id	sid	tid	token	lemma	pos
ejpam-3449	1	1	european	european	PROPN
ejpam-3449	1	2	journal	journal	PROPN
ejpam-3449	1	3	of	of	ADP
ejpam-3449	1	4	pure	pure	ADJ
ejpam-3449	1	5	and	and	CCONJ
ejpam-3449	1	6	applied	apply	VERB
ejpam-3449	1	7	mathematics	mathematic	NOUN
ejpam-3449	1	8	vol	vol	NOUN
ejpam-3449	1	9	.	.	PROPN
ejpam-3449	2	1	12	12	NUM
ejpam-3449	2	2	,	,	PUNCT
ejpam-3449	2	3	no	no	INTJ
ejpam-3449	2	4	.	.	NOUN
ejpam-3449	2	5	3	3	NUM
ejpam-3449	2	6	,	,	PUNCT
ejpam-3449	2	7	2019	2019	NUM
ejpam-3449	2	8	,	,	PUNCT
ejpam-3449	2	9	960	960	NUM
ejpam-3449	2	10	-	-	SYM
ejpam-3449	2	11	977	977	NUM
ejpam-3449	2	12	issn	issn	PROPN
ejpam-3449	2	13	1307	1307	NUM
ejpam-3449	2	14	-	-	SYM
ejpam-3449	2	15	5543	5543	NUM
ejpam-3449	2	16	–	–	PUNCT
ejpam-3449	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3449	2	18	published	publish	VERB
ejpam-3449	2	19	by	by	ADP
ejpam-3449	2	20	new	new	PROPN
ejpam-3449	2	21	york	york	PROPN
ejpam-3449	2	22	business	business	PROPN
ejpam-3449	2	23	global	global	ADJ
ejpam-3449	2	24	operation	operation	NOUN
ejpam-3449	2	25	on	on	ADP
ejpam-3449	2	26	fine	fine	ADJ
ejpam-3449	2	27	topology	topology	NOUN
ejpam-3449	2	28	p.	p.	PROPN
ejpam-3449	2	29	l.	l.	PROPN
ejpam-3449	2	30	powar1	powar1	PROPN
ejpam-3449	2	31	,	,	PUNCT
ejpam-3449	2	32	baravan	baravan	PROPN
ejpam-3449	2	33	a.	a.	PROPN
ejpam-3449	2	34	asaad2,3,∗	asaad2,3,∗	PROPN
ejpam-3449	2	35	,	,	PUNCT
ejpam-3449	2	36	k.	k.	PROPN
ejpam-3449	2	37	rajak4	rajak4	PROPN
ejpam-3449	2	38	,	,	PUNCT
ejpam-3449	2	39	r.	r.	PROPN
ejpam-3449	2	40	kushwaha1	kushwaha1	PROPN
ejpam-3449	2	41	1	1	NUM
ejpam-3449	2	42	department	department	NOUN
ejpam-3449	2	43	of	of	ADP
ejpam-3449	2	44	mathematics	mathematic	NOUN
ejpam-3449	2	45	,	,	PUNCT
ejpam-3449	2	46	rani	rani	PROPN
ejpam-3449	2	47	durgawati	durgawati	PROPN
ejpam-3449	2	48	university	university	PROPN
ejpam-3449	2	49	,	,	PUNCT
ejpam-3449	2	50	jabalpur	jabalpur	PROPN
ejpam-3449	2	51	,	,	PUNCT
ejpam-3449	2	52	(	(	PUNCT
ejpam-3449	2	53	m.	m.	NOUN
ejpam-3449	2	54	p.	p.	PROPN
ejpam-3449	2	55	)	)	PUNCT
ejpam-3449	2	56	,	,	PUNCT
ejpam-3449	2	57	india	india	PROPN
ejpam-3449	2	58	2	2	NUM
ejpam-3449	2	59	department	department	NOUN
ejpam-3449	2	60	of	of	ADP
ejpam-3449	2	61	computer	computer	NOUN
ejpam-3449	2	62	science	science	NOUN
ejpam-3449	2	63	,	,	PUNCT
ejpam-3449	2	64	college	college	NOUN
ejpam-3449	2	65	of	of	ADP
ejpam-3449	2	66	science	science	NOUN
ejpam-3449	2	67	,	,	PUNCT
ejpam-3449	2	68	cihan	cihan	VERB
ejpam-3449	2	69	university	university	NOUN
ejpam-3449	2	70	-	-	PUNCT
ejpam-3449	2	71	duhok	duhok	NOUN
ejpam-3449	2	72	,	,	PUNCT
ejpam-3449	2	73	iraq	iraq	PROPN
ejpam-3449	2	74	3	3	NUM
ejpam-3449	2	75	department	department	NOUN
ejpam-3449	2	76	of	of	ADP
ejpam-3449	2	77	mathematics	mathematic	NOUN
ejpam-3449	2	78	,	,	PUNCT
ejpam-3449	2	79	faculty	faculty	NOUN
ejpam-3449	2	80	of	of	ADP
ejpam-3449	2	81	science	science	NOUN
ejpam-3449	2	82	,	,	PUNCT
ejpam-3449	2	83	university	university	NOUN
ejpam-3449	2	84	of	of	ADP
ejpam-3449	2	85	zakho	zakho	PROPN
ejpam-3449	2	86	,	,	PUNCT
ejpam-3449	2	87	iraq	iraq	PROPN
ejpam-3449	2	88	4	4	NUM
ejpam-3449	2	89	department	department	NOUN
ejpam-3449	2	90	of	of	ADP
ejpam-3449	2	91	mathematics	mathematics	PROPN
ejpam-3449	2	92	,	,	PUNCT
ejpam-3449	2	93	st	st	PROPN
ejpam-3449	2	94	.	.	PROPN
ejpam-3449	2	95	aloysius	aloysius	PROPN
ejpam-3449	2	96	college	college	PROPN
ejpam-3449	2	97	(	(	PUNCT
ejpam-3449	2	98	autonomous	autonomous	ADJ
ejpam-3449	2	99	)	)	PUNCT
ejpam-3449	2	100	,	,	PUNCT
ejpam-3449	2	101	jabalpur	jabalpur	PROPN
ejpam-3449	2	102	,	,	PUNCT
ejpam-3449	2	103	(	(	PUNCT
ejpam-3449	2	104	m.	m.	NOUN
ejpam-3449	2	105	p.	p.	PROPN
ejpam-3449	2	106	)	)	PUNCT
ejpam-3449	2	107	,	,	PUNCT
ejpam-3449	2	108	india	india	PROPN
ejpam-3449	2	109	abstract	abstract	NOUN
ejpam-3449	2	110	.	.	PUNCT
ejpam-3449	3	1	this	this	DET
ejpam-3449	3	2	paper	paper	NOUN
ejpam-3449	3	3	introduces	introduce	VERB
ejpam-3449	3	4	the	the	DET
ejpam-3449	3	5	concept	concept	NOUN
ejpam-3449	3	6	of	of	ADP
ejpam-3449	3	7	an	an	DET
ejpam-3449	3	8	operation	operation	NOUN
ejpam-3449	3	9	γ	γ	NOUN
ejpam-3449	3	10	on	on	ADP
ejpam-3449	3	11	τf	τf	NUM
ejpam-3449	3	12	.	.	PUNCT
ejpam-3449	4	1	using	use	VERB
ejpam-3449	4	2	this	this	DET
ejpam-3449	4	3	operation	operation	NOUN
ejpam-3449	4	4	,	,	PUNCT
ejpam-3449	4	5	we	we	PRON
ejpam-3449	4	6	define	define	VERB
ejpam-3449	4	7	the	the	DET
ejpam-3449	4	8	concept	concept	NOUN
ejpam-3449	4	9	of	of	ADP
ejpam-3449	4	10	fγ	fγ	NOUN
ejpam-3449	4	11	-	-	PUNCT
ejpam-3449	4	12	open	open	ADJ
ejpam-3449	4	13	sets	set	NOUN
ejpam-3449	4	14	,	,	PUNCT
ejpam-3449	4	15	and	and	CCONJ
ejpam-3449	4	16	study	study	VERB
ejpam-3449	4	17	some	some	PRON
ejpam-3449	4	18	of	of	ADP
ejpam-3449	4	19	their	their	PRON
ejpam-3449	4	20	related	related	ADJ
ejpam-3449	4	21	notions	notion	NOUN
ejpam-3449	4	22	.	.	PUNCT
ejpam-3449	5	1	also	also	ADV
ejpam-3449	5	2	,	,	PUNCT
ejpam-3449	5	3	we	we	PRON
ejpam-3449	5	4	introduce	introduce	VERB
ejpam-3449	5	5	the	the	DET
ejpam-3449	5	6	concept	concept	NOUN
ejpam-3449	5	7	of	of	ADP
ejpam-3449	5	8	fγg.closed	fγg.close	VERB
ejpam-3449	5	9	sets	set	NOUN
ejpam-3449	5	10	and	and	CCONJ
ejpam-3449	5	11	then	then	ADV
ejpam-3449	5	12	study	study	VERB
ejpam-3449	5	13	some	some	PRON
ejpam-3449	5	14	of	of	ADP
ejpam-3449	5	15	its	its	PRON
ejpam-3449	5	16	properties	property	NOUN
ejpam-3449	5	17	.	.	PUNCT
ejpam-3449	6	1	moreover	moreover	ADV
ejpam-3449	6	2	,	,	PUNCT
ejpam-3449	6	3	we	we	PRON
ejpam-3449	6	4	introduce	introduce	VERB
ejpam-3449	6	5	and	and	CCONJ
ejpam-3449	6	6	investigate	investigate	VERB
ejpam-3449	6	7	some	some	DET
ejpam-3449	6	8	types	type	NOUN
ejpam-3449	6	9	of	of	ADP
ejpam-3449	6	10	fγ	fγ	NOUN
ejpam-3449	6	11	-	-	PUNCT
ejpam-3449	6	12	separation	separation	NOUN
ejpam-3449	6	13	axioms	axiom	NOUN
ejpam-3449	6	14	and	and	CCONJ
ejpam-3449	6	15	fγβ	fγβ	ADJ
ejpam-3449	6	16	-	-	PUNCT
ejpam-3449	6	17	continuous	continuous	ADJ
ejpam-3449	6	18	functions	function	NOUN
ejpam-3449	6	19	by	by	ADP
ejpam-3449	6	20	utilizing	utilize	VERB
ejpam-3449	6	21	the	the	DET
ejpam-3449	6	22	operation	operation	NOUN
ejpam-3449	6	23	γ	γ	NOUN
ejpam-3449	6	24	on	on	ADP
ejpam-3449	6	25	τf	τf	PROPN
ejpam-3449	6	26	.	.	PUNCT
ejpam-3449	7	1	finally	finally	ADV
ejpam-3449	7	2	,	,	PUNCT
ejpam-3449	7	3	some	some	DET
ejpam-3449	7	4	basic	basic	ADJ
ejpam-3449	7	5	properties	property	NOUN
ejpam-3449	7	6	of	of	ADP
ejpam-3449	7	7	functions	function	NOUN
ejpam-3449	7	8	with	with	ADP
ejpam-3449	7	9	fβ	fβ	ADV
ejpam-3449	7	10	-	-	PUNCT
ejpam-3449	7	11	closed	closed	ADJ
ejpam-3449	7	12	graphs	graph	NOUN
ejpam-3449	7	13	have	have	AUX
ejpam-3449	7	14	been	be	AUX
ejpam-3449	7	15	obtained	obtain	VERB
ejpam-3449	7	16	.	.	PUNCT
ejpam-3449	8	1	2010	2010	NUM
ejpam-3449	8	2	mathematics	mathematic	NOUN
ejpam-3449	8	3	subject	subject	NOUN
ejpam-3449	8	4	classifications	classification	NOUN
ejpam-3449	8	5	:	:	PUNCT
ejpam-3449	8	6	54a05	54a05	NUM
ejpam-3449	8	7	,	,	PUNCT
ejpam-3449	8	8	54a10	54a10	NUM
ejpam-3449	8	9	,	,	PUNCT
ejpam-3449	8	10	54c05	54c05	NUM
ejpam-3449	8	11	,	,	PUNCT
ejpam-3449	8	12	54c10	54c10	NUM
ejpam-3449	8	13	,	,	PUNCT
ejpam-3449	8	14	54d10	54d10	NUM
ejpam-3449	8	15	key	key	ADJ
ejpam-3449	8	16	words	word	NOUN
ejpam-3449	8	17	and	and	CCONJ
ejpam-3449	8	18	phrases	phrase	NOUN
ejpam-3449	8	19	:	:	PUNCT
ejpam-3449	8	20	fine	fine	ADJ
ejpam-3449	8	21	-	-	PUNCT
ejpam-3449	8	22	open	open	ADJ
ejpam-3449	8	23	sets	set	NOUN
ejpam-3449	8	24	,	,	PUNCT
ejpam-3449	8	25	fγ	fγ	NOUN
ejpam-3449	8	26	-	-	PUNCT
ejpam-3449	8	27	open	open	ADJ
ejpam-3449	8	28	sets	set	NOUN
ejpam-3449	8	29	,	,	PUNCT
ejpam-3449	8	30	fγg.closed	fγg.closed	ADJ
ejpam-3449	8	31	sets	set	NOUN
ejpam-3449	8	32	,	,	PUNCT
ejpam-3449	8	33	fγ	fγ	NOUN
ejpam-3449	8	34	-	-	PUNCT
ejpam-3449	8	35	separation	separation	NOUN
ejpam-3449	8	36	axioms	axiom	NOUN
ejpam-3449	8	37	,	,	PUNCT
ejpam-3449	8	38	fγβ	fγβ	ADJ
ejpam-3449	8	39	-	-	PUNCT
ejpam-3449	8	40	continuous	continuous	ADJ
ejpam-3449	8	41	functions	function	NOUN
ejpam-3449	8	42	,	,	PUNCT
ejpam-3449	8	43	fβ	fβ	ADJ
ejpam-3449	8	44	-	-	PUNCT
ejpam-3449	8	45	closed	closed	ADJ
ejpam-3449	8	46	graphs	graph	NOUN
ejpam-3449	8	47	1	1	NUM
ejpam-3449	8	48	.	.	PUNCT
ejpam-3449	9	1	introduction	introduction	NOUN
ejpam-3449	9	2	kasahara	kasahara	PROPN
ejpam-3449	10	1	[	[	X
ejpam-3449	10	2	11	11	NUM
ejpam-3449	10	3	]	]	PUNCT
ejpam-3449	10	4	introduced	introduce	VERB
ejpam-3449	10	5	the	the	DET
ejpam-3449	10	6	notion	notion	NOUN
ejpam-3449	10	7	of	of	ADP
ejpam-3449	10	8	an	an	DET
ejpam-3449	10	9	α	α	NOUN
ejpam-3449	10	10	operation	operation	NOUN
ejpam-3449	10	11	approaches	approach	NOUN
ejpam-3449	10	12	on	on	ADP
ejpam-3449	10	13	a	a	DET
ejpam-3449	10	14	class	class	NOUN
ejpam-3449	10	15	τ	τ	PROPN
ejpam-3449	10	16	of	of	ADP
ejpam-3449	10	17	sets	set	NOUN
ejpam-3449	10	18	and	and	CCONJ
ejpam-3449	10	19	studied	study	VERB
ejpam-3449	10	20	the	the	DET
ejpam-3449	10	21	concept	concept	NOUN
ejpam-3449	10	22	of	of	ADP
ejpam-3449	10	23	α	α	NOUN
ejpam-3449	10	24	-	-	ADJ
ejpam-3449	10	25	continuous	continuous	ADJ
ejpam-3449	10	26	functions	function	NOUN
ejpam-3449	10	27	with	with	ADP
ejpam-3449	10	28	α	α	NOUN
ejpam-3449	10	29	-	-	PUNCT
ejpam-3449	10	30	closed	closed	ADJ
ejpam-3449	10	31	graphs	graph	NOUN
ejpam-3449	10	32	and	and	CCONJ
ejpam-3449	10	33	α	α	NOUN
ejpam-3449	10	34	-	-	ADJ
ejpam-3449	10	35	compact	compact	ADJ
ejpam-3449	10	36	spaces	space	NOUN
ejpam-3449	10	37	.	.	PUNCT
ejpam-3449	11	1	after	after	ADP
ejpam-3449	11	2	this	this	PRON
ejpam-3449	11	3	,	,	PUNCT
ejpam-3449	11	4	jankovic	jankovic	PROPN
ejpam-3449	11	5	[	[	X
ejpam-3449	11	6	10	10	NUM
ejpam-3449	11	7	]	]	PUNCT
ejpam-3449	11	8	introduced	introduce	VERB
ejpam-3449	11	9	the	the	DET
ejpam-3449	11	10	concept	concept	NOUN
ejpam-3449	11	11	of	of	ADP
ejpam-3449	11	12	α	α	NOUN
ejpam-3449	11	13	-	-	NOUN
ejpam-3449	11	14	closure	closure	NOUN
ejpam-3449	11	15	of	of	ADP
ejpam-3449	11	16	a	a	DET
ejpam-3449	11	17	set	set	NOUN
ejpam-3449	11	18	in	in	ADP
ejpam-3449	11	19	x	x	PUNCT
ejpam-3449	11	20	via	via	ADP
ejpam-3449	11	21	α	α	NOUN
ejpam-3449	11	22	-	-	NOUN
ejpam-3449	11	23	operation	operation	NOUN
ejpam-3449	11	24	and	and	CCONJ
ejpam-3449	11	25	investigated	investigate	VERB
ejpam-3449	11	26	further	further	ADJ
ejpam-3449	11	27	characterizations	characterization	NOUN
ejpam-3449	11	28	of	of	ADP
ejpam-3449	11	29	function	function	NOUN
ejpam-3449	11	30	with	with	ADP
ejpam-3449	11	31	α	α	NOUN
ejpam-3449	11	32	-	-	PUNCT
ejpam-3449	11	33	closed	closed	ADJ
ejpam-3449	11	34	graph	graph	NOUN
ejpam-3449	11	35	.	.	PUNCT
ejpam-3449	12	1	later	later	ADV
ejpam-3449	12	2	,	,	PUNCT
ejpam-3449	12	3	ogata	ogata	PROPN
ejpam-3449	13	1	[	[	X
ejpam-3449	13	2	12	12	NUM
ejpam-3449	13	3	]	]	PUNCT
ejpam-3449	13	4	defined	define	VERB
ejpam-3449	13	5	and	and	CCONJ
ejpam-3449	13	6	studied	study	VERB
ejpam-3449	13	7	the	the	DET
ejpam-3449	13	8	concept	concept	NOUN
ejpam-3449	13	9	of	of	ADP
ejpam-3449	13	10	γ	γ	NOUN
ejpam-3449	13	11	-	-	ADJ
ejpam-3449	13	12	open	open	ADJ
ejpam-3449	13	13	sets	set	NOUN
ejpam-3449	13	14	,	,	PUNCT
ejpam-3449	13	15	and	and	CCONJ
ejpam-3449	13	16	applied	apply	VERB
ejpam-3449	13	17	it	it	PRON
ejpam-3449	13	18	to	to	PART
ejpam-3449	13	19	investigate	investigate	VERB
ejpam-3449	13	20	operation	operation	NOUN
ejpam-3449	13	21	-	-	PUNCT
ejpam-3449	13	22	functions	function	NOUN
ejpam-3449	13	23	and	and	CCONJ
ejpam-3449	13	24	operation	operation	NOUN
ejpam-3449	13	25	-	-	PUNCT
ejpam-3449	13	26	separation	separation	NOUN
ejpam-3449	13	27	axioms	axiom	NOUN
ejpam-3449	13	28	.	.	PUNCT
ejpam-3449	14	1	asaad	asaad	PROPN
ejpam-3449	14	2	et	et	PROPN
ejpam-3449	14	3	al	al	PROPN
ejpam-3449	14	4	.	.	PUNCT
ejpam-3449	15	1	[	[	X
ejpam-3449	15	2	7	7	X
ejpam-3449	15	3	]	]	PUNCT
ejpam-3449	15	4	introduced	introduce	VERB
ejpam-3449	15	5	the	the	DET
ejpam-3449	15	6	notion	notion	NOUN
ejpam-3449	15	7	of	of	ADP
ejpam-3449	15	8	γ	γ	X
ejpam-3449	15	9	-	-	ADJ
ejpam-3449	15	10	extremally	extremally	ADV
ejpam-3449	15	11	disconnected	disconnected	ADJ
ejpam-3449	15	12	spaces	space	NOUN
ejpam-3449	15	13	.	.	PUNCT
ejpam-3449	16	1	asaad	asaad	PROPN
ejpam-3449	16	2	et	et	PROPN
ejpam-3449	16	3	al	al	PROPN
ejpam-3449	16	4	.	.	PUNCT
ejpam-3449	17	1	[	[	X
ejpam-3449	17	2	5	5	NUM
ejpam-3449	17	3	]	]	PUNCT
ejpam-3449	17	4	studied	study	VERB
ejpam-3449	17	5	further	further	ADJ
ejpam-3449	17	6	characterizations	characterization	NOUN
ejpam-3449	17	7	of	of	ADP
ejpam-3449	17	8	γ	γ	X
ejpam-3449	17	9	-	-	ADJ
ejpam-3449	17	10	extremally	extremally	ADV
ejpam-3449	17	11	disconnected	disconnected	ADJ
ejpam-3449	17	12	spaces	space	NOUN
ejpam-3449	17	13	and	and	CCONJ
ejpam-3449	17	14	investigated	investigate	VERB
ejpam-3449	17	15	some	some	DET
ejpam-3449	17	16	relations	relation	NOUN
ejpam-3449	17	17	of	of	ADP
ejpam-3449	17	18	functions	function	NOUN
ejpam-3449	17	19	of	of	ADP
ejpam-3449	17	20	γ	γ	X
ejpam-3449	17	21	-	-	ADJ
ejpam-3449	17	22	extremally	extremally	ADV
ejpam-3449	17	23	disconnected	disconnected	ADJ
ejpam-3449	17	24	spaces	space	NOUN
ejpam-3449	17	25	.	.	PUNCT
ejpam-3449	18	1	asaad	asaad	PROPN
ejpam-3449	19	1	[	[	X
ejpam-3449	19	2	4	4	X
ejpam-3449	19	3	]	]	PUNCT
ejpam-3449	19	4	defined	define	VERB
ejpam-3449	19	5	a	a	DET
ejpam-3449	19	6	γ	γ	NOUN
ejpam-3449	19	7	operation	operation	NOUN
ejpam-3449	19	8	on	on	ADP
ejpam-3449	19	9	generalized	generalized	ADJ
ejpam-3449	19	10	open	open	ADJ
ejpam-3449	19	11	sets	set	NOUN
ejpam-3449	19	12	in	in	ADP
ejpam-3449	19	13	x	x	PUNCT
ejpam-3449	19	14	and	and	CCONJ
ejpam-3449	19	15	studied	study	VERB
ejpam-3449	19	16	its	its	PRON
ejpam-3449	19	17	applications	application	NOUN
ejpam-3449	19	18	.	.	PUNCT
ejpam-3449	20	1	in	in	ADP
ejpam-3449	20	2	2017	2017	NUM
ejpam-3449	20	3	-	-	SYM
ejpam-3449	20	4	2018	2018	NUM
ejpam-3449	20	5	,	,	PUNCT
ejpam-3449	20	6	ahmad	ahmad	PROPN
ejpam-3449	20	7	and	and	CCONJ
ejpam-3449	20	8	asaad	asaad	NOUN
ejpam-3449	20	9	(	(	PUNCT
ejpam-3449	20	10	[	[	X
ejpam-3449	20	11	1	1	NUM
ejpam-3449	20	12	]	]	PUNCT
ejpam-3449	20	13	,	,	PUNCT
ejpam-3449	20	14	[	[	X
ejpam-3449	20	15	6	6	NUM
ejpam-3449	20	16	]	]	PUNCT
ejpam-3449	20	17	)	)	PUNCT
ejpam-3449	20	18	introduced	introduce	VERB
ejpam-3449	20	19	an	an	DET
ejpam-3449	20	20	operation	operation	NOUN
ejpam-3449	20	21	γ	γ	NOUN
ejpam-3449	20	22	on	on	ADP
ejpam-3449	20	23	semi	semi	ADV
ejpam-3449	20	24	generalized	generalize	VERB
ejpam-3449	20	25	open	open	ADJ
ejpam-3449	20	26	subsets	subset	NOUN
ejpam-3449	20	27	of	of	ADP
ejpam-3449	20	28	x	x	PUNCT
ejpam-3449	20	29	and	and	CCONJ
ejpam-3449	20	30	discussed	discuss	VERB
ejpam-3449	20	31	some	some	DET
ejpam-3449	20	32	types	type	NOUN
ejpam-3449	20	33	of	of	ADP
ejpam-3449	20	34	separation	separation	NOUN
ejpam-3449	20	35	axioms	axiom	NOUN
ejpam-3449	20	36	,	,	PUNCT
ejpam-3449	20	37	functions	function	NOUN
ejpam-3449	20	38	and	and	CCONJ
ejpam-3449	20	39	closed	closed	ADJ
ejpam-3449	20	40	spaces	space	NOUN
ejpam-3449	20	41	with	with	ADP
ejpam-3449	20	42	respect	respect	NOUN
ejpam-3449	20	43	to	to	ADP
ejpam-3449	20	44	γ	γ	PROPN
ejpam-3449	20	45	.	.	PUNCT
ejpam-3449	20	46	recently	recently	ADV
ejpam-3449	20	47	,	,	PUNCT
ejpam-3449	20	48	asaad	asaad	NOUN
ejpam-3449	20	49	and	and	CCONJ
ejpam-3449	20	50	ameen	ameen	NOUN
ejpam-3449	21	1	[	[	X
ejpam-3449	21	2	8	8	NUM
ejpam-3449	21	3	]	]	PUNCT
ejpam-3449	21	4	introduced	introduce	VERB
ejpam-3449	21	5	an	an	DET
ejpam-3449	21	6	operation	operation	NOUN
ejpam-3449	21	7	on	on	ADP
ejpam-3449	21	8	gα	gα	NOUN
ejpam-3449	21	9	-	-	PUNCT
ejpam-3449	21	10	open	open	ADJ
ejpam-3449	21	11	sets	set	NOUN
ejpam-3449	21	12	and	and	CCONJ
ejpam-3449	21	13	studied	study	VERB
ejpam-3449	21	14	some	some	PRON
ejpam-3449	21	15	of	of	ADP
ejpam-3449	21	16	its	its	PRON
ejpam-3449	21	17	properties	property	NOUN
ejpam-3449	21	18	.	.	PUNCT
ejpam-3449	22	1	on	on	ADP
ejpam-3449	22	2	∗corresponding	∗corresponde	VERB
ejpam-3449	22	3	author	author	NOUN
ejpam-3449	22	4	.	.	PUNCT
ejpam-3449	23	1	doi	doi	NOUN
ejpam-3449	23	2	:	:	PUNCT
ejpam-3449	23	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3449	https://doi.org/10.29020/nybg.ejpam.v12i3.3449	PRON
ejpam-3449	23	4	email	email	NOUN
ejpam-3449	23	5	addresses	address	VERB
ejpam-3449	23	6	:	:	PUNCT
ejpam-3449	23	7	pvjrdvv@gamil.com	pvjrdvv@gamil.com	X
ejpam-3449	23	8	(	(	PUNCT
ejpam-3449	23	9	p.	p.	NOUN
ejpam-3449	23	10	l.	l.	PROPN
ejpam-3449	23	11	powar	powar	PROPN
ejpam-3449	23	12	)	)	PUNCT
ejpam-3449	23	13	,	,	PUNCT
ejpam-3449	23	14	baravan.asaad@uoz.edu.krd	baravan.asaad@uoz.edu.krd	PROPN
ejpam-3449	23	15	(	(	PUNCT
ejpam-3449	23	16	b.	b.	PROPN
ejpam-3449	23	17	a.	a.	PROPN
ejpam-3449	23	18	asaad	asaad	PROPN
ejpam-3449	23	19	)	)	PUNCT
ejpam-3449	23	20	,	,	PUNCT
ejpam-3449	23	21	kusumrajakrdvv@gmail.com	kusumrajakrdvv@gmail.com	PROPN
ejpam-3449	23	22	(	(	PUNCT
ejpam-3449	23	23	k.	k.	PROPN
ejpam-3449	23	24	rajak	rajak	PROPN
ejpam-3449	23	25	)	)	PUNCT
ejpam-3449	23	26	,	,	PUNCT
ejpam-3449	23	27	kushwaharam786@gmail.com	kushwaharam786@gmail.com	X
ejpam-3449	23	28	(	(	PUNCT
ejpam-3449	23	29	r.	r.	PROPN
ejpam-3449	23	30	kushwaha	kushwaha	PROPN
ejpam-3449	23	31	)	)	PUNCT
ejpam-3449	23	32	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3449	24	1	960	960	NUM
ejpam-3449	24	2	c	c	X
ejpam-3449	24	3	©	©	PROPN
ejpam-3449	24	4	2019	2019	NUM
ejpam-3449	24	5	ejpam	ejpam	NOUN
ejpam-3449	24	6	all	all	DET
ejpam-3449	24	7	rights	right	NOUN
ejpam-3449	24	8	reserved	reserve	VERB
ejpam-3449	24	9	.	.	PUNCT
ejpam-3449	25	1	b.	b.	PROPN
ejpam-3449	25	2	a.	a.	PROPN
ejpam-3449	25	3	asaad	asaad	PROPN
ejpam-3449	25	4	et	et	PROPN
ejpam-3449	25	5	al	al	PROPN
ejpam-3449	25	6	.	.	PUNCT
ejpam-3449	25	7	/	/	SYM
ejpam-3449	25	8	eur	eur	PROPN
ejpam-3449	25	9	.	.	PUNCT
ejpam-3449	26	1	j.	j.	PROPN
ejpam-3449	26	2	pure	pure	PROPN
ejpam-3449	26	3	appl	appl	PROPN
ejpam-3449	26	4	.	.	PROPN
ejpam-3449	26	5	math	math	PROPN
ejpam-3449	26	6	,	,	PUNCT
ejpam-3449	26	7	12	12	NUM
ejpam-3449	26	8	(	(	PUNCT
ejpam-3449	26	9	3	3	NUM
ejpam-3449	26	10	)	)	PUNCT
ejpam-3449	26	11	(	(	PUNCT
ejpam-3449	26	12	2019	2019	NUM
ejpam-3449	26	13	)	)	PUNCT
ejpam-3449	26	14	,	,	PUNCT
ejpam-3449	26	15	960	960	NUM
ejpam-3449	26	16	-	-	SYM
ejpam-3449	26	17	977	977	NUM
ejpam-3449	26	18	961	961	NUM
ejpam-3449	26	19	the	the	DET
ejpam-3449	26	20	other	other	ADJ
ejpam-3449	26	21	hand	hand	NOUN
ejpam-3449	26	22	,	,	PUNCT
ejpam-3449	26	23	powar	powar	NOUN
ejpam-3449	26	24	and	and	CCONJ
ejpam-3449	26	25	rajak	rajak	ADJ
ejpam-3449	27	1	[	[	X
ejpam-3449	27	2	13	13	NUM
ejpam-3449	27	3	]	]	PUNCT
ejpam-3449	27	4	defined	define	VERB
ejpam-3449	27	5	the	the	DET
ejpam-3449	27	6	concept	concept	NOUN
ejpam-3449	27	7	of	of	ADP
ejpam-3449	27	8	fine	fine	ADJ
ejpam-3449	27	9	-	-	PUNCT
ejpam-3449	27	10	open	open	ADJ
ejpam-3449	27	11	sets	set	NOUN
ejpam-3449	27	12	.	.	PUNCT
ejpam-3449	28	1	they	they	PRON
ejpam-3449	28	2	studied	study	VERB
ejpam-3449	28	3	fine	fine	ADJ
ejpam-3449	28	4	-	-	PUNCT
ejpam-3449	28	5	irresolute	irresolute	ADJ
ejpam-3449	28	6	homeomorphism	homeomorphism	NOUN
ejpam-3449	28	7	and	and	CCONJ
ejpam-3449	28	8	fine	fine	ADJ
ejpam-3449	28	9	-	-	PUNCT
ejpam-3449	28	10	quotient	quotient	NOUN
ejpam-3449	28	11	function	function	NOUN
ejpam-3449	28	12	.	.	PUNCT
ejpam-3449	29	1	the	the	DET
ejpam-3449	29	2	aim	aim	NOUN
ejpam-3449	29	3	of	of	ADP
ejpam-3449	29	4	this	this	DET
ejpam-3449	29	5	paper	paper	NOUN
ejpam-3449	29	6	is	be	AUX
ejpam-3449	29	7	to	to	PART
ejpam-3449	29	8	introduce	introduce	VERB
ejpam-3449	29	9	the	the	DET
ejpam-3449	29	10	concept	concept	NOUN
ejpam-3449	29	11	of	of	ADP
ejpam-3449	29	12	an	an	DET
ejpam-3449	29	13	operation	operation	NOUN
ejpam-3449	29	14	γ	γ	NOUN
ejpam-3449	29	15	on	on	ADP
ejpam-3449	29	16	τf	τf	ADP
ejpam-3449	29	17	and	and	CCONJ
ejpam-3449	29	18	to	to	PART
ejpam-3449	29	19	define	define	VERB
ejpam-3449	29	20	the	the	DET
ejpam-3449	29	21	notion	notion	NOUN
ejpam-3449	29	22	of	of	ADP
ejpam-3449	29	23	fγ	fγ	NOUN
ejpam-3449	29	24	-	-	PUNCT
ejpam-3449	29	25	open	open	ADJ
ejpam-3449	29	26	sets	set	NOUN
ejpam-3449	29	27	of	of	ADP
ejpam-3449	29	28	(	(	PUNCT
ejpam-3449	29	29	x	x	NOUN
ejpam-3449	29	30	,	,	PUNCT
ejpam-3449	29	31	τ	τ	PROPN
ejpam-3449	29	32	,	,	PUNCT
ejpam-3449	29	33	τf	τf	NUM
ejpam-3449	29	34	)	)	PUNCT
ejpam-3449	29	35	by	by	ADP
ejpam-3449	29	36	using	use	VERB
ejpam-3449	29	37	the	the	DET
ejpam-3449	29	38	operation	operation	NOUN
ejpam-3449	29	39	γ	γ	NOUN
ejpam-3449	29	40	on	on	ADP
ejpam-3449	29	41	τf	τf	PROPN
ejpam-3449	29	42	.	.	PUNCT
ejpam-3449	30	1	also	also	ADV
ejpam-3449	30	2	,	,	PUNCT
ejpam-3449	30	3	some	some	DET
ejpam-3449	30	4	notions	notion	NOUN
ejpam-3449	30	5	of	of	ADP
ejpam-3449	30	6	fγ	fγ	NOUN
ejpam-3449	30	7	-	-	PUNCT
ejpam-3449	30	8	open	open	ADJ
ejpam-3449	30	9	sets	set	NOUN
ejpam-3449	30	10	with	with	ADP
ejpam-3449	30	11	their	their	PRON
ejpam-3449	30	12	relationships	relationship	NOUN
ejpam-3449	30	13	are	be	AUX
ejpam-3449	30	14	studied	study	VERB
ejpam-3449	30	15	.	.	PUNCT
ejpam-3449	31	1	in	in	ADP
ejpam-3449	31	2	section	section	NOUN
ejpam-3449	31	3	4	4	NUM
ejpam-3449	31	4	,	,	PUNCT
ejpam-3449	31	5	we	we	PRON
ejpam-3449	31	6	introduce	introduce	VERB
ejpam-3449	31	7	the	the	DET
ejpam-3449	31	8	concept	concept	NOUN
ejpam-3449	31	9	of	of	ADP
ejpam-3449	31	10	fγg.closed	fγg.close	VERB
ejpam-3449	31	11	sets	set	NOUN
ejpam-3449	31	12	and	and	CCONJ
ejpam-3449	31	13	then	then	ADV
ejpam-3449	31	14	investigate	investigate	VERB
ejpam-3449	31	15	some	some	PRON
ejpam-3449	31	16	of	of	ADP
ejpam-3449	31	17	its	its	PRON
ejpam-3449	31	18	properties	property	NOUN
ejpam-3449	31	19	.	.	PUNCT
ejpam-3449	32	1	in	in	ADP
ejpam-3449	32	2	section	section	NOUN
ejpam-3449	32	3	5	5	NUM
ejpam-3449	32	4	,	,	PUNCT
ejpam-3449	32	5	some	some	DET
ejpam-3449	32	6	types	type	NOUN
ejpam-3449	32	7	of	of	ADP
ejpam-3449	32	8	fγ	fγ	NOUN
ejpam-3449	32	9	-	-	PUNCT
ejpam-3449	32	10	separation	separation	NOUN
ejpam-3449	32	11	axioms	axiom	NOUN
ejpam-3449	32	12	by	by	ADP
ejpam-3449	32	13	utilizing	utilize	VERB
ejpam-3449	32	14	the	the	DET
ejpam-3449	32	15	operation	operation	NOUN
ejpam-3449	32	16	γ	γ	NOUN
ejpam-3449	32	17	on	on	ADP
ejpam-3449	32	18	τf	τf	PROPN
ejpam-3449	32	19	are	be	AUX
ejpam-3449	32	20	introduced	introduce	VERB
ejpam-3449	32	21	and	and	CCONJ
ejpam-3449	32	22	investigated	investigate	VERB
ejpam-3449	32	23	.	.	PUNCT
ejpam-3449	33	1	in	in	ADP
ejpam-3449	33	2	the	the	DET
ejpam-3449	33	3	last	last	ADJ
ejpam-3449	33	4	two	two	NUM
ejpam-3449	33	5	sections	section	NOUN
ejpam-3449	33	6	,	,	PUNCT
ejpam-3449	33	7	some	some	DET
ejpam-3449	33	8	basic	basic	ADJ
ejpam-3449	33	9	properties	property	NOUN
ejpam-3449	33	10	of	of	ADP
ejpam-3449	33	11	fγβ	fγβ	ADJ
ejpam-3449	33	12	-	-	PUNCT
ejpam-3449	33	13	continuous	continuous	ADJ
ejpam-3449	33	14	functions	function	NOUN
ejpam-3449	33	15	with	with	ADP
ejpam-3449	33	16	fβ	fβ	ADV
ejpam-3449	33	17	-	-	PUNCT
ejpam-3449	33	18	closed	closed	ADJ
ejpam-3449	33	19	graphs	graph	NOUN
ejpam-3449	33	20	have	have	AUX
ejpam-3449	33	21	been	be	AUX
ejpam-3449	33	22	obtained	obtain	VERB
ejpam-3449	33	23	.	.	PUNCT
ejpam-3449	34	1	2	2	X
ejpam-3449	34	2	.	.	NUM
ejpam-3449	34	3	preliminaries	preliminary	NOUN
ejpam-3449	34	4	throughout	throughout	ADP
ejpam-3449	34	5	this	this	DET
ejpam-3449	34	6	paper	paper	NOUN
ejpam-3449	34	7	,	,	PUNCT
ejpam-3449	34	8	the	the	DET
ejpam-3449	34	9	space	space	NOUN
ejpam-3449	34	10	(	(	PUNCT
ejpam-3449	34	11	x	x	X
ejpam-3449	34	12	,	,	PUNCT
ejpam-3449	34	13	τ	τ	X
ejpam-3449	34	14	)	)	PUNCT
ejpam-3449	34	15	(	(	PUNCT
ejpam-3449	34	16	or	or	CCONJ
ejpam-3449	34	17	simply	simply	ADV
ejpam-3449	34	18	x	x	X
ejpam-3449	34	19	)	)	PUNCT
ejpam-3449	34	20	always	always	ADV
ejpam-3449	34	21	mean	mean	VERB
ejpam-3449	34	22	topological	topological	ADJ
ejpam-3449	34	23	space	space	NOUN
ejpam-3449	34	24	on	on	ADP
ejpam-3449	34	25	which	which	PRON
ejpam-3449	34	26	no	no	DET
ejpam-3449	34	27	separation	separation	NOUN
ejpam-3449	34	28	axioms	axiom	NOUN
ejpam-3449	34	29	are	be	AUX
ejpam-3449	34	30	assumed	assume	VERB
ejpam-3449	34	31	unless	unless	SCONJ
ejpam-3449	34	32	explicitly	explicitly	ADV
ejpam-3449	34	33	stated	state	VERB
ejpam-3449	34	34	.	.	PUNCT
ejpam-3449	35	1	definition	definition	NOUN
ejpam-3449	35	2	2.1	2.1	NUM
ejpam-3449	35	3	.	.	PUNCT
ejpam-3449	36	1	[	[	X
ejpam-3449	36	2	13	13	NUM
ejpam-3449	36	3	]	]	PUNCT
ejpam-3449	36	4	let	let	VERB
ejpam-3449	36	5	(	(	PUNCT
ejpam-3449	36	6	x	x	NOUN
ejpam-3449	36	7	,	,	PUNCT
ejpam-3449	36	8	τ	τ	X
ejpam-3449	36	9	)	)	PUNCT
ejpam-3449	36	10	be	be	VERB
ejpam-3449	36	11	a	a	DET
ejpam-3449	36	12	topological	topological	ADJ
ejpam-3449	36	13	space	space	NOUN
ejpam-3449	36	14	,	,	PUNCT
ejpam-3449	36	15	we	we	PRON
ejpam-3449	36	16	define	define	VERB
ejpam-3449	36	17	τ(aα	τ(aα	NOUN
ejpam-3449	36	18	)	)	PUNCT
ejpam-3449	36	19	=	=	SYM
ejpam-3449	36	20	τα(say)=	τα(say)=	NOUN
ejpam-3449	36	21	{	{	PUNCT
ejpam-3449	36	22	gα(6=	gα(6=	NOUN
ejpam-3449	36	23	x	x	NOUN
ejpam-3449	36	24	)	)	PUNCT
ejpam-3449	36	25	:	:	PUNCT
ejpam-3449	36	26	gα	gα	ADP
ejpam-3449	36	27	∩aα	∩aα	PROPN
ejpam-3449	36	28	6=	6=	PROPN
ejpam-3449	36	29	φ	φ	PROPN
ejpam-3449	36	30	,	,	PUNCT
ejpam-3449	36	31	for	for	ADP
ejpam-3449	36	32	aα	aα	NOUN
ejpam-3449	36	33	∈	∈	PROPN
ejpam-3449	36	34	τ	τ	X
ejpam-3449	36	35	and	and	CCONJ
ejpam-3449	36	36	aα	aα	PROPN
ejpam-3449	36	37	6=	6=	PROPN
ejpam-3449	36	38	φ	φ	PROPN
ejpam-3449	36	39	,	,	PUNCT
ejpam-3449	36	40	x.	x.	NOUN
ejpam-3449	36	41	for	for	ADP
ejpam-3449	36	42	some	some	DET
ejpam-3449	36	43	α	α	NOUN
ejpam-3449	36	44	∈	∈	PROPN
ejpam-3449	36	45	j	j	PROPN
ejpam-3449	36	46	,	,	PUNCT
ejpam-3449	36	47	where	where	SCONJ
ejpam-3449	36	48	j	j	PROPN
ejpam-3449	36	49	is	be	AUX
ejpam-3449	36	50	the	the	DET
ejpam-3449	36	51	index	index	NOUN
ejpam-3449	36	52	set	set	NOUN
ejpam-3449	36	53	}	}	PUNCT
ejpam-3449	36	54	.	.	PUNCT
ejpam-3449	37	1	now	now	ADV
ejpam-3449	37	2	,	,	PUNCT
ejpam-3449	37	3	define	define	VERB
ejpam-3449	37	4	τf	τf	ADP
ejpam-3449	37	5	=	=	SYM
ejpam-3449	37	6	{	{	PUNCT
ejpam-3449	37	7	φ	φ	PROPN
ejpam-3449	37	8	,	,	PUNCT
ejpam-3449	37	9	x}∪α	x}∪α	PUNCT
ejpam-3449	37	10	{	{	PUNCT
ejpam-3449	37	11	τα	τα	NOUN
ejpam-3449	37	12	}	}	PUNCT
ejpam-3449	37	13	.	.	PUNCT
ejpam-3449	38	1	the	the	DET
ejpam-3449	38	2	above	above	ADJ
ejpam-3449	38	3	collection	collection	NOUN
ejpam-3449	38	4	τf	τf	ADP
ejpam-3449	38	5	of	of	ADP
ejpam-3449	38	6	subsets	subset	NOUN
ejpam-3449	38	7	of	of	ADP
ejpam-3449	38	8	x	x	SYM
ejpam-3449	38	9	is	be	AUX
ejpam-3449	38	10	called	call	VERB
ejpam-3449	38	11	the	the	DET
ejpam-3449	38	12	fine	fine	ADJ
ejpam-3449	38	13	collection	collection	NOUN
ejpam-3449	38	14	of	of	ADP
ejpam-3449	38	15	subsets	subset	NOUN
ejpam-3449	38	16	of	of	ADP
ejpam-3449	38	17	x	x	PUNCT
ejpam-3449	38	18	and	and	CCONJ
ejpam-3449	38	19	(	(	PUNCT
ejpam-3449	38	20	x	x	NOUN
ejpam-3449	38	21	,	,	PUNCT
ejpam-3449	38	22	τ	τ	PROPN
ejpam-3449	38	23	,	,	PUNCT
ejpam-3449	38	24	τf	τf	PROPN
ejpam-3449	38	25	)	)	PUNCT
ejpam-3449	38	26	is	be	AUX
ejpam-3449	38	27	said	say	VERB
ejpam-3449	38	28	to	to	PART
ejpam-3449	38	29	be	be	AUX
ejpam-3449	38	30	the	the	DET
ejpam-3449	38	31	fine	fine	ADJ
ejpam-3449	38	32	space	space	NOUN
ejpam-3449	38	33	x	x	PUNCT
ejpam-3449	38	34	generated	generate	VERB
ejpam-3449	38	35	by	by	ADP
ejpam-3449	38	36	the	the	DET
ejpam-3449	38	37	topology	topology	NOUN
ejpam-3449	38	38	τ	τ	PROPN
ejpam-3449	38	39	on	on	ADP
ejpam-3449	38	40	x.	x.	PROPN
ejpam-3449	38	41	definition	definition	NOUN
ejpam-3449	38	42	2.2	2.2	NUM
ejpam-3449	38	43	.	.	PUNCT
ejpam-3449	39	1	[	[	X
ejpam-3449	39	2	13	13	NUM
ejpam-3449	39	3	]	]	PUNCT
ejpam-3449	39	4	a	a	DET
ejpam-3449	39	5	subset	subset	ADJ
ejpam-3449	39	6	u	u	NOUN
ejpam-3449	39	7	of	of	ADP
ejpam-3449	39	8	a	a	DET
ejpam-3449	39	9	fine	fine	ADJ
ejpam-3449	39	10	space	space	NOUN
ejpam-3449	39	11	x	x	PRON
ejpam-3449	39	12	is	be	AUX
ejpam-3449	39	13	said	say	VERB
ejpam-3449	39	14	to	to	PART
ejpam-3449	39	15	be	be	AUX
ejpam-3449	39	16	fine	fine	ADV
ejpam-3449	39	17	-	-	PUNCT
ejpam-3449	39	18	open	open	ADJ
ejpam-3449	39	19	in	in	ADP
ejpam-3449	39	20	x	x	NOUN
ejpam-3449	39	21	,	,	PUNCT
ejpam-3449	39	22	if	if	SCONJ
ejpam-3449	39	23	u	u	NOUN
ejpam-3449	39	24	belongs	belong	VERB
ejpam-3449	39	25	to	to	ADP
ejpam-3449	39	26	the	the	DET
ejpam-3449	39	27	collection	collection	NOUN
ejpam-3449	39	28	τf	τf	ADP
ejpam-3449	39	29	.	.	PUNCT
ejpam-3449	40	1	it	it	PRON
ejpam-3449	40	2	is	be	AUX
ejpam-3449	40	3	clear	clear	ADJ
ejpam-3449	40	4	that	that	SCONJ
ejpam-3449	40	5	every	every	DET
ejpam-3449	40	6	open	open	ADJ
ejpam-3449	40	7	set	set	NOUN
ejpam-3449	40	8	of	of	ADP
ejpam-3449	40	9	x	x	PUNCT
ejpam-3449	40	10	is	be	AUX
ejpam-3449	40	11	fine	fine	ADV
ejpam-3449	40	12	-	-	PUNCT
ejpam-3449	40	13	open	open	ADJ
ejpam-3449	40	14	in	in	ADP
ejpam-3449	40	15	x.	x.	NOUN
ejpam-3449	40	16	the	the	DET
ejpam-3449	40	17	complement	complement	NOUN
ejpam-3449	40	18	of	of	ADP
ejpam-3449	40	19	a	a	DET
ejpam-3449	40	20	fine	fine	ADV
ejpam-3449	40	21	-	-	PUNCT
ejpam-3449	40	22	open	open	ADJ
ejpam-3449	40	23	set	set	NOUN
ejpam-3449	40	24	of	of	ADP
ejpam-3449	40	25	x	x	PRON
ejpam-3449	40	26	is	be	AUX
ejpam-3449	40	27	called	call	VERB
ejpam-3449	40	28	the	the	DET
ejpam-3449	40	29	fine	fine	ADV
ejpam-3449	40	30	-	-	PUNCT
ejpam-3449	40	31	closed	close	VERB
ejpam-3449	40	32	in	in	ADP
ejpam-3449	40	33	x.	x.	NOUN
ejpam-3449	40	34	remark	remark	PROPN
ejpam-3449	40	35	2.3	2.3	NUM
ejpam-3449	40	36	.	.	PUNCT
ejpam-3449	41	1	[	[	X
ejpam-3449	41	2	13	13	NUM
ejpam-3449	41	3	]	]	PUNCT
ejpam-3449	41	4	let	let	VERB
ejpam-3449	41	5	(	(	PUNCT
ejpam-3449	41	6	x	x	NOUN
ejpam-3449	41	7	,	,	PUNCT
ejpam-3449	41	8	τ	τ	PROPN
ejpam-3449	41	9	,	,	PUNCT
ejpam-3449	41	10	τf	τf	NUM
ejpam-3449	41	11	)	)	PUNCT
ejpam-3449	41	12	be	be	AUX
ejpam-3449	41	13	a	a	DET
ejpam-3449	41	14	fine	fine	ADJ
ejpam-3449	41	15	space	space	NOUN
ejpam-3449	41	16	.	.	PUNCT
ejpam-3449	42	1	then	then	ADV
ejpam-3449	42	2	the	the	DET
ejpam-3449	42	3	following	following	NOUN
ejpam-3449	42	4	are	be	AUX
ejpam-3449	42	5	holds	hold	NOUN
ejpam-3449	42	6	.	.	PUNCT
ejpam-3449	43	1	(	(	PUNCT
ejpam-3449	43	2	i	i	NOUN
ejpam-3449	43	3	)	)	PUNCT
ejpam-3449	43	4	the	the	DET
ejpam-3449	43	5	arbitrary	arbitrary	ADJ
ejpam-3449	43	6	union	union	NOUN
ejpam-3449	43	7	of	of	ADP
ejpam-3449	43	8	any	any	DET
ejpam-3449	43	9	fine	fine	ADJ
ejpam-3449	43	10	-	-	PUNCT
ejpam-3449	43	11	open	open	ADJ
ejpam-3449	43	12	sets	set	NOUN
ejpam-3449	43	13	in	in	ADP
ejpam-3449	43	14	x	x	SYM
ejpam-3449	43	15	is	be	AUX
ejpam-3449	43	16	fine	fine	ADV
ejpam-3449	43	17	-	-	PUNCT
ejpam-3449	43	18	open	open	ADJ
ejpam-3449	43	19	of	of	ADP
ejpam-3449	43	20	x.	x.	PROPN
ejpam-3449	43	21	(	(	PUNCT
ejpam-3449	43	22	ii	ii	PROPN
ejpam-3449	43	23	)	)	PUNCT
ejpam-3449	43	24	the	the	DET
ejpam-3449	43	25	intersection	intersection	NOUN
ejpam-3449	43	26	of	of	ADP
ejpam-3449	43	27	two	two	NUM
ejpam-3449	43	28	fine	fine	ADJ
ejpam-3449	43	29	-	-	PUNCT
ejpam-3449	43	30	open	open	ADJ
ejpam-3449	43	31	sets	set	NOUN
ejpam-3449	43	32	need	need	AUX
ejpam-3449	43	33	not	not	PART
ejpam-3449	43	34	be	be	AUX
ejpam-3449	43	35	fine	fine	ADV
ejpam-3449	43	36	-	-	PUNCT
ejpam-3449	43	37	open	open	ADJ
ejpam-3449	43	38	.	.	PUNCT
ejpam-3449	44	1	definition	definition	NOUN
ejpam-3449	44	2	2.4	2.4	NUM
ejpam-3449	44	3	.	.	PUNCT
ejpam-3449	45	1	[	[	X
ejpam-3449	45	2	13	13	NUM
ejpam-3449	45	3	]	]	PUNCT
ejpam-3449	45	4	let	let	VERB
ejpam-3449	45	5	a	a	PRON
ejpam-3449	45	6	be	be	AUX
ejpam-3449	45	7	the	the	DET
ejpam-3449	45	8	subset	subset	NOUN
ejpam-3449	45	9	of	of	ADP
ejpam-3449	45	10	a	a	DET
ejpam-3449	45	11	fine	fine	ADJ
ejpam-3449	45	12	space	space	NOUN
ejpam-3449	46	1	x	x	NOUN
ejpam-3449	46	2	,	,	PUNCT
ejpam-3449	46	3	the	the	DET
ejpam-3449	46	4	fine	fine	ADJ
ejpam-3449	46	5	interior	interior	NOUN
ejpam-3449	46	6	of	of	ADP
ejpam-3449	46	7	a	a	PRON
ejpam-3449	46	8	is	be	AUX
ejpam-3449	46	9	defined	define	VERB
ejpam-3449	46	10	as	as	ADP
ejpam-3449	46	11	the	the	DET
ejpam-3449	46	12	union	union	NOUN
ejpam-3449	46	13	of	of	ADP
ejpam-3449	46	14	all	all	DET
ejpam-3449	46	15	fine	fine	ADJ
ejpam-3449	46	16	-	-	PUNCT
ejpam-3449	46	17	open	open	ADJ
ejpam-3449	46	18	sets	set	NOUN
ejpam-3449	46	19	contained	contain	VERB
ejpam-3449	46	20	in	in	ADP
ejpam-3449	46	21	a.	a.	NOUN
ejpam-3449	46	22	that	that	PRON
ejpam-3449	46	23	means	mean	VERB
ejpam-3449	46	24	,	,	PUNCT
ejpam-3449	46	25	the	the	DET
ejpam-3449	46	26	fine	fine	ADJ
ejpam-3449	46	27	interior	interior	NOUN
ejpam-3449	46	28	of	of	ADP
ejpam-3449	46	29	a	a	PRON
ejpam-3449	46	30	is	be	AUX
ejpam-3449	46	31	the	the	DET
ejpam-3449	46	32	largest	large	ADJ
ejpam-3449	46	33	fine	fine	ADJ
ejpam-3449	46	34	-	-	PUNCT
ejpam-3449	46	35	open	open	ADJ
ejpam-3449	46	36	set	set	NOUN
ejpam-3449	46	37	contained	contain	VERB
ejpam-3449	46	38	in	in	ADP
ejpam-3449	46	39	a	a	PRON
ejpam-3449	46	40	and	and	CCONJ
ejpam-3449	46	41	it	it	PRON
ejpam-3449	46	42	is	be	AUX
ejpam-3449	46	43	denoted	denote	VERB
ejpam-3449	46	44	by	by	ADP
ejpam-3449	46	45	fint(a	fint(a	PROPN
ejpam-3449	46	46	)	)	PUNCT
ejpam-3449	46	47	.	.	PUNCT
ejpam-3449	47	1	definition	definition	NOUN
ejpam-3449	47	2	2.5	2.5	NUM
ejpam-3449	47	3	.	.	PUNCT
ejpam-3449	48	1	[	[	X
ejpam-3449	48	2	13	13	NUM
ejpam-3449	48	3	]	]	PUNCT
ejpam-3449	48	4	let	let	VERB
ejpam-3449	48	5	a	a	PRON
ejpam-3449	48	6	be	be	AUX
ejpam-3449	48	7	the	the	DET
ejpam-3449	48	8	subset	subset	NOUN
ejpam-3449	48	9	of	of	ADP
ejpam-3449	48	10	a	a	DET
ejpam-3449	48	11	fine	fine	ADJ
ejpam-3449	48	12	space	space	NOUN
ejpam-3449	48	13	x	x	NOUN
ejpam-3449	48	14	,	,	PUNCT
ejpam-3449	48	15	the	the	DET
ejpam-3449	48	16	fine	fine	ADJ
ejpam-3449	48	17	closure	closure	NOUN
ejpam-3449	48	18	of	of	ADP
ejpam-3449	48	19	a	a	PRON
ejpam-3449	48	20	is	be	AUX
ejpam-3449	48	21	defined	define	VERB
ejpam-3449	48	22	as	as	ADP
ejpam-3449	48	23	the	the	DET
ejpam-3449	48	24	intersection	intersection	NOUN
ejpam-3449	48	25	of	of	ADP
ejpam-3449	48	26	all	all	DET
ejpam-3449	48	27	fine	fine	ADJ
ejpam-3449	48	28	-	-	PUNCT
ejpam-3449	48	29	closed	close	VERB
ejpam-3449	48	30	sets	set	NOUN
ejpam-3449	48	31	containing	contain	VERB
ejpam-3449	48	32	the	the	DET
ejpam-3449	48	33	set	set	NOUN
ejpam-3449	48	34	a.	a.	NOUN
ejpam-3449	48	35	that	that	PRON
ejpam-3449	48	36	means	mean	VERB
ejpam-3449	48	37	,	,	PUNCT
ejpam-3449	48	38	the	the	DET
ejpam-3449	48	39	fine	fine	ADJ
ejpam-3449	48	40	closure	closure	NOUN
ejpam-3449	48	41	of	of	ADP
ejpam-3449	48	42	a	a	PRON
ejpam-3449	48	43	is	be	AUX
ejpam-3449	48	44	the	the	DET
ejpam-3449	48	45	smallest	small	ADJ
ejpam-3449	48	46	fine	fine	ADJ
ejpam-3449	48	47	-	-	PUNCT
ejpam-3449	48	48	closed	close	VERB
ejpam-3449	48	49	set	set	NOUN
ejpam-3449	48	50	containing	contain	VERB
ejpam-3449	48	51	a	a	PRON
ejpam-3449	49	1	and	and	CCONJ
ejpam-3449	49	2	it	it	PRON
ejpam-3449	49	3	is	be	AUX
ejpam-3449	49	4	denoted	denote	VERB
ejpam-3449	49	5	by	by	ADP
ejpam-3449	49	6	fcl(a	fcl(a	PROPN
ejpam-3449	49	7	)	)	PUNCT
ejpam-3449	49	8	.	.	PUNCT
ejpam-3449	50	1	definition	definition	NOUN
ejpam-3449	50	2	2.6	2.6	NUM
ejpam-3449	50	3	.	.	PUNCT
ejpam-3449	51	1	[	[	X
ejpam-3449	51	2	12	12	NUM
ejpam-3449	51	3	]	]	PUNCT
ejpam-3449	51	4	an	an	DET
ejpam-3449	51	5	operation	operation	NOUN
ejpam-3449	51	6	γ	γ	NOUN
ejpam-3449	51	7	on	on	ADP
ejpam-3449	51	8	the	the	DET
ejpam-3449	51	9	topology	topology	NOUN
ejpam-3449	51	10	τ	τ	PROPN
ejpam-3449	51	11	on	on	ADP
ejpam-3449	51	12	x	x	X
ejpam-3449	51	13	is	be	AUX
ejpam-3449	51	14	a	a	DET
ejpam-3449	51	15	mapping	mapping	NOUN
ejpam-3449	51	16	γ	γ	X
ejpam-3449	51	17	:	:	PUNCT
ejpam-3449	51	18	τ	τ	PROPN
ejpam-3449	51	19	→	→	SYM
ejpam-3449	51	20	p	p	X
ejpam-3449	51	21	(	(	PUNCT
ejpam-3449	51	22	x	x	X
ejpam-3449	51	23	)	)	PUNCT
ejpam-3449	51	24	such	such	ADJ
ejpam-3449	51	25	that	that	SCONJ
ejpam-3449	51	26	u	u	PROPN
ejpam-3449	51	27	⊆	⊆	NUM
ejpam-3449	51	28	γ(u	γ(u	NOUN
ejpam-3449	51	29	)	)	PUNCT
ejpam-3449	51	30	for	for	ADP
ejpam-3449	51	31	each	each	DET
ejpam-3449	51	32	u	u	PROPN
ejpam-3449	51	33	∈	∈	PROPN
ejpam-3449	51	34	τ	τ	X
ejpam-3449	51	35	,	,	PUNCT
ejpam-3449	51	36	where	where	SCONJ
ejpam-3449	51	37	p	p	NOUN
ejpam-3449	51	38	(	(	PUNCT
ejpam-3449	51	39	x	x	X
ejpam-3449	51	40	)	)	PUNCT
ejpam-3449	51	41	is	be	AUX
ejpam-3449	51	42	the	the	DET
ejpam-3449	51	43	power	power	NOUN
ejpam-3449	51	44	set	set	NOUN
ejpam-3449	51	45	of	of	ADP
ejpam-3449	51	46	x	x	X
ejpam-3449	51	47	and	and	CCONJ
ejpam-3449	51	48	γ(u	γ(u	PROPN
ejpam-3449	51	49	)	)	PUNCT
ejpam-3449	51	50	denotes	denote	VERB
ejpam-3449	51	51	the	the	DET
ejpam-3449	51	52	value	value	NOUN
ejpam-3449	51	53	of	of	ADP
ejpam-3449	51	54	γ	γ	NOUN
ejpam-3449	51	55	at	at	ADP
ejpam-3449	51	56	u	u	PROPN
ejpam-3449	51	57	.	.	PUNCT
ejpam-3449	52	1	a	a	DET
ejpam-3449	52	2	nonempty	nonempty	NOUN
ejpam-3449	52	3	subset	subset	VERB
ejpam-3449	52	4	a	a	PRON
ejpam-3449	52	5	of	of	ADP
ejpam-3449	52	6	a	a	DET
ejpam-3449	52	7	topological	topological	ADJ
ejpam-3449	52	8	space	space	NOUN
ejpam-3449	52	9	(	(	PUNCT
ejpam-3449	52	10	x	x	X
ejpam-3449	52	11	,	,	PUNCT
ejpam-3449	52	12	τ	τ	X
ejpam-3449	52	13	)	)	PUNCT
ejpam-3449	52	14	with	with	ADP
ejpam-3449	52	15	an	an	DET
ejpam-3449	52	16	operation	operation	NOUN
ejpam-3449	52	17	γ	γ	NOUN
ejpam-3449	52	18	on	on	ADP
ejpam-3449	52	19	τ	τ	PROPN
ejpam-3449	52	20	is	be	AUX
ejpam-3449	52	21	said	say	VERB
ejpam-3449	52	22	to	to	PART
ejpam-3449	52	23	be	be	AUX
ejpam-3449	52	24	γ	γ	X
ejpam-3449	52	25	-	-	ADJ
ejpam-3449	52	26	open	open	ADJ
ejpam-3449	52	27	if	if	SCONJ
ejpam-3449	52	28	for	for	ADP
ejpam-3449	52	29	each	each	DET
ejpam-3449	52	30	x	x	SYM
ejpam-3449	52	31	∈	∈	PROPN
ejpam-3449	52	32	a	a	PRON
ejpam-3449	52	33	,	,	PUNCT
ejpam-3449	52	34	there	there	PRON
ejpam-3449	52	35	exists	exist	VERB
ejpam-3449	52	36	an	an	DET
ejpam-3449	52	37	open	open	ADJ
ejpam-3449	52	38	set	set	NOUN
ejpam-3449	52	39	u	u	NOUN
ejpam-3449	52	40	containing	contain	VERB
ejpam-3449	52	41	x	x	PUNCT
ejpam-3449	52	42	such	such	ADJ
ejpam-3449	52	43	that	that	SCONJ
ejpam-3449	52	44	γ(u	γ(u	NOUN
ejpam-3449	52	45	)	)	PUNCT
ejpam-3449	52	46	⊆	⊆	NUM
ejpam-3449	52	47	a.	a.	NOUN
ejpam-3449	52	48	the	the	DET
ejpam-3449	52	49	complement	complement	NOUN
ejpam-3449	52	50	of	of	ADP
ejpam-3449	52	51	a	a	DET
ejpam-3449	52	52	γ	γ	X
ejpam-3449	52	53	-	-	ADJ
ejpam-3449	52	54	open	open	ADJ
ejpam-3449	52	55	subset	subset	NOUN
ejpam-3449	52	56	of	of	ADP
ejpam-3449	52	57	a	a	DET
ejpam-3449	52	58	space	space	NOUN
ejpam-3449	52	59	x	x	PUNCT
ejpam-3449	52	60	as	as	ADP
ejpam-3449	52	61	γ	γ	NOUN
ejpam-3449	52	62	-	-	ADJ
ejpam-3449	52	63	closed	closed	ADJ
ejpam-3449	52	64	.	.	PUNCT
ejpam-3449	53	1	the	the	DET
ejpam-3449	53	2	family	family	NOUN
ejpam-3449	53	3	of	of	ADP
ejpam-3449	53	4	all	all	DET
ejpam-3449	53	5	γ	γ	ADJ
ejpam-3449	53	6	-	-	ADJ
ejpam-3449	53	7	open	open	ADJ
ejpam-3449	53	8	subsets	subset	NOUN
ejpam-3449	53	9	of	of	ADP
ejpam-3449	53	10	a	a	DET
ejpam-3449	53	11	space	space	NOUN
ejpam-3449	53	12	(	(	PUNCT
ejpam-3449	53	13	x	x	X
ejpam-3449	53	14	,	,	PUNCT
ejpam-3449	53	15	τ	τ	X
ejpam-3449	53	16	)	)	PUNCT
ejpam-3449	53	17	is	be	AUX
ejpam-3449	53	18	denoted	denote	VERB
ejpam-3449	53	19	by	by	ADP
ejpam-3449	53	20	τγ	τγ	PUNCT
ejpam-3449	53	21	.	.	PUNCT
ejpam-3449	54	1	b.	b.	PROPN
ejpam-3449	54	2	a.	a.	PROPN
ejpam-3449	54	3	asaad	asaad	PROPN
ejpam-3449	54	4	et	et	PROPN
ejpam-3449	54	5	al	al	PROPN
ejpam-3449	54	6	.	.	PUNCT
ejpam-3449	54	7	/	/	SYM
ejpam-3449	54	8	eur	eur	PROPN
ejpam-3449	54	9	.	.	PUNCT
ejpam-3449	55	1	j.	j.	PROPN
ejpam-3449	55	2	pure	pure	PROPN
ejpam-3449	55	3	appl	appl	PROPN
ejpam-3449	55	4	.	.	PROPN
ejpam-3449	55	5	math	math	PROPN
ejpam-3449	55	6	,	,	PUNCT
ejpam-3449	55	7	12	12	NUM
ejpam-3449	55	8	(	(	PUNCT
ejpam-3449	55	9	3	3	NUM
ejpam-3449	55	10	)	)	PUNCT
ejpam-3449	55	11	(	(	PUNCT
ejpam-3449	55	12	2019	2019	NUM
ejpam-3449	55	13	)	)	PUNCT
ejpam-3449	55	14	,	,	PUNCT
ejpam-3449	55	15	960	960	NUM
ejpam-3449	55	16	-	-	SYM
ejpam-3449	55	17	977	977	NUM
ejpam-3449	55	18	962	962	NUM
ejpam-3449	55	19	definition	definition	NOUN
ejpam-3449	55	20	2.7	2.7	NUM
ejpam-3449	55	21	.	.	PUNCT
ejpam-3449	56	1	[	[	X
ejpam-3449	56	2	10	10	NUM
ejpam-3449	56	3	]	]	X
ejpam-3449	56	4	a	a	DET
ejpam-3449	56	5	point	point	NOUN
ejpam-3449	56	6	x	x	X
ejpam-3449	56	7	∈	∈	NOUN
ejpam-3449	56	8	x	x	X
ejpam-3449	56	9	is	be	AUX
ejpam-3449	56	10	in	in	ADP
ejpam-3449	56	11	the	the	DET
ejpam-3449	56	12	γ	γ	NOUN
ejpam-3449	56	13	-	-	NOUN
ejpam-3449	56	14	closure	closure	NOUN
ejpam-3449	56	15	of	of	ADP
ejpam-3449	56	16	a	a	DET
ejpam-3449	56	17	set	set	NOUN
ejpam-3449	56	18	a	a	DET
ejpam-3449	56	19	⊆	⊆	NUM
ejpam-3449	56	20	x	x	SYM
ejpam-3449	56	21	if	if	SCONJ
ejpam-3449	56	22	γ(u	γ(u	NOUN
ejpam-3449	56	23	)	)	PUNCT
ejpam-3449	56	24	∩	∩	NOUN
ejpam-3449	56	25	a	a	DET
ejpam-3449	56	26	6=	6=	NUM
ejpam-3449	56	27	φ	φ	NOUN
ejpam-3449	56	28	for	for	ADP
ejpam-3449	56	29	each	each	DET
ejpam-3449	56	30	open	open	ADJ
ejpam-3449	56	31	set	set	VERB
ejpam-3449	56	32	u	u	NOUN
ejpam-3449	56	33	containing	contain	VERB
ejpam-3449	56	34	x.	x.	NOUN
ejpam-3449	56	35	the	the	DET
ejpam-3449	56	36	set	set	NOUN
ejpam-3449	56	37	of	of	ADP
ejpam-3449	56	38	all	all	DET
ejpam-3449	56	39	γ	γ	NOUN
ejpam-3449	56	40	-	-	PUNCT
ejpam-3449	56	41	closure	closure	NOUN
ejpam-3449	56	42	points	point	NOUN
ejpam-3449	56	43	of	of	ADP
ejpam-3449	56	44	a	a	PRON
ejpam-3449	56	45	is	be	AUX
ejpam-3449	56	46	called	call	VERB
ejpam-3449	56	47	γ	γ	NOUN
ejpam-3449	56	48	-	-	NOUN
ejpam-3449	56	49	closure	closure	NOUN
ejpam-3449	56	50	of	of	ADP
ejpam-3449	56	51	a	a	PRON
ejpam-3449	56	52	and	and	CCONJ
ejpam-3449	56	53	is	be	AUX
ejpam-3449	56	54	denoted	denote	VERB
ejpam-3449	56	55	by	by	ADP
ejpam-3449	56	56	clγ(a	clγ(a	PROPN
ejpam-3449	56	57	)	)	PUNCT
ejpam-3449	56	58	.	.	PUNCT
ejpam-3449	57	1	definition	definition	NOUN
ejpam-3449	57	2	2.8	2.8	NUM
ejpam-3449	57	3	.	.	PUNCT
ejpam-3449	58	1	[	[	X
ejpam-3449	58	2	12	12	NUM
ejpam-3449	58	3	]	]	PUNCT
ejpam-3449	58	4	a	a	DET
ejpam-3449	58	5	subset	subset	NOUN
ejpam-3449	58	6	a	a	PRON
ejpam-3449	58	7	of	of	ADP
ejpam-3449	58	8	(	(	PUNCT
ejpam-3449	58	9	x	x	PROPN
ejpam-3449	58	10	,	,	PUNCT
ejpam-3449	58	11	τ	τ	X
ejpam-3449	58	12	)	)	PUNCT
ejpam-3449	58	13	with	with	ADP
ejpam-3449	58	14	an	an	DET
ejpam-3449	58	15	operation	operation	NOUN
ejpam-3449	58	16	γ	γ	NOUN
ejpam-3449	58	17	on	on	ADP
ejpam-3449	58	18	τ	τ	PROPN
ejpam-3449	58	19	is	be	AUX
ejpam-3449	58	20	said	say	VERB
ejpam-3449	58	21	to	to	PART
ejpam-3449	58	22	be	be	AUX
ejpam-3449	58	23	γ	γ	X
ejpam-3449	58	24	-	-	PUNCT
ejpam-3449	58	25	g	g	NOUN
ejpam-3449	58	26	-	-	PUNCT
ejpam-3449	58	27	closed	closed	ADJ
ejpam-3449	58	28	if	if	SCONJ
ejpam-3449	58	29	clγ(a	clγ(a	PROPN
ejpam-3449	58	30	)	)	PUNCT
ejpam-3449	58	31	⊆	⊆	NUM
ejpam-3449	58	32	u	u	NOUN
ejpam-3449	58	33	whenever	whenever	SCONJ
ejpam-3449	58	34	a	a	DET
ejpam-3449	58	35	⊆	⊆	NUM
ejpam-3449	58	36	u	u	NOUN
ejpam-3449	58	37	and	and	CCONJ
ejpam-3449	58	38	u	u	NOUN
ejpam-3449	58	39	is	be	AUX
ejpam-3449	58	40	γ	γ	X
ejpam-3449	58	41	-	-	ADJ
ejpam-3449	58	42	open	open	ADJ
ejpam-3449	58	43	in	in	ADP
ejpam-3449	58	44	(	(	PUNCT
ejpam-3449	58	45	x	x	NOUN
ejpam-3449	58	46	,	,	PUNCT
ejpam-3449	58	47	τ	τ	PROPN
ejpam-3449	58	48	)	)	PUNCT
ejpam-3449	58	49	.	.	PUNCT
ejpam-3449	59	1	definition	definition	NOUN
ejpam-3449	59	2	2.9	2.9	NUM
ejpam-3449	59	3	.	.	PUNCT
ejpam-3449	60	1	[	[	X
ejpam-3449	60	2	12	12	NUM
ejpam-3449	60	3	]	]	PUNCT
ejpam-3449	60	4	a	a	DET
ejpam-3449	60	5	topological	topological	ADJ
ejpam-3449	60	6	space	space	NOUN
ejpam-3449	60	7	(	(	PUNCT
ejpam-3449	60	8	x	x	X
ejpam-3449	60	9	,	,	PUNCT
ejpam-3449	60	10	τ	τ	X
ejpam-3449	60	11	)	)	PUNCT
ejpam-3449	60	12	with	with	ADP
ejpam-3449	60	13	an	an	DET
ejpam-3449	60	14	operation	operation	NOUN
ejpam-3449	60	15	γ	γ	NOUN
ejpam-3449	60	16	on	on	ADP
ejpam-3449	60	17	τ	τ	PROPN
ejpam-3449	60	18	is	be	AUX
ejpam-3449	60	19	said	say	VERB
ejpam-3449	60	20	to	to	PART
ejpam-3449	60	21	be	be	AUX
ejpam-3449	60	22	(	(	PUNCT
ejpam-3449	60	23	i	i	NOUN
ejpam-3449	60	24	)	)	PUNCT
ejpam-3449	60	25	γ	γ	PROPN
ejpam-3449	60	26	-	-	PUNCT
ejpam-3449	60	27	t0	t0	PROPN
ejpam-3449	60	28	if	if	SCONJ
ejpam-3449	60	29	for	for	ADP
ejpam-3449	60	30	any	any	DET
ejpam-3449	60	31	two	two	NUM
ejpam-3449	60	32	distinct	distinct	ADJ
ejpam-3449	60	33	points	point	NOUN
ejpam-3449	60	34	x	x	NOUN
ejpam-3449	60	35	,	,	PUNCT
ejpam-3449	60	36	y	y	PROPN
ejpam-3449	60	37	in	in	ADP
ejpam-3449	60	38	x	x	SYM
ejpam-3449	60	39	,	,	PUNCT
ejpam-3449	60	40	there	there	PRON
ejpam-3449	60	41	exists	exist	VERB
ejpam-3449	60	42	an	an	DET
ejpam-3449	60	43	open	open	ADJ
ejpam-3449	60	44	set	set	NOUN
ejpam-3449	60	45	u	u	PRON
ejpam-3449	60	46	such	such	ADJ
ejpam-3449	60	47	that	that	SCONJ
ejpam-3449	60	48	x	x	SYM
ejpam-3449	60	49	∈	∈	PROPN
ejpam-3449	60	50	u	u	NOUN
ejpam-3449	60	51	and	and	CCONJ
ejpam-3449	60	52	y	y	PROPN
ejpam-3449	60	53	/∈	/∈	PUNCT
ejpam-3449	60	54	γ(u	γ(u	PROPN
ejpam-3449	60	55	)	)	PUNCT
ejpam-3449	60	56	or	or	CCONJ
ejpam-3449	60	57	y	y	PROPN
ejpam-3449	60	58	∈	∈	PROPN
ejpam-3449	60	59	u	u	NOUN
ejpam-3449	60	60	and	and	CCONJ
ejpam-3449	60	61	x	x	PROPN
ejpam-3449	60	62	/∈	/∈	PUNCT
ejpam-3449	60	63	γ(u	γ(u	PROPN
ejpam-3449	60	64	)	)	PUNCT
ejpam-3449	60	65	.	.	PUNCT
ejpam-3449	61	1	(	(	PUNCT
ejpam-3449	61	2	ii	ii	NOUN
ejpam-3449	61	3	)	)	PUNCT
ejpam-3449	61	4	γ	γ	PROPN
ejpam-3449	61	5	-	-	PUNCT
ejpam-3449	61	6	t1	t1	NOUN
ejpam-3449	61	7	if	if	SCONJ
ejpam-3449	61	8	for	for	ADP
ejpam-3449	61	9	any	any	DET
ejpam-3449	61	10	two	two	NUM
ejpam-3449	61	11	distinct	distinct	ADJ
ejpam-3449	61	12	points	point	NOUN
ejpam-3449	61	13	x	x	NOUN
ejpam-3449	61	14	,	,	PUNCT
ejpam-3449	61	15	y	y	PROPN
ejpam-3449	61	16	in	in	ADP
ejpam-3449	61	17	x	x	SYM
ejpam-3449	61	18	,	,	PUNCT
ejpam-3449	61	19	there	there	PRON
ejpam-3449	61	20	exist	exist	VERB
ejpam-3449	61	21	two	two	NUM
ejpam-3449	61	22	open	open	ADJ
ejpam-3449	61	23	sets	set	NOUN
ejpam-3449	61	24	u	u	NOUN
ejpam-3449	61	25	and	and	CCONJ
ejpam-3449	61	26	v	v	ADP
ejpam-3449	61	27	containing	contain	VERB
ejpam-3449	61	28	x	x	PROPN
ejpam-3449	61	29	and	and	CCONJ
ejpam-3449	61	30	y	y	PROPN
ejpam-3449	61	31	respectively	respectively	ADV
ejpam-3449	61	32	such	such	ADJ
ejpam-3449	61	33	that	that	SCONJ
ejpam-3449	61	34	y	y	PROPN
ejpam-3449	61	35	/∈	/∈	PUNCT
ejpam-3449	61	36	γ(u	γ(u	PROPN
ejpam-3449	61	37	)	)	PUNCT
ejpam-3449	61	38	and	and	CCONJ
ejpam-3449	61	39	x	x	NOUN
ejpam-3449	61	40	/∈	/∈	PUNCT
ejpam-3449	61	41	γ(v	γ(v	ADJ
ejpam-3449	61	42	)	)	PUNCT
ejpam-3449	61	43	.	.	PUNCT
ejpam-3449	62	1	(	(	PUNCT
ejpam-3449	62	2	iii	iii	X
ejpam-3449	62	3	)	)	PUNCT
ejpam-3449	62	4	γ	γ	PROPN
ejpam-3449	62	5	-	-	NOUN
ejpam-3449	62	6	t2	t2	NOUN
ejpam-3449	62	7	if	if	SCONJ
ejpam-3449	62	8	for	for	ADP
ejpam-3449	62	9	any	any	DET
ejpam-3449	62	10	two	two	NUM
ejpam-3449	62	11	distinct	distinct	ADJ
ejpam-3449	62	12	points	point	NOUN
ejpam-3449	62	13	x	x	NOUN
ejpam-3449	62	14	,	,	PUNCT
ejpam-3449	62	15	y	y	PROPN
ejpam-3449	62	16	in	in	ADP
ejpam-3449	62	17	x	x	SYM
ejpam-3449	62	18	,	,	PUNCT
ejpam-3449	62	19	there	there	PRON
ejpam-3449	62	20	exist	exist	VERB
ejpam-3449	62	21	two	two	NUM
ejpam-3449	62	22	open	open	ADJ
ejpam-3449	62	23	sets	set	NOUN
ejpam-3449	62	24	u	u	NOUN
ejpam-3449	62	25	and	and	CCONJ
ejpam-3449	62	26	v	v	ADP
ejpam-3449	62	27	containing	contain	VERB
ejpam-3449	62	28	x	x	PROPN
ejpam-3449	62	29	and	and	CCONJ
ejpam-3449	62	30	y	y	PROPN
ejpam-3449	62	31	respectively	respectively	ADV
ejpam-3449	62	32	such	such	ADJ
ejpam-3449	62	33	that	that	SCONJ
ejpam-3449	62	34	γ(u	γ(u	NOUN
ejpam-3449	62	35	)	)	PUNCT
ejpam-3449	62	36	∩	∩	NOUN
ejpam-3449	62	37	γ(v	γ(v	NOUN
ejpam-3449	62	38	)	)	PUNCT
ejpam-3449	62	39	=	=	SYM
ejpam-3449	63	1	φ	φ	PROPN
ejpam-3449	63	2	.	.	PUNCT
ejpam-3449	63	3	(	(	PUNCT
ejpam-3449	63	4	iv	iv	X
ejpam-3449	63	5	)	)	PUNCT
ejpam-3449	63	6	γ	γ	PROPN
ejpam-3449	63	7	-	-	PUNCT
ejpam-3449	63	8	t	t	PROPN
ejpam-3449	63	9	1	1	NUM
ejpam-3449	63	10	2	2	NUM
ejpam-3449	63	11	if	if	SCONJ
ejpam-3449	63	12	every	every	DET
ejpam-3449	63	13	γ	γ	PROPN
ejpam-3449	63	14	-	-	PUNCT
ejpam-3449	63	15	g	g	NOUN
ejpam-3449	63	16	-	-	PUNCT
ejpam-3449	63	17	closed	close	VERB
ejpam-3449	63	18	set	set	NOUN
ejpam-3449	63	19	in	in	ADP
ejpam-3449	63	20	x	x	PROPN
ejpam-3449	63	21	is	be	AUX
ejpam-3449	63	22	γ	γ	PRON
ejpam-3449	63	23	-	-	ADJ
ejpam-3449	63	24	closed	closed	ADJ
ejpam-3449	63	25	.	.	PUNCT
ejpam-3449	64	1	3	3	X
ejpam-3449	64	2	.	.	X
ejpam-3449	64	3	fγ	fγ	NOUN
ejpam-3449	64	4	-	-	PUNCT
ejpam-3449	64	5	open	open	NOUN
ejpam-3449	64	6	sets	set	VERB
ejpam-3449	64	7	an	an	DET
ejpam-3449	64	8	operation	operation	NOUN
ejpam-3449	64	9	γ	γ	NOUN
ejpam-3449	64	10	on	on	ADP
ejpam-3449	64	11	τf	τf	PROPN
ejpam-3449	64	12	is	be	AUX
ejpam-3449	64	13	a	a	DET
ejpam-3449	64	14	mapping	mapping	NOUN
ejpam-3449	64	15	γ	γ	NOUN
ejpam-3449	64	16	:	:	PUNCT
ejpam-3449	64	17	τf	τf	ADP
ejpam-3449	64	18	→	→	SYM
ejpam-3449	64	19	p	p	X
ejpam-3449	64	20	(	(	PUNCT
ejpam-3449	64	21	x	x	X
ejpam-3449	64	22	)	)	PUNCT
ejpam-3449	64	23	such	such	ADJ
ejpam-3449	64	24	that	that	SCONJ
ejpam-3449	64	25	u	u	PROPN
ejpam-3449	64	26	⊆	⊆	NUM
ejpam-3449	64	27	γ(u	γ(u	NOUN
ejpam-3449	64	28	)	)	PUNCT
ejpam-3449	64	29	for	for	ADP
ejpam-3449	64	30	every	every	DET
ejpam-3449	64	31	u	u	PROPN
ejpam-3449	64	32	∈	∈	PROPN
ejpam-3449	64	33	τf	τf	ADP
ejpam-3449	64	34	,	,	PUNCT
ejpam-3449	64	35	where	where	SCONJ
ejpam-3449	64	36	p	p	NOUN
ejpam-3449	64	37	(	(	PUNCT
ejpam-3449	64	38	x	x	X
ejpam-3449	64	39	)	)	PUNCT
ejpam-3449	64	40	is	be	AUX
ejpam-3449	64	41	the	the	DET
ejpam-3449	64	42	power	power	NOUN
ejpam-3449	64	43	set	set	NOUN
ejpam-3449	64	44	of	of	ADP
ejpam-3449	64	45	x	x	X
ejpam-3449	64	46	and	and	CCONJ
ejpam-3449	64	47	γ(u	γ(u	PROPN
ejpam-3449	64	48	)	)	PUNCT
ejpam-3449	64	49	is	be	AUX
ejpam-3449	64	50	the	the	DET
ejpam-3449	64	51	value	value	NOUN
ejpam-3449	64	52	of	of	ADP
ejpam-3449	64	53	γ	γ	NOUN
ejpam-3449	64	54	at	at	ADP
ejpam-3449	64	55	u	u	PROPN
ejpam-3449	64	56	.	.	PUNCT
ejpam-3449	65	1	from	from	ADP
ejpam-3449	65	2	this	this	PRON
ejpam-3449	65	3	,	,	PUNCT
ejpam-3449	65	4	we	we	PRON
ejpam-3449	65	5	can	can	AUX
ejpam-3449	65	6	easily	easily	ADV
ejpam-3449	65	7	to	to	PART
ejpam-3449	65	8	find	find	VERB
ejpam-3449	65	9	γ(x	γ(x	NOUN
ejpam-3449	65	10	)	)	PUNCT
ejpam-3449	66	1	=	=	SYM
ejpam-3449	67	1	x	x	X
ejpam-3449	67	2	for	for	ADP
ejpam-3449	67	3	any	any	DET
ejpam-3449	67	4	operation	operation	NOUN
ejpam-3449	67	5	γ	γ	NOUN
ejpam-3449	67	6	:	:	PUNCT
ejpam-3449	67	7	τf	τf	PROPN
ejpam-3449	67	8	→	→	SYM
ejpam-3449	67	9	p	p	X
ejpam-3449	67	10	(	(	PUNCT
ejpam-3449	67	11	x	x	NOUN
ejpam-3449	67	12	)	)	PUNCT
ejpam-3449	67	13	.	.	PUNCT
ejpam-3449	68	1	the	the	DET
ejpam-3449	68	2	operators	operator	NOUN
ejpam-3449	68	3	defined	define	VERB
ejpam-3449	68	4	by	by	ADP
ejpam-3449	68	5	γ(u	γ(u	PROPN
ejpam-3449	68	6	)	)	PUNCT
ejpam-3449	68	7	=	=	SYM
ejpam-3449	68	8	u	u	NOUN
ejpam-3449	68	9	,	,	PUNCT
ejpam-3449	68	10	γ(u	γ(u	PROPN
ejpam-3449	68	11	)	)	PUNCT
ejpam-3449	68	12	=	=	SYM
ejpam-3449	68	13	x	x	NOUN
ejpam-3449	68	14	,	,	PUNCT
ejpam-3449	68	15	γ(u	γ(u	X
ejpam-3449	68	16	)	)	PUNCT
ejpam-3449	68	17	=	=	SYM
ejpam-3449	68	18	fcl(u	fcl(u	PROPN
ejpam-3449	68	19	)	)	PUNCT
ejpam-3449	68	20	and	and	CCONJ
ejpam-3449	68	21	γ(u	γ(u	NOUN
ejpam-3449	68	22	)	)	PUNCT
ejpam-3449	68	23	=	=	PUNCT
ejpam-3449	68	24	fint(fcl(u	fint(fcl(u	NUM
ejpam-3449	68	25	)	)	PUNCT
ejpam-3449	68	26	)	)	PUNCT
ejpam-3449	68	27	are	be	AUX
ejpam-3449	68	28	all	all	PRON
ejpam-3449	68	29	examples	example	NOUN
ejpam-3449	68	30	of	of	ADP
ejpam-3449	68	31	the	the	DET
ejpam-3449	68	32	operation	operation	NOUN
ejpam-3449	68	33	γ	γ	PROPN
ejpam-3449	68	34	.	.	PROPN
ejpam-3449	68	35	definition	definition	NOUN
ejpam-3449	68	36	3.1	3.1	NUM
ejpam-3449	68	37	.	.	PUNCT
ejpam-3449	69	1	let	let	AUX
ejpam-3449	69	2	(	(	PUNCT
ejpam-3449	69	3	x	x	NOUN
ejpam-3449	69	4	,	,	PUNCT
ejpam-3449	69	5	τ	τ	PROPN
ejpam-3449	69	6	,	,	PUNCT
ejpam-3449	69	7	τf	τf	NUM
ejpam-3449	69	8	)	)	PUNCT
ejpam-3449	69	9	be	be	AUX
ejpam-3449	69	10	a	a	DET
ejpam-3449	69	11	fine	fine	ADJ
ejpam-3449	69	12	space	space	NOUN
ejpam-3449	69	13	and	and	CCONJ
ejpam-3449	69	14	γ	γ	X
ejpam-3449	69	15	:	:	PUNCT
ejpam-3449	69	16	τf	τf	PROPN
ejpam-3449	69	17	→	→	SYM
ejpam-3449	69	18	p	p	X
ejpam-3449	69	19	(	(	PUNCT
ejpam-3449	69	20	x	x	NOUN
ejpam-3449	69	21	)	)	PUNCT
ejpam-3449	69	22	be	be	AUX
ejpam-3449	69	23	an	an	DET
ejpam-3449	69	24	operation	operation	NOUN
ejpam-3449	69	25	on	on	ADP
ejpam-3449	69	26	τf	τf	PROPN
ejpam-3449	69	27	.	.	PUNCT
ejpam-3449	70	1	a	a	DET
ejpam-3449	70	2	nonempty	nonempty	ADV
ejpam-3449	70	3	set	set	VERB
ejpam-3449	70	4	a	a	PRON
ejpam-3449	70	5	of	of	ADP
ejpam-3449	70	6	x	x	SYM
ejpam-3449	70	7	is	be	AUX
ejpam-3449	70	8	said	say	VERB
ejpam-3449	70	9	to	to	PART
ejpam-3449	70	10	be	be	AUX
ejpam-3449	70	11	fγ	fγ	NOUN
ejpam-3449	70	12	-	-	PUNCT
ejpam-3449	70	13	open	open	ADJ
ejpam-3449	70	14	if	if	SCONJ
ejpam-3449	70	15	for	for	ADP
ejpam-3449	70	16	each	each	DET
ejpam-3449	70	17	x	x	SYM
ejpam-3449	70	18	∈	∈	PROPN
ejpam-3449	70	19	a	a	PRON
ejpam-3449	70	20	,	,	PUNCT
ejpam-3449	70	21	there	there	PRON
ejpam-3449	70	22	exists	exist	VERB
ejpam-3449	70	23	a	a	DET
ejpam-3449	70	24	fine	fine	ADV
ejpam-3449	70	25	-	-	PUNCT
ejpam-3449	70	26	open	open	NOUN
ejpam-3449	70	27	set	set	NOUN
ejpam-3449	70	28	u	u	PRON
ejpam-3449	70	29	such	such	ADJ
ejpam-3449	70	30	that	that	SCONJ
ejpam-3449	70	31	x	x	SYM
ejpam-3449	70	32	∈	∈	PROPN
ejpam-3449	70	33	u	u	NOUN
ejpam-3449	70	34	and	and	CCONJ
ejpam-3449	70	35	γ(u	γ(u	PROPN
ejpam-3449	70	36	)	)	PUNCT
ejpam-3449	70	37	⊆	⊆	NUM
ejpam-3449	70	38	a.	a.	NOUN
ejpam-3449	70	39	the	the	DET
ejpam-3449	70	40	complement	complement	NOUN
ejpam-3449	70	41	of	of	ADP
ejpam-3449	70	42	a	a	DET
ejpam-3449	70	43	fγ	fγ	ADV
ejpam-3449	70	44	-	-	PUNCT
ejpam-3449	70	45	open	open	ADJ
ejpam-3449	70	46	set	set	NOUN
ejpam-3449	70	47	of	of	ADP
ejpam-3449	70	48	x	x	PROPN
ejpam-3449	70	49	is	be	AUX
ejpam-3449	70	50	fγ	fγ	ADV
ejpam-3449	70	51	-	-	PUNCT
ejpam-3449	70	52	closed	closed	ADJ
ejpam-3449	70	53	.	.	PUNCT
ejpam-3449	71	1	suppose	suppose	VERB
ejpam-3449	71	2	that	that	SCONJ
ejpam-3449	71	3	the	the	DET
ejpam-3449	71	4	empty	empty	ADJ
ejpam-3449	71	5	set	set	NOUN
ejpam-3449	71	6	φ	φ	PROPN
ejpam-3449	71	7	is	be	AUX
ejpam-3449	71	8	also	also	ADV
ejpam-3449	71	9	fγ	fγ	ADV
ejpam-3449	71	10	-	-	PUNCT
ejpam-3449	71	11	open	open	NOUN
ejpam-3449	71	12	set	set	NOUN
ejpam-3449	71	13	for	for	ADP
ejpam-3449	71	14	any	any	DET
ejpam-3449	71	15	operation	operation	NOUN
ejpam-3449	71	16	γ	γ	NOUN
ejpam-3449	71	17	:	:	PUNCT
ejpam-3449	71	18	τf	τf	PROPN
ejpam-3449	71	19	→	→	SYM
ejpam-3449	71	20	p	p	X
ejpam-3449	71	21	(	(	PUNCT
ejpam-3449	71	22	x	x	NOUN
ejpam-3449	71	23	)	)	PUNCT
ejpam-3449	71	24	.	.	PUNCT
ejpam-3449	72	1	the	the	DET
ejpam-3449	72	2	family	family	NOUN
ejpam-3449	72	3	of	of	ADP
ejpam-3449	72	4	all	all	DET
ejpam-3449	72	5	fγ	fγ	NOUN
ejpam-3449	72	6	-	-	PUNCT
ejpam-3449	72	7	open	open	ADJ
ejpam-3449	72	8	subsets	subset	NOUN
ejpam-3449	72	9	of	of	ADP
ejpam-3449	72	10	a	a	DET
ejpam-3449	72	11	fine	fine	ADJ
ejpam-3449	72	12	space	space	NOUN
ejpam-3449	72	13	(	(	PUNCT
ejpam-3449	72	14	x	x	X
ejpam-3449	72	15	,	,	PUNCT
ejpam-3449	72	16	τ	τ	PROPN
ejpam-3449	72	17	,	,	PUNCT
ejpam-3449	72	18	τf	τf	PROPN
ejpam-3449	72	19	)	)	PUNCT
ejpam-3449	72	20	is	be	AUX
ejpam-3449	72	21	denoted	denote	VERB
ejpam-3449	72	22	by	by	ADP
ejpam-3449	72	23	τfγ	τfγ	X
ejpam-3449	72	24	.	.	PUNCT
ejpam-3449	73	1	theorem	theorem	ADJ
ejpam-3449	73	2	3.2	3.2	NUM
ejpam-3449	73	3	.	.	PUNCT
ejpam-3449	74	1	the	the	DET
ejpam-3449	74	2	union	union	NOUN
ejpam-3449	74	3	of	of	ADP
ejpam-3449	74	4	any	any	DET
ejpam-3449	74	5	collection	collection	NOUN
ejpam-3449	74	6	of	of	ADP
ejpam-3449	74	7	fγ	fγ	NOUN
ejpam-3449	74	8	-	-	PUNCT
ejpam-3449	74	9	open	open	ADJ
ejpam-3449	74	10	sets	set	NOUN
ejpam-3449	74	11	in	in	ADP
ejpam-3449	74	12	a	a	DET
ejpam-3449	74	13	fine	fine	ADJ
ejpam-3449	74	14	space	space	NOUN
ejpam-3449	74	15	(	(	PUNCT
ejpam-3449	74	16	x	x	X
ejpam-3449	74	17	,	,	PUNCT
ejpam-3449	74	18	τ	τ	PROPN
ejpam-3449	74	19	,	,	PUNCT
ejpam-3449	74	20	τf	τf	PROPN
ejpam-3449	74	21	)	)	PUNCT
ejpam-3449	74	22	is	be	AUX
ejpam-3449	74	23	a	a	DET
ejpam-3449	74	24	fγ	fγ	ADV
ejpam-3449	74	25	-	-	PUNCT
ejpam-3449	74	26	open	open	NOUN
ejpam-3449	74	27	set	set	NOUN
ejpam-3449	74	28	in	in	ADP
ejpam-3449	74	29	(	(	PUNCT
ejpam-3449	74	30	x	x	NOUN
ejpam-3449	74	31	,	,	PUNCT
ejpam-3449	74	32	τ	τ	PROPN
ejpam-3449	74	33	,	,	PUNCT
ejpam-3449	74	34	τf	τf	NUM
ejpam-3449	74	35	)	)	PUNCT
ejpam-3449	74	36	.	.	PUNCT
ejpam-3449	75	1	proof	proof	NOUN
ejpam-3449	75	2	.	.	PUNCT
ejpam-3449	76	1	let	let	VERB
ejpam-3449	76	2	x	x	X
ejpam-3449	76	3	∈	∈	PROPN
ejpam-3449	76	4	⋃	⋃	NOUN
ejpam-3449	76	5	α∈∆{aα	α∈∆{aα	NOUN
ejpam-3449	76	6	}	}	PUNCT
ejpam-3449	76	7	,	,	PUNCT
ejpam-3449	76	8	where	where	SCONJ
ejpam-3449	76	9	{	{	PUNCT
ejpam-3449	76	10	aα}α∈∆	aα}α∈∆	NOUN
ejpam-3449	76	11	be	be	AUX
ejpam-3449	76	12	a	a	DET
ejpam-3449	76	13	class	class	NOUN
ejpam-3449	76	14	of	of	ADP
ejpam-3449	76	15	fγ	fγ	NOUN
ejpam-3449	76	16	-	-	PUNCT
ejpam-3449	76	17	open	open	ADJ
ejpam-3449	76	18	sets	set	NOUN
ejpam-3449	76	19	in	in	ADP
ejpam-3449	76	20	x.	x.	NOUN
ejpam-3449	76	21	then	then	ADV
ejpam-3449	76	22	x	x	SYM
ejpam-3449	76	23	∈	∈	PROPN
ejpam-3449	76	24	aα	aα	NOUN
ejpam-3449	76	25	for	for	ADP
ejpam-3449	76	26	some	some	DET
ejpam-3449	76	27	α	α	NOUN
ejpam-3449	76	28	∈	∈	PROPN
ejpam-3449	77	1	∆.	∆.	NOUN
ejpam-3449	77	2	since	since	SCONJ
ejpam-3449	77	3	aα	aα	PROPN
ejpam-3449	77	4	is	be	AUX
ejpam-3449	77	5	fγ	fγ	NOUN
ejpam-3449	77	6	-	-	PUNCT
ejpam-3449	77	7	open	open	NOUN
ejpam-3449	77	8	set	set	NOUN
ejpam-3449	77	9	in	in	ADP
ejpam-3449	77	10	x	x	NOUN
ejpam-3449	77	11	,	,	PUNCT
ejpam-3449	77	12	then	then	ADV
ejpam-3449	77	13	there	there	PRON
ejpam-3449	77	14	exists	exist	VERB
ejpam-3449	77	15	a	a	DET
ejpam-3449	77	16	fine	fine	ADV
ejpam-3449	77	17	-	-	PUNCT
ejpam-3449	77	18	open	open	NOUN
ejpam-3449	77	19	set	set	VERB
ejpam-3449	77	20	v	v	ADP
ejpam-3449	77	21	such	such	ADJ
ejpam-3449	77	22	that	that	SCONJ
ejpam-3449	77	23	x	x	SYM
ejpam-3449	77	24	∈	∈	NOUN
ejpam-3449	77	25	v	v	ADP
ejpam-3449	77	26	⊆	⊆	NUM
ejpam-3449	77	27	γ(v	γ(v	NOUN
ejpam-3449	77	28	)	)	PUNCT
ejpam-3449	77	29	⊆	⊆	NUM
ejpam-3449	77	30	aα	aα	NOUN
ejpam-3449	77	31	⊆	⊆	NUM
ejpam-3449	77	32	⋃	⋃	NOUN
ejpam-3449	77	33	α∈∆{aα	α∈∆{aα	NOUN
ejpam-3449	77	34	}	}	PUNCT
ejpam-3449	77	35	.	.	PUNCT
ejpam-3449	78	1	therefore	therefore	ADV
ejpam-3449	78	2	,	,	PUNCT
ejpam-3449	78	3	⋃	⋃	NOUN
ejpam-3449	78	4	α∈∆{aα	α∈∆{aα	NOUN
ejpam-3449	78	5	}	}	PUNCT
ejpam-3449	78	6	is	be	AUX
ejpam-3449	78	7	a	a	DET
ejpam-3449	78	8	fγ	fγ	ADV
ejpam-3449	78	9	-	-	PUNCT
ejpam-3449	78	10	open	open	NOUN
ejpam-3449	78	11	set	set	NOUN
ejpam-3449	78	12	in	in	ADP
ejpam-3449	78	13	x.	x.	PROPN
ejpam-3449	78	14	example	example	NOUN
ejpam-3449	78	15	3.3	3.3	NUM
ejpam-3449	78	16	.	.	PUNCT
ejpam-3449	79	1	the	the	DET
ejpam-3449	79	2	intersection	intersection	NOUN
ejpam-3449	79	3	of	of	ADP
ejpam-3449	79	4	any	any	DET
ejpam-3449	79	5	two	two	NUM
ejpam-3449	79	6	fγ	fγ	ADV
ejpam-3449	79	7	-	-	PUNCT
ejpam-3449	79	8	open	open	ADJ
ejpam-3449	79	9	sets	set	NOUN
ejpam-3449	79	10	in	in	ADP
ejpam-3449	79	11	(	(	PUNCT
ejpam-3449	79	12	x	x	NOUN
ejpam-3449	79	13	,	,	PUNCT
ejpam-3449	79	14	τ	τ	PROPN
ejpam-3449	79	15	,	,	PUNCT
ejpam-3449	79	16	τf	τf	NUM
ejpam-3449	79	17	)	)	PUNCT
ejpam-3449	79	18	is	be	AUX
ejpam-3449	79	19	generally	generally	ADV
ejpam-3449	79	20	not	not	PART
ejpam-3449	79	21	a	a	DET
ejpam-3449	79	22	fγ	fγ	ADV
ejpam-3449	79	23	-	-	PUNCT
ejpam-3449	79	24	open	open	ADJ
ejpam-3449	79	25	sets	set	NOUN
ejpam-3449	79	26	.	.	PUNCT
ejpam-3449	80	1	to	to	PART
ejpam-3449	80	2	see	see	VERB
ejpam-3449	80	3	this	this	PRON
ejpam-3449	80	4	,	,	PUNCT
ejpam-3449	80	5	let	let	VERB
ejpam-3449	80	6	x	x	PUNCT
ejpam-3449	80	7	=	=	PRON
ejpam-3449	80	8	{	{	PUNCT
ejpam-3449	80	9	a	a	PRON
ejpam-3449	80	10	,	,	PUNCT
ejpam-3449	80	11	b	b	NOUN
ejpam-3449	80	12	,	,	PUNCT
ejpam-3449	80	13	c	c	NOUN
ejpam-3449	80	14	}	}	PUNCT
ejpam-3449	80	15	and	and	CCONJ
ejpam-3449	80	16	τ	τ	PROPN
ejpam-3449	80	17	=	=	SYM
ejpam-3449	80	18	p	p	X
ejpam-3449	80	19	(	(	PUNCT
ejpam-3449	80	20	x	x	NOUN
ejpam-3449	80	21	)	)	PUNCT
ejpam-3449	80	22	=	=	SYM
ejpam-3449	80	23	τf	τf	PROPN
ejpam-3449	80	24	.	.	PUNCT
ejpam-3449	81	1	let	let	VERB
ejpam-3449	81	2	γ	γ	NOUN
ejpam-3449	81	3	:	:	PUNCT
ejpam-3449	81	4	τf	τf	PROPN
ejpam-3449	81	5	→	→	SYM
ejpam-3449	81	6	p	p	X
ejpam-3449	81	7	(	(	PUNCT
ejpam-3449	81	8	x	x	NOUN
ejpam-3449	81	9	)	)	PUNCT
ejpam-3449	81	10	be	be	VERB
ejpam-3449	81	11	an	an	DET
ejpam-3449	81	12	b.	b.	PROPN
ejpam-3449	81	13	a.	a.	NOUN
ejpam-3449	81	14	asaad	asaad	PROPN
ejpam-3449	81	15	et	et	PROPN
ejpam-3449	82	1	al	al	PROPN
ejpam-3449	82	2	.	.	PUNCT
ejpam-3449	82	3	/	/	SYM
ejpam-3449	82	4	eur	eur	PROPN
ejpam-3449	82	5	.	.	PUNCT
ejpam-3449	83	1	j.	j.	PROPN
ejpam-3449	83	2	pure	pure	PROPN
ejpam-3449	83	3	appl	appl	PROPN
ejpam-3449	83	4	.	.	PROPN
ejpam-3449	83	5	math	math	PROPN
ejpam-3449	83	6	,	,	PUNCT
ejpam-3449	83	7	12	12	NUM
ejpam-3449	83	8	(	(	PUNCT
ejpam-3449	83	9	3	3	NUM
ejpam-3449	83	10	)	)	PUNCT
ejpam-3449	83	11	(	(	PUNCT
ejpam-3449	83	12	2019	2019	NUM
ejpam-3449	83	13	)	)	PUNCT
ejpam-3449	83	14	,	,	PUNCT
ejpam-3449	83	15	960	960	NUM
ejpam-3449	83	16	-	-	SYM
ejpam-3449	83	17	977	977	NUM
ejpam-3449	83	18	963	963	NUM
ejpam-3449	83	19	operation	operation	NOUN
ejpam-3449	83	20	on	on	ADP
ejpam-3449	83	21	τf	τf	ADV
ejpam-3449	83	22	defined	define	VERB
ejpam-3449	83	23	as	as	SCONJ
ejpam-3449	83	24	follows	follow	VERB
ejpam-3449	83	25	:	:	PUNCT
ejpam-3449	83	26	for	for	ADP
ejpam-3449	83	27	every	every	DET
ejpam-3449	83	28	a	a	DET
ejpam-3449	83	29	∈	∈	PROPN
ejpam-3449	83	30	τf	τf	ADP
ejpam-3449	83	31	γ(a	γ(a	PROPN
ejpam-3449	83	32	)	)	PUNCT
ejpam-3449	84	1	=	=	PRON
ejpam-3449	84	2	{	{	PUNCT
ejpam-3449	84	3	a	a	DET
ejpam-3449	84	4	if	if	SCONJ
ejpam-3449	84	5	a	a	PRON
ejpam-3449	84	6	6=	6=	NUM
ejpam-3449	84	7	{	{	PUNCT
ejpam-3449	84	8	c	c	NOUN
ejpam-3449	84	9	}	}	PUNCT
ejpam-3449	84	10	{	{	PUNCT
ejpam-3449	84	11	b	b	NOUN
ejpam-3449	84	12	,	,	PUNCT
ejpam-3449	84	13	c	c	NOUN
ejpam-3449	84	14	}	}	PUNCT
ejpam-3449	84	15	if	if	SCONJ
ejpam-3449	84	16	a	a	PRON
ejpam-3449	84	17	=	=	X
ejpam-3449	84	18	{	{	PUNCT
ejpam-3449	84	19	c	c	NOUN
ejpam-3449	84	20	}	}	PUNCT
ejpam-3449	84	21	thus	thus	ADV
ejpam-3449	84	22	,	,	PUNCT
ejpam-3449	84	23	τfγ	τfγ	AUX
ejpam-3449	84	24	=	=	SYM
ejpam-3449	84	25	p	p	X
ejpam-3449	84	26	(	(	PUNCT
ejpam-3449	84	27	x)\{c	x)\{c	PROPN
ejpam-3449	84	28	}	}	PUNCT
ejpam-3449	84	29	.	.	PUNCT
ejpam-3449	85	1	then	then	ADV
ejpam-3449	85	2	{	{	PUNCT
ejpam-3449	85	3	a	a	X
ejpam-3449	85	4	,	,	PUNCT
ejpam-3449	85	5	c	c	NOUN
ejpam-3449	85	6	}	}	PUNCT
ejpam-3449	85	7	∈	∈	NOUN
ejpam-3449	85	8	τfγ	τfγ	NOUN
ejpam-3449	85	9	and	and	CCONJ
ejpam-3449	85	10	{	{	PUNCT
ejpam-3449	85	11	b	b	NOUN
ejpam-3449	85	12	,	,	PUNCT
ejpam-3449	85	13	c	c	NOUN
ejpam-3449	85	14	}	}	PUNCT
ejpam-3449	85	15	∈	∈	NOUN
ejpam-3449	85	16	τfγ	τfγ	NOUN
ejpam-3449	85	17	,	,	PUNCT
ejpam-3449	85	18	but	but	CCONJ
ejpam-3449	85	19	{	{	PUNCT
ejpam-3449	85	20	a	a	X
ejpam-3449	85	21	,	,	PUNCT
ejpam-3449	85	22	c	c	NOUN
ejpam-3449	85	23	}	}	PUNCT
ejpam-3449	85	24	∩	∩	ADJ
ejpam-3449	85	25	{	{	PUNCT
ejpam-3449	85	26	b	b	NOUN
ejpam-3449	85	27	,	,	PUNCT
ejpam-3449	85	28	c	c	NOUN
ejpam-3449	85	29	}	}	PUNCT
ejpam-3449	85	30	=	=	SYM
ejpam-3449	85	31	{	{	PUNCT
ejpam-3449	85	32	c	c	NOUN
ejpam-3449	85	33	}	}	PUNCT
ejpam-3449	85	34	/∈	/∈	PUNCT
ejpam-3449	85	35	τfγ	τfγ	NOUN
ejpam-3449	85	36	.	.	PUNCT
ejpam-3449	86	1	therefore	therefore	ADV
ejpam-3449	86	2	,	,	PUNCT
ejpam-3449	86	3	τfγ	τfγ	X
ejpam-3449	86	4	does	do	AUX
ejpam-3449	86	5	not	not	PART
ejpam-3449	86	6	form	form	VERB
ejpam-3449	86	7	a	a	DET
ejpam-3449	86	8	topology	topology	NOUN
ejpam-3449	86	9	on	on	ADP
ejpam-3449	86	10	x.	x.	NOUN
ejpam-3449	87	1	it	it	PRON
ejpam-3449	87	2	is	be	AUX
ejpam-3449	87	3	clear	clear	ADJ
ejpam-3449	87	4	from	from	ADP
ejpam-3449	87	5	definition	definition	NOUN
ejpam-3449	87	6	3.1	3.1	NUM
ejpam-3449	87	7	that	that	PRON
ejpam-3449	87	8	every	every	DET
ejpam-3449	87	9	fγ	fγ	ADV
ejpam-3449	87	10	-	-	PUNCT
ejpam-3449	87	11	open	open	ADJ
ejpam-3449	87	12	set	set	NOUN
ejpam-3449	87	13	is	be	AUX
ejpam-3449	87	14	fine	fine	ADV
ejpam-3449	87	15	-	-	PUNCT
ejpam-3449	87	16	open	open	ADJ
ejpam-3449	87	17	in	in	ADP
ejpam-3449	87	18	(	(	PUNCT
ejpam-3449	87	19	x	x	NOUN
ejpam-3449	87	20	,	,	PUNCT
ejpam-3449	87	21	τ	τ	PROPN
ejpam-3449	87	22	,	,	PUNCT
ejpam-3449	87	23	τf	τf	NUM
ejpam-3449	87	24	)	)	PUNCT
ejpam-3449	87	25	(	(	PUNCT
ejpam-3449	87	26	that	that	PRON
ejpam-3449	87	27	is	is	ADV
ejpam-3449	87	28	,	,	PUNCT
ejpam-3449	87	29	τfγ	τfγ	VERB
ejpam-3449	87	30	⊆	⊆	NUM
ejpam-3449	87	31	τf	τf	NUM
ejpam-3449	87	32	)	)	PUNCT
ejpam-3449	87	33	.	.	PUNCT
ejpam-3449	88	1	but	but	CCONJ
ejpam-3449	88	2	the	the	DET
ejpam-3449	88	3	converse	converse	NOUN
ejpam-3449	88	4	need	need	AUX
ejpam-3449	88	5	not	not	PART
ejpam-3449	88	6	be	be	AUX
ejpam-3449	88	7	true	true	ADJ
ejpam-3449	88	8	as	as	SCONJ
ejpam-3449	88	9	shown	show	VERB
ejpam-3449	88	10	by	by	ADP
ejpam-3449	88	11	the	the	DET
ejpam-3449	88	12	following	follow	VERB
ejpam-3449	88	13	example	example	NOUN
ejpam-3449	88	14	.	.	PUNCT
ejpam-3449	89	1	example	example	NOUN
ejpam-3449	89	2	3.4	3.4	NUM
ejpam-3449	89	3	.	.	PUNCT
ejpam-3449	90	1	in	in	ADP
ejpam-3449	90	2	example	example	NOUN
ejpam-3449	90	3	3.3	3.3	NUM
ejpam-3449	90	4	,	,	PUNCT
ejpam-3449	90	5	the	the	DET
ejpam-3449	90	6	set	set	NOUN
ejpam-3449	90	7	{	{	PUNCT
ejpam-3449	90	8	c	c	NOUN
ejpam-3449	90	9	}	}	PUNCT
ejpam-3449	90	10	is	be	AUX
ejpam-3449	90	11	fine	fine	ADV
ejpam-3449	90	12	-	-	PUNCT
ejpam-3449	90	13	open	open	ADJ
ejpam-3449	90	14	,	,	PUNCT
ejpam-3449	90	15	but	but	CCONJ
ejpam-3449	90	16	it	it	PRON
ejpam-3449	90	17	is	be	AUX
ejpam-3449	90	18	not	not	PART
ejpam-3449	90	19	fγ	fγ	ADV
ejpam-3449	90	20	-	-	PUNCT
ejpam-3449	90	21	open	open	ADJ
ejpam-3449	90	22	.	.	PUNCT
ejpam-3449	91	1	definition	definition	NOUN
ejpam-3449	91	2	3.5	3.5	NUM
ejpam-3449	91	3	.	.	PUNCT
ejpam-3449	92	1	a	a	DET
ejpam-3449	92	2	fine	fine	ADJ
ejpam-3449	92	3	space	space	NOUN
ejpam-3449	92	4	(	(	PUNCT
ejpam-3449	92	5	x	x	X
ejpam-3449	92	6	,	,	PUNCT
ejpam-3449	92	7	τ	τ	PROPN
ejpam-3449	92	8	,	,	PUNCT
ejpam-3449	92	9	τf	τf	NUM
ejpam-3449	92	10	)	)	PUNCT
ejpam-3449	92	11	with	with	ADP
ejpam-3449	92	12	an	an	DET
ejpam-3449	92	13	operation	operation	NOUN
ejpam-3449	92	14	γ	γ	NOUN
ejpam-3449	92	15	on	on	ADP
ejpam-3449	92	16	τf	τf	PROPN
ejpam-3449	92	17	is	be	AUX
ejpam-3449	92	18	said	say	VERB
ejpam-3449	92	19	to	to	PART
ejpam-3449	92	20	be	be	AUX
ejpam-3449	92	21	fγ	fγ	NOUN
ejpam-3449	92	22	-	-	PUNCT
ejpam-3449	92	23	regular	regular	ADJ
ejpam-3449	92	24	if	if	SCONJ
ejpam-3449	92	25	for	for	ADP
ejpam-3449	92	26	each	each	DET
ejpam-3449	92	27	x	x	SYM
ejpam-3449	92	28	∈	∈	PROPN
ejpam-3449	92	29	x	x	X
ejpam-3449	92	30	and	and	CCONJ
ejpam-3449	92	31	for	for	ADP
ejpam-3449	92	32	each	each	DET
ejpam-3449	92	33	fine	fine	ADJ
ejpam-3449	92	34	-	-	PUNCT
ejpam-3449	92	35	open	open	ADJ
ejpam-3449	92	36	set	set	NOUN
ejpam-3449	92	37	u	u	NOUN
ejpam-3449	92	38	containing	contain	VERB
ejpam-3449	92	39	x	x	PRON
ejpam-3449	92	40	,	,	PUNCT
ejpam-3449	92	41	there	there	PRON
ejpam-3449	92	42	exists	exist	VERB
ejpam-3449	92	43	a	a	DET
ejpam-3449	92	44	fine	fine	ADV
ejpam-3449	92	45	-	-	PUNCT
ejpam-3449	92	46	open	open	NOUN
ejpam-3449	92	47	set	set	NOUN
ejpam-3449	92	48	w	w	ADP
ejpam-3449	92	49	such	such	ADJ
ejpam-3449	92	50	that	that	SCONJ
ejpam-3449	92	51	x	x	SYM
ejpam-3449	92	52	∈w	∈w	NOUN
ejpam-3449	92	53	and	and	CCONJ
ejpam-3449	92	54	γ(w	γ(w	X
ejpam-3449	92	55	)	)	PUNCT
ejpam-3449	93	1	⊆	⊆	NUM
ejpam-3449	93	2	u	u	NOUN
ejpam-3449	93	3	.	.	PUNCT
ejpam-3449	94	1	theorem	theorem	VERB
ejpam-3449	94	2	3.6	3.6	NUM
ejpam-3449	94	3	.	.	PUNCT
ejpam-3449	95	1	let	let	AUX
ejpam-3449	95	2	(	(	PUNCT
ejpam-3449	95	3	x	x	NOUN
ejpam-3449	95	4	,	,	PUNCT
ejpam-3449	95	5	τ	τ	PROPN
ejpam-3449	95	6	,	,	PUNCT
ejpam-3449	95	7	τf	τf	NUM
ejpam-3449	95	8	)	)	PUNCT
ejpam-3449	95	9	be	be	AUX
ejpam-3449	95	10	a	a	DET
ejpam-3449	95	11	fine	fine	ADJ
ejpam-3449	95	12	space	space	NOUN
ejpam-3449	95	13	and	and	CCONJ
ejpam-3449	95	14	γ	γ	X
ejpam-3449	95	15	:	:	PUNCT
ejpam-3449	95	16	τf	τf	PROPN
ejpam-3449	95	17	→	→	SYM
ejpam-3449	95	18	p	p	X
ejpam-3449	95	19	(	(	PUNCT
ejpam-3449	95	20	x	x	NOUN
ejpam-3449	95	21	)	)	PUNCT
ejpam-3449	95	22	be	be	AUX
ejpam-3449	95	23	an	an	DET
ejpam-3449	95	24	operation	operation	NOUN
ejpam-3449	95	25	on	on	ADP
ejpam-3449	95	26	τf	τf	PROPN
ejpam-3449	95	27	.	.	PUNCT
ejpam-3449	96	1	then	then	ADV
ejpam-3449	96	2	the	the	DET
ejpam-3449	96	3	following	follow	VERB
ejpam-3449	96	4	conditions	condition	NOUN
ejpam-3449	96	5	are	be	AUX
ejpam-3449	96	6	equivalent	equivalent	ADJ
ejpam-3449	96	7	:	:	PUNCT
ejpam-3449	96	8	(	(	PUNCT
ejpam-3449	96	9	i	i	NOUN
ejpam-3449	96	10	)	)	PUNCT
ejpam-3449	96	11	τf	τf	NOUN
ejpam-3449	97	1	=	=	PUNCT
ejpam-3449	97	2	τfγ	τfγ	NOUN
ejpam-3449	97	3	.	.	PUNCT
ejpam-3449	98	1	(	(	PUNCT
ejpam-3449	98	2	ii	ii	NOUN
ejpam-3449	98	3	)	)	PUNCT
ejpam-3449	98	4	(	(	PUNCT
ejpam-3449	98	5	x	x	X
ejpam-3449	98	6	,	,	PUNCT
ejpam-3449	98	7	τ	τ	PROPN
ejpam-3449	98	8	,	,	PUNCT
ejpam-3449	98	9	τf	τf	PROPN
ejpam-3449	98	10	)	)	PUNCT
ejpam-3449	98	11	is	be	AUX
ejpam-3449	98	12	a	a	DET
ejpam-3449	98	13	fγ	fγ	ADJ
ejpam-3449	98	14	-	-	PUNCT
ejpam-3449	98	15	regular	regular	ADJ
ejpam-3449	98	16	space	space	NOUN
ejpam-3449	98	17	.	.	PUNCT
ejpam-3449	99	1	(	(	PUNCT
ejpam-3449	99	2	iii	iii	X
ejpam-3449	99	3	)	)	PUNCT
ejpam-3449	99	4	for	for	ADP
ejpam-3449	99	5	every	every	DET
ejpam-3449	99	6	x	x	SYM
ejpam-3449	99	7	∈	∈	PROPN
ejpam-3449	99	8	x	x	X
ejpam-3449	99	9	and	and	CCONJ
ejpam-3449	99	10	for	for	ADP
ejpam-3449	99	11	every	every	DET
ejpam-3449	99	12	fine	fine	ADJ
ejpam-3449	99	13	-	-	PUNCT
ejpam-3449	99	14	open	open	ADJ
ejpam-3449	99	15	set	set	NOUN
ejpam-3449	99	16	u	u	NOUN
ejpam-3449	99	17	of	of	ADP
ejpam-3449	99	18	(	(	PUNCT
ejpam-3449	99	19	x	x	PROPN
ejpam-3449	99	20	,	,	PUNCT
ejpam-3449	99	21	τ	τ	PROPN
ejpam-3449	99	22	,	,	PUNCT
ejpam-3449	99	23	τf	τf	NOUN
ejpam-3449	99	24	)	)	PUNCT
ejpam-3449	99	25	containing	contain	VERB
ejpam-3449	99	26	x	x	X
ejpam-3449	99	27	,	,	PUNCT
ejpam-3449	99	28	there	there	PRON
ejpam-3449	99	29	exists	exist	VERB
ejpam-3449	99	30	a	a	DET
ejpam-3449	99	31	fγ	fγ	ADV
ejpam-3449	99	32	-	-	PUNCT
ejpam-3449	99	33	open	open	NOUN
ejpam-3449	99	34	set	set	NOUN
ejpam-3449	99	35	w	w	PROPN
ejpam-3449	99	36	of	of	ADP
ejpam-3449	99	37	(	(	PUNCT
ejpam-3449	99	38	x	x	PROPN
ejpam-3449	99	39	,	,	PUNCT
ejpam-3449	99	40	τ	τ	PROPN
ejpam-3449	99	41	,	,	PUNCT
ejpam-3449	99	42	τf	τf	NOUN
ejpam-3449	99	43	)	)	PUNCT
ejpam-3449	99	44	containing	contain	VERB
ejpam-3449	99	45	x	x	PUNCT
ejpam-3449	99	46	such	such	ADJ
ejpam-3449	99	47	that	that	SCONJ
ejpam-3449	99	48	w	w	ADP
ejpam-3449	99	49	⊆	⊆	NUM
ejpam-3449	99	50	u	u	NOUN
ejpam-3449	99	51	.	.	PUNCT
ejpam-3449	100	1	proof	proof	NOUN
ejpam-3449	100	2	.	.	PUNCT
ejpam-3449	101	1	(	(	PUNCT
ejpam-3449	101	2	1	1	X
ejpam-3449	101	3	)	)	PUNCT
ejpam-3449	101	4	⇒	⇒	NOUN
ejpam-3449	101	5	(	(	PUNCT
ejpam-3449	101	6	2	2	X
ejpam-3449	101	7	)	)	PUNCT
ejpam-3449	101	8	let	let	VERB
ejpam-3449	101	9	x	x	SYM
ejpam-3449	101	10	∈	∈	PROPN
ejpam-3449	101	11	x	x	X
ejpam-3449	101	12	and	and	CCONJ
ejpam-3449	101	13	u	u	PRON
ejpam-3449	101	14	be	be	VERB
ejpam-3449	101	15	a	a	DET
ejpam-3449	101	16	fine	fine	ADV
ejpam-3449	101	17	-	-	PUNCT
ejpam-3449	101	18	open	open	NOUN
ejpam-3449	101	19	set	set	NOUN
ejpam-3449	101	20	in	in	ADP
ejpam-3449	101	21	x	x	INTJ
ejpam-3449	101	22	such	such	ADJ
ejpam-3449	101	23	that	that	SCONJ
ejpam-3449	101	24	x	x	SYM
ejpam-3449	101	25	∈	∈	PROPN
ejpam-3449	101	26	u	u	NOUN
ejpam-3449	101	27	.	.	PUNCT
ejpam-3449	102	1	it	it	PRON
ejpam-3449	102	2	follows	follow	VERB
ejpam-3449	102	3	from	from	ADP
ejpam-3449	102	4	assumption	assumption	NOUN
ejpam-3449	102	5	that	that	SCONJ
ejpam-3449	102	6	u	u	NOUN
ejpam-3449	102	7	is	be	AUX
ejpam-3449	102	8	a	a	DET
ejpam-3449	102	9	fγ	fγ	ADV
ejpam-3449	102	10	-	-	PUNCT
ejpam-3449	102	11	open	open	ADJ
ejpam-3449	102	12	set	set	NOUN
ejpam-3449	102	13	.	.	PUNCT
ejpam-3449	103	1	this	this	PRON
ejpam-3449	103	2	implies	imply	VERB
ejpam-3449	103	3	that	that	SCONJ
ejpam-3449	103	4	there	there	PRON
ejpam-3449	103	5	exists	exist	VERB
ejpam-3449	103	6	a	a	DET
ejpam-3449	103	7	fine	fine	ADV
ejpam-3449	103	8	-	-	PUNCT
ejpam-3449	103	9	open	open	NOUN
ejpam-3449	103	10	set	set	NOUN
ejpam-3449	103	11	w	w	ADP
ejpam-3449	103	12	such	such	ADJ
ejpam-3449	103	13	that	that	SCONJ
ejpam-3449	103	14	x	x	SYM
ejpam-3449	103	15	∈w	∈w	NOUN
ejpam-3449	103	16	and	and	CCONJ
ejpam-3449	103	17	γ(w	γ(w	X
ejpam-3449	103	18	)	)	PUNCT
ejpam-3449	104	1	⊆	⊆	NUM
ejpam-3449	104	2	u	u	NOUN
ejpam-3449	104	3	.	.	PUNCT
ejpam-3449	105	1	therefore	therefore	ADV
ejpam-3449	105	2	,	,	PUNCT
ejpam-3449	105	3	the	the	DET
ejpam-3449	105	4	fine	fine	ADJ
ejpam-3449	105	5	space	space	NOUN
ejpam-3449	105	6	(	(	PUNCT
ejpam-3449	105	7	x	x	X
ejpam-3449	105	8	,	,	PUNCT
ejpam-3449	105	9	τ	τ	PROPN
ejpam-3449	105	10	,	,	PUNCT
ejpam-3449	105	11	τf	τf	PROPN
ejpam-3449	105	12	)	)	PUNCT
ejpam-3449	105	13	is	be	AUX
ejpam-3449	105	14	fγ	fγ	NOUN
ejpam-3449	105	15	-	-	PUNCT
ejpam-3449	105	16	regular	regular	NOUN
ejpam-3449	105	17	.	.	PUNCT
ejpam-3449	106	1	(	(	PUNCT
ejpam-3449	106	2	2	2	X
ejpam-3449	106	3	)	)	PUNCT
ejpam-3449	106	4	⇒	⇒	NOUN
ejpam-3449	106	5	(	(	PUNCT
ejpam-3449	106	6	3	3	X
ejpam-3449	106	7	)	)	PUNCT
ejpam-3449	106	8	let	let	VERB
ejpam-3449	106	9	x	x	SYM
ejpam-3449	106	10	∈	∈	PROPN
ejpam-3449	106	11	x	x	X
ejpam-3449	106	12	and	and	CCONJ
ejpam-3449	106	13	u	u	PRON
ejpam-3449	106	14	be	be	VERB
ejpam-3449	106	15	a	a	DET
ejpam-3449	106	16	fine	fine	ADV
ejpam-3449	106	17	-	-	PUNCT
ejpam-3449	106	18	open	open	NOUN
ejpam-3449	106	19	set	set	NOUN
ejpam-3449	106	20	in	in	ADP
ejpam-3449	106	21	(	(	PUNCT
ejpam-3449	106	22	x	x	NOUN
ejpam-3449	106	23	,	,	PUNCT
ejpam-3449	106	24	τ	τ	PROPN
ejpam-3449	106	25	,	,	PUNCT
ejpam-3449	106	26	τf	τf	NOUN
ejpam-3449	106	27	)	)	PUNCT
ejpam-3449	106	28	containing	contain	VERB
ejpam-3449	106	29	x.	x.	NOUN
ejpam-3449	106	30	then	then	ADV
ejpam-3449	106	31	by	by	ADP
ejpam-3449	106	32	(	(	PUNCT
ejpam-3449	106	33	2	2	NUM
ejpam-3449	106	34	)	)	PUNCT
ejpam-3449	106	35	,	,	PUNCT
ejpam-3449	106	36	there	there	PRON
ejpam-3449	106	37	is	be	VERB
ejpam-3449	106	38	a	a	DET
ejpam-3449	106	39	fine	fine	ADV
ejpam-3449	106	40	-	-	PUNCT
ejpam-3449	106	41	open	open	NOUN
ejpam-3449	106	42	set	set	NOUN
ejpam-3449	106	43	w	w	ADP
ejpam-3449	106	44	such	such	ADJ
ejpam-3449	106	45	that	that	SCONJ
ejpam-3449	106	46	x	x	SYM
ejpam-3449	106	47	∈	∈	PROPN
ejpam-3449	106	48	w	w	NOUN
ejpam-3449	106	49	⊆	⊆	NUM
ejpam-3449	106	50	γ(w	γ(w	X
ejpam-3449	106	51	)	)	PUNCT
ejpam-3449	106	52	⊆	⊆	NUM
ejpam-3449	106	53	u	u	NOUN
ejpam-3449	106	54	.	.	PUNCT
ejpam-3449	107	1	again	again	ADV
ejpam-3449	107	2	,	,	PUNCT
ejpam-3449	107	3	by	by	ADP
ejpam-3449	107	4	using	use	VERB
ejpam-3449	107	5	(	(	PUNCT
ejpam-3449	107	6	2	2	NUM
ejpam-3449	107	7	)	)	PUNCT
ejpam-3449	107	8	for	for	ADP
ejpam-3449	107	9	the	the	DET
ejpam-3449	107	10	set	set	PROPN
ejpam-3449	107	11	w	w	NOUN
ejpam-3449	107	12	,	,	PUNCT
ejpam-3449	107	13	it	it	PRON
ejpam-3449	107	14	is	be	AUX
ejpam-3449	107	15	shown	show	VERB
ejpam-3449	107	16	that	that	SCONJ
ejpam-3449	107	17	w	w	NOUN
ejpam-3449	107	18	is	be	AUX
ejpam-3449	107	19	fγ	fγ	ADV
ejpam-3449	107	20	-	-	PUNCT
ejpam-3449	107	21	open	open	ADJ
ejpam-3449	107	22	.	.	PUNCT
ejpam-3449	108	1	hence	hence	ADV
ejpam-3449	108	2	w	w	PROPN
ejpam-3449	108	3	is	be	AUX
ejpam-3449	108	4	a	a	DET
ejpam-3449	108	5	fγ	fγ	ADV
ejpam-3449	108	6	-	-	PUNCT
ejpam-3449	108	7	open	open	ADJ
ejpam-3449	108	8	set	set	NOUN
ejpam-3449	108	9	containing	contain	VERB
ejpam-3449	108	10	x	x	PUNCT
ejpam-3449	108	11	such	such	ADJ
ejpam-3449	108	12	that	that	SCONJ
ejpam-3449	108	13	w	w	ADP
ejpam-3449	108	14	⊆	⊆	NUM
ejpam-3449	108	15	u	u	NOUN
ejpam-3449	108	16	.	.	PUNCT
ejpam-3449	109	1	(	(	PUNCT
ejpam-3449	109	2	3	3	X
ejpam-3449	109	3	)	)	PUNCT
ejpam-3449	109	4	⇒	⇒	NOUN
ejpam-3449	109	5	(	(	PUNCT
ejpam-3449	109	6	1	1	X
ejpam-3449	109	7	)	)	PUNCT
ejpam-3449	109	8	by	by	ADP
ejpam-3449	109	9	applying	apply	VERB
ejpam-3449	109	10	the	the	DET
ejpam-3449	109	11	part	part	NOUN
ejpam-3449	109	12	(	(	PUNCT
ejpam-3449	109	13	3	3	NUM
ejpam-3449	109	14	)	)	PUNCT
ejpam-3449	109	15	and	and	CCONJ
ejpam-3449	109	16	theorem	theorem	VERB
ejpam-3449	109	17	3.2	3.2	NUM
ejpam-3449	109	18	,	,	PUNCT
ejpam-3449	109	19	it	it	PRON
ejpam-3449	109	20	follows	follow	VERB
ejpam-3449	109	21	that	that	SCONJ
ejpam-3449	109	22	every	every	DET
ejpam-3449	109	23	fine	fine	ADJ
ejpam-3449	109	24	-	-	PUNCT
ejpam-3449	109	25	open	open	ADJ
ejpam-3449	109	26	set	set	NOUN
ejpam-3449	109	27	of	of	ADP
ejpam-3449	109	28	x	x	PROPN
ejpam-3449	109	29	is	be	AUX
ejpam-3449	109	30	fγ	fγ	ADV
ejpam-3449	109	31	-	-	PUNCT
ejpam-3449	109	32	open	open	ADJ
ejpam-3449	109	33	in	in	ADP
ejpam-3449	109	34	x.	x.	NOUN
ejpam-3449	109	35	that	that	PRON
ejpam-3449	109	36	is	is	ADV
ejpam-3449	109	37	,	,	PUNCT
ejpam-3449	109	38	τf	τf	PRON
ejpam-3449	109	39	⊆	⊆	NUM
ejpam-3449	109	40	τfγ	τfγ	NOUN
ejpam-3449	109	41	.	.	PUNCT
ejpam-3449	110	1	but	but	CCONJ
ejpam-3449	110	2	in	in	ADP
ejpam-3449	110	3	general	general	ADJ
ejpam-3449	110	4	,	,	PUNCT
ejpam-3449	110	5	we	we	PRON
ejpam-3449	110	6	have	have	AUX
ejpam-3449	110	7	τfγ	τfγ	VERB
ejpam-3449	110	8	⊆	⊆	NUM
ejpam-3449	110	9	τf	τf	NOUN
ejpam-3449	110	10	.	.	PUNCT
ejpam-3449	111	1	therefore	therefore	ADV
ejpam-3449	111	2	,	,	PUNCT
ejpam-3449	111	3	τf	τf	ADP
ejpam-3449	111	4	=	=	PUNCT
ejpam-3449	111	5	τfγ	τfγ	X
ejpam-3449	111	6	.	.	PUNCT
ejpam-3449	112	1	definition	definition	NOUN
ejpam-3449	112	2	3.7	3.7	NUM
ejpam-3449	112	3	.	.	PUNCT
ejpam-3449	113	1	let	let	AUX
ejpam-3449	113	2	(	(	PUNCT
ejpam-3449	113	3	x	x	NOUN
ejpam-3449	113	4	,	,	PUNCT
ejpam-3449	113	5	τ	τ	PROPN
ejpam-3449	113	6	,	,	PUNCT
ejpam-3449	113	7	τf	τf	NUM
ejpam-3449	113	8	)	)	PUNCT
ejpam-3449	113	9	be	be	AUX
ejpam-3449	113	10	any	any	DET
ejpam-3449	113	11	fine	fine	ADJ
ejpam-3449	113	12	space	space	NOUN
ejpam-3449	113	13	.	.	PUNCT
ejpam-3449	114	1	an	an	DET
ejpam-3449	114	2	operation	operation	NOUN
ejpam-3449	114	3	γ	γ	NOUN
ejpam-3449	114	4	on	on	ADP
ejpam-3449	114	5	τf	τf	PROPN
ejpam-3449	114	6	is	be	AUX
ejpam-3449	114	7	said	say	VERB
ejpam-3449	114	8	to	to	PART
ejpam-3449	114	9	be	be	AUX
ejpam-3449	114	10	(	(	PUNCT
ejpam-3449	114	11	i	i	NOUN
ejpam-3449	114	12	)	)	PUNCT
ejpam-3449	114	13	fine	fine	ADJ
ejpam-3449	114	14	-	-	PUNCT
ejpam-3449	114	15	open	open	ADJ
ejpam-3449	114	16	if	if	SCONJ
ejpam-3449	114	17	for	for	ADP
ejpam-3449	114	18	each	each	DET
ejpam-3449	114	19	x	x	SYM
ejpam-3449	114	20	∈	∈	PROPN
ejpam-3449	114	21	x	x	X
ejpam-3449	114	22	and	and	CCONJ
ejpam-3449	114	23	for	for	ADP
ejpam-3449	114	24	every	every	DET
ejpam-3449	114	25	fine	fine	ADJ
ejpam-3449	114	26	-	-	PUNCT
ejpam-3449	114	27	open	open	NOUN
ejpam-3449	114	28	set	set	NOUN
ejpam-3449	114	29	u	u	NOUN
ejpam-3449	114	30	containing	contain	VERB
ejpam-3449	114	31	x	x	PRON
ejpam-3449	114	32	,	,	PUNCT
ejpam-3449	114	33	there	there	PRON
ejpam-3449	114	34	exists	exist	VERB
ejpam-3449	114	35	a	a	DET
ejpam-3449	114	36	fγ	fγ	ADV
ejpam-3449	114	37	-	-	PUNCT
ejpam-3449	114	38	open	open	NOUN
ejpam-3449	114	39	set	set	NOUN
ejpam-3449	114	40	w	w	NOUN
ejpam-3449	114	41	containing	contain	VERB
ejpam-3449	114	42	x	x	PUNCT
ejpam-3449	115	1	such	such	ADJ
ejpam-3449	115	2	that	that	SCONJ
ejpam-3449	115	3	w	w	ADP
ejpam-3449	115	4	⊆	⊆	NUM
ejpam-3449	115	5	γ(u	γ(u	NOUN
ejpam-3449	115	6	)	)	PUNCT
ejpam-3449	115	7	.	.	PUNCT
ejpam-3449	116	1	(	(	PUNCT
ejpam-3449	116	2	ii	ii	NOUN
ejpam-3449	116	3	)	)	PUNCT
ejpam-3449	116	4	fine	fine	ADJ
ejpam-3449	116	5	-	-	PUNCT
ejpam-3449	116	6	regular	regular	ADJ
ejpam-3449	116	7	if	if	SCONJ
ejpam-3449	116	8	for	for	ADP
ejpam-3449	116	9	each	each	DET
ejpam-3449	116	10	x	x	SYM
ejpam-3449	116	11	∈	∈	PROPN
ejpam-3449	116	12	x	x	X
ejpam-3449	116	13	and	and	CCONJ
ejpam-3449	116	14	for	for	ADP
ejpam-3449	116	15	every	every	DET
ejpam-3449	116	16	pair	pair	NOUN
ejpam-3449	116	17	of	of	ADP
ejpam-3449	116	18	fine	fine	ADJ
ejpam-3449	116	19	-	-	PUNCT
ejpam-3449	116	20	open	open	ADJ
ejpam-3449	116	21	sets	set	NOUN
ejpam-3449	116	22	u1	u1	NOUN
ejpam-3449	116	23	and	and	CCONJ
ejpam-3449	116	24	u2	u2	NOUN
ejpam-3449	116	25	such	such	ADJ
ejpam-3449	116	26	that	that	SCONJ
ejpam-3449	116	27	both	both	DET
ejpam-3449	116	28	containing	contain	VERB
ejpam-3449	116	29	x	x	X
ejpam-3449	116	30	,	,	PUNCT
ejpam-3449	116	31	there	there	PRON
ejpam-3449	116	32	exists	exist	VERB
ejpam-3449	116	33	a	a	DET
ejpam-3449	116	34	fine	fine	ADV
ejpam-3449	116	35	-	-	PUNCT
ejpam-3449	116	36	open	open	NOUN
ejpam-3449	116	37	set	set	NOUN
ejpam-3449	116	38	w	w	NOUN
ejpam-3449	116	39	containing	contain	VERB
ejpam-3449	116	40	x	x	PUNCT
ejpam-3449	116	41	such	such	ADJ
ejpam-3449	116	42	that	that	SCONJ
ejpam-3449	116	43	γ(w	γ(w	X
ejpam-3449	116	44	)	)	PUNCT
ejpam-3449	116	45	⊆	⊆	NUM
ejpam-3449	116	46	γ(u1	γ(u1	NOUN
ejpam-3449	116	47	)	)	PUNCT
ejpam-3449	116	48	∩	∩	NOUN
ejpam-3449	116	49	γ(u2	γ(u2	NOUN
ejpam-3449	116	50	)	)	PUNCT
ejpam-3449	116	51	.	.	PUNCT
ejpam-3449	117	1	b.	b.	PROPN
ejpam-3449	117	2	a.	a.	PROPN
ejpam-3449	117	3	asaad	asaad	PROPN
ejpam-3449	117	4	et	et	PROPN
ejpam-3449	117	5	al	al	PROPN
ejpam-3449	117	6	.	.	PUNCT
ejpam-3449	117	7	/	/	SYM
ejpam-3449	117	8	eur	eur	PROPN
ejpam-3449	117	9	.	.	PUNCT
ejpam-3449	118	1	j.	j.	PROPN
ejpam-3449	118	2	pure	pure	PROPN
ejpam-3449	118	3	appl	appl	PROPN
ejpam-3449	118	4	.	.	PROPN
ejpam-3449	118	5	math	math	PROPN
ejpam-3449	118	6	,	,	PUNCT
ejpam-3449	118	7	12	12	NUM
ejpam-3449	118	8	(	(	PUNCT
ejpam-3449	118	9	3	3	NUM
ejpam-3449	118	10	)	)	PUNCT
ejpam-3449	118	11	(	(	PUNCT
ejpam-3449	118	12	2019	2019	NUM
ejpam-3449	118	13	)	)	PUNCT
ejpam-3449	118	14	,	,	PUNCT
ejpam-3449	118	15	960	960	NUM
ejpam-3449	118	16	-	-	SYM
ejpam-3449	118	17	977	977	NUM
ejpam-3449	118	18	964	964	NUM
ejpam-3449	118	19	lemma	lemma	PROPN
ejpam-3449	118	20	3.8	3.8	NUM
ejpam-3449	118	21	.	.	PUNCT
ejpam-3449	119	1	let	let	VERB
ejpam-3449	119	2	a	a	DET
ejpam-3449	119	3	mapping	mapping	NOUN
ejpam-3449	119	4	γ	γ	NOUN
ejpam-3449	119	5	be	be	AUX
ejpam-3449	119	6	fine	fine	ADV
ejpam-3449	119	7	-	-	PUNCT
ejpam-3449	119	8	regular	regular	ADJ
ejpam-3449	119	9	operation	operation	NOUN
ejpam-3449	119	10	on	on	ADP
ejpam-3449	119	11	τf	τf	PROPN
ejpam-3449	119	12	.	.	PUNCT
ejpam-3449	120	1	if	if	SCONJ
ejpam-3449	120	2	a	a	PRON
ejpam-3449	120	3	and	and	CCONJ
ejpam-3449	120	4	b	b	NOUN
ejpam-3449	120	5	are	be	AUX
ejpam-3449	120	6	fγ	fγ	ADV
ejpam-3449	120	7	-	-	PUNCT
ejpam-3449	120	8	open	open	ADJ
ejpam-3449	120	9	sets	set	NOUN
ejpam-3449	120	10	in	in	ADP
ejpam-3449	120	11	a	a	DET
ejpam-3449	120	12	fine	fine	ADJ
ejpam-3449	120	13	space	space	NOUN
ejpam-3449	120	14	(	(	PUNCT
ejpam-3449	120	15	x	x	X
ejpam-3449	120	16	,	,	PUNCT
ejpam-3449	120	17	τ	τ	PROPN
ejpam-3449	120	18	,	,	PUNCT
ejpam-3449	120	19	τf	τf	NUM
ejpam-3449	120	20	)	)	PUNCT
ejpam-3449	120	21	,	,	PUNCT
ejpam-3449	120	22	then	then	ADV
ejpam-3449	120	23	a	a	DET
ejpam-3449	120	24	∩	∩	ADJ
ejpam-3449	120	25	b	b	NOUN
ejpam-3449	120	26	is	be	AUX
ejpam-3449	120	27	also	also	ADV
ejpam-3449	120	28	fγ	fγ	ADV
ejpam-3449	120	29	-	-	PUNCT
ejpam-3449	120	30	open	open	NOUN
ejpam-3449	120	31	set	set	NOUN
ejpam-3449	120	32	in	in	ADP
ejpam-3449	120	33	(	(	PUNCT
ejpam-3449	120	34	x	x	NOUN
ejpam-3449	120	35	,	,	PUNCT
ejpam-3449	120	36	τ	τ	PROPN
ejpam-3449	120	37	,	,	PUNCT
ejpam-3449	120	38	τf	τf	NUM
ejpam-3449	120	39	)	)	PUNCT
ejpam-3449	120	40	.	.	PUNCT
ejpam-3449	121	1	proof	proof	NOUN
ejpam-3449	121	2	.	.	PUNCT
ejpam-3449	122	1	suppose	suppose	VERB
ejpam-3449	122	2	x	x	SYM
ejpam-3449	122	3	∈	∈	PROPN
ejpam-3449	122	4	a	a	DET
ejpam-3449	122	5	∩	∩	ADJ
ejpam-3449	122	6	b	b	NOUN
ejpam-3449	122	7	for	for	ADP
ejpam-3449	122	8	any	any	DET
ejpam-3449	122	9	fγ	fγ	ADJ
ejpam-3449	122	10	-	-	PUNCT
ejpam-3449	122	11	open	open	NOUN
ejpam-3449	122	12	sets	set	NOUN
ejpam-3449	122	13	a	a	PRON
ejpam-3449	122	14	and	and	CCONJ
ejpam-3449	122	15	b	b	NOUN
ejpam-3449	122	16	in	in	ADP
ejpam-3449	122	17	(	(	PUNCT
ejpam-3449	122	18	x	x	NOUN
ejpam-3449	122	19	,	,	PUNCT
ejpam-3449	122	20	τ	τ	PROPN
ejpam-3449	122	21	,	,	PUNCT
ejpam-3449	122	22	τf	τf	NUM
ejpam-3449	122	23	)	)	PUNCT
ejpam-3449	122	24	both	both	PRON
ejpam-3449	122	25	containing	contain	VERB
ejpam-3449	122	26	x.	x.	NOUN
ejpam-3449	122	27	then	then	ADV
ejpam-3449	122	28	there	there	PRON
ejpam-3449	122	29	exist	exist	VERB
ejpam-3449	122	30	fine	fine	ADJ
ejpam-3449	122	31	-	-	PUNCT
ejpam-3449	122	32	open	open	ADJ
ejpam-3449	122	33	sets	set	NOUN
ejpam-3449	122	34	u1	u1	NOUN
ejpam-3449	122	35	and	and	CCONJ
ejpam-3449	122	36	u2	u2	NOUN
ejpam-3449	122	37	such	such	ADJ
ejpam-3449	122	38	that	that	SCONJ
ejpam-3449	122	39	x	x	SYM
ejpam-3449	122	40	∈	∈	PROPN
ejpam-3449	122	41	u1	u1	NOUN
ejpam-3449	122	42	⊆	⊆	NUM
ejpam-3449	122	43	a	a	PRON
ejpam-3449	122	44	and	and	CCONJ
ejpam-3449	122	45	x	x	SYM
ejpam-3449	122	46	∈	∈	PROPN
ejpam-3449	122	47	u2	u2	PROPN
ejpam-3449	122	48	⊆	⊆	NUM
ejpam-3449	122	49	b.	b.	NOUN
ejpam-3449	122	50	since	since	SCONJ
ejpam-3449	122	51	γ	γ	PROPN
ejpam-3449	122	52	is	be	AUX
ejpam-3449	122	53	a	a	DET
ejpam-3449	122	54	fine	fine	ADJ
ejpam-3449	122	55	-	-	PUNCT
ejpam-3449	122	56	regular	regular	ADJ
ejpam-3449	122	57	operation	operation	NOUN
ejpam-3449	122	58	on	on	ADP
ejpam-3449	122	59	τf	τf	PROPN
ejpam-3449	122	60	,	,	PUNCT
ejpam-3449	122	61	then	then	ADV
ejpam-3449	122	62	there	there	PRON
ejpam-3449	122	63	exists	exist	VERB
ejpam-3449	122	64	a	a	DET
ejpam-3449	122	65	fine	fine	ADV
ejpam-3449	122	66	-	-	PUNCT
ejpam-3449	122	67	open	open	NOUN
ejpam-3449	122	68	set	set	NOUN
ejpam-3449	122	69	w	w	NOUN
ejpam-3449	122	70	containing	contain	VERB
ejpam-3449	122	71	x	x	PUNCT
ejpam-3449	122	72	such	such	ADJ
ejpam-3449	122	73	that	that	SCONJ
ejpam-3449	122	74	γ(w	γ(w	X
ejpam-3449	122	75	)	)	PUNCT
ejpam-3449	122	76	⊆	⊆	NUM
ejpam-3449	122	77	γ(u1	γ(u1	NOUN
ejpam-3449	122	78	)	)	PUNCT
ejpam-3449	122	79	∩	∩	NOUN
ejpam-3449	122	80	γ(u2	γ(u2	NOUN
ejpam-3449	122	81	)	)	PUNCT
ejpam-3449	122	82	⊆	⊆	NUM
ejpam-3449	122	83	a	a	DET
ejpam-3449	122	84	∩b	∩b	NOUN
ejpam-3449	122	85	.	.	PUNCT
ejpam-3449	123	1	therefore	therefore	ADV
ejpam-3449	123	2	,	,	PUNCT
ejpam-3449	123	3	a	a	DET
ejpam-3449	123	4	∩b	∩b	NOUN
ejpam-3449	123	5	is	be	AUX
ejpam-3449	123	6	fγ	fγ	NOUN
ejpam-3449	123	7	-	-	PUNCT
ejpam-3449	123	8	open	open	NOUN
ejpam-3449	123	9	set	set	NOUN
ejpam-3449	123	10	in	in	ADP
ejpam-3449	123	11	(	(	PUNCT
ejpam-3449	123	12	x	x	NOUN
ejpam-3449	123	13	,	,	PUNCT
ejpam-3449	123	14	τ	τ	PROPN
ejpam-3449	123	15	,	,	PUNCT
ejpam-3449	123	16	τf	τf	NUM
ejpam-3449	123	17	)	)	PUNCT
ejpam-3449	123	18	.	.	PUNCT
ejpam-3449	124	1	remark	remark	PROPN
ejpam-3449	124	2	3.9	3.9	NUM
ejpam-3449	124	3	.	.	PUNCT
ejpam-3449	125	1	by	by	ADP
ejpam-3449	125	2	applying	apply	VERB
ejpam-3449	125	3	lemma	lemma	PROPN
ejpam-3449	125	4	3.8	3.8	NUM
ejpam-3449	125	5	,	,	PUNCT
ejpam-3449	125	6	it	it	PRON
ejpam-3449	125	7	is	be	AUX
ejpam-3449	125	8	easy	easy	ADJ
ejpam-3449	125	9	to	to	PART
ejpam-3449	125	10	show	show	VERB
ejpam-3449	125	11	that	that	SCONJ
ejpam-3449	125	12	τfγ	τfγ	VERB
ejpam-3449	125	13	forms	form	NOUN
ejpam-3449	125	14	a	a	DET
ejpam-3449	125	15	topology	topology	NOUN
ejpam-3449	125	16	on	on	ADP
ejpam-3449	125	17	x	x	PUNCT
ejpam-3449	125	18	for	for	ADP
ejpam-3449	125	19	any	any	DET
ejpam-3449	125	20	fine	fine	ADJ
ejpam-3449	125	21	-	-	PUNCT
ejpam-3449	125	22	regular	regular	ADJ
ejpam-3449	125	23	operation	operation	NOUN
ejpam-3449	125	24	γ	γ	NOUN
ejpam-3449	125	25	on	on	ADP
ejpam-3449	125	26	τf	τf	PROPN
ejpam-3449	125	27	.	.	PUNCT
ejpam-3449	126	1	definition	definition	NOUN
ejpam-3449	126	2	3.10	3.10	NUM
ejpam-3449	126	3	.	.	PUNCT
ejpam-3449	127	1	let	let	VERB
ejpam-3449	127	2	a	a	DET
ejpam-3449	127	3	be	be	AUX
ejpam-3449	127	4	any	any	DET
ejpam-3449	127	5	subset	subset	NOUN
ejpam-3449	127	6	of	of	ADP
ejpam-3449	127	7	a	a	DET
ejpam-3449	127	8	fine	fine	ADJ
ejpam-3449	127	9	space	space	NOUN
ejpam-3449	127	10	(	(	PUNCT
ejpam-3449	127	11	x	x	X
ejpam-3449	127	12	,	,	PUNCT
ejpam-3449	127	13	τ	τ	PROPN
ejpam-3449	127	14	,	,	PUNCT
ejpam-3449	127	15	τf	τf	NUM
ejpam-3449	127	16	)	)	PUNCT
ejpam-3449	127	17	and	and	CCONJ
ejpam-3449	127	18	γ	γ	X
ejpam-3449	127	19	be	be	AUX
ejpam-3449	127	20	an	an	DET
ejpam-3449	127	21	operation	operation	NOUN
ejpam-3449	127	22	on	on	ADP
ejpam-3449	127	23	τf	τf	PROPN
ejpam-3449	127	24	.	.	PUNCT
ejpam-3449	128	1	the	the	DET
ejpam-3449	128	2	point	point	NOUN
ejpam-3449	128	3	x	x	X
ejpam-3449	128	4	∈	∈	NOUN
ejpam-3449	128	5	x	x	PUNCT
ejpam-3449	128	6	is	be	AUX
ejpam-3449	128	7	said	say	VERB
ejpam-3449	128	8	to	to	PART
ejpam-3449	128	9	be	be	AUX
ejpam-3449	128	10	fγ	fγ	NOUN
ejpam-3449	128	11	-	-	PUNCT
ejpam-3449	128	12	closure	closure	NOUN
ejpam-3449	128	13	of	of	ADP
ejpam-3449	128	14	a	a	DET
ejpam-3449	128	15	if	if	SCONJ
ejpam-3449	128	16	γ(u	γ(u	NOUN
ejpam-3449	128	17	)	)	PUNCT
ejpam-3449	128	18	∩	∩	NOUN
ejpam-3449	128	19	a	a	DET
ejpam-3449	128	20	6=	6=	NUM
ejpam-3449	128	21	φ	φ	NOUN
ejpam-3449	128	22	for	for	ADP
ejpam-3449	128	23	each	each	DET
ejpam-3449	128	24	u	u	NOUN
ejpam-3449	128	25	∈	∈	PROPN
ejpam-3449	128	26	τf	τf	ADP
ejpam-3449	128	27	such	such	ADJ
ejpam-3449	128	28	that	that	SCONJ
ejpam-3449	128	29	x	x	SYM
ejpam-3449	128	30	∈	∈	PROPN
ejpam-3449	128	31	u	u	NOUN
ejpam-3449	128	32	.	.	PUNCT
ejpam-3449	129	1	we	we	PRON
ejpam-3449	129	2	denote	denote	VERB
ejpam-3449	129	3	fclγ(a	fclγ(a	PROPN
ejpam-3449	129	4	)	)	PUNCT
ejpam-3449	129	5	by	by	ADP
ejpam-3449	129	6	the	the	DET
ejpam-3449	129	7	fγ	fγ	NOUN
ejpam-3449	129	8	-	-	PUNCT
ejpam-3449	129	9	closure	closure	NOUN
ejpam-3449	129	10	of	of	ADP
ejpam-3449	129	11	a	a	PRON
ejpam-3449	129	12	which	which	PRON
ejpam-3449	129	13	is	be	AUX
ejpam-3449	129	14	the	the	DET
ejpam-3449	129	15	set	set	NOUN
ejpam-3449	129	16	of	of	ADP
ejpam-3449	129	17	all	all	DET
ejpam-3449	129	18	fγ	fγ	NOUN
ejpam-3449	129	19	-	-	PUNCT
ejpam-3449	129	20	closure	closure	NOUN
ejpam-3449	129	21	points	point	NOUN
ejpam-3449	129	22	of	of	ADP
ejpam-3449	129	23	a.	a.	NOUN
ejpam-3449	129	24	definition	definition	NOUN
ejpam-3449	129	25	3.11	3.11	NUM
ejpam-3449	129	26	.	.	PUNCT
ejpam-3449	130	1	let	let	VERB
ejpam-3449	130	2	a	a	DET
ejpam-3449	130	3	be	be	AUX
ejpam-3449	130	4	any	any	DET
ejpam-3449	130	5	subset	subset	NOUN
ejpam-3449	130	6	of	of	ADP
ejpam-3449	130	7	a	a	DET
ejpam-3449	130	8	fine	fine	ADJ
ejpam-3449	130	9	space	space	NOUN
ejpam-3449	130	10	(	(	PUNCT
ejpam-3449	130	11	x	x	X
ejpam-3449	130	12	,	,	PUNCT
ejpam-3449	130	13	τ	τ	PROPN
ejpam-3449	130	14	,	,	PUNCT
ejpam-3449	130	15	τf	τf	NUM
ejpam-3449	130	16	)	)	PUNCT
ejpam-3449	130	17	and	and	CCONJ
ejpam-3449	130	18	γ	γ	X
ejpam-3449	130	19	be	be	AUX
ejpam-3449	130	20	an	an	DET
ejpam-3449	130	21	operation	operation	NOUN
ejpam-3449	130	22	on	on	ADP
ejpam-3449	130	23	τf	τf	PROPN
ejpam-3449	130	24	.	.	PUNCT
ejpam-3449	131	1	we	we	PRON
ejpam-3449	131	2	define	define	VERB
ejpam-3449	131	3	τfγ	τfγ	NOUN
ejpam-3449	131	4	-	-	PUNCT
ejpam-3449	131	5	cl(a	cl(a	NUM
ejpam-3449	131	6	)	)	PUNCT
ejpam-3449	131	7	as	as	ADP
ejpam-3449	131	8	the	the	DET
ejpam-3449	131	9	intersection	intersection	NOUN
ejpam-3449	131	10	of	of	ADP
ejpam-3449	131	11	all	all	DET
ejpam-3449	131	12	fγ	fγ	NOUN
ejpam-3449	131	13	-	-	PUNCT
ejpam-3449	131	14	closed	close	VERB
ejpam-3449	131	15	sets	set	NOUN
ejpam-3449	131	16	of	of	ADP
ejpam-3449	131	17	x	x	PUNCT
ejpam-3449	131	18	containing	contain	VERB
ejpam-3449	131	19	a.	a.	NOUN
ejpam-3449	131	20	i.e.	i.e.	X
ejpam-3449	131	21	τfγ	τfγ	X
ejpam-3449	131	22	-	-	PUNCT
ejpam-3449	131	23	cl(a	cl(a	NUM
ejpam-3449	131	24	)	)	PUNCT
ejpam-3449	131	25	=	=	SYM
ejpam-3449	131	26	⋂	⋂	PROPN
ejpam-3449	131	27	{	{	PUNCT
ejpam-3449	131	28	f	f	NOUN
ejpam-3449	131	29	:	:	PUNCT
ejpam-3449	131	30	a	a	DET
ejpam-3449	131	31	⊆	⊆	NUM
ejpam-3449	131	32	f	f	NOUN
ejpam-3449	131	33	,	,	PUNCT
ejpam-3449	131	34	x\f	x\f	PROPN
ejpam-3449	131	35	∈	∈	PROPN
ejpam-3449	131	36	τfγ	τfγ	VERB
ejpam-3449	131	37	}	}	PUNCT
ejpam-3449	131	38	.	.	PUNCT
ejpam-3449	132	1	theorem	theorem	VERB
ejpam-3449	132	2	3.12	3.12	NUM
ejpam-3449	132	3	.	.	PUNCT
ejpam-3449	133	1	let	let	VERB
ejpam-3449	133	2	a	a	DET
ejpam-3449	133	3	be	be	AUX
ejpam-3449	133	4	any	any	DET
ejpam-3449	133	5	subset	subset	NOUN
ejpam-3449	133	6	of	of	ADP
ejpam-3449	133	7	a	a	DET
ejpam-3449	133	8	fine	fine	ADJ
ejpam-3449	133	9	space	space	NOUN
ejpam-3449	133	10	(	(	PUNCT
ejpam-3449	133	11	x	x	X
ejpam-3449	133	12	,	,	PUNCT
ejpam-3449	133	13	τ	τ	PROPN
ejpam-3449	133	14	,	,	PUNCT
ejpam-3449	133	15	τf	τf	NUM
ejpam-3449	133	16	)	)	PUNCT
ejpam-3449	133	17	and	and	CCONJ
ejpam-3449	133	18	γ	γ	X
ejpam-3449	133	19	be	be	AUX
ejpam-3449	133	20	an	an	DET
ejpam-3449	133	21	operation	operation	NOUN
ejpam-3449	133	22	on	on	ADP
ejpam-3449	133	23	τf	τf	PROPN
ejpam-3449	133	24	.	.	PUNCT
ejpam-3449	134	1	then	then	ADV
ejpam-3449	134	2	x	x	X
ejpam-3449	134	3	∈	∈	PROPN
ejpam-3449	134	4	τfγ	τfγ	NOUN
ejpam-3449	134	5	-	-	PUNCT
ejpam-3449	134	6	cl(a	cl(a	NUM
ejpam-3449	134	7	)	)	PUNCT
ejpam-3449	134	8	if	if	SCONJ
ejpam-3449	134	9	and	and	CCONJ
ejpam-3449	134	10	only	only	ADV
ejpam-3449	134	11	if	if	SCONJ
ejpam-3449	134	12	a	a	DET
ejpam-3449	134	13	∩	∩	ADJ
ejpam-3449	134	14	u	u	NOUN
ejpam-3449	134	15	6=	6=	PROPN
ejpam-3449	134	16	φ	φ	PROPN
ejpam-3449	134	17	for	for	ADP
ejpam-3449	134	18	every	every	DET
ejpam-3449	134	19	fγ	fγ	NOUN
ejpam-3449	134	20	-	-	PUNCT
ejpam-3449	134	21	open	open	NOUN
ejpam-3449	134	22	set	set	NOUN
ejpam-3449	134	23	u	u	NOUN
ejpam-3449	134	24	of	of	ADP
ejpam-3449	134	25	x	x	SYM
ejpam-3449	134	26	containing	contain	VERB
ejpam-3449	134	27	x.	x.	NOUN
ejpam-3449	134	28	proof	proof	NOUN
ejpam-3449	134	29	.	.	PUNCT
ejpam-3449	135	1	let	let	VERB
ejpam-3449	135	2	x	x	PUNCT
ejpam-3449	135	3	∈	∈	VERB
ejpam-3449	135	4	τfγ	τfγ	NOUN
ejpam-3449	135	5	-	-	PUNCT
ejpam-3449	135	6	cl(a	cl(a	NUM
ejpam-3449	135	7	)	)	PUNCT
ejpam-3449	135	8	and	and	CCONJ
ejpam-3449	135	9	let	let	VERB
ejpam-3449	135	10	a	a	DET
ejpam-3449	135	11	∩	∩	ADJ
ejpam-3449	135	12	u	u	NOUN
ejpam-3449	135	13	=	=	PROPN
ejpam-3449	135	14	φ	φ	PROPN
ejpam-3449	135	15	for	for	ADP
ejpam-3449	135	16	some	some	DET
ejpam-3449	135	17	fγ	fγ	ADV
ejpam-3449	135	18	-	-	PUNCT
ejpam-3449	135	19	open	open	NOUN
ejpam-3449	135	20	set	set	NOUN
ejpam-3449	135	21	u	u	NOUN
ejpam-3449	135	22	of	of	ADP
ejpam-3449	135	23	x	x	SYM
ejpam-3449	135	24	containing	contain	VERB
ejpam-3449	135	25	x.	x.	NOUN
ejpam-3449	135	26	then	then	ADV
ejpam-3449	135	27	a	a	DET
ejpam-3449	135	28	⊆	⊆	NUM
ejpam-3449	135	29	x\u	x\u	PROPN
ejpam-3449	135	30	and	and	CCONJ
ejpam-3449	135	31	x\u	x\u	PROPN
ejpam-3449	135	32	is	be	AUX
ejpam-3449	135	33	fγ	fγ	ADV
ejpam-3449	135	34	-	-	PUNCT
ejpam-3449	135	35	closed	close	VERB
ejpam-3449	135	36	set	set	NOUN
ejpam-3449	135	37	in	in	ADP
ejpam-3449	135	38	x.	x.	NOUN
ejpam-3449	136	1	so	so	ADV
ejpam-3449	136	2	τfγ	τfγ	NOUN
ejpam-3449	136	3	-	-	PUNCT
ejpam-3449	136	4	cl(a	cl(a	NUM
ejpam-3449	136	5	)	)	PUNCT
ejpam-3449	137	1	⊆	⊆	NUM
ejpam-3449	137	2	x\u	x\u	PROPN
ejpam-3449	137	3	.	.	PUNCT
ejpam-3449	138	1	thus	thus	ADV
ejpam-3449	138	2	,	,	PUNCT
ejpam-3449	138	3	x	x	PROPN
ejpam-3449	138	4	∈	∈	PROPN
ejpam-3449	138	5	x\u	x\u	PROPN
ejpam-3449	138	6	.	.	PUNCT
ejpam-3449	139	1	this	this	PRON
ejpam-3449	139	2	is	be	AUX
ejpam-3449	139	3	a	a	DET
ejpam-3449	139	4	contradiction	contradiction	NOUN
ejpam-3449	139	5	.	.	PUNCT
ejpam-3449	140	1	hence	hence	ADV
ejpam-3449	140	2	a	a	DET
ejpam-3449	140	3	∩	∩	ADJ
ejpam-3449	140	4	u	u	NOUN
ejpam-3449	140	5	6=	6=	PROPN
ejpam-3449	140	6	φ	φ	PROPN
ejpam-3449	140	7	for	for	ADP
ejpam-3449	140	8	every	every	DET
ejpam-3449	140	9	fγ	fγ	NOUN
ejpam-3449	140	10	-	-	PUNCT
ejpam-3449	140	11	open	open	NOUN
ejpam-3449	140	12	set	set	NOUN
ejpam-3449	140	13	u	u	NOUN
ejpam-3449	140	14	of	of	ADP
ejpam-3449	140	15	x	x	SYM
ejpam-3449	140	16	containing	contain	VERB
ejpam-3449	140	17	x.	x.	NOUN
ejpam-3449	140	18	conversely	conversely	ADV
ejpam-3449	140	19	,	,	PUNCT
ejpam-3449	140	20	suppose	suppose	VERB
ejpam-3449	140	21	that	that	SCONJ
ejpam-3449	140	22	x	x	X
ejpam-3449	140	23	/∈	/∈	PUNCT
ejpam-3449	140	24	τfγ	τfγ	NOUN
ejpam-3449	140	25	-	-	PUNCT
ejpam-3449	140	26	cl(a	cl(a	NUM
ejpam-3449	140	27	)	)	PUNCT
ejpam-3449	140	28	.	.	PUNCT
ejpam-3449	141	1	so	so	ADV
ejpam-3449	141	2	there	there	PRON
ejpam-3449	141	3	exists	exist	VERB
ejpam-3449	141	4	a	a	DET
ejpam-3449	141	5	fγ	fγ	ADV
ejpam-3449	141	6	-	-	PUNCT
ejpam-3449	141	7	closed	close	VERB
ejpam-3449	141	8	set	set	NOUN
ejpam-3449	141	9	f	f	PROPN
ejpam-3449	141	10	such	such	ADJ
ejpam-3449	141	11	that	that	SCONJ
ejpam-3449	141	12	a	a	DET
ejpam-3449	141	13	⊆	⊆	NUM
ejpam-3449	141	14	f	f	PROPN
ejpam-3449	141	15	and	and	CCONJ
ejpam-3449	141	16	x	x	PROPN
ejpam-3449	141	17	/∈	/∈	PROPN
ejpam-3449	142	1	f	f	PROPN
ejpam-3449	142	2	.	.	PUNCT
ejpam-3449	143	1	then	then	ADV
ejpam-3449	143	2	x\f	x\f	PRON
ejpam-3449	143	3	is	be	AUX
ejpam-3449	143	4	a	a	DET
ejpam-3449	143	5	fγ	fγ	ADV
ejpam-3449	143	6	-	-	PUNCT
ejpam-3449	143	7	open	open	NOUN
ejpam-3449	143	8	set	set	NOUN
ejpam-3449	143	9	such	such	ADJ
ejpam-3449	143	10	that	that	SCONJ
ejpam-3449	143	11	x	x	SYM
ejpam-3449	143	12	∈	∈	PROPN
ejpam-3449	143	13	x\f	x\f	PROPN
ejpam-3449	143	14	and	and	CCONJ
ejpam-3449	143	15	a	a	DET
ejpam-3449	143	16	∩	∩	NOUN
ejpam-3449	143	17	(	(	PUNCT
ejpam-3449	143	18	x\f	x\f	PROPN
ejpam-3449	143	19	)	)	PUNCT
ejpam-3449	144	1	=	=	SYM
ejpam-3449	144	2	φ	φ	X
ejpam-3449	144	3	.	.	PUNCT
ejpam-3449	145	1	contradiction	contradiction	NOUN
ejpam-3449	145	2	of	of	ADP
ejpam-3449	145	3	hypothesis	hypothesis	NOUN
ejpam-3449	145	4	.	.	PUNCT
ejpam-3449	146	1	therefore	therefore	ADV
ejpam-3449	146	2	,	,	PUNCT
ejpam-3449	146	3	x	x	PUNCT
ejpam-3449	146	4	∈	∈	PROPN
ejpam-3449	146	5	τfγ	τfγ	NOUN
ejpam-3449	146	6	-	-	PUNCT
ejpam-3449	146	7	cl(a	cl(a	NUM
ejpam-3449	146	8	)	)	PUNCT
ejpam-3449	146	9	.	.	PUNCT
ejpam-3449	147	1	lemma	lemma	PROPN
ejpam-3449	147	2	3.13	3.13	NUM
ejpam-3449	147	3	.	.	PUNCT
ejpam-3449	148	1	the	the	DET
ejpam-3449	148	2	following	follow	VERB
ejpam-3449	148	3	statements	statement	NOUN
ejpam-3449	148	4	are	be	AUX
ejpam-3449	148	5	true	true	ADJ
ejpam-3449	148	6	for	for	ADP
ejpam-3449	148	7	any	any	DET
ejpam-3449	148	8	subsets	subset	NOUN
ejpam-3449	148	9	a	a	PRON
ejpam-3449	148	10	and	and	CCONJ
ejpam-3449	148	11	b	b	NOUN
ejpam-3449	148	12	of	of	ADP
ejpam-3449	148	13	a	a	DET
ejpam-3449	148	14	fine	fine	ADJ
ejpam-3449	148	15	space	space	NOUN
ejpam-3449	148	16	(	(	PUNCT
ejpam-3449	148	17	x	x	X
ejpam-3449	148	18	,	,	PUNCT
ejpam-3449	148	19	τ	τ	PROPN
ejpam-3449	148	20	,	,	PUNCT
ejpam-3449	148	21	τf	τf	NUM
ejpam-3449	148	22	)	)	PUNCT
ejpam-3449	148	23	with	with	ADP
ejpam-3449	148	24	an	an	DET
ejpam-3449	148	25	operation	operation	NOUN
ejpam-3449	148	26	γ	γ	NOUN
ejpam-3449	148	27	on	on	ADP
ejpam-3449	148	28	τf	τf	PROPN
ejpam-3449	148	29	.	.	PUNCT
ejpam-3449	149	1	(	(	PUNCT
ejpam-3449	149	2	i	i	NOUN
ejpam-3449	149	3	)	)	PUNCT
ejpam-3449	149	4	fclγ(a	fclγ(a	PROPN
ejpam-3449	149	5	)	)	PUNCT
ejpam-3449	149	6	is	be	AUX
ejpam-3449	149	7	fine	fine	ADV
ejpam-3449	149	8	-	-	PUNCT
ejpam-3449	149	9	closed	close	VERB
ejpam-3449	149	10	set	set	NOUN
ejpam-3449	149	11	in	in	ADP
ejpam-3449	149	12	x	x	PUNCT
ejpam-3449	149	13	and	and	CCONJ
ejpam-3449	149	14	τfγ	τfγ	NOUN
ejpam-3449	149	15	-	-	PUNCT
ejpam-3449	149	16	cl(a	cl(a	NUM
ejpam-3449	149	17	)	)	PUNCT
ejpam-3449	149	18	is	be	AUX
ejpam-3449	149	19	fγ	fγ	ADV
ejpam-3449	149	20	-	-	PUNCT
ejpam-3449	149	21	closed	close	VERB
ejpam-3449	149	22	set	set	NOUN
ejpam-3449	149	23	in	in	ADP
ejpam-3449	149	24	x.	x.	PROPN
ejpam-3449	149	25	(	(	PUNCT
ejpam-3449	149	26	ii	ii	PROPN
ejpam-3449	149	27	)	)	PUNCT
ejpam-3449	149	28	a	a	DET
ejpam-3449	149	29	⊆	⊆	NUM
ejpam-3449	149	30	fclγ(a	fclγ(a	NOUN
ejpam-3449	149	31	)	)	PUNCT
ejpam-3449	149	32	⊆	⊆	NUM
ejpam-3449	149	33	τfγ	τfγ	NOUN
ejpam-3449	149	34	-	-	PUNCT
ejpam-3449	149	35	cl(a	cl(a	NUM
ejpam-3449	149	36	)	)	PUNCT
ejpam-3449	149	37	.	.	PUNCT
ejpam-3449	150	1	(	(	PUNCT
ejpam-3449	150	2	iii	iii	X
ejpam-3449	150	3	)	)	PUNCT
ejpam-3449	150	4	τfγ	τfγ	NOUN
ejpam-3449	150	5	-	-	PUNCT
ejpam-3449	150	6	cl(φ	cl(φ	NOUN
ejpam-3449	150	7	)	)	PUNCT
ejpam-3449	150	8	=	=	SYM
ejpam-3449	150	9	fclγ(φ	fclγ(φ	NOUN
ejpam-3449	150	10	)	)	PUNCT
ejpam-3449	150	11	=	=	SYM
ejpam-3449	150	12	φ	φ	PROPN
ejpam-3449	150	13	and	and	CCONJ
ejpam-3449	150	14	τfγ	τfγ	NOUN
ejpam-3449	150	15	-	-	PUNCT
ejpam-3449	150	16	cl(x	cl(x	NUM
ejpam-3449	150	17	)	)	PUNCT
ejpam-3449	150	18	=	=	SYM
ejpam-3449	150	19	fclγ(x	fclγ(x	PROPN
ejpam-3449	150	20	)	)	PUNCT
ejpam-3449	150	21	=	=	SYM
ejpam-3449	151	1	x.	x.	NOUN
ejpam-3449	151	2	(	(	PUNCT
ejpam-3449	151	3	iv	iv	X
ejpam-3449	151	4	)	)	PUNCT
ejpam-3449	151	5	(	(	PUNCT
ejpam-3449	151	6	a	a	X
ejpam-3449	151	7	)	)	PUNCT
ejpam-3449	151	8	a	a	PRON
ejpam-3449	151	9	is	be	AUX
ejpam-3449	151	10	fγ	fγ	NOUN
ejpam-3449	151	11	-	-	PUNCT
ejpam-3449	151	12	closed	closed	ADJ
ejpam-3449	151	13	if	if	SCONJ
ejpam-3449	152	1	and	and	CCONJ
ejpam-3449	152	2	only	only	ADV
ejpam-3449	152	3	if	if	SCONJ
ejpam-3449	152	4	τfγ	τfγ	X
ejpam-3449	152	5	-	-	PUNCT
ejpam-3449	152	6	cl(a	cl(a	NUM
ejpam-3449	152	7	)	)	PUNCT
ejpam-3449	152	8	=	=	SYM
ejpam-3449	152	9	a	a	PROPN
ejpam-3449	152	10	and	and	CCONJ
ejpam-3449	152	11	,	,	PUNCT
ejpam-3449	152	12	(	(	PUNCT
ejpam-3449	152	13	b	b	X
ejpam-3449	152	14	)	)	PUNCT
ejpam-3449	152	15	a	a	PRON
ejpam-3449	152	16	is	be	AUX
ejpam-3449	152	17	fγ	fγ	NOUN
ejpam-3449	152	18	-	-	PUNCT
ejpam-3449	152	19	closed	closed	ADJ
ejpam-3449	152	20	if	if	SCONJ
ejpam-3449	153	1	and	and	CCONJ
ejpam-3449	153	2	only	only	ADV
ejpam-3449	153	3	if	if	SCONJ
ejpam-3449	153	4	fclγ(a	fclγ(a	NOUN
ejpam-3449	153	5	)	)	PUNCT
ejpam-3449	153	6	=	=	SYM
ejpam-3449	153	7	a.	a.	NOUN
ejpam-3449	153	8	(	(	PUNCT
ejpam-3449	153	9	v	v	NOUN
ejpam-3449	153	10	)	)	PUNCT
ejpam-3449	153	11	if	if	SCONJ
ejpam-3449	153	12	a	a	DET
ejpam-3449	153	13	⊆	⊆	NUM
ejpam-3449	153	14	b	b	NOUN
ejpam-3449	153	15	,	,	PUNCT
ejpam-3449	153	16	then	then	ADV
ejpam-3449	153	17	τfγ	τfγ	NOUN
ejpam-3449	153	18	-	-	PUNCT
ejpam-3449	153	19	cl(a	cl(a	NUM
ejpam-3449	153	20	)	)	PUNCT
ejpam-3449	153	21	⊆	⊆	NUM
ejpam-3449	153	22	τfγ	τfγ	NOUN
ejpam-3449	153	23	-	-	PUNCT
ejpam-3449	153	24	cl(b	cl(b	NOUN
ejpam-3449	153	25	)	)	PUNCT
ejpam-3449	153	26	and	and	CCONJ
ejpam-3449	153	27	fclγ(a	fclγ(a	NOUN
ejpam-3449	153	28	)	)	PUNCT
ejpam-3449	153	29	⊆	⊆	NUM
ejpam-3449	153	30	fclγ(b	fclγ(b	NOUN
ejpam-3449	153	31	)	)	PUNCT
ejpam-3449	153	32	.	.	PUNCT
ejpam-3449	154	1	(	(	PUNCT
ejpam-3449	154	2	vi	vi	X
ejpam-3449	154	3	)	)	PUNCT
ejpam-3449	154	4	(	(	PUNCT
ejpam-3449	154	5	a	a	X
ejpam-3449	154	6	)	)	PUNCT
ejpam-3449	154	7	τfγ	τfγ	NOUN
ejpam-3449	154	8	-	-	PUNCT
ejpam-3449	154	9	cl(a	cl(a	NUM
ejpam-3449	154	10	∩	∩	ADJ
ejpam-3449	154	11	b	b	X
ejpam-3449	154	12	)	)	PUNCT
ejpam-3449	154	13	⊆	⊆	NUM
ejpam-3449	154	14	τfγ	τfγ	NOUN
ejpam-3449	154	15	-	-	PUNCT
ejpam-3449	154	16	cl(a	cl(a	NUM
ejpam-3449	154	17	)	)	PUNCT
ejpam-3449	154	18	∩	∩	ADJ
ejpam-3449	154	19	τfγ	τfγ	NOUN
ejpam-3449	154	20	-	-	PUNCT
ejpam-3449	154	21	cl(b	cl(b	NOUN
ejpam-3449	154	22	)	)	PUNCT
ejpam-3449	154	23	and	and	CCONJ
ejpam-3449	154	24	,	,	PUNCT
ejpam-3449	154	25	b.	b.	PROPN
ejpam-3449	154	26	a.	a.	PROPN
ejpam-3449	154	27	asaad	asaad	PROPN
ejpam-3449	154	28	et	et	PROPN
ejpam-3449	155	1	al	al	PROPN
ejpam-3449	155	2	.	.	PUNCT
ejpam-3449	155	3	/	/	SYM
ejpam-3449	155	4	eur	eur	PROPN
ejpam-3449	155	5	.	.	PUNCT
ejpam-3449	156	1	j.	j.	PROPN
ejpam-3449	156	2	pure	pure	PROPN
ejpam-3449	156	3	appl	appl	PROPN
ejpam-3449	156	4	.	.	PROPN
ejpam-3449	156	5	math	math	PROPN
ejpam-3449	156	6	,	,	PUNCT
ejpam-3449	156	7	12	12	NUM
ejpam-3449	156	8	(	(	PUNCT
ejpam-3449	156	9	3	3	NUM
ejpam-3449	156	10	)	)	PUNCT
ejpam-3449	156	11	(	(	PUNCT
ejpam-3449	156	12	2019	2019	NUM
ejpam-3449	156	13	)	)	PUNCT
ejpam-3449	156	14	,	,	PUNCT
ejpam-3449	156	15	960	960	NUM
ejpam-3449	156	16	-	-	SYM
ejpam-3449	156	17	977	977	NUM
ejpam-3449	156	18	965	965	NUM
ejpam-3449	156	19	(	(	PUNCT
ejpam-3449	156	20	b	b	NOUN
ejpam-3449	156	21	)	)	PUNCT
ejpam-3449	156	22	fclγ(a	fclγ(a	NOUN
ejpam-3449	156	23	∩	∩	ADJ
ejpam-3449	156	24	b	b	X
ejpam-3449	156	25	)	)	PUNCT
ejpam-3449	156	26	⊆	⊆	NUM
ejpam-3449	156	27	fclγ(a	fclγ(a	NOUN
ejpam-3449	156	28	)	)	PUNCT
ejpam-3449	156	29	∩	∩	ADJ
ejpam-3449	156	30	fclγ(b	fclγ(b	NOUN
ejpam-3449	156	31	)	)	PUNCT
ejpam-3449	156	32	.	.	PUNCT
ejpam-3449	157	1	(	(	PUNCT
ejpam-3449	157	2	vii	vii	PROPN
ejpam-3449	157	3	)	)	PUNCT
ejpam-3449	157	4	(	(	PUNCT
ejpam-3449	157	5	a	a	X
ejpam-3449	157	6	)	)	PUNCT
ejpam-3449	157	7	τfγ	τfγ	NOUN
ejpam-3449	157	8	-	-	PUNCT
ejpam-3449	157	9	cl(a	cl(a	NUM
ejpam-3449	157	10	)	)	PUNCT
ejpam-3449	157	11	∪	∪	ADP
ejpam-3449	157	12	τfγ	τfγ	NOUN
ejpam-3449	157	13	-	-	PUNCT
ejpam-3449	157	14	cl(b	cl(b	NOUN
ejpam-3449	157	15	)	)	PUNCT
ejpam-3449	157	16	⊆	⊆	NUM
ejpam-3449	157	17	τfγ	τfγ	NOUN
ejpam-3449	157	18	-	-	PUNCT
ejpam-3449	157	19	cl(a	cl(a	NUM
ejpam-3449	157	20	∪	∪	X
ejpam-3449	157	21	b	b	NOUN
ejpam-3449	157	22	)	)	PUNCT
ejpam-3449	157	23	and	and	CCONJ
ejpam-3449	157	24	,	,	PUNCT
ejpam-3449	157	25	(	(	PUNCT
ejpam-3449	157	26	b	b	X
ejpam-3449	157	27	)	)	PUNCT
ejpam-3449	157	28	fclγ(a	fclγ(a	NOUN
ejpam-3449	157	29	)	)	PUNCT
ejpam-3449	157	30	∪	∪	X
ejpam-3449	157	31	fclγ(b	fclγ(b	PROPN
ejpam-3449	157	32	)	)	PUNCT
ejpam-3449	157	33	⊆	⊆	NUM
ejpam-3449	157	34	fclγ(a	fclγ(a	NOUN
ejpam-3449	157	35	∪	∪	ADJ
ejpam-3449	157	36	b	b	NOUN
ejpam-3449	157	37	)	)	PUNCT
ejpam-3449	157	38	.	.	PUNCT
ejpam-3449	158	1	(	(	PUNCT
ejpam-3449	158	2	viii	viii	NOUN
ejpam-3449	158	3	)	)	PUNCT
ejpam-3449	158	4	τfγ	τfγ	NOUN
ejpam-3449	158	5	-	-	PUNCT
ejpam-3449	158	6	cl(τfγ	cl(τfγ	NOUN
ejpam-3449	158	7	-	-	PUNCT
ejpam-3449	158	8	cl(a	cl(a	NUM
ejpam-3449	158	9	)	)	PUNCT
ejpam-3449	158	10	)	)	PUNCT
ejpam-3449	159	1	=	=	PUNCT
ejpam-3449	159	2	τfγ	τfγ	NOUN
ejpam-3449	159	3	-	-	PUNCT
ejpam-3449	159	4	cl(a	cl(a	NUM
ejpam-3449	159	5	)	)	PUNCT
ejpam-3449	159	6	.	.	PUNCT
ejpam-3449	160	1	proof	proof	NOUN
ejpam-3449	160	2	.	.	PUNCT
ejpam-3449	161	1	straightforward	straightforward	ADJ
ejpam-3449	161	2	.	.	PUNCT
ejpam-3449	162	1	theorem	theorem	VERB
ejpam-3449	162	2	3.14	3.14	NUM
ejpam-3449	162	3	.	.	PUNCT
ejpam-3449	163	1	for	for	ADP
ejpam-3449	163	2	any	any	DET
ejpam-3449	163	3	subsets	subset	NOUN
ejpam-3449	163	4	a	a	PRON
ejpam-3449	163	5	,	,	PUNCT
ejpam-3449	163	6	b	b	PROPN
ejpam-3449	163	7	of	of	ADP
ejpam-3449	163	8	a	a	DET
ejpam-3449	163	9	fine	fine	ADJ
ejpam-3449	163	10	space	space	NOUN
ejpam-3449	163	11	(	(	PUNCT
ejpam-3449	163	12	x	x	X
ejpam-3449	163	13	,	,	PUNCT
ejpam-3449	163	14	τ	τ	PROPN
ejpam-3449	163	15	,	,	PUNCT
ejpam-3449	163	16	τf	τf	NUM
ejpam-3449	163	17	)	)	PUNCT
ejpam-3449	163	18	.	.	PUNCT
ejpam-3449	164	1	if	if	SCONJ
ejpam-3449	164	2	γ	γ	X
ejpam-3449	164	3	is	be	AUX
ejpam-3449	164	4	a	a	DET
ejpam-3449	164	5	fine	fine	ADJ
ejpam-3449	164	6	-	-	PUNCT
ejpam-3449	164	7	regular	regular	ADJ
ejpam-3449	164	8	operation	operation	NOUN
ejpam-3449	164	9	on	on	ADP
ejpam-3449	164	10	τf	τf	PROPN
ejpam-3449	164	11	,	,	PUNCT
ejpam-3449	164	12	then	then	ADV
ejpam-3449	164	13	(	(	PUNCT
ejpam-3449	164	14	i	i	NOUN
ejpam-3449	164	15	)	)	PUNCT
ejpam-3449	164	16	τfγ	τfγ	NOUN
ejpam-3449	164	17	-	-	PUNCT
ejpam-3449	164	18	cl(a	cl(a	NUM
ejpam-3449	164	19	)	)	PUNCT
ejpam-3449	164	20	∪	∪	ADP
ejpam-3449	164	21	τfγ	τfγ	NOUN
ejpam-3449	164	22	-	-	PUNCT
ejpam-3449	164	23	cl(b	cl(b	NOUN
ejpam-3449	164	24	)	)	PUNCT
ejpam-3449	164	25	=	=	SYM
ejpam-3449	164	26	τfγ	τfγ	NOUN
ejpam-3449	164	27	-	-	PUNCT
ejpam-3449	164	28	cl(a	cl(a	NUM
ejpam-3449	164	29	∪	∪	X
ejpam-3449	164	30	b	b	NOUN
ejpam-3449	164	31	)	)	PUNCT
ejpam-3449	164	32	.	.	PUNCT
ejpam-3449	165	1	(	(	PUNCT
ejpam-3449	165	2	ii	ii	NOUN
ejpam-3449	165	3	)	)	PUNCT
ejpam-3449	165	4	fclγ(a	fclγ(a	PROPN
ejpam-3449	165	5	)	)	PUNCT
ejpam-3449	165	6	∪	∪	X
ejpam-3449	165	7	fclγ(b	fclγ(b	NOUN
ejpam-3449	165	8	)	)	PUNCT
ejpam-3449	165	9	=	=	SYM
ejpam-3449	166	1	fclγ(a	fclγ(a	NOUN
ejpam-3449	166	2	∪	∪	VERB
ejpam-3449	166	3	b	b	NOUN
ejpam-3449	166	4	)	)	PUNCT
ejpam-3449	166	5	.	.	PUNCT
ejpam-3449	167	1	proof	proof	NOUN
ejpam-3449	167	2	.	.	PUNCT
ejpam-3449	168	1	(	(	PUNCT
ejpam-3449	168	2	1	1	X
ejpam-3449	168	3	)	)	PUNCT
ejpam-3449	168	4	it	it	PRON
ejpam-3449	168	5	is	be	AUX
ejpam-3449	168	6	enough	enough	ADJ
ejpam-3449	168	7	to	to	PART
ejpam-3449	168	8	prove	prove	VERB
ejpam-3449	168	9	that	that	SCONJ
ejpam-3449	168	10	τfγ	τfγ	NOUN
ejpam-3449	168	11	-	-	PUNCT
ejpam-3449	168	12	cl(a	cl(a	NUM
ejpam-3449	168	13	∪	∪	X
ejpam-3449	168	14	b	b	NOUN
ejpam-3449	168	15	)	)	PUNCT
ejpam-3449	168	16	⊆	⊆	NUM
ejpam-3449	168	17	τfγ	τfγ	NOUN
ejpam-3449	168	18	-	-	PUNCT
ejpam-3449	168	19	cl(a	cl(a	NUM
ejpam-3449	168	20	)	)	PUNCT
ejpam-3449	168	21	∪	∪	ADP
ejpam-3449	168	22	τfγ	τfγ	NOUN
ejpam-3449	168	23	-	-	PUNCT
ejpam-3449	168	24	cl(b	cl(b	NOUN
ejpam-3449	168	25	)	)	PUNCT
ejpam-3449	168	26	since	since	SCONJ
ejpam-3449	168	27	the	the	DET
ejpam-3449	168	28	other	other	ADJ
ejpam-3449	168	29	part	part	NOUN
ejpam-3449	168	30	follows	follow	VERB
ejpam-3449	168	31	directly	directly	ADV
ejpam-3449	168	32	from	from	ADP
ejpam-3449	168	33	lemma	lemma	PROPN
ejpam-3449	168	34	3.13	3.13	NUM
ejpam-3449	168	35	(	(	PUNCT
ejpam-3449	168	36	7	7	NUM
ejpam-3449	168	37	)	)	PUNCT
ejpam-3449	168	38	.	.	PUNCT
ejpam-3449	169	1	let	let	VERB
ejpam-3449	169	2	x	x	PRON
ejpam-3449	169	3	/∈	/∈	VERB
ejpam-3449	169	4	τfγ	τfγ	NOUN
ejpam-3449	169	5	-	-	PUNCT
ejpam-3449	169	6	cl(a	cl(a	NUM
ejpam-3449	169	7	)	)	PUNCT
ejpam-3449	169	8	∪	∪	ADP
ejpam-3449	169	9	τfγ	τfγ	NOUN
ejpam-3449	169	10	-	-	PUNCT
ejpam-3449	169	11	cl(b	cl(b	NOUN
ejpam-3449	169	12	)	)	PUNCT
ejpam-3449	169	13	.	.	PUNCT
ejpam-3449	170	1	then	then	ADV
ejpam-3449	170	2	by	by	ADP
ejpam-3449	170	3	using	use	VERB
ejpam-3449	170	4	theorem	theorem	NOUN
ejpam-3449	170	5	3.12	3.12	NUM
ejpam-3449	170	6	,	,	PUNCT
ejpam-3449	170	7	there	there	PRON
ejpam-3449	170	8	exist	exist	VERB
ejpam-3449	170	9	two	two	NUM
ejpam-3449	170	10	fγ	fγ	ADV
ejpam-3449	170	11	-	-	PUNCT
ejpam-3449	170	12	open	open	ADJ
ejpam-3449	170	13	sets	set	NOUN
ejpam-3449	170	14	u	u	NOUN
ejpam-3449	170	15	and	and	CCONJ
ejpam-3449	170	16	v	v	NOUN
ejpam-3449	170	17	containing	contain	VERB
ejpam-3449	170	18	x	x	PUNCT
ejpam-3449	170	19	such	such	ADJ
ejpam-3449	170	20	that	that	SCONJ
ejpam-3449	170	21	a	a	DET
ejpam-3449	170	22	∩	∩	ADJ
ejpam-3449	170	23	u	u	NOUN
ejpam-3449	170	24	=	=	PROPN
ejpam-3449	170	25	φ	φ	PROPN
ejpam-3449	170	26	and	and	CCONJ
ejpam-3449	170	27	b	b	PROPN
ejpam-3449	170	28	∩	∩	ADJ
ejpam-3449	170	29	v	v	X
ejpam-3449	170	30	=	=	SYM
ejpam-3449	170	31	φ	φ	PROPN
ejpam-3449	170	32	.	.	PUNCT
ejpam-3449	171	1	since	since	SCONJ
ejpam-3449	171	2	γ	γ	PROPN
ejpam-3449	171	3	is	be	AUX
ejpam-3449	171	4	a	a	DET
ejpam-3449	171	5	fine	fine	ADJ
ejpam-3449	171	6	-	-	PUNCT
ejpam-3449	171	7	regular	regular	ADJ
ejpam-3449	171	8	operation	operation	NOUN
ejpam-3449	171	9	on	on	ADP
ejpam-3449	171	10	τf	τf	PROPN
ejpam-3449	171	11	,	,	PUNCT
ejpam-3449	171	12	then	then	ADV
ejpam-3449	171	13	by	by	ADP
ejpam-3449	171	14	lemma	lemma	PROPN
ejpam-3449	171	15	3.8	3.8	NUM
ejpam-3449	171	16	,	,	PUNCT
ejpam-3449	171	17	u	u	PROPN
ejpam-3449	171	18	∩	∩	NOUN
ejpam-3449	171	19	v	v	NOUN
ejpam-3449	171	20	is	be	AUX
ejpam-3449	171	21	fγ	fγ	NOUN
ejpam-3449	171	22	-	-	PUNCT
ejpam-3449	171	23	open	open	ADJ
ejpam-3449	171	24	in	in	ADP
ejpam-3449	171	25	x	x	INTJ
ejpam-3449	171	26	such	such	ADJ
ejpam-3449	171	27	that	that	SCONJ
ejpam-3449	171	28	(	(	PUNCT
ejpam-3449	171	29	u	u	PROPN
ejpam-3449	171	30	∩	∩	ADJ
ejpam-3449	171	31	v	v	NOUN
ejpam-3449	171	32	)	)	PUNCT
ejpam-3449	171	33	∩	∩	NOUN
ejpam-3449	171	34	(	(	PUNCT
ejpam-3449	171	35	a	a	DET
ejpam-3449	171	36	∪	∪	X
ejpam-3449	171	37	b	b	NOUN
ejpam-3449	171	38	)	)	PUNCT
ejpam-3449	172	1	=	=	SYM
ejpam-3449	172	2	φ	φ	PROPN
ejpam-3449	172	3	.	.	PUNCT
ejpam-3449	173	1	therefore	therefore	ADV
ejpam-3449	173	2	,	,	PUNCT
ejpam-3449	173	3	we	we	PRON
ejpam-3449	173	4	have	have	VERB
ejpam-3449	173	5	x	x	X
ejpam-3449	173	6	/∈	/∈	ADP
ejpam-3449	173	7	τfγ	τfγ	NOUN
ejpam-3449	173	8	-	-	PUNCT
ejpam-3449	173	9	cl(a	cl(a	NUM
ejpam-3449	173	10	∪	∪	X
ejpam-3449	173	11	b	b	NOUN
ejpam-3449	173	12	)	)	PUNCT
ejpam-3449	173	13	and	and	CCONJ
ejpam-3449	173	14	hence	hence	ADV
ejpam-3449	173	15	τfγ	τfγ	NOUN
ejpam-3449	173	16	-	-	PUNCT
ejpam-3449	173	17	cl(a	cl(a	NUM
ejpam-3449	173	18	∪	∪	X
ejpam-3449	173	19	b	b	NOUN
ejpam-3449	173	20	)	)	PUNCT
ejpam-3449	173	21	⊆	⊆	NUM
ejpam-3449	173	22	τfγ	τfγ	NOUN
ejpam-3449	173	23	-	-	PUNCT
ejpam-3449	173	24	cl(a	cl(a	NUM
ejpam-3449	173	25	)	)	PUNCT
ejpam-3449	173	26	∪	∪	ADP
ejpam-3449	173	27	τfγ	τfγ	NOUN
ejpam-3449	173	28	-	-	PUNCT
ejpam-3449	173	29	cl(b	cl(b	NOUN
ejpam-3449	173	30	)	)	PUNCT
ejpam-3449	173	31	.	.	PUNCT
ejpam-3449	174	1	(	(	PUNCT
ejpam-3449	174	2	2	2	X
ejpam-3449	174	3	)	)	PUNCT
ejpam-3449	174	4	let	let	VERB
ejpam-3449	174	5	x	x	PRON
ejpam-3449	174	6	/∈	/∈	PUNCT
ejpam-3449	174	7	fclγ(a	fclγ(a	NOUN
ejpam-3449	174	8	)	)	PUNCT
ejpam-3449	174	9	∪	∪	PROPN
ejpam-3449	174	10	fclγ(b	fclγ(b	PROPN
ejpam-3449	174	11	)	)	PUNCT
ejpam-3449	174	12	.	.	PUNCT
ejpam-3449	175	1	then	then	ADV
ejpam-3449	175	2	there	there	PRON
ejpam-3449	175	3	exist	exist	VERB
ejpam-3449	175	4	fine	fine	ADJ
ejpam-3449	175	5	-	-	PUNCT
ejpam-3449	175	6	open	open	ADJ
ejpam-3449	175	7	sets	set	NOUN
ejpam-3449	175	8	u1	u1	NOUN
ejpam-3449	175	9	and	and	CCONJ
ejpam-3449	175	10	u2	u2	NOUN
ejpam-3449	175	11	such	such	ADJ
ejpam-3449	175	12	that	that	SCONJ
ejpam-3449	175	13	x	x	SYM
ejpam-3449	175	14	∈	∈	PROPN
ejpam-3449	175	15	u1	u1	NOUN
ejpam-3449	175	16	,	,	PUNCT
ejpam-3449	175	17	x	x	PROPN
ejpam-3449	175	18	∈	∈	PROPN
ejpam-3449	175	19	u2	u2	PROPN
ejpam-3449	175	20	,	,	PUNCT
ejpam-3449	175	21	a	a	DET
ejpam-3449	175	22	∩	∩	ADJ
ejpam-3449	175	23	γ(u1	γ(u1	NOUN
ejpam-3449	175	24	)	)	PUNCT
ejpam-3449	176	1	=	=	PUNCT
ejpam-3449	176	2	φ	φ	PROPN
ejpam-3449	176	3	and	and	CCONJ
ejpam-3449	176	4	a	a	DET
ejpam-3449	176	5	∩	∩	ADJ
ejpam-3449	176	6	γ(u2	γ(u2	NOUN
ejpam-3449	176	7	)	)	PUNCT
ejpam-3449	177	1	=	=	SYM
ejpam-3449	177	2	φ	φ	PROPN
ejpam-3449	177	3	.	.	PUNCT
ejpam-3449	178	1	since	since	SCONJ
ejpam-3449	178	2	γ	γ	PROPN
ejpam-3449	178	3	is	be	AUX
ejpam-3449	178	4	a	a	DET
ejpam-3449	178	5	fine	fine	ADJ
ejpam-3449	178	6	-	-	PUNCT
ejpam-3449	178	7	regular	regular	ADJ
ejpam-3449	178	8	operation	operation	NOUN
ejpam-3449	178	9	on	on	ADP
ejpam-3449	178	10	τf	τf	PROPN
ejpam-3449	178	11	,	,	PUNCT
ejpam-3449	178	12	then	then	ADV
ejpam-3449	178	13	there	there	PRON
ejpam-3449	178	14	exists	exist	VERB
ejpam-3449	178	15	a	a	DET
ejpam-3449	178	16	fine	fine	ADV
ejpam-3449	178	17	-	-	PUNCT
ejpam-3449	178	18	open	open	NOUN
ejpam-3449	178	19	set	set	NOUN
ejpam-3449	178	20	w	w	NOUN
ejpam-3449	178	21	containing	contain	VERB
ejpam-3449	178	22	x	x	PUNCT
ejpam-3449	178	23	such	such	ADJ
ejpam-3449	178	24	that	that	SCONJ
ejpam-3449	178	25	γ(w	γ(w	X
ejpam-3449	178	26	)	)	PUNCT
ejpam-3449	178	27	⊆	⊆	NUM
ejpam-3449	178	28	γ(u1	γ(u1	NOUN
ejpam-3449	178	29	)	)	PUNCT
ejpam-3449	178	30	∩	∩	NOUN
ejpam-3449	178	31	γ(u2	γ(u2	NOUN
ejpam-3449	178	32	)	)	PUNCT
ejpam-3449	178	33	.	.	PUNCT
ejpam-3449	179	1	thus	thus	ADV
ejpam-3449	179	2	,	,	PUNCT
ejpam-3449	179	3	we	we	PRON
ejpam-3449	179	4	have	have	VERB
ejpam-3449	179	5	(	(	PUNCT
ejpam-3449	179	6	a	a	DET
ejpam-3449	179	7	∪	∪	ADJ
ejpam-3449	179	8	b	b	NOUN
ejpam-3449	179	9	)	)	PUNCT
ejpam-3449	179	10	∩	∩	NOUN
ejpam-3449	179	11	γ(w	γ(w	X
ejpam-3449	179	12	)	)	PUNCT
ejpam-3449	180	1	⊆	⊆	X
ejpam-3449	180	2	(	(	PUNCT
ejpam-3449	180	3	a	a	DET
ejpam-3449	180	4	∪	∪	ADJ
ejpam-3449	180	5	b	b	NOUN
ejpam-3449	180	6	)	)	PUNCT
ejpam-3449	180	7	∩	∩	NOUN
ejpam-3449	180	8	(	(	PUNCT
ejpam-3449	180	9	γ(u1	γ(u1	NOUN
ejpam-3449	180	10	)	)	PUNCT
ejpam-3449	180	11	∩	∩	NOUN
ejpam-3449	180	12	γ(u2	γ(u2	NOUN
ejpam-3449	180	13	)	)	PUNCT
ejpam-3449	180	14	)	)	PUNCT
ejpam-3449	180	15	.	.	PUNCT
ejpam-3449	181	1	this	this	PRON
ejpam-3449	181	2	implies	imply	VERB
ejpam-3449	181	3	that	that	SCONJ
ejpam-3449	181	4	(	(	PUNCT
ejpam-3449	181	5	a	a	DET
ejpam-3449	181	6	∪	∪	ADJ
ejpam-3449	181	7	b	b	NOUN
ejpam-3449	181	8	)	)	PUNCT
ejpam-3449	181	9	∩	∩	NOUN
ejpam-3449	181	10	γ(w	γ(w	X
ejpam-3449	181	11	)	)	PUNCT
ejpam-3449	182	1	=	=	PUNCT
ejpam-3449	182	2	φ	φ	PROPN
ejpam-3449	182	3	since	since	SCONJ
ejpam-3449	182	4	(	(	PUNCT
ejpam-3449	182	5	a	a	DET
ejpam-3449	182	6	∪	∪	ADJ
ejpam-3449	182	7	b	b	NOUN
ejpam-3449	182	8	)	)	PUNCT
ejpam-3449	182	9	∩	∩	NOUN
ejpam-3449	182	10	(	(	PUNCT
ejpam-3449	182	11	γ(u1	γ(u1	NOUN
ejpam-3449	182	12	)	)	PUNCT
ejpam-3449	182	13	∩	∩	NOUN
ejpam-3449	182	14	γ(u2	γ(u2	NOUN
ejpam-3449	182	15	)	)	PUNCT
ejpam-3449	182	16	)	)	PUNCT
ejpam-3449	183	1	=	=	PUNCT
ejpam-3449	183	2	φ	φ	X
ejpam-3449	183	3	.	.	PUNCT
ejpam-3449	184	1	this	this	PRON
ejpam-3449	184	2	means	mean	VERB
ejpam-3449	184	3	that	that	SCONJ
ejpam-3449	184	4	x	x	X
ejpam-3449	184	5	/∈	/∈	PUNCT
ejpam-3449	184	6	fclγ(a	fclγ(a	NOUN
ejpam-3449	184	7	∪	∪	ADJ
ejpam-3449	184	8	b	b	NOUN
ejpam-3449	184	9	)	)	PUNCT
ejpam-3449	184	10	and	and	CCONJ
ejpam-3449	184	11	hence	hence	ADV
ejpam-3449	184	12	fclγ(a	fclγ(a	ADV
ejpam-3449	184	13	∪	∪	ADJ
ejpam-3449	184	14	b	b	NOUN
ejpam-3449	184	15	)	)	PUNCT
ejpam-3449	184	16	⊆	⊆	NUM
ejpam-3449	184	17	fclγ(a	fclγ(a	NOUN
ejpam-3449	184	18	)	)	PUNCT
ejpam-3449	184	19	∪	∪	X
ejpam-3449	184	20	fclγ(b	fclγ(b	PROPN
ejpam-3449	184	21	)	)	PUNCT
ejpam-3449	184	22	.	.	PUNCT
ejpam-3449	185	1	using	use	VERB
ejpam-3449	185	2	lemma	lemma	PROPN
ejpam-3449	185	3	3.13	3.13	NUM
ejpam-3449	185	4	(	(	PUNCT
ejpam-3449	185	5	7	7	NUM
ejpam-3449	185	6	)	)	PUNCT
ejpam-3449	185	7	,	,	PUNCT
ejpam-3449	185	8	we	we	PRON
ejpam-3449	185	9	have	have	VERB
ejpam-3449	185	10	the	the	DET
ejpam-3449	185	11	equality	equality	NOUN
ejpam-3449	185	12	.	.	PUNCT
ejpam-3449	186	1	theorem	theorem	VERB
ejpam-3449	186	2	3.15	3.15	NUM
ejpam-3449	186	3	.	.	PUNCT
ejpam-3449	187	1	let	let	VERB
ejpam-3449	187	2	a	a	DET
ejpam-3449	187	3	be	be	AUX
ejpam-3449	187	4	any	any	DET
ejpam-3449	187	5	subset	subset	NOUN
ejpam-3449	187	6	of	of	ADP
ejpam-3449	187	7	a	a	DET
ejpam-3449	187	8	fine	fine	ADJ
ejpam-3449	187	9	space	space	NOUN
ejpam-3449	187	10	(	(	PUNCT
ejpam-3449	187	11	x	x	X
ejpam-3449	187	12	,	,	PUNCT
ejpam-3449	187	13	τ	τ	PROPN
ejpam-3449	187	14	,	,	PUNCT
ejpam-3449	187	15	τf	τf	NUM
ejpam-3449	187	16	)	)	PUNCT
ejpam-3449	187	17	.	.	PUNCT
ejpam-3449	188	1	if	if	SCONJ
ejpam-3449	188	2	γ	γ	X
ejpam-3449	188	3	is	be	AUX
ejpam-3449	188	4	a	a	DET
ejpam-3449	188	5	fine	fine	ADJ
ejpam-3449	188	6	-	-	PUNCT
ejpam-3449	188	7	open	open	ADJ
ejpam-3449	188	8	operation	operation	NOUN
ejpam-3449	188	9	on	on	ADP
ejpam-3449	188	10	τf	τf	PROPN
ejpam-3449	188	11	,	,	PUNCT
ejpam-3449	188	12	then	then	ADV
ejpam-3449	188	13	fclγ(a	fclγ(a	ADJ
ejpam-3449	188	14	)	)	PUNCT
ejpam-3449	188	15	=	=	SYM
ejpam-3449	188	16	τfγ	τfγ	NOUN
ejpam-3449	188	17	-	-	PUNCT
ejpam-3449	188	18	cl(a	cl(a	NUM
ejpam-3449	188	19	)	)	PUNCT
ejpam-3449	188	20	,	,	PUNCT
ejpam-3449	188	21	fclγ(fclγ(a	fclγ(fclγ(a	NUM
ejpam-3449	188	22	)	)	PUNCT
ejpam-3449	188	23	)	)	PUNCT
ejpam-3449	189	1	=	=	SYM
ejpam-3449	189	2	fclγ(a	fclγ(a	NOUN
ejpam-3449	189	3	)	)	PUNCT
ejpam-3449	189	4	and	and	CCONJ
ejpam-3449	189	5	fclγ(a	fclγ(a	NOUN
ejpam-3449	189	6	)	)	PUNCT
ejpam-3449	189	7	is	be	AUX
ejpam-3449	189	8	fγ	fγ	ADV
ejpam-3449	189	9	-	-	PUNCT
ejpam-3449	189	10	closed	close	VERB
ejpam-3449	189	11	set	set	NOUN
ejpam-3449	189	12	in	in	ADP
ejpam-3449	189	13	x.	x.	NOUN
ejpam-3449	189	14	proof	proof	NOUN
ejpam-3449	189	15	.	.	PUNCT
ejpam-3449	190	1	by	by	ADP
ejpam-3449	190	2	lemma	lemma	PROPN
ejpam-3449	190	3	3.13	3.13	NUM
ejpam-3449	190	4	(	(	PUNCT
ejpam-3449	190	5	2	2	NUM
ejpam-3449	190	6	)	)	PUNCT
ejpam-3449	190	7	,	,	PUNCT
ejpam-3449	190	8	we	we	PRON
ejpam-3449	190	9	have	have	VERB
ejpam-3449	190	10	fclγ(a	fclγ(a	NOUN
ejpam-3449	190	11	)	)	PUNCT
ejpam-3449	190	12	⊆	⊆	NUM
ejpam-3449	190	13	τfγ	τfγ	NOUN
ejpam-3449	190	14	-	-	PUNCT
ejpam-3449	190	15	cl(a	cl(a	NUM
ejpam-3449	190	16	)	)	PUNCT
ejpam-3449	190	17	.	.	PUNCT
ejpam-3449	191	1	now	now	ADV
ejpam-3449	191	2	,	,	PUNCT
ejpam-3449	191	3	we	we	PRON
ejpam-3449	191	4	need	need	VERB
ejpam-3449	191	5	to	to	PART
ejpam-3449	191	6	show	show	VERB
ejpam-3449	191	7	that	that	SCONJ
ejpam-3449	191	8	τfγ	τfγ	NOUN
ejpam-3449	191	9	-	-	PUNCT
ejpam-3449	191	10	cl(a	cl(a	NUM
ejpam-3449	191	11	)	)	PUNCT
ejpam-3449	191	12	⊆	⊆	NUM
ejpam-3449	191	13	fclγ(a	fclγ(a	NOUN
ejpam-3449	191	14	)	)	PUNCT
ejpam-3449	191	15	.	.	PUNCT
ejpam-3449	192	1	let	let	VERB
ejpam-3449	192	2	x	x	X
ejpam-3449	192	3	/∈	/∈	PUNCT
ejpam-3449	192	4	fclγ(a	fclγ(a	NOUN
ejpam-3449	192	5	)	)	PUNCT
ejpam-3449	192	6	,	,	PUNCT
ejpam-3449	192	7	then	then	ADV
ejpam-3449	192	8	there	there	PRON
ejpam-3449	192	9	exists	exist	VERB
ejpam-3449	192	10	a	a	DET
ejpam-3449	192	11	fine	fine	ADV
ejpam-3449	192	12	-	-	PUNCT
ejpam-3449	192	13	open	open	ADJ
ejpam-3449	192	14	set	set	NOUN
ejpam-3449	192	15	u	u	NOUN
ejpam-3449	192	16	containing	contain	VERB
ejpam-3449	192	17	x	x	PUNCT
ejpam-3449	192	18	such	such	ADJ
ejpam-3449	192	19	that	that	SCONJ
ejpam-3449	192	20	a	a	DET
ejpam-3449	192	21	∩	∩	ADJ
ejpam-3449	192	22	γ(u	γ(u	NOUN
ejpam-3449	192	23	)	)	PUNCT
ejpam-3449	192	24	=	=	SYM
ejpam-3449	193	1	φ	φ	PROPN
ejpam-3449	193	2	.	.	PUNCT
ejpam-3449	194	1	since	since	SCONJ
ejpam-3449	194	2	γ	γ	PROPN
ejpam-3449	194	3	is	be	AUX
ejpam-3449	194	4	a	a	DET
ejpam-3449	194	5	fine	fine	ADV
ejpam-3449	194	6	-	-	PUNCT
ejpam-3449	194	7	open	open	ADJ
ejpam-3449	194	8	on	on	ADP
ejpam-3449	194	9	τf	τf	PROPN
ejpam-3449	194	10	,	,	PUNCT
ejpam-3449	194	11	then	then	ADV
ejpam-3449	194	12	there	there	PRON
ejpam-3449	194	13	exists	exist	VERB
ejpam-3449	194	14	a	a	DET
ejpam-3449	194	15	fγ	fγ	ADV
ejpam-3449	194	16	-	-	PUNCT
ejpam-3449	194	17	open	open	NOUN
ejpam-3449	194	18	set	set	NOUN
ejpam-3449	194	19	w	w	NOUN
ejpam-3449	194	20	containing	contain	VERB
ejpam-3449	194	21	x	x	PUNCT
ejpam-3449	194	22	such	such	ADJ
ejpam-3449	194	23	that	that	SCONJ
ejpam-3449	194	24	w	w	ADP
ejpam-3449	194	25	⊆	⊆	NUM
ejpam-3449	194	26	γ(u	γ(u	NOUN
ejpam-3449	194	27	)	)	PUNCT
ejpam-3449	194	28	.	.	PUNCT
ejpam-3449	195	1	so	so	ADV
ejpam-3449	195	2	a	a	DET
ejpam-3449	195	3	∩	∩	ADJ
ejpam-3449	195	4	w	w	NOUN
ejpam-3449	195	5	=	=	SYM
ejpam-3449	195	6	φ	φ	PROPN
ejpam-3449	195	7	and	and	CCONJ
ejpam-3449	195	8	hence	hence	ADV
ejpam-3449	195	9	by	by	ADP
ejpam-3449	195	10	theorem	theorem	NOUN
ejpam-3449	195	11	3.12	3.12	NUM
ejpam-3449	195	12	,	,	PUNCT
ejpam-3449	195	13	x	x	PROPN
ejpam-3449	195	14	/∈	/∈	PUNCT
ejpam-3449	195	15	τfγcl(a	τfγcl(a	NOUN
ejpam-3449	195	16	)	)	PUNCT
ejpam-3449	195	17	.	.	PUNCT
ejpam-3449	196	1	therefore	therefore	ADV
ejpam-3449	196	2	,	,	PUNCT
ejpam-3449	196	3	τfγ	τfγ	X
ejpam-3449	196	4	-	-	PUNCT
ejpam-3449	196	5	cl(a	cl(a	NUM
ejpam-3449	196	6	)	)	PUNCT
ejpam-3449	196	7	⊆	⊆	NUM
ejpam-3449	196	8	fclγ(a	fclγ(a	NOUN
ejpam-3449	196	9	)	)	PUNCT
ejpam-3449	196	10	.	.	PUNCT
ejpam-3449	197	1	hence	hence	ADV
ejpam-3449	197	2	fclγ(a	fclγ(a	NOUN
ejpam-3449	197	3	)	)	PUNCT
ejpam-3449	197	4	=	=	SYM
ejpam-3449	197	5	τfγ	τfγ	NOUN
ejpam-3449	197	6	-	-	PUNCT
ejpam-3449	197	7	cl(a	cl(a	NUM
ejpam-3449	197	8	)	)	PUNCT
ejpam-3449	197	9	.	.	PUNCT
ejpam-3449	198	1	moreover	moreover	ADV
ejpam-3449	198	2	,	,	PUNCT
ejpam-3449	198	3	using	use	VERB
ejpam-3449	198	4	the	the	DET
ejpam-3449	198	5	above	above	ADJ
ejpam-3449	198	6	result	result	NOUN
ejpam-3449	198	7	and	and	CCONJ
ejpam-3449	198	8	by	by	ADP
ejpam-3449	198	9	lemma	lemma	PROPN
ejpam-3449	198	10	3.13	3.13	NUM
ejpam-3449	198	11	(	(	PUNCT
ejpam-3449	198	12	8)	8)	NUM
ejpam-3449	198	13	,	,	PUNCT
ejpam-3449	198	14	we	we	PRON
ejpam-3449	198	15	get	get	VERB
ejpam-3449	198	16	fclγ(fclγ(a	fclγ(fclγ(a	ADJ
ejpam-3449	198	17	)	)	PUNCT
ejpam-3449	198	18	)	)	PUNCT
ejpam-3449	199	1	=	=	SYM
ejpam-3449	199	2	fclγ(a	fclγ(a	NOUN
ejpam-3449	199	3	)	)	PUNCT
ejpam-3449	199	4	and	and	CCONJ
ejpam-3449	199	5	by	by	ADP
ejpam-3449	199	6	lemma	lemma	PROPN
ejpam-3449	199	7	3.13	3.13	NUM
ejpam-3449	199	8	(	(	PUNCT
ejpam-3449	199	9	4b	4b	PROPN
ejpam-3449	199	10	)	)	PUNCT
ejpam-3449	199	11	,	,	PUNCT
ejpam-3449	199	12	we	we	PRON
ejpam-3449	199	13	obtain	obtain	VERB
ejpam-3449	199	14	fclγ(a	fclγ(a	NOUN
ejpam-3449	199	15	)	)	PUNCT
ejpam-3449	199	16	is	be	AUX
ejpam-3449	199	17	fγ	fγ	ADV
ejpam-3449	199	18	-	-	PUNCT
ejpam-3449	199	19	closed	close	VERB
ejpam-3449	199	20	set	set	NOUN
ejpam-3449	199	21	in	in	ADP
ejpam-3449	199	22	x.	x.	PROPN
ejpam-3449	199	23	b.	b.	PROPN
ejpam-3449	199	24	a.	a.	PROPN
ejpam-3449	199	25	asaad	asaad	PROPN
ejpam-3449	199	26	et	et	PROPN
ejpam-3449	200	1	al	al	PROPN
ejpam-3449	200	2	.	.	PUNCT
ejpam-3449	200	3	/	/	SYM
ejpam-3449	200	4	eur	eur	PROPN
ejpam-3449	200	5	.	.	PUNCT
ejpam-3449	201	1	j.	j.	PROPN
ejpam-3449	201	2	pure	pure	PROPN
ejpam-3449	201	3	appl	appl	PROPN
ejpam-3449	201	4	.	.	PROPN
ejpam-3449	201	5	math	math	PROPN
ejpam-3449	201	6	,	,	PUNCT
ejpam-3449	201	7	12	12	NUM
ejpam-3449	201	8	(	(	PUNCT
ejpam-3449	201	9	3	3	NUM
ejpam-3449	201	10	)	)	PUNCT
ejpam-3449	201	11	(	(	PUNCT
ejpam-3449	201	12	2019	2019	NUM
ejpam-3449	201	13	)	)	PUNCT
ejpam-3449	201	14	,	,	PUNCT
ejpam-3449	201	15	960	960	NUM
ejpam-3449	201	16	-	-	SYM
ejpam-3449	201	17	977	977	NUM
ejpam-3449	201	18	966	966	NUM
ejpam-3449	201	19	theorem	theorem	NOUN
ejpam-3449	201	20	3.16	3.16	NUM
ejpam-3449	201	21	.	.	PUNCT
ejpam-3449	202	1	let	let	VERB
ejpam-3449	202	2	a	a	DET
ejpam-3449	202	3	be	be	AUX
ejpam-3449	202	4	any	any	DET
ejpam-3449	202	5	subset	subset	NOUN
ejpam-3449	202	6	of	of	ADP
ejpam-3449	202	7	a	a	DET
ejpam-3449	202	8	fine	fine	ADJ
ejpam-3449	202	9	space	space	NOUN
ejpam-3449	202	10	(	(	PUNCT
ejpam-3449	202	11	x	x	X
ejpam-3449	202	12	,	,	PUNCT
ejpam-3449	202	13	τ	τ	PROPN
ejpam-3449	202	14	,	,	PUNCT
ejpam-3449	202	15	τf	τf	NUM
ejpam-3449	202	16	)	)	PUNCT
ejpam-3449	202	17	and	and	CCONJ
ejpam-3449	202	18	γ	γ	X
ejpam-3449	202	19	be	be	AUX
ejpam-3449	202	20	an	an	DET
ejpam-3449	202	21	operation	operation	NOUN
ejpam-3449	202	22	on	on	ADP
ejpam-3449	202	23	τf	τf	PROPN
ejpam-3449	202	24	.	.	PUNCT
ejpam-3449	203	1	then	then	ADV
ejpam-3449	203	2	the	the	DET
ejpam-3449	203	3	following	follow	VERB
ejpam-3449	203	4	statements	statement	NOUN
ejpam-3449	203	5	are	be	AUX
ejpam-3449	203	6	equivalent	equivalent	ADJ
ejpam-3449	203	7	:	:	PUNCT
ejpam-3449	203	8	(	(	PUNCT
ejpam-3449	203	9	i	i	NOUN
ejpam-3449	203	10	)	)	PUNCT
ejpam-3449	203	11	a	a	PRON
ejpam-3449	203	12	is	be	AUX
ejpam-3449	203	13	fγ	fγ	NOUN
ejpam-3449	203	14	-	-	PUNCT
ejpam-3449	203	15	open	open	ADJ
ejpam-3449	203	16	set	set	NOUN
ejpam-3449	203	17	.	.	PUNCT
ejpam-3449	204	1	(	(	PUNCT
ejpam-3449	204	2	ii	ii	NOUN
ejpam-3449	204	3	)	)	PUNCT
ejpam-3449	204	4	fclγ(x\a	fclγ(x\a	NOUN
ejpam-3449	204	5	)	)	PUNCT
ejpam-3449	204	6	=	=	SYM
ejpam-3449	205	1	x\a	x\a	PROPN
ejpam-3449	205	2	.	.	PUNCT
ejpam-3449	206	1	(	(	PUNCT
ejpam-3449	206	2	iii	iii	NOUN
ejpam-3449	206	3	)	)	PUNCT
ejpam-3449	206	4	τfγ	τfγ	NOUN
ejpam-3449	206	5	-	-	PUNCT
ejpam-3449	206	6	cl(x\a	cl(x\a	ADJ
ejpam-3449	206	7	)	)	PUNCT
ejpam-3449	206	8	=	=	PUNCT
ejpam-3449	207	1	x\a	x\a	PROPN
ejpam-3449	207	2	.	.	PUNCT
ejpam-3449	207	3	(	(	PUNCT
ejpam-3449	207	4	iv	iv	X
ejpam-3449	207	5	)	)	PUNCT
ejpam-3449	207	6	x\a	x\a	PROPN
ejpam-3449	207	7	is	be	AUX
ejpam-3449	207	8	fγ	fγ	ADV
ejpam-3449	207	9	-	-	PUNCT
ejpam-3449	207	10	closed	close	VERB
ejpam-3449	207	11	set	set	NOUN
ejpam-3449	207	12	.	.	PUNCT
ejpam-3449	208	1	proof	proof	NOUN
ejpam-3449	208	2	.	.	PUNCT
ejpam-3449	209	1	clear	clear	ADJ
ejpam-3449	209	2	.	.	PUNCT
ejpam-3449	210	1	lemma	lemma	PROPN
ejpam-3449	210	2	3.17	3.17	NUM
ejpam-3449	210	3	.	.	PUNCT
ejpam-3449	211	1	let	let	AUX
ejpam-3449	211	2	(	(	PUNCT
ejpam-3449	211	3	x	x	NOUN
ejpam-3449	211	4	,	,	PUNCT
ejpam-3449	211	5	τ	τ	PROPN
ejpam-3449	211	6	,	,	PUNCT
ejpam-3449	211	7	τf	τf	NUM
ejpam-3449	211	8	)	)	PUNCT
ejpam-3449	211	9	be	be	AUX
ejpam-3449	211	10	a	a	DET
ejpam-3449	211	11	fine	fine	ADJ
ejpam-3449	211	12	space	space	NOUN
ejpam-3449	211	13	and	and	CCONJ
ejpam-3449	211	14	γ	γ	NOUN
ejpam-3449	211	15	be	be	AUX
ejpam-3449	211	16	a	a	DET
ejpam-3449	211	17	fine	fine	ADJ
ejpam-3449	211	18	-	-	PUNCT
ejpam-3449	211	19	regular	regular	ADJ
ejpam-3449	211	20	operation	operation	NOUN
ejpam-3449	211	21	on	on	ADP
ejpam-3449	211	22	τf	τf	PROPN
ejpam-3449	211	23	.	.	PUNCT
ejpam-3449	212	1	then	then	ADV
ejpam-3449	212	2	τfγ	τfγ	VERB
ejpam-3449	212	3	-	-	PUNCT
ejpam-3449	212	4	cl(a	cl(a	NUM
ejpam-3449	212	5	)	)	PUNCT
ejpam-3449	212	6	∩	∩	NOUN
ejpam-3449	212	7	u	u	NOUN
ejpam-3449	212	8	⊆	⊆	NUM
ejpam-3449	212	9	τfγ	τfγ	X
ejpam-3449	212	10	-	-	PUNCT
ejpam-3449	212	11	cl(a	cl(a	NUM
ejpam-3449	212	12	∩	∩	ADJ
ejpam-3449	212	13	u	u	NOUN
ejpam-3449	212	14	)	)	PUNCT
ejpam-3449	212	15	holds	hold	VERB
ejpam-3449	212	16	for	for	ADP
ejpam-3449	212	17	every	every	DET
ejpam-3449	212	18	fγ	fγ	NOUN
ejpam-3449	212	19	-	-	PUNCT
ejpam-3449	212	20	open	open	ADJ
ejpam-3449	212	21	set	set	NOUN
ejpam-3449	212	22	u	u	NOUN
ejpam-3449	212	23	and	and	CCONJ
ejpam-3449	212	24	every	every	DET
ejpam-3449	212	25	subset	subset	VERB
ejpam-3449	212	26	a	a	PRON
ejpam-3449	212	27	of	of	ADP
ejpam-3449	212	28	x.	x.	NOUN
ejpam-3449	212	29	proof	proof	NOUN
ejpam-3449	212	30	.	.	PUNCT
ejpam-3449	213	1	suppose	suppose	VERB
ejpam-3449	213	2	that	that	SCONJ
ejpam-3449	213	3	x	x	PUNCT
ejpam-3449	213	4	∈	∈	PROPN
ejpam-3449	213	5	τfγ	τfγ	NOUN
ejpam-3449	213	6	-	-	PUNCT
ejpam-3449	213	7	cl(a	cl(a	NUM
ejpam-3449	213	8	)	)	PUNCT
ejpam-3449	213	9	∩	∩	NOUN
ejpam-3449	213	10	u	u	NOUN
ejpam-3449	213	11	for	for	ADP
ejpam-3449	213	12	every	every	DET
ejpam-3449	213	13	fγ	fγ	NOUN
ejpam-3449	213	14	-	-	PUNCT
ejpam-3449	213	15	open	open	ADJ
ejpam-3449	213	16	set	set	NOUN
ejpam-3449	213	17	u	u	NOUN
ejpam-3449	213	18	,	,	PUNCT
ejpam-3449	213	19	then	then	ADV
ejpam-3449	213	20	x	x	SYM
ejpam-3449	213	21	∈	∈	PROPN
ejpam-3449	213	22	τfγ	τfγ	NOUN
ejpam-3449	213	23	-	-	PUNCT
ejpam-3449	213	24	cl(a	cl(a	NUM
ejpam-3449	213	25	)	)	PUNCT
ejpam-3449	213	26	and	and	CCONJ
ejpam-3449	213	27	x	x	PUNCT
ejpam-3449	213	28	∈	∈	PROPN
ejpam-3449	213	29	u	u	NOUN
ejpam-3449	213	30	.	.	PUNCT
ejpam-3449	214	1	let	let	VERB
ejpam-3449	214	2	v	v	PART
ejpam-3449	214	3	be	be	AUX
ejpam-3449	214	4	any	any	DET
ejpam-3449	214	5	fγ	fγ	ADV
ejpam-3449	214	6	-	-	PUNCT
ejpam-3449	214	7	open	open	ADJ
ejpam-3449	214	8	set	set	NOUN
ejpam-3449	214	9	of	of	ADP
ejpam-3449	214	10	x	x	PUNCT
ejpam-3449	214	11	containing	contain	VERB
ejpam-3449	214	12	x.	x.	NOUN
ejpam-3449	214	13	since	since	SCONJ
ejpam-3449	214	14	γ	γ	PROPN
ejpam-3449	214	15	is	be	AUX
ejpam-3449	214	16	fine	fine	ADV
ejpam-3449	214	17	-	-	PUNCT
ejpam-3449	214	18	regular	regular	ADJ
ejpam-3449	214	19	on	on	ADP
ejpam-3449	214	20	τf	τf	PROPN
ejpam-3449	214	21	.	.	PUNCT
ejpam-3449	215	1	so	so	ADV
ejpam-3449	215	2	by	by	ADP
ejpam-3449	215	3	lemma	lemma	PROPN
ejpam-3449	215	4	3.8	3.8	NUM
ejpam-3449	215	5	,	,	PUNCT
ejpam-3449	215	6	u	u	PROPN
ejpam-3449	215	7	∩	∩	NOUN
ejpam-3449	215	8	v	v	NOUN
ejpam-3449	215	9	is	be	AUX
ejpam-3449	215	10	fγ	fγ	ADV
ejpam-3449	215	11	-	-	PUNCT
ejpam-3449	215	12	open	open	ADJ
ejpam-3449	215	13	set	set	NOUN
ejpam-3449	215	14	containing	contain	VERB
ejpam-3449	215	15	x.	x.	NOUN
ejpam-3449	215	16	since	since	SCONJ
ejpam-3449	215	17	x	x	PROPN
ejpam-3449	215	18	∈	∈	PROPN
ejpam-3449	215	19	τfγ	τfγ	NOUN
ejpam-3449	215	20	-	-	PUNCT
ejpam-3449	215	21	cl(a	cl(a	NUM
ejpam-3449	215	22	)	)	PUNCT
ejpam-3449	215	23	,	,	PUNCT
ejpam-3449	215	24	then	then	ADV
ejpam-3449	215	25	by	by	ADP
ejpam-3449	215	26	theorem	theorem	NOUN
ejpam-3449	215	27	3.12	3.12	NUM
ejpam-3449	215	28	,	,	PUNCT
ejpam-3449	215	29	we	we	PRON
ejpam-3449	215	30	have	have	VERB
ejpam-3449	215	31	a	a	DET
ejpam-3449	215	32	∩	∩	NOUN
ejpam-3449	215	33	(	(	PUNCT
ejpam-3449	215	34	u	u	PROPN
ejpam-3449	215	35	∩	∩	NOUN
ejpam-3449	215	36	v	v	NOUN
ejpam-3449	215	37	)	)	PUNCT
ejpam-3449	215	38	6=	6=	ADP
ejpam-3449	216	1	φ	φ	PROPN
ejpam-3449	216	2	.	.	PUNCT
ejpam-3449	217	1	this	this	PRON
ejpam-3449	217	2	means	mean	VERB
ejpam-3449	217	3	that	that	SCONJ
ejpam-3449	217	4	(	(	PUNCT
ejpam-3449	217	5	a	a	DET
ejpam-3449	217	6	∩	∩	ADJ
ejpam-3449	217	7	u	u	NOUN
ejpam-3449	217	8	)	)	PUNCT
ejpam-3449	217	9	∩	∩	PROPN
ejpam-3449	217	10	v	v	ADP
ejpam-3449	217	11	6=	6=	PROPN
ejpam-3449	217	12	φ	φ	PROPN
ejpam-3449	217	13	.	.	PUNCT
ejpam-3449	218	1	therefore	therefore	ADV
ejpam-3449	218	2	,	,	PUNCT
ejpam-3449	218	3	again	again	ADV
ejpam-3449	218	4	by	by	ADP
ejpam-3449	218	5	theorem	theorem	NOUN
ejpam-3449	218	6	3.12	3.12	NUM
ejpam-3449	218	7	,	,	PUNCT
ejpam-3449	218	8	we	we	PRON
ejpam-3449	218	9	obtain	obtain	VERB
ejpam-3449	218	10	that	that	SCONJ
ejpam-3449	218	11	x	x	PUNCT
ejpam-3449	218	12	∈	∈	PROPN
ejpam-3449	218	13	τfγ	τfγ	NOUN
ejpam-3449	218	14	-	-	PUNCT
ejpam-3449	218	15	cl(a	cl(a	NUM
ejpam-3449	218	16	∩	∩	ADJ
ejpam-3449	218	17	u	u	NOUN
ejpam-3449	218	18	)	)	PUNCT
ejpam-3449	218	19	.	.	PUNCT
ejpam-3449	219	1	thus	thus	ADV
ejpam-3449	219	2	,	,	PUNCT
ejpam-3449	219	3	τfγ	τfγ	NOUN
ejpam-3449	219	4	-	-	PUNCT
ejpam-3449	219	5	cl(a	cl(a	NUM
ejpam-3449	219	6	)	)	PUNCT
ejpam-3449	219	7	∩	∩	NOUN
ejpam-3449	219	8	u	u	NOUN
ejpam-3449	219	9	⊆	⊆	NUM
ejpam-3449	219	10	τfγ	τfγ	X
ejpam-3449	219	11	-	-	PUNCT
ejpam-3449	219	12	cl(a	cl(a	VERB
ejpam-3449	219	13	∩	∩	ADJ
ejpam-3449	219	14	u	u	NOUN
ejpam-3449	219	15	)	)	PUNCT
ejpam-3449	219	16	.	.	PUNCT
ejpam-3449	220	1	4	4	X
ejpam-3449	220	2	.	.	NUM
ejpam-3449	220	3	fγg.closed	fγg.close	VERB
ejpam-3449	220	4	sets	set	VERB
ejpam-3449	220	5	definition	definition	NOUN
ejpam-3449	220	6	4.1	4.1	NUM
ejpam-3449	220	7	.	.	PUNCT
ejpam-3449	221	1	a	a	DET
ejpam-3449	221	2	subset	subset	NOUN
ejpam-3449	221	3	a	a	PRON
ejpam-3449	221	4	of	of	ADP
ejpam-3449	221	5	a	a	DET
ejpam-3449	221	6	fine	fine	ADJ
ejpam-3449	221	7	space	space	NOUN
ejpam-3449	221	8	(	(	PUNCT
ejpam-3449	221	9	x	x	X
ejpam-3449	221	10	,	,	PUNCT
ejpam-3449	221	11	τ	τ	PROPN
ejpam-3449	221	12	,	,	PUNCT
ejpam-3449	221	13	τf	τf	NUM
ejpam-3449	221	14	)	)	PUNCT
ejpam-3449	221	15	with	with	ADP
ejpam-3449	221	16	an	an	DET
ejpam-3449	221	17	operation	operation	NOUN
ejpam-3449	221	18	γ	γ	NOUN
ejpam-3449	221	19	on	on	ADP
ejpam-3449	221	20	τf	τf	PROPN
ejpam-3449	221	21	is	be	AUX
ejpam-3449	221	22	said	say	VERB
ejpam-3449	221	23	to	to	PART
ejpam-3449	221	24	be	be	AUX
ejpam-3449	221	25	fγ	fγ	ADV
ejpam-3449	221	26	-	-	PUNCT
ejpam-3449	221	27	generalized	generalize	VERB
ejpam-3449	221	28	closed	close	VERB
ejpam-3449	221	29	(	(	PUNCT
ejpam-3449	221	30	briefly	briefly	ADV
ejpam-3449	221	31	fγg.closed	fγg.close	VERB
ejpam-3449	221	32	)	)	PUNCT
ejpam-3449	221	33	if	if	SCONJ
ejpam-3449	221	34	fclγ(a	fclγ(a	NOUN
ejpam-3449	221	35	)	)	PUNCT
ejpam-3449	221	36	⊆	⊆	NUM
ejpam-3449	221	37	u	u	NOUN
ejpam-3449	221	38	whenever	whenever	SCONJ
ejpam-3449	221	39	a	a	DET
ejpam-3449	221	40	⊆	⊆	NUM
ejpam-3449	221	41	u	u	NOUN
ejpam-3449	221	42	and	and	CCONJ
ejpam-3449	221	43	u	u	NOUN
ejpam-3449	221	44	is	be	AUX
ejpam-3449	221	45	a	a	DET
ejpam-3449	221	46	fγ	fγ	ADV
ejpam-3449	221	47	-	-	PUNCT
ejpam-3449	221	48	open	open	NOUN
ejpam-3449	221	49	set	set	NOUN
ejpam-3449	221	50	in	in	ADP
ejpam-3449	221	51	x.	x.	PROPN
ejpam-3449	221	52	lemma	lemma	PROPN
ejpam-3449	221	53	4.2	4.2	NUM
ejpam-3449	221	54	.	.	PUNCT
ejpam-3449	222	1	let	let	AUX
ejpam-3449	222	2	(	(	PUNCT
ejpam-3449	222	3	x	x	NOUN
ejpam-3449	222	4	,	,	PUNCT
ejpam-3449	222	5	τ	τ	PROPN
ejpam-3449	222	6	,	,	PUNCT
ejpam-3449	222	7	τf	τf	NUM
ejpam-3449	222	8	)	)	PUNCT
ejpam-3449	222	9	be	be	AUX
ejpam-3449	222	10	a	a	DET
ejpam-3449	222	11	fine	fine	ADJ
ejpam-3449	222	12	space	space	NOUN
ejpam-3449	222	13	and	and	CCONJ
ejpam-3449	222	14	γ	γ	NOUN
ejpam-3449	222	15	be	be	AUX
ejpam-3449	222	16	an	an	DET
ejpam-3449	222	17	operation	operation	NOUN
ejpam-3449	222	18	on	on	ADP
ejpam-3449	222	19	τf	τf	PROPN
ejpam-3449	222	20	.	.	PUNCT
ejpam-3449	223	1	a	a	DET
ejpam-3449	223	2	set	set	NOUN
ejpam-3449	223	3	a	a	DET
ejpam-3449	223	4	in	in	ADP
ejpam-3449	223	5	(	(	PUNCT
ejpam-3449	223	6	x	x	NOUN
ejpam-3449	223	7	,	,	PUNCT
ejpam-3449	223	8	τ	τ	PROPN
ejpam-3449	223	9	,	,	PUNCT
ejpam-3449	223	10	τf	τf	NUM
ejpam-3449	223	11	)	)	PUNCT
ejpam-3449	223	12	is	be	AUX
ejpam-3449	223	13	fγg.closed	fγg.close	VERB
ejpam-3449	223	14	if	if	SCONJ
ejpam-3449	223	15	and	and	CCONJ
ejpam-3449	223	16	only	only	ADV
ejpam-3449	223	17	if	if	SCONJ
ejpam-3449	223	18	a	a	DET
ejpam-3449	223	19	∩	∩	ADJ
ejpam-3449	223	20	τfγ	τfγ	NOUN
ejpam-3449	223	21	-	-	PUNCT
ejpam-3449	223	22	cl({x	cl({x	NOUN
ejpam-3449	223	23	}	}	PUNCT
ejpam-3449	223	24	)	)	PUNCT
ejpam-3449	223	25	6=	6=	ADP
ejpam-3449	223	26	φ	φ	PROPN
ejpam-3449	223	27	for	for	ADP
ejpam-3449	223	28	every	every	DET
ejpam-3449	223	29	x	x	PROPN
ejpam-3449	223	30	∈	∈	PROPN
ejpam-3449	223	31	fclγ(a	fclγ(a	NOUN
ejpam-3449	223	32	)	)	PUNCT
ejpam-3449	223	33	.	.	PUNCT
ejpam-3449	224	1	proof	proof	NOUN
ejpam-3449	224	2	.	.	PUNCT
ejpam-3449	225	1	suppose	suppose	VERB
ejpam-3449	225	2	a	a	PRON
ejpam-3449	225	3	is	be	AUX
ejpam-3449	225	4	fγg.closed	fγg.close	VERB
ejpam-3449	225	5	set	set	VERB
ejpam-3449	225	6	in	in	ADP
ejpam-3449	225	7	x	x	PUNCT
ejpam-3449	225	8	and	and	CCONJ
ejpam-3449	225	9	suppose	suppose	VERB
ejpam-3449	225	10	(	(	PUNCT
ejpam-3449	225	11	if	if	SCONJ
ejpam-3449	225	12	possible	possible	ADJ
ejpam-3449	225	13	)	)	PUNCT
ejpam-3449	225	14	that	that	SCONJ
ejpam-3449	225	15	there	there	PRON
ejpam-3449	225	16	exists	exist	VERB
ejpam-3449	225	17	an	an	DET
ejpam-3449	225	18	element	element	NOUN
ejpam-3449	225	19	x	x	SYM
ejpam-3449	225	20	∈	∈	PROPN
ejpam-3449	225	21	fclγ(a	fclγ(a	NOUN
ejpam-3449	225	22	)	)	PUNCT
ejpam-3449	225	23	such	such	ADJ
ejpam-3449	225	24	that	that	SCONJ
ejpam-3449	225	25	a∩	a∩	PROPN
ejpam-3449	225	26	τfγ	τfγ	PROPN
ejpam-3449	225	27	-	-	PUNCT
ejpam-3449	225	28	cl({x	cl({x	NOUN
ejpam-3449	225	29	}	}	PUNCT
ejpam-3449	225	30	)	)	PUNCT
ejpam-3449	226	1	=	=	SYM
ejpam-3449	226	2	φ	φ	PROPN
ejpam-3449	226	3	.	.	PUNCT
ejpam-3449	227	1	this	this	PRON
ejpam-3449	227	2	follows	follow	VERB
ejpam-3449	227	3	that	that	SCONJ
ejpam-3449	227	4	a	a	DET
ejpam-3449	227	5	⊆	⊆	NUM
ejpam-3449	227	6	x\τfγ	x\τfγ	NOUN
ejpam-3449	227	7	-	-	PUNCT
ejpam-3449	227	8	cl({x	cl({x	NOUN
ejpam-3449	227	9	}	}	PUNCT
ejpam-3449	227	10	)	)	PUNCT
ejpam-3449	227	11	.	.	PUNCT
ejpam-3449	228	1	since	since	SCONJ
ejpam-3449	228	2	τfγ	τfγ	NOUN
ejpam-3449	228	3	-	-	PUNCT
ejpam-3449	228	4	cl({x	cl({x	NOUN
ejpam-3449	228	5	}	}	PUNCT
ejpam-3449	228	6	)	)	PUNCT
ejpam-3449	228	7	is	be	AUX
ejpam-3449	228	8	fγ	fγ	NOUN
ejpam-3449	228	9	-	-	PUNCT
ejpam-3449	228	10	closed	close	VERB
ejpam-3449	228	11	implies	imply	VERB
ejpam-3449	228	12	x\τfγ	x\τfγ	PROPN
ejpam-3449	228	13	-	-	PUNCT
ejpam-3449	228	14	cl({x	cl({x	NOUN
ejpam-3449	228	15	}	}	PUNCT
ejpam-3449	228	16	)	)	PUNCT
ejpam-3449	228	17	is	be	AUX
ejpam-3449	228	18	fγ	fγ	NOUN
ejpam-3449	228	19	-	-	PUNCT
ejpam-3449	228	20	open	open	ADJ
ejpam-3449	228	21	and	and	CCONJ
ejpam-3449	228	22	a	a	PRON
ejpam-3449	228	23	is	be	AUX
ejpam-3449	228	24	fγg.closed	fγg.close	VERB
ejpam-3449	228	25	set	set	VERB
ejpam-3449	228	26	in	in	ADP
ejpam-3449	228	27	x.	x.	NOUN
ejpam-3449	228	28	then	then	ADV
ejpam-3449	228	29	,	,	PUNCT
ejpam-3449	228	30	we	we	PRON
ejpam-3449	228	31	have	have	VERB
ejpam-3449	228	32	that	that	DET
ejpam-3449	228	33	fclγ(a	fclγ(a	NOUN
ejpam-3449	228	34	)	)	PUNCT
ejpam-3449	228	35	⊆	⊆	NUM
ejpam-3449	228	36	x\τfγ	x\τfγ	PROPN
ejpam-3449	228	37	-	-	PUNCT
ejpam-3449	228	38	cl({x	cl({x	NOUN
ejpam-3449	228	39	}	}	PUNCT
ejpam-3449	228	40	)	)	PUNCT
ejpam-3449	228	41	.	.	PUNCT
ejpam-3449	229	1	this	this	PRON
ejpam-3449	229	2	means	mean	VERB
ejpam-3449	229	3	that	that	SCONJ
ejpam-3449	229	4	x	x	X
ejpam-3449	229	5	/∈	/∈	PUNCT
ejpam-3449	229	6	fclγ(a	fclγ(a	NOUN
ejpam-3449	229	7	)	)	PUNCT
ejpam-3449	229	8	.	.	PUNCT
ejpam-3449	230	1	this	this	PRON
ejpam-3449	230	2	is	be	AUX
ejpam-3449	230	3	a	a	DET
ejpam-3449	230	4	contradiction	contradiction	NOUN
ejpam-3449	230	5	.	.	PUNCT
ejpam-3449	231	1	hence	hence	ADV
ejpam-3449	231	2	a	a	DET
ejpam-3449	231	3	∩	∩	ADJ
ejpam-3449	231	4	τfγ	τfγ	NOUN
ejpam-3449	231	5	-	-	PUNCT
ejpam-3449	231	6	cl({x	cl({x	NOUN
ejpam-3449	231	7	}	}	PUNCT
ejpam-3449	231	8	)	)	PUNCT
ejpam-3449	232	1	6=	6=	ADP
ejpam-3449	232	2	φ	φ	X
ejpam-3449	232	3	.	.	PUNCT
ejpam-3449	233	1	conversely	conversely	ADV
ejpam-3449	233	2	,	,	PUNCT
ejpam-3449	233	3	let	let	VERB
ejpam-3449	233	4	u	u	PRON
ejpam-3449	233	5	∈	∈	PRON
ejpam-3449	233	6	τfγ	τfγ	VERB
ejpam-3449	233	7	such	such	ADJ
ejpam-3449	233	8	that	that	SCONJ
ejpam-3449	233	9	a	a	DET
ejpam-3449	233	10	⊆	⊆	NUM
ejpam-3449	233	11	u	u	NOUN
ejpam-3449	233	12	.	.	PUNCT
ejpam-3449	234	1	to	to	PART
ejpam-3449	234	2	show	show	VERB
ejpam-3449	234	3	that	that	SCONJ
ejpam-3449	234	4	fclγ(a	fclγ(a	NOUN
ejpam-3449	234	5	)	)	PUNCT
ejpam-3449	234	6	⊆	⊆	NUM
ejpam-3449	234	7	u	u	NOUN
ejpam-3449	234	8	.	.	PUNCT
ejpam-3449	235	1	let	let	VERB
ejpam-3449	235	2	x	x	PUNCT
ejpam-3449	235	3	∈	∈	PROPN
ejpam-3449	235	4	fclγ(a	fclγ(a	PROPN
ejpam-3449	235	5	)	)	PUNCT
ejpam-3449	235	6	.	.	PUNCT
ejpam-3449	236	1	then	then	ADV
ejpam-3449	236	2	by	by	ADP
ejpam-3449	236	3	hypothesis	hypothesis	NOUN
ejpam-3449	236	4	,	,	PUNCT
ejpam-3449	236	5	a	a	DET
ejpam-3449	236	6	∩	∩	ADJ
ejpam-3449	236	7	τfγ	τfγ	NOUN
ejpam-3449	236	8	-	-	PUNCT
ejpam-3449	236	9	cl({x	cl({x	NOUN
ejpam-3449	236	10	}	}	PUNCT
ejpam-3449	236	11	)	)	PUNCT
ejpam-3449	236	12	6=	6=	ADP
ejpam-3449	236	13	φ	φ	PROPN
ejpam-3449	236	14	.	.	PUNCT
ejpam-3449	237	1	so	so	ADV
ejpam-3449	237	2	there	there	PRON
ejpam-3449	237	3	exists	exist	VERB
ejpam-3449	237	4	an	an	DET
ejpam-3449	237	5	element	element	NOUN
ejpam-3449	237	6	y	y	PROPN
ejpam-3449	237	7	∈	∈	PROPN
ejpam-3449	237	8	a	a	DET
ejpam-3449	237	9	∩	∩	ADJ
ejpam-3449	237	10	τfγ	τfγ	NOUN
ejpam-3449	237	11	-	-	PUNCT
ejpam-3449	237	12	cl({x	cl({x	NOUN
ejpam-3449	237	13	}	}	PUNCT
ejpam-3449	237	14	)	)	PUNCT
ejpam-3449	237	15	.	.	PUNCT
ejpam-3449	238	1	thus	thus	ADV
ejpam-3449	238	2	y	y	PROPN
ejpam-3449	238	3	∈	∈	PROPN
ejpam-3449	238	4	a	a	DET
ejpam-3449	238	5	⊆	⊆	NUM
ejpam-3449	238	6	u	u	NOUN
ejpam-3449	238	7	and	and	CCONJ
ejpam-3449	238	8	y	y	PROPN
ejpam-3449	238	9	∈	∈	PROPN
ejpam-3449	238	10	τfγ	τfγ	PROPN
ejpam-3449	238	11	-	-	PUNCT
ejpam-3449	238	12	cl({x	cl({x	NOUN
ejpam-3449	238	13	}	}	PUNCT
ejpam-3449	238	14	)	)	PUNCT
ejpam-3449	238	15	.	.	PUNCT
ejpam-3449	239	1	by	by	ADP
ejpam-3449	239	2	theorem	theorem	NOUN
ejpam-3449	239	3	3.12	3.12	NUM
ejpam-3449	239	4	,	,	PUNCT
ejpam-3449	239	5	{	{	PUNCT
ejpam-3449	239	6	x	x	NOUN
ejpam-3449	239	7	}	}	PUNCT
ejpam-3449	239	8	∩	∩	ADJ
ejpam-3449	239	9	u	u	PROPN
ejpam-3449	239	10	6=	6=	PROPN
ejpam-3449	239	11	φ	φ	PROPN
ejpam-3449	239	12	.	.	PUNCT
ejpam-3449	240	1	hence	hence	ADV
ejpam-3449	240	2	x	x	SYM
ejpam-3449	240	3	∈	∈	PROPN
ejpam-3449	240	4	u	u	NOUN
ejpam-3449	240	5	and	and	CCONJ
ejpam-3449	240	6	so	so	ADV
ejpam-3449	240	7	fclγ(a	fclγ(a	ADJ
ejpam-3449	240	8	)	)	PUNCT
ejpam-3449	240	9	⊆	⊆	NUM
ejpam-3449	240	10	u	u	NOUN
ejpam-3449	240	11	.	.	PUNCT
ejpam-3449	241	1	therefore	therefore	ADV
ejpam-3449	241	2	,	,	PUNCT
ejpam-3449	241	3	a	a	PRON
ejpam-3449	241	4	is	be	AUX
ejpam-3449	241	5	fγg.closed	fγg.close	VERB
ejpam-3449	241	6	set	set	VERB
ejpam-3449	241	7	in	in	ADP
ejpam-3449	241	8	(	(	PUNCT
ejpam-3449	241	9	x	x	NOUN
ejpam-3449	241	10	,	,	PUNCT
ejpam-3449	241	11	τ	τ	PROPN
ejpam-3449	241	12	,	,	PUNCT
ejpam-3449	241	13	τf	τf	NUM
ejpam-3449	241	14	)	)	PUNCT
ejpam-3449	241	15	.	.	PUNCT
ejpam-3449	242	1	theorem	theorem	VERB
ejpam-3449	242	2	4.3	4.3	NUM
ejpam-3449	242	3	.	.	PUNCT
ejpam-3449	243	1	let	let	VERB
ejpam-3449	243	2	a	a	DET
ejpam-3449	243	3	be	be	AUX
ejpam-3449	243	4	a	a	DET
ejpam-3449	243	5	subset	subset	NOUN
ejpam-3449	243	6	of	of	ADP
ejpam-3449	243	7	fine	fine	ADJ
ejpam-3449	243	8	space	space	NOUN
ejpam-3449	243	9	(	(	PUNCT
ejpam-3449	243	10	x	x	X
ejpam-3449	243	11	,	,	PUNCT
ejpam-3449	243	12	τ	τ	PROPN
ejpam-3449	243	13	,	,	PUNCT
ejpam-3449	243	14	τf	τf	NUM
ejpam-3449	243	15	)	)	PUNCT
ejpam-3449	243	16	and	and	CCONJ
ejpam-3449	243	17	γ	γ	X
ejpam-3449	243	18	be	be	AUX
ejpam-3449	243	19	an	an	DET
ejpam-3449	243	20	operation	operation	NOUN
ejpam-3449	243	21	on	on	ADP
ejpam-3449	243	22	τf	τf	PROPN
ejpam-3449	243	23	.	.	PUNCT
ejpam-3449	244	1	if	if	SCONJ
ejpam-3449	244	2	a	a	PRON
ejpam-3449	244	3	is	be	AUX
ejpam-3449	244	4	fγg.closed	fγg.close	VERB
ejpam-3449	244	5	,	,	PUNCT
ejpam-3449	244	6	then	then	ADV
ejpam-3449	244	7	fclγ(a)\a	fclγ(a)\a	PUNCT
ejpam-3449	244	8	does	do	AUX
ejpam-3449	244	9	not	not	PART
ejpam-3449	244	10	contain	contain	VERB
ejpam-3449	244	11	any	any	DET
ejpam-3449	244	12	non	non	ADJ
ejpam-3449	244	13	-	-	ADJ
ejpam-3449	244	14	empty	empty	ADJ
ejpam-3449	244	15	fγ	fγ	NOUN
ejpam-3449	244	16	-	-	PUNCT
ejpam-3449	244	17	closed	close	VERB
ejpam-3449	244	18	set	set	NOUN
ejpam-3449	244	19	.	.	PUNCT
ejpam-3449	245	1	b.	b.	PROPN
ejpam-3449	245	2	a.	a.	PROPN
ejpam-3449	245	3	asaad	asaad	PROPN
ejpam-3449	245	4	et	et	PROPN
ejpam-3449	245	5	al	al	PROPN
ejpam-3449	245	6	.	.	PUNCT
ejpam-3449	245	7	/	/	SYM
ejpam-3449	245	8	eur	eur	PROPN
ejpam-3449	245	9	.	.	PUNCT
ejpam-3449	246	1	j.	j.	PROPN
ejpam-3449	246	2	pure	pure	PROPN
ejpam-3449	246	3	appl	appl	PROPN
ejpam-3449	246	4	.	.	PROPN
ejpam-3449	246	5	math	math	PROPN
ejpam-3449	246	6	,	,	PUNCT
ejpam-3449	246	7	12	12	NUM
ejpam-3449	246	8	(	(	PUNCT
ejpam-3449	246	9	3	3	NUM
ejpam-3449	246	10	)	)	PUNCT
ejpam-3449	246	11	(	(	PUNCT
ejpam-3449	246	12	2019	2019	NUM
ejpam-3449	246	13	)	)	PUNCT
ejpam-3449	246	14	,	,	PUNCT
ejpam-3449	246	15	960	960	NUM
ejpam-3449	246	16	-	-	SYM
ejpam-3449	246	17	977	977	NUM
ejpam-3449	246	18	967	967	NUM
ejpam-3449	246	19	proof	proof	NOUN
ejpam-3449	246	20	.	.	PUNCT
ejpam-3449	247	1	let	let	VERB
ejpam-3449	247	2	f	f	PRON
ejpam-3449	247	3	be	be	AUX
ejpam-3449	247	4	a	a	DET
ejpam-3449	247	5	non	non	ADJ
ejpam-3449	247	6	-	-	ADJ
ejpam-3449	247	7	empty	empty	ADJ
ejpam-3449	247	8	fγ	fγ	NOUN
ejpam-3449	247	9	-	-	PUNCT
ejpam-3449	247	10	closed	close	VERB
ejpam-3449	247	11	set	set	NOUN
ejpam-3449	247	12	in	in	ADP
ejpam-3449	247	13	x	x	PUNCT
ejpam-3449	247	14	such	such	ADJ
ejpam-3449	247	15	that	that	SCONJ
ejpam-3449	247	16	f	f	PROPN
ejpam-3449	247	17	⊆	⊆	NUM
ejpam-3449	247	18	fclγ(a)\a	fclγ(a)\a	NOUN
ejpam-3449	247	19	.	.	PUNCT
ejpam-3449	248	1	then	then	ADV
ejpam-3449	248	2	f	f	PROPN
ejpam-3449	248	3	⊆	⊆	NUM
ejpam-3449	248	4	x\a	x\a	PROPN
ejpam-3449	248	5	implies	imply	VERB
ejpam-3449	248	6	a	a	DET
ejpam-3449	248	7	⊆	⊆	NUM
ejpam-3449	248	8	x\f	x\f	PROPN
ejpam-3449	248	9	.	.	PUNCT
ejpam-3449	249	1	since	since	SCONJ
ejpam-3449	249	2	x\f	x\f	PROPN
ejpam-3449	249	3	is	be	AUX
ejpam-3449	249	4	fγ	fγ	ADV
ejpam-3449	249	5	-	-	PUNCT
ejpam-3449	249	6	open	open	NOUN
ejpam-3449	249	7	set	set	NOUN
ejpam-3449	249	8	and	and	CCONJ
ejpam-3449	249	9	a	a	PRON
ejpam-3449	249	10	is	be	AUX
ejpam-3449	249	11	fγg.closed	fγg.close	VERB
ejpam-3449	249	12	set	set	NOUN
ejpam-3449	249	13	,	,	PUNCT
ejpam-3449	249	14	then	then	ADV
ejpam-3449	249	15	fclγ(a	fclγ(a	NOUN
ejpam-3449	249	16	)	)	PUNCT
ejpam-3449	250	1	⊆	⊆	NUM
ejpam-3449	250	2	x\f	x\f	PROPN
ejpam-3449	250	3	.	.	PUNCT
ejpam-3449	251	1	that	that	PRON
ejpam-3449	251	2	is	be	AUX
ejpam-3449	251	3	f	f	PROPN
ejpam-3449	251	4	⊆	⊆	NUM
ejpam-3449	251	5	x\fclγ(a	x\fclγ(a	NOUN
ejpam-3449	251	6	)	)	PUNCT
ejpam-3449	251	7	.	.	PUNCT
ejpam-3449	252	1	hence	hence	ADV
ejpam-3449	252	2	f	f	PROPN
ejpam-3449	252	3	⊆	⊆	NUM
ejpam-3449	252	4	x\fclγ(a	x\fclγ(a	NOUN
ejpam-3449	252	5	)	)	PUNCT
ejpam-3449	252	6	∩	∩	NOUN
ejpam-3449	252	7	fclγ(a)\a	fclγ(a)\a	NUM
ejpam-3449	252	8	⊆	⊆	NUM
ejpam-3449	252	9	x\fclγ(a	x\fclγ(a	NUM
ejpam-3449	252	10	)	)	PUNCT
ejpam-3449	252	11	∩	∩	ADJ
ejpam-3449	252	12	fclγ(a	fclγ(a	NOUN
ejpam-3449	252	13	)	)	PUNCT
ejpam-3449	252	14	=	=	SYM
ejpam-3449	253	1	φ	φ	PROPN
ejpam-3449	253	2	.	.	PUNCT
ejpam-3449	254	1	this	this	PRON
ejpam-3449	254	2	shows	show	VERB
ejpam-3449	254	3	that	that	SCONJ
ejpam-3449	254	4	f	f	PROPN
ejpam-3449	254	5	=	=	SYM
ejpam-3449	254	6	φ	φ	PROPN
ejpam-3449	254	7	.	.	PUNCT
ejpam-3449	255	1	this	this	PRON
ejpam-3449	255	2	is	be	AUX
ejpam-3449	255	3	a	a	DET
ejpam-3449	255	4	contradiction	contradiction	NOUN
ejpam-3449	255	5	.	.	PUNCT
ejpam-3449	256	1	therefore	therefore	ADV
ejpam-3449	256	2	,	,	PUNCT
ejpam-3449	256	3	f	f	PROPN
ejpam-3449	256	4	6⊆	6⊆	PROPN
ejpam-3449	256	5	fclγ(a)\a	fclγ(a)\a	NOUN
ejpam-3449	256	6	.	.	PUNCT
ejpam-3449	256	7	theorem	theorem	VERB
ejpam-3449	256	8	4.4	4.4	NUM
ejpam-3449	256	9	.	.	PUNCT
ejpam-3449	257	1	if	if	SCONJ
ejpam-3449	257	2	γ	γ	X
ejpam-3449	257	3	:	:	PUNCT
ejpam-3449	257	4	τf	τf	PROPN
ejpam-3449	257	5	→	→	SYM
ejpam-3449	257	6	p	p	X
ejpam-3449	257	7	(	(	PUNCT
ejpam-3449	257	8	x	x	X
ejpam-3449	257	9	)	)	PUNCT
ejpam-3449	257	10	is	be	AUX
ejpam-3449	257	11	a	a	DET
ejpam-3449	257	12	fine	fine	ADJ
ejpam-3449	257	13	-	-	PUNCT
ejpam-3449	257	14	open	open	ADJ
ejpam-3449	257	15	operation	operation	NOUN
ejpam-3449	257	16	,	,	PUNCT
ejpam-3449	257	17	then	then	ADV
ejpam-3449	257	18	the	the	DET
ejpam-3449	257	19	converse	converse	NOUN
ejpam-3449	257	20	of	of	ADP
ejpam-3449	257	21	the	the	DET
ejpam-3449	257	22	theorem	theorem	NOUN
ejpam-3449	257	23	4.3	4.3	NUM
ejpam-3449	257	24	is	be	AUX
ejpam-3449	257	25	true	true	ADJ
ejpam-3449	257	26	.	.	PUNCT
ejpam-3449	258	1	proof	proof	NOUN
ejpam-3449	258	2	.	.	PUNCT
ejpam-3449	259	1	let	let	VERB
ejpam-3449	259	2	u	u	PRON
ejpam-3449	259	3	be	be	AUX
ejpam-3449	259	4	a	a	DET
ejpam-3449	259	5	fγ	fγ	ADV
ejpam-3449	259	6	-	-	PUNCT
ejpam-3449	259	7	open	open	NOUN
ejpam-3449	259	8	set	set	NOUN
ejpam-3449	259	9	in	in	ADP
ejpam-3449	259	10	(	(	PUNCT
ejpam-3449	259	11	x	x	NOUN
ejpam-3449	259	12	,	,	PUNCT
ejpam-3449	259	13	τ	τ	PROPN
ejpam-3449	259	14	,	,	PUNCT
ejpam-3449	259	15	τf	τf	NUM
ejpam-3449	259	16	)	)	PUNCT
ejpam-3449	259	17	such	such	ADJ
ejpam-3449	259	18	that	that	SCONJ
ejpam-3449	259	19	a	a	DET
ejpam-3449	259	20	⊆	⊆	NUM
ejpam-3449	259	21	u	u	NOUN
ejpam-3449	259	22	.	.	PUNCT
ejpam-3449	260	1	since	since	SCONJ
ejpam-3449	260	2	γ	γ	X
ejpam-3449	260	3	:	:	PUNCT
ejpam-3449	260	4	τf	τf	PROPN
ejpam-3449	260	5	→	→	SYM
ejpam-3449	260	6	p	p	X
ejpam-3449	260	7	(	(	PUNCT
ejpam-3449	260	8	x	x	X
ejpam-3449	260	9	)	)	PUNCT
ejpam-3449	260	10	is	be	AUX
ejpam-3449	260	11	a	a	DET
ejpam-3449	260	12	fine	fine	ADJ
ejpam-3449	260	13	-	-	PUNCT
ejpam-3449	260	14	open	open	ADJ
ejpam-3449	260	15	operation	operation	NOUN
ejpam-3449	260	16	,	,	PUNCT
ejpam-3449	260	17	then	then	ADV
ejpam-3449	260	18	by	by	ADP
ejpam-3449	260	19	theorem	theorem	NOUN
ejpam-3449	260	20	3.15	3.15	NUM
ejpam-3449	260	21	,	,	PUNCT
ejpam-3449	260	22	fclγ(a	fclγ(a	NOUN
ejpam-3449	260	23	)	)	PUNCT
ejpam-3449	260	24	is	be	AUX
ejpam-3449	260	25	fγ	fγ	ADV
ejpam-3449	260	26	-	-	PUNCT
ejpam-3449	260	27	closed	close	VERB
ejpam-3449	260	28	set	set	NOUN
ejpam-3449	260	29	in	in	ADP
ejpam-3449	260	30	x.	x.	NOUN
ejpam-3449	260	31	thus	thus	ADV
ejpam-3449	260	32	,	,	PUNCT
ejpam-3449	260	33	using	use	VERB
ejpam-3449	260	34	theorem	theorem	NOUN
ejpam-3449	260	35	3.2	3.2	NUM
ejpam-3449	260	36	,	,	PUNCT
ejpam-3449	260	37	we	we	PRON
ejpam-3449	260	38	have	have	AUX
ejpam-3449	260	39	fclγ(a	fclγ(a	NOUN
ejpam-3449	260	40	)	)	PUNCT
ejpam-3449	260	41	∩x\u	∩x\u	PROPN
ejpam-3449	260	42	is	be	AUX
ejpam-3449	260	43	a	a	DET
ejpam-3449	260	44	fγ	fγ	ADV
ejpam-3449	260	45	-	-	PUNCT
ejpam-3449	260	46	closed	close	VERB
ejpam-3449	260	47	set	set	NOUN
ejpam-3449	260	48	in	in	ADP
ejpam-3449	260	49	(	(	PUNCT
ejpam-3449	260	50	x	x	NOUN
ejpam-3449	260	51	,	,	PUNCT
ejpam-3449	260	52	τ	τ	PROPN
ejpam-3449	260	53	,	,	PUNCT
ejpam-3449	260	54	τf	τf	NUM
ejpam-3449	260	55	)	)	PUNCT
ejpam-3449	260	56	.	.	PUNCT
ejpam-3449	261	1	since	since	SCONJ
ejpam-3449	261	2	x\u	x\u	PROPN
ejpam-3449	261	3	⊆	⊆	NUM
ejpam-3449	261	4	x\a	x\a	PROPN
ejpam-3449	261	5	,	,	PUNCT
ejpam-3449	261	6	fclγ(a	fclγ(a	NOUN
ejpam-3449	261	7	)	)	PUNCT
ejpam-3449	261	8	∩x\u	∩x\u	PROPN
ejpam-3449	261	9	⊆	⊆	NUM
ejpam-3449	261	10	fclγ(a)\a	fclγ(a)\a	NOUN
ejpam-3449	261	11	.	.	PUNCT
ejpam-3449	262	1	using	use	VERB
ejpam-3449	262	2	the	the	DET
ejpam-3449	262	3	assumption	assumption	NOUN
ejpam-3449	262	4	of	of	ADP
ejpam-3449	262	5	the	the	DET
ejpam-3449	262	6	converse	converse	NOUN
ejpam-3449	262	7	of	of	ADP
ejpam-3449	262	8	the	the	DET
ejpam-3449	262	9	theorem	theorem	ADJ
ejpam-3449	262	10	4.3	4.3	NUM
ejpam-3449	262	11	,	,	PUNCT
ejpam-3449	262	12	fclγ(a	fclγ(a	NOUN
ejpam-3449	262	13	)	)	PUNCT
ejpam-3449	262	14	⊆	⊆	NUM
ejpam-3449	262	15	u	u	NOUN
ejpam-3449	262	16	.	.	PUNCT
ejpam-3449	263	1	therefore	therefore	ADV
ejpam-3449	263	2	,	,	PUNCT
ejpam-3449	263	3	a	a	PRON
ejpam-3449	263	4	is	be	AUX
ejpam-3449	263	5	fγg.closed	fγg.close	VERB
ejpam-3449	263	6	set	set	VERB
ejpam-3449	263	7	in	in	ADP
ejpam-3449	263	8	(	(	PUNCT
ejpam-3449	263	9	x	x	NOUN
ejpam-3449	263	10	,	,	PUNCT
ejpam-3449	263	11	τ	τ	PROPN
ejpam-3449	263	12	,	,	PUNCT
ejpam-3449	263	13	τf	τf	NUM
ejpam-3449	263	14	)	)	PUNCT
ejpam-3449	263	15	.	.	PUNCT
ejpam-3449	264	1	corollary	corollary	ADJ
ejpam-3449	264	2	4.5	4.5	NUM
ejpam-3449	264	3	.	.	PUNCT
ejpam-3449	265	1	let	let	VERB
ejpam-3449	265	2	a	a	DET
ejpam-3449	265	3	be	be	AUX
ejpam-3449	265	4	a	a	DET
ejpam-3449	265	5	fγg.closed	fγg.close	VERB
ejpam-3449	265	6	subset	subset	NOUN
ejpam-3449	265	7	of	of	ADP
ejpam-3449	265	8	fine	fine	ADJ
ejpam-3449	265	9	space	space	NOUN
ejpam-3449	265	10	(	(	PUNCT
ejpam-3449	265	11	x	x	X
ejpam-3449	265	12	,	,	PUNCT
ejpam-3449	265	13	τ	τ	PROPN
ejpam-3449	265	14	,	,	PUNCT
ejpam-3449	265	15	τf	τf	NUM
ejpam-3449	265	16	)	)	PUNCT
ejpam-3449	265	17	and	and	CCONJ
ejpam-3449	265	18	let	let	VERB
ejpam-3449	265	19	γ	γ	NOUN
ejpam-3449	265	20	be	be	AUX
ejpam-3449	265	21	an	an	DET
ejpam-3449	265	22	operation	operation	NOUN
ejpam-3449	265	23	on	on	ADP
ejpam-3449	265	24	τf	τf	PROPN
ejpam-3449	265	25	.	.	PUNCT
ejpam-3449	266	1	then	then	ADV
ejpam-3449	266	2	a	a	PRON
ejpam-3449	266	3	is	be	AUX
ejpam-3449	266	4	fγ	fγ	NOUN
ejpam-3449	266	5	-	-	PUNCT
ejpam-3449	266	6	closed	closed	ADJ
ejpam-3449	266	7	if	if	SCONJ
ejpam-3449	267	1	and	and	CCONJ
ejpam-3449	267	2	only	only	ADV
ejpam-3449	267	3	if	if	SCONJ
ejpam-3449	267	4	fclγ(a)\a	fclγ(a)\a	NUM
ejpam-3449	267	5	is	be	AUX
ejpam-3449	267	6	fγ	fγ	ADV
ejpam-3449	267	7	-	-	PUNCT
ejpam-3449	267	8	closed	close	VERB
ejpam-3449	267	9	set	set	NOUN
ejpam-3449	267	10	.	.	PUNCT
ejpam-3449	268	1	proof	proof	NOUN
ejpam-3449	268	2	.	.	PUNCT
ejpam-3449	269	1	let	let	VERB
ejpam-3449	269	2	a	a	DET
ejpam-3449	269	3	be	be	AUX
ejpam-3449	269	4	a	a	DET
ejpam-3449	269	5	fγ	fγ	ADV
ejpam-3449	269	6	-	-	PUNCT
ejpam-3449	269	7	closed	close	VERB
ejpam-3449	269	8	set	set	NOUN
ejpam-3449	269	9	in	in	ADP
ejpam-3449	269	10	(	(	PUNCT
ejpam-3449	269	11	x	x	NOUN
ejpam-3449	269	12	,	,	PUNCT
ejpam-3449	269	13	τ	τ	PROPN
ejpam-3449	269	14	,	,	PUNCT
ejpam-3449	269	15	τf	τf	NUM
ejpam-3449	269	16	)	)	PUNCT
ejpam-3449	269	17	.	.	PUNCT
ejpam-3449	270	1	then	then	ADV
ejpam-3449	270	2	by	by	ADP
ejpam-3449	270	3	lemma	lemma	PROPN
ejpam-3449	270	4	3.13	3.13	NUM
ejpam-3449	270	5	(	(	PUNCT
ejpam-3449	270	6	4b	4b	PROPN
ejpam-3449	270	7	)	)	PUNCT
ejpam-3449	270	8	,	,	PUNCT
ejpam-3449	270	9	fclγ(a	fclγ(a	NOUN
ejpam-3449	270	10	)	)	PUNCT
ejpam-3449	270	11	=	=	SYM
ejpam-3449	270	12	a	a	DET
ejpam-3449	270	13	and	and	CCONJ
ejpam-3449	270	14	hence	hence	ADV
ejpam-3449	270	15	fclγ(a)\a	fclγ(a)\a	ADJ
ejpam-3449	270	16	=	=	SYM
ejpam-3449	270	17	φ	φ	NUM
ejpam-3449	270	18	which	which	PRON
ejpam-3449	270	19	is	be	AUX
ejpam-3449	270	20	fγ	fγ	ADV
ejpam-3449	270	21	-	-	PUNCT
ejpam-3449	270	22	closed	close	VERB
ejpam-3449	270	23	set	set	NOUN
ejpam-3449	270	24	.	.	PUNCT
ejpam-3449	271	1	conversely	conversely	ADV
ejpam-3449	271	2	,	,	PUNCT
ejpam-3449	271	3	suppose	suppose	VERB
ejpam-3449	271	4	fclγ(a)\a	fclγ(a)\a	NUM
ejpam-3449	271	5	is	be	AUX
ejpam-3449	271	6	fγ	fγ	ADV
ejpam-3449	271	7	-	-	PUNCT
ejpam-3449	271	8	closed	close	VERB
ejpam-3449	271	9	and	and	CCONJ
ejpam-3449	271	10	a	a	PRON
ejpam-3449	271	11	is	be	AUX
ejpam-3449	271	12	fγg.closed	fγg.close	VERB
ejpam-3449	271	13	.	.	PUNCT
ejpam-3449	272	1	then	then	ADV
ejpam-3449	272	2	by	by	ADP
ejpam-3449	272	3	theorem	theorem	NOUN
ejpam-3449	272	4	4.3	4.3	NUM
ejpam-3449	272	5	,	,	PUNCT
ejpam-3449	272	6	fclγ(a)\a	fclγ(a)\a	PUNCT
ejpam-3449	272	7	does	do	AUX
ejpam-3449	272	8	not	not	PART
ejpam-3449	272	9	contain	contain	VERB
ejpam-3449	272	10	any	any	DET
ejpam-3449	272	11	non	non	ADJ
ejpam-3449	272	12	-	-	ADJ
ejpam-3449	272	13	empty	empty	ADJ
ejpam-3449	272	14	fγ	fγ	NOUN
ejpam-3449	272	15	-	-	PUNCT
ejpam-3449	272	16	closed	close	VERB
ejpam-3449	272	17	set	set	NOUN
ejpam-3449	272	18	and	and	CCONJ
ejpam-3449	272	19	since	since	SCONJ
ejpam-3449	272	20	fclγ(a)\a	fclγ(a)\a	NUM
ejpam-3449	272	21	is	be	AUX
ejpam-3449	272	22	fγ	fγ	ADV
ejpam-3449	272	23	-	-	PUNCT
ejpam-3449	272	24	closed	close	VERB
ejpam-3449	272	25	subset	subset	NOUN
ejpam-3449	272	26	of	of	ADP
ejpam-3449	272	27	itself	itself	PRON
ejpam-3449	272	28	,	,	PUNCT
ejpam-3449	272	29	then	then	ADV
ejpam-3449	272	30	fclγ(a)\a	fclγ(a)\a	PUNCT
ejpam-3449	272	31	=	=	SYM
ejpam-3449	272	32	φ	φ	PROPN
ejpam-3449	272	33	implies	imply	VERB
ejpam-3449	272	34	fclγ(a	fclγ(a	NOUN
ejpam-3449	272	35	)	)	PUNCT
ejpam-3449	272	36	∩	∩	NOUN
ejpam-3449	272	37	x\a	x\a	PUNCT
ejpam-3449	273	1	=	=	SYM
ejpam-3449	273	2	φ	φ	PROPN
ejpam-3449	273	3	.	.	PUNCT
ejpam-3449	274	1	hence	hence	ADV
ejpam-3449	274	2	fclγ(a	fclγ(a	NOUN
ejpam-3449	274	3	)	)	PUNCT
ejpam-3449	274	4	=	=	SYM
ejpam-3449	275	1	a.	a.	NOUN
ejpam-3449	275	2	this	this	PRON
ejpam-3449	275	3	follows	follow	VERB
ejpam-3449	275	4	from	from	ADP
ejpam-3449	275	5	lemma	lemma	PROPN
ejpam-3449	275	6	3.13	3.13	NUM
ejpam-3449	275	7	(	(	PUNCT
ejpam-3449	275	8	4b	4b	PROPN
ejpam-3449	275	9	)	)	PUNCT
ejpam-3449	275	10	that	that	SCONJ
ejpam-3449	275	11	a	a	PRON
ejpam-3449	275	12	is	be	AUX
ejpam-3449	275	13	fγ	fγ	NOUN
ejpam-3449	275	14	-	-	PUNCT
ejpam-3449	275	15	closed	close	VERB
ejpam-3449	275	16	set	set	NOUN
ejpam-3449	275	17	in	in	ADP
ejpam-3449	275	18	(	(	PUNCT
ejpam-3449	275	19	x	x	NOUN
ejpam-3449	275	20	,	,	PUNCT
ejpam-3449	275	21	τ	τ	PROPN
ejpam-3449	275	22	,	,	PUNCT
ejpam-3449	275	23	τf	τf	NUM
ejpam-3449	275	24	)	)	PUNCT
ejpam-3449	275	25	.	.	PUNCT
ejpam-3449	276	1	theorem	theorem	VERB
ejpam-3449	276	2	4.6	4.6	NUM
ejpam-3449	276	3	.	.	PUNCT
ejpam-3449	277	1	let	let	AUX
ejpam-3449	277	2	(	(	PUNCT
ejpam-3449	277	3	x	x	NOUN
ejpam-3449	277	4	,	,	PUNCT
ejpam-3449	277	5	τ	τ	X
ejpam-3449	277	6	)	)	PUNCT
ejpam-3449	277	7	be	be	VERB
ejpam-3449	277	8	a	a	DET
ejpam-3449	277	9	fine	fine	ADJ
ejpam-3449	277	10	space	space	NOUN
ejpam-3449	277	11	and	and	CCONJ
ejpam-3449	277	12	γ	γ	NOUN
ejpam-3449	277	13	be	be	AUX
ejpam-3449	277	14	an	an	DET
ejpam-3449	277	15	operation	operation	NOUN
ejpam-3449	277	16	on	on	ADP
ejpam-3449	277	17	τf	τf	PROPN
ejpam-3449	277	18	.	.	PUNCT
ejpam-3449	278	1	if	if	SCONJ
ejpam-3449	278	2	a	a	DET
ejpam-3449	278	3	subset	subset	NOUN
ejpam-3449	278	4	a	a	PRON
ejpam-3449	278	5	of	of	ADP
ejpam-3449	278	6	x	x	SYM
ejpam-3449	278	7	is	be	AUX
ejpam-3449	278	8	fγg.closed	fγg.close	VERB
ejpam-3449	278	9	and	and	CCONJ
ejpam-3449	278	10	fγ	fγ	ADV
ejpam-3449	278	11	-	-	PUNCT
ejpam-3449	278	12	open	open	ADJ
ejpam-3449	278	13	,	,	PUNCT
ejpam-3449	278	14	then	then	ADV
ejpam-3449	278	15	a	a	PRON
ejpam-3449	278	16	is	be	AUX
ejpam-3449	278	17	fγ	fγ	NOUN
ejpam-3449	278	18	-	-	PUNCT
ejpam-3449	278	19	closed	closed	ADJ
ejpam-3449	278	20	.	.	PUNCT
ejpam-3449	279	1	proof	proof	NOUN
ejpam-3449	279	2	.	.	PUNCT
ejpam-3449	280	1	since	since	SCONJ
ejpam-3449	280	2	a	a	PRON
ejpam-3449	280	3	is	be	AUX
ejpam-3449	280	4	fγg.closed	fγg.close	VERB
ejpam-3449	280	5	and	and	CCONJ
ejpam-3449	280	6	fγ	fγ	ADV
ejpam-3449	280	7	-	-	PUNCT
ejpam-3449	280	8	open	open	NOUN
ejpam-3449	280	9	set	set	NOUN
ejpam-3449	280	10	in	in	ADP
ejpam-3449	280	11	x	x	NOUN
ejpam-3449	280	12	,	,	PUNCT
ejpam-3449	280	13	then	then	ADV
ejpam-3449	280	14	fclγ(a	fclγ(a	NOUN
ejpam-3449	280	15	)	)	PUNCT
ejpam-3449	280	16	⊆	⊆	NUM
ejpam-3449	280	17	a	a	PRON
ejpam-3449	280	18	and	and	CCONJ
ejpam-3449	280	19	hence	hence	ADV
ejpam-3449	280	20	by	by	ADP
ejpam-3449	280	21	lemma	lemma	PROPN
ejpam-3449	280	22	3.13	3.13	NUM
ejpam-3449	280	23	(	(	PUNCT
ejpam-3449	280	24	4b	4b	PROPN
ejpam-3449	280	25	)	)	PUNCT
ejpam-3449	280	26	,	,	PUNCT
ejpam-3449	280	27	a	a	PRON
ejpam-3449	280	28	is	be	AUX
ejpam-3449	280	29	fγ	fγ	NOUN
ejpam-3449	280	30	-	-	PUNCT
ejpam-3449	280	31	closed	closed	ADJ
ejpam-3449	280	32	.	.	PUNCT
ejpam-3449	281	1	theorem	theorem	VERB
ejpam-3449	281	2	4.7	4.7	NUM
ejpam-3449	281	3	.	.	PUNCT
ejpam-3449	282	1	in	in	ADP
ejpam-3449	282	2	any	any	DET
ejpam-3449	282	3	fine	fine	ADJ
ejpam-3449	282	4	space	space	NOUN
ejpam-3449	282	5	(	(	PUNCT
ejpam-3449	282	6	x	x	X
ejpam-3449	282	7	,	,	PUNCT
ejpam-3449	282	8	τ	τ	PROPN
ejpam-3449	282	9	,	,	PUNCT
ejpam-3449	282	10	τf	τf	NUM
ejpam-3449	282	11	)	)	PUNCT
ejpam-3449	282	12	with	with	ADP
ejpam-3449	282	13	an	an	DET
ejpam-3449	282	14	operation	operation	NOUN
ejpam-3449	282	15	γ	γ	NOUN
ejpam-3449	282	16	on	on	ADP
ejpam-3449	282	17	τf	τf	PROPN
ejpam-3449	282	18	.	.	PUNCT
ejpam-3449	283	1	for	for	ADP
ejpam-3449	283	2	an	an	DET
ejpam-3449	283	3	element	element	NOUN
ejpam-3449	283	4	x	x	SYM
ejpam-3449	283	5	∈	∈	PROPN
ejpam-3449	283	6	x	x	NOUN
ejpam-3449	283	7	,	,	PUNCT
ejpam-3449	283	8	the	the	DET
ejpam-3449	283	9	set	set	NOUN
ejpam-3449	283	10	x\{x	x\{x	X
ejpam-3449	283	11	}	}	PUNCT
ejpam-3449	283	12	is	be	AUX
ejpam-3449	283	13	fγg.closed	fγg.close	VERB
ejpam-3449	283	14	or	or	CCONJ
ejpam-3449	283	15	fγ	fγ	ADV
ejpam-3449	283	16	-	-	PUNCT
ejpam-3449	283	17	open	open	ADJ
ejpam-3449	283	18	.	.	PUNCT
ejpam-3449	284	1	proof	proof	NOUN
ejpam-3449	284	2	.	.	PUNCT
ejpam-3449	285	1	suppose	suppose	VERB
ejpam-3449	285	2	that	that	SCONJ
ejpam-3449	285	3	x\{x	x\{x	PROPN
ejpam-3449	285	4	}	}	PUNCT
ejpam-3449	285	5	is	be	AUX
ejpam-3449	285	6	not	not	PART
ejpam-3449	285	7	fγ	fγ	ADV
ejpam-3449	285	8	-	-	PUNCT
ejpam-3449	285	9	open	open	ADJ
ejpam-3449	285	10	.	.	PUNCT
ejpam-3449	286	1	then	then	ADV
ejpam-3449	286	2	x	x	X
ejpam-3449	286	3	is	be	AUX
ejpam-3449	286	4	the	the	DET
ejpam-3449	286	5	only	only	ADJ
ejpam-3449	286	6	fγ	fγ	ADV
ejpam-3449	286	7	-	-	PUNCT
ejpam-3449	286	8	open	open	ADJ
ejpam-3449	286	9	set	set	NOUN
ejpam-3449	286	10	containing	contain	VERB
ejpam-3449	286	11	x\{x	x\{x	PROPN
ejpam-3449	286	12	}	}	PUNCT
ejpam-3449	286	13	.	.	PUNCT
ejpam-3449	287	1	this	this	PRON
ejpam-3449	287	2	implies	imply	VERB
ejpam-3449	287	3	that	that	SCONJ
ejpam-3449	287	4	fclγ(x\{x	fclγ(x\{x	ADJ
ejpam-3449	287	5	}	}	PUNCT
ejpam-3449	287	6	)	)	PUNCT
ejpam-3449	287	7	⊆	⊆	NUM
ejpam-3449	287	8	x.	x.	NOUN
ejpam-3449	287	9	thus	thus	ADV
ejpam-3449	287	10	x\{x	x\{x	NOUN
ejpam-3449	287	11	}	}	PUNCT
ejpam-3449	287	12	is	be	AUX
ejpam-3449	287	13	a	a	DET
ejpam-3449	287	14	fγg.closed	fγg.close	VERB
ejpam-3449	287	15	set	set	NOUN
ejpam-3449	287	16	in	in	ADP
ejpam-3449	287	17	x.	x.	PROPN
ejpam-3449	287	18	corollary	corollary	PROPN
ejpam-3449	287	19	4.8	4.8	NUM
ejpam-3449	287	20	.	.	PUNCT
ejpam-3449	288	1	in	in	ADP
ejpam-3449	288	2	any	any	DET
ejpam-3449	288	3	fine	fine	ADJ
ejpam-3449	288	4	space	space	NOUN
ejpam-3449	288	5	(	(	PUNCT
ejpam-3449	288	6	x	x	X
ejpam-3449	288	7	,	,	PUNCT
ejpam-3449	288	8	τ	τ	PROPN
ejpam-3449	288	9	,	,	PUNCT
ejpam-3449	288	10	τf	τf	NUM
ejpam-3449	288	11	)	)	PUNCT
ejpam-3449	288	12	with	with	ADP
ejpam-3449	288	13	an	an	DET
ejpam-3449	288	14	operation	operation	NOUN
ejpam-3449	288	15	γ	γ	NOUN
ejpam-3449	288	16	on	on	ADP
ejpam-3449	288	17	τf	τf	PROPN
ejpam-3449	288	18	.	.	PUNCT
ejpam-3449	289	1	for	for	ADP
ejpam-3449	289	2	an	an	DET
ejpam-3449	289	3	element	element	NOUN
ejpam-3449	289	4	x	x	SYM
ejpam-3449	289	5	∈	∈	PROPN
ejpam-3449	289	6	x	x	NOUN
ejpam-3449	289	7	,	,	PUNCT
ejpam-3449	289	8	either	either	CCONJ
ejpam-3449	289	9	the	the	DET
ejpam-3449	289	10	set	set	NOUN
ejpam-3449	289	11	{	{	PUNCT
ejpam-3449	289	12	x	x	NOUN
ejpam-3449	289	13	}	}	PUNCT
ejpam-3449	289	14	is	be	AUX
ejpam-3449	289	15	fγ	fγ	ADV
ejpam-3449	289	16	-	-	PUNCT
ejpam-3449	289	17	closed	close	VERB
ejpam-3449	289	18	or	or	CCONJ
ejpam-3449	289	19	the	the	DET
ejpam-3449	289	20	set	set	NOUN
ejpam-3449	289	21	x\{x	x\{x	X
ejpam-3449	289	22	}	}	PUNCT
ejpam-3449	289	23	is	be	AUX
ejpam-3449	289	24	fγg.closed	fγg.close	VERB
ejpam-3449	289	25	.	.	PUNCT
ejpam-3449	290	1	proof	proof	NOUN
ejpam-3449	290	2	.	.	PUNCT
ejpam-3449	291	1	suppose	suppose	VERB
ejpam-3449	291	2	{	{	PUNCT
ejpam-3449	291	3	x	x	NOUN
ejpam-3449	291	4	}	}	PUNCT
ejpam-3449	291	5	is	be	AUX
ejpam-3449	291	6	not	not	PART
ejpam-3449	291	7	fγ	fγ	ADV
ejpam-3449	291	8	-	-	PUNCT
ejpam-3449	291	9	closed	closed	ADJ
ejpam-3449	291	10	,	,	PUNCT
ejpam-3449	291	11	then	then	ADV
ejpam-3449	291	12	x\{x	x\{x	NOUN
ejpam-3449	291	13	}	}	PUNCT
ejpam-3449	291	14	is	be	AUX
ejpam-3449	291	15	not	not	PART
ejpam-3449	291	16	fγ	fγ	ADV
ejpam-3449	291	17	-	-	PUNCT
ejpam-3449	291	18	open	open	ADJ
ejpam-3449	291	19	.	.	PUNCT
ejpam-3449	292	1	hence	hence	ADV
ejpam-3449	292	2	by	by	ADP
ejpam-3449	292	3	theorem	theorem	NOUN
ejpam-3449	292	4	4.7	4.7	NUM
ejpam-3449	292	5	,	,	PUNCT
ejpam-3449	292	6	x\{x	x\{x	PROPN
ejpam-3449	292	7	}	}	PUNCT
ejpam-3449	292	8	is	be	AUX
ejpam-3449	292	9	fγg.closed	fγg.close	VERB
ejpam-3449	292	10	set	set	VERB
ejpam-3449	292	11	in	in	ADP
ejpam-3449	292	12	x.	x.	NOUN
ejpam-3449	292	13	definition	definition	NOUN
ejpam-3449	292	14	4.9	4.9	NUM
ejpam-3449	292	15	.	.	PUNCT
ejpam-3449	293	1	let	let	VERB
ejpam-3449	293	2	a	a	DET
ejpam-3449	293	3	be	be	AUX
ejpam-3449	293	4	any	any	DET
ejpam-3449	293	5	subset	subset	NOUN
ejpam-3449	293	6	of	of	ADP
ejpam-3449	293	7	a	a	DET
ejpam-3449	293	8	fine	fine	ADJ
ejpam-3449	293	9	space	space	NOUN
ejpam-3449	293	10	(	(	PUNCT
ejpam-3449	293	11	x	x	X
ejpam-3449	293	12	,	,	PUNCT
ejpam-3449	293	13	τ	τ	PROPN
ejpam-3449	293	14	,	,	PUNCT
ejpam-3449	293	15	τf	τf	NUM
ejpam-3449	293	16	)	)	PUNCT
ejpam-3449	293	17	and	and	CCONJ
ejpam-3449	293	18	γ	γ	X
ejpam-3449	293	19	be	be	AUX
ejpam-3449	293	20	an	an	DET
ejpam-3449	293	21	operation	operation	NOUN
ejpam-3449	293	22	on	on	ADP
ejpam-3449	293	23	τf	τf	PROPN
ejpam-3449	293	24	.	.	PUNCT
ejpam-3449	294	1	then	then	ADV
ejpam-3449	294	2	the	the	DET
ejpam-3449	294	3	τfγ	τfγ	NOUN
ejpam-3449	294	4	-	-	PUNCT
ejpam-3449	294	5	kernel	kernel	NOUN
ejpam-3449	294	6	of	of	ADP
ejpam-3449	294	7	a	a	PRON
ejpam-3449	294	8	is	be	AUX
ejpam-3449	294	9	denoted	denote	VERB
ejpam-3449	294	10	by	by	ADP
ejpam-3449	294	11	τfγ	τfγ	NOUN
ejpam-3449	294	12	-	-	PUNCT
ejpam-3449	294	13	ker(a	ker(a	VERB
ejpam-3449	294	14	)	)	PUNCT
ejpam-3449	294	15	and	and	CCONJ
ejpam-3449	294	16	is	be	AUX
ejpam-3449	294	17	defined	define	VERB
ejpam-3449	294	18	as	as	SCONJ
ejpam-3449	294	19	follows	follow	VERB
ejpam-3449	294	20	:	:	PUNCT
ejpam-3449	294	21	b.	b.	PROPN
ejpam-3449	294	22	a.	a.	PROPN
ejpam-3449	294	23	asaad	asaad	PROPN
ejpam-3449	294	24	et	et	PROPN
ejpam-3449	294	25	al	al	PROPN
ejpam-3449	294	26	.	.	PUNCT
ejpam-3449	294	27	/	/	SYM
ejpam-3449	294	28	eur	eur	PROPN
ejpam-3449	294	29	.	.	PUNCT
ejpam-3449	295	1	j.	j.	PROPN
ejpam-3449	295	2	pure	pure	PROPN
ejpam-3449	295	3	appl	appl	PROPN
ejpam-3449	295	4	.	.	PROPN
ejpam-3449	295	5	math	math	PROPN
ejpam-3449	295	6	,	,	PUNCT
ejpam-3449	295	7	12	12	NUM
ejpam-3449	295	8	(	(	PUNCT
ejpam-3449	295	9	3	3	NUM
ejpam-3449	295	10	)	)	PUNCT
ejpam-3449	295	11	(	(	PUNCT
ejpam-3449	295	12	2019	2019	NUM
ejpam-3449	295	13	)	)	PUNCT
ejpam-3449	295	14	,	,	PUNCT
ejpam-3449	295	15	960	960	NUM
ejpam-3449	295	16	-	-	SYM
ejpam-3449	295	17	977	977	NUM
ejpam-3449	295	18	968	968	NUM
ejpam-3449	295	19	τfγ	τfγ	NOUN
ejpam-3449	295	20	-	-	PUNCT
ejpam-3449	295	21	ker(a)=	ker(a)=	PROPN
ejpam-3449	295	22	∩{u	∩{u	NOUN
ejpam-3449	295	23	:	:	PUNCT
ejpam-3449	295	24	a	a	DET
ejpam-3449	295	25	⊆	⊆	NUM
ejpam-3449	295	26	u	u	NOUN
ejpam-3449	295	27	and	and	CCONJ
ejpam-3449	295	28	u	u	NOUN
ejpam-3449	295	29	∈	∈	PROPN
ejpam-3449	295	30	τfγ	τfγ	VERB
ejpam-3449	295	31	}	}	PUNCT
ejpam-3449	295	32	in	in	ADP
ejpam-3449	295	33	other	other	ADJ
ejpam-3449	295	34	words	word	NOUN
ejpam-3449	295	35	,	,	PUNCT
ejpam-3449	295	36	τfγ	τfγ	NOUN
ejpam-3449	295	37	-	-	PUNCT
ejpam-3449	295	38	ker(a	ker(a	VERB
ejpam-3449	295	39	)	)	PUNCT
ejpam-3449	295	40	is	be	AUX
ejpam-3449	295	41	the	the	DET
ejpam-3449	295	42	intersection	intersection	NOUN
ejpam-3449	295	43	of	of	ADP
ejpam-3449	295	44	all	all	DET
ejpam-3449	295	45	fγ	fγ	ADJ
ejpam-3449	295	46	-	-	PUNCT
ejpam-3449	295	47	open	open	ADJ
ejpam-3449	295	48	sets	set	NOUN
ejpam-3449	295	49	of	of	ADP
ejpam-3449	295	50	(	(	PUNCT
ejpam-3449	295	51	x	x	NOUN
ejpam-3449	295	52	,	,	PUNCT
ejpam-3449	295	53	τ	τ	PROPN
ejpam-3449	295	54	,	,	PUNCT
ejpam-3449	295	55	τf	τf	NOUN
ejpam-3449	295	56	)	)	PUNCT
ejpam-3449	295	57	containing	contain	VERB
ejpam-3449	295	58	a.	a.	NOUN
ejpam-3449	295	59	theorem	theorem	NOUN
ejpam-3449	295	60	4.10	4.10	NUM
ejpam-3449	295	61	.	.	PUNCT
ejpam-3449	296	1	let	let	VERB
ejpam-3449	296	2	a	a	DET
ejpam-3449	296	3	⊆	⊆	NUM
ejpam-3449	296	4	(	(	PUNCT
ejpam-3449	296	5	x	x	NOUN
ejpam-3449	296	6	,	,	PUNCT
ejpam-3449	296	7	τ	τ	PROPN
ejpam-3449	296	8	,	,	PUNCT
ejpam-3449	296	9	τf	τf	NUM
ejpam-3449	296	10	)	)	PUNCT
ejpam-3449	296	11	and	and	CCONJ
ejpam-3449	296	12	γ	γ	X
ejpam-3449	296	13	be	be	AUX
ejpam-3449	296	14	an	an	DET
ejpam-3449	296	15	operation	operation	NOUN
ejpam-3449	296	16	on	on	ADP
ejpam-3449	296	17	τf	τf	PROPN
ejpam-3449	296	18	.	.	PUNCT
ejpam-3449	297	1	then	then	ADV
ejpam-3449	297	2	a	a	PRON
ejpam-3449	297	3	is	be	AUX
ejpam-3449	297	4	fγg.closed	fγg.close	VERB
ejpam-3449	297	5	if	if	SCONJ
ejpam-3449	297	6	and	and	CCONJ
ejpam-3449	297	7	only	only	ADV
ejpam-3449	297	8	if	if	SCONJ
ejpam-3449	297	9	fclγ(a	fclγ(a	PROPN
ejpam-3449	297	10	)	)	PUNCT
ejpam-3449	297	11	⊆	⊆	NUM
ejpam-3449	297	12	τfγ	τfγ	X
ejpam-3449	297	13	-	-	PUNCT
ejpam-3449	297	14	ker(a	ker(a	NOUN
ejpam-3449	297	15	)	)	PUNCT
ejpam-3449	297	16	.	.	PUNCT
ejpam-3449	298	1	proof	proof	NOUN
ejpam-3449	298	2	.	.	PUNCT
ejpam-3449	299	1	suppose	suppose	VERB
ejpam-3449	299	2	that	that	SCONJ
ejpam-3449	299	3	a	a	PRON
ejpam-3449	299	4	is	be	AUX
ejpam-3449	299	5	fγg.closed	fγg.close	VERB
ejpam-3449	299	6	.	.	PUNCT
ejpam-3449	300	1	then	then	ADV
ejpam-3449	300	2	fclγ(a	fclγ(a	NOUN
ejpam-3449	300	3	)	)	PUNCT
ejpam-3449	300	4	⊆	⊆	NUM
ejpam-3449	300	5	u	u	NOUN
ejpam-3449	300	6	,	,	PUNCT
ejpam-3449	300	7	whenever	whenever	SCONJ
ejpam-3449	300	8	a	a	DET
ejpam-3449	300	9	⊆	⊆	NUM
ejpam-3449	300	10	u	u	NOUN
ejpam-3449	300	11	and	and	CCONJ
ejpam-3449	300	12	u	u	NOUN
ejpam-3449	300	13	is	be	AUX
ejpam-3449	300	14	fγ	fγ	NOUN
ejpam-3449	300	15	-	-	PUNCT
ejpam-3449	300	16	open	open	ADJ
ejpam-3449	300	17	.	.	PUNCT
ejpam-3449	301	1	let	let	VERB
ejpam-3449	301	2	x	x	PUNCT
ejpam-3449	301	3	∈	∈	PROPN
ejpam-3449	301	4	fclγ(a	fclγ(a	PROPN
ejpam-3449	301	5	)	)	PUNCT
ejpam-3449	301	6	.	.	PUNCT
ejpam-3449	302	1	then	then	ADV
ejpam-3449	302	2	by	by	ADP
ejpam-3449	302	3	lemma	lemma	PROPN
ejpam-3449	302	4	4.2	4.2	NUM
ejpam-3449	302	5	,	,	PUNCT
ejpam-3449	302	6	a	a	DET
ejpam-3449	302	7	∩	∩	ADJ
ejpam-3449	302	8	τfγ	τfγ	NOUN
ejpam-3449	302	9	-	-	PUNCT
ejpam-3449	302	10	cl({x	cl({x	NOUN
ejpam-3449	302	11	}	}	PUNCT
ejpam-3449	302	12	)	)	PUNCT
ejpam-3449	302	13	6=	6=	ADP
ejpam-3449	303	1	φ	φ	PROPN
ejpam-3449	303	2	.	.	PUNCT
ejpam-3449	304	1	so	so	ADV
ejpam-3449	304	2	there	there	PRON
ejpam-3449	304	3	exists	exist	VERB
ejpam-3449	304	4	a	a	DET
ejpam-3449	304	5	point	point	NOUN
ejpam-3449	304	6	z	z	NOUN
ejpam-3449	304	7	in	in	ADP
ejpam-3449	304	8	x	x	PUNCT
ejpam-3449	304	9	such	such	ADJ
ejpam-3449	304	10	that	that	SCONJ
ejpam-3449	304	11	z	z	PROPN
ejpam-3449	304	12	∈	∈	PROPN
ejpam-3449	304	13	a	a	DET
ejpam-3449	304	14	∩	∩	ADJ
ejpam-3449	304	15	τfγ	τfγ	NOUN
ejpam-3449	304	16	-	-	PUNCT
ejpam-3449	304	17	cl({x	cl({x	NOUN
ejpam-3449	304	18	}	}	PUNCT
ejpam-3449	304	19	)	)	PUNCT
ejpam-3449	304	20	implies	imply	VERB
ejpam-3449	304	21	that	that	SCONJ
ejpam-3449	304	22	z	z	PROPN
ejpam-3449	304	23	∈	∈	PROPN
ejpam-3449	304	24	a	a	DET
ejpam-3449	304	25	⊆	⊆	NUM
ejpam-3449	304	26	u	u	NOUN
ejpam-3449	304	27	and	and	CCONJ
ejpam-3449	304	28	z	z	NOUN
ejpam-3449	304	29	∈	∈	PROPN
ejpam-3449	304	30	τfγcl({x	τfγcl({x	ADP
ejpam-3449	304	31	}	}	PUNCT
ejpam-3449	304	32	)	)	PUNCT
ejpam-3449	304	33	.	.	PUNCT
ejpam-3449	305	1	by	by	ADP
ejpam-3449	305	2	theorem	theorem	NOUN
ejpam-3449	305	3	3.12	3.12	NUM
ejpam-3449	305	4	,	,	PUNCT
ejpam-3449	305	5	{	{	PUNCT
ejpam-3449	305	6	x	x	NOUN
ejpam-3449	305	7	}	}	PUNCT
ejpam-3449	305	8	∩	∩	ADJ
ejpam-3449	305	9	u	u	PROPN
ejpam-3449	305	10	6=	6=	PROPN
ejpam-3449	305	11	φ	φ	PROPN
ejpam-3449	305	12	.	.	PUNCT
ejpam-3449	306	1	hence	hence	ADV
ejpam-3449	306	2	we	we	PRON
ejpam-3449	306	3	show	show	VERB
ejpam-3449	306	4	that	that	SCONJ
ejpam-3449	306	5	x	x	PUNCT
ejpam-3449	306	6	∈	∈	PROPN
ejpam-3449	306	7	τfγ	τfγ	NOUN
ejpam-3449	306	8	-	-	PUNCT
ejpam-3449	306	9	ker(a	ker(a	NOUN
ejpam-3449	306	10	)	)	PUNCT
ejpam-3449	306	11	.	.	PUNCT
ejpam-3449	307	1	therefore	therefore	ADV
ejpam-3449	307	2	,	,	PUNCT
ejpam-3449	307	3	fclγ(a	fclγ(a	NOUN
ejpam-3449	307	4	)	)	PUNCT
ejpam-3449	307	5	⊆	⊆	NUM
ejpam-3449	307	6	τfγ	τfγ	X
ejpam-3449	307	7	-	-	PUNCT
ejpam-3449	307	8	ker(a	ker(a	NOUN
ejpam-3449	307	9	)	)	PUNCT
ejpam-3449	307	10	.	.	PUNCT
ejpam-3449	308	1	conversely	conversely	ADV
ejpam-3449	308	2	,	,	PUNCT
ejpam-3449	308	3	let	let	VERB
ejpam-3449	308	4	fclγ(a	fclγ(a	NOUN
ejpam-3449	308	5	)	)	PUNCT
ejpam-3449	308	6	⊆	⊆	NUM
ejpam-3449	308	7	τfγ	τfγ	X
ejpam-3449	308	8	-	-	PUNCT
ejpam-3449	308	9	ker(a	ker(a	NOUN
ejpam-3449	308	10	)	)	PUNCT
ejpam-3449	308	11	.	.	PUNCT
ejpam-3449	309	1	let	let	VERB
ejpam-3449	309	2	u	u	PRON
ejpam-3449	309	3	be	be	AUX
ejpam-3449	309	4	any	any	DET
ejpam-3449	309	5	fγ	fγ	ADV
ejpam-3449	309	6	-	-	PUNCT
ejpam-3449	309	7	open	open	ADJ
ejpam-3449	309	8	set	set	NOUN
ejpam-3449	309	9	containing	contain	VERB
ejpam-3449	309	10	a.	a.	NOUN
ejpam-3449	309	11	let	let	VERB
ejpam-3449	309	12	x	x	PRON
ejpam-3449	309	13	be	be	AUX
ejpam-3449	309	14	a	a	DET
ejpam-3449	309	15	point	point	NOUN
ejpam-3449	309	16	in	in	ADP
ejpam-3449	309	17	x	x	INTJ
ejpam-3449	309	18	such	such	ADJ
ejpam-3449	309	19	that	that	SCONJ
ejpam-3449	309	20	x	x	SYM
ejpam-3449	309	21	∈	∈	PROPN
ejpam-3449	309	22	fclγ(a	fclγ(a	NOUN
ejpam-3449	309	23	)	)	PUNCT
ejpam-3449	309	24	.	.	PUNCT
ejpam-3449	310	1	then	then	ADV
ejpam-3449	310	2	x	x	X
ejpam-3449	310	3	∈	∈	PROPN
ejpam-3449	310	4	τfγ	τfγ	NOUN
ejpam-3449	310	5	-	-	PUNCT
ejpam-3449	310	6	ker(a	ker(a	NOUN
ejpam-3449	310	7	)	)	PUNCT
ejpam-3449	310	8	.	.	PUNCT
ejpam-3449	311	1	namely	namely	ADV
ejpam-3449	311	2	,	,	PUNCT
ejpam-3449	311	3	we	we	PRON
ejpam-3449	311	4	have	have	VERB
ejpam-3449	311	5	x	x	X
ejpam-3449	311	6	∈	∈	PROPN
ejpam-3449	311	7	u	u	NOUN
ejpam-3449	311	8	,	,	PUNCT
ejpam-3449	311	9	because	because	SCONJ
ejpam-3449	311	10	a	a	DET
ejpam-3449	311	11	⊆	⊆	NUM
ejpam-3449	311	12	u	u	NOUN
ejpam-3449	311	13	and	and	CCONJ
ejpam-3449	311	14	u	u	NOUN
ejpam-3449	311	15	∈	∈	PROPN
ejpam-3449	311	16	τfγ	τfγ	NOUN
ejpam-3449	311	17	}	}	PUNCT
ejpam-3449	311	18	.	.	PUNCT
ejpam-3449	312	1	that	that	PRON
ejpam-3449	312	2	is	be	AUX
ejpam-3449	312	3	fclγ(a	fclγ(a	NOUN
ejpam-3449	312	4	)	)	PUNCT
ejpam-3449	312	5	⊆	⊆	NUM
ejpam-3449	312	6	τfγ	τfγ	NOUN
ejpam-3449	312	7	-	-	PUNCT
ejpam-3449	312	8	ker(a)⊆	ker(a)⊆	NOUN
ejpam-3449	312	9	u	u	NOUN
ejpam-3449	312	10	.	.	PUNCT
ejpam-3449	313	1	therefore	therefore	ADV
ejpam-3449	313	2	,	,	PUNCT
ejpam-3449	313	3	a	a	PRON
ejpam-3449	313	4	is	be	AUX
ejpam-3449	313	5	fγg.closed	fγg.close	VERB
ejpam-3449	313	6	set	set	VERB
ejpam-3449	313	7	in	in	ADP
ejpam-3449	313	8	x.	x.	PROPN
ejpam-3449	313	9	5	5	NUM
ejpam-3449	313	10	.	.	PUNCT
ejpam-3449	314	1	on	on	ADP
ejpam-3449	314	2	fγ	fγ	NOUN
ejpam-3449	314	3	-	-	PUNCT
ejpam-3449	314	4	separation	separation	NOUN
ejpam-3449	314	5	axioms	axiom	NOUN
ejpam-3449	314	6	definition	definition	NOUN
ejpam-3449	314	7	5.1	5.1	NUM
ejpam-3449	314	8	.	.	PUNCT
ejpam-3449	315	1	a	a	DET
ejpam-3449	315	2	fine	fine	ADJ
ejpam-3449	315	3	space	space	NOUN
ejpam-3449	315	4	(	(	PUNCT
ejpam-3449	315	5	x	x	X
ejpam-3449	315	6	,	,	PUNCT
ejpam-3449	315	7	τ	τ	PROPN
ejpam-3449	315	8	,	,	PUNCT
ejpam-3449	315	9	τf	τf	NUM
ejpam-3449	315	10	)	)	PUNCT
ejpam-3449	315	11	with	with	ADP
ejpam-3449	315	12	an	an	DET
ejpam-3449	315	13	operation	operation	NOUN
ejpam-3449	315	14	γ	γ	NOUN
ejpam-3449	315	15	on	on	ADP
ejpam-3449	315	16	τf	τf	PROPN
ejpam-3449	315	17	is	be	AUX
ejpam-3449	315	18	said	say	VERB
ejpam-3449	315	19	to	to	PART
ejpam-3449	315	20	be	be	AUX
ejpam-3449	315	21	(	(	PUNCT
ejpam-3449	315	22	i	i	NOUN
ejpam-3449	315	23	)	)	PUNCT
ejpam-3449	315	24	fγ	fγ	PROPN
ejpam-3449	315	25	-	-	PUNCT
ejpam-3449	315	26	t0	t0	PROPN
ejpam-3449	315	27	if	if	SCONJ
ejpam-3449	315	28	for	for	ADP
ejpam-3449	315	29	any	any	DET
ejpam-3449	315	30	two	two	NUM
ejpam-3449	315	31	distinct	distinct	ADJ
ejpam-3449	315	32	points	point	NOUN
ejpam-3449	315	33	x	x	NOUN
ejpam-3449	315	34	,	,	PUNCT
ejpam-3449	315	35	y	y	PROPN
ejpam-3449	315	36	in	in	ADP
ejpam-3449	315	37	x	x	SYM
ejpam-3449	315	38	,	,	PUNCT
ejpam-3449	315	39	there	there	PRON
ejpam-3449	315	40	exists	exist	VERB
ejpam-3449	315	41	a	a	DET
ejpam-3449	315	42	fine	fine	ADV
ejpam-3449	315	43	-	-	PUNCT
ejpam-3449	315	44	open	open	NOUN
ejpam-3449	315	45	set	set	NOUN
ejpam-3449	315	46	u	u	PRON
ejpam-3449	315	47	such	such	ADJ
ejpam-3449	315	48	that	that	SCONJ
ejpam-3449	315	49	x	x	SYM
ejpam-3449	315	50	∈	∈	PROPN
ejpam-3449	315	51	u	u	NOUN
ejpam-3449	315	52	and	and	CCONJ
ejpam-3449	315	53	y	y	PROPN
ejpam-3449	315	54	/∈	/∈	PUNCT
ejpam-3449	315	55	γ(u	γ(u	PROPN
ejpam-3449	315	56	)	)	PUNCT
ejpam-3449	315	57	or	or	CCONJ
ejpam-3449	315	58	y	y	PROPN
ejpam-3449	315	59	∈	∈	PROPN
ejpam-3449	315	60	u	u	NOUN
ejpam-3449	315	61	and	and	CCONJ
ejpam-3449	315	62	x	x	PROPN
ejpam-3449	315	63	/∈	/∈	PUNCT
ejpam-3449	315	64	γ(u	γ(u	PROPN
ejpam-3449	315	65	)	)	PUNCT
ejpam-3449	315	66	.	.	PUNCT
ejpam-3449	316	1	(	(	PUNCT
ejpam-3449	316	2	ii	ii	NOUN
ejpam-3449	316	3	)	)	PUNCT
ejpam-3449	316	4	fγ	fγ	PROPN
ejpam-3449	316	5	-	-	PUNCT
ejpam-3449	316	6	t	t	NOUN
ejpam-3449	316	7	∗0	∗0	PROPN
ejpam-3449	316	8	if	if	SCONJ
ejpam-3449	316	9	for	for	ADP
ejpam-3449	316	10	each	each	DET
ejpam-3449	316	11	pair	pair	NOUN
ejpam-3449	316	12	of	of	ADP
ejpam-3449	316	13	distinct	distinct	ADJ
ejpam-3449	316	14	points	point	NOUN
ejpam-3449	316	15	x	x	X
ejpam-3449	316	16	,	,	PUNCT
ejpam-3449	316	17	y	y	PROPN
ejpam-3449	316	18	in	in	ADP
ejpam-3449	316	19	x	x	SYM
ejpam-3449	316	20	,	,	PUNCT
ejpam-3449	316	21	there	there	PRON
ejpam-3449	316	22	exists	exist	VERB
ejpam-3449	316	23	a	a	DET
ejpam-3449	316	24	fγ	fγ	ADV
ejpam-3449	316	25	-	-	PUNCT
ejpam-3449	316	26	open	open	NOUN
ejpam-3449	316	27	set	set	NOUN
ejpam-3449	316	28	u	u	NOUN
ejpam-3449	316	29	containing	contain	VERB
ejpam-3449	316	30	one	one	NUM
ejpam-3449	316	31	of	of	ADP
ejpam-3449	316	32	the	the	DET
ejpam-3449	316	33	points	point	NOUN
ejpam-3449	316	34	but	but	CCONJ
ejpam-3449	316	35	not	not	PART
ejpam-3449	316	36	the	the	DET
ejpam-3449	316	37	other	other	ADJ
ejpam-3449	316	38	.	.	PUNCT
ejpam-3449	317	1	definition	definition	NOUN
ejpam-3449	317	2	5.2	5.2	NUM
ejpam-3449	317	3	.	.	PUNCT
ejpam-3449	318	1	a	a	DET
ejpam-3449	318	2	fine	fine	ADJ
ejpam-3449	318	3	space	space	NOUN
ejpam-3449	318	4	(	(	PUNCT
ejpam-3449	318	5	x	x	X
ejpam-3449	318	6	,	,	PUNCT
ejpam-3449	318	7	τ	τ	PROPN
ejpam-3449	318	8	,	,	PUNCT
ejpam-3449	318	9	τf	τf	NUM
ejpam-3449	318	10	)	)	PUNCT
ejpam-3449	318	11	with	with	ADP
ejpam-3449	318	12	an	an	DET
ejpam-3449	318	13	operation	operation	NOUN
ejpam-3449	318	14	γ	γ	NOUN
ejpam-3449	318	15	on	on	ADP
ejpam-3449	318	16	τf	τf	PROPN
ejpam-3449	318	17	is	be	AUX
ejpam-3449	318	18	said	say	VERB
ejpam-3449	318	19	to	to	PART
ejpam-3449	318	20	be	be	AUX
ejpam-3449	318	21	(	(	PUNCT
ejpam-3449	318	22	i	i	NOUN
ejpam-3449	318	23	)	)	PUNCT
ejpam-3449	318	24	fγ	fγ	PROPN
ejpam-3449	318	25	-	-	PUNCT
ejpam-3449	318	26	t1	t1	NOUN
ejpam-3449	318	27	if	if	SCONJ
ejpam-3449	318	28	for	for	ADP
ejpam-3449	318	29	any	any	DET
ejpam-3449	318	30	two	two	NUM
ejpam-3449	318	31	distinct	distinct	ADJ
ejpam-3449	318	32	points	point	NOUN
ejpam-3449	318	33	x	x	NOUN
ejpam-3449	318	34	,	,	PUNCT
ejpam-3449	318	35	y	y	PROPN
ejpam-3449	318	36	in	in	ADP
ejpam-3449	318	37	x	x	SYM
ejpam-3449	318	38	,	,	PUNCT
ejpam-3449	318	39	there	there	PRON
ejpam-3449	318	40	exist	exist	VERB
ejpam-3449	318	41	two	two	NUM
ejpam-3449	318	42	fine	fine	ADJ
ejpam-3449	318	43	-	-	PUNCT
ejpam-3449	318	44	open	open	ADJ
ejpam-3449	318	45	sets	set	NOUN
ejpam-3449	318	46	u	u	NOUN
ejpam-3449	318	47	and	and	CCONJ
ejpam-3449	318	48	v	v	ADP
ejpam-3449	318	49	such	such	ADJ
ejpam-3449	318	50	that	that	SCONJ
ejpam-3449	318	51	x	x	SYM
ejpam-3449	318	52	∈	∈	PROPN
ejpam-3449	318	53	u	u	NOUN
ejpam-3449	318	54	,	,	PUNCT
ejpam-3449	318	55	y	y	PROPN
ejpam-3449	318	56	/∈	/∈	PUNCT
ejpam-3449	318	57	γ(u	γ(u	PROPN
ejpam-3449	318	58	)	)	PUNCT
ejpam-3449	318	59	,	,	PUNCT
ejpam-3449	318	60	y	y	PROPN
ejpam-3449	318	61	∈	∈	PROPN
ejpam-3449	318	62	v	v	NOUN
ejpam-3449	318	63	and	and	CCONJ
ejpam-3449	318	64	x	x	NOUN
ejpam-3449	318	65	/∈	/∈	INTJ
ejpam-3449	318	66	γ(v	γ(v	ADJ
ejpam-3449	318	67	)	)	PUNCT
ejpam-3449	318	68	.	.	PUNCT
ejpam-3449	319	1	(	(	PUNCT
ejpam-3449	319	2	ii	ii	NOUN
ejpam-3449	319	3	)	)	PUNCT
ejpam-3449	319	4	fγ	fγ	PROPN
ejpam-3449	319	5	-	-	PUNCT
ejpam-3449	319	6	t	t	NOUN
ejpam-3449	319	7	∗1	∗1	PROPN
ejpam-3449	320	1	if	if	SCONJ
ejpam-3449	320	2	for	for	ADP
ejpam-3449	320	3	each	each	DET
ejpam-3449	320	4	pair	pair	NOUN
ejpam-3449	320	5	of	of	ADP
ejpam-3449	320	6	distinct	distinct	ADJ
ejpam-3449	320	7	points	point	NOUN
ejpam-3449	320	8	x	x	X
ejpam-3449	320	9	,	,	PUNCT
ejpam-3449	320	10	y	y	PROPN
ejpam-3449	320	11	in	in	ADP
ejpam-3449	320	12	x	x	SYM
ejpam-3449	320	13	,	,	PUNCT
ejpam-3449	320	14	there	there	PRON
ejpam-3449	320	15	exist	exist	VERB
ejpam-3449	320	16	two	two	NUM
ejpam-3449	320	17	fγ	fγ	ADV
ejpam-3449	320	18	-	-	PUNCT
ejpam-3449	320	19	open	open	ADJ
ejpam-3449	320	20	sets	set	NOUN
ejpam-3449	320	21	u	u	NOUN
ejpam-3449	320	22	and	and	CCONJ
ejpam-3449	320	23	v	v	ADP
ejpam-3449	320	24	such	such	ADJ
ejpam-3449	320	25	that	that	SCONJ
ejpam-3449	320	26	x	x	SYM
ejpam-3449	320	27	∈	∈	NOUN
ejpam-3449	320	28	u	u	NOUN
ejpam-3449	320	29	but	but	CCONJ
ejpam-3449	320	30	y	y	PROPN
ejpam-3449	320	31	/∈	/∈	PUNCT
ejpam-3449	320	32	u	u	PROPN
ejpam-3449	320	33	and	and	CCONJ
ejpam-3449	320	34	y	y	PROPN
ejpam-3449	320	35	∈	∈	PROPN
ejpam-3449	321	1	v	v	NOUN
ejpam-3449	322	1	but	but	CCONJ
ejpam-3449	322	2	x	x	SYM
ejpam-3449	322	3	/∈	/∈	NOUN
ejpam-3449	322	4	v	v	NOUN
ejpam-3449	322	5	.	.	PUNCT
ejpam-3449	323	1	definition	definition	NOUN
ejpam-3449	323	2	5.3	5.3	NUM
ejpam-3449	323	3	.	.	PUNCT
ejpam-3449	324	1	a	a	DET
ejpam-3449	324	2	fine	fine	ADJ
ejpam-3449	324	3	space	space	NOUN
ejpam-3449	324	4	(	(	PUNCT
ejpam-3449	324	5	x	x	X
ejpam-3449	324	6	,	,	PUNCT
ejpam-3449	324	7	τ	τ	PROPN
ejpam-3449	324	8	,	,	PUNCT
ejpam-3449	324	9	τf	τf	NUM
ejpam-3449	324	10	)	)	PUNCT
ejpam-3449	324	11	with	with	ADP
ejpam-3449	324	12	an	an	DET
ejpam-3449	324	13	operation	operation	NOUN
ejpam-3449	324	14	γ	γ	NOUN
ejpam-3449	324	15	on	on	ADP
ejpam-3449	324	16	τf	τf	PROPN
ejpam-3449	324	17	is	be	AUX
ejpam-3449	324	18	said	say	VERB
ejpam-3449	324	19	to	to	PART
ejpam-3449	324	20	be	be	AUX
ejpam-3449	324	21	(	(	PUNCT
ejpam-3449	324	22	i	i	NOUN
ejpam-3449	324	23	)	)	PUNCT
ejpam-3449	324	24	fγ	fγ	PROPN
ejpam-3449	324	25	-	-	PUNCT
ejpam-3449	324	26	t2	t2	NOUN
ejpam-3449	324	27	if	if	SCONJ
ejpam-3449	324	28	for	for	ADP
ejpam-3449	324	29	any	any	DET
ejpam-3449	324	30	two	two	NUM
ejpam-3449	324	31	distinct	distinct	ADJ
ejpam-3449	324	32	points	point	NOUN
ejpam-3449	325	1	x	x	NOUN
ejpam-3449	325	2	,	,	PUNCT
ejpam-3449	325	3	y	y	PROPN
ejpam-3449	325	4	in	in	ADP
ejpam-3449	325	5	x	x	SYM
ejpam-3449	325	6	,	,	PUNCT
ejpam-3449	325	7	there	there	PRON
ejpam-3449	325	8	exist	exist	VERB
ejpam-3449	325	9	two	two	NUM
ejpam-3449	325	10	fine	fine	ADJ
ejpam-3449	325	11	-	-	PUNCT
ejpam-3449	325	12	open	open	ADJ
ejpam-3449	325	13	sets	set	NOUN
ejpam-3449	325	14	u	u	NOUN
ejpam-3449	325	15	and	and	CCONJ
ejpam-3449	325	16	v	v	ADP
ejpam-3449	325	17	such	such	ADJ
ejpam-3449	325	18	that	that	SCONJ
ejpam-3449	325	19	x	x	SYM
ejpam-3449	325	20	∈	∈	PROPN
ejpam-3449	325	21	u	u	NOUN
ejpam-3449	325	22	,	,	PUNCT
ejpam-3449	325	23	y	y	PROPN
ejpam-3449	325	24	∈	∈	PROPN
ejpam-3449	325	25	v	v	NOUN
ejpam-3449	325	26	and	and	CCONJ
ejpam-3449	325	27	γ(u	γ(u	NOUN
ejpam-3449	325	28	)	)	PUNCT
ejpam-3449	325	29	∩	∩	NOUN
ejpam-3449	325	30	γ(v	γ(v	NOUN
ejpam-3449	325	31	)	)	PUNCT
ejpam-3449	325	32	=	=	SYM
ejpam-3449	326	1	φ	φ	PROPN
ejpam-3449	326	2	.	.	PUNCT
ejpam-3449	326	3	(	(	PUNCT
ejpam-3449	326	4	ii	ii	NOUN
ejpam-3449	326	5	)	)	PUNCT
ejpam-3449	326	6	fγ	fγ	PROPN
ejpam-3449	326	7	-	-	PUNCT
ejpam-3449	326	8	t	t	NOUN
ejpam-3449	326	9	∗2	∗2	PROPN
ejpam-3449	326	10	if	if	SCONJ
ejpam-3449	326	11	for	for	ADP
ejpam-3449	326	12	each	each	DET
ejpam-3449	326	13	pair	pair	NOUN
ejpam-3449	326	14	of	of	ADP
ejpam-3449	326	15	distinct	distinct	ADJ
ejpam-3449	326	16	points	point	NOUN
ejpam-3449	326	17	x	x	X
ejpam-3449	326	18	,	,	PUNCT
ejpam-3449	326	19	y	y	PROPN
ejpam-3449	326	20	in	in	ADP
ejpam-3449	326	21	x	x	SYM
ejpam-3449	326	22	,	,	PUNCT
ejpam-3449	326	23	there	there	PRON
ejpam-3449	326	24	exist	exist	VERB
ejpam-3449	326	25	fγ	fγ	ADV
ejpam-3449	326	26	-	-	PUNCT
ejpam-3449	326	27	open	open	ADJ
ejpam-3449	326	28	sets	set	NOUN
ejpam-3449	326	29	u	u	NOUN
ejpam-3449	326	30	and	and	CCONJ
ejpam-3449	326	31	v	v	ADP
ejpam-3449	326	32	such	such	ADJ
ejpam-3449	326	33	that	that	SCONJ
ejpam-3449	326	34	x	x	SYM
ejpam-3449	326	35	∈	∈	PROPN
ejpam-3449	326	36	u	u	NOUN
ejpam-3449	326	37	,	,	PUNCT
ejpam-3449	326	38	y	y	PROPN
ejpam-3449	326	39	∈	∈	PROPN
ejpam-3449	326	40	v	v	NOUN
ejpam-3449	326	41	and	and	CCONJ
ejpam-3449	326	42	u	u	NOUN
ejpam-3449	326	43	∩	∩	NOUN
ejpam-3449	326	44	v	v	NOUN
ejpam-3449	326	45	=	=	SYM
ejpam-3449	326	46	φ	φ	PROPN
ejpam-3449	326	47	.	.	PUNCT
ejpam-3449	327	1	definition	definition	NOUN
ejpam-3449	327	2	5.4	5.4	NUM
ejpam-3449	327	3	.	.	PUNCT
ejpam-3449	328	1	a	a	DET
ejpam-3449	328	2	fine	fine	ADJ
ejpam-3449	328	3	space	space	NOUN
ejpam-3449	328	4	(	(	PUNCT
ejpam-3449	328	5	x	x	X
ejpam-3449	328	6	,	,	PUNCT
ejpam-3449	328	7	τ	τ	PROPN
ejpam-3449	328	8	,	,	PUNCT
ejpam-3449	328	9	τf	τf	NUM
ejpam-3449	328	10	)	)	PUNCT
ejpam-3449	328	11	with	with	ADP
ejpam-3449	328	12	an	an	DET
ejpam-3449	328	13	operation	operation	NOUN
ejpam-3449	328	14	γ	γ	NOUN
ejpam-3449	328	15	on	on	ADP
ejpam-3449	328	16	τf	τf	PROPN
ejpam-3449	328	17	is	be	AUX
ejpam-3449	328	18	said	say	VERB
ejpam-3449	328	19	to	to	PART
ejpam-3449	328	20	be	be	AUX
ejpam-3449	328	21	fγ	fγ	PROPN
ejpam-3449	328	22	-	-	PUNCT
ejpam-3449	328	23	t	t	PROPN
ejpam-3449	328	24	1	1	NUM
ejpam-3449	328	25	2	2	NUM
ejpam-3449	328	26	if	if	SCONJ
ejpam-3449	328	27	every	every	DET
ejpam-3449	328	28	fγg.closed	fγg.close	VERB
ejpam-3449	328	29	set	set	VERB
ejpam-3449	328	30	in	in	ADP
ejpam-3449	328	31	x	x	PROPN
ejpam-3449	328	32	is	be	AUX
ejpam-3449	328	33	fγ	fγ	ADV
ejpam-3449	328	34	-	-	PUNCT
ejpam-3449	328	35	closed	close	VERB
ejpam-3449	328	36	set	set	NOUN
ejpam-3449	328	37	.	.	PUNCT
ejpam-3449	329	1	theorem	theorem	VERB
ejpam-3449	329	2	5.5	5.5	NUM
ejpam-3449	329	3	.	.	PUNCT
ejpam-3449	330	1	for	for	ADP
ejpam-3449	330	2	any	any	DET
ejpam-3449	330	3	fine	fine	ADJ
ejpam-3449	330	4	space	space	NOUN
ejpam-3449	330	5	(	(	PUNCT
ejpam-3449	330	6	x	x	X
ejpam-3449	330	7	,	,	PUNCT
ejpam-3449	330	8	τ	τ	PROPN
ejpam-3449	330	9	,	,	PUNCT
ejpam-3449	330	10	τf	τf	NUM
ejpam-3449	330	11	)	)	PUNCT
ejpam-3449	330	12	with	with	ADP
ejpam-3449	330	13	an	an	DET
ejpam-3449	330	14	operation	operation	NOUN
ejpam-3449	330	15	γ	γ	NOUN
ejpam-3449	330	16	on	on	ADP
ejpam-3449	330	17	τf	τf	PROPN
ejpam-3449	330	18	.	.	PUNCT
ejpam-3449	331	1	then	then	ADV
ejpam-3449	331	2	(	(	PUNCT
ejpam-3449	331	3	x	x	X
ejpam-3449	331	4	,	,	PUNCT
ejpam-3449	331	5	τ	τ	PROPN
ejpam-3449	331	6	,	,	PUNCT
ejpam-3449	331	7	τf	τf	PROPN
ejpam-3449	331	8	)	)	PUNCT
ejpam-3449	331	9	is	be	AUX
ejpam-3449	331	10	fγ	fγ	PROPN
ejpam-3449	331	11	-	-	PUNCT
ejpam-3449	331	12	t	t	PROPN
ejpam-3449	331	13	1	1	NUM
ejpam-3449	331	14	2	2	NUM
ejpam-3449	331	15	if	if	SCONJ
ejpam-3449	331	16	and	and	CCONJ
ejpam-3449	331	17	only	only	ADV
ejpam-3449	331	18	if	if	SCONJ
ejpam-3449	331	19	for	for	ADP
ejpam-3449	331	20	each	each	DET
ejpam-3449	331	21	point	point	NOUN
ejpam-3449	331	22	x	x	X
ejpam-3449	331	23	∈	∈	NOUN
ejpam-3449	331	24	x	x	NOUN
ejpam-3449	331	25	,	,	PUNCT
ejpam-3449	331	26	the	the	DET
ejpam-3449	331	27	set	set	NOUN
ejpam-3449	331	28	{	{	PUNCT
ejpam-3449	331	29	x	x	NOUN
ejpam-3449	331	30	}	}	PUNCT
ejpam-3449	331	31	is	be	AUX
ejpam-3449	331	32	fγ	fγ	ADV
ejpam-3449	331	33	-	-	PUNCT
ejpam-3449	331	34	closed	close	VERB
ejpam-3449	331	35	or	or	CCONJ
ejpam-3449	331	36	fγ	fγ	ADV
ejpam-3449	331	37	-	-	PUNCT
ejpam-3449	331	38	open	open	ADJ
ejpam-3449	331	39	.	.	PUNCT
ejpam-3449	332	1	proof	proof	NOUN
ejpam-3449	332	2	.	.	PUNCT
ejpam-3449	333	1	let	let	VERB
ejpam-3449	333	2	x	x	PRON
ejpam-3449	333	3	be	be	AUX
ejpam-3449	333	4	a	a	DET
ejpam-3449	333	5	fγ	fγ	PROPN
ejpam-3449	333	6	-	-	PUNCT
ejpam-3449	333	7	t	t	NOUN
ejpam-3449	333	8	1	1	NUM
ejpam-3449	333	9	2	2	NUM
ejpam-3449	333	10	space	space	NOUN
ejpam-3449	333	11	and	and	CCONJ
ejpam-3449	333	12	let	let	VERB
ejpam-3449	333	13	{	{	PUNCT
ejpam-3449	333	14	x	x	VERB
ejpam-3449	333	15	}	}	PUNCT
ejpam-3449	333	16	is	be	AUX
ejpam-3449	333	17	not	not	PART
ejpam-3449	333	18	fγ	fγ	ADV
ejpam-3449	333	19	-	-	PUNCT
ejpam-3449	333	20	closed	close	VERB
ejpam-3449	333	21	set	set	NOUN
ejpam-3449	333	22	in	in	ADP
ejpam-3449	333	23	(	(	PUNCT
ejpam-3449	333	24	x	x	NOUN
ejpam-3449	333	25	,	,	PUNCT
ejpam-3449	333	26	τ	τ	PROPN
ejpam-3449	333	27	,	,	PUNCT
ejpam-3449	333	28	τf	τf	NUM
ejpam-3449	333	29	)	)	PUNCT
ejpam-3449	333	30	.	.	PUNCT
ejpam-3449	334	1	by	by	ADP
ejpam-3449	334	2	corollary	corollary	ADJ
ejpam-3449	334	3	4.8	4.8	NUM
ejpam-3449	334	4	,	,	PUNCT
ejpam-3449	334	5	x\{x	x\{x	CCONJ
ejpam-3449	334	6	}	}	PUNCT
ejpam-3449	334	7	is	be	AUX
ejpam-3449	334	8	fγg.closed	fγg.close	VERB
ejpam-3449	334	9	.	.	PUNCT
ejpam-3449	335	1	since	since	SCONJ
ejpam-3449	335	2	(	(	PUNCT
ejpam-3449	335	3	x	x	X
ejpam-3449	335	4	,	,	PUNCT
ejpam-3449	335	5	τ	τ	PROPN
ejpam-3449	335	6	,	,	PUNCT
ejpam-3449	335	7	τf	τf	PROPN
ejpam-3449	335	8	)	)	PUNCT
ejpam-3449	335	9	is	be	AUX
ejpam-3449	335	10	fγ	fγ	PROPN
ejpam-3449	335	11	-	-	PUNCT
ejpam-3449	335	12	t	t	PROPN
ejpam-3449	335	13	1	1	NUM
ejpam-3449	335	14	2	2	NUM
ejpam-3449	335	15	,	,	PUNCT
ejpam-3449	335	16	then	then	ADV
ejpam-3449	335	17	x\{x	x\{x	NOUN
ejpam-3449	335	18	}	}	PUNCT
ejpam-3449	335	19	is	be	AUX
ejpam-3449	335	20	fγ	fγ	ADV
ejpam-3449	335	21	-	-	PUNCT
ejpam-3449	335	22	closed	close	VERB
ejpam-3449	335	23	set	set	NOUN
ejpam-3449	335	24	which	which	PRON
ejpam-3449	335	25	means	mean	VERB
ejpam-3449	335	26	that	that	SCONJ
ejpam-3449	335	27	{	{	PUNCT
ejpam-3449	335	28	x	x	X
ejpam-3449	335	29	}	}	PUNCT
ejpam-3449	335	30	is	be	AUX
ejpam-3449	335	31	fγ	fγ	ADV
ejpam-3449	335	32	-	-	PUNCT
ejpam-3449	335	33	open	open	NOUN
ejpam-3449	335	34	set	set	NOUN
ejpam-3449	335	35	in	in	ADP
ejpam-3449	335	36	x.	x.	PROPN
ejpam-3449	335	37	b.	b.	PROPN
ejpam-3449	335	38	a.	a.	PROPN
ejpam-3449	335	39	asaad	asaad	PROPN
ejpam-3449	335	40	et	et	PROPN
ejpam-3449	336	1	al	al	PROPN
ejpam-3449	336	2	.	.	PUNCT
ejpam-3449	336	3	/	/	SYM
ejpam-3449	336	4	eur	eur	PROPN
ejpam-3449	336	5	.	.	PUNCT
ejpam-3449	337	1	j.	j.	PROPN
ejpam-3449	337	2	pure	pure	PROPN
ejpam-3449	337	3	appl	appl	PROPN
ejpam-3449	337	4	.	.	PROPN
ejpam-3449	337	5	math	math	PROPN
ejpam-3449	337	6	,	,	PUNCT
ejpam-3449	337	7	12	12	NUM
ejpam-3449	337	8	(	(	PUNCT
ejpam-3449	337	9	3	3	NUM
ejpam-3449	337	10	)	)	PUNCT
ejpam-3449	337	11	(	(	PUNCT
ejpam-3449	337	12	2019	2019	NUM
ejpam-3449	337	13	)	)	PUNCT
ejpam-3449	337	14	,	,	PUNCT
ejpam-3449	337	15	960	960	NUM
ejpam-3449	337	16	-	-	SYM
ejpam-3449	337	17	977	977	NUM
ejpam-3449	337	18	969	969	NUM
ejpam-3449	337	19	conversely	conversely	ADV
ejpam-3449	337	20	,	,	PUNCT
ejpam-3449	337	21	let	let	VERB
ejpam-3449	337	22	f	f	PRON
ejpam-3449	337	23	be	be	AUX
ejpam-3449	337	24	any	any	DET
ejpam-3449	337	25	fγg.closed	fγg.close	VERB
ejpam-3449	337	26	set	set	NOUN
ejpam-3449	337	27	in	in	ADP
ejpam-3449	337	28	the	the	DET
ejpam-3449	337	29	fine	fine	ADJ
ejpam-3449	337	30	space	space	NOUN
ejpam-3449	337	31	(	(	PUNCT
ejpam-3449	337	32	x	x	X
ejpam-3449	337	33	,	,	PUNCT
ejpam-3449	337	34	τ	τ	PROPN
ejpam-3449	337	35	,	,	PUNCT
ejpam-3449	337	36	τf	τf	NUM
ejpam-3449	337	37	)	)	PUNCT
ejpam-3449	337	38	.	.	PUNCT
ejpam-3449	338	1	we	we	PRON
ejpam-3449	338	2	have	have	VERB
ejpam-3449	338	3	to	to	PART
ejpam-3449	338	4	show	show	VERB
ejpam-3449	338	5	that	that	SCONJ
ejpam-3449	338	6	f	f	PROPN
ejpam-3449	338	7	is	be	AUX
ejpam-3449	338	8	fγ	fγ	NOUN
ejpam-3449	338	9	-	-	PUNCT
ejpam-3449	338	10	closed	closed	ADJ
ejpam-3449	338	11	(	(	PUNCT
ejpam-3449	338	12	that	that	PRON
ejpam-3449	338	13	is	is	ADV
ejpam-3449	338	14	fclγ(f	fclγ(f	NOUN
ejpam-3449	338	15	)	)	PUNCT
ejpam-3449	339	1	=	=	SYM
ejpam-3449	339	2	f	f	PROPN
ejpam-3449	339	3	(	(	PUNCT
ejpam-3449	339	4	by	by	ADP
ejpam-3449	339	5	lemma	lemma	PROPN
ejpam-3449	339	6	3.13	3.13	NUM
ejpam-3449	339	7	(	(	PUNCT
ejpam-3449	339	8	4b	4b	PROPN
ejpam-3449	339	9	)	)	PUNCT
ejpam-3449	339	10	)	)	PUNCT
ejpam-3449	339	11	)	)	PUNCT
ejpam-3449	339	12	.	.	PUNCT
ejpam-3449	340	1	it	it	PRON
ejpam-3449	340	2	is	be	AUX
ejpam-3449	340	3	sufficient	sufficient	ADJ
ejpam-3449	340	4	to	to	PART
ejpam-3449	340	5	show	show	VERB
ejpam-3449	340	6	that	that	DET
ejpam-3449	340	7	fclγ(f	fclγ(f	NOUN
ejpam-3449	340	8	)	)	PUNCT
ejpam-3449	340	9	⊆	⊆	NUM
ejpam-3449	340	10	f	f	NOUN
ejpam-3449	340	11	.	.	PUNCT
ejpam-3449	341	1	let	let	VERB
ejpam-3449	341	2	x	x	SYM
ejpam-3449	341	3	∈	∈	PROPN
ejpam-3449	341	4	fclγ(f	fclγ(f	NOUN
ejpam-3449	341	5	)	)	PUNCT
ejpam-3449	341	6	.	.	PUNCT
ejpam-3449	342	1	by	by	ADP
ejpam-3449	342	2	hypothesis	hypothesis	NOUN
ejpam-3449	342	3	{	{	PUNCT
ejpam-3449	342	4	x	x	NOUN
ejpam-3449	342	5	}	}	PUNCT
ejpam-3449	342	6	is	be	AUX
ejpam-3449	342	7	fγ	fγ	ADV
ejpam-3449	342	8	-	-	PUNCT
ejpam-3449	342	9	closed	close	VERB
ejpam-3449	342	10	or	or	CCONJ
ejpam-3449	342	11	fγ	fγ	ADV
ejpam-3449	342	12	-	-	PUNCT
ejpam-3449	342	13	open	open	ADJ
ejpam-3449	342	14	for	for	ADP
ejpam-3449	342	15	each	each	DET
ejpam-3449	342	16	x	x	SYM
ejpam-3449	342	17	∈	∈	PROPN
ejpam-3449	342	18	x.	x.	NOUN
ejpam-3449	343	1	so	so	ADV
ejpam-3449	343	2	we	we	PRON
ejpam-3449	343	3	have	have	VERB
ejpam-3449	343	4	two	two	NUM
ejpam-3449	343	5	cases	case	NOUN
ejpam-3449	343	6	:	:	PUNCT
ejpam-3449	343	7	case	case	NOUN
ejpam-3449	343	8	(	(	PUNCT
ejpam-3449	343	9	1	1	NUM
ejpam-3449	343	10	):	):	PUNCT
ejpam-3449	343	11	if	if	SCONJ
ejpam-3449	343	12	{	{	PUNCT
ejpam-3449	343	13	x	x	NOUN
ejpam-3449	343	14	}	}	PUNCT
ejpam-3449	343	15	is	be	AUX
ejpam-3449	343	16	fγ	fγ	ADV
ejpam-3449	343	17	-	-	PUNCT
ejpam-3449	343	18	closed	close	VERB
ejpam-3449	343	19	set	set	NOUN
ejpam-3449	343	20	.	.	PUNCT
ejpam-3449	344	1	suppose	suppose	VERB
ejpam-3449	344	2	x	x	X
ejpam-3449	345	1	/∈	/∈	PUNCT
ejpam-3449	345	2	f	f	PROPN
ejpam-3449	345	3	,	,	PUNCT
ejpam-3449	345	4	then	then	ADV
ejpam-3449	345	5	x	x	SYM
ejpam-3449	345	6	∈	∈	PROPN
ejpam-3449	345	7	fclγ(f	fclγ(f	NOUN
ejpam-3449	345	8	)	)	PUNCT
ejpam-3449	345	9	\f	\f	PUNCT
ejpam-3449	345	10	contains	contain	VERB
ejpam-3449	345	11	a	a	DET
ejpam-3449	345	12	non	non	ADJ
ejpam-3449	345	13	-	-	ADJ
ejpam-3449	345	14	empty	empty	ADJ
ejpam-3449	345	15	fγ	fγ	NOUN
ejpam-3449	345	16	-	-	PUNCT
ejpam-3449	345	17	closed	close	VERB
ejpam-3449	345	18	set	set	NOUN
ejpam-3449	345	19	{	{	PUNCT
ejpam-3449	345	20	x	x	NOUN
ejpam-3449	345	21	}	}	PUNCT
ejpam-3449	345	22	.	.	PUNCT
ejpam-3449	346	1	a	a	DET
ejpam-3449	346	2	contradiction	contradiction	NOUN
ejpam-3449	346	3	since	since	SCONJ
ejpam-3449	346	4	f	f	PROPN
ejpam-3449	346	5	is	be	AUX
ejpam-3449	346	6	fγg.closed	fγg.close	VERB
ejpam-3449	346	7	set	set	VERB
ejpam-3449	346	8	and	and	CCONJ
ejpam-3449	346	9	according	accord	VERB
ejpam-3449	346	10	to	to	ADP
ejpam-3449	346	11	the	the	DET
ejpam-3449	346	12	theorem	theorem	NOUN
ejpam-3449	346	13	4.3	4.3	NUM
ejpam-3449	346	14	.	.	PUNCT
ejpam-3449	347	1	hence	hence	ADV
ejpam-3449	347	2	x	x	SYM
ejpam-3449	347	3	∈	∈	PROPN
ejpam-3449	347	4	f	f	X
ejpam-3449	347	5	.	.	PUNCT
ejpam-3449	348	1	this	this	PRON
ejpam-3449	348	2	follows	follow	VERB
ejpam-3449	348	3	that	that	DET
ejpam-3449	348	4	fclγ(f	fclγ(f	NOUN
ejpam-3449	348	5	)	)	PUNCT
ejpam-3449	348	6	⊆	⊆	NUM
ejpam-3449	348	7	f	f	NOUN
ejpam-3449	348	8	and	and	CCONJ
ejpam-3449	348	9	hence	hence	ADV
ejpam-3449	348	10	fclγ(f	fclγ(f	VERB
ejpam-3449	348	11	)	)	PUNCT
ejpam-3449	349	1	=	=	PUNCT
ejpam-3449	349	2	f	f	PROPN
ejpam-3449	349	3	.	.	PUNCT
ejpam-3449	350	1	this	this	PRON
ejpam-3449	350	2	means	mean	VERB
ejpam-3449	350	3	from	from	ADP
ejpam-3449	350	4	by	by	ADP
ejpam-3449	350	5	lemma	lemma	PROPN
ejpam-3449	350	6	3.13	3.13	NUM
ejpam-3449	350	7	(	(	PUNCT
ejpam-3449	350	8	4b	4b	PROPN
ejpam-3449	350	9	)	)	PUNCT
ejpam-3449	350	10	that	that	SCONJ
ejpam-3449	350	11	f	f	PROPN
ejpam-3449	350	12	is	be	AUX
ejpam-3449	350	13	fγ	fγ	ADV
ejpam-3449	350	14	-	-	PUNCT
ejpam-3449	350	15	closed	close	VERB
ejpam-3449	350	16	set	set	NOUN
ejpam-3449	350	17	in	in	ADP
ejpam-3449	350	18	(	(	PUNCT
ejpam-3449	350	19	x	x	NOUN
ejpam-3449	350	20	,	,	PUNCT
ejpam-3449	350	21	τ	τ	PROPN
ejpam-3449	350	22	,	,	PUNCT
ejpam-3449	350	23	τf	τf	NUM
ejpam-3449	350	24	)	)	PUNCT
ejpam-3449	350	25	.	.	PUNCT
ejpam-3449	351	1	thus	thus	ADV
ejpam-3449	351	2	(	(	PUNCT
ejpam-3449	351	3	x	x	X
ejpam-3449	351	4	,	,	PUNCT
ejpam-3449	351	5	τ	τ	PROPN
ejpam-3449	351	6	,	,	PUNCT
ejpam-3449	351	7	τf	τf	PROPN
ejpam-3449	351	8	)	)	PUNCT
ejpam-3449	351	9	is	be	AUX
ejpam-3449	351	10	fγ	fγ	PROPN
ejpam-3449	351	11	-	-	PUNCT
ejpam-3449	351	12	t	t	NOUN
ejpam-3449	351	13	1	1	NUM
ejpam-3449	351	14	2	2	NUM
ejpam-3449	351	15	space	space	NOUN
ejpam-3449	351	16	.	.	PUNCT
ejpam-3449	352	1	case	case	NOUN
ejpam-3449	352	2	(	(	PUNCT
ejpam-3449	352	3	2	2	NUM
ejpam-3449	352	4	):	):	PUNCT
ejpam-3449	352	5	if	if	SCONJ
ejpam-3449	352	6	{	{	PUNCT
ejpam-3449	352	7	x	x	NOUN
ejpam-3449	352	8	}	}	PUNCT
ejpam-3449	352	9	is	be	AUX
ejpam-3449	352	10	fγ	fγ	ADV
ejpam-3449	352	11	-	-	PUNCT
ejpam-3449	352	12	open	open	ADJ
ejpam-3449	352	13	set	set	NOUN
ejpam-3449	352	14	.	.	PUNCT
ejpam-3449	353	1	then	then	ADV
ejpam-3449	353	2	by	by	ADP
ejpam-3449	353	3	theorem	theorem	NOUN
ejpam-3449	353	4	3.12	3.12	NUM
ejpam-3449	353	5	,	,	PUNCT
ejpam-3449	353	6	f	f	PROPN
ejpam-3449	353	7	∩{x	∩{x	PROPN
ejpam-3449	353	8	}	}	PUNCT
ejpam-3449	353	9	6=	6=	NUM
ejpam-3449	353	10	φ	φ	NUM
ejpam-3449	353	11	which	which	PRON
ejpam-3449	353	12	implies	imply	VERB
ejpam-3449	353	13	that	that	SCONJ
ejpam-3449	353	14	x	x	SYM
ejpam-3449	353	15	∈	∈	PROPN
ejpam-3449	353	16	f	f	X
ejpam-3449	353	17	.	.	PUNCT
ejpam-3449	354	1	so	so	ADV
ejpam-3449	354	2	fclγ(f	fclγ(f	VERB
ejpam-3449	354	3	)	)	PUNCT
ejpam-3449	355	1	⊆	⊆	NUM
ejpam-3449	355	2	f	f	NOUN
ejpam-3449	355	3	.	.	PUNCT
ejpam-3449	356	1	thus	thus	ADV
ejpam-3449	356	2	by	by	ADP
ejpam-3449	356	3	lemma	lemma	PROPN
ejpam-3449	356	4	3.13	3.13	NUM
ejpam-3449	356	5	(	(	PUNCT
ejpam-3449	356	6	4b	4b	PROPN
ejpam-3449	356	7	)	)	PUNCT
ejpam-3449	356	8	,	,	PUNCT
ejpam-3449	356	9	f	f	PROPN
ejpam-3449	356	10	is	be	AUX
ejpam-3449	356	11	fγ	fγ	NOUN
ejpam-3449	356	12	-	-	PUNCT
ejpam-3449	356	13	closed	closed	ADJ
ejpam-3449	356	14	.	.	PUNCT
ejpam-3449	357	1	therefore	therefore	ADV
ejpam-3449	357	2	,	,	PUNCT
ejpam-3449	357	3	(	(	PUNCT
ejpam-3449	357	4	x	x	X
ejpam-3449	357	5	,	,	PUNCT
ejpam-3449	357	6	τ	τ	PROPN
ejpam-3449	357	7	,	,	PUNCT
ejpam-3449	357	8	τf	τf	PROPN
ejpam-3449	357	9	)	)	PUNCT
ejpam-3449	357	10	is	be	AUX
ejpam-3449	357	11	fγ	fγ	PROPN
ejpam-3449	357	12	-	-	PUNCT
ejpam-3449	357	13	t	t	NOUN
ejpam-3449	357	14	1	1	NUM
ejpam-3449	357	15	2	2	NUM
ejpam-3449	357	16	space	space	NOUN
ejpam-3449	357	17	.	.	PUNCT
ejpam-3449	358	1	theorem	theorem	VERB
ejpam-3449	358	2	5.6	5.6	NUM
ejpam-3449	358	3	.	.	PUNCT
ejpam-3449	359	1	for	for	ADP
ejpam-3449	359	2	any	any	DET
ejpam-3449	359	3	fine	fine	ADJ
ejpam-3449	359	4	space	space	NOUN
ejpam-3449	359	5	(	(	PUNCT
ejpam-3449	359	6	x	x	X
ejpam-3449	359	7	,	,	PUNCT
ejpam-3449	359	8	τ	τ	PROPN
ejpam-3449	359	9	,	,	PUNCT
ejpam-3449	359	10	τf	τf	NUM
ejpam-3449	359	11	)	)	PUNCT
ejpam-3449	359	12	with	with	ADP
ejpam-3449	359	13	an	an	DET
ejpam-3449	359	14	operation	operation	NOUN
ejpam-3449	359	15	γ	γ	NOUN
ejpam-3449	359	16	on	on	ADP
ejpam-3449	359	17	τf	τf	NUM
ejpam-3449	359	18	,	,	PUNCT
ejpam-3449	359	19	we	we	PRON
ejpam-3449	359	20	have	have	AUX
ejpam-3449	359	21	(	(	PUNCT
ejpam-3449	359	22	i	i	NOUN
ejpam-3449	359	23	)	)	PUNCT
ejpam-3449	359	24	let	let	VERB
ejpam-3449	359	25	γ	γ	NOUN
ejpam-3449	359	26	be	be	AUX
ejpam-3449	359	27	a	a	DET
ejpam-3449	359	28	fine	fine	ADJ
ejpam-3449	359	29	-	-	PUNCT
ejpam-3449	359	30	open	open	ADJ
ejpam-3449	359	31	operation	operation	NOUN
ejpam-3449	359	32	on	on	ADP
ejpam-3449	359	33	τf	τf	PROPN
ejpam-3449	359	34	.	.	PUNCT
ejpam-3449	360	1	then	then	ADV
ejpam-3449	360	2	a	a	DET
ejpam-3449	360	3	space	space	NOUN
ejpam-3449	360	4	x	x	PUNCT
ejpam-3449	360	5	is	be	AUX
ejpam-3449	360	6	a	a	DET
ejpam-3449	360	7	fγ	fγ	PROPN
ejpam-3449	360	8	-	-	PUNCT
ejpam-3449	360	9	t0	t0	NOUN
ejpam-3449	360	10	space	space	NOUN
ejpam-3449	360	11	if	if	SCONJ
ejpam-3449	360	12	and	and	CCONJ
ejpam-3449	360	13	only	only	ADV
ejpam-3449	360	14	if	if	SCONJ
ejpam-3449	360	15	fclγ({x	fclγ({x	PROPN
ejpam-3449	360	16	}	}	PUNCT
ejpam-3449	360	17	)	)	PUNCT
ejpam-3449	360	18	6=	6=	X
ejpam-3449	361	1	fclγ({y	fclγ({y	NOUN
ejpam-3449	361	2	}	}	PUNCT
ejpam-3449	361	3	)	)	PUNCT
ejpam-3449	361	4	,	,	PUNCT
ejpam-3449	361	5	for	for	ADP
ejpam-3449	361	6	every	every	DET
ejpam-3449	361	7	pair	pair	NOUN
ejpam-3449	361	8	x	x	X
ejpam-3449	361	9	,	,	PUNCT
ejpam-3449	361	10	y	y	PROPN
ejpam-3449	361	11	of	of	ADP
ejpam-3449	361	12	x	x	PUNCT
ejpam-3449	361	13	with	with	ADP
ejpam-3449	361	14	x	x	SYM
ejpam-3449	361	15	6=	6=	PROPN
ejpam-3449	361	16	y.	y.	PROPN
ejpam-3449	361	17	(	(	PUNCT
ejpam-3449	361	18	ii	ii	PROPN
ejpam-3449	361	19	)	)	PUNCT
ejpam-3449	361	20	a	a	DET
ejpam-3449	361	21	space	space	NOUN
ejpam-3449	361	22	x	x	PUNCT
ejpam-3449	361	23	is	be	AUX
ejpam-3449	361	24	fγ	fγ	PROPN
ejpam-3449	361	25	-	-	PUNCT
ejpam-3449	361	26	t	t	NOUN
ejpam-3449	361	27	∗0	∗0	PROPN
ejpam-3449	362	1	if	if	SCONJ
ejpam-3449	362	2	and	and	CCONJ
ejpam-3449	362	3	only	only	ADV
ejpam-3449	362	4	if	if	SCONJ
ejpam-3449	362	5	τfγ	τfγ	X
ejpam-3449	362	6	-	-	PUNCT
ejpam-3449	362	7	cl({x	cl({x	NOUN
ejpam-3449	362	8	}	}	PUNCT
ejpam-3449	362	9	)	)	PUNCT
ejpam-3449	362	10	6=	6=	X
ejpam-3449	362	11	τfγ	τfγ	NOUN
ejpam-3449	362	12	-	-	PUNCT
ejpam-3449	362	13	cl({y	cl({y	NOUN
ejpam-3449	362	14	}	}	PUNCT
ejpam-3449	362	15	)	)	PUNCT
ejpam-3449	362	16	,	,	PUNCT
ejpam-3449	362	17	for	for	ADP
ejpam-3449	362	18	every	every	DET
ejpam-3449	362	19	pair	pair	NOUN
ejpam-3449	362	20	of	of	ADP
ejpam-3449	362	21	distinct	distinct	ADJ
ejpam-3449	362	22	points	point	NOUN
ejpam-3449	362	23	x	x	X
ejpam-3449	362	24	,	,	PUNCT
ejpam-3449	362	25	y	y	PROPN
ejpam-3449	362	26	of	of	ADP
ejpam-3449	362	27	x.	x.	NOUN
ejpam-3449	362	28	proof	proof	NOUN
ejpam-3449	362	29	.	.	PUNCT
ejpam-3449	363	1	(	(	PUNCT
ejpam-3449	363	2	1	1	X
ejpam-3449	363	3	)	)	PUNCT
ejpam-3449	363	4	let	let	VERB
ejpam-3449	363	5	x	x	PRON
ejpam-3449	363	6	,	,	PUNCT
ejpam-3449	363	7	y	y	PROPN
ejpam-3449	363	8	be	be	VERB
ejpam-3449	363	9	any	any	DET
ejpam-3449	363	10	two	two	NUM
ejpam-3449	363	11	distinct	distinct	ADJ
ejpam-3449	363	12	points	point	NOUN
ejpam-3449	363	13	of	of	ADP
ejpam-3449	363	14	a	a	DET
ejpam-3449	363	15	fγ	fγ	PROPN
ejpam-3449	363	16	-	-	PUNCT
ejpam-3449	363	17	t0	t0	NOUN
ejpam-3449	363	18	space	space	NOUN
ejpam-3449	363	19	(	(	PUNCT
ejpam-3449	363	20	x	x	X
ejpam-3449	363	21	,	,	PUNCT
ejpam-3449	363	22	τ	τ	PROPN
ejpam-3449	363	23	,	,	PUNCT
ejpam-3449	363	24	τf	τf	NUM
ejpam-3449	363	25	)	)	PUNCT
ejpam-3449	363	26	.	.	PUNCT
ejpam-3449	364	1	then	then	ADV
ejpam-3449	364	2	by	by	ADP
ejpam-3449	364	3	definition	definition	NOUN
ejpam-3449	364	4	,	,	PUNCT
ejpam-3449	364	5	we	we	PRON
ejpam-3449	364	6	assume	assume	VERB
ejpam-3449	364	7	that	that	SCONJ
ejpam-3449	364	8	there	there	PRON
ejpam-3449	364	9	exists	exist	VERB
ejpam-3449	364	10	a	a	DET
ejpam-3449	364	11	fγ	fγ	ADV
ejpam-3449	364	12	-	-	PUNCT
ejpam-3449	364	13	open	open	NOUN
ejpam-3449	364	14	set	set	NOUN
ejpam-3449	364	15	u	u	PRON
ejpam-3449	364	16	such	such	ADJ
ejpam-3449	364	17	that	that	SCONJ
ejpam-3449	364	18	x	x	SYM
ejpam-3449	364	19	∈	∈	PROPN
ejpam-3449	364	20	u	u	NOUN
ejpam-3449	364	21	and	and	CCONJ
ejpam-3449	364	22	y	y	PROPN
ejpam-3449	364	23	/∈	/∈	PUNCT
ejpam-3449	364	24	γ(u	γ(u	PROPN
ejpam-3449	364	25	)	)	PUNCT
ejpam-3449	364	26	.	.	PUNCT
ejpam-3449	365	1	since	since	SCONJ
ejpam-3449	365	2	γ	γ	PROPN
ejpam-3449	365	3	is	be	AUX
ejpam-3449	365	4	a	a	DET
ejpam-3449	365	5	fine	fine	ADJ
ejpam-3449	365	6	-	-	PUNCT
ejpam-3449	365	7	open	open	ADJ
ejpam-3449	365	8	operation	operation	NOUN
ejpam-3449	365	9	on	on	ADP
ejpam-3449	365	10	τf	τf	PROPN
ejpam-3449	365	11	,	,	PUNCT
ejpam-3449	365	12	then	then	ADV
ejpam-3449	365	13	there	there	PRON
ejpam-3449	365	14	exists	exist	VERB
ejpam-3449	365	15	a	a	DET
ejpam-3449	365	16	fγ	fγ	ADV
ejpam-3449	365	17	-	-	PUNCT
ejpam-3449	365	18	open	open	NOUN
ejpam-3449	365	19	set	set	NOUN
ejpam-3449	365	20	w	w	ADP
ejpam-3449	365	21	such	such	ADJ
ejpam-3449	365	22	that	that	SCONJ
ejpam-3449	365	23	x	x	SYM
ejpam-3449	365	24	∈w	∈w	NOUN
ejpam-3449	365	25	and	and	CCONJ
ejpam-3449	365	26	w	w	ADP
ejpam-3449	365	27	⊆	⊆	NUM
ejpam-3449	365	28	γ(u	γ(u	NOUN
ejpam-3449	365	29	)	)	PUNCT
ejpam-3449	365	30	.	.	PUNCT
ejpam-3449	366	1	hence	hence	ADV
ejpam-3449	366	2	y	y	PROPN
ejpam-3449	366	3	∈	∈	PROPN
ejpam-3449	366	4	x\γ(u	x\γ(u	NOUN
ejpam-3449	366	5	)	)	PUNCT
ejpam-3449	367	1	⊆	⊆	NUM
ejpam-3449	367	2	x\w	x\w	X
ejpam-3449	367	3	.	.	PUNCT
ejpam-3449	368	1	since	since	SCONJ
ejpam-3449	368	2	x\w	x\w	PROPN
ejpam-3449	368	3	is	be	AUX
ejpam-3449	368	4	a	a	DET
ejpam-3449	368	5	fγ	fγ	ADV
ejpam-3449	368	6	-	-	PUNCT
ejpam-3449	368	7	closed	close	VERB
ejpam-3449	368	8	set	set	NOUN
ejpam-3449	368	9	in	in	ADP
ejpam-3449	368	10	(	(	PUNCT
ejpam-3449	368	11	x	x	NOUN
ejpam-3449	368	12	,	,	PUNCT
ejpam-3449	368	13	τ	τ	PROPN
ejpam-3449	368	14	,	,	PUNCT
ejpam-3449	368	15	τf	τf	NUM
ejpam-3449	368	16	)	)	PUNCT
ejpam-3449	368	17	.	.	PUNCT
ejpam-3449	369	1	then	then	ADV
ejpam-3449	369	2	we	we	PRON
ejpam-3449	369	3	obtain	obtain	VERB
ejpam-3449	369	4	that	that	PRON
ejpam-3449	369	5	fclγ({y	fclγ({y	NOUN
ejpam-3449	369	6	}	}	PUNCT
ejpam-3449	369	7	)	)	PUNCT
ejpam-3449	369	8	⊆	⊆	NUM
ejpam-3449	369	9	x\w	x\w	PROPN
ejpam-3449	369	10	and	and	CCONJ
ejpam-3449	369	11	therefore	therefore	ADV
ejpam-3449	369	12	fclγ({x	fclγ({x	PROPN
ejpam-3449	369	13	}	}	PUNCT
ejpam-3449	369	14	)	)	PUNCT
ejpam-3449	369	15	6=	6=	X
ejpam-3449	369	16	fclγ({y	fclγ({y	NOUN
ejpam-3449	369	17	}	}	PUNCT
ejpam-3449	369	18	)	)	PUNCT
ejpam-3449	369	19	.	.	PUNCT
ejpam-3449	370	1	conversely	conversely	ADV
ejpam-3449	370	2	,	,	PUNCT
ejpam-3449	370	3	suppose	suppose	VERB
ejpam-3449	370	4	for	for	ADP
ejpam-3449	370	5	any	any	DET
ejpam-3449	370	6	x	x	NOUN
ejpam-3449	370	7	,	,	PUNCT
ejpam-3449	370	8	y	y	PROPN
ejpam-3449	370	9	∈	∈	PROPN
ejpam-3449	370	10	x	x	PUNCT
ejpam-3449	370	11	with	with	ADP
ejpam-3449	370	12	x	x	SYM
ejpam-3449	370	13	6=	6=	PROPN
ejpam-3449	370	14	y	y	PROPN
ejpam-3449	370	15	,	,	PUNCT
ejpam-3449	370	16	we	we	PRON
ejpam-3449	370	17	have	have	VERB
ejpam-3449	370	18	fclγ({x	fclγ({x	NUM
ejpam-3449	370	19	}	}	PUNCT
ejpam-3449	370	20	)	)	PUNCT
ejpam-3449	370	21	6=	6=	X
ejpam-3449	371	1	fclγ({y	fclγ({y	NOUN
ejpam-3449	371	2	}	}	PUNCT
ejpam-3449	371	3	)	)	PUNCT
ejpam-3449	371	4	.	.	PUNCT
ejpam-3449	372	1	now	now	ADV
ejpam-3449	372	2	,	,	PUNCT
ejpam-3449	372	3	we	we	PRON
ejpam-3449	372	4	assume	assume	VERB
ejpam-3449	372	5	that	that	SCONJ
ejpam-3449	372	6	there	there	PRON
ejpam-3449	372	7	exists	exist	VERB
ejpam-3449	372	8	z	z	NOUN
ejpam-3449	372	9	∈	∈	PROPN
ejpam-3449	372	10	x	x	PUNCT
ejpam-3449	372	11	such	such	ADJ
ejpam-3449	372	12	that	that	SCONJ
ejpam-3449	372	13	z	z	PROPN
ejpam-3449	372	14	∈	∈	PROPN
ejpam-3449	372	15	fclγ({x	fclγ({x	PROPN
ejpam-3449	372	16	}	}	PUNCT
ejpam-3449	372	17	)	)	PUNCT
ejpam-3449	372	18	,	,	PUNCT
ejpam-3449	372	19	but	but	CCONJ
ejpam-3449	372	20	z	z	NOUN
ejpam-3449	372	21	/∈	/∈	PUNCT
ejpam-3449	373	1	fclγ({y	fclγ({y	NUM
ejpam-3449	373	2	}	}	PUNCT
ejpam-3449	373	3	)	)	PUNCT
ejpam-3449	373	4	.	.	PUNCT
ejpam-3449	374	1	if	if	SCONJ
ejpam-3449	374	2	x	x	PUNCT
ejpam-3449	374	3	∈	∈	PROPN
ejpam-3449	374	4	fclγ({y	fclγ({y	NOUN
ejpam-3449	374	5	}	}	PUNCT
ejpam-3449	374	6	)	)	PUNCT
ejpam-3449	374	7	,	,	PUNCT
ejpam-3449	374	8	then	then	ADV
ejpam-3449	374	9	{	{	PUNCT
ejpam-3449	374	10	x	x	NOUN
ejpam-3449	374	11	}	}	PUNCT
ejpam-3449	374	12	⊆	⊆	NUM
ejpam-3449	374	13	fclγ({y	fclγ({y	NOUN
ejpam-3449	374	14	}	}	PUNCT
ejpam-3449	374	15	)	)	PUNCT
ejpam-3449	374	16	,	,	PUNCT
ejpam-3449	374	17	which	which	PRON
ejpam-3449	374	18	implies	imply	VERB
ejpam-3449	374	19	that	that	SCONJ
ejpam-3449	374	20	fclγ({x	fclγ({x	PROPN
ejpam-3449	374	21	}	}	PUNCT
ejpam-3449	374	22	)	)	PUNCT
ejpam-3449	375	1	⊆	⊆	NUM
ejpam-3449	375	2	fclγ({y	fclγ({y	NOUN
ejpam-3449	375	3	}	}	PUNCT
ejpam-3449	375	4	)	)	PUNCT
ejpam-3449	375	5	(	(	PUNCT
ejpam-3449	375	6	by	by	ADP
ejpam-3449	375	7	lemma	lemma	PROPN
ejpam-3449	375	8	3.13	3.13	NUM
ejpam-3449	375	9	(	(	PUNCT
ejpam-3449	375	10	5	5	NUM
ejpam-3449	375	11	)	)	PUNCT
ejpam-3449	375	12	)	)	PUNCT
ejpam-3449	375	13	.	.	PUNCT
ejpam-3449	376	1	this	this	PRON
ejpam-3449	376	2	implies	imply	VERB
ejpam-3449	376	3	that	that	SCONJ
ejpam-3449	376	4	z	z	PROPN
ejpam-3449	376	5	∈	∈	PROPN
ejpam-3449	376	6	fclγ({y	fclγ({y	PROPN
ejpam-3449	376	7	}	}	PUNCT
ejpam-3449	376	8	)	)	PUNCT
ejpam-3449	376	9	.	.	PUNCT
ejpam-3449	377	1	this	this	DET
ejpam-3449	377	2	contradiction	contradiction	NOUN
ejpam-3449	377	3	shows	show	VERB
ejpam-3449	377	4	that	that	SCONJ
ejpam-3449	377	5	x	x	X
ejpam-3449	377	6	/∈	/∈	PUNCT
ejpam-3449	377	7	fclγ({y	fclγ({y	NUM
ejpam-3449	377	8	}	}	PUNCT
ejpam-3449	377	9	)	)	PUNCT
ejpam-3449	377	10	.	.	PUNCT
ejpam-3449	378	1	this	this	PRON
ejpam-3449	378	2	means	mean	VERB
ejpam-3449	378	3	that	that	SCONJ
ejpam-3449	378	4	by	by	ADP
ejpam-3449	378	5	definition	definition	NOUN
ejpam-3449	378	6	3.10	3.10	NUM
ejpam-3449	378	7	,	,	PUNCT
ejpam-3449	378	8	there	there	PRON
ejpam-3449	378	9	exists	exist	VERB
ejpam-3449	378	10	a	a	DET
ejpam-3449	378	11	fine	fine	ADV
ejpam-3449	378	12	-	-	PUNCT
ejpam-3449	378	13	open	open	NOUN
ejpam-3449	378	14	set	set	NOUN
ejpam-3449	378	15	u	u	PRON
ejpam-3449	378	16	such	such	ADJ
ejpam-3449	378	17	that	that	SCONJ
ejpam-3449	378	18	x	x	SYM
ejpam-3449	378	19	∈	∈	PROPN
ejpam-3449	378	20	u	u	NOUN
ejpam-3449	378	21	and	and	CCONJ
ejpam-3449	378	22	γ(u)∩{y	γ(u)∩{y	NOUN
ejpam-3449	378	23	}	}	PUNCT
ejpam-3449	378	24	=	=	SYM
ejpam-3449	378	25	φ	φ	PROPN
ejpam-3449	378	26	.	.	PUNCT
ejpam-3449	379	1	thus	thus	ADV
ejpam-3449	379	2	,	,	PUNCT
ejpam-3449	379	3	we	we	PRON
ejpam-3449	379	4	have	have	VERB
ejpam-3449	379	5	that	that	PRON
ejpam-3449	379	6	x	x	PUNCT
ejpam-3449	379	7	∈	∈	PROPN
ejpam-3449	379	8	u	u	NOUN
ejpam-3449	379	9	and	and	CCONJ
ejpam-3449	379	10	y	y	PROPN
ejpam-3449	379	11	/∈	/∈	PUNCT
ejpam-3449	379	12	γ(u	γ(u	PROPN
ejpam-3449	379	13	)	)	PUNCT
ejpam-3449	379	14	.	.	PUNCT
ejpam-3449	380	1	it	it	PRON
ejpam-3449	380	2	gives	give	VERB
ejpam-3449	380	3	that	that	SCONJ
ejpam-3449	380	4	the	the	DET
ejpam-3449	380	5	fine	fine	ADJ
ejpam-3449	380	6	space	space	NOUN
ejpam-3449	380	7	(	(	PUNCT
ejpam-3449	380	8	x	x	X
ejpam-3449	380	9	,	,	PUNCT
ejpam-3449	380	10	τ	τ	PROPN
ejpam-3449	380	11	,	,	PUNCT
ejpam-3449	380	12	τf	τf	PROPN
ejpam-3449	380	13	)	)	PUNCT
ejpam-3449	380	14	is	be	AUX
ejpam-3449	380	15	fγ	fγ	NOUN
ejpam-3449	380	16	-	-	PUNCT
ejpam-3449	380	17	t0	t0	NOUN
ejpam-3449	380	18	.	.	PUNCT
ejpam-3449	381	1	(	(	PUNCT
ejpam-3449	381	2	2	2	X
ejpam-3449	381	3	)	)	PUNCT
ejpam-3449	381	4	let	let	VERB
ejpam-3449	381	5	x	x	PRON
ejpam-3449	381	6	be	be	AUX
ejpam-3449	381	7	a	a	DET
ejpam-3449	381	8	fγ	fγ	PROPN
ejpam-3449	381	9	-	-	PUNCT
ejpam-3449	381	10	t	t	NOUN
ejpam-3449	381	11	∗0	∗0	NOUN
ejpam-3449	381	12	space	space	NOUN
ejpam-3449	381	13	and	and	CCONJ
ejpam-3449	381	14	x	x	NOUN
ejpam-3449	381	15	,	,	PUNCT
ejpam-3449	381	16	y	y	PROPN
ejpam-3449	381	17	be	be	VERB
ejpam-3449	381	18	any	any	DET
ejpam-3449	381	19	two	two	NUM
ejpam-3449	381	20	distinct	distinct	ADJ
ejpam-3449	381	21	points	point	NOUN
ejpam-3449	381	22	of	of	ADP
ejpam-3449	381	23	x.	x.	NOUN
ejpam-3449	381	24	then	then	ADV
ejpam-3449	381	25	there	there	PRON
ejpam-3449	381	26	exists	exist	VERB
ejpam-3449	381	27	a	a	DET
ejpam-3449	381	28	fγ	fγ	ADV
ejpam-3449	381	29	-	-	PUNCT
ejpam-3449	381	30	open	open	NOUN
ejpam-3449	381	31	set	set	NOUN
ejpam-3449	381	32	g	g	NOUN
ejpam-3449	381	33	containing	contain	VERB
ejpam-3449	381	34	x	x	PUNCT
ejpam-3449	381	35	or	or	CCONJ
ejpam-3449	381	36	y	y	PROPN
ejpam-3449	381	37	(	(	PUNCT
ejpam-3449	381	38	say	say	VERB
ejpam-3449	381	39	x	x	X
ejpam-3449	381	40	,	,	PUNCT
ejpam-3449	381	41	but	but	CCONJ
ejpam-3449	381	42	not	not	PART
ejpam-3449	381	43	y	y	NOUN
ejpam-3449	381	44	)	)	PUNCT
ejpam-3449	381	45	.	.	PUNCT
ejpam-3449	382	1	so	so	ADV
ejpam-3449	382	2	x\g	x\g	PROPN
ejpam-3449	382	3	is	be	AUX
ejpam-3449	382	4	a	a	DET
ejpam-3449	382	5	fγ	fγ	ADV
ejpam-3449	382	6	-	-	PUNCT
ejpam-3449	382	7	closed	close	VERB
ejpam-3449	382	8	set	set	NOUN
ejpam-3449	382	9	,	,	PUNCT
ejpam-3449	382	10	which	which	PRON
ejpam-3449	382	11	does	do	AUX
ejpam-3449	382	12	not	not	PART
ejpam-3449	382	13	contain	contain	VERB
ejpam-3449	382	14	x	x	PRON
ejpam-3449	382	15	,	,	PUNCT
ejpam-3449	382	16	but	but	CCONJ
ejpam-3449	382	17	contains	contain	VERB
ejpam-3449	382	18	y.	y.	NOUN
ejpam-3449	382	19	since	since	SCONJ
ejpam-3449	382	20	τfγ	τfγ	NOUN
ejpam-3449	382	21	-	-	PUNCT
ejpam-3449	382	22	cl({y	cl({y	NOUN
ejpam-3449	382	23	}	}	PUNCT
ejpam-3449	382	24	)	)	PUNCT
ejpam-3449	382	25	is	be	AUX
ejpam-3449	382	26	the	the	DET
ejpam-3449	382	27	smallest	small	ADJ
ejpam-3449	382	28	fγ	fγ	NOUN
ejpam-3449	382	29	-	-	PUNCT
ejpam-3449	382	30	closed	close	VERB
ejpam-3449	382	31	set	set	NOUN
ejpam-3449	382	32	containing	contain	VERB
ejpam-3449	382	33	y	y	PROPN
ejpam-3449	382	34	,	,	PUNCT
ejpam-3449	382	35	τfγ	τfγ	NOUN
ejpam-3449	382	36	-	-	PUNCT
ejpam-3449	382	37	cl({y	cl({y	NOUN
ejpam-3449	382	38	}	}	PUNCT
ejpam-3449	382	39	)	)	PUNCT
ejpam-3449	383	1	⊆	⊆	NUM
ejpam-3449	383	2	x\g	x\g	NOUN
ejpam-3449	383	3	,	,	PUNCT
ejpam-3449	383	4	and	and	CCONJ
ejpam-3449	383	5	so	so	ADV
ejpam-3449	383	6	x	x	X
ejpam-3449	383	7	/∈	/∈	PUNCT
ejpam-3449	383	8	τfγ	τfγ	NOUN
ejpam-3449	383	9	-	-	PUNCT
ejpam-3449	383	10	cl({y	cl({y	NOUN
ejpam-3449	383	11	}	}	PUNCT
ejpam-3449	383	12	)	)	PUNCT
ejpam-3449	383	13	.	.	PUNCT
ejpam-3449	384	1	therefore	therefore	ADV
ejpam-3449	384	2	,	,	PUNCT
ejpam-3449	384	3	τfγ	τfγ	X
ejpam-3449	384	4	-	-	PUNCT
ejpam-3449	384	5	cl({x	cl({x	NOUN
ejpam-3449	384	6	}	}	PUNCT
ejpam-3449	384	7	)	)	PUNCT
ejpam-3449	384	8	6=	6=	X
ejpam-3449	384	9	τfγ	τfγ	NOUN
ejpam-3449	384	10	-	-	PUNCT
ejpam-3449	384	11	cl({y	cl({y	NOUN
ejpam-3449	384	12	}	}	PUNCT
ejpam-3449	384	13	)	)	PUNCT
ejpam-3449	384	14	.	.	PUNCT
ejpam-3449	385	1	conversely	conversely	ADV
ejpam-3449	385	2	,	,	PUNCT
ejpam-3449	385	3	suppose	suppose	VERB
ejpam-3449	385	4	for	for	ADP
ejpam-3449	385	5	any	any	DET
ejpam-3449	385	6	x	x	NOUN
ejpam-3449	385	7	,	,	PUNCT
ejpam-3449	385	8	y	y	PROPN
ejpam-3449	385	9	∈	∈	PROPN
ejpam-3449	385	10	x	x	PUNCT
ejpam-3449	385	11	with	with	ADP
ejpam-3449	385	12	x	x	SYM
ejpam-3449	385	13	6=	6=	PROPN
ejpam-3449	385	14	y	y	PROPN
ejpam-3449	385	15	,	,	PUNCT
ejpam-3449	385	16	τfγ	τfγ	NOUN
ejpam-3449	385	17	-	-	PUNCT
ejpam-3449	385	18	cl({x	cl({x	NOUN
ejpam-3449	385	19	}	}	PUNCT
ejpam-3449	385	20	)	)	PUNCT
ejpam-3449	385	21	6=	6=	X
ejpam-3449	385	22	τfγ	τfγ	NOUN
ejpam-3449	385	23	-	-	PUNCT
ejpam-3449	385	24	cl({y	cl({y	NOUN
ejpam-3449	385	25	}	}	PUNCT
ejpam-3449	385	26	)	)	PUNCT
ejpam-3449	385	27	.	.	PUNCT
ejpam-3449	386	1	now	now	ADV
ejpam-3449	386	2	,	,	PUNCT
ejpam-3449	386	3	let	let	VERB
ejpam-3449	386	4	z	z	NOUN
ejpam-3449	386	5	∈	∈	PROPN
ejpam-3449	386	6	x	x	PUNCT
ejpam-3449	386	7	such	such	ADJ
ejpam-3449	386	8	that	that	SCONJ
ejpam-3449	386	9	z	z	NOUN
ejpam-3449	386	10	∈	∈	PROPN
ejpam-3449	386	11	τfγ	τfγ	PROPN
ejpam-3449	386	12	-	-	PUNCT
ejpam-3449	386	13	cl({x	cl({x	NOUN
ejpam-3449	386	14	}	}	PUNCT
ejpam-3449	386	15	)	)	PUNCT
ejpam-3449	386	16	,	,	PUNCT
ejpam-3449	386	17	but	but	CCONJ
ejpam-3449	386	18	z	z	NOUN
ejpam-3449	386	19	/∈	/∈	PUNCT
ejpam-3449	386	20	τfγ	τfγ	NOUN
ejpam-3449	386	21	-	-	PUNCT
ejpam-3449	386	22	cl({y	cl({y	NOUN
ejpam-3449	386	23	}	}	PUNCT
ejpam-3449	386	24	)	)	PUNCT
ejpam-3449	386	25	.	.	PUNCT
ejpam-3449	387	1	now	now	ADV
ejpam-3449	387	2	,	,	PUNCT
ejpam-3449	387	3	we	we	PRON
ejpam-3449	387	4	claim	claim	VERB
ejpam-3449	387	5	that	that	SCONJ
ejpam-3449	387	6	x	x	PUNCT
ejpam-3449	387	7	∈	∈	PROPN
ejpam-3449	387	8	τfγ	τfγ	NOUN
ejpam-3449	387	9	-	-	PUNCT
ejpam-3449	387	10	cl({y	cl({y	NOUN
ejpam-3449	387	11	}	}	PUNCT
ejpam-3449	387	12	)	)	PUNCT
ejpam-3449	387	13	.	.	PUNCT
ejpam-3449	388	1	for	for	ADP
ejpam-3449	388	2	,	,	PUNCT
ejpam-3449	388	3	if	if	SCONJ
ejpam-3449	388	4	x	x	X
ejpam-3449	388	5	∈	∈	PROPN
ejpam-3449	388	6	τfγ	τfγ	NOUN
ejpam-3449	388	7	-	-	PUNCT
ejpam-3449	388	8	cl({y	cl({y	NOUN
ejpam-3449	388	9	}	}	PUNCT
ejpam-3449	388	10	)	)	PUNCT
ejpam-3449	388	11	,	,	PUNCT
ejpam-3449	388	12	then	then	ADV
ejpam-3449	388	13	{	{	PUNCT
ejpam-3449	388	14	x	x	NOUN
ejpam-3449	388	15	}	}	PUNCT
ejpam-3449	388	16	⊆	⊆	NUM
ejpam-3449	388	17	τfγ	τfγ	NOUN
ejpam-3449	388	18	-	-	PUNCT
ejpam-3449	388	19	cl({y	cl({y	NOUN
ejpam-3449	388	20	}	}	PUNCT
ejpam-3449	388	21	)	)	PUNCT
ejpam-3449	388	22	,	,	PUNCT
ejpam-3449	388	23	which	which	PRON
ejpam-3449	388	24	implies	imply	VERB
ejpam-3449	388	25	that	that	SCONJ
ejpam-3449	388	26	τfγ	τfγ	VERB
ejpam-3449	388	27	-	-	PUNCT
ejpam-3449	388	28	cl({x	cl({x	NOUN
ejpam-3449	388	29	}	}	PUNCT
ejpam-3449	388	30	)	)	PUNCT
ejpam-3449	388	31	⊆	⊆	NUM
ejpam-3449	388	32	τfγcl({y	τfγcl({y	X
ejpam-3449	388	33	}	}	PUNCT
ejpam-3449	388	34	)	)	PUNCT
ejpam-3449	388	35	.	.	PUNCT
ejpam-3449	389	1	this	this	PRON
ejpam-3449	389	2	is	be	AUX
ejpam-3449	389	3	a	a	DET
ejpam-3449	389	4	contradiction	contradiction	NOUN
ejpam-3449	389	5	to	to	ADP
ejpam-3449	389	6	the	the	DET
ejpam-3449	389	7	fact	fact	NOUN
ejpam-3449	390	1	that	that	SCONJ
ejpam-3449	390	2	z	z	NOUN
ejpam-3449	390	3	/∈	/∈	PUNCT
ejpam-3449	390	4	τfγ	τfγ	NOUN
ejpam-3449	390	5	-	-	PUNCT
ejpam-3449	390	6	cl({y	cl({y	NOUN
ejpam-3449	390	7	}	}	PUNCT
ejpam-3449	390	8	)	)	PUNCT
ejpam-3449	390	9	.	.	PUNCT
ejpam-3449	391	1	hence	hence	ADV
ejpam-3449	391	2	x	x	PUNCT
ejpam-3449	391	3	belongs	belong	VERB
ejpam-3449	391	4	to	to	ADP
ejpam-3449	391	5	the	the	DET
ejpam-3449	391	6	fγ	fγ	ADV
ejpam-3449	391	7	-	-	PUNCT
ejpam-3449	391	8	open	open	NOUN
ejpam-3449	391	9	set	set	ADJ
ejpam-3449	391	10	x\τfγ	x\τfγ	PROPN
ejpam-3449	391	11	-	-	PUNCT
ejpam-3449	391	12	cl({y	cl({y	X
ejpam-3449	391	13	}	}	PUNCT
ejpam-3449	391	14	)	)	PUNCT
ejpam-3449	391	15	to	to	PART
ejpam-3449	391	16	which	which	PRON
ejpam-3449	391	17	y	y	PROPN
ejpam-3449	391	18	does	do	AUX
ejpam-3449	391	19	not	not	PART
ejpam-3449	391	20	belong	belong	VERB
ejpam-3449	391	21	.	.	PUNCT
ejpam-3449	392	1	it	it	PRON
ejpam-3449	392	2	gives	give	VERB
ejpam-3449	392	3	that	that	PRON
ejpam-3449	392	4	x	x	PRON
ejpam-3449	392	5	is	be	AUX
ejpam-3449	392	6	fγ	fγ	PROPN
ejpam-3449	392	7	-	-	PUNCT
ejpam-3449	392	8	t	t	NOUN
ejpam-3449	392	9	∗0	∗0	PROPN
ejpam-3449	392	10	space	space	NOUN
ejpam-3449	392	11	.	.	PUNCT
ejpam-3449	393	1	corollary	corollary	ADJ
ejpam-3449	393	2	5.7	5.7	NUM
ejpam-3449	393	3	.	.	PUNCT
ejpam-3449	393	4	suppose	suppose	VERB
ejpam-3449	393	5	that	that	SCONJ
ejpam-3449	393	6	γ	γ	PROPN
ejpam-3449	393	7	is	be	AUX
ejpam-3449	393	8	a	a	DET
ejpam-3449	393	9	fine	fine	ADJ
ejpam-3449	393	10	-	-	PUNCT
ejpam-3449	393	11	open	open	ADJ
ejpam-3449	393	12	operation	operation	NOUN
ejpam-3449	393	13	on	on	ADP
ejpam-3449	393	14	τf	τf	PROPN
ejpam-3449	393	15	.	.	PUNCT
ejpam-3449	394	1	a	a	DET
ejpam-3449	394	2	fine	fine	ADJ
ejpam-3449	394	3	space	space	NOUN
ejpam-3449	394	4	(	(	PUNCT
ejpam-3449	394	5	x	x	X
ejpam-3449	394	6	,	,	PUNCT
ejpam-3449	394	7	τ	τ	PROPN
ejpam-3449	394	8	,	,	PUNCT
ejpam-3449	394	9	τf	τf	PROPN
ejpam-3449	394	10	)	)	PUNCT
ejpam-3449	394	11	is	be	AUX
ejpam-3449	394	12	fγ	fγ	NOUN
ejpam-3449	394	13	-	-	PUNCT
ejpam-3449	394	14	t0	t0	NOUN
ejpam-3449	394	15	if	if	SCONJ
ejpam-3449	394	16	and	and	CCONJ
ejpam-3449	394	17	only	only	ADV
ejpam-3449	394	18	if	if	SCONJ
ejpam-3449	394	19	(	(	PUNCT
ejpam-3449	394	20	x	x	NOUN
ejpam-3449	394	21	,	,	PUNCT
ejpam-3449	394	22	τ	τ	PROPN
ejpam-3449	394	23	,	,	PUNCT
ejpam-3449	394	24	τf	τf	PROPN
ejpam-3449	394	25	)	)	PUNCT
ejpam-3449	394	26	is	be	AUX
ejpam-3449	394	27	fγ	fγ	PROPN
ejpam-3449	394	28	-	-	PUNCT
ejpam-3449	394	29	t	t	NOUN
ejpam-3449	394	30	∗0	∗0	PROPN
ejpam-3449	394	31	.	.	PUNCT
ejpam-3449	395	1	b.	b.	PROPN
ejpam-3449	395	2	a.	a.	PROPN
ejpam-3449	395	3	asaad	asaad	PROPN
ejpam-3449	395	4	et	et	PROPN
ejpam-3449	395	5	al	al	PROPN
ejpam-3449	395	6	.	.	PUNCT
ejpam-3449	395	7	/	/	SYM
ejpam-3449	395	8	eur	eur	PROPN
ejpam-3449	395	9	.	.	PUNCT
ejpam-3449	396	1	j.	j.	PROPN
ejpam-3449	396	2	pure	pure	PROPN
ejpam-3449	396	3	appl	appl	PROPN
ejpam-3449	396	4	.	.	PROPN
ejpam-3449	396	5	math	math	PROPN
ejpam-3449	396	6	,	,	PUNCT
ejpam-3449	396	7	12	12	NUM
ejpam-3449	396	8	(	(	PUNCT
ejpam-3449	396	9	3	3	NUM
ejpam-3449	396	10	)	)	PUNCT
ejpam-3449	396	11	(	(	PUNCT
ejpam-3449	396	12	2019	2019	NUM
ejpam-3449	396	13	)	)	PUNCT
ejpam-3449	396	14	,	,	PUNCT
ejpam-3449	396	15	960	960	NUM
ejpam-3449	396	16	-	-	SYM
ejpam-3449	396	17	977	977	NUM
ejpam-3449	396	18	970	970	NUM
ejpam-3449	396	19	proof	proof	NOUN
ejpam-3449	396	20	.	.	PUNCT
ejpam-3449	397	1	this	this	PRON
ejpam-3449	397	2	follows	follow	VERB
ejpam-3449	397	3	from	from	ADP
ejpam-3449	397	4	theorem	theorem	ADJ
ejpam-3449	397	5	5.6	5.6	NUM
ejpam-3449	397	6	and	and	CCONJ
ejpam-3449	397	7	the	the	DET
ejpam-3449	397	8	fact	fact	NOUN
ejpam-3449	397	9	that	that	SCONJ
ejpam-3449	397	10	fclγ(a	fclγ(a	NOUN
ejpam-3449	397	11	)	)	PUNCT
ejpam-3449	397	12	=	=	SYM
ejpam-3449	397	13	τfγ	τfγ	NOUN
ejpam-3449	397	14	-	-	PUNCT
ejpam-3449	397	15	cl(a	cl(a	NUM
ejpam-3449	397	16	)	)	PUNCT
ejpam-3449	397	17	for	for	ADP
ejpam-3449	397	18	anya	anya	PROPN
ejpam-3449	397	19	⊆	⊆	NUM
ejpam-3449	397	20	x	x	NOUN
ejpam-3449	397	21	holds	hold	VERB
ejpam-3449	397	22	under	under	ADP
ejpam-3449	397	23	the	the	DET
ejpam-3449	397	24	assumption	assumption	NOUN
ejpam-3449	397	25	that	that	SCONJ
ejpam-3449	397	26	γ	γ	PROPN
ejpam-3449	397	27	is	be	AUX
ejpam-3449	397	28	a	a	DET
ejpam-3449	397	29	fine	fine	ADJ
ejpam-3449	397	30	-	-	PUNCT
ejpam-3449	397	31	open	open	ADJ
ejpam-3449	397	32	operation	operation	NOUN
ejpam-3449	397	33	on	on	ADP
ejpam-3449	397	34	τf	τf	PROPN
ejpam-3449	397	35	(	(	PUNCT
ejpam-3449	397	36	see	see	VERB
ejpam-3449	397	37	theorem	theorem	NOUN
ejpam-3449	397	38	3.15	3.15	NUM
ejpam-3449	397	39	)	)	PUNCT
ejpam-3449	397	40	.	.	PUNCT
ejpam-3449	398	1	theorem	theorem	VERB
ejpam-3449	398	2	5.8	5.8	NUM
ejpam-3449	398	3	.	.	PUNCT
ejpam-3449	399	1	for	for	ADP
ejpam-3449	399	2	a	a	DET
ejpam-3449	399	3	fine	fine	ADJ
ejpam-3449	399	4	space	space	NOUN
ejpam-3449	399	5	(	(	PUNCT
ejpam-3449	399	6	x	x	X
ejpam-3449	399	7	,	,	PUNCT
ejpam-3449	399	8	τ	τ	PROPN
ejpam-3449	399	9	,	,	PUNCT
ejpam-3449	399	10	τf	τf	NUM
ejpam-3449	399	11	)	)	PUNCT
ejpam-3449	399	12	with	with	ADP
ejpam-3449	399	13	an	an	DET
ejpam-3449	399	14	operation	operation	NOUN
ejpam-3449	399	15	γ	γ	NOUN
ejpam-3449	399	16	on	on	ADP
ejpam-3449	399	17	τf	τf	PROPN
ejpam-3449	399	18	.	.	PUNCT
ejpam-3449	400	1	then	then	ADV
ejpam-3449	400	2	the	the	DET
ejpam-3449	400	3	following	follow	VERB
ejpam-3449	400	4	statements	statement	NOUN
ejpam-3449	400	5	are	be	AUX
ejpam-3449	400	6	true	true	ADJ
ejpam-3449	400	7	:	:	PUNCT
ejpam-3449	400	8	(	(	PUNCT
ejpam-3449	400	9	i	i	NOUN
ejpam-3449	400	10	)	)	PUNCT
ejpam-3449	400	11	(	(	PUNCT
ejpam-3449	400	12	x	x	X
ejpam-3449	400	13	,	,	PUNCT
ejpam-3449	400	14	τ	τ	PROPN
ejpam-3449	400	15	,	,	PUNCT
ejpam-3449	400	16	τf	τf	PROPN
ejpam-3449	400	17	)	)	PUNCT
ejpam-3449	400	18	is	be	AUX
ejpam-3449	400	19	fγ	fγ	PROPN
ejpam-3449	400	20	-	-	PUNCT
ejpam-3449	400	21	t1	t1	NOUN
ejpam-3449	400	22	.	.	PUNCT
ejpam-3449	401	1	(	(	PUNCT
ejpam-3449	401	2	ii	ii	NOUN
ejpam-3449	401	3	)	)	PUNCT
ejpam-3449	401	4	for	for	ADP
ejpam-3449	401	5	every	every	DET
ejpam-3449	401	6	point	point	NOUN
ejpam-3449	401	7	x	x	X
ejpam-3449	401	8	∈	∈	NOUN
ejpam-3449	401	9	x	x	NOUN
ejpam-3449	401	10	,	,	PUNCT
ejpam-3449	401	11	the	the	DET
ejpam-3449	401	12	set	set	NOUN
ejpam-3449	401	13	{	{	PUNCT
ejpam-3449	401	14	x	x	NOUN
ejpam-3449	401	15	}	}	PUNCT
ejpam-3449	401	16	is	be	AUX
ejpam-3449	401	17	fγ	fγ	ADV
ejpam-3449	401	18	-	-	PUNCT
ejpam-3449	401	19	closed	closed	ADJ
ejpam-3449	401	20	.	.	PUNCT
ejpam-3449	402	1	(	(	PUNCT
ejpam-3449	402	2	iii	iii	X
ejpam-3449	402	3	)	)	PUNCT
ejpam-3449	402	4	(	(	PUNCT
ejpam-3449	402	5	x	x	X
ejpam-3449	402	6	,	,	PUNCT
ejpam-3449	402	7	τ	τ	PROPN
ejpam-3449	402	8	,	,	PUNCT
ejpam-3449	402	9	τf	τf	PROPN
ejpam-3449	402	10	)	)	PUNCT
ejpam-3449	402	11	is	be	AUX
ejpam-3449	402	12	fγ	fγ	PROPN
ejpam-3449	402	13	-	-	PUNCT
ejpam-3449	402	14	t	t	NOUN
ejpam-3449	402	15	∗1	∗1	PROPN
ejpam-3449	402	16	.	.	PUNCT
ejpam-3449	403	1	proof	proof	NOUN
ejpam-3449	403	2	.	.	PUNCT
ejpam-3449	404	1	(	(	PUNCT
ejpam-3449	404	2	1	1	X
ejpam-3449	404	3	)	)	PUNCT
ejpam-3449	404	4	⇒	⇒	NOUN
ejpam-3449	404	5	(	(	PUNCT
ejpam-3449	404	6	2	2	X
ejpam-3449	404	7	)	)	PUNCT
ejpam-3449	404	8	let	let	VERB
ejpam-3449	404	9	x	x	PRON
ejpam-3449	404	10	be	be	AUX
ejpam-3449	404	11	a	a	DET
ejpam-3449	404	12	point	point	NOUN
ejpam-3449	404	13	of	of	ADP
ejpam-3449	404	14	an	an	DET
ejpam-3449	404	15	fγ	fγ	PROPN
ejpam-3449	404	16	-	-	PUNCT
ejpam-3449	404	17	t1	t1	NOUN
ejpam-3449	404	18	space	space	NOUN
ejpam-3449	404	19	(	(	PUNCT
ejpam-3449	404	20	x	x	X
ejpam-3449	404	21	,	,	PUNCT
ejpam-3449	404	22	τ	τ	PROPN
ejpam-3449	404	23	,	,	PUNCT
ejpam-3449	404	24	τf	τf	NUM
ejpam-3449	404	25	)	)	PUNCT
ejpam-3449	404	26	.	.	PUNCT
ejpam-3449	405	1	then	then	ADV
ejpam-3449	405	2	for	for	ADP
ejpam-3449	405	3	any	any	DET
ejpam-3449	405	4	point	point	NOUN
ejpam-3449	405	5	y	y	PROPN
ejpam-3449	405	6	∈	∈	PROPN
ejpam-3449	405	7	x	x	PUNCT
ejpam-3449	405	8	such	such	ADJ
ejpam-3449	405	9	that	that	SCONJ
ejpam-3449	405	10	x	x	PROPN
ejpam-3449	405	11	6=	6=	NUM
ejpam-3449	405	12	y	y	PROPN
ejpam-3449	405	13	,	,	PUNCT
ejpam-3449	405	14	there	there	PRON
ejpam-3449	405	15	exists	exist	VERB
ejpam-3449	405	16	a	a	DET
ejpam-3449	405	17	fine	fine	ADV
ejpam-3449	405	18	-	-	PUNCT
ejpam-3449	405	19	open	open	ADJ
ejpam-3449	405	20	set	set	NOUN
ejpam-3449	405	21	vy	vy	NOUN
ejpam-3449	405	22	such	such	ADJ
ejpam-3449	405	23	that	that	SCONJ
ejpam-3449	405	24	y	y	PROPN
ejpam-3449	405	25	∈	∈	PROPN
ejpam-3449	405	26	vy	vy	NOUN
ejpam-3449	405	27	but	but	CCONJ
ejpam-3449	405	28	x	x	X
ejpam-3449	405	29	/∈	/∈	PUNCT
ejpam-3449	405	30	γ(vy	γ(vy	ADJ
ejpam-3449	405	31	)	)	PUNCT
ejpam-3449	405	32	.	.	PUNCT
ejpam-3449	406	1	thus	thus	ADV
ejpam-3449	406	2	,	,	PUNCT
ejpam-3449	406	3	y	y	PROPN
ejpam-3449	406	4	∈	∈	PROPN
ejpam-3449	406	5	γ(vy	γ(vy	ADV
ejpam-3449	406	6	)	)	PUNCT
ejpam-3449	406	7	⊆	⊆	NUM
ejpam-3449	406	8	x\{x	x\{x	NUM
ejpam-3449	406	9	}	}	PUNCT
ejpam-3449	406	10	.	.	PUNCT
ejpam-3449	407	1	this	this	PRON
ejpam-3449	407	2	implies	imply	VERB
ejpam-3449	407	3	that	that	SCONJ
ejpam-3449	407	4	x\{x	x\{x	PROPN
ejpam-3449	407	5	}	}	PUNCT
ejpam-3449	407	6	=	=	PUNCT
ejpam-3449	407	7	∪{γ(vy	∪{γ(vy	NUM
ejpam-3449	407	8	)	)	PUNCT
ejpam-3449	407	9	:	:	PUNCT
ejpam-3449	408	1	y	y	PROPN
ejpam-3449	408	2	∈	∈	PROPN
ejpam-3449	408	3	x\{x	x\{x	PROPN
ejpam-3449	408	4	}	}	PUNCT
ejpam-3449	408	5	}	}	PUNCT
ejpam-3449	408	6	.	.	PUNCT
ejpam-3449	409	1	it	it	PRON
ejpam-3449	409	2	is	be	AUX
ejpam-3449	409	3	shown	show	VERB
ejpam-3449	409	4	that	that	SCONJ
ejpam-3449	409	5	x\{x	x\{x	NOUN
ejpam-3449	409	6	}	}	PUNCT
ejpam-3449	409	7	is	be	AUX
ejpam-3449	409	8	fγ	fγ	ADV
ejpam-3449	409	9	-	-	PUNCT
ejpam-3449	409	10	open	open	NOUN
ejpam-3449	409	11	set	set	NOUN
ejpam-3449	409	12	in	in	ADP
ejpam-3449	409	13	(	(	PUNCT
ejpam-3449	409	14	x	x	NOUN
ejpam-3449	409	15	,	,	PUNCT
ejpam-3449	409	16	τ	τ	PROPN
ejpam-3449	409	17	,	,	PUNCT
ejpam-3449	409	18	τf	τf	NUM
ejpam-3449	409	19	)	)	PUNCT
ejpam-3449	409	20	.	.	PUNCT
ejpam-3449	410	1	hence	hence	ADV
ejpam-3449	410	2	{	{	PUNCT
ejpam-3449	410	3	x	x	X
ejpam-3449	410	4	}	}	PUNCT
ejpam-3449	410	5	is	be	AUX
ejpam-3449	410	6	fγ	fγ	ADV
ejpam-3449	410	7	-	-	PUNCT
ejpam-3449	410	8	closed	close	VERB
ejpam-3449	410	9	set	set	NOUN
ejpam-3449	410	10	in	in	ADP
ejpam-3449	410	11	(	(	PUNCT
ejpam-3449	410	12	x	x	NOUN
ejpam-3449	410	13	,	,	PUNCT
ejpam-3449	410	14	τ	τ	PROPN
ejpam-3449	410	15	,	,	PUNCT
ejpam-3449	410	16	τf	τf	NUM
ejpam-3449	410	17	)	)	PUNCT
ejpam-3449	410	18	.	.	PUNCT
ejpam-3449	411	1	(	(	PUNCT
ejpam-3449	411	2	2	2	X
ejpam-3449	411	3	)	)	PUNCT
ejpam-3449	411	4	⇒	⇒	NOUN
ejpam-3449	411	5	(	(	PUNCT
ejpam-3449	411	6	3	3	X
ejpam-3449	411	7	)	)	PUNCT
ejpam-3449	411	8	suppose	suppose	VERB
ejpam-3449	411	9	every	every	DET
ejpam-3449	411	10	singleton	singleton	NOUN
ejpam-3449	411	11	set	set	VERB
ejpam-3449	411	12	in	in	ADP
ejpam-3449	411	13	x	x	PROPN
ejpam-3449	411	14	is	be	AUX
ejpam-3449	411	15	fγ	fγ	ADV
ejpam-3449	411	16	-	-	PUNCT
ejpam-3449	411	17	closed	closed	ADJ
ejpam-3449	411	18	.	.	PUNCT
ejpam-3449	412	1	let	let	VERB
ejpam-3449	412	2	x	x	PRON
ejpam-3449	412	3	,	,	PUNCT
ejpam-3449	412	4	y	y	PROPN
ejpam-3449	412	5	∈	∈	PROPN
ejpam-3449	412	6	x	x	PUNCT
ejpam-3449	412	7	such	such	ADJ
ejpam-3449	412	8	that	that	SCONJ
ejpam-3449	412	9	x	x	PRON
ejpam-3449	412	10	6=	6=	ADP
ejpam-3449	412	11	y.	y.	NOUN
ejpam-3449	412	12	this	this	PRON
ejpam-3449	412	13	implies	imply	VERB
ejpam-3449	412	14	that	that	SCONJ
ejpam-3449	412	15	x	x	SYM
ejpam-3449	412	16	∈	∈	PROPN
ejpam-3449	412	17	x\{y	x\{y	PROPN
ejpam-3449	412	18	}	}	PUNCT
ejpam-3449	412	19	.	.	PUNCT
ejpam-3449	413	1	by	by	ADP
ejpam-3449	413	2	hypothesis	hypothesis	NOUN
ejpam-3449	413	3	,	,	PUNCT
ejpam-3449	413	4	we	we	PRON
ejpam-3449	413	5	get	get	VERB
ejpam-3449	413	6	x\{y	x\{y	VERB
ejpam-3449	413	7	}	}	PUNCT
ejpam-3449	413	8	is	be	AUX
ejpam-3449	413	9	a	a	DET
ejpam-3449	413	10	fγ	fγ	ADV
ejpam-3449	413	11	-	-	PUNCT
ejpam-3449	413	12	open	open	ADJ
ejpam-3449	413	13	set	set	NOUN
ejpam-3449	413	14	contains	contain	VERB
ejpam-3449	413	15	x	x	PUNCT
ejpam-3449	413	16	but	but	CCONJ
ejpam-3449	413	17	not	not	PART
ejpam-3449	413	18	y.	y.	NOUN
ejpam-3449	413	19	similarly	similarly	ADV
ejpam-3449	413	20	x\{x	x\{x	X
ejpam-3449	413	21	}	}	PUNCT
ejpam-3449	413	22	is	be	AUX
ejpam-3449	413	23	a	a	DET
ejpam-3449	413	24	fγ	fγ	ADV
ejpam-3449	413	25	-	-	PUNCT
ejpam-3449	413	26	open	open	ADJ
ejpam-3449	413	27	set	set	NOUN
ejpam-3449	413	28	contains	contain	VERB
ejpam-3449	413	29	y	y	PROPN
ejpam-3449	413	30	but	but	CCONJ
ejpam-3449	413	31	not	not	PART
ejpam-3449	413	32	x.	x.	NOUN
ejpam-3449	413	33	therefore	therefore	ADV
ejpam-3449	413	34	,	,	PUNCT
ejpam-3449	413	35	x	x	X
ejpam-3449	413	36	is	be	AUX
ejpam-3449	413	37	fγ	fγ	PROPN
ejpam-3449	413	38	-	-	PUNCT
ejpam-3449	413	39	t	t	NOUN
ejpam-3449	413	40	∗1	∗1	PROPN
ejpam-3449	413	41	space	space	NOUN
ejpam-3449	413	42	.	.	PUNCT
ejpam-3449	414	1	(	(	PUNCT
ejpam-3449	414	2	3	3	X
ejpam-3449	414	3	)	)	PUNCT
ejpam-3449	414	4	⇒	⇒	NOUN
ejpam-3449	414	5	(	(	PUNCT
ejpam-3449	414	6	1	1	X
ejpam-3449	414	7	)	)	PUNCT
ejpam-3449	414	8	it	it	PRON
ejpam-3449	414	9	is	be	AUX
ejpam-3449	414	10	shown	show	VERB
ejpam-3449	414	11	that	that	SCONJ
ejpam-3449	414	12	if	if	SCONJ
ejpam-3449	414	13	x	x	PROPN
ejpam-3449	414	14	∈	∈	PROPN
ejpam-3449	414	15	u	u	NOUN
ejpam-3449	414	16	,	,	PUNCT
ejpam-3449	414	17	where	where	SCONJ
ejpam-3449	414	18	u	u	NOUN
ejpam-3449	414	19	∈	∈	NOUN
ejpam-3449	414	20	τfγ	τfγ	VERB
ejpam-3449	414	21	,	,	PUNCT
ejpam-3449	414	22	then	then	ADV
ejpam-3449	414	23	there	there	PRON
ejpam-3449	414	24	exist	exist	VERB
ejpam-3449	414	25	a	a	DET
ejpam-3449	414	26	fine	fine	ADV
ejpam-3449	414	27	-	-	PUNCT
ejpam-3449	414	28	open	open	NOUN
ejpam-3449	414	29	set	set	VERB
ejpam-3449	414	30	v	v	ADP
ejpam-3449	415	1	such	such	ADJ
ejpam-3449	415	2	that	that	SCONJ
ejpam-3449	415	3	x	x	SYM
ejpam-3449	415	4	∈	∈	NOUN
ejpam-3449	415	5	v	v	ADP
ejpam-3449	415	6	⊆	⊆	NUM
ejpam-3449	415	7	γ(v	γ(v	NOUN
ejpam-3449	415	8	)	)	PUNCT
ejpam-3449	415	9	⊆	⊆	NUM
ejpam-3449	415	10	u	u	NOUN
ejpam-3449	415	11	.	.	PUNCT
ejpam-3449	416	1	applying	apply	VERB
ejpam-3449	416	2	the	the	DET
ejpam-3449	416	3	part	part	NOUN
ejpam-3449	416	4	(	(	PUNCT
ejpam-3449	416	5	3	3	NUM
ejpam-3449	416	6	)	)	PUNCT
ejpam-3449	416	7	,	,	PUNCT
ejpam-3449	416	8	we	we	PRON
ejpam-3449	416	9	obtain	obtain	VERB
ejpam-3449	416	10	(	(	PUNCT
ejpam-3449	416	11	x	x	NOUN
ejpam-3449	416	12	,	,	PUNCT
ejpam-3449	416	13	τ	τ	PROPN
ejpam-3449	416	14	,	,	PUNCT
ejpam-3449	416	15	τf	τf	PROPN
ejpam-3449	416	16	)	)	PUNCT
ejpam-3449	416	17	is	be	AUX
ejpam-3449	416	18	fγ	fγ	PROPN
ejpam-3449	416	19	-	-	PUNCT
ejpam-3449	416	20	t1	t1	NOUN
ejpam-3449	416	21	.	.	PUNCT
ejpam-3449	417	1	theorem	theorem	VERB
ejpam-3449	417	2	5.9	5.9	NUM
ejpam-3449	417	3	.	.	PUNCT
ejpam-3449	418	1	for	for	ADP
ejpam-3449	418	2	any	any	DET
ejpam-3449	418	3	fine	fine	ADJ
ejpam-3449	418	4	space	space	NOUN
ejpam-3449	418	5	(	(	PUNCT
ejpam-3449	418	6	x	x	X
ejpam-3449	418	7	,	,	PUNCT
ejpam-3449	418	8	τ	τ	PROPN
ejpam-3449	418	9	,	,	PUNCT
ejpam-3449	418	10	τf	τf	NUM
ejpam-3449	418	11	)	)	PUNCT
ejpam-3449	418	12	and	and	CCONJ
ejpam-3449	418	13	any	any	DET
ejpam-3449	418	14	operation	operation	NOUN
ejpam-3449	418	15	γ	γ	NOUN
ejpam-3449	418	16	on	on	ADP
ejpam-3449	418	17	τf	τf	NUM
ejpam-3449	418	18	,	,	PUNCT
ejpam-3449	418	19	the	the	DET
ejpam-3449	418	20	following	follow	VERB
ejpam-3449	418	21	properties	property	NOUN
ejpam-3449	418	22	hold	hold	VERB
ejpam-3449	418	23	.	.	PUNCT
ejpam-3449	419	1	(	(	PUNCT
ejpam-3449	419	2	i	i	NOUN
ejpam-3449	419	3	)	)	PUNCT
ejpam-3449	419	4	every	every	DET
ejpam-3449	419	5	fγ	fγ	NOUN
ejpam-3449	419	6	-	-	PUNCT
ejpam-3449	419	7	t2	t2	NOUN
ejpam-3449	419	8	space	space	NOUN
ejpam-3449	419	9	is	be	AUX
ejpam-3449	419	10	fγ	fγ	NOUN
ejpam-3449	419	11	-	-	PUNCT
ejpam-3449	419	12	t1	t1	NOUN
ejpam-3449	419	13	.	.	PUNCT
ejpam-3449	420	1	(	(	PUNCT
ejpam-3449	420	2	ii	ii	NOUN
ejpam-3449	420	3	)	)	PUNCT
ejpam-3449	420	4	every	every	DET
ejpam-3449	420	5	fγ	fγ	PROPN
ejpam-3449	420	6	-	-	PUNCT
ejpam-3449	420	7	t1	t1	NOUN
ejpam-3449	420	8	space	space	NOUN
ejpam-3449	420	9	is	be	AUX
ejpam-3449	420	10	fγ	fγ	PROPN
ejpam-3449	420	11	-	-	PUNCT
ejpam-3449	420	12	t	t	PROPN
ejpam-3449	420	13	1	1	NUM
ejpam-3449	420	14	2	2	NUM
ejpam-3449	420	15	.	.	PUNCT
ejpam-3449	421	1	(	(	PUNCT
ejpam-3449	421	2	iii	iii	X
ejpam-3449	421	3	)	)	PUNCT
ejpam-3449	421	4	every	every	DET
ejpam-3449	421	5	fγ	fγ	PROPN
ejpam-3449	421	6	-	-	PUNCT
ejpam-3449	421	7	t	t	PROPN
ejpam-3449	421	8	1	1	NUM
ejpam-3449	421	9	2	2	NUM
ejpam-3449	421	10	space	space	NOUN
ejpam-3449	421	11	is	be	AUX
ejpam-3449	421	12	fγ	fγ	NOUN
ejpam-3449	421	13	-	-	PUNCT
ejpam-3449	421	14	t	t	NOUN
ejpam-3449	421	15	∗0	∗0	PROPN
ejpam-3449	421	16	.	.	PUNCT
ejpam-3449	422	1	(	(	PUNCT
ejpam-3449	422	2	iv	iv	X
ejpam-3449	422	3	)	)	PUNCT
ejpam-3449	422	4	every	every	DET
ejpam-3449	422	5	fγ	fγ	PROPN
ejpam-3449	422	6	-	-	PUNCT
ejpam-3449	422	7	t	t	NOUN
ejpam-3449	422	8	∗n	∗n	PROPN
ejpam-3449	422	9	space	space	NOUN
ejpam-3449	422	10	is	be	AUX
ejpam-3449	422	11	fγ	fγ	PROPN
ejpam-3449	422	12	-	-	PUNCT
ejpam-3449	422	13	t	t	NOUN
ejpam-3449	422	14	∗n−1	∗n−1	PROPN
ejpam-3449	422	15	,	,	PUNCT
ejpam-3449	422	16	where	where	SCONJ
ejpam-3449	422	17	n	n	X
ejpam-3449	422	18	∈	∈	PROPN
ejpam-3449	422	19	{	{	PUNCT
ejpam-3449	422	20	2	2	NUM
ejpam-3449	422	21	,	,	PUNCT
ejpam-3449	422	22	1	1	NUM
ejpam-3449	422	23	}	}	PUNCT
ejpam-3449	422	24	.	.	PUNCT
ejpam-3449	423	1	(	(	PUNCT
ejpam-3449	423	2	v	v	NOUN
ejpam-3449	423	3	)	)	PUNCT
ejpam-3449	423	4	every	every	DET
ejpam-3449	423	5	fγ	fγ	PROPN
ejpam-3449	423	6	-	-	PUNCT
ejpam-3449	423	7	t	t	NOUN
ejpam-3449	423	8	∗n	∗n	PROPN
ejpam-3449	423	9	space	space	NOUN
ejpam-3449	423	10	is	be	AUX
ejpam-3449	423	11	fγ	fγ	NOUN
ejpam-3449	423	12	-	-	PUNCT
ejpam-3449	423	13	tn	tn	NOUN
ejpam-3449	423	14	,	,	PUNCT
ejpam-3449	423	15	where	where	SCONJ
ejpam-3449	423	16	n	n	X
ejpam-3449	423	17	∈	∈	PROPN
ejpam-3449	423	18	{	{	PUNCT
ejpam-3449	423	19	2	2	NUM
ejpam-3449	423	20	,	,	PUNCT
ejpam-3449	423	21	0	0	NUM
ejpam-3449	423	22	}	}	PUNCT
ejpam-3449	423	23	.	.	PUNCT
ejpam-3449	424	1	proof	proof	NOUN
ejpam-3449	424	2	.	.	PUNCT
ejpam-3449	425	1	follows	follow	VERB
ejpam-3449	425	2	directly	directly	ADV
ejpam-3449	425	3	from	from	ADP
ejpam-3449	425	4	their	their	PRON
ejpam-3449	425	5	definitions	definition	NOUN
ejpam-3449	425	6	.	.	PUNCT
ejpam-3449	426	1	remark	remark	VERB
ejpam-3449	426	2	5.10	5.10	NUM
ejpam-3449	426	3	.	.	PUNCT
ejpam-3449	427	1	by	by	ADP
ejpam-3449	427	2	theorem	theorem	ADJ
ejpam-3449	427	3	5.9	5.9	NUM
ejpam-3449	427	4	and	and	CCONJ
ejpam-3449	427	5	theorem	theorem	VERB
ejpam-3449	427	6	5.8	5.8	NUM
ejpam-3449	427	7	,	,	PUNCT
ejpam-3449	427	8	we	we	PRON
ejpam-3449	427	9	obtain	obtain	VERB
ejpam-3449	427	10	the	the	DET
ejpam-3449	427	11	following	follow	VERB
ejpam-3449	427	12	diagram	diagram	NOUN
ejpam-3449	427	13	of	of	ADP
ejpam-3449	427	14	implications	implication	NOUN
ejpam-3449	427	15	.	.	PUNCT
ejpam-3449	428	1	moreover	moreover	ADV
ejpam-3449	428	2	,	,	PUNCT
ejpam-3449	428	3	the	the	DET
ejpam-3449	428	4	following	follow	VERB
ejpam-3449	428	5	examples	example	NOUN
ejpam-3449	428	6	5.11	5.11	NUM
ejpam-3449	428	7	,	,	PUNCT
ejpam-3449	428	8	5.12	5.12	NUM
ejpam-3449	428	9	,	,	PUNCT
ejpam-3449	428	10	5.13	5.13	NUM
ejpam-3449	428	11	and	and	CCONJ
ejpam-3449	428	12	5.14	5.14	NUM
ejpam-3449	428	13	below	below	ADP
ejpam-3449	428	14	show	show	VERB
ejpam-3449	428	15	that	that	SCONJ
ejpam-3449	428	16	the	the	DET
ejpam-3449	428	17	reverse	reverse	ADJ
ejpam-3449	428	18	implications	implication	NOUN
ejpam-3449	428	19	are	be	AUX
ejpam-3449	428	20	not	not	PART
ejpam-3449	428	21	true	true	ADJ
ejpam-3449	428	22	in	in	ADP
ejpam-3449	428	23	general	general	ADJ
ejpam-3449	428	24	.	.	PUNCT
ejpam-3449	429	1	fγ	fγ	PROPN
ejpam-3449	429	2	-	-	PUNCT
ejpam-3449	429	3	t	t	PROPN
ejpam-3449	429	4	∗2	∗2	PROPN
ejpam-3449	429	5	�	�	PROPN
ejpam-3449	429	6	�	�	PROPN
ejpam-3449	429	7	//	//	NUM
ejpam-3449	429	8	fγ	fγ	PROPN
ejpam-3449	429	9	-	-	PUNCT
ejpam-3449	429	10	t	t	NOUN
ejpam-3449	429	11	∗1	∗1	PROPN
ejpam-3449	429	12	�	�	PROPN
ejpam-3449	429	13	�	�	PROPN
ejpam-3449	429	14	//	//	NUM
ejpam-3449	429	15	fγ	fγ	PROPN
ejpam-3449	429	16	-	-	PUNCT
ejpam-3449	429	17	t	t	PROPN
ejpam-3449	429	18	∗0	∗0	PROPN
ejpam-3449	429	19	�	�	PROPN
ejpam-3449	429	20	�	�	PROPN
ejpam-3449	429	21	fγ	fγ	PROPN
ejpam-3449	429	22	-	-	PUNCT
ejpam-3449	429	23	t2	t2	PROPN
ejpam-3449	429	24	//	//	NUM
ejpam-3449	429	25	fγ	fγ	PROPN
ejpam-3449	429	26	-	-	PUNCT
ejpam-3449	429	27	t1	t1	NOUN
ejpam-3449	429	28	oo	oo	PROPN
ejpam-3449	429	29	//	//	NUM
ejpam-3449	429	30	fγ	fγ	PROPN
ejpam-3449	429	31	-	-	PUNCT
ejpam-3449	429	32	t	t	PROPN
ejpam-3449	429	33	1	1	NUM
ejpam-3449	429	34	2	2	NUM
ejpam-3449	429	35	;	;	PUNCT
ejpam-3449	429	36	;	;	PUNCT
ejpam-3449	429	37	wwwwwwwww	wwwwwwwww	PROPN
ejpam-3449	429	38	//	//	PROPN
ejpam-3449	429	39	fγ	fγ	PROPN
ejpam-3449	429	40	-	-	PUNCT
ejpam-3449	429	41	t0	t0	PROPN
ejpam-3449	429	42	γ	γ	PROPN
ejpam-3449	429	43	-	-	PUNCT
ejpam-3449	429	44	t2	t2	NOUN
ejpam-3449	429	45	oo	oo	NOUN
ejpam-3449	429	46	//	//	SYM
ejpam-3449	429	47	γ	γ	X
ejpam-3449	429	48	-	-	PUNCT
ejpam-3449	429	49	t1	t1	NOUN
ejpam-3449	429	50	oo	oo	PROPN
ejpam-3449	429	51	//	//	PUNCT
ejpam-3449	429	52	γ	γ	X
ejpam-3449	429	53	-	-	PUNCT
ejpam-3449	429	54	t	t	PROPN
ejpam-3449	429	55	1	1	NUM
ejpam-3449	429	56	2	2	NUM
ejpam-3449	429	57	oo	oo	NOUN
ejpam-3449	429	58	//	//	NUM
ejpam-3449	429	59	γ	γ	X
ejpam-3449	429	60	-	-	PUNCT
ejpam-3449	429	61	t0	t0	PROPN
ejpam-3449	429	62	oo	oo	INTJ
ejpam-3449	429	63	b.	b.	PROPN
ejpam-3449	429	64	a.	a.	PROPN
ejpam-3449	429	65	asaad	asaad	PROPN
ejpam-3449	429	66	et	et	PROPN
ejpam-3449	429	67	al	al	PROPN
ejpam-3449	429	68	.	.	PUNCT
ejpam-3449	429	69	/	/	SYM
ejpam-3449	429	70	eur	eur	PROPN
ejpam-3449	429	71	.	.	PUNCT
ejpam-3449	430	1	j.	j.	PROPN
ejpam-3449	430	2	pure	pure	PROPN
ejpam-3449	430	3	appl	appl	PROPN
ejpam-3449	430	4	.	.	PROPN
ejpam-3449	430	5	math	math	PROPN
ejpam-3449	430	6	,	,	PUNCT
ejpam-3449	430	7	12	12	NUM
ejpam-3449	430	8	(	(	PUNCT
ejpam-3449	430	9	3	3	NUM
ejpam-3449	430	10	)	)	PUNCT
ejpam-3449	430	11	(	(	PUNCT
ejpam-3449	430	12	2019	2019	NUM
ejpam-3449	430	13	)	)	PUNCT
ejpam-3449	430	14	,	,	PUNCT
ejpam-3449	430	15	960	960	NUM
ejpam-3449	430	16	-	-	SYM
ejpam-3449	430	17	977	977	NUM
ejpam-3449	430	18	971	971	NUM
ejpam-3449	430	19	example	example	NOUN
ejpam-3449	430	20	5.11	5.11	NUM
ejpam-3449	430	21	.	.	PUNCT
ejpam-3449	431	1	let	let	VERB
ejpam-3449	431	2	x	x	PUNCT
ejpam-3449	431	3	=	=	PRON
ejpam-3449	431	4	{	{	PUNCT
ejpam-3449	431	5	a	a	PRON
ejpam-3449	431	6	,	,	PUNCT
ejpam-3449	431	7	b	b	NOUN
ejpam-3449	431	8	,	,	PUNCT
ejpam-3449	431	9	c	c	NOUN
ejpam-3449	431	10	}	}	PUNCT
ejpam-3449	431	11	and	and	CCONJ
ejpam-3449	431	12	τ	τ	PROPN
ejpam-3449	431	13	=	=	PUNCT
ejpam-3449	431	14	{	{	PUNCT
ejpam-3449	431	15	φ	φ	PROPN
ejpam-3449	431	16	,	,	PUNCT
ejpam-3449	431	17	x	x	X
ejpam-3449	431	18	,	,	PUNCT
ejpam-3449	431	19	{	{	PUNCT
ejpam-3449	431	20	a	a	X
ejpam-3449	431	21	}	}	PUNCT
ejpam-3449	431	22	,	,	PUNCT
ejpam-3449	431	23	{	{	PUNCT
ejpam-3449	431	24	b	b	NOUN
ejpam-3449	431	25	}	}	PUNCT
ejpam-3449	431	26	,	,	PUNCT
ejpam-3449	431	27	{	{	PUNCT
ejpam-3449	431	28	a	a	PRON
ejpam-3449	431	29	,	,	PUNCT
ejpam-3449	431	30	b	b	NOUN
ejpam-3449	431	31	}	}	PUNCT
ejpam-3449	431	32	}	}	PUNCT
ejpam-3449	431	33	.	.	PUNCT
ejpam-3449	432	1	then	then	ADV
ejpam-3449	432	2	τf	τf	NOUN
ejpam-3449	432	3	=	=	PUNCT
ejpam-3449	432	4	τ	τ	X
ejpam-3449	432	5	∪	∪	X
ejpam-3449	432	6	{	{	PUNCT
ejpam-3449	432	7	{	{	PUNCT
ejpam-3449	432	8	a	a	NOUN
ejpam-3449	432	9	,	,	PUNCT
ejpam-3449	432	10	c	c	NOUN
ejpam-3449	432	11	}	}	PUNCT
ejpam-3449	432	12	,	,	PUNCT
ejpam-3449	432	13	{	{	PUNCT
ejpam-3449	432	14	b	b	X
ejpam-3449	432	15	,	,	PUNCT
ejpam-3449	432	16	c	c	NOUN
ejpam-3449	432	17	}	}	PUNCT
ejpam-3449	432	18	}	}	PUNCT
ejpam-3449	432	19	.	.	PUNCT
ejpam-3449	433	1	(	(	PUNCT
ejpam-3449	433	2	i	i	NOUN
ejpam-3449	433	3	)	)	PUNCT
ejpam-3449	433	4	define	define	VERB
ejpam-3449	433	5	an	an	DET
ejpam-3449	433	6	operation	operation	NOUN
ejpam-3449	433	7	γ	γ	NOUN
ejpam-3449	433	8	on	on	ADP
ejpam-3449	433	9	τf	τf	ADP
ejpam-3449	433	10	as	as	SCONJ
ejpam-3449	433	11	follows	follow	VERB
ejpam-3449	433	12	:	:	PUNCT
ejpam-3449	433	13	for	for	ADP
ejpam-3449	433	14	every	every	DET
ejpam-3449	433	15	a	a	DET
ejpam-3449	433	16	∈	∈	PROPN
ejpam-3449	433	17	τf	τf	ADP
ejpam-3449	433	18	γ(a	γ(a	PROPN
ejpam-3449	433	19	)	)	PUNCT
ejpam-3449	433	20	=	=	PUNCT
ejpam-3449	433	21			PUNCT
ejpam-3449	433	22	{	{	PUNCT
ejpam-3449	433	23	a	a	PROPN
ejpam-3449	433	24	,	,	PUNCT
ejpam-3449	433	25	b	b	NOUN
ejpam-3449	433	26	}	}	PUNCT
ejpam-3449	433	27	if	if	SCONJ
ejpam-3449	433	28	a	a	PRON
ejpam-3449	433	29	=	=	X
ejpam-3449	433	30	{	{	PUNCT
ejpam-3449	433	31	b	b	NOUN
ejpam-3449	433	32	}	}	PUNCT
ejpam-3449	433	33	{	{	PUNCT
ejpam-3449	433	34	b	b	NOUN
ejpam-3449	433	35	,	,	PUNCT
ejpam-3449	433	36	c	c	NOUN
ejpam-3449	433	37	}	}	PUNCT
ejpam-3449	433	38	if	if	SCONJ
ejpam-3449	433	39	a	a	PRON
ejpam-3449	433	40	=	=	X
ejpam-3449	433	41	{	{	PUNCT
ejpam-3449	433	42	c	c	NOUN
ejpam-3449	433	43	}	}	PUNCT
ejpam-3449	433	44	or	or	CCONJ
ejpam-3449	433	45	{	{	PUNCT
ejpam-3449	433	46	b	b	NOUN
ejpam-3449	433	47	,	,	PUNCT
ejpam-3449	433	48	c	c	NOUN
ejpam-3449	433	49	}	}	PUNCT
ejpam-3449	433	50	x	x	SYM
ejpam-3449	433	51	otherwise	otherwise	ADV
ejpam-3449	433	52	obviously	obviously	ADV
ejpam-3449	433	53	,	,	PUNCT
ejpam-3449	433	54	the	the	DET
ejpam-3449	433	55	space	space	NOUN
ejpam-3449	433	56	(	(	PUNCT
ejpam-3449	433	57	x	x	X
ejpam-3449	433	58	,	,	PUNCT
ejpam-3449	433	59	τ	τ	PROPN
ejpam-3449	433	60	,	,	PUNCT
ejpam-3449	433	61	τf	τf	PROPN
ejpam-3449	433	62	)	)	PUNCT
ejpam-3449	433	63	is	be	AUX
ejpam-3449	433	64	fγ	fγ	NOUN
ejpam-3449	433	65	-	-	PUNCT
ejpam-3449	433	66	t0	t0	NOUN
ejpam-3449	433	67	,	,	PUNCT
ejpam-3449	433	68	but	but	CCONJ
ejpam-3449	433	69	it	it	PRON
ejpam-3449	433	70	is	be	AUX
ejpam-3449	433	71	not	not	PART
ejpam-3449	433	72	fγ	fγ	PROPN
ejpam-3449	433	73	-	-	PUNCT
ejpam-3449	433	74	t	t	NOUN
ejpam-3449	433	75	∗0	∗0	PROPN
ejpam-3449	433	76	.	.	PUNCT
ejpam-3449	434	1	hence	hence	ADV
ejpam-3449	434	2	the	the	DET
ejpam-3449	434	3	fine	fine	ADJ
ejpam-3449	434	4	space	space	NOUN
ejpam-3449	434	5	(	(	PUNCT
ejpam-3449	434	6	x	x	X
ejpam-3449	434	7	,	,	PUNCT
ejpam-3449	434	8	τ	τ	PROPN
ejpam-3449	434	9	,	,	PUNCT
ejpam-3449	434	10	τf	τf	PROPN
ejpam-3449	434	11	)	)	PUNCT
ejpam-3449	434	12	is	be	AUX
ejpam-3449	434	13	not	not	PART
ejpam-3449	434	14	fγ	fγ	PROPN
ejpam-3449	434	15	-	-	PUNCT
ejpam-3449	434	16	t	t	PROPN
ejpam-3449	434	17	1	1	NUM
ejpam-3449	434	18	2	2	NUM
ejpam-3449	434	19	.	.	PUNCT
ejpam-3449	435	1	(	(	PUNCT
ejpam-3449	435	2	ii	ii	NOUN
ejpam-3449	435	3	)	)	PUNCT
ejpam-3449	435	4	let	let	VERB
ejpam-3449	435	5	γ	γ	NOUN
ejpam-3449	435	6	:	:	PUNCT
ejpam-3449	435	7	τf	τf	PROPN
ejpam-3449	435	8	→	→	SYM
ejpam-3449	435	9	p	p	X
ejpam-3449	435	10	(	(	PUNCT
ejpam-3449	435	11	x	x	NOUN
ejpam-3449	435	12	)	)	PUNCT
ejpam-3449	435	13	be	be	AUX
ejpam-3449	435	14	an	an	DET
ejpam-3449	435	15	operation	operation	NOUN
ejpam-3449	435	16	on	on	ADP
ejpam-3449	435	17	τf	τf	ADV
ejpam-3449	435	18	defined	define	VERB
ejpam-3449	435	19	as	as	SCONJ
ejpam-3449	435	20	follows	follow	VERB
ejpam-3449	435	21	:	:	PUNCT
ejpam-3449	435	22	for	for	ADP
ejpam-3449	435	23	every	every	DET
ejpam-3449	435	24	set	set	NOUN
ejpam-3449	435	25	a	a	DET
ejpam-3449	435	26	∈	∈	NOUN
ejpam-3449	435	27	τf	τf	ADP
ejpam-3449	435	28	γ(b	γ(b	NOUN
ejpam-3449	435	29	)	)	PUNCT
ejpam-3449	436	1	=	=	PRON
ejpam-3449	436	2	{	{	PUNCT
ejpam-3449	436	3	b	b	NOUN
ejpam-3449	436	4	if	if	SCONJ
ejpam-3449	436	5	b	b	X
ejpam-3449	436	6	=	=	X
ejpam-3449	436	7	{	{	PUNCT
ejpam-3449	436	8	a	a	NOUN
ejpam-3449	436	9	}	}	PUNCT
ejpam-3449	436	10	or	or	CCONJ
ejpam-3449	436	11	{	{	PUNCT
ejpam-3449	436	12	b	b	NOUN
ejpam-3449	436	13	}	}	PUNCT
ejpam-3449	436	14	or	or	CCONJ
ejpam-3449	436	15	{	{	PUNCT
ejpam-3449	436	16	a	a	DET
ejpam-3449	436	17	,	,	PUNCT
ejpam-3449	436	18	b	b	NOUN
ejpam-3449	436	19	}	}	PUNCT
ejpam-3449	436	20	or	or	CCONJ
ejpam-3449	436	21	{	{	PUNCT
ejpam-3449	436	22	b	b	NOUN
ejpam-3449	436	23	,	,	PUNCT
ejpam-3449	436	24	c	c	NOUN
ejpam-3449	436	25	}	}	PUNCT
ejpam-3449	436	26	x	x	SYM
ejpam-3449	436	27	otherwise	otherwise	ADV
ejpam-3449	436	28	thus	thus	ADV
ejpam-3449	436	29	,	,	PUNCT
ejpam-3449	436	30	τfγ	τfγ	AUX
ejpam-3449	436	31	=	=	SYM
ejpam-3449	436	32	{	{	PUNCT
ejpam-3449	436	33	φ	φ	NOUN
ejpam-3449	436	34	,	,	PUNCT
ejpam-3449	436	35	x	x	X
ejpam-3449	436	36	,	,	PUNCT
ejpam-3449	436	37	{	{	PUNCT
ejpam-3449	436	38	a	a	X
ejpam-3449	436	39	}	}	PUNCT
ejpam-3449	436	40	,	,	PUNCT
ejpam-3449	436	41	{	{	PUNCT
ejpam-3449	436	42	b	b	NOUN
ejpam-3449	436	43	}	}	PUNCT
ejpam-3449	436	44	,	,	PUNCT
ejpam-3449	436	45	{	{	PUNCT
ejpam-3449	436	46	a	a	DET
ejpam-3449	436	47	,	,	PUNCT
ejpam-3449	436	48	b	b	NOUN
ejpam-3449	436	49	}	}	PUNCT
ejpam-3449	436	50	,	,	PUNCT
ejpam-3449	436	51	{	{	PUNCT
ejpam-3449	436	52	b	b	X
ejpam-3449	436	53	,	,	PUNCT
ejpam-3449	436	54	c	c	NOUN
ejpam-3449	436	55	}	}	PUNCT
ejpam-3449	436	56	}	}	PUNCT
ejpam-3449	436	57	.	.	PUNCT
ejpam-3449	437	1	clearly	clearly	ADV
ejpam-3449	437	2	,	,	PUNCT
ejpam-3449	437	3	the	the	DET
ejpam-3449	437	4	space	space	NOUN
ejpam-3449	437	5	(	(	PUNCT
ejpam-3449	437	6	x	x	X
ejpam-3449	437	7	,	,	PUNCT
ejpam-3449	437	8	τ	τ	PROPN
ejpam-3449	437	9	,	,	PUNCT
ejpam-3449	437	10	τf	τf	PROPN
ejpam-3449	437	11	)	)	PUNCT
ejpam-3449	437	12	is	be	AUX
ejpam-3449	437	13	fγ	fγ	PROPN
ejpam-3449	437	14	-	-	PUNCT
ejpam-3449	437	15	t	t	PROPN
ejpam-3449	437	16	1	1	NUM
ejpam-3449	437	17	2	2	NUM
ejpam-3449	437	18	,	,	PUNCT
ejpam-3449	437	19	but	but	CCONJ
ejpam-3449	437	20	it	it	PRON
ejpam-3449	437	21	is	be	AUX
ejpam-3449	437	22	not	not	PART
ejpam-3449	437	23	fγ	fγ	NOUN
ejpam-3449	437	24	-	-	PUNCT
ejpam-3449	437	25	t1	t1	NOUN
ejpam-3449	437	26	.	.	PUNCT
ejpam-3449	437	27	example	example	NOUN
ejpam-3449	438	1	5.12	5.12	NUM
ejpam-3449	438	2	.	.	PUNCT
ejpam-3449	439	1	let	let	VERB
ejpam-3449	439	2	x	x	PUNCT
ejpam-3449	439	3	=	=	PRON
ejpam-3449	439	4	{	{	PUNCT
ejpam-3449	439	5	a	a	PRON
ejpam-3449	439	6	,	,	PUNCT
ejpam-3449	439	7	b	b	NOUN
ejpam-3449	439	8	,	,	PUNCT
ejpam-3449	439	9	c	c	NOUN
ejpam-3449	439	10	}	}	PUNCT
ejpam-3449	439	11	and	and	CCONJ
ejpam-3449	439	12	τ	τ	PROPN
ejpam-3449	439	13	=	=	PUNCT
ejpam-3449	439	14	{	{	PUNCT
ejpam-3449	439	15	φ	φ	PROPN
ejpam-3449	439	16	,	,	PUNCT
ejpam-3449	439	17	x	x	X
ejpam-3449	439	18	,	,	PUNCT
ejpam-3449	439	19	{	{	PUNCT
ejpam-3449	439	20	b	b	NOUN
ejpam-3449	439	21	}	}	PUNCT
ejpam-3449	439	22	}	}	PUNCT
ejpam-3449	439	23	.	.	PUNCT
ejpam-3449	440	1	then	then	ADV
ejpam-3449	440	2	τf	τf	NOUN
ejpam-3449	440	3	=	=	SYM
ejpam-3449	440	4	{	{	PUNCT
ejpam-3449	440	5	φ	φ	PROPN
ejpam-3449	440	6	,	,	PUNCT
ejpam-3449	440	7	x	x	PRON
ejpam-3449	440	8	,	,	PUNCT
ejpam-3449	440	9	{	{	PUNCT
ejpam-3449	440	10	b	b	NOUN
ejpam-3449	440	11	}	}	PUNCT
ejpam-3449	440	12	,	,	PUNCT
ejpam-3449	440	13	{	{	PUNCT
ejpam-3449	440	14	a	a	DET
ejpam-3449	440	15	,	,	PUNCT
ejpam-3449	440	16	b	b	NOUN
ejpam-3449	440	17	}	}	PUNCT
ejpam-3449	440	18	,	,	PUNCT
ejpam-3449	440	19	{	{	PUNCT
ejpam-3449	440	20	a	a	PRON
ejpam-3449	440	21	,	,	PUNCT
ejpam-3449	440	22	c	c	NOUN
ejpam-3449	440	23	}	}	PUNCT
ejpam-3449	440	24	}	}	PUNCT
ejpam-3449	440	25	.	.	PUNCT
ejpam-3449	441	1	let	let	VERB
ejpam-3449	441	2	γ	γ	NOUN
ejpam-3449	441	3	:	:	PUNCT
ejpam-3449	441	4	τf	τf	PROPN
ejpam-3449	441	5	→	→	SYM
ejpam-3449	441	6	p	p	X
ejpam-3449	441	7	(	(	PUNCT
ejpam-3449	441	8	x	x	NOUN
ejpam-3449	441	9	)	)	PUNCT
ejpam-3449	441	10	be	be	AUX
ejpam-3449	441	11	an	an	DET
ejpam-3449	441	12	operation	operation	NOUN
ejpam-3449	441	13	on	on	ADP
ejpam-3449	441	14	τf	τf	ADV
ejpam-3449	441	15	defined	define	VERB
ejpam-3449	441	16	as	as	SCONJ
ejpam-3449	441	17	follows	follow	VERB
ejpam-3449	441	18	:	:	PUNCT
ejpam-3449	441	19	for	for	ADP
ejpam-3449	441	20	every	every	DET
ejpam-3449	441	21	set	set	NOUN
ejpam-3449	441	22	a	a	DET
ejpam-3449	441	23	∈	∈	NOUN
ejpam-3449	441	24	τf	τf	ADP
ejpam-3449	441	25	γ(a	γ(a	PROPN
ejpam-3449	441	26	)	)	PUNCT
ejpam-3449	442	1	=	=	PRON
ejpam-3449	442	2	{	{	PUNCT
ejpam-3449	442	3	a	a	X
ejpam-3449	442	4	if	if	SCONJ
ejpam-3449	442	5	a	a	PRON
ejpam-3449	442	6	=	=	X
ejpam-3449	442	7	{	{	PUNCT
ejpam-3449	442	8	b	b	NOUN
ejpam-3449	442	9	}	}	PUNCT
ejpam-3449	442	10	or	or	CCONJ
ejpam-3449	442	11	{	{	PUNCT
ejpam-3449	442	12	a	a	PRON
ejpam-3449	442	13	,	,	PUNCT
ejpam-3449	442	14	b	b	NOUN
ejpam-3449	442	15	}	}	PUNCT
ejpam-3449	442	16	fcl(a	fcl(a	PROPN
ejpam-3449	442	17	)	)	PUNCT
ejpam-3449	442	18	otherwise	otherwise	ADV
ejpam-3449	442	19	thus	thus	ADV
ejpam-3449	442	20	,	,	PUNCT
ejpam-3449	442	21	τfγ	τfγ	AUX
ejpam-3449	442	22	=	=	SYM
ejpam-3449	442	23	{	{	PUNCT
ejpam-3449	442	24	φ	φ	NOUN
ejpam-3449	442	25	,	,	PUNCT
ejpam-3449	442	26	x	x	X
ejpam-3449	442	27	,	,	PUNCT
ejpam-3449	442	28	{	{	PUNCT
ejpam-3449	442	29	b	b	NOUN
ejpam-3449	442	30	}	}	PUNCT
ejpam-3449	442	31	,	,	PUNCT
ejpam-3449	442	32	{	{	PUNCT
ejpam-3449	442	33	a	a	DET
ejpam-3449	442	34	,	,	PUNCT
ejpam-3449	442	35	b	b	NOUN
ejpam-3449	442	36	}	}	PUNCT
ejpam-3449	442	37	}	}	PUNCT
ejpam-3449	442	38	.	.	PUNCT
ejpam-3449	443	1	then	then	ADV
ejpam-3449	443	2	the	the	DET
ejpam-3449	443	3	fine	fine	ADJ
ejpam-3449	443	4	space	space	NOUN
ejpam-3449	443	5	(	(	PUNCT
ejpam-3449	443	6	x	x	X
ejpam-3449	443	7	,	,	PUNCT
ejpam-3449	443	8	τ	τ	PROPN
ejpam-3449	443	9	,	,	PUNCT
ejpam-3449	443	10	τf	τf	PROPN
ejpam-3449	443	11	)	)	PUNCT
ejpam-3449	443	12	is	be	AUX
ejpam-3449	443	13	fγ	fγ	PROPN
ejpam-3449	443	14	-	-	PUNCT
ejpam-3449	443	15	t	t	NOUN
ejpam-3449	443	16	∗0	∗0	PROPN
ejpam-3449	443	17	,	,	PUNCT
ejpam-3449	443	18	but	but	CCONJ
ejpam-3449	443	19	it	it	PRON
ejpam-3449	443	20	is	be	AUX
ejpam-3449	443	21	not	not	PART
ejpam-3449	443	22	fγt	fγt	ADJ
ejpam-3449	443	23	1	1	NUM
ejpam-3449	443	24	2	2	NUM
ejpam-3449	443	25	.	.	PUNCT
ejpam-3449	444	1	since	since	SCONJ
ejpam-3449	444	2	{	{	PUNCT
ejpam-3449	444	3	b	b	X
ejpam-3449	444	4	,	,	PUNCT
ejpam-3449	444	5	c	c	NOUN
ejpam-3449	444	6	}	}	PUNCT
ejpam-3449	444	7	is	be	AUX
ejpam-3449	444	8	fγg.closed	fγg.close	VERB
ejpam-3449	444	9	set	set	VERB
ejpam-3449	444	10	in	in	ADP
ejpam-3449	444	11	(	(	PUNCT
ejpam-3449	444	12	x	x	NOUN
ejpam-3449	444	13	,	,	PUNCT
ejpam-3449	444	14	τ	τ	PROPN
ejpam-3449	444	15	,	,	PUNCT
ejpam-3449	444	16	τf	τf	PROPN
ejpam-3449	444	17	)	)	PUNCT
ejpam-3449	444	18	,	,	PUNCT
ejpam-3449	444	19	but	but	CCONJ
ejpam-3449	444	20	{	{	PUNCT
ejpam-3449	444	21	b	b	NOUN
ejpam-3449	444	22	,	,	PUNCT
ejpam-3449	444	23	c	c	NOUN
ejpam-3449	444	24	}	}	PUNCT
ejpam-3449	444	25	is	be	AUX
ejpam-3449	444	26	not	not	PART
ejpam-3449	444	27	fγ	fγ	ADV
ejpam-3449	444	28	-	-	PUNCT
ejpam-3449	444	29	closed	close	VERB
ejpam-3449	444	30	set	set	NOUN
ejpam-3449	444	31	in	in	ADP
ejpam-3449	444	32	(	(	PUNCT
ejpam-3449	444	33	x	x	NOUN
ejpam-3449	444	34	,	,	PUNCT
ejpam-3449	444	35	τ	τ	PROPN
ejpam-3449	444	36	,	,	PUNCT
ejpam-3449	444	37	τf	τf	NUM
ejpam-3449	444	38	)	)	PUNCT
ejpam-3449	444	39	.	.	PUNCT
ejpam-3449	445	1	therefore	therefore	ADV
ejpam-3449	445	2	,	,	PUNCT
ejpam-3449	445	3	(	(	PUNCT
ejpam-3449	445	4	x	x	X
ejpam-3449	445	5	,	,	PUNCT
ejpam-3449	445	6	τ	τ	PROPN
ejpam-3449	445	7	,	,	PUNCT
ejpam-3449	445	8	τf	τf	PROPN
ejpam-3449	445	9	)	)	PUNCT
ejpam-3449	445	10	is	be	AUX
ejpam-3449	445	11	not	not	PART
ejpam-3449	445	12	a	a	DET
ejpam-3449	445	13	fγ	fγ	PROPN
ejpam-3449	445	14	-	-	PUNCT
ejpam-3449	445	15	t	t	NOUN
ejpam-3449	445	16	∗1	∗1	PROPN
ejpam-3449	445	17	space	space	NOUN
ejpam-3449	445	18	.	.	PUNCT
ejpam-3449	446	1	example	example	NOUN
ejpam-3449	447	1	5.13	5.13	NUM
ejpam-3449	447	2	.	.	PUNCT
ejpam-3449	447	3	suppose	suppose	VERB
ejpam-3449	447	4	x	x	SYM
ejpam-3449	447	5	=	=	PRON
ejpam-3449	447	6	{	{	PUNCT
ejpam-3449	447	7	a	a	PRON
ejpam-3449	447	8	,	,	PUNCT
ejpam-3449	447	9	b	b	NOUN
ejpam-3449	447	10	,	,	PUNCT
ejpam-3449	447	11	c	c	NOUN
ejpam-3449	447	12	}	}	PUNCT
ejpam-3449	447	13	and	and	CCONJ
ejpam-3449	447	14	τ	τ	PROPN
ejpam-3449	447	15	=	=	PUNCT
ejpam-3449	447	16	all	all	DET
ejpam-3449	447	17	subsets	subset	NOUN
ejpam-3449	447	18	of	of	ADP
ejpam-3449	447	19	x.	x.	NOUN
ejpam-3449	447	20	define	define	VERB
ejpam-3449	447	21	an	an	DET
ejpam-3449	447	22	operation	operation	NOUN
ejpam-3449	447	23	γ	γ	NOUN
ejpam-3449	447	24	on	on	ADP
ejpam-3449	447	25	τf	τf	ADP
ejpam-3449	447	26	as	as	SCONJ
ejpam-3449	447	27	follows	follow	VERB
ejpam-3449	447	28	:	:	PUNCT
ejpam-3449	447	29	for	for	ADP
ejpam-3449	447	30	every	every	DET
ejpam-3449	447	31	a	a	DET
ejpam-3449	447	32	∈	∈	PROPN
ejpam-3449	447	33	τf	τf	ADP
ejpam-3449	447	34	γ(a	γ(a	PROPN
ejpam-3449	447	35	)	)	PUNCT
ejpam-3449	447	36	=	=	PRON
ejpam-3449	447	37	{	{	PUNCT
ejpam-3449	447	38	a	a	X
ejpam-3449	447	39	if	if	SCONJ
ejpam-3449	447	40	a	a	PRON
ejpam-3449	447	41	=	=	X
ejpam-3449	447	42	{	{	PUNCT
ejpam-3449	447	43	a	a	PROPN
ejpam-3449	447	44	,	,	PUNCT
ejpam-3449	447	45	b	b	NOUN
ejpam-3449	447	46	}	}	PUNCT
ejpam-3449	447	47	or	or	CCONJ
ejpam-3449	447	48	{	{	PUNCT
ejpam-3449	447	49	a	a	PRON
ejpam-3449	447	50	,	,	PUNCT
ejpam-3449	447	51	c	c	NOUN
ejpam-3449	447	52	}	}	PUNCT
ejpam-3449	447	53	or	or	CCONJ
ejpam-3449	447	54	{	{	PUNCT
ejpam-3449	447	55	b	b	NOUN
ejpam-3449	447	56	,	,	PUNCT
ejpam-3449	447	57	c	c	NOUN
ejpam-3449	447	58	}	}	PUNCT
ejpam-3449	447	59	x	x	SYM
ejpam-3449	447	60	otherwise	otherwise	ADV
ejpam-3449	447	61	therefore	therefore	ADV
ejpam-3449	447	62	,	,	PUNCT
ejpam-3449	447	63	(	(	PUNCT
ejpam-3449	447	64	x	x	X
ejpam-3449	447	65	,	,	PUNCT
ejpam-3449	447	66	τ	τ	PROPN
ejpam-3449	447	67	,	,	PUNCT
ejpam-3449	447	68	τf	τf	PROPN
ejpam-3449	447	69	)	)	PUNCT
ejpam-3449	447	70	is	be	AUX
ejpam-3449	447	71	fγ	fγ	PROPN
ejpam-3449	447	72	-	-	PUNCT
ejpam-3449	447	73	t	t	NOUN
ejpam-3449	447	74	∗1	∗1	PROPN
ejpam-3449	447	75	space	space	NOUN
ejpam-3449	447	76	,	,	PUNCT
ejpam-3449	447	77	and	and	CCONJ
ejpam-3449	447	78	by	by	ADP
ejpam-3449	447	79	theorem	theorem	NOUN
ejpam-3449	447	80	5.8	5.8	NUM
ejpam-3449	447	81	,	,	PUNCT
ejpam-3449	447	82	it	it	PRON
ejpam-3449	447	83	is	be	AUX
ejpam-3449	447	84	fγ	fγ	NOUN
ejpam-3449	447	85	-	-	PUNCT
ejpam-3449	447	86	t1	t1	NOUN
ejpam-3449	447	87	,	,	PUNCT
ejpam-3449	447	88	but	but	CCONJ
ejpam-3449	447	89	(	(	PUNCT
ejpam-3449	447	90	x	x	X
ejpam-3449	447	91	,	,	PUNCT
ejpam-3449	447	92	τ	τ	PROPN
ejpam-3449	447	93	,	,	PUNCT
ejpam-3449	447	94	τf	τf	PROPN
ejpam-3449	447	95	)	)	PUNCT
ejpam-3449	447	96	is	be	AUX
ejpam-3449	447	97	not	not	PART
ejpam-3449	447	98	fγ	fγ	NOUN
ejpam-3449	447	99	-	-	PUNCT
ejpam-3449	447	100	t2	t2	NOUN
ejpam-3449	447	101	and	and	CCONJ
ejpam-3449	447	102	hence	hence	ADV
ejpam-3449	447	103	it	it	PRON
ejpam-3449	447	104	is	be	AUX
ejpam-3449	447	105	not	not	PART
ejpam-3449	447	106	fγ	fγ	PROPN
ejpam-3449	447	107	-	-	PUNCT
ejpam-3449	447	108	t	t	NOUN
ejpam-3449	447	109	∗2	∗2	PROPN
ejpam-3449	447	110	.	.	PUNCT
ejpam-3449	448	1	example	example	NOUN
ejpam-3449	449	1	5.14	5.14	NUM
ejpam-3449	449	2	.	.	PUNCT
ejpam-3449	450	1	let	let	VERB
ejpam-3449	450	2	x	x	PUNCT
ejpam-3449	450	3	=	=	PRON
ejpam-3449	450	4	{	{	PUNCT
ejpam-3449	450	5	a	a	PRON
ejpam-3449	450	6	,	,	PUNCT
ejpam-3449	450	7	b	b	NOUN
ejpam-3449	450	8	,	,	PUNCT
ejpam-3449	450	9	c	c	NOUN
ejpam-3449	450	10	}	}	PUNCT
ejpam-3449	450	11	and	and	CCONJ
ejpam-3449	450	12	τ	τ	PROPN
ejpam-3449	450	13	=	=	PUNCT
ejpam-3449	450	14	{	{	PUNCT
ejpam-3449	450	15	φ	φ	PROPN
ejpam-3449	450	16	,	,	PUNCT
ejpam-3449	450	17	x	x	X
ejpam-3449	450	18	,	,	PUNCT
ejpam-3449	450	19	{	{	PUNCT
ejpam-3449	450	20	a	a	DET
ejpam-3449	450	21	,	,	PUNCT
ejpam-3449	450	22	b	b	NOUN
ejpam-3449	450	23	}	}	PUNCT
ejpam-3449	450	24	}	}	PUNCT
ejpam-3449	450	25	.	.	PUNCT
ejpam-3449	451	1	then	then	ADV
ejpam-3449	451	2	τf	τf	NOUN
ejpam-3449	451	3	=	=	PUNCT
ejpam-3449	451	4	τ	τ	X
ejpam-3449	451	5	∪	∪	X
ejpam-3449	451	6	{	{	PUNCT
ejpam-3449	451	7	{	{	PUNCT
ejpam-3449	451	8	a	a	NOUN
ejpam-3449	451	9	}	}	PUNCT
ejpam-3449	451	10	,	,	PUNCT
ejpam-3449	451	11	{	{	PUNCT
ejpam-3449	451	12	b	b	NOUN
ejpam-3449	451	13	}	}	PUNCT
ejpam-3449	451	14	,	,	PUNCT
ejpam-3449	451	15	{	{	PUNCT
ejpam-3449	451	16	a	a	X
ejpam-3449	451	17	,	,	PUNCT
ejpam-3449	451	18	c	c	NOUN
ejpam-3449	451	19	}	}	PUNCT
ejpam-3449	451	20	,	,	PUNCT
ejpam-3449	451	21	{	{	PUNCT
ejpam-3449	451	22	b	b	X
ejpam-3449	451	23	,	,	PUNCT
ejpam-3449	451	24	c	c	NOUN
ejpam-3449	451	25	}	}	PUNCT
ejpam-3449	451	26	}	}	PUNCT
ejpam-3449	451	27	.	.	PUNCT
ejpam-3449	452	1	define	define	VERB
ejpam-3449	452	2	an	an	DET
ejpam-3449	452	3	operation	operation	NOUN
ejpam-3449	452	4	γ	γ	NOUN
ejpam-3449	452	5	:	:	PUNCT
ejpam-3449	452	6	τf	τf	PROPN
ejpam-3449	452	7	→	→	SYM
ejpam-3449	452	8	p	p	X
ejpam-3449	452	9	(	(	PUNCT
ejpam-3449	452	10	x	x	X
ejpam-3449	452	11	)	)	PUNCT
ejpam-3449	452	12	by	by	ADP
ejpam-3449	452	13	γ(a	γ(a	NOUN
ejpam-3449	452	14	)	)	PUNCT
ejpam-3449	452	15	=	=	PUNCT
ejpam-3449	452	16	a	a	PRON
ejpam-3449	452	17	for	for	ADP
ejpam-3449	452	18	all	all	DET
ejpam-3449	452	19	a	a	DET
ejpam-3449	452	20	∈	∈	NOUN
ejpam-3449	452	21	τf	τf	PROPN
ejpam-3449	452	22	.	.	PUNCT
ejpam-3449	453	1	here	here	ADV
ejpam-3449	453	2	,	,	PUNCT
ejpam-3449	453	3	τfγ	τfγ	VERB
ejpam-3449	453	4	=	=	SYM
ejpam-3449	453	5	τf	τf	NOUN
ejpam-3449	453	6	and	and	CCONJ
ejpam-3449	453	7	τγ	τγ	X
ejpam-3449	453	8	=	=	SYM
ejpam-3449	453	9	τ	τ	PROPN
ejpam-3449	453	10	.	.	PUNCT
ejpam-3449	454	1	then	then	ADV
ejpam-3449	454	2	the	the	DET
ejpam-3449	454	3	fine	fine	ADJ
ejpam-3449	454	4	space	space	NOUN
ejpam-3449	454	5	(	(	PUNCT
ejpam-3449	454	6	x	x	X
ejpam-3449	454	7	,	,	PUNCT
ejpam-3449	454	8	τ	τ	PROPN
ejpam-3449	454	9	,	,	PUNCT
ejpam-3449	454	10	τf	τf	PROPN
ejpam-3449	454	11	)	)	PUNCT
ejpam-3449	454	12	is	be	AUX
ejpam-3449	454	13	fγ	fγ	NOUN
ejpam-3449	454	14	-	-	PUNCT
ejpam-3449	454	15	ti	ti	NOUN
ejpam-3449	454	16	,	,	PUNCT
ejpam-3449	454	17	but	but	CCONJ
ejpam-3449	454	18	it	it	PRON
ejpam-3449	454	19	is	be	AUX
ejpam-3449	454	20	not	not	PART
ejpam-3449	454	21	γ	γ	PROPN
ejpam-3449	454	22	-	-	PUNCT
ejpam-3449	454	23	ti	ti	NOUN
ejpam-3449	454	24	for	for	ADP
ejpam-3449	454	25	i	i	PROPN
ejpam-3449	454	26	=	=	SYM
ejpam-3449	454	27	0	0	NUM
ejpam-3449	454	28	,	,	PUNCT
ejpam-3449	454	29	1	1	NUM
ejpam-3449	454	30	2	2	NUM
ejpam-3449	454	31	,	,	PUNCT
ejpam-3449	454	32	1	1	NUM
ejpam-3449	454	33	,	,	PUNCT
ejpam-3449	454	34	2	2	NUM
ejpam-3449	454	35	.	.	PUNCT
ejpam-3449	454	36	b.	b.	PROPN
ejpam-3449	454	37	a.	a.	PROPN
ejpam-3449	454	38	asaad	asaad	PROPN
ejpam-3449	454	39	et	et	PROPN
ejpam-3449	455	1	al	al	PROPN
ejpam-3449	455	2	.	.	PUNCT
ejpam-3449	455	3	/	/	SYM
ejpam-3449	455	4	eur	eur	PROPN
ejpam-3449	455	5	.	.	PUNCT
ejpam-3449	456	1	j.	j.	PROPN
ejpam-3449	456	2	pure	pure	PROPN
ejpam-3449	456	3	appl	appl	PROPN
ejpam-3449	456	4	.	.	PROPN
ejpam-3449	456	5	math	math	PROPN
ejpam-3449	456	6	,	,	PUNCT
ejpam-3449	456	7	12	12	NUM
ejpam-3449	456	8	(	(	PUNCT
ejpam-3449	456	9	3	3	NUM
ejpam-3449	456	10	)	)	PUNCT
ejpam-3449	456	11	(	(	PUNCT
ejpam-3449	456	12	2019	2019	NUM
ejpam-3449	456	13	)	)	PUNCT
ejpam-3449	456	14	,	,	PUNCT
ejpam-3449	456	15	960	960	NUM
ejpam-3449	456	16	-	-	SYM
ejpam-3449	456	17	977	977	NUM
ejpam-3449	456	18	972	972	NUM
ejpam-3449	456	19	6	6	NUM
ejpam-3449	456	20	.	.	PUNCT
ejpam-3449	457	1	fγβ	fγβ	ADJ
ejpam-3449	457	2	-	-	PUNCT
ejpam-3449	457	3	continuous	continuous	ADJ
ejpam-3449	457	4	functions	function	NOUN
ejpam-3449	457	5	throughout	throughout	ADP
ejpam-3449	457	6	section	section	NOUN
ejpam-3449	457	7	6	6	NUM
ejpam-3449	457	8	and	and	CCONJ
ejpam-3449	457	9	section	section	NOUN
ejpam-3449	457	10	7	7	NUM
ejpam-3449	457	11	,	,	PUNCT
ejpam-3449	457	12	let	let	VERB
ejpam-3449	457	13	(	(	PUNCT
ejpam-3449	457	14	x	x	NOUN
ejpam-3449	457	15	,	,	PUNCT
ejpam-3449	457	16	τ	τ	PROPN
ejpam-3449	457	17	,	,	PUNCT
ejpam-3449	457	18	τf	τf	NUM
ejpam-3449	457	19	)	)	PUNCT
ejpam-3449	457	20	and	and	CCONJ
ejpam-3449	457	21	(	(	PUNCT
ejpam-3449	457	22	y	y	PROPN
ejpam-3449	457	23	,	,	PUNCT
ejpam-3449	457	24	σ	σ	PROPN
ejpam-3449	457	25	,	,	PUNCT
ejpam-3449	457	26	σf	σf	NOUN
ejpam-3449	457	27	)	)	PUNCT
ejpam-3449	457	28	be	be	AUX
ejpam-3449	457	29	two	two	NUM
ejpam-3449	457	30	fine	fine	ADJ
ejpam-3449	457	31	spaces	space	NOUN
ejpam-3449	457	32	and	and	CCONJ
ejpam-3449	457	33	let	let	VERB
ejpam-3449	457	34	γ	γ	NOUN
ejpam-3449	457	35	:	:	PUNCT
ejpam-3449	457	36	τf	τf	PROPN
ejpam-3449	457	37	→	→	SYM
ejpam-3449	457	38	p	p	X
ejpam-3449	457	39	(	(	PUNCT
ejpam-3449	457	40	x	x	NOUN
ejpam-3449	457	41	)	)	PUNCT
ejpam-3449	457	42	and	and	CCONJ
ejpam-3449	457	43	β	β	X
ejpam-3449	457	44	:	:	PUNCT
ejpam-3449	457	45	σf	σf	X
ejpam-3449	457	46	→	→	SYM
ejpam-3449	457	47	p	p	X
ejpam-3449	457	48	(	(	PUNCT
ejpam-3449	457	49	y	y	PROPN
ejpam-3449	457	50	)	)	PUNCT
ejpam-3449	457	51	be	be	AUX
ejpam-3449	457	52	operations	operation	NOUN
ejpam-3449	457	53	on	on	ADP
ejpam-3449	457	54	τf	τf	PRON
ejpam-3449	457	55	and	and	CCONJ
ejpam-3449	457	56	σf	σf	VERB
ejpam-3449	457	57	respectively	respectively	ADV
ejpam-3449	457	58	.	.	PUNCT
ejpam-3449	458	1	in	in	ADP
ejpam-3449	458	2	this	this	DET
ejpam-3449	458	3	section	section	NOUN
ejpam-3449	458	4	,	,	PUNCT
ejpam-3449	458	5	we	we	PRON
ejpam-3449	458	6	introduce	introduce	VERB
ejpam-3449	458	7	a	a	DET
ejpam-3449	458	8	new	new	ADJ
ejpam-3449	458	9	class	class	NOUN
ejpam-3449	458	10	of	of	ADP
ejpam-3449	458	11	functions	function	NOUN
ejpam-3449	458	12	called	call	VERB
ejpam-3449	458	13	fγβ	fγβ	ADV
ejpam-3449	458	14	-	-	NOUN
ejpam-3449	458	15	continuous	continuous	ADJ
ejpam-3449	458	16	.	.	PUNCT
ejpam-3449	459	1	some	some	DET
ejpam-3449	459	2	characterizations	characterization	NOUN
ejpam-3449	459	3	and	and	CCONJ
ejpam-3449	459	4	properties	property	NOUN
ejpam-3449	459	5	of	of	ADP
ejpam-3449	459	6	this	this	DET
ejpam-3449	459	7	function	function	NOUN
ejpam-3449	459	8	are	be	AUX
ejpam-3449	459	9	investigated	investigate	VERB
ejpam-3449	459	10	.	.	PUNCT
ejpam-3449	460	1	definition	definition	NOUN
ejpam-3449	460	2	6.1	6.1	NUM
ejpam-3449	460	3	.	.	PUNCT
ejpam-3449	461	1	a	a	DET
ejpam-3449	461	2	function	function	NOUN
ejpam-3449	461	3	h	h	NOUN
ejpam-3449	461	4	:	:	PUNCT
ejpam-3449	461	5	(	(	PUNCT
ejpam-3449	461	6	x	x	X
ejpam-3449	461	7	,	,	PUNCT
ejpam-3449	461	8	τ	τ	PROPN
ejpam-3449	461	9	,	,	PUNCT
ejpam-3449	461	10	τf	τf	NUM
ejpam-3449	461	11	)	)	PUNCT
ejpam-3449	461	12	→	→	SYM
ejpam-3449	461	13	(	(	PUNCT
ejpam-3449	461	14	y	y	PROPN
ejpam-3449	461	15	,	,	PUNCT
ejpam-3449	461	16	σ	σ	PROPN
ejpam-3449	461	17	,	,	PUNCT
ejpam-3449	461	18	σf	σf	NOUN
ejpam-3449	461	19	)	)	PUNCT
ejpam-3449	461	20	is	be	AUX
ejpam-3449	461	21	said	say	VERB
ejpam-3449	461	22	to	to	PART
ejpam-3449	461	23	be	be	AUX
ejpam-3449	461	24	fγβ	fγβ	ADV
ejpam-3449	461	25	-	-	ADJ
ejpam-3449	461	26	continuous	continuous	ADJ
ejpam-3449	461	27	if	if	SCONJ
ejpam-3449	461	28	for	for	ADP
ejpam-3449	461	29	each	each	DET
ejpam-3449	461	30	x	x	SYM
ejpam-3449	461	31	∈	∈	PROPN
ejpam-3449	461	32	x	x	X
ejpam-3449	461	33	and	and	CCONJ
ejpam-3449	461	34	each	each	DET
ejpam-3449	461	35	fine	fine	ADJ
ejpam-3449	461	36	-	-	PUNCT
ejpam-3449	461	37	open	open	NOUN
ejpam-3449	461	38	set	set	VERB
ejpam-3449	461	39	v	v	NOUN
ejpam-3449	461	40	containing	contain	VERB
ejpam-3449	461	41	h(x	h(x	PROPN
ejpam-3449	461	42	)	)	PUNCT
ejpam-3449	461	43	,	,	PUNCT
ejpam-3449	461	44	there	there	PRON
ejpam-3449	461	45	exists	exist	VERB
ejpam-3449	461	46	a	a	DET
ejpam-3449	461	47	fine	fine	ADV
ejpam-3449	461	48	-	-	PUNCT
ejpam-3449	461	49	open	open	ADJ
ejpam-3449	461	50	set	set	NOUN
ejpam-3449	461	51	u	u	NOUN
ejpam-3449	461	52	containing	contain	VERB
ejpam-3449	461	53	x	x	PUNCT
ejpam-3449	461	54	such	such	ADJ
ejpam-3449	461	55	that	that	DET
ejpam-3449	461	56	h(γ(u	h(γ(u	NOUN
ejpam-3449	461	57	)	)	PUNCT
ejpam-3449	461	58	)	)	PUNCT
ejpam-3449	462	1	⊆	⊆	NUM
ejpam-3449	462	2	β(v	β(v	NOUN
ejpam-3449	462	3	)	)	PUNCT
ejpam-3449	462	4	.	.	PUNCT
ejpam-3449	463	1	theorem	theorem	VERB
ejpam-3449	463	2	6.2	6.2	NUM
ejpam-3449	463	3	.	.	PUNCT
ejpam-3449	464	1	let	let	VERB
ejpam-3449	464	2	h	h	NOUN
ejpam-3449	464	3	:	:	PUNCT
ejpam-3449	464	4	(	(	PUNCT
ejpam-3449	464	5	x	x	X
ejpam-3449	464	6	,	,	PUNCT
ejpam-3449	464	7	τ	τ	PROPN
ejpam-3449	464	8	,	,	PUNCT
ejpam-3449	464	9	τf	τf	NOUN
ejpam-3449	464	10	)	)	PUNCT
ejpam-3449	464	11	→	→	SYM
ejpam-3449	464	12	(	(	PUNCT
ejpam-3449	464	13	y	y	PROPN
ejpam-3449	464	14	,	,	PUNCT
ejpam-3449	464	15	σ	σ	PROPN
ejpam-3449	464	16	,	,	PUNCT
ejpam-3449	464	17	σf	σf	NOUN
ejpam-3449	464	18	)	)	PUNCT
ejpam-3449	464	19	be	be	AUX
ejpam-3449	464	20	a	a	DET
ejpam-3449	464	21	fγβ	fγβ	ADJ
ejpam-3449	464	22	-	-	ADJ
ejpam-3449	464	23	continuous	continuous	ADJ
ejpam-3449	464	24	function	function	NOUN
ejpam-3449	464	25	,	,	PUNCT
ejpam-3449	464	26	then	then	ADV
ejpam-3449	464	27	,	,	PUNCT
ejpam-3449	464	28	(	(	PUNCT
ejpam-3449	464	29	i	i	NOUN
ejpam-3449	464	30	)	)	PUNCT
ejpam-3449	464	31	h(fclγ(a	h(fclγ(a	PROPN
ejpam-3449	464	32	)	)	PUNCT
ejpam-3449	464	33	)	)	PUNCT
ejpam-3449	465	1	⊆	⊆	NUM
ejpam-3449	465	2	fclβ(h(a	fclβ(h(a	PROPN
ejpam-3449	465	3	)	)	PUNCT
ejpam-3449	465	4	)	)	PUNCT
ejpam-3449	465	5	,	,	PUNCT
ejpam-3449	465	6	for	for	ADP
ejpam-3449	465	7	every	every	DET
ejpam-3449	465	8	a	a	DET
ejpam-3449	465	9	⊆	⊆	NUM
ejpam-3449	465	10	(	(	PUNCT
ejpam-3449	465	11	x	x	NOUN
ejpam-3449	465	12	,	,	PUNCT
ejpam-3449	465	13	τ	τ	PROPN
ejpam-3449	465	14	,	,	PUNCT
ejpam-3449	465	15	τf	τf	NUM
ejpam-3449	465	16	)	)	PUNCT
ejpam-3449	465	17	.	.	PUNCT
ejpam-3449	466	1	(	(	PUNCT
ejpam-3449	466	2	ii	ii	NOUN
ejpam-3449	466	3	)	)	PUNCT
ejpam-3449	466	4	h−1(f	h−1(f	PROPN
ejpam-3449	466	5	)	)	PUNCT
ejpam-3449	466	6	is	be	AUX
ejpam-3449	466	7	fγ	fγ	ADV
ejpam-3449	466	8	-	-	PUNCT
ejpam-3449	466	9	closed	close	VERB
ejpam-3449	466	10	set	set	NOUN
ejpam-3449	466	11	in	in	ADP
ejpam-3449	466	12	(	(	PUNCT
ejpam-3449	466	13	x	x	NOUN
ejpam-3449	466	14	,	,	PUNCT
ejpam-3449	466	15	τ	τ	PROPN
ejpam-3449	466	16	,	,	PUNCT
ejpam-3449	466	17	τf	τf	NUM
ejpam-3449	466	18	)	)	PUNCT
ejpam-3449	466	19	,	,	PUNCT
ejpam-3449	466	20	for	for	ADP
ejpam-3449	466	21	every	every	DET
ejpam-3449	466	22	fβ	fβ	ADJ
ejpam-3449	466	23	-	-	PUNCT
ejpam-3449	466	24	closed	closed	ADJ
ejpam-3449	466	25	set	set	ADJ
ejpam-3449	466	26	f	f	PROPN
ejpam-3449	466	27	of	of	ADP
ejpam-3449	466	28	(	(	PUNCT
ejpam-3449	466	29	y	y	PROPN
ejpam-3449	466	30	,	,	PUNCT
ejpam-3449	466	31	σ	σ	PROPN
ejpam-3449	466	32	,	,	PUNCT
ejpam-3449	466	33	σf	σf	NOUN
ejpam-3449	466	34	)	)	PUNCT
ejpam-3449	466	35	.	.	PUNCT
ejpam-3449	467	1	proof	proof	NOUN
ejpam-3449	467	2	.	.	PUNCT
ejpam-3449	468	1	(	(	PUNCT
ejpam-3449	468	2	1	1	X
ejpam-3449	468	3	)	)	PUNCT
ejpam-3449	468	4	let	let	VERB
ejpam-3449	468	5	y	y	PROPN
ejpam-3449	468	6	∈	∈	PROPN
ejpam-3449	468	7	h(fclγ(a	h(fclγ(a	PROPN
ejpam-3449	468	8	)	)	PUNCT
ejpam-3449	468	9	)	)	PUNCT
ejpam-3449	468	10	and	and	CCONJ
ejpam-3449	468	11	v	v	X
ejpam-3449	468	12	be	be	AUX
ejpam-3449	468	13	any	any	DET
ejpam-3449	468	14	fine	fine	ADJ
ejpam-3449	468	15	-	-	PUNCT
ejpam-3449	468	16	open	open	ADJ
ejpam-3449	468	17	set	set	NOUN
ejpam-3449	468	18	containing	contain	VERB
ejpam-3449	468	19	y.	y.	NOUN
ejpam-3449	468	20	then	then	ADV
ejpam-3449	468	21	by	by	ADP
ejpam-3449	468	22	hypothesis	hypothesis	NOUN
ejpam-3449	468	23	,	,	PUNCT
ejpam-3449	468	24	there	there	PRON
ejpam-3449	468	25	exists	exist	VERB
ejpam-3449	468	26	x	x	X
ejpam-3449	468	27	∈	∈	PROPN
ejpam-3449	468	28	x	x	X
ejpam-3449	468	29	and	and	CCONJ
ejpam-3449	468	30	fine	fine	ADV
ejpam-3449	468	31	-	-	PUNCT
ejpam-3449	468	32	open	open	ADJ
ejpam-3449	468	33	set	set	NOUN
ejpam-3449	468	34	u	u	NOUN
ejpam-3449	468	35	containing	contain	VERB
ejpam-3449	468	36	x	x	PUNCT
ejpam-3449	468	37	such	such	ADJ
ejpam-3449	468	38	that	that	SCONJ
ejpam-3449	468	39	h(x	h(x	PROPN
ejpam-3449	468	40	)	)	PUNCT
ejpam-3449	469	1	=	=	SYM
ejpam-3449	469	2	y	y	PROPN
ejpam-3449	469	3	and	and	CCONJ
ejpam-3449	469	4	h(γ(u	h(γ(u	NOUN
ejpam-3449	469	5	)	)	PUNCT
ejpam-3449	469	6	)	)	PUNCT
ejpam-3449	470	1	⊆	⊆	NUM
ejpam-3449	470	2	β(v	β(v	NOUN
ejpam-3449	470	3	)	)	PUNCT
ejpam-3449	470	4	.	.	PUNCT
ejpam-3449	471	1	since	since	SCONJ
ejpam-3449	471	2	x	x	PROPN
ejpam-3449	471	3	∈	∈	PROPN
ejpam-3449	471	4	fclγ(a	fclγ(a	PROPN
ejpam-3449	471	5	)	)	PUNCT
ejpam-3449	471	6	,	,	PUNCT
ejpam-3449	471	7	we	we	PRON
ejpam-3449	471	8	have	have	VERB
ejpam-3449	471	9	γ(u	γ(u	NOUN
ejpam-3449	471	10	)	)	PUNCT
ejpam-3449	471	11	∩	∩	NOUN
ejpam-3449	471	12	a	a	DET
ejpam-3449	471	13	6=	6=	NUM
ejpam-3449	471	14	φ	φ	PROPN
ejpam-3449	471	15	.	.	PUNCT
ejpam-3449	472	1	hence	hence	ADV
ejpam-3449	472	2	φ	φ	PROPN
ejpam-3449	472	3	6=	6=	SYM
ejpam-3449	472	4	h(γ(u	h(γ(u	NOUN
ejpam-3449	472	5	)	)	PUNCT
ejpam-3449	472	6	∩	∩	NOUN
ejpam-3449	472	7	a	a	X
ejpam-3449	472	8	)	)	PUNCT
ejpam-3449	472	9	⊆	⊆	NUM
ejpam-3449	472	10	h(γ(u	h(γ(u	NOUN
ejpam-3449	472	11	)	)	PUNCT
ejpam-3449	472	12	)	)	PUNCT
ejpam-3449	473	1	∩	∩	PROPN
ejpam-3449	473	2	h(a	h(a	PROPN
ejpam-3449	473	3	)	)	PUNCT
ejpam-3449	473	4	⊆	⊆	NUM
ejpam-3449	473	5	β(v	β(v	SYM
ejpam-3449	473	6	)	)	PUNCT
ejpam-3449	473	7	∩	∩	PROPN
ejpam-3449	473	8	h(a	h(a	PROPN
ejpam-3449	473	9	)	)	PUNCT
ejpam-3449	473	10	.	.	PUNCT
ejpam-3449	474	1	this	this	PRON
ejpam-3449	474	2	implies	imply	VERB
ejpam-3449	474	3	that	that	SCONJ
ejpam-3449	474	4	y	y	PROPN
ejpam-3449	474	5	∈	∈	PROPN
ejpam-3449	474	6	fclβ(h(a	fclβ(h(a	PROPN
ejpam-3449	474	7	)	)	PUNCT
ejpam-3449	474	8	)	)	PUNCT
ejpam-3449	474	9	.	.	PUNCT
ejpam-3449	475	1	therefore	therefore	ADV
ejpam-3449	475	2	,	,	PUNCT
ejpam-3449	475	3	h(fclγ(a	h(fclγ(a	NOUN
ejpam-3449	475	4	)	)	PUNCT
ejpam-3449	475	5	)	)	PUNCT
ejpam-3449	476	1	⊆	⊆	NUM
ejpam-3449	476	2	fclβ(h(a	fclβ(h(a	PROPN
ejpam-3449	476	3	)	)	PUNCT
ejpam-3449	476	4	)	)	PUNCT
ejpam-3449	476	5	.	.	PUNCT
ejpam-3449	477	1	(	(	PUNCT
ejpam-3449	477	2	2	2	X
ejpam-3449	477	3	)	)	PUNCT
ejpam-3449	477	4	let	let	VERB
ejpam-3449	477	5	f	f	PRON
ejpam-3449	477	6	be	be	AUX
ejpam-3449	477	7	any	any	DET
ejpam-3449	477	8	fβ	fβ	ADJ
ejpam-3449	477	9	-	-	PUNCT
ejpam-3449	477	10	closed	closed	ADJ
ejpam-3449	477	11	set	set	NOUN
ejpam-3449	477	12	of	of	ADP
ejpam-3449	477	13	(	(	PUNCT
ejpam-3449	477	14	y	y	PROPN
ejpam-3449	477	15	,	,	PUNCT
ejpam-3449	477	16	σ	σ	PROPN
ejpam-3449	477	17	,	,	PUNCT
ejpam-3449	477	18	σf	σf	NOUN
ejpam-3449	477	19	)	)	PUNCT
ejpam-3449	477	20	.	.	PUNCT
ejpam-3449	478	1	by	by	ADP
ejpam-3449	478	2	using	use	VERB
ejpam-3449	478	3	(	(	PUNCT
ejpam-3449	478	4	1	1	NUM
ejpam-3449	478	5	)	)	PUNCT
ejpam-3449	478	6	,	,	PUNCT
ejpam-3449	478	7	we	we	PRON
ejpam-3449	478	8	have	have	VERB
ejpam-3449	478	9	h(fclγ(h−1(f	h(fclγ(h−1(f	PROPN
ejpam-3449	478	10	)	)	PUNCT
ejpam-3449	478	11	)	)	PUNCT
ejpam-3449	478	12	)	)	PUNCT
ejpam-3449	479	1	⊆	⊆	NUM
ejpam-3449	479	2	fclβ(f	fclβ(f	NOUN
ejpam-3449	479	3	)	)	PUNCT
ejpam-3449	479	4	=	=	SYM
ejpam-3449	480	1	f	f	PROPN
ejpam-3449	480	2	.	.	PUNCT
ejpam-3449	481	1	therefore	therefore	ADV
ejpam-3449	481	2	,	,	PUNCT
ejpam-3449	481	3	fclγ(h−1(f	fclγ(h−1(f	ADJ
ejpam-3449	481	4	)	)	PUNCT
ejpam-3449	481	5	)	)	PUNCT
ejpam-3449	482	1	=	=	SYM
ejpam-3449	482	2	h−1(f	h−1(f	PROPN
ejpam-3449	482	3	)	)	PUNCT
ejpam-3449	482	4	.	.	PUNCT
ejpam-3449	483	1	hence	hence	ADV
ejpam-3449	483	2	h−1(f	h−1(f	PROPN
ejpam-3449	483	3	)	)	PUNCT
ejpam-3449	483	4	is	be	AUX
ejpam-3449	483	5	fγ	fγ	ADV
ejpam-3449	483	6	-	-	PUNCT
ejpam-3449	483	7	closed	close	VERB
ejpam-3449	483	8	set	set	NOUN
ejpam-3449	483	9	in	in	ADP
ejpam-3449	483	10	(	(	PUNCT
ejpam-3449	483	11	x	x	NOUN
ejpam-3449	483	12	,	,	PUNCT
ejpam-3449	483	13	τ	τ	PROPN
ejpam-3449	483	14	,	,	PUNCT
ejpam-3449	483	15	τf	τf	NUM
ejpam-3449	483	16	)	)	PUNCT
ejpam-3449	483	17	.	.	PUNCT
ejpam-3449	484	1	theorem	theorem	VERB
ejpam-3449	484	2	6.3	6.3	NUM
ejpam-3449	484	3	.	.	PUNCT
ejpam-3449	485	1	in	in	ADP
ejpam-3449	485	2	theorem	theorem	NOUN
ejpam-3449	485	3	6.2	6.2	NUM
ejpam-3449	485	4	,	,	PUNCT
ejpam-3449	485	5	the	the	DET
ejpam-3449	485	6	properties	property	NOUN
ejpam-3449	485	7	of	of	ADP
ejpam-3449	485	8	fγβ	fγβ	NOUN
ejpam-3449	485	9	-	-	PUNCT
ejpam-3449	485	10	continuity	continuity	NOUN
ejpam-3449	485	11	of	of	ADP
ejpam-3449	485	12	f	f	PROPN
ejpam-3449	485	13	,	,	PUNCT
ejpam-3449	485	14	(	(	PUNCT
ejpam-3449	485	15	1	1	X
ejpam-3449	485	16	)	)	PUNCT
ejpam-3449	485	17	and	and	CCONJ
ejpam-3449	485	18	(	(	PUNCT
ejpam-3449	485	19	2	2	X
ejpam-3449	485	20	)	)	PUNCT
ejpam-3449	485	21	are	be	AUX
ejpam-3449	485	22	equivalent	equivalent	ADJ
ejpam-3449	485	23	to	to	ADP
ejpam-3449	485	24	each	each	DET
ejpam-3449	485	25	other	other	ADJ
ejpam-3449	485	26	if	if	SCONJ
ejpam-3449	485	27	either	either	CCONJ
ejpam-3449	485	28	the	the	DET
ejpam-3449	485	29	fine	fine	ADJ
ejpam-3449	485	30	space	space	NOUN
ejpam-3449	485	31	(	(	PUNCT
ejpam-3449	485	32	y	y	PROPN
ejpam-3449	485	33	,	,	PUNCT
ejpam-3449	485	34	σ	σ	PROPN
ejpam-3449	485	35	,	,	PUNCT
ejpam-3449	485	36	σf	σf	NOUN
ejpam-3449	485	37	)	)	PUNCT
ejpam-3449	485	38	is	be	AUX
ejpam-3449	485	39	fβ	fβ	ADJ
ejpam-3449	485	40	-	-	PUNCT
ejpam-3449	485	41	regular	regular	ADJ
ejpam-3449	485	42	or	or	CCONJ
ejpam-3449	485	43	the	the	DET
ejpam-3449	485	44	operation	operation	NOUN
ejpam-3449	485	45	β	β	NOUN
ejpam-3449	485	46	is	be	AUX
ejpam-3449	485	47	fine	fine	ADV
ejpam-3449	485	48	-	-	PUNCT
ejpam-3449	485	49	open	open	ADJ
ejpam-3449	485	50	.	.	PUNCT
ejpam-3449	486	1	proof	proof	NOUN
ejpam-3449	486	2	.	.	PUNCT
ejpam-3449	487	1	it	it	PRON
ejpam-3449	487	2	follows	follow	VERB
ejpam-3449	487	3	from	from	ADP
ejpam-3449	487	4	the	the	DET
ejpam-3449	487	5	proof	proof	NOUN
ejpam-3449	487	6	of	of	ADP
ejpam-3449	487	7	theorem	theorem	ADJ
ejpam-3449	487	8	6.2	6.2	NUM
ejpam-3449	487	9	that	that	PRON
ejpam-3449	487	10	we	we	PRON
ejpam-3449	487	11	know	know	VERB
ejpam-3449	487	12	the	the	DET
ejpam-3449	487	13	following	follow	VERB
ejpam-3449	487	14	implications	implication	NOUN
ejpam-3449	487	15	:	:	PUNCT
ejpam-3449	487	16	”	"	PUNCT
ejpam-3449	487	17	fγβ	fγβ	NOUN
ejpam-3449	487	18	-	-	PUNCT
ejpam-3449	487	19	continuity	continuity	NOUN
ejpam-3449	487	20	of	of	ADP
ejpam-3449	487	21	h	h	NOUN
ejpam-3449	487	22	”	"	PUNCT
ejpam-3449	487	23	⇒	⇒	NOUN
ejpam-3449	487	24	(	(	PUNCT
ejpam-3449	487	25	1	1	NUM
ejpam-3449	487	26	)	)	PUNCT
ejpam-3449	487	27	⇒	⇒	NOUN
ejpam-3449	487	28	(	(	PUNCT
ejpam-3449	487	29	2	2	NUM
ejpam-3449	487	30	)	)	PUNCT
ejpam-3449	487	31	.	.	PUNCT
ejpam-3449	488	1	thus	thus	ADV
ejpam-3449	488	2	,	,	PUNCT
ejpam-3449	488	3	when	when	SCONJ
ejpam-3449	488	4	the	the	DET
ejpam-3449	488	5	fine	fine	ADJ
ejpam-3449	488	6	space	space	NOUN
ejpam-3449	488	7	(	(	PUNCT
ejpam-3449	488	8	y	y	PROPN
ejpam-3449	488	9	,	,	PUNCT
ejpam-3449	488	10	σ	σ	PROPN
ejpam-3449	488	11	,	,	PUNCT
ejpam-3449	488	12	σf	σf	NOUN
ejpam-3449	488	13	)	)	PUNCT
ejpam-3449	488	14	is	be	AUX
ejpam-3449	488	15	fβ	fβ	ADJ
ejpam-3449	488	16	-	-	PUNCT
ejpam-3449	488	17	regular	regular	ADJ
ejpam-3449	488	18	,	,	PUNCT
ejpam-3449	488	19	we	we	PRON
ejpam-3449	488	20	prove	prove	VERB
ejpam-3449	488	21	the	the	DET
ejpam-3449	488	22	implication	implication	NOUN
ejpam-3449	488	23	:	:	PUNCT
ejpam-3449	488	24	(	(	PUNCT
ejpam-3449	488	25	2	2	X
ejpam-3449	488	26	)	)	PUNCT
ejpam-3449	488	27	⇒	⇒	VERB
ejpam-3449	488	28	fγβ	fγβ	NOUN
ejpam-3449	488	29	-	-	PUNCT
ejpam-3449	488	30	continuity	continuity	NOUN
ejpam-3449	488	31	of	of	ADP
ejpam-3449	488	32	h.	h.	NOUN
ejpam-3449	488	33	let	let	VERB
ejpam-3449	489	1	x	x	SYM
ejpam-3449	489	2	∈	∈	PROPN
ejpam-3449	489	3	x	x	PUNCT
ejpam-3449	489	4	and	and	CCONJ
ejpam-3449	489	5	let	let	VERB
ejpam-3449	489	6	v	v	NUM
ejpam-3449	489	7	∈	∈	NOUN
ejpam-3449	489	8	σf	σf	VERB
ejpam-3449	489	9	such	such	ADJ
ejpam-3449	489	10	that	that	SCONJ
ejpam-3449	489	11	h(x	h(x	PROPN
ejpam-3449	489	12	)	)	PUNCT
ejpam-3449	489	13	∈	∈	PROPN
ejpam-3449	489	14	v	v	NOUN
ejpam-3449	489	15	.	.	PUNCT
ejpam-3449	490	1	since	since	SCONJ
ejpam-3449	490	2	(	(	PUNCT
ejpam-3449	490	3	y	y	PROPN
ejpam-3449	490	4	,	,	PUNCT
ejpam-3449	490	5	σ	σ	PROPN
ejpam-3449	490	6	,	,	PUNCT
ejpam-3449	490	7	σf	σf	NOUN
ejpam-3449	490	8	)	)	PUNCT
ejpam-3449	490	9	is	be	AUX
ejpam-3449	490	10	a	a	DET
ejpam-3449	490	11	fβ	fβ	ADJ
ejpam-3449	490	12	-	-	PUNCT
ejpam-3449	490	13	regular	regular	ADJ
ejpam-3449	490	14	space	space	NOUN
ejpam-3449	490	15	,	,	PUNCT
ejpam-3449	490	16	then	then	ADV
ejpam-3449	490	17	by	by	ADP
ejpam-3449	490	18	theorem	theorem	NOUN
ejpam-3449	490	19	3.6	3.6	NUM
ejpam-3449	490	20	,	,	PUNCT
ejpam-3449	490	21	v	v	ADP
ejpam-3449	490	22	∈	∈	PROPN
ejpam-3449	490	23	σgβ	σgβ	NOUN
ejpam-3449	490	24	.	.	PUNCT
ejpam-3449	491	1	by	by	ADP
ejpam-3449	491	2	using	use	VERB
ejpam-3449	491	3	(	(	PUNCT
ejpam-3449	491	4	2	2	NUM
ejpam-3449	491	5	)	)	PUNCT
ejpam-3449	491	6	of	of	ADP
ejpam-3449	491	7	theorem	theorem	ADJ
ejpam-3449	491	8	6.2	6.2	NUM
ejpam-3449	491	9	,	,	PUNCT
ejpam-3449	491	10	h−1(v	h−1(v	PROPN
ejpam-3449	491	11	)	)	PUNCT
ejpam-3449	492	1	∈	∈	NOUN
ejpam-3449	492	2	τfγ	τfγ	VERB
ejpam-3449	492	3	such	such	ADJ
ejpam-3449	492	4	that	that	SCONJ
ejpam-3449	492	5	x	x	SYM
ejpam-3449	492	6	∈	∈	PROPN
ejpam-3449	492	7	h−1(v	h−1(v	PROPN
ejpam-3449	492	8	)	)	PUNCT
ejpam-3449	492	9	.	.	PUNCT
ejpam-3449	493	1	so	so	ADV
ejpam-3449	493	2	there	there	PRON
ejpam-3449	493	3	exists	exist	VERB
ejpam-3449	493	4	a	a	DET
ejpam-3449	493	5	fine	fine	ADV
ejpam-3449	493	6	-	-	PUNCT
ejpam-3449	493	7	open	open	NOUN
ejpam-3449	493	8	set	set	NOUN
ejpam-3449	493	9	u	u	PRON
ejpam-3449	493	10	such	such	ADJ
ejpam-3449	493	11	that	that	SCONJ
ejpam-3449	493	12	x	x	SYM
ejpam-3449	493	13	∈	∈	PROPN
ejpam-3449	493	14	u	u	NOUN
ejpam-3449	493	15	and	and	CCONJ
ejpam-3449	493	16	γ(u	γ(u	PROPN
ejpam-3449	493	17	)	)	PUNCT
ejpam-3449	493	18	⊆	⊆	NUM
ejpam-3449	493	19	h−1(v	h−1(v	PROPN
ejpam-3449	493	20	)	)	PUNCT
ejpam-3449	493	21	.	.	PUNCT
ejpam-3449	494	1	this	this	PRON
ejpam-3449	494	2	implies	imply	VERB
ejpam-3449	494	3	that	that	SCONJ
ejpam-3449	494	4	h(γ(u	h(γ(u	NOUN
ejpam-3449	494	5	)	)	PUNCT
ejpam-3449	494	6	)	)	PUNCT
ejpam-3449	495	1	⊆	⊆	NUM
ejpam-3449	495	2	v	v	ADP
ejpam-3449	495	3	⊆	⊆	NUM
ejpam-3449	495	4	β(v	β(v	NOUN
ejpam-3449	495	5	)	)	PUNCT
ejpam-3449	495	6	.	.	PUNCT
ejpam-3449	496	1	therefore	therefore	ADV
ejpam-3449	496	2	,	,	PUNCT
ejpam-3449	496	3	h	h	NOUN
ejpam-3449	496	4	is	be	AUX
ejpam-3449	496	5	fγβ	fγβ	ADV
ejpam-3449	496	6	-	-	PUNCT
ejpam-3449	496	7	continuous	continuous	ADJ
ejpam-3449	496	8	.	.	PUNCT
ejpam-3449	497	1	now	now	ADV
ejpam-3449	497	2	,	,	PUNCT
ejpam-3449	497	3	when	when	SCONJ
ejpam-3449	497	4	β	β	X
ejpam-3449	497	5	is	be	AUX
ejpam-3449	497	6	a	a	DET
ejpam-3449	497	7	fine	fine	ADJ
ejpam-3449	497	8	-	-	PUNCT
ejpam-3449	497	9	open	open	ADJ
ejpam-3449	497	10	operation	operation	NOUN
ejpam-3449	497	11	,	,	PUNCT
ejpam-3449	497	12	we	we	PRON
ejpam-3449	497	13	show	show	VERB
ejpam-3449	497	14	the	the	DET
ejpam-3449	497	15	implication	implication	NOUN
ejpam-3449	497	16	:	:	PUNCT
ejpam-3449	497	17	(	(	PUNCT
ejpam-3449	497	18	2	2	X
ejpam-3449	497	19	)	)	PUNCT
ejpam-3449	497	20	⇒	⇒	VERB
ejpam-3449	497	21	fγβ	fγβ	NOUN
ejpam-3449	497	22	-	-	PUNCT
ejpam-3449	497	23	continuity	continuity	NOUN
ejpam-3449	497	24	of	of	ADP
ejpam-3449	497	25	h.	h.	NOUN
ejpam-3449	497	26	let	let	VERB
ejpam-3449	498	1	x	x	SYM
ejpam-3449	498	2	∈	∈	PROPN
ejpam-3449	498	3	x	x	PUNCT
ejpam-3449	498	4	and	and	CCONJ
ejpam-3449	498	5	let	let	VERB
ejpam-3449	498	6	v	v	NUM
ejpam-3449	498	7	∈	∈	NOUN
ejpam-3449	498	8	σf	σf	VERB
ejpam-3449	498	9	such	such	ADJ
ejpam-3449	498	10	that	that	SCONJ
ejpam-3449	498	11	h(x	h(x	PROPN
ejpam-3449	498	12	)	)	PUNCT
ejpam-3449	498	13	∈	∈	PROPN
ejpam-3449	498	14	v	v	NOUN
ejpam-3449	498	15	.	.	PUNCT
ejpam-3449	499	1	since	since	SCONJ
ejpam-3449	499	2	β	β	X
ejpam-3449	499	3	is	be	AUX
ejpam-3449	499	4	a	a	DET
ejpam-3449	499	5	fine	fine	ADJ
ejpam-3449	499	6	-	-	PUNCT
ejpam-3449	499	7	open	open	ADJ
ejpam-3449	499	8	operation	operation	NOUN
ejpam-3449	499	9	,	,	PUNCT
ejpam-3449	499	10	then	then	ADV
ejpam-3449	499	11	there	there	PRON
ejpam-3449	499	12	exists	exist	VERB
ejpam-3449	499	13	w	w	PROPN
ejpam-3449	499	14	∈	∈	PROPN
ejpam-3449	499	15	σgβ	σgβ	ADP
ejpam-3449	499	16	such	such	ADJ
ejpam-3449	499	17	that	that	SCONJ
ejpam-3449	499	18	h(x	h(x	PROPN
ejpam-3449	499	19	)	)	PUNCT
ejpam-3449	499	20	∈	∈	PROPN
ejpam-3449	499	21	w	w	NOUN
ejpam-3449	499	22	and	and	CCONJ
ejpam-3449	499	23	w	w	ADP
ejpam-3449	499	24	⊆	⊆	NUM
ejpam-3449	499	25	β(v	β(v	NOUN
ejpam-3449	499	26	)	)	PUNCT
ejpam-3449	499	27	.	.	PUNCT
ejpam-3449	500	1	by	by	ADP
ejpam-3449	500	2	using	use	VERB
ejpam-3449	500	3	(	(	PUNCT
ejpam-3449	500	4	2	2	NUM
ejpam-3449	500	5	)	)	PUNCT
ejpam-3449	500	6	of	of	ADP
ejpam-3449	500	7	theorem	theorem	ADJ
ejpam-3449	500	8	6.2	6.2	NUM
ejpam-3449	500	9	,	,	PUNCT
ejpam-3449	500	10	h−1(w	h−1(w	NOUN
ejpam-3449	500	11	)	)	PUNCT
ejpam-3449	500	12	∈	∈	NOUN
ejpam-3449	500	13	τfγ	τfγ	VERB
ejpam-3449	500	14	such	such	ADJ
ejpam-3449	500	15	that	that	SCONJ
ejpam-3449	500	16	x	x	SYM
ejpam-3449	500	17	∈	∈	PROPN
ejpam-3449	500	18	h−1(w	h−1(w	NOUN
ejpam-3449	500	19	)	)	PUNCT
ejpam-3449	500	20	.	.	PUNCT
ejpam-3449	501	1	so	so	ADV
ejpam-3449	501	2	there	there	PRON
ejpam-3449	501	3	exists	exist	VERB
ejpam-3449	501	4	a	a	DET
ejpam-3449	501	5	fine	fine	ADV
ejpam-3449	501	6	-	-	PUNCT
ejpam-3449	501	7	open	open	NOUN
ejpam-3449	501	8	set	set	NOUN
ejpam-3449	501	9	u	u	PRON
ejpam-3449	501	10	such	such	ADJ
ejpam-3449	501	11	that	that	SCONJ
ejpam-3449	501	12	x	x	SYM
ejpam-3449	501	13	∈	∈	PROPN
ejpam-3449	501	14	u	u	NOUN
ejpam-3449	501	15	and	and	CCONJ
ejpam-3449	501	16	γ(u	γ(u	PROPN
ejpam-3449	501	17	)	)	PUNCT
ejpam-3449	501	18	⊆	⊆	NUM
ejpam-3449	501	19	h−1(w	h−1(w	NOUN
ejpam-3449	501	20	)	)	PUNCT
ejpam-3449	501	21	⊆	⊆	NUM
ejpam-3449	501	22	h−1(β(v	h−1(β(v	NOUN
ejpam-3449	501	23	)	)	PUNCT
ejpam-3449	501	24	)	)	PUNCT
ejpam-3449	501	25	.	.	PUNCT
ejpam-3449	502	1	this	this	PRON
ejpam-3449	502	2	implies	imply	VERB
ejpam-3449	502	3	that	that	SCONJ
ejpam-3449	502	4	h(γ(u	h(γ(u	NOUN
ejpam-3449	502	5	)	)	PUNCT
ejpam-3449	502	6	)	)	PUNCT
ejpam-3449	503	1	⊆	⊆	NUM
ejpam-3449	503	2	β(v	β(v	NOUN
ejpam-3449	503	3	)	)	PUNCT
ejpam-3449	503	4	.	.	PUNCT
ejpam-3449	504	1	hence	hence	ADV
ejpam-3449	504	2	h	h	PROPN
ejpam-3449	504	3	is	be	AUX
ejpam-3449	504	4	fγβ	fγβ	ADV
ejpam-3449	504	5	-	-	PUNCT
ejpam-3449	504	6	continuous	continuous	ADJ
ejpam-3449	504	7	.	.	PUNCT
ejpam-3449	505	1	definition	definition	NOUN
ejpam-3449	505	2	6.4	6.4	NUM
ejpam-3449	505	3	.	.	PUNCT
ejpam-3449	506	1	a	a	DET
ejpam-3449	506	2	function	function	NOUN
ejpam-3449	506	3	h	h	NOUN
ejpam-3449	506	4	:	:	PUNCT
ejpam-3449	506	5	(	(	PUNCT
ejpam-3449	506	6	x	x	X
ejpam-3449	506	7	,	,	PUNCT
ejpam-3449	506	8	τ	τ	PROPN
ejpam-3449	506	9	,	,	PUNCT
ejpam-3449	506	10	τf	τf	NOUN
ejpam-3449	506	11	)	)	PUNCT
ejpam-3449	506	12	→	→	SYM
ejpam-3449	506	13	(	(	PUNCT
ejpam-3449	506	14	y	y	PROPN
ejpam-3449	506	15	,	,	PUNCT
ejpam-3449	506	16	σ	σ	PROPN
ejpam-3449	506	17	,	,	PUNCT
ejpam-3449	506	18	σf	σf	NOUN
ejpam-3449	506	19	)	)	PUNCT
ejpam-3449	506	20	is	be	AUX
ejpam-3449	506	21	said	say	VERB
ejpam-3449	506	22	to	to	PART
ejpam-3449	506	23	be	be	AUX
ejpam-3449	506	24	b.	b.	PROPN
ejpam-3449	506	25	a.	a.	PROPN
ejpam-3449	506	26	asaad	asaad	PROPN
ejpam-3449	506	27	et	et	PROPN
ejpam-3449	507	1	al	al	PROPN
ejpam-3449	507	2	.	.	PUNCT
ejpam-3449	507	3	/	/	SYM
ejpam-3449	507	4	eur	eur	PROPN
ejpam-3449	507	5	.	.	PUNCT
ejpam-3449	508	1	j.	j.	PROPN
ejpam-3449	508	2	pure	pure	PROPN
ejpam-3449	508	3	appl	appl	PROPN
ejpam-3449	508	4	.	.	PROPN
ejpam-3449	508	5	math	math	PROPN
ejpam-3449	508	6	,	,	PUNCT
ejpam-3449	508	7	12	12	NUM
ejpam-3449	508	8	(	(	PUNCT
ejpam-3449	508	9	3	3	NUM
ejpam-3449	508	10	)	)	PUNCT
ejpam-3449	508	11	(	(	PUNCT
ejpam-3449	508	12	2019	2019	NUM
ejpam-3449	508	13	)	)	PUNCT
ejpam-3449	508	14	,	,	PUNCT
ejpam-3449	508	15	960	960	NUM
ejpam-3449	508	16	-	-	SYM
ejpam-3449	508	17	977	977	NUM
ejpam-3449	508	18	973	973	NUM
ejpam-3449	508	19	(	(	PUNCT
ejpam-3449	508	20	i	i	NOUN
ejpam-3449	508	21	)	)	PUNCT
ejpam-3449	508	22	fγβ	fγβ	NOUN
ejpam-3449	508	23	-	-	PUNCT
ejpam-3449	508	24	closed	closed	ADJ
ejpam-3449	508	25	if	if	SCONJ
ejpam-3449	508	26	the	the	DET
ejpam-3449	508	27	image	image	NOUN
ejpam-3449	508	28	of	of	ADP
ejpam-3449	508	29	each	each	DET
ejpam-3449	508	30	fγ	fγ	ADV
ejpam-3449	508	31	-	-	PUNCT
ejpam-3449	508	32	closed	close	VERB
ejpam-3449	508	33	set	set	NOUN
ejpam-3449	508	34	of	of	ADP
ejpam-3449	508	35	x	x	PUNCT
ejpam-3449	508	36	is	be	AUX
ejpam-3449	508	37	fβ	fβ	ADV
ejpam-3449	508	38	-	-	PUNCT
ejpam-3449	508	39	closed	closed	ADJ
ejpam-3449	508	40	in	in	ADP
ejpam-3449	508	41	y	y	PROPN
ejpam-3449	508	42	.	.	PUNCT
ejpam-3449	509	1	(	(	PUNCT
ejpam-3449	509	2	ii	ii	NOUN
ejpam-3449	509	3	)	)	PUNCT
ejpam-3449	509	4	fβ	fβ	ADV
ejpam-3449	509	5	-	-	PUNCT
ejpam-3449	509	6	closed	closed	ADJ
ejpam-3449	509	7	if	if	SCONJ
ejpam-3449	509	8	the	the	DET
ejpam-3449	509	9	image	image	NOUN
ejpam-3449	509	10	of	of	ADP
ejpam-3449	509	11	each	each	DET
ejpam-3449	509	12	fine	fine	ADV
ejpam-3449	509	13	-	-	PUNCT
ejpam-3449	509	14	closed	close	VERB
ejpam-3449	509	15	set	set	NOUN
ejpam-3449	509	16	of	of	ADP
ejpam-3449	509	17	x	x	PUNCT
ejpam-3449	509	18	is	be	AUX
ejpam-3449	509	19	fβ	fβ	ADV
ejpam-3449	509	20	-	-	PUNCT
ejpam-3449	509	21	closed	closed	ADJ
ejpam-3449	509	22	in	in	ADP
ejpam-3449	509	23	y	y	PROPN
ejpam-3449	509	24	.	.	PUNCT
ejpam-3449	510	1	theorem	theorem	VERB
ejpam-3449	510	2	6.5	6.5	NUM
ejpam-3449	510	3	.	.	PUNCT
ejpam-3449	511	1	suppose	suppose	VERB
ejpam-3449	511	2	that	that	SCONJ
ejpam-3449	511	3	a	a	DET
ejpam-3449	511	4	function	function	NOUN
ejpam-3449	511	5	h	h	NOUN
ejpam-3449	511	6	:	:	PUNCT
ejpam-3449	511	7	(	(	PUNCT
ejpam-3449	511	8	x	x	X
ejpam-3449	511	9	,	,	PUNCT
ejpam-3449	511	10	τ	τ	PROPN
ejpam-3449	511	11	,	,	PUNCT
ejpam-3449	511	12	τf	τf	NUM
ejpam-3449	511	13	)	)	PUNCT
ejpam-3449	511	14	→	→	SYM
ejpam-3449	511	15	(	(	PUNCT
ejpam-3449	511	16	y	y	PROPN
ejpam-3449	511	17	,	,	PUNCT
ejpam-3449	511	18	σ	σ	PROPN
ejpam-3449	511	19	,	,	PUNCT
ejpam-3449	511	20	σf	σf	NOUN
ejpam-3449	511	21	)	)	PUNCT
ejpam-3449	511	22	is	be	AUX
ejpam-3449	511	23	both	both	PRON
ejpam-3449	511	24	fγβ	fγβ	ADV
ejpam-3449	511	25	-	-	ADJ
ejpam-3449	511	26	continuous	continuous	ADJ
ejpam-3449	511	27	and	and	CCONJ
ejpam-3449	511	28	fβ	fβ	ADV
ejpam-3449	511	29	-	-	PUNCT
ejpam-3449	511	30	closed	closed	ADJ
ejpam-3449	511	31	,	,	PUNCT
ejpam-3449	511	32	then	then	ADV
ejpam-3449	511	33	:	:	PUNCT
ejpam-3449	511	34	(	(	PUNCT
ejpam-3449	511	35	i	i	NOUN
ejpam-3449	511	36	)	)	PUNCT
ejpam-3449	511	37	for	for	ADP
ejpam-3449	511	38	every	every	DET
ejpam-3449	511	39	fγg.closed	fγg.close	VERB
ejpam-3449	511	40	set	set	VERB
ejpam-3449	511	41	a	a	PRON
ejpam-3449	511	42	of	of	ADP
ejpam-3449	511	43	(	(	PUNCT
ejpam-3449	511	44	x	x	PROPN
ejpam-3449	511	45	,	,	PUNCT
ejpam-3449	511	46	τ	τ	PROPN
ejpam-3449	511	47	,	,	PUNCT
ejpam-3449	511	48	τf	τf	NUM
ejpam-3449	511	49	)	)	PUNCT
ejpam-3449	511	50	,	,	PUNCT
ejpam-3449	511	51	the	the	DET
ejpam-3449	511	52	image	image	NOUN
ejpam-3449	511	53	h(a	h(a	PROPN
ejpam-3449	511	54	)	)	PUNCT
ejpam-3449	511	55	is	be	AUX
ejpam-3449	511	56	fβg.closed	fβg.close	VERB
ejpam-3449	511	57	in	in	ADP
ejpam-3449	511	58	(	(	PUNCT
ejpam-3449	511	59	y	y	PROPN
ejpam-3449	511	60	,	,	PUNCT
ejpam-3449	511	61	σ	σ	PROPN
ejpam-3449	511	62	,	,	PUNCT
ejpam-3449	511	63	σf	σf	NOUN
ejpam-3449	511	64	)	)	PUNCT
ejpam-3449	511	65	.	.	PUNCT
ejpam-3449	512	1	(	(	PUNCT
ejpam-3449	512	2	ii	ii	NOUN
ejpam-3449	512	3	)	)	PUNCT
ejpam-3449	512	4	for	for	ADP
ejpam-3449	512	5	every	every	DET
ejpam-3449	512	6	fβg.closed	fβg.close	VERB
ejpam-3449	512	7	set	set	NOUN
ejpam-3449	512	8	b	b	PROPN
ejpam-3449	512	9	of	of	ADP
ejpam-3449	512	10	(	(	PUNCT
ejpam-3449	512	11	y	y	PROPN
ejpam-3449	512	12	,	,	PUNCT
ejpam-3449	512	13	σ	σ	PROPN
ejpam-3449	512	14	,	,	PUNCT
ejpam-3449	512	15	σf	σf	NOUN
ejpam-3449	512	16	)	)	PUNCT
ejpam-3449	512	17	,	,	PUNCT
ejpam-3449	512	18	the	the	DET
ejpam-3449	512	19	inverse	inverse	NOUN
ejpam-3449	512	20	set	set	VERB
ejpam-3449	512	21	h−1(b	h−1(b	PROPN
ejpam-3449	512	22	)	)	PUNCT
ejpam-3449	512	23	is	be	AUX
ejpam-3449	512	24	fγg.closed	fγg.close	VERB
ejpam-3449	512	25	in	in	ADP
ejpam-3449	512	26	(	(	PUNCT
ejpam-3449	512	27	x	x	NOUN
ejpam-3449	512	28	,	,	PUNCT
ejpam-3449	512	29	τ	τ	PROPN
ejpam-3449	512	30	,	,	PUNCT
ejpam-3449	512	31	τf	τf	NUM
ejpam-3449	512	32	)	)	PUNCT
ejpam-3449	512	33	.	.	PUNCT
ejpam-3449	513	1	proof	proof	NOUN
ejpam-3449	513	2	.	.	PUNCT
ejpam-3449	514	1	(	(	PUNCT
ejpam-3449	514	2	1	1	X
ejpam-3449	514	3	)	)	PUNCT
ejpam-3449	514	4	let	let	VERB
ejpam-3449	514	5	g	g	NOUN
ejpam-3449	514	6	be	be	AUX
ejpam-3449	514	7	any	any	DET
ejpam-3449	514	8	fβ	fβ	ADJ
ejpam-3449	514	9	-	-	PUNCT
ejpam-3449	514	10	open	open	ADJ
ejpam-3449	514	11	set	set	NOUN
ejpam-3449	514	12	in	in	ADP
ejpam-3449	514	13	(	(	PUNCT
ejpam-3449	514	14	y	y	PROPN
ejpam-3449	514	15	,	,	PUNCT
ejpam-3449	514	16	σ	σ	PROPN
ejpam-3449	514	17	,	,	PUNCT
ejpam-3449	514	18	σf	σf	NOUN
ejpam-3449	514	19	)	)	PUNCT
ejpam-3449	514	20	such	such	ADJ
ejpam-3449	514	21	that	that	DET
ejpam-3449	514	22	h(a	h(a	PROPN
ejpam-3449	514	23	)	)	PUNCT
ejpam-3449	515	1	⊆	⊆	NUM
ejpam-3449	515	2	g.	g.	NOUN
ejpam-3449	515	3	since	since	SCONJ
ejpam-3449	515	4	h	h	PROPN
ejpam-3449	515	5	is	be	AUX
ejpam-3449	515	6	fγβ	fγβ	ADV
ejpam-3449	515	7	-	-	ADJ
ejpam-3449	515	8	continuous	continuous	ADJ
ejpam-3449	515	9	function	function	NOUN
ejpam-3449	515	10	,	,	PUNCT
ejpam-3449	515	11	then	then	ADV
ejpam-3449	515	12	by	by	ADP
ejpam-3449	515	13	using	use	VERB
ejpam-3449	515	14	theorem	theorem	ADJ
ejpam-3449	515	15	6.2	6.2	NUM
ejpam-3449	515	16	(	(	PUNCT
ejpam-3449	515	17	2	2	NUM
ejpam-3449	515	18	)	)	PUNCT
ejpam-3449	515	19	,	,	PUNCT
ejpam-3449	515	20	h−1(g	h−1(g	PROPN
ejpam-3449	515	21	)	)	PUNCT
ejpam-3449	515	22	is	be	AUX
ejpam-3449	515	23	fγ	fγ	ADV
ejpam-3449	515	24	-	-	PUNCT
ejpam-3449	515	25	open	open	NOUN
ejpam-3449	515	26	set	set	NOUN
ejpam-3449	515	27	in	in	ADP
ejpam-3449	515	28	(	(	PUNCT
ejpam-3449	515	29	x	x	NOUN
ejpam-3449	515	30	,	,	PUNCT
ejpam-3449	515	31	τ	τ	PROPN
ejpam-3449	515	32	,	,	PUNCT
ejpam-3449	515	33	τf	τf	NUM
ejpam-3449	515	34	)	)	PUNCT
ejpam-3449	515	35	.	.	PUNCT
ejpam-3449	516	1	since	since	SCONJ
ejpam-3449	516	2	a	a	PRON
ejpam-3449	516	3	is	be	AUX
ejpam-3449	516	4	fγg.closed	fγg.close	VERB
ejpam-3449	516	5	and	and	CCONJ
ejpam-3449	516	6	a	a	DET
ejpam-3449	516	7	⊆	⊆	NUM
ejpam-3449	516	8	h−1(g	h−1(g	NOUN
ejpam-3449	516	9	)	)	PUNCT
ejpam-3449	516	10	,	,	PUNCT
ejpam-3449	516	11	we	we	PRON
ejpam-3449	516	12	have	have	VERB
ejpam-3449	516	13	fclγ(a	fclγ(a	NOUN
ejpam-3449	516	14	)	)	PUNCT
ejpam-3449	516	15	⊆	⊆	NUM
ejpam-3449	516	16	h−1(g	h−1(g	NOUN
ejpam-3449	516	17	)	)	PUNCT
ejpam-3449	516	18	,	,	PUNCT
ejpam-3449	516	19	and	and	CCONJ
ejpam-3449	516	20	hence	hence	ADV
ejpam-3449	516	21	h(fclγ(a	h(fclγ(a	NUM
ejpam-3449	516	22	)	)	PUNCT
ejpam-3449	516	23	)	)	PUNCT
ejpam-3449	517	1	⊆	⊆	NUM
ejpam-3449	517	2	g.	g.	NOUN
ejpam-3449	517	3	thus	thus	ADV
ejpam-3449	517	4	,	,	PUNCT
ejpam-3449	517	5	by	by	ADP
ejpam-3449	517	6	lemma	lemma	PROPN
ejpam-3449	517	7	3.13	3.13	NUM
ejpam-3449	517	8	(	(	PUNCT
ejpam-3449	517	9	1	1	NUM
ejpam-3449	517	10	)	)	PUNCT
ejpam-3449	517	11	,	,	PUNCT
ejpam-3449	517	12	fclγ(a	fclγ(a	NOUN
ejpam-3449	517	13	)	)	PUNCT
ejpam-3449	517	14	is	be	AUX
ejpam-3449	517	15	fine	fine	ADV
ejpam-3449	517	16	-	-	PUNCT
ejpam-3449	517	17	closed	close	VERB
ejpam-3449	517	18	set	set	NOUN
ejpam-3449	517	19	and	and	CCONJ
ejpam-3449	517	20	since	since	SCONJ
ejpam-3449	517	21	h	h	NOUN
ejpam-3449	517	22	is	be	AUX
ejpam-3449	517	23	fβclosed	fβclose	VERB
ejpam-3449	517	24	,	,	PUNCT
ejpam-3449	517	25	then	then	ADV
ejpam-3449	517	26	h(fclγ(a	h(fclγ(a	NOUN
ejpam-3449	517	27	)	)	PUNCT
ejpam-3449	517	28	)	)	PUNCT
ejpam-3449	518	1	is	be	AUX
ejpam-3449	518	2	fβ	fβ	ADV
ejpam-3449	518	3	-	-	PUNCT
ejpam-3449	518	4	closed	closed	ADJ
ejpam-3449	518	5	set	set	NOUN
ejpam-3449	518	6	in	in	ADP
ejpam-3449	518	7	y	y	PROPN
ejpam-3449	518	8	.	.	PUNCT
ejpam-3449	519	1	therefore	therefore	ADV
ejpam-3449	519	2	,	,	PUNCT
ejpam-3449	519	3	fclβ(h(a	fclβ(h(a	PROPN
ejpam-3449	519	4	)	)	PUNCT
ejpam-3449	519	5	)	)	PUNCT
ejpam-3449	520	1	⊆	⊆	NUM
ejpam-3449	520	2	fclβ(h(fclγ(a	fclβ(h(fclγ(a	NOUN
ejpam-3449	520	3	)	)	PUNCT
ejpam-3449	520	4	)	)	PUNCT
ejpam-3449	520	5	)	)	PUNCT
ejpam-3449	521	1	=	=	PUNCT
ejpam-3449	521	2	h(fclγ(a	h(fclγ(a	NOUN
ejpam-3449	521	3	)	)	PUNCT
ejpam-3449	521	4	)	)	PUNCT
ejpam-3449	522	1	⊆	⊆	NUM
ejpam-3449	522	2	g.	g.	NOUN
ejpam-3449	522	3	this	this	PRON
ejpam-3449	522	4	implies	imply	VERB
ejpam-3449	522	5	that	that	SCONJ
ejpam-3449	522	6	h(a	h(a	PROPN
ejpam-3449	522	7	)	)	PUNCT
ejpam-3449	522	8	is	be	AUX
ejpam-3449	522	9	fβg.closed	fβg.close	VERB
ejpam-3449	522	10	in	in	ADP
ejpam-3449	522	11	(	(	PUNCT
ejpam-3449	522	12	y	y	PROPN
ejpam-3449	522	13	,	,	PUNCT
ejpam-3449	522	14	σ	σ	PROPN
ejpam-3449	522	15	,	,	PUNCT
ejpam-3449	522	16	σf	σf	NOUN
ejpam-3449	522	17	)	)	PUNCT
ejpam-3449	522	18	.	.	PUNCT
ejpam-3449	523	1	(	(	PUNCT
ejpam-3449	523	2	2	2	X
ejpam-3449	523	3	)	)	PUNCT
ejpam-3449	523	4	let	let	VERB
ejpam-3449	523	5	h	h	NOUN
ejpam-3449	523	6	be	be	AUX
ejpam-3449	523	7	any	any	DET
ejpam-3449	523	8	fγ	fγ	ADV
ejpam-3449	523	9	-	-	PUNCT
ejpam-3449	523	10	open	open	ADJ
ejpam-3449	523	11	set	set	NOUN
ejpam-3449	523	12	of	of	ADP
ejpam-3449	523	13	a	a	DET
ejpam-3449	523	14	fine	fine	ADJ
ejpam-3449	523	15	space	space	NOUN
ejpam-3449	523	16	(	(	PUNCT
ejpam-3449	523	17	x	x	X
ejpam-3449	523	18	,	,	PUNCT
ejpam-3449	523	19	τ	τ	PROPN
ejpam-3449	523	20	,	,	PUNCT
ejpam-3449	523	21	τf	τf	NUM
ejpam-3449	523	22	)	)	PUNCT
ejpam-3449	523	23	such	such	ADJ
ejpam-3449	523	24	that	that	SCONJ
ejpam-3449	523	25	h−1(b	h−1(b	PROPN
ejpam-3449	523	26	)	)	PUNCT
ejpam-3449	523	27	⊆	⊆	NUM
ejpam-3449	523	28	h.	h.	NOUN
ejpam-3449	523	29	let	let	VERB
ejpam-3449	523	30	c	c	NOUN
ejpam-3449	523	31	=	=	PUNCT
ejpam-3449	523	32	fclγ(h−1(b	fclγ(h−1(b	X
ejpam-3449	523	33	)	)	PUNCT
ejpam-3449	523	34	)	)	PUNCT
ejpam-3449	524	1	∩	∩	NOUN
ejpam-3449	524	2	(	(	PUNCT
ejpam-3449	524	3	x\h	x\h	PROPN
ejpam-3449	524	4	)	)	PUNCT
ejpam-3449	524	5	,	,	PUNCT
ejpam-3449	524	6	then	then	ADV
ejpam-3449	524	7	by	by	ADP
ejpam-3449	524	8	lemma	lemma	PROPN
ejpam-3449	524	9	3.13	3.13	NUM
ejpam-3449	524	10	(	(	PUNCT
ejpam-3449	524	11	1	1	NUM
ejpam-3449	524	12	)	)	PUNCT
ejpam-3449	524	13	,	,	PUNCT
ejpam-3449	524	14	c	c	PROPN
ejpam-3449	524	15	is	be	AUX
ejpam-3449	524	16	fine	fine	ADV
ejpam-3449	524	17	-	-	PUNCT
ejpam-3449	524	18	closed	close	VERB
ejpam-3449	524	19	set	set	NOUN
ejpam-3449	524	20	in	in	ADP
ejpam-3449	524	21	(	(	PUNCT
ejpam-3449	524	22	x	x	NOUN
ejpam-3449	524	23	,	,	PUNCT
ejpam-3449	524	24	τ	τ	PROPN
ejpam-3449	524	25	,	,	PUNCT
ejpam-3449	524	26	τf	τf	NUM
ejpam-3449	524	27	)	)	PUNCT
ejpam-3449	524	28	.	.	PUNCT
ejpam-3449	525	1	since	since	SCONJ
ejpam-3449	525	2	h	h	NOUN
ejpam-3449	525	3	is	be	AUX
ejpam-3449	525	4	fβ	fβ	ADV
ejpam-3449	525	5	-	-	PUNCT
ejpam-3449	525	6	closed	closed	ADJ
ejpam-3449	525	7	function	function	NOUN
ejpam-3449	525	8	.	.	PUNCT
ejpam-3449	526	1	then	then	ADV
ejpam-3449	526	2	h(c	h(c	PROPN
ejpam-3449	526	3	)	)	PUNCT
ejpam-3449	526	4	is	be	AUX
ejpam-3449	526	5	fβ	fβ	ADV
ejpam-3449	526	6	-	-	PUNCT
ejpam-3449	526	7	closed	closed	ADJ
ejpam-3449	526	8	in	in	ADP
ejpam-3449	526	9	(	(	PUNCT
ejpam-3449	526	10	y	y	PROPN
ejpam-3449	526	11	,	,	PUNCT
ejpam-3449	526	12	σ	σ	PROPN
ejpam-3449	526	13	,	,	PUNCT
ejpam-3449	526	14	σf	σf	NOUN
ejpam-3449	526	15	)	)	PUNCT
ejpam-3449	526	16	.	.	PUNCT
ejpam-3449	527	1	since	since	SCONJ
ejpam-3449	527	2	h	h	PROPN
ejpam-3449	527	3	is	be	AUX
ejpam-3449	527	4	fγβ	fγβ	ADV
ejpam-3449	527	5	-	-	ADJ
ejpam-3449	527	6	continuous	continuous	ADJ
ejpam-3449	527	7	function	function	NOUN
ejpam-3449	527	8	,	,	PUNCT
ejpam-3449	527	9	then	then	ADV
ejpam-3449	527	10	by	by	ADP
ejpam-3449	527	11	using	use	VERB
ejpam-3449	527	12	theorem	theorem	ADJ
ejpam-3449	527	13	6.2	6.2	NUM
ejpam-3449	527	14	(	(	PUNCT
ejpam-3449	527	15	1	1	NUM
ejpam-3449	527	16	)	)	PUNCT
ejpam-3449	527	17	,	,	PUNCT
ejpam-3449	527	18	we	we	PRON
ejpam-3449	527	19	have	have	VERB
ejpam-3449	527	20	h(c	h(c	PROPN
ejpam-3449	527	21	)	)	PUNCT
ejpam-3449	527	22	=	=	SYM
ejpam-3449	527	23	h(fclγ(h−1(b	h(fclγ(h−1(b	ADJ
ejpam-3449	527	24	)	)	PUNCT
ejpam-3449	527	25	)	)	PUNCT
ejpam-3449	527	26	)	)	PUNCT
ejpam-3449	528	1	∩	∩	PROPN
ejpam-3449	528	2	h(x\h	h(x\h	PROPN
ejpam-3449	528	3	)	)	PUNCT
ejpam-3449	528	4	⊆	⊆	NUM
ejpam-3449	528	5	fclβ(b	fclβ(b	NOUN
ejpam-3449	528	6	)	)	PUNCT
ejpam-3449	528	7	∩	∩	ADJ
ejpam-3449	528	8	h(x\h	h(x\h	PROPN
ejpam-3449	528	9	)	)	PUNCT
ejpam-3449	528	10	⊆	⊆	NUM
ejpam-3449	528	11	fclβ(b	fclβ(b	NOUN
ejpam-3449	528	12	)	)	PUNCT
ejpam-3449	528	13	∩	∩	NOUN
ejpam-3449	528	14	(	(	PUNCT
ejpam-3449	528	15	y	y	PROPN
ejpam-3449	528	16	\b	\b	NOUN
ejpam-3449	528	17	)	)	PUNCT
ejpam-3449	528	18	=	=	SYM
ejpam-3449	529	1	fclβ(b)\b	fclβ(b)\b	PROPN
ejpam-3449	529	2	.	.	PUNCT
ejpam-3449	530	1	this	this	PRON
ejpam-3449	530	2	implies	imply	VERB
ejpam-3449	530	3	from	from	ADP
ejpam-3449	530	4	theorem	theorem	ADJ
ejpam-3449	530	5	4.3	4.3	NUM
ejpam-3449	530	6	that	that	SCONJ
ejpam-3449	530	7	h(c	h(c	PROPN
ejpam-3449	530	8	)	)	PUNCT
ejpam-3449	530	9	=	=	SYM
ejpam-3449	530	10	φ	φ	PROPN
ejpam-3449	530	11	,	,	PUNCT
ejpam-3449	530	12	and	and	CCONJ
ejpam-3449	530	13	hence	hence	ADV
ejpam-3449	530	14	c	c	NOUN
ejpam-3449	530	15	=	=	SYM
ejpam-3449	530	16	φ	φ	PROPN
ejpam-3449	530	17	.	.	PUNCT
ejpam-3449	531	1	so	so	SCONJ
ejpam-3449	531	2	fclγ(h−1(b	fclγ(h−1(b	NOUN
ejpam-3449	531	3	)	)	PUNCT
ejpam-3449	531	4	)	)	PUNCT
ejpam-3449	532	1	⊆	⊆	NUM
ejpam-3449	532	2	h.	h.	PROPN
ejpam-3449	532	3	therefore	therefore	ADV
ejpam-3449	532	4	,	,	PUNCT
ejpam-3449	532	5	h−1(b	h−1(b	PROPN
ejpam-3449	532	6	)	)	PUNCT
ejpam-3449	532	7	is	be	AUX
ejpam-3449	532	8	fγg.closed	fγg.close	VERB
ejpam-3449	532	9	in	in	ADP
ejpam-3449	532	10	(	(	PUNCT
ejpam-3449	532	11	x	x	NOUN
ejpam-3449	532	12	,	,	PUNCT
ejpam-3449	532	13	τ	τ	PROPN
ejpam-3449	532	14	,	,	PUNCT
ejpam-3449	532	15	τf	τf	NUM
ejpam-3449	532	16	)	)	PUNCT
ejpam-3449	532	17	.	.	PUNCT
ejpam-3449	533	1	theorem	theorem	VERB
ejpam-3449	533	2	6.6	6.6	NUM
ejpam-3449	533	3	.	.	PUNCT
ejpam-3449	534	1	let	let	VERB
ejpam-3449	534	2	h	h	NOUN
ejpam-3449	534	3	:	:	PUNCT
ejpam-3449	534	4	(	(	PUNCT
ejpam-3449	534	5	x	x	X
ejpam-3449	534	6	,	,	PUNCT
ejpam-3449	534	7	τ	τ	PROPN
ejpam-3449	534	8	,	,	PUNCT
ejpam-3449	534	9	τf	τf	NOUN
ejpam-3449	534	10	)	)	PUNCT
ejpam-3449	534	11	→	→	SYM
ejpam-3449	534	12	(	(	PUNCT
ejpam-3449	534	13	y	y	PROPN
ejpam-3449	534	14	,	,	PUNCT
ejpam-3449	534	15	σ	σ	PROPN
ejpam-3449	534	16	,	,	PUNCT
ejpam-3449	534	17	σf	σf	NOUN
ejpam-3449	534	18	)	)	PUNCT
ejpam-3449	534	19	be	be	AUX
ejpam-3449	534	20	an	an	DET
ejpam-3449	534	21	injective	injective	ADJ
ejpam-3449	534	22	,	,	PUNCT
ejpam-3449	534	23	fγβ	fγβ	ADV
ejpam-3449	534	24	-	-	ADJ
ejpam-3449	534	25	continuous	continuous	ADJ
ejpam-3449	534	26	and	and	CCONJ
ejpam-3449	534	27	fβ	fβ	ADV
ejpam-3449	534	28	-	-	PUNCT
ejpam-3449	534	29	closed	closed	ADJ
ejpam-3449	534	30	function	function	NOUN
ejpam-3449	534	31	.	.	PUNCT
ejpam-3449	535	1	if	if	SCONJ
ejpam-3449	535	2	(	(	PUNCT
ejpam-3449	535	3	y	y	PROPN
ejpam-3449	535	4	,	,	PUNCT
ejpam-3449	535	5	σ	σ	PROPN
ejpam-3449	535	6	,	,	PUNCT
ejpam-3449	535	7	σf	σf	NOUN
ejpam-3449	535	8	)	)	PUNCT
ejpam-3449	535	9	is	be	AUX
ejpam-3449	535	10	fβ	fβ	ADJ
ejpam-3449	535	11	-	-	PUNCT
ejpam-3449	535	12	t	t	NOUN
ejpam-3449	535	13	1	1	NUM
ejpam-3449	535	14	2	2	NUM
ejpam-3449	535	15	,	,	PUNCT
ejpam-3449	535	16	then	then	ADV
ejpam-3449	535	17	(	(	PUNCT
ejpam-3449	535	18	x	x	X
ejpam-3449	535	19	,	,	PUNCT
ejpam-3449	535	20	τ	τ	PROPN
ejpam-3449	535	21	,	,	PUNCT
ejpam-3449	535	22	τf	τf	PROPN
ejpam-3449	535	23	)	)	PUNCT
ejpam-3449	535	24	is	be	AUX
ejpam-3449	535	25	fγ	fγ	PROPN
ejpam-3449	535	26	-	-	PUNCT
ejpam-3449	535	27	t	t	PROPN
ejpam-3449	535	28	1	1	NUM
ejpam-3449	535	29	2	2	NUM
ejpam-3449	535	30	.	.	PUNCT
ejpam-3449	536	1	proof	proof	NOUN
ejpam-3449	536	2	.	.	PUNCT
ejpam-3449	537	1	let	let	VERB
ejpam-3449	537	2	g	g	NOUN
ejpam-3449	537	3	be	be	AUX
ejpam-3449	537	4	any	any	DET
ejpam-3449	537	5	fγg.closed	fγg.close	VERB
ejpam-3449	537	6	set	set	NOUN
ejpam-3449	537	7	of	of	ADP
ejpam-3449	537	8	(	(	PUNCT
ejpam-3449	537	9	x	x	PROPN
ejpam-3449	537	10	,	,	PUNCT
ejpam-3449	537	11	τ	τ	PROPN
ejpam-3449	537	12	,	,	PUNCT
ejpam-3449	537	13	τf	τf	NUM
ejpam-3449	537	14	)	)	PUNCT
ejpam-3449	537	15	.	.	PUNCT
ejpam-3449	538	1	since	since	SCONJ
ejpam-3449	538	2	h	h	PROPN
ejpam-3449	538	3	is	be	AUX
ejpam-3449	538	4	fγβ	fγβ	ADV
ejpam-3449	538	5	-	-	ADJ
ejpam-3449	538	6	continuous	continuous	ADJ
ejpam-3449	538	7	and	and	CCONJ
ejpam-3449	538	8	fβ	fβ	ADV
ejpam-3449	538	9	-	-	PUNCT
ejpam-3449	538	10	closed	closed	ADJ
ejpam-3449	538	11	function	function	NOUN
ejpam-3449	538	12	.	.	PUNCT
ejpam-3449	539	1	then	then	ADV
ejpam-3449	539	2	by	by	ADP
ejpam-3449	539	3	theorem	theorem	ADJ
ejpam-3449	539	4	6.5	6.5	NUM
ejpam-3449	539	5	(	(	PUNCT
ejpam-3449	539	6	1	1	NUM
ejpam-3449	539	7	)	)	PUNCT
ejpam-3449	539	8	,	,	PUNCT
ejpam-3449	539	9	h(g	h(g	NOUN
ejpam-3449	539	10	)	)	PUNCT
ejpam-3449	539	11	is	be	AUX
ejpam-3449	539	12	fβg.closed	fβg.close	VERB
ejpam-3449	539	13	in	in	ADP
ejpam-3449	539	14	(	(	PUNCT
ejpam-3449	539	15	y	y	PROPN
ejpam-3449	539	16	,	,	PUNCT
ejpam-3449	539	17	σ	σ	PROPN
ejpam-3449	539	18	,	,	PUNCT
ejpam-3449	539	19	σf	σf	NOUN
ejpam-3449	539	20	)	)	PUNCT
ejpam-3449	539	21	.	.	PUNCT
ejpam-3449	540	1	since	since	SCONJ
ejpam-3449	540	2	(	(	PUNCT
ejpam-3449	540	3	y	y	PROPN
ejpam-3449	540	4	,	,	PUNCT
ejpam-3449	540	5	σ	σ	PROPN
ejpam-3449	540	6	,	,	PUNCT
ejpam-3449	540	7	σf	σf	NOUN
ejpam-3449	540	8	)	)	PUNCT
ejpam-3449	540	9	is	be	AUX
ejpam-3449	540	10	fβ	fβ	ADJ
ejpam-3449	540	11	-	-	PUNCT
ejpam-3449	540	12	t	t	NOUN
ejpam-3449	540	13	1	1	NUM
ejpam-3449	540	14	2	2	NUM
ejpam-3449	540	15	,	,	PUNCT
ejpam-3449	540	16	then	then	ADV
ejpam-3449	540	17	h(g	h(g	NOUN
ejpam-3449	540	18	)	)	PUNCT
ejpam-3449	540	19	is	be	AUX
ejpam-3449	540	20	fβ	fβ	ADV
ejpam-3449	540	21	-	-	PUNCT
ejpam-3449	540	22	closed	closed	ADJ
ejpam-3449	540	23	in	in	ADP
ejpam-3449	540	24	y	y	PROPN
ejpam-3449	540	25	.	.	PUNCT
ejpam-3449	541	1	again	again	ADV
ejpam-3449	541	2	,	,	PUNCT
ejpam-3449	541	3	since	since	SCONJ
ejpam-3449	541	4	h	h	NOUN
ejpam-3449	541	5	is	be	AUX
ejpam-3449	541	6	fγβ	fγβ	ADV
ejpam-3449	541	7	-	-	ADJ
ejpam-3449	541	8	continuous	continuous	ADJ
ejpam-3449	541	9	,	,	PUNCT
ejpam-3449	541	10	then	then	ADV
ejpam-3449	541	11	by	by	ADP
ejpam-3449	541	12	theorem	theorem	ADJ
ejpam-3449	541	13	6.2	6.2	NUM
ejpam-3449	541	14	(	(	PUNCT
ejpam-3449	541	15	2	2	NUM
ejpam-3449	541	16	)	)	PUNCT
ejpam-3449	541	17	,	,	PUNCT
ejpam-3449	541	18	h−1(h(g	h−1(h(g	NOUN
ejpam-3449	541	19	)	)	PUNCT
ejpam-3449	541	20	)	)	PUNCT
ejpam-3449	541	21	is	be	AUX
ejpam-3449	541	22	fγ	fγ	NOUN
ejpam-3449	541	23	-	-	PUNCT
ejpam-3449	541	24	closed	close	VERB
ejpam-3449	541	25	in	in	ADP
ejpam-3449	541	26	x.	x.	NOUN
ejpam-3449	541	27	hence	hence	ADV
ejpam-3449	541	28	g	g	PROPN
ejpam-3449	541	29	is	be	AUX
ejpam-3449	541	30	fγ	fγ	NOUN
ejpam-3449	541	31	-	-	PUNCT
ejpam-3449	541	32	closed	closed	ADJ
ejpam-3449	541	33	in	in	ADP
ejpam-3449	541	34	x	x	PUNCT
ejpam-3449	541	35	since	since	SCONJ
ejpam-3449	541	36	h	h	NOUN
ejpam-3449	541	37	is	be	AUX
ejpam-3449	541	38	injective	injective	ADJ
ejpam-3449	541	39	.	.	PUNCT
ejpam-3449	542	1	therefore	therefore	ADV
ejpam-3449	542	2	,	,	PUNCT
ejpam-3449	542	3	(	(	PUNCT
ejpam-3449	542	4	x	x	X
ejpam-3449	542	5	,	,	PUNCT
ejpam-3449	542	6	τ	τ	PROPN
ejpam-3449	542	7	,	,	PUNCT
ejpam-3449	542	8	τf	τf	PROPN
ejpam-3449	542	9	)	)	PUNCT
ejpam-3449	542	10	is	be	AUX
ejpam-3449	542	11	a	a	DET
ejpam-3449	542	12	fγ	fγ	PROPN
ejpam-3449	542	13	-	-	PUNCT
ejpam-3449	542	14	t	t	NOUN
ejpam-3449	542	15	1	1	NUM
ejpam-3449	542	16	2	2	NUM
ejpam-3449	542	17	space	space	NOUN
ejpam-3449	542	18	.	.	PUNCT
ejpam-3449	543	1	theorem	theorem	VERB
ejpam-3449	543	2	6.7	6.7	NUM
ejpam-3449	543	3	.	.	PUNCT
ejpam-3449	544	1	let	let	VERB
ejpam-3449	544	2	a	a	DET
ejpam-3449	544	3	function	function	NOUN
ejpam-3449	544	4	h	h	NOUN
ejpam-3449	544	5	:	:	PUNCT
ejpam-3449	544	6	(	(	PUNCT
ejpam-3449	544	7	x	x	X
ejpam-3449	544	8	,	,	PUNCT
ejpam-3449	544	9	τ	τ	PROPN
ejpam-3449	544	10	,	,	PUNCT
ejpam-3449	544	11	τf	τf	NOUN
ejpam-3449	544	12	)	)	PUNCT
ejpam-3449	544	13	→	→	SYM
ejpam-3449	544	14	(	(	PUNCT
ejpam-3449	544	15	y	y	PROPN
ejpam-3449	544	16	,	,	PUNCT
ejpam-3449	544	17	σ	σ	PROPN
ejpam-3449	544	18	,	,	PUNCT
ejpam-3449	544	19	σf	σf	NOUN
ejpam-3449	544	20	)	)	PUNCT
ejpam-3449	544	21	be	be	AUX
ejpam-3449	544	22	surjective	surjective	ADJ
ejpam-3449	544	23	,	,	PUNCT
ejpam-3449	544	24	fγβ	fγβ	ADJ
ejpam-3449	544	25	-	-	ADJ
ejpam-3449	544	26	continuous	continuous	ADJ
ejpam-3449	544	27	and	and	CCONJ
ejpam-3449	544	28	fβ	fβ	ADV
ejpam-3449	544	29	-	-	PUNCT
ejpam-3449	544	30	closed	closed	ADJ
ejpam-3449	544	31	.	.	PUNCT
ejpam-3449	545	1	if	if	SCONJ
ejpam-3449	545	2	(	(	PUNCT
ejpam-3449	545	3	x	x	NOUN
ejpam-3449	545	4	,	,	PUNCT
ejpam-3449	545	5	τ	τ	PROPN
ejpam-3449	545	6	,	,	PUNCT
ejpam-3449	545	7	τf	τf	PROPN
ejpam-3449	545	8	)	)	PUNCT
ejpam-3449	545	9	is	be	AUX
ejpam-3449	545	10	fγ	fγ	PROPN
ejpam-3449	545	11	-	-	PUNCT
ejpam-3449	545	12	t	t	PROPN
ejpam-3449	545	13	1	1	NUM
ejpam-3449	545	14	2	2	NUM
ejpam-3449	545	15	,	,	PUNCT
ejpam-3449	545	16	then	then	ADV
ejpam-3449	545	17	(	(	PUNCT
ejpam-3449	545	18	y	y	PROPN
ejpam-3449	545	19	,	,	PUNCT
ejpam-3449	545	20	σ	σ	PROPN
ejpam-3449	545	21	,	,	PUNCT
ejpam-3449	545	22	σf	σf	NOUN
ejpam-3449	545	23	)	)	PUNCT
ejpam-3449	545	24	is	be	AUX
ejpam-3449	545	25	fβ	fβ	ADJ
ejpam-3449	545	26	-	-	PUNCT
ejpam-3449	545	27	t	t	NOUN
ejpam-3449	545	28	1	1	NUM
ejpam-3449	545	29	2	2	NUM
ejpam-3449	545	30	.	.	PUNCT
ejpam-3449	546	1	proof	proof	NOUN
ejpam-3449	546	2	.	.	PUNCT
ejpam-3449	547	1	let	let	VERB
ejpam-3449	547	2	h	h	PRON
ejpam-3449	547	3	be	be	AUX
ejpam-3449	547	4	a	a	DET
ejpam-3449	547	5	fβg.closed	fβg.close	VERB
ejpam-3449	547	6	set	set	NOUN
ejpam-3449	547	7	of	of	ADP
ejpam-3449	547	8	(	(	PUNCT
ejpam-3449	547	9	y	y	PROPN
ejpam-3449	547	10	,	,	PUNCT
ejpam-3449	547	11	σ	σ	PROPN
ejpam-3449	547	12	,	,	PUNCT
ejpam-3449	547	13	σf	σf	NOUN
ejpam-3449	547	14	)	)	PUNCT
ejpam-3449	547	15	.	.	PUNCT
ejpam-3449	548	1	since	since	SCONJ
ejpam-3449	548	2	h	h	PROPN
ejpam-3449	548	3	is	be	AUX
ejpam-3449	548	4	fγβ	fγβ	ADV
ejpam-3449	548	5	-	-	ADJ
ejpam-3449	548	6	continuous	continuous	ADJ
ejpam-3449	548	7	and	and	CCONJ
ejpam-3449	548	8	fβ	fβ	ADV
ejpam-3449	548	9	-	-	PUNCT
ejpam-3449	548	10	closed	closed	ADJ
ejpam-3449	548	11	function	function	NOUN
ejpam-3449	548	12	.	.	PUNCT
ejpam-3449	549	1	then	then	ADV
ejpam-3449	549	2	by	by	ADP
ejpam-3449	549	3	theorem	theorem	ADJ
ejpam-3449	549	4	6.5	6.5	NUM
ejpam-3449	549	5	(	(	PUNCT
ejpam-3449	549	6	2	2	NUM
ejpam-3449	549	7	)	)	PUNCT
ejpam-3449	549	8	,	,	PUNCT
ejpam-3449	549	9	h−1(h	h−1(h	PROPN
ejpam-3449	549	10	)	)	PUNCT
ejpam-3449	549	11	is	be	AUX
ejpam-3449	549	12	fγg.closed	fγg.close	VERB
ejpam-3449	549	13	in	in	ADP
ejpam-3449	549	14	(	(	PUNCT
ejpam-3449	549	15	x	x	NOUN
ejpam-3449	549	16	,	,	PUNCT
ejpam-3449	549	17	τ	τ	PROPN
ejpam-3449	549	18	,	,	PUNCT
ejpam-3449	549	19	τf	τf	NUM
ejpam-3449	549	20	)	)	PUNCT
ejpam-3449	549	21	.	.	PUNCT
ejpam-3449	550	1	since	since	SCONJ
ejpam-3449	550	2	(	(	PUNCT
ejpam-3449	550	3	x	x	X
ejpam-3449	550	4	,	,	PUNCT
ejpam-3449	550	5	τ	τ	PROPN
ejpam-3449	550	6	,	,	PUNCT
ejpam-3449	550	7	τf	τf	PROPN
ejpam-3449	550	8	)	)	PUNCT
ejpam-3449	550	9	is	be	AUX
ejpam-3449	550	10	fγ	fγ	PROPN
ejpam-3449	550	11	-	-	PUNCT
ejpam-3449	550	12	t	t	PROPN
ejpam-3449	550	13	1	1	NUM
ejpam-3449	550	14	2	2	NUM
ejpam-3449	550	15	,	,	PUNCT
ejpam-3449	550	16	then	then	ADV
ejpam-3449	550	17	we	we	PRON
ejpam-3449	550	18	have	have	AUX
ejpam-3449	550	19	,	,	PUNCT
ejpam-3449	550	20	h−1(h	h−1(h	PROPN
ejpam-3449	550	21	)	)	PUNCT
ejpam-3449	550	22	is	be	AUX
ejpam-3449	550	23	fγ	fγ	ADV
ejpam-3449	550	24	-	-	PUNCT
ejpam-3449	550	25	closed	close	VERB
ejpam-3449	550	26	set	set	NOUN
ejpam-3449	550	27	in	in	ADP
ejpam-3449	550	28	x.	x.	NOUN
ejpam-3449	550	29	again	again	ADV
ejpam-3449	550	30	,	,	PUNCT
ejpam-3449	550	31	since	since	SCONJ
ejpam-3449	550	32	h	h	NOUN
ejpam-3449	550	33	is	be	AUX
ejpam-3449	550	34	fβ	fβ	ADV
ejpam-3449	550	35	-	-	PUNCT
ejpam-3449	550	36	closed	closed	ADJ
ejpam-3449	550	37	function	function	NOUN
ejpam-3449	550	38	,	,	PUNCT
ejpam-3449	550	39	then	then	ADV
ejpam-3449	550	40	h(h−1(h	h(h−1(h	PROPN
ejpam-3449	550	41	)	)	PUNCT
ejpam-3449	550	42	)	)	PUNCT
ejpam-3449	551	1	is	be	AUX
ejpam-3449	551	2	fβ	fβ	ADV
ejpam-3449	551	3	-	-	PUNCT
ejpam-3449	551	4	closed	closed	ADJ
ejpam-3449	551	5	in	in	ADP
ejpam-3449	551	6	y	y	PROPN
ejpam-3449	551	7	.	.	PUNCT
ejpam-3449	552	1	therefore	therefore	ADV
ejpam-3449	552	2	,	,	PUNCT
ejpam-3449	552	3	h	h	NOUN
ejpam-3449	552	4	is	be	AUX
ejpam-3449	552	5	fβ	fβ	ADV
ejpam-3449	552	6	-	-	PUNCT
ejpam-3449	552	7	closed	closed	ADJ
ejpam-3449	552	8	in	in	ADP
ejpam-3449	552	9	y	y	PROPN
ejpam-3449	552	10	since	since	SCONJ
ejpam-3449	552	11	h	h	PROPN
ejpam-3449	552	12	is	be	AUX
ejpam-3449	552	13	surjective	surjective	ADJ
ejpam-3449	552	14	.	.	PUNCT
ejpam-3449	553	1	hence	hence	ADV
ejpam-3449	553	2	(	(	PUNCT
ejpam-3449	553	3	y	y	PROPN
ejpam-3449	553	4	,	,	PUNCT
ejpam-3449	553	5	σ	σ	PROPN
ejpam-3449	553	6	,	,	PUNCT
ejpam-3449	553	7	σf	σf	NOUN
ejpam-3449	553	8	)	)	PUNCT
ejpam-3449	553	9	is	be	AUX
ejpam-3449	553	10	fβ	fβ	ADJ
ejpam-3449	553	11	-	-	PUNCT
ejpam-3449	553	12	t	t	NOUN
ejpam-3449	553	13	1	1	NUM
ejpam-3449	553	14	2	2	NUM
ejpam-3449	553	15	space	space	NOUN
ejpam-3449	553	16	.	.	PUNCT
ejpam-3449	554	1	b.	b.	PROPN
ejpam-3449	554	2	a.	a.	PROPN
ejpam-3449	554	3	asaad	asaad	PROPN
ejpam-3449	554	4	et	et	PROPN
ejpam-3449	554	5	al	al	PROPN
ejpam-3449	554	6	.	.	PUNCT
ejpam-3449	554	7	/	/	SYM
ejpam-3449	554	8	eur	eur	PROPN
ejpam-3449	554	9	.	.	PUNCT
ejpam-3449	555	1	j.	j.	PROPN
ejpam-3449	555	2	pure	pure	PROPN
ejpam-3449	555	3	appl	appl	PROPN
ejpam-3449	555	4	.	.	PROPN
ejpam-3449	555	5	math	math	PROPN
ejpam-3449	555	6	,	,	PUNCT
ejpam-3449	555	7	12	12	NUM
ejpam-3449	555	8	(	(	PUNCT
ejpam-3449	555	9	3	3	NUM
ejpam-3449	555	10	)	)	PUNCT
ejpam-3449	555	11	(	(	PUNCT
ejpam-3449	555	12	2019	2019	NUM
ejpam-3449	555	13	)	)	PUNCT
ejpam-3449	555	14	,	,	PUNCT
ejpam-3449	555	15	960	960	NUM
ejpam-3449	555	16	-	-	SYM
ejpam-3449	555	17	977	977	NUM
ejpam-3449	555	18	974	974	NUM
ejpam-3449	555	19	theorem	theorem	NOUN
ejpam-3449	555	20	6.8	6.8	NUM
ejpam-3449	555	21	.	.	PUNCT
ejpam-3449	556	1	if	if	SCONJ
ejpam-3449	556	2	a	a	DET
ejpam-3449	556	3	function	function	NOUN
ejpam-3449	556	4	h	h	NOUN
ejpam-3449	556	5	:	:	PUNCT
ejpam-3449	556	6	(	(	PUNCT
ejpam-3449	556	7	x	x	X
ejpam-3449	556	8	,	,	PUNCT
ejpam-3449	556	9	τ	τ	PROPN
ejpam-3449	556	10	,	,	PUNCT
ejpam-3449	556	11	τf	τf	NOUN
ejpam-3449	556	12	)	)	PUNCT
ejpam-3449	556	13	→	→	SYM
ejpam-3449	556	14	(	(	PUNCT
ejpam-3449	556	15	y	y	PROPN
ejpam-3449	556	16	,	,	PUNCT
ejpam-3449	556	17	σ	σ	PROPN
ejpam-3449	556	18	,	,	PUNCT
ejpam-3449	556	19	σf	σf	NOUN
ejpam-3449	556	20	)	)	PUNCT
ejpam-3449	556	21	is	be	AUX
ejpam-3449	556	22	injective	injective	ADJ
ejpam-3449	556	23	fγβ	fγβ	ADV
ejpam-3449	556	24	-	-	ADJ
ejpam-3449	556	25	continuous	continuous	ADJ
ejpam-3449	556	26	and	and	CCONJ
ejpam-3449	556	27	the	the	DET
ejpam-3449	556	28	fine	fine	ADJ
ejpam-3449	556	29	space	space	NOUN
ejpam-3449	556	30	(	(	PUNCT
ejpam-3449	556	31	y	y	PROPN
ejpam-3449	556	32	,	,	PUNCT
ejpam-3449	556	33	σ	σ	PROPN
ejpam-3449	556	34	,	,	PUNCT
ejpam-3449	556	35	σf	σf	NOUN
ejpam-3449	556	36	)	)	PUNCT
ejpam-3449	556	37	is	be	AUX
ejpam-3449	556	38	fβ	fβ	ADJ
ejpam-3449	556	39	-	-	PUNCT
ejpam-3449	556	40	t2	t2	NOUN
ejpam-3449	556	41	,	,	PUNCT
ejpam-3449	556	42	then	then	ADV
ejpam-3449	556	43	the	the	DET
ejpam-3449	556	44	fine	fine	ADJ
ejpam-3449	556	45	space	space	NOUN
ejpam-3449	556	46	(	(	PUNCT
ejpam-3449	556	47	x	x	X
ejpam-3449	556	48	,	,	PUNCT
ejpam-3449	556	49	τ	τ	PROPN
ejpam-3449	556	50	,	,	PUNCT
ejpam-3449	556	51	τf	τf	PROPN
ejpam-3449	556	52	)	)	PUNCT
ejpam-3449	556	53	is	be	AUX
ejpam-3449	556	54	fγ	fγ	NOUN
ejpam-3449	556	55	-	-	PUNCT
ejpam-3449	556	56	t2	t2	NOUN
ejpam-3449	556	57	.	.	PUNCT
ejpam-3449	557	1	proof	proof	NOUN
ejpam-3449	557	2	.	.	PUNCT
ejpam-3449	558	1	let	let	VERB
ejpam-3449	558	2	x1	x1	PROPN
ejpam-3449	558	3	and	and	CCONJ
ejpam-3449	558	4	x2	x2	PROPN
ejpam-3449	558	5	be	be	VERB
ejpam-3449	558	6	any	any	DET
ejpam-3449	558	7	distinct	distinct	ADJ
ejpam-3449	558	8	points	point	NOUN
ejpam-3449	558	9	of	of	ADP
ejpam-3449	558	10	a	a	DET
ejpam-3449	558	11	fine	fine	ADJ
ejpam-3449	558	12	space	space	NOUN
ejpam-3449	558	13	(	(	PUNCT
ejpam-3449	558	14	x	x	X
ejpam-3449	558	15	,	,	PUNCT
ejpam-3449	558	16	τ	τ	PROPN
ejpam-3449	558	17	,	,	PUNCT
ejpam-3449	558	18	τf	τf	NUM
ejpam-3449	558	19	)	)	PUNCT
ejpam-3449	558	20	.	.	PUNCT
ejpam-3449	559	1	since	since	SCONJ
ejpam-3449	559	2	h	h	NOUN
ejpam-3449	559	3	is	be	AUX
ejpam-3449	559	4	an	an	DET
ejpam-3449	559	5	injective	injective	ADJ
ejpam-3449	559	6	function	function	NOUN
ejpam-3449	559	7	and	and	CCONJ
ejpam-3449	559	8	(	(	PUNCT
ejpam-3449	559	9	y	y	PROPN
ejpam-3449	559	10	,	,	PUNCT
ejpam-3449	559	11	σ	σ	PROPN
ejpam-3449	559	12	,	,	PUNCT
ejpam-3449	559	13	σf	σf	NOUN
ejpam-3449	559	14	)	)	PUNCT
ejpam-3449	559	15	is	be	AUX
ejpam-3449	559	16	fβ	fβ	ADJ
ejpam-3449	559	17	-	-	PUNCT
ejpam-3449	559	18	t2	t2	NOUN
ejpam-3449	559	19	.	.	PUNCT
ejpam-3449	560	1	then	then	ADV
ejpam-3449	560	2	there	there	PRON
ejpam-3449	560	3	exist	exist	VERB
ejpam-3449	560	4	two	two	NUM
ejpam-3449	560	5	fine	fine	ADJ
ejpam-3449	560	6	-	-	PUNCT
ejpam-3449	560	7	open	open	ADJ
ejpam-3449	560	8	sets	set	NOUN
ejpam-3449	560	9	u1	u1	NOUN
ejpam-3449	560	10	and	and	CCONJ
ejpam-3449	560	11	u2	u2	NOUN
ejpam-3449	560	12	in	in	ADP
ejpam-3449	560	13	y	y	PROPN
ejpam-3449	560	14	such	such	ADJ
ejpam-3449	560	15	that	that	DET
ejpam-3449	560	16	f(x1	f(x1	ADJ
ejpam-3449	560	17	)	)	PUNCT
ejpam-3449	560	18	∈	∈	PROPN
ejpam-3449	560	19	u1	u1	NOUN
ejpam-3449	560	20	,	,	PUNCT
ejpam-3449	560	21	h(x2	h(x2	NOUN
ejpam-3449	560	22	)	)	PUNCT
ejpam-3449	560	23	∈	∈	PROPN
ejpam-3449	560	24	u2	u2	NOUN
ejpam-3449	560	25	and	and	CCONJ
ejpam-3449	560	26	β(u1	β(u1	NOUN
ejpam-3449	560	27	)	)	PUNCT
ejpam-3449	560	28	∩	∩	NOUN
ejpam-3449	560	29	β(u2	β(u2	NOUN
ejpam-3449	560	30	)	)	PUNCT
ejpam-3449	561	1	=	=	PUNCT
ejpam-3449	561	2	φ	φ	PROPN
ejpam-3449	561	3	.	.	PUNCT
ejpam-3449	562	1	since	since	SCONJ
ejpam-3449	562	2	h	h	PROPN
ejpam-3449	562	3	is	be	AUX
ejpam-3449	562	4	fγβ	fγβ	ADV
ejpam-3449	562	5	-	-	ADJ
ejpam-3449	562	6	continuous	continuous	ADJ
ejpam-3449	562	7	,	,	PUNCT
ejpam-3449	562	8	there	there	PRON
ejpam-3449	562	9	exist	exist	VERB
ejpam-3449	562	10	fine	fine	ADJ
ejpam-3449	562	11	-	-	PUNCT
ejpam-3449	562	12	open	open	ADJ
ejpam-3449	562	13	sets	set	NOUN
ejpam-3449	562	14	v1	v1	VERB
ejpam-3449	562	15	and	and	CCONJ
ejpam-3449	562	16	v2	v2	VERB
ejpam-3449	562	17	in	in	ADP
ejpam-3449	562	18	x	x	X
ejpam-3449	562	19	such	such	ADJ
ejpam-3449	562	20	that	that	SCONJ
ejpam-3449	562	21	x1	x1	PROPN
ejpam-3449	562	22	∈	∈	PROPN
ejpam-3449	562	23	v1	v1	NOUN
ejpam-3449	562	24	,	,	PUNCT
ejpam-3449	562	25	x2	x2	PROPN
ejpam-3449	562	26	∈	∈	PROPN
ejpam-3449	562	27	v2	v2	PROPN
ejpam-3449	562	28	,	,	PUNCT
ejpam-3449	562	29	h(γ(v1	h(γ(v1	NOUN
ejpam-3449	562	30	)	)	PUNCT
ejpam-3449	562	31	)	)	PUNCT
ejpam-3449	562	32	⊆	⊆	NUM
ejpam-3449	562	33	β(u1	β(u1	NUM
ejpam-3449	562	34	)	)	PUNCT
ejpam-3449	562	35	and	and	CCONJ
ejpam-3449	562	36	h(γ(v2	h(γ(v2	NOUN
ejpam-3449	562	37	)	)	PUNCT
ejpam-3449	562	38	)	)	PUNCT
ejpam-3449	562	39	⊆	⊆	NUM
ejpam-3449	562	40	β(u2	β(u2	NOUN
ejpam-3449	562	41	)	)	PUNCT
ejpam-3449	562	42	.	.	PUNCT
ejpam-3449	563	1	therefore	therefore	ADV
ejpam-3449	563	2	β(u1	β(u1	X
ejpam-3449	563	3	)	)	PUNCT
ejpam-3449	563	4	∩	∩	NOUN
ejpam-3449	563	5	β(u2	β(u2	NOUN
ejpam-3449	563	6	)	)	PUNCT
ejpam-3449	564	1	=	=	PUNCT
ejpam-3449	564	2	φ	φ	X
ejpam-3449	564	3	.	.	PUNCT
ejpam-3449	565	1	hence	hence	ADV
ejpam-3449	565	2	(	(	PUNCT
ejpam-3449	565	3	x	x	X
ejpam-3449	565	4	,	,	PUNCT
ejpam-3449	565	5	τ	τ	PROPN
ejpam-3449	565	6	,	,	PUNCT
ejpam-3449	565	7	τf	τf	PROPN
ejpam-3449	565	8	)	)	PUNCT
ejpam-3449	565	9	is	be	AUX
ejpam-3449	565	10	fγ	fγ	NOUN
ejpam-3449	565	11	-	-	PUNCT
ejpam-3449	565	12	t2	t2	NOUN
ejpam-3449	565	13	.	.	PUNCT
ejpam-3449	566	1	theorem	theorem	VERB
ejpam-3449	566	2	6.9	6.9	NUM
ejpam-3449	566	3	.	.	PUNCT
ejpam-3449	567	1	if	if	SCONJ
ejpam-3449	567	2	a	a	DET
ejpam-3449	567	3	function	function	NOUN
ejpam-3449	567	4	h	h	NOUN
ejpam-3449	567	5	:	:	PUNCT
ejpam-3449	567	6	(	(	PUNCT
ejpam-3449	567	7	x	x	X
ejpam-3449	567	8	,	,	PUNCT
ejpam-3449	567	9	τ	τ	PROPN
ejpam-3449	567	10	,	,	PUNCT
ejpam-3449	567	11	τf	τf	NOUN
ejpam-3449	567	12	)	)	PUNCT
ejpam-3449	567	13	→	→	SYM
ejpam-3449	567	14	(	(	PUNCT
ejpam-3449	567	15	y	y	PROPN
ejpam-3449	567	16	,	,	PUNCT
ejpam-3449	567	17	σ	σ	PROPN
ejpam-3449	567	18	,	,	PUNCT
ejpam-3449	567	19	σf	σf	NOUN
ejpam-3449	567	20	)	)	PUNCT
ejpam-3449	567	21	is	be	AUX
ejpam-3449	567	22	injective	injective	ADJ
ejpam-3449	567	23	fγβ	fγβ	ADV
ejpam-3449	567	24	-	-	ADJ
ejpam-3449	567	25	continuous	continuous	ADJ
ejpam-3449	567	26	and	and	CCONJ
ejpam-3449	567	27	the	the	DET
ejpam-3449	567	28	fine	fine	ADJ
ejpam-3449	567	29	space	space	NOUN
ejpam-3449	567	30	(	(	PUNCT
ejpam-3449	567	31	y	y	PROPN
ejpam-3449	567	32	,	,	PUNCT
ejpam-3449	567	33	σ	σ	PROPN
ejpam-3449	567	34	,	,	PUNCT
ejpam-3449	567	35	σf	σf	NOUN
ejpam-3449	567	36	)	)	PUNCT
ejpam-3449	567	37	is	be	AUX
ejpam-3449	567	38	fβ	fβ	ADJ
ejpam-3449	567	39	-	-	PUNCT
ejpam-3449	567	40	ti	ti	NOUN
ejpam-3449	567	41	,	,	PUNCT
ejpam-3449	567	42	then	then	ADV
ejpam-3449	567	43	the	the	DET
ejpam-3449	567	44	fine	fine	ADJ
ejpam-3449	567	45	space	space	NOUN
ejpam-3449	567	46	(	(	PUNCT
ejpam-3449	567	47	x	x	X
ejpam-3449	567	48	,	,	PUNCT
ejpam-3449	567	49	τ	τ	PROPN
ejpam-3449	567	50	,	,	PUNCT
ejpam-3449	567	51	τf	τf	PROPN
ejpam-3449	567	52	)	)	PUNCT
ejpam-3449	567	53	is	be	AUX
ejpam-3449	567	54	fγ	fγ	NOUN
ejpam-3449	567	55	-	-	PUNCT
ejpam-3449	567	56	ti	ti	NOUN
ejpam-3449	567	57	for	for	ADP
ejpam-3449	567	58	i	i	PRON
ejpam-3449	567	59	∈	∈	PROPN
ejpam-3449	567	60	{	{	PUNCT
ejpam-3449	567	61	0	0	NUM
ejpam-3449	567	62	,	,	PUNCT
ejpam-3449	567	63	1	1	NUM
ejpam-3449	567	64	}	}	PUNCT
ejpam-3449	567	65	.	.	PUNCT
ejpam-3449	568	1	proof	proof	NOUN
ejpam-3449	568	2	.	.	PUNCT
ejpam-3449	569	1	the	the	DET
ejpam-3449	569	2	proof	proof	NOUN
ejpam-3449	569	3	is	be	AUX
ejpam-3449	569	4	similar	similar	ADJ
ejpam-3449	569	5	to	to	AUX
ejpam-3449	569	6	theorem	theorem	VERB
ejpam-3449	569	7	6.8	6.8	NUM
ejpam-3449	569	8	.	.	PUNCT
ejpam-3449	570	1	definition	definition	NOUN
ejpam-3449	570	2	6.10	6.10	NUM
ejpam-3449	570	3	.	.	PUNCT
ejpam-3449	571	1	a	a	DET
ejpam-3449	571	2	function	function	NOUN
ejpam-3449	571	3	h	h	NOUN
ejpam-3449	571	4	:	:	PUNCT
ejpam-3449	571	5	(	(	PUNCT
ejpam-3449	571	6	x	x	X
ejpam-3449	571	7	,	,	PUNCT
ejpam-3449	571	8	τ	τ	PROPN
ejpam-3449	571	9	,	,	PUNCT
ejpam-3449	571	10	τf	τf	NOUN
ejpam-3449	571	11	)	)	PUNCT
ejpam-3449	571	12	→	→	SYM
ejpam-3449	571	13	(	(	PUNCT
ejpam-3449	571	14	y	y	PROPN
ejpam-3449	571	15	,	,	PUNCT
ejpam-3449	571	16	σ	σ	PROPN
ejpam-3449	571	17	,	,	PUNCT
ejpam-3449	571	18	σf	σf	NOUN
ejpam-3449	571	19	)	)	PUNCT
ejpam-3449	571	20	is	be	AUX
ejpam-3449	571	21	said	say	VERB
ejpam-3449	571	22	to	to	PART
ejpam-3449	571	23	be	be	AUX
ejpam-3449	571	24	fγβ	fγβ	NOUN
ejpam-3449	571	25	-	-	PUNCT
ejpam-3449	571	26	homeomorphism	homeomorphism	PROPN
ejpam-3449	571	27	if	if	SCONJ
ejpam-3449	571	28	h	h	NOUN
ejpam-3449	571	29	is	be	AUX
ejpam-3449	571	30	bijective	bijective	ADJ
ejpam-3449	571	31	,	,	PUNCT
ejpam-3449	571	32	fγβ	fγβ	ADV
ejpam-3449	571	33	-	-	ADJ
ejpam-3449	571	34	continuous	continuous	ADJ
ejpam-3449	571	35	and	and	CCONJ
ejpam-3449	571	36	h−1	h−1	PROPN
ejpam-3449	571	37	is	be	AUX
ejpam-3449	571	38	fβγ	fβγ	NOUN
ejpam-3449	571	39	-	-	PUNCT
ejpam-3449	571	40	continuous	continuous	ADJ
ejpam-3449	571	41	.	.	PUNCT
ejpam-3449	572	1	theorem	theorem	NOUN
ejpam-3449	572	2	6.11	6.11	NUM
ejpam-3449	572	3	.	.	PUNCT
ejpam-3449	573	1	assume	assume	VERB
ejpam-3449	573	2	that	that	SCONJ
ejpam-3449	573	3	a	a	DET
ejpam-3449	573	4	function	function	NOUN
ejpam-3449	573	5	h	h	NOUN
ejpam-3449	573	6	:	:	PUNCT
ejpam-3449	573	7	(	(	PUNCT
ejpam-3449	573	8	x	x	X
ejpam-3449	573	9	,	,	PUNCT
ejpam-3449	573	10	τ	τ	PROPN
ejpam-3449	573	11	,	,	PUNCT
ejpam-3449	573	12	τf	τf	NOUN
ejpam-3449	573	13	)	)	PUNCT
ejpam-3449	573	14	→	→	SYM
ejpam-3449	573	15	(	(	PUNCT
ejpam-3449	573	16	y	y	PROPN
ejpam-3449	573	17	,	,	PUNCT
ejpam-3449	573	18	σ	σ	PROPN
ejpam-3449	573	19	,	,	PUNCT
ejpam-3449	573	20	σf	σf	NOUN
ejpam-3449	573	21	)	)	PUNCT
ejpam-3449	573	22	is	be	AUX
ejpam-3449	573	23	fγβ	fγβ	NOUN
ejpam-3449	573	24	-	-	PUNCT
ejpam-3449	573	25	homeomorphism	homeomorphism	NOUN
ejpam-3449	573	26	.	.	PUNCT
ejpam-3449	574	1	if	if	SCONJ
ejpam-3449	574	2	(	(	PUNCT
ejpam-3449	574	3	x	x	NOUN
ejpam-3449	574	4	,	,	PUNCT
ejpam-3449	574	5	τ	τ	PROPN
ejpam-3449	574	6	,	,	PUNCT
ejpam-3449	574	7	τf	τf	PROPN
ejpam-3449	574	8	)	)	PUNCT
ejpam-3449	574	9	is	be	AUX
ejpam-3449	574	10	fγ	fγ	PROPN
ejpam-3449	574	11	-	-	PUNCT
ejpam-3449	574	12	t	t	PROPN
ejpam-3449	574	13	1	1	NUM
ejpam-3449	574	14	2	2	NUM
ejpam-3449	574	15	,	,	PUNCT
ejpam-3449	574	16	then	then	ADV
ejpam-3449	574	17	(	(	PUNCT
ejpam-3449	574	18	y	y	PROPN
ejpam-3449	574	19	,	,	PUNCT
ejpam-3449	574	20	σ	σ	PROPN
ejpam-3449	574	21	,	,	PUNCT
ejpam-3449	574	22	σf	σf	NOUN
ejpam-3449	574	23	)	)	PUNCT
ejpam-3449	574	24	is	be	AUX
ejpam-3449	574	25	fβ	fβ	ADJ
ejpam-3449	574	26	-	-	PUNCT
ejpam-3449	574	27	t	t	NOUN
ejpam-3449	574	28	1	1	NUM
ejpam-3449	574	29	2	2	NUM
ejpam-3449	574	30	.	.	PUNCT
ejpam-3449	575	1	proof	proof	NOUN
ejpam-3449	575	2	.	.	PUNCT
ejpam-3449	576	1	let	let	VERB
ejpam-3449	576	2	{	{	PUNCT
ejpam-3449	576	3	y	y	AUX
ejpam-3449	576	4	}	}	PUNCT
ejpam-3449	576	5	be	be	AUX
ejpam-3449	576	6	any	any	DET
ejpam-3449	576	7	singleton	singleton	NOUN
ejpam-3449	576	8	set	set	NOUN
ejpam-3449	576	9	of	of	ADP
ejpam-3449	576	10	(	(	PUNCT
ejpam-3449	576	11	y	y	PROPN
ejpam-3449	576	12	,	,	PUNCT
ejpam-3449	576	13	σ	σ	PROPN
ejpam-3449	576	14	,	,	PUNCT
ejpam-3449	576	15	σf	σf	NOUN
ejpam-3449	576	16	)	)	PUNCT
ejpam-3449	576	17	.	.	PUNCT
ejpam-3449	577	1	then	then	ADV
ejpam-3449	577	2	there	there	PRON
ejpam-3449	577	3	exists	exist	VERB
ejpam-3449	577	4	an	an	DET
ejpam-3449	577	5	element	element	NOUN
ejpam-3449	577	6	x	x	PUNCT
ejpam-3449	577	7	of	of	ADP
ejpam-3449	577	8	x	x	PRON
ejpam-3449	577	9	such	such	ADJ
ejpam-3449	577	10	that	that	SCONJ
ejpam-3449	577	11	y	y	PROPN
ejpam-3449	577	12	=	=	SYM
ejpam-3449	577	13	h(x	h(x	PROPN
ejpam-3449	577	14	)	)	PUNCT
ejpam-3449	577	15	.	.	PUNCT
ejpam-3449	578	1	so	so	ADV
ejpam-3449	578	2	by	by	ADP
ejpam-3449	578	3	hypothesis	hypothesis	NOUN
ejpam-3449	578	4	and	and	CCONJ
ejpam-3449	578	5	theorem	theorem	VERB
ejpam-3449	578	6	5.5	5.5	NUM
ejpam-3449	578	7	,	,	PUNCT
ejpam-3449	578	8	we	we	PRON
ejpam-3449	578	9	have	have	VERB
ejpam-3449	578	10	{	{	PUNCT
ejpam-3449	578	11	x	x	NOUN
ejpam-3449	578	12	}	}	PUNCT
ejpam-3449	578	13	is	be	AUX
ejpam-3449	578	14	fγ	fγ	ADV
ejpam-3449	578	15	-	-	PUNCT
ejpam-3449	578	16	closed	close	VERB
ejpam-3449	578	17	or	or	CCONJ
ejpam-3449	578	18	fγ	fγ	ADV
ejpam-3449	578	19	-	-	PUNCT
ejpam-3449	578	20	open	open	NOUN
ejpam-3449	578	21	set	set	NOUN
ejpam-3449	578	22	in	in	ADP
ejpam-3449	578	23	x.	x.	NOUN
ejpam-3449	578	24	by	by	ADP
ejpam-3449	578	25	using	use	VERB
ejpam-3449	578	26	theorem	theorem	ADJ
ejpam-3449	578	27	6.2	6.2	NUM
ejpam-3449	578	28	,	,	PUNCT
ejpam-3449	578	29	{	{	PUNCT
ejpam-3449	578	30	y	y	NOUN
ejpam-3449	578	31	}	}	PUNCT
ejpam-3449	578	32	is	be	AUX
ejpam-3449	578	33	fβ	fβ	ADV
ejpam-3449	578	34	-	-	PUNCT
ejpam-3449	578	35	closed	closed	ADJ
ejpam-3449	578	36	or	or	CCONJ
ejpam-3449	578	37	fβ	fβ	ADJ
ejpam-3449	578	38	-	-	PUNCT
ejpam-3449	578	39	open	open	ADJ
ejpam-3449	578	40	set	set	NOUN
ejpam-3449	578	41	.	.	PUNCT
ejpam-3449	579	1	hence	hence	ADV
ejpam-3449	579	2	the	the	DET
ejpam-3449	579	3	fine	fine	ADJ
ejpam-3449	579	4	space	space	NOUN
ejpam-3449	579	5	by	by	ADP
ejpam-3449	579	6	theorem	theorem	ADJ
ejpam-3449	579	7	5.5	5.5	NUM
ejpam-3449	579	8	,	,	PUNCT
ejpam-3449	579	9	(	(	PUNCT
ejpam-3449	579	10	y	y	PROPN
ejpam-3449	579	11	,	,	PUNCT
ejpam-3449	579	12	σ	σ	PROPN
ejpam-3449	579	13	,	,	PUNCT
ejpam-3449	579	14	σf	σf	NOUN
ejpam-3449	579	15	)	)	PUNCT
ejpam-3449	579	16	is	be	AUX
ejpam-3449	579	17	fβ	fβ	ADJ
ejpam-3449	579	18	-	-	PUNCT
ejpam-3449	579	19	t	t	NOUN
ejpam-3449	579	20	1	1	NUM
ejpam-3449	579	21	2	2	NUM
ejpam-3449	579	22	.	.	PUNCT
ejpam-3449	580	1	7	7	X
ejpam-3449	580	2	.	.	NUM
ejpam-3449	580	3	functions	function	NOUN
ejpam-3449	580	4	with	with	ADP
ejpam-3449	580	5	fβ	fβ	ADV
ejpam-3449	580	6	-	-	PUNCT
ejpam-3449	580	7	closed	closed	ADJ
ejpam-3449	580	8	graphs	graph	NOUN
ejpam-3449	580	9	for	for	ADP
ejpam-3449	580	10	a	a	DET
ejpam-3449	580	11	function	function	NOUN
ejpam-3449	580	12	h	h	NOUN
ejpam-3449	580	13	:	:	PUNCT
ejpam-3449	580	14	(	(	PUNCT
ejpam-3449	580	15	x	x	X
ejpam-3449	580	16	,	,	PUNCT
ejpam-3449	580	17	τ	τ	PROPN
ejpam-3449	580	18	,	,	PUNCT
ejpam-3449	580	19	τf	τf	NOUN
ejpam-3449	580	20	)	)	PUNCT
ejpam-3449	580	21	→	→	SYM
ejpam-3449	580	22	(	(	PUNCT
ejpam-3449	580	23	y	y	PROPN
ejpam-3449	580	24	,	,	PUNCT
ejpam-3449	580	25	σ	σ	PROPN
ejpam-3449	580	26	,	,	PUNCT
ejpam-3449	580	27	σf	σf	NOUN
ejpam-3449	580	28	)	)	PUNCT
ejpam-3449	580	29	,	,	PUNCT
ejpam-3449	580	30	the	the	DET
ejpam-3449	580	31	subset	subset	NOUN
ejpam-3449	580	32	{	{	PUNCT
ejpam-3449	580	33	(	(	PUNCT
ejpam-3449	580	34	x	x	NOUN
ejpam-3449	580	35	,	,	PUNCT
ejpam-3449	580	36	h(x	h(x	PROPN
ejpam-3449	580	37	)	)	PUNCT
ejpam-3449	580	38	)	)	PUNCT
ejpam-3449	580	39	:	:	PUNCT
ejpam-3449	581	1	x	x	X
ejpam-3449	581	2	∈	∈	NOUN
ejpam-3449	581	3	x	x	X
ejpam-3449	581	4	}	}	PUNCT
ejpam-3449	581	5	of	of	ADP
ejpam-3449	581	6	the	the	DET
ejpam-3449	581	7	product	product	NOUN
ejpam-3449	581	8	space	space	NOUN
ejpam-3449	581	9	(	(	PUNCT
ejpam-3449	581	10	x	x	SYM
ejpam-3449	581	11	×	×	PROPN
ejpam-3449	581	12	y	y	PROPN
ejpam-3449	581	13	,	,	PUNCT
ejpam-3449	581	14	τ	τ	PROPN
ejpam-3449	581	15	×	×	PROPN
ejpam-3449	581	16	σ	σ	PROPN
ejpam-3449	581	17	)	)	PUNCT
ejpam-3449	581	18	is	be	AUX
ejpam-3449	581	19	called	call	VERB
ejpam-3449	581	20	the	the	DET
ejpam-3449	581	21	graph	graph	NOUN
ejpam-3449	581	22	of	of	ADP
ejpam-3449	581	23	h	h	NOUN
ejpam-3449	581	24	and	and	CCONJ
ejpam-3449	581	25	is	be	AUX
ejpam-3449	581	26	denoted	denote	VERB
ejpam-3449	581	27	by	by	ADP
ejpam-3449	581	28	g(h	g(h	PROPN
ejpam-3449	581	29	)	)	PUNCT
ejpam-3449	582	1	[	[	X
ejpam-3449	582	2	9	9	NUM
ejpam-3449	582	3	]	]	PUNCT
ejpam-3449	582	4	.	.	PUNCT
ejpam-3449	583	1	in	in	ADP
ejpam-3449	583	2	this	this	DET
ejpam-3449	583	3	section	section	NOUN
ejpam-3449	583	4	,	,	PUNCT
ejpam-3449	583	5	we	we	PRON
ejpam-3449	583	6	further	far	ADV
ejpam-3449	583	7	investigate	investigate	VERB
ejpam-3449	583	8	general	general	ADJ
ejpam-3449	583	9	operator	operator	NOUN
ejpam-3449	583	10	approaches	approach	NOUN
ejpam-3449	583	11	of	of	ADP
ejpam-3449	583	12	closed	closed	ADJ
ejpam-3449	583	13	graphs	graph	NOUN
ejpam-3449	583	14	of	of	ADP
ejpam-3449	583	15	functions	function	NOUN
ejpam-3449	583	16	.	.	PUNCT
ejpam-3449	584	1	let	let	VERB
ejpam-3449	584	2	λ	λ	X
ejpam-3449	584	3	:	:	PUNCT
ejpam-3449	584	4	(	(	PUNCT
ejpam-3449	584	5	τ	τ	X
ejpam-3449	584	6	×	×	PROPN
ejpam-3449	584	7	σ)f	σ)f	PUNCT
ejpam-3449	584	8	→	→	SYM
ejpam-3449	584	9	p	p	X
ejpam-3449	584	10	(	(	PUNCT
ejpam-3449	584	11	x	x	PROPN
ejpam-3449	584	12	×	×	PROPN
ejpam-3449	584	13	y	y	PROPN
ejpam-3449	584	14	)	)	PUNCT
ejpam-3449	584	15	be	be	AUX
ejpam-3449	584	16	an	an	DET
ejpam-3449	584	17	operation	operation	NOUN
ejpam-3449	584	18	on	on	ADP
ejpam-3449	584	19	(	(	PUNCT
ejpam-3449	584	20	τ	τ	X
ejpam-3449	584	21	×	×	PROPN
ejpam-3449	584	22	σ)f	σ)f	PUNCT
ejpam-3449	584	23	.	.	PUNCT
ejpam-3449	585	1	definition	definition	NOUN
ejpam-3449	585	2	7.1	7.1	NUM
ejpam-3449	585	3	.	.	PUNCT
ejpam-3449	586	1	the	the	DET
ejpam-3449	586	2	graph	graph	NOUN
ejpam-3449	586	3	g(h	g(h	NUM
ejpam-3449	586	4	)	)	PUNCT
ejpam-3449	586	5	of	of	ADP
ejpam-3449	586	6	h	h	NOUN
ejpam-3449	586	7	:	:	PUNCT
ejpam-3449	586	8	(	(	PUNCT
ejpam-3449	586	9	x	x	X
ejpam-3449	586	10	,	,	PUNCT
ejpam-3449	586	11	τ	τ	PROPN
ejpam-3449	586	12	,	,	PUNCT
ejpam-3449	586	13	τf	τf	NOUN
ejpam-3449	586	14	)	)	PUNCT
ejpam-3449	586	15	→	→	SYM
ejpam-3449	586	16	(	(	PUNCT
ejpam-3449	586	17	y	y	PROPN
ejpam-3449	586	18	,	,	PUNCT
ejpam-3449	586	19	σ	σ	PROPN
ejpam-3449	586	20	,	,	PUNCT
ejpam-3449	586	21	σf	σf	NOUN
ejpam-3449	586	22	)	)	PUNCT
ejpam-3449	586	23	is	be	AUX
ejpam-3449	586	24	called	call	VERB
ejpam-3449	586	25	fβ	fβ	ADV
ejpam-3449	586	26	-	-	PUNCT
ejpam-3449	586	27	closed	closed	ADJ
ejpam-3449	586	28	if	if	SCONJ
ejpam-3449	586	29	for	for	ADP
ejpam-3449	586	30	each	each	DET
ejpam-3449	586	31	(	(	PUNCT
ejpam-3449	586	32	x	x	NOUN
ejpam-3449	586	33	,	,	PUNCT
ejpam-3449	586	34	y	y	NOUN
ejpam-3449	586	35	)	)	PUNCT
ejpam-3449	586	36	∈	∈	PROPN
ejpam-3449	586	37	(	(	PUNCT
ejpam-3449	586	38	x	x	SYM
ejpam-3449	586	39	×	×	PROPN
ejpam-3449	586	40	y	y	PROPN
ejpam-3449	586	41	)	)	PUNCT
ejpam-3449	586	42	\g(h	\g(h	PROPN
ejpam-3449	586	43	)	)	PUNCT
ejpam-3449	586	44	,	,	PUNCT
ejpam-3449	586	45	there	there	PRON
ejpam-3449	586	46	exist	exist	VERB
ejpam-3449	586	47	fine	fine	ADJ
ejpam-3449	586	48	-	-	PUNCT
ejpam-3449	586	49	open	open	ADJ
ejpam-3449	586	50	sets	set	VERB
ejpam-3449	586	51	u	u	NOUN
ejpam-3449	586	52	⊆	⊆	NUM
ejpam-3449	586	53	x	x	NOUN
ejpam-3449	586	54	and	and	CCONJ
ejpam-3449	586	55	v	v	ADP
ejpam-3449	586	56	⊆	⊆	NUM
ejpam-3449	586	57	y	y	NOUN
ejpam-3449	586	58	containing	contain	VERB
ejpam-3449	586	59	x	x	PROPN
ejpam-3449	586	60	and	and	CCONJ
ejpam-3449	586	61	y	y	PROPN
ejpam-3449	586	62	,	,	PUNCT
ejpam-3449	586	63	respectively	respectively	ADV
ejpam-3449	586	64	,	,	PUNCT
ejpam-3449	586	65	such	such	ADJ
ejpam-3449	586	66	that	that	SCONJ
ejpam-3449	586	67	(	(	PUNCT
ejpam-3449	586	68	u	u	NOUN
ejpam-3449	586	69	×	×	NOUN
ejpam-3449	586	70	β(v	β(v	NOUN
ejpam-3449	586	71	)	)	PUNCT
ejpam-3449	586	72	)	)	PUNCT
ejpam-3449	586	73	∩	∩	NOUN
ejpam-3449	586	74	g(h	g(h	NUM
ejpam-3449	586	75	)	)	PUNCT
ejpam-3449	587	1	=	=	SYM
ejpam-3449	587	2	φ	φ	PROPN
ejpam-3449	587	3	.	.	PUNCT
ejpam-3449	588	1	the	the	DET
ejpam-3449	588	2	proof	proof	NOUN
ejpam-3449	588	3	of	of	ADP
ejpam-3449	588	4	the	the	DET
ejpam-3449	588	5	following	follow	VERB
ejpam-3449	588	6	lemma	lemma	PROPN
ejpam-3449	588	7	follows	follow	VERB
ejpam-3449	588	8	directly	directly	ADV
ejpam-3449	588	9	from	from	ADP
ejpam-3449	588	10	the	the	DET
ejpam-3449	588	11	above	above	ADJ
ejpam-3449	588	12	definition	definition	NOUN
ejpam-3449	588	13	.	.	PUNCT
ejpam-3449	589	1	lemma	lemma	PROPN
ejpam-3449	589	2	7.2	7.2	NUM
ejpam-3449	589	3	.	.	PUNCT
ejpam-3449	590	1	a	a	DET
ejpam-3449	590	2	function	function	NOUN
ejpam-3449	590	3	h	h	NOUN
ejpam-3449	590	4	:	:	PUNCT
ejpam-3449	590	5	(	(	PUNCT
ejpam-3449	590	6	x	x	X
ejpam-3449	590	7	,	,	PUNCT
ejpam-3449	590	8	τ	τ	PROPN
ejpam-3449	590	9	,	,	PUNCT
ejpam-3449	590	10	τf	τf	NUM
ejpam-3449	590	11	)	)	PUNCT
ejpam-3449	590	12	→	→	SYM
ejpam-3449	590	13	(	(	PUNCT
ejpam-3449	590	14	y	y	PROPN
ejpam-3449	590	15	,	,	PUNCT
ejpam-3449	590	16	σ	σ	PROPN
ejpam-3449	590	17	,	,	PUNCT
ejpam-3449	590	18	σf	σf	NOUN
ejpam-3449	590	19	)	)	PUNCT
ejpam-3449	590	20	has	have	VERB
ejpam-3449	590	21	fβ	fβ	ADV
ejpam-3449	590	22	-	-	PUNCT
ejpam-3449	590	23	closed	closed	ADJ
ejpam-3449	590	24	graph	graph	NOUN
ejpam-3449	590	25	if	if	SCONJ
ejpam-3449	591	1	and	and	CCONJ
ejpam-3449	591	2	only	only	ADV
ejpam-3449	591	3	if	if	SCONJ
ejpam-3449	591	4	for	for	ADP
ejpam-3449	591	5	each	each	DET
ejpam-3449	591	6	(	(	PUNCT
ejpam-3449	591	7	x	x	NOUN
ejpam-3449	591	8	,	,	PUNCT
ejpam-3449	591	9	y	y	NOUN
ejpam-3449	591	10	)	)	PUNCT
ejpam-3449	591	11	∈	∈	PROPN
ejpam-3449	591	12	(	(	PUNCT
ejpam-3449	591	13	x	x	SYM
ejpam-3449	591	14	×	×	PROPN
ejpam-3449	591	15	y	y	PROPN
ejpam-3449	591	16	)	)	PUNCT
ejpam-3449	591	17	\g(h	\g(h	PROPN
ejpam-3449	591	18	)	)	PUNCT
ejpam-3449	591	19	,	,	PUNCT
ejpam-3449	591	20	there	there	PRON
ejpam-3449	591	21	exist	exist	VERB
ejpam-3449	591	22	u	u	PROPN
ejpam-3449	591	23	∈	∈	NOUN
ejpam-3449	591	24	τf	τf	ADP
ejpam-3449	591	25	containing	contain	VERB
ejpam-3449	591	26	x	x	PROPN
ejpam-3449	591	27	and	and	CCONJ
ejpam-3449	591	28	v	v	NOUN
ejpam-3449	591	29	∈	∈	NOUN
ejpam-3449	591	30	σf	σf	NOUN
ejpam-3449	591	31	containing	contain	VERB
ejpam-3449	591	32	y	y	PRON
ejpam-3449	591	33	such	such	ADJ
ejpam-3449	591	34	that	that	SCONJ
ejpam-3449	591	35	h(u	h(u	NOUN
ejpam-3449	591	36	)	)	PUNCT
ejpam-3449	591	37	∩	∩	NOUN
ejpam-3449	591	38	β(v	β(v	NOUN
ejpam-3449	591	39	)	)	PUNCT
ejpam-3449	592	1	=	=	SYM
ejpam-3449	592	2	φ	φ	PROPN
ejpam-3449	592	3	.	.	PUNCT
ejpam-3449	593	1	definition	definition	NOUN
ejpam-3449	593	2	7.3	7.3	NUM
ejpam-3449	593	3	.	.	PUNCT
ejpam-3449	594	1	an	an	DET
ejpam-3449	594	2	operation	operation	NOUN
ejpam-3449	594	3	λ	λ	NOUN
ejpam-3449	594	4	:	:	PUNCT
ejpam-3449	594	5	(	(	PUNCT
ejpam-3449	594	6	τ	τ	X
ejpam-3449	594	7	×	×	PROPN
ejpam-3449	594	8	σ)f	σ)f	PUNCT
ejpam-3449	594	9	→	→	SYM
ejpam-3449	594	10	p	p	X
ejpam-3449	594	11	(	(	PUNCT
ejpam-3449	594	12	x	x	PROPN
ejpam-3449	594	13	×	×	PROPN
ejpam-3449	594	14	y	y	PROPN
ejpam-3449	594	15	)	)	PUNCT
ejpam-3449	594	16	is	be	AUX
ejpam-3449	594	17	said	say	VERB
ejpam-3449	594	18	to	to	PART
ejpam-3449	594	19	be	be	AUX
ejpam-3449	594	20	fine	fine	ADV
ejpam-3449	594	21	-	-	PUNCT
ejpam-3449	594	22	associated	associate	VERB
ejpam-3449	594	23	with	with	ADP
ejpam-3449	594	24	γ	γ	PROPN
ejpam-3449	594	25	and	and	CCONJ
ejpam-3449	594	26	β	β	X
ejpam-3449	594	27	if	if	SCONJ
ejpam-3449	594	28	λ(u	λ(u	PROPN
ejpam-3449	594	29	×	×	NOUN
ejpam-3449	594	30	v	v	NOUN
ejpam-3449	594	31	)	)	PUNCT
ejpam-3449	594	32	=	=	SYM
ejpam-3449	594	33	γ(u)×	γ(u)×	PROPN
ejpam-3449	594	34	β(v	β(v	PROPN
ejpam-3449	594	35	)	)	PUNCT
ejpam-3449	594	36	holds	hold	VERB
ejpam-3449	594	37	for	for	ADP
ejpam-3449	594	38	each	each	DET
ejpam-3449	594	39	u	u	NOUN
ejpam-3449	594	40	∈	∈	PROPN
ejpam-3449	594	41	τf	τf	ADP
ejpam-3449	594	42	and	and	CCONJ
ejpam-3449	594	43	v	v	NOUN
ejpam-3449	594	44	∈	∈	NOUN
ejpam-3449	594	45	σf	σf	NOUN
ejpam-3449	594	46	.	.	PUNCT
ejpam-3449	595	1	b.	b.	PROPN
ejpam-3449	595	2	a.	a.	PROPN
ejpam-3449	595	3	asaad	asaad	PROPN
ejpam-3449	595	4	et	et	PROPN
ejpam-3449	595	5	al	al	PROPN
ejpam-3449	595	6	.	.	PUNCT
ejpam-3449	595	7	/	/	SYM
ejpam-3449	595	8	eur	eur	PROPN
ejpam-3449	595	9	.	.	PUNCT
ejpam-3449	596	1	j.	j.	PROPN
ejpam-3449	596	2	pure	pure	PROPN
ejpam-3449	596	3	appl	appl	PROPN
ejpam-3449	596	4	.	.	PROPN
ejpam-3449	596	5	math	math	PROPN
ejpam-3449	596	6	,	,	PUNCT
ejpam-3449	596	7	12	12	NUM
ejpam-3449	596	8	(	(	PUNCT
ejpam-3449	596	9	3	3	NUM
ejpam-3449	596	10	)	)	PUNCT
ejpam-3449	596	11	(	(	PUNCT
ejpam-3449	596	12	2019	2019	NUM
ejpam-3449	596	13	)	)	PUNCT
ejpam-3449	596	14	,	,	PUNCT
ejpam-3449	596	15	960	960	NUM
ejpam-3449	596	16	-	-	SYM
ejpam-3449	596	17	977	977	NUM
ejpam-3449	596	18	975	975	NUM
ejpam-3449	596	19	definition	definition	NOUN
ejpam-3449	596	20	7.4	7.4	NUM
ejpam-3449	596	21	.	.	PUNCT
ejpam-3449	597	1	the	the	DET
ejpam-3449	597	2	operation	operation	NOUN
ejpam-3449	597	3	λ	λ	X
ejpam-3449	597	4	:	:	PUNCT
ejpam-3449	597	5	(	(	PUNCT
ejpam-3449	597	6	τ	τ	X
ejpam-3449	597	7	×	×	PROPN
ejpam-3449	597	8	σ)f	σ)f	PUNCT
ejpam-3449	597	9	→	→	SYM
ejpam-3449	597	10	p	p	X
ejpam-3449	597	11	(	(	PUNCT
ejpam-3449	597	12	x	x	PROPN
ejpam-3449	597	13	×	×	PROPN
ejpam-3449	597	14	y	y	PROPN
ejpam-3449	597	15	)	)	PUNCT
ejpam-3449	597	16	is	be	AUX
ejpam-3449	597	17	said	say	VERB
ejpam-3449	597	18	to	to	PART
ejpam-3449	597	19	be	be	AUX
ejpam-3449	597	20	fine	fine	ADV
ejpam-3449	597	21	-	-	PUNCT
ejpam-3449	597	22	regular	regular	ADJ
ejpam-3449	597	23	with	with	ADP
ejpam-3449	597	24	respect	respect	NOUN
ejpam-3449	597	25	to	to	ADP
ejpam-3449	597	26	γ	γ	PROPN
ejpam-3449	597	27	and	and	CCONJ
ejpam-3449	597	28	β	β	PROPN
ejpam-3449	597	29	if	if	SCONJ
ejpam-3449	597	30	for	for	SCONJ
ejpam-3449	597	31	each	each	DET
ejpam-3449	597	32	(	(	PUNCT
ejpam-3449	597	33	x	x	NOUN
ejpam-3449	597	34	,	,	PUNCT
ejpam-3449	597	35	y	y	NOUN
ejpam-3449	597	36	)	)	PUNCT
ejpam-3449	597	37	∈	∈	PROPN
ejpam-3449	597	38	x	x	SYM
ejpam-3449	597	39	×	×	PROPN
ejpam-3449	597	40	y	y	PROPN
ejpam-3449	597	41	and	and	CCONJ
ejpam-3449	597	42	each	each	DET
ejpam-3449	597	43	fine	fine	ADJ
ejpam-3449	597	44	-	-	PUNCT
ejpam-3449	597	45	open	open	ADJ
ejpam-3449	597	46	set	set	NOUN
ejpam-3449	597	47	w	w	NOUN
ejpam-3449	597	48	containing	contain	VERB
ejpam-3449	597	49	(	(	PUNCT
ejpam-3449	597	50	x	x	NOUN
ejpam-3449	597	51	,	,	PUNCT
ejpam-3449	597	52	y	y	PROPN
ejpam-3449	597	53	)	)	PUNCT
ejpam-3449	597	54	,	,	PUNCT
ejpam-3449	597	55	there	there	PRON
ejpam-3449	597	56	exist	exist	VERB
ejpam-3449	597	57	fine	fine	ADJ
ejpam-3449	597	58	-	-	PUNCT
ejpam-3449	597	59	open	open	ADJ
ejpam-3449	597	60	sets	set	VERB
ejpam-3449	597	61	u	u	NOUN
ejpam-3449	597	62	in	in	ADP
ejpam-3449	597	63	x	x	X
ejpam-3449	597	64	and	and	CCONJ
ejpam-3449	597	65	v	v	NOUN
ejpam-3449	597	66	in	in	ADP
ejpam-3449	597	67	y	y	PRON
ejpam-3449	597	68	such	such	ADJ
ejpam-3449	597	69	that	that	SCONJ
ejpam-3449	597	70	x	x	SYM
ejpam-3449	597	71	∈	∈	PROPN
ejpam-3449	597	72	u	u	NOUN
ejpam-3449	597	73	,	,	PUNCT
ejpam-3449	597	74	y	y	PROPN
ejpam-3449	597	75	∈	∈	PROPN
ejpam-3449	597	76	v	v	NOUN
ejpam-3449	597	77	and	and	CCONJ
ejpam-3449	597	78	γ(u)×	γ(u)×	PROPN
ejpam-3449	597	79	β(v	β(v	PROPN
ejpam-3449	597	80	)	)	PUNCT
ejpam-3449	597	81	⊆	⊆	NUM
ejpam-3449	597	82	λ(w	λ(w	NOUN
ejpam-3449	597	83	)	)	PUNCT
ejpam-3449	597	84	.	.	PUNCT
ejpam-3449	598	1	theorem	theorem	VERB
ejpam-3449	598	2	7.5	7.5	NUM
ejpam-3449	598	3	.	.	PUNCT
ejpam-3449	599	1	let	let	VERB
ejpam-3449	599	2	λ	λ	X
ejpam-3449	599	3	:	:	PUNCT
ejpam-3449	599	4	(	(	PUNCT
ejpam-3449	599	5	τ	τ	X
ejpam-3449	599	6	×	×	PROPN
ejpam-3449	599	7	τ)f	τ)f	PUNCT
ejpam-3449	599	8	→	→	SYM
ejpam-3449	599	9	p	p	X
ejpam-3449	599	10	(	(	PUNCT
ejpam-3449	599	11	x	x	NOUN
ejpam-3449	599	12	×x	×x	X
ejpam-3449	599	13	)	)	PUNCT
ejpam-3449	599	14	be	be	VERB
ejpam-3449	599	15	a	a	DET
ejpam-3449	599	16	fine	fine	ADV
ejpam-3449	599	17	-	-	PUNCT
ejpam-3449	599	18	associated	associate	VERB
ejpam-3449	599	19	operation	operation	NOUN
ejpam-3449	599	20	with	with	ADP
ejpam-3449	599	21	γ	γ	PROPN
ejpam-3449	599	22	and	and	CCONJ
ejpam-3449	599	23	γ	γ	PROPN
ejpam-3449	599	24	.	.	PROPN
ejpam-3449	600	1	if	if	SCONJ
ejpam-3449	600	2	h	h	NOUN
ejpam-3449	600	3	:	:	PUNCT
ejpam-3449	600	4	(	(	PUNCT
ejpam-3449	600	5	x	x	X
ejpam-3449	600	6	,	,	PUNCT
ejpam-3449	600	7	τ	τ	PROPN
ejpam-3449	600	8	,	,	PUNCT
ejpam-3449	600	9	τf	τf	NUM
ejpam-3449	600	10	)	)	PUNCT
ejpam-3449	600	11	→	→	SYM
ejpam-3449	600	12	(	(	PUNCT
ejpam-3449	600	13	y	y	PROPN
ejpam-3449	600	14	,	,	PUNCT
ejpam-3449	600	15	σ	σ	PROPN
ejpam-3449	600	16	,	,	PUNCT
ejpam-3449	600	17	σf	σf	NOUN
ejpam-3449	600	18	)	)	PUNCT
ejpam-3449	600	19	is	be	AUX
ejpam-3449	600	20	a	a	DET
ejpam-3449	600	21	fγβ	fγβ	ADJ
ejpam-3449	600	22	-	-	ADJ
ejpam-3449	600	23	continuous	continuous	ADJ
ejpam-3449	600	24	function	function	NOUN
ejpam-3449	600	25	and	and	CCONJ
ejpam-3449	600	26	(	(	PUNCT
ejpam-3449	600	27	y	y	PROPN
ejpam-3449	600	28	,	,	PUNCT
ejpam-3449	600	29	σ	σ	PROPN
ejpam-3449	600	30	,	,	PUNCT
ejpam-3449	600	31	σf	σf	NOUN
ejpam-3449	600	32	)	)	PUNCT
ejpam-3449	600	33	is	be	AUX
ejpam-3449	600	34	a	a	DET
ejpam-3449	600	35	fβ	fβ	ADJ
ejpam-3449	600	36	-	-	PUNCT
ejpam-3449	600	37	t2	t2	NOUN
ejpam-3449	600	38	space	space	NOUN
ejpam-3449	600	39	,	,	PUNCT
ejpam-3449	600	40	then	then	ADV
ejpam-3449	600	41	the	the	DET
ejpam-3449	600	42	set	set	NOUN
ejpam-3449	600	43	a	a	X
ejpam-3449	600	44	=	=	X
ejpam-3449	600	45	{	{	PUNCT
ejpam-3449	600	46	(	(	PUNCT
ejpam-3449	600	47	x	x	NOUN
ejpam-3449	600	48	,	,	PUNCT
ejpam-3449	600	49	y	y	NOUN
ejpam-3449	600	50	)	)	PUNCT
ejpam-3449	600	51	∈	∈	PROPN
ejpam-3449	600	52	x	x	X
ejpam-3449	600	53	×x	×x	X
ejpam-3449	600	54	:	:	PUNCT
ejpam-3449	600	55	h(x	h(x	PROPN
ejpam-3449	600	56	)	)	PUNCT
ejpam-3449	600	57	=	=	PUNCT
ejpam-3449	601	1	h(y	h(y	ADV
ejpam-3449	601	2	)	)	PUNCT
ejpam-3449	601	3	}	}	PUNCT
ejpam-3449	601	4	is	be	AUX
ejpam-3449	601	5	a	a	DET
ejpam-3449	601	6	fλ	fλ	ADJ
ejpam-3449	601	7	-	-	ADJ
ejpam-3449	601	8	closed	closed	ADJ
ejpam-3449	601	9	set	set	NOUN
ejpam-3449	601	10	of	of	ADP
ejpam-3449	601	11	(	(	PUNCT
ejpam-3449	601	12	x	x	X
ejpam-3449	601	13	×x	×x	PROPN
ejpam-3449	601	14	,	,	PUNCT
ejpam-3449	601	15	τ	τ	PROPN
ejpam-3449	601	16	×	×	PROPN
ejpam-3449	601	17	τ	τ	PROPN
ejpam-3449	601	18	)	)	PUNCT
ejpam-3449	601	19	.	.	PUNCT
ejpam-3449	602	1	proof	proof	NOUN
ejpam-3449	602	2	.	.	PUNCT
ejpam-3449	603	1	we	we	PRON
ejpam-3449	603	2	want	want	VERB
ejpam-3449	603	3	to	to	PART
ejpam-3449	603	4	prove	prove	VERB
ejpam-3449	603	5	that	that	SCONJ
ejpam-3449	603	6	fclλ(a	fclλ(a	NOUN
ejpam-3449	603	7	)	)	PUNCT
ejpam-3449	603	8	⊆	⊆	NUM
ejpam-3449	603	9	a.	a.	NOUN
ejpam-3449	603	10	let	let	VERB
ejpam-3449	603	11	(	(	PUNCT
ejpam-3449	603	12	x	x	NOUN
ejpam-3449	603	13	,	,	PUNCT
ejpam-3449	603	14	y	y	NOUN
ejpam-3449	603	15	)	)	PUNCT
ejpam-3449	603	16	∈	∈	PROPN
ejpam-3449	603	17	(	(	PUNCT
ejpam-3449	603	18	x	x	NOUN
ejpam-3449	603	19	×x)\a	×x)\a	NOUN
ejpam-3449	603	20	.	.	NOUN
ejpam-3449	604	1	since	since	SCONJ
ejpam-3449	604	2	(	(	PUNCT
ejpam-3449	604	3	y	y	PROPN
ejpam-3449	604	4	,	,	PUNCT
ejpam-3449	604	5	σ	σ	PROPN
ejpam-3449	604	6	,	,	PUNCT
ejpam-3449	604	7	σf	σf	NOUN
ejpam-3449	604	8	)	)	PUNCT
ejpam-3449	604	9	is	be	AUX
ejpam-3449	604	10	fβ	fβ	ADJ
ejpam-3449	604	11	-	-	PUNCT
ejpam-3449	604	12	t2	t2	NOUN
ejpam-3449	604	13	.	.	PUNCT
ejpam-3449	605	1	then	then	ADV
ejpam-3449	605	2	there	there	PRON
ejpam-3449	605	3	exist	exist	VERB
ejpam-3449	605	4	two	two	NUM
ejpam-3449	605	5	fine	fine	ADJ
ejpam-3449	605	6	-	-	PUNCT
ejpam-3449	605	7	open	open	ADJ
ejpam-3449	605	8	sets	set	NOUN
ejpam-3449	605	9	u	u	NOUN
ejpam-3449	605	10	and	and	CCONJ
ejpam-3449	605	11	v	v	NOUN
ejpam-3449	605	12	in	in	ADP
ejpam-3449	605	13	(	(	PUNCT
ejpam-3449	605	14	y	y	PROPN
ejpam-3449	605	15	,	,	PUNCT
ejpam-3449	605	16	σ	σ	PROPN
ejpam-3449	605	17	,	,	PUNCT
ejpam-3449	605	18	σf	σf	NOUN
ejpam-3449	605	19	)	)	PUNCT
ejpam-3449	605	20	such	such	ADJ
ejpam-3449	605	21	that	that	SCONJ
ejpam-3449	605	22	h(x	h(x	PROPN
ejpam-3449	605	23	)	)	PUNCT
ejpam-3449	605	24	∈	∈	PROPN
ejpam-3449	605	25	u	u	NOUN
ejpam-3449	605	26	,	,	PUNCT
ejpam-3449	605	27	h(y	h(y	ADV
ejpam-3449	605	28	)	)	PUNCT
ejpam-3449	605	29	∈	∈	PROPN
ejpam-3449	605	30	v	v	NOUN
ejpam-3449	605	31	and	and	CCONJ
ejpam-3449	605	32	β(u	β(u	NOUN
ejpam-3449	605	33	)	)	PUNCT
ejpam-3449	605	34	∩	∩	NOUN
ejpam-3449	605	35	β(v	β(v	NOUN
ejpam-3449	605	36	)	)	PUNCT
ejpam-3449	605	37	=	=	SYM
ejpam-3449	606	1	φ	φ	X
ejpam-3449	606	2	.	.	PUNCT
ejpam-3449	607	1	moreover	moreover	ADV
ejpam-3449	607	2	,	,	PUNCT
ejpam-3449	607	3	for	for	ADP
ejpam-3449	607	4	u	u	NOUN
ejpam-3449	607	5	and	and	CCONJ
ejpam-3449	607	6	v	v	NOUN
ejpam-3449	607	7	there	there	PRON
ejpam-3449	607	8	exist	exist	VERB
ejpam-3449	607	9	fine	fine	ADJ
ejpam-3449	607	10	-	-	PUNCT
ejpam-3449	607	11	open	open	ADJ
ejpam-3449	607	12	sets	set	NOUN
ejpam-3449	607	13	r	r	NOUN
ejpam-3449	607	14	and	and	CCONJ
ejpam-3449	607	15	s	s	X
ejpam-3449	607	16	in	in	ADP
ejpam-3449	607	17	(	(	PUNCT
ejpam-3449	607	18	x	x	NOUN
ejpam-3449	607	19	,	,	PUNCT
ejpam-3449	607	20	τ	τ	PROPN
ejpam-3449	607	21	,	,	PUNCT
ejpam-3449	607	22	τf	τf	NUM
ejpam-3449	607	23	)	)	PUNCT
ejpam-3449	607	24	such	such	ADJ
ejpam-3449	607	25	that	that	SCONJ
ejpam-3449	607	26	x	x	SYM
ejpam-3449	607	27	∈	∈	PROPN
ejpam-3449	607	28	r	r	NOUN
ejpam-3449	607	29	,	,	PUNCT
ejpam-3449	607	30	y	y	PROPN
ejpam-3449	607	31	∈	∈	PROPN
ejpam-3449	607	32	s	s	X
ejpam-3449	607	33	and	and	CCONJ
ejpam-3449	607	34	h(γ(r	h(γ(r	NOUN
ejpam-3449	607	35	)	)	PUNCT
ejpam-3449	607	36	)	)	PUNCT
ejpam-3449	608	1	⊆	⊆	NUM
ejpam-3449	608	2	β(u	β(u	NUM
ejpam-3449	608	3	)	)	PUNCT
ejpam-3449	608	4	and	and	CCONJ
ejpam-3449	608	5	h(γ(s	h(γ(s	PROPN
ejpam-3449	608	6	)	)	PUNCT
ejpam-3449	608	7	)	)	PUNCT
ejpam-3449	609	1	⊆	⊆	NUM
ejpam-3449	609	2	β(v	β(v	NOUN
ejpam-3449	609	3	)	)	PUNCT
ejpam-3449	609	4	since	since	SCONJ
ejpam-3449	609	5	h	h	NOUN
ejpam-3449	609	6	is	be	AUX
ejpam-3449	609	7	fγβ	fγβ	ADV
ejpam-3449	609	8	-	-	PUNCT
ejpam-3449	609	9	continuous	continuous	ADJ
ejpam-3449	609	10	.	.	PUNCT
ejpam-3449	610	1	therefore	therefore	ADV
ejpam-3449	610	2	we	we	PRON
ejpam-3449	610	3	have	have	VERB
ejpam-3449	610	4	(	(	PUNCT
ejpam-3449	610	5	x	x	NOUN
ejpam-3449	610	6	,	,	PUNCT
ejpam-3449	610	7	y	y	PROPN
ejpam-3449	610	8	)	)	PUNCT
ejpam-3449	610	9	∈	∈	PROPN
ejpam-3449	610	10	γ(r	γ(r	PROPN
ejpam-3449	610	11	)	)	PUNCT
ejpam-3449	610	12	×	×	PROPN
ejpam-3449	610	13	γ(s	γ(	NOUN
ejpam-3449	610	14	)	)	PUNCT
ejpam-3449	611	1	=	=	PUNCT
ejpam-3449	612	1	λ(r	λ(r	X
ejpam-3449	612	2	×	×	PROPN
ejpam-3449	612	3	s	s	NOUN
ejpam-3449	612	4	)	)	PUNCT
ejpam-3449	612	5	∩	∩	NOUN
ejpam-3449	612	6	a	a	PRON
ejpam-3449	612	7	=	=	SYM
ejpam-3449	612	8	φ	φ	PROPN
ejpam-3449	612	9	because	because	SCONJ
ejpam-3449	612	10	r×	r×	PROPN
ejpam-3449	612	11	s	s	PROPN
ejpam-3449	612	12	∈	∈	PROPN
ejpam-3449	612	13	(	(	PUNCT
ejpam-3449	612	14	τ	τ	X
ejpam-3449	612	15	×	×	PROPN
ejpam-3449	612	16	τ)f	τ)f	PUNCT
ejpam-3449	612	17	.	.	PUNCT
ejpam-3449	613	1	this	this	PRON
ejpam-3449	613	2	shows	show	VERB
ejpam-3449	613	3	that	that	SCONJ
ejpam-3449	613	4	(	(	PUNCT
ejpam-3449	613	5	x	x	X
ejpam-3449	613	6	,	,	PUNCT
ejpam-3449	613	7	y	y	PROPN
ejpam-3449	613	8	)	)	PUNCT
ejpam-3449	613	9	/∈	/∈	PUNCT
ejpam-3449	614	1	fclλ(a	fclλ(a	NOUN
ejpam-3449	614	2	)	)	PUNCT
ejpam-3449	614	3	.	.	PUNCT
ejpam-3449	615	1	corollary	corollary	NOUN
ejpam-3449	615	2	7.6	7.6	NUM
ejpam-3449	615	3	.	.	PUNCT
ejpam-3449	616	1	suppose	suppose	VERB
ejpam-3449	616	2	λ	λ	X
ejpam-3449	616	3	:	:	PUNCT
ejpam-3449	616	4	(	(	PUNCT
ejpam-3449	616	5	τ	τ	X
ejpam-3449	616	6	×	×	PROPN
ejpam-3449	616	7	τ)f	τ)f	PUNCT
ejpam-3449	616	8	→	→	SYM
ejpam-3449	616	9	p	p	X
ejpam-3449	616	10	(	(	PUNCT
ejpam-3449	616	11	x	x	NOUN
ejpam-3449	616	12	×x	×x	X
ejpam-3449	616	13	)	)	PUNCT
ejpam-3449	616	14	is	be	AUX
ejpam-3449	616	15	fine	fine	ADV
ejpam-3449	616	16	-	-	PUNCT
ejpam-3449	616	17	associated	associate	VERB
ejpam-3449	616	18	operation	operation	NOUN
ejpam-3449	616	19	with	with	ADP
ejpam-3449	616	20	γ	γ	PROPN
ejpam-3449	616	21	and	and	CCONJ
ejpam-3449	616	22	γ	γ	NOUN
ejpam-3449	616	23	,	,	PUNCT
ejpam-3449	616	24	and	and	CCONJ
ejpam-3449	616	25	it	it	PRON
ejpam-3449	616	26	is	be	AUX
ejpam-3449	616	27	fine	fine	ADV
ejpam-3449	616	28	-	-	PUNCT
ejpam-3449	616	29	regular	regular	ADJ
ejpam-3449	616	30	with	with	ADP
ejpam-3449	616	31	γ	γ	NOUN
ejpam-3449	616	32	and	and	CCONJ
ejpam-3449	616	33	γ	γ	PROPN
ejpam-3449	616	34	.	.	PROPN
ejpam-3449	617	1	a	a	DET
ejpam-3449	617	2	fine	fine	ADJ
ejpam-3449	617	3	space	space	NOUN
ejpam-3449	617	4	(	(	PUNCT
ejpam-3449	617	5	x	x	X
ejpam-3449	617	6	,	,	PUNCT
ejpam-3449	617	7	τ	τ	PROPN
ejpam-3449	617	8	,	,	PUNCT
ejpam-3449	617	9	τf	τf	PROPN
ejpam-3449	617	10	)	)	PUNCT
ejpam-3449	617	11	is	be	AUX
ejpam-3449	617	12	fγ	fγ	NOUN
ejpam-3449	617	13	-	-	PUNCT
ejpam-3449	617	14	t2	t2	NOUN
ejpam-3449	617	15	if	if	SCONJ
ejpam-3449	617	16	and	and	CCONJ
ejpam-3449	617	17	only	only	ADV
ejpam-3449	617	18	if	if	SCONJ
ejpam-3449	617	19	the	the	DET
ejpam-3449	617	20	diagonal	diagonal	ADJ
ejpam-3449	617	21	set	set	VERB
ejpam-3449	617	22	4	4	NUM
ejpam-3449	617	23	=	=	SYM
ejpam-3449	617	24	{	{	PUNCT
ejpam-3449	617	25	(	(	PUNCT
ejpam-3449	617	26	x	x	NOUN
ejpam-3449	617	27	,	,	PUNCT
ejpam-3449	617	28	x	x	X
ejpam-3449	617	29	)	)	PUNCT
ejpam-3449	617	30	:	:	PUNCT
ejpam-3449	618	1	x	x	X
ejpam-3449	618	2	∈	∈	NOUN
ejpam-3449	618	3	x	x	PRON
ejpam-3449	618	4	}	}	PUNCT
ejpam-3449	618	5	is	be	AUX
ejpam-3449	618	6	fλ	fλ	NOUN
ejpam-3449	618	7	-	-	ADJ
ejpam-3449	618	8	closed	closed	ADJ
ejpam-3449	618	9	of	of	ADP
ejpam-3449	618	10	(	(	PUNCT
ejpam-3449	618	11	x	x	X
ejpam-3449	618	12	×x	×x	PROPN
ejpam-3449	618	13	,	,	PUNCT
ejpam-3449	618	14	τ	τ	PROPN
ejpam-3449	618	15	×	×	PROPN
ejpam-3449	618	16	τ	τ	PROPN
ejpam-3449	618	17	)	)	PUNCT
ejpam-3449	618	18	.	.	PUNCT
ejpam-3449	619	1	theorem	theorem	VERB
ejpam-3449	619	2	7.7	7.7	NUM
ejpam-3449	619	3	.	.	PUNCT
ejpam-3449	620	1	let	let	VERB
ejpam-3449	620	2	λ	λ	X
ejpam-3449	620	3	:	:	PUNCT
ejpam-3449	620	4	(	(	PUNCT
ejpam-3449	620	5	τ	τ	X
ejpam-3449	620	6	×	×	PROPN
ejpam-3449	620	7	σ)f	σ)f	PUNCT
ejpam-3449	620	8	→	→	SYM
ejpam-3449	620	9	p	p	X
ejpam-3449	620	10	(	(	PUNCT
ejpam-3449	620	11	x	x	PROPN
ejpam-3449	620	12	×	×	PROPN
ejpam-3449	620	13	y	y	PROPN
ejpam-3449	620	14	)	)	PUNCT
ejpam-3449	620	15	be	be	AUX
ejpam-3449	620	16	a	a	DET
ejpam-3449	620	17	fine	fine	ADV
ejpam-3449	620	18	-	-	PUNCT
ejpam-3449	620	19	associated	associate	VERB
ejpam-3449	620	20	operation	operation	NOUN
ejpam-3449	620	21	with	with	ADP
ejpam-3449	620	22	γ	γ	PROPN
ejpam-3449	620	23	and	and	CCONJ
ejpam-3449	620	24	β	β	NOUN
ejpam-3449	620	25	.	.	PUNCT
ejpam-3449	621	1	if	if	SCONJ
ejpam-3449	621	2	h	h	NOUN
ejpam-3449	621	3	:	:	PUNCT
ejpam-3449	621	4	(	(	PUNCT
ejpam-3449	621	5	x	x	X
ejpam-3449	621	6	,	,	PUNCT
ejpam-3449	621	7	τ	τ	PROPN
ejpam-3449	621	8	,	,	PUNCT
ejpam-3449	621	9	τf	τf	NOUN
ejpam-3449	621	10	)	)	PUNCT
ejpam-3449	621	11	→	→	SYM
ejpam-3449	621	12	(	(	PUNCT
ejpam-3449	621	13	y	y	PROPN
ejpam-3449	621	14	,	,	PUNCT
ejpam-3449	621	15	σ	σ	PROPN
ejpam-3449	621	16	,	,	PUNCT
ejpam-3449	621	17	σf	σf	NOUN
ejpam-3449	621	18	)	)	PUNCT
ejpam-3449	621	19	is	be	AUX
ejpam-3449	621	20	fγβ	fγβ	ADV
ejpam-3449	621	21	-	-	ADJ
ejpam-3449	621	22	continuous	continuous	ADJ
ejpam-3449	621	23	and	and	CCONJ
ejpam-3449	621	24	(	(	PUNCT
ejpam-3449	621	25	y	y	PROPN
ejpam-3449	621	26	,	,	PUNCT
ejpam-3449	621	27	σ	σ	PROPN
ejpam-3449	621	28	,	,	PUNCT
ejpam-3449	621	29	σf	σf	NOUN
ejpam-3449	621	30	)	)	PUNCT
ejpam-3449	621	31	is	be	AUX
ejpam-3449	621	32	fβ	fβ	ADJ
ejpam-3449	621	33	-	-	PUNCT
ejpam-3449	621	34	t2	t2	NOUN
ejpam-3449	621	35	,	,	PUNCT
ejpam-3449	621	36	then	then	ADV
ejpam-3449	621	37	the	the	DET
ejpam-3449	621	38	graph	graph	NOUN
ejpam-3449	621	39	of	of	ADP
ejpam-3449	621	40	h	h	NOUN
ejpam-3449	621	41	,	,	PUNCT
ejpam-3449	621	42	g(h	g(h	NUM
ejpam-3449	621	43	)	)	PUNCT
ejpam-3449	622	1	=	=	PRON
ejpam-3449	622	2	{	{	PUNCT
ejpam-3449	622	3	(	(	PUNCT
ejpam-3449	622	4	x	x	NOUN
ejpam-3449	622	5	,	,	PUNCT
ejpam-3449	622	6	h(x	h(x	PROPN
ejpam-3449	622	7	)	)	PUNCT
ejpam-3449	622	8	)	)	PUNCT
ejpam-3449	623	1	∈	∈	PROPN
ejpam-3449	623	2	x	x	SYM
ejpam-3449	623	3	×	×	PROPN
ejpam-3449	623	4	y	y	PROPN
ejpam-3449	623	5	}	}	PUNCT
ejpam-3449	623	6	is	be	AUX
ejpam-3449	623	7	a	a	DET
ejpam-3449	623	8	fλ	fλ	ADJ
ejpam-3449	623	9	-	-	ADJ
ejpam-3449	623	10	closed	closed	ADJ
ejpam-3449	623	11	set	set	NOUN
ejpam-3449	623	12	of	of	ADP
ejpam-3449	623	13	(	(	PUNCT
ejpam-3449	623	14	x	x	PROPN
ejpam-3449	623	15	×	×	PROPN
ejpam-3449	623	16	y	y	PROPN
ejpam-3449	623	17	,	,	PUNCT
ejpam-3449	623	18	τ	τ	PROPN
ejpam-3449	623	19	×	×	PROPN
ejpam-3449	623	20	σ	σ	PROPN
ejpam-3449	623	21	)	)	PUNCT
ejpam-3449	623	22	.	.	PUNCT
ejpam-3449	624	1	proof	proof	NOUN
ejpam-3449	624	2	.	.	PUNCT
ejpam-3449	625	1	the	the	DET
ejpam-3449	625	2	proof	proof	NOUN
ejpam-3449	625	3	is	be	AUX
ejpam-3449	625	4	similar	similar	ADJ
ejpam-3449	625	5	to	to	AUX
ejpam-3449	625	6	theorem	theorem	VERB
ejpam-3449	625	7	7.5	7.5	NUM
ejpam-3449	625	8	.	.	PUNCT
ejpam-3449	626	1	definition	definition	NOUN
ejpam-3449	626	2	7.8	7.8	NUM
ejpam-3449	626	3	.	.	PUNCT
ejpam-3449	627	1	let	let	AUX
ejpam-3449	627	2	(	(	PUNCT
ejpam-3449	627	3	x	x	NOUN
ejpam-3449	627	4	,	,	PUNCT
ejpam-3449	627	5	τ	τ	PROPN
ejpam-3449	627	6	,	,	PUNCT
ejpam-3449	627	7	τf	τf	NUM
ejpam-3449	627	8	)	)	PUNCT
ejpam-3449	627	9	be	be	AUX
ejpam-3449	627	10	a	a	DET
ejpam-3449	627	11	fine	fine	ADJ
ejpam-3449	627	12	space	space	NOUN
ejpam-3449	627	13	and	and	CCONJ
ejpam-3449	627	14	γ	γ	NOUN
ejpam-3449	627	15	be	be	AUX
ejpam-3449	627	16	an	an	DET
ejpam-3449	627	17	operation	operation	NOUN
ejpam-3449	627	18	on	on	ADP
ejpam-3449	627	19	τf	τf	PROPN
ejpam-3449	627	20	.	.	PUNCT
ejpam-3449	628	1	a	a	DET
ejpam-3449	628	2	subset	subset	NOUN
ejpam-3449	628	3	s	s	NOUN
ejpam-3449	628	4	of	of	ADP
ejpam-3449	628	5	x	x	VERB
ejpam-3449	628	6	is	be	AUX
ejpam-3449	628	7	said	say	VERB
ejpam-3449	628	8	to	to	PART
ejpam-3449	628	9	be	be	AUX
ejpam-3449	628	10	fγ	fγ	ADJ
ejpam-3449	628	11	-	-	PUNCT
ejpam-3449	628	12	compact	compact	ADJ
ejpam-3449	628	13	if	if	SCONJ
ejpam-3449	628	14	for	for	ADP
ejpam-3449	628	15	every	every	DET
ejpam-3449	628	16	fine	fine	ADJ
ejpam-3449	628	17	-	-	PUNCT
ejpam-3449	628	18	open	open	ADJ
ejpam-3449	628	19	cover	cover	NOUN
ejpam-3449	628	20	{	{	PUNCT
ejpam-3449	628	21	ui	ui	NOUN
ejpam-3449	628	22	,	,	PUNCT
ejpam-3449	628	23	i	i	PRON
ejpam-3449	628	24	∈	∈	PROPN
ejpam-3449	628	25	n	n	CCONJ
ejpam-3449	628	26	}	}	PUNCT
ejpam-3449	628	27	of	of	ADP
ejpam-3449	628	28	s	s	PROPN
ejpam-3449	628	29	,	,	PUNCT
ejpam-3449	628	30	there	there	PRON
ejpam-3449	628	31	exists	exist	VERB
ejpam-3449	628	32	a	a	DET
ejpam-3449	628	33	finite	finite	NOUN
ejpam-3449	628	34	subfamily	subfamily	ADV
ejpam-3449	628	35	{	{	PUNCT
ejpam-3449	628	36	u1	u1	NOUN
ejpam-3449	628	37	,	,	PUNCT
ejpam-3449	628	38	u2	u2	NOUN
ejpam-3449	628	39	,	,	PUNCT
ejpam-3449	628	40	...	...	PUNCT
ejpam-3449	628	41	,	,	PUNCT
ejpam-3449	628	42	un	un	PROPN
ejpam-3449	628	43	}	}	PUNCT
ejpam-3449	628	44	such	such	ADJ
ejpam-3449	628	45	that	that	PRON
ejpam-3449	628	46	s	s	VERB
ejpam-3449	628	47	⊆	⊆	NUM
ejpam-3449	628	48	γ(u1	γ(u1	NOUN
ejpam-3449	628	49	)	)	PUNCT
ejpam-3449	628	50	∪	∪	ADP
ejpam-3449	628	51	γ(u2	γ(u2	NOUN
ejpam-3449	628	52	)	)	PUNCT
ejpam-3449	628	53	∪	∪	NOUN
ejpam-3449	628	54	...	...	PUNCT
ejpam-3449	629	1	∪	∪	PROPN
ejpam-3449	629	2	γ(un	γ(un	PROPN
ejpam-3449	629	3	)	)	PUNCT
ejpam-3449	629	4	.	.	PUNCT
ejpam-3449	630	1	theorem	theorem	VERB
ejpam-3449	630	2	7.9	7.9	NUM
ejpam-3449	630	3	.	.	PUNCT
ejpam-3449	631	1	suppose	suppose	VERB
ejpam-3449	631	2	that	that	SCONJ
ejpam-3449	631	3	γ	γ	PROPN
ejpam-3449	631	4	is	be	AUX
ejpam-3449	631	5	fine	fine	ADV
ejpam-3449	631	6	-	-	PUNCT
ejpam-3449	631	7	regular	regular	ADJ
ejpam-3449	631	8	and	and	CCONJ
ejpam-3449	631	9	λ	λ	X
ejpam-3449	631	10	:	:	PUNCT
ejpam-3449	631	11	(	(	PUNCT
ejpam-3449	631	12	τ	τ	PROPN
ejpam-3449	631	13	×σ)f	×σ)f	PROPN
ejpam-3449	631	14	→	→	SYM
ejpam-3449	631	15	p	p	X
ejpam-3449	631	16	(	(	PUNCT
ejpam-3449	631	17	x	x	NOUN
ejpam-3449	631	18	×y	×y	PRON
ejpam-3449	631	19	)	)	PUNCT
ejpam-3449	631	20	is	be	AUX
ejpam-3449	631	21	fine	fine	ADV
ejpam-3449	631	22	-	-	PUNCT
ejpam-3449	631	23	regular	regular	ADJ
ejpam-3449	631	24	with	with	ADP
ejpam-3449	631	25	respect	respect	NOUN
ejpam-3449	631	26	to	to	ADP
ejpam-3449	631	27	γ	γ	PROPN
ejpam-3449	631	28	and	and	CCONJ
ejpam-3449	631	29	β	β	X
ejpam-3449	631	30	.	.	PUNCT
ejpam-3449	632	1	let	let	AUX
ejpam-3449	632	2	h	h	NOUN
ejpam-3449	632	3	:	:	PUNCT
ejpam-3449	632	4	(	(	PUNCT
ejpam-3449	632	5	x	x	X
ejpam-3449	632	6	,	,	PUNCT
ejpam-3449	632	7	τ	τ	PROPN
ejpam-3449	632	8	,	,	PUNCT
ejpam-3449	632	9	τf	τf	NUM
ejpam-3449	632	10	)	)	PUNCT
ejpam-3449	632	11	→	→	SYM
ejpam-3449	632	12	(	(	PUNCT
ejpam-3449	632	13	y	y	PROPN
ejpam-3449	632	14	,	,	PUNCT
ejpam-3449	632	15	σ	σ	PROPN
ejpam-3449	632	16	,	,	PUNCT
ejpam-3449	632	17	σf	σf	NOUN
ejpam-3449	632	18	)	)	PUNCT
ejpam-3449	632	19	be	be	AUX
ejpam-3449	632	20	a	a	DET
ejpam-3449	632	21	function	function	NOUN
ejpam-3449	632	22	whose	whose	DET
ejpam-3449	632	23	graph	graph	NOUN
ejpam-3449	632	24	g(h	g(h	PROPN
ejpam-3449	632	25	)	)	PUNCT
ejpam-3449	632	26	is	be	AUX
ejpam-3449	632	27	fλ	fλ	NOUN
ejpam-3449	632	28	-	-	ADJ
ejpam-3449	632	29	closed	closed	ADJ
ejpam-3449	632	30	in	in	ADP
ejpam-3449	632	31	(	(	PUNCT
ejpam-3449	632	32	x	x	SYM
ejpam-3449	632	33	×	×	PROPN
ejpam-3449	632	34	y	y	PROPN
ejpam-3449	632	35	,	,	PUNCT
ejpam-3449	632	36	τ	τ	PROPN
ejpam-3449	632	37	×	×	PROPN
ejpam-3449	632	38	σ	σ	PROPN
ejpam-3449	632	39	)	)	PUNCT
ejpam-3449	632	40	.	.	PUNCT
ejpam-3449	633	1	if	if	SCONJ
ejpam-3449	633	2	a	a	DET
ejpam-3449	633	3	subset	subset	NOUN
ejpam-3449	633	4	s	s	X
ejpam-3449	633	5	is	be	AUX
ejpam-3449	633	6	fβ	fβ	ADJ
ejpam-3449	633	7	-	-	ADJ
ejpam-3449	633	8	compact	compact	ADJ
ejpam-3449	633	9	in	in	ADP
ejpam-3449	633	10	(	(	PUNCT
ejpam-3449	633	11	y	y	PROPN
ejpam-3449	633	12	,	,	PUNCT
ejpam-3449	633	13	σ	σ	PROPN
ejpam-3449	633	14	,	,	PUNCT
ejpam-3449	633	15	σf	σf	NOUN
ejpam-3449	633	16	)	)	PUNCT
ejpam-3449	633	17	,	,	PUNCT
ejpam-3449	633	18	then	then	ADV
ejpam-3449	633	19	h−1(s	h−1(	VERB
ejpam-3449	633	20	)	)	PUNCT
ejpam-3449	633	21	is	be	AUX
ejpam-3449	633	22	fγ	fγ	NOUN
ejpam-3449	633	23	-	-	PUNCT
ejpam-3449	633	24	closed	close	VERB
ejpam-3449	633	25	in	in	ADP
ejpam-3449	633	26	(	(	PUNCT
ejpam-3449	633	27	x	x	NOUN
ejpam-3449	633	28	,	,	PUNCT
ejpam-3449	633	29	τ	τ	PROPN
ejpam-3449	633	30	,	,	PUNCT
ejpam-3449	633	31	τf	τf	NUM
ejpam-3449	633	32	)	)	PUNCT
ejpam-3449	633	33	.	.	PUNCT
ejpam-3449	634	1	proof	proof	NOUN
ejpam-3449	634	2	.	.	PUNCT
ejpam-3449	635	1	suppose	suppose	VERB
ejpam-3449	635	2	that	that	SCONJ
ejpam-3449	635	3	h−1(s	h−1(s	PROPN
ejpam-3449	635	4	)	)	PUNCT
ejpam-3449	635	5	is	be	AUX
ejpam-3449	635	6	not	not	PART
ejpam-3449	635	7	fγ	fγ	ADV
ejpam-3449	635	8	-	-	PUNCT
ejpam-3449	635	9	closed	closed	ADJ
ejpam-3449	635	10	then	then	ADV
ejpam-3449	635	11	there	there	PRON
ejpam-3449	635	12	exist	exist	VERB
ejpam-3449	635	13	a	a	DET
ejpam-3449	635	14	point	point	NOUN
ejpam-3449	635	15	x	x	PUNCT
ejpam-3449	635	16	such	such	ADJ
ejpam-3449	635	17	that	that	SCONJ
ejpam-3449	635	18	x	x	SYM
ejpam-3449	635	19	∈	∈	PROPN
ejpam-3449	635	20	fclγ(h−1(s	fclγ(h−1(	NOUN
ejpam-3449	635	21	)	)	PUNCT
ejpam-3449	635	22	)	)	PUNCT
ejpam-3449	636	1	and	and	CCONJ
ejpam-3449	636	2	x	x	X
ejpam-3449	636	3	6∈	6∈	NOUN
ejpam-3449	636	4	h−1(s	h−1(s	PROPN
ejpam-3449	636	5	)	)	PUNCT
ejpam-3449	636	6	.	.	PUNCT
ejpam-3449	637	1	since	since	SCONJ
ejpam-3449	637	2	(	(	PUNCT
ejpam-3449	637	3	x	x	X
ejpam-3449	637	4	,	,	PUNCT
ejpam-3449	637	5	s	s	PART
ejpam-3449	637	6	)	)	PUNCT
ejpam-3449	637	7	6∈	6∈	NOUN
ejpam-3449	637	8	g(h	g(h	NUM
ejpam-3449	637	9	)	)	PUNCT
ejpam-3449	637	10	and	and	CCONJ
ejpam-3449	637	11	each	each	DET
ejpam-3449	637	12	s	s	PROPN
ejpam-3449	637	13	∈	∈	PROPN
ejpam-3449	637	14	s	s	X
ejpam-3449	637	15	and	and	CCONJ
ejpam-3449	637	16	fclλ(g(h	fclλ(g(h	NOUN
ejpam-3449	637	17	)	)	PUNCT
ejpam-3449	637	18	)	)	PUNCT
ejpam-3449	638	1	⊆	⊆	NUM
ejpam-3449	638	2	g(h	g(h	NUM
ejpam-3449	638	3	)	)	PUNCT
ejpam-3449	638	4	,	,	PUNCT
ejpam-3449	638	5	there	there	PRON
ejpam-3449	638	6	exists	exist	VERB
ejpam-3449	638	7	a	a	DET
ejpam-3449	638	8	fine	fine	ADV
ejpam-3449	638	9	-	-	PUNCT
ejpam-3449	638	10	open	open	NOUN
ejpam-3449	638	11	set	set	NOUN
ejpam-3449	638	12	w	w	PROPN
ejpam-3449	638	13	of	of	ADP
ejpam-3449	638	14	(	(	PUNCT
ejpam-3449	638	15	x	x	PROPN
ejpam-3449	638	16	×	×	PROPN
ejpam-3449	638	17	y	y	PROPN
ejpam-3449	638	18	,	,	PUNCT
ejpam-3449	638	19	τ	τ	PROPN
ejpam-3449	638	20	×	×	PROPN
ejpam-3449	638	21	σ	σ	PROPN
ejpam-3449	638	22	)	)	PUNCT
ejpam-3449	638	23	such	such	ADJ
ejpam-3449	638	24	that	that	SCONJ
ejpam-3449	638	25	(	(	PUNCT
ejpam-3449	638	26	x	x	NOUN
ejpam-3449	638	27	,	,	PUNCT
ejpam-3449	638	28	s	s	PART
ejpam-3449	638	29	)	)	PUNCT
ejpam-3449	638	30	∈	∈	PROPN
ejpam-3449	638	31	w	w	PROPN
ejpam-3449	638	32	and	and	CCONJ
ejpam-3449	638	33	β(w	β(w	PUNCT
ejpam-3449	638	34	)	)	PUNCT
ejpam-3449	638	35	∩	∩	NOUN
ejpam-3449	638	36	g(h	g(h	NUM
ejpam-3449	638	37	)	)	PUNCT
ejpam-3449	638	38	=	=	SYM
ejpam-3449	639	1	φ	φ	PROPN
ejpam-3449	639	2	.	.	PUNCT
ejpam-3449	640	1	by	by	ADP
ejpam-3449	640	2	fine	fine	ADJ
ejpam-3449	640	3	-	-	PUNCT
ejpam-3449	640	4	regularity	regularity	NOUN
ejpam-3449	640	5	of	of	ADP
ejpam-3449	640	6	λ	λ	NOUN
ejpam-3449	640	7	,	,	PUNCT
ejpam-3449	640	8	for	for	ADP
ejpam-3449	640	9	each	each	DET
ejpam-3449	640	10	s	s	X
ejpam-3449	640	11	∈	∈	PROPN
ejpam-3449	640	12	s	s	X
ejpam-3449	640	13	we	we	PRON
ejpam-3449	640	14	can	can	AUX
ejpam-3449	640	15	take	take	VERB
ejpam-3449	640	16	two	two	NUM
ejpam-3449	640	17	fine	fine	ADJ
ejpam-3449	640	18	-	-	PUNCT
ejpam-3449	640	19	open	open	ADJ
ejpam-3449	640	20	sets	set	NOUN
ejpam-3449	640	21	u(s	u(s	ADJ
ejpam-3449	640	22	)	)	PUNCT
ejpam-3449	640	23	and	and	CCONJ
ejpam-3449	640	24	v	v	NOUN
ejpam-3449	640	25	(	(	PUNCT
ejpam-3449	640	26	s	s	NOUN
ejpam-3449	640	27	)	)	PUNCT
ejpam-3449	640	28	in	in	ADP
ejpam-3449	640	29	(	(	PUNCT
ejpam-3449	640	30	y	y	PROPN
ejpam-3449	640	31	,	,	PUNCT
ejpam-3449	640	32	σ	σ	PROPN
ejpam-3449	640	33	,	,	PUNCT
ejpam-3449	640	34	σf	σf	NOUN
ejpam-3449	640	35	)	)	PUNCT
ejpam-3449	640	36	such	such	ADJ
ejpam-3449	640	37	that	that	SCONJ
ejpam-3449	640	38	x	x	SYM
ejpam-3449	640	39	∈	∈	PROPN
ejpam-3449	640	40	u(s	u(s	PROPN
ejpam-3449	640	41	)	)	PUNCT
ejpam-3449	640	42	,	,	PUNCT
ejpam-3449	640	43	s	s	VERB
ejpam-3449	641	1	∈	∈	PROPN
ejpam-3449	641	2	v	v	ADP
ejpam-3449	641	3	(	(	PUNCT
ejpam-3449	641	4	s	s	NOUN
ejpam-3449	641	5	)	)	PUNCT
ejpam-3449	641	6	and	and	CCONJ
ejpam-3449	641	7	γ(u(s	γ(u(s	NUM
ejpam-3449	641	8	)	)	PUNCT
ejpam-3449	641	9	)	)	PUNCT
ejpam-3449	641	10	×	×	NOUN
ejpam-3449	641	11	β(v	β(v	NOUN
ejpam-3449	641	12	(	(	PUNCT
ejpam-3449	641	13	s	s	NOUN
ejpam-3449	641	14	)	)	PUNCT
ejpam-3449	641	15	)	)	PUNCT
ejpam-3449	642	1	⊆	⊆	NUM
ejpam-3449	642	2	λ(w	λ(w	NOUN
ejpam-3449	642	3	)	)	PUNCT
ejpam-3449	642	4	.	.	PUNCT
ejpam-3449	643	1	then	then	ADV
ejpam-3449	643	2	we	we	PRON
ejpam-3449	643	3	have	have	VERB
ejpam-3449	643	4	h(γ(u(s	h(γ(u(s	PROPN
ejpam-3449	643	5	)	)	PUNCT
ejpam-3449	643	6	)	)	PUNCT
ejpam-3449	643	7	)	)	PUNCT
ejpam-3449	643	8	∩	∩	NOUN
ejpam-3449	643	9	β(v	β(v	PROPN
ejpam-3449	643	10	(	(	PUNCT
ejpam-3449	643	11	s	s	NOUN
ejpam-3449	643	12	)	)	PUNCT
ejpam-3449	643	13	)	)	PUNCT
ejpam-3449	644	1	=	=	SYM
ejpam-3449	644	2	φ	φ	PROPN
ejpam-3449	644	3	.	.	PUNCT
ejpam-3449	645	1	since	since	SCONJ
ejpam-3449	645	2	{	{	PUNCT
ejpam-3449	645	3	v	v	X
ejpam-3449	645	4	(	(	PUNCT
ejpam-3449	645	5	s	s	NOUN
ejpam-3449	645	6	)	)	PUNCT
ejpam-3449	645	7	:	:	PUNCT
ejpam-3449	645	8	s	s	VERB
ejpam-3449	645	9	∈	∈	PROPN
ejpam-3449	645	10	s	s	AUX
ejpam-3449	645	11	}	}	PUNCT
ejpam-3449	645	12	is	be	AUX
ejpam-3449	645	13	fine	fine	ADV
ejpam-3449	645	14	-	-	PUNCT
ejpam-3449	645	15	open	open	ADJ
ejpam-3449	645	16	cover	cover	NOUN
ejpam-3449	645	17	of	of	ADP
ejpam-3449	645	18	s	s	NOUN
ejpam-3449	645	19	,	,	PUNCT
ejpam-3449	645	20	then	then	ADV
ejpam-3449	645	21	by	by	ADP
ejpam-3449	645	22	fγ	fγ	NOUN
ejpam-3449	645	23	-	-	PUNCT
ejpam-3449	645	24	compactness	compactness	NOUN
ejpam-3449	645	25	there	there	PRON
ejpam-3449	645	26	exists	exist	VERB
ejpam-3449	645	27	a	a	DET
ejpam-3449	645	28	finite	finite	ADJ
ejpam-3449	645	29	number	number	NOUN
ejpam-3449	645	30	s1	s1	NOUN
ejpam-3449	645	31	,	,	PUNCT
ejpam-3449	645	32	s2	s2	PROPN
ejpam-3449	645	33	,	,	PUNCT
ejpam-3449	645	34	...	...	PUNCT
ejpam-3449	645	35	,	,	PUNCT
ejpam-3449	645	36	sn	sn	PROPN
ejpam-3449	645	37	∈	∈	PROPN
ejpam-3449	645	38	s	s	VERB
ejpam-3449	645	39	such	such	ADJ
ejpam-3449	645	40	that	that	PRON
ejpam-3449	645	41	s	s	VERB
ejpam-3449	645	42	⊆	⊆	NUM
ejpam-3449	645	43	β(v	β(v	ADJ
ejpam-3449	645	44	(	(	PUNCT
ejpam-3449	645	45	s1	s1	NOUN
ejpam-3449	645	46	)	)	PUNCT
ejpam-3449	645	47	)	)	PUNCT
ejpam-3449	645	48	∪	∪	ADP
ejpam-3449	645	49	β(v	β(v	PROPN
ejpam-3449	645	50	(	(	PUNCT
ejpam-3449	645	51	s2	s2	PROPN
ejpam-3449	645	52	)	)	PUNCT
ejpam-3449	645	53	)	)	PUNCT
ejpam-3449	645	54	∪	∪	ADP
ejpam-3449	645	55	...	...	PUNCT
ejpam-3449	645	56	∪	∪	ADP
ejpam-3449	645	57	β(v	β(v	PROPN
ejpam-3449	645	58	(	(	PUNCT
ejpam-3449	645	59	sn	sn	PROPN
ejpam-3449	645	60	)	)	PUNCT
ejpam-3449	645	61	)	)	PUNCT
ejpam-3449	645	62	.	.	PUNCT
ejpam-3449	646	1	by	by	ADP
ejpam-3449	646	2	the	the	DET
ejpam-3449	646	3	fine	fine	ADJ
ejpam-3449	646	4	-	-	PUNCT
ejpam-3449	646	5	regularity	regularity	NOUN
ejpam-3449	646	6	of	of	ADP
ejpam-3449	646	7	γ	γ	X
ejpam-3449	646	8	,	,	PUNCT
ejpam-3449	646	9	there	there	PRON
ejpam-3449	646	10	exist	exist	VERB
ejpam-3449	646	11	a	a	DET
ejpam-3449	646	12	fine	fine	ADV
ejpam-3449	646	13	-	-	PUNCT
ejpam-3449	646	14	open	open	NOUN
ejpam-3449	646	15	set	set	NOUN
ejpam-3449	646	16	u	u	PRON
ejpam-3449	646	17	such	such	ADJ
ejpam-3449	646	18	that	that	SCONJ
ejpam-3449	646	19	x	x	SYM
ejpam-3449	646	20	∈	∈	PROPN
ejpam-3449	646	21	u	u	NOUN
ejpam-3449	646	22	,	,	PUNCT
ejpam-3449	646	23	γ(u	γ(u	PROPN
ejpam-3449	646	24	)	)	PUNCT
ejpam-3449	646	25	⊆	⊆	NUM
ejpam-3449	646	26	γ(u(s1	γ(u(s1	NOUN
ejpam-3449	646	27	)	)	PUNCT
ejpam-3449	646	28	)	)	PUNCT
ejpam-3449	646	29	∩	∩	NOUN
ejpam-3449	646	30	γ(u(s2	γ(u(s2	NOUN
ejpam-3449	646	31	)	)	PUNCT
ejpam-3449	646	32	)	)	PUNCT
ejpam-3449	646	33	∩	∩	NOUN
ejpam-3449	646	34	...	...	PUNCT
ejpam-3449	646	35	∩	∩	NOUN
ejpam-3449	646	36	γ(u(sn	γ(u(sn	VERB
ejpam-3449	646	37	)	)	PUNCT
ejpam-3449	646	38	)	)	PUNCT
ejpam-3449	646	39	.	.	PUNCT
ejpam-3449	647	1	therefore	therefore	ADV
ejpam-3449	647	2	,	,	PUNCT
ejpam-3449	647	3	we	we	PRON
ejpam-3449	647	4	have	have	VERB
ejpam-3449	647	5	γ(u)∩	γ(u)∩	PROPN
ejpam-3449	647	6	h−1(s	h−1(s	PROPN
ejpam-3449	647	7	)	)	PUNCT
ejpam-3449	647	8	⊆	⊆	NUM
ejpam-3449	647	9	u(si)∩	u(si)∩	NOUN
ejpam-3449	647	10	h−1(β(v	h−1(β(v	NOUN
ejpam-3449	647	11	(	(	PUNCT
ejpam-3449	647	12	si	si	NOUN
ejpam-3449	647	13	)	)	PUNCT
ejpam-3449	647	14	)	)	PUNCT
ejpam-3449	647	15	)	)	PUNCT
ejpam-3449	648	1	=	=	PUNCT
ejpam-3449	648	2	φ	φ	X
ejpam-3449	648	3	.	.	PUNCT
ejpam-3449	649	1	this	this	PRON
ejpam-3449	649	2	shows	show	VERB
ejpam-3449	649	3	that	that	SCONJ
ejpam-3449	649	4	x	x	PROPN
ejpam-3449	649	5	6∈	6∈	NOUN
ejpam-3449	649	6	fclγ(h−1(s	fclγ(h−1(	NOUN
ejpam-3449	649	7	)	)	PUNCT
ejpam-3449	649	8	)	)	PUNCT
ejpam-3449	649	9	.	.	PUNCT
ejpam-3449	650	1	this	this	PRON
ejpam-3449	650	2	is	be	AUX
ejpam-3449	650	3	a	a	DET
ejpam-3449	650	4	contradiction	contradiction	NOUN
ejpam-3449	650	5	.	.	PUNCT
ejpam-3449	651	1	therefore	therefore	ADV
ejpam-3449	651	2	,	,	PUNCT
ejpam-3449	651	3	h−1(s	h−1(s	PROPN
ejpam-3449	651	4	)	)	PUNCT
ejpam-3449	651	5	is	be	AUX
ejpam-3449	651	6	fγ	fγ	NOUN
ejpam-3449	651	7	-	-	PUNCT
ejpam-3449	651	8	closed	closed	ADJ
ejpam-3449	651	9	.	.	PUNCT
ejpam-3449	652	1	references	reference	NOUN
ejpam-3449	652	2	976	976	NUM
ejpam-3449	652	3	theorem	theorem	NOUN
ejpam-3449	652	4	7.10	7.10	NUM
ejpam-3449	652	5	.	.	PUNCT
ejpam-3449	652	6	suppose	suppose	VERB
ejpam-3449	652	7	that	that	SCONJ
ejpam-3449	652	8	the	the	DET
ejpam-3449	652	9	following	follow	VERB
ejpam-3449	652	10	condition	condition	NOUN
ejpam-3449	652	11	hold	hold	VERB
ejpam-3449	652	12	:	:	PUNCT
ejpam-3449	652	13	(	(	PUNCT
ejpam-3449	652	14	i	i	NOUN
ejpam-3449	652	15	)	)	PUNCT
ejpam-3449	652	16	γ	γ	NOUN
ejpam-3449	652	17	:	:	PUNCT
ejpam-3449	652	18	τf	τf	PROPN
ejpam-3449	652	19	→	→	SYM
ejpam-3449	652	20	p	p	X
ejpam-3449	652	21	(	(	PUNCT
ejpam-3449	652	22	x	x	X
ejpam-3449	652	23	)	)	PUNCT
ejpam-3449	652	24	is	be	AUX
ejpam-3449	652	25	fine	fine	ADV
ejpam-3449	652	26	-	-	PUNCT
ejpam-3449	652	27	open	open	ADJ
ejpam-3449	652	28	(	(	PUNCT
ejpam-3449	652	29	ii	ii	NOUN
ejpam-3449	652	30	)	)	PUNCT
ejpam-3449	652	31	β	β	NOUN
ejpam-3449	652	32	:	:	PUNCT
ejpam-3449	652	33	σf	σf	NOUN
ejpam-3449	652	34	→	→	SYM
ejpam-3449	652	35	p	p	X
ejpam-3449	652	36	(	(	PUNCT
ejpam-3449	652	37	y	y	PROPN
ejpam-3449	652	38	)	)	PUNCT
ejpam-3449	652	39	is	be	AUX
ejpam-3449	652	40	fine	fine	ADV
ejpam-3449	652	41	-	-	PUNCT
ejpam-3449	652	42	regular	regular	ADJ
ejpam-3449	652	43	,	,	PUNCT
ejpam-3449	652	44	and	and	CCONJ
ejpam-3449	652	45	(	(	PUNCT
ejpam-3449	652	46	iii	iii	X
ejpam-3449	652	47	)	)	PUNCT
ejpam-3449	652	48	λ	λ	NOUN
ejpam-3449	652	49	:	:	PUNCT
ejpam-3449	652	50	(	(	PUNCT
ejpam-3449	652	51	τ×σ)f	τ×σ)f	PUNCT
ejpam-3449	652	52	→	→	SYM
ejpam-3449	652	53	p	p	X
ejpam-3449	652	54	(	(	PUNCT
ejpam-3449	652	55	x×y	x×y	PROPN
ejpam-3449	652	56	)	)	PUNCT
ejpam-3449	652	57	is	be	AUX
ejpam-3449	652	58	associated	associate	VERB
ejpam-3449	652	59	with	with	ADP
ejpam-3449	652	60	γ	γ	PROPN
ejpam-3449	652	61	and	and	CCONJ
ejpam-3449	652	62	β	β	NOUN
ejpam-3449	652	63	,	,	PUNCT
ejpam-3449	652	64	and	and	CCONJ
ejpam-3449	652	65	λ	λ	PROPN
ejpam-3449	652	66	is	be	AUX
ejpam-3449	652	67	fine	fine	ADV
ejpam-3449	652	68	-	-	PUNCT
ejpam-3449	652	69	regular	regular	ADJ
ejpam-3449	652	70	with	with	ADP
ejpam-3449	652	71	respect	respect	NOUN
ejpam-3449	652	72	to	to	ADP
ejpam-3449	652	73	γ	γ	PROPN
ejpam-3449	652	74	and	and	CCONJ
ejpam-3449	652	75	β	β	X
ejpam-3449	652	76	.	.	PUNCT
ejpam-3449	653	1	let	let	AUX
ejpam-3449	653	2	h	h	NOUN
ejpam-3449	653	3	:	:	PUNCT
ejpam-3449	653	4	(	(	PUNCT
ejpam-3449	653	5	x	x	X
ejpam-3449	653	6	,	,	PUNCT
ejpam-3449	653	7	τ	τ	PROPN
ejpam-3449	653	8	,	,	PUNCT
ejpam-3449	653	9	τf	τf	NOUN
ejpam-3449	653	10	)	)	PUNCT
ejpam-3449	653	11	→	→	SYM
ejpam-3449	653	12	(	(	PUNCT
ejpam-3449	653	13	y	y	PROPN
ejpam-3449	653	14	,	,	PUNCT
ejpam-3449	653	15	σ	σ	PROPN
ejpam-3449	653	16	,	,	PUNCT
ejpam-3449	653	17	σf	σf	NOUN
ejpam-3449	653	18	)	)	PUNCT
ejpam-3449	653	19	be	be	AUX
ejpam-3449	653	20	a	a	DET
ejpam-3449	653	21	function	function	NOUN
ejpam-3449	653	22	whose	whose	DET
ejpam-3449	653	23	graph	graph	NOUN
ejpam-3449	653	24	g(h	g(h	PROPN
ejpam-3449	653	25	)	)	PUNCT
ejpam-3449	653	26	is	be	AUX
ejpam-3449	653	27	fλ	fλ	NOUN
ejpam-3449	653	28	-	-	ADJ
ejpam-3449	653	29	closed	closed	ADJ
ejpam-3449	653	30	in	in	ADP
ejpam-3449	653	31	(	(	PUNCT
ejpam-3449	653	32	x×y	x×y	PROPN
ejpam-3449	653	33	,	,	PUNCT
ejpam-3449	653	34	τ×σ	τ×σ	NUM
ejpam-3449	653	35	)	)	PUNCT
ejpam-3449	653	36	.	.	PUNCT
ejpam-3449	654	1	if	if	SCONJ
ejpam-3449	654	2	every	every	DET
ejpam-3449	654	3	cover	cover	NOUN
ejpam-3449	654	4	of	of	ADP
ejpam-3449	654	5	a	a	PRON
ejpam-3449	654	6	by	by	ADP
ejpam-3449	654	7	fγ	fγ	NOUN
ejpam-3449	654	8	-	-	PUNCT
ejpam-3449	654	9	open	open	ADJ
ejpam-3449	654	10	sets	set	NOUN
ejpam-3449	654	11	of	of	ADP
ejpam-3449	654	12	(	(	PUNCT
ejpam-3449	654	13	x	x	NOUN
ejpam-3449	654	14	,	,	PUNCT
ejpam-3449	654	15	τ	τ	PROPN
ejpam-3449	654	16	,	,	PUNCT
ejpam-3449	654	17	τf	τf	NUM
ejpam-3449	654	18	)	)	PUNCT
ejpam-3449	654	19	has	have	AUX
ejpam-3449	654	20	finite	finite	ADJ
ejpam-3449	654	21	sub	sub	NOUN
ejpam-3449	654	22	cover	cover	NOUN
ejpam-3449	654	23	,	,	PUNCT
ejpam-3449	654	24	then	then	ADV
ejpam-3449	654	25	h(a	h(a	PROPN
ejpam-3449	654	26	)	)	PUNCT
ejpam-3449	654	27	is	be	AUX
ejpam-3449	654	28	fβ	fβ	ADV
ejpam-3449	654	29	-	-	PUNCT
ejpam-3449	654	30	closed	closed	ADJ
ejpam-3449	654	31	in	in	ADP
ejpam-3449	654	32	(	(	PUNCT
ejpam-3449	654	33	y	y	PROPN
ejpam-3449	654	34	,	,	PUNCT
ejpam-3449	654	35	σ	σ	PROPN
ejpam-3449	654	36	,	,	PUNCT
ejpam-3449	654	37	σf	σf	NOUN
ejpam-3449	654	38	)	)	PUNCT
ejpam-3449	654	39	.	.	PUNCT
ejpam-3449	655	1	proof	proof	NOUN
ejpam-3449	655	2	.	.	PUNCT
ejpam-3449	656	1	similar	similar	ADJ
ejpam-3449	656	2	to	to	ADP
ejpam-3449	656	3	theorem	theorem	VERB
ejpam-3449	656	4	7.9	7.9	NUM
ejpam-3449	656	5	.	.	NOUN
ejpam-3449	656	6	8	8	NUM
ejpam-3449	656	7	.	.	PUNCT
ejpam-3449	656	8	conclusion	conclusion	NOUN
ejpam-3449	656	9	in	in	ADP
ejpam-3449	656	10	the	the	DET
ejpam-3449	656	11	present	present	ADJ
ejpam-3449	656	12	paper	paper	NOUN
ejpam-3449	656	13	,	,	PUNCT
ejpam-3449	656	14	the	the	DET
ejpam-3449	656	15	concepts	concept	NOUN
ejpam-3449	656	16	of	of	ADP
ejpam-3449	656	17	an	an	DET
ejpam-3449	656	18	operation	operation	NOUN
ejpam-3449	656	19	γ	γ	NOUN
ejpam-3449	656	20	on	on	ADP
ejpam-3449	656	21	τf	τf	PROPN
ejpam-3449	656	22	are	be	AUX
ejpam-3449	656	23	introduced	introduce	VERB
ejpam-3449	656	24	.	.	PUNCT
ejpam-3449	657	1	also	also	ADV
ejpam-3449	657	2	,	,	PUNCT
ejpam-3449	657	3	the	the	DET
ejpam-3449	657	4	concept	concept	NOUN
ejpam-3449	657	5	of	of	ADP
ejpam-3449	657	6	fγ	fγ	NOUN
ejpam-3449	657	7	-	-	PUNCT
ejpam-3449	657	8	open	open	ADJ
ejpam-3449	657	9	sets	set	NOUN
ejpam-3449	657	10	are	be	AUX
ejpam-3449	657	11	defined	define	VERB
ejpam-3449	657	12	,	,	PUNCT
ejpam-3449	657	13	and	and	CCONJ
ejpam-3449	657	14	some	some	PRON
ejpam-3449	657	15	of	of	ADP
ejpam-3449	657	16	their	their	PRON
ejpam-3449	657	17	properties	property	NOUN
ejpam-3449	657	18	are	be	AUX
ejpam-3449	657	19	studied	study	VERB
ejpam-3449	657	20	via	via	ADP
ejpam-3449	657	21	this	this	DET
ejpam-3449	657	22	operation	operation	NOUN
ejpam-3449	657	23	.	.	PUNCT
ejpam-3449	658	1	moreover	moreover	ADV
ejpam-3449	658	2	,	,	PUNCT
ejpam-3449	658	3	the	the	DET
ejpam-3449	658	4	concept	concept	NOUN
ejpam-3449	658	5	of	of	ADP
ejpam-3449	658	6	fγg.closed	fγg.close	VERB
ejpam-3449	658	7	sets	set	NOUN
ejpam-3449	658	8	are	be	AUX
ejpam-3449	658	9	studied	study	VERB
ejpam-3449	658	10	.	.	PUNCT
ejpam-3449	659	1	furthermore	furthermore	ADV
ejpam-3449	659	2	,	,	PUNCT
ejpam-3449	659	3	some	some	DET
ejpam-3449	659	4	types	type	NOUN
ejpam-3449	659	5	of	of	ADP
ejpam-3449	659	6	fγ	fγ	NOUN
ejpam-3449	659	7	-	-	PUNCT
ejpam-3449	659	8	separation	separation	NOUN
ejpam-3449	659	9	axioms	axiom	NOUN
ejpam-3449	659	10	and	and	CCONJ
ejpam-3449	659	11	fγβ	fγβ	ADJ
ejpam-3449	659	12	-	-	PUNCT
ejpam-3449	659	13	continuous	continuous	ADJ
ejpam-3449	659	14	functions	function	NOUN
ejpam-3449	659	15	are	be	AUX
ejpam-3449	659	16	investigated	investigate	VERB
ejpam-3449	659	17	.	.	PUNCT
ejpam-3449	660	1	in	in	ADP
ejpam-3449	660	2	addition	addition	NOUN
ejpam-3449	660	3	,	,	PUNCT
ejpam-3449	660	4	some	some	DET
ejpam-3449	660	5	basic	basic	ADJ
ejpam-3449	660	6	properties	property	NOUN
ejpam-3449	660	7	of	of	ADP
ejpam-3449	660	8	functions	function	NOUN
ejpam-3449	660	9	with	with	ADP
ejpam-3449	660	10	fβ	fβ	ADV
ejpam-3449	660	11	-	-	PUNCT
ejpam-3449	660	12	closed	closed	ADJ
ejpam-3449	660	13	graphs	graph	NOUN
ejpam-3449	660	14	are	be	AUX
ejpam-3449	660	15	obtained	obtain	VERB
ejpam-3449	660	16	.	.	PUNCT
ejpam-3449	661	1	references	reference	NOUN
ejpam-3449	661	2	[	[	X
ejpam-3449	661	3	1	1	NUM
ejpam-3449	661	4	]	]	X
ejpam-3449	661	5	n.	n.	PROPN
ejpam-3449	661	6	ahmad	ahmad	PROPN
ejpam-3449	661	7	and	and	CCONJ
ejpam-3449	661	8	b.a	b.a	PROPN
ejpam-3449	661	9	.	.	PROPN
ejpam-3449	661	10	asaad	asaad	PROPN
ejpam-3449	661	11	,	,	PUNCT
ejpam-3449	661	12	more	more	ADJ
ejpam-3449	661	13	properties	property	NOUN
ejpam-3449	661	14	of	of	ADP
ejpam-3449	661	15	an	an	DET
ejpam-3449	661	16	operation	operation	NOUN
ejpam-3449	661	17	on	on	ADP
ejpam-3449	661	18	semi	semi	ADJ
ejpam-3449	661	19	-	-	ADJ
ejpam-3449	661	20	generalized	generalized	ADJ
ejpam-3449	661	21	open	open	ADJ
ejpam-3449	661	22	sets	set	NOUN
ejpam-3449	661	23	,	,	PUNCT
ejpam-3449	661	24	italian	italian	ADJ
ejpam-3449	661	25	journal	journal	NOUN
ejpam-3449	661	26	of	of	ADP
ejpam-3449	661	27	pure	pure	ADJ
ejpam-3449	661	28	and	and	CCONJ
ejpam-3449	661	29	applied	applied	ADJ
ejpam-3449	661	30	mathematics	mathematic	NOUN
ejpam-3449	661	31	,	,	PUNCT
ejpam-3449	661	32	39	39	NUM
ejpam-3449	661	33	(	(	PUNCT
ejpam-3449	661	34	2018	2018	NUM
ejpam-3449	661	35	)	)	PUNCT
ejpam-3449	661	36	,	,	PUNCT
ejpam-3449	661	37	608	608	NUM
ejpam-3449	661	38	-	-	SYM
ejpam-3449	661	39	627	627	NUM
ejpam-3449	661	40	.	.	PUNCT
ejpam-3449	662	1	[	[	X
ejpam-3449	662	2	2	2	X
ejpam-3449	662	3	]	]	PUNCT
ejpam-3449	662	4	t.	t.	PROPN
ejpam-3449	662	5	m.	m.	PROPN
ejpam-3449	662	6	al	al	PROPN
ejpam-3449	662	7	-	-	PUNCT
ejpam-3449	662	8	shami	shami	PROPN
ejpam-3449	662	9	,	,	PUNCT
ejpam-3449	662	10	somewhere	somewhere	ADV
ejpam-3449	662	11	dense	dense	ADJ
ejpam-3449	662	12	sets	set	NOUN
ejpam-3449	662	13	and	and	CCONJ
ejpam-3449	662	14	st1	st1	PROPN
ejpam-3449	662	15	-	-	PUNCT
ejpam-3449	662	16	spaces	spaces	PROPN
ejpam-3449	662	17	,	,	PUNCT
ejpam-3449	662	18	punjab	punjab	PROPN
ejpam-3449	662	19	univ	univ	PROPN
ejpam-3449	662	20	.	.	PUNCT
ejpam-3449	663	1	j.	j.	PROPN
ejpam-3449	663	2	math	math	PROPN
ejpam-3449	663	3	.	.	PUNCT
ejpam-3449	664	1	(	(	PUNCT
ejpam-3449	664	2	lahore	lahore	NOUN
ejpam-3449	664	3	)	)	PUNCT
ejpam-3449	664	4	,	,	PUNCT
ejpam-3449	664	5	49	49	NUM
ejpam-3449	664	6	(	(	PUNCT
ejpam-3449	664	7	2	2	NUM
ejpam-3449	664	8	)	)	PUNCT
ejpam-3449	664	9	(	(	PUNCT
ejpam-3449	664	10	2017	2017	NUM
ejpam-3449	664	11	)	)	PUNCT
ejpam-3449	664	12	,	,	PUNCT
ejpam-3449	664	13	101	101	NUM
ejpam-3449	664	14	-	-	SYM
ejpam-3449	664	15	111	111	NUM
ejpam-3449	664	16	.	.	PUNCT
ejpam-3449	665	1	[	[	X
ejpam-3449	665	2	3	3	X
ejpam-3449	665	3	]	]	PUNCT
ejpam-3449	665	4	t.	t.	PROPN
ejpam-3449	665	5	m.	m.	PROPN
ejpam-3449	665	6	al	al	PROPN
ejpam-3449	665	7	-	-	PUNCT
ejpam-3449	665	8	shami	shami	PROPN
ejpam-3449	665	9	and	and	CCONJ
ejpam-3449	665	10	t.	t.	PROPN
ejpam-3449	665	11	noiri	noiri	PROPN
ejpam-3449	665	12	,	,	PUNCT
ejpam-3449	665	13	more	more	ADJ
ejpam-3449	665	14	notions	notion	NOUN
ejpam-3449	665	15	and	and	CCONJ
ejpam-3449	665	16	mappings	mapping	NOUN
ejpam-3449	665	17	via	via	ADP
ejpam-3449	665	18	somewhere	somewhere	ADJ
ejpam-3449	665	19	dense	dense	ADJ
ejpam-3449	665	20	sets	set	NOUN
ejpam-3449	665	21	,	,	PUNCT
ejpam-3449	665	22	afrika	afrika	ADJ
ejpam-3449	665	23	matematika	matematika	NOUN
ejpam-3449	665	24	,	,	PUNCT
ejpam-3449	665	25	(	(	PUNCT
ejpam-3449	665	26	2019	2019	NUM
ejpam-3449	665	27	)	)	PUNCT
ejpam-3449	665	28	.	.	PUNCT
ejpam-3449	666	1	[	[	X
ejpam-3449	666	2	4	4	NUM
ejpam-3449	666	3	]	]	X
ejpam-3449	666	4	b.a	b.a	PROPN
ejpam-3449	666	5	.	.	PROPN
ejpam-3449	666	6	asaad	asaad	PROPN
ejpam-3449	666	7	,	,	PUNCT
ejpam-3449	666	8	some	some	DET
ejpam-3449	666	9	applications	application	NOUN
ejpam-3449	666	10	of	of	ADP
ejpam-3449	666	11	generalized	generalized	ADJ
ejpam-3449	666	12	open	open	ADJ
ejpam-3449	666	13	sets	set	NOUN
ejpam-3449	666	14	via	via	ADP
ejpam-3449	666	15	operations	operation	NOUN
ejpam-3449	666	16	,	,	PUNCT
ejpam-3449	666	17	new	new	ADJ
ejpam-3449	666	18	trends	trend	NOUN
ejpam-3449	666	19	in	in	ADP
ejpam-3449	666	20	mathematical	mathematical	ADJ
ejpam-3449	666	21	sciences	science	NOUN
ejpam-3449	666	22	,	,	PUNCT
ejpam-3449	666	23	5	5	NUM
ejpam-3449	666	24	(	(	PUNCT
ejpam-3449	666	25	1	1	NUM
ejpam-3449	666	26	)	)	PUNCT
ejpam-3449	666	27	(	(	PUNCT
ejpam-3449	666	28	2017	2017	NUM
ejpam-3449	666	29	)	)	PUNCT
ejpam-3449	666	30	,	,	PUNCT
ejpam-3449	666	31	145	145	NUM
ejpam-3449	666	32	-	-	SYM
ejpam-3449	666	33	157	157	NUM
ejpam-3449	666	34	.	.	PUNCT
ejpam-3449	667	1	[	[	X
ejpam-3449	667	2	5	5	NUM
ejpam-3449	667	3	]	]	X
ejpam-3449	667	4	b.a	b.a	PROPN
ejpam-3449	667	5	.	.	PROPN
ejpam-3449	667	6	asaad	asaad	PROPN
ejpam-3449	667	7	and	and	CCONJ
ejpam-3449	667	8	n.	n.	PROPN
ejpam-3449	667	9	ahmad	ahmad	PROPN
ejpam-3449	667	10	,	,	PUNCT
ejpam-3449	667	11	further	further	ADJ
ejpam-3449	667	12	characterizations	characterization	NOUN
ejpam-3449	667	13	of	of	ADP
ejpam-3449	667	14	γ	γ	X
ejpam-3449	667	15	-	-	ADJ
ejpam-3449	667	16	extremally	extremally	ADV
ejpam-3449	667	17	disconnected	disconnected	ADJ
ejpam-3449	667	18	spaces	space	NOUN
ejpam-3449	667	19	,	,	PUNCT
ejpam-3449	667	20	international	international	ADJ
ejpam-3449	667	21	journal	journal	NOUN
ejpam-3449	667	22	of	of	ADP
ejpam-3449	667	23	pure	pure	ADJ
ejpam-3449	667	24	and	and	CCONJ
ejpam-3449	667	25	applied	applied	ADJ
ejpam-3449	667	26	mathematics	mathematic	NOUN
ejpam-3449	667	27	,	,	PUNCT
ejpam-3449	667	28	108	108	NUM
ejpam-3449	667	29	(	(	PUNCT
ejpam-3449	667	30	3	3	NUM
ejpam-3449	667	31	)	)	PUNCT
ejpam-3449	667	32	(	(	PUNCT
ejpam-3449	667	33	2016	2016	NUM
ejpam-3449	667	34	)	)	PUNCT
ejpam-3449	667	35	,	,	PUNCT
ejpam-3449	667	36	533549	533549	NUM
ejpam-3449	667	37	.	.	PUNCT
ejpam-3449	668	1	[	[	X
ejpam-3449	668	2	6	6	NUM
ejpam-3449	668	3	]	]	X
ejpam-3449	668	4	b.a	b.a	PROPN
ejpam-3449	668	5	.	.	PROPN
ejpam-3449	668	6	asaad	asaad	PROPN
ejpam-3449	668	7	and	and	CCONJ
ejpam-3449	668	8	n.	n.	PROPN
ejpam-3449	668	9	ahmad	ahmad	PROPN
ejpam-3449	668	10	,	,	PUNCT
ejpam-3449	668	11	operation	operation	NOUN
ejpam-3449	668	12	on	on	ADP
ejpam-3449	668	13	semi	semi	ADJ
ejpam-3449	668	14	generalized	generalized	ADJ
ejpam-3449	668	15	open	open	ADJ
ejpam-3449	668	16	sets	set	NOUN
ejpam-3449	668	17	with	with	ADP
ejpam-3449	668	18	its	its	PRON
ejpam-3449	668	19	separation	separation	NOUN
ejpam-3449	668	20	axioms	axiom	NOUN
ejpam-3449	668	21	,	,	PUNCT
ejpam-3449	668	22	aip	aip	PROPN
ejpam-3449	668	23	conference	conference	NOUN
ejpam-3449	668	24	proceedings	proceeding	NOUN
ejpam-3449	668	25	1905	1905	NUM
ejpam-3449	668	26	,	,	PUNCT
ejpam-3449	668	27	020001	020001	NUM
ejpam-3449	668	28	(	(	PUNCT
ejpam-3449	668	29	2017	2017	NUM
ejpam-3449	668	30	)	)	PUNCT
ejpam-3449	668	31	;	;	PUNCT
ejpam-3449	668	32	https://doi.org/10.1063/1.5012141	https://doi.org/10.1063/1.5012141	PROPN
ejpam-3449	668	33	.	.	PUNCT
ejpam-3449	669	1	[	[	X
ejpam-3449	669	2	7	7	NUM
ejpam-3449	669	3	]	]	X
ejpam-3449	669	4	b.a	b.a	PROPN
ejpam-3449	669	5	.	.	PROPN
ejpam-3449	669	6	asaad	asaad	PROPN
ejpam-3449	669	7	,	,	PUNCT
ejpam-3449	669	8	n.	n.	PROPN
ejpam-3449	669	9	ahmad	ahmad	PROPN
ejpam-3449	669	10	and	and	CCONJ
ejpam-3449	669	11	z.	z.	PROPN
ejpam-3449	669	12	omar	omar	PROPN
ejpam-3449	669	13	,	,	PUNCT
ejpam-3449	669	14	γ	γ	PROPN
ejpam-3449	669	15	-	-	ADJ
ejpam-3449	669	16	regular	regular	ADJ
ejpam-3449	669	17	-	-	PUNCT
ejpam-3449	669	18	open	open	ADJ
ejpam-3449	669	19	sets	set	NOUN
ejpam-3449	669	20	and	and	CCONJ
ejpam-3449	669	21	γ	γ	NOUN
ejpam-3449	669	22	-	-	PUNCT
ejpam-3449	669	23	extremally	extremally	ADV
ejpam-3449	669	24	disconnected	disconnected	ADJ
ejpam-3449	669	25	spaces	space	NOUN
ejpam-3449	669	26	,	,	PUNCT
ejpam-3449	669	27	mathematical	mathematical	ADJ
ejpam-3449	669	28	theory	theory	NOUN
ejpam-3449	669	29	and	and	CCONJ
ejpam-3449	669	30	modeling	modeling	NOUN
ejpam-3449	669	31	,	,	PUNCT
ejpam-3449	669	32	3	3	NUM
ejpam-3449	669	33	(	(	PUNCT
ejpam-3449	669	34	12	12	NUM
ejpam-3449	669	35	)	)	PUNCT
ejpam-3449	669	36	(	(	PUNCT
ejpam-3449	669	37	2013	2013	NUM
ejpam-3449	669	38	)	)	PUNCT
ejpam-3449	669	39	,	,	PUNCT
ejpam-3449	669	40	132	132	NUM
ejpam-3449	669	41	-	-	SYM
ejpam-3449	669	42	141	141	NUM
ejpam-3449	669	43	.	.	PUNCT
ejpam-3449	670	1	references	reference	NOUN
ejpam-3449	670	2	977	977	NUM
ejpam-3449	670	3	[	[	SYM
ejpam-3449	670	4	8	8	NUM
ejpam-3449	670	5	]	]	X
ejpam-3449	670	6	b.a	b.a	PROPN
ejpam-3449	670	7	.	.	PROPN
ejpam-3449	670	8	asaad	asaad	PROPN
ejpam-3449	670	9	and	and	CCONJ
ejpam-3449	670	10	z.a	z.a	PROPN
ejpam-3449	670	11	.	.	PROPN
ejpam-3449	670	12	ameen	ameen	PROPN
ejpam-3449	670	13	,	,	PUNCT
ejpam-3449	670	14	some	some	DET
ejpam-3449	670	15	properties	property	NOUN
ejpam-3449	670	16	of	of	ADP
ejpam-3449	670	17	an	an	DET
ejpam-3449	670	18	operation	operation	NOUN
ejpam-3449	670	19	on	on	ADP
ejpam-3449	670	20	gα	gα	NOUN
ejpam-3449	670	21	-	-	PUNCT
ejpam-3449	670	22	open	open	ADJ
ejpam-3449	670	23	sets	set	NOUN
ejpam-3449	670	24	,	,	PUNCT
ejpam-3449	670	25	new	new	ADJ
ejpam-3449	670	26	trends	trend	NOUN
ejpam-3449	670	27	in	in	ADP
ejpam-3449	670	28	mathematical	mathematical	ADJ
ejpam-3449	670	29	sciences	science	NOUN
ejpam-3449	670	30	,	,	PUNCT
ejpam-3449	670	31	7	7	NUM
ejpam-3449	670	32	2	2	NUM
ejpam-3449	670	33	(	(	PUNCT
ejpam-3449	670	34	2019	2019	NUM
ejpam-3449	670	35	)	)	PUNCT
ejpam-3449	670	36	,	,	PUNCT
ejpam-3449	670	37	150	150	NUM
ejpam-3449	670	38	-	-	SYM
ejpam-3449	670	39	158	158	NUM
ejpam-3449	670	40	.	.	PUNCT
ejpam-3449	671	1	[	[	X
ejpam-3449	671	2	9	9	NUM
ejpam-3449	671	3	]	]	PUNCT
ejpam-3449	671	4	t.	t.	PROPN
ejpam-3449	671	5	husain	husain	PROPN
ejpam-3449	671	6	,	,	PUNCT
ejpam-3449	671	7	topology	topology	NOUN
ejpam-3449	671	8	and	and	CCONJ
ejpam-3449	671	9	maps	map	NOUN
ejpam-3449	671	10	,	,	PUNCT
ejpam-3449	671	11	plenum	plenum	PROPN
ejpam-3449	671	12	press	press	PROPN
ejpam-3449	671	13	,	,	PUNCT
ejpam-3449	671	14	new	new	PROPN
ejpam-3449	671	15	york	york	PROPN
ejpam-3449	671	16	,	,	PUNCT
ejpam-3449	671	17	(	(	PUNCT
ejpam-3449	671	18	1977	1977	NUM
ejpam-3449	671	19	)	)	PUNCT
ejpam-3449	671	20	.	.	PUNCT
ejpam-3449	672	1	[	[	X
ejpam-3449	672	2	10	10	NUM
ejpam-3449	672	3	]	]	X
ejpam-3449	672	4	d.	d.	PROPN
ejpam-3449	672	5	s.	s.	PROPN
ejpam-3449	672	6	jankovic	jankovic	PROPN
ejpam-3449	672	7	,	,	PUNCT
ejpam-3449	672	8	on	on	ADP
ejpam-3449	672	9	functions	function	NOUN
ejpam-3449	672	10	with	with	ADP
ejpam-3449	672	11	α	α	NOUN
ejpam-3449	672	12	-	-	PUNCT
ejpam-3449	672	13	closed	closed	ADJ
ejpam-3449	672	14	graphs	graph	NOUN
ejpam-3449	672	15	,	,	PUNCT
ejpam-3449	672	16	glasnik	glasnik	PROPN
ejpam-3449	672	17	matematicki	matematicki	PROPN
ejpam-3449	672	18	,	,	PUNCT
ejpam-3449	672	19	18	18	NUM
ejpam-3449	672	20	38	38	NUM
ejpam-3449	672	21	(	(	PUNCT
ejpam-3449	672	22	1983	1983	NUM
ejpam-3449	672	23	)	)	PUNCT
ejpam-3449	672	24	,	,	PUNCT
ejpam-3449	672	25	141	141	NUM
ejpam-3449	672	26	-	-	SYM
ejpam-3449	672	27	148	148	NUM
ejpam-3449	672	28	.	.	PUNCT
ejpam-3449	673	1	[	[	X
ejpam-3449	673	2	11	11	NUM
ejpam-3449	673	3	]	]	PUNCT
ejpam-3449	673	4	s.	s.	PROPN
ejpam-3449	673	5	kasahara	kasahara	PROPN
ejpam-3449	673	6	,	,	PUNCT
ejpam-3449	673	7	operation	operation	NOUN
ejpam-3449	673	8	compact	compact	ADJ
ejpam-3449	673	9	spaces	space	NOUN
ejpam-3449	673	10	,	,	PUNCT
ejpam-3449	673	11	math	math	NOUN
ejpam-3449	673	12	.	.	PUNCT
ejpam-3449	674	1	japonica	japonica	PROPN
ejpam-3449	674	2	,	,	PUNCT
ejpam-3449	674	3	24	24	NUM
ejpam-3449	674	4	1	1	NUM
ejpam-3449	674	5	(	(	PUNCT
ejpam-3449	674	6	1979	1979	NUM
ejpam-3449	674	7	)	)	PUNCT
ejpam-3449	674	8	,	,	PUNCT
ejpam-3449	674	9	97	97	NUM
ejpam-3449	674	10	-	-	SYM
ejpam-3449	674	11	105	105	NUM
ejpam-3449	674	12	.	.	PUNCT
ejpam-3449	675	1	[	[	X
ejpam-3449	675	2	12	12	NUM
ejpam-3449	675	3	]	]	PUNCT
ejpam-3449	675	4	h.	h.	PROPN
ejpam-3449	675	5	ogata	ogata	PROPN
ejpam-3449	675	6	,	,	PUNCT
ejpam-3449	675	7	operation	operation	NOUN
ejpam-3449	675	8	on	on	ADP
ejpam-3449	675	9	topological	topological	ADJ
ejpam-3449	675	10	spaces	space	NOUN
ejpam-3449	675	11	and	and	CCONJ
ejpam-3449	675	12	associated	associate	VERB
ejpam-3449	675	13	topology	topology	NOUN
ejpam-3449	675	14	,	,	PUNCT
ejpam-3449	675	15	math	math	NOUN
ejpam-3449	675	16	.	.	PUNCT
ejpam-3449	676	1	japonica	japonica	PROPN
ejpam-3449	676	2	,	,	PUNCT
ejpam-3449	676	3	36	36	NUM
ejpam-3449	676	4	1	1	NUM
ejpam-3449	676	5	(	(	PUNCT
ejpam-3449	676	6	1991	1991	NUM
ejpam-3449	676	7	)	)	PUNCT
ejpam-3449	676	8	,	,	PUNCT
ejpam-3449	676	9	175	175	NUM
ejpam-3449	676	10	-	-	SYM
ejpam-3449	676	11	184	184	NUM
ejpam-3449	676	12	.	.	PUNCT
ejpam-3449	677	1	[	[	X
ejpam-3449	677	2	13	13	NUM
ejpam-3449	677	3	]	]	X
ejpam-3449	677	4	p.l	p.l	PROPN
ejpam-3449	677	5	.	.	PROPN
ejpam-3449	677	6	powar	powar	PROPN
ejpam-3449	677	7	and	and	CCONJ
ejpam-3449	677	8	k.	k.	PROPN
ejpam-3449	677	9	rajak	rajak	PROPN
ejpam-3449	677	10	,	,	PUNCT
ejpam-3449	677	11	fine	fine	ADJ
ejpam-3449	677	12	-	-	PUNCT
ejpam-3449	677	13	irresolute	irresolute	ADJ
ejpam-3449	677	14	mappings	mapping	NOUN
ejpam-3449	677	15	,	,	PUNCT
ejpam-3449	677	16	journal	journal	NOUN
ejpam-3449	677	17	of	of	ADP
ejpam-3449	677	18	advanced	advanced	ADJ
ejpam-3449	677	19	studies	study	NOUN
ejpam-3449	677	20	in	in	ADP
ejpam-3449	677	21	topology	topology	NOUN
ejpam-3449	677	22	,	,	PUNCT
ejpam-3449	677	23	3	3	NUM
ejpam-3449	677	24	4	4	NUM
ejpam-3449	677	25	(	(	PUNCT
ejpam-3449	677	26	2012	2012	NUM
ejpam-3449	677	27	)	)	PUNCT
ejpam-3449	677	28	,	,	PUNCT
ejpam-3449	677	29	125	125	NUM
ejpam-3449	677	30	-	-	SYM
ejpam-3449	677	31	139	139	NUM
ejpam-3449	677	32	.	.	PUNCT