72	,	,	PUNCT
ejpam-5962	202	73	β	β	X
ejpam-5962	202	74	/	/	SYM
ejpam-5962	202	75	1	1	NUM
ejpam-5962	202	76	,	,	PUNCT
ejpam-5962	202	77	β	β	X
ejpam-5962	202	78	/	/	SYM
ejpam-5962	202	79	2	2	NUM
ejpam-5962	202	80	)	)	PUNCT
ejpam-5962	202	81	is	be	AUX
ejpam-5962	202	82	pairwise	pairwise	NOUN
ejpam-5962	202	83	compact	compact	ADJ
ejpam-5962	202	84	closed	close	VERB
ejpam-5962	202	85	space	space	NOUN
ejpam-5962	202	86	.	.	PUNCT
ejpam-5962	203	1	define	define	VERB
ejpam-5962	203	2	ϑ	ϑ	PROPN
ejpam-5962	203	3	/	/	SYM
ejpam-5962	203	4	1	1	NUM
ejpam-5962	203	5	=	=	NOUN
ejpam-5962	203	6	{	{	PUNCT
ejpam-5962	203	7	φ−1(b	φ−1(b	PROPN
ejpam-5962	203	8	)	)	PUNCT
ejpam-5962	203	9	:	:	PUNCT
ejpam-5962	204	1	b	b	X
ejpam-5962	204	2	∈	∈	ADP
ejpam-5962	204	3	β	β	X
ejpam-5962	204	4	/	/	SYM
ejpam-5962	204	5	1	1	NUM
ejpam-5962	204	6	}	}	PUNCT
ejpam-5962	204	7	is	be	AUX
ejpam-5962	204	8	a	a	DET
ejpam-5962	204	9	topology	topology	NOUN
ejpam-5962	204	10	in	in	ADP
ejpam-5962	204	11	z	z	NOUN
ejpam-5962	204	12	such	such	ADJ
ejpam-5962	204	13	that	that	SCONJ
ejpam-5962	204	14	ϑ	ϑ	PROPN
ejpam-5962	204	15	/	/	SYM
ejpam-5962	204	16	1	1	NUM
ejpam-5962	204	17	≤	≤	NOUN
ejpam-5962	204	18	ϑ1	ϑ1	NOUN
ejpam-5962	204	19	and	and	CCONJ
ejpam-5962	204	20	τ	τ	PROPN
ejpam-5962	204	21	/	/	SYM
ejpam-5962	204	22	2	2	NUM
ejpam-5962	204	23	=	=	SYM
ejpam-5962	204	24	{	{	PUNCT
ejpam-5962	204	25	φ−1(a	φ−1(a	PROPN
ejpam-5962	204	26	)	)	PUNCT
ejpam-5962	204	27	:	:	PUNCT
ejpam-5962	204	28	a	a	DET
ejpam-5962	204	29	∈	∈	PROPN
ejpam-5962	204	30	β	β	X
ejpam-5962	204	31	/	/	SYM
ejpam-5962	204	32	2	2	NUM
ejpam-5962	204	33	}	}	PUNCT
ejpam-5962	204	34	is	be	AUX
ejpam-5962	204	35	a	a	DET
ejpam-5962	204	36	topology	topology	NOUN
ejpam-5962	204	37	in	in	ADP
ejpam-5962	204	38	z	z	NOUN
ejpam-5962	204	39	such	such	ADJ
ejpam-5962	204	40	that	that	SCONJ
ejpam-5962	204	41	ϑ	ϑ	PROPN
ejpam-5962	204	42	/	/	SYM
ejpam-5962	204	43	2	2	NUM
ejpam-5962	204	44	≤	≤	NOUN
ejpam-5962	204	45	ϑ2	ϑ2	NOUN
ejpam-5962	204	46	and	and	CCONJ
ejpam-5962	204	47	so	so	ADV
ejpam-5962	204	48	(	(	PUNCT
ejpam-5962	204	49	z	z	NOUN
ejpam-5962	204	50	,	,	PUNCT
ejpam-5962	204	51	ϑ	ϑ	X
ejpam-5962	204	52	/	/	SYM
ejpam-5962	204	53	1	1	NUM
ejpam-5962	204	54	,	,	PUNCT
ejpam-5962	204	55	ϑ	ϑ	X
ejpam-5962	204	56	/	/	SYM
ejpam-5962	204	57	2	2	NUM
ejpam-5962	204	58	)	)	PUNCT
ejpam-5962	204	59	is	be	AUX
ejpam-5962	204	60	pairwise	pairwise	PROPN
ejpam-5962	204	61	compact	compact	ADJ
ejpam-5962	204	62	closed	close	VERB
ejpam-5962	204	63	spacewhich	spacewhich	NOUN
ejpam-5962	204	64	is	be	AUX
ejpam-5962	204	65	in	in	ADP
ejpam-5962	204	66	opposition	opposition	NOUN
ejpam-5962	204	67	to	to	ADP
ejpam-5962	204	68	(	(	PUNCT
ejpam-5962	204	69	z	z	NOUN
ejpam-5962	204	70	,	,	PUNCT
ejpam-5962	204	71	ϑ1	ϑ1	NOUN
ejpam-5962	204	72	,	,	PUNCT
ejpam-5962	204	73	ϑ2	ϑ2	PROPN
ejpam-5962	204	74	)	)	PUNCT
ejpam-5962	204	75	is	be	AUX
ejpam-5962	204	76	pairwise	pairwise	NOUN
ejpam-5962	204	77	minimal	minimal	ADJ
ejpam-5962	204	78	compact	compact	ADJ
ejpam-5962	204	79	closed	closed	ADJ
ejpam-5962	204	80	space	space	NOUN
ejpam-5962	204	81	.	.	PUNCT
ejpam-5962	205	1	hence	hence	ADV
ejpam-5962	205	2	(	(	PUNCT
ejpam-5962	205	3	n	n	CCONJ
ejpam-5962	205	4	,	,	PUNCT
ejpam-5962	205	5	β1	β1	PROPN
ejpam-5962	205	6	,	,	PUNCT
ejpam-5962	205	7	β2	β2	NOUN
ejpam-5962	205	8	)	)	PUNCT
ejpam-5962	205	9	is	be	AUX
ejpam-5962	205	10	pairwise	pairwise	NOUN
ejpam-5962	205	11	minimal	minimal	ADJ
ejpam-5962	205	12	compact	compact	ADJ
ejpam-5962	205	13	closed	closed	ADJ
ejpam-5962	205	14	space	space	NOUN
ejpam-5962	205	15	.	.	PUNCT
ejpam-5962	206	1	theorem	theorem	VERB
ejpam-5962	206	2	5.3	5.3	NUM
ejpam-5962	206	3	.	.	PUNCT
ejpam-5962	207	1	in	in	ADP
ejpam-5962	207	2	the	the	DET
ejpam-5962	207	3	event	event	NOUN
ejpam-5962	207	4	that	that	SCONJ
ejpam-5962	207	5	(	(	PUNCT
ejpam-5962	207	6	z1	z1	PROPN
ejpam-5962	207	7	×z2	×z2	PROPN
ejpam-5962	207	8	,	,	PUNCT
ejpam-5962	207	9	ϑ1	ϑ1	PROPN
ejpam-5962	207	10	×	×	NOUN
ejpam-5962	207	11	ϑ1	ϑ1	NOUN
ejpam-5962	207	12	,	,	PUNCT
ejpam-5962	207	13	ϑ2	ϑ2	PROPN
ejpam-5962	207	14	×	×	NOUN
ejpam-5962	207	15	ϑ2	ϑ2	NOUN
ejpam-5962	207	16	)	)	PUNCT
ejpam-5962	207	17	is	be	AUX
ejpam-5962	207	18	pairwise	pairwise	NOUN
ejpam-5962	207	19	compact	compact	ADJ
ejpam-5962	207	20	closed	close	VERB
ejpam-5962	207	21	space	space	NOUN
ejpam-5962	207	22	.	.	PUNCT
ejpam-5962	208	1	subsequently	subsequently	ADV
ejpam-5962	208	2	,	,	PUNCT
ejpam-5962	208	3	each	each	PRON
ejpam-5962	208	4	(	(	PUNCT
ejpam-5962	208	5	z1	z1	PROPN
ejpam-5962	208	6	,	,	PUNCT
ejpam-5962	208	7	ϑ1	ϑ1	NOUN
ejpam-5962	208	8	,	,	PUNCT
ejpam-5962	208	9	ϑ2	ϑ2	PROPN
ejpam-5962	208	10	)	)	PUNCT
ejpam-5962	208	11	,	,	PUNCT
ejpam-5962	208	12	(	(	PUNCT
ejpam-5962	208	13	z2	z2	NOUN
ejpam-5962	208	14	,	,	PUNCT
ejpam-5962	208	15	ϑ1	ϑ1	NOUN
ejpam-5962	208	16	,	,	PUNCT
ejpam-5962	208	17	ϑ2	ϑ2	PROPN
ejpam-5962	208	18	)	)	PUNCT
ejpam-5962	208	19	is	be	AUX
ejpam-5962	208	20	pairwise	pairwise	NOUN
ejpam-5962	208	21	minimal	minimal	ADJ
ejpam-5962	208	22	compact	compact	ADJ
ejpam-5962	208	23	closed	closed	ADJ
ejpam-5962	208	24	space	space	NOUN
ejpam-5962	208	25	.	.	PUNCT
ejpam-5962	209	1	proof	proof	NOUN
ejpam-5962	209	2	.	.	PUNCT
ejpam-5962	210	1	because	because	SCONJ
ejpam-5962	210	2	(	(	PUNCT
ejpam-5962	210	3	z1×z2	z1×z2	PROPN
ejpam-5962	210	4	,	,	PUNCT
ejpam-5962	210	5	ϑ1×ϑ1	ϑ1×ϑ1	PROPN
ejpam-5962	210	6	,	,	PUNCT
ejpam-5962	210	7	ϑ2	ϑ2	PROPN
ejpam-5962	210	8	×ϑ2	×ϑ2	PROPN
ejpam-5962	210	9	)	)	PUNCT
ejpam-5962	210	10	is	be	AUX
ejpam-5962	210	11	pairwise	pairwise	NOUN
ejpam-5962	210	12	compact	compact	ADJ
ejpam-5962	210	13	,	,	PUNCT
ejpam-5962	210	14	then	then	ADV
ejpam-5962	210	15	each	each	PRON
ejpam-5962	210	16	(	(	PUNCT
ejpam-5962	210	17	z1	z1	PROPN
ejpam-5962	210	18	,	,	PUNCT
ejpam-5962	210	19	ϑ1	ϑ1	NOUN
ejpam-5962	210	20	,	,	PUNCT
ejpam-5962	210	21	ϑ2	ϑ2	PROPN
ejpam-5962	210	22	)	)	PUNCT
ejpam-5962	210	23	,	,	PUNCT
ejpam-5962	210	24	(	(	PUNCT
ejpam-5962	210	25	z2	z2	NOUN
ejpam-5962	210	26	,	,	PUNCT
ejpam-5962	210	27	ϑ1	ϑ1	NOUN
ejpam-5962	210	28	,	,	PUNCT
ejpam-5962	210	29	ϑ2	ϑ2	PROPN
ejpam-5962	210	30	)	)	PUNCT
ejpam-5962	210	31	is	be	AUX
ejpam-5962	210	32	pairwise	pairwise	NOUN
ejpam-5962	210	33	compact	compact	ADJ
ejpam-5962	210	34	too	too	ADV
ejpam-5962	210	35	.	.	PUNCT
ejpam-5962	211	1	in	in	ADP
ejpam-5962	211	2	the	the	DET
ejpam-5962	211	3	event	event	NOUN
ejpam-5962	211	4	that	that	SCONJ
ejpam-5962	211	5	{	{	PUNCT
ejpam-5962	211	6	z2	z2	NOUN
ejpam-5962	211	7	}	}	PUNCT
ejpam-5962	211	8	be	be	AUX
ejpam-5962	211	9	a	a	DET
ejpam-5962	211	10	fixed	fix	VERB
ejpam-5962	211	11	element	element	NOUN
ejpam-5962	211	12	in	in	ADP
ejpam-5962	211	13	(	(	PUNCT
ejpam-5962	211	14	z2	z2	PROPN
ejpam-5962	211	15	,	,	PUNCT
ejpam-5962	211	16	ϑ1	ϑ1	NOUN
ejpam-5962	211	17	,	,	PUNCT
ejpam-5962	211	18	ϑ2	ϑ2	PROPN
ejpam-5962	211	19	)	)	PUNCT
ejpam-5962	211	20	,	,	PUNCT
ejpam-5962	211	21	then	then	ADV
ejpam-5962	211	22	(	(	PUNCT
ejpam-5962	211	23	z1	z1	ADJ
ejpam-5962	211	24	,	,	PUNCT
ejpam-5962	211	25	ϑ1	ϑ1	NOUN
ejpam-5962	211	26	,	,	PUNCT
ejpam-5962	211	27	ϑ2)×{z2	ϑ2)×{z2	X
ejpam-5962	211	28	}	}	PUNCT
ejpam-5962	211	29	is	be	AUX
ejpam-5962	211	30	a	a	DET
ejpam-5962	211	31	subspace	subspace	NOUN
ejpam-5962	211	32	of	of	ADP
ejpam-5962	211	33	(	(	PUNCT
ejpam-5962	211	34	z1×z2	z1×z2	PROPN
ejpam-5962	211	35	,	,	PUNCT
ejpam-5962	211	36	ϑ1×ϑ1	ϑ1×ϑ1	PROPN
ejpam-5962	211	37	,	,	PUNCT
ejpam-5962	211	38	ϑ2	ϑ2	PROPN
ejpam-5962	211	39	×ϑ2	×ϑ2	PROPN
ejpam-5962	211	40	)	)	PUNCT
ejpam-5962	211	41	.	.	PUNCT
ejpam-5962	212	1	in	in	ADP
ejpam-5962	212	2	light	light	NOUN
ejpam-5962	212	3	of	of	ADP
ejpam-5962	212	4	this	this	PRON
ejpam-5962	212	5	(	(	PUNCT
ejpam-5962	212	6	z1	z1	PROPN
ejpam-5962	212	7	,	,	PUNCT
ejpam-5962	212	8	ϑ1	ϑ1	PROPN
ejpam-5962	212	9	,	,	PUNCT
ejpam-5962	212	10	ϑ2)×	ϑ2)×	X
ejpam-5962	212	11	{	{	PUNCT
ejpam-5962	212	12	z2	z2	PROPN
ejpam-5962	212	13	}	}	PUNCT
ejpam-5962	212	14	is	be	AUX
ejpam-5962	212	15	pairwise	pairwise	NOUN
ejpam-5962	212	16	compact	compact	ADJ
ejpam-5962	212	17	compact	compact	ADJ
ejpam-5962	212	18	closed	close	VERB
ejpam-5962	212	19	space	space	NOUN
ejpam-5962	212	20	.	.	PUNCT
ejpam-5962	213	1	but	but	CCONJ
ejpam-5962	213	2	(	(	PUNCT
ejpam-5962	213	3	z1	z1	ADJ
ejpam-5962	213	4	,	,	PUNCT
ejpam-5962	213	5	ϑ1	ϑ1	NOUN
ejpam-5962	213	6	,	,	PUNCT
ejpam-5962	213	7	ϑ2	ϑ2	PROPN
ejpam-5962	213	8	)	)	PUNCT
ejpam-5962	213	9	is	be	AUX
ejpam-5962	213	10	pairwise	pairwise	NOUN
ejpam-5962	213	11	homomorphic	homomorphic	ADJ
ejpam-5962	213	12	to	to	ADP
ejpam-5962	213	13	(	(	PUNCT
ejpam-5962	213	14	z1	z1	PROPN
ejpam-5962	213	15	,	,	PUNCT
ejpam-5962	213	16	ϑ1	ϑ1	NOUN
ejpam-5962	213	17	,	,	PUNCT
ejpam-5962	213	18	ϑ2	ϑ2	PROPN
ejpam-5962	213	19	)	)	PUNCT
ejpam-5962	213	20	×	×	NOUN
ejpam-5962	213	21	{	{	PUNCT
ejpam-5962	213	22	z2	z2	PROPN
ejpam-5962	213	23	}	}	PUNCT
ejpam-5962	213	24	.	.	PUNCT
ejpam-5962	214	1	it	it	PRON
ejpam-5962	214	2	follows	follow	VERB
ejpam-5962	214	3	from	from	ADP
ejpam-5962	214	4	this	this	PRON
ejpam-5962	214	5	that	that	SCONJ
ejpam-5962	214	6	(	(	PUNCT
ejpam-5962	214	7	z1	z1	NOUN
ejpam-5962	214	8	,	,	PUNCT
ejpam-5962	214	9	ϑ1	ϑ1	NOUN
ejpam-5962	214	10	,	,	PUNCT
ejpam-5962	214	11	ϑ2	ϑ2	PROPN
ejpam-5962	214	12	)	)	PUNCT
ejpam-5962	214	13	is	be	AUX
ejpam-5962	214	14	pairwise	pairwise	NOUN
ejpam-5962	214	15	compact	compact	ADJ
ejpam-5962	214	16	compact	compact	ADJ
ejpam-5962	214	17	closed	close	VERB
ejpam-5962	214	18	space	space	NOUN
ejpam-5962	214	19	.	.	PUNCT
ejpam-5962	215	1	by	by	ADP
ejpam-5962	215	2	theorem	theorem	NOUN
ejpam-5962	215	3	5.1	5.1	NUM
ejpam-5962	215	4	,	,	PUNCT
ejpam-5962	215	5	(	(	PUNCT
ejpam-5962	215	6	z1	z1	NOUN
ejpam-5962	215	7	,	,	PUNCT
ejpam-5962	215	8	ϑ1	ϑ1	NOUN
ejpam-5962	215	9	,	,	PUNCT
ejpam-5962	215	10	ϑ2	ϑ2	PROPN
ejpam-5962	215	11	)	)	PUNCT
ejpam-5962	215	12	is	be	AUX
ejpam-5962	215	13	pairwise	pairwise	NOUN
ejpam-5962	215	14	minimal	minimal	ADJ
ejpam-5962	215	15	compact	compact	ADJ
ejpam-5962	215	16	closed	closed	ADJ
ejpam-5962	215	17	space	space	NOUN
ejpam-5962	215	18	.	.	PUNCT
ejpam-5962	216	1	also	also	ADV
ejpam-5962	216	2	,	,	PUNCT
ejpam-5962	216	3	we	we	PRON
ejpam-5962	216	4	can	can	AUX
ejpam-5962	216	5	demonstrate	demonstrate	VERB
ejpam-5962	216	6	that	that	SCONJ
ejpam-5962	216	7	(	(	PUNCT
ejpam-5962	216	8	z2	z2	PROPN
ejpam-5962	216	9	,	,	PUNCT
ejpam-5962	216	10	ϑ1	ϑ1	NOUN
ejpam-5962	216	11	,	,	PUNCT
ejpam-5962	216	12	ϑ2	ϑ2	PROPN
ejpam-5962	216	13	)	)	PUNCT
ejpam-5962	216	14	is	be	AUX
ejpam-5962	216	15	pairwise	pairwise	NOUN
ejpam-5962	216	16	minimal	minimal	ADJ
ejpam-5962	216	17	compact	compact	ADJ
ejpam-5962	216	18	closed	closed	ADJ
ejpam-5962	216	19	space	space	NOUN
ejpam-5962	216	20	.	.	PUNCT
ejpam-5962	217	1	corollary	corollary	ADJ
ejpam-5962	217	2	generalizations	generalization	NOUN
ejpam-5962	217	3	of	of	ADP
ejpam-5962	217	4	the	the	DET
ejpam-5962	217	5	theorem	theorem	ADJ
ejpam-5962	217	6	5.3	5.3	NUM
ejpam-5962	217	7	findings	finding	NOUN
ejpam-5962	217	8	are	be	AUX
ejpam-5962	217	9	as	as	SCONJ
ejpam-5962	217	10	follows	follow	VERB
ejpam-5962	217	11	.	.	PUNCT
ejpam-5962	218	1	corollary	corollary	ADJ
ejpam-5962	218	2	5.1	5.1	NUM
ejpam-5962	218	3	.	.	PUNCT
ejpam-5962	219	1	if	if	SCONJ
ejpam-5962	219	2	z	z	NOUN
ejpam-5962	219	3	=	=	SYM
ejpam-5962	219	4	∏	∏	NUM
ejpam-5962	219	5	ρ∈λ	ρ∈λ	NOUN
ejpam-5962	219	6	zρ	zρ	NOUN
ejpam-5962	219	7	is	be	AUX
ejpam-5962	219	8	a	a	DET
ejpam-5962	219	9	pairwise	pairwise	NOUN
ejpam-5962	219	10	compact	compact	ADJ
ejpam-5962	219	11	closed	close	VERB
ejpam-5962	219	12	space	space	NOUN
ejpam-5962	219	13	,	,	PUNCT
ejpam-5962	219	14	then	then	ADV
ejpam-5962	219	15	each	each	DET
ejpam-5962	219	16	zα	zα	PROPN
ejpam-5962	219	17	is	be	AUX
ejpam-5962	219	18	pairwise	pairwise	PROPN
ejpam-5962	219	19	minimal	minimal	ADJ
ejpam-5962	219	20	compact	compact	ADJ
ejpam-5962	219	21	closed	closed	ADJ
ejpam-5962	219	22	space	space	NOUN
ejpam-5962	219	23	,	,	PUNCT
ejpam-5962	219	24	for	for	ADP
ejpam-5962	219	25	each	each	DET
ejpam-5962	219	26	ρ	ρ	PROPN
ejpam-5962	219	27	∈	∈	PROPN
ejpam-5962	219	28	λ	λ	PROPN
ejpam-5962	219	29	.	.	PUNCT
ejpam-5962	219	30	theorem	theorem	PROPN
ejpam-5962	219	31	5.4	5.4	NUM
ejpam-5962	219	32	.	.	PUNCT
ejpam-5962	220	1	suppose	suppose	VERB
ejpam-5962	220	2	that	that	SCONJ
ejpam-5962	220	3	φ	φ	PROPN
ejpam-5962	220	4	:	:	PUNCT
ejpam-5962	220	5	(	(	PUNCT
ejpam-5962	220	6	z	z	NOUN
ejpam-5962	220	7	,	,	PUNCT
ejpam-5962	220	8	ϑ1	ϑ1	NOUN
ejpam-5962	220	9	,	,	PUNCT
ejpam-5962	220	10	ϑ2	ϑ2	PROPN
ejpam-5962	220	11	)	)	PUNCT
ejpam-5962	220	12	−−−−−−−−→	−−−−−−−−→	NOUN
ejpam-5962	220	13	onto	onto	ADP
ejpam-5962	220	14	closed	close	VERB
ejpam-5962	220	15	(	(	PUNCT
ejpam-5962	220	16	n	n	CCONJ
ejpam-5962	220	17	,	,	PUNCT
ejpam-5962	220	18	β1	β1	PROPN
ejpam-5962	220	19	,	,	PUNCT
ejpam-5962	220	20	β2	β2	PROPN
ejpam-5962	220	21	)	)	PUNCT
ejpam-5962	220	22	be	be	VERB
ejpam-5962	220	23	pairwise	pairwise	NOUN
ejpam-5962	220	24	continuous	continuous	ADJ
ejpam-5962	220	25	function	function	NOUN
ejpam-5962	220	26	.	.	PUNCT
ejpam-5962	221	1	whenever	whenever	SCONJ
ejpam-5962	221	2	(	(	PUNCT
ejpam-5962	221	3	z	z	NOUN
ejpam-5962	221	4	,	,	PUNCT
ejpam-5962	221	5	ϑ1	ϑ1	NOUN
ejpam-5962	221	6	,	,	PUNCT
ejpam-5962	221	7	ϑ2	ϑ2	PROPN
ejpam-5962	221	8	)	)	PUNCT
ejpam-5962	221	9	is	be	AUX
ejpam-5962	221	10	pairwise	pairwise	NOUN
ejpam-5962	221	11	minimal	minimal	ADJ
ejpam-5962	221	12	compact	compact	ADJ
ejpam-5962	221	13	closed	closed	ADJ
ejpam-5962	221	14	space	space	NOUN
ejpam-5962	221	15	,	,	PUNCT
ejpam-5962	221	16	then	then	ADV
ejpam-5962	221	17	(	(	PUNCT
ejpam-5962	221	18	n	n	X
ejpam-5962	221	19	,	,	PUNCT
ejpam-5962	221	20	β1	β1	PROPN
ejpam-5962	221	21	,	,	PUNCT
ejpam-5962	221	22	β2	β2	NOUN
ejpam-5962	221	23	)	)	PUNCT
ejpam-5962	221	24	is	be	AUX
ejpam-5962	221	25	true	true	ADJ
ejpam-5962	221	26	.	.	PUNCT
ejpam-5962	222	1	proof	proof	NOUN
ejpam-5962	222	2	.	.	PUNCT
ejpam-5962	223	1	theorem	theorem	VERB
ejpam-5962	223	2	4.1	4.1	NUM
ejpam-5962	223	3	is	be	AUX
ejpam-5962	223	4	sufficient	sufficient	ADJ
ejpam-5962	223	5	to	to	PART
ejpam-5962	223	6	establish	establish	VERB
ejpam-5962	223	7	that	that	SCONJ
ejpam-5962	223	8	(	(	PUNCT
ejpam-5962	223	9	n	n	X
ejpam-5962	223	10	,	,	PUNCT
ejpam-5962	223	11	β1	β1	PROPN
ejpam-5962	223	12	,	,	PUNCT
ejpam-5962	223	13	β2	β2	NOUN
ejpam-5962	223	14	)	)	PUNCT
ejpam-5962	223	15	is	be	AUX
ejpam-5962	223	16	pairwise	pairwise	NOUN
ejpam-5962	223	17	compact	compact	ADJ
ejpam-5962	223	18	closed	close	VERB
ejpam-5962	223	19	space	space	NOUN
ejpam-5962	223	20	.	.	PUNCT
ejpam-5962	224	1	suppose	suppose	VERB
ejpam-5962	224	2	u	u	PRON
ejpam-5962	224	3	is	be	AUX
ejpam-5962	224	4	β1−compact	β1−compact	PRON
ejpam-5962	224	5	set	set	VERB
ejpam-5962	224	6	in	in	ADP
ejpam-5962	224	7	(	(	PUNCT
ejpam-5962	224	8	n	n	CCONJ
ejpam-5962	224	9	,	,	PUNCT
ejpam-5962	224	10	β1	β1	PROPN
ejpam-5962	224	11	,	,	PUNCT
ejpam-5962	224	12	β2).to	β2).to	PART
ejpam-5962	224	13	demonstrate	demonstrate	VERB
ejpam-5962	224	14	that	that	SCONJ
ejpam-5962	224	15	(	(	PUNCT
ejpam-5962	224	16	n	n	X
ejpam-5962	224	17	,	,	PUNCT
ejpam-5962	224	18	β1	β1	PROPN
ejpam-5962	224	19	,	,	PUNCT
ejpam-5962	224	20	β2	β2	NOUN
ejpam-5962	224	21	)	)	PUNCT
ejpam-5962	224	22	is	be	AUX
ejpam-5962	224	23	β2−closed	β2−close	VERB
ejpam-5962	224	24	in	in	ADP
ejpam-5962	224	25	(	(	PUNCT
ejpam-5962	224	26	n	n	CCONJ
ejpam-5962	224	27	,	,	PUNCT
ejpam-5962	224	28	β1	β1	PROPN
ejpam-5962	224	29	,	,	PUNCT
ejpam-5962	224	30	β2).given	β2).given	SCONJ
ejpam-5962	224	31	that	that	SCONJ
ejpam-5962	224	32	φ	φ	PROPN
ejpam-5962	224	33	is	be	AUX
ejpam-5962	224	34	pairwise	pairwise	NOUN
ejpam-5962	224	35	closed	close	VERB
ejpam-5962	224	36	continuous	continuous	ADJ
ejpam-5962	224	37	function	function	NOUN
ejpam-5962	224	38	,	,	PUNCT
ejpam-5962	224	39	then	then	ADV
ejpam-5962	224	40	φ−1(z	φ−1(z	PROPN
ejpam-5962	224	41	)	)	PUNCT
ejpam-5962	224	42	is	be	AUX
ejpam-5962	224	43	ϑ1−compact	ϑ1−compact	NOUN
ejpam-5962	224	44	in	in	ADP
ejpam-5962	224	45	(	(	PUNCT
ejpam-5962	224	46	z	z	NOUN
ejpam-5962	224	47	,	,	PUNCT
ejpam-5962	224	48	ϑ1	ϑ1	NOUN
ejpam-5962	224	49	,	,	PUNCT
ejpam-5962	224	50	ϑ2	ϑ2	PROPN
ejpam-5962	224	51	)	)	PUNCT
ejpam-5962	224	52	,	,	PUNCT
ejpam-5962	224	53	and	and	CCONJ
ejpam-5962	224	54	although	although	SCONJ
ejpam-5962	224	55	(	(	PUNCT
ejpam-5962	224	56	z	z	NOUN
ejpam-5962	224	57	,	,	PUNCT
ejpam-5962	224	58	ϑ1	ϑ1	NOUN
ejpam-5962	224	59	,	,	PUNCT
ejpam-5962	224	60	ϑ2	ϑ2	PROPN
ejpam-5962	224	61	)	)	PUNCT
ejpam-5962	224	62	is	be	AUX
ejpam-5962	224	63	pairwise	pairwise	NOUN
ejpam-5962	224	64	minimal	minimal	ADJ
ejpam-5962	224	65	compact	compact	ADJ
ejpam-5962	224	66	closed	close	VERB
ejpam-5962	224	67	space	space	NOUN
ejpam-5962	224	68	,	,	PUNCT
ejpam-5962	224	69	so	so	CCONJ
ejpam-5962	224	70	(	(	PUNCT
ejpam-5962	224	71	z	z	NOUN
ejpam-5962	224	72	,	,	PUNCT
ejpam-5962	224	73	ϑ1	ϑ1	NOUN
ejpam-5962	224	74	,	,	PUNCT
ejpam-5962	224	75	ϑ2	ϑ2	PROPN
ejpam-5962	224	76	)	)	PUNCT
ejpam-5962	224	77	is	be	AUX
ejpam-5962	224	78	pairwise	pairwise	NOUN
ejpam-5962	224	79	minimal	minimal	ADJ
ejpam-5962	224	80	compact	compact	ADJ
ejpam-5962	224	81	closed	close	VERB
ejpam-5962	224	82	space	space	NOUN
ejpam-5962	224	83	so	so	SCONJ
ejpam-5962	224	84	φ−1(z	φ−1(z	NOUN
ejpam-5962	224	85	)	)	PUNCT
ejpam-5962	224	86	is	be	AUX
ejpam-5962	224	87	ϑ2	ϑ2	PROPN
ejpam-5962	224	88	−closed	−close	VERB
ejpam-5962	224	89	in	in	ADP
ejpam-5962	224	90	(	(	PUNCT
ejpam-5962	224	91	z	z	NOUN
ejpam-5962	224	92	,	,	PUNCT
ejpam-5962	224	93	ϑ1	ϑ1	NOUN
ejpam-5962	224	94	,	,	PUNCT
ejpam-5962	224	95	ϑ2	ϑ2	PROPN
ejpam-5962	224	96	)	)	PUNCT
ejpam-5962	224	97	.	.	PUNCT
ejpam-5962	225	1	however	however	ADV
ejpam-5962	225	2	,	,	PUNCT
ejpam-5962	225	3	because	because	SCONJ
ejpam-5962	225	4	φ	φ	PROPN
ejpam-5962	225	5	is	be	AUX
ejpam-5962	225	6	pairwise	pairwise	NOUN
ejpam-5962	225	7	onto	onto	ADP
ejpam-5962	225	8	,	,	PUNCT
ejpam-5962	225	9	so	so	ADV
ejpam-5962	225	10	φ	φ	PROPN
ejpam-5962	225	11	(	(	PUNCT
ejpam-5962	225	12	φ−1(u	φ−1(u	PROPN
ejpam-5962	225	13	)	)	PUNCT
ejpam-5962	226	1	=	=	SYM
ejpam-5962	226	2	u	u	PROPN
ejpam-5962	226	3	is	be	AUX
ejpam-5962	226	4	β2	β2	VERB
ejpam-5962	226	5	−closed	−close	VERB
ejpam-5962	226	6	in	in	ADP
ejpam-5962	226	7	(	(	PUNCT
ejpam-5962	226	8	n	n	CCONJ
ejpam-5962	226	9	,	,	PUNCT
ejpam-5962	226	10	β1	β1	NOUN
ejpam-5962	226	11	,	,	PUNCT
ejpam-5962	226	12	β2	β2	PROPN
ejpam-5962	226	13	)	)	PUNCT
ejpam-5962	226	14	.	.	PUNCT
ejpam-5962	227	1	similar	similar	ADJ
ejpam-5962	227	2	to	to	ADP
ejpam-5962	227	3	howv	howv	PROPN
ejpam-5962	227	4	is	be	AUX
ejpam-5962	227	5	β2−compact	β2−compact	NOUN
ejpam-5962	227	6	set	set	VERB
ejpam-5962	227	7	in	in	ADP
ejpam-5962	227	8	(	(	PUNCT
ejpam-5962	227	9	n	n	CCONJ
ejpam-5962	227	10	,	,	PUNCT
ejpam-5962	227	11	β1	β1	NOUN
ejpam-5962	227	12	,	,	PUNCT
ejpam-5962	227	13	β2	β2	NOUN
ejpam-5962	227	14	)	)	PUNCT
ejpam-5962	227	15	,	,	PUNCT
ejpam-5962	227	16	so	so	CCONJ
ejpam-5962	227	17	(	(	PUNCT
ejpam-5962	227	18	n	n	CCONJ
ejpam-5962	227	19	,	,	PUNCT
ejpam-5962	227	20	β1	β1	PROPN
ejpam-5962	227	21	,	,	PUNCT
ejpam-5962	227	22	β2	β2	NOUN
ejpam-5962	227	23	)	)	PUNCT
ejpam-5962	227	24	is	be	AUX
ejpam-5962	227	25	pairwise	pairwise	NOUN
ejpam-5962	227	26	compact	compact	ADJ
ejpam-5962	227	27	closed	close	VERB
ejpam-5962	227	28	space	space	NOUN
ejpam-5962	227	29	.	.	PUNCT
ejpam-5962	228	1	given	give	VERB
ejpam-5962	228	2	that	that	SCONJ
ejpam-5962	228	3	(	(	PUNCT
ejpam-5962	228	4	z	z	NOUN
ejpam-5962	228	5	,	,	PUNCT
ejpam-5962	228	6	ϑ1	ϑ1	NOUN
ejpam-5962	228	7	,	,	PUNCT
ejpam-5962	228	8	ϑ2	ϑ2	PROPN
ejpam-5962	228	9	)	)	PUNCT
ejpam-5962	228	10	is	be	AUX
ejpam-5962	228	11	pairwise	pairwise	NOUN
ejpam-5962	228	12	compact	compact	ADJ
ejpam-5962	228	13	and	and	CCONJ
ejpam-5962	228	14	φ	φ	PROPN
ejpam-5962	228	15	is	be	AUX
ejpam-5962	228	16	pairwise	pairwise	NOUN
ejpam-5962	228	17	onto	onto	ADP
ejpam-5962	228	18	closed	closed	ADJ
ejpam-5962	228	19	function	function	NOUN
ejpam-5962	228	20	φ(z	φ(z	PROPN
ejpam-5962	228	21	)	)	PUNCT
ejpam-5962	228	22	=	=	SYM
ejpam-5962	228	23	n	n	X
ejpam-5962	228	24	,	,	PUNCT
ejpam-5962	228	25	so	so	CCONJ
ejpam-5962	228	26	(	(	PUNCT
ejpam-5962	228	27	n	n	CCONJ
ejpam-5962	228	28	,	,	PUNCT
ejpam-5962	228	29	β1	β1	PROPN
ejpam-5962	228	30	,	,	PUNCT
ejpam-5962	228	31	β2	β2	NOUN
ejpam-5962	228	32	)	)	PUNCT
ejpam-5962	228	33	is	be	AUX
ejpam-5962	228	34	pairwise	pairwise	NOUN
ejpam-5962	228	35	compact	compact	ADJ
ejpam-5962	228	36	.	.	PUNCT
ejpam-5962	229	1	as	as	ADP
ejpam-5962	229	2	a	a	DET
ejpam-5962	229	3	result	result	NOUN
ejpam-5962	229	4	,	,	PUNCT
ejpam-5962	229	5	according	accord	VERB
ejpam-5962	229	6	to	to	ADP
ejpam-5962	229	7	theorem	theorem	ADJ
ejpam-5962	229	8	5.2	5.2	NUM
ejpam-5962	229	9	,	,	PUNCT
ejpam-5962	229	10	(	(	PUNCT
ejpam-5962	229	11	n	n	X
ejpam-5962	229	12	,	,	PUNCT
ejpam-5962	229	13	β1	β1	PROPN
ejpam-5962	229	14	,	,	PUNCT
ejpam-5962	229	15	β2	β2	NOUN
ejpam-5962	229	16	)	)	PUNCT
ejpam-5962	229	17	is	be	AUX
ejpam-5962	229	18	pairwise	pairwise	NOUN
ejpam-5962	229	19	minimal	minimal	ADJ
ejpam-5962	229	20	compact	compact	ADJ
ejpam-5962	229	21	closed	closed	ADJ
ejpam-5962	229	22	space	space	NOUN
ejpam-5962	229	23	.	.	PUNCT
ejpam-5962	230	1	theorem	theorem	VERB
ejpam-5962	230	2	5.5	5.5	NUM
ejpam-5962	230	3	.	.	PUNCT
ejpam-5962	231	1	if	if	SCONJ
ejpam-5962	231	2	ψ	ψ	X
ejpam-5962	231	3	:	:	PUNCT
ejpam-5962	231	4	(	(	PUNCT
ejpam-5962	231	5	n	n	X
ejpam-5962	231	6	,	,	PUNCT
ejpam-5962	231	7	β1	β1	NOUN
ejpam-5962	231	8	,	,	PUNCT
ejpam-5962	231	9	β2	β2	NOUN
ejpam-5962	231	10	)	)	PUNCT
ejpam-5962	231	11	→	→	SYM
ejpam-5962	231	12	(	(	PUNCT
ejpam-5962	231	13	z	z	NOUN
ejpam-5962	231	14	,	,	PUNCT
ejpam-5962	231	15	ϑ1	ϑ1	NOUN
ejpam-5962	231	16	,	,	PUNCT
ejpam-5962	231	17	ϑ2	ϑ2	PROPN
ejpam-5962	231	18	)	)	PUNCT
ejpam-5962	231	19	is	be	AUX
ejpam-5962	231	20	pairwise	pairwise	NOUN
ejpam-5962	231	21	hoemorphism	hoemorphism	NOUN
ejpam-5962	231	22	,	,	PUNCT
ejpam-5962	231	23	then	then	ADV
ejpam-5962	231	24	(	(	PUNCT
ejpam-5962	231	25	z	z	NOUN
ejpam-5962	231	26	,	,	PUNCT
ejpam-5962	231	27	ϑ1	ϑ1	NOUN
ejpam-5962	231	28	,	,	PUNCT
ejpam-5962	231	29	ϑ2	ϑ2	PROPN
ejpam-5962	231	30	)	)	PUNCT
ejpam-5962	231	31	,	,	PUNCT
ejpam-5962	231	32	(	(	PUNCT
ejpam-5962	231	33	n	n	CCONJ
ejpam-5962	231	34	,	,	PUNCT
ejpam-5962	231	35	β	β	X
ejpam-5962	231	36	\	\	PROPN
ejpam-5962	231	37	1	1	NUM
ejpam-5962	231	38	,	,	PUNCT
ejpam-5962	231	39	β	β	NOUN
ejpam-5962	231	40	\	\	PROPN
ejpam-5962	231	41	2	2	NUM
ejpam-5962	231	42	)	)	PUNCT
ejpam-5962	231	43	is	be	AUX
ejpam-5962	231	44	pairwise	pairwise	NOUN
ejpam-5962	231	45	compact	compact	ADJ
ejpam-5962	231	46	closed	close	VERB
ejpam-5962	231	47	space	space	NOUN
ejpam-5962	231	48	,	,	PUNCT
ejpam-5962	231	49	while	while	SCONJ
ejpam-5962	231	50	else	else	ADV
ejpam-5962	231	51	(	(	PUNCT
ejpam-5962	231	52	z	z	NOUN
ejpam-5962	231	53	,	,	PUNCT
ejpam-5962	231	54	ϑ1	ϑ1	NOUN
ejpam-5962	231	55	,	,	PUNCT
ejpam-5962	231	56	ϑ2	ϑ2	PROPN
ejpam-5962	231	57	)	)	PUNCT
ejpam-5962	231	58	is	be	AUX
ejpam-5962	231	59	pairwise	pairwise	NOUN
ejpam-5962	231	60	compact	compact	ADJ
ejpam-5962	231	61	open	open	ADJ
ejpam-5962	231	62	space	space	NOUN
ejpam-5962	231	63	.	.	PUNCT
ejpam-5962	232	1	a.	a.	NOUN
ejpam-5962	232	2	a.	a.	PROPN
ejpam-5962	232	3	atoom	atoom	PROPN
ejpam-5962	232	4	et	et	PROPN
ejpam-5962	232	5	al	al	PROPN
ejpam-5962	232	6	.	.	PUNCT
ejpam-5962	232	7	/	/	SYM
ejpam-5962	232	8	eur	eur	PROPN
ejpam-5962	232	9	.	.	PUNCT
ejpam-5962	233	1	j.	j.	PROPN
ejpam-5962	233	2	pure	pure	PROPN
ejpam-5962	233	3	appl	appl	PROPN
ejpam-5962	233	4	.	.	PROPN
ejpam-5962	233	5	math	math	PROPN
ejpam-5962	233	6	,	,	PUNCT
ejpam-5962	233	7	18	18	NUM
ejpam-5962	233	8	(	(	PUNCT
ejpam-5962	233	9	2	2	NUM
ejpam-5962	233	10	)	)	PUNCT
ejpam-5962	233	11	(	(	PUNCT
ejpam-5962	233	12	2025	2025	NUM
ejpam-5962	233	13	)	)	PUNCT
ejpam-5962	233	14	,	,	PUNCT
ejpam-5962	233	15	5962	5962	NUM
ejpam-5962	233	16	9	9	NUM
ejpam-5962	233	17	of	of	ADP
ejpam-5962	233	18	17	17	NUM
ejpam-5962	233	19	proof	proof	NOUN
ejpam-5962	233	20	.	.	PUNCT
ejpam-5962	234	1	assuming	assume	VERB
ejpam-5962	234	2	(	(	PUNCT
ejpam-5962	234	3	z	z	NOUN
ejpam-5962	234	4	,	,	PUNCT
ejpam-5962	234	5	ϑ1	ϑ1	NOUN
ejpam-5962	234	6	,	,	PUNCT
ejpam-5962	234	7	ϑ2	ϑ2	PROPN
ejpam-5962	234	8	)	)	PUNCT
ejpam-5962	234	9	be	be	AUX
ejpam-5962	234	10	pairwise	pairwise	NOUN
ejpam-5962	234	11	compact	compact	ADJ
ejpam-5962	234	12	closed	close	VERB
ejpam-5962	234	13	space	space	NOUN
ejpam-5962	234	14	,	,	PUNCT
ejpam-5962	234	15	and	and	CCONJ
ejpam-5962	234	16	a	a	DET
ejpam-5962	234	17	function	function	NOUN
ejpam-5962	234	18	ψ	ψ	X
ejpam-5962	234	19	:	:	PUNCT
ejpam-5962	234	20	(	(	PUNCT
ejpam-5962	234	21	n	n	X
ejpam-5962	234	22	,	,	PUNCT
ejpam-5962	234	23	β1	β1	NOUN
ejpam-5962	234	24	,	,	PUNCT
ejpam-5962	234	25	β2	β2	NOUN
ejpam-5962	234	26	)	)	PUNCT
ejpam-5962	234	27	→	→	SYM
ejpam-5962	234	28	(	(	PUNCT
ejpam-5962	234	29	z	z	NOUN
ejpam-5962	234	30	,	,	PUNCT
ejpam-5962	234	31	ϑ1	ϑ1	NOUN
ejpam-5962	234	32	,	,	PUNCT
ejpam-5962	234	33	ϑ2	ϑ2	PROPN
ejpam-5962	234	34	)	)	PUNCT
ejpam-5962	234	35	be	be	VERB
ejpam-5962	234	36	a	a	DET
ejpam-5962	234	37	pairwise	pairwise	NOUN
ejpam-5962	234	38	continuous	continuous	ADJ
ejpam-5962	234	39	function	function	NOUN
ejpam-5962	234	40	therefore	therefore	ADV
ejpam-5962	234	41	(	(	PUNCT
ejpam-5962	234	42	n	n	X
ejpam-5962	234	43	,	,	PUNCT
ejpam-5962	234	44	β	β	X
ejpam-5962	234	45	\	\	PROPN
ejpam-5962	234	46	1	1	NUM
ejpam-5962	234	47	,	,	PUNCT
ejpam-5962	234	48	β	β	NOUN
ejpam-5962	234	49	\	\	PROPN
ejpam-5962	234	50	2	2	NUM
ejpam-5962	234	51	)	)	PUNCT
ejpam-5962	234	52	be	be	AUX
ejpam-5962	234	53	pairwise	pairwise	NOUN
ejpam-5962	234	54	compact	compact	ADJ
ejpam-5962	234	55	.	.	PUNCT
ejpam-5962	235	1	in	in	ADP
ejpam-5962	235	2	order	order	NOUN
ejpam-5962	235	3	to	to	PART
ejpam-5962	235	4	demonstrate	demonstrate	VERB
ejpam-5962	235	5	ψ	ψ	NOUN
ejpam-5962	235	6	is	be	AUX
ejpam-5962	235	7	pairwise	pairwise	NOUN
ejpam-5962	235	8	hoemorphism	hoemorphism	NOUN
ejpam-5962	235	9	.	.	PUNCT
ejpam-5962	236	1	let	let	VERB
ejpam-5962	236	2	u	u	PRON
ejpam-5962	236	3	be	be	AUX
ejpam-5962	236	4	any	any	DET
ejpam-5962	236	5	β1−compact	β1−compact	NOUN
ejpam-5962	236	6	in	in	ADP
ejpam-5962	236	7	(	(	PUNCT
ejpam-5962	236	8	n	n	CCONJ
ejpam-5962	236	9	,	,	PUNCT
ejpam-5962	236	10	β1	β1	NOUN
ejpam-5962	236	11	,	,	PUNCT
ejpam-5962	236	12	β2	β2	PROPN
ejpam-5962	236	13	)	)	PUNCT
ejpam-5962	236	14	,	,	PUNCT
ejpam-5962	236	15	then	then	ADV
ejpam-5962	236	16	u	u	NOUN
ejpam-5962	236	17	is	be	AUX
ejpam-5962	236	18	β2−closed	β2−close	VERB
ejpam-5962	236	19	set	set	VERB
ejpam-5962	236	20	.	.	PUNCT
ejpam-5962	237	1	due	due	ADP
ejpam-5962	237	2	to	to	ADP
ejpam-5962	237	3	the	the	DET
ejpam-5962	237	4	fact	fact	NOUN
ejpam-5962	237	5	that	that	SCONJ
ejpam-5962	237	6	(	(	PUNCT
ejpam-5962	237	7	z	z	X
ejpam-5962	237	8	,	,	PUNCT
ejpam-5962	237	9	ϑ1	ϑ1	NOUN
ejpam-5962	237	10	,	,	PUNCT
ejpam-5962	237	11	ϑ2	ϑ2	PROPN
ejpam-5962	237	12	)	)	PUNCT
ejpam-5962	237	13	is	be	AUX
ejpam-5962	237	14	pairwise	pairwise	NOUN
ejpam-5962	237	15	compact	compact	ADJ
ejpam-5962	237	16	closed	close	VERB
ejpam-5962	237	17	space	space	NOUN
ejpam-5962	237	18	,	,	PUNCT
ejpam-5962	237	19	then	then	ADV
ejpam-5962	237	20	ψ(u	ψ(u	PROPN
ejpam-5962	237	21	)	)	PUNCT
ejpam-5962	237	22	=	=	PUNCT
ejpam-5962	237	23	(	(	PUNCT
ejpam-5962	237	24	ψ−1)−1(u	ψ−1)−1(u	PROPN
ejpam-5962	237	25	)	)	PUNCT
ejpam-5962	237	26	is	be	AUX
ejpam-5962	237	27	ϑ2−compact	ϑ2−compact	NOUN
ejpam-5962	237	28	in	in	ADP
ejpam-5962	237	29	(	(	PUNCT
ejpam-5962	237	30	z	z	NOUN
ejpam-5962	237	31	,	,	PUNCT
ejpam-5962	237	32	ϑ1	ϑ1	NOUN
ejpam-5962	237	33	,	,	PUNCT
ejpam-5962	237	34	ϑ2	ϑ2	PROPN
ejpam-5962	237	35	)	)	PUNCT
ejpam-5962	237	36	and	and	CCONJ
ejpam-5962	237	37	ψ(u	ψ(u	PROPN
ejpam-5962	237	38	)	)	PUNCT
ejpam-5962	237	39	is	be	AUX
ejpam-5962	237	40	ϑ1−closed	ϑ1−close	VERB
ejpam-5962	237	41	in	in	ADP
ejpam-5962	237	42	(	(	PUNCT
ejpam-5962	237	43	z	z	NOUN
ejpam-5962	237	44	,	,	PUNCT
ejpam-5962	237	45	ϑ1	ϑ1	NOUN
ejpam-5962	237	46	,	,	PUNCT
ejpam-5962	237	47	ϑ2	ϑ2	PROPN
ejpam-5962	237	48	)	)	PUNCT
ejpam-5962	237	49	,	,	PUNCT
ejpam-5962	237	50	as	as	ADP
ejpam-5962	237	51	a	a	DET
ejpam-5962	237	52	result	result	NOUN
ejpam-5962	237	53	ψ−1	ψ−1	PROPN
ejpam-5962	237	54	:	:	PUNCT
ejpam-5962	237	55	(	(	PUNCT
ejpam-5962	237	56	z	z	NOUN
ejpam-5962	237	57	,	,	PUNCT
ejpam-5962	237	58	ϑ1	ϑ1	NOUN
ejpam-5962	237	59	,	,	PUNCT
ejpam-5962	237	60	ϑ2	ϑ2	PROPN
ejpam-5962	237	61	)	)	PUNCT
ejpam-5962	237	62	→	→	SYM
ejpam-5962	237	63	(	(	PUNCT
ejpam-5962	237	64	y	y	PROPN
ejpam-5962	237	65	,	,	PUNCT
ejpam-5962	237	66	σ1	σ1	PROPN
ejpam-5962	237	67	,	,	PUNCT
ejpam-5962	237	68	σ2	σ2	PROPN
ejpam-5962	237	69	)	)	PUNCT
ejpam-5962	237	70	is	be	AUX
ejpam-5962	237	71	pairwise	pairwise	NOUN
ejpam-5962	237	72	continuous	continuous	ADJ
ejpam-5962	237	73	function	function	NOUN
ejpam-5962	237	74	,	,	PUNCT
ejpam-5962	237	75	yet	yet	CCONJ
ejpam-5962	237	76	ψ	ψ	X
ejpam-5962	237	77	is	be	AUX
ejpam-5962	237	78	pairwise	pairwise	NOUN
ejpam-5962	237	79	continuous	continuous	ADJ
ejpam-5962	237	80	function	function	NOUN
ejpam-5962	237	81	.	.	PUNCT
ejpam-5962	238	1	thus	thus	ADV
ejpam-5962	238	2	,	,	PUNCT
ejpam-5962	238	3	ψ	ψ	X
ejpam-5962	238	4	is	be	AUX
ejpam-5962	238	5	pairwise	pairwise	NOUN
ejpam-5962	238	6	hoemorphism	hoemorphism	NOUN
ejpam-5962	238	7	.	.	PUNCT
ejpam-5962	239	1	in	in	ADP
ejpam-5962	239	2	order	order	NOUN
ejpam-5962	239	3	to	to	PART
ejpam-5962	239	4	demonstrate	demonstrate	VERB
ejpam-5962	239	5	that	that	SCONJ
ejpam-5962	239	6	(	(	PUNCT
ejpam-5962	239	7	z	z	NOUN
ejpam-5962	239	8	,	,	PUNCT
ejpam-5962	239	9	ϑ1	ϑ1	NOUN
ejpam-5962	239	10	,	,	PUNCT
ejpam-5962	239	11	ϑ2	ϑ2	PROPN
ejpam-5962	239	12	)	)	PUNCT
ejpam-5962	239	13	is	be	AUX
ejpam-5962	239	14	pairwise	pairwise	NOUN
ejpam-5962	239	15	compact	compact	ADJ
ejpam-5962	239	16	compact	compact	ADJ
ejpam-5962	239	17	closed	close	VERB
ejpam-5962	239	18	space	space	NOUN
ejpam-5962	239	19	.	.	PUNCT
ejpam-5962	240	1	allowing	allow	VERB
ejpam-5962	240	2	the	the	DET
ejpam-5962	240	3	pairwise	pairwise	NOUN
ejpam-5962	240	4	continuous	continuous	ADJ
ejpam-5962	240	5	function	function	NOUN
ejpam-5962	240	6	ψ	ψ	NOUN
ejpam-5962	240	7	:	:	PUNCT
ejpam-5962	240	8	(	(	PUNCT
ejpam-5962	240	9	n	n	X
ejpam-5962	240	10	,	,	PUNCT
ejpam-5962	240	11	β1	β1	NOUN
ejpam-5962	240	12	,	,	PUNCT
ejpam-5962	240	13	β2	β2	NOUN
ejpam-5962	240	14	)	)	PUNCT
ejpam-5962	240	15	→	→	SYM
ejpam-5962	240	16	(	(	PUNCT
ejpam-5962	240	17	z	z	NOUN
ejpam-5962	240	18	,	,	PUNCT
ejpam-5962	240	19	ϑ1	ϑ1	NOUN
ejpam-5962	240	20	,	,	PUNCT
ejpam-5962	240	21	ϑ2	ϑ2	PROPN
ejpam-5962	240	22	)	)	PUNCT
ejpam-5962	240	23	is	be	AUX
ejpam-5962	240	24	pairwise	pairwise	NOUN
ejpam-5962	240	25	hoemorphism	hoemorphism	NOUN
ejpam-5962	240	26	.	.	PUNCT
ejpam-5962	241	1	because	because	SCONJ
ejpam-5962	241	2	every	every	DET
ejpam-5962	241	3	pairwise	pairwise	NOUN
ejpam-5962	241	4	minimal	minimal	ADJ
ejpam-5962	241	5	compact	compact	ADJ
ejpam-5962	241	6	closed	close	VERB
ejpam-5962	241	7	space	space	NOUN
ejpam-5962	241	8	is	be	AUX
ejpam-5962	241	9	pairwise	pairwise	NOUN
ejpam-5962	241	10	compact	compact	ADJ
ejpam-5962	241	11	closed	close	VERB
ejpam-5962	241	12	space	space	NOUN
ejpam-5962	241	13	.	.	PUNCT
ejpam-5962	242	1	it	it	PRON
ejpam-5962	242	2	is	be	AUX
ejpam-5962	242	3	sufficient	sufficient	ADJ
ejpam-5962	242	4	to	to	PART
ejpam-5962	242	5	demonstrate	demonstrate	VERB
ejpam-5962	242	6	that	that	SCONJ
ejpam-5962	242	7	(	(	PUNCT
ejpam-5962	242	8	z	z	NOUN
ejpam-5962	242	9	,	,	PUNCT
ejpam-5962	242	10	ϑ1	ϑ1	NOUN
ejpam-5962	242	11	,	,	PUNCT
ejpam-5962	242	12	ϑ2	ϑ2	PROPN
ejpam-5962	242	13	)	)	PUNCT
ejpam-5962	242	14	is	be	AUX
ejpam-5962	242	15	pairwise	pairwise	NOUN
ejpam-5962	242	16	minimal	minimal	ADJ
ejpam-5962	242	17	compact	compact	ADJ
ejpam-5962	242	18	closed	closed	ADJ
ejpam-5962	242	19	space	space	NOUN
ejpam-5962	242	20	.	.	PUNCT
ejpam-5962	243	1	take	take	VERB
ejpam-5962	243	2	(	(	PUNCT
ejpam-5962	243	3	z	z	NOUN
ejpam-5962	243	4	,	,	PUNCT
ejpam-5962	243	5	ϑ1	ϑ1	NOUN
ejpam-5962	243	6	,	,	PUNCT
ejpam-5962	243	7	ϑ2	ϑ2	PROPN
ejpam-5962	243	8	)	)	PUNCT
ejpam-5962	243	9	⊂	⊂	PROPN
ejpam-5962	243	10	(	(	PUNCT
ejpam-5962	243	11	z	z	X
ejpam-5962	243	12	,	,	PUNCT
ejpam-5962	243	13	ϑ	ϑ	X
ejpam-5962	243	14	\	\	PROPN
ejpam-5962	243	15	1	1	NUM
ejpam-5962	243	16	,	,	PUNCT
ejpam-5962	243	17	ϑ	ϑ	X
ejpam-5962	243	18	\	\	PROPN
ejpam-5962	243	19	2	2	NUM
ejpam-5962	243	20	)	)	PUNCT
ejpam-5962	243	21	,	,	PUNCT
ejpam-5962	243	22	it	it	PRON
ejpam-5962	243	23	is	be	AUX
ejpam-5962	243	24	mean	mean	VERB
ejpam-5962	244	1	ϑ1	ϑ1	PROPN
ejpam-5962	244	2	⊂	⊂	PROPN
ejpam-5962	244	3	ϑ	ϑ	X
ejpam-5962	244	4	\	\	PROPN
ejpam-5962	244	5	1	1	NUM
ejpam-5962	244	6	,	,	PUNCT
ejpam-5962	244	7	ϑ2	ϑ2	PROPN
ejpam-5962	244	8	⊂	⊂	PROPN
ejpam-5962	244	9	ϑ	ϑ	X
ejpam-5962	244	10	\	\	PROPN
ejpam-5962	244	11	2	2	NUM
ejpam-5962	244	12	and	and	CCONJ
ejpam-5962	244	13	λ:(z	λ:(z	PROPN
ejpam-5962	244	14	,	,	PUNCT
ejpam-5962	244	15	ϑ1	ϑ1	NOUN
ejpam-5962	244	16	,	,	PUNCT
ejpam-5962	244	17	ϑ2	ϑ2	PROPN
ejpam-5962	244	18	)	)	PUNCT
ejpam-5962	244	19	→	→	SYM
ejpam-5962	244	20	(	(	PUNCT
ejpam-5962	244	21	z	z	NOUN
ejpam-5962	244	22	,	,	PUNCT
ejpam-5962	244	23	ϑ	ϑ	X
ejpam-5962	244	24	\	\	PROPN
ejpam-5962	244	25	1	1	NUM
ejpam-5962	244	26	,	,	PUNCT
ejpam-5962	244	27	ϑ	ϑ	X
ejpam-5962	244	28	\	\	PROPN
ejpam-5962	244	29	2	2	NUM
ejpam-5962	244	30	)	)	PUNCT
ejpam-5962	244	31	be	be	AUX
ejpam-5962	244	32	pairwise	pairwise	NOUN
ejpam-5962	244	33	continuous	continuous	ADJ
ejpam-5962	244	34	function	function	NOUN
ejpam-5962	244	35	,	,	PUNCT
ejpam-5962	244	36	nevertheless	nevertheless	ADV
ejpam-5962	244	37	is	be	AUX
ejpam-5962	244	38	not	not	PART
ejpam-5962	244	39	pairwise	pairwise	NOUN
ejpam-5962	244	40	hoemorphism	hoemorphism	NOUN
ejpam-5962	244	41	,	,	PUNCT
ejpam-5962	244	42	so	so	ADV
ejpam-5962	244	43	ϑ1	ϑ1	PROPN
ejpam-5962	244	44	,	,	PUNCT
ejpam-5962	244	45	ϑ2	ϑ2	PROPN
ejpam-5962	244	46	is	be	AUX
ejpam-5962	244	47	not	not	PART
ejpam-5962	244	48	maximal	maximal	ADJ
ejpam-5962	244	49	compact	compact	ADJ
ejpam-5962	244	50	.	.	PUNCT
ejpam-5962	245	1	consequently	consequently	ADV
ejpam-5962	245	2	,	,	PUNCT
ejpam-5962	245	3	(	(	PUNCT
ejpam-5962	245	4	z	z	NOUN
ejpam-5962	245	5	,	,	PUNCT
ejpam-5962	245	6	ϑ1	ϑ1	NOUN
ejpam-5962	245	7	,	,	PUNCT
ejpam-5962	245	8	ϑ2	ϑ2	PROPN
ejpam-5962	245	9	)	)	PUNCT
ejpam-5962	245	10	is	be	AUX
ejpam-5962	245	11	pairwise	pairwise	NOUN
ejpam-5962	245	12	minimal	minimal	ADJ
ejpam-5962	245	13	compact	compact	ADJ
ejpam-5962	245	14	closed	closed	ADJ
ejpam-5962	245	15	space	space	NOUN
ejpam-5962	245	16	.	.	PUNCT
ejpam-5962	246	1	furthermore	furthermore	ADV
ejpam-5962	246	2	,	,	PUNCT
ejpam-5962	246	3	(	(	PUNCT
ejpam-5962	246	4	z	z	NOUN
ejpam-5962	246	5	,	,	PUNCT
ejpam-5962	246	6	ϑ1	ϑ1	NOUN
ejpam-5962	246	7	,	,	PUNCT
ejpam-5962	246	8	ϑ2	ϑ2	PROPN
ejpam-5962	246	9	)	)	PUNCT
ejpam-5962	246	10	is	be	AUX
ejpam-5962	246	11	pairwise	pairwise	NOUN
ejpam-5962	246	12	compact	compact	ADJ
ejpam-5962	246	13	closed	close	VERB
ejpam-5962	246	14	space	space	NOUN
ejpam-5962	246	15	.	.	PUNCT
ejpam-5962	247	1	corollary	corollary	ADJ
ejpam-5962	247	2	5.2	5.2	NUM
ejpam-5962	247	3	.	.	PUNCT
ejpam-5962	248	1	let	let	VERB
ejpam-5962	248	2	’s	’s	PRON
ejpam-5962	248	3	say	say	VERB
ejpam-5962	248	4	that	that	SCONJ
ejpam-5962	248	5	a	a	DET
ejpam-5962	248	6	function	function	NOUN
ejpam-5962	248	7	φ	φ	NOUN
ejpam-5962	248	8	:	:	PUNCT
ejpam-5962	248	9	(	(	PUNCT
ejpam-5962	248	10	z	z	NOUN
ejpam-5962	248	11	,	,	PUNCT
ejpam-5962	248	12	ϑ1	ϑ1	NOUN
ejpam-5962	248	13	,	,	PUNCT
ejpam-5962	248	14	ϑ2	ϑ2	PROPN
ejpam-5962	248	15	)	)	PUNCT
ejpam-5962	248	16	→	→	SYM
ejpam-5962	248	17	(	(	PUNCT
ejpam-5962	248	18	n	n	CCONJ
ejpam-5962	248	19	,	,	PUNCT
ejpam-5962	248	20	β1	β1	PROPN
ejpam-5962	248	21	,	,	PUNCT
ejpam-5962	248	22	β2)be	β2)be	PROPN
ejpam-5962	248	23	pairwise	pairwise	NOUN
ejpam-5962	248	24	onto	onto	ADP
ejpam-5962	248	25	continuous	continuous	ADJ
ejpam-5962	248	26	function	function	NOUN
ejpam-5962	248	27	and	and	CCONJ
ejpam-5962	248	28	(	(	PUNCT
ejpam-5962	248	29	n	n	CCONJ
ejpam-5962	248	30	,	,	PUNCT
ejpam-5962	248	31	β1	β1	PROPN
ejpam-5962	248	32	,	,	PUNCT
ejpam-5962	248	33	β2	β2	NOUN
ejpam-5962	248	34	)	)	PUNCT
ejpam-5962	248	35	is	be	AUX
ejpam-5962	248	36	pairwise	pairwise	NOUN
ejpam-5962	248	37	compact	compact	ADJ
ejpam-5962	248	38	closed	close	VERB
ejpam-5962	248	39	space	space	NOUN
ejpam-5962	248	40	.	.	PUNCT
ejpam-5962	249	1	as	as	ADP
ejpam-5962	249	2	(	(	PUNCT
ejpam-5962	249	3	z	z	NOUN
ejpam-5962	249	4	,	,	PUNCT
ejpam-5962	249	5	ϑ1	ϑ1	NOUN
ejpam-5962	249	6	,	,	PUNCT
ejpam-5962	249	7	ϑ2	ϑ2	PROPN
ejpam-5962	249	8	)	)	PUNCT
ejpam-5962	249	9	is	be	AUX
ejpam-5962	249	10	pairwise	pairwise	NOUN
ejpam-5962	249	11	compact	compact	ADJ
ejpam-5962	249	12	hausdroff	hausdroff	NOUN
ejpam-5962	249	13	,	,	PUNCT
ejpam-5962	249	14	then	then	ADV
ejpam-5962	249	15	(	(	PUNCT
ejpam-5962	249	16	n	n	X
ejpam-5962	249	17	,	,	PUNCT
ejpam-5962	249	18	β1	β1	PROPN
ejpam-5962	249	19	,	,	PUNCT
ejpam-5962	249	20	β2	β2	NOUN
ejpam-5962	249	21	)	)	PUNCT
ejpam-5962	249	22	follows	follow	VERB
ejpam-5962	249	23	.	.	PUNCT
ejpam-5962	250	1	proof	proof	NOUN
ejpam-5962	250	2	.	.	PUNCT
ejpam-5962	251	1	given	give	VERB
ejpam-5962	251	2	that	that	SCONJ
ejpam-5962	251	3	(	(	PUNCT
ejpam-5962	251	4	z	z	NOUN
ejpam-5962	251	5	,	,	PUNCT
ejpam-5962	251	6	ϑ1	ϑ1	NOUN
ejpam-5962	251	7	,	,	PUNCT
ejpam-5962	251	8	ϑ2	ϑ2	PROPN
ejpam-5962	251	9	)	)	PUNCT
ejpam-5962	251	10	is	be	AUX
ejpam-5962	251	11	pairwise	pairwise	NOUN
ejpam-5962	251	12	compact	compact	ADJ
ejpam-5962	251	13	hausdroff	hausdroff	NOUN
ejpam-5962	251	14	and	and	CCONJ
ejpam-5962	251	15	φ	φ	PROPN
ejpam-5962	251	16	is	be	AUX
ejpam-5962	251	17	pairwise	pairwise	NOUN
ejpam-5962	251	18	onto	onto	ADP
ejpam-5962	251	19	continuous	continuous	ADJ
ejpam-5962	251	20	function	function	NOUN
ejpam-5962	251	21	.	.	PUNCT
ejpam-5962	252	1	therefore	therefore	ADV
ejpam-5962	252	2	,	,	PUNCT
ejpam-5962	252	3	(	(	PUNCT
ejpam-5962	252	4	n	n	X
ejpam-5962	252	5	,	,	PUNCT
ejpam-5962	252	6	β1	β1	PROPN
ejpam-5962	252	7	,	,	PUNCT
ejpam-5962	252	8	β2	β2	NOUN
ejpam-5962	252	9	)	)	PUNCT
ejpam-5962	252	10	is	be	AUX
ejpam-5962	252	11	pairwise	pairwise	NOUN
ejpam-5962	252	12	compact	compact	ADJ
ejpam-5962	252	13	hausdroff	hausdroff	NOUN
ejpam-5962	252	14	and	and	CCONJ
ejpam-5962	252	15	pairwise	pairwise	NOUN
ejpam-5962	252	16	compact	compact	ADJ
ejpam-5962	252	17	closed	close	VERB
ejpam-5962	252	18	space	space	NOUN
ejpam-5962	252	19	.	.	PUNCT
ejpam-5962	253	1	theorem	theorem	VERB
ejpam-5962	253	2	5.6	5.6	NUM
ejpam-5962	253	3	.	.	PUNCT
ejpam-5962	254	1	let	let	VERB
ejpam-5962	254	2	φ	φ	PROPN
ejpam-5962	254	3	:	:	PUNCT
ejpam-5962	254	4	(	(	PUNCT
ejpam-5962	254	5	z	z	NOUN
ejpam-5962	254	6	,	,	PUNCT
ejpam-5962	254	7	ϑ1	ϑ1	PROPN
ejpam-5962	254	8	,	,	PUNCT
ejpam-5962	254	9	ϑ2)one	ϑ2)one	NOUN
ejpam-5962	254	10	to	to	ADP
ejpam-5962	254	11	one−−−−−−−→	one−−−−−−−→	PROPN
ejpam-5962	254	12	(	(	PUNCT
ejpam-5962	254	13	n	n	CCONJ
ejpam-5962	254	14	,	,	PUNCT
ejpam-5962	254	15	β1	β1	PROPN
ejpam-5962	254	16	,	,	PUNCT
ejpam-5962	254	17	β2	β2	PROPN
ejpam-5962	254	18	)	)	PUNCT
ejpam-5962	254	19	be	be	VERB
ejpam-5962	254	20	pairwise	pairwise	NOUN
ejpam-5962	254	21	k−continuous	k−continuous	NOUN
ejpam-5962	254	22	function	function	NOUN
ejpam-5962	254	23	.	.	PUNCT
ejpam-5962	255	1	if	if	SCONJ
ejpam-5962	255	2	(	(	PUNCT
ejpam-5962	255	3	n	n	X
ejpam-5962	255	4	,	,	PUNCT
ejpam-5962	255	5	β1	β1	PROPN
ejpam-5962	255	6	,	,	PUNCT
ejpam-5962	255	7	β2	β2	NOUN
ejpam-5962	255	8	)	)	PUNCT
ejpam-5962	255	9	is	be	AUX
ejpam-5962	255	10	pairwise	pairwise	NOUN
ejpam-5962	255	11	compact	compact	ADJ
ejpam-5962	255	12	closed	close	VERB
ejpam-5962	255	13	space	space	NOUN
ejpam-5962	255	14	,	,	PUNCT
ejpam-5962	255	15	then	then	ADV
ejpam-5962	255	16	z	z	NOUN
ejpam-5962	255	17	=	=	SYM
ejpam-5962	255	18	φ−1(n	φ−1(n	PROPN
ejpam-5962	255	19	)	)	PUNCT
ejpam-5962	255	20	is	be	AUX
ejpam-5962	255	21	pairwise	pairwise	NOUN
ejpam-5962	255	22	compact	compact	ADJ
ejpam-5962	255	23	closed	close	VERB
ejpam-5962	255	24	space	space	NOUN
ejpam-5962	255	25	.	.	PUNCT
ejpam-5962	256	1	proof	proof	NOUN
ejpam-5962	256	2	.	.	PUNCT
ejpam-5962	257	1	to	to	PART
ejpam-5962	257	2	demonstrate	demonstrate	VERB
ejpam-5962	257	3	that	that	SCONJ
ejpam-5962	257	4	u	u	PRON
ejpam-5962	257	5	be	be	VERB
ejpam-5962	257	6	ϑ1−compact	ϑ1−compact	NOUN
ejpam-5962	257	7	in	in	ADP
ejpam-5962	257	8	(	(	PUNCT
ejpam-5962	257	9	z	z	NOUN
ejpam-5962	257	10	,	,	PUNCT
ejpam-5962	257	11	ϑ1	ϑ1	NOUN
ejpam-5962	257	12	,	,	PUNCT
ejpam-5962	257	13	ϑ2	ϑ2	PROPN
ejpam-5962	257	14	)	)	PUNCT
ejpam-5962	257	15	,	,	PUNCT
ejpam-5962	257	16	let	let	VERB
ejpam-5962	257	17	’s	’s	PRON
ejpam-5962	257	18	assume	assume	VERB
ejpam-5962	257	19	that	that	SCONJ
ejpam-5962	257	20	u	u	NOUN
ejpam-5962	257	21	is	be	AUX
ejpam-5962	257	22	ϑ1−closed	ϑ1−close	VERB
ejpam-5962	257	23	in	in	ADP
ejpam-5962	257	24	(	(	PUNCT
ejpam-5962	257	25	z	z	NOUN
ejpam-5962	257	26	,	,	PUNCT
ejpam-5962	257	27	ϑ1	ϑ1	NOUN
ejpam-5962	257	28	,	,	PUNCT
ejpam-5962	257	29	ϑ2	ϑ2	PROPN
ejpam-5962	257	30	)	)	PUNCT
ejpam-5962	257	31	.	.	PUNCT
ejpam-5962	258	1	u	u	NOUN
ejpam-5962	258	2	is	be	AUX
ejpam-5962	258	3	ϑ1−compact	ϑ1−compact	NOUN
ejpam-5962	258	4	in	in	ADP
ejpam-5962	258	5	(	(	PUNCT
ejpam-5962	258	6	z	z	NOUN
ejpam-5962	258	7	,	,	PUNCT
ejpam-5962	258	8	ϑ1	ϑ1	NOUN
ejpam-5962	258	9	,	,	PUNCT
ejpam-5962	258	10	ϑ2	ϑ2	PROPN
ejpam-5962	258	11	)	)	PUNCT
ejpam-5962	258	12	,	,	PUNCT
ejpam-5962	258	13	which	which	PRON
ejpam-5962	258	14	means	mean	VERB
ejpam-5962	258	15	that	that	SCONJ
ejpam-5962	258	16	φ(u	φ(u	NOUN
ejpam-5962	258	17	)	)	PUNCT
ejpam-5962	258	18	is	be	AUX
ejpam-5962	258	19	β1−compact	β1−compact	ADJ
ejpam-5962	258	20	in	in	ADP
ejpam-5962	258	21	(	(	PUNCT
ejpam-5962	258	22	n	n	CCONJ
ejpam-5962	258	23	,	,	PUNCT
ejpam-5962	258	24	β1	β1	PROPN
ejpam-5962	258	25	,	,	PUNCT
ejpam-5962	258	26	β2).given	β2).given	SCONJ
ejpam-5962	258	27	that	that	SCONJ
ejpam-5962	258	28	φ	φ	PROPN
ejpam-5962	258	29	is	be	AUX
ejpam-5962	258	30	pairwisek−continuous	pairwisek−continuous	ADJ
ejpam-5962	258	31	function	function	NOUN
ejpam-5962	258	32	and	and	CCONJ
ejpam-5962	258	33	(	(	PUNCT
ejpam-5962	258	34	n	n	CCONJ
ejpam-5962	258	35	,	,	PUNCT
ejpam-5962	258	36	β1	β1	PROPN
ejpam-5962	258	37	,	,	PUNCT
ejpam-5962	258	38	β2	β2	NOUN
ejpam-5962	258	39	)	)	PUNCT
ejpam-5962	258	40	is	be	AUX
ejpam-5962	258	41	pairwise	pairwise	NOUN
ejpam-5962	258	42	compact	compact	ADJ
ejpam-5962	258	43	closed	close	VERB
ejpam-5962	258	44	space	space	NOUN
ejpam-5962	258	45	,	,	PUNCT
ejpam-5962	258	46	φ(u	φ(u	NOUN
ejpam-5962	258	47	)	)	PUNCT
ejpam-5962	258	48	is	be	AUX
ejpam-5962	258	49	β2−closed	β2−close	VERB
ejpam-5962	258	50	in	in	ADP
ejpam-5962	258	51	(	(	PUNCT
ejpam-5962	258	52	n	n	CCONJ
ejpam-5962	258	53	,	,	PUNCT
ejpam-5962	258	54	β1	β1	NOUN
ejpam-5962	258	55	,	,	PUNCT
ejpam-5962	258	56	β2	β2	PROPN
ejpam-5962	258	57	)	)	PUNCT
ejpam-5962	258	58	.	.	PUNCT
ejpam-5962	259	1	however	however	ADV
ejpam-5962	259	2	,	,	PUNCT
ejpam-5962	259	3	if	if	SCONJ
ejpam-5962	259	4	φ	φ	PROPN
ejpam-5962	259	5	is	be	AUX
ejpam-5962	259	6	be	be	AUX
ejpam-5962	259	7	pairwise	pairwise	NOUN
ejpam-5962	259	8	continuous	continuous	ADJ
ejpam-5962	259	9	function	function	NOUN
ejpam-5962	259	10	and	and	CCONJ
ejpam-5962	259	11	one	one	NUM
ejpam-5962	259	12	to	to	ADP
ejpam-5962	259	13	one	one	NUM
ejpam-5962	259	14	,	,	PUNCT
ejpam-5962	259	15	φ−1(φ(u	φ−1(φ(u	PROPN
ejpam-5962	259	16	)	)	PUNCT
ejpam-5962	259	17	)	)	PUNCT
ejpam-5962	260	1	=	=	SYM
ejpam-5962	260	2	u	u	NOUN
ejpam-5962	260	3	is	be	AUX
ejpam-5962	260	4	ϑ2−closed	ϑ2−close	VERB
ejpam-5962	260	5	in	in	ADP
ejpam-5962	260	6	(	(	PUNCT
ejpam-5962	260	7	z	z	NOUN
ejpam-5962	260	8	,	,	PUNCT
ejpam-5962	260	9	ϑ1	ϑ1	NOUN
ejpam-5962	260	10	,	,	PUNCT
ejpam-5962	260	11	ϑ2	ϑ2	PROPN
ejpam-5962	260	12	)	)	PUNCT
ejpam-5962	260	13	as	as	ADP
ejpam-5962	260	14	a	a	DET
ejpam-5962	260	15	result	result	NOUN
ejpam-5962	260	16	,	,	PUNCT
ejpam-5962	260	17	so	so	SCONJ
ejpam-5962	260	18	z	z	NOUN
ejpam-5962	260	19	=	=	SYM
ejpam-5962	260	20	φ−1(u	φ−1(u	PROPN
ejpam-5962	260	21	)	)	PUNCT
ejpam-5962	260	22	is	be	AUX
ejpam-5962	260	23	pairwise	pairwise	NOUN
ejpam-5962	260	24	compact	compact	ADJ
ejpam-5962	260	25	closed	close	VERB
ejpam-5962	260	26	space	space	NOUN
ejpam-5962	260	27	.	.	PUNCT
ejpam-5962	261	1	v	v	NOUN
ejpam-5962	261	2	is	be	AUX
ejpam-5962	261	3	ϑ2−compact	ϑ2−compact	NOUN
ejpam-5962	261	4	in	in	ADP
ejpam-5962	261	5	(	(	PUNCT
ejpam-5962	261	6	z	z	NOUN
ejpam-5962	261	7	,	,	PUNCT
ejpam-5962	261	8	ϑ1	ϑ1	NOUN
ejpam-5962	261	9	,	,	PUNCT
ejpam-5962	261	10	ϑ2	ϑ2	PROPN
ejpam-5962	261	11	)	)	PUNCT
ejpam-5962	261	12	.	.	PUNCT
ejpam-5962	262	1	the	the	DET
ejpam-5962	262	2	outcome	outcome	NOUN
ejpam-5962	262	3	is	be	AUX
ejpam-5962	262	4	received	receive	VERB
ejpam-5962	262	5	.	.	PUNCT
ejpam-5962	263	1	if	if	SCONJ
ejpam-5962	263	2	we	we	PRON
ejpam-5962	263	3	apply	apply	VERB
ejpam-5962	263	4	the	the	DET
ejpam-5962	263	5	same	same	ADJ
ejpam-5962	263	6	theorem	theorem	ADJ
ejpam-5962	263	7	stages	stage	NOUN
ejpam-5962	263	8	,	,	PUNCT
ejpam-5962	263	9	we	we	PRON
ejpam-5962	263	10	will	will	AUX
ejpam-5962	263	11	obtain	obtain	VERB
ejpam-5962	263	12	the	the	DET
ejpam-5962	263	13	following	follow	VERB
ejpam-5962	263	14	corollary	corollary	NOUN
ejpam-5962	263	15	.	.	PUNCT
ejpam-5962	264	1	corollary	corollary	ADJ
ejpam-5962	264	2	5.3	5.3	NUM
ejpam-5962	264	3	.	.	PUNCT
ejpam-5962	265	1	let	let	VERB
ejpam-5962	265	2	φ	φ	PROPN
ejpam-5962	265	3	:	:	PUNCT
ejpam-5962	265	4	(	(	PUNCT
ejpam-5962	265	5	z	z	NOUN
ejpam-5962	265	6	,	,	PUNCT
ejpam-5962	265	7	ϑ1	ϑ1	NOUN
ejpam-5962	265	8	,	,	PUNCT
ejpam-5962	265	9	ϑ2	ϑ2	PROPN
ejpam-5962	265	10	)	)	PUNCT
ejpam-5962	265	11	−−−−−−−→	−−−−−−−→	NOUN
ejpam-5962	265	12	one	one	NUM
ejpam-5962	265	13	to	to	ADP
ejpam-5962	265	14	one	one	NUM
ejpam-5962	265	15	(	(	PUNCT
ejpam-5962	265	16	n	n	CCONJ
ejpam-5962	265	17	,	,	PUNCT
ejpam-5962	265	18	β1	β1	PROPN
ejpam-5962	265	19	,	,	PUNCT
ejpam-5962	265	20	β2	β2	PROPN
ejpam-5962	265	21	)	)	PUNCT
ejpam-5962	265	22	be	be	VERB
ejpam-5962	265	23	pairwise	pairwise	NOUN
ejpam-5962	265	24	compact	compact	ADJ
ejpam-5962	265	25	,	,	PUNCT
ejpam-5962	265	26	pairwise	pairwise	VERB
ejpam-5962	265	27	continuous	continuous	ADJ
ejpam-5962	265	28	function	function	NOUN
ejpam-5962	265	29	.	.	PUNCT
ejpam-5962	266	1	if	if	SCONJ
ejpam-5962	266	2	(	(	PUNCT
ejpam-5962	266	3	n	n	X
ejpam-5962	266	4	,	,	PUNCT
ejpam-5962	266	5	β1	β1	PROPN
ejpam-5962	266	6	,	,	PUNCT
ejpam-5962	266	7	β2	β2	NOUN
ejpam-5962	266	8	)	)	PUNCT
ejpam-5962	266	9	is	be	AUX
ejpam-5962	266	10	pairwise	pairwise	NOUN
ejpam-5962	266	11	minimal	minimal	ADJ
ejpam-5962	266	12	compact	compact	ADJ
ejpam-5962	266	13	closed	closed	ADJ
ejpam-5962	266	14	space	space	NOUN
ejpam-5962	266	15	,	,	PUNCT
ejpam-5962	266	16	then	then	ADV
ejpam-5962	266	17	z	z	NOUN
ejpam-5962	266	18	=	=	SYM
ejpam-5962	266	19	φ−1(n	φ−1(n	PROPN
ejpam-5962	266	20	)	)	PUNCT
ejpam-5962	266	21	is	be	AUX
ejpam-5962	266	22	pairwise	pairwise	NOUN
ejpam-5962	266	23	minimal	minimal	ADJ
ejpam-5962	266	24	compact	compact	ADJ
ejpam-5962	266	25	closed	closed	ADJ
ejpam-5962	266	26	space	space	NOUN
ejpam-5962	266	27	.	.	PUNCT
ejpam-5962	267	1	theorem	theorem	VERB
ejpam-5962	267	2	5.7	5.7	NUM
ejpam-5962	267	3	.	.	PUNCT
ejpam-5962	268	1	every	every	DET
ejpam-5962	268	2	pairwise	pairwise	NOUN
ejpam-5962	268	3	k−function	k−function	NOUN
ejpam-5962	268	4	between	between	ADP
ejpam-5962	268	5	pairwise	pairwise	NOUN
ejpam-5962	268	6	minimal	minimal	ADJ
ejpam-5962	268	7	compact	compact	ADJ
ejpam-5962	268	8	closed	close	VERB
ejpam-5962	268	9	space	space	NOUN
ejpam-5962	268	10	can	can	AUX
ejpam-5962	268	11	be	be	AUX
ejpam-5962	268	12	both	both	PRON
ejpam-5962	268	13	pairwise	pairwise	VERB
ejpam-5962	268	14	continuous	continuous	ADJ
ejpam-5962	268	15	and	and	CCONJ
ejpam-5962	268	16	pairwise	pairwise	NOUN
ejpam-5962	268	17	closed	close	VERB
ejpam-5962	268	18	.	.	PUNCT
ejpam-5962	269	1	a.	a.	NOUN
ejpam-5962	269	2	a.	a.	PROPN
ejpam-5962	269	3	atoom	atoom	PROPN
ejpam-5962	269	4	et	et	PROPN
ejpam-5962	269	5	al	al	PROPN
ejpam-5962	269	6	.	.	PUNCT
ejpam-5962	269	7	/	/	SYM
ejpam-5962	269	8	eur	eur	PROPN
ejpam-5962	269	9	.	.	PUNCT
ejpam-5962	270	1	j.	j.	PROPN
ejpam-5962	270	2	pure	pure	PROPN
ejpam-5962	270	3	appl	appl	PROPN
ejpam-5962	270	4	.	.	PROPN
ejpam-5962	270	5	math	math	PROPN
ejpam-5962	270	6	,	,	PUNCT
ejpam-5962	270	7	18	18	NUM
ejpam-5962	270	8	(	(	PUNCT
ejpam-5962	270	9	2	2	NUM
ejpam-5962	270	10	)	)	PUNCT
ejpam-5962	270	11	(	(	PUNCT
ejpam-5962	270	12	2025	2025	NUM
ejpam-5962	270	13	)	)	PUNCT
ejpam-5962	270	14	,	,	PUNCT
ejpam-5962	270	15	5962	5962	NUM
ejpam-5962	270	16	10	10	NUM
ejpam-5962	270	17	of	of	ADP
ejpam-5962	270	18	17	17	NUM
ejpam-5962	270	19	proof	proof	NOUN
ejpam-5962	270	20	.	.	PUNCT
ejpam-5962	271	1	assume	assume	VERB
ejpam-5962	271	2	that	that	SCONJ
ejpam-5962	271	3	φ	φ	PROPN
ejpam-5962	271	4	:	:	PUNCT
ejpam-5962	271	5	(	(	PUNCT
ejpam-5962	271	6	z	z	NOUN
ejpam-5962	271	7	,	,	PUNCT
ejpam-5962	271	8	ϑ1	ϑ1	NOUN
ejpam-5962	271	9	,	,	PUNCT
ejpam-5962	271	10	ϑ2	ϑ2	PROPN
ejpam-5962	271	11	)	)	PUNCT
ejpam-5962	271	12	→	→	SYM
ejpam-5962	271	13	(	(	PUNCT
ejpam-5962	271	14	n	n	CCONJ
ejpam-5962	271	15	,	,	PUNCT
ejpam-5962	271	16	β1	β1	PROPN
ejpam-5962	271	17	,	,	PUNCT
ejpam-5962	271	18	β2	β2	NOUN
ejpam-5962	271	19	)	)	PUNCT
ejpam-5962	271	20	are	be	AUX
ejpam-5962	271	21	pairwisek−function	pairwisek−function	NOUN
ejpam-5962	271	22	and	and	CCONJ
ejpam-5962	271	23	(	(	PUNCT
ejpam-5962	271	24	z	z	NOUN
ejpam-5962	271	25	,	,	PUNCT
ejpam-5962	271	26	ϑ1	ϑ1	NOUN
ejpam-5962	271	27	,	,	PUNCT
ejpam-5962	271	28	ϑ2	ϑ2	PROPN
ejpam-5962	271	29	)	)	PUNCT
ejpam-5962	271	30	,	,	PUNCT
ejpam-5962	271	31	(	(	PUNCT
ejpam-5962	271	32	n	n	X
ejpam-5962	271	33	,	,	PUNCT
ejpam-5962	271	34	β1	β1	PROPN
ejpam-5962	271	35	,	,	PUNCT
ejpam-5962	271	36	β2	β2	NOUN
ejpam-5962	271	37	)	)	PUNCT
ejpam-5962	271	38	are	be	AUX
ejpam-5962	271	39	pairwise	pairwise	NOUN
ejpam-5962	271	40	minimal	minimal	ADJ
ejpam-5962	271	41	compact	compact	ADJ
ejpam-5962	271	42	closed	closed	ADJ
ejpam-5962	271	43	space	space	NOUN
ejpam-5962	271	44	.	.	PUNCT
ejpam-5962	272	1	given	give	VERB
ejpam-5962	272	2	that	that	SCONJ
ejpam-5962	272	3	φ	φ	PROPN
ejpam-5962	272	4	is	be	AUX
ejpam-5962	272	5	pairwise	pairwise	NOUN
ejpam-5962	272	6	continuous	continuous	ADJ
ejpam-5962	272	7	and	and	CCONJ
ejpam-5962	272	8	that	that	SCONJ
ejpam-5962	272	9	(	(	PUNCT
ejpam-5962	272	10	n	n	X
ejpam-5962	272	11	,	,	PUNCT
ejpam-5962	272	12	β1	β1	PROPN
ejpam-5962	272	13	,	,	PUNCT
ejpam-5962	272	14	β2	β2	NOUN
ejpam-5962	272	15	)	)	PUNCT
ejpam-5962	272	16	is	be	AUX
ejpam-5962	272	17	pairwise	pairwise	NOUN
ejpam-5962	272	18	minimal	minimal	ADJ
ejpam-5962	272	19	compact	compact	ADJ
ejpam-5962	272	20	closed	closed	ADJ
ejpam-5962	272	21	space	space	NOUN
ejpam-5962	272	22	.	.	PUNCT
ejpam-5962	273	1	consequently	consequently	ADV
ejpam-5962	273	2	,	,	PUNCT
ejpam-5962	273	3	if	if	SCONJ
ejpam-5962	273	4	u	u	NOUN
ejpam-5962	273	5	is	be	AUX
ejpam-5962	273	6	β1−closed	β1−close	VERB
ejpam-5962	273	7	in	in	ADP
ejpam-5962	273	8	(	(	PUNCT
ejpam-5962	273	9	n	n	CCONJ
ejpam-5962	273	10	,	,	PUNCT
ejpam-5962	273	11	β1	β1	NOUN
ejpam-5962	273	12	,	,	PUNCT
ejpam-5962	273	13	β2	β2	NOUN
ejpam-5962	273	14	)	)	PUNCT
ejpam-5962	273	15	,	,	PUNCT
ejpam-5962	273	16	so	so	CCONJ
ejpam-5962	273	17	u	u	NOUN
ejpam-5962	273	18	is	be	AUX
ejpam-5962	273	19	β2−compact	β2−compact	ADJ
ejpam-5962	273	20	.	.	PUNCT
ejpam-5962	274	1	as	as	ADP
ejpam-5962	274	2	a	a	DET
ejpam-5962	274	3	result	result	NOUN
ejpam-5962	274	4	of	of	ADP
ejpam-5962	274	5	the	the	DET
ejpam-5962	274	6	fact	fact	NOUN
ejpam-5962	274	7	that	that	SCONJ
ejpam-5962	274	8	φ	φ	PROPN
ejpam-5962	274	9	is	be	AUX
ejpam-5962	274	10	pairwise	pairwise	PROPN
ejpam-5962	274	11	k−function	k−function	NOUN
ejpam-5962	274	12	,	,	PUNCT
ejpam-5962	274	13	φ−1(u	φ−1(u	PROPN
ejpam-5962	274	14	)	)	PUNCT
ejpam-5962	274	15	is	be	AUX
ejpam-5962	274	16	now	now	ADV
ejpam-5962	274	17	ϑ2−compact	ϑ2−compact	NOUN
ejpam-5962	274	18	in	in	ADP
ejpam-5962	274	19	(	(	PUNCT
ejpam-5962	274	20	z	z	NOUN
ejpam-5962	274	21	,	,	PUNCT
ejpam-5962	274	22	ϑ1	ϑ1	NOUN
ejpam-5962	274	23	,	,	PUNCT
ejpam-5962	274	24	ϑ2	ϑ2	PROPN
ejpam-5962	274	25	)	)	PUNCT
ejpam-5962	274	26	,	,	PUNCT
ejpam-5962	274	27	yet(z	yet(z	PROPN
ejpam-5962	274	28	,	,	PUNCT
ejpam-5962	274	29	ϑ1	ϑ1	NOUN
ejpam-5962	274	30	,	,	PUNCT
ejpam-5962	274	31	ϑ2	ϑ2	PROPN
ejpam-5962	274	32	)	)	PUNCT
ejpam-5962	274	33	is	be	AUX
ejpam-5962	274	34	minimal	minimal	ADJ
ejpam-5962	274	35	compact	compact	ADJ
ejpam-5962	274	36	closed	closed	ADJ
ejpam-5962	274	37	space	space	NOUN
ejpam-5962	274	38	.	.	PUNCT
ejpam-5962	275	1	simillarly	simillarly	ADJ
ejpam-5962	275	2	forv	forv	NOUN
ejpam-5962	275	3	is	be	AUX
ejpam-5962	275	4	β2−closed	β2−close	VERB
ejpam-5962	275	5	in	in	ADP
ejpam-5962	275	6	(	(	PUNCT
ejpam-5962	275	7	n	n	CCONJ
ejpam-5962	275	8	,	,	PUNCT
ejpam-5962	275	9	β1	β1	NOUN
ejpam-5962	275	10	,	,	PUNCT
ejpam-5962	275	11	β2	β2	PROPN
ejpam-5962	275	12	)	)	PUNCT
ejpam-5962	275	13	.	.	PUNCT
ejpam-5962	276	1	as	as	ADP
ejpam-5962	276	2	a	a	DET
ejpam-5962	276	3	result	result	NOUN
ejpam-5962	276	4	,	,	PUNCT
ejpam-5962	276	5	φ	φ	PROPN
ejpam-5962	276	6	is	be	AUX
ejpam-5962	276	7	pairwise	pairwise	NOUN
ejpam-5962	276	8	continuous	continuous	ADJ
ejpam-5962	276	9	.	.	PUNCT
ejpam-5962	277	1	now	now	ADV
ejpam-5962	277	2	,	,	PUNCT
ejpam-5962	277	3	φ	φ	PROPN
ejpam-5962	277	4	is	be	AUX
ejpam-5962	277	5	pairwise	pairwise	NOUN
ejpam-5962	277	6	closed	closed	ADJ
ejpam-5962	277	7	,	,	PUNCT
ejpam-5962	277	8	if	if	SCONJ
ejpam-5962	277	9	r	r	NOUN
ejpam-5962	277	10	is	be	AUX
ejpam-5962	277	11	ϑ2−compact	ϑ2−compact	NOUN
ejpam-5962	277	12	in	in	ADP
ejpam-5962	277	13	(	(	PUNCT
ejpam-5962	277	14	z	z	NOUN
ejpam-5962	277	15	,	,	PUNCT
ejpam-5962	277	16	ϑ1	ϑ1	NOUN
ejpam-5962	277	17	,	,	PUNCT
ejpam-5962	277	18	ϑ2	ϑ2	PROPN
ejpam-5962	277	19	)	)	PUNCT
ejpam-5962	277	20	,	,	PUNCT
ejpam-5962	277	21	then	then	ADV
ejpam-5962	277	22	φ(r	φ(r	ADJ
ejpam-5962	277	23	)	)	PUNCT
ejpam-5962	277	24	is	be	AUX
ejpam-5962	277	25	β2−compact	β2−compact	ADJ
ejpam-5962	277	26	in	in	ADP
ejpam-5962	277	27	(	(	PUNCT
ejpam-5962	277	28	n	n	CCONJ
ejpam-5962	277	29	,	,	PUNCT
ejpam-5962	277	30	β1	β1	NOUN
ejpam-5962	277	31	,	,	PUNCT
ejpam-5962	277	32	β2	β2	PROPN
ejpam-5962	277	33	)	)	PUNCT
ejpam-5962	277	34	.	.	PUNCT
ejpam-5962	278	1	this	this	PRON
ejpam-5962	278	2	means	mean	VERB
ejpam-5962	278	3	that	that	SCONJ
ejpam-5962	278	4	since	since	SCONJ
ejpam-5962	278	5	φ	φ	PROPN
ejpam-5962	278	6	is	be	AUX
ejpam-5962	278	7	pairwise	pairwise	PROPN
ejpam-5962	278	8	k−function	k−function	NOUN
ejpam-5962	278	9	and	and	CCONJ
ejpam-5962	278	10	(	(	PUNCT
ejpam-5962	278	11	n	n	CCONJ
ejpam-5962	278	12	,	,	PUNCT
ejpam-5962	278	13	β1	β1	PROPN
ejpam-5962	278	14	,	,	PUNCT
ejpam-5962	278	15	β2	β2	NOUN
ejpam-5962	278	16	)	)	PUNCT
ejpam-5962	278	17	is	be	AUX
ejpam-5962	278	18	pairwise	pairwise	NOUN
ejpam-5962	278	19	minimal	minimal	ADJ
ejpam-5962	278	20	compact	compact	ADJ
ejpam-5962	278	21	closed	closed	ADJ
ejpam-5962	278	22	space	space	NOUN
ejpam-5962	278	23	.	.	PUNCT
ejpam-5962	279	1	as	as	ADP
ejpam-5962	279	2	a	a	DET
ejpam-5962	279	3	result	result	NOUN
ejpam-5962	279	4	,	,	PUNCT
ejpam-5962	279	5	φ(r	φ(r	ADJ
ejpam-5962	279	6	)	)	PUNCT
ejpam-5962	279	7	is	be	AUX
ejpam-5962	279	8	β1−closed	β1−close	VERB
ejpam-5962	279	9	in	in	ADP
ejpam-5962	279	10	(	(	PUNCT
ejpam-5962	279	11	n	n	CCONJ
ejpam-5962	279	12	,	,	PUNCT
ejpam-5962	279	13	β1	β1	NOUN
ejpam-5962	279	14	,	,	PUNCT
ejpam-5962	279	15	β2	β2	PROPN
ejpam-5962	279	16	)	)	PUNCT
ejpam-5962	279	17	,	,	PUNCT
ejpam-5962	279	18	φ	φ	PROPN
ejpam-5962	279	19	is	be	AUX
ejpam-5962	279	20	pairwise	pairwise	NOUN
ejpam-5962	279	21	closed	close	VERB
ejpam-5962	279	22	.	.	PUNCT
ejpam-5962	280	1	theorem	theorem	VERB
ejpam-5962	280	2	5.8	5.8	PROPN
ejpam-5962	280	3	.	.	PUNCT
ejpam-5962	281	1	assume	assume	VERB
ejpam-5962	281	2	φ	φ	PROPN
ejpam-5962	281	3	:	:	PUNCT
ejpam-5962	281	4	(	(	PUNCT
ejpam-5962	281	5	z	z	NOUN
ejpam-5962	281	6	,	,	PUNCT
ejpam-5962	281	7	ϑ1	ϑ1	NOUN
ejpam-5962	281	8	,	,	PUNCT
ejpam-5962	281	9	ϑ2	ϑ2	PROPN
ejpam-5962	281	10	)	)	PUNCT
ejpam-5962	281	11	→	→	SYM
ejpam-5962	281	12	(	(	PUNCT
ejpam-5962	281	13	n	n	CCONJ
ejpam-5962	281	14	,	,	PUNCT
ejpam-5962	281	15	β1	β1	PROPN
ejpam-5962	281	16	,	,	PUNCT
ejpam-5962	281	17	β2	β2	PROPN
ejpam-5962	281	18	)	)	PUNCT
ejpam-5962	281	19	be	be	VERB
ejpam-5962	281	20	pairwise	pairwise	NOUN
ejpam-5962	281	21	k−onto	k−onto	ADP
ejpam-5962	281	22	function	function	NOUN
ejpam-5962	281	23	and	and	CCONJ
ejpam-5962	281	24	pairwise	pairwise	NOUN
ejpam-5962	281	25	closed	closed	ADJ
ejpam-5962	281	26	function	function	NOUN
ejpam-5962	281	27	.	.	PUNCT
ejpam-5962	282	1	if	if	SCONJ
ejpam-5962	282	2	(	(	PUNCT
ejpam-5962	282	3	z	z	NOUN
ejpam-5962	282	4	,	,	PUNCT
ejpam-5962	282	5	ϑ1	ϑ1	NOUN
ejpam-5962	282	6	,	,	PUNCT
ejpam-5962	282	7	ϑ2	ϑ2	PROPN
ejpam-5962	282	8	)	)	PUNCT
ejpam-5962	282	9	is	be	AUX
ejpam-5962	282	10	pairwise	pairwise	NOUN
ejpam-5962	282	11	minimal	minimal	ADJ
ejpam-5962	282	12	compact	compact	ADJ
ejpam-5962	282	13	closed	closed	ADJ
ejpam-5962	282	14	space	space	NOUN
ejpam-5962	282	15	,	,	PUNCT
ejpam-5962	282	16	then	then	ADV
ejpam-5962	282	17	(	(	PUNCT
ejpam-5962	282	18	n	n	X
ejpam-5962	282	19	,	,	PUNCT
ejpam-5962	282	20	β1	β1	PROPN
ejpam-5962	282	21	,	,	PUNCT
ejpam-5962	282	22	β2	β2	NOUN
ejpam-5962	282	23	)	)	PUNCT
ejpam-5962	282	24	is	be	AUX
ejpam-5962	282	25	true	true	ADJ
ejpam-5962	282	26	.	.	PUNCT
ejpam-5962	283	1	proof	proof	NOUN
ejpam-5962	283	2	.	.	PUNCT
ejpam-5962	284	1	as	as	SCONJ
ejpam-5962	284	2	every	every	DET
ejpam-5962	284	3	(	(	PUNCT
ejpam-5962	284	4	z	z	NOUN
ejpam-5962	284	5	,	,	PUNCT
ejpam-5962	284	6	ϑ1	ϑ1	NOUN
ejpam-5962	284	7	,	,	PUNCT
ejpam-5962	284	8	ϑ2	ϑ2	PROPN
ejpam-5962	284	9	)	)	PUNCT
ejpam-5962	284	10	is	be	AUX
ejpam-5962	284	11	pairwise	pairwise	NOUN
ejpam-5962	284	12	minimal	minimal	ADJ
ejpam-5962	284	13	compact	compact	ADJ
ejpam-5962	284	14	closed	close	VERB
ejpam-5962	284	15	space	space	NOUN
ejpam-5962	284	16	and	and	CCONJ
ejpam-5962	284	17	φ	φ	PROPN
ejpam-5962	284	18	is	be	AUX
ejpam-5962	284	19	pairwise	pairwise	NOUN
ejpam-5962	284	20	k−onto	k−onto	ADP
ejpam-5962	284	21	function	function	NOUN
ejpam-5962	284	22	,	,	PUNCT
ejpam-5962	284	23	then	then	ADV
ejpam-5962	284	24	n	n	PROPN
ejpam-5962	284	25	=	=	SYM
ejpam-5962	284	26	φ(z	φ(z	PROPN
ejpam-5962	284	27	)	)	PUNCT
ejpam-5962	284	28	and	and	CCONJ
ejpam-5962	284	29	every	every	DET
ejpam-5962	284	30	pairwise	pairwise	NOUN
ejpam-5962	284	31	minimal	minimal	ADJ
ejpam-5962	284	32	compact	compact	ADJ
ejpam-5962	284	33	closed	close	VERB
ejpam-5962	284	34	space	space	NOUN
ejpam-5962	284	35	is	be	AUX
ejpam-5962	285	1	pairwise	pairwise	NOUN
ejpam-5962	285	2	compact	compact	ADJ
ejpam-5962	285	3	,	,	PUNCT
ejpam-5962	285	4	(	(	PUNCT
ejpam-5962	285	5	n	n	X
ejpam-5962	285	6	,	,	PUNCT
ejpam-5962	285	7	β1	β1	PROPN
ejpam-5962	285	8	,	,	PUNCT
ejpam-5962	285	9	β2	β2	NOUN
ejpam-5962	285	10	)	)	PUNCT
ejpam-5962	285	11	is	be	AUX
ejpam-5962	285	12	pairwise	pairwise	NOUN
ejpam-5962	285	13	minimal	minimal	ADJ
ejpam-5962	285	14	compact	compact	ADJ
ejpam-5962	285	15	closed	closed	ADJ
ejpam-5962	285	16	space	space	NOUN
ejpam-5962	285	17	.	.	PUNCT
ejpam-5962	286	1	if	if	SCONJ
ejpam-5962	286	2	we	we	PRON
ejpam-5962	286	3	apply	apply	VERB
ejpam-5962	286	4	the	the	DET
ejpam-5962	286	5	same	same	ADJ
ejpam-5962	286	6	theorem	theorem	ADJ
ejpam-5962	286	7	stages	stage	NOUN
ejpam-5962	286	8	,	,	PUNCT
ejpam-5962	286	9	we	we	PRON
ejpam-5962	286	10	will	will	AUX
ejpam-5962	286	11	obtain	obtain	VERB
ejpam-5962	286	12	the	the	DET
ejpam-5962	286	13	following	follow	VERB
ejpam-5962	286	14	corollary	corollary	ADJ
ejpam-5962	286	15	:	:	PUNCT
ejpam-5962	286	16	corollary	corollary	ADJ
ejpam-5962	286	17	5.4	5.4	NUM
ejpam-5962	286	18	.	.	PUNCT
ejpam-5962	287	1	take	take	VERB
ejpam-5962	287	2	φ	φ	NOUN
ejpam-5962	287	3	:	:	PUNCT
ejpam-5962	287	4	(	(	PUNCT
ejpam-5962	287	5	z	z	NOUN
ejpam-5962	287	6	,	,	PUNCT
ejpam-5962	287	7	ϑ1	ϑ1	NOUN
ejpam-5962	287	8	,	,	PUNCT
ejpam-5962	287	9	ϑ2	ϑ2	PROPN
ejpam-5962	287	10	)	)	PUNCT
ejpam-5962	287	11	→	→	SYM
ejpam-5962	287	12	(	(	PUNCT
ejpam-5962	287	13	n	n	CCONJ
ejpam-5962	287	14	,	,	PUNCT
ejpam-5962	287	15	β1	β1	PROPN
ejpam-5962	287	16	,	,	PUNCT
ejpam-5962	287	17	β2	β2	NOUN
ejpam-5962	287	18	)	)	PUNCT
ejpam-5962	287	19	is	be	AUX
ejpam-5962	287	20	pairwise	pairwise	NOUN
ejpam-5962	287	21	k−onto	k−onto	ADP
ejpam-5962	287	22	function	function	NOUN
ejpam-5962	287	23	and	and	CCONJ
ejpam-5962	287	24	pairwise	pairwise	NOUN
ejpam-5962	287	25	closed	closed	ADJ
ejpam-5962	287	26	function	function	NOUN
ejpam-5962	287	27	.	.	PUNCT
ejpam-5962	288	1	in	in	ADP
ejpam-5962	288	2	the	the	DET
ejpam-5962	288	3	event	event	NOUN
ejpam-5962	288	4	where	where	SCONJ
ejpam-5962	288	5	(	(	PUNCT
ejpam-5962	288	6	n	n	X
ejpam-5962	288	7	,	,	PUNCT
ejpam-5962	288	8	β1	β1	PROPN
ejpam-5962	288	9	,	,	PUNCT
ejpam-5962	288	10	β2	β2	NOUN
ejpam-5962	288	11	)	)	PUNCT
ejpam-5962	288	12	is	be	AUX
ejpam-5962	288	13	pairwise	pairwise	NOUN
ejpam-5962	288	14	minimal	minimal	ADJ
ejpam-5962	288	15	compact	compact	ADJ
ejpam-5962	288	16	closed	closed	ADJ
ejpam-5962	288	17	space	space	NOUN
ejpam-5962	288	18	,	,	PUNCT
ejpam-5962	288	19	then	then	ADV
ejpam-5962	288	20	z	z	NOUN
ejpam-5962	288	21	=	=	SYM
ejpam-5962	288	22	φ−1(n	φ−1(n	PROPN
ejpam-5962	288	23	)	)	PUNCT
ejpam-5962	288	24	holds	hold	VERB
ejpam-5962	288	25	true	true	ADJ
ejpam-5962	288	26	.	.	PUNCT
ejpam-5962	289	1	6	6	X
ejpam-5962	289	2	.	.	X
ejpam-5962	289	3	new	new	ADJ
ejpam-5962	289	4	remarks	remark	NOUN
ejpam-5962	289	5	of	of	ADP
ejpam-5962	289	6	pairwise	pairwise	NOUN
ejpam-5962	289	7	lindelöf	lindelöf	NOUN
ejpam-5962	289	8	closed	close	VERB
ejpam-5962	289	9	spaces	space	VERB
ejpam-5962	289	10	the	the	DET
ejpam-5962	289	11	advanced	advanced	ADJ
ejpam-5962	289	12	characteristics	characteristic	NOUN
ejpam-5962	289	13	of	of	ADP
ejpam-5962	289	14	the	the	DET
ejpam-5962	289	15	pairwise	pairwise	NOUN
ejpam-5962	289	16	minimal	minimal	ADJ
ejpam-5962	289	17	lindelöf	lindelöf	NOUN
ejpam-5962	289	18	closed	close	VERB
ejpam-5962	289	19	spaces	space	NOUN
ejpam-5962	289	20	are	be	AUX
ejpam-5962	289	21	highlighted	highlight	VERB
ejpam-5962	289	22	in	in	ADP
ejpam-5962	289	23	this	this	DET
ejpam-5962	289	24	part	part	NOUN
ejpam-5962	289	25	,	,	PUNCT
ejpam-5962	289	26	along	along	ADP
ejpam-5962	289	27	with	with	ADP
ejpam-5962	289	28	some	some	DET
ejpam-5962	289	29	peculiarities	peculiarity	NOUN
ejpam-5962	289	30	of	of	ADP
ejpam-5962	289	31	the	the	DET
ejpam-5962	289	32	cartesian	cartesian	ADJ
ejpam-5962	289	33	process	process	NOUN
ejpam-5962	289	34	of	of	ADP
ejpam-5962	289	35	multiplication	multiplication	NOUN
ejpam-5962	289	36	of	of	ADP
ejpam-5962	289	37	these	these	DET
ejpam-5962	289	38	spaces	space	NOUN
ejpam-5962	289	39	in	in	ADP
ejpam-5962	289	40	special	special	ADJ
ejpam-5962	289	41	circumstances	circumstance	NOUN
ejpam-5962	289	42	.	.	PUNCT
ejpam-5962	290	1	definition	definition	NOUN
ejpam-5962	290	2	6.1	6.1	NUM
ejpam-5962	290	3	.	.	PUNCT
ejpam-5962	291	1	let	let	AUX
ejpam-5962	291	2	(	(	PUNCT
ejpam-5962	291	3	z	z	NOUN
ejpam-5962	291	4	,	,	PUNCT
ejpam-5962	291	5	ϑ1	ϑ1	NOUN
ejpam-5962	291	6	,	,	PUNCT
ejpam-5962	291	7	ϑ2	ϑ2	PROPN
ejpam-5962	291	8	)	)	PUNCT
ejpam-5962	291	9	be	be	VERB
ejpam-5962	291	10	a	a	DET
ejpam-5962	291	11	topological	topological	ADJ
ejpam-5962	291	12	space	space	NOUN
ejpam-5962	291	13	.	.	PUNCT
ejpam-5962	292	1	we	we	PRON
ejpam-5962	292	2	define	define	VERB
ejpam-5962	292	3	(	(	PUNCT
ejpam-5962	292	4	z	z	NOUN
ejpam-5962	292	5	,	,	PUNCT
ejpam-5962	292	6	ϑ1	ϑ1	NOUN
ejpam-5962	292	7	,	,	PUNCT
ejpam-5962	292	8	ϑ2	ϑ2	PROPN
ejpam-5962	292	9	)	)	PUNCT
ejpam-5962	292	10	is	be	AUX
ejpam-5962	292	11	pairwise	pairwise	NOUN
ejpam-5962	292	12	lindelöf	lindelöf	NOUN
ejpam-5962	292	13	closed	close	VERB
ejpam-5962	292	14	spaces	space	NOUN
ejpam-5962	292	15	,	,	PUNCT
ejpam-5962	292	16	when	when	SCONJ
ejpam-5962	292	17	each	each	DET
ejpam-5962	292	18	ϑ1−lindelöf	ϑ1−lindelöf	PROPN
ejpam-5962	292	19	subset	subset	VERB
ejpam-5962	292	20	of	of	ADP
ejpam-5962	292	21	(	(	PUNCT
ejpam-5962	292	22	z	z	NOUN
ejpam-5962	292	23	,	,	PUNCT
ejpam-5962	292	24	ϑ1	ϑ1	NOUN
ejpam-5962	292	25	,	,	PUNCT
ejpam-5962	292	26	ϑ2	ϑ2	PROPN
ejpam-5962	292	27	)	)	PUNCT
ejpam-5962	292	28	is	be	AUX
ejpam-5962	292	29	ϑ2−closed	ϑ2−close	VERB
ejpam-5962	292	30	in	in	ADP
ejpam-5962	292	31	(	(	PUNCT
ejpam-5962	292	32	z	z	NOUN
ejpam-5962	292	33	,	,	PUNCT
ejpam-5962	292	34	ϑ1	ϑ1	NOUN
ejpam-5962	292	35	,	,	PUNCT
ejpam-5962	292	36	ϑ2	ϑ2	PROPN
ejpam-5962	292	37	)	)	PUNCT
ejpam-5962	292	38	and	and	CCONJ
ejpam-5962	292	39	ϑ2−lindelöf	ϑ2−lindelöf	VERB
ejpam-5962	292	40	subspace	subspace	NOUN
ejpam-5962	292	41	of	of	ADP
ejpam-5962	292	42	(	(	PUNCT
ejpam-5962	292	43	z	z	NOUN
ejpam-5962	292	44	,	,	PUNCT
ejpam-5962	292	45	ϑ1	ϑ1	NOUN
ejpam-5962	292	46	,	,	PUNCT
ejpam-5962	292	47	ϑ2	ϑ2	PROPN
ejpam-5962	292	48	)	)	PUNCT
ejpam-5962	292	49	is	be	AUX
ejpam-5962	292	50	ϑ1−closed	ϑ1−close	VERB
ejpam-5962	292	51	in	in	ADP
ejpam-5962	292	52	(	(	PUNCT
ejpam-5962	292	53	z	z	NOUN
ejpam-5962	292	54	,	,	PUNCT
ejpam-5962	292	55	ϑ1	ϑ1	NOUN
ejpam-5962	292	56	,	,	PUNCT
ejpam-5962	292	57	ϑ2	ϑ2	PROPN
ejpam-5962	292	58	)	)	PUNCT
ejpam-5962	292	59	.	.	PUNCT
ejpam-5962	293	1	remark	remark	VERB
ejpam-5962	293	2	6.1	6.1	NUM
ejpam-5962	293	3	.	.	PUNCT
ejpam-5962	294	1	there	there	PRON
ejpam-5962	294	2	are	be	VERB
ejpam-5962	294	3	pairwise	pairwise	NOUN
ejpam-5962	294	4	lindelöf	lindelöf	NOUN
ejpam-5962	294	5	closed	close	VERB
ejpam-5962	294	6	spaces	space	NOUN
ejpam-5962	294	7	for	for	ADP
ejpam-5962	294	8	every	every	DET
ejpam-5962	294	9	pairwise	pairwise	NOUN
ejpam-5962	294	10	compact	compact	ADJ
ejpam-5962	294	11	closed	closed	ADJ
ejpam-5962	294	12	spaces	space	NOUN
ejpam-5962	294	13	.	.	PUNCT
ejpam-5962	294	14	example	example	NOUN
ejpam-5962	294	15	6.1	6.1	NUM
ejpam-5962	294	16	.	.	PUNCT
ejpam-5962	295	1	(	(	PUNCT
ejpam-5962	295	2	r,ϑs	r,ϑs	NUM
ejpam-5962	295	3	,	,	PUNCT
ejpam-5962	295	4	ϑl	ϑl	NOUN
ejpam-5962	295	5	)	)	PUNCT
ejpam-5962	295	6	is	be	AUX
ejpam-5962	295	7	not	not	PART
ejpam-5962	295	8	pairwise	pairwise	NOUN
ejpam-5962	295	9	lindelöf	lindelöf	NOUN
ejpam-5962	295	10	space	space	NOUN
ejpam-5962	295	11	.	.	PUNCT
ejpam-5962	296	1	due	due	ADP
ejpam-5962	296	2	to	to	ADP
ejpam-5962	296	3	the	the	DET
ejpam-5962	296	4	fact	fact	NOUN
ejpam-5962	296	5	that	that	SCONJ
ejpam-5962	296	6	u	u	NOUN
ejpam-5962	296	7	is	be	AUX
ejpam-5962	296	8	ϑs−open	ϑs−open	NOUN
ejpam-5962	296	9	subset	subset	VERB
ejpam-5962	296	10	,	,	PUNCT
ejpam-5962	296	11	then	then	ADV
ejpam-5962	296	12	u	u	NOUN
ejpam-5962	296	13	is	be	AUX
ejpam-5962	296	14	ϑs−lindelöf	ϑs−lindelöf	NOUN
ejpam-5962	296	15	.	.	PUNCT
ejpam-5962	297	1	u	u	NOUN
ejpam-5962	297	2	is	be	AUX
ejpam-5962	297	3	not	not	PART
ejpam-5962	297	4	τl−closed	τl−close	VERB
ejpam-5962	297	5	though	though	ADV
ejpam-5962	297	6	.	.	PUNCT
ejpam-5962	298	1	the	the	DET
ejpam-5962	298	2	example	example	NOUN
ejpam-5962	298	3	below	below	ADV
ejpam-5962	298	4	demonstrates	demonstrate	VERB
ejpam-5962	298	5	that	that	SCONJ
ejpam-5962	298	6	pairwise	pairwise	PROPN
ejpam-5962	298	7	lindelöf	lindelöf	NOUN
ejpam-5962	298	8	closed	close	VERB
ejpam-5962	298	9	spaces	space	NOUN
ejpam-5962	298	10	are	be	AUX
ejpam-5962	298	11	not	not	PART
ejpam-5962	298	12	always	always	ADV
ejpam-5962	298	13	represented	represent	VERB
ejpam-5962	298	14	by	by	ADP
ejpam-5962	298	15	their	their	PRON
ejpam-5962	298	16	continuous	continuous	ADJ
ejpam-5962	298	17	images	image	NOUN
ejpam-5962	298	18	.	.	PUNCT
ejpam-5962	298	19	example	example	NOUN
ejpam-5962	299	1	6.2	6.2	NUM
ejpam-5962	299	2	.	.	PUNCT
ejpam-5962	299	3	assume	assume	VERB
ejpam-5962	299	4	that	that	SCONJ
ejpam-5962	299	5	φ	φ	PROPN
ejpam-5962	299	6	:	:	PUNCT
ejpam-5962	299	7	(	(	PUNCT
ejpam-5962	299	8	r,ϑd	r,ϑd	PROPN
ejpam-5962	299	9	,	,	PUNCT
ejpam-5962	299	10	ϑd	ϑd	NOUN
ejpam-5962	299	11	)	)	PUNCT
ejpam-5962	299	12	→	→	SYM
ejpam-5962	299	13	(	(	PUNCT
ejpam-5962	299	14	r,ϑind	r,ϑind	NOUN
ejpam-5962	299	15	,	,	PUNCT
ejpam-5962	299	16	ϑind	ϑind	NOUN
ejpam-5962	299	17	)	)	PUNCT
ejpam-5962	299	18	is	be	AUX
ejpam-5962	299	19	pairwise	pairwise	NOUN
ejpam-5962	299	20	continuous	continuous	ADJ
ejpam-5962	299	21	function	function	NOUN
ejpam-5962	299	22	.	.	PUNCT
ejpam-5962	300	1	as	as	ADP
ejpam-5962	300	2	a	a	DET
ejpam-5962	300	3	result	result	NOUN
ejpam-5962	300	4	,	,	PUNCT
ejpam-5962	300	5	whereas	whereas	SCONJ
ejpam-5962	300	6	(	(	PUNCT
ejpam-5962	300	7	r,ϑd	r,ϑd	NOUN
ejpam-5962	300	8	,	,	PUNCT
ejpam-5962	300	9	ϑd	ϑd	NOUN
ejpam-5962	300	10	)	)	PUNCT
ejpam-5962	300	11	is	be	AUX
ejpam-5962	300	12	pairwise	pairwise	NOUN
ejpam-5962	300	13	lindelöf	lindelöf	NOUN
ejpam-5962	300	14	closed	close	VERB
ejpam-5962	300	15	space	space	NOUN
ejpam-5962	300	16	,	,	PUNCT
ejpam-5962	300	17	but	but	CCONJ
ejpam-5962	300	18	(	(	PUNCT
ejpam-5962	300	19	r,ϑind	r,ϑind	NOUN
ejpam-5962	300	20	,	,	PUNCT
ejpam-5962	300	21	ϑind	ϑind	NOUN
ejpam-5962	300	22	)	)	PUNCT
ejpam-5962	300	23	is	be	AUX
ejpam-5962	300	24	not	not	PART
ejpam-5962	300	25	pairwise	pairwise	NOUN
ejpam-5962	300	26	lindelöf	lindelöf	NOUN
ejpam-5962	300	27	closed	close	VERB
ejpam-5962	300	28	space	space	NOUN
ejpam-5962	300	29	.	.	PUNCT
ejpam-5962	301	1	a.	a.	NOUN
ejpam-5962	301	2	a.	a.	PROPN
ejpam-5962	301	3	atoom	atoom	PROPN
ejpam-5962	301	4	et	et	PROPN
ejpam-5962	301	5	al	al	PROPN
ejpam-5962	301	6	.	.	PUNCT
ejpam-5962	301	7	/	/	SYM
ejpam-5962	301	8	eur	eur	PROPN
ejpam-5962	301	9	.	.	PUNCT
ejpam-5962	302	1	j.	j.	PROPN
ejpam-5962	302	2	pure	pure	PROPN
ejpam-5962	302	3	appl	appl	PROPN
ejpam-5962	302	4	.	.	PROPN
ejpam-5962	302	5	math	math	PROPN
ejpam-5962	302	6	,	,	PUNCT
ejpam-5962	302	7	18	18	NUM
ejpam-5962	302	8	(	(	PUNCT
ejpam-5962	302	9	2	2	NUM
ejpam-5962	302	10	)	)	PUNCT
ejpam-5962	302	11	(	(	PUNCT
ejpam-5962	302	12	2025	2025	NUM
ejpam-5962	302	13	)	)	PUNCT
ejpam-5962	302	14	,	,	PUNCT
ejpam-5962	302	15	5962	5962	NUM
ejpam-5962	302	16	11	11	NUM
ejpam-5962	302	17	of	of	ADP
ejpam-5962	302	18	17	17	NUM
ejpam-5962	302	19	theorem	theorem	NOUN
ejpam-5962	302	20	6.1	6.1	NUM
ejpam-5962	302	21	.	.	PUNCT
ejpam-5962	303	1	while	while	SCONJ
ejpam-5962	303	2	φ	φ	PROPN
ejpam-5962	303	3	:	:	PUNCT
ejpam-5962	303	4	(	(	PUNCT
ejpam-5962	303	5	z	z	NOUN
ejpam-5962	303	6	,	,	PUNCT
ejpam-5962	303	7	ϑ1	ϑ1	PROPN
ejpam-5962	303	8	,	,	PUNCT
ejpam-5962	303	9	ϑ2)injection−−−−−−−→	ϑ2)injection−−−−−−−→	NOUN
ejpam-5962	303	10	(	(	PUNCT
ejpam-5962	303	11	n	n	CCONJ
ejpam-5962	303	12	,	,	PUNCT
ejpam-5962	303	13	β1	β1	PROPN
ejpam-5962	303	14	,	,	PUNCT
ejpam-5962	303	15	β2	β2	PROPN
ejpam-5962	303	16	)	)	PUNCT
ejpam-5962	303	17	be	be	VERB
ejpam-5962	303	18	pairwise	pairwise	NOUN
ejpam-5962	303	19	injection	injection	NOUN
ejpam-5962	303	20	continuous	continuous	ADJ
ejpam-5962	303	21	function	function	NOUN
ejpam-5962	303	22	from	from	ADP
ejpam-5962	303	23	(	(	PUNCT
ejpam-5962	303	24	z	z	NOUN
ejpam-5962	303	25	,	,	PUNCT
ejpam-5962	303	26	ϑ1	ϑ1	NOUN
ejpam-5962	303	27	,	,	PUNCT
ejpam-5962	303	28	ϑ2	ϑ2	PROPN
ejpam-5962	303	29	)	)	PUNCT
ejpam-5962	303	30	into	into	ADP
ejpam-5962	303	31	pairwise	pairwise	NOUN
ejpam-5962	303	32	lindelöf	lindelöf	NOUN
ejpam-5962	303	33	closed	close	VERB
ejpam-5962	303	34	space	space	NOUN
ejpam-5962	303	35	(	(	PUNCT
ejpam-5962	303	36	n	n	X
ejpam-5962	303	37	,	,	PUNCT
ejpam-5962	303	38	β1	β1	PROPN
ejpam-5962	303	39	,	,	PUNCT
ejpam-5962	303	40	β2	β2	PROPN
ejpam-5962	303	41	)	)	PUNCT
ejpam-5962	303	42	,	,	PUNCT
ejpam-5962	303	43	therefore	therefore	ADV
ejpam-5962	303	44	(	(	PUNCT
ejpam-5962	303	45	z	z	NOUN
ejpam-5962	303	46	,	,	PUNCT
ejpam-5962	303	47	ϑ1	ϑ1	NOUN
ejpam-5962	303	48	,	,	PUNCT
ejpam-5962	303	49	ϑ2	ϑ2	PROPN
ejpam-5962	303	50	)	)	PUNCT
ejpam-5962	303	51	is	be	AUX
ejpam-5962	303	52	too	too	ADV
ejpam-5962	303	53	.	.	PUNCT
ejpam-5962	304	1	proof	proof	NOUN
ejpam-5962	304	2	.	.	PUNCT
ejpam-5962	305	1	suppose	suppose	VERB
ejpam-5962	305	2	that	that	SCONJ
ejpam-5962	305	3	t	t	PROPN
ejpam-5962	305	4	is	be	AUX
ejpam-5962	305	5	any	any	DET
ejpam-5962	305	6	ϑ1−lindelöf	ϑ1−lindelöf	PROPN
ejpam-5962	305	7	subset	subset	NOUN
ejpam-5962	305	8	of	of	ADP
ejpam-5962	305	9	(	(	PUNCT
ejpam-5962	305	10	z	z	NOUN
ejpam-5962	305	11	,	,	PUNCT
ejpam-5962	305	12	ϑ1	ϑ1	NOUN
ejpam-5962	305	13	,	,	PUNCT
ejpam-5962	305	14	ϑ2	ϑ2	PROPN
ejpam-5962	305	15	)	)	PUNCT
ejpam-5962	305	16	,	,	PUNCT
ejpam-5962	305	17	then	then	ADV
ejpam-5962	305	18	φ(t	φ(t	PROPN
ejpam-5962	305	19	)	)	PUNCT
ejpam-5962	305	20	is	be	AUX
ejpam-5962	305	21	β1−lindelöf	β1−lindelöf	PROPN
ejpam-5962	305	22	subset	subset	VERB
ejpam-5962	305	23	in	in	ADP
ejpam-5962	305	24	(	(	PUNCT
ejpam-5962	305	25	n	n	CCONJ
ejpam-5962	305	26	,	,	PUNCT
ejpam-5962	305	27	β1	β1	NOUN
ejpam-5962	305	28	,	,	PUNCT
ejpam-5962	305	29	β2	β2	PROPN
ejpam-5962	305	30	)	)	PUNCT
ejpam-5962	305	31	.	.	PUNCT
ejpam-5962	306	1	given	give	VERB
ejpam-5962	306	2	that	that	SCONJ
ejpam-5962	306	3	(	(	PUNCT
ejpam-5962	306	4	n	n	X
ejpam-5962	306	5	,	,	PUNCT
ejpam-5962	306	6	β1	β1	PROPN
ejpam-5962	306	7	,	,	PUNCT
ejpam-5962	306	8	β2	β2	NOUN
ejpam-5962	306	9	)	)	PUNCT
ejpam-5962	306	10	is	be	AUX
ejpam-5962	306	11	pairwise	pairwise	NOUN
ejpam-5962	306	12	closed	close	VERB
ejpam-5962	306	13	lindelöf	lindelöf	NOUN
ejpam-5962	306	14	space	space	NOUN
ejpam-5962	306	15	,	,	PUNCT
ejpam-5962	306	16	then	then	ADV
ejpam-5962	306	17	φ(t	φ(t	PROPN
ejpam-5962	306	18	)	)	PUNCT
ejpam-5962	306	19	is	be	AUX
ejpam-5962	306	20	β2−closed	β2−close	VERB
ejpam-5962	306	21	of	of	ADP
ejpam-5962	306	22	(	(	PUNCT
ejpam-5962	306	23	n	n	X
ejpam-5962	306	24	,	,	PUNCT
ejpam-5962	306	25	β1	β1	PROPN
ejpam-5962	306	26	,	,	PUNCT
ejpam-5962	306	27	β2	β2	PROPN
ejpam-5962	306	28	)	)	PUNCT
ejpam-5962	306	29	and	and	CCONJ
ejpam-5962	306	30	φ	φ	PROPN
ejpam-5962	306	31	is	be	AUX
ejpam-5962	306	32	pairwise	pairwise	NOUN
ejpam-5962	306	33	injection	injection	NOUN
ejpam-5962	306	34	continuous	continuous	ADJ
ejpam-5962	306	35	function	function	NOUN
ejpam-5962	306	36	,	,	PUNCT
ejpam-5962	306	37	then	then	ADV
ejpam-5962	306	38	φ−1(φ(t	φ−1(φ(t	ADV
ejpam-5962	306	39	)	)	PUNCT
ejpam-5962	307	1	=	=	SYM
ejpam-5962	307	2	t	t	PROPN
ejpam-5962	307	3	is	be	AUX
ejpam-5962	307	4	ϑ2−closed	ϑ2−close	VERB
ejpam-5962	307	5	subset	subset	NOUN
ejpam-5962	307	6	of	of	ADP
ejpam-5962	307	7	(	(	PUNCT
ejpam-5962	307	8	z	z	NOUN
ejpam-5962	307	9	,	,	PUNCT
ejpam-5962	307	10	ϑ1	ϑ1	NOUN
ejpam-5962	307	11	,	,	PUNCT
ejpam-5962	307	12	ϑ2	ϑ2	PROPN
ejpam-5962	307	13	)	)	PUNCT
ejpam-5962	307	14	.	.	PUNCT
ejpam-5962	308	1	simillarly	simillarly	ADV
ejpam-5962	308	2	for	for	ADP
ejpam-5962	308	3	j	j	PROPN
ejpam-5962	308	4	is	be	AUX
ejpam-5962	308	5	ϑ2−lindelöf	ϑ2−lindelöf	PROPN
ejpam-5962	308	6	subset	subset	NOUN
ejpam-5962	308	7	of	of	ADP
ejpam-5962	308	8	(	(	PUNCT
ejpam-5962	308	9	z	z	NOUN
ejpam-5962	308	10	,	,	PUNCT
ejpam-5962	308	11	ϑ1	ϑ1	NOUN
ejpam-5962	308	12	,	,	PUNCT
ejpam-5962	308	13	ϑ2	ϑ2	PROPN
ejpam-5962	308	14	)	)	PUNCT
ejpam-5962	308	15	.	.	PUNCT
ejpam-5962	309	1	the	the	DET
ejpam-5962	309	2	(	(	PUNCT
ejpam-5962	309	3	z	z	NOUN
ejpam-5962	309	4	,	,	PUNCT
ejpam-5962	309	5	ϑ1	ϑ1	NOUN
ejpam-5962	309	6	,	,	PUNCT
ejpam-5962	309	7	ϑ2	ϑ2	PROPN
ejpam-5962	309	8	)	)	PUNCT
ejpam-5962	309	9	is	be	AUX
ejpam-5962	309	10	ϑ2	ϑ2	NOUN
ejpam-5962	309	11	-	-	PUNCT
ejpam-5962	309	12	lindelöf	lindelöf	NOUN
ejpam-5962	309	13	subset	subset	VERB
ejpam-5962	309	14	behaves	behave	VERB
ejpam-5962	309	15	similarly	similarly	ADV
ejpam-5962	309	16	for	for	ADP
ejpam-5962	309	17	j	j	PROPN
ejpam-5962	309	18	.	.	PUNCT
ejpam-5962	310	1	consequently	consequently	ADV
ejpam-5962	310	2	,	,	PUNCT
ejpam-5962	310	3	pairwise	pairwise	PROPN
ejpam-5962	310	4	lindelöf	lindelöf	NOUN
ejpam-5962	310	5	closed	close	VERB
ejpam-5962	310	6	space	space	NOUN
ejpam-5962	310	7	(	(	PUNCT
ejpam-5962	310	8	z	z	NOUN
ejpam-5962	310	9	,	,	PUNCT
ejpam-5962	310	10	ϑ1	ϑ1	NOUN
ejpam-5962	310	11	,	,	PUNCT
ejpam-5962	310	12	ϑ2	ϑ2	NOUN
ejpam-5962	310	13	)	)	PUNCT
ejpam-5962	310	14	exists	exist	VERB
ejpam-5962	310	15	.	.	PUNCT
ejpam-5962	311	1	theorem	theorem	VERB
ejpam-5962	311	2	6.2	6.2	NUM
ejpam-5962	311	3	.	.	PUNCT
ejpam-5962	312	1	being	be	AUX
ejpam-5962	312	2	a	a	DET
ejpam-5962	312	3	pairwise	pairwise	NOUN
ejpam-5962	312	4	lindelöf	lindelöf	NOUN
ejpam-5962	312	5	closed	close	VERB
ejpam-5962	312	6	space	space	NOUN
ejpam-5962	312	7	has	have	VERB
ejpam-5962	312	8	the	the	DET
ejpam-5962	312	9	bitopological	bitopological	ADJ
ejpam-5962	312	10	characteristic	characteristic	NOUN
ejpam-5962	312	11	.	.	PUNCT
ejpam-5962	313	1	proof	proof	NOUN
ejpam-5962	313	2	.	.	PUNCT
ejpam-5962	314	1	letting	let	VERB
ejpam-5962	314	2	(	(	PUNCT
ejpam-5962	314	3	z	z	NOUN
ejpam-5962	314	4	,	,	PUNCT
ejpam-5962	314	5	ϑz1	ϑz1	X
ejpam-5962	314	6	,	,	PUNCT
ejpam-5962	314	7	ϑz2	ϑz2	PROPN
ejpam-5962	314	8	)	)	PUNCT
ejpam-5962	314	9	be	be	VERB
ejpam-5962	314	10	a	a	DET
ejpam-5962	314	11	pairwise	pairwise	NOUN
ejpam-5962	314	12	lindelöf	lindelöf	NOUN
ejpam-5962	314	13	closed	close	VERB
ejpam-5962	314	14	space	space	NOUN
ejpam-5962	314	15	and	and	CCONJ
ejpam-5962	314	16	(	(	PUNCT
ejpam-5962	314	17	n,ϑn1	n,ϑn1	PROPN
ejpam-5962	314	18	,	,	PUNCT
ejpam-5962	314	19	ϑn2	ϑn2	X
ejpam-5962	314	20	)	)	PUNCT
ejpam-5962	314	21	be	be	AUX
ejpam-5962	314	22	a	a	DET
ejpam-5962	314	23	subspace	subspace	NOUN
ejpam-5962	314	24	of	of	ADP
ejpam-5962	314	25	(	(	PUNCT
ejpam-5962	314	26	z	z	NOUN
ejpam-5962	314	27	,	,	PUNCT
ejpam-5962	314	28	ϑz1	ϑz1	X
ejpam-5962	314	29	,	,	PUNCT
ejpam-5962	314	30	ϑz2	ϑz2	PROPN
ejpam-5962	314	31	)	)	PUNCT
ejpam-5962	314	32	.	.	PUNCT
ejpam-5962	315	1	given	give	VERB
ejpam-5962	315	2	φ	φ	PROPN
ejpam-5962	315	3	:	:	PUNCT
ejpam-5962	315	4	(	(	PUNCT
ejpam-5962	315	5	z	z	NOUN
ejpam-5962	315	6	,	,	PUNCT
ejpam-5962	315	7	ϑz1	ϑz1	X
ejpam-5962	315	8	,	,	PUNCT
ejpam-5962	315	9	ϑz2	ϑz2	PROPN
ejpam-5962	315	10	)	)	PUNCT
ejpam-5962	315	11	→	→	SYM
ejpam-5962	315	12	(	(	PUNCT
ejpam-5962	315	13	n,ϑn1	n,ϑn1	PROPN
ejpam-5962	315	14	,	,	PUNCT
ejpam-5962	315	15	ϑn2	ϑn2	X
ejpam-5962	315	16	)	)	PUNCT
ejpam-5962	315	17	be	be	VERB
ejpam-5962	315	18	pairwise	pairwise	NOUN
ejpam-5962	315	19	homeomorphism	homeomorphism	NOUN
ejpam-5962	315	20	and	and	CCONJ
ejpam-5962	315	21	u	u	NOUN
ejpam-5962	315	22	be	be	AUX
ejpam-5962	315	23	ϑn1−lindelöf	ϑn1−lindelöf	NOUN
ejpam-5962	315	24	subset	subset	VERB
ejpam-5962	315	25	of	of	ADP
ejpam-5962	315	26	(	(	PUNCT
ejpam-5962	315	27	n,ϑn1	n,ϑn1	PROPN
ejpam-5962	315	28	,	,	PUNCT
ejpam-5962	315	29	ϑn2	ϑn2	PROPN
ejpam-5962	315	30	)	)	PUNCT
ejpam-5962	315	31	.	.	PUNCT
ejpam-5962	316	1	granted	grant	VERB
ejpam-5962	316	2	that	that	SCONJ
ejpam-5962	316	3	(	(	PUNCT
ejpam-5962	316	4	z	z	NOUN
ejpam-5962	316	5	,	,	PUNCT
ejpam-5962	316	6	ϑz1	ϑz1	X
ejpam-5962	316	7	,	,	PUNCT
ejpam-5962	316	8	ϑz2	ϑz2	PROPN
ejpam-5962	316	9	)	)	PUNCT
ejpam-5962	316	10	is	be	AUX
ejpam-5962	316	11	a	a	DET
ejpam-5962	316	12	pairwise	pairwise	NOUN
ejpam-5962	316	13	lindelöf	lindelöf	NOUN
ejpam-5962	316	14	closed	close	VERB
ejpam-5962	316	15	space	space	NOUN
ejpam-5962	316	16	,	,	PUNCT
ejpam-5962	316	17	so	so	ADV
ejpam-5962	316	18	φ−1(u	φ−1(u	PROPN
ejpam-5962	316	19	)	)	PUNCT
ejpam-5962	316	20	is	be	AUX
ejpam-5962	316	21	ϑz2−closed	ϑz2−close	VERB
ejpam-5962	316	22	in	in	ADP
ejpam-5962	316	23	(	(	PUNCT
ejpam-5962	316	24	z	z	NOUN
ejpam-5962	316	25	,	,	PUNCT
ejpam-5962	316	26	ϑz1	ϑz1	X
ejpam-5962	316	27	,	,	PUNCT
ejpam-5962	316	28	ϑz2	ϑz2	PROPN
ejpam-5962	316	29	)	)	PUNCT
ejpam-5962	316	30	.	.	PUNCT
ejpam-5962	317	1	as	as	ADP
ejpam-5962	317	2	a	a	DET
ejpam-5962	317	3	result	result	NOUN
ejpam-5962	317	4	,	,	PUNCT
ejpam-5962	317	5	φ−1(φ(u	φ−1(φ(u	PROPN
ejpam-5962	317	6	)	)	PUNCT
ejpam-5962	318	1	=	=	SYM
ejpam-5962	318	2	u	u	NOUN
ejpam-5962	318	3	is	be	AUX
ejpam-5962	318	4	ϑn2−closed	ϑn2−close	VERB
ejpam-5962	318	5	in	in	ADP
ejpam-5962	318	6	(	(	PUNCT
ejpam-5962	318	7	n,ϑn1	n,ϑn1	INTJ
ejpam-5962	318	8	,	,	PUNCT
ejpam-5962	318	9	ϑn2).similar	ϑn2).similar	PROPN
ejpam-5962	318	10	conditions	condition	NOUN
ejpam-5962	318	11	apply	apply	VERB
ejpam-5962	318	12	v	v	PRON
ejpam-5962	318	13	be	be	NOUN
ejpam-5962	318	14	ϑn2−lindelöf	ϑn2−lindelöf	NOUN
ejpam-5962	318	15	subset	subset	VERB
ejpam-5962	318	16	of	of	ADP
ejpam-5962	318	17	(	(	PUNCT
ejpam-5962	318	18	n,ϑn1	n,ϑn1	PROPN
ejpam-5962	318	19	,	,	PUNCT
ejpam-5962	318	20	ϑn2	ϑn2	PROPN
ejpam-5962	318	21	)	)	PUNCT
ejpam-5962	318	22	.	.	PUNCT
ejpam-5962	319	1	therefore	therefore	ADV
ejpam-5962	319	2	,	,	PUNCT
ejpam-5962	319	3	(	(	PUNCT
ejpam-5962	319	4	n,ϑn1	n,ϑn1	X
ejpam-5962	319	5	,	,	PUNCT
ejpam-5962	319	6	ϑn2	ϑn2	X
ejpam-5962	319	7	)	)	PUNCT
ejpam-5962	319	8	is	be	AUX
ejpam-5962	319	9	pairwise	pairwise	NOUN
ejpam-5962	319	10	lindelöf	lindelöf	NOUN
ejpam-5962	319	11	closed	close	VERB
ejpam-5962	319	12	space	space	NOUN
ejpam-5962	319	13	.	.	PUNCT
ejpam-5962	320	1	theorem	theorem	VERB
ejpam-5962	320	2	6.3	6.3	NUM
ejpam-5962	320	3	.	.	PUNCT
ejpam-5962	321	1	being	be	AUX
ejpam-5962	321	2	a	a	DET
ejpam-5962	321	3	pairwise	pairwise	NOUN
ejpam-5962	321	4	lindelöf	lindelöf	NOUN
ejpam-5962	321	5	closed	close	VERB
ejpam-5962	321	6	space	space	NOUN
ejpam-5962	321	7	is	be	AUX
ejpam-5962	321	8	an	an	DET
ejpam-5962	321	9	inherited	inherit	VERB
ejpam-5962	321	10	quality	quality	NOUN
ejpam-5962	321	11	.	.	PUNCT
ejpam-5962	322	1	proof	proof	NOUN
ejpam-5962	322	2	.	.	PUNCT
ejpam-5962	323	1	assuming	assume	VERB
ejpam-5962	323	2	(	(	PUNCT
ejpam-5962	323	3	z	z	NOUN
ejpam-5962	323	4	,	,	PUNCT
ejpam-5962	323	5	ϑz1	ϑz1	X
ejpam-5962	323	6	,	,	PUNCT
ejpam-5962	323	7	ϑz2	ϑz2	PROPN
ejpam-5962	323	8	)	)	PUNCT
ejpam-5962	323	9	be	be	VERB
ejpam-5962	323	10	a	a	DET
ejpam-5962	323	11	pairwise	pairwise	NOUN
ejpam-5962	323	12	closed	close	VERB
ejpam-5962	323	13	lindelöf	lindelöf	NOUN
ejpam-5962	323	14	space	space	NOUN
ejpam-5962	323	15	,	,	PUNCT
ejpam-5962	323	16	(	(	PUNCT
ejpam-5962	323	17	n,ϑn1	n,ϑn1	INTJ
ejpam-5962	323	18	,	,	PUNCT
ejpam-5962	323	19	ϑn2	ϑn2	X
ejpam-5962	323	20	)	)	PUNCT
ejpam-5962	323	21	be	be	AUX
ejpam-5962	323	22	a	a	DET
ejpam-5962	323	23	subspace	subspace	NOUN
ejpam-5962	323	24	of	of	ADP
ejpam-5962	323	25	(	(	PUNCT
ejpam-5962	323	26	z	z	NOUN
ejpam-5962	323	27	,	,	PUNCT
ejpam-5962	323	28	ϑz1	ϑz1	X
ejpam-5962	323	29	,	,	PUNCT
ejpam-5962	323	30	ϑz2	ϑz2	PROPN
ejpam-5962	323	31	)	)	PUNCT
ejpam-5962	323	32	and	and	CCONJ
ejpam-5962	323	33	u	u	PRON
ejpam-5962	323	34	be	be	VERB
ejpam-5962	323	35	ϑn1−lindelöf	ϑn1−lindelöf	NOUN
ejpam-5962	323	36	subset	subset	VERB
ejpam-5962	323	37	of	of	ADP
ejpam-5962	323	38	(	(	PUNCT
ejpam-5962	323	39	n,ϑn1	n,ϑn1	PROPN
ejpam-5962	323	40	,	,	PUNCT
ejpam-5962	323	41	ϑn2	ϑn2	PROPN
ejpam-5962	323	42	)	)	PUNCT
ejpam-5962	323	43	,	,	PUNCT
ejpam-5962	323	44	therefore	therefore	ADV
ejpam-5962	323	45	u	u	NOUN
ejpam-5962	323	46	is	be	AUX
ejpam-5962	323	47	ϑz1−lindelöf	ϑz1−lindelöf	NOUN
ejpam-5962	323	48	subset	subset	VERB
ejpam-5962	323	49	of	of	ADP
ejpam-5962	323	50	(	(	PUNCT
ejpam-5962	323	51	z	z	NOUN
ejpam-5962	323	52	,	,	PUNCT
ejpam-5962	323	53	ϑz1	ϑz1	X
ejpam-5962	323	54	,	,	PUNCT
ejpam-5962	323	55	ϑz2	ϑz2	PROPN
ejpam-5962	323	56	)	)	PUNCT
ejpam-5962	323	57	.	.	PUNCT
ejpam-5962	324	1	however	however	ADV
ejpam-5962	324	2	,	,	PUNCT
ejpam-5962	324	3	(	(	PUNCT
ejpam-5962	324	4	z	z	X
ejpam-5962	324	5	,	,	PUNCT
ejpam-5962	324	6	ϑz1	ϑz1	X
ejpam-5962	324	7	,	,	PUNCT
ejpam-5962	324	8	ϑz2	ϑz2	PROPN
ejpam-5962	324	9	)	)	PUNCT
ejpam-5962	324	10	is	be	AUX
ejpam-5962	324	11	a	a	DET
ejpam-5962	324	12	pairwise	pairwise	NOUN
ejpam-5962	324	13	closed	close	VERB
ejpam-5962	324	14	lindelöf	lindelöf	NOUN
ejpam-5962	324	15	space	space	NOUN
ejpam-5962	324	16	,	,	PUNCT
ejpam-5962	324	17	so	so	CCONJ
ejpam-5962	324	18	u	u	NOUN
ejpam-5962	324	19	is	be	AUX
ejpam-5962	324	20	ϑz2−closed	ϑz2−close	VERB
ejpam-5962	324	21	in	in	ADP
ejpam-5962	324	22	(	(	PUNCT
ejpam-5962	324	23	z	z	NOUN
ejpam-5962	324	24	,	,	PUNCT
ejpam-5962	324	25	ϑz1	ϑz1	X
ejpam-5962	324	26	,	,	PUNCT
ejpam-5962	324	27	ϑz2	ϑz2	PROPN
ejpam-5962	324	28	)	)	PUNCT
ejpam-5962	324	29	.	.	PUNCT
ejpam-5962	325	1	nevertheless	nevertheless	ADV
ejpam-5962	325	2	,	,	PUNCT
ejpam-5962	325	3	u	u	NOUN
ejpam-5962	325	4	=	=	SYM
ejpam-5962	325	5	u	u	PROPN
ejpam-5962	325	6	∩	∩	NOUN
ejpam-5962	325	7	n	n	PRON
ejpam-5962	325	8	is	be	AUX
ejpam-5962	325	9	ϑn2−closed	ϑn2−close	VERB
ejpam-5962	325	10	in	in	ADP
ejpam-5962	325	11	(	(	PUNCT
ejpam-5962	325	12	n,ϑn1	n,ϑn1	PROPN
ejpam-5962	325	13	,	,	PUNCT
ejpam-5962	325	14	ϑn2	ϑn2	PROPN
ejpam-5962	325	15	)	)	PUNCT
ejpam-5962	325	16	.	.	PUNCT
ejpam-5962	326	1	the	the	DET
ejpam-5962	326	2	actually	actually	ADV
ejpam-5962	326	3	imply	imply	VERB
ejpam-5962	326	4	(	(	PUNCT
ejpam-5962	326	5	n,ϑn1	n,ϑn1	NOUN
ejpam-5962	326	6	,	,	PUNCT
ejpam-5962	326	7	ϑn2	ϑn2	X
ejpam-5962	326	8	)	)	PUNCT
ejpam-5962	326	9	is	be	AUX
ejpam-5962	326	10	pairwise	pairwise	NOUN
ejpam-5962	326	11	lindelöf	lindelöf	NOUN
ejpam-5962	326	12	closed	close	VERB
ejpam-5962	326	13	space	space	NOUN
ejpam-5962	326	14	.	.	PUNCT
ejpam-5962	327	1	7	7	X
ejpam-5962	327	2	.	.	X
ejpam-5962	327	3	some	some	DET
ejpam-5962	327	4	characterisations	characterisation	NOUN
ejpam-5962	327	5	of	of	ADP
ejpam-5962	327	6	pairwise	pairwise	PROPN
ejpam-5962	327	7	minimal	minimal	ADJ
ejpam-5962	327	8	closed	close	VERB
ejpam-5962	327	9	lindelöf	lindelöf	NOUN
ejpam-5962	327	10	spaces	space	VERB
ejpam-5962	327	11	more	more	ADJ
ejpam-5962	327	12	findings	finding	NOUN
ejpam-5962	327	13	about	about	ADP
ejpam-5962	327	14	the	the	DET
ejpam-5962	327	15	pairwise	pairwise	NOUN
ejpam-5962	327	16	minimal	minimal	ADJ
ejpam-5962	327	17	lindelöf	lindelöf	NOUN
ejpam-5962	327	18	closed	close	VERB
ejpam-5962	327	19	space	space	NOUN
ejpam-5962	327	20	’s	’s	PART
ejpam-5962	327	21	topological	topological	ADJ
ejpam-5962	327	22	properties	property	NOUN
ejpam-5962	327	23	are	be	AUX
ejpam-5962	327	24	presented	present	VERB
ejpam-5962	327	25	in	in	ADP
ejpam-5962	327	26	this	this	DET
ejpam-5962	327	27	part	part	NOUN
ejpam-5962	327	28	,	,	PUNCT
ejpam-5962	327	29	along	along	ADP
ejpam-5962	327	30	with	with	ADP
ejpam-5962	327	31	a	a	DET
ejpam-5962	327	32	diagram	diagram	NOUN
ejpam-5962	327	33	illustrating	illustrate	VERB
ejpam-5962	327	34	the	the	DET
ejpam-5962	327	35	main	main	ADJ
ejpam-5962	327	36	connection	connection	NOUN
ejpam-5962	327	37	between	between	ADP
ejpam-5962	327	38	these	these	DET
ejpam-5962	327	39	spaces	space	NOUN
ejpam-5962	327	40	.	.	PUNCT
ejpam-5962	328	1	definition	definition	NOUN
ejpam-5962	328	2	7.1	7.1	NUM
ejpam-5962	328	3	.	.	PUNCT
ejpam-5962	329	1	a	a	DET
ejpam-5962	329	2	bitopological	bitopological	ADJ
ejpam-5962	329	3	space	space	NOUN
ejpam-5962	329	4	(	(	PUNCT
ejpam-5962	329	5	z	z	NOUN
ejpam-5962	329	6	,	,	PUNCT
ejpam-5962	329	7	ϑ1	ϑ1	NOUN
ejpam-5962	329	8	,	,	PUNCT
ejpam-5962	329	9	ϑ2	ϑ2	PROPN
ejpam-5962	329	10	)	)	PUNCT
ejpam-5962	329	11	is	be	AUX
ejpam-5962	329	12	considered	consider	VERB
ejpam-5962	329	13	to	to	PART
ejpam-5962	329	14	be	be	AUX
ejpam-5962	329	15	pairwise	pairwise	NOUN
ejpam-5962	329	16	minimal	minimal	ADJ
ejpam-5962	329	17	lindelöf	lindelöf	NOUN
ejpam-5962	329	18	closed	close	VERB
ejpam-5962	329	19	space	space	NOUN
ejpam-5962	329	20	,	,	PUNCT
ejpam-5962	329	21	when	when	SCONJ
ejpam-5962	329	22	and	and	CCONJ
ejpam-5962	329	23	only	only	ADV
ejpam-5962	329	24	when	when	SCONJ
ejpam-5962	329	25	ϑ	ϑ	X
ejpam-5962	329	26	/	/	SYM
ejpam-5962	329	27	1	1	NUM
ejpam-5962	329	28	≤	≤	NOUN
ejpam-5962	329	29	ϑ1	ϑ1	NOUN
ejpam-5962	329	30	,	,	PUNCT
ejpam-5962	329	31	ϑ	ϑ	X
ejpam-5962	329	32	/	/	SYM
ejpam-5962	329	33	2	2	NUM
ejpam-5962	329	34	≤	≤	NOUN
ejpam-5962	329	35	ϑ2	ϑ2	NOUN
ejpam-5962	329	36	and	and	CCONJ
ejpam-5962	329	37	(	(	PUNCT
ejpam-5962	329	38	z	z	NOUN
ejpam-5962	329	39	,	,	PUNCT
ejpam-5962	329	40	ϑ	ϑ	X
ejpam-5962	329	41	/	/	SYM
ejpam-5962	329	42	1	1	NUM
ejpam-5962	329	43	,	,	PUNCT
ejpam-5962	329	44	ϑ	ϑ	X
ejpam-5962	329	45	/	/	SYM
ejpam-5962	329	46	2	2	NUM
ejpam-5962	329	47	)	)	PUNCT
ejpam-5962	329	48	is	be	AUX
ejpam-5962	329	49	not	not	PART
ejpam-5962	329	50	pairwise	pairwise	NOUN
ejpam-5962	329	51	lindelöf	lindelöf	NOUN
ejpam-5962	329	52	closed	close	VERB
ejpam-5962	329	53	space	space	NOUN
ejpam-5962	329	54	.	.	PUNCT
ejpam-5962	330	1	theorem	theorem	VERB
ejpam-5962	330	2	7.1	7.1	NUM
ejpam-5962	330	3	.	.	PUNCT
ejpam-5962	331	1	any	any	DET
ejpam-5962	331	2	pairwise	pairwise	NOUN
ejpam-5962	331	3	lindelöf	lindelöf	NOUN
ejpam-5962	331	4	closed	close	VERB
ejpam-5962	331	5	space	space	NOUN
ejpam-5962	331	6	is	be	AUX
ejpam-5962	331	7	a	a	DET
ejpam-5962	331	8	pairwise	pairwise	NOUN
ejpam-5962	331	9	minimal	minimal	ADJ
ejpam-5962	331	10	lindelöf	lindelöf	NOUN
ejpam-5962	331	11	closed	close	VERB
ejpam-5962	331	12	space	space	NOUN
ejpam-5962	331	13	.	.	PUNCT
ejpam-5962	332	1	proof	proof	NOUN
ejpam-5962	332	2	.	.	PUNCT
ejpam-5962	333	1	while	while	SCONJ
ejpam-5962	333	2	(	(	PUNCT
ejpam-5962	333	3	z	z	NOUN
ejpam-5962	333	4	,	,	PUNCT
ejpam-5962	333	5	ϑ1	ϑ1	NOUN
ejpam-5962	333	6	,	,	PUNCT
ejpam-5962	333	7	ϑ2	ϑ2	PROPN
ejpam-5962	333	8	)	)	PUNCT
ejpam-5962	333	9	be	be	VERB
ejpam-5962	333	10	pairwise	pairwise	NOUN
ejpam-5962	333	11	lindelöf	lindelöf	NOUN
ejpam-5962	333	12	closed	close	VERB
ejpam-5962	333	13	space	space	NOUN
ejpam-5962	333	14	and	and	CCONJ
ejpam-5962	333	15	is	be	AUX
ejpam-5962	333	16	not	not	PART
ejpam-5962	333	17	pairwise	pairwise	NOUN
ejpam-5962	333	18	minimal	minimal	ADJ
ejpam-5962	333	19	lindelöf	lindelöf	NOUN
ejpam-5962	333	20	closed	close	VERB
ejpam-5962	333	21	space	space	NOUN
ejpam-5962	333	22	,	,	PUNCT
ejpam-5962	333	23	subsequently	subsequently	ADV
ejpam-5962	333	24	there	there	PRON
ejpam-5962	333	25	are	be	VERB
ejpam-5962	333	26	ϑ	ϑ	X
ejpam-5962	333	27	/	/	SYM
ejpam-5962	333	28	1	1	NUM
ejpam-5962	333	29	,	,	PUNCT
ejpam-5962	333	30	ϑ	ϑ	X
ejpam-5962	333	31	/	/	SYM
ejpam-5962	333	32	2	2	NUM
ejpam-5962	333	33	make	make	VERB
ejpam-5962	333	34	ϑ	ϑ	NOUN
ejpam-5962	333	35	/	/	SYM
ejpam-5962	333	36	1	1	NUM
ejpam-5962	333	37	≤	≤	NOUN
ejpam-5962	333	38	ϑ1	ϑ1	NOUN
ejpam-5962	333	39	,	,	PUNCT
ejpam-5962	333	40	ϑ	ϑ	X
ejpam-5962	333	41	/	/	SYM
ejpam-5962	333	42	2	2	NUM
ejpam-5962	333	43	≤	≤	NOUN
ejpam-5962	333	44	ϑ2	ϑ2	NOUN
ejpam-5962	333	45	and	and	CCONJ
ejpam-5962	333	46	a.	a.	NOUN
ejpam-5962	333	47	a.	a.	NOUN
ejpam-5962	333	48	atoom	atoom	PROPN
ejpam-5962	333	49	et	et	PROPN
ejpam-5962	333	50	al	al	PROPN
ejpam-5962	333	51	.	.	PUNCT
ejpam-5962	333	52	/	/	SYM
ejpam-5962	333	53	eur	eur	PROPN
ejpam-5962	333	54	.	.	PUNCT
ejpam-5962	334	1	j.	j.	PROPN
ejpam-5962	334	2	pure	pure	PROPN
ejpam-5962	334	3	appl	appl	PROPN
ejpam-5962	334	4	.	.	PROPN
ejpam-5962	334	5	math	math	PROPN
ejpam-5962	334	6	,	,	PUNCT
ejpam-5962	334	7	18	18	NUM
ejpam-5962	334	8	(	(	PUNCT
ejpam-5962	334	9	2	2	NUM
ejpam-5962	334	10	)	)	PUNCT
ejpam-5962	334	11	(	(	PUNCT
ejpam-5962	334	12	2025	2025	NUM
ejpam-5962	334	13	)	)	PUNCT
ejpam-5962	334	14	,	,	PUNCT
ejpam-5962	334	15	5962	5962	NUM
ejpam-5962	334	16	12	12	NUM
ejpam-5962	334	17	of	of	ADP
ejpam-5962	334	18	17	17	NUM
ejpam-5962	334	19	(	(	PUNCT
ejpam-5962	334	20	z	z	NOUN
ejpam-5962	334	21	,	,	PUNCT
ejpam-5962	334	22	ϑ	ϑ	X
ejpam-5962	334	23	/	/	SYM
ejpam-5962	334	24	1	1	NUM
ejpam-5962	334	25	,	,	PUNCT
ejpam-5962	334	26	ϑ	ϑ	X
ejpam-5962	334	27	/	/	SYM
ejpam-5962	334	28	2	2	NUM
ejpam-5962	334	29	)	)	PUNCT
ejpam-5962	334	30	is	be	AUX
ejpam-5962	334	31	pairwise	pairwise	NOUN
ejpam-5962	334	32	closed	close	VERB
ejpam-5962	334	33	lindelöf	lindelöf	NOUN
ejpam-5962	334	34	space	space	NOUN
ejpam-5962	334	35	.	.	PUNCT
ejpam-5962	335	1	as	as	ADP
ejpam-5962	335	2	ix	ix	ADV
ejpam-5962	335	3	:	:	PUNCT
ejpam-5962	335	4	(	(	PUNCT
ejpam-5962	335	5	z	z	NOUN
ejpam-5962	335	6	,	,	PUNCT
ejpam-5962	335	7	ϑ1	ϑ1	NOUN
ejpam-5962	335	8	,	,	PUNCT
ejpam-5962	335	9	ϑ2	ϑ2	PROPN
ejpam-5962	335	10	)	)	PUNCT
ejpam-5962	335	11	→	→	SYM
ejpam-5962	335	12	(	(	PUNCT
ejpam-5962	335	13	z	z	NOUN
ejpam-5962	335	14	,	,	PUNCT
ejpam-5962	335	15	ϑ	ϑ	X
ejpam-5962	335	16	/	/	SYM
ejpam-5962	335	17	1	1	NUM
ejpam-5962	335	18	,	,	PUNCT
ejpam-5962	335	19	ϑ	ϑ	X
ejpam-5962	335	20	/	/	SYM
ejpam-5962	335	21	2	2	NUM
ejpam-5962	335	22	)	)	PUNCT
ejpam-5962	335	23	be	be	AUX
ejpam-5962	335	24	pairwise	pairwise	NOUN
ejpam-5962	335	25	identity	identity	NOUN
ejpam-5962	335	26	,	,	PUNCT
ejpam-5962	335	27	pairwise	pairwise	NOUN
ejpam-5962	335	28	continuous	continuous	ADJ
ejpam-5962	335	29	,	,	PUNCT
ejpam-5962	335	30	pairwise	pairwise	NOUN
ejpam-5962	335	31	bijection	bijection	NOUN
ejpam-5962	335	32	,	,	PUNCT
ejpam-5962	335	33	and	and	CCONJ
ejpam-5962	335	34	pairwise	pairwise	NOUN
ejpam-5962	335	35	closed	close	VERB
ejpam-5962	335	36	function	function	NOUN
ejpam-5962	335	37	,	,	PUNCT
ejpam-5962	335	38	after	after	ADP
ejpam-5962	335	39	which	which	PRON
ejpam-5962	335	40	ix	ix	ADV
ejpam-5962	335	41	is	be	AUX
ejpam-5962	335	42	pairwise	pairwise	NOUN
ejpam-5962	335	43	homeomorphism	homeomorphism	NOUN
ejpam-5962	335	44	,	,	PUNCT
ejpam-5962	335	45	so	so	SCONJ
ejpam-5962	335	46	ϑ	ϑ	ADJ
ejpam-5962	335	47	/	/	SYM
ejpam-5962	335	48	1	1	NUM
ejpam-5962	335	49	=	=	SYM
ejpam-5962	335	50	ϑ1	ϑ1	PROPN
ejpam-5962	335	51	,	,	PUNCT
ejpam-5962	335	52	ϑ	ϑ	X
ejpam-5962	335	53	/	/	SYM
ejpam-5962	335	54	2	2	NUM
ejpam-5962	335	55	=	=	SYM
ejpam-5962	335	56	ϑ2	ϑ2	NOUN
ejpam-5962	335	57	.	.	PUNCT
ejpam-5962	336	1	contradiction	contradiction	NOUN
ejpam-5962	336	2	results	result	NOUN
ejpam-5962	336	3	.	.	PUNCT
ejpam-5962	337	1	therefore	therefore	ADV
ejpam-5962	337	2	,	,	PUNCT
ejpam-5962	337	3	(	(	PUNCT
ejpam-5962	337	4	z	z	NOUN
ejpam-5962	337	5	,	,	PUNCT
ejpam-5962	337	6	ϑ1	ϑ1	NOUN
ejpam-5962	337	7	,	,	PUNCT
ejpam-5962	337	8	ϑ2	ϑ2	PROPN
ejpam-5962	337	9	)	)	PUNCT
ejpam-5962	337	10	is	be	AUX
ejpam-5962	337	11	pairwise	pairwise	NOUN
ejpam-5962	337	12	minimal	minimal	ADJ
ejpam-5962	337	13	closed	close	VERB
ejpam-5962	337	14	lindelöf	lindelöf	NOUN
ejpam-5962	337	15	space	space	NOUN
ejpam-5962	337	16	.	.	PUNCT
ejpam-5962	337	17	example	example	NOUN
ejpam-5962	338	1	7.1	7.1	NUM
ejpam-5962	338	2	.	.	PUNCT
ejpam-5962	339	1	while	while	SCONJ
ejpam-5962	339	2	z	z	NOUN
ejpam-5962	339	3	is	be	AUX
ejpam-5962	339	4	pairwise	pairwise	NOUN
ejpam-5962	339	5	countable	countable	ADJ
ejpam-5962	339	6	set	set	NOUN
ejpam-5962	339	7	,	,	PUNCT
ejpam-5962	339	8	after	after	ADP
ejpam-5962	339	9	which	which	PRON
ejpam-5962	339	10	(	(	PUNCT
ejpam-5962	339	11	z	z	NOUN
ejpam-5962	339	12	,	,	PUNCT
ejpam-5962	339	13	ϑd	ϑd	NOUN
ejpam-5962	339	14	,	,	PUNCT
ejpam-5962	339	15	ϑd	ϑd	NOUN
ejpam-5962	339	16	)	)	PUNCT
ejpam-5962	339	17	is	be	AUX
ejpam-5962	339	18	pairwise	pairwise	NOUN
ejpam-5962	339	19	minimal	minimal	ADJ
ejpam-5962	339	20	lindelöf	lindelöf	NOUN
ejpam-5962	339	21	closed	close	VERB
ejpam-5962	339	22	space	space	NOUN
ejpam-5962	339	23	.	.	PUNCT
ejpam-5962	340	1	remark	remark	VERB
ejpam-5962	340	2	7.1	7.1	NUM
ejpam-5962	340	3	.	.	PUNCT
ejpam-5962	341	1	as	as	SCONJ
ejpam-5962	341	2	demonstrated	demonstrate	VERB
ejpam-5962	341	3	by	by	ADP
ejpam-5962	341	4	the	the	DET
ejpam-5962	341	5	following	follow	VERB
ejpam-5962	341	6	example	example	NOUN
ejpam-5962	341	7	,	,	PUNCT
ejpam-5962	341	8	pairwise	pairwise	PROPN
ejpam-5962	341	9	minimal	minimal	ADJ
ejpam-5962	341	10	closed	close	VERB
ejpam-5962	341	11	lindelöf	lindelöf	NOUN
ejpam-5962	341	12	space	space	NOUN
ejpam-5962	341	13	is	be	AUX
ejpam-5962	341	14	not	not	PART
ejpam-5962	341	15	always	always	ADV
ejpam-5962	341	16	the	the	DET
ejpam-5962	341	17	continuous	continuous	ADJ
ejpam-5962	341	18	image	image	NOUN
ejpam-5962	341	19	of	of	ADP
ejpam-5962	341	20	pairwise	pairwise	NOUN
ejpam-5962	341	21	minimal	minimal	ADJ
ejpam-5962	341	22	closed	close	VERB
ejpam-5962	341	23	lindelöf	lindelöf	NOUN
ejpam-5962	341	24	space	space	NOUN
ejpam-5962	341	25	.	.	PUNCT
ejpam-5962	341	26	example	example	NOUN
ejpam-5962	341	27	7.2	7.2	NUM
ejpam-5962	341	28	.	.	PUNCT
ejpam-5962	342	1	assuming	assume	VERB
ejpam-5962	342	2	z	z	AUX
ejpam-5962	342	3	be	be	AUX
ejpam-5962	342	4	countable	countable	ADJ
ejpam-5962	342	5	set	set	NOUN
ejpam-5962	342	6	and	and	CCONJ
ejpam-5962	342	7	ix	ix	INTJ
ejpam-5962	342	8	:	:	PUNCT
ejpam-5962	342	9	(	(	PUNCT
ejpam-5962	342	10	z	z	NOUN
ejpam-5962	342	11	,	,	PUNCT
ejpam-5962	342	12	ϑd	ϑd	NOUN
ejpam-5962	342	13	,	,	PUNCT
ejpam-5962	342	14	ϑd	ϑd	NOUN
ejpam-5962	342	15	)	)	PUNCT
ejpam-5962	342	16	→	→	SYM
ejpam-5962	342	17	(	(	PUNCT
ejpam-5962	342	18	z	z	NOUN
ejpam-5962	342	19	,	,	PUNCT
ejpam-5962	342	20	ϑind	ϑind	ADJ
ejpam-5962	342	21	,	,	PUNCT
ejpam-5962	342	22	ϑind	ϑind	NOUN
ejpam-5962	342	23	)	)	PUNCT
ejpam-5962	342	24	be	be	VERB
ejpam-5962	342	25	pairwise	pairwise	NOUN
ejpam-5962	342	26	identity	identity	NOUN
ejpam-5962	342	27	function	function	NOUN
ejpam-5962	342	28	on	on	ADP
ejpam-5962	342	29	z	z	PROPN
ejpam-5962	342	30	,	,	PUNCT
ejpam-5962	342	31	(	(	PUNCT
ejpam-5962	342	32	z	z	NOUN
ejpam-5962	342	33	,	,	PUNCT
ejpam-5962	342	34	ϑd	ϑd	NOUN
ejpam-5962	342	35	,	,	PUNCT
ejpam-5962	342	36	ϑd	ϑd	NOUN
ejpam-5962	342	37	)	)	PUNCT
ejpam-5962	342	38	is	be	AUX
ejpam-5962	342	39	pairwise	pairwise	NOUN
ejpam-5962	342	40	minimal	minimal	ADJ
ejpam-5962	342	41	lindelöf	lindelöf	NOUN
ejpam-5962	342	42	closed	close	VERB
ejpam-5962	342	43	space	space	NOUN
ejpam-5962	342	44	,	,	PUNCT
ejpam-5962	342	45	however	however	ADV
ejpam-5962	342	46	(	(	PUNCT
ejpam-5962	342	47	z	z	NOUN
ejpam-5962	342	48	,	,	PUNCT
ejpam-5962	342	49	ϑind	ϑind	ADJ
ejpam-5962	342	50	,	,	PUNCT
ejpam-5962	342	51	ϑind	ϑind	NOUN
ejpam-5962	342	52	)	)	PUNCT
ejpam-5962	342	53	is	be	AUX
ejpam-5962	342	54	not	not	PART
ejpam-5962	342	55	pairwise	pairwise	NOUN
ejpam-5962	342	56	minimal	minimal	ADJ
ejpam-5962	342	57	lindelöf	lindelöf	NOUN
ejpam-5962	342	58	closed	close	VERB
ejpam-5962	342	59	space	space	NOUN
ejpam-5962	342	60	.	.	PUNCT
ejpam-5962	343	1	theorem	theorem	VERB
ejpam-5962	343	2	7.2	7.2	NUM
ejpam-5962	343	3	.	.	PUNCT
ejpam-5962	344	1	a	a	DET
ejpam-5962	344	2	bitopological	bitopological	ADJ
ejpam-5962	344	3	property	property	NOUN
ejpam-5962	344	4	is	be	AUX
ejpam-5962	344	5	the	the	DET
ejpam-5962	344	6	state	state	NOUN
ejpam-5962	344	7	of	of	ADP
ejpam-5962	344	8	having	have	VERB
ejpam-5962	344	9	pairwise	pairwise	NOUN
ejpam-5962	344	10	minimal	minimal	ADJ
ejpam-5962	344	11	lindelöf	lindelöf	NOUN
ejpam-5962	344	12	closed	close	VERB
ejpam-5962	344	13	space	space	NOUN
ejpam-5962	344	14	.	.	PUNCT
ejpam-5962	345	1	proof	proof	NOUN
ejpam-5962	345	2	.	.	PUNCT
ejpam-5962	346	1	let	let	VERB
ejpam-5962	346	2	(	(	PUNCT
ejpam-5962	346	3	z	z	NOUN
ejpam-5962	346	4	,	,	PUNCT
ejpam-5962	346	5	ϑz1	ϑz1	X
ejpam-5962	346	6	,	,	PUNCT
ejpam-5962	346	7	ϑz2	ϑz2	PROPN
ejpam-5962	346	8	)	)	PUNCT
ejpam-5962	346	9	be	be	VERB
ejpam-5962	346	10	a	a	DET
ejpam-5962	346	11	pairwise	pairwise	NOUN
ejpam-5962	346	12	minimal	minimal	ADJ
ejpam-5962	346	13	closed	close	VERB
ejpam-5962	346	14	lindelöf	lindelöf	NOUN
ejpam-5962	346	15	space	space	NOUN
ejpam-5962	346	16	and	and	CCONJ
ejpam-5962	346	17	φ	φ	NOUN
ejpam-5962	346	18	:	:	PUNCT
ejpam-5962	346	19	(	(	PUNCT
ejpam-5962	346	20	z	z	NOUN
ejpam-5962	346	21	,	,	PUNCT
ejpam-5962	346	22	ϑz1	ϑz1	X
ejpam-5962	346	23	,	,	PUNCT
ejpam-5962	346	24	ϑz2	ϑz2	PROPN
ejpam-5962	346	25	)	)	PUNCT
ejpam-5962	346	26	→	→	SYM
ejpam-5962	346	27	(	(	PUNCT
ejpam-5962	346	28	n,ϑn1	n,ϑn1	PROPN
ejpam-5962	346	29	,	,	PUNCT
ejpam-5962	346	30	ϑn2	ϑn2	X
ejpam-5962	346	31	)	)	PUNCT
ejpam-5962	346	32	be	be	AUX
ejpam-5962	346	33	a	a	DET
ejpam-5962	346	34	pairwise	pairwise	NOUN
ejpam-5962	346	35	homeomorphism	homeomorphism	NOUN
ejpam-5962	346	36	and	and	CCONJ
ejpam-5962	346	37	(	(	PUNCT
ejpam-5962	346	38	n,ϑn1	n,ϑn1	PROPN
ejpam-5962	346	39	,	,	PUNCT
ejpam-5962	346	40	ϑn2	ϑn2	X
ejpam-5962	346	41	)	)	PUNCT
ejpam-5962	346	42	is	be	AUX
ejpam-5962	346	43	pairwise	pairwise	NOUN
ejpam-5962	346	44	closed	close	VERB
ejpam-5962	346	45	lindelöf	lindelöf	NOUN
ejpam-5962	346	46	space	space	NOUN
ejpam-5962	346	47	and	and	CCONJ
ejpam-5962	346	48	is	be	AUX
ejpam-5962	346	49	not	not	PART
ejpam-5962	346	50	pairwise	pairwise	NOUN
ejpam-5962	346	51	minimal	minimal	ADJ
ejpam-5962	346	52	lindelöf	lindelöf	NOUN
ejpam-5962	346	53	closed	close	VERB
ejpam-5962	346	54	space	space	NOUN
ejpam-5962	346	55	.	.	PUNCT
ejpam-5962	347	1	therefore	therefore	ADV
ejpam-5962	347	2	,	,	PUNCT
ejpam-5962	347	3	there	there	PRON
ejpam-5962	347	4	are	be	VERB
ejpam-5962	347	5	ϑ	ϑ	ADJ
ejpam-5962	347	6	/	/	SYM
ejpam-5962	347	7	n1	n1	ADJ
ejpam-5962	347	8	≤	≤	ADV
ejpam-5962	347	9	ϑn1	ϑn1	NOUN
ejpam-5962	347	10	,	,	PUNCT
ejpam-5962	347	11	ϑ	ϑ	X
ejpam-5962	347	12	/	/	SYM
ejpam-5962	347	13	n2	n2	ADJ
ejpam-5962	347	14	≤	≤	PROPN
ejpam-5962	347	15	ϑn2	ϑn2	ADV
ejpam-5962	347	16	,	,	PUNCT
ejpam-5962	347	17	and	and	CCONJ
ejpam-5962	347	18	that	that	SCONJ
ejpam-5962	347	19	such	such	ADJ
ejpam-5962	347	20	(	(	PUNCT
ejpam-5962	347	21	n,ϑ	n,ϑ	ADJ
ejpam-5962	347	22	/	/	SYM
ejpam-5962	347	23	n1	n1	PROPN
ejpam-5962	347	24	,	,	PUNCT
ejpam-5962	347	25	ϑ	ϑ	X
ejpam-5962	347	26	/	/	SYM
ejpam-5962	347	27	n2	n2	NOUN
ejpam-5962	347	28	)	)	PUNCT
ejpam-5962	347	29	is	be	AUX
ejpam-5962	347	30	pairwise	pairwise	NOUN
ejpam-5962	347	31	lindelöf	lindelöf	NOUN
ejpam-5962	347	32	closed	close	VERB
ejpam-5962	347	33	space	space	NOUN
ejpam-5962	347	34	.	.	PUNCT
ejpam-5962	348	1	suppose	suppose	VERB
ejpam-5962	348	2	u	u	NOUN
ejpam-5962	348	3	is	be	AUX
ejpam-5962	348	4	ϑ	ϑ	AUX
ejpam-5962	348	5	/	/	SYM
ejpam-5962	348	6	n1−set	n1−set	VERB
ejpam-5962	348	7	in	in	ADP
ejpam-5962	348	8	(	(	PUNCT
ejpam-5962	348	9	n,ϑn1	n,ϑn1	INTJ
ejpam-5962	348	10	,	,	PUNCT
ejpam-5962	348	11	ϑn2),such	ϑn2),such	ADV
ejpam-5962	348	12	that	that	SCONJ
ejpam-5962	348	13	φ−1(u	φ−1(u	PROPN
ejpam-5962	348	14	)	)	PUNCT
ejpam-5962	348	15	is	be	AUX
ejpam-5962	348	16	ϑz1−set	ϑz1−set	VERB
ejpam-5962	348	17	in	in	ADP
ejpam-5962	348	18	(	(	PUNCT
ejpam-5962	348	19	z	z	NOUN
ejpam-5962	348	20	,	,	PUNCT
ejpam-5962	348	21	ϑz1	ϑz1	X
ejpam-5962	348	22	,	,	PUNCT
ejpam-5962	348	23	ϑz2	ϑz2	PROPN
ejpam-5962	348	24	)	)	PUNCT
ejpam-5962	348	25	,	,	PUNCT
ejpam-5962	348	26	so	so	SCONJ
ejpam-5962	348	27	ϑ	ϑ	X
ejpam-5962	348	28	/	/	SYM
ejpam-5962	348	29	z1	z1	ADJ
ejpam-5962	348	30	≤	≤	NOUN
ejpam-5962	348	31	ϑz1	ϑz1	X
ejpam-5962	348	32	,	,	PUNCT
ejpam-5962	348	33	but	but	CCONJ
ejpam-5962	348	34	also	also	ADV
ejpam-5962	348	35	forv	forv	NOUN
ejpam-5962	348	36	is	be	AUX
ejpam-5962	348	37	ϑ	ϑ	AUX
ejpam-5962	348	38	/	/	SYM
ejpam-5962	348	39	n2−set	n2−set	NOUN
ejpam-5962	348	40	in	in	ADP
ejpam-5962	348	41	(	(	PUNCT
ejpam-5962	348	42	n,ϑn1	n,ϑn1	NOUN
ejpam-5962	348	43	,	,	PUNCT
ejpam-5962	348	44	ϑn2	ϑn2	PROPN
ejpam-5962	348	45	)	)	PUNCT
ejpam-5962	348	46	,	,	PUNCT
ejpam-5962	348	47	φ	φ	PROPN
ejpam-5962	348	48	−1(v	−1(v	PROPN
ejpam-5962	348	49	)	)	PUNCT
ejpam-5962	348	50	is	be	AUX
ejpam-5962	348	51	ϑz2−set	ϑz2−set	VERB
ejpam-5962	348	52	in	in	ADP
ejpam-5962	348	53	(	(	PUNCT
ejpam-5962	348	54	z	z	NOUN
ejpam-5962	348	55	,	,	PUNCT
ejpam-5962	348	56	ϑz1	ϑz1	X
ejpam-5962	348	57	,	,	PUNCT
ejpam-5962	348	58	ϑz2	ϑz2	PROPN
ejpam-5962	348	59	)	)	PUNCT
ejpam-5962	348	60	,	,	PUNCT
ejpam-5962	348	61	so	so	SCONJ
ejpam-5962	348	62	ϑ	ϑ	X
ejpam-5962	348	63	/	/	SYM
ejpam-5962	348	64	z1	z1	ADJ
ejpam-5962	348	65	≤	≤	NOUN
ejpam-5962	348	66	ϑz1	ϑz1	X
ejpam-5962	348	67	.	.	PUNCT
ejpam-5962	349	1	consequently	consequently	ADV
ejpam-5962	349	2	,	,	PUNCT
ejpam-5962	349	3	(	(	PUNCT
ejpam-5962	349	4	z	z	X
ejpam-5962	349	5	,	,	PUNCT
ejpam-5962	349	6	ϑ	ϑ	X
ejpam-5962	349	7	/	/	SYM
ejpam-5962	349	8	z1	z1	PROPN
ejpam-5962	349	9	,	,	PUNCT
ejpam-5962	349	10	ϑ	ϑ	X
ejpam-5962	349	11	/	/	SYM
ejpam-5962	349	12	z2	z2	NOUN
ejpam-5962	349	13	)	)	PUNCT
ejpam-5962	349	14	is	be	AUX
ejpam-5962	349	15	pairwise	pairwise	NOUN
ejpam-5962	349	16	lindelöf	lindelöf	NOUN
ejpam-5962	349	17	closed	close	VERB
ejpam-5962	349	18	space	space	NOUN
ejpam-5962	349	19	,	,	PUNCT
ejpam-5962	349	20	which	which	PRON
ejpam-5962	349	21	is	be	AUX
ejpam-5962	349	22	contradiction	contradiction	NOUN
ejpam-5962	349	23	with	with	ADP
ejpam-5962	349	24	(	(	PUNCT
ejpam-5962	349	25	z	z	NOUN
ejpam-5962	349	26	,	,	PUNCT
ejpam-5962	349	27	ϑz1	ϑz1	X
ejpam-5962	349	28	,	,	PUNCT
ejpam-5962	349	29	ϑz2	ϑz2	PROPN
ejpam-5962	349	30	)	)	PUNCT
ejpam-5962	349	31	be	be	VERB
ejpam-5962	349	32	a	a	DET
ejpam-5962	349	33	pairwise	pairwise	NOUN
ejpam-5962	349	34	minimal	minimal	ADJ
ejpam-5962	349	35	lindelöf	lindelöf	NOUN
ejpam-5962	349	36	closed	close	VERB
ejpam-5962	349	37	space	space	NOUN
ejpam-5962	349	38	.	.	PUNCT
ejpam-5962	350	1	therefore	therefore	ADV
ejpam-5962	350	2	,	,	PUNCT
ejpam-5962	350	3	(	(	PUNCT
ejpam-5962	350	4	n,ϑn1	n,ϑn1	X
ejpam-5962	350	5	,	,	PUNCT
ejpam-5962	350	6	ϑn2	ϑn2	X
ejpam-5962	350	7	)	)	PUNCT
ejpam-5962	350	8	is	be	AUX
ejpam-5962	350	9	pairwise	pairwise	NOUN
ejpam-5962	350	10	minimal	minimal	ADJ
ejpam-5962	350	11	lindelöf	lindelöf	NOUN
ejpam-5962	350	12	closed	close	VERB
ejpam-5962	350	13	space	space	NOUN
ejpam-5962	350	14	.	.	PUNCT
ejpam-5962	351	1	the	the	DET
ejpam-5962	351	2	following	follow	VERB
ejpam-5962	351	3	corollaries	corollary	NOUN
ejpam-5962	351	4	have	have	VERB
ejpam-5962	351	5	the	the	DET
ejpam-5962	351	6	same	same	ADJ
ejpam-5962	351	7	theorem	theorem	NOUN
ejpam-5962	351	8	-	-	NOUN
ejpam-5962	351	9	proof	proof	NOUN
ejpam-5962	351	10	as	as	ADP
ejpam-5962	351	11	the	the	DET
ejpam-5962	351	12	following	following	ADJ
ejpam-5962	351	13	ones	one	NOUN
ejpam-5962	351	14	.	.	PUNCT
ejpam-5962	352	1	corollary	corollary	ADJ
ejpam-5962	352	2	7.1	7.1	NUM
ejpam-5962	352	3	.	.	PUNCT
ejpam-5962	353	1	let	let	VERB
ejpam-5962	353	2	(	(	PUNCT
ejpam-5962	353	3	z	z	NOUN
ejpam-5962	353	4	,	,	PUNCT
ejpam-5962	353	5	ϑz1	ϑz1	X
ejpam-5962	353	6	,	,	PUNCT
ejpam-5962	353	7	ϑz2	ϑz2	PROPN
ejpam-5962	353	8	)	)	PUNCT
ejpam-5962	353	9	be	be	VERB
ejpam-5962	353	10	a	a	DET
ejpam-5962	353	11	pairwise	pairwise	NOUN
ejpam-5962	353	12	lindelöf	lindelöf	NOUN
ejpam-5962	353	13	closed	close	VERB
ejpam-5962	353	14	space	space	NOUN
ejpam-5962	353	15	and	and	CCONJ
ejpam-5962	353	16	(	(	PUNCT
ejpam-5962	353	17	n,ϑn1	n,ϑn1	PROPN
ejpam-5962	353	18	,	,	PUNCT
ejpam-5962	353	19	ϑn2	ϑn2	X
ejpam-5962	353	20	)	)	PUNCT
ejpam-5962	353	21	be	be	VERB
ejpam-5962	353	22	pairwise	pairwise	NOUN
ejpam-5962	353	23	closed	close	VERB
ejpam-5962	353	24	subspace	subspace	NOUN
ejpam-5962	353	25	of	of	ADP
ejpam-5962	353	26	(	(	PUNCT
ejpam-5962	353	27	z	z	NOUN
ejpam-5962	353	28	,	,	PUNCT
ejpam-5962	353	29	ϑz1	ϑz1	X
ejpam-5962	353	30	,	,	PUNCT
ejpam-5962	353	31	ϑz2	ϑz2	PROPN
ejpam-5962	353	32	)	)	PUNCT
ejpam-5962	353	33	,	,	PUNCT
ejpam-5962	353	34	then	then	ADV
ejpam-5962	353	35	(	(	PUNCT
ejpam-5962	353	36	n,ϑn1	n,ϑn1	NOUN
ejpam-5962	353	37	,	,	PUNCT
ejpam-5962	353	38	ϑn2	ϑn2	X
ejpam-5962	353	39	)	)	PUNCT
ejpam-5962	353	40	is	be	AUX
ejpam-5962	353	41	pairwise	pairwise	NOUN
ejpam-5962	353	42	lindelöf	lindelöf	NOUN
ejpam-5962	353	43	closed	close	VERB
ejpam-5962	353	44	space	space	NOUN
ejpam-5962	353	45	.	.	PUNCT
ejpam-5962	354	1	corollary	corollary	ADJ
ejpam-5962	354	2	7.2	7.2	NUM
ejpam-5962	354	3	.	.	PUNCT
ejpam-5962	355	1	when	when	SCONJ
ejpam-5962	355	2	(	(	PUNCT
ejpam-5962	355	3	z	z	NOUN
ejpam-5962	355	4	,	,	PUNCT
ejpam-5962	355	5	ϑz1	ϑz1	X
ejpam-5962	355	6	,	,	PUNCT
ejpam-5962	355	7	ϑz2	ϑz2	PROPN
ejpam-5962	355	8	)	)	PUNCT
ejpam-5962	355	9	be	be	VERB
ejpam-5962	355	10	a	a	DET
ejpam-5962	355	11	pairwise	pairwise	NOUN
ejpam-5962	355	12	minimal	minimal	ADJ
ejpam-5962	355	13	lindelöf	lindelöf	NOUN
ejpam-5962	355	14	closed	close	VERB
ejpam-5962	355	15	space	space	NOUN
ejpam-5962	355	16	and	and	CCONJ
ejpam-5962	355	17	(	(	PUNCT
ejpam-5962	355	18	n,ϑn1	n,ϑn1	PROPN
ejpam-5962	355	19	,	,	PUNCT
ejpam-5962	355	20	ϑn2	ϑn2	X
ejpam-5962	355	21	)	)	PUNCT
ejpam-5962	355	22	be	be	VERB
ejpam-5962	355	23	pairwise	pairwise	NOUN
ejpam-5962	355	24	closed	close	VERB
ejpam-5962	355	25	subspace	subspace	NOUN
ejpam-5962	355	26	of	of	ADP
ejpam-5962	355	27	(	(	PUNCT
ejpam-5962	355	28	z	z	NOUN
ejpam-5962	355	29	,	,	PUNCT
ejpam-5962	355	30	ϑz1	ϑz1	X
ejpam-5962	355	31	,	,	PUNCT
ejpam-5962	355	32	ϑz2	ϑz2	PROPN
ejpam-5962	355	33	)	)	PUNCT
ejpam-5962	355	34	,	,	PUNCT
ejpam-5962	355	35	after	after	ADP
ejpam-5962	355	36	which	which	PRON
ejpam-5962	355	37	(	(	PUNCT
ejpam-5962	355	38	n,ϑn1	n,ϑn1	NUM
ejpam-5962	355	39	,	,	PUNCT
ejpam-5962	355	40	ϑn2	ϑn2	X
ejpam-5962	355	41	)	)	PUNCT
ejpam-5962	355	42	is	be	AUX
ejpam-5962	355	43	pairwise	pairwise	NOUN
ejpam-5962	355	44	minimal	minimal	ADJ
ejpam-5962	355	45	lindelöf	lindelöf	NOUN
ejpam-5962	355	46	closed	close	VERB
ejpam-5962	355	47	space	space	NOUN
ejpam-5962	355	48	.	.	PUNCT
ejpam-5962	356	1	theorem	theorem	VERB
ejpam-5962	356	2	7.3	7.3	NUM
ejpam-5962	356	3	.	.	PUNCT
ejpam-5962	357	1	assuming	assume	VERB
ejpam-5962	357	2	that	that	SCONJ
ejpam-5962	357	3	(	(	PUNCT
ejpam-5962	357	4	z1×z2	z1×z2	PROPN
ejpam-5962	357	5	,	,	PUNCT
ejpam-5962	357	6	ϑ1×ϑ1	ϑ1×ϑ1	PROPN
ejpam-5962	357	7	,	,	PUNCT
ejpam-5962	357	8	ϑ2	ϑ2	PROPN
ejpam-5962	357	9	×ϑ2	×ϑ2	PROPN
ejpam-5962	357	10	)	)	PUNCT
ejpam-5962	357	11	is	be	AUX
ejpam-5962	357	12	pairwise	pairwise	NOUN
ejpam-5962	357	13	lindelöf	lindelöf	NOUN
ejpam-5962	357	14	closed	close	VERB
ejpam-5962	357	15	space	space	NOUN
ejpam-5962	357	16	.	.	PUNCT
ejpam-5962	358	1	therefore	therefore	ADV
ejpam-5962	358	2	,	,	PUNCT
ejpam-5962	358	3	each	each	PRON
ejpam-5962	358	4	(	(	PUNCT
ejpam-5962	358	5	z1	z1	PROPN
ejpam-5962	358	6	,	,	PUNCT
ejpam-5962	358	7	ϑ1	ϑ1	NOUN
ejpam-5962	358	8	,	,	PUNCT
ejpam-5962	358	9	ϑ2	ϑ2	PROPN
ejpam-5962	358	10	)	)	PUNCT
ejpam-5962	358	11	,	,	PUNCT
ejpam-5962	358	12	(	(	PUNCT
ejpam-5962	358	13	z2	z2	NOUN
ejpam-5962	358	14	,	,	PUNCT
ejpam-5962	358	15	ϑ1	ϑ1	NOUN
ejpam-5962	358	16	,	,	PUNCT
ejpam-5962	358	17	ϑ2	ϑ2	PROPN
ejpam-5962	358	18	)	)	PUNCT
ejpam-5962	358	19	is	be	AUX
ejpam-5962	358	20	pairwise	pairwise	NOUN
ejpam-5962	358	21	minimal	minimal	ADJ
ejpam-5962	358	22	lindelöf	lindelöf	NOUN
ejpam-5962	358	23	closed	close	VERB
ejpam-5962	358	24	space	space	NOUN
ejpam-5962	358	25	.	.	PUNCT
ejpam-5962	359	1	proof	proof	NOUN
ejpam-5962	359	2	.	.	PUNCT
ejpam-5962	360	1	lindelöf	lindelöf	NOUN
ejpam-5962	360	2	closed	close	VERB
ejpam-5962	360	3	space	space	NOUN
ejpam-5962	360	4	has	have	AUX
ejpam-5962	360	5	the	the	DET
ejpam-5962	360	6	property	property	NOUN
ejpam-5962	360	7	of	of	ADP
ejpam-5962	360	8	being	be	AUX
ejpam-5962	360	9	pairwise	pairwise	NOUN
ejpam-5962	360	10	minimal	minimal	ADJ
ejpam-5962	360	11	,	,	PUNCT
ejpam-5962	360	12	which	which	PRON
ejpam-5962	360	13	is	be	AUX
ejpam-5962	360	14	a	a	DET
ejpam-5962	360	15	bitopological	bitopological	ADJ
ejpam-5962	360	16	property	property	NOUN
ejpam-5962	360	17	,	,	PUNCT
ejpam-5962	360	18	if	if	SCONJ
ejpam-5962	360	19	{	{	PUNCT
ejpam-5962	360	20	x2	x2	NOUN
ejpam-5962	360	21	}	}	PUNCT
ejpam-5962	360	22	be	be	VERB
ejpam-5962	360	23	a	a	DET
ejpam-5962	360	24	fixed	fix	VERB
ejpam-5962	360	25	element	element	NOUN
ejpam-5962	360	26	in	in	ADP
ejpam-5962	360	27	(	(	PUNCT
ejpam-5962	360	28	z2	z2	PROPN
ejpam-5962	360	29	,	,	PUNCT
ejpam-5962	360	30	ϑ1	ϑ1	NOUN
ejpam-5962	360	31	,	,	PUNCT
ejpam-5962	360	32	ϑ2	ϑ2	PROPN
ejpam-5962	360	33	)	)	PUNCT
ejpam-5962	360	34	,	,	PUNCT
ejpam-5962	360	35	then	then	ADV
ejpam-5962	360	36	(	(	PUNCT
ejpam-5962	360	37	z1	z1	ADJ
ejpam-5962	360	38	,	,	PUNCT
ejpam-5962	360	39	ϑ1	ϑ1	NOUN
ejpam-5962	360	40	,	,	PUNCT
ejpam-5962	360	41	ϑ2)×{z2	ϑ2)×{z2	X
ejpam-5962	360	42	}	}	PUNCT
ejpam-5962	360	43	is	be	AUX
ejpam-5962	360	44	a	a	DET
ejpam-5962	360	45	subspace	subspace	NOUN
ejpam-5962	360	46	of	of	ADP
ejpam-5962	360	47	(	(	PUNCT
ejpam-5962	360	48	z1	z1	PROPN
ejpam-5962	360	49	×	×	PROPN
ejpam-5962	360	50	z2	z2	PROPN
ejpam-5962	360	51	,	,	PUNCT
ejpam-5962	360	52	ϑ1	ϑ1	PROPN
ejpam-5962	360	53	×	×	NOUN
ejpam-5962	360	54	ϑ1	ϑ1	NOUN
ejpam-5962	360	55	,	,	PUNCT
ejpam-5962	360	56	ϑ2	ϑ2	PROPN
ejpam-5962	360	57	×	×	NOUN
ejpam-5962	360	58	ϑ2).therefore	ϑ2).therefore	PROPN
ejpam-5962	360	59	(	(	PUNCT
ejpam-5962	360	60	z1	z1	NOUN
ejpam-5962	360	61	,	,	PUNCT
ejpam-5962	360	62	ϑ1	ϑ1	NOUN
ejpam-5962	360	63	,	,	PUNCT
ejpam-5962	360	64	ϑ2	ϑ2	PROPN
ejpam-5962	360	65	)	)	PUNCT
ejpam-5962	360	66	×	×	NOUN
ejpam-5962	360	67	{	{	PUNCT
ejpam-5962	360	68	z2	z2	NOUN
ejpam-5962	360	69	}	}	PUNCT
ejpam-5962	360	70	is	be	AUX
ejpam-5962	360	71	pairwise	pairwise	NOUN
ejpam-5962	360	72	lindelöf	lindelöf	NOUN
ejpam-5962	360	73	closed	close	VERB
ejpam-5962	360	74	space	space	NOUN
ejpam-5962	360	75	.	.	PUNCT
ejpam-5962	361	1	but	but	CCONJ
ejpam-5962	361	2	(	(	PUNCT
ejpam-5962	361	3	z1	z1	ADJ
ejpam-5962	361	4	,	,	PUNCT
ejpam-5962	361	5	ϑ1	ϑ1	NOUN
ejpam-5962	361	6	,	,	PUNCT
ejpam-5962	361	7	ϑ2	ϑ2	PROPN
ejpam-5962	361	8	)	)	PUNCT
ejpam-5962	361	9	×	×	NOUN
ejpam-5962	361	10	{	{	PUNCT
ejpam-5962	361	11	z2	z2	NOUN
ejpam-5962	361	12	}	}	PUNCT
ejpam-5962	361	13	is	be	AUX
ejpam-5962	361	14	pairwise	pairwise	NOUN
ejpam-5962	361	15	homomorphic	homomorphic	ADJ
ejpam-5962	361	16	to	to	ADP
ejpam-5962	361	17	(	(	PUNCT
ejpam-5962	361	18	z1	z1	PROPN
ejpam-5962	361	19	,	,	PUNCT
ejpam-5962	361	20	ϑ1	ϑ1	NOUN
ejpam-5962	361	21	,	,	PUNCT
ejpam-5962	361	22	ϑ2	ϑ2	PROPN
ejpam-5962	361	23	)	)	PUNCT
ejpam-5962	361	24	.	.	PUNCT
ejpam-5962	362	1	by	by	ADP
ejpam-5962	362	2	a.	a.	PROPN
ejpam-5962	362	3	a.	a.	PROPN
ejpam-5962	362	4	atoom	atoom	PROPN
ejpam-5962	362	5	et	et	PROPN
ejpam-5962	362	6	al	al	PROPN
ejpam-5962	362	7	.	.	PUNCT
ejpam-5962	362	8	/	/	SYM
ejpam-5962	362	9	eur	eur	PROPN
ejpam-5962	362	10	.	.	PUNCT
ejpam-5962	363	1	j.	j.	PROPN
ejpam-5962	363	2	pure	pure	PROPN
ejpam-5962	363	3	appl	appl	PROPN
ejpam-5962	363	4	.	.	PROPN
ejpam-5962	363	5	math	math	PROPN
ejpam-5962	363	6	,	,	PUNCT
ejpam-5962	363	7	18	18	NUM
ejpam-5962	363	8	(	(	PUNCT
ejpam-5962	363	9	2	2	NUM
ejpam-5962	363	10	)	)	PUNCT
ejpam-5962	363	11	(	(	PUNCT
ejpam-5962	363	12	2025	2025	NUM
ejpam-5962	363	13	)	)	PUNCT
ejpam-5962	363	14	,	,	PUNCT
ejpam-5962	363	15	5962	5962	NUM
ejpam-5962	363	16	13	13	NUM
ejpam-5962	363	17	of	of	ADP
ejpam-5962	363	18	17	17	NUM
ejpam-5962	363	19	theorem	theorem	VERB
ejpam-5962	363	20	7.2	7.2	NUM
ejpam-5962	363	21	,	,	PUNCT
ejpam-5962	363	22	(	(	PUNCT
ejpam-5962	363	23	z1	z1	NOUN
ejpam-5962	363	24	,	,	PUNCT
ejpam-5962	363	25	ϑ1	ϑ1	NOUN
ejpam-5962	363	26	,	,	PUNCT
ejpam-5962	363	27	ϑ2	ϑ2	PROPN
ejpam-5962	363	28	)	)	PUNCT
ejpam-5962	363	29	is	be	AUX
ejpam-5962	363	30	pairwise	pairwise	NOUN
ejpam-5962	363	31	lindelöf	lindelöf	NOUN
ejpam-5962	363	32	closed	close	VERB
ejpam-5962	363	33	space	space	NOUN
ejpam-5962	363	34	.	.	PUNCT
ejpam-5962	364	1	now	now	ADV
ejpam-5962	364	2	since	since	SCONJ
ejpam-5962	364	3	every	every	DET
ejpam-5962	364	4	pairwise	pairwise	NOUN
ejpam-5962	364	5	lindelöf	lindelöf	NOUN
ejpam-5962	364	6	closed	close	VERB
ejpam-5962	364	7	space	space	NOUN
ejpam-5962	364	8	is	be	AUX
ejpam-5962	364	9	pairwise	pairwise	NOUN
ejpam-5962	364	10	minimal	minimal	ADJ
ejpam-5962	364	11	lindelöf	lindelöf	NOUN
ejpam-5962	364	12	closed	close	VERB
ejpam-5962	364	13	space	space	NOUN
ejpam-5962	364	14	,	,	PUNCT
ejpam-5962	364	15	therefore	therefore	ADV
ejpam-5962	364	16	(	(	PUNCT
ejpam-5962	364	17	z1	z1	ADJ
ejpam-5962	364	18	,	,	PUNCT
ejpam-5962	364	19	ϑ1	ϑ1	NOUN
ejpam-5962	364	20	,	,	PUNCT
ejpam-5962	364	21	ϑ2	ϑ2	PROPN
ejpam-5962	364	22	)	)	PUNCT
ejpam-5962	364	23	is	be	AUX
ejpam-5962	364	24	pairwise	pairwise	NOUN
ejpam-5962	364	25	minimal	minimal	ADJ
ejpam-5962	364	26	lindelöf	lindelöf	NOUN
ejpam-5962	364	27	closed	close	VERB
ejpam-5962	364	28	space.similar	space.similar	PROPN
ejpam-5962	364	29	to	to	ADP
ejpam-5962	364	30	that	that	PRON
ejpam-5962	364	31	,	,	PUNCT
ejpam-5962	364	32	we	we	PRON
ejpam-5962	364	33	can	can	AUX
ejpam-5962	364	34	demonstrate	demonstrate	VERB
ejpam-5962	364	35	(	(	PUNCT
ejpam-5962	364	36	z2	z2	PROPN
ejpam-5962	364	37	,	,	PUNCT
ejpam-5962	364	38	ϑ1	ϑ1	NOUN
ejpam-5962	364	39	,	,	PUNCT
ejpam-5962	364	40	ϑ2	ϑ2	PROPN
ejpam-5962	364	41	)	)	PUNCT
ejpam-5962	364	42	is	be	AUX
ejpam-5962	364	43	pairwise	pairwise	NOUN
ejpam-5962	364	44	minimal	minimal	ADJ
ejpam-5962	364	45	lindelöf	lindelöf	NOUN
ejpam-5962	364	46	closed	close	VERB
ejpam-5962	364	47	space	space	NOUN
ejpam-5962	364	48	.	.	PUNCT
ejpam-5962	365	1	the	the	DET
ejpam-5962	365	2	outcomes	outcome	NOUN
ejpam-5962	365	3	of	of	ADP
ejpam-5962	365	4	theorem	theorem	ADJ
ejpam-5962	365	5	7.3	7.3	NUM
ejpam-5962	365	6	are	be	AUX
ejpam-5962	365	7	generalized	generalize	VERB
ejpam-5962	365	8	in	in	ADP
ejpam-5962	365	9	the	the	DET
ejpam-5962	365	10	following	following	ADJ
ejpam-5962	365	11	way	way	NOUN
ejpam-5962	365	12	.	.	PUNCT
ejpam-5962	366	1	corollary	corollary	ADJ
ejpam-5962	366	2	7.3	7.3	NUM
ejpam-5962	366	3	.	.	PUNCT
ejpam-5962	367	1	if	if	SCONJ
ejpam-5962	367	2	z	z	NOUN
ejpam-5962	367	3	=	=	SYM
ejpam-5962	367	4	∏	∏	NUM
ejpam-5962	367	5	α∈ω	α∈ω	NOUN
ejpam-5962	367	6	zα	zα	PROPN
ejpam-5962	367	7	is	be	AUX
ejpam-5962	367	8	a	a	DET
ejpam-5962	367	9	pairwise	pairwise	NOUN
ejpam-5962	367	10	lindelöf	lindelöf	NOUN
ejpam-5962	367	11	closed	close	VERB
ejpam-5962	367	12	space	space	NOUN
ejpam-5962	367	13	,	,	PUNCT
ejpam-5962	367	14	then	then	ADV
ejpam-5962	367	15	each	each	DET
ejpam-5962	367	16	zα	zα	PROPN
ejpam-5962	367	17	is	be	AUX
ejpam-5962	367	18	pairwise	pairwise	PROPN
ejpam-5962	367	19	minimal	minimal	ADJ
ejpam-5962	367	20	lindelöf	lindelöf	NOUN
ejpam-5962	367	21	closed	close	VERB
ejpam-5962	367	22	space	space	NOUN
ejpam-5962	367	23	,	,	PUNCT
ejpam-5962	367	24	for	for	ADP
ejpam-5962	367	25	each	each	DET
ejpam-5962	367	26	α	α	PROPN
ejpam-5962	367	27	∈	∈	PROPN
ejpam-5962	367	28	φ	φ	PROPN
ejpam-5962	367	29	.	.	PROPN
ejpam-5962	367	30	8	8	NUM
ejpam-5962	367	31	.	.	PUNCT
ejpam-5962	368	1	a	a	DET
ejpam-5962	368	2	new	new	ADJ
ejpam-5962	368	3	defition	defition	NOUN
ejpam-5962	368	4	of	of	ADP
ejpam-5962	368	5	pairwise	pairwise	PROPN
ejpam-5962	368	6	minimal	minimal	ADJ
ejpam-5962	368	7	hausdroff	hausdroff	NOUN
ejpam-5962	368	8	spaces	space	NOUN
ejpam-5962	368	9	we	we	PRON
ejpam-5962	368	10	provide	provide	VERB
ejpam-5962	368	11	a	a	DET
ejpam-5962	368	12	novel	novel	ADJ
ejpam-5962	368	13	definition	definition	NOUN
ejpam-5962	368	14	of	of	ADP
ejpam-5962	368	15	pairwise	pairwise	NOUN
ejpam-5962	368	16	minimal	minimal	ADJ
ejpam-5962	368	17	hausdroff	hausdroff	NOUN
ejpam-5962	368	18	spaces	space	NOUN
ejpam-5962	368	19	in	in	ADP
ejpam-5962	368	20	this	this	DET
ejpam-5962	368	21	section	section	NOUN
ejpam-5962	368	22	,	,	PUNCT
ejpam-5962	368	23	along	along	ADP
ejpam-5962	368	24	with	with	ADP
ejpam-5962	368	25	some	some	PRON
ejpam-5962	368	26	of	of	ADP
ejpam-5962	368	27	its	its	PRON
ejpam-5962	368	28	related	related	ADJ
ejpam-5962	368	29	features	feature	NOUN
ejpam-5962	368	30	.	.	PUNCT
ejpam-5962	369	1	definition	definition	NOUN
ejpam-5962	369	2	8.1	8.1	NUM
ejpam-5962	369	3	.	.	PUNCT
ejpam-5962	370	1	can	can	AUX
ejpam-5962	370	2	let	let	VERB
ejpam-5962	370	3	(	(	PUNCT
ejpam-5962	370	4	z	z	NOUN
ejpam-5962	370	5	,	,	PUNCT
ejpam-5962	370	6	ϑ1	ϑ1	NOUN
ejpam-5962	370	7	,	,	PUNCT
ejpam-5962	370	8	ϑ2	ϑ2	PROPN
ejpam-5962	370	9	)	)	PUNCT
ejpam-5962	370	10	be	be	VERB
ejpam-5962	370	11	pairwise	pairwise	NOUN
ejpam-5962	370	12	hausdroff	hausdroff	NOUN
ejpam-5962	370	13	space	space	NOUN
ejpam-5962	370	14	.	.	PUNCT
ejpam-5962	371	1	a	a	DET
ejpam-5962	371	2	bitopological	bitopological	ADJ
ejpam-5962	371	3	space	space	NOUN
ejpam-5962	371	4	(	(	PUNCT
ejpam-5962	371	5	z	z	NOUN
ejpam-5962	371	6	,	,	PUNCT
ejpam-5962	371	7	ϑ1	ϑ1	NOUN
ejpam-5962	371	8	,	,	PUNCT
ejpam-5962	371	9	ϑ2	ϑ2	PROPN
ejpam-5962	371	10	)	)	PUNCT
ejpam-5962	371	11	is	be	AUX
ejpam-5962	371	12	allegedly	allegedly	ADV
ejpam-5962	371	13	pairwise	pairwise	VERB
ejpam-5962	371	14	minimal	minimal	ADJ
ejpam-5962	371	15	hausdroff	hausdroff	NOUN
ejpam-5962	371	16	space	space	NOUN
ejpam-5962	371	17	,	,	PUNCT
ejpam-5962	371	18	only	only	ADV
ejpam-5962	371	19	if	if	SCONJ
ejpam-5962	371	20	and	and	CCONJ
ejpam-5962	371	21	only	only	ADV
ejpam-5962	371	22	ϑ	ϑ	X
ejpam-5962	371	23	/	/	SYM
ejpam-5962	371	24	1	1	NUM
ejpam-5962	371	25	≤	≤	NOUN
ejpam-5962	371	26	ϑ1	ϑ1	NOUN
ejpam-5962	371	27	,	,	PUNCT
ejpam-5962	371	28	ϑ	ϑ	X
ejpam-5962	371	29	/	/	SYM
ejpam-5962	371	30	2	2	NUM
ejpam-5962	371	31	≤	≤	NOUN
ejpam-5962	371	32	ϑ2	ϑ2	NOUN
ejpam-5962	371	33	and	and	CCONJ
ejpam-5962	371	34	(	(	PUNCT
ejpam-5962	371	35	z	z	NOUN
ejpam-5962	371	36	,	,	PUNCT
ejpam-5962	371	37	ϑ	ϑ	X
ejpam-5962	371	38	/	/	SYM
ejpam-5962	371	39	1	1	NUM
ejpam-5962	371	40	,	,	PUNCT
ejpam-5962	371	41	ϑ	ϑ	X
ejpam-5962	371	42	/	/	SYM
ejpam-5962	371	43	2	2	NUM
ejpam-5962	371	44	)	)	PUNCT
ejpam-5962	371	45	is	be	AUX
ejpam-5962	371	46	not	not	PART
ejpam-5962	371	47	pairwise	pairwise	NOUN
ejpam-5962	371	48	hausdroff	hausdroff	NOUN
ejpam-5962	371	49	space	space	NOUN
ejpam-5962	371	50	.	.	PUNCT
ejpam-5962	372	1	theorem	theorem	VERB
ejpam-5962	372	2	8.1	8.1	NUM
ejpam-5962	372	3	.	.	PUNCT
ejpam-5962	373	1	every	every	DET
ejpam-5962	373	2	pairwise	pairwise	NOUN
ejpam-5962	373	3	locally	locally	ADV
ejpam-5962	373	4	compact	compact	ADJ
ejpam-5962	373	5	minimal	minimal	ADJ
ejpam-5962	373	6	compact	compact	ADJ
ejpam-5962	373	7	closed	close	VERB
ejpam-5962	373	8	space	space	NOUN
ejpam-5962	373	9	is	be	AUX
ejpam-5962	373	10	pairwise	pairwise	NOUN
ejpam-5962	373	11	minimal	minimal	ADJ
ejpam-5962	373	12	hausdroff	hausdroff	NOUN
ejpam-5962	373	13	space	space	NOUN
ejpam-5962	373	14	.	.	PUNCT
ejpam-5962	374	1	proof	proof	NOUN
ejpam-5962	374	2	.	.	PUNCT
ejpam-5962	375	1	suppose	suppose	VERB
ejpam-5962	375	2	(	(	PUNCT
ejpam-5962	375	3	z	z	NOUN
ejpam-5962	375	4	,	,	PUNCT
ejpam-5962	375	5	ϑz1	ϑz1	X
ejpam-5962	375	6	,	,	PUNCT
ejpam-5962	375	7	ϑz2	ϑz2	PROPN
ejpam-5962	375	8	)	)	PUNCT
ejpam-5962	375	9	is	be	AUX
ejpam-5962	375	10	a	a	DET
ejpam-5962	375	11	pairwise	pairwise	NOUN
ejpam-5962	375	12	locally	locally	ADV
ejpam-5962	375	13	compact	compact	ADJ
ejpam-5962	375	14	minimal	minimal	ADJ
ejpam-5962	375	15	compact	compact	ADJ
ejpam-5962	375	16	closed	close	VERB
ejpam-5962	375	17	space	space	NOUN
ejpam-5962	375	18	,	,	PUNCT
ejpam-5962	375	19	so	so	CCONJ
ejpam-5962	375	20	(	(	PUNCT
ejpam-5962	375	21	z	z	NOUN
ejpam-5962	375	22	,	,	PUNCT
ejpam-5962	375	23	ϑz1	ϑz1	X
ejpam-5962	375	24	,	,	PUNCT
ejpam-5962	375	25	ϑz2	ϑz2	PROPN
ejpam-5962	375	26	)	)	PUNCT
ejpam-5962	375	27	is	be	AUX
ejpam-5962	375	28	pairwise	pairwise	NOUN
ejpam-5962	375	29	locally	locally	ADV
ejpam-5962	375	30	compact	compact	ADJ
ejpam-5962	375	31	and	and	CCONJ
ejpam-5962	375	32	pairwise	pairwise	NOUN
ejpam-5962	375	33	compact	compact	ADJ
ejpam-5962	375	34	closed	close	VERB
ejpam-5962	375	35	space	space	NOUN
ejpam-5962	375	36	.	.	PUNCT
ejpam-5962	376	1	consequently	consequently	ADV
ejpam-5962	376	2	,	,	PUNCT
ejpam-5962	376	3	(	(	PUNCT
ejpam-5962	376	4	z	z	X
ejpam-5962	376	5	,	,	PUNCT
ejpam-5962	376	6	ϑz1	ϑz1	X
ejpam-5962	376	7	,	,	PUNCT
ejpam-5962	376	8	ϑz2	ϑz2	PROPN
ejpam-5962	376	9	)	)	PUNCT
ejpam-5962	376	10	is	be	AUX
ejpam-5962	376	11	pairwise	pairwise	NOUN
ejpam-5962	376	12	hausdroff	hausdroff	NOUN
ejpam-5962	376	13	space	space	NOUN
ejpam-5962	376	14	.	.	PUNCT
ejpam-5962	377	1	suppose	suppose	VERB
ejpam-5962	377	2	(	(	PUNCT
ejpam-5962	377	3	z	z	NOUN
ejpam-5962	377	4	,	,	PUNCT
ejpam-5962	377	5	ϑz1	ϑz1	X
ejpam-5962	377	6	,	,	PUNCT
ejpam-5962	377	7	ϑz2	ϑz2	PROPN
ejpam-5962	377	8	)	)	PUNCT
ejpam-5962	377	9	is	be	AUX
ejpam-5962	377	10	not	not	PART
ejpam-5962	377	11	pairwise	pairwise	NOUN
ejpam-5962	377	12	minimal	minimal	ADJ
ejpam-5962	377	13	hausdroff	hausdroff	NOUN
ejpam-5962	377	14	space	space	NOUN
ejpam-5962	377	15	,	,	PUNCT
ejpam-5962	377	16	so	so	SCONJ
ejpam-5962	377	17	there	there	PRON
ejpam-5962	377	18	exists	exist	VERB
ejpam-5962	377	19	ϑ	ϑ	X
ejpam-5962	377	20	/	/	SYM
ejpam-5962	377	21	z1	z1	ADJ
ejpam-5962	377	22	≤	≤	NOUN
ejpam-5962	377	23	ϑz1	ϑz1	X
ejpam-5962	377	24	,	,	PUNCT
ejpam-5962	377	25	ϑ	ϑ	X
ejpam-5962	377	26	/	/	SYM
ejpam-5962	377	27	z2	z2	PROPN
ejpam-5962	377	28	≤	≤	NOUN
ejpam-5962	377	29	ϑz2	ϑz2	PROPN
ejpam-5962	377	30	,	,	PUNCT
ejpam-5962	377	31	like	like	ADP
ejpam-5962	377	32	that	that	PRON
ejpam-5962	377	33	(	(	PUNCT
ejpam-5962	377	34	z	z	NOUN
ejpam-5962	377	35	,	,	PUNCT
ejpam-5962	377	36	ϑ	ϑ	X
ejpam-5962	377	37	/	/	SYM
ejpam-5962	377	38	z1	z1	PROPN
ejpam-5962	377	39	,	,	PUNCT
ejpam-5962	377	40	ϑ	ϑ	X
ejpam-5962	377	41	/	/	SYM
ejpam-5962	377	42	z2	z2	NOUN
ejpam-5962	377	43	)	)	PUNCT
ejpam-5962	377	44	is	be	AUX
ejpam-5962	377	45	pairwise	pairwise	NOUN
ejpam-5962	377	46	hausdroff	hausdroff	NOUN
ejpam-5962	377	47	space	space	NOUN
ejpam-5962	377	48	,	,	PUNCT
ejpam-5962	377	49	implies	imply	VERB
ejpam-5962	377	50	(	(	PUNCT
ejpam-5962	377	51	z	z	NOUN
ejpam-5962	377	52	,	,	PUNCT
ejpam-5962	377	53	ϑ	ϑ	X
ejpam-5962	377	54	/	/	SYM
ejpam-5962	377	55	z1	z1	PROPN
ejpam-5962	377	56	,	,	PUNCT
ejpam-5962	377	57	ϑ	ϑ	X
ejpam-5962	377	58	/	/	SYM
ejpam-5962	377	59	z2	z2	NOUN
ejpam-5962	377	60	)	)	PUNCT
ejpam-5962	377	61	is	be	AUX
ejpam-5962	377	62	pairwise	pairwise	NOUN
ejpam-5962	377	63	compact	compact	ADJ
ejpam-5962	377	64	closed	close	VERB
ejpam-5962	377	65	space	space	NOUN
ejpam-5962	377	66	.	.	PUNCT
ejpam-5962	378	1	consequently	consequently	ADV
ejpam-5962	378	2	,	,	PUNCT
ejpam-5962	378	3	a	a	DET
ejpam-5962	378	4	contradiction	contradiction	NOUN
ejpam-5962	378	5	results	result	VERB
ejpam-5962	378	6	.	.	PUNCT
ejpam-5962	379	1	therefore	therefore	ADV
ejpam-5962	379	2	(	(	PUNCT
ejpam-5962	379	3	z	z	NOUN
ejpam-5962	379	4	,	,	PUNCT
ejpam-5962	379	5	ϑz1	ϑz1	X
ejpam-5962	379	6	,	,	PUNCT
ejpam-5962	379	7	ϑz2	ϑz2	PROPN
ejpam-5962	379	8	)	)	PUNCT
ejpam-5962	379	9	is	be	AUX
ejpam-5962	379	10	pairwise	pairwise	NOUN
ejpam-5962	379	11	minimal	minimal	ADJ
ejpam-5962	379	12	hausdroff	hausdroff	NOUN
ejpam-5962	379	13	space	space	NOUN
ejpam-5962	379	14	.	.	PUNCT
ejpam-5962	380	1	the	the	DET
ejpam-5962	380	2	following	follow	VERB
ejpam-5962	380	3	corollary	corollary	NOUN
ejpam-5962	380	4	’s	’s	PART
ejpam-5962	380	5	proof	proof	NOUN
ejpam-5962	380	6	resembles	resemble	VERB
ejpam-5962	380	7	that	that	PRON
ejpam-5962	380	8	of	of	ADP
ejpam-5962	380	9	the	the	DET
ejpam-5962	380	10	aforementioned	aforementione	VERB
ejpam-5962	380	11	theorem	theorem	NOUN
ejpam-5962	380	12	.	.	PROPN
ejpam-5962	380	13	corollary	corollary	ADJ
ejpam-5962	380	14	8.1	8.1	NUM
ejpam-5962	380	15	.	.	PUNCT
ejpam-5962	381	1	for	for	ADP
ejpam-5962	381	2	each	each	DET
ejpam-5962	381	3	pairwise	pairwise	NOUN
ejpam-5962	381	4	locally	locally	ADV
ejpam-5962	381	5	compact	compact	ADJ
ejpam-5962	381	6	minimal	minimal	ADJ
ejpam-5962	381	7	lindelöf	lindelöf	NOUN
ejpam-5962	381	8	closed	close	VERB
ejpam-5962	381	9	space	space	NOUN
ejpam-5962	381	10	is	be	AUX
ejpam-5962	381	11	pairwise	pairwise	NOUN
ejpam-5962	381	12	minimal	minimal	ADJ
ejpam-5962	381	13	hausdroff	hausdroff	NOUN
ejpam-5962	381	14	space	space	NOUN
ejpam-5962	381	15	.	.	PUNCT
ejpam-5962	382	1	theorem	theorem	VERB
ejpam-5962	382	2	8.2	8.2	NUM
ejpam-5962	382	3	.	.	PUNCT
ejpam-5962	383	1	every	every	DET
ejpam-5962	383	2	pairwise	pairwise	NOUN
ejpam-5962	383	3	hausdroff	hausdroff	VERB
ejpam-5962	383	4	minimal	minimal	ADJ
ejpam-5962	383	5	compact	compact	ADJ
ejpam-5962	383	6	closed	close	VERB
ejpam-5962	383	7	space	space	NOUN
ejpam-5962	383	8	is	be	AUX
ejpam-5962	383	9	pairwise	pairwise	NOUN
ejpam-5962	383	10	minimal	minimal	ADJ
ejpam-5962	383	11	hausdroff	hausdroff	NOUN
ejpam-5962	383	12	space	space	NOUN
ejpam-5962	383	13	.	.	PUNCT
ejpam-5962	384	1	proof	proof	NOUN
ejpam-5962	384	2	.	.	PUNCT
ejpam-5962	385	1	let	let	VERB
ejpam-5962	385	2	(	(	PUNCT
ejpam-5962	385	3	z	z	NOUN
ejpam-5962	385	4	,	,	PUNCT
ejpam-5962	385	5	ϑ1	ϑ1	NOUN
ejpam-5962	385	6	,	,	PUNCT
ejpam-5962	385	7	ϑ2	ϑ2	PROPN
ejpam-5962	385	8	)	)	PUNCT
ejpam-5962	385	9	be	be	VERB
ejpam-5962	385	10	pairwise	pairwise	NOUN
ejpam-5962	385	11	hausdroff	hausdroff	NOUN
ejpam-5962	385	12	minimal	minimal	ADJ
ejpam-5962	385	13	compact	compact	ADJ
ejpam-5962	385	14	closed	closed	ADJ
ejpam-5962	385	15	space	space	NOUN
ejpam-5962	385	16	,	,	PUNCT
ejpam-5962	385	17	then	then	ADV
ejpam-5962	385	18	(	(	PUNCT
ejpam-5962	385	19	z	z	NOUN
ejpam-5962	385	20	,	,	PUNCT
ejpam-5962	385	21	ϑ1	ϑ1	NOUN
ejpam-5962	385	22	,	,	PUNCT
ejpam-5962	385	23	ϑ2	ϑ2	PROPN
ejpam-5962	385	24	)	)	PUNCT
ejpam-5962	385	25	is	be	AUX
ejpam-5962	385	26	pairwise	pairwise	NOUN
ejpam-5962	385	27	hausdroff	hausdroff	NOUN
ejpam-5962	385	28	compact	compact	ADJ
ejpam-5962	385	29	closed	close	VERB
ejpam-5962	385	30	space	space	NOUN
ejpam-5962	385	31	and	and	CCONJ
ejpam-5962	385	32	(	(	PUNCT
ejpam-5962	385	33	z	z	NOUN
ejpam-5962	385	34	,	,	PUNCT
ejpam-5962	385	35	ϑ1	ϑ1	NOUN
ejpam-5962	385	36	,	,	PUNCT
ejpam-5962	385	37	ϑ2	ϑ2	PROPN
ejpam-5962	385	38	)	)	PUNCT
ejpam-5962	385	39	is	be	AUX
ejpam-5962	385	40	not	not	PART
ejpam-5962	385	41	pairwise	pairwise	NOUN
ejpam-5962	385	42	minimal	minimal	ADJ
ejpam-5962	385	43	hausdroff	hausdroff	NOUN
ejpam-5962	385	44	space	space	NOUN
ejpam-5962	385	45	,	,	PUNCT
ejpam-5962	385	46	hence	hence	ADV
ejpam-5962	385	47	,	,	PUNCT
ejpam-5962	385	48	there	there	PRON
ejpam-5962	385	49	are	be	VERB
ejpam-5962	385	50	ϑ	ϑ	PROPN
ejpam-5962	385	51	/	/	SYM
ejpam-5962	385	52	1	1	NUM
ejpam-5962	385	53	,	,	PUNCT
ejpam-5962	385	54	ϑ	ϑ	X
ejpam-5962	385	55	/	/	SYM
ejpam-5962	385	56	2	2	NUM
ejpam-5962	385	57	such	such	ADJ
ejpam-5962	385	58	that	that	SCONJ
ejpam-5962	385	59	,	,	PUNCT
ejpam-5962	385	60	ϑ	ϑ	X
ejpam-5962	385	61	/	/	SYM
ejpam-5962	385	62	1	1	NUM
ejpam-5962	385	63	≤	≤	NOUN
ejpam-5962	385	64	ϑ1	ϑ1	NOUN
ejpam-5962	385	65	,	,	PUNCT
ejpam-5962	385	66	ϑ	ϑ	X
ejpam-5962	385	67	/	/	SYM
ejpam-5962	385	68	2	2	NUM
ejpam-5962	385	69	≤	≤	NOUN
ejpam-5962	385	70	ϑ2	ϑ2	NOUN
ejpam-5962	385	71	and	and	CCONJ
ejpam-5962	385	72	(	(	PUNCT
ejpam-5962	385	73	z	z	NOUN
ejpam-5962	385	74	,	,	PUNCT
ejpam-5962	385	75	ϑ	ϑ	X
ejpam-5962	385	76	/	/	SYM
ejpam-5962	385	77	1	1	NUM
ejpam-5962	385	78	,	,	PUNCT
ejpam-5962	385	79	ϑ	ϑ	X
ejpam-5962	385	80	/	/	SYM
ejpam-5962	385	81	2	2	NUM
ejpam-5962	385	82	)	)	PUNCT
ejpam-5962	385	83	is	be	AUX
ejpam-5962	385	84	pairwise	pairwise	NOUN
ejpam-5962	385	85	hausdroff	hausdroff	NOUN
ejpam-5962	385	86	space	space	NOUN
ejpam-5962	385	87	and	and	CCONJ
ejpam-5962	385	88	so	so	ADV
ejpam-5962	385	89	(	(	PUNCT
ejpam-5962	385	90	z	z	NOUN
ejpam-5962	385	91	,	,	PUNCT
ejpam-5962	385	92	ϑ	ϑ	X
ejpam-5962	385	93	/	/	SYM
ejpam-5962	385	94	1	1	NUM
ejpam-5962	385	95	,	,	PUNCT
ejpam-5962	385	96	ϑ	ϑ	X
ejpam-5962	385	97	/	/	SYM
ejpam-5962	385	98	2	2	NUM
ejpam-5962	385	99	)	)	PUNCT
ejpam-5962	385	100	is	be	AUX
ejpam-5962	385	101	pairwise	pairwise	NOUN
ejpam-5962	385	102	compact	compact	ADJ
ejpam-5962	385	103	closed	close	VERB
ejpam-5962	385	104	space	space	NOUN
ejpam-5962	385	105	.	.	PUNCT
ejpam-5962	386	1	a	a	DET
ejpam-5962	386	2	contradiction	contradiction	NOUN
ejpam-5962	386	3	results	result	VERB
ejpam-5962	386	4	because	because	SCONJ
ejpam-5962	386	5	(	(	PUNCT
ejpam-5962	386	6	z	z	X
ejpam-5962	386	7	,	,	PUNCT
ejpam-5962	386	8	ϑ1	ϑ1	NOUN
ejpam-5962	386	9	,	,	PUNCT
ejpam-5962	386	10	ϑ2	ϑ2	PROPN
ejpam-5962	386	11	)	)	PUNCT
ejpam-5962	386	12	be	be	VERB
ejpam-5962	386	13	pairwise	pairwise	NOUN
ejpam-5962	386	14	minimal	minimal	ADJ
ejpam-5962	386	15	compact	compact	ADJ
ejpam-5962	386	16	closed	closed	ADJ
ejpam-5962	386	17	space	space	NOUN
ejpam-5962	386	18	.	.	PUNCT
ejpam-5962	387	1	hence	hence	ADV
ejpam-5962	387	2	(	(	PUNCT
ejpam-5962	387	3	z	z	NOUN
ejpam-5962	387	4	,	,	PUNCT
ejpam-5962	387	5	ϑ1	ϑ1	NOUN
ejpam-5962	387	6	,	,	PUNCT
ejpam-5962	387	7	ϑ2	ϑ2	PROPN
ejpam-5962	387	8	)	)	PUNCT
ejpam-5962	387	9	is	be	AUX
ejpam-5962	387	10	pairwise	pairwise	NOUN
ejpam-5962	387	11	minimal	minimal	ADJ
ejpam-5962	387	12	hausdroff	hausdroff	NOUN
ejpam-5962	387	13	space	space	NOUN
ejpam-5962	387	14	.	.	PUNCT
ejpam-5962	388	1	the	the	DET
ejpam-5962	388	2	following	follow	VERB
ejpam-5962	388	3	corollary	corollary	NOUN
ejpam-5962	388	4	’s	’s	PART
ejpam-5962	388	5	proof	proof	NOUN
ejpam-5962	388	6	is	be	AUX
ejpam-5962	388	7	equivalent	equivalent	ADJ
ejpam-5962	388	8	to	to	ADP
ejpam-5962	388	9	that	that	PRON
ejpam-5962	388	10	of	of	ADP
ejpam-5962	388	11	the	the	DET
ejpam-5962	388	12	aforementioned	aforementione	VERB
ejpam-5962	388	13	theorem	theorem	NOUN
ejpam-5962	388	14	.	.	PUNCT
ejpam-5962	388	15	a.	a.	PROPN
ejpam-5962	388	16	a.	a.	PROPN
ejpam-5962	388	17	atoom	atoom	PROPN
ejpam-5962	388	18	et	et	PROPN
ejpam-5962	388	19	al	al	PROPN
ejpam-5962	388	20	.	.	PUNCT
ejpam-5962	388	21	/	/	SYM
ejpam-5962	388	22	eur	eur	PROPN
ejpam-5962	388	23	.	.	PUNCT
ejpam-5962	389	1	j.	j.	PROPN
ejpam-5962	389	2	pure	pure	PROPN
ejpam-5962	389	3	appl	appl	PROPN
ejpam-5962	389	4	.	.	PROPN
ejpam-5962	389	5	math	math	PROPN
ejpam-5962	389	6	,	,	PUNCT
ejpam-5962	389	7	18	18	NUM
ejpam-5962	389	8	(	(	PUNCT
ejpam-5962	389	9	2	2	NUM
ejpam-5962	389	10	)	)	PUNCT
ejpam-5962	389	11	(	(	PUNCT
ejpam-5962	389	12	2025	2025	NUM
ejpam-5962	389	13	)	)	PUNCT
ejpam-5962	389	14	,	,	PUNCT
ejpam-5962	389	15	5962	5962	NUM
ejpam-5962	389	16	14	14	NUM
ejpam-5962	389	17	of	of	ADP
ejpam-5962	389	18	17	17	NUM
ejpam-5962	389	19	corollary	corollary	ADJ
ejpam-5962	389	20	8.2	8.2	NUM
ejpam-5962	389	21	.	.	PUNCT
ejpam-5962	390	1	each	each	DET
ejpam-5962	390	2	pairwise	pairwise	NOUN
ejpam-5962	390	3	hausdroff	hausdroff	NOUN
ejpam-5962	390	4	minimal	minimal	ADJ
ejpam-5962	390	5	compact	compact	ADJ
ejpam-5962	390	6	closed	close	VERB
ejpam-5962	390	7	space	space	NOUN
ejpam-5962	390	8	is	be	AUX
ejpam-5962	390	9	pairwise	pairwise	NOUN
ejpam-5962	390	10	minimal	minimal	ADJ
ejpam-5962	390	11	compact	compact	ADJ
ejpam-5962	390	12	closed	closed	ADJ
ejpam-5962	390	13	space	space	NOUN
ejpam-5962	390	14	.	.	PUNCT
ejpam-5962	391	1	theorem	theorem	VERB
ejpam-5962	391	2	8.3	8.3	NUM
ejpam-5962	391	3	.	.	PUNCT
ejpam-5962	392	1	every	every	DET
ejpam-5962	392	2	pairwise	pairwise	NOUN
ejpam-5962	392	3	regular	regular	ADJ
ejpam-5962	392	4	minimal	minimal	ADJ
ejpam-5962	392	5	compact	compact	ADJ
ejpam-5962	392	6	closed	close	VERB
ejpam-5962	392	7	space	space	NOUN
ejpam-5962	392	8	is	be	AUX
ejpam-5962	392	9	pairwise	pairwise	NOUN
ejpam-5962	392	10	minimal	minimal	ADJ
ejpam-5962	392	11	hausdroff	hausdroff	NOUN
ejpam-5962	392	12	space	space	NOUN
ejpam-5962	392	13	.	.	PUNCT
ejpam-5962	393	1	proof	proof	NOUN
ejpam-5962	393	2	.	.	PUNCT
ejpam-5962	394	1	let	let	VERB
ejpam-5962	394	2	(	(	PUNCT
ejpam-5962	394	3	z	z	NOUN
ejpam-5962	394	4	,	,	PUNCT
ejpam-5962	394	5	ϑ1	ϑ1	NOUN
ejpam-5962	394	6	,	,	PUNCT
ejpam-5962	394	7	ϑ2	ϑ2	PROPN
ejpam-5962	394	8	)	)	PUNCT
ejpam-5962	394	9	be	be	VERB
ejpam-5962	394	10	pairwise	pairwise	NOUN
ejpam-5962	394	11	regular	regular	ADJ
ejpam-5962	394	12	minimal	minimal	ADJ
ejpam-5962	394	13	compact	compact	ADJ
ejpam-5962	394	14	closed	closed	ADJ
ejpam-5962	394	15	space	space	NOUN
ejpam-5962	394	16	,	,	PUNCT
ejpam-5962	394	17	then	then	ADV
ejpam-5962	394	18	(	(	PUNCT
ejpam-5962	394	19	z	z	NOUN
ejpam-5962	394	20	,	,	PUNCT
ejpam-5962	394	21	ϑ1	ϑ1	NOUN
ejpam-5962	394	22	,	,	PUNCT
ejpam-5962	394	23	ϑ2	ϑ2	PROPN
ejpam-5962	394	24	)	)	PUNCT
ejpam-5962	394	25	is	be	AUX
ejpam-5962	394	26	pairwise	pairwise	NOUN
ejpam-5962	394	27	regular	regular	ADJ
ejpam-5962	394	28	compact	compact	ADJ
ejpam-5962	394	29	closed	closed	ADJ
ejpam-5962	394	30	space	space	NOUN
ejpam-5962	394	31	.	.	PUNCT
ejpam-5962	395	1	since	since	SCONJ
ejpam-5962	395	2	every	every	DET
ejpam-5962	395	3	pairwise	pairwise	NOUN
ejpam-5962	395	4	compact	compact	ADJ
ejpam-5962	395	5	closed	close	VERB
ejpam-5962	395	6	space	space	NOUN
ejpam-5962	395	7	is	be	AUX
ejpam-5962	395	8	pairwise	pairwise	NOUN
ejpam-5962	395	9	t1−	t1−	NOUN
ejpam-5962	395	10	space	space	NOUN
ejpam-5962	395	11	.	.	PUNCT
ejpam-5962	396	1	hence	hence	ADV
ejpam-5962	396	2	(	(	PUNCT
ejpam-5962	396	3	z	z	NOUN
ejpam-5962	396	4	,	,	PUNCT
ejpam-5962	396	5	ϑ1	ϑ1	NOUN
ejpam-5962	396	6	,	,	PUNCT
ejpam-5962	396	7	ϑ2	ϑ2	PROPN
ejpam-5962	396	8	)	)	PUNCT
ejpam-5962	396	9	is	be	AUX
ejpam-5962	396	10	regular	regular	ADJ
ejpam-5962	396	11	and	and	CCONJ
ejpam-5962	396	12	t1−	t1−	NOUN
ejpam-5962	396	13	space	space	NOUN
ejpam-5962	397	1	so	so	SCONJ
ejpam-5962	397	2	it	it	PRON
ejpam-5962	397	3	is	be	AUX
ejpam-5962	397	4	t2−	t2−	NOUN
ejpam-5962	397	5	space	space	NOUN
ejpam-5962	397	6	.	.	PUNCT
ejpam-5962	398	1	suppose	suppose	VERB
ejpam-5962	398	2	(	(	PUNCT
ejpam-5962	398	3	z	z	NOUN
ejpam-5962	398	4	,	,	PUNCT
ejpam-5962	398	5	ϑ1	ϑ1	NOUN
ejpam-5962	398	6	,	,	PUNCT
ejpam-5962	398	7	ϑ2	ϑ2	PROPN
ejpam-5962	398	8	)	)	PUNCT
ejpam-5962	398	9	is	be	AUX
ejpam-5962	398	10	not	not	PART
ejpam-5962	398	11	pairwise	pairwise	NOUN
ejpam-5962	398	12	minimal	minimal	ADJ
ejpam-5962	398	13	hausdroff	hausdroff	NOUN
ejpam-5962	398	14	space	space	NOUN
ejpam-5962	398	15	,	,	PUNCT
ejpam-5962	398	16	so	so	SCONJ
ejpam-5962	398	17	there	there	PRON
ejpam-5962	398	18	exist	exist	VERB
ejpam-5962	398	19	ϑ	ϑ	PROPN
ejpam-5962	398	20	/	/	SYM
ejpam-5962	398	21	1	1	NUM
ejpam-5962	398	22	,	,	PUNCT
ejpam-5962	398	23	ϑ	ϑ	X
ejpam-5962	398	24	/	/	SYM
ejpam-5962	398	25	2	2	NUM
ejpam-5962	398	26	such	such	ADJ
ejpam-5962	398	27	that	that	SCONJ
ejpam-5962	398	28	,	,	PUNCT
ejpam-5962	398	29	ϑ	ϑ	X
ejpam-5962	398	30	/	/	SYM
ejpam-5962	398	31	1	1	NUM
ejpam-5962	398	32	≤	≤	NOUN
ejpam-5962	398	33	ϑ1	ϑ1	NOUN
ejpam-5962	398	34	,	,	PUNCT
ejpam-5962	398	35	ϑ	ϑ	X
ejpam-5962	398	36	/	/	SYM
ejpam-5962	398	37	2	2	NUM
ejpam-5962	398	38	≤	≤	NOUN
ejpam-5962	398	39	ϑ2	ϑ2	NOUN
ejpam-5962	398	40	and	and	CCONJ
ejpam-5962	398	41	(	(	PUNCT
ejpam-5962	398	42	z	z	NOUN
ejpam-5962	398	43	,	,	PUNCT
ejpam-5962	398	44	ϑ	ϑ	X
ejpam-5962	398	45	/	/	SYM
ejpam-5962	398	46	1	1	NUM
ejpam-5962	398	47	,	,	PUNCT
ejpam-5962	398	48	ϑ	ϑ	X
ejpam-5962	398	49	/	/	SYM
ejpam-5962	398	50	2	2	NUM
ejpam-5962	398	51	)	)	PUNCT
ejpam-5962	398	52	is	be	AUX
ejpam-5962	398	53	pairwise	pairwise	NOUN
ejpam-5962	398	54	compact	compact	ADJ
ejpam-5962	398	55	closed	close	VERB
ejpam-5962	398	56	space	space	NOUN
ejpam-5962	398	57	,	,	PUNCT
ejpam-5962	398	58	which	which	PRON
ejpam-5962	398	59	is	be	AUX
ejpam-5962	398	60	incongruous	incongruous	ADJ
ejpam-5962	398	61	;	;	PUNCT
ejpam-5962	398	62	as	as	ADP
ejpam-5962	398	63	a	a	DET
ejpam-5962	398	64	result	result	NOUN
ejpam-5962	398	65	(	(	PUNCT
ejpam-5962	398	66	z	z	NOUN
ejpam-5962	398	67	,	,	PUNCT
ejpam-5962	398	68	ϑ1	ϑ1	NOUN
ejpam-5962	398	69	,	,	PUNCT
ejpam-5962	398	70	ϑ2	ϑ2	PROPN
ejpam-5962	398	71	)	)	PUNCT
ejpam-5962	398	72	is	be	AUX
ejpam-5962	398	73	pairwise	pairwise	NOUN
ejpam-5962	398	74	minimal	minimal	ADJ
ejpam-5962	398	75	hausdroff	hausdroff	NOUN
ejpam-5962	398	76	space	space	NOUN
ejpam-5962	398	77	.	.	PUNCT
ejpam-5962	399	1	(	(	PUNCT
ejpam-5962	399	2	z	z	X
ejpam-5962	399	3	,	,	PUNCT
ejpam-5962	399	4	ϑ1	ϑ1	NOUN
ejpam-5962	399	5	,	,	PUNCT
ejpam-5962	399	6	ϑ2	ϑ2	PROPN
ejpam-5962	399	7	)	)	PUNCT
ejpam-5962	399	8	,	,	PUNCT
ejpam-5962	399	9	(	(	PUNCT
ejpam-5962	399	10	n	n	X
ejpam-5962	399	11	,	,	PUNCT
ejpam-5962	399	12	β1	β1	PROPN
ejpam-5962	399	13	,	,	PUNCT
ejpam-5962	399	14	β2	β2	NOUN
ejpam-5962	399	15	)	)	PUNCT
ejpam-5962	399	16	theorem	theorem	VERB
ejpam-5962	399	17	8.4	8.4	NUM
ejpam-5962	399	18	.	.	PUNCT
ejpam-5962	400	1	suppose	suppose	VERB
ejpam-5962	400	2	(	(	PUNCT
ejpam-5962	400	3	z	z	NOUN
ejpam-5962	400	4	×	×	NOUN
ejpam-5962	400	5	n	n	CCONJ
ejpam-5962	400	6	,	,	PUNCT
ejpam-5962	400	7	ϑ1	ϑ1	PROPN
ejpam-5962	400	8	×	×	NOUN
ejpam-5962	400	9	β1	β1	PROPN
ejpam-5962	400	10	,	,	PUNCT
ejpam-5962	400	11	ϑ2	ϑ2	PROPN
ejpam-5962	400	12	×	×	NOUN
ejpam-5962	400	13	β2	β2	NOUN
ejpam-5962	400	14	)	)	PUNCT
ejpam-5962	400	15	is	be	AUX
ejpam-5962	400	16	pairwise	pairwise	NOUN
ejpam-5962	400	17	regular	regular	ADJ
ejpam-5962	400	18	compact	compact	ADJ
ejpam-5962	400	19	closed	closed	ADJ
ejpam-5962	400	20	space	space	NOUN
ejpam-5962	400	21	,	,	PUNCT
ejpam-5962	400	22	then	then	ADV
ejpam-5962	400	23	each	each	PRON
ejpam-5962	400	24	(	(	PUNCT
ejpam-5962	400	25	z	z	NOUN
ejpam-5962	400	26	,	,	PUNCT
ejpam-5962	400	27	ϑ1	ϑ1	NOUN
ejpam-5962	400	28	,	,	PUNCT
ejpam-5962	400	29	ϑ2	ϑ2	PROPN
ejpam-5962	400	30	)	)	PUNCT
ejpam-5962	400	31	,	,	PUNCT
ejpam-5962	400	32	(	(	PUNCT
ejpam-5962	400	33	n	n	X
ejpam-5962	400	34	,	,	PUNCT
ejpam-5962	400	35	β1	β1	PROPN
ejpam-5962	400	36	,	,	PUNCT
ejpam-5962	400	37	β2	β2	NOUN
ejpam-5962	400	38	)	)	PUNCT
ejpam-5962	400	39	is	be	AUX
ejpam-5962	400	40	pairwise	pairwise	NOUN
ejpam-5962	400	41	minimal	minimal	ADJ
ejpam-5962	400	42	hausdroff	hausdroff	NOUN
ejpam-5962	400	43	space	space	NOUN
ejpam-5962	400	44	.	.	PUNCT
ejpam-5962	401	1	proof	proof	NOUN
ejpam-5962	401	2	.	.	PUNCT
ejpam-5962	402	1	since	since	SCONJ
ejpam-5962	402	2	(	(	PUNCT
ejpam-5962	402	3	z	z	NOUN
ejpam-5962	402	4	,	,	PUNCT
ejpam-5962	402	5	ϑ1	ϑ1	NOUN
ejpam-5962	402	6	,	,	PUNCT
ejpam-5962	402	7	ϑ2	ϑ2	PROPN
ejpam-5962	402	8	)	)	PUNCT
ejpam-5962	402	9	,	,	PUNCT
ejpam-5962	402	10	(	(	PUNCT
ejpam-5962	402	11	n	n	X
ejpam-5962	402	12	,	,	PUNCT
ejpam-5962	402	13	β1	β1	PROPN
ejpam-5962	402	14	,	,	PUNCT
ejpam-5962	402	15	β2	β2	NOUN
ejpam-5962	402	16	)	)	PUNCT
ejpam-5962	402	17	is	be	AUX
ejpam-5962	402	18	pairwise	pairwise	NOUN
ejpam-5962	402	19	compact	compact	ADJ
ejpam-5962	402	20	closed	close	VERB
ejpam-5962	402	21	space	space	NOUN
ejpam-5962	402	22	,	,	PUNCT
ejpam-5962	402	23	so	so	SCONJ
ejpam-5962	402	24	each	each	PRON
ejpam-5962	402	25	(	(	PUNCT
ejpam-5962	402	26	z	z	NOUN
ejpam-5962	402	27	,	,	PUNCT
ejpam-5962	402	28	ϑ1	ϑ1	NOUN
ejpam-5962	402	29	,	,	PUNCT
ejpam-5962	402	30	ϑ2	ϑ2	PROPN
ejpam-5962	402	31	)	)	PUNCT
ejpam-5962	402	32	,	,	PUNCT
ejpam-5962	402	33	(	(	PUNCT
ejpam-5962	402	34	n	n	X
ejpam-5962	402	35	,	,	PUNCT
ejpam-5962	402	36	β1	β1	PROPN
ejpam-5962	402	37	,	,	PUNCT
ejpam-5962	402	38	β2	β2	NOUN
ejpam-5962	402	39	)	)	PUNCT
ejpam-5962	402	40	is	be	AUX
ejpam-5962	402	41	pairwise	pairwise	NOUN
ejpam-5962	402	42	minimal	minimal	ADJ
ejpam-5962	402	43	compact	compact	ADJ
ejpam-5962	402	44	closed	closed	ADJ
ejpam-5962	402	45	space	space	NOUN
ejpam-5962	402	46	,	,	PUNCT
ejpam-5962	402	47	and	and	CCONJ
ejpam-5962	402	48	therefore	therefore	ADV
ejpam-5962	402	49	(	(	PUNCT
ejpam-5962	402	50	z	z	NOUN
ejpam-5962	402	51	,	,	PUNCT
ejpam-5962	402	52	ϑ1	ϑ1	NOUN
ejpam-5962	402	53	,	,	PUNCT
ejpam-5962	402	54	ϑ2	ϑ2	PROPN
ejpam-5962	402	55	)	)	PUNCT
ejpam-5962	402	56	,	,	PUNCT
ejpam-5962	402	57	(	(	PUNCT
ejpam-5962	402	58	n	n	X
ejpam-5962	402	59	,	,	PUNCT
ejpam-5962	402	60	β1	β1	PROPN
ejpam-5962	402	61	,	,	PUNCT
ejpam-5962	402	62	β2	β2	NOUN
ejpam-5962	402	63	)	)	PUNCT
ejpam-5962	402	64	is	be	AUX
ejpam-5962	402	65	pairwise	pairwise	NOUN
ejpam-5962	402	66	regular	regular	NOUN
ejpam-5962	402	67	,	,	PUNCT
ejpam-5962	402	68	then	then	ADV
ejpam-5962	402	69	it	it	PRON
ejpam-5962	402	70	is	be	AUX
ejpam-5962	402	71	pairwise	pairwise	NOUN
ejpam-5962	402	72	minimal	minimal	ADJ
ejpam-5962	402	73	hausdroff	hausdroff	NOUN
ejpam-5962	402	74	space	space	NOUN
ejpam-5962	402	75	.	.	PUNCT
ejpam-5962	403	1	theorem	theorem	VERB
ejpam-5962	403	2	8.5	8.5	NUM
ejpam-5962	403	3	.	.	PUNCT
ejpam-5962	404	1	if	if	SCONJ
ejpam-5962	404	2	(	(	PUNCT
ejpam-5962	404	3	z	z	NOUN
ejpam-5962	404	4	,	,	PUNCT
ejpam-5962	404	5	ϑ1	ϑ1	NOUN
ejpam-5962	404	6	,	,	PUNCT
ejpam-5962	404	7	ϑ2	ϑ2	PROPN
ejpam-5962	404	8	)	)	PUNCT
ejpam-5962	404	9	,	,	PUNCT
ejpam-5962	404	10	(	(	PUNCT
ejpam-5962	404	11	n	n	X
ejpam-5962	404	12	,	,	PUNCT
ejpam-5962	404	13	β1	β1	PROPN
ejpam-5962	404	14	,	,	PUNCT
ejpam-5962	404	15	β2	β2	NOUN
ejpam-5962	404	16	)	)	PUNCT
ejpam-5962	404	17	are	be	AUX
ejpam-5962	404	18	pairwise	pairwise	NOUN
ejpam-5962	404	19	hausdroff	hausdroff	NOUN
ejpam-5962	404	20	compact	compact	ADJ
ejpam-5962	404	21	closed	close	VERB
ejpam-5962	404	22	space	space	NOUN
ejpam-5962	404	23	,	,	PUNCT
ejpam-5962	404	24	(	(	PUNCT
ejpam-5962	404	25	z	z	NOUN
ejpam-5962	404	26	×n	×n	NUM
ejpam-5962	404	27	,	,	PUNCT
ejpam-5962	404	28	ϑ1	ϑ1	PROPN
ejpam-5962	404	29	×	×	NOUN
ejpam-5962	404	30	β1	β1	PROPN
ejpam-5962	404	31	,	,	PUNCT
ejpam-5962	404	32	ϑ2	ϑ2	PROPN
ejpam-5962	404	33	×	×	NOUN
ejpam-5962	404	34	β2	β2	NOUN
ejpam-5962	404	35	)	)	PUNCT
ejpam-5962	404	36	is	be	AUX
ejpam-5962	404	37	pairwise	pairwise	NOUN
ejpam-5962	404	38	regular	regular	ADJ
ejpam-5962	404	39	minimal	minimal	ADJ
ejpam-5962	404	40	compact	compact	ADJ
ejpam-5962	404	41	closed	closed	ADJ
ejpam-5962	404	42	space	space	NOUN
ejpam-5962	404	43	.	.	PUNCT
ejpam-5962	405	1	proof	proof	NOUN
ejpam-5962	405	2	.	.	PUNCT
ejpam-5962	406	1	since	since	SCONJ
ejpam-5962	406	2	(	(	PUNCT
ejpam-5962	406	3	z	z	NOUN
ejpam-5962	406	4	,	,	PUNCT
ejpam-5962	406	5	ϑ1	ϑ1	NOUN
ejpam-5962	406	6	,	,	PUNCT
ejpam-5962	406	7	ϑ2	ϑ2	PROPN
ejpam-5962	406	8	)	)	PUNCT
ejpam-5962	406	9	,	,	PUNCT
ejpam-5962	406	10	(	(	PUNCT
ejpam-5962	406	11	n	n	X
ejpam-5962	406	12	,	,	PUNCT
ejpam-5962	406	13	β1	β1	PROPN
ejpam-5962	406	14	,	,	PUNCT
ejpam-5962	406	15	β2	β2	NOUN
ejpam-5962	406	16	)	)	PUNCT
ejpam-5962	406	17	are	be	AUX
ejpam-5962	406	18	pairwise	pairwise	NOUN
ejpam-5962	406	19	hausdroff	hausdroff	NOUN
ejpam-5962	406	20	compact	compact	ADJ
ejpam-5962	406	21	closed	closed	ADJ
ejpam-5962	406	22	space	space	NOUN
ejpam-5962	406	23	,	,	PUNCT
ejpam-5962	406	24	then	then	ADV
ejpam-5962	406	25	(	(	PUNCT
ejpam-5962	406	26	z×n	z×n	PROPN
ejpam-5962	406	27	,	,	PUNCT
ejpam-5962	406	28	ϑ1×β1	ϑ1×β1	NOUN
ejpam-5962	406	29	,	,	PUNCT
ejpam-5962	406	30	ϑ2	ϑ2	PROPN
ejpam-5962	406	31	×β2	×β2	PROPN
ejpam-5962	406	32	)	)	PUNCT
ejpam-5962	406	33	is	be	AUX
ejpam-5962	406	34	pairwise	pairwise	NOUN
ejpam-5962	406	35	hausdroff	hausdroff	NOUN
ejpam-5962	406	36	compact	compact	ADJ
ejpam-5962	406	37	closed	close	VERB
ejpam-5962	406	38	space	space	NOUN
ejpam-5962	406	39	,	,	PUNCT
ejpam-5962	406	40	so	so	ADV
ejpam-5962	406	41	by	by	ADP
ejpam-5962	406	42	theorem	theorem	NOUN
ejpam-5962	406	43	8.3	8.3	NUM
ejpam-5962	406	44	,	,	PUNCT
ejpam-5962	406	45	(	(	PUNCT
ejpam-5962	406	46	z	z	NOUN
ejpam-5962	406	47	×n	×n	NUM
ejpam-5962	406	48	,	,	PUNCT
ejpam-5962	406	49	ϑ1	ϑ1	PROPN
ejpam-5962	406	50	×	×	NOUN
ejpam-5962	406	51	β1	β1	PROPN
ejpam-5962	406	52	,	,	PUNCT
ejpam-5962	406	53	ϑ2	ϑ2	PROPN
ejpam-5962	406	54	×	×	NOUN
ejpam-5962	406	55	β2	β2	NOUN
ejpam-5962	406	56	)	)	PUNCT
ejpam-5962	406	57	is	be	AUX
ejpam-5962	406	58	pairwise	pairwise	NOUN
ejpam-5962	406	59	compact	compact	ADJ
ejpam-5962	406	60	closed	close	VERB
ejpam-5962	406	61	space	space	NOUN
ejpam-5962	406	62	,	,	PUNCT
ejpam-5962	406	63	and	and	CCONJ
ejpam-5962	406	64	so	so	ADV
ejpam-5962	406	65	is	be	AUX
ejpam-5962	406	66	pairwise	pairwise	NOUN
ejpam-5962	406	67	minimal	minimal	ADJ
ejpam-5962	406	68	compact	compact	ADJ
ejpam-5962	406	69	closed	closed	ADJ
ejpam-5962	406	70	space	space	NOUN
ejpam-5962	406	71	,	,	PUNCT
ejpam-5962	406	72	by	by	ADP
ejpam-5962	406	73	theorem	theorem	NOUN
ejpam-5962	406	74	8.4	8.4	NUM
ejpam-5962	406	75	,	,	PUNCT
ejpam-5962	406	76	(	(	PUNCT
ejpam-5962	406	77	z	z	NOUN
ejpam-5962	406	78	×	×	NOUN
ejpam-5962	406	79	n	n	CCONJ
ejpam-5962	406	80	,	,	PUNCT
ejpam-5962	406	81	ϑ1	ϑ1	PROPN
ejpam-5962	406	82	×	×	NOUN
ejpam-5962	406	83	β1	β1	PROPN
ejpam-5962	406	84	,	,	PUNCT
ejpam-5962	406	85	ϑ2	ϑ2	PROPN
ejpam-5962	406	86	×	×	NOUN
ejpam-5962	406	87	β2	β2	NOUN
ejpam-5962	406	88	)	)	PUNCT
ejpam-5962	406	89	is	be	AUX
ejpam-5962	406	90	pairwise	pairwise	NOUN
ejpam-5962	406	91	regular	regular	ADJ
ejpam-5962	406	92	minimal	minimal	ADJ
ejpam-5962	406	93	compact	compact	ADJ
ejpam-5962	406	94	closed	closed	ADJ
ejpam-5962	406	95	space	space	NOUN
ejpam-5962	406	96	.	.	PUNCT
ejpam-5962	407	1	corollary	corollary	ADJ
ejpam-5962	407	2	8.3	8.3	NUM
ejpam-5962	407	3	.	.	PUNCT
ejpam-5962	408	1	every	every	DET
ejpam-5962	408	2	pairwise	pairwise	NOUN
ejpam-5962	408	3	lindelöf	lindelöf	NOUN
ejpam-5962	408	4	closed	close	VERB
ejpam-5962	408	5	space	space	NOUN
ejpam-5962	408	6	is	be	AUX
ejpam-5962	408	7	pairwise	pairwise	NOUN
ejpam-5962	408	8	compact	compact	ADJ
ejpam-5962	408	9	closed	close	VERB
ejpam-5962	408	10	space	space	NOUN
ejpam-5962	408	11	.	.	PUNCT
ejpam-5962	409	1	theorem	theorem	VERB
ejpam-5962	409	2	8.6	8.6	NUM
ejpam-5962	409	3	.	.	PUNCT
ejpam-5962	410	1	for	for	ADP
ejpam-5962	410	2	pairwise	pairwise	NOUN
ejpam-5962	410	3	closed	close	VERB
ejpam-5962	410	4	compact	compact	ADJ
ejpam-5962	410	5	p−space	p−space	NOUN
ejpam-5962	410	6	(	(	PUNCT
ejpam-5962	410	7	z	z	NOUN
ejpam-5962	410	8	,	,	PUNCT
ejpam-5962	410	9	ϑ1	ϑ1	NOUN
ejpam-5962	410	10	,	,	PUNCT
ejpam-5962	410	11	ϑ2	ϑ2	PROPN
ejpam-5962	410	12	)	)	PUNCT
ejpam-5962	410	13	,	,	PUNCT
ejpam-5962	410	14	the	the	DET
ejpam-5962	410	15	following	follow	VERB
ejpam-5962	410	16	is	be	AUX
ejpam-5962	410	17	equivalent	equivalent	ADJ
ejpam-5962	410	18	:	:	PUNCT
ejpam-5962	410	19	let	let	VERB
ejpam-5962	410	20	(	(	PUNCT
ejpam-5962	410	21	z	z	NOUN
ejpam-5962	410	22	,	,	PUNCT
ejpam-5962	410	23	ϑ1	ϑ1	NOUN
ejpam-5962	410	24	,	,	PUNCT
ejpam-5962	410	25	ϑ2	ϑ2	PROPN
ejpam-5962	410	26	)	)	PUNCT
ejpam-5962	410	27	is	be	AUX
ejpam-5962	410	28	pairwise	pairwise	NOUN
ejpam-5962	410	29	minimal	minimal	ADJ
ejpam-5962	410	30	hausdroff	hausdroff	NOUN
ejpam-5962	410	31	space	space	NOUN
ejpam-5962	410	32	,	,	PUNCT
ejpam-5962	410	33	if	if	SCONJ
ejpam-5962	410	34	and	and	CCONJ
ejpam-5962	410	35	only	only	ADV
ejpam-5962	410	36	if	if	SCONJ
ejpam-5962	410	37	(	(	PUNCT
ejpam-5962	410	38	z	z	NOUN
ejpam-5962	410	39	,	,	PUNCT
ejpam-5962	410	40	ϑ1	ϑ1	NOUN
ejpam-5962	410	41	,	,	PUNCT
ejpam-5962	410	42	ϑ2	ϑ2	PROPN
ejpam-5962	410	43	)	)	PUNCT
ejpam-5962	410	44	is	be	AUX
ejpam-5962	410	45	pairwise	pairwise	NOUN
ejpam-5962	410	46	hausdroff	hausdroff	NOUN
ejpam-5962	410	47	minimal	minimal	ADJ
ejpam-5962	410	48	lindelöf	lindelöf	NOUN
ejpam-5962	410	49	closed	close	VERB
ejpam-5962	410	50	space	space	NOUN
ejpam-5962	410	51	.	.	PUNCT
ejpam-5962	411	1	proof	proof	NOUN
ejpam-5962	411	2	.	.	PUNCT
ejpam-5962	412	1	⇒let	⇒let	PROPN
ejpam-5962	412	2	(	(	PUNCT
ejpam-5962	412	3	z	z	NOUN
ejpam-5962	412	4	,	,	PUNCT
ejpam-5962	412	5	ϑ1	ϑ1	NOUN
ejpam-5962	412	6	,	,	PUNCT
ejpam-5962	412	7	ϑ2	ϑ2	PROPN
ejpam-5962	412	8	)	)	PUNCT
ejpam-5962	412	9	is	be	AUX
ejpam-5962	412	10	pairwise	pairwise	NOUN
ejpam-5962	412	11	minimal	minimal	ADJ
ejpam-5962	412	12	hausdroff	hausdroff	NOUN
ejpam-5962	412	13	space	space	NOUN
ejpam-5962	412	14	,	,	PUNCT
ejpam-5962	412	15	(	(	PUNCT
ejpam-5962	412	16	z	z	NOUN
ejpam-5962	412	17	,	,	PUNCT
ejpam-5962	412	18	ϑ1	ϑ1	NOUN
ejpam-5962	412	19	,	,	PUNCT
ejpam-5962	412	20	ϑ2	ϑ2	PROPN
ejpam-5962	412	21	)	)	PUNCT
ejpam-5962	412	22	is	be	AUX
ejpam-5962	412	23	pairwise	pairwise	NOUN
ejpam-5962	412	24	hausdroff	hausdroff	NOUN
ejpam-5962	412	25	space	space	NOUN
ejpam-5962	412	26	,	,	PUNCT
ejpam-5962	412	27	so	so	CCONJ
ejpam-5962	412	28	(	(	PUNCT
ejpam-5962	412	29	z	z	NOUN
ejpam-5962	412	30	,	,	PUNCT
ejpam-5962	412	31	ϑ1	ϑ1	NOUN
ejpam-5962	412	32	,	,	PUNCT
ejpam-5962	412	33	ϑ2	ϑ2	PROPN
ejpam-5962	412	34	)	)	PUNCT
ejpam-5962	412	35	is	be	AUX
ejpam-5962	412	36	pairwise	pairwise	NOUN
ejpam-5962	412	37	compact	compact	ADJ
ejpam-5962	412	38	closed	close	VERB
ejpam-5962	412	39	space	space	NOUN
ejpam-5962	412	40	,	,	PUNCT
ejpam-5962	412	41	so	so	ADV
ejpam-5962	413	1	pairwise	pairwise	PROPN
ejpam-5962	413	2	lindelöf	lindelöf	NOUN
ejpam-5962	413	3	closed	close	VERB
ejpam-5962	413	4	space	space	NOUN
ejpam-5962	413	5	.	.	PUNCT
ejpam-5962	414	1	hence	hence	ADV
ejpam-5962	414	2	(	(	PUNCT
ejpam-5962	414	3	z	z	NOUN
ejpam-5962	414	4	,	,	PUNCT
ejpam-5962	414	5	ϑ1	ϑ1	NOUN
ejpam-5962	414	6	,	,	PUNCT
ejpam-5962	414	7	ϑ2	ϑ2	PROPN
ejpam-5962	414	8	)	)	PUNCT
ejpam-5962	414	9	is	be	AUX
ejpam-5962	414	10	pairwise	pairwise	NOUN
ejpam-5962	414	11	minimal	minimal	ADJ
ejpam-5962	414	12	lindelöf	lindelöf	NOUN
ejpam-5962	414	13	closed	close	VERB
ejpam-5962	414	14	space	space	NOUN
ejpam-5962	414	15	.	.	PUNCT
ejpam-5962	415	1	⇐	⇐	PROPN
ejpam-5962	415	2	let	let	VERB
ejpam-5962	415	3	(	(	PUNCT
ejpam-5962	415	4	z	z	NOUN
ejpam-5962	415	5	,	,	PUNCT
ejpam-5962	415	6	ϑ1	ϑ1	NOUN
ejpam-5962	415	7	,	,	PUNCT
ejpam-5962	415	8	ϑ2	ϑ2	PROPN
ejpam-5962	415	9	)	)	PUNCT
ejpam-5962	415	10	is	be	AUX
ejpam-5962	415	11	pairwise	pairwise	NOUN
ejpam-5962	415	12	hausdroff	hausdroff	NOUN
ejpam-5962	415	13	minimal	minimal	ADJ
ejpam-5962	415	14	lindelöf	lindelöf	NOUN
ejpam-5962	415	15	closed	close	VERB
ejpam-5962	415	16	space	space	NOUN
ejpam-5962	415	17	,	,	PUNCT
ejpam-5962	415	18	then	then	ADV
ejpam-5962	415	19	(	(	PUNCT
ejpam-5962	415	20	z	z	NOUN
ejpam-5962	415	21	,	,	PUNCT
ejpam-5962	415	22	ϑ1	ϑ1	NOUN
ejpam-5962	415	23	,	,	PUNCT
ejpam-5962	415	24	ϑ2	ϑ2	PROPN
ejpam-5962	415	25	)	)	PUNCT
ejpam-5962	415	26	is	be	AUX
ejpam-5962	415	27	pairwise	pairwise	NOUN
ejpam-5962	415	28	hausdroff	hausdroff	NOUN
ejpam-5962	415	29	lindelöf	lindelöf	NOUN
ejpam-5962	415	30	closed	close	VERB
ejpam-5962	415	31	space	space	NOUN
ejpam-5962	415	32	,	,	PUNCT
ejpam-5962	415	33	so	so	CCONJ
ejpam-5962	415	34	(	(	PUNCT
ejpam-5962	415	35	z	z	NOUN
ejpam-5962	415	36	,	,	PUNCT
ejpam-5962	415	37	ϑ1	ϑ1	NOUN
ejpam-5962	415	38	,	,	PUNCT
ejpam-5962	415	39	ϑ2	ϑ2	PROPN
ejpam-5962	415	40	)	)	PUNCT
ejpam-5962	415	41	is	be	AUX
ejpam-5962	415	42	pairwise	pairwise	NOUN
ejpam-5962	415	43	compact	compact	ADJ
ejpam-5962	415	44	closed	close	VERB
ejpam-5962	415	45	space	space	NOUN
ejpam-5962	415	46	,	,	PUNCT
ejpam-5962	415	47	and	and	CCONJ
ejpam-5962	415	48	so	so	ADV
ejpam-5962	415	49	(	(	PUNCT
ejpam-5962	415	50	z	z	NOUN
ejpam-5962	415	51	,	,	PUNCT
ejpam-5962	415	52	ϑ1	ϑ1	NOUN
ejpam-5962	415	53	,	,	PUNCT
ejpam-5962	415	54	ϑ2	ϑ2	PROPN
ejpam-5962	415	55	)	)	PUNCT
ejpam-5962	415	56	is	be	AUX
ejpam-5962	415	57	pairwise	pairwise	NOUN
ejpam-5962	415	58	minimal	minimal	ADJ
ejpam-5962	415	59	lindelöf	lindelöf	NOUN
ejpam-5962	415	60	closed	close	VERB
ejpam-5962	415	61	space	space	NOUN
ejpam-5962	415	62	.	.	PUNCT
ejpam-5962	416	1	hence	hence	ADV
ejpam-5962	416	2	by	by	ADP
ejpam-5962	416	3	theorem	theorem	NOUN
ejpam-5962	416	4	8.6	8.6	NUM
ejpam-5962	416	5	(	(	PUNCT
ejpam-5962	416	6	z	z	NOUN
ejpam-5962	416	7	,	,	PUNCT
ejpam-5962	416	8	ϑ1	ϑ1	NOUN
ejpam-5962	416	9	,	,	PUNCT
ejpam-5962	416	10	ϑ2	ϑ2	PROPN
ejpam-5962	416	11	)	)	PUNCT
ejpam-5962	416	12	is	be	AUX
ejpam-5962	416	13	pairwise	pairwise	NOUN
ejpam-5962	416	14	minimal	minimal	ADJ
ejpam-5962	416	15	hausdroff	hausdroff	NOUN
ejpam-5962	416	16	space	space	NOUN
ejpam-5962	416	17	a.	a.	NOUN
ejpam-5962	416	18	a.	a.	PROPN
ejpam-5962	416	19	atoom	atoom	PROPN
ejpam-5962	416	20	et	et	PROPN
ejpam-5962	416	21	al	al	PROPN
ejpam-5962	416	22	.	.	PUNCT
ejpam-5962	416	23	/	/	SYM
ejpam-5962	416	24	eur	eur	PROPN
ejpam-5962	416	25	.	.	PUNCT
ejpam-5962	417	1	j.	j.	PROPN
ejpam-5962	417	2	pure	pure	PROPN
ejpam-5962	417	3	appl	appl	PROPN
ejpam-5962	417	4	.	.	PROPN
ejpam-5962	417	5	math	math	PROPN
ejpam-5962	417	6	,	,	PUNCT
ejpam-5962	417	7	18	18	NUM
ejpam-5962	417	8	(	(	PUNCT
ejpam-5962	417	9	2	2	NUM
ejpam-5962	417	10	)	)	PUNCT
ejpam-5962	417	11	(	(	PUNCT
ejpam-5962	417	12	2025	2025	NUM
ejpam-5962	417	13	)	)	PUNCT
ejpam-5962	417	14	,	,	PUNCT
ejpam-5962	417	15	5962	5962	NUM
ejpam-5962	417	16	15	15	NUM
ejpam-5962	417	17	of	of	ADP
ejpam-5962	417	18	17	17	NUM
ejpam-5962	417	19	theorem	theorem	VERB
ejpam-5962	417	20	8.7	8.7	NUM
ejpam-5962	417	21	.	.	PUNCT
ejpam-5962	418	1	for	for	ADP
ejpam-5962	418	2	pairwise	pairwise	NOUN
ejpam-5962	418	3	closed	close	VERB
ejpam-5962	418	4	compact	compact	ADJ
ejpam-5962	418	5	p−space	p−space	NOUN
ejpam-5962	418	6	(	(	PUNCT
ejpam-5962	418	7	z	z	NOUN
ejpam-5962	418	8	,	,	PUNCT
ejpam-5962	418	9	ϑ1	ϑ1	NOUN
ejpam-5962	418	10	,	,	PUNCT
ejpam-5962	418	11	ϑ2	ϑ2	PROPN
ejpam-5962	418	12	)	)	PUNCT
ejpam-5962	418	13	,	,	PUNCT
ejpam-5962	418	14	the	the	DET
ejpam-5962	418	15	following	follow	VERB
ejpam-5962	418	16	is	be	AUX
ejpam-5962	418	17	equivalent	equivalent	ADJ
ejpam-5962	418	18	:	:	PUNCT
ejpam-5962	418	19	let	let	VERB
ejpam-5962	418	20	(	(	PUNCT
ejpam-5962	418	21	z	z	NOUN
ejpam-5962	418	22	,	,	PUNCT
ejpam-5962	418	23	ϑ1	ϑ1	NOUN
ejpam-5962	418	24	,	,	PUNCT
ejpam-5962	418	25	ϑ2	ϑ2	PROPN
ejpam-5962	418	26	)	)	PUNCT
ejpam-5962	418	27	is	be	AUX
ejpam-5962	418	28	pairwise	pairwise	NOUN
ejpam-5962	418	29	minimal	minimal	ADJ
ejpam-5962	418	30	compact	compact	ADJ
ejpam-5962	418	31	space	space	NOUN
ejpam-5962	418	32	,	,	PUNCT
ejpam-5962	418	33	if	if	SCONJ
ejpam-5962	418	34	and	and	CCONJ
ejpam-5962	418	35	only	only	ADV
ejpam-5962	418	36	if	if	SCONJ
ejpam-5962	418	37	(	(	PUNCT
ejpam-5962	418	38	z	z	NOUN
ejpam-5962	418	39	,	,	PUNCT
ejpam-5962	418	40	ϑ1	ϑ1	NOUN
ejpam-5962	418	41	,	,	PUNCT
ejpam-5962	418	42	ϑ2	ϑ2	PROPN
ejpam-5962	418	43	)	)	PUNCT
ejpam-5962	418	44	is	be	AUX
ejpam-5962	418	45	pairwise	pairwise	NOUN
ejpam-5962	418	46	minimal	minimal	ADJ
ejpam-5962	418	47	lindelöf	lindelöf	NOUN
ejpam-5962	418	48	closed	close	VERB
ejpam-5962	418	49	space	space	NOUN
ejpam-5962	418	50	.	.	PUNCT
ejpam-5962	419	1	proof	proof	NOUN
ejpam-5962	419	2	.	.	PUNCT
ejpam-5962	420	1	⇒	⇒	NOUN
ejpam-5962	420	2	let	let	VERB
ejpam-5962	420	3	(	(	PUNCT
ejpam-5962	420	4	z	z	NOUN
ejpam-5962	420	5	,	,	PUNCT
ejpam-5962	420	6	ϑ1	ϑ1	NOUN
ejpam-5962	420	7	,	,	PUNCT
ejpam-5962	420	8	ϑ2	ϑ2	PROPN
ejpam-5962	420	9	)	)	PUNCT
ejpam-5962	420	10	is	be	AUX
ejpam-5962	420	11	pairwise	pairwise	NOUN
ejpam-5962	420	12	minimal	minimal	ADJ
ejpam-5962	420	13	compact	compact	ADJ
ejpam-5962	420	14	space	space	NOUN
ejpam-5962	420	15	,	,	PUNCT
ejpam-5962	420	16	then	then	ADV
ejpam-5962	420	17	(	(	PUNCT
ejpam-5962	420	18	z	z	NOUN
ejpam-5962	420	19	,	,	PUNCT
ejpam-5962	420	20	ϑ1	ϑ1	NOUN
ejpam-5962	420	21	,	,	PUNCT
ejpam-5962	420	22	ϑ2	ϑ2	PROPN
ejpam-5962	420	23	)	)	PUNCT
ejpam-5962	420	24	is	be	AUX
ejpam-5962	420	25	pairwise	pairwise	NOUN
ejpam-5962	420	26	compact	compact	ADJ
ejpam-5962	420	27	space	space	NOUN
ejpam-5962	420	28	,	,	PUNCT
ejpam-5962	420	29	so	so	CCONJ
ejpam-5962	420	30	(	(	PUNCT
ejpam-5962	420	31	z	z	NOUN
ejpam-5962	420	32	,	,	PUNCT
ejpam-5962	420	33	ϑ1	ϑ1	NOUN
ejpam-5962	420	34	,	,	PUNCT
ejpam-5962	420	35	ϑ2	ϑ2	PROPN
ejpam-5962	420	36	)	)	PUNCT
ejpam-5962	420	37	is	be	AUX
ejpam-5962	420	38	pairwise	pairwise	NOUN
ejpam-5962	420	39	t2	t2	NOUN
ejpam-5962	420	40	.	.	PUNCT
ejpam-5962	421	1	since	since	SCONJ
ejpam-5962	421	2	(	(	PUNCT
ejpam-5962	421	3	z	z	NOUN
ejpam-5962	421	4	,	,	PUNCT
ejpam-5962	421	5	ϑ1	ϑ1	NOUN
ejpam-5962	421	6	,	,	PUNCT
ejpam-5962	421	7	ϑ2	ϑ2	PROPN
ejpam-5962	421	8	)	)	PUNCT
ejpam-5962	421	9	is	be	AUX
ejpam-5962	421	10	p−space	p−space	NOUN
ejpam-5962	421	11	and	and	CCONJ
ejpam-5962	421	12	pairwise	pairwise	NOUN
ejpam-5962	421	13	compact	compact	ADJ
ejpam-5962	421	14	closed	close	VERB
ejpam-5962	421	15	space	space	NOUN
ejpam-5962	421	16	,	,	PUNCT
ejpam-5962	421	17	then	then	ADV
ejpam-5962	421	18	(	(	PUNCT
ejpam-5962	421	19	z	z	NOUN
ejpam-5962	421	20	,	,	PUNCT
ejpam-5962	421	21	ϑ1	ϑ1	NOUN
ejpam-5962	421	22	,	,	PUNCT
ejpam-5962	421	23	ϑ2	ϑ2	PROPN
ejpam-5962	421	24	)	)	PUNCT
ejpam-5962	421	25	is	be	AUX
ejpam-5962	421	26	pairwise	pairwise	NOUN
ejpam-5962	421	27	lindelöf	lindelöf	NOUN
ejpam-5962	421	28	closed	close	VERB
ejpam-5962	421	29	space	space	NOUN
ejpam-5962	421	30	.	.	PUNCT
ejpam-5962	422	1	hence	hence	ADV
ejpam-5962	422	2	(	(	PUNCT
ejpam-5962	422	3	z	z	NOUN
ejpam-5962	422	4	,	,	PUNCT
ejpam-5962	422	5	ϑ1	ϑ1	NOUN
ejpam-5962	422	6	,	,	PUNCT
ejpam-5962	422	7	ϑ2	ϑ2	PROPN
ejpam-5962	422	8	)	)	PUNCT
ejpam-5962	422	9	is	be	AUX
ejpam-5962	422	10	pairwise	pairwise	NOUN
ejpam-5962	422	11	minimal	minimal	ADJ
ejpam-5962	422	12	lindelöf	lindelöf	NOUN
ejpam-5962	422	13	closed	close	VERB
ejpam-5962	422	14	space	space	NOUN
ejpam-5962	422	15	.	.	PUNCT
ejpam-5962	423	1	⇐	⇐	PROPN
ejpam-5962	423	2	let	let	VERB
ejpam-5962	423	3	(	(	PUNCT
ejpam-5962	423	4	z	z	NOUN
ejpam-5962	423	5	,	,	PUNCT
ejpam-5962	423	6	ϑ1	ϑ1	NOUN
ejpam-5962	423	7	,	,	PUNCT
ejpam-5962	423	8	ϑ2	ϑ2	PROPN
ejpam-5962	423	9	)	)	PUNCT
ejpam-5962	423	10	is	be	AUX
ejpam-5962	423	11	pairwise	pairwise	NOUN
ejpam-5962	423	12	minimal	minimal	ADJ
ejpam-5962	423	13	lindelöf	lindelöf	NOUN
ejpam-5962	423	14	closed	close	VERB
ejpam-5962	423	15	space	space	NOUN
ejpam-5962	423	16	,	,	PUNCT
ejpam-5962	423	17	then	then	ADV
ejpam-5962	423	18	(	(	PUNCT
ejpam-5962	423	19	z	z	NOUN
ejpam-5962	423	20	,	,	PUNCT
ejpam-5962	423	21	ϑ1	ϑ1	NOUN
ejpam-5962	423	22	,	,	PUNCT
ejpam-5962	423	23	ϑ2	ϑ2	PROPN
ejpam-5962	423	24	)	)	PUNCT
ejpam-5962	423	25	is	be	AUX
ejpam-5962	423	26	pairwise	pairwise	NOUN
ejpam-5962	423	27	lindelöf	lindelöf	NOUN
ejpam-5962	423	28	closed	close	VERB
ejpam-5962	423	29	space	space	NOUN
ejpam-5962	423	30	,	,	PUNCT
ejpam-5962	423	31	so	so	CCONJ
ejpam-5962	423	32	(	(	PUNCT
ejpam-5962	423	33	z	z	NOUN
ejpam-5962	423	34	,	,	PUNCT
ejpam-5962	423	35	ϑ1	ϑ1	NOUN
ejpam-5962	423	36	,	,	PUNCT
ejpam-5962	423	37	ϑ2	ϑ2	PROPN
ejpam-5962	423	38	)	)	PUNCT
ejpam-5962	423	39	is	be	AUX
ejpam-5962	423	40	pairwise	pairwise	NOUN
ejpam-5962	423	41	compact	compact	ADJ
ejpam-5962	423	42	closed	close	VERB
ejpam-5962	423	43	space	space	NOUN
ejpam-5962	423	44	.	.	PUNCT
ejpam-5962	424	1	hence	hence	ADV
ejpam-5962	424	2	(	(	PUNCT
ejpam-5962	424	3	z	z	NOUN
ejpam-5962	424	4	,	,	PUNCT
ejpam-5962	424	5	ϑ1	ϑ1	NOUN
ejpam-5962	424	6	,	,	PUNCT
ejpam-5962	424	7	ϑ2	ϑ2	PROPN
ejpam-5962	424	8	)	)	PUNCT
ejpam-5962	424	9	is	be	AUX
ejpam-5962	424	10	pairwise	pairwise	NOUN
ejpam-5962	424	11	minimal	minimal	ADJ
ejpam-5962	424	12	compact	compact	ADJ
ejpam-5962	424	13	space	space	NOUN
ejpam-5962	424	14	.	.	PUNCT
ejpam-5962	425	1	9	9	X
ejpam-5962	425	2	.	.	X
ejpam-5962	425	3	types	type	NOUN
ejpam-5962	425	4	of	of	ADP
ejpam-5962	425	5	minimal	minimal	ADJ
ejpam-5962	425	6	spaces	space	NOUN
ejpam-5962	425	7	in	in	ADP
ejpam-5962	425	8	bitopological	bitopological	ADJ
ejpam-5962	425	9	spaces	space	NOUN
ejpam-5962	425	10	;	;	PUNCT
ejpam-5962	425	11	application	application	NOUN
ejpam-5962	425	12	minimal	minimal	ADJ
ejpam-5962	425	13	space	space	NOUN
ejpam-5962	425	14	in	in	ADP
ejpam-5962	425	15	bitopological	bitopological	ADJ
ejpam-5962	425	16	spaces	space	NOUN
ejpam-5962	425	17	provide	provide	VERB
ejpam-5962	425	18	intriguing	intriguing	ADJ
ejpam-5962	425	19	opportunities	opportunity	NOUN
ejpam-5962	425	20	for	for	ADP
ejpam-5962	425	21	future	future	ADJ
ejpam-5962	425	22	and	and	CCONJ
ejpam-5962	425	23	predictive	predictive	ADJ
ejpam-5962	425	24	applications	application	NOUN
ejpam-5962	425	25	.	.	PUNCT
ejpam-5962	426	1	these	these	DET
ejpam-5962	426	2	space	space	NOUN
ejpam-5962	426	3	provide	provide	VERB
ejpam-5962	426	4	a	a	DET
ejpam-5962	426	5	foundation	foundation	NOUN
ejpam-5962	426	6	for	for	ADP
ejpam-5962	426	7	simplifying	simplify	VERB
ejpam-5962	426	8	complicated	complicated	ADJ
ejpam-5962	426	9	systems	system	NOUN
ejpam-5962	426	10	by	by	ADP
ejpam-5962	426	11	focusing	focus	VERB
ejpam-5962	426	12	on	on	ADP
ejpam-5962	426	13	critical	critical	ADJ
ejpam-5962	426	14	components	component	NOUN
ejpam-5962	426	15	and	and	CCONJ
ejpam-5962	426	16	relationships	relationship	NOUN
ejpam-5962	426	17	,	,	PUNCT
ejpam-5962	426	18	making	make	VERB
ejpam-5962	426	19	it	it	PRON
ejpam-5962	426	20	easier	easy	ADJ
ejpam-5962	426	21	to	to	PART
ejpam-5962	426	22	study	study	VERB
ejpam-5962	426	23	and	and	CCONJ
ejpam-5962	426	24	anticipate	anticipate	VERB
ejpam-5962	426	25	actions	action	NOUN
ejpam-5962	426	26	in	in	ADP
ejpam-5962	426	27	multivariable	multivariable	ADJ
ejpam-5962	426	28	environments	environment	NOUN
ejpam-5962	426	29	.	.	PUNCT
ejpam-5962	427	1	traditional	traditional	ADJ
ejpam-5962	427	2	approaches	approach	NOUN
ejpam-5962	427	3	frequently	frequently	ADV
ejpam-5962	427	4	struggle	struggle	VERB
ejpam-5962	427	5	with	with	ADP
ejpam-5962	427	6	qualitative	qualitative	ADJ
ejpam-5962	427	7	features	feature	NOUN
ejpam-5962	427	8	of	of	ADP
ejpam-5962	427	9	systems	system	NOUN
ejpam-5962	427	10	,	,	PUNCT
ejpam-5962	427	11	such	such	ADJ
ejpam-5962	427	12	as	as	ADP
ejpam-5962	427	13	those	those	PRON
ejpam-5962	427	14	seen	see	VERB
ejpam-5962	427	15	in	in	ADP
ejpam-5962	427	16	social	social	ADJ
ejpam-5962	427	17	or	or	CCONJ
ejpam-5962	427	18	educational	educational	ADJ
ejpam-5962	427	19	contexts	context	NOUN
ejpam-5962	427	20	where	where	SCONJ
ejpam-5962	427	21	quantification	quantification	NOUN
ejpam-5962	427	22	is	be	AUX
ejpam-5962	427	23	problematic	problematic	ADJ
ejpam-5962	427	24	.	.	PUNCT
ejpam-5962	428	1	by	by	ADP
ejpam-5962	428	2	reducing	reduce	VERB
ejpam-5962	428	3	the	the	DET
ejpam-5962	428	4	system	system	NOUN
ejpam-5962	428	5	to	to	ADP
ejpam-5962	428	6	its	its	PRON
ejpam-5962	428	7	most	most	ADV
ejpam-5962	428	8	basic	basic	ADJ
ejpam-5962	428	9	structure	structure	NOUN
ejpam-5962	428	10	,	,	PUNCT
ejpam-5962	428	11	we	we	PRON
ejpam-5962	428	12	may	may	AUX
ejpam-5962	428	13	better	well	ADV
ejpam-5962	428	14	describe	describe	VERB
ejpam-5962	428	15	and	and	CCONJ
ejpam-5962	428	16	comprehend	comprehend	VERB
ejpam-5962	428	17	the	the	DET
ejpam-5962	428	18	underlying	underlie	VERB
ejpam-5962	428	19	dynamics	dynamic	NOUN
ejpam-5962	428	20	,	,	PUNCT
ejpam-5962	428	21	allowing	allow	VERB
ejpam-5962	428	22	for	for	ADP
ejpam-5962	428	23	more	more	ADV
ejpam-5962	428	24	accurate	accurate	ADJ
ejpam-5962	428	25	predictions	prediction	NOUN
ejpam-5962	428	26	and	and	CCONJ
ejpam-5962	428	27	insights	insight	NOUN
ejpam-5962	428	28	.	.	PUNCT
ejpam-5962	429	1	potentially	potentially	ADV
ejpam-5962	429	2	improve	improve	VERB
ejpam-5962	429	3	medical	medical	ADJ
ejpam-5962	429	4	decision	decision	NOUN
ejpam-5962	429	5	-	-	PUNCT
ejpam-5962	429	6	making	make	VERB
ejpam-5962	429	7	processes	process	NOUN
ejpam-5962	429	8	.	.	PUNCT
ejpam-5962	430	1	by	by	ADP
ejpam-5962	430	2	using	use	VERB
ejpam-5962	430	3	simple	simple	ADJ
ejpam-5962	430	4	structures	structure	NOUN
ejpam-5962	430	5	,	,	PUNCT
ejpam-5962	430	6	we	we	PRON
ejpam-5962	430	7	were	be	AUX
ejpam-5962	430	8	able	able	ADJ
ejpam-5962	430	9	to	to	PART
ejpam-5962	430	10	speed	speed	VERB
ejpam-5962	430	11	the	the	DET
ejpam-5962	430	12	analysis	analysis	NOUN
ejpam-5962	430	13	of	of	ADP
ejpam-5962	430	14	complicated	complicated	ADJ
ejpam-5962	430	15	medical	medical	ADJ
ejpam-5962	430	16	data	datum	NOUN
ejpam-5962	430	17	,	,	PUNCT
ejpam-5962	430	18	focusing	focus	VERB
ejpam-5962	430	19	on	on	ADP
ejpam-5962	430	20	the	the	DET
ejpam-5962	430	21	reduction	reduction	NOUN
ejpam-5962	430	22	and	and	CCONJ
ejpam-5962	430	23	fundamental	fundamental	ADJ
ejpam-5962	430	24	decision	decision	NOUN
ejpam-5962	430	25	qualities	quality	NOUN
ejpam-5962	430	26	.	.	PUNCT
ejpam-5962	431	1	this	this	PRON
ejpam-5962	431	2	would	would	AUX
ejpam-5962	431	3	enable	enable	VERB
ejpam-5962	431	4	a	a	DET
ejpam-5962	431	5	more	more	ADV
ejpam-5962	431	6	realistic	realistic	ADJ
ejpam-5962	431	7	comparison	comparison	NOUN
ejpam-5962	431	8	of	of	ADP
ejpam-5962	431	9	decision	decision	NOUN
ejpam-5962	431	10	-	-	PUNCT
ejpam-5962	431	11	making	make	VERB
ejpam-5962	431	12	outcomes	outcome	NOUN
ejpam-5962	431	13	among	among	ADP
ejpam-5962	431	14	patients	patient	NOUN
ejpam-5962	431	15	with	with	ADP
ejpam-5962	431	16	comparable	comparable	ADJ
ejpam-5962	431	17	and	and	CCONJ
ejpam-5962	431	18	dissimilar	dissimilar	ADJ
ejpam-5962	431	19	symptoms	symptom	NOUN
ejpam-5962	431	20	.	.	PUNCT
ejpam-5962	432	1	furthermore	furthermore	ADV
ejpam-5962	432	2	,	,	PUNCT
ejpam-5962	432	3	combining	combine	VERB
ejpam-5962	432	4	minimal	minimal	ADJ
ejpam-5962	432	5	spaces	space	NOUN
ejpam-5962	432	6	with	with	ADP
ejpam-5962	432	7	a	a	DET
ejpam-5962	432	8	variable	variable	ADJ
ejpam-5962	432	9	precision	precision	NOUN
ejpam-5962	432	10	rough	rough	ADJ
ejpam-5962	432	11	set	set	NOUN
ejpam-5962	432	12	model	model	NOUN
ejpam-5962	432	13	may	may	AUX
ejpam-5962	432	14	improve	improve	VERB
ejpam-5962	432	15	the	the	DET
ejpam-5962	432	16	accuracy	accuracy	NOUN
ejpam-5962	432	17	and	and	CCONJ
ejpam-5962	432	18	reliability	reliability	NOUN
ejpam-5962	432	19	of	of	ADP
ejpam-5962	432	20	medical	medical	ADJ
ejpam-5962	432	21	diagnosis	diagnosis	NOUN
ejpam-5962	432	22	and	and	CCONJ
ejpam-5962	432	23	treatment	treatment	NOUN
ejpam-5962	432	24	regimens.in	regimens.in	PROPN
ejpam-5962	432	25	machine	machine	NOUN
ejpam-5962	432	26	learning	learning	NOUN
ejpam-5962	432	27	,	,	PUNCT
ejpam-5962	432	28	ai	ai	VERB
ejpam-5962	432	29	and	and	CCONJ
ejpam-5962	432	30	big	big	ADJ
ejpam-5962	432	31	data	datum	NOUN
ejpam-5962	432	32	;	;	PUNCT
ejpam-5962	432	33	using	use	VERB
ejpam-5962	432	34	minimal	minimal	ADJ
ejpam-5962	432	35	compact	compact	ADJ
ejpam-5962	432	36	and	and	CCONJ
ejpam-5962	432	37	lindelöf	lindelöf	NOUN
ejpam-5962	432	38	spaces	space	VERB
ejpam-5962	432	39	in	in	ADP
ejpam-5962	432	40	bitopological	bitopological	ADJ
ejpam-5962	432	41	systems	system	NOUN
ejpam-5962	432	42	would	would	AUX
ejpam-5962	432	43	improve	improve	VERB
ejpam-5962	432	44	data	datum	NOUN
ejpam-5962	432	45	processing	processing	NOUN
ejpam-5962	432	46	by	by	ADP
ejpam-5962	432	47	identifying	identify	VERB
ejpam-5962	432	48	essential	essential	ADJ
ejpam-5962	432	49	subsets	subset	NOUN
ejpam-5962	432	50	and	and	CCONJ
ejpam-5962	432	51	optimizing	optimize	VERB
ejpam-5962	432	52	sampling	sample	VERB
ejpam-5962	432	53	across	across	ADP
ejpam-5962	432	54	dual	dual	ADJ
ejpam-5962	432	55	topologies	topology	NOUN
ejpam-5962	432	56	.	.	PUNCT
ejpam-5962	433	1	this	this	PRON
ejpam-5962	433	2	would	would	AUX
ejpam-5962	433	3	minimize	minimize	VERB
ejpam-5962	433	4	dataset	dataset	ADJ
ejpam-5962	433	5	size	size	NOUN
ejpam-5962	433	6	,	,	PUNCT
ejpam-5962	433	7	increase	increase	VERB
ejpam-5962	433	8	computational	computational	ADJ
ejpam-5962	433	9	efficiency	efficiency	NOUN
ejpam-5962	433	10	,	,	PUNCT
ejpam-5962	433	11	and	and	CCONJ
ejpam-5962	433	12	preserve	preserve	VERB
ejpam-5962	433	13	accuracy	accuracy	NOUN
ejpam-5962	433	14	,	,	PUNCT
ejpam-5962	433	15	making	make	VERB
ejpam-5962	433	16	predictive	predictive	ADJ
ejpam-5962	433	17	models	model	NOUN
ejpam-5962	433	18	more	more	ADV
ejpam-5962	433	19	scalable	scalable	ADJ
ejpam-5962	433	20	and	and	CCONJ
ejpam-5962	433	21	adaptable	adaptable	ADJ
ejpam-5962	433	22	to	to	ADP
ejpam-5962	433	23	complex	complex	ADJ
ejpam-5962	433	24	systems	system	NOUN
ejpam-5962	433	25	with	with	ADP
ejpam-5962	433	26	multiple	multiple	ADJ
ejpam-5962	433	27	topologies	topology	NOUN
ejpam-5962	433	28	.	.	PUNCT
ejpam-5962	434	1	when	when	SCONJ
ejpam-5962	434	2	applied	apply	VERB
ejpam-5962	434	3	to	to	ADP
ejpam-5962	434	4	urban	urban	ADJ
ejpam-5962	434	5	planning	planning	NOUN
ejpam-5962	434	6	and	and	CCONJ
ejpam-5962	434	7	smart	smart	ADJ
ejpam-5962	434	8	cities	city	NOUN
ejpam-5962	434	9	,	,	PUNCT
ejpam-5962	434	10	it	it	PRON
ejpam-5962	434	11	has	have	VERB
ejpam-5962	434	12	the	the	DET
ejpam-5962	434	13	potential	potential	NOUN
ejpam-5962	434	14	to	to	PART
ejpam-5962	434	15	optimize	optimize	VERB
ejpam-5962	434	16	city	city	NOUN
ejpam-5962	434	17	layouts	layout	NOUN
ejpam-5962	434	18	and	and	CCONJ
ejpam-5962	434	19	infrastructure	infrastructure	NOUN
ejpam-5962	434	20	by	by	ADP
ejpam-5962	434	21	taking	take	VERB
ejpam-5962	434	22	into	into	ADP
ejpam-5962	434	23	account	account	NOUN
ejpam-5962	434	24	several	several	ADJ
ejpam-5962	434	25	variables	variable	NOUN
ejpam-5962	434	26	at	at	ADP
ejpam-5962	434	27	once	once	ADV
ejpam-5962	434	28	.	.	PUNCT
ejpam-5962	435	1	minimal	minimal	ADJ
ejpam-5962	435	2	compact	compact	ADJ
ejpam-5962	435	3	areas	area	NOUN
ejpam-5962	435	4	allow	allow	VERB
ejpam-5962	435	5	for	for	ADP
ejpam-5962	435	6	effective	effective	ADJ
ejpam-5962	435	7	distribution	distribution	NOUN
ejpam-5962	435	8	of	of	ADP
ejpam-5962	435	9	facilities	facility	NOUN
ejpam-5962	435	10	while	while	SCONJ
ejpam-5962	435	11	balancing	balance	VERB
ejpam-5962	435	12	physical	physical	ADJ
ejpam-5962	435	13	land	land	NOUN
ejpam-5962	435	14	use	use	NOUN
ejpam-5962	435	15	and	and	CCONJ
ejpam-5962	435	16	social	social	ADJ
ejpam-5962	435	17	connectivity	connectivity	NOUN
ejpam-5962	435	18	,	,	PUNCT
ejpam-5962	435	19	resulting	result	VERB
ejpam-5962	435	20	in	in	ADP
ejpam-5962	435	21	more	more	ADV
ejpam-5962	435	22	adaptive	adaptive	ADJ
ejpam-5962	435	23	urban	urban	ADJ
ejpam-5962	435	24	environments	environment	NOUN
ejpam-5962	435	25	.	.	PUNCT
ejpam-5962	436	1	meanwhile	meanwhile	ADV
ejpam-5962	436	2	,	,	PUNCT
ejpam-5962	436	3	lindelöf	lindelöf	NOUN
ejpam-5962	436	4	spaces	space	NOUN
ejpam-5962	436	5	could	could	AUX
ejpam-5962	436	6	improve	improve	VERB
ejpam-5962	436	7	the	the	DET
ejpam-5962	436	8	architecture	architecture	NOUN
ejpam-5962	436	9	of	of	ADP
ejpam-5962	436	10	interconnected	interconnected	ADJ
ejpam-5962	436	11	networks	network	NOUN
ejpam-5962	436	12	by	by	ADP
ejpam-5962	436	13	identifying	identify	VERB
ejpam-5962	436	14	minimal	minimal	ADJ
ejpam-5962	436	15	hubs	hub	NOUN
ejpam-5962	436	16	that	that	PRON
ejpam-5962	436	17	service	service	VERB
ejpam-5962	436	18	various	various	ADJ
ejpam-5962	436	19	connections	connection	NOUN
ejpam-5962	436	20	,	,	PUNCT
ejpam-5962	436	21	allowing	allow	VERB
ejpam-5962	436	22	for	for	ADP
ejpam-5962	436	23	scalable	scalable	ADJ
ejpam-5962	436	24	infrastructure	infrastructure	NOUN
ejpam-5962	436	25	that	that	PRON
ejpam-5962	436	26	can	can	AUX
ejpam-5962	436	27	meet	meet	VERB
ejpam-5962	436	28	changing	change	VERB
ejpam-5962	436	29	demands	demand	NOUN
ejpam-5962	436	30	without	without	ADP
ejpam-5962	436	31	requiring	require	VERB
ejpam-5962	436	32	proportional	proportional	ADJ
ejpam-5962	436	33	resource	resource	NOUN
ejpam-5962	436	34	increases	increase	NOUN
ejpam-5962	436	35	.	.	PUNCT
ejpam-5962	437	1	overall	overall	ADV
ejpam-5962	437	2	,	,	PUNCT
ejpam-5962	437	3	this	this	DET
ejpam-5962	437	4	strategy	strategy	NOUN
ejpam-5962	437	5	would	would	AUX
ejpam-5962	437	6	result	result	VERB
ejpam-5962	437	7	in	in	ADP
ejpam-5962	437	8	smarter	smart	ADJ
ejpam-5962	437	9	,	,	PUNCT
ejpam-5962	437	10	more	more	ADV
ejpam-5962	437	11	resilient	resilient	ADJ
ejpam-5962	437	12	city	city	NOUN
ejpam-5962	437	13	designs.the	designs.the	DET
ejpam-5962	437	14	unifying	unify	VERB
ejpam-5962	437	15	thread	thread	NOUN
ejpam-5962	437	16	running	run	VERB
ejpam-5962	437	17	across	across	ADP
ejpam-5962	437	18	all	all	DET
ejpam-5962	437	19	applications	application	NOUN
ejpam-5962	437	20	is	be	AUX
ejpam-5962	437	21	efficiency	efficiency	NOUN
ejpam-5962	437	22	.	.	PUNCT
ejpam-5962	438	1	minimal	minimal	ADJ
ejpam-5962	438	2	compact	compact	ADJ
ejpam-5962	438	3	and	and	CCONJ
ejpam-5962	438	4	lindelöf	lindelöf	NOUN
ejpam-5962	438	5	spaces	space	NOUN
ejpam-5962	438	6	give	give	VERB
ejpam-5962	438	7	frameworks	framework	NOUN
ejpam-5962	438	8	for	for	ADP
ejpam-5962	438	9	a.	a.	NOUN
ejpam-5962	438	10	a.	a.	NOUN
ejpam-5962	438	11	atoom	atoom	PROPN
ejpam-5962	438	12	et	et	PROPN
ejpam-5962	438	13	al	al	PROPN
ejpam-5962	438	14	.	.	PUNCT
ejpam-5962	438	15	/	/	SYM
ejpam-5962	438	16	eur	eur	PROPN
ejpam-5962	438	17	.	.	PUNCT
ejpam-5962	439	1	j.	j.	PROPN
ejpam-5962	439	2	pure	pure	PROPN
ejpam-5962	439	3	appl	appl	PROPN
ejpam-5962	439	4	.	.	PROPN
ejpam-5962	439	5	math	math	PROPN
ejpam-5962	439	6	,	,	PUNCT
ejpam-5962	439	7	18	18	NUM
ejpam-5962	439	8	(	(	PUNCT
ejpam-5962	439	9	2	2	NUM
ejpam-5962	439	10	)	)	PUNCT
ejpam-5962	439	11	(	(	PUNCT
ejpam-5962	439	12	2025	2025	NUM
ejpam-5962	439	13	)	)	PUNCT
ejpam-5962	439	14	,	,	PUNCT
ejpam-5962	439	15	5962	5962	NUM
ejpam-5962	439	16	16	16	NUM
ejpam-5962	439	17	of	of	ADP
ejpam-5962	439	18	17	17	NUM
ejpam-5962	439	19	getting	get	VERB
ejpam-5962	439	20	optimal	optimal	ADJ
ejpam-5962	439	21	results	result	NOUN
ejpam-5962	439	22	with	with	ADP
ejpam-5962	439	23	little	little	ADJ
ejpam-5962	439	24	resources	resource	NOUN
ejpam-5962	439	25	while	while	SCONJ
ejpam-5962	439	26	improving	improve	VERB
ejpam-5962	439	27	predictability	predictability	NOUN
ejpam-5962	439	28	and	and	CCONJ
ejpam-5962	439	29	scalability	scalability	NOUN
ejpam-5962	439	30	in	in	ADP
ejpam-5962	439	31	complicated	complicated	ADJ
ejpam-5962	439	32	systems	system	NOUN
ejpam-5962	439	33	.	.	PUNCT
ejpam-5962	440	1	10	10	NUM
ejpam-5962	440	2	.	.	PUNCT
ejpam-5962	441	1	conclusions	conclusion	NOUN
ejpam-5962	441	2	the	the	DET
ejpam-5962	441	3	relationships	relationship	NOUN
ejpam-5962	441	4	among	among	ADP
ejpam-5962	441	5	pairwise	pairwise	NOUN
ejpam-5962	441	6	minimal	minimal	ADJ
ejpam-5962	441	7	compact	compact	ADJ
ejpam-5962	441	8	closed	closed	ADJ
ejpam-5962	441	9	spaces	space	NOUN
ejpam-5962	441	10	,	,	PUNCT
ejpam-5962	441	11	pairwise	pairwise	PROPN
ejpam-5962	441	12	minimal	minimal	ADJ
ejpam-5962	441	13	lindelöf	lindelöf	NOUN
ejpam-5962	441	14	closed	close	VERB
ejpam-5962	441	15	spaces	space	NOUN
ejpam-5962	441	16	,	,	PUNCT
ejpam-5962	441	17	and	and	CCONJ
ejpam-5962	441	18	pairwise	pairwise	PROPN
ejpam-5962	441	19	minimal	minimal	ADJ
ejpam-5962	441	20	hausdorff	hausdorff	NOUN
ejpam-5962	441	21	spaces	space	NOUN
ejpam-5962	441	22	in	in	ADP
ejpam-5962	441	23	bitopological	bitopological	ADJ
ejpam-5962	441	24	spaces	space	NOUN
ejpam-5962	441	25	were	be	AUX
ejpam-5962	441	26	examined	examine	VERB
ejpam-5962	441	27	in	in	ADP
ejpam-5962	441	28	this	this	DET
ejpam-5962	441	29	study	study	NOUN
ejpam-5962	441	30	.	.	PUNCT
ejpam-5962	442	1	according	accord	VERB
ejpam-5962	442	2	to	to	ADP
ejpam-5962	442	3	the	the	DET
ejpam-5962	442	4	compact	compact	ADJ
ejpam-5962	442	5	,	,	PUNCT
ejpam-5962	442	6	lindelöf	lindelöf	PROPN
ejpam-5962	442	7	,	,	PUNCT
ejpam-5962	442	8	and	and	CCONJ
ejpam-5962	442	9	hausdorff	hausdorff	NOUN
ejpam-5962	442	10	spaces	space	NOUN
ejpam-5962	442	11	notion	notion	NOUN
ejpam-5962	442	12	that	that	PRON
ejpam-5962	442	13	is	be	AUX
ejpam-5962	442	14	here	here	ADV
ejpam-5962	442	15	proposed	propose	VERB
ejpam-5962	442	16	,	,	PUNCT
ejpam-5962	442	17	the	the	DET
ejpam-5962	442	18	study	study	NOUN
ejpam-5962	442	19	determined	determine	VERB
ejpam-5962	442	20	the	the	DET
ejpam-5962	442	21	prerequisites	prerequisite	NOUN
ejpam-5962	442	22	for	for	ADP
ejpam-5962	442	23	harmonizing	harmonize	VERB
ejpam-5962	442	24	the	the	DET
ejpam-5962	442	25	closed	closed	ADJ
ejpam-5962	442	26	sets	set	NOUN
ejpam-5962	442	27	.	.	PUNCT
ejpam-5962	443	1	we	we	PRON
ejpam-5962	443	2	looked	look	VERB
ejpam-5962	443	3	at	at	ADP
ejpam-5962	443	4	the	the	DET
ejpam-5962	443	5	relationship	relationship	NOUN
ejpam-5962	443	6	between	between	ADP
ejpam-5962	443	7	these	these	DET
ejpam-5962	443	8	two	two	NUM
ejpam-5962	443	9	ideas	idea	NOUN
ejpam-5962	443	10	and	and	CCONJ
ejpam-5962	443	11	described	describe	VERB
ejpam-5962	443	12	them	they	PRON
ejpam-5962	443	13	using	use	VERB
ejpam-5962	443	14	several	several	ADJ
ejpam-5962	443	15	sets	set	NOUN
ejpam-5962	443	16	.	.	PUNCT
ejpam-5962	444	1	this	this	DET
ejpam-5962	444	2	study	study	NOUN
ejpam-5962	444	3	’s	’s	PART
ejpam-5962	444	4	secondary	secondary	ADJ
ejpam-5962	444	5	goal	goal	NOUN
ejpam-5962	444	6	was	be	AUX
ejpam-5962	444	7	to	to	PART
ejpam-5962	444	8	draw	draw	VERB
ejpam-5962	444	9	attention	attention	NOUN
ejpam-5962	444	10	to	to	ADP
ejpam-5962	444	11	some	some	DET
ejpam-5962	444	12	intricate	intricate	ADJ
ejpam-5962	444	13	closed	close	VERB
ejpam-5962	444	14	-	-	PUNCT
ejpam-5962	444	15	set	set	VERB
ejpam-5962	444	16	features	feature	NOUN
ejpam-5962	444	17	and	and	CCONJ
ejpam-5962	444	18	some	some	DET
ejpam-5962	444	19	peculiarities	peculiarity	NOUN
ejpam-5962	444	20	of	of	ADP
ejpam-5962	444	21	the	the	DET
ejpam-5962	444	22	cartesian	cartesian	ADJ
ejpam-5962	444	23	process	process	NOUN
ejpam-5962	444	24	of	of	ADP
ejpam-5962	444	25	multiplying	multiply	VERB
ejpam-5962	444	26	these	these	DET
ejpam-5962	444	27	functions	function	NOUN
ejpam-5962	444	28	in	in	ADP
ejpam-5962	444	29	specific	specific	ADJ
ejpam-5962	444	30	circumstances	circumstance	NOUN
ejpam-5962	444	31	.	.	PUNCT
ejpam-5962	445	1	furthermore	furthermore	ADV
ejpam-5962	445	2	,	,	PUNCT
ejpam-5962	445	3	key	key	ADJ
ejpam-5962	445	4	aspects	aspect	NOUN
ejpam-5962	445	5	of	of	ADP
ejpam-5962	445	6	these	these	DET
ejpam-5962	445	7	concepts	concept	NOUN
ejpam-5962	445	8	as	as	ADV
ejpam-5962	445	9	well	well	ADV
ejpam-5962	445	10	as	as	ADP
ejpam-5962	445	11	a	a	DET
ejpam-5962	445	12	few	few	ADJ
ejpam-5962	445	13	instructive	instructive	ADJ
ejpam-5962	445	14	situations	situation	NOUN
ejpam-5962	445	15	were	be	AUX
ejpam-5962	445	16	carefully	carefully	ADV
ejpam-5962	445	17	investigated	investigate	VERB
ejpam-5962	445	18	.	.	PUNCT
ejpam-5962	446	1	we	we	PRON
ejpam-5962	446	2	identified	identify	VERB
ejpam-5962	446	3	their	their	PRON
ejpam-5962	446	4	fundamental	fundamental	ADJ
ejpam-5962	446	5	characteristics	characteristic	NOUN
ejpam-5962	446	6	in	in	ADP
ejpam-5962	446	7	general	general	ADJ
ejpam-5962	446	8	and	and	CCONJ
ejpam-5962	446	9	made	make	VERB
ejpam-5962	446	10	clear	clear	ADJ
ejpam-5962	446	11	the	the	DET
ejpam-5962	446	12	requirements	requirement	NOUN
ejpam-5962	446	13	for	for	ADP
ejpam-5962	446	14	establishing	establish	VERB
ejpam-5962	446	15	similar	similar	ADJ
ejpam-5962	446	16	linkages	linkage	NOUN
ejpam-5962	446	17	between	between	ADP
ejpam-5962	446	18	them	they	PRON
ejpam-5962	446	19	.	.	PUNCT
ejpam-5962	447	1	we	we	PRON
ejpam-5962	447	2	went	go	VERB
ejpam-5962	447	3	through	through	ADP
ejpam-5962	447	4	their	their	PRON
ejpam-5962	447	5	main	main	ADJ
ejpam-5962	447	6	traits	trait	NOUN
ejpam-5962	447	7	and	and	CCONJ
ejpam-5962	447	8	demonstrated	demonstrate	VERB
ejpam-5962	447	9	how	how	SCONJ
ejpam-5962	447	10	they	they	PRON
ejpam-5962	447	11	work	work	VERB
ejpam-5962	447	12	together	together	ADV
ejpam-5962	447	13	.	.	PUNCT
ejpam-5962	448	1	additionally	additionally	ADV
ejpam-5962	448	2	,	,	PUNCT
ejpam-5962	448	3	the	the	DET
ejpam-5962	448	4	report	report	NOUN
ejpam-5962	448	5	highlighted	highlight	VERB
ejpam-5962	448	6	the	the	DET
ejpam-5962	448	7	characteristics	characteristic	NOUN
ejpam-5962	448	8	of	of	ADP
ejpam-5962	448	9	these	these	DET
ejpam-5962	448	10	functions	function	NOUN
ejpam-5962	448	11	and	and	CCONJ
ejpam-5962	448	12	offered	offer	VERB
ejpam-5962	448	13	numerous	numerous	ADJ
ejpam-5962	448	14	examples	example	NOUN
ejpam-5962	448	15	of	of	ADP
ejpam-5962	448	16	them	they	PRON
ejpam-5962	448	17	.	.	PUNCT
ejpam-5962	449	1	the	the	DET
ejpam-5962	449	2	exploration	exploration	NOUN
ejpam-5962	449	3	of	of	ADP
ejpam-5962	449	4	the	the	DET
ejpam-5962	449	5	various	various	ADJ
ejpam-5962	449	6	potential	potential	ADJ
ejpam-5962	449	7	futures	future	NOUN
ejpam-5962	449	8	for	for	ADP
ejpam-5962	449	9	these	these	DET
ejpam-5962	449	10	functions	function	NOUN
ejpam-5962	449	11	will	will	AUX
ejpam-5962	449	12	begin	begin	VERB
ejpam-5962	449	13	with	with	ADP
ejpam-5962	449	14	these	these	DET
ejpam-5962	449	15	spaces	space	NOUN
ejpam-5962	449	16	.	.	PUNCT
ejpam-5962	450	1	further	further	ADJ
ejpam-5962	450	2	variations	variation	NOUN
ejpam-5962	450	3	of	of	ADP
ejpam-5962	450	4	these	these	DET
ejpam-5962	450	5	regions	region	NOUN
ejpam-5962	450	6	may	may	AUX
ejpam-5962	450	7	be	be	AUX
ejpam-5962	450	8	explored	explore	VERB
ejpam-5962	450	9	in	in	ADP
ejpam-5962	450	10	future	future	ADJ
ejpam-5962	450	11	research	research	NOUN
ejpam-5962	450	12	[	[	X
ejpam-5962	450	13	17	17	NUM
ejpam-5962	450	14	]	]	PUNCT
ejpam-5962	450	15	,	,	PUNCT
ejpam-5962	450	16	[	[	X
ejpam-5962	450	17	18	18	NUM
ejpam-5962	450	18	]	]	PUNCT
ejpam-5962	450	19	,	,	PUNCT
ejpam-5962	450	20	[	[	X
ejpam-5962	450	21	19],[20	19],[20	X
ejpam-5962	450	22	]	]	X
ejpam-5962	450	23	,	,	PUNCT
ejpam-5962	450	24	[	[	X
ejpam-5962	450	25	21	21	NUM
ejpam-5962	450	26	]	]	PUNCT
ejpam-5962	450	27	,	,	PUNCT
ejpam-5962	450	28	and	and	CCONJ
ejpam-5962	450	29	[	[	X
ejpam-5962	450	30	22	22	NUM
ejpam-5962	450	31	]	]	PUNCT
ejpam-5962	450	32	respectively	respectively	ADV
ejpam-5962	450	33	.	.	PUNCT
ejpam-5962	451	1	acknowledgements	acknowledgement	NOUN
ejpam-5962	451	2	the	the	DET
ejpam-5962	451	3	authors	author	NOUN
ejpam-5962	451	4	are	be	AUX
ejpam-5962	451	5	grateful	grateful	ADJ
ejpam-5962	451	6	to	to	ADP
ejpam-5962	451	7	the	the	DET
ejpam-5962	451	8	anonymous	anonymous	ADJ
ejpam-5962	451	9	reviewers	reviewer	NOUN
ejpam-5962	451	10	for	for	ADP
ejpam-5962	451	11	their	their	PRON
ejpam-5962	451	12	constructive	constructive	ADJ
ejpam-5962	451	13	criticism	criticism	NOUN
ejpam-5962	451	14	and	and	CCONJ
ejpam-5962	451	15	helpful	helpful	ADJ
ejpam-5962	451	16	comments	comment	NOUN
ejpam-5962	451	17	.	.	PUNCT
ejpam-5962	452	1	references	reference	NOUN
ejpam-5962	452	2	[	[	X
ejpam-5962	452	3	1	1	NUM
ejpam-5962	452	4	]	]	PUNCT
ejpam-5962	452	5	a.	a.	PROPN
ejpam-5962	452	6	s.	s.	PROPN
ejpam-5962	452	7	parhomenko	parhomenko	PROPN
ejpam-5962	452	8	.	.	PUNCT
ejpam-5962	453	1	über	über	PROPN
ejpam-5962	453	2	eineindeutige	eineindeutige	ADJ
ejpam-5962	453	3	stetige	stetige	NOUN
ejpam-5962	453	4	abbildungen	abbildungen	NOUN
ejpam-5962	453	5	.	.	PUNCT
ejpam-5962	454	1	matematicheskii	matematicheskii	PROPN
ejpam-5962	454	2	sbornik	sbornik	PROPN
ejpam-5962	454	3	,	,	PUNCT
ejpam-5962	454	4	5(47):197–210	5(47):197–210	NUM
ejpam-5962	454	5	,	,	PUNCT
ejpam-5962	454	6	1939	1939	NUM
ejpam-5962	454	7	.	.	PUNCT
ejpam-5962	455	1	[	[	X
ejpam-5962	455	2	2	2	X
ejpam-5962	455	3	]	]	PUNCT
ejpam-5962	455	4	e.	e.	PROPN
ejpam-5962	455	5	hewitt	hewitt	PROPN
ejpam-5962	455	6	.	.	PUNCT
ejpam-5962	456	1	a	a	DET
ejpam-5962	456	2	problem	problem	NOUN
ejpam-5962	456	3	of	of	ADP
ejpam-5962	456	4	set	set	NOUN
ejpam-5962	456	5	-	-	PUNCT
ejpam-5962	456	6	theoretic	theoretic	NOUN
ejpam-5962	456	7	topology	topology	NOUN
ejpam-5962	456	8	.	.	PUNCT
ejpam-5962	457	1	duke	duke	PROPN
ejpam-5962	457	2	mathematical	mathematical	PROPN
ejpam-5962	457	3	journal	journal	PROPN
ejpam-5962	457	4	,	,	PUNCT
ejpam-5962	457	5	10(2):309–333	10(2):309–333	PROPN
ejpam-5962	457	6	,	,	PUNCT
ejpam-5962	457	7	1943	1943	NUM
ejpam-5962	457	8	.	.	PUNCT
ejpam-5962	458	1	[	[	X
ejpam-5962	458	2	3	3	X
ejpam-5962	458	3	]	]	X
ejpam-5962	458	4	r.	r.	NOUN
ejpam-5962	458	5	vaidyanathaswamy	vaidyanathaswamy	PROPN
ejpam-5962	458	6	.	.	PUNCT
ejpam-5962	459	1	set	set	VERB
ejpam-5962	459	2	topology	topology	NOUN
ejpam-5962	459	3	.	.	PUNCT
ejpam-5962	460	1	1947	1947	NUM
ejpam-5962	460	2	.	.	PUNCT
ejpam-5962	461	1	[	[	X
ejpam-5962	461	2	4	4	NUM
ejpam-5962	461	3	]	]	PUNCT
ejpam-5962	461	4	a.	a.	NOUN
ejpam-5962	461	5	ramanathan	ramanathan	PROPN
ejpam-5962	461	6	.	.	PUNCT
ejpam-5962	462	1	a	a	DET
ejpam-5962	462	2	characterization	characterization	NOUN
ejpam-5962	462	3	of	of	ADP
ejpam-5962	462	4	maximal	maximal	ADJ
ejpam-5962	462	5	-	-	PUNCT
ejpam-5962	462	6	hausdorff	hausdorff	NOUN
ejpam-5962	462	7	spaces	space	NOUN
ejpam-5962	462	8	.	.	PUNCT
ejpam-5962	463	1	journal	journal	NOUN
ejpam-5962	463	2	of	of	ADP
ejpam-5962	463	3	the	the	DET
ejpam-5962	463	4	indian	indian	PROPN
ejpam-5962	463	5	mathematical	mathematical	ADJ
ejpam-5962	463	6	society	society	NOUN
ejpam-5962	463	7	,	,	PUNCT
ejpam-5962	463	8	11:73–80	11:73–80	PROPN
ejpam-5962	463	9	,	,	PUNCT
ejpam-5962	463	10	1947	1947	NUM
ejpam-5962	463	11	.	.	PUNCT
ejpam-5962	464	1	[	[	X
ejpam-5962	464	2	5	5	NUM
ejpam-5962	464	3	]	]	PUNCT
ejpam-5962	464	4	a.	a.	NOUN
ejpam-5962	464	5	ramanathan	ramanathan	PROPN
ejpam-5962	464	6	.	.	PUNCT
ejpam-5962	465	1	maximal	maximal	ADJ
ejpam-5962	465	2	-	-	PUNCT
ejpam-5962	465	3	hausdorff	hausdorff	NOUN
ejpam-5962	465	4	spaces	space	NOUN
ejpam-5962	465	5	.	.	PUNCT
ejpam-5962	466	1	proceedings	proceeding	NOUN
ejpam-5962	466	2	of	of	ADP
ejpam-5962	466	3	the	the	DET
ejpam-5962	466	4	indian	indian	PROPN
ejpam-5962	466	5	academy	academy	PROPN
ejpam-5962	466	6	of	of	ADP
ejpam-5962	466	7	sciences	sciences	PROPN
ejpam-5962	466	8	,	,	PUNCT
ejpam-5962	466	9	section	section	NOUN
ejpam-5962	466	10	a	a	PRON
ejpam-5962	466	11	,	,	PUNCT
ejpam-5962	466	12	26(1):31–42	26(1):31–42	NUM
ejpam-5962	466	13	,	,	PUNCT
ejpam-5962	466	14	1947	1947	NUM
ejpam-5962	466	15	.	.	PUNCT
ejpam-5962	467	1	[	[	X
ejpam-5962	467	2	6	6	NUM
ejpam-5962	467	3	]	]	X
ejpam-5962	467	4	h.	h.	PROPN
ejpam-5962	467	5	tong	tong	PROPN
ejpam-5962	467	6	.	.	PUNCT
ejpam-5962	468	1	note	note	NOUN
ejpam-5962	468	2	on	on	ADP
ejpam-5962	468	3	minimal	minimal	ADJ
ejpam-5962	468	4	bicompact	bicompact	ADJ
ejpam-5962	468	5	spaces	space	NOUN
ejpam-5962	468	6	.	.	PUNCT
ejpam-5962	469	1	bulletin	bulletin	NOUN
ejpam-5962	469	2	of	of	ADP
ejpam-5962	469	3	the	the	DET
ejpam-5962	469	4	american	american	PROPN
ejpam-5962	469	5	mathematical	mathematical	PROPN
ejpam-5962	469	6	society	society	NOUN
ejpam-5962	469	7	,	,	PUNCT
ejpam-5962	469	8	54(5):478–479	54(5):478–479	PROPN
ejpam-5962	469	9	,	,	PUNCT
ejpam-5962	469	10	1948	1948	NUM
ejpam-5962	469	11	.	.	PUNCT
ejpam-5962	470	1	[	[	X
ejpam-5962	470	2	7	7	NUM
ejpam-5962	470	3	]	]	PUNCT
ejpam-5962	470	4	a.	a.	NOUN
ejpam-5962	470	5	ramanathan	ramanathan	PROPN
ejpam-5962	470	6	.	.	PUNCT
ejpam-5962	471	1	minimal	minimal	ADJ
ejpam-5962	471	2	-	-	PUNCT
ejpam-5962	471	3	bicompact	bicompact	ADJ
ejpam-5962	471	4	spaces	space	NOUN
ejpam-5962	471	5	.	.	PUNCT
ejpam-5962	472	1	journal	journal	NOUN
ejpam-5962	472	2	of	of	ADP
ejpam-5962	472	3	the	the	DET
ejpam-5962	472	4	indian	indian	PROPN
ejpam-5962	472	5	mathematical	mathematical	ADJ
ejpam-5962	472	6	society	society	NOUN
ejpam-5962	472	7	,	,	PUNCT
ejpam-5962	472	8	12:40–46	12:40–46	NUM
ejpam-5962	472	9	,	,	PUNCT
ejpam-5962	472	10	1948	1948	NUM
ejpam-5962	472	11	.	.	PUNCT
ejpam-5962	473	1	[	[	X
ejpam-5962	473	2	8	8	NUM
ejpam-5962	473	3	]	]	X
ejpam-5962	473	4	n.	n.	PROPN
ejpam-5962	473	5	smythe	smythe	PROPN
ejpam-5962	473	6	and	and	CCONJ
ejpam-5962	473	7	c.	c.	PROPN
ejpam-5962	473	8	a.	a.	PROPN
ejpam-5962	473	9	wilkins	wilkins	PROPN
ejpam-5962	473	10	.	.	PUNCT
ejpam-5962	474	1	minimal	minimal	ADJ
ejpam-5962	474	2	hausdorff	hausdorff	NOUN
ejpam-5962	474	3	and	and	CCONJ
ejpam-5962	474	4	maximal	maximal	ADJ
ejpam-5962	474	5	compact	compact	ADJ
ejpam-5962	474	6	spaces	space	NOUN
ejpam-5962	474	7	.	.	PUNCT
ejpam-5962	475	1	journal	journal	NOUN
ejpam-5962	475	2	of	of	ADP
ejpam-5962	475	3	the	the	DET
ejpam-5962	475	4	australian	australian	ADJ
ejpam-5962	475	5	mathematical	mathematical	ADJ
ejpam-5962	475	6	society	society	NOUN
ejpam-5962	475	7	,	,	PUNCT
ejpam-5962	475	8	3(2):167–171	3(2):167–171	NUM
ejpam-5962	475	9	,	,	PUNCT
ejpam-5962	475	10	1963	1963	NUM
ejpam-5962	475	11	.	.	PUNCT
ejpam-5962	476	1	a.	a.	NOUN
ejpam-5962	476	2	a.	a.	PROPN
ejpam-5962	476	3	atoom	atoom	PROPN
ejpam-5962	476	4	et	et	PROPN
ejpam-5962	476	5	al	al	PROPN
ejpam-5962	476	6	.	.	PUNCT
ejpam-5962	476	7	/	/	SYM
ejpam-5962	476	8	eur	eur	PROPN
ejpam-5962	476	9	.	.	PUNCT
ejpam-5962	477	1	j.	j.	PROPN
ejpam-5962	477	2	pure	pure	PROPN
ejpam-5962	477	3	appl	appl	PROPN
ejpam-5962	477	4	.	.	PROPN
ejpam-5962	477	5	math	math	PROPN
ejpam-5962	477	6	,	,	PUNCT
ejpam-5962	477	7	18	18	NUM
ejpam-5962	477	8	(	(	PUNCT
ejpam-5962	477	9	2	2	NUM
ejpam-5962	477	10	)	)	PUNCT
ejpam-5962	477	11	(	(	PUNCT
ejpam-5962	477	12	2025	2025	NUM
ejpam-5962	477	13	)	)	PUNCT
ejpam-5962	477	14	,	,	PUNCT
ejpam-5962	477	15	5962	5962	NUM
ejpam-5962	477	16	17	17	NUM
ejpam-5962	477	17	of	of	ADP
ejpam-5962	477	18	17	17	NUM
ejpam-5962	477	19	[	[	SYM
ejpam-5962	477	20	9	9	NUM
ejpam-5962	477	21	]	]	X
ejpam-5962	477	22	r.	r.	PROPN
ejpam-5962	477	23	larson	larson	PROPN
ejpam-5962	477	24	.	.	PROPN
ejpam-5962	478	1	complementary	complementary	ADJ
ejpam-5962	478	2	topological	topological	ADJ
ejpam-5962	478	3	properties	property	NOUN
ejpam-5962	478	4	.	.	PUNCT
ejpam-5962	479	1	notices	notice	NOUN
ejpam-5962	479	2	of	of	ADP
ejpam-5962	479	3	the	the	DET
ejpam-5962	479	4	american	american	PROPN
ejpam-5962	479	5	mathematical	mathematical	PROPN
ejpam-5962	479	6	society	society	NOUN
ejpam-5962	479	7	,	,	PUNCT
ejpam-5962	479	8	20	20	NUM
ejpam-5962	479	9	:	:	PUNCT
ejpam-5962	479	10	a–176	a–176	PROPN
ejpam-5962	479	11	,	,	PUNCT
ejpam-5962	479	12	1973	1973	NUM
ejpam-5962	479	13	.	.	PUNCT
ejpam-5962	480	1	[	[	X
ejpam-5962	480	2	10	10	NUM
ejpam-5962	480	3	]	]	X
ejpam-5962	480	4	p.	p.	NOUN
ejpam-5962	480	5	fletcher	fletcher	PROPN
ejpam-5962	480	6	et	et	PROPN
ejpam-5962	480	7	al	al	PROPN
ejpam-5962	480	8	.	.	PUNCT
ejpam-5962	481	1	the	the	DET
ejpam-5962	481	2	comparison	comparison	NOUN
ejpam-5962	481	3	of	of	ADP
ejpam-5962	481	4	topologies	topology	NOUN
ejpam-5962	481	5	.	.	PUNCT
ejpam-5962	482	1	duke	duke	PROPN
ejpam-5962	482	2	mathematical	mathematical	PROPN
ejpam-5962	482	3	journal	journal	PROPN
ejpam-5962	482	4	,	,	PUNCT
ejpam-5962	482	5	36(2):325–331	36(2):325–331	NUM
ejpam-5962	482	6	,	,	PUNCT
ejpam-5962	482	7	1969	1969	NUM
ejpam-5962	482	8	.	.	PUNCT
ejpam-5962	483	1	[	[	X
ejpam-5962	483	2	11	11	NUM
ejpam-5962	483	3	]	]	X
ejpam-5962	483	4	w.	w.	PROPN
ejpam-5962	483	5	g.	g.	PROPN
ejpam-5962	483	6	fleissner	fleissner	PROPN
ejpam-5962	483	7	.	.	PUNCT
ejpam-5962	484	1	a	a	DET
ejpam-5962	484	2	tb	tb	NOUN
ejpam-5962	484	3	space	space	NOUN
ejpam-5962	484	4	which	which	PRON
ejpam-5962	484	5	is	be	AUX
ejpam-5962	484	6	not	not	PART
ejpam-5962	484	7	katetov	katetov	ADJ
ejpam-5962	484	8	tb	tb	NOUN
ejpam-5962	484	9	.	.	PUNCT
ejpam-5962	485	1	rocky	rocky	ADJ
ejpam-5962	485	2	mountain	mountain	PROPN
ejpam-5962	485	3	journal	journal	NOUN
ejpam-5962	485	4	of	of	ADP
ejpam-5962	485	5	mathematics	mathematic	NOUN
ejpam-5962	485	6	,	,	PUNCT
ejpam-5962	485	7	10(3):661–663	10(3):661–663	NUM
ejpam-5962	485	8	,	,	PUNCT
ejpam-5962	485	9	1980	1980	NUM
ejpam-5962	485	10	.	.	PUNCT
ejpam-5962	486	1	[	[	X
ejpam-5962	486	2	12	12	NUM
ejpam-5962	486	3	]	]	X
ejpam-5962	486	4	d.	d.	PROPN
ejpam-5962	486	5	b.	b.	PROPN
ejpam-5962	486	6	gauld	gauld	PROPN
ejpam-5962	486	7	,	,	PUNCT
ejpam-5962	486	8	m.	m.	PROPN
ejpam-5962	486	9	mršević	mršević	PROPN
ejpam-5962	486	10	,	,	PUNCT
ejpam-5962	486	11	i.	i.	PROPN
ejpam-5962	486	12	l.	l.	PROPN
ejpam-5962	486	13	reilly	reilly	PROPN
ejpam-5962	486	14	,	,	PUNCT
ejpam-5962	486	15	and	and	CCONJ
ejpam-5962	486	16	m.	m.	PROPN
ejpam-5962	486	17	k.	k.	PROPN
ejpam-5962	486	18	vamanamurthy	vamanamurthy	PROPN
ejpam-5962	486	19	.	.	PUNCT
ejpam-5962	487	1	co	co	VERB
ejpam-5962	487	2	-	-	NOUN
ejpam-5962	487	3	lindelöf	lindelöf	NOUN
ejpam-5962	487	4	topologies	topology	NOUN
ejpam-5962	487	5	and	and	CCONJ
ejpam-5962	487	6	l	l	ADJ
ejpam-5962	487	7	-	-	ADJ
ejpam-5962	487	8	continuous	continuous	ADJ
ejpam-5962	487	9	functions	function	NOUN
ejpam-5962	487	10	.	.	PUNCT
ejpam-5962	488	1	glasnik	glasnik	PROPN
ejpam-5962	488	2	matematički	matematički	PROPN
ejpam-5962	488	3	,	,	PUNCT
ejpam-5962	488	4	19(39):297–308	19(39):297–308	NUM
ejpam-5962	488	5	,	,	PUNCT
ejpam-5962	488	6	1984	1984	NUM
ejpam-5962	488	7	.	.	PUNCT
ejpam-5962	489	1	[	[	X
ejpam-5962	489	2	13	13	NUM
ejpam-5962	489	3	]	]	PUNCT
ejpam-5962	489	4	j.	j.	PROPN
ejpam-5962	489	5	van	van	PROPN
ejpam-5962	489	6	mill	mill	PROPN
ejpam-5962	489	7	.	.	PUNCT
ejpam-5962	490	1	the	the	DET
ejpam-5962	490	2	infinite	infinite	ADJ
ejpam-5962	490	3	-	-	PUNCT
ejpam-5962	490	4	dimensional	dimensional	ADJ
ejpam-5962	490	5	topology	topology	NOUN
ejpam-5962	490	6	of	of	ADP
ejpam-5962	490	7	function	function	NOUN
ejpam-5962	490	8	spaces	space	NOUN
ejpam-5962	490	9	.	.	PUNCT
ejpam-5962	491	1	north	north	NOUN
ejpam-5962	491	2	-	-	PUNCT
ejpam-5962	491	3	holland	holland	PROPN
ejpam-5962	491	4	mathematical	mathematical	PROPN
ejpam-5962	491	5	library	library	NOUN
ejpam-5962	491	6	,	,	PUNCT
ejpam-5962	491	7	64	64	NUM
ejpam-5962	491	8	,	,	PUNCT
ejpam-5962	491	9	2001	2001	NUM
ejpam-5962	491	10	.	.	PUNCT
ejpam-5962	492	1	[	[	X
ejpam-5962	492	2	14	14	NUM
ejpam-5962	492	3	]	]	X
ejpam-5962	492	4	j.	j.	PROPN
ejpam-5962	492	5	c.	c.	PROPN
ejpam-5962	492	6	kelly	kelly	PROPN
ejpam-5962	492	7	.	.	PUNCT
ejpam-5962	493	1	bitopological	bitopological	ADJ
ejpam-5962	493	2	spaces	space	NOUN
ejpam-5962	493	3	.	.	PUNCT
ejpam-5962	494	1	proceedings	proceeding	NOUN
ejpam-5962	494	2	of	of	ADP
ejpam-5962	494	3	the	the	DET
ejpam-5962	494	4	london	london	PROPN
ejpam-5962	494	5	mathematical	mathematical	ADJ
ejpam-5962	494	6	society	society	NOUN
ejpam-5962	494	7	,	,	PUNCT
ejpam-5962	494	8	13(1):71–89	13(1):71–89	NUM
ejpam-5962	494	9	,	,	PUNCT
ejpam-5962	494	10	1963	1963	NUM
ejpam-5962	494	11	.	.	PUNCT
ejpam-5962	495	1	[	[	X
ejpam-5962	495	2	15	15	NUM
ejpam-5962	495	3	]	]	X
ejpam-5962	495	4	r.	r.	PROPN
ejpam-5962	495	5	engelking	engelke	VERB
ejpam-5962	495	6	.	.	PUNCT
ejpam-5962	496	1	general	general	ADJ
ejpam-5962	496	2	topology	topology	PROPN
ejpam-5962	496	3	.	.	PUNCT
ejpam-5962	497	1	sigma	sigma	PROPN
ejpam-5962	497	2	series	series	PROPN
ejpam-5962	497	3	in	in	ADP
ejpam-5962	497	4	pure	pure	ADJ
ejpam-5962	497	5	mathematics	mathematic	NOUN
ejpam-5962	497	6	,	,	PUNCT
ejpam-5962	497	7	6	6	NUM
ejpam-5962	497	8	,	,	PUNCT
ejpam-5962	497	9	1989	1989	NUM
ejpam-5962	497	10	.	.	PUNCT
ejpam-5962	498	1	[	[	X
ejpam-5962	498	2	16	16	NUM
ejpam-5962	498	3	]	]	PUNCT
ejpam-5962	498	4	a.	a.	NOUN
ejpam-5962	498	5	fora	fora	NOUN
ejpam-5962	498	6	and	and	CCONJ
ejpam-5962	498	7	h.	h.	PROPN
ejpam-5962	498	8	hdeib	hdeib	PROPN
ejpam-5962	498	9	.	.	PUNCT
ejpam-5962	499	1	on	on	ADP
ejpam-5962	499	2	pairwise	pairwise	PROPN
ejpam-5962	499	3	lindelöf	lindelöf	NOUN
ejpam-5962	499	4	spaces	space	VERB
ejpam-5962	499	5	.	.	PUNCT
ejpam-5962	500	1	revista	revista	PROPN
ejpam-5962	500	2	colombiana	colombiana	PROPN
ejpam-5962	500	3	de	de	X
ejpam-5962	500	4	matemáticas	matemáticas	PROPN
ejpam-5962	500	5	,	,	PUNCT
ejpam-5962	500	6	17(1	17(1	NUM
ejpam-5962	500	7	-	-	SYM
ejpam-5962	500	8	2):37–58	2):37–58	NUM
ejpam-5962	500	9	,	,	PUNCT
ejpam-5962	500	10	1983	1983	NUM
ejpam-5962	500	11	.	.	PUNCT
ejpam-5962	501	1	[	[	X
ejpam-5962	501	2	17	17	NUM
ejpam-5962	501	3	]	]	X
ejpam-5962	501	4	r.	r.	PROPN
ejpam-5962	501	5	alrababah	alrababah	PROPN
ejpam-5962	501	6	,	,	PUNCT
ejpam-5962	501	7	a.	a.	PROPN
ejpam-5962	501	8	amourah	amourah	PROPN
ejpam-5962	501	9	,	,	PUNCT
ejpam-5962	501	10	j.	j.	PROPN
ejpam-5962	501	11	salah	salah	PROPN
ejpam-5962	501	12	,	,	PUNCT
ejpam-5962	501	13	r.	r.	PROPN
ejpam-5962	501	14	ahmad	ahmad	PROPN
ejpam-5962	501	15	,	,	PUNCT
ejpam-5962	501	16	and	and	CCONJ
ejpam-5962	501	17	a.	a.	NOUN
ejpam-5962	501	18	a.	a.	NOUN
ejpam-5962	501	19	atoom	atoom	PROPN
ejpam-5962	501	20	.	.	PUNCT
ejpam-5962	502	1	new	new	ADJ
ejpam-5962	502	2	results	result	NOUN
ejpam-5962	502	3	on	on	ADP
ejpam-5962	502	4	difference	difference	NOUN
ejpam-5962	502	5	paracompactness	paracompactness	NOUN
ejpam-5962	502	6	in	in	ADP
ejpam-5962	502	7	topological	topological	ADJ
ejpam-5962	502	8	spaces	space	NOUN
ejpam-5962	502	9	.	.	PUNCT
ejpam-5962	503	1	european	european	ADJ
ejpam-5962	503	2	journal	journal	PROPN
ejpam-5962	503	3	of	of	ADP
ejpam-5962	503	4	pure	pure	ADJ
ejpam-5962	503	5	and	and	CCONJ
ejpam-5962	503	6	applied	applied	ADJ
ejpam-5962	503	7	mathematics	mathematic	NOUN
ejpam-5962	503	8	,	,	PUNCT
ejpam-5962	503	9	17(4):2990–3003	17(4):2990–3003	NUM
ejpam-5962	503	10	,	,	PUNCT
ejpam-5962	503	11	2024	2024	NUM
ejpam-5962	503	12	.	.	PUNCT
ejpam-5962	504	1	[	[	X
ejpam-5962	504	2	18	18	NUM
ejpam-5962	504	3	]	]	PUNCT
ejpam-5962	504	4	a.	a.	NOUN
ejpam-5962	504	5	a.	a.	NOUN
ejpam-5962	504	6	atoom	atoom	PROPN
ejpam-5962	504	7	.	.	PUNCT
ejpam-5962	505	1	study	study	NOUN
ejpam-5962	505	2	of	of	ADP
ejpam-5962	505	3	pairwise	pairwise	NOUN
ejpam-5962	505	4	-	-	PUNCT
ejpam-5962	505	5	ω	ω	NOUN
ejpam-5962	505	6	-	-	ADJ
ejpam-5962	505	7	compact	compact	ADJ
ejpam-5962	505	8	spaces	space	NOUN
ejpam-5962	505	9	.	.	PUNCT
ejpam-5962	506	1	global	global	ADJ
ejpam-5962	506	2	journal	journal	PROPN
ejpam-5962	506	3	of	of	ADP
ejpam-5962	506	4	mathematics	mathematic	NOUN
ejpam-5962	506	5	,	,	PUNCT
ejpam-5962	506	6	14(2):1453–1459	14(2):1453–1459	NUM
ejpam-5962	506	7	,	,	PUNCT
ejpam-5962	506	8	2018	2018	NUM
ejpam-5962	506	9	.	.	PUNCT
ejpam-5962	507	1	[	[	X
ejpam-5962	507	2	19	19	NUM
ejpam-5962	507	3	]	]	PUNCT
ejpam-5962	507	4	a.	a.	NOUN
ejpam-5962	507	5	a.	a.	NOUN
ejpam-5962	507	6	atoom	atoom	PROPN
ejpam-5962	507	7	.	.	PUNCT
ejpam-5962	508	1	on	on	ADP
ejpam-5962	508	2	pairwise	pairwise	NOUN
ejpam-5962	508	3	-	-	PUNCT
ejpam-5962	508	4	ω	ω	NOUN
ejpam-5962	508	5	-	-	PUNCT
ejpam-5962	508	6	perfect	perfect	ADJ
ejpam-5962	508	7	functions	function	NOUN
ejpam-5962	508	8	.	.	PUNCT
ejpam-5962	509	1	journal	journal	NOUN
ejpam-5962	509	2	of	of	ADP
ejpam-5962	509	3	mathematics	mathematic	NOUN
ejpam-5962	509	4	and	and	CCONJ
ejpam-5962	509	5	computer	computer	NOUN
ejpam-5962	509	6	science	science	NOUN
ejpam-5962	509	7	,	,	PUNCT
ejpam-5962	509	8	12(1):1–11	12(1):1–11	NUM
ejpam-5962	509	9	,	,	PUNCT
ejpam-5962	509	10	2022	2022	NUM
ejpam-5962	509	11	.	.	PUNCT
ejpam-5962	510	1	[	[	X
ejpam-5962	510	2	20	20	NUM
ejpam-5962	510	3	]	]	PUNCT
ejpam-5962	510	4	a.	a.	NOUN
ejpam-5962	510	5	a.	a.	NOUN
ejpam-5962	510	6	atoom	atoom	PROPN
ejpam-5962	510	7	,	,	PUNCT
ejpam-5962	510	8	r.	r.	PROPN
ejpam-5962	510	9	alrababah	alrababah	PROPN
ejpam-5962	510	10	,	,	PUNCT
ejpam-5962	510	11	m.	m.	NOUN
ejpam-5962	510	12	alholi	alholi	PROPN
ejpam-5962	510	13	,	,	PUNCT
ejpam-5962	510	14	h.	h.	PROPN
ejpam-5962	510	15	qoqazeh	qoqazeh	PROPN
ejpam-5962	510	16	,	,	PUNCT
ejpam-5962	510	17	a.	a.	NOUN
ejpam-5962	510	18	alnana	alnana	PROPN
ejpam-5962	510	19	,	,	PUNCT
ejpam-5962	510	20	and	and	CCONJ
ejpam-5962	510	21	d.	d.	PROPN
ejpam-5962	510	22	a.	a.	PROPN
ejpam-5962	510	23	mahmoud	mahmoud	PROPN
ejpam-5962	510	24	.	.	PUNCT
ejpam-5962	511	1	exploring	explore	VERB
ejpam-5962	511	2	the	the	DET
ejpam-5962	511	3	difference	difference	NOUN
ejpam-5962	511	4	paralindelöf	paralindelöf	NOUN
ejpam-5962	511	5	in	in	ADP
ejpam-5962	511	6	topological	topological	ADJ
ejpam-5962	511	7	spaces	space	NOUN
ejpam-5962	511	8	.	.	PUNCT
ejpam-5962	512	1	international	international	ADJ
ejpam-5962	512	2	journal	journal	NOUN
ejpam-5962	512	3	of	of	ADP
ejpam-5962	512	4	analysis	analysis	NOUN
ejpam-5962	512	5	and	and	CCONJ
ejpam-5962	512	6	applications	application	NOUN
ejpam-5962	512	7	,	,	PUNCT
ejpam-5962	512	8	23:24	23:24	NUM
ejpam-5962	512	9	,	,	PUNCT
ejpam-5962	512	10	2025	2025	NUM
ejpam-5962	512	11	.	.	PUNCT
ejpam-5962	513	1	[	[	X
ejpam-5962	513	2	21	21	NUM
ejpam-5962	513	3	]	]	X
ejpam-5962	513	4	f.	f.	PROPN
ejpam-5962	513	5	bani	bani	PROPN
ejpam-5962	513	6	-	-	PUNCT
ejpam-5962	513	7	ahmad	ahmad	PROPN
ejpam-5962	513	8	,	,	PUNCT
ejpam-5962	513	9	o.	o.	PROPN
ejpam-5962	513	10	alsayyed	alsayye	VERB
ejpam-5962	513	11	,	,	PUNCT
ejpam-5962	513	12	and	and	CCONJ
ejpam-5962	513	13	a.	a.	NOUN
ejpam-5962	513	14	a.	a.	NOUN
ejpam-5962	513	15	atoom	atoom	PROPN
ejpam-5962	513	16	.	.	PUNCT
ejpam-5962	514	1	some	some	DET
ejpam-5962	514	2	new	new	ADJ
ejpam-5962	514	3	results	result	NOUN
ejpam-5962	514	4	of	of	ADP
ejpam-5962	514	5	difference	difference	NOUN
ejpam-5962	514	6	perfect	perfect	ADJ
ejpam-5962	514	7	functions	function	NOUN
ejpam-5962	514	8	in	in	ADP
ejpam-5962	514	9	topological	topological	ADJ
ejpam-5962	514	10	spaces	space	NOUN
ejpam-5962	514	11	.	.	PUNCT
ejpam-5962	515	1	aims	aim	VERB
ejpam-5962	515	2	mathematics	mathematic	NOUN
ejpam-5962	515	3	,	,	PUNCT
ejpam-5962	515	4	7(11):20058–20065	7(11):20058–20065	NOUN
ejpam-5962	515	5	,	,	PUNCT
ejpam-5962	515	6	2022	2022	NUM
ejpam-5962	515	7	.	.	PUNCT
ejpam-5962	516	1	[	[	X
ejpam-5962	516	2	22	22	NUM
ejpam-5962	516	3	]	]	X
ejpam-5962	516	4	h.	h.	PROPN
ejpam-5962	516	5	qoqazeh	qoqazeh	PROPN
ejpam-5962	516	6	,	,	PUNCT
ejpam-5962	516	7	a.	a.	NOUN
ejpam-5962	516	8	a.	a.	NOUN
ejpam-5962	516	9	atoom	atoom	PROPN
ejpam-5962	516	10	,	,	PUNCT
ejpam-5962	516	11	m.	m.	NOUN
ejpam-5962	516	12	alholi	alholi	PROPN
ejpam-5962	516	13	,	,	PUNCT
ejpam-5962	516	14	e.	e.	PROPN
ejpam-5962	516	15	almuhur	almuhur	PROPN
ejpam-5962	516	16	,	,	PUNCT
ejpam-5962	516	17	e.	e.	PROPN
ejpam-5962	516	18	hussein	hussein	PROPN
ejpam-5962	516	19	,	,	PUNCT
ejpam-5962	516	20	a.	a.	NOUN
ejpam-5962	516	21	owledat	owledat	NOUN
ejpam-5962	516	22	,	,	PUNCT
ejpam-5962	516	23	and	and	CCONJ
ejpam-5962	516	24	a.	a.	PROPN
ejpam-5962	516	25	al	al	PROPN
ejpam-5962	516	26	-	-	PROPN
ejpam-5962	516	27	nana	nana	PROPN
ejpam-5962	516	28	.	.	PUNCT
ejpam-5962	517	1	kc	kc	NOUN
ejpam-5962	517	2	-	-	PUNCT
ejpam-5962	517	3	bitopological	bitopological	ADJ
ejpam-5962	517	4	spaces	space	NOUN
ejpam-5962	517	5	.	.	PUNCT
ejpam-5962	518	1	aims	aim	VERB
ejpam-5962	518	2	mathematics	mathematic	NOUN
ejpam-5962	518	3	,	,	PUNCT
ejpam-5962	518	4	9(12):32182–32199	9(12):32182–32199	NUM
ejpam-5962	518	5	,	,	PUNCT
ejpam-5962	518	6	2024	2024	NUM
ejpam-5962	518	7	.	.	PUNCT