id	sid	tid	token	lemma	pos
ejpam-1783	1	1	european	european	PROPN
ejpam-1783	1	2	journal	journal	PROPN
ejpam-1783	1	3	of	of	ADP
ejpam-1783	1	4	pure	pure	ADJ
ejpam-1783	1	5	and	and	CCONJ
ejpam-1783	1	6	applied	apply	VERB
ejpam-1783	1	7	mathematics	mathematic	NOUN
ejpam-1783	1	8	vol	vol	NOUN
ejpam-1783	1	9	.	.	PROPN
ejpam-1783	2	1	6	6	NUM
ejpam-1783	2	2	,	,	PUNCT
ejpam-1783	2	3	no	no	INTJ
ejpam-1783	2	4	.	.	NOUN
ejpam-1783	2	5	3	3	NUM
ejpam-1783	2	6	,	,	PUNCT
ejpam-1783	2	7	2013	2013	NUM
ejpam-1783	2	8	,	,	PUNCT
ejpam-1783	2	9	352	352	NUM
ejpam-1783	2	10	-	-	SYM
ejpam-1783	2	11	362	362	NUM
ejpam-1783	2	12	issn	issn	PROPN
ejpam-1783	2	13	1307	1307	NUM
ejpam-1783	2	14	-	-	SYM
ejpam-1783	2	15	5543	5543	NUM
ejpam-1783	2	16	–	–	PUNCT
ejpam-1783	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1783	2	18	on	on	ADP
ejpam-1783	2	19	decompositions	decomposition	NOUN
ejpam-1783	2	20	of	of	ADP
ejpam-1783	2	21	continuity	continuity	NOUN
ejpam-1783	2	22	and	and	CCONJ
ejpam-1783	2	23	complete	complete	ADJ
ejpam-1783	2	24	continuity	continuity	NOUN
ejpam-1783	2	25	in	in	ADP
ejpam-1783	2	26	ideal	ideal	ADJ
ejpam-1783	2	27	topological	topological	ADJ
ejpam-1783	2	28	spaces	space	NOUN
ejpam-1783	3	1	e.	e.	PROPN
ejpam-1783	3	2	hatir	hatir	PROPN
ejpam-1783	3	3	konya	konya	PROPN
ejpam-1783	3	4	n.e	n.e	PROPN
ejpam-1783	3	5	.	.	PROPN
ejpam-1783	3	6	university	university	PROPN
ejpam-1783	3	7	,	,	PUNCT
ejpam-1783	3	8	education	education	NOUN
ejpam-1783	3	9	faculty	faculty	NOUN
ejpam-1783	3	10	,	,	PUNCT
ejpam-1783	3	11	meram	meram	PROPN
ejpam-1783	3	12	,	,	PUNCT
ejpam-1783	3	13	konya	konya	PROPN
ejpam-1783	3	14	,	,	PUNCT
ejpam-1783	3	15	turkey	turkey	PROPN
ejpam-1783	3	16	abstract	abstract	NOUN
ejpam-1783	3	17	.	.	PUNCT
ejpam-1783	4	1	we	we	PRON
ejpam-1783	4	2	define	define	VERB
ejpam-1783	4	3	new	new	ADJ
ejpam-1783	4	4	classes	class	NOUN
ejpam-1783	4	5	of	of	ADP
ejpam-1783	4	6	sets	set	NOUN
ejpam-1783	4	7	called	call	VERB
ejpam-1783	4	8	δβi	δβi	DET
ejpam-1783	4	9	-open	-open	NOUN
ejpam-1783	4	10	set	set	NOUN
ejpam-1783	4	11	,	,	PUNCT
ejpam-1783	4	12	δα−	δα−	PUNCT
ejpam-1783	4	13	i	i	PRON
ejpam-1783	4	14	-open	-open	VERB
ejpam-1783	4	15	set	set	NOUN
ejpam-1783	4	16	,	,	PUNCT
ejpam-1783	4	17	δβ	δβ	NOUN
ejpam-1783	4	18	−	−	PROPN
ejpam-1783	4	19	i−set	i−set	NOUN
ejpam-1783	4	20	,	,	PUNCT
ejpam-1783	4	21	semi∗	semi∗	NOUN
ejpam-1783	4	22	−	−	PROPN
ejpam-1783	5	1	i	i	PRON
ejpam-1783	5	2	open	open	VERB
ejpam-1783	5	3	set	set	VERB
ejpam-1783	5	4	,	,	PUNCT
ejpam-1783	5	5	sδi	sδi	ADJ
ejpam-1783	5	6	−	−	ADP
ejpam-1783	5	7	g	g	NOUN
ejpam-1783	5	8	-	-	PUNCT
ejpam-1783	5	9	closed	close	VERB
ejpam-1783	5	10	set	set	NOUN
ejpam-1783	5	11	in	in	ADP
ejpam-1783	5	12	ideal	ideal	ADJ
ejpam-1783	5	13	topological	topological	ADJ
ejpam-1783	5	14	spaces	space	NOUN
ejpam-1783	5	15	.	.	PUNCT
ejpam-1783	6	1	using	use	VERB
ejpam-1783	6	2	these	these	DET
ejpam-1783	6	3	sets	set	NOUN
ejpam-1783	6	4	,	,	PUNCT
ejpam-1783	6	5	we	we	PRON
ejpam-1783	6	6	obtain	obtain	VERB
ejpam-1783	6	7	decompositions	decomposition	NOUN
ejpam-1783	6	8	of	of	ADP
ejpam-1783	6	9	continuity	continuity	NOUN
ejpam-1783	6	10	and	and	CCONJ
ejpam-1783	6	11	complete	complete	ADJ
ejpam-1783	6	12	continuity	continuity	NOUN
ejpam-1783	6	13	in	in	ADP
ejpam-1783	6	14	ideal	ideal	ADJ
ejpam-1783	6	15	topological	topological	ADJ
ejpam-1783	6	16	spaces	space	NOUN
ejpam-1783	6	17	.	.	PUNCT
ejpam-1783	7	1	also	also	ADV
ejpam-1783	7	2	,	,	PUNCT
ejpam-1783	7	3	we	we	PRON
ejpam-1783	7	4	investigate	investigate	VERB
ejpam-1783	7	5	some	some	DET
ejpam-1783	7	6	properties	property	NOUN
ejpam-1783	7	7	of	of	ADP
ejpam-1783	7	8	these	these	DET
ejpam-1783	7	9	sets	set	NOUN
ejpam-1783	7	10	and	and	CCONJ
ejpam-1783	7	11	relationship	relationship	VERB
ejpam-1783	7	12	other	other	ADJ
ejpam-1783	7	13	generalized	generalized	ADJ
ejpam-1783	7	14	sets	set	NOUN
ejpam-1783	7	15	.	.	PUNCT
ejpam-1783	8	1	2010	2010	NUM
ejpam-1783	8	2	mathematics	mathematic	NOUN
ejpam-1783	8	3	subject	subject	NOUN
ejpam-1783	8	4	classifications	classification	NOUN
ejpam-1783	8	5	:	:	PUNCT
ejpam-1783	8	6	54c08	54c08	NUM
ejpam-1783	8	7	,	,	PUNCT
ejpam-1783	8	8	54c10	54c10	NUM
ejpam-1783	8	9	;	;	PUNCT
ejpam-1783	8	10	54a05	54a05	NUM
ejpam-1783	8	11	key	key	ADJ
ejpam-1783	8	12	words	word	NOUN
ejpam-1783	8	13	and	and	CCONJ
ejpam-1783	8	14	phrases	phrase	NOUN
ejpam-1783	8	15	:	:	PUNCT
ejpam-1783	8	16	ideal	ideal	ADJ
ejpam-1783	8	17	topological	topological	ADJ
ejpam-1783	8	18	spaces	space	NOUN
ejpam-1783	8	19	,	,	PUNCT
ejpam-1783	8	20	δβ	δβ	NOUN
ejpam-1783	8	21	-	-	PUNCT
ejpam-1783	8	22	open	open	NOUN
ejpam-1783	8	23	set	set	NOUN
ejpam-1783	8	24	,	,	PUNCT
ejpam-1783	8	25	δβi	δβi	DET
ejpam-1783	8	26	-open	-open	NOUN
ejpam-1783	8	27	set	set	VERB
ejpam-1783	8	28	1	1	NUM
ejpam-1783	8	29	.	.	PUNCT
ejpam-1783	8	30	introduction	introduction	NOUN
ejpam-1783	8	31	and	and	CCONJ
ejpam-1783	8	32	preliminaries	preliminary	NOUN
ejpam-1783	8	33	recently	recently	ADV
ejpam-1783	8	34	,	,	PUNCT
ejpam-1783	8	35	ekici	ekici	NOUN
ejpam-1783	8	36	and	and	CCONJ
ejpam-1783	8	37	noiri	noiri	ADV
ejpam-1783	9	1	[	[	X
ejpam-1783	9	2	3	3	X
ejpam-1783	9	3	]	]	PUNCT
ejpam-1783	9	4	have	have	AUX
ejpam-1783	9	5	introduced	introduce	VERB
ejpam-1783	9	6	pre∗−	pre∗−	ADJ
ejpam-1783	9	7	i	i	PRON
ejpam-1783	9	8	-open	-open	VERB
ejpam-1783	9	9	sets	set	VERB
ejpam-1783	9	10	to	to	PART
ejpam-1783	9	11	obtain	obtain	VERB
ejpam-1783	9	12	a	a	DET
ejpam-1783	9	13	decomposition	decomposition	NOUN
ejpam-1783	9	14	of	of	ADP
ejpam-1783	9	15	continuity	continuity	NOUN
ejpam-1783	9	16	and	and	CCONJ
ejpam-1783	9	17	defined	define	VERB
ejpam-1783	9	18	α∗	α∗	NOUN
ejpam-1783	9	19	−	−	NOUN
ejpam-1783	9	20	i	i	PRON
ejpam-1783	9	21	-open	-open	VERB
ejpam-1783	9	22	sets	set	NOUN
ejpam-1783	9	23	and	and	CCONJ
ejpam-1783	9	24	showed	show	VERB
ejpam-1783	9	25	that	that	SCONJ
ejpam-1783	9	26	the	the	DET
ejpam-1783	9	27	family	family	NOUN
ejpam-1783	9	28	of	of	ADP
ejpam-1783	9	29	α∗	α∗	NOUN
ejpam-1783	9	30	−	−	PROPN
ejpam-1783	9	31	i	i	PRON
ejpam-1783	9	32	-open	-open	VERB
ejpam-1783	9	33	sets	set	NOUN
ejpam-1783	9	34	is	be	AUX
ejpam-1783	9	35	a	a	DET
ejpam-1783	9	36	topology	topology	NOUN
ejpam-1783	9	37	in	in	ADP
ejpam-1783	9	38	ideal	ideal	ADJ
ejpam-1783	9	39	topological	topological	ADJ
ejpam-1783	9	40	space	space	NOUN
ejpam-1783	9	41	.	.	PUNCT
ejpam-1783	10	1	in	in	ADP
ejpam-1783	10	2	[	[	X
ejpam-1783	10	3	14	14	NUM
ejpam-1783	10	4	]	]	PUNCT
ejpam-1783	10	5	,	,	PUNCT
ejpam-1783	10	6	the	the	DET
ejpam-1783	10	7	authors	author	NOUN
ejpam-1783	10	8	have	have	AUX
ejpam-1783	10	9	studied	study	VERB
ejpam-1783	10	10	some	some	DET
ejpam-1783	10	11	new	new	ADJ
ejpam-1783	10	12	classes	class	NOUN
ejpam-1783	10	13	of	of	ADP
ejpam-1783	10	14	functions	function	NOUN
ejpam-1783	10	15	in	in	ADP
ejpam-1783	10	16	ideal	ideal	ADJ
ejpam-1783	10	17	topological	topological	ADJ
ejpam-1783	10	18	spaces	space	NOUN
ejpam-1783	10	19	.	.	PUNCT
ejpam-1783	11	1	in	in	ADP
ejpam-1783	11	2	this	this	DET
ejpam-1783	11	3	paper	paper	NOUN
ejpam-1783	11	4	,	,	PUNCT
ejpam-1783	11	5	we	we	PRON
ejpam-1783	11	6	define	define	VERB
ejpam-1783	11	7	new	new	ADJ
ejpam-1783	11	8	classes	class	NOUN
ejpam-1783	11	9	of	of	ADP
ejpam-1783	11	10	sets	set	NOUN
ejpam-1783	11	11	called	call	VERB
ejpam-1783	11	12	δβi	δβi	DET
ejpam-1783	11	13	open	open	ADJ
ejpam-1783	11	14	set	set	NOUN
ejpam-1783	11	15	,	,	PUNCT
ejpam-1783	11	16	δα−	δα−	PUNCT
ejpam-1783	11	17	i	i	PRON
ejpam-1783	11	18	-open	-open	VERB
ejpam-1783	11	19	set	set	VERB
ejpam-1783	11	20	,	,	PUNCT
ejpam-1783	11	21	δβ−	δβ−	PROPN
ejpam-1783	12	1	i	i	PRON
ejpam-1783	12	2	-set	-set	NUM
ejpam-1783	12	3	,	,	PUNCT
ejpam-1783	12	4	semi∗−	semi∗−	VERB
ejpam-1783	12	5	i	i	PRON
ejpam-1783	12	6	-open	-open	VERB
ejpam-1783	12	7	set	set	VERB
ejpam-1783	12	8	,	,	PUNCT
ejpam-1783	12	9	sδi−	sδi−	PROPN
ejpam-1783	12	10	g	g	NOUN
ejpam-1783	12	11	-	-	PUNCT
ejpam-1783	12	12	closed	close	VERB
ejpam-1783	12	13	set	set	NOUN
ejpam-1783	12	14	in	in	ADP
ejpam-1783	12	15	ideal	ideal	ADJ
ejpam-1783	12	16	topological	topological	ADJ
ejpam-1783	12	17	spaces	space	NOUN
ejpam-1783	12	18	.	.	PUNCT
ejpam-1783	13	1	using	use	VERB
ejpam-1783	13	2	these	these	DET
ejpam-1783	13	3	sets	set	NOUN
ejpam-1783	13	4	,	,	PUNCT
ejpam-1783	13	5	we	we	PRON
ejpam-1783	13	6	obtain	obtain	VERB
ejpam-1783	13	7	decompositions	decomposition	NOUN
ejpam-1783	13	8	of	of	ADP
ejpam-1783	13	9	continuity	continuity	NOUN
ejpam-1783	13	10	and	and	CCONJ
ejpam-1783	13	11	complete	complete	ADJ
ejpam-1783	13	12	continuity	continuity	NOUN
ejpam-1783	13	13	in	in	ADP
ejpam-1783	13	14	ideal	ideal	ADJ
ejpam-1783	13	15	topological	topological	ADJ
ejpam-1783	13	16	spaces	space	NOUN
ejpam-1783	13	17	.	.	PUNCT
ejpam-1783	14	1	also	also	ADV
ejpam-1783	14	2	,	,	PUNCT
ejpam-1783	14	3	we	we	PRON
ejpam-1783	14	4	investigate	investigate	VERB
ejpam-1783	14	5	some	some	DET
ejpam-1783	14	6	properties	property	NOUN
ejpam-1783	14	7	of	of	ADP
ejpam-1783	14	8	these	these	DET
ejpam-1783	14	9	sets	set	NOUN
ejpam-1783	14	10	and	and	CCONJ
ejpam-1783	14	11	relationship	relationship	VERB
ejpam-1783	14	12	other	other	ADJ
ejpam-1783	14	13	generalized	generalized	ADJ
ejpam-1783	14	14	sets	set	NOUN
ejpam-1783	14	15	.	.	PUNCT
ejpam-1783	15	1	throughout	throughout	ADP
ejpam-1783	15	2	this	this	DET
ejpam-1783	15	3	paper	paper	NOUN
ejpam-1783	15	4	,	,	PUNCT
ejpam-1783	15	5	spaces	space	VERB
ejpam-1783	15	6	(	(	PUNCT
ejpam-1783	15	7	x	x	X
ejpam-1783	15	8	,	,	PUNCT
ejpam-1783	15	9	τ	τ	PROPN
ejpam-1783	15	10	)	)	PUNCT
ejpam-1783	15	11	and	and	CCONJ
ejpam-1783	15	12	(	(	PUNCT
ejpam-1783	15	13	y	y	PROPN
ejpam-1783	15	14	,	,	PUNCT
ejpam-1783	15	15	σ	σ	PROPN
ejpam-1783	15	16	)	)	PUNCT
ejpam-1783	15	17	(	(	PUNCT
ejpam-1783	15	18	or	or	CCONJ
ejpam-1783	15	19	simply	simply	ADV
ejpam-1783	15	20	x	x	X
ejpam-1783	15	21	and	and	CCONJ
ejpam-1783	15	22	y	y	PROPN
ejpam-1783	15	23	)	)	PUNCT
ejpam-1783	15	24	,	,	PUNCT
ejpam-1783	15	25	always	always	ADV
ejpam-1783	15	26	mean	mean	VERB
ejpam-1783	15	27	topological	topological	ADJ
ejpam-1783	15	28	spaces	space	NOUN
ejpam-1783	15	29	on	on	ADP
ejpam-1783	15	30	which	which	PRON
ejpam-1783	15	31	no	no	DET
ejpam-1783	15	32	separation	separation	NOUN
ejpam-1783	15	33	axiom	axiom	NOUN
ejpam-1783	15	34	is	be	AUX
ejpam-1783	15	35	assumed	assume	VERB
ejpam-1783	15	36	.	.	PUNCT
ejpam-1783	16	1	for	for	ADP
ejpam-1783	16	2	a	a	DET
ejpam-1783	16	3	subset	subset	NOUN
ejpam-1783	16	4	a	a	PRON
ejpam-1783	16	5	of	of	ADP
ejpam-1783	16	6	a	a	DET
ejpam-1783	16	7	topological	topological	ADJ
ejpam-1783	16	8	space	space	NOUN
ejpam-1783	16	9	(	(	PUNCT
ejpam-1783	16	10	x	x	X
ejpam-1783	16	11	,	,	PUNCT
ejpam-1783	16	12	τ	τ	PROPN
ejpam-1783	16	13	)	)	PUNCT
ejpam-1783	16	14	,	,	PUNCT
ejpam-1783	16	15	cl(a	cl(a	NUM
ejpam-1783	16	16	)	)	PUNCT
ejpam-1783	16	17	and	and	CCONJ
ejpam-1783	16	18	int(a	int(a	PROPN
ejpam-1783	16	19	)	)	PUNCT
ejpam-1783	16	20	will	will	AUX
ejpam-1783	16	21	denote	denote	VERB
ejpam-1783	16	22	the	the	DET
ejpam-1783	16	23	closure	closure	NOUN
ejpam-1783	16	24	and	and	CCONJ
ejpam-1783	16	25	interior	interior	NOUN
ejpam-1783	16	26	of	of	ADP
ejpam-1783	16	27	a	a	DET
ejpam-1783	16	28	in	in	ADP
ejpam-1783	16	29	(	(	PUNCT
ejpam-1783	16	30	x	x	INTJ
ejpam-1783	16	31	,	,	PUNCT
ejpam-1783	16	32	τ	τ	PROPN
ejpam-1783	16	33	)	)	PUNCT
ejpam-1783	16	34	,	,	PUNCT
ejpam-1783	16	35	respectively	respectively	ADV
ejpam-1783	16	36	.	.	PUNCT
ejpam-1783	17	1	a	a	DET
ejpam-1783	17	2	subset	subset	NOUN
ejpam-1783	17	3	of	of	ADP
ejpam-1783	17	4	a	a	DET
ejpam-1783	17	5	space	space	NOUN
ejpam-1783	17	6	(	(	PUNCT
ejpam-1783	17	7	x	x	X
ejpam-1783	17	8	,	,	PUNCT
ejpam-1783	17	9	τ	τ	X
ejpam-1783	17	10	)	)	PUNCT
ejpam-1783	17	11	is	be	AUX
ejpam-1783	17	12	said	say	VERB
ejpam-1783	17	13	to	to	PART
ejpam-1783	17	14	be	be	AUX
ejpam-1783	17	15	regular	regular	ADJ
ejpam-1783	17	16	open	open	ADJ
ejpam-1783	17	17	(	(	PUNCT
ejpam-1783	17	18	resp	resp	NOUN
ejpam-1783	17	19	.	.	PUNCT
ejpam-1783	18	1	regular	regular	ADJ
ejpam-1783	18	2	closed	closed	ADJ
ejpam-1783	18	3	)	)	PUNCT
ejpam-1783	19	1	[	[	X
ejpam-1783	19	2	12	12	NUM
ejpam-1783	19	3	]	]	X
ejpam-1783	19	4	if	if	SCONJ
ejpam-1783	19	5	a=	a=	ADV
ejpam-1783	19	6	int(cl(a	int(cl(a	PROPN
ejpam-1783	19	7	)	)	PUNCT
ejpam-1783	19	8	)	)	PUNCT
ejpam-1783	19	9	(	(	PUNCT
ejpam-1783	19	10	resp	resp	NOUN
ejpam-1783	19	11	.	.	PUNCT
ejpam-1783	20	1	a=	a=	PROPN
ejpam-1783	20	2	cl(int(a	cl(int(a	PROPN
ejpam-1783	20	3	)	)	PUNCT
ejpam-1783	20	4	)	)	PUNCT
ejpam-1783	20	5	)	)	PUNCT
ejpam-1783	20	6	.	.	PUNCT
ejpam-1783	21	1	a	a	PRON
ejpam-1783	21	2	is	be	AUX
ejpam-1783	21	3	called	call	VERB
ejpam-1783	21	4	δ	δ	NOUN
ejpam-1783	21	5	-	-	NOUN
ejpam-1783	21	6	open	open	ADJ
ejpam-1783	21	7	[	[	X
ejpam-1783	21	8	12	12	NUM
ejpam-1783	21	9	]	]	X
ejpam-1783	21	10	if	if	SCONJ
ejpam-1783	21	11	for	for	ADP
ejpam-1783	21	12	each	each	DET
ejpam-1783	21	13	x	x	SYM
ejpam-1783	21	14	∈	∈	PROPN
ejpam-1783	21	15	a	a	PRON
ejpam-1783	21	16	,	,	PUNCT
ejpam-1783	21	17	there	there	PRON
ejpam-1783	21	18	exists	exist	VERB
ejpam-1783	21	19	a	a	DET
ejpam-1783	21	20	regular	regular	ADJ
ejpam-1783	21	21	open	open	ADJ
ejpam-1783	21	22	set	set	NOUN
ejpam-1783	21	23	g	g	PROPN
ejpam-1783	21	24	such	such	ADJ
ejpam-1783	21	25	that	that	SCONJ
ejpam-1783	21	26	x	x	SYM
ejpam-1783	21	27	∈	∈	PROPN
ejpam-1783	21	28	g	g	PROPN
ejpam-1783	21	29	⊂	⊂	PROPN
ejpam-1783	21	30	a.	a.	NOUN
ejpam-1783	21	31	the	the	DET
ejpam-1783	21	32	complement	complement	NOUN
ejpam-1783	21	33	of	of	ADP
ejpam-1783	21	34	a	a	DET
ejpam-1783	21	35	del	del	PRON
ejpam-1783	21	36	ta	ta	NOUN
ejpam-1783	21	37	-	-	PUNCT
ejpam-1783	21	38	open	open	ADJ
ejpam-1783	21	39	set	set	NOUN
ejpam-1783	21	40	is	be	AUX
ejpam-1783	21	41	called	call	VERB
ejpam-1783	21	42	δ	δ	PROPN
ejpam-1783	21	43	-	-	PUNCT
ejpam-1783	21	44	closed	closed	ADJ
ejpam-1783	21	45	.	.	PUNCT
ejpam-1783	22	1	a	a	DET
ejpam-1783	22	2	point	point	NOUN
ejpam-1783	22	3	x	x	X
ejpam-1783	22	4	∈	∈	NOUN
ejpam-1783	22	5	x	x	PUNCT
ejpam-1783	22	6	is	be	AUX
ejpam-1783	22	7	called	call	VERB
ejpam-1783	22	8	a	a	DET
ejpam-1783	22	9	δ	δ	NOUN
ejpam-1783	22	10	-	-	PUNCT
ejpam-1783	22	11	cluster	cluster	NOUN
ejpam-1783	22	12	point	point	NOUN
ejpam-1783	22	13	of	of	ADP
ejpam-1783	22	14	a	a	DET
ejpam-1783	22	15	if	if	SCONJ
ejpam-1783	22	16	int(cl(u))∩a	int(cl(u))∩a	NOUN
ejpam-1783	22	17	6=∅	6=∅	NUM
ejpam-1783	22	18	for	for	ADP
ejpam-1783	22	19	each	each	DET
ejpam-1783	22	20	open	open	ADJ
ejpam-1783	22	21	set	set	VERB
ejpam-1783	22	22	u	u	NOUN
ejpam-1783	22	23	containing	contain	VERB
ejpam-1783	22	24	x	x	X
ejpam-1783	22	25	.	.	PUNCT
ejpam-1783	23	1	the	the	DET
ejpam-1783	23	2	set	set	NOUN
ejpam-1783	23	3	of	of	ADP
ejpam-1783	23	4	all	all	DET
ejpam-1783	23	5	δ	δ	NOUN
ejpam-1783	23	6	-	-	PUNCT
ejpam-1783	23	7	cluster	cluster	NOUN
ejpam-1783	23	8	points	point	NOUN
ejpam-1783	23	9	of	of	ADP
ejpam-1783	23	10	a	a	PRON
ejpam-1783	23	11	is	be	AUX
ejpam-1783	23	12	called	call	VERB
ejpam-1783	23	13	the	the	DET
ejpam-1783	23	14	δ	δ	NOUN
ejpam-1783	23	15	-	-	NOUN
ejpam-1783	23	16	closure	closure	NOUN
ejpam-1783	23	17	of	of	ADP
ejpam-1783	23	18	a	a	PRON
ejpam-1783	23	19	and	and	CCONJ
ejpam-1783	23	20	is	be	AUX
ejpam-1783	23	21	denoted	denote	VERB
ejpam-1783	23	22	by	by	ADP
ejpam-1783	23	23	clδ(a	clδ(a	NOUN
ejpam-1783	23	24	)	)	PUNCT
ejpam-1783	23	25	.	.	PUNCT
ejpam-1783	24	1	the	the	DET
ejpam-1783	24	2	δ	δ	PROPN
ejpam-1783	24	3	-	-	NOUN
ejpam-1783	24	4	interior	interior	NOUN
ejpam-1783	24	5	of	of	ADP
ejpam-1783	24	6	a	a	PRON
ejpam-1783	24	7	is	be	AUX
ejpam-1783	24	8	the	the	DET
ejpam-1783	24	9	union	union	NOUN
ejpam-1783	24	10	of	of	ADP
ejpam-1783	24	11	all	all	DET
ejpam-1783	24	12	regular	regular	ADJ
ejpam-1783	24	13	open	open	ADJ
ejpam-1783	24	14	sets	set	NOUN
ejpam-1783	24	15	of	of	ADP
ejpam-1783	24	16	x	x	PUNCT
ejpam-1783	24	17	contained	contain	VERB
ejpam-1783	24	18	in	in	ADP
ejpam-1783	24	19	a	a	PRON
ejpam-1783	24	20	and	and	CCONJ
ejpam-1783	24	21	it	it	PRON
ejpam-1783	24	22	is	be	AUX
ejpam-1783	24	23	denoted	denote	VERB
ejpam-1783	24	24	by	by	ADP
ejpam-1783	24	25	intδ(a	intδ(a	NOUN
ejpam-1783	24	26	)	)	PUNCT
ejpam-1783	24	27	.	.	PUNCT
ejpam-1783	25	1	email	email	NOUN
ejpam-1783	25	2	address	address	NOUN
ejpam-1783	25	3	:	:	PUNCT
ejpam-1783	26	1	hatir10@yahoo.com	hatir10@yahoo.com	X
ejpam-1783	26	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1783	27	1	352	352	NUM
ejpam-1783	27	2	c	c	AUX
ejpam-1783	27	3	©	©	PROPN
ejpam-1783	27	4	2013	2013	NUM
ejpam-1783	27	5	ejpam	ejpam	NOUN
ejpam-1783	27	6	all	all	DET
ejpam-1783	27	7	rights	right	NOUN
ejpam-1783	27	8	reserved	reserve	VERB
ejpam-1783	27	9	.	.	PUNCT
ejpam-1783	28	1	e.	e.	PROPN
ejpam-1783	28	2	hatir	hatir	PROPN
ejpam-1783	28	3	/	/	SYM
ejpam-1783	28	4	eur	eur	PROPN
ejpam-1783	28	5	.	.	PUNCT
ejpam-1783	29	1	j.	j.	PROPN
ejpam-1783	29	2	pure	pure	PROPN
ejpam-1783	29	3	appl	appl	PROPN
ejpam-1783	29	4	.	.	PROPN
ejpam-1783	29	5	math	math	PROPN
ejpam-1783	29	6	,	,	PUNCT
ejpam-1783	29	7	6	6	NUM
ejpam-1783	29	8	(	(	PUNCT
ejpam-1783	29	9	2013	2013	NUM
ejpam-1783	29	10	)	)	PUNCT
ejpam-1783	29	11	,	,	PUNCT
ejpam-1783	29	12	352	352	NUM
ejpam-1783	29	13	-	-	SYM
ejpam-1783	29	14	362	362	NUM
ejpam-1783	29	15	353	353	NUM
ejpam-1783	29	16	an	an	DET
ejpam-1783	29	17	ideal	ideal	NOUN
ejpam-1783	30	1	i	i	PRON
ejpam-1783	30	2	on	on	ADP
ejpam-1783	30	3	a	a	DET
ejpam-1783	30	4	topological	topological	ADJ
ejpam-1783	30	5	space	space	NOUN
ejpam-1783	30	6	(	(	PUNCT
ejpam-1783	30	7	x	x	X
ejpam-1783	30	8	,	,	PUNCT
ejpam-1783	30	9	τ	τ	X
ejpam-1783	30	10	)	)	PUNCT
ejpam-1783	30	11	is	be	AUX
ejpam-1783	30	12	a	a	DET
ejpam-1783	30	13	nonempty	nonempty	ADJ
ejpam-1783	30	14	collection	collection	NOUN
ejpam-1783	30	15	of	of	ADP
ejpam-1783	30	16	subsets	subset	NOUN
ejpam-1783	30	17	of	of	ADP
ejpam-1783	30	18	x	x	PUNCT
ejpam-1783	30	19	which	which	PRON
ejpam-1783	30	20	satisfies	satisfy	VERB
ejpam-1783	30	21	i	i	PRON
ejpam-1783	30	22	)	)	PUNCT
ejpam-1783	31	1	a	a	PRON
ejpam-1783	31	2	∈	∈	NOUN
ejpam-1783	32	1	i	i	PRON
ejpam-1783	32	2	and	and	CCONJ
ejpam-1783	32	3	b	b	PROPN
ejpam-1783	32	4	⊂	⊂	PROPN
ejpam-1783	32	5	a	a	PRON
ejpam-1783	32	6	implies	imply	VERB
ejpam-1783	32	7	b	b	X
ejpam-1783	32	8	∈	∈	PROPN
ejpam-1783	32	9	i	i	PRON
ejpam-1783	32	10	,	,	PUNCT
ejpam-1783	32	11	ii	ii	PROPN
ejpam-1783	32	12	)	)	PUNCT
ejpam-1783	32	13	a	a	DET
ejpam-1783	32	14	∈	∈	PROPN
ejpam-1783	32	15	i	i	PRON
ejpam-1783	32	16	and	and	CCONJ
ejpam-1783	32	17	b	b	X
ejpam-1783	32	18	∈	∈	PROPN
ejpam-1783	32	19	i	i	PRON
ejpam-1783	32	20	implies	imply	VERB
ejpam-1783	32	21	a∪	a∪	PROPN
ejpam-1783	33	1	b	b	X
ejpam-1783	33	2	∈	∈	PROPN
ejpam-1783	34	1	i	i	PRON
ejpam-1783	34	2	.	.	PUNCT
ejpam-1783	35	1	an	an	DET
ejpam-1783	35	2	ideal	ideal	ADJ
ejpam-1783	35	3	topological	topological	ADJ
ejpam-1783	35	4	space	space	NOUN
ejpam-1783	35	5	is	be	AUX
ejpam-1783	35	6	a	a	DET
ejpam-1783	35	7	topological	topological	ADJ
ejpam-1783	35	8	space	space	NOUN
ejpam-1783	35	9	(	(	PUNCT
ejpam-1783	35	10	x	x	X
ejpam-1783	35	11	,	,	PUNCT
ejpam-1783	35	12	τ	τ	PROPN
ejpam-1783	35	13	)	)	PUNCT
ejpam-1783	35	14	with	with	ADP
ejpam-1783	35	15	an	an	DET
ejpam-1783	35	16	ideal	ideal	ADJ
ejpam-1783	35	17	i	i	PRON
ejpam-1783	35	18	on	on	ADP
ejpam-1783	35	19	x	x	X
ejpam-1783	35	20	and	and	CCONJ
ejpam-1783	35	21	if	if	SCONJ
ejpam-1783	35	22	p(x	p(x	PROPN
ejpam-1783	35	23	)	)	PUNCT
ejpam-1783	35	24	is	be	AUX
ejpam-1783	35	25	the	the	DET
ejpam-1783	35	26	set	set	NOUN
ejpam-1783	35	27	of	of	ADP
ejpam-1783	35	28	all	all	DET
ejpam-1783	35	29	subsets	subset	NOUN
ejpam-1783	35	30	of	of	ADP
ejpam-1783	35	31	x	x	PRON
ejpam-1783	35	32	,	,	PUNCT
ejpam-1783	35	33	a	a	DET
ejpam-1783	35	34	set	set	NOUN
ejpam-1783	35	35	operator	operator	NOUN
ejpam-1783	35	36	(	(	PUNCT
ejpam-1783	35	37	·	·	PUNCT
ejpam-1783	35	38	)	)	PUNCT
ejpam-1783	35	39	∗	∗	NOUN
ejpam-1783	35	40	:	:	PUNCT
ejpam-1783	35	41	p(x	p(x	PROPN
ejpam-1783	35	42	)	)	PUNCT
ejpam-1783	35	43	→	→	SYM
ejpam-1783	35	44	p(x	p(x	PROPN
ejpam-1783	35	45	)	)	PUNCT
ejpam-1783	35	46	called	call	VERB
ejpam-1783	35	47	a	a	DET
ejpam-1783	35	48	local	local	ADJ
ejpam-1783	35	49	function	function	NOUN
ejpam-1783	35	50	[	[	X
ejpam-1783	35	51	8	8	NUM
ejpam-1783	35	52	]	]	PUNCT
ejpam-1783	35	53	of	of	ADP
ejpam-1783	35	54	a	a	PRON
ejpam-1783	35	55	with	with	ADP
ejpam-1783	35	56	respect	respect	NOUN
ejpam-1783	35	57	to	to	ADP
ejpam-1783	35	58	τ	τ	PROPN
ejpam-1783	36	1	and	and	CCONJ
ejpam-1783	36	2	i	i	PRON
ejpam-1783	36	3	is	be	AUX
ejpam-1783	36	4	defined	define	VERB
ejpam-1783	36	5	as	as	SCONJ
ejpam-1783	36	6	follows	follow	VERB
ejpam-1783	36	7	:	:	PUNCT
ejpam-1783	36	8	for	for	ADP
ejpam-1783	36	9	a	a	DET
ejpam-1783	36	10	⊂	⊂	PROPN
ejpam-1783	36	11	x	x	X
ejpam-1783	36	12	,	,	PUNCT
ejpam-1783	36	13	a∗(i	a∗(i	PROPN
ejpam-1783	36	14	)	)	PUNCT
ejpam-1783	36	15	=	=	SYM
ejpam-1783	36	16	�	�	PROPN
ejpam-1783	36	17	x	x	SYM
ejpam-1783	36	18	∈	∈	PROPN
ejpam-1783	36	19	x	x	X
ejpam-1783	36	20	:	:	PUNCT
ejpam-1783	36	21	u	u	NOUN
ejpam-1783	36	22	∩	∩	NOUN
ejpam-1783	36	23	a	a	X
ejpam-1783	36	24	/∈	/∈	PUNCT
ejpam-1783	36	25	i	i	PRON
ejpam-1783	36	26	for	for	ADP
ejpam-1783	36	27	every	every	DET
ejpam-1783	36	28	u	u	PROPN
ejpam-1783	36	29	∈	∈	PROPN
ejpam-1783	36	30	τ(x	τ(x	NOUN
ejpam-1783	36	31	)	)	PUNCT
ejpam-1783	36	32	where	where	SCONJ
ejpam-1783	36	33	τ(x	τ(x	NOUN
ejpam-1783	36	34	)	)	PUNCT
ejpam-1783	36	35	=	=	PRON
ejpam-1783	36	36	{	{	PUNCT
ejpam-1783	36	37	u	u	X
ejpam-1783	36	38	∈	∈	PROPN
ejpam-1783	36	39	τ	τ	X
ejpam-1783	36	40	:	:	PUNCT
ejpam-1783	36	41	x	x	SYM
ejpam-1783	36	42	∈	∈	PROPN
ejpam-1783	36	43	u	u	NOUN
ejpam-1783	36	44	}	}	PUNCT
ejpam-1783	36	45	.	.	PUNCT
ejpam-1783	37	1	we	we	PRON
ejpam-1783	37	2	simply	simply	ADV
ejpam-1783	37	3	write	write	VERB
ejpam-1783	37	4	a∗	a∗	PROPN
ejpam-1783	37	5	instead	instead	ADV
ejpam-1783	37	6	of	of	ADP
ejpam-1783	37	7	a∗(i	a∗(i	PROPN
ejpam-1783	37	8	,	,	PUNCT
ejpam-1783	37	9	τ	τ	PROPN
ejpam-1783	37	10	)	)	PUNCT
ejpam-1783	37	11	.	.	PUNCT
ejpam-1783	38	1	x	x	PUNCT
ejpam-1783	38	2	∗	∗	NOUN
ejpam-1783	38	3	is	be	AUX
ejpam-1783	38	4	often	often	ADV
ejpam-1783	38	5	a	a	DET
ejpam-1783	38	6	proper	proper	ADJ
ejpam-1783	38	7	subset	subset	NOUN
ejpam-1783	38	8	of	of	ADP
ejpam-1783	38	9	x	x	X
ejpam-1783	38	10	.	.	PUNCT
ejpam-1783	39	1	the	the	DET
ejpam-1783	39	2	hypothesis	hypothesis	NOUN
ejpam-1783	39	3	x	x	PUNCT
ejpam-1783	39	4	=	=	PUNCT
ejpam-1783	39	5	x	x	SYM
ejpam-1783	39	6	∗	∗	NOUN
ejpam-1783	39	7	[	[	X
ejpam-1783	39	8	6	6	NUM
ejpam-1783	39	9	]	]	PUNCT
ejpam-1783	39	10	is	be	AUX
ejpam-1783	39	11	equivalent	equivalent	ADJ
ejpam-1783	39	12	to	to	ADP
ejpam-1783	39	13	the	the	DET
ejpam-1783	39	14	hypothesis	hypothesis	NOUN
ejpam-1783	39	15	τ	τ	PROPN
ejpam-1783	39	16	∩	∩	PROPN
ejpam-1783	39	17	i	i	NOUN
ejpam-1783	39	18	=	=	PUNCT
ejpam-1783	39	19	∅.	∅.	VERB
ejpam-1783	39	20	for	for	ADP
ejpam-1783	39	21	every	every	DET
ejpam-1783	39	22	ideal	ideal	ADJ
ejpam-1783	39	23	topological	topological	ADJ
ejpam-1783	39	24	space	space	NOUN
ejpam-1783	39	25	,	,	PUNCT
ejpam-1783	39	26	there	there	PRON
ejpam-1783	39	27	exists	exist	VERB
ejpam-1783	39	28	a	a	DET
ejpam-1783	39	29	topology	topology	NOUN
ejpam-1783	39	30	τ∗(i	τ∗(i	PROPN
ejpam-1783	39	31	)	)	PUNCT
ejpam-1783	39	32	or	or	CCONJ
ejpam-1783	39	33	briefly	briefly	ADV
ejpam-1783	39	34	τ∗	τ∗	PROPN
ejpam-1783	39	35	,	,	PUNCT
ejpam-1783	39	36	finer	fine	ADJ
ejpam-1783	39	37	than	than	ADP
ejpam-1783	39	38	τ	τ	PROPN
ejpam-1783	39	39	,	,	PUNCT
ejpam-1783	39	40	generated	generate	VERB
ejpam-1783	39	41	by	by	ADP
ejpam-1783	39	42	β(i	β(i	X
ejpam-1783	39	43	,	,	PUNCT
ejpam-1783	39	44	τ	τ	X
ejpam-1783	39	45	)	)	PUNCT
ejpam-1783	39	46	=	=	SYM
ejpam-1783	39	47	{	{	PUNCT
ejpam-1783	39	48	u	u	NOUN
ejpam-1783	39	49	\	\	PROPN
ejpam-1783	39	50	i	i	PRON
ejpam-1783	39	51	:	:	PUNCT
ejpam-1783	39	52	u	u	PROPN
ejpam-1783	39	53	∈	∈	PROPN
ejpam-1783	39	54	τ	τ	X
ejpam-1783	40	1	and	and	CCONJ
ejpam-1783	40	2	i	i	PRON
ejpam-1783	40	3	∈	∈	PROPN
ejpam-1783	40	4	i	i	X
ejpam-1783	40	5	}	}	PUNCT
ejpam-1783	40	6	,	,	PUNCT
ejpam-1783	40	7	but	but	CCONJ
ejpam-1783	40	8	in	in	ADP
ejpam-1783	40	9	general	general	ADJ
ejpam-1783	40	10	β(i	β(i	X
ejpam-1783	40	11	,	,	PUNCT
ejpam-1783	40	12	τ	τ	X
ejpam-1783	40	13	)	)	PUNCT
ejpam-1783	40	14	is	be	AUX
ejpam-1783	40	15	not	not	PART
ejpam-1783	40	16	always	always	ADV
ejpam-1783	40	17	a	a	DET
ejpam-1783	40	18	topology	topology	NOUN
ejpam-1783	41	1	[	[	X
ejpam-1783	41	2	7	7	NUM
ejpam-1783	41	3	]	]	PUNCT
ejpam-1783	41	4	.	.	PUNCT
ejpam-1783	42	1	additionally	additionally	ADV
ejpam-1783	42	2	,	,	PUNCT
ejpam-1783	42	3	cl∗(a	cl∗(a	NOUN
ejpam-1783	42	4	)	)	PUNCT
ejpam-1783	42	5	=	=	PUNCT
ejpam-1783	43	1	a∪	a∪	DET
ejpam-1783	43	2	a∗	a∗	PROPN
ejpam-1783	43	3	defines	define	VERB
ejpam-1783	43	4	a	a	DET
ejpam-1783	43	5	kuratowski	kuratowski	ADJ
ejpam-1783	43	6	closure	closure	NOUN
ejpam-1783	43	7	operator	operator	NOUN
ejpam-1783	43	8	for	for	ADP
ejpam-1783	43	9	τ∗(i	τ∗(i	PROPN
ejpam-1783	43	10	)	)	PUNCT
ejpam-1783	43	11	.	.	PUNCT
ejpam-1783	44	1	if	if	SCONJ
ejpam-1783	44	2	i	i	PRON
ejpam-1783	44	3	is	be	AUX
ejpam-1783	44	4	an	an	DET
ejpam-1783	44	5	ideal	ideal	NOUN
ejpam-1783	44	6	on	on	ADP
ejpam-1783	44	7	x	x	NOUN
ejpam-1783	44	8	,	,	PUNCT
ejpam-1783	44	9	then	then	ADV
ejpam-1783	44	10	(	(	PUNCT
ejpam-1783	44	11	x	x	X
ejpam-1783	44	12	,	,	PUNCT
ejpam-1783	44	13	τ	τ	PROPN
ejpam-1783	44	14	,	,	PUNCT
ejpam-1783	44	15	i	i	PROPN
ejpam-1783	44	16	)	)	PUNCT
ejpam-1783	44	17	is	be	AUX
ejpam-1783	44	18	called	call	VERB
ejpam-1783	44	19	an	an	DET
ejpam-1783	44	20	ideal	ideal	ADJ
ejpam-1783	44	21	topological	topological	ADJ
ejpam-1783	44	22	space	space	NOUN
ejpam-1783	44	23	or	or	CCONJ
ejpam-1783	44	24	simply	simply	ADV
ejpam-1783	44	25	an	an	DET
ejpam-1783	44	26	ideal	ideal	ADJ
ejpam-1783	44	27	space	space	NOUN
ejpam-1783	44	28	.	.	PUNCT
ejpam-1783	45	1	a	a	DET
ejpam-1783	45	2	subset	subset	NOUN
ejpam-1783	45	3	a	a	PRON
ejpam-1783	45	4	of	of	ADP
ejpam-1783	45	5	an	an	DET
ejpam-1783	45	6	ideal	ideal	ADJ
ejpam-1783	45	7	space	space	NOUN
ejpam-1783	45	8	(	(	PUNCT
ejpam-1783	45	9	x	x	X
ejpam-1783	45	10	,	,	PUNCT
ejpam-1783	45	11	τ	τ	PROPN
ejpam-1783	45	12	,	,	PUNCT
ejpam-1783	45	13	i	i	PROPN
ejpam-1783	45	14	)	)	PUNCT
ejpam-1783	45	15	is	be	AUX
ejpam-1783	45	16	said	say	VERB
ejpam-1783	45	17	to	to	PART
ejpam-1783	45	18	be	be	AUX
ejpam-1783	45	19	r−	r−	NOUN
ejpam-1783	45	20	i	i	PRON
ejpam-1783	45	21	-open	-open	VERB
ejpam-1783	46	1	[	[	X
ejpam-1783	46	2	14	14	NUM
ejpam-1783	46	3	]	]	PUNCT
ejpam-1783	46	4	if	if	SCONJ
ejpam-1783	46	5	a=	a=	ADV
ejpam-1783	46	6	int(cl∗(a	int(cl∗(a	NOUN
ejpam-1783	46	7	)	)	PUNCT
ejpam-1783	46	8	)	)	PUNCT
ejpam-1783	46	9	.	.	PUNCT
ejpam-1783	47	1	a	a	DET
ejpam-1783	47	2	point	point	NOUN
ejpam-1783	47	3	x	x	X
ejpam-1783	47	4	in	in	ADP
ejpam-1783	47	5	an	an	DET
ejpam-1783	47	6	ideal	ideal	ADJ
ejpam-1783	47	7	space	space	NOUN
ejpam-1783	47	8	(	(	PUNCT
ejpam-1783	47	9	x	x	X
ejpam-1783	47	10	,	,	PUNCT
ejpam-1783	47	11	τ	τ	PROPN
ejpam-1783	47	12	,	,	PUNCT
ejpam-1783	47	13	i	i	PROPN
ejpam-1783	47	14	)	)	PUNCT
ejpam-1783	47	15	is	be	AUX
ejpam-1783	47	16	called	call	VERB
ejpam-1783	47	17	a	a	DET
ejpam-1783	47	18	δi−	δi−	NOUN
ejpam-1783	47	19	cluster	cluster	NOUN
ejpam-1783	47	20	point	point	NOUN
ejpam-1783	47	21	of	of	ADP
ejpam-1783	47	22	a	a	PRON
ejpam-1783	47	23	if	if	SCONJ
ejpam-1783	47	24	int(cl∗(u))∩a	int(cl∗(u))∩a	NOUN
ejpam-1783	47	25	6=∅	6=∅	NUM
ejpam-1783	47	26	for	for	ADP
ejpam-1783	47	27	each	each	DET
ejpam-1783	47	28	neighborhood	neighborhood	NOUN
ejpam-1783	47	29	u	u	NOUN
ejpam-1783	47	30	of	of	ADP
ejpam-1783	47	31	x	x	X
ejpam-1783	47	32	.	.	PUNCT
ejpam-1783	48	1	the	the	DET
ejpam-1783	48	2	set	set	NOUN
ejpam-1783	48	3	of	of	ADP
ejpam-1783	48	4	all	all	DET
ejpam-1783	48	5	δi	δi	NOUN
ejpam-1783	48	6	-cluster	-cluster	NOUN
ejpam-1783	48	7	points	point	NOUN
ejpam-1783	48	8	of	of	ADP
ejpam-1783	48	9	a	a	PRON
ejpam-1783	48	10	is	be	AUX
ejpam-1783	48	11	called	call	VERB
ejpam-1783	48	12	the	the	DET
ejpam-1783	48	13	δi	δi	PROPN
ejpam-1783	48	14	-closure	-closure	NOUN
ejpam-1783	48	15	of	of	ADP
ejpam-1783	48	16	a	a	PRON
ejpam-1783	48	17	and	and	CCONJ
ejpam-1783	48	18	is	be	AUX
ejpam-1783	48	19	denoted	denote	VERB
ejpam-1783	48	20	by	by	ADP
ejpam-1783	48	21	δcli(a	δcli(a	PROPN
ejpam-1783	48	22	)	)	PUNCT
ejpam-1783	48	23	.	.	PUNCT
ejpam-1783	49	1	a	a	PRON
ejpam-1783	49	2	is	be	AUX
ejpam-1783	49	3	said	say	VERB
ejpam-1783	49	4	to	to	PART
ejpam-1783	49	5	be	be	AUX
ejpam-1783	49	6	δi	δi	ADV
ejpam-1783	49	7	-closed	-close	VERB
ejpam-1783	49	8	[	[	X
ejpam-1783	49	9	14	14	NUM
ejpam-1783	49	10	]	]	PUNCT
ejpam-1783	49	11	if	if	SCONJ
ejpam-1783	49	12	δcli(a	δcli(a	ADJ
ejpam-1783	49	13	)	)	PUNCT
ejpam-1783	49	14	=	=	VERB
ejpam-1783	49	15	a.	a.	NOUN
ejpam-1783	49	16	the	the	DET
ejpam-1783	49	17	complement	complement	NOUN
ejpam-1783	49	18	of	of	ADP
ejpam-1783	49	19	δi	δi	ADV
ejpam-1783	49	20	-closed	-close	VERB
ejpam-1783	49	21	set	set	NOUN
ejpam-1783	49	22	is	be	AUX
ejpam-1783	49	23	called	call	VERB
ejpam-1783	49	24	δi	δi	NOUN
ejpam-1783	49	25	-open	-open	NOUN
ejpam-1783	49	26	set	set	NOUN
ejpam-1783	49	27	.	.	PUNCT
ejpam-1783	50	1	lemma	lemma	PROPN
ejpam-1783	50	2	1	1	NUM
ejpam-1783	50	3	(	(	PUNCT
ejpam-1783	50	4	[	[	X
ejpam-1783	50	5	7	7	NUM
ejpam-1783	50	6	]	]	NUM
ejpam-1783	50	7	)	)	PUNCT
ejpam-1783	50	8	.	.	PUNCT
ejpam-1783	51	1	let	let	AUX
ejpam-1783	51	2	(	(	PUNCT
ejpam-1783	51	3	x	x	X
ejpam-1783	51	4	,	,	PUNCT
ejpam-1783	51	5	τ	τ	PROPN
ejpam-1783	51	6	,	,	PUNCT
ejpam-1783	51	7	i	i	PRON
ejpam-1783	51	8	)	)	PUNCT
ejpam-1783	51	9	be	be	VERB
ejpam-1783	51	10	an	an	DET
ejpam-1783	51	11	ideal	ideal	ADJ
ejpam-1783	51	12	topological	topological	ADJ
ejpam-1783	51	13	space	space	NOUN
ejpam-1783	51	14	and	and	CCONJ
ejpam-1783	51	15	a	a	DET
ejpam-1783	51	16	,	,	PUNCT
ejpam-1783	51	17	b	b	PROPN
ejpam-1783	51	18	be	be	AUX
ejpam-1783	51	19	subsets	subset	NOUN
ejpam-1783	51	20	of	of	ADP
ejpam-1783	51	21	x	x	PROPN
ejpam-1783	51	22	.	.	PUNCT
ejpam-1783	52	1	1	1	X
ejpam-1783	52	2	.	.	X
ejpam-1783	53	1	if	if	SCONJ
ejpam-1783	53	2	a⊂	a⊂	NOUN
ejpam-1783	53	3	b	b	NOUN
ejpam-1783	53	4	,	,	PUNCT
ejpam-1783	53	5	then	then	ADV
ejpam-1783	53	6	a∗	a∗	PROPN
ejpam-1783	53	7	⊂	⊂	PROPN
ejpam-1783	53	8	b∗	b∗	ADJ
ejpam-1783	53	9	2	2	X
ejpam-1783	53	10	.	.	PUNCT
ejpam-1783	54	1	if	if	SCONJ
ejpam-1783	54	2	g	g	PROPN
ejpam-1783	54	3	∈	∈	PROPN
ejpam-1783	54	4	τ	τ	PROPN
ejpam-1783	54	5	,	,	PUNCT
ejpam-1783	54	6	then	then	ADV
ejpam-1783	54	7	g	g	PROPN
ejpam-1783	54	8	∩	∩	ADJ
ejpam-1783	54	9	a∗	a∗	PROPN
ejpam-1783	54	10	⊂	⊂	PROPN
ejpam-1783	54	11	(	(	PUNCT
ejpam-1783	54	12	g	g	PROPN
ejpam-1783	54	13	∩	∩	NOUN
ejpam-1783	54	14	a)∗	a)∗	PROPN
ejpam-1783	54	15	3	3	X
ejpam-1783	54	16	.	.	PUNCT
ejpam-1783	54	17	a∗	a∗	PROPN
ejpam-1783	54	18	=	=	SYM
ejpam-1783	54	19	cl(a∗)⊂	cl(a∗)⊂	PROPN
ejpam-1783	54	20	cl(a	cl(a	NUM
ejpam-1783	54	21	)	)	PUNCT
ejpam-1783	54	22	.	.	PUNCT
ejpam-1783	55	1	definition	definition	NOUN
ejpam-1783	55	2	1	1	NUM
ejpam-1783	55	3	.	.	PUNCT
ejpam-1783	56	1	a	a	DET
ejpam-1783	56	2	subset	subset	NOUN
ejpam-1783	56	3	a	a	PRON
ejpam-1783	56	4	of	of	ADP
ejpam-1783	56	5	an	an	DET
ejpam-1783	56	6	ideal	ideal	ADJ
ejpam-1783	56	7	topological	topological	ADJ
ejpam-1783	56	8	space	space	NOUN
ejpam-1783	56	9	(	(	PUNCT
ejpam-1783	56	10	x	x	X
ejpam-1783	56	11	,	,	PUNCT
ejpam-1783	56	12	τ	τ	PROPN
ejpam-1783	56	13	,	,	PUNCT
ejpam-1783	56	14	i	i	PROPN
ejpam-1783	56	15	)	)	PUNCT
ejpam-1783	56	16	is	be	AUX
ejpam-1783	56	17	called	call	VERB
ejpam-1783	56	18	a	a	PRON
ejpam-1783	56	19	)	)	PUNCT
ejpam-1783	56	20	α	α	NOUN
ejpam-1783	56	21	-	-	ADJ
ejpam-1783	56	22	open	open	ADJ
ejpam-1783	56	23	[	[	X
ejpam-1783	56	24	10	10	NUM
ejpam-1783	56	25	]	]	X
ejpam-1783	56	26	if	if	SCONJ
ejpam-1783	56	27	a⊂	a⊂	ADP
ejpam-1783	56	28	int(cl(int(a	int(cl(int(a	NOUN
ejpam-1783	56	29	)	)	PUNCT
ejpam-1783	56	30	)	)	PUNCT
ejpam-1783	56	31	)	)	PUNCT
ejpam-1783	57	1	b	b	X
ejpam-1783	57	2	)	)	PUNCT
ejpam-1783	57	3	preopen	preopen	NOUN
ejpam-1783	58	1	[	[	X
ejpam-1783	58	2	9	9	NUM
ejpam-1783	58	3	]	]	X
ejpam-1783	58	4	if	if	SCONJ
ejpam-1783	58	5	a⊂	a⊂	PRON
ejpam-1783	58	6	int(cl(a	int(cl(a	NOUN
ejpam-1783	58	7	)	)	PUNCT
ejpam-1783	58	8	)	)	PUNCT
ejpam-1783	59	1	c	c	X
ejpam-1783	59	2	)	)	PUNCT
ejpam-1783	59	3	pre−	pre−	NOUN
ejpam-1783	59	4	i	i	PRON
ejpam-1783	59	5	-open	-open	VERB
ejpam-1783	60	1	[	[	X
ejpam-1783	60	2	2	2	NUM
ejpam-1783	60	3	]	]	PUNCT
ejpam-1783	60	4	if	if	SCONJ
ejpam-1783	60	5	a⊂	a⊂	PRON
ejpam-1783	60	6	int(cl∗(a	int(cl∗(a	NOUN
ejpam-1783	60	7	)	)	PUNCT
ejpam-1783	60	8	)	)	PUNCT
ejpam-1783	61	1	d	d	X
ejpam-1783	61	2	)	)	PUNCT
ejpam-1783	61	3	α−	α−	ADP
ejpam-1783	61	4	i	i	PRON
ejpam-1783	61	5	-open	-open	VERB
ejpam-1783	62	1	[	[	X
ejpam-1783	62	2	4	4	NUM
ejpam-1783	62	3	]	]	X
ejpam-1783	62	4	if	if	SCONJ
ejpam-1783	62	5	a⊂	a⊂	NOUN
ejpam-1783	62	6	int(cl∗(int(a	int(cl∗(int(a	PROPN
ejpam-1783	62	7	)	)	PUNCT
ejpam-1783	62	8	)	)	PUNCT
ejpam-1783	62	9	)	)	PUNCT
ejpam-1783	63	1	e	e	X
ejpam-1783	63	2	)	)	PUNCT
ejpam-1783	63	3	δ	δ	NOUN
ejpam-1783	63	4	-	-	NOUN
ejpam-1783	63	5	preopen	preopen	ADJ
ejpam-1783	64	1	[	[	X
ejpam-1783	64	2	11	11	NUM
ejpam-1783	64	3	]	]	PUNCT
ejpam-1783	64	4	if	if	SCONJ
ejpam-1783	64	5	a⊂	a⊂	NOUN
ejpam-1783	64	6	int(clδ(a	int(clδ(a	NOUN
ejpam-1783	64	7	)	)	PUNCT
ejpam-1783	64	8	)	)	PUNCT
ejpam-1783	65	1	f	f	X
ejpam-1783	65	2	)	)	PUNCT
ejpam-1783	65	3	pre∗−	pre∗−	NUM
ejpam-1783	65	4	i	i	PRON
ejpam-1783	65	5	-open	-open	VERB
ejpam-1783	66	1	[	[	X
ejpam-1783	66	2	3	3	NUM
ejpam-1783	66	3	]	]	PUNCT
ejpam-1783	66	4	if	if	SCONJ
ejpam-1783	66	5	a⊂	a⊂	NOUN
ejpam-1783	66	6	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	66	7	)	)	PUNCT
ejpam-1783	66	8	)	)	PUNCT
ejpam-1783	66	9	g	g	NOUN
ejpam-1783	66	10	)	)	PUNCT
ejpam-1783	67	1	α∗−	α∗−	PROPN
ejpam-1783	68	1	i	i	PRON
ejpam-1783	68	2	-open	-open	VERB
ejpam-1783	69	1	[	[	X
ejpam-1783	69	2	3	3	NUM
ejpam-1783	69	3	]	]	PUNCT
ejpam-1783	69	4	if	if	SCONJ
ejpam-1783	69	5	a⊂	a⊂	NOUN
ejpam-1783	69	6	int(cl∗(intδ(a	int(cl∗(intδ(a	NOUN
ejpam-1783	69	7	)	)	PUNCT
ejpam-1783	69	8	)	)	PUNCT
ejpam-1783	69	9	)	)	PUNCT
ejpam-1783	69	10	h	h	X
ejpam-1783	69	11	)	)	PUNCT
ejpam-1783	69	12	strongly	strongly	ADV
ejpam-1783	69	13	α−	α−	ADP
ejpam-1783	69	14	i	i	PRON
ejpam-1783	69	15	-open	-open	VERB
ejpam-1783	70	1	[	[	X
ejpam-1783	70	2	3	3	NUM
ejpam-1783	70	3	]	]	PUNCT
ejpam-1783	70	4	if	if	SCONJ
ejpam-1783	70	5	a⊂	a⊂	PRON
ejpam-1783	70	6	int(cl∗(δint	int(cl∗(δint	PROPN
ejpam-1783	70	7	i(a	i(a	PROPN
ejpam-1783	70	8	)	)	PUNCT
ejpam-1783	70	9	)	)	PUNCT
ejpam-1783	70	10	)	)	PUNCT
ejpam-1783	71	1	i	i	NOUN
ejpam-1783	71	2	)	)	PUNCT
ejpam-1783	71	3	β∗i	β∗i	PUNCT
ejpam-1783	71	4	-open	-open	VERB
ejpam-1783	72	1	[	[	X
ejpam-1783	72	2	3	3	NUM
ejpam-1783	72	3	]	]	X
ejpam-1783	72	4	if	if	SCONJ
ejpam-1783	72	5	a⊂	a⊂	PRON
ejpam-1783	72	6	cl∗(int(clδ(a	cl∗(int(clδ(a	NUM
ejpam-1783	72	7	)	)	PUNCT
ejpam-1783	72	8	)	)	PUNCT
ejpam-1783	72	9	)	)	PUNCT
ejpam-1783	72	10	j	j	PROPN
ejpam-1783	72	11	)	)	PUNCT
ejpam-1783	72	12	t	t	PROPN
ejpam-1783	72	13	−	−	PROPN
ejpam-1783	73	1	i	i	PRON
ejpam-1783	73	2	-set	-set	PUNCT
ejpam-1783	74	1	[	[	X
ejpam-1783	74	2	5	5	X
ejpam-1783	74	3	]	]	X
ejpam-1783	74	4	if	if	SCONJ
ejpam-1783	74	5	int(cl∗(a	int(cl∗(a	NOUN
ejpam-1783	74	6	)	)	PUNCT
ejpam-1783	74	7	)	)	PUNCT
ejpam-1783	75	1	=	=	PUNCT
ejpam-1783	75	2	int(a	int(a	PROPN
ejpam-1783	75	3	)	)	PUNCT
ejpam-1783	75	4	k	k	NOUN
ejpam-1783	75	5	)	)	PUNCT
ejpam-1783	75	6	δβ∗i	δβ∗i	VERB
ejpam-1783	75	7	-open	-open	NOUN
ejpam-1783	75	8	[	[	X
ejpam-1783	75	9	13	13	NUM
ejpam-1783	75	10	]	]	PUNCT
ejpam-1783	75	11	if	if	SCONJ
ejpam-1783	75	12	a⊂	a⊂	NOUN
ejpam-1783	75	13	cl∗(int(δcli(a	cl∗(int(δcli(a	NOUN
ejpam-1783	75	14	)	)	PUNCT
ejpam-1783	75	15	)	)	PUNCT
ejpam-1783	75	16	)	)	PUNCT
ejpam-1783	76	1	e.	e.	PROPN
ejpam-1783	76	2	hatir	hatir	PROPN
ejpam-1783	76	3	/	/	SYM
ejpam-1783	76	4	eur	eur	PROPN
ejpam-1783	76	5	.	.	PUNCT
ejpam-1783	77	1	j.	j.	PROPN
ejpam-1783	77	2	pure	pure	PROPN
ejpam-1783	77	3	appl	appl	PROPN
ejpam-1783	77	4	.	.	PROPN
ejpam-1783	77	5	math	math	PROPN
ejpam-1783	77	6	,	,	PUNCT
ejpam-1783	77	7	6	6	NUM
ejpam-1783	77	8	(	(	PUNCT
ejpam-1783	77	9	2013	2013	NUM
ejpam-1783	77	10	)	)	PUNCT
ejpam-1783	77	11	,	,	PUNCT
ejpam-1783	77	12	352	352	NUM
ejpam-1783	77	13	-	-	SYM
ejpam-1783	77	14	362	362	NUM
ejpam-1783	77	15	354	354	NUM
ejpam-1783	77	16	2	2	NUM
ejpam-1783	77	17	.	.	PUNCT
ejpam-1783	77	18	δβi	δβi	PRON
ejpam-1783	77	19	-open	-open	NOUN
ejpam-1783	77	20	sets	set	NOUN
ejpam-1783	77	21	definition	definition	NOUN
ejpam-1783	77	22	2	2	NUM
ejpam-1783	77	23	.	.	PUNCT
ejpam-1783	78	1	a	a	DET
ejpam-1783	78	2	subset	subset	NOUN
ejpam-1783	78	3	a	a	PRON
ejpam-1783	78	4	of	of	ADP
ejpam-1783	78	5	an	an	DET
ejpam-1783	78	6	ideal	ideal	NOUN
ejpam-1783	78	7	space(x	space(x	PROPN
ejpam-1783	78	8	,	,	PUNCT
ejpam-1783	78	9	τ	τ	PROPN
ejpam-1783	78	10	,	,	PUNCT
ejpam-1783	78	11	i	i	PROPN
ejpam-1783	78	12	)	)	PUNCT
ejpam-1783	78	13	is	be	AUX
ejpam-1783	78	14	said	say	VERB
ejpam-1783	78	15	to	to	PART
ejpam-1783	78	16	be	be	AUX
ejpam-1783	78	17	δβi	δβi	DET
ejpam-1783	78	18	-open	-open	ADJ
ejpam-1783	78	19	if	if	SCONJ
ejpam-1783	78	20	a⊂	a⊂	NOUN
ejpam-1783	78	21	cl(int(δcli(a	cl(int(δcli(a	NOUN
ejpam-1783	78	22	)	)	PUNCT
ejpam-1783	78	23	)	)	PUNCT
ejpam-1783	78	24	)	)	PUNCT
ejpam-1783	78	25	.	.	PUNCT
ejpam-1783	79	1	remark	remark	PROPN
ejpam-1783	79	2	1	1	NUM
ejpam-1783	79	3	.	.	PUNCT
ejpam-1783	80	1	the	the	DET
ejpam-1783	80	2	following	follow	VERB
ejpam-1783	80	3	diagram	diagram	NOUN
ejpam-1783	80	4	holds	hold	VERB
ejpam-1783	80	5	for	for	ADP
ejpam-1783	80	6	a	a	DET
ejpam-1783	80	7	subset	subset	NOUN
ejpam-1783	80	8	a	a	PRON
ejpam-1783	80	9	of	of	ADP
ejpam-1783	80	10	an	an	DET
ejpam-1783	80	11	ideal	ideal	ADJ
ejpam-1783	80	12	space	space	NOUN
ejpam-1783	80	13	(	(	PUNCT
ejpam-1783	80	14	x	x	X
ejpam-1783	80	15	,	,	PUNCT
ejpam-1783	80	16	τ	τ	PROPN
ejpam-1783	80	17	,	,	PUNCT
ejpam-1783	80	18	i	i	PROPN
ejpam-1783	80	19	)	)	PUNCT
ejpam-1783	80	20	.	.	PUNCT
ejpam-1783	81	1	open	open	ADJ
ejpam-1783	81	2	↓	↓	NOUN
ejpam-1783	82	1	α−	α−	ADP
ejpam-1783	82	2	i	i	PRON
ejpam-1783	82	3	-open	-open	VERB
ejpam-1783	82	4	→	→	PUNCT
ejpam-1783	82	5	pre−i	pre−i	X
ejpam-1783	82	6	-open	-open	NOUN
ejpam-1783	82	7	→	→	SYM
ejpam-1783	82	8	pre∗−	pre∗−	ADJ
ejpam-1783	82	9	i	i	PRON
ejpam-1783	82	10	-open	-open	VERB
ejpam-1783	82	11	→	→	PUNCT
ejpam-1783	82	12	δβ∗i	δβ∗i	NOUN
ejpam-1783	82	13	-open	-open	NOUN
ejpam-1783	82	14	→	→	SYM
ejpam-1783	82	15	δβi	δβi	PRON
ejpam-1783	82	16	-open	-open	NOUN
ejpam-1783	82	17	↓	↓	PROPN
ejpam-1783	82	18	↓	↓	PROPN
ejpam-1783	82	19	↓	↓	PROPN
ejpam-1783	82	20	↓	↓	PROPN
ejpam-1783	82	21	↓	↓	PROPN
ejpam-1783	82	22	α	α	X
ejpam-1783	82	23	-	-	ADJ
ejpam-1783	82	24	open	open	ADJ
ejpam-1783	82	25	→	→	SYM
ejpam-1783	82	26	preopen	preopen	ADJ
ejpam-1783	82	27	→	→	SYM
ejpam-1783	82	28	δ	δ	NOUN
ejpam-1783	82	29	-	-	PUNCT
ejpam-1783	82	30	preopen	preopen	ADJ
ejpam-1783	82	31	→	→	SYM
ejpam-1783	82	32	β∗i	β∗i	PUNCT
ejpam-1783	82	33	-open	-open	NOUN
ejpam-1783	82	34	→	→	SYM
ejpam-1783	82	35	δβ	δβ	NOUN
ejpam-1783	82	36	-	-	PUNCT
ejpam-1783	82	37	open	open	ADJ
ejpam-1783	82	38	figure	figure	NOUN
ejpam-1783	82	39	1	1	NUM
ejpam-1783	82	40	:	:	PUNCT
ejpam-1783	82	41	diagram	diagram	VERB
ejpam-1783	82	42	none	none	NOUN
ejpam-1783	82	43	of	of	ADP
ejpam-1783	82	44	these	these	DET
ejpam-1783	82	45	implications	implication	NOUN
ejpam-1783	82	46	is	be	AUX
ejpam-1783	82	47	reversible	reversible	ADJ
ejpam-1783	82	48	,	,	PUNCT
ejpam-1783	82	49	as	as	SCONJ
ejpam-1783	82	50	shown	show	VERB
ejpam-1783	82	51	in	in	ADP
ejpam-1783	82	52	the	the	DET
ejpam-1783	82	53	following	following	ADJ
ejpam-1783	82	54	example	example	NOUN
ejpam-1783	82	55	and	and	CCONJ
ejpam-1783	83	1	in	in	ADP
ejpam-1783	83	2	[	[	X
ejpam-1783	83	3	3	3	X
ejpam-1783	83	4	]	]	PUNCT
ejpam-1783	83	5	example	example	NOUN
ejpam-1783	83	6	1	1	X
ejpam-1783	83	7	.	.	PUNCT
ejpam-1783	84	1	let	let	VERB
ejpam-1783	84	2	x	x	PUNCT
ejpam-1783	84	3	=	=	PRON
ejpam-1783	84	4	{	{	PUNCT
ejpam-1783	84	5	a	a	PRON
ejpam-1783	84	6	,	,	PUNCT
ejpam-1783	84	7	b	b	NOUN
ejpam-1783	84	8	,	,	PUNCT
ejpam-1783	84	9	c	c	NOUN
ejpam-1783	84	10	,	,	PUNCT
ejpam-1783	84	11	d	d	NOUN
ejpam-1783	84	12	}	}	PUNCT
ejpam-1783	84	13	,	,	PUNCT
ejpam-1783	84	14	τ	τ	X
ejpam-1783	84	15	=	=	PUNCT
ejpam-1783	84	16	{	{	PUNCT
ejpam-1783	84	17	x	x	NOUN
ejpam-1783	84	18	,	,	PUNCT
ejpam-1783	84	19	∅	∅	NOUN
ejpam-1783	84	20	,	,	PUNCT
ejpam-1783	84	21	{	{	PUNCT
ejpam-1783	84	22	a	a	NOUN
ejpam-1783	84	23	}	}	PUNCT
ejpam-1783	84	24	,	,	PUNCT
ejpam-1783	84	25	{	{	PUNCT
ejpam-1783	84	26	b	b	NOUN
ejpam-1783	84	27	}	}	PUNCT
ejpam-1783	84	28	,	,	PUNCT
ejpam-1783	84	29	{	{	PUNCT
ejpam-1783	84	30	a	a	DET
ejpam-1783	84	31	,	,	PUNCT
ejpam-1783	84	32	b	b	NOUN
ejpam-1783	84	33	}	}	PUNCT
ejpam-1783	84	34	,	,	PUNCT
ejpam-1783	84	35	{	{	PUNCT
ejpam-1783	84	36	a	a	X
ejpam-1783	84	37	,	,	PUNCT
ejpam-1783	84	38	c	c	NOUN
ejpam-1783	84	39	}	}	PUNCT
ejpam-1783	84	40	,	,	PUNCT
ejpam-1783	84	41	{	{	PUNCT
ejpam-1783	84	42	a	a	PRON
ejpam-1783	84	43	,	,	PUNCT
ejpam-1783	84	44	b	b	NOUN
ejpam-1783	84	45	,	,	PUNCT
ejpam-1783	84	46	c	c	NOUN
ejpam-1783	84	47	}	}	PUNCT
ejpam-1783	84	48	}	}	PUNCT
ejpam-1783	84	49	and	and	CCONJ
ejpam-1783	84	50	i	i	PRON
ejpam-1783	84	51	=	=	SYM
ejpam-1783	84	52	p(x	p(x	PROPN
ejpam-1783	84	53	)	)	PUNCT
ejpam-1783	84	54	.	.	PUNCT
ejpam-1783	85	1	then	then	ADV
ejpam-1783	85	2	the	the	DET
ejpam-1783	85	3	set	set	NOUN
ejpam-1783	85	4	{	{	PUNCT
ejpam-1783	85	5	c	c	NOUN
ejpam-1783	85	6	,	,	PUNCT
ejpam-1783	85	7	d	d	NOUN
ejpam-1783	85	8	}	}	PUNCT
ejpam-1783	85	9	is	be	AUX
ejpam-1783	85	10	δβ−open	δβ−open	ADJ
ejpam-1783	85	11	,	,	PUNCT
ejpam-1783	85	12	but	but	CCONJ
ejpam-1783	85	13	it	it	PRON
ejpam-1783	85	14	is	be	AUX
ejpam-1783	85	15	not	not	PART
ejpam-1783	85	16	δβi	δβi	ADJ
ejpam-1783	85	17	-open	-open	NOUN
ejpam-1783	85	18	.	.	PUNCT
ejpam-1783	86	1	the	the	DET
ejpam-1783	86	2	set	set	NOUN
ejpam-1783	86	3	{	{	PUNCT
ejpam-1783	86	4	b	b	NOUN
ejpam-1783	86	5	,	,	PUNCT
ejpam-1783	86	6	d	d	NOUN
ejpam-1783	86	7	}	}	PUNCT
ejpam-1783	86	8	is	be	AUX
ejpam-1783	86	9	δβi	δβi	DET
ejpam-1783	86	10	-open	-open	NOUN
ejpam-1783	86	11	set	set	NOUN
ejpam-1783	86	12	,	,	PUNCT
ejpam-1783	86	13	but	but	CCONJ
ejpam-1783	86	14	it	it	PRON
ejpam-1783	86	15	is	be	AUX
ejpam-1783	86	16	not	not	PART
ejpam-1783	86	17	both	both	PRON
ejpam-1783	86	18	β∗i	β∗i	PUNCT
ejpam-1783	86	19	-open	-open	ADJ
ejpam-1783	86	20	and	and	CCONJ
ejpam-1783	86	21	δβ∗i	δβ∗i	NOUN
ejpam-1783	86	22	-open	-open	NOUN
ejpam-1783	86	23	.	.	PUNCT
ejpam-1783	87	1	if	if	SCONJ
ejpam-1783	87	2	we	we	PRON
ejpam-1783	87	3	take	take	VERB
ejpam-1783	87	4	i	i	PRON
ejpam-1783	87	5	=	=	PUNCT
ejpam-1783	87	6	{	{	PUNCT
ejpam-1783	87	7	∅	∅	NOUN
ejpam-1783	87	8	}	}	PUNCT
ejpam-1783	87	9	,	,	PUNCT
ejpam-1783	87	10	then	then	ADV
ejpam-1783	87	11	the	the	DET
ejpam-1783	87	12	set	set	NOUN
ejpam-1783	87	13	{	{	PUNCT
ejpam-1783	87	14	c	c	NOUN
ejpam-1783	87	15	,	,	PUNCT
ejpam-1783	87	16	d	d	NOUN
ejpam-1783	87	17	}	}	PUNCT
ejpam-1783	87	18	is	be	AUX
ejpam-1783	87	19	δβi	δβi	DET
ejpam-1783	87	20	-open	-open	NOUN
ejpam-1783	87	21	,	,	PUNCT
ejpam-1783	87	22	but	but	CCONJ
ejpam-1783	87	23	it	it	PRON
ejpam-1783	87	24	is	be	AUX
ejpam-1783	87	25	not	not	PART
ejpam-1783	87	26	pre∗	pre∗	ADJ
ejpam-1783	87	27	−	−	NOUN
ejpam-1783	88	1	i	i	PRON
ejpam-1783	88	2	-open	-open	VERB
ejpam-1783	88	3	.	.	PUNCT
ejpam-1783	89	1	the	the	DET
ejpam-1783	89	2	family	family	NOUN
ejpam-1783	89	3	of	of	ADP
ejpam-1783	89	4	all	all	DET
ejpam-1783	89	5	δβi	δβi	ADJ
ejpam-1783	89	6	-open	-open	NOUN
ejpam-1783	89	7	(	(	PUNCT
ejpam-1783	89	8	resp	resp	NOUN
ejpam-1783	89	9	.	.	PUNCT
ejpam-1783	90	1	δβi	δβi	ADJ
ejpam-1783	90	2	-closed	-close	VERB
ejpam-1783	90	3	)	)	PUNCT
ejpam-1783	90	4	sets	set	NOUN
ejpam-1783	90	5	of	of	ADP
ejpam-1783	90	6	x	x	SYM
ejpam-1783	90	7	is	be	AUX
ejpam-1783	90	8	denoted	denote	VERB
ejpam-1783	90	9	by	by	ADP
ejpam-1783	90	10	δβ	δβ	NOUN
ejpam-1783	90	11	io(x	io(x	PUNCT
ejpam-1783	90	12	)	)	PUNCT
ejpam-1783	90	13	(	(	PUNCT
ejpam-1783	90	14	resp	resp	NOUN
ejpam-1783	90	15	.	.	PUNCT
ejpam-1783	91	1	δβ	δβ	NOUN
ejpam-1783	91	2	ic(x	ic(x	NOUN
ejpam-1783	91	3	)	)	PUNCT
ejpam-1783	91	4	)	)	PUNCT
ejpam-1783	91	5	.	.	PUNCT
ejpam-1783	92	1	definition	definition	NOUN
ejpam-1783	92	2	3	3	X
ejpam-1783	92	3	.	.	PUNCT
ejpam-1783	93	1	let	let	AUX
ejpam-1783	93	2	(	(	PUNCT
ejpam-1783	93	3	x	x	X
ejpam-1783	93	4	,	,	PUNCT
ejpam-1783	93	5	τ	τ	PROPN
ejpam-1783	93	6	,	,	PUNCT
ejpam-1783	93	7	i	i	PRON
ejpam-1783	93	8	)	)	PUNCT
ejpam-1783	93	9	be	be	VERB
ejpam-1783	93	10	an	an	DET
ejpam-1783	93	11	ideal	ideal	ADJ
ejpam-1783	93	12	space	space	NOUN
ejpam-1783	93	13	.	.	PUNCT
ejpam-1783	94	1	a	a	X
ejpam-1783	94	2	)	)	PUNCT
ejpam-1783	94	3	the	the	DET
ejpam-1783	94	4	union	union	NOUN
ejpam-1783	94	5	of	of	ADP
ejpam-1783	94	6	all	all	DET
ejpam-1783	94	7	δβi	δβi	ADJ
ejpam-1783	94	8	-open	-open	NOUN
ejpam-1783	94	9	sets	set	NOUN
ejpam-1783	94	10	contained	contain	VERB
ejpam-1783	94	11	in	in	ADP
ejpam-1783	94	12	a	a	PRON
ejpam-1783	94	13	is	be	AUX
ejpam-1783	94	14	called	call	VERB
ejpam-1783	94	15	the	the	DET
ejpam-1783	94	16	δβi	δβi	ADJ
ejpam-1783	94	17	-interior	-interior	NOUN
ejpam-1783	94	18	of	of	ADP
ejpam-1783	94	19	a	a	PRON
ejpam-1783	94	20	and	and	CCONJ
ejpam-1783	94	21	is	be	AUX
ejpam-1783	94	22	denoted	denote	VERB
ejpam-1783	94	23	by	by	ADP
ejpam-1783	94	24	δβ	δβ	PROPN
ejpam-1783	94	25	int	int	PROPN
ejpam-1783	94	26	i(a	i(a	PROPN
ejpam-1783	94	27	)	)	PUNCT
ejpam-1783	94	28	b	b	NOUN
ejpam-1783	94	29	)	)	PUNCT
ejpam-1783	94	30	the	the	DET
ejpam-1783	94	31	intersection	intersection	NOUN
ejpam-1783	94	32	of	of	ADP
ejpam-1783	94	33	all	all	DET
ejpam-1783	94	34	δβi	δβi	ADJ
ejpam-1783	94	35	-closed	-close	VERB
ejpam-1783	94	36	sets	set	NOUN
ejpam-1783	94	37	containing	contain	VERB
ejpam-1783	94	38	a	a	PRON
ejpam-1783	94	39	is	be	AUX
ejpam-1783	94	40	called	call	VERB
ejpam-1783	94	41	the	the	DET
ejpam-1783	94	42	δβi	δβi	ADJ
ejpam-1783	94	43	-closure	-closure	NOUN
ejpam-1783	94	44	of	of	ADP
ejpam-1783	94	45	a	a	PRON
ejpam-1783	94	46	and	and	CCONJ
ejpam-1783	94	47	is	be	AUX
ejpam-1783	94	48	denoted	denote	VERB
ejpam-1783	94	49	by	by	ADP
ejpam-1783	94	50	δβcli(a	δβcli(a	NOUN
ejpam-1783	94	51	)	)	PUNCT
ejpam-1783	94	52	.	.	PUNCT
ejpam-1783	95	1	theorem	theorem	NOUN
ejpam-1783	95	2	1	1	NUM
ejpam-1783	95	3	.	.	PUNCT
ejpam-1783	96	1	the	the	DET
ejpam-1783	96	2	following	follow	VERB
ejpam-1783	96	3	properties	property	NOUN
ejpam-1783	96	4	hold	hold	VERB
ejpam-1783	96	5	for	for	ADP
ejpam-1783	96	6	the	the	DET
ejpam-1783	96	7	δβi	δβi	ADJ
ejpam-1783	96	8	-closure	-closure	NOUN
ejpam-1783	96	9	of	of	ADP
ejpam-1783	96	10	a	a	DET
ejpam-1783	96	11	set	set	NOUN
ejpam-1783	96	12	a	a	PRON
ejpam-1783	96	13	in	in	ADP
ejpam-1783	96	14	a	a	DET
ejpam-1783	96	15	space	space	NOUN
ejpam-1783	96	16	(	(	PUNCT
ejpam-1783	96	17	x	x	X
ejpam-1783	96	18	,	,	PUNCT
ejpam-1783	96	19	τ	τ	PROPN
ejpam-1783	96	20	,	,	PUNCT
ejpam-1783	96	21	i	i	PROPN
ejpam-1783	96	22	)	)	PUNCT
ejpam-1783	96	23	.	.	PUNCT
ejpam-1783	97	1	a	a	X
ejpam-1783	97	2	)	)	PUNCT
ejpam-1783	97	3	a	a	PRON
ejpam-1783	97	4	is	be	AUX
ejpam-1783	97	5	δβi	δβi	NOUN
ejpam-1783	97	6	-closed	-close	VERB
ejpam-1783	97	7	in	in	ADP
ejpam-1783	97	8	x	x	PUNCT
ejpam-1783	97	9	if	if	SCONJ
ejpam-1783	98	1	and	and	CCONJ
ejpam-1783	98	2	only	only	ADV
ejpam-1783	98	3	if	if	SCONJ
ejpam-1783	98	4	a=	a=	ADJ
ejpam-1783	98	5	δβcli(a	δβcli(a	NOUN
ejpam-1783	98	6	)	)	PUNCT
ejpam-1783	98	7	,	,	PUNCT
ejpam-1783	98	8	b	b	X
ejpam-1783	98	9	)	)	PUNCT
ejpam-1783	98	10	δβcli(a)⊂	δβcli(a)⊂	NOUN
ejpam-1783	98	11	δβcli(b	δβcli(b	PROPN
ejpam-1783	98	12	)	)	PUNCT
ejpam-1783	99	1	whenever	whenever	SCONJ
ejpam-1783	99	2	a⊂	a⊂	X
ejpam-1783	99	3	b	b	X
ejpam-1783	99	4	⊂	⊂	X
ejpam-1783	99	5	x	x	X
ejpam-1783	99	6	,	,	PUNCT
ejpam-1783	99	7	c	c	NOUN
ejpam-1783	99	8	)	)	PUNCT
ejpam-1783	99	9	δβcli(a	δβcli(a	NOUN
ejpam-1783	99	10	)	)	PUNCT
ejpam-1783	99	11	is	be	AUX
ejpam-1783	99	12	δβi	δβi	PRON
ejpam-1783	99	13	-closed	-close	VERB
ejpam-1783	99	14	,	,	PUNCT
ejpam-1783	99	15	d	d	NOUN
ejpam-1783	99	16	)	)	PUNCT
ejpam-1783	99	17	δβcli(δβcli(a	δβcli(δβcli(a	NOUN
ejpam-1783	99	18	)	)	PUNCT
ejpam-1783	99	19	)	)	PUNCT
ejpam-1783	100	1	=	=	SYM
ejpam-1783	100	2	δβcli(a	δβcli(a	NOUN
ejpam-1783	100	3	)	)	PUNCT
ejpam-1783	100	4	,	,	PUNCT
ejpam-1783	100	5	e	e	X
ejpam-1783	100	6	)	)	PUNCT
ejpam-1783	100	7	x	x	SYM
ejpam-1783	100	8	∈	∈	PROPN
ejpam-1783	100	9	δβcli(a	δβcli(a	NOUN
ejpam-1783	100	10	)	)	PUNCT
ejpam-1783	100	11	if	if	SCONJ
ejpam-1783	100	12	a∩	a∩	PROPN
ejpam-1783	100	13	u	u	NOUN
ejpam-1783	100	14	6=∅	6=∅	NUM
ejpam-1783	100	15	for	for	ADP
ejpam-1783	100	16	every	every	DET
ejpam-1783	100	17	δβi	δβi	ADJ
ejpam-1783	100	18	-open	-open	NOUN
ejpam-1783	100	19	set	set	NOUN
ejpam-1783	100	20	containing	contain	VERB
ejpam-1783	100	21	x.	x.	NOUN
ejpam-1783	100	22	proof	proof	NOUN
ejpam-1783	100	23	.	.	PUNCT
ejpam-1783	101	1	straightforward	straightforward	ADJ
ejpam-1783	101	2	.	.	PUNCT
ejpam-1783	102	1	we	we	PRON
ejpam-1783	102	2	give	give	VERB
ejpam-1783	102	3	the	the	DET
ejpam-1783	102	4	following	follow	VERB
ejpam-1783	102	5	lemma	lemma	PROPN
ejpam-1783	102	6	using	use	VERB
ejpam-1783	102	7	in	in	ADP
ejpam-1783	102	8	the	the	DET
ejpam-1783	102	9	sequel	sequel	NOUN
ejpam-1783	102	10	.	.	PUNCT
ejpam-1783	103	1	lemma	lemma	PROPN
ejpam-1783	103	2	2	2	X
ejpam-1783	103	3	.	.	PUNCT
ejpam-1783	103	4	let	let	VERB
ejpam-1783	103	5	a	a	DET
ejpam-1783	103	6	be	be	AUX
ejpam-1783	103	7	a	a	DET
ejpam-1783	103	8	subset	subset	NOUN
ejpam-1783	103	9	of	of	ADP
ejpam-1783	103	10	a	a	DET
ejpam-1783	103	11	space	space	NOUN
ejpam-1783	103	12	(	(	PUNCT
ejpam-1783	103	13	x	x	X
ejpam-1783	103	14	,	,	PUNCT
ejpam-1783	103	15	τ	τ	PROPN
ejpam-1783	103	16	,	,	PUNCT
ejpam-1783	103	17	i	i	PROPN
ejpam-1783	103	18	)	)	PUNCT
ejpam-1783	103	19	.	.	PUNCT
ejpam-1783	104	1	then	then	ADV
ejpam-1783	104	2	a	a	X
ejpam-1783	104	3	)	)	PUNCT
ejpam-1783	104	4	δcli(a)∩	δcli(a)∩	PROPN
ejpam-1783	104	5	u	u	NOUN
ejpam-1783	104	6	⊂	⊂	PROPN
ejpam-1783	104	7	δcli(a∩	δcli(a∩	PROPN
ejpam-1783	104	8	u	u	NOUN
ejpam-1783	104	9	)	)	PUNCT
ejpam-1783	104	10	,	,	PUNCT
ejpam-1783	104	11	for	for	ADP
ejpam-1783	104	12	any	any	DET
ejpam-1783	104	13	δi	δi	NOUN
ejpam-1783	104	14	-open	-open	NOUN
ejpam-1783	104	15	set	set	VERB
ejpam-1783	104	16	u	u	NOUN
ejpam-1783	104	17	in	in	ADP
ejpam-1783	104	18	x	x	SYM
ejpam-1783	104	19	,	,	PUNCT
ejpam-1783	104	20	e.	e.	PROPN
ejpam-1783	104	21	hatir	hatir	PROPN
ejpam-1783	104	22	/	/	SYM
ejpam-1783	104	23	eur	eur	PROPN
ejpam-1783	104	24	.	.	PUNCT
ejpam-1783	105	1	j.	j.	PROPN
ejpam-1783	105	2	pure	pure	PROPN
ejpam-1783	105	3	appl	appl	PROPN
ejpam-1783	105	4	.	.	PROPN
ejpam-1783	105	5	math	math	PROPN
ejpam-1783	105	6	,	,	PUNCT
ejpam-1783	105	7	6	6	NUM
ejpam-1783	105	8	(	(	PUNCT
ejpam-1783	105	9	2013	2013	NUM
ejpam-1783	105	10	)	)	PUNCT
ejpam-1783	105	11	,	,	PUNCT
ejpam-1783	105	12	352	352	NUM
ejpam-1783	105	13	-	-	SYM
ejpam-1783	105	14	362	362	NUM
ejpam-1783	105	15	355	355	NUM
ejpam-1783	105	16	b	b	NOUN
ejpam-1783	105	17	)	)	PUNCT
ejpam-1783	105	18	δint	δint	NOUN
ejpam-1783	105	19	i(a∪	i(a∪	NOUN
ejpam-1783	105	20	f)⊂	f)⊂	VERB
ejpam-1783	105	21	δint	δint	NOUN
ejpam-1783	105	22	i(a)∪	i(a)∪	PROPN
ejpam-1783	105	23	f	f	PROPN
ejpam-1783	105	24	,	,	PUNCT
ejpam-1783	105	25	for	for	ADP
ejpam-1783	105	26	any	any	DET
ejpam-1783	105	27	δi	δi	NOUN
ejpam-1783	105	28	-closed	-close	VERB
ejpam-1783	105	29	set	set	VERB
ejpam-1783	105	30	f	f	NOUN
ejpam-1783	105	31	in	in	ADP
ejpam-1783	105	32	x	x	PROPN
ejpam-1783	105	33	.	.	PUNCT
ejpam-1783	106	1	proposition	proposition	NOUN
ejpam-1783	106	2	1	1	NUM
ejpam-1783	106	3	.	.	PUNCT
ejpam-1783	107	1	let	let	VERB
ejpam-1783	107	2	(	(	PUNCT
ejpam-1783	107	3	x	x	X
ejpam-1783	107	4	,	,	PUNCT
ejpam-1783	107	5	τ	τ	PROPN
ejpam-1783	107	6	,	,	PUNCT
ejpam-1783	107	7	i	i	PRON
ejpam-1783	107	8	)	)	PUNCT
ejpam-1783	107	9	be	be	VERB
ejpam-1783	107	10	an	an	DET
ejpam-1783	107	11	ideal	ideal	ADJ
ejpam-1783	107	12	space	space	NOUN
ejpam-1783	107	13	.	.	PUNCT
ejpam-1783	108	1	if	if	SCONJ
ejpam-1783	108	2	a⊂	a⊂	DET
ejpam-1783	108	3	b	b	X
ejpam-1783	108	4	⊂	⊂	X
ejpam-1783	108	5	δcli(a	δcli(a	PROPN
ejpam-1783	108	6	)	)	PUNCT
ejpam-1783	108	7	and	and	CCONJ
ejpam-1783	108	8	b	b	X
ejpam-1783	108	9	be	be	AUX
ejpam-1783	108	10	a	a	DET
ejpam-1783	108	11	δβi	δβi	ADJ
ejpam-1783	108	12	-open	-open	NOUN
ejpam-1783	108	13	,	,	PUNCT
ejpam-1783	108	14	then	then	ADV
ejpam-1783	108	15	a	a	PRON
ejpam-1783	108	16	is	be	AUX
ejpam-1783	108	17	δβi	δβi	DET
ejpam-1783	108	18	-open	-open	NOUN
ejpam-1783	108	19	.	.	PUNCT
ejpam-1783	109	1	proof	proof	NOUN
ejpam-1783	109	2	.	.	PUNCT
ejpam-1783	110	1	let	let	VERB
ejpam-1783	110	2	a⊂	a⊂	NOUN
ejpam-1783	110	3	b	b	NOUN
ejpam-1783	110	4	⊂	⊂	X
ejpam-1783	110	5	δcli(a	δcli(a	PROPN
ejpam-1783	110	6	)	)	PUNCT
ejpam-1783	110	7	and	and	CCONJ
ejpam-1783	110	8	b	b	X
ejpam-1783	110	9	be	be	AUX
ejpam-1783	110	10	a	a	DET
ejpam-1783	110	11	δβi	δβi	ADJ
ejpam-1783	110	12	-open	-open	NOUN
ejpam-1783	110	13	.	.	PUNCT
ejpam-1783	111	1	then	then	ADV
ejpam-1783	111	2	we	we	PRON
ejpam-1783	111	3	have	have	VERB
ejpam-1783	111	4	δcli(a	δcli(a	ADJ
ejpam-1783	111	5	)	)	PUNCT
ejpam-1783	111	6	=	=	SYM
ejpam-1783	111	7	δcli(b	δcli(b	PROPN
ejpam-1783	111	8	)	)	PUNCT
ejpam-1783	111	9	.	.	PUNCT
ejpam-1783	112	1	thus	thus	ADV
ejpam-1783	112	2	,	,	PUNCT
ejpam-1783	112	3	a⊂	a⊂	X
ejpam-1783	112	4	b	b	X
ejpam-1783	112	5	⊂	⊂	X
ejpam-1783	112	6	cl(int(δcli(b	cl(int(δcli(b	NUM
ejpam-1783	112	7	)	)	PUNCT
ejpam-1783	112	8	)	)	PUNCT
ejpam-1783	112	9	)	)	PUNCT
ejpam-1783	113	1	=	=	PUNCT
ejpam-1783	113	2	cl(int(δcli(a	cl(int(δcli(a	PROPN
ejpam-1783	113	3	)	)	PUNCT
ejpam-1783	113	4	)	)	PUNCT
ejpam-1783	113	5	)	)	PUNCT
ejpam-1783	114	1	and	and	CCONJ
ejpam-1783	114	2	hence	hence	ADV
ejpam-1783	114	3	a	a	PRON
ejpam-1783	114	4	is	be	AUX
ejpam-1783	114	5	δβi	δβi	DET
ejpam-1783	114	6	-open	-open	ADJ
ejpam-1783	114	7	set	set	NOUN
ejpam-1783	114	8	.	.	PUNCT
ejpam-1783	115	1	proposition	proposition	NOUN
ejpam-1783	115	2	2	2	NUM
ejpam-1783	115	3	.	.	PUNCT
ejpam-1783	116	1	let	let	AUX
ejpam-1783	116	2	(	(	PUNCT
ejpam-1783	116	3	x	x	X
ejpam-1783	116	4	,	,	PUNCT
ejpam-1783	116	5	τ	τ	PROPN
ejpam-1783	116	6	,	,	PUNCT
ejpam-1783	116	7	i	i	PRON
ejpam-1783	116	8	)	)	PUNCT
ejpam-1783	116	9	be	be	VERB
ejpam-1783	116	10	an	an	DET
ejpam-1783	116	11	ideal	ideal	ADJ
ejpam-1783	116	12	space	space	NOUN
ejpam-1783	116	13	.	.	PUNCT
ejpam-1783	117	1	if	if	SCONJ
ejpam-1783	117	2	a⊂	a⊂	PRON
ejpam-1783	117	3	b	b	X
ejpam-1783	117	4	⊂	⊂	X
ejpam-1783	117	5	cl(a	cl(a	X
ejpam-1783	117	6	)	)	PUNCT
ejpam-1783	117	7	and	and	CCONJ
ejpam-1783	117	8	a	a	PRON
ejpam-1783	117	9	be	be	AUX
ejpam-1783	117	10	a	a	DET
ejpam-1783	117	11	δβi	δβi	ADJ
ejpam-1783	117	12	-open	-open	NOUN
ejpam-1783	117	13	,	,	PUNCT
ejpam-1783	117	14	then	then	ADV
ejpam-1783	117	15	b	b	PROPN
ejpam-1783	117	16	is	be	AUX
ejpam-1783	117	17	δβi	δβi	DET
ejpam-1783	117	18	-open	-open	NOUN
ejpam-1783	117	19	.	.	PUNCT
ejpam-1783	118	1	proof	proof	NOUN
ejpam-1783	118	2	.	.	PUNCT
ejpam-1783	119	1	let	let	VERB
ejpam-1783	119	2	a⊂	a⊂	NOUN
ejpam-1783	119	3	b	b	PROPN
ejpam-1783	119	4	⊂	⊂	PROPN
ejpam-1783	119	5	cl(a	cl(a	X
ejpam-1783	119	6	)	)	PUNCT
ejpam-1783	119	7	and	and	CCONJ
ejpam-1783	119	8	a	a	PRON
ejpam-1783	119	9	be	be	AUX
ejpam-1783	119	10	δβi	δβi	ADJ
ejpam-1783	119	11	-open	-open	NOUN
ejpam-1783	119	12	.	.	PUNCT
ejpam-1783	120	1	then	then	ADV
ejpam-1783	120	2	a⊂	a⊂	VERB
ejpam-1783	120	3	cl(int(δcli(a	cl(int(δcli(a	NOUN
ejpam-1783	120	4	)	)	PUNCT
ejpam-1783	120	5	)	)	PUNCT
ejpam-1783	120	6	)	)	PUNCT
ejpam-1783	120	7	.	.	PUNCT
ejpam-1783	121	1	since	since	SCONJ
ejpam-1783	121	2	b	b	PROPN
ejpam-1783	121	3	⊂	⊂	PROPN
ejpam-1783	121	4	cl(a	cl(a	X
ejpam-1783	121	5	)	)	PUNCT
ejpam-1783	121	6	,	,	PUNCT
ejpam-1783	121	7	then	then	ADV
ejpam-1783	121	8	b	b	PROPN
ejpam-1783	121	9	⊂	⊂	PROPN
ejpam-1783	121	10	cl(cl(int(δcli(a	cl(cl(int(δcli(a	PROPN
ejpam-1783	121	11	)	)	PUNCT
ejpam-1783	121	12	)	)	PUNCT
ejpam-1783	121	13	)	)	PUNCT
ejpam-1783	121	14	)	)	PUNCT
ejpam-1783	122	1	=	=	PUNCT
ejpam-1783	122	2	cl(int(δcli(a)))⊂	cl(int(δcli(a)))⊂	NOUN
ejpam-1783	122	3	cl(int(δcli(b	cl(int(δcli(b	NUM
ejpam-1783	122	4	)	)	PUNCT
ejpam-1783	122	5	)	)	PUNCT
ejpam-1783	122	6	)	)	PUNCT
ejpam-1783	122	7	.	.	PUNCT
ejpam-1783	123	1	thus	thus	ADV
ejpam-1783	123	2	b	b	X
ejpam-1783	123	3	is	be	AUX
ejpam-1783	123	4	δβi	δβi	DET
ejpam-1783	123	5	-open	-open	ADJ
ejpam-1783	123	6	set	set	NOUN
ejpam-1783	123	7	.	.	PUNCT
ejpam-1783	124	1	corollary	corollary	ADJ
ejpam-1783	124	2	1	1	NUM
ejpam-1783	124	3	.	.	PUNCT
ejpam-1783	125	1	let	let	VERB
ejpam-1783	125	2	(	(	PUNCT
ejpam-1783	125	3	x	x	X
ejpam-1783	125	4	,	,	PUNCT
ejpam-1783	125	5	τ	τ	PROPN
ejpam-1783	125	6	,	,	PUNCT
ejpam-1783	125	7	i	i	PRON
ejpam-1783	125	8	)	)	PUNCT
ejpam-1783	125	9	be	be	VERB
ejpam-1783	125	10	an	an	DET
ejpam-1783	125	11	ideal	ideal	ADJ
ejpam-1783	125	12	space	space	NOUN
ejpam-1783	125	13	.	.	PUNCT
ejpam-1783	126	1	if	if	SCONJ
ejpam-1783	126	2	a	a	PRON
ejpam-1783	126	3	is	be	AUX
ejpam-1783	126	4	δβi	δβi	DET
ejpam-1783	126	5	-open	-open	NOUN
ejpam-1783	126	6	,	,	PUNCT
ejpam-1783	126	7	then	then	ADV
ejpam-1783	126	8	cl(a	cl(a	NUM
ejpam-1783	126	9	)	)	PUNCT
ejpam-1783	126	10	is	be	AUX
ejpam-1783	126	11	δβi	δβi	DET
ejpam-1783	126	12	-open	-open	NOUN
ejpam-1783	126	13	.	.	PUNCT
ejpam-1783	127	1	proposition	proposition	NOUN
ejpam-1783	127	2	3	3	X
ejpam-1783	127	3	.	.	PUNCT
ejpam-1783	128	1	let	let	VERB
ejpam-1783	128	2	(	(	PUNCT
ejpam-1783	128	3	x	x	X
ejpam-1783	128	4	,	,	PUNCT
ejpam-1783	128	5	τ	τ	PROPN
ejpam-1783	128	6	,	,	PUNCT
ejpam-1783	128	7	i	i	PRON
ejpam-1783	128	8	)	)	PUNCT
ejpam-1783	128	9	be	be	VERB
ejpam-1783	128	10	an	an	DET
ejpam-1783	128	11	ideal	ideal	ADJ
ejpam-1783	128	12	space	space	NOUN
ejpam-1783	128	13	and	and	CCONJ
ejpam-1783	128	14	a⊂	a⊂	PRON
ejpam-1783	128	15	x	x	VERB
ejpam-1783	128	16	is	be	AUX
ejpam-1783	128	17	δβi	δβi	NOUN
ejpam-1783	128	18	-closed	-close	VERB
ejpam-1783	128	19	if	if	SCONJ
ejpam-1783	128	20	and	and	CCONJ
ejpam-1783	128	21	only	only	ADV
ejpam-1783	128	22	if	if	SCONJ
ejpam-1783	128	23	c	c	PROPN
ejpam-1783	128	24	l(int(δint	l(int(δint	VERB
ejpam-1783	128	25	i(a)))⊂	i(a)))⊂	ADJ
ejpam-1783	128	26	a.	a.	NOUN
ejpam-1783	128	27	proof	proof	NOUN
ejpam-1783	128	28	.	.	PUNCT
ejpam-1783	129	1	let	let	VERB
ejpam-1783	129	2	a∈	a∈	PROPN
ejpam-1783	129	3	δβ	δβ	VERB
ejpam-1783	129	4	ic(x	ic(x	NOUN
ejpam-1783	129	5	)	)	PUNCT
ejpam-1783	129	6	⇐	⇐	ADJ
ejpam-1783	129	7	⇒	⇒	NOUN
ejpam-1783	129	8	x	x	PUNCT
ejpam-1783	129	9	−	−	PROPN
ejpam-1783	129	10	a∈	a∈	PROPN
ejpam-1783	129	11	δβ	δβ	NOUN
ejpam-1783	129	12	io(x	io(x	PUNCT
ejpam-1783	129	13	)	)	PUNCT
ejpam-1783	129	14	.	.	PUNCT
ejpam-1783	130	1	⇐	⇐	ADJ
ejpam-1783	130	2	⇒	⇒	NOUN
ejpam-1783	130	3	x	x	X
ejpam-1783	130	4	−	−	ADP
ejpam-1783	130	5	a⊂	a⊂	PUNCT
ejpam-1783	130	6	cl(int(δcli(x	cl(int(δcli(x	NOUN
ejpam-1783	130	7	−	−	PROPN
ejpam-1783	130	8	a	a	NOUN
ejpam-1783	130	9	)	)	PUNCT
ejpam-1783	130	10	)	)	PUNCT
ejpam-1783	130	11	)	)	PUNCT
ejpam-1783	131	1	=	=	NOUN
ejpam-1783	131	2	cl(int(x	cl(int(x	NOUN
ejpam-1783	131	3	−δint	−δint	X
ejpam-1783	131	4	i(a	i(a	PROPN
ejpam-1783	131	5	)	)	PUNCT
ejpam-1783	131	6	)	)	PUNCT
ejpam-1783	131	7	)	)	PUNCT
ejpam-1783	132	1	=	=	PRON
ejpam-1783	132	2	cl(x	cl(x	NUM
ejpam-1783	132	3	−	−	PROPN
ejpam-1783	132	4	cl(δint	cl(δint	PROPN
ejpam-1783	132	5	i(a	i(a	PROPN
ejpam-1783	132	6	)	)	PUNCT
ejpam-1783	132	7	)	)	PUNCT
ejpam-1783	132	8	)	)	PUNCT
ejpam-1783	133	1	=	=	PUNCT
ejpam-1783	133	2	x	x	SYM
ejpam-1783	133	3	−	−	PROPN
ejpam-1783	133	4	int(cl(δint	int(cl(δint	NOUN
ejpam-1783	133	5	i(a	i(a	PROPN
ejpam-1783	133	6	)	)	PUNCT
ejpam-1783	133	7	)	)	PUNCT
ejpam-1783	133	8	)	)	PUNCT
ejpam-1783	134	1	⇐	⇐	ADJ
ejpam-1783	134	2	⇒	⇒	PROPN
ejpam-1783	134	3	int(cl(δint	int(cl(δint	VERB
ejpam-1783	134	4	i(a)))⊂	i(a)))⊂	X
ejpam-1783	134	5	a.	a.	NOUN
ejpam-1783	134	6	remark	remark	NOUN
ejpam-1783	134	7	2	2	NUM
ejpam-1783	134	8	.	.	PUNCT
ejpam-1783	135	1	the	the	DET
ejpam-1783	135	2	intersection	intersection	NOUN
ejpam-1783	135	3	of	of	ADP
ejpam-1783	135	4	any	any	DET
ejpam-1783	135	5	two	two	NUM
ejpam-1783	135	6	δβi	δβi	NOUN
ejpam-1783	135	7	-open	-open	NOUN
ejpam-1783	135	8	sets	set	NOUN
ejpam-1783	135	9	need	need	AUX
ejpam-1783	135	10	not	not	PART
ejpam-1783	135	11	be	be	AUX
ejpam-1783	135	12	δβi	δβi	DET
ejpam-1783	135	13	-open	-open	NOUN
ejpam-1783	135	14	set	set	VERB
ejpam-1783	135	15	as	as	SCONJ
ejpam-1783	135	16	shown	show	VERB
ejpam-1783	135	17	example	example	NOUN
ejpam-1783	135	18	below	below	ADV
ejpam-1783	135	19	.	.	PUNCT
ejpam-1783	136	1	example	example	NOUN
ejpam-1783	137	1	2	2	NUM
ejpam-1783	137	2	.	.	PUNCT
ejpam-1783	137	3	let	let	VERB
ejpam-1783	137	4	x	x	PUNCT
ejpam-1783	137	5	=	=	PRON
ejpam-1783	137	6	{	{	PUNCT
ejpam-1783	137	7	a	a	PRON
ejpam-1783	137	8	,	,	PUNCT
ejpam-1783	137	9	b	b	NOUN
ejpam-1783	137	10	,	,	PUNCT
ejpam-1783	137	11	c	c	NOUN
ejpam-1783	137	12	,	,	PUNCT
ejpam-1783	137	13	d	d	NOUN
ejpam-1783	137	14	}	}	PUNCT
ejpam-1783	137	15	,	,	PUNCT
ejpam-1783	137	16	τ	τ	X
ejpam-1783	137	17	=	=	PUNCT
ejpam-1783	137	18	{	{	PUNCT
ejpam-1783	137	19	x	x	NOUN
ejpam-1783	137	20	,	,	PUNCT
ejpam-1783	137	21	∅	∅	NOUN
ejpam-1783	137	22	,	,	PUNCT
ejpam-1783	137	23	{	{	PUNCT
ejpam-1783	137	24	a	a	NOUN
ejpam-1783	137	25	}	}	PUNCT
ejpam-1783	137	26	,	,	PUNCT
ejpam-1783	137	27	{	{	PUNCT
ejpam-1783	137	28	b	b	NOUN
ejpam-1783	137	29	}	}	PUNCT
ejpam-1783	137	30	,	,	PUNCT
ejpam-1783	137	31	{	{	PUNCT
ejpam-1783	137	32	a	a	DET
ejpam-1783	137	33	,	,	PUNCT
ejpam-1783	137	34	b	b	NOUN
ejpam-1783	137	35	}	}	PUNCT
ejpam-1783	137	36	,	,	PUNCT
ejpam-1783	137	37	{	{	PUNCT
ejpam-1783	137	38	a	a	X
ejpam-1783	137	39	,	,	PUNCT
ejpam-1783	137	40	c	c	NOUN
ejpam-1783	137	41	}	}	PUNCT
ejpam-1783	137	42	,	,	PUNCT
ejpam-1783	137	43	{	{	PUNCT
ejpam-1783	137	44	a	a	PRON
ejpam-1783	137	45	,	,	PUNCT
ejpam-1783	137	46	b	b	NOUN
ejpam-1783	137	47	,	,	PUNCT
ejpam-1783	137	48	c	c	NOUN
ejpam-1783	137	49	}	}	PUNCT
ejpam-1783	137	50	}	}	PUNCT
ejpam-1783	137	51	and	and	CCONJ
ejpam-1783	137	52	i	i	PRON
ejpam-1783	137	53	=	=	SYM
ejpam-1783	137	54	p(x	p(x	PROPN
ejpam-1783	137	55	)	)	PUNCT
ejpam-1783	137	56	.	.	PUNCT
ejpam-1783	138	1	hence	hence	ADV
ejpam-1783	138	2	{	{	PUNCT
ejpam-1783	138	3	b	b	X
ejpam-1783	138	4	,	,	PUNCT
ejpam-1783	138	5	d	d	NOUN
ejpam-1783	138	6	}	}	PUNCT
ejpam-1783	138	7	,	,	PUNCT
ejpam-1783	138	8	{	{	PUNCT
ejpam-1783	138	9	a	a	X
ejpam-1783	138	10	,	,	PUNCT
ejpam-1783	138	11	c	c	NOUN
ejpam-1783	138	12	,	,	PUNCT
ejpam-1783	138	13	d	d	NOUN
ejpam-1783	138	14	}	}	PUNCT
ejpam-1783	138	15	are	be	AUX
ejpam-1783	138	16	δβi	δβi	PRON
ejpam-1783	138	17	-open	-open	NOUN
ejpam-1783	138	18	sets	set	NOUN
ejpam-1783	138	19	,	,	PUNCT
ejpam-1783	138	20	but	but	CCONJ
ejpam-1783	138	21	the	the	DET
ejpam-1783	138	22	set	set	NOUN
ejpam-1783	138	23	{	{	PUNCT
ejpam-1783	138	24	d	d	NOUN
ejpam-1783	138	25	}	}	PUNCT
ejpam-1783	138	26	is	be	AUX
ejpam-1783	138	27	not	not	PART
ejpam-1783	138	28	δβi	δβi	ADJ
ejpam-1783	138	29	-open	-open	NOUN
ejpam-1783	138	30	.	.	PUNCT
ejpam-1783	139	1	definition	definition	NOUN
ejpam-1783	139	2	4	4	NUM
ejpam-1783	139	3	.	.	PUNCT
ejpam-1783	140	1	a	a	DET
ejpam-1783	140	2	subset	subset	NOUN
ejpam-1783	140	3	a	a	PRON
ejpam-1783	140	4	of	of	ADP
ejpam-1783	140	5	an	an	DET
ejpam-1783	140	6	ideal	ideal	ADJ
ejpam-1783	140	7	space	space	NOUN
ejpam-1783	140	8	(	(	PUNCT
ejpam-1783	140	9	x	x	X
ejpam-1783	140	10	,	,	PUNCT
ejpam-1783	140	11	τ	τ	PROPN
ejpam-1783	140	12	,	,	PUNCT
ejpam-1783	140	13	i	i	PROPN
ejpam-1783	140	14	)	)	PUNCT
ejpam-1783	140	15	is	be	AUX
ejpam-1783	140	16	said	say	VERB
ejpam-1783	140	17	to	to	PART
ejpam-1783	140	18	be	be	AUX
ejpam-1783	140	19	δα−i	δα−i	NOUN
ejpam-1783	140	20	-open	-open	NOUN
ejpam-1783	140	21	if	if	SCONJ
ejpam-1783	140	22	a⊂	a⊂	PRON
ejpam-1783	140	23	int(cl(δint	int(cl(δint	NOUN
ejpam-1783	140	24	i(a	i(a	NOUN
ejpam-1783	140	25	)	)	PUNCT
ejpam-1783	140	26	)	)	PUNCT
ejpam-1783	140	27	)	)	PUNCT
ejpam-1783	140	28	.	.	PUNCT
ejpam-1783	141	1	the	the	DET
ejpam-1783	141	2	family	family	NOUN
ejpam-1783	141	3	of	of	ADP
ejpam-1783	141	4	all	all	PRON
ejpam-1783	141	5	δα−	δα−	PROPN
ejpam-1783	141	6	i	i	PRON
ejpam-1783	141	7	-open	-open	ADJ
ejpam-1783	141	8	(	(	PUNCT
ejpam-1783	141	9	resp	resp	NOUN
ejpam-1783	141	10	.	.	PUNCT
ejpam-1783	142	1	δα−	δα−	PUNCT
ejpam-1783	142	2	i	i	PRON
ejpam-1783	142	3	-closed	-closed	ADJ
ejpam-1783	142	4	)	)	PUNCT
ejpam-1783	142	5	sets	set	NOUN
ejpam-1783	142	6	of	of	ADP
ejpam-1783	142	7	x	x	SYM
ejpam-1783	142	8	is	be	AUX
ejpam-1783	142	9	denoted	denote	VERB
ejpam-1783	142	10	by	by	ADP
ejpam-1783	142	11	δαio(x	δαio(x	PROPN
ejpam-1783	142	12	)	)	PUNCT
ejpam-1783	142	13	(	(	PUNCT
ejpam-1783	142	14	resp	resp	NOUN
ejpam-1783	142	15	.	.	PUNCT
ejpam-1783	143	1	δαic(x	δαic(x	NOUN
ejpam-1783	143	2	)	)	PUNCT
ejpam-1783	143	3	)	)	PUNCT
ejpam-1783	143	4	.	.	PUNCT
ejpam-1783	144	1	it	it	PRON
ejpam-1783	144	2	is	be	AUX
ejpam-1783	144	3	obvious	obvious	ADJ
ejpam-1783	144	4	that	that	SCONJ
ejpam-1783	144	5	every	every	DET
ejpam-1783	144	6	δi	δi	PROPN
ejpam-1783	144	7	-open	-open	NOUN
ejpam-1783	144	8	set	set	NOUN
ejpam-1783	144	9	is	be	AUX
ejpam-1783	144	10	δα−	δα−	PUNCT
ejpam-1783	144	11	i	i	PRON
ejpam-1783	144	12	-open	-open	VERB
ejpam-1783	144	13	.	.	PUNCT
ejpam-1783	145	1	proposition	proposition	NOUN
ejpam-1783	145	2	4	4	NUM
ejpam-1783	145	3	.	.	PUNCT
ejpam-1783	146	1	let	let	VERB
ejpam-1783	146	2	(	(	PUNCT
ejpam-1783	146	3	x	x	X
ejpam-1783	146	4	,	,	PUNCT
ejpam-1783	146	5	τ	τ	PROPN
ejpam-1783	146	6	,	,	PUNCT
ejpam-1783	146	7	i	i	PRON
ejpam-1783	146	8	)	)	PUNCT
ejpam-1783	146	9	be	be	VERB
ejpam-1783	146	10	an	an	DET
ejpam-1783	146	11	ideal	ideal	ADJ
ejpam-1783	146	12	topological	topological	ADJ
ejpam-1783	146	13	space	space	NOUN
ejpam-1783	146	14	.	.	PUNCT
ejpam-1783	147	1	then	then	ADV
ejpam-1783	147	2	,	,	PUNCT
ejpam-1783	147	3	the	the	DET
ejpam-1783	147	4	family	family	NOUN
ejpam-1783	147	5	of	of	ADP
ejpam-1783	147	6	δα−	δα−	PROPN
ejpam-1783	147	7	i	i	PRON
ejpam-1783	147	8	-open	-open	NOUN
ejpam-1783	147	9	sets	set	NOUN
ejpam-1783	147	10	is	be	AUX
ejpam-1783	147	11	a	a	DET
ejpam-1783	147	12	topology	topology	NOUN
ejpam-1783	147	13	for	for	ADP
ejpam-1783	147	14	x	x	X
ejpam-1783	147	15	.	.	PUNCT
ejpam-1783	148	1	proof	proof	NOUN
ejpam-1783	148	2	.	.	PUNCT
ejpam-1783	149	1	it	it	PRON
ejpam-1783	149	2	is	be	AUX
ejpam-1783	149	3	obvious	obvious	ADJ
ejpam-1783	149	4	that	that	SCONJ
ejpam-1783	149	5	∅	∅	NOUN
ejpam-1783	150	1	and	and	CCONJ
ejpam-1783	150	2	x	x	X
ejpam-1783	150	3	are	be	AUX
ejpam-1783	150	4	δα−	δα−	PUNCT
ejpam-1783	150	5	i	i	PRON
ejpam-1783	150	6	-open	-open	NOUN
ejpam-1783	150	7	sets	set	NOUN
ejpam-1783	150	8	.	.	PUNCT
ejpam-1783	151	1	let	let	VERB
ejpam-1783	151	2	a	a	DET
ejpam-1783	151	3	,	,	PUNCT
ejpam-1783	151	4	b	b	PROPN
ejpam-1783	151	5	be	be	AUX
ejpam-1783	151	6	δα−	δα−	PROPN
ejpam-1783	151	7	i	i	PRON
ejpam-1783	151	8	-open	-open	NOUN
ejpam-1783	151	9	sets	set	NOUN
ejpam-1783	151	10	.	.	PUNCT
ejpam-1783	152	1	then	then	ADV
ejpam-1783	152	2	a∩	a∩	PROPN
ejpam-1783	152	3	b	b	PROPN
ejpam-1783	152	4	⊂int(cl(δcli(a)))∩	⊂int(cl(δcli(a)))∩	NOUN
ejpam-1783	152	5	int(cl(δcli(b	int(cl(δcli(b	PROPN
ejpam-1783	152	6	)	)	PUNCT
ejpam-1783	152	7	)	)	PUNCT
ejpam-1783	152	8	)	)	PUNCT
ejpam-1783	153	1	=	=	NOUN
ejpam-1783	153	2	int(cl(δint	int(cl(δint	NOUN
ejpam-1783	153	3	i(a))∩	i(a))∩	NOUN
ejpam-1783	153	4	int(cl(δint	int(cl(δint	NOUN
ejpam-1783	153	5	i(b	i(b	NOUN
ejpam-1783	153	6	)	)	PUNCT
ejpam-1783	153	7	)	)	PUNCT
ejpam-1783	153	8	)	)	PUNCT
ejpam-1783	153	9	)	)	PUNCT
ejpam-1783	154	1	e.	e.	PROPN
ejpam-1783	154	2	hatir	hatir	PROPN
ejpam-1783	154	3	/	/	SYM
ejpam-1783	154	4	eur	eur	PROPN
ejpam-1783	154	5	.	.	PUNCT
ejpam-1783	155	1	j.	j.	PROPN
ejpam-1783	155	2	pure	pure	PROPN
ejpam-1783	155	3	appl	appl	PROPN
ejpam-1783	155	4	.	.	PROPN
ejpam-1783	155	5	math	math	PROPN
ejpam-1783	155	6	,	,	PUNCT
ejpam-1783	155	7	6	6	NUM
ejpam-1783	155	8	(	(	PUNCT
ejpam-1783	155	9	2013	2013	NUM
ejpam-1783	155	10	)	)	PUNCT
ejpam-1783	155	11	,	,	PUNCT
ejpam-1783	155	12	352	352	NUM
ejpam-1783	155	13	-	-	SYM
ejpam-1783	155	14	362	362	NUM
ejpam-1783	155	15	356	356	NUM
ejpam-1783	155	16	⊂int(cl(δint	⊂int(cl(δint	PROPN
ejpam-1783	155	17	i(a)∩	i(a)∩	NOUN
ejpam-1783	155	18	cl(δint	cl(δint	PROPN
ejpam-1783	155	19	i(b	i(b	NOUN
ejpam-1783	155	20	)	)	PUNCT
ejpam-1783	155	21	)	)	PUNCT
ejpam-1783	155	22	)	)	PUNCT
ejpam-1783	156	1	=	=	PRON
ejpam-1783	156	2	int(cl(int(δint	int(cl(int(δint	NOUN
ejpam-1783	156	3	i(a))∩	i(a))∩	NOUN
ejpam-1783	156	4	cl(δint	cl(δint	PROPN
ejpam-1783	156	5	i(b	i(b	NOUN
ejpam-1783	156	6	)	)	PUNCT
ejpam-1783	156	7	)	)	PUNCT
ejpam-1783	156	8	)	)	PUNCT
ejpam-1783	156	9	)	)	PUNCT
ejpam-1783	157	1	⊂int(cl(cl(δint	⊂int(cl(cl(δint	CCONJ
ejpam-1783	157	2	i(a)∩δint	i(a)∩δint	PROPN
ejpam-1783	157	3	i(b	i(b	PROPN
ejpam-1783	157	4	)	)	PUNCT
ejpam-1783	157	5	)	)	PUNCT
ejpam-1783	157	6	)	)	PUNCT
ejpam-1783	157	7	)	)	PUNCT
ejpam-1783	158	1	=	=	PRON
ejpam-1783	158	2	int(cl(δint	int(cl(δint	VERB
ejpam-1783	158	3	i(a∩	i(a∩	PROPN
ejpam-1783	158	4	b	b	NOUN
ejpam-1783	158	5	)	)	PUNCT
ejpam-1783	158	6	)	)	PUNCT
ejpam-1783	158	7	)	)	PUNCT
ejpam-1783	159	1	hence	hence	ADV
ejpam-1783	159	2	,	,	PUNCT
ejpam-1783	159	3	a∩	a∩	PROPN
ejpam-1783	159	4	b	b	PROPN
ejpam-1783	159	5	is	be	AUX
ejpam-1783	159	6	a	a	DET
ejpam-1783	159	7	δα−	δα−	PUNCT
ejpam-1783	159	8	i	i	PRON
ejpam-1783	159	9	-open	-open	NOUN
ejpam-1783	159	10	set	set	VERB
ejpam-1783	159	11	.	.	PUNCT
ejpam-1783	160	1	for	for	ADP
ejpam-1783	160	2	the	the	DET
ejpam-1783	160	3	last	last	ADJ
ejpam-1783	160	4	axiom	axiom	NOUN
ejpam-1783	160	5	of	of	ADP
ejpam-1783	160	6	topology	topology	NOUN
ejpam-1783	160	7	,	,	PUNCT
ejpam-1783	160	8	let	let	VERB
ejpam-1783	160	9	ai	ai	AUX
ejpam-1783	160	10	be	be	AUX
ejpam-1783	160	11	δα−	δα−	PROPN
ejpam-1783	160	12	i	i	PRON
ejpam-1783	160	13	-open	-open	NOUN
ejpam-1783	160	14	sets	set	NOUN
ejpam-1783	160	15	for	for	ADP
ejpam-1783	160	16	i	i	PRON
ejpam-1783	160	17	∈	∈	PROPN
ejpam-1783	161	1	i	i	PRON
ejpam-1783	161	2	.	.	PUNCT
ejpam-1783	162	1	then	then	ADV
ejpam-1783	162	2	ai	ai	VERB
ejpam-1783	162	3	⊂	⊂	PROPN
ejpam-1783	162	4	int(cl(δint	int(cl(δint	NOUN
ejpam-1783	162	5	i(ai)))⊂	i(ai)))⊂	NOUN
ejpam-1783	162	6	int(cl(δint	int(cl(δint	NOUN
ejpam-1783	162	7	i(∪i∈iai	i(∪i∈iai	ADJ
ejpam-1783	162	8	)	)	PUNCT
ejpam-1783	162	9	)	)	PUNCT
ejpam-1783	162	10	)	)	PUNCT
ejpam-1783	162	11	.	.	PUNCT
ejpam-1783	163	1	thus	thus	ADV
ejpam-1783	163	2	,	,	PUNCT
ejpam-1783	163	3	∪i∈iai	∪i∈iai	PROPN
ejpam-1783	163	4	⊂	⊂	PROPN
ejpam-1783	163	5	int(cl(δint	int(cl(δint	NOUN
ejpam-1783	163	6	i(∪i∈iai	i(∪i∈iai	ADJ
ejpam-1783	163	7	)	)	PUNCT
ejpam-1783	163	8	)	)	PUNCT
ejpam-1783	163	9	)	)	PUNCT
ejpam-1783	163	10	.	.	PUNCT
ejpam-1783	164	1	this	this	PRON
ejpam-1783	164	2	implies	imply	VERB
ejpam-1783	164	3	that	that	SCONJ
ejpam-1783	164	4	∪i∈iai	∪i∈iai	PROPN
ejpam-1783	164	5	is	be	AUX
ejpam-1783	164	6	a	a	DET
ejpam-1783	164	7	δα−	δα−	PUNCT
ejpam-1783	164	8	i	i	PRON
ejpam-1783	164	9	-open	-open	NOUN
ejpam-1783	164	10	set	set	NOUN
ejpam-1783	164	11	.	.	PUNCT
ejpam-1783	165	1	proposition	proposition	NOUN
ejpam-1783	165	2	5	5	NUM
ejpam-1783	165	3	.	.	PUNCT
ejpam-1783	166	1	let	let	VERB
ejpam-1783	166	2	(	(	PUNCT
ejpam-1783	166	3	x	x	X
ejpam-1783	166	4	,	,	PUNCT
ejpam-1783	166	5	τ	τ	PROPN
ejpam-1783	166	6	,	,	PUNCT
ejpam-1783	166	7	i	i	PRON
ejpam-1783	166	8	)	)	PUNCT
ejpam-1783	166	9	be	be	VERB
ejpam-1783	166	10	an	an	DET
ejpam-1783	166	11	ideal	ideal	ADJ
ejpam-1783	166	12	space	space	NOUN
ejpam-1783	166	13	.	.	PUNCT
ejpam-1783	167	1	if	if	SCONJ
ejpam-1783	167	2	a	a	PRON
ejpam-1783	167	3	is	be	AUX
ejpam-1783	167	4	δβi	δβi	DET
ejpam-1783	167	5	-open	-open	ADJ
ejpam-1783	167	6	and	and	CCONJ
ejpam-1783	167	7	b	b	NOUN
ejpam-1783	167	8	is	be	AUX
ejpam-1783	167	9	δα−	δα−	PROPN
ejpam-1783	167	10	i	i	PRON
ejpam-1783	167	11	-open	-open	VERB
ejpam-1783	167	12	,	,	PUNCT
ejpam-1783	167	13	then	then	ADV
ejpam-1783	167	14	a∩	a∩	PROPN
ejpam-1783	167	15	b	b	PROPN
ejpam-1783	167	16	is	be	AUX
ejpam-1783	167	17	δβi	δβi	DET
ejpam-1783	167	18	-open	-open	NOUN
ejpam-1783	167	19	.	.	PUNCT
ejpam-1783	168	1	proof	proof	NOUN
ejpam-1783	168	2	.	.	PUNCT
ejpam-1783	169	1	let	let	VERB
ejpam-1783	169	2	a	a	DET
ejpam-1783	169	3	∈	∈	NOUN
ejpam-1783	169	4	δβ	δβ	NOUN
ejpam-1783	169	5	io(x	io(x	PUNCT
ejpam-1783	169	6	)	)	PUNCT
ejpam-1783	169	7	and	and	CCONJ
ejpam-1783	169	8	b	b	X
ejpam-1783	169	9	∈	∈	PROPN
ejpam-1783	169	10	δαio(x	δαio(x	NOUN
ejpam-1783	169	11	)	)	PUNCT
ejpam-1783	169	12	.	.	PUNCT
ejpam-1783	170	1	then	then	ADV
ejpam-1783	170	2	,	,	PUNCT
ejpam-1783	170	3	we	we	PRON
ejpam-1783	170	4	have	have	VERB
ejpam-1783	170	5	a	a	DET
ejpam-1783	170	6	⊂	⊂	PROPN
ejpam-1783	170	7	cl(int(δcli(a	cl(int(δcli(a	PROPN
ejpam-1783	170	8	)	)	PUNCT
ejpam-1783	170	9	)	)	PUNCT
ejpam-1783	170	10	)	)	PUNCT
ejpam-1783	171	1	and	and	CCONJ
ejpam-1783	171	2	b	b	X
ejpam-1783	171	3	⊂	⊂	PROPN
ejpam-1783	171	4	int(cl(δint	int(cl(δint	PROPN
ejpam-1783	171	5	i(b	i(b	NOUN
ejpam-1783	171	6	)	)	PUNCT
ejpam-1783	171	7	)	)	PUNCT
ejpam-1783	171	8	)	)	PUNCT
ejpam-1783	171	9	,	,	PUNCT
ejpam-1783	171	10	respectively	respectively	ADV
ejpam-1783	171	11	.	.	PUNCT
ejpam-1783	172	1	this	this	PRON
ejpam-1783	172	2	implies	imply	VERB
ejpam-1783	172	3	that	that	SCONJ
ejpam-1783	172	4	a∩	a∩	PROPN
ejpam-1783	172	5	b	b	PROPN
ejpam-1783	172	6	⊂cl(int(δcli(a)))∩	⊂cl(int(δcli(a)))∩	PROPN
ejpam-1783	172	7	int(cl(δint	int(cl(δint	PROPN
ejpam-1783	172	8	i(b	i(b	NOUN
ejpam-1783	172	9	)	)	PUNCT
ejpam-1783	172	10	)	)	PUNCT
ejpam-1783	172	11	)	)	PUNCT
ejpam-1783	173	1	⊂cl(int((int(δcli(a))))∩	⊂cl(int((int(δcli(a))))∩	NOUN
ejpam-1783	173	2	(	(	PUNCT
ejpam-1783	173	3	cl(δint	cl(δint	NOUN
ejpam-1783	173	4	i(b	i(b	NOUN
ejpam-1783	173	5	)	)	PUNCT
ejpam-1783	173	6	)	)	PUNCT
ejpam-1783	173	7	)	)	PUNCT
ejpam-1783	173	8	)	)	PUNCT
ejpam-1783	173	9	)	)	PUNCT
ejpam-1783	174	1	⊂cl(int(cl(δcli(a)∩δint	⊂cl(int(cl(δcli(a)∩δint	VERB
ejpam-1783	174	2	i(b))))⊂	i(b))))⊂	PROPN
ejpam-1783	174	3	cl(int(cl(δcli(a∩	cl(int(cl(δcli(a∩	PROPN
ejpam-1783	174	4	b	b	NOUN
ejpam-1783	174	5	)	)	PUNCT
ejpam-1783	174	6	)	)	PUNCT
ejpam-1783	174	7	)	)	PUNCT
ejpam-1783	174	8	)	)	PUNCT
ejpam-1783	175	1	⊂cl(int(δcli(δcli(a∩	⊂cl(int(δcli(δcli(a∩	PROPN
ejpam-1783	175	2	b	b	NOUN
ejpam-1783	175	3	)	)	PUNCT
ejpam-1783	175	4	)	)	PUNCT
ejpam-1783	175	5	)	)	PUNCT
ejpam-1783	175	6	)	)	PUNCT
ejpam-1783	176	1	=	=	PUNCT
ejpam-1783	176	2	cl(int(δcli(a∩	cl(int(δcli(a∩	NUM
ejpam-1783	176	3	b	b	NOUN
ejpam-1783	176	4	)	)	PUNCT
ejpam-1783	176	5	)	)	PUNCT
ejpam-1783	176	6	)	)	PUNCT
ejpam-1783	176	7	.	.	PUNCT
ejpam-1783	177	1	corollary	corollary	ADJ
ejpam-1783	177	2	2	2	NUM
ejpam-1783	177	3	.	.	PUNCT
ejpam-1783	178	1	a	a	DET
ejpam-1783	178	2	set	set	NOUN
ejpam-1783	178	3	a	a	PRON
ejpam-1783	178	4	in	in	ADP
ejpam-1783	178	5	(	(	PUNCT
ejpam-1783	178	6	x	x	INTJ
ejpam-1783	178	7	,	,	PUNCT
ejpam-1783	178	8	τ	τ	PROPN
ejpam-1783	178	9	,	,	PUNCT
ejpam-1783	178	10	i	i	PROPN
ejpam-1783	178	11	)	)	PUNCT
ejpam-1783	178	12	is	be	AUX
ejpam-1783	178	13	a	a	DET
ejpam-1783	178	14	δβi	δβi	NOUN
ejpam-1783	178	15	-open	-open	NOUN
ejpam-1783	178	16	if	if	SCONJ
ejpam-1783	179	1	and	and	CCONJ
ejpam-1783	179	2	only	only	ADV
ejpam-1783	179	3	if	if	SCONJ
ejpam-1783	179	4	u	u	NOUN
ejpam-1783	179	5	∩a∈	∩a∈	VERB
ejpam-1783	179	6	δβ	δβ	NOUN
ejpam-1783	179	7	io(x	io(x	PUNCT
ejpam-1783	179	8	)	)	PUNCT
ejpam-1783	179	9	,	,	PUNCT
ejpam-1783	179	10	for	for	ADP
ejpam-1783	179	11	every	every	DET
ejpam-1783	179	12	δi	δi	PROPN
ejpam-1783	179	13	-open	-open	NOUN
ejpam-1783	179	14	set	set	NOUN
ejpam-1783	179	15	u	u	NOUN
ejpam-1783	179	16	of	of	ADP
ejpam-1783	179	17	(	(	PUNCT
ejpam-1783	179	18	x	x	PROPN
ejpam-1783	179	19	,	,	PUNCT
ejpam-1783	179	20	τ	τ	PROPN
ejpam-1783	179	21	,	,	PUNCT
ejpam-1783	179	22	i	i	PROPN
ejpam-1783	179	23	)	)	PUNCT
ejpam-1783	179	24	.	.	PUNCT
ejpam-1783	180	1	proof	proof	NOUN
ejpam-1783	180	2	.	.	PUNCT
ejpam-1783	181	1	let	let	VERB
ejpam-1783	181	2	a	a	PRON
ejpam-1783	181	3	be	be	AUX
ejpam-1783	181	4	a	a	DET
ejpam-1783	181	5	δβi	δβi	ADJ
ejpam-1783	181	6	-open	-open	NOUN
ejpam-1783	181	7	set	set	NOUN
ejpam-1783	181	8	.	.	PUNCT
ejpam-1783	182	1	then	then	ADV
ejpam-1783	182	2	we	we	PRON
ejpam-1783	182	3	have	have	VERB
ejpam-1783	182	4	u	u	NOUN
ejpam-1783	182	5	∩	∩	ADJ
ejpam-1783	182	6	a⊂u	a⊂u	ADJ
ejpam-1783	182	7	∩	∩	ADJ
ejpam-1783	182	8	cl(int(δcli(a	cl(int(δcli(a	PROPN
ejpam-1783	182	9	)	)	PUNCT
ejpam-1783	182	10	)	)	PUNCT
ejpam-1783	182	11	)	)	PUNCT
ejpam-1783	183	1	=	=	NOUN
ejpam-1783	183	2	int(u)∩	int(u)∩	X
ejpam-1783	183	3	cl(int(δcli(a)))⊂	cl(int(δcli(a)))⊂	NOUN
ejpam-1783	183	4	cl(int(u)∩	cl(int(u)∩	PROPN
ejpam-1783	183	5	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	183	6	)	)	PUNCT
ejpam-1783	183	7	)	)	PUNCT
ejpam-1783	183	8	)	)	PUNCT
ejpam-1783	184	1	=	=	NOUN
ejpam-1783	184	2	cl(int(u	cl(int(u	X
ejpam-1783	184	3	∩δcli(a)))⊂	∩δcli(a)))⊂	PUNCT
ejpam-1783	184	4	cl(int(δcli(u	cl(int(δcli(u	PROPN
ejpam-1783	184	5	∩	∩	NOUN
ejpam-1783	184	6	a	a	X
ejpam-1783	184	7	)	)	PUNCT
ejpam-1783	184	8	)	)	PUNCT
ejpam-1783	184	9	)	)	PUNCT
ejpam-1783	184	10	by	by	ADP
ejpam-1783	184	11	lemma	lemma	PROPN
ejpam-1783	184	12	2	2	NUM
ejpam-1783	184	13	.	.	PUNCT
ejpam-1783	184	14	hence	hence	ADV
ejpam-1783	184	15	u	u	PROPN
ejpam-1783	184	16	∩	∩	PROPN
ejpam-1783	184	17	a∈	a∈	PROPN
ejpam-1783	184	18	δβ	δβ	NOUN
ejpam-1783	184	19	io(x	io(x	PUNCT
ejpam-1783	184	20	)	)	PUNCT
ejpam-1783	184	21	.	.	PUNCT
ejpam-1783	185	1	definition	definition	NOUN
ejpam-1783	185	2	5	5	NUM
ejpam-1783	185	3	.	.	PUNCT
ejpam-1783	186	1	a	a	DET
ejpam-1783	186	2	subset	subset	NOUN
ejpam-1783	186	3	a	a	PRON
ejpam-1783	186	4	of	of	ADP
ejpam-1783	186	5	an	an	DET
ejpam-1783	186	6	ideal	ideal	ADJ
ejpam-1783	186	7	space	space	NOUN
ejpam-1783	186	8	(	(	PUNCT
ejpam-1783	186	9	x	x	X
ejpam-1783	186	10	,	,	PUNCT
ejpam-1783	186	11	τ	τ	PROPN
ejpam-1783	186	12	,	,	PUNCT
ejpam-1783	186	13	i	i	PROPN
ejpam-1783	186	14	)	)	PUNCT
ejpam-1783	186	15	is	be	AUX
ejpam-1783	186	16	said	say	VERB
ejpam-1783	186	17	to	to	PART
ejpam-1783	186	18	be	be	AUX
ejpam-1783	186	19	a	a	DET
ejpam-1783	186	20	)	)	PUNCT
ejpam-1783	186	21	strongly−t	strongly−t	NOUN
ejpam-1783	186	22	−	−	PROPN
ejpam-1783	187	1	i	i	PRON
ejpam-1783	187	2	-set	-set	PUNCT
ejpam-1783	188	1	[	[	X
ejpam-1783	188	2	3	3	X
ejpam-1783	188	3	]	]	PUNCT
ejpam-1783	188	4	if	if	SCONJ
ejpam-1783	188	5	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	188	6	)	)	PUNCT
ejpam-1783	188	7	)	)	PUNCT
ejpam-1783	189	1	=	=	PUNCT
ejpam-1783	189	2	int(a	int(a	PROPN
ejpam-1783	189	3	)	)	PUNCT
ejpam-1783	189	4	b	b	NOUN
ejpam-1783	189	5	)	)	PUNCT
ejpam-1783	189	6	δβ	δβ	NOUN
ejpam-1783	189	7	−	−	PROPN
ejpam-1783	189	8	t	t	NOUN
ejpam-1783	189	9	-	-	PUNCT
ejpam-1783	189	10	set	set	VERB
ejpam-1783	189	11	[	[	X
ejpam-1783	189	12	5	5	NUM
ejpam-1783	189	13	]	]	PUNCT
ejpam-1783	189	14	if	if	SCONJ
ejpam-1783	189	15	c	c	NOUN
ejpam-1783	189	16	l(int(clδ(a	l(int(clδ(a	NOUN
ejpam-1783	189	17	)	)	PUNCT
ejpam-1783	189	18	)	)	PUNCT
ejpam-1783	189	19	)	)	PUNCT
ejpam-1783	190	1	=	=	PUNCT
ejpam-1783	190	2	int(a	int(a	NOUN
ejpam-1783	190	3	)	)	PUNCT
ejpam-1783	190	4	c	c	NOUN
ejpam-1783	190	5	)	)	PUNCT
ejpam-1783	190	6	δβ	δβ	NOUN
ejpam-1783	190	7	−	−	PROPN
ejpam-1783	190	8	t	t	NOUN
ejpam-1783	191	1	−	−	PROPN
ejpam-1783	191	2	i	i	PRON
ejpam-1783	191	3	-set	-set	VERB
ejpam-1783	191	4	if	if	SCONJ
ejpam-1783	191	5	c	c	PROPN
ejpam-1783	191	6	l(int(δcli(a	l(int(δcli(a	PROPN
ejpam-1783	191	7	)	)	PUNCT
ejpam-1783	191	8	)	)	PUNCT
ejpam-1783	191	9	)	)	PUNCT
ejpam-1783	192	1	=	=	PUNCT
ejpam-1783	192	2	int(a	int(a	NOUN
ejpam-1783	192	3	)	)	PUNCT
ejpam-1783	192	4	d	d	NOUN
ejpam-1783	192	5	)	)	PUNCT
ejpam-1783	192	6	δα∗−	δα∗−	NOUN
ejpam-1783	193	1	i	i	PRON
ejpam-1783	193	2	-set	-set	VERB
ejpam-1783	193	3	if	if	SCONJ
ejpam-1783	193	4	int(cl(δint	int(cl(δint	NOUN
ejpam-1783	193	5	i(a	i(a	PROPN
ejpam-1783	193	6	)	)	PUNCT
ejpam-1783	193	7	)	)	PUNCT
ejpam-1783	193	8	)	)	PUNCT
ejpam-1783	194	1	=	=	SYM
ejpam-1783	194	2	δint	δint	NOUN
ejpam-1783	194	3	i(a	i(a	PROPN
ejpam-1783	194	4	)	)	PUNCT
ejpam-1783	194	5	e.	e.	PROPN
ejpam-1783	194	6	hatir	hatir	PROPN
ejpam-1783	194	7	/	/	SYM
ejpam-1783	194	8	eur	eur	PROPN
ejpam-1783	194	9	.	.	PUNCT
ejpam-1783	195	1	j.	j.	PROPN
ejpam-1783	195	2	pure	pure	PROPN
ejpam-1783	195	3	appl	appl	PROPN
ejpam-1783	195	4	.	.	PROPN
ejpam-1783	195	5	math	math	PROPN
ejpam-1783	195	6	,	,	PUNCT
ejpam-1783	195	7	6	6	NUM
ejpam-1783	195	8	(	(	PUNCT
ejpam-1783	195	9	2013	2013	NUM
ejpam-1783	195	10	)	)	PUNCT
ejpam-1783	195	11	,	,	PUNCT
ejpam-1783	195	12	352	352	NUM
ejpam-1783	195	13	-	-	SYM
ejpam-1783	195	14	362	362	NUM
ejpam-1783	195	15	357	357	NUM
ejpam-1783	195	16	proposition	proposition	NOUN
ejpam-1783	195	17	6	6	NUM
ejpam-1783	195	18	.	.	PUNCT
ejpam-1783	196	1	a	a	PRON
ejpam-1783	196	2	)	)	PUNCT
ejpam-1783	196	3	δβ	δβ	NOUN
ejpam-1783	196	4	−	−	PROPN
ejpam-1783	196	5	t	t	NOUN
ejpam-1783	196	6	-	-	PUNCT
ejpam-1783	196	7	set	set	NOUN
ejpam-1783	196	8	is	be	AUX
ejpam-1783	196	9	a	a	DET
ejpam-1783	196	10	δβ	δβ	NOUN
ejpam-1783	196	11	−	−	PROPN
ejpam-1783	196	12	t	t	NOUN
ejpam-1783	196	13	−	−	PROPN
ejpam-1783	197	1	i	i	PRON
ejpam-1783	197	2	-set	-set	VERB
ejpam-1783	197	3	.	.	PUNCT
ejpam-1783	198	1	b	b	X
ejpam-1783	198	2	)	)	PUNCT
ejpam-1783	198	3	a	a	DET
ejpam-1783	198	4	δβ	δβ	NOUN
ejpam-1783	198	5	−	−	PROPN
ejpam-1783	198	6	t	t	NOUN
ejpam-1783	199	1	−	−	NOUN
ejpam-1783	199	2	i	i	PRON
ejpam-1783	199	3	-set	-set	VERB
ejpam-1783	199	4	is	be	AUX
ejpam-1783	199	5	a	a	DET
ejpam-1783	199	6	strongly−t	strongly−t	NUM
ejpam-1783	199	7	−	−	PROPN
ejpam-1783	200	1	i	i	PRON
ejpam-1783	200	2	-set	-set	ADJ
ejpam-1783	200	3	.	.	PUNCT
ejpam-1783	201	1	proof	proof	NOUN
ejpam-1783	201	2	.	.	PUNCT
ejpam-1783	202	1	obvious	obvious	ADJ
ejpam-1783	202	2	.	.	PUNCT
ejpam-1783	203	1	proposition	proposition	NOUN
ejpam-1783	203	2	7	7	NUM
ejpam-1783	203	3	.	.	PUNCT
ejpam-1783	204	1	let	let	VERB
ejpam-1783	204	2	a	a	PRON
ejpam-1783	204	3	and	and	CCONJ
ejpam-1783	204	4	b	b	NOUN
ejpam-1783	204	5	be	be	AUX
ejpam-1783	204	6	subsets	subset	NOUN
ejpam-1783	204	7	of	of	ADP
ejpam-1783	204	8	an	an	DET
ejpam-1783	204	9	ideal	ideal	ADJ
ejpam-1783	204	10	space	space	NOUN
ejpam-1783	204	11	(	(	PUNCT
ejpam-1783	204	12	x	x	X
ejpam-1783	204	13	,	,	PUNCT
ejpam-1783	204	14	τ	τ	PROPN
ejpam-1783	204	15	,	,	PUNCT
ejpam-1783	204	16	i	i	PROPN
ejpam-1783	204	17	)	)	PUNCT
ejpam-1783	204	18	.	.	PUNCT
ejpam-1783	205	1	if	if	SCONJ
ejpam-1783	205	2	a	a	PRON
ejpam-1783	205	3	and	and	CCONJ
ejpam-1783	205	4	b	b	NOUN
ejpam-1783	205	5	are	be	AUX
ejpam-1783	205	6	δβ	δβ	NOUN
ejpam-1783	205	7	−	−	PROPN
ejpam-1783	205	8	t	t	NOUN
ejpam-1783	205	9	−	−	NOUN
ejpam-1783	206	1	i	i	PRON
ejpam-1783	206	2	-sets	-set	NOUN
ejpam-1783	206	3	,	,	PUNCT
ejpam-1783	206	4	then	then	ADV
ejpam-1783	206	5	a∩	a∩	PROPN
ejpam-1783	206	6	b	b	PROPN
ejpam-1783	206	7	is	be	AUX
ejpam-1783	206	8	a	a	DET
ejpam-1783	206	9	δβ	δβ	NOUN
ejpam-1783	206	10	−	−	PROPN
ejpam-1783	206	11	t	t	NOUN
ejpam-1783	206	12	−	−	PROPN
ejpam-1783	207	1	i	i	PRON
ejpam-1783	207	2	-set	-set	ADJ
ejpam-1783	207	3	.	.	PUNCT
ejpam-1783	208	1	proof	proof	NOUN
ejpam-1783	208	2	.	.	PUNCT
ejpam-1783	209	1	let	let	VERB
ejpam-1783	209	2	a	a	PRON
ejpam-1783	209	3	and	and	CCONJ
ejpam-1783	209	4	b	b	NOUN
ejpam-1783	209	5	be	be	AUX
ejpam-1783	209	6	δβ	δβ	NOUN
ejpam-1783	209	7	−	−	PROPN
ejpam-1783	209	8	t	t	NOUN
ejpam-1783	209	9	−	−	NOUN
ejpam-1783	210	1	i	i	PRON
ejpam-1783	210	2	-sets	-set	VERB
ejpam-1783	210	3	.	.	PUNCT
ejpam-1783	211	1	then	then	ADV
ejpam-1783	211	2	int(a∩	int(a∩	PROPN
ejpam-1783	211	3	b)⊂cl(int(δcli(a∩	b)⊂cl(int(δcli(a∩	PROPN
ejpam-1783	211	4	b	b	PROPN
ejpam-1783	211	5	)	)	PUNCT
ejpam-1783	211	6	)	)	PUNCT
ejpam-1783	211	7	)	)	PUNCT
ejpam-1783	212	1	⊂cl(int(δcli(a)∩δcli(b	⊂cl(int(δcli(a)∩δcli(b	PROPN
ejpam-1783	212	2	)	)	PUNCT
ejpam-1783	212	3	)	)	PUNCT
ejpam-1783	212	4	)	)	PUNCT
ejpam-1783	213	1	=	=	NOUN
ejpam-1783	213	2	cl(int(δcli(a))∩	cl(int(δcli(a))∩	NOUN
ejpam-1783	213	3	int(δcli(b	int(δcli(b	NOUN
ejpam-1783	213	4	)	)	PUNCT
ejpam-1783	213	5	)	)	PUNCT
ejpam-1783	213	6	)	)	PUNCT
ejpam-1783	214	1	⊂cl(int(δcli(a)))∩	⊂cl(int(δcli(a)))∩	NOUN
ejpam-1783	214	2	cl(int(δcli(b	cl(int(δcli(b	NUM
ejpam-1783	214	3	)	)	PUNCT
ejpam-1783	214	4	)	)	PUNCT
ejpam-1783	214	5	)	)	PUNCT
ejpam-1783	215	1	=	=	NOUN
ejpam-1783	215	2	int(a)∩	int(a)∩	X
ejpam-1783	215	3	int(b	int(b	X
ejpam-1783	215	4	)	)	PUNCT
ejpam-1783	215	5	=	=	PROPN
ejpam-1783	215	6	int(a∩	int(a∩	PROPN
ejpam-1783	215	7	b	b	PROPN
ejpam-1783	215	8	)	)	PUNCT
ejpam-1783	215	9	this	this	PRON
ejpam-1783	215	10	implies	imply	VERB
ejpam-1783	215	11	that	that	SCONJ
ejpam-1783	215	12	a∩	a∩	PROPN
ejpam-1783	215	13	b	b	PROPN
ejpam-1783	215	14	is	be	AUX
ejpam-1783	215	15	a	a	DET
ejpam-1783	215	16	δβ	δβ	NOUN
ejpam-1783	215	17	−	−	PROPN
ejpam-1783	215	18	t	t	NOUN
ejpam-1783	215	19	−	−	PROPN
ejpam-1783	215	20	i	i	PRON
ejpam-1783	215	21	-set	-set	VERB
ejpam-1783	215	22	.	.	PUNCT
ejpam-1783	216	1	definition	definition	NOUN
ejpam-1783	216	2	6	6	NUM
ejpam-1783	216	3	.	.	PUNCT
ejpam-1783	217	1	let	let	VERB
ejpam-1783	217	2	(	(	PUNCT
ejpam-1783	217	3	x	x	X
ejpam-1783	217	4	,	,	PUNCT
ejpam-1783	217	5	τ	τ	PROPN
ejpam-1783	217	6	,	,	PUNCT
ejpam-1783	217	7	i	i	PRON
ejpam-1783	217	8	)	)	PUNCT
ejpam-1783	217	9	be	be	VERB
ejpam-1783	217	10	an	an	DET
ejpam-1783	217	11	ideal	ideal	ADJ
ejpam-1783	217	12	space	space	NOUN
ejpam-1783	217	13	.	.	PUNCT
ejpam-1783	218	1	a	a	X
ejpam-1783	218	2	)	)	PUNCT
ejpam-1783	218	3	a	a	DET
ejpam-1783	218	4	subset	subset	NOUN
ejpam-1783	218	5	a	a	DET
ejpam-1783	218	6	in	in	ADP
ejpam-1783	218	7	x	x	SYM
ejpam-1783	218	8	is	be	AUX
ejpam-1783	218	9	said	say	VERB
ejpam-1783	218	10	to	to	PART
ejpam-1783	218	11	be	be	AUX
ejpam-1783	218	12	δβ	δβ	NOUN
ejpam-1783	218	13	−	−	PROPN
ejpam-1783	218	14	b	b	NOUN
ejpam-1783	219	1	−	−	PROPN
ejpam-1783	220	1	i	i	PRON
ejpam-1783	220	2	-set	-set	X
ejpam-1783	220	3	(	(	PUNCT
ejpam-1783	220	4	resp	resp	NOUN
ejpam-1783	220	5	.	.	PUNCT
ejpam-1783	221	1	stronglyb	stronglyb	NOUN
ejpam-1783	221	2	−	−	PROPN
ejpam-1783	222	1	i	i	PRON
ejpam-1783	222	2	-set	-set	PUNCT
ejpam-1783	223	1	[	[	X
ejpam-1783	223	2	3	3	NUM
ejpam-1783	223	3	]	]	PUNCT
ejpam-1783	223	4	,	,	PUNCT
ejpam-1783	223	5	δβ	δβ	VERB
ejpam-1783	223	6	−	−	PROPN
ejpam-1783	223	7	b	b	NOUN
ejpam-1783	223	8	-	-	PUNCT
ejpam-1783	223	9	set	set	VERB
ejpam-1783	223	10	[	[	X
ejpam-1783	223	11	5	5	NUM
ejpam-1783	223	12	]	]	PUNCT
ejpam-1783	223	13	)	)	PUNCT
ejpam-1783	223	14	if	if	SCONJ
ejpam-1783	223	15	there	there	PRON
ejpam-1783	223	16	is	be	VERB
ejpam-1783	223	17	a	a	DET
ejpam-1783	223	18	u	u	PROPN
ejpam-1783	223	19	∈	∈	PROPN
ejpam-1783	223	20	τ	τ	X
ejpam-1783	223	21	and	and	CCONJ
ejpam-1783	223	22	a	a	DET
ejpam-1783	223	23	δβ	δβ	NOUN
ejpam-1783	223	24	−	−	PROPN
ejpam-1783	223	25	t	t	NOUN
ejpam-1783	224	1	−	−	PROPN
ejpam-1783	225	1	i	i	PRON
ejpam-1783	225	2	-set	-set	X
ejpam-1783	225	3	(	(	PUNCT
ejpam-1783	225	4	resp	resp	NOUN
ejpam-1783	225	5	.	.	PUNCT
ejpam-1783	226	1	strongly−t	strongly−t	NOUN
ejpam-1783	226	2	−	−	PROPN
ejpam-1783	227	1	i	i	PRON
ejpam-1783	227	2	-set	-set	NUM
ejpam-1783	227	3	,	,	PUNCT
ejpam-1783	227	4	δβ	δβ	NOUN
ejpam-1783	227	5	−	−	PROPN
ejpam-1783	227	6	t	t	NOUN
ejpam-1783	227	7	-	-	PUNCT
ejpam-1783	227	8	set	set	NOUN
ejpam-1783	227	9	)	)	PUNCT
ejpam-1783	227	10	v	v	NOUN
ejpam-1783	227	11	in	in	ADP
ejpam-1783	227	12	x	x	PUNCT
ejpam-1783	227	13	such	such	ADJ
ejpam-1783	227	14	that	that	SCONJ
ejpam-1783	227	15	a=	a=	PROPN
ejpam-1783	227	16	u	u	NOUN
ejpam-1783	227	17	∩	∩	NOUN
ejpam-1783	227	18	v	v	NOUN
ejpam-1783	227	19	.	.	PUNCT
ejpam-1783	228	1	b	b	X
ejpam-1783	228	2	)	)	PUNCT
ejpam-1783	228	3	a	a	DET
ejpam-1783	228	4	subset	subset	NOUN
ejpam-1783	228	5	a	a	DET
ejpam-1783	228	6	in	in	ADP
ejpam-1783	228	7	x	x	SYM
ejpam-1783	228	8	is	be	AUX
ejpam-1783	228	9	said	say	VERB
ejpam-1783	228	10	to	to	PART
ejpam-1783	228	11	be	be	AUX
ejpam-1783	228	12	δ−	δ−	PROPN
ejpam-1783	228	13	c	c	NOUN
ejpam-1783	228	14	-	-	PUNCT
ejpam-1783	228	15	set	set	VERB
ejpam-1783	228	16	if	if	SCONJ
ejpam-1783	228	17	there	there	PRON
ejpam-1783	228	18	is	be	VERB
ejpam-1783	228	19	a	a	DET
ejpam-1783	228	20	δi	δi	NOUN
ejpam-1783	228	21	-open	-open	NOUN
ejpam-1783	228	22	set	set	VERB
ejpam-1783	228	23	u	u	NOUN
ejpam-1783	228	24	in	in	ADP
ejpam-1783	228	25	x	x	X
ejpam-1783	228	26	and	and	CCONJ
ejpam-1783	228	27	a	a	DET
ejpam-1783	228	28	δα∗	δα∗	NOUN
ejpam-1783	228	29	−	−	PROPN
ejpam-1783	229	1	i	i	PRON
ejpam-1783	229	2	-set	-set	VERB
ejpam-1783	229	3	v	v	NOUN
ejpam-1783	229	4	in	in	ADP
ejpam-1783	229	5	x	x	PUNCT
ejpam-1783	229	6	such	such	ADJ
ejpam-1783	229	7	that	that	SCONJ
ejpam-1783	229	8	a=	a=	PROPN
ejpam-1783	229	9	u	u	NOUN
ejpam-1783	229	10	∩	∩	ADJ
ejpam-1783	229	11	v	v	NOUN
ejpam-1783	229	12	.	.	PUNCT
ejpam-1783	230	1	proposition	proposition	NOUN
ejpam-1783	230	2	8	8	NUM
ejpam-1783	230	3	.	.	PUNCT
ejpam-1783	231	1	a	a	X
ejpam-1783	231	2	)	)	PUNCT
ejpam-1783	231	3	a	a	DET
ejpam-1783	231	4	δβ	δβ	NOUN
ejpam-1783	231	5	−	−	PROPN
ejpam-1783	231	6	t	t	NOUN
ejpam-1783	232	1	−	−	PROPN
ejpam-1783	232	2	i	i	PRON
ejpam-1783	232	3	-set	-set	VERB
ejpam-1783	232	4	a	a	PRON
ejpam-1783	232	5	is	be	AUX
ejpam-1783	232	6	a	a	DET
ejpam-1783	232	7	δβ	δβ	NOUN
ejpam-1783	232	8	−	−	NOUN
ejpam-1783	232	9	b−	b−	NOUN
ejpam-1783	232	10	i	i	PRON
ejpam-1783	232	11	-set	-set	VERB
ejpam-1783	232	12	.	.	PUNCT
ejpam-1783	233	1	b	b	X
ejpam-1783	233	2	)	)	PUNCT
ejpam-1783	233	3	an	an	DET
ejpam-1783	233	4	open	open	ADJ
ejpam-1783	233	5	set	set	NOUN
ejpam-1783	233	6	is	be	AUX
ejpam-1783	233	7	a	a	DET
ejpam-1783	233	8	δβ	δβ	NOUN
ejpam-1783	233	9	−	−	NOUN
ejpam-1783	233	10	b−	b−	NOUN
ejpam-1783	233	11	i	i	PRON
ejpam-1783	233	12	-set	-set	VERB
ejpam-1783	233	13	.	.	PUNCT
ejpam-1783	234	1	c	c	X
ejpam-1783	234	2	)	)	PUNCT
ejpam-1783	234	3	a	a	DET
ejpam-1783	234	4	δi	δi	NOUN
ejpam-1783	234	5	-open	-open	NOUN
ejpam-1783	234	6	set	set	NOUN
ejpam-1783	234	7	is	be	AUX
ejpam-1783	234	8	a	a	DET
ejpam-1783	234	9	δ−	δ−	PROPN
ejpam-1783	234	10	c	c	NOUN
ejpam-1783	234	11	-	-	PUNCT
ejpam-1783	234	12	set	set	VERB
ejpam-1783	234	13	.	.	PUNCT
ejpam-1783	235	1	proposition	proposition	NOUN
ejpam-1783	235	2	9	9	NUM
ejpam-1783	235	3	.	.	PUNCT
ejpam-1783	236	1	a	a	X
ejpam-1783	236	2	)	)	PUNCT
ejpam-1783	236	3	a	a	DET
ejpam-1783	236	4	δβ	δβ	NOUN
ejpam-1783	236	5	−	−	NOUN
ejpam-1783	236	6	b	b	X
ejpam-1783	236	7	-	-	PUNCT
ejpam-1783	236	8	set	set	NOUN
ejpam-1783	236	9	is	be	AUX
ejpam-1783	236	10	a	a	DET
ejpam-1783	236	11	δβ	δβ	NOUN
ejpam-1783	236	12	−	−	NOUN
ejpam-1783	236	13	b−	b−	NOUN
ejpam-1783	236	14	i	i	PRON
ejpam-1783	236	15	-set	-set	VERB
ejpam-1783	236	16	.	.	PUNCT
ejpam-1783	237	1	b	b	X
ejpam-1783	237	2	)	)	PUNCT
ejpam-1783	237	3	a	a	DET
ejpam-1783	237	4	δβ	δβ	NOUN
ejpam-1783	237	5	−	−	PROPN
ejpam-1783	237	6	b−	b−	NOUN
ejpam-1783	238	1	i	i	PRON
ejpam-1783	238	2	-set	-set	VERB
ejpam-1783	238	3	is	be	AUX
ejpam-1783	238	4	a	a	DET
ejpam-1783	238	5	stronglyb−	stronglyb−	PROPN
ejpam-1783	238	6	i	i	PRON
ejpam-1783	238	7	-set	-set	ADJ
ejpam-1783	238	8	.	.	PUNCT
ejpam-1783	239	1	remark	remark	PROPN
ejpam-1783	239	2	3	3	NUM
ejpam-1783	239	3	.	.	PUNCT
ejpam-1783	240	1	the	the	DET
ejpam-1783	240	2	converses	converse	NOUN
ejpam-1783	240	3	of	of	ADP
ejpam-1783	240	4	the	the	DET
ejpam-1783	240	5	statements	statement	NOUN
ejpam-1783	240	6	in	in	ADP
ejpam-1783	240	7	proposition	proposition	NOUN
ejpam-1783	240	8	6	6	NUM
ejpam-1783	240	9	and	and	CCONJ
ejpam-1783	240	10	proposition	proposition	NOUN
ejpam-1783	240	11	9	9	NUM
ejpam-1783	240	12	are	be	AUX
ejpam-1783	240	13	false	false	ADJ
ejpam-1783	240	14	as	as	ADP
ejpam-1783	240	15	in	in	ADP
ejpam-1783	240	16	the	the	DET
ejpam-1783	240	17	following	follow	VERB
ejpam-1783	240	18	example	example	NOUN
ejpam-1783	240	19	.	.	PUNCT
ejpam-1783	241	1	example	example	NOUN
ejpam-1783	242	1	3	3	X
ejpam-1783	242	2	.	.	PUNCT
ejpam-1783	242	3	let	let	VERB
ejpam-1783	242	4	x	x	PUNCT
ejpam-1783	242	5	=	=	PRON
ejpam-1783	242	6	{	{	PUNCT
ejpam-1783	242	7	a	a	PRON
ejpam-1783	242	8	,	,	PUNCT
ejpam-1783	242	9	b	b	NOUN
ejpam-1783	242	10	,	,	PUNCT
ejpam-1783	242	11	c	c	NOUN
ejpam-1783	242	12	,	,	PUNCT
ejpam-1783	242	13	d	d	NOUN
ejpam-1783	242	14	}	}	PUNCT
ejpam-1783	242	15	,	,	PUNCT
ejpam-1783	242	16	τ=	τ=	X
ejpam-1783	242	17	{	{	PUNCT
ejpam-1783	242	18	x	x	NOUN
ejpam-1783	242	19	,	,	PUNCT
ejpam-1783	242	20	∅	∅	NOUN
ejpam-1783	242	21	,	,	PUNCT
ejpam-1783	242	22	{	{	PUNCT
ejpam-1783	242	23	a	a	NOUN
ejpam-1783	242	24	}	}	PUNCT
ejpam-1783	242	25	,	,	PUNCT
ejpam-1783	242	26	{	{	PUNCT
ejpam-1783	242	27	a	a	X
ejpam-1783	242	28	,	,	PUNCT
ejpam-1783	242	29	c	c	NOUN
ejpam-1783	242	30	}	}	PUNCT
ejpam-1783	242	31	,	,	PUNCT
ejpam-1783	242	32	{	{	PUNCT
ejpam-1783	242	33	a	a	DET
ejpam-1783	242	34	,	,	PUNCT
ejpam-1783	242	35	b	b	NOUN
ejpam-1783	242	36	,	,	PUNCT
ejpam-1783	242	37	c	c	NOUN
ejpam-1783	242	38	}	}	PUNCT
ejpam-1783	242	39	,	,	PUNCT
ejpam-1783	242	40	{	{	PUNCT
ejpam-1783	242	41	c	c	X
ejpam-1783	242	42	,	,	PUNCT
ejpam-1783	242	43	d	d	NOUN
ejpam-1783	242	44	}	}	PUNCT
ejpam-1783	242	45	,	,	PUNCT
ejpam-1783	242	46	{	{	PUNCT
ejpam-1783	242	47	c	c	NOUN
ejpam-1783	242	48	}	}	PUNCT
ejpam-1783	242	49	,	,	PUNCT
ejpam-1783	242	50	{	{	PUNCT
ejpam-1783	242	51	a	a	X
ejpam-1783	242	52	,	,	PUNCT
ejpam-1783	242	53	c	c	NOUN
ejpam-1783	242	54	,	,	PUNCT
ejpam-1783	242	55	d	d	NOUN
ejpam-1783	242	56	}	}	PUNCT
ejpam-1783	242	57	}	}	PUNCT
ejpam-1783	242	58	and	and	CCONJ
ejpam-1783	242	59	i	i	PRON
ejpam-1783	242	60	=	=	PUNCT
ejpam-1783	242	61	{	{	PUNCT
ejpam-1783	242	62	∅	∅	NOUN
ejpam-1783	242	63	,	,	PUNCT
ejpam-1783	242	64	{	{	PUNCT
ejpam-1783	242	65	c	c	NOUN
ejpam-1783	242	66	}	}	PUNCT
ejpam-1783	242	67	}	}	PUNCT
ejpam-1783	242	68	.	.	PUNCT
ejpam-1783	243	1	hence	hence	ADV
ejpam-1783	243	2	{	{	PUNCT
ejpam-1783	243	3	c	c	X
ejpam-1783	243	4	,	,	PUNCT
ejpam-1783	243	5	d	d	NOUN
ejpam-1783	243	6	}	}	PUNCT
ejpam-1783	243	7	is	be	AUX
ejpam-1783	243	8	strongly−t−	strongly−t−	PROPN
ejpam-1783	243	9	i	i	PRON
ejpam-1783	243	10	-set	-set	X
ejpam-1783	243	11	(	(	PUNCT
ejpam-1783	243	12	resp	resp	NOUN
ejpam-1783	243	13	.	.	PUNCT
ejpam-1783	244	1	strongly	strongly	ADV
ejpam-1783	244	2	b−	b−	PROPN
ejpam-1783	244	3	i	i	PRON
ejpam-1783	244	4	-set	-set	NUM
ejpam-1783	244	5	)	)	PUNCT
ejpam-1783	244	6	,	,	PUNCT
ejpam-1783	244	7	but	but	CCONJ
ejpam-1783	244	8	it	it	PRON
ejpam-1783	244	9	is	be	AUX
ejpam-1783	244	10	not	not	PART
ejpam-1783	244	11	δβ	δβ	NOUN
ejpam-1783	244	12	−	−	PROPN
ejpam-1783	245	1	t−	t−	PROPN
ejpam-1783	245	2	i	i	PRON
ejpam-1783	245	3	set	set	VERB
ejpam-1783	245	4	(	(	PUNCT
ejpam-1783	245	5	resp	resp	NOUN
ejpam-1783	245	6	.	.	PUNCT
ejpam-1783	246	1	δβ	δβ	NOUN
ejpam-1783	246	2	-b	-b	PUNCT
ejpam-1783	246	3	-	-	PROPN
ejpam-1783	246	4	i	i	NOUN
ejpam-1783	246	5	-	-	PUNCT
ejpam-1783	246	6	set	set	NOUN
ejpam-1783	246	7	)	)	PUNCT
ejpam-1783	246	8	.	.	PUNCT
ejpam-1783	247	1	{	{	PUNCT
ejpam-1783	247	2	d	d	X
ejpam-1783	247	3	}	}	PUNCT
ejpam-1783	247	4	is	be	AUX
ejpam-1783	247	5	δβ	δβ	NOUN
ejpam-1783	248	1	−	−	PROPN
ejpam-1783	248	2	t	t	NOUN
ejpam-1783	248	3	−	−	PROPN
ejpam-1783	249	1	i	i	PRON
ejpam-1783	249	2	-set	-set	X
ejpam-1783	249	3	(	(	PUNCT
ejpam-1783	249	4	resp	resp	NOUN
ejpam-1783	249	5	.	.	PUNCT
ejpam-1783	250	1	δβ	δβ	NOUN
ejpam-1783	250	2	−	−	PROPN
ejpam-1783	250	3	b−	b−	PROPN
ejpam-1783	250	4	i	i	PRON
ejpam-1783	250	5	-set	-set	NUM
ejpam-1783	250	6	)	)	PUNCT
ejpam-1783	250	7	,	,	PUNCT
ejpam-1783	250	8	but	but	CCONJ
ejpam-1783	250	9	it	it	PRON
ejpam-1783	250	10	is	be	AUX
ejpam-1783	250	11	not	not	PART
ejpam-1783	250	12	δβ	δβ	NOUN
ejpam-1783	251	1	−	−	PROPN
ejpam-1783	251	2	t	t	NOUN
ejpam-1783	251	3	-	-	PUNCT
ejpam-1783	251	4	set	set	VERB
ejpam-1783	251	5	(	(	PUNCT
ejpam-1783	251	6	resp	resp	NOUN
ejpam-1783	251	7	.	.	PUNCT
ejpam-1783	252	1	δβ	δβ	NOUN
ejpam-1783	252	2	−	−	NOUN
ejpam-1783	252	3	b	b	NOUN
ejpam-1783	252	4	-	-	PUNCT
ejpam-1783	252	5	set	set	NOUN
ejpam-1783	252	6	)	)	PUNCT
ejpam-1783	252	7	.	.	PUNCT
ejpam-1783	253	1	lemma	lemma	PROPN
ejpam-1783	253	2	3	3	X
ejpam-1783	253	3	.	.	PUNCT
ejpam-1783	254	1	let	let	AUX
ejpam-1783	254	2	(	(	PUNCT
ejpam-1783	254	3	x	x	X
ejpam-1783	254	4	,	,	PUNCT
ejpam-1783	254	5	τ	τ	PROPN
ejpam-1783	254	6	,	,	PUNCT
ejpam-1783	254	7	i	i	PRON
ejpam-1783	254	8	)	)	PUNCT
ejpam-1783	254	9	be	be	VERB
ejpam-1783	254	10	an	an	DET
ejpam-1783	254	11	ideal	ideal	ADJ
ejpam-1783	254	12	space	space	NOUN
ejpam-1783	254	13	and	and	CCONJ
ejpam-1783	254	14	a	a	DET
ejpam-1783	254	15	be	be	AUX
ejpam-1783	254	16	a	a	DET
ejpam-1783	254	17	subset	subset	NOUN
ejpam-1783	254	18	of	of	ADP
ejpam-1783	254	19	x	x	PROPN
ejpam-1783	254	20	.	.	PUNCT
ejpam-1783	255	1	e.	e.	PROPN
ejpam-1783	255	2	hatir	hatir	PROPN
ejpam-1783	255	3	/	/	SYM
ejpam-1783	255	4	eur	eur	PROPN
ejpam-1783	255	5	.	.	PUNCT
ejpam-1783	256	1	j.	j.	PROPN
ejpam-1783	256	2	pure	pure	PROPN
ejpam-1783	256	3	appl	appl	PROPN
ejpam-1783	256	4	.	.	PROPN
ejpam-1783	256	5	math	math	PROPN
ejpam-1783	256	6	,	,	PUNCT
ejpam-1783	256	7	6	6	NUM
ejpam-1783	256	8	(	(	PUNCT
ejpam-1783	256	9	2013	2013	NUM
ejpam-1783	256	10	)	)	PUNCT
ejpam-1783	256	11	,	,	PUNCT
ejpam-1783	256	12	352	352	NUM
ejpam-1783	256	13	-	-	SYM
ejpam-1783	256	14	362	362	NUM
ejpam-1783	256	15	358	358	NUM
ejpam-1783	256	16	a	a	X
ejpam-1783	256	17	)	)	PUNCT
ejpam-1783	256	18	if	if	SCONJ
ejpam-1783	256	19	a	a	PRON
ejpam-1783	256	20	is	be	AUX
ejpam-1783	256	21	open	open	ADJ
ejpam-1783	256	22	,	,	PUNCT
ejpam-1783	256	23	then	then	ADV
ejpam-1783	256	24	δcli(a	δcli(a	ADJ
ejpam-1783	256	25	)	)	PUNCT
ejpam-1783	256	26	=	=	SYM
ejpam-1783	256	27	cl(a	cl(a	X
ejpam-1783	256	28	)	)	PUNCT
ejpam-1783	256	29	,	,	PUNCT
ejpam-1783	256	30	b	b	X
ejpam-1783	256	31	)	)	PUNCT
ejpam-1783	256	32	if	if	SCONJ
ejpam-1783	256	33	a	a	PRON
ejpam-1783	256	34	is	be	AUX
ejpam-1783	256	35	closed	closed	ADJ
ejpam-1783	256	36	,	,	PUNCT
ejpam-1783	256	37	then	then	ADV
ejpam-1783	256	38	δint	δint	NOUN
ejpam-1783	256	39	i(a	i(a	PROPN
ejpam-1783	256	40	)	)	PUNCT
ejpam-1783	256	41	=	=	PUNCT
ejpam-1783	257	1	int(a	int(a	PROPN
ejpam-1783	257	2	)	)	PUNCT
ejpam-1783	257	3	.	.	PUNCT
ejpam-1783	258	1	proof	proof	NOUN
ejpam-1783	258	2	.	.	PUNCT
ejpam-1783	259	1	a	a	PRON
ejpam-1783	259	2	)	)	PUNCT
ejpam-1783	259	3	since	since	SCONJ
ejpam-1783	259	4	every	every	DET
ejpam-1783	259	5	δi	δi	NOUN
ejpam-1783	259	6	-open	-open	NOUN
ejpam-1783	259	7	set	set	NOUN
ejpam-1783	259	8	is	be	AUX
ejpam-1783	259	9	open	open	ADJ
ejpam-1783	259	10	,	,	PUNCT
ejpam-1783	259	11	we	we	PRON
ejpam-1783	259	12	have	have	VERB
ejpam-1783	259	13	cl(a)⊂	cl(a)⊂	ADJ
ejpam-1783	259	14	δcli(a	δcli(a	ADJ
ejpam-1783	259	15	)	)	PUNCT
ejpam-1783	260	1	[	[	X
ejpam-1783	260	2	14	14	NUM
ejpam-1783	260	3	]	]	PUNCT
ejpam-1783	260	4	.	.	PUNCT
ejpam-1783	261	1	conversely	conversely	ADV
ejpam-1783	261	2	,	,	PUNCT
ejpam-1783	261	3	let	let	VERB
ejpam-1783	261	4	x	x	PRON
ejpam-1783	261	5	/∈	/∈	PUNCT
ejpam-1783	261	6	cl(a	cl(a	NUM
ejpam-1783	261	7	)	)	PUNCT
ejpam-1783	261	8	.	.	PUNCT
ejpam-1783	262	1	then	then	ADV
ejpam-1783	262	2	there	there	PRON
ejpam-1783	262	3	exists	exist	VERB
ejpam-1783	262	4	an	an	DET
ejpam-1783	262	5	open	open	ADJ
ejpam-1783	262	6	set	set	NOUN
ejpam-1783	262	7	u	u	NOUN
ejpam-1783	262	8	containing	contain	VERB
ejpam-1783	262	9	x	x	PUNCT
ejpam-1783	262	10	such	such	ADJ
ejpam-1783	262	11	that	that	SCONJ
ejpam-1783	262	12	u	u	PROPN
ejpam-1783	262	13	∩	∩	NOUN
ejpam-1783	262	14	a=∅.	a=∅.	VERB
ejpam-1783	262	15	since	since	SCONJ
ejpam-1783	262	16	a	a	PRON
ejpam-1783	262	17	is	be	AUX
ejpam-1783	262	18	an	an	DET
ejpam-1783	262	19	open	open	ADJ
ejpam-1783	262	20	set	set	NOUN
ejpam-1783	262	21	,	,	PUNCT
ejpam-1783	262	22	int(cl(u))∩	int(cl(u))∩	NOUN
ejpam-1783	262	23	a=	a=	NOUN
ejpam-1783	262	24	∅	∅	NOUN
ejpam-1783	262	25	and	and	CCONJ
ejpam-1783	262	26	we	we	PRON
ejpam-1783	262	27	know	know	VERB
ejpam-1783	262	28	that	that	SCONJ
ejpam-1783	262	29	int(cl∗(u	int(cl∗(u	PROPN
ejpam-1783	262	30	)	)	PUNCT
ejpam-1783	262	31	)	)	PUNCT
ejpam-1783	263	1	⊂	⊂	PROPN
ejpam-1783	263	2	int(cl(u	int(cl(u	PROPN
ejpam-1783	263	3	)	)	PUNCT
ejpam-1783	263	4	)	)	PUNCT
ejpam-1783	263	5	,	,	PUNCT
ejpam-1783	263	6	i.e.	i.e.	X
ejpam-1783	263	7	int(cl∗(u))∩	int(cl∗(u))∩	NOUN
ejpam-1783	263	8	a=∅.	a=∅.	PRON
ejpam-1783	263	9	this	this	PRON
ejpam-1783	263	10	means	mean	VERB
ejpam-1783	263	11	that	that	SCONJ
ejpam-1783	263	12	x	x	SYM
ejpam-1783	263	13	/∈	/∈	PUNCT
ejpam-1783	263	14	δcli(a	δcli(a	ADJ
ejpam-1783	263	15	)	)	PUNCT
ejpam-1783	263	16	.	.	PUNCT
ejpam-1783	264	1	so	so	ADV
ejpam-1783	264	2	,	,	PUNCT
ejpam-1783	264	3	we	we	PRON
ejpam-1783	264	4	get	get	VERB
ejpam-1783	264	5	the	the	DET
ejpam-1783	264	6	result	result	NOUN
ejpam-1783	264	7	.	.	PUNCT
ejpam-1783	265	1	b	b	X
ejpam-1783	265	2	)	)	PUNCT
ejpam-1783	265	3	this	this	PRON
ejpam-1783	265	4	follows	follow	VERB
ejpam-1783	265	5	from	from	ADP
ejpam-1783	265	6	(	(	PUNCT
ejpam-1783	265	7	a	a	NOUN
ejpam-1783	265	8	)	)	PUNCT
ejpam-1783	265	9	.	.	PUNCT
ejpam-1783	266	1	theorem	theorem	NOUN
ejpam-1783	266	2	2	2	NUM
ejpam-1783	266	3	.	.	X
ejpam-1783	266	4	for	for	ADP
ejpam-1783	266	5	a	a	DET
ejpam-1783	266	6	subset	subset	NOUN
ejpam-1783	266	7	a	a	PRON
ejpam-1783	266	8	of	of	ADP
ejpam-1783	266	9	an	an	DET
ejpam-1783	266	10	ideal	ideal	ADJ
ejpam-1783	266	11	space	space	NOUN
ejpam-1783	266	12	(	(	PUNCT
ejpam-1783	266	13	x	x	X
ejpam-1783	266	14	,	,	PUNCT
ejpam-1783	266	15	τ	τ	PROPN
ejpam-1783	266	16	,	,	PUNCT
ejpam-1783	266	17	i	i	PROPN
ejpam-1783	266	18	)	)	PUNCT
ejpam-1783	266	19	,	,	PUNCT
ejpam-1783	266	20	the	the	DET
ejpam-1783	266	21	following	follow	VERB
ejpam-1783	266	22	properties	property	NOUN
ejpam-1783	266	23	are	be	AUX
ejpam-1783	266	24	equivalent	equivalent	ADJ
ejpam-1783	266	25	;	;	PUNCT
ejpam-1783	266	26	a	a	X
ejpam-1783	266	27	)	)	PUNCT
ejpam-1783	266	28	a	a	PRON
ejpam-1783	266	29	is	be	AUX
ejpam-1783	266	30	regular	regular	ADJ
ejpam-1783	266	31	open	open	ADJ
ejpam-1783	266	32	,	,	PUNCT
ejpam-1783	266	33	b	b	NOUN
ejpam-1783	266	34	)	)	PUNCT
ejpam-1783	266	35	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	266	36	)	)	PUNCT
ejpam-1783	266	37	)	)	PUNCT
ejpam-1783	267	1	=	=	SYM
ejpam-1783	267	2	a	a	PRON
ejpam-1783	267	3	,	,	PUNCT
ejpam-1783	267	4	c	c	NOUN
ejpam-1783	267	5	)	)	PUNCT
ejpam-1783	267	6	a	a	PRON
ejpam-1783	267	7	is	be	AUX
ejpam-1783	267	8	pre∗−	pre∗−	ADJ
ejpam-1783	267	9	i	i	PRON
ejpam-1783	267	10	-open	-open	VERB
ejpam-1783	267	11	and	and	CCONJ
ejpam-1783	267	12	a	a	DET
ejpam-1783	267	13	strongly−t	strongly−t	NOUN
ejpam-1783	267	14	−	−	PROPN
ejpam-1783	268	1	i	i	PRON
ejpam-1783	268	2	-set	-set	ADJ
ejpam-1783	268	3	.	.	PUNCT
ejpam-1783	269	1	proof	proof	NOUN
ejpam-1783	269	2	.	.	PUNCT
ejpam-1783	270	1	a	a	PRON
ejpam-1783	270	2	)	)	PUNCT
ejpam-1783	270	3	=	=	NOUN
ejpam-1783	270	4	⇒	⇒	NOUN
ejpam-1783	270	5	b	b	NUM
ejpam-1783	270	6	)	)	PUNCT
ejpam-1783	270	7	.	.	PUNCT
ejpam-1783	271	1	let	let	VERB
ejpam-1783	271	2	a	a	PRON
ejpam-1783	271	3	be	be	AUX
ejpam-1783	271	4	regular	regular	ADJ
ejpam-1783	271	5	open	open	ADJ
ejpam-1783	271	6	.	.	PUNCT
ejpam-1783	272	1	then	then	ADV
ejpam-1783	272	2	a	a	PRON
ejpam-1783	272	3	is	be	AUX
ejpam-1783	272	4	open	open	ADJ
ejpam-1783	272	5	and	and	CCONJ
ejpam-1783	272	6	by	by	ADP
ejpam-1783	272	7	lemma	lemma	PROPN
ejpam-1783	272	8	3	3	NUM
ejpam-1783	272	9	,	,	PUNCT
ejpam-1783	272	10	δcli(a	δcli(a	ADJ
ejpam-1783	272	11	)	)	PUNCT
ejpam-1783	272	12	=	=	NOUN
ejpam-1783	272	13	cl(a	cl(a	X
ejpam-1783	272	14	)	)	PUNCT
ejpam-1783	272	15	.	.	PUNCT
ejpam-1783	273	1	therefore	therefore	ADV
ejpam-1783	273	2	,	,	PUNCT
ejpam-1783	273	3	we	we	PRON
ejpam-1783	273	4	have	have	VERB
ejpam-1783	273	5	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	273	6	)	)	PUNCT
ejpam-1783	273	7	)	)	PUNCT
ejpam-1783	274	1	=	=	SYM
ejpam-1783	274	2	int(cl(a	int(cl(a	PROPN
ejpam-1783	274	3	)	)	PUNCT
ejpam-1783	274	4	)	)	PUNCT
ejpam-1783	275	1	=	=	PUNCT
ejpam-1783	275	2	a.	a.	NOUN
ejpam-1783	275	3	b	b	X
ejpam-1783	275	4	)	)	PUNCT
ejpam-1783	275	5	=	=	NOUN
ejpam-1783	275	6	⇒	⇒	NOUN
ejpam-1783	275	7	c	c	NOUN
ejpam-1783	275	8	)	)	PUNCT
ejpam-1783	275	9	.	.	PUNCT
ejpam-1783	276	1	straightforward	straightforward	ADJ
ejpam-1783	276	2	.	.	PUNCT
ejpam-1783	277	1	c	c	X
ejpam-1783	277	2	)	)	PUNCT
ejpam-1783	277	3	=	=	VERB
ejpam-1783	277	4	⇒	⇒	NOUN
ejpam-1783	277	5	a	a	PRON
ejpam-1783	277	6	)	)	PUNCT
ejpam-1783	277	7	.	.	PUNCT
ejpam-1783	278	1	let	let	VERB
ejpam-1783	278	2	a	a	DET
ejpam-1783	278	3	be	be	AUX
ejpam-1783	278	4	pre∗−	pre∗−	ADJ
ejpam-1783	279	1	i	i	PRON
ejpam-1783	279	2	-open	-open	VERB
ejpam-1783	279	3	and	and	CCONJ
ejpam-1783	279	4	strongly−t	strongly−t	NOUN
ejpam-1783	279	5	−	−	PROPN
ejpam-1783	280	1	i	i	PRON
ejpam-1783	280	2	-set	-set	VERB
ejpam-1783	280	3	.	.	PUNCT
ejpam-1783	281	1	then	then	ADV
ejpam-1783	281	2	a⊂	a⊂	PUNCT
ejpam-1783	281	3	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	281	4	)	)	PUNCT
ejpam-1783	281	5	)	)	PUNCT
ejpam-1783	282	1	=	=	PUNCT
ejpam-1783	282	2	int(a)⊂	int(a)⊂	PROPN
ejpam-1783	282	3	a	a	PRON
ejpam-1783	282	4	and	and	CCONJ
ejpam-1783	282	5	a	a	PRON
ejpam-1783	282	6	is	be	AUX
ejpam-1783	282	7	open	open	ADJ
ejpam-1783	282	8	,	,	PUNCT
ejpam-1783	282	9	a=	a=	NOUN
ejpam-1783	282	10	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	282	11	)	)	PUNCT
ejpam-1783	282	12	)	)	PUNCT
ejpam-1783	283	1	=	=	SYM
ejpam-1783	283	2	int(cl(a	int(cl(a	PROPN
ejpam-1783	283	3	)	)	PUNCT
ejpam-1783	283	4	)	)	PUNCT
ejpam-1783	283	5	.	.	PUNCT
ejpam-1783	284	1	theorem	theorem	NOUN
ejpam-1783	284	2	3	3	X
ejpam-1783	284	3	.	.	PUNCT
ejpam-1783	285	1	let	let	VERB
ejpam-1783	285	2	a	a	DET
ejpam-1783	285	3	be	be	AUX
ejpam-1783	285	4	a	a	DET
ejpam-1783	285	5	subset	subset	NOUN
ejpam-1783	285	6	of	of	ADP
ejpam-1783	285	7	an	an	DET
ejpam-1783	285	8	ideal	ideal	ADJ
ejpam-1783	285	9	space	space	NOUN
ejpam-1783	285	10	(	(	PUNCT
ejpam-1783	285	11	x	x	X
ejpam-1783	285	12	,	,	PUNCT
ejpam-1783	285	13	τ	τ	PROPN
ejpam-1783	285	14	,	,	PUNCT
ejpam-1783	285	15	i	i	PROPN
ejpam-1783	285	16	)	)	PUNCT
ejpam-1783	285	17	.	.	PUNCT
ejpam-1783	286	1	then	then	ADV
ejpam-1783	286	2	the	the	DET
ejpam-1783	286	3	following	follow	VERB
ejpam-1783	286	4	properties	property	NOUN
ejpam-1783	286	5	are	be	AUX
ejpam-1783	286	6	equivalent	equivalent	ADJ
ejpam-1783	286	7	;	;	PUNCT
ejpam-1783	286	8	a	a	X
ejpam-1783	286	9	)	)	PUNCT
ejpam-1783	286	10	a	a	PRON
ejpam-1783	286	11	is	be	AUX
ejpam-1783	286	12	open	open	ADJ
ejpam-1783	286	13	,	,	PUNCT
ejpam-1783	286	14	b	b	X
ejpam-1783	286	15	)	)	PUNCT
ejpam-1783	286	16	a	a	PRON
ejpam-1783	286	17	is	be	AUX
ejpam-1783	286	18	pre∗−	pre∗−	ADJ
ejpam-1783	286	19	i	i	PRON
ejpam-1783	286	20	-open	-open	VERB
ejpam-1783	286	21	and	and	CCONJ
ejpam-1783	286	22	a	a	DET
ejpam-1783	286	23	strongly	strongly	ADV
ejpam-1783	286	24	b−	b−	NOUN
ejpam-1783	286	25	i	i	PRON
ejpam-1783	286	26	-set	-set	X
ejpam-1783	286	27	,	,	PUNCT
ejpam-1783	286	28	c	c	X
ejpam-1783	286	29	)	)	PUNCT
ejpam-1783	286	30	a	a	PRON
ejpam-1783	286	31	is	be	AUX
ejpam-1783	286	32	δβi	δβi	DET
ejpam-1783	286	33	-open	-open	ADJ
ejpam-1783	286	34	and	and	CCONJ
ejpam-1783	286	35	a	a	DET
ejpam-1783	286	36	δβ	δβ	NOUN
ejpam-1783	286	37	−	−	PROPN
ejpam-1783	286	38	b−	b−	NOUN
ejpam-1783	286	39	i	i	PRON
ejpam-1783	286	40	-set	-set	VERB
ejpam-1783	286	41	.	.	PUNCT
ejpam-1783	287	1	proof	proof	NOUN
ejpam-1783	287	2	.	.	PUNCT
ejpam-1783	288	1	a)	a)	PUNCT
ejpam-1783	288	2	⇐	⇐	ADJ
ejpam-1783	288	3	⇒	⇒	PROPN
ejpam-1783	288	4	b	b	X
ejpam-1783	288	5	)	)	PUNCT
ejpam-1783	288	6	it	it	PRON
ejpam-1783	288	7	follows	follow	VERB
ejpam-1783	288	8	from	from	ADP
ejpam-1783	288	9	[	[	X
ejpam-1783	288	10	3	3	NUM
ejpam-1783	288	11	,	,	PUNCT
ejpam-1783	288	12	theorem	theorem	VERB
ejpam-1783	288	13	33	33	NUM
ejpam-1783	288	14	]	]	SYM
ejpam-1783	288	15	a	a	X
ejpam-1783	288	16	)	)	PUNCT
ejpam-1783	288	17	=	=	NOUN
ejpam-1783	288	18	⇒	⇒	NOUN
ejpam-1783	288	19	c	c	NOUN
ejpam-1783	288	20	)	)	PUNCT
ejpam-1783	288	21	diagram	diagram	NOUN
ejpam-1783	288	22	1	1	NUM
ejpam-1783	288	23	and	and	CCONJ
ejpam-1783	288	24	proposition	proposition	NOUN
ejpam-1783	288	25	8	8	NUM
ejpam-1783	288	26	c	c	NOUN
ejpam-1783	288	27	)	)	PUNCT
ejpam-1783	289	1	=	=	VERB
ejpam-1783	289	2	⇒	⇒	NOUN
ejpam-1783	289	3	a	a	PRON
ejpam-1783	289	4	)	)	PUNCT
ejpam-1783	289	5	let	let	VERB
ejpam-1783	289	6	a	a	PRON
ejpam-1783	289	7	be	be	AUX
ejpam-1783	289	8	a	a	DET
ejpam-1783	289	9	δβi	δβi	NOUN
ejpam-1783	289	10	-open	-open	NOUN
ejpam-1783	289	11	and	and	CCONJ
ejpam-1783	289	12	a	a	DET
ejpam-1783	289	13	δβ	δβ	NOUN
ejpam-1783	289	14	−	−	PROPN
ejpam-1783	289	15	b−	b−	NOUN
ejpam-1783	289	16	i	i	PRON
ejpam-1783	289	17	-set	-set	VERB
ejpam-1783	289	18	.	.	PUNCT
ejpam-1783	290	1	then	then	ADV
ejpam-1783	290	2	there	there	PRON
ejpam-1783	290	3	exist	exist	VERB
ejpam-1783	290	4	an	an	DET
ejpam-1783	290	5	open	open	ADJ
ejpam-1783	290	6	set	set	NOUN
ejpam-1783	290	7	u	u	NOUN
ejpam-1783	290	8	and	and	CCONJ
ejpam-1783	290	9	a	a	DET
ejpam-1783	290	10	δβ	δβ	NOUN
ejpam-1783	290	11	−	−	PROPN
ejpam-1783	290	12	t	t	NOUN
ejpam-1783	290	13	−	−	PROPN
ejpam-1783	291	1	i	i	PRON
ejpam-1783	291	2	-set	-set	VERB
ejpam-1783	291	3	v	v	NOUN
ejpam-1783	291	4	in	in	ADP
ejpam-1783	291	5	x	x	PUNCT
ejpam-1783	291	6	such	such	ADJ
ejpam-1783	291	7	that	that	SCONJ
ejpam-1783	291	8	a=	a=	PROPN
ejpam-1783	291	9	u	u	NOUN
ejpam-1783	291	10	∩	∩	NOUN
ejpam-1783	291	11	v	v	NOUN
ejpam-1783	291	12	.	.	PUNCT
ejpam-1783	292	1	since	since	SCONJ
ejpam-1783	292	2	v	v	NOUN
ejpam-1783	292	3	is	be	AUX
ejpam-1783	292	4	δβ	δβ	NOUN
ejpam-1783	292	5	−	−	PROPN
ejpam-1783	292	6	t	t	NOUN
ejpam-1783	292	7	−	−	PROPN
ejpam-1783	293	1	i	i	PRON
ejpam-1783	293	2	-set	-set	VERB
ejpam-1783	293	3	and	and	CCONJ
ejpam-1783	293	4	a	a	PRON
ejpam-1783	293	5	is	be	AUX
ejpam-1783	293	6	δβi	δβi	DET
ejpam-1783	293	7	-open	-open	NOUN
ejpam-1783	293	8	,	,	PUNCT
ejpam-1783	293	9	then	then	ADV
ejpam-1783	293	10	a⊂cl(int(δcli(a	a⊂cl(int(δcli(a	PROPN
ejpam-1783	293	11	)	)	PUNCT
ejpam-1783	293	12	)	)	PUNCT
ejpam-1783	293	13	)	)	PUNCT
ejpam-1783	294	1	=	=	PRON
ejpam-1783	294	2	cl(int(δcli(u	cl(int(δcli(u	PROPN
ejpam-1783	294	3	∩	∩	NOUN
ejpam-1783	294	4	v	v	NOUN
ejpam-1783	294	5	)	)	PUNCT
ejpam-1783	294	6	)	)	PUNCT
ejpam-1783	294	7	)	)	PUNCT
ejpam-1783	295	1	⊂cl(int(δcli(u)∩δcli(v	⊂cl(int(δcli(u)∩δcli(v	PROPN
ejpam-1783	295	2	)	)	PUNCT
ejpam-1783	295	3	)	)	PUNCT
ejpam-1783	295	4	)	)	PUNCT
ejpam-1783	296	1	=	=	NOUN
ejpam-1783	296	2	cl(int(δcli(u))∩	cl(int(δcli(u))∩	NOUN
ejpam-1783	296	3	int(δcli(v	int(δcli(v	NOUN
ejpam-1783	296	4	)	)	PUNCT
ejpam-1783	296	5	)	)	PUNCT
ejpam-1783	296	6	)	)	PUNCT
ejpam-1783	297	1	⊂cl(int(δcli(u)))∩	⊂cl(int(δcli(u)))∩	PROPN
ejpam-1783	297	2	cl(int(δcli(v	cl(int(δcli(v	PROPN
ejpam-1783	297	3	)	)	PUNCT
ejpam-1783	297	4	)	)	PUNCT
ejpam-1783	297	5	)	)	PUNCT
ejpam-1783	298	1	=	=	PRON
ejpam-1783	298	2	cl(int(δcli(u)))∩	cl(int(δcli(u)))∩	VERB
ejpam-1783	298	3	int(v	int(v	NOUN
ejpam-1783	298	4	)	)	PUNCT
ejpam-1783	298	5	.	.	PUNCT
ejpam-1783	299	1	thus	thus	ADV
ejpam-1783	299	2	,	,	PUNCT
ejpam-1783	299	3	a	a	DET
ejpam-1783	299	4	=	=	NOUN
ejpam-1783	299	5	u	u	NOUN
ejpam-1783	299	6	∩	∩	NOUN
ejpam-1783	299	7	v	v	NOUN
ejpam-1783	299	8	=	=	SYM
ejpam-1783	299	9	(	(	PUNCT
ejpam-1783	299	10	u	u	NOUN
ejpam-1783	299	11	∩	∩	ADJ
ejpam-1783	299	12	v	v	NOUN
ejpam-1783	299	13	)	)	PUNCT
ejpam-1783	299	14	∩	∩	NOUN
ejpam-1783	299	15	u	u	PROPN
ejpam-1783	299	16	⊂	⊂	PROPN
ejpam-1783	299	17	cl(int(δcli(u)))∩	cl(int(δcli(u)))∩	VERB
ejpam-1783	299	18	int(v	int(v	NOUN
ejpam-1783	299	19	)	)	PUNCT
ejpam-1783	299	20	∩	∩	PROPN
ejpam-1783	299	21	u	u	PROPN
ejpam-1783	299	22	e.	e.	PROPN
ejpam-1783	299	23	hatir	hatir	PROPN
ejpam-1783	299	24	/	/	SYM
ejpam-1783	299	25	eur	eur	PROPN
ejpam-1783	299	26	.	.	PUNCT
ejpam-1783	300	1	j.	j.	PROPN
ejpam-1783	300	2	pure	pure	PROPN
ejpam-1783	300	3	appl	appl	PROPN
ejpam-1783	300	4	.	.	PROPN
ejpam-1783	300	5	math	math	PROPN
ejpam-1783	300	6	,	,	PUNCT
ejpam-1783	300	7	6	6	NUM
ejpam-1783	300	8	(	(	PUNCT
ejpam-1783	300	9	2013	2013	NUM
ejpam-1783	300	10	)	)	PUNCT
ejpam-1783	300	11	,	,	PUNCT
ejpam-1783	300	12	352	352	NUM
ejpam-1783	300	13	-	-	SYM
ejpam-1783	300	14	362	362	NUM
ejpam-1783	300	15	359	359	NUM
ejpam-1783	300	16	=	=	NOUN
ejpam-1783	300	17	u	u	NOUN
ejpam-1783	300	18	∩	∩	X
ejpam-1783	300	19	int(v	int(v	NOUN
ejpam-1783	300	20	)	)	PUNCT
ejpam-1783	300	21	and	and	CCONJ
ejpam-1783	300	22	u	u	PROPN
ejpam-1783	300	23	∩	∩	X
ejpam-1783	300	24	int(v	int(v	PROPN
ejpam-1783	300	25	)	)	PUNCT
ejpam-1783	300	26	⊂	⊂	PROPN
ejpam-1783	300	27	u	u	PROPN
ejpam-1783	300	28	∩	∩	NOUN
ejpam-1783	300	29	v	v	NOUN
ejpam-1783	300	30	=	=	NOUN
ejpam-1783	300	31	a.	a.	NOUN
ejpam-1783	300	32	hence	hence	ADV
ejpam-1783	300	33	a=	a=	VERB
ejpam-1783	300	34	u	u	NOUN
ejpam-1783	300	35	∩	∩	X
ejpam-1783	300	36	int(v	int(v	NOUN
ejpam-1783	300	37	)	)	PUNCT
ejpam-1783	300	38	and	and	CCONJ
ejpam-1783	300	39	a	a	PRON
ejpam-1783	300	40	is	be	AUX
ejpam-1783	300	41	an	an	DET
ejpam-1783	300	42	open	open	ADJ
ejpam-1783	300	43	set	set	NOUN
ejpam-1783	300	44	.	.	PUNCT
ejpam-1783	301	1	theorem	theorem	ADJ
ejpam-1783	301	2	4	4	NUM
ejpam-1783	301	3	.	.	PUNCT
ejpam-1783	302	1	let	let	VERB
ejpam-1783	302	2	a	a	DET
ejpam-1783	302	3	be	be	AUX
ejpam-1783	302	4	a	a	DET
ejpam-1783	302	5	subset	subset	NOUN
ejpam-1783	302	6	of	of	ADP
ejpam-1783	302	7	an	an	DET
ejpam-1783	302	8	ideal	ideal	ADJ
ejpam-1783	302	9	space	space	NOUN
ejpam-1783	302	10	(	(	PUNCT
ejpam-1783	302	11	x	x	X
ejpam-1783	302	12	,	,	PUNCT
ejpam-1783	302	13	τ	τ	PROPN
ejpam-1783	302	14	,	,	PUNCT
ejpam-1783	302	15	i	i	PROPN
ejpam-1783	302	16	)	)	PUNCT
ejpam-1783	302	17	.	.	PUNCT
ejpam-1783	303	1	then	then	ADV
ejpam-1783	303	2	the	the	DET
ejpam-1783	303	3	following	follow	VERB
ejpam-1783	303	4	properties	property	NOUN
ejpam-1783	303	5	are	be	AUX
ejpam-1783	303	6	equivalent	equivalent	ADJ
ejpam-1783	303	7	;	;	PUNCT
ejpam-1783	303	8	a	a	X
ejpam-1783	303	9	)	)	PUNCT
ejpam-1783	303	10	a	a	PRON
ejpam-1783	303	11	is	be	AUX
ejpam-1783	303	12	δi	δi	ADP
ejpam-1783	303	13	-open	-open	NOUN
ejpam-1783	303	14	,	,	PUNCT
ejpam-1783	303	15	b	b	NOUN
ejpam-1783	303	16	)	)	PUNCT
ejpam-1783	303	17	a	a	PRON
ejpam-1783	303	18	is	be	AUX
ejpam-1783	303	19	δα−	δα−	PROPN
ejpam-1783	303	20	i	i	PRON
ejpam-1783	303	21	-open	-open	ADJ
ejpam-1783	303	22	and	and	CCONJ
ejpam-1783	303	23	a	a	DET
ejpam-1783	303	24	δ−	δ−	ADJ
ejpam-1783	303	25	c	c	NOUN
ejpam-1783	303	26	-	-	PUNCT
ejpam-1783	303	27	set	set	VERB
ejpam-1783	303	28	.	.	PUNCT
ejpam-1783	304	1	proof	proof	NOUN
ejpam-1783	304	2	.	.	PUNCT
ejpam-1783	305	1	the	the	DET
ejpam-1783	305	2	proof	proof	NOUN
ejpam-1783	305	3	is	be	AUX
ejpam-1783	305	4	similar	similar	ADJ
ejpam-1783	305	5	with	with	ADP
ejpam-1783	305	6	theorem	theorem	ADJ
ejpam-1783	305	7	3	3	NUM
ejpam-1783	305	8	3	3	NUM
ejpam-1783	305	9	.	.	PUNCT
ejpam-1783	306	1	decompositions	decomposition	NOUN
ejpam-1783	306	2	of	of	ADP
ejpam-1783	306	3	continuity	continuity	NOUN
ejpam-1783	306	4	and	and	CCONJ
ejpam-1783	306	5	δi	δi	VERB
ejpam-1783	306	6	-continuity	-continuity	ADJ
ejpam-1783	306	7	definition	definition	NOUN
ejpam-1783	306	8	7	7	NUM
ejpam-1783	306	9	.	.	PUNCT
ejpam-1783	307	1	a	a	X
ejpam-1783	307	2	)	)	PUNCT
ejpam-1783	307	3	let	let	VERB
ejpam-1783	307	4	f	f	X
ejpam-1783	307	5	:	:	PUNCT
ejpam-1783	307	6	(	(	PUNCT
ejpam-1783	307	7	x	x	X
ejpam-1783	307	8	,	,	PUNCT
ejpam-1783	307	9	τ	τ	PROPN
ejpam-1783	307	10	,	,	PUNCT
ejpam-1783	307	11	i	i	NOUN
ejpam-1783	307	12	)	)	PUNCT
ejpam-1783	307	13	→	→	SYM
ejpam-1783	307	14	(	(	PUNCT
ejpam-1783	307	15	y	y	PROPN
ejpam-1783	307	16	,	,	PUNCT
ejpam-1783	307	17	σ	σ	PROPN
ejpam-1783	307	18	)	)	PUNCT
ejpam-1783	307	19	be	be	AUX
ejpam-1783	307	20	a	a	DET
ejpam-1783	307	21	function	function	NOUN
ejpam-1783	307	22	.	.	PUNCT
ejpam-1783	308	1	if	if	SCONJ
ejpam-1783	308	2	for	for	ADP
ejpam-1783	308	3	each	each	DET
ejpam-1783	308	4	v	v	NUM
ejpam-1783	308	5	∈	∈	PROPN
ejpam-1783	308	6	σ	σ	PROPN
ejpam-1783	308	7	,	,	PUNCT
ejpam-1783	308	8	f	f	PROPN
ejpam-1783	308	9	−1(v	−1(v	PROPN
ejpam-1783	308	10	)	)	PUNCT
ejpam-1783	308	11	is	be	AUX
ejpam-1783	308	12	a	a	DET
ejpam-1783	308	13	δβi	δβi	ADJ
ejpam-1783	308	14	-open	-open	NOUN
ejpam-1783	308	15	(	(	PUNCT
ejpam-1783	308	16	resp	resp	NOUN
ejpam-1783	308	17	.	.	PUNCT
ejpam-1783	309	1	δβ	δβ	NOUN
ejpam-1783	309	2	−	−	PROPN
ejpam-1783	309	3	b−	b−	PROPN
ejpam-1783	309	4	i	i	PRON
ejpam-1783	309	5	-set	-set	NUM
ejpam-1783	309	6	)	)	PUNCT
ejpam-1783	309	7	,	,	PUNCT
ejpam-1783	309	8	then	then	ADV
ejpam-1783	309	9	f	f	PROPN
ejpam-1783	309	10	is	be	AUX
ejpam-1783	309	11	said	say	VERB
ejpam-1783	309	12	to	to	PART
ejpam-1783	309	13	be	be	AUX
ejpam-1783	309	14	δ−β	δ−β	ADJ
ejpam-1783	309	15	−	−	PROPN
ejpam-1783	310	1	i	i	PRON
ejpam-1783	310	2	-continuous	-continuous	ADJ
ejpam-1783	310	3	(	(	PUNCT
ejpam-1783	310	4	resp	resp	NOUN
ejpam-1783	310	5	.	.	PUNCT
ejpam-1783	311	1	δβ	δβ	NOUN
ejpam-1783	311	2	−	−	PROPN
ejpam-1783	311	3	b−	b−	NOUN
ejpam-1783	311	4	i	i	PRON
ejpam-1783	311	5	continuous	continuous	ADJ
ejpam-1783	311	6	)	)	PUNCT
ejpam-1783	311	7	.	.	PUNCT
ejpam-1783	312	1	b	b	X
ejpam-1783	312	2	)	)	PUNCT
ejpam-1783	312	3	let	let	VERB
ejpam-1783	312	4	f	f	X
ejpam-1783	312	5	:	:	PUNCT
ejpam-1783	312	6	(	(	PUNCT
ejpam-1783	312	7	x	x	X
ejpam-1783	312	8	,	,	PUNCT
ejpam-1783	312	9	τ	τ	PROPN
ejpam-1783	312	10	,	,	PUNCT
ejpam-1783	312	11	i)→	i)→	ADJ
ejpam-1783	312	12	(	(	PUNCT
ejpam-1783	312	13	y	y	PROPN
ejpam-1783	312	14	,	,	PUNCT
ejpam-1783	312	15	σ	σ	PROPN
ejpam-1783	312	16	,	,	PUNCT
ejpam-1783	312	17	j	j	PROPN
ejpam-1783	312	18	)	)	PUNCT
ejpam-1783	312	19	be	be	AUX
ejpam-1783	312	20	a	a	DET
ejpam-1783	312	21	function	function	NOUN
ejpam-1783	312	22	.	.	PUNCT
ejpam-1783	313	1	if	if	SCONJ
ejpam-1783	313	2	for	for	SCONJ
ejpam-1783	313	3	each	each	DET
ejpam-1783	313	4	δi	δi	NOUN
ejpam-1783	313	5	-open	-open	NOUN
ejpam-1783	313	6	set	set	VERB
ejpam-1783	313	7	v	v	NOUN
ejpam-1783	313	8	in	in	ADP
ejpam-1783	313	9	y	y	PROPN
ejpam-1783	313	10	,	,	PUNCT
ejpam-1783	313	11	f	f	PROPN
ejpam-1783	313	12	−1(v	−1(v	PROPN
ejpam-1783	313	13	)	)	PUNCT
ejpam-1783	313	14	is	be	AUX
ejpam-1783	313	15	a	a	DET
ejpam-1783	313	16	δi	δi	NOUN
ejpam-1783	313	17	-open	-open	NOUN
ejpam-1783	313	18	,	,	PUNCT
ejpam-1783	313	19	then	then	ADV
ejpam-1783	313	20	f	f	PROPN
ejpam-1783	313	21	is	be	AUX
ejpam-1783	313	22	said	say	VERB
ejpam-1783	313	23	to	to	PART
ejpam-1783	313	24	be	be	AUX
ejpam-1783	313	25	δ−	δ−	PROPN
ejpam-1783	313	26	i	i	PRON
ejpam-1783	313	27	-continuous	-continuous	ADJ
ejpam-1783	313	28	[	[	X
ejpam-1783	313	29	10	10	NUM
ejpam-1783	313	30	]	]	PUNCT
ejpam-1783	313	31	.	.	PUNCT
ejpam-1783	314	1	c	c	X
ejpam-1783	314	2	)	)	PUNCT
ejpam-1783	314	3	let	let	VERB
ejpam-1783	314	4	f	f	NOUN
ejpam-1783	314	5	:	:	PUNCT
ejpam-1783	314	6	(	(	PUNCT
ejpam-1783	314	7	x	x	X
ejpam-1783	314	8	,	,	PUNCT
ejpam-1783	314	9	τ	τ	PROPN
ejpam-1783	314	10	,	,	PUNCT
ejpam-1783	314	11	i)→	i)→	ADJ
ejpam-1783	314	12	(	(	PUNCT
ejpam-1783	314	13	y	y	PROPN
ejpam-1783	314	14	,	,	PUNCT
ejpam-1783	314	15	σ	σ	PROPN
ejpam-1783	314	16	,	,	PUNCT
ejpam-1783	314	17	j	j	PROPN
ejpam-1783	314	18	)	)	PUNCT
ejpam-1783	314	19	be	be	AUX
ejpam-1783	314	20	a	a	DET
ejpam-1783	314	21	function	function	NOUN
ejpam-1783	314	22	.	.	PUNCT
ejpam-1783	315	1	if	if	SCONJ
ejpam-1783	315	2	for	for	SCONJ
ejpam-1783	315	3	each	each	DET
ejpam-1783	315	4	δi	δi	NOUN
ejpam-1783	315	5	-open	-open	NOUN
ejpam-1783	315	6	set	set	VERB
ejpam-1783	315	7	v	v	NOUN
ejpam-1783	315	8	in	in	ADP
ejpam-1783	315	9	y	y	PROPN
ejpam-1783	315	10	,	,	PUNCT
ejpam-1783	315	11	f	f	PROPN
ejpam-1783	315	12	−1(v	−1(v	PROPN
ejpam-1783	315	13	)	)	PUNCT
ejpam-1783	315	14	is	be	AUX
ejpam-1783	315	15	a	a	DET
ejpam-1783	315	16	δα−	δα−	PROPN
ejpam-1783	315	17	i	i	PRON
ejpam-1783	315	18	open	open	VERB
ejpam-1783	315	19	(	(	PUNCT
ejpam-1783	315	20	resp	resp	NOUN
ejpam-1783	315	21	.	.	PUNCT
ejpam-1783	316	1	δ−	δ−	PROPN
ejpam-1783	316	2	c	c	NOUN
ejpam-1783	316	3	-	-	PUNCT
ejpam-1783	316	4	set	set	NOUN
ejpam-1783	316	5	)	)	PUNCT
ejpam-1783	316	6	,	,	PUNCT
ejpam-1783	316	7	then	then	ADV
ejpam-1783	316	8	f	f	PROPN
ejpam-1783	316	9	is	be	AUX
ejpam-1783	316	10	said	say	VERB
ejpam-1783	316	11	to	to	PART
ejpam-1783	316	12	be	be	AUX
ejpam-1783	316	13	δα−	δα−	PROPN
ejpam-1783	317	1	i	i	PRON
ejpam-1783	317	2	-continuous	-continuous	ADJ
ejpam-1783	317	3	(	(	PUNCT
ejpam-1783	317	4	resp	resp	NOUN
ejpam-1783	317	5	.	.	PUNCT
ejpam-1783	318	1	δ−	δ−	ADJ
ejpam-1783	318	2	c	c	NOUN
ejpam-1783	318	3	-	-	ADJ
ejpam-1783	318	4	continuous	continuous	ADJ
ejpam-1783	318	5	)	)	PUNCT
ejpam-1783	318	6	.	.	PUNCT
ejpam-1783	319	1	by	by	ADP
ejpam-1783	319	2	theorem	theorem	NOUN
ejpam-1783	319	3	3	3	NUM
ejpam-1783	319	4	,	,	PUNCT
ejpam-1783	319	5	we	we	PRON
ejpam-1783	319	6	obtain	obtain	VERB
ejpam-1783	319	7	the	the	DET
ejpam-1783	319	8	following	follow	VERB
ejpam-1783	319	9	theorem	theorem	VERB
ejpam-1783	319	10	.	.	PUNCT
ejpam-1783	319	11	theorem	theorem	NOUN
ejpam-1783	319	12	5	5	NUM
ejpam-1783	319	13	.	.	X
ejpam-1783	319	14	for	for	ADP
ejpam-1783	319	15	a	a	DET
ejpam-1783	319	16	function	function	NOUN
ejpam-1783	319	17	f	f	NOUN
ejpam-1783	319	18	:	:	PUNCT
ejpam-1783	319	19	(	(	PUNCT
ejpam-1783	319	20	x	x	X
ejpam-1783	319	21	,	,	PUNCT
ejpam-1783	319	22	τ	τ	PROPN
ejpam-1783	319	23	,	,	PUNCT
ejpam-1783	319	24	i)→	i)→	ADJ
ejpam-1783	319	25	(	(	PUNCT
ejpam-1783	319	26	y	y	PROPN
ejpam-1783	319	27	,	,	PUNCT
ejpam-1783	319	28	σ	σ	PROPN
ejpam-1783	319	29	)	)	PUNCT
ejpam-1783	319	30	,	,	PUNCT
ejpam-1783	319	31	the	the	DET
ejpam-1783	319	32	following	follow	VERB
ejpam-1783	319	33	properties	property	NOUN
ejpam-1783	319	34	are	be	AUX
ejpam-1783	319	35	equivalent	equivalent	ADJ
ejpam-1783	319	36	;	;	PUNCT
ejpam-1783	319	37	a	a	X
ejpam-1783	319	38	)	)	PUNCT
ejpam-1783	319	39	f	f	PROPN
ejpam-1783	319	40	is	be	AUX
ejpam-1783	319	41	continuous	continuous	ADJ
ejpam-1783	319	42	,	,	PUNCT
ejpam-1783	319	43	b	b	X
ejpam-1783	319	44	)	)	PUNCT
ejpam-1783	319	45	f	f	PROPN
ejpam-1783	319	46	is	be	AUX
ejpam-1783	319	47	δ−	δ−	PROPN
ejpam-1783	319	48	β	β	NOUN
ejpam-1783	319	49	−	−	PROPN
ejpam-1783	320	1	i	i	PRON
ejpam-1783	320	2	-continuous	-continuous	ADJ
ejpam-1783	320	3	and	and	CCONJ
ejpam-1783	320	4	δβ	δβ	NOUN
ejpam-1783	320	5	−	−	PROPN
ejpam-1783	320	6	b−	b−	NOUN
ejpam-1783	320	7	i	i	PRON
ejpam-1783	320	8	-continuous	-continuous	PROPN
ejpam-1783	320	9	.	.	PUNCT
ejpam-1783	321	1	remark	remark	NOUN
ejpam-1783	321	2	4	4	NUM
ejpam-1783	321	3	.	.	PUNCT
ejpam-1783	322	1	δ−β−	δ−β−	PRON
ejpam-1783	323	1	i	i	PRON
ejpam-1783	323	2	-continuity	-continuity	PROPN
ejpam-1783	323	3	and	and	CCONJ
ejpam-1783	323	4	δβ−b−	δβ−b−	PROPN
ejpam-1783	323	5	i	i	PRON
ejpam-1783	323	6	-continuity	-continuity	PROPN
ejpam-1783	323	7	are	be	AUX
ejpam-1783	323	8	independent	independent	ADJ
ejpam-1783	323	9	notions	notion	NOUN
ejpam-1783	323	10	of	of	ADP
ejpam-1783	323	11	each	each	DET
ejpam-1783	323	12	other	other	ADJ
ejpam-1783	323	13	.	.	PUNCT
ejpam-1783	323	14	example	example	NOUN
ejpam-1783	324	1	4	4	X
ejpam-1783	324	2	.	.	PUNCT
ejpam-1783	324	3	let	let	VERB
ejpam-1783	324	4	x	x	SYM
ejpam-1783	324	5	=	=	PUNCT
ejpam-1783	324	6	y	y	PROPN
ejpam-1783	324	7	=	=	PUNCT
ejpam-1783	324	8	{	{	PUNCT
ejpam-1783	324	9	a	a	PRON
ejpam-1783	324	10	,	,	PUNCT
ejpam-1783	324	11	b	b	NOUN
ejpam-1783	324	12	,	,	PUNCT
ejpam-1783	324	13	c	c	NOUN
ejpam-1783	324	14	,	,	PUNCT
ejpam-1783	324	15	d	d	NOUN
ejpam-1783	324	16	}	}	PUNCT
ejpam-1783	324	17	,	,	PUNCT
ejpam-1783	324	18	τ	τ	X
ejpam-1783	324	19	=	=	PUNCT
ejpam-1783	324	20	{	{	PUNCT
ejpam-1783	324	21	x	x	NOUN
ejpam-1783	324	22	,	,	PUNCT
ejpam-1783	324	23	∅	∅	NOUN
ejpam-1783	324	24	,	,	PUNCT
ejpam-1783	324	25	{	{	PUNCT
ejpam-1783	324	26	a	a	NOUN
ejpam-1783	324	27	}	}	PUNCT
ejpam-1783	324	28	,	,	PUNCT
ejpam-1783	324	29	{	{	PUNCT
ejpam-1783	324	30	a	a	X
ejpam-1783	324	31	,	,	PUNCT
ejpam-1783	324	32	c	c	NOUN
ejpam-1783	324	33	}	}	PUNCT
ejpam-1783	324	34	,	,	PUNCT
ejpam-1783	324	35	{	{	PUNCT
ejpam-1783	324	36	a	a	DET
ejpam-1783	324	37	,	,	PUNCT
ejpam-1783	324	38	b	b	NOUN
ejpam-1783	324	39	,	,	PUNCT
ejpam-1783	324	40	c	c	NOUN
ejpam-1783	324	41	}	}	PUNCT
ejpam-1783	324	42	,	,	PUNCT
ejpam-1783	324	43	{	{	PUNCT
ejpam-1783	324	44	c	c	X
ejpam-1783	324	45	,	,	PUNCT
ejpam-1783	324	46	d	d	NOUN
ejpam-1783	324	47	}	}	PUNCT
ejpam-1783	324	48	,	,	PUNCT
ejpam-1783	324	49	{	{	PUNCT
ejpam-1783	324	50	c	c	NOUN
ejpam-1783	324	51	}	}	PUNCT
ejpam-1783	324	52	,	,	PUNCT
ejpam-1783	324	53	{	{	PUNCT
ejpam-1783	324	54	a	a	X
ejpam-1783	324	55	,	,	PUNCT
ejpam-1783	324	56	c	c	NOUN
ejpam-1783	324	57	,	,	PUNCT
ejpam-1783	324	58	d	d	NOUN
ejpam-1783	324	59	}	}	PUNCT
ejpam-1783	324	60	}	}	PUNCT
ejpam-1783	324	61	and	and	CCONJ
ejpam-1783	324	62	i	i	PRON
ejpam-1783	324	63	=	=	PUNCT
ejpam-1783	324	64	{	{	PUNCT
ejpam-1783	324	65	∅	∅	NOUN
ejpam-1783	324	66	,	,	PUNCT
ejpam-1783	324	67	{	{	PUNCT
ejpam-1783	324	68	c	c	NOUN
ejpam-1783	324	69	}	}	PUNCT
ejpam-1783	324	70	}	}	PUNCT
ejpam-1783	324	71	and	and	CCONJ
ejpam-1783	324	72	σ	σ	NUM
ejpam-1783	324	73	=	=	SYM
ejpam-1783	324	74	{	{	PUNCT
ejpam-1783	324	75	∅	∅	NOUN
ejpam-1783	324	76	,	,	PUNCT
ejpam-1783	324	77	y	y	PROPN
ejpam-1783	324	78	,	,	PUNCT
ejpam-1783	324	79	{	{	PUNCT
ejpam-1783	324	80	a	a	PRON
ejpam-1783	324	81	,	,	PUNCT
ejpam-1783	324	82	c	c	NOUN
ejpam-1783	324	83	}	}	PUNCT
ejpam-1783	324	84	}	}	PUNCT
ejpam-1783	324	85	.	.	PUNCT
ejpam-1783	325	1	define	define	VERB
ejpam-1783	325	2	a	a	DET
ejpam-1783	325	3	function	function	NOUN
ejpam-1783	325	4	f	f	NOUN
ejpam-1783	325	5	:	:	PUNCT
ejpam-1783	325	6	(	(	PUNCT
ejpam-1783	325	7	x	x	X
ejpam-1783	325	8	,	,	PUNCT
ejpam-1783	325	9	τ	τ	PROPN
ejpam-1783	325	10	,	,	PUNCT
ejpam-1783	325	11	i)→	i)→	ADJ
ejpam-1783	325	12	(	(	PUNCT
ejpam-1783	325	13	y	y	PROPN
ejpam-1783	325	14	,	,	PUNCT
ejpam-1783	325	15	σ	σ	PROPN
ejpam-1783	325	16	)	)	PUNCT
ejpam-1783	325	17	such	such	ADJ
ejpam-1783	325	18	that	that	SCONJ
ejpam-1783	325	19	f	f	PROPN
ejpam-1783	325	20	(	(	PUNCT
ejpam-1783	325	21	x	x	X
ejpam-1783	325	22	)	)	PUNCT
ejpam-1783	325	23	=	=	PUNCT
ejpam-1783	326	1	x.	x.	NOUN
ejpam-1783	326	2	then	then	ADV
ejpam-1783	326	3	f	f	PROPN
ejpam-1783	326	4	is	be	AUX
ejpam-1783	326	5	δ−	δ−	PROPN
ejpam-1783	326	6	β	β	NOUN
ejpam-1783	326	7	−	−	PROPN
ejpam-1783	327	1	i	i	PRON
ejpam-1783	327	2	-continuous	-continuous	ADJ
ejpam-1783	327	3	,	,	PUNCT
ejpam-1783	327	4	but	but	CCONJ
ejpam-1783	327	5	it	it	PRON
ejpam-1783	327	6	is	be	AUX
ejpam-1783	327	7	not	not	PART
ejpam-1783	327	8	δβ	δβ	NOUN
ejpam-1783	328	1	−	−	PROPN
ejpam-1783	328	2	b	b	NOUN
ejpam-1783	328	3	−	−	NOUN
ejpam-1783	329	1	i	i	PRON
ejpam-1783	329	2	-continuous	-continuous	ADJ
ejpam-1783	329	3	.	.	PUNCT
ejpam-1783	330	1	if	if	SCONJ
ejpam-1783	330	2	we	we	PRON
ejpam-1783	330	3	change	change	VERB
ejpam-1783	330	4	the	the	DET
ejpam-1783	330	5	topology	topology	NOUN
ejpam-1783	330	6	on	on	ADP
ejpam-1783	330	7	y	y	PROPN
ejpam-1783	330	8	as	as	ADP
ejpam-1783	330	9	σ1	σ1	PROPN
ejpam-1783	330	10	=	=	SYM
ejpam-1783	330	11	{	{	PUNCT
ejpam-1783	330	12	∅	∅	NOUN
ejpam-1783	330	13	,	,	PUNCT
ejpam-1783	330	14	y	y	PROPN
ejpam-1783	330	15	,	,	PUNCT
ejpam-1783	330	16	{	{	PUNCT
ejpam-1783	330	17	d	d	NOUN
ejpam-1783	330	18	}	}	PUNCT
ejpam-1783	330	19	}	}	PUNCT
ejpam-1783	330	20	in	in	ADP
ejpam-1783	330	21	the	the	DET
ejpam-1783	330	22	function	function	NOUN
ejpam-1783	330	23	f	f	NOUN
ejpam-1783	330	24	:	:	PUNCT
ejpam-1783	330	25	(	(	PUNCT
ejpam-1783	330	26	x	x	X
ejpam-1783	330	27	,	,	PUNCT
ejpam-1783	330	28	τ	τ	PROPN
ejpam-1783	330	29	,	,	PUNCT
ejpam-1783	330	30	i)→	i)→	ADJ
ejpam-1783	330	31	(	(	PUNCT
ejpam-1783	330	32	y	y	PROPN
ejpam-1783	330	33	,	,	PUNCT
ejpam-1783	330	34	σ1	σ1	PROPN
ejpam-1783	330	35	)	)	PUNCT
ejpam-1783	330	36	defined	define	VERB
ejpam-1783	330	37	as	as	ADP
ejpam-1783	330	38	f	f	PROPN
ejpam-1783	330	39	(	(	PUNCT
ejpam-1783	330	40	x	x	NOUN
ejpam-1783	330	41	)	)	PUNCT
ejpam-1783	330	42	=	=	SYM
ejpam-1783	331	1	x	x	X
ejpam-1783	331	2	,	,	PUNCT
ejpam-1783	331	3	then	then	ADV
ejpam-1783	331	4	f	f	PROPN
ejpam-1783	331	5	is	be	AUX
ejpam-1783	331	6	δβ	δβ	NOUN
ejpam-1783	331	7	−	−	PROPN
ejpam-1783	331	8	b−	b−	NOUN
ejpam-1783	331	9	i	i	PRON
ejpam-1783	331	10	-continuous	-continuous	ADJ
ejpam-1783	331	11	,	,	PUNCT
ejpam-1783	331	12	but	but	CCONJ
ejpam-1783	331	13	it	it	PRON
ejpam-1783	331	14	is	be	AUX
ejpam-1783	331	15	not	not	PART
ejpam-1783	331	16	δ−	δ−	ADJ
ejpam-1783	331	17	β	β	NOUN
ejpam-1783	331	18	−	−	NOUN
ejpam-1783	332	1	i	i	PRON
ejpam-1783	332	2	-continuous	-continuous	ADJ
ejpam-1783	332	3	.	.	PUNCT
ejpam-1783	333	1	theorem	theorem	VERB
ejpam-1783	333	2	6	6	NUM
ejpam-1783	333	3	.	.	PUNCT
ejpam-1783	333	4	for	for	ADP
ejpam-1783	333	5	a	a	DET
ejpam-1783	333	6	function	function	NOUN
ejpam-1783	333	7	f	f	NOUN
ejpam-1783	333	8	:	:	PUNCT
ejpam-1783	333	9	(	(	PUNCT
ejpam-1783	333	10	x	x	X
ejpam-1783	333	11	,	,	PUNCT
ejpam-1783	333	12	τ	τ	PROPN
ejpam-1783	333	13	,	,	PUNCT
ejpam-1783	333	14	i)→	i)→	ADJ
ejpam-1783	333	15	(	(	PUNCT
ejpam-1783	333	16	y	y	PROPN
ejpam-1783	333	17	,	,	PUNCT
ejpam-1783	333	18	σ	σ	PROPN
ejpam-1783	333	19	,	,	PUNCT
ejpam-1783	333	20	j	j	PROPN
ejpam-1783	333	21	)	)	PUNCT
ejpam-1783	333	22	,	,	PUNCT
ejpam-1783	333	23	the	the	DET
ejpam-1783	333	24	following	follow	VERB
ejpam-1783	333	25	properties	property	NOUN
ejpam-1783	333	26	are	be	AUX
ejpam-1783	333	27	equivalent	equivalent	ADJ
ejpam-1783	333	28	;	;	PUNCT
ejpam-1783	333	29	a	a	X
ejpam-1783	333	30	)	)	PUNCT
ejpam-1783	333	31	f	f	PROPN
ejpam-1783	333	32	is	be	AUX
ejpam-1783	333	33	δ−	δ−	PROPN
ejpam-1783	333	34	i	i	PROPN
ejpam-1783	333	35	-continuous	-continuous	ADJ
ejpam-1783	333	36	,	,	PUNCT
ejpam-1783	333	37	b	b	NOUN
ejpam-1783	333	38	)	)	PUNCT
ejpam-1783	333	39	f	f	PROPN
ejpam-1783	333	40	is	be	AUX
ejpam-1783	333	41	δα−	δα−	PROPN
ejpam-1783	333	42	i	i	PRON
ejpam-1783	333	43	-continuous	-continuous	ADJ
ejpam-1783	333	44	and	and	CCONJ
ejpam-1783	333	45	δ−	δ−	PROPN
ejpam-1783	333	46	c	c	NOUN
ejpam-1783	333	47	-	-	PUNCT
ejpam-1783	333	48	continuous	continuous	ADJ
ejpam-1783	333	49	.	.	PUNCT
ejpam-1783	334	1	remark	remark	NOUN
ejpam-1783	334	2	5	5	NUM
ejpam-1783	334	3	.	.	PUNCT
ejpam-1783	334	4	δα−	δα−	PUNCT
ejpam-1783	335	1	i	i	PRON
ejpam-1783	335	2	-continuity	-continuity	ADJ
ejpam-1783	335	3	and	and	CCONJ
ejpam-1783	335	4	δ−	δ−	PROPN
ejpam-1783	335	5	c	c	NOUN
ejpam-1783	335	6	-	-	PUNCT
ejpam-1783	335	7	continuity	continuity	NOUN
ejpam-1783	335	8	are	be	AUX
ejpam-1783	335	9	independent	independent	ADJ
ejpam-1783	335	10	notions	notion	NOUN
ejpam-1783	335	11	of	of	ADP
ejpam-1783	335	12	each	each	DET
ejpam-1783	335	13	other	other	ADJ
ejpam-1783	335	14	.	.	PUNCT
ejpam-1783	336	1	e.	e.	PROPN
ejpam-1783	336	2	hatir	hatir	PROPN
ejpam-1783	336	3	/	/	SYM
ejpam-1783	336	4	eur	eur	PROPN
ejpam-1783	336	5	.	.	PUNCT
ejpam-1783	337	1	j.	j.	PROPN
ejpam-1783	337	2	pure	pure	PROPN
ejpam-1783	337	3	appl	appl	PROPN
ejpam-1783	337	4	.	.	PROPN
ejpam-1783	337	5	math	math	PROPN
ejpam-1783	337	6	,	,	PUNCT
ejpam-1783	337	7	6	6	NUM
ejpam-1783	337	8	(	(	PUNCT
ejpam-1783	337	9	2013	2013	NUM
ejpam-1783	337	10	)	)	PUNCT
ejpam-1783	337	11	,	,	PUNCT
ejpam-1783	337	12	352	352	NUM
ejpam-1783	337	13	-	-	SYM
ejpam-1783	337	14	362	362	NUM
ejpam-1783	337	15	360	360	NUM
ejpam-1783	337	16	example	example	NOUN
ejpam-1783	337	17	5	5	NUM
ejpam-1783	337	18	.	.	PUNCT
ejpam-1783	338	1	let	let	VERB
ejpam-1783	338	2	x	x	SYM
ejpam-1783	338	3	=	=	PUNCT
ejpam-1783	338	4	y	y	PROPN
ejpam-1783	338	5	=	=	PUNCT
ejpam-1783	338	6	{	{	PUNCT
ejpam-1783	338	7	a	a	PRON
ejpam-1783	338	8	,	,	PUNCT
ejpam-1783	338	9	b	b	NOUN
ejpam-1783	338	10	,	,	PUNCT
ejpam-1783	338	11	c	c	NOUN
ejpam-1783	338	12	,	,	PUNCT
ejpam-1783	338	13	d	d	NOUN
ejpam-1783	338	14	}	}	PUNCT
ejpam-1783	338	15	,	,	PUNCT
ejpam-1783	338	16	τ	τ	X
ejpam-1783	338	17	=	=	PUNCT
ejpam-1783	338	18	{	{	PUNCT
ejpam-1783	338	19	x	x	NOUN
ejpam-1783	338	20	,	,	PUNCT
ejpam-1783	338	21	∅	∅	NOUN
ejpam-1783	338	22	,	,	PUNCT
ejpam-1783	338	23	{	{	PUNCT
ejpam-1783	338	24	a	a	NOUN
ejpam-1783	338	25	}	}	PUNCT
ejpam-1783	338	26	,	,	PUNCT
ejpam-1783	338	27	{	{	PUNCT
ejpam-1783	338	28	a	a	X
ejpam-1783	338	29	,	,	PUNCT
ejpam-1783	338	30	c	c	NOUN
ejpam-1783	338	31	}	}	PUNCT
ejpam-1783	338	32	,	,	PUNCT
ejpam-1783	338	33	{	{	PUNCT
ejpam-1783	338	34	a	a	DET
ejpam-1783	338	35	,	,	PUNCT
ejpam-1783	338	36	b	b	NOUN
ejpam-1783	338	37	,	,	PUNCT
ejpam-1783	338	38	c	c	NOUN
ejpam-1783	338	39	}	}	PUNCT
ejpam-1783	338	40	,	,	PUNCT
ejpam-1783	338	41	{	{	PUNCT
ejpam-1783	338	42	c	c	X
ejpam-1783	338	43	,	,	PUNCT
ejpam-1783	338	44	d	d	NOUN
ejpam-1783	338	45	}	}	PUNCT
ejpam-1783	338	46	,	,	PUNCT
ejpam-1783	338	47	{	{	PUNCT
ejpam-1783	338	48	c	c	NOUN
ejpam-1783	338	49	}	}	PUNCT
ejpam-1783	338	50	,	,	PUNCT
ejpam-1783	338	51	{	{	PUNCT
ejpam-1783	338	52	a	a	X
ejpam-1783	338	53	,	,	PUNCT
ejpam-1783	338	54	c	c	NOUN
ejpam-1783	338	55	,	,	PUNCT
ejpam-1783	338	56	d	d	NOUN
ejpam-1783	338	57	}	}	PUNCT
ejpam-1783	338	58	}	}	PUNCT
ejpam-1783	338	59	and	and	CCONJ
ejpam-1783	338	60	i	i	PRON
ejpam-1783	338	61	=	=	PUNCT
ejpam-1783	338	62	{	{	PUNCT
ejpam-1783	338	63	∅	∅	NOUN
ejpam-1783	338	64	,	,	PUNCT
ejpam-1783	338	65	{	{	PUNCT
ejpam-1783	338	66	c	c	NOUN
ejpam-1783	338	67	}	}	PUNCT
ejpam-1783	338	68	}	}	PUNCT
ejpam-1783	338	69	.	.	PUNCT
ejpam-1783	339	1	also	also	ADV
ejpam-1783	339	2	let	let	VERB
ejpam-1783	339	3	σ	σ	NOUN
ejpam-1783	339	4	=	=	PRON
ejpam-1783	339	5	{	{	PUNCT
ejpam-1783	339	6	∅	∅	NOUN
ejpam-1783	339	7	,	,	PUNCT
ejpam-1783	339	8	y	y	PROPN
ejpam-1783	339	9	,	,	PUNCT
ejpam-1783	339	10	{	{	PUNCT
ejpam-1783	339	11	b	b	NOUN
ejpam-1783	339	12	,	,	PUNCT
ejpam-1783	339	13	c	c	NOUN
ejpam-1783	339	14	}	}	PUNCT
ejpam-1783	339	15	}	}	PUNCT
ejpam-1783	339	16	and	and	CCONJ
ejpam-1783	339	17	j	j	PROPN
ejpam-1783	339	18	=	=	SYM
ejpam-1783	339	19	p(x	p(x	PROPN
ejpam-1783	339	20	)	)	PUNCT
ejpam-1783	339	21	.	.	PUNCT
ejpam-1783	340	1	define	define	VERB
ejpam-1783	340	2	a	a	DET
ejpam-1783	340	3	function	function	NOUN
ejpam-1783	340	4	f	f	NOUN
ejpam-1783	340	5	:	:	PUNCT
ejpam-1783	340	6	(	(	PUNCT
ejpam-1783	340	7	x	x	X
ejpam-1783	340	8	,	,	PUNCT
ejpam-1783	340	9	τ	τ	PROPN
ejpam-1783	340	10	,	,	PUNCT
ejpam-1783	340	11	i)→	i)→	ADJ
ejpam-1783	340	12	(	(	PUNCT
ejpam-1783	340	13	y	y	PROPN
ejpam-1783	340	14	,	,	PUNCT
ejpam-1783	340	15	σ	σ	PROPN
ejpam-1783	340	16	,	,	PUNCT
ejpam-1783	340	17	j	j	PROPN
ejpam-1783	340	18	)	)	PUNCT
ejpam-1783	340	19	such	such	ADJ
ejpam-1783	340	20	that	that	SCONJ
ejpam-1783	340	21	f	f	PROPN
ejpam-1783	340	22	(	(	PUNCT
ejpam-1783	340	23	x	x	X
ejpam-1783	340	24	)	)	PUNCT
ejpam-1783	340	25	=	=	SYM
ejpam-1783	341	1	x.then	x.then	PROPN
ejpam-1783	341	2	f	f	PROPN
ejpam-1783	341	3	is	be	AUX
ejpam-1783	341	4	δ−	δ−	ADJ
ejpam-1783	341	5	c	c	NOUN
ejpam-1783	341	6	-	-	ADJ
ejpam-1783	341	7	continuous	continuous	ADJ
ejpam-1783	341	8	,	,	PUNCT
ejpam-1783	341	9	but	but	CCONJ
ejpam-1783	341	10	it	it	PRON
ejpam-1783	341	11	is	be	AUX
ejpam-1783	341	12	not	not	PART
ejpam-1783	341	13	δα−	δα−	PROPN
ejpam-1783	342	1	i	i	PRON
ejpam-1783	342	2	-continuous	-continuous	ADJ
ejpam-1783	342	3	.	.	PUNCT
ejpam-1783	343	1	if	if	SCONJ
ejpam-1783	343	2	we	we	PRON
ejpam-1783	343	3	change	change	VERB
ejpam-1783	343	4	the	the	DET
ejpam-1783	343	5	topology	topology	NOUN
ejpam-1783	343	6	on	on	ADP
ejpam-1783	343	7	y	y	PROPN
ejpam-1783	343	8	as	as	ADP
ejpam-1783	343	9	σ1	σ1	PROPN
ejpam-1783	343	10	=	=	SYM
ejpam-1783	343	11	{	{	PUNCT
ejpam-1783	343	12	∅	∅	NOUN
ejpam-1783	343	13	,	,	PUNCT
ejpam-1783	343	14	y	y	PROPN
ejpam-1783	343	15	,	,	PUNCT
ejpam-1783	343	16	{	{	PUNCT
ejpam-1783	343	17	a	a	PRON
ejpam-1783	343	18	,	,	PUNCT
ejpam-1783	343	19	c	c	NOUN
ejpam-1783	343	20	}	}	PUNCT
ejpam-1783	343	21	}	}	PUNCT
ejpam-1783	343	22	and	and	CCONJ
ejpam-1783	343	23	j	j	PROPN
ejpam-1783	343	24	=	=	SYM
ejpam-1783	343	25	p(x	p(x	PROPN
ejpam-1783	343	26	)	)	PUNCT
ejpam-1783	343	27	in	in	ADP
ejpam-1783	343	28	the	the	DET
ejpam-1783	343	29	function	function	NOUN
ejpam-1783	343	30	f	f	NOUN
ejpam-1783	343	31	:	:	PUNCT
ejpam-1783	343	32	(	(	PUNCT
ejpam-1783	343	33	x	x	X
ejpam-1783	343	34	,	,	PUNCT
ejpam-1783	343	35	τ	τ	PROPN
ejpam-1783	343	36	,	,	PUNCT
ejpam-1783	343	37	i)→	i)→	ADJ
ejpam-1783	343	38	(	(	PUNCT
ejpam-1783	343	39	y	y	PROPN
ejpam-1783	343	40	,	,	PUNCT
ejpam-1783	343	41	σ1	σ1	PROPN
ejpam-1783	343	42	,	,	PUNCT
ejpam-1783	343	43	j	j	PROPN
ejpam-1783	343	44	)	)	PUNCT
ejpam-1783	343	45	such	such	ADJ
ejpam-1783	343	46	that	that	SCONJ
ejpam-1783	343	47	f	f	PROPN
ejpam-1783	343	48	(	(	PUNCT
ejpam-1783	343	49	x	x	X
ejpam-1783	343	50	)	)	PUNCT
ejpam-1783	343	51	=	=	SYM
ejpam-1783	343	52	x	x	X
ejpam-1783	343	53	,	,	PUNCT
ejpam-1783	343	54	then	then	ADV
ejpam-1783	343	55	f	f	PROPN
ejpam-1783	343	56	is	be	AUX
ejpam-1783	343	57	δα−	δα−	PROPN
ejpam-1783	343	58	i	i	PRON
ejpam-1783	343	59	-continuous	-continuous	ADJ
ejpam-1783	343	60	,	,	PUNCT
ejpam-1783	343	61	but	but	CCONJ
ejpam-1783	343	62	it	it	PRON
ejpam-1783	343	63	is	be	AUX
ejpam-1783	343	64	not	not	PART
ejpam-1783	343	65	δ−	δ−	ADJ
ejpam-1783	343	66	c	c	NOUN
ejpam-1783	343	67	-	-	ADJ
ejpam-1783	343	68	continuous	continuous	ADJ
ejpam-1783	343	69	.	.	PUNCT
ejpam-1783	344	1	4	4	X
ejpam-1783	344	2	.	.	X
ejpam-1783	344	3	decomposition	decomposition	NOUN
ejpam-1783	344	4	of	of	ADP
ejpam-1783	344	5	complete	complete	ADJ
ejpam-1783	344	6	continuity	continuity	NOUN
ejpam-1783	344	7	definition	definition	NOUN
ejpam-1783	344	8	8	8	NUM
ejpam-1783	344	9	.	.	PUNCT
ejpam-1783	345	1	a	a	DET
ejpam-1783	345	2	subset	subset	NOUN
ejpam-1783	345	3	a	a	PRON
ejpam-1783	345	4	of	of	ADP
ejpam-1783	345	5	an	an	DET
ejpam-1783	345	6	ideal	ideal	ADJ
ejpam-1783	345	7	space	space	NOUN
ejpam-1783	345	8	(	(	PUNCT
ejpam-1783	345	9	x	x	X
ejpam-1783	345	10	,	,	PUNCT
ejpam-1783	345	11	τ	τ	PROPN
ejpam-1783	345	12	,	,	PUNCT
ejpam-1783	345	13	i	i	PROPN
ejpam-1783	345	14	)	)	PUNCT
ejpam-1783	345	15	is	be	AUX
ejpam-1783	345	16	said	say	VERB
ejpam-1783	345	17	to	to	PART
ejpam-1783	345	18	be	be	AUX
ejpam-1783	345	19	semi∗−	semi∗−	ADJ
ejpam-1783	345	20	i	i	PRON
ejpam-1783	345	21	-open	-open	VERB
ejpam-1783	345	22	(	(	PUNCT
ejpam-1783	345	23	resp	resp	NOUN
ejpam-1783	345	24	.	.	PUNCT
ejpam-1783	346	1	semi∗−	semi∗−	NOUN
ejpam-1783	346	2	i	i	PRON
ejpam-1783	346	3	closed	close	VERB
ejpam-1783	346	4	)	)	PUNCT
ejpam-1783	346	5	set	set	VERB
ejpam-1783	346	6	if	if	SCONJ
ejpam-1783	346	7	a⊂	a⊂	PRON
ejpam-1783	346	8	cl(δint	cl(δint	NOUN
ejpam-1783	346	9	i(a	i(a	PROPN
ejpam-1783	346	10	)	)	PUNCT
ejpam-1783	346	11	)	)	PUNCT
ejpam-1783	347	1	(	(	PUNCT
ejpam-1783	347	2	resp	resp	NOUN
ejpam-1783	347	3	.	.	PUNCT
ejpam-1783	348	1	int(δcli(a))⊂	int(δcli(a))⊂	ADP
ejpam-1783	348	2	a	a	X
ejpam-1783	348	3	)	)	PUNCT
ejpam-1783	348	4	the	the	DET
ejpam-1783	348	5	intersection	intersection	NOUN
ejpam-1783	348	6	of	of	ADP
ejpam-1783	348	7	all	all	DET
ejpam-1783	348	8	semi∗−	semi∗−	NOUN
ejpam-1783	348	9	i	i	PRON
ejpam-1783	348	10	-closed	-close	VERB
ejpam-1783	348	11	sets	set	NOUN
ejpam-1783	348	12	containing	contain	VERB
ejpam-1783	348	13	a	a	PRON
ejpam-1783	348	14	is	be	AUX
ejpam-1783	348	15	called	call	VERB
ejpam-1783	348	16	semi∗−δ−	semi∗−δ−	ADJ
ejpam-1783	348	17	i	i	PRON
ejpam-1783	348	18	-closure	-closure	NOUN
ejpam-1783	348	19	of	of	ADP
ejpam-1783	348	20	a	a	PRON
ejpam-1783	348	21	and	and	CCONJ
ejpam-1783	348	22	denoted	denote	VERB
ejpam-1783	348	23	by	by	ADP
ejpam-1783	348	24	sδcli(a	sδcli(a	NOUN
ejpam-1783	348	25	)	)	PUNCT
ejpam-1783	348	26	.	.	PUNCT
ejpam-1783	349	1	theorem	theorem	ADJ
ejpam-1783	349	2	7	7	NUM
ejpam-1783	349	3	.	.	PUNCT
ejpam-1783	350	1	let	let	VERB
ejpam-1783	350	2	a	a	DET
ejpam-1783	350	3	be	be	AUX
ejpam-1783	350	4	a	a	DET
ejpam-1783	350	5	subset	subset	NOUN
ejpam-1783	350	6	of	of	ADP
ejpam-1783	350	7	an	an	DET
ejpam-1783	350	8	ideal	ideal	ADJ
ejpam-1783	350	9	space	space	NOUN
ejpam-1783	350	10	(	(	PUNCT
ejpam-1783	350	11	x	x	X
ejpam-1783	350	12	,	,	PUNCT
ejpam-1783	350	13	τ	τ	PROPN
ejpam-1783	350	14	,	,	PUNCT
ejpam-1783	350	15	i	i	PROPN
ejpam-1783	350	16	)	)	PUNCT
ejpam-1783	350	17	.	.	PUNCT
ejpam-1783	351	1	then	then	ADV
ejpam-1783	351	2	sδcli(a	sδcli(a	VERB
ejpam-1783	351	3	)	)	PUNCT
ejpam-1783	351	4	=	=	PUNCT
ejpam-1783	351	5	a∪	a∪	PRON
ejpam-1783	351	6	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	351	7	)	)	PUNCT
ejpam-1783	351	8	)	)	PUNCT
ejpam-1783	351	9	.	.	PUNCT
ejpam-1783	352	1	proof	proof	NOUN
ejpam-1783	352	2	.	.	PUNCT
ejpam-1783	353	1	since	since	SCONJ
ejpam-1783	353	2	int(δcli(a∪	int(δcli(a∪	PROPN
ejpam-1783	353	3	int(δcli(a))))⊂int(δcli(a)∪δcli(int(δcli(a	int(δcli(a))))⊂int(δcli(a)∪δcli(int(δcli(a	PROPN
ejpam-1783	353	4	)	)	PUNCT
ejpam-1783	353	5	)	)	PUNCT
ejpam-1783	353	6	)	)	PUNCT
ejpam-1783	353	7	)	)	PUNCT
ejpam-1783	354	1	=	=	X
ejpam-1783	354	2	int(δcli(a))⊂	int(δcli(a))⊂	X
ejpam-1783	354	3	a∪	a∪	X
ejpam-1783	354	4	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	354	5	)	)	PUNCT
ejpam-1783	354	6	)	)	PUNCT
ejpam-1783	354	7	,	,	PUNCT
ejpam-1783	354	8	a∪	a∪	PROPN
ejpam-1783	354	9	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	354	10	)	)	PUNCT
ejpam-1783	354	11	)	)	PUNCT
ejpam-1783	354	12	is	be	AUX
ejpam-1783	354	13	semi∗−	semi∗−	ADJ
ejpam-1783	354	14	i	i	PRON
ejpam-1783	354	15	-closed	-close	VERB
ejpam-1783	354	16	containing	contain	VERB
ejpam-1783	354	17	a	a	DET
ejpam-1783	354	18	and	and	CCONJ
ejpam-1783	354	19	hence	hence	ADV
ejpam-1783	354	20	sδcli(a)⊂	sδcli(a)⊂	X
ejpam-1783	354	21	a∪	a∪	PROPN
ejpam-1783	354	22	int(δcli(a	int(δcli(a	PROPN
ejpam-1783	354	23	)	)	PUNCT
ejpam-1783	354	24	)	)	PUNCT
ejpam-1783	354	25	.	.	PUNCT
ejpam-1783	355	1	on	on	ADP
ejpam-1783	355	2	the	the	DET
ejpam-1783	355	3	other	other	ADJ
ejpam-1783	355	4	hand	hand	NOUN
ejpam-1783	355	5	,	,	PUNCT
ejpam-1783	355	6	since	since	SCONJ
ejpam-1783	355	7	sδcli(a	sδcli(a	NOUN
ejpam-1783	355	8	)	)	PUNCT
ejpam-1783	355	9	is	be	AUX
ejpam-1783	355	10	semi∗−	semi∗−	ADJ
ejpam-1783	355	11	i	i	PRON
ejpam-1783	355	12	-closed	-close	VERB
ejpam-1783	355	13	,	,	PUNCT
ejpam-1783	355	14	int(δcli(a))⊂	int(δcli(a))⊂	ADJ
ejpam-1783	355	15	int(δcli(sδcli(a)))⊂	int(δcli(sδcli(a)))⊂	NOUN
ejpam-1783	355	16	sδcli(a	sδcli(a	NOUN
ejpam-1783	355	17	)	)	PUNCT
ejpam-1783	355	18	.	.	PUNCT
ejpam-1783	356	1	thus	thus	ADV
ejpam-1783	356	2	a∪	a∪	ADP
ejpam-1783	356	3	int(δcli(a))⊂	int(δcli(a))⊂	NOUN
ejpam-1783	356	4	sδcli(a	sδcli(a	NOUN
ejpam-1783	356	5	)	)	PUNCT
ejpam-1783	356	6	.	.	PUNCT
ejpam-1783	357	1	definition	definition	NOUN
ejpam-1783	357	2	9	9	NUM
ejpam-1783	357	3	.	.	PUNCT
ejpam-1783	358	1	a	a	DET
ejpam-1783	358	2	subset	subset	NOUN
ejpam-1783	358	3	a	a	PRON
ejpam-1783	358	4	of	of	ADP
ejpam-1783	358	5	an	an	DET
ejpam-1783	358	6	ideal	ideal	ADJ
ejpam-1783	358	7	space	space	NOUN
ejpam-1783	358	8	(	(	PUNCT
ejpam-1783	358	9	x	x	X
ejpam-1783	358	10	,	,	PUNCT
ejpam-1783	358	11	τ	τ	PROPN
ejpam-1783	358	12	,	,	PUNCT
ejpam-1783	358	13	i	i	PROPN
ejpam-1783	358	14	)	)	PUNCT
ejpam-1783	358	15	is	be	AUX
ejpam-1783	358	16	said	say	VERB
ejpam-1783	358	17	to	to	PART
ejpam-1783	358	18	be	be	AUX
ejpam-1783	358	19	semi	semi	ADV
ejpam-1783	358	20	−	−	NOUN
ejpam-1783	358	21	δi	δi	ADV
ejpam-1783	358	22	-generalized	-generalize	VERB
ejpam-1783	358	23	-	-	PUNCT
ejpam-1783	358	24	closed	closed	ADJ
ejpam-1783	358	25	(	(	PUNCT
ejpam-1783	358	26	briefly	briefly	ADV
ejpam-1783	358	27	,	,	PUNCT
ejpam-1783	358	28	sδi	sδi	ADJ
ejpam-1783	358	29	−	−	ADP
ejpam-1783	358	30	g	g	NOUN
ejpam-1783	358	31	-	-	PUNCT
ejpam-1783	358	32	closed	closed	ADJ
ejpam-1783	358	33	)	)	PUNCT
ejpam-1783	359	1	if	if	SCONJ
ejpam-1783	359	2	sδcli(a)⊂	sδcli(a)⊂	NOUN
ejpam-1783	359	3	u	u	NOUN
ejpam-1783	359	4	,	,	PUNCT
ejpam-1783	359	5	whenever	whenever	SCONJ
ejpam-1783	359	6	a⊂	a⊂	PUNCT
ejpam-1783	359	7	u	u	NOUN
ejpam-1783	359	8	and	and	CCONJ
ejpam-1783	359	9	u	u	NOUN
ejpam-1783	359	10	is	be	AUX
ejpam-1783	359	11	pre∗−	pre∗−	ADJ
ejpam-1783	359	12	i	i	PRON
ejpam-1783	359	13	-open	-open	VERB
ejpam-1783	359	14	.	.	PUNCT
ejpam-1783	359	15	theorem	theorem	VERB
ejpam-1783	359	16	8	8	NUM
ejpam-1783	359	17	.	.	PUNCT
ejpam-1783	360	1	for	for	ADP
ejpam-1783	360	2	a	a	DET
ejpam-1783	360	3	subset	subset	NOUN
ejpam-1783	360	4	a	a	PRON
ejpam-1783	360	5	of	of	ADP
ejpam-1783	360	6	an	an	DET
ejpam-1783	360	7	ideal	ideal	ADJ
ejpam-1783	360	8	space	space	NOUN
ejpam-1783	360	9	(	(	PUNCT
ejpam-1783	360	10	x	x	X
ejpam-1783	360	11	,	,	PUNCT
ejpam-1783	360	12	τ	τ	PROPN
ejpam-1783	360	13	,	,	PUNCT
ejpam-1783	360	14	i	i	PROPN
ejpam-1783	360	15	)	)	PUNCT
ejpam-1783	360	16	,	,	PUNCT
ejpam-1783	360	17	the	the	DET
ejpam-1783	360	18	following	follow	VERB
ejpam-1783	360	19	properties	property	NOUN
ejpam-1783	360	20	are	be	AUX
ejpam-1783	360	21	equivalent	equivalent	ADJ
ejpam-1783	360	22	;	;	PUNCT
ejpam-1783	360	23	a	a	X
ejpam-1783	360	24	)	)	PUNCT
ejpam-1783	360	25	a	a	PRON
ejpam-1783	360	26	is	be	AUX
ejpam-1783	360	27	regular	regular	ADJ
ejpam-1783	360	28	open	open	ADJ
ejpam-1783	360	29	,	,	PUNCT
ejpam-1783	360	30	b	b	X
ejpam-1783	360	31	)	)	PUNCT
ejpam-1783	360	32	a	a	PRON
ejpam-1783	360	33	is	be	AUX
ejpam-1783	360	34	pre∗−	pre∗−	ADJ
ejpam-1783	360	35	i	i	PRON
ejpam-1783	360	36	-open	-open	VERB
ejpam-1783	360	37	and	and	CCONJ
ejpam-1783	360	38	semi−δi	semi−δi	VERB
ejpam-1783	360	39	-generalized	-generalize	VERB
ejpam-1783	360	40	-	-	PUNCT
ejpam-1783	360	41	closed	closed	ADJ
ejpam-1783	360	42	.	.	PUNCT
ejpam-1783	361	1	proof	proof	NOUN
ejpam-1783	361	2	.	.	PUNCT
ejpam-1783	362	1	(	(	PUNCT
ejpam-1783	362	2	a	a	X
ejpam-1783	362	3	)	)	PUNCT
ejpam-1783	362	4	=	=	NOUN
ejpam-1783	362	5	⇒	⇒	NOUN
ejpam-1783	362	6	(	(	PUNCT
ejpam-1783	362	7	b	b	NOUN
ejpam-1783	362	8	)	)	PUNCT
ejpam-1783	362	9	.	.	PUNCT
ejpam-1783	363	1	let	let	VERB
ejpam-1783	363	2	a	a	PRON
ejpam-1783	363	3	be	be	AUX
ejpam-1783	363	4	a	a	DET
ejpam-1783	363	5	regular	regular	ADJ
ejpam-1783	363	6	open	open	NOUN
ejpam-1783	363	7	.	.	PUNCT
ejpam-1783	364	1	since	since	SCONJ
ejpam-1783	364	2	every	every	DET
ejpam-1783	364	3	regular	regular	ADJ
ejpam-1783	364	4	open	open	ADJ
ejpam-1783	364	5	set	set	NOUN
ejpam-1783	364	6	is	be	AUX
ejpam-1783	364	7	pre∗	pre∗	NOUN
ejpam-1783	364	8	−	−	NOUN
ejpam-1783	365	1	i	i	PRON
ejpam-1783	365	2	-open	-open	VERB
ejpam-1783	365	3	,	,	PUNCT
ejpam-1783	365	4	a	a	PRON
ejpam-1783	365	5	is	be	AUX
ejpam-1783	365	6	pre∗	pre∗	NOUN
ejpam-1783	365	7	−	−	NOUN
ejpam-1783	366	1	i	i	PRON
ejpam-1783	366	2	-open	-open	VERB
ejpam-1783	366	3	.	.	PUNCT
ejpam-1783	367	1	by	by	ADP
ejpam-1783	367	2	sδcli(a	sδcli(a	ADP
ejpam-1783	367	3	)	)	PUNCT
ejpam-1783	367	4	=	=	PUNCT
ejpam-1783	367	5	a∪	a∪	DET
ejpam-1783	367	6	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	367	7	)	)	PUNCT
ejpam-1783	367	8	)	)	PUNCT
ejpam-1783	367	9	=	=	SYM
ejpam-1783	367	10	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	367	11	)	)	PUNCT
ejpam-1783	367	12	)	)	PUNCT
ejpam-1783	368	1	=	=	SYM
ejpam-1783	368	2	int(cl(a	int(cl(a	PROPN
ejpam-1783	368	3	)	)	PUNCT
ejpam-1783	368	4	)	)	PUNCT
ejpam-1783	369	1	=	=	PUNCT
ejpam-1783	369	2	a	a	PRON
ejpam-1783	369	3	and	and	CCONJ
ejpam-1783	369	4	theorem	theorem	VERB
ejpam-1783	369	5	2	2	NUM
ejpam-1783	369	6	,	,	PUNCT
ejpam-1783	369	7	a	a	PRON
ejpam-1783	369	8	is	be	AUX
ejpam-1783	369	9	sδi	sδi	NOUN
ejpam-1783	369	10	−	−	ADP
ejpam-1783	369	11	g	g	NOUN
ejpam-1783	369	12	-	-	PUNCT
ejpam-1783	369	13	closed	closed	ADJ
ejpam-1783	369	14	.	.	PUNCT
ejpam-1783	370	1	(	(	PUNCT
ejpam-1783	370	2	b	b	X
ejpam-1783	370	3	)	)	PUNCT
ejpam-1783	370	4	=	=	NOUN
ejpam-1783	370	5	⇒	⇒	NOUN
ejpam-1783	370	6	(	(	PUNCT
ejpam-1783	370	7	a	a	NOUN
ejpam-1783	370	8	)	)	PUNCT
ejpam-1783	370	9	.	.	PUNCT
ejpam-1783	371	1	let	let	VERB
ejpam-1783	371	2	a	a	DET
ejpam-1783	371	3	be	be	AUX
ejpam-1783	371	4	pre∗	pre∗	NOUN
ejpam-1783	371	5	−	−	NOUN
ejpam-1783	372	1	i	i	PRON
ejpam-1783	372	2	-open	-open	ADJ
ejpam-1783	372	3	and	and	CCONJ
ejpam-1783	372	4	a	a	DET
ejpam-1783	372	5	sδi	sδi	NOUN
ejpam-1783	372	6	−	−	NOUN
ejpam-1783	372	7	g	g	NOUN
ejpam-1783	372	8	-	-	PUNCT
ejpam-1783	372	9	closed	close	VERB
ejpam-1783	372	10	set	set	NOUN
ejpam-1783	372	11	.	.	PUNCT
ejpam-1783	373	1	then	then	ADV
ejpam-1783	373	2	sδcli(a	sδcli(a	PROPN
ejpam-1783	373	3	)	)	PUNCT
ejpam-1783	373	4	⊂	⊂	PROPN
ejpam-1783	373	5	a	a	PRON
ejpam-1783	373	6	and	and	CCONJ
ejpam-1783	373	7	hence	hence	ADV
ejpam-1783	373	8	a	a	PRON
ejpam-1783	373	9	is	be	AUX
ejpam-1783	373	10	strong	strong	ADJ
ejpam-1783	373	11	semi−i	semi−i	PROPN
ejpam-1783	373	12	-closed	-closed	PROPN
ejpam-1783	373	13	.	.	PUNCT
ejpam-1783	374	1	therefore	therefore	ADV
ejpam-1783	374	2	,	,	PUNCT
ejpam-1783	374	3	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	374	4	)	)	PUNCT
ejpam-1783	374	5	)	)	PUNCT
ejpam-1783	375	1	⊂	⊂	PROPN
ejpam-1783	375	2	a.	a.	PROPN
ejpam-1783	375	3	since	since	SCONJ
ejpam-1783	375	4	a	a	PRON
ejpam-1783	375	5	is	be	AUX
ejpam-1783	375	6	pre∗	pre∗	NOUN
ejpam-1783	375	7	−	−	NOUN
ejpam-1783	376	1	i	i	PRON
ejpam-1783	376	2	-open	-open	VERB
ejpam-1783	376	3	,	,	PUNCT
ejpam-1783	376	4	a⊂	a⊂	NOUN
ejpam-1783	376	5	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	376	6	)	)	PUNCT
ejpam-1783	376	7	)	)	PUNCT
ejpam-1783	376	8	and	and	CCONJ
ejpam-1783	376	9	int(δcli(a	int(δcli(a	NOUN
ejpam-1783	376	10	)	)	PUNCT
ejpam-1783	377	1	=	=	PUNCT
ejpam-1783	377	2	a.	a.	NOUN
ejpam-1783	377	3	thus	thus	ADV
ejpam-1783	377	4	,	,	PUNCT
ejpam-1783	377	5	by	by	ADP
ejpam-1783	377	6	theorem	theorem	NOUN
ejpam-1783	377	7	2	2	NUM
ejpam-1783	377	8	,	,	PUNCT
ejpam-1783	377	9	a	a	PRON
ejpam-1783	377	10	is	be	AUX
ejpam-1783	377	11	regular	regular	ADJ
ejpam-1783	377	12	open	open	ADJ
ejpam-1783	377	13	.	.	PUNCT
ejpam-1783	378	1	to	to	PART
ejpam-1783	378	2	obtain	obtain	VERB
ejpam-1783	378	3	decomposition	decomposition	NOUN
ejpam-1783	378	4	of	of	ADP
ejpam-1783	378	5	complete	complete	ADJ
ejpam-1783	378	6	continuity	continuity	NOUN
ejpam-1783	378	7	,	,	PUNCT
ejpam-1783	378	8	we	we	PRON
ejpam-1783	378	9	introduce	introduce	VERB
ejpam-1783	378	10	the	the	DET
ejpam-1783	378	11	following	follow	VERB
ejpam-1783	378	12	new	new	ADJ
ejpam-1783	378	13	functions	function	NOUN
ejpam-1783	378	14	.	.	PUNCT
ejpam-1783	379	1	references	reference	NOUN
ejpam-1783	379	2	361	361	NUM
ejpam-1783	379	3	definition	definition	NOUN
ejpam-1783	379	4	10	10	NUM
ejpam-1783	379	5	.	.	PUNCT
ejpam-1783	380	1	a	a	DET
ejpam-1783	380	2	function	function	NOUN
ejpam-1783	380	3	f	f	NOUN
ejpam-1783	380	4	:	:	PUNCT
ejpam-1783	380	5	(	(	PUNCT
ejpam-1783	380	6	x	x	X
ejpam-1783	380	7	,	,	PUNCT
ejpam-1783	380	8	τ)→	τ)→	PROPN
ejpam-1783	380	9	(	(	PUNCT
ejpam-1783	380	10	y	y	PROPN
ejpam-1783	380	11	,	,	PUNCT
ejpam-1783	380	12	σ	σ	PROPN
ejpam-1783	380	13	)	)	PUNCT
ejpam-1783	380	14	is	be	AUX
ejpam-1783	380	15	said	say	VERB
ejpam-1783	380	16	to	to	PART
ejpam-1783	380	17	be	be	AUX
ejpam-1783	380	18	completely	completely	ADV
ejpam-1783	380	19	continuous	continuous	ADJ
ejpam-1783	381	1	[	[	X
ejpam-1783	381	2	1	1	NUM
ejpam-1783	381	3	]	]	X
ejpam-1783	381	4	if	if	SCONJ
ejpam-1783	381	5	for	for	ADP
ejpam-1783	381	6	each	each	DET
ejpam-1783	381	7	v	v	NUM
ejpam-1783	381	8	∈	∈	PROPN
ejpam-1783	381	9	σ	σ	PROPN
ejpam-1783	381	10	,	,	PUNCT
ejpam-1783	381	11	f	f	PROPN
ejpam-1783	381	12	−1(v	−1(v	PROPN
ejpam-1783	381	13	)	)	PUNCT
ejpam-1783	381	14	is	be	AUX
ejpam-1783	381	15	regular	regular	ADJ
ejpam-1783	381	16	open	open	ADJ
ejpam-1783	381	17	in	in	ADP
ejpam-1783	381	18	(	(	PUNCT
ejpam-1783	381	19	x	x	INTJ
ejpam-1783	381	20	,	,	PUNCT
ejpam-1783	381	21	τ	τ	PROPN
ejpam-1783	381	22	)	)	PUNCT
ejpam-1783	381	23	.	.	PUNCT
ejpam-1783	382	1	definition	definition	NOUN
ejpam-1783	382	2	11	11	NUM
ejpam-1783	382	3	.	.	PUNCT
ejpam-1783	383	1	a	a	DET
ejpam-1783	383	2	function	function	NOUN
ejpam-1783	383	3	f	f	NOUN
ejpam-1783	383	4	:	:	PUNCT
ejpam-1783	383	5	(	(	PUNCT
ejpam-1783	383	6	x	x	X
ejpam-1783	383	7	,	,	PUNCT
ejpam-1783	383	8	τ	τ	PROPN
ejpam-1783	383	9	,	,	PUNCT
ejpam-1783	383	10	i	i	NOUN
ejpam-1783	383	11	)	)	PUNCT
ejpam-1783	383	12	→	→	SYM
ejpam-1783	383	13	(	(	PUNCT
ejpam-1783	383	14	y	y	PROPN
ejpam-1783	383	15	,	,	PUNCT
ejpam-1783	383	16	σ	σ	PROPN
ejpam-1783	383	17	)	)	PUNCT
ejpam-1783	383	18	is	be	AUX
ejpam-1783	383	19	said	say	VERB
ejpam-1783	383	20	to	to	PART
ejpam-1783	383	21	be	be	AUX
ejpam-1783	383	22	pre∗	pre∗	NOUN
ejpam-1783	383	23	−	−	PROPN
ejpam-1783	384	1	i	i	PRON
ejpam-1783	384	2	-continuous	-continuous	ADJ
ejpam-1783	384	3	[	[	X
ejpam-1783	384	4	3	3	NUM
ejpam-1783	384	5	]	]	PUNCT
ejpam-1783	384	6	(	(	PUNCT
ejpam-1783	384	7	resp	resp	NOUN
ejpam-1783	384	8	.	.	PUNCT
ejpam-1783	385	1	contra	contra	PROPN
ejpam-1783	385	2	sδi	sδi	PROPN
ejpam-1783	386	1	−	−	PROPN
ejpam-1783	386	2	g	g	NOUN
ejpam-1783	386	3	-	-	PUNCT
ejpam-1783	386	4	continuous	continuous	ADJ
ejpam-1783	386	5	)	)	PUNCT
ejpam-1783	386	6	if	if	SCONJ
ejpam-1783	386	7	for	for	ADP
ejpam-1783	386	8	each	each	DET
ejpam-1783	386	9	v	v	NUM
ejpam-1783	386	10	∈	∈	PROPN
ejpam-1783	386	11	σ	σ	PROPN
ejpam-1783	386	12	,	,	PUNCT
ejpam-1783	386	13	f	f	PROPN
ejpam-1783	386	14	−1(v	−1(v	PROPN
ejpam-1783	386	15	)	)	PUNCT
ejpam-1783	386	16	is	be	AUX
ejpam-1783	386	17	pre∗	pre∗	NOUN
ejpam-1783	386	18	−	−	NOUN
ejpam-1783	387	1	i	i	PRON
ejpam-1783	387	2	-open	-open	VERB
ejpam-1783	387	3	(	(	PUNCT
ejpam-1783	387	4	resp	resp	NOUN
ejpam-1783	387	5	.	.	PUNCT
ejpam-1783	388	1	sδi	sδi	PROPN
ejpam-1783	388	2	−	−	ADP
ejpam-1783	388	3	g	g	NOUN
ejpam-1783	388	4	-	-	PUNCT
ejpam-1783	388	5	closed	closed	ADJ
ejpam-1783	388	6	)	)	PUNCT
ejpam-1783	388	7	in	in	ADP
ejpam-1783	388	8	(	(	PUNCT
ejpam-1783	388	9	x	x	INTJ
ejpam-1783	388	10	,	,	PUNCT
ejpam-1783	388	11	τ	τ	PROPN
ejpam-1783	388	12	,	,	PUNCT
ejpam-1783	388	13	i	i	PROPN
ejpam-1783	388	14	)	)	PUNCT
ejpam-1783	388	15	.	.	PUNCT
ejpam-1783	389	1	by	by	ADP
ejpam-1783	389	2	theorem	theorem	NOUN
ejpam-1783	389	3	8	8	NUM
ejpam-1783	389	4	,	,	PUNCT
ejpam-1783	389	5	we	we	PRON
ejpam-1783	389	6	obtain	obtain	VERB
ejpam-1783	389	7	the	the	DET
ejpam-1783	389	8	following	follow	VERB
ejpam-1783	389	9	decomposition	decomposition	NOUN
ejpam-1783	389	10	of	of	ADP
ejpam-1783	389	11	complete	complete	ADJ
ejpam-1783	389	12	continuity	continuity	NOUN
ejpam-1783	389	13	.	.	PUNCT
ejpam-1783	390	1	theorem	theorem	VERB
ejpam-1783	390	2	9	9	NUM
ejpam-1783	390	3	.	.	PUNCT
ejpam-1783	391	1	for	for	ADP
ejpam-1783	391	2	a	a	DET
ejpam-1783	391	3	function	function	NOUN
ejpam-1783	391	4	f	f	NOUN
ejpam-1783	391	5	:	:	PUNCT
ejpam-1783	391	6	(	(	PUNCT
ejpam-1783	391	7	x	x	X
ejpam-1783	391	8	,	,	PUNCT
ejpam-1783	391	9	τ	τ	PROPN
ejpam-1783	391	10	,	,	PUNCT
ejpam-1783	391	11	i)→	i)→	ADJ
ejpam-1783	391	12	(	(	PUNCT
ejpam-1783	391	13	y	y	PROPN
ejpam-1783	391	14	,	,	PUNCT
ejpam-1783	391	15	σ	σ	PROPN
ejpam-1783	391	16	)	)	PUNCT
ejpam-1783	391	17	,	,	PUNCT
ejpam-1783	391	18	the	the	DET
ejpam-1783	391	19	following	follow	VERB
ejpam-1783	391	20	properties	property	NOUN
ejpam-1783	391	21	are	be	AUX
ejpam-1783	391	22	equivalent	equivalent	ADJ
ejpam-1783	391	23	;	;	PUNCT
ejpam-1783	391	24	a	a	X
ejpam-1783	391	25	)	)	PUNCT
ejpam-1783	391	26	f	f	NOUN
ejpam-1783	391	27	is	be	AUX
ejpam-1783	391	28	completely	completely	ADV
ejpam-1783	391	29	continuous	continuous	ADJ
ejpam-1783	391	30	,	,	PUNCT
ejpam-1783	391	31	b	b	NOUN
ejpam-1783	391	32	)	)	PUNCT
ejpam-1783	391	33	f	f	PROPN
ejpam-1783	391	34	is	be	AUX
ejpam-1783	391	35	pre∗−	pre∗−	ADJ
ejpam-1783	391	36	i	i	PRON
ejpam-1783	391	37	-continuous	-continuous	ADJ
ejpam-1783	391	38	and	and	CCONJ
ejpam-1783	391	39	contra	contra	PROPN
ejpam-1783	391	40	sδi	sδi	PROPN
ejpam-1783	391	41	−	−	PROPN
ejpam-1783	391	42	g	g	NOUN
ejpam-1783	391	43	-	-	PUNCT
ejpam-1783	391	44	continuous	continuous	ADJ
ejpam-1783	391	45	.	.	PUNCT
ejpam-1783	392	1	remark	remark	NOUN
ejpam-1783	392	2	6	6	NUM
ejpam-1783	392	3	.	.	PUNCT
ejpam-1783	393	1	by	by	ADP
ejpam-1783	393	2	the	the	DET
ejpam-1783	393	3	following	follow	VERB
ejpam-1783	393	4	example	example	NOUN
ejpam-1783	393	5	,	,	PUNCT
ejpam-1783	393	6	pre∗	pre∗	NOUN
ejpam-1783	393	7	−	−	PROPN
ejpam-1783	394	1	i	i	PRON
ejpam-1783	394	2	-continuity	-continuity	PROPN
ejpam-1783	394	3	and	and	CCONJ
ejpam-1783	394	4	contra	contra	PROPN
ejpam-1783	394	5	sδi	sδi	PROPN
ejpam-1783	394	6	−	−	PROPN
ejpam-1783	394	7	g	g	NOUN
ejpam-1783	394	8	-	-	PUNCT
ejpam-1783	394	9	continuity	continuity	NOUN
ejpam-1783	394	10	are	be	AUX
ejpam-1783	394	11	independent	independent	ADJ
ejpam-1783	394	12	concepts	concept	NOUN
ejpam-1783	394	13	.	.	PUNCT
ejpam-1783	395	1	example	example	NOUN
ejpam-1783	395	2	6	6	NUM
ejpam-1783	395	3	.	.	PUNCT
ejpam-1783	396	1	let	let	VERB
ejpam-1783	396	2	x	x	SYM
ejpam-1783	396	3	=	=	PUNCT
ejpam-1783	396	4	y	y	PROPN
ejpam-1783	396	5	=	=	PUNCT
ejpam-1783	396	6	{	{	PUNCT
ejpam-1783	396	7	a	a	PRON
ejpam-1783	396	8	,	,	PUNCT
ejpam-1783	396	9	b	b	NOUN
ejpam-1783	396	10	,	,	PUNCT
ejpam-1783	396	11	c	c	NOUN
ejpam-1783	396	12	,	,	PUNCT
ejpam-1783	396	13	d	d	NOUN
ejpam-1783	396	14	}	}	PUNCT
ejpam-1783	396	15	,	,	PUNCT
ejpam-1783	396	16	τ	τ	X
ejpam-1783	396	17	=	=	PUNCT
ejpam-1783	396	18	{	{	PUNCT
ejpam-1783	396	19	x	x	NOUN
ejpam-1783	396	20	,	,	PUNCT
ejpam-1783	396	21	∅	∅	NOUN
ejpam-1783	396	22	,	,	PUNCT
ejpam-1783	396	23	{	{	PUNCT
ejpam-1783	396	24	a	a	NOUN
ejpam-1783	396	25	}	}	PUNCT
ejpam-1783	396	26	,	,	PUNCT
ejpam-1783	396	27	{	{	PUNCT
ejpam-1783	396	28	a	a	X
ejpam-1783	396	29	,	,	PUNCT
ejpam-1783	396	30	c	c	NOUN
ejpam-1783	396	31	}	}	PUNCT
ejpam-1783	396	32	,	,	PUNCT
ejpam-1783	396	33	{	{	PUNCT
ejpam-1783	396	34	a	a	DET
ejpam-1783	396	35	,	,	PUNCT
ejpam-1783	396	36	b	b	NOUN
ejpam-1783	396	37	,	,	PUNCT
ejpam-1783	396	38	c	c	NOUN
ejpam-1783	396	39	}	}	PUNCT
ejpam-1783	396	40	,	,	PUNCT
ejpam-1783	396	41	{	{	PUNCT
ejpam-1783	396	42	c	c	X
ejpam-1783	396	43	,	,	PUNCT
ejpam-1783	396	44	d	d	NOUN
ejpam-1783	396	45	}	}	PUNCT
ejpam-1783	396	46	,	,	PUNCT
ejpam-1783	396	47	{	{	PUNCT
ejpam-1783	396	48	c	c	NOUN
ejpam-1783	396	49	}	}	PUNCT
ejpam-1783	396	50	,	,	PUNCT
ejpam-1783	396	51	{	{	PUNCT
ejpam-1783	396	52	a	a	X
ejpam-1783	396	53	,	,	PUNCT
ejpam-1783	396	54	c	c	NOUN
ejpam-1783	396	55	,	,	PUNCT
ejpam-1783	396	56	d	d	NOUN
ejpam-1783	396	57	}	}	PUNCT
ejpam-1783	396	58	}	}	PUNCT
ejpam-1783	396	59	and	and	CCONJ
ejpam-1783	396	60	i	i	PRON
ejpam-1783	396	61	=	=	PUNCT
ejpam-1783	396	62	{	{	PUNCT
ejpam-1783	396	63	∅	∅	NOUN
ejpam-1783	396	64	,	,	PUNCT
ejpam-1783	396	65	{	{	PUNCT
ejpam-1783	396	66	c	c	NOUN
ejpam-1783	396	67	}	}	PUNCT
ejpam-1783	396	68	}	}	PUNCT
ejpam-1783	396	69	and	and	CCONJ
ejpam-1783	396	70	σ	σ	NUM
ejpam-1783	396	71	=	=	SYM
ejpam-1783	396	72	{	{	PUNCT
ejpam-1783	396	73	∅	∅	NOUN
ejpam-1783	396	74	,	,	PUNCT
ejpam-1783	396	75	y	y	PROPN
ejpam-1783	396	76	,	,	PUNCT
ejpam-1783	396	77	{	{	PUNCT
ejpam-1783	396	78	a	a	PRON
ejpam-1783	396	79	,	,	PUNCT
ejpam-1783	396	80	c	c	NOUN
ejpam-1783	396	81	}	}	PUNCT
ejpam-1783	396	82	}	}	PUNCT
ejpam-1783	396	83	as	as	ADP
ejpam-1783	396	84	in	in	ADP
ejpam-1783	396	85	example	example	NOUN
ejpam-1783	396	86	4	4	NUM
ejpam-1783	396	87	.	.	PUNCT
ejpam-1783	396	88	define	define	VERB
ejpam-1783	396	89	a	a	DET
ejpam-1783	396	90	function	function	NOUN
ejpam-1783	396	91	f	f	NOUN
ejpam-1783	396	92	:	:	PUNCT
ejpam-1783	396	93	(	(	PUNCT
ejpam-1783	396	94	x	x	X
ejpam-1783	396	95	,	,	PUNCT
ejpam-1783	396	96	τ	τ	PROPN
ejpam-1783	396	97	,	,	PUNCT
ejpam-1783	396	98	i	i	NOUN
ejpam-1783	396	99	)	)	PUNCT
ejpam-1783	396	100	→	→	SYM
ejpam-1783	396	101	(	(	PUNCT
ejpam-1783	396	102	y	y	PROPN
ejpam-1783	396	103	,	,	PUNCT
ejpam-1783	396	104	σ	σ	PROPN
ejpam-1783	396	105	)	)	PUNCT
ejpam-1783	396	106	such	such	ADJ
ejpam-1783	396	107	that	that	SCONJ
ejpam-1783	396	108	f	f	PROPN
ejpam-1783	396	109	(	(	PUNCT
ejpam-1783	396	110	x	x	X
ejpam-1783	396	111	)	)	PUNCT
ejpam-1783	396	112	=	=	PUNCT
ejpam-1783	397	1	x.	x.	NOUN
ejpam-1783	397	2	then	then	ADV
ejpam-1783	397	3	f	f	PROPN
ejpam-1783	397	4	is	be	AUX
ejpam-1783	397	5	pre∗−	pre∗−	ADJ
ejpam-1783	397	6	i	i	PRON
ejpam-1783	397	7	-continuous	-continuous	ADJ
ejpam-1783	397	8	,	,	PUNCT
ejpam-1783	397	9	but	but	CCONJ
ejpam-1783	397	10	it	it	PRON
ejpam-1783	397	11	is	be	AUX
ejpam-1783	397	12	not	not	PART
ejpam-1783	397	13	contra	contra	PROPN
ejpam-1783	397	14	sδi	sδi	NOUN
ejpam-1783	397	15	−	−	PROPN
ejpam-1783	398	1	g	g	NOUN
ejpam-1783	398	2	-	-	PUNCT
ejpam-1783	398	3	continuous	continuous	ADJ
ejpam-1783	398	4	.	.	PUNCT
ejpam-1783	399	1	if	if	SCONJ
ejpam-1783	399	2	we	we	PRON
ejpam-1783	399	3	change	change	VERB
ejpam-1783	399	4	the	the	DET
ejpam-1783	399	5	topology	topology	NOUN
ejpam-1783	399	6	on	on	ADP
ejpam-1783	399	7	y	y	PROPN
ejpam-1783	399	8	as	as	ADP
ejpam-1783	399	9	σ1	σ1	PROPN
ejpam-1783	399	10	=	=	SYM
ejpam-1783	399	11	{	{	PUNCT
ejpam-1783	399	12	∅	∅	NOUN
ejpam-1783	399	13	,	,	PUNCT
ejpam-1783	399	14	y	y	PROPN
ejpam-1783	399	15	,	,	PUNCT
ejpam-1783	399	16	{	{	PUNCT
ejpam-1783	399	17	b	b	NOUN
ejpam-1783	399	18	}	}	PUNCT
ejpam-1783	399	19	}	}	PUNCT
ejpam-1783	399	20	in	in	ADP
ejpam-1783	399	21	the	the	DET
ejpam-1783	399	22	function	function	NOUN
ejpam-1783	399	23	f	f	NOUN
ejpam-1783	399	24	:	:	PUNCT
ejpam-1783	399	25	(	(	PUNCT
ejpam-1783	399	26	x	x	X
ejpam-1783	399	27	,	,	PUNCT
ejpam-1783	399	28	τ	τ	PROPN
ejpam-1783	399	29	,	,	PUNCT
ejpam-1783	399	30	i)→	i)→	ADJ
ejpam-1783	399	31	(	(	PUNCT
ejpam-1783	399	32	y	y	PROPN
ejpam-1783	399	33	,	,	PUNCT
ejpam-1783	399	34	σ1	σ1	PROPN
ejpam-1783	399	35	)	)	PUNCT
ejpam-1783	399	36	defined	define	VERB
ejpam-1783	399	37	as	as	ADP
ejpam-1783	399	38	f	f	PROPN
ejpam-1783	399	39	(	(	PUNCT
ejpam-1783	399	40	x	x	NOUN
ejpam-1783	399	41	)	)	PUNCT
ejpam-1783	399	42	=	=	SYM
ejpam-1783	400	1	x	x	X
ejpam-1783	400	2	,	,	PUNCT
ejpam-1783	400	3	then	then	ADV
ejpam-1783	400	4	f	f	PROPN
ejpam-1783	400	5	is	be	AUX
ejpam-1783	400	6	contra	contra	PROPN
ejpam-1783	400	7	sδi	sδi	PROPN
ejpam-1783	400	8	−	−	PROPN
ejpam-1783	401	1	g	g	NOUN
ejpam-1783	401	2	-	-	PUNCT
ejpam-1783	401	3	continuous	continuous	ADJ
ejpam-1783	401	4	,	,	PUNCT
ejpam-1783	401	5	but	but	CCONJ
ejpam-1783	401	6	it	it	PRON
ejpam-1783	401	7	is	be	AUX
ejpam-1783	401	8	not	not	PART
ejpam-1783	401	9	pre∗−	pre∗−	ADJ
ejpam-1783	401	10	i	i	PRON
ejpam-1783	401	11	-continuous	-continuous	ADJ
ejpam-1783	401	12	.	.	PUNCT
ejpam-1783	402	1	references	reference	NOUN
ejpam-1783	402	2	[	[	X
ejpam-1783	402	3	1	1	X
ejpam-1783	402	4	]	]	PUNCT
ejpam-1783	402	5	s.	s.	PROPN
ejpam-1783	402	6	p.	p.	PROPN
ejpam-1783	402	7	arya	arya	PROPN
ejpam-1783	402	8	and	and	CCONJ
ejpam-1783	402	9	r.	r.	PROPN
ejpam-1783	402	10	gupta	gupta	PROPN
ejpam-1783	402	11	.	.	PUNCT
ejpam-1783	403	1	on	on	ADP
ejpam-1783	403	2	strongly	strongly	ADV
ejpam-1783	403	3	continuous	continuous	ADJ
ejpam-1783	403	4	mappings	mapping	NOUN
ejpam-1783	403	5	,	,	PUNCT
ejpam-1783	403	6	kyungpook	kyungpook	PROPN
ejpam-1783	403	7	mathematical	mathematical	ADJ
ejpam-1783	403	8	journal	journal	NOUN
ejpam-1783	403	9	,	,	PUNCT
ejpam-1783	403	10	14	14	NUM
ejpam-1783	403	11	,	,	PUNCT
ejpam-1783	403	12	131	131	NUM
ejpam-1783	403	13	-	-	SYM
ejpam-1783	403	14	143	143	NUM
ejpam-1783	403	15	.	.	PUNCT
ejpam-1783	403	16	1974	1974	NUM
ejpam-1783	403	17	.	.	PUNCT
ejpam-1783	404	1	[	[	X
ejpam-1783	404	2	2	2	X
ejpam-1783	404	3	]	]	PUNCT
ejpam-1783	404	4	j.	j.	PROPN
ejpam-1783	404	5	dontchev	dontchev	PROPN
ejpam-1783	404	6	.	.	PUNCT
ejpam-1783	405	1	on	on	ADP
ejpam-1783	405	2	pre	pre	ADJ
ejpam-1783	405	3	-	-	ADJ
ejpam-1783	405	4	i	i	PRON
ejpam-1783	405	5	-	-	PUNCT
ejpam-1783	405	6	open	open	ADJ
ejpam-1783	405	7	sets	set	NOUN
ejpam-1783	405	8	and	and	CCONJ
ejpam-1783	405	9	a	a	DET
ejpam-1783	405	10	decomposition	decomposition	NOUN
ejpam-1783	405	11	of	of	ADP
ejpam-1783	405	12	i	i	NOUN
ejpam-1783	405	13	-	-	PUNCT
ejpam-1783	405	14	continuity	continuity	NOUN
ejpam-1783	405	15	,	,	PUNCT
ejpam-1783	405	16	banyan	banyan	ADJ
ejpam-1783	405	17	mathematical	mathematical	ADJ
ejpam-1783	405	18	journal	journal	NOUN
ejpam-1783	405	19	,	,	PUNCT
ejpam-1783	405	20	2	2	NUM
ejpam-1783	405	21	.	.	NUM
ejpam-1783	405	22	1996	1996	NUM
ejpam-1783	405	23	.	.	PUNCT
ejpam-1783	406	1	[	[	X
ejpam-1783	406	2	3	3	X
ejpam-1783	406	3	]	]	X
ejpam-1783	406	4	e.	e.	PROPN
ejpam-1783	406	5	ekici	ekici	PROPN
ejpam-1783	406	6	and	and	CCONJ
ejpam-1783	406	7	t.	t.	PROPN
ejpam-1783	406	8	noiri	noiri	PROPN
ejpam-1783	406	9	.	.	PUNCT
ejpam-1783	407	1	on	on	ADP
ejpam-1783	407	2	subsets	subset	NOUN
ejpam-1783	407	3	and	and	CCONJ
ejpam-1783	407	4	decompositions	decomposition	NOUN
ejpam-1783	407	5	of	of	ADP
ejpam-1783	407	6	continuity	continuity	NOUN
ejpam-1783	407	7	in	in	ADP
ejpam-1783	407	8	ideal	ideal	ADJ
ejpam-1783	407	9	topological	topological	ADJ
ejpam-1783	407	10	spaces	space	NOUN
ejpam-1783	407	11	,	,	PUNCT
ejpam-1783	407	12	the	the	DET
ejpam-1783	407	13	arabian	arabian	ADJ
ejpam-1783	407	14	journal	journal	NOUN
ejpam-1783	407	15	for	for	ADP
ejpam-1783	407	16	science	science	NOUN
ejpam-1783	407	17	and	and	CCONJ
ejpam-1783	407	18	engineering	engineering	NOUN
ejpam-1783	407	19	,	,	PUNCT
ejpam-1783	407	20	34(1a	34(1a	NUM
ejpam-1783	407	21	)	)	PUNCT
ejpam-1783	407	22	,	,	PUNCT
ejpam-1783	407	23	165	165	NUM
ejpam-1783	407	24	-	-	SYM
ejpam-1783	407	25	177	177	NUM
ejpam-1783	407	26	.	.	PUNCT
ejpam-1783	407	27	2009	2009	NUM
ejpam-1783	407	28	.	.	PUNCT
ejpam-1783	408	1	[	[	X
ejpam-1783	408	2	4	4	X
ejpam-1783	408	3	]	]	X
ejpam-1783	408	4	e.	e.	PROPN
ejpam-1783	408	5	hatir	hatir	PROPN
ejpam-1783	408	6	and	and	CCONJ
ejpam-1783	408	7	t.	t.	PROPN
ejpam-1783	408	8	noiri	noiri	PROPN
ejpam-1783	408	9	.	.	PUNCT
ejpam-1783	409	1	on	on	ADP
ejpam-1783	409	2	decompositions	decomposition	NOUN
ejpam-1783	409	3	of	of	ADP
ejpam-1783	409	4	continuity	continuity	NOUN
ejpam-1783	409	5	via	via	ADP
ejpam-1783	409	6	idealization	idealization	NOUN
ejpam-1783	409	7	,	,	PUNCT
ejpam-1783	409	8	acta	acta	PROPN
ejpam-1783	409	9	mathematica	mathematica	PROPN
ejpam-1783	409	10	hungarica	hungarica	PROPN
ejpam-1783	409	11	,	,	PUNCT
ejpam-1783	409	12	96	96	NUM
ejpam-1783	409	13	,	,	PUNCT
ejpam-1783	409	14	341	341	NUM
ejpam-1783	409	15	-	-	SYM
ejpam-1783	409	16	349	349	NUM
ejpam-1783	409	17	.	.	PUNCT
ejpam-1783	409	18	2002	2002	NUM
ejpam-1783	409	19	.	.	PUNCT
ejpam-1783	410	1	[	[	X
ejpam-1783	410	2	5	5	X
ejpam-1783	410	3	]	]	PUNCT
ejpam-1783	410	4	e.	e.	PROPN
ejpam-1783	410	5	hatir	hatir	PROPN
ejpam-1783	410	6	and	and	CCONJ
ejpam-1783	410	7	t.	t.	PROPN
ejpam-1783	410	8	noiri	noiri	PROPN
ejpam-1783	410	9	.	.	PUNCT
ejpam-1783	411	1	decomposition	decomposition	NOUN
ejpam-1783	411	2	of	of	ADP
ejpam-1783	411	3	continuity	continuity	NOUN
ejpam-1783	411	4	and	and	CCONJ
ejpam-1783	411	5	complete	complete	ADJ
ejpam-1783	411	6	continuity	continuity	NOUN
ejpam-1783	411	7	,	,	PUNCT
ejpam-1783	411	8	acta	acta	PROPN
ejpam-1783	411	9	mathematica	mathematica	PROPN
ejpam-1783	411	10	hungarica	hungarica	PROPN
ejpam-1783	411	11	,	,	PUNCT
ejpam-1783	411	12	113(4	113(4	NUM
ejpam-1783	411	13	)	)	PUNCT
ejpam-1783	411	14	,	,	PUNCT
ejpam-1783	411	15	281	281	NUM
ejpam-1783	411	16	-	-	SYM
ejpam-1783	411	17	287	287	NUM
ejpam-1783	411	18	.	.	PUNCT
ejpam-1783	412	1	2006	2006	NUM
ejpam-1783	412	2	.	.	PUNCT
ejpam-1783	413	1	[	[	X
ejpam-1783	413	2	6	6	NUM
ejpam-1783	413	3	]	]	PUNCT
ejpam-1783	413	4	e.	e.	PROPN
ejpam-1783	413	5	hayashi	hayashi	PROPN
ejpam-1783	413	6	.	.	PUNCT
ejpam-1783	414	1	topologies	topology	NOUN
ejpam-1783	414	2	defined	define	VERB
ejpam-1783	414	3	by	by	ADP
ejpam-1783	414	4	local	local	ADJ
ejpam-1783	414	5	properties	property	NOUN
ejpam-1783	414	6	,	,	PUNCT
ejpam-1783	414	7	mathematische	mathematische	NOUN
ejpam-1783	414	8	annalen	annalen	PROPN
ejpam-1783	414	9	,	,	PUNCT
ejpam-1783	414	10	156	156	NUM
ejpam-1783	414	11	,	,	PUNCT
ejpam-1783	414	12	205215	205215	NUM
ejpam-1783	414	13	.	.	PUNCT
ejpam-1783	414	14	1964	1964	NUM
ejpam-1783	414	15	.	.	PUNCT
ejpam-1783	415	1	[	[	X
ejpam-1783	415	2	7	7	X
ejpam-1783	415	3	]	]	X
ejpam-1783	415	4	d.	d.	PROPN
ejpam-1783	415	5	janković	janković	PROPN
ejpam-1783	415	6	and	and	CCONJ
ejpam-1783	415	7	t.	t.	PROPN
ejpam-1783	415	8	r.	r.	PROPN
ejpam-1783	415	9	hamlett	hamlett	PROPN
ejpam-1783	415	10	.	.	PUNCT
ejpam-1783	416	1	new	new	ADJ
ejpam-1783	416	2	topologies	topology	NOUN
ejpam-1783	416	3	from	from	ADP
ejpam-1783	416	4	old	old	ADJ
ejpam-1783	416	5	via	via	ADP
ejpam-1783	416	6	ideals	ideal	NOUN
ejpam-1783	416	7	,	,	PUNCT
ejpam-1783	416	8	american	american	PROPN
ejpam-1783	416	9	mathematical	mathematical	PROPN
ejpam-1783	416	10	monthly	monthly	ADV
ejpam-1783	416	11	,	,	PUNCT
ejpam-1783	416	12	97	97	NUM
ejpam-1783	416	13	,	,	PUNCT
ejpam-1783	416	14	295	295	NUM
ejpam-1783	416	15	-	-	SYM
ejpam-1783	416	16	310	310	NUM
ejpam-1783	416	17	.	.	NOUN
ejpam-1783	416	18	1990	1990	NUM
ejpam-1783	416	19	.	.	PUNCT
ejpam-1783	417	1	[	[	X
ejpam-1783	417	2	8	8	X
ejpam-1783	417	3	]	]	PUNCT
ejpam-1783	417	4	k.	k.	PROPN
ejpam-1783	417	5	kuratowski	kuratowski	PROPN
ejpam-1783	417	6	.	.	PUNCT
ejpam-1783	418	1	topology	topology	PROPN
ejpam-1783	418	2	,	,	PUNCT
ejpam-1783	418	3	vol.1	vol.1	PROPN
ejpam-1783	418	4	,	,	PUNCT
ejpam-1783	418	5	new	new	PROPN
ejpam-1783	418	6	york	york	PROPN
ejpam-1783	418	7	:	:	PUNCT
ejpam-1783	418	8	academic	academic	ADJ
ejpam-1783	418	9	press	press	NOUN
ejpam-1783	418	10	,	,	PUNCT
ejpam-1783	418	11	1966	1966	NUM
ejpam-1783	418	12	.	.	PUNCT
ejpam-1783	419	1	references	reference	NOUN
ejpam-1783	419	2	362	362	NUM
ejpam-1783	420	1	[	[	X
ejpam-1783	420	2	9	9	NUM
ejpam-1783	420	3	]	]	PUNCT
ejpam-1783	420	4	a.	a.	NOUN
ejpam-1783	420	5	s.	s.	PROPN
ejpam-1783	420	6	mashhour	mashhour	PROPN
ejpam-1783	420	7	,	,	PUNCT
ejpam-1783	420	8	m.	m.	PROPN
ejpam-1783	420	9	e.	e.	PROPN
ejpam-1783	420	10	abd	abd	PROPN
ejpam-1783	421	1	el	el	PROPN
ejpam-1783	421	2	-	-	PROPN
ejpam-1783	421	3	monsef	monsef	ADJ
ejpam-1783	421	4	,	,	PUNCT
ejpam-1783	421	5	and	and	CCONJ
ejpam-1783	421	6	s.	s.	PROPN
ejpam-1783	421	7	n.	n.	PROPN
ejpam-1783	421	8	el	el	PROPN
ejpam-1783	421	9	-	-	PROPN
ejpam-1783	421	10	deeb	deeb	PROPN
ejpam-1783	421	11	.	.	PUNCT
ejpam-1783	422	1	on	on	ADP
ejpam-1783	422	2	precontinuous	precontinuous	ADJ
ejpam-1783	422	3	and	and	CCONJ
ejpam-1783	422	4	weak	weak	ADJ
ejpam-1783	422	5	precontinuous	precontinuous	ADJ
ejpam-1783	422	6	mappings	mapping	NOUN
ejpam-1783	422	7	,	,	PUNCT
ejpam-1783	422	8	proceedings	proceeding	NOUN
ejpam-1783	422	9	of	of	ADP
ejpam-1783	422	10	the	the	DET
ejpam-1783	422	11	mathematical	mathematical	ADJ
ejpam-1783	422	12	and	and	CCONJ
ejpam-1783	422	13	physical	physical	ADJ
ejpam-1783	422	14	society	society	NOUN
ejpam-1783	422	15	of	of	ADP
ejpam-1783	422	16	egypt	egypt	PROPN
ejpam-1783	422	17	,	,	PUNCT
ejpam-1783	422	18	53	53	NUM
ejpam-1783	422	19	,	,	PUNCT
ejpam-1783	422	20	47	47	NUM
ejpam-1783	422	21	-	-	SYM
ejpam-1783	422	22	53	53	NUM
ejpam-1783	422	23	.	.	NUM
ejpam-1783	422	24	1982	1982	NUM
ejpam-1783	422	25	.	.	PUNCT
ejpam-1783	423	1	[	[	X
ejpam-1783	423	2	10	10	NUM
ejpam-1783	423	3	]	]	PUNCT
ejpam-1783	423	4	a.	a.	NOUN
ejpam-1783	423	5	s.	s.	PROPN
ejpam-1783	423	6	mashhour	mashhour	PROPN
ejpam-1783	423	7	,	,	PUNCT
ejpam-1783	423	8	i.	i.	PROPN
ejpam-1783	423	9	a.	a.	PROPN
ejpam-1783	423	10	hasanein	hasanein	PROPN
ejpam-1783	423	11	,	,	PUNCT
ejpam-1783	423	12	and	and	CCONJ
ejpam-1783	423	13	s.	s.	PROPN
ejpam-1783	423	14	n.	n.	PROPN
ejpam-1783	423	15	el	el	PROPN
ejpam-1783	423	16	-	-	PROPN
ejpam-1783	423	17	deeb	deeb	PROPN
ejpam-1783	423	18	.	.	PUNCT
ejpam-1783	424	1	α	α	X
ejpam-1783	424	2	-	-	ADJ
ejpam-1783	424	3	continuous	continuous	ADJ
ejpam-1783	424	4	and	and	CCONJ
ejpam-1783	424	5	α	α	NOUN
ejpam-1783	424	6	-	-	ADJ
ejpam-1783	424	7	open	open	ADJ
ejpam-1783	424	8	mappings	mapping	NOUN
ejpam-1783	424	9	,	,	PUNCT
ejpam-1783	424	10	acta	acta	PROPN
ejpam-1783	424	11	mathematica	mathematica	PROPN
ejpam-1783	424	12	hungarica	hungarica	PROPN
ejpam-1783	424	13	,	,	PUNCT
ejpam-1783	424	14	41	41	NUM
ejpam-1783	424	15	,	,	PUNCT
ejpam-1783	424	16	213	213	NUM
ejpam-1783	424	17	-	-	SYM
ejpam-1783	424	18	218	218	NUM
ejpam-1783	424	19	.	.	PUNCT
ejpam-1783	425	1	1983	1983	NUM
ejpam-1783	425	2	.	.	PUNCT
ejpam-1783	426	1	[	[	X
ejpam-1783	426	2	11	11	NUM
ejpam-1783	426	3	]	]	PUNCT
ejpam-1783	426	4	s.	s.	PROPN
ejpam-1783	426	5	raychaudhuri	raychaudhuri	PROPN
ejpam-1783	426	6	and	and	CCONJ
ejpam-1783	426	7	m.	m.	PROPN
ejpam-1783	426	8	n.	n.	PROPN
ejpam-1783	426	9	mukherjee	mukherjee	PROPN
ejpam-1783	426	10	.	.	PUNCT
ejpam-1783	427	1	on	on	ADP
ejpam-1783	427	2	δ	δ	PROPN
ejpam-1783	427	3	-	-	PUNCT
ejpam-1783	427	4	almost	almost	ADV
ejpam-1783	427	5	continuity	continuity	NOUN
ejpam-1783	427	6	and	and	CCONJ
ejpam-1783	427	7	δ	δ	NOUN
ejpam-1783	427	8	-	-	PUNCT
ejpam-1783	427	9	preopen	preopen	ADJ
ejpam-1783	427	10	sets	set	NOUN
ejpam-1783	427	11	,	,	PUNCT
ejpam-1783	427	12	bulletin	bulletin	NOUN
ejpam-1783	427	13	of	of	ADP
ejpam-1783	427	14	the	the	DET
ejpam-1783	427	15	institude	institude	NOUN
ejpam-1783	427	16	of	of	ADP
ejpam-1783	427	17	mathematics	mathematic	NOUN
ejpam-1783	427	18	,	,	PUNCT
ejpam-1783	427	19	academia	academia	PROPN
ejpam-1783	427	20	sinica	sinica	PROPN
ejpam-1783	427	21	,	,	PUNCT
ejpam-1783	427	22	2(4	2(4	NUM
ejpam-1783	427	23	)	)	PUNCT
ejpam-1783	427	24	,	,	PUNCT
ejpam-1783	427	25	357	357	NUM
ejpam-1783	427	26	-	-	SYM
ejpam-1783	427	27	366	366	NUM
ejpam-1783	427	28	.	.	PUNCT
ejpam-1783	427	29	1993	1993	NUM
ejpam-1783	427	30	.	.	PUNCT
ejpam-1783	428	1	[	[	X
ejpam-1783	428	2	12	12	NUM
ejpam-1783	428	3	]	]	X
ejpam-1783	428	4	n.	n.	NOUN
ejpam-1783	428	5	v.	v.	ADP
ejpam-1783	428	6	velićko	velićko	PROPN
ejpam-1783	428	7	.	.	PUNCT
ejpam-1783	429	1	h	h	NOUN
ejpam-1783	429	2	-	-	PUNCT
ejpam-1783	429	3	closed	close	VERB
ejpam-1783	429	4	topological	topological	ADJ
ejpam-1783	429	5	spaces	space	NOUN
ejpam-1783	429	6	,	,	PUNCT
ejpam-1783	429	7	american	american	PROPN
ejpam-1783	429	8	mathematical	mathematical	ADJ
ejpam-1783	429	9	society	society	NOUN
ejpam-1783	429	10	translation	translation	NOUN
ejpam-1783	429	11	,	,	PUNCT
ejpam-1783	429	12	78(2	78(2	PROPN
ejpam-1783	429	13	)	)	PUNCT
ejpam-1783	429	14	,	,	PUNCT
ejpam-1783	429	15	103	103	NUM
ejpam-1783	429	16	-	-	SYM
ejpam-1783	429	17	118	118	NUM
ejpam-1783	429	18	.	.	PUNCT
ejpam-1783	429	19	1968	1968	NUM
ejpam-1783	429	20	.	.	PUNCT
ejpam-1783	430	1	[	[	X
ejpam-1783	430	2	13	13	NUM
ejpam-1783	430	3	]	]	X
ejpam-1783	430	4	y.	y.	NOUN
ejpam-1783	430	5	yazlık	yazlık	PROPN
ejpam-1783	430	6	.	.	PUNCT
ejpam-1783	431	1	δβ∗i	δβ∗i	NOUN
ejpam-1783	431	2	-open	-open	NOUN
ejpam-1783	431	3	sets	set	NOUN
ejpam-1783	431	4	and	and	CCONJ
ejpam-1783	431	5	decomposition	decomposition	NOUN
ejpam-1783	431	6	of	of	ADP
ejpam-1783	431	7	continuity	continuity	NOUN
ejpam-1783	431	8	in	in	ADP
ejpam-1783	431	9	ideal	ideal	ADJ
ejpam-1783	431	10	topological	topological	ADJ
ejpam-1783	431	11	spaces	space	NOUN
ejpam-1783	431	12	,	,	PUNCT
ejpam-1783	431	13	msc	msc	PROPN
ejpam-1783	431	14	thesis	thesis	PROPN
ejpam-1783	431	15	,	,	PUNCT
ejpam-1783	431	16	selcuk	selcuk	PROPN
ejpam-1783	431	17	university	university	NOUN
ejpam-1783	431	18	,	,	PUNCT
ejpam-1783	431	19	2009	2009	NUM
ejpam-1783	432	1	.	.	PUNCT
ejpam-1783	433	1	[	[	X
ejpam-1783	433	2	14	14	NUM
ejpam-1783	433	3	]	]	X
ejpam-1783	433	4	s.	s.	PROPN
ejpam-1783	433	5	yuksel	yuksel	PROPN
ejpam-1783	433	6	,	,	PUNCT
ejpam-1783	433	7	a.	a.	NOUN
ejpam-1783	433	8	acikgöz	acikgöz	NOUN
ejpam-1783	433	9	,	,	PUNCT
ejpam-1783	433	10	and	and	CCONJ
ejpam-1783	433	11	t.	t.	PROPN
ejpam-1783	433	12	noiri	noiri	PROPN
ejpam-1783	433	13	.	.	PUNCT
ejpam-1783	434	1	on	on	ADP
ejpam-1783	434	2	δ	δ	PROPN
ejpam-1783	434	3	−	−	PROPN
ejpam-1783	435	1	i	i	PRON
ejpam-1783	435	2	-continuous	-continuous	ADJ
ejpam-1783	435	3	functions	function	NOUN
ejpam-1783	435	4	,	,	PUNCT
ejpam-1783	435	5	turkish	turkish	ADJ
ejpam-1783	435	6	journal	journal	NOUN
ejpam-1783	435	7	of	of	ADP
ejpam-1783	435	8	mathematics	mathematic	NOUN
ejpam-1783	435	9	,	,	PUNCT
ejpam-1783	435	10	29	29	NUM
ejpam-1783	435	11	,	,	PUNCT
ejpam-1783	435	12	39	39	NUM
ejpam-1783	435	13	-	-	SYM
ejpam-1783	435	14	51	51	NUM
ejpam-1783	435	15	.	.	PUNCT
ejpam-1783	435	16	2005	2005	NUM
ejpam-1783	435	17	.	.	PUNCT