id	sid	tid	token	lemma	pos
ejpam-865	1	1	4_865_beceren.dvi	4_865_beceren.dvi	NUM
ejpam-865	1	2	european	european	PROPN
ejpam-865	1	3	journal	journal	PROPN
ejpam-865	1	4	of	of	ADP
ejpam-865	1	5	pure	pure	ADJ
ejpam-865	1	6	and	and	CCONJ
ejpam-865	1	7	applied	apply	VERB
ejpam-865	1	8	mathematics	mathematic	NOUN
ejpam-865	1	9	vol	vol	NOUN
ejpam-865	1	10	.	.	PROPN
ejpam-865	1	11	4	4	NUM
ejpam-865	1	12	,	,	PUNCT
ejpam-865	1	13	no	no	INTJ
ejpam-865	1	14	.	.	NOUN
ejpam-865	1	15	4	4	NUM
ejpam-865	1	16	,	,	PUNCT
ejpam-865	1	17	2011	2011	NUM
ejpam-865	1	18	,	,	PUNCT
ejpam-865	1	19	361	361	NUM
ejpam-865	1	20	-	-	SYM
ejpam-865	1	21	369	369	NUM
ejpam-865	1	22	issn	issn	PROPN
ejpam-865	1	23	1307	1307	NUM
ejpam-865	1	24	-	-	SYM
ejpam-865	1	25	5543	5543	NUM
ejpam-865	1	26	–	–	PUNCT
ejpam-865	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-865	1	28	on	on	ADP
ejpam-865	1	29	δα	δα	ADP
ejpam-865	1	30	,	,	PUNCT
ejpam-865	1	31	δp	δp	ADP
ejpam-865	1	32	and	and	CCONJ
ejpam-865	1	33	δs	δs	NOUN
ejpam-865	1	34	-	-	PUNCT
ejpam-865	1	35	irresolute	irresolute	ADJ
ejpam-865	1	36	functions	function	NOUN
ejpam-865	1	37	yusuf	yusuf	PROPN
ejpam-865	1	38	beceren1,∗	beceren1,∗	PROPN
ejpam-865	1	39	,	,	PUNCT
ejpam-865	1	40	takashi	takashi	PROPN
ejpam-865	1	41	noiri	noiri	PROPN
ejpam-865	1	42	2	2	NUM
ejpam-865	1	43	1	1	NUM
ejpam-865	1	44	department	department	NOUN
ejpam-865	1	45	of	of	ADP
ejpam-865	1	46	mathematics	mathematic	NOUN
ejpam-865	1	47	,	,	PUNCT
ejpam-865	1	48	faculty	faculty	NOUN
ejpam-865	1	49	of	of	ADP
ejpam-865	1	50	sciences	science	NOUN
ejpam-865	1	51	,	,	PUNCT
ejpam-865	1	52	selçuk	selçuk	PROPN
ejpam-865	1	53	university	university	PROPN
ejpam-865	1	54	,	,	PUNCT
ejpam-865	1	55	kampus	kampus	PROPN
ejpam-865	1	56	,	,	PUNCT
ejpam-865	1	57	konya	konya	PROPN
ejpam-865	1	58	42031	42031	NUM
ejpam-865	1	59	,	,	PUNCT
ejpam-865	1	60	turkey	turkey	PROPN
ejpam-865	1	61	.	.	PUNCT
ejpam-865	2	1	2	2	NUM
ejpam-865	2	2	department	department	NOUN
ejpam-865	2	3	of	of	ADP
ejpam-865	2	4	mathematics	mathematic	NOUN
ejpam-865	2	5	,	,	PUNCT
ejpam-865	2	6	yatsushiro	yatsushiro	PROPN
ejpam-865	2	7	college	college	PROPN
ejpam-865	2	8	of	of	ADP
ejpam-865	2	9	technology	technology	NOUN
ejpam-865	2	10	,	,	PUNCT
ejpam-865	2	11	yatsushiro	yatsushiro	PROPN
ejpam-865	2	12	,	,	PUNCT
ejpam-865	2	13	kumamoto	kumamoto	PROPN
ejpam-865	2	14	,	,	PUNCT
ejpam-865	2	15	866	866	NUM
ejpam-865	2	16	-	-	PUNCT
ejpam-865	2	17	8501	8501	NUM
ejpam-865	2	18	,	,	PUNCT
ejpam-865	2	19	japan	japan	PROPN
ejpam-865	2	20	.	.	PUNCT
ejpam-865	3	1	abstract	abstract	PROPN
ejpam-865	3	2	.	.	PUNCT
ejpam-865	4	1	in	in	ADP
ejpam-865	4	2	this	this	DET
ejpam-865	4	3	paper	paper	NOUN
ejpam-865	4	4	is	be	AUX
ejpam-865	4	5	to	to	PART
ejpam-865	4	6	introduce	introduce	VERB
ejpam-865	4	7	and	and	CCONJ
ejpam-865	4	8	investigate	investigate	VERB
ejpam-865	4	9	new	new	ADJ
ejpam-865	4	10	classes	class	NOUN
ejpam-865	4	11	of	of	ADP
ejpam-865	4	12	various	various	ADJ
ejpam-865	4	13	irresolute	irresolute	ADJ
ejpam-865	4	14	functions	function	NOUN
ejpam-865	4	15	and	and	CCONJ
ejpam-865	4	16	obtain	obtain	VERB
ejpam-865	4	17	some	some	PRON
ejpam-865	4	18	of	of	ADP
ejpam-865	4	19	their	their	PRON
ejpam-865	4	20	properties	property	NOUN
ejpam-865	4	21	in	in	ADP
ejpam-865	4	22	topological	topological	ADJ
ejpam-865	4	23	spaces	space	NOUN
ejpam-865	4	24	.	.	PUNCT
ejpam-865	5	1	2000	2000	NUM
ejpam-865	5	2	mathematics	mathematic	NOUN
ejpam-865	5	3	subject	subject	NOUN
ejpam-865	5	4	classifications	classification	NOUN
ejpam-865	5	5	:	:	PUNCT
ejpam-865	5	6	54c10	54c10	NUM
ejpam-865	5	7	,	,	PUNCT
ejpam-865	5	8	54c08	54c08	NUM
ejpam-865	5	9	,	,	PUNCT
ejpam-865	5	10	54a05	54a05	NUM
ejpam-865	5	11	.	.	PUNCT
ejpam-865	6	1	key	key	ADJ
ejpam-865	6	2	words	word	NOUN
ejpam-865	6	3	and	and	CCONJ
ejpam-865	6	4	phrases	phrase	NOUN
ejpam-865	6	5	:	:	PUNCT
ejpam-865	6	6	α	α	X
ejpam-865	6	7	-	-	ADJ
ejpam-865	6	8	open	open	ADJ
ejpam-865	6	9	set	set	NOUN
ejpam-865	6	10	,	,	PUNCT
ejpam-865	6	11	preopen	preopen	ADJ
ejpam-865	6	12	set	set	NOUN
ejpam-865	6	13	,	,	PUNCT
ejpam-865	6	14	semi	semi	ADJ
ejpam-865	6	15	-	-	ADJ
ejpam-865	6	16	open	open	ADJ
ejpam-865	6	17	set	set	NOUN
ejpam-865	6	18	,	,	PUNCT
ejpam-865	6	19	δα	δα	NOUN
ejpam-865	6	20	-	-	PUNCT
ejpam-865	6	21	irresolute	irresolute	ADJ
ejpam-865	6	22	function	function	NOUN
ejpam-865	6	23	,	,	PUNCT
ejpam-865	6	24	δp	δp	NOUN
ejpam-865	6	25	-	-	PUNCT
ejpam-865	6	26	irresolute	irresolute	ADJ
ejpam-865	6	27	function	function	NOUN
ejpam-865	6	28	,	,	PUNCT
ejpam-865	6	29	δs	δs	NOUN
ejpam-865	6	30	-	-	PUNCT
ejpam-865	6	31	irresolute	irresolute	ADJ
ejpam-865	6	32	function	function	NOUN
ejpam-865	6	33	.	.	PUNCT
ejpam-865	7	1	1	1	X
ejpam-865	7	2	.	.	X
ejpam-865	7	3	introduction	introduction	NOUN
ejpam-865	7	4	recall	recall	VERB
ejpam-865	7	5	the	the	DET
ejpam-865	7	6	concepts	concept	NOUN
ejpam-865	7	7	of	of	ADP
ejpam-865	7	8	α	α	NOUN
ejpam-865	7	9	-	-	ADJ
ejpam-865	7	10	open	open	ADJ
ejpam-865	7	11	[	[	X
ejpam-865	7	12	26	26	NUM
ejpam-865	7	13	]	]	PUNCT
ejpam-865	7	14	(	(	PUNCT
ejpam-865	7	15	resp	resp	NOUN
ejpam-865	7	16	.	.	PUNCT
ejpam-865	8	1	semi	semi	ADJ
ejpam-865	8	2	-	-	ADJ
ejpam-865	8	3	open	open	ADJ
ejpam-865	8	4	[	[	X
ejpam-865	8	5	15	15	NUM
ejpam-865	8	6	]	]	PUNCT
ejpam-865	8	7	,	,	PUNCT
ejpam-865	8	8	preopen	preopen	ADJ
ejpam-865	8	9	[	[	X
ejpam-865	8	10	18	18	NUM
ejpam-865	8	11	]	]	PUNCT
ejpam-865	8	12	,	,	PUNCT
ejpam-865	8	13	β	β	X
ejpam-865	8	14	-open	-open	NOUN
ejpam-865	9	1	[	[	X
ejpam-865	9	2	11	11	NUM
ejpam-865	9	3	]	]	SYM
ejpam-865	9	4	)	)	PUNCT
ejpam-865	9	5	sets	set	NOUN
ejpam-865	9	6	and	and	CCONJ
ejpam-865	9	7	semi	semi	ADV
ejpam-865	9	8	α	α	NOUN
ejpam-865	9	9	-	-	ADJ
ejpam-865	9	10	irresolute	irresolute	ADJ
ejpam-865	9	11	[	[	X
ejpam-865	9	12	2	2	NUM
ejpam-865	9	13	]	]	PUNCT
ejpam-865	9	14	(	(	PUNCT
ejpam-865	9	15	resp	resp	NOUN
ejpam-865	9	16	.	.	PUNCT
ejpam-865	10	1	semi	semi	ADV
ejpam-865	10	2	α	α	PROPN
ejpam-865	10	3	-	-	ADJ
ejpam-865	10	4	preirresolute	preirresolute	NOUN
ejpam-865	10	5	[	[	X
ejpam-865	10	6	3	3	NUM
ejpam-865	10	7	]	]	SYM
ejpam-865	10	8	)	)	PUNCT
ejpam-865	10	9	functions	function	NOUN
ejpam-865	10	10	in	in	ADP
ejpam-865	10	11	topological	topological	ADJ
ejpam-865	10	12	spaces	space	NOUN
ejpam-865	10	13	.	.	PUNCT
ejpam-865	11	1	the	the	DET
ejpam-865	11	2	main	main	ADJ
ejpam-865	11	3	purpose	purpose	NOUN
ejpam-865	11	4	of	of	ADP
ejpam-865	11	5	this	this	DET
ejpam-865	11	6	paper	paper	NOUN
ejpam-865	11	7	is	be	AUX
ejpam-865	11	8	to	to	PART
ejpam-865	11	9	define	define	VERB
ejpam-865	11	10	and	and	CCONJ
ejpam-865	11	11	study	study	VERB
ejpam-865	11	12	the	the	DET
ejpam-865	11	13	notions	notion	NOUN
ejpam-865	11	14	of	of	ADP
ejpam-865	11	15	new	new	ADJ
ejpam-865	11	16	classes	class	NOUN
ejpam-865	11	17	of	of	ADP
ejpam-865	11	18	functions	function	NOUN
ejpam-865	11	19	,	,	PUNCT
ejpam-865	11	20	namely	namely	ADV
ejpam-865	11	21	δα	δα	NOUN
ejpam-865	11	22	-	-	PUNCT
ejpam-865	11	23	irresolute	irresolute	ADJ
ejpam-865	11	24	,	,	PUNCT
ejpam-865	11	25	δp	δp	PRON
ejpam-865	11	26	-	-	PUNCT
ejpam-865	11	27	irresolute	irresolute	ADJ
ejpam-865	11	28	and	and	CCONJ
ejpam-865	11	29	δs	δs	NOUN
ejpam-865	11	30	-	-	PUNCT
ejpam-865	11	31	irresolute	irresolute	ADJ
ejpam-865	11	32	functions	function	NOUN
ejpam-865	11	33	,	,	PUNCT
ejpam-865	11	34	and	and	CCONJ
ejpam-865	11	35	to	to	PART
ejpam-865	11	36	give	give	VERB
ejpam-865	11	37	some	some	DET
ejpam-865	11	38	properties	property	NOUN
ejpam-865	11	39	of	of	ADP
ejpam-865	11	40	these	these	DET
ejpam-865	11	41	functions	function	NOUN
ejpam-865	11	42	in	in	ADP
ejpam-865	11	43	topological	topological	ADJ
ejpam-865	11	44	spaces	space	NOUN
ejpam-865	11	45	.	.	PUNCT
ejpam-865	12	1	2	2	X
ejpam-865	12	2	.	.	NUM
ejpam-865	12	3	preliminaries	preliminary	NOUN
ejpam-865	12	4	throughout	throughout	ADP
ejpam-865	12	5	this	this	DET
ejpam-865	12	6	paper	paper	NOUN
ejpam-865	12	7	,	,	PUNCT
ejpam-865	12	8	spaces	space	NOUN
ejpam-865	12	9	always	always	ADV
ejpam-865	12	10	mean	mean	VERB
ejpam-865	12	11	topological	topological	ADJ
ejpam-865	12	12	spaces	space	NOUN
ejpam-865	12	13	and	and	CCONJ
ejpam-865	12	14	f	f	NOUN
ejpam-865	12	15	:	:	PUNCT
ejpam-865	12	16	x	x	X
ejpam-865	12	17	→	→	SYM
ejpam-865	12	18	y	y	PROPN
ejpam-865	12	19	denotes	denote	VERB
ejpam-865	12	20	a	a	DET
ejpam-865	12	21	single	single	ADJ
ejpam-865	12	22	valued	value	VERB
ejpam-865	12	23	function	function	NOUN
ejpam-865	12	24	of	of	ADP
ejpam-865	12	25	a	a	DET
ejpam-865	12	26	space	space	NOUN
ejpam-865	12	27	(	(	PUNCT
ejpam-865	12	28	x	x	X
ejpam-865	12	29	,	,	PUNCT
ejpam-865	12	30	τ	τ	PROPN
ejpam-865	12	31	)	)	PUNCT
ejpam-865	12	32	into	into	ADP
ejpam-865	12	33	a	a	DET
ejpam-865	12	34	space	space	NOUN
ejpam-865	12	35	(	(	PUNCT
ejpam-865	12	36	y	y	PROPN
ejpam-865	12	37	,	,	PUNCT
ejpam-865	12	38	σ	σ	PROPN
ejpam-865	12	39	)	)	PUNCT
ejpam-865	12	40	.	.	PUNCT
ejpam-865	13	1	let	let	VERB
ejpam-865	13	2	s	s	PRON
ejpam-865	13	3	be	be	AUX
ejpam-865	13	4	a	a	DET
ejpam-865	13	5	subset	subset	NOUN
ejpam-865	13	6	of	of	ADP
ejpam-865	13	7	a	a	DET
ejpam-865	13	8	space	space	NOUN
ejpam-865	13	9	(	(	PUNCT
ejpam-865	13	10	x	x	X
ejpam-865	13	11	,	,	PUNCT
ejpam-865	13	12	τ	τ	PROPN
ejpam-865	13	13	)	)	PUNCT
ejpam-865	13	14	.	.	PUNCT
ejpam-865	14	1	the	the	DET
ejpam-865	14	2	closure	closure	NOUN
ejpam-865	14	3	and	and	CCONJ
ejpam-865	14	4	the	the	DET
ejpam-865	14	5	interior	interior	NOUN
ejpam-865	14	6	of	of	ADP
ejpam-865	14	7	s	s	NOUN
ejpam-865	14	8	are	be	AUX
ejpam-865	14	9	denoted	denote	VERB
ejpam-865	14	10	by	by	ADP
ejpam-865	14	11	cl(s	cl(	NOUN
ejpam-865	14	12	)	)	PUNCT
ejpam-865	14	13	and	and	CCONJ
ejpam-865	14	14	int(s	int(s	PROPN
ejpam-865	14	15	)	)	PUNCT
ejpam-865	14	16	,	,	PUNCT
ejpam-865	14	17	respectively	respectively	ADV
ejpam-865	14	18	.	.	PUNCT
ejpam-865	15	1	here	here	ADV
ejpam-865	15	2	we	we	PRON
ejpam-865	15	3	recall	recall	VERB
ejpam-865	15	4	the	the	DET
ejpam-865	15	5	following	follow	VERB
ejpam-865	15	6	known	know	VERB
ejpam-865	15	7	definitions	definition	NOUN
ejpam-865	15	8	and	and	CCONJ
ejpam-865	15	9	properties	property	NOUN
ejpam-865	15	10	.	.	PUNCT
ejpam-865	16	1	definition	definition	NOUN
ejpam-865	16	2	1	1	NUM
ejpam-865	16	3	.	.	PUNCT
ejpam-865	17	1	a	a	DET
ejpam-865	17	2	subset	subset	NOUN
ejpam-865	17	3	s	s	NOUN
ejpam-865	17	4	of	of	ADP
ejpam-865	17	5	a	a	DET
ejpam-865	17	6	space	space	NOUN
ejpam-865	17	7	(	(	PUNCT
ejpam-865	17	8	x	x	X
ejpam-865	17	9	,	,	PUNCT
ejpam-865	17	10	τ	τ	X
ejpam-865	17	11	)	)	PUNCT
ejpam-865	17	12	is	be	AUX
ejpam-865	17	13	said	say	VERB
ejpam-865	17	14	to	to	PART
ejpam-865	17	15	be	be	AUX
ejpam-865	17	16	α	α	X
ejpam-865	17	17	-	-	ADJ
ejpam-865	17	18	open	open	ADJ
ejpam-865	17	19	[	[	X
ejpam-865	17	20	26	26	NUM
ejpam-865	17	21	]	]	PUNCT
ejpam-865	17	22	(	(	PUNCT
ejpam-865	17	23	resp	resp	NOUN
ejpam-865	17	24	.	.	PUNCT
ejpam-865	18	1	semi	semi	ADJ
ejpam-865	18	2	-	-	ADJ
ejpam-865	18	3	open	open	ADJ
ejpam-865	18	4	[	[	X
ejpam-865	18	5	15	15	NUM
ejpam-865	18	6	]	]	PUNCT
ejpam-865	18	7	,	,	PUNCT
ejpam-865	18	8	preopen	preopen	ADJ
ejpam-865	18	9	[	[	X
ejpam-865	18	10	18	18	NUM
ejpam-865	18	11	]	]	PUNCT
ejpam-865	18	12	,	,	PUNCT
ejpam-865	18	13	β	β	X
ejpam-865	18	14	-open	-open	NOUN
ejpam-865	19	1	[	[	X
ejpam-865	19	2	11	11	NUM
ejpam-865	19	3	]	]	SYM
ejpam-865	19	4	)	)	PUNCT
ejpam-865	19	5	if	if	SCONJ
ejpam-865	19	6	s	s	VERB
ejpam-865	19	7	⊂	⊂	X
ejpam-865	19	8	int(cl(int(s	int(cl(int(s	PROPN
ejpam-865	19	9	)	)	PUNCT
ejpam-865	19	10	)	)	PUNCT
ejpam-865	19	11	)	)	PUNCT
ejpam-865	20	1	(	(	PUNCT
ejpam-865	20	2	resp	resp	NOUN
ejpam-865	20	3	.	.	PUNCT
ejpam-865	21	1	s	s	PART
ejpam-865	21	2	⊂	⊂	PROPN
ejpam-865	21	3	cl(int(s	cl(int(s	PROPN
ejpam-865	21	4	)	)	PUNCT
ejpam-865	21	5	)	)	PUNCT
ejpam-865	22	1	,	,	PUNCT
ejpam-865	22	2	s	s	PROPN
ejpam-865	22	3	⊂	⊂	PROPN
ejpam-865	22	4	int(cl(s	int(cl(s	PROPN
ejpam-865	22	5	)	)	PUNCT
ejpam-865	22	6	)	)	PUNCT
ejpam-865	22	7	,	,	PUNCT
ejpam-865	22	8	s	s	PROPN
ejpam-865	22	9	⊂	⊂	PROPN
ejpam-865	22	10	cl(int(cl(s	cl(int(cl(s	PROPN
ejpam-865	22	11	)	)	PUNCT
ejpam-865	22	12	)	)	PUNCT
ejpam-865	22	13	)	)	PUNCT
ejpam-865	22	14	)	)	PUNCT
ejpam-865	22	15	.	.	PUNCT
ejpam-865	23	1	∗corresponding	∗corresponde	VERB
ejpam-865	23	2	author	author	NOUN
ejpam-865	23	3	.	.	PUNCT
ejpam-865	24	1	email	email	NOUN
ejpam-865	24	2	addresses	address	NOUN
ejpam-865	24	3	:	:	PUNCT
ejpam-865	24	4	ybe	ybe	PROPN
ejpam-865	24	5	eren	eren	PROPN
ejpam-865	24	6	�	�	PROPN
ejpam-865	24	7	sel	sel	PROPN
ejpam-865	24	8	uk.edu.tr	uk.edu.tr	PROPN
ejpam-865	24	9	(	(	PUNCT
ejpam-865	24	10	y.	y.	PROPN
ejpam-865	24	11	beceren	beceren	PROPN
ejpam-865	24	12	)	)	PUNCT
ejpam-865	24	13	,	,	PUNCT
ejpam-865	24	14	t.noiri	t.noiri	ADV
ejpam-865	24	15	�	�	NOUN
ejpam-865	24	16	nifty	nifty	ADJ
ejpam-865	24	17	.	.	PUNCT
ejpam-865	25	1	om	om	PROPN
ejpam-865	25	2	(	(	PUNCT
ejpam-865	25	3	t.	t.	PROPN
ejpam-865	25	4	noiri	noiri	PROPN
ejpam-865	25	5	)	)	PUNCT
ejpam-865	25	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-865	26	1	361	361	NUM
ejpam-865	26	2	c	c	X
ejpam-865	26	3	©	©	PROPN
ejpam-865	26	4	2011	2011	NUM
ejpam-865	26	5	ejpam	ejpam	VERB
ejpam-865	26	6	all	all	DET
ejpam-865	26	7	rights	right	NOUN
ejpam-865	26	8	reserved	reserve	VERB
ejpam-865	26	9	.	.	PUNCT
ejpam-865	27	1	y.	y.	PROPN
ejpam-865	27	2	beceren	beceren	PROPN
ejpam-865	27	3	,	,	PUNCT
ejpam-865	27	4	t.	t.	PROPN
ejpam-865	27	5	noiri	noiri	PROPN
ejpam-865	27	6	/	/	SYM
ejpam-865	27	7	eur	eur	PROPN
ejpam-865	27	8	.	.	PUNCT
ejpam-865	28	1	j.	j.	PROPN
ejpam-865	28	2	pure	pure	PROPN
ejpam-865	28	3	appl	appl	PROPN
ejpam-865	28	4	.	.	PROPN
ejpam-865	28	5	math	math	PROPN
ejpam-865	28	6	,	,	PUNCT
ejpam-865	28	7	4	4	NUM
ejpam-865	28	8	(	(	PUNCT
ejpam-865	28	9	2011	2011	NUM
ejpam-865	28	10	)	)	PUNCT
ejpam-865	28	11	,	,	PUNCT
ejpam-865	28	12	361	361	NUM
ejpam-865	28	13	-	-	SYM
ejpam-865	28	14	369	369	NUM
ejpam-865	28	15	362	362	NUM
ejpam-865	28	16	a	a	DET
ejpam-865	28	17	point	point	NOUN
ejpam-865	28	18	x	x	X
ejpam-865	28	19	∈	∈	NOUN
ejpam-865	28	20	x	x	PUNCT
ejpam-865	28	21	is	be	AUX
ejpam-865	28	22	called	call	VERB
ejpam-865	28	23	the	the	DET
ejpam-865	28	24	δ	δ	NOUN
ejpam-865	28	25	-	-	PUNCT
ejpam-865	28	26	cluster	cluster	NOUN
ejpam-865	28	27	point	point	NOUN
ejpam-865	28	28	of	of	ADP
ejpam-865	28	29	a	a	PRON
ejpam-865	28	30	if	if	SCONJ
ejpam-865	28	31	a∩	a∩	PROPN
ejpam-865	28	32	int(cl(u	int(cl(u	PROPN
ejpam-865	28	33	)	)	PUNCT
ejpam-865	28	34	)	)	PUNCT
ejpam-865	29	1	6=	6=	ADP
ejpam-865	29	2	∅	∅	NOUN
ejpam-865	29	3	for	for	ADP
ejpam-865	29	4	every	every	DET
ejpam-865	29	5	open	open	ADJ
ejpam-865	29	6	set	set	NOUN
ejpam-865	29	7	u	u	NOUN
ejpam-865	29	8	of	of	ADP
ejpam-865	29	9	x	x	SYM
ejpam-865	29	10	containing	contain	VERB
ejpam-865	29	11	x	x	PUNCT
ejpam-865	29	12	.	.	PUNCT
ejpam-865	30	1	the	the	DET
ejpam-865	30	2	set	set	NOUN
ejpam-865	30	3	of	of	ADP
ejpam-865	30	4	all	all	DET
ejpam-865	30	5	δ	δ	NOUN
ejpam-865	30	6	-	-	PUNCT
ejpam-865	30	7	cluster	cluster	NOUN
ejpam-865	30	8	points	point	NOUN
ejpam-865	30	9	of	of	ADP
ejpam-865	30	10	a	a	PRON
ejpam-865	30	11	is	be	AUX
ejpam-865	30	12	called	call	VERB
ejpam-865	30	13	the	the	DET
ejpam-865	30	14	δ	δ	NOUN
ejpam-865	30	15	-	-	PUNCT
ejpam-865	30	16	cluster	cluster	NOUN
ejpam-865	30	17	of	of	ADP
ejpam-865	30	18	a	a	PRON
ejpam-865	30	19	,	,	PUNCT
ejpam-865	30	20	denoted	denote	VERB
ejpam-865	30	21	by	by	ADP
ejpam-865	30	22	clδ(a	clδ(a	NOUN
ejpam-865	30	23	)	)	PUNCT
ejpam-865	30	24	.	.	PUNCT
ejpam-865	31	1	a	a	DET
ejpam-865	31	2	subset	subset	NOUN
ejpam-865	31	3	a	a	PRON
ejpam-865	31	4	of	of	ADP
ejpam-865	31	5	x	x	PRON
ejpam-865	31	6	is	be	AUX
ejpam-865	31	7	called	call	VERB
ejpam-865	31	8	δ	δ	PROPN
ejpam-865	31	9	-	-	PUNCT
ejpam-865	31	10	closed	closed	ADJ
ejpam-865	31	11	[	[	X
ejpam-865	31	12	27	27	NUM
ejpam-865	31	13	]	]	X
ejpam-865	31	14	if	if	SCONJ
ejpam-865	31	15	a=	a=	ADV
ejpam-865	31	16	clδ(a	clδ(a	NOUN
ejpam-865	31	17	)	)	PUNCT
ejpam-865	31	18	.	.	PUNCT
ejpam-865	32	1	the	the	DET
ejpam-865	32	2	complement	complement	NOUN
ejpam-865	32	3	of	of	ADP
ejpam-865	32	4	a	a	DET
ejpam-865	32	5	δ	δ	NOUN
ejpam-865	32	6	-	-	PUNCT
ejpam-865	32	7	closed	close	VERB
ejpam-865	32	8	set	set	NOUN
ejpam-865	32	9	is	be	AUX
ejpam-865	32	10	called	call	VERB
ejpam-865	32	11	δ	δ	NOUN
ejpam-865	32	12	-	-	ADJ
ejpam-865	32	13	open	open	ADJ
ejpam-865	32	14	[	[	X
ejpam-865	32	15	27	27	NUM
ejpam-865	32	16	]	]	PUNCT
ejpam-865	32	17	.	.	PUNCT
ejpam-865	33	1	a	a	DET
ejpam-865	33	2	subset	subset	NOUN
ejpam-865	33	3	a	a	PRON
ejpam-865	33	4	of	of	ADP
ejpam-865	33	5	x	x	SYM
ejpam-865	33	6	is	be	AUX
ejpam-865	33	7	said	say	VERB
ejpam-865	33	8	to	to	PART
ejpam-865	33	9	be	be	AUX
ejpam-865	33	10	a	a	DET
ejpam-865	33	11	δ	δ	NOUN
ejpam-865	33	12	-	-	PUNCT
ejpam-865	33	13	semiopen	semiopen	ADJ
ejpam-865	34	1	[	[	X
ejpam-865	34	2	23	23	NUM
ejpam-865	34	3	]	]	PUNCT
ejpam-865	34	4	if	if	SCONJ
ejpam-865	34	5	there	there	PRON
ejpam-865	34	6	exists	exist	VERB
ejpam-865	34	7	a	a	DET
ejpam-865	34	8	δ	δ	NOUN
ejpam-865	34	9	-	-	ADJ
ejpam-865	34	10	open	open	ADJ
ejpam-865	34	11	set	set	VERB
ejpam-865	34	12	u	u	NOUN
ejpam-865	34	13	of	of	ADP
ejpam-865	34	14	x	x	SYM
ejpam-865	34	15	such	such	ADJ
ejpam-865	34	16	that	that	SCONJ
ejpam-865	34	17	u	u	PROPN
ejpam-865	34	18	⊂	⊂	PROPN
ejpam-865	34	19	a	a	DET
ejpam-865	34	20	⊂	⊂	PROPN
ejpam-865	34	21	cl(u	cl(u	PROPN
ejpam-865	34	22	)	)	PUNCT
ejpam-865	34	23	.	.	PUNCT
ejpam-865	35	1	the	the	DET
ejpam-865	35	2	complement	complement	NOUN
ejpam-865	35	3	of	of	ADP
ejpam-865	35	4	a	a	DET
ejpam-865	35	5	δ	δ	NOUN
ejpam-865	35	6	-	-	PUNCT
ejpam-865	35	7	semiopen	semiopen	ADJ
ejpam-865	35	8	set	set	NOUN
ejpam-865	35	9	is	be	AUX
ejpam-865	35	10	called	call	VERB
ejpam-865	35	11	δ	δ	NOUN
ejpam-865	35	12	-	-	PUNCT
ejpam-865	35	13	semiclosed	semiclose	VERB
ejpam-865	35	14	set	set	NOUN
ejpam-865	35	15	.	.	PUNCT
ejpam-865	36	1	a	a	DET
ejpam-865	36	2	point	point	NOUN
ejpam-865	36	3	x	x	X
ejpam-865	36	4	∈	∈	NOUN
ejpam-865	36	5	x	x	PUNCT
ejpam-865	36	6	is	be	AUX
ejpam-865	36	7	called	call	VERB
ejpam-865	36	8	the	the	DET
ejpam-865	36	9	δ	δ	NOUN
ejpam-865	36	10	-	-	PUNCT
ejpam-865	36	11	semicluster	semicluster	ADJ
ejpam-865	36	12	point	point	NOUN
ejpam-865	36	13	of	of	ADP
ejpam-865	36	14	a	a	PRON
ejpam-865	36	15	if	if	SCONJ
ejpam-865	36	16	a∩	a∩	PROPN
ejpam-865	36	17	u	u	PROPN
ejpam-865	36	18	6=	6=	NOUN
ejpam-865	36	19	∅	∅	NOUN
ejpam-865	36	20	for	for	ADP
ejpam-865	36	21	every	every	DET
ejpam-865	36	22	δ	δ	PROPN
ejpam-865	36	23	-	-	PUNCT
ejpam-865	36	24	semiopen	semiopen	VERB
ejpam-865	36	25	set	set	VERB
ejpam-865	36	26	u	u	NOUN
ejpam-865	36	27	of	of	ADP
ejpam-865	36	28	x	x	SYM
ejpam-865	36	29	containing	contain	VERB
ejpam-865	36	30	x	x	PUNCT
ejpam-865	36	31	.	.	PUNCT
ejpam-865	37	1	the	the	DET
ejpam-865	37	2	set	set	NOUN
ejpam-865	37	3	of	of	ADP
ejpam-865	37	4	all	all	DET
ejpam-865	37	5	δ	δ	NOUN
ejpam-865	37	6	-	-	PUNCT
ejpam-865	37	7	semicluster	semicluster	ADJ
ejpam-865	37	8	points	point	NOUN
ejpam-865	37	9	of	of	ADP
ejpam-865	37	10	a	a	PRON
ejpam-865	37	11	is	be	AUX
ejpam-865	37	12	called	call	VERB
ejpam-865	37	13	the	the	DET
ejpam-865	37	14	δ	δ	NOUN
ejpam-865	37	15	-	-	PUNCT
ejpam-865	37	16	semiclosure	semiclosure	NOUN
ejpam-865	37	17	[	[	X
ejpam-865	37	18	23	23	NUM
ejpam-865	37	19	]	]	PUNCT
ejpam-865	37	20	of	of	ADP
ejpam-865	37	21	a	a	PRON
ejpam-865	37	22	,	,	PUNCT
ejpam-865	37	23	denoted	denote	VERB
ejpam-865	37	24	by	by	ADP
ejpam-865	37	25	δcls(a	δcls(a	PROPN
ejpam-865	37	26	)	)	PUNCT
ejpam-865	37	27	.	.	PUNCT
ejpam-865	38	1	the	the	DET
ejpam-865	38	2	family	family	NOUN
ejpam-865	38	3	of	of	ADP
ejpam-865	38	4	all	all	DET
ejpam-865	38	5	α	α	NOUN
ejpam-865	38	6	-	-	ADJ
ejpam-865	38	7	open	open	ADJ
ejpam-865	38	8	(	(	PUNCT
ejpam-865	38	9	resp	resp	NOUN
ejpam-865	38	10	.	.	PUNCT
ejpam-865	39	1	semi	semi	ADJ
ejpam-865	39	2	-	-	ADJ
ejpam-865	39	3	open	open	ADJ
ejpam-865	39	4	,	,	PUNCT
ejpam-865	39	5	preopen	preopen	ADJ
ejpam-865	39	6	,	,	PUNCT
ejpam-865	39	7	β	β	X
ejpam-865	39	8	-open	-open	PROPN
ejpam-865	39	9	,	,	PUNCT
ejpam-865	39	10	δ	δ	NOUN
ejpam-865	39	11	-	-	ADJ
ejpam-865	39	12	open	open	ADJ
ejpam-865	39	13	,	,	PUNCT
ejpam-865	39	14	δ	δ	NOUN
ejpam-865	39	15	-	-	PUNCT
ejpam-865	39	16	semiopen	semiopen	ADJ
ejpam-865	39	17	)	)	PUNCT
ejpam-865	39	18	sets	set	NOUN
ejpam-865	39	19	in	in	ADP
ejpam-865	39	20	a	a	DET
ejpam-865	39	21	space	space	NOUN
ejpam-865	39	22	(	(	PUNCT
ejpam-865	39	23	x	x	X
ejpam-865	39	24	,	,	PUNCT
ejpam-865	39	25	τ	τ	X
ejpam-865	39	26	)	)	PUNCT
ejpam-865	39	27	is	be	AUX
ejpam-865	39	28	denoted	denote	VERB
ejpam-865	39	29	by	by	ADP
ejpam-865	39	30	τα	τα	NOUN
ejpam-865	39	31	=	=	SYM
ejpam-865	39	32	α(x	α(x	PROPN
ejpam-865	39	33	)	)	PUNCT
ejpam-865	39	34	(	(	PUNCT
ejpam-865	39	35	resp	resp	NOUN
ejpam-865	39	36	.	.	PUNCT
ejpam-865	39	37	so(x	so(x	PROPN
ejpam-865	39	38	)	)	PUNCT
ejpam-865	39	39	,	,	PUNCT
ejpam-865	39	40	po(x	po(x	NUM
ejpam-865	39	41	)	)	PUNCT
ejpam-865	39	42	,	,	PUNCT
ejpam-865	39	43	βo(x	βo(x	PUNCT
ejpam-865	39	44	)	)	PUNCT
ejpam-865	39	45	,	,	PUNCT
ejpam-865	39	46	δo(x	δo(x	NUM
ejpam-865	39	47	)	)	PUNCT
ejpam-865	39	48	,	,	PUNCT
ejpam-865	39	49	δso(x	δso(x	PROPN
ejpam-865	39	50	)	)	PUNCT
ejpam-865	39	51	)	)	PUNCT
ejpam-865	39	52	.	.	PUNCT
ejpam-865	40	1	it	it	PRON
ejpam-865	40	2	is	be	AUX
ejpam-865	40	3	shown	show	VERB
ejpam-865	40	4	in	in	ADP
ejpam-865	40	5	[	[	X
ejpam-865	40	6	26	26	NUM
ejpam-865	40	7	]	]	PUNCT
ejpam-865	40	8	that	that	PRON
ejpam-865	40	9	τα	τα	NOUN
ejpam-865	40	10	is	be	AUX
ejpam-865	40	11	a	a	DET
ejpam-865	40	12	topology	topology	NOUN
ejpam-865	40	13	for	for	ADP
ejpam-865	40	14	x	x	X
ejpam-865	40	15	.	.	PUNCT
ejpam-865	41	1	moreover	moreover	ADV
ejpam-865	41	2	,	,	PUNCT
ejpam-865	41	3	τ	τ	PROPN
ejpam-865	41	4	⊂	⊂	X
ejpam-865	41	5	τα	τα	X
ejpam-865	41	6	=	=	X
ejpam-865	41	7	po(x	po(x	NUM
ejpam-865	41	8	)	)	PUNCT
ejpam-865	41	9	∩	∩	NOUN
ejpam-865	41	10	so(x	so(x	NUM
ejpam-865	41	11	)	)	PUNCT
ejpam-865	42	1	⊂	⊂	PROPN
ejpam-865	42	2	βo(x	βo(x	PUNCT
ejpam-865	42	3	)	)	PUNCT
ejpam-865	42	4	.	.	PUNCT
ejpam-865	43	1	the	the	DET
ejpam-865	43	2	complement	complement	NOUN
ejpam-865	43	3	of	of	ADP
ejpam-865	43	4	an	an	DET
ejpam-865	43	5	α	α	NOUN
ejpam-865	43	6	-	-	ADJ
ejpam-865	43	7	open	open	ADJ
ejpam-865	43	8	(	(	PUNCT
ejpam-865	43	9	resp	resp	NOUN
ejpam-865	43	10	.	.	PUNCT
ejpam-865	44	1	preopen	preopen	ADJ
ejpam-865	44	2	,	,	PUNCT
ejpam-865	44	3	semi	semi	ADJ
ejpam-865	44	4	-	-	ADJ
ejpam-865	44	5	open	open	ADJ
ejpam-865	44	6	)	)	PUNCT
ejpam-865	44	7	set	set	NOUN
ejpam-865	44	8	is	be	AUX
ejpam-865	44	9	said	say	VERB
ejpam-865	44	10	to	to	PART
ejpam-865	44	11	be	be	AUX
ejpam-865	44	12	α	α	PRON
ejpam-865	44	13	-	-	ADJ
ejpam-865	44	14	closed	closed	ADJ
ejpam-865	44	15	[	[	X
ejpam-865	44	16	17	17	NUM
ejpam-865	44	17	]	]	PUNCT
ejpam-865	44	18	(	(	PUNCT
ejpam-865	44	19	resp	resp	NOUN
ejpam-865	44	20	.	.	PUNCT
ejpam-865	45	1	preclosed	preclose	VERB
ejpam-865	45	2	[	[	X
ejpam-865	45	3	18	18	NUM
ejpam-865	45	4	]	]	PUNCT
ejpam-865	45	5	,	,	PUNCT
ejpam-865	45	6	semi	semi	ADJ
ejpam-865	45	7	-	-	ADJ
ejpam-865	45	8	closed	closed	ADJ
ejpam-865	45	9	[	[	X
ejpam-865	45	10	8	8	NUM
ejpam-865	45	11	]	]	NUM
ejpam-865	45	12	)	)	PUNCT
ejpam-865	45	13	.	.	PUNCT
ejpam-865	46	1	the	the	DET
ejpam-865	46	2	intersection	intersection	NOUN
ejpam-865	46	3	of	of	ADP
ejpam-865	46	4	all	all	DET
ejpam-865	46	5	α	α	PRON
ejpam-865	46	6	-	-	ADJ
ejpam-865	46	7	closed	closed	ADJ
ejpam-865	46	8	(	(	PUNCT
ejpam-865	46	9	resp	resp	NOUN
ejpam-865	46	10	.	.	PUNCT
ejpam-865	46	11	preclosed	preclose	VERB
ejpam-865	46	12	,	,	PUNCT
ejpam-865	46	13	semi	semi	ADJ
ejpam-865	46	14	-	-	ADJ
ejpam-865	46	15	closed	closed	ADJ
ejpam-865	46	16	)	)	PUNCT
ejpam-865	46	17	sets	set	NOUN
ejpam-865	46	18	in	in	ADP
ejpam-865	46	19	(	(	PUNCT
ejpam-865	46	20	x	x	INTJ
ejpam-865	46	21	,	,	PUNCT
ejpam-865	46	22	τ	τ	X
ejpam-865	46	23	)	)	PUNCT
ejpam-865	46	24	containing	contain	VERB
ejpam-865	46	25	a	a	DET
ejpam-865	46	26	subset	subset	NOUN
ejpam-865	46	27	a	a	PRON
ejpam-865	46	28	is	be	AUX
ejpam-865	46	29	called	call	VERB
ejpam-865	46	30	the	the	DET
ejpam-865	46	31	α	α	NOUN
ejpam-865	46	32	-	-	NOUN
ejpam-865	46	33	closure	closure	NOUN
ejpam-865	46	34	[	[	X
ejpam-865	46	35	17	17	NUM
ejpam-865	46	36	]	]	X
ejpam-865	46	37	(	(	PUNCT
ejpam-865	46	38	resp	resp	NOUN
ejpam-865	46	39	.	.	PUNCT
ejpam-865	47	1	preclosure	preclosure	ADJ
ejpam-865	48	1	[	[	X
ejpam-865	48	2	10	10	NUM
ejpam-865	48	3	]	]	PUNCT
ejpam-865	48	4	,	,	PUNCT
ejpam-865	48	5	semi	semi	ADJ
ejpam-865	48	6	-	-	NOUN
ejpam-865	48	7	closure	closure	ADJ
ejpam-865	48	8	[	[	X
ejpam-865	48	9	8	8	NUM
ejpam-865	48	10	]	]	SYM
ejpam-865	48	11	)	)	PUNCT
ejpam-865	48	12	of	of	ADP
ejpam-865	48	13	a	a	PRON
ejpam-865	48	14	,	,	PUNCT
ejpam-865	48	15	denoted	denote	VERB
ejpam-865	48	16	by	by	ADP
ejpam-865	48	17	αcl(a	αcl(a	NUM
ejpam-865	48	18	)	)	PUNCT
ejpam-865	48	19	(	(	PUNCT
ejpam-865	48	20	resp	resp	NOUN
ejpam-865	48	21	.	.	PUNCT
ejpam-865	49	1	pcl(a	pcl(a	NUM
ejpam-865	49	2	)	)	PUNCT
ejpam-865	49	3	,	,	PUNCT
ejpam-865	49	4	sc	sc	PROPN
ejpam-865	49	5	l(a	l(a	PROPN
ejpam-865	49	6	)	)	PUNCT
ejpam-865	49	7	)	)	PUNCT
ejpam-865	49	8	.	.	PUNCT
ejpam-865	50	1	the	the	DET
ejpam-865	50	2	union	union	NOUN
ejpam-865	50	3	of	of	ADP
ejpam-865	50	4	all	all	DET
ejpam-865	50	5	α	α	NOUN
ejpam-865	50	6	-	-	ADJ
ejpam-865	50	7	open	open	ADJ
ejpam-865	50	8	(	(	PUNCT
ejpam-865	50	9	resp	resp	NOUN
ejpam-865	50	10	.	.	PUNCT
ejpam-865	51	1	preopen	preopen	ADJ
ejpam-865	51	2	,	,	PUNCT
ejpam-865	51	3	semi	semi	ADJ
ejpam-865	51	4	-	-	ADJ
ejpam-865	51	5	open	open	ADJ
ejpam-865	51	6	,	,	PUNCT
ejpam-865	51	7	δ	δ	NOUN
ejpam-865	51	8	-	-	ADJ
ejpam-865	51	9	open	open	ADJ
ejpam-865	51	10	)	)	PUNCT
ejpam-865	51	11	sets	set	NOUN
ejpam-865	51	12	of	of	ADP
ejpam-865	51	13	x	x	PUNCT
ejpam-865	51	14	contained	contain	VERB
ejpam-865	51	15	in	in	ADP
ejpam-865	51	16	a	a	PRON
ejpam-865	51	17	is	be	AUX
ejpam-865	51	18	called	call	VERB
ejpam-865	51	19	the	the	DET
ejpam-865	51	20	α	α	NOUN
ejpam-865	51	21	-	-	NOUN
ejpam-865	51	22	interior	interior	ADJ
ejpam-865	51	23	[	[	X
ejpam-865	51	24	1	1	NUM
ejpam-865	51	25	]	]	PUNCT
ejpam-865	51	26	(	(	PUNCT
ejpam-865	51	27	resp	resp	NOUN
ejpam-865	51	28	.	.	PUNCT
ejpam-865	52	1	preinterior	preinterior	PROPN
ejpam-865	53	1	[	[	X
ejpam-865	53	2	19	19	NUM
ejpam-865	53	3	]	]	PUNCT
ejpam-865	53	4	,	,	PUNCT
ejpam-865	53	5	semi	semi	ADJ
ejpam-865	53	6	-	-	ADJ
ejpam-865	53	7	interior	interior	ADJ
ejpam-865	53	8	[	[	X
ejpam-865	53	9	8	8	NUM
ejpam-865	53	10	]	]	PUNCT
ejpam-865	53	11	,	,	PUNCT
ejpam-865	53	12	δ	δ	PROPN
ejpam-865	53	13	-	-	NOUN
ejpam-865	53	14	interior	interior	ADJ
ejpam-865	53	15	[	[	X
ejpam-865	53	16	27	27	NUM
ejpam-865	53	17	]	]	PUNCT
ejpam-865	53	18	)	)	PUNCT
ejpam-865	53	19	of	of	ADP
ejpam-865	53	20	a	a	PRON
ejpam-865	53	21	and	and	CCONJ
ejpam-865	53	22	is	be	AUX
ejpam-865	53	23	denoted	denote	VERB
ejpam-865	53	24	by	by	ADP
ejpam-865	53	25	αlnt(a	αlnt(a	PROPN
ejpam-865	53	26	)	)	PUNCT
ejpam-865	53	27	(	(	PUNCT
ejpam-865	53	28	resp	resp	NOUN
ejpam-865	53	29	.	.	PUNCT
ejpam-865	54	1	plnt(a	plnt(a	PROPN
ejpam-865	54	2	)	)	PUNCT
ejpam-865	54	3	,	,	PUNCT
ejpam-865	54	4	sint(a	sint(a	PROPN
ejpam-865	54	5	)	)	PUNCT
ejpam-865	54	6	,	,	PUNCT
ejpam-865	54	7	intδ(a	intδ(a	NOUN
ejpam-865	54	8	)	)	PUNCT
ejpam-865	54	9	)	)	PUNCT
ejpam-865	54	10	.	.	PUNCT
ejpam-865	55	1	a	a	DET
ejpam-865	55	2	subset	subset	NOUN
ejpam-865	55	3	s	s	NOUN
ejpam-865	55	4	of	of	ADP
ejpam-865	55	5	a	a	DET
ejpam-865	55	6	space	space	NOUN
ejpam-865	55	7	(	(	PUNCT
ejpam-865	55	8	x	x	X
ejpam-865	55	9	,	,	PUNCT
ejpam-865	55	10	τ	τ	X
ejpam-865	55	11	)	)	PUNCT
ejpam-865	55	12	is	be	AUX
ejpam-865	55	13	δ	δ	PROPN
ejpam-865	55	14	-	-	PUNCT
ejpam-865	55	15	semiopen	semiopen	ADJ
ejpam-865	56	1	[	[	X
ejpam-865	56	2	23	23	NUM
ejpam-865	56	3	]	]	PUNCT
ejpam-865	56	4	(	(	PUNCT
ejpam-865	56	5	resp	resp	NOUN
ejpam-865	56	6	.	.	PUNCT
ejpam-865	57	1	δ	δ	PROPN
ejpam-865	57	2	-	-	PUNCT
ejpam-865	57	3	semiclosed	semiclose	VERB
ejpam-865	57	4	)	)	PUNCT
ejpam-865	57	5	if	if	SCONJ
ejpam-865	57	6	s	s	VERB
ejpam-865	57	7	⊂	⊂	PROPN
ejpam-865	57	8	cl(intδ(s	cl(intδ(s	PROPN
ejpam-865	57	9	)	)	PUNCT
ejpam-865	57	10	)	)	PUNCT
ejpam-865	58	1	(	(	PUNCT
ejpam-865	58	2	resp	resp	NOUN
ejpam-865	58	3	.	.	PUNCT
ejpam-865	59	1	int(clδ(s))⊂	int(clδ(s))⊂	X
ejpam-865	59	2	s	s	X
ejpam-865	59	3	)	)	PUNCT
ejpam-865	59	4	.	.	PUNCT
ejpam-865	60	1	lemma	lemma	PROPN
ejpam-865	60	2	1	1	NUM
ejpam-865	60	3	(	(	PUNCT
ejpam-865	60	4	park	park	NOUN
ejpam-865	60	5	et	et	NOUN
ejpam-865	60	6	al	al	PROPN
ejpam-865	60	7	.	.	PUNCT
ejpam-865	61	1	[	[	X
ejpam-865	61	2	23	23	NUM
ejpam-865	61	3	]	]	PUNCT
ejpam-865	61	4	)	)	PUNCT
ejpam-865	61	5	.	.	PUNCT
ejpam-865	62	1	the	the	DET
ejpam-865	62	2	intersection	intersection	NOUN
ejpam-865	62	3	(	(	PUNCT
ejpam-865	62	4	resp	resp	NOUN
ejpam-865	62	5	.	.	PUNCT
ejpam-865	62	6	union	union	NOUN
ejpam-865	62	7	)	)	PUNCT
ejpam-865	62	8	of	of	ADP
ejpam-865	62	9	arbitrary	arbitrary	ADJ
ejpam-865	62	10	collection	collection	NOUN
ejpam-865	62	11	of	of	ADP
ejpam-865	62	12	δsemiclosed	δsemiclosed	ADJ
ejpam-865	62	13	(	(	PUNCT
ejpam-865	62	14	resp	resp	NOUN
ejpam-865	62	15	.	.	PUNCT
ejpam-865	63	1	δ	δ	PROPN
ejpam-865	63	2	-	-	PUNCT
ejpam-865	63	3	semiopen	semiopen	ADJ
ejpam-865	63	4	)	)	PUNCT
ejpam-865	63	5	sets	set	NOUN
ejpam-865	63	6	in	in	ADP
ejpam-865	63	7	(	(	PUNCT
ejpam-865	63	8	x	x	NOUN
ejpam-865	63	9	,	,	PUNCT
ejpam-865	63	10	τ	τ	X
ejpam-865	63	11	)	)	PUNCT
ejpam-865	63	12	is	be	AUX
ejpam-865	63	13	δ	δ	PROPN
ejpam-865	63	14	-	-	PUNCT
ejpam-865	63	15	semiclosed	semiclose	VERB
ejpam-865	63	16	(	(	PUNCT
ejpam-865	63	17	resp	resp	NOUN
ejpam-865	63	18	.	.	PUNCT
ejpam-865	64	1	δ	δ	PROPN
ejpam-865	64	2	-	-	PUNCT
ejpam-865	64	3	semiopen	semiopen	ADJ
ejpam-865	64	4	)	)	PUNCT
ejpam-865	64	5	.	.	PUNCT
ejpam-865	65	1	and	and	CCONJ
ejpam-865	65	2	a	a	DET
ejpam-865	65	3	⊂	⊂	X
ejpam-865	65	4	x	x	X
ejpam-865	65	5	is	be	AUX
ejpam-865	65	6	δ	δ	PROPN
ejpam-865	65	7	-	-	PUNCT
ejpam-865	65	8	semiclosed	semiclose	VERB
ejpam-865	65	9	if	if	SCONJ
ejpam-865	65	10	and	and	CCONJ
ejpam-865	65	11	only	only	ADV
ejpam-865	65	12	if	if	SCONJ
ejpam-865	65	13	a=	a=	VERB
ejpam-865	65	14	δcls(a	δcls(a	VERB
ejpam-865	65	15	)	)	PUNCT
ejpam-865	65	16	.	.	PUNCT
ejpam-865	66	1	lemma	lemma	PROPN
ejpam-865	66	2	2	2	NUM
ejpam-865	66	3	(	(	PUNCT
ejpam-865	66	4	[	[	X
ejpam-865	66	5	7	7	NUM
ejpam-865	66	6	,	,	PUNCT
ejpam-865	66	7	10	10	NUM
ejpam-865	66	8	,	,	PUNCT
ejpam-865	66	9	22	22	NUM
ejpam-865	66	10	,	,	PUNCT
ejpam-865	66	11	14	14	NUM
ejpam-865	66	12	]	]	PUNCT
ejpam-865	66	13	)	)	PUNCT
ejpam-865	66	14	.	.	PUNCT
ejpam-865	67	1	let	let	VERB
ejpam-865	67	2	{	{	PUNCT
ejpam-865	67	3	xλ	xλ	NOUN
ejpam-865	67	4	:	:	PUNCT
ejpam-865	67	5	λ	λ	X
ejpam-865	67	6	∈	∈	PROPN
ejpam-865	67	7	λ	λ	PROPN
ejpam-865	67	8	}	}	PUNCT
ejpam-865	67	9	be	be	VERB
ejpam-865	67	10	any	any	DET
ejpam-865	67	11	family	family	NOUN
ejpam-865	67	12	of	of	ADP
ejpam-865	67	13	topological	topological	ADJ
ejpam-865	67	14	spaces	space	NOUN
ejpam-865	67	15	and	and	CCONJ
ejpam-865	67	16	uλi	uλi	NOUN
ejpam-865	67	17	be	be	AUX
ejpam-865	67	18	a	a	DET
ejpam-865	67	19	nonempty	nonempty	ADJ
ejpam-865	67	20	subset	subset	NOUN
ejpam-865	67	21	of	of	ADP
ejpam-865	67	22	xλi	xλi	PROPN
ejpam-865	67	23	for	for	ADP
ejpam-865	67	24	each	each	DET
ejpam-865	67	25	i	i	NOUN
ejpam-865	67	26	=	=	NOUN
ejpam-865	67	27	1,2	1,2	NUM
ejpam-865	67	28	,	,	PUNCT
ejpam-865	67	29	.	.	PUNCT
ejpam-865	67	30	.	.	PUNCT
ejpam-865	67	31	.	.	PUNCT
ejpam-865	68	1	,	,	PUNCT
ejpam-865	68	2	n.	n.	NOUN
ejpam-865	68	3	then	then	ADV
ejpam-865	68	4	u	u	X
ejpam-865	68	5	=	=	SYM
ejpam-865	68	6	πλ6	πλ6	PROPN
ejpam-865	68	7	=	=	SYM
ejpam-865	68	8	λi	λi	NOUN
ejpam-865	68	9	xλ	xλ	PROPN
ejpam-865	68	10	×	×	PROPN
ejpam-865	68	11	π	π	PROPN
ejpam-865	68	12	n	n	CCONJ
ejpam-865	68	13	i=1uλi	i=1uλi	PROPN
ejpam-865	68	14	is	be	AUX
ejpam-865	68	15	a	a	DET
ejpam-865	68	16	nonempty	nonempty	ADV
ejpam-865	68	17	α	α	NOUN
ejpam-865	68	18	-	-	ADJ
ejpam-865	68	19	open	open	ADJ
ejpam-865	68	20	[	[	X
ejpam-865	68	21	7	7	NUM
ejpam-865	68	22	]	]	X
ejpam-865	68	23	(	(	PUNCT
ejpam-865	68	24	resp	resp	NOUN
ejpam-865	68	25	.	.	PUNCT
ejpam-865	69	1	preopen	preopen	ADJ
ejpam-865	70	1	[	[	X
ejpam-865	70	2	10	10	NUM
ejpam-865	70	3	]	]	PUNCT
ejpam-865	70	4	,	,	PUNCT
ejpam-865	70	5	semi	semi	ADJ
ejpam-865	70	6	-	-	ADJ
ejpam-865	70	7	open	open	ADJ
ejpam-865	70	8	[	[	X
ejpam-865	70	9	22	22	NUM
ejpam-865	70	10	]	]	PUNCT
ejpam-865	70	11	,	,	PUNCT
ejpam-865	70	12	δ	δ	PROPN
ejpam-865	70	13	-	-	PUNCT
ejpam-865	70	14	semiopen	semiopen	VERB
ejpam-865	71	1	[	[	X
ejpam-865	71	2	14	14	NUM
ejpam-865	71	3	]	]	PUNCT
ejpam-865	71	4	)	)	PUNCT
ejpam-865	71	5	subset	subset	NOUN
ejpam-865	71	6	of	of	ADP
ejpam-865	71	7	πxλ	πxλ	INTJ
ejpam-865	71	8	if	if	SCONJ
ejpam-865	72	1	and	and	CCONJ
ejpam-865	72	2	only	only	ADV
ejpam-865	72	3	if	if	SCONJ
ejpam-865	72	4	uλi	uλi	NOUN
ejpam-865	72	5	is	be	AUX
ejpam-865	72	6	α	α	NOUN
ejpam-865	72	7	-	-	ADJ
ejpam-865	72	8	open	open	ADJ
ejpam-865	72	9	(	(	PUNCT
ejpam-865	72	10	resp	resp	NOUN
ejpam-865	72	11	.	.	PUNCT
ejpam-865	73	1	preopen	preopen	ADJ
ejpam-865	73	2	,	,	PUNCT
ejpam-865	73	3	semi	semi	ADJ
ejpam-865	73	4	-	-	ADJ
ejpam-865	73	5	open	open	ADJ
ejpam-865	73	6	,	,	PUNCT
ejpam-865	73	7	δ	δ	NOUN
ejpam-865	73	8	-	-	PUNCT
ejpam-865	73	9	semiopen	semiopen	ADJ
ejpam-865	73	10	)	)	PUNCT
ejpam-865	73	11	in	in	ADP
ejpam-865	73	12	xλi	xλi	PROPN
ejpam-865	73	13	for	for	ADP
ejpam-865	73	14	each	each	PRON
ejpam-865	73	15	i	i	NOUN
ejpam-865	73	16	=	=	NOUN
ejpam-865	73	17	1,2	1,2	NUM
ejpam-865	73	18	,	,	PUNCT
ejpam-865	73	19	.	.	PUNCT
ejpam-865	73	20	.	.	PUNCT
ejpam-865	74	1	.	.	PUNCT
ejpam-865	75	1	,	,	PUNCT
ejpam-865	75	2	n.	n.	PROPN
ejpam-865	75	3	lemma	lemma	PROPN
ejpam-865	75	4	3	3	X
ejpam-865	75	5	.	.	PUNCT
ejpam-865	76	1	let	let	VERB
ejpam-865	76	2	a	a	PRON
ejpam-865	76	3	and	and	CCONJ
ejpam-865	76	4	b	b	NOUN
ejpam-865	76	5	be	be	AUX
ejpam-865	76	6	subsets	subset	NOUN
ejpam-865	76	7	of	of	ADP
ejpam-865	76	8	a	a	DET
ejpam-865	76	9	space	space	NOUN
ejpam-865	76	10	(	(	PUNCT
ejpam-865	76	11	x	x	X
ejpam-865	76	12	,	,	PUNCT
ejpam-865	76	13	τ	τ	PROPN
ejpam-865	76	14	)	)	PUNCT
ejpam-865	76	15	.	.	PUNCT
ejpam-865	77	1	then	then	ADV
ejpam-865	77	2	we	we	PRON
ejpam-865	77	3	have	have	VERB
ejpam-865	77	4	(	(	PUNCT
ejpam-865	77	5	1	1	X
ejpam-865	77	6	)	)	PUNCT
ejpam-865	77	7	if	if	SCONJ
ejpam-865	77	8	aεδso(x	aεδso(x	VERB
ejpam-865	77	9	)	)	PUNCT
ejpam-865	77	10	and	and	CCONJ
ejpam-865	77	11	bεδo(x	bεδo(x	PROPN
ejpam-865	77	12	)	)	PUNCT
ejpam-865	77	13	,	,	PUNCT
ejpam-865	77	14	then	then	ADV
ejpam-865	77	15	a∩	a∩	PROPN
ejpam-865	77	16	bεδso(b	bεδso(b	PROPN
ejpam-865	77	17	)	)	PUNCT
ejpam-865	78	1	[	[	X
ejpam-865	78	2	14	14	NUM
ejpam-865	78	3	]	]	PUNCT
ejpam-865	78	4	.	.	PUNCT
ejpam-865	79	1	(	(	PUNCT
ejpam-865	79	2	2	2	X
ejpam-865	79	3	)	)	PUNCT
ejpam-865	79	4	if	if	SCONJ
ejpam-865	79	5	aεδso(b	aεδso(b	PROPN
ejpam-865	79	6	)	)	PUNCT
ejpam-865	79	7	and	and	CCONJ
ejpam-865	79	8	bεδo(x	bεδo(x	PROPN
ejpam-865	79	9	)	)	PUNCT
ejpam-865	79	10	,	,	PUNCT
ejpam-865	79	11	then	then	ADV
ejpam-865	79	12	aεδso(x	aεδso(x	VERB
ejpam-865	79	13	)	)	PUNCT
ejpam-865	80	1	[	[	X
ejpam-865	80	2	6	6	NUM
ejpam-865	80	3	]	]	PUNCT
ejpam-865	80	4	.	.	PUNCT
ejpam-865	81	1	definition	definition	NOUN
ejpam-865	81	2	2	2	NUM
ejpam-865	81	3	.	.	PUNCT
ejpam-865	82	1	a	a	DET
ejpam-865	82	2	function	function	NOUN
ejpam-865	82	3	f	f	NOUN
ejpam-865	82	4	:	:	PUNCT
ejpam-865	82	5	(	(	PUNCT
ejpam-865	82	6	x	x	X
ejpam-865	82	7	,	,	PUNCT
ejpam-865	82	8	τ)→	τ)→	PROPN
ejpam-865	82	9	(	(	PUNCT
ejpam-865	82	10	y	y	PROPN
ejpam-865	82	11	,	,	PUNCT
ejpam-865	82	12	σ	σ	PROPN
ejpam-865	82	13	)	)	PUNCT
ejpam-865	82	14	is	be	AUX
ejpam-865	82	15	said	say	VERB
ejpam-865	82	16	to	to	PART
ejpam-865	82	17	be	be	AUX
ejpam-865	82	18	:	:	PUNCT
ejpam-865	82	19	•	•	NUM
ejpam-865	82	20	semi	semi	VERB
ejpam-865	82	21	α	α	X
ejpam-865	82	22	-	-	ADJ
ejpam-865	82	23	irresolute	irresolute	ADJ
ejpam-865	82	24	[	[	X
ejpam-865	82	25	2	2	NUM
ejpam-865	82	26	]	]	PUNCT
ejpam-865	82	27	if	if	SCONJ
ejpam-865	82	28	f	f	PROPN
ejpam-865	82	29	−1(v	−1(v	PROPN
ejpam-865	82	30	)	)	PUNCT
ejpam-865	82	31	is	be	AUX
ejpam-865	82	32	semi	semi	ADJ
ejpam-865	82	33	-	-	ADJ
ejpam-865	82	34	open	open	ADJ
ejpam-865	82	35	set	set	NOUN
ejpam-865	82	36	in	in	ADP
ejpam-865	82	37	x	x	PUNCT
ejpam-865	82	38	for	for	ADP
ejpam-865	82	39	every	every	DET
ejpam-865	82	40	α	α	NOUN
ejpam-865	82	41	-	-	ADJ
ejpam-865	82	42	open	open	ADJ
ejpam-865	82	43	subset	subset	NOUN
ejpam-865	82	44	v	v	NOUN
ejpam-865	82	45	of	of	ADP
ejpam-865	82	46	y	y	PROPN
ejpam-865	82	47	.	.	PUNCT
ejpam-865	83	1	•	•	NUM
ejpam-865	83	2	semi	semi	ADV
ejpam-865	83	3	α	α	NOUN
ejpam-865	83	4	-	-	ADJ
ejpam-865	83	5	preirresolute	preirresolute	NOUN
ejpam-865	84	1	[	[	X
ejpam-865	84	2	3	3	NUM
ejpam-865	84	3	]	]	PUNCT
ejpam-865	84	4	if	if	SCONJ
ejpam-865	84	5	f	f	PROPN
ejpam-865	84	6	−1(v	−1(v	PROPN
ejpam-865	84	7	)	)	PUNCT
ejpam-865	84	8	is	be	AUX
ejpam-865	84	9	semi	semi	ADJ
ejpam-865	84	10	-	-	ADJ
ejpam-865	84	11	open	open	ADJ
ejpam-865	84	12	set	set	NOUN
ejpam-865	84	13	in	in	ADP
ejpam-865	84	14	x	x	PUNCT
ejpam-865	84	15	for	for	ADP
ejpam-865	84	16	every	every	DET
ejpam-865	84	17	preopen	preopen	NOUN
ejpam-865	84	18	subset	subset	VERB
ejpam-865	84	19	v	v	NOUN
ejpam-865	84	20	of	of	ADP
ejpam-865	84	21	y	y	PROPN
ejpam-865	84	22	.	.	PUNCT
ejpam-865	85	1	•	•	NUM
ejpam-865	85	2	(	(	PUNCT
ejpam-865	85	3	δ	δ	NOUN
ejpam-865	85	4	,	,	PUNCT
ejpam-865	85	5	β)-irresolute	β)-irresolute	PUNCT
ejpam-865	86	1	[	[	X
ejpam-865	86	2	6	6	NUM
ejpam-865	86	3	]	]	PUNCT
ejpam-865	86	4	if	if	SCONJ
ejpam-865	86	5	f	f	PROPN
ejpam-865	86	6	−1(v	−1(v	PROPN
ejpam-865	86	7	)	)	PUNCT
ejpam-865	86	8	is	be	AUX
ejpam-865	86	9	δ	δ	PROPN
ejpam-865	86	10	-	-	PUNCT
ejpam-865	86	11	semiopen	semiopen	ADJ
ejpam-865	86	12	set	set	VERB
ejpam-865	86	13	in	in	ADP
ejpam-865	86	14	x	x	PUNCT
ejpam-865	86	15	for	for	ADP
ejpam-865	86	16	every	every	DET
ejpam-865	86	17	β	β	X
ejpam-865	86	18	-open	-open	NOUN
ejpam-865	86	19	subset	subset	NOUN
ejpam-865	86	20	v	v	NOUN
ejpam-865	86	21	of	of	ADP
ejpam-865	86	22	y	y	PROPN
ejpam-865	86	23	.	.	PUNCT
ejpam-865	87	1	•	•	NUM
ejpam-865	87	2	δ	δ	NOUN
ejpam-865	87	3	-	-	PUNCT
ejpam-865	87	4	semi	semi	ADV
ejpam-865	87	5	-	-	ADJ
ejpam-865	87	6	continuous	continuous	ADJ
ejpam-865	87	7	[	[	X
ejpam-865	87	8	25	25	NUM
ejpam-865	87	9	]	]	PUNCT
ejpam-865	87	10	if	if	SCONJ
ejpam-865	87	11	f	f	PROPN
ejpam-865	87	12	−1(v	−1(v	PROPN
ejpam-865	87	13	)	)	PUNCT
ejpam-865	87	14	is	be	AUX
ejpam-865	87	15	δ	δ	PROPN
ejpam-865	87	16	-	-	PUNCT
ejpam-865	87	17	semiopen	semiopen	ADJ
ejpam-865	87	18	set	set	VERB
ejpam-865	87	19	in	in	ADP
ejpam-865	87	20	x	x	PUNCT
ejpam-865	87	21	for	for	ADP
ejpam-865	87	22	every	every	DET
ejpam-865	87	23	open	open	NOUN
ejpam-865	87	24	subset	subset	NOUN
ejpam-865	87	25	v	v	NOUN
ejpam-865	87	26	of	of	ADP
ejpam-865	87	27	y	y	PROPN
ejpam-865	87	28	.	.	PUNCT
ejpam-865	88	1	•	•	NUM
ejpam-865	88	2	α	α	X
ejpam-865	88	3	-	-	NOUN
ejpam-865	88	4	irresolute	irresolute	ADJ
ejpam-865	88	5	[	[	X
ejpam-865	88	6	17	17	NUM
ejpam-865	88	7	]	]	PUNCT
ejpam-865	88	8	if	if	SCONJ
ejpam-865	88	9	f	f	PROPN
ejpam-865	88	10	−1(v	−1(v	PROPN
ejpam-865	88	11	)	)	PUNCT
ejpam-865	88	12	is	be	AUX
ejpam-865	88	13	α	α	X
ejpam-865	88	14	-	-	ADJ
ejpam-865	88	15	open	open	ADJ
ejpam-865	88	16	set	set	NOUN
ejpam-865	88	17	in	in	ADP
ejpam-865	88	18	x	x	PUNCT
ejpam-865	88	19	for	for	ADP
ejpam-865	88	20	every	every	DET
ejpam-865	88	21	α	α	NOUN
ejpam-865	88	22	-	-	ADJ
ejpam-865	88	23	open	open	ADJ
ejpam-865	88	24	subset	subset	NOUN
ejpam-865	88	25	v	v	NOUN
ejpam-865	88	26	of	of	ADP
ejpam-865	88	27	y	y	PROPN
ejpam-865	88	28	.	.	PUNCT
ejpam-865	89	1	y.	y.	PROPN
ejpam-865	89	2	beceren	beceren	PROPN
ejpam-865	89	3	,	,	PUNCT
ejpam-865	89	4	t.	t.	PROPN
ejpam-865	89	5	noiri	noiri	PROPN
ejpam-865	89	6	/	/	SYM
ejpam-865	89	7	eur	eur	PROPN
ejpam-865	89	8	.	.	PUNCT
ejpam-865	90	1	j.	j.	PROPN
ejpam-865	90	2	pure	pure	PROPN
ejpam-865	90	3	appl	appl	PROPN
ejpam-865	90	4	.	.	PROPN
ejpam-865	90	5	math	math	PROPN
ejpam-865	90	6	,	,	PUNCT
ejpam-865	90	7	4	4	NUM
ejpam-865	90	8	(	(	PUNCT
ejpam-865	90	9	2011	2011	NUM
ejpam-865	90	10	)	)	PUNCT
ejpam-865	90	11	,	,	PUNCT
ejpam-865	90	12	361	361	NUM
ejpam-865	90	13	-	-	SYM
ejpam-865	90	14	369	369	NUM
ejpam-865	90	15	363	363	NUM
ejpam-865	90	16	•	•	NUM
ejpam-865	90	17	preirresolute	preirresolute	NOUN
ejpam-865	91	1	[	[	X
ejpam-865	91	2	24	24	NUM
ejpam-865	91	3	]	]	PUNCT
ejpam-865	91	4	if	if	SCONJ
ejpam-865	91	5	f	f	PROPN
ejpam-865	91	6	−1(v	−1(v	PROPN
ejpam-865	91	7	)	)	PUNCT
ejpam-865	91	8	is	be	AUX
ejpam-865	91	9	preopen	preopen	ADJ
ejpam-865	91	10	set	set	VERB
ejpam-865	91	11	in	in	ADP
ejpam-865	91	12	x	x	PUNCT
ejpam-865	91	13	for	for	ADP
ejpam-865	91	14	every	every	DET
ejpam-865	91	15	preopen	preopen	NOUN
ejpam-865	91	16	subset	subset	VERB
ejpam-865	91	17	v	v	NOUN
ejpam-865	91	18	of	of	ADP
ejpam-865	91	19	y	y	PROPN
ejpam-865	91	20	.	.	PUNCT
ejpam-865	92	1	•	•	NUM
ejpam-865	92	2	irresolute	irresolute	ADJ
ejpam-865	93	1	[	[	X
ejpam-865	93	2	9	9	NUM
ejpam-865	93	3	]	]	PUNCT
ejpam-865	93	4	if	if	SCONJ
ejpam-865	93	5	f	f	PROPN
ejpam-865	93	6	−1(v	−1(v	PROPN
ejpam-865	93	7	)	)	PUNCT
ejpam-865	93	8	is	be	AUX
ejpam-865	93	9	semi	semi	ADJ
ejpam-865	93	10	-	-	ADJ
ejpam-865	93	11	open	open	ADJ
ejpam-865	93	12	set	set	NOUN
ejpam-865	93	13	in	in	ADP
ejpam-865	93	14	x	x	PUNCT
ejpam-865	93	15	for	for	ADP
ejpam-865	93	16	every	every	DET
ejpam-865	93	17	semi	semi	ADJ
ejpam-865	93	18	-	-	ADJ
ejpam-865	93	19	open	open	ADJ
ejpam-865	93	20	subset	subset	ADJ
ejpam-865	93	21	v	v	NOUN
ejpam-865	93	22	of	of	ADP
ejpam-865	93	23	y	y	PROPN
ejpam-865	93	24	.	.	PUNCT
ejpam-865	94	1	3	3	X
ejpam-865	94	2	.	.	X
ejpam-865	94	3	δα	δα	PROPN
ejpam-865	94	4	,	,	PUNCT
ejpam-865	94	5	δp	δp	ADP
ejpam-865	94	6	and	and	CCONJ
ejpam-865	94	7	δs	δs	NOUN
ejpam-865	94	8	-	-	PUNCT
ejpam-865	94	9	irresolute	irresolute	ADJ
ejpam-865	94	10	functions	function	NOUN
ejpam-865	94	11	definition	definition	NOUN
ejpam-865	94	12	3	3	NUM
ejpam-865	94	13	.	.	PUNCT
ejpam-865	95	1	a	a	DET
ejpam-865	95	2	function	function	NOUN
ejpam-865	95	3	f	f	NOUN
ejpam-865	95	4	:	:	PUNCT
ejpam-865	95	5	(	(	PUNCT
ejpam-865	95	6	x	x	X
ejpam-865	95	7	,	,	PUNCT
ejpam-865	95	8	τ)→	τ)→	PROPN
ejpam-865	95	9	(	(	PUNCT
ejpam-865	95	10	y	y	PROPN
ejpam-865	95	11	,	,	PUNCT
ejpam-865	95	12	σ	σ	PROPN
ejpam-865	95	13	)	)	PUNCT
ejpam-865	95	14	is	be	AUX
ejpam-865	95	15	said	say	VERB
ejpam-865	95	16	to	to	PART
ejpam-865	95	17	be	be	AUX
ejpam-865	95	18	δα	δα	NOUN
ejpam-865	95	19	-	-	PUNCT
ejpam-865	95	20	irresolute	irresolute	ADJ
ejpam-865	95	21	,	,	PUNCT
ejpam-865	95	22	δp	δp	PRON
ejpam-865	95	23	-	-	PUNCT
ejpam-865	95	24	irresolute	irresolute	ADJ
ejpam-865	95	25	and	and	CCONJ
ejpam-865	95	26	δsirresolute	δsirresolute	VERB
ejpam-865	95	27	if	if	SCONJ
ejpam-865	95	28	f	f	PROPN
ejpam-865	95	29	−1(v	−1(v	PROPN
ejpam-865	95	30	)	)	PUNCT
ejpam-865	95	31	is	be	AUX
ejpam-865	95	32	δ	δ	PROPN
ejpam-865	95	33	-	-	PUNCT
ejpam-865	95	34	semiopen	semiopen	ADJ
ejpam-865	95	35	set	set	VERB
ejpam-865	95	36	in	in	ADP
ejpam-865	95	37	x	x	PUNCT
ejpam-865	95	38	for	for	ADP
ejpam-865	95	39	every	every	DET
ejpam-865	95	40	α	α	NOUN
ejpam-865	95	41	-	-	ADJ
ejpam-865	95	42	open	open	ADJ
ejpam-865	95	43	(	(	PUNCT
ejpam-865	95	44	resp	resp	NOUN
ejpam-865	95	45	.	.	PUNCT
ejpam-865	96	1	preopen	preopen	ADJ
ejpam-865	96	2	,	,	PUNCT
ejpam-865	96	3	semi	semi	ADJ
ejpam-865	96	4	-	-	ADJ
ejpam-865	96	5	open	open	ADJ
ejpam-865	96	6	)	)	PUNCT
ejpam-865	96	7	subset	subset	VERB
ejpam-865	96	8	v	v	NOUN
ejpam-865	96	9	of	of	ADP
ejpam-865	96	10	y	y	PROPN
ejpam-865	96	11	.	.	PUNCT
ejpam-865	97	1	from	from	ADP
ejpam-865	97	2	the	the	DET
ejpam-865	97	3	definitions	definition	NOUN
ejpam-865	97	4	,	,	PUNCT
ejpam-865	97	5	we	we	PRON
ejpam-865	97	6	have	have	VERB
ejpam-865	97	7	the	the	DET
ejpam-865	97	8	following	follow	VERB
ejpam-865	97	9	relationships	relationship	NOUN
ejpam-865	97	10	:	:	PUNCT
ejpam-865	97	11	(	(	PUNCT
ejpam-865	97	12	δ	δ	X
ejpam-865	97	13	,	,	PUNCT
ejpam-865	97	14	β)−	β)−	ADJ
ejpam-865	97	15	irresoluteness	irresoluteness	NOUN
ejpam-865	97	16	→	→	SYM
ejpam-865	97	17	δp−	δp−	NUM
ejpam-865	97	18	irresoluteness	irresoluteness	NOUN
ejpam-865	97	19	→	→	PUNCT
ejpam-865	97	20	semi−α−	semi−α−	NOUN
ejpam-865	97	21	preirresoluteness	preirresoluteness	NOUN
ejpam-865	97	22	↓	↓	NOUN
ejpam-865	97	23	↓	↓	PROPN
ejpam-865	97	24	↓	↓	PROPN
ejpam-865	97	25	δs−	δs−	PROPN
ejpam-865	97	26	irresoluteness	irresoluteness	PROPN
ejpam-865	97	27	→	→	SYM
ejpam-865	97	28	δα−	δα−	PROPN
ejpam-865	97	29	irresoluteness	irresoluteness	NOUN
ejpam-865	97	30	→	→	SYM
ejpam-865	97	31	semi−α−	semi−α−	PROPN
ejpam-865	97	32	irresoluteness	irresoluteness	NOUN
ejpam-865	97	33	however	however	ADV
ejpam-865	97	34	the	the	DET
ejpam-865	97	35	converses	converse	NOUN
ejpam-865	97	36	of	of	ADP
ejpam-865	97	37	the	the	DET
ejpam-865	97	38	above	above	ADJ
ejpam-865	97	39	implications	implication	NOUN
ejpam-865	97	40	are	be	AUX
ejpam-865	97	41	not	not	PART
ejpam-865	97	42	true	true	ADJ
ejpam-865	97	43	in	in	ADP
ejpam-865	97	44	general	general	ADJ
ejpam-865	97	45	by	by	ADP
ejpam-865	97	46	the	the	DET
ejpam-865	97	47	following	follow	VERB
ejpam-865	97	48	examples	example	NOUN
ejpam-865	97	49	.	.	PUNCT
ejpam-865	98	1	example	example	NOUN
ejpam-865	99	1	1	1	NUM
ejpam-865	99	2	.	.	PUNCT
ejpam-865	99	3	let	let	VERB
ejpam-865	99	4	x	x	PUNCT
ejpam-865	99	5	=	=	PRON
ejpam-865	99	6	{	{	PUNCT
ejpam-865	99	7	a	a	PRON
ejpam-865	99	8	,	,	PUNCT
ejpam-865	99	9	b	b	NOUN
ejpam-865	99	10	,	,	PUNCT
ejpam-865	99	11	c	c	NOUN
ejpam-865	99	12	}	}	PUNCT
ejpam-865	99	13	with	with	ADP
ejpam-865	99	14	topologies	topology	NOUN
ejpam-865	99	15	τ	τ	X
ejpam-865	99	16	=	=	SYM
ejpam-865	99	17	{	{	PUNCT
ejpam-865	99	18	x	x	NOUN
ejpam-865	99	19	,	,	PUNCT
ejpam-865	99	20	∅	∅	NOUN
ejpam-865	99	21	,	,	PUNCT
ejpam-865	99	22	{	{	PUNCT
ejpam-865	99	23	a	a	PRON
ejpam-865	99	24	,	,	PUNCT
ejpam-865	99	25	b	b	NOUN
ejpam-865	99	26	}	}	PUNCT
ejpam-865	99	27	}	}	PUNCT
ejpam-865	99	28	andσ	andσ	NOUN
ejpam-865	99	29	=	=	SYM
ejpam-865	99	30	{	{	PUNCT
ejpam-865	99	31	x	x	NOUN
ejpam-865	99	32	,	,	PUNCT
ejpam-865	99	33	∅	∅	NOUN
ejpam-865	99	34	,	,	PUNCT
ejpam-865	99	35	{	{	PUNCT
ejpam-865	99	36	a	a	X
ejpam-865	99	37	}	}	PUNCT
ejpam-865	99	38	,	,	PUNCT
ejpam-865	99	39	{	{	PUNCT
ejpam-865	99	40	b	b	NOUN
ejpam-865	99	41	}	}	PUNCT
ejpam-865	99	42	,	,	PUNCT
ejpam-865	99	43	{	{	PUNCT
ejpam-865	99	44	a	a	DET
ejpam-865	99	45	,	,	PUNCT
ejpam-865	99	46	b	b	NOUN
ejpam-865	99	47	}	}	PUNCT
ejpam-865	99	48	}	}	PUNCT
ejpam-865	99	49	.	.	PUNCT
ejpam-865	100	1	let	let	VERB
ejpam-865	100	2	a	a	DET
ejpam-865	100	3	function	function	NOUN
ejpam-865	100	4	f	f	NOUN
ejpam-865	100	5	:	:	PUNCT
ejpam-865	100	6	(	(	PUNCT
ejpam-865	100	7	x	x	X
ejpam-865	100	8	,	,	PUNCT
ejpam-865	100	9	τ)→	τ)→	PROPN
ejpam-865	100	10	(	(	PUNCT
ejpam-865	100	11	x	x	X
ejpam-865	100	12	,	,	PUNCT
ejpam-865	100	13	σ	σ	PROPN
ejpam-865	100	14	)	)	PUNCT
ejpam-865	100	15	be	be	AUX
ejpam-865	100	16	defined	define	VERB
ejpam-865	100	17	by	by	ADP
ejpam-865	100	18	f	f	PROPN
ejpam-865	100	19	(	(	PUNCT
ejpam-865	100	20	a	a	X
ejpam-865	100	21	)	)	PUNCT
ejpam-865	100	22	=	=	SYM
ejpam-865	100	23	f	f	X
ejpam-865	100	24	(	(	PUNCT
ejpam-865	100	25	b	b	NOUN
ejpam-865	100	26	)	)	PUNCT
ejpam-865	100	27	=	=	PUNCT
ejpam-865	100	28	a	a	PROPN
ejpam-865	100	29	and	and	CCONJ
ejpam-865	100	30	f	f	PROPN
ejpam-865	100	31	(	(	PUNCT
ejpam-865	100	32	c	c	NOUN
ejpam-865	100	33	)	)	PUNCT
ejpam-865	101	1	=	=	SYM
ejpam-865	101	2	c.	c.	NOUN
ejpam-865	101	3	then	then	ADV
ejpam-865	101	4	f	f	PROPN
ejpam-865	101	5	is	be	AUX
ejpam-865	101	6	semi	semi	ADV
ejpam-865	101	7	α	α	X
ejpam-865	101	8	-	-	ADJ
ejpam-865	101	9	preirresolute	preirresolute	NOUN
ejpam-865	101	10	and	and	CCONJ
ejpam-865	101	11	hence	hence	ADV
ejpam-865	101	12	semi	semi	ADV
ejpam-865	101	13	α	α	NOUN
ejpam-865	101	14	-	-	ADJ
ejpam-865	101	15	irresolute	irresolute	ADJ
ejpam-865	101	16	but	but	CCONJ
ejpam-865	101	17	it	it	PRON
ejpam-865	101	18	is	be	AUX
ejpam-865	101	19	neither	neither	DET
ejpam-865	101	20	δα	δα	NOUN
ejpam-865	101	21	-	-	PUNCT
ejpam-865	101	22	irresolute	irresolute	ADJ
ejpam-865	101	23	,	,	PUNCT
ejpam-865	101	24	δs	δs	NOUN
ejpam-865	101	25	-	-	PUNCT
ejpam-865	101	26	irresolute	irresolute	ADJ
ejpam-865	101	27	nor	nor	CCONJ
ejpam-865	101	28	δpirresolute	δpirresolute	NOUN
ejpam-865	101	29	.	.	PUNCT
ejpam-865	101	30	example	example	NOUN
ejpam-865	102	1	2	2	NUM
ejpam-865	102	2	.	.	PUNCT
ejpam-865	102	3	let	let	VERB
ejpam-865	102	4	x	x	PUNCT
ejpam-865	102	5	=	=	PRON
ejpam-865	102	6	{	{	PUNCT
ejpam-865	102	7	a	a	PRON
ejpam-865	102	8	,	,	PUNCT
ejpam-865	102	9	b	b	NOUN
ejpam-865	102	10	,	,	PUNCT
ejpam-865	102	11	c	c	NOUN
ejpam-865	102	12	,	,	PUNCT
ejpam-865	102	13	d	d	NOUN
ejpam-865	102	14	}	}	PUNCT
ejpam-865	102	15	with	with	ADP
ejpam-865	102	16	topologies	topology	NOUN
ejpam-865	102	17	τ	τ	X
ejpam-865	102	18	=	=	SYM
ejpam-865	102	19	{	{	PUNCT
ejpam-865	102	20	x	x	NOUN
ejpam-865	102	21	,	,	PUNCT
ejpam-865	102	22	∅	∅	NOUN
ejpam-865	102	23	,	,	PUNCT
ejpam-865	102	24	{	{	PUNCT
ejpam-865	102	25	a	a	PRON
ejpam-865	102	26	,	,	PUNCT
ejpam-865	102	27	b	b	NOUN
ejpam-865	102	28	,	,	PUNCT
ejpam-865	102	29	c	c	NOUN
ejpam-865	102	30	}	}	PUNCT
ejpam-865	102	31	}	}	PUNCT
ejpam-865	102	32	and	and	CCONJ
ejpam-865	102	33	σ	σ	X
ejpam-865	102	34	=	=	SYM
ejpam-865	102	35	{	{	PUNCT
ejpam-865	102	36	x	x	NOUN
ejpam-865	102	37	,	,	PUNCT
ejpam-865	102	38	∅	∅	NOUN
ejpam-865	102	39	,	,	PUNCT
ejpam-865	102	40	{	{	PUNCT
ejpam-865	102	41	a	a	X
ejpam-865	102	42	}	}	PUNCT
ejpam-865	102	43	,	,	PUNCT
ejpam-865	102	44	{	{	PUNCT
ejpam-865	102	45	b	b	NOUN
ejpam-865	102	46	,	,	PUNCT
ejpam-865	102	47	c	c	NOUN
ejpam-865	102	48	}	}	PUNCT
ejpam-865	102	49	,	,	PUNCT
ejpam-865	102	50	{	{	PUNCT
ejpam-865	102	51	a	a	PRON
ejpam-865	102	52	,	,	PUNCT
ejpam-865	102	53	b	b	NOUN
ejpam-865	102	54	,	,	PUNCT
ejpam-865	102	55	c	c	NOUN
ejpam-865	102	56	}	}	PUNCT
ejpam-865	102	57	}	}	PUNCT
ejpam-865	102	58	.	.	PUNCT
ejpam-865	103	1	let	let	VERB
ejpam-865	103	2	a	a	DET
ejpam-865	103	3	function	function	NOUN
ejpam-865	103	4	f	f	NOUN
ejpam-865	103	5	:	:	PUNCT
ejpam-865	103	6	(	(	PUNCT
ejpam-865	103	7	x	x	X
ejpam-865	103	8	,	,	PUNCT
ejpam-865	103	9	τ)→	τ)→	PROPN
ejpam-865	103	10	(	(	PUNCT
ejpam-865	103	11	x	x	X
ejpam-865	103	12	,	,	PUNCT
ejpam-865	103	13	σ	σ	PROPN
ejpam-865	103	14	)	)	PUNCT
ejpam-865	103	15	be	be	AUX
ejpam-865	103	16	defined	define	VERB
ejpam-865	103	17	by	by	ADP
ejpam-865	103	18	f	f	PROPN
ejpam-865	103	19	(	(	PUNCT
ejpam-865	103	20	a	a	X
ejpam-865	103	21	)	)	PUNCT
ejpam-865	104	1	=	=	SYM
ejpam-865	104	2	f	f	X
ejpam-865	104	3	(	(	PUNCT
ejpam-865	104	4	b	b	NOUN
ejpam-865	104	5	)	)	PUNCT
ejpam-865	104	6	=	=	SYM
ejpam-865	105	1	f	f	X
ejpam-865	105	2	(	(	PUNCT
ejpam-865	105	3	c	c	NOUN
ejpam-865	105	4	)	)	PUNCT
ejpam-865	105	5	=	=	SYM
ejpam-865	105	6	b	b	PROPN
ejpam-865	105	7	and	and	CCONJ
ejpam-865	105	8	f	f	PROPN
ejpam-865	105	9	(	(	PUNCT
ejpam-865	105	10	d	d	NOUN
ejpam-865	105	11	)	)	PUNCT
ejpam-865	106	1	=	=	SYM
ejpam-865	106	2	c.	c.	NOUN
ejpam-865	106	3	then	then	ADV
ejpam-865	106	4	f	f	PROPN
ejpam-865	106	5	is	be	AUX
ejpam-865	106	6	δs	δs	NOUN
ejpam-865	106	7	-	-	PUNCT
ejpam-865	106	8	irresolute	irresolute	ADJ
ejpam-865	106	9	and	and	CCONJ
ejpam-865	106	10	hence	hence	ADV
ejpam-865	106	11	δα	δα	NOUN
ejpam-865	106	12	-	-	PUNCT
ejpam-865	106	13	irresolute	irresolute	ADJ
ejpam-865	106	14	but	but	CCONJ
ejpam-865	106	15	it	it	PRON
ejpam-865	106	16	is	be	AUX
ejpam-865	106	17	not	not	PART
ejpam-865	106	18	semi	semi	ADV
ejpam-865	106	19	α	α	NOUN
ejpam-865	106	20	-	-	ADJ
ejpam-865	106	21	preirresolute	preirresolute	NOUN
ejpam-865	106	22	.	.	PUNCT
ejpam-865	107	1	theorem	theorem	NOUN
ejpam-865	107	2	1	1	NUM
ejpam-865	107	3	.	.	X
ejpam-865	107	4	for	for	ADP
ejpam-865	107	5	a	a	DET
ejpam-865	107	6	function	function	NOUN
ejpam-865	107	7	f	f	NOUN
ejpam-865	107	8	:	:	PUNCT
ejpam-865	107	9	(	(	PUNCT
ejpam-865	107	10	x	x	X
ejpam-865	107	11	,	,	PUNCT
ejpam-865	107	12	τ)→	τ)→	PROPN
ejpam-865	107	13	(	(	PUNCT
ejpam-865	107	14	y	y	PROPN
ejpam-865	107	15	,	,	PUNCT
ejpam-865	107	16	σ	σ	PROPN
ejpam-865	107	17	)	)	PUNCT
ejpam-865	107	18	,	,	PUNCT
ejpam-865	107	19	the	the	DET
ejpam-865	107	20	following	follow	VERB
ejpam-865	107	21	are	be	AUX
ejpam-865	107	22	equivalent	equivalent	ADJ
ejpam-865	107	23	:	:	PUNCT
ejpam-865	107	24	(	(	PUNCT
ejpam-865	107	25	a	a	X
ejpam-865	107	26	)	)	PUNCT
ejpam-865	107	27	f	f	PROPN
ejpam-865	107	28	is	be	AUX
ejpam-865	107	29	δα	δα	NOUN
ejpam-865	107	30	-	-	PUNCT
ejpam-865	107	31	irresolute	irresolute	ADJ
ejpam-865	107	32	;	;	PUNCT
ejpam-865	107	33	(	(	PUNCT
ejpam-865	107	34	b	b	X
ejpam-865	107	35	)	)	PUNCT
ejpam-865	107	36	f	f	NOUN
ejpam-865	107	37	:	:	PUNCT
ejpam-865	107	38	(	(	PUNCT
ejpam-865	107	39	x	x	X
ejpam-865	107	40	,	,	PUNCT
ejpam-865	107	41	τ)→	τ)→	PROPN
ejpam-865	107	42	(	(	PUNCT
ejpam-865	107	43	y	y	PROPN
ejpam-865	107	44	,	,	PUNCT
ejpam-865	107	45	σα	σα	PROPN
ejpam-865	107	46	)	)	PUNCT
ejpam-865	107	47	is	be	AUX
ejpam-865	107	48	δ	δ	PROPN
ejpam-865	107	49	-	-	PUNCT
ejpam-865	107	50	semi	semi	ADV
ejpam-865	107	51	-	-	ADJ
ejpam-865	107	52	continuous	continuous	ADJ
ejpam-865	107	53	;	;	PUNCT
ejpam-865	107	54	(	(	PUNCT
ejpam-865	107	55	c	c	X
ejpam-865	107	56	)	)	PUNCT
ejpam-865	107	57	for	for	ADP
ejpam-865	107	58	each	each	DET
ejpam-865	107	59	x	x	SYM
ejpam-865	107	60	∈	∈	PROPN
ejpam-865	107	61	x	x	X
ejpam-865	107	62	and	and	CCONJ
ejpam-865	107	63	each	each	DET
ejpam-865	107	64	α	α	NOUN
ejpam-865	107	65	-	-	ADJ
ejpam-865	107	66	open	open	ADJ
ejpam-865	107	67	set	set	NOUN
ejpam-865	107	68	v	v	NOUN
ejpam-865	107	69	of	of	ADP
ejpam-865	107	70	y	y	PROPN
ejpam-865	107	71	containing	contain	VERB
ejpam-865	107	72	f	f	PROPN
ejpam-865	107	73	(	(	PUNCT
ejpam-865	107	74	x	x	NOUN
ejpam-865	107	75	)	)	PUNCT
ejpam-865	107	76	,	,	PUNCT
ejpam-865	107	77	there	there	PRON
ejpam-865	107	78	exists	exist	VERB
ejpam-865	107	79	a	a	DET
ejpam-865	107	80	δ	δ	NOUN
ejpam-865	107	81	-	-	PUNCT
ejpam-865	107	82	semiopen	semiopen	VERB
ejpam-865	107	83	set	set	VERB
ejpam-865	107	84	u	u	NOUN
ejpam-865	107	85	of	of	ADP
ejpam-865	107	86	x	x	PUNCT
ejpam-865	107	87	containing	contain	VERB
ejpam-865	107	88	x	x	PUNCT
ejpam-865	107	89	such	such	ADJ
ejpam-865	107	90	that	that	SCONJ
ejpam-865	107	91	f	f	PROPN
ejpam-865	107	92	(	(	PUNCT
ejpam-865	107	93	u)⊂	u)⊂	NOUN
ejpam-865	107	94	v	v	VERB
ejpam-865	107	95	;	;	PUNCT
ejpam-865	107	96	(	(	PUNCT
ejpam-865	107	97	d	d	X
ejpam-865	107	98	)	)	PUNCT
ejpam-865	107	99	f	f	PROPN
ejpam-865	107	100	−1(v	−1(v	PROPN
ejpam-865	107	101	)	)	PUNCT
ejpam-865	108	1	⊂	⊂	PROPN
ejpam-865	108	2	cl(intδ	cl(intδ	PROPN
ejpam-865	108	3	(	(	PUNCT
ejpam-865	108	4	f	f	PROPN
ejpam-865	108	5	−1(v	−1(v	PROPN
ejpam-865	108	6	)	)	PUNCT
ejpam-865	108	7	)	)	PUNCT
ejpam-865	108	8	)	)	PUNCT
ejpam-865	109	1	for	for	ADP
ejpam-865	109	2	every	every	DET
ejpam-865	109	3	α	α	NOUN
ejpam-865	109	4	-	-	ADJ
ejpam-865	109	5	open	open	ADJ
ejpam-865	109	6	set	set	NOUN
ejpam-865	109	7	v	v	NOUN
ejpam-865	109	8	of	of	ADP
ejpam-865	109	9	y	y	PROPN
ejpam-865	109	10	;	;	PUNCT
ejpam-865	109	11	(	(	PUNCT
ejpam-865	109	12	e	e	X
ejpam-865	109	13	)	)	PUNCT
ejpam-865	109	14	f	f	PROPN
ejpam-865	109	15	−1(f	−1(f	PROPN
ejpam-865	109	16	)	)	PUNCT
ejpam-865	109	17	is	be	AUX
ejpam-865	109	18	δ	δ	PROPN
ejpam-865	109	19	-	-	PUNCT
ejpam-865	109	20	semiclosed	semiclose	VERB
ejpam-865	109	21	in	in	ADP
ejpam-865	109	22	x	x	PUNCT
ejpam-865	109	23	for	for	ADP
ejpam-865	109	24	every	every	DET
ejpam-865	109	25	α	α	PRON
ejpam-865	109	26	-	-	ADJ
ejpam-865	109	27	closed	closed	ADJ
ejpam-865	109	28	set	set	ADJ
ejpam-865	109	29	f	f	PROPN
ejpam-865	109	30	of	of	ADP
ejpam-865	109	31	y	y	PROPN
ejpam-865	109	32	;	;	PUNCT
ejpam-865	109	33	(	(	PUNCT
ejpam-865	109	34	f	f	X
ejpam-865	109	35	)	)	PUNCT
ejpam-865	109	36	int(clδ	int(clδ	NOUN
ejpam-865	109	37	(	(	PUNCT
ejpam-865	109	38	f	f	PROPN
ejpam-865	109	39	−1(b	−1(b	NOUN
ejpam-865	109	40	)	)	PUNCT
ejpam-865	109	41	)	)	PUNCT
ejpam-865	109	42	)	)	PUNCT
ejpam-865	110	1	⊂	⊂	PROPN
ejpam-865	110	2	f	f	PROPN
ejpam-865	110	3	−1(αcl(b	−1(αcl(b	PROPN
ejpam-865	110	4	)	)	PUNCT
ejpam-865	110	5	)	)	PUNCT
ejpam-865	111	1	for	for	ADP
ejpam-865	111	2	every	every	DET
ejpam-865	111	3	subset	subset	NOUN
ejpam-865	111	4	b	b	PROPN
ejpam-865	111	5	of	of	ADP
ejpam-865	111	6	y	y	PROPN
ejpam-865	111	7	;	;	PUNCT
ejpam-865	111	8	(	(	PUNCT
ejpam-865	111	9	g	g	NOUN
ejpam-865	111	10	)	)	PUNCT
ejpam-865	111	11	f	f	NOUN
ejpam-865	111	12	(	(	PUNCT
ejpam-865	111	13	int(clδ(a)))⊂	int(clδ(a)))⊂	NOUN
ejpam-865	111	14	αcl	αcl	NOUN
ejpam-865	111	15	(	(	PUNCT
ejpam-865	111	16	f	f	X
ejpam-865	111	17	(	(	PUNCT
ejpam-865	111	18	a	a	NOUN
ejpam-865	111	19	)	)	PUNCT
ejpam-865	111	20	)	)	PUNCT
ejpam-865	111	21	for	for	ADP
ejpam-865	111	22	every	every	DET
ejpam-865	111	23	subset	subset	NOUN
ejpam-865	111	24	a	a	PRON
ejpam-865	111	25	of	of	ADP
ejpam-865	111	26	x	x	X
ejpam-865	111	27	.	.	PUNCT
ejpam-865	112	1	y.	y.	PROPN
ejpam-865	112	2	beceren	beceren	PROPN
ejpam-865	112	3	,	,	PUNCT
ejpam-865	112	4	t.	t.	PROPN
ejpam-865	112	5	noiri	noiri	PROPN
ejpam-865	112	6	/	/	SYM
ejpam-865	112	7	eur	eur	PROPN
ejpam-865	112	8	.	.	PUNCT
ejpam-865	113	1	j.	j.	PROPN
ejpam-865	113	2	pure	pure	PROPN
ejpam-865	113	3	appl	appl	PROPN
ejpam-865	113	4	.	.	PROPN
ejpam-865	113	5	math	math	PROPN
ejpam-865	113	6	,	,	PUNCT
ejpam-865	113	7	4	4	NUM
ejpam-865	113	8	(	(	PUNCT
ejpam-865	113	9	2011	2011	NUM
ejpam-865	113	10	)	)	PUNCT
ejpam-865	113	11	,	,	PUNCT
ejpam-865	113	12	361	361	NUM
ejpam-865	113	13	-	-	SYM
ejpam-865	113	14	369	369	NUM
ejpam-865	113	15	364	364	NUM
ejpam-865	113	16	proof	proof	NOUN
ejpam-865	113	17	.	.	PUNCT
ejpam-865	114	1	(	(	PUNCT
ejpam-865	114	2	a	a	X
ejpam-865	114	3	)	)	PUNCT
ejpam-865	114	4	⇒	⇒	NOUN
ejpam-865	114	5	(	(	PUNCT
ejpam-865	114	6	b	b	NOUN
ejpam-865	114	7	)	)	PUNCT
ejpam-865	114	8	.	.	PUNCT
ejpam-865	115	1	let	let	VERB
ejpam-865	115	2	x	x	PUNCT
ejpam-865	115	3	∈	∈	PROPN
ejpam-865	115	4	x	x	X
ejpam-865	115	5	and	and	CCONJ
ejpam-865	115	6	v	v	X
ejpam-865	115	7	be	be	AUX
ejpam-865	115	8	any	any	DET
ejpam-865	115	9	α	α	NOUN
ejpam-865	115	10	-	-	ADJ
ejpam-865	115	11	open	open	ADJ
ejpam-865	115	12	set	set	NOUN
ejpam-865	115	13	of	of	ADP
ejpam-865	115	14	y	y	PROPN
ejpam-865	115	15	containing	contain	VERB
ejpam-865	115	16	f	f	PROPN
ejpam-865	115	17	(	(	PUNCT
ejpam-865	115	18	x	x	NOUN
ejpam-865	115	19	)	)	PUNCT
ejpam-865	115	20	.	.	PUNCT
ejpam-865	116	1	by	by	ADP
ejpam-865	116	2	definition	definition	NOUN
ejpam-865	116	3	3	3	NUM
ejpam-865	116	4	,	,	PUNCT
ejpam-865	116	5	f	f	PROPN
ejpam-865	116	6	−1(v	−1(v	PROPN
ejpam-865	116	7	)	)	PUNCT
ejpam-865	116	8	εδso(x	εδso(x	NOUN
ejpam-865	116	9	)	)	PUNCT
ejpam-865	116	10	containing	contain	VERB
ejpam-865	116	11	x	x	PUNCT
ejpam-865	116	12	and	and	CCONJ
ejpam-865	116	13	hence	hence	ADV
ejpam-865	116	14	f	f	X
ejpam-865	116	15	:	:	PUNCT
ejpam-865	116	16	(	(	PUNCT
ejpam-865	116	17	x	x	X
ejpam-865	116	18	,	,	PUNCT
ejpam-865	116	19	τ)→	τ)→	PROPN
ejpam-865	116	20	(	(	PUNCT
ejpam-865	116	21	y	y	PROPN
ejpam-865	116	22	,	,	PUNCT
ejpam-865	116	23	σα	σα	PROPN
ejpam-865	116	24	)	)	PUNCT
ejpam-865	116	25	is	be	AUX
ejpam-865	116	26	δ	δ	PROPN
ejpam-865	116	27	-	-	PUNCT
ejpam-865	116	28	semi	semi	ADV
ejpam-865	116	29	-	-	ADJ
ejpam-865	116	30	continuous	continuous	ADJ
ejpam-865	116	31	.	.	PUNCT
ejpam-865	117	1	(	(	PUNCT
ejpam-865	117	2	b	b	X
ejpam-865	117	3	)	)	PUNCT
ejpam-865	117	4	⇒	⇒	NOUN
ejpam-865	117	5	(	(	PUNCT
ejpam-865	117	6	c	c	NOUN
ejpam-865	117	7	)	)	PUNCT
ejpam-865	117	8	.	.	PUNCT
ejpam-865	118	1	let	let	VERB
ejpam-865	118	2	x	x	PUNCT
ejpam-865	118	3	∈	∈	PROPN
ejpam-865	118	4	x	x	X
ejpam-865	118	5	and	and	CCONJ
ejpam-865	118	6	v	v	X
ejpam-865	118	7	be	be	AUX
ejpam-865	118	8	any	any	DET
ejpam-865	118	9	α	α	NOUN
ejpam-865	118	10	-	-	ADJ
ejpam-865	118	11	open	open	ADJ
ejpam-865	118	12	set	set	NOUN
ejpam-865	118	13	of	of	ADP
ejpam-865	118	14	y	y	PROPN
ejpam-865	118	15	containing	contain	VERB
ejpam-865	118	16	f	f	PROPN
ejpam-865	118	17	(	(	PUNCT
ejpam-865	118	18	x	x	NOUN
ejpam-865	118	19	)	)	PUNCT
ejpam-865	118	20	.	.	PUNCT
ejpam-865	119	1	set	set	VERB
ejpam-865	119	2	u	u	NOUN
ejpam-865	119	3	=	=	PUNCT
ejpam-865	119	4	f	f	PROPN
ejpam-865	119	5	−1(v	−1(v	PROPN
ejpam-865	119	6	)	)	PUNCT
ejpam-865	119	7	,	,	PUNCT
ejpam-865	119	8	then	then	ADV
ejpam-865	119	9	by	by	ADP
ejpam-865	119	10	(	(	PUNCT
ejpam-865	119	11	b	b	NOUN
ejpam-865	119	12	)	)	PUNCT
ejpam-865	119	13	,	,	PUNCT
ejpam-865	119	14	u	u	PROPN
ejpam-865	119	15	is	be	AUX
ejpam-865	119	16	a	a	DET
ejpam-865	119	17	δ	δ	NOUN
ejpam-865	119	18	-	-	PUNCT
ejpam-865	119	19	semiopen	semiopen	ADJ
ejpam-865	119	20	set	set	NOUN
ejpam-865	119	21	of	of	ADP
ejpam-865	119	22	x	x	PUNCT
ejpam-865	119	23	containing	contain	VERB
ejpam-865	119	24	x	x	PROPN
ejpam-865	119	25	and	and	CCONJ
ejpam-865	119	26	f	f	PROPN
ejpam-865	119	27	(	(	PUNCT
ejpam-865	119	28	u)⊂	u)⊂	NOUN
ejpam-865	119	29	v	v	NOUN
ejpam-865	119	30	.	.	PUNCT
ejpam-865	120	1	(	(	PUNCT
ejpam-865	120	2	c	c	X
ejpam-865	120	3	)	)	PUNCT
ejpam-865	120	4	⇒	⇒	NOUN
ejpam-865	120	5	(	(	PUNCT
ejpam-865	120	6	d	d	NOUN
ejpam-865	120	7	)	)	PUNCT
ejpam-865	120	8	.	.	PUNCT
ejpam-865	121	1	let	let	VERB
ejpam-865	121	2	v	v	PART
ejpam-865	121	3	be	be	AUX
ejpam-865	121	4	any	any	DET
ejpam-865	121	5	α	α	NOUN
ejpam-865	121	6	-	-	ADJ
ejpam-865	121	7	open	open	ADJ
ejpam-865	121	8	subset	subset	NOUN
ejpam-865	121	9	of	of	ADP
ejpam-865	121	10	y	y	PROPN
ejpam-865	121	11	and	and	CCONJ
ejpam-865	121	12	x	x	SYM
ejpam-865	121	13	∈	∈	PROPN
ejpam-865	121	14	f	f	PROPN
ejpam-865	121	15	−1(v	−1(v	NOUN
ejpam-865	121	16	)	)	PUNCT
ejpam-865	121	17	.	.	PUNCT
ejpam-865	122	1	by	by	ADP
ejpam-865	122	2	(	(	PUNCT
ejpam-865	122	3	c	c	NOUN
ejpam-865	122	4	)	)	PUNCT
ejpam-865	122	5	,	,	PUNCT
ejpam-865	122	6	there	there	PRON
ejpam-865	122	7	exists	exist	VERB
ejpam-865	122	8	a	a	DET
ejpam-865	122	9	δsemiopen	δsemiopen	ADJ
ejpam-865	122	10	set	set	VERB
ejpam-865	122	11	u	u	NOUN
ejpam-865	122	12	of	of	ADP
ejpam-865	122	13	x	x	PUNCT
ejpam-865	122	14	containing	contain	VERB
ejpam-865	122	15	x	x	PUNCT
ejpam-865	122	16	such	such	ADJ
ejpam-865	122	17	that	that	SCONJ
ejpam-865	122	18	f	f	PROPN
ejpam-865	122	19	(	(	PUNCT
ejpam-865	122	20	u)⊂	u)⊂	NOUN
ejpam-865	122	21	v	v	NOUN
ejpam-865	122	22	.	.	PUNCT
ejpam-865	123	1	therefore	therefore	ADV
ejpam-865	123	2	,	,	PUNCT
ejpam-865	123	3	we	we	PRON
ejpam-865	123	4	obtain	obtain	VERB
ejpam-865	123	5	x	x	PUNCT
ejpam-865	123	6	∈	∈	X
ejpam-865	123	7	u	u	NOUN
ejpam-865	123	8	⊂	⊂	X
ejpam-865	123	9	cl(intδ(u))⊂	cl(intδ(u))⊂	X
ejpam-865	124	1	cl(intδ	cl(intδ	ADV
ejpam-865	124	2	(	(	PUNCT
ejpam-865	124	3	f	f	PROPN
ejpam-865	124	4	−1(v	−1(v	PROPN
ejpam-865	124	5	)	)	PUNCT
ejpam-865	124	6	)	)	PUNCT
ejpam-865	124	7	)	)	PUNCT
ejpam-865	125	1	and	and	CCONJ
ejpam-865	125	2	hence	hence	ADV
ejpam-865	125	3	f	f	PROPN
ejpam-865	125	4	−1(v	−1(v	PROPN
ejpam-865	125	5	)	)	PUNCT
ejpam-865	126	1	⊂	⊂	PROPN
ejpam-865	126	2	cl(intδ	cl(intδ	PROPN
ejpam-865	126	3	(	(	PUNCT
ejpam-865	126	4	f	f	PROPN
ejpam-865	126	5	−1(v	−1(v	PROPN
ejpam-865	126	6	)	)	PUNCT
ejpam-865	126	7	)	)	PUNCT
ejpam-865	126	8	)	)	PUNCT
ejpam-865	126	9	.	.	PUNCT
ejpam-865	127	1	(	(	PUNCT
ejpam-865	127	2	d	d	X
ejpam-865	127	3	)	)	PUNCT
ejpam-865	127	4	⇒	⇒	NOUN
ejpam-865	127	5	(	(	PUNCT
ejpam-865	127	6	e	e	NOUN
ejpam-865	127	7	)	)	PUNCT
ejpam-865	127	8	.	.	PUNCT
ejpam-865	128	1	let	let	VERB
ejpam-865	128	2	f	f	PRON
ejpam-865	128	3	be	be	AUX
ejpam-865	128	4	any	any	DET
ejpam-865	128	5	α	α	NOUN
ejpam-865	128	6	-	-	PUNCT
ejpam-865	128	7	closed	closed	ADJ
ejpam-865	128	8	subset	subset	NOUN
ejpam-865	128	9	of	of	ADP
ejpam-865	128	10	y	y	PROPN
ejpam-865	128	11	.	.	PUNCT
ejpam-865	129	1	set	set	VERB
ejpam-865	129	2	v	v	NUM
ejpam-865	129	3	=	=	SYM
ejpam-865	129	4	y	y	PROPN
ejpam-865	129	5	−	−	PROPN
ejpam-865	130	1	f	f	PROPN
ejpam-865	130	2	,	,	PUNCT
ejpam-865	130	3	then	then	ADV
ejpam-865	130	4	v	v	NOUN
ejpam-865	130	5	is	be	AUX
ejpam-865	130	6	α	α	NOUN
ejpam-865	130	7	-	-	NOUN
ejpam-865	130	8	open	open	ADJ
ejpam-865	130	9	in	in	ADP
ejpam-865	130	10	y	y	PROPN
ejpam-865	130	11	.	.	PUNCT
ejpam-865	131	1	by	by	ADP
ejpam-865	131	2	(	(	PUNCT
ejpam-865	131	3	d	d	NOUN
ejpam-865	131	4	)	)	PUNCT
ejpam-865	131	5	,	,	PUNCT
ejpam-865	131	6	we	we	PRON
ejpam-865	131	7	have	have	VERB
ejpam-865	131	8	f	f	PROPN
ejpam-865	131	9	−1(v	−1(v	PROPN
ejpam-865	131	10	)	)	PUNCT
ejpam-865	132	1	⊂	⊂	PROPN
ejpam-865	132	2	cl(intδ	cl(intδ	PROPN
ejpam-865	132	3	(	(	PUNCT
ejpam-865	132	4	f	f	PROPN
ejpam-865	132	5	−1(v	−1(v	PROPN
ejpam-865	132	6	)	)	PUNCT
ejpam-865	132	7	)	)	PUNCT
ejpam-865	132	8	)	)	PUNCT
ejpam-865	132	9	and	and	CCONJ
ejpam-865	132	10	hence	hence	ADV
ejpam-865	132	11	f	f	PROPN
ejpam-865	132	12	−1(f	−1(f	PROPN
ejpam-865	132	13	)	)	PUNCT
ejpam-865	132	14	=	=	SYM
ejpam-865	132	15	x−	x−	PROPN
ejpam-865	132	16	(	(	PUNCT
ejpam-865	132	17	f	f	PROPN
ejpam-865	132	18	−1(y−f	−1(y−f	PROPN
ejpam-865	132	19	)	)	PUNCT
ejpam-865	132	20	)	)	PUNCT
ejpam-865	133	1	=	=	PUNCT
ejpam-865	133	2	x−	x−	PROPN
ejpam-865	133	3	f	f	PROPN
ejpam-865	133	4	−1(v	−1(v	PROPN
ejpam-865	133	5	)	)	PUNCT
ejpam-865	133	6	is	be	AUX
ejpam-865	133	7	δ	δ	PROPN
ejpam-865	133	8	-	-	PUNCT
ejpam-865	133	9	semiclosed	semiclose	VERB
ejpam-865	133	10	in	in	ADP
ejpam-865	133	11	x	x	X
ejpam-865	133	12	.	.	PUNCT
ejpam-865	134	1	(	(	PUNCT
ejpam-865	134	2	e	e	NOUN
ejpam-865	134	3	)	)	PUNCT
ejpam-865	134	4	⇒	⇒	NOUN
ejpam-865	134	5	(	(	PUNCT
ejpam-865	134	6	f	f	X
ejpam-865	134	7	)	)	PUNCT
ejpam-865	134	8	.	.	PUNCT
ejpam-865	135	1	let	let	VERB
ejpam-865	135	2	b	b	X
ejpam-865	135	3	be	be	AUX
ejpam-865	135	4	any	any	DET
ejpam-865	135	5	subset	subset	NOUN
ejpam-865	135	6	of	of	ADP
ejpam-865	135	7	y	y	PROPN
ejpam-865	135	8	.	.	PUNCT
ejpam-865	136	1	since	since	SCONJ
ejpam-865	136	2	αcl(b	αcl(b	PROPN
ejpam-865	136	3	)	)	PUNCT
ejpam-865	136	4	is	be	AUX
ejpam-865	136	5	α	α	NOUN
ejpam-865	136	6	-	-	VERB
ejpam-865	136	7	closed	closed	ADJ
ejpam-865	136	8	in	in	ADP
ejpam-865	136	9	y	y	PROPN
ejpam-865	136	10	,	,	PUNCT
ejpam-865	136	11	f	f	PROPN
ejpam-865	136	12	−1(αcl(b	−1(αcl(b	PROPN
ejpam-865	136	13	)	)	PUNCT
ejpam-865	136	14	)	)	PUNCT
ejpam-865	137	1	is	be	AUX
ejpam-865	137	2	δ	δ	PROPN
ejpam-865	137	3	-	-	PUNCT
ejpam-865	137	4	semiclosed	semiclose	VERB
ejpam-865	137	5	in	in	ADP
ejpam-865	137	6	x	x	PUNCT
ejpam-865	137	7	and	and	CCONJ
ejpam-865	137	8	hence	hence	ADV
ejpam-865	137	9	int(clδ	int(clδ	NOUN
ejpam-865	137	10	(	(	PUNCT
ejpam-865	137	11	f	f	PROPN
ejpam-865	137	12	−1(αcl(b	−1(αcl(b	PROPN
ejpam-865	137	13	)	)	PUNCT
ejpam-865	137	14	)	)	PUNCT
ejpam-865	137	15	)	)	PUNCT
ejpam-865	137	16	)	)	PUNCT
ejpam-865	138	1	⊂	⊂	PROPN
ejpam-865	138	2	f	f	X
ejpam-865	138	3	−1(αcl(b	−1(αcl(b	PROPN
ejpam-865	138	4	)	)	PUNCT
ejpam-865	138	5	)	)	PUNCT
ejpam-865	138	6	.	.	PUNCT
ejpam-865	139	1	thus	thus	ADV
ejpam-865	139	2	we	we	PRON
ejpam-865	139	3	have	have	VERB
ejpam-865	139	4	int(clδ	int(clδ	NOUN
ejpam-865	139	5	(	(	PUNCT
ejpam-865	139	6	f	f	X
ejpam-865	139	7	−1(b)))⊂	−1(b)))⊂	PROPN
ejpam-865	139	8	f	f	PROPN
ejpam-865	139	9	−1(αcl(b	−1(αcl(b	PROPN
ejpam-865	139	10	)	)	PUNCT
ejpam-865	139	11	)	)	PUNCT
ejpam-865	139	12	.	.	PUNCT
ejpam-865	140	1	(	(	PUNCT
ejpam-865	140	2	f)⇒	f)⇒	PROPN
ejpam-865	140	3	(	(	PUNCT
ejpam-865	140	4	g	g	NOUN
ejpam-865	140	5	)	)	PUNCT
ejpam-865	140	6	.	.	PUNCT
ejpam-865	141	1	let	let	VERB
ejpam-865	141	2	a	a	DET
ejpam-865	141	3	be	be	AUX
ejpam-865	141	4	any	any	DET
ejpam-865	141	5	subset	subset	NOUN
ejpam-865	141	6	of	of	ADP
ejpam-865	141	7	x	x	X
ejpam-865	141	8	.	.	PUNCT
ejpam-865	142	1	by	by	ADP
ejpam-865	142	2	(	(	PUNCT
ejpam-865	142	3	f	f	PROPN
ejpam-865	142	4	)	)	PUNCT
ejpam-865	142	5	,	,	PUNCT
ejpam-865	142	6	we	we	PRON
ejpam-865	142	7	obtain	obtain	VERB
ejpam-865	142	8	int(clδ(a))⊂	int(clδ(a))⊂	NUM
ejpam-865	142	9	int(clδ	int(clδ	NOUN
ejpam-865	142	10	(	(	PUNCT
ejpam-865	142	11	f	f	PROPN
ejpam-865	142	12	−1	−1	PROPN
ejpam-865	142	13	(	(	PUNCT
ejpam-865	142	14	f	f	PROPN
ejpam-865	142	15	(	(	PUNCT
ejpam-865	142	16	a))))⊂	a))))⊂	PROPN
ejpam-865	142	17	f	f	PROPN
ejpam-865	142	18	−1(αcl	−1(αcl	PROPN
ejpam-865	142	19	(	(	PUNCT
ejpam-865	142	20	f	f	PROPN
ejpam-865	142	21	(	(	PUNCT
ejpam-865	142	22	a	a	NOUN
ejpam-865	142	23	)	)	PUNCT
ejpam-865	142	24	)	)	PUNCT
ejpam-865	142	25	)	)	PUNCT
ejpam-865	142	26	and	and	CCONJ
ejpam-865	142	27	hence	hence	ADV
ejpam-865	142	28	f	f	PROPN
ejpam-865	142	29	(	(	PUNCT
ejpam-865	142	30	int(clδ(a)))⊂	int(clδ(a)))⊂	NOUN
ejpam-865	142	31	αcl	αcl	NOUN
ejpam-865	142	32	(	(	PUNCT
ejpam-865	142	33	f	f	X
ejpam-865	142	34	(	(	PUNCT
ejpam-865	142	35	a	a	NOUN
ejpam-865	142	36	)	)	PUNCT
ejpam-865	142	37	)	)	PUNCT
ejpam-865	142	38	.	.	PUNCT
ejpam-865	143	1	(	(	PUNCT
ejpam-865	143	2	g	g	NOUN
ejpam-865	143	3	)	)	PUNCT
ejpam-865	143	4	⇒	⇒	NOUN
ejpam-865	143	5	(	(	PUNCT
ejpam-865	143	6	a	a	X
ejpam-865	143	7	)	)	PUNCT
ejpam-865	143	8	.	.	PUNCT
ejpam-865	144	1	let	let	VERB
ejpam-865	144	2	v	v	PART
ejpam-865	144	3	be	be	AUX
ejpam-865	144	4	any	any	DET
ejpam-865	144	5	α	α	NOUN
ejpam-865	144	6	-	-	ADJ
ejpam-865	144	7	open	open	ADJ
ejpam-865	144	8	subset	subset	NOUN
ejpam-865	144	9	of	of	ADP
ejpam-865	144	10	y	y	PROPN
ejpam-865	144	11	.	.	PUNCT
ejpam-865	145	1	since	since	SCONJ
ejpam-865	145	2	f	f	PROPN
ejpam-865	145	3	−1(y	−1(y	DET
ejpam-865	145	4	−	−	PROPN
ejpam-865	145	5	v	v	NOUN
ejpam-865	145	6	)	)	PUNCT
ejpam-865	145	7	=	=	PUNCT
ejpam-865	146	1	x	x	PUNCT
ejpam-865	146	2	−	−	PROPN
ejpam-865	146	3	f	f	PROPN
ejpam-865	146	4	−1(v	−1(v	PROPN
ejpam-865	146	5	)	)	PUNCT
ejpam-865	146	6	is	be	AUX
ejpam-865	146	7	a	a	DET
ejpam-865	146	8	subset	subset	NOUN
ejpam-865	146	9	of	of	ADP
ejpam-865	146	10	x	x	X
ejpam-865	146	11	and	and	CCONJ
ejpam-865	146	12	by	by	ADP
ejpam-865	146	13	(	(	PUNCT
ejpam-865	146	14	g	g	NOUN
ejpam-865	146	15	)	)	PUNCT
ejpam-865	146	16	,	,	PUNCT
ejpam-865	146	17	we	we	PRON
ejpam-865	146	18	obtain	obtain	VERB
ejpam-865	146	19	f	f	PROPN
ejpam-865	146	20	(	(	PUNCT
ejpam-865	146	21	int(clδ	int(clδ	PROPN
ejpam-865	146	22	(	(	PUNCT
ejpam-865	146	23	f	f	PROPN
ejpam-865	146	24	−1(y	−1(y	ADJ
ejpam-865	146	25	−	−	PROPN
ejpam-865	146	26	v	v	NOUN
ejpam-865	146	27	)	)	PUNCT
ejpam-865	146	28	)	)	PUNCT
ejpam-865	146	29	)	)	PUNCT
ejpam-865	146	30	)	)	PUNCT
ejpam-865	147	1	⊂	⊂	PROPN
ejpam-865	147	2	αcl	αcl	NOUN
ejpam-865	147	3	(	(	PUNCT
ejpam-865	147	4	f	f	PROPN
ejpam-865	147	5	(	(	PUNCT
ejpam-865	147	6	f	f	PROPN
ejpam-865	147	7	−1(y	−1(y	X
ejpam-865	147	8	−	−	PROPN
ejpam-865	147	9	v	v	NOUN
ejpam-865	147	10	)	)	PUNCT
ejpam-865	147	11	)	)	PUNCT
ejpam-865	147	12	)	)	PUNCT
ejpam-865	148	1	⊂	⊂	PROPN
ejpam-865	148	2	αcl(y	αcl(y	NUM
ejpam-865	148	3	−	−	PROPN
ejpam-865	148	4	v	v	NOUN
ejpam-865	148	5	)	)	PUNCT
ejpam-865	148	6	=	=	SYM
ejpam-865	148	7	y	y	PROPN
ejpam-865	148	8	−αint(v	−αint(v	NOUN
ejpam-865	148	9	)	)	PUNCT
ejpam-865	149	1	=	=	PUNCT
ejpam-865	150	1	y	y	PROPN
ejpam-865	150	2	−	−	PROPN
ejpam-865	150	3	v	v	NOUN
ejpam-865	150	4	and	and	CCONJ
ejpam-865	150	5	hence	hence	ADV
ejpam-865	150	6	x	x	NOUN
ejpam-865	150	7	−	−	NOUN
ejpam-865	151	1	cl(intδ	cl(intδ	ADV
ejpam-865	151	2	(	(	PUNCT
ejpam-865	151	3	f	f	PROPN
ejpam-865	151	4	−1(v	−1(v	PROPN
ejpam-865	151	5	)	)	PUNCT
ejpam-865	151	6	)	)	PUNCT
ejpam-865	151	7	)	)	PUNCT
ejpam-865	152	1	=	=	X
ejpam-865	152	2	int(clδ(x	int(clδ(x	ADP
ejpam-865	152	3	−	−	PROPN
ejpam-865	152	4	f	f	PROPN
ejpam-865	152	5	−1(v	−1(v	PROPN
ejpam-865	152	6	)	)	PUNCT
ejpam-865	152	7	)	)	PUNCT
ejpam-865	152	8	)	)	PUNCT
ejpam-865	153	1	=	=	SYM
ejpam-865	153	2	int(clδ	int(clδ	NOUN
ejpam-865	153	3	(	(	PUNCT
ejpam-865	153	4	f	f	PROPN
ejpam-865	153	5	−1(y	−1(y	ADP
ejpam-865	153	6	−	−	PROPN
ejpam-865	153	7	v	v	NOUN
ejpam-865	153	8	)	)	PUNCT
ejpam-865	153	9	)	)	PUNCT
ejpam-865	153	10	)	)	PUNCT
ejpam-865	154	1	⊂	⊂	PROPN
ejpam-865	154	2	f	f	X
ejpam-865	154	3	−1	−1	PROPN
ejpam-865	154	4	(	(	PUNCT
ejpam-865	154	5	f	f	PROPN
ejpam-865	154	6	(	(	PUNCT
ejpam-865	154	7	int(clδ	int(clδ	PROPN
ejpam-865	154	8	(	(	PUNCT
ejpam-865	154	9	f	f	PROPN
ejpam-865	154	10	−1(y	−1(y	ADJ
ejpam-865	154	11	−	−	PROPN
ejpam-865	154	12	v	v	NOUN
ejpam-865	154	13	)	)	PUNCT
ejpam-865	154	14	)	)	PUNCT
ejpam-865	154	15	)	)	PUNCT
ejpam-865	154	16	)	)	PUNCT
ejpam-865	154	17	)	)	PUNCT
ejpam-865	155	1	⊂	⊂	PROPN
ejpam-865	155	2	f	f	X
ejpam-865	156	1	−1(y	−1(y	PRON
ejpam-865	156	2	−	−	PROPN
ejpam-865	156	3	v	v	NOUN
ejpam-865	156	4	)	)	PUNCT
ejpam-865	157	1	=	=	NOUN
ejpam-865	157	2	x	x	SYM
ejpam-865	157	3	−	−	PROPN
ejpam-865	157	4	f	f	PROPN
ejpam-865	157	5	−1(v	−1(v	PROPN
ejpam-865	157	6	)	)	PUNCT
ejpam-865	157	7	.	.	PUNCT
ejpam-865	158	1	therefore	therefore	ADV
ejpam-865	158	2	,	,	PUNCT
ejpam-865	158	3	we	we	PRON
ejpam-865	158	4	have	have	VERB
ejpam-865	158	5	f	f	PROPN
ejpam-865	158	6	−1(v	−1(v	PROPN
ejpam-865	158	7	)	)	PUNCT
ejpam-865	159	1	⊂	⊂	PROPN
ejpam-865	159	2	cl(intδ	cl(intδ	PROPN
ejpam-865	159	3	(	(	PUNCT
ejpam-865	159	4	f	f	PROPN
ejpam-865	159	5	−1(v	−1(v	PROPN
ejpam-865	159	6	)	)	PUNCT
ejpam-865	159	7	)	)	PUNCT
ejpam-865	159	8	)	)	PUNCT
ejpam-865	159	9	and	and	CCONJ
ejpam-865	159	10	hence	hence	ADV
ejpam-865	159	11	f	f	PROPN
ejpam-865	159	12	−1(v	−1(v	PROPN
ejpam-865	159	13	)	)	PUNCT
ejpam-865	159	14	is	be	AUX
ejpam-865	159	15	δ	δ	PROPN
ejpam-865	159	16	-	-	PUNCT
ejpam-865	159	17	semiopen	semiopen	ADJ
ejpam-865	159	18	in	in	ADP
ejpam-865	159	19	x	x	X
ejpam-865	159	20	.	.	PUNCT
ejpam-865	160	1	thus	thus	ADV
ejpam-865	160	2	the	the	DET
ejpam-865	160	3	function	function	NOUN
ejpam-865	160	4	f	f	PROPN
ejpam-865	160	5	is	be	AUX
ejpam-865	160	6	δα	δα	NOUN
ejpam-865	160	7	-	-	PUNCT
ejpam-865	160	8	irresolute	irresolute	ADJ
ejpam-865	160	9	.	.	PUNCT
ejpam-865	161	1	now	now	ADV
ejpam-865	161	2	,	,	PUNCT
ejpam-865	161	3	the	the	DET
ejpam-865	161	4	proofs	proof	NOUN
ejpam-865	161	5	of	of	ADP
ejpam-865	161	6	the	the	DET
ejpam-865	161	7	following	follow	VERB
ejpam-865	161	8	two	two	NUM
ejpam-865	161	9	theorems	theorem	NOUN
ejpam-865	161	10	are	be	AUX
ejpam-865	161	11	similar	similar	ADJ
ejpam-865	161	12	to	to	ADP
ejpam-865	161	13	theorem	theorem	VERB
ejpam-865	161	14	1	1	NUM
ejpam-865	161	15	and	and	CCONJ
ejpam-865	161	16	are	be	AUX
ejpam-865	161	17	thus	thus	ADV
ejpam-865	161	18	omitted	omit	VERB
ejpam-865	161	19	.	.	PUNCT
ejpam-865	162	1	theorem	theorem	NOUN
ejpam-865	162	2	2	2	NUM
ejpam-865	162	3	.	.	PUNCT
ejpam-865	163	1	the	the	DET
ejpam-865	163	2	following	follow	VERB
ejpam-865	163	3	are	be	AUX
ejpam-865	163	4	equivalent	equivalent	ADJ
ejpam-865	163	5	for	for	ADP
ejpam-865	163	6	a	a	DET
ejpam-865	163	7	function	function	NOUN
ejpam-865	163	8	f	f	NOUN
ejpam-865	163	9	:	:	PUNCT
ejpam-865	163	10	(	(	PUNCT
ejpam-865	163	11	x	x	X
ejpam-865	163	12	,	,	PUNCT
ejpam-865	163	13	τ)→	τ)→	PROPN
ejpam-865	163	14	(	(	PUNCT
ejpam-865	163	15	y	y	PROPN
ejpam-865	163	16	,	,	PUNCT
ejpam-865	163	17	σ	σ	PROPN
ejpam-865	163	18	):	):	PUNCT
ejpam-865	163	19	(	(	PUNCT
ejpam-865	163	20	a	a	X
ejpam-865	163	21	)	)	PUNCT
ejpam-865	163	22	f	f	PROPN
ejpam-865	163	23	is	be	AUX
ejpam-865	163	24	δp	δp	PRON
ejpam-865	163	25	-	-	PUNCT
ejpam-865	163	26	irresolute	irresolute	ADJ
ejpam-865	163	27	;	;	PUNCT
ejpam-865	163	28	(	(	PUNCT
ejpam-865	163	29	b	b	X
ejpam-865	163	30	)	)	PUNCT
ejpam-865	163	31	for	for	ADP
ejpam-865	163	32	each	each	DET
ejpam-865	163	33	x	x	SYM
ejpam-865	163	34	∈	∈	PROPN
ejpam-865	163	35	x	x	X
ejpam-865	163	36	and	and	CCONJ
ejpam-865	163	37	each	each	DET
ejpam-865	163	38	preopen	preopen	NOUN
ejpam-865	163	39	set	set	VERB
ejpam-865	163	40	v	v	NUM
ejpam-865	163	41	of	of	ADP
ejpam-865	163	42	y	y	PROPN
ejpam-865	163	43	containing	contain	VERB
ejpam-865	163	44	f	f	PROPN
ejpam-865	163	45	(	(	PUNCT
ejpam-865	163	46	x	x	NOUN
ejpam-865	163	47	)	)	PUNCT
ejpam-865	163	48	,	,	PUNCT
ejpam-865	163	49	there	there	PRON
ejpam-865	163	50	exists	exist	VERB
ejpam-865	163	51	a	a	DET
ejpam-865	163	52	δ	δ	NOUN
ejpam-865	163	53	-	-	PUNCT
ejpam-865	163	54	semiopen	semiopen	VERB
ejpam-865	163	55	set	set	VERB
ejpam-865	163	56	u	u	NOUN
ejpam-865	163	57	of	of	ADP
ejpam-865	163	58	x	x	PUNCT
ejpam-865	163	59	containing	contain	VERB
ejpam-865	163	60	x	x	PUNCT
ejpam-865	163	61	such	such	ADJ
ejpam-865	163	62	that	that	SCONJ
ejpam-865	163	63	f	f	PROPN
ejpam-865	163	64	(	(	PUNCT
ejpam-865	163	65	u)⊂	u)⊂	NOUN
ejpam-865	163	66	v	v	ADJ
ejpam-865	163	67	;	;	PUNCT
ejpam-865	163	68	(	(	PUNCT
ejpam-865	163	69	c	c	X
ejpam-865	163	70	)	)	PUNCT
ejpam-865	163	71	f	f	PROPN
ejpam-865	163	72	−1(v	−1(v	PROPN
ejpam-865	163	73	)	)	PUNCT
ejpam-865	164	1	⊂	⊂	PROPN
ejpam-865	164	2	cl(intδ	cl(intδ	PROPN
ejpam-865	164	3	(	(	PUNCT
ejpam-865	164	4	f	f	PROPN
ejpam-865	164	5	−1(v	−1(v	PROPN
ejpam-865	164	6	)	)	PUNCT
ejpam-865	164	7	)	)	PUNCT
ejpam-865	164	8	)	)	PUNCT
ejpam-865	164	9	for	for	ADP
ejpam-865	164	10	every	every	DET
ejpam-865	164	11	preopen	preopen	NOUN
ejpam-865	164	12	set	set	VERB
ejpam-865	164	13	v	v	NOUN
ejpam-865	164	14	of	of	ADP
ejpam-865	164	15	y	y	PROPN
ejpam-865	164	16	;	;	PUNCT
ejpam-865	164	17	(	(	PUNCT
ejpam-865	164	18	d	d	X
ejpam-865	164	19	)	)	PUNCT
ejpam-865	164	20	f	f	PROPN
ejpam-865	164	21	−1(f	−1(f	PROPN
ejpam-865	164	22	)	)	PUNCT
ejpam-865	164	23	is	be	AUX
ejpam-865	164	24	δ	δ	PROPN
ejpam-865	164	25	-	-	PUNCT
ejpam-865	164	26	semiclosed	semiclose	VERB
ejpam-865	164	27	in	in	ADP
ejpam-865	164	28	x	x	PUNCT
ejpam-865	164	29	for	for	ADP
ejpam-865	164	30	every	every	DET
ejpam-865	164	31	preclosed	preclose	VERB
ejpam-865	164	32	set	set	VERB
ejpam-865	164	33	f	f	PROPN
ejpam-865	164	34	of	of	ADP
ejpam-865	164	35	y	y	PROPN
ejpam-865	164	36	;	;	PUNCT
ejpam-865	164	37	(	(	PUNCT
ejpam-865	164	38	e	e	NOUN
ejpam-865	164	39	)	)	PUNCT
ejpam-865	164	40	int(clδ	int(clδ	NOUN
ejpam-865	164	41	(	(	PUNCT
ejpam-865	164	42	f	f	PROPN
ejpam-865	164	43	−1(b	−1(b	NOUN
ejpam-865	164	44	)	)	PUNCT
ejpam-865	164	45	)	)	PUNCT
ejpam-865	164	46	)	)	PUNCT
ejpam-865	165	1	⊂	⊂	PROPN
ejpam-865	165	2	f	f	X
ejpam-865	165	3	−1(pcl(b	−1(pcl(b	PROPN
ejpam-865	165	4	)	)	PUNCT
ejpam-865	165	5	)	)	PUNCT
ejpam-865	166	1	for	for	ADP
ejpam-865	166	2	every	every	DET
ejpam-865	166	3	subset	subset	NOUN
ejpam-865	166	4	b	b	PROPN
ejpam-865	166	5	of	of	ADP
ejpam-865	166	6	y	y	PROPN
ejpam-865	166	7	;	;	PUNCT
ejpam-865	166	8	(	(	PUNCT
ejpam-865	166	9	f	f	X
ejpam-865	166	10	)	)	PUNCT
ejpam-865	166	11	f	f	PROPN
ejpam-865	166	12	(	(	PUNCT
ejpam-865	166	13	int(clδ(a)))⊂	int(clδ(a)))⊂	PROPN
ejpam-865	166	14	pcl	pcl	PROPN
ejpam-865	166	15	(	(	PUNCT
ejpam-865	166	16	f	f	PROPN
ejpam-865	166	17	(	(	PUNCT
ejpam-865	166	18	a	a	NOUN
ejpam-865	166	19	)	)	PUNCT
ejpam-865	166	20	)	)	PUNCT
ejpam-865	166	21	for	for	ADP
ejpam-865	166	22	every	every	DET
ejpam-865	166	23	subset	subset	NOUN
ejpam-865	166	24	a	a	PRON
ejpam-865	166	25	of	of	ADP
ejpam-865	166	26	x	x	X
ejpam-865	166	27	.	.	PUNCT
ejpam-865	167	1	y.	y.	PROPN
ejpam-865	167	2	beceren	beceren	PROPN
ejpam-865	167	3	,	,	PUNCT
ejpam-865	167	4	t.	t.	PROPN
ejpam-865	167	5	noiri	noiri	PROPN
ejpam-865	167	6	/	/	SYM
ejpam-865	167	7	eur	eur	PROPN
ejpam-865	167	8	.	.	PUNCT
ejpam-865	168	1	j.	j.	PROPN
ejpam-865	168	2	pure	pure	PROPN
ejpam-865	168	3	appl	appl	PROPN
ejpam-865	168	4	.	.	PROPN
ejpam-865	168	5	math	math	PROPN
ejpam-865	168	6	,	,	PUNCT
ejpam-865	168	7	4	4	NUM
ejpam-865	168	8	(	(	PUNCT
ejpam-865	168	9	2011	2011	NUM
ejpam-865	168	10	)	)	PUNCT
ejpam-865	168	11	,	,	PUNCT
ejpam-865	168	12	361	361	NUM
ejpam-865	168	13	-	-	SYM
ejpam-865	168	14	369	369	NUM
ejpam-865	168	15	365	365	NUM
ejpam-865	168	16	theorem	theorem	NOUN
ejpam-865	168	17	3	3	NUM
ejpam-865	168	18	.	.	X
ejpam-865	168	19	for	for	ADP
ejpam-865	168	20	a	a	DET
ejpam-865	168	21	function	function	NOUN
ejpam-865	168	22	f	f	NOUN
ejpam-865	168	23	:	:	PUNCT
ejpam-865	168	24	(	(	PUNCT
ejpam-865	168	25	x	x	X
ejpam-865	168	26	,	,	PUNCT
ejpam-865	168	27	τ)→	τ)→	PROPN
ejpam-865	168	28	(	(	PUNCT
ejpam-865	168	29	y	y	PROPN
ejpam-865	168	30	,	,	PUNCT
ejpam-865	168	31	σ	σ	PROPN
ejpam-865	168	32	)	)	PUNCT
ejpam-865	168	33	,	,	PUNCT
ejpam-865	168	34	the	the	DET
ejpam-865	168	35	following	follow	VERB
ejpam-865	168	36	are	be	AUX
ejpam-865	168	37	equivalent	equivalent	ADJ
ejpam-865	168	38	:	:	PUNCT
ejpam-865	168	39	(	(	PUNCT
ejpam-865	168	40	a	a	X
ejpam-865	168	41	)	)	PUNCT
ejpam-865	168	42	f	f	PROPN
ejpam-865	168	43	is	be	AUX
ejpam-865	168	44	δs	δs	NOUN
ejpam-865	168	45	-	-	PUNCT
ejpam-865	168	46	irresolute	irresolute	ADJ
ejpam-865	168	47	;	;	PUNCT
ejpam-865	168	48	(	(	PUNCT
ejpam-865	168	49	b	b	X
ejpam-865	168	50	)	)	PUNCT
ejpam-865	168	51	for	for	ADP
ejpam-865	168	52	each	each	DET
ejpam-865	168	53	x	x	SYM
ejpam-865	168	54	∈	∈	PROPN
ejpam-865	168	55	x	x	X
ejpam-865	168	56	and	and	CCONJ
ejpam-865	168	57	each	each	PRON
ejpam-865	168	58	semi	semi	ADJ
ejpam-865	168	59	-	-	ADJ
ejpam-865	168	60	open	open	ADJ
ejpam-865	168	61	set	set	VERB
ejpam-865	168	62	v	v	NOUN
ejpam-865	168	63	of	of	ADP
ejpam-865	168	64	y	y	PROPN
ejpam-865	168	65	containing	contain	VERB
ejpam-865	168	66	f	f	PROPN
ejpam-865	168	67	(	(	PUNCT
ejpam-865	168	68	x	x	NOUN
ejpam-865	168	69	)	)	PUNCT
ejpam-865	168	70	,	,	PUNCT
ejpam-865	168	71	there	there	PRON
ejpam-865	168	72	exists	exist	VERB
ejpam-865	168	73	a	a	DET
ejpam-865	168	74	δ	δ	NOUN
ejpam-865	168	75	-	-	PUNCT
ejpam-865	168	76	semiopen	semiopen	VERB
ejpam-865	168	77	set	set	VERB
ejpam-865	168	78	u	u	NOUN
ejpam-865	168	79	of	of	ADP
ejpam-865	168	80	x	x	PUNCT
ejpam-865	168	81	containing	contain	VERB
ejpam-865	168	82	x	x	PUNCT
ejpam-865	168	83	such	such	ADJ
ejpam-865	168	84	that	that	SCONJ
ejpam-865	168	85	f	f	PROPN
ejpam-865	168	86	(	(	PUNCT
ejpam-865	168	87	u)⊂	u)⊂	NOUN
ejpam-865	168	88	v	v	VERB
ejpam-865	168	89	;	;	PUNCT
ejpam-865	168	90	(	(	PUNCT
ejpam-865	168	91	c	c	X
ejpam-865	168	92	)	)	PUNCT
ejpam-865	168	93	f	f	PROPN
ejpam-865	168	94	−1(v	−1(v	PROPN
ejpam-865	168	95	)	)	PUNCT
ejpam-865	169	1	⊂	⊂	PROPN
ejpam-865	170	1	cl(intδ	cl(intδ	PROPN
ejpam-865	170	2	(	(	PUNCT
ejpam-865	170	3	f	f	PROPN
ejpam-865	170	4	−1(v	−1(v	PROPN
ejpam-865	170	5	)	)	PUNCT
ejpam-865	170	6	)	)	PUNCT
ejpam-865	170	7	)	)	PUNCT
ejpam-865	171	1	for	for	ADP
ejpam-865	171	2	every	every	DET
ejpam-865	171	3	semi	semi	ADJ
ejpam-865	171	4	-	-	ADJ
ejpam-865	171	5	open	open	ADJ
ejpam-865	171	6	set	set	VERB
ejpam-865	171	7	v	v	NOUN
ejpam-865	171	8	of	of	ADP
ejpam-865	171	9	y	y	PROPN
ejpam-865	171	10	;	;	PUNCT
ejpam-865	171	11	(	(	PUNCT
ejpam-865	171	12	d	d	X
ejpam-865	171	13	)	)	PUNCT
ejpam-865	171	14	f	f	PROPN
ejpam-865	171	15	−1(f	−1(f	PROPN
ejpam-865	171	16	)	)	PUNCT
ejpam-865	171	17	is	be	AUX
ejpam-865	171	18	δ	δ	PROPN
ejpam-865	171	19	-	-	PUNCT
ejpam-865	171	20	semiclosed	semiclose	VERB
ejpam-865	171	21	in	in	ADP
ejpam-865	171	22	x	x	PUNCT
ejpam-865	171	23	for	for	ADP
ejpam-865	171	24	every	every	DET
ejpam-865	171	25	semi	semi	ADJ
ejpam-865	171	26	-	-	ADJ
ejpam-865	171	27	closed	closed	ADJ
ejpam-865	171	28	set	set	ADJ
ejpam-865	171	29	f	f	PROPN
ejpam-865	171	30	of	of	ADP
ejpam-865	171	31	y	y	PROPN
ejpam-865	171	32	;	;	PUNCT
ejpam-865	171	33	(	(	PUNCT
ejpam-865	171	34	e	e	NOUN
ejpam-865	171	35	)	)	PUNCT
ejpam-865	171	36	int(clδ	int(clδ	NOUN
ejpam-865	171	37	(	(	PUNCT
ejpam-865	171	38	f	f	PROPN
ejpam-865	171	39	−1(b	−1(b	NOUN
ejpam-865	171	40	)	)	PUNCT
ejpam-865	171	41	)	)	PUNCT
ejpam-865	171	42	)	)	PUNCT
ejpam-865	172	1	⊂	⊂	PROPN
ejpam-865	172	2	f	f	PROPN
ejpam-865	172	3	−1(sc	−1(sc	PROPN
ejpam-865	172	4	l(b	l(b	PROPN
ejpam-865	172	5	)	)	PUNCT
ejpam-865	172	6	)	)	PUNCT
ejpam-865	172	7	for	for	ADP
ejpam-865	172	8	every	every	DET
ejpam-865	172	9	subset	subset	NOUN
ejpam-865	172	10	b	b	PROPN
ejpam-865	172	11	of	of	ADP
ejpam-865	172	12	y	y	PROPN
ejpam-865	172	13	;	;	PUNCT
ejpam-865	172	14	(	(	PUNCT
ejpam-865	172	15	f	f	X
ejpam-865	172	16	)	)	PUNCT
ejpam-865	172	17	f	f	PROPN
ejpam-865	172	18	(	(	PUNCT
ejpam-865	172	19	int(clδ(a)))⊂	int(clδ(a)))⊂	PROPN
ejpam-865	172	20	sc	sc	PROPN
ejpam-865	172	21	l	l	PROPN
ejpam-865	172	22	(	(	PUNCT
ejpam-865	172	23	f	f	X
ejpam-865	172	24	(	(	PUNCT
ejpam-865	172	25	a	a	NOUN
ejpam-865	172	26	)	)	PUNCT
ejpam-865	172	27	)	)	PUNCT
ejpam-865	172	28	for	for	ADP
ejpam-865	172	29	every	every	DET
ejpam-865	172	30	subset	subset	NOUN
ejpam-865	172	31	a	a	PRON
ejpam-865	172	32	of	of	ADP
ejpam-865	172	33	x	x	PRON
ejpam-865	172	34	.	.	PUNCT
ejpam-865	173	1	the	the	DET
ejpam-865	173	2	proofs	proof	NOUN
ejpam-865	173	3	of	of	ADP
ejpam-865	173	4	the	the	DET
ejpam-865	173	5	other	other	ADJ
ejpam-865	173	6	parts	part	NOUN
ejpam-865	173	7	of	of	ADP
ejpam-865	173	8	the	the	DET
ejpam-865	173	9	following	follow	VERB
ejpam-865	173	10	theorems	theorem	NOUN
ejpam-865	173	11	follow	follow	VERB
ejpam-865	173	12	by	by	ADP
ejpam-865	173	13	a	a	DET
ejpam-865	173	14	similar	similar	ADJ
ejpam-865	173	15	way	way	NOUN
ejpam-865	173	16	and	and	CCONJ
ejpam-865	173	17	are	be	AUX
ejpam-865	173	18	thus	thus	ADV
ejpam-865	173	19	omitted	omit	VERB
ejpam-865	173	20	.	.	PUNCT
ejpam-865	174	1	theorem	theorem	ADJ
ejpam-865	174	2	4	4	NUM
ejpam-865	174	3	.	.	PUNCT
ejpam-865	175	1	let	let	VERB
ejpam-865	175	2	f	f	NOUN
ejpam-865	175	3	:	:	PUNCT
ejpam-865	175	4	x	x	X
ejpam-865	175	5	→	→	SYM
ejpam-865	175	6	y	y	X
ejpam-865	175	7	be	be	AUX
ejpam-865	175	8	a	a	DET
ejpam-865	175	9	function	function	NOUN
ejpam-865	175	10	and	and	CCONJ
ejpam-865	175	11	g	g	NOUN
ejpam-865	175	12	:	:	PUNCT
ejpam-865	175	13	x	x	SYM
ejpam-865	175	14	→	→	SYM
ejpam-865	175	15	x	x	SYM
ejpam-865	175	16	×	×	NOUN
ejpam-865	175	17	y	y	PROPN
ejpam-865	175	18	the	the	DET
ejpam-865	175	19	graph	graph	NOUN
ejpam-865	175	20	function	function	NOUN
ejpam-865	175	21	,	,	PUNCT
ejpam-865	175	22	given	give	VERB
ejpam-865	175	23	by	by	ADP
ejpam-865	175	24	g(x	g(x	NOUN
ejpam-865	175	25	)	)	PUNCT
ejpam-865	175	26	=	=	SYM
ejpam-865	176	1	(	(	PUNCT
ejpam-865	176	2	x	x	INTJ
ejpam-865	176	3	,	,	PUNCT
ejpam-865	176	4	f	f	PROPN
ejpam-865	176	5	(	(	PUNCT
ejpam-865	176	6	x	x	NOUN
ejpam-865	176	7	)	)	PUNCT
ejpam-865	176	8	)	)	PUNCT
ejpam-865	176	9	for	for	ADP
ejpam-865	176	10	every	every	DET
ejpam-865	176	11	x	x	SYM
ejpam-865	176	12	∈	∈	PROPN
ejpam-865	176	13	x	x	X
ejpam-865	176	14	.	.	PUNCT
ejpam-865	177	1	then	then	ADV
ejpam-865	177	2	f	f	PROPN
ejpam-865	177	3	is	be	AUX
ejpam-865	177	4	δα	δα	NOUN
ejpam-865	177	5	-	-	ADJ
ejpam-865	177	6	irresolute	irresolute	ADJ
ejpam-865	177	7	(	(	PUNCT
ejpam-865	177	8	resp	resp	NOUN
ejpam-865	177	9	.	.	PUNCT
ejpam-865	178	1	δp	δp	PRON
ejpam-865	178	2	-	-	PUNCT
ejpam-865	178	3	irresolute	irresolute	ADJ
ejpam-865	178	4	,	,	PUNCT
ejpam-865	178	5	δs	δs	NOUN
ejpam-865	178	6	-	-	PUNCT
ejpam-865	178	7	irresolute	irresolute	NOUN
ejpam-865	178	8	)	)	PUNCT
ejpam-865	178	9	if	if	SCONJ
ejpam-865	178	10	g	g	PROPN
ejpam-865	178	11	is	be	AUX
ejpam-865	178	12	δα	δα	NOUN
ejpam-865	178	13	-	-	ADJ
ejpam-865	178	14	irresolute	irresolute	ADJ
ejpam-865	178	15	(	(	PUNCT
ejpam-865	178	16	resp	resp	NOUN
ejpam-865	178	17	.	.	PUNCT
ejpam-865	179	1	δp	δp	PRON
ejpam-865	179	2	-	-	PUNCT
ejpam-865	179	3	irresolute	irresolute	ADJ
ejpam-865	179	4	,	,	PUNCT
ejpam-865	179	5	δs	δs	NOUN
ejpam-865	179	6	-	-	PUNCT
ejpam-865	179	7	irresolute	irresolute	NOUN
ejpam-865	179	8	)	)	PUNCT
ejpam-865	179	9	.	.	PUNCT
ejpam-865	180	1	proof	proof	NOUN
ejpam-865	180	2	.	.	PUNCT
ejpam-865	181	1	let	let	VERB
ejpam-865	181	2	x	x	PUNCT
ejpam-865	181	3	∈	∈	PROPN
ejpam-865	181	4	x	x	X
ejpam-865	181	5	and	and	CCONJ
ejpam-865	181	6	v	v	X
ejpam-865	181	7	be	be	AUX
ejpam-865	181	8	any	any	DET
ejpam-865	181	9	α	α	NOUN
ejpam-865	181	10	-	-	ADJ
ejpam-865	181	11	open	open	ADJ
ejpam-865	181	12	(	(	PUNCT
ejpam-865	181	13	resp	resp	NOUN
ejpam-865	181	14	.	.	PUNCT
ejpam-865	182	1	preopen	preopen	ADJ
ejpam-865	182	2	,	,	PUNCT
ejpam-865	182	3	semi	semi	ADJ
ejpam-865	182	4	-	-	ADJ
ejpam-865	182	5	open	open	ADJ
ejpam-865	182	6	)	)	PUNCT
ejpam-865	182	7	set	set	NOUN
ejpam-865	182	8	of	of	ADP
ejpam-865	182	9	y	y	PROPN
ejpam-865	182	10	containing	contain	VERB
ejpam-865	182	11	f	f	PROPN
ejpam-865	182	12	(	(	PUNCT
ejpam-865	182	13	x	x	NOUN
ejpam-865	182	14	)	)	PUNCT
ejpam-865	182	15	.	.	PUNCT
ejpam-865	183	1	then	then	ADV
ejpam-865	183	2	,	,	PUNCT
ejpam-865	183	3	by	by	ADP
ejpam-865	183	4	lemma	lemma	PROPN
ejpam-865	183	5	2	2	NUM
ejpam-865	183	6	,	,	PUNCT
ejpam-865	183	7	the	the	DET
ejpam-865	183	8	set	set	NOUN
ejpam-865	183	9	x	x	SYM
ejpam-865	183	10	×	×	NOUN
ejpam-865	183	11	v	v	NOUN
ejpam-865	183	12	is	be	AUX
ejpam-865	183	13	α	α	NOUN
ejpam-865	183	14	-	-	ADJ
ejpam-865	183	15	open	open	ADJ
ejpam-865	183	16	(	(	PUNCT
ejpam-865	183	17	resp	resp	NOUN
ejpam-865	183	18	.	.	PUNCT
ejpam-865	184	1	preopen	preopen	ADJ
ejpam-865	184	2	,	,	PUNCT
ejpam-865	184	3	semi	semi	ADJ
ejpam-865	184	4	-	-	ADJ
ejpam-865	184	5	open	open	ADJ
ejpam-865	184	6	)	)	PUNCT
ejpam-865	184	7	in	in	ADP
ejpam-865	184	8	x	x	SYM
ejpam-865	184	9	×	×	PROPN
ejpam-865	184	10	y	y	NOUN
ejpam-865	184	11	containing	contain	VERB
ejpam-865	184	12	g(x	g(x	NOUN
ejpam-865	184	13	)	)	PUNCT
ejpam-865	184	14	.	.	PUNCT
ejpam-865	185	1	since	since	SCONJ
ejpam-865	185	2	g	g	PROPN
ejpam-865	185	3	is	be	AUX
ejpam-865	185	4	δα	δα	NOUN
ejpam-865	185	5	-	-	ADJ
ejpam-865	185	6	irresolute	irresolute	ADJ
ejpam-865	185	7	(	(	PUNCT
ejpam-865	185	8	resp	resp	NOUN
ejpam-865	185	9	.	.	PUNCT
ejpam-865	186	1	δp	δp	PRON
ejpam-865	186	2	-	-	PUNCT
ejpam-865	186	3	irresolute	irresolute	ADJ
ejpam-865	186	4	,	,	PUNCT
ejpam-865	186	5	δs	δs	NOUN
ejpam-865	186	6	-	-	PUNCT
ejpam-865	186	7	irresolute	irresolute	NOUN
ejpam-865	186	8	)	)	PUNCT
ejpam-865	186	9	,	,	PUNCT
ejpam-865	186	10	there	there	PRON
ejpam-865	186	11	exists	exist	VERB
ejpam-865	186	12	a	a	DET
ejpam-865	186	13	δ	δ	NOUN
ejpam-865	186	14	-	-	PUNCT
ejpam-865	186	15	semiopen	semiopen	VERB
ejpam-865	186	16	set	set	VERB
ejpam-865	186	17	u	u	NOUN
ejpam-865	186	18	of	of	ADP
ejpam-865	186	19	x	x	PUNCT
ejpam-865	186	20	containing	contain	VERB
ejpam-865	186	21	x	x	PUNCT
ejpam-865	186	22	such	such	ADJ
ejpam-865	186	23	that	that	DET
ejpam-865	186	24	g(u)⊂	g(u)⊂	NOUN
ejpam-865	186	25	x	x	X
ejpam-865	186	26	×	×	NOUN
ejpam-865	186	27	v	v	NOUN
ejpam-865	187	1	and	and	CCONJ
ejpam-865	187	2	hence	hence	ADV
ejpam-865	187	3	f	f	PROPN
ejpam-865	187	4	(	(	PUNCT
ejpam-865	187	5	u)⊂	u)⊂	NOUN
ejpam-865	187	6	v	v	NOUN
ejpam-865	187	7	.	.	PUNCT
ejpam-865	188	1	thus	thus	ADV
ejpam-865	188	2	f	f	PROPN
ejpam-865	188	3	is	be	AUX
ejpam-865	188	4	δα	δα	NOUN
ejpam-865	188	5	-	-	ADJ
ejpam-865	188	6	irresolute	irresolute	ADJ
ejpam-865	188	7	(	(	PUNCT
ejpam-865	188	8	resp	resp	NOUN
ejpam-865	188	9	.	.	PUNCT
ejpam-865	189	1	δp	δp	PRON
ejpam-865	189	2	-	-	PUNCT
ejpam-865	189	3	irresolute	irresolute	ADJ
ejpam-865	189	4	,	,	PUNCT
ejpam-865	189	5	δs	δs	NOUN
ejpam-865	189	6	-	-	PUNCT
ejpam-865	189	7	irresolute	irresolute	NOUN
ejpam-865	189	8	)	)	PUNCT
ejpam-865	189	9	.	.	PUNCT
ejpam-865	190	1	theorem	theorem	NOUN
ejpam-865	190	2	5	5	NUM
ejpam-865	190	3	.	.	PUNCT
ejpam-865	191	1	if	if	SCONJ
ejpam-865	191	2	a	a	DET
ejpam-865	191	3	function	function	NOUN
ejpam-865	191	4	f	f	NOUN
ejpam-865	191	5	:	:	PUNCT
ejpam-865	191	6	x	x	X
ejpam-865	191	7	→	→	PUNCT
ejpam-865	191	8	πyλ	πyλ	PROPN
ejpam-865	191	9	is	be	AUX
ejpam-865	191	10	δα	δα	NOUN
ejpam-865	191	11	-	-	ADJ
ejpam-865	191	12	irresolute	irresolute	ADJ
ejpam-865	191	13	(	(	PUNCT
ejpam-865	191	14	resp	resp	NOUN
ejpam-865	191	15	.	.	PUNCT
ejpam-865	192	1	δp	δp	PRON
ejpam-865	192	2	-	-	PUNCT
ejpam-865	192	3	irresolute	irresolute	ADJ
ejpam-865	192	4	,	,	PUNCT
ejpam-865	192	5	δs	δs	NOUN
ejpam-865	192	6	-	-	PUNCT
ejpam-865	192	7	irresolute	irresolute	NOUN
ejpam-865	192	8	)	)	PUNCT
ejpam-865	192	9	,	,	PUNCT
ejpam-865	192	10	then	then	ADV
ejpam-865	192	11	pλo	pλo	INTJ
ejpam-865	192	12	f	f	X
ejpam-865	193	1	:	:	PUNCT
ejpam-865	193	2	x	x	X
ejpam-865	193	3	→	→	SYM
ejpam-865	193	4	yλ	yλ	PROPN
ejpam-865	193	5	is	be	AUX
ejpam-865	193	6	δα	δα	NOUN
ejpam-865	193	7	-	-	ADJ
ejpam-865	193	8	irresolute	irresolute	ADJ
ejpam-865	193	9	(	(	PUNCT
ejpam-865	193	10	resp	resp	NOUN
ejpam-865	193	11	.	.	PUNCT
ejpam-865	194	1	δp	δp	PRON
ejpam-865	194	2	-	-	PUNCT
ejpam-865	194	3	irresolute	irresolute	ADJ
ejpam-865	194	4	,	,	PUNCT
ejpam-865	194	5	δs	δs	NOUN
ejpam-865	194	6	-	-	PUNCT
ejpam-865	194	7	irresolute	irresolute	NOUN
ejpam-865	194	8	)	)	PUNCT
ejpam-865	195	1	for	for	ADP
ejpam-865	195	2	each	each	DET
ejpam-865	195	3	λ	λ	PROPN
ejpam-865	195	4	∈	∈	PROPN
ejpam-865	195	5	λ	λ	PROPN
ejpam-865	195	6	,	,	PUNCT
ejpam-865	195	7	where	where	SCONJ
ejpam-865	195	8	pλ	pλ	PROPN
ejpam-865	195	9	is	be	AUX
ejpam-865	195	10	the	the	DET
ejpam-865	195	11	projection	projection	NOUN
ejpam-865	195	12	of	of	ADP
ejpam-865	195	13	πyλ	πyλ	PRON
ejpam-865	195	14	onto	onto	ADP
ejpam-865	195	15	yλ	yλ	PROPN
ejpam-865	195	16	.	.	PUNCT
ejpam-865	195	17	proof	proof	NOUN
ejpam-865	195	18	.	.	PUNCT
ejpam-865	196	1	let	let	VERB
ejpam-865	196	2	vλ	vλ	INTJ
ejpam-865	196	3	be	be	AUX
ejpam-865	196	4	any	any	DET
ejpam-865	196	5	α	α	NOUN
ejpam-865	196	6	-	-	ADJ
ejpam-865	196	7	open	open	ADJ
ejpam-865	196	8	(	(	PUNCT
ejpam-865	196	9	resp	resp	NOUN
ejpam-865	196	10	.	.	PUNCT
ejpam-865	197	1	preopen	preopen	ADJ
ejpam-865	197	2	,	,	PUNCT
ejpam-865	197	3	semi	semi	ADJ
ejpam-865	197	4	-	-	ADJ
ejpam-865	197	5	open	open	ADJ
ejpam-865	197	6	)	)	PUNCT
ejpam-865	197	7	set	set	NOUN
ejpam-865	197	8	of	of	ADP
ejpam-865	197	9	yλ	yλ	PROPN
ejpam-865	197	10	.	.	PUNCT
ejpam-865	198	1	since	since	SCONJ
ejpam-865	198	2	pλ	pλ	PROPN
ejpam-865	198	3	is	be	AUX
ejpam-865	198	4	continuous	continuous	ADJ
ejpam-865	198	5	and	and	CCONJ
ejpam-865	198	6	open	open	ADJ
ejpam-865	198	7	,	,	PUNCT
ejpam-865	198	8	it	it	PRON
ejpam-865	198	9	is	be	AUX
ejpam-865	198	10	α	α	NOUN
ejpam-865	198	11	-	-	NOUN
ejpam-865	198	12	irresolute	irresolute	ADJ
ejpam-865	198	13	[	[	X
ejpam-865	198	14	20	20	NUM
ejpam-865	198	15	,	,	PUNCT
ejpam-865	198	16	theorem	theorem	VERB
ejpam-865	198	17	3.2	3.2	NUM
ejpam-865	198	18	]	]	PUNCT
ejpam-865	198	19	(	(	PUNCT
ejpam-865	198	20	resp	resp	NOUN
ejpam-865	198	21	.	.	PUNCT
ejpam-865	199	1	preirresolute	preirresolute	PROPN
ejpam-865	200	1	[	[	X
ejpam-865	200	2	20	20	NUM
ejpam-865	200	3	,	,	PUNCT
ejpam-865	200	4	theorem	theorem	VERB
ejpam-865	200	5	3.4	3.4	NUM
ejpam-865	200	6	]	]	PUNCT
ejpam-865	200	7	,	,	PUNCT
ejpam-865	200	8	irresolute	irresolute	VERB
ejpam-865	201	1	[	[	X
ejpam-865	201	2	9	9	NUM
ejpam-865	201	3	,	,	PUNCT
ejpam-865	201	4	theorem	theorem	VERB
ejpam-865	201	5	1.2	1.2	NUM
ejpam-865	201	6	]	]	PUNCT
ejpam-865	201	7	)	)	PUNCT
ejpam-865	201	8	and	and	CCONJ
ejpam-865	201	9	hence	hence	ADV
ejpam-865	201	10	p−1	p−1	PROPN
ejpam-865	201	11	λ	λ	PROPN
ejpam-865	201	12	(	(	PUNCT
ejpam-865	201	13	vλ	vλ	PROPN
ejpam-865	201	14	)	)	PUNCT
ejpam-865	201	15	is	be	AUX
ejpam-865	201	16	α	α	X
ejpam-865	201	17	-	-	ADJ
ejpam-865	201	18	open	open	ADJ
ejpam-865	201	19	(	(	PUNCT
ejpam-865	201	20	resp	resp	NOUN
ejpam-865	201	21	.	.	PUNCT
ejpam-865	202	1	preopen	preopen	ADJ
ejpam-865	202	2	,	,	PUNCT
ejpam-865	202	3	semi	semi	ADJ
ejpam-865	202	4	-	-	ADJ
ejpam-865	202	5	open	open	ADJ
ejpam-865	202	6	)	)	PUNCT
ejpam-865	202	7	inπyλ	inπyλ	NOUN
ejpam-865	202	8	.	.	PUNCT
ejpam-865	203	1	since	since	SCONJ
ejpam-865	203	2	f	f	PROPN
ejpam-865	203	3	is	be	AUX
ejpam-865	203	4	δα	δα	NOUN
ejpam-865	203	5	-	-	ADJ
ejpam-865	203	6	irresolute	irresolute	ADJ
ejpam-865	203	7	(	(	PUNCT
ejpam-865	203	8	resp	resp	NOUN
ejpam-865	203	9	.	.	PUNCT
ejpam-865	204	1	δp	δp	PRON
ejpam-865	204	2	-	-	PUNCT
ejpam-865	204	3	irresolute	irresolute	ADJ
ejpam-865	204	4	,	,	PUNCT
ejpam-865	204	5	δs	δs	NOUN
ejpam-865	204	6	-	-	PUNCT
ejpam-865	204	7	irresolute	irresolute	NOUN
ejpam-865	204	8	)	)	PUNCT
ejpam-865	204	9	,	,	PUNCT
ejpam-865	204	10	then	then	ADV
ejpam-865	204	11	f	f	X
ejpam-865	204	12	−1(p−1	−1(p−1	PROPN
ejpam-865	204	13	λ	λ	X
ejpam-865	204	14	(	(	PUNCT
ejpam-865	204	15	vλ	vλ	PROPN
ejpam-865	204	16	)	)	PUNCT
ejpam-865	204	17	)	)	PUNCT
ejpam-865	205	1	=	=	PUNCT
ejpam-865	205	2	(	(	PUNCT
ejpam-865	205	3	pλo	pλo	PROPN
ejpam-865	205	4	f	f	PROPN
ejpam-865	205	5	)	)	PUNCT
ejpam-865	205	6	−1(vλ	−1(vλ	NOUN
ejpam-865	205	7	)	)	PUNCT
ejpam-865	205	8	is	be	AUX
ejpam-865	205	9	δ	δ	PROPN
ejpam-865	205	10	-	-	PUNCT
ejpam-865	205	11	semiopen	semiopen	ADJ
ejpam-865	205	12	in	in	ADP
ejpam-865	205	13	x	x	X
ejpam-865	205	14	.	.	PUNCT
ejpam-865	206	1	hence	hence	ADV
ejpam-865	206	2	pλo	pλo	PROPN
ejpam-865	206	3	f	f	PROPN
ejpam-865	206	4	is	be	AUX
ejpam-865	206	5	δα	δα	NOUN
ejpam-865	206	6	-	-	ADJ
ejpam-865	206	7	irresolute	irresolute	ADJ
ejpam-865	206	8	(	(	PUNCT
ejpam-865	206	9	resp	resp	NOUN
ejpam-865	206	10	.	.	PUNCT
ejpam-865	207	1	δp	δp	PRON
ejpam-865	207	2	-	-	PUNCT
ejpam-865	207	3	irresolute	irresolute	ADJ
ejpam-865	207	4	,	,	PUNCT
ejpam-865	207	5	δs	δs	NOUN
ejpam-865	207	6	-	-	PUNCT
ejpam-865	207	7	irresolute	irresolute	NOUN
ejpam-865	207	8	)	)	PUNCT
ejpam-865	208	1	for	for	ADP
ejpam-865	208	2	each	each	DET
ejpam-865	208	3	λ	λ	PROPN
ejpam-865	208	4	∈	∈	PROPN
ejpam-865	208	5	λ	λ	PROPN
ejpam-865	208	6	.	.	PUNCT
ejpam-865	208	7	theorem	theorem	VERB
ejpam-865	208	8	6	6	NUM
ejpam-865	208	9	.	.	PUNCT
ejpam-865	209	1	if	if	SCONJ
ejpam-865	209	2	the	the	DET
ejpam-865	209	3	product	product	NOUN
ejpam-865	209	4	function	function	VERB
ejpam-865	209	5	f	f	NOUN
ejpam-865	209	6	:	:	PUNCT
ejpam-865	209	7	πxλ	πxλ	X
ejpam-865	209	8	→	→	PUNCT
ejpam-865	209	9	πyλ	πyλ	PROPN
ejpam-865	209	10	is	be	AUX
ejpam-865	209	11	δα	δα	NOUN
ejpam-865	209	12	-	-	ADJ
ejpam-865	209	13	irresolute	irresolute	ADJ
ejpam-865	209	14	(	(	PUNCT
ejpam-865	209	15	resp	resp	NOUN
ejpam-865	209	16	.	.	PUNCT
ejpam-865	210	1	δp	δp	ADP
ejpam-865	210	2	-	-	PUNCT
ejpam-865	210	3	irresolute	irresolute	ADJ
ejpam-865	210	4	,	,	PUNCT
ejpam-865	210	5	δsirresolute	δsirresolute	NOUN
ejpam-865	210	6	)	)	PUNCT
ejpam-865	211	1	,	,	PUNCT
ejpam-865	211	2	then	then	ADV
ejpam-865	211	3	fλ	fλ	INTJ
ejpam-865	211	4	:	:	PUNCT
ejpam-865	211	5	xλ→	xλ→	PROPN
ejpam-865	212	1	yλ	yλ	PROPN
ejpam-865	212	2	is	be	AUX
ejpam-865	212	3	δα	δα	NOUN
ejpam-865	212	4	-	-	ADJ
ejpam-865	212	5	irresolute	irresolute	ADJ
ejpam-865	212	6	(	(	PUNCT
ejpam-865	212	7	resp	resp	NOUN
ejpam-865	212	8	.	.	PUNCT
ejpam-865	213	1	δp	δp	PRON
ejpam-865	213	2	-	-	PUNCT
ejpam-865	213	3	irresolute	irresolute	ADJ
ejpam-865	213	4	,	,	PUNCT
ejpam-865	213	5	δs	δs	NOUN
ejpam-865	213	6	-	-	PUNCT
ejpam-865	213	7	irresolute	irresolute	NOUN
ejpam-865	213	8	)	)	PUNCT
ejpam-865	214	1	for	for	ADP
ejpam-865	214	2	each	each	DET
ejpam-865	214	3	λ	λ	PROPN
ejpam-865	214	4	∈	∈	PROPN
ejpam-865	214	5	λ	λ	PROPN
ejpam-865	214	6	.	.	PUNCT
ejpam-865	214	7	proof	proof	NOUN
ejpam-865	214	8	.	.	PUNCT
ejpam-865	215	1	let	let	VERB
ejpam-865	215	2	λ0	λ0	NOUN
ejpam-865	215	3	∈	∈	NOUN
ejpam-865	215	4	λ	λ	NOUN
ejpam-865	215	5	be	be	VERB
ejpam-865	215	6	an	an	DET
ejpam-865	215	7	arbitrary	arbitrary	ADJ
ejpam-865	215	8	fixed	fix	VERB
ejpam-865	215	9	index	index	NOUN
ejpam-865	215	10	and	and	CCONJ
ejpam-865	215	11	vλ0	vλ0	NOUN
ejpam-865	215	12	be	be	AUX
ejpam-865	215	13	any	any	DET
ejpam-865	215	14	α	α	NOUN
ejpam-865	215	15	-	-	ADJ
ejpam-865	215	16	open	open	ADJ
ejpam-865	215	17	(	(	PUNCT
ejpam-865	215	18	resp	resp	NOUN
ejpam-865	215	19	.	.	PUNCT
ejpam-865	216	1	preopen	preopen	ADJ
ejpam-865	216	2	,	,	PUNCT
ejpam-865	216	3	semiopen	semiopen	ADJ
ejpam-865	216	4	)	)	PUNCT
ejpam-865	216	5	set	set	NOUN
ejpam-865	216	6	of	of	ADP
ejpam-865	216	7	yλ0	yλ0	PROPN
ejpam-865	216	8	.	.	PUNCT
ejpam-865	217	1	then	then	ADV
ejpam-865	217	2	πyλ	πyλ	PRON
ejpam-865	217	3	×	×	NOUN
ejpam-865	217	4	vλ0	vλ0	NOUN
ejpam-865	217	5	is	be	AUX
ejpam-865	217	6	α	α	NOUN
ejpam-865	217	7	-	-	ADJ
ejpam-865	217	8	open	open	ADJ
ejpam-865	217	9	(	(	PUNCT
ejpam-865	217	10	resp	resp	NOUN
ejpam-865	217	11	.	.	PUNCT
ejpam-865	218	1	preopen	preopen	ADJ
ejpam-865	218	2	,	,	PUNCT
ejpam-865	218	3	semi	semi	ADJ
ejpam-865	218	4	-	-	ADJ
ejpam-865	218	5	open	open	ADJ
ejpam-865	218	6	)	)	PUNCT
ejpam-865	218	7	in	in	ADP
ejpam-865	218	8	πyλ	πyλ	PROPN
ejpam-865	218	9	by	by	ADP
ejpam-865	218	10	lemma	lemma	PROPN
ejpam-865	218	11	2	2	NUM
ejpam-865	218	12	,	,	PUNCT
ejpam-865	218	13	where	where	SCONJ
ejpam-865	218	14	λ0	λ0	NOUN
ejpam-865	218	15	6=	6=	ADP
ejpam-865	218	16	λ	λ	PROPN
ejpam-865	218	17	∈	∈	PROPN
ejpam-865	218	18	λ	λ	PROPN
ejpam-865	218	19	.	.	PUNCT
ejpam-865	219	1	since	since	SCONJ
ejpam-865	219	2	f	f	PROPN
ejpam-865	219	3	is	be	AUX
ejpam-865	219	4	δα	δα	NOUN
ejpam-865	219	5	-	-	ADJ
ejpam-865	219	6	irresolute	irresolute	ADJ
ejpam-865	219	7	(	(	PUNCT
ejpam-865	219	8	resp	resp	NOUN
ejpam-865	219	9	.	.	PUNCT
ejpam-865	220	1	δp	δp	PRON
ejpam-865	220	2	-	-	PUNCT
ejpam-865	220	3	irresolute	irresolute	ADJ
ejpam-865	220	4	,	,	PUNCT
ejpam-865	220	5	δs	δs	NOUN
ejpam-865	220	6	-	-	PUNCT
ejpam-865	220	7	irresolute	irresolute	NOUN
ejpam-865	220	8	)	)	PUNCT
ejpam-865	220	9	,	,	PUNCT
ejpam-865	220	10	then	then	ADV
ejpam-865	220	11	f	f	PROPN
ejpam-865	220	12	−1(πyλ×	−1(πyλ×	VERB
ejpam-865	220	13	vλ0	vλ0	NOUN
ejpam-865	220	14	)	)	PUNCT
ejpam-865	221	1	=	=	PUNCT
ejpam-865	221	2	πxλ×	πxλ×	PUNCT
ejpam-865	221	3	f	f	NOUN
ejpam-865	221	4	−1	−1	NOUN
ejpam-865	221	5	λ0	λ0	NOUN
ejpam-865	221	6	(	(	PUNCT
ejpam-865	221	7	vλ0	vλ0	NOUN
ejpam-865	221	8	)	)	PUNCT
ejpam-865	221	9	is	be	AUX
ejpam-865	221	10	δ	δ	PROPN
ejpam-865	221	11	-	-	PUNCT
ejpam-865	221	12	semiopen	semiopen	ADJ
ejpam-865	221	13	in	in	ADP
ejpam-865	221	14	πxλ	πxλ	ADV
ejpam-865	221	15	and	and	CCONJ
ejpam-865	221	16	hence	hence	ADV
ejpam-865	221	17	,	,	PUNCT
ejpam-865	221	18	by	by	ADP
ejpam-865	221	19	lemma	lemma	PROPN
ejpam-865	221	20	2	2	NUM
ejpam-865	221	21	,	,	PUNCT
ejpam-865	221	22	f	f	NOUN
ejpam-865	221	23	−1	−1	NOUN
ejpam-865	221	24	λ0	λ0	NOUN
ejpam-865	221	25	(	(	PUNCT
ejpam-865	221	26	vλ0	vλ0	NOUN
ejpam-865	221	27	)	)	PUNCT
ejpam-865	221	28	is	be	AUX
ejpam-865	221	29	δ	δ	PROPN
ejpam-865	221	30	-	-	PUNCT
ejpam-865	221	31	semiopen	semiopen	ADJ
ejpam-865	221	32	in	in	ADP
ejpam-865	221	33	xλ0	xλ0	PROPN
ejpam-865	221	34	.	.	PUNCT
ejpam-865	222	1	this	this	PRON
ejpam-865	222	2	implies	imply	VERB
ejpam-865	222	3	that	that	SCONJ
ejpam-865	222	4	fλ0	fλ0	PROPN
ejpam-865	222	5	is	be	AUX
ejpam-865	222	6	δα	δα	NOUN
ejpam-865	222	7	-	-	ADJ
ejpam-865	222	8	irresolute	irresolute	ADJ
ejpam-865	222	9	(	(	PUNCT
ejpam-865	222	10	resp	resp	NOUN
ejpam-865	222	11	.	.	PUNCT
ejpam-865	223	1	δp	δp	PRON
ejpam-865	223	2	-	-	PUNCT
ejpam-865	223	3	irresolute	irresolute	ADJ
ejpam-865	223	4	,	,	PUNCT
ejpam-865	223	5	δs	δs	NOUN
ejpam-865	223	6	-	-	PUNCT
ejpam-865	223	7	irresolute	irresolute	NOUN
ejpam-865	223	8	)	)	PUNCT
ejpam-865	223	9	.	.	PUNCT
ejpam-865	224	1	y.	y.	PROPN
ejpam-865	224	2	beceren	beceren	PROPN
ejpam-865	224	3	,	,	PUNCT
ejpam-865	224	4	t.	t.	PROPN
ejpam-865	224	5	noiri	noiri	PROPN
ejpam-865	224	6	/	/	SYM
ejpam-865	224	7	eur	eur	PROPN
ejpam-865	224	8	.	.	PUNCT
ejpam-865	225	1	j.	j.	PROPN
ejpam-865	225	2	pure	pure	PROPN
ejpam-865	225	3	appl	appl	PROPN
ejpam-865	225	4	.	.	PROPN
ejpam-865	225	5	math	math	PROPN
ejpam-865	225	6	,	,	PUNCT
ejpam-865	225	7	4	4	NUM
ejpam-865	225	8	(	(	PUNCT
ejpam-865	225	9	2011	2011	NUM
ejpam-865	225	10	)	)	PUNCT
ejpam-865	225	11	,	,	PUNCT
ejpam-865	225	12	361	361	NUM
ejpam-865	225	13	-	-	SYM
ejpam-865	225	14	369	369	NUM
ejpam-865	225	15	366	366	NUM
ejpam-865	225	16	theorem	theorem	NOUN
ejpam-865	225	17	7	7	NUM
ejpam-865	225	18	.	.	PUNCT
ejpam-865	226	1	if	if	SCONJ
ejpam-865	226	2	f	f	PROPN
ejpam-865	226	3	:	:	PUNCT
ejpam-865	226	4	(	(	PUNCT
ejpam-865	226	5	x	x	X
ejpam-865	226	6	,	,	PUNCT
ejpam-865	226	7	τ	τ	PROPN
ejpam-865	226	8	)	)	PUNCT
ejpam-865	226	9	→	→	SYM
ejpam-865	226	10	(	(	PUNCT
ejpam-865	226	11	y	y	PROPN
ejpam-865	226	12	,	,	PUNCT
ejpam-865	226	13	σ	σ	PROPN
ejpam-865	226	14	)	)	PUNCT
ejpam-865	226	15	is	be	AUX
ejpam-865	226	16	δα	δα	NOUN
ejpam-865	226	17	-	-	ADJ
ejpam-865	226	18	irresolute	irresolute	ADJ
ejpam-865	226	19	(	(	PUNCT
ejpam-865	226	20	resp	resp	NOUN
ejpam-865	226	21	.	.	PUNCT
ejpam-865	227	1	δp	δp	PRON
ejpam-865	227	2	-	-	PUNCT
ejpam-865	227	3	irresolute	irresolute	ADJ
ejpam-865	227	4	,	,	PUNCT
ejpam-865	227	5	δs	δs	NOUN
ejpam-865	227	6	-	-	PUNCT
ejpam-865	227	7	irresolute	irresolute	NOUN
ejpam-865	227	8	)	)	PUNCT
ejpam-865	227	9	and	and	CCONJ
ejpam-865	227	10	a	a	PRON
ejpam-865	227	11	is	be	AUX
ejpam-865	227	12	a	a	DET
ejpam-865	227	13	δ	δ	NOUN
ejpam-865	227	14	-	-	ADJ
ejpam-865	227	15	open	open	ADJ
ejpam-865	227	16	subset	subset	NOUN
ejpam-865	227	17	of	of	ADP
ejpam-865	227	18	x	x	PRON
ejpam-865	227	19	,	,	PUNCT
ejpam-865	227	20	then	then	ADV
ejpam-865	228	1	the	the	DET
ejpam-865	228	2	restriction	restriction	NOUN
ejpam-865	228	3	f	f	X
ejpam-865	228	4	/	/	SYM
ejpam-865	228	5	a	a	PRON
ejpam-865	228	6	:	:	PUNCT
ejpam-865	228	7	a→	a→	PUNCT
ejpam-865	228	8	y	y	PROPN
ejpam-865	228	9	is	be	AUX
ejpam-865	228	10	δα	δα	NOUN
ejpam-865	228	11	-	-	ADJ
ejpam-865	228	12	irresolute	irresolute	ADJ
ejpam-865	228	13	(	(	PUNCT
ejpam-865	228	14	resp	resp	NOUN
ejpam-865	228	15	.	.	PUNCT
ejpam-865	229	1	δp	δp	PRON
ejpam-865	229	2	-	-	PUNCT
ejpam-865	229	3	irresolute	irresolute	ADJ
ejpam-865	229	4	,	,	PUNCT
ejpam-865	229	5	δs	δs	NOUN
ejpam-865	229	6	-	-	PUNCT
ejpam-865	229	7	irresolute	irresolute	NOUN
ejpam-865	229	8	)	)	PUNCT
ejpam-865	229	9	.	.	PUNCT
ejpam-865	230	1	proof	proof	NOUN
ejpam-865	230	2	.	.	PUNCT
ejpam-865	231	1	let	let	VERB
ejpam-865	231	2	v	v	PART
ejpam-865	231	3	be	be	AUX
ejpam-865	231	4	any	any	DET
ejpam-865	231	5	α	α	NOUN
ejpam-865	231	6	-	-	ADJ
ejpam-865	231	7	open	open	ADJ
ejpam-865	231	8	(	(	PUNCT
ejpam-865	231	9	resp	resp	NOUN
ejpam-865	231	10	.	.	PUNCT
ejpam-865	232	1	preopen	preopen	ADJ
ejpam-865	232	2	,	,	PUNCT
ejpam-865	232	3	semi	semi	ADJ
ejpam-865	232	4	-	-	ADJ
ejpam-865	232	5	open	open	ADJ
ejpam-865	232	6	)	)	PUNCT
ejpam-865	232	7	set	set	NOUN
ejpam-865	232	8	of	of	ADP
ejpam-865	232	9	y	y	PROPN
ejpam-865	232	10	.	.	PUNCT
ejpam-865	233	1	since	since	SCONJ
ejpam-865	233	2	f	f	PROPN
ejpam-865	233	3	is	be	AUX
ejpam-865	233	4	δα	δα	NOUN
ejpam-865	233	5	-	-	ADJ
ejpam-865	233	6	irresolute	irresolute	ADJ
ejpam-865	233	7	(	(	PUNCT
ejpam-865	233	8	resp	resp	NOUN
ejpam-865	233	9	.	.	PUNCT
ejpam-865	234	1	δp	δp	PRON
ejpam-865	234	2	-	-	PUNCT
ejpam-865	234	3	irresolute	irresolute	ADJ
ejpam-865	234	4	,	,	PUNCT
ejpam-865	234	5	δs	δs	NOUN
ejpam-865	234	6	-	-	PUNCT
ejpam-865	234	7	irresolute	irresolute	NOUN
ejpam-865	234	8	)	)	PUNCT
ejpam-865	234	9	,	,	PUNCT
ejpam-865	234	10	then	then	ADV
ejpam-865	234	11	f	f	PROPN
ejpam-865	234	12	−1(v	−1(v	PROPN
ejpam-865	234	13	)	)	PUNCT
ejpam-865	234	14	is	be	AUX
ejpam-865	234	15	δ	δ	PROPN
ejpam-865	234	16	-	-	PUNCT
ejpam-865	234	17	semiopen	semiopen	ADJ
ejpam-865	234	18	in	in	ADP
ejpam-865	234	19	x	x	X
ejpam-865	234	20	.	.	PUNCT
ejpam-865	235	1	since	since	SCONJ
ejpam-865	235	2	a	a	PRON
ejpam-865	235	3	is	be	AUX
ejpam-865	235	4	δ	δ	NOUN
ejpam-865	235	5	-	-	ADJ
ejpam-865	235	6	open	open	ADJ
ejpam-865	235	7	in	in	ADP
ejpam-865	235	8	x	x	X
ejpam-865	235	9	,	,	PUNCT
ejpam-865	235	10	(	(	PUNCT
ejpam-865	235	11	f	f	X
ejpam-865	235	12	/	/	SYM
ejpam-865	235	13	a	a	NOUN
ejpam-865	235	14	)	)	PUNCT
ejpam-865	235	15	−1(v	−1(v	NOUN
ejpam-865	235	16	)	)	PUNCT
ejpam-865	236	1	=	=	SYM
ejpam-865	236	2	a∩	a∩	PROPN
ejpam-865	236	3	f	f	PROPN
ejpam-865	236	4	−1(v	−1(v	PROPN
ejpam-865	236	5	)	)	PUNCT
ejpam-865	236	6	is	be	AUX
ejpam-865	236	7	δ	δ	PROPN
ejpam-865	236	8	-	-	PUNCT
ejpam-865	236	9	semiopen	semiopen	ADJ
ejpam-865	236	10	in	in	ADP
ejpam-865	236	11	a	a	PRON
ejpam-865	236	12	by	by	ADP
ejpam-865	236	13	the	the	DET
ejpam-865	236	14	condition	condition	NOUN
ejpam-865	236	15	(	(	PUNCT
ejpam-865	236	16	1	1	NUM
ejpam-865	236	17	)	)	PUNCT
ejpam-865	236	18	of	of	ADP
ejpam-865	236	19	lemma	lemma	PROPN
ejpam-865	236	20	3	3	NUM
ejpam-865	236	21	.	.	PUNCT
ejpam-865	237	1	hence	hence	ADV
ejpam-865	237	2	f	f	PROPN
ejpam-865	237	3	/	/	SYM
ejpam-865	237	4	a	a	PRON
ejpam-865	237	5	is	be	AUX
ejpam-865	237	6	δα	δα	NOUN
ejpam-865	237	7	-	-	ADJ
ejpam-865	237	8	irresolute	irresolute	ADJ
ejpam-865	237	9	(	(	PUNCT
ejpam-865	237	10	resp	resp	NOUN
ejpam-865	237	11	.	.	PUNCT
ejpam-865	238	1	δp	δp	PRON
ejpam-865	238	2	-	-	PUNCT
ejpam-865	238	3	irresolute	irresolute	ADJ
ejpam-865	238	4	,	,	PUNCT
ejpam-865	238	5	δs	δs	NOUN
ejpam-865	238	6	-	-	PUNCT
ejpam-865	238	7	irresolute	irresolute	NOUN
ejpam-865	238	8	)	)	PUNCT
ejpam-865	238	9	.	.	PUNCT
ejpam-865	239	1	theorem	theorem	ADJ
ejpam-865	239	2	8	8	NUM
ejpam-865	239	3	.	.	PUNCT
ejpam-865	240	1	let	let	VERB
ejpam-865	240	2	f	f	NOUN
ejpam-865	240	3	:	:	PUNCT
ejpam-865	240	4	(	(	PUNCT
ejpam-865	240	5	x	x	X
ejpam-865	240	6	,	,	PUNCT
ejpam-865	240	7	τ)→	τ)→	PROPN
ejpam-865	240	8	(	(	PUNCT
ejpam-865	240	9	y	y	PROPN
ejpam-865	240	10	,	,	PUNCT
ejpam-865	240	11	σ	σ	PROPN
ejpam-865	240	12	)	)	PUNCT
ejpam-865	240	13	be	be	AUX
ejpam-865	240	14	a	a	DET
ejpam-865	240	15	function	function	NOUN
ejpam-865	240	16	and	and	CCONJ
ejpam-865	240	17	{	{	PUNCT
ejpam-865	240	18	aλ	aλ	X
ejpam-865	240	19	:	:	PUNCT
ejpam-865	240	20	λ	λ	PROPN
ejpam-865	240	21	∈	∈	PROPN
ejpam-865	240	22	λ	λ	PROPN
ejpam-865	240	23	}	}	PUNCT
ejpam-865	240	24	be	be	VERB
ejpam-865	240	25	a	a	DET
ejpam-865	240	26	cover	cover	NOUN
ejpam-865	240	27	of	of	ADP
ejpam-865	240	28	x	x	PUNCT
ejpam-865	240	29	by	by	ADP
ejpam-865	240	30	δ	δ	PROPN
ejpam-865	240	31	-	-	ADJ
ejpam-865	240	32	open	open	ADJ
ejpam-865	240	33	sets	set	NOUN
ejpam-865	240	34	of	of	ADP
ejpam-865	240	35	(	(	PUNCT
ejpam-865	240	36	x	x	INTJ
ejpam-865	240	37	,	,	PUNCT
ejpam-865	240	38	τ	τ	PROPN
ejpam-865	240	39	)	)	PUNCT
ejpam-865	240	40	.	.	PUNCT
ejpam-865	241	1	then	then	ADV
ejpam-865	241	2	f	f	PROPN
ejpam-865	241	3	is	be	AUX
ejpam-865	241	4	δα	δα	NOUN
ejpam-865	241	5	-	-	ADJ
ejpam-865	241	6	irresolute	irresolute	ADJ
ejpam-865	241	7	(	(	PUNCT
ejpam-865	241	8	resp	resp	NOUN
ejpam-865	241	9	.	.	PUNCT
ejpam-865	242	1	δp	δp	PRON
ejpam-865	242	2	-	-	PUNCT
ejpam-865	242	3	irresolute	irresolute	ADJ
ejpam-865	242	4	,	,	PUNCT
ejpam-865	242	5	δs	δs	NOUN
ejpam-865	242	6	-	-	PUNCT
ejpam-865	242	7	irresolute	irresolute	NOUN
ejpam-865	242	8	)	)	PUNCT
ejpam-865	242	9	if	if	SCONJ
ejpam-865	242	10	f	f	PROPN
ejpam-865	242	11	/	/	SYM
ejpam-865	242	12	aλ	aλ	PROPN
ejpam-865	242	13	:	:	PUNCT
ejpam-865	242	14	aλ	aλ	PROPN
ejpam-865	242	15	→	→	SYM
ejpam-865	242	16	y	y	PROPN
ejpam-865	242	17	is	be	AUX
ejpam-865	242	18	δα	δα	NOUN
ejpam-865	242	19	-	-	ADJ
ejpam-865	242	20	irresolute	irresolute	ADJ
ejpam-865	242	21	(	(	PUNCT
ejpam-865	242	22	resp	resp	NOUN
ejpam-865	242	23	.	.	PUNCT
ejpam-865	243	1	δp	δp	PRON
ejpam-865	243	2	-	-	PUNCT
ejpam-865	243	3	irresolute	irresolute	ADJ
ejpam-865	243	4	,	,	PUNCT
ejpam-865	243	5	δs	δs	NOUN
ejpam-865	243	6	-	-	PUNCT
ejpam-865	243	7	irresolute	irresolute	NOUN
ejpam-865	243	8	)	)	PUNCT
ejpam-865	244	1	for	for	ADP
ejpam-865	244	2	each	each	DET
ejpam-865	244	3	λ	λ	PROPN
ejpam-865	244	4	∈	∈	PROPN
ejpam-865	244	5	λ	λ	PROPN
ejpam-865	244	6	.	.	PUNCT
ejpam-865	244	7	proof	proof	NOUN
ejpam-865	244	8	.	.	PUNCT
ejpam-865	245	1	let	let	VERB
ejpam-865	245	2	v	v	PART
ejpam-865	245	3	be	be	AUX
ejpam-865	245	4	any	any	DET
ejpam-865	245	5	α	α	NOUN
ejpam-865	245	6	-	-	ADJ
ejpam-865	245	7	open	open	ADJ
ejpam-865	245	8	(	(	PUNCT
ejpam-865	245	9	resp	resp	NOUN
ejpam-865	245	10	.	.	PUNCT
ejpam-865	246	1	preopen	preopen	ADJ
ejpam-865	246	2	,	,	PUNCT
ejpam-865	246	3	semi	semi	ADJ
ejpam-865	246	4	-	-	ADJ
ejpam-865	246	5	open	open	ADJ
ejpam-865	246	6	)	)	PUNCT
ejpam-865	246	7	set	set	NOUN
ejpam-865	246	8	of	of	ADP
ejpam-865	246	9	y	y	PROPN
ejpam-865	246	10	.	.	PUNCT
ejpam-865	247	1	since	since	SCONJ
ejpam-865	247	2	f	f	PROPN
ejpam-865	247	3	/	/	SYM
ejpam-865	247	4	aλ	aλ	PROPN
ejpam-865	247	5	is	be	AUX
ejpam-865	247	6	δα	δα	NOUN
ejpam-865	247	7	-	-	ADJ
ejpam-865	247	8	irresolute	irresolute	ADJ
ejpam-865	247	9	(	(	PUNCT
ejpam-865	247	10	resp	resp	NOUN
ejpam-865	247	11	.	.	PUNCT
ejpam-865	248	1	δp	δp	PRON
ejpam-865	248	2	-	-	PUNCT
ejpam-865	248	3	irresolute	irresolute	ADJ
ejpam-865	248	4	,	,	PUNCT
ejpam-865	248	5	δs	δs	NOUN
ejpam-865	248	6	-	-	PUNCT
ejpam-865	248	7	irresolute	irresolute	NOUN
ejpam-865	248	8	)	)	PUNCT
ejpam-865	249	1	,	,	PUNCT
ejpam-865	249	2	then	then	ADV
ejpam-865	249	3	(	(	PUNCT
ejpam-865	249	4	f	f	X
ejpam-865	249	5	/	/	SYM
ejpam-865	249	6	aλ	aλ	PROPN
ejpam-865	249	7	)	)	PUNCT
ejpam-865	249	8	−1(v	−1(v	NOUN
ejpam-865	249	9	)	)	PUNCT
ejpam-865	250	1	=	=	PUNCT
ejpam-865	250	2	f	f	PROPN
ejpam-865	250	3	−1(v	−1(v	PROPN
ejpam-865	250	4	)	)	PUNCT
ejpam-865	250	5	∩	∩	NOUN
ejpam-865	250	6	aλ	aλ	ADP
ejpam-865	250	7	is	be	AUX
ejpam-865	250	8	δ	δ	PROPN
ejpam-865	250	9	-	-	PUNCT
ejpam-865	250	10	semiopen	semiopen	ADJ
ejpam-865	250	11	in	in	ADP
ejpam-865	250	12	aλ	aλ	PROPN
ejpam-865	250	13	.	.	PUNCT
ejpam-865	251	1	since	since	SCONJ
ejpam-865	251	2	aλ	aλ	PROPN
ejpam-865	251	3	is	be	AUX
ejpam-865	251	4	δ	δ	NOUN
ejpam-865	251	5	-	-	ADJ
ejpam-865	251	6	open	open	ADJ
ejpam-865	251	7	in	in	ADP
ejpam-865	251	8	x	x	X
ejpam-865	251	9	,	,	PUNCT
ejpam-865	251	10	by	by	ADP
ejpam-865	251	11	the	the	DET
ejpam-865	251	12	condition	condition	NOUN
ejpam-865	251	13	(	(	PUNCT
ejpam-865	251	14	2	2	NUM
ejpam-865	251	15	)	)	PUNCT
ejpam-865	251	16	of	of	ADP
ejpam-865	251	17	lemma	lemma	PROPN
ejpam-865	251	18	3	3	NUM
ejpam-865	251	19	,	,	PUNCT
ejpam-865	251	20	(	(	PUNCT
ejpam-865	251	21	f	f	X
ejpam-865	251	22	/	/	SYM
ejpam-865	251	23	aλ	aλ	PROPN
ejpam-865	251	24	)	)	PUNCT
ejpam-865	251	25	−1(v	−1(v	PROPN
ejpam-865	251	26	)	)	PUNCT
ejpam-865	251	27	is	be	AUX
ejpam-865	251	28	δ	δ	PROPN
ejpam-865	251	29	-	-	PUNCT
ejpam-865	251	30	semiopen	semiopen	ADJ
ejpam-865	251	31	in	in	ADP
ejpam-865	251	32	x	x	PUNCT
ejpam-865	251	33	for	for	ADP
ejpam-865	251	34	λ	λ	PROPN
ejpam-865	251	35	∈	∈	PROPN
ejpam-865	251	36	λ	λ	PROPN
ejpam-865	251	37	.	.	PUNCT
ejpam-865	252	1	therefore	therefore	ADV
ejpam-865	252	2	f	f	PROPN
ejpam-865	252	3	−1(v	−1(v	PROPN
ejpam-865	252	4	)	)	PUNCT
ejpam-865	253	1	=	=	PUNCT
ejpam-865	254	1	x	x	NOUN
ejpam-865	254	2	∩	∩	X
ejpam-865	254	3	f	f	PROPN
ejpam-865	254	4	−1(v	−1(v	PROPN
ejpam-865	254	5	)	)	PUNCT
ejpam-865	254	6	=	=	PUNCT
ejpam-865	254	7	∪{aλ	∪{aλ	PROPN
ejpam-865	254	8	∩	∩	PROPN
ejpam-865	254	9	f	f	PROPN
ejpam-865	254	10	−1(v	−1(v	PROPN
ejpam-865	254	11	)	)	PUNCT
ejpam-865	254	12	:	:	PUNCT
ejpam-865	255	1	λ	λ	X
ejpam-865	255	2	∈	∈	PROPN
ejpam-865	255	3	λ	λ	X
ejpam-865	255	4	}	}	PUNCT
ejpam-865	255	5	=	=	SYM
ejpam-865	255	6	∪	∪	X
ejpam-865	255	7	{	{	PUNCT
ejpam-865	255	8	(	(	PUNCT
ejpam-865	255	9	f	f	X
ejpam-865	255	10	/	/	SYM
ejpam-865	255	11	aλ	aλ	PROPN
ejpam-865	255	12	)	)	PUNCT
ejpam-865	255	13	−1(v	−1(v	PROPN
ejpam-865	255	14	)	)	PUNCT
ejpam-865	255	15	:	:	PUNCT
ejpam-865	256	1	λ	λ	X
ejpam-865	256	2	∈	∈	PROPN
ejpam-865	256	3	λ	λ	PROPN
ejpam-865	256	4	}	}	PUNCT
ejpam-865	256	5	is	be	AUX
ejpam-865	256	6	δ	δ	PROPN
ejpam-865	256	7	-	-	PUNCT
ejpam-865	256	8	semiopen	semiopen	ADJ
ejpam-865	256	9	in	in	ADP
ejpam-865	256	10	x	x	PRON
ejpam-865	256	11	because	because	SCONJ
ejpam-865	256	12	the	the	DET
ejpam-865	256	13	union	union	NOUN
ejpam-865	256	14	of	of	ADP
ejpam-865	256	15	δ	δ	PROPN
ejpam-865	256	16	-	-	PUNCT
ejpam-865	256	17	semiopen	semiopen	ADJ
ejpam-865	256	18	sets	set	NOUN
ejpam-865	256	19	is	be	AUX
ejpam-865	256	20	a	a	DET
ejpam-865	256	21	δ	δ	NOUN
ejpam-865	256	22	-	-	PUNCT
ejpam-865	256	23	semiopen	semiopen	ADJ
ejpam-865	256	24	set	set	VERB
ejpam-865	256	25	by	by	ADP
ejpam-865	256	26	lemma	lemma	PROPN
ejpam-865	256	27	1	1	NUM
ejpam-865	256	28	.	.	PUNCT
ejpam-865	257	1	hence	hence	ADV
ejpam-865	257	2	f	f	PROPN
ejpam-865	257	3	is	be	AUX
ejpam-865	257	4	δα	δα	NOUN
ejpam-865	257	5	-	-	ADJ
ejpam-865	257	6	irresolute	irresolute	ADJ
ejpam-865	257	7	(	(	PUNCT
ejpam-865	257	8	resp	resp	NOUN
ejpam-865	257	9	.	.	PUNCT
ejpam-865	258	1	δp	δp	PRON
ejpam-865	258	2	-	-	PUNCT
ejpam-865	258	3	irresolute	irresolute	ADJ
ejpam-865	258	4	,	,	PUNCT
ejpam-865	258	5	δs	δs	NOUN
ejpam-865	258	6	-	-	PUNCT
ejpam-865	258	7	irresolute	irresolute	NOUN
ejpam-865	258	8	)	)	PUNCT
ejpam-865	258	9	.	.	PUNCT
ejpam-865	259	1	theorem	theorem	NOUN
ejpam-865	259	2	9	9	NUM
ejpam-865	259	3	.	.	PUNCT
ejpam-865	260	1	let	let	VERB
ejpam-865	260	2	f	f	NOUN
ejpam-865	260	3	:	:	PUNCT
ejpam-865	260	4	x	x	X
ejpam-865	260	5	→	→	SYM
ejpam-865	260	6	y	y	PROPN
ejpam-865	260	7	and	and	CCONJ
ejpam-865	260	8	g	g	PROPN
ejpam-865	260	9	:	:	PUNCT
ejpam-865	260	10	y	y	PROPN
ejpam-865	260	11	→	→	SYM
ejpam-865	260	12	z	z	AUX
ejpam-865	260	13	be	be	AUX
ejpam-865	260	14	functions	function	NOUN
ejpam-865	260	15	.	.	PUNCT
ejpam-865	261	1	then	then	ADV
ejpam-865	261	2	the	the	DET
ejpam-865	261	3	composition	composition	NOUN
ejpam-865	261	4	go	go	VERB
ejpam-865	261	5	f	f	NOUN
ejpam-865	261	6	:	:	PUNCT
ejpam-865	261	7	x	x	X
ejpam-865	261	8	→	→	SYM
ejpam-865	261	9	z	z	PROPN
ejpam-865	261	10	is	be	AUX
ejpam-865	261	11	δα	δα	NOUN
ejpam-865	261	12	-	-	ADJ
ejpam-865	261	13	irresolute	irresolute	ADJ
ejpam-865	261	14	(	(	PUNCT
ejpam-865	261	15	resp	resp	NOUN
ejpam-865	261	16	.	.	PUNCT
ejpam-865	262	1	δp	δp	PRON
ejpam-865	262	2	-	-	PUNCT
ejpam-865	262	3	irresolute	irresolute	ADJ
ejpam-865	262	4	,	,	PUNCT
ejpam-865	262	5	δs	δs	NOUN
ejpam-865	262	6	-	-	PUNCT
ejpam-865	262	7	irresolute	irresolute	NOUN
ejpam-865	262	8	)	)	PUNCT
ejpam-865	262	9	if	if	SCONJ
ejpam-865	262	10	f	f	PROPN
ejpam-865	262	11	is	be	AUX
ejpam-865	262	12	δα	δα	NOUN
ejpam-865	262	13	-	-	ADJ
ejpam-865	262	14	irresolute	irresolute	ADJ
ejpam-865	262	15	(	(	PUNCT
ejpam-865	262	16	resp	resp	NOUN
ejpam-865	262	17	.	.	PUNCT
ejpam-865	263	1	δp	δp	PRON
ejpam-865	263	2	-	-	PUNCT
ejpam-865	263	3	irresolute	irresolute	ADJ
ejpam-865	263	4	,	,	PUNCT
ejpam-865	263	5	δs	δs	NOUN
ejpam-865	263	6	-	-	PUNCT
ejpam-865	263	7	irresolute	irresolute	NOUN
ejpam-865	263	8	)	)	PUNCT
ejpam-865	263	9	and	and	CCONJ
ejpam-865	263	10	g	g	PROPN
ejpam-865	263	11	is	be	AUX
ejpam-865	263	12	α	α	NOUN
ejpam-865	263	13	-	-	NOUN
ejpam-865	263	14	irresolute	irresolute	ADJ
ejpam-865	263	15	(	(	PUNCT
ejpam-865	263	16	resp	resp	NOUN
ejpam-865	263	17	.	.	PUNCT
ejpam-865	264	1	preirresolute	preirresolute	PROPN
ejpam-865	264	2	,	,	PUNCT
ejpam-865	264	3	irresolute	irresolute	ADJ
ejpam-865	264	4	)	)	PUNCT
ejpam-865	264	5	.	.	PUNCT
ejpam-865	265	1	proof	proof	NOUN
ejpam-865	265	2	.	.	PUNCT
ejpam-865	266	1	let	let	VERB
ejpam-865	266	2	w	w	NOUN
ejpam-865	266	3	be	be	AUX
ejpam-865	266	4	any	any	DET
ejpam-865	266	5	α	α	NOUN
ejpam-865	266	6	-	-	ADJ
ejpam-865	266	7	open	open	ADJ
ejpam-865	266	8	(	(	PUNCT
ejpam-865	266	9	resp	resp	NOUN
ejpam-865	266	10	.	.	PUNCT
ejpam-865	267	1	preopen	preopen	ADJ
ejpam-865	267	2	,	,	PUNCT
ejpam-865	267	3	semi	semi	ADJ
ejpam-865	267	4	-	-	ADJ
ejpam-865	267	5	open	open	ADJ
ejpam-865	267	6	)	)	PUNCT
ejpam-865	267	7	subset	subset	NOUN
ejpam-865	267	8	of	of	ADP
ejpam-865	267	9	z	z	PROPN
ejpam-865	267	10	.	.	PUNCT
ejpam-865	268	1	since	since	SCONJ
ejpam-865	268	2	g	g	PROPN
ejpam-865	268	3	is	be	AUX
ejpam-865	268	4	α	α	NOUN
ejpam-865	268	5	-	-	NOUN
ejpam-865	268	6	irresolute	irresolute	ADJ
ejpam-865	268	7	(	(	PUNCT
ejpam-865	268	8	resp	resp	NOUN
ejpam-865	268	9	.	.	PUNCT
ejpam-865	269	1	preirresolute	preirresolute	PROPN
ejpam-865	269	2	,	,	PUNCT
ejpam-865	269	3	irresolute	irresolute	ADJ
ejpam-865	269	4	)	)	PUNCT
ejpam-865	269	5	,	,	PUNCT
ejpam-865	269	6	g−1(w	g−1(w	PROPN
ejpam-865	269	7	)	)	PUNCT
ejpam-865	269	8	is	be	AUX
ejpam-865	269	9	α	α	X
ejpam-865	269	10	-	-	ADJ
ejpam-865	269	11	open	open	ADJ
ejpam-865	269	12	(	(	PUNCT
ejpam-865	269	13	resp	resp	NOUN
ejpam-865	269	14	.	.	PUNCT
ejpam-865	270	1	preopen	preopen	ADJ
ejpam-865	270	2	,	,	PUNCT
ejpam-865	270	3	semi	semi	ADJ
ejpam-865	270	4	-	-	ADJ
ejpam-865	270	5	open	open	ADJ
ejpam-865	270	6	)	)	PUNCT
ejpam-865	270	7	in	in	ADP
ejpam-865	270	8	y	y	PROPN
ejpam-865	270	9	.	.	PUNCT
ejpam-865	271	1	since	since	SCONJ
ejpam-865	271	2	f	f	PROPN
ejpam-865	271	3	is	be	AUX
ejpam-865	271	4	δα	δα	NOUN
ejpam-865	271	5	-	-	ADJ
ejpam-865	271	6	irresolute	irresolute	ADJ
ejpam-865	271	7	(	(	PUNCT
ejpam-865	271	8	resp	resp	NOUN
ejpam-865	271	9	.	.	PUNCT
ejpam-865	272	1	δp	δp	PRON
ejpam-865	272	2	-	-	PUNCT
ejpam-865	272	3	irresolute	irresolute	ADJ
ejpam-865	272	4	,	,	PUNCT
ejpam-865	272	5	δs	δs	NOUN
ejpam-865	272	6	-	-	PUNCT
ejpam-865	272	7	irresolute	irresolute	NOUN
ejpam-865	272	8	)	)	PUNCT
ejpam-865	273	1	,	,	PUNCT
ejpam-865	273	2	then	then	ADV
ejpam-865	273	3	(	(	PUNCT
ejpam-865	273	4	go	go	VERB
ejpam-865	273	5	f	f	NOUN
ejpam-865	273	6	)	)	PUNCT
ejpam-865	273	7	−1(w	−1(w	ADV
ejpam-865	273	8	)	)	PUNCT
ejpam-865	274	1	=	=	SYM
ejpam-865	274	2	f	f	NOUN
ejpam-865	274	3	−1(g−1(w	−1(g−1(w	NOUN
ejpam-865	274	4	)	)	PUNCT
ejpam-865	275	1	)	)	PUNCT
ejpam-865	275	2	is	be	AUX
ejpam-865	275	3	δ	δ	PROPN
ejpam-865	275	4	-	-	PUNCT
ejpam-865	275	5	semiopen	semiopen	ADJ
ejpam-865	275	6	in	in	ADP
ejpam-865	275	7	x	x	PUNCT
ejpam-865	275	8	and	and	CCONJ
ejpam-865	275	9	hence	hence	ADV
ejpam-865	275	10	go	go	VERB
ejpam-865	275	11	f	f	PROPN
ejpam-865	275	12	is	be	AUX
ejpam-865	275	13	δα	δα	NOUN
ejpam-865	275	14	-	-	ADJ
ejpam-865	275	15	irresolute	irresolute	ADJ
ejpam-865	275	16	(	(	PUNCT
ejpam-865	275	17	resp	resp	NOUN
ejpam-865	275	18	.	.	PUNCT
ejpam-865	276	1	δp	δp	PRON
ejpam-865	276	2	-	-	PUNCT
ejpam-865	276	3	irresolute	irresolute	ADJ
ejpam-865	276	4	,	,	PUNCT
ejpam-865	276	5	δs	δs	NOUN
ejpam-865	276	6	-	-	PUNCT
ejpam-865	276	7	irresolute	irresolute	NOUN
ejpam-865	276	8	)	)	PUNCT
ejpam-865	276	9	.	.	PUNCT
ejpam-865	277	1	we	we	PRON
ejpam-865	277	2	recall	recall	VERB
ejpam-865	277	3	that	that	SCONJ
ejpam-865	277	4	a	a	DET
ejpam-865	277	5	space	space	NOUN
ejpam-865	277	6	(	(	PUNCT
ejpam-865	277	7	x	x	X
ejpam-865	277	8	,	,	PUNCT
ejpam-865	277	9	τ	τ	X
ejpam-865	277	10	)	)	PUNCT
ejpam-865	277	11	is	be	AUX
ejpam-865	277	12	said	say	VERB
ejpam-865	277	13	to	to	PART
ejpam-865	277	14	be	be	AUX
ejpam-865	277	15	submaximal	submaximal	ADJ
ejpam-865	277	16	[	[	X
ejpam-865	277	17	4	4	NUM
ejpam-865	277	18	]	]	PUNCT
ejpam-865	277	19	if	if	SCONJ
ejpam-865	277	20	every	every	DET
ejpam-865	277	21	dense	dense	ADJ
ejpam-865	277	22	subset	subset	NOUN
ejpam-865	277	23	of	of	ADP
ejpam-865	277	24	x	x	PUNCT
ejpam-865	277	25	is	be	AUX
ejpam-865	277	26	open	open	ADJ
ejpam-865	277	27	in	in	ADP
ejpam-865	277	28	x	x	PUNCT
ejpam-865	277	29	and	and	CCONJ
ejpam-865	277	30	extremally	extremally	ADV
ejpam-865	277	31	disconnected	disconnect	VERB
ejpam-865	277	32	[	[	X
ejpam-865	277	33	26	26	NUM
ejpam-865	277	34	]	]	X
ejpam-865	277	35	if	if	SCONJ
ejpam-865	277	36	the	the	DET
ejpam-865	277	37	closure	closure	NOUN
ejpam-865	277	38	of	of	ADP
ejpam-865	277	39	each	each	DET
ejpam-865	277	40	open	open	ADJ
ejpam-865	277	41	subset	subset	NOUN
ejpam-865	277	42	of	of	ADP
ejpam-865	277	43	x	x	PUNCT
ejpam-865	277	44	is	be	AUX
ejpam-865	277	45	open	open	ADJ
ejpam-865	277	46	in	in	ADP
ejpam-865	277	47	x	x	X
ejpam-865	277	48	.	.	PUNCT
ejpam-865	278	1	the	the	DET
ejpam-865	278	2	following	follow	VERB
ejpam-865	278	3	theorem	theorem	NOUN
ejpam-865	278	4	follows	follow	VERB
ejpam-865	278	5	from	from	ADP
ejpam-865	278	6	the	the	DET
ejpam-865	278	7	fact	fact	NOUN
ejpam-865	278	8	that	that	SCONJ
ejpam-865	278	9	if	if	SCONJ
ejpam-865	278	10	(	(	PUNCT
ejpam-865	278	11	x	x	X
ejpam-865	278	12	,	,	PUNCT
ejpam-865	278	13	τ	τ	X
ejpam-865	278	14	)	)	PUNCT
ejpam-865	278	15	is	be	AUX
ejpam-865	278	16	a	a	DET
ejpam-865	278	17	submaximal	submaximal	ADJ
ejpam-865	278	18	and	and	CCONJ
ejpam-865	278	19	extremally	extremally	ADV
ejpam-865	278	20	disconnected	disconnected	ADJ
ejpam-865	278	21	space	space	NOUN
ejpam-865	278	22	,	,	PUNCT
ejpam-865	278	23	then	then	ADV
ejpam-865	278	24	τ	τ	PROPN
ejpam-865	278	25	=	=	SYM
ejpam-865	278	26	τα	τα	NOUN
ejpam-865	278	27	=	=	X
ejpam-865	278	28	so(x	so(x	X
ejpam-865	278	29	)	)	PUNCT
ejpam-865	279	1	=	=	SYM
ejpam-865	279	2	po(x	po(x	X
ejpam-865	279	3	)	)	PUNCT
ejpam-865	279	4	=	=	PUNCT
ejpam-865	279	5	βo(x	βo(x	PUNCT
ejpam-865	279	6	)	)	PUNCT
ejpam-865	280	1	[	[	X
ejpam-865	280	2	12	12	NUM
ejpam-865	280	3	,	,	PUNCT
ejpam-865	280	4	21	21	NUM
ejpam-865	280	5	]	]	PUNCT
ejpam-865	280	6	.	.	PUNCT
ejpam-865	281	1	theorem	theorem	ADJ
ejpam-865	281	2	10	10	NUM
ejpam-865	281	3	.	.	PUNCT
ejpam-865	282	1	let	let	AUX
ejpam-865	282	2	(	(	PUNCT
ejpam-865	282	3	y	y	PROPN
ejpam-865	282	4	,	,	PUNCT
ejpam-865	282	5	σ	σ	PROPN
ejpam-865	282	6	)	)	PUNCT
ejpam-865	282	7	be	be	VERB
ejpam-865	282	8	a	a	DET
ejpam-865	282	9	submaximal	submaximal	ADJ
ejpam-865	282	10	and	and	CCONJ
ejpam-865	282	11	extremally	extremally	ADV
ejpam-865	282	12	disconnected	disconnected	ADJ
ejpam-865	282	13	space	space	NOUN
ejpam-865	282	14	and	and	CCONJ
ejpam-865	282	15	let	let	VERB
ejpam-865	282	16	f	f	X
ejpam-865	282	17	:	:	PUNCT
ejpam-865	282	18	(	(	PUNCT
ejpam-865	282	19	x	x	X
ejpam-865	282	20	,	,	PUNCT
ejpam-865	282	21	τ)→	τ)→	PROPN
ejpam-865	282	22	(	(	PUNCT
ejpam-865	282	23	y	y	PROPN
ejpam-865	282	24	,	,	PUNCT
ejpam-865	282	25	σ	σ	PROPN
ejpam-865	282	26	)	)	PUNCT
ejpam-865	282	27	be	be	AUX
ejpam-865	282	28	a	a	DET
ejpam-865	282	29	function	function	NOUN
ejpam-865	282	30	.	.	PUNCT
ejpam-865	283	1	then	then	ADV
ejpam-865	283	2	we	we	PRON
ejpam-865	283	3	have	have	VERB
ejpam-865	283	4	δα	δα	NOUN
ejpam-865	283	5	-	-	PUNCT
ejpam-865	283	6	irresoluteness⇔	irresoluteness⇔	NOUN
ejpam-865	283	7	δp	δp	NOUN
ejpam-865	283	8	-	-	PUNCT
ejpam-865	283	9	irresoluteness⇔	irresoluteness⇔	NOUN
ejpam-865	283	10	δs−	δs−	NUM
ejpam-865	283	11	irresoluteness⇔	irresoluteness⇔	PROPN
ejpam-865	283	12	(	(	PUNCT
ejpam-865	283	13	δ	δ	NOUN
ejpam-865	283	14	,	,	PUNCT
ejpam-865	283	15	β)-irresoluteness	β)-irresoluteness	PROPN
ejpam-865	283	16	.	.	PUNCT
ejpam-865	284	1	recall	recall	VERB
ejpam-865	284	2	that	that	SCONJ
ejpam-865	284	3	a	a	DET
ejpam-865	284	4	topological	topological	ADJ
ejpam-865	284	5	space	space	NOUN
ejpam-865	284	6	(	(	PUNCT
ejpam-865	284	7	x	x	X
ejpam-865	284	8	,	,	PUNCT
ejpam-865	284	9	τ	τ	X
ejpam-865	284	10	)	)	PUNCT
ejpam-865	284	11	is	be	AUX
ejpam-865	284	12	called	call	VERB
ejpam-865	284	13	α	α	DET
ejpam-865	284	14	−	−	PROPN
ejpam-865	284	15	t2	t2	NOUN
ejpam-865	284	16	[	[	X
ejpam-865	284	17	17	17	NUM
ejpam-865	284	18	]	]	X
ejpam-865	284	19	(	(	PUNCT
ejpam-865	284	20	resp	resp	NOUN
ejpam-865	284	21	.	.	PUNCT
ejpam-865	285	1	pre	pre	ADJ
ejpam-865	285	2	-	-	NOUN
ejpam-865	285	3	t2	t2	ADJ
ejpam-865	285	4	[	[	X
ejpam-865	285	5	13	13	NUM
ejpam-865	285	6	]	]	PUNCT
ejpam-865	285	7	,	,	PUNCT
ejpam-865	285	8	semi	semi	ADJ
ejpam-865	285	9	-	-	NOUN
ejpam-865	285	10	t2	t2	ADJ
ejpam-865	285	11	[	[	X
ejpam-865	285	12	16	16	NUM
ejpam-865	285	13	]	]	PUNCT
ejpam-865	285	14	,	,	PUNCT
ejpam-865	285	15	δ	δ	PROPN
ejpam-865	285	16	-	-	PUNCT
ejpam-865	285	17	semi	semi	NOUN
ejpam-865	285	18	-	-	NOUN
ejpam-865	285	19	t2	t2	ADJ
ejpam-865	285	20	[	[	X
ejpam-865	285	21	5	5	NUM
ejpam-865	285	22	]	]	X
ejpam-865	285	23	if	if	SCONJ
ejpam-865	285	24	for	for	ADP
ejpam-865	285	25	any	any	DET
ejpam-865	285	26	distinct	distinct	ADJ
ejpam-865	285	27	pair	pair	NOUN
ejpam-865	285	28	of	of	ADP
ejpam-865	285	29	points	point	NOUN
ejpam-865	285	30	x	x	PUNCT
ejpam-865	285	31	and	and	CCONJ
ejpam-865	285	32	y	y	PROPN
ejpam-865	285	33	in	in	ADP
ejpam-865	285	34	x	x	SYM
ejpam-865	285	35	,	,	PUNCT
ejpam-865	285	36	there	there	PRON
ejpam-865	285	37	exist	exist	VERB
ejpam-865	285	38	uεα(x	uεα(x	NOUN
ejpam-865	285	39	,	,	PUNCT
ejpam-865	285	40	x	x	NOUN
ejpam-865	285	41	)	)	PUNCT
ejpam-865	285	42	and	and	CCONJ
ejpam-865	285	43	vεα(x	vεα(x	PROPN
ejpam-865	285	44	,	,	PUNCT
ejpam-865	285	45	y	y	PROPN
ejpam-865	285	46	)	)	PUNCT
ejpam-865	285	47	(	(	PUNCT
ejpam-865	285	48	resp	resp	NOUN
ejpam-865	285	49	.	.	PUNCT
ejpam-865	286	1	uεpo(x	uεpo(x	PROPN
ejpam-865	286	2	,	,	PUNCT
ejpam-865	286	3	x	x	NOUN
ejpam-865	286	4	)	)	PUNCT
ejpam-865	286	5	and	and	CCONJ
ejpam-865	286	6	vεpo(x	vεpo(x	PRON
ejpam-865	286	7	,	,	PUNCT
ejpam-865	286	8	y	y	PROPN
ejpam-865	286	9	)	)	PUNCT
ejpam-865	286	10	,	,	PUNCT
ejpam-865	286	11	uεso(x	uεso(x	PROPN
ejpam-865	286	12	,	,	PUNCT
ejpam-865	286	13	x	x	NOUN
ejpam-865	286	14	)	)	PUNCT
ejpam-865	286	15	and	and	CCONJ
ejpam-865	286	16	vεso(x	vεso(x	PROPN
ejpam-865	286	17	,	,	PUNCT
ejpam-865	286	18	y	y	PROPN
ejpam-865	286	19	)	)	PUNCT
ejpam-865	286	20	,	,	PUNCT
ejpam-865	286	21	uεδso(x	uεδso(x	PROPN
ejpam-865	286	22	,	,	PUNCT
ejpam-865	286	23	x	x	NOUN
ejpam-865	286	24	)	)	PUNCT
ejpam-865	286	25	and	and	CCONJ
ejpam-865	286	26	vεδso(x	vεδso(x	NUM
ejpam-865	286	27	,	,	PUNCT
ejpam-865	286	28	y	y	PROPN
ejpam-865	286	29	)	)	PUNCT
ejpam-865	286	30	)	)	PUNCT
ejpam-865	286	31	such	such	ADJ
ejpam-865	286	32	that	that	SCONJ
ejpam-865	286	33	u	u	PROPN
ejpam-865	286	34	∩	∩	NOUN
ejpam-865	286	35	v	v	NOUN
ejpam-865	286	36	=	=	PUNCT
ejpam-865	286	37	∅.	∅.	NOUN
ejpam-865	286	38	theorem	theorem	VERB
ejpam-865	286	39	11	11	NUM
ejpam-865	286	40	.	.	PUNCT
ejpam-865	287	1	if	if	SCONJ
ejpam-865	287	2	f	f	PROPN
ejpam-865	287	3	:	:	PUNCT
ejpam-865	287	4	(	(	PUNCT
ejpam-865	287	5	x	x	X
ejpam-865	287	6	,	,	PUNCT
ejpam-865	287	7	τ)→	τ)→	PROPN
ejpam-865	287	8	(	(	PUNCT
ejpam-865	287	9	y	y	PROPN
ejpam-865	287	10	,	,	PUNCT
ejpam-865	287	11	σ	σ	PROPN
ejpam-865	287	12	)	)	PUNCT
ejpam-865	287	13	is	be	AUX
ejpam-865	287	14	δα	δα	NOUN
ejpam-865	287	15	-	-	ADJ
ejpam-865	287	16	irresolute	irresolute	ADJ
ejpam-865	287	17	(	(	PUNCT
ejpam-865	287	18	resp	resp	NOUN
ejpam-865	287	19	.	.	PUNCT
ejpam-865	288	1	δp	δp	PRON
ejpam-865	288	2	-	-	PUNCT
ejpam-865	288	3	irresolute	irresolute	ADJ
ejpam-865	288	4	,	,	PUNCT
ejpam-865	288	5	δs	δs	NOUN
ejpam-865	288	6	-	-	PUNCT
ejpam-865	288	7	irresolute	irresolute	NOUN
ejpam-865	288	8	)	)	PUNCT
ejpam-865	289	1	injection	injection	NOUN
ejpam-865	289	2	and	and	CCONJ
ejpam-865	289	3	y	y	NOUN
ejpam-865	289	4	is	be	AUX
ejpam-865	289	5	α−	α−	ADP
ejpam-865	289	6	t2	t2	PROPN
ejpam-865	289	7	(	(	PUNCT
ejpam-865	289	8	resp	resp	NOUN
ejpam-865	289	9	.	.	PUNCT
ejpam-865	290	1	pre	pre	ADJ
ejpam-865	290	2	-	-	NOUN
ejpam-865	290	3	t2	t2	ADJ
ejpam-865	290	4	,	,	PUNCT
ejpam-865	290	5	semi	semi	ADJ
ejpam-865	290	6	-	-	NOUN
ejpam-865	290	7	t2	t2	ADJ
ejpam-865	290	8	)	)	PUNCT
ejpam-865	290	9	,	,	PUNCT
ejpam-865	290	10	then	then	ADV
ejpam-865	290	11	x	x	PUNCT
ejpam-865	290	12	is	be	AUX
ejpam-865	290	13	δ	δ	NOUN
ejpam-865	290	14	-	-	PUNCT
ejpam-865	290	15	semi	semi	NOUN
ejpam-865	290	16	-	-	NOUN
ejpam-865	290	17	t2	t2	NOUN
ejpam-865	290	18	.	.	PUNCT
ejpam-865	291	1	y.	y.	PROPN
ejpam-865	291	2	beceren	beceren	PROPN
ejpam-865	291	3	,	,	PUNCT
ejpam-865	291	4	t.	t.	PROPN
ejpam-865	291	5	noiri	noiri	PROPN
ejpam-865	291	6	/	/	SYM
ejpam-865	291	7	eur	eur	PROPN
ejpam-865	291	8	.	.	PUNCT
ejpam-865	292	1	j.	j.	PROPN
ejpam-865	292	2	pure	pure	PROPN
ejpam-865	292	3	appl	appl	PROPN
ejpam-865	292	4	.	.	PROPN
ejpam-865	292	5	math	math	PROPN
ejpam-865	292	6	,	,	PUNCT
ejpam-865	292	7	4	4	NUM
ejpam-865	292	8	(	(	PUNCT
ejpam-865	292	9	2011	2011	NUM
ejpam-865	292	10	)	)	PUNCT
ejpam-865	292	11	,	,	PUNCT
ejpam-865	292	12	361	361	NUM
ejpam-865	292	13	-	-	SYM
ejpam-865	292	14	369	369	NUM
ejpam-865	292	15	367	367	NUM
ejpam-865	292	16	proof	proof	NOUN
ejpam-865	292	17	.	.	PUNCT
ejpam-865	293	1	let	let	VERB
ejpam-865	293	2	x	x	PRON
ejpam-865	293	3	and	and	CCONJ
ejpam-865	293	4	y	y	PROPN
ejpam-865	293	5	be	be	AUX
ejpam-865	293	6	distinct	distinct	ADJ
ejpam-865	293	7	points	point	NOUN
ejpam-865	293	8	of	of	ADP
ejpam-865	293	9	x	x	X
ejpam-865	293	10	.	.	PUNCT
ejpam-865	294	1	then	then	ADV
ejpam-865	294	2	f	f	PROPN
ejpam-865	294	3	(	(	PUNCT
ejpam-865	294	4	x	x	X
ejpam-865	294	5	)	)	PUNCT
ejpam-865	294	6	6=	6=	ADP
ejpam-865	294	7	f	f	PROPN
ejpam-865	294	8	(	(	PUNCT
ejpam-865	294	9	y	y	PROPN
ejpam-865	294	10	)	)	PUNCT
ejpam-865	294	11	.	.	PUNCT
ejpam-865	295	1	since	since	SCONJ
ejpam-865	295	2	y	y	PROPN
ejpam-865	295	3	is	be	AUX
ejpam-865	295	4	α−	α−	ADP
ejpam-865	295	5	t2	t2	PROPN
ejpam-865	295	6	(	(	PUNCT
ejpam-865	295	7	resp	resp	NOUN
ejpam-865	295	8	.	.	PUNCT
ejpam-865	296	1	pret2	pret2	ADJ
ejpam-865	296	2	,	,	PUNCT
ejpam-865	296	3	semi	semi	ADJ
ejpam-865	296	4	-	-	NOUN
ejpam-865	296	5	t2	t2	ADJ
ejpam-865	296	6	)	)	PUNCT
ejpam-865	296	7	,	,	PUNCT
ejpam-865	296	8	there	there	PRON
ejpam-865	296	9	exist	exist	VERB
ejpam-865	296	10	disjoint	disjoint	NOUN
ejpam-865	296	11	α	α	NOUN
ejpam-865	296	12	-	-	ADJ
ejpam-865	296	13	open	open	ADJ
ejpam-865	296	14	(	(	PUNCT
ejpam-865	296	15	resp	resp	NOUN
ejpam-865	296	16	.	.	PUNCT
ejpam-865	297	1	preopen	preopen	ADJ
ejpam-865	297	2	,	,	PUNCT
ejpam-865	297	3	semi	semi	ADJ
ejpam-865	297	4	-	-	ADJ
ejpam-865	297	5	open	open	ADJ
ejpam-865	297	6	)	)	PUNCT
ejpam-865	297	7	sets	set	VERB
ejpam-865	297	8	v	v	NOUN
ejpam-865	297	9	and	and	CCONJ
ejpam-865	297	10	w	w	NOUN
ejpam-865	297	11	containing	contain	VERB
ejpam-865	297	12	f	f	PROPN
ejpam-865	297	13	(	(	PUNCT
ejpam-865	297	14	x	x	NOUN
ejpam-865	297	15	)	)	PUNCT
ejpam-865	298	1	and	and	CCONJ
ejpam-865	298	2	f	f	PROPN
ejpam-865	298	3	(	(	PUNCT
ejpam-865	298	4	y	y	NOUN
ejpam-865	298	5	)	)	PUNCT
ejpam-865	298	6	,	,	PUNCT
ejpam-865	298	7	respectively	respectively	ADV
ejpam-865	298	8	.	.	PUNCT
ejpam-865	299	1	since	since	SCONJ
ejpam-865	299	2	f	f	PROPN
ejpam-865	299	3	is	be	AUX
ejpam-865	299	4	δα	δα	NOUN
ejpam-865	299	5	-	-	ADJ
ejpam-865	299	6	irresolute	irresolute	ADJ
ejpam-865	299	7	(	(	PUNCT
ejpam-865	299	8	resp	resp	NOUN
ejpam-865	299	9	.	.	PUNCT
ejpam-865	300	1	δp	δp	PRON
ejpam-865	300	2	-	-	PUNCT
ejpam-865	300	3	irresolute	irresolute	ADJ
ejpam-865	300	4	,	,	PUNCT
ejpam-865	300	5	δs	δs	NOUN
ejpam-865	300	6	-	-	PUNCT
ejpam-865	300	7	irresolute	irresolute	NOUN
ejpam-865	300	8	)	)	PUNCT
ejpam-865	300	9	,	,	PUNCT
ejpam-865	300	10	there	there	PRON
ejpam-865	300	11	exist	exist	VERB
ejpam-865	300	12	δ	δ	PROPN
ejpam-865	300	13	-	-	PUNCT
ejpam-865	300	14	semiopen	semiopen	VERB
ejpam-865	300	15	sets	set	VERB
ejpam-865	300	16	u	u	NOUN
ejpam-865	300	17	and	and	CCONJ
ejpam-865	300	18	h	h	NOUN
ejpam-865	300	19	containing	contain	VERB
ejpam-865	300	20	x	x	PROPN
ejpam-865	300	21	and	and	CCONJ
ejpam-865	300	22	y	y	PROPN
ejpam-865	300	23	,	,	PUNCT
ejpam-865	300	24	respectively	respectively	ADV
ejpam-865	300	25	,	,	PUNCT
ejpam-865	300	26	such	such	ADJ
ejpam-865	300	27	that	that	SCONJ
ejpam-865	300	28	f	f	PROPN
ejpam-865	300	29	(	(	PUNCT
ejpam-865	300	30	u	u	NOUN
ejpam-865	300	31	)	)	PUNCT
ejpam-865	300	32	⊂	⊂	PROPN
ejpam-865	300	33	v	v	PROPN
ejpam-865	300	34	and	and	CCONJ
ejpam-865	300	35	f	f	PROPN
ejpam-865	300	36	(	(	PUNCT
ejpam-865	300	37	h)⊂w	h)⊂w	VERB
ejpam-865	300	38	.	.	PUNCT
ejpam-865	301	1	it	it	PRON
ejpam-865	301	2	follows	follow	VERB
ejpam-865	301	3	that	that	SCONJ
ejpam-865	301	4	u	u	PROPN
ejpam-865	301	5	∩	∩	ADJ
ejpam-865	301	6	h	h	NOUN
ejpam-865	301	7	=	=	PUNCT
ejpam-865	301	8	∅.	∅.	ADP
ejpam-865	301	9	this	this	PRON
ejpam-865	301	10	shows	show	VERB
ejpam-865	301	11	that	that	SCONJ
ejpam-865	301	12	x	x	PRON
ejpam-865	301	13	is	be	AUX
ejpam-865	301	14	δ	δ	NOUN
ejpam-865	301	15	-	-	PUNCT
ejpam-865	301	16	semi	semi	NOUN
ejpam-865	301	17	-	-	NOUN
ejpam-865	301	18	t2	t2	NOUN
ejpam-865	301	19	.	.	PUNCT
ejpam-865	302	1	lemma	lemma	PROPN
ejpam-865	302	2	4	4	NUM
ejpam-865	302	3	(	(	PUNCT
ejpam-865	302	4	lee	lee	PROPN
ejpam-865	302	5	et	et	PROPN
ejpam-865	302	6	.	.	PUNCT
ejpam-865	303	1	al	al	PROPN
ejpam-865	303	2	.	.	PUNCT
ejpam-865	304	1	[	[	X
ejpam-865	304	2	14	14	NUM
ejpam-865	304	3	]	]	PUNCT
ejpam-865	304	4	)	)	PUNCT
ejpam-865	304	5	.	.	PUNCT
ejpam-865	305	1	if	if	SCONJ
ejpam-865	305	2	ai	ai	NOUN
ejpam-865	305	3	is	be	AUX
ejpam-865	305	4	a	a	DET
ejpam-865	305	5	δ	δ	NOUN
ejpam-865	305	6	-	-	PUNCT
ejpam-865	305	7	semiopen	semiopen	ADJ
ejpam-865	305	8	set	set	NOUN
ejpam-865	305	9	of	of	ADP
ejpam-865	305	10	x	x	PROPN
ejpam-865	305	11	i(i	i(i	PROPN
ejpam-865	305	12	=	=	SYM
ejpam-865	305	13	1,2	1,2	NUM
ejpam-865	305	14	)	)	PUNCT
ejpam-865	305	15	,	,	PUNCT
ejpam-865	305	16	then	then	ADV
ejpam-865	305	17	a1×	a1×	PROPN
ejpam-865	305	18	a2	a2	PROPN
ejpam-865	305	19	is	be	AUX
ejpam-865	305	20	δ	δ	PROPN
ejpam-865	305	21	-	-	PUNCT
ejpam-865	305	22	semiopen	semiopen	ADJ
ejpam-865	305	23	in	in	ADP
ejpam-865	305	24	x1×	x1×	PROPN
ejpam-865	305	25	x2	x2	PROPN
ejpam-865	305	26	.	.	PUNCT
ejpam-865	306	1	theorem	theorem	VERB
ejpam-865	306	2	12	12	NUM
ejpam-865	306	3	.	.	PUNCT
ejpam-865	307	1	if	if	SCONJ
ejpam-865	307	2	f	f	PROPN
ejpam-865	307	3	:	:	PUNCT
ejpam-865	307	4	(	(	PUNCT
ejpam-865	307	5	x	x	X
ejpam-865	307	6	,	,	PUNCT
ejpam-865	307	7	τ)→	τ)→	PROPN
ejpam-865	307	8	(	(	PUNCT
ejpam-865	307	9	y	y	PROPN
ejpam-865	307	10	,	,	PUNCT
ejpam-865	307	11	σ	σ	PROPN
ejpam-865	307	12	)	)	PUNCT
ejpam-865	307	13	is	be	AUX
ejpam-865	307	14	δα	δα	NOUN
ejpam-865	307	15	-	-	ADJ
ejpam-865	307	16	irresolute	irresolute	ADJ
ejpam-865	307	17	(	(	PUNCT
ejpam-865	307	18	resp	resp	NOUN
ejpam-865	307	19	.	.	PUNCT
ejpam-865	308	1	δp	δp	PRON
ejpam-865	308	2	-	-	PUNCT
ejpam-865	308	3	irresolute	irresolute	ADJ
ejpam-865	308	4	,	,	PUNCT
ejpam-865	308	5	δs	δs	NOUN
ejpam-865	308	6	-	-	PUNCT
ejpam-865	308	7	irresolute	irresolute	NOUN
ejpam-865	308	8	)	)	PUNCT
ejpam-865	308	9	and	and	CCONJ
ejpam-865	308	10	y	y	PROPN
ejpam-865	308	11	is	be	AUX
ejpam-865	308	12	α−	α−	ADP
ejpam-865	308	13	t2	t2	PROPN
ejpam-865	308	14	(	(	PUNCT
ejpam-865	308	15	resp	resp	NOUN
ejpam-865	308	16	.	.	PUNCT
ejpam-865	309	1	pre	pre	ADJ
ejpam-865	309	2	-	-	NOUN
ejpam-865	309	3	t2	t2	ADJ
ejpam-865	309	4	,	,	PUNCT
ejpam-865	309	5	semi	semi	ADJ
ejpam-865	309	6	-	-	NOUN
ejpam-865	309	7	t2	t2	ADJ
ejpam-865	309	8	)	)	PUNCT
ejpam-865	309	9	,	,	PUNCT
ejpam-865	309	10	then	then	ADV
ejpam-865	309	11	the	the	DET
ejpam-865	309	12	set	set	NOUN
ejpam-865	309	13	e	e	NOUN
ejpam-865	309	14	=	=	PRON
ejpam-865	309	15	{	{	PUNCT
ejpam-865	309	16	(	(	PUNCT
ejpam-865	309	17	x	x	INTJ
ejpam-865	309	18	,	,	PUNCT
ejpam-865	309	19	y	y	PROPN
ejpam-865	309	20	)	)	PUNCT
ejpam-865	309	21	:	:	PUNCT
ejpam-865	310	1	f	f	X
ejpam-865	310	2	(	(	PUNCT
ejpam-865	310	3	x	x	X
ejpam-865	310	4	)	)	PUNCT
ejpam-865	310	5	=	=	SYM
ejpam-865	310	6	f	f	PROPN
ejpam-865	310	7	(	(	PUNCT
ejpam-865	310	8	y	y	NOUN
ejpam-865	310	9	)	)	PUNCT
ejpam-865	310	10	}	}	PUNCT
ejpam-865	310	11	is	be	AUX
ejpam-865	310	12	δ	δ	PROPN
ejpam-865	310	13	-	-	PUNCT
ejpam-865	310	14	semiclosed	semiclose	VERB
ejpam-865	310	15	in	in	ADP
ejpam-865	310	16	x	x	X
ejpam-865	310	17	×x	×x	X
ejpam-865	310	18	.	.	PUNCT
ejpam-865	311	1	proof	proof	NOUN
ejpam-865	311	2	.	.	PUNCT
ejpam-865	312	1	suppose	suppose	VERB
ejpam-865	312	2	that	that	SCONJ
ejpam-865	312	3	(	(	PUNCT
ejpam-865	312	4	x	x	X
ejpam-865	312	5	,	,	PUNCT
ejpam-865	312	6	y	y	PROPN
ejpam-865	312	7	)	)	PUNCT
ejpam-865	312	8	/∈	/∈	PUNCT
ejpam-865	313	1	e.	e.	PROPN
ejpam-865	314	1	then	then	ADV
ejpam-865	314	2	f	f	PROPN
ejpam-865	314	3	(	(	PUNCT
ejpam-865	314	4	x	x	X
ejpam-865	314	5	)	)	PUNCT
ejpam-865	314	6	6=	6=	ADP
ejpam-865	314	7	f	f	PROPN
ejpam-865	314	8	(	(	PUNCT
ejpam-865	314	9	y	y	PROPN
ejpam-865	314	10	)	)	PUNCT
ejpam-865	314	11	.	.	PUNCT
ejpam-865	315	1	since	since	SCONJ
ejpam-865	315	2	y	y	PROPN
ejpam-865	315	3	is	be	AUX
ejpam-865	315	4	α−	α−	ADP
ejpam-865	315	5	t2	t2	PROPN
ejpam-865	315	6	(	(	PUNCT
ejpam-865	315	7	resp	resp	NOUN
ejpam-865	315	8	.	.	PUNCT
ejpam-865	316	1	pre	pre	ADJ
ejpam-865	316	2	-	-	NOUN
ejpam-865	316	3	t2	t2	ADJ
ejpam-865	316	4	,	,	PUNCT
ejpam-865	316	5	semit2	semit2	NOUN
ejpam-865	316	6	)	)	PUNCT
ejpam-865	316	7	,	,	PUNCT
ejpam-865	316	8	there	there	PRON
ejpam-865	316	9	exist	exist	VERB
ejpam-865	316	10	vεα(y	vεα(y	PROPN
ejpam-865	316	11	,	,	PUNCT
ejpam-865	316	12	f	f	PROPN
ejpam-865	316	13	(	(	PUNCT
ejpam-865	316	14	x	x	NOUN
ejpam-865	316	15	)	)	PUNCT
ejpam-865	316	16	)	)	PUNCT
ejpam-865	316	17	and	and	CCONJ
ejpam-865	316	18	wεα(y	wεα(y	PROPN
ejpam-865	316	19	,	,	PUNCT
ejpam-865	316	20	f	f	PROPN
ejpam-865	316	21	(	(	PUNCT
ejpam-865	316	22	y	y	NOUN
ejpam-865	316	23	)	)	PUNCT
ejpam-865	316	24	)	)	PUNCT
ejpam-865	317	1	(	(	PUNCT
ejpam-865	317	2	resp	resp	NOUN
ejpam-865	317	3	.	.	PUNCT
ejpam-865	318	1	vεpo(y	vεpo(y	PROPN
ejpam-865	318	2	,	,	PUNCT
ejpam-865	318	3	f	f	PROPN
ejpam-865	318	4	(	(	PUNCT
ejpam-865	318	5	x	x	NOUN
ejpam-865	318	6	)	)	PUNCT
ejpam-865	318	7	)	)	PUNCT
ejpam-865	318	8	and	and	CCONJ
ejpam-865	318	9	wεpo(y	wεpo(y	PROPN
ejpam-865	318	10	,	,	PUNCT
ejpam-865	318	11	f	f	PROPN
ejpam-865	318	12	(	(	PUNCT
ejpam-865	318	13	y	y	NOUN
ejpam-865	318	14	)	)	PUNCT
ejpam-865	318	15	)	)	PUNCT
ejpam-865	318	16	,	,	PUNCT
ejpam-865	318	17	vεso(y	vεso(y	NUM
ejpam-865	318	18	,	,	PUNCT
ejpam-865	318	19	f	f	PROPN
ejpam-865	318	20	(	(	PUNCT
ejpam-865	318	21	x	x	NOUN
ejpam-865	318	22	)	)	PUNCT
ejpam-865	318	23	)	)	PUNCT
ejpam-865	318	24	and	and	CCONJ
ejpam-865	318	25	wεso(y	wεso(y	PROPN
ejpam-865	318	26	,	,	PUNCT
ejpam-865	318	27	f	f	PROPN
ejpam-865	318	28	(	(	PUNCT
ejpam-865	318	29	y	y	NOUN
ejpam-865	318	30	)	)	PUNCT
ejpam-865	318	31	)	)	PUNCT
ejpam-865	318	32	)	)	PUNCT
ejpam-865	319	1	such	such	ADJ
ejpam-865	319	2	that	that	DET
ejpam-865	319	3	v	v	NOUN
ejpam-865	319	4	∩w	∩w	NOUN
ejpam-865	319	5	=	=	PUNCT
ejpam-865	319	6	∅.	∅.	NOUN
ejpam-865	319	7	since	since	SCONJ
ejpam-865	319	8	f	f	PROPN
ejpam-865	319	9	is	be	AUX
ejpam-865	319	10	δα	δα	NOUN
ejpam-865	319	11	-	-	ADJ
ejpam-865	319	12	irresolute	irresolute	ADJ
ejpam-865	319	13	(	(	PUNCT
ejpam-865	319	14	resp	resp	NOUN
ejpam-865	319	15	.	.	PUNCT
ejpam-865	320	1	δp	δp	PRON
ejpam-865	320	2	-	-	PUNCT
ejpam-865	320	3	irresolute	irresolute	ADJ
ejpam-865	320	4	,	,	PUNCT
ejpam-865	320	5	δs	δs	NOUN
ejpam-865	320	6	-	-	PUNCT
ejpam-865	320	7	irresolute	irresolute	NOUN
ejpam-865	320	8	)	)	PUNCT
ejpam-865	320	9	,	,	PUNCT
ejpam-865	320	10	there	there	PRON
ejpam-865	320	11	exist	exist	VERB
ejpam-865	320	12	δ	δ	PROPN
ejpam-865	320	13	-	-	PUNCT
ejpam-865	320	14	semiopen	semiopen	VERB
ejpam-865	320	15	sets	set	VERB
ejpam-865	320	16	u	u	NOUN
ejpam-865	320	17	and	and	CCONJ
ejpam-865	320	18	h	h	NOUN
ejpam-865	320	19	containing	contain	VERB
ejpam-865	320	20	x	x	PROPN
ejpam-865	320	21	and	and	CCONJ
ejpam-865	320	22	y	y	PROPN
ejpam-865	320	23	,	,	PUNCT
ejpam-865	320	24	respectively	respectively	ADV
ejpam-865	320	25	,	,	PUNCT
ejpam-865	320	26	such	such	ADJ
ejpam-865	320	27	that	that	SCONJ
ejpam-865	320	28	f	f	PROPN
ejpam-865	320	29	(	(	PUNCT
ejpam-865	320	30	u)⊂	u)⊂	CCONJ
ejpam-865	320	31	v	v	NOUN
ejpam-865	320	32	and	and	CCONJ
ejpam-865	320	33	f	f	PROPN
ejpam-865	320	34	(	(	PUNCT
ejpam-865	320	35	h)⊂w	h)⊂w	NOUN
ejpam-865	320	36	.	.	PUNCT
ejpam-865	321	1	set	set	VERB
ejpam-865	321	2	g	g	PROPN
ejpam-865	321	3	=	=	SYM
ejpam-865	321	4	u	u	NOUN
ejpam-865	321	5	×h	×h	NOUN
ejpam-865	321	6	.	.	PUNCT
ejpam-865	322	1	by	by	ADP
ejpam-865	322	2	lemma	lemma	PROPN
ejpam-865	322	3	4	4	NUM
ejpam-865	322	4	,	,	PUNCT
ejpam-865	322	5	(	(	PUNCT
ejpam-865	322	6	x	x	X
ejpam-865	322	7	,	,	PUNCT
ejpam-865	322	8	y	y	PROPN
ejpam-865	322	9	)	)	PUNCT
ejpam-865	322	10	∈	∈	PROPN
ejpam-865	323	1	g	g	NOUN
ejpam-865	323	2	∈	∈	PROPN
ejpam-865	323	3	δso(x	δso(x	X
ejpam-865	323	4	×	×	NOUN
ejpam-865	323	5	x	x	PUNCT
ejpam-865	323	6	)	)	PUNCT
ejpam-865	323	7	and	and	CCONJ
ejpam-865	323	8	g	g	NOUN
ejpam-865	323	9	∩	∩	ADJ
ejpam-865	323	10	e	e	NOUN
ejpam-865	323	11	=	=	PUNCT
ejpam-865	323	12	∅.	∅.	PRON
ejpam-865	323	13	this	this	PRON
ejpam-865	323	14	means	mean	VERB
ejpam-865	323	15	that	that	SCONJ
ejpam-865	323	16	δcls(e)⊂	δcls(e)⊂	NOUN
ejpam-865	323	17	e	e	NOUN
ejpam-865	323	18	and	and	CCONJ
ejpam-865	323	19	hence	hence	ADV
ejpam-865	323	20	the	the	DET
ejpam-865	323	21	set	set	NOUN
ejpam-865	323	22	e	e	NOUN
ejpam-865	323	23	is	be	AUX
ejpam-865	323	24	δ	δ	PROPN
ejpam-865	323	25	-	-	PUNCT
ejpam-865	323	26	semiclosed	semiclose	VERB
ejpam-865	323	27	in	in	ADP
ejpam-865	323	28	x	x	X
ejpam-865	323	29	×	×	PROPN
ejpam-865	323	30	x	x	X
ejpam-865	323	31	.	.	PUNCT
ejpam-865	324	1	definition	definition	NOUN
ejpam-865	324	2	4	4	NUM
ejpam-865	324	3	.	.	PUNCT
ejpam-865	325	1	for	for	ADP
ejpam-865	325	2	a	a	DET
ejpam-865	325	3	function	function	NOUN
ejpam-865	325	4	f	f	NOUN
ejpam-865	325	5	:	:	PUNCT
ejpam-865	325	6	x	x	X
ejpam-865	325	7	→	→	SYM
ejpam-865	325	8	y	y	PROPN
ejpam-865	325	9	,	,	PUNCT
ejpam-865	325	10	the	the	DET
ejpam-865	325	11	graph	graph	NOUN
ejpam-865	325	12	g	g	PROPN
ejpam-865	325	13	(	(	PUNCT
ejpam-865	325	14	f	f	PROPN
ejpam-865	325	15	)	)	PUNCT
ejpam-865	325	16	=	=	PRON
ejpam-865	326	1	{	{	PUNCT
ejpam-865	326	2	(	(	PUNCT
ejpam-865	326	3	x	x	INTJ
ejpam-865	326	4	,	,	PUNCT
ejpam-865	326	5	f	f	PROPN
ejpam-865	326	6	(	(	PUNCT
ejpam-865	326	7	x	x	NOUN
ejpam-865	326	8	)	)	PUNCT
ejpam-865	326	9	)	)	PUNCT
ejpam-865	326	10	:	:	PUNCT
ejpam-865	327	1	x	x	X
ejpam-865	327	2	∈	∈	NOUN
ejpam-865	327	3	x	x	PUNCT
ejpam-865	327	4	}	}	PUNCT
ejpam-865	327	5	is	be	AUX
ejpam-865	327	6	called	call	VERB
ejpam-865	327	7	δαclosed	δαclosed	ADJ
ejpam-865	327	8	(	(	PUNCT
ejpam-865	327	9	resp	resp	NOUN
ejpam-865	327	10	.	.	PUNCT
ejpam-865	328	1	δp	δp	PRON
ejpam-865	328	2	-	-	PUNCT
ejpam-865	328	3	closed	closed	ADJ
ejpam-865	328	4	,	,	PUNCT
ejpam-865	328	5	δs	δs	NOUN
ejpam-865	328	6	-	-	PUNCT
ejpam-865	328	7	closed	closed	ADJ
ejpam-865	328	8	)	)	PUNCT
ejpam-865	328	9	if	if	SCONJ
ejpam-865	328	10	for	for	ADP
ejpam-865	328	11	each	each	DET
ejpam-865	328	12	(	(	PUNCT
ejpam-865	328	13	x	x	PROPN
ejpam-865	328	14	,	,	PUNCT
ejpam-865	328	15	y	y	PROPN
ejpam-865	328	16	)	)	PUNCT
ejpam-865	328	17	∈	∈	PROPN
ejpam-865	328	18	(	(	PUNCT
ejpam-865	328	19	x	x	SYM
ejpam-865	328	20	×	×	PROPN
ejpam-865	328	21	y	y	PROPN
ejpam-865	328	22	)	)	PUNCT
ejpam-865	328	23	−	−	PROPN
ejpam-865	329	1	g	g	PROPN
ejpam-865	329	2	(	(	PUNCT
ejpam-865	329	3	f	f	PROPN
ejpam-865	329	4	)	)	PUNCT
ejpam-865	329	5	,	,	PUNCT
ejpam-865	329	6	there	there	PRON
ejpam-865	329	7	exist	exist	VERB
ejpam-865	329	8	uεδso(x	uεδso(x	PROPN
ejpam-865	329	9	,	,	PUNCT
ejpam-865	329	10	x	x	NOUN
ejpam-865	329	11	)	)	PUNCT
ejpam-865	329	12	and	and	CCONJ
ejpam-865	329	13	vεα(y	vεα(y	PROPN
ejpam-865	329	14	,	,	PUNCT
ejpam-865	329	15	y	y	PROPN
ejpam-865	329	16	)	)	PUNCT
ejpam-865	329	17	(	(	PUNCT
ejpam-865	329	18	resp	resp	NOUN
ejpam-865	329	19	.	.	PUNCT
ejpam-865	330	1	vεpo(y	vεpo(y	PROPN
ejpam-865	330	2	,	,	PUNCT
ejpam-865	330	3	y	y	PROPN
ejpam-865	330	4	)	)	PUNCT
ejpam-865	330	5	,	,	PUNCT
ejpam-865	330	6	vεso(y	vεso(y	X
ejpam-865	330	7	,	,	PUNCT
ejpam-865	330	8	y	y	NOUN
ejpam-865	330	9	)	)	PUNCT
ejpam-865	330	10	)	)	PUNCT
ejpam-865	331	1	such	such	ADJ
ejpam-865	331	2	that	that	SCONJ
ejpam-865	331	3	(	(	PUNCT
ejpam-865	331	4	u	u	NOUN
ejpam-865	331	5	×	×	PROPN
ejpam-865	331	6	v	v	NOUN
ejpam-865	331	7	)	)	PUNCT
ejpam-865	331	8	∩	∩	ADJ
ejpam-865	331	9	g	g	PROPN
ejpam-865	331	10	(	(	PUNCT
ejpam-865	331	11	f	f	PROPN
ejpam-865	331	12	)	)	PUNCT
ejpam-865	331	13	=	=	SYM
ejpam-865	331	14	∅.	∅.	NOUN
ejpam-865	331	15	theorem	theorem	VERB
ejpam-865	331	16	13	13	NUM
ejpam-865	331	17	.	.	PUNCT
ejpam-865	332	1	if	if	SCONJ
ejpam-865	332	2	f	f	PROPN
ejpam-865	332	3	:	:	PUNCT
ejpam-865	332	4	x	x	X
ejpam-865	332	5	→	→	SYM
ejpam-865	332	6	y	y	PROPN
ejpam-865	332	7	is	be	AUX
ejpam-865	332	8	δα	δα	NOUN
ejpam-865	332	9	-	-	ADJ
ejpam-865	332	10	irresolute	irresolute	ADJ
ejpam-865	332	11	(	(	PUNCT
ejpam-865	332	12	resp	resp	NOUN
ejpam-865	332	13	.	.	PUNCT
ejpam-865	333	1	δp	δp	PRON
ejpam-865	333	2	-	-	PUNCT
ejpam-865	333	3	irresolute	irresolute	ADJ
ejpam-865	333	4	,	,	PUNCT
ejpam-865	333	5	δs	δs	NOUN
ejpam-865	333	6	-	-	PUNCT
ejpam-865	333	7	irresolute	irresolute	NOUN
ejpam-865	333	8	)	)	PUNCT
ejpam-865	333	9	and	and	CCONJ
ejpam-865	333	10	y	y	PROPN
ejpam-865	333	11	is	be	AUX
ejpam-865	333	12	α−	α−	ADP
ejpam-865	333	13	t2	t2	PROPN
ejpam-865	333	14	(	(	PUNCT
ejpam-865	333	15	resp	resp	NOUN
ejpam-865	333	16	.	.	PUNCT
ejpam-865	334	1	pre	pre	ADJ
ejpam-865	334	2	-	-	NOUN
ejpam-865	334	3	t2	t2	ADJ
ejpam-865	334	4	,	,	PUNCT
ejpam-865	334	5	semi	semi	ADJ
ejpam-865	334	6	-	-	NOUN
ejpam-865	334	7	t2	t2	ADJ
ejpam-865	334	8	)	)	PUNCT
ejpam-865	334	9	,	,	PUNCT
ejpam-865	334	10	then	then	ADV
ejpam-865	334	11	g	g	PROPN
ejpam-865	334	12	(	(	PUNCT
ejpam-865	334	13	f	f	PROPN
ejpam-865	334	14	)	)	PUNCT
ejpam-865	334	15	is	be	AUX
ejpam-865	334	16	δα	δα	NOUN
ejpam-865	334	17	-	-	ADJ
ejpam-865	334	18	closed	closed	ADJ
ejpam-865	334	19	(	(	PUNCT
ejpam-865	334	20	resp	resp	NOUN
ejpam-865	334	21	.	.	PUNCT
ejpam-865	335	1	δp	δp	PRON
ejpam-865	335	2	-	-	PUNCT
ejpam-865	335	3	closed	closed	ADJ
ejpam-865	335	4	,	,	PUNCT
ejpam-865	335	5	δs	δs	NOUN
ejpam-865	335	6	-	-	PUNCT
ejpam-865	335	7	closed	closed	ADJ
ejpam-865	335	8	)	)	PUNCT
ejpam-865	335	9	in	in	ADP
ejpam-865	335	10	x	x	X
ejpam-865	335	11	×	×	PROPN
ejpam-865	335	12	y	y	PROPN
ejpam-865	335	13	.	.	PUNCT
ejpam-865	336	1	proof	proof	NOUN
ejpam-865	336	2	.	.	PUNCT
ejpam-865	337	1	let	let	VERB
ejpam-865	337	2	(	(	PUNCT
ejpam-865	337	3	x	x	X
ejpam-865	337	4	,	,	PUNCT
ejpam-865	337	5	y	y	PROPN
ejpam-865	337	6	)	)	PUNCT
ejpam-865	337	7	∈	∈	PROPN
ejpam-865	337	8	(	(	PUNCT
ejpam-865	337	9	x	x	SYM
ejpam-865	337	10	×	×	PROPN
ejpam-865	337	11	y	y	PROPN
ejpam-865	337	12	)	)	PUNCT
ejpam-865	338	1	−	−	PROPN
ejpam-865	338	2	g	g	PROPN
ejpam-865	338	3	(	(	PUNCT
ejpam-865	338	4	f	f	PROPN
ejpam-865	338	5	)	)	PUNCT
ejpam-865	338	6	.	.	PUNCT
ejpam-865	339	1	this	this	PRON
ejpam-865	339	2	implies	imply	VERB
ejpam-865	339	3	that	that	SCONJ
ejpam-865	339	4	f	f	PROPN
ejpam-865	339	5	(	(	PUNCT
ejpam-865	339	6	x	x	X
ejpam-865	339	7	)	)	PUNCT
ejpam-865	339	8	6=	6=	PUNCT
ejpam-865	340	1	y.	y.	NOUN
ejpam-865	340	2	since	since	SCONJ
ejpam-865	340	3	y	y	PROPN
ejpam-865	340	4	is	be	AUX
ejpam-865	340	5	α	α	NUM
ejpam-865	340	6	−	−	PROPN
ejpam-865	340	7	t2	t2	NOUN
ejpam-865	340	8	(	(	PUNCT
ejpam-865	340	9	resp	resp	NOUN
ejpam-865	340	10	.	.	PUNCT
ejpam-865	341	1	pre	pre	ADJ
ejpam-865	341	2	-	-	NOUN
ejpam-865	341	3	t2	t2	ADJ
ejpam-865	341	4	,	,	PUNCT
ejpam-865	341	5	semi	semi	ADJ
ejpam-865	341	6	-	-	NOUN
ejpam-865	341	7	t2	t2	ADJ
ejpam-865	341	8	)	)	PUNCT
ejpam-865	341	9	,	,	PUNCT
ejpam-865	341	10	there	there	PRON
ejpam-865	341	11	exist	exist	VERB
ejpam-865	341	12	disjoint	disjoint	NOUN
ejpam-865	341	13	α	α	NOUN
ejpam-865	341	14	-	-	ADJ
ejpam-865	341	15	open	open	ADJ
ejpam-865	341	16	(	(	PUNCT
ejpam-865	341	17	resp	resp	NOUN
ejpam-865	341	18	.	.	PUNCT
ejpam-865	342	1	preopen	preopen	ADJ
ejpam-865	342	2	,	,	PUNCT
ejpam-865	342	3	semi	semi	ADJ
ejpam-865	342	4	-	-	ADJ
ejpam-865	342	5	open	open	ADJ
ejpam-865	342	6	)	)	PUNCT
ejpam-865	342	7	sets	set	VERB
ejpam-865	342	8	v	v	NOUN
ejpam-865	342	9	and	and	CCONJ
ejpam-865	342	10	w	w	NOUN
ejpam-865	342	11	in	in	ADP
ejpam-865	342	12	y	y	PROPN
ejpam-865	342	13	containing	contain	VERB
ejpam-865	342	14	f	f	X
ejpam-865	342	15	(	(	PUNCT
ejpam-865	342	16	x	x	NOUN
ejpam-865	342	17	)	)	PUNCT
ejpam-865	342	18	and	and	CCONJ
ejpam-865	342	19	y	y	PROPN
ejpam-865	342	20	,	,	PUNCT
ejpam-865	342	21	respectively	respectively	ADV
ejpam-865	342	22	.	.	PUNCT
ejpam-865	343	1	since	since	SCONJ
ejpam-865	343	2	f	f	PROPN
ejpam-865	343	3	is	be	AUX
ejpam-865	343	4	δα	δα	NOUN
ejpam-865	343	5	-	-	ADJ
ejpam-865	343	6	irresolute	irresolute	ADJ
ejpam-865	343	7	(	(	PUNCT
ejpam-865	343	8	resp	resp	NOUN
ejpam-865	343	9	.	.	PUNCT
ejpam-865	344	1	δp	δp	ADP
ejpam-865	344	2	-	-	PUNCT
ejpam-865	344	3	irresolute	irresolute	ADJ
ejpam-865	344	4	,	,	PUNCT
ejpam-865	344	5	δsirresolute	δsirresolute	NOUN
ejpam-865	344	6	)	)	PUNCT
ejpam-865	345	1	,	,	PUNCT
ejpam-865	345	2	there	there	PRON
ejpam-865	345	3	exists	exist	VERB
ejpam-865	345	4	a	a	DET
ejpam-865	345	5	δ	δ	NOUN
ejpam-865	345	6	-	-	PUNCT
ejpam-865	345	7	semiopen	semiopen	VERB
ejpam-865	345	8	set	set	VERB
ejpam-865	345	9	u	u	NOUN
ejpam-865	345	10	of	of	ADP
ejpam-865	345	11	x	x	PUNCT
ejpam-865	345	12	containing	contain	VERB
ejpam-865	345	13	x	x	PUNCT
ejpam-865	345	14	such	such	ADJ
ejpam-865	345	15	that	that	SCONJ
ejpam-865	345	16	f	f	PROPN
ejpam-865	345	17	(	(	PUNCT
ejpam-865	345	18	u)⊂	u)⊂	NOUN
ejpam-865	345	19	v	v	NOUN
ejpam-865	345	20	.	.	PUNCT
ejpam-865	346	1	therefore	therefore	ADV
ejpam-865	346	2	f	f	PROPN
ejpam-865	346	3	(	(	PUNCT
ejpam-865	346	4	u	u	NOUN
ejpam-865	346	5	)	)	PUNCT
ejpam-865	346	6	∩w	∩w	NOUN
ejpam-865	346	7	=	=	NOUN
ejpam-865	346	8	∅	∅	NOUN
ejpam-865	346	9	and	and	CCONJ
ejpam-865	346	10	hence	hence	ADV
ejpam-865	346	11	(	(	PUNCT
ejpam-865	346	12	u	u	NOUN
ejpam-865	346	13	×w	×w	NOUN
ejpam-865	346	14	)	)	PUNCT
ejpam-865	346	15	∩	∩	PROPN
ejpam-865	346	16	g	g	PROPN
ejpam-865	346	17	(	(	PUNCT
ejpam-865	346	18	f	f	PROPN
ejpam-865	346	19	)	)	PUNCT
ejpam-865	346	20	=	=	PUNCT
ejpam-865	346	21	∅.	∅.	VERB
ejpam-865	346	22	thus	thus	ADV
ejpam-865	346	23	g	g	PROPN
ejpam-865	346	24	(	(	PUNCT
ejpam-865	346	25	f	f	PROPN
ejpam-865	346	26	)	)	PUNCT
ejpam-865	346	27	is	be	AUX
ejpam-865	346	28	δα	δα	NOUN
ejpam-865	346	29	-	-	ADJ
ejpam-865	346	30	closed	closed	ADJ
ejpam-865	346	31	(	(	PUNCT
ejpam-865	346	32	resp	resp	NOUN
ejpam-865	346	33	.	.	PUNCT
ejpam-865	347	1	δp	δp	PRON
ejpam-865	347	2	-	-	PUNCT
ejpam-865	347	3	closed	closed	ADJ
ejpam-865	347	4	,	,	PUNCT
ejpam-865	347	5	δs	δs	NOUN
ejpam-865	347	6	-	-	PUNCT
ejpam-865	347	7	closed	closed	ADJ
ejpam-865	347	8	)	)	PUNCT
ejpam-865	347	9	in	in	ADP
ejpam-865	347	10	x	x	X
ejpam-865	347	11	×	×	PROPN
ejpam-865	347	12	y	y	PROPN
ejpam-865	347	13	.	.	PUNCT
ejpam-865	348	1	theorem	theorem	VERB
ejpam-865	348	2	14	14	NUM
ejpam-865	348	3	.	.	PUNCT
ejpam-865	349	1	if	if	SCONJ
ejpam-865	349	2	f	f	PROPN
ejpam-865	349	3	:	:	PUNCT
ejpam-865	349	4	x	x	X
ejpam-865	349	5	→	→	SYM
ejpam-865	349	6	y	y	PROPN
ejpam-865	349	7	is	be	AUX
ejpam-865	349	8	δα	δα	NOUN
ejpam-865	349	9	-	-	ADJ
ejpam-865	349	10	irresolute	irresolute	ADJ
ejpam-865	349	11	(	(	PUNCT
ejpam-865	349	12	resp	resp	NOUN
ejpam-865	349	13	.	.	PUNCT
ejpam-865	350	1	δp	δp	PRON
ejpam-865	350	2	-	-	PUNCT
ejpam-865	350	3	irresolute	irresolute	ADJ
ejpam-865	350	4	,	,	PUNCT
ejpam-865	350	5	δs	δs	NOUN
ejpam-865	350	6	-	-	PUNCT
ejpam-865	350	7	irresolute	irresolute	NOUN
ejpam-865	350	8	)	)	PUNCT
ejpam-865	350	9	injection	injection	NOUN
ejpam-865	350	10	with	with	ADP
ejpam-865	350	11	a	a	DET
ejpam-865	350	12	δα	δα	NOUN
ejpam-865	350	13	-	-	PUNCT
ejpam-865	350	14	closed	closed	ADJ
ejpam-865	350	15	(	(	PUNCT
ejpam-865	350	16	resp	resp	NOUN
ejpam-865	350	17	.	.	PUNCT
ejpam-865	351	1	δp	δp	PRON
ejpam-865	351	2	-	-	PUNCT
ejpam-865	351	3	closed	closed	ADJ
ejpam-865	351	4	,	,	PUNCT
ejpam-865	351	5	δs	δs	NOUN
ejpam-865	351	6	-	-	PUNCT
ejpam-865	351	7	closed	closed	ADJ
ejpam-865	351	8	)	)	PUNCT
ejpam-865	351	9	graph	graph	NOUN
ejpam-865	351	10	,	,	PUNCT
ejpam-865	351	11	then	then	ADV
ejpam-865	351	12	x	x	PUNCT
ejpam-865	351	13	is	be	AUX
ejpam-865	351	14	δ	δ	NOUN
ejpam-865	351	15	-	-	PUNCT
ejpam-865	351	16	semi	semi	NOUN
ejpam-865	351	17	-	-	NOUN
ejpam-865	351	18	t2	t2	NOUN
ejpam-865	351	19	.	.	PUNCT
ejpam-865	352	1	proof	proof	NOUN
ejpam-865	352	2	.	.	PUNCT
ejpam-865	353	1	let	let	VERB
ejpam-865	353	2	x	x	PRON
ejpam-865	353	3	and	and	CCONJ
ejpam-865	353	4	y	y	PROPN
ejpam-865	353	5	be	be	AUX
ejpam-865	353	6	any	any	DET
ejpam-865	353	7	distinct	distinct	ADJ
ejpam-865	353	8	points	point	NOUN
ejpam-865	353	9	of	of	ADP
ejpam-865	353	10	x	x	X
ejpam-865	353	11	.	.	PUNCT
ejpam-865	354	1	then	then	ADV
ejpam-865	354	2	f	f	PROPN
ejpam-865	354	3	(	(	PUNCT
ejpam-865	354	4	x	x	X
ejpam-865	354	5	)	)	PUNCT
ejpam-865	354	6	6=	6=	ADP
ejpam-865	354	7	f	f	PROPN
ejpam-865	354	8	(	(	PUNCT
ejpam-865	354	9	y	y	NOUN
ejpam-865	354	10	)	)	PUNCT
ejpam-865	354	11	and	and	CCONJ
ejpam-865	354	12	hence	hence	ADV
ejpam-865	354	13	(	(	PUNCT
ejpam-865	354	14	x	x	INTJ
ejpam-865	354	15	,	,	PUNCT
ejpam-865	354	16	f	f	PROPN
ejpam-865	354	17	(	(	PUNCT
ejpam-865	354	18	y	y	NOUN
ejpam-865	354	19	)	)	PUNCT
ejpam-865	354	20	)	)	PUNCT
ejpam-865	355	1	∈	∈	PROPN
ejpam-865	355	2	(	(	PUNCT
ejpam-865	355	3	x	x	SYM
ejpam-865	355	4	×	×	PROPN
ejpam-865	355	5	y	y	PROPN
ejpam-865	355	6	)	)	PUNCT
ejpam-865	355	7	−	−	PROPN
ejpam-865	356	1	g	g	PROPN
ejpam-865	356	2	(	(	PUNCT
ejpam-865	356	3	f	f	PROPN
ejpam-865	356	4	)	)	PUNCT
ejpam-865	356	5	.	.	PUNCT
ejpam-865	357	1	since	since	SCONJ
ejpam-865	357	2	g	g	PROPN
ejpam-865	357	3	(	(	PUNCT
ejpam-865	357	4	f	f	PROPN
ejpam-865	357	5	)	)	PUNCT
ejpam-865	357	6	is	be	AUX
ejpam-865	357	7	δα	δα	NOUN
ejpam-865	357	8	-	-	ADJ
ejpam-865	357	9	closed	closed	ADJ
ejpam-865	357	10	(	(	PUNCT
ejpam-865	357	11	resp	resp	NOUN
ejpam-865	357	12	.	.	PUNCT
ejpam-865	358	1	δp	δp	PRON
ejpam-865	358	2	-	-	PUNCT
ejpam-865	358	3	closed	closed	ADJ
ejpam-865	358	4	,	,	PUNCT
ejpam-865	358	5	δs	δs	NOUN
ejpam-865	358	6	-	-	PUNCT
ejpam-865	358	7	closed	closed	ADJ
ejpam-865	358	8	)	)	PUNCT
ejpam-865	358	9	,	,	PUNCT
ejpam-865	358	10	there	there	PRON
ejpam-865	358	11	exist	exist	VERB
ejpam-865	358	12	uεδso(x	uεδso(x	PROPN
ejpam-865	358	13	,	,	PUNCT
ejpam-865	358	14	x	x	NOUN
ejpam-865	358	15	)	)	PUNCT
ejpam-865	358	16	and	and	CCONJ
ejpam-865	358	17	vεα(y	vεα(y	PROPN
ejpam-865	358	18	,	,	PUNCT
ejpam-865	358	19	f	f	PROPN
ejpam-865	358	20	(	(	PUNCT
ejpam-865	358	21	y	y	NOUN
ejpam-865	358	22	)	)	PUNCT
ejpam-865	358	23	)	)	PUNCT
ejpam-865	359	1	(	(	PUNCT
ejpam-865	359	2	resp	resp	NOUN
ejpam-865	359	3	.	.	PUNCT
ejpam-865	360	1	vεpo(y	vεpo(y	PROPN
ejpam-865	360	2	,	,	PUNCT
ejpam-865	360	3	f	f	PROPN
ejpam-865	360	4	(	(	PUNCT
ejpam-865	360	5	y	y	NOUN
ejpam-865	360	6	)	)	PUNCT
ejpam-865	360	7	)	)	PUNCT
ejpam-865	360	8	,	,	PUNCT
ejpam-865	360	9	vεso(y	vεso(y	NUM
ejpam-865	360	10	,	,	PUNCT
ejpam-865	360	11	f	f	PROPN
ejpam-865	360	12	(	(	PUNCT
ejpam-865	360	13	y	y	NOUN
ejpam-865	360	14	)	)	PUNCT
ejpam-865	360	15	)	)	PUNCT
ejpam-865	360	16	)	)	PUNCT
ejpam-865	361	1	such	such	ADJ
ejpam-865	361	2	that	that	SCONJ
ejpam-865	361	3	(	(	PUNCT
ejpam-865	361	4	u	u	NOUN
ejpam-865	361	5	×	×	PROPN
ejpam-865	361	6	v	v	NOUN
ejpam-865	361	7	)	)	PUNCT
ejpam-865	361	8	∩	∩	PROPN
ejpam-865	361	9	g	g	PROPN
ejpam-865	361	10	(	(	PUNCT
ejpam-865	361	11	f	f	PROPN
ejpam-865	361	12	)	)	PUNCT
ejpam-865	361	13	=	=	NOUN
ejpam-865	361	14	∅	∅	NOUN
ejpam-865	361	15	and	and	CCONJ
ejpam-865	361	16	hence	hence	ADV
ejpam-865	361	17	f	f	PROPN
ejpam-865	361	18	(	(	PUNCT
ejpam-865	361	19	u)∩	u)∩	PROPN
ejpam-865	361	20	v	v	X
ejpam-865	361	21	=	=	PUNCT
ejpam-865	361	22	∅.	∅.	NOUN
ejpam-865	361	23	since	since	SCONJ
ejpam-865	361	24	f	f	PROPN
ejpam-865	361	25	is	be	AUX
ejpam-865	361	26	δα	δα	NOUN
ejpam-865	361	27	-	-	ADJ
ejpam-865	361	28	irresolute	irresolute	ADJ
ejpam-865	361	29	(	(	PUNCT
ejpam-865	361	30	resp	resp	NOUN
ejpam-865	361	31	.	.	PUNCT
ejpam-865	361	32	δp	δp	PRON
ejpam-865	361	33	-	-	PUNCT
ejpam-865	361	34	irresolute	irresolute	ADJ
ejpam-865	361	35	,	,	PUNCT
ejpam-865	361	36	δs	δs	NOUN
ejpam-865	361	37	-	-	PUNCT
ejpam-865	361	38	irresolute	irresolute	NOUN
ejpam-865	361	39	)	)	PUNCT
ejpam-865	361	40	,	,	PUNCT
ejpam-865	361	41	there	there	PRON
ejpam-865	361	42	exists	exist	VERB
ejpam-865	361	43	gεδso(x	gεδso(x	VERB
ejpam-865	361	44	,	,	PUNCT
ejpam-865	361	45	y	y	PROPN
ejpam-865	361	46	)	)	PUNCT
ejpam-865	361	47	such	such	ADJ
ejpam-865	361	48	that	that	SCONJ
ejpam-865	361	49	f	f	PROPN
ejpam-865	361	50	(	(	PUNCT
ejpam-865	361	51	g)⊂	g)⊂	PROPN
ejpam-865	361	52	v	v	NOUN
ejpam-865	361	53	.	.	PUNCT
ejpam-865	362	1	thus	thus	ADV
ejpam-865	362	2	we	we	PRON
ejpam-865	362	3	have	have	VERB
ejpam-865	362	4	f	f	PROPN
ejpam-865	362	5	(	(	PUNCT
ejpam-865	362	6	u)∩	u)∩	PROPN
ejpam-865	362	7	f	f	PROPN
ejpam-865	362	8	(	(	PUNCT
ejpam-865	362	9	g	g	NOUN
ejpam-865	362	10	)	)	PUNCT
ejpam-865	362	11	=	=	NOUN
ejpam-865	362	12	∅	∅	NOUN
ejpam-865	362	13	and	and	CCONJ
ejpam-865	362	14	hence	hence	ADV
ejpam-865	362	15	u	u	NOUN
ejpam-865	362	16	∩	∩	NOUN
ejpam-865	362	17	g	g	NOUN
ejpam-865	362	18	=	=	PUNCT
ejpam-865	362	19	∅.	∅.	ADP
ejpam-865	362	20	this	this	PRON
ejpam-865	362	21	shows	show	VERB
ejpam-865	362	22	that	that	SCONJ
ejpam-865	362	23	x	x	PRON
ejpam-865	362	24	is	be	AUX
ejpam-865	362	25	δ	δ	NOUN
ejpam-865	362	26	-	-	PUNCT
ejpam-865	362	27	semi	semi	NOUN
ejpam-865	362	28	-	-	NOUN
ejpam-865	362	29	t2	t2	ADJ
ejpam-865	362	30	.	.	PUNCT
ejpam-865	363	1	references	reference	NOUN
ejpam-865	363	2	368	368	NUM
ejpam-865	363	3	references	reference	NOUN
ejpam-865	363	4	[	[	X
ejpam-865	363	5	1	1	NUM
ejpam-865	363	6	]	]	PUNCT
ejpam-865	363	7	d	d	PROPN
ejpam-865	363	8	andrijević.	andrijević.	PROPN
ejpam-865	363	9	some	some	DET
ejpam-865	363	10	properties	property	NOUN
ejpam-865	363	11	of	of	ADP
ejpam-865	363	12	the	the	DET
ejpam-865	363	13	topolgy	topolgy	NOUN
ejpam-865	363	14	of	of	ADP
ejpam-865	363	15	α	α	NOUN
ejpam-865	363	16	-	-	PUNCT
ejpam-865	363	17	sets	set	NOUN
ejpam-865	363	18	.	.	PUNCT
ejpam-865	364	1	mat	mat	X
ejpam-865	364	2	.	.	PROPN
ejpam-865	364	3	vesnik	vesnik	PROPN
ejpam-865	364	4	,	,	PUNCT
ejpam-865	364	5	36:1–10	36:1–10	NUM
ejpam-865	364	6	,	,	PUNCT
ejpam-865	364	7	1984	1984	NUM
ejpam-865	364	8	.	.	PUNCT
ejpam-865	365	1	[	[	X
ejpam-865	365	2	2	2	NUM
ejpam-865	365	3	]	]	PUNCT
ejpam-865	365	4	y	y	PROPN
ejpam-865	365	5	beceren	beceren	PROPN
ejpam-865	365	6	.	.	PUNCT
ejpam-865	366	1	on	on	ADP
ejpam-865	366	2	semi	semi	ADJ
ejpam-865	366	3	α	α	NOUN
ejpam-865	366	4	-	-	PUNCT
ejpam-865	366	5	irresolute	irresolute	ADJ
ejpam-865	366	6	functions	function	NOUN
ejpam-865	366	7	.	.	PUNCT
ejpam-865	367	1	j.	j.	PROPN
ejpam-865	367	2	indian	indian	PROPN
ejpam-865	367	3	acad	acad	PROPN
ejpam-865	367	4	.	.	PUNCT
ejpam-865	368	1	math	math	NOUN
ejpam-865	368	2	.	.	PUNCT
ejpam-865	368	3	,	,	PUNCT
ejpam-865	369	1	22:353–362	22:353–362	NUM
ejpam-865	369	2	,	,	PUNCT
ejpam-865	369	3	2000	2000	NUM
ejpam-865	369	4	.	.	PUNCT
ejpam-865	370	1	[	[	X
ejpam-865	370	2	3	3	NUM
ejpam-865	370	3	]	]	X
ejpam-865	370	4	y	y	PROPN
ejpam-865	370	5	beceren	beceren	PROPN
ejpam-865	370	6	.	.	PUNCT
ejpam-865	371	1	strongly	strongly	ADV
ejpam-865	371	2	semi	semi	ADJ
ejpam-865	371	3	β	β	X
ejpam-865	371	4	-irresolute	-irresolute	ADJ
ejpam-865	371	5	functions	function	NOUN
ejpam-865	371	6	and	and	CCONJ
ejpam-865	371	7	semi	semi	ADV
ejpam-865	371	8	α	α	PROPN
ejpam-865	371	9	-	-	PUNCT
ejpam-865	371	10	preirresolute	preirresolute	ADJ
ejpam-865	371	11	functions	function	NOUN
ejpam-865	371	12	.	.	PUNCT
ejpam-865	372	1	far	far	PROPN
ejpam-865	372	2	east	east	PROPN
ejpam-865	372	3	j.	j.	PROPN
ejpam-865	372	4	math	math	PROPN
ejpam-865	372	5	.	.	PUNCT
ejpam-865	373	1	sci	sci	PROPN
ejpam-865	373	2	.	.	PUNCT
ejpam-865	373	3	(	(	PUNCT
ejpam-865	373	4	fjms	fjms	PROPN
ejpam-865	373	5	)	)	PUNCT
ejpam-865	373	6	,	,	PUNCT
ejpam-865	373	7	3:973–983	3:973–983	NUM
ejpam-865	373	8	,	,	PUNCT
ejpam-865	373	9	2001	2001	NUM
ejpam-865	373	10	.	.	PUNCT
ejpam-865	374	1	[	[	X
ejpam-865	374	2	4	4	X
ejpam-865	374	3	]	]	PUNCT
ejpam-865	374	4	n	n	X
ejpam-865	374	5	bourbaki	bourbaki	VERB
ejpam-865	374	6	.	.	PUNCT
ejpam-865	375	1	elements	element	NOUN
ejpam-865	375	2	of	of	ADP
ejpam-865	375	3	mathematics	mathematic	NOUN
ejpam-865	375	4	,	,	PUNCT
ejpam-865	375	5	general	general	ADJ
ejpam-865	375	6	topology	topology	NOUN
ejpam-865	375	7	,	,	PUNCT
ejpam-865	375	8	part	part	NOUN
ejpam-865	375	9	1,hermann	1,hermann	NUM
ejpam-865	375	10	.	.	PUNCT
ejpam-865	376	1	addison	addison	PROPN
ejpam-865	376	2	-	-	PUNCT
ejpam-865	376	3	wesley	wesley	PROPN
ejpam-865	376	4	publishing	publishing	PROPN
ejpam-865	376	5	co.	co.	PROPN
ejpam-865	376	6	reading	reading	PROPN
ejpam-865	376	7	,	,	PUNCT
ejpam-865	376	8	mass	mass	PROPN
ejpam-865	376	9	.	.	PUNCT
ejpam-865	376	10	paris	paris	PROPN
ejpam-865	376	11	,	,	PUNCT
ejpam-865	376	12	1966	1966	NUM
ejpam-865	376	13	.	.	PUNCT
ejpam-865	377	1	[	[	X
ejpam-865	377	2	5	5	NUM
ejpam-865	377	3	]	]	X
ejpam-865	377	4	m	m	VERB
ejpam-865	377	5	caldas	caldas	PROPN
ejpam-865	377	6	,	,	PUNCT
ejpam-865	377	7	d	d	PROPN
ejpam-865	377	8	georgiou	georgiou	PROPN
ejpam-865	377	9	,	,	PUNCT
ejpam-865	377	10	s	s	PART
ejpam-865	377	11	jafari	jafari	X
ejpam-865	377	12	,	,	PUNCT
ejpam-865	377	13	and	and	CCONJ
ejpam-865	377	14	t	t	PROPN
ejpam-865	377	15	noiri	noiri	PROPN
ejpam-865	377	16	.	.	PUNCT
ejpam-865	378	1	more	more	ADV
ejpam-865	378	2	on	on	ADP
ejpam-865	378	3	δ	δ	PROPN
ejpam-865	378	4	-	-	PUNCT
ejpam-865	378	5	semiopen	semiopen	ADJ
ejpam-865	378	6	sets	set	NOUN
ejpam-865	378	7	.	.	PUNCT
ejpam-865	379	1	note	note	VERB
ejpam-865	379	2	mat	mat	NOUN
ejpam-865	379	3	.	.	PROPN
ejpam-865	379	4	,	,	PUNCT
ejpam-865	379	5	22:113–126	22:113–126	NUM
ejpam-865	379	6	,	,	PUNCT
ejpam-865	379	7	2003	2003	NUM
ejpam-865	379	8	.	.	PUNCT
ejpam-865	380	1	[	[	X
ejpam-865	380	2	6	6	NUM
ejpam-865	380	3	]	]	X
ejpam-865	380	4	m	m	VERB
ejpam-865	380	5	caldas	caldas	PROPN
ejpam-865	380	6	,	,	PUNCT
ejpam-865	380	7	s	s	PART
ejpam-865	380	8	jafari	jafari	ADJ
ejpam-865	380	9	,	,	PUNCT
ejpam-865	380	10	and	and	CCONJ
ejpam-865	380	11	r	r	NOUN
ejpam-865	380	12	saraf	saraf	NOUN
ejpam-865	380	13	.	.	PUNCT
ejpam-865	381	1	on	on	ADP
ejpam-865	381	2	a	a	DET
ejpam-865	381	3	non	non	ADJ
ejpam-865	381	4	-	-	ADJ
ejpam-865	381	5	continuous	continuous	ADJ
ejpam-865	381	6	and	and	CCONJ
ejpam-865	381	7	stronger	strong	ADJ
ejpam-865	381	8	form	form	NOUN
ejpam-865	381	9	of	of	ADP
ejpam-865	381	10	levine	levine	PROPN
ejpam-865	381	11	’s	’s	PART
ejpam-865	381	12	semi	semi	ADJ
ejpam-865	381	13	-	-	ADJ
ejpam-865	381	14	continuous	continuous	ADJ
ejpam-865	381	15	functions	function	NOUN
ejpam-865	381	16	.	.	PUNCT
ejpam-865	381	17	math	math	NOUN
ejpam-865	381	18	.	.	PUNCT
ejpam-865	382	1	commun	commun	PROPN
ejpam-865	382	2	.	.	PROPN
ejpam-865	382	3	,	,	PUNCT
ejpam-865	382	4	14:19–25	14:19–25	NUM
ejpam-865	382	5	,	,	PUNCT
ejpam-865	382	6	2009	2009	NUM
ejpam-865	382	7	.	.	PUNCT
ejpam-865	383	1	[	[	X
ejpam-865	383	2	7	7	X
ejpam-865	383	3	]	]	X
ejpam-865	383	4	g	g	PROPN
ejpam-865	383	5	chae	chae	PROPN
ejpam-865	383	6	,	,	PUNCT
ejpam-865	383	7	t	t	PROPN
ejpam-865	383	8	noiri	noiri	PROPN
ejpam-865	383	9	,	,	PUNCT
ejpam-865	383	10	and	and	CCONJ
ejpam-865	383	11	d	d	PROPN
ejpam-865	383	12	lee	lee	PROPN
ejpam-865	383	13	.	.	PUNCT
ejpam-865	384	1	on	on	ADP
ejpam-865	384	2	na	na	ADJ
ejpam-865	384	3	-	-	ADJ
ejpam-865	384	4	continuous	continuous	ADJ
ejpam-865	384	5	functions	function	NOUN
ejpam-865	384	6	.	.	PUNCT
ejpam-865	385	1	kyungpook	kyungpook	PROPN
ejpam-865	385	2	math	math	PROPN
ejpam-865	385	3	.	.	PUNCT
ejpam-865	386	1	j.	j.	PROPN
ejpam-865	386	2	,	,	PUNCT
ejpam-865	386	3	26:73–79	26:73–79	PROPN
ejpam-865	386	4	,	,	PUNCT
ejpam-865	386	5	1986	1986	NUM
ejpam-865	386	6	.	.	PUNCT
ejpam-865	387	1	[	[	X
ejpam-865	387	2	8	8	NUM
ejpam-865	387	3	]	]	X
ejpam-865	387	4	s	s	VERB
ejpam-865	387	5	crossley	crossley	NOUN
ejpam-865	387	6	and	and	CCONJ
ejpam-865	387	7	s	s	VERB
ejpam-865	387	8	hildebrand	hildebrand	NOUN
ejpam-865	387	9	.	.	PUNCT
ejpam-865	388	1	semi	semi	ADJ
ejpam-865	388	2	-	-	NOUN
ejpam-865	388	3	closure	closure	ADJ
ejpam-865	388	4	.	.	PUNCT
ejpam-865	389	1	texas	texas	PROPN
ejpam-865	389	2	j.	j.	PROPN
ejpam-865	389	3	sci	sci	PROPN
ejpam-865	389	4	.	.	PROPN
ejpam-865	389	5	,	,	PUNCT
ejpam-865	389	6	22:99–112	22:99–112	NUM
ejpam-865	389	7	,	,	PUNCT
ejpam-865	389	8	1971	1971	NUM
ejpam-865	389	9	.	.	PUNCT
ejpam-865	390	1	[	[	X
ejpam-865	390	2	9	9	NUM
ejpam-865	390	3	]	]	X
ejpam-865	390	4	s	s	VERB
ejpam-865	390	5	crossley	crossley	NOUN
ejpam-865	390	6	and	and	CCONJ
ejpam-865	390	7	s	s	VERB
ejpam-865	390	8	hildebrand	hildebrand	NOUN
ejpam-865	390	9	.	.	PUNCT
ejpam-865	391	1	semi	semi	ADJ
ejpam-865	391	2	-	-	ADJ
ejpam-865	391	3	topological	topological	ADJ
ejpam-865	391	4	properties	property	NOUN
ejpam-865	391	5	.	.	PUNCT
ejpam-865	392	1	fund	fund	NOUN
ejpam-865	392	2	math	math	PROPN
ejpam-865	392	3	.	.	PUNCT
ejpam-865	392	4	,	,	PUNCT
ejpam-865	393	1	74:233–254	74:233–254	PROPN
ejpam-865	393	2	,	,	PUNCT
ejpam-865	393	3	1972	1972	NUM
ejpam-865	393	4	.	.	PUNCT
ejpam-865	394	1	[	[	X
ejpam-865	394	2	10	10	NUM
ejpam-865	394	3	]	]	SYM
ejpam-865	394	4	s	s	PART
ejpam-865	394	5	el	el	PROPN
ejpam-865	394	6	-	-	PUNCT
ejpam-865	394	7	deeb	deeb	PROPN
ejpam-865	394	8	,	,	PUNCT
ejpam-865	394	9	i	i	PRON
ejpam-865	394	10	hasanein	hasanein	VERB
ejpam-865	394	11	,	,	PUNCT
ejpam-865	394	12	a	a	DET
ejpam-865	394	13	mashhour	mashhour	NOUN
ejpam-865	394	14	,	,	PUNCT
ejpam-865	394	15	and	and	CCONJ
ejpam-865	394	16	t	t	PROPN
ejpam-865	394	17	noiri	noiri	PROPN
ejpam-865	394	18	.	.	PUNCT
ejpam-865	395	1	on	on	ADP
ejpam-865	395	2	p	p	NOUN
ejpam-865	395	3	-	-	PUNCT
ejpam-865	395	4	regular	regular	ADJ
ejpam-865	395	5	spaces	space	NOUN
ejpam-865	395	6	.	.	PUNCT
ejpam-865	396	1	bull	bull	NOUN
ejpam-865	396	2	.	.	PUNCT
ejpam-865	397	1	math	math	NOUN
ejpam-865	397	2	.	.	PUNCT
ejpam-865	398	1	soc	soc	PROPN
ejpam-865	398	2	.	.	PUNCT
ejpam-865	399	1	sci	sci	PROPN
ejpam-865	399	2	.	.	PROPN
ejpam-865	399	3	math	math	PROPN
ejpam-865	399	4	.	.	PUNCT
ejpam-865	400	1	r.	r.	PROPN
ejpam-865	400	2	s.	s.	PROPN
ejpam-865	400	3	roumanie	roumanie	PROPN
ejpam-865	400	4	(	(	PUNCT
ejpam-865	400	5	n.	n.	PROPN
ejpam-865	400	6	s.	s.	PROPN
ejpam-865	400	7	)	)	PUNCT
ejpam-865	400	8	,	,	PUNCT
ejpam-865	400	9	27(75):311–315	27(75):311–315	NUM
ejpam-865	400	10	,	,	PUNCT
ejpam-865	400	11	1983	1983	NUM
ejpam-865	400	12	.	.	PUNCT
ejpam-865	401	1	[	[	X
ejpam-865	401	2	11	11	NUM
ejpam-865	401	3	]	]	X
ejpam-865	401	4	m	m	VERB
ejpam-865	401	5	abd	abd	PROPN
ejpam-865	401	6	el	el	PROPN
ejpam-865	401	7	-	-	PROPN
ejpam-865	401	8	monsef	monsef	ADJ
ejpam-865	401	9	,	,	PUNCT
ejpam-865	401	10	s	s	PART
ejpam-865	401	11	el	el	PROPN
ejpam-865	401	12	-	-	PUNCT
ejpam-865	401	13	deeb	deeb	PROPN
ejpam-865	401	14	,	,	PUNCT
ejpam-865	401	15	and	and	CCONJ
ejpam-865	401	16	r	r	NOUN
ejpam-865	401	17	mahmoud	mahmoud	PROPN
ejpam-865	401	18	.	.	PUNCT
ejpam-865	402	1	β	β	X
ejpam-865	402	2	-open	-open	PROPN
ejpam-865	402	3	sets	set	NOUN
ejpam-865	402	4	and	and	CCONJ
ejpam-865	402	5	β	β	X
ejpam-865	402	6	-continuous	-continuous	ADJ
ejpam-865	402	7	mapping	mapping	NOUN
ejpam-865	402	8	.	.	PUNCT
ejpam-865	403	1	bull	bull	NOUN
ejpam-865	403	2	.	.	PUNCT
ejpam-865	404	1	fac	fac	PROPN
ejpam-865	404	2	.	.	PUNCT
ejpam-865	405	1	sci	sci	PROPN
ejpam-865	405	2	.	.	PUNCT
ejpam-865	405	3	assiut	assiut	PROPN
ejpam-865	405	4	univ	univ	PROPN
ejpam-865	405	5	.	.	PUNCT
ejpam-865	406	1	a	a	DET
ejpam-865	406	2	,	,	PUNCT
ejpam-865	406	3	12:77–90	12:77–90	NUM
ejpam-865	406	4	,	,	PUNCT
ejpam-865	406	5	1983	1983	NUM
ejpam-865	406	6	.	.	PUNCT
ejpam-865	407	1	[	[	X
ejpam-865	407	2	12	12	NUM
ejpam-865	407	3	]	]	X
ejpam-865	407	4	d	d	NOUN
ejpam-865	407	5	janković.	janković.	PROPN
ejpam-865	407	6	on	on	ADP
ejpam-865	407	7	locally	locally	ADV
ejpam-865	407	8	irreducible	irreducible	ADJ
ejpam-865	407	9	spaces	space	NOUN
ejpam-865	407	10	.	.	PUNCT
ejpam-865	408	1	ann	ann	PROPN
ejpam-865	408	2	.	.	PUNCT
ejpam-865	408	3	soc	soc	PROPN
ejpam-865	408	4	.	.	PUNCT
ejpam-865	409	1	sci	sci	PROPN
ejpam-865	409	2	.	.	PROPN
ejpam-865	410	1	bruxelles	bruxelles	PROPN
ejpam-865	410	2	sér	sér	PROPN
ejpam-865	410	3	.	.	PUNCT
ejpam-865	411	1	i	i	PRON
ejpam-865	411	2	,	,	PUNCT
ejpam-865	411	3	97:59–72	97:59–72	NUM
ejpam-865	411	4	,	,	PUNCT
ejpam-865	411	5	1983	1983	NUM
ejpam-865	411	6	.	.	PUNCT
ejpam-865	412	1	[	[	X
ejpam-865	412	2	13	13	NUM
ejpam-865	412	3	]	]	PUNCT
ejpam-865	412	4	a	a	DET
ejpam-865	412	5	kar	kar	NOUN
ejpam-865	412	6	and	and	CCONJ
ejpam-865	412	7	p	p	NOUN
ejpam-865	412	8	bhattacharyya	bhattacharyya	ADJ
ejpam-865	412	9	.	.	PUNCT
ejpam-865	413	1	some	some	DET
ejpam-865	413	2	weak	weak	ADJ
ejpam-865	413	3	separation	separation	NOUN
ejpam-865	413	4	axioms	axiom	NOUN
ejpam-865	413	5	.	.	PUNCT
ejpam-865	414	1	bull	bull	NOUN
ejpam-865	414	2	.	.	PUNCT
ejpam-865	415	1	calcutta	calcutta	PROPN
ejpam-865	415	2	math	math	PROPN
ejpam-865	415	3	.	.	PUNCT
ejpam-865	416	1	soc	soc	PROPN
ejpam-865	416	2	.	.	PUNCT
ejpam-865	416	3	,	,	PUNCT
ejpam-865	416	4	82:415–422	82:415–422	NUM
ejpam-865	416	5	,	,	PUNCT
ejpam-865	416	6	1990	1990	NUM
ejpam-865	416	7	.	.	PUNCT
ejpam-865	417	1	[	[	X
ejpam-865	417	2	14	14	NUM
ejpam-865	417	3	]	]	SYM
ejpam-865	417	4	b	b	X
ejpam-865	417	5	lee	lee	PROPN
ejpam-865	417	6	,	,	PUNCT
ejpam-865	417	7	m	m	VERB
ejpam-865	417	8	son	son	NOUN
ejpam-865	417	9	,	,	PUNCT
ejpam-865	417	10	and	and	CCONJ
ejpam-865	417	11	j	j	PROPN
ejpam-865	417	12	park	park	NOUN
ejpam-865	417	13	.	.	PUNCT
ejpam-865	418	1	δ	δ	PROPN
ejpam-865	418	2	-	-	PUNCT
ejpam-865	418	3	semiopen	semiopen	ADJ
ejpam-865	418	4	sets	set	NOUN
ejpam-865	418	5	and	and	CCONJ
ejpam-865	418	6	its	its	PRON
ejpam-865	418	7	applications	application	NOUN
ejpam-865	418	8	.	.	PUNCT
ejpam-865	419	1	far	far	PROPN
ejpam-865	419	2	east	east	PROPN
ejpam-865	419	3	j.	j.	PROPN
ejpam-865	419	4	math	math	PROPN
ejpam-865	419	5	.	.	PUNCT
ejpam-865	420	1	sci	sci	PROPN
ejpam-865	420	2	.	.	PUNCT
ejpam-865	420	3	(	(	PUNCT
ejpam-865	420	4	fjms	fjms	PROPN
ejpam-865	420	5	)	)	PUNCT
ejpam-865	420	6	,	,	PUNCT
ejpam-865	420	7	3:745–759	3:745–759	NUM
ejpam-865	420	8	,	,	PUNCT
ejpam-865	420	9	2001	2001	NUM
ejpam-865	420	10	.	.	PUNCT
ejpam-865	421	1	[	[	X
ejpam-865	421	2	15	15	NUM
ejpam-865	421	3	]	]	PUNCT
ejpam-865	421	4	n	n	DET
ejpam-865	421	5	levine	levine	PROPN
ejpam-865	421	6	.	.	PUNCT
ejpam-865	422	1	semi	semi	ADV
ejpam-865	422	2	open	open	ADJ
ejpam-865	422	3	sets	set	NOUN
ejpam-865	422	4	and	and	CCONJ
ejpam-865	422	5	semi	semi	ADJ
ejpam-865	422	6	continuity	continuity	NOUN
ejpam-865	422	7	in	in	ADP
ejpam-865	422	8	topological	topological	ADJ
ejpam-865	422	9	spaces	space	NOUN
ejpam-865	422	10	.	.	PUNCT
ejpam-865	423	1	amer	amer	PROPN
ejpam-865	423	2	.	.	PUNCT
ejpam-865	423	3	math	math	PROPN
ejpam-865	423	4	.	.	PUNCT
ejpam-865	424	1	monthly	monthly	ADJ
ejpam-865	424	2	,	,	PUNCT
ejpam-865	424	3	70:36–41	70:36–41	NUM
ejpam-865	424	4	,	,	PUNCT
ejpam-865	424	5	1963	1963	NUM
ejpam-865	424	6	.	.	PUNCT
ejpam-865	425	1	[	[	X
ejpam-865	425	2	16	16	NUM
ejpam-865	425	3	]	]	SYM
ejpam-865	425	4	s	s	PART
ejpam-865	425	5	maheshwari	maheshwari	NOUN
ejpam-865	425	6	and	and	CCONJ
ejpam-865	425	7	r	r	NOUN
ejpam-865	425	8	prasad	prasad	PROPN
ejpam-865	425	9	.	.	PUNCT
ejpam-865	426	1	some	some	DET
ejpam-865	426	2	new	new	ADJ
ejpam-865	426	3	separation	separation	NOUN
ejpam-865	426	4	axioms	axiom	VERB
ejpam-865	426	5	.	.	PUNCT
ejpam-865	427	1	ann	ann	PROPN
ejpam-865	427	2	.	.	PUNCT
ejpam-865	427	3	soc	soc	PROPN
ejpam-865	427	4	.	.	PUNCT
ejpam-865	428	1	sci	sci	PROPN
ejpam-865	428	2	.	.	PROPN
ejpam-865	429	1	bruxelles	bruxelles	PROPN
ejpam-865	429	2	sér	sér	PROPN
ejpam-865	429	3	.	.	PUNCT
ejpam-865	430	1	i	i	PRON
ejpam-865	430	2	,	,	PUNCT
ejpam-865	430	3	89:395–402	89:395–402	PROPN
ejpam-865	430	4	,	,	PUNCT
ejpam-865	430	5	1975	1975	NUM
ejpam-865	430	6	.	.	PUNCT
ejpam-865	431	1	[	[	X
ejpam-865	431	2	17	17	NUM
ejpam-865	431	3	]	]	SYM
ejpam-865	431	4	s	s	PART
ejpam-865	431	5	maheshwari	maheshwari	NOUN
ejpam-865	431	6	and	and	CCONJ
ejpam-865	431	7	s	s	PART
ejpam-865	431	8	thakur	thakur	PROPN
ejpam-865	431	9	.	.	PUNCT
ejpam-865	432	1	on	on	ADP
ejpam-865	432	2	α	α	NOUN
ejpam-865	432	3	-	-	PUNCT
ejpam-865	432	4	irresolute	irresolute	ADJ
ejpam-865	432	5	mappings	mapping	NOUN
ejpam-865	432	6	.	.	PUNCT
ejpam-865	433	1	tamkang	tamkang	PROPN
ejpam-865	433	2	j.	j.	PROPN
ejpam-865	433	3	math	math	PROPN
ejpam-865	433	4	.	.	PUNCT
ejpam-865	433	5	,	,	PUNCT
ejpam-865	433	6	11:209–214	11:209–214	PROPN
ejpam-865	433	7	,	,	PUNCT
ejpam-865	433	8	1980	1980	NUM
ejpam-865	433	9	.	.	PUNCT
ejpam-865	434	1	references	reference	NOUN
ejpam-865	434	2	369	369	NUM
ejpam-865	435	1	[	[	X
ejpam-865	435	2	18	18	NUM
ejpam-865	435	3	]	]	PUNCT
ejpam-865	435	4	a	a	DET
ejpam-865	435	5	mashhour	mashhour	NOUN
ejpam-865	435	6	,	,	PUNCT
ejpam-865	435	7	m	m	VERB
ejpam-865	435	8	abd	abd	PROPN
ejpam-865	435	9	el	el	PROPN
ejpam-865	435	10	-	-	NOUN
ejpam-865	435	11	monsef	monsef	ADJ
ejpam-865	435	12	,	,	PUNCT
ejpam-865	435	13	and	and	CCONJ
ejpam-865	435	14	s	s	VERB
ejpam-865	435	15	el	el	PROPN
ejpam-865	435	16	-	-	PUNCT
ejpam-865	435	17	deeb	deeb	PROPN
ejpam-865	435	18	.	.	PUNCT
ejpam-865	436	1	on	on	ADP
ejpam-865	436	2	precontinuous	precontinuous	ADJ
ejpam-865	436	3	and	and	CCONJ
ejpam-865	436	4	weak	weak	ADJ
ejpam-865	436	5	precontinuous	precontinuous	ADJ
ejpam-865	436	6	mappings	mapping	NOUN
ejpam-865	436	7	.	.	PUNCT
ejpam-865	437	1	proc	proc	NOUN
ejpam-865	437	2	.	.	PUNCT
ejpam-865	438	1	math	math	NOUN
ejpam-865	438	2	.	.	PUNCT
ejpam-865	439	1	phys	phy	NOUN
ejpam-865	439	2	.	.	PUNCT
ejpam-865	440	1	soc	soc	PROPN
ejpam-865	440	2	.	.	PUNCT
ejpam-865	441	1	egypt	egypt	PROPN
ejpam-865	441	2	,	,	PUNCT
ejpam-865	441	3	53:47–53	53:47–53	NUM
ejpam-865	441	4	,	,	PUNCT
ejpam-865	441	5	1982	1982	NUM
ejpam-865	441	6	.	.	PUNCT
ejpam-865	442	1	[	[	X
ejpam-865	442	2	19	19	NUM
ejpam-865	442	3	]	]	X
ejpam-865	442	4	a	a	DET
ejpam-865	442	5	mashhour	mashhour	NOUN
ejpam-865	442	6	,	,	PUNCT
ejpam-865	442	7	m	m	VERB
ejpam-865	442	8	abd	abd	PROPN
ejpam-865	442	9	el	el	PROPN
ejpam-865	442	10	-	-	NOUN
ejpam-865	442	11	monsef	monsef	ADJ
ejpam-865	442	12	,	,	PUNCT
ejpam-865	442	13	and	and	CCONJ
ejpam-865	442	14	i	i	PRON
ejpam-865	442	15	hasanein	hasanein	VERB
ejpam-865	442	16	.	.	PUNCT
ejpam-865	443	1	on	on	ADP
ejpam-865	443	2	pretopological	pretopological	ADJ
ejpam-865	443	3	spaces	space	NOUN
ejpam-865	443	4	.	.	PUNCT
ejpam-865	444	1	bull	bull	NOUN
ejpam-865	444	2	.	.	PUNCT
ejpam-865	445	1	math	math	NOUN
ejpam-865	445	2	.	.	PUNCT
ejpam-865	446	1	soc	soc	PROPN
ejpam-865	446	2	.	.	PUNCT
ejpam-865	447	1	sci	sci	PROPN
ejpam-865	447	2	.	.	PROPN
ejpam-865	447	3	math	math	PROPN
ejpam-865	447	4	.	.	PUNCT
ejpam-865	448	1	r.	r.	PROPN
ejpam-865	448	2	s.	s.	PROPN
ejpam-865	448	3	roumanie	roumanie	PROPN
ejpam-865	448	4	(	(	PUNCT
ejpam-865	448	5	n.	n.	PROPN
ejpam-865	448	6	s.	s.	PROPN
ejpam-865	448	7	)	)	PUNCT
ejpam-865	448	8	,	,	PUNCT
ejpam-865	448	9	28	28	NUM
ejpam-865	448	10	(	(	PUNCT
ejpam-865	448	11	76):39–45	76):39–45	NUM
ejpam-865	448	12	,	,	PUNCT
ejpam-865	448	13	1984	1984	NUM
ejpam-865	448	14	.	.	PUNCT
ejpam-865	449	1	[	[	X
ejpam-865	449	2	20	20	NUM
ejpam-865	449	3	]	]	PUNCT
ejpam-865	449	4	a	a	DET
ejpam-865	449	5	mashhour	mashhour	NOUN
ejpam-865	449	6	,	,	PUNCT
ejpam-865	449	7	i	i	PRON
ejpam-865	449	8	hasanein	hasanein	VERB
ejpam-865	449	9	,	,	PUNCT
ejpam-865	449	10	and	and	CCONJ
ejpam-865	449	11	s	s	VERB
ejpam-865	449	12	el	el	PROPN
ejpam-865	449	13	-	-	PUNCT
ejpam-865	449	14	deeb	deeb	PROPN
ejpam-865	449	15	.	.	PUNCT
ejpam-865	450	1	α	α	X
ejpam-865	450	2	-	-	ADJ
ejpam-865	450	3	continuous	continuous	ADJ
ejpam-865	450	4	and	and	CCONJ
ejpam-865	450	5	α	α	NOUN
ejpam-865	450	6	-	-	ADJ
ejpam-865	450	7	open	open	ADJ
ejpam-865	450	8	mappings	mapping	NOUN
ejpam-865	450	9	.	.	PUNCT
ejpam-865	451	1	acta	acta	PROPN
ejpam-865	451	2	math	math	PROPN
ejpam-865	451	3	.	.	PUNCT
ejpam-865	452	1	hungar	hungar	PROPN
ejpam-865	452	2	.	.	PUNCT
ejpam-865	452	3	,	,	PUNCT
ejpam-865	452	4	41:213–218	41:213–218	PROPN
ejpam-865	452	5	,	,	PUNCT
ejpam-865	452	6	1983	1983	NUM
ejpam-865	452	7	.	.	PUNCT
ejpam-865	453	1	[	[	X
ejpam-865	453	2	21	21	NUM
ejpam-865	453	3	]	]	X
ejpam-865	453	4	a	a	DET
ejpam-865	453	5	nasef	nasef	NOUN
ejpam-865	453	6	and	and	CCONJ
ejpam-865	453	7	t	t	PROPN
ejpam-865	453	8	noiri	noiri	PROPN
ejpam-865	453	9	.	.	PUNCT
ejpam-865	454	1	strong	strong	ADJ
ejpam-865	454	2	forms	form	NOUN
ejpam-865	454	3	of	of	ADP
ejpam-865	454	4	faint	faint	ADJ
ejpam-865	454	5	continuity	continuity	NOUN
ejpam-865	454	6	.	.	PUNCT
ejpam-865	455	1	mem	mem	PROPN
ejpam-865	455	2	.	.	PUNCT
ejpam-865	455	3	fac	fac	PROPN
ejpam-865	455	4	.	.	PUNCT
ejpam-865	456	1	sci	sci	PROPN
ejpam-865	456	2	.	.	PROPN
ejpam-865	456	3	kochi	kochi	PROPN
ejpam-865	456	4	univ	univ	PROPN
ejpam-865	456	5	.	.	PUNCT
ejpam-865	457	1	ser	ser	PROPN
ejpam-865	457	2	.	.	PUNCT
ejpam-865	458	1	a	a	DET
ejpam-865	458	2	math	math	NOUN
ejpam-865	458	3	.	.	PUNCT
ejpam-865	458	4	,	,	PUNCT
ejpam-865	458	5	19:21–28	19:21–28	NUM
ejpam-865	458	6	,	,	PUNCT
ejpam-865	458	7	1998	1998	NUM
ejpam-865	458	8	.	.	PUNCT
ejpam-865	459	1	[	[	X
ejpam-865	459	2	22	22	NUM
ejpam-865	459	3	]	]	PUNCT
ejpam-865	459	4	t	t	PROPN
ejpam-865	459	5	noiri	noiri	PROPN
ejpam-865	459	6	.	.	PUNCT
ejpam-865	460	1	remarks	remark	NOUN
ejpam-865	460	2	on	on	ADP
ejpam-865	460	3	semi	semi	ADJ
ejpam-865	460	4	-	-	ADJ
ejpam-865	460	5	open	open	ADJ
ejpam-865	460	6	mappings	mapping	NOUN
ejpam-865	460	7	.	.	PUNCT
ejpam-865	461	1	bull	bull	NOUN
ejpam-865	461	2	.	.	PUNCT
ejpam-865	462	1	calcutta	calcutta	PROPN
ejpam-865	462	2	math	math	PROPN
ejpam-865	462	3	.	.	PUNCT
ejpam-865	463	1	soc	soc	PROPN
ejpam-865	463	2	.	.	PUNCT
ejpam-865	463	3	,	,	PUNCT
ejpam-865	464	1	65:197–201	65:197–201	PROPN
ejpam-865	464	2	,	,	PUNCT
ejpam-865	464	3	1973	1973	NUM
ejpam-865	464	4	.	.	PUNCT
ejpam-865	465	1	[	[	X
ejpam-865	465	2	23	23	NUM
ejpam-865	465	3	]	]	X
ejpam-865	465	4	j	j	PROPN
ejpam-865	465	5	park	park	PROPN
ejpam-865	465	6	,	,	PUNCT
ejpam-865	465	7	b	b	PROPN
ejpam-865	465	8	lee	lee	PROPN
ejpam-865	465	9	,	,	PUNCT
ejpam-865	465	10	and	and	CCONJ
ejpam-865	465	11	m	m	PROPN
ejpam-865	465	12	son	son	NOUN
ejpam-865	465	13	.	.	PUNCT
ejpam-865	466	1	on	on	ADP
ejpam-865	466	2	δ	δ	PROPN
ejpam-865	466	3	-	-	PUNCT
ejpam-865	466	4	semiopen	semiopen	ADJ
ejpam-865	466	5	sets	set	NOUN
ejpam-865	466	6	in	in	ADP
ejpam-865	466	7	topological	topological	ADJ
ejpam-865	466	8	spaces	space	NOUN
ejpam-865	466	9	.	.	PUNCT
ejpam-865	467	1	j.	j.	PROPN
ejpam-865	467	2	indian	indian	PROPN
ejpam-865	467	3	acad	acad	PROPN
ejpam-865	467	4	.	.	PUNCT
ejpam-865	468	1	math	math	NOUN
ejpam-865	468	2	.	.	PUNCT
ejpam-865	468	3	,	,	PUNCT
ejpam-865	468	4	19:59–67	19:59–67	NUM
ejpam-865	468	5	,	,	PUNCT
ejpam-865	468	6	1997	1997	NUM
ejpam-865	468	7	.	.	PUNCT
ejpam-865	469	1	[	[	X
ejpam-865	469	2	24	24	NUM
ejpam-865	469	3	]	]	X
ejpam-865	470	1	i	i	PRON
ejpam-865	470	2	reilly	reilly	ADV
ejpam-865	470	3	and	and	CCONJ
ejpam-865	470	4	m	m	PROPN
ejpam-865	470	5	vamanamurthy	vamanamurthy	ADJ
ejpam-865	470	6	.	.	PUNCT
ejpam-865	471	1	on	on	ADP
ejpam-865	471	2	α	α	NOUN
ejpam-865	471	3	-	-	NOUN
ejpam-865	471	4	continuity	continuity	NOUN
ejpam-865	471	5	in	in	ADP
ejpam-865	471	6	topological	topological	ADJ
ejpam-865	471	7	spaces	space	NOUN
ejpam-865	471	8	.	.	PUNCT
ejpam-865	472	1	acta	acta	PROPN
ejpam-865	472	2	math	math	PROPN
ejpam-865	472	3	.	.	PUNCT
ejpam-865	473	1	hungar	hungar	PROPN
ejpam-865	473	2	.	.	PUNCT
ejpam-865	473	3	,	,	PUNCT
ejpam-865	474	1	45:27–32	45:27–32	NUM
ejpam-865	474	2	,	,	PUNCT
ejpam-865	474	3	1985	1985	NUM
ejpam-865	474	4	.	.	PUNCT
ejpam-865	475	1	[	[	X
ejpam-865	475	2	25	25	NUM
ejpam-865	475	3	]	]	X
ejpam-865	475	4	m	m	VERB
ejpam-865	475	5	son	son	NOUN
ejpam-865	475	6	.	.	PUNCT
ejpam-865	476	1	on	on	ADP
ejpam-865	476	2	δ	δ	PROPN
ejpam-865	476	3	-	-	PUNCT
ejpam-865	476	4	semiopen	semiopen	ADJ
ejpam-865	476	5	sets	set	NOUN
ejpam-865	476	6	and	and	CCONJ
ejpam-865	476	7	δ	δ	NOUN
ejpam-865	476	8	-	-	PUNCT
ejpam-865	476	9	semicontinuous	semicontinuous	ADJ
ejpam-865	476	10	functions	function	NOUN
ejpam-865	476	11	.	.	PUNCT
ejpam-865	477	1	phd	phd	NOUN
ejpam-865	477	2	thesis	thesis	PROPN
ejpam-865	477	3	,	,	PUNCT
ejpam-865	477	4	dong	dong	PROPN
ejpam-865	477	5	univ	univ	PROPN
ejpam-865	477	6	.	.	PROPN
ejpam-865	477	7	,	,	PUNCT
ejpam-865	477	8	1999	1999	NUM
ejpam-865	477	9	.	.	PUNCT
ejpam-865	478	1	[	[	X
ejpam-865	478	2	26	26	NUM
ejpam-865	478	3	]	]	X
ejpam-865	478	4	o	o	X
ejpam-865	478	5	njåstad	njåstad	NOUN
ejpam-865	478	6	.	.	PUNCT
ejpam-865	479	1	on	on	ADP
ejpam-865	479	2	some	some	DET
ejpam-865	479	3	classes	class	NOUN
ejpam-865	479	4	of	of	ADP
ejpam-865	479	5	nearly	nearly	ADV
ejpam-865	479	6	open	open	ADJ
ejpam-865	479	7	sets	set	NOUN
ejpam-865	479	8	.	.	PUNCT
ejpam-865	480	1	pacific	pacific	PROPN
ejpam-865	480	2	j.	j.	PROPN
ejpam-865	480	3	math	math	PROPN
ejpam-865	480	4	.	.	PUNCT
ejpam-865	480	5	,	,	PUNCT
ejpam-865	480	6	15:961–970	15:961–970	PROPN
ejpam-865	480	7	,	,	PUNCT
ejpam-865	480	8	1965	1965	NUM
ejpam-865	480	9	.	.	PUNCT
ejpam-865	481	1	[	[	X
ejpam-865	481	2	27	27	NUM
ejpam-865	481	3	]	]	PUNCT
ejpam-865	481	4	n	n	PRON
ejpam-865	481	5	veličko	veličko	PROPN
ejpam-865	481	6	.	.	PUNCT
ejpam-865	482	1	h	h	NOUN
ejpam-865	482	2	-	-	PUNCT
ejpam-865	482	3	closed	close	VERB
ejpam-865	482	4	topological	topological	ADJ
ejpam-865	482	5	spaces	space	NOUN
ejpam-865	482	6	.	.	PUNCT
ejpam-865	483	1	amer	amer	PROPN
ejpam-865	483	2	.	.	PUNCT
ejpam-865	483	3	math	math	PROPN
ejpam-865	483	4	.	.	PUNCT
ejpam-865	484	1	soc	soc	PROPN
ejpam-865	484	2	.	.	PUNCT
ejpam-865	485	1	transl	transl	PROPN
ejpam-865	485	2	.	.	PUNCT
ejpam-865	485	3	,	,	PUNCT
ejpam-865	485	4	(	(	PUNCT
ejpam-865	485	5	2)78:103–118	2)78:103–118	NUM
ejpam-865	485	6	,	,	PUNCT
ejpam-865	485	7	1968	1968	NUM
ejpam-865	485	8	.	.	PUNCT