id	sid	tid	token	lemma	pos
ejpam-3483	1	1	european	european	PROPN
ejpam-3483	1	2	journal	journal	PROPN
ejpam-3483	1	3	of	of	ADP
ejpam-3483	1	4	pure	pure	ADJ
ejpam-3483	1	5	and	and	CCONJ
ejpam-3483	1	6	applied	apply	VERB
ejpam-3483	1	7	mathematics	mathematic	NOUN
ejpam-3483	1	8	vol	vol	NOUN
ejpam-3483	1	9	.	.	PROPN
ejpam-3483	2	1	12	12	NUM
ejpam-3483	2	2	,	,	PUNCT
ejpam-3483	2	3	no	no	INTJ
ejpam-3483	2	4	.	.	NOUN
ejpam-3483	2	5	3	3	NUM
ejpam-3483	2	6	,	,	PUNCT
ejpam-3483	2	7	2019	2019	NUM
ejpam-3483	2	8	,	,	PUNCT
ejpam-3483	2	9	1231	1231	NUM
ejpam-3483	2	10	-	-	SYM
ejpam-3483	2	11	1247	1247	NUM
ejpam-3483	2	12	issn	issn	PROPN
ejpam-3483	2	13	1307	1307	NUM
ejpam-3483	2	14	-	-	SYM
ejpam-3483	2	15	5543	5543	NUM
ejpam-3483	2	16	–	–	PUNCT
ejpam-3483	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3483	2	18	published	publish	VERB
ejpam-3483	2	19	by	by	ADP
ejpam-3483	2	20	new	new	PROPN
ejpam-3483	2	21	york	york	PROPN
ejpam-3483	2	22	business	business	PROPN
ejpam-3483	2	23	global	global	PROPN
ejpam-3483	2	24	supra	supra	PROPN
ejpam-3483	2	25	b	b	PROPN
ejpam-3483	2	26	maps	map	NOUN
ejpam-3483	2	27	via	via	ADP
ejpam-3483	2	28	topological	topological	ADJ
ejpam-3483	2	29	ordered	order	VERB
ejpam-3483	2	30	spaces	space	NOUN
ejpam-3483	2	31	baravan	baravan	PROPN
ejpam-3483	2	32	a.	a.	PROPN
ejpam-3483	2	33	asaad1,2,∗	asaad1,2,∗	PROPN
ejpam-3483	2	34	,	,	PUNCT
ejpam-3483	2	35	mohammed	mohammed	PROPN
ejpam-3483	2	36	k.	k.	PROPN
ejpam-3483	2	37	tahat3	tahat3	PROPN
ejpam-3483	2	38	,	,	PUNCT
ejpam-3483	2	39	tareq	tareq	PROPN
ejpam-3483	2	40	m.	m.	PROPN
ejpam-3483	2	41	al	al	PROPN
ejpam-3483	2	42	-	-	PUNCT
ejpam-3483	2	43	shami4	shami4	NOUN
ejpam-3483	2	44	1	1	NUM
ejpam-3483	2	45	department	department	NOUN
ejpam-3483	2	46	of	of	ADP
ejpam-3483	2	47	computer	computer	NOUN
ejpam-3483	2	48	science	science	NOUN
ejpam-3483	2	49	,	,	PUNCT
ejpam-3483	2	50	college	college	NOUN
ejpam-3483	2	51	of	of	ADP
ejpam-3483	2	52	science	science	NOUN
ejpam-3483	2	53	,	,	PUNCT
ejpam-3483	2	54	cihan	cihan	VERB
ejpam-3483	2	55	university	university	NOUN
ejpam-3483	2	56	-	-	PUNCT
ejpam-3483	2	57	duhok	duhok	NOUN
ejpam-3483	2	58	,	,	PUNCT
ejpam-3483	2	59	kurdistan	kurdistan	ADJ
ejpam-3483	2	60	region	region	NOUN
ejpam-3483	2	61	,	,	PUNCT
ejpam-3483	2	62	iraq	iraq	PROPN
ejpam-3483	2	63	2	2	NUM
ejpam-3483	2	64	department	department	NOUN
ejpam-3483	2	65	of	of	ADP
ejpam-3483	2	66	mathematics	mathematic	NOUN
ejpam-3483	2	67	,	,	PUNCT
ejpam-3483	2	68	faculty	faculty	NOUN
ejpam-3483	2	69	of	of	ADP
ejpam-3483	2	70	science	science	NOUN
ejpam-3483	2	71	,	,	PUNCT
ejpam-3483	2	72	university	university	NOUN
ejpam-3483	2	73	of	of	ADP
ejpam-3483	2	74	zakho	zakho	PROPN
ejpam-3483	2	75	,	,	PUNCT
ejpam-3483	2	76	kurdistan	kurdistan	ADJ
ejpam-3483	2	77	region	region	NOUN
ejpam-3483	2	78	,	,	PUNCT
ejpam-3483	2	79	iraq	iraq	PROPN
ejpam-3483	2	80	3	3	NUM
ejpam-3483	2	81	saudi	saudi	PROPN
ejpam-3483	2	82	electronic	electronic	ADJ
ejpam-3483	2	83	university	university	NOUN
ejpam-3483	2	84	,	,	PUNCT
ejpam-3483	2	85	saudi	saudi	PROPN
ejpam-3483	2	86	arabia	arabia	PROPN
ejpam-3483	2	87	4	4	NUM
ejpam-3483	2	88	department	department	NOUN
ejpam-3483	2	89	of	of	ADP
ejpam-3483	2	90	mathematics	mathematic	NOUN
ejpam-3483	2	91	,	,	PUNCT
ejpam-3483	2	92	sana’a	sana’a	NOUN
ejpam-3483	2	93	university	university	NOUN
ejpam-3483	2	94	,	,	PUNCT
ejpam-3483	2	95	sana’a	sana’a	NOUN
ejpam-3483	2	96	,	,	PUNCT
ejpam-3483	2	97	yemen	yemen	PROPN
ejpam-3483	2	98	abstract	abstract	NOUN
ejpam-3483	2	99	.	.	PUNCT
ejpam-3483	3	1	the	the	DET
ejpam-3483	3	2	authors	author	NOUN
ejpam-3483	3	3	utilize	utilize	VERB
ejpam-3483	3	4	the	the	DET
ejpam-3483	3	5	notions	notion	NOUN
ejpam-3483	3	6	of	of	ADP
ejpam-3483	3	7	increasing	increase	VERB
ejpam-3483	3	8	,	,	PUNCT
ejpam-3483	3	9	decreasing	decrease	VERB
ejpam-3483	3	10	and	and	CCONJ
ejpam-3483	3	11	balancing	balance	VERB
ejpam-3483	3	12	supra	supra	PROPN
ejpam-3483	3	13	b	b	NOUN
ejpam-3483	3	14	-	-	PUNCT
ejpam-3483	3	15	open	open	ADJ
ejpam-3483	3	16	sets	set	NOUN
ejpam-3483	3	17	to	to	PART
ejpam-3483	3	18	introduce	introduce	VERB
ejpam-3483	3	19	and	and	CCONJ
ejpam-3483	3	20	study	study	VERB
ejpam-3483	3	21	several	several	ADJ
ejpam-3483	3	22	types	type	NOUN
ejpam-3483	3	23	of	of	ADP
ejpam-3483	3	24	supra	supra	PROPN
ejpam-3483	3	25	continuous	continuous	ADJ
ejpam-3483	3	26	,	,	PUNCT
ejpam-3483	3	27	supra	supra	PROPN
ejpam-3483	3	28	open	open	ADJ
ejpam-3483	3	29	,	,	PUNCT
ejpam-3483	3	30	supra	supra	PROPN
ejpam-3483	3	31	closed	closed	ADJ
ejpam-3483	3	32	and	and	CCONJ
ejpam-3483	3	33	supra	supra	PROPN
ejpam-3483	3	34	homeomorphism	homeomorphism	PROPN
ejpam-3483	3	35	maps	map	NOUN
ejpam-3483	3	36	in	in	ADP
ejpam-3483	3	37	supra	supra	PROPN
ejpam-3483	3	38	topological	topological	ADJ
ejpam-3483	3	39	ordered	order	VERB
ejpam-3483	3	40	spaces	space	NOUN
ejpam-3483	3	41	.	.	PUNCT
ejpam-3483	4	1	they	they	PRON
ejpam-3483	4	2	give	give	VERB
ejpam-3483	4	3	the	the	DET
ejpam-3483	4	4	equivalent	equivalent	ADJ
ejpam-3483	4	5	conditions	condition	NOUN
ejpam-3483	4	6	for	for	ADP
ejpam-3483	4	7	each	each	DET
ejpam-3483	4	8	one	one	NUM
ejpam-3483	4	9	of	of	ADP
ejpam-3483	4	10	these	these	DET
ejpam-3483	4	11	notions	notion	NOUN
ejpam-3483	4	12	and	and	CCONJ
ejpam-3483	4	13	illustrate	illustrate	VERB
ejpam-3483	4	14	the	the	DET
ejpam-3483	4	15	relationships	relationship	NOUN
ejpam-3483	4	16	among	among	ADP
ejpam-3483	4	17	them	they	PRON
ejpam-3483	4	18	with	with	ADP
ejpam-3483	4	19	the	the	DET
ejpam-3483	4	20	help	help	NOUN
ejpam-3483	4	21	of	of	ADP
ejpam-3483	4	22	examples	example	NOUN
ejpam-3483	4	23	.	.	PUNCT
ejpam-3483	5	1	apart	apart	ADV
ejpam-3483	5	2	from	from	ADP
ejpam-3483	5	3	that	that	PRON
ejpam-3483	5	4	,	,	PUNCT
ejpam-3483	5	5	they	they	PRON
ejpam-3483	5	6	investigate	investigate	VERB
ejpam-3483	5	7	under	under	ADP
ejpam-3483	5	8	which	which	DET
ejpam-3483	5	9	conditions	condition	NOUN
ejpam-3483	5	10	these	these	DET
ejpam-3483	5	11	maps	map	NOUN
ejpam-3483	5	12	preserve	preserve	VERB
ejpam-3483	5	13	some	some	DET
ejpam-3483	5	14	separation	separation	NOUN
ejpam-3483	5	15	axioms	axiom	NOUN
ejpam-3483	5	16	between	between	ADP
ejpam-3483	5	17	supra	supra	PROPN
ejpam-3483	5	18	topological	topological	ADJ
ejpam-3483	5	19	ordered	order	VERB
ejpam-3483	5	20	spaces	space	NOUN
ejpam-3483	5	21	.	.	PUNCT
ejpam-3483	6	1	2010	2010	NUM
ejpam-3483	6	2	mathematics	mathematic	NOUN
ejpam-3483	6	3	subject	subject	NOUN
ejpam-3483	6	4	classifications	classification	NOUN
ejpam-3483	6	5	:	:	PUNCT
ejpam-3483	6	6	54f05	54f05	NUM
ejpam-3483	6	7	,	,	PUNCT
ejpam-3483	6	8	54f15	54f15	NUM
ejpam-3483	6	9	key	key	ADJ
ejpam-3483	6	10	words	word	NOUN
ejpam-3483	6	11	and	and	CCONJ
ejpam-3483	6	12	phrases	phrase	NOUN
ejpam-3483	6	13	:	:	PUNCT
ejpam-3483	6	14	i(d	i(d	NOUN
ejpam-3483	6	15	,	,	PUNCT
ejpam-3483	6	16	b)-supra	b)-supra	NOUN
ejpam-3483	6	17	b	b	X
ejpam-3483	6	18	-	-	PUNCT
ejpam-3483	6	19	continuous	continuous	ADJ
ejpam-3483	6	20	map	map	NOUN
ejpam-3483	6	21	,	,	PUNCT
ejpam-3483	6	22	i(d	i(d	NOUN
ejpam-3483	6	23	,	,	PUNCT
ejpam-3483	6	24	b)-supra	b)-supra	NOUN
ejpam-3483	6	25	b	b	X
ejpam-3483	6	26	-	-	PUNCT
ejpam-3483	6	27	open	open	ADJ
ejpam-3483	6	28	map	map	NOUN
ejpam-3483	6	29	,	,	PUNCT
ejpam-3483	6	30	i(d	i(d	NOUN
ejpam-3483	6	31	,	,	PUNCT
ejpam-3483	6	32	b)-supra	b)-supra	PUNCT
ejpam-3483	6	33	b	b	X
ejpam-3483	6	34	-	-	PUNCT
ejpam-3483	6	35	homeomorphism	homeomorphism	PROPN
ejpam-3483	6	36	map	map	NOUN
ejpam-3483	6	37	,	,	PUNCT
ejpam-3483	6	38	ordered	order	VERB
ejpam-3483	6	39	supra	supra	PROPN
ejpam-3483	6	40	b	b	PROPN
ejpam-3483	6	41	-	-	PUNCT
ejpam-3483	6	42	separation	separation	NOUN
ejpam-3483	6	43	axioms	axiom	VERB
ejpam-3483	6	44	1	1	NUM
ejpam-3483	6	45	.	.	PUNCT
ejpam-3483	6	46	introduction	introduction	NOUN
ejpam-3483	6	47	the	the	DET
ejpam-3483	6	48	concept	concept	NOUN
ejpam-3483	6	49	of	of	ADP
ejpam-3483	6	50	topological	topological	ADJ
ejpam-3483	6	51	ordered	order	VERB
ejpam-3483	6	52	spaces	space	NOUN
ejpam-3483	6	53	has	have	AUX
ejpam-3483	6	54	been	be	AUX
ejpam-3483	6	55	initiated	initiate	VERB
ejpam-3483	6	56	by	by	ADP
ejpam-3483	6	57	nachbin	nachbin	PROPN
ejpam-3483	7	1	[	[	X
ejpam-3483	7	2	26	26	NUM
ejpam-3483	7	3	]	]	PUNCT
ejpam-3483	7	4	in	in	ADP
ejpam-3483	7	5	1965	1965	NUM
ejpam-3483	7	6	.	.	PUNCT
ejpam-3483	8	1	in	in	ADP
ejpam-3483	8	2	1968	1968	NUM
ejpam-3483	8	3	,	,	PUNCT
ejpam-3483	8	4	mccartan	mccartan	ADJ
ejpam-3483	8	5	[	[	X
ejpam-3483	8	6	25	25	NUM
ejpam-3483	8	7	]	]	PUNCT
ejpam-3483	8	8	carried	carry	VERB
ejpam-3483	8	9	out	out	ADP
ejpam-3483	8	10	a	a	DET
ejpam-3483	8	11	detailed	detailed	ADJ
ejpam-3483	8	12	study	study	NOUN
ejpam-3483	8	13	about	about	ADP
ejpam-3483	8	14	ordered	order	VERB
ejpam-3483	8	15	separation	separation	NOUN
ejpam-3483	8	16	axioms	axiom	NOUN
ejpam-3483	8	17	.	.	PUNCT
ejpam-3483	9	1	he	he	PRON
ejpam-3483	9	2	distinguished	distinguish	VERB
ejpam-3483	9	3	between	between	ADP
ejpam-3483	9	4	two	two	NUM
ejpam-3483	9	5	types	type	NOUN
ejpam-3483	9	6	of	of	ADP
ejpam-3483	9	7	these	these	DET
ejpam-3483	9	8	axioms	axiom	NOUN
ejpam-3483	9	9	,	,	PUNCT
ejpam-3483	9	10	one	one	NUM
ejpam-3483	9	11	of	of	ADP
ejpam-3483	9	12	the	the	DET
ejpam-3483	9	13	them	they	PRON
ejpam-3483	9	14	depend	depend	VERB
ejpam-3483	9	15	on	on	ADP
ejpam-3483	9	16	monotone	monotone	ADJ
ejpam-3483	9	17	supra	supra	ADJ
ejpam-3483	9	18	neighborhoods	neighborhood	NOUN
ejpam-3483	9	19	and	and	CCONJ
ejpam-3483	9	20	the	the	DET
ejpam-3483	9	21	other	other	ADJ
ejpam-3483	9	22	depend	depend	VERB
ejpam-3483	9	23	on	on	ADP
ejpam-3483	9	24	monotone	monotone	ADJ
ejpam-3483	9	25	supra	supra	PROPN
ejpam-3483	9	26	open	open	ADJ
ejpam-3483	9	27	neighborhoods	neighborhood	NOUN
ejpam-3483	9	28	.	.	PUNCT
ejpam-3483	10	1	arya	arya	PROPN
ejpam-3483	10	2	and	and	CCONJ
ejpam-3483	10	3	gupta	gupta	PROPN
ejpam-3483	11	1	[	[	X
ejpam-3483	11	2	16	16	NUM
ejpam-3483	11	3	]	]	PUNCT
ejpam-3483	11	4	introduced	introduce	VERB
ejpam-3483	11	5	the	the	DET
ejpam-3483	11	6	concepts	concept	NOUN
ejpam-3483	11	7	of	of	ADP
ejpam-3483	11	8	semi	semi	ADJ
ejpam-3483	11	9	t1	t1	NOUN
ejpam-3483	11	10	-	-	PUNCT
ejpam-3483	11	11	ordered	order	VERB
ejpam-3483	11	12	and	and	CCONJ
ejpam-3483	11	13	semi	semi	ADV
ejpam-3483	11	14	t2	t2	NOUN
ejpam-3483	11	15	-	-	PUNCT
ejpam-3483	11	16	ordered	order	VERB
ejpam-3483	11	17	spaces	space	NOUN
ejpam-3483	11	18	.	.	PUNCT
ejpam-3483	12	1	kumar	kumar	PROPN
ejpam-3483	13	1	[	[	X
ejpam-3483	13	2	23	23	NUM
ejpam-3483	13	3	]	]	PUNCT
ejpam-3483	13	4	studied	study	VERB
ejpam-3483	13	5	the	the	DET
ejpam-3483	13	6	concepts	concept	NOUN
ejpam-3483	13	7	of	of	ADP
ejpam-3483	13	8	continuity	continuity	NOUN
ejpam-3483	13	9	,	,	PUNCT
ejpam-3483	13	10	openness	openness	NOUN
ejpam-3483	13	11	,	,	PUNCT
ejpam-3483	13	12	closedness	closedness	NOUN
ejpam-3483	13	13	and	and	CCONJ
ejpam-3483	13	14	homeomorphism	homeomorphism	PROPN
ejpam-3483	13	15	between	between	ADP
ejpam-3483	13	16	topological	topological	ADJ
ejpam-3483	13	17	ordered	order	VERB
ejpam-3483	13	18	spaces	space	NOUN
ejpam-3483	13	19	.	.	PUNCT
ejpam-3483	14	1	mashhour	mashhour	INTJ
ejpam-3483	14	2	et	et	PROPN
ejpam-3483	14	3	al	al	PROPN
ejpam-3483	14	4	.	.	PUNCT
ejpam-3483	15	1	[	[	X
ejpam-3483	15	2	24	24	NUM
ejpam-3483	15	3	]	]	PUNCT
ejpam-3483	15	4	introduced	introduce	VERB
ejpam-3483	15	5	a	a	DET
ejpam-3483	15	6	notion	notion	NOUN
ejpam-3483	15	7	of	of	ADP
ejpam-3483	15	8	supra	supra	PROPN
ejpam-3483	15	9	topological	topological	ADJ
ejpam-3483	15	10	spaces	space	NOUN
ejpam-3483	15	11	and	and	CCONJ
ejpam-3483	15	12	generalized	generalize	VERB
ejpam-3483	15	13	some	some	DET
ejpam-3483	15	14	properties	property	NOUN
ejpam-3483	15	15	of	of	ADP
ejpam-3483	15	16	topological	topological	ADJ
ejpam-3483	15	17	spaces	space	NOUN
ejpam-3483	15	18	to	to	ADP
ejpam-3483	15	19	supra	supra	PROPN
ejpam-3483	15	20	topological	topological	ADJ
ejpam-3483	15	21	spaces	space	NOUN
ejpam-3483	15	22	such	such	ADJ
ejpam-3483	15	23	as	as	ADP
ejpam-3483	15	24	continuity	continuity	NOUN
ejpam-3483	15	25	and	and	CCONJ
ejpam-3483	15	26	some	some	DET
ejpam-3483	15	27	separation	separation	NOUN
ejpam-3483	15	28	axioms	axiom	VERB
ejpam-3483	15	29	.	.	PUNCT
ejpam-3483	16	1	das	das	PROPN
ejpam-3483	16	2	[	[	X
ejpam-3483	16	3	17	17	NUM
ejpam-3483	16	4	]	]	PUNCT
ejpam-3483	16	5	introduced	introduce	VERB
ejpam-3483	16	6	ordered	order	VERB
ejpam-3483	16	7	separation	separation	NOUN
ejpam-3483	16	8	axioms	axiom	NOUN
ejpam-3483	16	9	in	in	ADP
ejpam-3483	16	10	supra	supra	PROPN
ejpam-3483	16	11	topological	topological	ADJ
ejpam-3483	16	12	ordered	order	VERB
ejpam-3483	16	13	spaces	space	NOUN
ejpam-3483	16	14	and	and	CCONJ
ejpam-3483	16	15	discussed	discuss	VERB
ejpam-3483	16	16	the	the	DET
ejpam-3483	16	17	validity	validity	NOUN
ejpam-3483	16	18	of	of	ADP
ejpam-3483	16	19	the	the	DET
ejpam-3483	16	20	results	result	NOUN
ejpam-3483	16	21	obtained	obtain	VERB
ejpam-3483	16	22	by	by	ADP
ejpam-3483	16	23	[	[	X
ejpam-3483	16	24	25	25	NUM
ejpam-3483	16	25	]	]	PUNCT
ejpam-3483	16	26	on	on	ADP
ejpam-3483	16	27	some	some	DET
ejpam-3483	16	28	∗corresponding	∗corresponde	VERB
ejpam-3483	16	29	author	author	NOUN
ejpam-3483	16	30	.	.	PUNCT
ejpam-3483	17	1	doi	doi	NOUN
ejpam-3483	17	2	:	:	PUNCT
ejpam-3483	17	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3483	https://doi.org/10.29020/nybg.ejpam.v12i3.3483	PROPN
ejpam-3483	17	4	email	email	NOUN
ejpam-3483	17	5	addresses	address	NOUN
ejpam-3483	17	6	:	:	PUNCT
ejpam-3483	17	7	baravan.asaad@uoz.edu.krd	baravan.asaad@uoz.edu.krd	NOUN
ejpam-3483	17	8	(	(	PUNCT
ejpam-3483	17	9	b.	b.	PROPN
ejpam-3483	17	10	a.	a.	PROPN
ejpam-3483	17	11	asaad	asaad	PROPN
ejpam-3483	17	12	)	)	PUNCT
ejpam-3483	17	13	,	,	PUNCT
ejpam-3483	17	14	just.tahat@gmail.com	just.tahat@gmail.com	X
ejpam-3483	17	15	(	(	PUNCT
ejpam-3483	17	16	mohammed	mohammed	PROPN
ejpam-3483	17	17	k.	k.	PROPN
ejpam-3483	17	18	tahat	tahat	PROPN
ejpam-3483	17	19	)	)	PUNCT
ejpam-3483	17	20	,	,	PUNCT
ejpam-3483	17	21	tareqalshami83@gmail.com	tareqalshami83@gmail.com	X
ejpam-3483	17	22	(	(	PUNCT
ejpam-3483	17	23	t.	t.	PROPN
ejpam-3483	17	24	m.	m.	PROPN
ejpam-3483	17	25	al	al	PROPN
ejpam-3483	17	26	-	-	PUNCT
ejpam-3483	17	27	shami	shami	PROPN
ejpam-3483	17	28	)	)	PUNCT
ejpam-3483	17	29	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3483	18	1	1231	1231	NUM
ejpam-3483	19	1	c	c	X
ejpam-3483	19	2	©	©	PROPN
ejpam-3483	19	3	2019	2019	NUM
ejpam-3483	19	4	ejpam	ejpam	NOUN
ejpam-3483	19	5	all	all	DET
ejpam-3483	19	6	rights	right	NOUN
ejpam-3483	19	7	reserved	reserve	VERB
ejpam-3483	19	8	.	.	PUNCT
ejpam-3483	20	1	b.	b.	PROPN
ejpam-3483	20	2	a.	a.	PROPN
ejpam-3483	20	3	asaad	asaad	PROPN
ejpam-3483	20	4	,	,	PUNCT
ejpam-3483	20	5	m.	m.	PROPN
ejpam-3483	20	6	k.	k.	PROPN
ejpam-3483	20	7	tahat	tahat	PROPN
ejpam-3483	20	8	,	,	PUNCT
ejpam-3483	20	9	t.	t.	PROPN
ejpam-3483	20	10	m.	m.	PROPN
ejpam-3483	20	11	al	al	PROPN
ejpam-3483	20	12	-	-	PUNCT
ejpam-3483	20	13	shami	shami	PROPN
ejpam-3483	20	14	/	/	PUNCT
ejpam-3483	20	15	eur	eur	PROPN
ejpam-3483	20	16	.	.	PUNCT
ejpam-3483	21	1	j.	j.	PROPN
ejpam-3483	21	2	pure	pure	PROPN
ejpam-3483	21	3	appl	appl	PROPN
ejpam-3483	21	4	.	.	PROPN
ejpam-3483	21	5	math	math	PROPN
ejpam-3483	21	6	,	,	PUNCT
ejpam-3483	21	7	12	12	NUM
ejpam-3483	21	8	(	(	PUNCT
ejpam-3483	21	9	3	3	NUM
ejpam-3483	21	10	)	)	PUNCT
ejpam-3483	21	11	(	(	PUNCT
ejpam-3483	21	12	2019	2019	NUM
ejpam-3483	21	13	)	)	PUNCT
ejpam-3483	21	14	,	,	PUNCT
ejpam-3483	21	15	1231	1231	NUM
ejpam-3483	21	16	-	-	SYM
ejpam-3483	21	17	1247	1247	NUM
ejpam-3483	21	18	1232	1232	NUM
ejpam-3483	21	19	ordered	order	VERB
ejpam-3483	21	20	spaces	space	NOUN
ejpam-3483	21	21	.	.	PUNCT
ejpam-3483	22	1	in	in	ADP
ejpam-3483	22	2	2016	2016	NUM
ejpam-3483	22	3	,	,	PUNCT
ejpam-3483	22	4	abo	abo	NOUN
ejpam-3483	22	5	-	-	PUNCT
ejpam-3483	22	6	elhamayel	elhamayel	NOUN
ejpam-3483	22	7	and	and	CCONJ
ejpam-3483	22	8	al	al	PROPN
ejpam-3483	22	9	-	-	PUNCT
ejpam-3483	22	10	shami	shami	PROPN
ejpam-3483	22	11	[	[	X
ejpam-3483	22	12	1	1	X
ejpam-3483	22	13	]	]	PUNCT
ejpam-3483	22	14	introduced	introduce	VERB
ejpam-3483	22	15	and	and	CCONJ
ejpam-3483	22	16	studied	study	VERB
ejpam-3483	22	17	some	some	DET
ejpam-3483	22	18	new	new	ADJ
ejpam-3483	22	19	maps	map	NOUN
ejpam-3483	22	20	between	between	ADP
ejpam-3483	22	21	supra	supra	PROPN
ejpam-3483	22	22	topological	topological	ADJ
ejpam-3483	22	23	spaces	space	NOUN
ejpam-3483	22	24	.	.	PUNCT
ejpam-3483	23	1	el	el	PROPN
ejpam-3483	23	2	-	-	PUNCT
ejpam-3483	23	3	shafei	shafei	NOUN
ejpam-3483	23	4	et	et	PROPN
ejpam-3483	23	5	al	al	PROPN
ejpam-3483	23	6	.	.	PUNCT
ejpam-3483	24	1	[	[	X
ejpam-3483	24	2	20	20	NUM
ejpam-3483	24	3	]	]	SYM
ejpam-3483	24	4	formulated	formulate	VERB
ejpam-3483	24	5	strong	strong	ADJ
ejpam-3483	24	6	separation	separation	NOUN
ejpam-3483	24	7	axioms	axiom	NOUN
ejpam-3483	24	8	via	via	ADP
ejpam-3483	24	9	supra	supra	PROPN
ejpam-3483	24	10	topological	topological	PROPN
ejpam-3483	24	11	ordered	order	VERB
ejpam-3483	24	12	spaces	space	NOUN
ejpam-3483	24	13	.	.	PUNCT
ejpam-3483	25	1	sayed	say	VERB
ejpam-3483	25	2	and	and	CCONJ
ejpam-3483	25	3	noiri	noiri	ADV
ejpam-3483	26	1	[	[	X
ejpam-3483	26	2	27	27	NUM
ejpam-3483	26	3	]	]	PUNCT
ejpam-3483	26	4	introduced	introduce	VERB
ejpam-3483	26	5	and	and	CCONJ
ejpam-3483	26	6	studied	study	VERB
ejpam-3483	26	7	supra	supra	PROPN
ejpam-3483	26	8	b	b	NOUN
ejpam-3483	26	9	-	-	PUNCT
ejpam-3483	26	10	open	open	ADJ
ejpam-3483	26	11	sets	set	NOUN
ejpam-3483	26	12	and	and	CCONJ
ejpam-3483	26	13	supra	supra	PROPN
ejpam-3483	26	14	b	b	NOUN
ejpam-3483	26	15	-	-	PUNCT
ejpam-3483	26	16	continuous	continuous	ADJ
ejpam-3483	26	17	maps	map	NOUN
ejpam-3483	26	18	.	.	PUNCT
ejpam-3483	27	1	in	in	ADP
ejpam-3483	27	2	[	[	X
ejpam-3483	27	3	2	2	NUM
ejpam-3483	27	4	,	,	PUNCT
ejpam-3483	27	5	6	6	NUM
ejpam-3483	27	6	,	,	PUNCT
ejpam-3483	27	7	8	8	NUM
ejpam-3483	27	8	]	]	PUNCT
ejpam-3483	27	9	,	,	PUNCT
ejpam-3483	27	10	al	al	PROPN
ejpam-3483	27	11	-	-	PUNCT
ejpam-3483	27	12	shami	shami	PROPN
ejpam-3483	27	13	investigated	investigate	VERB
ejpam-3483	27	14	the	the	DET
ejpam-3483	27	15	properties	property	NOUN
ejpam-3483	27	16	of	of	ADP
ejpam-3483	27	17	new	new	ADJ
ejpam-3483	27	18	types	type	NOUN
ejpam-3483	27	19	of	of	ADP
ejpam-3483	27	20	supra	supra	ADJ
ejpam-3483	27	21	compact	compact	ADJ
ejpam-3483	27	22	spaces	space	NOUN
ejpam-3483	27	23	,	,	PUNCT
ejpam-3483	27	24	and	and	CCONJ
ejpam-3483	27	25	in	in	ADP
ejpam-3483	27	26	[	[	X
ejpam-3483	27	27	3	3	NUM
ejpam-3483	27	28	,	,	PUNCT
ejpam-3483	27	29	18	18	NUM
ejpam-3483	27	30	]	]	PUNCT
ejpam-3483	27	31	,	,	PUNCT
ejpam-3483	27	32	the	the	DET
ejpam-3483	27	33	authors	author	NOUN
ejpam-3483	27	34	presented	present	VERB
ejpam-3483	27	35	two	two	NUM
ejpam-3483	27	36	kinds	kind	NOUN
ejpam-3483	27	37	of	of	ADP
ejpam-3483	27	38	generalized	generalized	ADJ
ejpam-3483	27	39	supra	supra	ADJ
ejpam-3483	27	40	open	open	ADJ
ejpam-3483	27	41	sets	set	NOUN
ejpam-3483	27	42	,	,	PUNCT
ejpam-3483	27	43	namely	namely	ADV
ejpam-3483	27	44	supra	supra	ADJ
ejpam-3483	27	45	semi	semi	ADV
ejpam-3483	27	46	open	open	ADJ
ejpam-3483	27	47	and	and	CCONJ
ejpam-3483	27	48	supra	supra	ADJ
ejpam-3483	27	49	r	r	NOUN
ejpam-3483	27	50	-	-	PUNCT
ejpam-3483	27	51	open	open	ADJ
ejpam-3483	27	52	sets	set	NOUN
ejpam-3483	27	53	.	.	PUNCT
ejpam-3483	28	1	in	in	ADP
ejpam-3483	28	2	[	[	X
ejpam-3483	28	3	5	5	NUM
ejpam-3483	28	4	,	,	PUNCT
ejpam-3483	28	5	7	7	NUM
ejpam-3483	28	6	,	,	PUNCT
ejpam-3483	28	7	15	15	NUM
ejpam-3483	28	8	,	,	PUNCT
ejpam-3483	28	9	19	19	NUM
ejpam-3483	28	10	,	,	PUNCT
ejpam-3483	28	11	21	21	NUM
ejpam-3483	28	12	]	]	PUNCT
ejpam-3483	28	13	,	,	PUNCT
ejpam-3483	28	14	the	the	DET
ejpam-3483	28	15	authors	author	NOUN
ejpam-3483	28	16	employed	employ	VERB
ejpam-3483	28	17	some	some	DET
ejpam-3483	28	18	generalizations	generalization	NOUN
ejpam-3483	28	19	of	of	ADP
ejpam-3483	28	20	supra	supra	ADJ
ejpam-3483	28	21	open	open	ADJ
ejpam-3483	28	22	sets	set	NOUN
ejpam-3483	28	23	to	to	PART
ejpam-3483	28	24	define	define	VERB
ejpam-3483	28	25	new	new	ADJ
ejpam-3483	28	26	types	type	NOUN
ejpam-3483	28	27	of	of	ADP
ejpam-3483	28	28	ordered	order	VERB
ejpam-3483	28	29	maps	map	NOUN
ejpam-3483	28	30	.	.	PUNCT
ejpam-3483	29	1	it	it	PRON
ejpam-3483	29	2	is	be	AUX
ejpam-3483	29	3	noteworthy	noteworthy	ADJ
ejpam-3483	29	4	that	that	SCONJ
ejpam-3483	29	5	the	the	DET
ejpam-3483	29	6	study	study	NOUN
ejpam-3483	29	7	concerning	concern	VERB
ejpam-3483	29	8	soft	soft	ADJ
ejpam-3483	29	9	topological	topological	ADJ
ejpam-3483	29	10	ordered	order	VERB
ejpam-3483	29	11	spaces	space	NOUN
ejpam-3483	29	12	was	be	AUX
ejpam-3483	29	13	done	do	VERB
ejpam-3483	29	14	in	in	ADP
ejpam-3483	29	15	[	[	X
ejpam-3483	29	16	10	10	NUM
ejpam-3483	29	17	]	]	PUNCT
ejpam-3483	29	18	and	and	CCONJ
ejpam-3483	29	19	the	the	DET
ejpam-3483	29	20	studies	study	NOUN
ejpam-3483	29	21	concerning	concern	VERB
ejpam-3483	29	22	various	various	ADJ
ejpam-3483	29	23	types	type	NOUN
ejpam-3483	29	24	of	of	ADP
ejpam-3483	29	25	soft	soft	ADJ
ejpam-3483	29	26	ordered	order	VERB
ejpam-3483	29	27	maps	map	NOUN
ejpam-3483	29	28	were	be	AUX
ejpam-3483	29	29	done	do	VERB
ejpam-3483	29	30	in	in	ADP
ejpam-3483	29	31	[	[	X
ejpam-3483	29	32	9	9	NUM
ejpam-3483	29	33	,	,	PUNCT
ejpam-3483	29	34	11–13	11–13	NUM
ejpam-3483	29	35	,	,	PUNCT
ejpam-3483	29	36	22	22	NUM
ejpam-3483	29	37	]	]	PUNCT
ejpam-3483	29	38	.	.	PUNCT
ejpam-3483	30	1	the	the	DET
ejpam-3483	30	2	aim	aim	NOUN
ejpam-3483	30	3	of	of	ADP
ejpam-3483	30	4	the	the	DET
ejpam-3483	30	5	present	present	ADJ
ejpam-3483	30	6	paper	paper	NOUN
ejpam-3483	30	7	is	be	AUX
ejpam-3483	30	8	to	to	PART
ejpam-3483	30	9	establish	establish	VERB
ejpam-3483	30	10	some	some	DET
ejpam-3483	30	11	types	type	NOUN
ejpam-3483	30	12	of	of	ADP
ejpam-3483	30	13	maps	map	NOUN
ejpam-3483	30	14	on	on	ADP
ejpam-3483	30	15	supra	supra	ADJ
ejpam-3483	30	16	topological	topological	ADJ
ejpam-3483	30	17	spaces	space	NOUN
ejpam-3483	30	18	,	,	PUNCT
ejpam-3483	30	19	namely	namely	ADV
ejpam-3483	30	20	x	x	ADJ
ejpam-3483	30	21	-	-	ADJ
ejpam-3483	30	22	supra	supra	ADJ
ejpam-3483	30	23	b	b	NOUN
ejpam-3483	30	24	-	-	PUNCT
ejpam-3483	30	25	continuous	continuous	ADJ
ejpam-3483	30	26	,	,	PUNCT
ejpam-3483	30	27	x	x	ADJ
ejpam-3483	30	28	-	-	ADJ
ejpam-3483	30	29	supra	supra	ADJ
ejpam-3483	30	30	b	b	NOUN
ejpam-3483	30	31	-	-	PUNCT
ejpam-3483	30	32	open	open	ADJ
ejpam-3483	30	33	,	,	PUNCT
ejpam-3483	30	34	x	x	ADJ
ejpam-3483	30	35	-	-	ADJ
ejpam-3483	30	36	supra	supra	ADJ
ejpam-3483	30	37	b	b	NOUN
ejpam-3483	30	38	-	-	PUNCT
ejpam-3483	30	39	closed	closed	ADJ
ejpam-3483	30	40	and	and	CCONJ
ejpam-3483	30	41	x	x	NOUN
ejpam-3483	30	42	-	-	ADJ
ejpam-3483	30	43	supra	supra	ADJ
ejpam-3483	30	44	b	b	NOUN
ejpam-3483	30	45	-	-	PUNCT
ejpam-3483	30	46	homeomorphism	homeomorphism	PROPN
ejpam-3483	30	47	maps	map	NOUN
ejpam-3483	30	48	,	,	PUNCT
ejpam-3483	30	49	where	where	SCONJ
ejpam-3483	30	50	x∈	x∈	PROPN
ejpam-3483	30	51	{	{	PUNCT
ejpam-3483	30	52	i	i	PROPN
ejpam-3483	30	53	,	,	PUNCT
ejpam-3483	30	54	d	d	PROPN
ejpam-3483	30	55	,	,	PUNCT
ejpam-3483	30	56	b	b	NOUN
ejpam-3483	30	57	}	}	PUNCT
ejpam-3483	30	58	.	.	PUNCT
ejpam-3483	31	1	the	the	DET
ejpam-3483	31	2	equivalent	equivalent	ADJ
ejpam-3483	31	3	conditions	condition	NOUN
ejpam-3483	31	4	for	for	ADP
ejpam-3483	31	5	these	these	DET
ejpam-3483	31	6	maps	map	NOUN
ejpam-3483	31	7	are	be	AUX
ejpam-3483	31	8	investigated	investigate	VERB
ejpam-3483	31	9	and	and	CCONJ
ejpam-3483	31	10	the	the	DET
ejpam-3483	31	11	relationships	relationship	NOUN
ejpam-3483	31	12	among	among	ADP
ejpam-3483	31	13	them	they	PRON
ejpam-3483	31	14	are	be	AUX
ejpam-3483	31	15	shown	show	VERB
ejpam-3483	31	16	with	with	ADP
ejpam-3483	31	17	the	the	DET
ejpam-3483	31	18	help	help	NOUN
ejpam-3483	31	19	of	of	ADP
ejpam-3483	31	20	examples	example	NOUN
ejpam-3483	31	21	.	.	PUNCT
ejpam-3483	32	1	also	also	ADV
ejpam-3483	32	2	,	,	PUNCT
ejpam-3483	32	3	the	the	DET
ejpam-3483	32	4	sufficient	sufficient	ADJ
ejpam-3483	32	5	conditions	condition	NOUN
ejpam-3483	32	6	for	for	SCONJ
ejpam-3483	32	7	these	these	DET
ejpam-3483	32	8	maps	map	NOUN
ejpam-3483	32	9	to	to	PART
ejpam-3483	32	10	preserve	preserve	VERB
ejpam-3483	32	11	some	some	DET
ejpam-3483	32	12	separation	separation	NOUN
ejpam-3483	32	13	axioms	axiom	NOUN
ejpam-3483	32	14	are	be	AUX
ejpam-3483	32	15	given	give	VERB
ejpam-3483	32	16	.	.	PUNCT
ejpam-3483	33	1	it	it	PRON
ejpam-3483	33	2	can	can	AUX
ejpam-3483	33	3	be	be	AUX
ejpam-3483	33	4	observed	observe	VERB
ejpam-3483	33	5	that	that	SCONJ
ejpam-3483	33	6	many	many	ADJ
ejpam-3483	33	7	of	of	ADP
ejpam-3483	33	8	the	the	DET
ejpam-3483	33	9	findings	finding	NOUN
ejpam-3483	33	10	that	that	PRON
ejpam-3483	33	11	raised	raise	VERB
ejpam-3483	33	12	at	at	ADP
ejpam-3483	33	13	herein	herein	NOUN
ejpam-3483	33	14	are	be	AUX
ejpam-3483	33	15	generalizations	generalization	NOUN
ejpam-3483	33	16	of	of	ADP
ejpam-3483	33	17	those	those	DET
ejpam-3483	33	18	findings	finding	NOUN
ejpam-3483	33	19	obtained	obtain	VERB
ejpam-3483	33	20	in	in	ADP
ejpam-3483	33	21	[	[	X
ejpam-3483	33	22	1	1	NUM
ejpam-3483	33	23	]	]	PUNCT
ejpam-3483	33	24	.	.	PUNCT
ejpam-3483	34	1	2	2	X
ejpam-3483	34	2	.	.	NUM
ejpam-3483	34	3	preliminaries	preliminary	NOUN
ejpam-3483	34	4	a	a	DET
ejpam-3483	34	5	topological	topological	ADJ
ejpam-3483	34	6	ordered	order	VERB
ejpam-3483	34	7	space	space	NOUN
ejpam-3483	34	8	is	be	AUX
ejpam-3483	34	9	a	a	DET
ejpam-3483	34	10	triple	triple	ADJ
ejpam-3483	34	11	(	(	PUNCT
ejpam-3483	34	12	x	x	NOUN
ejpam-3483	34	13	,	,	PUNCT
ejpam-3483	34	14	τ	τ	PROPN
ejpam-3483	34	15	,	,	PUNCT
ejpam-3483	34	16	�	�	PROPN
ejpam-3483	34	17	)	)	PUNCT
ejpam-3483	34	18	,	,	PUNCT
ejpam-3483	34	19	where	where	SCONJ
ejpam-3483	34	20	(	(	PUNCT
ejpam-3483	34	21	x	x	X
ejpam-3483	34	22	,	,	PUNCT
ejpam-3483	34	23	τ	τ	X
ejpam-3483	34	24	)	)	PUNCT
ejpam-3483	34	25	is	be	AUX
ejpam-3483	34	26	a	a	DET
ejpam-3483	34	27	topological	topological	ADJ
ejpam-3483	34	28	space	space	NOUN
ejpam-3483	34	29	and	and	CCONJ
ejpam-3483	34	30	(	(	PUNCT
ejpam-3483	34	31	x	x	NOUN
ejpam-3483	34	32	,	,	PUNCT
ejpam-3483	34	33	�	�	PROPN
ejpam-3483	34	34	)	)	PUNCT
ejpam-3483	34	35	is	be	AUX
ejpam-3483	34	36	a	a	DET
ejpam-3483	34	37	partially	partially	ADV
ejpam-3483	34	38	ordered	order	VERB
ejpam-3483	34	39	set	set	NOUN
ejpam-3483	34	40	.	.	PUNCT
ejpam-3483	35	1	from	from	ADP
ejpam-3483	35	2	now	now	ADV
ejpam-3483	35	3	on	on	ADV
ejpam-3483	35	4	,	,	PUNCT
ejpam-3483	35	5	the	the	DET
ejpam-3483	35	6	notations	notation	NOUN
ejpam-3483	35	7	τ	τ	X
ejpam-3483	35	8	µ	µ	NOUN
ejpam-3483	35	9	and	and	CCONJ
ejpam-3483	35	10	4	4	NUM
ejpam-3483	35	11	respectively	respectively	ADV
ejpam-3483	35	12	refer	refer	VERB
ejpam-3483	35	13	to	to	ADP
ejpam-3483	35	14	a	a	DET
ejpam-3483	35	15	topology	topology	NOUN
ejpam-3483	35	16	,	,	PUNCT
ejpam-3483	35	17	a	a	DET
ejpam-3483	35	18	supra	supra	ADJ
ejpam-3483	35	19	topology	topology	NOUN
ejpam-3483	35	20	and	and	CCONJ
ejpam-3483	35	21	the	the	DET
ejpam-3483	35	22	diagonal	diagonal	ADJ
ejpam-3483	35	23	relation	relation	NOUN
ejpam-3483	35	24	on	on	ADP
ejpam-3483	35	25	a	a	DET
ejpam-3483	35	26	non	non	X
ejpam-3483	35	27	empty	empty	ADJ
ejpam-3483	35	28	set	set	NOUN
ejpam-3483	35	29	x	x	PUNCT
ejpam-3483	35	30	or	or	CCONJ
ejpam-3483	35	31	y	y	PROPN
ejpam-3483	35	32	.	.	PUNCT
ejpam-3483	36	1	we	we	PRON
ejpam-3483	36	2	start	start	VERB
ejpam-3483	36	3	this	this	DET
ejpam-3483	36	4	section	section	NOUN
ejpam-3483	36	5	with	with	ADP
ejpam-3483	36	6	recalling	recall	VERB
ejpam-3483	36	7	some	some	DET
ejpam-3483	36	8	definitions	definition	NOUN
ejpam-3483	36	9	and	and	CCONJ
ejpam-3483	36	10	results	result	NOUN
ejpam-3483	36	11	which	which	PRON
ejpam-3483	36	12	are	be	AUX
ejpam-3483	36	13	necessary	necessary	ADJ
ejpam-3483	36	14	for	for	ADP
ejpam-3483	36	15	the	the	DET
ejpam-3483	36	16	sequel	sequel	NOUN
ejpam-3483	36	17	of	of	ADP
ejpam-3483	36	18	this	this	DET
ejpam-3483	36	19	study	study	NOUN
ejpam-3483	36	20	.	.	PUNCT
ejpam-3483	37	1	definition	definition	NOUN
ejpam-3483	37	2	1	1	NUM
ejpam-3483	37	3	.	.	PUNCT
ejpam-3483	38	1	[	[	X
ejpam-3483	38	2	26	26	NUM
ejpam-3483	38	3	]	]	PUNCT
ejpam-3483	38	4	let	let	VERB
ejpam-3483	38	5	a	a	DET
ejpam-3483	38	6	∈	∈	PROPN
ejpam-3483	38	7	x	x	X
ejpam-3483	38	8	and	and	CCONJ
ejpam-3483	38	9	b	b	NOUN
ejpam-3483	38	10	be	be	AUX
ejpam-3483	38	11	a	a	DET
ejpam-3483	38	12	subset	subset	NOUN
ejpam-3483	38	13	of	of	ADP
ejpam-3483	38	14	a	a	DET
ejpam-3483	38	15	partially	partially	ADV
ejpam-3483	38	16	ordered	order	VERB
ejpam-3483	38	17	set	set	NOUN
ejpam-3483	38	18	(	(	PUNCT
ejpam-3483	38	19	x	x	NOUN
ejpam-3483	38	20	,	,	PUNCT
ejpam-3483	38	21	�	�	PROPN
ejpam-3483	38	22	)	)	PUNCT
ejpam-3483	38	23	.	.	PUNCT
ejpam-3483	39	1	then	then	ADV
ejpam-3483	39	2	:	:	PUNCT
ejpam-3483	39	3	(	(	PUNCT
ejpam-3483	39	4	i	i	NOUN
ejpam-3483	39	5	)	)	PUNCT
ejpam-3483	39	6	i(a	i(a	PROPN
ejpam-3483	39	7	)	)	PUNCT
ejpam-3483	39	8	=	=	PRON
ejpam-3483	40	1	{	{	PUNCT
ejpam-3483	40	2	x	x	PUNCT
ejpam-3483	40	3	∈	∈	PROPN
ejpam-3483	40	4	x	x	X
ejpam-3483	40	5	:	:	PUNCT
ejpam-3483	40	6	a	a	DET
ejpam-3483	40	7	�	�	PROPN
ejpam-3483	40	8	x	x	NOUN
ejpam-3483	40	9	}	}	PUNCT
ejpam-3483	40	10	and	and	CCONJ
ejpam-3483	40	11	d(a	d(a	PROPN
ejpam-3483	40	12	)	)	PUNCT
ejpam-3483	40	13	=	=	PRON
ejpam-3483	40	14	{	{	PUNCT
ejpam-3483	40	15	x	x	PUNCT
ejpam-3483	40	16	∈	∈	NOUN
ejpam-3483	40	17	x	x	X
ejpam-3483	40	18	:	:	PUNCT
ejpam-3483	40	19	x	x	PUNCT
ejpam-3483	40	20	�	�	PROPN
ejpam-3483	40	21	a	a	PRON
ejpam-3483	40	22	}	}	PUNCT
ejpam-3483	40	23	.	.	PUNCT
ejpam-3483	41	1	(	(	PUNCT
ejpam-3483	41	2	ii	ii	NOUN
ejpam-3483	41	3	)	)	PUNCT
ejpam-3483	41	4	i(b	i(b	NOUN
ejpam-3483	41	5	)	)	PUNCT
ejpam-3483	42	1	=	=	SYM
ejpam-3483	42	2	⋃	⋃	NOUN
ejpam-3483	42	3	{	{	PUNCT
ejpam-3483	42	4	i(b	i(b	PROPN
ejpam-3483	42	5	)	)	PUNCT
ejpam-3483	42	6	:	:	PUNCT
ejpam-3483	42	7	b	b	X
ejpam-3483	42	8	∈	∈	ADJ
ejpam-3483	42	9	b	b	NOUN
ejpam-3483	42	10	}	}	PUNCT
ejpam-3483	42	11	and	and	CCONJ
ejpam-3483	42	12	d(b	d(b	NOUN
ejpam-3483	42	13	)	)	PUNCT
ejpam-3483	43	1	=	=	SYM
ejpam-3483	43	2	⋃	⋃	NOUN
ejpam-3483	43	3	{	{	PUNCT
ejpam-3483	43	4	d(b	d(b	NOUN
ejpam-3483	43	5	)	)	PUNCT
ejpam-3483	43	6	:	:	PUNCT
ejpam-3483	43	7	b	b	X
ejpam-3483	43	8	∈	∈	PROPN
ejpam-3483	43	9	b	b	NOUN
ejpam-3483	43	10	}	}	PUNCT
ejpam-3483	43	11	.	.	PUNCT
ejpam-3483	44	1	(	(	PUNCT
ejpam-3483	44	2	iii	iii	X
ejpam-3483	44	3	)	)	PUNCT
ejpam-3483	44	4	a	a	DET
ejpam-3483	44	5	set	set	NOUN
ejpam-3483	44	6	b	b	NOUN
ejpam-3483	44	7	is	be	AUX
ejpam-3483	44	8	called	call	VERB
ejpam-3483	44	9	increasing	increase	VERB
ejpam-3483	44	10	(	(	PUNCT
ejpam-3483	44	11	resp	resp	NOUN
ejpam-3483	44	12	.	.	PUNCT
ejpam-3483	45	1	decreasing	decrease	VERB
ejpam-3483	45	2	)	)	PUNCT
ejpam-3483	45	3	,	,	PUNCT
ejpam-3483	45	4	if	if	SCONJ
ejpam-3483	45	5	b	b	NOUN
ejpam-3483	45	6	=	=	SYM
ejpam-3483	45	7	i(b	i(b	NOUN
ejpam-3483	45	8	)	)	PUNCT
ejpam-3483	45	9	(	(	PUNCT
ejpam-3483	45	10	resp	resp	NOUN
ejpam-3483	45	11	.	.	PUNCT
ejpam-3483	46	1	b	b	X
ejpam-3483	46	2	=	=	PUNCT
ejpam-3483	46	3	d(b	d(b	PROPN
ejpam-3483	46	4	)	)	PUNCT
ejpam-3483	46	5	)	)	PUNCT
ejpam-3483	46	6	.	.	PUNCT
ejpam-3483	47	1	definition	definition	NOUN
ejpam-3483	47	2	2	2	NUM
ejpam-3483	47	3	.	.	PUNCT
ejpam-3483	48	1	[	[	X
ejpam-3483	48	2	23	23	NUM
ejpam-3483	48	3	]	]	PUNCT
ejpam-3483	48	4	a	a	DET
ejpam-3483	48	5	subset	subset	NOUN
ejpam-3483	48	6	b	b	NOUN
ejpam-3483	48	7	of	of	ADP
ejpam-3483	48	8	a	a	DET
ejpam-3483	48	9	partially	partially	ADV
ejpam-3483	48	10	ordered	order	VERB
ejpam-3483	48	11	set	set	NOUN
ejpam-3483	48	12	(	(	PUNCT
ejpam-3483	48	13	x	x	NOUN
ejpam-3483	48	14	,	,	PUNCT
ejpam-3483	48	15	�	�	PROPN
ejpam-3483	48	16	)	)	PUNCT
ejpam-3483	48	17	is	be	AUX
ejpam-3483	48	18	called	call	VERB
ejpam-3483	48	19	balancing	balance	VERB
ejpam-3483	48	20	if	if	SCONJ
ejpam-3483	48	21	it	it	PRON
ejpam-3483	48	22	is	be	AUX
ejpam-3483	48	23	increasing	increase	VERB
ejpam-3483	48	24	and	and	CCONJ
ejpam-3483	48	25	decreasing	decrease	VERB
ejpam-3483	48	26	.	.	PUNCT
ejpam-3483	49	1	definition	definition	NOUN
ejpam-3483	49	2	3	3	NUM
ejpam-3483	49	3	.	.	PUNCT
ejpam-3483	50	1	[	[	X
ejpam-3483	50	2	1	1	X
ejpam-3483	50	3	]	]	PUNCT
ejpam-3483	50	4	a	a	DET
ejpam-3483	50	5	map	map	NOUN
ejpam-3483	50	6	g	g	NOUN
ejpam-3483	50	7	:	:	PUNCT
ejpam-3483	50	8	(	(	PUNCT
ejpam-3483	50	9	x	x	X
ejpam-3483	50	10	,	,	PUNCT
ejpam-3483	50	11	τ)→	τ)→	PROPN
ejpam-3483	50	12	(	(	PUNCT
ejpam-3483	50	13	y	y	PROPN
ejpam-3483	50	14	,	,	PUNCT
ejpam-3483	50	15	µ	µ	NOUN
ejpam-3483	50	16	)	)	PUNCT
ejpam-3483	50	17	is	be	AUX
ejpam-3483	50	18	said	say	VERB
ejpam-3483	50	19	to	to	PART
ejpam-3483	50	20	be	be	AUX
ejpam-3483	50	21	supra	supra	ADJ
ejpam-3483	50	22	open	open	ADJ
ejpam-3483	50	23	(	(	PUNCT
ejpam-3483	50	24	resp	resp	NOUN
ejpam-3483	50	25	.	.	PUNCT
ejpam-3483	51	1	supra	supra	PROPN
ejpam-3483	51	2	closed	close	VERB
ejpam-3483	51	3	)	)	PUNCT
ejpam-3483	51	4	if	if	SCONJ
ejpam-3483	51	5	the	the	DET
ejpam-3483	51	6	image	image	NOUN
ejpam-3483	51	7	of	of	ADP
ejpam-3483	51	8	any	any	DET
ejpam-3483	51	9	open	open	ADJ
ejpam-3483	51	10	(	(	PUNCT
ejpam-3483	51	11	resp	resp	NOUN
ejpam-3483	51	12	.	.	PUNCT
ejpam-3483	52	1	closed	closed	ADJ
ejpam-3483	52	2	)	)	PUNCT
ejpam-3483	52	3	subset	subset	NOUN
ejpam-3483	52	4	of	of	ADP
ejpam-3483	52	5	x	x	PUNCT
ejpam-3483	52	6	is	be	AUX
ejpam-3483	52	7	a	a	DET
ejpam-3483	52	8	supra	supra	ADJ
ejpam-3483	52	9	open	open	ADJ
ejpam-3483	52	10	(	(	PUNCT
ejpam-3483	52	11	resp	resp	NOUN
ejpam-3483	52	12	.	.	PUNCT
ejpam-3483	53	1	supra	supra	PROPN
ejpam-3483	53	2	closed	close	VERB
ejpam-3483	53	3	)	)	PUNCT
ejpam-3483	53	4	subset	subset	NOUN
ejpam-3483	53	5	of	of	ADP
ejpam-3483	53	6	y	y	PROPN
ejpam-3483	53	7	.	.	PUNCT
ejpam-3483	54	1	definition	definition	NOUN
ejpam-3483	54	2	4	4	NUM
ejpam-3483	54	3	.	.	PUNCT
ejpam-3483	55	1	[	[	X
ejpam-3483	55	2	24	24	NUM
ejpam-3483	55	3	]	]	PUNCT
ejpam-3483	55	4	(	(	PUNCT
ejpam-3483	55	5	i	i	NOUN
ejpam-3483	55	6	)	)	PUNCT
ejpam-3483	55	7	a	a	DET
ejpam-3483	55	8	map	map	NOUN
ejpam-3483	55	9	g	g	NOUN
ejpam-3483	55	10	:	:	PUNCT
ejpam-3483	55	11	(	(	PUNCT
ejpam-3483	55	12	x,µ)→	x,µ)→	X
ejpam-3483	55	13	(	(	PUNCT
ejpam-3483	55	14	y	y	PROPN
ejpam-3483	55	15	,	,	PUNCT
ejpam-3483	55	16	τ	τ	PROPN
ejpam-3483	55	17	)	)	PUNCT
ejpam-3483	55	18	is	be	AUX
ejpam-3483	55	19	said	say	VERB
ejpam-3483	55	20	to	to	PART
ejpam-3483	55	21	be	be	AUX
ejpam-3483	55	22	supra	supra	ADJ
ejpam-3483	55	23	continuous	continuous	ADJ
ejpam-3483	55	24	if	if	SCONJ
ejpam-3483	55	25	the	the	DET
ejpam-3483	55	26	inverse	inverse	ADJ
ejpam-3483	55	27	image	image	NOUN
ejpam-3483	55	28	of	of	ADP
ejpam-3483	55	29	each	each	DET
ejpam-3483	55	30	open	open	ADJ
ejpam-3483	55	31	subset	subset	NOUN
ejpam-3483	55	32	of	of	ADP
ejpam-3483	55	33	y	y	PROPN
ejpam-3483	55	34	is	be	AUX
ejpam-3483	55	35	a	a	DET
ejpam-3483	55	36	supra	supra	ADJ
ejpam-3483	55	37	open	open	ADJ
ejpam-3483	55	38	subset	subset	NOUN
ejpam-3483	55	39	of	of	ADP
ejpam-3483	55	40	x.	x.	PROPN
ejpam-3483	55	41	b.	b.	PROPN
ejpam-3483	55	42	a.	a.	PROPN
ejpam-3483	55	43	asaad	asaad	PROPN
ejpam-3483	55	44	,	,	PUNCT
ejpam-3483	55	45	m.	m.	PROPN
ejpam-3483	55	46	k.	k.	PROPN
ejpam-3483	55	47	tahat	tahat	PROPN
ejpam-3483	55	48	,	,	PUNCT
ejpam-3483	55	49	t.	t.	PROPN
ejpam-3483	55	50	m.	m.	PROPN
ejpam-3483	55	51	al	al	PROPN
ejpam-3483	55	52	-	-	PUNCT
ejpam-3483	55	53	shami	shami	PROPN
ejpam-3483	55	54	/	/	PUNCT
ejpam-3483	55	55	eur	eur	PROPN
ejpam-3483	55	56	.	.	PUNCT
ejpam-3483	56	1	j.	j.	PROPN
ejpam-3483	56	2	pure	pure	PROPN
ejpam-3483	56	3	appl	appl	PROPN
ejpam-3483	56	4	.	.	PROPN
ejpam-3483	56	5	math	math	PROPN
ejpam-3483	56	6	,	,	PUNCT
ejpam-3483	56	7	12	12	NUM
ejpam-3483	56	8	(	(	PUNCT
ejpam-3483	56	9	3	3	NUM
ejpam-3483	56	10	)	)	PUNCT
ejpam-3483	56	11	(	(	PUNCT
ejpam-3483	56	12	2019	2019	NUM
ejpam-3483	56	13	)	)	PUNCT
ejpam-3483	56	14	,	,	PUNCT
ejpam-3483	56	15	1231	1231	NUM
ejpam-3483	56	16	-	-	SYM
ejpam-3483	56	17	1247	1247	NUM
ejpam-3483	56	18	1233	1233	NUM
ejpam-3483	56	19	(	(	PUNCT
ejpam-3483	56	20	ii	ii	NOUN
ejpam-3483	56	21	)	)	PUNCT
ejpam-3483	56	22	let	let	VERB
ejpam-3483	56	23	τ	τ	PROPN
ejpam-3483	56	24	be	be	AUX
ejpam-3483	56	25	a	a	DET
ejpam-3483	56	26	topology	topology	NOUN
ejpam-3483	56	27	and	and	CCONJ
ejpam-3483	56	28	µ	µ	NOUN
ejpam-3483	56	29	be	be	AUX
ejpam-3483	56	30	a	a	DET
ejpam-3483	56	31	supra	supra	ADJ
ejpam-3483	56	32	topology	topology	NOUN
ejpam-3483	56	33	on	on	ADP
ejpam-3483	56	34	x.	x.	NOUN
ejpam-3483	57	1	we	we	PRON
ejpam-3483	57	2	say	say	VERB
ejpam-3483	57	3	that	that	SCONJ
ejpam-3483	57	4	µ	µ	NOUN
ejpam-3483	57	5	is	be	AUX
ejpam-3483	57	6	associated	associate	VERB
ejpam-3483	57	7	supra	supra	ADJ
ejpam-3483	57	8	topology	topology	NOUN
ejpam-3483	57	9	with	with	ADP
ejpam-3483	57	10	τ	τ	PROPN
ejpam-3483	57	11	if	if	SCONJ
ejpam-3483	57	12	τ	τ	PROPN
ejpam-3483	57	13	⊆	⊆	NUM
ejpam-3483	57	14	µ.	µ.	NOUN
ejpam-3483	57	15	definition	definition	NOUN
ejpam-3483	57	16	5	5	NUM
ejpam-3483	57	17	.	.	PUNCT
ejpam-3483	58	1	[	[	X
ejpam-3483	58	2	27	27	NUM
ejpam-3483	58	3	]	]	PUNCT
ejpam-3483	58	4	a	a	DET
ejpam-3483	58	5	subset	subset	NOUN
ejpam-3483	58	6	e	e	X
ejpam-3483	58	7	of	of	ADP
ejpam-3483	58	8	(	(	PUNCT
ejpam-3483	58	9	x,µ	x,µ	NOUN
ejpam-3483	58	10	)	)	PUNCT
ejpam-3483	58	11	is	be	AUX
ejpam-3483	58	12	called	call	VERB
ejpam-3483	58	13	supra	supra	PROPN
ejpam-3483	58	14	b	b	NOUN
ejpam-3483	58	15	-	-	PUNCT
ejpam-3483	58	16	open	open	ADJ
ejpam-3483	58	17	if	if	SCONJ
ejpam-3483	58	18	e	e	PROPN
ejpam-3483	58	19	⊆	⊆	NUM
ejpam-3483	58	20	int(cl(e	int(cl(e	NOUN
ejpam-3483	58	21	)	)	PUNCT
ejpam-3483	58	22	)	)	PUNCT
ejpam-3483	59	1	⋃	⋃	NOUN
ejpam-3483	59	2	cl(int(e	cl(int(e	NOUN
ejpam-3483	59	3	)	)	PUNCT
ejpam-3483	59	4	)	)	PUNCT
ejpam-3483	60	1	and	and	CCONJ
ejpam-3483	60	2	its	its	PRON
ejpam-3483	60	3	complement	complement	NOUN
ejpam-3483	60	4	is	be	AUX
ejpam-3483	60	5	called	call	VERB
ejpam-3483	60	6	supra	supra	PROPN
ejpam-3483	60	7	b	b	NOUN
ejpam-3483	60	8	-	-	PUNCT
ejpam-3483	60	9	closed	closed	ADJ
ejpam-3483	60	10	.	.	PUNCT
ejpam-3483	61	1	definition	definition	NOUN
ejpam-3483	61	2	6	6	NUM
ejpam-3483	61	3	.	.	PUNCT
ejpam-3483	62	1	[	[	X
ejpam-3483	62	2	27	27	NUM
ejpam-3483	62	3	]	]	X
ejpam-3483	62	4	a	a	DET
ejpam-3483	62	5	map	map	NOUN
ejpam-3483	62	6	g	g	NOUN
ejpam-3483	62	7	:	:	PUNCT
ejpam-3483	62	8	(	(	PUNCT
ejpam-3483	62	9	x	x	X
ejpam-3483	62	10	,	,	PUNCT
ejpam-3483	62	11	τ)→	τ)→	PROPN
ejpam-3483	62	12	(	(	PUNCT
ejpam-3483	62	13	y	y	PROPN
ejpam-3483	62	14	,	,	PUNCT
ejpam-3483	62	15	θ	θ	PROPN
ejpam-3483	62	16	)	)	PUNCT
ejpam-3483	62	17	is	be	AUX
ejpam-3483	62	18	said	say	VERB
ejpam-3483	62	19	to	to	PART
ejpam-3483	62	20	be	be	AUX
ejpam-3483	62	21	:	:	PUNCT
ejpam-3483	62	22	(	(	PUNCT
ejpam-3483	62	23	i	i	NOUN
ejpam-3483	62	24	)	)	PUNCT
ejpam-3483	62	25	supra	supra	PROPN
ejpam-3483	62	26	b	b	X
ejpam-3483	62	27	-	-	PUNCT
ejpam-3483	62	28	continuous	continuous	ADJ
ejpam-3483	62	29	if	if	SCONJ
ejpam-3483	62	30	the	the	DET
ejpam-3483	62	31	inverse	inverse	ADJ
ejpam-3483	62	32	image	image	NOUN
ejpam-3483	62	33	of	of	ADP
ejpam-3483	62	34	each	each	DET
ejpam-3483	62	35	open	open	ADJ
ejpam-3483	62	36	subset	subset	NOUN
ejpam-3483	62	37	of	of	ADP
ejpam-3483	62	38	y	y	PROPN
ejpam-3483	62	39	is	be	AUX
ejpam-3483	62	40	a	a	DET
ejpam-3483	62	41	supra	supra	PROPN
ejpam-3483	62	42	b	b	NOUN
ejpam-3483	62	43	-	-	PUNCT
ejpam-3483	62	44	open	open	ADJ
ejpam-3483	62	45	subset	subset	NOUN
ejpam-3483	62	46	of	of	ADP
ejpam-3483	62	47	x.	x.	PROPN
ejpam-3483	62	48	(	(	PUNCT
ejpam-3483	62	49	ii	ii	PROPN
ejpam-3483	62	50	)	)	PUNCT
ejpam-3483	62	51	supra	supra	PROPN
ejpam-3483	62	52	b	b	X
ejpam-3483	62	53	-	-	PUNCT
ejpam-3483	62	54	open	open	ADJ
ejpam-3483	62	55	(	(	PUNCT
ejpam-3483	62	56	resp	resp	NOUN
ejpam-3483	62	57	.	.	PUNCT
ejpam-3483	63	1	supra	supra	PROPN
ejpam-3483	63	2	b	b	PROPN
ejpam-3483	63	3	-	-	PUNCT
ejpam-3483	63	4	closed	closed	ADJ
ejpam-3483	63	5	)	)	PUNCT
ejpam-3483	63	6	if	if	SCONJ
ejpam-3483	63	7	the	the	DET
ejpam-3483	63	8	image	image	NOUN
ejpam-3483	63	9	of	of	ADP
ejpam-3483	63	10	each	each	PRON
ejpam-3483	63	11	open	open	ADJ
ejpam-3483	63	12	(	(	PUNCT
ejpam-3483	63	13	resp	resp	NOUN
ejpam-3483	63	14	.	.	PUNCT
ejpam-3483	64	1	closed	closed	ADJ
ejpam-3483	64	2	)	)	PUNCT
ejpam-3483	64	3	subset	subset	NOUN
ejpam-3483	64	4	of	of	ADP
ejpam-3483	64	5	x	x	PUNCT
ejpam-3483	64	6	is	be	AUX
ejpam-3483	64	7	a	a	DET
ejpam-3483	64	8	supra	supra	PROPN
ejpam-3483	64	9	b	b	NOUN
ejpam-3483	64	10	-	-	PUNCT
ejpam-3483	64	11	open	open	ADJ
ejpam-3483	64	12	(	(	PUNCT
ejpam-3483	64	13	resp	resp	NOUN
ejpam-3483	64	14	.	.	PUNCT
ejpam-3483	65	1	supra	supra	PROPN
ejpam-3483	65	2	b	b	PROPN
ejpam-3483	65	3	-	-	PUNCT
ejpam-3483	65	4	closed	closed	ADJ
ejpam-3483	65	5	)	)	PUNCT
ejpam-3483	65	6	subset	subset	NOUN
ejpam-3483	65	7	of	of	ADP
ejpam-3483	65	8	y	y	PROPN
ejpam-3483	65	9	.	.	PUNCT
ejpam-3483	66	1	hereafter	hereafter	ADV
ejpam-3483	66	2	,	,	PUNCT
ejpam-3483	66	3	we	we	PRON
ejpam-3483	66	4	give	give	VERB
ejpam-3483	66	5	a	a	DET
ejpam-3483	66	6	concept	concept	NOUN
ejpam-3483	66	7	of	of	ADP
ejpam-3483	66	8	supra	supra	PROPN
ejpam-3483	66	9	b	b	PROPN
ejpam-3483	66	10	-	-	PUNCT
ejpam-3483	66	11	homeomorphism	homeomorphism	PROPN
ejpam-3483	66	12	maps	map	NOUN
ejpam-3483	66	13	.	.	PUNCT
ejpam-3483	67	1	definition	definition	NOUN
ejpam-3483	67	2	7	7	NUM
ejpam-3483	67	3	.	.	PUNCT
ejpam-3483	68	1	a	a	DET
ejpam-3483	68	2	map	map	NOUN
ejpam-3483	68	3	g	g	NOUN
ejpam-3483	68	4	:	:	PUNCT
ejpam-3483	68	5	(	(	PUNCT
ejpam-3483	68	6	x	x	X
ejpam-3483	68	7	,	,	PUNCT
ejpam-3483	68	8	τ	τ	X
ejpam-3483	68	9	)	)	PUNCT
ejpam-3483	68	10	→	→	SYM
ejpam-3483	68	11	(	(	PUNCT
ejpam-3483	68	12	y	y	PROPN
ejpam-3483	68	13	,	,	PUNCT
ejpam-3483	68	14	θ	θ	PROPN
ejpam-3483	68	15	)	)	PUNCT
ejpam-3483	68	16	is	be	AUX
ejpam-3483	68	17	said	say	VERB
ejpam-3483	68	18	to	to	PART
ejpam-3483	68	19	be	be	AUX
ejpam-3483	68	20	supra	supra	PROPN
ejpam-3483	68	21	b	b	NOUN
ejpam-3483	68	22	-	-	PUNCT
ejpam-3483	68	23	homeomorphism	homeomorphism	PROPN
ejpam-3483	68	24	if	if	SCONJ
ejpam-3483	68	25	it	it	PRON
ejpam-3483	68	26	is	be	AUX
ejpam-3483	68	27	bijective	bijective	ADJ
ejpam-3483	68	28	,	,	PUNCT
ejpam-3483	68	29	supra	supra	PROPN
ejpam-3483	68	30	b	b	NOUN
ejpam-3483	68	31	-	-	PUNCT
ejpam-3483	68	32	continuous	continuous	ADJ
ejpam-3483	68	33	and	and	CCONJ
ejpam-3483	68	34	supra	supra	ADJ
ejpam-3483	68	35	b	b	NOUN
ejpam-3483	68	36	-	-	PUNCT
ejpam-3483	68	37	open	open	ADJ
ejpam-3483	68	38	.	.	PUNCT
ejpam-3483	69	1	definition	definition	NOUN
ejpam-3483	69	2	8	8	NUM
ejpam-3483	69	3	.	.	PUNCT
ejpam-3483	70	1	a	a	DET
ejpam-3483	70	2	map	map	NOUN
ejpam-3483	70	3	f	f	X
ejpam-3483	70	4	:	:	PUNCT
ejpam-3483	70	5	(	(	PUNCT
ejpam-3483	70	6	x,	x,	NUM
ejpam-3483	70	7	�	�	PROPN
ejpam-3483	70	8	1)→	1)→	NUM
ejpam-3483	70	9	(	(	PUNCT
ejpam-3483	70	10	y,	y,	PROPN
ejpam-3483	70	11	�	�	PROPN
ejpam-3483	70	12	2	2	NUM
ejpam-3483	70	13	)	)	PUNCT
ejpam-3483	70	14	is	be	AUX
ejpam-3483	70	15	called	call	VERB
ejpam-3483	70	16	:	:	PUNCT
ejpam-3483	70	17	(	(	PUNCT
ejpam-3483	70	18	i	i	NOUN
ejpam-3483	70	19	)	)	PUNCT
ejpam-3483	70	20	order	order	NOUN
ejpam-3483	70	21	preserving	preserve	VERB
ejpam-3483	70	22	(	(	PUNCT
ejpam-3483	70	23	or	or	CCONJ
ejpam-3483	70	24	increasing	increase	VERB
ejpam-3483	70	25	)	)	PUNCT
ejpam-3483	70	26	if	if	SCONJ
ejpam-3483	70	27	a	a	DET
ejpam-3483	70	28	�	�	PROPN
ejpam-3483	70	29	1	1	NUM
ejpam-3483	70	30	b	b	PROPN
ejpam-3483	70	31	,	,	PUNCT
ejpam-3483	70	32	then	then	ADV
ejpam-3483	70	33	f(a	f(a	PROPN
ejpam-3483	70	34	)	)	PUNCT
ejpam-3483	70	35	�	�	PROPN
ejpam-3483	70	36	2	2	NUM
ejpam-3483	70	37	f(b	f(b	PROPN
ejpam-3483	70	38	)	)	PUNCT
ejpam-3483	70	39	for	for	ADP
ejpam-3483	70	40	each	each	DET
ejpam-3483	70	41	a	a	NOUN
ejpam-3483	70	42	,	,	PUNCT
ejpam-3483	70	43	b	b	X
ejpam-3483	70	44	∈	∈	PROPN
ejpam-3483	70	45	x.	x.	NOUN
ejpam-3483	70	46	(	(	PUNCT
ejpam-3483	70	47	ii	ii	NOUN
ejpam-3483	70	48	)	)	PUNCT
ejpam-3483	70	49	order	order	NOUN
ejpam-3483	70	50	embedding	embed	VERB
ejpam-3483	70	51	provided	provide	VERB
ejpam-3483	70	52	that	that	SCONJ
ejpam-3483	70	53	a	a	DET
ejpam-3483	70	54	�	�	PROPN
ejpam-3483	70	55	1	1	NUM
ejpam-3483	70	56	b	b	NOUN
ejpam-3483	70	57	if	if	SCONJ
ejpam-3483	70	58	and	and	CCONJ
ejpam-3483	70	59	only	only	ADV
ejpam-3483	70	60	if	if	SCONJ
ejpam-3483	70	61	f(a	f(a	PROPN
ejpam-3483	70	62	)	)	PUNCT
ejpam-3483	70	63	�	�	PROPN
ejpam-3483	70	64	2	2	NUM
ejpam-3483	70	65	f(b	f(b	PROPN
ejpam-3483	70	66	)	)	PUNCT
ejpam-3483	70	67	for	for	ADP
ejpam-3483	70	68	each	each	DET
ejpam-3483	70	69	a	a	NOUN
ejpam-3483	70	70	,	,	PUNCT
ejpam-3483	70	71	b	b	X
ejpam-3483	70	72	∈	∈	PROPN
ejpam-3483	70	73	x.	x.	NOUN
ejpam-3483	70	74	theorem	theorem	VERB
ejpam-3483	70	75	1	1	NUM
ejpam-3483	70	76	.	.	PUNCT
ejpam-3483	71	1	(	(	PUNCT
ejpam-3483	71	2	i	i	NOUN
ejpam-3483	71	3	)	)	PUNCT
ejpam-3483	71	4	if	if	SCONJ
ejpam-3483	71	5	g	g	NOUN
ejpam-3483	71	6	:	:	PUNCT
ejpam-3483	71	7	(	(	PUNCT
ejpam-3483	71	8	x,	x,	NUM
ejpam-3483	71	9	�	�	PROPN
ejpam-3483	71	10	1)→	1)→	NUM
ejpam-3483	71	11	(	(	PUNCT
ejpam-3483	71	12	y,	y,	PROPN
ejpam-3483	71	13	�	�	PROPN
ejpam-3483	71	14	2	2	NUM
ejpam-3483	71	15	)	)	PUNCT
ejpam-3483	71	16	is	be	AUX
ejpam-3483	71	17	an	an	DET
ejpam-3483	71	18	increasing	increase	VERB
ejpam-3483	71	19	map	map	NOUN
ejpam-3483	71	20	,	,	PUNCT
ejpam-3483	71	21	then	then	ADV
ejpam-3483	71	22	the	the	DET
ejpam-3483	71	23	inverse	inverse	ADJ
ejpam-3483	71	24	image	image	NOUN
ejpam-3483	71	25	of	of	ADP
ejpam-3483	71	26	each	each	DET
ejpam-3483	71	27	an	an	DET
ejpam-3483	71	28	increasing	increase	VERB
ejpam-3483	71	29	(	(	PUNCT
ejpam-3483	71	30	resp	resp	NOUN
ejpam-3483	71	31	.	.	PUNCT
ejpam-3483	72	1	a	a	DET
ejpam-3483	72	2	decreasing	decrease	VERB
ejpam-3483	72	3	)	)	PUNCT
ejpam-3483	72	4	subset	subset	NOUN
ejpam-3483	72	5	of	of	ADP
ejpam-3483	72	6	y	y	PROPN
ejpam-3483	72	7	is	be	AUX
ejpam-3483	72	8	increasing	increase	VERB
ejpam-3483	72	9	(	(	PUNCT
ejpam-3483	72	10	resp	resp	NOUN
ejpam-3483	72	11	.	.	PUNCT
ejpam-3483	73	1	decreasing	decrease	VERB
ejpam-3483	73	2	)	)	PUNCT
ejpam-3483	73	3	.	.	PUNCT
ejpam-3483	74	1	(	(	PUNCT
ejpam-3483	74	2	ii	ii	NOUN
ejpam-3483	74	3	)	)	PUNCT
ejpam-3483	74	4	if	if	SCONJ
ejpam-3483	74	5	g	g	PROPN
ejpam-3483	74	6	:	:	PUNCT
ejpam-3483	74	7	(	(	PUNCT
ejpam-3483	74	8	x,	x,	NUM
ejpam-3483	74	9	�	�	NOUN
ejpam-3483	74	10	1	1	NUM
ejpam-3483	74	11	)	)	PUNCT
ejpam-3483	74	12	→	→	SYM
ejpam-3483	74	13	(	(	PUNCT
ejpam-3483	74	14	y,	y,	PROPN
ejpam-3483	74	15	�	�	PROPN
ejpam-3483	74	16	2	2	NUM
ejpam-3483	74	17	)	)	PUNCT
ejpam-3483	74	18	is	be	AUX
ejpam-3483	74	19	a	a	DET
ejpam-3483	74	20	decreasing	decrease	VERB
ejpam-3483	74	21	map	map	NOUN
ejpam-3483	74	22	,	,	PUNCT
ejpam-3483	74	23	then	then	ADV
ejpam-3483	74	24	the	the	DET
ejpam-3483	74	25	inverse	inverse	ADJ
ejpam-3483	74	26	image	image	NOUN
ejpam-3483	74	27	of	of	ADP
ejpam-3483	74	28	each	each	DET
ejpam-3483	74	29	an	an	DET
ejpam-3483	74	30	increasing	increase	VERB
ejpam-3483	74	31	(	(	PUNCT
ejpam-3483	74	32	resp	resp	NOUN
ejpam-3483	74	33	.	.	PUNCT
ejpam-3483	75	1	a	a	DET
ejpam-3483	75	2	decreasing	decrease	VERB
ejpam-3483	75	3	)	)	PUNCT
ejpam-3483	75	4	subset	subset	NOUN
ejpam-3483	75	5	of	of	ADP
ejpam-3483	75	6	y	y	PROPN
ejpam-3483	75	7	is	be	AUX
ejpam-3483	75	8	decreasing	decrease	VERB
ejpam-3483	75	9	(	(	PUNCT
ejpam-3483	75	10	resp	resp	NOUN
ejpam-3483	75	11	.	.	PUNCT
ejpam-3483	76	1	increasing	increase	VERB
ejpam-3483	76	2	)	)	PUNCT
ejpam-3483	76	3	.	.	PUNCT
ejpam-3483	77	1	definition	definition	NOUN
ejpam-3483	77	2	9	9	NUM
ejpam-3483	77	3	.	.	PUNCT
ejpam-3483	78	1	[	[	X
ejpam-3483	78	2	24	24	NUM
ejpam-3483	78	3	,	,	PUNCT
ejpam-3483	78	4	27	27	NUM
ejpam-3483	78	5	]	]	PUNCT
ejpam-3483	78	6	let	let	VERB
ejpam-3483	78	7	e	e	PRON
ejpam-3483	78	8	be	be	AUX
ejpam-3483	78	9	a	a	DET
ejpam-3483	78	10	subset	subset	NOUN
ejpam-3483	78	11	of	of	ADP
ejpam-3483	78	12	a	a	DET
ejpam-3483	78	13	supra	supra	ADJ
ejpam-3483	78	14	topological	topological	ADJ
ejpam-3483	78	15	space	space	NOUN
ejpam-3483	78	16	(	(	PUNCT
ejpam-3483	78	17	x,µ	x,µ	NOUN
ejpam-3483	78	18	)	)	PUNCT
ejpam-3483	78	19	.	.	PUNCT
ejpam-3483	79	1	then	then	ADV
ejpam-3483	79	2	:	:	PUNCT
ejpam-3483	79	3	(	(	PUNCT
ejpam-3483	79	4	i	i	NOUN
ejpam-3483	79	5	)	)	PUNCT
ejpam-3483	79	6	supra	supra	PROPN
ejpam-3483	79	7	interior	interior	NOUN
ejpam-3483	79	8	of	of	ADP
ejpam-3483	79	9	e	e	PROPN
ejpam-3483	79	10	,	,	PUNCT
ejpam-3483	79	11	denoted	denote	VERB
ejpam-3483	79	12	by	by	ADP
ejpam-3483	79	13	sint(e	sint(e	PROPN
ejpam-3483	79	14	)	)	PUNCT
ejpam-3483	79	15	,	,	PUNCT
ejpam-3483	79	16	is	be	AUX
ejpam-3483	79	17	the	the	DET
ejpam-3483	79	18	union	union	NOUN
ejpam-3483	79	19	of	of	ADP
ejpam-3483	79	20	all	all	DET
ejpam-3483	79	21	supra	supra	PROPN
ejpam-3483	79	22	open	open	ADJ
ejpam-3483	79	23	sets	set	NOUN
ejpam-3483	79	24	contained	contain	VERB
ejpam-3483	79	25	in	in	ADP
ejpam-3483	79	26	e.	e.	PROPN
ejpam-3483	79	27	(	(	PUNCT
ejpam-3483	79	28	ii	ii	PROPN
ejpam-3483	79	29	)	)	PUNCT
ejpam-3483	79	30	supra	supra	ADJ
ejpam-3483	79	31	closure	closure	NOUN
ejpam-3483	79	32	of	of	ADP
ejpam-3483	79	33	e	e	NOUN
ejpam-3483	79	34	,	,	PUNCT
ejpam-3483	79	35	denoted	denote	VERB
ejpam-3483	79	36	by	by	ADP
ejpam-3483	79	37	scl(e	scl(e	PROPN
ejpam-3483	79	38	)	)	PUNCT
ejpam-3483	79	39	,	,	PUNCT
ejpam-3483	79	40	is	be	AUX
ejpam-3483	79	41	the	the	DET
ejpam-3483	79	42	intersection	intersection	NOUN
ejpam-3483	79	43	of	of	ADP
ejpam-3483	79	44	all	all	DET
ejpam-3483	79	45	supra	supra	PROPN
ejpam-3483	79	46	closed	close	VERB
ejpam-3483	79	47	sets	set	NOUN
ejpam-3483	79	48	containing	contain	VERB
ejpam-3483	79	49	e.	e.	PROPN
ejpam-3483	79	50	(	(	PUNCT
ejpam-3483	79	51	iii	iii	PROPN
ejpam-3483	79	52	)	)	PUNCT
ejpam-3483	79	53	supra	supra	PROPN
ejpam-3483	79	54	b	b	PROPN
ejpam-3483	79	55	-	-	PUNCT
ejpam-3483	79	56	interior	interior	NOUN
ejpam-3483	79	57	of	of	ADP
ejpam-3483	79	58	e	e	PROPN
ejpam-3483	79	59	,	,	PUNCT
ejpam-3483	79	60	denoted	denote	VERB
ejpam-3483	79	61	by	by	ADP
ejpam-3483	79	62	sbint(e	sbint(e	PROPN
ejpam-3483	79	63	)	)	PUNCT
ejpam-3483	79	64	,	,	PUNCT
ejpam-3483	79	65	is	be	AUX
ejpam-3483	79	66	the	the	DET
ejpam-3483	79	67	union	union	NOUN
ejpam-3483	79	68	of	of	ADP
ejpam-3483	79	69	all	all	DET
ejpam-3483	79	70	supra	supra	PROPN
ejpam-3483	79	71	b	b	NOUN
ejpam-3483	79	72	-	-	PUNCT
ejpam-3483	79	73	open	open	ADJ
ejpam-3483	79	74	sets	set	NOUN
ejpam-3483	79	75	contained	contain	VERB
ejpam-3483	79	76	in	in	ADP
ejpam-3483	79	77	e.	e.	PROPN
ejpam-3483	79	78	(	(	PUNCT
ejpam-3483	79	79	iv	iv	PROPN
ejpam-3483	79	80	)	)	PUNCT
ejpam-3483	79	81	supra	supra	PROPN
ejpam-3483	79	82	b	b	NOUN
ejpam-3483	79	83	-	-	PUNCT
ejpam-3483	79	84	closure	closure	NOUN
ejpam-3483	79	85	of	of	ADP
ejpam-3483	79	86	e	e	NOUN
ejpam-3483	79	87	,	,	PUNCT
ejpam-3483	79	88	denoted	denote	VERB
ejpam-3483	79	89	by	by	ADP
ejpam-3483	79	90	sbcl(e	sbcl(e	PROPN
ejpam-3483	79	91	)	)	PUNCT
ejpam-3483	79	92	,	,	PUNCT
ejpam-3483	79	93	is	be	AUX
ejpam-3483	79	94	the	the	DET
ejpam-3483	79	95	intersection	intersection	NOUN
ejpam-3483	79	96	of	of	ADP
ejpam-3483	79	97	all	all	DET
ejpam-3483	79	98	supra	supra	PROPN
ejpam-3483	79	99	b	b	PROPN
ejpam-3483	79	100	-	-	PUNCT
ejpam-3483	79	101	closed	closed	ADJ
ejpam-3483	79	102	sets	set	NOUN
ejpam-3483	79	103	containing	contain	VERB
ejpam-3483	79	104	e.	e.	PROPN
ejpam-3483	79	105	definition	definition	NOUN
ejpam-3483	79	106	10	10	NUM
ejpam-3483	79	107	.	.	PUNCT
ejpam-3483	80	1	[	[	X
ejpam-3483	80	2	25	25	NUM
ejpam-3483	80	3	]	]	PUNCT
ejpam-3483	80	4	a	a	DET
ejpam-3483	80	5	topological	topological	ADJ
ejpam-3483	80	6	ordered	order	VERB
ejpam-3483	80	7	space	space	NOUN
ejpam-3483	80	8	(	(	PUNCT
ejpam-3483	80	9	x	x	X
ejpam-3483	80	10	,	,	PUNCT
ejpam-3483	80	11	τ	τ	PROPN
ejpam-3483	80	12	,	,	PUNCT
ejpam-3483	80	13	�	�	PROPN
ejpam-3483	80	14	)	)	PUNCT
ejpam-3483	80	15	is	be	AUX
ejpam-3483	80	16	called	call	VERB
ejpam-3483	80	17	:	:	PUNCT
ejpam-3483	80	18	(	(	PUNCT
ejpam-3483	80	19	i	i	NOUN
ejpam-3483	80	20	)	)	PUNCT
ejpam-3483	80	21	lower	low	ADJ
ejpam-3483	80	22	t1	t1	NOUN
ejpam-3483	80	23	-	-	PUNCT
ejpam-3483	80	24	ordered	order	VERB
ejpam-3483	80	25	if	if	SCONJ
ejpam-3483	80	26	for	for	ADP
ejpam-3483	80	27	each	each	DET
ejpam-3483	80	28	a	a	NOUN
ejpam-3483	80	29	,	,	PUNCT
ejpam-3483	80	30	b	b	X
ejpam-3483	80	31	∈	∈	PROPN
ejpam-3483	80	32	x	x	X
ejpam-3483	80	33	such	such	ADJ
ejpam-3483	80	34	that	that	SCONJ
ejpam-3483	80	35	a	a	DET
ejpam-3483	80	36	6	6	NUM
ejpam-3483	80	37	�	�	PROPN
ejpam-3483	80	38	b	b	PROPN
ejpam-3483	80	39	,	,	PUNCT
ejpam-3483	80	40	there	there	PRON
ejpam-3483	80	41	exists	exist	VERB
ejpam-3483	80	42	an	an	DET
ejpam-3483	80	43	increasing	increase	VERB
ejpam-3483	80	44	neighborhood	neighborhood	NOUN
ejpam-3483	80	45	g	g	NOUN
ejpam-3483	80	46	of	of	ADP
ejpam-3483	80	47	a	a	PRON
ejpam-3483	80	48	does	do	AUX
ejpam-3483	80	49	not	not	PART
ejpam-3483	80	50	contain	contain	VERB
ejpam-3483	80	51	b.	b.	PROPN
ejpam-3483	80	52	b.	b.	PROPN
ejpam-3483	80	53	a.	a.	PROPN
ejpam-3483	80	54	asaad	asaad	PROPN
ejpam-3483	80	55	,	,	PUNCT
ejpam-3483	80	56	m.	m.	PROPN
ejpam-3483	80	57	k.	k.	PROPN
ejpam-3483	80	58	tahat	tahat	PROPN
ejpam-3483	80	59	,	,	PUNCT
ejpam-3483	80	60	t.	t.	PROPN
ejpam-3483	80	61	m.	m.	PROPN
ejpam-3483	80	62	al	al	PROPN
ejpam-3483	80	63	-	-	PUNCT
ejpam-3483	80	64	shami	shami	PROPN
ejpam-3483	80	65	/	/	PUNCT
ejpam-3483	80	66	eur	eur	PROPN
ejpam-3483	80	67	.	.	PUNCT
ejpam-3483	81	1	j.	j.	PROPN
ejpam-3483	81	2	pure	pure	PROPN
ejpam-3483	81	3	appl	appl	PROPN
ejpam-3483	81	4	.	.	PROPN
ejpam-3483	81	5	math	math	PROPN
ejpam-3483	81	6	,	,	PUNCT
ejpam-3483	81	7	12	12	NUM
ejpam-3483	81	8	(	(	PUNCT
ejpam-3483	81	9	3	3	NUM
ejpam-3483	81	10	)	)	PUNCT
ejpam-3483	81	11	(	(	PUNCT
ejpam-3483	81	12	2019	2019	NUM
ejpam-3483	81	13	)	)	PUNCT
ejpam-3483	81	14	,	,	PUNCT
ejpam-3483	81	15	1231	1231	NUM
ejpam-3483	81	16	-	-	SYM
ejpam-3483	81	17	1247	1247	NUM
ejpam-3483	81	18	1234	1234	NUM
ejpam-3483	81	19	(	(	PUNCT
ejpam-3483	81	20	ii	ii	NOUN
ejpam-3483	81	21	)	)	PUNCT
ejpam-3483	81	22	upper	upper	ADJ
ejpam-3483	81	23	t1	t1	NOUN
ejpam-3483	81	24	-	-	PUNCT
ejpam-3483	81	25	ordered	order	VERB
ejpam-3483	81	26	if	if	SCONJ
ejpam-3483	81	27	for	for	ADP
ejpam-3483	81	28	each	each	DET
ejpam-3483	81	29	a	a	NOUN
ejpam-3483	81	30	,	,	PUNCT
ejpam-3483	81	31	b	b	X
ejpam-3483	81	32	∈	∈	PROPN
ejpam-3483	81	33	x	x	X
ejpam-3483	81	34	such	such	ADJ
ejpam-3483	81	35	that	that	SCONJ
ejpam-3483	81	36	a	a	DET
ejpam-3483	81	37	6	6	NUM
ejpam-3483	81	38	�	�	PROPN
ejpam-3483	81	39	b	b	PROPN
ejpam-3483	82	1	,	,	PUNCT
ejpam-3483	82	2	there	there	PRON
ejpam-3483	82	3	exists	exist	VERB
ejpam-3483	82	4	a	a	DET
ejpam-3483	82	5	decreasing	decrease	VERB
ejpam-3483	82	6	neighborhood	neighborhood	NOUN
ejpam-3483	82	7	g	g	NOUN
ejpam-3483	82	8	of	of	ADP
ejpam-3483	82	9	b	b	NOUN
ejpam-3483	82	10	does	do	AUX
ejpam-3483	82	11	not	not	PART
ejpam-3483	82	12	contain	contain	VERB
ejpam-3483	82	13	a.	a.	NOUN
ejpam-3483	82	14	(	(	PUNCT
ejpam-3483	82	15	iii	iii	NOUN
ejpam-3483	82	16	)	)	PUNCT
ejpam-3483	82	17	t0	t0	NOUN
ejpam-3483	82	18	-	-	PUNCT
ejpam-3483	82	19	ordered	order	VERB
ejpam-3483	82	20	if	if	SCONJ
ejpam-3483	82	21	it	it	PRON
ejpam-3483	82	22	is	be	AUX
ejpam-3483	82	23	lower	low	ADJ
ejpam-3483	82	24	t1	t1	NOUN
ejpam-3483	82	25	-	-	PUNCT
ejpam-3483	82	26	ordered	ordered	ADJ
ejpam-3483	82	27	or	or	CCONJ
ejpam-3483	82	28	upper	upper	ADJ
ejpam-3483	82	29	t1	t1	NOUN
ejpam-3483	82	30	-	-	PUNCT
ejpam-3483	82	31	ordered	order	VERB
ejpam-3483	82	32	.	.	PUNCT
ejpam-3483	83	1	(	(	PUNCT
ejpam-3483	83	2	iv	iv	X
ejpam-3483	83	3	)	)	PUNCT
ejpam-3483	83	4	t1	t1	NOUN
ejpam-3483	83	5	-	-	PUNCT
ejpam-3483	83	6	ordered	order	VERB
ejpam-3483	83	7	if	if	SCONJ
ejpam-3483	83	8	it	it	PRON
ejpam-3483	83	9	is	be	AUX
ejpam-3483	83	10	both	both	CCONJ
ejpam-3483	83	11	lower	low	ADJ
ejpam-3483	83	12	t1	t1	NOUN
ejpam-3483	83	13	-	-	PUNCT
ejpam-3483	83	14	ordered	order	VERB
ejpam-3483	83	15	and	and	CCONJ
ejpam-3483	83	16	upper	upper	ADJ
ejpam-3483	83	17	t1	t1	NOUN
ejpam-3483	83	18	-	-	PUNCT
ejpam-3483	83	19	ordered	order	VERB
ejpam-3483	83	20	.	.	PUNCT
ejpam-3483	84	1	(	(	PUNCT
ejpam-3483	84	2	v	v	NOUN
ejpam-3483	84	3	)	)	PUNCT
ejpam-3483	84	4	t2	t2	NOUN
ejpam-3483	84	5	-	-	PUNCT
ejpam-3483	84	6	ordered	order	VERB
ejpam-3483	84	7	if	if	SCONJ
ejpam-3483	84	8	for	for	ADP
ejpam-3483	84	9	every	every	DET
ejpam-3483	84	10	a	a	PROPN
ejpam-3483	84	11	,	,	PUNCT
ejpam-3483	84	12	b	b	X
ejpam-3483	84	13	∈	∈	PROPN
ejpam-3483	84	14	x	x	X
ejpam-3483	84	15	such	such	ADJ
ejpam-3483	84	16	that	that	SCONJ
ejpam-3483	84	17	a	a	DET
ejpam-3483	84	18	6	6	NUM
ejpam-3483	84	19	�	�	PROPN
ejpam-3483	84	20	b	b	NOUN
ejpam-3483	84	21	,	,	PUNCT
ejpam-3483	84	22	there	there	PRON
ejpam-3483	84	23	exist	exist	VERB
ejpam-3483	84	24	an	an	DET
ejpam-3483	84	25	increasing	increase	VERB
ejpam-3483	84	26	neighborhood	neighborhood	NOUN
ejpam-3483	84	27	w1	w1	NOUN
ejpam-3483	84	28	of	of	ADP
ejpam-3483	84	29	a	a	PRON
ejpam-3483	84	30	and	and	CCONJ
ejpam-3483	84	31	a	a	DET
ejpam-3483	84	32	decreasing	decrease	VERB
ejpam-3483	84	33	w2	w2	NOUN
ejpam-3483	84	34	of	of	ADP
ejpam-3483	84	35	b	b	PROPN
ejpam-3483	84	36	such	such	ADJ
ejpam-3483	84	37	that	that	DET
ejpam-3483	84	38	w1	w1	NOUN
ejpam-3483	84	39	⋂	⋂	PROPN
ejpam-3483	84	40	w2	w2	NOUN
ejpam-3483	84	41	=	=	PRON
ejpam-3483	84	42	∅.	∅.	NOUN
ejpam-3483	84	43	remark	remark	NOUN
ejpam-3483	84	44	1	1	NUM
ejpam-3483	84	45	.	.	PUNCT
ejpam-3483	84	46	mccartan	mccartan	PROPN
ejpam-3483	85	1	[	[	X
ejpam-3483	85	2	25	25	NUM
ejpam-3483	85	3	]	]	PUNCT
ejpam-3483	85	4	named	name	VERB
ejpam-3483	85	5	the	the	DET
ejpam-3483	85	6	axioms	axiom	NOUN
ejpam-3483	85	7	mentioned	mention	VERB
ejpam-3483	85	8	in	in	ADP
ejpam-3483	85	9	the	the	DET
ejpam-3483	85	10	above	above	ADJ
ejpam-3483	85	11	definition	definition	NOUN
ejpam-3483	85	12	,	,	PUNCT
ejpam-3483	85	13	strong	strong	ADJ
ejpam-3483	85	14	ti	ti	ADJ
ejpam-3483	85	15	-	-	ADJ
ejpam-3483	85	16	ordered	order	VERB
ejpam-3483	85	17	spaces	space	NOUN
ejpam-3483	85	18	instead	instead	ADV
ejpam-3483	85	19	of	of	ADP
ejpam-3483	85	20	ti	ti	ADV
ejpam-3483	85	21	-	-	ADJ
ejpam-3483	85	22	ordered	order	VERB
ejpam-3483	85	23	spaces	space	NOUN
ejpam-3483	85	24	when	when	SCONJ
ejpam-3483	85	25	the	the	DET
ejpam-3483	85	26	word	word	NOUN
ejpam-3483	85	27	of	of	ADP
ejpam-3483	85	28	a	a	DET
ejpam-3483	85	29	neighborhood	neighborhood	NOUN
ejpam-3483	85	30	is	be	AUX
ejpam-3483	85	31	replaced	replace	VERB
ejpam-3483	85	32	by	by	ADP
ejpam-3483	85	33	an	an	DET
ejpam-3483	85	34	open	open	ADJ
ejpam-3483	85	35	set	set	NOUN
ejpam-3483	85	36	.	.	PUNCT
ejpam-3483	86	1	definition	definition	NOUN
ejpam-3483	86	2	11	11	NUM
ejpam-3483	86	3	.	.	PUNCT
ejpam-3483	87	1	[	[	X
ejpam-3483	87	2	20	20	NUM
ejpam-3483	87	3	]	]	PUNCT
ejpam-3483	87	4	a	a	DET
ejpam-3483	87	5	supra	supra	PROPN
ejpam-3483	87	6	topological	topological	ADJ
ejpam-3483	87	7	ordered	order	VERB
ejpam-3483	87	8	space	space	NOUN
ejpam-3483	87	9	(	(	PUNCT
ejpam-3483	87	10	x,µ	x,µ	NOUN
ejpam-3483	87	11	,	,	PUNCT
ejpam-3483	87	12	�	�	PROPN
ejpam-3483	87	13	)	)	PUNCT
ejpam-3483	87	14	is	be	AUX
ejpam-3483	87	15	called	call	VERB
ejpam-3483	87	16	:	:	PUNCT
ejpam-3483	87	17	(	(	PUNCT
ejpam-3483	87	18	i	i	NOUN
ejpam-3483	87	19	)	)	PUNCT
ejpam-3483	87	20	lower	low	ADJ
ejpam-3483	87	21	sst1	sst1	NOUN
ejpam-3483	87	22	-	-	PUNCT
ejpam-3483	87	23	ordered	order	VERB
ejpam-3483	87	24	if	if	SCONJ
ejpam-3483	87	25	for	for	ADP
ejpam-3483	87	26	each	each	DET
ejpam-3483	87	27	a	a	NOUN
ejpam-3483	87	28	,	,	PUNCT
ejpam-3483	87	29	b	b	X
ejpam-3483	87	30	∈	∈	PROPN
ejpam-3483	87	31	x	x	X
ejpam-3483	87	32	such	such	ADJ
ejpam-3483	87	33	that	that	SCONJ
ejpam-3483	87	34	a	a	DET
ejpam-3483	87	35	6	6	NUM
ejpam-3483	87	36	�	�	PROPN
ejpam-3483	87	37	b	b	PROPN
ejpam-3483	87	38	,	,	PUNCT
ejpam-3483	87	39	there	there	PRON
ejpam-3483	87	40	exists	exist	VERB
ejpam-3483	87	41	an	an	DET
ejpam-3483	87	42	increasing	increase	VERB
ejpam-3483	87	43	supra	supra	NOUN
ejpam-3483	87	44	open	open	ADJ
ejpam-3483	87	45	set	set	VERB
ejpam-3483	87	46	g	g	NOUN
ejpam-3483	87	47	containing	contain	VERB
ejpam-3483	87	48	a	a	PRON
ejpam-3483	87	49	does	do	AUX
ejpam-3483	87	50	not	not	PART
ejpam-3483	87	51	contain	contain	VERB
ejpam-3483	87	52	b.	b.	PROPN
ejpam-3483	87	53	(	(	PUNCT
ejpam-3483	87	54	ii	ii	NOUN
ejpam-3483	87	55	)	)	PUNCT
ejpam-3483	87	56	upper	upper	ADJ
ejpam-3483	87	57	sst1	sst1	NOUN
ejpam-3483	87	58	-	-	PUNCT
ejpam-3483	87	59	ordered	order	VERB
ejpam-3483	87	60	if	if	SCONJ
ejpam-3483	87	61	for	for	ADP
ejpam-3483	87	62	each	each	DET
ejpam-3483	87	63	a	a	NOUN
ejpam-3483	87	64	,	,	PUNCT
ejpam-3483	87	65	b	b	X
ejpam-3483	87	66	∈	∈	PROPN
ejpam-3483	87	67	x	x	X
ejpam-3483	87	68	such	such	ADJ
ejpam-3483	87	69	that	that	SCONJ
ejpam-3483	87	70	a	a	DET
ejpam-3483	87	71	6	6	NUM
ejpam-3483	87	72	�	�	PROPN
ejpam-3483	87	73	b	b	PROPN
ejpam-3483	87	74	,	,	PUNCT
ejpam-3483	87	75	there	there	PRON
ejpam-3483	87	76	exists	exist	VERB
ejpam-3483	87	77	a	a	DET
ejpam-3483	87	78	decreasing	decrease	VERB
ejpam-3483	87	79	supra	supra	NOUN
ejpam-3483	87	80	open	open	ADJ
ejpam-3483	87	81	set	set	VERB
ejpam-3483	87	82	g	g	NOUN
ejpam-3483	87	83	containing	contain	VERB
ejpam-3483	87	84	b	b	NOUN
ejpam-3483	87	85	does	do	AUX
ejpam-3483	87	86	not	not	PART
ejpam-3483	87	87	contain	contain	VERB
ejpam-3483	87	88	a.	a.	NOUN
ejpam-3483	87	89	(	(	PUNCT
ejpam-3483	87	90	iii	iii	NOUN
ejpam-3483	87	91	)	)	PUNCT
ejpam-3483	87	92	sst0	sst0	PROPN
ejpam-3483	87	93	-	-	PUNCT
ejpam-3483	87	94	ordered	order	VERB
ejpam-3483	87	95	if	if	SCONJ
ejpam-3483	87	96	it	it	PRON
ejpam-3483	87	97	is	be	AUX
ejpam-3483	87	98	lower	low	ADJ
ejpam-3483	87	99	sst1	sst1	NOUN
ejpam-3483	87	100	-	-	PUNCT
ejpam-3483	87	101	ordered	order	VERB
ejpam-3483	87	102	or	or	CCONJ
ejpam-3483	87	103	upper	upper	ADJ
ejpam-3483	87	104	sst1	sst1	NOUN
ejpam-3483	87	105	-	-	PUNCT
ejpam-3483	87	106	ordered	order	VERB
ejpam-3483	87	107	.	.	PUNCT
ejpam-3483	88	1	(	(	PUNCT
ejpam-3483	88	2	iv	iv	X
ejpam-3483	88	3	)	)	PUNCT
ejpam-3483	88	4	sst1	sst1	NOUN
ejpam-3483	88	5	-	-	PUNCT
ejpam-3483	88	6	ordered	order	VERB
ejpam-3483	88	7	if	if	SCONJ
ejpam-3483	88	8	it	it	PRON
ejpam-3483	88	9	is	be	AUX
ejpam-3483	88	10	both	both	PRON
ejpam-3483	88	11	lower	low	ADJ
ejpam-3483	88	12	sst1	sst1	NOUN
ejpam-3483	88	13	-	-	PUNCT
ejpam-3483	88	14	ordered	order	VERB
ejpam-3483	88	15	and	and	CCONJ
ejpam-3483	88	16	upper	upper	ADJ
ejpam-3483	88	17	t1	t1	NOUN
ejpam-3483	88	18	-	-	PUNCT
ejpam-3483	88	19	ordered	order	VERB
ejpam-3483	88	20	.	.	PUNCT
ejpam-3483	89	1	(	(	PUNCT
ejpam-3483	89	2	v	v	NOUN
ejpam-3483	89	3	)	)	PUNCT
ejpam-3483	89	4	sst2	sst2	NOUN
ejpam-3483	89	5	-	-	PUNCT
ejpam-3483	89	6	ordered	order	VERB
ejpam-3483	89	7	if	if	SCONJ
ejpam-3483	89	8	for	for	ADP
ejpam-3483	89	9	every	every	DET
ejpam-3483	89	10	a	a	PROPN
ejpam-3483	89	11	,	,	PUNCT
ejpam-3483	89	12	b	b	X
ejpam-3483	89	13	∈	∈	PROPN
ejpam-3483	89	14	x	x	X
ejpam-3483	89	15	such	such	ADJ
ejpam-3483	89	16	that	that	SCONJ
ejpam-3483	89	17	a	a	DET
ejpam-3483	89	18	6	6	NUM
ejpam-3483	89	19	�	�	PROPN
ejpam-3483	89	20	b	b	NOUN
ejpam-3483	89	21	,	,	PUNCT
ejpam-3483	89	22	there	there	PRON
ejpam-3483	89	23	exist	exist	VERB
ejpam-3483	89	24	a	a	DET
ejpam-3483	89	25	supra	supra	PROPN
ejpam-3483	89	26	open	open	ADJ
ejpam-3483	89	27	set	set	VERB
ejpam-3483	89	28	w1	w1	NOUN
ejpam-3483	89	29	containing	contain	VERB
ejpam-3483	89	30	a	a	PRON
ejpam-3483	89	31	and	and	CCONJ
ejpam-3483	89	32	a	a	DET
ejpam-3483	89	33	supra	supra	PROPN
ejpam-3483	89	34	open	open	ADJ
ejpam-3483	89	35	set	set	VERB
ejpam-3483	89	36	w2	w2	NOUN
ejpam-3483	89	37	containing	contain	VERB
ejpam-3483	89	38	b	b	PROPN
ejpam-3483	89	39	such	such	ADJ
ejpam-3483	89	40	that	that	DET
ejpam-3483	89	41	w1	w1	NOUN
ejpam-3483	89	42	⋂	⋂	PROPN
ejpam-3483	89	43	w2	w2	NOUN
ejpam-3483	89	44	=	=	PUNCT
ejpam-3483	89	45	∅.	∅.	PRON
ejpam-3483	89	46	3	3	NUM
ejpam-3483	89	47	.	.	PUNCT
ejpam-3483	90	1	supra	supra	PROPN
ejpam-3483	90	2	b	b	X
ejpam-3483	90	3	-	-	PUNCT
ejpam-3483	90	4	continuous	continuous	ADJ
ejpam-3483	90	5	maps	map	NOUN
ejpam-3483	90	6	the	the	DET
ejpam-3483	90	7	concepts	concept	NOUN
ejpam-3483	90	8	of	of	ADP
ejpam-3483	90	9	i	i	PROPN
ejpam-3483	90	10	-	-	PUNCT
ejpam-3483	90	11	supra	supra	PROPN
ejpam-3483	91	1	b	b	NOUN
ejpam-3483	91	2	-	-	PUNCT
ejpam-3483	91	3	continuous	continuous	ADJ
ejpam-3483	91	4	,	,	PUNCT
ejpam-3483	91	5	d	d	ADJ
ejpam-3483	91	6	-	-	PUNCT
ejpam-3483	91	7	supra	supra	ADJ
ejpam-3483	91	8	b	b	NOUN
ejpam-3483	91	9	-	-	PUNCT
ejpam-3483	91	10	continuous	continuous	ADJ
ejpam-3483	91	11	and	and	CCONJ
ejpam-3483	91	12	b	b	NOUN
ejpam-3483	91	13	-	-	PUNCT
ejpam-3483	91	14	supra	supra	ADJ
ejpam-3483	91	15	b	b	NOUN
ejpam-3483	91	16	-	-	PUNCT
ejpam-3483	91	17	continuous	continuous	ADJ
ejpam-3483	91	18	maps	map	NOUN
ejpam-3483	91	19	are	be	AUX
ejpam-3483	91	20	presented	present	VERB
ejpam-3483	91	21	and	and	CCONJ
ejpam-3483	91	22	their	their	PRON
ejpam-3483	91	23	main	main	ADJ
ejpam-3483	91	24	properties	property	NOUN
ejpam-3483	91	25	are	be	AUX
ejpam-3483	91	26	investigated	investigate	VERB
ejpam-3483	91	27	.	.	PUNCT
ejpam-3483	92	1	the	the	DET
ejpam-3483	92	2	relationships	relationship	NOUN
ejpam-3483	92	3	among	among	ADP
ejpam-3483	92	4	them	they	PRON
ejpam-3483	92	5	are	be	AUX
ejpam-3483	92	6	illustrated	illustrate	VERB
ejpam-3483	92	7	with	with	ADP
ejpam-3483	92	8	the	the	DET
ejpam-3483	92	9	help	help	NOUN
ejpam-3483	92	10	of	of	ADP
ejpam-3483	92	11	examples	example	NOUN
ejpam-3483	92	12	.	.	PUNCT
ejpam-3483	93	1	the	the	DET
ejpam-3483	93	2	conditions	condition	NOUN
ejpam-3483	93	3	under	under	ADP
ejpam-3483	93	4	which	which	PRON
ejpam-3483	93	5	such	such	DET
ejpam-3483	93	6	these	these	DET
ejpam-3483	93	7	types	type	NOUN
ejpam-3483	93	8	of	of	ADP
ejpam-3483	93	9	supra	supra	PROPN
ejpam-3483	93	10	b	b	PROPN
ejpam-3483	93	11	-	-	PUNCT
ejpam-3483	93	12	continuous	continuous	ADJ
ejpam-3483	93	13	maps	map	NOUN
ejpam-3483	93	14	preserve	preserve	VERB
ejpam-3483	93	15	some	some	DET
ejpam-3483	93	16	ordered	order	VERB
ejpam-3483	93	17	supra	supra	PROPN
ejpam-3483	93	18	b	b	NOUN
ejpam-3483	93	19	-	-	PUNCT
ejpam-3483	93	20	separation	separation	NOUN
ejpam-3483	93	21	axioms	axiom	NOUN
ejpam-3483	93	22	are	be	AUX
ejpam-3483	93	23	studied	study	VERB
ejpam-3483	93	24	.	.	PUNCT
ejpam-3483	94	1	definition	definition	NOUN
ejpam-3483	94	2	12	12	NUM
ejpam-3483	94	3	.	.	PUNCT
ejpam-3483	95	1	a	a	DET
ejpam-3483	95	2	subset	subset	ADJ
ejpam-3483	95	3	e	e	X
ejpam-3483	95	4	of	of	ADP
ejpam-3483	95	5	(	(	PUNCT
ejpam-3483	95	6	x,µ	x,µ	NOUN
ejpam-3483	95	7	,	,	PUNCT
ejpam-3483	95	8	�	�	PROPN
ejpam-3483	95	9	)	)	PUNCT
ejpam-3483	95	10	is	be	AUX
ejpam-3483	95	11	said	say	VERB
ejpam-3483	95	12	to	to	PART
ejpam-3483	95	13	be	be	AUX
ejpam-3483	95	14	:	:	PUNCT
ejpam-3483	95	15	(	(	PUNCT
ejpam-3483	95	16	i	i	NOUN
ejpam-3483	95	17	)	)	PUNCT
ejpam-3483	95	18	i	i	PROPN
ejpam-3483	95	19	-	-	PUNCT
ejpam-3483	95	20	supra	supra	PROPN
ejpam-3483	95	21	(	(	PUNCT
ejpam-3483	95	22	resp	resp	NOUN
ejpam-3483	95	23	.	.	PUNCT
ejpam-3483	96	1	d	d	X
ejpam-3483	96	2	-	-	PUNCT
ejpam-3483	96	3	supra	supra	ADJ
ejpam-3483	96	4	,	,	PUNCT
ejpam-3483	96	5	b	b	NOUN
ejpam-3483	96	6	-	-	PUNCT
ejpam-3483	96	7	supra	supra	ADJ
ejpam-3483	96	8	)	)	PUNCT
ejpam-3483	96	9	b	b	X
ejpam-3483	96	10	-	-	PUNCT
ejpam-3483	96	11	open	open	ADJ
ejpam-3483	96	12	if	if	SCONJ
ejpam-3483	96	13	it	it	PRON
ejpam-3483	96	14	is	be	AUX
ejpam-3483	96	15	supra	supra	ADJ
ejpam-3483	96	16	b	b	NOUN
ejpam-3483	96	17	-	-	PUNCT
ejpam-3483	96	18	open	open	ADJ
ejpam-3483	96	19	and	and	CCONJ
ejpam-3483	96	20	increasing	increase	VERB
ejpam-3483	96	21	(	(	PUNCT
ejpam-3483	96	22	resp	resp	NOUN
ejpam-3483	96	23	.	.	PUNCT
ejpam-3483	97	1	decreasing	decrease	VERB
ejpam-3483	97	2	,	,	PUNCT
ejpam-3483	97	3	balancing	balancing	NOUN
ejpam-3483	97	4	)	)	PUNCT
ejpam-3483	97	5	.	.	PUNCT
ejpam-3483	98	1	(	(	PUNCT
ejpam-3483	98	2	ii	ii	X
ejpam-3483	98	3	)	)	PUNCT
ejpam-3483	98	4	i	i	PROPN
ejpam-3483	98	5	-	-	PUNCT
ejpam-3483	98	6	supra	supra	PROPN
ejpam-3483	98	7	(	(	PUNCT
ejpam-3483	98	8	resp	resp	NOUN
ejpam-3483	98	9	.	.	PUNCT
ejpam-3483	99	1	d	d	X
ejpam-3483	99	2	-	-	PUNCT
ejpam-3483	99	3	supra	supra	ADJ
ejpam-3483	99	4	,	,	PUNCT
ejpam-3483	99	5	b	b	NOUN
ejpam-3483	99	6	-	-	PUNCT
ejpam-3483	99	7	supra	supra	ADJ
ejpam-3483	99	8	)	)	PUNCT
ejpam-3483	99	9	b	b	X
ejpam-3483	99	10	-	-	PUNCT
ejpam-3483	99	11	closed	closed	ADJ
ejpam-3483	99	12	if	if	SCONJ
ejpam-3483	99	13	it	it	PRON
ejpam-3483	99	14	is	be	AUX
ejpam-3483	99	15	supra	supra	ADJ
ejpam-3483	99	16	b	b	PROPN
ejpam-3483	99	17	-	-	PUNCT
ejpam-3483	99	18	closed	closed	ADJ
ejpam-3483	99	19	and	and	CCONJ
ejpam-3483	99	20	increasing	increase	VERB
ejpam-3483	99	21	(	(	PUNCT
ejpam-3483	99	22	resp	resp	NOUN
ejpam-3483	99	23	.	.	PUNCT
ejpam-3483	100	1	decreasing	decrease	VERB
ejpam-3483	100	2	,	,	PUNCT
ejpam-3483	100	3	balancing	balancing	NOUN
ejpam-3483	100	4	)	)	PUNCT
ejpam-3483	100	5	.	.	PUNCT
ejpam-3483	101	1	definition	definition	NOUN
ejpam-3483	101	2	13	13	NUM
ejpam-3483	101	3	.	.	PUNCT
ejpam-3483	102	1	a	a	DET
ejpam-3483	102	2	map	map	NOUN
ejpam-3483	102	3	f	f	X
ejpam-3483	102	4	:	:	PUNCT
ejpam-3483	102	5	(	(	PUNCT
ejpam-3483	102	6	x,µ,	x,µ,	PROPN
ejpam-3483	102	7	�	�	PROPN
ejpam-3483	102	8	)→	)→	PROPN
ejpam-3483	102	9	(	(	PUNCT
ejpam-3483	102	10	y	y	PROPN
ejpam-3483	102	11	,	,	PUNCT
ejpam-3483	102	12	τ	τ	PROPN
ejpam-3483	102	13	)	)	PUNCT
ejpam-3483	102	14	is	be	AUX
ejpam-3483	102	15	said	say	VERB
ejpam-3483	102	16	to	to	PART
ejpam-3483	102	17	be	be	AUX
ejpam-3483	102	18	:	:	PUNCT
ejpam-3483	102	19	b.	b.	PROPN
ejpam-3483	102	20	a.	a.	PROPN
ejpam-3483	102	21	asaad	asaad	PROPN
ejpam-3483	102	22	,	,	PUNCT
ejpam-3483	102	23	m.	m.	PROPN
ejpam-3483	102	24	k.	k.	PROPN
ejpam-3483	102	25	tahat	tahat	PROPN
ejpam-3483	102	26	,	,	PUNCT
ejpam-3483	102	27	t.	t.	PROPN
ejpam-3483	102	28	m.	m.	PROPN
ejpam-3483	102	29	al	al	PROPN
ejpam-3483	102	30	-	-	PUNCT
ejpam-3483	102	31	shami	shami	PROPN
ejpam-3483	102	32	/	/	PUNCT
ejpam-3483	102	33	eur	eur	PROPN
ejpam-3483	102	34	.	.	PUNCT
ejpam-3483	103	1	j.	j.	PROPN
ejpam-3483	103	2	pure	pure	PROPN
ejpam-3483	103	3	appl	appl	PROPN
ejpam-3483	103	4	.	.	PROPN
ejpam-3483	103	5	math	math	PROPN
ejpam-3483	103	6	,	,	PUNCT
ejpam-3483	103	7	12	12	NUM
ejpam-3483	103	8	(	(	PUNCT
ejpam-3483	103	9	3	3	NUM
ejpam-3483	103	10	)	)	PUNCT
ejpam-3483	103	11	(	(	PUNCT
ejpam-3483	103	12	2019	2019	NUM
ejpam-3483	103	13	)	)	PUNCT
ejpam-3483	103	14	,	,	PUNCT
ejpam-3483	103	15	1231	1231	NUM
ejpam-3483	103	16	-	-	SYM
ejpam-3483	103	17	1247	1247	NUM
ejpam-3483	103	18	1235	1235	NUM
ejpam-3483	103	19	(	(	PUNCT
ejpam-3483	103	20	i	i	NOUN
ejpam-3483	103	21	)	)	PUNCT
ejpam-3483	103	22	i	i	PROPN
ejpam-3483	103	23	-	-	PUNCT
ejpam-3483	103	24	supra	supra	PROPN
ejpam-3483	103	25	(	(	PUNCT
ejpam-3483	103	26	resp	resp	NOUN
ejpam-3483	103	27	.	.	PUNCT
ejpam-3483	104	1	d	d	X
ejpam-3483	104	2	-	-	PUNCT
ejpam-3483	104	3	supra	supra	ADJ
ejpam-3483	104	4	,	,	PUNCT
ejpam-3483	104	5	b	b	NOUN
ejpam-3483	104	6	-	-	PUNCT
ejpam-3483	104	7	supra	supra	ADJ
ejpam-3483	104	8	)	)	PUNCT
ejpam-3483	105	1	b	b	X
ejpam-3483	105	2	-	-	PUNCT
ejpam-3483	105	3	continuous	continuous	ADJ
ejpam-3483	105	4	at	at	ADP
ejpam-3483	105	5	p	p	PROPN
ejpam-3483	105	6	∈	∈	PROPN
ejpam-3483	105	7	x	x	PUNCT
ejpam-3483	105	8	if	if	SCONJ
ejpam-3483	105	9	for	for	ADP
ejpam-3483	105	10	each	each	DET
ejpam-3483	105	11	open	open	ADJ
ejpam-3483	105	12	set	set	VERB
ejpam-3483	105	13	h	h	NOUN
ejpam-3483	105	14	containing	contain	VERB
ejpam-3483	105	15	f(p	f(p	PROPN
ejpam-3483	105	16	)	)	PUNCT
ejpam-3483	105	17	,	,	PUNCT
ejpam-3483	105	18	there	there	PRON
ejpam-3483	105	19	exists	exist	VERB
ejpam-3483	105	20	an	an	DET
ejpam-3483	105	21	i	i	NOUN
ejpam-3483	105	22	-	-	PUNCT
ejpam-3483	105	23	supra	supra	PROPN
ejpam-3483	105	24	(	(	PUNCT
ejpam-3483	105	25	resp	resp	NOUN
ejpam-3483	105	26	.	.	PUNCT
ejpam-3483	106	1	a	a	DET
ejpam-3483	106	2	d	d	NOUN
ejpam-3483	106	3	-	-	PUNCT
ejpam-3483	106	4	supra	supra	ADJ
ejpam-3483	106	5	,	,	PUNCT
ejpam-3483	106	6	a	a	DET
ejpam-3483	106	7	b	b	NOUN
ejpam-3483	106	8	-	-	PUNCT
ejpam-3483	106	9	supra	supra	ADJ
ejpam-3483	106	10	)	)	PUNCT
ejpam-3483	106	11	b	b	X
ejpam-3483	106	12	-	-	PUNCT
ejpam-3483	106	13	open	open	ADJ
ejpam-3483	106	14	set	set	NOUN
ejpam-3483	106	15	g	g	NOUN
ejpam-3483	106	16	containing	contain	VERB
ejpam-3483	106	17	p	p	NOUN
ejpam-3483	106	18	such	such	ADJ
ejpam-3483	106	19	that	that	DET
ejpam-3483	106	20	f(g	f(g	NOUN
ejpam-3483	106	21	)	)	PUNCT
ejpam-3483	106	22	⊆	⊆	NUM
ejpam-3483	106	23	h.	h.	PROPN
ejpam-3483	106	24	(	(	PUNCT
ejpam-3483	106	25	ii	ii	NOUN
ejpam-3483	106	26	)	)	PUNCT
ejpam-3483	106	27	i	i	PROPN
ejpam-3483	106	28	-	-	PUNCT
ejpam-3483	106	29	supra	supra	PROPN
ejpam-3483	106	30	(	(	PUNCT
ejpam-3483	106	31	resp	resp	NOUN
ejpam-3483	106	32	.	.	PUNCT
ejpam-3483	107	1	d	d	X
ejpam-3483	107	2	-	-	PUNCT
ejpam-3483	107	3	supra	supra	ADJ
ejpam-3483	107	4	,	,	PUNCT
ejpam-3483	107	5	b	b	NOUN
ejpam-3483	107	6	-	-	PUNCT
ejpam-3483	107	7	supra	supra	ADJ
ejpam-3483	107	8	)	)	PUNCT
ejpam-3483	108	1	b	b	NOUN
ejpam-3483	108	2	-	-	PUNCT
ejpam-3483	108	3	continuous	continuous	ADJ
ejpam-3483	108	4	if	if	SCONJ
ejpam-3483	108	5	it	it	PRON
ejpam-3483	108	6	is	be	AUX
ejpam-3483	108	7	i	i	PROPN
ejpam-3483	108	8	-	-	PUNCT
ejpam-3483	108	9	supra	supra	PROPN
ejpam-3483	108	10	(	(	PUNCT
ejpam-3483	108	11	resp	resp	NOUN
ejpam-3483	108	12	.	.	PUNCT
ejpam-3483	109	1	d	d	X
ejpam-3483	109	2	-	-	PUNCT
ejpam-3483	109	3	supra	supra	ADJ
ejpam-3483	109	4	,	,	PUNCT
ejpam-3483	109	5	b	b	NOUN
ejpam-3483	109	6	-	-	PUNCT
ejpam-3483	109	7	supra	supra	ADJ
ejpam-3483	109	8	)	)	PUNCT
ejpam-3483	110	1	b	b	X
ejpam-3483	110	2	-	-	PUNCT
ejpam-3483	110	3	continuous	continuous	ADJ
ejpam-3483	110	4	at	at	ADP
ejpam-3483	110	5	each	each	DET
ejpam-3483	110	6	point	point	NOUN
ejpam-3483	110	7	p	p	PROPN
ejpam-3483	110	8	∈	∈	PROPN
ejpam-3483	110	9	x.	x.	NOUN
ejpam-3483	110	10	theorem	theorem	VERB
ejpam-3483	110	11	2	2	NUM
ejpam-3483	110	12	.	.	PUNCT
ejpam-3483	111	1	a	a	DET
ejpam-3483	111	2	map	map	NOUN
ejpam-3483	111	3	f	f	X
ejpam-3483	111	4	:	:	PUNCT
ejpam-3483	111	5	(	(	PUNCT
ejpam-3483	111	6	x,µ	x,µ	NOUN
ejpam-3483	111	7	,	,	PUNCT
ejpam-3483	111	8	�	�	PROPN
ejpam-3483	111	9	)	)	PUNCT
ejpam-3483	111	10	→	→	SYM
ejpam-3483	111	11	(	(	PUNCT
ejpam-3483	111	12	y	y	PROPN
ejpam-3483	111	13	,	,	PUNCT
ejpam-3483	111	14	τ	τ	PROPN
ejpam-3483	111	15	)	)	PUNCT
ejpam-3483	111	16	is	be	AUX
ejpam-3483	111	17	i	i	PROPN
ejpam-3483	111	18	-	-	PUNCT
ejpam-3483	111	19	supra	supra	PROPN
ejpam-3483	111	20	(	(	PUNCT
ejpam-3483	111	21	resp	resp	NOUN
ejpam-3483	111	22	.	.	PUNCT
ejpam-3483	112	1	d	d	X
ejpam-3483	112	2	-	-	PUNCT
ejpam-3483	112	3	supra	supra	ADJ
ejpam-3483	112	4	,	,	PUNCT
ejpam-3483	112	5	b	b	NOUN
ejpam-3483	112	6	-	-	PUNCT
ejpam-3483	112	7	supra	supra	ADJ
ejpam-3483	112	8	)	)	PUNCT
ejpam-3483	113	1	bcontinuous	bcontinuous	ADJ
ejpam-3483	113	2	if	if	SCONJ
ejpam-3483	113	3	and	and	CCONJ
ejpam-3483	113	4	only	only	ADV
ejpam-3483	113	5	if	if	SCONJ
ejpam-3483	113	6	the	the	DET
ejpam-3483	113	7	inverse	inverse	ADJ
ejpam-3483	113	8	image	image	NOUN
ejpam-3483	113	9	of	of	ADP
ejpam-3483	113	10	each	each	DET
ejpam-3483	113	11	open	open	ADJ
ejpam-3483	113	12	subset	subset	NOUN
ejpam-3483	113	13	of	of	ADP
ejpam-3483	113	14	y	y	PROPN
ejpam-3483	113	15	is	be	AUX
ejpam-3483	113	16	an	an	DET
ejpam-3483	113	17	i	i	NOUN
ejpam-3483	113	18	-	-	PUNCT
ejpam-3483	113	19	supra	supra	PROPN
ejpam-3483	113	20	(	(	PUNCT
ejpam-3483	113	21	resp	resp	NOUN
ejpam-3483	113	22	.	.	PUNCT
ejpam-3483	114	1	a	a	DET
ejpam-3483	114	2	d	d	NOUN
ejpam-3483	114	3	-	-	PUNCT
ejpam-3483	114	4	supra	supra	ADJ
ejpam-3483	114	5	,	,	PUNCT
ejpam-3483	114	6	a	a	DET
ejpam-3483	114	7	b	b	NOUN
ejpam-3483	114	8	-	-	PUNCT
ejpam-3483	114	9	supra	supra	ADJ
ejpam-3483	114	10	)	)	PUNCT
ejpam-3483	114	11	b	b	X
ejpam-3483	114	12	-	-	PUNCT
ejpam-3483	114	13	open	open	ADJ
ejpam-3483	114	14	subset	subset	NOUN
ejpam-3483	114	15	of	of	ADP
ejpam-3483	114	16	x.	x.	NOUN
ejpam-3483	114	17	proof	proof	NOUN
ejpam-3483	114	18	.	.	PUNCT
ejpam-3483	115	1	we	we	PRON
ejpam-3483	115	2	only	only	ADV
ejpam-3483	115	3	prove	prove	VERB
ejpam-3483	115	4	the	the	DET
ejpam-3483	115	5	theorem	theorem	NOUN
ejpam-3483	115	6	in	in	ADP
ejpam-3483	115	7	the	the	DET
ejpam-3483	115	8	case	case	NOUN
ejpam-3483	115	9	of	of	ADP
ejpam-3483	115	10	f	f	PROPN
ejpam-3483	115	11	is	be	AUX
ejpam-3483	115	12	an	an	DET
ejpam-3483	115	13	i	i	PROPN
ejpam-3483	115	14	-	-	PUNCT
ejpam-3483	115	15	supra	supra	PROPN
ejpam-3483	115	16	b	b	NOUN
ejpam-3483	115	17	-	-	PUNCT
ejpam-3483	115	18	continuous	continuous	ADJ
ejpam-3483	115	19	map	map	NOUN
ejpam-3483	115	20	and	and	CCONJ
ejpam-3483	115	21	the	the	DET
ejpam-3483	115	22	other	other	ADJ
ejpam-3483	115	23	cases	case	NOUN
ejpam-3483	115	24	follow	follow	VERB
ejpam-3483	115	25	similar	similar	ADJ
ejpam-3483	115	26	lines	line	NOUN
ejpam-3483	115	27	.	.	PUNCT
ejpam-3483	116	1	to	to	PART
ejpam-3483	116	2	prove	prove	VERB
ejpam-3483	116	3	the	the	DET
ejpam-3483	116	4	necessary	necessary	ADJ
ejpam-3483	116	5	part	part	NOUN
ejpam-3483	116	6	,	,	PUNCT
ejpam-3483	116	7	let	let	VERB
ejpam-3483	116	8	g	g	PRON
ejpam-3483	116	9	be	be	AUX
ejpam-3483	116	10	an	an	DET
ejpam-3483	116	11	open	open	ADJ
ejpam-3483	116	12	subset	subset	NOUN
ejpam-3483	116	13	of	of	ADP
ejpam-3483	116	14	y	y	PROPN
ejpam-3483	116	15	,	,	PUNCT
ejpam-3483	116	16	then	then	ADV
ejpam-3483	116	17	we	we	PRON
ejpam-3483	116	18	have	have	VERB
ejpam-3483	116	19	the	the	DET
ejpam-3483	116	20	following	follow	VERB
ejpam-3483	116	21	two	two	NUM
ejpam-3483	116	22	cases	case	NOUN
ejpam-3483	116	23	:	:	PUNCT
ejpam-3483	116	24	(	(	PUNCT
ejpam-3483	116	25	i	i	NOUN
ejpam-3483	116	26	)	)	PUNCT
ejpam-3483	116	27	f−1(g	f−1(g	PROPN
ejpam-3483	116	28	)	)	PUNCT
ejpam-3483	117	1	=	=	PUNCT
ejpam-3483	117	2	∅	∅	NOUN
ejpam-3483	117	3	which	which	PRON
ejpam-3483	117	4	is	be	AUX
ejpam-3483	117	5	an	an	DET
ejpam-3483	117	6	i	i	PROPN
ejpam-3483	117	7	-	-	PUNCT
ejpam-3483	117	8	supra	supra	PROPN
ejpam-3483	117	9	b	b	NOUN
ejpam-3483	117	10	-	-	PUNCT
ejpam-3483	117	11	open	open	ADJ
ejpam-3483	117	12	subset	subset	NOUN
ejpam-3483	117	13	of	of	ADP
ejpam-3483	117	14	x.	x.	PROPN
ejpam-3483	117	15	(	(	PUNCT
ejpam-3483	117	16	ii	ii	PROPN
ejpam-3483	117	17	)	)	PUNCT
ejpam-3483	117	18	f−1(g	f−1(g	PROPN
ejpam-3483	117	19	)	)	PUNCT
ejpam-3483	117	20	6=	6=	ADP
ejpam-3483	117	21	∅.	∅.	VERB
ejpam-3483	117	22	by	by	ADP
ejpam-3483	117	23	choosing	choose	VERB
ejpam-3483	117	24	p	p	NOUN
ejpam-3483	117	25	∈	∈	PROPN
ejpam-3483	117	26	x	x	PUNCT
ejpam-3483	117	27	such	such	ADJ
ejpam-3483	117	28	that	that	SCONJ
ejpam-3483	117	29	p	p	PROPN
ejpam-3483	117	30	∈	∈	PROPN
ejpam-3483	117	31	f−1(g	f−1(g	PROPN
ejpam-3483	117	32	)	)	PUNCT
ejpam-3483	117	33	,	,	PUNCT
ejpam-3483	117	34	we	we	PRON
ejpam-3483	117	35	obtain	obtain	VERB
ejpam-3483	117	36	f(p	f(p	NOUN
ejpam-3483	117	37	)	)	PUNCT
ejpam-3483	117	38	∈	∈	PROPN
ejpam-3483	118	1	g.	g.	NOUN
ejpam-3483	119	1	so	so	ADV
ejpam-3483	119	2	there	there	PRON
ejpam-3483	119	3	exists	exist	VERB
ejpam-3483	119	4	an	an	DET
ejpam-3483	119	5	i	i	PROPN
ejpam-3483	119	6	-	-	PUNCT
ejpam-3483	119	7	supra	supra	PROPN
ejpam-3483	119	8	b	b	NOUN
ejpam-3483	119	9	-	-	PUNCT
ejpam-3483	119	10	open	open	ADJ
ejpam-3483	119	11	set	set	ADJ
ejpam-3483	119	12	hp	hp	NOUN
ejpam-3483	119	13	containing	contain	VERB
ejpam-3483	119	14	p	p	NOUN
ejpam-3483	119	15	such	such	ADJ
ejpam-3483	119	16	that	that	SCONJ
ejpam-3483	119	17	f(hp	f(hp	PROPN
ejpam-3483	119	18	)	)	PUNCT
ejpam-3483	119	19	⊆	⊆	NUM
ejpam-3483	119	20	g.	g.	NOUN
ejpam-3483	119	21	since	since	SCONJ
ejpam-3483	119	22	p	p	PROPN
ejpam-3483	119	23	is	be	AUX
ejpam-3483	119	24	chosen	choose	VERB
ejpam-3483	119	25	randomly	randomly	ADV
ejpam-3483	119	26	,	,	PUNCT
ejpam-3483	119	27	then	then	ADV
ejpam-3483	119	28	f−1(g	f−1(g	PROPN
ejpam-3483	119	29	)	)	PUNCT
ejpam-3483	120	1	=	=	PUNCT
ejpam-3483	120	2	⋃	⋃	NOUN
ejpam-3483	120	3	p∈f−1(g)hp	p∈f−1(g)hp	NOUN
ejpam-3483	120	4	.	.	PUNCT
ejpam-3483	121	1	thus	thus	ADV
ejpam-3483	121	2	f−1(g	f−1(g	PROPN
ejpam-3483	121	3	)	)	PUNCT
ejpam-3483	121	4	is	be	AUX
ejpam-3483	121	5	an	an	DET
ejpam-3483	121	6	i	i	PROPN
ejpam-3483	121	7	-	-	PUNCT
ejpam-3483	121	8	supra	supra	PROPN
ejpam-3483	121	9	b	b	NOUN
ejpam-3483	121	10	-	-	PUNCT
ejpam-3483	121	11	open	open	ADJ
ejpam-3483	121	12	subset	subset	NOUN
ejpam-3483	121	13	of	of	ADP
ejpam-3483	121	14	x.	x.	NOUN
ejpam-3483	121	15	to	to	PART
ejpam-3483	121	16	prove	prove	VERB
ejpam-3483	121	17	the	the	DET
ejpam-3483	121	18	sufficient	sufficient	ADJ
ejpam-3483	121	19	part	part	NOUN
ejpam-3483	121	20	,	,	PUNCT
ejpam-3483	121	21	let	let	VERB
ejpam-3483	121	22	g	g	PRON
ejpam-3483	121	23	be	be	AUX
ejpam-3483	121	24	an	an	DET
ejpam-3483	121	25	open	open	ADJ
ejpam-3483	121	26	subset	subset	NOUN
ejpam-3483	121	27	of	of	ADP
ejpam-3483	121	28	y	y	PROPN
ejpam-3483	121	29	containing	contain	VERB
ejpam-3483	121	30	f(p	f(p	PROPN
ejpam-3483	121	31	)	)	PUNCT
ejpam-3483	121	32	.	.	PUNCT
ejpam-3483	122	1	then	then	ADV
ejpam-3483	122	2	p	p	PROPN
ejpam-3483	122	3	∈	∈	PROPN
ejpam-3483	122	4	f−1(g	f−1(g	PROPN
ejpam-3483	122	5	)	)	PUNCT
ejpam-3483	122	6	.	.	PUNCT
ejpam-3483	123	1	by	by	ADP
ejpam-3483	123	2	hypothesis	hypothesis	NOUN
ejpam-3483	123	3	,	,	PUNCT
ejpam-3483	123	4	f−1(g	f−1(g	PROPN
ejpam-3483	123	5	)	)	PUNCT
ejpam-3483	123	6	is	be	AUX
ejpam-3483	123	7	an	an	DET
ejpam-3483	123	8	i	i	PROPN
ejpam-3483	123	9	-	-	PUNCT
ejpam-3483	123	10	supra	supra	PROPN
ejpam-3483	123	11	b	b	NOUN
ejpam-3483	123	12	-	-	PUNCT
ejpam-3483	123	13	open	open	ADJ
ejpam-3483	123	14	set	set	NOUN
ejpam-3483	123	15	.	.	PUNCT
ejpam-3483	124	1	since	since	SCONJ
ejpam-3483	124	2	f(f−1(g	f(f−1(g	PROPN
ejpam-3483	124	3	)	)	PUNCT
ejpam-3483	124	4	)	)	PUNCT
ejpam-3483	125	1	⊆	⊆	NUM
ejpam-3483	125	2	g	g	NOUN
ejpam-3483	125	3	,	,	PUNCT
ejpam-3483	125	4	then	then	ADV
ejpam-3483	125	5	f	f	PROPN
ejpam-3483	125	6	is	be	AUX
ejpam-3483	125	7	an	an	DET
ejpam-3483	125	8	i	i	PROPN
ejpam-3483	125	9	-	-	PUNCT
ejpam-3483	125	10	supra	supra	PROPN
ejpam-3483	125	11	b	b	NOUN
ejpam-3483	125	12	-	-	PUNCT
ejpam-3483	125	13	continuous	continuous	ADJ
ejpam-3483	125	14	at	at	ADP
ejpam-3483	125	15	p	p	PROPN
ejpam-3483	125	16	∈	∈	PROPN
ejpam-3483	125	17	x	x	X
ejpam-3483	125	18	and	and	CCONJ
ejpam-3483	125	19	since	since	SCONJ
ejpam-3483	125	20	p	p	NOUN
ejpam-3483	125	21	is	be	AUX
ejpam-3483	125	22	chosen	choose	VERB
ejpam-3483	125	23	randomly	randomly	ADV
ejpam-3483	125	24	,	,	PUNCT
ejpam-3483	125	25	then	then	ADV
ejpam-3483	125	26	f	f	PROPN
ejpam-3483	125	27	is	be	AUX
ejpam-3483	125	28	i	i	PROPN
ejpam-3483	125	29	-	-	PUNCT
ejpam-3483	125	30	supra	supra	PROPN
ejpam-3483	125	31	b	b	NOUN
ejpam-3483	125	32	-	-	PUNCT
ejpam-3483	125	33	continuous	continuous	ADJ
ejpam-3483	125	34	.	.	PUNCT
ejpam-3483	126	1	remark	remark	NOUN
ejpam-3483	126	2	2	2	NUM
ejpam-3483	126	3	.	.	PUNCT
ejpam-3483	127	1	(	(	PUNCT
ejpam-3483	127	2	i	i	NOUN
ejpam-3483	127	3	)	)	PUNCT
ejpam-3483	127	4	every	every	DET
ejpam-3483	127	5	i	i	PROPN
ejpam-3483	127	6	-	-	PUNCT
ejpam-3483	127	7	supra	supra	PROPN
ejpam-3483	127	8	(	(	PUNCT
ejpam-3483	127	9	d	d	NOUN
ejpam-3483	127	10	-	-	PUNCT
ejpam-3483	127	11	supra	supra	ADJ
ejpam-3483	127	12	,	,	PUNCT
ejpam-3483	127	13	b	b	NOUN
ejpam-3483	127	14	-	-	PUNCT
ejpam-3483	127	15	supra	supra	ADJ
ejpam-3483	127	16	)	)	PUNCT
ejpam-3483	127	17	b	b	X
ejpam-3483	127	18	-	-	PUNCT
ejpam-3483	127	19	continuous	continuous	ADJ
ejpam-3483	127	20	map	map	NOUN
ejpam-3483	127	21	is	be	AUX
ejpam-3483	127	22	supra	supra	ADJ
ejpam-3483	127	23	b	b	NOUN
ejpam-3483	127	24	-	-	PUNCT
ejpam-3483	127	25	continuous	continuous	ADJ
ejpam-3483	127	26	.	.	PUNCT
ejpam-3483	128	1	(	(	PUNCT
ejpam-3483	128	2	ii	ii	NOUN
ejpam-3483	128	3	)	)	PUNCT
ejpam-3483	128	4	every	every	DET
ejpam-3483	128	5	b	b	X
ejpam-3483	128	6	-	-	PUNCT
ejpam-3483	128	7	supra	supra	ADJ
ejpam-3483	128	8	b	b	NOUN
ejpam-3483	128	9	-	-	PUNCT
ejpam-3483	128	10	continuous	continuous	ADJ
ejpam-3483	128	11	map	map	NOUN
ejpam-3483	128	12	is	be	AUX
ejpam-3483	128	13	i	i	PROPN
ejpam-3483	128	14	-	-	PUNCT
ejpam-3483	128	15	supra	supra	PROPN
ejpam-3483	128	16	(	(	PUNCT
ejpam-3483	128	17	d	d	NOUN
ejpam-3483	128	18	-	-	PUNCT
ejpam-3483	128	19	supra	supra	ADJ
ejpam-3483	128	20	)	)	PUNCT
ejpam-3483	128	21	b	b	NOUN
ejpam-3483	128	22	-	-	PUNCT
ejpam-3483	128	23	continuous	continuous	ADJ
ejpam-3483	128	24	.	.	PUNCT
ejpam-3483	129	1	the	the	DET
ejpam-3483	129	2	following	follow	VERB
ejpam-3483	129	3	two	two	NUM
ejpam-3483	129	4	examples	example	NOUN
ejpam-3483	129	5	illustrate	illustrate	VERB
ejpam-3483	129	6	that	that	SCONJ
ejpam-3483	129	7	the	the	DET
ejpam-3483	129	8	above	above	ADJ
ejpam-3483	129	9	remark	remark	NOUN
ejpam-3483	129	10	can	can	AUX
ejpam-3483	129	11	not	not	PART
ejpam-3483	129	12	be	be	AUX
ejpam-3483	129	13	reversed	reverse	VERB
ejpam-3483	129	14	,	,	PUNCT
ejpam-3483	129	15	in	in	ADP
ejpam-3483	129	16	general	general	ADJ
ejpam-3483	129	17	.	.	PUNCT
ejpam-3483	130	1	example	example	NOUN
ejpam-3483	131	1	1	1	NUM
ejpam-3483	131	2	.	.	PUNCT
ejpam-3483	131	3	let	let	VERB
ejpam-3483	131	4	a	a	DET
ejpam-3483	131	5	supra	supra	ADJ
ejpam-3483	131	6	topology	topology	NOUN
ejpam-3483	131	7	µ	µ	X
ejpam-3483	131	8	=	=	SYM
ejpam-3483	131	9	{	{	PUNCT
ejpam-3483	131	10	∅	∅	NOUN
ejpam-3483	131	11	,	,	PUNCT
ejpam-3483	131	12	x	x	X
ejpam-3483	131	13	,	,	PUNCT
ejpam-3483	131	14	{	{	PUNCT
ejpam-3483	131	15	a	a	X
ejpam-3483	131	16	}	}	PUNCT
ejpam-3483	131	17	,	,	PUNCT
ejpam-3483	131	18	{	{	PUNCT
ejpam-3483	131	19	b	b	NOUN
ejpam-3483	131	20	}	}	PUNCT
ejpam-3483	131	21	,	,	PUNCT
ejpam-3483	131	22	{	{	PUNCT
ejpam-3483	131	23	a	a	PRON
ejpam-3483	131	24	,	,	PUNCT
ejpam-3483	131	25	b	b	NOUN
ejpam-3483	131	26	}	}	PUNCT
ejpam-3483	131	27	}	}	PUNCT
ejpam-3483	131	28	and	and	CCONJ
ejpam-3483	131	29	a	a	DET
ejpam-3483	131	30	topology	topology	NOUN
ejpam-3483	131	31	τ	τ	X
ejpam-3483	131	32	=	=	SYM
ejpam-3483	131	33	{	{	PUNCT
ejpam-3483	131	34	∅	∅	NOUN
ejpam-3483	131	35	,	,	PUNCT
ejpam-3483	131	36	y	y	PROPN
ejpam-3483	131	37	,	,	PUNCT
ejpam-3483	131	38	{	{	PUNCT
ejpam-3483	131	39	x	x	NOUN
ejpam-3483	131	40	}	}	PUNCT
ejpam-3483	131	41	}	}	PUNCT
ejpam-3483	131	42	on	on	ADP
ejpam-3483	131	43	x	x	X
ejpam-3483	131	44	=	=	X
ejpam-3483	131	45	{	{	PUNCT
ejpam-3483	131	46	a	a	PRON
ejpam-3483	131	47	,	,	PUNCT
ejpam-3483	131	48	b	b	NOUN
ejpam-3483	131	49	,	,	PUNCT
ejpam-3483	131	50	c	c	NOUN
ejpam-3483	131	51	,	,	PUNCT
ejpam-3483	131	52	d	d	NOUN
ejpam-3483	131	53	}	}	PUNCT
ejpam-3483	131	54	and	and	CCONJ
ejpam-3483	131	55	y	y	PROPN
ejpam-3483	131	56	=	=	SYM
ejpam-3483	131	57	{	{	PUNCT
ejpam-3483	131	58	x	x	PROPN
ejpam-3483	131	59	,	,	PUNCT
ejpam-3483	131	60	y	y	PROPN
ejpam-3483	131	61	,	,	PUNCT
ejpam-3483	131	62	z	z	NOUN
ejpam-3483	131	63	}	}	PUNCT
ejpam-3483	131	64	,	,	PUNCT
ejpam-3483	131	65	respectively	respectively	ADV
ejpam-3483	131	66	.	.	PUNCT
ejpam-3483	132	1	let	let	VERB
ejpam-3483	132	2	a	a	DET
ejpam-3483	132	3	partial	partial	ADJ
ejpam-3483	132	4	order	order	NOUN
ejpam-3483	132	5	relation	relation	NOUN
ejpam-3483	132	6	�	�	NOUN
ejpam-3483	132	7	=	=	NOUN
ejpam-3483	132	8	4	4	NUM
ejpam-3483	132	9	⋃	⋃	NOUN
ejpam-3483	132	10	{	{	PUNCT
ejpam-3483	132	11	(	(	PUNCT
ejpam-3483	132	12	a	a	DET
ejpam-3483	132	13	,	,	PUNCT
ejpam-3483	132	14	b	b	NOUN
ejpam-3483	132	15	)	)	PUNCT
ejpam-3483	132	16	,	,	PUNCT
ejpam-3483	132	17	(	(	PUNCT
ejpam-3483	132	18	b	b	X
ejpam-3483	132	19	,	,	PUNCT
ejpam-3483	132	20	d	d	NOUN
ejpam-3483	132	21	)	)	PUNCT
ejpam-3483	132	22	,	,	PUNCT
ejpam-3483	132	23	(	(	PUNCT
ejpam-3483	132	24	a	a	DET
ejpam-3483	132	25	,	,	PUNCT
ejpam-3483	132	26	d	d	NOUN
ejpam-3483	132	27	)	)	PUNCT
ejpam-3483	132	28	}	}	PUNCT
ejpam-3483	132	29	on	on	ADP
ejpam-3483	132	30	x	x	PUNCT
ejpam-3483	132	31	and	and	CCONJ
ejpam-3483	132	32	let	let	VERB
ejpam-3483	132	33	a	a	DET
ejpam-3483	132	34	map	map	NOUN
ejpam-3483	132	35	f	f	X
ejpam-3483	132	36	:	:	PUNCT
ejpam-3483	132	37	(	(	PUNCT
ejpam-3483	132	38	x,µ	x,µ	NOUN
ejpam-3483	132	39	,	,	PUNCT
ejpam-3483	132	40	�	�	PROPN
ejpam-3483	132	41	)	)	PUNCT
ejpam-3483	132	42	→	→	SYM
ejpam-3483	132	43	(	(	PUNCT
ejpam-3483	132	44	y	y	PROPN
ejpam-3483	132	45	,	,	PUNCT
ejpam-3483	132	46	τ	τ	PROPN
ejpam-3483	132	47	)	)	PUNCT
ejpam-3483	132	48	be	be	AUX
ejpam-3483	132	49	defined	define	VERB
ejpam-3483	132	50	as	as	ADP
ejpam-3483	132	51	follows	follow	VERB
ejpam-3483	132	52	,	,	PUNCT
ejpam-3483	132	53	f(a	f(a	NOUN
ejpam-3483	132	54	)	)	PUNCT
ejpam-3483	132	55	=	=	SYM
ejpam-3483	132	56	f(c	f(c	PROPN
ejpam-3483	132	57	)	)	PUNCT
ejpam-3483	132	58	=	=	SYM
ejpam-3483	132	59	f(d	f(d	PROPN
ejpam-3483	132	60	)	)	PUNCT
ejpam-3483	132	61	=	=	SYM
ejpam-3483	132	62	x	x	X
ejpam-3483	132	63	and	and	CCONJ
ejpam-3483	132	64	f(b	f(b	PROPN
ejpam-3483	132	65	)	)	PUNCT
ejpam-3483	133	1	=	=	VERB
ejpam-3483	133	2	y.	y.	NOUN
ejpam-3483	133	3	obviously	obviously	ADV
ejpam-3483	133	4	,	,	PUNCT
ejpam-3483	133	5	f	f	PROPN
ejpam-3483	133	6	is	be	AUX
ejpam-3483	133	7	supra	supra	ADJ
ejpam-3483	133	8	b	b	NOUN
ejpam-3483	133	9	-	-	PUNCT
ejpam-3483	133	10	continuous	continuous	ADJ
ejpam-3483	133	11	.	.	PUNCT
ejpam-3483	134	1	on	on	ADP
ejpam-3483	134	2	the	the	DET
ejpam-3483	134	3	other	other	ADJ
ejpam-3483	134	4	hand	hand	NOUN
ejpam-3483	134	5	,	,	PUNCT
ejpam-3483	134	6	f−1({x	f−1({x	NOUN
ejpam-3483	134	7	}	}	PUNCT
ejpam-3483	134	8	)	)	PUNCT
ejpam-3483	135	1	=	=	PRON
ejpam-3483	135	2	{	{	PUNCT
ejpam-3483	135	3	a	a	X
ejpam-3483	135	4	,	,	PUNCT
ejpam-3483	135	5	c	c	NOUN
ejpam-3483	135	6	,	,	PUNCT
ejpam-3483	135	7	d	d	NOUN
ejpam-3483	135	8	}	}	PUNCT
ejpam-3483	135	9	is	be	AUX
ejpam-3483	135	10	neither	neither	CCONJ
ejpam-3483	135	11	a	a	DET
ejpam-3483	135	12	decreasing	decreasing	NOUN
ejpam-3483	135	13	nor	nor	CCONJ
ejpam-3483	135	14	an	an	DET
ejpam-3483	135	15	increasing	increase	VERB
ejpam-3483	135	16	supra	supra	ADJ
ejpam-3483	135	17	b	b	NOUN
ejpam-3483	135	18	-	-	PUNCT
ejpam-3483	135	19	open	open	ADJ
ejpam-3483	135	20	subset	subset	NOUN
ejpam-3483	135	21	of	of	ADP
ejpam-3483	135	22	x.	x.	PROPN
ejpam-3483	135	23	then	then	ADV
ejpam-3483	135	24	f	f	PROPN
ejpam-3483	135	25	is	be	AUX
ejpam-3483	135	26	not	not	PART
ejpam-3483	135	27	i	i	PROPN
ejpam-3483	135	28	-	-	PUNCT
ejpam-3483	135	29	supra	supra	ADJ
ejpam-3483	135	30	(	(	PUNCT
ejpam-3483	135	31	d	d	NOUN
ejpam-3483	135	32	-	-	PUNCT
ejpam-3483	135	33	supra	supra	ADJ
ejpam-3483	135	34	,	,	PUNCT
ejpam-3483	135	35	b	b	NOUN
ejpam-3483	135	36	-	-	PUNCT
ejpam-3483	135	37	supra	supra	ADJ
ejpam-3483	135	38	)	)	PUNCT
ejpam-3483	135	39	b	b	NOUN
ejpam-3483	135	40	-	-	PUNCT
ejpam-3483	135	41	continuous	continuous	ADJ
ejpam-3483	135	42	.	.	PUNCT
ejpam-3483	135	43	example	example	NOUN
ejpam-3483	136	1	2	2	NUM
ejpam-3483	136	2	.	.	X
ejpam-3483	136	3	we	we	PRON
ejpam-3483	136	4	replace	replace	VERB
ejpam-3483	136	5	only	only	ADV
ejpam-3483	136	6	a	a	DET
ejpam-3483	136	7	partial	partial	ADJ
ejpam-3483	136	8	order	order	NOUN
ejpam-3483	136	9	relation	relation	NOUN
ejpam-3483	136	10	in	in	ADP
ejpam-3483	136	11	example	example	NOUN
ejpam-3483	136	12	(	(	PUNCT
ejpam-3483	136	13	1	1	X
ejpam-3483	136	14	)	)	PUNCT
ejpam-3483	136	15	by	by	ADP
ejpam-3483	136	16	�	�	NOUN
ejpam-3483	136	17	=	=	PROPN
ejpam-3483	136	18	4	4	NUM
ejpam-3483	136	19	⋃	⋃	NOUN
ejpam-3483	136	20	{	{	PUNCT
ejpam-3483	136	21	(	(	PUNCT
ejpam-3483	136	22	b	b	NOUN
ejpam-3483	136	23	,	,	PUNCT
ejpam-3483	136	24	d	d	NOUN
ejpam-3483	136	25	)	)	PUNCT
ejpam-3483	136	26	}	}	PUNCT
ejpam-3483	136	27	.	.	PUNCT
ejpam-3483	137	1	then	then	ADV
ejpam-3483	137	2	a	a	DET
ejpam-3483	137	3	map	map	NOUN
ejpam-3483	137	4	f	f	NOUN
ejpam-3483	137	5	is	be	AUX
ejpam-3483	137	6	i	i	PROPN
ejpam-3483	137	7	-	-	PUNCT
ejpam-3483	137	8	supra	supra	PROPN
ejpam-3483	137	9	b	b	NOUN
ejpam-3483	137	10	-	-	PUNCT
ejpam-3483	137	11	continuous	continuous	ADJ
ejpam-3483	137	12	,	,	PUNCT
ejpam-3483	137	13	but	but	CCONJ
ejpam-3483	137	14	not	not	PART
ejpam-3483	137	15	b	b	NOUN
ejpam-3483	137	16	-	-	PUNCT
ejpam-3483	137	17	supra	supra	ADJ
ejpam-3483	137	18	b	b	NOUN
ejpam-3483	137	19	-	-	PUNCT
ejpam-3483	137	20	continuous	continuous	ADJ
ejpam-3483	137	21	.	.	PUNCT
ejpam-3483	138	1	definition	definition	NOUN
ejpam-3483	138	2	14	14	NUM
ejpam-3483	138	3	.	.	PUNCT
ejpam-3483	139	1	let	let	VERB
ejpam-3483	139	2	e	e	PRON
ejpam-3483	139	3	be	be	AUX
ejpam-3483	139	4	a	a	DET
ejpam-3483	139	5	subset	subset	NOUN
ejpam-3483	139	6	of	of	ADP
ejpam-3483	139	7	(	(	PUNCT
ejpam-3483	139	8	x,µ	x,µ	NOUN
ejpam-3483	139	9	,	,	PUNCT
ejpam-3483	139	10	�	�	PROPN
ejpam-3483	139	11	)	)	PUNCT
ejpam-3483	139	12	.	.	PUNCT
ejpam-3483	140	1	then	then	ADV
ejpam-3483	140	2	(	(	PUNCT
ejpam-3483	140	3	i	i	NOUN
ejpam-3483	140	4	)	)	PUNCT
ejpam-3483	140	5	eisbo	eisbo	PROPN
ejpam-3483	140	6	=	=	SYM
ejpam-3483	140	7	⋃	⋃	PROPN
ejpam-3483	140	8	{	{	PUNCT
ejpam-3483	140	9	g	g	NOUN
ejpam-3483	140	10	:	:	PUNCT
ejpam-3483	140	11	g	g	PROPN
ejpam-3483	140	12	is	be	AUX
ejpam-3483	140	13	an	an	DET
ejpam-3483	140	14	i	i	PROPN
ejpam-3483	140	15	-	-	PUNCT
ejpam-3483	140	16	supra	supra	PROPN
ejpam-3483	140	17	b	b	NOUN
ejpam-3483	140	18	-	-	PUNCT
ejpam-3483	140	19	open	open	ADJ
ejpam-3483	140	20	set	set	NOUN
ejpam-3483	140	21	contained	contain	VERB
ejpam-3483	140	22	in	in	ADP
ejpam-3483	140	23	e	e	NOUN
ejpam-3483	140	24	}	}	PUNCT
ejpam-3483	140	25	.	.	PUNCT
ejpam-3483	141	1	b.	b.	PROPN
ejpam-3483	141	2	a.	a.	PROPN
ejpam-3483	141	3	asaad	asaad	PROPN
ejpam-3483	141	4	,	,	PUNCT
ejpam-3483	141	5	m.	m.	PROPN
ejpam-3483	141	6	k.	k.	PROPN
ejpam-3483	141	7	tahat	tahat	PROPN
ejpam-3483	141	8	,	,	PUNCT
ejpam-3483	141	9	t.	t.	PROPN
ejpam-3483	141	10	m.	m.	PROPN
ejpam-3483	141	11	al	al	PROPN
ejpam-3483	141	12	-	-	PUNCT
ejpam-3483	141	13	shami	shami	PROPN
ejpam-3483	141	14	/	/	PUNCT
ejpam-3483	141	15	eur	eur	PROPN
ejpam-3483	141	16	.	.	PUNCT
ejpam-3483	142	1	j.	j.	PROPN
ejpam-3483	142	2	pure	pure	PROPN
ejpam-3483	142	3	appl	appl	PROPN
ejpam-3483	142	4	.	.	PROPN
ejpam-3483	142	5	math	math	PROPN
ejpam-3483	142	6	,	,	PUNCT
ejpam-3483	142	7	12	12	NUM
ejpam-3483	142	8	(	(	PUNCT
ejpam-3483	142	9	3	3	NUM
ejpam-3483	142	10	)	)	PUNCT
ejpam-3483	142	11	(	(	PUNCT
ejpam-3483	142	12	2019	2019	NUM
ejpam-3483	142	13	)	)	PUNCT
ejpam-3483	142	14	,	,	PUNCT
ejpam-3483	142	15	1231	1231	NUM
ejpam-3483	142	16	-	-	SYM
ejpam-3483	142	17	1247	1247	NUM
ejpam-3483	142	18	1236	1236	NUM
ejpam-3483	142	19	(	(	PUNCT
ejpam-3483	142	20	ii	ii	NOUN
ejpam-3483	142	21	)	)	PUNCT
ejpam-3483	142	22	edsbo	edsbo	NOUN
ejpam-3483	142	23	=	=	SYM
ejpam-3483	142	24	⋃	⋃	PROPN
ejpam-3483	142	25	{	{	PUNCT
ejpam-3483	142	26	g	g	NOUN
ejpam-3483	142	27	:	:	PUNCT
ejpam-3483	142	28	g	g	PROPN
ejpam-3483	142	29	is	be	AUX
ejpam-3483	142	30	a	a	DET
ejpam-3483	142	31	d	d	ADJ
ejpam-3483	142	32	-	-	PUNCT
ejpam-3483	142	33	supra	supra	ADJ
ejpam-3483	142	34	b	b	NOUN
ejpam-3483	142	35	-	-	PUNCT
ejpam-3483	142	36	open	open	ADJ
ejpam-3483	142	37	set	set	NOUN
ejpam-3483	142	38	contained	contain	VERB
ejpam-3483	142	39	in	in	ADP
ejpam-3483	142	40	e	e	NOUN
ejpam-3483	142	41	}	}	PUNCT
ejpam-3483	142	42	.	.	PUNCT
ejpam-3483	143	1	(	(	PUNCT
ejpam-3483	143	2	iii	iii	X
ejpam-3483	143	3	)	)	PUNCT
ejpam-3483	143	4	ebsbo	ebsbo	NOUN
ejpam-3483	143	5	=	=	SYM
ejpam-3483	143	6	⋃	⋃	PROPN
ejpam-3483	143	7	{	{	PUNCT
ejpam-3483	143	8	g	g	NOUN
ejpam-3483	143	9	:	:	PUNCT
ejpam-3483	143	10	g	g	PROPN
ejpam-3483	143	11	is	be	AUX
ejpam-3483	143	12	a	a	DET
ejpam-3483	143	13	b	b	PROPN
ejpam-3483	143	14	-	-	PUNCT
ejpam-3483	143	15	supra	supra	ADJ
ejpam-3483	143	16	b	b	NOUN
ejpam-3483	143	17	-	-	PUNCT
ejpam-3483	143	18	open	open	ADJ
ejpam-3483	143	19	set	set	NOUN
ejpam-3483	143	20	contained	contain	VERB
ejpam-3483	143	21	in	in	ADP
ejpam-3483	143	22	e	e	NOUN
ejpam-3483	143	23	}	}	PUNCT
ejpam-3483	143	24	.	.	PUNCT
ejpam-3483	144	1	(	(	PUNCT
ejpam-3483	144	2	iv	iv	X
ejpam-3483	144	3	)	)	PUNCT
ejpam-3483	144	4	eisbcl	eisbcl	NOUN
ejpam-3483	145	1	=	=	SYM
ejpam-3483	145	2	⋂	⋂	PROPN
ejpam-3483	145	3	{	{	PUNCT
ejpam-3483	145	4	h	h	NOUN
ejpam-3483	145	5	:	:	PUNCT
ejpam-3483	145	6	h	h	NOUN
ejpam-3483	145	7	is	be	AUX
ejpam-3483	145	8	an	an	DET
ejpam-3483	145	9	i	i	PROPN
ejpam-3483	145	10	-	-	PUNCT
ejpam-3483	145	11	supra	supra	PROPN
ejpam-3483	145	12	b	b	PROPN
ejpam-3483	145	13	-	-	PUNCT
ejpam-3483	145	14	closed	closed	ADJ
ejpam-3483	145	15	set	set	NOUN
ejpam-3483	145	16	containing	contain	VERB
ejpam-3483	145	17	e	e	NOUN
ejpam-3483	145	18	}	}	PUNCT
ejpam-3483	145	19	.	.	PUNCT
ejpam-3483	146	1	(	(	PUNCT
ejpam-3483	146	2	v	v	NOUN
ejpam-3483	146	3	)	)	PUNCT
ejpam-3483	146	4	edsbcl	edsbcl	NOUN
ejpam-3483	146	5	=	=	SYM
ejpam-3483	146	6	⋂	⋂	PROPN
ejpam-3483	146	7	{	{	PUNCT
ejpam-3483	146	8	h	h	NOUN
ejpam-3483	146	9	:	:	PUNCT
ejpam-3483	146	10	h	h	NOUN
ejpam-3483	146	11	is	be	AUX
ejpam-3483	146	12	a	a	DET
ejpam-3483	146	13	d	d	ADJ
ejpam-3483	146	14	-	-	PUNCT
ejpam-3483	146	15	supra	supra	ADJ
ejpam-3483	146	16	b	b	NOUN
ejpam-3483	146	17	-	-	PUNCT
ejpam-3483	146	18	closed	closed	ADJ
ejpam-3483	146	19	set	set	NOUN
ejpam-3483	146	20	containing	contain	VERB
ejpam-3483	146	21	e	e	NOUN
ejpam-3483	146	22	}	}	PUNCT
ejpam-3483	146	23	.	.	PUNCT
ejpam-3483	147	1	(	(	PUNCT
ejpam-3483	147	2	vi	vi	NOUN
ejpam-3483	147	3	)	)	PUNCT
ejpam-3483	147	4	ebsbcl	ebsbcl	NOUN
ejpam-3483	148	1	=	=	SYM
ejpam-3483	148	2	⋂	⋂	PROPN
ejpam-3483	148	3	{	{	PUNCT
ejpam-3483	148	4	h	h	NOUN
ejpam-3483	148	5	:	:	PUNCT
ejpam-3483	148	6	h	h	PROPN
ejpam-3483	148	7	is	be	AUX
ejpam-3483	148	8	a	a	DET
ejpam-3483	148	9	b	b	PROPN
ejpam-3483	148	10	-	-	PUNCT
ejpam-3483	148	11	supra	supra	ADJ
ejpam-3483	148	12	b	b	NOUN
ejpam-3483	148	13	-	-	PUNCT
ejpam-3483	148	14	closed	closed	ADJ
ejpam-3483	148	15	set	set	NOUN
ejpam-3483	148	16	containing	contain	VERB
ejpam-3483	148	17	e	e	NOUN
ejpam-3483	148	18	}	}	PUNCT
ejpam-3483	148	19	.	.	PUNCT
ejpam-3483	149	1	lemma	lemma	PROPN
ejpam-3483	149	2	1	1	X
ejpam-3483	149	3	.	.	PUNCT
ejpam-3483	150	1	let	let	VERB
ejpam-3483	150	2	e	e	PRON
ejpam-3483	150	3	be	be	AUX
ejpam-3483	150	4	a	a	DET
ejpam-3483	150	5	subset	subset	NOUN
ejpam-3483	150	6	of	of	ADP
ejpam-3483	150	7	(	(	PUNCT
ejpam-3483	150	8	x,µ	x,µ	NOUN
ejpam-3483	150	9	,	,	PUNCT
ejpam-3483	150	10	�	�	PROPN
ejpam-3483	150	11	)	)	PUNCT
ejpam-3483	150	12	.	.	PUNCT
ejpam-3483	151	1	then	then	ADV
ejpam-3483	151	2	:	:	PUNCT
ejpam-3483	151	3	(	(	PUNCT
ejpam-3483	151	4	i	i	NOUN
ejpam-3483	151	5	)	)	PUNCT
ejpam-3483	151	6	(	(	PUNCT
ejpam-3483	151	7	edsbcl)c	edsbcl)c	X
ejpam-3483	151	8	=	=	SYM
ejpam-3483	151	9	(	(	PUNCT
ejpam-3483	151	10	ec)isbo	ec)isbo	NOUN
ejpam-3483	151	11	.	.	PUNCT
ejpam-3483	152	1	(	(	PUNCT
ejpam-3483	152	2	ii	ii	NOUN
ejpam-3483	152	3	)	)	PUNCT
ejpam-3483	152	4	(	(	PUNCT
ejpam-3483	152	5	eisbcl)c	eisbcl)c	X
ejpam-3483	152	6	=	=	SYM
ejpam-3483	152	7	(	(	PUNCT
ejpam-3483	152	8	ec)dsbo	ec)dsbo	NOUN
ejpam-3483	152	9	.	.	PUNCT
ejpam-3483	153	1	(	(	PUNCT
ejpam-3483	153	2	iii	iii	NOUN
ejpam-3483	153	3	)	)	PUNCT
ejpam-3483	153	4	(	(	PUNCT
ejpam-3483	153	5	ebsbcl)c	ebsbcl)c	PROPN
ejpam-3483	153	6	=	=	SYM
ejpam-3483	153	7	(	(	PUNCT
ejpam-3483	153	8	ec)bsbo	ec)bsbo	NOUN
ejpam-3483	153	9	.	.	PUNCT
ejpam-3483	154	1	proof	proof	NOUN
ejpam-3483	154	2	.	.	PUNCT
ejpam-3483	155	1	(	(	PUNCT
ejpam-3483	155	2	i	i	NOUN
ejpam-3483	155	3	)	)	PUNCT
ejpam-3483	155	4	(	(	PUNCT
ejpam-3483	155	5	edsbcl)c	edsbcl)c	X
ejpam-3483	155	6	=	=	PUNCT
ejpam-3483	155	7	{	{	PUNCT
ejpam-3483	155	8	⋃	⋃	NOUN
ejpam-3483	155	9	f	f	NOUN
ejpam-3483	155	10	:	:	PUNCT
ejpam-3483	155	11	f	f	PROPN
ejpam-3483	155	12	is	be	AUX
ejpam-3483	155	13	a	a	DET
ejpam-3483	155	14	d	d	ADJ
ejpam-3483	155	15	-	-	PUNCT
ejpam-3483	155	16	supra	supra	ADJ
ejpam-3483	155	17	b	b	NOUN
ejpam-3483	155	18	-	-	PUNCT
ejpam-3483	155	19	closed	closed	ADJ
ejpam-3483	155	20	set	set	NOUN
ejpam-3483	155	21	containing	contain	VERB
ejpam-3483	155	22	e}c	e}c	PROPN
ejpam-3483	155	23	=	=	PUNCT
ejpam-3483	155	24	⋂	⋂	PROPN
ejpam-3483	155	25	{	{	PUNCT
ejpam-3483	155	26	f	f	NOUN
ejpam-3483	155	27	c	c	PROPN
ejpam-3483	155	28	:	:	PUNCT
ejpam-3483	155	29	f	f	PROPN
ejpam-3483	155	30	c	c	NOUN
ejpam-3483	155	31	is	be	AUX
ejpam-3483	155	32	an	an	DET
ejpam-3483	155	33	i	i	PROPN
ejpam-3483	155	34	-	-	PUNCT
ejpam-3483	155	35	supra	supra	PROPN
ejpam-3483	155	36	b	b	NOUN
ejpam-3483	155	37	-	-	PUNCT
ejpam-3483	155	38	open	open	ADJ
ejpam-3483	155	39	set	set	NOUN
ejpam-3483	155	40	contained	contain	VERB
ejpam-3483	155	41	in	in	ADP
ejpam-3483	155	42	ec	ec	PROPN
ejpam-3483	155	43	}	}	PUNCT
ejpam-3483	155	44	=	=	SYM
ejpam-3483	155	45	(	(	PUNCT
ejpam-3483	155	46	ec)isbo	ec)isbo	NOUN
ejpam-3483	155	47	.	.	PUNCT
ejpam-3483	156	1	the	the	DET
ejpam-3483	156	2	proofs	proof	NOUN
ejpam-3483	156	3	of	of	ADP
ejpam-3483	156	4	(	(	PUNCT
ejpam-3483	156	5	ii	ii	NOUN
ejpam-3483	156	6	)	)	PUNCT
ejpam-3483	156	7	and	and	CCONJ
ejpam-3483	156	8	(	(	PUNCT
ejpam-3483	156	9	iii	iii	X
ejpam-3483	156	10	)	)	PUNCT
ejpam-3483	156	11	are	be	AUX
ejpam-3483	156	12	similar	similar	ADJ
ejpam-3483	156	13	to	to	ADP
ejpam-3483	156	14	that	that	PRON
ejpam-3483	156	15	of	of	ADP
ejpam-3483	156	16	(	(	PUNCT
ejpam-3483	156	17	i	i	NOUN
ejpam-3483	156	18	)	)	PUNCT
ejpam-3483	156	19	.	.	PUNCT
ejpam-3483	157	1	theorem	theorem	NOUN
ejpam-3483	157	2	3	3	X
ejpam-3483	157	3	.	.	PUNCT
ejpam-3483	158	1	let	let	VERB
ejpam-3483	158	2	g	g	NOUN
ejpam-3483	158	3	:	:	PUNCT
ejpam-3483	158	4	(	(	PUNCT
ejpam-3483	158	5	x,µ,	x,µ,	PROPN
ejpam-3483	158	6	�	�	PROPN
ejpam-3483	158	7	)→	)→	PROPN
ejpam-3483	158	8	(	(	PUNCT
ejpam-3483	158	9	y	y	PROPN
ejpam-3483	158	10	,	,	PUNCT
ejpam-3483	158	11	τ	τ	PROPN
ejpam-3483	158	12	)	)	PUNCT
ejpam-3483	158	13	be	be	VERB
ejpam-3483	158	14	a	a	DET
ejpam-3483	158	15	map	map	NOUN
ejpam-3483	158	16	.	.	PUNCT
ejpam-3483	159	1	then	then	ADV
ejpam-3483	159	2	the	the	DET
ejpam-3483	159	3	following	follow	VERB
ejpam-3483	159	4	five	five	NUM
ejpam-3483	159	5	statements	statement	NOUN
ejpam-3483	159	6	are	be	AUX
ejpam-3483	159	7	equivalent	equivalent	ADJ
ejpam-3483	159	8	:	:	PUNCT
ejpam-3483	159	9	(	(	PUNCT
ejpam-3483	159	10	i	i	NOUN
ejpam-3483	159	11	)	)	PUNCT
ejpam-3483	159	12	g	g	PROPN
ejpam-3483	159	13	is	be	AUX
ejpam-3483	159	14	i	i	PROPN
ejpam-3483	159	15	-	-	PUNCT
ejpam-3483	159	16	supra	supra	PROPN
ejpam-3483	159	17	b	b	NOUN
ejpam-3483	159	18	-	-	NOUN
ejpam-3483	159	19	continuous	continuous	ADJ
ejpam-3483	159	20	;	;	PUNCT
ejpam-3483	159	21	(	(	PUNCT
ejpam-3483	159	22	ii	ii	NOUN
ejpam-3483	159	23	)	)	PUNCT
ejpam-3483	159	24	the	the	DET
ejpam-3483	159	25	inverse	inverse	ADJ
ejpam-3483	159	26	image	image	NOUN
ejpam-3483	159	27	of	of	ADP
ejpam-3483	159	28	each	each	DET
ejpam-3483	159	29	closed	closed	ADJ
ejpam-3483	159	30	subset	subset	NOUN
ejpam-3483	159	31	of	of	ADP
ejpam-3483	159	32	y	y	PROPN
ejpam-3483	159	33	is	be	AUX
ejpam-3483	159	34	a	a	DET
ejpam-3483	159	35	d	d	ADJ
ejpam-3483	159	36	-	-	PUNCT
ejpam-3483	159	37	supra	supra	ADJ
ejpam-3483	159	38	b	b	NOUN
ejpam-3483	159	39	-	-	PUNCT
ejpam-3483	159	40	closed	closed	ADJ
ejpam-3483	159	41	subset	subset	NOUN
ejpam-3483	159	42	of	of	ADP
ejpam-3483	159	43	x	x	PROPN
ejpam-3483	159	44	;	;	PUNCT
ejpam-3483	159	45	(	(	PUNCT
ejpam-3483	159	46	iii	iii	X
ejpam-3483	159	47	)	)	PUNCT
ejpam-3483	159	48	(	(	PUNCT
ejpam-3483	159	49	g−1(h))dsbcl	g−1(h))dsbcl	X
ejpam-3483	159	50	⊆	⊆	NUM
ejpam-3483	159	51	g−1(cl(h	g−1(cl(h	NOUN
ejpam-3483	159	52	)	)	PUNCT
ejpam-3483	159	53	)	)	PUNCT
ejpam-3483	159	54	for	for	ADP
ejpam-3483	159	55	every	every	DET
ejpam-3483	159	56	h	h	NOUN
ejpam-3483	159	57	⊆	⊆	NUM
ejpam-3483	159	58	y	y	NOUN
ejpam-3483	159	59	;	;	PUNCT
ejpam-3483	159	60	(	(	PUNCT
ejpam-3483	159	61	iv	iv	X
ejpam-3483	159	62	)	)	PUNCT
ejpam-3483	159	63	g(adsbcl	g(adsbcl	NOUN
ejpam-3483	159	64	)	)	PUNCT
ejpam-3483	159	65	⊆	⊆	NUM
ejpam-3483	159	66	cl(g(a	cl(g(a	NOUN
ejpam-3483	159	67	)	)	PUNCT
ejpam-3483	159	68	)	)	PUNCT
ejpam-3483	159	69	for	for	ADP
ejpam-3483	159	70	every	every	DET
ejpam-3483	159	71	a	a	DET
ejpam-3483	159	72	⊆	⊆	NUM
ejpam-3483	159	73	x	x	SYM
ejpam-3483	159	74	;	;	PUNCT
ejpam-3483	159	75	(	(	PUNCT
ejpam-3483	159	76	v	v	NOUN
ejpam-3483	159	77	)	)	PUNCT
ejpam-3483	159	78	g−1(int(h	g−1(int(h	NOUN
ejpam-3483	159	79	)	)	PUNCT
ejpam-3483	159	80	)	)	PUNCT
ejpam-3483	160	1	⊆	⊆	X
ejpam-3483	160	2	(	(	PUNCT
ejpam-3483	160	3	g−1(h))isbo	g−1(h))isbo	NOUN
ejpam-3483	160	4	for	for	ADP
ejpam-3483	160	5	every	every	DET
ejpam-3483	160	6	h	h	NOUN
ejpam-3483	160	7	⊆	⊆	NUM
ejpam-3483	160	8	y	y	NOUN
ejpam-3483	160	9	.	.	PUNCT
ejpam-3483	161	1	proof	proof	NOUN
ejpam-3483	161	2	.	.	PUNCT
ejpam-3483	162	1	(	(	PUNCT
ejpam-3483	162	2	i	i	NOUN
ejpam-3483	162	3	)	)	PUNCT
ejpam-3483	162	4	⇒	⇒	PROPN
ejpam-3483	162	5	(	(	PUNCT
ejpam-3483	162	6	ii	ii	PROPN
ejpam-3483	162	7	):	):	PUNCT
ejpam-3483	162	8	consider	consider	VERB
ejpam-3483	162	9	h	h	NOUN
ejpam-3483	162	10	is	be	AUX
ejpam-3483	162	11	a	a	DET
ejpam-3483	162	12	closed	closed	ADJ
ejpam-3483	162	13	subset	subset	NOUN
ejpam-3483	162	14	of	of	ADP
ejpam-3483	162	15	y	y	PROPN
ejpam-3483	162	16	.	.	PUNCT
ejpam-3483	163	1	then	then	ADV
ejpam-3483	163	2	hc	hc	PROPN
ejpam-3483	163	3	is	be	AUX
ejpam-3483	163	4	open	open	ADJ
ejpam-3483	163	5	.	.	PUNCT
ejpam-3483	164	1	therefore	therefore	ADV
ejpam-3483	164	2	g−1(hc	g−1(hc	PROPN
ejpam-3483	164	3	)	)	PUNCT
ejpam-3483	164	4	=	=	PUNCT
ejpam-3483	165	1	(	(	PUNCT
ejpam-3483	165	2	g−1(h))c	g−1(h))c	PROPN
ejpam-3483	165	3	is	be	AUX
ejpam-3483	165	4	an	an	DET
ejpam-3483	165	5	i	i	PROPN
ejpam-3483	165	6	-	-	PUNCT
ejpam-3483	165	7	supra	supra	PROPN
ejpam-3483	165	8	b	b	NOUN
ejpam-3483	165	9	-	-	PUNCT
ejpam-3483	165	10	open	open	ADJ
ejpam-3483	165	11	subset	subset	NOUN
ejpam-3483	165	12	of	of	ADP
ejpam-3483	165	13	x.	x.	PROPN
ejpam-3483	165	14	so	so	PROPN
ejpam-3483	165	15	g−1(h	g−1(h	PROPN
ejpam-3483	165	16	)	)	PUNCT
ejpam-3483	165	17	is	be	AUX
ejpam-3483	165	18	d	d	ADJ
ejpam-3483	165	19	-	-	PUNCT
ejpam-3483	165	20	supra	supra	ADJ
ejpam-3483	165	21	b	b	NOUN
ejpam-3483	165	22	-	-	PUNCT
ejpam-3483	165	23	closed	closed	ADJ
ejpam-3483	165	24	.	.	PUNCT
ejpam-3483	166	1	(	(	PUNCT
ejpam-3483	166	2	ii)⇒	ii)⇒	X
ejpam-3483	166	3	(	(	PUNCT
ejpam-3483	166	4	iii	iii	NOUN
ejpam-3483	166	5	):	):	PUNCT
ejpam-3483	166	6	for	for	ADP
ejpam-3483	166	7	any	any	DET
ejpam-3483	166	8	subset	subset	ADJ
ejpam-3483	166	9	h	h	NOUN
ejpam-3483	166	10	of	of	ADP
ejpam-3483	166	11	y	y	PROPN
ejpam-3483	166	12	,	,	PUNCT
ejpam-3483	166	13	we	we	PRON
ejpam-3483	166	14	have	have	AUX
ejpam-3483	166	15	cl(h	cl(h	VERB
ejpam-3483	166	16	)	)	PUNCT
ejpam-3483	166	17	is	be	AUX
ejpam-3483	166	18	closed	close	VERB
ejpam-3483	166	19	.	.	PUNCT
ejpam-3483	167	1	since	since	SCONJ
ejpam-3483	167	2	g−1(cl(h	g−1(cl(h	NOUN
ejpam-3483	167	3	)	)	PUNCT
ejpam-3483	167	4	)	)	PUNCT
ejpam-3483	167	5	is	be	AUX
ejpam-3483	167	6	a	a	DET
ejpam-3483	167	7	d	d	ADJ
ejpam-3483	167	8	-	-	PUNCT
ejpam-3483	167	9	supra	supra	ADJ
ejpam-3483	167	10	b	b	NOUN
ejpam-3483	167	11	-	-	PUNCT
ejpam-3483	167	12	closed	closed	ADJ
ejpam-3483	167	13	subset	subset	NOUN
ejpam-3483	167	14	of	of	ADP
ejpam-3483	167	15	x	x	PRON
ejpam-3483	167	16	,	,	PUNCT
ejpam-3483	167	17	then	then	ADV
ejpam-3483	167	18	(	(	PUNCT
ejpam-3483	167	19	g−1(h))dsbcl	g−1(h))dsbcl	X
ejpam-3483	167	20	⊆	⊆	NUM
ejpam-3483	167	21	(	(	PUNCT
ejpam-3483	167	22	g−1(cl(h))dsbcl	g−1(cl(h))dsbcl	NOUN
ejpam-3483	167	23	=	=	NOUN
ejpam-3483	167	24	g−1(cl(h	g−1(cl(h	NOUN
ejpam-3483	167	25	)	)	PUNCT
ejpam-3483	167	26	)	)	PUNCT
ejpam-3483	167	27	.	.	PUNCT
ejpam-3483	168	1	(	(	PUNCT
ejpam-3483	168	2	iii	iii	X
ejpam-3483	168	3	)	)	PUNCT
ejpam-3483	168	4	⇒	⇒	NOUN
ejpam-3483	168	5	(	(	PUNCT
ejpam-3483	168	6	iv	iv	NUM
ejpam-3483	168	7	):	):	PUNCT
ejpam-3483	168	8	consider	consider	VERB
ejpam-3483	168	9	a	a	PRON
ejpam-3483	168	10	is	be	AUX
ejpam-3483	168	11	a	a	DET
ejpam-3483	168	12	subset	subset	NOUN
ejpam-3483	168	13	of	of	ADP
ejpam-3483	168	14	x.	x.	NOUN
ejpam-3483	168	15	then	then	ADV
ejpam-3483	168	16	adsbcl	adsbcl	VERB
ejpam-3483	168	17	⊆	⊆	NUM
ejpam-3483	168	18	(	(	PUNCT
ejpam-3483	168	19	g−1(g(a)))dsbcl	g−1(g(a)))dsbcl	VERB
ejpam-3483	168	20	⊆	⊆	NUM
ejpam-3483	168	21	g−1(cl(g(a	g−1(cl(g(a	NOUN
ejpam-3483	168	22	)	)	PUNCT
ejpam-3483	168	23	)	)	PUNCT
ejpam-3483	168	24	.	.	PUNCT
ejpam-3483	169	1	therefore	therefore	ADV
ejpam-3483	169	2	g(adsbcl	g(adsbcl	NOUN
ejpam-3483	169	3	)	)	PUNCT
ejpam-3483	169	4	⊆	⊆	NUM
ejpam-3483	169	5	g(g−1(cl(g(a	g(g−1(cl(g(a	NOUN
ejpam-3483	169	6	)	)	PUNCT
ejpam-3483	169	7	)	)	PUNCT
ejpam-3483	169	8	)	)	PUNCT
ejpam-3483	170	1	⊆	⊆	NUM
ejpam-3483	170	2	cl(g(a	cl(g(a	NOUN
ejpam-3483	170	3	)	)	PUNCT
ejpam-3483	170	4	)	)	PUNCT
ejpam-3483	170	5	.	.	PUNCT
ejpam-3483	171	1	(	(	PUNCT
ejpam-3483	171	2	iv)⇒	iv)⇒	X
ejpam-3483	171	3	(	(	PUNCT
ejpam-3483	171	4	v	v	NOUN
ejpam-3483	171	5	):	):	PUNCT
ejpam-3483	171	6	let	let	VERB
ejpam-3483	171	7	h	h	PRON
ejpam-3483	171	8	be	be	AUX
ejpam-3483	171	9	a	a	DET
ejpam-3483	171	10	subset	subset	NOUN
ejpam-3483	171	11	of	of	ADP
ejpam-3483	171	12	y	y	PROPN
ejpam-3483	171	13	.	.	PUNCT
ejpam-3483	172	1	by	by	ADP
ejpam-3483	172	2	lemma	lemma	PROPN
ejpam-3483	172	3	(	(	PUNCT
ejpam-3483	172	4	1	1	NUM
ejpam-3483	172	5	)	)	PUNCT
ejpam-3483	172	6	,	,	PUNCT
ejpam-3483	172	7	we	we	PRON
ejpam-3483	172	8	obtain	obtain	VERB
ejpam-3483	172	9	g(x	g(x	PROPN
ejpam-3483	172	10	−	−	PROPN
ejpam-3483	172	11	(	(	PUNCT
ejpam-3483	172	12	g−1(h))isbo	g−1(h))isbo	PROPN
ejpam-3483	172	13	)	)	PUNCT
ejpam-3483	172	14	=	=	NOUN
ejpam-3483	172	15	g(((g−1(h))c)dsbcl	g(((g−1(h))c)dsbcl	NOUN
ejpam-3483	172	16	)	)	PUNCT
ejpam-3483	172	17	.	.	PUNCT
ejpam-3483	173	1	by	by	ADP
ejpam-3483	173	2	(	(	PUNCT
ejpam-3483	173	3	iv	iv	X
ejpam-3483	173	4	)	)	PUNCT
ejpam-3483	173	5	g(((g−1(h))c)dsbcl	g(((g−1(h))c)dsbcl	NOUN
ejpam-3483	173	6	)	)	PUNCT
ejpam-3483	173	7	⊆	⊆	NUM
ejpam-3483	173	8	cl(g(g−1(h))c	cl(g(g−1(h))c	PROPN
ejpam-3483	173	9	)	)	PUNCT
ejpam-3483	173	10	=	=	PUNCT
ejpam-3483	173	11	cl(g(g−1(hc	cl(g(g−1(hc	PROPN
ejpam-3483	173	12	)	)	PUNCT
ejpam-3483	173	13	)	)	PUNCT
ejpam-3483	173	14	)	)	PUNCT
ejpam-3483	174	1	⊆	⊆	NUM
ejpam-3483	174	2	cl(y	cl(y	NUM
ejpam-3483	174	3	−	−	NOUN
ejpam-3483	174	4	h	h	NOUN
ejpam-3483	174	5	)	)	PUNCT
ejpam-3483	174	6	=	=	SYM
ejpam-3483	175	1	y	y	PROPN
ejpam-3483	175	2	−	−	PROPN
ejpam-3483	175	3	int(h	int(h	PROPN
ejpam-3483	175	4	)	)	PUNCT
ejpam-3483	175	5	.	.	PUNCT
ejpam-3483	176	1	therefore	therefore	ADV
ejpam-3483	176	2	(	(	PUNCT
ejpam-3483	176	3	x	x	X
ejpam-3483	176	4	−	−	PROPN
ejpam-3483	176	5	(	(	PUNCT
ejpam-3483	176	6	g−1(h))isbo	g−1(h))isbo	PROPN
ejpam-3483	176	7	)	)	PUNCT
ejpam-3483	176	8	⊆	⊆	NUM
ejpam-3483	176	9	g−1(y	g−1(y	PROPN
ejpam-3483	176	10	−	−	PROPN
ejpam-3483	176	11	int(h	int(h	NOUN
ejpam-3483	176	12	)	)	PUNCT
ejpam-3483	176	13	)	)	PUNCT
ejpam-3483	177	1	=	=	PUNCT
ejpam-3483	177	2	x	x	X
ejpam-3483	177	3	−	−	NOUN
ejpam-3483	177	4	g−1(int(h	g−1(int(h	NOUN
ejpam-3483	177	5	)	)	PUNCT
ejpam-3483	177	6	)	)	PUNCT
ejpam-3483	177	7	.	.	PUNCT
ejpam-3483	178	1	thus	thus	ADV
ejpam-3483	178	2	g−1(int(h	g−1(int(h	VERB
ejpam-3483	178	3	)	)	PUNCT
ejpam-3483	178	4	)	)	PUNCT
ejpam-3483	179	1	⊆	⊆	NUM
ejpam-3483	179	2	(	(	PUNCT
ejpam-3483	179	3	g−1(h))isbo	g−1(h))isbo	NOUN
ejpam-3483	179	4	.	.	PUNCT
ejpam-3483	180	1	(	(	PUNCT
ejpam-3483	180	2	v)⇒	v)⇒	PROPN
ejpam-3483	180	3	(	(	PUNCT
ejpam-3483	180	4	i	i	NOUN
ejpam-3483	180	5	):	):	PUNCT
ejpam-3483	180	6	consider	consider	VERB
ejpam-3483	180	7	h	h	NOUN
ejpam-3483	180	8	is	be	AUX
ejpam-3483	180	9	an	an	DET
ejpam-3483	180	10	open	open	ADJ
ejpam-3483	180	11	subset	subset	NOUN
ejpam-3483	180	12	of	of	ADP
ejpam-3483	180	13	y	y	PROPN
ejpam-3483	180	14	.	.	PUNCT
ejpam-3483	181	1	then	then	ADV
ejpam-3483	181	2	g−1(h	g−1(h	PROPN
ejpam-3483	181	3	)	)	PUNCT
ejpam-3483	181	4	=	=	SYM
ejpam-3483	181	5	g−1(int(h	g−1(int(h	NOUN
ejpam-3483	181	6	)	)	PUNCT
ejpam-3483	181	7	)	)	PUNCT
ejpam-3483	182	1	⊆	⊆	X
ejpam-3483	182	2	(	(	PUNCT
ejpam-3483	182	3	g−1(h))isbo	g−1(h))isbo	PROPN
ejpam-3483	182	4	.	.	PROPN
ejpam-3483	183	1	from	from	ADP
ejpam-3483	183	2	the	the	DET
ejpam-3483	183	3	fact	fact	NOUN
ejpam-3483	183	4	that	that	SCONJ
ejpam-3483	183	5	(	(	PUNCT
ejpam-3483	183	6	g−1(h))isbo	g−1(h))isbo	PROPN
ejpam-3483	183	7	⊆	⊆	NUM
ejpam-3483	183	8	g−1(h	g−1(h	PROPN
ejpam-3483	183	9	)	)	PUNCT
ejpam-3483	183	10	,	,	PUNCT
ejpam-3483	183	11	we	we	PRON
ejpam-3483	183	12	have	have	AUX
ejpam-3483	183	13	g−1(h	g−1(h	PROPN
ejpam-3483	183	14	)	)	PUNCT
ejpam-3483	183	15	is	be	AUX
ejpam-3483	183	16	an	an	DET
ejpam-3483	183	17	i	i	PROPN
ejpam-3483	183	18	-	-	PUNCT
ejpam-3483	183	19	supra	supra	PROPN
ejpam-3483	183	20	b	b	NOUN
ejpam-3483	183	21	-	-	PUNCT
ejpam-3483	183	22	open	open	ADJ
ejpam-3483	183	23	subset	subset	NOUN
ejpam-3483	183	24	of	of	ADP
ejpam-3483	183	25	x.	x.	NOUN
ejpam-3483	183	26	thus	thus	ADV
ejpam-3483	183	27	g	g	PROPN
ejpam-3483	183	28	is	be	AUX
ejpam-3483	183	29	i	i	PROPN
ejpam-3483	183	30	-	-	PUNCT
ejpam-3483	183	31	supra	supra	PROPN
ejpam-3483	183	32	b	b	NOUN
ejpam-3483	183	33	-	-	PUNCT
ejpam-3483	183	34	continuous	continuous	ADJ
ejpam-3483	183	35	.	.	PUNCT
ejpam-3483	184	1	b.	b.	PROPN
ejpam-3483	184	2	a.	a.	PROPN
ejpam-3483	184	3	asaad	asaad	PROPN
ejpam-3483	184	4	,	,	PUNCT
ejpam-3483	184	5	m.	m.	PROPN
ejpam-3483	184	6	k.	k.	PROPN
ejpam-3483	184	7	tahat	tahat	PROPN
ejpam-3483	184	8	,	,	PUNCT
ejpam-3483	184	9	t.	t.	PROPN
ejpam-3483	184	10	m.	m.	PROPN
ejpam-3483	184	11	al	al	PROPN
ejpam-3483	184	12	-	-	PUNCT
ejpam-3483	184	13	shami	shami	PROPN
ejpam-3483	184	14	/	/	PUNCT
ejpam-3483	184	15	eur	eur	PROPN
ejpam-3483	184	16	.	.	PUNCT
ejpam-3483	185	1	j.	j.	PROPN
ejpam-3483	185	2	pure	pure	PROPN
ejpam-3483	185	3	appl	appl	PROPN
ejpam-3483	185	4	.	.	PROPN
ejpam-3483	185	5	math	math	PROPN
ejpam-3483	185	6	,	,	PUNCT
ejpam-3483	185	7	12	12	NUM
ejpam-3483	185	8	(	(	PUNCT
ejpam-3483	185	9	3	3	NUM
ejpam-3483	185	10	)	)	PUNCT
ejpam-3483	185	11	(	(	PUNCT
ejpam-3483	185	12	2019	2019	NUM
ejpam-3483	185	13	)	)	PUNCT
ejpam-3483	185	14	,	,	PUNCT
ejpam-3483	185	15	1231	1231	NUM
ejpam-3483	185	16	-	-	SYM
ejpam-3483	185	17	1247	1247	NUM
ejpam-3483	185	18	1237	1237	NUM
ejpam-3483	185	19	theorem	theorem	NOUN
ejpam-3483	185	20	4	4	NUM
ejpam-3483	185	21	.	.	PUNCT
ejpam-3483	186	1	let	let	VERB
ejpam-3483	186	2	g	g	NOUN
ejpam-3483	186	3	:	:	PUNCT
ejpam-3483	186	4	(	(	PUNCT
ejpam-3483	186	5	x,µ,	x,µ,	PROPN
ejpam-3483	186	6	�	�	PROPN
ejpam-3483	186	7	)→	)→	PROPN
ejpam-3483	186	8	(	(	PUNCT
ejpam-3483	186	9	y	y	PROPN
ejpam-3483	186	10	,	,	PUNCT
ejpam-3483	186	11	τ	τ	PROPN
ejpam-3483	186	12	)	)	PUNCT
ejpam-3483	186	13	be	be	VERB
ejpam-3483	186	14	a	a	DET
ejpam-3483	186	15	map	map	NOUN
ejpam-3483	186	16	.	.	PUNCT
ejpam-3483	187	1	then	then	ADV
ejpam-3483	187	2	the	the	DET
ejpam-3483	187	3	following	follow	VERB
ejpam-3483	187	4	five	five	NUM
ejpam-3483	187	5	statements	statement	NOUN
ejpam-3483	187	6	are	be	AUX
ejpam-3483	187	7	equivalent	equivalent	ADJ
ejpam-3483	187	8	:	:	PUNCT
ejpam-3483	187	9	(	(	PUNCT
ejpam-3483	187	10	i	i	NOUN
ejpam-3483	187	11	)	)	PUNCT
ejpam-3483	187	12	g	g	PROPN
ejpam-3483	187	13	is	be	AUX
ejpam-3483	187	14	d	d	NOUN
ejpam-3483	187	15	-	-	PUNCT
ejpam-3483	187	16	supra	supra	ADJ
ejpam-3483	187	17	b	b	NOUN
ejpam-3483	187	18	-	-	NOUN
ejpam-3483	187	19	continuous	continuous	ADJ
ejpam-3483	187	20	;	;	PUNCT
ejpam-3483	187	21	(	(	PUNCT
ejpam-3483	187	22	ii	ii	NOUN
ejpam-3483	187	23	)	)	PUNCT
ejpam-3483	187	24	the	the	DET
ejpam-3483	187	25	inverse	inverse	ADJ
ejpam-3483	187	26	image	image	NOUN
ejpam-3483	187	27	of	of	ADP
ejpam-3483	187	28	each	each	DET
ejpam-3483	187	29	closed	closed	ADJ
ejpam-3483	187	30	subset	subset	NOUN
ejpam-3483	187	31	of	of	ADP
ejpam-3483	187	32	y	y	PROPN
ejpam-3483	187	33	is	be	AUX
ejpam-3483	187	34	an	an	DET
ejpam-3483	187	35	i	i	PROPN
ejpam-3483	187	36	-	-	PUNCT
ejpam-3483	187	37	supra	supra	PROPN
ejpam-3483	187	38	b	b	PROPN
ejpam-3483	187	39	-	-	PUNCT
ejpam-3483	187	40	closed	closed	ADJ
ejpam-3483	187	41	subset	subset	NOUN
ejpam-3483	187	42	of	of	ADP
ejpam-3483	187	43	x	x	PROPN
ejpam-3483	187	44	;	;	PUNCT
ejpam-3483	187	45	(	(	PUNCT
ejpam-3483	187	46	iii	iii	X
ejpam-3483	187	47	)	)	PUNCT
ejpam-3483	187	48	(	(	PUNCT
ejpam-3483	187	49	g−1(h))isbcl	g−1(h))isbcl	X
ejpam-3483	187	50	⊆	⊆	NUM
ejpam-3483	187	51	g−1(cl(h	g−1(cl(h	NOUN
ejpam-3483	187	52	)	)	PUNCT
ejpam-3483	187	53	)	)	PUNCT
ejpam-3483	187	54	for	for	ADP
ejpam-3483	187	55	every	every	DET
ejpam-3483	187	56	h	h	NOUN
ejpam-3483	187	57	⊆	⊆	NUM
ejpam-3483	187	58	y	y	NOUN
ejpam-3483	187	59	;	;	PUNCT
ejpam-3483	187	60	(	(	PUNCT
ejpam-3483	187	61	iv	iv	X
ejpam-3483	187	62	)	)	PUNCT
ejpam-3483	187	63	g(aisbcl	g(aisbcl	NOUN
ejpam-3483	187	64	)	)	PUNCT
ejpam-3483	187	65	⊆	⊆	NUM
ejpam-3483	187	66	cl(g(a	cl(g(a	NOUN
ejpam-3483	187	67	)	)	PUNCT
ejpam-3483	187	68	)	)	PUNCT
ejpam-3483	187	69	for	for	ADP
ejpam-3483	187	70	every	every	DET
ejpam-3483	187	71	a	a	DET
ejpam-3483	187	72	⊆	⊆	NUM
ejpam-3483	187	73	x	x	SYM
ejpam-3483	187	74	;	;	PUNCT
ejpam-3483	187	75	(	(	PUNCT
ejpam-3483	187	76	v	v	NOUN
ejpam-3483	187	77	)	)	PUNCT
ejpam-3483	187	78	g−1(int(h	g−1(int(h	NOUN
ejpam-3483	187	79	)	)	PUNCT
ejpam-3483	187	80	)	)	PUNCT
ejpam-3483	188	1	⊆	⊆	NUM
ejpam-3483	188	2	(	(	PUNCT
ejpam-3483	188	3	g−1(h))dsbo	g−1(h))dsbo	PROPN
ejpam-3483	188	4	for	for	ADP
ejpam-3483	188	5	every	every	DET
ejpam-3483	188	6	h	h	NOUN
ejpam-3483	188	7	⊆	⊆	NUM
ejpam-3483	188	8	y	y	NOUN
ejpam-3483	188	9	.	.	PUNCT
ejpam-3483	189	1	proof	proof	NOUN
ejpam-3483	189	2	.	.	PUNCT
ejpam-3483	190	1	the	the	DET
ejpam-3483	190	2	proof	proof	NOUN
ejpam-3483	190	3	is	be	AUX
ejpam-3483	190	4	similar	similar	ADJ
ejpam-3483	190	5	to	to	ADP
ejpam-3483	190	6	that	that	PRON
ejpam-3483	190	7	of	of	ADP
ejpam-3483	190	8	theorem	theorem	ADJ
ejpam-3483	190	9	3	3	NUM
ejpam-3483	190	10	.	.	PUNCT
ejpam-3483	190	11	theorem	theorem	NOUN
ejpam-3483	190	12	5	5	NUM
ejpam-3483	190	13	.	.	PUNCT
ejpam-3483	191	1	let	let	VERB
ejpam-3483	191	2	g	g	NOUN
ejpam-3483	191	3	:	:	PUNCT
ejpam-3483	191	4	(	(	PUNCT
ejpam-3483	191	5	x,µ,	x,µ,	PROPN
ejpam-3483	191	6	�	�	PROPN
ejpam-3483	191	7	)→	)→	PROPN
ejpam-3483	191	8	(	(	PUNCT
ejpam-3483	191	9	y	y	PROPN
ejpam-3483	191	10	,	,	PUNCT
ejpam-3483	191	11	τ	τ	PROPN
ejpam-3483	191	12	)	)	PUNCT
ejpam-3483	191	13	be	be	VERB
ejpam-3483	191	14	a	a	DET
ejpam-3483	191	15	map	map	NOUN
ejpam-3483	191	16	.	.	PUNCT
ejpam-3483	192	1	then	then	ADV
ejpam-3483	192	2	the	the	DET
ejpam-3483	192	3	following	follow	VERB
ejpam-3483	192	4	five	five	NUM
ejpam-3483	192	5	statements	statement	NOUN
ejpam-3483	192	6	are	be	AUX
ejpam-3483	192	7	equivalent	equivalent	ADJ
ejpam-3483	192	8	:	:	PUNCT
ejpam-3483	192	9	(	(	PUNCT
ejpam-3483	192	10	i	i	NOUN
ejpam-3483	192	11	)	)	PUNCT
ejpam-3483	192	12	g	g	PROPN
ejpam-3483	192	13	is	be	AUX
ejpam-3483	192	14	b	b	NOUN
ejpam-3483	192	15	-	-	PUNCT
ejpam-3483	192	16	supra	supra	ADJ
ejpam-3483	192	17	b	b	NOUN
ejpam-3483	192	18	-	-	NOUN
ejpam-3483	192	19	continuous	continuous	ADJ
ejpam-3483	192	20	;	;	PUNCT
ejpam-3483	192	21	(	(	PUNCT
ejpam-3483	192	22	ii	ii	NOUN
ejpam-3483	192	23	)	)	PUNCT
ejpam-3483	192	24	the	the	DET
ejpam-3483	192	25	inverse	inverse	ADJ
ejpam-3483	192	26	image	image	NOUN
ejpam-3483	192	27	of	of	ADP
ejpam-3483	192	28	each	each	DET
ejpam-3483	192	29	closed	closed	ADJ
ejpam-3483	192	30	subset	subset	NOUN
ejpam-3483	192	31	of	of	ADP
ejpam-3483	192	32	y	y	PROPN
ejpam-3483	192	33	is	be	AUX
ejpam-3483	192	34	a	a	DET
ejpam-3483	192	35	b	b	PROPN
ejpam-3483	192	36	-	-	PUNCT
ejpam-3483	192	37	supra	supra	ADJ
ejpam-3483	192	38	b	b	NOUN
ejpam-3483	192	39	-	-	PUNCT
ejpam-3483	192	40	closed	closed	ADJ
ejpam-3483	192	41	subset	subset	NOUN
ejpam-3483	192	42	of	of	ADP
ejpam-3483	192	43	x	x	PROPN
ejpam-3483	192	44	;	;	PUNCT
ejpam-3483	192	45	(	(	PUNCT
ejpam-3483	192	46	iii	iii	X
ejpam-3483	192	47	)	)	PUNCT
ejpam-3483	192	48	(	(	PUNCT
ejpam-3483	192	49	g−1(h))bsbcl	g−1(h))bsbcl	X
ejpam-3483	192	50	⊆	⊆	NUM
ejpam-3483	192	51	g−1(cl(h	g−1(cl(h	NOUN
ejpam-3483	192	52	)	)	PUNCT
ejpam-3483	192	53	)	)	PUNCT
ejpam-3483	192	54	for	for	ADP
ejpam-3483	192	55	every	every	DET
ejpam-3483	192	56	h	h	NOUN
ejpam-3483	192	57	⊆	⊆	NUM
ejpam-3483	192	58	y	y	NOUN
ejpam-3483	192	59	;	;	PUNCT
ejpam-3483	192	60	(	(	PUNCT
ejpam-3483	192	61	iv	iv	X
ejpam-3483	192	62	)	)	PUNCT
ejpam-3483	192	63	g(absbcl	g(absbcl	NOUN
ejpam-3483	192	64	)	)	PUNCT
ejpam-3483	192	65	⊆	⊆	NUM
ejpam-3483	192	66	cl(g(a	cl(g(a	NOUN
ejpam-3483	192	67	)	)	PUNCT
ejpam-3483	192	68	)	)	PUNCT
ejpam-3483	192	69	for	for	ADP
ejpam-3483	192	70	every	every	DET
ejpam-3483	192	71	a	a	DET
ejpam-3483	192	72	⊆	⊆	NUM
ejpam-3483	192	73	x	x	SYM
ejpam-3483	192	74	;	;	PUNCT
ejpam-3483	192	75	(	(	PUNCT
ejpam-3483	192	76	v	v	NOUN
ejpam-3483	192	77	)	)	PUNCT
ejpam-3483	192	78	g−1(int(h	g−1(int(h	NOUN
ejpam-3483	192	79	)	)	PUNCT
ejpam-3483	192	80	)	)	PUNCT
ejpam-3483	193	1	⊆	⊆	NUM
ejpam-3483	193	2	(	(	PUNCT
ejpam-3483	193	3	g−1(h))bsbo	g−1(h))bsbo	NOUN
ejpam-3483	193	4	for	for	ADP
ejpam-3483	193	5	every	every	DET
ejpam-3483	193	6	h	h	NOUN
ejpam-3483	193	7	⊆	⊆	NUM
ejpam-3483	193	8	y	y	NOUN
ejpam-3483	193	9	.	.	PUNCT
ejpam-3483	194	1	proof	proof	NOUN
ejpam-3483	194	2	.	.	PUNCT
ejpam-3483	195	1	the	the	DET
ejpam-3483	195	2	proof	proof	NOUN
ejpam-3483	195	3	is	be	AUX
ejpam-3483	195	4	similar	similar	ADJ
ejpam-3483	195	5	to	to	ADP
ejpam-3483	195	6	that	that	PRON
ejpam-3483	195	7	of	of	ADP
ejpam-3483	195	8	theorem	theorem	ADJ
ejpam-3483	195	9	3	3	NUM
ejpam-3483	195	10	.	.	PUNCT
ejpam-3483	195	11	definition	definition	NOUN
ejpam-3483	195	12	15	15	NUM
ejpam-3483	195	13	.	.	PUNCT
ejpam-3483	196	1	a	a	DET
ejpam-3483	196	2	supra	supra	PROPN
ejpam-3483	196	3	topological	topological	ADJ
ejpam-3483	196	4	ordered	order	VERB
ejpam-3483	196	5	space	space	NOUN
ejpam-3483	196	6	(	(	PUNCT
ejpam-3483	196	7	x,µ	x,µ	NOUN
ejpam-3483	196	8	,	,	PUNCT
ejpam-3483	196	9	�	�	PROPN
ejpam-3483	196	10	)	)	PUNCT
ejpam-3483	196	11	is	be	AUX
ejpam-3483	196	12	called	call	VERB
ejpam-3483	196	13	:	:	PUNCT
ejpam-3483	196	14	(	(	PUNCT
ejpam-3483	196	15	i	i	NOUN
ejpam-3483	196	16	)	)	PUNCT
ejpam-3483	196	17	lower	low	ADJ
ejpam-3483	196	18	strong	strong	ADJ
ejpam-3483	196	19	supra	supra	ADJ
ejpam-3483	196	20	bt1	bt1	NOUN
ejpam-3483	196	21	-	-	PUNCT
ejpam-3483	196	22	ordered	order	VERB
ejpam-3483	196	23	(	(	PUNCT
ejpam-3483	196	24	briefly	briefly	ADV
ejpam-3483	196	25	,	,	PUNCT
ejpam-3483	196	26	lower	low	ADJ
ejpam-3483	196	27	ssbt1	ssbt1	NOUN
ejpam-3483	196	28	-	-	PUNCT
ejpam-3483	196	29	ordered	order	VERB
ejpam-3483	196	30	)	)	PUNCT
ejpam-3483	196	31	if	if	SCONJ
ejpam-3483	196	32	for	for	ADP
ejpam-3483	196	33	each	each	DET
ejpam-3483	196	34	a	a	NOUN
ejpam-3483	196	35	,	,	PUNCT
ejpam-3483	196	36	b	b	X
ejpam-3483	196	37	∈	∈	PROPN
ejpam-3483	196	38	x	x	X
ejpam-3483	196	39	such	such	ADJ
ejpam-3483	196	40	that	that	SCONJ
ejpam-3483	196	41	a	a	DET
ejpam-3483	196	42	6	6	NUM
ejpam-3483	196	43	�	�	PROPN
ejpam-3483	196	44	b	b	PROPN
ejpam-3483	196	45	,	,	PUNCT
ejpam-3483	196	46	there	there	PRON
ejpam-3483	196	47	exists	exist	VERB
ejpam-3483	196	48	an	an	DET
ejpam-3483	196	49	increasing	increase	VERB
ejpam-3483	196	50	supra	supra	ADJ
ejpam-3483	196	51	b	b	NOUN
ejpam-3483	196	52	-	-	PUNCT
ejpam-3483	196	53	open	open	ADJ
ejpam-3483	196	54	set	set	NOUN
ejpam-3483	196	55	g	g	NOUN
ejpam-3483	196	56	containing	contain	VERB
ejpam-3483	196	57	a	a	PRON
ejpam-3483	196	58	does	do	AUX
ejpam-3483	196	59	not	not	PART
ejpam-3483	196	60	contain	contain	VERB
ejpam-3483	196	61	b.	b.	PROPN
ejpam-3483	196	62	(	(	PUNCT
ejpam-3483	196	63	i	i	NOUN
ejpam-3483	196	64	)	)	PUNCT
ejpam-3483	196	65	upper	upper	ADJ
ejpam-3483	196	66	strong	strong	ADJ
ejpam-3483	196	67	supra	supra	PROPN
ejpam-3483	196	68	bt1	bt1	PROPN
ejpam-3483	196	69	-	-	PUNCT
ejpam-3483	196	70	ordered	order	VERB
ejpam-3483	196	71	(	(	PUNCT
ejpam-3483	196	72	briefly	briefly	ADV
ejpam-3483	196	73	,	,	PUNCT
ejpam-3483	196	74	upper	upper	ADJ
ejpam-3483	196	75	ssbt1	ssbt1	NOUN
ejpam-3483	196	76	-	-	PUNCT
ejpam-3483	196	77	ordered	order	VERB
ejpam-3483	196	78	)	)	PUNCT
ejpam-3483	196	79	if	if	SCONJ
ejpam-3483	196	80	for	for	ADP
ejpam-3483	196	81	each	each	DET
ejpam-3483	196	82	a	a	NOUN
ejpam-3483	196	83	,	,	PUNCT
ejpam-3483	196	84	b	b	X
ejpam-3483	196	85	∈	∈	PROPN
ejpam-3483	196	86	x	x	X
ejpam-3483	196	87	such	such	ADJ
ejpam-3483	196	88	that	that	SCONJ
ejpam-3483	196	89	a	a	DET
ejpam-3483	196	90	6	6	NUM
ejpam-3483	196	91	�	�	PROPN
ejpam-3483	196	92	b	b	PROPN
ejpam-3483	196	93	,	,	PUNCT
ejpam-3483	196	94	there	there	PRON
ejpam-3483	196	95	exists	exist	VERB
ejpam-3483	196	96	a	a	DET
ejpam-3483	196	97	decreasing	decrease	VERB
ejpam-3483	196	98	supra	supra	ADJ
ejpam-3483	196	99	b	b	NOUN
ejpam-3483	196	100	-	-	PUNCT
ejpam-3483	196	101	open	open	ADJ
ejpam-3483	196	102	set	set	NOUN
ejpam-3483	196	103	g	g	NOUN
ejpam-3483	196	104	containing	contain	VERB
ejpam-3483	196	105	b	b	NOUN
ejpam-3483	196	106	does	do	AUX
ejpam-3483	196	107	not	not	PART
ejpam-3483	196	108	contain	contain	VERB
ejpam-3483	196	109	a.	a.	NOUN
ejpam-3483	196	110	(	(	PUNCT
ejpam-3483	196	111	ii	ii	NOUN
ejpam-3483	196	112	)	)	PUNCT
ejpam-3483	196	113	ssbt0	ssbt0	NOUN
ejpam-3483	196	114	-	-	PUNCT
ejpam-3483	196	115	ordered	order	VERB
ejpam-3483	196	116	if	if	SCONJ
ejpam-3483	196	117	it	it	PRON
ejpam-3483	196	118	is	be	AUX
ejpam-3483	196	119	lower	low	ADJ
ejpam-3483	196	120	ssbt1	ssbt1	NOUN
ejpam-3483	196	121	-	-	PUNCT
ejpam-3483	196	122	ordered	order	VERB
ejpam-3483	196	123	or	or	CCONJ
ejpam-3483	196	124	upper	upper	ADJ
ejpam-3483	196	125	ssbt1	ssbt1	NOUN
ejpam-3483	196	126	-	-	PUNCT
ejpam-3483	196	127	ordered	order	VERB
ejpam-3483	196	128	.	.	PUNCT
ejpam-3483	197	1	(	(	PUNCT
ejpam-3483	197	2	iii	iii	NOUN
ejpam-3483	197	3	)	)	PUNCT
ejpam-3483	197	4	ssbt1	ssbt1	NOUN
ejpam-3483	197	5	-	-	PUNCT
ejpam-3483	197	6	ordered	order	VERB
ejpam-3483	197	7	if	if	SCONJ
ejpam-3483	197	8	it	it	PRON
ejpam-3483	197	9	is	be	AUX
ejpam-3483	197	10	lower	low	ADJ
ejpam-3483	197	11	ssbt1	ssbt1	NOUN
ejpam-3483	197	12	-	-	PUNCT
ejpam-3483	197	13	ordered	order	VERB
ejpam-3483	197	14	and	and	CCONJ
ejpam-3483	197	15	upper	upper	ADJ
ejpam-3483	197	16	ssbt1	ssbt1	NOUN
ejpam-3483	197	17	-	-	PUNCT
ejpam-3483	197	18	ordered	order	VERB
ejpam-3483	197	19	.	.	PUNCT
ejpam-3483	198	1	(	(	PUNCT
ejpam-3483	198	2	iv	iv	X
ejpam-3483	198	3	)	)	PUNCT
ejpam-3483	198	4	ssbt2	ssbt2	NOUN
ejpam-3483	198	5	-	-	PUNCT
ejpam-3483	198	6	ordered	order	VERB
ejpam-3483	198	7	if	if	SCONJ
ejpam-3483	198	8	for	for	ADP
ejpam-3483	198	9	every	every	DET
ejpam-3483	198	10	a	a	PROPN
ejpam-3483	198	11	,	,	PUNCT
ejpam-3483	198	12	b	b	X
ejpam-3483	198	13	∈	∈	PROPN
ejpam-3483	198	14	x	x	X
ejpam-3483	198	15	such	such	ADJ
ejpam-3483	198	16	that	that	SCONJ
ejpam-3483	198	17	a	a	DET
ejpam-3483	198	18	6	6	NUM
ejpam-3483	198	19	�	�	PROPN
ejpam-3483	198	20	b	b	NOUN
ejpam-3483	198	21	,	,	PUNCT
ejpam-3483	198	22	there	there	PRON
ejpam-3483	198	23	exist	exist	VERB
ejpam-3483	198	24	disjoint	disjoint	ADJ
ejpam-3483	198	25	supra	supra	PROPN
ejpam-3483	198	26	b	b	NOUN
ejpam-3483	198	27	-	-	PUNCT
ejpam-3483	198	28	open	open	ADJ
ejpam-3483	198	29	sets	set	VERB
ejpam-3483	198	30	w1	w1	NOUN
ejpam-3483	198	31	and	and	CCONJ
ejpam-3483	198	32	w2	w2	NOUN
ejpam-3483	198	33	containing	contain	VERB
ejpam-3483	198	34	a	a	PRON
ejpam-3483	198	35	and	and	CCONJ
ejpam-3483	198	36	b	b	NOUN
ejpam-3483	198	37	,	,	PUNCT
ejpam-3483	198	38	respectively	respectively	ADV
ejpam-3483	198	39	,	,	PUNCT
ejpam-3483	198	40	such	such	ADJ
ejpam-3483	198	41	that	that	DET
ejpam-3483	198	42	w1	w1	NOUN
ejpam-3483	198	43	is	be	AUX
ejpam-3483	198	44	increasing	increase	VERB
ejpam-3483	198	45	and	and	CCONJ
ejpam-3483	198	46	w2	w2	NOUN
ejpam-3483	198	47	is	be	AUX
ejpam-3483	198	48	decreasing	decrease	VERB
ejpam-3483	198	49	.	.	PUNCT
ejpam-3483	199	1	b.	b.	PROPN
ejpam-3483	199	2	a.	a.	PROPN
ejpam-3483	199	3	asaad	asaad	PROPN
ejpam-3483	199	4	,	,	PUNCT
ejpam-3483	199	5	m.	m.	PROPN
ejpam-3483	199	6	k.	k.	PROPN
ejpam-3483	199	7	tahat	tahat	PROPN
ejpam-3483	199	8	,	,	PUNCT
ejpam-3483	199	9	t.	t.	PROPN
ejpam-3483	199	10	m.	m.	PROPN
ejpam-3483	199	11	al	al	PROPN
ejpam-3483	199	12	-	-	PUNCT
ejpam-3483	199	13	shami	shami	PROPN
ejpam-3483	199	14	/	/	PUNCT
ejpam-3483	199	15	eur	eur	PROPN
ejpam-3483	199	16	.	.	PUNCT
ejpam-3483	200	1	j.	j.	PROPN
ejpam-3483	200	2	pure	pure	PROPN
ejpam-3483	200	3	appl	appl	PROPN
ejpam-3483	200	4	.	.	PROPN
ejpam-3483	200	5	math	math	PROPN
ejpam-3483	200	6	,	,	PUNCT
ejpam-3483	200	7	12	12	NUM
ejpam-3483	200	8	(	(	PUNCT
ejpam-3483	200	9	3	3	NUM
ejpam-3483	200	10	)	)	PUNCT
ejpam-3483	200	11	(	(	PUNCT
ejpam-3483	200	12	2019	2019	NUM
ejpam-3483	200	13	)	)	PUNCT
ejpam-3483	200	14	,	,	PUNCT
ejpam-3483	200	15	1231	1231	NUM
ejpam-3483	200	16	-	-	SYM
ejpam-3483	200	17	1247	1247	NUM
ejpam-3483	200	18	1238	1238	NUM
ejpam-3483	200	19	theorem	theorem	VERB
ejpam-3483	200	20	6	6	NUM
ejpam-3483	200	21	.	.	PUNCT
ejpam-3483	201	1	let	let	VERB
ejpam-3483	201	2	a	a	DET
ejpam-3483	201	3	bijective	bijective	ADJ
ejpam-3483	201	4	map	map	NOUN
ejpam-3483	201	5	f	f	X
ejpam-3483	201	6	:	:	PUNCT
ejpam-3483	201	7	(	(	PUNCT
ejpam-3483	201	8	x,µ,	x,µ,	PROPN
ejpam-3483	201	9	�	�	PROPN
ejpam-3483	201	10	1	1	NUM
ejpam-3483	201	11	)	)	PUNCT
ejpam-3483	201	12	→	→	SYM
ejpam-3483	201	13	(	(	PUNCT
ejpam-3483	201	14	y	y	NOUN
ejpam-3483	201	15	,	,	PUNCT
ejpam-3483	201	16	τ,	τ,	NOUN
ejpam-3483	201	17	�	�	X
ejpam-3483	201	18	2	2	NUM
ejpam-3483	201	19	)	)	PUNCT
ejpam-3483	201	20	be	be	VERB
ejpam-3483	201	21	i	i	PROPN
ejpam-3483	201	22	-	-	PUNCT
ejpam-3483	201	23	supra	supra	PROPN
ejpam-3483	201	24	b	b	NOUN
ejpam-3483	201	25	-	-	PUNCT
ejpam-3483	201	26	continuous	continuous	ADJ
ejpam-3483	201	27	and	and	CCONJ
ejpam-3483	201	28	f−1	f−1	PROPN
ejpam-3483	201	29	be	be	VERB
ejpam-3483	201	30	an	an	DET
ejpam-3483	201	31	order	order	NOUN
ejpam-3483	201	32	preserving	preserve	VERB
ejpam-3483	201	33	map	map	NOUN
ejpam-3483	201	34	.	.	PUNCT
ejpam-3483	202	1	if	if	SCONJ
ejpam-3483	202	2	(	(	PUNCT
ejpam-3483	202	3	y	y	NOUN
ejpam-3483	202	4	,	,	PUNCT
ejpam-3483	202	5	τ,	τ,	NOUN
ejpam-3483	202	6	�	�	X
ejpam-3483	202	7	2	2	NUM
ejpam-3483	202	8	)	)	PUNCT
ejpam-3483	202	9	is	be	AUX
ejpam-3483	202	10	lower	low	ADJ
ejpam-3483	202	11	t1	t1	NOUN
ejpam-3483	202	12	-	-	PUNCT
ejpam-3483	202	13	ordered	order	VERB
ejpam-3483	202	14	,	,	PUNCT
ejpam-3483	202	15	then	then	ADV
ejpam-3483	202	16	(	(	PUNCT
ejpam-3483	202	17	x,µ,	x,µ,	PROPN
ejpam-3483	202	18	�	�	PROPN
ejpam-3483	202	19	1	1	NUM
ejpam-3483	202	20	)	)	PUNCT
ejpam-3483	202	21	is	be	AUX
ejpam-3483	202	22	lower	low	ADJ
ejpam-3483	202	23	ssbt1	ssbt1	NOUN
ejpam-3483	202	24	-	-	PUNCT
ejpam-3483	202	25	ordered	order	VERB
ejpam-3483	202	26	.	.	PUNCT
ejpam-3483	203	1	proof	proof	NOUN
ejpam-3483	203	2	.	.	PUNCT
ejpam-3483	204	1	let	let	VERB
ejpam-3483	204	2	a	a	DET
ejpam-3483	204	3	,	,	PUNCT
ejpam-3483	204	4	b	b	X
ejpam-3483	204	5	∈	∈	PROPN
ejpam-3483	204	6	x	x	X
ejpam-3483	204	7	such	such	ADJ
ejpam-3483	204	8	that	that	SCONJ
ejpam-3483	204	9	a	a	DET
ejpam-3483	204	10	�	�	PROPN
ejpam-3483	204	11	1	1	NUM
ejpam-3483	204	12	b.	b.	NOUN
ejpam-3483	204	13	then	then	ADV
ejpam-3483	204	14	there	there	PRON
ejpam-3483	204	15	exist	exist	VERB
ejpam-3483	204	16	x	x	NOUN
ejpam-3483	204	17	,	,	PUNCT
ejpam-3483	204	18	y	y	PROPN
ejpam-3483	204	19	∈	∈	PROPN
ejpam-3483	204	20	y	y	PROPN
ejpam-3483	204	21	such	such	ADJ
ejpam-3483	204	22	that	that	SCONJ
ejpam-3483	204	23	x	x	X
ejpam-3483	204	24	=	=	SYM
ejpam-3483	204	25	f(a	f(a	PROPN
ejpam-3483	204	26	)	)	PUNCT
ejpam-3483	204	27	,	,	PUNCT
ejpam-3483	204	28	y	y	PROPN
ejpam-3483	204	29	=	=	SYM
ejpam-3483	204	30	f(b	f(b	PROPN
ejpam-3483	204	31	)	)	PUNCT
ejpam-3483	204	32	.	.	PUNCT
ejpam-3483	205	1	since	since	SCONJ
ejpam-3483	205	2	f−1	f−1	PROPN
ejpam-3483	205	3	is	be	AUX
ejpam-3483	205	4	order	order	NOUN
ejpam-3483	205	5	preserving	preserve	VERB
ejpam-3483	205	6	,	,	PUNCT
ejpam-3483	205	7	then	then	ADV
ejpam-3483	205	8	x	x	SYM
ejpam-3483	205	9	�	�	PROPN
ejpam-3483	205	10	2	2	NUM
ejpam-3483	205	11	y	y	PROPN
ejpam-3483	205	12	and	and	CCONJ
ejpam-3483	205	13	since	since	SCONJ
ejpam-3483	205	14	(	(	PUNCT
ejpam-3483	205	15	y	y	PROPN
ejpam-3483	205	16	,	,	PUNCT
ejpam-3483	205	17	τ,	τ,	NOUN
ejpam-3483	205	18	�	�	X
ejpam-3483	205	19	2	2	NUM
ejpam-3483	205	20	)	)	PUNCT
ejpam-3483	205	21	is	be	AUX
ejpam-3483	205	22	lower	low	ADJ
ejpam-3483	205	23	t1	t1	NOUN
ejpam-3483	205	24	-	-	PUNCT
ejpam-3483	205	25	ordered	order	VERB
ejpam-3483	205	26	,	,	PUNCT
ejpam-3483	205	27	then	then	ADV
ejpam-3483	205	28	there	there	PRON
ejpam-3483	205	29	exists	exist	VERB
ejpam-3483	205	30	an	an	DET
ejpam-3483	205	31	increasing	increase	VERB
ejpam-3483	205	32	neighborhood	neighborhood	NOUN
ejpam-3483	205	33	w	w	NOUN
ejpam-3483	205	34	of	of	ADP
ejpam-3483	205	35	x	x	PROPN
ejpam-3483	205	36	in	in	ADP
ejpam-3483	205	37	y	y	PRON
ejpam-3483	205	38	such	such	ADJ
ejpam-3483	205	39	that	that	SCONJ
ejpam-3483	205	40	y	y	PROPN
ejpam-3483	205	41	6∈	6∈	PROPN
ejpam-3483	205	42	w	w	PROPN
ejpam-3483	205	43	.	.	PUNCT
ejpam-3483	206	1	therefore	therefore	ADV
ejpam-3483	206	2	there	there	PRON
ejpam-3483	206	3	exists	exist	VERB
ejpam-3483	206	4	an	an	DET
ejpam-3483	206	5	open	open	ADJ
ejpam-3483	206	6	set	set	NOUN
ejpam-3483	206	7	g	g	PROPN
ejpam-3483	206	8	such	such	ADJ
ejpam-3483	206	9	that	that	SCONJ
ejpam-3483	206	10	x	x	SYM
ejpam-3483	206	11	∈	∈	NOUN
ejpam-3483	206	12	g	g	NOUN
ejpam-3483	206	13	⊆	⊆	NUM
ejpam-3483	206	14	w	w	NOUN
ejpam-3483	206	15	.	.	PUNCT
ejpam-3483	207	1	since	since	SCONJ
ejpam-3483	207	2	f	f	PROPN
ejpam-3483	207	3	is	be	AUX
ejpam-3483	207	4	i	i	PROPN
ejpam-3483	207	5	-	-	PUNCT
ejpam-3483	207	6	supra	supra	PROPN
ejpam-3483	207	7	b	b	NOUN
ejpam-3483	207	8	-	-	PUNCT
ejpam-3483	207	9	continuous	continuous	ADJ
ejpam-3483	207	10	,	,	PUNCT
ejpam-3483	207	11	then	then	ADV
ejpam-3483	207	12	a	a	DET
ejpam-3483	207	13	∈	∈	PROPN
ejpam-3483	207	14	f−1(g	f−1(g	NOUN
ejpam-3483	207	15	)	)	PUNCT
ejpam-3483	207	16	which	which	PRON
ejpam-3483	207	17	is	be	AUX
ejpam-3483	207	18	an	an	DET
ejpam-3483	207	19	i	i	PROPN
ejpam-3483	207	20	-	-	PUNCT
ejpam-3483	207	21	supra	supra	PROPN
ejpam-3483	207	22	b	b	NOUN
ejpam-3483	207	23	-	-	PUNCT
ejpam-3483	207	24	open	open	ADJ
ejpam-3483	207	25	set	set	NOUN
ejpam-3483	207	26	and	and	CCONJ
ejpam-3483	207	27	since	since	SCONJ
ejpam-3483	207	28	f	f	PROPN
ejpam-3483	207	29	is	be	AUX
ejpam-3483	207	30	bijective	bijective	ADJ
ejpam-3483	207	31	,	,	PUNCT
ejpam-3483	207	32	then	then	ADV
ejpam-3483	207	33	b	b	PROPN
ejpam-3483	207	34	6∈	6∈	PROPN
ejpam-3483	207	35	f−1(g	f−1(g	PROPN
ejpam-3483	207	36	)	)	PUNCT
ejpam-3483	207	37	.	.	PUNCT
ejpam-3483	208	1	thus	thus	ADV
ejpam-3483	208	2	(	(	PUNCT
ejpam-3483	208	3	x,µ,	x,µ,	PROPN
ejpam-3483	208	4	�	�	PROPN
ejpam-3483	208	5	1	1	NUM
ejpam-3483	208	6	)	)	PUNCT
ejpam-3483	208	7	is	be	AUX
ejpam-3483	208	8	lower	low	ADJ
ejpam-3483	208	9	ssbt1	ssbt1	NOUN
ejpam-3483	208	10	-	-	PUNCT
ejpam-3483	208	11	ordered	order	VERB
ejpam-3483	208	12	.	.	PUNCT
ejpam-3483	209	1	theorem	theorem	ADJ
ejpam-3483	209	2	7	7	NUM
ejpam-3483	209	3	.	.	PUNCT
ejpam-3483	210	1	let	let	VERB
ejpam-3483	210	2	a	a	DET
ejpam-3483	210	3	bijective	bijective	ADJ
ejpam-3483	210	4	map	map	NOUN
ejpam-3483	210	5	f	f	X
ejpam-3483	210	6	:	:	PUNCT
ejpam-3483	210	7	(	(	PUNCT
ejpam-3483	210	8	x,µ,	x,µ,	PROPN
ejpam-3483	210	9	�	�	PROPN
ejpam-3483	210	10	1)→	1)→	NUM
ejpam-3483	210	11	(	(	PUNCT
ejpam-3483	210	12	y	y	PROPN
ejpam-3483	210	13	,	,	PUNCT
ejpam-3483	210	14	τ,	τ,	NOUN
ejpam-3483	210	15	�	�	X
ejpam-3483	210	16	2	2	NUM
ejpam-3483	210	17	)	)	PUNCT
ejpam-3483	210	18	be	be	AUX
ejpam-3483	210	19	d	d	ADJ
ejpam-3483	210	20	-	-	PUNCT
ejpam-3483	210	21	supra	supra	ADJ
ejpam-3483	210	22	b	b	NOUN
ejpam-3483	210	23	-	-	PUNCT
ejpam-3483	210	24	continuous	continuous	ADJ
ejpam-3483	210	25	and	and	CCONJ
ejpam-3483	210	26	f−1	f−1	PROPN
ejpam-3483	210	27	be	be	VERB
ejpam-3483	210	28	an	an	DET
ejpam-3483	210	29	order	order	NOUN
ejpam-3483	210	30	preserving	preserve	VERB
ejpam-3483	210	31	map	map	NOUN
ejpam-3483	210	32	.	.	PUNCT
ejpam-3483	211	1	if	if	SCONJ
ejpam-3483	211	2	(	(	PUNCT
ejpam-3483	211	3	y	y	NOUN
ejpam-3483	211	4	,	,	PUNCT
ejpam-3483	211	5	τ,	τ,	NOUN
ejpam-3483	211	6	�	�	X
ejpam-3483	211	7	2	2	NUM
ejpam-3483	211	8	)	)	PUNCT
ejpam-3483	211	9	is	be	AUX
ejpam-3483	211	10	upper	upper	ADJ
ejpam-3483	211	11	t1	t1	NOUN
ejpam-3483	211	12	-	-	PUNCT
ejpam-3483	211	13	ordered	order	VERB
ejpam-3483	211	14	,	,	PUNCT
ejpam-3483	211	15	then	then	ADV
ejpam-3483	211	16	(	(	PUNCT
ejpam-3483	211	17	x,µ,	x,µ,	PROPN
ejpam-3483	211	18	�	�	PROPN
ejpam-3483	211	19	1	1	NUM
ejpam-3483	211	20	)	)	PUNCT
ejpam-3483	211	21	is	be	AUX
ejpam-3483	211	22	upper	upper	ADJ
ejpam-3483	211	23	ssbt1	ssbt1	NOUN
ejpam-3483	211	24	-	-	PUNCT
ejpam-3483	211	25	ordered	order	VERB
ejpam-3483	211	26	.	.	PUNCT
ejpam-3483	212	1	proof	proof	NOUN
ejpam-3483	212	2	.	.	PUNCT
ejpam-3483	213	1	the	the	DET
ejpam-3483	213	2	proof	proof	NOUN
ejpam-3483	213	3	is	be	AUX
ejpam-3483	213	4	similar	similar	ADJ
ejpam-3483	213	5	to	to	ADP
ejpam-3483	213	6	that	that	PRON
ejpam-3483	213	7	of	of	ADP
ejpam-3483	213	8	theorem	theorem	NOUN
ejpam-3483	213	9	(	(	PUNCT
ejpam-3483	213	10	6	6	NUM
ejpam-3483	213	11	)	)	PUNCT
ejpam-3483	213	12	.	.	PUNCT
ejpam-3483	214	1	theorem	theorem	ADJ
ejpam-3483	214	2	8	8	NUM
ejpam-3483	214	3	.	.	PUNCT
ejpam-3483	215	1	let	let	VERB
ejpam-3483	215	2	a	a	DET
ejpam-3483	215	3	bijective	bijective	ADJ
ejpam-3483	215	4	map	map	NOUN
ejpam-3483	215	5	f	f	X
ejpam-3483	215	6	:	:	PUNCT
ejpam-3483	215	7	(	(	PUNCT
ejpam-3483	215	8	x,µ,	x,µ,	PROPN
ejpam-3483	215	9	�	�	PROPN
ejpam-3483	215	10	1)→	1)→	NUM
ejpam-3483	215	11	(	(	PUNCT
ejpam-3483	215	12	y	y	PROPN
ejpam-3483	215	13	,	,	PUNCT
ejpam-3483	215	14	τ,	τ,	NOUN
ejpam-3483	215	15	�	�	X
ejpam-3483	215	16	2	2	NUM
ejpam-3483	215	17	)	)	PUNCT
ejpam-3483	215	18	be	be	AUX
ejpam-3483	215	19	b	b	NOUN
ejpam-3483	215	20	-	-	PUNCT
ejpam-3483	215	21	supra	supra	ADJ
ejpam-3483	215	22	b	b	NOUN
ejpam-3483	215	23	-	-	PUNCT
ejpam-3483	215	24	continuous	continuous	ADJ
ejpam-3483	215	25	and	and	CCONJ
ejpam-3483	215	26	f−1	f−1	PROPN
ejpam-3483	215	27	be	be	VERB
ejpam-3483	215	28	an	an	DET
ejpam-3483	215	29	order	order	NOUN
ejpam-3483	215	30	preserving	preserve	VERB
ejpam-3483	215	31	map	map	NOUN
ejpam-3483	215	32	.	.	PUNCT
ejpam-3483	216	1	if	if	SCONJ
ejpam-3483	216	2	(	(	PUNCT
ejpam-3483	216	3	y	y	NOUN
ejpam-3483	216	4	,	,	PUNCT
ejpam-3483	216	5	τ,	τ,	NOUN
ejpam-3483	216	6	�	�	X
ejpam-3483	216	7	2	2	NUM
ejpam-3483	216	8	)	)	PUNCT
ejpam-3483	216	9	is	be	AUX
ejpam-3483	216	10	ti	ti	ADJ
ejpam-3483	216	11	-	-	ADJ
ejpam-3483	216	12	ordered	order	VERB
ejpam-3483	216	13	,	,	PUNCT
ejpam-3483	216	14	then	then	ADV
ejpam-3483	216	15	(	(	PUNCT
ejpam-3483	216	16	x,µ,	x,µ,	PROPN
ejpam-3483	216	17	�	�	PROPN
ejpam-3483	216	18	1	1	NUM
ejpam-3483	216	19	)	)	PUNCT
ejpam-3483	216	20	is	be	AUX
ejpam-3483	216	21	ssbt1ordered	ssbt1ordere	VERB
ejpam-3483	216	22	for	for	ADP
ejpam-3483	216	23	i	i	PROPN
ejpam-3483	216	24	=	=	SYM
ejpam-3483	216	25	0	0	NUM
ejpam-3483	216	26	,	,	PUNCT
ejpam-3483	216	27	1	1	NUM
ejpam-3483	216	28	,	,	PUNCT
ejpam-3483	216	29	2	2	NUM
ejpam-3483	216	30	.	.	PUNCT
ejpam-3483	216	31	proof	proof	NOUN
ejpam-3483	216	32	.	.	PUNCT
ejpam-3483	217	1	we	we	PRON
ejpam-3483	217	2	only	only	ADV
ejpam-3483	217	3	prove	prove	VERB
ejpam-3483	217	4	the	the	DET
ejpam-3483	217	5	theorem	theorem	NOUN
ejpam-3483	217	6	in	in	ADP
ejpam-3483	217	7	the	the	DET
ejpam-3483	217	8	case	case	NOUN
ejpam-3483	217	9	of	of	ADP
ejpam-3483	217	10	i	i	PRON
ejpam-3483	217	11	=	=	PROPN
ejpam-3483	217	12	2	2	NUM
ejpam-3483	217	13	and	and	CCONJ
ejpam-3483	217	14	one	one	NUM
ejpam-3483	217	15	can	can	AUX
ejpam-3483	217	16	prove	prove	VERB
ejpam-3483	217	17	the	the	DET
ejpam-3483	217	18	theorem	theorem	NOUN
ejpam-3483	217	19	in	in	ADP
ejpam-3483	217	20	the	the	DET
ejpam-3483	217	21	case	case	NOUN
ejpam-3483	217	22	of	of	ADP
ejpam-3483	217	23	i	i	PRON
ejpam-3483	217	24	=	=	PROPN
ejpam-3483	217	25	0	0	NUM
ejpam-3483	217	26	,	,	PUNCT
ejpam-3483	217	27	1	1	NUM
ejpam-3483	217	28	in	in	ADP
ejpam-3483	217	29	a	a	DET
ejpam-3483	217	30	similar	similar	ADJ
ejpam-3483	217	31	way	way	NOUN
ejpam-3483	217	32	.	.	PUNCT
ejpam-3483	218	1	let	let	VERB
ejpam-3483	218	2	a	a	DET
ejpam-3483	218	3	,	,	PUNCT
ejpam-3483	218	4	b	b	X
ejpam-3483	218	5	∈	∈	PROPN
ejpam-3483	218	6	x	x	X
ejpam-3483	218	7	such	such	ADJ
ejpam-3483	218	8	that	that	SCONJ
ejpam-3483	218	9	a	a	DET
ejpam-3483	218	10	�	�	PROPN
ejpam-3483	218	11	1	1	NUM
ejpam-3483	218	12	b.	b.	NOUN
ejpam-3483	218	13	then	then	ADV
ejpam-3483	218	14	there	there	PRON
ejpam-3483	218	15	exist	exist	VERB
ejpam-3483	218	16	x	x	NOUN
ejpam-3483	218	17	,	,	PUNCT
ejpam-3483	218	18	y	y	PROPN
ejpam-3483	218	19	∈	∈	PROPN
ejpam-3483	218	20	y	y	PROPN
ejpam-3483	218	21	such	such	ADJ
ejpam-3483	218	22	that	that	SCONJ
ejpam-3483	218	23	x	x	X
ejpam-3483	218	24	=	=	SYM
ejpam-3483	218	25	f(a	f(a	PROPN
ejpam-3483	218	26	)	)	PUNCT
ejpam-3483	218	27	and	and	CCONJ
ejpam-3483	218	28	y	y	PROPN
ejpam-3483	218	29	=	=	SYM
ejpam-3483	218	30	f(b	f(b	PROPN
ejpam-3483	218	31	)	)	PUNCT
ejpam-3483	218	32	.	.	PUNCT
ejpam-3483	219	1	since	since	SCONJ
ejpam-3483	219	2	f−1	f−1	PROPN
ejpam-3483	219	3	is	be	AUX
ejpam-3483	219	4	order	order	NOUN
ejpam-3483	219	5	preserving	preserve	VERB
ejpam-3483	219	6	,	,	PUNCT
ejpam-3483	219	7	then	then	ADV
ejpam-3483	219	8	x	x	SYM
ejpam-3483	219	9	�	�	PROPN
ejpam-3483	219	10	2	2	NUM
ejpam-3483	219	11	y	y	PROPN
ejpam-3483	219	12	and	and	CCONJ
ejpam-3483	219	13	since	since	SCONJ
ejpam-3483	219	14	(	(	PUNCT
ejpam-3483	219	15	y	y	PROPN
ejpam-3483	219	16	,	,	PUNCT
ejpam-3483	219	17	τ,	τ,	NOUN
ejpam-3483	219	18	�	�	X
ejpam-3483	219	19	2	2	NUM
ejpam-3483	219	20	)	)	PUNCT
ejpam-3483	219	21	is	be	AUX
ejpam-3483	219	22	t2	t2	NOUN
ejpam-3483	219	23	-	-	PUNCT
ejpam-3483	219	24	ordered	order	VERB
ejpam-3483	219	25	,	,	PUNCT
ejpam-3483	219	26	then	then	ADV
ejpam-3483	219	27	there	there	PRON
ejpam-3483	219	28	are	be	VERB
ejpam-3483	219	29	disjoint	disjoint	NOUN
ejpam-3483	219	30	neighborhoods	neighborhood	NOUN
ejpam-3483	219	31	w1	w1	NOUN
ejpam-3483	219	32	and	and	CCONJ
ejpam-3483	219	33	w2	w2	NOUN
ejpam-3483	219	34	of	of	ADP
ejpam-3483	219	35	x	x	PROPN
ejpam-3483	219	36	and	and	CCONJ
ejpam-3483	219	37	y	y	PROPN
ejpam-3483	219	38	,	,	PUNCT
ejpam-3483	219	39	respectively	respectively	ADV
ejpam-3483	219	40	.	.	PUNCT
ejpam-3483	220	1	therefore	therefore	ADV
ejpam-3483	220	2	there	there	PRON
ejpam-3483	220	3	are	be	VERB
ejpam-3483	220	4	disjoint	disjoint	ADJ
ejpam-3483	220	5	open	open	ADJ
ejpam-3483	220	6	sets	set	NOUN
ejpam-3483	220	7	g	g	NOUN
ejpam-3483	220	8	and	and	CCONJ
ejpam-3483	220	9	h	h	NOUN
ejpam-3483	220	10	containing	contain	VERB
ejpam-3483	220	11	x	x	PROPN
ejpam-3483	220	12	and	and	CCONJ
ejpam-3483	220	13	y	y	PROPN
ejpam-3483	220	14	,	,	PUNCT
ejpam-3483	220	15	respectively	respectively	ADV
ejpam-3483	220	16	.	.	PUNCT
ejpam-3483	221	1	since	since	SCONJ
ejpam-3483	221	2	f	f	PROPN
ejpam-3483	221	3	is	be	AUX
ejpam-3483	221	4	b	b	NOUN
ejpam-3483	221	5	-	-	PUNCT
ejpam-3483	221	6	supra	supra	ADJ
ejpam-3483	221	7	b	b	NOUN
ejpam-3483	221	8	-	-	PUNCT
ejpam-3483	221	9	continuous	continuous	ADJ
ejpam-3483	221	10	,	,	PUNCT
ejpam-3483	221	11	then	then	ADV
ejpam-3483	221	12	a	a	DET
ejpam-3483	221	13	∈	∈	PROPN
ejpam-3483	221	14	f−1(g	f−1(g	NOUN
ejpam-3483	221	15	)	)	PUNCT
ejpam-3483	221	16	and	and	CCONJ
ejpam-3483	221	17	b	b	PROPN
ejpam-3483	221	18	∈	∈	PROPN
ejpam-3483	221	19	f−1(h	f−1(h	PROPN
ejpam-3483	221	20	)	)	PUNCT
ejpam-3483	221	21	which	which	PRON
ejpam-3483	221	22	are	be	AUX
ejpam-3483	221	23	b	b	PROPN
ejpam-3483	221	24	-	-	PUNCT
ejpam-3483	221	25	supra	supra	ADJ
ejpam-3483	221	26	b	b	NOUN
ejpam-3483	221	27	-	-	PUNCT
ejpam-3483	221	28	open	open	ADJ
ejpam-3483	221	29	subsets	subset	NOUN
ejpam-3483	221	30	of	of	ADP
ejpam-3483	221	31	x.	x.	NOUN
ejpam-3483	221	32	obviously	obviously	ADV
ejpam-3483	221	33	,	,	PUNCT
ejpam-3483	221	34	f−1(g	f−1(g	PROPN
ejpam-3483	221	35	)	)	PUNCT
ejpam-3483	221	36	⋂	⋂	PROPN
ejpam-3483	221	37	f−1(h	f−1(h	PROPN
ejpam-3483	221	38	)	)	PUNCT
ejpam-3483	221	39	=	=	PUNCT
ejpam-3483	221	40	∅.	∅.	VERB
ejpam-3483	221	41	thus	thus	ADV
ejpam-3483	221	42	(	(	PUNCT
ejpam-3483	221	43	x,µ,	x,µ,	PROPN
ejpam-3483	221	44	�	�	PROPN
ejpam-3483	221	45	1	1	NUM
ejpam-3483	221	46	)	)	PUNCT
ejpam-3483	221	47	is	be	AUX
ejpam-3483	221	48	an	an	DET
ejpam-3483	221	49	ssbt2	ssbt2	NOUN
ejpam-3483	221	50	-	-	PUNCT
ejpam-3483	221	51	ordered	order	VERB
ejpam-3483	221	52	space	space	NOUN
ejpam-3483	221	53	.	.	PUNCT
ejpam-3483	222	1	theorem	theorem	NOUN
ejpam-3483	222	2	9	9	NUM
ejpam-3483	222	3	.	.	PUNCT
ejpam-3483	223	1	consider	consider	VERB
ejpam-3483	223	2	a	a	DET
ejpam-3483	223	3	bijective	bijective	ADJ
ejpam-3483	223	4	soft	soft	ADJ
ejpam-3483	223	5	map	map	NOUN
ejpam-3483	223	6	f	f	X
ejpam-3483	223	7	:	:	PUNCT
ejpam-3483	223	8	(	(	PUNCT
ejpam-3483	223	9	x,µ,	x,µ,	PROPN
ejpam-3483	223	10	�	�	PROPN
ejpam-3483	223	11	1)→	1)→	NUM
ejpam-3483	223	12	(	(	PUNCT
ejpam-3483	223	13	y	y	PROPN
ejpam-3483	223	14	,	,	PUNCT
ejpam-3483	223	15	τ,	τ,	NOUN
ejpam-3483	223	16	�	�	X
ejpam-3483	223	17	2	2	NUM
ejpam-3483	223	18	)	)	PUNCT
ejpam-3483	223	19	is	be	AUX
ejpam-3483	223	20	supra	supra	ADJ
ejpam-3483	223	21	b	b	NOUN
ejpam-3483	223	22	-	-	PUNCT
ejpam-3483	223	23	continuous	continuous	ADJ
ejpam-3483	223	24	such	such	ADJ
ejpam-3483	223	25	that	that	SCONJ
ejpam-3483	223	26	f	f	PROPN
ejpam-3483	223	27	is	be	AUX
ejpam-3483	223	28	ordered	order	VERB
ejpam-3483	223	29	embedding	embed	VERB
ejpam-3483	223	30	.	.	PUNCT
ejpam-3483	224	1	if	if	SCONJ
ejpam-3483	224	2	(	(	PUNCT
ejpam-3483	224	3	y	y	NOUN
ejpam-3483	224	4	,	,	PUNCT
ejpam-3483	224	5	τ,	τ,	NOUN
ejpam-3483	224	6	�	�	X
ejpam-3483	224	7	2	2	NUM
ejpam-3483	224	8	)	)	PUNCT
ejpam-3483	224	9	is	be	AUX
ejpam-3483	224	10	strong	strong	ADJ
ejpam-3483	224	11	ti	ti	ADJ
ejpam-3483	224	12	-	-	ADJ
ejpam-3483	224	13	ordered	order	VERB
ejpam-3483	224	14	,	,	PUNCT
ejpam-3483	224	15	then	then	ADV
ejpam-3483	224	16	(	(	PUNCT
ejpam-3483	224	17	x,µ,	x,µ,	PROPN
ejpam-3483	224	18	�	�	PROPN
ejpam-3483	224	19	1	1	NUM
ejpam-3483	224	20	)	)	PUNCT
ejpam-3483	224	21	is	be	AUX
ejpam-3483	224	22	ssbti	ssbti	NOUN
ejpam-3483	224	23	-	-	PUNCT
ejpam-3483	224	24	ordered	order	VERB
ejpam-3483	224	25	for	for	ADP
ejpam-3483	224	26	i	i	PROPN
ejpam-3483	224	27	=	=	SYM
ejpam-3483	224	28	0	0	NUM
ejpam-3483	224	29	,	,	PUNCT
ejpam-3483	224	30	1	1	NUM
ejpam-3483	224	31	,	,	PUNCT
ejpam-3483	224	32	2	2	NUM
ejpam-3483	224	33	.	.	PUNCT
ejpam-3483	225	1	proof	proof	NOUN
ejpam-3483	225	2	.	.	PUNCT
ejpam-3483	226	1	we	we	PRON
ejpam-3483	226	2	only	only	ADV
ejpam-3483	226	3	prove	prove	VERB
ejpam-3483	226	4	the	the	DET
ejpam-3483	226	5	theorem	theorem	NOUN
ejpam-3483	226	6	in	in	ADP
ejpam-3483	226	7	the	the	DET
ejpam-3483	226	8	case	case	NOUN
ejpam-3483	226	9	of	of	ADP
ejpam-3483	226	10	i	i	PRON
ejpam-3483	226	11	=	=	PROPN
ejpam-3483	226	12	2	2	NUM
ejpam-3483	226	13	and	and	CCONJ
ejpam-3483	226	14	one	one	NUM
ejpam-3483	226	15	can	can	AUX
ejpam-3483	226	16	prove	prove	VERB
ejpam-3483	226	17	the	the	DET
ejpam-3483	226	18	theorem	theorem	NOUN
ejpam-3483	226	19	in	in	ADP
ejpam-3483	226	20	the	the	DET
ejpam-3483	226	21	case	case	NOUN
ejpam-3483	226	22	of	of	ADP
ejpam-3483	226	23	i	i	PRON
ejpam-3483	226	24	=	=	PROPN
ejpam-3483	226	25	0	0	NUM
ejpam-3483	226	26	,	,	PUNCT
ejpam-3483	226	27	1	1	NUM
ejpam-3483	226	28	in	in	ADP
ejpam-3483	226	29	a	a	DET
ejpam-3483	226	30	similar	similar	ADJ
ejpam-3483	226	31	way	way	NOUN
ejpam-3483	226	32	.	.	PUNCT
ejpam-3483	227	1	let	let	VERB
ejpam-3483	227	2	a	a	DET
ejpam-3483	227	3	,	,	PUNCT
ejpam-3483	227	4	b	b	X
ejpam-3483	227	5	∈	∈	PROPN
ejpam-3483	227	6	x	x	X
ejpam-3483	227	7	such	such	ADJ
ejpam-3483	227	8	that	that	SCONJ
ejpam-3483	227	9	a	a	DET
ejpam-3483	227	10	�	�	PROPN
ejpam-3483	227	11	1	1	NUM
ejpam-3483	227	12	b.	b.	NOUN
ejpam-3483	227	13	then	then	ADV
ejpam-3483	227	14	there	there	PRON
ejpam-3483	227	15	exist	exist	VERB
ejpam-3483	227	16	x	x	NOUN
ejpam-3483	227	17	,	,	PUNCT
ejpam-3483	227	18	y	y	PROPN
ejpam-3483	227	19	∈	∈	PROPN
ejpam-3483	227	20	y	y	PROPN
ejpam-3483	227	21	such	such	ADJ
ejpam-3483	227	22	that	that	SCONJ
ejpam-3483	227	23	x	x	X
ejpam-3483	227	24	=	=	SYM
ejpam-3483	227	25	f(a	f(a	PROPN
ejpam-3483	227	26	)	)	PUNCT
ejpam-3483	227	27	and	and	CCONJ
ejpam-3483	227	28	y	y	PROPN
ejpam-3483	227	29	=	=	SYM
ejpam-3483	227	30	f(b	f(b	PROPN
ejpam-3483	227	31	)	)	PUNCT
ejpam-3483	227	32	.	.	PUNCT
ejpam-3483	228	1	since	since	SCONJ
ejpam-3483	228	2	f	f	PROPN
ejpam-3483	228	3	is	be	AUX
ejpam-3483	228	4	ordered	order	VERB
ejpam-3483	228	5	embedding	embed	VERB
ejpam-3483	228	6	,	,	PUNCT
ejpam-3483	228	7	then	then	ADV
ejpam-3483	228	8	x	x	SYM
ejpam-3483	228	9	�	�	PROPN
ejpam-3483	228	10	2	2	NUM
ejpam-3483	228	11	y.	y.	NOUN
ejpam-3483	228	12	since	since	SCONJ
ejpam-3483	228	13	(	(	PUNCT
ejpam-3483	228	14	y	y	PROPN
ejpam-3483	228	15	,	,	PUNCT
ejpam-3483	228	16	τ,	τ,	NOUN
ejpam-3483	228	17	�	�	X
ejpam-3483	228	18	2	2	NUM
ejpam-3483	228	19	)	)	PUNCT
ejpam-3483	228	20	is	be	AUX
ejpam-3483	228	21	strong	strong	ADJ
ejpam-3483	228	22	t2	t2	NOUN
ejpam-3483	228	23	-	-	PUNCT
ejpam-3483	228	24	ordered	order	VERB
ejpam-3483	228	25	,	,	PUNCT
ejpam-3483	228	26	then	then	ADV
ejpam-3483	228	27	there	there	PRON
ejpam-3483	228	28	exist	exist	VERB
ejpam-3483	228	29	disjoint	disjoint	ADJ
ejpam-3483	228	30	open	open	ADJ
ejpam-3483	228	31	sets	set	NOUN
ejpam-3483	228	32	g	g	NOUN
ejpam-3483	228	33	and	and	CCONJ
ejpam-3483	228	34	h	h	NOUN
ejpam-3483	228	35	containing	contain	VERB
ejpam-3483	228	36	x	x	PROPN
ejpam-3483	228	37	and	and	CCONJ
ejpam-3483	228	38	y	y	PROPN
ejpam-3483	228	39	,	,	PUNCT
ejpam-3483	228	40	respectively	respectively	ADV
ejpam-3483	228	41	,	,	PUNCT
ejpam-3483	228	42	such	such	ADJ
ejpam-3483	228	43	that	that	SCONJ
ejpam-3483	228	44	g	g	PROPN
ejpam-3483	228	45	is	be	AUX
ejpam-3483	228	46	increasing	increase	VERB
ejpam-3483	228	47	and	and	CCONJ
ejpam-3483	228	48	h	h	NOUN
ejpam-3483	228	49	is	be	AUX
ejpam-3483	228	50	decreasing	decrease	VERB
ejpam-3483	228	51	.	.	PUNCT
ejpam-3483	229	1	since	since	SCONJ
ejpam-3483	229	2	f	f	PROPN
ejpam-3483	229	3	is	be	AUX
ejpam-3483	229	4	supra	supra	ADJ
ejpam-3483	229	5	b	b	NOUN
ejpam-3483	229	6	-	-	PUNCT
ejpam-3483	229	7	continuous	continuous	ADJ
ejpam-3483	229	8	and	and	CCONJ
ejpam-3483	229	9	order	order	NOUN
ejpam-3483	229	10	preserving	preserve	VERB
ejpam-3483	229	11	,	,	PUNCT
ejpam-3483	229	12	then	then	ADV
ejpam-3483	229	13	f−1(g	f−1(g	PROPN
ejpam-3483	229	14	)	)	PUNCT
ejpam-3483	229	15	is	be	AUX
ejpam-3483	229	16	an	an	DET
ejpam-3483	229	17	i	i	PROPN
ejpam-3483	229	18	-	-	PUNCT
ejpam-3483	229	19	supra	supra	PROPN
ejpam-3483	229	20	b	b	NOUN
ejpam-3483	229	21	-	-	PUNCT
ejpam-3483	229	22	open	open	ADJ
ejpam-3483	229	23	set	set	NOUN
ejpam-3483	229	24	containing	contain	VERB
ejpam-3483	229	25	a	a	PRON
ejpam-3483	229	26	,	,	PUNCT
ejpam-3483	229	27	f−1(h	f−1(h	PROPN
ejpam-3483	229	28	)	)	PUNCT
ejpam-3483	229	29	is	be	AUX
ejpam-3483	229	30	a	a	DET
ejpam-3483	229	31	d	d	ADJ
ejpam-3483	229	32	-	-	PUNCT
ejpam-3483	229	33	supra	supra	ADJ
ejpam-3483	229	34	b	b	NOUN
ejpam-3483	229	35	-	-	PUNCT
ejpam-3483	229	36	open	open	ADJ
ejpam-3483	229	37	set	set	NOUN
ejpam-3483	229	38	containing	contain	VERB
ejpam-3483	229	39	b	b	PROPN
ejpam-3483	229	40	and	and	CCONJ
ejpam-3483	229	41	f−1(g	f−1(g	NUM
ejpam-3483	229	42	)	)	PUNCT
ejpam-3483	230	1	⋂	⋂	PROPN
ejpam-3483	230	2	f−1(h	f−1(h	PROPN
ejpam-3483	230	3	)	)	PUNCT
ejpam-3483	231	1	=	=	PUNCT
ejpam-3483	231	2	∅.	∅.	VERB
ejpam-3483	231	3	hence	hence	ADV
ejpam-3483	231	4	(	(	PUNCT
ejpam-3483	231	5	x,µ,	x,µ,	PROPN
ejpam-3483	231	6	�	�	PROPN
ejpam-3483	231	7	1	1	NUM
ejpam-3483	231	8	)	)	PUNCT
ejpam-3483	231	9	is	be	AUX
ejpam-3483	231	10	ssbt2	ssbt2	NOUN
ejpam-3483	231	11	-	-	PUNCT
ejpam-3483	231	12	ordered	order	VERB
ejpam-3483	231	13	.	.	PUNCT
ejpam-3483	232	1	theorem	theorem	ADJ
ejpam-3483	232	2	10	10	NUM
ejpam-3483	232	3	.	.	PUNCT
ejpam-3483	233	1	consider	consider	VERB
ejpam-3483	233	2	an	an	DET
ejpam-3483	233	3	injective	injective	ADJ
ejpam-3483	233	4	soft	soft	ADJ
ejpam-3483	233	5	map	map	NOUN
ejpam-3483	234	1	f	f	NOUN
ejpam-3483	234	2	:	:	PUNCT
ejpam-3483	234	3	(	(	PUNCT
ejpam-3483	234	4	x,µ	x,µ	NOUN
ejpam-3483	234	5	,	,	PUNCT
ejpam-3483	234	6	�	�	PROPN
ejpam-3483	234	7	)	)	PUNCT
ejpam-3483	234	8	→	→	SYM
ejpam-3483	234	9	(	(	PUNCT
ejpam-3483	234	10	y	y	PROPN
ejpam-3483	234	11	,	,	PUNCT
ejpam-3483	234	12	τ	τ	X
ejpam-3483	234	13	)	)	PUNCT
ejpam-3483	234	14	is	be	AUX
ejpam-3483	234	15	b	b	NOUN
ejpam-3483	234	16	-	-	PUNCT
ejpam-3483	234	17	supra	supra	ADJ
ejpam-3483	234	18	bcontinuous	bcontinuous	NOUN
ejpam-3483	234	19	.	.	PUNCT
ejpam-3483	235	1	if	if	SCONJ
ejpam-3483	235	2	(	(	PUNCT
ejpam-3483	235	3	y	y	PROPN
ejpam-3483	235	4	,	,	PUNCT
ejpam-3483	235	5	τ	τ	X
ejpam-3483	235	6	)	)	PUNCT
ejpam-3483	235	7	is	be	AUX
ejpam-3483	235	8	ti	ti	NOUN
ejpam-3483	235	9	-	-	NOUN
ejpam-3483	235	10	space	space	NOUN
ejpam-3483	235	11	,	,	PUNCT
ejpam-3483	235	12	then	then	ADV
ejpam-3483	235	13	(	(	PUNCT
ejpam-3483	235	14	x,µ	x,µ	NOUN
ejpam-3483	235	15	,	,	PUNCT
ejpam-3483	235	16	�	�	PROPN
ejpam-3483	235	17	)	)	PUNCT
ejpam-3483	235	18	is	be	AUX
ejpam-3483	235	19	ssbti	ssbti	NOUN
ejpam-3483	235	20	-	-	PUNCT
ejpam-3483	235	21	ordered	order	VERB
ejpam-3483	235	22	for	for	ADP
ejpam-3483	235	23	i	i	PROPN
ejpam-3483	235	24	=	=	SYM
ejpam-3483	235	25	1	1	NUM
ejpam-3483	235	26	,	,	PUNCT
ejpam-3483	235	27	2	2	NUM
ejpam-3483	235	28	.	.	PUNCT
ejpam-3483	235	29	b.	b.	PROPN
ejpam-3483	235	30	a.	a.	PROPN
ejpam-3483	235	31	asaad	asaad	PROPN
ejpam-3483	235	32	,	,	PUNCT
ejpam-3483	235	33	m.	m.	PROPN
ejpam-3483	235	34	k.	k.	PROPN
ejpam-3483	235	35	tahat	tahat	PROPN
ejpam-3483	235	36	,	,	PUNCT
ejpam-3483	235	37	t.	t.	PROPN
ejpam-3483	235	38	m.	m.	PROPN
ejpam-3483	235	39	al	al	PROPN
ejpam-3483	235	40	-	-	PUNCT
ejpam-3483	235	41	shami	shami	PROPN
ejpam-3483	235	42	/	/	PUNCT
ejpam-3483	235	43	eur	eur	PROPN
ejpam-3483	235	44	.	.	PUNCT
ejpam-3483	236	1	j.	j.	PROPN
ejpam-3483	236	2	pure	pure	PROPN
ejpam-3483	236	3	appl	appl	PROPN
ejpam-3483	236	4	.	.	PROPN
ejpam-3483	236	5	math	math	PROPN
ejpam-3483	236	6	,	,	PUNCT
ejpam-3483	236	7	12	12	NUM
ejpam-3483	236	8	(	(	PUNCT
ejpam-3483	236	9	3	3	NUM
ejpam-3483	236	10	)	)	PUNCT
ejpam-3483	236	11	(	(	PUNCT
ejpam-3483	236	12	2019	2019	NUM
ejpam-3483	236	13	)	)	PUNCT
ejpam-3483	236	14	,	,	PUNCT
ejpam-3483	236	15	1231	1231	NUM
ejpam-3483	236	16	-	-	SYM
ejpam-3483	236	17	1247	1247	NUM
ejpam-3483	236	18	1239	1239	NUM
ejpam-3483	236	19	proof	proof	NOUN
ejpam-3483	236	20	.	.	PUNCT
ejpam-3483	237	1	we	we	PRON
ejpam-3483	237	2	prove	prove	VERB
ejpam-3483	237	3	the	the	DET
ejpam-3483	237	4	theorem	theorem	NOUN
ejpam-3483	237	5	in	in	ADP
ejpam-3483	237	6	case	case	NOUN
ejpam-3483	237	7	of	of	ADP
ejpam-3483	237	8	i	i	PRON
ejpam-3483	237	9	=	=	PROPN
ejpam-3483	237	10	2	2	NUM
ejpam-3483	237	11	and	and	CCONJ
ejpam-3483	237	12	the	the	DET
ejpam-3483	237	13	other	other	ADJ
ejpam-3483	237	14	case	case	NOUN
ejpam-3483	237	15	is	be	AUX
ejpam-3483	237	16	made	make	VERB
ejpam-3483	237	17	similarly	similarly	ADV
ejpam-3483	237	18	.	.	PUNCT
ejpam-3483	238	1	let	let	VERB
ejpam-3483	238	2	a	a	DET
ejpam-3483	238	3	,	,	PUNCT
ejpam-3483	238	4	b	b	X
ejpam-3483	238	5	∈	∈	PROPN
ejpam-3483	238	6	x	x	X
ejpam-3483	238	7	such	such	ADJ
ejpam-3483	238	8	that	that	SCONJ
ejpam-3483	238	9	a	a	DET
ejpam-3483	238	10	�	�	PROPN
ejpam-3483	238	11	1	1	NUM
ejpam-3483	238	12	b.	b.	NOUN
ejpam-3483	238	13	then	then	ADV
ejpam-3483	238	14	there	there	PRON
ejpam-3483	238	15	exist	exist	VERB
ejpam-3483	238	16	x	x	NOUN
ejpam-3483	238	17	,	,	PUNCT
ejpam-3483	238	18	y	y	PROPN
ejpam-3483	238	19	∈	∈	PROPN
ejpam-3483	238	20	y	y	PROPN
ejpam-3483	238	21	such	such	ADJ
ejpam-3483	238	22	that	that	DET
ejpam-3483	238	23	f(a	f(a	NOUN
ejpam-3483	238	24	)	)	PUNCT
ejpam-3483	239	1	=	=	SYM
ejpam-3483	239	2	x	x	NOUN
ejpam-3483	239	3	,	,	PUNCT
ejpam-3483	239	4	f(b	f(b	PROPN
ejpam-3483	239	5	)	)	PUNCT
ejpam-3483	239	6	=	=	SYM
ejpam-3483	239	7	y	y	PROPN
ejpam-3483	239	8	and	and	CCONJ
ejpam-3483	239	9	x	x	PROPN
ejpam-3483	239	10	6=	6=	ADP
ejpam-3483	239	11	y.	y.	NOUN
ejpam-3483	239	12	since	since	SCONJ
ejpam-3483	239	13	(	(	PUNCT
ejpam-3483	239	14	y	y	PROPN
ejpam-3483	239	15	,	,	PUNCT
ejpam-3483	239	16	τ	τ	X
ejpam-3483	239	17	)	)	PUNCT
ejpam-3483	239	18	is	be	AUX
ejpam-3483	239	19	a	a	DET
ejpam-3483	239	20	t2	t2	NOUN
ejpam-3483	239	21	-	-	PUNCT
ejpam-3483	239	22	space	space	NOUN
ejpam-3483	239	23	,	,	PUNCT
ejpam-3483	239	24	then	then	ADV
ejpam-3483	239	25	there	there	PRON
ejpam-3483	239	26	exist	exist	VERB
ejpam-3483	239	27	disjoint	disjoint	ADJ
ejpam-3483	239	28	open	open	ADJ
ejpam-3483	239	29	sets	set	NOUN
ejpam-3483	239	30	g	g	NOUN
ejpam-3483	239	31	and	and	CCONJ
ejpam-3483	239	32	h	h	NOUN
ejpam-3483	239	33	such	such	ADJ
ejpam-3483	239	34	that	that	SCONJ
ejpam-3483	239	35	x	x	SYM
ejpam-3483	239	36	∈	∈	PROPN
ejpam-3483	239	37	g	g	PROPN
ejpam-3483	239	38	and	and	CCONJ
ejpam-3483	239	39	y	y	PROPN
ejpam-3483	239	40	∈	∈	PROPN
ejpam-3483	239	41	h.	h.	NOUN
ejpam-3483	239	42	therefore	therefore	ADV
ejpam-3483	239	43	a	a	DET
ejpam-3483	239	44	∈	∈	PROPN
ejpam-3483	239	45	f−1(g	f−1(g	NOUN
ejpam-3483	239	46	)	)	PUNCT
ejpam-3483	239	47	and	and	CCONJ
ejpam-3483	239	48	b	b	PROPN
ejpam-3483	239	49	∈	∈	PROPN
ejpam-3483	239	50	f−1(h	f−1(h	PROPN
ejpam-3483	239	51	)	)	PUNCT
ejpam-3483	239	52	which	which	PRON
ejpam-3483	239	53	are	be	AUX
ejpam-3483	239	54	b	b	PROPN
ejpam-3483	239	55	-	-	PUNCT
ejpam-3483	239	56	supra	supra	ADJ
ejpam-3483	239	57	b	b	NOUN
ejpam-3483	239	58	-	-	PUNCT
ejpam-3483	239	59	open	open	ADJ
ejpam-3483	239	60	subsets	subset	NOUN
ejpam-3483	239	61	of	of	ADP
ejpam-3483	239	62	x.	x.	NOUN
ejpam-3483	239	63	obviously	obviously	ADV
ejpam-3483	239	64	,	,	PUNCT
ejpam-3483	239	65	f−1(g	f−1(g	PROPN
ejpam-3483	239	66	)	)	PUNCT
ejpam-3483	239	67	⋂	⋂	PROPN
ejpam-3483	239	68	f−1(h	f−1(h	PROPN
ejpam-3483	239	69	)	)	PUNCT
ejpam-3483	239	70	=	=	PUNCT
ejpam-3483	239	71	∅.	∅.	VERB
ejpam-3483	239	72	thus	thus	ADV
ejpam-3483	239	73	(	(	PUNCT
ejpam-3483	239	74	x,µ	x,µ	NOUN
ejpam-3483	239	75	,	,	PUNCT
ejpam-3483	239	76	�	�	PROPN
ejpam-3483	239	77	)	)	PUNCT
ejpam-3483	239	78	is	be	AUX
ejpam-3483	239	79	an	an	DET
ejpam-3483	239	80	ssbt2	ssbt2	NOUN
ejpam-3483	239	81	-	-	PUNCT
ejpam-3483	239	82	ordered	order	VERB
ejpam-3483	239	83	space	space	NOUN
ejpam-3483	239	84	.	.	PUNCT
ejpam-3483	240	1	4	4	X
ejpam-3483	240	2	.	.	X
ejpam-3483	240	3	supra	supra	PROPN
ejpam-3483	240	4	b	b	PROPN
ejpam-3483	240	5	-	-	PUNCT
ejpam-3483	240	6	open	open	ADJ
ejpam-3483	240	7	and	and	CCONJ
ejpam-3483	240	8	supra	supra	ADJ
ejpam-3483	240	9	b	b	PROPN
ejpam-3483	240	10	-	-	PUNCT
ejpam-3483	240	11	closed	close	VERB
ejpam-3483	240	12	maps	map	NOUN
ejpam-3483	240	13	in	in	ADP
ejpam-3483	240	14	this	this	DET
ejpam-3483	240	15	section	section	NOUN
ejpam-3483	240	16	,	,	PUNCT
ejpam-3483	240	17	we	we	PRON
ejpam-3483	240	18	introduce	introduce	VERB
ejpam-3483	240	19	the	the	DET
ejpam-3483	240	20	concepts	concept	NOUN
ejpam-3483	240	21	of	of	ADP
ejpam-3483	240	22	i	i	PROPN
ejpam-3483	240	23	-	-	PUNCT
ejpam-3483	240	24	supra	supra	PROPN
ejpam-3483	240	25	b	b	NOUN
ejpam-3483	240	26	-	-	PUNCT
ejpam-3483	240	27	open	open	ADJ
ejpam-3483	240	28	(	(	PUNCT
ejpam-3483	240	29	i	i	NOUN
ejpam-3483	240	30	-	-	PUNCT
ejpam-3483	240	31	supra	supra	PROPN
ejpam-3483	240	32	b	b	PROPN
ejpam-3483	240	33	-	-	PUNCT
ejpam-3483	240	34	closed	closed	ADJ
ejpam-3483	240	35	)	)	PUNCT
ejpam-3483	240	36	,	,	PUNCT
ejpam-3483	240	37	d	d	X
ejpam-3483	240	38	-	-	PUNCT
ejpam-3483	240	39	supra	supra	ADJ
ejpam-3483	240	40	b	b	NOUN
ejpam-3483	240	41	-	-	PUNCT
ejpam-3483	240	42	open	open	ADJ
ejpam-3483	240	43	(	(	PUNCT
ejpam-3483	240	44	d	d	NOUN
ejpam-3483	240	45	-	-	ADJ
ejpam-3483	240	46	supra	supra	ADJ
ejpam-3483	240	47	b	b	NOUN
ejpam-3483	240	48	-	-	PUNCT
ejpam-3483	240	49	closed	closed	ADJ
ejpam-3483	240	50	)	)	PUNCT
ejpam-3483	240	51	and	and	CCONJ
ejpam-3483	240	52	b	b	X
ejpam-3483	240	53	-	-	PUNCT
ejpam-3483	240	54	supra	supra	ADJ
ejpam-3483	240	55	b	b	NOUN
ejpam-3483	240	56	-	-	PUNCT
ejpam-3483	240	57	open	open	ADJ
ejpam-3483	240	58	(	(	PUNCT
ejpam-3483	240	59	b	b	NOUN
ejpam-3483	240	60	-	-	PUNCT
ejpam-3483	240	61	supra	supra	ADJ
ejpam-3483	240	62	b	b	NOUN
ejpam-3483	240	63	-	-	PUNCT
ejpam-3483	240	64	closed	closed	ADJ
ejpam-3483	240	65	)	)	PUNCT
ejpam-3483	240	66	maps	map	NOUN
ejpam-3483	240	67	.	.	PUNCT
ejpam-3483	241	1	we	we	PRON
ejpam-3483	241	2	demonstrate	demonstrate	VERB
ejpam-3483	241	3	their	their	PRON
ejpam-3483	241	4	main	main	ADJ
ejpam-3483	241	5	properties	property	NOUN
ejpam-3483	241	6	and	and	CCONJ
ejpam-3483	241	7	illustrate	illustrate	VERB
ejpam-3483	241	8	the	the	DET
ejpam-3483	241	9	relationships	relationship	NOUN
ejpam-3483	241	10	among	among	ADP
ejpam-3483	241	11	them	they	PRON
ejpam-3483	241	12	with	with	ADP
ejpam-3483	241	13	the	the	DET
ejpam-3483	241	14	help	help	NOUN
ejpam-3483	241	15	of	of	ADP
ejpam-3483	241	16	examples	example	NOUN
ejpam-3483	241	17	.	.	PUNCT
ejpam-3483	242	1	definition	definition	NOUN
ejpam-3483	242	2	16	16	NUM
ejpam-3483	242	3	.	.	PUNCT
ejpam-3483	243	1	a	a	DET
ejpam-3483	243	2	map	map	NOUN
ejpam-3483	243	3	g	g	NOUN
ejpam-3483	243	4	:	:	PUNCT
ejpam-3483	243	5	(	(	PUNCT
ejpam-3483	243	6	x	x	X
ejpam-3483	243	7	,	,	PUNCT
ejpam-3483	243	8	τ)→	τ)→	PROPN
ejpam-3483	243	9	(	(	PUNCT
ejpam-3483	243	10	y	y	PROPN
ejpam-3483	243	11	,	,	PUNCT
ejpam-3483	243	12	µ	µ	NUM
ejpam-3483	243	13	,	,	PUNCT
ejpam-3483	243	14	�	�	PROPN
ejpam-3483	243	15	)	)	PUNCT
ejpam-3483	243	16	is	be	AUX
ejpam-3483	243	17	said	say	VERB
ejpam-3483	243	18	to	to	PART
ejpam-3483	243	19	be	be	AUX
ejpam-3483	243	20	:	:	PUNCT
ejpam-3483	243	21	(	(	PUNCT
ejpam-3483	243	22	i	i	NOUN
ejpam-3483	243	23	)	)	PUNCT
ejpam-3483	243	24	i	i	PROPN
ejpam-3483	243	25	-	-	PUNCT
ejpam-3483	243	26	supra	supra	PROPN
ejpam-3483	243	27	(	(	PUNCT
ejpam-3483	243	28	resp	resp	NOUN
ejpam-3483	243	29	.	.	PUNCT
ejpam-3483	244	1	d	d	X
ejpam-3483	244	2	-	-	PUNCT
ejpam-3483	244	3	supra	supra	ADJ
ejpam-3483	244	4	,	,	PUNCT
ejpam-3483	244	5	b	b	NOUN
ejpam-3483	244	6	-	-	PUNCT
ejpam-3483	244	7	supra	supra	ADJ
ejpam-3483	244	8	)	)	PUNCT
ejpam-3483	244	9	b	b	X
ejpam-3483	244	10	-	-	PUNCT
ejpam-3483	244	11	open	open	ADJ
ejpam-3483	244	12	if	if	SCONJ
ejpam-3483	244	13	the	the	DET
ejpam-3483	244	14	image	image	NOUN
ejpam-3483	244	15	of	of	ADP
ejpam-3483	244	16	any	any	DET
ejpam-3483	244	17	open	open	ADJ
ejpam-3483	244	18	subset	subset	NOUN
ejpam-3483	244	19	of	of	ADP
ejpam-3483	244	20	x	x	PUNCT
ejpam-3483	244	21	is	be	AUX
ejpam-3483	244	22	an	an	DET
ejpam-3483	244	23	i	i	NOUN
ejpam-3483	244	24	-	-	PUNCT
ejpam-3483	244	25	supra	supra	PROPN
ejpam-3483	244	26	(	(	PUNCT
ejpam-3483	244	27	resp	resp	NOUN
ejpam-3483	244	28	.	.	PUNCT
ejpam-3483	245	1	a	a	DET
ejpam-3483	245	2	d	d	NOUN
ejpam-3483	245	3	-	-	PUNCT
ejpam-3483	245	4	supra	supra	ADJ
ejpam-3483	245	5	,	,	PUNCT
ejpam-3483	245	6	a	a	DET
ejpam-3483	245	7	b	b	NOUN
ejpam-3483	245	8	-	-	PUNCT
ejpam-3483	245	9	supra	supra	ADJ
ejpam-3483	245	10	)	)	PUNCT
ejpam-3483	245	11	b	b	X
ejpam-3483	245	12	-	-	PUNCT
ejpam-3483	245	13	open	open	ADJ
ejpam-3483	245	14	subset	subset	NOUN
ejpam-3483	245	15	of	of	ADP
ejpam-3483	245	16	y	y	PROPN
ejpam-3483	245	17	.	.	PUNCT
ejpam-3483	246	1	(	(	PUNCT
ejpam-3483	246	2	ii	ii	X
ejpam-3483	246	3	)	)	PUNCT
ejpam-3483	246	4	i	i	PROPN
ejpam-3483	246	5	-	-	PUNCT
ejpam-3483	246	6	supra	supra	PROPN
ejpam-3483	246	7	(	(	PUNCT
ejpam-3483	246	8	resp	resp	NOUN
ejpam-3483	246	9	.	.	PUNCT
ejpam-3483	247	1	d	d	X
ejpam-3483	247	2	-	-	PUNCT
ejpam-3483	247	3	supra	supra	ADJ
ejpam-3483	247	4	,	,	PUNCT
ejpam-3483	247	5	b	b	NOUN
ejpam-3483	247	6	-	-	PUNCT
ejpam-3483	247	7	supra	supra	ADJ
ejpam-3483	247	8	)	)	PUNCT
ejpam-3483	247	9	b	b	X
ejpam-3483	247	10	-	-	PUNCT
ejpam-3483	247	11	closed	closed	ADJ
ejpam-3483	247	12	if	if	SCONJ
ejpam-3483	247	13	the	the	DET
ejpam-3483	247	14	image	image	NOUN
ejpam-3483	247	15	of	of	ADP
ejpam-3483	247	16	any	any	DET
ejpam-3483	247	17	closed	closed	ADJ
ejpam-3483	247	18	subset	subset	NOUN
ejpam-3483	247	19	of	of	ADP
ejpam-3483	247	20	x	x	PUNCT
ejpam-3483	247	21	is	be	AUX
ejpam-3483	247	22	an	an	DET
ejpam-3483	247	23	i	i	NOUN
ejpam-3483	247	24	-	-	PUNCT
ejpam-3483	247	25	supra	supra	PROPN
ejpam-3483	247	26	(	(	PUNCT
ejpam-3483	247	27	resp	resp	NOUN
ejpam-3483	247	28	.	.	PUNCT
ejpam-3483	248	1	a	a	DET
ejpam-3483	248	2	d	d	NOUN
ejpam-3483	248	3	-	-	PUNCT
ejpam-3483	248	4	supra	supra	ADJ
ejpam-3483	248	5	,	,	PUNCT
ejpam-3483	248	6	a	a	DET
ejpam-3483	248	7	b	b	NOUN
ejpam-3483	248	8	-	-	PUNCT
ejpam-3483	248	9	supra	supra	ADJ
ejpam-3483	248	10	)	)	PUNCT
ejpam-3483	248	11	b	b	X
ejpam-3483	248	12	-	-	PUNCT
ejpam-3483	248	13	closed	closed	ADJ
ejpam-3483	248	14	subset	subset	NOUN
ejpam-3483	248	15	of	of	ADP
ejpam-3483	248	16	y	y	PROPN
ejpam-3483	248	17	.	.	PUNCT
ejpam-3483	249	1	remark	remark	PROPN
ejpam-3483	249	2	3	3	NUM
ejpam-3483	249	3	.	.	PUNCT
ejpam-3483	250	1	(	(	PUNCT
ejpam-3483	250	2	i	i	NOUN
ejpam-3483	250	3	)	)	PUNCT
ejpam-3483	250	4	every	every	DET
ejpam-3483	250	5	i	i	PROPN
ejpam-3483	250	6	-	-	PUNCT
ejpam-3483	250	7	supra	supra	PROPN
ejpam-3483	250	8	(	(	PUNCT
ejpam-3483	250	9	d	d	NOUN
ejpam-3483	250	10	-	-	PUNCT
ejpam-3483	250	11	supra	supra	ADJ
ejpam-3483	250	12	,	,	PUNCT
ejpam-3483	250	13	b	b	NOUN
ejpam-3483	250	14	-	-	PUNCT
ejpam-3483	250	15	supra	supra	ADJ
ejpam-3483	250	16	)	)	PUNCT
ejpam-3483	250	17	b	b	X
ejpam-3483	250	18	-	-	PUNCT
ejpam-3483	250	19	open	open	ADJ
ejpam-3483	250	20	map	map	NOUN
ejpam-3483	250	21	is	be	AUX
ejpam-3483	250	22	supra	supra	ADJ
ejpam-3483	250	23	b	b	NOUN
ejpam-3483	250	24	-	-	PUNCT
ejpam-3483	250	25	open	open	ADJ
ejpam-3483	250	26	.	.	PUNCT
ejpam-3483	251	1	(	(	PUNCT
ejpam-3483	251	2	ii	ii	NOUN
ejpam-3483	251	3	)	)	PUNCT
ejpam-3483	251	4	every	every	DET
ejpam-3483	251	5	i	i	PROPN
ejpam-3483	251	6	-	-	PUNCT
ejpam-3483	251	7	supra	supra	PROPN
ejpam-3483	251	8	(	(	PUNCT
ejpam-3483	251	9	d	d	NOUN
ejpam-3483	251	10	-	-	PUNCT
ejpam-3483	251	11	supra	supra	ADJ
ejpam-3483	251	12	,	,	PUNCT
ejpam-3483	251	13	b	b	NOUN
ejpam-3483	251	14	-	-	PUNCT
ejpam-3483	251	15	supra	supra	ADJ
ejpam-3483	251	16	)	)	PUNCT
ejpam-3483	251	17	b	b	X
ejpam-3483	251	18	-	-	PUNCT
ejpam-3483	251	19	closed	closed	ADJ
ejpam-3483	251	20	map	map	NOUN
ejpam-3483	251	21	is	be	AUX
ejpam-3483	251	22	supra	supra	ADJ
ejpam-3483	251	23	b	b	NOUN
ejpam-3483	251	24	-	-	PUNCT
ejpam-3483	251	25	closed	closed	ADJ
ejpam-3483	251	26	.	.	PUNCT
ejpam-3483	252	1	(	(	PUNCT
ejpam-3483	252	2	iii	iii	X
ejpam-3483	252	3	)	)	PUNCT
ejpam-3483	252	4	every	every	DET
ejpam-3483	252	5	b	b	NOUN
ejpam-3483	252	6	-	-	PUNCT
ejpam-3483	252	7	supra	supra	ADJ
ejpam-3483	252	8	b	b	NOUN
ejpam-3483	252	9	-	-	PUNCT
ejpam-3483	252	10	open	open	ADJ
ejpam-3483	252	11	map	map	NOUN
ejpam-3483	252	12	is	be	AUX
ejpam-3483	252	13	i	i	PROPN
ejpam-3483	252	14	-	-	PUNCT
ejpam-3483	252	15	supra	supra	PROPN
ejpam-3483	252	16	(	(	PUNCT
ejpam-3483	252	17	d	d	NOUN
ejpam-3483	252	18	-	-	PUNCT
ejpam-3483	252	19	supra	supra	ADJ
ejpam-3483	252	20	)	)	PUNCT
ejpam-3483	252	21	b	b	X
ejpam-3483	252	22	-	-	PUNCT
ejpam-3483	252	23	open	open	ADJ
ejpam-3483	252	24	.	.	PUNCT
ejpam-3483	253	1	(	(	PUNCT
ejpam-3483	253	2	iv	iv	X
ejpam-3483	253	3	)	)	PUNCT
ejpam-3483	253	4	every	every	DET
ejpam-3483	253	5	b	b	NOUN
ejpam-3483	253	6	-	-	PUNCT
ejpam-3483	253	7	supra	supra	ADJ
ejpam-3483	253	8	b	b	NOUN
ejpam-3483	253	9	-	-	PUNCT
ejpam-3483	253	10	closed	closed	ADJ
ejpam-3483	253	11	map	map	NOUN
ejpam-3483	253	12	is	be	AUX
ejpam-3483	253	13	i	i	PROPN
ejpam-3483	253	14	-	-	PUNCT
ejpam-3483	253	15	supra	supra	PROPN
ejpam-3483	253	16	(	(	PUNCT
ejpam-3483	253	17	d	d	NOUN
ejpam-3483	253	18	-	-	PUNCT
ejpam-3483	253	19	supra	supra	ADJ
ejpam-3483	253	20	)	)	PUNCT
ejpam-3483	253	21	b	b	NOUN
ejpam-3483	253	22	-	-	PUNCT
ejpam-3483	253	23	closed	closed	ADJ
ejpam-3483	253	24	.	.	PUNCT
ejpam-3483	254	1	the	the	DET
ejpam-3483	254	2	following	follow	VERB
ejpam-3483	254	3	two	two	NUM
ejpam-3483	254	4	examples	example	NOUN
ejpam-3483	254	5	illustrate	illustrate	VERB
ejpam-3483	254	6	that	that	SCONJ
ejpam-3483	254	7	the	the	DET
ejpam-3483	254	8	converse	converse	NOUN
ejpam-3483	254	9	of	of	ADP
ejpam-3483	254	10	the	the	DET
ejpam-3483	254	11	properties	property	NOUN
ejpam-3483	254	12	mentioned	mention	VERB
ejpam-3483	254	13	in	in	ADP
ejpam-3483	254	14	the	the	DET
ejpam-3483	254	15	above	above	ADJ
ejpam-3483	254	16	remark	remark	NOUN
ejpam-3483	254	17	need	need	AUX
ejpam-3483	254	18	not	not	PART
ejpam-3483	254	19	be	be	AUX
ejpam-3483	254	20	true	true	ADJ
ejpam-3483	254	21	in	in	ADP
ejpam-3483	254	22	general	general	ADJ
ejpam-3483	254	23	.	.	PUNCT
ejpam-3483	255	1	example	example	NOUN
ejpam-3483	256	1	3	3	X
ejpam-3483	256	2	.	.	PUNCT
ejpam-3483	256	3	let	let	VERB
ejpam-3483	256	4	a	a	DET
ejpam-3483	256	5	topology	topology	NOUN
ejpam-3483	256	6	τ	τ	NOUN
ejpam-3483	256	7	=	=	SYM
ejpam-3483	256	8	{	{	PUNCT
ejpam-3483	256	9	∅	∅	NOUN
ejpam-3483	256	10	,	,	PUNCT
ejpam-3483	256	11	x	x	X
ejpam-3483	256	12	,	,	PUNCT
ejpam-3483	256	13	{	{	PUNCT
ejpam-3483	256	14	1	1	NUM
ejpam-3483	256	15	,	,	PUNCT
ejpam-3483	256	16	2	2	NUM
ejpam-3483	256	17	}	}	PUNCT
ejpam-3483	256	18	}	}	PUNCT
ejpam-3483	256	19	and	and	CCONJ
ejpam-3483	256	20	a	a	DET
ejpam-3483	256	21	partial	partial	ADJ
ejpam-3483	256	22	order	order	NOUN
ejpam-3483	256	23	relation	relation	NOUN
ejpam-3483	256	24	�	�	NOUN
ejpam-3483	256	25	=	=	NOUN
ejpam-3483	256	26	4	4	NUM
ejpam-3483	256	27	⋃	⋃	NOUN
ejpam-3483	256	28	{	{	PUNCT
ejpam-3483	256	29	(	(	PUNCT
ejpam-3483	256	30	1	1	NUM
ejpam-3483	256	31	,	,	PUNCT
ejpam-3483	256	32	3	3	NUM
ejpam-3483	256	33	)	)	PUNCT
ejpam-3483	256	34	,	,	PUNCT
ejpam-3483	256	35	(	(	PUNCT
ejpam-3483	256	36	3	3	NUM
ejpam-3483	256	37	,	,	PUNCT
ejpam-3483	256	38	2)(1	2)(1	NUM
ejpam-3483	256	39	,	,	PUNCT
ejpam-3483	256	40	2	2	NUM
ejpam-3483	256	41	)	)	PUNCT
ejpam-3483	256	42	}	}	PUNCT
ejpam-3483	256	43	on	on	ADP
ejpam-3483	256	44	x	x	X
ejpam-3483	256	45	=	=	SYM
ejpam-3483	256	46	{	{	PUNCT
ejpam-3483	256	47	1	1	NUM
ejpam-3483	256	48	,	,	PUNCT
ejpam-3483	256	49	2	2	NUM
ejpam-3483	256	50	,	,	PUNCT
ejpam-3483	256	51	3	3	NUM
ejpam-3483	256	52	}	}	PUNCT
ejpam-3483	256	53	.	.	PUNCT
ejpam-3483	257	1	let	let	VERB
ejpam-3483	257	2	µ	µ	X
ejpam-3483	257	3	=	=	SYM
ejpam-3483	257	4	{	{	PUNCT
ejpam-3483	257	5	∅	∅	NOUN
ejpam-3483	257	6	,	,	PUNCT
ejpam-3483	257	7	x	x	X
ejpam-3483	257	8	,	,	PUNCT
ejpam-3483	257	9	{	{	PUNCT
ejpam-3483	257	10	1	1	NUM
ejpam-3483	257	11	}	}	PUNCT
ejpam-3483	257	12	,	,	PUNCT
ejpam-3483	257	13	{	{	PUNCT
ejpam-3483	257	14	1	1	NUM
ejpam-3483	257	15	,	,	PUNCT
ejpam-3483	257	16	2	2	NUM
ejpam-3483	257	17	}	}	PUNCT
ejpam-3483	257	18	,	,	PUNCT
ejpam-3483	257	19	{	{	PUNCT
ejpam-3483	257	20	1	1	NUM
ejpam-3483	257	21	,	,	PUNCT
ejpam-3483	257	22	3	3	NUM
ejpam-3483	257	23	}	}	PUNCT
ejpam-3483	257	24	}	}	PUNCT
ejpam-3483	257	25	be	be	AUX
ejpam-3483	257	26	a	a	DET
ejpam-3483	257	27	associated	associated	ADJ
ejpam-3483	257	28	supra	supra	NOUN
ejpam-3483	257	29	topology	topology	NOUN
ejpam-3483	257	30	with	with	ADP
ejpam-3483	257	31	τ	τ	PROPN
ejpam-3483	257	32	.	.	PUNCT
ejpam-3483	258	1	the	the	DET
ejpam-3483	258	2	identity	identity	NOUN
ejpam-3483	258	3	map	map	NOUN
ejpam-3483	258	4	f	f	X
ejpam-3483	258	5	:	:	PUNCT
ejpam-3483	258	6	(	(	PUNCT
ejpam-3483	258	7	x	x	X
ejpam-3483	258	8	,	,	PUNCT
ejpam-3483	258	9	τ)→	τ)→	PROPN
ejpam-3483	258	10	(	(	PUNCT
ejpam-3483	258	11	x,µ	x,µ	NOUN
ejpam-3483	258	12	,	,	PUNCT
ejpam-3483	258	13	�	�	PROPN
ejpam-3483	258	14	)	)	PUNCT
ejpam-3483	258	15	is	be	AUX
ejpam-3483	258	16	supra	supra	ADJ
ejpam-3483	258	17	b	b	NOUN
ejpam-3483	258	18	-	-	PUNCT
ejpam-3483	258	19	open	open	ADJ
ejpam-3483	258	20	and	and	CCONJ
ejpam-3483	258	21	supra	supra	ADJ
ejpam-3483	258	22	b	b	PROPN
ejpam-3483	258	23	-	-	PUNCT
ejpam-3483	258	24	closed	closed	ADJ
ejpam-3483	258	25	.	.	PUNCT
ejpam-3483	259	1	on	on	ADP
ejpam-3483	259	2	the	the	DET
ejpam-3483	259	3	other	other	ADJ
ejpam-3483	259	4	hand	hand	NOUN
ejpam-3483	259	5	,	,	PUNCT
ejpam-3483	259	6	f({1	f({1	NOUN
ejpam-3483	259	7	,	,	PUNCT
ejpam-3483	259	8	2	2	NUM
ejpam-3483	259	9	}	}	PUNCT
ejpam-3483	259	10	)	)	PUNCT
ejpam-3483	260	1	=	=	PRON
ejpam-3483	260	2	{	{	PUNCT
ejpam-3483	260	3	1	1	NUM
ejpam-3483	260	4	,	,	PUNCT
ejpam-3483	260	5	2	2	NUM
ejpam-3483	260	6	}	}	PUNCT
ejpam-3483	260	7	is	be	AUX
ejpam-3483	260	8	neither	neither	CCONJ
ejpam-3483	260	9	an	an	DET
ejpam-3483	260	10	increasing	increasing	NOUN
ejpam-3483	260	11	nor	nor	CCONJ
ejpam-3483	260	12	a	a	DET
ejpam-3483	260	13	decreasing	decrease	VERB
ejpam-3483	260	14	supra	supra	ADJ
ejpam-3483	260	15	b	b	NOUN
ejpam-3483	260	16	-	-	PUNCT
ejpam-3483	260	17	open	open	ADJ
ejpam-3483	260	18	subset	subset	NOUN
ejpam-3483	260	19	of	of	ADP
ejpam-3483	260	20	y	y	PROPN
ejpam-3483	260	21	.	.	PUNCT
ejpam-3483	261	1	so	so	ADV
ejpam-3483	261	2	that	that	SCONJ
ejpam-3483	261	3	f	f	PROPN
ejpam-3483	261	4	is	be	AUX
ejpam-3483	261	5	not	not	PART
ejpam-3483	261	6	x	x	ADJ
ejpam-3483	261	7	-	-	ADJ
ejpam-3483	261	8	supra	supra	ADJ
ejpam-3483	261	9	b	b	NOUN
ejpam-3483	261	10	-	-	PUNCT
ejpam-3483	261	11	open	open	ADJ
ejpam-3483	261	12	map	map	NOUN
ejpam-3483	261	13	for	for	ADP
ejpam-3483	261	14	x	x	PROPN
ejpam-3483	261	15	∈	∈	PROPN
ejpam-3483	261	16	{	{	PUNCT
ejpam-3483	261	17	i	i	NOUN
ejpam-3483	261	18	,	,	PUNCT
ejpam-3483	261	19	d	d	PROPN
ejpam-3483	261	20	,	,	PUNCT
ejpam-3483	261	21	b	b	NOUN
ejpam-3483	261	22	}	}	PUNCT
ejpam-3483	261	23	.	.	PUNCT
ejpam-3483	262	1	also	also	ADV
ejpam-3483	262	2	,	,	PUNCT
ejpam-3483	262	3	f({3	f({3	ADJ
ejpam-3483	262	4	}	}	PUNCT
ejpam-3483	262	5	)	)	PUNCT
ejpam-3483	262	6	=	=	PRON
ejpam-3483	262	7	{	{	PUNCT
ejpam-3483	262	8	3	3	NUM
ejpam-3483	262	9	}	}	PUNCT
ejpam-3483	262	10	is	be	AUX
ejpam-3483	262	11	neither	neither	CCONJ
ejpam-3483	262	12	an	an	DET
ejpam-3483	262	13	increasing	increasing	NOUN
ejpam-3483	262	14	nor	nor	CCONJ
ejpam-3483	262	15	a	a	DET
ejpam-3483	262	16	decreasing	decrease	VERB
ejpam-3483	262	17	supra	supra	ADJ
ejpam-3483	262	18	b	b	NOUN
ejpam-3483	262	19	-	-	PUNCT
ejpam-3483	262	20	closed	closed	ADJ
ejpam-3483	262	21	subset	subset	NOUN
ejpam-3483	262	22	of	of	ADP
ejpam-3483	262	23	y	y	PROPN
ejpam-3483	262	24	.	.	PUNCT
ejpam-3483	263	1	so	so	ADV
ejpam-3483	263	2	that	that	SCONJ
ejpam-3483	263	3	f	f	PROPN
ejpam-3483	263	4	is	be	AUX
ejpam-3483	263	5	not	not	PART
ejpam-3483	263	6	x	x	ADJ
ejpam-3483	263	7	-	-	ADJ
ejpam-3483	263	8	supra	supra	ADJ
ejpam-3483	263	9	b	b	NOUN
ejpam-3483	263	10	-	-	PUNCT
ejpam-3483	263	11	closed	closed	ADJ
ejpam-3483	263	12	map	map	NOUN
ejpam-3483	263	13	for	for	ADP
ejpam-3483	263	14	x	x	PROPN
ejpam-3483	263	15	∈	∈	PROPN
ejpam-3483	263	16	{	{	PUNCT
ejpam-3483	263	17	i	i	NOUN
ejpam-3483	263	18	,	,	PUNCT
ejpam-3483	263	19	d	d	PROPN
ejpam-3483	263	20	,	,	PUNCT
ejpam-3483	263	21	b	b	NOUN
ejpam-3483	263	22	}	}	PUNCT
ejpam-3483	263	23	.	.	PUNCT
ejpam-3483	264	1	example	example	NOUN
ejpam-3483	265	1	4	4	NUM
ejpam-3483	265	2	.	.	X
ejpam-3483	265	3	we	we	PRON
ejpam-3483	265	4	replace	replace	VERB
ejpam-3483	265	5	only	only	ADV
ejpam-3483	265	6	a	a	DET
ejpam-3483	265	7	partial	partial	ADJ
ejpam-3483	265	8	order	order	NOUN
ejpam-3483	265	9	relation	relation	NOUN
ejpam-3483	265	10	in	in	ADP
ejpam-3483	265	11	example	example	NOUN
ejpam-3483	265	12	(	(	PUNCT
ejpam-3483	265	13	3	3	X
ejpam-3483	265	14	)	)	PUNCT
ejpam-3483	265	15	by	by	ADP
ejpam-3483	265	16	�	�	NOUN
ejpam-3483	265	17	=	=	PROPN
ejpam-3483	265	18	4	4	NUM
ejpam-3483	265	19	⋃	⋃	NOUN
ejpam-3483	265	20	{	{	PUNCT
ejpam-3483	265	21	(	(	PUNCT
ejpam-3483	265	22	1	1	NUM
ejpam-3483	265	23	,	,	PUNCT
ejpam-3483	265	24	3	3	NUM
ejpam-3483	265	25	)	)	PUNCT
ejpam-3483	265	26	,	,	PUNCT
ejpam-3483	265	27	(	(	PUNCT
ejpam-3483	265	28	1	1	NUM
ejpam-3483	265	29	,	,	PUNCT
ejpam-3483	265	30	2	2	NUM
ejpam-3483	265	31	)	)	PUNCT
ejpam-3483	265	32	}	}	PUNCT
ejpam-3483	265	33	.	.	PUNCT
ejpam-3483	266	1	then	then	ADV
ejpam-3483	266	2	a	a	DET
ejpam-3483	266	3	map	map	NOUN
ejpam-3483	266	4	f	f	NOUN
ejpam-3483	266	5	is	be	AUX
ejpam-3483	266	6	d	d	ADJ
ejpam-3483	266	7	-	-	PUNCT
ejpam-3483	266	8	supra	supra	ADJ
ejpam-3483	266	9	b	b	NOUN
ejpam-3483	266	10	-	-	PUNCT
ejpam-3483	266	11	open	open	ADJ
ejpam-3483	266	12	,	,	PUNCT
ejpam-3483	266	13	but	but	CCONJ
ejpam-3483	266	14	is	be	AUX
ejpam-3483	266	15	not	not	PART
ejpam-3483	266	16	b	b	NOUN
ejpam-3483	266	17	-	-	PUNCT
ejpam-3483	266	18	supra	supra	ADJ
ejpam-3483	266	19	b	b	NOUN
ejpam-3483	266	20	-	-	PUNCT
ejpam-3483	266	21	open	open	ADJ
ejpam-3483	266	22	.	.	PUNCT
ejpam-3483	267	1	also	also	ADV
ejpam-3483	267	2	,	,	PUNCT
ejpam-3483	267	3	it	it	PRON
ejpam-3483	267	4	is	be	AUX
ejpam-3483	267	5	i	i	PROPN
ejpam-3483	267	6	-	-	PUNCT
ejpam-3483	267	7	supra	supra	PROPN
ejpam-3483	267	8	b	b	PROPN
ejpam-3483	267	9	-	-	PUNCT
ejpam-3483	267	10	closed	closed	ADJ
ejpam-3483	267	11	,	,	PUNCT
ejpam-3483	267	12	but	but	CCONJ
ejpam-3483	267	13	is	be	AUX
ejpam-3483	267	14	not	not	PART
ejpam-3483	267	15	b	b	NOUN
ejpam-3483	267	16	-	-	PUNCT
ejpam-3483	267	17	supra	supra	ADJ
ejpam-3483	267	18	b	b	NOUN
ejpam-3483	267	19	-	-	PUNCT
ejpam-3483	267	20	closed	closed	ADJ
ejpam-3483	267	21	.	.	PUNCT
ejpam-3483	268	1	theorem	theorem	VERB
ejpam-3483	268	2	11	11	NUM
ejpam-3483	268	3	.	.	PUNCT
ejpam-3483	269	1	the	the	DET
ejpam-3483	269	2	following	follow	VERB
ejpam-3483	269	3	statements	statement	NOUN
ejpam-3483	269	4	are	be	AUX
ejpam-3483	269	5	equivalent	equivalent	ADJ
ejpam-3483	269	6	,	,	PUNCT
ejpam-3483	269	7	for	for	ADP
ejpam-3483	269	8	a	a	DET
ejpam-3483	269	9	map	map	NOUN
ejpam-3483	269	10	f	f	X
ejpam-3483	269	11	:	:	PUNCT
ejpam-3483	269	12	(	(	PUNCT
ejpam-3483	269	13	x	x	X
ejpam-3483	269	14	,	,	PUNCT
ejpam-3483	269	15	τ)→	τ)→	PROPN
ejpam-3483	269	16	(	(	PUNCT
ejpam-3483	269	17	y	y	PROPN
ejpam-3483	269	18	,	,	PUNCT
ejpam-3483	269	19	µ	µ	NUM
ejpam-3483	269	20	,	,	PUNCT
ejpam-3483	269	21	�	�	PROPN
ejpam-3483	269	22	):	):	PUNCT
ejpam-3483	269	23	b.	b.	PROPN
ejpam-3483	269	24	a.	a.	PROPN
ejpam-3483	269	25	asaad	asaad	PROPN
ejpam-3483	269	26	,	,	PUNCT
ejpam-3483	269	27	m.	m.	PROPN
ejpam-3483	269	28	k.	k.	PROPN
ejpam-3483	269	29	tahat	tahat	PROPN
ejpam-3483	269	30	,	,	PUNCT
ejpam-3483	269	31	t.	t.	PROPN
ejpam-3483	269	32	m.	m.	PROPN
ejpam-3483	269	33	al	al	PROPN
ejpam-3483	269	34	-	-	PUNCT
ejpam-3483	269	35	shami	shami	PROPN
ejpam-3483	269	36	/	/	PUNCT
ejpam-3483	269	37	eur	eur	PROPN
ejpam-3483	269	38	.	.	PUNCT
ejpam-3483	270	1	j.	j.	PROPN
ejpam-3483	270	2	pure	pure	PROPN
ejpam-3483	270	3	appl	appl	PROPN
ejpam-3483	270	4	.	.	PROPN
ejpam-3483	270	5	math	math	PROPN
ejpam-3483	270	6	,	,	PUNCT
ejpam-3483	270	7	12	12	NUM
ejpam-3483	270	8	(	(	PUNCT
ejpam-3483	270	9	3	3	NUM
ejpam-3483	270	10	)	)	PUNCT
ejpam-3483	270	11	(	(	PUNCT
ejpam-3483	270	12	2019	2019	NUM
ejpam-3483	270	13	)	)	PUNCT
ejpam-3483	270	14	,	,	PUNCT
ejpam-3483	270	15	1231	1231	NUM
ejpam-3483	270	16	-	-	SYM
ejpam-3483	270	17	1247	1247	NUM
ejpam-3483	270	18	1240	1240	NUM
ejpam-3483	270	19	(	(	PUNCT
ejpam-3483	270	20	i	i	NOUN
ejpam-3483	270	21	)	)	PUNCT
ejpam-3483	270	22	f	f	PROPN
ejpam-3483	270	23	is	be	AUX
ejpam-3483	270	24	i	i	PROPN
ejpam-3483	270	25	-	-	PUNCT
ejpam-3483	270	26	supra	supra	PROPN
ejpam-3483	270	27	b	b	NOUN
ejpam-3483	270	28	-	-	PUNCT
ejpam-3483	270	29	open	open	ADJ
ejpam-3483	270	30	;	;	PUNCT
ejpam-3483	270	31	(	(	PUNCT
ejpam-3483	270	32	ii	ii	NOUN
ejpam-3483	270	33	)	)	PUNCT
ejpam-3483	270	34	int(f−1(h	int(f−1(h	PROPN
ejpam-3483	270	35	)	)	PUNCT
ejpam-3483	270	36	)	)	PUNCT
ejpam-3483	271	1	⊆	⊆	NUM
ejpam-3483	271	2	f−1(h	f−1(h	PROPN
ejpam-3483	271	3	isbo	isbo	NOUN
ejpam-3483	271	4	)	)	PUNCT
ejpam-3483	271	5	for	for	ADP
ejpam-3483	271	6	every	every	DET
ejpam-3483	271	7	h	h	NOUN
ejpam-3483	271	8	⊆	⊆	NUM
ejpam-3483	271	9	y	y	NOUN
ejpam-3483	271	10	;	;	PUNCT
ejpam-3483	271	11	(	(	PUNCT
ejpam-3483	271	12	iii	iii	X
ejpam-3483	271	13	)	)	PUNCT
ejpam-3483	271	14	f(int(g	f(int(g	NOUN
ejpam-3483	271	15	)	)	PUNCT
ejpam-3483	271	16	)	)	PUNCT
ejpam-3483	272	1	⊆	⊆	NUM
ejpam-3483	272	2	(	(	PUNCT
ejpam-3483	272	3	f(g))isbo	f(g))isbo	PROPN
ejpam-3483	272	4	for	for	ADP
ejpam-3483	272	5	every	every	DET
ejpam-3483	272	6	g	g	PROPN
ejpam-3483	272	7	⊆	⊆	NUM
ejpam-3483	272	8	x.	x.	NOUN
ejpam-3483	272	9	proof	proof	NOUN
ejpam-3483	272	10	.	.	PUNCT
ejpam-3483	273	1	(	(	PUNCT
ejpam-3483	273	2	i	i	NOUN
ejpam-3483	273	3	)	)	PUNCT
ejpam-3483	273	4	⇒	⇒	PROPN
ejpam-3483	273	5	(	(	PUNCT
ejpam-3483	273	6	ii	ii	PROPN
ejpam-3483	273	7	):	):	PUNCT
ejpam-3483	273	8	since	since	SCONJ
ejpam-3483	273	9	int(f−1(h	int(f−1(h	NOUN
ejpam-3483	273	10	)	)	PUNCT
ejpam-3483	273	11	)	)	PUNCT
ejpam-3483	273	12	is	be	AUX
ejpam-3483	273	13	an	an	DET
ejpam-3483	273	14	open	open	ADJ
ejpam-3483	273	15	subset	subset	NOUN
ejpam-3483	273	16	of	of	ADP
ejpam-3483	273	17	x	x	PRON
ejpam-3483	273	18	,	,	PUNCT
ejpam-3483	273	19	then	then	ADV
ejpam-3483	273	20	f(int(f−1(h	f(int(f−1(h	PROPN
ejpam-3483	273	21	)	)	PUNCT
ejpam-3483	273	22	)	)	PUNCT
ejpam-3483	273	23	)	)	PUNCT
ejpam-3483	274	1	is	be	AUX
ejpam-3483	274	2	an	an	DET
ejpam-3483	274	3	i	i	PROPN
ejpam-3483	274	4	-	-	PUNCT
ejpam-3483	274	5	supra	supra	PROPN
ejpam-3483	274	6	b	b	NOUN
ejpam-3483	274	7	-	-	PUNCT
ejpam-3483	274	8	open	open	ADJ
ejpam-3483	274	9	subset	subset	NOUN
ejpam-3483	274	10	of	of	ADP
ejpam-3483	274	11	y	y	PROPN
ejpam-3483	274	12	.	.	PUNCT
ejpam-3483	275	1	obviously	obviously	ADV
ejpam-3483	275	2	,	,	PUNCT
ejpam-3483	275	3	f(int(f−1(h	f(int(f−1(h	PROPN
ejpam-3483	275	4	)	)	PUNCT
ejpam-3483	275	5	)	)	PUNCT
ejpam-3483	275	6	)	)	PUNCT
ejpam-3483	276	1	⊆	⊆	NUM
ejpam-3483	276	2	f(f−1(h	f(f−1(h	NUM
ejpam-3483	276	3	)	)	PUNCT
ejpam-3483	276	4	)	)	PUNCT
ejpam-3483	277	1	⊆	⊆	NUM
ejpam-3483	277	2	h.	h.	PROPN
ejpam-3483	277	3	so	so	ADV
ejpam-3483	277	4	int(f−1(h	int(f−1(h	NOUN
ejpam-3483	277	5	)	)	PUNCT
ejpam-3483	277	6	)	)	PUNCT
ejpam-3483	278	1	⊆	⊆	NUM
ejpam-3483	278	2	f−1(h	f−1(h	PROPN
ejpam-3483	278	3	isbo	isbo	NOUN
ejpam-3483	278	4	)	)	PUNCT
ejpam-3483	278	5	.	.	PUNCT
ejpam-3483	279	1	(	(	PUNCT
ejpam-3483	279	2	ii)⇒	ii)⇒	X
ejpam-3483	279	3	(	(	PUNCT
ejpam-3483	279	4	iii	iii	NOUN
ejpam-3483	279	5	):	):	PUNCT
ejpam-3483	279	6	set	set	VERB
ejpam-3483	279	7	h	h	NOUN
ejpam-3483	279	8	=	=	PUNCT
ejpam-3483	279	9	f(g	f(g	PROPN
ejpam-3483	279	10	)	)	PUNCT
ejpam-3483	279	11	in	in	ADP
ejpam-3483	279	12	(	(	PUNCT
ejpam-3483	279	13	ii	ii	NOUN
ejpam-3483	279	14	)	)	PUNCT
ejpam-3483	279	15	.	.	PUNCT
ejpam-3483	280	1	then	then	ADV
ejpam-3483	280	2	int(f−1(f(g	int(f−1(f(g	PROPN
ejpam-3483	280	3	)	)	PUNCT
ejpam-3483	280	4	)	)	PUNCT
ejpam-3483	280	5	)	)	PUNCT
ejpam-3483	281	1	⊆	⊆	NUM
ejpam-3483	281	2	f−1((f(g))isbo	f−1((f(g))isbo	NOUN
ejpam-3483	281	3	)	)	PUNCT
ejpam-3483	281	4	.	.	PUNCT
ejpam-3483	282	1	since	since	SCONJ
ejpam-3483	282	2	int(g	int(g	PROPN
ejpam-3483	282	3	)	)	PUNCT
ejpam-3483	282	4	⊆	⊆	NUM
ejpam-3483	282	5	f−1((f(g))isbo	f−1((f(g))isbo	NOUN
ejpam-3483	282	6	)	)	PUNCT
ejpam-3483	282	7	,	,	PUNCT
ejpam-3483	282	8	then	then	ADV
ejpam-3483	282	9	f(int(g	f(int(g	NOUN
ejpam-3483	282	10	)	)	PUNCT
ejpam-3483	282	11	)	)	PUNCT
ejpam-3483	283	1	⊆	⊆	NUM
ejpam-3483	283	2	(	(	PUNCT
ejpam-3483	283	3	f(g))isbo	f(g))isbo	PROPN
ejpam-3483	283	4	.	.	PUNCT
ejpam-3483	283	5	(	(	PUNCT
ejpam-3483	283	6	iii	iii	X
ejpam-3483	283	7	)	)	PUNCT
ejpam-3483	283	8	⇒	⇒	NOUN
ejpam-3483	283	9	(	(	PUNCT
ejpam-3483	283	10	i	i	NOUN
ejpam-3483	283	11	):	):	PUNCT
ejpam-3483	283	12	let	let	VERB
ejpam-3483	283	13	g	g	PRON
ejpam-3483	283	14	be	be	AUX
ejpam-3483	283	15	an	an	DET
ejpam-3483	283	16	open	open	ADJ
ejpam-3483	283	17	subset	subset	NOUN
ejpam-3483	283	18	of	of	ADP
ejpam-3483	283	19	x.	x.	PROPN
ejpam-3483	283	20	then	then	ADV
ejpam-3483	283	21	f(int(g	f(int(g	NOUN
ejpam-3483	283	22	)	)	PUNCT
ejpam-3483	283	23	)	)	PUNCT
ejpam-3483	284	1	=	=	PUNCT
ejpam-3483	284	2	f(g	f(g	NOUN
ejpam-3483	284	3	)	)	PUNCT
ejpam-3483	284	4	⊆	⊆	NUM
ejpam-3483	284	5	(	(	PUNCT
ejpam-3483	284	6	f(g))isbo	f(g))isbo	PROPN
ejpam-3483	284	7	.	.	PUNCT
ejpam-3483	285	1	so	so	ADV
ejpam-3483	285	2	f(g	f(g	NOUN
ejpam-3483	285	3	)	)	PUNCT
ejpam-3483	285	4	is	be	AUX
ejpam-3483	285	5	an	an	DET
ejpam-3483	285	6	i	i	PROPN
ejpam-3483	285	7	-	-	PUNCT
ejpam-3483	285	8	supra	supra	PROPN
ejpam-3483	285	9	b	b	NOUN
ejpam-3483	285	10	-	-	PUNCT
ejpam-3483	285	11	open	open	ADJ
ejpam-3483	285	12	set	set	NOUN
ejpam-3483	285	13	.	.	PUNCT
ejpam-3483	286	1	thus	thus	ADV
ejpam-3483	286	2	f	f	PROPN
ejpam-3483	286	3	is	be	AUX
ejpam-3483	286	4	an	an	DET
ejpam-3483	286	5	i	i	PROPN
ejpam-3483	286	6	-	-	PUNCT
ejpam-3483	286	7	supra	supra	PROPN
ejpam-3483	286	8	b	b	NOUN
ejpam-3483	286	9	-	-	PUNCT
ejpam-3483	286	10	open	open	ADJ
ejpam-3483	286	11	map	map	NOUN
ejpam-3483	286	12	.	.	PUNCT
ejpam-3483	287	1	the	the	DET
ejpam-3483	287	2	following	follow	VERB
ejpam-3483	287	3	two	two	NUM
ejpam-3483	287	4	results	result	NOUN
ejpam-3483	287	5	can	can	AUX
ejpam-3483	287	6	be	be	AUX
ejpam-3483	287	7	proved	prove	VERB
ejpam-3483	287	8	similarly	similarly	ADV
ejpam-3483	287	9	.	.	PUNCT
ejpam-3483	288	1	theorem	theorem	NOUN
ejpam-3483	288	2	12	12	NUM
ejpam-3483	288	3	.	.	PUNCT
ejpam-3483	289	1	the	the	DET
ejpam-3483	289	2	following	follow	VERB
ejpam-3483	289	3	statements	statement	NOUN
ejpam-3483	289	4	are	be	AUX
ejpam-3483	289	5	equivalent	equivalent	ADJ
ejpam-3483	289	6	,	,	PUNCT
ejpam-3483	289	7	for	for	ADP
ejpam-3483	289	8	a	a	DET
ejpam-3483	289	9	map	map	NOUN
ejpam-3483	289	10	f	f	X
ejpam-3483	289	11	:	:	PUNCT
ejpam-3483	289	12	(	(	PUNCT
ejpam-3483	289	13	x	x	X
ejpam-3483	289	14	,	,	PUNCT
ejpam-3483	289	15	τ)→	τ)→	PROPN
ejpam-3483	289	16	(	(	PUNCT
ejpam-3483	289	17	y	y	PROPN
ejpam-3483	289	18	,	,	PUNCT
ejpam-3483	289	19	µ	µ	NUM
ejpam-3483	289	20	,	,	PUNCT
ejpam-3483	289	21	�	�	PROPN
ejpam-3483	289	22	):	):	PUNCT
ejpam-3483	289	23	(	(	PUNCT
ejpam-3483	289	24	i	i	NOUN
ejpam-3483	289	25	)	)	PUNCT
ejpam-3483	289	26	f	f	PROPN
ejpam-3483	289	27	is	be	AUX
ejpam-3483	289	28	d	d	ADJ
ejpam-3483	289	29	-	-	PUNCT
ejpam-3483	289	30	supra	supra	ADJ
ejpam-3483	289	31	b	b	NOUN
ejpam-3483	289	32	-	-	PUNCT
ejpam-3483	289	33	open	open	ADJ
ejpam-3483	289	34	;	;	PUNCT
ejpam-3483	289	35	(	(	PUNCT
ejpam-3483	289	36	ii	ii	NOUN
ejpam-3483	289	37	)	)	PUNCT
ejpam-3483	289	38	int(f−1(h	int(f−1(h	PROPN
ejpam-3483	289	39	)	)	PUNCT
ejpam-3483	289	40	)	)	PUNCT
ejpam-3483	290	1	⊆	⊆	NUM
ejpam-3483	290	2	f−1(hdsbo	f−1(hdsbo	NOUN
ejpam-3483	290	3	)	)	PUNCT
ejpam-3483	290	4	for	for	ADP
ejpam-3483	290	5	every	every	DET
ejpam-3483	290	6	h	h	NOUN
ejpam-3483	290	7	⊆	⊆	NUM
ejpam-3483	290	8	y	y	NOUN
ejpam-3483	290	9	;	;	PUNCT
ejpam-3483	290	10	(	(	PUNCT
ejpam-3483	290	11	iii	iii	X
ejpam-3483	290	12	)	)	PUNCT
ejpam-3483	290	13	f(int(g	f(int(g	NOUN
ejpam-3483	290	14	)	)	PUNCT
ejpam-3483	290	15	)	)	PUNCT
ejpam-3483	291	1	⊆	⊆	NUM
ejpam-3483	291	2	(	(	PUNCT
ejpam-3483	291	3	f(g))dsbo	f(g))dsbo	PROPN
ejpam-3483	291	4	for	for	ADP
ejpam-3483	291	5	every	every	DET
ejpam-3483	291	6	g	g	PROPN
ejpam-3483	291	7	⊆	⊆	NUM
ejpam-3483	291	8	x.	x.	NOUN
ejpam-3483	291	9	theorem	theorem	VERB
ejpam-3483	291	10	13	13	NUM
ejpam-3483	291	11	.	.	PUNCT
ejpam-3483	292	1	the	the	DET
ejpam-3483	292	2	following	follow	VERB
ejpam-3483	292	3	statements	statement	NOUN
ejpam-3483	292	4	are	be	AUX
ejpam-3483	292	5	equivalent	equivalent	ADJ
ejpam-3483	292	6	,	,	PUNCT
ejpam-3483	292	7	for	for	ADP
ejpam-3483	292	8	a	a	DET
ejpam-3483	292	9	map	map	NOUN
ejpam-3483	292	10	f	f	X
ejpam-3483	292	11	:	:	PUNCT
ejpam-3483	292	12	(	(	PUNCT
ejpam-3483	292	13	x	x	X
ejpam-3483	292	14	,	,	PUNCT
ejpam-3483	292	15	τ)→	τ)→	PROPN
ejpam-3483	292	16	(	(	PUNCT
ejpam-3483	292	17	y	y	PROPN
ejpam-3483	292	18	,	,	PUNCT
ejpam-3483	292	19	µ	µ	NUM
ejpam-3483	292	20	,	,	PUNCT
ejpam-3483	292	21	�	�	PROPN
ejpam-3483	292	22	):	):	PUNCT
ejpam-3483	292	23	(	(	PUNCT
ejpam-3483	292	24	i	i	NOUN
ejpam-3483	292	25	)	)	PUNCT
ejpam-3483	292	26	f	f	PROPN
ejpam-3483	292	27	is	be	AUX
ejpam-3483	292	28	b	b	NOUN
ejpam-3483	292	29	-	-	PUNCT
ejpam-3483	292	30	supra	supra	ADJ
ejpam-3483	292	31	b	b	NOUN
ejpam-3483	292	32	-	-	PUNCT
ejpam-3483	292	33	open	open	ADJ
ejpam-3483	292	34	;	;	PUNCT
ejpam-3483	292	35	(	(	PUNCT
ejpam-3483	292	36	ii	ii	NOUN
ejpam-3483	292	37	)	)	PUNCT
ejpam-3483	292	38	int(f−1(h	int(f−1(h	PROPN
ejpam-3483	292	39	)	)	PUNCT
ejpam-3483	292	40	)	)	PUNCT
ejpam-3483	293	1	⊆	⊆	NUM
ejpam-3483	293	2	f−1(hbsbo	f−1(hbsbo	NOUN
ejpam-3483	293	3	)	)	PUNCT
ejpam-3483	293	4	for	for	ADP
ejpam-3483	293	5	every	every	DET
ejpam-3483	293	6	h	h	NOUN
ejpam-3483	293	7	⊆	⊆	NUM
ejpam-3483	293	8	y	y	NOUN
ejpam-3483	293	9	;	;	PUNCT
ejpam-3483	293	10	(	(	PUNCT
ejpam-3483	293	11	iii	iii	X
ejpam-3483	293	12	)	)	PUNCT
ejpam-3483	293	13	f(int(g	f(int(g	NOUN
ejpam-3483	293	14	)	)	PUNCT
ejpam-3483	293	15	)	)	PUNCT
ejpam-3483	294	1	⊆	⊆	NUM
ejpam-3483	294	2	(	(	PUNCT
ejpam-3483	294	3	f(g))bsbo	f(g))bsbo	NOUN
ejpam-3483	294	4	for	for	ADP
ejpam-3483	294	5	every	every	DET
ejpam-3483	294	6	g	g	PROPN
ejpam-3483	294	7	⊆	⊆	NUM
ejpam-3483	294	8	x.	x.	NOUN
ejpam-3483	294	9	theorem	theorem	VERB
ejpam-3483	294	10	14	14	NUM
ejpam-3483	294	11	.	.	PUNCT
ejpam-3483	295	1	we	we	PRON
ejpam-3483	295	2	have	have	VERB
ejpam-3483	295	3	the	the	DET
ejpam-3483	295	4	following	follow	VERB
ejpam-3483	295	5	results	result	NOUN
ejpam-3483	295	6	for	for	ADP
ejpam-3483	295	7	a	a	DET
ejpam-3483	295	8	map	map	NOUN
ejpam-3483	295	9	f	f	X
ejpam-3483	295	10	:	:	PUNCT
ejpam-3483	295	11	(	(	PUNCT
ejpam-3483	295	12	x	x	X
ejpam-3483	295	13	,	,	PUNCT
ejpam-3483	295	14	τ)→	τ)→	PROPN
ejpam-3483	295	15	(	(	PUNCT
ejpam-3483	295	16	y	y	PROPN
ejpam-3483	295	17	,	,	PUNCT
ejpam-3483	295	18	µ	µ	NOUN
ejpam-3483	295	19	,	,	PUNCT
ejpam-3483	295	20	�	�	PROPN
ejpam-3483	295	21	)	)	PUNCT
ejpam-3483	295	22	.	.	PUNCT
ejpam-3483	296	1	(	(	PUNCT
ejpam-3483	296	2	i	i	NOUN
ejpam-3483	296	3	)	)	PUNCT
ejpam-3483	296	4	f	f	PROPN
ejpam-3483	296	5	is	be	AUX
ejpam-3483	296	6	i	i	PROPN
ejpam-3483	296	7	-	-	PUNCT
ejpam-3483	296	8	supra	supra	PROPN
ejpam-3483	296	9	b	b	PROPN
ejpam-3483	296	10	-	-	PUNCT
ejpam-3483	296	11	closed	closed	ADJ
ejpam-3483	296	12	if	if	SCONJ
ejpam-3483	297	1	and	and	CCONJ
ejpam-3483	297	2	only	only	ADV
ejpam-3483	297	3	if	if	SCONJ
ejpam-3483	297	4	(	(	PUNCT
ejpam-3483	297	5	f(g))isbcl	f(g))isbcl	NOUN
ejpam-3483	297	6	⊆	⊆	NUM
ejpam-3483	297	7	f(cl(g	f(cl(g	NOUN
ejpam-3483	297	8	)	)	PUNCT
ejpam-3483	297	9	)	)	PUNCT
ejpam-3483	297	10	for	for	ADP
ejpam-3483	297	11	any	any	DET
ejpam-3483	297	12	g	g	NOUN
ejpam-3483	297	13	⊆	⊆	NUM
ejpam-3483	297	14	x.	x.	NOUN
ejpam-3483	297	15	(	(	PUNCT
ejpam-3483	297	16	ii	ii	PROPN
ejpam-3483	297	17	)	)	PUNCT
ejpam-3483	297	18	f	f	PROPN
ejpam-3483	297	19	is	be	AUX
ejpam-3483	297	20	d	d	ADJ
ejpam-3483	297	21	-	-	PUNCT
ejpam-3483	297	22	supra	supra	ADJ
ejpam-3483	297	23	b	b	NOUN
ejpam-3483	297	24	-	-	PUNCT
ejpam-3483	297	25	closed	closed	ADJ
ejpam-3483	297	26	if	if	SCONJ
ejpam-3483	297	27	and	and	CCONJ
ejpam-3483	297	28	only	only	ADV
ejpam-3483	297	29	if	if	SCONJ
ejpam-3483	297	30	(	(	PUNCT
ejpam-3483	297	31	f(g))dsbcl	f(g))dsbcl	X
ejpam-3483	297	32	⊆	⊆	NUM
ejpam-3483	297	33	f(cl(g	f(cl(g	NOUN
ejpam-3483	297	34	)	)	PUNCT
ejpam-3483	297	35	)	)	PUNCT
ejpam-3483	297	36	for	for	ADP
ejpam-3483	297	37	any	any	DET
ejpam-3483	297	38	g	g	NOUN
ejpam-3483	297	39	⊆	⊆	NUM
ejpam-3483	297	40	x.	x.	NOUN
ejpam-3483	297	41	(	(	PUNCT
ejpam-3483	297	42	iii	iii	X
ejpam-3483	297	43	)	)	PUNCT
ejpam-3483	297	44	f	f	PROPN
ejpam-3483	297	45	is	be	AUX
ejpam-3483	297	46	b	b	NOUN
ejpam-3483	297	47	-	-	PUNCT
ejpam-3483	297	48	supra	supra	ADJ
ejpam-3483	297	49	b	b	NOUN
ejpam-3483	297	50	-	-	PUNCT
ejpam-3483	297	51	closed	closed	ADJ
ejpam-3483	297	52	if	if	SCONJ
ejpam-3483	297	53	and	and	CCONJ
ejpam-3483	297	54	only	only	ADV
ejpam-3483	297	55	if	if	SCONJ
ejpam-3483	297	56	(	(	PUNCT
ejpam-3483	297	57	f(g))bsbcl	f(g))bsbcl	NOUN
ejpam-3483	297	58	⊆	⊆	NUM
ejpam-3483	297	59	f(cl(g	f(cl(g	NOUN
ejpam-3483	297	60	)	)	PUNCT
ejpam-3483	297	61	)	)	PUNCT
ejpam-3483	297	62	for	for	ADP
ejpam-3483	297	63	any	any	DET
ejpam-3483	297	64	g	g	NOUN
ejpam-3483	297	65	⊆	⊆	NUM
ejpam-3483	297	66	x.	x.	NOUN
ejpam-3483	297	67	proof	proof	NOUN
ejpam-3483	297	68	.	.	PUNCT
ejpam-3483	298	1	(	(	PUNCT
ejpam-3483	298	2	i	i	NOUN
ejpam-3483	298	3	)	)	PUNCT
ejpam-3483	298	4	necessity	necessity	NOUN
ejpam-3483	298	5	:	:	PUNCT
ejpam-3483	298	6	consider	consider	VERB
ejpam-3483	298	7	f	f	PROPN
ejpam-3483	298	8	is	be	AUX
ejpam-3483	298	9	an	an	DET
ejpam-3483	298	10	i	i	PROPN
ejpam-3483	298	11	-	-	PUNCT
ejpam-3483	298	12	supra	supra	PROPN
ejpam-3483	298	13	b	b	PROPN
ejpam-3483	298	14	-	-	PUNCT
ejpam-3483	298	15	closed	closed	ADJ
ejpam-3483	298	16	map	map	NOUN
ejpam-3483	298	17	.	.	PUNCT
ejpam-3483	299	1	then	then	ADV
ejpam-3483	299	2	f(cl(g	f(cl(g	NOUN
ejpam-3483	299	3	)	)	PUNCT
ejpam-3483	299	4	)	)	PUNCT
ejpam-3483	299	5	is	be	AUX
ejpam-3483	299	6	an	an	DET
ejpam-3483	299	7	i	i	PROPN
ejpam-3483	299	8	-	-	PUNCT
ejpam-3483	299	9	supra	supra	PROPN
ejpam-3483	299	10	b	b	PROPN
ejpam-3483	299	11	-	-	PUNCT
ejpam-3483	299	12	closed	closed	ADJ
ejpam-3483	299	13	subset	subset	NOUN
ejpam-3483	299	14	of	of	ADP
ejpam-3483	299	15	y	y	PROPN
ejpam-3483	299	16	.	.	PUNCT
ejpam-3483	300	1	since	since	SCONJ
ejpam-3483	300	2	f(g	f(g	NOUN
ejpam-3483	300	3	)	)	PUNCT
ejpam-3483	300	4	⊆	⊆	NUM
ejpam-3483	300	5	f(cl(g	f(cl(g	NOUN
ejpam-3483	300	6	)	)	PUNCT
ejpam-3483	300	7	)	)	PUNCT
ejpam-3483	300	8	,	,	PUNCT
ejpam-3483	300	9	then	then	ADV
ejpam-3483	300	10	(	(	PUNCT
ejpam-3483	300	11	f(g))isbcl	f(g))isbcl	NOUN
ejpam-3483	300	12	⊆	⊆	NUM
ejpam-3483	300	13	f(cl(g	f(cl(g	NOUN
ejpam-3483	300	14	)	)	PUNCT
ejpam-3483	300	15	)	)	PUNCT
ejpam-3483	300	16	.	.	PUNCT
ejpam-3483	301	1	sufficiency	sufficiency	NOUN
ejpam-3483	301	2	:	:	PUNCT
ejpam-3483	301	3	consider	consider	VERB
ejpam-3483	301	4	b	b	NOUN
ejpam-3483	301	5	is	be	AUX
ejpam-3483	301	6	a	a	DET
ejpam-3483	301	7	closed	closed	ADJ
ejpam-3483	301	8	subset	subset	NOUN
ejpam-3483	301	9	of	of	ADP
ejpam-3483	301	10	x.	x.	PROPN
ejpam-3483	301	11	then	then	ADV
ejpam-3483	301	12	f(b	f(b	PROPN
ejpam-3483	301	13	)	)	PUNCT
ejpam-3483	302	1	⊆	⊆	NUM
ejpam-3483	302	2	(	(	PUNCT
ejpam-3483	302	3	f(b))isbcl	f(b))isbcl	PROPN
ejpam-3483	302	4	⊆	⊆	NUM
ejpam-3483	302	5	f(cl(b	f(cl(b	PROPN
ejpam-3483	302	6	)	)	PUNCT
ejpam-3483	302	7	)	)	PUNCT
ejpam-3483	303	1	=	=	SYM
ejpam-3483	303	2	f(b	f(b	PROPN
ejpam-3483	303	3	)	)	PUNCT
ejpam-3483	303	4	.	.	PUNCT
ejpam-3483	304	1	therefore	therefore	ADV
ejpam-3483	304	2	f(b	f(b	X
ejpam-3483	304	3	)	)	PUNCT
ejpam-3483	304	4	=	=	PRON
ejpam-3483	304	5	(	(	PUNCT
ejpam-3483	304	6	f(b))isbcl	f(b))isbcl	X
ejpam-3483	304	7	.	.	PUNCT
ejpam-3483	305	1	thus	thus	ADV
ejpam-3483	305	2	f(b	f(b	X
ejpam-3483	305	3	)	)	PUNCT
ejpam-3483	305	4	is	be	AUX
ejpam-3483	305	5	an	an	DET
ejpam-3483	305	6	i	i	PROPN
ejpam-3483	305	7	-	-	PUNCT
ejpam-3483	305	8	supra	supra	PROPN
ejpam-3483	305	9	b	b	PROPN
ejpam-3483	305	10	-	-	PUNCT
ejpam-3483	305	11	closed	closed	ADJ
ejpam-3483	305	12	set	set	NOUN
ejpam-3483	305	13	.	.	PUNCT
ejpam-3483	306	1	hence	hence	ADV
ejpam-3483	306	2	f	f	PROPN
ejpam-3483	306	3	is	be	AUX
ejpam-3483	306	4	an	an	DET
ejpam-3483	306	5	i	i	PROPN
ejpam-3483	306	6	-	-	PUNCT
ejpam-3483	306	7	supra	supra	PROPN
ejpam-3483	306	8	b	b	PROPN
ejpam-3483	306	9	-	-	PUNCT
ejpam-3483	306	10	closed	closed	ADJ
ejpam-3483	306	11	map	map	NOUN
ejpam-3483	306	12	.	.	PUNCT
ejpam-3483	307	1	the	the	DET
ejpam-3483	307	2	proofs	proof	NOUN
ejpam-3483	307	3	of	of	ADP
ejpam-3483	307	4	(	(	PUNCT
ejpam-3483	307	5	ii	ii	NOUN
ejpam-3483	307	6	)	)	PUNCT
ejpam-3483	307	7	and	and	CCONJ
ejpam-3483	307	8	(	(	PUNCT
ejpam-3483	307	9	iii	iii	X
ejpam-3483	307	10	)	)	PUNCT
ejpam-3483	307	11	are	be	AUX
ejpam-3483	307	12	similar	similar	ADJ
ejpam-3483	307	13	to	to	ADP
ejpam-3483	307	14	that	that	PRON
ejpam-3483	307	15	of	of	ADP
ejpam-3483	307	16	(	(	PUNCT
ejpam-3483	307	17	i	i	NOUN
ejpam-3483	307	18	)	)	PUNCT
ejpam-3483	307	19	.	.	PUNCT
ejpam-3483	308	1	theorem	theorem	NOUN
ejpam-3483	308	2	15	15	NUM
ejpam-3483	308	3	.	.	PUNCT
ejpam-3483	309	1	let	let	VERB
ejpam-3483	309	2	f	f	NOUN
ejpam-3483	309	3	:	:	PUNCT
ejpam-3483	309	4	(	(	PUNCT
ejpam-3483	309	5	x	x	X
ejpam-3483	309	6	,	,	PUNCT
ejpam-3483	309	7	τ,	τ,	NOUN
ejpam-3483	309	8	�	�	X
ejpam-3483	309	9	1	1	NUM
ejpam-3483	309	10	)	)	PUNCT
ejpam-3483	309	11	→	→	SYM
ejpam-3483	309	12	(	(	PUNCT
ejpam-3483	309	13	y	y	PROPN
ejpam-3483	309	14	,	,	PUNCT
ejpam-3483	309	15	µ,	µ,	X
ejpam-3483	309	16	�	�	PROPN
ejpam-3483	309	17	2	2	NUM
ejpam-3483	309	18	)	)	PUNCT
ejpam-3483	309	19	be	be	AUX
ejpam-3483	309	20	a	a	DET
ejpam-3483	309	21	bijective	bijective	ADJ
ejpam-3483	309	22	map	map	NOUN
ejpam-3483	309	23	.	.	PUNCT
ejpam-3483	310	1	then	then	ADV
ejpam-3483	310	2	we	we	PRON
ejpam-3483	310	3	have	have	VERB
ejpam-3483	310	4	the	the	DET
ejpam-3483	310	5	following	follow	VERB
ejpam-3483	310	6	results	result	NOUN
ejpam-3483	310	7	.	.	PUNCT
ejpam-3483	311	1	b.	b.	PROPN
ejpam-3483	311	2	a.	a.	PROPN
ejpam-3483	311	3	asaad	asaad	PROPN
ejpam-3483	311	4	,	,	PUNCT
ejpam-3483	311	5	m.	m.	PROPN
ejpam-3483	311	6	k.	k.	PROPN
ejpam-3483	311	7	tahat	tahat	PROPN
ejpam-3483	311	8	,	,	PUNCT
ejpam-3483	311	9	t.	t.	PROPN
ejpam-3483	311	10	m.	m.	PROPN
ejpam-3483	311	11	al	al	PROPN
ejpam-3483	311	12	-	-	PUNCT
ejpam-3483	311	13	shami	shami	PROPN
ejpam-3483	311	14	/	/	PUNCT
ejpam-3483	311	15	eur	eur	PROPN
ejpam-3483	311	16	.	.	PUNCT
ejpam-3483	312	1	j.	j.	PROPN
ejpam-3483	312	2	pure	pure	PROPN
ejpam-3483	312	3	appl	appl	PROPN
ejpam-3483	312	4	.	.	PROPN
ejpam-3483	312	5	math	math	PROPN
ejpam-3483	312	6	,	,	PUNCT
ejpam-3483	312	7	12	12	NUM
ejpam-3483	312	8	(	(	PUNCT
ejpam-3483	312	9	3	3	NUM
ejpam-3483	312	10	)	)	PUNCT
ejpam-3483	312	11	(	(	PUNCT
ejpam-3483	312	12	2019	2019	NUM
ejpam-3483	312	13	)	)	PUNCT
ejpam-3483	312	14	,	,	PUNCT
ejpam-3483	312	15	1231	1231	NUM
ejpam-3483	312	16	-	-	SYM
ejpam-3483	312	17	1247	1247	NUM
ejpam-3483	312	18	1241	1241	NUM
ejpam-3483	312	19	(	(	PUNCT
ejpam-3483	312	20	i	i	NOUN
ejpam-3483	312	21	)	)	PUNCT
ejpam-3483	312	22	f	f	PROPN
ejpam-3483	312	23	is	be	AUX
ejpam-3483	312	24	i	i	PROPN
ejpam-3483	312	25	-	-	PUNCT
ejpam-3483	312	26	supra	supra	PROPN
ejpam-3483	312	27	b	b	NOUN
ejpam-3483	312	28	-	-	PUNCT
ejpam-3483	312	29	open	open	ADJ
ejpam-3483	312	30	if	if	SCONJ
ejpam-3483	313	1	and	and	CCONJ
ejpam-3483	313	2	only	only	ADV
ejpam-3483	313	3	if	if	SCONJ
ejpam-3483	313	4	it	it	PRON
ejpam-3483	313	5	is	be	AUX
ejpam-3483	313	6	d	d	ADJ
ejpam-3483	313	7	-	-	PUNCT
ejpam-3483	313	8	supra	supra	ADJ
ejpam-3483	313	9	b	b	NOUN
ejpam-3483	313	10	-	-	PUNCT
ejpam-3483	313	11	closed	closed	ADJ
ejpam-3483	313	12	.	.	PUNCT
ejpam-3483	314	1	(	(	PUNCT
ejpam-3483	314	2	ii	ii	X
ejpam-3483	314	3	)	)	PUNCT
ejpam-3483	314	4	f	f	PROPN
ejpam-3483	314	5	is	be	AUX
ejpam-3483	314	6	d	d	ADJ
ejpam-3483	314	7	-	-	PUNCT
ejpam-3483	314	8	supra	supra	ADJ
ejpam-3483	314	9	b	b	NOUN
ejpam-3483	314	10	-	-	PUNCT
ejpam-3483	314	11	open	open	ADJ
ejpam-3483	314	12	if	if	SCONJ
ejpam-3483	314	13	and	and	CCONJ
ejpam-3483	314	14	only	only	ADV
ejpam-3483	314	15	if	if	SCONJ
ejpam-3483	314	16	it	it	PRON
ejpam-3483	314	17	is	be	AUX
ejpam-3483	314	18	i	i	PROPN
ejpam-3483	314	19	-	-	PUNCT
ejpam-3483	314	20	supra	supra	PROPN
ejpam-3483	314	21	b	b	PROPN
ejpam-3483	314	22	-	-	PUNCT
ejpam-3483	314	23	closed	closed	ADJ
ejpam-3483	314	24	.	.	PUNCT
ejpam-3483	315	1	(	(	PUNCT
ejpam-3483	315	2	iii	iii	X
ejpam-3483	315	3	)	)	PUNCT
ejpam-3483	315	4	f	f	PROPN
ejpam-3483	315	5	is	be	AUX
ejpam-3483	315	6	b	b	NOUN
ejpam-3483	315	7	-	-	PUNCT
ejpam-3483	315	8	supra	supra	ADJ
ejpam-3483	315	9	b	b	NOUN
ejpam-3483	315	10	-	-	PUNCT
ejpam-3483	315	11	open	open	ADJ
ejpam-3483	315	12	if	if	SCONJ
ejpam-3483	315	13	and	and	CCONJ
ejpam-3483	315	14	only	only	ADV
ejpam-3483	315	15	if	if	SCONJ
ejpam-3483	315	16	it	it	PRON
ejpam-3483	315	17	is	be	AUX
ejpam-3483	315	18	b	b	NOUN
ejpam-3483	315	19	-	-	PUNCT
ejpam-3483	315	20	supra	supra	ADJ
ejpam-3483	315	21	b	b	NOUN
ejpam-3483	315	22	-	-	PUNCT
ejpam-3483	315	23	closed	closed	ADJ
ejpam-3483	315	24	.	.	PUNCT
ejpam-3483	316	1	proof	proof	NOUN
ejpam-3483	316	2	.	.	PUNCT
ejpam-3483	317	1	(	(	PUNCT
ejpam-3483	317	2	i	i	NOUN
ejpam-3483	317	3	)	)	PUNCT
ejpam-3483	317	4	necessity	necessity	NOUN
ejpam-3483	317	5	:	:	PUNCT
ejpam-3483	317	6	let	let	VERB
ejpam-3483	317	7	f	f	PRON
ejpam-3483	317	8	be	be	AUX
ejpam-3483	317	9	an	an	DET
ejpam-3483	317	10	i	i	PROPN
ejpam-3483	317	11	-	-	PUNCT
ejpam-3483	317	12	supra	supra	PROPN
ejpam-3483	317	13	b	b	NOUN
ejpam-3483	317	14	-	-	PUNCT
ejpam-3483	317	15	open	open	ADJ
ejpam-3483	317	16	map	map	NOUN
ejpam-3483	317	17	and	and	CCONJ
ejpam-3483	317	18	let	let	VERB
ejpam-3483	317	19	g	g	PRON
ejpam-3483	317	20	be	be	AUX
ejpam-3483	317	21	a	a	DET
ejpam-3483	317	22	closed	closed	ADJ
ejpam-3483	317	23	subset	subset	NOUN
ejpam-3483	317	24	of	of	ADP
ejpam-3483	317	25	x.	x.	PROPN
ejpam-3483	317	26	then	then	ADV
ejpam-3483	317	27	gc	gc	PROPN
ejpam-3483	317	28	is	be	AUX
ejpam-3483	317	29	open	open	ADJ
ejpam-3483	317	30	.	.	PUNCT
ejpam-3483	318	1	since	since	SCONJ
ejpam-3483	318	2	f	f	PROPN
ejpam-3483	318	3	is	be	AUX
ejpam-3483	318	4	bijective	bijective	ADJ
ejpam-3483	318	5	,	,	PUNCT
ejpam-3483	318	6	then	then	ADV
ejpam-3483	318	7	f(gc	f(gc	NUM
ejpam-3483	318	8	)	)	PUNCT
ejpam-3483	319	1	=	=	SYM
ejpam-3483	319	2	(	(	PUNCT
ejpam-3483	319	3	f(g))c	f(g))c	PROPN
ejpam-3483	319	4	is	be	AUX
ejpam-3483	319	5	i	i	PROPN
ejpam-3483	319	6	-	-	PUNCT
ejpam-3483	319	7	supra	supra	PROPN
ejpam-3483	319	8	b	b	NOUN
ejpam-3483	319	9	-	-	PUNCT
ejpam-3483	319	10	open	open	ADJ
ejpam-3483	319	11	.	.	PUNCT
ejpam-3483	320	1	therefore	therefore	ADV
ejpam-3483	320	2	f(g	f(g	PROPN
ejpam-3483	320	3	)	)	PUNCT
ejpam-3483	320	4	is	be	AUX
ejpam-3483	320	5	a	a	DET
ejpam-3483	320	6	d	d	ADJ
ejpam-3483	320	7	-	-	PUNCT
ejpam-3483	320	8	supra	supra	ADJ
ejpam-3483	320	9	b	b	NOUN
ejpam-3483	320	10	-	-	PUNCT
ejpam-3483	320	11	closed	closed	ADJ
ejpam-3483	320	12	subset	subset	NOUN
ejpam-3483	320	13	of	of	ADP
ejpam-3483	320	14	y	y	PROPN
ejpam-3483	320	15	.	.	PUNCT
ejpam-3483	321	1	thus	thus	ADV
ejpam-3483	321	2	f	f	PROPN
ejpam-3483	321	3	is	be	AUX
ejpam-3483	321	4	d	d	ADJ
ejpam-3483	321	5	-	-	PUNCT
ejpam-3483	321	6	supra	supra	ADJ
ejpam-3483	321	7	b	b	NOUN
ejpam-3483	321	8	-	-	PUNCT
ejpam-3483	321	9	closed	closed	ADJ
ejpam-3483	321	10	.	.	PUNCT
ejpam-3483	322	1	sufficiency	sufficiency	NOUN
ejpam-3483	322	2	:	:	PUNCT
ejpam-3483	322	3	let	let	VERB
ejpam-3483	322	4	f	f	PRON
ejpam-3483	322	5	be	be	AUX
ejpam-3483	322	6	a	a	DET
ejpam-3483	322	7	d	d	ADJ
ejpam-3483	322	8	-	-	PUNCT
ejpam-3483	322	9	supra	supra	ADJ
ejpam-3483	322	10	b	b	NOUN
ejpam-3483	322	11	-	-	PUNCT
ejpam-3483	322	12	closed	closed	ADJ
ejpam-3483	322	13	map	map	NOUN
ejpam-3483	322	14	and	and	CCONJ
ejpam-3483	322	15	let	let	VERB
ejpam-3483	322	16	b	b	X
ejpam-3483	322	17	be	be	AUX
ejpam-3483	322	18	an	an	DET
ejpam-3483	322	19	open	open	ADJ
ejpam-3483	322	20	subset	subset	NOUN
ejpam-3483	322	21	of	of	ADP
ejpam-3483	322	22	x.	x.	PROPN
ejpam-3483	322	23	then	then	ADV
ejpam-3483	322	24	bc	bc	PROPN
ejpam-3483	322	25	is	be	AUX
ejpam-3483	322	26	closed	closed	ADJ
ejpam-3483	322	27	.	.	PUNCT
ejpam-3483	323	1	since	since	SCONJ
ejpam-3483	323	2	f	f	PROPN
ejpam-3483	323	3	is	be	AUX
ejpam-3483	323	4	bijective	bijective	ADJ
ejpam-3483	323	5	,	,	PUNCT
ejpam-3483	323	6	then	then	ADV
ejpam-3483	323	7	f(bc	f(bc	NUM
ejpam-3483	323	8	)	)	PUNCT
ejpam-3483	324	1	=	=	NOUN
ejpam-3483	325	1	(	(	PUNCT
ejpam-3483	325	2	f(b))c	f(b))c	PROPN
ejpam-3483	325	3	is	be	AUX
ejpam-3483	325	4	d	d	NOUN
ejpam-3483	325	5	-	-	ADJ
ejpam-3483	325	6	supra	supra	ADJ
ejpam-3483	325	7	b	b	NOUN
ejpam-3483	325	8	-	-	PUNCT
ejpam-3483	325	9	closed	closed	ADJ
ejpam-3483	325	10	.	.	PUNCT
ejpam-3483	326	1	therefore	therefore	ADV
ejpam-3483	326	2	f(b	f(b	PROPN
ejpam-3483	326	3	)	)	PUNCT
ejpam-3483	326	4	is	be	AUX
ejpam-3483	326	5	i	i	PROPN
ejpam-3483	326	6	-	-	PUNCT
ejpam-3483	326	7	supra	supra	PROPN
ejpam-3483	326	8	b	b	NOUN
ejpam-3483	326	9	-	-	PUNCT
ejpam-3483	326	10	open	open	ADJ
ejpam-3483	326	11	.	.	PUNCT
ejpam-3483	327	1	thus	thus	ADV
ejpam-3483	327	2	f	f	PROPN
ejpam-3483	327	3	is	be	AUX
ejpam-3483	327	4	i	i	PROPN
ejpam-3483	327	5	-	-	PUNCT
ejpam-3483	327	6	supra	supra	PROPN
ejpam-3483	327	7	b	b	PROPN
ejpam-3483	327	8	-	-	PUNCT
ejpam-3483	327	9	closed	closed	ADJ
ejpam-3483	327	10	.	.	PUNCT
ejpam-3483	328	1	the	the	DET
ejpam-3483	328	2	proofs	proof	NOUN
ejpam-3483	328	3	of	of	ADP
ejpam-3483	328	4	(	(	PUNCT
ejpam-3483	328	5	ii	ii	NOUN
ejpam-3483	328	6	)	)	PUNCT
ejpam-3483	328	7	and	and	CCONJ
ejpam-3483	328	8	(	(	PUNCT
ejpam-3483	328	9	iii	iii	X
ejpam-3483	328	10	)	)	PUNCT
ejpam-3483	328	11	are	be	AUX
ejpam-3483	328	12	similar	similar	ADJ
ejpam-3483	328	13	to	to	ADP
ejpam-3483	328	14	that	that	PRON
ejpam-3483	328	15	of	of	ADP
ejpam-3483	328	16	(	(	PUNCT
ejpam-3483	328	17	i	i	NOUN
ejpam-3483	328	18	)	)	PUNCT
ejpam-3483	328	19	.	.	PUNCT
ejpam-3483	329	1	theorem	theorem	VERB
ejpam-3483	329	2	16	16	NUM
ejpam-3483	329	3	.	.	PUNCT
ejpam-3483	330	1	the	the	DET
ejpam-3483	330	2	following	follow	VERB
ejpam-3483	330	3	two	two	NUM
ejpam-3483	330	4	statements	statement	NOUN
ejpam-3483	330	5	hold	hold	VERB
ejpam-3483	330	6	.	.	PUNCT
ejpam-3483	331	1	(	(	PUNCT
ejpam-3483	331	2	i	i	NOUN
ejpam-3483	331	3	)	)	PUNCT
ejpam-3483	331	4	if	if	SCONJ
ejpam-3483	331	5	the	the	DET
ejpam-3483	331	6	maps	map	NOUN
ejpam-3483	331	7	f	f	X
ejpam-3483	331	8	:	:	PUNCT
ejpam-3483	331	9	(	(	PUNCT
ejpam-3483	331	10	x	x	X
ejpam-3483	331	11	,	,	PUNCT
ejpam-3483	331	12	τ	τ	X
ejpam-3483	331	13	)	)	PUNCT
ejpam-3483	331	14	→	→	SYM
ejpam-3483	331	15	(	(	PUNCT
ejpam-3483	331	16	y	y	PROPN
ejpam-3483	331	17	,	,	PUNCT
ejpam-3483	331	18	θ	θ	PROPN
ejpam-3483	331	19	)	)	PUNCT
ejpam-3483	331	20	is	be	AUX
ejpam-3483	331	21	open	open	ADJ
ejpam-3483	331	22	and	and	CCONJ
ejpam-3483	331	23	g	g	NOUN
ejpam-3483	331	24	:	:	PUNCT
ejpam-3483	331	25	(	(	PUNCT
ejpam-3483	331	26	y	y	PROPN
ejpam-3483	331	27	,	,	PUNCT
ejpam-3483	331	28	θ	θ	NOUN
ejpam-3483	331	29	)	)	PUNCT
ejpam-3483	331	30	→	→	SYM
ejpam-3483	331	31	(	(	PUNCT
ejpam-3483	331	32	z	z	NOUN
ejpam-3483	331	33	,	,	PUNCT
ejpam-3483	331	34	ν	ν	PROPN
ejpam-3483	331	35	,	,	PUNCT
ejpam-3483	331	36	�	�	PROPN
ejpam-3483	331	37	)	)	PUNCT
ejpam-3483	331	38	is	be	AUX
ejpam-3483	331	39	i	i	PROPN
ejpam-3483	331	40	-	-	PUNCT
ejpam-3483	331	41	supra	supra	PROPN
ejpam-3483	331	42	(	(	PUNCT
ejpam-3483	331	43	resp	resp	NOUN
ejpam-3483	331	44	.	.	PUNCT
ejpam-3483	332	1	d	d	X
ejpam-3483	332	2	-	-	PUNCT
ejpam-3483	332	3	supra	supra	ADJ
ejpam-3483	332	4	,	,	PUNCT
ejpam-3483	332	5	b	b	NOUN
ejpam-3483	332	6	-	-	PUNCT
ejpam-3483	332	7	supra	supra	ADJ
ejpam-3483	332	8	)	)	PUNCT
ejpam-3483	332	9	b	b	X
ejpam-3483	332	10	-	-	PUNCT
ejpam-3483	332	11	open	open	ADJ
ejpam-3483	332	12	,	,	PUNCT
ejpam-3483	332	13	then	then	ADV
ejpam-3483	332	14	a	a	DET
ejpam-3483	332	15	map	map	NOUN
ejpam-3483	332	16	g	g	PROPN
ejpam-3483	332	17	◦	◦	NOUN
ejpam-3483	332	18	f	f	PROPN
ejpam-3483	332	19	is	be	AUX
ejpam-3483	332	20	i	i	PROPN
ejpam-3483	332	21	-	-	PUNCT
ejpam-3483	332	22	supra	supra	PROPN
ejpam-3483	332	23	(	(	PUNCT
ejpam-3483	332	24	resp	resp	NOUN
ejpam-3483	332	25	.	.	PUNCT
ejpam-3483	333	1	d	d	X
ejpam-3483	333	2	-	-	PUNCT
ejpam-3483	333	3	supra	supra	ADJ
ejpam-3483	333	4	,	,	PUNCT
ejpam-3483	333	5	b	b	NOUN
ejpam-3483	333	6	-	-	PUNCT
ejpam-3483	333	7	supra	supra	ADJ
ejpam-3483	333	8	)	)	PUNCT
ejpam-3483	333	9	b	b	X
ejpam-3483	333	10	-	-	PUNCT
ejpam-3483	333	11	open	open	ADJ
ejpam-3483	333	12	.	.	PUNCT
ejpam-3483	334	1	(	(	PUNCT
ejpam-3483	334	2	ii	ii	NOUN
ejpam-3483	334	3	)	)	PUNCT
ejpam-3483	334	4	if	if	SCONJ
ejpam-3483	334	5	the	the	DET
ejpam-3483	334	6	maps	map	NOUN
ejpam-3483	334	7	f	f	X
ejpam-3483	334	8	:	:	PUNCT
ejpam-3483	334	9	(	(	PUNCT
ejpam-3483	334	10	x	x	X
ejpam-3483	334	11	,	,	PUNCT
ejpam-3483	334	12	τ	τ	X
ejpam-3483	334	13	)	)	PUNCT
ejpam-3483	334	14	→	→	SYM
ejpam-3483	334	15	(	(	PUNCT
ejpam-3483	334	16	y	y	PROPN
ejpam-3483	334	17	,	,	PUNCT
ejpam-3483	334	18	θ	θ	PROPN
ejpam-3483	334	19	)	)	PUNCT
ejpam-3483	334	20	is	be	AUX
ejpam-3483	334	21	closed	closed	ADJ
ejpam-3483	334	22	and	and	CCONJ
ejpam-3483	334	23	g	g	NOUN
ejpam-3483	334	24	:	:	PUNCT
ejpam-3483	334	25	(	(	PUNCT
ejpam-3483	334	26	y	y	PROPN
ejpam-3483	334	27	,	,	PUNCT
ejpam-3483	334	28	θ	θ	NOUN
ejpam-3483	334	29	)	)	PUNCT
ejpam-3483	334	30	→	→	SYM
ejpam-3483	334	31	(	(	PUNCT
ejpam-3483	334	32	z	z	NOUN
ejpam-3483	334	33	,	,	PUNCT
ejpam-3483	334	34	ν	ν	PROPN
ejpam-3483	334	35	,	,	PUNCT
ejpam-3483	334	36	�	�	PROPN
ejpam-3483	334	37	)	)	PUNCT
ejpam-3483	334	38	is	be	AUX
ejpam-3483	334	39	i	i	PROPN
ejpam-3483	334	40	-	-	PUNCT
ejpam-3483	334	41	supra	supra	PROPN
ejpam-3483	334	42	(	(	PUNCT
ejpam-3483	334	43	resp	resp	NOUN
ejpam-3483	334	44	.	.	PUNCT
ejpam-3483	335	1	d	d	X
ejpam-3483	335	2	-	-	PUNCT
ejpam-3483	335	3	supra	supra	ADJ
ejpam-3483	335	4	,	,	PUNCT
ejpam-3483	335	5	b	b	NOUN
ejpam-3483	335	6	-	-	PUNCT
ejpam-3483	335	7	supra	supra	ADJ
ejpam-3483	335	8	)	)	PUNCT
ejpam-3483	335	9	b	b	NOUN
ejpam-3483	335	10	-	-	PUNCT
ejpam-3483	335	11	closed	closed	ADJ
ejpam-3483	335	12	,	,	PUNCT
ejpam-3483	335	13	then	then	ADV
ejpam-3483	335	14	a	a	DET
ejpam-3483	335	15	map	map	NOUN
ejpam-3483	335	16	g	g	PROPN
ejpam-3483	335	17	◦	◦	NOUN
ejpam-3483	335	18	f	f	PROPN
ejpam-3483	335	19	is	be	AUX
ejpam-3483	335	20	i	i	PROPN
ejpam-3483	335	21	-	-	PUNCT
ejpam-3483	335	22	supra	supra	PROPN
ejpam-3483	335	23	(	(	PUNCT
ejpam-3483	335	24	resp	resp	NOUN
ejpam-3483	335	25	.	.	PUNCT
ejpam-3483	336	1	d	d	X
ejpam-3483	336	2	-	-	PUNCT
ejpam-3483	336	3	supra	supra	ADJ
ejpam-3483	336	4	,	,	PUNCT
ejpam-3483	336	5	b	b	NOUN
ejpam-3483	336	6	-	-	PUNCT
ejpam-3483	336	7	supra	supra	ADJ
ejpam-3483	336	8	)	)	PUNCT
ejpam-3483	336	9	b	b	NOUN
ejpam-3483	336	10	-	-	PUNCT
ejpam-3483	336	11	closed	closed	ADJ
ejpam-3483	336	12	.	.	PUNCT
ejpam-3483	337	1	proof	proof	NOUN
ejpam-3483	337	2	.	.	PUNCT
ejpam-3483	338	1	the	the	DET
ejpam-3483	338	2	proof	proof	NOUN
ejpam-3483	338	3	is	be	AUX
ejpam-3483	338	4	straightforward	straightforward	ADJ
ejpam-3483	338	5	.	.	PUNCT
ejpam-3483	339	1	theorem	theorem	NOUN
ejpam-3483	339	2	17	17	NUM
ejpam-3483	339	3	.	.	PUNCT
ejpam-3483	340	1	if	if	SCONJ
ejpam-3483	340	2	the	the	DET
ejpam-3483	340	3	maps	map	NOUN
ejpam-3483	340	4	g	g	PROPN
ejpam-3483	340	5	◦	◦	NOUN
ejpam-3483	340	6	f	f	PROPN
ejpam-3483	340	7	is	be	AUX
ejpam-3483	340	8	i	i	PROPN
ejpam-3483	340	9	-	-	PUNCT
ejpam-3483	340	10	supra	supra	PROPN
ejpam-3483	340	11	(	(	PUNCT
ejpam-3483	340	12	resp	resp	NOUN
ejpam-3483	340	13	.	.	PUNCT
ejpam-3483	341	1	d	d	X
ejpam-3483	341	2	-	-	PUNCT
ejpam-3483	341	3	supra	supra	ADJ
ejpam-3483	341	4	,	,	PUNCT
ejpam-3483	341	5	b	b	NOUN
ejpam-3483	341	6	-	-	PUNCT
ejpam-3483	341	7	supra	supra	ADJ
ejpam-3483	341	8	)	)	PUNCT
ejpam-3483	341	9	b	b	X
ejpam-3483	341	10	-	-	PUNCT
ejpam-3483	341	11	open	open	ADJ
ejpam-3483	341	12	and	and	CCONJ
ejpam-3483	341	13	f	f	X
ejpam-3483	341	14	:	:	PUNCT
ejpam-3483	341	15	(	(	PUNCT
ejpam-3483	341	16	x	x	X
ejpam-3483	341	17	,	,	PUNCT
ejpam-3483	341	18	τ	τ	X
ejpam-3483	341	19	)	)	PUNCT
ejpam-3483	341	20	→	→	SYM
ejpam-3483	341	21	(	(	PUNCT
ejpam-3483	341	22	y	y	PROPN
ejpam-3483	341	23	,	,	PUNCT
ejpam-3483	341	24	θ	θ	PROPN
ejpam-3483	341	25	)	)	PUNCT
ejpam-3483	341	26	is	be	AUX
ejpam-3483	341	27	surjective	surjective	ADJ
ejpam-3483	341	28	and	and	CCONJ
ejpam-3483	341	29	continuous	continuous	ADJ
ejpam-3483	341	30	,	,	PUNCT
ejpam-3483	341	31	then	then	ADV
ejpam-3483	341	32	a	a	DET
ejpam-3483	341	33	map	map	NOUN
ejpam-3483	341	34	g	g	NOUN
ejpam-3483	341	35	:	:	PUNCT
ejpam-3483	341	36	(	(	PUNCT
ejpam-3483	341	37	y	y	PROPN
ejpam-3483	341	38	,	,	PUNCT
ejpam-3483	341	39	θ	θ	NOUN
ejpam-3483	341	40	)	)	PUNCT
ejpam-3483	341	41	→	→	SYM
ejpam-3483	341	42	(	(	PUNCT
ejpam-3483	341	43	z	z	NOUN
ejpam-3483	341	44	,	,	PUNCT
ejpam-3483	341	45	ν	ν	PROPN
ejpam-3483	341	46	,	,	PUNCT
ejpam-3483	341	47	�	�	PROPN
ejpam-3483	341	48	)	)	PUNCT
ejpam-3483	341	49	is	be	AUX
ejpam-3483	341	50	i	i	PROPN
ejpam-3483	341	51	-	-	PUNCT
ejpam-3483	341	52	supra	supra	PROPN
ejpam-3483	341	53	(	(	PUNCT
ejpam-3483	341	54	resp	resp	NOUN
ejpam-3483	341	55	.	.	PUNCT
ejpam-3483	342	1	d	d	X
ejpam-3483	342	2	-	-	PUNCT
ejpam-3483	342	3	supra	supra	ADJ
ejpam-3483	342	4	,	,	PUNCT
ejpam-3483	342	5	b	b	NOUN
ejpam-3483	342	6	-	-	PUNCT
ejpam-3483	342	7	supra	supra	ADJ
ejpam-3483	342	8	)	)	PUNCT
ejpam-3483	342	9	b	b	X
ejpam-3483	342	10	-	-	PUNCT
ejpam-3483	342	11	open	open	ADJ
ejpam-3483	342	12	.	.	PUNCT
ejpam-3483	343	1	proof	proof	NOUN
ejpam-3483	343	2	.	.	PUNCT
ejpam-3483	344	1	consider	consider	VERB
ejpam-3483	344	2	f	f	PROPN
ejpam-3483	344	3	is	be	AUX
ejpam-3483	344	4	a	a	DET
ejpam-3483	344	5	continuous	continuous	ADJ
ejpam-3483	344	6	map	map	NOUN
ejpam-3483	344	7	and	and	CCONJ
ejpam-3483	344	8	let	let	VERB
ejpam-3483	344	9	g	g	PRON
ejpam-3483	344	10	be	be	AUX
ejpam-3483	344	11	an	an	DET
ejpam-3483	344	12	open	open	ADJ
ejpam-3483	344	13	subset	subset	NOUN
ejpam-3483	344	14	of	of	ADP
ejpam-3483	344	15	y	y	PROPN
ejpam-3483	344	16	.	.	PUNCT
ejpam-3483	345	1	then	then	ADV
ejpam-3483	345	2	f−1(g	f−1(g	PROPN
ejpam-3483	345	3	)	)	PUNCT
ejpam-3483	345	4	is	be	AUX
ejpam-3483	345	5	an	an	DET
ejpam-3483	345	6	open	open	ADJ
ejpam-3483	345	7	subset	subset	NOUN
ejpam-3483	345	8	of	of	ADP
ejpam-3483	345	9	x.	x.	NOUN
ejpam-3483	345	10	since	since	SCONJ
ejpam-3483	345	11	g	g	PROPN
ejpam-3483	345	12	◦	◦	PROPN
ejpam-3483	345	13	f	f	PROPN
ejpam-3483	345	14	is	be	AUX
ejpam-3483	345	15	i	i	PROPN
ejpam-3483	345	16	-	-	PUNCT
ejpam-3483	345	17	supra	supra	PROPN
ejpam-3483	345	18	b	b	NOUN
ejpam-3483	345	19	-	-	PUNCT
ejpam-3483	345	20	open	open	ADJ
ejpam-3483	345	21	(	(	PUNCT
ejpam-3483	345	22	resp	resp	NOUN
ejpam-3483	345	23	.	.	PUNCT
ejpam-3483	346	1	d	d	X
ejpam-3483	346	2	-	-	PUNCT
ejpam-3483	346	3	supra	supra	ADJ
ejpam-3483	346	4	,	,	PUNCT
ejpam-3483	346	5	b	b	NOUN
ejpam-3483	346	6	-	-	PUNCT
ejpam-3483	346	7	supra	supra	NOUN
ejpam-3483	346	8	)	)	PUNCT
ejpam-3483	346	9	and	and	CCONJ
ejpam-3483	346	10	f	f	PROPN
ejpam-3483	346	11	is	be	AUX
ejpam-3483	346	12	surjective	surjective	ADJ
ejpam-3483	346	13	,	,	PUNCT
ejpam-3483	346	14	then	then	ADV
ejpam-3483	346	15	(	(	PUNCT
ejpam-3483	346	16	g	g	PROPN
ejpam-3483	346	17	◦	◦	NOUN
ejpam-3483	346	18	f)(f−1(g	f)(f−1(g	PROPN
ejpam-3483	346	19	)	)	PUNCT
ejpam-3483	346	20	)	)	PUNCT
ejpam-3483	347	1	=	=	SYM
ejpam-3483	347	2	g(g	g(g	PROPN
ejpam-3483	347	3	)	)	PUNCT
ejpam-3483	347	4	is	be	AUX
ejpam-3483	347	5	an	an	DET
ejpam-3483	347	6	i	i	PROPN
ejpam-3483	347	7	-	-	PUNCT
ejpam-3483	347	8	supra	supra	PROPN
ejpam-3483	347	9	b	b	NOUN
ejpam-3483	347	10	-	-	PUNCT
ejpam-3483	347	11	open	open	ADJ
ejpam-3483	347	12	(	(	PUNCT
ejpam-3483	347	13	resp	resp	NOUN
ejpam-3483	347	14	.	.	PUNCT
ejpam-3483	348	1	a	a	DET
ejpam-3483	348	2	d	d	NOUN
ejpam-3483	348	3	-	-	PUNCT
ejpam-3483	348	4	supra	supra	ADJ
ejpam-3483	348	5	,	,	PUNCT
ejpam-3483	348	6	a	a	DET
ejpam-3483	348	7	b	b	NOUN
ejpam-3483	348	8	-	-	PUNCT
ejpam-3483	348	9	supra	supra	ADJ
ejpam-3483	348	10	)	)	PUNCT
ejpam-3483	348	11	subset	subset	NOUN
ejpam-3483	348	12	of	of	ADP
ejpam-3483	348	13	z.	z.	PROPN
ejpam-3483	348	14	hence	hence	ADV
ejpam-3483	348	15	g	g	PROPN
ejpam-3483	348	16	is	be	AUX
ejpam-3483	348	17	i	i	PROPN
ejpam-3483	348	18	-	-	PUNCT
ejpam-3483	348	19	supra	supra	PROPN
ejpam-3483	348	20	b	b	NOUN
ejpam-3483	348	21	-	-	PUNCT
ejpam-3483	348	22	open	open	ADJ
ejpam-3483	348	23	(	(	PUNCT
ejpam-3483	348	24	resp	resp	NOUN
ejpam-3483	348	25	.	.	PUNCT
ejpam-3483	349	1	d	d	X
ejpam-3483	349	2	-	-	PUNCT
ejpam-3483	349	3	supra	supra	ADJ
ejpam-3483	349	4	,	,	PUNCT
ejpam-3483	349	5	b	b	NOUN
ejpam-3483	349	6	-	-	PUNCT
ejpam-3483	349	7	supra	supra	NOUN
ejpam-3483	349	8	)	)	PUNCT
ejpam-3483	349	9	.	.	PUNCT
ejpam-3483	350	1	proposition	proposition	NOUN
ejpam-3483	350	2	1	1	NUM
ejpam-3483	350	3	.	.	PUNCT
ejpam-3483	351	1	if	if	SCONJ
ejpam-3483	351	2	the	the	DET
ejpam-3483	351	3	maps	map	NOUN
ejpam-3483	351	4	g	g	PROPN
ejpam-3483	351	5	◦	◦	NOUN
ejpam-3483	351	6	f	f	X
ejpam-3483	351	7	:	:	PUNCT
ejpam-3483	351	8	(	(	PUNCT
ejpam-3483	351	9	x	x	X
ejpam-3483	351	10	,	,	PUNCT
ejpam-3483	351	11	τ,	τ,	NOUN
ejpam-3483	351	12	�	�	X
ejpam-3483	351	13	1	1	NUM
ejpam-3483	351	14	)	)	PUNCT
ejpam-3483	351	15	→	→	SYM
ejpam-3483	351	16	(	(	PUNCT
ejpam-3483	351	17	z	z	NOUN
ejpam-3483	351	18	,	,	PUNCT
ejpam-3483	351	19	µ,	µ,	X
ejpam-3483	351	20	�	�	PROPN
ejpam-3483	351	21	3	3	NUM
ejpam-3483	351	22	)	)	PUNCT
ejpam-3483	351	23	is	be	AUX
ejpam-3483	351	24	closed	close	VERB
ejpam-3483	351	25	and	and	CCONJ
ejpam-3483	351	26	g	g	NOUN
ejpam-3483	351	27	:	:	PUNCT
ejpam-3483	351	28	(	(	PUNCT
ejpam-3483	351	29	y	y	NOUN
ejpam-3483	351	30	,	,	PUNCT
ejpam-3483	351	31	θ,	θ,	NOUN
ejpam-3483	351	32	�	�	X
ejpam-3483	351	33	2	2	NUM
ejpam-3483	351	34	)	)	PUNCT
ejpam-3483	351	35	→	→	SYM
ejpam-3483	351	36	(	(	PUNCT
ejpam-3483	351	37	z	z	NOUN
ejpam-3483	351	38	,	,	PUNCT
ejpam-3483	351	39	µ,	µ,	X
ejpam-3483	351	40	�	�	PROPN
ejpam-3483	351	41	3	3	NUM
ejpam-3483	351	42	)	)	PUNCT
ejpam-3483	351	43	is	be	AUX
ejpam-3483	351	44	injective	injective	ADJ
ejpam-3483	351	45	and	and	CCONJ
ejpam-3483	351	46	i	i	NOUN
ejpam-3483	351	47	-	-	PUNCT
ejpam-3483	351	48	supra	supra	PROPN
ejpam-3483	351	49	(	(	PUNCT
ejpam-3483	351	50	resp	resp	NOUN
ejpam-3483	351	51	.	.	PUNCT
ejpam-3483	352	1	d	d	X
ejpam-3483	352	2	-	-	PUNCT
ejpam-3483	352	3	supra	supra	ADJ
ejpam-3483	352	4	,	,	PUNCT
ejpam-3483	352	5	b	b	NOUN
ejpam-3483	352	6	-	-	PUNCT
ejpam-3483	352	7	supra	supra	ADJ
ejpam-3483	352	8	)	)	PUNCT
ejpam-3483	353	1	b	b	X
ejpam-3483	353	2	-	-	PUNCT
ejpam-3483	353	3	continuous	continuous	ADJ
ejpam-3483	353	4	,	,	PUNCT
ejpam-3483	353	5	then	then	ADV
ejpam-3483	353	6	a	a	DET
ejpam-3483	353	7	map	map	NOUN
ejpam-3483	353	8	f	f	X
ejpam-3483	353	9	:	:	PUNCT
ejpam-3483	353	10	(	(	PUNCT
ejpam-3483	353	11	x	x	X
ejpam-3483	353	12	,	,	PUNCT
ejpam-3483	353	13	τ,	τ,	NOUN
ejpam-3483	353	14	�	�	X
ejpam-3483	353	15	1)→	1)→	NUM
ejpam-3483	353	16	(	(	PUNCT
ejpam-3483	353	17	y	y	PROPN
ejpam-3483	353	18	,	,	PUNCT
ejpam-3483	353	19	θ,	θ,	NOUN
ejpam-3483	353	20	�	�	NOUN
ejpam-3483	353	21	2	2	NUM
ejpam-3483	353	22	)	)	PUNCT
ejpam-3483	353	23	is	be	AUX
ejpam-3483	353	24	d	d	NOUN
ejpam-3483	353	25	-	-	PUNCT
ejpam-3483	353	26	supra	supra	ADJ
ejpam-3483	353	27	(	(	PUNCT
ejpam-3483	353	28	resp	resp	NOUN
ejpam-3483	353	29	.	.	PUNCT
ejpam-3483	354	1	i	i	PROPN
ejpam-3483	354	2	-	-	PUNCT
ejpam-3483	354	3	supra	supra	PROPN
ejpam-3483	354	4	,	,	PUNCT
ejpam-3483	354	5	b	b	NOUN
ejpam-3483	354	6	-	-	PUNCT
ejpam-3483	354	7	supra	supra	ADJ
ejpam-3483	354	8	)	)	PUNCT
ejpam-3483	354	9	b	b	NOUN
ejpam-3483	354	10	-	-	PUNCT
ejpam-3483	354	11	closed	closed	ADJ
ejpam-3483	354	12	.	.	PUNCT
ejpam-3483	355	1	proof	proof	NOUN
ejpam-3483	355	2	.	.	PUNCT
ejpam-3483	356	1	consider	consider	VERB
ejpam-3483	356	2	g	g	NOUN
ejpam-3483	356	3	◦	◦	NOUN
ejpam-3483	356	4	f	f	X
ejpam-3483	356	5	is	be	AUX
ejpam-3483	356	6	a	a	DET
ejpam-3483	356	7	closed	closed	ADJ
ejpam-3483	356	8	map	map	NOUN
ejpam-3483	356	9	and	and	CCONJ
ejpam-3483	356	10	let	let	VERB
ejpam-3483	356	11	g	g	PRON
ejpam-3483	356	12	be	be	AUX
ejpam-3483	356	13	a	a	DET
ejpam-3483	356	14	closed	closed	ADJ
ejpam-3483	356	15	subset	subset	NOUN
ejpam-3483	356	16	of	of	ADP
ejpam-3483	356	17	x.	x.	NOUN
ejpam-3483	356	18	then	then	ADV
ejpam-3483	356	19	(	(	PUNCT
ejpam-3483	356	20	g	g	NOUN
ejpam-3483	356	21	◦	◦	NOUN
ejpam-3483	356	22	f)(g	f)(g	NOUN
ejpam-3483	356	23	)	)	PUNCT
ejpam-3483	356	24	is	be	AUX
ejpam-3483	356	25	a	a	DET
ejpam-3483	356	26	closed	closed	ADJ
ejpam-3483	356	27	subset	subset	NOUN
ejpam-3483	356	28	of	of	ADP
ejpam-3483	356	29	z.	z.	PROPN
ejpam-3483	356	30	since	since	SCONJ
ejpam-3483	356	31	g	g	PROPN
ejpam-3483	356	32	is	be	AUX
ejpam-3483	356	33	injective	injective	ADJ
ejpam-3483	356	34	and	and	CCONJ
ejpam-3483	356	35	i	i	PROPN
ejpam-3483	356	36	-	-	PUNCT
ejpam-3483	356	37	supra	supra	PROPN
ejpam-3483	356	38	b	b	NOUN
ejpam-3483	356	39	-	-	PUNCT
ejpam-3483	356	40	continuous	continuous	ADJ
ejpam-3483	356	41	,	,	PUNCT
ejpam-3483	356	42	then	then	ADV
ejpam-3483	356	43	g−1(g	g−1(g	PROPN
ejpam-3483	356	44	◦	◦	NOUN
ejpam-3483	356	45	f	f	NOUN
ejpam-3483	356	46	)	)	PUNCT
ejpam-3483	356	47	=	=	SYM
ejpam-3483	356	48	f(g	f(g	NOUN
ejpam-3483	356	49	)	)	PUNCT
ejpam-3483	356	50	is	be	AUX
ejpam-3483	356	51	a	a	DET
ejpam-3483	356	52	d	d	ADJ
ejpam-3483	356	53	-	-	PUNCT
ejpam-3483	356	54	supra	supra	ADJ
ejpam-3483	356	55	b	b	NOUN
ejpam-3483	356	56	-	-	PUNCT
ejpam-3483	356	57	closed	closed	ADJ
ejpam-3483	356	58	subset	subset	NOUN
ejpam-3483	356	59	of	of	ADP
ejpam-3483	356	60	y	y	PROPN
ejpam-3483	356	61	.	.	PUNCT
ejpam-3483	357	1	hence	hence	ADV
ejpam-3483	357	2	f	f	PROPN
ejpam-3483	357	3	is	be	AUX
ejpam-3483	357	4	d	d	ADJ
ejpam-3483	357	5	-	-	PUNCT
ejpam-3483	357	6	supra	supra	ADJ
ejpam-3483	357	7	b	b	NOUN
ejpam-3483	357	8	-	-	PUNCT
ejpam-3483	357	9	closed	closed	ADJ
ejpam-3483	357	10	.	.	PUNCT
ejpam-3483	358	1	a	a	DET
ejpam-3483	358	2	similar	similar	ADJ
ejpam-3483	358	3	proof	proof	NOUN
ejpam-3483	358	4	can	can	AUX
ejpam-3483	358	5	be	be	AUX
ejpam-3483	358	6	given	give	VERB
ejpam-3483	358	7	for	for	ADP
ejpam-3483	358	8	the	the	DET
ejpam-3483	358	9	cases	case	NOUN
ejpam-3483	358	10	between	between	ADP
ejpam-3483	358	11	parentheses	parenthesis	NOUN
ejpam-3483	358	12	.	.	PUNCT
ejpam-3483	359	1	proposition	proposition	NOUN
ejpam-3483	359	2	2	2	NUM
ejpam-3483	359	3	.	.	PUNCT
ejpam-3483	360	1	we	we	PRON
ejpam-3483	360	2	have	have	VERB
ejpam-3483	360	3	the	the	DET
ejpam-3483	360	4	following	follow	VERB
ejpam-3483	360	5	results	result	NOUN
ejpam-3483	360	6	for	for	ADP
ejpam-3483	360	7	a	a	DET
ejpam-3483	360	8	bijective	bijective	ADJ
ejpam-3483	360	9	map	map	NOUN
ejpam-3483	361	1	f	f	X
ejpam-3483	361	2	:	:	PUNCT
ejpam-3483	361	3	(	(	PUNCT
ejpam-3483	361	4	x	x	X
ejpam-3483	361	5	,	,	PUNCT
ejpam-3483	361	6	τ,	τ,	NOUN
ejpam-3483	361	7	�	�	X
ejpam-3483	361	8	1)→	1)→	NUM
ejpam-3483	361	9	(	(	PUNCT
ejpam-3483	361	10	y	y	NOUN
ejpam-3483	361	11	,	,	PUNCT
ejpam-3483	361	12	θ,	θ,	NOUN
ejpam-3483	361	13	�	�	X
ejpam-3483	361	14	2	2	NUM
ejpam-3483	361	15	)	)	PUNCT
ejpam-3483	361	16	.	.	PUNCT
ejpam-3483	362	1	b.	b.	PROPN
ejpam-3483	362	2	a.	a.	PROPN
ejpam-3483	362	3	asaad	asaad	PROPN
ejpam-3483	362	4	,	,	PUNCT
ejpam-3483	362	5	m.	m.	PROPN
ejpam-3483	362	6	k.	k.	PROPN
ejpam-3483	362	7	tahat	tahat	PROPN
ejpam-3483	362	8	,	,	PUNCT
ejpam-3483	362	9	t.	t.	PROPN
ejpam-3483	362	10	m.	m.	PROPN
ejpam-3483	362	11	al	al	PROPN
ejpam-3483	362	12	-	-	PUNCT
ejpam-3483	362	13	shami	shami	PROPN
ejpam-3483	362	14	/	/	PUNCT
ejpam-3483	362	15	eur	eur	PROPN
ejpam-3483	362	16	.	.	PUNCT
ejpam-3483	363	1	j.	j.	PROPN
ejpam-3483	363	2	pure	pure	PROPN
ejpam-3483	363	3	appl	appl	PROPN
ejpam-3483	363	4	.	.	PROPN
ejpam-3483	363	5	math	math	PROPN
ejpam-3483	363	6	,	,	PUNCT
ejpam-3483	363	7	12	12	NUM
ejpam-3483	363	8	(	(	PUNCT
ejpam-3483	363	9	3	3	NUM
ejpam-3483	363	10	)	)	PUNCT
ejpam-3483	363	11	(	(	PUNCT
ejpam-3483	363	12	2019	2019	NUM
ejpam-3483	363	13	)	)	PUNCT
ejpam-3483	363	14	,	,	PUNCT
ejpam-3483	363	15	1231	1231	NUM
ejpam-3483	363	16	-	-	SYM
ejpam-3483	363	17	1247	1247	NUM
ejpam-3483	363	18	1242	1242	NUM
ejpam-3483	363	19	(	(	PUNCT
ejpam-3483	363	20	i	i	NOUN
ejpam-3483	363	21	)	)	PUNCT
ejpam-3483	363	22	f	f	PROPN
ejpam-3483	363	23	is	be	AUX
ejpam-3483	363	24	i	i	PROPN
ejpam-3483	363	25	-	-	PUNCT
ejpam-3483	363	26	supra	supra	PROPN
ejpam-3483	363	27	(	(	PUNCT
ejpam-3483	363	28	resp	resp	NOUN
ejpam-3483	363	29	.	.	PUNCT
ejpam-3483	364	1	d	d	X
ejpam-3483	364	2	-	-	PUNCT
ejpam-3483	364	3	supra	supra	ADJ
ejpam-3483	364	4	,	,	PUNCT
ejpam-3483	364	5	b	b	NOUN
ejpam-3483	364	6	-	-	PUNCT
ejpam-3483	364	7	supra	supra	ADJ
ejpam-3483	364	8	)	)	PUNCT
ejpam-3483	364	9	b	b	X
ejpam-3483	364	10	-	-	PUNCT
ejpam-3483	364	11	open	open	ADJ
ejpam-3483	364	12	if	if	SCONJ
ejpam-3483	364	13	and	and	CCONJ
ejpam-3483	364	14	only	only	ADV
ejpam-3483	364	15	if	if	SCONJ
ejpam-3483	364	16	f−1	f−1	PROPN
ejpam-3483	364	17	is	be	AUX
ejpam-3483	364	18	i	i	NOUN
ejpam-3483	364	19	-	-	PUNCT
ejpam-3483	364	20	supra	supra	PROPN
ejpam-3483	364	21	(	(	PUNCT
ejpam-3483	364	22	resp	resp	NOUN
ejpam-3483	364	23	.	.	PUNCT
ejpam-3483	365	1	dsupra	dsupra	ADJ
ejpam-3483	365	2	,	,	PUNCT
ejpam-3483	365	3	b	b	X
ejpam-3483	365	4	-	-	PUNCT
ejpam-3483	365	5	supra	supra	ADJ
ejpam-3483	365	6	)	)	PUNCT
ejpam-3483	365	7	b	b	NOUN
ejpam-3483	365	8	-	-	PUNCT
ejpam-3483	365	9	continuous	continuous	ADJ
ejpam-3483	365	10	.	.	PUNCT
ejpam-3483	366	1	(	(	PUNCT
ejpam-3483	366	2	ii	ii	X
ejpam-3483	366	3	)	)	PUNCT
ejpam-3483	366	4	f	f	PROPN
ejpam-3483	366	5	is	be	AUX
ejpam-3483	366	6	d	d	NOUN
ejpam-3483	366	7	-	-	PUNCT
ejpam-3483	366	8	supra	supra	ADJ
ejpam-3483	366	9	(	(	PUNCT
ejpam-3483	366	10	resp	resp	NOUN
ejpam-3483	366	11	.	.	PUNCT
ejpam-3483	367	1	i	i	PROPN
ejpam-3483	367	2	-	-	PUNCT
ejpam-3483	367	3	supra	supra	PROPN
ejpam-3483	367	4	,	,	PUNCT
ejpam-3483	367	5	b	b	NOUN
ejpam-3483	367	6	-	-	PUNCT
ejpam-3483	367	7	supra	supra	ADJ
ejpam-3483	367	8	)	)	PUNCT
ejpam-3483	367	9	b	b	X
ejpam-3483	367	10	-	-	PUNCT
ejpam-3483	367	11	closed	closed	ADJ
ejpam-3483	367	12	if	if	SCONJ
ejpam-3483	367	13	and	and	CCONJ
ejpam-3483	367	14	only	only	ADV
ejpam-3483	367	15	if	if	SCONJ
ejpam-3483	367	16	f−1	f−1	PROPN
ejpam-3483	367	17	is	be	AUX
ejpam-3483	367	18	i	i	NOUN
ejpam-3483	367	19	-	-	PUNCT
ejpam-3483	367	20	supra	supra	PROPN
ejpam-3483	367	21	(	(	PUNCT
ejpam-3483	367	22	resp	resp	NOUN
ejpam-3483	367	23	.	.	PUNCT
ejpam-3483	368	1	d	d	X
ejpam-3483	368	2	-	-	PUNCT
ejpam-3483	368	3	supra	supra	ADJ
ejpam-3483	368	4	,	,	PUNCT
ejpam-3483	368	5	b	b	NOUN
ejpam-3483	368	6	-	-	PUNCT
ejpam-3483	368	7	supra	supra	ADJ
ejpam-3483	368	8	)	)	PUNCT
ejpam-3483	368	9	b	b	NOUN
ejpam-3483	368	10	-	-	PUNCT
ejpam-3483	368	11	continuous	continuous	ADJ
ejpam-3483	368	12	.	.	PUNCT
ejpam-3483	369	1	proof	proof	NOUN
ejpam-3483	369	2	.	.	PUNCT
ejpam-3483	370	1	(	(	PUNCT
ejpam-3483	370	2	i	i	NOUN
ejpam-3483	370	3	)	)	PUNCT
ejpam-3483	370	4	we	we	PRON
ejpam-3483	370	5	prove	prove	VERB
ejpam-3483	370	6	(	(	PUNCT
ejpam-3483	370	7	i	i	NOUN
ejpam-3483	370	8	)	)	PUNCT
ejpam-3483	370	9	when	when	SCONJ
ejpam-3483	370	10	f	f	PROPN
ejpam-3483	370	11	is	be	AUX
ejpam-3483	370	12	a	a	DET
ejpam-3483	370	13	b	b	PROPN
ejpam-3483	370	14	-	-	PUNCT
ejpam-3483	370	15	supra	supra	ADJ
ejpam-3483	370	16	b	b	NOUN
ejpam-3483	370	17	-	-	PUNCT
ejpam-3483	370	18	open	open	ADJ
ejpam-3483	370	19	map	map	NOUN
ejpam-3483	370	20	,	,	PUNCT
ejpam-3483	370	21	and	and	CCONJ
ejpam-3483	370	22	the	the	DET
ejpam-3483	370	23	other	other	ADJ
ejpam-3483	370	24	cases	case	NOUN
ejpam-3483	370	25	follow	follow	VERB
ejpam-3483	370	26	similar	similar	ADJ
ejpam-3483	370	27	lines	line	NOUN
ejpam-3483	370	28	.	.	PUNCT
ejpam-3483	371	1	′	′	NUM
ejpam-3483	371	2	⇒′	⇒′	PROPN
ejpam-3483	371	3	let	let	VERB
ejpam-3483	371	4	f	f	PRON
ejpam-3483	371	5	be	be	AUX
ejpam-3483	371	6	a	a	DET
ejpam-3483	371	7	b	b	NOUN
ejpam-3483	371	8	-	-	PUNCT
ejpam-3483	371	9	supra	supra	ADJ
ejpam-3483	371	10	b	b	NOUN
ejpam-3483	371	11	-	-	PUNCT
ejpam-3483	371	12	open	open	ADJ
ejpam-3483	371	13	map	map	NOUN
ejpam-3483	371	14	and	and	CCONJ
ejpam-3483	371	15	let	let	VERB
ejpam-3483	371	16	g	g	PRON
ejpam-3483	371	17	be	be	AUX
ejpam-3483	371	18	an	an	DET
ejpam-3483	371	19	open	open	ADJ
ejpam-3483	371	20	subset	subset	NOUN
ejpam-3483	371	21	of	of	ADP
ejpam-3483	371	22	x.	x.	NOUN
ejpam-3483	371	23	then	then	ADV
ejpam-3483	371	24	(	(	PUNCT
ejpam-3483	371	25	f−1)−1(g	f−1)−1(g	PROPN
ejpam-3483	371	26	)	)	PUNCT
ejpam-3483	371	27	=	=	SYM
ejpam-3483	371	28	f(g	f(g	NOUN
ejpam-3483	371	29	)	)	PUNCT
ejpam-3483	371	30	is	be	AUX
ejpam-3483	371	31	a	a	DET
ejpam-3483	371	32	b	b	PROPN
ejpam-3483	371	33	-	-	PUNCT
ejpam-3483	371	34	supra	supra	ADJ
ejpam-3483	371	35	b	b	NOUN
ejpam-3483	371	36	-	-	PUNCT
ejpam-3483	371	37	open	open	ADJ
ejpam-3483	371	38	subset	subset	NOUN
ejpam-3483	371	39	of	of	ADP
ejpam-3483	371	40	y	y	PROPN
ejpam-3483	371	41	.	.	PUNCT
ejpam-3483	372	1	therefore	therefore	ADV
ejpam-3483	372	2	f−1	f−1	PROPN
ejpam-3483	372	3	is	be	AUX
ejpam-3483	372	4	a	a	DET
ejpam-3483	372	5	b	b	PROPN
ejpam-3483	372	6	-	-	PUNCT
ejpam-3483	372	7	supra	supra	ADJ
ejpam-3483	372	8	b	b	NOUN
ejpam-3483	372	9	-	-	PUNCT
ejpam-3483	372	10	continuous	continuous	ADJ
ejpam-3483	372	11	.	.	PUNCT
ejpam-3483	373	1	′	′	NUM
ejpam-3483	373	2	⇐	⇐	NOUN
ejpam-3483	373	3	′	′	NOUN
ejpam-3483	373	4	let	let	VERB
ejpam-3483	373	5	g	g	NOUN
ejpam-3483	373	6	be	be	AUX
ejpam-3483	373	7	an	an	DET
ejpam-3483	373	8	open	open	ADJ
ejpam-3483	373	9	subset	subset	NOUN
ejpam-3483	373	10	of	of	ADP
ejpam-3483	373	11	x	x	PUNCT
ejpam-3483	373	12	and	and	CCONJ
ejpam-3483	373	13	f−1	f−1	PROPN
ejpam-3483	373	14	be	be	AUX
ejpam-3483	373	15	a	a	DET
ejpam-3483	373	16	b	b	NOUN
ejpam-3483	373	17	-	-	PUNCT
ejpam-3483	373	18	supra	supra	ADJ
ejpam-3483	373	19	b	b	NOUN
ejpam-3483	373	20	-	-	PUNCT
ejpam-3483	373	21	continuous	continuous	ADJ
ejpam-3483	373	22	map	map	NOUN
ejpam-3483	373	23	.	.	PUNCT
ejpam-3483	374	1	then	then	ADV
ejpam-3483	374	2	f(g	f(g	NOUN
ejpam-3483	374	3	)	)	PUNCT
ejpam-3483	374	4	=	=	PUNCT
ejpam-3483	374	5	(	(	PUNCT
ejpam-3483	374	6	f−1)−1(g	f−1)−1(g	PROPN
ejpam-3483	374	7	)	)	PUNCT
ejpam-3483	374	8	is	be	AUX
ejpam-3483	374	9	a	a	DET
ejpam-3483	374	10	b	b	PROPN
ejpam-3483	374	11	-	-	PUNCT
ejpam-3483	374	12	supra	supra	ADJ
ejpam-3483	374	13	b	b	NOUN
ejpam-3483	374	14	-	-	PUNCT
ejpam-3483	374	15	open	open	ADJ
ejpam-3483	374	16	subset	subset	NOUN
ejpam-3483	374	17	of	of	ADP
ejpam-3483	374	18	y	y	PROPN
ejpam-3483	374	19	.	.	PUNCT
ejpam-3483	375	1	therefore	therefore	ADV
ejpam-3483	375	2	f	f	PROPN
ejpam-3483	375	3	is	be	AUX
ejpam-3483	375	4	b	b	NOUN
ejpam-3483	375	5	-	-	PUNCT
ejpam-3483	375	6	supra	supra	ADJ
ejpam-3483	375	7	b	b	NOUN
ejpam-3483	375	8	-	-	PUNCT
ejpam-3483	375	9	open	open	ADJ
ejpam-3483	375	10	.	.	PUNCT
ejpam-3483	376	1	(	(	PUNCT
ejpam-3483	376	2	ii	ii	NOUN
ejpam-3483	376	3	)	)	PUNCT
ejpam-3483	376	4	similarly	similarly	ADV
ejpam-3483	376	5	,	,	PUNCT
ejpam-3483	376	6	one	one	PRON
ejpam-3483	376	7	can	can	AUX
ejpam-3483	376	8	prove	prove	VERB
ejpam-3483	376	9	(	(	PUNCT
ejpam-3483	376	10	ii	ii	NOUN
ejpam-3483	376	11	)	)	PUNCT
ejpam-3483	376	12	.	.	PUNCT
ejpam-3483	377	1	theorem	theorem	NOUN
ejpam-3483	377	2	18	18	NUM
ejpam-3483	377	3	.	.	PUNCT
ejpam-3483	378	1	let	let	VERB
ejpam-3483	378	2	a	a	DET
ejpam-3483	378	3	bijective	bijective	ADJ
ejpam-3483	378	4	map	map	NOUN
ejpam-3483	378	5	f	f	X
ejpam-3483	378	6	:	:	PUNCT
ejpam-3483	378	7	(	(	PUNCT
ejpam-3483	378	8	x	x	X
ejpam-3483	378	9	,	,	PUNCT
ejpam-3483	378	10	τ,	τ,	NOUN
ejpam-3483	378	11	�	�	X
ejpam-3483	378	12	1)→	1)→	NUM
ejpam-3483	378	13	(	(	PUNCT
ejpam-3483	378	14	y	y	PROPN
ejpam-3483	378	15	,	,	PUNCT
ejpam-3483	378	16	µ,	µ,	X
ejpam-3483	378	17	�	�	PROPN
ejpam-3483	378	18	2	2	NUM
ejpam-3483	378	19	)	)	PUNCT
ejpam-3483	378	20	be	be	VERB
ejpam-3483	378	21	i	i	PROPN
ejpam-3483	378	22	-	-	PUNCT
ejpam-3483	378	23	supra	supra	PROPN
ejpam-3483	378	24	b	b	NOUN
ejpam-3483	378	25	-	-	PUNCT
ejpam-3483	378	26	open	open	ADJ
ejpam-3483	378	27	(	(	PUNCT
ejpam-3483	378	28	d	d	NOUN
ejpam-3483	378	29	-	-	ADJ
ejpam-3483	378	30	supra	supra	ADJ
ejpam-3483	378	31	b	b	NOUN
ejpam-3483	378	32	-	-	PUNCT
ejpam-3483	378	33	closed	closed	ADJ
ejpam-3483	378	34	)	)	PUNCT
ejpam-3483	378	35	and	and	CCONJ
ejpam-3483	378	36	order	order	NOUN
ejpam-3483	378	37	preserving	preserve	VERB
ejpam-3483	378	38	.	.	PUNCT
ejpam-3483	379	1	if	if	SCONJ
ejpam-3483	379	2	(	(	PUNCT
ejpam-3483	379	3	x	x	X
ejpam-3483	379	4	,	,	PUNCT
ejpam-3483	379	5	τ,	τ,	NOUN
ejpam-3483	379	6	�	�	X
ejpam-3483	379	7	1	1	NUM
ejpam-3483	379	8	)	)	PUNCT
ejpam-3483	379	9	is	be	AUX
ejpam-3483	379	10	lower	low	ADJ
ejpam-3483	379	11	t1	t1	NOUN
ejpam-3483	379	12	-	-	PUNCT
ejpam-3483	379	13	ordered	order	VERB
ejpam-3483	379	14	,	,	PUNCT
ejpam-3483	379	15	then	then	ADV
ejpam-3483	379	16	(	(	PUNCT
ejpam-3483	379	17	y	y	PROPN
ejpam-3483	379	18	,	,	PUNCT
ejpam-3483	379	19	µ,	µ,	X
ejpam-3483	379	20	�	�	PROPN
ejpam-3483	379	21	2	2	NUM
ejpam-3483	379	22	)	)	PUNCT
ejpam-3483	379	23	is	be	AUX
ejpam-3483	379	24	lower	low	ADJ
ejpam-3483	379	25	ssbt1	ssbt1	NOUN
ejpam-3483	379	26	-	-	PUNCT
ejpam-3483	379	27	ordered	order	VERB
ejpam-3483	379	28	.	.	PUNCT
ejpam-3483	380	1	proof	proof	NOUN
ejpam-3483	380	2	.	.	PUNCT
ejpam-3483	381	1	we	we	PRON
ejpam-3483	381	2	prove	prove	VERB
ejpam-3483	381	3	the	the	DET
ejpam-3483	381	4	theorem	theorem	NOUN
ejpam-3483	381	5	when	when	SCONJ
ejpam-3483	381	6	a	a	DET
ejpam-3483	381	7	map	map	NOUN
ejpam-3483	381	8	f	f	NOUN
ejpam-3483	381	9	is	be	AUX
ejpam-3483	381	10	i	i	PROPN
ejpam-3483	381	11	-	-	PUNCT
ejpam-3483	381	12	supra	supra	PROPN
ejpam-3483	381	13	b	b	NOUN
ejpam-3483	381	14	-	-	PUNCT
ejpam-3483	381	15	open	open	ADJ
ejpam-3483	381	16	.	.	PUNCT
ejpam-3483	382	1	let	let	VERB
ejpam-3483	382	2	x	x	PRON
ejpam-3483	382	3	,	,	PUNCT
ejpam-3483	382	4	y	y	PROPN
ejpam-3483	382	5	∈	∈	PROPN
ejpam-3483	382	6	y	y	PROPN
ejpam-3483	382	7	such	such	ADJ
ejpam-3483	382	8	that	that	SCONJ
ejpam-3483	382	9	x	x	SYM
ejpam-3483	382	10	�	�	PROPN
ejpam-3483	382	11	2	2	NUM
ejpam-3483	382	12	y.	y.	NOUN
ejpam-3483	382	13	since	since	SCONJ
ejpam-3483	382	14	f	f	PROPN
ejpam-3483	382	15	is	be	AUX
ejpam-3483	382	16	bijective	bijective	ADJ
ejpam-3483	382	17	,	,	PUNCT
ejpam-3483	382	18	then	then	ADV
ejpam-3483	382	19	there	there	PRON
ejpam-3483	382	20	exist	exist	VERB
ejpam-3483	382	21	a	a	DET
ejpam-3483	382	22	,	,	PUNCT
ejpam-3483	382	23	b	b	X
ejpam-3483	382	24	∈	∈	PROPN
ejpam-3483	382	25	x	x	X
ejpam-3483	382	26	such	such	ADJ
ejpam-3483	382	27	that	that	SCONJ
ejpam-3483	382	28	a	a	DET
ejpam-3483	382	29	=	=	NOUN
ejpam-3483	382	30	f−1(x	f−1(x	NOUN
ejpam-3483	382	31	)	)	PUNCT
ejpam-3483	382	32	and	and	CCONJ
ejpam-3483	382	33	b	b	X
ejpam-3483	382	34	=	=	SYM
ejpam-3483	382	35	f−1(y	f−1(y	PROPN
ejpam-3483	382	36	)	)	PUNCT
ejpam-3483	382	37	and	and	CCONJ
ejpam-3483	382	38	since	since	SCONJ
ejpam-3483	382	39	f	f	PROPN
ejpam-3483	382	40	is	be	AUX
ejpam-3483	382	41	order	order	NOUN
ejpam-3483	382	42	preserving	preserve	VERB
ejpam-3483	382	43	,	,	PUNCT
ejpam-3483	382	44	then	then	ADV
ejpam-3483	382	45	a	a	DET
ejpam-3483	382	46	�	�	PROPN
ejpam-3483	382	47	1	1	NUM
ejpam-3483	382	48	b.	b.	NOUN
ejpam-3483	382	49	by	by	ADP
ejpam-3483	382	50	hypothesis	hypothesis	NOUN
ejpam-3483	382	51	(	(	PUNCT
ejpam-3483	382	52	x	x	NOUN
ejpam-3483	382	53	,	,	PUNCT
ejpam-3483	382	54	τ,	τ,	NOUN
ejpam-3483	382	55	�	�	X
ejpam-3483	382	56	1	1	NUM
ejpam-3483	382	57	)	)	PUNCT
ejpam-3483	382	58	is	be	AUX
ejpam-3483	382	59	a	a	DET
ejpam-3483	382	60	lower	low	ADJ
ejpam-3483	382	61	t1	t1	NOUN
ejpam-3483	382	62	-	-	PUNCT
ejpam-3483	382	63	ordered	order	VERB
ejpam-3483	382	64	space	space	NOUN
ejpam-3483	382	65	,	,	PUNCT
ejpam-3483	382	66	then	then	ADV
ejpam-3483	382	67	there	there	PRON
ejpam-3483	382	68	exists	exist	VERB
ejpam-3483	382	69	an	an	DET
ejpam-3483	382	70	increasing	increase	VERB
ejpam-3483	382	71	neighborhood	neighborhood	NOUN
ejpam-3483	382	72	w	w	NOUN
ejpam-3483	382	73	of	of	ADP
ejpam-3483	382	74	a	a	PRON
ejpam-3483	382	75	in	in	ADP
ejpam-3483	382	76	x	x	PROPN
ejpam-3483	382	77	such	such	ADJ
ejpam-3483	382	78	that	that	DET
ejpam-3483	382	79	b	b	PROPN
ejpam-3483	382	80	6∈	6∈	NOUN
ejpam-3483	382	81	w	w	PROPN
ejpam-3483	382	82	.	.	PUNCT
ejpam-3483	383	1	therefore	therefore	ADV
ejpam-3483	383	2	there	there	PRON
ejpam-3483	383	3	exists	exist	VERB
ejpam-3483	383	4	an	an	DET
ejpam-3483	383	5	open	open	ADJ
ejpam-3483	383	6	set	set	NOUN
ejpam-3483	383	7	g	g	PROPN
ejpam-3483	383	8	such	such	DET
ejpam-3483	383	9	that	that	SCONJ
ejpam-3483	383	10	a	a	DET
ejpam-3483	383	11	∈	∈	NOUN
ejpam-3483	383	12	g	g	NOUN
ejpam-3483	383	13	⊆	⊆	NUM
ejpam-3483	383	14	w	w	NOUN
ejpam-3483	383	15	.	.	PUNCT
ejpam-3483	384	1	thus	thus	ADV
ejpam-3483	384	2	x	x	X
ejpam-3483	384	3	∈	∈	PROPN
ejpam-3483	384	4	f(g	f(g	NOUN
ejpam-3483	384	5	)	)	PUNCT
ejpam-3483	384	6	which	which	PRON
ejpam-3483	384	7	is	be	AUX
ejpam-3483	384	8	an	an	DET
ejpam-3483	384	9	i	i	PROPN
ejpam-3483	384	10	-	-	PUNCT
ejpam-3483	384	11	supra	supra	PROPN
ejpam-3483	384	12	b	b	NOUN
ejpam-3483	384	13	-	-	PUNCT
ejpam-3483	384	14	open	open	ADJ
ejpam-3483	384	15	subset	subset	NOUN
ejpam-3483	384	16	of	of	ADP
ejpam-3483	384	17	y	y	PROPN
ejpam-3483	384	18	.	.	PUNCT
ejpam-3483	385	1	since	since	SCONJ
ejpam-3483	385	2	f	f	PROPN
ejpam-3483	385	3	is	be	AUX
ejpam-3483	385	4	bijective	bijective	ADJ
ejpam-3483	385	5	,	,	PUNCT
ejpam-3483	385	6	then	then	ADV
ejpam-3483	385	7	y	y	PROPN
ejpam-3483	385	8	6∈	6∈	PROPN
ejpam-3483	385	9	f(g	f(g	PROPN
ejpam-3483	385	10	)	)	PUNCT
ejpam-3483	385	11	.	.	PUNCT
ejpam-3483	386	1	hence	hence	ADV
ejpam-3483	386	2	(	(	PUNCT
ejpam-3483	386	3	y	y	PROPN
ejpam-3483	386	4	,	,	PUNCT
ejpam-3483	386	5	µ,	µ,	X
ejpam-3483	386	6	�	�	PROPN
ejpam-3483	386	7	2	2	NUM
ejpam-3483	386	8	)	)	PUNCT
ejpam-3483	386	9	is	be	AUX
ejpam-3483	386	10	a	a	DET
ejpam-3483	386	11	lower	low	ADJ
ejpam-3483	386	12	ssbt1	ssbt1	NOUN
ejpam-3483	386	13	-	-	PUNCT
ejpam-3483	386	14	ordered	order	VERB
ejpam-3483	386	15	space	space	NOUN
ejpam-3483	386	16	.	.	PUNCT
ejpam-3483	387	1	theorem	theorem	VERB
ejpam-3483	387	2	4.9	4.9	NUM
ejpam-3483	387	3	says	say	VERB
ejpam-3483	387	4	that	that	SCONJ
ejpam-3483	387	5	a	a	DET
ejpam-3483	387	6	bijective	bijective	ADJ
ejpam-3483	387	7	map	map	NOUN
ejpam-3483	387	8	is	be	AUX
ejpam-3483	387	9	i	i	PROPN
ejpam-3483	387	10	-	-	PUNCT
ejpam-3483	387	11	supra	supra	PROPN
ejpam-3483	387	12	b	b	NOUN
ejpam-3483	387	13	-	-	PUNCT
ejpam-3483	387	14	open	open	ADJ
ejpam-3483	387	15	if	if	SCONJ
ejpam-3483	387	16	and	and	CCONJ
ejpam-3483	387	17	only	only	ADV
ejpam-3483	387	18	if	if	SCONJ
ejpam-3483	387	19	it	it	PRON
ejpam-3483	387	20	is	be	AUX
ejpam-3483	387	21	d	d	ADJ
ejpam-3483	387	22	-	-	PUNCT
ejpam-3483	387	23	supra	supra	ADJ
ejpam-3483	387	24	b	b	NOUN
ejpam-3483	387	25	-	-	PUNCT
ejpam-3483	387	26	closed	closed	ADJ
ejpam-3483	387	27	.	.	PUNCT
ejpam-3483	388	1	so	so	ADV
ejpam-3483	388	2	the	the	DET
ejpam-3483	388	3	result	result	NOUN
ejpam-3483	388	4	holds	hold	VERB
ejpam-3483	388	5	for	for	ADP
ejpam-3483	388	6	a	a	DET
ejpam-3483	388	7	d	d	ADJ
ejpam-3483	388	8	-	-	PUNCT
ejpam-3483	388	9	supra	supra	ADJ
ejpam-3483	388	10	b	b	NOUN
ejpam-3483	388	11	-	-	PUNCT
ejpam-3483	388	12	closed	closed	ADJ
ejpam-3483	388	13	map	map	NOUN
ejpam-3483	388	14	.	.	PUNCT
ejpam-3483	389	1	theorem	theorem	NOUN
ejpam-3483	389	2	19	19	NUM
ejpam-3483	389	3	.	.	PUNCT
ejpam-3483	390	1	let	let	VERB
ejpam-3483	390	2	a	a	DET
ejpam-3483	390	3	bijective	bijective	ADJ
ejpam-3483	390	4	map	map	NOUN
ejpam-3483	390	5	f	f	X
ejpam-3483	390	6	:	:	PUNCT
ejpam-3483	390	7	(	(	PUNCT
ejpam-3483	390	8	x	x	X
ejpam-3483	390	9	,	,	PUNCT
ejpam-3483	390	10	τ,	τ,	NOUN
ejpam-3483	390	11	�	�	X
ejpam-3483	390	12	1)→	1)→	NUM
ejpam-3483	390	13	(	(	PUNCT
ejpam-3483	390	14	y	y	PROPN
ejpam-3483	390	15	,	,	PUNCT
ejpam-3483	390	16	µ,	µ,	X
ejpam-3483	390	17	�	�	PROPN
ejpam-3483	390	18	2	2	NUM
ejpam-3483	390	19	)	)	PUNCT
ejpam-3483	390	20	be	be	AUX
ejpam-3483	390	21	d	d	ADJ
ejpam-3483	390	22	-	-	PUNCT
ejpam-3483	390	23	supra	supra	ADJ
ejpam-3483	390	24	b	b	NOUN
ejpam-3483	390	25	-	-	PUNCT
ejpam-3483	390	26	open	open	ADJ
ejpam-3483	390	27	(	(	PUNCT
ejpam-3483	390	28	i	i	NOUN
ejpam-3483	390	29	-	-	PUNCT
ejpam-3483	390	30	supra	supra	PROPN
ejpam-3483	390	31	b	b	PROPN
ejpam-3483	390	32	-	-	PUNCT
ejpam-3483	390	33	closed	closed	ADJ
ejpam-3483	390	34	)	)	PUNCT
ejpam-3483	390	35	and	and	CCONJ
ejpam-3483	390	36	order	order	NOUN
ejpam-3483	390	37	preserving	preserve	VERB
ejpam-3483	390	38	.	.	PUNCT
ejpam-3483	391	1	if	if	SCONJ
ejpam-3483	391	2	(	(	PUNCT
ejpam-3483	391	3	x	x	X
ejpam-3483	391	4	,	,	PUNCT
ejpam-3483	391	5	τ,	τ,	NOUN
ejpam-3483	391	6	�	�	X
ejpam-3483	391	7	1	1	NUM
ejpam-3483	391	8	)	)	PUNCT
ejpam-3483	391	9	is	be	AUX
ejpam-3483	391	10	upper	upper	ADJ
ejpam-3483	391	11	t1	t1	NOUN
ejpam-3483	391	12	-	-	PUNCT
ejpam-3483	391	13	ordered	order	VERB
ejpam-3483	391	14	,	,	PUNCT
ejpam-3483	391	15	then	then	ADV
ejpam-3483	391	16	(	(	PUNCT
ejpam-3483	391	17	y	y	PROPN
ejpam-3483	391	18	,	,	PUNCT
ejpam-3483	391	19	µ,	µ,	X
ejpam-3483	391	20	�	�	PROPN
ejpam-3483	391	21	2	2	NUM
ejpam-3483	391	22	)	)	PUNCT
ejpam-3483	391	23	is	be	AUX
ejpam-3483	391	24	upper	upper	ADJ
ejpam-3483	391	25	ssbt1	ssbt1	NOUN
ejpam-3483	391	26	-	-	PUNCT
ejpam-3483	391	27	ordered	order	VERB
ejpam-3483	391	28	.	.	PUNCT
ejpam-3483	392	1	proof	proof	NOUN
ejpam-3483	392	2	.	.	PUNCT
ejpam-3483	393	1	the	the	DET
ejpam-3483	393	2	proof	proof	NOUN
ejpam-3483	393	3	is	be	AUX
ejpam-3483	393	4	similar	similar	ADJ
ejpam-3483	393	5	to	to	ADP
ejpam-3483	393	6	that	that	PRON
ejpam-3483	393	7	of	of	ADP
ejpam-3483	393	8	theorem	theorem	NOUN
ejpam-3483	393	9	(	(	PUNCT
ejpam-3483	393	10	18	18	NUM
ejpam-3483	393	11	)	)	PUNCT
ejpam-3483	393	12	.	.	PUNCT
ejpam-3483	394	1	theorem	theorem	NOUN
ejpam-3483	394	2	20	20	NUM
ejpam-3483	394	3	.	.	PUNCT
ejpam-3483	395	1	let	let	VERB
ejpam-3483	395	2	a	a	DET
ejpam-3483	395	3	bijective	bijective	ADJ
ejpam-3483	395	4	map	map	NOUN
ejpam-3483	395	5	f	f	X
ejpam-3483	395	6	:	:	PUNCT
ejpam-3483	395	7	(	(	PUNCT
ejpam-3483	395	8	x	x	X
ejpam-3483	395	9	,	,	PUNCT
ejpam-3483	395	10	τ,	τ,	NOUN
ejpam-3483	395	11	�	�	X
ejpam-3483	395	12	1)→	1)→	NUM
ejpam-3483	395	13	(	(	PUNCT
ejpam-3483	395	14	y	y	PROPN
ejpam-3483	395	15	,	,	PUNCT
ejpam-3483	395	16	µ,	µ,	X
ejpam-3483	395	17	�	�	PROPN
ejpam-3483	395	18	2	2	NUM
ejpam-3483	395	19	)	)	PUNCT
ejpam-3483	395	20	be	be	AUX
ejpam-3483	395	21	b	b	NOUN
ejpam-3483	395	22	-	-	PUNCT
ejpam-3483	395	23	supra	supra	ADJ
ejpam-3483	395	24	b	b	NOUN
ejpam-3483	395	25	-	-	PUNCT
ejpam-3483	395	26	open	open	ADJ
ejpam-3483	395	27	(	(	PUNCT
ejpam-3483	395	28	b	b	NOUN
ejpam-3483	395	29	-	-	PUNCT
ejpam-3483	395	30	supra	supra	ADJ
ejpam-3483	395	31	b	b	NOUN
ejpam-3483	395	32	-	-	PUNCT
ejpam-3483	395	33	closed	closed	ADJ
ejpam-3483	395	34	)	)	PUNCT
ejpam-3483	395	35	and	and	CCONJ
ejpam-3483	395	36	order	order	NOUN
ejpam-3483	395	37	preserving	preserve	VERB
ejpam-3483	395	38	.	.	PUNCT
ejpam-3483	396	1	if	if	SCONJ
ejpam-3483	396	2	(	(	PUNCT
ejpam-3483	396	3	x	x	X
ejpam-3483	396	4	,	,	PUNCT
ejpam-3483	396	5	τ,	τ,	NOUN
ejpam-3483	396	6	�	�	X
ejpam-3483	396	7	1	1	NUM
ejpam-3483	396	8	)	)	PUNCT
ejpam-3483	396	9	is	be	AUX
ejpam-3483	396	10	ti	ti	ADJ
ejpam-3483	396	11	-	-	ADJ
ejpam-3483	396	12	ordered	order	VERB
ejpam-3483	396	13	,	,	PUNCT
ejpam-3483	396	14	then	then	ADV
ejpam-3483	396	15	(	(	PUNCT
ejpam-3483	396	16	y	y	PROPN
ejpam-3483	396	17	,	,	PUNCT
ejpam-3483	396	18	µ,	µ,	X
ejpam-3483	396	19	�	�	PROPN
ejpam-3483	396	20	2	2	NUM
ejpam-3483	396	21	)	)	PUNCT
ejpam-3483	396	22	is	be	AUX
ejpam-3483	396	23	ssbti	ssbti	NOUN
ejpam-3483	396	24	-	-	PUNCT
ejpam-3483	396	25	ordered	order	VERB
ejpam-3483	396	26	for	for	ADP
ejpam-3483	396	27	i	i	PROPN
ejpam-3483	396	28	=	=	SYM
ejpam-3483	396	29	0	0	NUM
ejpam-3483	396	30	,	,	PUNCT
ejpam-3483	396	31	1	1	NUM
ejpam-3483	396	32	,	,	PUNCT
ejpam-3483	396	33	2	2	NUM
ejpam-3483	396	34	.	.	PUNCT
ejpam-3483	397	1	proof	proof	NOUN
ejpam-3483	397	2	.	.	PUNCT
ejpam-3483	398	1	we	we	PRON
ejpam-3483	398	2	only	only	ADV
ejpam-3483	398	3	prove	prove	VERB
ejpam-3483	398	4	the	the	DET
ejpam-3483	398	5	theorem	theorem	NOUN
ejpam-3483	398	6	when	when	SCONJ
ejpam-3483	398	7	a	a	DET
ejpam-3483	398	8	map	map	NOUN
ejpam-3483	398	9	f	f	NOUN
ejpam-3483	398	10	is	be	AUX
ejpam-3483	398	11	b	b	NOUN
ejpam-3483	398	12	-	-	PUNCT
ejpam-3483	398	13	supra	supra	ADJ
ejpam-3483	398	14	b	b	NOUN
ejpam-3483	398	15	-	-	PUNCT
ejpam-3483	398	16	open	open	ADJ
ejpam-3483	398	17	and	and	CCONJ
ejpam-3483	398	18	in	in	ADP
ejpam-3483	398	19	the	the	DET
ejpam-3483	398	20	case	case	NOUN
ejpam-3483	398	21	of	of	ADP
ejpam-3483	398	22	i	i	PRON
ejpam-3483	398	23	=	=	NOUN
ejpam-3483	398	24	2	2	X
ejpam-3483	398	25	.	.	PUNCT
ejpam-3483	399	1	the	the	DET
ejpam-3483	399	2	other	other	ADJ
ejpam-3483	399	3	cases	case	NOUN
ejpam-3483	399	4	can	can	AUX
ejpam-3483	399	5	be	be	AUX
ejpam-3483	399	6	made	make	VERB
ejpam-3483	399	7	similarly	similarly	ADV
ejpam-3483	399	8	.	.	PUNCT
ejpam-3483	400	1	for	for	ADP
ejpam-3483	400	2	all	all	DET
ejpam-3483	400	3	x	x	NOUN
ejpam-3483	400	4	,	,	PUNCT
ejpam-3483	400	5	y	y	PROPN
ejpam-3483	400	6	∈	∈	PROPN
ejpam-3483	400	7	y	y	PROPN
ejpam-3483	400	8	such	such	ADJ
ejpam-3483	400	9	that	that	SCONJ
ejpam-3483	400	10	x	x	SYM
ejpam-3483	400	11	�	�	PROPN
ejpam-3483	400	12	2	2	NUM
ejpam-3483	400	13	y	y	PROPN
ejpam-3483	400	14	,	,	PUNCT
ejpam-3483	400	15	there	there	PRON
ejpam-3483	400	16	are	be	VERB
ejpam-3483	400	17	a	a	DET
ejpam-3483	400	18	,	,	PUNCT
ejpam-3483	400	19	b	b	X
ejpam-3483	400	20	∈	∈	PROPN
ejpam-3483	400	21	x	x	X
ejpam-3483	400	22	such	such	ADJ
ejpam-3483	400	23	that	that	SCONJ
ejpam-3483	400	24	a	a	DET
ejpam-3483	400	25	=	=	NOUN
ejpam-3483	400	26	f−1(x	f−1(x	NOUN
ejpam-3483	400	27	)	)	PUNCT
ejpam-3483	400	28	,	,	PUNCT
ejpam-3483	400	29	b	b	X
ejpam-3483	400	30	=	=	SYM
ejpam-3483	400	31	f−1(y	f−1(y	PROPN
ejpam-3483	400	32	)	)	PUNCT
ejpam-3483	400	33	.	.	PUNCT
ejpam-3483	401	1	since	since	SCONJ
ejpam-3483	401	2	f	f	PROPN
ejpam-3483	401	3	is	be	AUX
ejpam-3483	401	4	order	order	NOUN
ejpam-3483	401	5	preserving	preserve	VERB
ejpam-3483	401	6	,	,	PUNCT
ejpam-3483	401	7	then	then	ADV
ejpam-3483	401	8	a	a	DET
ejpam-3483	401	9	�	�	PROPN
ejpam-3483	401	10	1	1	NUM
ejpam-3483	401	11	b.	b.	NOUN
ejpam-3483	401	12	since	since	SCONJ
ejpam-3483	401	13	(	(	PUNCT
ejpam-3483	401	14	x	x	X
ejpam-3483	401	15	,	,	PUNCT
ejpam-3483	401	16	τ,	τ,	NOUN
ejpam-3483	401	17	�	�	X
ejpam-3483	401	18	1	1	NUM
ejpam-3483	401	19	)	)	PUNCT
ejpam-3483	401	20	is	be	AUX
ejpam-3483	401	21	a	a	DET
ejpam-3483	401	22	t2	t2	NOUN
ejpam-3483	401	23	-	-	PUNCT
ejpam-3483	401	24	ordered	order	VERB
ejpam-3483	401	25	space	space	NOUN
ejpam-3483	401	26	,	,	PUNCT
ejpam-3483	401	27	then	then	ADV
ejpam-3483	401	28	b.	b.	PROPN
ejpam-3483	401	29	a.	a.	PROPN
ejpam-3483	401	30	asaad	asaad	PROPN
ejpam-3483	401	31	,	,	PUNCT
ejpam-3483	401	32	m.	m.	PROPN
ejpam-3483	401	33	k.	k.	PROPN
ejpam-3483	401	34	tahat	tahat	PROPN
ejpam-3483	401	35	,	,	PUNCT
ejpam-3483	401	36	t.	t.	PROPN
ejpam-3483	401	37	m.	m.	PROPN
ejpam-3483	401	38	al	al	PROPN
ejpam-3483	401	39	-	-	PUNCT
ejpam-3483	401	40	shami	shami	PROPN
ejpam-3483	401	41	/	/	PUNCT
ejpam-3483	401	42	eur	eur	PROPN
ejpam-3483	401	43	.	.	PUNCT
ejpam-3483	402	1	j.	j.	PROPN
ejpam-3483	402	2	pure	pure	PROPN
ejpam-3483	402	3	appl	appl	PROPN
ejpam-3483	402	4	.	.	PROPN
ejpam-3483	402	5	math	math	PROPN
ejpam-3483	402	6	,	,	PUNCT
ejpam-3483	402	7	12	12	NUM
ejpam-3483	402	8	(	(	PUNCT
ejpam-3483	402	9	3	3	NUM
ejpam-3483	402	10	)	)	PUNCT
ejpam-3483	402	11	(	(	PUNCT
ejpam-3483	402	12	2019	2019	NUM
ejpam-3483	402	13	)	)	PUNCT
ejpam-3483	402	14	,	,	PUNCT
ejpam-3483	402	15	1231	1231	NUM
ejpam-3483	402	16	-	-	SYM
ejpam-3483	402	17	1247	1247	NUM
ejpam-3483	402	18	1243	1243	NUM
ejpam-3483	402	19	there	there	PRON
ejpam-3483	402	20	exist	exist	VERB
ejpam-3483	402	21	disjoint	disjoint	NOUN
ejpam-3483	402	22	neighborhoods	neighborhood	NOUN
ejpam-3483	402	23	w1	w1	NOUN
ejpam-3483	402	24	and	and	CCONJ
ejpam-3483	402	25	w2	w2	NOUN
ejpam-3483	402	26	of	of	ADP
ejpam-3483	402	27	a	a	PRON
ejpam-3483	402	28	and	and	CCONJ
ejpam-3483	402	29	b	b	NOUN
ejpam-3483	402	30	,	,	PUNCT
ejpam-3483	402	31	respectively	respectively	ADV
ejpam-3483	402	32	,	,	PUNCT
ejpam-3483	402	33	such	such	ADJ
ejpam-3483	402	34	that	that	DET
ejpam-3483	402	35	w1	w1	NOUN
ejpam-3483	402	36	is	be	AUX
ejpam-3483	402	37	increasing	increase	VERB
ejpam-3483	402	38	and	and	CCONJ
ejpam-3483	402	39	w2	w2	NOUN
ejpam-3483	402	40	is	be	AUX
ejpam-3483	402	41	decreasing	decrease	VERB
ejpam-3483	402	42	.	.	PUNCT
ejpam-3483	403	1	therefore	therefore	ADV
ejpam-3483	403	2	there	there	PRON
ejpam-3483	403	3	are	be	VERB
ejpam-3483	403	4	disjoint	disjoint	ADJ
ejpam-3483	403	5	open	open	ADJ
ejpam-3483	403	6	sets	set	NOUN
ejpam-3483	403	7	g	g	NOUN
ejpam-3483	403	8	and	and	CCONJ
ejpam-3483	403	9	h	h	NOUN
ejpam-3483	403	10	such	such	ADJ
ejpam-3483	403	11	that	that	SCONJ
ejpam-3483	403	12	a	a	DET
ejpam-3483	403	13	∈	∈	NOUN
ejpam-3483	403	14	g	g	ADP
ejpam-3483	403	15	⊆	⊆	NUM
ejpam-3483	403	16	w1	w1	NOUN
ejpam-3483	403	17	and	and	CCONJ
ejpam-3483	403	18	b	b	NOUN
ejpam-3483	403	19	∈	∈	PROPN
ejpam-3483	403	20	h	h	NOUN
ejpam-3483	403	21	⊆	⊆	NUM
ejpam-3483	403	22	w2	w2	NOUN
ejpam-3483	403	23	.	.	PUNCT
ejpam-3483	404	1	thus	thus	ADV
ejpam-3483	404	2	x	x	X
ejpam-3483	404	3	∈	∈	PROPN
ejpam-3483	404	4	f(g	f(g	NOUN
ejpam-3483	404	5	)	)	PUNCT
ejpam-3483	404	6	and	and	CCONJ
ejpam-3483	404	7	y	y	PROPN
ejpam-3483	404	8	∈	∈	PROPN
ejpam-3483	404	9	f(h	f(h	PROPN
ejpam-3483	404	10	)	)	PUNCT
ejpam-3483	404	11	which	which	PRON
ejpam-3483	404	12	are	be	AUX
ejpam-3483	404	13	b	b	PROPN
ejpam-3483	404	14	-	-	PUNCT
ejpam-3483	404	15	supra	supra	ADJ
ejpam-3483	404	16	b	b	NOUN
ejpam-3483	404	17	-	-	PUNCT
ejpam-3483	404	18	open	open	ADJ
ejpam-3483	404	19	sets	set	NOUN
ejpam-3483	404	20	.	.	PUNCT
ejpam-3483	405	1	since	since	SCONJ
ejpam-3483	405	2	f	f	PROPN
ejpam-3483	405	3	is	be	AUX
ejpam-3483	405	4	bijective	bijective	ADJ
ejpam-3483	405	5	,	,	PUNCT
ejpam-3483	405	6	then	then	ADV
ejpam-3483	405	7	f(g	f(g	NOUN
ejpam-3483	405	8	)	)	PUNCT
ejpam-3483	405	9	⋂	⋂	PROPN
ejpam-3483	405	10	f(h	f(h	PROPN
ejpam-3483	405	11	)	)	PUNCT
ejpam-3483	406	1	=	=	PUNCT
ejpam-3483	406	2	∅.	∅.	VERB
ejpam-3483	406	3	hence	hence	ADV
ejpam-3483	406	4	(	(	PUNCT
ejpam-3483	406	5	y	y	PROPN
ejpam-3483	406	6	,	,	PUNCT
ejpam-3483	406	7	µ,	µ,	X
ejpam-3483	406	8	�	�	PROPN
ejpam-3483	406	9	2	2	NUM
ejpam-3483	406	10	)	)	PUNCT
ejpam-3483	406	11	is	be	AUX
ejpam-3483	406	12	an	an	DET
ejpam-3483	406	13	ssbt2	ssbt2	NOUN
ejpam-3483	406	14	-	-	PUNCT
ejpam-3483	406	15	ordered	order	VERB
ejpam-3483	406	16	space	space	NOUN
ejpam-3483	406	17	.	.	PUNCT
ejpam-3483	407	1	theorem	theorem	PROPN
ejpam-3483	407	2	21	21	NUM
ejpam-3483	407	3	.	.	PUNCT
ejpam-3483	408	1	consider	consider	VERB
ejpam-3483	408	2	a	a	DET
ejpam-3483	408	3	bijective	bijective	ADJ
ejpam-3483	408	4	map	map	NOUN
ejpam-3483	409	1	f	f	X
ejpam-3483	409	2	:	:	PUNCT
ejpam-3483	409	3	(	(	PUNCT
ejpam-3483	409	4	x	x	X
ejpam-3483	409	5	,	,	PUNCT
ejpam-3483	409	6	τ,	τ,	NOUN
ejpam-3483	409	7	�	�	X
ejpam-3483	409	8	1	1	NUM
ejpam-3483	409	9	)	)	PUNCT
ejpam-3483	409	10	→	→	SYM
ejpam-3483	409	11	(	(	PUNCT
ejpam-3483	409	12	y	y	PROPN
ejpam-3483	409	13	,	,	PUNCT
ejpam-3483	409	14	µ,	µ,	X
ejpam-3483	409	15	�	�	PROPN
ejpam-3483	409	16	2	2	NUM
ejpam-3483	409	17	)	)	PUNCT
ejpam-3483	409	18	is	be	AUX
ejpam-3483	409	19	supra	supra	ADJ
ejpam-3483	409	20	b	b	NOUN
ejpam-3483	409	21	-	-	PUNCT
ejpam-3483	409	22	open	open	VERB
ejpam-3483	409	23	such	such	ADJ
ejpam-3483	409	24	that	that	SCONJ
ejpam-3483	409	25	f	f	PROPN
ejpam-3483	409	26	and	and	CCONJ
ejpam-3483	409	27	f−1	f−1	PROPN
ejpam-3483	409	28	are	be	AUX
ejpam-3483	409	29	order	order	NOUN
ejpam-3483	409	30	preserving	preserve	VERB
ejpam-3483	409	31	.	.	PUNCT
ejpam-3483	410	1	if	if	SCONJ
ejpam-3483	410	2	(	(	PUNCT
ejpam-3483	410	3	x	x	X
ejpam-3483	410	4	,	,	PUNCT
ejpam-3483	410	5	τ,	τ,	NOUN
ejpam-3483	410	6	�	�	X
ejpam-3483	410	7	1	1	NUM
ejpam-3483	410	8	)	)	PUNCT
ejpam-3483	410	9	is	be	AUX
ejpam-3483	410	10	strong	strong	ADJ
ejpam-3483	410	11	ti	ti	ADJ
ejpam-3483	410	12	-	-	ADJ
ejpam-3483	410	13	ordered	order	VERB
ejpam-3483	410	14	,	,	PUNCT
ejpam-3483	410	15	then	then	ADV
ejpam-3483	410	16	(	(	PUNCT
ejpam-3483	410	17	y	y	PROPN
ejpam-3483	410	18	,	,	PUNCT
ejpam-3483	410	19	µ,	µ,	X
ejpam-3483	410	20	�	�	PROPN
ejpam-3483	410	21	2	2	NUM
ejpam-3483	410	22	)	)	PUNCT
ejpam-3483	410	23	is	be	AUX
ejpam-3483	410	24	ssbti	ssbti	NOUN
ejpam-3483	410	25	-	-	PUNCT
ejpam-3483	410	26	ordered	order	VERB
ejpam-3483	410	27	for	for	ADP
ejpam-3483	410	28	i	i	PROPN
ejpam-3483	410	29	=	=	SYM
ejpam-3483	410	30	0	0	NUM
ejpam-3483	410	31	,	,	PUNCT
ejpam-3483	410	32	1	1	NUM
ejpam-3483	410	33	,	,	PUNCT
ejpam-3483	410	34	2	2	NUM
ejpam-3483	410	35	.	.	PUNCT
ejpam-3483	411	1	proof	proof	NOUN
ejpam-3483	411	2	.	.	PUNCT
ejpam-3483	412	1	we	we	PRON
ejpam-3483	412	2	prove	prove	VERB
ejpam-3483	412	3	the	the	DET
ejpam-3483	412	4	theorem	theorem	NOUN
ejpam-3483	412	5	in	in	ADP
ejpam-3483	412	6	case	case	NOUN
ejpam-3483	412	7	of	of	ADP
ejpam-3483	412	8	i	i	PRON
ejpam-3483	412	9	=	=	NOUN
ejpam-3483	413	1	2	2	X
ejpam-3483	413	2	.	.	PUNCT
ejpam-3483	413	3	let	let	VERB
ejpam-3483	413	4	x	x	PRON
ejpam-3483	413	5	,	,	PUNCT
ejpam-3483	413	6	y	y	PROPN
ejpam-3483	413	7	∈	∈	PROPN
ejpam-3483	413	8	y	y	PROPN
ejpam-3483	413	9	such	such	ADJ
ejpam-3483	413	10	that	that	SCONJ
ejpam-3483	413	11	x	x	SYM
ejpam-3483	413	12	�	�	PROPN
ejpam-3483	413	13	2	2	NUM
ejpam-3483	413	14	y.	y.	NOUN
ejpam-3483	413	15	then	then	ADV
ejpam-3483	413	16	there	there	PRON
ejpam-3483	413	17	exist	exist	VERB
ejpam-3483	413	18	a	a	DET
ejpam-3483	413	19	,	,	PUNCT
ejpam-3483	413	20	b	b	X
ejpam-3483	413	21	∈	∈	PROPN
ejpam-3483	413	22	x	x	X
ejpam-3483	413	23	such	such	ADJ
ejpam-3483	413	24	that	that	SCONJ
ejpam-3483	413	25	a	a	DET
ejpam-3483	413	26	=	=	NOUN
ejpam-3483	413	27	f−1(x	f−1(x	NOUN
ejpam-3483	413	28	)	)	PUNCT
ejpam-3483	413	29	and	and	CCONJ
ejpam-3483	413	30	b	b	X
ejpam-3483	413	31	=	=	SYM
ejpam-3483	413	32	f−1(y	f−1(y	PROPN
ejpam-3483	413	33	)	)	PUNCT
ejpam-3483	413	34	.	.	PUNCT
ejpam-3483	414	1	since	since	SCONJ
ejpam-3483	414	2	f	f	PROPN
ejpam-3483	414	3	is	be	AUX
ejpam-3483	414	4	order	order	NOUN
ejpam-3483	414	5	preserving	preserve	VERB
ejpam-3483	414	6	,	,	PUNCT
ejpam-3483	414	7	then	then	ADV
ejpam-3483	414	8	a	a	DET
ejpam-3483	414	9	�	�	PROPN
ejpam-3483	414	10	1	1	NUM
ejpam-3483	414	11	b.	b.	NOUN
ejpam-3483	414	12	since	since	SCONJ
ejpam-3483	414	13	(	(	PUNCT
ejpam-3483	414	14	x	x	X
ejpam-3483	414	15	,	,	PUNCT
ejpam-3483	414	16	τ,	τ,	NOUN
ejpam-3483	414	17	�	�	X
ejpam-3483	414	18	1	1	NUM
ejpam-3483	414	19	)	)	PUNCT
ejpam-3483	414	20	is	be	AUX
ejpam-3483	414	21	a	a	DET
ejpam-3483	414	22	strong	strong	ADJ
ejpam-3483	414	23	t2	t2	NOUN
ejpam-3483	414	24	-	-	PUNCT
ejpam-3483	414	25	ordered	order	VERB
ejpam-3483	414	26	space	space	NOUN
ejpam-3483	414	27	,	,	PUNCT
ejpam-3483	414	28	then	then	ADV
ejpam-3483	414	29	there	there	PRON
ejpam-3483	414	30	exist	exist	VERB
ejpam-3483	414	31	disjoint	disjoint	NOUN
ejpam-3483	414	32	an	an	DET
ejpam-3483	414	33	increasing	increase	VERB
ejpam-3483	414	34	open	open	ADJ
ejpam-3483	414	35	set	set	NOUN
ejpam-3483	414	36	g	g	NOUN
ejpam-3483	414	37	containing	contain	VERB
ejpam-3483	414	38	a	a	DET
ejpam-3483	414	39	and	and	CCONJ
ejpam-3483	414	40	a	a	DET
ejpam-3483	414	41	decreasing	decrease	VERB
ejpam-3483	414	42	open	open	ADJ
ejpam-3483	414	43	set	set	ADJ
ejpam-3483	414	44	h	h	NOUN
ejpam-3483	414	45	containing	contain	VERB
ejpam-3483	414	46	b.	b.	PROPN
ejpam-3483	414	47	by	by	ADP
ejpam-3483	414	48	hypothesis	hypothesis	NOUN
ejpam-3483	414	49	,	,	PUNCT
ejpam-3483	414	50	f	f	PROPN
ejpam-3483	414	51	is	be	AUX
ejpam-3483	414	52	bijective	bijective	ADJ
ejpam-3483	414	53	and	and	CCONJ
ejpam-3483	414	54	supra	supra	PROPN
ejpam-3483	414	55	b	b	PROPN
ejpam-3483	414	56	-	-	PUNCT
ejpam-3483	414	57	open	open	ADJ
ejpam-3483	414	58	,	,	PUNCT
ejpam-3483	414	59	and	and	CCONJ
ejpam-3483	414	60	f−1	f−1	PROPN
ejpam-3483	414	61	is	be	AUX
ejpam-3483	414	62	order	order	NOUN
ejpam-3483	414	63	preserving	preserve	VERB
ejpam-3483	414	64	,	,	PUNCT
ejpam-3483	414	65	then	then	ADV
ejpam-3483	414	66	f(g	f(g	NOUN
ejpam-3483	414	67	)	)	PUNCT
ejpam-3483	414	68	is	be	AUX
ejpam-3483	414	69	an	an	DET
ejpam-3483	414	70	i	i	PROPN
ejpam-3483	414	71	-	-	PUNCT
ejpam-3483	414	72	supra	supra	PROPN
ejpam-3483	414	73	b	b	NOUN
ejpam-3483	414	74	-	-	PUNCT
ejpam-3483	414	75	open	open	ADJ
ejpam-3483	414	76	set	set	NOUN
ejpam-3483	414	77	containing	contain	VERB
ejpam-3483	414	78	x	x	SYM
ejpam-3483	414	79	,	,	PUNCT
ejpam-3483	414	80	f(h	f(h	PROPN
ejpam-3483	414	81	)	)	PUNCT
ejpam-3483	414	82	is	be	AUX
ejpam-3483	414	83	a	a	DET
ejpam-3483	414	84	d	d	ADJ
ejpam-3483	414	85	-	-	PUNCT
ejpam-3483	414	86	supra	supra	ADJ
ejpam-3483	414	87	b	b	NOUN
ejpam-3483	414	88	-	-	PUNCT
ejpam-3483	414	89	open	open	ADJ
ejpam-3483	414	90	set	set	NOUN
ejpam-3483	414	91	containing	contain	VERB
ejpam-3483	414	92	y	y	PROPN
ejpam-3483	414	93	and	and	CCONJ
ejpam-3483	414	94	f(g	f(g	PROPN
ejpam-3483	414	95	)	)	PUNCT
ejpam-3483	414	96	⋂	⋂	PROPN
ejpam-3483	414	97	f(h	f(h	PROPN
ejpam-3483	414	98	)	)	PUNCT
ejpam-3483	415	1	=	=	PUNCT
ejpam-3483	415	2	∅.	∅.	VERB
ejpam-3483	415	3	therefore	therefore	ADV
ejpam-3483	415	4	(	(	PUNCT
ejpam-3483	415	5	y	y	PROPN
ejpam-3483	415	6	,	,	PUNCT
ejpam-3483	415	7	µ,	µ,	X
ejpam-3483	415	8	�	�	PROPN
ejpam-3483	415	9	2	2	NUM
ejpam-3483	415	10	)	)	PUNCT
ejpam-3483	415	11	is	be	AUX
ejpam-3483	415	12	ssbt2	ssbt2	NOUN
ejpam-3483	415	13	-	-	PUNCT
ejpam-3483	415	14	ordered	order	VERB
ejpam-3483	415	15	.	.	PUNCT
ejpam-3483	416	1	similarly	similarly	ADV
ejpam-3483	416	2	,	,	PUNCT
ejpam-3483	416	3	one	one	PRON
ejpam-3483	416	4	can	can	AUX
ejpam-3483	416	5	prove	prove	VERB
ejpam-3483	416	6	theorem	theorem	VERB
ejpam-3483	416	7	in	in	ADP
ejpam-3483	416	8	the	the	DET
ejpam-3483	416	9	cases	case	NOUN
ejpam-3483	416	10	of	of	ADP
ejpam-3483	416	11	i	i	NOUN
ejpam-3483	416	12	=	=	NOUN
ejpam-3483	416	13	0	0	NUM
ejpam-3483	416	14	,	,	PUNCT
ejpam-3483	416	15	1	1	NUM
ejpam-3483	416	16	.	.	X
ejpam-3483	416	17	theorem	theorem	NOUN
ejpam-3483	416	18	22	22	NUM
ejpam-3483	416	19	.	.	PUNCT
ejpam-3483	417	1	consider	consider	VERB
ejpam-3483	417	2	a	a	DET
ejpam-3483	417	3	bijective	bijective	ADJ
ejpam-3483	417	4	map	map	NOUN
ejpam-3483	418	1	f	f	X
ejpam-3483	418	2	:	:	PUNCT
ejpam-3483	418	3	(	(	PUNCT
ejpam-3483	418	4	x	x	X
ejpam-3483	418	5	,	,	PUNCT
ejpam-3483	418	6	τ,	τ,	NOUN
ejpam-3483	418	7	�	�	X
ejpam-3483	418	8	1)→	1)→	NUM
ejpam-3483	418	9	(	(	PUNCT
ejpam-3483	418	10	y	y	PROPN
ejpam-3483	418	11	,	,	PUNCT
ejpam-3483	418	12	µ,	µ,	X
ejpam-3483	418	13	�	�	PROPN
ejpam-3483	418	14	2	2	NUM
ejpam-3483	418	15	)	)	PUNCT
ejpam-3483	418	16	is	be	AUX
ejpam-3483	418	17	supra	supra	PROPN
ejpam-3483	418	18	b	b	PROPN
ejpam-3483	418	19	-	-	PUNCT
ejpam-3483	418	20	closed	close	VERB
ejpam-3483	418	21	such	such	ADJ
ejpam-3483	418	22	that	that	SCONJ
ejpam-3483	418	23	f	f	PROPN
ejpam-3483	418	24	and	and	CCONJ
ejpam-3483	418	25	f−1	f−1	PROPN
ejpam-3483	418	26	are	be	AUX
ejpam-3483	418	27	order	order	NOUN
ejpam-3483	418	28	preserving	preserve	VERB
ejpam-3483	418	29	.	.	PUNCT
ejpam-3483	419	1	if	if	SCONJ
ejpam-3483	419	2	(	(	PUNCT
ejpam-3483	419	3	x	x	X
ejpam-3483	419	4	,	,	PUNCT
ejpam-3483	419	5	τ,	τ,	NOUN
ejpam-3483	419	6	�	�	X
ejpam-3483	419	7	1	1	NUM
ejpam-3483	419	8	)	)	PUNCT
ejpam-3483	419	9	is	be	AUX
ejpam-3483	419	10	strong	strong	ADJ
ejpam-3483	419	11	ti	ti	ADJ
ejpam-3483	419	12	-	-	ADJ
ejpam-3483	419	13	ordered	order	VERB
ejpam-3483	419	14	,	,	PUNCT
ejpam-3483	419	15	then	then	ADV
ejpam-3483	419	16	(	(	PUNCT
ejpam-3483	419	17	y	y	PROPN
ejpam-3483	419	18	,	,	PUNCT
ejpam-3483	419	19	µ,	µ,	X
ejpam-3483	419	20	�	�	PROPN
ejpam-3483	419	21	2	2	NUM
ejpam-3483	419	22	)	)	PUNCT
ejpam-3483	419	23	is	be	AUX
ejpam-3483	419	24	ssbti	ssbti	NOUN
ejpam-3483	419	25	-	-	PUNCT
ejpam-3483	419	26	ordered	order	VERB
ejpam-3483	419	27	for	for	ADP
ejpam-3483	419	28	i	i	PROPN
ejpam-3483	419	29	=	=	SYM
ejpam-3483	419	30	0	0	NUM
ejpam-3483	419	31	,	,	PUNCT
ejpam-3483	419	32	1	1	NUM
ejpam-3483	419	33	,	,	PUNCT
ejpam-3483	419	34	2	2	NUM
ejpam-3483	419	35	.	.	PUNCT
ejpam-3483	420	1	proof	proof	NOUN
ejpam-3483	420	2	.	.	PUNCT
ejpam-3483	421	1	the	the	DET
ejpam-3483	421	2	proof	proof	NOUN
ejpam-3483	421	3	is	be	AUX
ejpam-3483	421	4	similar	similar	ADJ
ejpam-3483	421	5	to	to	ADP
ejpam-3483	421	6	that	that	PRON
ejpam-3483	421	7	of	of	ADP
ejpam-3483	421	8	theorem	theorem	NOUN
ejpam-3483	421	9	(	(	PUNCT
ejpam-3483	421	10	21	21	NUM
ejpam-3483	421	11	)	)	PUNCT
ejpam-3483	421	12	.	.	PUNCT
ejpam-3483	422	1	5	5	X
ejpam-3483	422	2	.	.	X
ejpam-3483	422	3	supra	supra	PROPN
ejpam-3483	422	4	b	b	PROPN
ejpam-3483	422	5	-	-	PUNCT
ejpam-3483	422	6	homeomorphism	homeomorphism	PROPN
ejpam-3483	422	7	maps	map	VERB
ejpam-3483	422	8	the	the	DET
ejpam-3483	422	9	concepts	concept	NOUN
ejpam-3483	422	10	of	of	ADP
ejpam-3483	422	11	i	i	PROPN
ejpam-3483	422	12	-	-	PUNCT
ejpam-3483	422	13	supra	supra	PROPN
ejpam-3483	422	14	b	b	PROPN
ejpam-3483	422	15	-	-	PUNCT
ejpam-3483	422	16	homeomorphism	homeomorphism	ADJ
ejpam-3483	422	17	,	,	PUNCT
ejpam-3483	422	18	d	d	X
ejpam-3483	422	19	-	-	PUNCT
ejpam-3483	422	20	supra	supra	ADJ
ejpam-3483	422	21	b	b	NOUN
ejpam-3483	422	22	-	-	PUNCT
ejpam-3483	422	23	homeomorphism	homeomorphism	PROPN
ejpam-3483	422	24	and	and	CCONJ
ejpam-3483	422	25	b	b	X
ejpam-3483	422	26	-	-	PUNCT
ejpam-3483	422	27	supra	supra	ADJ
ejpam-3483	422	28	bhomeomorphism	bhomeomorphism	NOUN
ejpam-3483	422	29	maps	map	NOUN
ejpam-3483	422	30	are	be	AUX
ejpam-3483	422	31	introduced	introduce	VERB
ejpam-3483	422	32	and	and	CCONJ
ejpam-3483	422	33	many	many	ADJ
ejpam-3483	422	34	of	of	ADP
ejpam-3483	422	35	their	their	PRON
ejpam-3483	422	36	properties	property	NOUN
ejpam-3483	422	37	are	be	AUX
ejpam-3483	422	38	established	establish	VERB
ejpam-3483	422	39	.	.	PUNCT
ejpam-3483	423	1	some	some	DET
ejpam-3483	423	2	illustrative	illustrative	ADJ
ejpam-3483	423	3	examples	example	NOUN
ejpam-3483	423	4	are	be	AUX
ejpam-3483	423	5	provided	provide	VERB
ejpam-3483	423	6	.	.	PUNCT
ejpam-3483	424	1	definition	definition	NOUN
ejpam-3483	424	2	17	17	NUM
ejpam-3483	424	3	.	.	PUNCT
ejpam-3483	425	1	let	let	VERB
ejpam-3483	425	2	τ	τ	PROPN
ejpam-3483	425	3	?	?	PUNCT
ejpam-3483	425	4	and	and	CCONJ
ejpam-3483	425	5	θ	θ	X
ejpam-3483	425	6	?	?	PROPN
ejpam-3483	425	7	be	be	AUX
ejpam-3483	425	8	associated	associate	VERB
ejpam-3483	425	9	supra	supra	ADJ
ejpam-3483	425	10	topologies	topology	NOUN
ejpam-3483	425	11	with	with	ADP
ejpam-3483	425	12	τ	τ	PROPN
ejpam-3483	425	13	and	and	CCONJ
ejpam-3483	425	14	θ	θ	PROPN
ejpam-3483	425	15	,	,	PUNCT
ejpam-3483	425	16	respectively	respectively	ADV
ejpam-3483	425	17	.	.	PUNCT
ejpam-3483	426	1	a	a	DET
ejpam-3483	426	2	bijective	bijective	ADJ
ejpam-3483	426	3	map	map	NOUN
ejpam-3483	426	4	g	g	NOUN
ejpam-3483	426	5	:	:	PUNCT
ejpam-3483	426	6	(	(	PUNCT
ejpam-3483	426	7	x	x	X
ejpam-3483	426	8	,	,	PUNCT
ejpam-3483	426	9	τ,	τ,	NOUN
ejpam-3483	426	10	�	�	X
ejpam-3483	426	11	1	1	NUM
ejpam-3483	426	12	)	)	PUNCT
ejpam-3483	426	13	→	→	SYM
ejpam-3483	426	14	(	(	PUNCT
ejpam-3483	426	15	y	y	NOUN
ejpam-3483	426	16	,	,	PUNCT
ejpam-3483	426	17	θ,	θ,	NOUN
ejpam-3483	426	18	�	�	NOUN
ejpam-3483	426	19	2	2	NUM
ejpam-3483	426	20	)	)	PUNCT
ejpam-3483	426	21	is	be	AUX
ejpam-3483	426	22	called	call	VERB
ejpam-3483	426	23	i	i	PRON
ejpam-3483	426	24	-	-	PUNCT
ejpam-3483	426	25	supra	supra	PROPN
ejpam-3483	426	26	(	(	PUNCT
ejpam-3483	426	27	resp	resp	NOUN
ejpam-3483	426	28	.	.	PUNCT
ejpam-3483	427	1	d	d	X
ejpam-3483	427	2	-	-	PUNCT
ejpam-3483	427	3	supra	supra	ADJ
ejpam-3483	427	4	,	,	PUNCT
ejpam-3483	427	5	b	b	NOUN
ejpam-3483	427	6	-	-	PUNCT
ejpam-3483	427	7	supra	supra	ADJ
ejpam-3483	427	8	)	)	PUNCT
ejpam-3483	427	9	b	b	NOUN
ejpam-3483	427	10	-	-	PUNCT
ejpam-3483	427	11	homeomorphism	homeomorphism	PROPN
ejpam-3483	427	12	if	if	SCONJ
ejpam-3483	427	13	it	it	PRON
ejpam-3483	427	14	is	be	AUX
ejpam-3483	427	15	i	i	PROPN
ejpam-3483	427	16	-	-	PUNCT
ejpam-3483	427	17	supra	supra	PROPN
ejpam-3483	427	18	b	b	NOUN
ejpam-3483	427	19	-	-	PUNCT
ejpam-3483	427	20	continuous	continuous	ADJ
ejpam-3483	427	21	and	and	CCONJ
ejpam-3483	427	22	i	i	NOUN
ejpam-3483	427	23	-	-	PUNCT
ejpam-3483	427	24	supra	supra	PROPN
ejpam-3483	427	25	b	b	NOUN
ejpam-3483	427	26	-	-	PUNCT
ejpam-3483	427	27	open	open	ADJ
ejpam-3483	427	28	(	(	PUNCT
ejpam-3483	427	29	resp	resp	NOUN
ejpam-3483	427	30	.	.	PUNCT
ejpam-3483	428	1	d	d	X
ejpam-3483	428	2	-	-	PUNCT
ejpam-3483	428	3	supra	supra	ADJ
ejpam-3483	428	4	bcontinuous	bcontinuous	NOUN
ejpam-3483	428	5	and	and	CCONJ
ejpam-3483	428	6	d	d	NOUN
ejpam-3483	428	7	-	-	ADJ
ejpam-3483	428	8	supra	supra	ADJ
ejpam-3483	428	9	b	b	NOUN
ejpam-3483	428	10	-	-	PUNCT
ejpam-3483	428	11	open	open	ADJ
ejpam-3483	428	12	,	,	PUNCT
ejpam-3483	428	13	b	b	X
ejpam-3483	428	14	-	-	PUNCT
ejpam-3483	428	15	supra	supra	ADJ
ejpam-3483	428	16	b	b	NOUN
ejpam-3483	428	17	-	-	PUNCT
ejpam-3483	428	18	continuous	continuous	ADJ
ejpam-3483	428	19	and	and	CCONJ
ejpam-3483	428	20	b	b	NOUN
ejpam-3483	428	21	-	-	PUNCT
ejpam-3483	428	22	supra	supra	ADJ
ejpam-3483	428	23	b	b	NOUN
ejpam-3483	428	24	-	-	PUNCT
ejpam-3483	428	25	open	open	ADJ
ejpam-3483	428	26	)	)	PUNCT
ejpam-3483	428	27	.	.	PUNCT
ejpam-3483	429	1	remark	remark	PROPN
ejpam-3483	429	2	4	4	NUM
ejpam-3483	429	3	.	.	PUNCT
ejpam-3483	430	1	(	(	PUNCT
ejpam-3483	430	2	i	i	NOUN
ejpam-3483	430	3	)	)	PUNCT
ejpam-3483	430	4	every	every	DET
ejpam-3483	430	5	i	i	PROPN
ejpam-3483	430	6	-	-	PUNCT
ejpam-3483	430	7	supra	supra	PROPN
ejpam-3483	430	8	(	(	PUNCT
ejpam-3483	430	9	d	d	NOUN
ejpam-3483	430	10	-	-	PUNCT
ejpam-3483	430	11	supra	supra	ADJ
ejpam-3483	430	12	,	,	PUNCT
ejpam-3483	430	13	b	b	NOUN
ejpam-3483	430	14	-	-	PUNCT
ejpam-3483	430	15	supra	supra	ADJ
ejpam-3483	430	16	)	)	PUNCT
ejpam-3483	430	17	b	b	NOUN
ejpam-3483	430	18	-	-	PUNCT
ejpam-3483	430	19	homeomorphism	homeomorphism	PROPN
ejpam-3483	430	20	map	map	NOUN
ejpam-3483	430	21	is	be	AUX
ejpam-3483	430	22	supra	supra	ADJ
ejpam-3483	430	23	bhomeomorphism	bhomeomorphism	NOUN
ejpam-3483	430	24	.	.	PUNCT
ejpam-3483	431	1	(	(	PUNCT
ejpam-3483	431	2	ii	ii	NOUN
ejpam-3483	431	3	)	)	PUNCT
ejpam-3483	431	4	every	every	DET
ejpam-3483	431	5	b	b	X
ejpam-3483	431	6	-	-	PUNCT
ejpam-3483	431	7	supra	supra	ADJ
ejpam-3483	431	8	b	b	NOUN
ejpam-3483	431	9	-	-	PUNCT
ejpam-3483	431	10	homeomorphism	homeomorphism	PROPN
ejpam-3483	431	11	map	map	NOUN
ejpam-3483	431	12	is	be	AUX
ejpam-3483	431	13	i	i	PROPN
ejpam-3483	431	14	-	-	PUNCT
ejpam-3483	431	15	supra	supra	PROPN
ejpam-3483	431	16	(	(	PUNCT
ejpam-3483	431	17	d	d	NOUN
ejpam-3483	431	18	-	-	PUNCT
ejpam-3483	431	19	supra	supra	ADJ
ejpam-3483	431	20	)	)	PUNCT
ejpam-3483	431	21	b	b	NOUN
ejpam-3483	431	22	-	-	PUNCT
ejpam-3483	431	23	homeomorphism	homeomorphism	PROPN
ejpam-3483	431	24	.	.	PUNCT
ejpam-3483	432	1	the	the	DET
ejpam-3483	432	2	following	follow	VERB
ejpam-3483	432	3	two	two	NUM
ejpam-3483	432	4	examples	example	NOUN
ejpam-3483	432	5	illustrate	illustrate	VERB
ejpam-3483	432	6	that	that	SCONJ
ejpam-3483	432	7	the	the	DET
ejpam-3483	432	8	above	above	ADJ
ejpam-3483	432	9	remark	remark	NOUN
ejpam-3483	432	10	can	can	AUX
ejpam-3483	432	11	not	not	PART
ejpam-3483	432	12	be	be	AUX
ejpam-3483	432	13	reversed	reverse	VERB
ejpam-3483	432	14	,	,	PUNCT
ejpam-3483	432	15	in	in	ADP
ejpam-3483	432	16	general	general	ADJ
ejpam-3483	432	17	.	.	PUNCT
ejpam-3483	433	1	b.	b.	PROPN
ejpam-3483	433	2	a.	a.	PROPN
ejpam-3483	433	3	asaad	asaad	PROPN
ejpam-3483	433	4	,	,	PUNCT
ejpam-3483	433	5	m.	m.	PROPN
ejpam-3483	433	6	k.	k.	PROPN
ejpam-3483	433	7	tahat	tahat	PROPN
ejpam-3483	433	8	,	,	PUNCT
ejpam-3483	433	9	t.	t.	PROPN
ejpam-3483	433	10	m.	m.	PROPN
ejpam-3483	433	11	al	al	PROPN
ejpam-3483	433	12	-	-	PUNCT
ejpam-3483	433	13	shami	shami	PROPN
ejpam-3483	433	14	/	/	PUNCT
ejpam-3483	433	15	eur	eur	PROPN
ejpam-3483	433	16	.	.	PUNCT
ejpam-3483	434	1	j.	j.	PROPN
ejpam-3483	434	2	pure	pure	PROPN
ejpam-3483	434	3	appl	appl	PROPN
ejpam-3483	434	4	.	.	PROPN
ejpam-3483	434	5	math	math	PROPN
ejpam-3483	434	6	,	,	PUNCT
ejpam-3483	434	7	12	12	NUM
ejpam-3483	434	8	(	(	PUNCT
ejpam-3483	434	9	3	3	NUM
ejpam-3483	434	10	)	)	PUNCT
ejpam-3483	434	11	(	(	PUNCT
ejpam-3483	434	12	2019	2019	NUM
ejpam-3483	434	13	)	)	PUNCT
ejpam-3483	434	14	,	,	PUNCT
ejpam-3483	434	15	1231	1231	NUM
ejpam-3483	434	16	-	-	SYM
ejpam-3483	434	17	1247	1247	NUM
ejpam-3483	434	18	1244	1244	NUM
ejpam-3483	434	19	example	example	NOUN
ejpam-3483	434	20	5	5	NUM
ejpam-3483	434	21	.	.	PUNCT
ejpam-3483	435	1	let	let	VERB
ejpam-3483	435	2	a	a	DET
ejpam-3483	435	3	topology	topology	NOUN
ejpam-3483	435	4	τ	τ	NOUN
ejpam-3483	435	5	=	=	SYM
ejpam-3483	435	6	{	{	PUNCT
ejpam-3483	435	7	∅	∅	NOUN
ejpam-3483	435	8	,	,	PUNCT
ejpam-3483	435	9	x	x	X
ejpam-3483	435	10	,	,	PUNCT
ejpam-3483	435	11	{	{	PUNCT
ejpam-3483	435	12	a	a	X
ejpam-3483	435	13	,	,	PUNCT
ejpam-3483	435	14	c	c	NOUN
ejpam-3483	435	15	}	}	PUNCT
ejpam-3483	435	16	}	}	PUNCT
ejpam-3483	435	17	on	on	ADP
ejpam-3483	435	18	x	x	X
ejpam-3483	435	19	=	=	X
ejpam-3483	435	20	{	{	PUNCT
ejpam-3483	435	21	a	a	PRON
ejpam-3483	435	22	,	,	PUNCT
ejpam-3483	435	23	b	b	NOUN
ejpam-3483	435	24	,	,	PUNCT
ejpam-3483	435	25	c	c	NOUN
ejpam-3483	435	26	}	}	PUNCT
ejpam-3483	435	27	,	,	PUNCT
ejpam-3483	435	28	a	a	DET
ejpam-3483	435	29	supra	supra	ADJ
ejpam-3483	435	30	topology	topology	NOUN
ejpam-3483	435	31	associated	associate	VERB
ejpam-3483	435	32	with	with	ADP
ejpam-3483	435	33	τ	τ	PROPN
ejpam-3483	435	34	be	be	AUX
ejpam-3483	435	35	{	{	PUNCT
ejpam-3483	435	36	∅	∅	NOUN
ejpam-3483	435	37	,	,	PUNCT
ejpam-3483	435	38	x	x	X
ejpam-3483	435	39	,	,	PUNCT
ejpam-3483	435	40	{	{	PUNCT
ejpam-3483	435	41	a	a	X
ejpam-3483	435	42	}	}	PUNCT
ejpam-3483	435	43	,	,	PUNCT
ejpam-3483	435	44	{	{	PUNCT
ejpam-3483	435	45	a	a	PRON
ejpam-3483	435	46	,	,	PUNCT
ejpam-3483	435	47	c	c	NOUN
ejpam-3483	435	48	}	}	PUNCT
ejpam-3483	435	49	}	}	PUNCT
ejpam-3483	435	50	and	and	CCONJ
ejpam-3483	435	51	a	a	DET
ejpam-3483	435	52	partial	partial	ADJ
ejpam-3483	435	53	order	order	NOUN
ejpam-3483	435	54	relation	relation	NOUN
ejpam-3483	435	55	�	�	NOUN
ejpam-3483	435	56	1=	1=	X
ejpam-3483	435	57	4	4	NUM
ejpam-3483	435	58	⋃	⋃	NOUN
ejpam-3483	435	59	{	{	PUNCT
ejpam-3483	435	60	(	(	PUNCT
ejpam-3483	435	61	c	c	NOUN
ejpam-3483	435	62	,	,	PUNCT
ejpam-3483	435	63	a	a	NOUN
ejpam-3483	435	64	)	)	PUNCT
ejpam-3483	435	65	,	,	PUNCT
ejpam-3483	435	66	(	(	PUNCT
ejpam-3483	435	67	c	c	X
ejpam-3483	435	68	,	,	PUNCT
ejpam-3483	435	69	b	b	NOUN
ejpam-3483	435	70	)	)	PUNCT
ejpam-3483	435	71	}	}	PUNCT
ejpam-3483	435	72	.	.	PUNCT
ejpam-3483	436	1	let	let	VERB
ejpam-3483	436	2	a	a	DET
ejpam-3483	436	3	topology	topology	NOUN
ejpam-3483	436	4	θ	θ	NOUN
ejpam-3483	436	5	=	=	SYM
ejpam-3483	436	6	{	{	PUNCT
ejpam-3483	436	7	∅	∅	NOUN
ejpam-3483	436	8	,	,	PUNCT
ejpam-3483	436	9	y	y	PROPN
ejpam-3483	436	10	,	,	PUNCT
ejpam-3483	436	11	{	{	PUNCT
ejpam-3483	436	12	y	y	PROPN
ejpam-3483	436	13	,	,	PUNCT
ejpam-3483	436	14	z	z	NOUN
ejpam-3483	436	15	}	}	PUNCT
ejpam-3483	436	16	}	}	PUNCT
ejpam-3483	436	17	on	on	ADP
ejpam-3483	436	18	y	y	PROPN
ejpam-3483	436	19	=	=	PUNCT
ejpam-3483	436	20	{	{	PUNCT
ejpam-3483	436	21	x	x	PROPN
ejpam-3483	436	22	,	,	PUNCT
ejpam-3483	436	23	y	y	PROPN
ejpam-3483	436	24	,	,	PUNCT
ejpam-3483	436	25	z	z	NOUN
ejpam-3483	436	26	}	}	PUNCT
ejpam-3483	436	27	,	,	PUNCT
ejpam-3483	436	28	a	a	DET
ejpam-3483	436	29	supra	supra	ADJ
ejpam-3483	436	30	topology	topology	NOUN
ejpam-3483	436	31	associated	associate	VERB
ejpam-3483	436	32	with	with	ADP
ejpam-3483	436	33	θ	θ	PROPN
ejpam-3483	436	34	be	be	AUX
ejpam-3483	436	35	{	{	PUNCT
ejpam-3483	436	36	∅	∅	NOUN
ejpam-3483	436	37	,	,	PUNCT
ejpam-3483	436	38	y	y	PROPN
ejpam-3483	436	39	,	,	PUNCT
ejpam-3483	436	40	{	{	PUNCT
ejpam-3483	436	41	y	y	NOUN
ejpam-3483	436	42	}	}	PUNCT
ejpam-3483	436	43	,	,	PUNCT
ejpam-3483	436	44	{	{	PUNCT
ejpam-3483	436	45	y	y	NOUN
ejpam-3483	436	46	,	,	PUNCT
ejpam-3483	436	47	z	z	NOUN
ejpam-3483	436	48	}	}	PUNCT
ejpam-3483	436	49	}	}	PUNCT
ejpam-3483	436	50	and	and	CCONJ
ejpam-3483	436	51	a	a	DET
ejpam-3483	436	52	partial	partial	ADJ
ejpam-3483	436	53	order	order	NOUN
ejpam-3483	436	54	relation	relation	NOUN
ejpam-3483	436	55	�	�	NOUN
ejpam-3483	436	56	2=	2=	NUM
ejpam-3483	436	57	4	4	NUM
ejpam-3483	436	58	⋃	⋃	NOUN
ejpam-3483	436	59	{	{	PUNCT
ejpam-3483	436	60	(	(	PUNCT
ejpam-3483	436	61	y	y	PROPN
ejpam-3483	436	62	,	,	PUNCT
ejpam-3483	436	63	z	z	NOUN
ejpam-3483	436	64	)	)	PUNCT
ejpam-3483	436	65	}	}	PUNCT
ejpam-3483	436	66	on	on	ADP
ejpam-3483	436	67	y	y	PROPN
ejpam-3483	436	68	.	.	PUNCT
ejpam-3483	437	1	a	a	DET
ejpam-3483	437	2	map	map	NOUN
ejpam-3483	437	3	f	f	X
ejpam-3483	437	4	:	:	PUNCT
ejpam-3483	437	5	(	(	PUNCT
ejpam-3483	437	6	x	x	X
ejpam-3483	437	7	,	,	PUNCT
ejpam-3483	437	8	τ,	τ,	NOUN
ejpam-3483	437	9	�	�	X
ejpam-3483	437	10	1	1	NUM
ejpam-3483	437	11	)	)	PUNCT
ejpam-3483	437	12	→	→	SYM
ejpam-3483	437	13	(	(	PUNCT
ejpam-3483	437	14	y	y	NOUN
ejpam-3483	437	15	,	,	PUNCT
ejpam-3483	437	16	θ,	θ,	NOUN
ejpam-3483	437	17	�	�	NOUN
ejpam-3483	437	18	2	2	NUM
ejpam-3483	437	19	)	)	PUNCT
ejpam-3483	437	20	is	be	AUX
ejpam-3483	437	21	defined	define	VERB
ejpam-3483	437	22	as	as	ADP
ejpam-3483	437	23	f(a	f(a	NOUN
ejpam-3483	437	24	)	)	PUNCT
ejpam-3483	438	1	=	=	SYM
ejpam-3483	438	2	y	y	PROPN
ejpam-3483	438	3	,	,	PUNCT
ejpam-3483	438	4	f(b	f(b	PROPN
ejpam-3483	438	5	)	)	PUNCT
ejpam-3483	438	6	=	=	SYM
ejpam-3483	438	7	z	z	NOUN
ejpam-3483	438	8	and	and	CCONJ
ejpam-3483	438	9	f(c	f(c	PROPN
ejpam-3483	438	10	)	)	PUNCT
ejpam-3483	438	11	=	=	PUNCT
ejpam-3483	439	1	x.	x.	NOUN
ejpam-3483	439	2	now	now	ADV
ejpam-3483	439	3	,	,	PUNCT
ejpam-3483	439	4	f	f	PROPN
ejpam-3483	439	5	is	be	AUX
ejpam-3483	439	6	supra	supra	PROPN
ejpam-3483	439	7	b	b	PROPN
ejpam-3483	439	8	-	-	PUNCT
ejpam-3483	439	9	homeomorphism	homeomorphism	NOUN
ejpam-3483	439	10	,	,	PUNCT
ejpam-3483	439	11	but	but	CCONJ
ejpam-3483	439	12	is	be	AUX
ejpam-3483	439	13	not	not	PART
ejpam-3483	439	14	x	x	ADJ
ejpam-3483	439	15	-	-	ADJ
ejpam-3483	439	16	supra	supra	ADJ
ejpam-3483	439	17	b	b	NOUN
ejpam-3483	439	18	-	-	PUNCT
ejpam-3483	439	19	homeomorphism	homeomorphism	PROPN
ejpam-3483	439	20	for	for	ADP
ejpam-3483	439	21	x	x	PROPN
ejpam-3483	439	22	∈	∈	PROPN
ejpam-3483	439	23	{	{	PUNCT
ejpam-3483	439	24	i	i	NOUN
ejpam-3483	439	25	,	,	PUNCT
ejpam-3483	439	26	d	d	PROPN
ejpam-3483	439	27	,	,	PUNCT
ejpam-3483	439	28	b	b	NOUN
ejpam-3483	439	29	}	}	PUNCT
ejpam-3483	439	30	.	.	PUNCT
ejpam-3483	440	1	example	example	NOUN
ejpam-3483	441	1	6	6	NUM
ejpam-3483	441	2	.	.	PUNCT
ejpam-3483	442	1	we	we	PRON
ejpam-3483	442	2	replace	replace	VERB
ejpam-3483	442	3	only	only	ADV
ejpam-3483	442	4	a	a	DET
ejpam-3483	442	5	partial	partial	ADJ
ejpam-3483	442	6	order	order	NOUN
ejpam-3483	442	7	relation	relation	NOUN
ejpam-3483	442	8	�	�	NOUN
ejpam-3483	442	9	1	1	NUM
ejpam-3483	442	10	in	in	ADP
ejpam-3483	442	11	example	example	NOUN
ejpam-3483	442	12	(	(	PUNCT
ejpam-3483	442	13	5	5	NUM
ejpam-3483	442	14	)	)	PUNCT
ejpam-3483	442	15	by	by	ADP
ejpam-3483	442	16	�	�	NOUN
ejpam-3483	442	17	=	=	PROPN
ejpam-3483	442	18	4	4	NUM
ejpam-3483	442	19	⋃	⋃	NOUN
ejpam-3483	442	20	{	{	PUNCT
ejpam-3483	442	21	(	(	PUNCT
ejpam-3483	442	22	a	a	PRON
ejpam-3483	442	23	,	,	PUNCT
ejpam-3483	442	24	c	c	NOUN
ejpam-3483	442	25	)	)	PUNCT
ejpam-3483	442	26	}	}	PUNCT
ejpam-3483	442	27	.	.	PUNCT
ejpam-3483	443	1	then	then	ADV
ejpam-3483	443	2	a	a	DET
ejpam-3483	443	3	map	map	NOUN
ejpam-3483	443	4	f	f	NOUN
ejpam-3483	443	5	is	be	AUX
ejpam-3483	443	6	d	d	ADJ
ejpam-3483	443	7	-	-	PUNCT
ejpam-3483	443	8	supra	supra	ADJ
ejpam-3483	443	9	b	b	NOUN
ejpam-3483	443	10	-	-	PUNCT
ejpam-3483	443	11	homeomorphism	homeomorphism	NOUN
ejpam-3483	443	12	,	,	PUNCT
ejpam-3483	443	13	but	but	CCONJ
ejpam-3483	443	14	not	not	PART
ejpam-3483	443	15	b	b	NOUN
ejpam-3483	443	16	-	-	PUNCT
ejpam-3483	443	17	supra	supra	ADJ
ejpam-3483	443	18	b	b	NOUN
ejpam-3483	443	19	-	-	PUNCT
ejpam-3483	443	20	homeomorphism	homeomorphism	PROPN
ejpam-3483	443	21	.	.	PUNCT
ejpam-3483	444	1	theorem	theorem	NOUN
ejpam-3483	444	2	23	23	NUM
ejpam-3483	444	3	.	.	PUNCT
ejpam-3483	445	1	let	let	VERB
ejpam-3483	445	2	a	a	DET
ejpam-3483	445	3	map	map	NOUN
ejpam-3483	445	4	f	f	X
ejpam-3483	445	5	:	:	PUNCT
ejpam-3483	445	6	(	(	PUNCT
ejpam-3483	445	7	x	x	X
ejpam-3483	445	8	,	,	PUNCT
ejpam-3483	445	9	τ,	τ,	NOUN
ejpam-3483	445	10	�	�	X
ejpam-3483	445	11	1)→	1)→	NUM
ejpam-3483	445	12	(	(	PUNCT
ejpam-3483	445	13	y	y	PROPN
ejpam-3483	445	14	,	,	PUNCT
ejpam-3483	445	15	θ,	θ,	NOUN
ejpam-3483	445	16	�	�	NOUN
ejpam-3483	445	17	2	2	NUM
ejpam-3483	445	18	)	)	PUNCT
ejpam-3483	445	19	be	be	AUX
ejpam-3483	445	20	bijective	bijective	ADJ
ejpam-3483	445	21	and	and	CCONJ
ejpam-3483	445	22	i	i	PROPN
ejpam-3483	445	23	-	-	PUNCT
ejpam-3483	445	24	supra	supra	PROPN
ejpam-3483	445	25	b	b	NOUN
ejpam-3483	445	26	-	-	PUNCT
ejpam-3483	445	27	continuous	continuous	ADJ
ejpam-3483	445	28	.	.	PUNCT
ejpam-3483	446	1	then	then	ADV
ejpam-3483	446	2	the	the	DET
ejpam-3483	446	3	following	follow	VERB
ejpam-3483	446	4	statements	statement	NOUN
ejpam-3483	446	5	are	be	AUX
ejpam-3483	446	6	equivalent	equivalent	ADJ
ejpam-3483	446	7	:	:	PUNCT
ejpam-3483	446	8	(	(	PUNCT
ejpam-3483	446	9	i	i	NOUN
ejpam-3483	446	10	)	)	PUNCT
ejpam-3483	446	11	f	f	PROPN
ejpam-3483	446	12	is	be	AUX
ejpam-3483	446	13	i	i	PROPN
ejpam-3483	446	14	-	-	PUNCT
ejpam-3483	446	15	supra	supra	PROPN
ejpam-3483	446	16	b	b	PROPN
ejpam-3483	446	17	-	-	PUNCT
ejpam-3483	446	18	homeomorphism	homeomorphism	X
ejpam-3483	446	19	;	;	PUNCT
ejpam-3483	446	20	(	(	PUNCT
ejpam-3483	446	21	ii	ii	X
ejpam-3483	446	22	)	)	PUNCT
ejpam-3483	446	23	f−1	f−1	PROPN
ejpam-3483	446	24	is	be	AUX
ejpam-3483	446	25	i	i	PROPN
ejpam-3483	446	26	-	-	PUNCT
ejpam-3483	446	27	supra	supra	PROPN
ejpam-3483	446	28	b	b	NOUN
ejpam-3483	446	29	-	-	NOUN
ejpam-3483	446	30	continuous	continuous	ADJ
ejpam-3483	446	31	;	;	PUNCT
ejpam-3483	446	32	(	(	PUNCT
ejpam-3483	446	33	iii	iii	X
ejpam-3483	446	34	)	)	PUNCT
ejpam-3483	446	35	f	f	PROPN
ejpam-3483	446	36	is	be	AUX
ejpam-3483	446	37	d	d	ADJ
ejpam-3483	446	38	-	-	PUNCT
ejpam-3483	446	39	supra	supra	ADJ
ejpam-3483	446	40	b	b	NOUN
ejpam-3483	446	41	-	-	PUNCT
ejpam-3483	446	42	closed	closed	ADJ
ejpam-3483	446	43	.	.	PUNCT
ejpam-3483	447	1	proof	proof	NOUN
ejpam-3483	447	2	.	.	PUNCT
ejpam-3483	448	1	(	(	PUNCT
ejpam-3483	448	2	i	i	NOUN
ejpam-3483	448	3	)	)	PUNCT
ejpam-3483	448	4	⇒	⇒	PROPN
ejpam-3483	448	5	(	(	PUNCT
ejpam-3483	448	6	ii	ii	PROPN
ejpam-3483	448	7	):	):	PUNCT
ejpam-3483	448	8	let	let	VERB
ejpam-3483	448	9	g	g	PRON
ejpam-3483	448	10	be	be	AUX
ejpam-3483	448	11	an	an	DET
ejpam-3483	448	12	open	open	ADJ
ejpam-3483	448	13	subset	subset	NOUN
ejpam-3483	448	14	of	of	ADP
ejpam-3483	448	15	x.	x.	NOUN
ejpam-3483	448	16	then	then	ADV
ejpam-3483	448	17	(	(	PUNCT
ejpam-3483	448	18	f−1)−1(g	f−1)−1(g	PROPN
ejpam-3483	448	19	)	)	PUNCT
ejpam-3483	448	20	=	=	SYM
ejpam-3483	448	21	f(g	f(g	NOUN
ejpam-3483	448	22	)	)	PUNCT
ejpam-3483	448	23	is	be	AUX
ejpam-3483	448	24	an	an	DET
ejpam-3483	448	25	i	i	PROPN
ejpam-3483	448	26	-	-	PUNCT
ejpam-3483	448	27	supra	supra	PROPN
ejpam-3483	448	28	b	b	NOUN
ejpam-3483	448	29	-	-	PUNCT
ejpam-3483	448	30	open	open	ADJ
ejpam-3483	448	31	set	set	NOUN
ejpam-3483	448	32	in	in	ADP
ejpam-3483	448	33	y	y	PROPN
ejpam-3483	448	34	.	.	PUNCT
ejpam-3483	449	1	therefore	therefore	ADV
ejpam-3483	449	2	f−1	f−1	PROPN
ejpam-3483	449	3	is	be	AUX
ejpam-3483	449	4	i	i	PROPN
ejpam-3483	449	5	-	-	PUNCT
ejpam-3483	449	6	supra	supra	PROPN
ejpam-3483	449	7	b	b	NOUN
ejpam-3483	449	8	-	-	PUNCT
ejpam-3483	449	9	continuous	continuous	ADJ
ejpam-3483	449	10	.	.	PUNCT
ejpam-3483	450	1	(	(	PUNCT
ejpam-3483	450	2	ii	ii	NOUN
ejpam-3483	450	3	)	)	PUNCT
ejpam-3483	450	4	⇒	⇒	NOUN
ejpam-3483	450	5	(	(	PUNCT
ejpam-3483	450	6	iii	iii	X
ejpam-3483	450	7	):	):	PUNCT
ejpam-3483	450	8	it	it	PRON
ejpam-3483	450	9	follows	follow	VERB
ejpam-3483	450	10	from	from	ADP
ejpam-3483	450	11	(	(	PUNCT
ejpam-3483	450	12	ii	ii	NOUN
ejpam-3483	450	13	)	)	PUNCT
ejpam-3483	450	14	of	of	ADP
ejpam-3483	450	15	theorem	theorem	NOUN
ejpam-3483	450	16	4.13	4.13	NUM
ejpam-3483	450	17	.	.	PUNCT
ejpam-3483	451	1	(	(	PUNCT
ejpam-3483	451	2	iii	iii	X
ejpam-3483	451	3	)	)	PUNCT
ejpam-3483	451	4	⇒	⇒	NOUN
ejpam-3483	451	5	(	(	PUNCT
ejpam-3483	451	6	i	i	NOUN
ejpam-3483	451	7	):	):	PUNCT
ejpam-3483	451	8	let	let	VERB
ejpam-3483	451	9	g	g	PRON
ejpam-3483	451	10	be	be	AUX
ejpam-3483	451	11	an	an	DET
ejpam-3483	451	12	open	open	ADJ
ejpam-3483	451	13	subset	subset	NOUN
ejpam-3483	451	14	of	of	ADP
ejpam-3483	451	15	x.	x.	PROPN
ejpam-3483	451	16	then	then	ADV
ejpam-3483	451	17	gc	gc	PROPN
ejpam-3483	451	18	is	be	AUX
ejpam-3483	451	19	a	a	DET
ejpam-3483	451	20	closed	closed	ADJ
ejpam-3483	451	21	set	set	NOUN
ejpam-3483	451	22	and	and	CCONJ
ejpam-3483	451	23	f(gc	f(gc	NOUN
ejpam-3483	451	24	)	)	PUNCT
ejpam-3483	451	25	=	=	SYM
ejpam-3483	452	1	(	(	PUNCT
ejpam-3483	452	2	f(g))c	f(g))c	PROPN
ejpam-3483	452	3	is	be	AUX
ejpam-3483	452	4	d	d	ADJ
ejpam-3483	452	5	-	-	ADJ
ejpam-3483	452	6	supra	supra	ADJ
ejpam-3483	452	7	b	b	NOUN
ejpam-3483	452	8	-	-	PUNCT
ejpam-3483	452	9	closed	closed	ADJ
ejpam-3483	452	10	.	.	PUNCT
ejpam-3483	453	1	therefore	therefore	ADV
ejpam-3483	453	2	f(g	f(g	PROPN
ejpam-3483	453	3	)	)	PUNCT
ejpam-3483	453	4	is	be	AUX
ejpam-3483	453	5	an	an	DET
ejpam-3483	453	6	i	i	PROPN
ejpam-3483	453	7	-	-	PUNCT
ejpam-3483	453	8	supra	supra	PROPN
ejpam-3483	453	9	b	b	NOUN
ejpam-3483	453	10	-	-	PUNCT
ejpam-3483	453	11	open	open	ADJ
ejpam-3483	453	12	subset	subset	NOUN
ejpam-3483	453	13	of	of	ADP
ejpam-3483	453	14	y	y	PROPN
ejpam-3483	453	15	.	.	PUNCT
ejpam-3483	454	1	thus	thus	ADV
ejpam-3483	454	2	f	f	PROPN
ejpam-3483	454	3	is	be	AUX
ejpam-3483	454	4	i	i	PROPN
ejpam-3483	454	5	-	-	PUNCT
ejpam-3483	454	6	supra	supra	PROPN
ejpam-3483	454	7	b	b	NOUN
ejpam-3483	454	8	-	-	PUNCT
ejpam-3483	454	9	open	open	ADJ
ejpam-3483	454	10	.	.	PUNCT
ejpam-3483	455	1	hence	hence	ADV
ejpam-3483	455	2	f	f	PROPN
ejpam-3483	455	3	is	be	AUX
ejpam-3483	455	4	an	an	DET
ejpam-3483	455	5	i	i	PROPN
ejpam-3483	455	6	-	-	PUNCT
ejpam-3483	455	7	supra	supra	PROPN
ejpam-3483	455	8	b	b	PROPN
ejpam-3483	455	9	-	-	PUNCT
ejpam-3483	455	10	homeomorphism	homeomorphism	PROPN
ejpam-3483	455	11	map	map	NOUN
ejpam-3483	455	12	.	.	PUNCT
ejpam-3483	456	1	the	the	DET
ejpam-3483	456	2	following	follow	VERB
ejpam-3483	456	3	two	two	NUM
ejpam-3483	456	4	results	result	NOUN
ejpam-3483	456	5	can	can	AUX
ejpam-3483	456	6	be	be	AUX
ejpam-3483	456	7	proved	prove	VERB
ejpam-3483	456	8	similarly	similarly	ADV
ejpam-3483	456	9	.	.	PUNCT
ejpam-3483	457	1	theorem	theorem	NOUN
ejpam-3483	457	2	24	24	NUM
ejpam-3483	457	3	.	.	PUNCT
ejpam-3483	458	1	let	let	VERB
ejpam-3483	458	2	a	a	DET
ejpam-3483	458	3	map	map	NOUN
ejpam-3483	458	4	f	f	X
ejpam-3483	458	5	:	:	PUNCT
ejpam-3483	458	6	(	(	PUNCT
ejpam-3483	458	7	x	x	X
ejpam-3483	458	8	,	,	PUNCT
ejpam-3483	458	9	τ,	τ,	NOUN
ejpam-3483	458	10	�	�	X
ejpam-3483	458	11	1)→	1)→	NUM
ejpam-3483	458	12	(	(	PUNCT
ejpam-3483	458	13	y	y	PROPN
ejpam-3483	458	14	,	,	PUNCT
ejpam-3483	458	15	θ,	θ,	NOUN
ejpam-3483	458	16	�	�	NOUN
ejpam-3483	458	17	2	2	NUM
ejpam-3483	458	18	)	)	PUNCT
ejpam-3483	458	19	be	be	AUX
ejpam-3483	458	20	bijective	bijective	ADJ
ejpam-3483	458	21	and	and	CCONJ
ejpam-3483	458	22	d	d	NOUN
ejpam-3483	458	23	-	-	ADJ
ejpam-3483	458	24	supra	supra	ADJ
ejpam-3483	459	1	b	b	NOUN
ejpam-3483	459	2	-	-	PUNCT
ejpam-3483	459	3	continuous	continuous	ADJ
ejpam-3483	459	4	.	.	PUNCT
ejpam-3483	460	1	then	then	ADV
ejpam-3483	460	2	the	the	DET
ejpam-3483	460	3	following	follow	VERB
ejpam-3483	460	4	statements	statement	NOUN
ejpam-3483	460	5	are	be	AUX
ejpam-3483	460	6	equivalent	equivalent	ADJ
ejpam-3483	460	7	:	:	PUNCT
ejpam-3483	460	8	(	(	PUNCT
ejpam-3483	460	9	i	i	NOUN
ejpam-3483	460	10	)	)	PUNCT
ejpam-3483	460	11	f	f	PROPN
ejpam-3483	460	12	is	be	AUX
ejpam-3483	460	13	d	d	ADJ
ejpam-3483	460	14	-	-	PUNCT
ejpam-3483	460	15	supra	supra	ADJ
ejpam-3483	460	16	b	b	NOUN
ejpam-3483	460	17	-	-	PUNCT
ejpam-3483	460	18	homeomorphism	homeomorphism	X
ejpam-3483	460	19	;	;	PUNCT
ejpam-3483	460	20	(	(	PUNCT
ejpam-3483	460	21	ii	ii	X
ejpam-3483	460	22	)	)	PUNCT
ejpam-3483	460	23	f−1	f−1	PROPN
ejpam-3483	460	24	is	be	AUX
ejpam-3483	460	25	d	d	ADJ
ejpam-3483	460	26	-	-	PUNCT
ejpam-3483	460	27	supra	supra	ADJ
ejpam-3483	460	28	b	b	NOUN
ejpam-3483	460	29	-	-	NOUN
ejpam-3483	460	30	continuous	continuous	ADJ
ejpam-3483	460	31	;	;	PUNCT
ejpam-3483	460	32	(	(	PUNCT
ejpam-3483	460	33	iii	iii	X
ejpam-3483	460	34	)	)	PUNCT
ejpam-3483	460	35	f	f	PROPN
ejpam-3483	460	36	is	be	AUX
ejpam-3483	460	37	i	i	PROPN
ejpam-3483	460	38	-	-	PUNCT
ejpam-3483	460	39	supra	supra	PROPN
ejpam-3483	460	40	b	b	PROPN
ejpam-3483	460	41	-	-	PUNCT
ejpam-3483	460	42	closed	closed	ADJ
ejpam-3483	460	43	.	.	PUNCT
ejpam-3483	461	1	theorem	theorem	VERB
ejpam-3483	461	2	25	25	NUM
ejpam-3483	461	3	.	.	PUNCT
ejpam-3483	462	1	let	let	VERB
ejpam-3483	462	2	a	a	DET
ejpam-3483	462	3	map	map	NOUN
ejpam-3483	462	4	f	f	X
ejpam-3483	462	5	:	:	PUNCT
ejpam-3483	462	6	(	(	PUNCT
ejpam-3483	462	7	x	x	X
ejpam-3483	462	8	,	,	PUNCT
ejpam-3483	462	9	τ,	τ,	NOUN
ejpam-3483	462	10	�	�	X
ejpam-3483	462	11	1)→	1)→	NUM
ejpam-3483	462	12	(	(	PUNCT
ejpam-3483	462	13	y	y	PROPN
ejpam-3483	462	14	,	,	PUNCT
ejpam-3483	462	15	θ,	θ,	NOUN
ejpam-3483	462	16	�	�	NOUN
ejpam-3483	462	17	2	2	NUM
ejpam-3483	462	18	)	)	PUNCT
ejpam-3483	462	19	be	be	AUX
ejpam-3483	462	20	bijective	bijective	ADJ
ejpam-3483	462	21	and	and	CCONJ
ejpam-3483	462	22	b	b	X
ejpam-3483	462	23	-	-	PUNCT
ejpam-3483	462	24	supra	supra	ADJ
ejpam-3483	463	1	b	b	NOUN
ejpam-3483	463	2	-	-	PUNCT
ejpam-3483	463	3	continuous	continuous	ADJ
ejpam-3483	463	4	.	.	PUNCT
ejpam-3483	464	1	then	then	ADV
ejpam-3483	464	2	the	the	DET
ejpam-3483	464	3	following	follow	VERB
ejpam-3483	464	4	statements	statement	NOUN
ejpam-3483	464	5	are	be	AUX
ejpam-3483	464	6	equivalent	equivalent	ADJ
ejpam-3483	464	7	:	:	PUNCT
ejpam-3483	464	8	(	(	PUNCT
ejpam-3483	464	9	i	i	NOUN
ejpam-3483	464	10	)	)	PUNCT
ejpam-3483	464	11	f	f	PROPN
ejpam-3483	464	12	is	be	AUX
ejpam-3483	464	13	b	b	NOUN
ejpam-3483	464	14	-	-	PUNCT
ejpam-3483	464	15	supra	supra	ADJ
ejpam-3483	464	16	b	b	NOUN
ejpam-3483	464	17	-	-	PUNCT
ejpam-3483	464	18	homeomorphism	homeomorphism	X
ejpam-3483	464	19	;	;	PUNCT
ejpam-3483	464	20	(	(	PUNCT
ejpam-3483	464	21	ii	ii	X
ejpam-3483	464	22	)	)	PUNCT
ejpam-3483	464	23	f−1	f−1	PROPN
ejpam-3483	464	24	is	be	AUX
ejpam-3483	464	25	b	b	NOUN
ejpam-3483	464	26	-	-	PUNCT
ejpam-3483	464	27	supra	supra	ADJ
ejpam-3483	464	28	b	b	NOUN
ejpam-3483	464	29	-	-	NOUN
ejpam-3483	464	30	continuous	continuous	ADJ
ejpam-3483	464	31	;	;	PUNCT
ejpam-3483	464	32	(	(	PUNCT
ejpam-3483	464	33	iii	iii	X
ejpam-3483	464	34	)	)	PUNCT
ejpam-3483	464	35	f	f	PROPN
ejpam-3483	464	36	is	be	AUX
ejpam-3483	464	37	b	b	NOUN
ejpam-3483	464	38	-	-	PUNCT
ejpam-3483	464	39	supra	supra	ADJ
ejpam-3483	464	40	b	b	NOUN
ejpam-3483	464	41	-	-	PUNCT
ejpam-3483	464	42	closed	closed	ADJ
ejpam-3483	464	43	.	.	PUNCT
ejpam-3483	465	1	theorem	theorem	NOUN
ejpam-3483	465	2	26	26	NUM
ejpam-3483	465	3	.	.	PUNCT
ejpam-3483	466	1	let	let	VERB
ejpam-3483	466	2	f	f	NOUN
ejpam-3483	466	3	:	:	PUNCT
ejpam-3483	466	4	(	(	PUNCT
ejpam-3483	466	5	x	x	X
ejpam-3483	466	6	,	,	PUNCT
ejpam-3483	466	7	τ,	τ,	NOUN
ejpam-3483	466	8	�	�	X
ejpam-3483	466	9	1)→	1)→	NUM
ejpam-3483	466	10	(	(	PUNCT
ejpam-3483	466	11	y	y	PROPN
ejpam-3483	466	12	,	,	PUNCT
ejpam-3483	466	13	θ,	θ,	NOUN
ejpam-3483	466	14	�	�	NOUN
ejpam-3483	466	15	2	2	NUM
ejpam-3483	466	16	)	)	PUNCT
ejpam-3483	466	17	be	be	AUX
ejpam-3483	466	18	a	a	DET
ejpam-3483	466	19	supra	supra	PROPN
ejpam-3483	466	20	b	b	PROPN
ejpam-3483	466	21	-	-	PUNCT
ejpam-3483	466	22	homeomorphism	homeomorphism	PROPN
ejpam-3483	466	23	map	map	NOUN
ejpam-3483	466	24	such	such	ADJ
ejpam-3483	466	25	that	that	SCONJ
ejpam-3483	466	26	f	f	PROPN
ejpam-3483	466	27	and	and	CCONJ
ejpam-3483	466	28	f−1	f−1	PROPN
ejpam-3483	466	29	are	be	AUX
ejpam-3483	466	30	order	order	NOUN
ejpam-3483	466	31	preserving	preserve	VERB
ejpam-3483	466	32	.	.	PUNCT
ejpam-3483	467	1	if	if	SCONJ
ejpam-3483	467	2	x	x	X
ejpam-3483	467	3	(	(	PUNCT
ejpam-3483	467	4	resp	resp	NOUN
ejpam-3483	467	5	.	.	PUNCT
ejpam-3483	468	1	y	y	PROPN
ejpam-3483	468	2	)	)	PUNCT
ejpam-3483	468	3	is	be	AUX
ejpam-3483	468	4	strong	strong	ADJ
ejpam-3483	468	5	ti	ti	ADJ
ejpam-3483	468	6	-	-	ADJ
ejpam-3483	468	7	ordered	order	VERB
ejpam-3483	468	8	,	,	PUNCT
ejpam-3483	468	9	then	then	ADV
ejpam-3483	468	10	y	y	PROPN
ejpam-3483	468	11	(	(	PUNCT
ejpam-3483	468	12	resp	resp	PROPN
ejpam-3483	468	13	.	.	PUNCT
ejpam-3483	469	1	x	x	X
ejpam-3483	469	2	)	)	PUNCT
ejpam-3483	469	3	is	be	AUX
ejpam-3483	469	4	ssbti	ssbti	NOUN
ejpam-3483	469	5	-	-	PUNCT
ejpam-3483	469	6	ordered	order	VERB
ejpam-3483	469	7	for	for	ADP
ejpam-3483	469	8	i	i	PROPN
ejpam-3483	469	9	=	=	SYM
ejpam-3483	469	10	0	0	NUM
ejpam-3483	469	11	,	,	PUNCT
ejpam-3483	469	12	1	1	NUM
ejpam-3483	469	13	,	,	PUNCT
ejpam-3483	469	14	2	2	NUM
ejpam-3483	469	15	.	.	PUNCT
ejpam-3483	469	16	references	reference	NOUN
ejpam-3483	469	17	1245	1245	NUM
ejpam-3483	469	18	proof	proof	NOUN
ejpam-3483	469	19	.	.	PUNCT
ejpam-3483	470	1	(	(	PUNCT
ejpam-3483	470	2	i	i	NOUN
ejpam-3483	470	3	)	)	PUNCT
ejpam-3483	470	4	let	let	VERB
ejpam-3483	470	5	x	x	PRON
ejpam-3483	470	6	be	be	AUX
ejpam-3483	470	7	a	a	DET
ejpam-3483	470	8	strong	strong	ADJ
ejpam-3483	470	9	ti	ti	ADJ
ejpam-3483	470	10	-	-	ADJ
ejpam-3483	470	11	ordered	order	VERB
ejpam-3483	470	12	space	space	NOUN
ejpam-3483	470	13	,	,	PUNCT
ejpam-3483	470	14	then	then	ADV
ejpam-3483	470	15	by	by	ADP
ejpam-3483	470	16	theorem	theorem	NOUN
ejpam-3483	470	17	21	21	NUM
ejpam-3483	470	18	,	,	PUNCT
ejpam-3483	470	19	y	y	PROPN
ejpam-3483	470	20	is	be	AUX
ejpam-3483	470	21	an	an	DET
ejpam-3483	470	22	ssbti	ssbti	NOUN
ejpam-3483	470	23	-	-	PUNCT
ejpam-3483	470	24	ordered	order	VERB
ejpam-3483	470	25	space	space	NOUN
ejpam-3483	470	26	for	for	ADP
ejpam-3483	470	27	i	i	PROPN
ejpam-3483	470	28	=	=	SYM
ejpam-3483	470	29	0	0	NUM
ejpam-3483	470	30	,	,	PUNCT
ejpam-3483	470	31	1	1	NUM
ejpam-3483	470	32	,	,	PUNCT
ejpam-3483	470	33	2	2	NUM
ejpam-3483	470	34	.	.	PUNCT
ejpam-3483	470	35	(	(	PUNCT
ejpam-3483	470	36	ii	ii	NOUN
ejpam-3483	470	37	)	)	PUNCT
ejpam-3483	470	38	let	let	VERB
ejpam-3483	470	39	y	y	PRON
ejpam-3483	470	40	be	be	AUX
ejpam-3483	470	41	a	a	DET
ejpam-3483	470	42	strong	strong	ADJ
ejpam-3483	470	43	ti	ti	ADJ
ejpam-3483	470	44	-	-	ADJ
ejpam-3483	470	45	ordered	order	VERB
ejpam-3483	470	46	space	space	NOUN
ejpam-3483	470	47	,	,	PUNCT
ejpam-3483	470	48	then	then	ADV
ejpam-3483	470	49	by	by	ADP
ejpam-3483	470	50	theorem	theorem	NOUN
ejpam-3483	470	51	8	8	NUM
ejpam-3483	470	52	,	,	PUNCT
ejpam-3483	470	53	x	x	X
ejpam-3483	470	54	is	be	AUX
ejpam-3483	470	55	an	an	DET
ejpam-3483	470	56	ssbti	ssbti	NOUN
ejpam-3483	470	57	-	-	PUNCT
ejpam-3483	470	58	ordered	order	VERB
ejpam-3483	470	59	space	space	NOUN
ejpam-3483	470	60	for	for	ADP
ejpam-3483	470	61	i	i	PROPN
ejpam-3483	470	62	=	=	SYM
ejpam-3483	470	63	0	0	NUM
ejpam-3483	470	64	,	,	PUNCT
ejpam-3483	470	65	1	1	NUM
ejpam-3483	470	66	,	,	PUNCT
ejpam-3483	470	67	2	2	NUM
ejpam-3483	470	68	.	.	NOUN
ejpam-3483	470	69	6	6	NUM
ejpam-3483	470	70	.	.	X
ejpam-3483	470	71	conclusion	conclusion	NOUN
ejpam-3483	470	72	in	in	ADP
ejpam-3483	470	73	the	the	DET
ejpam-3483	470	74	present	present	ADJ
ejpam-3483	470	75	paper	paper	NOUN
ejpam-3483	470	76	,	,	PUNCT
ejpam-3483	471	1	the	the	DET
ejpam-3483	471	2	concepts	concept	NOUN
ejpam-3483	471	3	of	of	ADP
ejpam-3483	471	4	i	i	PROPN
ejpam-3483	471	5	-	-	PUNCT
ejpam-3483	471	6	supra	supra	PROPN
ejpam-3483	471	7	b	b	NOUN
ejpam-3483	471	8	-	-	PUNCT
ejpam-3483	471	9	continuous	continuous	ADJ
ejpam-3483	471	10	(	(	PUNCT
ejpam-3483	471	11	i	i	NOUN
ejpam-3483	471	12	-	-	PUNCT
ejpam-3483	471	13	supra	supra	PROPN
ejpam-3483	471	14	b	b	NOUN
ejpam-3483	471	15	-	-	PUNCT
ejpam-3483	471	16	open	open	ADJ
ejpam-3483	471	17	,	,	PUNCT
ejpam-3483	471	18	i	i	PROPN
ejpam-3483	471	19	-	-	PUNCT
ejpam-3483	471	20	supra	supra	PROPN
ejpam-3483	471	21	bclosed	bclose	VERB
ejpam-3483	471	22	,	,	PUNCT
ejpam-3483	471	23	i	i	PROPN
ejpam-3483	471	24	-	-	PUNCT
ejpam-3483	471	25	supra	supra	PROPN
ejpam-3483	471	26	b	b	PROPN
ejpam-3483	471	27	-	-	PUNCT
ejpam-3483	471	28	homeomorphism	homeomorphism	ADJ
ejpam-3483	471	29	)	)	PUNCT
ejpam-3483	471	30	maps	map	NOUN
ejpam-3483	471	31	,	,	PUNCT
ejpam-3483	471	32	d	d	X
ejpam-3483	471	33	-	-	PUNCT
ejpam-3483	471	34	supra	supra	ADJ
ejpam-3483	471	35	b	b	NOUN
ejpam-3483	471	36	-	-	ADJ
ejpam-3483	471	37	continuous	continuous	ADJ
ejpam-3483	471	38	(	(	PUNCT
ejpam-3483	471	39	d	d	NOUN
ejpam-3483	471	40	-	-	ADJ
ejpam-3483	471	41	supra	supra	ADJ
ejpam-3483	471	42	b	b	NOUN
ejpam-3483	471	43	-	-	PUNCT
ejpam-3483	471	44	open	open	ADJ
ejpam-3483	471	45	,	,	PUNCT
ejpam-3483	471	46	d	d	ADJ
ejpam-3483	471	47	-	-	PUNCT
ejpam-3483	471	48	supra	supra	ADJ
ejpam-3483	471	49	b	b	NOUN
ejpam-3483	471	50	-	-	PUNCT
ejpam-3483	471	51	closed	closed	ADJ
ejpam-3483	471	52	,	,	PUNCT
ejpam-3483	471	53	d	d	ADJ
ejpam-3483	471	54	-	-	PUNCT
ejpam-3483	471	55	supra	supra	ADJ
ejpam-3483	471	56	b	b	NOUN
ejpam-3483	471	57	-	-	PUNCT
ejpam-3483	471	58	homeomorphism	homeomorphism	ADJ
ejpam-3483	471	59	)	)	PUNCT
ejpam-3483	471	60	maps	map	NOUN
ejpam-3483	471	61	and	and	CCONJ
ejpam-3483	471	62	b	b	X
ejpam-3483	471	63	-	-	PUNCT
ejpam-3483	471	64	supra	supra	ADJ
ejpam-3483	471	65	b	b	NOUN
ejpam-3483	471	66	-	-	PUNCT
ejpam-3483	471	67	continuous	continuous	ADJ
ejpam-3483	471	68	(	(	PUNCT
ejpam-3483	471	69	b	b	NOUN
ejpam-3483	471	70	-	-	PUNCT
ejpam-3483	471	71	supra	supra	ADJ
ejpam-3483	471	72	b	b	NOUN
ejpam-3483	471	73	-	-	PUNCT
ejpam-3483	471	74	open	open	ADJ
ejpam-3483	471	75	,	,	PUNCT
ejpam-3483	471	76	bsupra	bsupra	ADJ
ejpam-3483	471	77	b	b	PROPN
ejpam-3483	471	78	-	-	PUNCT
ejpam-3483	471	79	closed	closed	ADJ
ejpam-3483	471	80	,	,	PUNCT
ejpam-3483	471	81	b	b	X
ejpam-3483	471	82	-	-	PUNCT
ejpam-3483	471	83	supra	supra	ADJ
ejpam-3483	471	84	b	b	NOUN
ejpam-3483	471	85	-	-	PUNCT
ejpam-3483	471	86	homeomorphism	homeomorphism	ADJ
ejpam-3483	471	87	)	)	PUNCT
ejpam-3483	471	88	maps	map	NOUN
ejpam-3483	471	89	are	be	AUX
ejpam-3483	471	90	given	give	VERB
ejpam-3483	471	91	and	and	CCONJ
ejpam-3483	471	92	studied	study	VERB
ejpam-3483	471	93	.	.	PUNCT
ejpam-3483	472	1	the	the	DET
ejpam-3483	472	2	equivalent	equivalent	ADJ
ejpam-3483	472	3	conditions	condition	NOUN
ejpam-3483	472	4	for	for	ADP
ejpam-3483	472	5	the	the	DET
ejpam-3483	472	6	concepts	concept	NOUN
ejpam-3483	472	7	given	give	VERB
ejpam-3483	472	8	herein	herein	NOUN
ejpam-3483	472	9	are	be	AUX
ejpam-3483	472	10	presented	present	VERB
ejpam-3483	472	11	and	and	CCONJ
ejpam-3483	472	12	the	the	DET
ejpam-3483	472	13	relationships	relationship	NOUN
ejpam-3483	472	14	among	among	ADP
ejpam-3483	472	15	them	they	PRON
ejpam-3483	472	16	are	be	AUX
ejpam-3483	472	17	showed	show	VERB
ejpam-3483	472	18	with	with	ADP
ejpam-3483	472	19	the	the	DET
ejpam-3483	472	20	help	help	NOUN
ejpam-3483	472	21	of	of	ADP
ejpam-3483	472	22	illustrative	illustrative	ADJ
ejpam-3483	472	23	examples	example	NOUN
ejpam-3483	472	24	.	.	PUNCT
ejpam-3483	473	1	the	the	DET
ejpam-3483	473	2	sufficient	sufficient	ADJ
ejpam-3483	473	3	conditions	condition	NOUN
ejpam-3483	473	4	for	for	SCONJ
ejpam-3483	473	5	maps	map	NOUN
ejpam-3483	473	6	to	to	PART
ejpam-3483	473	7	preserve	preserve	VERB
ejpam-3483	473	8	some	some	DET
ejpam-3483	473	9	separation	separation	NOUN
ejpam-3483	473	10	axioms	axiom	NOUN
ejpam-3483	473	11	which	which	PRON
ejpam-3483	473	12	introduced	introduce	VERB
ejpam-3483	473	13	in	in	ADP
ejpam-3483	473	14	[	[	X
ejpam-3483	473	15	16	16	NUM
ejpam-3483	473	16	,	,	PUNCT
ejpam-3483	473	17	20	20	NUM
ejpam-3483	473	18	,	,	PUNCT
ejpam-3483	473	19	25	25	NUM
ejpam-3483	473	20	]	]	PUNCT
ejpam-3483	473	21	are	be	AUX
ejpam-3483	473	22	demonstrated	demonstrate	VERB
ejpam-3483	473	23	.	.	PUNCT
ejpam-3483	474	1	in	in	ADP
ejpam-3483	474	2	the	the	DET
ejpam-3483	474	3	next	next	ADJ
ejpam-3483	474	4	work	work	NOUN
ejpam-3483	474	5	,	,	PUNCT
ejpam-3483	474	6	we	we	PRON
ejpam-3483	474	7	plan	plan	VERB
ejpam-3483	474	8	to	to	PART
ejpam-3483	474	9	use	use	VERB
ejpam-3483	474	10	a	a	DET
ejpam-3483	474	11	notion	notion	NOUN
ejpam-3483	474	12	of	of	ADP
ejpam-3483	474	13	somewhere	somewhere	ADJ
ejpam-3483	474	14	dense	dense	ADJ
ejpam-3483	474	15	sets	set	NOUN
ejpam-3483	474	16	[	[	X
ejpam-3483	474	17	4	4	NUM
ejpam-3483	474	18	,	,	PUNCT
ejpam-3483	474	19	14	14	NUM
ejpam-3483	474	20	]	]	PUNCT
ejpam-3483	474	21	to	to	PART
ejpam-3483	474	22	define	define	VERB
ejpam-3483	474	23	various	various	ADJ
ejpam-3483	474	24	kinds	kind	NOUN
ejpam-3483	474	25	of	of	ADP
ejpam-3483	474	26	maps	map	NOUN
ejpam-3483	474	27	in	in	ADP
ejpam-3483	474	28	topological	topological	ADJ
ejpam-3483	474	29	ordered	order	VERB
ejpam-3483	474	30	spaces	space	NOUN
ejpam-3483	474	31	.	.	PUNCT
ejpam-3483	475	1	conflict	conflict	NOUN
ejpam-3483	475	2	of	of	ADP
ejpam-3483	475	3	interest	interest	NOUN
ejpam-3483	475	4	the	the	DET
ejpam-3483	475	5	authors	author	NOUN
ejpam-3483	475	6	declare	declare	VERB
ejpam-3483	475	7	that	that	SCONJ
ejpam-3483	475	8	there	there	PRON
ejpam-3483	475	9	is	be	VERB
ejpam-3483	475	10	no	no	DET
ejpam-3483	475	11	conflict	conflict	NOUN
ejpam-3483	475	12	of	of	ADP
ejpam-3483	475	13	interest	interest	NOUN
ejpam-3483	475	14	regarding	regard	VERB
ejpam-3483	475	15	the	the	DET
ejpam-3483	475	16	publication	publication	NOUN
ejpam-3483	475	17	of	of	ADP
ejpam-3483	475	18	this	this	DET
ejpam-3483	475	19	paper	paper	NOUN
ejpam-3483	475	20	.	.	PUNCT
ejpam-3483	476	1	acknowledgements	acknowledgement	NOUN
ejpam-3483	476	2	the	the	DET
ejpam-3483	476	3	authors	author	NOUN
ejpam-3483	476	4	would	would	AUX
ejpam-3483	476	5	like	like	VERB
ejpam-3483	476	6	to	to	PART
ejpam-3483	476	7	thank	thank	VERB
ejpam-3483	476	8	the	the	DET
ejpam-3483	476	9	reviewers	reviewer	NOUN
ejpam-3483	476	10	for	for	ADP
ejpam-3483	476	11	their	their	PRON
ejpam-3483	476	12	valuable	valuable	ADJ
ejpam-3483	476	13	comments	comment	NOUN
ejpam-3483	476	14	which	which	PRON
ejpam-3483	476	15	improved	improve	VERB
ejpam-3483	476	16	the	the	DET
ejpam-3483	476	17	presentation	presentation	NOUN
ejpam-3483	476	18	of	of	ADP
ejpam-3483	476	19	this	this	DET
ejpam-3483	476	20	paper	paper	NOUN
ejpam-3483	476	21	.	.	PUNCT
ejpam-3483	477	1	references	reference	NOUN
ejpam-3483	477	2	[	[	X
ejpam-3483	477	3	1	1	NUM
ejpam-3483	477	4	]	]	PUNCT
ejpam-3483	477	5	m.	m.	NOUN
ejpam-3483	477	6	abo	abo	NOUN
ejpam-3483	477	7	-	-	PUNCT
ejpam-3483	477	8	elhamayel	elhamayel	NOUN
ejpam-3483	477	9	and	and	CCONJ
ejpam-3483	477	10	t.	t.	PROPN
ejpam-3483	477	11	m.	m.	PROPN
ejpam-3483	477	12	al	al	PROPN
ejpam-3483	477	13	-	-	PUNCT
ejpam-3483	477	14	shami	shami	PROPN
ejpam-3483	477	15	,	,	PUNCT
ejpam-3483	477	16	supra	supra	PROPN
ejpam-3483	477	17	homeomorphism	homeomorphism	PROPN
ejpam-3483	477	18	in	in	ADP
ejpam-3483	477	19	supra	supra	PROPN
ejpam-3483	477	20	topological	topological	PROPN
ejpam-3483	477	21	ordered	order	VERB
ejpam-3483	477	22	spaces	space	NOUN
ejpam-3483	477	23	,	,	PUNCT
ejpam-3483	477	24	facta	facta	PROPN
ejpam-3483	477	25	universitatis	universitatis	PROPN
ejpam-3483	477	26	,	,	PUNCT
ejpam-3483	477	27	series	series	NOUN
ejpam-3483	477	28	:	:	PUNCT
ejpam-3483	477	29	mathematics	mathematic	NOUN
ejpam-3483	477	30	and	and	CCONJ
ejpam-3483	477	31	informatics	informatic	NOUN
ejpam-3483	477	32	,	,	PUNCT
ejpam-3483	477	33	31	31	NUM
ejpam-3483	477	34	(	(	PUNCT
ejpam-3483	477	35	5	5	NUM
ejpam-3483	477	36	)	)	PUNCT
ejpam-3483	477	37	(	(	PUNCT
ejpam-3483	477	38	2016	2016	NUM
ejpam-3483	477	39	)	)	PUNCT
ejpam-3483	477	40	1091	1091	NUM
ejpam-3483	477	41	-	-	SYM
ejpam-3483	477	42	1106	1106	NUM
ejpam-3483	478	1	[	[	X
ejpam-3483	478	2	2	2	NUM
ejpam-3483	478	3	]	]	PUNCT
ejpam-3483	478	4	t.	t.	PROPN
ejpam-3483	478	5	m.	m.	PROPN
ejpam-3483	478	6	al	al	PROPN
ejpam-3483	478	7	-	-	PUNCT
ejpam-3483	478	8	shami	shami	PROPN
ejpam-3483	478	9	,	,	PUNCT
ejpam-3483	478	10	some	some	DET
ejpam-3483	478	11	results	result	NOUN
ejpam-3483	478	12	related	relate	VERB
ejpam-3483	478	13	to	to	ADP
ejpam-3483	478	14	supra	supra	PROPN
ejpam-3483	478	15	topological	topological	ADJ
ejpam-3483	478	16	spaces	space	NOUN
ejpam-3483	478	17	,	,	PUNCT
ejpam-3483	478	18	journal	journal	NOUN
ejpam-3483	478	19	of	of	ADP
ejpam-3483	478	20	advanced	advanced	ADJ
ejpam-3483	478	21	studies	study	NOUN
ejpam-3483	478	22	in	in	ADP
ejpam-3483	478	23	topology	topology	NOUN
ejpam-3483	478	24	,	,	PUNCT
ejpam-3483	478	25	7	7	NUM
ejpam-3483	478	26	(	(	PUNCT
ejpam-3483	478	27	4	4	NUM
ejpam-3483	478	28	)	)	PUNCT
ejpam-3483	478	29	(	(	PUNCT
ejpam-3483	478	30	2016	2016	NUM
ejpam-3483	478	31	)	)	PUNCT
ejpam-3483	478	32	283	283	NUM
ejpam-3483	478	33	-	-	SYM
ejpam-3483	478	34	294	294	NUM
ejpam-3483	479	1	[	[	X
ejpam-3483	479	2	3	3	X
ejpam-3483	479	3	]	]	PUNCT
ejpam-3483	479	4	t.	t.	PROPN
ejpam-3483	479	5	m.	m.	PROPN
ejpam-3483	479	6	al	al	PROPN
ejpam-3483	479	7	-	-	PUNCT
ejpam-3483	479	8	shami	shami	PROPN
ejpam-3483	479	9	,	,	PUNCT
ejpam-3483	479	10	on	on	ADP
ejpam-3483	479	11	supra	supra	PROPN
ejpam-3483	479	12	semi	semi	ADV
ejpam-3483	479	13	open	open	ADJ
ejpam-3483	479	14	sets	set	NOUN
ejpam-3483	479	15	and	and	CCONJ
ejpam-3483	479	16	some	some	DET
ejpam-3483	479	17	applications	application	NOUN
ejpam-3483	479	18	on	on	ADP
ejpam-3483	479	19	topological	topological	ADJ
ejpam-3483	479	20	spaces	space	NOUN
ejpam-3483	479	21	,	,	PUNCT
ejpam-3483	479	22	journal	journal	NOUN
ejpam-3483	479	23	of	of	ADP
ejpam-3483	479	24	advanced	advanced	ADJ
ejpam-3483	479	25	studies	study	NOUN
ejpam-3483	479	26	in	in	ADP
ejpam-3483	479	27	topology	topology	NOUN
ejpam-3483	479	28	,	,	PUNCT
ejpam-3483	479	29	8	8	NUM
ejpam-3483	479	30	(	(	PUNCT
ejpam-3483	479	31	2	2	NUM
ejpam-3483	479	32	)	)	PUNCT
ejpam-3483	479	33	(	(	PUNCT
ejpam-3483	479	34	2017	2017	NUM
ejpam-3483	479	35	)	)	PUNCT
ejpam-3483	479	36	144	144	NUM
ejpam-3483	479	37	-	-	SYM
ejpam-3483	479	38	153	153	NUM
ejpam-3483	480	1	[	[	X
ejpam-3483	480	2	4	4	NUM
ejpam-3483	480	3	]	]	PUNCT
ejpam-3483	480	4	t.	t.	PROPN
ejpam-3483	480	5	m.	m.	PROPN
ejpam-3483	480	6	al	al	PROPN
ejpam-3483	480	7	-	-	PUNCT
ejpam-3483	480	8	shami	shami	PROPN
ejpam-3483	480	9	,	,	PUNCT
ejpam-3483	480	10	somewhere	somewhere	ADV
ejpam-3483	480	11	dense	dense	ADJ
ejpam-3483	480	12	sets	set	NOUN
ejpam-3483	480	13	and	and	CCONJ
ejpam-3483	480	14	st1	st1	PROPN
ejpam-3483	480	15	-	-	PUNCT
ejpam-3483	480	16	spaces	spaces	PROPN
ejpam-3483	480	17	,	,	PUNCT
ejpam-3483	480	18	punjab	punjab	PROPN
ejpam-3483	480	19	university	university	NOUN
ejpam-3483	480	20	journal	journal	NOUN
ejpam-3483	480	21	of	of	ADP
ejpam-3483	480	22	mathematics	mathematic	NOUN
ejpam-3483	480	23	,	,	PUNCT
ejpam-3483	480	24	49	49	NUM
ejpam-3483	480	25	(	(	PUNCT
ejpam-3483	480	26	2	2	NUM
ejpam-3483	480	27	)	)	PUNCT
ejpam-3483	480	28	(	(	PUNCT
ejpam-3483	480	29	2017	2017	NUM
ejpam-3483	480	30	)	)	PUNCT
ejpam-3483	480	31	101	101	NUM
ejpam-3483	480	32	-	-	PUNCT
ejpam-3483	480	33	111	111	NUM
ejpam-3483	480	34	references	reference	NOUN
ejpam-3483	480	35	1246	1246	NUM
ejpam-3483	480	36	[	[	X
ejpam-3483	480	37	5	5	X
ejpam-3483	480	38	]	]	PUNCT
ejpam-3483	480	39	t.	t.	PROPN
ejpam-3483	480	40	m.	m.	PROPN
ejpam-3483	480	41	al	al	PROPN
ejpam-3483	480	42	-	-	PUNCT
ejpam-3483	480	43	shami	shami	PROPN
ejpam-3483	480	44	,	,	PUNCT
ejpam-3483	480	45	supra	supra	PROPN
ejpam-3483	480	46	β	β	NOUN
ejpam-3483	480	47	-	-	ADJ
ejpam-3483	480	48	bicontinuous	bicontinuous	ADJ
ejpam-3483	480	49	maps	map	NOUN
ejpam-3483	480	50	via	via	ADP
ejpam-3483	480	51	topological	topological	ADJ
ejpam-3483	480	52	ordered	order	VERB
ejpam-3483	480	53	spaces	space	NOUN
ejpam-3483	480	54	,	,	PUNCT
ejpam-3483	480	55	mathematical	mathematical	ADJ
ejpam-3483	480	56	sciences	science	NOUN
ejpam-3483	480	57	letters	letter	NOUN
ejpam-3483	480	58	,	,	PUNCT
ejpam-3483	480	59	6	6	NUM
ejpam-3483	480	60	(	(	PUNCT
ejpam-3483	480	61	3	3	NUM
ejpam-3483	480	62	)	)	PUNCT
ejpam-3483	480	63	(	(	PUNCT
ejpam-3483	480	64	2017	2017	NUM
ejpam-3483	480	65	)	)	PUNCT
ejpam-3483	480	66	239	239	NUM
ejpam-3483	480	67	-	-	SYM
ejpam-3483	480	68	247	247	NUM
ejpam-3483	480	69	[	[	SYM
ejpam-3483	480	70	6	6	NUM
ejpam-3483	480	71	]	]	PUNCT
ejpam-3483	480	72	t.	t.	PROPN
ejpam-3483	480	73	m.	m.	PROPN
ejpam-3483	480	74	al	al	PROPN
ejpam-3483	480	75	-	-	PUNCT
ejpam-3483	480	76	shami	shami	PROPN
ejpam-3483	480	77	,	,	PUNCT
ejpam-3483	480	78	utilizing	utilize	VERB
ejpam-3483	480	79	supra	supra	PROPN
ejpam-3483	480	80	α	α	PROPN
ejpam-3483	480	81	-	-	ADJ
ejpam-3483	480	82	open	open	ADJ
ejpam-3483	480	83	sets	set	NOUN
ejpam-3483	480	84	to	to	PART
ejpam-3483	480	85	generate	generate	VERB
ejpam-3483	480	86	new	new	ADJ
ejpam-3483	480	87	types	type	NOUN
ejpam-3483	480	88	of	of	ADP
ejpam-3483	480	89	supra	supra	ADJ
ejpam-3483	480	90	compact	compact	ADJ
ejpam-3483	480	91	and	and	CCONJ
ejpam-3483	480	92	supra	supra	ADJ
ejpam-3483	480	93	lindelöf	lindelöf	PROPN
ejpam-3483	480	94	spaces	space	NOUN
ejpam-3483	480	95	,	,	PUNCT
ejpam-3483	480	96	facta	facta	PROPN
ejpam-3483	480	97	universitatis	universitatis	PROPN
ejpam-3483	480	98	,	,	PUNCT
ejpam-3483	480	99	series	series	NOUN
ejpam-3483	480	100	:	:	PUNCT
ejpam-3483	480	101	mathematics	mathematic	NOUN
ejpam-3483	480	102	and	and	CCONJ
ejpam-3483	480	103	informatics	informatic	NOUN
ejpam-3483	480	104	,	,	PUNCT
ejpam-3483	480	105	32	32	NUM
ejpam-3483	480	106	(	(	PUNCT
ejpam-3483	480	107	1	1	NUM
ejpam-3483	480	108	)	)	PUNCT
ejpam-3483	480	109	(	(	PUNCT
ejpam-3483	480	110	2017	2017	NUM
ejpam-3483	480	111	)	)	PUNCT
ejpam-3483	480	112	151	151	NUM
ejpam-3483	480	113	-	-	SYM
ejpam-3483	480	114	162	162	NUM
ejpam-3483	481	1	[	[	X
ejpam-3483	481	2	7	7	X
ejpam-3483	481	3	]	]	PUNCT
ejpam-3483	481	4	t.	t.	PROPN
ejpam-3483	481	5	m.	m.	PROPN
ejpam-3483	481	6	al	al	PROPN
ejpam-3483	481	7	-	-	PUNCT
ejpam-3483	481	8	shami	shami	PROPN
ejpam-3483	481	9	,	,	PUNCT
ejpam-3483	481	10	on	on	ADP
ejpam-3483	481	11	some	some	DET
ejpam-3483	481	12	maps	map	NOUN
ejpam-3483	481	13	in	in	ADP
ejpam-3483	481	14	supra	supra	PROPN
ejpam-3483	481	15	topological	topological	PROPN
ejpam-3483	481	16	ordered	order	VERB
ejpam-3483	481	17	spaces	space	NOUN
ejpam-3483	481	18	,	,	PUNCT
ejpam-3483	481	19	journal	journal	NOUN
ejpam-3483	481	20	of	of	ADP
ejpam-3483	481	21	new	new	ADJ
ejpam-3483	481	22	theory	theory	NOUN
ejpam-3483	481	23	,	,	PUNCT
ejpam-3483	481	24	20	20	NUM
ejpam-3483	481	25	(	(	PUNCT
ejpam-3483	481	26	2018	2018	NUM
ejpam-3483	481	27	)	)	PUNCT
ejpam-3483	481	28	76	76	NUM
ejpam-3483	481	29	-	-	SYM
ejpam-3483	481	30	92	92	NUM
ejpam-3483	482	1	[	[	SYM
ejpam-3483	482	2	8	8	NUM
ejpam-3483	482	3	]	]	PUNCT
ejpam-3483	482	4	t.	t.	PROPN
ejpam-3483	482	5	m.	m.	PROPN
ejpam-3483	482	6	al	al	PROPN
ejpam-3483	482	7	-	-	PUNCT
ejpam-3483	482	8	shami	shami	PROPN
ejpam-3483	482	9	,	,	PUNCT
ejpam-3483	482	10	supra	supra	ADJ
ejpam-3483	482	11	semi	semi	NOUN
ejpam-3483	482	12	-	-	NOUN
ejpam-3483	482	13	compactness	compactness	NOUN
ejpam-3483	482	14	via	via	ADP
ejpam-3483	482	15	supra	supra	PROPN
ejpam-3483	482	16	topological	topological	PROPN
ejpam-3483	482	17	spaces	space	NOUN
ejpam-3483	482	18	,	,	PUNCT
ejpam-3483	482	19	journal	journal	NOUN
ejpam-3483	482	20	of	of	ADP
ejpam-3483	482	21	taibah	taibah	PROPN
ejpam-3483	482	22	university	university	PROPN
ejpam-3483	482	23	for	for	ADP
ejpam-3483	482	24	science	science	NOUN
ejpam-3483	482	25	,	,	PUNCT
ejpam-3483	482	26	12	12	NUM
ejpam-3483	482	27	(	(	PUNCT
ejpam-3483	482	28	3	3	NUM
ejpam-3483	482	29	)	)	PUNCT
ejpam-3483	482	30	(	(	PUNCT
ejpam-3483	482	31	2018	2018	NUM
ejpam-3483	482	32	)	)	PUNCT
ejpam-3483	482	33	338	338	NUM
ejpam-3483	482	34	-	-	SYM
ejpam-3483	482	35	343	343	NUM
ejpam-3483	482	36	[	[	X
ejpam-3483	482	37	9	9	NUM
ejpam-3483	482	38	]	]	PUNCT
ejpam-3483	482	39	t.	t.	PROPN
ejpam-3483	482	40	m.	m.	PROPN
ejpam-3483	482	41	al	al	PROPN
ejpam-3483	482	42	-	-	PUNCT
ejpam-3483	482	43	shami	shami	PROPN
ejpam-3483	482	44	and	and	CCONJ
ejpam-3483	482	45	m.	m.	PROPN
ejpam-3483	482	46	e.	e.	PROPN
ejpam-3483	482	47	el	el	PROPN
ejpam-3483	482	48	-	-	PROPN
ejpam-3483	482	49	shafei	shafei	PROPN
ejpam-3483	482	50	,	,	PUNCT
ejpam-3483	482	51	some	some	DET
ejpam-3483	482	52	types	type	NOUN
ejpam-3483	482	53	of	of	ADP
ejpam-3483	482	54	soft	soft	ADJ
ejpam-3483	482	55	ordered	order	VERB
ejpam-3483	482	56	maps	map	NOUN
ejpam-3483	482	57	via	via	ADP
ejpam-3483	482	58	soft	soft	ADJ
ejpam-3483	482	59	pre	pre	ADJ
ejpam-3483	482	60	open	open	ADJ
ejpam-3483	482	61	sets	set	NOUN
ejpam-3483	482	62	,	,	PUNCT
ejpam-3483	482	63	applied	apply	VERB
ejpam-3483	482	64	mathematics	mathematics	PROPN
ejpam-3483	482	65	&	&	CCONJ
ejpam-3483	482	66	information	information	NOUN
ejpam-3483	482	67	sciences	sciences	PROPN
ejpam-3483	482	68	,	,	PUNCT
ejpam-3483	482	69	13	13	NUM
ejpam-3483	482	70	(	(	PUNCT
ejpam-3483	482	71	5	5	NUM
ejpam-3483	482	72	)	)	PUNCT
ejpam-3483	482	73	(	(	PUNCT
ejpam-3483	482	74	2019	2019	NUM
ejpam-3483	482	75	)	)	PUNCT
ejpam-3483	482	76	accepted	accept	VERB
ejpam-3483	482	77	[	[	X
ejpam-3483	482	78	10	10	NUM
ejpam-3483	482	79	]	]	PUNCT
ejpam-3483	482	80	t.	t.	PROPN
ejpam-3483	482	81	m.	m.	PROPN
ejpam-3483	482	82	al	al	PROPN
ejpam-3483	482	83	-	-	PUNCT
ejpam-3483	482	84	shami	shami	PROPN
ejpam-3483	482	85	,	,	PUNCT
ejpam-3483	483	1	m.	m.	PROPN
ejpam-3483	483	2	e.	e.	PROPN
ejpam-3483	483	3	el	el	PROPN
ejpam-3483	483	4	-	-	PROPN
ejpam-3483	483	5	shafei	shafei	PROPN
ejpam-3483	483	6	and	and	CCONJ
ejpam-3483	483	7	m.	m.	NOUN
ejpam-3483	483	8	abo	abo	NOUN
ejpam-3483	483	9	-	-	PUNCT
ejpam-3483	483	10	elhamayel	elhamayel	NOUN
ejpam-3483	483	11	,	,	PUNCT
ejpam-3483	483	12	on	on	ADP
ejpam-3483	483	13	soft	soft	ADJ
ejpam-3483	483	14	topological	topological	ADJ
ejpam-3483	483	15	ordered	order	VERB
ejpam-3483	483	16	spaces	space	NOUN
ejpam-3483	483	17	,	,	PUNCT
ejpam-3483	483	18	journal	journal	NOUN
ejpam-3483	483	19	of	of	ADP
ejpam-3483	483	20	king	king	PROPN
ejpam-3483	483	21	saud	saud	PROPN
ejpam-3483	483	22	university	university	PROPN
ejpam-3483	483	23	-	-	PUNCT
ejpam-3483	483	24	science	science	NOUN
ejpam-3483	483	25	,	,	PUNCT
ejpam-3483	483	26	https://doi.org/10.1016/j.jksus.2018.06.005	https://doi.org/10.1016/j.jksus.2018.06.005	NOUN
ejpam-3483	483	27	[	[	X
ejpam-3483	483	28	11	11	NUM
ejpam-3483	483	29	]	]	PUNCT
ejpam-3483	483	30	t.	t.	PROPN
ejpam-3483	483	31	m.	m.	PROPN
ejpam-3483	483	32	al	al	PROPN
ejpam-3483	483	33	-	-	PUNCT
ejpam-3483	483	34	shami	shami	PROPN
ejpam-3483	483	35	,	,	PUNCT
ejpam-3483	483	36	m.	m.	PROPN
ejpam-3483	483	37	e.	e.	PROPN
ejpam-3483	483	38	el	el	PROPN
ejpam-3483	483	39	-	-	PROPN
ejpam-3483	483	40	shafei	shafei	PROPN
ejpam-3483	483	41	and	and	CCONJ
ejpam-3483	483	42	m.	m.	NOUN
ejpam-3483	483	43	abo	abo	NOUN
ejpam-3483	483	44	-	-	PUNCT
ejpam-3483	483	45	elhamayel	elhamayel	NOUN
ejpam-3483	483	46	,	,	PUNCT
ejpam-3483	483	47	on	on	ADP
ejpam-3483	483	48	soft	soft	ADJ
ejpam-3483	483	49	ordered	order	VERB
ejpam-3483	483	50	maps	map	NOUN
ejpam-3483	483	51	,	,	PUNCT
ejpam-3483	483	52	general	general	ADJ
ejpam-3483	483	53	letters	letter	NOUN
ejpam-3483	483	54	in	in	ADP
ejpam-3483	483	55	mathematics	mathematic	NOUN
ejpam-3483	483	56	,	,	PUNCT
ejpam-3483	483	57	5	5	NUM
ejpam-3483	483	58	(	(	PUNCT
ejpam-3483	483	59	3	3	NUM
ejpam-3483	483	60	)	)	PUNCT
ejpam-3483	483	61	(	(	PUNCT
ejpam-3483	483	62	2018	2018	NUM
ejpam-3483	483	63	)	)	PUNCT
ejpam-3483	483	64	118	118	NUM
ejpam-3483	483	65	-	-	SYM
ejpam-3483	483	66	131	131	NUM
ejpam-3483	484	1	[	[	X
ejpam-3483	484	2	12	12	NUM
ejpam-3483	484	3	]	]	PUNCT
ejpam-3483	484	4	t.	t.	PROPN
ejpam-3483	484	5	m.	m.	PROPN
ejpam-3483	484	6	al	al	PROPN
ejpam-3483	484	7	-	-	PUNCT
ejpam-3483	484	8	shami	shami	PROPN
ejpam-3483	484	9	,	,	PUNCT
ejpam-3483	485	1	m.	m.	PROPN
ejpam-3483	485	2	e.	e.	PROPN
ejpam-3483	485	3	el	el	PROPN
ejpam-3483	485	4	-	-	PROPN
ejpam-3483	485	5	shafei	shafei	PROPN
ejpam-3483	485	6	and	and	CCONJ
ejpam-3483	485	7	m.	m.	NOUN
ejpam-3483	485	8	abo	abo	NOUN
ejpam-3483	485	9	-	-	PUNCT
ejpam-3483	485	10	elhamayel	elhamayel	ADJ
ejpam-3483	485	11	,	,	PUNCT
ejpam-3483	485	12	new	new	ADJ
ejpam-3483	485	13	types	type	NOUN
ejpam-3483	485	14	of	of	ADP
ejpam-3483	485	15	soft	soft	ADJ
ejpam-3483	485	16	ordered	order	VERB
ejpam-3483	485	17	mappings	mapping	NOUN
ejpam-3483	485	18	via	via	ADP
ejpam-3483	485	19	soft	soft	ADJ
ejpam-3483	485	20	α	α	NOUN
ejpam-3483	485	21	-	-	ADJ
ejpam-3483	485	22	open	open	ADJ
ejpam-3483	485	23	sets	set	NOUN
ejpam-3483	485	24	,	,	PUNCT
ejpam-3483	485	25	italian	italian	ADJ
ejpam-3483	485	26	journal	journal	NOUN
ejpam-3483	485	27	of	of	ADP
ejpam-3483	485	28	pure	pure	ADJ
ejpam-3483	485	29	and	and	CCONJ
ejpam-3483	485	30	applied	applied	ADJ
ejpam-3483	485	31	mathematics	mathematic	NOUN
ejpam-3483	485	32	,	,	PUNCT
ejpam-3483	485	33	41	41	NUM
ejpam-3483	485	34	(	(	PUNCT
ejpam-3483	485	35	2	2	NUM
ejpam-3483	485	36	)	)	PUNCT
ejpam-3483	485	37	(	(	PUNCT
ejpam-3483	485	38	2019	2019	NUM
ejpam-3483	485	39	)	)	PUNCT
ejpam-3483	485	40	accepted	accept	VERB
ejpam-3483	485	41	[	[	X
ejpam-3483	485	42	13	13	NUM
ejpam-3483	485	43	]	]	PUNCT
ejpam-3483	485	44	t.	t.	PROPN
ejpam-3483	485	45	m.	m.	PROPN
ejpam-3483	485	46	al	al	PROPN
ejpam-3483	485	47	-	-	PUNCT
ejpam-3483	485	48	shami	shami	PROPN
ejpam-3483	485	49	,	,	PUNCT
ejpam-3483	486	1	m.	m.	PROPN
ejpam-3483	486	2	e.	e.	PROPN
ejpam-3483	486	3	el	el	PROPN
ejpam-3483	486	4	-	-	PROPN
ejpam-3483	486	5	shafei	shafei	PROPN
ejpam-3483	486	6	and	and	CCONJ
ejpam-3483	486	7	b.	b.	PROPN
ejpam-3483	486	8	a.	a.	PROPN
ejpam-3483	486	9	asaad	asaad	PROPN
ejpam-3483	486	10	,	,	PUNCT
ejpam-3483	486	11	other	other	ADJ
ejpam-3483	486	12	kinds	kind	NOUN
ejpam-3483	486	13	of	of	ADP
ejpam-3483	486	14	soft	soft	ADJ
ejpam-3483	486	15	β	β	NOUN
ejpam-3483	486	16	mappings	mapping	NOUN
ejpam-3483	486	17	via	via	ADP
ejpam-3483	486	18	soft	soft	ADJ
ejpam-3483	486	19	topological	topological	ADJ
ejpam-3483	486	20	ordered	order	VERB
ejpam-3483	486	21	spaces	space	NOUN
ejpam-3483	486	22	,	,	PUNCT
ejpam-3483	486	23	european	european	PROPN
ejpam-3483	486	24	journal	journal	PROPN
ejpam-3483	486	25	of	of	ADP
ejpam-3483	486	26	pure	pure	ADJ
ejpam-3483	486	27	and	and	CCONJ
ejpam-3483	486	28	applied	applied	ADJ
ejpam-3483	486	29	mathematics	mathematic	NOUN
ejpam-3483	486	30	,	,	PUNCT
ejpam-3483	486	31	12	12	NUM
ejpam-3483	486	32	(	(	PUNCT
ejpam-3483	486	33	1	1	NUM
ejpam-3483	486	34	)	)	PUNCT
ejpam-3483	486	35	(	(	PUNCT
ejpam-3483	486	36	2019	2019	NUM
ejpam-3483	486	37	)	)	PUNCT
ejpam-3483	486	38	176	176	NUM
ejpam-3483	486	39	-	-	SYM
ejpam-3483	486	40	193	193	NUM
ejpam-3483	487	1	[	[	X
ejpam-3483	487	2	14	14	NUM
ejpam-3483	487	3	]	]	PUNCT
ejpam-3483	487	4	t.	t.	PROPN
ejpam-3483	487	5	m.	m.	PROPN
ejpam-3483	487	6	al	al	PROPN
ejpam-3483	487	7	-	-	PUNCT
ejpam-3483	487	8	shami	shami	PROPN
ejpam-3483	487	9	and	and	CCONJ
ejpam-3483	487	10	t.noiri	t.noiri	ADV
ejpam-3483	487	11	,	,	PUNCT
ejpam-3483	487	12	more	more	ADJ
ejpam-3483	487	13	notions	notion	NOUN
ejpam-3483	487	14	and	and	CCONJ
ejpam-3483	487	15	mappings	mapping	NOUN
ejpam-3483	487	16	via	via	ADP
ejpam-3483	487	17	somewhere	somewhere	ADJ
ejpam-3483	487	18	dense	dense	ADJ
ejpam-3483	487	19	sets	set	NOUN
ejpam-3483	487	20	,	,	PUNCT
ejpam-3483	487	21	afrika	afrika	ADJ
ejpam-3483	487	22	matematika	matematika	NOUN
ejpam-3483	487	23	,	,	PUNCT
ejpam-3483	487	24	(	(	PUNCT
ejpam-3483	487	25	2019	2019	NUM
ejpam-3483	487	26	)	)	PUNCT
ejpam-3483	487	27	,	,	PUNCT
ejpam-3483	487	28	https://doi.org/10.1007/s13370-019-00700-4	https://doi.org/10.1007/s13370-019-00700-4	NUM
ejpam-3483	487	29	.	.	PUNCT
ejpam-3483	488	1	[	[	X
ejpam-3483	488	2	15	15	NUM
ejpam-3483	488	3	]	]	X
ejpam-3483	488	4	t.	t.	PROPN
ejpam-3483	488	5	m.	m.	PROPN
ejpam-3483	488	6	al	al	PROPN
ejpam-3483	488	7	-	-	PUNCT
ejpam-3483	488	8	shami	shami	PROPN
ejpam-3483	488	9	and	and	CCONJ
ejpam-3483	488	10	m.	m.	PROPN
ejpam-3483	488	11	k.	k.	PROPN
ejpam-3483	488	12	tahat	tahat	PROPN
ejpam-3483	488	13	,	,	PUNCT
ejpam-3483	488	14	i	i	PRON
ejpam-3483	488	15	(	(	PUNCT
ejpam-3483	488	16	d	d	PROPN
ejpam-3483	488	17	,	,	PUNCT
ejpam-3483	488	18	b)-supra	b)-supra	PUNCT
ejpam-3483	488	19	pre	pre	X
ejpam-3483	488	20	maps	map	NOUN
ejpam-3483	488	21	via	via	ADP
ejpam-3483	488	22	supra	supra	PROPN
ejpam-3483	488	23	topological	topological	PROPN
ejpam-3483	488	24	ordered	order	VERB
ejpam-3483	488	25	spaces	space	NOUN
ejpam-3483	488	26	,	,	PUNCT
ejpam-3483	488	27	journal	journal	NOUN
ejpam-3483	488	28	of	of	ADP
ejpam-3483	488	29	progressive	progressive	ADJ
ejpam-3483	488	30	research	research	NOUN
ejpam-3483	488	31	in	in	ADP
ejpam-3483	488	32	mathematics	mathematic	NOUN
ejpam-3483	488	33	,	,	PUNCT
ejpam-3483	488	34	12	12	NUM
ejpam-3483	488	35	(	(	PUNCT
ejpam-3483	488	36	3	3	NUM
ejpam-3483	488	37	)	)	PUNCT
ejpam-3483	488	38	(	(	PUNCT
ejpam-3483	488	39	2017	2017	NUM
ejpam-3483	488	40	)	)	PUNCT
ejpam-3483	488	41	19892001	19892001	NUM
ejpam-3483	489	1	[	[	X
ejpam-3483	489	2	16	16	NUM
ejpam-3483	489	3	]	]	PUNCT
ejpam-3483	489	4	s.	s.	PROPN
ejpam-3483	489	5	d.	d.	PROPN
ejpam-3483	489	6	arya	arya	PROPN
ejpam-3483	489	7	and	and	CCONJ
ejpam-3483	489	8	k.	k.	PROPN
ejpam-3483	489	9	gupta	gupta	PROPN
ejpam-3483	489	10	,	,	PUNCT
ejpam-3483	489	11	new	new	ADJ
ejpam-3483	489	12	separation	separation	NOUN
ejpam-3483	489	13	axioms	axiom	NOUN
ejpam-3483	489	14	in	in	ADP
ejpam-3483	489	15	topological	topological	ADJ
ejpam-3483	489	16	ordered	order	VERB
ejpam-3483	489	17	spaces	space	NOUN
ejpam-3483	489	18	,	,	PUNCT
ejpam-3483	489	19	indain	indain	NOUN
ejpam-3483	489	20	journal	journal	NOUN
ejpam-3483	489	21	pure	pure	ADJ
ejpam-3483	489	22	and	and	CCONJ
ejpam-3483	489	23	applied	applied	ADJ
ejpam-3483	489	24	mathematics	mathematic	NOUN
ejpam-3483	489	25	,	,	PUNCT
ejpam-3483	489	26	22	22	NUM
ejpam-3483	489	27	(	(	PUNCT
ejpam-3483	489	28	1991	1991	NUM
ejpam-3483	489	29	)	)	PUNCT
ejpam-3483	489	30	461	461	NUM
ejpam-3483	489	31	-	-	NUM
ejpam-3483	489	32	468	468	NUM
ejpam-3483	490	1	[	[	X
ejpam-3483	490	2	17	17	NUM
ejpam-3483	490	3	]	]	PUNCT
ejpam-3483	490	4	p.	p.	PROPN
ejpam-3483	490	5	das	das	PROPN
ejpam-3483	490	6	,	,	PUNCT
ejpam-3483	490	7	separation	separation	NOUN
ejpam-3483	490	8	axioms	axiom	NOUN
ejpam-3483	490	9	in	in	ADP
ejpam-3483	490	10	ordered	order	VERB
ejpam-3483	490	11	spaces	space	NOUN
ejpam-3483	490	12	,	,	PUNCT
ejpam-3483	490	13	soochow	soochow	PROPN
ejpam-3483	490	14	journal	journal	NOUN
ejpam-3483	490	15	of	of	ADP
ejpam-3483	490	16	mathematics	mathematic	NOUN
ejpam-3483	490	17	,	,	PUNCT
ejpam-3483	490	18	30	30	NUM
ejpam-3483	490	19	(	(	PUNCT
ejpam-3483	490	20	4	4	NUM
ejpam-3483	490	21	)	)	PUNCT
ejpam-3483	490	22	(	(	PUNCT
ejpam-3483	490	23	2004	2004	NUM
ejpam-3483	490	24	)	)	PUNCT
ejpam-3483	490	25	447	447	NUM
ejpam-3483	490	26	-	-	SYM
ejpam-3483	490	27	454	454	NUM
ejpam-3483	491	1	[	[	X
ejpam-3483	491	2	18	18	NUM
ejpam-3483	491	3	]	]	PUNCT
ejpam-3483	491	4	m.	m.	PROPN
ejpam-3483	491	5	e.	e.	PROPN
ejpam-3483	491	6	el	el	PROPN
ejpam-3483	491	7	-	-	PROPN
ejpam-3483	491	8	shafei	shafei	PROPN
ejpam-3483	491	9	,	,	PUNCT
ejpam-3483	491	10	m.	m.	NOUN
ejpam-3483	491	11	abo	abo	NOUN
ejpam-3483	491	12	-	-	PUNCT
ejpam-3483	491	13	elhamayel	elhamayel	NOUN
ejpam-3483	491	14	and	and	CCONJ
ejpam-3483	491	15	t.	t.	PROPN
ejpam-3483	491	16	m.	m.	PROPN
ejpam-3483	491	17	al	al	PROPN
ejpam-3483	491	18	-	-	PUNCT
ejpam-3483	491	19	shami	shami	PROPN
ejpam-3483	491	20	,	,	PUNCT
ejpam-3483	491	21	on	on	ADP
ejpam-3483	491	22	supra	supra	ADJ
ejpam-3483	491	23	r	r	NOUN
ejpam-3483	491	24	-	-	PUNCT
ejpam-3483	491	25	open	open	ADJ
ejpam-3483	491	26	sets	set	NOUN
ejpam-3483	491	27	and	and	CCONJ
ejpam-3483	491	28	some	some	DET
ejpam-3483	491	29	applications	application	NOUN
ejpam-3483	491	30	on	on	ADP
ejpam-3483	491	31	topological	topological	ADJ
ejpam-3483	491	32	spaces	space	NOUN
ejpam-3483	491	33	,	,	PUNCT
ejpam-3483	491	34	journal	journal	NOUN
ejpam-3483	491	35	of	of	ADP
ejpam-3483	491	36	progressive	progressive	ADJ
ejpam-3483	491	37	research	research	NOUN
ejpam-3483	491	38	in	in	ADP
ejpam-3483	491	39	mathematics	mathematic	NOUN
ejpam-3483	491	40	,	,	PUNCT
ejpam-3483	491	41	8	8	NUM
ejpam-3483	491	42	(	(	PUNCT
ejpam-3483	491	43	2	2	NUM
ejpam-3483	491	44	)	)	PUNCT
ejpam-3483	491	45	(	(	PUNCT
ejpam-3483	491	46	2016	2016	NUM
ejpam-3483	491	47	)	)	PUNCT
ejpam-3483	491	48	1237	1237	NUM
ejpam-3483	491	49	-	-	SYM
ejpam-3483	491	50	1248	1248	NUM
ejpam-3483	491	51	references	reference	NOUN
ejpam-3483	491	52	1247	1247	NUM
ejpam-3483	491	53	[	[	X
ejpam-3483	491	54	19	19	NUM
ejpam-3483	491	55	]	]	PUNCT
ejpam-3483	491	56	m.	m.	PROPN
ejpam-3483	491	57	e.	e.	PROPN
ejpam-3483	491	58	el	el	PROPN
ejpam-3483	491	59	-	-	PROPN
ejpam-3483	491	60	shafei	shafei	PROPN
ejpam-3483	491	61	,	,	PUNCT
ejpam-3483	491	62	m.	m.	NOUN
ejpam-3483	491	63	abo	abo	NOUN
ejpam-3483	491	64	-	-	PUNCT
ejpam-3483	491	65	elhamayel	elhamayel	NOUN
ejpam-3483	491	66	and	and	CCONJ
ejpam-3483	491	67	t.	t.	PROPN
ejpam-3483	491	68	m.	m.	PROPN
ejpam-3483	491	69	al	al	PROPN
ejpam-3483	491	70	-	-	PUNCT
ejpam-3483	491	71	shami	shami	PROPN
ejpam-3483	491	72	,	,	PUNCT
ejpam-3483	491	73	generating	generate	VERB
ejpam-3483	491	74	ordered	order	VERB
ejpam-3483	491	75	maps	map	NOUN
ejpam-3483	491	76	via	via	ADP
ejpam-3483	491	77	supra	supra	PROPN
ejpam-3483	491	78	topological	topological	PROPN
ejpam-3483	491	79	ordered	order	VERB
ejpam-3483	491	80	spaces	space	NOUN
ejpam-3483	491	81	,	,	PUNCT
ejpam-3483	491	82	international	international	ADJ
ejpam-3483	491	83	journal	journal	NOUN
ejpam-3483	491	84	of	of	ADP
ejpam-3483	491	85	modern	modern	ADJ
ejpam-3483	491	86	mathematical	mathematical	ADJ
ejpam-3483	491	87	sciences	science	NOUN
ejpam-3483	491	88	,	,	PUNCT
ejpam-3483	491	89	15	15	NUM
ejpam-3483	491	90	(	(	PUNCT
ejpam-3483	491	91	3	3	NUM
ejpam-3483	491	92	)	)	PUNCT
ejpam-3483	491	93	(	(	PUNCT
ejpam-3483	491	94	2017	2017	NUM
ejpam-3483	491	95	)	)	PUNCT
ejpam-3483	491	96	339	339	NUM
ejpam-3483	491	97	-	-	SYM
ejpam-3483	491	98	357	357	NUM
ejpam-3483	491	99	[	[	SYM
ejpam-3483	491	100	20	20	NUM
ejpam-3483	491	101	]	]	PUNCT
ejpam-3483	491	102	m.	m.	PROPN
ejpam-3483	491	103	e.	e.	PROPN
ejpam-3483	491	104	el	el	PROPN
ejpam-3483	491	105	-	-	PROPN
ejpam-3483	491	106	shafei	shafei	PROPN
ejpam-3483	491	107	,	,	PUNCT
ejpam-3483	491	108	m.	m.	NOUN
ejpam-3483	491	109	abo	abo	NOUN
ejpam-3483	491	110	-	-	PUNCT
ejpam-3483	491	111	elhamayel	elhamayel	NOUN
ejpam-3483	491	112	and	and	CCONJ
ejpam-3483	491	113	t.	t.	PROPN
ejpam-3483	491	114	m.	m.	PROPN
ejpam-3483	491	115	al	al	PROPN
ejpam-3483	491	116	-	-	PUNCT
ejpam-3483	491	117	shami	shami	PROPN
ejpam-3483	491	118	,	,	PUNCT
ejpam-3483	491	119	strong	strong	ADJ
ejpam-3483	491	120	separation	separation	NOUN
ejpam-3483	491	121	axioms	axiom	NOUN
ejpam-3483	491	122	in	in	ADP
ejpam-3483	491	123	supra	supra	PROPN
ejpam-3483	491	124	topological	topological	ADJ
ejpam-3483	491	125	ordered	order	VERB
ejpam-3483	491	126	spaces	space	NOUN
ejpam-3483	491	127	,	,	PUNCT
ejpam-3483	491	128	mathematical	mathematical	ADJ
ejpam-3483	491	129	sciences	science	NOUN
ejpam-3483	491	130	letters	letter	NOUN
ejpam-3483	491	131	,	,	PUNCT
ejpam-3483	491	132	6	6	NUM
ejpam-3483	491	133	(	(	PUNCT
ejpam-3483	491	134	3	3	NUM
ejpam-3483	491	135	)	)	PUNCT
ejpam-3483	491	136	(	(	PUNCT
ejpam-3483	491	137	2017	2017	NUM
ejpam-3483	491	138	)	)	PUNCT
ejpam-3483	491	139	271	271	NUM
ejpam-3483	491	140	-	-	SYM
ejpam-3483	491	141	277	277	NUM
ejpam-3483	491	142	[	[	X
ejpam-3483	491	143	21	21	NUM
ejpam-3483	491	144	]	]	PUNCT
ejpam-3483	491	145	m.	m.	PROPN
ejpam-3483	491	146	e.	e.	PROPN
ejpam-3483	491	147	el	el	PROPN
ejpam-3483	491	148	-	-	PROPN
ejpam-3483	491	149	shafei	shafei	PROPN
ejpam-3483	491	150	,	,	PUNCT
ejpam-3483	491	151	m.	m.	NOUN
ejpam-3483	491	152	abo	abo	NOUN
ejpam-3483	491	153	-	-	PUNCT
ejpam-3483	491	154	elhamayel	elhamayel	NOUN
ejpam-3483	491	155	and	and	CCONJ
ejpam-3483	491	156	t.	t.	PROPN
ejpam-3483	491	157	m.	m.	PROPN
ejpam-3483	491	158	al	al	PROPN
ejpam-3483	491	159	-	-	PUNCT
ejpam-3483	491	160	shami	shami	PROPN
ejpam-3483	491	161	,	,	PUNCT
ejpam-3483	491	162	supra	supra	PROPN
ejpam-3483	491	163	r	r	PROPN
ejpam-3483	491	164	-	-	PUNCT
ejpam-3483	491	165	homeomorphism	homeomorphism	PROPN
ejpam-3483	491	166	in	in	ADP
ejpam-3483	491	167	supra	supra	PROPN
ejpam-3483	491	168	topological	topological	PROPN
ejpam-3483	491	169	ordered	order	VERB
ejpam-3483	491	170	spaces	space	NOUN
ejpam-3483	491	171	,	,	PUNCT
ejpam-3483	491	172	international	international	ADJ
ejpam-3483	491	173	journal	journal	NOUN
ejpam-3483	491	174	of	of	ADP
ejpam-3483	491	175	algebra	algebra	PROPN
ejpam-3483	491	176	and	and	CCONJ
ejpam-3483	491	177	statistics	statistic	NOUN
ejpam-3483	491	178	,	,	PUNCT
ejpam-3483	491	179	6	6	NUM
ejpam-3483	491	180	(	(	PUNCT
ejpam-3483	491	181	1	1	NUM
ejpam-3483	491	182	-	-	SYM
ejpam-3483	491	183	2	2	NUM
ejpam-3483	491	184	)	)	PUNCT
ejpam-3483	491	185	(	(	PUNCT
ejpam-3483	491	186	2017	2017	NUM
ejpam-3483	491	187	)	)	PUNCT
ejpam-3483	491	188	158	158	NUM
ejpam-3483	491	189	-	-	SYM
ejpam-3483	491	190	167	167	NUM
ejpam-3483	491	191	[	[	X
ejpam-3483	491	192	22	22	NUM
ejpam-3483	491	193	]	]	PUNCT
ejpam-3483	491	194	m.	m.	PROPN
ejpam-3483	492	1	e.	e.	PROPN
ejpam-3483	492	2	el	el	PROPN
ejpam-3483	492	3	-	-	PROPN
ejpam-3483	492	4	shafei	shafei	PROPN
ejpam-3483	492	5	and	and	CCONJ
ejpam-3483	492	6	t.	t.	PROPN
ejpam-3483	492	7	m.	m.	PROPN
ejpam-3483	492	8	al	al	PROPN
ejpam-3483	492	9	-	-	PUNCT
ejpam-3483	492	10	shami	shami	PROPN
ejpam-3483	492	11	,	,	PUNCT
ejpam-3483	492	12	some	some	DET
ejpam-3483	492	13	new	new	ADJ
ejpam-3483	492	14	types	type	NOUN
ejpam-3483	492	15	of	of	ADP
ejpam-3483	492	16	soft	soft	ADJ
ejpam-3483	492	17	b	b	NOUN
ejpam-3483	492	18	-	-	PUNCT
ejpam-3483	492	19	ordered	order	VERB
ejpam-3483	492	20	mappings	mapping	NOUN
ejpam-3483	492	21	,	,	PUNCT
ejpam-3483	492	22	international	international	ADJ
ejpam-3483	492	23	journal	journal	NOUN
ejpam-3483	492	24	of	of	ADP
ejpam-3483	492	25	advances	advance	NOUN
ejpam-3483	492	26	in	in	ADP
ejpam-3483	492	27	mathematics	mathematic	NOUN
ejpam-3483	492	28	,	,	PUNCT
ejpam-3483	492	29	2019	2019	NUM
ejpam-3483	492	30	(	(	PUNCT
ejpam-3483	492	31	3	3	NUM
ejpam-3483	492	32	)	)	PUNCT
ejpam-3483	492	33	(	(	PUNCT
ejpam-3483	492	34	2019	2019	NUM
ejpam-3483	492	35	)	)	PUNCT
ejpam-3483	492	36	1	1	NUM
ejpam-3483	492	37	-	-	SYM
ejpam-3483	492	38	14	14	NUM
ejpam-3483	492	39	[	[	X
ejpam-3483	492	40	23	23	NUM
ejpam-3483	492	41	]	]	PUNCT
ejpam-3483	492	42	m.	m.	PROPN
ejpam-3483	492	43	k.	k.	PROPN
ejpam-3483	492	44	r.	r.	PROPN
ejpam-3483	492	45	s.	s.	PROPN
ejpam-3483	492	46	v.	v.	PROPN
ejpam-3483	492	47	kumar	kumar	PROPN
ejpam-3483	492	48	,	,	PUNCT
ejpam-3483	492	49	homeomorphism	homeomorphism	PROPN
ejpam-3483	492	50	in	in	ADP
ejpam-3483	492	51	topological	topological	ADJ
ejpam-3483	492	52	ordered	order	VERB
ejpam-3483	492	53	spaces	space	NOUN
ejpam-3483	492	54	,	,	PUNCT
ejpam-3483	492	55	acta	acta	PROPN
ejpam-3483	492	56	ciencia	ciencia	PROPN
ejpam-3483	492	57	indian	indian	PROPN
ejpam-3483	492	58	,	,	PUNCT
ejpam-3483	492	59	xxviii(m)(1	xxviii(m)(1	PROPN
ejpam-3483	492	60	)	)	PUNCT
ejpam-3483	492	61	(	(	PUNCT
ejpam-3483	492	62	2012	2012	NUM
ejpam-3483	492	63	)	)	PUNCT
ejpam-3483	492	64	67	67	NUM
ejpam-3483	492	65	-	-	SYM
ejpam-3483	492	66	76	76	NUM
ejpam-3483	493	1	[	[	X
ejpam-3483	493	2	24	24	NUM
ejpam-3483	493	3	]	]	PUNCT
ejpam-3483	493	4	a.	a.	NOUN
ejpam-3483	493	5	s.	s.	PROPN
ejpam-3483	493	6	mashhour	mashhour	PROPN
ejpam-3483	493	7	,	,	PUNCT
ejpam-3483	493	8	a.	a.	PROPN
ejpam-3483	493	9	a.	a.	PROPN
ejpam-3483	493	10	allam	allam	PROPN
ejpam-3483	493	11	,	,	PUNCT
ejpam-3483	493	12	f.	f.	PROPN
ejpam-3483	493	13	s.	s.	PROPN
ejpam-3483	493	14	mahmoud	mahmoud	PROPN
ejpam-3483	493	15	and	and	CCONJ
ejpam-3483	493	16	f.	f.	PROPN
ejpam-3483	493	17	h.	h.	PROPN
ejpam-3483	493	18	khedr	khedr	PROPN
ejpam-3483	493	19	,	,	PUNCT
ejpam-3483	493	20	on	on	ADP
ejpam-3483	493	21	supra	supra	PROPN
ejpam-3483	493	22	topological	topological	ADJ
ejpam-3483	493	23	spaces	space	NOUN
ejpam-3483	493	24	,	,	PUNCT
ejpam-3483	493	25	indian	indian	ADJ
ejpam-3483	493	26	journal	journal	NOUN
ejpam-3483	493	27	of	of	ADP
ejpam-3483	493	28	pure	pure	ADJ
ejpam-3483	493	29	and	and	CCONJ
ejpam-3483	493	30	applied	applied	ADJ
ejpam-3483	493	31	mathematic	mathematic	ADJ
ejpam-3483	493	32	,	,	PUNCT
ejpam-3483	493	33	14	14	NUM
ejpam-3483	493	34	(	(	PUNCT
ejpam-3483	493	35	4	4	NUM
ejpam-3483	493	36	)	)	PUNCT
ejpam-3483	493	37	(	(	PUNCT
ejpam-3483	493	38	1983	1983	NUM
ejpam-3483	493	39	)	)	PUNCT
ejpam-3483	493	40	502	502	NUM
ejpam-3483	493	41	-	-	SYM
ejpam-3483	493	42	510	510	NUM
ejpam-3483	493	43	[	[	X
ejpam-3483	493	44	25	25	NUM
ejpam-3483	493	45	]	]	PUNCT
ejpam-3483	493	46	s.	s.	PROPN
ejpam-3483	493	47	d.	d.	PROPN
ejpam-3483	493	48	mccartan	mccartan	PROPN
ejpam-3483	493	49	,	,	PUNCT
ejpam-3483	493	50	separation	separation	NOUN
ejpam-3483	493	51	axioms	axiom	NOUN
ejpam-3483	493	52	for	for	ADP
ejpam-3483	493	53	topological	topological	ADJ
ejpam-3483	493	54	ordered	order	VERB
ejpam-3483	493	55	spaces	space	NOUN
ejpam-3483	493	56	,	,	PUNCT
ejpam-3483	493	57	mathematical	mathematical	ADJ
ejpam-3483	493	58	proceedings	proceeding	NOUN
ejpam-3483	493	59	of	of	ADP
ejpam-3483	493	60	the	the	DET
ejpam-3483	493	61	cambridge	cambridge	PROPN
ejpam-3483	493	62	philosophical	philosophical	ADJ
ejpam-3483	493	63	society	society	NOUN
ejpam-3483	493	64	,	,	PUNCT
ejpam-3483	493	65	64	64	NUM
ejpam-3483	493	66	(	(	PUNCT
ejpam-3483	493	67	1986	1986	NUM
ejpam-3483	493	68	)	)	PUNCT
ejpam-3483	494	1	965	965	NUM
ejpam-3483	494	2	-	-	SYM
ejpam-3483	494	3	973	973	NUM
ejpam-3483	494	4	[	[	X
ejpam-3483	494	5	26	26	NUM
ejpam-3483	494	6	]	]	X
ejpam-3483	494	7	l.	l.	PROPN
ejpam-3483	494	8	nachbin	nachbin	PROPN
ejpam-3483	494	9	,	,	PUNCT
ejpam-3483	494	10	topology	topology	NOUN
ejpam-3483	494	11	and	and	CCONJ
ejpam-3483	494	12	ordered	order	VERB
ejpam-3483	494	13	,	,	PUNCT
ejpam-3483	494	14	d.	d.	PROPN
ejpam-3483	494	15	van	van	PROPN
ejpam-3483	494	16	nostrand	nostrand	PROPN
ejpam-3483	494	17	inc	inc	PROPN
ejpam-3483	494	18	.	.	PROPN
ejpam-3483	494	19	princeton	princeton	PROPN
ejpam-3483	494	20	,	,	PUNCT
ejpam-3483	494	21	new	new	PROPN
ejpam-3483	494	22	jersey	jersey	PROPN
ejpam-3483	494	23	,	,	PUNCT
ejpam-3483	494	24	(	(	PUNCT
ejpam-3483	494	25	1965	1965	NUM
ejpam-3483	494	26	)	)	PUNCT
ejpam-3483	495	1	[	[	X
ejpam-3483	495	2	27	27	NUM
ejpam-3483	495	3	]	]	X
ejpam-3483	495	4	o.	o.	PROPN
ejpam-3483	495	5	r.	r.	PROPN
ejpam-3483	495	6	sayed	sayed	PROPN
ejpam-3483	495	7	and	and	CCONJ
ejpam-3483	495	8	t.	t.	PROPN
ejpam-3483	495	9	noiri	noiri	PROPN
ejpam-3483	495	10	,	,	PUNCT
ejpam-3483	495	11	on	on	ADP
ejpam-3483	495	12	supra	supra	PROPN
ejpam-3483	495	13	b	b	NOUN
ejpam-3483	495	14	-	-	PUNCT
ejpam-3483	495	15	open	open	ADJ
ejpam-3483	495	16	sets	set	NOUN
ejpam-3483	495	17	and	and	CCONJ
ejpam-3483	495	18	supra	supra	PROPN
ejpam-3483	495	19	b	b	NOUN
ejpam-3483	495	20	-	-	PUNCT
ejpam-3483	495	21	continuity	continuity	NOUN
ejpam-3483	495	22	on	on	ADP
ejpam-3483	495	23	topological	topological	ADJ
ejpam-3483	495	24	spaces	space	NOUN
ejpam-3483	495	25	,	,	PUNCT
ejpam-3483	495	26	european	european	PROPN
ejpam-3483	495	27	journal	journal	PROPN
ejpam-3483	495	28	of	of	ADP
ejpam-3483	495	29	pure	pure	ADJ
ejpam-3483	495	30	and	and	CCONJ
ejpam-3483	495	31	applied	applied	ADJ
ejpam-3483	495	32	mathematics	mathematic	NOUN
ejpam-3483	495	33	,	,	PUNCT
ejpam-3483	495	34	3	3	NUM
ejpam-3483	495	35	(	(	PUNCT
ejpam-3483	495	36	2010	2010	NUM
ejpam-3483	495	37	)	)	PUNCT
ejpam-3483	495	38	295	295	NUM
ejpam-3483	495	39	-	-	SYM
ejpam-3483	495	40	302	302	NUM
ejpam-3483	495	41	.	.	PUNCT