id	sid	tid	token	lemma	pos
ejpam-3502	1	1	european	european	PROPN
ejpam-3502	1	2	journal	journal	PROPN
ejpam-3502	1	3	of	of	ADP
ejpam-3502	1	4	pure	pure	ADJ
ejpam-3502	1	5	and	and	CCONJ
ejpam-3502	1	6	applied	apply	VERB
ejpam-3502	1	7	mathematics	mathematic	NOUN
ejpam-3502	1	8	vol	vol	NOUN
ejpam-3502	1	9	.	.	PROPN
ejpam-3502	2	1	12	12	NUM
ejpam-3502	2	2	,	,	PUNCT
ejpam-3502	2	3	no	no	INTJ
ejpam-3502	2	4	.	.	NOUN
ejpam-3502	2	5	4	4	NUM
ejpam-3502	2	6	,	,	PUNCT
ejpam-3502	2	7	2019	2019	NUM
ejpam-3502	2	8	,	,	PUNCT
ejpam-3502	2	9	1553	1553	NUM
ejpam-3502	2	10	-	-	SYM
ejpam-3502	2	11	1566	1566	NUM
ejpam-3502	2	12	issn	issn	PROPN
ejpam-3502	2	13	1307	1307	NUM
ejpam-3502	2	14	-	-	SYM
ejpam-3502	2	15	5543	5543	NUM
ejpam-3502	2	16	–	–	PUNCT
ejpam-3502	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3502	2	18	published	publish	VERB
ejpam-3502	2	19	by	by	ADP
ejpam-3502	2	20	new	new	PROPN
ejpam-3502	2	21	york	york	PROPN
ejpam-3502	2	22	business	business	PROPN
ejpam-3502	2	23	global	global	ADJ
ejpam-3502	2	24	functions	function	NOUN
ejpam-3502	2	25	on	on	ADP
ejpam-3502	2	26	n	n	CCONJ
ejpam-3502	2	27	-	-	PUNCT
ejpam-3502	2	28	generalized	generalize	VERB
ejpam-3502	2	29	topological	topological	ADJ
ejpam-3502	2	30	spaces	space	NOUN
ejpam-3502	2	31	cherry	cherry	PROPN
ejpam-3502	2	32	mae	mae	PROPN
ejpam-3502	2	33	r.	r.	PROPN
ejpam-3502	2	34	balingit1,∗	balingit1,∗	PROPN
ejpam-3502	2	35	,	,	PUNCT
ejpam-3502	2	36	julius	julius	PROPN
ejpam-3502	2	37	v.	v.	PROPN
ejpam-3502	2	38	benitez2	benitez2	PROPN
ejpam-3502	2	39	1	1	NUM
ejpam-3502	2	40	department	department	NOUN
ejpam-3502	2	41	of	of	ADP
ejpam-3502	2	42	mathematics	mathematic	NOUN
ejpam-3502	2	43	,	,	PUNCT
ejpam-3502	2	44	college	college	NOUN
ejpam-3502	2	45	of	of	ADP
ejpam-3502	2	46	arts	art	NOUN
ejpam-3502	2	47	and	and	CCONJ
ejpam-3502	2	48	sciences	science	NOUN
ejpam-3502	2	49	,	,	PUNCT
ejpam-3502	2	50	central	central	ADJ
ejpam-3502	2	51	mindanao	mindanao	PROPN
ejpam-3502	2	52	university	university	NOUN
ejpam-3502	2	53	,	,	PUNCT
ejpam-3502	2	54	maramag	maramag	NOUN
ejpam-3502	2	55	,	,	PUNCT
ejpam-3502	2	56	bukidnon	bukidnon	NOUN
ejpam-3502	2	57	,	,	PUNCT
ejpam-3502	2	58	philippines	philippines	PROPN
ejpam-3502	2	59	2	2	NUM
ejpam-3502	2	60	department	department	NOUN
ejpam-3502	2	61	of	of	ADP
ejpam-3502	2	62	mathematics	mathematic	NOUN
ejpam-3502	2	63	and	and	CCONJ
ejpam-3502	2	64	statistics	statistic	NOUN
ejpam-3502	2	65	,	,	PUNCT
ejpam-3502	2	66	college	college	NOUN
ejpam-3502	2	67	of	of	ADP
ejpam-3502	2	68	science	science	NOUN
ejpam-3502	2	69	and	and	CCONJ
ejpam-3502	2	70	mathematics	mathematic	NOUN
ejpam-3502	2	71	,	,	PUNCT
ejpam-3502	2	72	mindanao	mindanao	PROPN
ejpam-3502	2	73	state	state	PROPN
ejpam-3502	2	74	university	university	PROPN
ejpam-3502	2	75	-	-	PUNCT
ejpam-3502	2	76	iligan	iligan	PROPN
ejpam-3502	2	77	institute	institute	PROPN
ejpam-3502	2	78	of	of	ADP
ejpam-3502	2	79	technology	technology	PROPN
ejpam-3502	2	80	,	,	PUNCT
ejpam-3502	2	81	iligan	iligan	PROPN
ejpam-3502	2	82	city	city	PROPN
ejpam-3502	2	83	,	,	PUNCT
ejpam-3502	2	84	philippines	philippine	NOUN
ejpam-3502	2	85	abstract	abstract	ADJ
ejpam-3502	2	86	.	.	PUNCT
ejpam-3502	3	1	an	an	DET
ejpam-3502	3	2	n	n	ADV
ejpam-3502	3	3	-	-	PUNCT
ejpam-3502	3	4	generalized	generalize	VERB
ejpam-3502	3	5	topological	topological	ADJ
ejpam-3502	3	6	(	(	PUNCT
ejpam-3502	3	7	n	n	CCONJ
ejpam-3502	3	8	-	-	PUNCT
ejpam-3502	3	9	gt	gt	NOUN
ejpam-3502	3	10	)	)	PUNCT
ejpam-3502	3	11	space	space	NOUN
ejpam-3502	3	12	is	be	AUX
ejpam-3502	3	13	a	a	DET
ejpam-3502	3	14	pair	pair	NOUN
ejpam-3502	3	15	(	(	PUNCT
ejpam-3502	3	16	x	x	NOUN
ejpam-3502	3	17	,	,	PUNCT
ejpam-3502	3	18	g	g	NOUN
ejpam-3502	3	19	)	)	PUNCT
ejpam-3502	3	20	of	of	ADP
ejpam-3502	3	21	a	a	DET
ejpam-3502	3	22	nonempty	nonempty	ADV
ejpam-3502	3	23	set	set	VERB
ejpam-3502	3	24	x	x	PUNCT
ejpam-3502	3	25	and	and	CCONJ
ejpam-3502	3	26	a	a	DET
ejpam-3502	3	27	collection	collection	NOUN
ejpam-3502	3	28	g	g	NOUN
ejpam-3502	3	29	of	of	ADP
ejpam-3502	3	30	n	n	PROPN
ejpam-3502	3	31	(	(	PUNCT
ejpam-3502	3	32	n	n	CCONJ
ejpam-3502	3	33	∈	∈	PROPN
ejpam-3502	3	34	n	n	CCONJ
ejpam-3502	3	35	)	)	PUNCT
ejpam-3502	3	36	distinct	distinct	ADJ
ejpam-3502	3	37	generalized	generalized	ADJ
ejpam-3502	3	38	topologies	topology	NOUN
ejpam-3502	3	39	(	(	PUNCT
ejpam-3502	3	40	in	in	ADP
ejpam-3502	3	41	the	the	DET
ejpam-3502	3	42	sense	sense	NOUN
ejpam-3502	3	43	of	of	ADP
ejpam-3502	3	44	a.	a.	NOUN
ejpam-3502	3	45	császár	császár	PROPN
ejpam-3502	3	46	[	[	X
ejpam-3502	3	47	1	1	NUM
ejpam-3502	3	48	]	]	PUNCT
ejpam-3502	3	49	)	)	PUNCT
ejpam-3502	3	50	on	on	ADP
ejpam-3502	3	51	the	the	DET
ejpam-3502	3	52	set	set	NOUN
ejpam-3502	3	53	x.	x.	NOUN
ejpam-3502	3	54	in	in	ADP
ejpam-3502	3	55	this	this	DET
ejpam-3502	3	56	paper	paper	NOUN
ejpam-3502	3	57	,	,	PUNCT
ejpam-3502	3	58	we	we	PRON
ejpam-3502	3	59	look	look	VERB
ejpam-3502	3	60	into	into	ADP
ejpam-3502	3	61	g	g	PROPN
ejpam-3502	3	62	-continuous	-continuous	ADJ
ejpam-3502	3	63	maps	map	NOUN
ejpam-3502	3	64	,	,	PUNCT
ejpam-3502	3	65	g	g	NOUN
ejpam-3502	3	66	-open	-open	NOUN
ejpam-3502	3	67	and	and	CCONJ
ejpam-3502	3	68	g	g	NOUN
ejpam-3502	3	69	-closed	-close	VERB
ejpam-3502	3	70	maps	map	NOUN
ejpam-3502	3	71	,	,	PUNCT
ejpam-3502	3	72	as	as	ADV
ejpam-3502	3	73	well	well	ADV
ejpam-3502	3	74	as	as	ADP
ejpam-3502	3	75	g	g	PROPN
ejpam-3502	3	76	-homeomorphisms	-homeomorphism	NOUN
ejpam-3502	3	77	in	in	ADP
ejpam-3502	3	78	terms	term	NOUN
ejpam-3502	3	79	of	of	ADP
ejpam-3502	3	80	n	n	CCONJ
ejpam-3502	3	81	-	-	PUNCT
ejpam-3502	3	82	gt	gt	PROPN
ejpam-3502	3	83	spaces	space	NOUN
ejpam-3502	3	84	and	and	CCONJ
ejpam-3502	3	85	establish	establish	VERB
ejpam-3502	3	86	some	some	PRON
ejpam-3502	3	87	of	of	ADP
ejpam-3502	3	88	their	their	PRON
ejpam-3502	3	89	basic	basic	ADJ
ejpam-3502	3	90	properties	property	NOUN
ejpam-3502	3	91	and	and	CCONJ
ejpam-3502	3	92	relationships	relationship	NOUN
ejpam-3502	3	93	.	.	PUNCT
ejpam-3502	4	1	moreover	moreover	ADV
ejpam-3502	4	2	,	,	PUNCT
ejpam-3502	4	3	these	these	DET
ejpam-3502	4	4	notions	notion	NOUN
ejpam-3502	4	5	are	be	AUX
ejpam-3502	4	6	also	also	ADV
ejpam-3502	4	7	examined	examine	VERB
ejpam-3502	4	8	with	with	ADP
ejpam-3502	4	9	respect	respect	NOUN
ejpam-3502	4	10	to	to	ADP
ejpam-3502	4	11	the	the	DET
ejpam-3502	4	12	component	component	NOUN
ejpam-3502	4	13	generalized	generalize	VERB
ejpam-3502	4	14	topologies	topology	NOUN
ejpam-3502	4	15	of	of	ADP
ejpam-3502	4	16	the	the	DET
ejpam-3502	4	17	underlying	underlie	VERB
ejpam-3502	4	18	spaces	space	NOUN
ejpam-3502	4	19	by	by	ADP
ejpam-3502	4	20	defining	define	VERB
ejpam-3502	4	21	and	and	CCONJ
ejpam-3502	4	22	characterizing	characterize	VERB
ejpam-3502	4	23	pairwise	pairwise	NOUN
ejpam-3502	4	24	versions	version	NOUN
ejpam-3502	4	25	of	of	ADP
ejpam-3502	4	26	the	the	DET
ejpam-3502	4	27	said	say	VERB
ejpam-3502	4	28	types	type	NOUN
ejpam-3502	4	29	of	of	ADP
ejpam-3502	4	30	mappings	mapping	NOUN
ejpam-3502	4	31	.	.	PUNCT
ejpam-3502	5	1	2010	2010	NUM
ejpam-3502	5	2	mathematics	mathematic	NOUN
ejpam-3502	5	3	subject	subject	NOUN
ejpam-3502	5	4	classifications	classification	NOUN
ejpam-3502	5	5	:	:	PUNCT
ejpam-3502	5	6	54a05	54a05	NUM
ejpam-3502	5	7	,	,	PUNCT
ejpam-3502	5	8	54c05	54c05	NUM
ejpam-3502	5	9	,	,	PUNCT
ejpam-3502	5	10	54c08	54c08	NUM
ejpam-3502	5	11	,	,	PUNCT
ejpam-3502	5	12	54c10	54c10	NUM
ejpam-3502	5	13	,	,	PUNCT
ejpam-3502	5	14	54h99	54h99	NUM
ejpam-3502	5	15	key	key	ADJ
ejpam-3502	5	16	words	word	NOUN
ejpam-3502	5	17	and	and	CCONJ
ejpam-3502	5	18	phrases	phrase	NOUN
ejpam-3502	5	19	:	:	PUNCT
ejpam-3502	5	20	g	g	PROPN
ejpam-3502	5	21	-continuous	-continuous	ADJ
ejpam-3502	5	22	map	map	NOUN
ejpam-3502	5	23	,	,	PUNCT
ejpam-3502	5	24	g	g	PROPN
ejpam-3502	5	25	-open	-open	NOUN
ejpam-3502	5	26	map	map	NOUN
ejpam-3502	5	27	,	,	PUNCT
ejpam-3502	5	28	g	g	PROPN
ejpam-3502	5	29	-homeomorphism	-homeomorphism	NOUN
ejpam-3502	5	30	1	1	NUM
ejpam-3502	5	31	.	.	PUNCT
ejpam-3502	6	1	introduction	introduction	NOUN
ejpam-3502	6	2	open	open	ADJ
ejpam-3502	6	3	sets	set	NOUN
ejpam-3502	6	4	play	play	VERB
ejpam-3502	6	5	as	as	ADP
ejpam-3502	6	6	a	a	DET
ejpam-3502	6	7	fundamental	fundamental	ADJ
ejpam-3502	6	8	notion	notion	NOUN
ejpam-3502	6	9	that	that	PRON
ejpam-3502	6	10	underlies	underlie	VERB
ejpam-3502	6	11	almost	almost	ADV
ejpam-3502	6	12	any	any	PRON
ejpam-3502	6	13	other	other	ADJ
ejpam-3502	6	14	topological	topological	ADJ
ejpam-3502	6	15	concept	concept	NOUN
ejpam-3502	6	16	.	.	PUNCT
ejpam-3502	7	1	when	when	SCONJ
ejpam-3502	7	2	a.	a.	NOUN
ejpam-3502	7	3	császár	császár	PROPN
ejpam-3502	7	4	[	[	X
ejpam-3502	7	5	1	1	X
ejpam-3502	7	6	]	]	PUNCT
ejpam-3502	7	7	in	in	ADP
ejpam-3502	7	8	2002	2002	NUM
ejpam-3502	7	9	weakened	weaken	VERB
ejpam-3502	7	10	the	the	DET
ejpam-3502	7	11	conditions	condition	NOUN
ejpam-3502	7	12	that	that	PRON
ejpam-3502	7	13	are	be	AUX
ejpam-3502	7	14	to	to	PART
ejpam-3502	7	15	be	be	AUX
ejpam-3502	7	16	satisfied	satisfy	VERB
ejpam-3502	7	17	by	by	ADP
ejpam-3502	7	18	an	an	DET
ejpam-3502	7	19	open	open	ADJ
ejpam-3502	7	20	set	set	NOUN
ejpam-3502	7	21	,	,	PUNCT
ejpam-3502	7	22	the	the	DET
ejpam-3502	7	23	landscape	landscape	NOUN
ejpam-3502	7	24	of	of	ADP
ejpam-3502	7	25	topological	topological	ADJ
ejpam-3502	7	26	spaces	space	NOUN
ejpam-3502	7	27	widened	widen	VERB
ejpam-3502	7	28	significantly	significantly	ADV
ejpam-3502	7	29	.	.	PUNCT
ejpam-3502	8	1	in	in	ADP
ejpam-3502	8	2	[	[	X
ejpam-3502	8	3	1	1	NUM
ejpam-3502	8	4	]	]	PUNCT
ejpam-3502	8	5	,	,	PUNCT
ejpam-3502	8	6	he	he	PRON
ejpam-3502	8	7	defined	define	VERB
ejpam-3502	8	8	a	a	DET
ejpam-3502	8	9	generalized	generalized	ADJ
ejpam-3502	8	10	topological	topological	ADJ
ejpam-3502	8	11	space	space	NOUN
ejpam-3502	8	12	(	(	PUNCT
ejpam-3502	8	13	briefly	briefly	ADV
ejpam-3502	8	14	,	,	PUNCT
ejpam-3502	8	15	gt	gt	PROPN
ejpam-3502	8	16	space	space	NOUN
ejpam-3502	8	17	)	)	PUNCT
ejpam-3502	8	18	(	(	PUNCT
ejpam-3502	8	19	x,µ	x,µ	NOUN
ejpam-3502	8	20	)	)	PUNCT
ejpam-3502	8	21	as	as	SCONJ
ejpam-3502	8	22	a	a	DET
ejpam-3502	8	23	pair	pair	NOUN
ejpam-3502	8	24	of	of	ADP
ejpam-3502	8	25	a	a	DET
ejpam-3502	8	26	nonempty	nonempty	ADV
ejpam-3502	8	27	set	set	VERB
ejpam-3502	8	28	x	x	PUNCT
ejpam-3502	8	29	and	and	CCONJ
ejpam-3502	8	30	an	an	DET
ejpam-3502	8	31	associated	associated	ADJ
ejpam-3502	8	32	family	family	NOUN
ejpam-3502	8	33	µ	µ	NOUN
ejpam-3502	8	34	of	of	ADP
ejpam-3502	8	35	subsets	subset	NOUN
ejpam-3502	8	36	of	of	ADP
ejpam-3502	8	37	x	x	PUNCT
ejpam-3502	8	38	satisfying	satisfy	VERB
ejpam-3502	8	39	only	only	ADV
ejpam-3502	8	40	the	the	DET
ejpam-3502	8	41	conditions	condition	NOUN
ejpam-3502	8	42	that	that	PRON
ejpam-3502	8	43	∅	∅	VERB
ejpam-3502	8	44	∈	∈	PROPN
ejpam-3502	8	45	µ	µ	X
ejpam-3502	8	46	and	and	CCONJ
ejpam-3502	8	47	an	an	DET
ejpam-3502	8	48	arbitrary	arbitrary	ADJ
ejpam-3502	8	49	union	union	NOUN
ejpam-3502	8	50	of	of	ADP
ejpam-3502	8	51	sets	set	NOUN
ejpam-3502	8	52	in	in	ADP
ejpam-3502	8	53	µ	µ	PRON
ejpam-3502	8	54	belongs	belong	VERB
ejpam-3502	8	55	to	to	PART
ejpam-3502	8	56	µ.	µ.	VERB
ejpam-3502	8	57	naturally	naturally	ADV
ejpam-3502	8	58	,	,	PUNCT
ejpam-3502	8	59	the	the	DET
ejpam-3502	8	60	elements	element	NOUN
ejpam-3502	8	61	of	of	ADP
ejpam-3502	8	62	µ	µ	NOUN
ejpam-3502	8	63	are	be	AUX
ejpam-3502	8	64	termed	term	VERB
ejpam-3502	8	65	µ-open	µ-open	NOUN
ejpam-3502	8	66	sets	set	NOUN
ejpam-3502	8	67	.	.	PUNCT
ejpam-3502	9	1	in	in	ADP
ejpam-3502	9	2	the	the	DET
ejpam-3502	9	3	same	same	ADJ
ejpam-3502	9	4	space	space	NOUN
ejpam-3502	9	5	,	,	PUNCT
ejpam-3502	9	6	the	the	DET
ejpam-3502	9	7	µ-closure	µ-closure	NOUN
ejpam-3502	9	8	cµ(a	cµ(a	NUM
ejpam-3502	9	9	)	)	PUNCT
ejpam-3502	9	10	of	of	ADP
ejpam-3502	9	11	a	a	DET
ejpam-3502	9	12	subset	subset	NOUN
ejpam-3502	9	13	a	a	PRON
ejpam-3502	9	14	of	of	ADP
ejpam-3502	9	15	x	x	PRON
ejpam-3502	9	16	is	be	AUX
ejpam-3502	9	17	also	also	ADV
ejpam-3502	9	18	defined	define	VERB
ejpam-3502	9	19	as	as	ADP
ejpam-3502	9	20	the	the	DET
ejpam-3502	9	21	intersection	intersection	NOUN
ejpam-3502	9	22	of	of	ADP
ejpam-3502	9	23	all	all	DET
ejpam-3502	9	24	µ-closed	µ-close	VERB
ejpam-3502	9	25	sets	set	NOUN
ejpam-3502	9	26	containing	contain	VERB
ejpam-3502	9	27	a	a	DET
ejpam-3502	9	28	while	while	NOUN
ejpam-3502	9	29	the	the	DET
ejpam-3502	9	30	µ-interior	µ-interior	NOUN
ejpam-3502	9	31	iµ(a	iµ(a	NOUN
ejpam-3502	9	32	)	)	PUNCT
ejpam-3502	9	33	of	of	ADP
ejpam-3502	9	34	a	a	PRON
ejpam-3502	9	35	is	be	AUX
ejpam-3502	9	36	the	the	DET
ejpam-3502	9	37	union	union	NOUN
ejpam-3502	9	38	of	of	ADP
ejpam-3502	9	39	all	all	DET
ejpam-3502	9	40	µ-open	µ-open	NOUN
ejpam-3502	9	41	sets	set	NOUN
ejpam-3502	9	42	contained	contain	VERB
ejpam-3502	9	43	in	in	ADP
ejpam-3502	9	44	a	a	DET
ejpam-3502	9	45	[	[	X
ejpam-3502	9	46	1	1	NUM
ejpam-3502	9	47	]	]	PUNCT
ejpam-3502	9	48	.	.	PUNCT
ejpam-3502	10	1	other	other	ADJ
ejpam-3502	10	2	basic	basic	ADJ
ejpam-3502	10	3	properties	property	NOUN
ejpam-3502	10	4	of	of	ADP
ejpam-3502	10	5	a	a	DET
ejpam-3502	10	6	gt	gt	PROPN
ejpam-3502	10	7	space	space	NOUN
ejpam-3502	10	8	were	be	AUX
ejpam-3502	10	9	cited	cite	VERB
ejpam-3502	10	10	in	in	ADP
ejpam-3502	10	11	[	[	X
ejpam-3502	10	12	6	6	NUM
ejpam-3502	10	13	]	]	PUNCT
ejpam-3502	10	14	and	and	CCONJ
ejpam-3502	10	15	[	[	X
ejpam-3502	10	16	5	5	NUM
ejpam-3502	10	17	]	]	PUNCT
ejpam-3502	10	18	.	.	PUNCT
ejpam-3502	11	1	following	follow	VERB
ejpam-3502	11	2	this	this	DET
ejpam-3502	11	3	generalization	generalization	NOUN
ejpam-3502	11	4	,	,	PUNCT
ejpam-3502	11	5	the	the	DET
ejpam-3502	11	6	idea	idea	NOUN
ejpam-3502	11	7	of	of	ADP
ejpam-3502	11	8	utilizing	utilize	VERB
ejpam-3502	11	9	two	two	NUM
ejpam-3502	11	10	or	or	CCONJ
ejpam-3502	11	11	more	more	ADJ
ejpam-3502	11	12	gts	gts	NOUN
ejpam-3502	11	13	to	to	PART
ejpam-3502	11	14	form	form	VERB
ejpam-3502	11	15	a	a	DET
ejpam-3502	11	16	new	new	ADJ
ejpam-3502	11	17	type	type	NOUN
ejpam-3502	11	18	of	of	ADP
ejpam-3502	11	19	topological	topological	ADJ
ejpam-3502	11	20	space	space	NOUN
ejpam-3502	11	21	were	be	AUX
ejpam-3502	11	22	deeply	deeply	ADV
ejpam-3502	11	23	explored	explore	VERB
ejpam-3502	11	24	in	in	ADP
ejpam-3502	11	25	many	many	ADJ
ejpam-3502	11	26	succeeding	succeed	VERB
ejpam-3502	11	27	studies	study	NOUN
ejpam-3502	11	28	.	.	PUNCT
ejpam-3502	12	1	some	some	PRON
ejpam-3502	12	2	of	of	ADP
ejpam-3502	12	3	these	these	DET
ejpam-3502	12	4	results	result	NOUN
ejpam-3502	12	5	are	be	AUX
ejpam-3502	12	6	seen	see	VERB
ejpam-3502	12	7	in	in	ADP
ejpam-3502	12	8	[	[	X
ejpam-3502	12	9	5	5	NUM
ejpam-3502	12	10	]	]	PUNCT
ejpam-3502	12	11	,	,	PUNCT
ejpam-3502	12	12	[	[	X
ejpam-3502	12	13	8	8	NUM
ejpam-3502	12	14	]	]	PUNCT
ejpam-3502	12	15	,	,	PUNCT
ejpam-3502	12	16	[	[	X
ejpam-3502	12	17	9	9	NUM
ejpam-3502	12	18	]	]	PUNCT
ejpam-3502	12	19	,	,	PUNCT
ejpam-3502	12	20	[	[	X
ejpam-3502	12	21	10	10	NUM
ejpam-3502	12	22	]	]	PUNCT
ejpam-3502	12	23	,	,	PUNCT
ejpam-3502	12	24	[	[	X
ejpam-3502	12	25	12	12	NUM
ejpam-3502	12	26	]	]	PUNCT
ejpam-3502	12	27	,	,	PUNCT
ejpam-3502	12	28	[	[	X
ejpam-3502	12	29	13	13	NUM
ejpam-3502	12	30	]	]	PUNCT
ejpam-3502	12	31	,	,	PUNCT
ejpam-3502	12	32	[	[	X
ejpam-3502	12	33	14	14	NUM
ejpam-3502	12	34	]	]	PUNCT
ejpam-3502	12	35	,	,	PUNCT
ejpam-3502	12	36	[	[	X
ejpam-3502	12	37	15	15	NUM
ejpam-3502	12	38	]	]	PUNCT
ejpam-3502	12	39	,	,	PUNCT
ejpam-3502	12	40	[	[	X
ejpam-3502	12	41	16	16	NUM
ejpam-3502	12	42	]	]	PUNCT
ejpam-3502	12	43	,	,	PUNCT
ejpam-3502	12	44	[	[	X
ejpam-3502	12	45	17	17	NUM
ejpam-3502	12	46	]	]	PUNCT
ejpam-3502	12	47	,	,	PUNCT
ejpam-3502	12	48	and	and	CCONJ
ejpam-3502	12	49	[	[	X
ejpam-3502	12	50	19	19	NUM
ejpam-3502	12	51	]	]	PUNCT
ejpam-3502	12	52	.	.	PUNCT
ejpam-3502	13	1	in	in	ADP
ejpam-3502	13	2	particular	particular	ADJ
ejpam-3502	13	3	,	,	PUNCT
ejpam-3502	13	4	∗corresponding	∗corresponde	VERB
ejpam-3502	13	5	author	author	NOUN
ejpam-3502	13	6	.	.	PUNCT
ejpam-3502	14	1	doi	doi	NOUN
ejpam-3502	14	2	:	:	PUNCT
ejpam-3502	15	1	https://doi.org/10.29020/nybg.ejpam.v12i4.3502	https://doi.org/10.29020/nybg.ejpam.v12i4.3502	VERB
ejpam-3502	15	2	email	email	NOUN
ejpam-3502	15	3	addresses	address	NOUN
ejpam-3502	15	4	:	:	PUNCT
ejpam-3502	15	5	cmrbalingit@gmail.com	cmrbalingit@gmail.com	X
ejpam-3502	15	6	(	(	PUNCT
ejpam-3502	15	7	c.	c.	PROPN
ejpam-3502	15	8	balingit	balingit	PROPN
ejpam-3502	15	9	)	)	PUNCT
ejpam-3502	15	10	,	,	PUNCT
ejpam-3502	15	11	julius.benitez@g.msuiit.edu.ph	julius.benitez@g.msuiit.edu.ph	PROPN
ejpam-3502	15	12	(	(	PUNCT
ejpam-3502	15	13	j.	j.	PROPN
ejpam-3502	15	14	benitez	benitez	PROPN
ejpam-3502	15	15	)	)	PUNCT
ejpam-3502	15	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3502	15	17	1553	1553	NUM
ejpam-3502	16	1	c	c	NOUN
ejpam-3502	16	2	©	©	PROPN
ejpam-3502	16	3	2019	2019	NUM
ejpam-3502	16	4	ejpam	ejpam	NOUN
ejpam-3502	16	5	all	all	DET
ejpam-3502	16	6	rights	right	NOUN
ejpam-3502	16	7	reserved	reserve	VERB
ejpam-3502	16	8	.	.	PUNCT
ejpam-3502	17	1	c.	c.	PROPN
ejpam-3502	17	2	balingit	balingit	PROPN
ejpam-3502	17	3	,	,	PUNCT
ejpam-3502	17	4	j.	j.	PROPN
ejpam-3502	17	5	benitez	benitez	PROPN
ejpam-3502	17	6	/	/	PUNCT
ejpam-3502	17	7	eur	eur	PROPN
ejpam-3502	17	8	.	.	PUNCT
ejpam-3502	18	1	j.	j.	PROPN
ejpam-3502	18	2	pure	pure	PROPN
ejpam-3502	18	3	appl	appl	PROPN
ejpam-3502	18	4	.	.	PROPN
ejpam-3502	18	5	math	math	PROPN
ejpam-3502	18	6	,	,	PUNCT
ejpam-3502	18	7	12	12	NUM
ejpam-3502	18	8	(	(	PUNCT
ejpam-3502	18	9	4	4	NUM
ejpam-3502	18	10	)	)	PUNCT
ejpam-3502	18	11	(	(	PUNCT
ejpam-3502	18	12	2019	2019	NUM
ejpam-3502	18	13	)	)	PUNCT
ejpam-3502	18	14	,	,	PUNCT
ejpam-3502	18	15	1553	1553	NUM
ejpam-3502	18	16	-	-	SYM
ejpam-3502	18	17	1566	1566	NUM
ejpam-3502	18	18	1554	1554	NUM
ejpam-3502	18	19	an	an	DET
ejpam-3502	18	20	n	n	ADV
ejpam-3502	18	21	-	-	PUNCT
ejpam-3502	18	22	generalized	generalize	VERB
ejpam-3502	18	23	topological	topological	ADJ
ejpam-3502	18	24	space	space	NOUN
ejpam-3502	18	25	(	(	PUNCT
ejpam-3502	18	26	briefly	briefly	ADV
ejpam-3502	18	27	,	,	PUNCT
ejpam-3502	18	28	n	n	CCONJ
ejpam-3502	18	29	-	-	PUNCT
ejpam-3502	18	30	gt	gt	PROPN
ejpam-3502	18	31	space	space	NOUN
ejpam-3502	18	32	)	)	PUNCT
ejpam-3502	18	33	is	be	AUX
ejpam-3502	18	34	defined	define	VERB
ejpam-3502	18	35	in	in	ADP
ejpam-3502	18	36	[	[	X
ejpam-3502	18	37	2	2	NUM
ejpam-3502	18	38	]	]	PUNCT
ejpam-3502	18	39	as	as	ADP
ejpam-3502	18	40	a	a	DET
ejpam-3502	18	41	pair	pair	NOUN
ejpam-3502	18	42	(	(	PUNCT
ejpam-3502	18	43	x	x	X
ejpam-3502	18	44	,	,	PUNCT
ejpam-3502	18	45	g	g	NOUN
ejpam-3502	18	46	)	)	PUNCT
ejpam-3502	18	47	,	,	PUNCT
ejpam-3502	18	48	where	where	SCONJ
ejpam-3502	18	49	x	x	PRON
ejpam-3502	18	50	is	be	AUX
ejpam-3502	18	51	a	a	DET
ejpam-3502	18	52	nonempty	nonempty	ADV
ejpam-3502	18	53	set	set	VERB
ejpam-3502	18	54	and	and	CCONJ
ejpam-3502	18	55	g	g	NOUN
ejpam-3502	18	56	=	=	PUNCT
ejpam-3502	18	57	{	{	PUNCT
ejpam-3502	18	58	µ1	µ1	PROPN
ejpam-3502	18	59	,	,	PUNCT
ejpam-3502	18	60	.	.	PUNCT
ejpam-3502	18	61	.	.	PUNCT
ejpam-3502	19	1	.	.	PUNCT
ejpam-3502	20	1	,	,	PUNCT
ejpam-3502	20	2	µn	µn	PROPN
ejpam-3502	20	3	}	}	PUNCT
ejpam-3502	20	4	is	be	AUX
ejpam-3502	20	5	a	a	DET
ejpam-3502	20	6	finite	finite	ADJ
ejpam-3502	20	7	collection	collection	NOUN
ejpam-3502	20	8	of	of	ADP
ejpam-3502	20	9	n	n	DET
ejpam-3502	20	10	gts	gts	NOUN
ejpam-3502	20	11	on	on	ADP
ejpam-3502	20	12	x	x	PRON
ejpam-3502	20	13	,	,	PUNCT
ejpam-3502	20	14	for	for	ADP
ejpam-3502	20	15	some	some	DET
ejpam-3502	20	16	n	n	PRON
ejpam-3502	20	17	∈	∈	PROPN
ejpam-3502	20	18	n.	n.	NOUN
ejpam-3502	20	19	in	in	ADP
ejpam-3502	20	20	this	this	DET
ejpam-3502	20	21	space	space	NOUN
ejpam-3502	20	22	,	,	PUNCT
ejpam-3502	20	23	the	the	DET
ejpam-3502	20	24	g	g	PROPN
ejpam-3502	20	25	-closure	-closure	NOUN
ejpam-3502	20	26	of	of	ADP
ejpam-3502	20	27	a	a	DET
ejpam-3502	20	28	⊆	⊆	NUM
ejpam-3502	20	29	x	x	NOUN
ejpam-3502	20	30	,	,	PUNCT
ejpam-3502	20	31	denoted	denote	VERB
ejpam-3502	20	32	by	by	ADP
ejpam-3502	20	33	cg	cg	NOUN
ejpam-3502	20	34	(	(	PUNCT
ejpam-3502	20	35	a	a	NOUN
ejpam-3502	20	36	)	)	PUNCT
ejpam-3502	20	37	,	,	PUNCT
ejpam-3502	20	38	is	be	AUX
ejpam-3502	20	39	the	the	DET
ejpam-3502	20	40	intersection	intersection	NOUN
ejpam-3502	20	41	of	of	ADP
ejpam-3502	20	42	all	all	DET
ejpam-3502	20	43	sets	set	NOUN
ejpam-3502	20	44	f	f	NOUN
ejpam-3502	20	45	containing	contain	VERB
ejpam-3502	20	46	a	a	DET
ejpam-3502	20	47	where	where	SCONJ
ejpam-3502	20	48	f	f	NOUN
ejpam-3502	20	49	=	=	NOUN
ejpam-3502	20	50	x	x	PROPN
ejpam-3502	20	51	\g	\g	NOUN
ejpam-3502	20	52	for	for	ADP
ejpam-3502	20	53	some	some	DET
ejpam-3502	20	54	g	g	NOUN
ejpam-3502	20	55	∈	∈	NOUN
ejpam-3502	20	56	∪nj=1µj	∪nj=1µj	ADP
ejpam-3502	20	57	while	while	SCONJ
ejpam-3502	20	58	its	its	PRON
ejpam-3502	20	59	g	g	PROPN
ejpam-3502	20	60	-interior	-interior	NOUN
ejpam-3502	20	61	,	,	PUNCT
ejpam-3502	20	62	denoted	denote	VERB
ejpam-3502	20	63	by	by	ADP
ejpam-3502	20	64	ig	ig	PROPN
ejpam-3502	20	65	(	(	PUNCT
ejpam-3502	20	66	a	a	NOUN
ejpam-3502	20	67	)	)	PUNCT
ejpam-3502	20	68	,	,	PUNCT
ejpam-3502	20	69	is	be	AUX
ejpam-3502	20	70	the	the	DET
ejpam-3502	20	71	union	union	NOUN
ejpam-3502	20	72	of	of	ADP
ejpam-3502	20	73	all	all	DET
ejpam-3502	20	74	sets	set	NOUN
ejpam-3502	20	75	g	g	NOUN
ejpam-3502	20	76	contained	contain	VERB
ejpam-3502	20	77	in	in	ADP
ejpam-3502	20	78	a	a	PRON
ejpam-3502	20	79	for	for	ADP
ejpam-3502	20	80	some	some	DET
ejpam-3502	20	81	g	g	NOUN
ejpam-3502	20	82	∈	∈	NOUN
ejpam-3502	20	83	∪nj=1µj	∪nj=1µj	X
ejpam-3502	20	84	.	.	PUNCT
ejpam-3502	21	1	consequently	consequently	ADV
ejpam-3502	21	2	,	,	PUNCT
ejpam-3502	21	3	a	a	DET
ejpam-3502	21	4	⊆	⊆	NUM
ejpam-3502	21	5	x	x	NOUN
ejpam-3502	21	6	is	be	AUX
ejpam-3502	21	7	said	say	VERB
ejpam-3502	21	8	to	to	PART
ejpam-3502	21	9	be	be	AUX
ejpam-3502	21	10	g	g	NOUN
ejpam-3502	21	11	-closed	-close	VERB
ejpam-3502	21	12	if	if	SCONJ
ejpam-3502	21	13	cg	cg	NOUN
ejpam-3502	21	14	(	(	PUNCT
ejpam-3502	21	15	a	a	NOUN
ejpam-3502	21	16	)	)	PUNCT
ejpam-3502	21	17	=	=	SYM
ejpam-3502	22	1	a	a	PRON
ejpam-3502	23	1	and	and	CCONJ
ejpam-3502	23	2	is	be	AUX
ejpam-3502	23	3	g	g	PROPN
ejpam-3502	23	4	-open	-open	ADJ
ejpam-3502	23	5	if	if	SCONJ
ejpam-3502	23	6	ig	ig	PROPN
ejpam-3502	23	7	(	(	PUNCT
ejpam-3502	23	8	a	a	NOUN
ejpam-3502	23	9	)	)	PUNCT
ejpam-3502	24	1	=	=	NOUN
ejpam-3502	24	2	a.	a.	NOUN
ejpam-3502	24	3	these	these	PRON
ejpam-3502	24	4	mentioned	mention	VERB
ejpam-3502	24	5	sets	set	NOUN
ejpam-3502	24	6	in	in	ADP
ejpam-3502	24	7	an	an	DET
ejpam-3502	24	8	n	n	CCONJ
ejpam-3502	24	9	-	-	PUNCT
ejpam-3502	24	10	gt	gt	PROPN
ejpam-3502	24	11	space	space	NOUN
ejpam-3502	24	12	naturally	naturally	ADV
ejpam-3502	24	13	satisfy	satisfy	VERB
ejpam-3502	24	14	basic	basic	ADJ
ejpam-3502	24	15	properties	property	NOUN
ejpam-3502	24	16	analogous	analogous	ADJ
ejpam-3502	24	17	to	to	ADP
ejpam-3502	24	18	that	that	PRON
ejpam-3502	24	19	of	of	ADP
ejpam-3502	24	20	a	a	DET
ejpam-3502	24	21	gt	gt	PROPN
ejpam-3502	24	22	.	.	PUNCT
ejpam-3502	25	1	most	most	ADV
ejpam-3502	25	2	relevant	relevant	ADJ
ejpam-3502	25	3	in	in	ADP
ejpam-3502	25	4	this	this	DET
ejpam-3502	25	5	paper	paper	NOUN
ejpam-3502	25	6	are	be	AUX
ejpam-3502	25	7	that	that	SCONJ
ejpam-3502	25	8	the	the	DET
ejpam-3502	25	9	arbitrary	arbitrary	ADJ
ejpam-3502	25	10	union	union	NOUN
ejpam-3502	25	11	g	g	PROPN
ejpam-3502	25	12	-open	-open	PROPN
ejpam-3502	25	13	sets	set	NOUN
ejpam-3502	25	14	is	be	AUX
ejpam-3502	25	15	also	also	ADV
ejpam-3502	25	16	g	g	NOUN
ejpam-3502	25	17	-open	-open	ADJ
ejpam-3502	25	18	and	and	CCONJ
ejpam-3502	25	19	the	the	DET
ejpam-3502	25	20	arbitrary	arbitrary	ADJ
ejpam-3502	25	21	intersection	intersection	NOUN
ejpam-3502	25	22	of	of	ADP
ejpam-3502	25	23	g	g	NOUN
ejpam-3502	25	24	-closed	-close	VERB
ejpam-3502	25	25	sets	set	NOUN
ejpam-3502	25	26	is	be	AUX
ejpam-3502	25	27	also	also	ADV
ejpam-3502	25	28	g	g	PROPN
ejpam-3502	25	29	-closed	-close	VERB
ejpam-3502	25	30	.	.	PUNCT
ejpam-3502	26	1	also	also	ADV
ejpam-3502	26	2	,	,	PUNCT
ejpam-3502	26	3	each	each	DET
ejpam-3502	26	4	µj	µj	ADJ
ejpam-3502	26	5	-	-	PUNCT
ejpam-3502	26	6	open	open	ADJ
ejpam-3502	26	7	set	set	NOUN
ejpam-3502	26	8	is	be	AUX
ejpam-3502	26	9	g	g	NOUN
ejpam-3502	26	10	-open	-open	NOUN
ejpam-3502	26	11	for	for	ADP
ejpam-3502	26	12	all	all	DET
ejpam-3502	26	13	j	j	NOUN
ejpam-3502	26	14	=	=	SYM
ejpam-3502	26	15	1	1	NUM
ejpam-3502	26	16	,	,	PUNCT
ejpam-3502	26	17	.	.	PUNCT
ejpam-3502	26	18	.	.	PUNCT
ejpam-3502	27	1	.	.	PUNCT
ejpam-3502	28	1	,	,	PUNCT
ejpam-3502	28	2	n	n	CCONJ
ejpam-3502	28	3	so	so	ADV
ejpam-3502	28	4	that	that	SCONJ
ejpam-3502	28	5	for	for	ADP
ejpam-3502	28	6	any	any	DET
ejpam-3502	28	7	g	g	NOUN
ejpam-3502	28	8	-open	-open	NOUN
ejpam-3502	28	9	set	set	VERB
ejpam-3502	28	10	a	a	PRON
ejpam-3502	28	11	,	,	PUNCT
ejpam-3502	28	12	we	we	PRON
ejpam-3502	28	13	can	can	AUX
ejpam-3502	28	14	always	always	ADV
ejpam-3502	28	15	find	find	VERB
ejpam-3502	28	16	a	a	DET
ejpam-3502	28	17	j	j	NOUN
ejpam-3502	28	18	and	and	CCONJ
ejpam-3502	28	19	a	a	DET
ejpam-3502	28	20	µj	µj	NOUN
ejpam-3502	28	21	-	-	PUNCT
ejpam-3502	28	22	open	open	ADJ
ejpam-3502	28	23	set	set	ADJ
ejpam-3502	28	24	uj	uj	NUM
ejpam-3502	29	1	such	such	ADJ
ejpam-3502	29	2	that	that	DET
ejpam-3502	29	3	uj	uj	PROPN
ejpam-3502	29	4	⊆	⊆	NUM
ejpam-3502	29	5	a.	a.	NOUN
ejpam-3502	29	6	additionally	additionally	ADV
ejpam-3502	29	7	,	,	PUNCT
ejpam-3502	29	8	by	by	ADP
ejpam-3502	29	9	definition	definition	NOUN
ejpam-3502	29	10	of	of	ADP
ejpam-3502	29	11	g	g	PROPN
ejpam-3502	29	12	-interior	-interior	NOUN
ejpam-3502	29	13	and	and	CCONJ
ejpam-3502	29	14	g	g	NOUN
ejpam-3502	29	15	-closure	-closure	NOUN
ejpam-3502	29	16	,	,	PUNCT
ejpam-3502	29	17	for	for	ADP
ejpam-3502	29	18	each	each	PRON
ejpam-3502	29	19	a	a	DET
ejpam-3502	29	20	⊆	⊆	NUM
ejpam-3502	29	21	x	x	SYM
ejpam-3502	29	22	,	,	PUNCT
ejpam-3502	29	23	we	we	PRON
ejpam-3502	29	24	have	have	VERB
ejpam-3502	29	25	ig	ig	PROPN
ejpam-3502	29	26	(	(	PUNCT
ejpam-3502	29	27	a	a	NOUN
ejpam-3502	29	28	)	)	PUNCT
ejpam-3502	29	29	⊆	⊆	PROPN
ejpam-3502	29	30	a	a	PRON
ejpam-3502	29	31	and	and	CCONJ
ejpam-3502	29	32	a	a	DET
ejpam-3502	29	33	⊆	⊆	NUM
ejpam-3502	29	34	cg	cg	NOUN
ejpam-3502	29	35	(	(	PUNCT
ejpam-3502	29	36	a	a	NOUN
ejpam-3502	29	37	)	)	PUNCT
ejpam-3502	29	38	.	.	PUNCT
ejpam-3502	30	1	on	on	ADP
ejpam-3502	30	2	a	a	DET
ejpam-3502	30	3	finer	fine	ADJ
ejpam-3502	30	4	note	note	NOUN
ejpam-3502	30	5	,	,	PUNCT
ejpam-3502	30	6	it	it	PRON
ejpam-3502	30	7	is	be	AUX
ejpam-3502	30	8	observed	observe	VERB
ejpam-3502	30	9	that	that	SCONJ
ejpam-3502	30	10	ig	ig	PROPN
ejpam-3502	30	11	(	(	PUNCT
ejpam-3502	30	12	a	a	NOUN
ejpam-3502	30	13	)	)	PUNCT
ejpam-3502	30	14	=	=	NOUN
ejpam-3502	30	15	n⋃	n⋃	PUNCT
ejpam-3502	30	16	k=1	k=1	PROPN
ejpam-3502	30	17	iµk(a	iµk(a	PROPN
ejpam-3502	30	18	)	)	PUNCT
ejpam-3502	30	19	and	and	CCONJ
ejpam-3502	30	20	cg	cg	X
ejpam-3502	30	21	(	(	PUNCT
ejpam-3502	30	22	a	a	X
ejpam-3502	30	23	)	)	PUNCT
ejpam-3502	30	24	=	=	SYM
ejpam-3502	30	25	n⋂	n⋂	NOUN
ejpam-3502	30	26	k=1	k=1	X
ejpam-3502	30	27	cµk(a	cµk(a	NOUN
ejpam-3502	30	28	)	)	PUNCT
ejpam-3502	30	29	.	.	PUNCT
ejpam-3502	31	1	functions	function	NOUN
ejpam-3502	31	2	that	that	PRON
ejpam-3502	31	3	arise	arise	VERB
ejpam-3502	31	4	from	from	ADP
ejpam-3502	31	5	these	these	DET
ejpam-3502	31	6	new	new	ADJ
ejpam-3502	31	7	spaces	space	NOUN
ejpam-3502	31	8	were	be	AUX
ejpam-3502	31	9	also	also	ADV
ejpam-3502	31	10	studied	study	VERB
ejpam-3502	31	11	in	in	ADP
ejpam-3502	31	12	detail	detail	NOUN
ejpam-3502	31	13	.	.	PUNCT
ejpam-3502	32	1	they	they	PRON
ejpam-3502	32	2	were	be	AUX
ejpam-3502	32	3	modified	modify	VERB
ejpam-3502	32	4	to	to	PART
ejpam-3502	32	5	fit	fit	VERB
ejpam-3502	32	6	the	the	DET
ejpam-3502	32	7	definition	definition	NOUN
ejpam-3502	32	8	of	of	ADP
ejpam-3502	32	9	open	open	ADJ
ejpam-3502	32	10	sets	set	NOUN
ejpam-3502	32	11	in	in	ADP
ejpam-3502	32	12	each	each	PRON
ejpam-3502	32	13	of	of	ADP
ejpam-3502	32	14	these	these	DET
ejpam-3502	32	15	domains	domain	NOUN
ejpam-3502	32	16	.	.	PUNCT
ejpam-3502	33	1	among	among	ADP
ejpam-3502	33	2	the	the	DET
ejpam-3502	33	3	popular	popular	ADJ
ejpam-3502	33	4	types	type	NOUN
ejpam-3502	33	5	of	of	ADP
ejpam-3502	33	6	functions	function	NOUN
ejpam-3502	33	7	tackled	tackle	VERB
ejpam-3502	33	8	are	be	AUX
ejpam-3502	33	9	the	the	DET
ejpam-3502	33	10	continuous	continuous	ADJ
ejpam-3502	33	11	maps	map	NOUN
ejpam-3502	33	12	,	,	PUNCT
ejpam-3502	33	13	open	open	ADJ
ejpam-3502	33	14	and	and	CCONJ
ejpam-3502	33	15	closed	closed	ADJ
ejpam-3502	33	16	maps	map	NOUN
ejpam-3502	33	17	,	,	PUNCT
ejpam-3502	33	18	as	as	ADV
ejpam-3502	33	19	well	well	ADV
ejpam-3502	33	20	as	as	ADP
ejpam-3502	33	21	homeomorphisms	homeomorphisms	PROPN
ejpam-3502	33	22	(	(	PUNCT
ejpam-3502	33	23	see	see	VERB
ejpam-3502	33	24	[	[	X
ejpam-3502	33	25	3	3	NUM
ejpam-3502	33	26	]	]	PUNCT
ejpam-3502	33	27	,	,	PUNCT
ejpam-3502	33	28	[	[	X
ejpam-3502	33	29	4	4	NUM
ejpam-3502	33	30	]	]	PUNCT
ejpam-3502	33	31	,	,	PUNCT
ejpam-3502	33	32	[	[	X
ejpam-3502	33	33	6	6	NUM
ejpam-3502	33	34	]	]	PUNCT
ejpam-3502	33	35	and	and	CCONJ
ejpam-3502	33	36	[	[	X
ejpam-3502	33	37	11	11	NUM
ejpam-3502	33	38	]	]	PUNCT
ejpam-3502	33	39	,	,	PUNCT
ejpam-3502	33	40	[	[	X
ejpam-3502	33	41	18	18	NUM
ejpam-3502	33	42	]	]	NUM
ejpam-3502	33	43	)	)	PUNCT
ejpam-3502	33	44	.	.	PUNCT
ejpam-3502	34	1	this	this	DET
ejpam-3502	34	2	paper	paper	NOUN
ejpam-3502	34	3	intends	intend	VERB
ejpam-3502	34	4	to	to	PART
ejpam-3502	34	5	examine	examine	VERB
ejpam-3502	34	6	new	new	ADJ
ejpam-3502	34	7	variations	variation	NOUN
ejpam-3502	34	8	of	of	ADP
ejpam-3502	34	9	continuity	continuity	NOUN
ejpam-3502	34	10	,	,	PUNCT
ejpam-3502	34	11	open	open	ADJ
ejpam-3502	34	12	maps	map	NOUN
ejpam-3502	34	13	and	and	CCONJ
ejpam-3502	34	14	homeomorphisms	homeomorphism	NOUN
ejpam-3502	34	15	in	in	ADP
ejpam-3502	34	16	terms	term	NOUN
ejpam-3502	34	17	of	of	ADP
ejpam-3502	34	18	n	n	CCONJ
ejpam-3502	34	19	-	-	PUNCT
ejpam-3502	34	20	gt	gt	PROPN
ejpam-3502	34	21	spaces	space	NOUN
ejpam-3502	34	22	and	and	CCONJ
ejpam-3502	34	23	to	to	PART
ejpam-3502	34	24	inquire	inquire	VERB
ejpam-3502	34	25	into	into	ADP
ejpam-3502	34	26	the	the	DET
ejpam-3502	34	27	idea	idea	NOUN
ejpam-3502	34	28	of	of	ADP
ejpam-3502	34	29	localizing	localize	VERB
ejpam-3502	34	30	these	these	DET
ejpam-3502	34	31	mappings	mapping	NOUN
ejpam-3502	34	32	to	to	ADP
ejpam-3502	34	33	the	the	DET
ejpam-3502	34	34	component	component	NOUN
ejpam-3502	34	35	gts	gts	NOUN
ejpam-3502	34	36	of	of	ADP
ejpam-3502	34	37	the	the	DET
ejpam-3502	34	38	underlying	underlying	ADJ
ejpam-3502	34	39	spaces	space	NOUN
ejpam-3502	34	40	.	.	PUNCT
ejpam-3502	35	1	2	2	X
ejpam-3502	35	2	.	.	X
ejpam-3502	35	3	g	g	PROPN
ejpam-3502	35	4	-continuous	-continuous	ADJ
ejpam-3502	35	5	functions	function	NOUN
ejpam-3502	35	6	we	we	PRON
ejpam-3502	35	7	first	first	ADV
ejpam-3502	35	8	define	define	VERB
ejpam-3502	35	9	and	and	CCONJ
ejpam-3502	35	10	establish	establish	VERB
ejpam-3502	35	11	the	the	DET
ejpam-3502	35	12	existence	existence	NOUN
ejpam-3502	35	13	of	of	ADP
ejpam-3502	35	14	g	g	PROPN
ejpam-3502	35	15	-continuous	-continuous	ADJ
ejpam-3502	35	16	maps	map	NOUN
ejpam-3502	35	17	:	:	PUNCT
ejpam-3502	35	18	definition	definition	NOUN
ejpam-3502	35	19	2.1	2.1	NUM
ejpam-3502	35	20	.	.	PUNCT
ejpam-3502	36	1	let	let	VERB
ejpam-3502	36	2	(	(	PUNCT
ejpam-3502	36	3	x	x	NOUN
ejpam-3502	36	4	,	,	PUNCT
ejpam-3502	36	5	gx	gx	PROPN
ejpam-3502	36	6	)	)	PUNCT
ejpam-3502	36	7	and	and	CCONJ
ejpam-3502	36	8	(	(	PUNCT
ejpam-3502	36	9	y	y	PROPN
ejpam-3502	36	10	,	,	PUNCT
ejpam-3502	36	11	gy	gy	NOUN
ejpam-3502	36	12	)	)	PUNCT
ejpam-3502	36	13	be	be	AUX
ejpam-3502	36	14	m	m	PROPN
ejpam-3502	36	15	-	-	PUNCT
ejpam-3502	36	16	gt	gt	PROPN
ejpam-3502	36	17	and	and	CCONJ
ejpam-3502	36	18	n	n	CCONJ
ejpam-3502	36	19	-	-	PUNCT
ejpam-3502	36	20	gt	gt	PROPN
ejpam-3502	36	21	spaces	space	NOUN
ejpam-3502	36	22	,	,	PUNCT
ejpam-3502	36	23	respectively	respectively	ADV
ejpam-3502	36	24	,	,	PUNCT
ejpam-3502	36	25	where	where	SCONJ
ejpam-3502	36	26	gx	gx	PROPN
ejpam-3502	36	27	=	=	PUNCT
ejpam-3502	36	28	{	{	PUNCT
ejpam-3502	36	29	µ1	µ1	PROPN
ejpam-3502	36	30	,	,	PUNCT
ejpam-3502	36	31	.	.	PUNCT
ejpam-3502	36	32	.	.	PUNCT
ejpam-3502	36	33	.	.	PUNCT
ejpam-3502	37	1	,	,	PUNCT
ejpam-3502	37	2	µm	µm	ADP
ejpam-3502	37	3	}	}	PUNCT
ejpam-3502	37	4	and	and	CCONJ
ejpam-3502	37	5	gy	gy	NOUN
ejpam-3502	37	6	=	=	SYM
ejpam-3502	37	7	{	{	PUNCT
ejpam-3502	37	8	ν1	ν1	NOUN
ejpam-3502	37	9	,	,	PUNCT
ejpam-3502	37	10	.	.	PUNCT
ejpam-3502	37	11	.	.	PUNCT
ejpam-3502	38	1	.	.	PUNCT
ejpam-3502	39	1	,	,	PUNCT
ejpam-3502	39	2	νn	νn	AUX
ejpam-3502	39	3	}	}	PUNCT
ejpam-3502	39	4	for	for	ADP
ejpam-3502	39	5	some	some	DET
ejpam-3502	39	6	m	m	NOUN
ejpam-3502	39	7	,	,	PUNCT
ejpam-3502	39	8	n	n	PROPN
ejpam-3502	39	9	∈	∈	PROPN
ejpam-3502	39	10	n.	n.	NOUN
ejpam-3502	39	11	a	a	DET
ejpam-3502	39	12	function	function	NOUN
ejpam-3502	39	13	f	f	NOUN
ejpam-3502	40	1	:	:	PUNCT
ejpam-3502	40	2	x	x	X
ejpam-3502	40	3	→	→	SYM
ejpam-3502	40	4	y	y	PROPN
ejpam-3502	40	5	is	be	AUX
ejpam-3502	40	6	said	say	VERB
ejpam-3502	40	7	to	to	PART
ejpam-3502	40	8	be	be	AUX
ejpam-3502	40	9	g	g	NOUN
ejpam-3502	40	10	-continuous	-continuous	ADJ
ejpam-3502	40	11	at	at	ADP
ejpam-3502	40	12	a	a	DET
ejpam-3502	40	13	point	point	NOUN
ejpam-3502	40	14	x	x	SYM
ejpam-3502	40	15	∈	∈	NOUN
ejpam-3502	40	16	x	x	INTJ
ejpam-3502	40	17	if	if	SCONJ
ejpam-3502	40	18	for	for	ADP
ejpam-3502	40	19	each	each	DET
ejpam-3502	40	20	gy	gy	NOUN
ejpam-3502	40	21	-open	-open	NOUN
ejpam-3502	40	22	set	set	VERB
ejpam-3502	40	23	v	v	NOUN
ejpam-3502	40	24	containing	contain	VERB
ejpam-3502	40	25	f(x	f(x	PROPN
ejpam-3502	40	26	)	)	PUNCT
ejpam-3502	40	27	,	,	PUNCT
ejpam-3502	40	28	there	there	PRON
ejpam-3502	40	29	exists	exist	VERB
ejpam-3502	40	30	a	a	DET
ejpam-3502	40	31	gx	gx	PROPN
ejpam-3502	40	32	-	-	PUNCT
ejpam-3502	40	33	open	open	ADJ
ejpam-3502	40	34	set	set	NOUN
ejpam-3502	40	35	u	u	NOUN
ejpam-3502	40	36	containing	contain	VERB
ejpam-3502	40	37	x	x	PUNCT
ejpam-3502	40	38	such	such	ADJ
ejpam-3502	40	39	that	that	DET
ejpam-3502	40	40	f(u	f(u	PROPN
ejpam-3502	40	41	)	)	PUNCT
ejpam-3502	40	42	⊆	⊆	NUM
ejpam-3502	40	43	v	v	NOUN
ejpam-3502	40	44	.	.	PUNCT
ejpam-3502	41	1	the	the	DET
ejpam-3502	41	2	function	function	NOUN
ejpam-3502	41	3	f	f	NOUN
ejpam-3502	41	4	:	:	PUNCT
ejpam-3502	41	5	x	x	X
ejpam-3502	41	6	→	→	SYM
ejpam-3502	41	7	y	y	PROPN
ejpam-3502	41	8	is	be	AUX
ejpam-3502	41	9	g	g	NOUN
ejpam-3502	41	10	-continuous	-continuous	ADJ
ejpam-3502	41	11	if	if	SCONJ
ejpam-3502	41	12	it	it	PRON
ejpam-3502	41	13	is	be	AUX
ejpam-3502	41	14	continuous	continuous	ADJ
ejpam-3502	41	15	at	at	ADP
ejpam-3502	41	16	all	all	DET
ejpam-3502	41	17	points	point	NOUN
ejpam-3502	41	18	x	x	X
ejpam-3502	41	19	∈	∈	PROPN
ejpam-3502	41	20	x.	x.	NOUN
ejpam-3502	41	21	example	example	NOUN
ejpam-3502	42	1	2.2	2.2	NUM
ejpam-3502	42	2	.	.	PUNCT
ejpam-3502	43	1	let	let	VERB
ejpam-3502	43	2	m	m	PRON
ejpam-3502	43	3	,	,	PUNCT
ejpam-3502	43	4	n	n	PROPN
ejpam-3502	43	5	∈	∈	PROPN
ejpam-3502	43	6	n	n	CCONJ
ejpam-3502	43	7	where	where	SCONJ
ejpam-3502	43	8	m	m	VERB
ejpam-3502	43	9	≤	≤	ADJ
ejpam-3502	43	10	n	n	CCONJ
ejpam-3502	43	11	and	and	CCONJ
ejpam-3502	43	12	consider	consider	VERB
ejpam-3502	43	13	the	the	DET
ejpam-3502	43	14	m	m	PROPN
ejpam-3502	43	15	-	-	PUNCT
ejpam-3502	43	16	gt	gt	PROPN
ejpam-3502	43	17	space	space	NOUN
ejpam-3502	43	18	(	(	PUNCT
ejpam-3502	43	19	x	x	NOUN
ejpam-3502	43	20	,	,	PUNCT
ejpam-3502	43	21	gx	gx	PROPN
ejpam-3502	43	22	)	)	PUNCT
ejpam-3502	44	1	where	where	SCONJ
ejpam-3502	44	2	x	x	X
ejpam-3502	44	3	=	=	PUNCT
ejpam-3502	45	1	[	[	X
ejpam-3502	45	2	0,m	0,m	X
ejpam-3502	45	3	]	]	X
ejpam-3502	45	4	×	×	NOUN
ejpam-3502	45	5	r+	r+	NOUN
ejpam-3502	45	6	0	0	NUM
ejpam-3502	45	7	and	and	CCONJ
ejpam-3502	45	8	gx	gx	PROPN
ejpam-3502	45	9	=	=	PROPN
ejpam-3502	45	10	{	{	PUNCT
ejpam-3502	45	11	µ1	µ1	PROPN
ejpam-3502	45	12	,	,	PUNCT
ejpam-3502	45	13	.	.	PUNCT
ejpam-3502	45	14	.	.	PUNCT
ejpam-3502	45	15	.	.	PUNCT
ejpam-3502	46	1	,	,	PUNCT
ejpam-3502	46	2	µm	µm	ADP
ejpam-3502	46	3	}	}	PUNCT
ejpam-3502	46	4	such	such	ADJ
ejpam-3502	46	5	that	that	SCONJ
ejpam-3502	46	6	µj	µj	PROPN
ejpam-3502	46	7	=	=	PUNCT
ejpam-3502	46	8	{	{	PUNCT
ejpam-3502	46	9	∅	∅	NOUN
ejpam-3502	46	10	}	}	PUNCT
ejpam-3502	46	11	∪	∪	X
ejpam-3502	46	12	{	{	PUNCT
ejpam-3502	46	13	rjs	rjs	NOUN
ejpam-3502	46	14	:	:	PUNCT
ejpam-3502	46	15	s	s	X
ejpam-3502	46	16	≥	≥	NOUN
ejpam-3502	46	17	0	0	NUM
ejpam-3502	46	18	}	}	PUNCT
ejpam-3502	46	19	with	with	ADP
ejpam-3502	46	20	rjs	rjs	NOUN
ejpam-3502	46	21	=	=	SYM
ejpam-3502	46	22	{	{	PUNCT
ejpam-3502	46	23	(	(	PUNCT
ejpam-3502	46	24	x	x	NOUN
ejpam-3502	46	25	,	,	PUNCT
ejpam-3502	46	26	y	y	PROPN
ejpam-3502	46	27	)	)	PUNCT
ejpam-3502	46	28	:	:	PUNCT
ejpam-3502	47	1	j	j	PROPN
ejpam-3502	47	2	−	−	PROPN
ejpam-3502	47	3	1	1	NUM
ejpam-3502	47	4	≤	≤	NUM
ejpam-3502	47	5	x	x	PUNCT
ejpam-3502	47	6	≤	≤	NUM
ejpam-3502	47	7	j	j	PROPN
ejpam-3502	47	8	,	,	PUNCT
ejpam-3502	47	9	y	y	PROPN
ejpam-3502	47	10	≥	≥	NUM
ejpam-3502	47	11	s	s	PART
ejpam-3502	47	12	}	}	PUNCT
ejpam-3502	47	13	,	,	PUNCT
ejpam-3502	47	14	and	and	CCONJ
ejpam-3502	47	15	the	the	DET
ejpam-3502	47	16	n	n	CCONJ
ejpam-3502	47	17	-	-	PUNCT
ejpam-3502	47	18	gt	gt	PROPN
ejpam-3502	47	19	space	space	NOUN
ejpam-3502	47	20	(	(	PUNCT
ejpam-3502	47	21	y	y	NOUN
ejpam-3502	47	22	,	,	PUNCT
ejpam-3502	47	23	gy	gy	NOUN
ejpam-3502	47	24	)	)	PUNCT
ejpam-3502	47	25	where	where	SCONJ
ejpam-3502	47	26	y	y	NOUN
ejpam-3502	47	27	=	=	PUNCT
ejpam-3502	48	1	[	[	X
ejpam-3502	48	2	0	0	NUM
ejpam-3502	48	3	,	,	PUNCT
ejpam-3502	48	4	n	n	CCONJ
ejpam-3502	48	5	]	]	PUNCT
ejpam-3502	48	6	⊆	⊆	NUM
ejpam-3502	48	7	r	r	NOUN
ejpam-3502	48	8	and	and	CCONJ
ejpam-3502	48	9	gy	gy	NOUN
ejpam-3502	48	10	=	=	SYM
ejpam-3502	48	11	{	{	PUNCT
ejpam-3502	48	12	ν1	ν1	NOUN
ejpam-3502	48	13	,	,	PUNCT
ejpam-3502	48	14	.	.	PUNCT
ejpam-3502	48	15	.	.	PUNCT
ejpam-3502	49	1	.	.	PUNCT
ejpam-3502	50	1	,	,	PUNCT
ejpam-3502	50	2	νn	νn	X
ejpam-3502	50	3	}	}	PUNCT
ejpam-3502	50	4	such	such	ADJ
ejpam-3502	50	5	that	that	DET
ejpam-3502	50	6	νk	νk	NOUN
ejpam-3502	50	7	=	=	NOUN
ejpam-3502	50	8	{	{	PUNCT
ejpam-3502	50	9	∅	∅	NOUN
ejpam-3502	50	10	}	}	PUNCT
ejpam-3502	50	11	∪	∪	X
ejpam-3502	50	12	{	{	PUNCT
ejpam-3502	50	13	[	[	X
ejpam-3502	50	14	0	0	NUM
ejpam-3502	50	15	,	,	PUNCT
ejpam-3502	50	16	t	t	PROPN
ejpam-3502	50	17	]	]	PUNCT
ejpam-3502	50	18	:	:	PUNCT
ejpam-3502	50	19	t	t	X
ejpam-3502	50	20	=	=	SYM
ejpam-3502	50	21	1	1	NUM
ejpam-3502	50	22	,	,	PUNCT
ejpam-3502	50	23	.	.	PUNCT
ejpam-3502	50	24	.	.	PUNCT
ejpam-3502	50	25	.	.	PUNCT
ejpam-3502	51	1	,	,	PUNCT
ejpam-3502	51	2	k	k	X
ejpam-3502	51	3	}	}	PUNCT
ejpam-3502	51	4	.	.	PUNCT
ejpam-3502	52	1	define	define	VERB
ejpam-3502	52	2	f	f	NOUN
ejpam-3502	52	3	:	:	PUNCT
ejpam-3502	52	4	x	x	X
ejpam-3502	52	5	→	→	PUNCT
ejpam-3502	52	6	y	y	PROPN
ejpam-3502	52	7	such	such	ADJ
ejpam-3502	52	8	that	that	PRON
ejpam-3502	52	9	(	(	PUNCT
ejpam-3502	52	10	a	a	PRON
ejpam-3502	52	11	,	,	PUNCT
ejpam-3502	52	12	b	b	NOUN
ejpam-3502	52	13	)	)	PUNCT
ejpam-3502	52	14	7→	7→	NUM
ejpam-3502	52	15	a.	a.	NOUN
ejpam-3502	52	16	for	for	ADP
ejpam-3502	52	17	each	each	DET
ejpam-3502	52	18	(	(	PUNCT
ejpam-3502	52	19	a	a	PRON
ejpam-3502	52	20	,	,	PUNCT
ejpam-3502	52	21	b	b	NOUN
ejpam-3502	52	22	)	)	PUNCT
ejpam-3502	52	23	∈	∈	PROPN
ejpam-3502	52	24	x	x	NOUN
ejpam-3502	52	25	,	,	PUNCT
ejpam-3502	52	26	there	there	PRON
ejpam-3502	52	27	is	be	VERB
ejpam-3502	52	28	a	a	DET
ejpam-3502	52	29	j0	j0	NUM
ejpam-3502	52	30	such	such	ADJ
ejpam-3502	52	31	that	that	SCONJ
ejpam-3502	52	32	j0−	j0−	NOUN
ejpam-3502	52	33	1	1	NUM
ejpam-3502	52	34	<	<	X
ejpam-3502	52	35	a	a	DET
ejpam-3502	52	36	≤	≤	PROPN
ejpam-3502	52	37	j0	j0	PROPN
ejpam-3502	52	38	and	and	CCONJ
ejpam-3502	52	39	,	,	PUNCT
ejpam-3502	52	40	therefore	therefore	ADV
ejpam-3502	52	41	,	,	PUNCT
ejpam-3502	52	42	(	(	PUNCT
ejpam-3502	52	43	a	a	PRON
ejpam-3502	52	44	,	,	PUNCT
ejpam-3502	52	45	b	b	NOUN
ejpam-3502	52	46	)	)	PUNCT
ejpam-3502	52	47	∈	∈	PROPN
ejpam-3502	52	48	rj00	rj00	PROPN
ejpam-3502	52	49	.	.	PUNCT
ejpam-3502	53	1	now	now	ADV
ejpam-3502	53	2	,	,	PUNCT
ejpam-3502	53	3	the	the	DET
ejpam-3502	53	4	gy	gy	NOUN
ejpam-3502	53	5	-open	-open	PROPN
ejpam-3502	53	6	sets	set	NOUN
ejpam-3502	53	7	containing	contain	VERB
ejpam-3502	53	8	f(a	f(a	NOUN
ejpam-3502	53	9	,	,	PUNCT
ejpam-3502	53	10	b	b	NOUN
ejpam-3502	53	11	)	)	PUNCT
ejpam-3502	53	12	=	=	NOUN
ejpam-3502	54	1	a	a	PRON
ejpam-3502	54	2	are	be	AUX
ejpam-3502	54	3	precisely	precisely	ADV
ejpam-3502	54	4	the	the	DET
ejpam-3502	54	5	intervals	interval	NOUN
ejpam-3502	54	6	[	[	X
ejpam-3502	54	7	0	0	NUM
ejpam-3502	54	8	,	,	PUNCT
ejpam-3502	54	9	t	t	PROPN
ejpam-3502	54	10	]	]	PUNCT
ejpam-3502	54	11	,	,	PUNCT
ejpam-3502	54	12	where	where	SCONJ
ejpam-3502	54	13	j0	j0	PROPN
ejpam-3502	54	14	≤	≤	PROPN
ejpam-3502	54	15	t	t	PROPN
ejpam-3502	54	16	≤	≤	NUM
ejpam-3502	54	17	n.	n.	NOUN
ejpam-3502	54	18	now	now	ADV
ejpam-3502	54	19	,	,	PUNCT
ejpam-3502	54	20	for	for	ADP
ejpam-3502	54	21	each	each	DET
ejpam-3502	54	22	t	t	PROPN
ejpam-3502	54	23	,	,	PUNCT
ejpam-3502	54	24	f(rj00	f(rj00	PROPN
ejpam-3502	54	25	)	)	PUNCT
ejpam-3502	54	26	=	=	PUNCT
ejpam-3502	55	1	[	[	X
ejpam-3502	55	2	j0	j0	NUM
ejpam-3502	55	3	−	−	PROPN
ejpam-3502	55	4	1	1	NUM
ejpam-3502	55	5	,	,	PUNCT
ejpam-3502	55	6	j0	j0	PROPN
ejpam-3502	55	7	]	]	PUNCT
ejpam-3502	55	8	⊆	⊆	NUM
ejpam-3502	55	9	[	[	X
ejpam-3502	55	10	0	0	NUM
ejpam-3502	55	11	,	,	PUNCT
ejpam-3502	55	12	t	t	PROPN
ejpam-3502	55	13	]	]	PUNCT
ejpam-3502	55	14	.	.	PUNCT
ejpam-3502	56	1	this	this	PRON
ejpam-3502	56	2	means	mean	VERB
ejpam-3502	56	3	that	that	SCONJ
ejpam-3502	56	4	f	f	PROPN
ejpam-3502	56	5	is	be	AUX
ejpam-3502	56	6	g	g	NOUN
ejpam-3502	56	7	-continuous	-continuous	ADJ
ejpam-3502	56	8	at	at	ADP
ejpam-3502	56	9	(	(	PUNCT
ejpam-3502	56	10	a	a	DET
ejpam-3502	56	11	,	,	PUNCT
ejpam-3502	56	12	b	b	NOUN
ejpam-3502	56	13	)	)	PUNCT
ejpam-3502	56	14	and	and	CCONJ
ejpam-3502	56	15	because	because	SCONJ
ejpam-3502	56	16	(	(	PUNCT
ejpam-3502	56	17	a	a	PRON
ejpam-3502	56	18	,	,	PUNCT
ejpam-3502	56	19	b	b	NOUN
ejpam-3502	56	20	)	)	PUNCT
ejpam-3502	56	21	∈	∈	PROPN
ejpam-3502	56	22	x	x	PUNCT
ejpam-3502	56	23	is	be	AUX
ejpam-3502	56	24	arbitrary	arbitrary	ADJ
ejpam-3502	56	25	,	,	PUNCT
ejpam-3502	56	26	f	f	PROPN
ejpam-3502	56	27	is	be	AUX
ejpam-3502	56	28	therefore	therefore	ADV
ejpam-3502	56	29	g	g	PROPN
ejpam-3502	56	30	-continuous	-continuous	ADJ
ejpam-3502	56	31	.	.	PUNCT
ejpam-3502	57	1	this	this	DET
ejpam-3502	57	2	type	type	NOUN
ejpam-3502	57	3	of	of	ADP
ejpam-3502	57	4	mapping	mapping	NOUN
ejpam-3502	57	5	also	also	ADV
ejpam-3502	57	6	manifests	manifest	VERB
ejpam-3502	57	7	for	for	ADP
ejpam-3502	57	8	vertex	vertex	NOUN
ejpam-3502	57	9	and	and	CCONJ
ejpam-3502	57	10	arc	arc	NOUN
ejpam-3502	57	11	sets	set	NOUN
ejpam-3502	57	12	of	of	ADP
ejpam-3502	57	13	a	a	DET
ejpam-3502	57	14	directed	direct	VERB
ejpam-3502	57	15	graph	graph	NOUN
ejpam-3502	57	16	as	as	ADP
ejpam-3502	57	17	in	in	ADP
ejpam-3502	57	18	the	the	DET
ejpam-3502	57	19	following	following	NOUN
ejpam-3502	57	20	:	:	PUNCT
ejpam-3502	57	21	c.	c.	PROPN
ejpam-3502	57	22	balingit	balingit	PROPN
ejpam-3502	57	23	,	,	PUNCT
ejpam-3502	57	24	j.	j.	PROPN
ejpam-3502	57	25	benitez	benitez	PROPN
ejpam-3502	57	26	/	/	PUNCT
ejpam-3502	57	27	eur	eur	PROPN
ejpam-3502	57	28	.	.	PUNCT
ejpam-3502	58	1	j.	j.	PROPN
ejpam-3502	58	2	pure	pure	PROPN
ejpam-3502	58	3	appl	appl	PROPN
ejpam-3502	58	4	.	.	PROPN
ejpam-3502	58	5	math	math	PROPN
ejpam-3502	58	6	,	,	PUNCT
ejpam-3502	58	7	12	12	NUM
ejpam-3502	58	8	(	(	PUNCT
ejpam-3502	58	9	4	4	NUM
ejpam-3502	58	10	)	)	PUNCT
ejpam-3502	58	11	(	(	PUNCT
ejpam-3502	58	12	2019	2019	NUM
ejpam-3502	58	13	)	)	PUNCT
ejpam-3502	58	14	,	,	PUNCT
ejpam-3502	58	15	1553	1553	NUM
ejpam-3502	58	16	-	-	SYM
ejpam-3502	58	17	1566	1566	NUM
ejpam-3502	58	18	1555	1555	NUM
ejpam-3502	58	19	example	example	NOUN
ejpam-3502	58	20	2.3	2.3	NUM
ejpam-3502	58	21	.	.	PUNCT
ejpam-3502	59	1	let	let	VERB
ejpam-3502	59	2	d	d	PRON
ejpam-3502	59	3	be	be	AUX
ejpam-3502	59	4	a	a	DET
ejpam-3502	59	5	directed	direct	VERB
ejpam-3502	59	6	graph	graph	NOUN
ejpam-3502	59	7	with	with	ADP
ejpam-3502	59	8	no	no	DET
ejpam-3502	59	9	loops	loop	NOUN
ejpam-3502	59	10	and	and	CCONJ
ejpam-3502	59	11	multiple	multiple	ADJ
ejpam-3502	59	12	edges	edge	NOUN
ejpam-3502	59	13	and	and	CCONJ
ejpam-3502	59	14	with	with	ADP
ejpam-3502	59	15	finite	finite	ADJ
ejpam-3502	59	16	vertex	vertex	NOUN
ejpam-3502	59	17	set	set	VERB
ejpam-3502	59	18	v	v	NOUN
ejpam-3502	59	19	(	(	PUNCT
ejpam-3502	59	20	d	d	NOUN
ejpam-3502	59	21	)	)	PUNCT
ejpam-3502	59	22	and	and	CCONJ
ejpam-3502	59	23	arc	arc	NOUN
ejpam-3502	59	24	set	set	VERB
ejpam-3502	59	25	e(d	e(d	PROPN
ejpam-3502	59	26	)	)	PUNCT
ejpam-3502	59	27	and	and	CCONJ
ejpam-3502	59	28	let	let	VERB
ejpam-3502	59	29	p1	p1	PROPN
ejpam-3502	59	30	,	,	PUNCT
ejpam-3502	59	31	.	.	PUNCT
ejpam-3502	59	32	.	.	PUNCT
ejpam-3502	60	1	.	.	PUNCT
ejpam-3502	61	1	,	,	PUNCT
ejpam-3502	61	2	pn	pn	PROPN
ejpam-3502	61	3	be	be	AUX
ejpam-3502	61	4	the	the	DET
ejpam-3502	61	5	distinct	distinct	ADJ
ejpam-3502	61	6	maximal	maximal	ADJ
ejpam-3502	61	7	nontrivial	nontrivial	ADJ
ejpam-3502	61	8	paths	path	NOUN
ejpam-3502	61	9	in	in	ADP
ejpam-3502	61	10	d.	d.	PROPN
ejpam-3502	61	11	for	for	ADP
ejpam-3502	61	12	each	each	PRON
ejpam-3502	61	13	j	j	PROPN
ejpam-3502	62	1	=	=	SYM
ejpam-3502	62	2	1	1	NUM
ejpam-3502	62	3	,	,	PUNCT
ejpam-3502	62	4	.	.	PUNCT
ejpam-3502	62	5	.	.	PUNCT
ejpam-3502	63	1	.	.	PUNCT
ejpam-3502	64	1	,	,	PUNCT
ejpam-3502	64	2	n	n	CCONJ
ejpam-3502	64	3	,	,	PUNCT
ejpam-3502	64	4	let	let	VERB
ejpam-3502	64	5	µj	µj	PART
ejpam-3502	64	6	be	be	AUX
ejpam-3502	64	7	a	a	DET
ejpam-3502	64	8	family	family	NOUN
ejpam-3502	64	9	of	of	ADP
ejpam-3502	64	10	subsets	subset	NOUN
ejpam-3502	64	11	of	of	ADP
ejpam-3502	64	12	v	v	NOUN
ejpam-3502	64	13	(	(	PUNCT
ejpam-3502	64	14	d	d	NOUN
ejpam-3502	64	15	)	)	PUNCT
ejpam-3502	64	16	containing	contain	VERB
ejpam-3502	64	17	precisely	precisely	ADV
ejpam-3502	64	18	the	the	DET
ejpam-3502	64	19	empty	empty	ADJ
ejpam-3502	64	20	set	set	NOUN
ejpam-3502	64	21	and	and	CCONJ
ejpam-3502	64	22	all	all	DET
ejpam-3502	64	23	subsets	subset	NOUN
ejpam-3502	64	24	of	of	ADP
ejpam-3502	64	25	v	v	NOUN
ejpam-3502	64	26	(	(	PUNCT
ejpam-3502	64	27	d	d	NOUN
ejpam-3502	64	28	)	)	PUNCT
ejpam-3502	64	29	whose	whose	DET
ejpam-3502	64	30	elements	element	NOUN
ejpam-3502	64	31	induce	induce	VERB
ejpam-3502	64	32	a	a	DET
ejpam-3502	64	33	union	union	NOUN
ejpam-3502	64	34	of	of	ADP
ejpam-3502	64	35	subpaths	subpath	NOUN
ejpam-3502	64	36	of	of	ADP
ejpam-3502	64	37	the	the	DET
ejpam-3502	64	38	maximal	maximal	ADJ
ejpam-3502	64	39	path	path	NOUN
ejpam-3502	64	40	pj	pj	PROPN
ejpam-3502	64	41	.	.	PUNCT
ejpam-3502	65	1	then	then	ADV
ejpam-3502	65	2	each	each	PRON
ejpam-3502	65	3	µj	µj	PROPN
ejpam-3502	65	4	is	be	AUX
ejpam-3502	65	5	a	a	DET
ejpam-3502	65	6	gt	gt	PROPN
ejpam-3502	65	7	on	on	ADP
ejpam-3502	65	8	v	v	NUM
ejpam-3502	65	9	(	(	PUNCT
ejpam-3502	65	10	d	d	NOUN
ejpam-3502	65	11	)	)	PUNCT
ejpam-3502	65	12	and	and	CCONJ
ejpam-3502	65	13	consequently	consequently	ADV
ejpam-3502	65	14	,	,	PUNCT
ejpam-3502	65	15	if	if	SCONJ
ejpam-3502	65	16	g	g	PROPN
ejpam-3502	65	17	=	=	SYM
ejpam-3502	65	18	{	{	PUNCT
ejpam-3502	65	19	µ1	µ1	PROPN
ejpam-3502	65	20	,	,	PUNCT
ejpam-3502	65	21	.	.	PUNCT
ejpam-3502	65	22	.	.	PUNCT
ejpam-3502	65	23	.	.	PUNCT
ejpam-3502	66	1	,	,	PUNCT
ejpam-3502	66	2	µn	µn	PROPN
ejpam-3502	66	3	}	}	PUNCT
ejpam-3502	66	4	,	,	PUNCT
ejpam-3502	66	5	then	then	ADV
ejpam-3502	66	6	(	(	PUNCT
ejpam-3502	66	7	v	v	X
ejpam-3502	66	8	(	(	PUNCT
ejpam-3502	66	9	d),g	d),g	NOUN
ejpam-3502	66	10	)	)	PUNCT
ejpam-3502	66	11	is	be	AUX
ejpam-3502	66	12	an	an	DET
ejpam-3502	66	13	n	n	CCONJ
ejpam-3502	66	14	-	-	PUNCT
ejpam-3502	66	15	gt	gt	NOUN
ejpam-3502	66	16	space	space	NOUN
ejpam-3502	66	17	.	.	PUNCT
ejpam-3502	67	1	moreover	moreover	ADV
ejpam-3502	67	2	,	,	PUNCT
ejpam-3502	67	3	for	for	ADP
ejpam-3502	67	4	each	each	PRON
ejpam-3502	67	5	k	k	NOUN
ejpam-3502	67	6	=	=	SYM
ejpam-3502	67	7	1	1	NUM
ejpam-3502	67	8	,	,	PUNCT
ejpam-3502	67	9	.	.	PUNCT
ejpam-3502	67	10	.	.	PUNCT
ejpam-3502	67	11	.	.	PUNCT
ejpam-3502	68	1	,	,	PUNCT
ejpam-3502	68	2	n	n	CCONJ
ejpam-3502	68	3	,	,	PUNCT
ejpam-3502	68	4	let	let	VERB
ejpam-3502	68	5	ek	ek	PRON
ejpam-3502	68	6	be	be	AUX
ejpam-3502	68	7	the	the	DET
ejpam-3502	68	8	collection	collection	NOUN
ejpam-3502	68	9	of	of	ADP
ejpam-3502	68	10	arcs	arc	NOUN
ejpam-3502	68	11	in	in	ADP
ejpam-3502	68	12	the	the	DET
ejpam-3502	68	13	maximal	maximal	ADJ
ejpam-3502	68	14	path	path	NOUN
ejpam-3502	68	15	pk	pk	NOUN
ejpam-3502	68	16	and	and	CCONJ
ejpam-3502	68	17	νk	νk	NOUN
ejpam-3502	68	18	=	=	VERB
ejpam-3502	68	19	p(ek	p(ek	X
ejpam-3502	68	20	)	)	PUNCT
ejpam-3502	68	21	be	be	VERB
ejpam-3502	68	22	the	the	DET
ejpam-3502	68	23	power	power	NOUN
ejpam-3502	68	24	set	set	NOUN
ejpam-3502	68	25	of	of	ADP
ejpam-3502	68	26	ek	ek	PROPN
ejpam-3502	68	27	.	.	PROPN
ejpam-3502	69	1	clearly	clearly	ADV
ejpam-3502	69	2	,	,	PUNCT
ejpam-3502	69	3	each	each	DET
ejpam-3502	69	4	νk	νk	NOUN
ejpam-3502	69	5	is	be	AUX
ejpam-3502	69	6	a	a	DET
ejpam-3502	69	7	gt	gt	PROPN
ejpam-3502	69	8	on	on	ADP
ejpam-3502	69	9	e(d	e(d	PROPN
ejpam-3502	69	10	)	)	PUNCT
ejpam-3502	69	11	and	and	CCONJ
ejpam-3502	69	12	so	so	ADV
ejpam-3502	69	13	if	if	SCONJ
ejpam-3502	69	14	we	we	PRON
ejpam-3502	69	15	put	put	VERB
ejpam-3502	69	16	ge	ge	PROPN
ejpam-3502	69	17	=	=	PRON
ejpam-3502	69	18	{	{	PUNCT
ejpam-3502	69	19	ν1	ν1	NOUN
ejpam-3502	69	20	,	,	PUNCT
ejpam-3502	69	21	.	.	PUNCT
ejpam-3502	69	22	.	.	PUNCT
ejpam-3502	70	1	.	.	PUNCT
ejpam-3502	71	1	,	,	PUNCT
ejpam-3502	71	2	νn	νn	AUX
ejpam-3502	71	3	}	}	PUNCT
ejpam-3502	71	4	,	,	PUNCT
ejpam-3502	71	5	then	then	ADV
ejpam-3502	71	6	(	(	PUNCT
ejpam-3502	71	7	e(d),ge	e(d),ge	NOUN
ejpam-3502	71	8	)	)	PUNCT
ejpam-3502	71	9	is	be	AUX
ejpam-3502	71	10	also	also	ADV
ejpam-3502	71	11	an	an	DET
ejpam-3502	71	12	n	n	NUM
ejpam-3502	71	13	-	-	PUNCT
ejpam-3502	71	14	gt	gt	NOUN
ejpam-3502	71	15	space	space	NOUN
ejpam-3502	71	16	.	.	PUNCT
ejpam-3502	72	1	define	define	VERB
ejpam-3502	72	2	ϕ	ϕ	NOUN
ejpam-3502	72	3	:	:	PUNCT
ejpam-3502	72	4	e(d)→	e(d)→	NOUN
ejpam-3502	72	5	v	v	INTJ
ejpam-3502	72	6	(	(	PUNCT
ejpam-3502	72	7	d	d	NOUN
ejpam-3502	72	8	)	)	PUNCT
ejpam-3502	72	9	such	such	ADJ
ejpam-3502	72	10	that	that	PRON
ejpam-3502	72	11	for	for	ADP
ejpam-3502	72	12	e	e	NOUN
ejpam-3502	72	13	=	=	NOUN
ejpam-3502	72	14	uv	uv	PROPN
ejpam-3502	72	15	∈	∈	PROPN
ejpam-3502	72	16	e(g	e(g	PROPN
ejpam-3502	72	17	)	)	PUNCT
ejpam-3502	72	18	,	,	PUNCT
ejpam-3502	72	19	ϕ(e	ϕ(e	PROPN
ejpam-3502	72	20	)	)	PUNCT
ejpam-3502	73	1	=	=	PUNCT
ejpam-3502	73	2	u.	u.	VERB
ejpam-3502	73	3	if	if	SCONJ
ejpam-3502	73	4	u	u	NOUN
ejpam-3502	73	5	is	be	AUX
ejpam-3502	73	6	a	a	DET
ejpam-3502	73	7	gv	gv	NOUN
ejpam-3502	73	8	-open	-open	NOUN
ejpam-3502	73	9	set	set	NOUN
ejpam-3502	73	10	containing	contain	VERB
ejpam-3502	73	11	ϕ(e	ϕ(e	PROPN
ejpam-3502	73	12	)	)	PUNCT
ejpam-3502	74	1	=	=	SYM
ejpam-3502	74	2	u	u	NOUN
ejpam-3502	74	3	,	,	PUNCT
ejpam-3502	74	4	then	then	ADV
ejpam-3502	74	5	we	we	PRON
ejpam-3502	74	6	can	can	AUX
ejpam-3502	74	7	find	find	VERB
ejpam-3502	74	8	a	a	DET
ejpam-3502	74	9	k	k	NOUN
ejpam-3502	74	10	and	and	CCONJ
ejpam-3502	74	11	a	a	DET
ejpam-3502	74	12	gk	gk	PROPN
ejpam-3502	74	13	⊆	⊆	NUM
ejpam-3502	74	14	u	u	NOUN
ejpam-3502	74	15	such	such	ADJ
ejpam-3502	74	16	that	that	SCONJ
ejpam-3502	74	17	u	u	PROPN
ejpam-3502	74	18	∈	∈	PROPN
ejpam-3502	74	19	gk	gk	PROPN
ejpam-3502	74	20	∈	∈	PROPN
ejpam-3502	74	21	µk	µk	NOUN
ejpam-3502	74	22	.	.	PUNCT
ejpam-3502	75	1	now	now	ADV
ejpam-3502	75	2	,	,	PUNCT
ejpam-3502	75	3	the	the	DET
ejpam-3502	75	4	vertices	vertex	NOUN
ejpam-3502	75	5	in	in	ADP
ejpam-3502	75	6	gk	gk	PROPN
ejpam-3502	75	7	form	form	NOUN
ejpam-3502	75	8	a	a	DET
ejpam-3502	75	9	union	union	NOUN
ejpam-3502	75	10	of	of	ADP
ejpam-3502	75	11	subpaths	subpath	NOUN
ejpam-3502	75	12	of	of	ADP
ejpam-3502	75	13	the	the	DET
ejpam-3502	75	14	maximal	maximal	ADJ
ejpam-3502	75	15	path	path	NOUN
ejpam-3502	75	16	pk	pk	NOUN
ejpam-3502	75	17	and	and	CCONJ
ejpam-3502	75	18	with	with	ADP
ejpam-3502	75	19	arcs	arc	NOUN
ejpam-3502	75	20	from	from	ADP
ejpam-3502	75	21	ek	ek	PROPN
ejpam-3502	75	22	.	.	PUNCT
ejpam-3502	76	1	let	let	AUX
ejpam-3502	76	2	e∗k	e∗k	VERB
ejpam-3502	76	3	be	be	AUX
ejpam-3502	76	4	the	the	DET
ejpam-3502	76	5	collection	collection	NOUN
ejpam-3502	76	6	of	of	ADP
ejpam-3502	76	7	arcs	arc	NOUN
ejpam-3502	76	8	formed	form	VERB
ejpam-3502	76	9	by	by	ADP
ejpam-3502	76	10	the	the	DET
ejpam-3502	76	11	vertices	vertex	NOUN
ejpam-3502	76	12	in	in	ADP
ejpam-3502	76	13	gk	gk	PROPN
ejpam-3502	76	14	.	.	PUNCT
ejpam-3502	77	1	by	by	ADP
ejpam-3502	77	2	the	the	DET
ejpam-3502	77	3	definition	definition	NOUN
ejpam-3502	77	4	of	of	ADP
ejpam-3502	77	5	ge	ge	PROPN
ejpam-3502	77	6	,	,	PUNCT
ejpam-3502	77	7	e∗k	e∗k	PROPN
ejpam-3502	77	8	∈	∈	PROPN
ejpam-3502	77	9	νk	νk	NOUN
ejpam-3502	78	1	and	and	CCONJ
ejpam-3502	78	2	so	so	ADV
ejpam-3502	78	3	it	it	PRON
ejpam-3502	78	4	is	be	AUX
ejpam-3502	78	5	ge	ge	NOUN
ejpam-3502	78	6	-	-	VERB
ejpam-3502	78	7	open	open	ADJ
ejpam-3502	78	8	,	,	PUNCT
ejpam-3502	78	9	with	with	ADP
ejpam-3502	78	10	ϕ(e∗k	ϕ(e∗k	PROPN
ejpam-3502	78	11	)	)	PUNCT
ejpam-3502	78	12	⊆	⊆	NUM
ejpam-3502	78	13	gk	gk	PROPN
ejpam-3502	78	14	⊆	⊆	NUM
ejpam-3502	78	15	u	u	NOUN
ejpam-3502	78	16	.	.	PUNCT
ejpam-3502	79	1	this	this	PRON
ejpam-3502	79	2	implies	imply	VERB
ejpam-3502	79	3	that	that	SCONJ
ejpam-3502	79	4	ϕ	ϕ	NOUN
ejpam-3502	79	5	is	be	AUX
ejpam-3502	79	6	g	g	NOUN
ejpam-3502	79	7	-continuous	-continuous	ADJ
ejpam-3502	79	8	on	on	ADP
ejpam-3502	79	9	e	e	PROPN
ejpam-3502	79	10	∈	∈	PROPN
ejpam-3502	79	11	e(d	e(d	PROPN
ejpam-3502	79	12	)	)	PUNCT
ejpam-3502	79	13	.	.	PUNCT
ejpam-3502	80	1	by	by	ADP
ejpam-3502	80	2	the	the	DET
ejpam-3502	80	3	arbitrary	arbitrary	ADJ
ejpam-3502	80	4	nature	nature	NOUN
ejpam-3502	80	5	of	of	ADP
ejpam-3502	80	6	e	e	PROPN
ejpam-3502	80	7	,	,	PUNCT
ejpam-3502	80	8	ϕ	ϕ	PROPN
ejpam-3502	80	9	is	be	AUX
ejpam-3502	80	10	g	g	NOUN
ejpam-3502	80	11	-continuous	-continuous	ADJ
ejpam-3502	80	12	.	.	PUNCT
ejpam-3502	81	1	in	in	ADP
ejpam-3502	81	2	the	the	DET
ejpam-3502	81	3	succeeding	succeed	VERB
ejpam-3502	81	4	discussions	discussion	NOUN
ejpam-3502	81	5	,	,	PUNCT
ejpam-3502	81	6	we	we	PRON
ejpam-3502	81	7	assume	assume	VERB
ejpam-3502	81	8	that	that	SCONJ
ejpam-3502	81	9	(	(	PUNCT
ejpam-3502	81	10	x	x	NOUN
ejpam-3502	81	11	,	,	PUNCT
ejpam-3502	81	12	gx	gx	PROPN
ejpam-3502	81	13	)	)	PUNCT
ejpam-3502	81	14	and	and	CCONJ
ejpam-3502	81	15	(	(	PUNCT
ejpam-3502	81	16	y	y	PROPN
ejpam-3502	81	17	,	,	PUNCT
ejpam-3502	81	18	gy	gy	NOUN
ejpam-3502	81	19	)	)	PUNCT
ejpam-3502	81	20	are	be	AUX
ejpam-3502	81	21	m	m	PROPN
ejpam-3502	81	22	-	-	PUNCT
ejpam-3502	81	23	gt	gt	PROPN
ejpam-3502	81	24	and	and	CCONJ
ejpam-3502	81	25	n	n	CCONJ
ejpam-3502	81	26	-	-	PUNCT
ejpam-3502	81	27	gt	gt	PROPN
ejpam-3502	81	28	spaces	space	NOUN
ejpam-3502	81	29	,	,	PUNCT
ejpam-3502	81	30	respectively	respectively	ADV
ejpam-3502	81	31	,	,	PUNCT
ejpam-3502	81	32	where	where	SCONJ
ejpam-3502	81	33	gx	gx	PROPN
ejpam-3502	81	34	=	=	PUNCT
ejpam-3502	81	35	{	{	PUNCT
ejpam-3502	81	36	µ1	µ1	PROPN
ejpam-3502	81	37	,	,	PUNCT
ejpam-3502	81	38	.	.	PUNCT
ejpam-3502	81	39	.	.	PUNCT
ejpam-3502	82	1	.	.	PUNCT
ejpam-3502	83	1	,	,	PUNCT
ejpam-3502	83	2	µm	µm	ADP
ejpam-3502	83	3	}	}	PUNCT
ejpam-3502	83	4	and	and	CCONJ
ejpam-3502	83	5	gy	gy	NOUN
ejpam-3502	83	6	=	=	SYM
ejpam-3502	83	7	{	{	PUNCT
ejpam-3502	83	8	ν1	ν1	NOUN
ejpam-3502	83	9	,	,	PUNCT
ejpam-3502	83	10	.	.	PUNCT
ejpam-3502	83	11	.	.	PUNCT
ejpam-3502	84	1	.	.	PUNCT
ejpam-3502	85	1	,	,	PUNCT
ejpam-3502	85	2	νn	νn	AUX
ejpam-3502	85	3	}	}	PUNCT
ejpam-3502	85	4	for	for	ADP
ejpam-3502	85	5	some	some	DET
ejpam-3502	85	6	m	m	NOUN
ejpam-3502	85	7	,	,	PUNCT
ejpam-3502	85	8	n	n	PROPN
ejpam-3502	85	9	∈	∈	PROPN
ejpam-3502	85	10	n	n	NOUN
ejpam-3502	85	11	and	and	CCONJ
ejpam-3502	85	12	adapt	adapt	VERB
ejpam-3502	85	13	the	the	DET
ejpam-3502	85	14	notations	notation	NOUN
ejpam-3502	85	15	u	u	NOUN
ejpam-3502	85	16	=	=	NOUN
ejpam-3502	86	1	m⋃	m⋃	NOUN
ejpam-3502	86	2	j=1	j=1	PROPN
ejpam-3502	86	3	µj	µj	PROPN
ejpam-3502	86	4	and	and	CCONJ
ejpam-3502	86	5	v	v	NOUN
ejpam-3502	86	6	=	=	PUNCT
ejpam-3502	86	7	n⋃	n⋃	X
ejpam-3502	86	8	k=1	k=1	X
ejpam-3502	86	9	νk	νk	X
ejpam-3502	86	10	.	.	NOUN
ejpam-3502	87	1	for	for	ADP
ejpam-3502	87	2	convenience	convenience	NOUN
ejpam-3502	87	3	,	,	PUNCT
ejpam-3502	87	4	we	we	PRON
ejpam-3502	87	5	also	also	ADV
ejpam-3502	87	6	adapt	adapt	VERB
ejpam-3502	87	7	the	the	DET
ejpam-3502	87	8	notations	notation	NOUN
ejpam-3502	87	9	cx(a	cx(a	NOUN
ejpam-3502	87	10	)	)	PUNCT
ejpam-3502	87	11	and	and	CCONJ
ejpam-3502	87	12	ix(a	ix(a	NOUN
ejpam-3502	87	13	)	)	PUNCT
ejpam-3502	87	14	to	to	PART
ejpam-3502	87	15	signify	signify	VERB
ejpam-3502	87	16	the	the	DET
ejpam-3502	87	17	gx	gx	PROPN
ejpam-3502	87	18	-closure	-closure	PROPN
ejpam-3502	87	19	and	and	CCONJ
ejpam-3502	87	20	gx	gx	PROPN
ejpam-3502	87	21	-interior	-interior	NOUN
ejpam-3502	87	22	whenever	whenever	SCONJ
ejpam-3502	87	23	a	a	DET
ejpam-3502	87	24	⊆	⊆	NUM
ejpam-3502	87	25	x.	x.	NOUN
ejpam-3502	87	26	theorem	theorem	VERB
ejpam-3502	87	27	2.4	2.4	NUM
ejpam-3502	87	28	.	.	PUNCT
ejpam-3502	88	1	a	a	DET
ejpam-3502	88	2	function	function	NOUN
ejpam-3502	88	3	f	f	NOUN
ejpam-3502	88	4	:	:	PUNCT
ejpam-3502	88	5	x	x	X
ejpam-3502	88	6	→	→	SYM
ejpam-3502	88	7	y	y	PROPN
ejpam-3502	88	8	is	be	AUX
ejpam-3502	88	9	g	g	NOUN
ejpam-3502	88	10	-continuous	-continuous	ADJ
ejpam-3502	88	11	if	if	SCONJ
ejpam-3502	88	12	and	and	CCONJ
ejpam-3502	88	13	only	only	ADV
ejpam-3502	88	14	if	if	SCONJ
ejpam-3502	88	15	f−1(v	f−1(v	PROPN
ejpam-3502	88	16	)	)	PUNCT
ejpam-3502	88	17	is	be	AUX
ejpam-3502	88	18	gx	gx	PROPN
ejpam-3502	88	19	-	-	PUNCT
ejpam-3502	88	20	open	open	ADJ
ejpam-3502	88	21	for	for	SCONJ
ejpam-3502	88	22	every	every	DET
ejpam-3502	88	23	gy	gy	NOUN
ejpam-3502	88	24	-open	-open	NOUN
ejpam-3502	88	25	set	set	VERB
ejpam-3502	88	26	v	v	NOUN
ejpam-3502	88	27	.	.	PUNCT
ejpam-3502	89	1	proof	proof	NOUN
ejpam-3502	89	2	.	.	PUNCT
ejpam-3502	90	1	if	if	SCONJ
ejpam-3502	90	2	v	v	NOUN
ejpam-3502	90	3	is	be	AUX
ejpam-3502	90	4	a	a	DET
ejpam-3502	90	5	gy	gy	NOUN
ejpam-3502	90	6	-open	-open	NOUN
ejpam-3502	90	7	set	set	NOUN
ejpam-3502	90	8	and	and	CCONJ
ejpam-3502	90	9	x	x	PART
ejpam-3502	90	10	∈	∈	PROPN
ejpam-3502	90	11	f−1(v	f−1(v	NOUN
ejpam-3502	90	12	)	)	PUNCT
ejpam-3502	90	13	,	,	PUNCT
ejpam-3502	90	14	then	then	ADV
ejpam-3502	90	15	f(x	f(x	PROPN
ejpam-3502	90	16	)	)	PUNCT
ejpam-3502	90	17	∈	∈	PROPN
ejpam-3502	90	18	v	v	NOUN
ejpam-3502	90	19	and	and	CCONJ
ejpam-3502	90	20	since	since	SCONJ
ejpam-3502	90	21	f	f	PROPN
ejpam-3502	90	22	is	be	AUX
ejpam-3502	90	23	g	g	PROPN
ejpam-3502	90	24	-continuous	-continuous	ADJ
ejpam-3502	90	25	,	,	PUNCT
ejpam-3502	90	26	we	we	PRON
ejpam-3502	90	27	can	can	AUX
ejpam-3502	90	28	find	find	VERB
ejpam-3502	90	29	a	a	DET
ejpam-3502	90	30	gx	gx	PROPN
ejpam-3502	90	31	-open	-open	NOUN
ejpam-3502	90	32	set	set	VERB
ejpam-3502	90	33	ux	ux	NOUN
ejpam-3502	90	34	containing	contain	VERB
ejpam-3502	90	35	x	x	PUNCT
ejpam-3502	90	36	such	such	ADJ
ejpam-3502	90	37	that	that	SCONJ
ejpam-3502	90	38	f(ux	f(ux	NOUN
ejpam-3502	90	39	)	)	PUNCT
ejpam-3502	90	40	⊆	⊆	NUM
ejpam-3502	90	41	v	v	NOUN
ejpam-3502	90	42	.	.	PUNCT
ejpam-3502	91	1	consequently	consequently	ADV
ejpam-3502	91	2	,	,	PUNCT
ejpam-3502	91	3	ux	ux	PROPN
ejpam-3502	91	4	⊆	⊆	NUM
ejpam-3502	91	5	f−1(v	f−1(v	NOUN
ejpam-3502	91	6	)	)	PUNCT
ejpam-3502	91	7	and	and	CCONJ
ejpam-3502	91	8	so	so	ADV
ejpam-3502	91	9	f−1(v	f−1(v	PROPN
ejpam-3502	91	10	)	)	PUNCT
ejpam-3502	92	1	⊆	⊆	NUM
ejpam-3502	92	2	⋃	⋃	PROPN
ejpam-3502	92	3	x∈f−1(v	x∈f−1(v	PROPN
ejpam-3502	92	4	)	)	PUNCT
ejpam-3502	92	5	ux	ux	PROPN
ejpam-3502	92	6	⊆	⊆	NUM
ejpam-3502	92	7	f−1(v	f−1(v	NOUN
ejpam-3502	92	8	)	)	PUNCT
ejpam-3502	92	9	.	.	PUNCT
ejpam-3502	93	1	hence	hence	ADV
ejpam-3502	93	2	,	,	PUNCT
ejpam-3502	93	3	f−1(v	f−1(v	PROPN
ejpam-3502	93	4	)	)	PUNCT
ejpam-3502	94	1	=	=	PUNCT
ejpam-3502	94	2	⋃	⋃	PROPN
ejpam-3502	94	3	x∈f−1(v	x∈f−1(v	X
ejpam-3502	94	4	)	)	PUNCT
ejpam-3502	95	1	ux	ux	PROPN
ejpam-3502	95	2	is	be	AUX
ejpam-3502	95	3	gx	gx	PROPN
ejpam-3502	95	4	-open	-open	NOUN
ejpam-3502	95	5	.	.	PUNCT
ejpam-3502	96	1	conversely	conversely	ADV
ejpam-3502	96	2	,	,	PUNCT
ejpam-3502	96	3	if	if	SCONJ
ejpam-3502	96	4	x	x	SYM
ejpam-3502	96	5	∈	∈	PROPN
ejpam-3502	96	6	x	x	X
ejpam-3502	96	7	and	and	CCONJ
ejpam-3502	96	8	v	v	NOUN
ejpam-3502	96	9	is	be	AUX
ejpam-3502	96	10	a	a	DET
ejpam-3502	96	11	gy	gy	NOUN
ejpam-3502	96	12	-open	-open	NOUN
ejpam-3502	96	13	set	set	NOUN
ejpam-3502	96	14	containing	contain	VERB
ejpam-3502	96	15	f(x	f(x	PROPN
ejpam-3502	96	16	)	)	PUNCT
ejpam-3502	96	17	,	,	PUNCT
ejpam-3502	96	18	then	then	ADV
ejpam-3502	96	19	u	u	X
ejpam-3502	96	20	=	=	PROPN
ejpam-3502	96	21	f−1(v	f−1(v	PROPN
ejpam-3502	96	22	)	)	PUNCT
ejpam-3502	96	23	is	be	AUX
ejpam-3502	96	24	a	a	DET
ejpam-3502	96	25	gx	gx	PROPN
ejpam-3502	96	26	open	open	ADJ
ejpam-3502	96	27	set	set	NOUN
ejpam-3502	96	28	containing	contain	VERB
ejpam-3502	96	29	x	x	PUNCT
ejpam-3502	96	30	such	such	ADJ
ejpam-3502	96	31	that	that	DET
ejpam-3502	96	32	f(u	f(u	PROPN
ejpam-3502	96	33	)	)	PUNCT
ejpam-3502	96	34	=	=	SYM
ejpam-3502	96	35	v	v	NOUN
ejpam-3502	96	36	.	.	PUNCT
ejpam-3502	97	1	since	since	SCONJ
ejpam-3502	97	2	x	x	PRON
ejpam-3502	97	3	is	be	AUX
ejpam-3502	97	4	arbitrary	arbitrary	ADJ
ejpam-3502	97	5	,	,	PUNCT
ejpam-3502	97	6	we	we	PRON
ejpam-3502	97	7	see	see	VERB
ejpam-3502	97	8	that	that	SCONJ
ejpam-3502	97	9	f	f	PROPN
ejpam-3502	97	10	is	be	AUX
ejpam-3502	97	11	continuous	continuous	ADJ
ejpam-3502	97	12	.	.	PUNCT
ejpam-3502	98	1	�	�	PROPN
ejpam-3502	98	2	a	a	DET
ejpam-3502	98	3	g	g	PROPN
ejpam-3502	98	4	-continuous	-continuous	ADJ
ejpam-3502	98	5	map	map	NOUN
ejpam-3502	98	6	also	also	ADV
ejpam-3502	98	7	satisfy	satisfy	VERB
ejpam-3502	98	8	the	the	DET
ejpam-3502	98	9	following	follow	VERB
ejpam-3502	98	10	properties	property	NOUN
ejpam-3502	98	11	which	which	PRON
ejpam-3502	98	12	are	be	AUX
ejpam-3502	98	13	analogous	analogous	ADJ
ejpam-3502	98	14	to	to	ADP
ejpam-3502	98	15	that	that	PRON
ejpam-3502	98	16	of	of	ADP
ejpam-3502	98	17	a	a	DET
ejpam-3502	98	18	continuous	continuous	ADJ
ejpam-3502	98	19	map	map	NOUN
ejpam-3502	98	20	as	as	ADP
ejpam-3502	98	21	in	in	ADP
ejpam-3502	98	22	[	[	X
ejpam-3502	98	23	7	7	NUM
ejpam-3502	98	24	]	]	NUM
ejpam-3502	98	25	:	:	PUNCT
ejpam-3502	98	26	theorem	theorem	VERB
ejpam-3502	98	27	2.5	2.5	NUM
ejpam-3502	98	28	.	.	PUNCT
ejpam-3502	99	1	let	let	VERB
ejpam-3502	99	2	f	f	NOUN
ejpam-3502	99	3	:	:	PUNCT
ejpam-3502	99	4	x	x	X
ejpam-3502	99	5	→	→	SYM
ejpam-3502	99	6	y	y	X
ejpam-3502	99	7	be	be	AUX
ejpam-3502	99	8	a	a	DET
ejpam-3502	99	9	map	map	NOUN
ejpam-3502	99	10	.	.	PUNCT
ejpam-3502	100	1	then	then	ADV
ejpam-3502	100	2	the	the	DET
ejpam-3502	100	3	following	follow	VERB
ejpam-3502	100	4	statements	statement	NOUN
ejpam-3502	100	5	are	be	AUX
ejpam-3502	100	6	equivalent	equivalent	ADJ
ejpam-3502	100	7	:	:	PUNCT
ejpam-3502	100	8	1	1	X
ejpam-3502	100	9	.	.	X
ejpam-3502	100	10	f	f	PROPN
ejpam-3502	100	11	is	be	AUX
ejpam-3502	100	12	g	g	NOUN
ejpam-3502	100	13	-continuous	-continuous	ADJ
ejpam-3502	100	14	;	;	PUNCT
ejpam-3502	100	15	2	2	X
ejpam-3502	100	16	.	.	X
ejpam-3502	100	17	f−1(b	f−1(b	PROPN
ejpam-3502	100	18	)	)	PUNCT
ejpam-3502	100	19	is	be	AUX
ejpam-3502	100	20	gx	gx	PROPN
ejpam-3502	100	21	-	-	PUNCT
ejpam-3502	100	22	closed	closed	ADJ
ejpam-3502	100	23	for	for	ADP
ejpam-3502	100	24	each	each	DET
ejpam-3502	100	25	gy	gy	NOUN
ejpam-3502	100	26	-closed	-close	VERB
ejpam-3502	100	27	set	set	NOUN
ejpam-3502	100	28	b	b	NOUN
ejpam-3502	100	29	;	;	PUNCT
ejpam-3502	100	30	3	3	NUM
ejpam-3502	100	31	.	.	PUNCT
ejpam-3502	100	32	f(cx(a	f(cx(a	NOUN
ejpam-3502	100	33	)	)	PUNCT
ejpam-3502	100	34	)	)	PUNCT
ejpam-3502	101	1	⊆	⊆	NUM
ejpam-3502	101	2	cy	cy	PROPN
ejpam-3502	101	3	(	(	PUNCT
ejpam-3502	101	4	f(a	f(a	NOUN
ejpam-3502	101	5	)	)	PUNCT
ejpam-3502	101	6	)	)	PUNCT
ejpam-3502	101	7	for	for	ADP
ejpam-3502	101	8	any	any	DET
ejpam-3502	101	9	a	a	DET
ejpam-3502	101	10	⊆	⊆	NUM
ejpam-3502	101	11	x	x	NOUN
ejpam-3502	101	12	;	;	PUNCT
ejpam-3502	101	13	and	and	CCONJ
ejpam-3502	101	14	4	4	X
ejpam-3502	101	15	.	.	X
ejpam-3502	101	16	cx	cx	PROPN
ejpam-3502	101	17	(	(	PUNCT
ejpam-3502	101	18	f−1(b	f−1(b	PROPN
ejpam-3502	101	19	)	)	PUNCT
ejpam-3502	101	20	)	)	PUNCT
ejpam-3502	102	1	⊆	⊆	NUM
ejpam-3502	102	2	f−1(cy	f−1(cy	NOUN
ejpam-3502	102	3	(	(	PUNCT
ejpam-3502	102	4	b	b	NOUN
ejpam-3502	102	5	)	)	PUNCT
ejpam-3502	102	6	)	)	PUNCT
ejpam-3502	102	7	for	for	ADP
ejpam-3502	102	8	any	any	DET
ejpam-3502	102	9	b	b	PROPN
ejpam-3502	102	10	⊆	⊆	NUM
ejpam-3502	102	11	y	y	PROPN
ejpam-3502	102	12	.	.	PUNCT
ejpam-3502	103	1	c.	c.	PROPN
ejpam-3502	103	2	balingit	balingit	PROPN
ejpam-3502	103	3	,	,	PUNCT
ejpam-3502	103	4	j.	j.	PROPN
ejpam-3502	103	5	benitez	benitez	PROPN
ejpam-3502	103	6	/	/	PUNCT
ejpam-3502	103	7	eur	eur	PROPN
ejpam-3502	103	8	.	.	PUNCT
ejpam-3502	104	1	j.	j.	PROPN
ejpam-3502	104	2	pure	pure	PROPN
ejpam-3502	104	3	appl	appl	PROPN
ejpam-3502	104	4	.	.	PROPN
ejpam-3502	104	5	math	math	PROPN
ejpam-3502	104	6	,	,	PUNCT
ejpam-3502	104	7	12	12	NUM
ejpam-3502	104	8	(	(	PUNCT
ejpam-3502	104	9	4	4	NUM
ejpam-3502	104	10	)	)	PUNCT
ejpam-3502	104	11	(	(	PUNCT
ejpam-3502	104	12	2019	2019	NUM
ejpam-3502	104	13	)	)	PUNCT
ejpam-3502	104	14	,	,	PUNCT
ejpam-3502	104	15	1553	1553	NUM
ejpam-3502	104	16	-	-	SYM
ejpam-3502	104	17	1566	1566	NUM
ejpam-3502	104	18	1556	1556	NUM
ejpam-3502	104	19	remark	remark	NOUN
ejpam-3502	104	20	2.6	2.6	NUM
ejpam-3502	104	21	.	.	PUNCT
ejpam-3502	105	1	if	if	SCONJ
ejpam-3502	105	2	f	f	PROPN
ejpam-3502	105	3	:	:	PUNCT
ejpam-3502	105	4	x	x	X
ejpam-3502	105	5	→	→	SYM
ejpam-3502	105	6	y	y	PROPN
ejpam-3502	105	7	is	be	AUX
ejpam-3502	105	8	a	a	DET
ejpam-3502	105	9	g	g	NOUN
ejpam-3502	105	10	-continuous	-continuous	ADJ
ejpam-3502	105	11	map	map	NOUN
ejpam-3502	105	12	such	such	ADJ
ejpam-3502	105	13	that	that	SCONJ
ejpam-3502	105	14	f(x	f(x	PROPN
ejpam-3502	105	15	)	)	PUNCT
ejpam-3502	105	16	∈	∈	PROPN
ejpam-3502	105	17	⋃	⋃	NOUN
ejpam-3502	105	18	g∈v	g∈v	NOUN
ejpam-3502	105	19	g	g	NOUN
ejpam-3502	105	20	,	,	PUNCT
ejpam-3502	105	21	then	then	ADV
ejpam-3502	105	22	(	(	PUNCT
ejpam-3502	105	23	x	x	X
ejpam-3502	105	24	,	,	PUNCT
ejpam-3502	105	25	gx	gx	PROPN
ejpam-3502	105	26	)	)	PUNCT
ejpam-3502	105	27	is	be	AUX
ejpam-3502	105	28	strong	strong	ADJ
ejpam-3502	105	29	.	.	PUNCT
ejpam-3502	106	1	this	this	PRON
ejpam-3502	106	2	is	be	AUX
ejpam-3502	106	3	so	so	ADV
ejpam-3502	106	4	since	since	SCONJ
ejpam-3502	106	5	for	for	ADP
ejpam-3502	106	6	each	each	DET
ejpam-3502	106	7	x	x	SYM
ejpam-3502	106	8	∈	∈	PROPN
ejpam-3502	106	9	x	x	PUNCT
ejpam-3502	106	10	there	there	PRON
ejpam-3502	106	11	is	be	VERB
ejpam-3502	106	12	a	a	DET
ejpam-3502	106	13	gy	gy	NOUN
ejpam-3502	106	14	-open	-open	NOUN
ejpam-3502	106	15	set	set	VERB
ejpam-3502	106	16	v	v	NOUN
ejpam-3502	106	17	containing	contain	VERB
ejpam-3502	106	18	f(x	f(x	PROPN
ejpam-3502	106	19	)	)	PUNCT
ejpam-3502	106	20	and	and	CCONJ
ejpam-3502	106	21	consequently	consequently	ADV
ejpam-3502	106	22	a	a	DET
ejpam-3502	106	23	corresponding	correspond	VERB
ejpam-3502	106	24	ux	ux	NOUN
ejpam-3502	106	25	containing	contain	VERB
ejpam-3502	106	26	x	x	PUNCT
ejpam-3502	106	27	such	such	ADJ
ejpam-3502	106	28	that	that	SCONJ
ejpam-3502	106	29	f(ux	f(ux	NOUN
ejpam-3502	106	30	)	)	PUNCT
ejpam-3502	106	31	⊆	⊆	NUM
ejpam-3502	106	32	v	v	NOUN
ejpam-3502	106	33	.	.	PUNCT
ejpam-3502	107	1	this	this	PRON
ejpam-3502	107	2	indicates	indicate	VERB
ejpam-3502	107	3	that	that	SCONJ
ejpam-3502	107	4	x	x	PROPN
ejpam-3502	107	5	⊆	⊆	NUM
ejpam-3502	107	6	⋃	⋃	NOUN
ejpam-3502	107	7	x∈x	x∈x	NOUN
ejpam-3502	107	8	ux	ux	NOUN
ejpam-3502	107	9	⊆	⊆	NUM
ejpam-3502	107	10	x	x	PUNCT
ejpam-3502	107	11	and	and	CCONJ
ejpam-3502	107	12	(	(	PUNCT
ejpam-3502	107	13	x	x	NOUN
ejpam-3502	107	14	,	,	PUNCT
ejpam-3502	107	15	gx	gx	PROPN
ejpam-3502	107	16	)	)	PUNCT
ejpam-3502	107	17	is	be	AUX
ejpam-3502	107	18	therefore	therefore	ADV
ejpam-3502	107	19	strong	strong	ADJ
ejpam-3502	107	20	.	.	PUNCT
ejpam-3502	108	1	the	the	DET
ejpam-3502	108	2	notion	notion	NOUN
ejpam-3502	108	3	of	of	ADP
ejpam-3502	108	4	a	a	DET
ejpam-3502	108	5	(	(	PUNCT
ejpam-3502	108	6	µ	µ	NOUN
ejpam-3502	108	7	,	,	PUNCT
ejpam-3502	108	8	ν)(j	ν)(j	ADJ
ejpam-3502	108	9	,	,	PUNCT
ejpam-3502	108	10	k)-continuous	k)-continuous	ADJ
ejpam-3502	108	11	map	map	NOUN
ejpam-3502	108	12	,	,	PUNCT
ejpam-3502	108	13	where	where	SCONJ
ejpam-3502	108	14	j	j	PROPN
ejpam-3502	108	15	,	,	PUNCT
ejpam-3502	108	16	k	k	PROPN
ejpam-3502	108	17	=	=	SYM
ejpam-3502	108	18	1	1	NUM
ejpam-3502	108	19	,	,	PUNCT
ejpam-3502	108	20	2	2	NUM
ejpam-3502	108	21	are	be	AUX
ejpam-3502	108	22	distinct	distinct	ADJ
ejpam-3502	108	23	,	,	PUNCT
ejpam-3502	108	24	analogously	analogously	ADV
ejpam-3502	108	25	defined	define	VERB
ejpam-3502	108	26	for	for	ADP
ejpam-3502	108	27	a	a	DET
ejpam-3502	108	28	bigeneralized	bigeneralize	VERB
ejpam-3502	108	29	topological	topological	ADJ
ejpam-3502	108	30	space	space	NOUN
ejpam-3502	108	31	seen	see	VERB
ejpam-3502	108	32	in	in	ADP
ejpam-3502	108	33	[	[	X
ejpam-3502	108	34	6	6	NUM
ejpam-3502	108	35	]	]	PUNCT
ejpam-3502	108	36	,	,	PUNCT
ejpam-3502	108	37	may	may	AUX
ejpam-3502	108	38	be	be	AUX
ejpam-3502	108	39	extended	extend	VERB
ejpam-3502	108	40	to	to	ADP
ejpam-3502	108	41	maps	map	NOUN
ejpam-3502	108	42	between	between	ADP
ejpam-3502	108	43	an	an	DET
ejpam-3502	108	44	m	m	PROPN
ejpam-3502	108	45	-	-	PUNCT
ejpam-3502	108	46	gt	gt	PROPN
ejpam-3502	108	47	space	space	NOUN
ejpam-3502	108	48	and	and	CCONJ
ejpam-3502	108	49	n	n	CCONJ
ejpam-3502	108	50	-	-	PUNCT
ejpam-3502	108	51	gt	gt	PROPN
ejpam-3502	108	52	space	space	NOUN
ejpam-3502	108	53	:	:	PUNCT
ejpam-3502	108	54	definition	definition	NOUN
ejpam-3502	108	55	2.7	2.7	NUM
ejpam-3502	108	56	.	.	PUNCT
ejpam-3502	109	1	for	for	ADP
ejpam-3502	109	2	a	a	DET
ejpam-3502	109	3	pair	pair	NOUN
ejpam-3502	109	4	of	of	ADP
ejpam-3502	109	5	distinct	distinct	ADJ
ejpam-3502	109	6	j	j	PROPN
ejpam-3502	109	7	,	,	PUNCT
ejpam-3502	109	8	k	k	PROPN
ejpam-3502	109	9	where	where	SCONJ
ejpam-3502	109	10	1	1	NUM
ejpam-3502	109	11	≤	≤	NUM
ejpam-3502	109	12	j	j	PROPN
ejpam-3502	109	13	≤	≤	NOUN
ejpam-3502	109	14	m	m	PROPN
ejpam-3502	109	15	and	and	CCONJ
ejpam-3502	109	16	1	1	NUM
ejpam-3502	109	17	≤	≤	NUM
ejpam-3502	109	18	k	k	X
ejpam-3502	109	19	≤	≤	PROPN
ejpam-3502	109	20	n	n	CCONJ
ejpam-3502	109	21	,	,	PUNCT
ejpam-3502	109	22	a	a	DET
ejpam-3502	109	23	function	function	NOUN
ejpam-3502	109	24	f	f	NOUN
ejpam-3502	109	25	:	:	PUNCT
ejpam-3502	109	26	x	x	X
ejpam-3502	109	27	→	→	SYM
ejpam-3502	109	28	y	y	PROPN
ejpam-3502	109	29	is	be	AUX
ejpam-3502	109	30	(	(	PUNCT
ejpam-3502	109	31	µ	µ	NOUN
ejpam-3502	109	32	,	,	PUNCT
ejpam-3502	109	33	ν)(j	ν)(j	NOUN
ejpam-3502	109	34	,	,	PUNCT
ejpam-3502	109	35	k)-continuous	k)-continuous	ADJ
ejpam-3502	109	36	at	at	ADP
ejpam-3502	109	37	a	a	DET
ejpam-3502	109	38	point	point	NOUN
ejpam-3502	109	39	x	x	PUNCT
ejpam-3502	109	40	if	if	SCONJ
ejpam-3502	109	41	for	for	ADP
ejpam-3502	109	42	each	each	DET
ejpam-3502	109	43	νk	νk	NOUN
ejpam-3502	109	44	-	-	ADJ
ejpam-3502	109	45	open	open	ADJ
ejpam-3502	109	46	set	set	VERB
ejpam-3502	109	47	v	v	NOUN
ejpam-3502	109	48	containing	contain	VERB
ejpam-3502	109	49	f(x	f(x	PROPN
ejpam-3502	109	50	)	)	PUNCT
ejpam-3502	109	51	there	there	PRON
ejpam-3502	109	52	is	be	VERB
ejpam-3502	109	53	a	a	DET
ejpam-3502	109	54	µj	µj	NOUN
ejpam-3502	109	55	-	-	PUNCT
ejpam-3502	109	56	open	open	ADJ
ejpam-3502	109	57	set	set	NOUN
ejpam-3502	109	58	u	u	NOUN
ejpam-3502	109	59	containing	contain	VERB
ejpam-3502	109	60	x	x	PUNCT
ejpam-3502	109	61	such	such	ADJ
ejpam-3502	109	62	that	that	DET
ejpam-3502	109	63	f(u	f(u	PROPN
ejpam-3502	109	64	)	)	PUNCT
ejpam-3502	109	65	⊆	⊆	NUM
ejpam-3502	109	66	v	v	NOUN
ejpam-3502	109	67	.	.	PUNCT
ejpam-3502	110	1	if	if	SCONJ
ejpam-3502	110	2	f	f	PROPN
ejpam-3502	110	3	is	be	AUX
ejpam-3502	110	4	(	(	PUNCT
ejpam-3502	110	5	µ	µ	NOUN
ejpam-3502	110	6	,	,	PUNCT
ejpam-3502	110	7	ν)(j	ν)(j	NOUN
ejpam-3502	110	8	,	,	PUNCT
ejpam-3502	110	9	k)-continuous	k)-continuous	ADJ
ejpam-3502	110	10	at	at	ADV
ejpam-3502	110	11	all	all	DET
ejpam-3502	110	12	points	point	NOUN
ejpam-3502	110	13	x	x	PUNCT
ejpam-3502	110	14	∈	∈	NOUN
ejpam-3502	110	15	x	x	NOUN
ejpam-3502	110	16	,	,	PUNCT
ejpam-3502	110	17	then	then	ADV
ejpam-3502	110	18	we	we	PRON
ejpam-3502	110	19	say	say	VERB
ejpam-3502	110	20	f	f	PROPN
ejpam-3502	110	21	is	be	AUX
ejpam-3502	110	22	(	(	PUNCT
ejpam-3502	110	23	µ	µ	NOUN
ejpam-3502	110	24	,	,	PUNCT
ejpam-3502	110	25	ν)(j	ν)(j	NOUN
ejpam-3502	110	26	,	,	PUNCT
ejpam-3502	110	27	k)-continuous	k)-continuous	ADJ
ejpam-3502	110	28	.	.	PUNCT
ejpam-3502	110	29	example	example	NOUN
ejpam-3502	111	1	2.8	2.8	NUM
ejpam-3502	111	2	.	.	PUNCT
ejpam-3502	112	1	let	let	VERB
ejpam-3502	112	2	m	m	PRON
ejpam-3502	112	3	,	,	PUNCT
ejpam-3502	112	4	n	n	PROPN
ejpam-3502	112	5	∈	∈	PROPN
ejpam-3502	112	6	n	n	CCONJ
ejpam-3502	112	7	where	where	SCONJ
ejpam-3502	112	8	m	m	VERB
ejpam-3502	112	9	≥	≥	NOUN
ejpam-3502	112	10	n	n	CCONJ
ejpam-3502	112	11	and	and	CCONJ
ejpam-3502	112	12	consider	consider	VERB
ejpam-3502	112	13	the	the	DET
ejpam-3502	112	14	m	m	PROPN
ejpam-3502	112	15	-	-	PUNCT
ejpam-3502	112	16	gt	gt	PROPN
ejpam-3502	112	17	space	space	NOUN
ejpam-3502	112	18	(	(	PUNCT
ejpam-3502	112	19	x	x	NOUN
ejpam-3502	112	20	,	,	PUNCT
ejpam-3502	112	21	gx	gx	PROPN
ejpam-3502	112	22	)	)	PUNCT
ejpam-3502	112	23	where	where	SCONJ
ejpam-3502	112	24	x	x	PUNCT
ejpam-3502	112	25	and	and	CCONJ
ejpam-3502	112	26	gx	gx	PROPN
ejpam-3502	112	27	be	be	AUX
ejpam-3502	112	28	the	the	DET
ejpam-3502	112	29	same	same	ADJ
ejpam-3502	112	30	as	as	SCONJ
ejpam-3502	112	31	defined	define	VERB
ejpam-3502	112	32	in	in	ADP
ejpam-3502	112	33	example	example	NOUN
ejpam-3502	112	34	2.2	2.2	NUM
ejpam-3502	112	35	.	.	PUNCT
ejpam-3502	113	1	in	in	ADP
ejpam-3502	113	2	this	this	DET
ejpam-3502	113	3	case	case	NOUN
ejpam-3502	113	4	,	,	PUNCT
ejpam-3502	113	5	let	let	VERB
ejpam-3502	113	6	y	y	NOUN
ejpam-3502	113	7	=	=	PUNCT
ejpam-3502	114	1	[	[	X
ejpam-3502	114	2	0	0	NUM
ejpam-3502	114	3	,	,	PUNCT
ejpam-3502	114	4	n	n	CCONJ
ejpam-3502	114	5	]	]	PUNCT
ejpam-3502	114	6	and	and	CCONJ
ejpam-3502	114	7	for	for	ADP
ejpam-3502	114	8	each	each	PRON
ejpam-3502	114	9	k	k	NOUN
ejpam-3502	114	10	=	=	SYM
ejpam-3502	114	11	1	1	NUM
ejpam-3502	114	12	,	,	PUNCT
ejpam-3502	114	13	.	.	PUNCT
ejpam-3502	114	14	.	.	PUNCT
ejpam-3502	115	1	.	.	PUNCT
ejpam-3502	116	1	,	,	PUNCT
ejpam-3502	116	2	n	n	CCONJ
ejpam-3502	116	3	,	,	PUNCT
ejpam-3502	116	4	define	define	VERB
ejpam-3502	116	5	νk	νk	NOUN
ejpam-3502	116	6	=	=	SYM
ejpam-3502	116	7	{	{	PUNCT
ejpam-3502	116	8	∅	∅	NOUN
ejpam-3502	116	9	}	}	PUNCT
ejpam-3502	116	10	∪	∪	X
ejpam-3502	116	11	{	{	PUNCT
ejpam-3502	116	12	[	[	X
ejpam-3502	116	13	0	0	NUM
ejpam-3502	116	14	,	,	PUNCT
ejpam-3502	116	15	n−	n−	NOUN
ejpam-3502	116	16	t+	t+	NOUN
ejpam-3502	116	17	1	1	NUM
ejpam-3502	116	18	]	]	PUNCT
ejpam-3502	116	19	;	;	PUNCT
ejpam-3502	116	20	t	t	X
ejpam-3502	116	21	=	=	SYM
ejpam-3502	116	22	1	1	NUM
ejpam-3502	116	23	,	,	PUNCT
ejpam-3502	116	24	.	.	PUNCT
ejpam-3502	116	25	.	.	PUNCT
ejpam-3502	117	1	.	.	PUNCT
ejpam-3502	118	1	,	,	PUNCT
ejpam-3502	118	2	k	k	X
ejpam-3502	118	3	}	}	PUNCT
ejpam-3502	118	4	.	.	PUNCT
ejpam-3502	119	1	observe	observe	VERB
ejpam-3502	119	2	that	that	SCONJ
ejpam-3502	119	3	(	(	PUNCT
ejpam-3502	119	4	y	y	NOUN
ejpam-3502	119	5	,	,	PUNCT
ejpam-3502	119	6	gy	gy	PROPN
ejpam-3502	119	7	)	)	PUNCT
ejpam-3502	119	8	is	be	AUX
ejpam-3502	119	9	an	an	DET
ejpam-3502	119	10	n	n	CCONJ
ejpam-3502	119	11	-	-	PUNCT
ejpam-3502	119	12	gt	gt	NOUN
ejpam-3502	119	13	space	space	NOUN
ejpam-3502	119	14	.	.	PUNCT
ejpam-3502	120	1	define	define	VERB
ejpam-3502	120	2	the	the	DET
ejpam-3502	120	3	map	map	NOUN
ejpam-3502	121	1	f	f	X
ejpam-3502	121	2	:	:	PUNCT
ejpam-3502	121	3	y	y	PROPN
ejpam-3502	121	4	→	→	SYM
ejpam-3502	121	5	x	x	PROPN
ejpam-3502	121	6	as	as	ADP
ejpam-3502	121	7	f(y	f(y	NOUN
ejpam-3502	121	8	)	)	PUNCT
ejpam-3502	121	9	=	=	PUNCT
ejpam-3502	121	10	(	(	PUNCT
ejpam-3502	121	11	n−y	n−y	PROPN
ejpam-3502	121	12	n	n	PRON
ejpam-3502	121	13	,	,	PUNCT
ejpam-3502	121	14	n	n	PROPN
ejpam-3502	121	15	)	)	PUNCT
ejpam-3502	121	16	.	.	PUNCT
ejpam-3502	122	1	let	let	VERB
ejpam-3502	122	2	y	y	PROPN
ejpam-3502	122	3	∈	∈	PROPN
ejpam-3502	122	4	y	y	PROPN
ejpam-3502	122	5	and	and	CCONJ
ejpam-3502	122	6	v	v	NOUN
ejpam-3502	122	7	be	be	AUX
ejpam-3502	122	8	a	a	DET
ejpam-3502	122	9	µ1	µ1	NOUN
ejpam-3502	122	10	-	-	PUNCT
ejpam-3502	122	11	open	open	ADJ
ejpam-3502	122	12	set	set	NOUN
ejpam-3502	122	13	containing	contain	VERB
ejpam-3502	122	14	f(y	f(y	NOUN
ejpam-3502	122	15	)	)	PUNCT
ejpam-3502	122	16	=	=	PUNCT
ejpam-3502	122	17	(	(	PUNCT
ejpam-3502	122	18	n−y	n−y	PROPN
ejpam-3502	122	19	n	n	PRON
ejpam-3502	122	20	,	,	PUNCT
ejpam-3502	122	21	n	n	PROPN
ejpam-3502	122	22	)	)	PUNCT
ejpam-3502	122	23	.	.	PUNCT
ejpam-3502	123	1	then	then	ADV
ejpam-3502	123	2	v	v	NOUN
ejpam-3502	123	3	is	be	AUX
ejpam-3502	123	4	of	of	ADP
ejpam-3502	123	5	the	the	DET
ejpam-3502	123	6	form	form	NOUN
ejpam-3502	123	7	r1	r1	PROPN
ejpam-3502	123	8	b	b	PROPN
ejpam-3502	123	9	,	,	PUNCT
ejpam-3502	123	10	where	where	SCONJ
ejpam-3502	123	11	b	b	X
ejpam-3502	123	12	≤	≤	X
ejpam-3502	123	13	n.	n.	NOUN
ejpam-3502	123	14	now	now	ADV
ejpam-3502	123	15	,	,	PUNCT
ejpam-3502	123	16	y	y	PROPN
ejpam-3502	123	17	=	=	PUNCT
ejpam-3502	124	1	[	[	X
ejpam-3502	124	2	0	0	NUM
ejpam-3502	124	3	,	,	PUNCT
ejpam-3502	124	4	n	n	CCONJ
ejpam-3502	124	5	]	]	PUNCT
ejpam-3502	124	6	is	be	AUX
ejpam-3502	124	7	a	a	DET
ejpam-3502	124	8	νm	νm	ADJ
ejpam-3502	124	9	-	-	ADJ
ejpam-3502	124	10	open	open	ADJ
ejpam-3502	124	11	set	set	NOUN
ejpam-3502	124	12	containing	contain	VERB
ejpam-3502	124	13	y	y	PROPN
ejpam-3502	124	14	with	with	ADP
ejpam-3502	124	15	f([0	f([0	PROPN
ejpam-3502	124	16	,	,	PUNCT
ejpam-3502	124	17	n	n	CCONJ
ejpam-3502	124	18	]	]	PUNCT
ejpam-3502	124	19	)	)	PUNCT
ejpam-3502	125	1	=	=	SYM
ejpam-3502	125	2	{	{	PUNCT
ejpam-3502	125	3	(	(	PUNCT
ejpam-3502	125	4	x	x	NOUN
ejpam-3502	125	5	,	,	PUNCT
ejpam-3502	125	6	n	n	CCONJ
ejpam-3502	125	7	)	)	PUNCT
ejpam-3502	125	8	:	:	PUNCT
ejpam-3502	125	9	0	0	NUM
ejpam-3502	125	10	≤	≤	NUM
ejpam-3502	125	11	x	x	SYM
ejpam-3502	125	12	≤	≤	NUM
ejpam-3502	125	13	1	1	NUM
ejpam-3502	125	14	}	}	SYM
ejpam-3502	125	15	⊆	⊆	NUM
ejpam-3502	125	16	r1	r1	NOUN
ejpam-3502	125	17	n	n	CCONJ
ejpam-3502	125	18	⊆	⊆	NUM
ejpam-3502	125	19	r1	r1	PROPN
ejpam-3502	125	20	b	b	PROPN
ejpam-3502	125	21	for	for	ADP
ejpam-3502	125	22	all	all	DET
ejpam-3502	125	23	b	b	PROPN
ejpam-3502	125	24	≤	≤	X
ejpam-3502	125	25	n.	n.	NOUN
ejpam-3502	125	26	hence	hence	ADV
ejpam-3502	125	27	,	,	PUNCT
ejpam-3502	125	28	f	f	PROPN
ejpam-3502	125	29	is	be	AUX
ejpam-3502	125	30	(	(	PUNCT
ejpam-3502	125	31	ν	ν	NOUN
ejpam-3502	125	32	,	,	PUNCT
ejpam-3502	125	33	µ)(m,1)-continuous	µ)(m,1)-continuous	ADJ
ejpam-3502	125	34	at	at	ADP
ejpam-3502	125	35	y	y	PROPN
ejpam-3502	125	36	and	and	CCONJ
ejpam-3502	125	37	since	since	SCONJ
ejpam-3502	125	38	y	y	PROPN
ejpam-3502	125	39	is	be	AUX
ejpam-3502	125	40	arbitrary	arbitrary	ADJ
ejpam-3502	125	41	,	,	PUNCT
ejpam-3502	125	42	f	f	PROPN
ejpam-3502	125	43	is	be	AUX
ejpam-3502	125	44	in	in	ADP
ejpam-3502	125	45	fact	fact	NOUN
ejpam-3502	125	46	(	(	PUNCT
ejpam-3502	125	47	ν	ν	NOUN
ejpam-3502	125	48	,	,	PUNCT
ejpam-3502	125	49	µ)(m,1)-continuous	µ)(m,1)-continuous	ADJ
ejpam-3502	125	50	.	.	PUNCT
ejpam-3502	126	1	in	in	ADP
ejpam-3502	126	2	the	the	DET
ejpam-3502	126	3	next	next	ADJ
ejpam-3502	126	4	results	result	NOUN
ejpam-3502	126	5	,	,	PUNCT
ejpam-3502	126	6	some	some	DET
ejpam-3502	126	7	relationships	relationship	NOUN
ejpam-3502	126	8	between	between	ADP
ejpam-3502	126	9	g	g	PROPN
ejpam-3502	126	10	-continuity	-continuity	PROPN
ejpam-3502	126	11	and	and	CCONJ
ejpam-3502	126	12	(	(	PUNCT
ejpam-3502	126	13	µ	µ	NOUN
ejpam-3502	126	14	,	,	PUNCT
ejpam-3502	126	15	ν)(j	ν)(j	NOUN
ejpam-3502	126	16	,	,	PUNCT
ejpam-3502	126	17	k)-continuity	k)-continuity	NOUN
ejpam-3502	126	18	are	be	AUX
ejpam-3502	126	19	established	establish	VERB
ejpam-3502	126	20	:	:	PUNCT
ejpam-3502	126	21	theorem	theorem	VERB
ejpam-3502	126	22	2.9	2.9	NUM
ejpam-3502	126	23	.	.	PUNCT
ejpam-3502	127	1	a	a	DET
ejpam-3502	127	2	function	function	NOUN
ejpam-3502	127	3	f	f	NOUN
ejpam-3502	127	4	:	:	PUNCT
ejpam-3502	127	5	x	x	X
ejpam-3502	127	6	→	→	SYM
ejpam-3502	127	7	y	y	PROPN
ejpam-3502	127	8	is	be	AUX
ejpam-3502	127	9	g	g	NOUN
ejpam-3502	127	10	-continuous	-continuous	ADJ
ejpam-3502	127	11	at	at	ADP
ejpam-3502	127	12	a	a	DET
ejpam-3502	127	13	point	point	NOUN
ejpam-3502	127	14	x	x	SYM
ejpam-3502	127	15	∈	∈	NOUN
ejpam-3502	127	16	x	x	INTJ
ejpam-3502	127	17	if	if	SCONJ
ejpam-3502	128	1	and	and	CCONJ
ejpam-3502	128	2	only	only	ADV
ejpam-3502	128	3	if	if	SCONJ
ejpam-3502	128	4	for	for	ADP
ejpam-3502	128	5	each	each	PRON
ejpam-3502	128	6	k	k	NOUN
ejpam-3502	128	7	=	=	SYM
ejpam-3502	128	8	1	1	NUM
ejpam-3502	128	9	,	,	PUNCT
ejpam-3502	128	10	.	.	PUNCT
ejpam-3502	128	11	.	.	PUNCT
ejpam-3502	129	1	.	.	PUNCT
ejpam-3502	130	1	,	,	PUNCT
ejpam-3502	130	2	n	n	CCONJ
ejpam-3502	130	3	,	,	PUNCT
ejpam-3502	130	4	there	there	PRON
ejpam-3502	130	5	exists	exist	VERB
ejpam-3502	130	6	1	1	NUM
ejpam-3502	130	7	≤	≤	NUM
ejpam-3502	130	8	j	j	PROPN
ejpam-3502	130	9	≤	≤	NUM
ejpam-3502	130	10	m	m	VERB
ejpam-3502	130	11	such	such	ADJ
ejpam-3502	130	12	that	that	SCONJ
ejpam-3502	130	13	f	f	PROPN
ejpam-3502	130	14	is	be	AUX
ejpam-3502	130	15	(	(	PUNCT
ejpam-3502	130	16	µ	µ	NOUN
ejpam-3502	130	17	,	,	PUNCT
ejpam-3502	130	18	ν)(j	ν)(j	NOUN
ejpam-3502	130	19	,	,	PUNCT
ejpam-3502	130	20	k)-continuous	k)-continuous	ADJ
ejpam-3502	130	21	at	at	ADP
ejpam-3502	130	22	x.	x.	NOUN
ejpam-3502	130	23	proof	proof	PROPN
ejpam-3502	130	24	.	.	PUNCT
ejpam-3502	131	1	suppose	suppose	VERB
ejpam-3502	131	2	that	that	SCONJ
ejpam-3502	131	3	f	f	PROPN
ejpam-3502	131	4	is	be	AUX
ejpam-3502	131	5	g	g	NOUN
ejpam-3502	131	6	-continuous	-continuous	ADJ
ejpam-3502	131	7	at	at	ADP
ejpam-3502	131	8	x	x	X
ejpam-3502	131	9	∈	∈	PROPN
ejpam-3502	131	10	x	x	NOUN
ejpam-3502	131	11	,	,	PUNCT
ejpam-3502	131	12	k	k	PROPN
ejpam-3502	131	13	∈	∈	PROPN
ejpam-3502	131	14	{	{	PUNCT
ejpam-3502	131	15	1	1	NUM
ejpam-3502	131	16	,	,	PUNCT
ejpam-3502	131	17	.	.	PUNCT
ejpam-3502	131	18	.	.	PUNCT
ejpam-3502	132	1	.	.	PUNCT
ejpam-3502	133	1	,	,	PUNCT
ejpam-3502	133	2	n	n	CCONJ
ejpam-3502	133	3	}	}	PUNCT
ejpam-3502	133	4	and	and	CCONJ
ejpam-3502	133	5	vk	vk	PROPN
ejpam-3502	133	6	is	be	AUX
ejpam-3502	133	7	a	a	DET
ejpam-3502	133	8	νk	νk	NOUN
ejpam-3502	133	9	-	-	ADJ
ejpam-3502	133	10	open	open	ADJ
ejpam-3502	133	11	set	set	NOUN
ejpam-3502	133	12	containing	contain	VERB
ejpam-3502	133	13	f(x	f(x	PROPN
ejpam-3502	133	14	)	)	PUNCT
ejpam-3502	133	15	.	.	PUNCT
ejpam-3502	134	1	then	then	ADV
ejpam-3502	134	2	vk	vk	PROPN
ejpam-3502	134	3	is	be	AUX
ejpam-3502	134	4	gy	gy	NOUN
ejpam-3502	134	5	-open	-open	ADJ
ejpam-3502	134	6	and	and	CCONJ
ejpam-3502	134	7	since	since	SCONJ
ejpam-3502	134	8	f	f	PROPN
ejpam-3502	134	9	is	be	AUX
ejpam-3502	134	10	g	g	PROPN
ejpam-3502	134	11	-continuous	-continuous	ADJ
ejpam-3502	134	12	,	,	PUNCT
ejpam-3502	134	13	we	we	PRON
ejpam-3502	134	14	can	can	AUX
ejpam-3502	134	15	find	find	VERB
ejpam-3502	134	16	a	a	DET
ejpam-3502	134	17	gx	gx	PROPN
ejpam-3502	134	18	-open	-open	PROPN
ejpam-3502	134	19	set	set	NOUN
ejpam-3502	134	20	u	u	NOUN
ejpam-3502	134	21	containing	contain	VERB
ejpam-3502	134	22	x	x	PUNCT
ejpam-3502	134	23	such	such	ADJ
ejpam-3502	134	24	that	that	DET
ejpam-3502	134	25	f(u	f(u	PROPN
ejpam-3502	134	26	)	)	PUNCT
ejpam-3502	134	27	⊆	⊆	NUM
ejpam-3502	134	28	vk	vk	NOUN
ejpam-3502	134	29	.	.	PUNCT
ejpam-3502	135	1	since	since	SCONJ
ejpam-3502	135	2	u	u	NOUN
ejpam-3502	135	3	is	be	AUX
ejpam-3502	135	4	gx	gx	PROPN
ejpam-3502	135	5	-open	-open	NOUN
ejpam-3502	135	6	,	,	PUNCT
ejpam-3502	135	7	there	there	PRON
ejpam-3502	135	8	is	be	VERB
ejpam-3502	135	9	a	a	DET
ejpam-3502	135	10	1	1	NUM
ejpam-3502	135	11	≤	≤	NUM
ejpam-3502	135	12	j	j	PROPN
ejpam-3502	135	13	≤	≤	NUM
ejpam-3502	135	14	m	m	VERB
ejpam-3502	135	15	such	such	ADJ
ejpam-3502	135	16	that	that	SCONJ
ejpam-3502	135	17	for	for	ADP
ejpam-3502	135	18	some	some	DET
ejpam-3502	135	19	hj	hj	PROPN
ejpam-3502	135	20	∈	∈	PROPN
ejpam-3502	135	21	µj	µj	PROPN
ejpam-3502	135	22	,	,	PUNCT
ejpam-3502	135	23	we	we	PRON
ejpam-3502	135	24	have	have	VERB
ejpam-3502	135	25	x	x	NOUN
ejpam-3502	135	26	∈	∈	PROPN
ejpam-3502	135	27	hj	hj	VERB
ejpam-3502	135	28	⊆	⊆	NUM
ejpam-3502	135	29	u	u	NOUN
ejpam-3502	135	30	and	and	CCONJ
ejpam-3502	135	31	f(hj	f(hj	NOUN
ejpam-3502	135	32	)	)	PUNCT
ejpam-3502	135	33	⊆	⊆	NUM
ejpam-3502	135	34	f(u	f(u	PROPN
ejpam-3502	135	35	)	)	PUNCT
ejpam-3502	135	36	⊆	⊆	NUM
ejpam-3502	135	37	vk	vk	NOUN
ejpam-3502	135	38	.	.	PUNCT
ejpam-3502	136	1	thus	thus	ADV
ejpam-3502	136	2	,	,	PUNCT
ejpam-3502	136	3	f	f	PROPN
ejpam-3502	136	4	is	be	AUX
ejpam-3502	136	5	(	(	PUNCT
ejpam-3502	136	6	µ	µ	NOUN
ejpam-3502	136	7	,	,	PUNCT
ejpam-3502	136	8	ν)(j	ν)(j	NOUN
ejpam-3502	136	9	,	,	PUNCT
ejpam-3502	136	10	k)-continuous	k)-continuous	ADJ
ejpam-3502	136	11	at	at	ADP
ejpam-3502	136	12	x	x	SYM
ejpam-3502	136	13	∈	∈	PROPN
ejpam-3502	136	14	x.	x.	NOUN
ejpam-3502	136	15	conversely	conversely	ADV
ejpam-3502	136	16	,	,	PUNCT
ejpam-3502	136	17	suppose	suppose	VERB
ejpam-3502	136	18	that	that	SCONJ
ejpam-3502	136	19	v	v	NOUN
ejpam-3502	136	20	is	be	AUX
ejpam-3502	136	21	a	a	DET
ejpam-3502	136	22	gy	gy	NOUN
ejpam-3502	136	23	-open	-open	NOUN
ejpam-3502	136	24	set	set	NOUN
ejpam-3502	136	25	containing	contain	VERB
ejpam-3502	136	26	f(x	f(x	PROPN
ejpam-3502	136	27	)	)	PUNCT
ejpam-3502	136	28	.	.	PUNCT
ejpam-3502	137	1	then	then	ADV
ejpam-3502	137	2	for	for	ADP
ejpam-3502	137	3	some	some	DET
ejpam-3502	137	4	k	k	NOUN
ejpam-3502	137	5	,	,	PUNCT
ejpam-3502	137	6	there	there	PRON
ejpam-3502	137	7	is	be	VERB
ejpam-3502	137	8	a	a	DET
ejpam-3502	137	9	gk	gk	PROPN
ejpam-3502	137	10	∈	∈	PROPN
ejpam-3502	137	11	νk	νk	ADP
ejpam-3502	137	12	such	such	ADJ
ejpam-3502	137	13	that	that	SCONJ
ejpam-3502	137	14	f(x	f(x	PROPN
ejpam-3502	137	15	)	)	PUNCT
ejpam-3502	137	16	∈	∈	PROPN
ejpam-3502	137	17	gk	gk	PROPN
ejpam-3502	137	18	⊆	⊆	NUM
ejpam-3502	137	19	v	v	NOUN
ejpam-3502	137	20	.	.	PUNCT
ejpam-3502	138	1	by	by	ADP
ejpam-3502	138	2	assumption	assumption	NOUN
ejpam-3502	138	3	,	,	PUNCT
ejpam-3502	138	4	for	for	ADP
ejpam-3502	138	5	some	some	DET
ejpam-3502	138	6	1	1	NUM
ejpam-3502	138	7	≤	≤	NUM
ejpam-3502	138	8	j	j	PROPN
ejpam-3502	138	9	≤	≤	PROPN
ejpam-3502	138	10	m	m	PROPN
ejpam-3502	138	11	,	,	PUNCT
ejpam-3502	138	12	we	we	PRON
ejpam-3502	138	13	can	can	AUX
ejpam-3502	138	14	find	find	VERB
ejpam-3502	138	15	a	a	DET
ejpam-3502	138	16	µj	µj	NOUN
ejpam-3502	138	17	-	-	PUNCT
ejpam-3502	138	18	open	open	ADJ
ejpam-3502	138	19	(	(	PUNCT
ejpam-3502	138	20	and	and	CCONJ
ejpam-3502	138	21	hence	hence	ADV
ejpam-3502	138	22	,	,	PUNCT
ejpam-3502	138	23	g	g	PROPN
ejpam-3502	138	24	-open	-open	NOUN
ejpam-3502	138	25	)	)	PUNCT
ejpam-3502	138	26	set	set	VERB
ejpam-3502	138	27	u	u	NOUN
ejpam-3502	138	28	containing	contain	VERB
ejpam-3502	138	29	x	x	PUNCT
ejpam-3502	138	30	such	such	ADJ
ejpam-3502	138	31	that	that	DET
ejpam-3502	138	32	f(u	f(u	PROPN
ejpam-3502	138	33	)	)	PUNCT
ejpam-3502	138	34	⊆	⊆	NUM
ejpam-3502	138	35	gk	gk	PROPN
ejpam-3502	138	36	⊆	⊆	NUM
ejpam-3502	138	37	v	v	NOUN
ejpam-3502	138	38	.	.	PUNCT
ejpam-3502	139	1	thus	thus	ADV
ejpam-3502	139	2	,	,	PUNCT
ejpam-3502	139	3	f	f	PROPN
ejpam-3502	139	4	is	be	AUX
ejpam-3502	139	5	g	g	PROPN
ejpam-3502	139	6	-continuous	-continuous	ADJ
ejpam-3502	139	7	at	at	ADP
ejpam-3502	139	8	x.	x.	PROPN
ejpam-3502	139	9	�	�	PROPN
ejpam-3502	139	10	theorem	theorem	VERB
ejpam-3502	139	11	2.9	2.9	NUM
ejpam-3502	139	12	implies	imply	VERB
ejpam-3502	139	13	that	that	SCONJ
ejpam-3502	139	14	to	to	PART
ejpam-3502	139	15	inspect	inspect	VERB
ejpam-3502	139	16	for	for	ADP
ejpam-3502	139	17	g	g	PROPN
ejpam-3502	139	18	-continuity	-continuity	PROPN
ejpam-3502	139	19	at	at	ADP
ejpam-3502	139	20	a	a	DET
ejpam-3502	139	21	point	point	NOUN
ejpam-3502	139	22	of	of	ADP
ejpam-3502	139	23	the	the	DET
ejpam-3502	139	24	domain	domain	NOUN
ejpam-3502	139	25	,	,	PUNCT
ejpam-3502	139	26	we	we	PRON
ejpam-3502	139	27	may	may	AUX
ejpam-3502	139	28	simply	simply	ADV
ejpam-3502	139	29	find	find	VERB
ejpam-3502	139	30	for	for	ADP
ejpam-3502	139	31	each	each	DET
ejpam-3502	139	32	component	component	NOUN
ejpam-3502	139	33	gt	gt	PROPN
ejpam-3502	139	34	of	of	ADP
ejpam-3502	139	35	(	(	PUNCT
ejpam-3502	139	36	y	y	PROPN
ejpam-3502	139	37	,	,	PUNCT
ejpam-3502	139	38	gy	gy	PROPN
ejpam-3502	139	39	)	)	PUNCT
ejpam-3502	139	40	a	a	DET
ejpam-3502	139	41	corresponding	correspond	VERB
ejpam-3502	139	42	component	component	NOUN
ejpam-3502	139	43	gt	gt	PROPN
ejpam-3502	139	44	of	of	ADP
ejpam-3502	139	45	(	(	PUNCT
ejpam-3502	139	46	x	x	PROPN
ejpam-3502	139	47	,	,	PUNCT
ejpam-3502	139	48	gx	gx	PROPN
ejpam-3502	139	49	)	)	PUNCT
ejpam-3502	139	50	for	for	ADP
ejpam-3502	139	51	which	which	PRON
ejpam-3502	139	52	the	the	DET
ejpam-3502	139	53	continuity	continuity	NOUN
ejpam-3502	139	54	in	in	ADP
ejpam-3502	139	55	the	the	DET
ejpam-3502	139	56	sense	sense	NOUN
ejpam-3502	139	57	of	of	ADP
ejpam-3502	139	58	definition	definition	NOUN
ejpam-3502	139	59	2.7	2.7	NUM
ejpam-3502	139	60	holds	hold	NOUN
ejpam-3502	139	61	.	.	PUNCT
ejpam-3502	140	1	some	some	DET
ejpam-3502	140	2	properties	property	NOUN
ejpam-3502	140	3	of	of	ADP
ejpam-3502	140	4	(	(	PUNCT
ejpam-3502	140	5	µ	µ	NOUN
ejpam-3502	140	6	,	,	PUNCT
ejpam-3502	140	7	ν)(j	ν)(j	NOUN
ejpam-3502	140	8	,	,	PUNCT
ejpam-3502	140	9	k)-continuity	k)-continuity	NOUN
ejpam-3502	140	10	can	can	AUX
ejpam-3502	140	11	be	be	AUX
ejpam-3502	140	12	drawn	draw	VERB
ejpam-3502	140	13	by	by	ADP
ejpam-3502	140	14	a	a	DET
ejpam-3502	140	15	simple	simple	ADJ
ejpam-3502	140	16	extension	extension	NOUN
ejpam-3502	140	17	of	of	ADP
ejpam-3502	140	18	those	those	PRON
ejpam-3502	140	19	that	that	PRON
ejpam-3502	140	20	are	be	AUX
ejpam-3502	140	21	enumerated	enumerate	VERB
ejpam-3502	140	22	in	in	ADP
ejpam-3502	140	23	[	[	X
ejpam-3502	140	24	6	6	NUM
ejpam-3502	140	25	]	]	X
ejpam-3502	140	26	:	:	PUNCT
ejpam-3502	140	27	c.	c.	PROPN
ejpam-3502	140	28	balingit	balingit	PROPN
ejpam-3502	140	29	,	,	PUNCT
ejpam-3502	140	30	j.	j.	PROPN
ejpam-3502	140	31	benitez	benitez	PROPN
ejpam-3502	140	32	/	/	PUNCT
ejpam-3502	140	33	eur	eur	PROPN
ejpam-3502	140	34	.	.	PUNCT
ejpam-3502	141	1	j.	j.	PROPN
ejpam-3502	141	2	pure	pure	PROPN
ejpam-3502	141	3	appl	appl	PROPN
ejpam-3502	141	4	.	.	PROPN
ejpam-3502	141	5	math	math	PROPN
ejpam-3502	141	6	,	,	PUNCT
ejpam-3502	141	7	12	12	NUM
ejpam-3502	141	8	(	(	PUNCT
ejpam-3502	141	9	4	4	NUM
ejpam-3502	141	10	)	)	PUNCT
ejpam-3502	141	11	(	(	PUNCT
ejpam-3502	141	12	2019	2019	NUM
ejpam-3502	141	13	)	)	PUNCT
ejpam-3502	141	14	,	,	PUNCT
ejpam-3502	141	15	1553	1553	NUM
ejpam-3502	141	16	-	-	SYM
ejpam-3502	141	17	1566	1566	NUM
ejpam-3502	141	18	1557	1557	NUM
ejpam-3502	141	19	theorem	theorem	VERB
ejpam-3502	141	20	2.10	2.10	NUM
ejpam-3502	141	21	.	.	PUNCT
ejpam-3502	142	1	let	let	VERB
ejpam-3502	142	2	f	f	NOUN
ejpam-3502	142	3	:	:	PUNCT
ejpam-3502	142	4	x	x	X
ejpam-3502	142	5	→	→	SYM
ejpam-3502	142	6	y	y	X
ejpam-3502	142	7	be	be	AUX
ejpam-3502	142	8	a	a	DET
ejpam-3502	142	9	map	map	NOUN
ejpam-3502	142	10	.	.	PUNCT
ejpam-3502	143	1	the	the	DET
ejpam-3502	143	2	following	follow	VERB
ejpam-3502	143	3	statements	statement	NOUN
ejpam-3502	143	4	are	be	AUX
ejpam-3502	143	5	equivalent	equivalent	ADJ
ejpam-3502	143	6	:	:	PUNCT
ejpam-3502	143	7	1	1	X
ejpam-3502	143	8	.	.	X
ejpam-3502	143	9	f	f	PROPN
ejpam-3502	143	10	is	be	AUX
ejpam-3502	143	11	(	(	PUNCT
ejpam-3502	143	12	µ	µ	NOUN
ejpam-3502	143	13	,	,	PUNCT
ejpam-3502	143	14	ν)(j	ν)(j	NOUN
ejpam-3502	143	15	,	,	PUNCT
ejpam-3502	143	16	k)-continuous	k)-continuous	ADJ
ejpam-3502	143	17	at	at	ADP
ejpam-3502	143	18	a	a	DET
ejpam-3502	143	19	point	point	NOUN
ejpam-3502	143	20	x	x	X
ejpam-3502	143	21	∈	∈	PROPN
ejpam-3502	143	22	x	x	X
ejpam-3502	143	23	;	;	PUNCT
ejpam-3502	143	24	2	2	X
ejpam-3502	143	25	.	.	X
ejpam-3502	143	26	x	x	SYM
ejpam-3502	143	27	∈	∈	PROPN
ejpam-3502	143	28	iµj	iµj	NOUN
ejpam-3502	143	29	(	(	PUNCT
ejpam-3502	143	30	f−1(v	f−1(v	PROPN
ejpam-3502	143	31	)	)	PUNCT
ejpam-3502	143	32	)	)	PUNCT
ejpam-3502	143	33	for	for	ADP
ejpam-3502	143	34	each	each	DET
ejpam-3502	143	35	νk	νk	NOUN
ejpam-3502	143	36	-	-	ADJ
ejpam-3502	143	37	open	open	ADJ
ejpam-3502	143	38	set	set	VERB
ejpam-3502	143	39	v	v	NOUN
ejpam-3502	143	40	containing	contain	VERB
ejpam-3502	143	41	f(x	f(x	PROPN
ejpam-3502	143	42	)	)	PUNCT
ejpam-3502	143	43	;	;	PUNCT
ejpam-3502	143	44	3	3	X
ejpam-3502	143	45	.	.	X
ejpam-3502	143	46	x	x	SYM
ejpam-3502	143	47	∈	∈	PROPN
ejpam-3502	143	48	iµj	iµj	NOUN
ejpam-3502	143	49	(	(	PUNCT
ejpam-3502	143	50	f−1(b	f−1(b	PROPN
ejpam-3502	143	51	)	)	PUNCT
ejpam-3502	143	52	)	)	PUNCT
ejpam-3502	143	53	for	for	ADP
ejpam-3502	143	54	each	each	DET
ejpam-3502	143	55	b	b	NOUN
ejpam-3502	143	56	⊆	⊆	NUM
ejpam-3502	143	57	y	y	NUM
ejpam-3502	143	58	such	such	ADJ
ejpam-3502	143	59	that	that	SCONJ
ejpam-3502	143	60	x	x	SYM
ejpam-3502	143	61	∈	∈	PROPN
ejpam-3502	143	62	f−1(iνk(b	f−1(iνk(b	NOUN
ejpam-3502	143	63	)	)	PUNCT
ejpam-3502	143	64	)	)	PUNCT
ejpam-3502	143	65	;	;	PUNCT
ejpam-3502	143	66	and	and	CCONJ
ejpam-3502	143	67	4	4	X
ejpam-3502	143	68	.	.	X
ejpam-3502	143	69	x	x	SYM
ejpam-3502	143	70	∈	∈	PROPN
ejpam-3502	143	71	f−1(f	f−1(f	PROPN
ejpam-3502	143	72	)	)	PUNCT
ejpam-3502	143	73	for	for	ADP
ejpam-3502	143	74	all	all	DET
ejpam-3502	143	75	νk	νk	NOUN
ejpam-3502	143	76	-	-	ADJ
ejpam-3502	143	77	closed	closed	ADJ
ejpam-3502	143	78	set	set	NOUN
ejpam-3502	143	79	f	f	PROPN
ejpam-3502	143	80	such	such	ADJ
ejpam-3502	143	81	that	that	SCONJ
ejpam-3502	143	82	x	x	SYM
ejpam-3502	143	83	∈	∈	NOUN
ejpam-3502	143	84	cµj	cµj	NOUN
ejpam-3502	143	85	(	(	PUNCT
ejpam-3502	143	86	f−1(f	f−1(f	PROPN
ejpam-3502	143	87	)	)	PUNCT
ejpam-3502	143	88	)	)	PUNCT
ejpam-3502	143	89	.	.	PUNCT
ejpam-3502	144	1	theorem	theorem	VERB
ejpam-3502	144	2	2.11	2.11	NUM
ejpam-3502	144	3	.	.	PUNCT
ejpam-3502	145	1	let	let	VERB
ejpam-3502	145	2	f	f	NOUN
ejpam-3502	145	3	:	:	PUNCT
ejpam-3502	145	4	x	x	X
ejpam-3502	145	5	→	→	SYM
ejpam-3502	145	6	y	y	X
ejpam-3502	145	7	be	be	AUX
ejpam-3502	145	8	a	a	DET
ejpam-3502	145	9	map	map	NOUN
ejpam-3502	145	10	.	.	PUNCT
ejpam-3502	146	1	the	the	DET
ejpam-3502	146	2	following	follow	VERB
ejpam-3502	146	3	statements	statement	NOUN
ejpam-3502	146	4	are	be	AUX
ejpam-3502	146	5	equivalent	equivalent	ADJ
ejpam-3502	146	6	:	:	PUNCT
ejpam-3502	146	7	1	1	X
ejpam-3502	146	8	.	.	X
ejpam-3502	146	9	f	f	PROPN
ejpam-3502	146	10	is	be	AUX
ejpam-3502	146	11	(	(	PUNCT
ejpam-3502	146	12	µ	µ	NOUN
ejpam-3502	146	13	,	,	PUNCT
ejpam-3502	146	14	ν)(j	ν)(j	NOUN
ejpam-3502	146	15	,	,	PUNCT
ejpam-3502	146	16	k)-continuous	k)-continuous	ADJ
ejpam-3502	146	17	;	;	PUNCT
ejpam-3502	146	18	2	2	X
ejpam-3502	146	19	.	.	X
ejpam-3502	146	20	f−1(v	f−1(v	NOUN
ejpam-3502	146	21	)	)	PUNCT
ejpam-3502	147	1	=	=	PUNCT
ejpam-3502	147	2	iµj	iµj	NOUN
ejpam-3502	147	3	(	(	PUNCT
ejpam-3502	147	4	f	f	PROPN
ejpam-3502	147	5	−1(v	−1(v	PROPN
ejpam-3502	147	6	)	)	PUNCT
ejpam-3502	147	7	)	)	PUNCT
ejpam-3502	147	8	for	for	ADP
ejpam-3502	147	9	each	each	DET
ejpam-3502	147	10	νk	νk	NOUN
ejpam-3502	147	11	-	-	ADJ
ejpam-3502	147	12	open	open	ADJ
ejpam-3502	147	13	set	set	VERB
ejpam-3502	147	14	v	v	NOUN
ejpam-3502	147	15	;	;	PUNCT
ejpam-3502	147	16	3	3	X
ejpam-3502	147	17	.	.	X
ejpam-3502	147	18	f−1(iνk(b	f−1(iνk(b	NUM
ejpam-3502	147	19	)	)	PUNCT
ejpam-3502	147	20	)	)	PUNCT
ejpam-3502	148	1	⊆	⊆	NUM
ejpam-3502	148	2	iµj	iµj	NOUN
ejpam-3502	148	3	(	(	PUNCT
ejpam-3502	148	4	f−1(b	f−1(b	PROPN
ejpam-3502	148	5	)	)	PUNCT
ejpam-3502	148	6	)	)	PUNCT
ejpam-3502	148	7	for	for	ADP
ejpam-3502	148	8	each	each	DET
ejpam-3502	148	9	b	b	PROPN
ejpam-3502	148	10	⊆	⊆	NUM
ejpam-3502	148	11	y	y	NOUN
ejpam-3502	148	12	;	;	PUNCT
ejpam-3502	148	13	and	and	CCONJ
ejpam-3502	148	14	4	4	X
ejpam-3502	148	15	.	.	X
ejpam-3502	148	16	cµj	cµj	NOUN
ejpam-3502	148	17	(	(	PUNCT
ejpam-3502	148	18	f	f	PROPN
ejpam-3502	148	19	−1(f	−1(f	PROPN
ejpam-3502	148	20	)	)	PUNCT
ejpam-3502	148	21	)	)	PUNCT
ejpam-3502	149	1	=	=	SYM
ejpam-3502	149	2	f−1(f	f−1(f	PROPN
ejpam-3502	149	3	)	)	PUNCT
ejpam-3502	149	4	for	for	ADP
ejpam-3502	149	5	all	all	DET
ejpam-3502	149	6	νk	νk	NOUN
ejpam-3502	149	7	-	-	ADJ
ejpam-3502	149	8	closed	closed	ADJ
ejpam-3502	149	9	set	set	ADJ
ejpam-3502	149	10	f	f	PROPN
ejpam-3502	149	11	.	.	PUNCT
ejpam-3502	150	1	in	in	ADP
ejpam-3502	150	2	view	view	NOUN
ejpam-3502	150	3	of	of	ADP
ejpam-3502	150	4	definition	definition	NOUN
ejpam-3502	150	5	2.7	2.7	NUM
ejpam-3502	150	6	,	,	PUNCT
ejpam-3502	150	7	(	(	PUNCT
ejpam-3502	150	8	µ	µ	NOUN
ejpam-3502	150	9	,	,	PUNCT
ejpam-3502	150	10	ν)(j	ν)(j	NOUN
ejpam-3502	150	11	,	,	PUNCT
ejpam-3502	150	12	k)-continuity	k)-continuity	NOUN
ejpam-3502	150	13	may	may	AUX
ejpam-3502	150	14	occur	occur	VERB
ejpam-3502	150	15	for	for	ADP
ejpam-3502	150	16	each	each	DET
ejpam-3502	150	17	pair	pair	NOUN
ejpam-3502	150	18	of	of	ADP
ejpam-3502	150	19	indices	index	NOUN
ejpam-3502	150	20	j	j	PROPN
ejpam-3502	150	21	and	and	CCONJ
ejpam-3502	150	22	k	k	PROPN
ejpam-3502	150	23	;	;	PUNCT
ejpam-3502	150	24	and	and	CCONJ
ejpam-3502	150	25	thence	thence	NOUN
ejpam-3502	150	26	we	we	PRON
ejpam-3502	150	27	have	have	VERB
ejpam-3502	150	28	another	another	DET
ejpam-3502	150	29	type	type	NOUN
ejpam-3502	150	30	of	of	ADP
ejpam-3502	150	31	continuity	continuity	NOUN
ejpam-3502	150	32	formally	formally	ADV
ejpam-3502	150	33	stated	state	VERB
ejpam-3502	150	34	as	as	SCONJ
ejpam-3502	150	35	follows	follow	VERB
ejpam-3502	150	36	:	:	PUNCT
ejpam-3502	150	37	definition	definition	NOUN
ejpam-3502	150	38	2.12	2.12	NUM
ejpam-3502	150	39	.	.	PUNCT
ejpam-3502	151	1	let	let	VERB
ejpam-3502	151	2	(	(	PUNCT
ejpam-3502	151	3	x	x	NOUN
ejpam-3502	151	4	,	,	PUNCT
ejpam-3502	151	5	gx	gx	PROPN
ejpam-3502	151	6	)	)	PUNCT
ejpam-3502	151	7	and	and	CCONJ
ejpam-3502	151	8	(	(	PUNCT
ejpam-3502	151	9	y	y	PROPN
ejpam-3502	151	10	,	,	PUNCT
ejpam-3502	151	11	gy	gy	NOUN
ejpam-3502	151	12	)	)	PUNCT
ejpam-3502	151	13	be	be	AUX
ejpam-3502	151	14	m	m	PROPN
ejpam-3502	151	15	-	-	PUNCT
ejpam-3502	151	16	gt	gt	PROPN
ejpam-3502	151	17	and	and	CCONJ
ejpam-3502	151	18	n	n	CCONJ
ejpam-3502	151	19	-	-	PUNCT
ejpam-3502	151	20	gt	gt	PROPN
ejpam-3502	151	21	spaces	space	NOUN
ejpam-3502	151	22	,	,	PUNCT
ejpam-3502	151	23	respectively	respectively	ADV
ejpam-3502	151	24	,	,	PUNCT
ejpam-3502	151	25	where	where	SCONJ
ejpam-3502	151	26	gx	gx	PROPN
ejpam-3502	151	27	=	=	PUNCT
ejpam-3502	151	28	{	{	PUNCT
ejpam-3502	151	29	µ1	µ1	PROPN
ejpam-3502	151	30	,	,	PUNCT
ejpam-3502	151	31	.	.	PUNCT
ejpam-3502	151	32	.	.	PUNCT
ejpam-3502	151	33	.	.	PUNCT
ejpam-3502	152	1	,	,	PUNCT
ejpam-3502	152	2	µm	µm	ADP
ejpam-3502	152	3	}	}	PUNCT
ejpam-3502	152	4	and	and	CCONJ
ejpam-3502	152	5	gy	gy	NOUN
ejpam-3502	152	6	=	=	SYM
ejpam-3502	152	7	{	{	PUNCT
ejpam-3502	152	8	ν1	ν1	NOUN
ejpam-3502	152	9	,	,	PUNCT
ejpam-3502	152	10	.	.	PUNCT
ejpam-3502	152	11	.	.	PUNCT
ejpam-3502	153	1	.	.	PUNCT
ejpam-3502	154	1	,	,	PUNCT
ejpam-3502	154	2	νn	νn	AUX
ejpam-3502	154	3	}	}	PUNCT
ejpam-3502	154	4	for	for	ADP
ejpam-3502	154	5	some	some	DET
ejpam-3502	154	6	m	m	NOUN
ejpam-3502	154	7	,	,	PUNCT
ejpam-3502	154	8	n	n	PROPN
ejpam-3502	154	9	∈	∈	PROPN
ejpam-3502	154	10	n.	n.	NOUN
ejpam-3502	154	11	a	a	DET
ejpam-3502	154	12	function	function	NOUN
ejpam-3502	154	13	f	f	NOUN
ejpam-3502	155	1	:	:	PUNCT
ejpam-3502	155	2	x	x	X
ejpam-3502	155	3	→	→	SYM
ejpam-3502	155	4	y	y	PROPN
ejpam-3502	155	5	is	be	AUX
ejpam-3502	155	6	called	call	VERB
ejpam-3502	155	7	pairwise	pairwise	NOUN
ejpam-3502	155	8	(	(	PUNCT
ejpam-3502	155	9	µ	µ	NOUN
ejpam-3502	155	10	,	,	PUNCT
ejpam-3502	155	11	ν)-continuous	ν)-continuous	ADJ
ejpam-3502	155	12	if	if	SCONJ
ejpam-3502	155	13	for	for	ADP
ejpam-3502	155	14	each	each	DET
ejpam-3502	155	15	pair	pair	NOUN
ejpam-3502	155	16	j	j	PROPN
ejpam-3502	155	17	,	,	PUNCT
ejpam-3502	155	18	k	k	PROPN
ejpam-3502	155	19	where	where	SCONJ
ejpam-3502	155	20	1	1	NUM
ejpam-3502	155	21	≤	≤	NUM
ejpam-3502	155	22	j	j	PROPN
ejpam-3502	155	23	≤	≤	NOUN
ejpam-3502	155	24	m	m	PROPN
ejpam-3502	155	25	and	and	CCONJ
ejpam-3502	155	26	1	1	NUM
ejpam-3502	155	27	≤	≤	NUM
ejpam-3502	155	28	k	k	X
ejpam-3502	155	29	≤	≤	PROPN
ejpam-3502	155	30	n	n	CCONJ
ejpam-3502	155	31	,	,	PUNCT
ejpam-3502	155	32	f	f	PROPN
ejpam-3502	155	33	is	be	AUX
ejpam-3502	155	34	(	(	PUNCT
ejpam-3502	155	35	µ	µ	NOUN
ejpam-3502	155	36	,	,	PUNCT
ejpam-3502	155	37	ν)(j	ν)(j	NOUN
ejpam-3502	155	38	,	,	PUNCT
ejpam-3502	155	39	k)-continuous	k)-continuous	ADJ
ejpam-3502	155	40	.	.	PUNCT
ejpam-3502	155	41	example	example	NOUN
ejpam-3502	156	1	2.13	2.13	NUM
ejpam-3502	156	2	.	.	NOUN
ejpam-3502	157	1	1	1	X
ejpam-3502	157	2	.	.	X
ejpam-3502	158	1	let	let	VERB
ejpam-3502	158	2	(	(	PUNCT
ejpam-3502	158	3	x	x	NOUN
ejpam-3502	158	4	,	,	PUNCT
ejpam-3502	158	5	g1	g1	PROPN
ejpam-3502	158	6	)	)	PUNCT
ejpam-3502	158	7	and	and	CCONJ
ejpam-3502	158	8	(	(	PUNCT
ejpam-3502	158	9	x	x	X
ejpam-3502	158	10	,	,	PUNCT
ejpam-3502	158	11	g2	g2	PROPN
ejpam-3502	158	12	)	)	PUNCT
ejpam-3502	158	13	be	be	AUX
ejpam-3502	158	14	strong	strong	ADJ
ejpam-3502	158	15	m	m	PROPN
ejpam-3502	158	16	-	-	PUNCT
ejpam-3502	158	17	gt	gt	PROPN
ejpam-3502	158	18	and	and	CCONJ
ejpam-3502	158	19	n	n	CCONJ
ejpam-3502	158	20	-	-	PUNCT
ejpam-3502	158	21	gt	gt	PROPN
ejpam-3502	158	22	spaces	space	NOUN
ejpam-3502	158	23	,	,	PUNCT
ejpam-3502	158	24	respectively	respectively	ADV
ejpam-3502	158	25	,	,	PUNCT
ejpam-3502	158	26	over	over	ADP
ejpam-3502	158	27	the	the	DET
ejpam-3502	158	28	same	same	ADJ
ejpam-3502	158	29	set	set	NOUN
ejpam-3502	158	30	x	x	PUNCT
ejpam-3502	158	31	and	and	CCONJ
ejpam-3502	158	32	c	c	NOUN
ejpam-3502	158	33	∈	∈	PROPN
ejpam-3502	158	34	x.	x.	NOUN
ejpam-3502	159	1	if	if	SCONJ
ejpam-3502	159	2	f	f	X
ejpam-3502	159	3	:	:	PUNCT
ejpam-3502	159	4	x	x	X
ejpam-3502	159	5	→	→	PUNCT
ejpam-3502	159	6	x	x	SYM
ejpam-3502	159	7	is	be	AUX
ejpam-3502	159	8	the	the	DET
ejpam-3502	159	9	constant	constant	ADJ
ejpam-3502	159	10	function	function	NOUN
ejpam-3502	159	11	defined	define	VERB
ejpam-3502	159	12	by	by	ADP
ejpam-3502	159	13	f(x	f(x	PROPN
ejpam-3502	159	14	)	)	PUNCT
ejpam-3502	160	1	=	=	SYM
ejpam-3502	161	1	c	c	X
ejpam-3502	161	2	,	,	PUNCT
ejpam-3502	161	3	then	then	ADV
ejpam-3502	161	4	for	for	ADP
ejpam-3502	161	5	each	each	PRON
ejpam-3502	161	6	k	k	NOUN
ejpam-3502	161	7	=	=	SYM
ejpam-3502	161	8	1	1	NUM
ejpam-3502	161	9	,	,	PUNCT
ejpam-3502	161	10	.	.	PUNCT
ejpam-3502	161	11	.	.	PUNCT
ejpam-3502	161	12	.	.	PUNCT
ejpam-3502	161	13	,	,	PUNCT
ejpam-3502	162	1	n	n	CCONJ
ejpam-3502	162	2	and	and	CCONJ
ejpam-3502	162	3	for	for	ADP
ejpam-3502	162	4	each	each	DET
ejpam-3502	162	5	νk	νk	ADJ
ejpam-3502	162	6	-	-	ADJ
ejpam-3502	162	7	open	open	ADJ
ejpam-3502	162	8	set	set	VERB
ejpam-3502	162	9	vk	vk	NOUN
ejpam-3502	162	10	containing	contain	VERB
ejpam-3502	162	11	c	c	NOUN
ejpam-3502	162	12	,	,	PUNCT
ejpam-3502	162	13	f(gj	f(gj	NUM
ejpam-3502	162	14	)	)	PUNCT
ejpam-3502	162	15	⊆	⊆	NUM
ejpam-3502	162	16	{	{	PUNCT
ejpam-3502	162	17	c	c	NOUN
ejpam-3502	162	18	}	}	PUNCT
ejpam-3502	162	19	⊆	⊆	NUM
ejpam-3502	162	20	vk	vk	NOUN
ejpam-3502	162	21	for	for	ADP
ejpam-3502	162	22	all	all	DET
ejpam-3502	162	23	sets	set	NOUN
ejpam-3502	162	24	gj	gj	NOUN
ejpam-3502	162	25	∈	∈	PROPN
ejpam-3502	162	26	µj	µj	X
ejpam-3502	162	27	.	.	PUNCT
ejpam-3502	163	1	thus	thus	ADV
ejpam-3502	163	2	,	,	PUNCT
ejpam-3502	163	3	f	f	PROPN
ejpam-3502	163	4	is	be	AUX
ejpam-3502	163	5	(	(	PUNCT
ejpam-3502	163	6	µ	µ	NOUN
ejpam-3502	163	7	,	,	PUNCT
ejpam-3502	163	8	ν)(j	ν)(j	NOUN
ejpam-3502	163	9	,	,	PUNCT
ejpam-3502	163	10	k)-continuous	k)-continuous	ADJ
ejpam-3502	163	11	at	at	ADP
ejpam-3502	163	12	any	any	DET
ejpam-3502	163	13	point	point	NOUN
ejpam-3502	163	14	x	x	X
ejpam-3502	163	15	∈	∈	NOUN
ejpam-3502	163	16	x	x	X
ejpam-3502	163	17	and	and	CCONJ
ejpam-3502	163	18	any	any	DET
ejpam-3502	163	19	pair	pair	NOUN
ejpam-3502	163	20	j	j	PROPN
ejpam-3502	163	21	,	,	PUNCT
ejpam-3502	163	22	k.	k.	PROPN
ejpam-3502	163	23	as	as	ADP
ejpam-3502	163	24	a	a	DET
ejpam-3502	163	25	result	result	NOUN
ejpam-3502	163	26	,	,	PUNCT
ejpam-3502	163	27	f	f	PROPN
ejpam-3502	163	28	is	be	AUX
ejpam-3502	163	29	pairwise	pairwise	NOUN
ejpam-3502	163	30	(	(	PUNCT
ejpam-3502	163	31	µ	µ	NOUN
ejpam-3502	163	32	,	,	PUNCT
ejpam-3502	163	33	ν)-continuous	ν)-continuous	ADJ
ejpam-3502	163	34	.	.	NOUN
ejpam-3502	164	1	2	2	X
ejpam-3502	164	2	.	.	X
ejpam-3502	164	3	in	in	ADP
ejpam-3502	164	4	example	example	NOUN
ejpam-3502	164	5	2.8	2.8	NUM
ejpam-3502	164	6	,	,	PUNCT
ejpam-3502	164	7	we	we	PRON
ejpam-3502	164	8	observe	observe	VERB
ejpam-3502	164	9	that	that	SCONJ
ejpam-3502	164	10	for	for	ADP
ejpam-3502	164	11	a	a	DET
ejpam-3502	164	12	pair	pair	NOUN
ejpam-3502	164	13	s	s	PROPN
ejpam-3502	164	14	,	,	PUNCT
ejpam-3502	164	15	t	t	PROPN
ejpam-3502	164	16	∈	∈	PROPN
ejpam-3502	164	17	n	n	CCONJ
ejpam-3502	164	18	where	where	SCONJ
ejpam-3502	164	19	1	1	NUM
ejpam-3502	164	20	≤	≤	NOUN
ejpam-3502	164	21	s	s	PART
ejpam-3502	164	22	≤	≤	NUM
ejpam-3502	164	23	n	n	PRON
ejpam-3502	164	24	and	and	CCONJ
ejpam-3502	164	25	1	1	NUM
ejpam-3502	164	26	≤	≤	NOUN
ejpam-3502	164	27	t	t	NOUN
ejpam-3502	164	28	≤	≤	NOUN
ejpam-3502	164	29	m	m	PROPN
ejpam-3502	164	30	and	and	CCONJ
ejpam-3502	164	31	for	for	ADP
ejpam-3502	164	32	y	y	PROPN
ejpam-3502	164	33	∈	∈	PROPN
ejpam-3502	164	34	y	y	PROPN
ejpam-3502	164	35	,	,	PUNCT
ejpam-3502	164	36	0	0	NUM
ejpam-3502	164	37	≤	≤	NUM
ejpam-3502	164	38	n−y	n−y	NOUN
ejpam-3502	164	39	n	n	CCONJ
ejpam-3502	164	40	≤	≤	NUM
ejpam-3502	164	41	1	1	NUM
ejpam-3502	164	42	which	which	PRON
ejpam-3502	164	43	means	mean	VERB
ejpam-3502	164	44	that	that	SCONJ
ejpam-3502	164	45	f(y	f(y	NOUN
ejpam-3502	164	46	)	)	PUNCT
ejpam-3502	164	47	∈	∈	PROPN
ejpam-3502	164	48	r1	r1	NOUN
ejpam-3502	164	49	0	0	PUNCT
ejpam-3502	165	1	and	and	CCONJ
ejpam-3502	165	2	so	so	ADV
ejpam-3502	165	3	if	if	SCONJ
ejpam-3502	165	4	t	t	PROPN
ejpam-3502	165	5	6=	6=	NUM
ejpam-3502	165	6	1	1	NUM
ejpam-3502	165	7	,	,	PUNCT
ejpam-3502	165	8	f	f	PROPN
ejpam-3502	165	9	vacuously	vacuously	ADV
ejpam-3502	165	10	satisfies	satisfy	VERB
ejpam-3502	165	11	(	(	PUNCT
ejpam-3502	165	12	ν	ν	NOUN
ejpam-3502	165	13	,	,	PUNCT
ejpam-3502	165	14	µ)(s	µ)(s	NOUN
ejpam-3502	165	15	,	,	PUNCT
ejpam-3502	165	16	t)-continuity	t)-continuity	NOUN
ejpam-3502	165	17	on	on	ADP
ejpam-3502	165	18	y.	y.	PROPN
ejpam-3502	165	19	now	now	ADV
ejpam-3502	165	20	,	,	PUNCT
ejpam-3502	165	21	if	if	SCONJ
ejpam-3502	165	22	t	t	PROPN
ejpam-3502	165	23	=	=	SYM
ejpam-3502	165	24	1	1	NUM
ejpam-3502	165	25	,	,	PUNCT
ejpam-3502	165	26	we	we	PRON
ejpam-3502	165	27	note	note	VERB
ejpam-3502	165	28	that	that	SCONJ
ejpam-3502	165	29	y	y	PROPN
ejpam-3502	165	30	=	=	PUNCT
ejpam-3502	166	1	[	[	X
ejpam-3502	166	2	0	0	NUM
ejpam-3502	166	3	,	,	PUNCT
ejpam-3502	166	4	n	n	CCONJ
ejpam-3502	166	5	]	]	PUNCT
ejpam-3502	166	6	is	be	AUX
ejpam-3502	166	7	νs	νs	NOUN
ejpam-3502	166	8	-	-	ADJ
ejpam-3502	166	9	open	open	ADJ
ejpam-3502	166	10	for	for	ADP
ejpam-3502	166	11	all	all	PRON
ejpam-3502	166	12	s	s	PART
ejpam-3502	166	13	=	=	NOUN
ejpam-3502	166	14	1	1	NUM
ejpam-3502	166	15	,	,	PUNCT
ejpam-3502	166	16	.	.	PUNCT
ejpam-3502	166	17	.	.	PUNCT
ejpam-3502	167	1	.	.	PUNCT
ejpam-3502	168	1	,	,	PUNCT
ejpam-3502	168	2	n	n	NOUN
ejpam-3502	168	3	and	and	CCONJ
ejpam-3502	168	4	recall	recall	VERB
ejpam-3502	168	5	that	that	SCONJ
ejpam-3502	168	6	the	the	DET
ejpam-3502	168	7	µ1	µ1	ADV
ejpam-3502	168	8	-	-	PUNCT
ejpam-3502	168	9	open	open	ADJ
ejpam-3502	168	10	set	set	NOUN
ejpam-3502	168	11	containing	contain	VERB
ejpam-3502	168	12	f(y	f(y	NOUN
ejpam-3502	168	13	)	)	PUNCT
ejpam-3502	168	14	are	be	AUX
ejpam-3502	168	15	precisely	precisely	ADV
ejpam-3502	168	16	the	the	DET
ejpam-3502	168	17	sets	set	NOUN
ejpam-3502	168	18	r1	r1	PROPN
ejpam-3502	168	19	b	b	PROPN
ejpam-3502	168	20	where	where	SCONJ
ejpam-3502	168	21	b	b	NOUN
ejpam-3502	168	22	≤	≤	NOUN
ejpam-3502	168	23	n	n	CCONJ
ejpam-3502	168	24	with	with	ADP
ejpam-3502	168	25	f([0	f([0	NOUN
ejpam-3502	168	26	,	,	PUNCT
ejpam-3502	168	27	n	n	CCONJ
ejpam-3502	168	28	]	]	PUNCT
ejpam-3502	168	29	)	)	PUNCT
ejpam-3502	168	30	⊆	⊆	NUM
ejpam-3502	168	31	r1	r1	PROPN
ejpam-3502	168	32	b	b	PROPN
ejpam-3502	168	33	.	.	PUNCT
ejpam-3502	169	1	this	this	PRON
ejpam-3502	169	2	indicates	indicate	VERB
ejpam-3502	169	3	that	that	SCONJ
ejpam-3502	169	4	f	f	PROPN
ejpam-3502	169	5	is	be	AUX
ejpam-3502	169	6	(	(	PUNCT
ejpam-3502	169	7	ν	ν	NOUN
ejpam-3502	169	8	,	,	PUNCT
ejpam-3502	169	9	µ)(s	µ)(s	NOUN
ejpam-3502	169	10	,	,	PUNCT
ejpam-3502	169	11	t)continuous	t)continuous	ADJ
ejpam-3502	169	12	at	at	ADP
ejpam-3502	169	13	y.	y.	NOUN
ejpam-3502	169	14	from	from	ADP
ejpam-3502	169	15	these	these	DET
ejpam-3502	169	16	cases	case	NOUN
ejpam-3502	169	17	,	,	PUNCT
ejpam-3502	169	18	we	we	PRON
ejpam-3502	169	19	can	can	AUX
ejpam-3502	169	20	see	see	VERB
ejpam-3502	169	21	that	that	PRON
ejpam-3502	169	22	with	with	ADP
ejpam-3502	169	23	the	the	DET
ejpam-3502	169	24	arbitrary	arbitrary	ADJ
ejpam-3502	169	25	nature	nature	NOUN
ejpam-3502	169	26	of	of	ADP
ejpam-3502	169	27	y	y	PROPN
ejpam-3502	169	28	,	,	PUNCT
ejpam-3502	169	29	f	f	PROPN
ejpam-3502	169	30	is	be	AUX
ejpam-3502	169	31	pairwise	pairwise	NOUN
ejpam-3502	169	32	(	(	PUNCT
ejpam-3502	169	33	ν	ν	NOUN
ejpam-3502	169	34	,	,	PUNCT
ejpam-3502	169	35	µ)-continuous	µ)-continuous	ADJ
ejpam-3502	169	36	.	.	NOUN
ejpam-3502	169	37	3	3	X
ejpam-3502	169	38	.	.	X
ejpam-3502	169	39	consider	consider	VERB
ejpam-3502	169	40	the	the	DET
ejpam-3502	169	41	graph	graph	NOUN
ejpam-3502	169	42	d∗	d∗	NOUN
ejpam-3502	169	43	and	and	CCONJ
ejpam-3502	169	44	the	the	DET
ejpam-3502	169	45	n	n	CCONJ
ejpam-3502	169	46	-	-	PUNCT
ejpam-3502	169	47	gt	gt	PROPN
ejpam-3502	169	48	spaces	space	NOUN
ejpam-3502	169	49	(	(	PUNCT
ejpam-3502	169	50	v	v	NOUN
ejpam-3502	169	51	(	(	PUNCT
ejpam-3502	169	52	d∗),gv	d∗),gv	PROPN
ejpam-3502	169	53	)	)	PUNCT
ejpam-3502	169	54	and	and	CCONJ
ejpam-3502	169	55	(	(	PUNCT
ejpam-3502	169	56	e(d∗),ge	e(d∗),ge	NOUN
ejpam-3502	169	57	)	)	PUNCT
ejpam-3502	169	58	as	as	SCONJ
ejpam-3502	169	59	described	describe	VERB
ejpam-3502	169	60	in	in	ADP
ejpam-3502	169	61	example	example	NOUN
ejpam-3502	169	62	2.3	2.3	NUM
ejpam-3502	169	63	.	.	PUNCT
ejpam-3502	170	1	define	define	VERB
ejpam-3502	170	2	the	the	DET
ejpam-3502	170	3	mapping	mapping	NOUN
ejpam-3502	170	4	g	g	NOUN
ejpam-3502	170	5	:	:	PUNCT
ejpam-3502	170	6	e(d∗	e(d∗	X
ejpam-3502	170	7	)	)	PUNCT
ejpam-3502	170	8	→	→	SYM
ejpam-3502	170	9	v	v	X
ejpam-3502	170	10	(	(	PUNCT
ejpam-3502	170	11	d∗	d∗	PROPN
ejpam-3502	170	12	)	)	PUNCT
ejpam-3502	170	13	by	by	ADP
ejpam-3502	170	14	g(e	g(e	PROPN
ejpam-3502	170	15	)	)	PUNCT
ejpam-3502	171	1	=	=	SYM
ejpam-3502	171	2	u	u	NOUN
ejpam-3502	171	3	for	for	ADP
ejpam-3502	171	4	each	each	DET
ejpam-3502	171	5	e	e	NOUN
ejpam-3502	171	6	=	=	PUNCT
ejpam-3502	171	7	uv	uv	PROPN
ejpam-3502	171	8	∈	∈	PROPN
ejpam-3502	171	9	e(d∗	e(d∗	NOUN
ejpam-3502	171	10	)	)	PUNCT
ejpam-3502	171	11	.	.	PUNCT
ejpam-3502	172	1	let	let	VERB
ejpam-3502	172	2	j	j	PROPN
ejpam-3502	172	3	,	,	PUNCT
ejpam-3502	172	4	k	k	PROPN
ejpam-3502	172	5	∈	∈	PROPN
ejpam-3502	172	6	{	{	PUNCT
ejpam-3502	172	7	1	1	NUM
ejpam-3502	172	8	,	,	PUNCT
ejpam-3502	172	9	.	.	PUNCT
ejpam-3502	172	10	.	.	PUNCT
ejpam-3502	173	1	.	.	PUNCT
ejpam-3502	173	2	,	,	PUNCT
ejpam-3502	174	1	n	n	CCONJ
ejpam-3502	174	2	}	}	PUNCT
ejpam-3502	174	3	and	and	CCONJ
ejpam-3502	174	4	e	e	PROPN
ejpam-3502	174	5	∈	∈	PROPN
ejpam-3502	174	6	e(d∗	e(d∗	NOUN
ejpam-3502	174	7	)	)	PUNCT
ejpam-3502	174	8	.	.	PUNCT
ejpam-3502	175	1	if	if	SCONJ
ejpam-3502	175	2	e	e	PROPN
ejpam-3502	175	3	=	=	PUNCT
ejpam-3502	175	4	ei	ei	PROPN
ejpam-3502	175	5	for	for	ADP
ejpam-3502	175	6	some	some	DET
ejpam-3502	175	7	i	i	NOUN
ejpam-3502	175	8	=	=	NOUN
ejpam-3502	175	9	1	1	NUM
ejpam-3502	175	10	,	,	PUNCT
ejpam-3502	175	11	.	.	PUNCT
ejpam-3502	175	12	.	.	PUNCT
ejpam-3502	175	13	.	.	PUNCT
ejpam-3502	176	1	,	,	PUNCT
ejpam-3502	176	2	s	s	VERB
ejpam-3502	176	3	−	−	PROPN
ejpam-3502	176	4	1	1	NUM
ejpam-3502	176	5	,	,	PUNCT
ejpam-3502	176	6	then	then	ADV
ejpam-3502	176	7	g(e	g(e	PROPN
ejpam-3502	176	8	)	)	PUNCT
ejpam-3502	177	1	=	=	PUNCT
ejpam-3502	177	2	g(ei	g(ei	NOUN
ejpam-3502	177	3	)	)	PUNCT
ejpam-3502	177	4	=	=	SYM
ejpam-3502	177	5	vi	vi	PROPN
ejpam-3502	177	6	.	.	NOUN
ejpam-3502	177	7	notice	notice	VERB
ejpam-3502	177	8	that	that	SCONJ
ejpam-3502	177	9	µk	µk	X
ejpam-3502	177	10	-	-	PUNCT
ejpam-3502	177	11	open	open	ADJ
ejpam-3502	177	12	sets	set	NOUN
ejpam-3502	177	13	v	v	ADP
ejpam-3502	177	14	containing	contain	VERB
ejpam-3502	177	15	vi	vi	PROPN
ejpam-3502	177	16	must	must	AUX
ejpam-3502	177	17	contain	contain	VERB
ejpam-3502	177	18	either	either	CCONJ
ejpam-3502	177	19	both	both	CCONJ
ejpam-3502	177	20	vi−1	vi−1	PROPN
ejpam-3502	177	21	and	and	CCONJ
ejpam-3502	177	22	vi	vi	NOUN
ejpam-3502	177	23	or	or	CCONJ
ejpam-3502	177	24	both	both	DET
ejpam-3502	177	25	vi	vi	NOUN
ejpam-3502	177	26	and	and	CCONJ
ejpam-3502	177	27	vi+1	vi+1	NOUN
ejpam-3502	177	28	.	.	PUNCT
ejpam-3502	178	1	for	for	ADP
ejpam-3502	178	2	the	the	DET
ejpam-3502	178	3	former	former	ADJ
ejpam-3502	178	4	case	case	NOUN
ejpam-3502	178	5	,	,	PUNCT
ejpam-3502	178	6	we	we	PRON
ejpam-3502	178	7	take	take	VERB
ejpam-3502	178	8	the	the	DET
ejpam-3502	178	9	νj	νj	NOUN
ejpam-3502	178	10	-	-	PUNCT
ejpam-3502	178	11	open	open	ADJ
ejpam-3502	178	12	set	set	ADJ
ejpam-3502	178	13	c.	c.	PROPN
ejpam-3502	178	14	balingit	balingit	PROPN
ejpam-3502	178	15	,	,	PUNCT
ejpam-3502	178	16	j.	j.	PROPN
ejpam-3502	178	17	benitez	benitez	PROPN
ejpam-3502	178	18	/	/	PUNCT
ejpam-3502	178	19	eur	eur	PROPN
ejpam-3502	178	20	.	.	PUNCT
ejpam-3502	179	1	j.	j.	PROPN
ejpam-3502	179	2	pure	pure	PROPN
ejpam-3502	179	3	appl	appl	PROPN
ejpam-3502	179	4	.	.	PROPN
ejpam-3502	179	5	math	math	PROPN
ejpam-3502	179	6	,	,	PUNCT
ejpam-3502	179	7	12	12	NUM
ejpam-3502	179	8	(	(	PUNCT
ejpam-3502	179	9	4	4	NUM
ejpam-3502	179	10	)	)	PUNCT
ejpam-3502	179	11	(	(	PUNCT
ejpam-3502	179	12	2019	2019	NUM
ejpam-3502	179	13	)	)	PUNCT
ejpam-3502	179	14	,	,	PUNCT
ejpam-3502	179	15	1553	1553	NUM
ejpam-3502	179	16	-	-	SYM
ejpam-3502	179	17	1566	1566	NUM
ejpam-3502	179	18	1558	1558	NUM
ejpam-3502	179	19	figure	figure	NOUN
ejpam-3502	179	20	1	1	NUM
ejpam-3502	179	21	:	:	PUNCT
ejpam-3502	179	22	directed	direct	VERB
ejpam-3502	179	23	graph	graph	NOUN
ejpam-3502	179	24	d∗	d∗	NOUN
ejpam-3502	179	25	for	for	ADP
ejpam-3502	179	26	example	example	NOUN
ejpam-3502	179	27	2.13	2.13	NUM
ejpam-3502	179	28	(	(	PUNCT
ejpam-3502	179	29	3	3	NUM
ejpam-3502	179	30	)	)	PUNCT
ejpam-3502	179	31	.	.	PUNCT
ejpam-3502	180	1	u1	u1	NOUN
ejpam-3502	180	2	=	=	SYM
ejpam-3502	180	3	{	{	PUNCT
ejpam-3502	180	4	ei−1	ei−1	PROPN
ejpam-3502	180	5	,	,	PUNCT
ejpam-3502	180	6	ei	ei	NOUN
ejpam-3502	180	7	}	}	PUNCT
ejpam-3502	180	8	,	,	PUNCT
ejpam-3502	180	9	and	and	CCONJ
ejpam-3502	180	10	for	for	ADP
ejpam-3502	180	11	the	the	DET
ejpam-3502	180	12	latter	latter	ADJ
ejpam-3502	180	13	,	,	PUNCT
ejpam-3502	180	14	take	take	VERB
ejpam-3502	180	15	u2	u2	NOUN
ejpam-3502	180	16	=	=	SYM
ejpam-3502	180	17	{	{	PUNCT
ejpam-3502	180	18	ei	ei	NOUN
ejpam-3502	180	19	}	}	PUNCT
ejpam-3502	180	20	.	.	PUNCT
ejpam-3502	181	1	these	these	PRON
ejpam-3502	181	2	sets	set	VERB
ejpam-3502	181	3	both	both	DET
ejpam-3502	181	4	contain	contain	VERB
ejpam-3502	181	5	e	e	NOUN
ejpam-3502	181	6	=	=	SYM
ejpam-3502	181	7	ei	ei	NOUN
ejpam-3502	181	8	and	and	CCONJ
ejpam-3502	181	9	since	since	SCONJ
ejpam-3502	181	10	g(u1	g(u1	NOUN
ejpam-3502	181	11	)	)	PUNCT
ejpam-3502	182	1	=	=	PRON
ejpam-3502	182	2	{	{	PUNCT
ejpam-3502	182	3	vi−1	vi−1	PROPN
ejpam-3502	182	4	,	,	PUNCT
ejpam-3502	182	5	vi	vi	NOUN
ejpam-3502	182	6	}	}	PUNCT
ejpam-3502	182	7	⊆	⊆	NUM
ejpam-3502	182	8	v	v	NOUN
ejpam-3502	182	9	and	and	CCONJ
ejpam-3502	182	10	g(u2	g(u2	NOUN
ejpam-3502	182	11	)	)	PUNCT
ejpam-3502	183	1	=	=	PRON
ejpam-3502	183	2	{	{	PUNCT
ejpam-3502	183	3	vi	vi	NOUN
ejpam-3502	183	4	}	}	PUNCT
ejpam-3502	183	5	⊆	⊆	NUM
ejpam-3502	183	6	v	v	NOUN
ejpam-3502	183	7	.	.	PUNCT
ejpam-3502	184	1	on	on	ADP
ejpam-3502	184	2	the	the	DET
ejpam-3502	184	3	other	other	ADJ
ejpam-3502	184	4	hand	hand	NOUN
ejpam-3502	184	5	,	,	PUNCT
ejpam-3502	184	6	if	if	SCONJ
ejpam-3502	184	7	e	e	NOUN
ejpam-3502	184	8	=	=	PUNCT
ejpam-3502	184	9	e∗i	e∗i	PUNCT
ejpam-3502	184	10	for	for	ADP
ejpam-3502	184	11	some	some	DET
ejpam-3502	184	12	i	i	NOUN
ejpam-3502	184	13	=	=	NOUN
ejpam-3502	184	14	1	1	NUM
ejpam-3502	184	15	,	,	PUNCT
ejpam-3502	184	16	.	.	PUNCT
ejpam-3502	184	17	.	.	PUNCT
ejpam-3502	184	18	.	.	PUNCT
ejpam-3502	185	1	,	,	PUNCT
ejpam-3502	185	2	n	n	CCONJ
ejpam-3502	185	3	,	,	PUNCT
ejpam-3502	185	4	then	then	ADV
ejpam-3502	185	5	g(e	g(e	PROPN
ejpam-3502	185	6	)	)	PUNCT
ejpam-3502	186	1	=	=	PUNCT
ejpam-3502	186	2	vs	vs	ADP
ejpam-3502	186	3	for	for	ADP
ejpam-3502	186	4	each	each	DET
ejpam-3502	186	5	µk	µk	NOUN
ejpam-3502	186	6	-	-	PUNCT
ejpam-3502	186	7	open	open	ADJ
ejpam-3502	186	8	set	set	NOUN
ejpam-3502	186	9	v	v	NOUN
ejpam-3502	186	10	containing	contain	VERB
ejpam-3502	186	11	vs	vs	ADP
ejpam-3502	186	12	,	,	PUNCT
ejpam-3502	186	13	u	u	NOUN
ejpam-3502	186	14	=	=	X
ejpam-3502	186	15	{	{	PUNCT
ejpam-3502	186	16	ej	ej	NOUN
ejpam-3502	186	17	}	}	PUNCT
ejpam-3502	186	18	is	be	AUX
ejpam-3502	186	19	νj	νj	ADV
ejpam-3502	186	20	-	-	PUNCT
ejpam-3502	186	21	open	open	ADJ
ejpam-3502	186	22	and	and	CCONJ
ejpam-3502	186	23	g(ej	g(ej	PROPN
ejpam-3502	186	24	)	)	PUNCT
ejpam-3502	186	25	=	=	PUNCT
ejpam-3502	186	26	{	{	PUNCT
ejpam-3502	186	27	vs	vs	ADP
ejpam-3502	186	28	}	}	PUNCT
ejpam-3502	186	29	⊆	⊆	NUM
ejpam-3502	186	30	v	v	NOUN
ejpam-3502	186	31	.	.	PUNCT
ejpam-3502	187	1	hence	hence	ADV
ejpam-3502	187	2	,	,	PUNCT
ejpam-3502	187	3	g	g	PROPN
ejpam-3502	187	4	is	be	AUX
ejpam-3502	187	5	(	(	PUNCT
ejpam-3502	187	6	ν	ν	NOUN
ejpam-3502	187	7	,	,	PUNCT
ejpam-3502	187	8	µ)(j	µ)(j	ADJ
ejpam-3502	187	9	,	,	PUNCT
ejpam-3502	187	10	k)-continuous	k)-continuous	ADJ
ejpam-3502	187	11	at	at	ADP
ejpam-3502	187	12	e	e	PROPN
ejpam-3502	187	13	∈	∈	PROPN
ejpam-3502	187	14	e(d∗	e(d∗	NOUN
ejpam-3502	187	15	)	)	PUNCT
ejpam-3502	187	16	.	.	PUNCT
ejpam-3502	188	1	with	with	ADP
ejpam-3502	188	2	j	j	PROPN
ejpam-3502	188	3	,	,	PUNCT
ejpam-3502	188	4	k	k	PROPN
ejpam-3502	188	5	and	and	CCONJ
ejpam-3502	188	6	e	e	PROPN
ejpam-3502	188	7	arbitrary	arbitrary	ADJ
ejpam-3502	188	8	,	,	PUNCT
ejpam-3502	188	9	we	we	PRON
ejpam-3502	188	10	see	see	VERB
ejpam-3502	188	11	that	that	SCONJ
ejpam-3502	188	12	g	g	PROPN
ejpam-3502	188	13	is	be	AUX
ejpam-3502	188	14	pairwise	pairwise	NOUN
ejpam-3502	188	15	(	(	PUNCT
ejpam-3502	188	16	ν	ν	NOUN
ejpam-3502	188	17	,	,	PUNCT
ejpam-3502	188	18	µ)-continuous	µ)-continuous	ADJ
ejpam-3502	188	19	.	.	PUNCT
ejpam-3502	189	1	if	if	SCONJ
ejpam-3502	189	2	every	every	DET
ejpam-3502	189	3	µj	µj	PROPN
ejpam-3502	189	4	is	be	AUX
ejpam-3502	189	5	a	a	DET
ejpam-3502	189	6	strong	strong	ADJ
ejpam-3502	189	7	gt	gt	NOUN
ejpam-3502	189	8	on	on	ADP
ejpam-3502	189	9	x	x	SYM
ejpam-3502	189	10	,	,	PUNCT
ejpam-3502	189	11	and	and	CCONJ
ejpam-3502	189	12	f	f	X
ejpam-3502	189	13	:	:	PUNCT
ejpam-3502	189	14	x	x	X
ejpam-3502	189	15	→	→	SYM
ejpam-3502	189	16	y	y	PROPN
ejpam-3502	189	17	is	be	AUX
ejpam-3502	189	18	defined	define	VERB
ejpam-3502	189	19	by	by	ADP
ejpam-3502	189	20	f(x	f(x	PROPN
ejpam-3502	189	21	)	)	PUNCT
ejpam-3502	190	1	=	=	SYM
ejpam-3502	190	2	c	c	NOUN
ejpam-3502	190	3	for	for	ADP
ejpam-3502	190	4	some	some	DET
ejpam-3502	190	5	c	c	NOUN
ejpam-3502	190	6	∈	∈	PROPN
ejpam-3502	190	7	y	y	PROPN
ejpam-3502	190	8	,	,	PUNCT
ejpam-3502	190	9	then	then	ADV
ejpam-3502	190	10	for	for	ADP
ejpam-3502	190	11	a	a	DET
ejpam-3502	190	12	pair	pair	NOUN
ejpam-3502	190	13	of	of	ADP
ejpam-3502	190	14	fixed	fix	VERB
ejpam-3502	190	15	indices	index	NOUN
ejpam-3502	190	16	j	j	PROPN
ejpam-3502	190	17	,	,	PUNCT
ejpam-3502	190	18	k	k	PROPN
ejpam-3502	190	19	,	,	PUNCT
ejpam-3502	190	20	and	and	CCONJ
ejpam-3502	190	21	for	for	ADP
ejpam-3502	190	22	a	a	DET
ejpam-3502	190	23	νk	νk	NOUN
ejpam-3502	190	24	-	-	ADJ
ejpam-3502	190	25	open	open	ADJ
ejpam-3502	190	26	set	set	VERB
ejpam-3502	190	27	vk	vk	NOUN
ejpam-3502	190	28	containing	contain	VERB
ejpam-3502	190	29	c	c	NOUN
ejpam-3502	190	30	,	,	PUNCT
ejpam-3502	190	31	f(uj	f(uj	PROPN
ejpam-3502	190	32	)	)	PUNCT
ejpam-3502	190	33	=	=	PUNCT
ejpam-3502	190	34	{	{	PUNCT
ejpam-3502	190	35	c	c	NOUN
ejpam-3502	190	36	}	}	PUNCT
ejpam-3502	190	37	⊆	⊆	NUM
ejpam-3502	190	38	vk	vk	NOUN
ejpam-3502	190	39	for	for	ADP
ejpam-3502	190	40	all	all	DET
ejpam-3502	190	41	µj	µj	ADJ
ejpam-3502	190	42	-	-	PUNCT
ejpam-3502	190	43	open	open	ADJ
ejpam-3502	190	44	set	set	ADJ
ejpam-3502	190	45	uj	uj	PROPN
ejpam-3502	190	46	.	.	PUNCT
ejpam-3502	191	1	since	since	SCONJ
ejpam-3502	191	2	each	each	DET
ejpam-3502	191	3	µj	µj	PROPN
ejpam-3502	191	4	is	be	AUX
ejpam-3502	191	5	strong	strong	ADJ
ejpam-3502	191	6	,	,	PUNCT
ejpam-3502	191	7	there	there	PRON
ejpam-3502	191	8	is	be	VERB
ejpam-3502	191	9	such	such	ADJ
ejpam-3502	191	10	µj	µj	PROPN
ejpam-3502	191	11	-	-	PUNCT
ejpam-3502	191	12	open	open	ADJ
ejpam-3502	191	13	set	set	ADJ
ejpam-3502	191	14	u∗j	u∗j	NUM
ejpam-3502	191	15	containing	contain	VERB
ejpam-3502	191	16	x	x	PUNCT
ejpam-3502	191	17	whose	whose	DET
ejpam-3502	191	18	image	image	NOUN
ejpam-3502	191	19	is	be	AUX
ejpam-3502	191	20	contained	contain	VERB
ejpam-3502	191	21	in	in	ADP
ejpam-3502	191	22	vk	vk	PROPN
ejpam-3502	191	23	.	.	PUNCT
ejpam-3502	192	1	with	with	ADP
ejpam-3502	192	2	j	j	PROPN
ejpam-3502	192	3	,	,	PUNCT
ejpam-3502	192	4	k	k	PROPN
ejpam-3502	192	5	held	hold	VERB
ejpam-3502	192	6	arbitrary	arbitrary	ADJ
ejpam-3502	192	7	,	,	PUNCT
ejpam-3502	192	8	we	we	PRON
ejpam-3502	192	9	see	see	VERB
ejpam-3502	192	10	that	that	SCONJ
ejpam-3502	192	11	f	f	PROPN
ejpam-3502	192	12	is	be	AUX
ejpam-3502	192	13	(	(	PUNCT
ejpam-3502	192	14	µ	µ	NOUN
ejpam-3502	192	15	,	,	PUNCT
ejpam-3502	192	16	ν)-continuous	ν)-continuous	ADJ
ejpam-3502	192	17	.	.	PUNCT
ejpam-3502	193	1	if	if	SCONJ
ejpam-3502	193	2	,	,	PUNCT
ejpam-3502	193	3	on	on	ADP
ejpam-3502	193	4	the	the	DET
ejpam-3502	193	5	other	other	ADJ
ejpam-3502	193	6	hand	hand	NOUN
ejpam-3502	193	7	,	,	PUNCT
ejpam-3502	193	8	f	f	X
ejpam-3502	193	9	:	:	PUNCT
ejpam-3502	193	10	x	x	X
ejpam-3502	193	11	→	→	SYM
ejpam-3502	193	12	y	y	PROPN
ejpam-3502	193	13	is	be	AUX
ejpam-3502	193	14	a	a	DET
ejpam-3502	193	15	map	map	NOUN
ejpam-3502	193	16	such	such	ADJ
ejpam-3502	193	17	that	that	SCONJ
ejpam-3502	193	18	f(x	f(x	PROPN
ejpam-3502	193	19	)	)	PUNCT
ejpam-3502	193	20	⊆	⊆	NUM
ejpam-3502	193	21	y	y	PROPN
ejpam-3502	193	22	\	\	PROPN
ejpam-3502	193	23	(	(	PUNCT
ejpam-3502	193	24	⋃	⋃	NOUN
ejpam-3502	193	25	g∈v	g∈v	NOUN
ejpam-3502	193	26	g	g	NOUN
ejpam-3502	193	27	)	)	PUNCT
ejpam-3502	193	28	6=	6=	ADP
ejpam-3502	193	29	∅	∅	NOUN
ejpam-3502	193	30	,	,	PUNCT
ejpam-3502	193	31	then	then	ADV
ejpam-3502	193	32	f	f	PROPN
ejpam-3502	193	33	is	be	AUX
ejpam-3502	193	34	immediately	immediately	ADV
ejpam-3502	193	35	pairwise	pairwise	NOUN
ejpam-3502	193	36	(	(	PUNCT
ejpam-3502	193	37	µ	µ	NOUN
ejpam-3502	193	38	,	,	PUNCT
ejpam-3502	193	39	ν)-continuous	ν)-continuous	PROPN
ejpam-3502	193	40	.	.	PROPN
ejpam-3502	194	1	remark	remark	PROPN
ejpam-3502	194	2	2.14	2.14	NUM
ejpam-3502	194	3	.	.	PUNCT
ejpam-3502	195	1	if	if	SCONJ
ejpam-3502	195	2	f	f	PROPN
ejpam-3502	195	3	:	:	PUNCT
ejpam-3502	195	4	x	x	X
ejpam-3502	195	5	→	→	SYM
ejpam-3502	195	6	y	y	PROPN
ejpam-3502	195	7	is	be	AUX
ejpam-3502	195	8	pairwise	pairwise	NOUN
ejpam-3502	195	9	(	(	PUNCT
ejpam-3502	195	10	µ	µ	NOUN
ejpam-3502	195	11	,	,	PUNCT
ejpam-3502	195	12	ν)-continuous	ν)-continuous	ADJ
ejpam-3502	195	13	,	,	PUNCT
ejpam-3502	195	14	x	x	SYM
ejpam-3502	195	15	∈	∈	PROPN
ejpam-3502	195	16	x	x	X
ejpam-3502	195	17	and	and	CCONJ
ejpam-3502	195	18	v	v	NOUN
ejpam-3502	195	19	is	be	AUX
ejpam-3502	195	20	a	a	DET
ejpam-3502	195	21	g	g	NOUN
ejpam-3502	195	22	-open	-open	NOUN
ejpam-3502	195	23	set	set	NOUN
ejpam-3502	195	24	containing	contain	VERB
ejpam-3502	195	25	f(x	f(x	PROPN
ejpam-3502	195	26	)	)	PUNCT
ejpam-3502	195	27	,	,	PUNCT
ejpam-3502	195	28	then	then	ADV
ejpam-3502	195	29	for	for	ADP
ejpam-3502	195	30	some	some	PRON
ejpam-3502	195	31	k	k	NOUN
ejpam-3502	195	32	there	there	PRON
ejpam-3502	195	33	exists	exist	VERB
ejpam-3502	195	34	a	a	DET
ejpam-3502	195	35	νk	νk	NOUN
ejpam-3502	195	36	-	-	ADJ
ejpam-3502	195	37	open	open	ADJ
ejpam-3502	195	38	subset	subset	ADJ
ejpam-3502	195	39	gk	gk	PROPN
ejpam-3502	195	40	of	of	ADP
ejpam-3502	195	41	v	v	NOUN
ejpam-3502	196	1	such	such	ADJ
ejpam-3502	196	2	that	that	DET
ejpam-3502	196	3	f(x	f(x	PROPN
ejpam-3502	196	4	)	)	PUNCT
ejpam-3502	196	5	∈	∈	PROPN
ejpam-3502	196	6	gk	gk	PROPN
ejpam-3502	196	7	.	.	PROPN
ejpam-3502	197	1	for	for	ADP
ejpam-3502	197	2	any	any	DET
ejpam-3502	197	3	j	j	NOUN
ejpam-3502	197	4	,	,	PUNCT
ejpam-3502	197	5	there	there	PRON
ejpam-3502	197	6	is	be	VERB
ejpam-3502	197	7	a	a	DET
ejpam-3502	197	8	µj	µj	NOUN
ejpam-3502	197	9	-	-	PUNCT
ejpam-3502	197	10	open	open	ADJ
ejpam-3502	197	11	(	(	PUNCT
ejpam-3502	197	12	hence	hence	ADV
ejpam-3502	197	13	,	,	PUNCT
ejpam-3502	197	14	gx	gx	PROPN
ejpam-3502	197	15	-	-	ADJ
ejpam-3502	197	16	open	open	ADJ
ejpam-3502	197	17	)	)	PUNCT
ejpam-3502	197	18	set	set	VERB
ejpam-3502	197	19	u	u	PRON
ejpam-3502	197	20	such	such	ADJ
ejpam-3502	197	21	that	that	SCONJ
ejpam-3502	197	22	x	x	SYM
ejpam-3502	197	23	∈	∈	PROPN
ejpam-3502	197	24	u	u	NOUN
ejpam-3502	197	25	and	and	CCONJ
ejpam-3502	197	26	f(u	f(u	PROPN
ejpam-3502	197	27	)	)	PUNCT
ejpam-3502	197	28	⊆	⊆	NUM
ejpam-3502	197	29	gk	gk	PROPN
ejpam-3502	197	30	⊆	⊆	NUM
ejpam-3502	197	31	v	v	NOUN
ejpam-3502	197	32	.	.	PUNCT
ejpam-3502	198	1	thus	thus	ADV
ejpam-3502	198	2	,	,	PUNCT
ejpam-3502	198	3	f	f	PROPN
ejpam-3502	198	4	is	be	AUX
ejpam-3502	198	5	g	g	NOUN
ejpam-3502	198	6	-continuous	-continuous	ADJ
ejpam-3502	198	7	whenever	whenever	SCONJ
ejpam-3502	198	8	it	it	PRON
ejpam-3502	198	9	is	be	AUX
ejpam-3502	198	10	pairwise	pairwise	NOUN
ejpam-3502	198	11	(	(	PUNCT
ejpam-3502	198	12	µ	µ	NOUN
ejpam-3502	198	13	,	,	PUNCT
ejpam-3502	198	14	ν)-continuous	ν)-continuous	ADJ
ejpam-3502	198	15	.	.	PUNCT
ejpam-3502	199	1	the	the	DET
ejpam-3502	199	2	next	next	ADJ
ejpam-3502	199	3	theorem	theorem	NOUN
ejpam-3502	199	4	provides	provide	VERB
ejpam-3502	199	5	some	some	DET
ejpam-3502	199	6	characterizations	characterization	NOUN
ejpam-3502	199	7	for	for	ADP
ejpam-3502	199	8	a	a	DET
ejpam-3502	199	9	pairwise	pairwise	NOUN
ejpam-3502	199	10	(	(	PUNCT
ejpam-3502	199	11	µ	µ	NUM
ejpam-3502	199	12	,	,	PUNCT
ejpam-3502	199	13	ν)-continuous	ν)-continuous	ADJ
ejpam-3502	199	14	map	map	NOUN
ejpam-3502	199	15	:	:	PUNCT
ejpam-3502	199	16	theorem	theorem	NOUN
ejpam-3502	199	17	2.15	2.15	NUM
ejpam-3502	199	18	.	.	PUNCT
ejpam-3502	200	1	let	let	VERB
ejpam-3502	200	2	f	f	NOUN
ejpam-3502	200	3	:	:	PUNCT
ejpam-3502	200	4	x	x	X
ejpam-3502	200	5	→	→	SYM
ejpam-3502	200	6	y	y	X
ejpam-3502	200	7	be	be	AUX
ejpam-3502	200	8	a	a	DET
ejpam-3502	200	9	map	map	NOUN
ejpam-3502	200	10	.	.	PUNCT
ejpam-3502	201	1	the	the	DET
ejpam-3502	201	2	following	follow	VERB
ejpam-3502	201	3	statements	statement	NOUN
ejpam-3502	201	4	are	be	AUX
ejpam-3502	201	5	equivalent	equivalent	ADJ
ejpam-3502	201	6	:	:	PUNCT
ejpam-3502	201	7	1	1	X
ejpam-3502	201	8	.	.	X
ejpam-3502	201	9	f	f	PROPN
ejpam-3502	201	10	is	be	AUX
ejpam-3502	201	11	pairwise	pairwise	NOUN
ejpam-3502	201	12	(	(	PUNCT
ejpam-3502	201	13	µ	µ	NOUN
ejpam-3502	201	14	,	,	PUNCT
ejpam-3502	201	15	ν)-continuous	ν)-continuous	ADJ
ejpam-3502	201	16	;	;	PUNCT
ejpam-3502	201	17	2	2	X
ejpam-3502	201	18	.	.	X
ejpam-3502	201	19	f−1(v	f−1(v	PROPN
ejpam-3502	201	20	)	)	PUNCT
ejpam-3502	201	21	is	be	AUX
ejpam-3502	201	22	µj	µj	NOUN
ejpam-3502	201	23	-	-	PUNCT
ejpam-3502	201	24	open	open	ADJ
ejpam-3502	201	25	for	for	ADP
ejpam-3502	201	26	each	each	DET
ejpam-3502	201	27	gy	gy	NOUN
ejpam-3502	201	28	-open	-open	NOUN
ejpam-3502	201	29	set	set	VERB
ejpam-3502	201	30	v	v	NOUN
ejpam-3502	201	31	and	and	CCONJ
ejpam-3502	201	32	for	for	ADP
ejpam-3502	201	33	each	each	PRON
ejpam-3502	201	34	j	j	NOUN
ejpam-3502	201	35	=	=	SYM
ejpam-3502	201	36	1	1	NUM
ejpam-3502	201	37	,	,	PUNCT
ejpam-3502	201	38	.	.	PUNCT
ejpam-3502	201	39	.	.	PUNCT
ejpam-3502	202	1	.	.	PUNCT
ejpam-3502	203	1	,	,	PUNCT
ejpam-3502	203	2	m	m	PROPN
ejpam-3502	203	3	;	;	PUNCT
ejpam-3502	203	4	3	3	X
ejpam-3502	203	5	.	.	NUM
ejpam-3502	203	6	f−1(igy	f−1(igy	X
ejpam-3502	203	7	(	(	PUNCT
ejpam-3502	203	8	b	b	NOUN
ejpam-3502	203	9	)	)	PUNCT
ejpam-3502	203	10	)	)	PUNCT
ejpam-3502	204	1	⊆	⊆	NUM
ejpam-3502	204	2	iµj	iµj	NOUN
ejpam-3502	204	3	(	(	PUNCT
ejpam-3502	204	4	f−1(b	f−1(b	PROPN
ejpam-3502	204	5	)	)	PUNCT
ejpam-3502	204	6	)	)	PUNCT
ejpam-3502	204	7	for	for	ADP
ejpam-3502	204	8	all	all	DET
ejpam-3502	204	9	b	b	NOUN
ejpam-3502	204	10	⊆	⊆	NUM
ejpam-3502	204	11	y	y	PROPN
ejpam-3502	204	12	and	and	CCONJ
ejpam-3502	204	13	for	for	ADP
ejpam-3502	204	14	all	all	PRON
ejpam-3502	204	15	j	j	NOUN
ejpam-3502	204	16	=	=	SYM
ejpam-3502	204	17	1	1	NUM
ejpam-3502	204	18	,	,	PUNCT
ejpam-3502	204	19	.	.	PUNCT
ejpam-3502	204	20	.	.	PUNCT
ejpam-3502	204	21	.	.	PUNCT
ejpam-3502	205	1	,	,	PUNCT
ejpam-3502	205	2	m	m	PROPN
ejpam-3502	205	3	;	;	PUNCT
ejpam-3502	205	4	and	and	CCONJ
ejpam-3502	205	5	4	4	X
ejpam-3502	205	6	.	.	X
ejpam-3502	205	7	f−1(f	f−1(f	PROPN
ejpam-3502	205	8	)	)	PUNCT
ejpam-3502	205	9	is	be	AUX
ejpam-3502	205	10	µj	µj	PROPN
ejpam-3502	205	11	-	-	PUNCT
ejpam-3502	205	12	closed	closed	ADJ
ejpam-3502	205	13	for	for	ADP
ejpam-3502	205	14	all	all	DET
ejpam-3502	205	15	gy	gy	NOUN
ejpam-3502	205	16	-closed	-close	VERB
ejpam-3502	205	17	sets	set	NOUN
ejpam-3502	205	18	f	f	NOUN
ejpam-3502	205	19	.	.	PUNCT
ejpam-3502	206	1	proof	proof	NOUN
ejpam-3502	206	2	.	.	PUNCT
ejpam-3502	207	1	(	(	PUNCT
ejpam-3502	207	2	1	1	X
ejpam-3502	207	3	)	)	PUNCT
ejpam-3502	207	4	⇒	⇒	NOUN
ejpam-3502	207	5	(	(	PUNCT
ejpam-3502	207	6	2	2	X
ejpam-3502	207	7	)	)	PUNCT
ejpam-3502	207	8	if	if	SCONJ
ejpam-3502	207	9	f	f	PROPN
ejpam-3502	207	10	is	be	AUX
ejpam-3502	207	11	pairwise	pairwise	NOUN
ejpam-3502	207	12	(	(	PUNCT
ejpam-3502	207	13	µ	µ	NOUN
ejpam-3502	207	14	,	,	PUNCT
ejpam-3502	207	15	ν)-continuous	ν)-continuous	ADJ
ejpam-3502	207	16	and	and	CCONJ
ejpam-3502	207	17	v	v	NOUN
ejpam-3502	207	18	is	be	AUX
ejpam-3502	207	19	a	a	DET
ejpam-3502	207	20	gy	gy	NOUN
ejpam-3502	207	21	-open	-open	NOUN
ejpam-3502	207	22	set	set	NOUN
ejpam-3502	207	23	,	,	PUNCT
ejpam-3502	207	24	then	then	ADV
ejpam-3502	207	25	v	v	AUX
ejpam-3502	207	26	=	=	SYM
ejpam-3502	207	27	igy	igy	PROPN
ejpam-3502	207	28	(	(	PUNCT
ejpam-3502	207	29	v	v	NOUN
ejpam-3502	207	30	)	)	PUNCT
ejpam-3502	207	31	=	=	PUNCT
ejpam-3502	207	32	n⋃	n⋃	ADP
ejpam-3502	207	33	k=1	k=1	X
ejpam-3502	207	34	iνk(v	iνk(v	PROPN
ejpam-3502	207	35	)	)	PUNCT
ejpam-3502	207	36	.	.	PUNCT
ejpam-3502	208	1	now	now	ADV
ejpam-3502	208	2	,	,	PUNCT
ejpam-3502	208	3	each	each	DET
ejpam-3502	208	4	iνk(v	iνk(v	PROPN
ejpam-3502	208	5	)	)	PUNCT
ejpam-3502	208	6	∈	∈	PROPN
ejpam-3502	208	7	νk	νk	NOUN
ejpam-3502	208	8	.	.	PUNCT
ejpam-3502	208	9	by	by	ADP
ejpam-3502	208	10	theorem	theorem	ADJ
ejpam-3502	208	11	2.11	2.11	NUM
ejpam-3502	208	12	(	(	PUNCT
ejpam-3502	208	13	2	2	NUM
ejpam-3502	208	14	)	)	PUNCT
ejpam-3502	208	15	,	,	PUNCT
ejpam-3502	208	16	for	for	ADP
ejpam-3502	208	17	each	each	DET
ejpam-3502	208	18	j	j	PROPN
ejpam-3502	208	19	=	=	SYM
ejpam-3502	208	20	1	1	NUM
ejpam-3502	208	21	,	,	PUNCT
ejpam-3502	208	22	.	.	PUNCT
ejpam-3502	208	23	.	.	PUNCT
ejpam-3502	208	24	.	.	PUNCT
ejpam-3502	209	1	,	,	PUNCT
ejpam-3502	209	2	m	m	PROPN
ejpam-3502	209	3	,	,	PUNCT
ejpam-3502	209	4	f−1(iνk(v	f−1(iνk(v	NOUN
ejpam-3502	209	5	)	)	PUNCT
ejpam-3502	209	6	)	)	PUNCT
ejpam-3502	210	1	=	=	SYM
ejpam-3502	210	2	iµj	iµj	NOUN
ejpam-3502	210	3	(	(	PUNCT
ejpam-3502	210	4	f	f	PROPN
ejpam-3502	210	5	−1(iνk(v	−1(iνk(v	PROPN
ejpam-3502	210	6	)	)	PUNCT
ejpam-3502	210	7	)	)	PUNCT
ejpam-3502	210	8	)	)	PUNCT
ejpam-3502	210	9	and	and	CCONJ
ejpam-3502	210	10	is	be	AUX
ejpam-3502	210	11	therefore	therefore	ADV
ejpam-3502	210	12	µj	µj	ADJ
ejpam-3502	210	13	-	-	PUNCT
ejpam-3502	210	14	open	open	ADJ
ejpam-3502	210	15	.	.	PUNCT
ejpam-3502	211	1	as	as	ADP
ejpam-3502	211	2	a	a	DET
ejpam-3502	211	3	result	result	NOUN
ejpam-3502	211	4	,	,	PUNCT
ejpam-3502	211	5	f−1(v	f−1(v	NOUN
ejpam-3502	211	6	)	)	PUNCT
ejpam-3502	212	1	=	=	SYM
ejpam-3502	212	2	c.	c.	PROPN
ejpam-3502	212	3	balingit	balingit	PROPN
ejpam-3502	212	4	,	,	PUNCT
ejpam-3502	212	5	j.	j.	PROPN
ejpam-3502	212	6	benitez	benitez	PROPN
ejpam-3502	212	7	/	/	PUNCT
ejpam-3502	212	8	eur	eur	PROPN
ejpam-3502	212	9	.	.	PUNCT
ejpam-3502	213	1	j.	j.	PROPN
ejpam-3502	213	2	pure	pure	PROPN
ejpam-3502	213	3	appl	appl	PROPN
ejpam-3502	213	4	.	.	PROPN
ejpam-3502	213	5	math	math	PROPN
ejpam-3502	213	6	,	,	PUNCT
ejpam-3502	213	7	12	12	NUM
ejpam-3502	213	8	(	(	PUNCT
ejpam-3502	213	9	4	4	NUM
ejpam-3502	213	10	)	)	PUNCT
ejpam-3502	213	11	(	(	PUNCT
ejpam-3502	213	12	2019	2019	NUM
ejpam-3502	213	13	)	)	PUNCT
ejpam-3502	213	14	,	,	PUNCT
ejpam-3502	213	15	1553	1553	NUM
ejpam-3502	213	16	-	-	SYM
ejpam-3502	213	17	1566	1566	NUM
ejpam-3502	213	18	1559	1559	NUM
ejpam-3502	213	19	n⋃	n⋃	X
ejpam-3502	213	20	k=1	k=1	PROPN
ejpam-3502	213	21	f−1(iνk(v	f−1(iνk(v	PROPN
ejpam-3502	213	22	)	)	PUNCT
ejpam-3502	213	23	)	)	PUNCT
ejpam-3502	213	24	is	be	AUX
ejpam-3502	213	25	µj	µj	NOUN
ejpam-3502	213	26	-	-	PUNCT
ejpam-3502	213	27	open	open	ADJ
ejpam-3502	213	28	for	for	ADP
ejpam-3502	213	29	every	every	DET
ejpam-3502	213	30	j	j	NOUN
ejpam-3502	213	31	=	=	SYM
ejpam-3502	213	32	1	1	NUM
ejpam-3502	213	33	,	,	PUNCT
ejpam-3502	213	34	.	.	PUNCT
ejpam-3502	213	35	.	.	PUNCT
ejpam-3502	213	36	.	.	PUNCT
ejpam-3502	214	1	,	,	PUNCT
ejpam-3502	214	2	m.	m.	NOUN
ejpam-3502	214	3	(	(	PUNCT
ejpam-3502	214	4	2	2	NUM
ejpam-3502	214	5	)	)	PUNCT
ejpam-3502	214	6	⇒	⇒	NOUN
ejpam-3502	214	7	(	(	PUNCT
ejpam-3502	214	8	3	3	X
ejpam-3502	214	9	)	)	PUNCT
ejpam-3502	214	10	suppose	suppose	VERB
ejpam-3502	214	11	that	that	SCONJ
ejpam-3502	214	12	b	b	PROPN
ejpam-3502	214	13	⊆	⊆	NUM
ejpam-3502	214	14	y	y	NOUN
ejpam-3502	214	15	.	.	PUNCT
ejpam-3502	215	1	then	then	ADV
ejpam-3502	215	2	igy	igy	PROPN
ejpam-3502	215	3	(	(	PUNCT
ejpam-3502	215	4	b	b	NOUN
ejpam-3502	215	5	)	)	PUNCT
ejpam-3502	215	6	is	be	AUX
ejpam-3502	215	7	gy	gy	NOUN
ejpam-3502	215	8	-open	-open	NOUN
ejpam-3502	215	9	.	.	PUNCT
ejpam-3502	216	1	by	by	ADP
ejpam-3502	216	2	assumption	assumption	NOUN
ejpam-3502	216	3	,	,	PUNCT
ejpam-3502	216	4	f−1(igy	f−1(igy	X
ejpam-3502	216	5	(	(	PUNCT
ejpam-3502	216	6	b	b	NOUN
ejpam-3502	216	7	)	)	PUNCT
ejpam-3502	216	8	)	)	PUNCT
ejpam-3502	216	9	is	be	AUX
ejpam-3502	216	10	µj	µj	NOUN
ejpam-3502	216	11	-	-	PUNCT
ejpam-3502	216	12	open	open	ADJ
ejpam-3502	216	13	for	for	ADP
ejpam-3502	216	14	each	each	PRON
ejpam-3502	216	15	j	j	NOUN
ejpam-3502	216	16	=	=	SYM
ejpam-3502	216	17	1	1	NUM
ejpam-3502	216	18	,	,	PUNCT
ejpam-3502	216	19	.	.	PUNCT
ejpam-3502	216	20	.	.	PUNCT
ejpam-3502	217	1	.	.	PUNCT
ejpam-3502	218	1	,	,	PUNCT
ejpam-3502	218	2	m	m	PRON
ejpam-3502	218	3	,	,	PUNCT
ejpam-3502	218	4	implying	imply	VERB
ejpam-3502	218	5	that	that	SCONJ
ejpam-3502	218	6	f−1(igy	f−1(igy	X
ejpam-3502	218	7	(	(	PUNCT
ejpam-3502	218	8	b	b	NOUN
ejpam-3502	218	9	)	)	PUNCT
ejpam-3502	218	10	)	)	PUNCT
ejpam-3502	219	1	=	=	SYM
ejpam-3502	219	2	iµj	iµj	NOUN
ejpam-3502	219	3	(	(	PUNCT
ejpam-3502	219	4	f	f	PROPN
ejpam-3502	219	5	−1(igy	−1(igy	PROPN
ejpam-3502	219	6	(	(	PUNCT
ejpam-3502	219	7	b	b	NOUN
ejpam-3502	219	8	)	)	PUNCT
ejpam-3502	219	9	)	)	PUNCT
ejpam-3502	219	10	)	)	PUNCT
ejpam-3502	220	1	⊆	⊆	NUM
ejpam-3502	220	2	iµj	iµj	NOUN
ejpam-3502	220	3	(	(	PUNCT
ejpam-3502	220	4	f	f	PROPN
ejpam-3502	220	5	−1(b	−1(b	NOUN
ejpam-3502	220	6	)	)	PUNCT
ejpam-3502	220	7	)	)	PUNCT
ejpam-3502	220	8	for	for	ADP
ejpam-3502	220	9	each	each	DET
ejpam-3502	220	10	j	j	PROPN
ejpam-3502	220	11	=	=	SYM
ejpam-3502	220	12	1	1	NUM
ejpam-3502	220	13	,	,	PUNCT
ejpam-3502	220	14	.	.	PUNCT
ejpam-3502	220	15	.	.	PUNCT
ejpam-3502	220	16	.	.	PUNCT
ejpam-3502	221	1	,	,	PUNCT
ejpam-3502	221	2	m.	m.	NOUN
ejpam-3502	221	3	(	(	PUNCT
ejpam-3502	221	4	3	3	NUM
ejpam-3502	221	5	)	)	PUNCT
ejpam-3502	221	6	⇒	⇒	NOUN
ejpam-3502	221	7	(	(	PUNCT
ejpam-3502	221	8	1	1	NUM
ejpam-3502	221	9	)	)	PUNCT
ejpam-3502	221	10	for	for	ADP
ejpam-3502	221	11	a	a	DET
ejpam-3502	221	12	pair	pair	NOUN
ejpam-3502	221	13	j	j	PROPN
ejpam-3502	221	14	,	,	PUNCT
ejpam-3502	221	15	k	k	PROPN
ejpam-3502	221	16	,	,	PUNCT
ejpam-3502	221	17	and	and	CCONJ
ejpam-3502	221	18	for	for	ADP
ejpam-3502	221	19	b	b	PROPN
ejpam-3502	221	20	⊆	⊆	NUM
ejpam-3502	221	21	y	y	PROPN
ejpam-3502	221	22	,	,	PUNCT
ejpam-3502	221	23	iνk(b	iνk(b	PROPN
ejpam-3502	221	24	)	)	PUNCT
ejpam-3502	221	25	is	be	AUX
ejpam-3502	221	26	νk	νk	NOUN
ejpam-3502	221	27	-	-	ADJ
ejpam-3502	221	28	open	open	ADJ
ejpam-3502	221	29	and	and	CCONJ
ejpam-3502	221	30	is	be	AUX
ejpam-3502	221	31	therefore	therefore	ADV
ejpam-3502	221	32	gy	gy	PROPN
ejpam-3502	221	33	-open	-open	PROPN
ejpam-3502	221	34	.	.	PUNCT
ejpam-3502	222	1	thus	thus	ADV
ejpam-3502	222	2	,	,	PUNCT
ejpam-3502	222	3	by	by	ADP
ejpam-3502	222	4	statement	statement	NOUN
ejpam-3502	222	5	(	(	PUNCT
ejpam-3502	222	6	3	3	NUM
ejpam-3502	222	7	)	)	PUNCT
ejpam-3502	222	8	,	,	PUNCT
ejpam-3502	222	9	f−1(iνk(b	f−1(iνk(b	NOUN
ejpam-3502	222	10	)	)	PUNCT
ejpam-3502	222	11	)	)	PUNCT
ejpam-3502	222	12	=	=	NUM
ejpam-3502	222	13	f−1(igy	f−1(igy	X
ejpam-3502	222	14	(	(	PUNCT
ejpam-3502	222	15	iνk(b	iνk(b	NOUN
ejpam-3502	222	16	)	)	PUNCT
ejpam-3502	222	17	)	)	PUNCT
ejpam-3502	222	18	)	)	PUNCT
ejpam-3502	223	1	⊆	⊆	NUM
ejpam-3502	223	2	iµj	iµj	NOUN
ejpam-3502	223	3	(	(	PUNCT
ejpam-3502	223	4	f−1(iνk(b	f−1(iνk(b	NOUN
ejpam-3502	223	5	)	)	PUNCT
ejpam-3502	223	6	)	)	PUNCT
ejpam-3502	223	7	)	)	PUNCT
ejpam-3502	224	1	⊆	⊆	NUM
ejpam-3502	224	2	iµj	iµj	NOUN
ejpam-3502	224	3	(	(	PUNCT
ejpam-3502	224	4	f−1(b	f−1(b	PROPN
ejpam-3502	224	5	)	)	PUNCT
ejpam-3502	224	6	)	)	PUNCT
ejpam-3502	224	7	.	.	PUNCT
ejpam-3502	225	1	by	by	ADP
ejpam-3502	225	2	the	the	DET
ejpam-3502	225	3	equivalence	equivalence	NOUN
ejpam-3502	225	4	in	in	ADP
ejpam-3502	225	5	theorem	theorem	NOUN
ejpam-3502	225	6	2.11	2.11	NUM
ejpam-3502	225	7	,	,	PUNCT
ejpam-3502	225	8	and	and	CCONJ
ejpam-3502	225	9	since	since	SCONJ
ejpam-3502	225	10	j	j	PROPN
ejpam-3502	225	11	,	,	PUNCT
ejpam-3502	225	12	k	k	PROPN
ejpam-3502	225	13	are	be	AUX
ejpam-3502	225	14	arbitrarily	arbitrarily	ADV
ejpam-3502	225	15	chosen	choose	VERB
ejpam-3502	225	16	,	,	PUNCT
ejpam-3502	225	17	we	we	PRON
ejpam-3502	225	18	see	see	VERB
ejpam-3502	225	19	that	that	SCONJ
ejpam-3502	225	20	f	f	PROPN
ejpam-3502	225	21	is	be	AUX
ejpam-3502	225	22	pairwise	pairwise	NOUN
ejpam-3502	225	23	(	(	PUNCT
ejpam-3502	225	24	µ	µ	NOUN
ejpam-3502	225	25	,	,	PUNCT
ejpam-3502	225	26	ν)-continuous	ν)-continuous	ADJ
ejpam-3502	225	27	.	.	PUNCT
ejpam-3502	226	1	(	(	PUNCT
ejpam-3502	226	2	4	4	X
ejpam-3502	226	3	)	)	PUNCT
ejpam-3502	226	4	⇔	⇔	X
ejpam-3502	226	5	(	(	PUNCT
ejpam-3502	226	6	2	2	NUM
ejpam-3502	226	7	)	)	PUNCT
ejpam-3502	226	8	this	this	DET
ejpam-3502	226	9	equivalence	equivalence	NOUN
ejpam-3502	226	10	follows	follow	VERB
ejpam-3502	226	11	from	from	ADP
ejpam-3502	226	12	the	the	DET
ejpam-3502	226	13	fact	fact	NOUN
ejpam-3502	226	14	that	that	SCONJ
ejpam-3502	226	15	f−1(y	f−1(y	PROPN
ejpam-3502	226	16	\f	\f	X
ejpam-3502	226	17	)	)	PUNCT
ejpam-3502	227	1	=	=	PUNCT
ejpam-3502	227	2	x	x	PUNCT
ejpam-3502	227	3	\f−1(f	\f−1(f	NOUN
ejpam-3502	227	4	)	)	PUNCT
ejpam-3502	227	5	for	for	ADP
ejpam-3502	227	6	any	any	DET
ejpam-3502	227	7	f	f	PROPN
ejpam-3502	227	8	⊆	⊆	NUM
ejpam-3502	227	9	y	y	PROPN
ejpam-3502	227	10	.	.	PUNCT
ejpam-3502	227	11	�	�	PROPN
ejpam-3502	228	1	3	3	NUM
ejpam-3502	228	2	.	.	PUNCT
ejpam-3502	229	1	g	g	NOUN
ejpam-3502	229	2	-open	-open	PROPN
ejpam-3502	229	3	and	and	CCONJ
ejpam-3502	229	4	g	g	NOUN
ejpam-3502	229	5	-closed	-close	VERB
ejpam-3502	229	6	maps	map	NOUN
ejpam-3502	229	7	now	now	ADV
ejpam-3502	229	8	,	,	PUNCT
ejpam-3502	229	9	we	we	PRON
ejpam-3502	229	10	define	define	VERB
ejpam-3502	229	11	and	and	CCONJ
ejpam-3502	229	12	examine	examine	VERB
ejpam-3502	229	13	g	g	PROPN
ejpam-3502	229	14	-open	-open	PROPN
ejpam-3502	229	15	and	and	CCONJ
ejpam-3502	229	16	g	g	NOUN
ejpam-3502	229	17	-closed	-close	VERB
ejpam-3502	229	18	maps	map	NOUN
ejpam-3502	229	19	on	on	ADP
ejpam-3502	229	20	n	n	CCONJ
ejpam-3502	229	21	-	-	PUNCT
ejpam-3502	229	22	gt	gt	PROPN
ejpam-3502	229	23	spaces	space	VERB
ejpam-3502	229	24	:	:	PUNCT
ejpam-3502	229	25	definition	definition	NOUN
ejpam-3502	229	26	3.1	3.1	NUM
ejpam-3502	229	27	.	.	PUNCT
ejpam-3502	230	1	let	let	VERB
ejpam-3502	230	2	(	(	PUNCT
ejpam-3502	230	3	x	x	NOUN
ejpam-3502	230	4	,	,	PUNCT
ejpam-3502	230	5	gx	gx	PROPN
ejpam-3502	230	6	)	)	PUNCT
ejpam-3502	230	7	and	and	CCONJ
ejpam-3502	230	8	(	(	PUNCT
ejpam-3502	230	9	y	y	PROPN
ejpam-3502	230	10	,	,	PUNCT
ejpam-3502	230	11	gy	gy	NOUN
ejpam-3502	230	12	)	)	PUNCT
ejpam-3502	230	13	be	be	AUX
ejpam-3502	230	14	m	m	PROPN
ejpam-3502	230	15	-	-	PUNCT
ejpam-3502	230	16	gt	gt	PROPN
ejpam-3502	230	17	and	and	CCONJ
ejpam-3502	230	18	n	n	CCONJ
ejpam-3502	230	19	-	-	PUNCT
ejpam-3502	230	20	gt	gt	PROPN
ejpam-3502	230	21	spaces	space	NOUN
ejpam-3502	230	22	,	,	PUNCT
ejpam-3502	230	23	respectively	respectively	ADV
ejpam-3502	230	24	,	,	PUNCT
ejpam-3502	230	25	where	where	SCONJ
ejpam-3502	230	26	gx	gx	PROPN
ejpam-3502	230	27	=	=	PUNCT
ejpam-3502	230	28	{	{	PUNCT
ejpam-3502	230	29	µ1	µ1	PROPN
ejpam-3502	230	30	,	,	PUNCT
ejpam-3502	230	31	.	.	PUNCT
ejpam-3502	230	32	.	.	PUNCT
ejpam-3502	230	33	.	.	PUNCT
ejpam-3502	231	1	,	,	PUNCT
ejpam-3502	231	2	µm	µm	ADP
ejpam-3502	231	3	}	}	PUNCT
ejpam-3502	231	4	and	and	CCONJ
ejpam-3502	231	5	gy	gy	NOUN
ejpam-3502	231	6	=	=	SYM
ejpam-3502	231	7	{	{	PUNCT
ejpam-3502	231	8	ν1	ν1	NOUN
ejpam-3502	231	9	,	,	PUNCT
ejpam-3502	231	10	.	.	PUNCT
ejpam-3502	231	11	.	.	PUNCT
ejpam-3502	232	1	.	.	PUNCT
ejpam-3502	233	1	,	,	PUNCT
ejpam-3502	233	2	νn	νn	AUX
ejpam-3502	233	3	}	}	PUNCT
ejpam-3502	233	4	for	for	ADP
ejpam-3502	233	5	some	some	DET
ejpam-3502	233	6	m	m	NOUN
ejpam-3502	233	7	,	,	PUNCT
ejpam-3502	233	8	n	n	PROPN
ejpam-3502	233	9	∈	∈	NOUN
ejpam-3502	233	10	n	n	NOUN
ejpam-3502	234	1	and	and	CCONJ
ejpam-3502	234	2	let	let	VERB
ejpam-3502	234	3	f	f	NOUN
ejpam-3502	234	4	:	:	PUNCT
ejpam-3502	234	5	x	x	X
ejpam-3502	234	6	→	→	SYM
ejpam-3502	234	7	y	y	X
ejpam-3502	234	8	be	be	AUX
ejpam-3502	234	9	a	a	DET
ejpam-3502	234	10	map	map	NOUN
ejpam-3502	234	11	.	.	PUNCT
ejpam-3502	235	1	f	f	PROPN
ejpam-3502	235	2	is	be	AUX
ejpam-3502	235	3	called	call	VERB
ejpam-3502	235	4	g	g	PROPN
ejpam-3502	235	5	-open	-open	ADJ
ejpam-3502	235	6	map	map	NOUN
ejpam-3502	236	1	[	[	X
ejpam-3502	236	2	resp	resp	NOUN
ejpam-3502	236	3	.	.	PUNCT
ejpam-3502	237	1	g	g	NOUN
ejpam-3502	237	2	-closed	-close	VERB
ejpam-3502	237	3	map	map	NOUN
ejpam-3502	237	4	]	]	X
ejpam-3502	237	5	if	if	SCONJ
ejpam-3502	237	6	f(a	f(a	PROPN
ejpam-3502	237	7	)	)	PUNCT
ejpam-3502	237	8	is	be	AUX
ejpam-3502	237	9	gy	gy	NOUN
ejpam-3502	237	10	-open	-open	PROPN
ejpam-3502	238	1	[	[	X
ejpam-3502	238	2	resp	resp	NOUN
ejpam-3502	238	3	.	.	PUNCT
ejpam-3502	239	1	gy	gy	PROPN
ejpam-3502	239	2	-closed	-closed	PROPN
ejpam-3502	239	3	]	]	PUNCT
ejpam-3502	239	4	for	for	ADP
ejpam-3502	239	5	each	each	DET
ejpam-3502	239	6	gx	gx	PROPN
ejpam-3502	239	7	-	-	PUNCT
ejpam-3502	239	8	open	open	ADJ
ejpam-3502	239	9	[	[	X
ejpam-3502	239	10	resp	resp	NOUN
ejpam-3502	239	11	.	.	PUNCT
ejpam-3502	240	1	gx	gx	PROPN
ejpam-3502	240	2	-	-	PUNCT
ejpam-3502	240	3	closed	closed	ADJ
ejpam-3502	240	4	]	]	PUNCT
ejpam-3502	240	5	set	set	VERB
ejpam-3502	240	6	a.	a.	NOUN
ejpam-3502	240	7	example	example	NOUN
ejpam-3502	240	8	3.2	3.2	NUM
ejpam-3502	240	9	.	.	PUNCT
ejpam-3502	241	1	consider	consider	VERB
ejpam-3502	241	2	the	the	DET
ejpam-3502	241	3	following	follow	VERB
ejpam-3502	241	4	examples	example	NOUN
ejpam-3502	241	5	:	:	PUNCT
ejpam-3502	242	1	1	1	X
ejpam-3502	242	2	.	.	X
ejpam-3502	242	3	let	let	VERB
ejpam-3502	242	4	(	(	PUNCT
ejpam-3502	242	5	x	x	NOUN
ejpam-3502	242	6	,	,	PUNCT
ejpam-3502	242	7	gx	gx	PROPN
ejpam-3502	242	8	)	)	PUNCT
ejpam-3502	242	9	and	and	CCONJ
ejpam-3502	242	10	(	(	PUNCT
ejpam-3502	242	11	y	y	PROPN
ejpam-3502	242	12	,	,	PUNCT
ejpam-3502	242	13	gy	gy	NOUN
ejpam-3502	242	14	)	)	PUNCT
ejpam-3502	242	15	and	and	CCONJ
ejpam-3502	242	16	f	f	X
ejpam-3502	242	17	:	:	PUNCT
ejpam-3502	242	18	x	x	X
ejpam-3502	242	19	→	→	SYM
ejpam-3502	242	20	y	y	PROPN
ejpam-3502	242	21	be	be	AUX
ejpam-3502	242	22	as	as	ADV
ejpam-3502	242	23	defined	define	VERB
ejpam-3502	242	24	in	in	ADP
ejpam-3502	242	25	example	example	NOUN
ejpam-3502	242	26	2.2	2.2	NUM
ejpam-3502	242	27	.	.	PUNCT
ejpam-3502	243	1	if	if	SCONJ
ejpam-3502	243	2	(	(	PUNCT
ejpam-3502	243	3	a	a	PRON
ejpam-3502	243	4	,	,	PUNCT
ejpam-3502	243	5	b	b	NOUN
ejpam-3502	243	6	)	)	PUNCT
ejpam-3502	243	7	∈	∈	PROPN
ejpam-3502	243	8	x	x	NOUN
ejpam-3502	243	9	,	,	PUNCT
ejpam-3502	243	10	then	then	ADV
ejpam-3502	243	11	there	there	PRON
ejpam-3502	243	12	is	be	VERB
ejpam-3502	243	13	a	a	DET
ejpam-3502	243	14	j0	j0	NUM
ejpam-3502	243	15	such	such	ADJ
ejpam-3502	243	16	that	that	SCONJ
ejpam-3502	243	17	j0	j0	PROPN
ejpam-3502	243	18	−	−	PROPN
ejpam-3502	243	19	1	1	NUM
ejpam-3502	243	20	<	<	X
ejpam-3502	243	21	a	a	DET
ejpam-3502	243	22	≤	≤	PROPN
ejpam-3502	243	23	j0	j0	PROPN
ejpam-3502	243	24	.	.	PUNCT
ejpam-3502	244	1	define	define	VERB
ejpam-3502	244	2	f∗	f∗	NOUN
ejpam-3502	244	3	:	:	PUNCT
ejpam-3502	244	4	x	x	X
ejpam-3502	244	5	→	→	PUNCT
ejpam-3502	244	6	y	y	NUM
ejpam-3502	244	7	such	such	ADJ
ejpam-3502	244	8	that	that	SCONJ
ejpam-3502	244	9	f∗(a	f∗(a	NOUN
ejpam-3502	244	10	,	,	PUNCT
ejpam-3502	244	11	b	b	NOUN
ejpam-3502	244	12	)	)	PUNCT
ejpam-3502	244	13	=	=	SYM
ejpam-3502	244	14	j0−a	j0−a	PROPN
ejpam-3502	244	15	j0	j0	PROPN
ejpam-3502	244	16	.	.	PUNCT
ejpam-3502	245	1	for	for	ADP
ejpam-3502	245	2	each	each	DET
ejpam-3502	245	3	j	j	PROPN
ejpam-3502	245	4	=	=	SYM
ejpam-3502	245	5	1	1	NUM
ejpam-3502	245	6	,	,	PUNCT
ejpam-3502	245	7	.	.	PUNCT
ejpam-3502	245	8	.	.	PUNCT
ejpam-3502	245	9	.	.	PUNCT
ejpam-3502	246	1	,	,	PUNCT
ejpam-3502	246	2	m	m	VERB
ejpam-3502	246	3	and	and	CCONJ
ejpam-3502	246	4	for	for	ADP
ejpam-3502	246	5	each	each	PRON
ejpam-3502	246	6	s	s	PART
ejpam-3502	246	7	≥	≥	NOUN
ejpam-3502	246	8	0	0	NUM
ejpam-3502	246	9	,	,	PUNCT
ejpam-3502	246	10	f∗(rjs	f∗(rjs	NUM
ejpam-3502	246	11	)	)	PUNCT
ejpam-3502	247	1	=	=	PUNCT
ejpam-3502	248	1	[	[	X
ejpam-3502	248	2	0	0	NUM
ejpam-3502	248	3	,	,	PUNCT
ejpam-3502	248	4	1	1	NUM
ejpam-3502	248	5	]	]	PUNCT
ejpam-3502	248	6	,	,	PUNCT
ejpam-3502	248	7	which	which	PRON
ejpam-3502	248	8	is	be	AUX
ejpam-3502	248	9	a	a	DET
ejpam-3502	248	10	gy	gy	NOUN
ejpam-3502	248	11	-open	-open	NOUN
ejpam-3502	248	12	set	set	NOUN
ejpam-3502	248	13	.	.	PUNCT
ejpam-3502	249	1	but	but	CCONJ
ejpam-3502	249	2	each	each	DET
ejpam-3502	249	3	gx	gx	PROPN
ejpam-3502	249	4	-open	-open	PROPN
ejpam-3502	249	5	set	set	VERB
ejpam-3502	249	6	u	u	NOUN
ejpam-3502	249	7	⊆	⊆	NUM
ejpam-3502	249	8	x	x	NOUN
ejpam-3502	249	9	is	be	AUX
ejpam-3502	249	10	the	the	DET
ejpam-3502	249	11	union	union	NOUN
ejpam-3502	249	12	of	of	ADP
ejpam-3502	249	13	sets	set	NOUN
ejpam-3502	249	14	rjs	rjs	X
ejpam-3502	249	15	;	;	PUNCT
ejpam-3502	249	16	thus	thus	ADV
ejpam-3502	249	17	,	,	PUNCT
ejpam-3502	249	18	f∗	f∗	NOUN
ejpam-3502	249	19	is	be	AUX
ejpam-3502	249	20	a	a	DET
ejpam-3502	249	21	g	g	NOUN
ejpam-3502	249	22	-open	-open	NOUN
ejpam-3502	249	23	map	map	NOUN
ejpam-3502	249	24	.	.	PUNCT
ejpam-3502	250	1	however	however	ADV
ejpam-3502	250	2	,	,	PUNCT
ejpam-3502	250	3	for	for	ADP
ejpam-3502	250	4	the	the	DET
ejpam-3502	250	5	gx	gx	PROPN
ejpam-3502	250	6	-closed	-closed	PROPN
ejpam-3502	250	7	set	set	NOUN
ejpam-3502	250	8	f	f	X
ejpam-3502	250	9	=	=	PRON
ejpam-3502	250	10	{	{	PUNCT
ejpam-3502	250	11	(	(	PUNCT
ejpam-3502	250	12	x	x	NOUN
ejpam-3502	250	13	,	,	PUNCT
ejpam-3502	250	14	y	y	PROPN
ejpam-3502	250	15	)	)	PUNCT
ejpam-3502	250	16	:	:	PUNCT
ejpam-3502	250	17	0	0	NUM
ejpam-3502	250	18	≤	≤	NUM
ejpam-3502	250	19	x	x	SYM
ejpam-3502	250	20	≤	≤	NUM
ejpam-3502	250	21	1	1	NUM
ejpam-3502	250	22	,	,	PUNCT
ejpam-3502	250	23	0	0	NUM
ejpam-3502	250	24	≤	≤	NUM
ejpam-3502	251	1	y	y	PROPN
ejpam-3502	251	2	<	<	X
ejpam-3502	251	3	n	n	CCONJ
ejpam-3502	251	4	}	}	PUNCT
ejpam-3502	251	5	,	,	PUNCT
ejpam-3502	251	6	we	we	PRON
ejpam-3502	251	7	see	see	VERB
ejpam-3502	251	8	that	that	PRON
ejpam-3502	251	9	f∗(f	f∗(f	PROPN
ejpam-3502	251	10	)	)	PUNCT
ejpam-3502	252	1	=	=	PUNCT
ejpam-3502	253	1	[	[	X
ejpam-3502	253	2	0	0	NUM
ejpam-3502	253	3	,	,	PUNCT
ejpam-3502	253	4	1	1	NUM
ejpam-3502	253	5	]	]	PUNCT
ejpam-3502	253	6	is	be	AUX
ejpam-3502	253	7	not	not	PART
ejpam-3502	253	8	a	a	DET
ejpam-3502	253	9	gy	gy	NOUN
ejpam-3502	253	10	-closed	-close	VERB
ejpam-3502	253	11	set	set	NOUN
ejpam-3502	253	12	.	.	PUNCT
ejpam-3502	254	1	hence	hence	ADV
ejpam-3502	254	2	,	,	PUNCT
ejpam-3502	254	3	f∗	f∗	NOUN
ejpam-3502	254	4	is	be	AUX
ejpam-3502	254	5	not	not	PART
ejpam-3502	254	6	a	a	DET
ejpam-3502	254	7	g	g	NOUN
ejpam-3502	254	8	-closed	-close	VERB
ejpam-3502	254	9	map	map	NOUN
ejpam-3502	254	10	.	.	PUNCT
ejpam-3502	255	1	2	2	X
ejpam-3502	255	2	.	.	X
ejpam-3502	255	3	recall	recall	VERB
ejpam-3502	255	4	the	the	DET
ejpam-3502	255	5	spaces	space	NOUN
ejpam-3502	255	6	(	(	PUNCT
ejpam-3502	255	7	v	v	NOUN
ejpam-3502	255	8	(	(	PUNCT
ejpam-3502	255	9	d),gv	d),gv	X
ejpam-3502	255	10	)	)	PUNCT
ejpam-3502	255	11	and	and	CCONJ
ejpam-3502	255	12	(	(	PUNCT
ejpam-3502	255	13	e(d),ge	e(d),ge	PROPN
ejpam-3502	255	14	)	)	PUNCT
ejpam-3502	255	15	described	describe	VERB
ejpam-3502	255	16	in	in	ADP
ejpam-3502	255	17	example	example	NOUN
ejpam-3502	255	18	2.3	2.3	NUM
ejpam-3502	255	19	.	.	PUNCT
ejpam-3502	256	1	observe	observe	VERB
ejpam-3502	256	2	that	that	SCONJ
ejpam-3502	256	3	each	each	DET
ejpam-3502	256	4	u	u	PROPN
ejpam-3502	256	5	∈	∈	PROPN
ejpam-3502	256	6	v	v	NOUN
ejpam-3502	256	7	(	(	PUNCT
ejpam-3502	256	8	d	d	NOUN
ejpam-3502	256	9	)	)	PUNCT
ejpam-3502	256	10	is	be	AUX
ejpam-3502	256	11	in	in	ADP
ejpam-3502	256	12	some	some	DET
ejpam-3502	256	13	maximal	maximal	ADJ
ejpam-3502	256	14	path	path	NOUN
ejpam-3502	256	15	pi	pi	NOUN
ejpam-3502	256	16	in	in	ADP
ejpam-3502	256	17	d.	d.	PROPN
ejpam-3502	256	18	let	let	VERB
ejpam-3502	256	19	s	s	NOUN
ejpam-3502	256	20	=	=	VERB
ejpam-3502	256	21	max{i	max{i	X
ejpam-3502	256	22	:	:	PUNCT
ejpam-3502	256	23	u	u	PROPN
ejpam-3502	256	24	∈	∈	PROPN
ejpam-3502	256	25	v	v	ADP
ejpam-3502	256	26	(	(	PUNCT
ejpam-3502	256	27	pi	pi	NOUN
ejpam-3502	256	28	)	)	PUNCT
ejpam-3502	256	29	}	}	PUNCT
ejpam-3502	256	30	and	and	CCONJ
ejpam-3502	256	31	denote	denote	VERB
ejpam-3502	256	32	ps	ps	NOUN
ejpam-3502	256	33	=	=	PUNCT
ejpam-3502	257	1	[	[	X
ejpam-3502	257	2	u(s,1	u(s,1	NOUN
ejpam-3502	257	3	)	)	PUNCT
ejpam-3502	257	4	,	,	PUNCT
ejpam-3502	257	5	.	.	PUNCT
ejpam-3502	257	6	.	.	PUNCT
ejpam-3502	258	1	.	.	PUNCT
ejpam-3502	259	1	,	,	PUNCT
ejpam-3502	259	2	u(s	u(s	PROPN
ejpam-3502	259	3	,	,	PUNCT
ejpam-3502	259	4	k	k	NOUN
ejpam-3502	259	5	)	)	PUNCT
ejpam-3502	259	6	]	]	PUNCT
ejpam-3502	259	7	.	.	PUNCT
ejpam-3502	260	1	then	then	ADV
ejpam-3502	260	2	for	for	ADP
ejpam-3502	260	3	every	every	DET
ejpam-3502	260	4	u	u	PROPN
ejpam-3502	260	5	∈	∈	PROPN
ejpam-3502	260	6	u	u	NOUN
ejpam-3502	260	7	,	,	PUNCT
ejpam-3502	260	8	there	there	PRON
ejpam-3502	260	9	corresponds	correspond	VERB
ejpam-3502	260	10	a	a	DET
ejpam-3502	260	11	unique	unique	ADJ
ejpam-3502	260	12	pair	pair	NOUN
ejpam-3502	260	13	(	(	PUNCT
ejpam-3502	260	14	s	s	X
ejpam-3502	260	15	,	,	PUNCT
ejpam-3502	260	16	d	d	NOUN
ejpam-3502	260	17	)	)	PUNCT
ejpam-3502	260	18	such	such	ADJ
ejpam-3502	260	19	that	that	DET
ejpam-3502	260	20	u	u	NOUN
ejpam-3502	260	21	=	=	PROPN
ejpam-3502	260	22	u(s	u(s	PROPN
ejpam-3502	260	23	,	,	PUNCT
ejpam-3502	260	24	d	d	NOUN
ejpam-3502	260	25	)	)	PUNCT
ejpam-3502	260	26	for	for	ADP
ejpam-3502	260	27	some	some	DET
ejpam-3502	260	28	1	1	NUM
ejpam-3502	260	29	≤	≤	NUM
ejpam-3502	260	30	d	d	NOUN
ejpam-3502	260	31	≤	≤	PROPN
ejpam-3502	260	32	k.	k.	NOUN
ejpam-3502	260	33	define	define	VERB
ejpam-3502	260	34	the	the	DET
ejpam-3502	260	35	map	map	NOUN
ejpam-3502	261	1	ϕ∗	ϕ∗	INTJ
ejpam-3502	261	2	:	:	PUNCT
ejpam-3502	261	3	v	v	NOUN
ejpam-3502	261	4	(	(	PUNCT
ejpam-3502	261	5	d	d	NOUN
ejpam-3502	261	6	)	)	PUNCT
ejpam-3502	261	7	→	→	SYM
ejpam-3502	261	8	e(d	e(d	PROPN
ejpam-3502	261	9	)	)	PUNCT
ejpam-3502	261	10	by	by	ADP
ejpam-3502	261	11	ϕ∗(u	ϕ∗(u	NOUN
ejpam-3502	261	12	)	)	PUNCT
ejpam-3502	261	13	=	=	PRON
ejpam-3502	261	14	{	{	PUNCT
ejpam-3502	261	15	e(s	e(s	PROPN
ejpam-3502	261	16	,	,	PUNCT
ejpam-3502	261	17	k−1	k−1	PROPN
ejpam-3502	261	18	)	)	PUNCT
ejpam-3502	261	19	=	=	PUNCT
ejpam-3502	262	1	u(s	u(s	ADJ
ejpam-3502	262	2	,	,	PUNCT
ejpam-3502	262	3	k−1)u(s	k−1)u(s	PRON
ejpam-3502	262	4	,	,	PUNCT
ejpam-3502	262	5	k	k	NOUN
ejpam-3502	262	6	)	)	PUNCT
ejpam-3502	262	7	,	,	PUNCT
ejpam-3502	262	8	if	if	SCONJ
ejpam-3502	262	9	d	d	PROPN
ejpam-3502	262	10	=	=	SYM
ejpam-3502	262	11	k	k	X
ejpam-3502	262	12	e(s	e(s	PROPN
ejpam-3502	262	13	,	,	PUNCT
ejpam-3502	262	14	d	d	NOUN
ejpam-3502	262	15	)	)	PUNCT
ejpam-3502	262	16	=	=	SYM
ejpam-3502	262	17	u(s	u(s	ADJ
ejpam-3502	262	18	,	,	PUNCT
ejpam-3502	262	19	d)u(s	d)u(s	NUM
ejpam-3502	262	20	,	,	PUNCT
ejpam-3502	262	21	d+1	d+1	NOUN
ejpam-3502	262	22	)	)	PUNCT
ejpam-3502	262	23	,	,	PUNCT
ejpam-3502	262	24	if	if	SCONJ
ejpam-3502	262	25	d	d	PROPN
ejpam-3502	262	26	6=	6=	PROPN
ejpam-3502	262	27	k	k	X
ejpam-3502	262	28	.	.	PUNCT
ejpam-3502	263	1	by	by	ADP
ejpam-3502	263	2	the	the	DET
ejpam-3502	263	3	uniqueness	uniqueness	NOUN
ejpam-3502	263	4	of	of	ADP
ejpam-3502	263	5	s	s	PROPN
ejpam-3502	263	6	,	,	PUNCT
ejpam-3502	263	7	we	we	PRON
ejpam-3502	263	8	see	see	VERB
ejpam-3502	263	9	that	that	DET
ejpam-3502	263	10	ϕ∗	ϕ∗	NOUN
ejpam-3502	263	11	is	be	AUX
ejpam-3502	263	12	a	a	DET
ejpam-3502	263	13	well	well	ADV
ejpam-3502	263	14	-	-	PUNCT
ejpam-3502	263	15	defined	define	VERB
ejpam-3502	263	16	map	map	NOUN
ejpam-3502	263	17	.	.	PUNCT
ejpam-3502	264	1	also	also	ADV
ejpam-3502	264	2	,	,	PUNCT
ejpam-3502	264	3	by	by	ADP
ejpam-3502	264	4	definition	definition	NOUN
ejpam-3502	264	5	of	of	ADP
ejpam-3502	264	6	the	the	DET
ejpam-3502	264	7	n	n	CCONJ
ejpam-3502	264	8	-	-	PUNCT
ejpam-3502	264	9	gt	gt	PROPN
ejpam-3502	264	10	space	space	NOUN
ejpam-3502	264	11	(	(	PUNCT
ejpam-3502	264	12	e(d),ge	e(d),ge	PROPN
ejpam-3502	264	13	)	)	PUNCT
ejpam-3502	264	14	,	,	PUNCT
ejpam-3502	264	15	{	{	PUNCT
ejpam-3502	264	16	e	e	X
ejpam-3502	264	17	}	}	PUNCT
ejpam-3502	264	18	is	be	AUX
ejpam-3502	264	19	ge	ge	NOUN
ejpam-3502	264	20	-	-	NOUN
ejpam-3502	264	21	open	open	ADJ
ejpam-3502	264	22	for	for	ADP
ejpam-3502	264	23	every	every	DET
ejpam-3502	264	24	arc	arc	NOUN
ejpam-3502	264	25	e	e	PROPN
ejpam-3502	264	26	∈	∈	PROPN
ejpam-3502	264	27	e(d	e(d	PROPN
ejpam-3502	264	28	)	)	PUNCT
ejpam-3502	264	29	.	.	PUNCT
ejpam-3502	265	1	hence	hence	ADV
ejpam-3502	265	2	,	,	PUNCT
ejpam-3502	265	3	if	if	SCONJ
ejpam-3502	265	4	u	u	PROPN
ejpam-3502	265	5	⊆	⊆	NUM
ejpam-3502	265	6	v	v	ADP
ejpam-3502	265	7	(	(	PUNCT
ejpam-3502	265	8	d	d	NOUN
ejpam-3502	265	9	)	)	PUNCT
ejpam-3502	265	10	is	be	AUX
ejpam-3502	265	11	gv	gv	AUX
ejpam-3502	265	12	-open	-open	ADJ
ejpam-3502	265	13	,	,	PUNCT
ejpam-3502	265	14	then	then	ADV
ejpam-3502	265	15	ϕ∗(u	ϕ∗(u	PROPN
ejpam-3502	265	16	)	)	PUNCT
ejpam-3502	265	17	=	=	SYM
ejpam-3502	265	18	⋃	⋃	NOUN
ejpam-3502	265	19	u∈u	u∈u	ADJ
ejpam-3502	265	20	ϕ∗(u	ϕ∗(u	NOUN
ejpam-3502	265	21	)	)	PUNCT
ejpam-3502	265	22	is	be	AUX
ejpam-3502	265	23	ge	ge	NOUN
ejpam-3502	265	24	-	-	ADJ
ejpam-3502	265	25	open	open	ADJ
ejpam-3502	265	26	.	.	PUNCT
ejpam-3502	266	1	in	in	ADP
ejpam-3502	266	2	turn	turn	NOUN
ejpam-3502	266	3	,	,	PUNCT
ejpam-3502	266	4	ϕ∗	ϕ∗	ADJ
ejpam-3502	266	5	:	:	PUNCT
ejpam-3502	266	6	v	v	NOUN
ejpam-3502	266	7	(	(	PUNCT
ejpam-3502	266	8	d	d	NOUN
ejpam-3502	266	9	)	)	PUNCT
ejpam-3502	266	10	→	→	SYM
ejpam-3502	266	11	e(d	e(d	PROPN
ejpam-3502	266	12	)	)	PUNCT
ejpam-3502	266	13	is	be	AUX
ejpam-3502	266	14	a	a	DET
ejpam-3502	266	15	c.	c.	NOUN
ejpam-3502	266	16	balingit	balingit	PROPN
ejpam-3502	266	17	,	,	PUNCT
ejpam-3502	266	18	j.	j.	PROPN
ejpam-3502	266	19	benitez	benitez	PROPN
ejpam-3502	266	20	/	/	PUNCT
ejpam-3502	266	21	eur	eur	PROPN
ejpam-3502	266	22	.	.	PUNCT
ejpam-3502	267	1	j.	j.	PROPN
ejpam-3502	267	2	pure	pure	PROPN
ejpam-3502	267	3	appl	appl	PROPN
ejpam-3502	267	4	.	.	PROPN
ejpam-3502	267	5	math	math	PROPN
ejpam-3502	267	6	,	,	PUNCT
ejpam-3502	267	7	12	12	NUM
ejpam-3502	267	8	(	(	PUNCT
ejpam-3502	267	9	4	4	NUM
ejpam-3502	267	10	)	)	PUNCT
ejpam-3502	267	11	(	(	PUNCT
ejpam-3502	267	12	2019	2019	NUM
ejpam-3502	267	13	)	)	PUNCT
ejpam-3502	267	14	,	,	PUNCT
ejpam-3502	267	15	1553	1553	NUM
ejpam-3502	267	16	-	-	SYM
ejpam-3502	267	17	1566	1566	NUM
ejpam-3502	267	18	1560	1560	NUM
ejpam-3502	267	19	g	g	NOUN
ejpam-3502	267	20	-open	-open	NOUN
ejpam-3502	267	21	map	map	NOUN
ejpam-3502	267	22	.	.	PUNCT
ejpam-3502	268	1	meanwhile	meanwhile	ADV
ejpam-3502	268	2	,	,	PUNCT
ejpam-3502	268	3	for	for	ADP
ejpam-3502	268	4	any	any	DET
ejpam-3502	268	5	gv	gv	ADV
ejpam-3502	268	6	-closed	-close	VERB
ejpam-3502	268	7	set	set	VERB
ejpam-3502	268	8	f	f	NOUN
ejpam-3502	268	9	,	,	PUNCT
ejpam-3502	268	10	we	we	PRON
ejpam-3502	268	11	see	see	VERB
ejpam-3502	268	12	that	that	DET
ejpam-3502	268	13	ϕ∗(f	ϕ∗(f	PROPN
ejpam-3502	268	14	)	)	PUNCT
ejpam-3502	268	15	is	be	AUX
ejpam-3502	268	16	definitely	definitely	ADV
ejpam-3502	268	17	a	a	DET
ejpam-3502	268	18	ge	ge	PROPN
ejpam-3502	268	19	-	-	PUNCT
ejpam-3502	268	20	closed	close	VERB
ejpam-3502	268	21	set	set	NOUN
ejpam-3502	268	22	.	.	PUNCT
ejpam-3502	269	1	that	that	PRON
ejpam-3502	269	2	is	is	ADV
ejpam-3502	269	3	,	,	PUNCT
ejpam-3502	269	4	ϕ∗	ϕ∗	PROPN
ejpam-3502	269	5	is	be	AUX
ejpam-3502	269	6	a	a	DET
ejpam-3502	269	7	g	g	NOUN
ejpam-3502	269	8	-closed	-close	VERB
ejpam-3502	269	9	map	map	NOUN
ejpam-3502	269	10	.	.	PUNCT
ejpam-3502	270	1	g	g	NOUN
ejpam-3502	270	2	-open	-open	PROPN
ejpam-3502	270	3	and	and	CCONJ
ejpam-3502	270	4	g	g	NOUN
ejpam-3502	270	5	-closed	-close	VERB
ejpam-3502	270	6	maps	map	NOUN
ejpam-3502	270	7	naturally	naturally	ADV
ejpam-3502	270	8	satisfy	satisfy	VERB
ejpam-3502	270	9	the	the	DET
ejpam-3502	270	10	following	follow	VERB
ejpam-3502	270	11	inherent	inherent	ADJ
ejpam-3502	270	12	properties	property	NOUN
ejpam-3502	270	13	of	of	ADP
ejpam-3502	270	14	open	open	ADJ
ejpam-3502	270	15	and	and	CCONJ
ejpam-3502	270	16	closed	closed	ADJ
ejpam-3502	270	17	maps	map	NOUN
ejpam-3502	270	18	in	in	ADP
ejpam-3502	270	19	the	the	DET
ejpam-3502	270	20	sense	sense	NOUN
ejpam-3502	270	21	of	of	ADP
ejpam-3502	270	22	the	the	DET
ejpam-3502	270	23	ordinary	ordinary	ADJ
ejpam-3502	270	24	topological	topological	ADJ
ejpam-3502	270	25	spaces	space	NOUN
ejpam-3502	270	26	:	:	PUNCT
ejpam-3502	270	27	theorem	theorem	VERB
ejpam-3502	270	28	3.3	3.3	NUM
ejpam-3502	270	29	.	.	PUNCT
ejpam-3502	271	1	let	let	VERB
ejpam-3502	271	2	f	f	NOUN
ejpam-3502	271	3	:	:	PUNCT
ejpam-3502	271	4	x	x	X
ejpam-3502	271	5	→	→	SYM
ejpam-3502	271	6	y	y	X
ejpam-3502	271	7	be	be	AUX
ejpam-3502	271	8	a	a	DET
ejpam-3502	271	9	map	map	NOUN
ejpam-3502	271	10	and	and	CCONJ
ejpam-3502	271	11	s	s	VERB
ejpam-3502	271	12	⊆	⊆	NUM
ejpam-3502	271	13	y	y	NOUN
ejpam-3502	271	14	.	.	PUNCT
ejpam-3502	272	1	1	1	X
ejpam-3502	272	2	.	.	X
ejpam-3502	273	1	if	if	SCONJ
ejpam-3502	273	2	f	f	PROPN
ejpam-3502	273	3	is	be	AUX
ejpam-3502	273	4	a	a	DET
ejpam-3502	273	5	g	g	NOUN
ejpam-3502	273	6	-open	-open	NOUN
ejpam-3502	273	7	map	map	NOUN
ejpam-3502	273	8	and	and	CCONJ
ejpam-3502	273	9	a	a	PRON
ejpam-3502	273	10	is	be	AUX
ejpam-3502	273	11	a	a	DET
ejpam-3502	273	12	gx	gx	PROPN
ejpam-3502	273	13	-	-	PUNCT
ejpam-3502	273	14	closed	closed	ADJ
ejpam-3502	273	15	set	set	NOUN
ejpam-3502	273	16	containing	contain	VERB
ejpam-3502	273	17	f−1(s	f−1(s	PROPN
ejpam-3502	273	18	)	)	PUNCT
ejpam-3502	273	19	,	,	PUNCT
ejpam-3502	273	20	then	then	ADV
ejpam-3502	273	21	there	there	PRON
ejpam-3502	273	22	is	be	VERB
ejpam-3502	273	23	a	a	DET
ejpam-3502	273	24	gy	gy	NOUN
ejpam-3502	273	25	-closed	-close	VERB
ejpam-3502	273	26	set	set	NOUN
ejpam-3502	273	27	b	b	NOUN
ejpam-3502	273	28	containing	contain	VERB
ejpam-3502	273	29	s	s	PRON
ejpam-3502	273	30	such	such	ADJ
ejpam-3502	273	31	that	that	DET
ejpam-3502	273	32	f−1(b	f−1(b	PROPN
ejpam-3502	273	33	)	)	PUNCT
ejpam-3502	273	34	⊆	⊆	NUM
ejpam-3502	273	35	a.	a.	NOUN
ejpam-3502	273	36	2	2	NUM
ejpam-3502	273	37	.	.	PUNCT
ejpam-3502	274	1	if	if	SCONJ
ejpam-3502	274	2	f	f	PROPN
ejpam-3502	274	3	is	be	AUX
ejpam-3502	274	4	a	a	DET
ejpam-3502	274	5	g	g	NOUN
ejpam-3502	274	6	-closed	-close	VERB
ejpam-3502	274	7	map	map	NOUN
ejpam-3502	274	8	and	and	CCONJ
ejpam-3502	274	9	u	u	NOUN
ejpam-3502	274	10	is	be	AUX
ejpam-3502	274	11	a	a	DET
ejpam-3502	274	12	gx	gx	PROPN
ejpam-3502	274	13	-	-	PUNCT
ejpam-3502	274	14	open	open	ADJ
ejpam-3502	274	15	set	set	NOUN
ejpam-3502	274	16	containing	contain	VERB
ejpam-3502	274	17	f−1(s	f−1(s	PROPN
ejpam-3502	274	18	)	)	PUNCT
ejpam-3502	274	19	,	,	PUNCT
ejpam-3502	274	20	then	then	ADV
ejpam-3502	274	21	there	there	PRON
ejpam-3502	274	22	is	be	VERB
ejpam-3502	274	23	a	a	DET
ejpam-3502	274	24	gy	gy	NOUN
ejpam-3502	274	25	-open	-open	NOUN
ejpam-3502	274	26	set	set	NOUN
ejpam-3502	274	27	set	set	VERB
ejpam-3502	274	28	v	v	NOUN
ejpam-3502	274	29	containing	contain	VERB
ejpam-3502	274	30	s	s	PRON
ejpam-3502	274	31	such	such	ADJ
ejpam-3502	274	32	that	that	DET
ejpam-3502	274	33	f−1(v	f−1(v	NOUN
ejpam-3502	274	34	)	)	PUNCT
ejpam-3502	275	1	⊆	⊆	NUM
ejpam-3502	275	2	u	u	NOUN
ejpam-3502	275	3	.	.	PUNCT
ejpam-3502	276	1	corollary	corollary	ADJ
ejpam-3502	276	2	3.4	3.4	NUM
ejpam-3502	276	3	.	.	PUNCT
ejpam-3502	277	1	if	if	SCONJ
ejpam-3502	277	2	f	f	PROPN
ejpam-3502	277	3	:	:	PUNCT
ejpam-3502	277	4	x	x	X
ejpam-3502	277	5	→	→	SYM
ejpam-3502	277	6	y	y	PROPN
ejpam-3502	277	7	is	be	AUX
ejpam-3502	277	8	a	a	DET
ejpam-3502	277	9	g	g	NOUN
ejpam-3502	277	10	-closed	-close	VERB
ejpam-3502	277	11	map	map	NOUN
ejpam-3502	277	12	,	,	PUNCT
ejpam-3502	277	13	y	y	PROPN
ejpam-3502	277	14	∈	∈	PROPN
ejpam-3502	277	15	y	y	PROPN
ejpam-3502	277	16	and	and	CCONJ
ejpam-3502	277	17	u	u	PROPN
ejpam-3502	277	18	is	be	AUX
ejpam-3502	277	19	a	a	DET
ejpam-3502	277	20	gx	gx	PROPN
ejpam-3502	277	21	-	-	PUNCT
ejpam-3502	277	22	open	open	ADJ
ejpam-3502	277	23	set	set	NOUN
ejpam-3502	277	24	such	such	ADJ
ejpam-3502	277	25	that	that	SCONJ
ejpam-3502	277	26	f−1({y	f−1({y	NOUN
ejpam-3502	277	27	}	}	PUNCT
ejpam-3502	277	28	)	)	PUNCT
ejpam-3502	278	1	⊆	⊆	NUM
ejpam-3502	278	2	u	u	NOUN
ejpam-3502	278	3	,	,	PUNCT
ejpam-3502	278	4	then	then	ADV
ejpam-3502	278	5	y	y	PROPN
ejpam-3502	278	6	∈	∈	PROPN
ejpam-3502	278	7	iy	iy	PROPN
ejpam-3502	278	8	(	(	PUNCT
ejpam-3502	278	9	f(cx(u	f(cx(u	NOUN
ejpam-3502	278	10	)	)	PUNCT
ejpam-3502	278	11	)	)	PUNCT
ejpam-3502	278	12	)	)	PUNCT
ejpam-3502	278	13	.	.	PUNCT
ejpam-3502	279	1	theorem	theorem	VERB
ejpam-3502	279	2	3.5	3.5	NUM
ejpam-3502	279	3	.	.	PUNCT
ejpam-3502	280	1	let	let	VERB
ejpam-3502	280	2	f	f	NOUN
ejpam-3502	280	3	:	:	PUNCT
ejpam-3502	280	4	x	x	X
ejpam-3502	280	5	→	→	SYM
ejpam-3502	280	6	y	y	X
ejpam-3502	280	7	be	be	AUX
ejpam-3502	280	8	a	a	DET
ejpam-3502	280	9	map	map	NOUN
ejpam-3502	280	10	.	.	PUNCT
ejpam-3502	281	1	the	the	DET
ejpam-3502	281	2	following	follow	VERB
ejpam-3502	281	3	statements	statement	NOUN
ejpam-3502	281	4	are	be	AUX
ejpam-3502	281	5	equivalent	equivalent	ADJ
ejpam-3502	281	6	:	:	PUNCT
ejpam-3502	281	7	1	1	X
ejpam-3502	281	8	.	.	X
ejpam-3502	281	9	f	f	PROPN
ejpam-3502	281	10	is	be	AUX
ejpam-3502	281	11	a	a	DET
ejpam-3502	281	12	g	g	NOUN
ejpam-3502	281	13	-open	-open	NOUN
ejpam-3502	281	14	map	map	NOUN
ejpam-3502	281	15	;	;	PUNCT
ejpam-3502	281	16	2	2	X
ejpam-3502	281	17	.	.	X
ejpam-3502	281	18	f(ix(a	f(ix(a	NOUN
ejpam-3502	281	19	)	)	PUNCT
ejpam-3502	281	20	)	)	PUNCT
ejpam-3502	282	1	⊆	⊆	NUM
ejpam-3502	282	2	iy	iy	PROPN
ejpam-3502	282	3	(	(	PUNCT
ejpam-3502	282	4	f(a	f(a	NOUN
ejpam-3502	282	5	)	)	PUNCT
ejpam-3502	282	6	)	)	PUNCT
ejpam-3502	282	7	for	for	ADP
ejpam-3502	282	8	every	every	DET
ejpam-3502	282	9	a	a	DET
ejpam-3502	282	10	⊆	⊆	NUM
ejpam-3502	282	11	x	x	NOUN
ejpam-3502	282	12	;	;	PUNCT
ejpam-3502	282	13	and	and	CCONJ
ejpam-3502	282	14	3	3	X
ejpam-3502	282	15	.	.	X
ejpam-3502	282	16	for	for	ADP
ejpam-3502	282	17	each	each	DET
ejpam-3502	282	18	x	x	SYM
ejpam-3502	282	19	∈	∈	PROPN
ejpam-3502	282	20	x	x	X
ejpam-3502	282	21	and	and	CCONJ
ejpam-3502	282	22	for	for	ADP
ejpam-3502	282	23	every	every	DET
ejpam-3502	282	24	gx	gx	PROPN
ejpam-3502	282	25	-	-	PUNCT
ejpam-3502	282	26	open	open	ADJ
ejpam-3502	282	27	set	set	NOUN
ejpam-3502	282	28	u	u	NOUN
ejpam-3502	282	29	containing	contain	VERB
ejpam-3502	282	30	x	x	PRON
ejpam-3502	282	31	,	,	PUNCT
ejpam-3502	282	32	there	there	PRON
ejpam-3502	282	33	exists	exist	VERB
ejpam-3502	282	34	a	a	DET
ejpam-3502	282	35	gy	gy	NOUN
ejpam-3502	282	36	-open	-open	NOUN
ejpam-3502	282	37	set	set	NOUN
ejpam-3502	282	38	w	w	NOUN
ejpam-3502	282	39	containing	contain	VERB
ejpam-3502	282	40	f(x	f(x	PROPN
ejpam-3502	282	41	)	)	PUNCT
ejpam-3502	282	42	such	such	ADJ
ejpam-3502	282	43	that	that	SCONJ
ejpam-3502	282	44	w	w	PROPN
ejpam-3502	282	45	⊆	⊆	NUM
ejpam-3502	282	46	f(u	f(u	PROPN
ejpam-3502	282	47	)	)	PUNCT
ejpam-3502	282	48	.	.	PUNCT
ejpam-3502	283	1	theorem	theorem	VERB
ejpam-3502	283	2	3.6	3.6	NUM
ejpam-3502	283	3	.	.	PUNCT
ejpam-3502	284	1	a	a	DET
ejpam-3502	284	2	map	map	NOUN
ejpam-3502	284	3	f	f	X
ejpam-3502	284	4	:	:	PUNCT
ejpam-3502	284	5	x	x	X
ejpam-3502	284	6	→	→	SYM
ejpam-3502	284	7	y	y	PROPN
ejpam-3502	284	8	is	be	AUX
ejpam-3502	284	9	a	a	DET
ejpam-3502	284	10	g	g	NOUN
ejpam-3502	284	11	-closed	-close	VERB
ejpam-3502	284	12	map	map	NOUN
ejpam-3502	284	13	if	if	SCONJ
ejpam-3502	284	14	and	and	CCONJ
ejpam-3502	284	15	only	only	ADV
ejpam-3502	284	16	if	if	SCONJ
ejpam-3502	284	17	cy	cy	PROPN
ejpam-3502	284	18	(	(	PUNCT
ejpam-3502	284	19	f(a	f(a	NOUN
ejpam-3502	284	20	)	)	PUNCT
ejpam-3502	284	21	)	)	PUNCT
ejpam-3502	284	22	⊆	⊆	NUM
ejpam-3502	284	23	f(cx(a	f(cx(a	NOUN
ejpam-3502	284	24	)	)	PUNCT
ejpam-3502	284	25	)	)	PUNCT
ejpam-3502	284	26	for	for	SCONJ
ejpam-3502	284	27	each	each	PRON
ejpam-3502	284	28	a	a	DET
ejpam-3502	284	29	⊆	⊆	NUM
ejpam-3502	284	30	x.	x.	NOUN
ejpam-3502	284	31	theorem	theorem	VERB
ejpam-3502	284	32	3.7	3.7	NUM
ejpam-3502	284	33	.	.	PUNCT
ejpam-3502	285	1	let	let	VERB
ejpam-3502	285	2	f	f	NOUN
ejpam-3502	285	3	:	:	PUNCT
ejpam-3502	285	4	x	x	X
ejpam-3502	285	5	→	→	SYM
ejpam-3502	285	6	y	y	X
ejpam-3502	285	7	be	be	AUX
ejpam-3502	285	8	a	a	DET
ejpam-3502	285	9	map	map	NOUN
ejpam-3502	285	10	.	.	PUNCT
ejpam-3502	286	1	the	the	DET
ejpam-3502	286	2	following	follow	VERB
ejpam-3502	286	3	statements	statement	NOUN
ejpam-3502	286	4	are	be	AUX
ejpam-3502	286	5	equivalent	equivalent	ADJ
ejpam-3502	286	6	:	:	PUNCT
ejpam-3502	286	7	1	1	X
ejpam-3502	286	8	.	.	X
ejpam-3502	286	9	f	f	PROPN
ejpam-3502	286	10	is	be	AUX
ejpam-3502	286	11	a	a	DET
ejpam-3502	286	12	g	g	NOUN
ejpam-3502	286	13	-closed	-close	VERB
ejpam-3502	286	14	map	map	NOUN
ejpam-3502	286	15	;	;	PUNCT
ejpam-3502	286	16	2	2	X
ejpam-3502	286	17	.	.	X
ejpam-3502	287	1	if	if	SCONJ
ejpam-3502	287	2	a	a	DET
ejpam-3502	287	3	⊆	⊆	NUM
ejpam-3502	287	4	x	x	X
ejpam-3502	287	5	is	be	AUX
ejpam-3502	287	6	a	a	DET
ejpam-3502	287	7	gx	gx	PROPN
ejpam-3502	287	8	-	-	PUNCT
ejpam-3502	287	9	open	open	ADJ
ejpam-3502	287	10	set	set	NOUN
ejpam-3502	287	11	,	,	PUNCT
ejpam-3502	287	12	then	then	ADV
ejpam-3502	287	13	s	s	VERB
ejpam-3502	287	14	=	=	PUNCT
ejpam-3502	287	15	{	{	PUNCT
ejpam-3502	287	16	y	y	NOUN
ejpam-3502	287	17	:	:	PUNCT
ejpam-3502	287	18	f−1({y	f−1({y	PROPN
ejpam-3502	287	19	}	}	PUNCT
ejpam-3502	287	20	)	)	PUNCT
ejpam-3502	287	21	⊆	⊆	X
ejpam-3502	287	22	a	a	PRON
ejpam-3502	287	23	}	}	PUNCT
ejpam-3502	287	24	is	be	AUX
ejpam-3502	287	25	a	a	DET
ejpam-3502	287	26	gy	gy	NOUN
ejpam-3502	287	27	-open	-open	NOUN
ejpam-3502	287	28	set	set	NOUN
ejpam-3502	287	29	;	;	PUNCT
ejpam-3502	287	30	and	and	CCONJ
ejpam-3502	287	31	3	3	X
ejpam-3502	287	32	.	.	X
ejpam-3502	288	1	if	if	SCONJ
ejpam-3502	288	2	b	b	PROPN
ejpam-3502	288	3	⊆	⊆	NUM
ejpam-3502	288	4	x	x	X
ejpam-3502	288	5	is	be	AUX
ejpam-3502	288	6	a	a	DET
ejpam-3502	288	7	gx	gx	PROPN
ejpam-3502	288	8	-	-	PUNCT
ejpam-3502	288	9	closed	closed	ADJ
ejpam-3502	288	10	set	set	NOUN
ejpam-3502	288	11	,	,	PUNCT
ejpam-3502	288	12	then	then	ADV
ejpam-3502	288	13	t	t	PROPN
ejpam-3502	288	14	=	=	PUNCT
ejpam-3502	288	15	{	{	PUNCT
ejpam-3502	288	16	y	y	NOUN
ejpam-3502	288	17	:	:	PUNCT
ejpam-3502	288	18	f−1({y	f−1({y	PROPN
ejpam-3502	288	19	}	}	PUNCT
ejpam-3502	288	20	)	)	PUNCT
ejpam-3502	288	21	∩b	∩b	NOUN
ejpam-3502	288	22	6=	6=	PUNCT
ejpam-3502	288	23	∅	∅	NOUN
ejpam-3502	288	24	}	}	PUNCT
ejpam-3502	288	25	is	be	AUX
ejpam-3502	288	26	a	a	DET
ejpam-3502	288	27	gy	gy	NOUN
ejpam-3502	288	28	-closed	-close	VERB
ejpam-3502	288	29	set	set	NOUN
ejpam-3502	288	30	.	.	PUNCT
ejpam-3502	289	1	we	we	PRON
ejpam-3502	289	2	now	now	ADV
ejpam-3502	289	3	establish	establish	VERB
ejpam-3502	289	4	the	the	DET
ejpam-3502	289	5	equivalence	equivalence	NOUN
ejpam-3502	289	6	of	of	ADP
ejpam-3502	289	7	g	g	NOUN
ejpam-3502	289	8	-open	-open	ADJ
ejpam-3502	289	9	and	and	CCONJ
ejpam-3502	289	10	g	g	NOUN
ejpam-3502	289	11	-closed	-close	VERB
ejpam-3502	289	12	maps	map	NOUN
ejpam-3502	289	13	involving	involve	VERB
ejpam-3502	289	14	bijective	bijective	ADJ
ejpam-3502	289	15	mappings	mapping	NOUN
ejpam-3502	289	16	:	:	PUNCT
ejpam-3502	289	17	theorem	theorem	VERB
ejpam-3502	289	18	3.8	3.8	NUM
ejpam-3502	289	19	.	.	PUNCT
ejpam-3502	290	1	if	if	SCONJ
ejpam-3502	290	2	f	f	PROPN
ejpam-3502	290	3	:	:	PUNCT
ejpam-3502	290	4	x	x	X
ejpam-3502	290	5	→	→	SYM
ejpam-3502	290	6	y	y	PROPN
ejpam-3502	290	7	is	be	AUX
ejpam-3502	290	8	bijective	bijective	ADJ
ejpam-3502	290	9	,	,	PUNCT
ejpam-3502	290	10	then	then	ADV
ejpam-3502	290	11	f	f	PROPN
ejpam-3502	290	12	is	be	AUX
ejpam-3502	290	13	a	a	DET
ejpam-3502	290	14	g	g	NOUN
ejpam-3502	290	15	-open	-open	NOUN
ejpam-3502	290	16	map	map	NOUN
ejpam-3502	290	17	if	if	SCONJ
ejpam-3502	290	18	and	and	CCONJ
ejpam-3502	290	19	only	only	ADV
ejpam-3502	290	20	if	if	SCONJ
ejpam-3502	290	21	f	f	PROPN
ejpam-3502	290	22	is	be	AUX
ejpam-3502	290	23	a	a	DET
ejpam-3502	290	24	g	g	NOUN
ejpam-3502	290	25	-closed	-close	VERB
ejpam-3502	290	26	map	map	NOUN
ejpam-3502	290	27	.	.	PUNCT
ejpam-3502	291	1	proof	proof	NOUN
ejpam-3502	291	2	.	.	PUNCT
ejpam-3502	292	1	observe	observe	VERB
ejpam-3502	292	2	that	that	SCONJ
ejpam-3502	292	3	for	for	ADP
ejpam-3502	292	4	a	a	DET
ejpam-3502	292	5	subset	subset	ADJ
ejpam-3502	292	6	u	u	NOUN
ejpam-3502	292	7	of	of	ADP
ejpam-3502	292	8	x	x	PROPN
ejpam-3502	292	9	,	,	PUNCT
ejpam-3502	292	10	f(x\u	f(x\u	PROPN
ejpam-3502	292	11	)	)	PUNCT
ejpam-3502	292	12	=	=	SYM
ejpam-3502	292	13	y	y	PROPN
ejpam-3502	292	14	\f(u	\f(u	PROPN
ejpam-3502	292	15	)	)	PUNCT
ejpam-3502	292	16	if	if	SCONJ
ejpam-3502	292	17	and	and	CCONJ
ejpam-3502	292	18	only	only	ADV
ejpam-3502	292	19	if	if	SCONJ
ejpam-3502	292	20	f	f	PROPN
ejpam-3502	292	21	is	be	AUX
ejpam-3502	292	22	bijective	bijective	ADJ
ejpam-3502	292	23	.	.	PUNCT
ejpam-3502	293	1	thus	thus	ADV
ejpam-3502	293	2	,	,	PUNCT
ejpam-3502	293	3	if	if	SCONJ
ejpam-3502	293	4	f	f	PROPN
ejpam-3502	293	5	is	be	AUX
ejpam-3502	293	6	a	a	DET
ejpam-3502	293	7	g	g	NOUN
ejpam-3502	293	8	-open	-open	NOUN
ejpam-3502	293	9	map	map	NOUN
ejpam-3502	293	10	and	and	CCONJ
ejpam-3502	293	11	u	u	NOUN
ejpam-3502	293	12	is	be	AUX
ejpam-3502	293	13	g	g	NOUN
ejpam-3502	293	14	-closed	-close	VERB
ejpam-3502	293	15	,	,	PUNCT
ejpam-3502	293	16	then	then	ADV
ejpam-3502	293	17	f(x\u	f(x\u	PROPN
ejpam-3502	293	18	)	)	PUNCT
ejpam-3502	293	19	=	=	SYM
ejpam-3502	293	20	y	y	PROPN
ejpam-3502	293	21	\f(u	\f(u	PROPN
ejpam-3502	293	22	)	)	PUNCT
ejpam-3502	293	23	is	be	AUX
ejpam-3502	293	24	g	g	PROPN
ejpam-3502	293	25	-open	-open	ADJ
ejpam-3502	293	26	so	so	SCONJ
ejpam-3502	293	27	that	that	SCONJ
ejpam-3502	293	28	f(u	f(u	NOUN
ejpam-3502	293	29	)	)	PUNCT
ejpam-3502	293	30	is	be	AUX
ejpam-3502	293	31	g	g	NOUN
ejpam-3502	293	32	-closed	-close	VERB
ejpam-3502	293	33	.	.	PUNCT
ejpam-3502	294	1	that	that	PRON
ejpam-3502	294	2	is	be	AUX
ejpam-3502	294	3	,	,	PUNCT
ejpam-3502	294	4	f	f	PROPN
ejpam-3502	294	5	is	be	AUX
ejpam-3502	294	6	also	also	ADV
ejpam-3502	294	7	a	a	DET
ejpam-3502	294	8	g	g	NOUN
ejpam-3502	294	9	-closed	-close	VERB
ejpam-3502	294	10	map	map	NOUN
ejpam-3502	294	11	.	.	PUNCT
ejpam-3502	295	1	similarly	similarly	ADV
ejpam-3502	295	2	,	,	PUNCT
ejpam-3502	295	3	if	if	SCONJ
ejpam-3502	295	4	f	f	PROPN
ejpam-3502	295	5	is	be	AUX
ejpam-3502	295	6	a	a	DET
ejpam-3502	295	7	g	g	NOUN
ejpam-3502	295	8	-closed	-close	VERB
ejpam-3502	295	9	map	map	NOUN
ejpam-3502	295	10	,	,	PUNCT
ejpam-3502	295	11	then	then	ADV
ejpam-3502	295	12	f	f	PROPN
ejpam-3502	295	13	is	be	AUX
ejpam-3502	295	14	also	also	ADV
ejpam-3502	295	15	a	a	DET
ejpam-3502	295	16	g	g	NOUN
ejpam-3502	295	17	-open	-open	NOUN
ejpam-3502	295	18	map	map	NOUN
ejpam-3502	295	19	.	.	PUNCT
ejpam-3502	296	1	�	�	PROPN
ejpam-3502	296	2	definition	definition	NOUN
ejpam-3502	296	3	3.9	3.9	NUM
ejpam-3502	296	4	.	.	PUNCT
ejpam-3502	297	1	let	let	VERB
ejpam-3502	297	2	(	(	PUNCT
ejpam-3502	297	3	x	x	NOUN
ejpam-3502	297	4	,	,	PUNCT
ejpam-3502	297	5	gx	gx	PROPN
ejpam-3502	297	6	)	)	PUNCT
ejpam-3502	297	7	and	and	CCONJ
ejpam-3502	297	8	(	(	PUNCT
ejpam-3502	297	9	y	y	PROPN
ejpam-3502	297	10	,	,	PUNCT
ejpam-3502	297	11	gy	gy	NOUN
ejpam-3502	297	12	)	)	PUNCT
ejpam-3502	297	13	be	be	AUX
ejpam-3502	297	14	m	m	PROPN
ejpam-3502	297	15	-	-	PUNCT
ejpam-3502	297	16	gt	gt	PROPN
ejpam-3502	297	17	and	and	CCONJ
ejpam-3502	297	18	n	n	CCONJ
ejpam-3502	297	19	-	-	PUNCT
ejpam-3502	297	20	gt	gt	PROPN
ejpam-3502	297	21	spaces	space	NOUN
ejpam-3502	297	22	,	,	PUNCT
ejpam-3502	297	23	respectively	respectively	ADV
ejpam-3502	297	24	,	,	PUNCT
ejpam-3502	297	25	where	where	SCONJ
ejpam-3502	297	26	gx	gx	PROPN
ejpam-3502	297	27	=	=	PUNCT
ejpam-3502	297	28	{	{	PUNCT
ejpam-3502	297	29	µ1	µ1	PROPN
ejpam-3502	297	30	,	,	PUNCT
ejpam-3502	297	31	.	.	PUNCT
ejpam-3502	297	32	.	.	PUNCT
ejpam-3502	297	33	.	.	PUNCT
ejpam-3502	298	1	,	,	PUNCT
ejpam-3502	298	2	µm	µm	ADP
ejpam-3502	298	3	}	}	PUNCT
ejpam-3502	298	4	and	and	CCONJ
ejpam-3502	298	5	gy	gy	NOUN
ejpam-3502	298	6	=	=	SYM
ejpam-3502	298	7	{	{	PUNCT
ejpam-3502	298	8	ν1	ν1	NOUN
ejpam-3502	298	9	,	,	PUNCT
ejpam-3502	298	10	.	.	PUNCT
ejpam-3502	298	11	.	.	PUNCT
ejpam-3502	299	1	.	.	PUNCT
ejpam-3502	300	1	,	,	PUNCT
ejpam-3502	300	2	νn	νn	AUX
ejpam-3502	300	3	}	}	PUNCT
ejpam-3502	300	4	for	for	ADP
ejpam-3502	300	5	some	some	DET
ejpam-3502	300	6	m	m	NOUN
ejpam-3502	300	7	,	,	PUNCT
ejpam-3502	300	8	n	n	PROPN
ejpam-3502	300	9	∈	∈	PROPN
ejpam-3502	300	10	n.	n.	NOUN
ejpam-3502	300	11	furthermore	furthermore	ADV
ejpam-3502	300	12	,	,	PUNCT
ejpam-3502	300	13	let	let	VERB
ejpam-3502	300	14	f	f	PRON
ejpam-3502	300	15	:	:	PUNCT
ejpam-3502	300	16	x	x	X
ejpam-3502	300	17	→	→	SYM
ejpam-3502	300	18	y	y	X
ejpam-3502	300	19	be	be	AUX
ejpam-3502	300	20	a	a	DET
ejpam-3502	300	21	map	map	NOUN
ejpam-3502	300	22	.	.	PUNCT
ejpam-3502	301	1	c.	c.	PROPN
ejpam-3502	301	2	balingit	balingit	PROPN
ejpam-3502	301	3	,	,	PUNCT
ejpam-3502	301	4	j.	j.	PROPN
ejpam-3502	301	5	benitez	benitez	PROPN
ejpam-3502	301	6	/	/	PUNCT
ejpam-3502	301	7	eur	eur	PROPN
ejpam-3502	301	8	.	.	PUNCT
ejpam-3502	302	1	j.	j.	PROPN
ejpam-3502	302	2	pure	pure	PROPN
ejpam-3502	302	3	appl	appl	PROPN
ejpam-3502	302	4	.	.	PROPN
ejpam-3502	302	5	math	math	PROPN
ejpam-3502	302	6	,	,	PUNCT
ejpam-3502	302	7	12	12	NUM
ejpam-3502	302	8	(	(	PUNCT
ejpam-3502	302	9	4	4	NUM
ejpam-3502	302	10	)	)	PUNCT
ejpam-3502	302	11	(	(	PUNCT
ejpam-3502	302	12	2019	2019	NUM
ejpam-3502	302	13	)	)	PUNCT
ejpam-3502	302	14	,	,	PUNCT
ejpam-3502	302	15	1553	1553	NUM
ejpam-3502	302	16	-	-	SYM
ejpam-3502	302	17	1566	1566	NUM
ejpam-3502	302	18	1561	1561	NUM
ejpam-3502	302	19	1	1	NUM
ejpam-3502	302	20	.	.	PUNCT
ejpam-3502	303	1	f	f	PROPN
ejpam-3502	303	2	is	be	AUX
ejpam-3502	303	3	called	call	VERB
ejpam-3502	303	4	a	a	DET
ejpam-3502	303	5	(	(	PUNCT
ejpam-3502	303	6	µ	µ	NOUN
ejpam-3502	303	7	,	,	PUNCT
ejpam-3502	303	8	ν)(j	ν)(j	NOUN
ejpam-3502	303	9	,	,	PUNCT
ejpam-3502	303	10	k)-open	k)-open	NOUN
ejpam-3502	303	11	map	map	NOUN
ejpam-3502	304	1	[	[	X
ejpam-3502	304	2	resp	resp	NOUN
ejpam-3502	304	3	.	.	PUNCT
ejpam-3502	305	1	(	(	PUNCT
ejpam-3502	305	2	µ	µ	NOUN
ejpam-3502	305	3	,	,	PUNCT
ejpam-3502	305	4	ν)(j	ν)(j	NOUN
ejpam-3502	305	5	,	,	PUNCT
ejpam-3502	305	6	k)-closed	k)-closed	ADJ
ejpam-3502	305	7	map	map	NOUN
ejpam-3502	305	8	]	]	X
ejpam-3502	305	9	if	if	SCONJ
ejpam-3502	305	10	f(u	f(u	PROPN
ejpam-3502	305	11	)	)	PUNCT
ejpam-3502	305	12	is	be	AUX
ejpam-3502	305	13	a	a	DET
ejpam-3502	305	14	νk	νk	NOUN
ejpam-3502	305	15	-	-	ADJ
ejpam-3502	305	16	open	open	ADJ
ejpam-3502	305	17	[	[	X
ejpam-3502	305	18	resp	resp	NOUN
ejpam-3502	305	19	.	.	PUNCT
ejpam-3502	306	1	νk	νk	VERB
ejpam-3502	306	2	-	-	VERB
ejpam-3502	306	3	closed	closed	ADJ
ejpam-3502	306	4	]	]	PUNCT
ejpam-3502	306	5	set	set	VERB
ejpam-3502	306	6	for	for	ADP
ejpam-3502	306	7	every	every	DET
ejpam-3502	306	8	µj	µj	PROPN
ejpam-3502	306	9	-	-	PUNCT
ejpam-3502	306	10	open	open	ADJ
ejpam-3502	306	11	[	[	X
ejpam-3502	306	12	resp	resp	NOUN
ejpam-3502	306	13	.	.	PUNCT
ejpam-3502	307	1	µj	µj	PROPN
ejpam-3502	307	2	-	-	PUNCT
ejpam-3502	307	3	closed	closed	ADJ
ejpam-3502	307	4	]	]	PUNCT
ejpam-3502	307	5	set	set	VERB
ejpam-3502	307	6	u	u	NOUN
ejpam-3502	307	7	⊆	⊆	NUM
ejpam-3502	307	8	x.	x.	NOUN
ejpam-3502	307	9	2	2	NUM
ejpam-3502	307	10	.	.	X
ejpam-3502	308	1	f	f	PROPN
ejpam-3502	308	2	is	be	AUX
ejpam-3502	308	3	called	call	VERB
ejpam-3502	308	4	a	a	DET
ejpam-3502	308	5	pairwise	pairwise	NOUN
ejpam-3502	308	6	(	(	PUNCT
ejpam-3502	308	7	µ	µ	NOUN
ejpam-3502	308	8	,	,	PUNCT
ejpam-3502	308	9	ν)-open	ν)-open	PRON
ejpam-3502	308	10	map	map	VERB
ejpam-3502	309	1	[	[	X
ejpam-3502	309	2	resp	resp	NOUN
ejpam-3502	309	3	.	.	PUNCT
ejpam-3502	310	1	pairwise	pairwise	NOUN
ejpam-3502	310	2	(	(	PUNCT
ejpam-3502	310	3	µ	µ	NOUN
ejpam-3502	310	4	,	,	PUNCT
ejpam-3502	310	5	ν)-closed	ν)-closed	ADJ
ejpam-3502	310	6	map	map	NOUN
ejpam-3502	310	7	]	]	X
ejpam-3502	310	8	if	if	SCONJ
ejpam-3502	310	9	for	for	ADP
ejpam-3502	310	10	each	each	DET
ejpam-3502	310	11	pair	pair	NOUN
ejpam-3502	310	12	j	j	PROPN
ejpam-3502	310	13	,	,	PUNCT
ejpam-3502	310	14	k	k	PROPN
ejpam-3502	310	15	where	where	SCONJ
ejpam-3502	310	16	1	1	NUM
ejpam-3502	310	17	≤	≤	NUM
ejpam-3502	310	18	j	j	PROPN
ejpam-3502	310	19	≤	≤	NOUN
ejpam-3502	310	20	m	m	PROPN
ejpam-3502	310	21	and	and	CCONJ
ejpam-3502	310	22	1	1	NUM
ejpam-3502	310	23	≤	≤	NUM
ejpam-3502	310	24	k	k	X
ejpam-3502	310	25	≤	≤	PROPN
ejpam-3502	310	26	n	n	CCONJ
ejpam-3502	310	27	,	,	PUNCT
ejpam-3502	310	28	f	f	PROPN
ejpam-3502	310	29	is	be	AUX
ejpam-3502	310	30	a	a	DET
ejpam-3502	310	31	(	(	PUNCT
ejpam-3502	310	32	µ	µ	NOUN
ejpam-3502	310	33	,	,	PUNCT
ejpam-3502	310	34	ν)(j	ν)(j	NOUN
ejpam-3502	310	35	,	,	PUNCT
ejpam-3502	310	36	k)-open	k)-open	NOUN
ejpam-3502	310	37	map	map	NOUN
ejpam-3502	311	1	[	[	X
ejpam-3502	311	2	resp	resp	NOUN
ejpam-3502	311	3	.	.	PUNCT
ejpam-3502	312	1	(	(	PUNCT
ejpam-3502	312	2	µ	µ	NOUN
ejpam-3502	312	3	,	,	PUNCT
ejpam-3502	312	4	ν)(j	ν)(j	NOUN
ejpam-3502	312	5	,	,	PUNCT
ejpam-3502	312	6	k)-closed	k)-closed	ADJ
ejpam-3502	312	7	map	map	NOUN
ejpam-3502	312	8	]	]	PUNCT
ejpam-3502	312	9	.	.	PUNCT
ejpam-3502	313	1	notice	notice	VERB
ejpam-3502	313	2	that	that	SCONJ
ejpam-3502	313	3	if	if	SCONJ
ejpam-3502	313	4	both	both	DET
ejpam-3502	313	5	(	(	PUNCT
ejpam-3502	313	6	x	x	NOUN
ejpam-3502	313	7	,	,	PUNCT
ejpam-3502	313	8	gx	gx	PROPN
ejpam-3502	313	9	)	)	PUNCT
ejpam-3502	313	10	and	and	CCONJ
ejpam-3502	313	11	(	(	PUNCT
ejpam-3502	313	12	y	y	PROPN
ejpam-3502	313	13	,	,	PUNCT
ejpam-3502	313	14	gy	gy	NOUN
ejpam-3502	313	15	)	)	PUNCT
ejpam-3502	313	16	are	be	AUX
ejpam-3502	313	17	1	1	NUM
ejpam-3502	313	18	-	-	PUNCT
ejpam-3502	313	19	gt	gt	PROPN
ejpam-3502	313	20	spaces	space	NOUN
ejpam-3502	313	21	,	,	PUNCT
ejpam-3502	313	22	then	then	ADV
ejpam-3502	313	23	it	it	PRON
ejpam-3502	313	24	immediately	immediately	ADV
ejpam-3502	313	25	follows	follow	VERB
ejpam-3502	313	26	that	that	SCONJ
ejpam-3502	313	27	f	f	X
ejpam-3502	313	28	:	:	PUNCT
ejpam-3502	313	29	x	x	X
ejpam-3502	313	30	→	→	SYM
ejpam-3502	313	31	y	y	PROPN
ejpam-3502	313	32	is	be	AUX
ejpam-3502	313	33	a	a	DET
ejpam-3502	313	34	g	g	NOUN
ejpam-3502	313	35	-open	-open	NOUN
ejpam-3502	313	36	map	map	NOUN
ejpam-3502	314	1	if	if	SCONJ
ejpam-3502	314	2	and	and	CCONJ
ejpam-3502	314	3	only	only	ADV
ejpam-3502	314	4	if	if	SCONJ
ejpam-3502	314	5	f	f	PROPN
ejpam-3502	314	6	is	be	AUX
ejpam-3502	314	7	a	a	DET
ejpam-3502	314	8	(	(	PUNCT
ejpam-3502	314	9	µ	µ	NUM
ejpam-3502	314	10	,	,	PUNCT
ejpam-3502	314	11	ν)(1,1)-open	ν)(1,1)-open	NUM
ejpam-3502	314	12	map	map	NOUN
ejpam-3502	314	13	.	.	PUNCT
ejpam-3502	315	1	furthermore	furthermore	ADV
ejpam-3502	315	2	,	,	PUNCT
ejpam-3502	315	3	a	a	DET
ejpam-3502	315	4	(	(	PUNCT
ejpam-3502	315	5	µ	µ	NOUN
ejpam-3502	315	6	,	,	PUNCT
ejpam-3502	315	7	ν)(j	ν)(j	NOUN
ejpam-3502	315	8	,	,	PUNCT
ejpam-3502	315	9	k)-open	k)-open	NOUN
ejpam-3502	315	10	map	map	NOUN
ejpam-3502	316	1	[	[	X
ejpam-3502	316	2	resp	resp	NOUN
ejpam-3502	316	3	.	.	PUNCT
ejpam-3502	317	1	(	(	PUNCT
ejpam-3502	317	2	µ	µ	NOUN
ejpam-3502	317	3	,	,	PUNCT
ejpam-3502	317	4	ν)(j	ν)(j	NOUN
ejpam-3502	317	5	,	,	PUNCT
ejpam-3502	317	6	k)-closed	k)-close	VERB
ejpam-3502	317	7	map	map	NOUN
ejpam-3502	317	8	]	]	PUNCT
ejpam-3502	317	9	may	may	AUX
ejpam-3502	317	10	not	not	PART
ejpam-3502	317	11	be	be	AUX
ejpam-3502	317	12	a	a	DET
ejpam-3502	317	13	g	g	NOUN
ejpam-3502	317	14	-open	-open	ADJ
ejpam-3502	317	15	map	map	NOUN
ejpam-3502	318	1	[	[	X
ejpam-3502	318	2	resp	resp	NOUN
ejpam-3502	318	3	.	.	PUNCT
ejpam-3502	319	1	g	g	PROPN
ejpam-3502	319	2	closed	closed	ADJ
ejpam-3502	319	3	map	map	NOUN
ejpam-3502	319	4	]	]	PUNCT
ejpam-3502	319	5	.	.	PUNCT
ejpam-3502	320	1	on	on	ADP
ejpam-3502	320	2	the	the	DET
ejpam-3502	320	3	other	other	ADJ
ejpam-3502	320	4	hand	hand	NOUN
ejpam-3502	320	5	,	,	PUNCT
ejpam-3502	320	6	a	a	DET
ejpam-3502	320	7	g	g	NOUN
ejpam-3502	320	8	-open	-open	ADJ
ejpam-3502	320	9	map	map	NOUN
ejpam-3502	321	1	[	[	X
ejpam-3502	321	2	resp	resp	NOUN
ejpam-3502	321	3	.	.	PUNCT
ejpam-3502	322	1	g	g	NOUN
ejpam-3502	322	2	-closed	-close	VERB
ejpam-3502	322	3	map	map	NOUN
ejpam-3502	322	4	]	]	PUNCT
ejpam-3502	322	5	may	may	AUX
ejpam-3502	322	6	also	also	ADV
ejpam-3502	322	7	not	not	PART
ejpam-3502	322	8	be	be	AUX
ejpam-3502	322	9	a	a	DET
ejpam-3502	322	10	(	(	PUNCT
ejpam-3502	322	11	µ	µ	NOUN
ejpam-3502	322	12	,	,	PUNCT
ejpam-3502	322	13	ν)(j	ν)(j	NOUN
ejpam-3502	322	14	,	,	PUNCT
ejpam-3502	322	15	k)-open	k)-open	NOUN
ejpam-3502	322	16	map	map	NOUN
ejpam-3502	323	1	[	[	X
ejpam-3502	323	2	resp	resp	NOUN
ejpam-3502	323	3	.	.	PUNCT
ejpam-3502	324	1	(	(	PUNCT
ejpam-3502	324	2	µ	µ	NOUN
ejpam-3502	324	3	,	,	PUNCT
ejpam-3502	324	4	ν)(j	ν)(j	NOUN
ejpam-3502	324	5	,	,	PUNCT
ejpam-3502	324	6	k)-closed	k)-closed	ADJ
ejpam-3502	324	7	map	map	NOUN
ejpam-3502	324	8	]	]	PUNCT
ejpam-3502	324	9	.	.	PUNCT
ejpam-3502	325	1	these	these	PRON
ejpam-3502	325	2	are	be	AUX
ejpam-3502	325	3	illustrated	illustrate	VERB
ejpam-3502	325	4	in	in	ADP
ejpam-3502	325	5	the	the	DET
ejpam-3502	325	6	following	follow	VERB
ejpam-3502	325	7	example	example	NOUN
ejpam-3502	325	8	:	:	PUNCT
ejpam-3502	325	9	example	example	NOUN
ejpam-3502	325	10	3.10	3.10	NUM
ejpam-3502	325	11	.	.	PUNCT
ejpam-3502	326	1	let	let	VERB
ejpam-3502	326	2	x	x	PRON
ejpam-3502	326	3	and	and	CCONJ
ejpam-3502	326	4	y	y	PROPN
ejpam-3502	326	5	be	be	AUX
ejpam-3502	326	6	infinite	infinite	ADJ
ejpam-3502	326	7	sets	set	NOUN
ejpam-3502	326	8	and	and	CCONJ
ejpam-3502	326	9	{	{	PUNCT
ejpam-3502	326	10	p1	p1	NOUN
ejpam-3502	326	11	,	,	PUNCT
ejpam-3502	326	12	.	.	PUNCT
ejpam-3502	326	13	.	.	PUNCT
ejpam-3502	327	1	.	.	PUNCT
ejpam-3502	328	1	,	,	PUNCT
ejpam-3502	328	2	pm	pm	NOUN
ejpam-3502	328	3	}	}	PUNCT
ejpam-3502	328	4	and	and	CCONJ
ejpam-3502	328	5	{	{	PUNCT
ejpam-3502	328	6	q1	q1	NOUN
ejpam-3502	328	7	,	,	PUNCT
ejpam-3502	328	8	.	.	PUNCT
ejpam-3502	328	9	.	.	PUNCT
ejpam-3502	329	1	.	.	PUNCT
ejpam-3502	330	1	,	,	PUNCT
ejpam-3502	330	2	qn	qn	PART
ejpam-3502	330	3	}	}	PUNCT
ejpam-3502	330	4	be	be	VERB
ejpam-3502	330	5	some	some	DET
ejpam-3502	330	6	partitions	partition	NOUN
ejpam-3502	330	7	of	of	ADP
ejpam-3502	330	8	x	x	X
ejpam-3502	330	9	and	and	CCONJ
ejpam-3502	330	10	y	y	PROPN
ejpam-3502	330	11	,	,	PUNCT
ejpam-3502	330	12	respectively	respectively	ADV
ejpam-3502	330	13	.	.	PUNCT
ejpam-3502	331	1	putting	put	VERB
ejpam-3502	331	2	gx	gx	PROPN
ejpam-3502	331	3	=	=	PUNCT
ejpam-3502	331	4	{	{	PUNCT
ejpam-3502	331	5	µj	µj	X
ejpam-3502	331	6	:	:	PUNCT
ejpam-3502	331	7	j	j	PROPN
ejpam-3502	331	8	=	=	SYM
ejpam-3502	331	9	1	1	NUM
ejpam-3502	331	10	,	,	PUNCT
ejpam-3502	331	11	.	.	PUNCT
ejpam-3502	331	12	.	.	PUNCT
ejpam-3502	332	1	.	.	PUNCT
ejpam-3502	333	1	,	,	PUNCT
ejpam-3502	333	2	m	m	VERB
ejpam-3502	333	3	}	}	PUNCT
ejpam-3502	333	4	and	and	CCONJ
ejpam-3502	333	5	gy	gy	NOUN
ejpam-3502	333	6	=	=	PUNCT
ejpam-3502	333	7	{	{	PUNCT
ejpam-3502	333	8	νk	νk	X
ejpam-3502	333	9	:	:	PUNCT
ejpam-3502	333	10	k	k	NOUN
ejpam-3502	333	11	=	=	SYM
ejpam-3502	333	12	1	1	NUM
ejpam-3502	333	13	,	,	PUNCT
ejpam-3502	333	14	.	.	PUNCT
ejpam-3502	333	15	.	.	PUNCT
ejpam-3502	334	1	.	.	PUNCT
ejpam-3502	335	1	,	,	PUNCT
ejpam-3502	335	2	n	n	CCONJ
ejpam-3502	335	3	}	}	PUNCT
ejpam-3502	335	4	where	where	SCONJ
ejpam-3502	335	5	µj	µj	PROPN
ejpam-3502	335	6	=	=	SYM
ejpam-3502	335	7	p(pj	p(pj	X
ejpam-3502	335	8	)	)	PUNCT
ejpam-3502	335	9	and	and	CCONJ
ejpam-3502	335	10	νk	νk	NOUN
ejpam-3502	335	11	=	=	SYM
ejpam-3502	335	12	p(qk	p(qk	X
ejpam-3502	335	13	)	)	PUNCT
ejpam-3502	335	14	,	,	PUNCT
ejpam-3502	335	15	we	we	PRON
ejpam-3502	335	16	come	come	VERB
ejpam-3502	335	17	up	up	ADP
ejpam-3502	335	18	with	with	ADP
ejpam-3502	335	19	the	the	DET
ejpam-3502	335	20	m	m	PROPN
ejpam-3502	335	21	-	-	PUNCT
ejpam-3502	335	22	gt	gt	PROPN
ejpam-3502	335	23	space	space	NOUN
ejpam-3502	335	24	(	(	PUNCT
ejpam-3502	335	25	x	x	NOUN
ejpam-3502	335	26	,	,	PUNCT
ejpam-3502	335	27	gx	gx	PROPN
ejpam-3502	335	28	)	)	PUNCT
ejpam-3502	335	29	and	and	CCONJ
ejpam-3502	335	30	the	the	DET
ejpam-3502	335	31	n	n	CCONJ
ejpam-3502	335	32	-	-	PUNCT
ejpam-3502	335	33	gt	gt	PROPN
ejpam-3502	335	34	space	space	NOUN
ejpam-3502	335	35	(	(	PUNCT
ejpam-3502	335	36	y	y	NOUN
ejpam-3502	335	37	,	,	PUNCT
ejpam-3502	335	38	gy	gy	NOUN
ejpam-3502	335	39	)	)	PUNCT
ejpam-3502	335	40	.	.	PUNCT
ejpam-3502	336	1	1	1	X
ejpam-3502	336	2	.	.	X
ejpam-3502	337	1	if	if	SCONJ
ejpam-3502	337	2	,	,	PUNCT
ejpam-3502	337	3	in	in	ADP
ejpam-3502	337	4	general	general	ADJ
ejpam-3502	337	5	,	,	PUNCT
ejpam-3502	337	6	f	f	X
ejpam-3502	337	7	:	:	PUNCT
ejpam-3502	337	8	x	x	X
ejpam-3502	337	9	→	→	SYM
ejpam-3502	337	10	y	y	PROPN
ejpam-3502	337	11	is	be	AUX
ejpam-3502	337	12	the	the	DET
ejpam-3502	337	13	constant	constant	ADJ
ejpam-3502	337	14	map	map	NOUN
ejpam-3502	337	15	f(x	f(x	PROPN
ejpam-3502	337	16	)	)	PUNCT
ejpam-3502	338	1	=	=	SYM
ejpam-3502	338	2	c	c	X
ejpam-3502	338	3	,	,	PUNCT
ejpam-3502	338	4	then	then	ADV
ejpam-3502	338	5	for	for	ADP
ejpam-3502	338	6	the	the	DET
ejpam-3502	338	7	fixed	fix	VERB
ejpam-3502	338	8	k∗	k∗	NOUN
ejpam-3502	338	9	(	(	PUNCT
ejpam-3502	338	10	where	where	SCONJ
ejpam-3502	338	11	c	c	PROPN
ejpam-3502	338	12	∈	∈	PROPN
ejpam-3502	338	13	qk∗	qk∗	NOUN
ejpam-3502	338	14	)	)	PUNCT
ejpam-3502	338	15	,	,	PUNCT
ejpam-3502	338	16	f	f	PROPN
ejpam-3502	338	17	is	be	AUX
ejpam-3502	338	18	a	a	DET
ejpam-3502	338	19	(	(	PUNCT
ejpam-3502	338	20	µ	µ	NOUN
ejpam-3502	338	21	,	,	PUNCT
ejpam-3502	338	22	ν)(j	ν)(j	PROPN
ejpam-3502	338	23	,	,	PUNCT
ejpam-3502	338	24	k	k	PROPN
ejpam-3502	338	25	∗)-open	∗)-open	PROPN
ejpam-3502	338	26	map	map	NOUN
ejpam-3502	338	27	and	and	CCONJ
ejpam-3502	338	28	,	,	PUNCT
ejpam-3502	338	29	in	in	ADP
ejpam-3502	338	30	fact	fact	NOUN
ejpam-3502	338	31	,	,	PUNCT
ejpam-3502	338	32	also	also	ADV
ejpam-3502	338	33	a	a	DET
ejpam-3502	338	34	g	g	NOUN
ejpam-3502	338	35	-open	-open	NOUN
ejpam-3502	338	36	map	map	NOUN
ejpam-3502	338	37	.	.	PUNCT
ejpam-3502	339	1	2	2	X
ejpam-3502	339	2	.	.	X
ejpam-3502	339	3	in	in	ADP
ejpam-3502	339	4	particular	particular	ADJ
ejpam-3502	339	5	,	,	PUNCT
ejpam-3502	339	6	consider	consider	VERB
ejpam-3502	339	7	the	the	DET
ejpam-3502	339	8	case	case	NOUN
ejpam-3502	339	9	where	where	SCONJ
ejpam-3502	339	10	x	x	SYM
ejpam-3502	339	11	=	=	SYM
ejpam-3502	339	12	y	y	PROPN
ejpam-3502	339	13	and	and	CCONJ
ejpam-3502	339	14	m	m	PROPN
ejpam-3502	339	15	=	=	SYM
ejpam-3502	339	16	n	n	CCONJ
ejpam-3502	339	17	,	,	PUNCT
ejpam-3502	339	18	while	while	SCONJ
ejpam-3502	339	19	pj	pj	PROPN
ejpam-3502	339	20	6=	6=	PROPN
ejpam-3502	339	21	qk	qk	NOUN
ejpam-3502	339	22	for	for	ADP
ejpam-3502	339	23	any	any	DET
ejpam-3502	339	24	j	j	PROPN
ejpam-3502	339	25	,	,	PUNCT
ejpam-3502	339	26	k.	k.	PROPN
ejpam-3502	340	1	then	then	ADV
ejpam-3502	340	2	if	if	SCONJ
ejpam-3502	340	3	f	f	PRON
ejpam-3502	340	4	:	:	PUNCT
ejpam-3502	340	5	x	x	X
ejpam-3502	340	6	→	→	SYM
ejpam-3502	340	7	y	y	PROPN
ejpam-3502	340	8	is	be	AUX
ejpam-3502	340	9	the	the	DET
ejpam-3502	340	10	identity	identity	NOUN
ejpam-3502	340	11	map	map	NOUN
ejpam-3502	340	12	,	,	PUNCT
ejpam-3502	340	13	it	it	PRON
ejpam-3502	340	14	is	be	AUX
ejpam-3502	340	15	easy	easy	ADJ
ejpam-3502	340	16	to	to	PART
ejpam-3502	340	17	see	see	VERB
ejpam-3502	340	18	that	that	SCONJ
ejpam-3502	340	19	f	f	PROPN
ejpam-3502	340	20	is	be	AUX
ejpam-3502	340	21	a	a	DET
ejpam-3502	340	22	g	g	NOUN
ejpam-3502	340	23	-open	-open	NOUN
ejpam-3502	340	24	map	map	NOUN
ejpam-3502	340	25	.	.	PUNCT
ejpam-3502	341	1	however	however	ADV
ejpam-3502	341	2	,	,	PUNCT
ejpam-3502	341	3	f	f	PROPN
ejpam-3502	341	4	is	be	AUX
ejpam-3502	341	5	not	not	PART
ejpam-3502	341	6	a	a	DET
ejpam-3502	341	7	(	(	PUNCT
ejpam-3502	341	8	µ	µ	NOUN
ejpam-3502	341	9	,	,	PUNCT
ejpam-3502	341	10	ν)(j	ν)(j	NOUN
ejpam-3502	341	11	,	,	PUNCT
ejpam-3502	341	12	k)-open	k)-open	NOUN
ejpam-3502	341	13	map	map	NOUN
ejpam-3502	341	14	for	for	ADP
ejpam-3502	341	15	any	any	DET
ejpam-3502	341	16	pair	pair	NOUN
ejpam-3502	341	17	j	j	PROPN
ejpam-3502	341	18	,	,	PUNCT
ejpam-3502	341	19	k	k	PROPN
ejpam-3502	341	20	due	due	ADP
ejpam-3502	341	21	to	to	ADP
ejpam-3502	341	22	our	our	PRON
ejpam-3502	341	23	choice	choice	NOUN
ejpam-3502	341	24	of	of	ADP
ejpam-3502	341	25	partitions	partition	NOUN
ejpam-3502	341	26	.	.	PUNCT
ejpam-3502	342	1	3	3	X
ejpam-3502	342	2	.	.	PUNCT
ejpam-3502	342	3	now	now	ADV
ejpam-3502	342	4	,	,	PUNCT
ejpam-3502	342	5	consider	consider	VERB
ejpam-3502	342	6	the	the	DET
ejpam-3502	342	7	case	case	NOUN
ejpam-3502	342	8	where	where	SCONJ
ejpam-3502	342	9	x	x	PUNCT
ejpam-3502	342	10	6=	6=	ADP
ejpam-3502	342	11	y	y	PROPN
ejpam-3502	342	12	,	,	PUNCT
ejpam-3502	342	13	∅	∅	NOUN
ejpam-3502	342	14	6=	6=	ADP
ejpam-3502	342	15	a	a	DET
ejpam-3502	342	16	⊂	⊂	PROPN
ejpam-3502	342	17	x	x	X
ejpam-3502	342	18	and	and	CCONJ
ejpam-3502	342	19	∅	∅	NOUN
ejpam-3502	342	20	6=	6=	SYM
ejpam-3502	342	21	b	b	X
ejpam-3502	342	22	⊂	⊂	PROPN
ejpam-3502	342	23	y	y	PROPN
ejpam-3502	342	24	,	,	PUNCT
ejpam-3502	342	25	µ1	µ1	PROPN
ejpam-3502	342	26	=	=	SYM
ejpam-3502	342	27	p(a	p(a	PROPN
ejpam-3502	342	28	)	)	PUNCT
ejpam-3502	342	29	,	,	PUNCT
ejpam-3502	342	30	µ2	µ2	PROPN
ejpam-3502	342	31	=	=	SYM
ejpam-3502	342	32	p(x\a	p(x\a	PROPN
ejpam-3502	342	33	)	)	PUNCT
ejpam-3502	342	34	and	and	CCONJ
ejpam-3502	342	35	ν1	ν1	NOUN
ejpam-3502	342	36	=	=	SYM
ejpam-3502	342	37	p(b	p(b	PROPN
ejpam-3502	342	38	)	)	PUNCT
ejpam-3502	342	39	.	.	PUNCT
ejpam-3502	343	1	if	if	SCONJ
ejpam-3502	343	2	gx	gx	PROPN
ejpam-3502	343	3	=	=	SYM
ejpam-3502	343	4	{	{	PUNCT
ejpam-3502	343	5	µ1	µ1	PROPN
ejpam-3502	343	6	,	,	PUNCT
ejpam-3502	343	7	µ2	µ2	PROPN
ejpam-3502	343	8	}	}	PUNCT
ejpam-3502	343	9	and	and	CCONJ
ejpam-3502	343	10	gy	gy	NOUN
ejpam-3502	343	11	=	=	SYM
ejpam-3502	343	12	{	{	PUNCT
ejpam-3502	343	13	ν1	ν1	NOUN
ejpam-3502	343	14	}	}	PUNCT
ejpam-3502	343	15	,	,	PUNCT
ejpam-3502	343	16	then	then	ADV
ejpam-3502	343	17	(	(	PUNCT
ejpam-3502	343	18	x	x	X
ejpam-3502	343	19	,	,	PUNCT
ejpam-3502	343	20	gx	gx	PROPN
ejpam-3502	343	21	)	)	PUNCT
ejpam-3502	343	22	is	be	AUX
ejpam-3502	343	23	a	a	DET
ejpam-3502	343	24	2	2	NUM
ejpam-3502	343	25	-	-	PUNCT
ejpam-3502	343	26	gt	gt	NOUN
ejpam-3502	343	27	space	space	NOUN
ejpam-3502	343	28	and	and	CCONJ
ejpam-3502	343	29	(	(	PUNCT
ejpam-3502	343	30	y	y	PROPN
ejpam-3502	343	31	,	,	PUNCT
ejpam-3502	343	32	gy	gy	PROPN
ejpam-3502	343	33	)	)	PUNCT
ejpam-3502	343	34	is	be	AUX
ejpam-3502	343	35	a	a	DET
ejpam-3502	343	36	1	1	NUM
ejpam-3502	343	37	-	-	PUNCT
ejpam-3502	343	38	gt	gt	NOUN
ejpam-3502	343	39	space	space	NOUN
ejpam-3502	343	40	.	.	PUNCT
ejpam-3502	344	1	furthermore	furthermore	ADV
ejpam-3502	344	2	,	,	PUNCT
ejpam-3502	344	3	if	if	SCONJ
ejpam-3502	344	4	c1	c1	PROPN
ejpam-3502	344	5	∈	∈	PROPN
ejpam-3502	344	6	b	b	PROPN
ejpam-3502	344	7	and	and	CCONJ
ejpam-3502	344	8	c2	c2	PROPN
ejpam-3502	344	9	∈	∈	PROPN
ejpam-3502	344	10	y	y	PROPN
ejpam-3502	344	11	\b	\b	NOUN
ejpam-3502	344	12	are	be	AUX
ejpam-3502	344	13	fixed	fix	VERB
ejpam-3502	344	14	and	and	CCONJ
ejpam-3502	344	15	f	f	X
ejpam-3502	344	16	:	:	PUNCT
ejpam-3502	344	17	x	x	X
ejpam-3502	344	18	→	→	SYM
ejpam-3502	344	19	y	y	PROPN
ejpam-3502	344	20	is	be	AUX
ejpam-3502	344	21	defined	define	VERB
ejpam-3502	344	22	as	as	ADP
ejpam-3502	344	23	f(x	f(x	PROPN
ejpam-3502	344	24	)	)	PUNCT
ejpam-3502	345	1	=	=	PRON
ejpam-3502	345	2	{	{	PUNCT
ejpam-3502	345	3	c1	c1	NOUN
ejpam-3502	345	4	,	,	PUNCT
ejpam-3502	345	5	if	if	SCONJ
ejpam-3502	345	6	x	x	PROPN
ejpam-3502	345	7	∈	∈	PROPN
ejpam-3502	345	8	a	a	DET
ejpam-3502	345	9	c2	c2	PROPN
ejpam-3502	345	10	,	,	PUNCT
ejpam-3502	345	11	if	if	SCONJ
ejpam-3502	345	12	x	x	SYM
ejpam-3502	345	13	∈	∈	PROPN
ejpam-3502	345	14	x\a	x\a	PUNCT
ejpam-3502	345	15	,	,	PUNCT
ejpam-3502	345	16	then	then	ADV
ejpam-3502	345	17	f	f	PROPN
ejpam-3502	345	18	is	be	AUX
ejpam-3502	345	19	a	a	DET
ejpam-3502	345	20	(	(	PUNCT
ejpam-3502	345	21	µ	µ	NUM
ejpam-3502	345	22	,	,	PUNCT
ejpam-3502	345	23	ν)(1,1)-open	ν)(1,1)-open	NOUN
ejpam-3502	345	24	map	map	NOUN
ejpam-3502	345	25	but	but	CCONJ
ejpam-3502	345	26	not	not	PART
ejpam-3502	345	27	a	a	DET
ejpam-3502	345	28	g	g	NOUN
ejpam-3502	345	29	-open	-open	NOUN
ejpam-3502	345	30	map	map	NOUN
ejpam-3502	345	31	since	since	SCONJ
ejpam-3502	345	32	f(x	f(x	NOUN
ejpam-3502	345	33	)	)	PUNCT
ejpam-3502	346	1	=	=	PRON
ejpam-3502	346	2	{	{	PUNCT
ejpam-3502	346	3	c1	c1	PROPN
ejpam-3502	346	4	,	,	PUNCT
ejpam-3502	346	5	c2	c2	PROPN
ejpam-3502	346	6	}	}	PUNCT
ejpam-3502	346	7	is	be	AUX
ejpam-3502	346	8	not	not	PART
ejpam-3502	346	9	gy	gy	PROPN
ejpam-3502	346	10	-open	-open	PROPN
ejpam-3502	346	11	.	.	PUNCT
ejpam-3502	346	12	example	example	NOUN
ejpam-3502	347	1	3.11	3.11	NUM
ejpam-3502	347	2	.	.	PUNCT
ejpam-3502	348	1	to	to	PART
ejpam-3502	348	2	illustrate	illustrate	VERB
ejpam-3502	348	3	a	a	DET
ejpam-3502	348	4	pairwise	pairwise	NOUN
ejpam-3502	348	5	(	(	PUNCT
ejpam-3502	348	6	µ	µ	NOUN
ejpam-3502	348	7	,	,	PUNCT
ejpam-3502	348	8	ν)-open	ν)-open	NOUN
ejpam-3502	348	9	map	map	NOUN
ejpam-3502	348	10	,	,	PUNCT
ejpam-3502	348	11	we	we	PRON
ejpam-3502	348	12	simply	simply	ADV
ejpam-3502	348	13	recall	recall	VERB
ejpam-3502	348	14	the	the	DET
ejpam-3502	348	15	mapping	mapping	NOUN
ejpam-3502	348	16	f	f	NOUN
ejpam-3502	348	17	in	in	ADP
ejpam-3502	348	18	example	example	NOUN
ejpam-3502	348	19	3.2	3.2	NUM
ejpam-3502	348	20	(	(	PUNCT
ejpam-3502	348	21	1.ii	1.ii	NUM
ejpam-3502	348	22	)	)	PUNCT
ejpam-3502	348	23	.	.	PUNCT
ejpam-3502	349	1	this	this	PRON
ejpam-3502	349	2	is	be	AUX
ejpam-3502	349	3	so	so	SCONJ
ejpam-3502	349	4	since	since	SCONJ
ejpam-3502	349	5	the	the	DET
ejpam-3502	349	6	image	image	NOUN
ejpam-3502	349	7	of	of	ADP
ejpam-3502	349	8	each	each	DET
ejpam-3502	349	9	g	g	PROPN
ejpam-3502	349	10	-open	-open	NOUN
ejpam-3502	349	11	set	set	NOUN
ejpam-3502	349	12	(	(	PUNCT
ejpam-3502	349	13	and	and	CCONJ
ejpam-3502	349	14	hence	hence	ADV
ejpam-3502	349	15	of	of	ADP
ejpam-3502	349	16	any	any	DET
ejpam-3502	349	17	µj	µj	NOUN
ejpam-3502	349	18	-	-	PUNCT
ejpam-3502	349	19	open	open	ADJ
ejpam-3502	349	20	set	set	NOUN
ejpam-3502	349	21	)	)	PUNCT
ejpam-3502	349	22	is	be	AUX
ejpam-3502	349	23	[	[	X
ejpam-3502	349	24	0	0	NUM
ejpam-3502	349	25	,	,	PUNCT
ejpam-3502	349	26	1	1	NUM
ejpam-3502	349	27	]	]	PUNCT
ejpam-3502	349	28	which	which	PRON
ejpam-3502	349	29	is	be	AUX
ejpam-3502	349	30	νk	νk	NOUN
ejpam-3502	349	31	-	-	VERB
ejpam-3502	349	32	open	open	ADJ
ejpam-3502	349	33	for	for	ADP
ejpam-3502	349	34	all	all	PRON
ejpam-3502	350	1	k.	k.	PROPN
ejpam-3502	350	2	a	a	DET
ejpam-3502	350	3	(	(	PUNCT
ejpam-3502	350	4	µ	µ	NOUN
ejpam-3502	350	5	,	,	PUNCT
ejpam-3502	350	6	ν)(j	ν)(j	NOUN
ejpam-3502	350	7	,	,	PUNCT
ejpam-3502	350	8	k)-open	k)-open	NOUN
ejpam-3502	350	9	map	map	NOUN
ejpam-3502	350	10	and	and	CCONJ
ejpam-3502	350	11	a	a	DET
ejpam-3502	350	12	(	(	PUNCT
ejpam-3502	350	13	µ	µ	NOUN
ejpam-3502	350	14	,	,	PUNCT
ejpam-3502	350	15	ν)(j	ν)(j	NOUN
ejpam-3502	350	16	,	,	PUNCT
ejpam-3502	350	17	k)-closed	k)-close	VERB
ejpam-3502	350	18	map	map	NOUN
ejpam-3502	350	19	inherits	inherit	VERB
ejpam-3502	350	20	similar	similar	ADJ
ejpam-3502	350	21	and	and	CCONJ
ejpam-3502	350	22	corresponding	corresponding	ADJ
ejpam-3502	350	23	properties	property	NOUN
ejpam-3502	350	24	as	as	SCONJ
ejpam-3502	350	25	established	establish	VERB
ejpam-3502	350	26	in	in	ADP
ejpam-3502	350	27	the	the	DET
ejpam-3502	350	28	previous	previous	ADJ
ejpam-3502	350	29	results	result	NOUN
ejpam-3502	350	30	in	in	ADP
ejpam-3502	350	31	this	this	DET
ejpam-3502	350	32	section	section	NOUN
ejpam-3502	350	33	since	since	SCONJ
ejpam-3502	350	34	a	a	DET
ejpam-3502	350	35	(	(	PUNCT
ejpam-3502	350	36	µ	µ	NOUN
ejpam-3502	350	37	,	,	PUNCT
ejpam-3502	350	38	ν)(j	ν)(j	NOUN
ejpam-3502	350	39	,	,	PUNCT
ejpam-3502	350	40	k)-open	k)-open	NOUN
ejpam-3502	350	41	map	map	NOUN
ejpam-3502	350	42	and	and	CCONJ
ejpam-3502	350	43	a	a	DET
ejpam-3502	350	44	(	(	PUNCT
ejpam-3502	350	45	µ	µ	NOUN
ejpam-3502	350	46	,	,	PUNCT
ejpam-3502	350	47	ν)(j	ν)(j	NOUN
ejpam-3502	350	48	,	,	PUNCT
ejpam-3502	350	49	k)-closed	k)-close	VERB
ejpam-3502	350	50	maps	map	NOUN
ejpam-3502	350	51	are	be	AUX
ejpam-3502	350	52	analogous	analogous	ADJ
ejpam-3502	350	53	to	to	ADP
ejpam-3502	350	54	a	a	DET
ejpam-3502	350	55	g	g	NOUN
ejpam-3502	350	56	-open	-open	NOUN
ejpam-3502	350	57	map	map	NOUN
ejpam-3502	350	58	and	and	CCONJ
ejpam-3502	350	59	a	a	DET
ejpam-3502	350	60	g	g	NOUN
ejpam-3502	350	61	-closed	-close	VERB
ejpam-3502	350	62	map	map	NOUN
ejpam-3502	350	63	,	,	PUNCT
ejpam-3502	350	64	respectively	respectively	ADV
ejpam-3502	350	65	,	,	PUNCT
ejpam-3502	350	66	when	when	SCONJ
ejpam-3502	350	67	the	the	DET
ejpam-3502	350	68	underlying	underlying	ADJ
ejpam-3502	350	69	spaces	space	NOUN
ejpam-3502	350	70	involved	involve	VERB
ejpam-3502	350	71	are	be	AUX
ejpam-3502	350	72	both	both	PRON
ejpam-3502	350	73	1	1	NUM
ejpam-3502	350	74	-	-	PUNCT
ejpam-3502	350	75	gt	gt	PROPN
ejpam-3502	350	76	spaces	space	NOUN
ejpam-3502	350	77	.	.	PUNCT
ejpam-3502	351	1	c.	c.	PROPN
ejpam-3502	351	2	balingit	balingit	PROPN
ejpam-3502	351	3	,	,	PUNCT
ejpam-3502	351	4	j.	j.	PROPN
ejpam-3502	351	5	benitez	benitez	PROPN
ejpam-3502	351	6	/	/	PUNCT
ejpam-3502	351	7	eur	eur	PROPN
ejpam-3502	351	8	.	.	PUNCT
ejpam-3502	352	1	j.	j.	PROPN
ejpam-3502	352	2	pure	pure	PROPN
ejpam-3502	352	3	appl	appl	PROPN
ejpam-3502	352	4	.	.	PROPN
ejpam-3502	352	5	math	math	PROPN
ejpam-3502	352	6	,	,	PUNCT
ejpam-3502	352	7	12	12	NUM
ejpam-3502	352	8	(	(	PUNCT
ejpam-3502	352	9	4	4	NUM
ejpam-3502	352	10	)	)	PUNCT
ejpam-3502	352	11	(	(	PUNCT
ejpam-3502	352	12	2019	2019	NUM
ejpam-3502	352	13	)	)	PUNCT
ejpam-3502	352	14	,	,	PUNCT
ejpam-3502	352	15	1553	1553	NUM
ejpam-3502	352	16	-	-	SYM
ejpam-3502	352	17	1566	1566	NUM
ejpam-3502	352	18	1562	1562	NUM
ejpam-3502	352	19	we	we	PRON
ejpam-3502	352	20	now	now	ADV
ejpam-3502	352	21	present	present	VERB
ejpam-3502	352	22	some	some	DET
ejpam-3502	352	23	observations	observation	NOUN
ejpam-3502	352	24	showing	show	VERB
ejpam-3502	352	25	relationships	relationship	NOUN
ejpam-3502	352	26	of	of	ADP
ejpam-3502	352	27	the	the	DET
ejpam-3502	352	28	mentioned	mention	VERB
ejpam-3502	352	29	typed	type	VERB
ejpam-3502	352	30	of	of	ADP
ejpam-3502	352	31	open	open	ADJ
ejpam-3502	352	32	maps	map	NOUN
ejpam-3502	352	33	:	:	PUNCT
ejpam-3502	352	34	theorem	theorem	VERB
ejpam-3502	352	35	3.12	3.12	NUM
ejpam-3502	352	36	.	.	PUNCT
ejpam-3502	353	1	if	if	SCONJ
ejpam-3502	353	2	for	for	ADP
ejpam-3502	353	3	each	each	DET
ejpam-3502	353	4	j	j	NOUN
ejpam-3502	353	5	there	there	PRON
ejpam-3502	353	6	is	be	VERB
ejpam-3502	353	7	a	a	DET
ejpam-3502	353	8	k	k	NOUN
ejpam-3502	353	9	such	such	ADJ
ejpam-3502	353	10	that	that	SCONJ
ejpam-3502	353	11	f	f	PROPN
ejpam-3502	353	12	is	be	AUX
ejpam-3502	353	13	a	a	DET
ejpam-3502	353	14	(	(	PUNCT
ejpam-3502	353	15	µ	µ	NOUN
ejpam-3502	353	16	,	,	PUNCT
ejpam-3502	353	17	ν)(j	ν)(j	NUM
ejpam-3502	353	18	,	,	PUNCT
ejpam-3502	353	19	k)-open	k)-open	NOUN
ejpam-3502	353	20	map	map	NOUN
ejpam-3502	353	21	,	,	PUNCT
ejpam-3502	353	22	then	then	ADV
ejpam-3502	353	23	f	f	PROPN
ejpam-3502	353	24	is	be	AUX
ejpam-3502	353	25	a	a	DET
ejpam-3502	353	26	g	g	NOUN
ejpam-3502	353	27	-open	-open	NOUN
ejpam-3502	353	28	map	map	NOUN
ejpam-3502	353	29	.	.	PUNCT
ejpam-3502	354	1	proof	proof	NOUN
ejpam-3502	354	2	.	.	PUNCT
ejpam-3502	355	1	let	let	VERB
ejpam-3502	355	2	u	u	PRON
ejpam-3502	355	3	be	be	AUX
ejpam-3502	355	4	a	a	DET
ejpam-3502	355	5	gx	gx	PROPN
ejpam-3502	355	6	-open	-open	NOUN
ejpam-3502	355	7	set	set	NOUN
ejpam-3502	355	8	.	.	PUNCT
ejpam-3502	356	1	then	then	ADV
ejpam-3502	356	2	for	for	ADP
ejpam-3502	356	3	each	each	DET
ejpam-3502	356	4	x	x	SYM
ejpam-3502	356	5	∈	∈	PROPN
ejpam-3502	356	6	u	u	NOUN
ejpam-3502	356	7	,	,	PUNCT
ejpam-3502	356	8	there	there	PRON
ejpam-3502	356	9	exists	exist	VERB
ejpam-3502	356	10	a	a	DET
ejpam-3502	356	11	j	j	NOUN
ejpam-3502	356	12	and	and	CCONJ
ejpam-3502	356	13	a	a	DET
ejpam-3502	356	14	µj	µj	ADJ
ejpam-3502	356	15	-	-	PUNCT
ejpam-3502	356	16	open	open	ADJ
ejpam-3502	356	17	set	set	ADJ
ejpam-3502	356	18	ox	ox	NOUN
ejpam-3502	356	19	such	such	ADJ
ejpam-3502	356	20	that	that	SCONJ
ejpam-3502	356	21	x	x	SYM
ejpam-3502	356	22	∈	∈	PROPN
ejpam-3502	356	23	ox	ox	NOUN
ejpam-3502	356	24	⊆	⊆	NUM
ejpam-3502	356	25	u	u	NOUN
ejpam-3502	356	26	.	.	PUNCT
ejpam-3502	357	1	by	by	ADP
ejpam-3502	357	2	assumption	assumption	NOUN
ejpam-3502	357	3	,	,	PUNCT
ejpam-3502	357	4	there	there	PRON
ejpam-3502	357	5	exists	exist	VERB
ejpam-3502	357	6	a	a	DET
ejpam-3502	357	7	k	k	NOUN
ejpam-3502	357	8	such	such	ADJ
ejpam-3502	357	9	that	that	SCONJ
ejpam-3502	357	10	f(ox	f(ox	PROPN
ejpam-3502	357	11	)	)	PUNCT
ejpam-3502	357	12	is	be	AUX
ejpam-3502	357	13	νk	νk	NOUN
ejpam-3502	357	14	-	-	ADJ
ejpam-3502	357	15	open	open	ADJ
ejpam-3502	357	16	.	.	PUNCT
ejpam-3502	358	1	as	as	ADP
ejpam-3502	358	2	a	a	DET
ejpam-3502	358	3	result	result	NOUN
ejpam-3502	358	4	,	,	PUNCT
ejpam-3502	358	5	f(u	f(u	PROPN
ejpam-3502	358	6	)	)	PUNCT
ejpam-3502	359	1	=	=	SYM
ejpam-3502	360	1	f	f	X
ejpam-3502	360	2	(	(	PUNCT
ejpam-3502	360	3	⋃	⋃	PROPN
ejpam-3502	360	4	x∈u	x∈u	PROPN
ejpam-3502	360	5	ox	ox	NOUN
ejpam-3502	360	6	)	)	PUNCT
ejpam-3502	360	7	=	=	SYM
ejpam-3502	360	8	⋃	⋃	ADP
ejpam-3502	360	9	x∈u	x∈u	ADJ
ejpam-3502	360	10	f(ox	f(ox	PROPN
ejpam-3502	360	11	)	)	PUNCT
ejpam-3502	360	12	is	be	AUX
ejpam-3502	360	13	a	a	DET
ejpam-3502	360	14	gy	gy	NOUN
ejpam-3502	360	15	-open	-open	NOUN
ejpam-3502	360	16	set	set	NOUN
ejpam-3502	360	17	.	.	PUNCT
ejpam-3502	361	1	since	since	SCONJ
ejpam-3502	361	2	u	u	NOUN
ejpam-3502	361	3	is	be	AUX
ejpam-3502	361	4	arbitrary	arbitrary	ADJ
ejpam-3502	361	5	,	,	PUNCT
ejpam-3502	361	6	we	we	PRON
ejpam-3502	361	7	say	say	VERB
ejpam-3502	361	8	that	that	SCONJ
ejpam-3502	361	9	f	f	PROPN
ejpam-3502	361	10	is	be	AUX
ejpam-3502	361	11	a	a	DET
ejpam-3502	361	12	g	g	NOUN
ejpam-3502	361	13	-open	-open	NOUN
ejpam-3502	361	14	map	map	NOUN
ejpam-3502	361	15	.	.	PUNCT
ejpam-3502	362	1	�	�	PROPN
ejpam-3502	362	2	the	the	DET
ejpam-3502	362	3	converse	converse	NOUN
ejpam-3502	362	4	of	of	ADP
ejpam-3502	362	5	theorem	theorem	ADJ
ejpam-3502	362	6	3.12	3.12	NUM
ejpam-3502	362	7	is	be	AUX
ejpam-3502	362	8	not	not	PART
ejpam-3502	362	9	generally	generally	ADV
ejpam-3502	362	10	true	true	ADJ
ejpam-3502	362	11	as	as	SCONJ
ejpam-3502	362	12	seen	see	VERB
ejpam-3502	362	13	in	in	ADP
ejpam-3502	362	14	example	example	NOUN
ejpam-3502	362	15	3.10	3.10	NUM
ejpam-3502	362	16	(	(	PUNCT
ejpam-3502	362	17	2	2	NUM
ejpam-3502	362	18	)	)	PUNCT
ejpam-3502	362	19	.	.	PUNCT
ejpam-3502	363	1	corollary	corollary	ADJ
ejpam-3502	363	2	3.13	3.13	NUM
ejpam-3502	363	3	.	.	PUNCT
ejpam-3502	364	1	if	if	SCONJ
ejpam-3502	364	2	f	f	PROPN
ejpam-3502	364	3	is	be	AUX
ejpam-3502	364	4	a	a	DET
ejpam-3502	364	5	pairwise	pairwise	NOUN
ejpam-3502	364	6	(	(	PUNCT
ejpam-3502	364	7	µ	µ	NOUN
ejpam-3502	364	8	,	,	PUNCT
ejpam-3502	364	9	ν)-open	ν)-open	NOUN
ejpam-3502	364	10	map	map	NOUN
ejpam-3502	364	11	,	,	PUNCT
ejpam-3502	364	12	then	then	ADV
ejpam-3502	364	13	f	f	PROPN
ejpam-3502	364	14	is	be	AUX
ejpam-3502	364	15	a	a	DET
ejpam-3502	364	16	g	g	NOUN
ejpam-3502	364	17	-open	-open	NOUN
ejpam-3502	364	18	map	map	NOUN
ejpam-3502	364	19	.	.	PUNCT
ejpam-3502	365	1	proof	proof	NOUN
ejpam-3502	365	2	.	.	PUNCT
ejpam-3502	366	1	this	this	PRON
ejpam-3502	366	2	is	be	AUX
ejpam-3502	366	3	immediate	immediate	ADJ
ejpam-3502	366	4	from	from	ADP
ejpam-3502	366	5	the	the	DET
ejpam-3502	366	6	definition	definition	NOUN
ejpam-3502	366	7	of	of	ADP
ejpam-3502	366	8	a	a	DET
ejpam-3502	366	9	pairwise	pairwise	NOUN
ejpam-3502	366	10	(	(	PUNCT
ejpam-3502	366	11	µ	µ	NOUN
ejpam-3502	366	12	,	,	PUNCT
ejpam-3502	366	13	ν)-open	ν)-open	NOUN
ejpam-3502	366	14	map	map	VERB
ejpam-3502	366	15	and	and	CCONJ
ejpam-3502	366	16	then	then	ADV
ejpam-3502	366	17	applying	apply	VERB
ejpam-3502	366	18	theorem	theorem	ADJ
ejpam-3502	366	19	3.12	3.12	NUM
ejpam-3502	366	20	.	.	PUNCT
ejpam-3502	366	21	�	�	PROPN
ejpam-3502	366	22	theorem	theorem	VERB
ejpam-3502	366	23	3.14	3.14	NUM
ejpam-3502	366	24	.	.	PUNCT
ejpam-3502	367	1	a	a	DET
ejpam-3502	367	2	mapping	mapping	NOUN
ejpam-3502	367	3	f	f	NOUN
ejpam-3502	367	4	:	:	PUNCT
ejpam-3502	367	5	x	x	X
ejpam-3502	367	6	→	→	SYM
ejpam-3502	367	7	y	y	PROPN
ejpam-3502	367	8	is	be	AUX
ejpam-3502	367	9	a	a	DET
ejpam-3502	367	10	pairwise	pairwise	NOUN
ejpam-3502	367	11	(	(	PUNCT
ejpam-3502	367	12	µ	µ	NOUN
ejpam-3502	367	13	,	,	PUNCT
ejpam-3502	367	14	ν)-open	ν)-open	PUNCT
ejpam-3502	367	15	map	map	VERB
ejpam-3502	367	16	if	if	SCONJ
ejpam-3502	367	17	and	and	CCONJ
ejpam-3502	367	18	only	only	ADV
ejpam-3502	367	19	if	if	SCONJ
ejpam-3502	367	20	for	for	ADP
ejpam-3502	367	21	each	each	DET
ejpam-3502	367	22	j	j	NOUN
ejpam-3502	367	23	and	and	CCONJ
ejpam-3502	367	24	for	for	ADP
ejpam-3502	367	25	each	each	DET
ejpam-3502	367	26	µj	µj	NOUN
ejpam-3502	367	27	-	-	PUNCT
ejpam-3502	367	28	open	open	ADJ
ejpam-3502	367	29	set	set	NOUN
ejpam-3502	367	30	u	u	PROPN
ejpam-3502	367	31	,	,	PUNCT
ejpam-3502	367	32	f(u	f(u	PROPN
ejpam-3502	367	33	)	)	PUNCT
ejpam-3502	367	34	∈	∈	PROPN
ejpam-3502	367	35	n⋂	n⋂	NOUN
ejpam-3502	367	36	k=1	k=1	VERB
ejpam-3502	367	37	νk	νk	X
ejpam-3502	367	38	.	.	PUNCT
ejpam-3502	367	39	proof	proof	NOUN
ejpam-3502	367	40	.	.	PUNCT
ejpam-3502	368	1	let	let	VERB
ejpam-3502	368	2	f	f	NOUN
ejpam-3502	368	3	:	:	PUNCT
ejpam-3502	368	4	x	x	X
ejpam-3502	368	5	→	→	SYM
ejpam-3502	368	6	y	y	X
ejpam-3502	368	7	be	be	AUX
ejpam-3502	368	8	a	a	DET
ejpam-3502	368	9	map	map	NOUN
ejpam-3502	368	10	,	,	PUNCT
ejpam-3502	368	11	j	j	PROPN
ejpam-3502	368	12	∈	∈	PROPN
ejpam-3502	368	13	{	{	PUNCT
ejpam-3502	368	14	1	1	NUM
ejpam-3502	368	15	,	,	PUNCT
ejpam-3502	368	16	.	.	PUNCT
ejpam-3502	368	17	.	.	PUNCT
ejpam-3502	368	18	.	.	PUNCT
ejpam-3502	369	1	,	,	PUNCT
ejpam-3502	369	2	m	m	VERB
ejpam-3502	369	3	}	}	PUNCT
ejpam-3502	369	4	and	and	CCONJ
ejpam-3502	369	5	u	u	PRON
ejpam-3502	369	6	be	be	VERB
ejpam-3502	369	7	a	a	DET
ejpam-3502	369	8	µj	µj	NOUN
ejpam-3502	369	9	-	-	PUNCT
ejpam-3502	369	10	open	open	ADJ
ejpam-3502	369	11	set	set	NOUN
ejpam-3502	369	12	.	.	PUNCT
ejpam-3502	370	1	if	if	SCONJ
ejpam-3502	370	2	f	f	PROPN
ejpam-3502	370	3	is	be	AUX
ejpam-3502	370	4	a	a	DET
ejpam-3502	370	5	pairwise	pairwise	NOUN
ejpam-3502	370	6	(	(	PUNCT
ejpam-3502	370	7	µ	µ	NOUN
ejpam-3502	370	8	,	,	PUNCT
ejpam-3502	370	9	ν)-open	ν)-open	NOUN
ejpam-3502	370	10	map	map	NOUN
ejpam-3502	370	11	,	,	PUNCT
ejpam-3502	370	12	then	then	ADV
ejpam-3502	370	13	for	for	ADP
ejpam-3502	370	14	every	every	DET
ejpam-3502	370	15	k	k	PROPN
ejpam-3502	370	16	,	,	PUNCT
ejpam-3502	370	17	f(u	f(u	PROPN
ejpam-3502	370	18	)	)	PUNCT
ejpam-3502	370	19	is	be	AUX
ejpam-3502	370	20	µk	µk	ADV
ejpam-3502	370	21	-	-	PUNCT
ejpam-3502	370	22	open	open	ADJ
ejpam-3502	370	23	so	so	SCONJ
ejpam-3502	370	24	that	that	SCONJ
ejpam-3502	370	25	f(u	f(u	PROPN
ejpam-3502	370	26	)	)	PUNCT
ejpam-3502	370	27	∈	∈	PROPN
ejpam-3502	370	28	n⋂	n⋂	NOUN
ejpam-3502	370	29	k=1	k=1	VERB
ejpam-3502	371	1	νk	νk	X
ejpam-3502	371	2	.	.	PUNCT
ejpam-3502	372	1	the	the	DET
ejpam-3502	372	2	converse	converse	NOUN
ejpam-3502	372	3	is	be	AUX
ejpam-3502	372	4	similarly	similarly	ADV
ejpam-3502	372	5	outright	outright	ADJ
ejpam-3502	372	6	.	.	PUNCT
ejpam-3502	373	1	�	�	PROPN
ejpam-3502	373	2	corollary	corollary	NOUN
ejpam-3502	373	3	3.15	3.15	NUM
ejpam-3502	373	4	.	.	PUNCT
ejpam-3502	374	1	if	if	SCONJ
ejpam-3502	374	2	for	for	ADP
ejpam-3502	374	3	each	each	DET
ejpam-3502	374	4	j	j	NOUN
ejpam-3502	374	5	and	and	CCONJ
ejpam-3502	374	6	for	for	ADP
ejpam-3502	374	7	each	each	DET
ejpam-3502	374	8	µj	µj	NOUN
ejpam-3502	374	9	-	-	PUNCT
ejpam-3502	374	10	open	open	ADJ
ejpam-3502	374	11	set	set	NOUN
ejpam-3502	374	12	u	u	PROPN
ejpam-3502	374	13	,	,	PUNCT
ejpam-3502	374	14	f(u	f(u	PROPN
ejpam-3502	374	15	)	)	PUNCT
ejpam-3502	374	16	∈	∈	PROPN
ejpam-3502	374	17	n⋂	n⋂	NOUN
ejpam-3502	374	18	k=1	k=1	VERB
ejpam-3502	375	1	νk	νk	X
ejpam-3502	375	2	,	,	PUNCT
ejpam-3502	375	3	then	then	ADV
ejpam-3502	375	4	f	f	PROPN
ejpam-3502	375	5	is	be	AUX
ejpam-3502	375	6	a	a	DET
ejpam-3502	375	7	g	g	NOUN
ejpam-3502	375	8	-open	-open	NOUN
ejpam-3502	375	9	map	map	NOUN
ejpam-3502	375	10	.	.	PUNCT
ejpam-3502	376	1	proof	proof	NOUN
ejpam-3502	376	2	.	.	PUNCT
ejpam-3502	377	1	this	this	DET
ejpam-3502	377	2	relationship	relationship	NOUN
ejpam-3502	377	3	is	be	AUX
ejpam-3502	377	4	a	a	DET
ejpam-3502	377	5	direct	direct	ADJ
ejpam-3502	377	6	consequence	consequence	NOUN
ejpam-3502	377	7	of	of	ADP
ejpam-3502	377	8	theorem	theorem	ADJ
ejpam-3502	377	9	3.14	3.14	NUM
ejpam-3502	377	10	and	and	CCONJ
ejpam-3502	377	11	corollary	corollary	ADJ
ejpam-3502	377	12	3.13	3.13	NUM
ejpam-3502	377	13	.	.	PUNCT
ejpam-3502	378	1	�	�	PROPN
ejpam-3502	378	2	4	4	NUM
ejpam-3502	378	3	.	.	PUNCT
ejpam-3502	379	1	g	g	NOUN
ejpam-3502	379	2	-homeomorphisms	-homeomorphism	NOUN
ejpam-3502	379	3	this	this	DET
ejpam-3502	379	4	section	section	NOUN
ejpam-3502	379	5	basically	basically	ADV
ejpam-3502	379	6	displays	display	VERB
ejpam-3502	379	7	the	the	DET
ejpam-3502	379	8	relationships	relationship	NOUN
ejpam-3502	379	9	of	of	ADP
ejpam-3502	379	10	g	g	PROPN
ejpam-3502	379	11	-continuous	-continuous	ADJ
ejpam-3502	379	12	maps	map	NOUN
ejpam-3502	379	13	to	to	ADP
ejpam-3502	379	14	g	g	NOUN
ejpam-3502	379	15	-open	-open	ADJ
ejpam-3502	379	16	and	and	CCONJ
ejpam-3502	379	17	g	g	NOUN
ejpam-3502	379	18	-closed	-close	VERB
ejpam-3502	379	19	maps	map	NOUN
ejpam-3502	379	20	in	in	ADP
ejpam-3502	379	21	form	form	NOUN
ejpam-3502	379	22	of	of	ADP
ejpam-3502	379	23	g	g	PROPN
ejpam-3502	379	24	-homeomorphisms	-homeomorphism	NOUN
ejpam-3502	379	25	.	.	PUNCT
ejpam-3502	380	1	in	in	ADP
ejpam-3502	380	2	the	the	DET
ejpam-3502	380	3	sense	sense	NOUN
ejpam-3502	380	4	of	of	ADP
ejpam-3502	380	5	ordinary	ordinary	ADJ
ejpam-3502	380	6	topological	topological	ADJ
ejpam-3502	380	7	spaces	space	NOUN
ejpam-3502	380	8	,	,	PUNCT
ejpam-3502	380	9	the	the	DET
ejpam-3502	380	10	existence	existence	NOUN
ejpam-3502	380	11	of	of	ADP
ejpam-3502	380	12	homeomorphisms	homeomorphism	NOUN
ejpam-3502	380	13	between	between	ADP
ejpam-3502	380	14	two	two	NUM
ejpam-3502	380	15	topological	topological	ADJ
ejpam-3502	380	16	spaces	space	NOUN
ejpam-3502	380	17	identifies	identify	VERB
ejpam-3502	380	18	an	an	DET
ejpam-3502	380	19	equivalence	equivalence	NOUN
ejpam-3502	380	20	of	of	ADP
ejpam-3502	380	21	their	their	PRON
ejpam-3502	380	22	structures	structure	NOUN
ejpam-3502	380	23	.	.	PUNCT
ejpam-3502	381	1	here	here	ADV
ejpam-3502	381	2	,	,	PUNCT
ejpam-3502	381	3	we	we	PRON
ejpam-3502	381	4	investigate	investigate	VERB
ejpam-3502	381	5	whether	whether	SCONJ
ejpam-3502	381	6	the	the	DET
ejpam-3502	381	7	existence	existence	NOUN
ejpam-3502	381	8	of	of	ADP
ejpam-3502	381	9	such	such	ADJ
ejpam-3502	381	10	likeness	likeness	NOUN
ejpam-3502	381	11	extends	extend	VERB
ejpam-3502	381	12	this	this	DET
ejpam-3502	381	13	time	time	NOUN
ejpam-3502	381	14	to	to	ADP
ejpam-3502	381	15	n	n	CCONJ
ejpam-3502	381	16	-	-	PUNCT
ejpam-3502	381	17	gt	gt	PROPN
ejpam-3502	381	18	spaces	space	NOUN
ejpam-3502	381	19	.	.	PUNCT
ejpam-3502	382	1	definition	definition	NOUN
ejpam-3502	382	2	4.1	4.1	NUM
ejpam-3502	382	3	.	.	PUNCT
ejpam-3502	383	1	let	let	VERB
ejpam-3502	383	2	(	(	PUNCT
ejpam-3502	383	3	x	x	NOUN
ejpam-3502	383	4	,	,	PUNCT
ejpam-3502	383	5	gx	gx	PROPN
ejpam-3502	383	6	)	)	PUNCT
ejpam-3502	383	7	and	and	CCONJ
ejpam-3502	383	8	(	(	PUNCT
ejpam-3502	383	9	y	y	PROPN
ejpam-3502	383	10	,	,	PUNCT
ejpam-3502	383	11	gy	gy	NOUN
ejpam-3502	383	12	)	)	PUNCT
ejpam-3502	383	13	be	be	AUX
ejpam-3502	383	14	m	m	PROPN
ejpam-3502	383	15	-	-	PUNCT
ejpam-3502	383	16	gt	gt	PROPN
ejpam-3502	383	17	and	and	CCONJ
ejpam-3502	383	18	n	n	CCONJ
ejpam-3502	383	19	-	-	PUNCT
ejpam-3502	383	20	gt	gt	PROPN
ejpam-3502	383	21	spaces	space	NOUN
ejpam-3502	383	22	,	,	PUNCT
ejpam-3502	383	23	respectively	respectively	ADV
ejpam-3502	383	24	,	,	PUNCT
ejpam-3502	383	25	where	where	SCONJ
ejpam-3502	383	26	gx	gx	PROPN
ejpam-3502	383	27	=	=	PUNCT
ejpam-3502	383	28	{	{	PUNCT
ejpam-3502	383	29	µ1	µ1	PROPN
ejpam-3502	383	30	,	,	PUNCT
ejpam-3502	383	31	.	.	PUNCT
ejpam-3502	383	32	.	.	PUNCT
ejpam-3502	383	33	.	.	PUNCT
ejpam-3502	384	1	,	,	PUNCT
ejpam-3502	384	2	µm	µm	ADP
ejpam-3502	384	3	}	}	PUNCT
ejpam-3502	384	4	and	and	CCONJ
ejpam-3502	384	5	gy	gy	NOUN
ejpam-3502	384	6	=	=	SYM
ejpam-3502	384	7	{	{	PUNCT
ejpam-3502	384	8	ν1	ν1	NOUN
ejpam-3502	384	9	,	,	PUNCT
ejpam-3502	384	10	.	.	PUNCT
ejpam-3502	384	11	.	.	PUNCT
ejpam-3502	385	1	.	.	PUNCT
ejpam-3502	386	1	,	,	PUNCT
ejpam-3502	386	2	νn	νn	AUX
ejpam-3502	386	3	}	}	PUNCT
ejpam-3502	386	4	for	for	ADP
ejpam-3502	386	5	some	some	DET
ejpam-3502	386	6	m	m	NOUN
ejpam-3502	386	7	,	,	PUNCT
ejpam-3502	386	8	n	n	PROPN
ejpam-3502	386	9	∈	∈	PROPN
ejpam-3502	386	10	n.	n.	PROPN
ejpam-3502	386	11	c.	c.	PROPN
ejpam-3502	386	12	balingit	balingit	PROPN
ejpam-3502	386	13	,	,	PUNCT
ejpam-3502	386	14	j.	j.	PROPN
ejpam-3502	386	15	benitez	benitez	PROPN
ejpam-3502	386	16	/	/	PUNCT
ejpam-3502	386	17	eur	eur	PROPN
ejpam-3502	386	18	.	.	PUNCT
ejpam-3502	387	1	j.	j.	PROPN
ejpam-3502	387	2	pure	pure	PROPN
ejpam-3502	387	3	appl	appl	PROPN
ejpam-3502	387	4	.	.	PROPN
ejpam-3502	387	5	math	math	PROPN
ejpam-3502	387	6	,	,	PUNCT
ejpam-3502	387	7	12	12	NUM
ejpam-3502	387	8	(	(	PUNCT
ejpam-3502	387	9	4	4	NUM
ejpam-3502	387	10	)	)	PUNCT
ejpam-3502	387	11	(	(	PUNCT
ejpam-3502	387	12	2019	2019	NUM
ejpam-3502	387	13	)	)	PUNCT
ejpam-3502	387	14	,	,	PUNCT
ejpam-3502	387	15	1553	1553	NUM
ejpam-3502	387	16	-	-	SYM
ejpam-3502	387	17	1566	1566	NUM
ejpam-3502	387	18	1563	1563	NUM
ejpam-3502	387	19	1	1	NUM
ejpam-3502	387	20	.	.	PUNCT
ejpam-3502	388	1	a	a	DET
ejpam-3502	388	2	bijective	bijective	ADJ
ejpam-3502	388	3	map	map	NOUN
ejpam-3502	388	4	f	f	X
ejpam-3502	388	5	:	:	PUNCT
ejpam-3502	388	6	x	x	X
ejpam-3502	388	7	→	→	SYM
ejpam-3502	388	8	y	y	PROPN
ejpam-3502	388	9	is	be	AUX
ejpam-3502	388	10	a	a	DET
ejpam-3502	388	11	g	g	NOUN
ejpam-3502	388	12	-homeomorphism	-homeomorphism	NOUN
ejpam-3502	388	13	if	if	SCONJ
ejpam-3502	388	14	both	both	DET
ejpam-3502	388	15	f	f	PROPN
ejpam-3502	388	16	and	and	CCONJ
ejpam-3502	388	17	f−1	f−1	PROPN
ejpam-3502	388	18	are	be	AUX
ejpam-3502	388	19	g	g	NOUN
ejpam-3502	388	20	continuous	continuous	ADJ
ejpam-3502	388	21	maps	map	NOUN
ejpam-3502	388	22	.	.	PUNCT
ejpam-3502	389	1	in	in	ADP
ejpam-3502	389	2	this	this	DET
ejpam-3502	389	3	case	case	NOUN
ejpam-3502	389	4	,	,	PUNCT
ejpam-3502	389	5	we	we	PRON
ejpam-3502	389	6	use	use	VERB
ejpam-3502	389	7	the	the	DET
ejpam-3502	389	8	notation	notation	NOUN
ejpam-3502	389	9	f	f	NOUN
ejpam-3502	389	10	:	:	PUNCT
ejpam-3502	389	11	x	x	X
ejpam-3502	389	12	g∼=	g∼=	PUNCT
ejpam-3502	389	13	y	y	PROPN
ejpam-3502	389	14	to	to	PART
ejpam-3502	389	15	denote	denote	VERB
ejpam-3502	389	16	that	that	SCONJ
ejpam-3502	389	17	f	f	PROPN
ejpam-3502	389	18	is	be	AUX
ejpam-3502	389	19	a	a	DET
ejpam-3502	389	20	g	g	NOUN
ejpam-3502	389	21	-homeomorphism	-homeomorphism	NOUN
ejpam-3502	389	22	.	.	PUNCT
ejpam-3502	390	1	2	2	X
ejpam-3502	390	2	.	.	X
ejpam-3502	390	3	if	if	SCONJ
ejpam-3502	390	4	there	there	PRON
ejpam-3502	390	5	exists	exist	VERB
ejpam-3502	390	6	a	a	DET
ejpam-3502	390	7	g	g	PROPN
ejpam-3502	390	8	-homeomorphism	-homeomorphism	NOUN
ejpam-3502	390	9	f	f	NOUN
ejpam-3502	390	10	:	:	PUNCT
ejpam-3502	390	11	x	x	SYM
ejpam-3502	390	12	g∼=	g∼=	NUM
ejpam-3502	390	13	y	y	PROPN
ejpam-3502	390	14	,	,	PUNCT
ejpam-3502	390	15	then	then	ADV
ejpam-3502	390	16	we	we	PRON
ejpam-3502	390	17	say	say	VERB
ejpam-3502	390	18	that	that	SCONJ
ejpam-3502	390	19	the	the	DET
ejpam-3502	390	20	spaces	space	NOUN
ejpam-3502	390	21	x	x	X
ejpam-3502	390	22	and	and	CCONJ
ejpam-3502	390	23	y	y	PROPN
ejpam-3502	390	24	are	be	AUX
ejpam-3502	390	25	g	g	PROPN
ejpam-3502	390	26	-homeomorphic	-homeomorphic	PROPN
ejpam-3502	390	27	.	.	PUNCT
ejpam-3502	390	28	example	example	NOUN
ejpam-3502	390	29	4.2	4.2	NUM
ejpam-3502	390	30	.	.	PUNCT
ejpam-3502	391	1	by	by	ADP
ejpam-3502	391	2	the	the	DET
ejpam-3502	391	3	definition	definition	NOUN
ejpam-3502	391	4	of	of	ADP
ejpam-3502	391	5	the	the	DET
ejpam-3502	391	6	spaces	space	NOUN
ejpam-3502	391	7	(	(	PUNCT
ejpam-3502	391	8	x	x	NOUN
ejpam-3502	391	9	,	,	PUNCT
ejpam-3502	391	10	g1	g1	PROPN
ejpam-3502	391	11	)	)	PUNCT
ejpam-3502	391	12	and	and	CCONJ
ejpam-3502	391	13	(	(	PUNCT
ejpam-3502	391	14	x	x	X
ejpam-3502	391	15	,	,	PUNCT
ejpam-3502	391	16	g2	g2	PROPN
ejpam-3502	391	17	)	)	PUNCT
ejpam-3502	391	18	in	in	ADP
ejpam-3502	391	19	example	example	NOUN
ejpam-3502	391	20	3.10	3.10	NUM
ejpam-3502	391	21	(	(	PUNCT
ejpam-3502	391	22	2	2	NUM
ejpam-3502	391	23	)	)	PUNCT
ejpam-3502	391	24	,	,	PUNCT
ejpam-3502	391	25	we	we	PRON
ejpam-3502	391	26	see	see	VERB
ejpam-3502	391	27	that	that	SCONJ
ejpam-3502	391	28	the	the	DET
ejpam-3502	391	29	identity	identity	NOUN
ejpam-3502	391	30	map	map	NOUN
ejpam-3502	391	31	between	between	ADP
ejpam-3502	391	32	these	these	DET
ejpam-3502	391	33	particular	particular	ADJ
ejpam-3502	391	34	spaces	space	NOUN
ejpam-3502	391	35	easily	easily	ADV
ejpam-3502	391	36	provides	provide	VERB
ejpam-3502	391	37	a	a	DET
ejpam-3502	391	38	g	g	NOUN
ejpam-3502	391	39	homeomorphic	homeomorphic	ADJ
ejpam-3502	391	40	map	map	NOUN
ejpam-3502	391	41	.	.	PUNCT
ejpam-3502	392	1	in	in	ADP
ejpam-3502	392	2	a	a	DET
ejpam-3502	392	3	wider	wide	ADJ
ejpam-3502	392	4	sense	sense	NOUN
ejpam-3502	392	5	,	,	PUNCT
ejpam-3502	392	6	if	if	SCONJ
ejpam-3502	392	7	f	f	X
ejpam-3502	392	8	:	:	PUNCT
ejpam-3502	392	9	x	x	X
ejpam-3502	392	10	→	→	SYM
ejpam-3502	392	11	y	y	PROPN
ejpam-3502	392	12	is	be	AUX
ejpam-3502	392	13	any	any	DET
ejpam-3502	392	14	bijection	bijection	NOUN
ejpam-3502	392	15	and	and	CCONJ
ejpam-3502	392	16	(	(	PUNCT
ejpam-3502	392	17	x	x	NOUN
ejpam-3502	392	18	,	,	PUNCT
ejpam-3502	392	19	gx	gx	PROPN
ejpam-3502	392	20	)	)	PUNCT
ejpam-3502	392	21	and	and	CCONJ
ejpam-3502	392	22	(	(	PUNCT
ejpam-3502	392	23	y	y	PROPN
ejpam-3502	392	24	,	,	PUNCT
ejpam-3502	392	25	gy	gy	NOUN
ejpam-3502	392	26	)	)	PUNCT
ejpam-3502	392	27	are	be	AUX
ejpam-3502	392	28	as	as	ADV
ejpam-3502	392	29	defined	define	VERB
ejpam-3502	392	30	in	in	ADP
ejpam-3502	392	31	example	example	NOUN
ejpam-3502	392	32	3.10	3.10	NUM
ejpam-3502	392	33	,	,	PUNCT
ejpam-3502	392	34	then	then	ADV
ejpam-3502	392	35	f	f	PROPN
ejpam-3502	392	36	is	be	AUX
ejpam-3502	392	37	in	in	ADP
ejpam-3502	392	38	fact	fact	NOUN
ejpam-3502	392	39	a	a	DET
ejpam-3502	392	40	g	g	PROPN
ejpam-3502	392	41	-homeomorphism	-homeomorphism	NOUN
ejpam-3502	392	42	.	.	PUNCT
ejpam-3502	393	1	however	however	ADV
ejpam-3502	393	2	,	,	PUNCT
ejpam-3502	393	3	it	it	PRON
ejpam-3502	393	4	should	should	AUX
ejpam-3502	393	5	be	be	AUX
ejpam-3502	393	6	noted	note	VERB
ejpam-3502	393	7	that	that	SCONJ
ejpam-3502	393	8	not	not	PART
ejpam-3502	393	9	every	every	DET
ejpam-3502	393	10	bijective	bijective	ADJ
ejpam-3502	393	11	mapping	mapping	NOUN
ejpam-3502	393	12	is	be	AUX
ejpam-3502	393	13	a	a	DET
ejpam-3502	393	14	g	g	PROPN
ejpam-3502	393	15	-homeomorphism	-homeomorphism	NOUN
ejpam-3502	393	16	:	:	PUNCT
ejpam-3502	393	17	see	see	VERB
ejpam-3502	393	18	this	this	PRON
ejpam-3502	393	19	by	by	ADP
ejpam-3502	393	20	simply	simply	ADV
ejpam-3502	393	21	dropping	drop	VERB
ejpam-3502	393	22	qn	qn	INTJ
ejpam-3502	393	23	(	(	PUNCT
ejpam-3502	393	24	or	or	CCONJ
ejpam-3502	393	25	any	any	PRON
ejpam-3502	393	26	of	of	ADP
ejpam-3502	393	27	the	the	DET
ejpam-3502	393	28	component	component	NOUN
ejpam-3502	393	29	gts	gts	NOUN
ejpam-3502	393	30	)	)	PUNCT
ejpam-3502	393	31	in	in	ADP
ejpam-3502	393	32	the	the	DET
ejpam-3502	393	33	n	n	CCONJ
ejpam-3502	393	34	-	-	PUNCT
ejpam-3502	393	35	gt	gt	PROPN
ejpam-3502	393	36	space	space	NOUN
ejpam-3502	393	37	(	(	PUNCT
ejpam-3502	393	38	y	y	NOUN
ejpam-3502	393	39	,	,	PUNCT
ejpam-3502	393	40	gy	gy	NOUN
ejpam-3502	393	41	)	)	PUNCT
ejpam-3502	393	42	in	in	ADP
ejpam-3502	393	43	the	the	DET
ejpam-3502	393	44	same	same	ADJ
ejpam-3502	393	45	example	example	NOUN
ejpam-3502	393	46	.	.	PUNCT
ejpam-3502	394	1	example	example	NOUN
ejpam-3502	394	2	4.2	4.2	NUM
ejpam-3502	394	3	suggests	suggest	VERB
ejpam-3502	394	4	that	that	SCONJ
ejpam-3502	394	5	even	even	ADV
ejpam-3502	394	6	if	if	SCONJ
ejpam-3502	394	7	f	f	X
ejpam-3502	394	8	:	:	PUNCT
ejpam-3502	394	9	x	x	X
ejpam-3502	394	10	g∼=	g∼=	NUM
ejpam-3502	394	11	y	y	PROPN
ejpam-3502	394	12	,	,	PUNCT
ejpam-3502	394	13	it	it	PRON
ejpam-3502	394	14	is	be	AUX
ejpam-3502	394	15	not	not	PART
ejpam-3502	394	16	a	a	DET
ejpam-3502	394	17	guarantee	guarantee	NOUN
ejpam-3502	394	18	that	that	SCONJ
ejpam-3502	394	19	the	the	DET
ejpam-3502	394	20	spaces	space	NOUN
ejpam-3502	394	21	x	x	X
ejpam-3502	394	22	and	and	CCONJ
ejpam-3502	394	23	y	y	PROPN
ejpam-3502	394	24	are	be	AUX
ejpam-3502	394	25	equivalent	equivalent	ADJ
ejpam-3502	394	26	in	in	ADP
ejpam-3502	394	27	terms	term	NOUN
ejpam-3502	394	28	of	of	ADP
ejpam-3502	394	29	their	their	PRON
ejpam-3502	394	30	component	component	NOUN
ejpam-3502	394	31	gts	gts	NOUN
ejpam-3502	394	32	.	.	PUNCT
ejpam-3502	395	1	in	in	ADP
ejpam-3502	395	2	other	other	ADJ
ejpam-3502	395	3	words	word	NOUN
ejpam-3502	395	4	,	,	PUNCT
ejpam-3502	395	5	a	a	DET
ejpam-3502	395	6	component	component	NOUN
ejpam-3502	395	7	gt	gt	INTJ
ejpam-3502	395	8	µj	µj	PROPN
ejpam-3502	395	9	in	in	ADP
ejpam-3502	395	10	gx	gx	PROPN
ejpam-3502	395	11	may	may	AUX
ejpam-3502	395	12	not	not	PART
ejpam-3502	395	13	coincide	coincide	VERB
ejpam-3502	395	14	to	to	ADP
ejpam-3502	395	15	any	any	DET
ejpam-3502	395	16	νk	νk	NOUN
ejpam-3502	395	17	in	in	ADP
ejpam-3502	395	18	gy	gy	NOUN
ejpam-3502	395	19	even	even	ADV
ejpam-3502	395	20	if	if	SCONJ
ejpam-3502	395	21	x	x	PRON
ejpam-3502	395	22	is	be	AUX
ejpam-3502	395	23	g	g	NOUN
ejpam-3502	395	24	-homeomorphic	-homeomorphic	ADJ
ejpam-3502	395	25	to	to	ADP
ejpam-3502	395	26	y	y	PROPN
ejpam-3502	395	27	.	.	PUNCT
ejpam-3502	396	1	theorem	theorem	VERB
ejpam-3502	396	2	4.3	4.3	NUM
ejpam-3502	396	3	.	.	PUNCT
ejpam-3502	397	1	let	let	VERB
ejpam-3502	397	2	f	f	NOUN
ejpam-3502	397	3	:	:	PUNCT
ejpam-3502	397	4	x	x	X
ejpam-3502	397	5	→	→	SYM
ejpam-3502	397	6	y	y	X
ejpam-3502	397	7	be	be	AUX
ejpam-3502	397	8	a	a	DET
ejpam-3502	397	9	bijective	bijective	ADJ
ejpam-3502	397	10	map	map	NOUN
ejpam-3502	397	11	.	.	PUNCT
ejpam-3502	398	1	then	then	ADV
ejpam-3502	398	2	the	the	DET
ejpam-3502	398	3	following	follow	VERB
ejpam-3502	398	4	statements	statement	NOUN
ejpam-3502	398	5	are	be	AUX
ejpam-3502	398	6	equivalent	equivalent	ADJ
ejpam-3502	398	7	:	:	PUNCT
ejpam-3502	398	8	1	1	X
ejpam-3502	398	9	.	.	X
ejpam-3502	398	10	f	f	PROPN
ejpam-3502	398	11	is	be	AUX
ejpam-3502	398	12	a	a	DET
ejpam-3502	398	13	g	g	NOUN
ejpam-3502	398	14	-homeomorphism	-homeomorphism	NOUN
ejpam-3502	398	15	;	;	PUNCT
ejpam-3502	398	16	2	2	NUM
ejpam-3502	398	17	.	.	X
ejpam-3502	398	18	f	f	PROPN
ejpam-3502	398	19	is	be	AUX
ejpam-3502	398	20	a	a	DET
ejpam-3502	398	21	g	g	NOUN
ejpam-3502	398	22	-continuous	-continuous	ADJ
ejpam-3502	398	23	and	and	CCONJ
ejpam-3502	398	24	g	g	NOUN
ejpam-3502	398	25	-open	-open	NOUN
ejpam-3502	398	26	map	map	NOUN
ejpam-3502	398	27	;	;	PUNCT
ejpam-3502	398	28	3	3	X
ejpam-3502	398	29	.	.	X
ejpam-3502	398	30	f	f	PROPN
ejpam-3502	398	31	is	be	AUX
ejpam-3502	398	32	a	a	DET
ejpam-3502	398	33	g	g	NOUN
ejpam-3502	398	34	-continuous	-continuous	ADJ
ejpam-3502	398	35	and	and	CCONJ
ejpam-3502	398	36	g	g	NOUN
ejpam-3502	398	37	-closed	-close	VERB
ejpam-3502	398	38	map	map	NOUN
ejpam-3502	398	39	;	;	PUNCT
ejpam-3502	398	40	4	4	NUM
ejpam-3502	398	41	.	.	PUNCT
ejpam-3502	398	42	f(cx(a	f(cx(a	NOUN
ejpam-3502	398	43	)	)	PUNCT
ejpam-3502	398	44	)	)	PUNCT
ejpam-3502	399	1	=	=	SYM
ejpam-3502	399	2	cy	cy	PROPN
ejpam-3502	399	3	(	(	PUNCT
ejpam-3502	399	4	f(a	f(a	NOUN
ejpam-3502	399	5	)	)	PUNCT
ejpam-3502	399	6	)	)	PUNCT
ejpam-3502	399	7	for	for	ADP
ejpam-3502	399	8	every	every	DET
ejpam-3502	399	9	a	a	DET
ejpam-3502	399	10	⊆	⊆	NUM
ejpam-3502	399	11	x	x	NOUN
ejpam-3502	399	12	;	;	PUNCT
ejpam-3502	399	13	and	and	CCONJ
ejpam-3502	399	14	5	5	X
ejpam-3502	399	15	.	.	X
ejpam-3502	399	16	f(ix(a	f(ix(a	NOUN
ejpam-3502	399	17	)	)	PUNCT
ejpam-3502	399	18	)	)	PUNCT
ejpam-3502	400	1	=	=	SYM
ejpam-3502	400	2	iy	iy	PROPN
ejpam-3502	400	3	(	(	PUNCT
ejpam-3502	400	4	f(a	f(a	NOUN
ejpam-3502	400	5	)	)	PUNCT
ejpam-3502	400	6	)	)	PUNCT
ejpam-3502	400	7	for	for	ADP
ejpam-3502	400	8	every	every	DET
ejpam-3502	400	9	a	a	DET
ejpam-3502	400	10	⊆	⊆	NUM
ejpam-3502	400	11	x.	x.	NOUN
ejpam-3502	400	12	proof	proof	NOUN
ejpam-3502	400	13	.	.	PUNCT
ejpam-3502	401	1	suppose	suppose	VERB
ejpam-3502	401	2	f	f	X
ejpam-3502	401	3	:	:	PUNCT
ejpam-3502	401	4	x	x	X
ejpam-3502	401	5	→	→	SYM
ejpam-3502	401	6	y	y	PROPN
ejpam-3502	401	7	is	be	AUX
ejpam-3502	401	8	a	a	DET
ejpam-3502	401	9	bijective	bijective	ADJ
ejpam-3502	401	10	map	map	NOUN
ejpam-3502	401	11	.	.	PUNCT
ejpam-3502	402	1	(	(	PUNCT
ejpam-3502	402	2	1	1	X
ejpam-3502	402	3	)	)	PUNCT
ejpam-3502	402	4	⇔	⇔	X
ejpam-3502	402	5	(	(	PUNCT
ejpam-3502	402	6	2	2	NUM
ejpam-3502	402	7	)	)	PUNCT
ejpam-3502	402	8	note	note	NOUN
ejpam-3502	402	9	that	that	SCONJ
ejpam-3502	402	10	f	f	PROPN
ejpam-3502	402	11	is	be	AUX
ejpam-3502	402	12	a	a	DET
ejpam-3502	402	13	g	g	NOUN
ejpam-3502	402	14	-homeomorphism	-homeomorphism	NOUN
ejpam-3502	402	15	if	if	SCONJ
ejpam-3502	402	16	and	and	CCONJ
ejpam-3502	402	17	only	only	ADV
ejpam-3502	402	18	if	if	SCONJ
ejpam-3502	402	19	f	f	PROPN
ejpam-3502	402	20	is	be	AUX
ejpam-3502	402	21	g	g	PROPN
ejpam-3502	402	22	-continuous	-continuous	ADJ
ejpam-3502	402	23	and	and	CCONJ
ejpam-3502	402	24	f−1	f−1	PROPN
ejpam-3502	402	25	is	be	AUX
ejpam-3502	402	26	also	also	ADV
ejpam-3502	402	27	g	g	NOUN
ejpam-3502	402	28	-continuous	-continuous	ADJ
ejpam-3502	402	29	.	.	PUNCT
ejpam-3502	403	1	as	as	ADP
ejpam-3502	403	2	such	such	ADJ
ejpam-3502	403	3	,	,	PUNCT
ejpam-3502	403	4	theorem	theorem	VERB
ejpam-3502	403	5	2.4	2.4	NUM
ejpam-3502	403	6	provides	provide	VERB
ejpam-3502	403	7	that	that	PRON
ejpam-3502	403	8	for	for	ADP
ejpam-3502	403	9	every	every	DET
ejpam-3502	403	10	gx	gx	PROPN
ejpam-3502	403	11	-open	-open	PROPN
ejpam-3502	403	12	set	set	NOUN
ejpam-3502	403	13	u	u	NOUN
ejpam-3502	403	14	,	,	PUNCT
ejpam-3502	403	15	(	(	PUNCT
ejpam-3502	403	16	f−1)−1(u	f−1)−1(u	NOUN
ejpam-3502	403	17	)	)	PUNCT
ejpam-3502	403	18	=	=	SYM
ejpam-3502	403	19	f(u	f(u	PROPN
ejpam-3502	403	20	)	)	PUNCT
ejpam-3502	403	21	is	be	AUX
ejpam-3502	403	22	gy	gy	NOUN
ejpam-3502	403	23	-open	-open	NOUN
ejpam-3502	403	24	.	.	PUNCT
ejpam-3502	404	1	this	this	PRON
ejpam-3502	404	2	means	mean	VERB
ejpam-3502	404	3	that	that	SCONJ
ejpam-3502	404	4	f	f	PROPN
ejpam-3502	404	5	is	be	AUX
ejpam-3502	404	6	also	also	ADV
ejpam-3502	404	7	g	g	PROPN
ejpam-3502	404	8	-open	-open	NOUN
ejpam-3502	404	9	map	map	NOUN
ejpam-3502	404	10	,	,	PUNCT
ejpam-3502	404	11	and	and	CCONJ
ejpam-3502	404	12	conversely	conversely	ADV
ejpam-3502	404	13	.	.	PUNCT
ejpam-3502	405	1	(	(	PUNCT
ejpam-3502	405	2	2)⇔	2)⇔	NUM
ejpam-3502	405	3	(	(	PUNCT
ejpam-3502	405	4	3	3	NUM
ejpam-3502	405	5	)	)	PUNCT
ejpam-3502	405	6	because	because	SCONJ
ejpam-3502	405	7	f	f	PROPN
ejpam-3502	405	8	is	be	AUX
ejpam-3502	405	9	bijective	bijective	ADJ
ejpam-3502	405	10	,	,	PUNCT
ejpam-3502	405	11	these	these	DET
ejpam-3502	405	12	directions	direction	NOUN
ejpam-3502	405	13	follow	follow	VERB
ejpam-3502	405	14	immediately	immediately	ADV
ejpam-3502	405	15	from	from	ADP
ejpam-3502	405	16	theorem	theorem	ADJ
ejpam-3502	405	17	3.8	3.8	NUM
ejpam-3502	405	18	.	.	PUNCT
ejpam-3502	406	1	(	(	PUNCT
ejpam-3502	406	2	3)⇔	3)⇔	NUM
ejpam-3502	406	3	(	(	PUNCT
ejpam-3502	406	4	4	4	NUM
ejpam-3502	406	5	)	)	PUNCT
ejpam-3502	406	6	this	this	PRON
ejpam-3502	406	7	follows	follow	VERB
ejpam-3502	406	8	immediately	immediately	ADV
ejpam-3502	406	9	from	from	ADP
ejpam-3502	406	10	theorems	theorem	NOUN
ejpam-3502	406	11	2.5	2.5	NUM
ejpam-3502	406	12	and	and	CCONJ
ejpam-3502	406	13	3.6	3.6	NUM
ejpam-3502	406	14	.	.	PUNCT
ejpam-3502	407	1	(	(	PUNCT
ejpam-3502	407	2	2	2	X
ejpam-3502	407	3	)	)	PUNCT
ejpam-3502	407	4	⇔	⇔	NOUN
ejpam-3502	407	5	(	(	PUNCT
ejpam-3502	407	6	5	5	NUM
ejpam-3502	407	7	)	)	PUNCT
ejpam-3502	407	8	from	from	ADP
ejpam-3502	407	9	theorem	theorem	ADJ
ejpam-3502	407	10	3.5	3.5	NUM
ejpam-3502	407	11	,	,	PUNCT
ejpam-3502	407	12	f	f	PROPN
ejpam-3502	407	13	is	be	AUX
ejpam-3502	407	14	a	a	DET
ejpam-3502	407	15	g	g	NOUN
ejpam-3502	407	16	-open	-open	NOUN
ejpam-3502	407	17	map	map	NOUN
ejpam-3502	407	18	if	if	SCONJ
ejpam-3502	407	19	and	and	CCONJ
ejpam-3502	407	20	only	only	ADV
ejpam-3502	407	21	if	if	SCONJ
ejpam-3502	407	22	f(ix(a	f(ix(a	NOUN
ejpam-3502	407	23	)	)	PUNCT
ejpam-3502	407	24	)	)	PUNCT
ejpam-3502	408	1	⊆	⊆	NUM
ejpam-3502	408	2	iy	iy	PROPN
ejpam-3502	408	3	(	(	PUNCT
ejpam-3502	408	4	f(a	f(a	NOUN
ejpam-3502	408	5	)	)	PUNCT
ejpam-3502	408	6	)	)	PUNCT
ejpam-3502	408	7	.	.	PUNCT
ejpam-3502	409	1	also	also	ADV
ejpam-3502	409	2	,	,	PUNCT
ejpam-3502	409	3	since	since	SCONJ
ejpam-3502	409	4	f	f	PROPN
ejpam-3502	409	5	is	be	AUX
ejpam-3502	409	6	both	both	PRON
ejpam-3502	409	7	bijective	bijective	ADJ
ejpam-3502	409	8	and	and	CCONJ
ejpam-3502	409	9	g	g	NOUN
ejpam-3502	409	10	-continuous	-continuous	ADJ
ejpam-3502	409	11	,	,	PUNCT
ejpam-3502	409	12	f−1(iy	f−1(iy	PROPN
ejpam-3502	409	13	(	(	PUNCT
ejpam-3502	409	14	f(a	f(a	NOUN
ejpam-3502	409	15	)	)	PUNCT
ejpam-3502	409	16	)	)	PUNCT
ejpam-3502	409	17	)	)	PUNCT
ejpam-3502	409	18	is	be	AUX
ejpam-3502	409	19	gx	gx	PROPN
ejpam-3502	409	20	-open	-open	NOUN
ejpam-3502	409	21	and	and	CCONJ
ejpam-3502	409	22	f−1(iy	f−1(iy	PROPN
ejpam-3502	409	23	(	(	PUNCT
ejpam-3502	409	24	f(a	f(a	NOUN
ejpam-3502	409	25	)	)	PUNCT
ejpam-3502	409	26	)	)	PUNCT
ejpam-3502	409	27	)	)	PUNCT
ejpam-3502	410	1	⊆	⊆	NUM
ejpam-3502	410	2	f−1(f(a	f−1(f(a	NOUN
ejpam-3502	410	3	)	)	PUNCT
ejpam-3502	410	4	)	)	PUNCT
ejpam-3502	411	1	=	=	PUNCT
ejpam-3502	411	2	a	a	DET
ejpam-3502	411	3	implying	imply	VERB
ejpam-3502	411	4	that	that	SCONJ
ejpam-3502	411	5	f−1(iy	f−1(iy	PROPN
ejpam-3502	411	6	(	(	PUNCT
ejpam-3502	411	7	f(a	f(a	NOUN
ejpam-3502	411	8	)	)	PUNCT
ejpam-3502	411	9	)	)	PUNCT
ejpam-3502	411	10	)	)	PUNCT
ejpam-3502	412	1	⊆	⊆	NUM
ejpam-3502	412	2	ix(a	ix(a	NOUN
ejpam-3502	412	3	)	)	PUNCT
ejpam-3502	412	4	.	.	PUNCT
ejpam-3502	413	1	as	as	ADP
ejpam-3502	413	2	a	a	DET
ejpam-3502	413	3	result	result	NOUN
ejpam-3502	413	4	,	,	PUNCT
ejpam-3502	413	5	iy	iy	PROPN
ejpam-3502	413	6	(	(	PUNCT
ejpam-3502	413	7	f(a	f(a	NOUN
ejpam-3502	413	8	)	)	PUNCT
ejpam-3502	413	9	)	)	PUNCT
ejpam-3502	413	10	⊆	⊆	NUM
ejpam-3502	413	11	f(ix(a	f(ix(a	NOUN
ejpam-3502	413	12	)	)	PUNCT
ejpam-3502	413	13	)	)	PUNCT
ejpam-3502	413	14	.	.	PUNCT
ejpam-3502	414	1	conversely	conversely	ADV
ejpam-3502	414	2	,	,	PUNCT
ejpam-3502	414	3	we	we	PRON
ejpam-3502	414	4	only	only	ADV
ejpam-3502	414	5	need	need	VERB
ejpam-3502	414	6	to	to	PART
ejpam-3502	414	7	show	show	VERB
ejpam-3502	414	8	that	that	SCONJ
ejpam-3502	414	9	f−1(b	f−1(b	PROPN
ejpam-3502	414	10	)	)	PUNCT
ejpam-3502	414	11	is	be	AUX
ejpam-3502	414	12	gx	gx	PROPN
ejpam-3502	414	13	-open	-open	PROPN
ejpam-3502	414	14	for	for	ADP
ejpam-3502	414	15	any	any	DET
ejpam-3502	414	16	gy	gy	NOUN
ejpam-3502	414	17	-open	-open	NOUN
ejpam-3502	414	18	set	set	NOUN
ejpam-3502	414	19	b	b	NOUN
ejpam-3502	414	20	whenever	whenever	SCONJ
ejpam-3502	414	21	(	(	PUNCT
ejpam-3502	414	22	5	5	X
ejpam-3502	414	23	)	)	PUNCT
ejpam-3502	414	24	holds	hold	VERB
ejpam-3502	414	25	.	.	PUNCT
ejpam-3502	415	1	indeed	indeed	ADV
ejpam-3502	415	2	,	,	PUNCT
ejpam-3502	415	3	if	if	SCONJ
ejpam-3502	415	4	b	b	NOUN
ejpam-3502	415	5	is	be	AUX
ejpam-3502	415	6	gy	gy	NOUN
ejpam-3502	415	7	-open	-open	NOUN
ejpam-3502	415	8	,	,	PUNCT
ejpam-3502	415	9	(	(	PUNCT
ejpam-3502	415	10	5	5	X
ejpam-3502	415	11	)	)	PUNCT
ejpam-3502	415	12	provides	provide	VERB
ejpam-3502	415	13	that	that	DET
ejpam-3502	415	14	f(ix(f−1(b	f(ix(f−1(b	NOUN
ejpam-3502	415	15	)	)	PUNCT
ejpam-3502	415	16	)	)	PUNCT
ejpam-3502	415	17	)	)	PUNCT
ejpam-3502	416	1	=	=	SYM
ejpam-3502	416	2	iy	iy	INTJ
ejpam-3502	416	3	(	(	PUNCT
ejpam-3502	416	4	f(f−1(b	f(f−1(b	PROPN
ejpam-3502	416	5	)	)	PUNCT
ejpam-3502	416	6	)	)	PUNCT
ejpam-3502	416	7	)	)	PUNCT
ejpam-3502	417	1	=	=	SYM
ejpam-3502	417	2	iy	iy	X
ejpam-3502	417	3	(	(	PUNCT
ejpam-3502	417	4	b	b	NOUN
ejpam-3502	417	5	)	)	PUNCT
ejpam-3502	417	6	=	=	SYM
ejpam-3502	417	7	b.	b.	PROPN
ejpam-3502	417	8	c.	c.	PROPN
ejpam-3502	417	9	balingit	balingit	PROPN
ejpam-3502	417	10	,	,	PUNCT
ejpam-3502	417	11	j.	j.	PROPN
ejpam-3502	417	12	benitez	benitez	PROPN
ejpam-3502	417	13	/	/	PUNCT
ejpam-3502	417	14	eur	eur	PROPN
ejpam-3502	417	15	.	.	PUNCT
ejpam-3502	418	1	j.	j.	PROPN
ejpam-3502	418	2	pure	pure	PROPN
ejpam-3502	418	3	appl	appl	PROPN
ejpam-3502	418	4	.	.	PROPN
ejpam-3502	418	5	math	math	PROPN
ejpam-3502	418	6	,	,	PUNCT
ejpam-3502	418	7	12	12	NUM
ejpam-3502	418	8	(	(	PUNCT
ejpam-3502	418	9	4	4	NUM
ejpam-3502	418	10	)	)	PUNCT
ejpam-3502	418	11	(	(	PUNCT
ejpam-3502	418	12	2019	2019	NUM
ejpam-3502	418	13	)	)	PUNCT
ejpam-3502	418	14	,	,	PUNCT
ejpam-3502	418	15	1553	1553	NUM
ejpam-3502	418	16	-	-	SYM
ejpam-3502	418	17	1566	1566	NUM
ejpam-3502	418	18	1564	1564	NUM
ejpam-3502	418	19	thus	thus	ADV
ejpam-3502	418	20	,	,	PUNCT
ejpam-3502	418	21	ix(f−1(b	ix(f−1(b	NOUN
ejpam-3502	418	22	)	)	PUNCT
ejpam-3502	418	23	)	)	PUNCT
ejpam-3502	419	1	=	=	SYM
ejpam-3502	419	2	f−1(b	f−1(b	PROPN
ejpam-3502	419	3	)	)	PUNCT
ejpam-3502	419	4	is	be	AUX
ejpam-3502	419	5	a	a	DET
ejpam-3502	419	6	gx	gx	PROPN
ejpam-3502	419	7	-open	-open	NOUN
ejpam-3502	419	8	set	set	NOUN
ejpam-3502	419	9	which	which	PRON
ejpam-3502	419	10	,	,	PUNCT
ejpam-3502	419	11	in	in	ADP
ejpam-3502	419	12	turn	turn	NOUN
ejpam-3502	419	13	,	,	PUNCT
ejpam-3502	419	14	shows	show	VERB
ejpam-3502	419	15	that	that	SCONJ
ejpam-3502	419	16	f	f	PROPN
ejpam-3502	419	17	is	be	AUX
ejpam-3502	419	18	also	also	ADV
ejpam-3502	419	19	g	g	PROPN
ejpam-3502	419	20	continuous	continuous	ADJ
ejpam-3502	419	21	.	.	PUNCT
ejpam-3502	420	1	�	�	PROPN
ejpam-3502	420	2	definition	definition	NOUN
ejpam-3502	420	3	4.4	4.4	NUM
ejpam-3502	420	4	.	.	PUNCT
ejpam-3502	421	1	let	let	VERB
ejpam-3502	421	2	(	(	PUNCT
ejpam-3502	421	3	x	x	NOUN
ejpam-3502	421	4	,	,	PUNCT
ejpam-3502	421	5	gx	gx	PROPN
ejpam-3502	421	6	)	)	PUNCT
ejpam-3502	421	7	and	and	CCONJ
ejpam-3502	421	8	(	(	PUNCT
ejpam-3502	421	9	y	y	PROPN
ejpam-3502	421	10	,	,	PUNCT
ejpam-3502	421	11	gy	gy	NOUN
ejpam-3502	421	12	)	)	PUNCT
ejpam-3502	421	13	be	be	AUX
ejpam-3502	421	14	m	m	PROPN
ejpam-3502	421	15	-	-	PUNCT
ejpam-3502	421	16	gt	gt	PROPN
ejpam-3502	421	17	and	and	CCONJ
ejpam-3502	421	18	n	n	CCONJ
ejpam-3502	421	19	-	-	PUNCT
ejpam-3502	421	20	gt	gt	PROPN
ejpam-3502	421	21	spaces	space	NOUN
ejpam-3502	421	22	,	,	PUNCT
ejpam-3502	421	23	respectively	respectively	ADV
ejpam-3502	421	24	,	,	PUNCT
ejpam-3502	421	25	where	where	SCONJ
ejpam-3502	421	26	gx	gx	PROPN
ejpam-3502	421	27	=	=	PUNCT
ejpam-3502	421	28	{	{	PUNCT
ejpam-3502	421	29	µ1	µ1	PROPN
ejpam-3502	421	30	,	,	PUNCT
ejpam-3502	421	31	.	.	PUNCT
ejpam-3502	421	32	.	.	PUNCT
ejpam-3502	421	33	.	.	PUNCT
ejpam-3502	422	1	,	,	PUNCT
ejpam-3502	422	2	µm	µm	ADP
ejpam-3502	422	3	}	}	PUNCT
ejpam-3502	422	4	and	and	CCONJ
ejpam-3502	422	5	gy	gy	NOUN
ejpam-3502	422	6	=	=	SYM
ejpam-3502	422	7	{	{	PUNCT
ejpam-3502	422	8	ν1	ν1	NOUN
ejpam-3502	422	9	,	,	PUNCT
ejpam-3502	422	10	.	.	PUNCT
ejpam-3502	422	11	.	.	PUNCT
ejpam-3502	423	1	.	.	PUNCT
ejpam-3502	424	1	,	,	PUNCT
ejpam-3502	424	2	νn	νn	AUX
ejpam-3502	424	3	}	}	PUNCT
ejpam-3502	424	4	for	for	ADP
ejpam-3502	424	5	some	some	DET
ejpam-3502	424	6	m	m	NOUN
ejpam-3502	424	7	,	,	PUNCT
ejpam-3502	424	8	n	n	PROPN
ejpam-3502	424	9	∈	∈	NOUN
ejpam-3502	424	10	n	n	NOUN
ejpam-3502	425	1	and	and	CCONJ
ejpam-3502	425	2	let	let	VERB
ejpam-3502	425	3	f	f	NOUN
ejpam-3502	425	4	:	:	PUNCT
ejpam-3502	425	5	x	x	X
ejpam-3502	425	6	→	→	SYM
ejpam-3502	425	7	y	y	X
ejpam-3502	425	8	be	be	AUX
ejpam-3502	425	9	a	a	DET
ejpam-3502	425	10	bijective	bijective	ADJ
ejpam-3502	425	11	map	map	NOUN
ejpam-3502	425	12	.	.	PUNCT
ejpam-3502	426	1	1	1	X
ejpam-3502	426	2	.	.	X
ejpam-3502	426	3	f	f	PROPN
ejpam-3502	426	4	is	be	AUX
ejpam-3502	426	5	called	call	VERB
ejpam-3502	426	6	a	a	DET
ejpam-3502	426	7	(	(	PUNCT
ejpam-3502	426	8	µ	µ	NOUN
ejpam-3502	426	9	,	,	PUNCT
ejpam-3502	426	10	ν)(j	ν)(j	NOUN
ejpam-3502	426	11	,	,	PUNCT
ejpam-3502	426	12	k)-homeomorphism	k)-homeomorphism	PUNCT
ejpam-3502	426	13	if	if	SCONJ
ejpam-3502	426	14	f	f	PROPN
ejpam-3502	426	15	is	be	AUX
ejpam-3502	426	16	a	a	DET
ejpam-3502	426	17	(	(	PUNCT
ejpam-3502	426	18	µ	µ	NOUN
ejpam-3502	426	19	,	,	PUNCT
ejpam-3502	426	20	ν)(j	ν)(j	ADJ
ejpam-3502	426	21	,	,	PUNCT
ejpam-3502	426	22	k)-continuous	k)-continuous	ADJ
ejpam-3502	426	23	map	map	NOUN
ejpam-3502	426	24	and	and	CCONJ
ejpam-3502	426	25	f−1	f−1	PROPN
ejpam-3502	426	26	is	be	AUX
ejpam-3502	426	27	a	a	DET
ejpam-3502	426	28	(	(	PUNCT
ejpam-3502	426	29	ν	ν	NOUN
ejpam-3502	426	30	,	,	PUNCT
ejpam-3502	426	31	µ)(k	µ)(k	ADP
ejpam-3502	426	32	,	,	PUNCT
ejpam-3502	426	33	j)-continuous	j)-continuous	ADJ
ejpam-3502	426	34	map	map	NOUN
ejpam-3502	426	35	and	and	CCONJ
ejpam-3502	426	36	we	we	PRON
ejpam-3502	426	37	write	write	VERB
ejpam-3502	426	38	f	f	PROPN
ejpam-3502	426	39	:	:	PUNCT
ejpam-3502	426	40	x	x	SYM
ejpam-3502	426	41	(	(	PUNCT
ejpam-3502	426	42	j	j	NOUN
ejpam-3502	426	43	,	,	PUNCT
ejpam-3502	426	44	k)∼=	k)∼=	NOUN
ejpam-3502	426	45	y	y	NOUN
ejpam-3502	426	46	.	.	PUNCT
ejpam-3502	427	1	2	2	X
ejpam-3502	427	2	.	.	X
ejpam-3502	427	3	f	f	PROPN
ejpam-3502	427	4	is	be	AUX
ejpam-3502	427	5	called	call	VERB
ejpam-3502	427	6	a	a	DET
ejpam-3502	427	7	pairwise	pairwise	NOUN
ejpam-3502	427	8	(	(	PUNCT
ejpam-3502	427	9	µ	µ	NOUN
ejpam-3502	427	10	,	,	PUNCT
ejpam-3502	427	11	ν)-homeomorphism	ν)-homeomorphism	PUNCT
ejpam-3502	427	12	if	if	SCONJ
ejpam-3502	427	13	for	for	ADP
ejpam-3502	427	14	each	each	DET
ejpam-3502	427	15	pair	pair	NOUN
ejpam-3502	427	16	j	j	PROPN
ejpam-3502	427	17	,	,	PUNCT
ejpam-3502	427	18	k	k	PROPN
ejpam-3502	427	19	,	,	PUNCT
ejpam-3502	427	20	f	f	PROPN
ejpam-3502	427	21	is	be	AUX
ejpam-3502	427	22	a	a	DET
ejpam-3502	427	23	(	(	PUNCT
ejpam-3502	427	24	µ	µ	NOUN
ejpam-3502	427	25	,	,	PUNCT
ejpam-3502	427	26	ν)(j	ν)(j	NOUN
ejpam-3502	427	27	,	,	PUNCT
ejpam-3502	427	28	k)homeomorphism	k)homeomorphism	PROPN
ejpam-3502	427	29	.	.	PUNCT
ejpam-3502	428	1	in	in	ADP
ejpam-3502	428	2	this	this	DET
ejpam-3502	428	3	case	case	NOUN
ejpam-3502	428	4	,	,	PUNCT
ejpam-3502	428	5	we	we	PRON
ejpam-3502	428	6	write	write	VERB
ejpam-3502	428	7	f	f	PROPN
ejpam-3502	428	8	:	:	PUNCT
ejpam-3502	428	9	x	x	PUNCT
ejpam-3502	428	10	pw∼=	pw∼=	NOUN
ejpam-3502	428	11	y	y	PROPN
ejpam-3502	428	12	.	.	PUNCT
ejpam-3502	429	1	by	by	ADP
ejpam-3502	429	2	the	the	DET
ejpam-3502	429	3	definition	definition	NOUN
ejpam-3502	429	4	of	of	ADP
ejpam-3502	429	5	(	(	PUNCT
ejpam-3502	429	6	µ	µ	NOUN
ejpam-3502	429	7	,	,	PUNCT
ejpam-3502	429	8	ν)(j	ν)(j	NOUN
ejpam-3502	429	9	,	,	PUNCT
ejpam-3502	429	10	k)-homeomorphism	k)-homeomorphism	NOUN
ejpam-3502	429	11	,	,	PUNCT
ejpam-3502	429	12	it	it	PRON
ejpam-3502	429	13	is	be	AUX
ejpam-3502	429	14	easy	easy	ADJ
ejpam-3502	429	15	to	to	PART
ejpam-3502	429	16	see	see	VERB
ejpam-3502	429	17	that	that	SCONJ
ejpam-3502	429	18	f	f	PROPN
ejpam-3502	429	19	is	be	AUX
ejpam-3502	429	20	pairwise	pairwise	NOUN
ejpam-3502	429	21	(	(	PUNCT
ejpam-3502	429	22	µ	µ	NOUN
ejpam-3502	429	23	,	,	PUNCT
ejpam-3502	429	24	ν)-homeomorphism	ν)-homeomorphism	PUNCT
ejpam-3502	429	25	if	if	SCONJ
ejpam-3502	429	26	and	and	CCONJ
ejpam-3502	429	27	only	only	ADV
ejpam-3502	429	28	if	if	SCONJ
ejpam-3502	429	29	f	f	PROPN
ejpam-3502	429	30	is	be	AUX
ejpam-3502	429	31	a	a	DET
ejpam-3502	429	32	pairwise	pairwise	NOUN
ejpam-3502	429	33	(	(	PUNCT
ejpam-3502	429	34	µ	µ	NOUN
ejpam-3502	429	35	,	,	PUNCT
ejpam-3502	429	36	ν)-continuous	ν)-continuous	ADJ
ejpam-3502	429	37	map	map	NOUN
ejpam-3502	429	38	and	and	CCONJ
ejpam-3502	429	39	f−1	f−1	PROPN
ejpam-3502	429	40	is	be	AUX
ejpam-3502	429	41	a	a	DET
ejpam-3502	429	42	pairwise	pairwise	NOUN
ejpam-3502	429	43	(	(	PUNCT
ejpam-3502	429	44	ν	ν	NOUN
ejpam-3502	429	45	,	,	PUNCT
ejpam-3502	429	46	µ)-continuous	µ)-continuous	ADJ
ejpam-3502	429	47	map	map	NOUN
ejpam-3502	429	48	.	.	PUNCT
ejpam-3502	430	1	theorem	theorem	VERB
ejpam-3502	430	2	4.5	4.5	NUM
ejpam-3502	430	3	.	.	PUNCT
ejpam-3502	431	1	if	if	SCONJ
ejpam-3502	431	2	f	f	PROPN
ejpam-3502	431	3	is	be	AUX
ejpam-3502	431	4	a	a	DET
ejpam-3502	431	5	pairwise	pairwise	NOUN
ejpam-3502	431	6	(	(	PUNCT
ejpam-3502	431	7	µ	µ	NOUN
ejpam-3502	431	8	,	,	PUNCT
ejpam-3502	431	9	ν)-homeomorphism	ν)-homeomorphism	NOUN
ejpam-3502	431	10	,	,	PUNCT
ejpam-3502	431	11	then	then	ADV
ejpam-3502	431	12	f	f	PROPN
ejpam-3502	431	13	is	be	AUX
ejpam-3502	431	14	a	a	DET
ejpam-3502	431	15	g	g	NOUN
ejpam-3502	431	16	-homeomorphism	-homeomorphism	NOUN
ejpam-3502	431	17	.	.	PUNCT
ejpam-3502	432	1	proof	proof	NOUN
ejpam-3502	432	2	.	.	PUNCT
ejpam-3502	433	1	if	if	SCONJ
ejpam-3502	433	2	f	f	PROPN
ejpam-3502	433	3	is	be	AUX
ejpam-3502	433	4	a	a	DET
ejpam-3502	433	5	pairwise	pairwise	NOUN
ejpam-3502	433	6	(	(	PUNCT
ejpam-3502	433	7	µ	µ	NOUN
ejpam-3502	433	8	,	,	PUNCT
ejpam-3502	433	9	ν)-homeomorphism	ν)-homeomorphism	NOUN
ejpam-3502	433	10	,	,	PUNCT
ejpam-3502	433	11	then	then	ADV
ejpam-3502	433	12	f	f	PROPN
ejpam-3502	433	13	is	be	AUX
ejpam-3502	433	14	a	a	DET
ejpam-3502	433	15	pairwise	pairwise	NOUN
ejpam-3502	433	16	(	(	PUNCT
ejpam-3502	433	17	µ	µ	NOUN
ejpam-3502	433	18	,	,	PUNCT
ejpam-3502	433	19	ν)-continuous	ν)-continuous	ADJ
ejpam-3502	433	20	map	map	NOUN
ejpam-3502	433	21	and	and	CCONJ
ejpam-3502	433	22	f−1	f−1	PROPN
ejpam-3502	433	23	is	be	AUX
ejpam-3502	433	24	a	a	DET
ejpam-3502	433	25	pairwise	pairwise	NOUN
ejpam-3502	433	26	(	(	PUNCT
ejpam-3502	433	27	ν	ν	NOUN
ejpam-3502	433	28	,	,	PUNCT
ejpam-3502	433	29	µ)-continuous	µ)-continuous	ADJ
ejpam-3502	433	30	map	map	NOUN
ejpam-3502	433	31	.	.	PUNCT
ejpam-3502	434	1	by	by	ADP
ejpam-3502	434	2	remark	remark	NOUN
ejpam-3502	434	3	2.14	2.14	NUM
ejpam-3502	434	4	,	,	PUNCT
ejpam-3502	434	5	f	f	PROPN
ejpam-3502	434	6	and	and	CCONJ
ejpam-3502	434	7	f−1	f−1	PROPN
ejpam-3502	434	8	are	be	AUX
ejpam-3502	434	9	g	g	NOUN
ejpam-3502	434	10	-continuous	-continuous	ADJ
ejpam-3502	434	11	maps	map	NOUN
ejpam-3502	434	12	.	.	PUNCT
ejpam-3502	435	1	thus	thus	ADV
ejpam-3502	435	2	,	,	PUNCT
ejpam-3502	435	3	f	f	PROPN
ejpam-3502	435	4	is	be	AUX
ejpam-3502	435	5	a	a	DET
ejpam-3502	435	6	g	g	PROPN
ejpam-3502	435	7	-homeomorphism	-homeomorphism	NOUN
ejpam-3502	435	8	.	.	PUNCT
ejpam-3502	436	1	�	�	PROPN
ejpam-3502	436	2	theorem	theorem	VERB
ejpam-3502	436	3	4.6	4.6	NUM
ejpam-3502	436	4	.	.	PUNCT
ejpam-3502	437	1	if	if	SCONJ
ejpam-3502	437	2	f	f	PROPN
ejpam-3502	437	3	is	be	AUX
ejpam-3502	437	4	a	a	DET
ejpam-3502	437	5	pairwise	pairwise	NOUN
ejpam-3502	437	6	(	(	PUNCT
ejpam-3502	437	7	µ	µ	NOUN
ejpam-3502	437	8	,	,	PUNCT
ejpam-3502	437	9	ν)-homeomorphism	ν)-homeomorphism	NOUN
ejpam-3502	437	10	,	,	PUNCT
ejpam-3502	437	11	then	then	ADV
ejpam-3502	437	12	µ1	µ1	PROPN
ejpam-3502	437	13	=	=	SYM
ejpam-3502	437	14	·	·	PUNCT
ejpam-3502	437	15	·	·	PUNCT
ejpam-3502	437	16	·	·	PUNCT
ejpam-3502	438	1	=	=	SYM
ejpam-3502	438	2	µm	µm	NOUN
ejpam-3502	438	3	and	and	CCONJ
ejpam-3502	438	4	ν1	ν1	NOUN
ejpam-3502	438	5	=	=	SYM
ejpam-3502	438	6	·	·	PUNCT
ejpam-3502	438	7	·	·	PUNCT
ejpam-3502	438	8	·	·	PUNCT
ejpam-3502	439	1	=	=	PUNCT
ejpam-3502	439	2	νn	νn	X
ejpam-3502	439	3	.	.	NOUN
ejpam-3502	439	4	proof	proof	NOUN
ejpam-3502	439	5	.	.	PUNCT
ejpam-3502	440	1	we	we	PRON
ejpam-3502	440	2	first	first	ADV
ejpam-3502	440	3	show	show	VERB
ejpam-3502	440	4	that	that	SCONJ
ejpam-3502	440	5	if	if	SCONJ
ejpam-3502	440	6	f	f	X
ejpam-3502	440	7	:	:	PUNCT
ejpam-3502	440	8	x	x	X
ejpam-3502	440	9	(	(	PUNCT
ejpam-3502	440	10	j	j	NOUN
ejpam-3502	440	11	,	,	PUNCT
ejpam-3502	440	12	k)∼=	k)∼=	NOUN
ejpam-3502	440	13	y	y	NOUN
ejpam-3502	440	14	for	for	ADP
ejpam-3502	440	15	each	each	DET
ejpam-3502	440	16	pair	pair	PROPN
ejpam-3502	440	17	j	j	PROPN
ejpam-3502	440	18	,	,	PUNCT
ejpam-3502	440	19	k	k	PROPN
ejpam-3502	440	20	of	of	ADP
ejpam-3502	440	21	indices	index	NOUN
ejpam-3502	440	22	,	,	PUNCT
ejpam-3502	440	23	then	then	ADV
ejpam-3502	440	24	{	{	PUNCT
ejpam-3502	440	25	f(u	f(u	PROPN
ejpam-3502	440	26	)	)	PUNCT
ejpam-3502	440	27	:	:	PUNCT
ejpam-3502	440	28	u	u	PROPN
ejpam-3502	440	29	∈	∈	NOUN
ejpam-3502	440	30	µj	µj	PROPN
ejpam-3502	440	31	}	}	PUNCT
ejpam-3502	440	32	=	=	SYM
ejpam-3502	440	33	νk	νk	X
ejpam-3502	440	34	.	.	PUNCT
ejpam-3502	440	35	indeed	indeed	ADV
ejpam-3502	440	36	,	,	PUNCT
ejpam-3502	440	37	if	if	SCONJ
ejpam-3502	440	38	u	u	PROPN
ejpam-3502	440	39	∈	∈	PROPN
ejpam-3502	440	40	µj	µj	X
ejpam-3502	440	41	,	,	PUNCT
ejpam-3502	440	42	then	then	ADV
ejpam-3502	440	43	f(u	f(u	PROPN
ejpam-3502	440	44	)	)	PUNCT
ejpam-3502	440	45	∈	∈	PROPN
ejpam-3502	440	46	νk	νk	NOUN
ejpam-3502	440	47	since	since	SCONJ
ejpam-3502	440	48	f	f	PROPN
ejpam-3502	440	49	is	be	AUX
ejpam-3502	440	50	also	also	ADV
ejpam-3502	440	51	a	a	DET
ejpam-3502	440	52	(	(	PUNCT
ejpam-3502	440	53	µ	µ	NOUN
ejpam-3502	440	54	,	,	PUNCT
ejpam-3502	440	55	ν)(j	ν)(j	NOUN
ejpam-3502	440	56	,	,	PUNCT
ejpam-3502	440	57	k)-open	k)-open	VERB
ejpam-3502	440	58	as	as	SCONJ
ejpam-3502	440	59	implied	imply	VERB
ejpam-3502	440	60	by	by	ADP
ejpam-3502	440	61	definition	definition	NOUN
ejpam-3502	440	62	4.4	4.4	NUM
ejpam-3502	440	63	and	and	CCONJ
ejpam-3502	440	64	the	the	DET
ejpam-3502	440	65	equivalence	equivalence	NOUN
ejpam-3502	440	66	of	of	ADP
ejpam-3502	440	67	(	(	PUNCT
ejpam-3502	440	68	1	1	NUM
ejpam-3502	440	69	)	)	PUNCT
ejpam-3502	440	70	and	and	CCONJ
ejpam-3502	440	71	(	(	PUNCT
ejpam-3502	440	72	2	2	X
ejpam-3502	440	73	)	)	PUNCT
ejpam-3502	440	74	in	in	ADP
ejpam-3502	440	75	theorems	theorem	NOUN
ejpam-3502	440	76	2.11	2.11	NUM
ejpam-3502	440	77	and	and	CCONJ
ejpam-3502	440	78	2.15	2.15	NUM
ejpam-3502	440	79	.	.	PUNCT
ejpam-3502	441	1	also	also	ADV
ejpam-3502	441	2	,	,	PUNCT
ejpam-3502	441	3	if	if	SCONJ
ejpam-3502	441	4	v	v	ADP
ejpam-3502	441	5	∈	∈	PROPN
ejpam-3502	441	6	νk	νk	NOUN
ejpam-3502	441	7	,	,	PUNCT
ejpam-3502	441	8	f	f	PROPN
ejpam-3502	441	9	−1(v	−1(v	PROPN
ejpam-3502	441	10	)	)	PUNCT
ejpam-3502	441	11	∈	∈	PROPN
ejpam-3502	441	12	µj	µj	PROPN
ejpam-3502	441	13	since	since	SCONJ
ejpam-3502	441	14	f	f	PROPN
ejpam-3502	441	15	is	be	AUX
ejpam-3502	441	16	(	(	PUNCT
ejpam-3502	441	17	µ	µ	NOUN
ejpam-3502	441	18	,	,	PUNCT
ejpam-3502	441	19	ν)(j	ν)(j	NOUN
ejpam-3502	441	20	,	,	PUNCT
ejpam-3502	441	21	k)-continuous	k)-continuous	ADJ
ejpam-3502	441	22	,	,	PUNCT
ejpam-3502	441	23	implying	imply	VERB
ejpam-3502	441	24	that	that	SCONJ
ejpam-3502	441	25	v	v	NOUN
ejpam-3502	441	26	=	=	SYM
ejpam-3502	441	27	f(f−1(v	f(f−1(v	PROPN
ejpam-3502	441	28	)	)	PUNCT
ejpam-3502	441	29	)	)	PUNCT
ejpam-3502	442	1	∈	∈	PROPN
ejpam-3502	442	2	{	{	PUNCT
ejpam-3502	442	3	f(u	f(u	PROPN
ejpam-3502	442	4	)	)	PUNCT
ejpam-3502	442	5	:	:	PUNCT
ejpam-3502	443	1	u	u	PROPN
ejpam-3502	443	2	∈	∈	PROPN
ejpam-3502	443	3	µj	µj	PROPN
ejpam-3502	443	4	}	}	PUNCT
ejpam-3502	443	5	.	.	PUNCT
ejpam-3502	444	1	similarly	similarly	ADV
ejpam-3502	444	2	,	,	PUNCT
ejpam-3502	444	3	{	{	PUNCT
ejpam-3502	444	4	f−1(v	f−1(v	PROPN
ejpam-3502	444	5	)	)	PUNCT
ejpam-3502	444	6	:	:	PUNCT
ejpam-3502	444	7	v	v	X
ejpam-3502	444	8	∈	∈	NOUN
ejpam-3502	444	9	νk	νk	NOUN
ejpam-3502	444	10	}	}	PUNCT
ejpam-3502	444	11	=	=	SYM
ejpam-3502	444	12	µj	µj	PROPN
ejpam-3502	444	13	.	.	PUNCT
ejpam-3502	445	1	now	now	ADV
ejpam-3502	445	2	,	,	PUNCT
ejpam-3502	445	3	if	if	SCONJ
ejpam-3502	445	4	f	f	PROPN
ejpam-3502	445	5	:	:	PUNCT
ejpam-3502	445	6	x	x	X
ejpam-3502	445	7	pw∼=	pw∼=	PROPN
ejpam-3502	445	8	y	y	PROPN
ejpam-3502	445	9	,	,	PUNCT
ejpam-3502	445	10	then	then	ADV
ejpam-3502	445	11	for	for	ADP
ejpam-3502	445	12	a	a	DET
ejpam-3502	445	13	fixed	fix	VERB
ejpam-3502	445	14	µj	µj	NOUN
ejpam-3502	445	15	,	,	PUNCT
ejpam-3502	445	16	{	{	PUNCT
ejpam-3502	445	17	f(u	f(u	PROPN
ejpam-3502	445	18	)	)	PUNCT
ejpam-3502	445	19	:	:	PUNCT
ejpam-3502	445	20	u	u	PROPN
ejpam-3502	445	21	∈	∈	NOUN
ejpam-3502	445	22	µj	µj	PROPN
ejpam-3502	445	23	}	}	PUNCT
ejpam-3502	445	24	=	=	PUNCT
ejpam-3502	445	25	νk	νk	NOUN
ejpam-3502	445	26	for	for	ADP
ejpam-3502	445	27	all	all	PRON
ejpam-3502	445	28	k	k	NOUN
ejpam-3502	445	29	=	=	SYM
ejpam-3502	445	30	1	1	NUM
ejpam-3502	445	31	,	,	PUNCT
ejpam-3502	445	32	.	.	PUNCT
ejpam-3502	445	33	.	.	PUNCT
ejpam-3502	445	34	.	.	PUNCT
ejpam-3502	446	1	,	,	PUNCT
ejpam-3502	446	2	n.	n.	NOUN
ejpam-3502	446	3	that	that	PRON
ejpam-3502	446	4	is	be	AUX
ejpam-3502	446	5	,	,	PUNCT
ejpam-3502	446	6	ν1	ν1	NOUN
ejpam-3502	446	7	=	=	PUNCT
ejpam-3502	446	8	.	.	PUNCT
ejpam-3502	446	9	.	.	PUNCT
ejpam-3502	446	10	.	.	PUNCT
ejpam-3502	447	1	=	=	PUNCT
ejpam-3502	447	2	νn	νn	X
ejpam-3502	447	3	.	.	NOUN
ejpam-3502	448	1	in	in	ADP
ejpam-3502	448	2	the	the	DET
ejpam-3502	448	3	same	same	ADJ
ejpam-3502	448	4	manner	manner	NOUN
ejpam-3502	448	5	,	,	PUNCT
ejpam-3502	448	6	for	for	ADP
ejpam-3502	448	7	a	a	DET
ejpam-3502	448	8	fixed	fix	VERB
ejpam-3502	448	9	νk	νk	NOUN
ejpam-3502	448	10	,	,	PUNCT
ejpam-3502	448	11	{	{	PUNCT
ejpam-3502	448	12	f−1(v	f−1(v	PROPN
ejpam-3502	448	13	)	)	PUNCT
ejpam-3502	448	14	:	:	PUNCT
ejpam-3502	448	15	v	v	X
ejpam-3502	448	16	∈	∈	NOUN
ejpam-3502	448	17	νk	νk	NOUN
ejpam-3502	448	18	}	}	PUNCT
ejpam-3502	448	19	=	=	SYM
ejpam-3502	448	20	µj	µj	PROPN
ejpam-3502	448	21	for	for	ADP
ejpam-3502	448	22	all	all	PRON
ejpam-3502	448	23	j	j	NOUN
ejpam-3502	448	24	=	=	SYM
ejpam-3502	448	25	1	1	NUM
ejpam-3502	448	26	,	,	PUNCT
ejpam-3502	448	27	.	.	PUNCT
ejpam-3502	448	28	.	.	PUNCT
ejpam-3502	448	29	.	.	PUNCT
ejpam-3502	449	1	,	,	PUNCT
ejpam-3502	449	2	m	m	VERB
ejpam-3502	449	3	which	which	PRON
ejpam-3502	449	4	indicates	indicate	VERB
ejpam-3502	449	5	that	that	SCONJ
ejpam-3502	449	6	µ1	µ1	PROPN
ejpam-3502	449	7	=	=	PUNCT
ejpam-3502	449	8	.	.	PUNCT
ejpam-3502	449	9	.	.	PUNCT
ejpam-3502	449	10	.	.	PUNCT
ejpam-3502	450	1	=	=	PUNCT
ejpam-3502	450	2	µm	µm	NOUN
ejpam-3502	450	3	.	.	PROPN
ejpam-3502	450	4	�	�	PROPN
ejpam-3502	450	5	in	in	ADP
ejpam-3502	450	6	general	general	ADJ
ejpam-3502	450	7	,	,	PUNCT
ejpam-3502	450	8	the	the	DET
ejpam-3502	450	9	converse	converse	NOUN
ejpam-3502	450	10	of	of	ADP
ejpam-3502	450	11	theorem	theorem	ADJ
ejpam-3502	450	12	4.6	4.6	NUM
ejpam-3502	450	13	may	may	AUX
ejpam-3502	450	14	not	not	PART
ejpam-3502	450	15	hold	hold	VERB
ejpam-3502	450	16	.	.	PUNCT
ejpam-3502	451	1	acknowledgements	acknowledgement	NOUN
ejpam-3502	451	2	the	the	DET
ejpam-3502	451	3	authors	author	NOUN
ejpam-3502	451	4	express	express	VERB
ejpam-3502	451	5	sincerest	sincere	ADJ
ejpam-3502	451	6	gratitude	gratitude	NOUN
ejpam-3502	451	7	to	to	ADP
ejpam-3502	451	8	central	central	ADJ
ejpam-3502	451	9	mindanao	mindanao	PROPN
ejpam-3502	451	10	university	university	PROPN
ejpam-3502	451	11	,	,	PUNCT
ejpam-3502	451	12	msu	msu	PROPN
ejpam-3502	451	13	-	-	PUNCT
ejpam-3502	451	14	iligan	iligan	PROPN
ejpam-3502	451	15	institute	institute	PROPN
ejpam-3502	451	16	of	of	ADP
ejpam-3502	451	17	technology	technology	PROPN
ejpam-3502	451	18	and	and	CCONJ
ejpam-3502	451	19	the	the	DET
ejpam-3502	451	20	dost	dost	NOUN
ejpam-3502	451	21	-	-	PUNCT
ejpam-3502	451	22	asthrdp	asthrdp	NOUN
ejpam-3502	451	23	for	for	ADP
ejpam-3502	451	24	the	the	DET
ejpam-3502	451	25	materialization	materialization	NOUN
ejpam-3502	451	26	of	of	ADP
ejpam-3502	451	27	this	this	DET
ejpam-3502	451	28	paper	paper	NOUN
ejpam-3502	451	29	.	.	PUNCT
ejpam-3502	452	1	references	reference	NOUN
ejpam-3502	452	2	1565	1565	NUM
ejpam-3502	452	3	references	reference	NOUN
ejpam-3502	452	4	[	[	X
ejpam-3502	452	5	1	1	NUM
ejpam-3502	452	6	]	]	PUNCT
ejpam-3502	452	7	á.	á.	PROPN
ejpam-3502	452	8	császár	császár	PROPN
ejpam-3502	452	9	.	.	PUNCT
ejpam-3502	453	1	generalized	generalized	ADJ
ejpam-3502	453	2	topology	topology	NOUN
ejpam-3502	453	3	,	,	PUNCT
ejpam-3502	453	4	generalized	generalize	VERB
ejpam-3502	453	5	continuity	continuity	NOUN
ejpam-3502	453	6	.	.	PUNCT
ejpam-3502	454	1	acta	acta	PROPN
ejpam-3502	454	2	mathematica	mathematica	PROPN
ejpam-3502	454	3	hungarica	hungarica	PROPN
ejpam-3502	454	4	,	,	PUNCT
ejpam-3502	454	5	96	96	NUM
ejpam-3502	454	6	(	(	PUNCT
ejpam-3502	454	7	4):351	4):351	NOUN
ejpam-3502	454	8	-	-	SYM
ejpam-3502	454	9	357	357	NUM
ejpam-3502	454	10	,	,	PUNCT
ejpam-3502	454	11	2002	2002	NUM
ejpam-3502	454	12	.	.	PUNCT
ejpam-3502	455	1	[	[	X
ejpam-3502	455	2	2	2	NUM
ejpam-3502	455	3	]	]	PUNCT
ejpam-3502	455	4	c.	c.	NOUN
ejpam-3502	455	5	balingit	balingit	PROPN
ejpam-3502	455	6	and	and	CCONJ
ejpam-3502	455	7	j.	j.	PROPN
ejpam-3502	455	8	benitez	benitez	PROPN
ejpam-3502	455	9	.	.	PUNCT
ejpam-3502	456	1	on	on	ADP
ejpam-3502	456	2	n	n	CCONJ
ejpam-3502	456	3	-	-	PUNCT
ejpam-3502	456	4	generalized	generalize	VERB
ejpam-3502	456	5	topological	topological	ADJ
ejpam-3502	456	6	spaces	space	NOUN
ejpam-3502	456	7	.	.	PUNCT
ejpam-3502	457	1	manuscript	manuscript	NOUN
ejpam-3502	457	2	submitted	submit	VERB
ejpam-3502	457	3	for	for	ADP
ejpam-3502	457	4	publication	publication	NOUN
ejpam-3502	457	5	,	,	PUNCT
ejpam-3502	457	6	2019	2019	NUM
ejpam-3502	457	7	[	[	SYM
ejpam-3502	457	8	3	3	NUM
ejpam-3502	457	9	]	]	X
ejpam-3502	457	10	c.	c.	NOUN
ejpam-3502	457	11	balingit	balingit	PROPN
ejpam-3502	457	12	and	and	CCONJ
ejpam-3502	457	13	f.	f.	PROPN
ejpam-3502	457	14	jamil	jamil	PROPN
ejpam-3502	457	15	.	.	PUNCT
ejpam-3502	458	1	on	on	ADP
ejpam-3502	458	2	continuous	continuous	ADJ
ejpam-3502	458	3	functions	function	NOUN
ejpam-3502	458	4	in	in	ADP
ejpam-3502	458	5	trigeneralized	trigeneralize	VERB
ejpam-3502	458	6	topological	topological	ADJ
ejpam-3502	458	7	spaces	space	NOUN
ejpam-3502	458	8	.	.	PUNCT
ejpam-3502	459	1	asia	asia	PROPN
ejpam-3502	459	2	pacific	pacific	PROPN
ejpam-3502	459	3	journal	journal	PROPN
ejpam-3502	459	4	of	of	ADP
ejpam-3502	459	5	science	science	NOUN
ejpam-3502	459	6	,	,	PUNCT
ejpam-3502	459	7	mathematics	mathematic	NOUN
ejpam-3502	459	8	and	and	CCONJ
ejpam-3502	459	9	engineering	engineering	NOUN
ejpam-3502	459	10	,	,	PUNCT
ejpam-3502	459	11	3(2):1	3(2):1	PROPN
ejpam-3502	459	12	-	-	SYM
ejpam-3502	459	13	16	16	NUM
ejpam-3502	459	14	,	,	PUNCT
ejpam-3502	459	15	2015	2015	NUM
ejpam-3502	459	16	.	.	PUNCT
ejpam-3502	460	1	[	[	X
ejpam-3502	460	2	4	4	X
ejpam-3502	460	3	]	]	PUNCT
ejpam-3502	460	4	c.	c.	PROPN
ejpam-3502	460	5	boonpok	boonpok	PROPN
ejpam-3502	460	6	.	.	PUNCT
ejpam-3502	461	1	bicontinuous	bicontinuous	ADJ
ejpam-3502	461	2	maps	map	NOUN
ejpam-3502	461	3	in	in	ADP
ejpam-3502	461	4	biclosure	biclosure	NOUN
ejpam-3502	461	5	spaces	space	NOUN
ejpam-3502	461	6	.	.	PUNCT
ejpam-3502	462	1	international	international	ADJ
ejpam-3502	462	2	journal	journal	PROPN
ejpam-3502	462	3	of	of	ADP
ejpam-3502	462	4	contemporary	contemporary	PROPN
ejpam-3502	462	5	mathematical	mathematical	PROPN
ejpam-3502	462	6	sciences	sciences	PROPN
ejpam-3502	462	7	,	,	PUNCT
ejpam-3502	462	8	5(2):51	5(2):51	PROPN
ejpam-3502	462	9	-	-	SYM
ejpam-3502	462	10	59	59	NUM
ejpam-3502	462	11	,	,	PUNCT
ejpam-3502	462	12	2010	2010	NUM
ejpam-3502	462	13	.	.	PUNCT
ejpam-3502	463	1	[	[	X
ejpam-3502	463	2	5	5	X
ejpam-3502	463	3	]	]	PUNCT
ejpam-3502	463	4	c.	c.	PROPN
ejpam-3502	463	5	boonpok	boonpok	PROPN
ejpam-3502	463	6	.	.	PUNCT
ejpam-3502	464	1	weakly	weakly	ADJ
ejpam-3502	464	2	open	open	ADJ
ejpam-3502	464	3	functions	function	NOUN
ejpam-3502	464	4	on	on	ADP
ejpam-3502	464	5	bigeneralized	bigeneralize	VERB
ejpam-3502	464	6	topological	topological	ADJ
ejpam-3502	464	7	spaces	space	NOUN
ejpam-3502	464	8	.	.	PUNCT
ejpam-3502	465	1	international	international	ADJ
ejpam-3502	465	2	journal	journal	PROPN
ejpam-3502	465	3	of	of	ADP
ejpam-3502	465	4	mathematical	mathematical	ADJ
ejpam-3502	465	5	analysis	analysis	NOUN
ejpam-3502	465	6	,	,	PUNCT
ejpam-3502	465	7	4(18):891	4(18):891	NUM
ejpam-3502	465	8	-	-	SYM
ejpam-3502	465	9	897	897	NUM
ejpam-3502	465	10	,	,	PUNCT
ejpam-3502	465	11	2010	2010	NUM
ejpam-3502	465	12	.	.	PUNCT
ejpam-3502	466	1	[	[	X
ejpam-3502	466	2	6	6	NUM
ejpam-3502	466	3	]	]	PUNCT
ejpam-3502	466	4	c.	c.	PROPN
ejpam-3502	466	5	boonpok	boonpok	PROPN
ejpam-3502	466	6	,	,	PUNCT
ejpam-3502	466	7	t.	t.	PROPN
ejpam-3502	466	8	duangphui	duangphui	PROPN
ejpam-3502	466	9	,	,	PUNCT
ejpam-3502	466	10	and	and	CCONJ
ejpam-3502	466	11	c.	c.	PROPN
ejpam-3502	466	12	viriyapong	viriyapong	PROPN
ejpam-3502	466	13	.	.	PUNCT
ejpam-3502	467	1	continuous	continuous	ADJ
ejpam-3502	467	2	functions	function	NOUN
ejpam-3502	467	3	on	on	ADP
ejpam-3502	467	4	bigeneralized	bigeneralize	VERB
ejpam-3502	467	5	topological	topological	ADJ
ejpam-3502	467	6	spaces	space	NOUN
ejpam-3502	467	7	.	.	PUNCT
ejpam-3502	468	1	international	international	ADJ
ejpam-3502	468	2	journal	journal	PROPN
ejpam-3502	468	3	of	of	ADP
ejpam-3502	468	4	mathematical	mathematical	ADJ
ejpam-3502	468	5	analysis	analysis	NOUN
ejpam-3502	468	6	,	,	PUNCT
ejpam-3502	468	7	5(24):11651174	5(24):11651174	NUM
ejpam-3502	468	8	,	,	PUNCT
ejpam-3502	468	9	2011	2011	NUM
ejpam-3502	468	10	.	.	PUNCT
ejpam-3502	469	1	[	[	X
ejpam-3502	469	2	7	7	X
ejpam-3502	469	3	]	]	X
ejpam-3502	469	4	j.	j.	PROPN
ejpam-3502	469	5	dugundji	dugundji	PROPN
ejpam-3502	469	6	.	.	PUNCT
ejpam-3502	469	7	topology	topology	PROPN
ejpam-3502	469	8	.	.	PUNCT
ejpam-3502	470	1	allyn	allyn	PROPN
ejpam-3502	470	2	and	and	CCONJ
ejpam-3502	470	3	bacon	bacon	PROPN
ejpam-3502	470	4	,	,	PUNCT
ejpam-3502	470	5	boston	boston	PROPN
ejpam-3502	470	6	,	,	PUNCT
ejpam-3502	470	7	1966	1966	NUM
ejpam-3502	470	8	.	.	PUNCT
ejpam-3502	471	1	[	[	X
ejpam-3502	471	2	8	8	X
ejpam-3502	471	3	]	]	PUNCT
ejpam-3502	471	4	j.	j.	PROPN
ejpam-3502	471	5	kelly	kelly	PROPN
ejpam-3502	471	6	.	.	PUNCT
ejpam-3502	472	1	bitopological	bitopological	ADJ
ejpam-3502	472	2	spaces	space	NOUN
ejpam-3502	472	3	.	.	PUNCT
ejpam-3502	473	1	proceedings	proceeding	NOUN
ejpam-3502	473	2	,	,	PUNCT
ejpam-3502	473	3	london	london	PROPN
ejpam-3502	473	4	mathematical	mathematical	ADJ
ejpam-3502	473	5	society	society	NOUN
ejpam-3502	473	6	,	,	PUNCT
ejpam-3502	473	7	13(3):7189	13(3):7189	NUM
ejpam-3502	473	8	,	,	PUNCT
ejpam-3502	473	9	1963	1963	NUM
ejpam-3502	473	10	.	.	PUNCT
ejpam-3502	474	1	[	[	X
ejpam-3502	474	2	9	9	NUM
ejpam-3502	474	3	]	]	PUNCT
ejpam-3502	474	4	m.	m.	NOUN
ejpam-3502	474	5	kovar	kovar	PROPN
ejpam-3502	474	6	.	.	PUNCT
ejpam-3502	475	1	on	on	ADP
ejpam-3502	475	2	3	3	NUM
ejpam-3502	475	3	-	-	PUNCT
ejpam-3502	475	4	topological	topological	ADJ
ejpam-3502	475	5	version	version	NOUN
ejpam-3502	475	6	of	of	ADP
ejpam-3502	475	7	θ	θ	NOUN
ejpam-3502	475	8	-	-	NOUN
ejpam-3502	475	9	regularity	regularity	NOUN
ejpam-3502	475	10	.	.	PUNCT
ejpam-3502	476	1	international	international	ADJ
ejpam-3502	476	2	journal	journal	PROPN
ejpam-3502	476	3	of	of	ADP
ejpam-3502	476	4	mathematics	mathematics	PROPN
ejpam-3502	476	5	and	and	CCONJ
ejpam-3502	476	6	mathematical	mathematical	ADJ
ejpam-3502	476	7	sciences	science	NOUN
ejpam-3502	476	8	,	,	PUNCT
ejpam-3502	476	9	23(6):393	23(6):393	NUM
ejpam-3502	476	10	-	-	SYM
ejpam-3502	476	11	398	398	NUM
ejpam-3502	476	12	,	,	PUNCT
ejpam-3502	476	13	2000	2000	NUM
ejpam-3502	476	14	.	.	PUNCT
ejpam-3502	477	1	[	[	X
ejpam-3502	477	2	10	10	NUM
ejpam-3502	477	3	]	]	X
ejpam-3502	477	4	s.	s.	PROPN
ejpam-3502	477	5	maragathavalli	maragathavalli	PROPN
ejpam-3502	477	6	and	and	CCONJ
ejpam-3502	477	7	m.	m.	PROPN
ejpam-3502	477	8	sheikh	sheikh	PROPN
ejpam-3502	477	9	john	john	PROPN
ejpam-3502	477	10	.	.	PUNCT
ejpam-3502	478	1	strongly	strongly	ADV
ejpam-3502	478	2	αg∗-closed	αg∗-close	VERB
ejpam-3502	478	3	sets	set	NOUN
ejpam-3502	478	4	in	in	ADP
ejpam-3502	478	5	bitopological	bitopological	ADJ
ejpam-3502	478	6	spaces	space	NOUN
ejpam-3502	478	7	.	.	PUNCT
ejpam-3502	479	1	international	international	ADJ
ejpam-3502	479	2	journal	journal	PROPN
ejpam-3502	479	3	of	of	ADP
ejpam-3502	479	4	contemporary	contemporary	PROPN
ejpam-3502	479	5	mathematical	mathematical	PROPN
ejpam-3502	479	6	sciences	sciences	PROPN
ejpam-3502	479	7	,	,	PUNCT
ejpam-3502	479	8	5(17):805	5(17):805	NUM
ejpam-3502	479	9	-	-	PUNCT
ejpam-3502	479	10	813	813	NUM
ejpam-3502	479	11	,	,	PUNCT
ejpam-3502	479	12	2010	2010	NUM
ejpam-3502	479	13	.	.	PUNCT
ejpam-3502	480	1	[	[	X
ejpam-3502	480	2	11	11	NUM
ejpam-3502	480	3	]	]	PUNCT
ejpam-3502	480	4	w.	w.	PROPN
ejpam-3502	480	5	k.	k.	PROPN
ejpam-3502	480	6	min	min	PROPN
ejpam-3502	480	7	and	and	CCONJ
ejpam-3502	480	8	y.	y.	PROPN
ejpam-3502	480	9	k.	k.	PROPN
ejpam-3502	480	10	kim	kim	PROPN
ejpam-3502	480	11	.	.	PUNCT
ejpam-3502	481	1	quasi	quasi	ADJ
ejpam-3502	481	2	-	-	ADJ
ejpam-3502	481	3	generalized	generalized	ADJ
ejpam-3502	481	4	open	open	ADJ
ejpam-3502	481	5	sets	set	NOUN
ejpam-3502	481	6	and	and	CCONJ
ejpam-3502	481	7	quasi	quasi	ADJ
ejpam-3502	481	8	-	-	ADJ
ejpam-3502	481	9	generalized	generalized	ADJ
ejpam-3502	481	10	continuity	continuity	NOUN
ejpam-3502	481	11	on	on	ADP
ejpam-3502	481	12	bigeneralized	bigeneralize	VERB
ejpam-3502	481	13	topological	topological	ADJ
ejpam-3502	481	14	spaces	space	NOUN
ejpam-3502	481	15	.	.	PUNCT
ejpam-3502	482	1	honam	honam	PROPN
ejpam-3502	482	2	mathematical	mathematical	PROPN
ejpam-3502	482	3	journal	journal	PROPN
ejpam-3502	482	4	,	,	PUNCT
ejpam-3502	482	5	4(32):619	4(32):619	NUM
ejpam-3502	482	6	-	-	SYM
ejpam-3502	482	7	624	624	NUM
ejpam-3502	482	8	,	,	PUNCT
ejpam-3502	482	9	2010	2010	NUM
ejpam-3502	482	10	.	.	PUNCT
ejpam-3502	483	1	[	[	X
ejpam-3502	483	2	12	12	NUM
ejpam-3502	483	3	]	]	X
ejpam-3502	483	4	c.	c.	PROPN
ejpam-3502	483	5	mukundhan	mukundhan	PROPN
ejpam-3502	483	6	and	and	CCONJ
ejpam-3502	483	7	n.	n.	PROPN
ejpam-3502	483	8	nagaveni	nagaveni	PROPN
ejpam-3502	483	9	.	.	PUNCT
ejpam-3502	484	1	a	a	DET
ejpam-3502	484	2	weaker	weak	ADJ
ejpam-3502	484	3	form	form	NOUN
ejpam-3502	484	4	of	of	ADP
ejpam-3502	484	5	a	a	DET
ejpam-3502	484	6	generalized	generalize	VERB
ejpam-3502	484	7	closed	closed	ADJ
ejpam-3502	484	8	set	set	NOUN
ejpam-3502	484	9	.	.	PUNCT
ejpam-3502	485	1	international	international	ADJ
ejpam-3502	485	2	journal	journal	PROPN
ejpam-3502	485	3	of	of	ADP
ejpam-3502	485	4	contemporary	contemporary	PROPN
ejpam-3502	485	5	mathematical	mathematical	PROPN
ejpam-3502	485	6	sciences	sciences	PROPN
ejpam-3502	485	7	,	,	PUNCT
ejpam-3502	485	8	6:949	6:949	NUM
ejpam-3502	485	9	-	-	SYM
ejpam-3502	485	10	961	961	NUM
ejpam-3502	485	11	,	,	PUNCT
ejpam-3502	485	12	2011	2011	NUM
ejpam-3502	485	13	.	.	PUNCT
ejpam-3502	486	1	[	[	X
ejpam-3502	486	2	13	13	NUM
ejpam-3502	486	3	]	]	X
ejpam-3502	486	4	d.	d.	PROPN
ejpam-3502	486	5	v.	v.	PROPN
ejpam-3502	486	6	mukundhan	mukundhan	PROPN
ejpam-3502	486	7	.	.	PUNCT
ejpam-3502	487	1	introduction	introduction	NOUN
ejpam-3502	487	2	to	to	ADP
ejpam-3502	487	3	quad	quad	PROPN
ejpam-3502	487	4	topological	topological	ADJ
ejpam-3502	487	5	spaces	space	NOUN
ejpam-3502	487	6	.	.	PUNCT
ejpam-3502	488	1	international	international	ADJ
ejpam-3502	488	2	journal	journal	PROPN
ejpam-3502	488	3	of	of	ADP
ejpam-3502	488	4	scientific	scientific	ADJ
ejpam-3502	488	5	and	and	CCONJ
ejpam-3502	488	6	engineering	engineering	NOUN
ejpam-3502	488	7	research	research	NOUN
ejpam-3502	488	8	,	,	PUNCT
ejpam-3502	488	9	4:2483	4:2483	PROPN
ejpam-3502	488	10	-	-	SYM
ejpam-3502	488	11	2485	2485	NUM
ejpam-3502	488	12	,	,	PUNCT
ejpam-3502	488	13	2013	2013	NUM
ejpam-3502	488	14	.	.	PUNCT
ejpam-3502	489	1	[	[	X
ejpam-3502	489	2	14	14	NUM
ejpam-3502	489	3	]	]	X
ejpam-3502	489	4	s.	s.	PROPN
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ejpam-3502	489	6	.	.	PUNCT
ejpam-3502	490	1	a	a	DET
ejpam-3502	490	2	study	study	NOUN
ejpam-3502	490	3	of	of	ADP
ejpam-3502	490	4	tri	tri	ADJ
ejpam-3502	490	5	-	-	ADJ
ejpam-3502	490	6	topological	topological	ADJ
ejpam-3502	490	7	spaces	space	NOUN
ejpam-3502	490	8	.	.	PUNCT
ejpam-3502	491	1	phd	phd	NOUN
ejpam-3502	491	2	thesis	thesis	PROPN
ejpam-3502	491	3	.	.	PUNCT
ejpam-3502	492	1	shodhganga.inflibnet.ac.in	shodhganga.inflibnet.ac.in	PROPN
ejpam-3502	492	2	,	,	PUNCT
ejpam-3502	492	3	2014	2014	NUM
ejpam-3502	492	4	.	.	PUNCT
ejpam-3502	493	1	[	[	X
ejpam-3502	493	2	15	15	NUM
ejpam-3502	493	3	]	]	PUNCT
ejpam-3502	493	4	a.	a.	NOUN
ejpam-3502	493	5	piekosz	piekosz	NOUN
ejpam-3502	493	6	.	.	PUNCT
ejpam-3502	494	1	on	on	ADP
ejpam-3502	494	2	generalized	generalized	ADJ
ejpam-3502	494	3	topological	topological	ADJ
ejpam-3502	494	4	spaces	space	NOUN
ejpam-3502	494	5	i.	i.	PROPN
ejpam-3502	494	6	annales	annale	VERB
ejpam-3502	494	7	polinici	polinici	PROPN
ejpam-3502	494	8	mathematici	mathematici	PROPN
ejpam-3502	494	9	,	,	PUNCT
ejpam-3502	494	10	107:217	107:217	PROPN
ejpam-3502	494	11	-	-	PUNCT
ejpam-3502	494	12	241	241	NUM
ejpam-3502	494	13	,	,	PUNCT
ejpam-3502	494	14	2013	2013	NUM
ejpam-3502	494	15	.	.	PUNCT
ejpam-3502	495	1	references	reference	NOUN
ejpam-3502	495	2	1566	1566	NUM
ejpam-3502	496	1	[	[	X
ejpam-3502	496	2	16	16	NUM
ejpam-3502	496	3	]	]	X
ejpam-3502	496	4	u.	u.	PROPN
ejpam-3502	496	5	tapi	tapi	PROPN
ejpam-3502	496	6	and	and	CCONJ
ejpam-3502	496	7	r.	r.	PROPN
ejpam-3502	496	8	sharma	sharma	PROPN
ejpam-3502	496	9	.	.	PUNCT
ejpam-3502	497	1	αt	αt	NOUN
ejpam-3502	497	2	open	open	ADJ
ejpam-3502	497	3	sets	set	NOUN
ejpam-3502	497	4	in	in	ADP
ejpam-3502	497	5	tri	tri	ADJ
ejpam-3502	497	6	topological	topological	ADJ
ejpam-3502	497	7	space	space	NOUN
ejpam-3502	497	8	.	.	PUNCT
ejpam-3502	498	1	international	international	ADJ
ejpam-3502	498	2	journal	journal	NOUN
ejpam-3502	498	3	of	of	ADP
ejpam-3502	498	4	innovative	innovative	ADJ
ejpam-3502	498	5	research	research	NOUN
ejpam-3502	498	6	in	in	ADP
ejpam-3502	498	7	science	science	NOUN
ejpam-3502	498	8	and	and	CCONJ
ejpam-3502	498	9	engineering	engineering	NOUN
ejpam-3502	498	10	,	,	PUNCT
ejpam-3502	498	11	3:464	3:464	ADV
ejpam-3502	498	12	-	-	PUNCT
ejpam-3502	498	13	471	471	NUM
ejpam-3502	498	14	,	,	PUNCT
ejpam-3502	498	15	2017	2017	NUM
ejpam-3502	498	16	.	.	PUNCT
ejpam-3502	499	1	[	[	X
ejpam-3502	499	2	17	17	NUM
ejpam-3502	499	3	]	]	PUNCT
ejpam-3502	499	4	m.	m.	NOUN
ejpam-3502	499	5	thivagar	thivagar	NOUN
ejpam-3502	499	6	,	,	PUNCT
ejpam-3502	499	7	et	et	NOUN
ejpam-3502	499	8	.	.	PUNCT
ejpam-3502	500	1	al	al	PROPN
ejpam-3502	500	2	.	.	PROPN
ejpam-3502	501	1	on	on	ADP
ejpam-3502	501	2	new	new	ADJ
ejpam-3502	501	3	structure	structure	NOUN
ejpam-3502	501	4	of	of	ADP
ejpam-3502	501	5	n	n	DET
ejpam-3502	501	6	-topology	-topology	NOUN
ejpam-3502	501	7	.	.	PUNCT
ejpam-3502	502	1	cogent	cogent	NOUN
ejpam-3502	502	2	mathematics	mathematic	NOUN
ejpam-3502	502	3	,	,	PUNCT
ejpam-3502	502	4	3	3	NUM
ejpam-3502	502	5	:	:	SYM
ejpam-3502	502	6	2016	2016	NUM
ejpam-3502	502	7	.	.	PUNCT
ejpam-3502	503	1	[	[	X
ejpam-3502	503	2	18	18	NUM
ejpam-3502	503	3	]	]	PUNCT
ejpam-3502	503	4	a.	a.	NOUN
ejpam-3502	503	5	h.	h.	PROPN
ejpam-3502	503	6	zakari	zakari	PROPN
ejpam-3502	503	7	.	.	PUNCT
ejpam-3502	504	1	almost	almost	ADV
ejpam-3502	504	2	homeomorphisms	homeomorphism	VERB
ejpam-3502	504	3	on	on	ADP
ejpam-3502	504	4	bigeneralized	bigeneralize	VERB
ejpam-3502	504	5	topological	topological	ADJ
ejpam-3502	504	6	spaces	space	NOUN
ejpam-3502	504	7	.	.	PUNCT
ejpam-3502	505	1	international	international	ADJ
ejpam-3502	505	2	mathematical	mathematical	PROPN
ejpam-3502	505	3	forum	forum	PROPN
ejpam-3502	505	4	,	,	PUNCT
ejpam-3502	505	5	8(38):51	8(38):51	PROPN
ejpam-3502	505	6	-	-	SYM
ejpam-3502	505	7	59	59	NUM
ejpam-3502	505	8	,	,	PUNCT
ejpam-3502	505	9	2010	2010	NUM
ejpam-3502	505	10	.	.	PUNCT
ejpam-3502	506	1	[	[	X
ejpam-3502	506	2	19	19	NUM
ejpam-3502	506	3	]	]	X
ejpam-3502	506	4	i.	i.	NOUN
ejpam-3502	506	5	zvina	zvina	PROPN
ejpam-3502	506	6	.	.	PUNCT
ejpam-3502	507	1	introduction	introduction	NOUN
ejpam-3502	507	2	to	to	ADP
ejpam-3502	507	3	generalized	generalize	VERB
ejpam-3502	507	4	topological	topological	ADJ
ejpam-3502	507	5	space	space	NOUN
ejpam-3502	507	6	.	.	PUNCT
ejpam-3502	508	1	applied	apply	VERB
ejpam-3502	508	2	general	general	ADJ
ejpam-3502	508	3	topology	topology	NOUN
ejpam-3502	508	4	(	(	PUNCT
ejpam-3502	508	5	universidad	universidad	PROPN
ejpam-3502	508	6	politecnica	politecnica	PROPN
ejpam-3502	508	7	de	de	PROPN
ejpam-3502	508	8	valencia	valencia	PROPN
ejpam-3502	508	9	)	)	PUNCT
ejpam-3502	508	10	,	,	PUNCT
ejpam-3502	508	11	12(1):46	12(1):46	NUM
ejpam-3502	508	12	-	-	SYM
ejpam-3502	508	13	66	66	NUM
ejpam-3502	508	14	,	,	PUNCT
ejpam-3502	508	15	2011	2011	NUM
ejpam-3502	508	16	.	.	PUNCT