id	sid	tid	token	lemma	pos
ejpam-1068	1	1	5_roy.dvi	5_roy.dvi	NUM
ejpam-1068	1	2	european	european	ADJ
ejpam-1068	1	3	journal	journal	PROPN
ejpam-1068	1	4	of	of	ADP
ejpam-1068	1	5	pure	pure	ADJ
ejpam-1068	1	6	and	and	CCONJ
ejpam-1068	1	7	applied	apply	VERB
ejpam-1068	1	8	mathematics	mathematic	NOUN
ejpam-1068	1	9	vol	vol	NOUN
ejpam-1068	1	10	.	.	PROPN
ejpam-1068	2	1	6	6	NUM
ejpam-1068	2	2	,	,	PUNCT
ejpam-1068	2	3	no	no	INTJ
ejpam-1068	2	4	.	.	NOUN
ejpam-1068	2	5	1	1	NUM
ejpam-1068	2	6	,	,	PUNCT
ejpam-1068	2	7	2013	2013	NUM
ejpam-1068	2	8	,	,	PUNCT
ejpam-1068	2	9	44	44	NUM
ejpam-1068	2	10	-	-	SYM
ejpam-1068	2	11	52	52	NUM
ejpam-1068	2	12	issn	issn	PROPN
ejpam-1068	2	13	1307	1307	NUM
ejpam-1068	2	14	-	-	SYM
ejpam-1068	2	15	5543	5543	NUM
ejpam-1068	2	16	–	–	PUNCT
ejpam-1068	3	1	www.ejpam.com	www.ejpam.com	X
ejpam-1068	3	2	separation	separation	NOUN
ejpam-1068	3	3	axioms	axiom	VERB
ejpam-1068	3	4	on	on	ADP
ejpam-1068	3	5	topological	topological	ADJ
ejpam-1068	3	6	spaces	space	NOUN
ejpam-1068	3	7	a	a	DET
ejpam-1068	3	8	unified	unified	ADJ
ejpam-1068	3	9	version	version	NOUN
ejpam-1068	3	10	bishwambhar	bishwambhar	NOUN
ejpam-1068	3	11	roy1,∗	roy1,∗	NOUN
ejpam-1068	3	12	,	,	PUNCT
ejpam-1068	3	13	ritu	ritu	PROPN
ejpam-1068	3	14	sen2	sen2	PROPN
ejpam-1068	3	15	,	,	PUNCT
ejpam-1068	3	16	takashi	takashi	PROPN
ejpam-1068	3	17	noiri3	noiri3	PROPN
ejpam-1068	4	1	1	1	NUM
ejpam-1068	4	2	department	department	NOUN
ejpam-1068	4	3	of	of	ADP
ejpam-1068	4	4	mathematics	mathematic	NOUN
ejpam-1068	4	5	,	,	PUNCT
ejpam-1068	4	6	women	woman	NOUN
ejpam-1068	4	7	’s	’s	PART
ejpam-1068	4	8	christian	christian	PROPN
ejpam-1068	4	9	college	college	NOUN
ejpam-1068	4	10	,	,	PUNCT
ejpam-1068	4	11	6	6	NUM
ejpam-1068	4	12	,	,	PUNCT
ejpam-1068	4	13	greek	greek	ADJ
ejpam-1068	4	14	church	church	NOUN
ejpam-1068	4	15	row	row	NOUN
ejpam-1068	4	16	,	,	PUNCT
ejpam-1068	4	17	kolkata-700	kolkata-700	PROPN
ejpam-1068	4	18	026	026	NUM
ejpam-1068	4	19	,	,	PUNCT
ejpam-1068	4	20	india	india	PROPN
ejpam-1068	4	21	2	2	NUM
ejpam-1068	4	22	department	department	NOUN
ejpam-1068	4	23	of	of	ADP
ejpam-1068	4	24	mathematics	mathematic	NOUN
ejpam-1068	4	25	,	,	PUNCT
ejpam-1068	4	26	s.	s.	PROPN
ejpam-1068	4	27	a.	a.	PROPN
ejpam-1068	4	28	jaipuria	jaipuria	PROPN
ejpam-1068	4	29	college	college	PROPN
ejpam-1068	4	30	,	,	PUNCT
ejpam-1068	4	31	10	10	NUM
ejpam-1068	4	32	,	,	PUNCT
ejpam-1068	4	33	raja	raja	PROPN
ejpam-1068	4	34	naba	naba	PROPN
ejpam-1068	4	35	krishna	krishna	PROPN
ejpam-1068	4	36	street	street	PROPN
ejpam-1068	4	37	,	,	PUNCT
ejpam-1068	4	38	kolkata	kolkata	VERB
ejpam-1068	4	39	700	700	NUM
ejpam-1068	4	40	005	005	NUM
ejpam-1068	4	41	,	,	PUNCT
ejpam-1068	4	42	india	india	PROPN
ejpam-1068	4	43	3	3	NUM
ejpam-1068	4	44	2949	2949	NUM
ejpam-1068	4	45	-	-	SYM
ejpam-1068	4	46	1	1	NUM
ejpam-1068	4	47	shiokita	shiokita	NOUN
ejpam-1068	4	48	-	-	PUNCT
ejpam-1068	4	49	cho	cho	ADJ
ejpam-1068	4	50	,	,	PUNCT
ejpam-1068	4	51	hinagu	hinagu	ADJ
ejpam-1068	4	52	,	,	PUNCT
ejpam-1068	4	53	yatsushiro	yatsushiro	PROPN
ejpam-1068	4	54	-	-	PUNCT
ejpam-1068	4	55	shi	shi	PROPN
ejpam-1068	4	56	,	,	PUNCT
ejpam-1068	4	57	kumamoto	kumamoto	PROPN
ejpam-1068	4	58	-	-	PUNCT
ejpam-1068	4	59	ken	ken	PROPN
ejpam-1068	4	60	,	,	PUNCT
ejpam-1068	4	61	japan	japan	PROPN
ejpam-1068	4	62	abstract	abstract	PROPN
ejpam-1068	4	63	.	.	PUNCT
ejpam-1068	5	1	in	in	ADP
ejpam-1068	5	2	this	this	DET
ejpam-1068	5	3	paper	paper	NOUN
ejpam-1068	5	4	,	,	PUNCT
ejpam-1068	5	5	a	a	DET
ejpam-1068	5	6	new	new	ADJ
ejpam-1068	5	7	kind	kind	NOUN
ejpam-1068	5	8	of	of	ADP
ejpam-1068	5	9	sets	set	NOUN
ejpam-1068	5	10	called	call	VERB
ejpam-1068	5	11	generalized	generalized	ADJ
ejpam-1068	5	12	ψ	ψ	NOUN
ejpam-1068	5	13	-	-	ADJ
ejpam-1068	5	14	closed	closed	ADJ
ejpam-1068	5	15	(	(	PUNCT
ejpam-1068	5	16	briefly	briefly	ADV
ejpam-1068	5	17	gψ	gψ	ADV
ejpam-1068	5	18	-	-	PUNCT
ejpam-1068	5	19	closed	closed	ADJ
ejpam-1068	5	20	)	)	PUNCT
ejpam-1068	5	21	sets	set	NOUN
ejpam-1068	5	22	are	be	AUX
ejpam-1068	5	23	introduced	introduce	VERB
ejpam-1068	5	24	and	and	CCONJ
ejpam-1068	5	25	studied	study	VERB
ejpam-1068	5	26	in	in	ADP
ejpam-1068	5	27	a	a	DET
ejpam-1068	5	28	topological	topological	ADJ
ejpam-1068	5	29	space	space	NOUN
ejpam-1068	5	30	by	by	ADP
ejpam-1068	5	31	using	use	VERB
ejpam-1068	5	32	the	the	DET
ejpam-1068	5	33	concept	concept	NOUN
ejpam-1068	5	34	of	of	ADP
ejpam-1068	5	35	operation	operation	NOUN
ejpam-1068	5	36	on	on	ADP
ejpam-1068	5	37	topological	topological	ADJ
ejpam-1068	5	38	space	space	NOUN
ejpam-1068	5	39	.	.	PUNCT
ejpam-1068	6	1	the	the	DET
ejpam-1068	6	2	class	class	NOUN
ejpam-1068	6	3	of	of	ADP
ejpam-1068	6	4	all	all	DET
ejpam-1068	6	5	gψ	gψ	ADJ
ejpam-1068	6	6	-	-	PUNCT
ejpam-1068	6	7	closed	closed	ADJ
ejpam-1068	6	8	sets	set	NOUN
ejpam-1068	6	9	is	be	AUX
ejpam-1068	6	10	strictly	strictly	ADV
ejpam-1068	6	11	larger	large	ADJ
ejpam-1068	6	12	than	than	ADP
ejpam-1068	6	13	the	the	DET
ejpam-1068	6	14	class	class	NOUN
ejpam-1068	6	15	of	of	ADP
ejpam-1068	6	16	all	all	DET
ejpam-1068	6	17	ψ	ψ	ADJ
ejpam-1068	6	18	-	-	ADJ
ejpam-1068	6	19	closed	closed	ADJ
ejpam-1068	6	20	sets	set	NOUN
ejpam-1068	6	21	.	.	PUNCT
ejpam-1068	7	1	some	some	PRON
ejpam-1068	7	2	of	of	ADP
ejpam-1068	7	3	their	their	PRON
ejpam-1068	7	4	properties	property	NOUN
ejpam-1068	7	5	are	be	AUX
ejpam-1068	7	6	investigated	investigate	VERB
ejpam-1068	7	7	here	here	ADV
ejpam-1068	7	8	.	.	PUNCT
ejpam-1068	8	1	finally	finally	ADV
ejpam-1068	8	2	,	,	PUNCT
ejpam-1068	8	3	some	some	DET
ejpam-1068	8	4	characterizations	characterization	NOUN
ejpam-1068	8	5	of	of	ADP
ejpam-1068	8	6	ψg	ψg	NOUN
ejpam-1068	8	7	-regular	-regular	PROPN
ejpam-1068	8	8	and	and	CCONJ
ejpam-1068	8	9	ψg	ψg	NOUN
ejpam-1068	8	10	-normal	-normal	ADJ
ejpam-1068	8	11	spaces	space	NOUN
ejpam-1068	8	12	have	have	AUX
ejpam-1068	8	13	been	be	AUX
ejpam-1068	8	14	given	give	VERB
ejpam-1068	8	15	.	.	PUNCT
ejpam-1068	9	1	2010	2010	NUM
ejpam-1068	9	2	mathematics	mathematic	NOUN
ejpam-1068	9	3	subject	subject	NOUN
ejpam-1068	9	4	classifications	classification	NOUN
ejpam-1068	9	5	:	:	PUNCT
ejpam-1068	9	6	54d10	54d10	NUM
ejpam-1068	9	7	,	,	PUNCT
ejpam-1068	9	8	54d15	54d15	NUM
ejpam-1068	9	9	,	,	PUNCT
ejpam-1068	9	10	54c08	54c08	NUM
ejpam-1068	9	11	,	,	PUNCT
ejpam-1068	9	12	54c10	54c10	NUM
ejpam-1068	9	13	key	key	ADJ
ejpam-1068	9	14	words	word	NOUN
ejpam-1068	9	15	and	and	CCONJ
ejpam-1068	9	16	phrases	phrase	NOUN
ejpam-1068	9	17	:	:	PUNCT
ejpam-1068	9	18	ψ	ψ	X
ejpam-1068	9	19	-	-	ADJ
ejpam-1068	9	20	open	open	ADJ
ejpam-1068	9	21	set	set	NOUN
ejpam-1068	9	22	,	,	PUNCT
ejpam-1068	9	23	gψ	gψ	ADJ
ejpam-1068	9	24	-	-	PUNCT
ejpam-1068	9	25	closed	closed	ADJ
ejpam-1068	9	26	set	set	NOUN
ejpam-1068	9	27	,	,	PUNCT
ejpam-1068	9	28	ψg	ψg	NOUN
ejpam-1068	9	29	-regular	-regular	PROPN
ejpam-1068	9	30	,	,	PUNCT
ejpam-1068	9	31	ψg	ψg	X
ejpam-1068	9	32	-normal	-normal	ADJ
ejpam-1068	9	33	space	space	NOUN
ejpam-1068	9	34	1	1	NUM
ejpam-1068	9	35	.	.	PUNCT
ejpam-1068	10	1	introduction	introduction	NOUN
ejpam-1068	10	2	it	it	PRON
ejpam-1068	10	3	is	be	AUX
ejpam-1068	10	4	observed	observe	VERB
ejpam-1068	10	5	from	from	ADP
ejpam-1068	10	6	literature	literature	NOUN
ejpam-1068	10	7	that	that	SCONJ
ejpam-1068	10	8	there	there	PRON
ejpam-1068	10	9	has	have	AUX
ejpam-1068	10	10	been	be	AUX
ejpam-1068	10	11	a	a	DET
ejpam-1068	10	12	considerable	considerable	ADJ
ejpam-1068	10	13	work	work	NOUN
ejpam-1068	10	14	on	on	ADP
ejpam-1068	10	15	different	different	ADJ
ejpam-1068	10	16	relatively	relatively	ADV
ejpam-1068	10	17	weak	weak	ADJ
ejpam-1068	10	18	forms	form	NOUN
ejpam-1068	10	19	of	of	ADP
ejpam-1068	10	20	separation	separation	NOUN
ejpam-1068	10	21	axioms	axiom	NOUN
ejpam-1068	10	22	,	,	PUNCT
ejpam-1068	10	23	like	like	ADP
ejpam-1068	10	24	regularity	regularity	NOUN
ejpam-1068	10	25	and	and	CCONJ
ejpam-1068	10	26	normality	normality	NOUN
ejpam-1068	10	27	axioms	axiom	NOUN
ejpam-1068	10	28	in	in	ADP
ejpam-1068	10	29	particular	particular	ADJ
ejpam-1068	10	30	;	;	PUNCT
ejpam-1068	10	31	several	several	ADJ
ejpam-1068	10	32	other	other	ADJ
ejpam-1068	10	33	neighbouring	neighbouring	ADJ
ejpam-1068	10	34	forms	form	NOUN
ejpam-1068	10	35	of	of	ADP
ejpam-1068	10	36	them	they	PRON
ejpam-1068	10	37	have	have	AUX
ejpam-1068	10	38	also	also	ADV
ejpam-1068	10	39	been	be	AUX
ejpam-1068	10	40	studied	study	VERB
ejpam-1068	10	41	in	in	ADP
ejpam-1068	10	42	many	many	ADJ
ejpam-1068	10	43	papers	paper	NOUN
ejpam-1068	10	44	.	.	PUNCT
ejpam-1068	11	1	for	for	ADP
ejpam-1068	11	2	instance	instance	NOUN
ejpam-1068	11	3	,	,	PUNCT
ejpam-1068	11	4	p	p	NOUN
ejpam-1068	11	5	-	-	PUNCT
ejpam-1068	11	6	regular	regular	ADJ
ejpam-1068	12	1	[	[	X
ejpam-1068	12	2	7	7	NUM
ejpam-1068	12	3	]	]	PUNCT
ejpam-1068	12	4	,	,	PUNCT
ejpam-1068	12	5	p	p	NOUN
ejpam-1068	12	6	-	-	PUNCT
ejpam-1068	12	7	normal	normal	ADJ
ejpam-1068	12	8	[	[	X
ejpam-1068	12	9	18	18	NUM
ejpam-1068	12	10	]	]	PUNCT
ejpam-1068	12	11	,	,	PUNCT
ejpam-1068	12	12	s	s	NOUN
ejpam-1068	12	13	-	-	ADJ
ejpam-1068	12	14	regular	regular	ADJ
ejpam-1068	13	1	[	[	X
ejpam-1068	13	2	10	10	NUM
ejpam-1068	13	3	]	]	PUNCT
ejpam-1068	13	4	,	,	PUNCT
ejpam-1068	13	5	s	s	NOUN
ejpam-1068	13	6	-	-	ADJ
ejpam-1068	13	7	normal	normal	ADJ
ejpam-1068	13	8	[	[	X
ejpam-1068	13	9	11	11	NUM
ejpam-1068	13	10	]	]	X
ejpam-1068	13	11	δp	δp	NOUN
ejpam-1068	13	12	-	-	ADJ
ejpam-1068	13	13	normal	normal	ADJ
ejpam-1068	13	14	[	[	X
ejpam-1068	13	15	6	6	NUM
ejpam-1068	13	16	]	]	PUNCT
ejpam-1068	13	17	,	,	PUNCT
ejpam-1068	13	18	β	β	X
ejpam-1068	13	19	-regular	-regular	ADJ
ejpam-1068	14	1	[	[	X
ejpam-1068	14	2	1	1	NUM
ejpam-1068	14	3	]	]	PUNCT
ejpam-1068	14	4	and	and	CCONJ
ejpam-1068	14	5	β	β	X
ejpam-1068	14	6	-normal	-normal	ADJ
ejpam-1068	14	7	[	[	X
ejpam-1068	14	8	12	12	NUM
ejpam-1068	14	9	]	]	PUNCT
ejpam-1068	14	10	are	be	AUX
ejpam-1068	14	11	some	some	PRON
ejpam-1068	14	12	of	of	ADP
ejpam-1068	14	13	the	the	DET
ejpam-1068	14	14	variant	variant	ADJ
ejpam-1068	14	15	forms	form	NOUN
ejpam-1068	14	16	of	of	ADP
ejpam-1068	14	17	regularity	regularity	NOUN
ejpam-1068	14	18	and	and	CCONJ
ejpam-1068	14	19	normality	normality	NOUN
ejpam-1068	14	20	properties	property	NOUN
ejpam-1068	14	21	,	,	PUNCT
ejpam-1068	14	22	that	that	PRON
ejpam-1068	14	23	have	have	AUX
ejpam-1068	14	24	been	be	AUX
ejpam-1068	14	25	investigated	investigate	VERB
ejpam-1068	14	26	by	by	ADP
ejpam-1068	14	27	different	different	ADJ
ejpam-1068	14	28	researchers	researcher	NOUN
ejpam-1068	14	29	as	as	ADP
ejpam-1068	14	30	separate	separate	ADJ
ejpam-1068	14	31	entities	entity	NOUN
ejpam-1068	14	32	.	.	PUNCT
ejpam-1068	15	1	recently	recently	ADV
ejpam-1068	15	2	,	,	PUNCT
ejpam-1068	15	3	noiri	noiri	PROPN
ejpam-1068	15	4	and	and	CCONJ
ejpam-1068	15	5	roy	roy	PROPN
ejpam-1068	15	6	[	[	X
ejpam-1068	15	7	15	15	NUM
ejpam-1068	15	8	]	]	PUNCT
ejpam-1068	15	9	has	have	AUX
ejpam-1068	15	10	also	also	ADV
ejpam-1068	15	11	introduced	introduce	VERB
ejpam-1068	15	12	the	the	DET
ejpam-1068	15	13	concept	concept	NOUN
ejpam-1068	15	14	of	of	ADP
ejpam-1068	15	15	µg	µg	NOUN
ejpam-1068	15	16	-	-	PUNCT
ejpam-1068	15	17	regularity	regularity	NOUN
ejpam-1068	15	18	and	and	CCONJ
ejpam-1068	15	19	µg	µg	NOUN
ejpam-1068	15	20	-	-	PUNCT
ejpam-1068	15	21	normality	normality	NOUN
ejpam-1068	15	22	by	by	ADP
ejpam-1068	15	23	using	use	VERB
ejpam-1068	15	24	the	the	DET
ejpam-1068	15	25	concept	concept	NOUN
ejpam-1068	15	26	of	of	ADP
ejpam-1068	15	27	generalized	generalized	ADJ
ejpam-1068	15	28	topology	topology	NOUN
ejpam-1068	15	29	towards	towards	ADP
ejpam-1068	15	30	such	such	DET
ejpam-1068	15	31	an	an	DET
ejpam-1068	15	32	unified	unified	ADJ
ejpam-1068	15	33	version	version	NOUN
ejpam-1068	15	34	.	.	PUNCT
ejpam-1068	16	1	as	as	SCONJ
ejpam-1068	16	2	can	can	AUX
ejpam-1068	16	3	be	be	AUX
ejpam-1068	16	4	observed	observe	VERB
ejpam-1068	16	5	,	,	PUNCT
ejpam-1068	16	6	all	all	DET
ejpam-1068	16	7	these	these	DET
ejpam-1068	16	8	variations	variation	NOUN
ejpam-1068	16	9	have	have	AUX
ejpam-1068	16	10	been	be	AUX
ejpam-1068	16	11	effected	effect	VERB
ejpam-1068	16	12	by	by	ADP
ejpam-1068	16	13	using	use	VERB
ejpam-1068	16	14	different	different	ADJ
ejpam-1068	16	15	types	type	NOUN
ejpam-1068	16	16	of	of	ADP
ejpam-1068	16	17	operators	operator	NOUN
ejpam-1068	16	18	like	like	ADP
ejpam-1068	16	19	int	int	NOUN
ejpam-1068	16	20	,	,	PUNCT
ejpam-1068	16	21	intcl	intcl	NOUN
ejpam-1068	16	22	,	,	PUNCT
ejpam-1068	16	23	intclδ	intclδ	NOUN
ejpam-1068	16	24	,	,	PUNCT
ejpam-1068	16	25	clint	clint	NOUN
ejpam-1068	16	26	,	,	PUNCT
ejpam-1068	16	27	intclint	intclint	NOUN
ejpam-1068	16	28	,	,	PUNCT
ejpam-1068	16	29	clintcl	clintcl	NOUN
ejpam-1068	16	30	,	,	PUNCT
ejpam-1068	16	31	where	where	SCONJ
ejpam-1068	16	32	int	int	NOUN
ejpam-1068	16	33	and	and	CCONJ
ejpam-1068	16	34	cl	cl	NOUN
ejpam-1068	16	35	respectively	respectively	ADV
ejpam-1068	16	36	stand	stand	VERB
ejpam-1068	16	37	for	for	ADP
ejpam-1068	16	38	interior	interior	ADJ
ejpam-1068	16	39	and	and	CCONJ
ejpam-1068	16	40	closure	closure	NOUN
ejpam-1068	16	41	operators	operator	NOUN
ejpam-1068	16	42	,	,	PUNCT
ejpam-1068	16	43	and	and	CCONJ
ejpam-1068	16	44	clδ	clδ	NOUN
ejpam-1068	16	45	denotes	denote	VERB
ejpam-1068	16	46	the	the	DET
ejpam-1068	16	47	δ	δ	PROPN
ejpam-1068	16	48	-	-	PUNCT
ejpam-1068	16	49	closure	closure	NOUN
ejpam-1068	16	50	operator	operator	NOUN
ejpam-1068	16	51	.	.	PUNCT
ejpam-1068	17	1	the	the	DET
ejpam-1068	17	2	concept	concept	NOUN
ejpam-1068	17	3	of	of	ADP
ejpam-1068	17	4	a	a	DET
ejpam-1068	17	5	generalized	generalized	ADJ
ejpam-1068	17	6	type	type	NOUN
ejpam-1068	17	7	of	of	ADP
ejpam-1068	17	8	operator	operator	NOUN
ejpam-1068	17	9	,	,	PUNCT
ejpam-1068	17	10	called	call	VERB
ejpam-1068	17	11	operation	operation	NOUN
ejpam-1068	17	12	on	on	ADP
ejpam-1068	17	13	the	the	DET
ejpam-1068	17	14	power	power	NOUN
ejpam-1068	17	15	set	set	NOUN
ejpam-1068	17	16	p	p	PROPN
ejpam-1068	17	17	(	(	PUNCT
ejpam-1068	17	18	x	x	NOUN
ejpam-1068	17	19	)	)	PUNCT
ejpam-1068	17	20	of	of	ADP
ejpam-1068	17	21	a	a	DET
ejpam-1068	17	22	topological	topological	ADJ
ejpam-1068	17	23	space	space	NOUN
ejpam-1068	17	24	(	(	PUNCT
ejpam-1068	17	25	x	x	X
ejpam-1068	17	26	,	,	PUNCT
ejpam-1068	17	27	τ	τ	X
ejpam-1068	17	28	)	)	PUNCT
ejpam-1068	17	29	was	be	AUX
ejpam-1068	17	30	introduced	introduce	VERB
ejpam-1068	17	31	by	by	ADP
ejpam-1068	17	32	[	[	X
ejpam-1068	17	33	3	3	NUM
ejpam-1068	17	34	]	]	PUNCT
ejpam-1068	17	35	.	.	PUNCT
ejpam-1068	18	1	it	it	PRON
ejpam-1068	18	2	turns	turn	VERB
ejpam-1068	18	3	out	out	ADP
ejpam-1068	18	4	from	from	ADP
ejpam-1068	18	5	the	the	DET
ejpam-1068	18	6	investigations	investigation	NOUN
ejpam-1068	18	7	that	that	PRON
ejpam-1068	18	8	by	by	ADP
ejpam-1068	18	9	judicious	judicious	ADJ
ejpam-1068	18	10	use	use	NOUN
ejpam-1068	18	11	of	of	ADP
ejpam-1068	18	12	the	the	DET
ejpam-1068	18	13	notion	notion	NOUN
ejpam-1068	18	14	of	of	ADP
ejpam-1068	18	15	’	'	PUNCT
ejpam-1068	18	16	operation	operation	NOUN
ejpam-1068	18	17	’	'	PUNCT
ejpam-1068	18	18	,	,	PUNCT
ejpam-1068	18	19	one	one	PRON
ejpam-1068	18	20	can	can	AUX
ejpam-1068	18	21	∗corresponding	∗corresponde	VERB
ejpam-1068	18	22	author	author	NOUN
ejpam-1068	18	23	.	.	PUNCT
ejpam-1068	19	1	email	email	NOUN
ejpam-1068	19	2	addresses	address	NOUN
ejpam-1068	19	3	:	:	PUNCT
ejpam-1068	19	4	bishwambhar_roy	bishwambhar_roy	X
ejpam-1068	19	5	�	�	NOUN
ejpam-1068	19	6	yahoo	yahoo	PROPN
ejpam-1068	19	7	.	.	PUNCT
ejpam-1068	20	1	o.in	o.in	PROPN
ejpam-1068	20	2	(	(	PUNCT
ejpam-1068	20	3	b.	b.	PROPN
ejpam-1068	20	4	roy	roy	PROPN
ejpam-1068	20	5	)	)	PUNCT
ejpam-1068	20	6	,	,	PUNCT
ejpam-1068	20	7	ritu_sen29	ritu_sen29	PROPN
ejpam-1068	20	8	�	�	PROPN
ejpam-1068	20	9	yahoo	yahoo	PROPN
ejpam-1068	20	10	.	.	PUNCT
ejpam-1068	21	1	o.in	o.in	PROPN
ejpam-1068	21	2	(	(	PUNCT
ejpam-1068	21	3	r.	r.	PROPN
ejpam-1068	21	4	sen	sen	PROPN
ejpam-1068	21	5	)	)	PUNCT
ejpam-1068	21	6	,	,	PUNCT
ejpam-1068	21	7	t.noiri	t.noiri	ADV
ejpam-1068	21	8	�	�	NOUN
ejpam-1068	21	9	nifty	nifty	ADJ
ejpam-1068	21	10	.	.	PUNCT
ejpam-1068	22	1	om	om	PROPN
ejpam-1068	22	2	(	(	PUNCT
ejpam-1068	22	3	t.	t.	PROPN
ejpam-1068	22	4	noiri	noiri	PROPN
ejpam-1068	22	5	)	)	PUNCT
ejpam-1068	22	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1068	23	1	44	44	NUM
ejpam-1068	23	2	c	c	X
ejpam-1068	23	3	©	©	PROPN
ejpam-1068	23	4	2013	2013	NUM
ejpam-1068	23	5	ejpam	ejpam	NOUN
ejpam-1068	23	6	all	all	DET
ejpam-1068	23	7	rights	right	NOUN
ejpam-1068	23	8	reserved	reserve	VERB
ejpam-1068	23	9	.	.	PUNCT
ejpam-1068	24	1	b.	b.	PROPN
ejpam-1068	24	2	roy	roy	PROPN
ejpam-1068	24	3	,	,	PUNCT
ejpam-1068	24	4	r.	r.	PROPN
ejpam-1068	24	5	sen	sen	PROPN
ejpam-1068	24	6	,	,	PUNCT
ejpam-1068	24	7	t.	t.	PROPN
ejpam-1068	24	8	noiri	noiri	PROPN
ejpam-1068	24	9	/	/	SYM
ejpam-1068	24	10	eur	eur	PROPN
ejpam-1068	24	11	.	.	PUNCT
ejpam-1068	25	1	j.	j.	PROPN
ejpam-1068	25	2	pure	pure	PROPN
ejpam-1068	25	3	appl	appl	PROPN
ejpam-1068	25	4	.	.	PROPN
ejpam-1068	25	5	math	math	PROPN
ejpam-1068	25	6	,	,	PUNCT
ejpam-1068	25	7	6	6	NUM
ejpam-1068	25	8	(	(	PUNCT
ejpam-1068	25	9	2013	2013	NUM
ejpam-1068	25	10	)	)	PUNCT
ejpam-1068	25	11	,	,	PUNCT
ejpam-1068	25	12	44	44	NUM
ejpam-1068	25	13	-	-	SYM
ejpam-1068	25	14	52	52	NUM
ejpam-1068	25	15	45	45	NUM
ejpam-1068	25	16	give	give	VERB
ejpam-1068	25	17	generalized	generalized	ADJ
ejpam-1068	25	18	definitions	definition	NOUN
ejpam-1068	25	19	of	of	ADP
ejpam-1068	25	20	regularity	regularity	NOUN
ejpam-1068	25	21	and	and	CCONJ
ejpam-1068	25	22	normality	normality	NOUN
ejpam-1068	25	23	axioms	axiom	NOUN
ejpam-1068	25	24	from	from	ADP
ejpam-1068	25	25	which	which	PRON
ejpam-1068	25	26	the	the	DET
ejpam-1068	25	27	definitions	definition	NOUN
ejpam-1068	25	28	of	of	ADP
ejpam-1068	25	29	different	different	ADJ
ejpam-1068	25	30	varied	varied	ADJ
ejpam-1068	25	31	forms	form	NOUN
ejpam-1068	25	32	of	of	ADP
ejpam-1068	25	33	such	such	ADJ
ejpam-1068	25	34	properties	property	NOUN
ejpam-1068	25	35	and	and	CCONJ
ejpam-1068	25	36	many	many	ADJ
ejpam-1068	25	37	known	know	VERB
ejpam-1068	25	38	results	result	NOUN
ejpam-1068	25	39	thereon	thereon	NOUN
ejpam-1068	25	40	follow	follow	VERB
ejpam-1068	25	41	as	as	ADP
ejpam-1068	25	42	particular	particular	ADJ
ejpam-1068	25	43	consequences	consequence	NOUN
ejpam-1068	25	44	.	.	PUNCT
ejpam-1068	26	1	2	2	X
ejpam-1068	26	2	.	.	X
ejpam-1068	26	3	main	main	ADJ
ejpam-1068	26	4	results	result	NOUN
ejpam-1068	26	5	2.1	2.1	NUM
ejpam-1068	26	6	.	.	PUNCT
ejpam-1068	27	1	properties	property	NOUN
ejpam-1068	27	2	of	of	ADP
ejpam-1068	27	3	gψ	gψ	ADV
ejpam-1068	27	4	-	-	PUNCT
ejpam-1068	27	5	closed	closed	ADJ
ejpam-1068	27	6	sets	set	NOUN
ejpam-1068	27	7	we	we	PRON
ejpam-1068	27	8	now	now	ADV
ejpam-1068	27	9	begin	begin	VERB
ejpam-1068	27	10	by	by	ADP
ejpam-1068	27	11	recalling	recall	VERB
ejpam-1068	27	12	a	a	DET
ejpam-1068	27	13	few	few	ADJ
ejpam-1068	27	14	definitions	definition	NOUN
ejpam-1068	27	15	and	and	CCONJ
ejpam-1068	27	16	observe	observe	VERB
ejpam-1068	27	17	that	that	SCONJ
ejpam-1068	27	18	many	many	ADJ
ejpam-1068	27	19	of	of	ADP
ejpam-1068	27	20	the	the	DET
ejpam-1068	27	21	existing	exist	VERB
ejpam-1068	27	22	relevant	relevant	ADJ
ejpam-1068	27	23	definitions	definition	NOUN
ejpam-1068	27	24	considered	consider	VERB
ejpam-1068	27	25	in	in	ADP
ejpam-1068	27	26	various	various	ADJ
ejpam-1068	27	27	papers	paper	NOUN
ejpam-1068	27	28	turn	turn	VERB
ejpam-1068	27	29	out	out	ADP
ejpam-1068	27	30	to	to	PART
ejpam-1068	27	31	be	be	AUX
ejpam-1068	27	32	special	special	ADJ
ejpam-1068	27	33	cases	case	NOUN
ejpam-1068	27	34	of	of	ADP
ejpam-1068	27	35	the	the	DET
ejpam-1068	27	36	ones	one	NOUN
ejpam-1068	27	37	given	give	VERB
ejpam-1068	27	38	below	below	ADV
ejpam-1068	27	39	.	.	PUNCT
ejpam-1068	28	1	definition	definition	NOUN
ejpam-1068	28	2	1	1	NUM
ejpam-1068	28	3	(	(	PUNCT
ejpam-1068	28	4	[	[	X
ejpam-1068	28	5	3	3	NUM
ejpam-1068	28	6	]	]	PUNCT
ejpam-1068	28	7	)	)	PUNCT
ejpam-1068	28	8	.	.	PUNCT
ejpam-1068	29	1	let	let	AUX
ejpam-1068	29	2	(	(	PUNCT
ejpam-1068	29	3	x	x	X
ejpam-1068	29	4	,	,	PUNCT
ejpam-1068	29	5	τ	τ	X
ejpam-1068	29	6	)	)	PUNCT
ejpam-1068	29	7	be	be	VERB
ejpam-1068	29	8	a	a	DET
ejpam-1068	29	9	topological	topological	ADJ
ejpam-1068	29	10	space	space	NOUN
ejpam-1068	29	11	.	.	PUNCT
ejpam-1068	30	1	a	a	DET
ejpam-1068	30	2	mappingψ	mappingψ	NOUN
ejpam-1068	30	3	:p	:p	INTJ
ejpam-1068	30	4	(	(	PUNCT
ejpam-1068	30	5	x	x	X
ejpam-1068	30	6	)	)	PUNCT
ejpam-1068	30	7	→p	→p	PROPN
ejpam-1068	30	8	(	(	PUNCT
ejpam-1068	30	9	x	x	X
ejpam-1068	30	10	)	)	PUNCT
ejpam-1068	30	11	is	be	AUX
ejpam-1068	30	12	called	call	VERB
ejpam-1068	30	13	an	an	DET
ejpam-1068	30	14	operation	operation	NOUN
ejpam-1068	30	15	on	on	ADP
ejpam-1068	30	16	p	p	PROPN
ejpam-1068	30	17	(	(	PUNCT
ejpam-1068	30	18	x	x	PROPN
ejpam-1068	30	19	)	)	PUNCT
ejpam-1068	30	20	,	,	PUNCT
ejpam-1068	30	21	wherep	wherep	NOUN
ejpam-1068	30	22	(	(	PUNCT
ejpam-1068	30	23	x	x	X
ejpam-1068	30	24	)	)	PUNCT
ejpam-1068	30	25	denotes	denote	NOUN
ejpam-1068	30	26	as	as	ADP
ejpam-1068	30	27	usual	usual	ADJ
ejpam-1068	30	28	the	the	DET
ejpam-1068	30	29	power	power	NOUN
ejpam-1068	30	30	set	set	NOUN
ejpam-1068	30	31	of	of	ADP
ejpam-1068	30	32	x	x	SYM
ejpam-1068	30	33	,	,	PUNCT
ejpam-1068	30	34	if	if	SCONJ
ejpam-1068	30	35	for	for	ADP
ejpam-1068	30	36	each	each	DET
ejpam-1068	30	37	a∈	a∈	PROPN
ejpam-1068	30	38	p	p	PROPN
ejpam-1068	30	39	(	(	PUNCT
ejpam-1068	30	40	x	x	PROPN
ejpam-1068	30	41	)	)	PUNCT
ejpam-1068	30	42	\{∅	\{∅	PROPN
ejpam-1068	30	43	}	}	PUNCT
ejpam-1068	30	44	,	,	PUNCT
ejpam-1068	30	45	inta⊆ψ(a	inta⊆ψ(a	PROPN
ejpam-1068	30	46	)	)	PUNCT
ejpam-1068	30	47	and	and	CCONJ
ejpam-1068	30	48	ψ(∅	ψ(∅	NOUN
ejpam-1068	30	49	)	)	PUNCT
ejpam-1068	30	50	=	=	NOUN
ejpam-1068	30	51	∅.	∅.	ADP
ejpam-1068	30	52	the	the	DET
ejpam-1068	30	53	set	set	NOUN
ejpam-1068	30	54	of	of	ADP
ejpam-1068	30	55	all	all	DET
ejpam-1068	30	56	operations	operation	NOUN
ejpam-1068	30	57	on	on	ADP
ejpam-1068	30	58	a	a	DET
ejpam-1068	30	59	space	space	NOUN
ejpam-1068	30	60	x	x	PUNCT
ejpam-1068	30	61	will	will	AUX
ejpam-1068	30	62	be	be	AUX
ejpam-1068	30	63	denoted	denote	VERB
ejpam-1068	30	64	by	by	ADP
ejpam-1068	30	65	o	o	PROPN
ejpam-1068	30	66	(	(	PUNCT
ejpam-1068	30	67	x	x	PROPN
ejpam-1068	30	68	)	)	PUNCT
ejpam-1068	30	69	.	.	PUNCT
ejpam-1068	31	1	remark	remark	PROPN
ejpam-1068	31	2	1	1	NUM
ejpam-1068	31	3	.	.	PUNCT
ejpam-1068	32	1	it	it	PRON
ejpam-1068	32	2	is	be	AUX
ejpam-1068	32	3	easy	easy	ADJ
ejpam-1068	32	4	to	to	PART
ejpam-1068	32	5	check	check	VERB
ejpam-1068	32	6	that	that	SCONJ
ejpam-1068	32	7	some	some	DET
ejpam-1068	32	8	examples	example	NOUN
ejpam-1068	32	9	of	of	ADP
ejpam-1068	32	10	operations	operation	NOUN
ejpam-1068	32	11	on	on	ADP
ejpam-1068	32	12	a	a	DET
ejpam-1068	32	13	space	space	NOUN
ejpam-1068	32	14	x	x	PRON
ejpam-1068	32	15	are	be	AUX
ejpam-1068	32	16	the	the	DET
ejpam-1068	32	17	well	well	ADV
ejpam-1068	32	18	known	know	VERB
ejpam-1068	32	19	operators	operator	NOUN
ejpam-1068	32	20	viz	viz	VERB
ejpam-1068	32	21	.	.	PUNCT
ejpam-1068	33	1	int	int	PROPN
ejpam-1068	33	2	,	,	PUNCT
ejpam-1068	33	3	intcl	intcl	NOUN
ejpam-1068	33	4	,	,	PUNCT
ejpam-1068	33	5	intclδ	intclδ	NOUN
ejpam-1068	33	6	,	,	PUNCT
ejpam-1068	33	7	cl	cl	NOUN
ejpam-1068	33	8	int	int	NOUN
ejpam-1068	33	9	,	,	PUNCT
ejpam-1068	33	10	intclint	intclint	NOUN
ejpam-1068	33	11	,	,	PUNCT
ejpam-1068	33	12	cl	cl	NOUN
ejpam-1068	33	13	intcl	intcl	NOUN
ejpam-1068	33	14	.	.	PUNCT
ejpam-1068	34	1	definition	definition	NOUN
ejpam-1068	34	2	2	2	NUM
ejpam-1068	34	3	(	(	PUNCT
ejpam-1068	34	4	[	[	X
ejpam-1068	34	5	3	3	NUM
ejpam-1068	34	6	]	]	PUNCT
ejpam-1068	34	7	)	)	PUNCT
ejpam-1068	34	8	.	.	PUNCT
ejpam-1068	35	1	let	let	VERB
ejpam-1068	35	2	ψ	ψ	PART
ejpam-1068	35	3	denote	denote	VERB
ejpam-1068	35	4	an	an	DET
ejpam-1068	35	5	operation	operation	NOUN
ejpam-1068	35	6	on	on	ADP
ejpam-1068	35	7	a	a	DET
ejpam-1068	35	8	space	space	NOUN
ejpam-1068	35	9	(	(	PUNCT
ejpam-1068	35	10	x	x	X
ejpam-1068	35	11	,	,	PUNCT
ejpam-1068	35	12	τ	τ	PROPN
ejpam-1068	35	13	)	)	PUNCT
ejpam-1068	35	14	.	.	PUNCT
ejpam-1068	36	1	then	then	ADV
ejpam-1068	36	2	a	a	DET
ejpam-1068	36	3	subset	subset	NOUN
ejpam-1068	36	4	a	a	PRON
ejpam-1068	36	5	of	of	ADP
ejpam-1068	36	6	x	x	PRON
ejpam-1068	36	7	is	be	AUX
ejpam-1068	36	8	called	call	VERB
ejpam-1068	36	9	ψ	ψ	NOUN
ejpam-1068	36	10	-	-	ADJ
ejpam-1068	36	11	open	open	ADJ
ejpam-1068	36	12	if	if	SCONJ
ejpam-1068	36	13	a⊆	a⊆	PROPN
ejpam-1068	36	14	ψ(a	ψ(a	PROPN
ejpam-1068	36	15	)	)	PUNCT
ejpam-1068	36	16	.	.	PUNCT
ejpam-1068	37	1	complements	complement	NOUN
ejpam-1068	37	2	of	of	ADP
ejpam-1068	37	3	ψ	ψ	VERB
ejpam-1068	37	4	-	-	ADJ
ejpam-1068	37	5	open	open	ADJ
ejpam-1068	37	6	sets	set	NOUN
ejpam-1068	37	7	will	will	AUX
ejpam-1068	37	8	be	be	AUX
ejpam-1068	37	9	called	call	VERB
ejpam-1068	37	10	ψ	ψ	ADJ
ejpam-1068	37	11	-	-	ADJ
ejpam-1068	37	12	closed	closed	ADJ
ejpam-1068	37	13	sets	set	NOUN
ejpam-1068	37	14	.	.	PUNCT
ejpam-1068	38	1	the	the	DET
ejpam-1068	38	2	family	family	NOUN
ejpam-1068	38	3	of	of	ADP
ejpam-1068	38	4	all	all	DET
ejpam-1068	38	5	ψ	ψ	NOUN
ejpam-1068	38	6	-	-	ADJ
ejpam-1068	38	7	open	open	ADJ
ejpam-1068	38	8	(	(	PUNCT
ejpam-1068	38	9	resp	resp	NOUN
ejpam-1068	38	10	.	.	PUNCT
ejpam-1068	39	1	ψ	ψ	X
ejpam-1068	39	2	-	-	ADJ
ejpam-1068	39	3	closed	closed	ADJ
ejpam-1068	39	4	)	)	PUNCT
ejpam-1068	39	5	subsets	subset	NOUN
ejpam-1068	39	6	of	of	ADP
ejpam-1068	39	7	x	x	PROPN
ejpam-1068	39	8	is	be	AUX
ejpam-1068	39	9	denoted	denote	VERB
ejpam-1068	39	10	by	by	ADP
ejpam-1068	39	11	ψo	ψo	PRON
ejpam-1068	39	12	(	(	PUNCT
ejpam-1068	39	13	x	x	X
ejpam-1068	39	14	)	)	PUNCT
ejpam-1068	39	15	(	(	PUNCT
ejpam-1068	39	16	resp	resp	NOUN
ejpam-1068	39	17	.	.	PUNCT
ejpam-1068	40	1	ψc	ψc	VERB
ejpam-1068	40	2	(	(	PUNCT
ejpam-1068	40	3	x	x	NOUN
ejpam-1068	40	4	)	)	PUNCT
ejpam-1068	40	5	)	)	PUNCT
ejpam-1068	40	6	.	.	PUNCT
ejpam-1068	41	1	remark	remark	NOUN
ejpam-1068	41	2	2	2	NUM
ejpam-1068	41	3	.	.	PUNCT
ejpam-1068	42	1	it	it	PRON
ejpam-1068	42	2	is	be	AUX
ejpam-1068	42	3	clear	clear	ADJ
ejpam-1068	42	4	that	that	SCONJ
ejpam-1068	42	5	ifψ	ifψ	NOUN
ejpam-1068	42	6	stands	stand	VERB
ejpam-1068	42	7	for	for	ADP
ejpam-1068	42	8	any	any	PRON
ejpam-1068	42	9	of	of	ADP
ejpam-1068	42	10	the	the	DET
ejpam-1068	42	11	operators	operator	NOUN
ejpam-1068	42	12	int	int	PROPN
ejpam-1068	42	13	,	,	PUNCT
ejpam-1068	42	14	intcl	intcl	NOUN
ejpam-1068	42	15	,	,	PUNCT
ejpam-1068	42	16	intclδ	intclδ	NOUN
ejpam-1068	42	17	,	,	PUNCT
ejpam-1068	42	18	cl	cl	NOUN
ejpam-1068	42	19	int	int	NOUN
ejpam-1068	42	20	,	,	PUNCT
ejpam-1068	42	21	intclint	intclint	NOUN
ejpam-1068	42	22	,	,	PUNCT
ejpam-1068	42	23	cl	cl	NOUN
ejpam-1068	42	24	intcl	intcl	NOUN
ejpam-1068	42	25	,	,	PUNCT
ejpam-1068	42	26	then	then	ADV
ejpam-1068	42	27	ψ	ψ	NOUN
ejpam-1068	42	28	-	-	NOUN
ejpam-1068	42	29	openness	openness	NOUN
ejpam-1068	42	30	of	of	ADP
ejpam-1068	42	31	a	a	DET
ejpam-1068	42	32	subset	subset	NOUN
ejpam-1068	42	33	a	a	PRON
ejpam-1068	42	34	of	of	ADP
ejpam-1068	42	35	x	x	SYM
ejpam-1068	42	36	coincides	coincide	NOUN
ejpam-1068	42	37	with	with	ADP
ejpam-1068	42	38	respectively	respectively	ADV
ejpam-1068	42	39	the	the	DET
ejpam-1068	42	40	openness	openness	NOUN
ejpam-1068	42	41	,	,	PUNCT
ejpam-1068	42	42	preopenness	preopenness	NOUN
ejpam-1068	42	43	,	,	PUNCT
ejpam-1068	42	44	δ	δ	PROPN
ejpam-1068	42	45	-	-	PUNCT
ejpam-1068	42	46	preopenness	preopenness	NOUN
ejpam-1068	42	47	,	,	PUNCT
ejpam-1068	42	48	semi	semi	ADJ
ejpam-1068	42	49	-	-	NOUN
ejpam-1068	42	50	openness	openness	ADJ
ejpam-1068	42	51	,	,	PUNCT
ejpam-1068	42	52	α	α	NOUN
ejpam-1068	42	53	-	-	NOUN
ejpam-1068	42	54	openness	openness	NOUN
ejpam-1068	42	55	and	and	CCONJ
ejpam-1068	42	56	β	β	NOUN
ejpam-1068	42	57	-openness	-openness	NOUN
ejpam-1068	42	58	of	of	ADP
ejpam-1068	42	59	a	a	DET
ejpam-1068	42	60	[	[	X
ejpam-1068	42	61	see	see	NOUN
ejpam-1068	42	62	5	5	NUM
ejpam-1068	42	63	,	,	PUNCT
ejpam-1068	42	64	14	14	NUM
ejpam-1068	42	65	,	,	PUNCT
ejpam-1068	42	66	19	19	NUM
ejpam-1068	42	67	,	,	PUNCT
ejpam-1068	42	68	13	13	NUM
ejpam-1068	42	69	,	,	PUNCT
ejpam-1068	42	70	11	11	NUM
ejpam-1068	42	71	,	,	PUNCT
ejpam-1068	42	72	12	12	NUM
ejpam-1068	42	73	]	]	PUNCT
ejpam-1068	42	74	.	.	PUNCT
ejpam-1068	43	1	definition	definition	NOUN
ejpam-1068	43	2	3	3	NUM
ejpam-1068	43	3	(	(	PUNCT
ejpam-1068	43	4	[	[	X
ejpam-1068	43	5	3	3	NUM
ejpam-1068	43	6	]	]	PUNCT
ejpam-1068	43	7	)	)	PUNCT
ejpam-1068	43	8	.	.	PUNCT
ejpam-1068	44	1	let	let	VERB
ejpam-1068	44	2	(	(	PUNCT
ejpam-1068	44	3	x	x	X
ejpam-1068	44	4	,	,	PUNCT
ejpam-1068	44	5	τ	τ	X
ejpam-1068	44	6	)	)	PUNCT
ejpam-1068	44	7	be	be	VERB
ejpam-1068	44	8	a	a	DET
ejpam-1068	44	9	topological	topological	ADJ
ejpam-1068	44	10	space	space	NOUN
ejpam-1068	44	11	,	,	PUNCT
ejpam-1068	44	12	ψ	ψ	NOUN
ejpam-1068	44	13	∈	∈	PROPN
ejpam-1068	44	14	o	o	X
ejpam-1068	44	15	(	(	PUNCT
ejpam-1068	44	16	x	x	SYM
ejpam-1068	44	17	)	)	PUNCT
ejpam-1068	44	18	and	and	CCONJ
ejpam-1068	44	19	a⊆	a⊆	NOUN
ejpam-1068	44	20	x	x	X
ejpam-1068	44	21	.	.	PUNCT
ejpam-1068	45	1	then	then	ADV
ejpam-1068	45	2	the	the	DET
ejpam-1068	45	3	intersection	intersection	NOUN
ejpam-1068	45	4	of	of	ADP
ejpam-1068	45	5	all	all	DET
ejpam-1068	45	6	ψ	ψ	ADJ
ejpam-1068	45	7	-	-	ADJ
ejpam-1068	45	8	closed	closed	ADJ
ejpam-1068	45	9	sets	set	NOUN
ejpam-1068	45	10	containing	contain	VERB
ejpam-1068	45	11	a	a	PRON
ejpam-1068	45	12	is	be	AUX
ejpam-1068	45	13	called	call	VERB
ejpam-1068	45	14	the	the	DET
ejpam-1068	45	15	ψ	ψ	NOUN
ejpam-1068	45	16	-	-	NOUN
ejpam-1068	45	17	closure	closure	NOUN
ejpam-1068	45	18	of	of	ADP
ejpam-1068	45	19	a	a	PRON
ejpam-1068	45	20	,	,	PUNCT
ejpam-1068	45	21	denoted	denote	VERB
ejpam-1068	45	22	by	by	ADP
ejpam-1068	45	23	ψ	ψ	NOUN
ejpam-1068	45	24	-	-	ADJ
ejpam-1068	45	25	cla	cla	ADJ
ejpam-1068	45	26	;	;	PUNCT
ejpam-1068	45	27	alternately	alternately	ADV
ejpam-1068	45	28	,	,	PUNCT
ejpam-1068	45	29	ψ	ψ	X
ejpam-1068	45	30	-	-	PUNCT
ejpam-1068	45	31	cla	cla	ADJ
ejpam-1068	45	32	is	be	AUX
ejpam-1068	45	33	the	the	DET
ejpam-1068	45	34	smallest	small	ADJ
ejpam-1068	45	35	ψ	ψ	ADJ
ejpam-1068	45	36	-	-	ADJ
ejpam-1068	45	37	closed	closed	ADJ
ejpam-1068	45	38	set	set	NOUN
ejpam-1068	45	39	containing	contain	VERB
ejpam-1068	45	40	a.	a.	NOUN
ejpam-1068	45	41	the	the	DET
ejpam-1068	45	42	union	union	NOUN
ejpam-1068	45	43	of	of	ADP
ejpam-1068	45	44	all	all	DET
ejpam-1068	45	45	ψ	ψ	ADJ
ejpam-1068	45	46	-	-	ADJ
ejpam-1068	45	47	open	open	ADJ
ejpam-1068	45	48	subsets	subset	NOUN
ejpam-1068	45	49	of	of	ADP
ejpam-1068	45	50	g	g	PROPN
ejpam-1068	45	51	is	be	AUX
ejpam-1068	45	52	the	the	DET
ejpam-1068	45	53	ψ	ψ	NOUN
ejpam-1068	45	54	-	-	NOUN
ejpam-1068	45	55	interior	interior	ADJ
ejpam-1068	45	56	of	of	ADP
ejpam-1068	45	57	g	g	NOUN
ejpam-1068	45	58	,	,	PUNCT
ejpam-1068	45	59	denoted	denote	VERB
ejpam-1068	45	60	by	by	ADP
ejpam-1068	45	61	ψ	ψ	NOUN
ejpam-1068	45	62	-	-	NOUN
ejpam-1068	45	63	intg	intg	ADJ
ejpam-1068	45	64	.	.	PUNCT
ejpam-1068	46	1	it	it	PRON
ejpam-1068	46	2	is	be	AUX
ejpam-1068	46	3	known	know	VERB
ejpam-1068	46	4	from	from	ADP
ejpam-1068	46	5	[	[	X
ejpam-1068	46	6	8	8	NUM
ejpam-1068	46	7	]	]	PUNCT
ejpam-1068	46	8	that	that	SCONJ
ejpam-1068	46	9	x	x	SYM
ejpam-1068	46	10	∈	∈	NOUN
ejpam-1068	46	11	ψ	ψ	X
ejpam-1068	46	12	−	−	PUNCT
ejpam-1068	46	13	cla	cla	PROPN
ejpam-1068	46	14	iff	iff	PROPN
ejpam-1068	46	15	a	a	DET
ejpam-1068	46	16	∩	∩	ADJ
ejpam-1068	46	17	u	u	NOUN
ejpam-1068	46	18	6=	6=	NOUN
ejpam-1068	46	19	∅	∅	NOUN
ejpam-1068	46	20	,	,	PUNCT
ejpam-1068	46	21	for	for	ADP
ejpam-1068	46	22	all	all	DET
ejpam-1068	46	23	u	u	NOUN
ejpam-1068	46	24	with	with	ADP
ejpam-1068	46	25	x	x	PROPN
ejpam-1068	46	26	∈	∈	PROPN
ejpam-1068	46	27	u	u	NOUN
ejpam-1068	46	28	∈	∈	PROPN
ejpam-1068	46	29	ψo	ψo	X
ejpam-1068	46	30	(	(	PUNCT
ejpam-1068	46	31	x	x	X
ejpam-1068	46	32	)	)	PUNCT
ejpam-1068	47	1	and	and	CCONJ
ejpam-1068	47	2	x	x	PUNCT
ejpam-1068	47	3	∈	∈	PROPN
ejpam-1068	47	4	ψ−	ψ−	VERB
ejpam-1068	47	5	intg	intg	PROPN
ejpam-1068	47	6	iff	iff	PROPN
ejpam-1068	47	7	∃	∃	PROPN
ejpam-1068	47	8	x	x	PROPN
ejpam-1068	47	9	∈	∈	PROPN
ejpam-1068	47	10	u	u	NOUN
ejpam-1068	47	11	∈	∈	PROPN
ejpam-1068	47	12	ψo	ψo	X
ejpam-1068	47	13	(	(	PUNCT
ejpam-1068	47	14	x	x	X
ejpam-1068	47	15	)	)	PUNCT
ejpam-1068	47	16	such	such	ADJ
ejpam-1068	47	17	that	that	SCONJ
ejpam-1068	47	18	x	x	SYM
ejpam-1068	47	19	∈	∈	PROPN
ejpam-1068	47	20	u	u	NOUN
ejpam-1068	47	21	⊆	⊆	NUM
ejpam-1068	47	22	g.	g.	NOUN
ejpam-1068	47	23	in	in	ADP
ejpam-1068	47	24	[	[	X
ejpam-1068	47	25	8	8	NUM
ejpam-1068	47	26	]	]	PUNCT
ejpam-1068	47	27	,	,	PUNCT
ejpam-1068	47	28	it	it	PRON
ejpam-1068	47	29	is	be	AUX
ejpam-1068	47	30	also	also	ADV
ejpam-1068	47	31	shown	show	VERB
ejpam-1068	47	32	that	that	SCONJ
ejpam-1068	47	33	x	x	NOUN
ejpam-1068	47	34	\ψ−	\ψ−	ADV
ejpam-1068	47	35	clg	clg	NOUN
ejpam-1068	47	36	=	=	PRON
ejpam-1068	47	37	ψ−	ψ−	NOUN
ejpam-1068	47	38	int(x	int(x	NOUN
ejpam-1068	47	39	\	\	NOUN
ejpam-1068	47	40	g	g	NOUN
ejpam-1068	47	41	)	)	PUNCT
ejpam-1068	47	42	.	.	PUNCT
ejpam-1068	48	1	remark	remark	PROPN
ejpam-1068	48	2	3	3	NUM
ejpam-1068	48	3	.	.	PUNCT
ejpam-1068	49	1	obviously	obviously	ADV
ejpam-1068	49	2	if	if	SCONJ
ejpam-1068	49	3	one	one	PRON
ejpam-1068	49	4	takes	take	VERB
ejpam-1068	49	5	interior	interior	NOUN
ejpam-1068	49	6	as	as	ADP
ejpam-1068	49	7	the	the	DET
ejpam-1068	49	8	operationψ	operationψ	NOUN
ejpam-1068	49	9	,	,	PUNCT
ejpam-1068	49	10	thenψ	thenψ	NOUN
ejpam-1068	49	11	-	-	PUNCT
ejpam-1068	49	12	closure	closure	NOUN
ejpam-1068	49	13	becomes	become	VERB
ejpam-1068	49	14	equivalent	equivalent	ADJ
ejpam-1068	49	15	to	to	ADP
ejpam-1068	49	16	the	the	DET
ejpam-1068	49	17	usual	usual	ADJ
ejpam-1068	49	18	closure	closure	NOUN
ejpam-1068	49	19	.	.	PUNCT
ejpam-1068	50	1	similarly	similarly	ADV
ejpam-1068	50	2	,	,	PUNCT
ejpam-1068	50	3	ψ	ψ	NOUN
ejpam-1068	50	4	-	-	NOUN
ejpam-1068	50	5	closure	closure	NOUN
ejpam-1068	50	6	becomes	becomes	AUX
ejpam-1068	50	7	pcl	pcl	PROPN
ejpam-1068	50	8	,	,	PUNCT
ejpam-1068	50	9	pclδ	pclδ	NOUN
ejpam-1068	50	10	,	,	PUNCT
ejpam-1068	50	11	scl	scl	PROPN
ejpam-1068	50	12	,	,	PUNCT
ejpam-1068	50	13	α	α	NOUN
ejpam-1068	50	14	-	-	NOUN
ejpam-1068	50	15	cl	cl	NOUN
ejpam-1068	50	16	,	,	PUNCT
ejpam-1068	50	17	β	β	X
ejpam-1068	50	18	-cl	-cl	NOUN
ejpam-1068	50	19	,	,	PUNCT
ejpam-1068	50	20	ifψ	ifψ	PRON
ejpam-1068	50	21	is	be	AUX
ejpam-1068	50	22	taken	take	VERB
ejpam-1068	50	23	to	to	PART
ejpam-1068	50	24	stand	stand	VERB
ejpam-1068	50	25	for	for	ADP
ejpam-1068	50	26	the	the	DET
ejpam-1068	50	27	operators	operator	NOUN
ejpam-1068	50	28	intcl	intcl	PROPN
ejpam-1068	50	29	,	,	PUNCT
ejpam-1068	50	30	intclδ	intclδ	NOUN
ejpam-1068	50	31	,	,	PUNCT
ejpam-1068	50	32	cl	cl	NOUN
ejpam-1068	50	33	int	int	NOUN
ejpam-1068	50	34	,	,	PUNCT
ejpam-1068	50	35	intclint	intclint	NOUN
ejpam-1068	50	36	and	and	CCONJ
ejpam-1068	50	37	clintcl	clintcl	VERB
ejpam-1068	50	38	respectively	respectively	ADV
ejpam-1068	50	39	[	[	X
ejpam-1068	50	40	see	see	VERB
ejpam-1068	50	41	14	14	NUM
ejpam-1068	50	42	,	,	PUNCT
ejpam-1068	50	43	19	19	NUM
ejpam-1068	50	44	,	,	PUNCT
ejpam-1068	50	45	13	13	NUM
ejpam-1068	50	46	,	,	PUNCT
ejpam-1068	50	47	11	11	NUM
ejpam-1068	50	48	,	,	PUNCT
ejpam-1068	50	49	12	12	NUM
ejpam-1068	50	50	,	,	PUNCT
ejpam-1068	50	51	for	for	ADP
ejpam-1068	50	52	details	detail	NOUN
ejpam-1068	50	53	]	]	PUNCT
ejpam-1068	50	54	.	.	PUNCT
ejpam-1068	51	1	definition	definition	NOUN
ejpam-1068	51	2	4	4	NUM
ejpam-1068	51	3	.	.	PUNCT
ejpam-1068	52	1	let	let	VERB
ejpam-1068	52	2	ψ	ψ	PART
ejpam-1068	52	3	be	be	AUX
ejpam-1068	52	4	an	an	DET
ejpam-1068	52	5	operation	operation	NOUN
ejpam-1068	52	6	on	on	ADP
ejpam-1068	52	7	a	a	DET
ejpam-1068	52	8	topological	topological	ADJ
ejpam-1068	52	9	space	space	NOUN
ejpam-1068	52	10	(	(	PUNCT
ejpam-1068	52	11	x	x	X
ejpam-1068	52	12	,	,	PUNCT
ejpam-1068	52	13	τ	τ	PROPN
ejpam-1068	52	14	)	)	PUNCT
ejpam-1068	52	15	.	.	PUNCT
ejpam-1068	53	1	then	then	ADV
ejpam-1068	53	2	a	a	DET
ejpam-1068	53	3	⊆	⊆	NUM
ejpam-1068	53	4	x	x	NUM
ejpam-1068	53	5	is	be	AUX
ejpam-1068	53	6	called	call	VERB
ejpam-1068	53	7	a	a	DET
ejpam-1068	53	8	generalized	generalized	ADJ
ejpam-1068	53	9	ψ	ψ	ADJ
ejpam-1068	53	10	-	-	ADJ
ejpam-1068	53	11	closed	closed	ADJ
ejpam-1068	53	12	set	set	NOUN
ejpam-1068	53	13	(	(	PUNCT
ejpam-1068	53	14	or	or	CCONJ
ejpam-1068	53	15	simply	simply	ADV
ejpam-1068	53	16	gψ	gψ	ADJ
ejpam-1068	53	17	-	-	PUNCT
ejpam-1068	53	18	closed	closed	ADJ
ejpam-1068	53	19	set	set	NOUN
ejpam-1068	53	20	)	)	PUNCT
ejpam-1068	53	21	if	if	SCONJ
ejpam-1068	53	22	ψ−	ψ−	VERB
ejpam-1068	53	23	cl(a	cl(a	PUNCT
ejpam-1068	53	24	)	)	PUNCT
ejpam-1068	53	25	⊆	⊆	NUM
ejpam-1068	53	26	u	u	NOUN
ejpam-1068	53	27	whenever	whenever	SCONJ
ejpam-1068	53	28	a	a	DET
ejpam-1068	53	29	⊆	⊆	NUM
ejpam-1068	53	30	u	u	NOUN
ejpam-1068	53	31	∈	∈	PROPN
ejpam-1068	53	32	τ	τ	PROPN
ejpam-1068	53	33	.	.	PUNCT
ejpam-1068	54	1	the	the	DET
ejpam-1068	54	2	complement	complement	NOUN
ejpam-1068	54	3	of	of	ADP
ejpam-1068	54	4	a	a	DET
ejpam-1068	54	5	gψ	gψ	ADV
ejpam-1068	54	6	-	-	PUNCT
ejpam-1068	54	7	closed	closed	ADJ
ejpam-1068	54	8	set	set	NOUN
ejpam-1068	54	9	is	be	AUX
ejpam-1068	54	10	called	call	VERB
ejpam-1068	54	11	a	a	DET
ejpam-1068	54	12	generalized	generalized	ADJ
ejpam-1068	54	13	ψ	ψ	NOUN
ejpam-1068	54	14	-	-	ADJ
ejpam-1068	54	15	open	open	ADJ
ejpam-1068	54	16	(	(	PUNCT
ejpam-1068	54	17	or	or	CCONJ
ejpam-1068	54	18	simply	simply	ADV
ejpam-1068	54	19	gψ	gψ	ADJ
ejpam-1068	54	20	-	-	PUNCT
ejpam-1068	54	21	open	open	ADJ
ejpam-1068	54	22	)	)	PUNCT
ejpam-1068	54	23	set	set	NOUN
ejpam-1068	54	24	.	.	PUNCT
ejpam-1068	55	1	b.	b.	PROPN
ejpam-1068	55	2	roy	roy	PROPN
ejpam-1068	55	3	,	,	PUNCT
ejpam-1068	55	4	r.	r.	PROPN
ejpam-1068	55	5	sen	sen	PROPN
ejpam-1068	55	6	,	,	PUNCT
ejpam-1068	55	7	t.	t.	PROPN
ejpam-1068	55	8	noiri	noiri	PROPN
ejpam-1068	55	9	/	/	SYM
ejpam-1068	55	10	eur	eur	PROPN
ejpam-1068	55	11	.	.	PUNCT
ejpam-1068	56	1	j.	j.	PROPN
ejpam-1068	56	2	pure	pure	PROPN
ejpam-1068	56	3	appl	appl	PROPN
ejpam-1068	56	4	.	.	PROPN
ejpam-1068	56	5	math	math	PROPN
ejpam-1068	56	6	,	,	PUNCT
ejpam-1068	56	7	6	6	NUM
ejpam-1068	56	8	(	(	PUNCT
ejpam-1068	56	9	2013	2013	NUM
ejpam-1068	56	10	)	)	PUNCT
ejpam-1068	56	11	,	,	PUNCT
ejpam-1068	56	12	44	44	NUM
ejpam-1068	56	13	-	-	SYM
ejpam-1068	56	14	52	52	NUM
ejpam-1068	56	15	46	46	NUM
ejpam-1068	56	16	remark	remark	NOUN
ejpam-1068	56	17	4	4	NUM
ejpam-1068	56	18	.	.	PUNCT
ejpam-1068	57	1	(	(	PUNCT
ejpam-1068	57	2	i	i	NOUN
ejpam-1068	57	3	)	)	PUNCT
ejpam-1068	57	4	let	let	VERB
ejpam-1068	57	5	ψ	ψ	PART
ejpam-1068	57	6	be	be	AUX
ejpam-1068	57	7	an	an	DET
ejpam-1068	57	8	operation	operation	NOUN
ejpam-1068	57	9	on	on	ADP
ejpam-1068	57	10	a	a	DET
ejpam-1068	57	11	topological	topological	ADJ
ejpam-1068	57	12	space	space	NOUN
ejpam-1068	57	13	(	(	PUNCT
ejpam-1068	57	14	x	x	X
ejpam-1068	57	15	,	,	PUNCT
ejpam-1068	57	16	τ	τ	PROPN
ejpam-1068	57	17	)	)	PUNCT
ejpam-1068	57	18	.	.	PUNCT
ejpam-1068	58	1	then	then	ADV
ejpam-1068	58	2	every	every	DET
ejpam-1068	58	3	gψ	gψ	ADV
ejpam-1068	58	4	-	-	PUNCT
ejpam-1068	58	5	closed	closed	ADJ
ejpam-1068	58	6	set	set	NOUN
ejpam-1068	58	7	reduces	reduce	VERB
ejpam-1068	58	8	to	to	ADP
ejpam-1068	58	9	a	a	DET
ejpam-1068	58	10	g	g	NOUN
ejpam-1068	58	11	-	-	PUNCT
ejpam-1068	58	12	closed	closed	ADJ
ejpam-1068	58	13	[	[	X
ejpam-1068	58	14	9	9	NUM
ejpam-1068	58	15	]	]	PUNCT
ejpam-1068	58	16	(	(	PUNCT
ejpam-1068	58	17	resp	resp	NOUN
ejpam-1068	58	18	.	.	PUNCT
ejpam-1068	59	1	gp	gp	NOUN
ejpam-1068	59	2	-	-	PUNCT
ejpam-1068	59	3	closed	closed	ADJ
ejpam-1068	59	4	[	[	X
ejpam-1068	59	5	17	17	NUM
ejpam-1068	59	6	]	]	PUNCT
ejpam-1068	59	7	,	,	PUNCT
ejpam-1068	59	8	gs	gs	NOUN
ejpam-1068	59	9	-	-	PUNCT
ejpam-1068	59	10	closed	closed	ADJ
ejpam-1068	59	11	[	[	X
ejpam-1068	59	12	2	2	NUM
ejpam-1068	59	13	]	]	PUNCT
ejpam-1068	59	14	,	,	PUNCT
ejpam-1068	59	15	αg	αg	NOUN
ejpam-1068	59	16	-	-	PUNCT
ejpam-1068	59	17	closed	closed	ADJ
ejpam-1068	59	18	[	[	X
ejpam-1068	59	19	13	13	NUM
ejpam-1068	59	20	]	]	PUNCT
ejpam-1068	59	21	,	,	PUNCT
ejpam-1068	59	22	gδp	gδp	PROPN
ejpam-1068	59	23	-	-	PUNCT
ejpam-1068	59	24	closed	close	VERB
ejpam-1068	60	1	[	[	X
ejpam-1068	60	2	6	6	NUM
ejpam-1068	60	3	]	]	PUNCT
ejpam-1068	60	4	,	,	PUNCT
ejpam-1068	60	5	gsp	gsp	NOUN
ejpam-1068	60	6	-	-	PUNCT
ejpam-1068	60	7	closed	close	VERB
ejpam-1068	60	8	[	[	X
ejpam-1068	60	9	4	4	NUM
ejpam-1068	60	10	]	]	PUNCT
ejpam-1068	60	11	)	)	PUNCT
ejpam-1068	60	12	set	set	VERB
ejpam-1068	60	13	if	if	SCONJ
ejpam-1068	60	14	one	one	PRON
ejpam-1068	60	15	takes	take	VERB
ejpam-1068	60	16	ψ	ψ	NOUN
ejpam-1068	60	17	to	to	PART
ejpam-1068	60	18	be	be	AUX
ejpam-1068	60	19	int	int	NOUN
ejpam-1068	60	20	(	(	PUNCT
ejpam-1068	60	21	resp	resp	NOUN
ejpam-1068	60	22	.	.	PUNCT
ejpam-1068	60	23	intcl	intcl	PROPN
ejpam-1068	60	24	,	,	PUNCT
ejpam-1068	60	25	cl	cl	NOUN
ejpam-1068	60	26	int	int	NOUN
ejpam-1068	60	27	,	,	PUNCT
ejpam-1068	60	28	intclint	intclint	NOUN
ejpam-1068	60	29	,	,	PUNCT
ejpam-1068	60	30	intclδ	intclδ	NOUN
ejpam-1068	60	31	,	,	PUNCT
ejpam-1068	60	32	cl	cl	NOUN
ejpam-1068	60	33	intcl	intcl	NOUN
ejpam-1068	60	34	)	)	PUNCT
ejpam-1068	60	35	.	.	PUNCT
ejpam-1068	61	1	(	(	PUNCT
ejpam-1068	61	2	ii	ii	NOUN
ejpam-1068	61	3	)	)	PUNCT
ejpam-1068	61	4	for	for	ADP
ejpam-1068	61	5	an	an	DET
ejpam-1068	61	6	operation	operation	NOUN
ejpam-1068	61	7	ψ	ψ	NOUN
ejpam-1068	61	8	on	on	ADP
ejpam-1068	61	9	a	a	DET
ejpam-1068	61	10	topological	topological	ADJ
ejpam-1068	61	11	space	space	NOUN
ejpam-1068	61	12	(	(	PUNCT
ejpam-1068	61	13	x	x	X
ejpam-1068	61	14	,	,	PUNCT
ejpam-1068	61	15	τ	τ	PROPN
ejpam-1068	61	16	)	)	PUNCT
ejpam-1068	61	17	,	,	PUNCT
ejpam-1068	61	18	every	every	DET
ejpam-1068	61	19	ψ	ψ	VERB
ejpam-1068	61	20	-	-	ADJ
ejpam-1068	61	21	closed	closed	ADJ
ejpam-1068	61	22	set	set	NOUN
ejpam-1068	61	23	is	be	AUX
ejpam-1068	61	24	a	a	DET
ejpam-1068	61	25	gψ	gψ	ADV
ejpam-1068	61	26	-	-	PUNCT
ejpam-1068	61	27	closed	closed	ADJ
ejpam-1068	61	28	set	set	NOUN
ejpam-1068	61	29	.	.	PUNCT
ejpam-1068	62	1	in	in	ADP
ejpam-1068	62	2	fact	fact	NOUN
ejpam-1068	62	3	,	,	PUNCT
ejpam-1068	62	4	if	if	SCONJ
ejpam-1068	62	5	a	a	PRON
ejpam-1068	62	6	is	be	AUX
ejpam-1068	62	7	a	a	DET
ejpam-1068	62	8	ψ	ψ	NOUN
ejpam-1068	62	9	-	-	VERB
ejpam-1068	62	10	closed	closed	ADJ
ejpam-1068	62	11	with	with	ADP
ejpam-1068	62	12	a	a	DET
ejpam-1068	62	13	⊆	⊆	NUM
ejpam-1068	62	14	u	u	NOUN
ejpam-1068	62	15	∈	∈	PROPN
ejpam-1068	62	16	τ	τ	PROPN
ejpam-1068	62	17	,	,	PUNCT
ejpam-1068	62	18	then	then	ADV
ejpam-1068	62	19	a	a	DET
ejpam-1068	62	20	=	=	PUNCT
ejpam-1068	62	21	ψ−	ψ−	NOUN
ejpam-1068	62	22	cl(a	cl(a	NUM
ejpam-1068	62	23	)	)	PUNCT
ejpam-1068	62	24	⊆	⊆	NUM
ejpam-1068	62	25	u	u	NOUN
ejpam-1068	62	26	,	,	PUNCT
ejpam-1068	62	27	so	so	SCONJ
ejpam-1068	62	28	that	that	SCONJ
ejpam-1068	62	29	a	a	PRON
ejpam-1068	62	30	is	be	AUX
ejpam-1068	62	31	gψ	gψ	ADJ
ejpam-1068	62	32	-	-	PUNCT
ejpam-1068	62	33	closed	closed	ADJ
ejpam-1068	62	34	.	.	PUNCT
ejpam-1068	63	1	that	that	SCONJ
ejpam-1068	63	2	the	the	DET
ejpam-1068	63	3	converse	converse	NOUN
ejpam-1068	63	4	is	be	AUX
ejpam-1068	63	5	false	false	ADJ
ejpam-1068	63	6	as	as	SCONJ
ejpam-1068	63	7	shown	show	VERB
ejpam-1068	63	8	by	by	ADP
ejpam-1068	63	9	the	the	DET
ejpam-1068	63	10	following	follow	VERB
ejpam-1068	63	11	example	example	NOUN
ejpam-1068	63	12	.	.	PUNCT
ejpam-1068	64	1	example	example	NOUN
ejpam-1068	65	1	1	1	NUM
ejpam-1068	65	2	.	.	PUNCT
ejpam-1068	65	3	let	let	VERB
ejpam-1068	65	4	x	x	PUNCT
ejpam-1068	65	5	=	=	PRON
ejpam-1068	65	6	{	{	PUNCT
ejpam-1068	65	7	a	a	PRON
ejpam-1068	65	8	,	,	PUNCT
ejpam-1068	65	9	b	b	NOUN
ejpam-1068	65	10	,	,	PUNCT
ejpam-1068	65	11	c	c	NOUN
ejpam-1068	65	12	,	,	PUNCT
ejpam-1068	65	13	d	d	NOUN
ejpam-1068	65	14	}	}	PUNCT
ejpam-1068	65	15	and	and	CCONJ
ejpam-1068	65	16	τ	τ	PROPN
ejpam-1068	65	17	=	=	SYM
ejpam-1068	65	18	{	{	PUNCT
ejpam-1068	65	19	∅	∅	NOUN
ejpam-1068	65	20	,	,	PUNCT
ejpam-1068	65	21	x	x	INTJ
ejpam-1068	65	22	,	,	PUNCT
ejpam-1068	65	23	{	{	PUNCT
ejpam-1068	65	24	a	a	NOUN
ejpam-1068	65	25	}	}	PUNCT
ejpam-1068	65	26	,	,	PUNCT
ejpam-1068	65	27	{	{	PUNCT
ejpam-1068	65	28	a	a	DET
ejpam-1068	65	29	,	,	PUNCT
ejpam-1068	65	30	b	b	NOUN
ejpam-1068	65	31	}	}	PUNCT
ejpam-1068	65	32	,	,	PUNCT
ejpam-1068	65	33	{	{	PUNCT
ejpam-1068	65	34	a	a	PRON
ejpam-1068	65	35	,	,	PUNCT
ejpam-1068	65	36	b	b	NOUN
ejpam-1068	65	37	,	,	PUNCT
ejpam-1068	65	38	c	c	NOUN
ejpam-1068	65	39	}	}	PUNCT
ejpam-1068	65	40	}	}	PUNCT
ejpam-1068	65	41	.	.	PUNCT
ejpam-1068	66	1	consider	consider	VERB
ejpam-1068	66	2	the	the	DET
ejpam-1068	66	3	map	map	NOUN
ejpam-1068	66	4	ψ	ψ	X
ejpam-1068	66	5	:	:	PUNCT
ejpam-1068	66	6	p	p	X
ejpam-1068	66	7	(	(	PUNCT
ejpam-1068	66	8	x	x	X
ejpam-1068	66	9	)	)	PUNCT
ejpam-1068	66	10	→p	→p	PROPN
ejpam-1068	66	11	(	(	PUNCT
ejpam-1068	66	12	x	x	X
ejpam-1068	66	13	)	)	PUNCT
ejpam-1068	66	14	defined	define	VERB
ejpam-1068	66	15	by	by	ADP
ejpam-1068	66	16	ψ({a	ψ({a	PROPN
ejpam-1068	66	17	}	}	PUNCT
ejpam-1068	66	18	)	)	PUNCT
ejpam-1068	67	1	=	=	SYM
ejpam-1068	67	2	ψ({a	ψ({a	PROPN
ejpam-1068	67	3	,	,	PUNCT
ejpam-1068	67	4	c	c	NOUN
ejpam-1068	67	5	}	}	PUNCT
ejpam-1068	67	6	)	)	PUNCT
ejpam-1068	68	1	=	=	SYM
ejpam-1068	68	2	ψ({a	ψ({a	PROPN
ejpam-1068	68	3	,	,	PUNCT
ejpam-1068	68	4	d	d	NOUN
ejpam-1068	68	5	}	}	PUNCT
ejpam-1068	68	6	)	)	PUNCT
ejpam-1068	69	1	=	=	SYM
ejpam-1068	69	2	ψ({a	ψ({a	PROPN
ejpam-1068	69	3	,	,	PUNCT
ejpam-1068	69	4	b	b	NOUN
ejpam-1068	69	5	}	}	PUNCT
ejpam-1068	69	6	)	)	PUNCT
ejpam-1068	70	1	=	=	SYM
ejpam-1068	70	2	ψ({a	ψ({a	PROPN
ejpam-1068	70	3	,	,	PUNCT
ejpam-1068	70	4	b	b	NOUN
ejpam-1068	70	5	,	,	PUNCT
ejpam-1068	70	6	c	c	NOUN
ejpam-1068	70	7	}	}	PUNCT
ejpam-1068	70	8	)	)	PUNCT
ejpam-1068	71	1	=	=	SYM
ejpam-1068	71	2	ψ({a	ψ({a	PROPN
ejpam-1068	71	3	,	,	PUNCT
ejpam-1068	71	4	b	b	NOUN
ejpam-1068	71	5	,	,	PUNCT
ejpam-1068	71	6	d	d	NOUN
ejpam-1068	71	7	}	}	PUNCT
ejpam-1068	71	8	)	)	PUNCT
ejpam-1068	72	1	=	=	SYM
ejpam-1068	72	2	ψ({a	ψ({a	PROPN
ejpam-1068	72	3	,	,	PUNCT
ejpam-1068	72	4	c	c	X
ejpam-1068	72	5	,	,	PUNCT
ejpam-1068	72	6	d	d	NOUN
ejpam-1068	72	7	}	}	PUNCT
ejpam-1068	72	8	)	)	PUNCT
ejpam-1068	73	1	=	=	NOUN
ejpam-1068	73	2	ψ(x	ψ(x	NOUN
ejpam-1068	73	3	)	)	PUNCT
ejpam-1068	74	1	=	=	SYM
ejpam-1068	74	2	x	x	X
ejpam-1068	74	3	,	,	PUNCT
ejpam-1068	74	4	ψ({b	ψ({b	PROPN
ejpam-1068	74	5	}	}	PUNCT
ejpam-1068	74	6	)	)	PUNCT
ejpam-1068	75	1	=	=	SYM
ejpam-1068	75	2	ψ({c	ψ({c	NOUN
ejpam-1068	75	3	}	}	PUNCT
ejpam-1068	75	4	)	)	PUNCT
ejpam-1068	76	1	=	=	SYM
ejpam-1068	76	2	ψ({d	ψ({d	NOUN
ejpam-1068	76	3	}	}	PUNCT
ejpam-1068	76	4	)	)	PUNCT
ejpam-1068	77	1	=	=	X
ejpam-1068	77	2	ψ({c	ψ({c	NOUN
ejpam-1068	77	3	,	,	PUNCT
ejpam-1068	77	4	d	d	NOUN
ejpam-1068	77	5	}	}	PUNCT
ejpam-1068	77	6	)	)	PUNCT
ejpam-1068	78	1	=	=	SYM
ejpam-1068	78	2	ψ({b	ψ({b	PROPN
ejpam-1068	78	3	,	,	PUNCT
ejpam-1068	78	4	c	c	NOUN
ejpam-1068	78	5	}	}	PUNCT
ejpam-1068	78	6	)	)	PUNCT
ejpam-1068	79	1	=	=	SYM
ejpam-1068	79	2	ψ({b	ψ({b	ADJ
ejpam-1068	79	3	,	,	PUNCT
ejpam-1068	79	4	d	d	NOUN
ejpam-1068	79	5	}	}	PUNCT
ejpam-1068	79	6	)	)	PUNCT
ejpam-1068	80	1	=	=	SYM
ejpam-1068	80	2	ψ({b	ψ({b	PROPN
ejpam-1068	80	3	,	,	PUNCT
ejpam-1068	80	4	c	c	X
ejpam-1068	80	5	,	,	PUNCT
ejpam-1068	80	6	d	d	NOUN
ejpam-1068	80	7	}	}	PUNCT
ejpam-1068	80	8	)	)	PUNCT
ejpam-1068	80	9	=	=	SYM
ejpam-1068	80	10	∅	∅	NOUN
ejpam-1068	80	11	and	and	CCONJ
ejpam-1068	80	12	ψ({∅	ψ({∅	NOUN
ejpam-1068	80	13	}	}	PUNCT
ejpam-1068	80	14	)	)	PUNCT
ejpam-1068	81	1	=	=	NOUN
ejpam-1068	81	2	∅.	∅.	PRON
ejpam-1068	81	3	thenψ	thenψ	NOUN
ejpam-1068	81	4	is	be	AUX
ejpam-1068	81	5	an	an	DET
ejpam-1068	81	6	operation	operation	NOUN
ejpam-1068	81	7	on	on	ADP
ejpam-1068	81	8	the	the	DET
ejpam-1068	81	9	topological	topological	ADJ
ejpam-1068	81	10	space	space	NOUN
ejpam-1068	81	11	(	(	PUNCT
ejpam-1068	81	12	x	x	X
ejpam-1068	81	13	,	,	PUNCT
ejpam-1068	81	14	τ	τ	PROPN
ejpam-1068	81	15	)	)	PUNCT
ejpam-1068	81	16	.	.	PUNCT
ejpam-1068	82	1	it	it	PRON
ejpam-1068	82	2	is	be	AUX
ejpam-1068	82	3	easy	easy	ADJ
ejpam-1068	82	4	to	to	PART
ejpam-1068	82	5	check	check	VERB
ejpam-1068	82	6	that	that	SCONJ
ejpam-1068	82	7	{	{	PUNCT
ejpam-1068	82	8	a	a	PRON
ejpam-1068	82	9	,	,	PUNCT
ejpam-1068	82	10	d	d	NOUN
ejpam-1068	82	11	}	}	PUNCT
ejpam-1068	82	12	is	be	AUX
ejpam-1068	82	13	gψ	gψ	ADV
ejpam-1068	82	14	-	-	PUNCT
ejpam-1068	82	15	closed	closed	ADJ
ejpam-1068	82	16	but	but	CCONJ
ejpam-1068	82	17	not	not	PART
ejpam-1068	82	18	ψ	ψ	VERB
ejpam-1068	82	19	-	-	VERB
ejpam-1068	82	20	closed	closed	ADJ
ejpam-1068	82	21	.	.	PUNCT
ejpam-1068	83	1	the	the	DET
ejpam-1068	83	2	next	next	ADJ
ejpam-1068	83	3	example	example	NOUN
ejpam-1068	83	4	shows	show	VERB
ejpam-1068	83	5	that	that	SCONJ
ejpam-1068	83	6	the	the	DET
ejpam-1068	83	7	union	union	NOUN
ejpam-1068	83	8	(	(	PUNCT
ejpam-1068	83	9	intersection	intersection	NOUN
ejpam-1068	83	10	)	)	PUNCT
ejpam-1068	83	11	of	of	ADP
ejpam-1068	83	12	two	two	NUM
ejpam-1068	83	13	gψ	gψ	ADJ
ejpam-1068	83	14	-	-	PUNCT
ejpam-1068	83	15	closed	closed	ADJ
ejpam-1068	83	16	sets	set	NOUN
ejpam-1068	83	17	is	be	AUX
ejpam-1068	83	18	not	not	PART
ejpam-1068	83	19	in	in	ADP
ejpam-1068	83	20	general	general	ADJ
ejpam-1068	83	21	gψ	gψ	ADV
ejpam-1068	83	22	-	-	PUNCT
ejpam-1068	83	23	closed	closed	ADJ
ejpam-1068	83	24	.	.	PUNCT
ejpam-1068	84	1	example	example	NOUN
ejpam-1068	85	1	2	2	NUM
ejpam-1068	85	2	.	.	PUNCT
ejpam-1068	85	3	(	(	PUNCT
ejpam-1068	85	4	a	a	X
ejpam-1068	85	5	)	)	PUNCT
ejpam-1068	85	6	let	let	VERB
ejpam-1068	85	7	x	x	PUNCT
ejpam-1068	85	8	=	=	PRON
ejpam-1068	85	9	{	{	PUNCT
ejpam-1068	85	10	a	a	PRON
ejpam-1068	85	11	,	,	PUNCT
ejpam-1068	85	12	b	b	NOUN
ejpam-1068	85	13	,	,	PUNCT
ejpam-1068	85	14	c	c	NOUN
ejpam-1068	85	15	}	}	PUNCT
ejpam-1068	85	16	and	and	CCONJ
ejpam-1068	85	17	τ	τ	PROPN
ejpam-1068	85	18	=	=	SYM
ejpam-1068	85	19	{	{	PUNCT
ejpam-1068	85	20	∅	∅	NOUN
ejpam-1068	85	21	,	,	PUNCT
ejpam-1068	85	22	{	{	PUNCT
ejpam-1068	85	23	a	a	X
ejpam-1068	85	24	}	}	PUNCT
ejpam-1068	85	25	,	,	PUNCT
ejpam-1068	85	26	{	{	PUNCT
ejpam-1068	85	27	a	a	DET
ejpam-1068	85	28	,	,	PUNCT
ejpam-1068	85	29	b	b	NOUN
ejpam-1068	85	30	}	}	PUNCT
ejpam-1068	85	31	,	,	PUNCT
ejpam-1068	85	32	x	x	SYM
ejpam-1068	85	33	}	}	PUNCT
ejpam-1068	85	34	.	.	PUNCT
ejpam-1068	86	1	then	then	ADV
ejpam-1068	86	2	(	(	PUNCT
ejpam-1068	86	3	x	x	X
ejpam-1068	86	4	,	,	PUNCT
ejpam-1068	86	5	τ	τ	X
ejpam-1068	86	6	)	)	PUNCT
ejpam-1068	86	7	is	be	AUX
ejpam-1068	86	8	a	a	DET
ejpam-1068	86	9	topological	topological	ADJ
ejpam-1068	86	10	space	space	NOUN
ejpam-1068	86	11	.	.	PUNCT
ejpam-1068	87	1	consider	consider	VERB
ejpam-1068	87	2	the	the	DET
ejpam-1068	87	3	mapping	mapping	NOUN
ejpam-1068	87	4	ψ	ψ	X
ejpam-1068	87	5	:	:	PUNCT
ejpam-1068	87	6	p	p	X
ejpam-1068	87	7	(	(	PUNCT
ejpam-1068	87	8	x	x	NOUN
ejpam-1068	87	9	)	)	PUNCT
ejpam-1068	87	10	→	→	SYM
ejpam-1068	87	11	p	p	X
ejpam-1068	87	12	(	(	PUNCT
ejpam-1068	87	13	x	x	NOUN
ejpam-1068	87	14	)	)	PUNCT
ejpam-1068	87	15	defined	define	VERB
ejpam-1068	87	16	by	by	ADP
ejpam-1068	87	17	ψ(∅	ψ(∅	NOUN
ejpam-1068	87	18	)	)	PUNCT
ejpam-1068	87	19	=	=	SYM
ejpam-1068	87	20	ψ({b	ψ({b	PROPN
ejpam-1068	87	21	}	}	PUNCT
ejpam-1068	87	22	)	)	PUNCT
ejpam-1068	87	23	=	=	SYM
ejpam-1068	87	24	ψ({c	ψ({c	NOUN
ejpam-1068	87	25	}	}	PUNCT
ejpam-1068	87	26	)	)	PUNCT
ejpam-1068	88	1	=	=	SYM
ejpam-1068	88	2	∅	∅	NOUN
ejpam-1068	88	3	,	,	PUNCT
ejpam-1068	88	4	ψ({a	ψ({a	PROPN
ejpam-1068	88	5	}	}	PUNCT
ejpam-1068	88	6	)	)	PUNCT
ejpam-1068	88	7	=	=	PRON
ejpam-1068	88	8	{	{	PUNCT
ejpam-1068	88	9	a	a	NOUN
ejpam-1068	88	10	}	}	PUNCT
ejpam-1068	88	11	,	,	PUNCT
ejpam-1068	88	12	ψ({b	ψ({b	PROPN
ejpam-1068	88	13	,	,	PUNCT
ejpam-1068	88	14	c	c	NOUN
ejpam-1068	88	15	}	}	PUNCT
ejpam-1068	88	16	)	)	PUNCT
ejpam-1068	88	17	=	=	PRON
ejpam-1068	88	18	{	{	PUNCT
ejpam-1068	88	19	b	b	NOUN
ejpam-1068	88	20	,	,	PUNCT
ejpam-1068	88	21	c	c	NOUN
ejpam-1068	88	22	}	}	PUNCT
ejpam-1068	88	23	,	,	PUNCT
ejpam-1068	88	24	ψ({a	ψ({a	PROPN
ejpam-1068	88	25	,	,	PUNCT
ejpam-1068	88	26	c	c	NOUN
ejpam-1068	88	27	}	}	PUNCT
ejpam-1068	88	28	)	)	PUNCT
ejpam-1068	88	29	=	=	PRON
ejpam-1068	88	30	{	{	PUNCT
ejpam-1068	88	31	a	a	X
ejpam-1068	88	32	,	,	PUNCT
ejpam-1068	88	33	c	c	NOUN
ejpam-1068	88	34	}	}	PUNCT
ejpam-1068	88	35	,	,	PUNCT
ejpam-1068	88	36	ψ({a	ψ({a	PROPN
ejpam-1068	88	37	,	,	PUNCT
ejpam-1068	88	38	b	b	NOUN
ejpam-1068	88	39	}	}	PUNCT
ejpam-1068	88	40	)	)	PUNCT
ejpam-1068	88	41	=	=	PRON
ejpam-1068	88	42	{	{	PUNCT
ejpam-1068	88	43	a	a	PRON
ejpam-1068	88	44	,	,	PUNCT
ejpam-1068	88	45	b	b	NOUN
ejpam-1068	88	46	}	}	PUNCT
ejpam-1068	88	47	and	and	CCONJ
ejpam-1068	88	48	ψ(x	ψ(x	NOUN
ejpam-1068	88	49	)	)	PUNCT
ejpam-1068	89	1	=	=	PUNCT
ejpam-1068	90	1	x	x	X
ejpam-1068	90	2	.	.	PUNCT
ejpam-1068	91	1	then	then	ADV
ejpam-1068	91	2	ψ	ψ	X
ejpam-1068	91	3	is	be	AUX
ejpam-1068	91	4	an	an	DET
ejpam-1068	91	5	operation	operation	NOUN
ejpam-1068	91	6	on	on	ADP
ejpam-1068	91	7	the	the	DET
ejpam-1068	91	8	topological	topological	ADJ
ejpam-1068	91	9	space	space	NOUN
ejpam-1068	91	10	(	(	PUNCT
ejpam-1068	91	11	x	x	X
ejpam-1068	91	12	,	,	PUNCT
ejpam-1068	91	13	τ	τ	PROPN
ejpam-1068	91	14	)	)	PUNCT
ejpam-1068	91	15	.	.	PUNCT
ejpam-1068	92	1	it	it	PRON
ejpam-1068	92	2	can	can	AUX
ejpam-1068	92	3	be	be	AUX
ejpam-1068	92	4	easily	easily	ADV
ejpam-1068	92	5	verified	verify	VERB
ejpam-1068	92	6	that	that	SCONJ
ejpam-1068	92	7	a	a	PRON
ejpam-1068	92	8	=	=	X
ejpam-1068	92	9	{	{	PUNCT
ejpam-1068	92	10	a	a	NOUN
ejpam-1068	92	11	}	}	PUNCT
ejpam-1068	92	12	and	and	CCONJ
ejpam-1068	92	13	b	b	X
ejpam-1068	92	14	=	=	PRON
ejpam-1068	92	15	{	{	PUNCT
ejpam-1068	92	16	b	b	NOUN
ejpam-1068	92	17	}	}	PUNCT
ejpam-1068	92	18	are	be	AUX
ejpam-1068	92	19	two	two	NUM
ejpam-1068	92	20	gψ	gψ	ADV
ejpam-1068	92	21	-	-	PUNCT
ejpam-1068	92	22	closed	closed	ADJ
ejpam-1068	92	23	sets	set	NOUN
ejpam-1068	92	24	but	but	CCONJ
ejpam-1068	92	25	their	their	PRON
ejpam-1068	92	26	union	union	NOUN
ejpam-1068	92	27	a∪	a∪	NOUN
ejpam-1068	92	28	b	b	X
ejpam-1068	92	29	=	=	PUNCT
ejpam-1068	92	30	{	{	PUNCT
ejpam-1068	92	31	a	a	PROPN
ejpam-1068	92	32	,	,	PUNCT
ejpam-1068	92	33	b	b	NOUN
ejpam-1068	92	34	}	}	PUNCT
ejpam-1068	92	35	is	be	AUX
ejpam-1068	92	36	not	not	PART
ejpam-1068	92	37	a	a	DET
ejpam-1068	92	38	gψ	gψ	ADV
ejpam-1068	92	39	-	-	PUNCT
ejpam-1068	92	40	open	open	ADJ
ejpam-1068	92	41	set	set	NOUN
ejpam-1068	92	42	.	.	PUNCT
ejpam-1068	93	1	(	(	PUNCT
ejpam-1068	93	2	b)let	b)let	NOUN
ejpam-1068	93	3	x	x	SYM
ejpam-1068	93	4	=	=	PRON
ejpam-1068	93	5	{	{	PUNCT
ejpam-1068	93	6	a	a	PRON
ejpam-1068	93	7	,	,	PUNCT
ejpam-1068	93	8	b	b	NOUN
ejpam-1068	93	9	,	,	PUNCT
ejpam-1068	93	10	c	c	NOUN
ejpam-1068	93	11	}	}	PUNCT
ejpam-1068	93	12	and	and	CCONJ
ejpam-1068	93	13	τ	τ	PROPN
ejpam-1068	93	14	=	=	SYM
ejpam-1068	93	15	{	{	PUNCT
ejpam-1068	93	16	∅	∅	NOUN
ejpam-1068	93	17	,	,	PUNCT
ejpam-1068	93	18	{	{	PUNCT
ejpam-1068	93	19	a	a	X
ejpam-1068	93	20	}	}	PUNCT
ejpam-1068	93	21	,	,	PUNCT
ejpam-1068	93	22	x	x	SYM
ejpam-1068	93	23	}	}	PUNCT
ejpam-1068	93	24	.	.	PUNCT
ejpam-1068	94	1	then	then	ADV
ejpam-1068	94	2	(	(	PUNCT
ejpam-1068	94	3	x	x	X
ejpam-1068	94	4	,	,	PUNCT
ejpam-1068	94	5	τ	τ	X
ejpam-1068	94	6	)	)	PUNCT
ejpam-1068	94	7	is	be	AUX
ejpam-1068	94	8	a	a	DET
ejpam-1068	94	9	topological	topological	ADJ
ejpam-1068	94	10	space	space	NOUN
ejpam-1068	94	11	.	.	PUNCT
ejpam-1068	95	1	consider	consider	VERB
ejpam-1068	95	2	the	the	DET
ejpam-1068	95	3	mapping	mapping	NOUN
ejpam-1068	95	4	ψ	ψ	X
ejpam-1068	95	5	:p	:p	PROPN
ejpam-1068	95	6	(	(	PUNCT
ejpam-1068	95	7	x	x	X
ejpam-1068	95	8	)	)	PUNCT
ejpam-1068	95	9	→p	→p	PROPN
ejpam-1068	95	10	(	(	PUNCT
ejpam-1068	95	11	x	x	X
ejpam-1068	95	12	)	)	PUNCT
ejpam-1068	95	13	defined	define	VERB
ejpam-1068	95	14	by	by	ADP
ejpam-1068	95	15	ψ(∅	ψ(∅	NOUN
ejpam-1068	95	16	)	)	PUNCT
ejpam-1068	95	17	=	=	NOUN
ejpam-1068	95	18	∅	∅	NOUN
ejpam-1068	95	19	,	,	PUNCT
ejpam-1068	95	20	ψ({a	ψ({a	PROPN
ejpam-1068	95	21	}	}	PUNCT
ejpam-1068	95	22	)	)	PUNCT
ejpam-1068	96	1	=	=	PRON
ejpam-1068	96	2	{	{	PUNCT
ejpam-1068	96	3	a	a	NOUN
ejpam-1068	96	4	}	}	PUNCT
ejpam-1068	96	5	,	,	PUNCT
ejpam-1068	96	6	ψ({b	ψ({b	PROPN
ejpam-1068	96	7	}	}	PUNCT
ejpam-1068	96	8	)	)	PUNCT
ejpam-1068	96	9	=	=	SYM
ejpam-1068	96	10	ψ({c	ψ({c	NOUN
ejpam-1068	96	11	}	}	PUNCT
ejpam-1068	96	12	)	)	PUNCT
ejpam-1068	97	1	=	=	SYM
ejpam-1068	97	2	ψ({b	ψ({b	PROPN
ejpam-1068	97	3	,	,	PUNCT
ejpam-1068	97	4	c	c	NOUN
ejpam-1068	97	5	}	}	PUNCT
ejpam-1068	97	6	)	)	PUNCT
ejpam-1068	97	7	=	=	SYM
ejpam-1068	97	8	∅	∅	NOUN
ejpam-1068	97	9	,	,	PUNCT
ejpam-1068	97	10	ψ({a	ψ({a	PROPN
ejpam-1068	97	11	,	,	PUNCT
ejpam-1068	97	12	b	b	NOUN
ejpam-1068	97	13	}	}	PUNCT
ejpam-1068	97	14	)	)	PUNCT
ejpam-1068	98	1	=	=	SYM
ejpam-1068	98	2	ψ({a	ψ({a	PROPN
ejpam-1068	98	3	,	,	PUNCT
ejpam-1068	98	4	c	c	NOUN
ejpam-1068	98	5	}	}	PUNCT
ejpam-1068	98	6	)	)	PUNCT
ejpam-1068	98	7	=	=	PRON
ejpam-1068	98	8	{	{	PUNCT
ejpam-1068	98	9	a	a	NOUN
ejpam-1068	98	10	}	}	PUNCT
ejpam-1068	98	11	and	and	CCONJ
ejpam-1068	98	12	ψ(x	ψ(x	NOUN
ejpam-1068	98	13	)	)	PUNCT
ejpam-1068	99	1	=	=	PUNCT
ejpam-1068	100	1	x	x	X
ejpam-1068	100	2	on	on	ADP
ejpam-1068	100	3	the	the	DET
ejpam-1068	100	4	space	space	NOUN
ejpam-1068	100	5	x	x	X
ejpam-1068	100	6	.	.	PUNCT
ejpam-1068	101	1	then	then	ADV
ejpam-1068	101	2	ψ	ψ	X
ejpam-1068	101	3	is	be	AUX
ejpam-1068	101	4	an	an	DET
ejpam-1068	101	5	operation	operation	NOUN
ejpam-1068	101	6	on	on	ADP
ejpam-1068	101	7	the	the	DET
ejpam-1068	101	8	topological	topological	ADJ
ejpam-1068	101	9	space	space	NOUN
ejpam-1068	101	10	(	(	PUNCT
ejpam-1068	101	11	x	x	X
ejpam-1068	101	12	,	,	PUNCT
ejpam-1068	101	13	τ	τ	PROPN
ejpam-1068	101	14	)	)	PUNCT
ejpam-1068	101	15	.	.	PUNCT
ejpam-1068	102	1	it	it	PRON
ejpam-1068	102	2	is	be	AUX
ejpam-1068	102	3	easy	easy	ADJ
ejpam-1068	102	4	to	to	PART
ejpam-1068	102	5	verify	verify	VERB
ejpam-1068	102	6	that	that	SCONJ
ejpam-1068	103	1	a	a	PRON
ejpam-1068	103	2	=	=	X
ejpam-1068	103	3	{	{	PUNCT
ejpam-1068	103	4	a	a	NOUN
ejpam-1068	103	5	,	,	PUNCT
ejpam-1068	103	6	c	c	NOUN
ejpam-1068	103	7	}	}	PUNCT
ejpam-1068	103	8	and	and	CCONJ
ejpam-1068	103	9	b	b	X
ejpam-1068	103	10	=	=	NOUN
ejpam-1068	103	11	{	{	PUNCT
ejpam-1068	103	12	a	a	PROPN
ejpam-1068	103	13	,	,	PUNCT
ejpam-1068	103	14	b	b	X
ejpam-1068	103	15	}	}	PUNCT
ejpam-1068	103	16	are	be	AUX
ejpam-1068	103	17	two	two	NUM
ejpam-1068	103	18	gψ	gψ	ADV
ejpam-1068	103	19	-	-	PUNCT
ejpam-1068	103	20	closed	closed	ADJ
ejpam-1068	103	21	sets	set	NOUN
ejpam-1068	103	22	in	in	ADP
ejpam-1068	103	23	(	(	PUNCT
ejpam-1068	103	24	x	x	INTJ
ejpam-1068	103	25	,	,	PUNCT
ejpam-1068	103	26	τ	τ	PROPN
ejpam-1068	103	27	)	)	PUNCT
ejpam-1068	103	28	but	but	CCONJ
ejpam-1068	103	29	a∩	a∩	PROPN
ejpam-1068	103	30	b	b	X
ejpam-1068	103	31	=	=	X
ejpam-1068	103	32	{	{	PUNCT
ejpam-1068	103	33	a	a	PRON
ejpam-1068	103	34	}	}	PUNCT
ejpam-1068	103	35	is	be	AUX
ejpam-1068	103	36	not	not	PART
ejpam-1068	103	37	gψ	gψ	ADV
ejpam-1068	103	38	-	-	PUNCT
ejpam-1068	103	39	closed	closed	ADJ
ejpam-1068	103	40	.	.	PUNCT
ejpam-1068	104	1	theorem	theorem	NOUN
ejpam-1068	104	2	1	1	NUM
ejpam-1068	104	3	.	.	PUNCT
ejpam-1068	105	1	let	let	VERB
ejpam-1068	105	2	ψ	ψ	PART
ejpam-1068	105	3	be	be	AUX
ejpam-1068	105	4	an	an	DET
ejpam-1068	105	5	operation	operation	NOUN
ejpam-1068	105	6	on	on	ADP
ejpam-1068	105	7	a	a	DET
ejpam-1068	105	8	topological	topological	ADJ
ejpam-1068	105	9	space	space	NOUN
ejpam-1068	105	10	(	(	PUNCT
ejpam-1068	105	11	x	x	X
ejpam-1068	105	12	,	,	PUNCT
ejpam-1068	105	13	τ	τ	PROPN
ejpam-1068	105	14	)	)	PUNCT
ejpam-1068	105	15	.	.	PUNCT
ejpam-1068	106	1	if	if	SCONJ
ejpam-1068	106	2	a	a	PRON
ejpam-1068	106	3	is	be	AUX
ejpam-1068	106	4	gψ	gψ	ADJ
ejpam-1068	106	5	-	-	PUNCT
ejpam-1068	106	6	closed	closed	ADJ
ejpam-1068	106	7	,	,	PUNCT
ejpam-1068	106	8	then	then	ADV
ejpam-1068	106	9	ψ−	ψ−	VERB
ejpam-1068	106	10	cl(a	cl(a	X
ejpam-1068	106	11	)	)	PUNCT
ejpam-1068	106	12	\	\	NOUN
ejpam-1068	107	1	a	a	PRON
ejpam-1068	107	2	does	do	AUX
ejpam-1068	107	3	not	not	PART
ejpam-1068	107	4	contain	contain	VERB
ejpam-1068	107	5	any	any	DET
ejpam-1068	107	6	non	non	ADJ
ejpam-1068	107	7	-	-	ADJ
ejpam-1068	107	8	empty	empty	ADJ
ejpam-1068	107	9	closed	closed	ADJ
ejpam-1068	107	10	set	set	NOUN
ejpam-1068	107	11	.	.	PUNCT
ejpam-1068	108	1	proof	proof	NOUN
ejpam-1068	108	2	.	.	PUNCT
ejpam-1068	109	1	let	let	VERB
ejpam-1068	109	2	f	f	PRON
ejpam-1068	109	3	be	be	AUX
ejpam-1068	109	4	a	a	DET
ejpam-1068	109	5	closed	closed	ADJ
ejpam-1068	109	6	subset	subset	NOUN
ejpam-1068	109	7	of	of	ADP
ejpam-1068	109	8	x	x	SYM
ejpam-1068	109	9	such	such	ADJ
ejpam-1068	109	10	that	that	SCONJ
ejpam-1068	109	11	f	f	PROPN
ejpam-1068	109	12	⊆ψ−cl(a)\a	⊆ψ−cl(a)\a	NOUN
ejpam-1068	109	13	,	,	PUNCT
ejpam-1068	109	14	where	where	SCONJ
ejpam-1068	109	15	a	a	PRON
ejpam-1068	109	16	is	be	AUX
ejpam-1068	109	17	gψ	gψ	ADJ
ejpam-1068	109	18	-	-	PUNCT
ejpam-1068	109	19	closed	closed	ADJ
ejpam-1068	109	20	.	.	PUNCT
ejpam-1068	110	1	then	then	ADV
ejpam-1068	110	2	x	x	SYM
ejpam-1068	110	3	\	\	PROPN
ejpam-1068	110	4	f	f	PROPN
ejpam-1068	110	5	is	be	AUX
ejpam-1068	110	6	open	open	ADJ
ejpam-1068	110	7	,	,	PUNCT
ejpam-1068	110	8	a⊆	a⊆	VERB
ejpam-1068	110	9	x	x	SYM
ejpam-1068	111	1	\	\	PROPN
ejpam-1068	111	2	f	f	PROPN
ejpam-1068	111	3	and	and	CCONJ
ejpam-1068	111	4	a	a	PRON
ejpam-1068	111	5	is	be	AUX
ejpam-1068	111	6	gψ	gψ	ADV
ejpam-1068	111	7	-	-	PUNCT
ejpam-1068	111	8	closed	closed	ADJ
ejpam-1068	111	9	,	,	PUNCT
ejpam-1068	111	10	so	so	ADV
ejpam-1068	111	11	ψ−	ψ−	PROPN
ejpam-1068	111	12	cl(a	cl(a	PUNCT
ejpam-1068	111	13	)	)	PUNCT
ejpam-1068	111	14	⊆	⊆	NUM
ejpam-1068	111	15	x	x	SYM
ejpam-1068	111	16	\	\	PROPN
ejpam-1068	111	17	f	f	PROPN
ejpam-1068	111	18	and	and	CCONJ
ejpam-1068	111	19	thus	thus	ADV
ejpam-1068	111	20	f	f	PROPN
ejpam-1068	111	21	⊆	⊆	NUM
ejpam-1068	111	22	x	x	SYM
ejpam-1068	111	23	\ψ−	\ψ−	NOUN
ejpam-1068	111	24	cl(a	cl(a	NUM
ejpam-1068	111	25	)	)	PUNCT
ejpam-1068	111	26	.	.	PUNCT
ejpam-1068	112	1	thus	thus	ADV
ejpam-1068	112	2	f	f	PROPN
ejpam-1068	112	3	⊆	⊆	NUM
ejpam-1068	112	4	(	(	PUNCT
ejpam-1068	112	5	x	x	NOUN
ejpam-1068	112	6	\ψ−	\ψ−	NOUN
ejpam-1068	112	7	cl(a))∩ψ−	cl(a))∩ψ−	PROPN
ejpam-1068	112	8	cl(a	cl(a	NUM
ejpam-1068	112	9	)	)	PUNCT
ejpam-1068	112	10	=	=	SYM
ejpam-1068	112	11	∅	∅	NOUN
ejpam-1068	112	12	and	and	CCONJ
ejpam-1068	112	13	hence	hence	ADV
ejpam-1068	112	14	f	f	NOUN
ejpam-1068	112	15	=	=	PUNCT
ejpam-1068	112	16	∅.	∅.	PRON
ejpam-1068	112	17	corollary	corollary	ADJ
ejpam-1068	112	18	1	1	NUM
ejpam-1068	112	19	.	.	PUNCT
ejpam-1068	113	1	let	let	VERB
ejpam-1068	113	2	ψ	ψ	PART
ejpam-1068	113	3	be	be	AUX
ejpam-1068	113	4	an	an	DET
ejpam-1068	113	5	operation	operation	NOUN
ejpam-1068	113	6	on	on	ADP
ejpam-1068	113	7	a	a	DET
ejpam-1068	113	8	topological	topological	ADJ
ejpam-1068	113	9	space	space	NOUN
ejpam-1068	113	10	(	(	PUNCT
ejpam-1068	113	11	x	x	X
ejpam-1068	113	12	,	,	PUNCT
ejpam-1068	113	13	τ	τ	PROPN
ejpam-1068	113	14	)	)	PUNCT
ejpam-1068	113	15	and	and	CCONJ
ejpam-1068	113	16	a⊆	a⊆	NOUN
ejpam-1068	113	17	x	x	PUNCT
ejpam-1068	113	18	be	be	AUX
ejpam-1068	113	19	a	a	DET
ejpam-1068	113	20	gψ	gψ	ADV
ejpam-1068	113	21	-	-	PUNCT
ejpam-1068	113	22	closed	closed	ADJ
ejpam-1068	113	23	set	set	NOUN
ejpam-1068	113	24	.	.	PUNCT
ejpam-1068	114	1	then	then	ADV
ejpam-1068	114	2	a	a	PRON
ejpam-1068	114	3	is	be	AUX
ejpam-1068	114	4	ψ	ψ	ADJ
ejpam-1068	114	5	-	-	ADJ
ejpam-1068	114	6	closed	closed	ADJ
ejpam-1068	114	7	iff	iff	NOUN
ejpam-1068	114	8	ψ−	ψ−	PROPN
ejpam-1068	114	9	cl(a	cl(a	NUM
ejpam-1068	114	10	)	)	PUNCT
ejpam-1068	114	11	\	\	NOUN
ejpam-1068	115	1	a	a	PRON
ejpam-1068	115	2	is	be	AUX
ejpam-1068	115	3	closed	closed	ADJ
ejpam-1068	115	4	.	.	PUNCT
ejpam-1068	116	1	b.	b.	PROPN
ejpam-1068	116	2	roy	roy	PROPN
ejpam-1068	116	3	,	,	PUNCT
ejpam-1068	116	4	r.	r.	PROPN
ejpam-1068	116	5	sen	sen	PROPN
ejpam-1068	116	6	,	,	PUNCT
ejpam-1068	116	7	t.	t.	PROPN
ejpam-1068	116	8	noiri	noiri	PROPN
ejpam-1068	116	9	/	/	SYM
ejpam-1068	116	10	eur	eur	PROPN
ejpam-1068	116	11	.	.	PUNCT
ejpam-1068	117	1	j.	j.	PROPN
ejpam-1068	117	2	pure	pure	PROPN
ejpam-1068	117	3	appl	appl	PROPN
ejpam-1068	117	4	.	.	PROPN
ejpam-1068	117	5	math	math	PROPN
ejpam-1068	117	6	,	,	PUNCT
ejpam-1068	117	7	6	6	NUM
ejpam-1068	117	8	(	(	PUNCT
ejpam-1068	117	9	2013	2013	NUM
ejpam-1068	117	10	)	)	PUNCT
ejpam-1068	117	11	,	,	PUNCT
ejpam-1068	117	12	44	44	NUM
ejpam-1068	117	13	-	-	SYM
ejpam-1068	117	14	52	52	NUM
ejpam-1068	117	15	47	47	NUM
ejpam-1068	117	16	proof	proof	NOUN
ejpam-1068	117	17	.	.	PUNCT
ejpam-1068	118	1	let	let	VERB
ejpam-1068	118	2	a	a	PRON
ejpam-1068	118	3	be	be	AUX
ejpam-1068	118	4	a	a	DET
ejpam-1068	118	5	gψ	gψ	ADV
ejpam-1068	118	6	-	-	PUNCT
ejpam-1068	118	7	closed	closed	ADJ
ejpam-1068	118	8	set	set	NOUN
ejpam-1068	118	9	.	.	PUNCT
ejpam-1068	119	1	if	if	SCONJ
ejpam-1068	119	2	a	a	PRON
ejpam-1068	119	3	is	be	AUX
ejpam-1068	119	4	ψ	ψ	NOUN
ejpam-1068	119	5	-	-	ADJ
ejpam-1068	119	6	closed	closed	ADJ
ejpam-1068	119	7	,	,	PUNCT
ejpam-1068	119	8	ψ−	ψ−	NOUN
ejpam-1068	119	9	cl(a	cl(a	NUM
ejpam-1068	119	10	)	)	PUNCT
ejpam-1068	119	11	\	\	PROPN
ejpam-1068	119	12	a=	a=	ADJ
ejpam-1068	119	13	∅	∅	NOUN
ejpam-1068	119	14	,	,	PUNCT
ejpam-1068	119	15	and	and	CCONJ
ejpam-1068	119	16	thus	thus	ADV
ejpam-1068	119	17	ψ−	ψ−	VERB
ejpam-1068	119	18	cl(a	cl(a	X
ejpam-1068	119	19	)	)	PUNCT
ejpam-1068	119	20	\	\	NOUN
ejpam-1068	120	1	a	a	PRON
ejpam-1068	120	2	becomes	become	VERB
ejpam-1068	120	3	a	a	DET
ejpam-1068	120	4	closed	closed	ADJ
ejpam-1068	120	5	set	set	NOUN
ejpam-1068	120	6	.	.	PUNCT
ejpam-1068	121	1	conversely	conversely	ADV
ejpam-1068	121	2	,	,	PUNCT
ejpam-1068	121	3	let	let	VERB
ejpam-1068	121	4	ψ−	ψ−	VERB
ejpam-1068	121	5	cl(a	cl(a	X
ejpam-1068	121	6	)	)	PUNCT
ejpam-1068	121	7	\	\	NOUN
ejpam-1068	122	1	a	a	DET
ejpam-1068	122	2	be	be	AUX
ejpam-1068	122	3	a	a	DET
ejpam-1068	122	4	closed	closed	ADJ
ejpam-1068	122	5	set	set	NOUN
ejpam-1068	122	6	,	,	PUNCT
ejpam-1068	122	7	where	where	SCONJ
ejpam-1068	122	8	a	a	PRON
ejpam-1068	122	9	is	be	AUX
ejpam-1068	122	10	gψ	gψ	ADJ
ejpam-1068	122	11	-	-	PUNCT
ejpam-1068	122	12	closed	closed	ADJ
ejpam-1068	122	13	.	.	PUNCT
ejpam-1068	123	1	then	then	ADV
ejpam-1068	123	2	by	by	ADP
ejpam-1068	123	3	theorem	theorem	NOUN
ejpam-1068	123	4	1	1	NUM
ejpam-1068	123	5	,	,	PUNCT
ejpam-1068	123	6	ψ−	ψ−	VERB
ejpam-1068	123	7	cl(a	cl(a	NUM
ejpam-1068	123	8	)	)	PUNCT
ejpam-1068	123	9	\a	\a	VERB
ejpam-1068	123	10	does	do	AUX
ejpam-1068	123	11	not	not	PART
ejpam-1068	123	12	contain	contain	VERB
ejpam-1068	123	13	any	any	DET
ejpam-1068	123	14	non	non	ADJ
ejpam-1068	123	15	-	-	ADJ
ejpam-1068	123	16	empty	empty	ADJ
ejpam-1068	123	17	closed	closed	ADJ
ejpam-1068	123	18	set	set	NOUN
ejpam-1068	123	19	.	.	PUNCT
ejpam-1068	124	1	since	since	SCONJ
ejpam-1068	124	2	ψ−	ψ−	PROPN
ejpam-1068	124	3	cl(a	cl(a	NUM
ejpam-1068	124	4	)	)	PUNCT
ejpam-1068	124	5	\a	\a	VERB
ejpam-1068	124	6	is	be	AUX
ejpam-1068	124	7	a	a	DET
ejpam-1068	124	8	closed	closed	ADJ
ejpam-1068	124	9	subset	subset	NOUN
ejpam-1068	124	10	of	of	ADP
ejpam-1068	124	11	itself	itself	PRON
ejpam-1068	124	12	,	,	PUNCT
ejpam-1068	124	13	ψ−	ψ−	VERB
ejpam-1068	124	14	cl(a	cl(a	NUM
ejpam-1068	124	15	)	)	PUNCT
ejpam-1068	124	16	\	\	NOUN
ejpam-1068	124	17	a=	a=	ADJ
ejpam-1068	124	18	∅	∅	NOUN
ejpam-1068	124	19	and	and	CCONJ
ejpam-1068	124	20	hence	hence	ADV
ejpam-1068	124	21	a	a	PRON
ejpam-1068	124	22	is	be	AUX
ejpam-1068	124	23	ψ	ψ	ADJ
ejpam-1068	124	24	-	-	ADJ
ejpam-1068	124	25	closed	closed	ADJ
ejpam-1068	124	26	.	.	PUNCT
ejpam-1068	125	1	theorem	theorem	NOUN
ejpam-1068	125	2	2	2	NUM
ejpam-1068	125	3	.	.	PUNCT
ejpam-1068	125	4	a	a	DET
ejpam-1068	125	5	subset	subset	NOUN
ejpam-1068	125	6	a	a	PRON
ejpam-1068	125	7	of	of	ADP
ejpam-1068	125	8	a	a	DET
ejpam-1068	125	9	topological	topological	ADJ
ejpam-1068	125	10	space	space	NOUN
ejpam-1068	125	11	(	(	PUNCT
ejpam-1068	125	12	x	x	X
ejpam-1068	125	13	,	,	PUNCT
ejpam-1068	125	14	τ	τ	PROPN
ejpam-1068	125	15	)	)	PUNCT
ejpam-1068	125	16	with	with	ADP
ejpam-1068	125	17	an	an	DET
ejpam-1068	125	18	operation	operation	NOUN
ejpam-1068	125	19	ψ	ψ	NOUN
ejpam-1068	125	20	on	on	ADP
ejpam-1068	125	21	it	it	PRON
ejpam-1068	125	22	is	be	AUX
ejpam-1068	125	23	gψ	gψ	ADV
ejpam-1068	125	24	-	-	PUNCT
ejpam-1068	125	25	closed	closed	ADJ
ejpam-1068	125	26	iff	iff	PROPN
ejpam-1068	125	27	cl({x})∩	cl({x})∩	PROPN
ejpam-1068	125	28	a	a	DET
ejpam-1068	125	29	6=	6=	NOUN
ejpam-1068	125	30	∅	∅	NOUN
ejpam-1068	125	31	for	for	ADP
ejpam-1068	125	32	every	every	DET
ejpam-1068	125	33	x	x	X
ejpam-1068	125	34	∈ψ−	∈ψ−	PROPN
ejpam-1068	125	35	cl(a	cl(a	NUM
ejpam-1068	125	36	)	)	PUNCT
ejpam-1068	125	37	.	.	PUNCT
ejpam-1068	126	1	proof	proof	NOUN
ejpam-1068	126	2	.	.	PUNCT
ejpam-1068	127	1	let	let	VERB
ejpam-1068	127	2	a	a	PRON
ejpam-1068	127	3	be	be	AUX
ejpam-1068	127	4	a	a	DET
ejpam-1068	127	5	gψ	gψ	ADV
ejpam-1068	127	6	-	-	PUNCT
ejpam-1068	127	7	closed	closed	ADJ
ejpam-1068	127	8	set	set	NOUN
ejpam-1068	127	9	in	in	ADP
ejpam-1068	127	10	x	x	PUNCT
ejpam-1068	127	11	and	and	CCONJ
ejpam-1068	127	12	suppose	suppose	VERB
ejpam-1068	127	13	if	if	SCONJ
ejpam-1068	127	14	possible	possible	ADJ
ejpam-1068	127	15	that	that	SCONJ
ejpam-1068	127	16	there	there	PRON
ejpam-1068	127	17	exists	exist	VERB
ejpam-1068	127	18	an	an	DET
ejpam-1068	127	19	x	x	X
ejpam-1068	127	20	∈ψ−	∈ψ−	NOUN
ejpam-1068	127	21	cl(a	cl(a	NUM
ejpam-1068	127	22	)	)	PUNCT
ejpam-1068	127	23	such	such	ADJ
ejpam-1068	127	24	that	that	SCONJ
ejpam-1068	127	25	cl({x})∩	cl({x})∩	NOUN
ejpam-1068	127	26	a=	a=	VERB
ejpam-1068	127	27	∅.	∅.	X
ejpam-1068	127	28	therefore	therefore	ADV
ejpam-1068	127	29	a⊆	a⊆	VERB
ejpam-1068	127	30	x	x	SYM
ejpam-1068	127	31	\	\	NOUN
ejpam-1068	127	32	cl({x	cl({x	NUM
ejpam-1068	127	33	}	}	PUNCT
ejpam-1068	127	34	)	)	PUNCT
ejpam-1068	127	35	,	,	PUNCT
ejpam-1068	127	36	and	and	CCONJ
ejpam-1068	127	37	so	so	ADV
ejpam-1068	127	38	ψ−	ψ−	VERB
ejpam-1068	127	39	cl(a	cl(a	PUNCT
ejpam-1068	127	40	)	)	PUNCT
ejpam-1068	127	41	⊆	⊆	NUM
ejpam-1068	127	42	x	x	SYM
ejpam-1068	127	43	\	\	NOUN
ejpam-1068	127	44	cl({x	cl({x	NUM
ejpam-1068	127	45	}	}	PUNCT
ejpam-1068	127	46	)	)	PUNCT
ejpam-1068	127	47	.	.	PUNCT
ejpam-1068	128	1	hence	hence	ADV
ejpam-1068	128	2	x	x	X
ejpam-1068	128	3	6∈ψ−	6∈ψ−	NUM
ejpam-1068	128	4	cl(a	cl(a	NUM
ejpam-1068	128	5	)	)	PUNCT
ejpam-1068	128	6	,	,	PUNCT
ejpam-1068	129	1	which	which	PRON
ejpam-1068	129	2	is	be	AUX
ejpam-1068	129	3	a	a	DET
ejpam-1068	129	4	contradiction	contradiction	NOUN
ejpam-1068	129	5	.	.	PUNCT
ejpam-1068	130	1	conversely	conversely	ADV
ejpam-1068	130	2	,	,	PUNCT
ejpam-1068	130	3	suppose	suppose	VERB
ejpam-1068	130	4	that	that	SCONJ
ejpam-1068	130	5	the	the	DET
ejpam-1068	130	6	condition	condition	NOUN
ejpam-1068	130	7	of	of	ADP
ejpam-1068	130	8	the	the	DET
ejpam-1068	130	9	theorem	theorem	NOUN
ejpam-1068	130	10	holds	hold	VERB
ejpam-1068	130	11	and	and	CCONJ
ejpam-1068	130	12	let	let	VERB
ejpam-1068	130	13	u	u	PRON
ejpam-1068	130	14	be	be	AUX
ejpam-1068	130	15	any	any	DET
ejpam-1068	130	16	open	open	ADJ
ejpam-1068	130	17	set	set	NOUN
ejpam-1068	130	18	containing	contain	VERB
ejpam-1068	130	19	a.	a.	NOUN
ejpam-1068	130	20	let	let	NOUN
ejpam-1068	130	21	x	x	PUNCT
ejpam-1068	130	22	∈ψ−	∈ψ−	PROPN
ejpam-1068	130	23	cl(a	cl(a	NUM
ejpam-1068	130	24	)	)	PUNCT
ejpam-1068	130	25	.	.	PUNCT
ejpam-1068	131	1	then	then	ADV
ejpam-1068	131	2	by	by	ADP
ejpam-1068	131	3	hypothesis	hypothesis	NOUN
ejpam-1068	131	4	cl({x})∩	cl({x})∩	NOUN
ejpam-1068	131	5	a	a	DET
ejpam-1068	131	6	6=	6=	NOUN
ejpam-1068	131	7	∅	∅	NOUN
ejpam-1068	131	8	,	,	PUNCT
ejpam-1068	131	9	so	so	SCONJ
ejpam-1068	131	10	there	there	PRON
ejpam-1068	131	11	exists	exist	VERB
ejpam-1068	131	12	z	z	PROPN
ejpam-1068	131	13	∈	∈	PROPN
ejpam-1068	131	14	cl({x	cl({x	PRON
ejpam-1068	131	15	}	}	PUNCT
ejpam-1068	131	16	)	)	PUNCT
ejpam-1068	131	17	∩	∩	NOUN
ejpam-1068	131	18	a	a	PRON
ejpam-1068	131	19	and	and	CCONJ
ejpam-1068	131	20	so	so	ADV
ejpam-1068	131	21	z	z	NOUN
ejpam-1068	131	22	∈	∈	PROPN
ejpam-1068	131	23	a	a	DET
ejpam-1068	131	24	⊆	⊆	NUM
ejpam-1068	131	25	u	u	NOUN
ejpam-1068	131	26	.	.	PUNCT
ejpam-1068	132	1	thus	thus	ADV
ejpam-1068	132	2	{	{	PUNCT
ejpam-1068	132	3	x	x	NOUN
ejpam-1068	132	4	}	}	PUNCT
ejpam-1068	132	5	∩	∩	ADJ
ejpam-1068	132	6	u	u	NOUN
ejpam-1068	132	7	6=	6=	ADP
ejpam-1068	132	8	∅.	∅.	VERB
ejpam-1068	132	9	hence	hence	ADV
ejpam-1068	132	10	x	x	PART
ejpam-1068	132	11	∈	∈	PROPN
ejpam-1068	132	12	u	u	NOUN
ejpam-1068	132	13	,	,	PUNCT
ejpam-1068	132	14	which	which	PRON
ejpam-1068	132	15	implies	imply	VERB
ejpam-1068	132	16	that	that	SCONJ
ejpam-1068	132	17	ψ−	ψ−	PROPN
ejpam-1068	132	18	cl(a	cl(a	PUNCT
ejpam-1068	132	19	)	)	PUNCT
ejpam-1068	132	20	⊆	⊆	NUM
ejpam-1068	132	21	u	u	NOUN
ejpam-1068	132	22	.	.	PUNCT
ejpam-1068	133	1	theorem	theorem	NOUN
ejpam-1068	133	2	3	3	X
ejpam-1068	133	3	.	.	PUNCT
ejpam-1068	134	1	let	let	VERB
ejpam-1068	134	2	ψ	ψ	PART
ejpam-1068	134	3	be	be	AUX
ejpam-1068	134	4	an	an	DET
ejpam-1068	134	5	operation	operation	NOUN
ejpam-1068	134	6	on	on	ADP
ejpam-1068	134	7	a	a	DET
ejpam-1068	134	8	topological	topological	ADJ
ejpam-1068	134	9	space	space	NOUN
ejpam-1068	134	10	(	(	PUNCT
ejpam-1068	134	11	x	x	X
ejpam-1068	134	12	,	,	PUNCT
ejpam-1068	134	13	τ	τ	PROPN
ejpam-1068	134	14	)	)	PUNCT
ejpam-1068	134	15	and	and	CCONJ
ejpam-1068	134	16	a⊆	a⊆	PROPN
ejpam-1068	134	17	b	b	PRON
ejpam-1068	134	18	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	134	19	cl(a	cl(a	NUM
ejpam-1068	134	20	)	)	PUNCT
ejpam-1068	134	21	,	,	PUNCT
ejpam-1068	134	22	where	where	SCONJ
ejpam-1068	134	23	a	a	PRON
ejpam-1068	134	24	is	be	AUX
ejpam-1068	134	25	gψ	gψ	ADJ
ejpam-1068	134	26	-	-	PUNCT
ejpam-1068	134	27	closed	closed	ADJ
ejpam-1068	134	28	.	.	PUNCT
ejpam-1068	135	1	then	then	ADV
ejpam-1068	135	2	b	b	PROPN
ejpam-1068	135	3	is	be	AUX
ejpam-1068	135	4	gψ	gψ	ADV
ejpam-1068	135	5	-	-	PUNCT
ejpam-1068	135	6	closed	closed	ADJ
ejpam-1068	135	7	.	.	PUNCT
ejpam-1068	136	1	proof	proof	NOUN
ejpam-1068	136	2	.	.	PUNCT
ejpam-1068	137	1	let	let	VERB
ejpam-1068	137	2	b	b	NOUN
ejpam-1068	137	3	⊆	⊆	NUM
ejpam-1068	137	4	u	u	NOUN
ejpam-1068	137	5	∈	∈	PROPN
ejpam-1068	137	6	τ	τ	PROPN
ejpam-1068	137	7	.	.	PUNCT
ejpam-1068	138	1	since	since	SCONJ
ejpam-1068	138	2	a	a	PRON
ejpam-1068	138	3	is	be	AUX
ejpam-1068	138	4	gψ	gψ	ADV
ejpam-1068	138	5	-	-	PUNCT
ejpam-1068	138	6	closed	closed	ADJ
ejpam-1068	138	7	and	and	CCONJ
ejpam-1068	138	8	a⊆	a⊆	NOUN
ejpam-1068	138	9	u	u	NOUN
ejpam-1068	138	10	,	,	PUNCT
ejpam-1068	138	11	ψ−	ψ−	PROPN
ejpam-1068	138	12	cl(a	cl(a	NUM
ejpam-1068	138	13	)	)	PUNCT
ejpam-1068	138	14	⊆	⊆	NUM
ejpam-1068	138	15	u	u	NOUN
ejpam-1068	138	16	.	.	PUNCT
ejpam-1068	139	1	now	now	ADV
ejpam-1068	139	2	,	,	PUNCT
ejpam-1068	139	3	b	b	PROPN
ejpam-1068	139	4	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	139	5	cl(a	cl(a	X
ejpam-1068	139	6	)	)	PUNCT
ejpam-1068	139	7	implies	imply	VERB
ejpam-1068	139	8	ψ−	ψ−	VERB
ejpam-1068	139	9	cl(b	cl(b	NOUN
ejpam-1068	139	10	)	)	PUNCT
ejpam-1068	139	11	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	139	12	cl(a	cl(a	NUM
ejpam-1068	139	13	)	)	PUNCT
ejpam-1068	139	14	and	and	CCONJ
ejpam-1068	139	15	hence	hence	ADV
ejpam-1068	139	16	ψ−	ψ−	VERB
ejpam-1068	139	17	cl(b	cl(b	NOUN
ejpam-1068	139	18	)	)	PUNCT
ejpam-1068	140	1	⊆	⊆	NUM
ejpam-1068	140	2	u	u	NOUN
ejpam-1068	140	3	.	.	PUNCT
ejpam-1068	141	1	theorem	theorem	ADJ
ejpam-1068	141	2	4	4	NUM
ejpam-1068	141	3	.	.	PUNCT
ejpam-1068	142	1	let	let	AUX
ejpam-1068	142	2	(	(	PUNCT
ejpam-1068	142	3	x	x	X
ejpam-1068	142	4	,	,	PUNCT
ejpam-1068	142	5	τ	τ	X
ejpam-1068	142	6	)	)	PUNCT
ejpam-1068	142	7	be	be	VERB
ejpam-1068	142	8	a	a	DET
ejpam-1068	142	9	topological	topological	ADJ
ejpam-1068	142	10	space	space	NOUN
ejpam-1068	142	11	and	and	CCONJ
ejpam-1068	142	12	ψ	ψ	AUX
ejpam-1068	142	13	be	be	AUX
ejpam-1068	142	14	an	an	DET
ejpam-1068	142	15	operation	operation	NOUN
ejpam-1068	142	16	on	on	ADP
ejpam-1068	142	17	x	x	X
ejpam-1068	142	18	.	.	PUNCT
ejpam-1068	143	1	then	then	ADV
ejpam-1068	143	2	a	a	PRON
ejpam-1068	143	3	is	be	AUX
ejpam-1068	143	4	gψ	gψ	ADJ
ejpam-1068	143	5	-	-	PUNCT
ejpam-1068	143	6	open	open	ADJ
ejpam-1068	143	7	iff	iff	PROPN
ejpam-1068	143	8	f	f	PROPN
ejpam-1068	143	9	⊆ψ−	⊆ψ−	PROPN
ejpam-1068	143	10	int(a	int(a	PROPN
ejpam-1068	143	11	)	)	PUNCT
ejpam-1068	143	12	whenever	whenever	SCONJ
ejpam-1068	143	13	f	f	PROPN
ejpam-1068	143	14	⊆	⊆	PROPN
ejpam-1068	143	15	a	a	PRON
ejpam-1068	143	16	and	and	CCONJ
ejpam-1068	143	17	f	f	PROPN
ejpam-1068	143	18	is	be	AUX
ejpam-1068	143	19	closed	closed	ADJ
ejpam-1068	143	20	.	.	PUNCT
ejpam-1068	144	1	proof	proof	NOUN
ejpam-1068	144	2	.	.	PUNCT
ejpam-1068	145	1	let	let	VERB
ejpam-1068	145	2	a	a	PRON
ejpam-1068	145	3	be	be	AUX
ejpam-1068	145	4	a	a	DET
ejpam-1068	145	5	gψ	gψ	ADV
ejpam-1068	145	6	-	-	PUNCT
ejpam-1068	145	7	open	open	ADJ
ejpam-1068	145	8	set	set	NOUN
ejpam-1068	145	9	and	and	CCONJ
ejpam-1068	145	10	f	f	PROPN
ejpam-1068	145	11	⊆	⊆	PROPN
ejpam-1068	145	12	a	a	PRON
ejpam-1068	145	13	,	,	PUNCT
ejpam-1068	145	14	where	where	SCONJ
ejpam-1068	145	15	f	f	PROPN
ejpam-1068	145	16	is	be	AUX
ejpam-1068	145	17	closed	closed	ADJ
ejpam-1068	145	18	.	.	PUNCT
ejpam-1068	146	1	then	then	ADV
ejpam-1068	146	2	x	x	X
ejpam-1068	146	3	\	\	PROPN
ejpam-1068	146	4	a	a	PRON
ejpam-1068	146	5	is	be	AUX
ejpam-1068	146	6	a	a	DET
ejpam-1068	146	7	gψ	gψ	ADV
ejpam-1068	146	8	-	-	PUNCT
ejpam-1068	146	9	closed	closed	ADJ
ejpam-1068	146	10	set	set	NOUN
ejpam-1068	146	11	contained	contain	VERB
ejpam-1068	146	12	in	in	ADP
ejpam-1068	146	13	the	the	DET
ejpam-1068	146	14	open	open	ADJ
ejpam-1068	146	15	set	set	NOUN
ejpam-1068	146	16	x	x	NOUN
ejpam-1068	146	17	\	\	PROPN
ejpam-1068	146	18	f	f	X
ejpam-1068	146	19	.	.	PUNCT
ejpam-1068	147	1	hence	hence	ADV
ejpam-1068	147	2	ψ−	ψ−	VERB
ejpam-1068	147	3	cl(x	cl(x	X
ejpam-1068	147	4	\	\	NOUN
ejpam-1068	147	5	a)⊆	a)⊆	X
ejpam-1068	147	6	x	x	SYM
ejpam-1068	147	7	\	\	PROPN
ejpam-1068	147	8	f	f	PROPN
ejpam-1068	147	9	,	,	PUNCT
ejpam-1068	147	10	i.e.	i.e.	X
ejpam-1068	147	11	,	,	PUNCT
ejpam-1068	147	12	x	x	X
ejpam-1068	147	13	\ψ−	\ψ−	NOUN
ejpam-1068	147	14	int(a	int(a	NOUN
ejpam-1068	147	15	)	)	PUNCT
ejpam-1068	147	16	⊆	⊆	NUM
ejpam-1068	147	17	x	x	SYM
ejpam-1068	147	18	\	\	PROPN
ejpam-1068	147	19	f	f	X
ejpam-1068	147	20	.	.	PUNCT
ejpam-1068	148	1	so	so	ADV
ejpam-1068	148	2	f	f	PROPN
ejpam-1068	148	3	⊆ψ−	⊆ψ−	PROPN
ejpam-1068	148	4	int(a	int(a	PROPN
ejpam-1068	148	5	)	)	PUNCT
ejpam-1068	148	6	.	.	PUNCT
ejpam-1068	149	1	conversely	conversely	ADV
ejpam-1068	149	2	,	,	PUNCT
ejpam-1068	149	3	suppose	suppose	VERB
ejpam-1068	149	4	that	that	SCONJ
ejpam-1068	149	5	f	f	PROPN
ejpam-1068	149	6	⊆	⊆	NUM
ejpam-1068	149	7	ψ	ψ	X
ejpam-1068	149	8	−	−	PROPN
ejpam-1068	149	9	int(a	int(a	NOUN
ejpam-1068	149	10	)	)	PUNCT
ejpam-1068	149	11	for	for	ADP
ejpam-1068	149	12	any	any	DET
ejpam-1068	149	13	closed	closed	ADJ
ejpam-1068	149	14	set	set	NOUN
ejpam-1068	149	15	f	f	PROPN
ejpam-1068	149	16	whenever	whenever	SCONJ
ejpam-1068	149	17	f	f	PROPN
ejpam-1068	149	18	⊆	⊆	NUM
ejpam-1068	149	19	a.	a.	NOUN
ejpam-1068	149	20	let	let	VERB
ejpam-1068	149	21	x	x	SYM
ejpam-1068	149	22	\a⊆	\a⊆	NUM
ejpam-1068	149	23	u	u	NOUN
ejpam-1068	149	24	,	,	PUNCT
ejpam-1068	149	25	where	where	SCONJ
ejpam-1068	149	26	u	u	PROPN
ejpam-1068	149	27	∈	∈	PROPN
ejpam-1068	149	28	τ	τ	PROPN
ejpam-1068	149	29	.	.	PUNCT
ejpam-1068	150	1	then	then	ADV
ejpam-1068	150	2	x	x	X
ejpam-1068	150	3	\u	\u	X
ejpam-1068	150	4	⊆	⊆	SYM
ejpam-1068	150	5	a	a	PRON
ejpam-1068	150	6	and	and	CCONJ
ejpam-1068	150	7	x	x	SYM
ejpam-1068	150	8	\u	\u	X
ejpam-1068	150	9	is	be	AUX
ejpam-1068	150	10	closed	close	VERB
ejpam-1068	150	11	.	.	PUNCT
ejpam-1068	151	1	by	by	ADP
ejpam-1068	151	2	assumption	assumption	NOUN
ejpam-1068	151	3	,	,	PUNCT
ejpam-1068	151	4	x	x	X
ejpam-1068	151	5	\u	\u	X
ejpam-1068	151	6	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	151	7	int(a	int(a	NOUN
ejpam-1068	151	8	)	)	PUNCT
ejpam-1068	151	9	and	and	CCONJ
ejpam-1068	151	10	henceψ−cl(x	henceψ−cl(x	PROPN
ejpam-1068	151	11	\a	\a	NUM
ejpam-1068	151	12	)	)	PUNCT
ejpam-1068	151	13	=	=	SYM
ejpam-1068	151	14	x	x	SYM
ejpam-1068	151	15	\ψ−int(a	\ψ−int(a	PROPN
ejpam-1068	151	16	)	)	PUNCT
ejpam-1068	151	17	⊆	⊆	NUM
ejpam-1068	151	18	u	u	NOUN
ejpam-1068	151	19	.	.	PUNCT
ejpam-1068	152	1	hence	hence	ADV
ejpam-1068	152	2	x	x	PUNCT
ejpam-1068	152	3	\a	\a	ADJ
ejpam-1068	152	4	is	be	AUX
ejpam-1068	152	5	gψ	gψ	ADJ
ejpam-1068	152	6	-	-	PUNCT
ejpam-1068	152	7	closed	closed	ADJ
ejpam-1068	152	8	and	and	CCONJ
ejpam-1068	152	9	hence	hence	ADV
ejpam-1068	152	10	a	a	PRON
ejpam-1068	152	11	is	be	AUX
ejpam-1068	152	12	gψ	gψ	ADJ
ejpam-1068	152	13	-	-	PUNCT
ejpam-1068	152	14	open	open	ADJ
ejpam-1068	152	15	.	.	PUNCT
ejpam-1068	153	1	theorem	theorem	NOUN
ejpam-1068	153	2	5	5	NUM
ejpam-1068	153	3	.	.	PUNCT
ejpam-1068	154	1	let	let	VERB
ejpam-1068	154	2	ψ	ψ	PART
ejpam-1068	154	3	be	be	AUX
ejpam-1068	154	4	an	an	DET
ejpam-1068	154	5	operation	operation	NOUN
ejpam-1068	154	6	on	on	ADP
ejpam-1068	154	7	a	a	DET
ejpam-1068	154	8	topological	topological	ADJ
ejpam-1068	154	9	space	space	NOUN
ejpam-1068	154	10	(	(	PUNCT
ejpam-1068	154	11	x	x	X
ejpam-1068	154	12	,	,	PUNCT
ejpam-1068	154	13	τ	τ	PROPN
ejpam-1068	154	14	)	)	PUNCT
ejpam-1068	154	15	.	.	PUNCT
ejpam-1068	155	1	then	then	ADV
ejpam-1068	155	2	the	the	DET
ejpam-1068	155	3	following	follow	VERB
ejpam-1068	155	4	are	be	AUX
ejpam-1068	155	5	equivalent	equivalent	ADJ
ejpam-1068	155	6	:	:	PUNCT
ejpam-1068	155	7	(	(	PUNCT
ejpam-1068	155	8	i	i	NOUN
ejpam-1068	155	9	)	)	PUNCT
ejpam-1068	155	10	every	every	DET
ejpam-1068	155	11	open	open	ADJ
ejpam-1068	155	12	set	set	NOUN
ejpam-1068	155	13	of	of	ADP
ejpam-1068	155	14	x	x	PUNCT
ejpam-1068	155	15	is	be	AUX
ejpam-1068	155	16	ψ	ψ	VERB
ejpam-1068	155	17	-	-	ADJ
ejpam-1068	155	18	closed	closed	ADJ
ejpam-1068	155	19	.	.	PUNCT
ejpam-1068	156	1	(	(	PUNCT
ejpam-1068	156	2	ii	ii	NOUN
ejpam-1068	156	3	)	)	PUNCT
ejpam-1068	156	4	every	every	DET
ejpam-1068	156	5	subset	subset	NOUN
ejpam-1068	156	6	of	of	ADP
ejpam-1068	156	7	x	x	PUNCT
ejpam-1068	156	8	is	be	AUX
ejpam-1068	156	9	gψ	gψ	ADV
ejpam-1068	156	10	-	-	PUNCT
ejpam-1068	156	11	closed	closed	ADJ
ejpam-1068	156	12	.	.	PUNCT
ejpam-1068	157	1	proof	proof	NOUN
ejpam-1068	157	2	.	.	PUNCT
ejpam-1068	158	1	(	(	PUNCT
ejpam-1068	158	2	i)⇒	i)⇒	PROPN
ejpam-1068	158	3	(	(	PUNCT
ejpam-1068	158	4	ii	ii	NOUN
ejpam-1068	158	5	)	)	PUNCT
ejpam-1068	158	6	:	:	PUNCT
ejpam-1068	158	7	let	let	VERB
ejpam-1068	158	8	a⊆	a⊆	PUNCT
ejpam-1068	158	9	u	u	PRON
ejpam-1068	158	10	∈	∈	PROPN
ejpam-1068	158	11	τ	τ	PROPN
ejpam-1068	158	12	.	.	PUNCT
ejpam-1068	159	1	then	then	ADV
ejpam-1068	159	2	by	by	ADP
ejpam-1068	159	3	(	(	PUNCT
ejpam-1068	159	4	i	i	NOUN
ejpam-1068	159	5	)	)	PUNCT
ejpam-1068	159	6	,	,	PUNCT
ejpam-1068	159	7	u	u	PROPN
ejpam-1068	159	8	is	be	AUX
ejpam-1068	159	9	ψ	ψ	VERB
ejpam-1068	159	10	-	-	ADJ
ejpam-1068	159	11	closed	closed	ADJ
ejpam-1068	159	12	so	so	ADV
ejpam-1068	159	13	ψ−	ψ−	VERB
ejpam-1068	159	14	cl(a	cl(a	NUM
ejpam-1068	159	15	)	)	PUNCT
ejpam-1068	159	16	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	159	17	cl(u	cl(u	NOUN
ejpam-1068	159	18	)	)	PUNCT
ejpam-1068	159	19	=	=	SYM
ejpam-1068	159	20	u	u	NOUN
ejpam-1068	159	21	.	.	PUNCT
ejpam-1068	160	1	thus	thus	ADV
ejpam-1068	160	2	a	a	PRON
ejpam-1068	160	3	is	be	AUX
ejpam-1068	160	4	gψ	gψ	ADV
ejpam-1068	160	5	-	-	PUNCT
ejpam-1068	160	6	closed	closed	ADJ
ejpam-1068	160	7	.	.	PUNCT
ejpam-1068	161	1	(	(	PUNCT
ejpam-1068	161	2	ii	ii	NOUN
ejpam-1068	161	3	)	)	PUNCT
ejpam-1068	161	4	⇒	⇒	NOUN
ejpam-1068	161	5	(	(	PUNCT
ejpam-1068	161	6	i	i	NOUN
ejpam-1068	161	7	)	)	PUNCT
ejpam-1068	161	8	:	:	PUNCT
ejpam-1068	161	9	let	let	VERB
ejpam-1068	161	10	u	u	PRON
ejpam-1068	161	11	∈	∈	PROPN
ejpam-1068	161	12	τ	τ	PROPN
ejpam-1068	161	13	.	.	PUNCT
ejpam-1068	162	1	then	then	ADV
ejpam-1068	162	2	by	by	ADP
ejpam-1068	162	3	(	(	PUNCT
ejpam-1068	162	4	ii	ii	NOUN
ejpam-1068	162	5	)	)	PUNCT
ejpam-1068	162	6	,	,	PUNCT
ejpam-1068	162	7	u	u	PROPN
ejpam-1068	162	8	is	be	AUX
ejpam-1068	162	9	gψ	gψ	ADV
ejpam-1068	162	10	-	-	PUNCT
ejpam-1068	162	11	closed	closed	ADJ
ejpam-1068	162	12	and	and	CCONJ
ejpam-1068	162	13	hence	hence	ADV
ejpam-1068	162	14	ψ−	ψ−	VERB
ejpam-1068	162	15	cl(u	cl(u	NOUN
ejpam-1068	162	16	)	)	PUNCT
ejpam-1068	162	17	⊆	⊆	NUM
ejpam-1068	162	18	u	u	NOUN
ejpam-1068	162	19	,	,	PUNCT
ejpam-1068	162	20	showing	show	VERB
ejpam-1068	162	21	u	u	PRON
ejpam-1068	162	22	to	to	PART
ejpam-1068	162	23	be	be	AUX
ejpam-1068	162	24	ψ	ψ	NOUN
ejpam-1068	162	25	-	-	ADJ
ejpam-1068	162	26	closed	closed	ADJ
ejpam-1068	162	27	.	.	PUNCT
ejpam-1068	163	1	b.	b.	PROPN
ejpam-1068	163	2	roy	roy	PROPN
ejpam-1068	163	3	,	,	PUNCT
ejpam-1068	163	4	r.	r.	PROPN
ejpam-1068	163	5	sen	sen	PROPN
ejpam-1068	163	6	,	,	PUNCT
ejpam-1068	163	7	t.	t.	PROPN
ejpam-1068	163	8	noiri	noiri	PROPN
ejpam-1068	163	9	/	/	SYM
ejpam-1068	163	10	eur	eur	PROPN
ejpam-1068	163	11	.	.	PUNCT
ejpam-1068	164	1	j.	j.	PROPN
ejpam-1068	164	2	pure	pure	PROPN
ejpam-1068	164	3	appl	appl	PROPN
ejpam-1068	164	4	.	.	PROPN
ejpam-1068	164	5	math	math	PROPN
ejpam-1068	164	6	,	,	PUNCT
ejpam-1068	164	7	6	6	NUM
ejpam-1068	164	8	(	(	PUNCT
ejpam-1068	164	9	2013	2013	NUM
ejpam-1068	164	10	)	)	PUNCT
ejpam-1068	164	11	,	,	PUNCT
ejpam-1068	164	12	44	44	NUM
ejpam-1068	164	13	-	-	SYM
ejpam-1068	164	14	52	52	NUM
ejpam-1068	164	15	48	48	NUM
ejpam-1068	164	16	theorem	theorem	NOUN
ejpam-1068	164	17	6	6	NUM
ejpam-1068	164	18	.	.	PUNCT
ejpam-1068	165	1	let	let	VERB
ejpam-1068	165	2	ψ	ψ	PART
ejpam-1068	165	3	be	be	AUX
ejpam-1068	165	4	an	an	DET
ejpam-1068	165	5	operation	operation	NOUN
ejpam-1068	165	6	on	on	ADP
ejpam-1068	165	7	a	a	DET
ejpam-1068	165	8	topological	topological	ADJ
ejpam-1068	165	9	space	space	NOUN
ejpam-1068	165	10	(	(	PUNCT
ejpam-1068	165	11	x	x	X
ejpam-1068	165	12	,	,	PUNCT
ejpam-1068	165	13	τ	τ	PROPN
ejpam-1068	165	14	)	)	PUNCT
ejpam-1068	165	15	.	.	PUNCT
ejpam-1068	166	1	if	if	SCONJ
ejpam-1068	166	2	a	a	PRON
ejpam-1068	166	3	is	be	AUX
ejpam-1068	166	4	an	an	DET
ejpam-1068	166	5	open	open	ADJ
ejpam-1068	166	6	and	and	CCONJ
ejpam-1068	166	7	gψ	gψ	ADV
ejpam-1068	166	8	-	-	PUNCT
ejpam-1068	166	9	closed	closed	ADJ
ejpam-1068	166	10	subset	subset	NOUN
ejpam-1068	166	11	of	of	ADP
ejpam-1068	166	12	x	x	X
ejpam-1068	166	13	,	,	PUNCT
ejpam-1068	166	14	then	then	ADV
ejpam-1068	166	15	a	a	PRON
ejpam-1068	166	16	is	be	AUX
ejpam-1068	166	17	ψ	ψ	ADJ
ejpam-1068	166	18	-	-	ADJ
ejpam-1068	166	19	closed	closed	ADJ
ejpam-1068	166	20	.	.	PUNCT
ejpam-1068	167	1	proof	proof	NOUN
ejpam-1068	167	2	.	.	PUNCT
ejpam-1068	168	1	similar	similar	ADJ
ejpam-1068	168	2	to	to	ADP
ejpam-1068	168	3	the	the	DET
ejpam-1068	168	4	proof	proof	NOUN
ejpam-1068	168	5	of	of	ADP
ejpam-1068	168	6	theorem	theorem	NOUN
ejpam-1068	168	7	5((ii)⇒	5((ii)⇒	NUM
ejpam-1068	168	8	(	(	PUNCT
ejpam-1068	168	9	i	i	NOUN
ejpam-1068	168	10	)	)	PUNCT
ejpam-1068	168	11	)	)	PUNCT
ejpam-1068	168	12	.	.	PUNCT
ejpam-1068	169	1	theorem	theorem	VERB
ejpam-1068	169	2	7	7	NUM
ejpam-1068	169	3	.	.	PUNCT
ejpam-1068	170	1	let	let	VERB
ejpam-1068	170	2	ψ	ψ	PART
ejpam-1068	170	3	be	be	AUX
ejpam-1068	170	4	an	an	DET
ejpam-1068	170	5	operation	operation	NOUN
ejpam-1068	170	6	on	on	ADP
ejpam-1068	170	7	a	a	DET
ejpam-1068	170	8	topological	topological	ADJ
ejpam-1068	170	9	space	space	NOUN
ejpam-1068	170	10	(	(	PUNCT
ejpam-1068	170	11	x	x	X
ejpam-1068	170	12	,	,	PUNCT
ejpam-1068	170	13	τ	τ	PROPN
ejpam-1068	170	14	)	)	PUNCT
ejpam-1068	170	15	.	.	PUNCT
ejpam-1068	171	1	if	if	SCONJ
ejpam-1068	171	2	a	a	DET
ejpam-1068	171	3	subset	subset	NOUN
ejpam-1068	171	4	a	a	PRON
ejpam-1068	171	5	of	of	ADP
ejpam-1068	171	6	x	x	PRON
ejpam-1068	171	7	is	be	AUX
ejpam-1068	171	8	gψ	gψ	ADJ
ejpam-1068	171	9	-	-	PUNCT
ejpam-1068	171	10	open	open	ADJ
ejpam-1068	171	11	,	,	PUNCT
ejpam-1068	171	12	then	then	ADV
ejpam-1068	171	13	u	u	NOUN
ejpam-1068	171	14	=	=	NOUN
ejpam-1068	171	15	x	x	INTJ
ejpam-1068	171	16	whenever	whenever	SCONJ
ejpam-1068	171	17	u	u	NOUN
ejpam-1068	171	18	is	be	AUX
ejpam-1068	171	19	open	open	ADJ
ejpam-1068	171	20	and	and	CCONJ
ejpam-1068	171	21	ψ−	ψ−	VERB
ejpam-1068	171	22	int(a)∪	int(a)∪	PROPN
ejpam-1068	171	23	(	(	PUNCT
ejpam-1068	171	24	x	x	SYM
ejpam-1068	171	25	\	\	PROPN
ejpam-1068	171	26	a)⊆	a)⊆	X
ejpam-1068	171	27	u.	u.	NOUN
ejpam-1068	171	28	proof	proof	NOUN
ejpam-1068	171	29	.	.	PUNCT
ejpam-1068	172	1	let	let	VERB
ejpam-1068	172	2	u	u	PRON
ejpam-1068	172	3	∈	∈	PROPN
ejpam-1068	172	4	τ	τ	X
ejpam-1068	172	5	and	and	CCONJ
ejpam-1068	172	6	ψ−	ψ−	PROPN
ejpam-1068	172	7	int(a)∪	int(a)∪	PROPN
ejpam-1068	173	1	(	(	PUNCT
ejpam-1068	173	2	x	x	SYM
ejpam-1068	173	3	\	\	PROPN
ejpam-1068	173	4	a)⊆	a)⊆	X
ejpam-1068	173	5	u	u	NOUN
ejpam-1068	173	6	for	for	ADP
ejpam-1068	173	7	a	a	DET
ejpam-1068	173	8	gψ	gψ	ADV
ejpam-1068	173	9	-	-	PUNCT
ejpam-1068	173	10	open	open	ADJ
ejpam-1068	173	11	set	set	NOUN
ejpam-1068	173	12	a.	a.	NOUN
ejpam-1068	173	13	then	then	ADV
ejpam-1068	173	14	x	x	SYM
ejpam-1068	173	15	\u	\u	X
ejpam-1068	173	16	⊆	⊆	X
ejpam-1068	173	17	(	(	PUNCT
ejpam-1068	173	18	x	x	NOUN
ejpam-1068	173	19	\ψ−	\ψ−	ADJ
ejpam-1068	173	20	int(a))∩a	int(a))∩a	NOUN
ejpam-1068	173	21	,	,	PUNCT
ejpam-1068	173	22	i.e.	i.e.	X
ejpam-1068	173	23	,	,	PUNCT
ejpam-1068	173	24	x	x	X
ejpam-1068	173	25	\u	\u	X
ejpam-1068	173	26	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	173	27	cl(x	cl(x	X
ejpam-1068	173	28	\	\	PROPN
ejpam-1068	173	29	a	a	PRON
ejpam-1068	173	30	)	)	PUNCT
ejpam-1068	173	31	\	\	NOUN
ejpam-1068	173	32	(	(	PUNCT
ejpam-1068	173	33	x	x	SYM
ejpam-1068	173	34	\a	\a	NUM
ejpam-1068	173	35	)	)	PUNCT
ejpam-1068	173	36	.	.	PUNCT
ejpam-1068	174	1	since	since	SCONJ
ejpam-1068	174	2	x	x	PRON
ejpam-1068	174	3	\a	\a	ADJ
ejpam-1068	174	4	is	be	AUX
ejpam-1068	174	5	gψ	gψ	ADJ
ejpam-1068	174	6	-	-	PUNCT
ejpam-1068	174	7	closed	closed	ADJ
ejpam-1068	174	8	,	,	PUNCT
ejpam-1068	174	9	by	by	ADP
ejpam-1068	174	10	theorem	theorem	NOUN
ejpam-1068	174	11	1	1	NUM
ejpam-1068	174	12	,	,	PUNCT
ejpam-1068	174	13	x	x	SYM
ejpam-1068	174	14	\	\	NOUN
ejpam-1068	174	15	u	u	NOUN
ejpam-1068	174	16	=	=	NOUN
ejpam-1068	174	17	∅	∅	NOUN
ejpam-1068	174	18	and	and	CCONJ
ejpam-1068	174	19	hence	hence	ADV
ejpam-1068	174	20	u	u	NOUN
ejpam-1068	175	1	=	=	NOUN
ejpam-1068	175	2	x	x	X
ejpam-1068	175	3	.	.	PUNCT
ejpam-1068	176	1	theorem	theorem	ADJ
ejpam-1068	176	2	8	8	NUM
ejpam-1068	176	3	.	.	PUNCT
ejpam-1068	177	1	for	for	ADP
ejpam-1068	177	2	a	a	DET
ejpam-1068	177	3	t1	t1	PROPN
ejpam-1068	177	4	topological	topological	ADJ
ejpam-1068	177	5	space	space	NOUN
ejpam-1068	177	6	(	(	PUNCT
ejpam-1068	177	7	x	x	X
ejpam-1068	177	8	,	,	PUNCT
ejpam-1068	177	9	τ	τ	PROPN
ejpam-1068	177	10	)	)	PUNCT
ejpam-1068	177	11	with	with	ADP
ejpam-1068	177	12	an	an	DET
ejpam-1068	177	13	operation	operation	NOUN
ejpam-1068	177	14	ψ	ψ	NOUN
ejpam-1068	177	15	on	on	ADP
ejpam-1068	177	16	it	it	PRON
ejpam-1068	177	17	,	,	PUNCT
ejpam-1068	177	18	every	every	DET
ejpam-1068	177	19	gψ	gψ	ADV
ejpam-1068	177	20	-	-	PUNCT
ejpam-1068	177	21	closed	closed	ADJ
ejpam-1068	177	22	set	set	NOUN
ejpam-1068	177	23	is	be	AUX
ejpam-1068	177	24	ψ	ψ	ADJ
ejpam-1068	177	25	-	-	ADJ
ejpam-1068	177	26	closed	closed	ADJ
ejpam-1068	177	27	.	.	PUNCT
ejpam-1068	178	1	proof	proof	NOUN
ejpam-1068	178	2	.	.	PUNCT
ejpam-1068	179	1	let	let	VERB
ejpam-1068	179	2	a	a	PRON
ejpam-1068	179	3	be	be	AUX
ejpam-1068	179	4	a	a	DET
ejpam-1068	179	5	gψ	gψ	ADV
ejpam-1068	179	6	-	-	PUNCT
ejpam-1068	179	7	closed	closed	ADJ
ejpam-1068	179	8	subset	subset	NOUN
ejpam-1068	179	9	of	of	ADP
ejpam-1068	179	10	a	a	DET
ejpam-1068	179	11	t1	t1	ADJ
ejpam-1068	179	12	-	-	PUNCT
ejpam-1068	179	13	topological	topological	ADJ
ejpam-1068	179	14	space	space	NOUN
ejpam-1068	179	15	(	(	PUNCT
ejpam-1068	179	16	x	x	X
ejpam-1068	179	17	,	,	PUNCT
ejpam-1068	179	18	τ	τ	PROPN
ejpam-1068	179	19	)	)	PUNCT
ejpam-1068	179	20	and	and	CCONJ
ejpam-1068	179	21	x	x	PUNCT
ejpam-1068	179	22	∈ψ−cl(a	∈ψ−cl(a	PROPN
ejpam-1068	179	23	)	)	PUNCT
ejpam-1068	179	24	.	.	PUNCT
ejpam-1068	180	1	then	then	ADV
ejpam-1068	180	2	by	by	ADP
ejpam-1068	180	3	t1	t1	PROPN
ejpam-1068	180	4	-	-	NOUN
ejpam-1068	180	5	ness	ness	NOUN
ejpam-1068	180	6	of	of	ADP
ejpam-1068	180	7	x	x	SYM
ejpam-1068	180	8	,	,	PUNCT
ejpam-1068	180	9	{	{	PUNCT
ejpam-1068	180	10	x	x	NOUN
ejpam-1068	180	11	}	}	PUNCT
ejpam-1068	180	12	is	be	AUX
ejpam-1068	180	13	a	a	DET
ejpam-1068	180	14	closed	closed	ADJ
ejpam-1068	180	15	set	set	NOUN
ejpam-1068	180	16	.	.	PUNCT
ejpam-1068	181	1	thus	thus	ADV
ejpam-1068	181	2	by	by	ADP
ejpam-1068	181	3	theorem	theorem	NOUN
ejpam-1068	181	4	1	1	NUM
ejpam-1068	181	5	,	,	PUNCT
ejpam-1068	181	6	x	x	PROPN
ejpam-1068	181	7	6∈ψ−	6∈ψ−	NUM
ejpam-1068	181	8	cl(a)\a	cl(a)\a	NOUN
ejpam-1068	181	9	.	.	PUNCT
ejpam-1068	182	1	since	since	SCONJ
ejpam-1068	182	2	x	x	PRON
ejpam-1068	182	3	∈ψ−	∈ψ−	PROPN
ejpam-1068	182	4	cl(a	cl(a	NUM
ejpam-1068	182	5	)	)	PUNCT
ejpam-1068	182	6	,	,	PUNCT
ejpam-1068	182	7	then	then	ADV
ejpam-1068	182	8	x	x	PART
ejpam-1068	182	9	∈	∈	NOUN
ejpam-1068	182	10	a.	a.	NOUN
ejpam-1068	182	11	this	this	PRON
ejpam-1068	182	12	shows	show	VERB
ejpam-1068	182	13	that	that	SCONJ
ejpam-1068	182	14	ψ−	ψ−	PROPN
ejpam-1068	182	15	cl(a	cl(a	PUNCT
ejpam-1068	182	16	)	)	PUNCT
ejpam-1068	182	17	⊆	⊆	NUM
ejpam-1068	182	18	a	a	PRON
ejpam-1068	182	19	or	or	CCONJ
ejpam-1068	182	20	equivalently	equivalently	ADV
ejpam-1068	182	21	that	that	PRON
ejpam-1068	182	22	ψ−	ψ−	VERB
ejpam-1068	182	23	cl(a	cl(a	PUNCT
ejpam-1068	182	24	)	)	PUNCT
ejpam-1068	183	1	=	=	PUNCT
ejpam-1068	183	2	a.	a.	NOUN
ejpam-1068	183	3	2.2	2.2	NUM
ejpam-1068	183	4	.	.	PUNCT
ejpam-1068	184	1	properties	property	NOUN
ejpam-1068	184	2	of	of	ADP
ejpam-1068	184	3	ψg	ψg	NOUN
ejpam-1068	184	4	-	-	ADJ
ejpam-1068	184	5	regular	regular	ADJ
ejpam-1068	184	6	and	and	CCONJ
ejpam-1068	184	7	ψg	ψg	NOUN
ejpam-1068	184	8	-	-	ADJ
ejpam-1068	184	9	normal	normal	ADJ
ejpam-1068	184	10	spaces	space	NOUN
ejpam-1068	184	11	definition	definition	NOUN
ejpam-1068	184	12	5	5	NUM
ejpam-1068	184	13	.	.	PUNCT
ejpam-1068	185	1	let	let	AUX
ejpam-1068	185	2	(	(	PUNCT
ejpam-1068	185	3	x	x	X
ejpam-1068	185	4	,	,	PUNCT
ejpam-1068	185	5	τ	τ	X
ejpam-1068	185	6	)	)	PUNCT
ejpam-1068	185	7	be	be	VERB
ejpam-1068	185	8	a	a	DET
ejpam-1068	185	9	topological	topological	ADJ
ejpam-1068	185	10	space	space	NOUN
ejpam-1068	185	11	and	and	CCONJ
ejpam-1068	185	12	ψ	ψ	AUX
ejpam-1068	185	13	be	be	AUX
ejpam-1068	185	14	an	an	DET
ejpam-1068	185	15	operation	operation	NOUN
ejpam-1068	185	16	on	on	ADP
ejpam-1068	185	17	x	x	X
ejpam-1068	185	18	.	.	PUNCT
ejpam-1068	186	1	then	then	ADV
ejpam-1068	186	2	(	(	PUNCT
ejpam-1068	186	3	x	x	X
ejpam-1068	186	4	,	,	PUNCT
ejpam-1068	186	5	τ	τ	X
ejpam-1068	186	6	)	)	PUNCT
ejpam-1068	186	7	is	be	AUX
ejpam-1068	186	8	said	say	VERB
ejpam-1068	186	9	to	to	PART
ejpam-1068	186	10	be	be	AUX
ejpam-1068	186	11	ψg	ψg	NOUN
ejpam-1068	186	12	-regular	-regular	ADJ
ejpam-1068	186	13	if	if	SCONJ
ejpam-1068	186	14	for	for	ADP
ejpam-1068	186	15	each	each	DET
ejpam-1068	186	16	closed	close	VERB
ejpam-1068	186	17	set	set	VERB
ejpam-1068	186	18	f	f	PROPN
ejpam-1068	186	19	of	of	ADP
ejpam-1068	186	20	x	x	PUNCT
ejpam-1068	186	21	not	not	PART
ejpam-1068	186	22	containing	contain	VERB
ejpam-1068	186	23	x	x	PUNCT
ejpam-1068	186	24	there	there	PRON
ejpam-1068	186	25	exist	exist	VERB
ejpam-1068	186	26	disjoint	disjoint	NOUN
ejpam-1068	186	27	ψ	ψ	ADJ
ejpam-1068	186	28	-	-	ADJ
ejpam-1068	186	29	open	open	ADJ
ejpam-1068	186	30	sets	set	NOUN
ejpam-1068	186	31	u	u	NOUN
ejpam-1068	186	32	and	and	CCONJ
ejpam-1068	186	33	v	v	ADP
ejpam-1068	186	34	such	such	ADJ
ejpam-1068	186	35	that	that	SCONJ
ejpam-1068	186	36	x	x	SYM
ejpam-1068	186	37	∈	∈	PROPN
ejpam-1068	186	38	u	u	PROPN
ejpam-1068	186	39	,	,	PUNCT
ejpam-1068	186	40	f	f	PROPN
ejpam-1068	186	41	⊆	⊆	NUM
ejpam-1068	186	42	v	v	NOUN
ejpam-1068	186	43	.	.	PUNCT
ejpam-1068	187	1	remark	remark	PROPN
ejpam-1068	187	2	5	5	NUM
ejpam-1068	187	3	.	.	PUNCT
ejpam-1068	188	1	let	let	VERB
ejpam-1068	188	2	ψ	ψ	PART
ejpam-1068	188	3	be	be	AUX
ejpam-1068	188	4	an	an	DET
ejpam-1068	188	5	operation	operation	NOUN
ejpam-1068	188	6	on	on	ADP
ejpam-1068	188	7	a	a	DET
ejpam-1068	188	8	space	space	NOUN
ejpam-1068	188	9	(	(	PUNCT
ejpam-1068	188	10	x	x	X
ejpam-1068	188	11	,	,	PUNCT
ejpam-1068	188	12	τ	τ	PROPN
ejpam-1068	188	13	)	)	PUNCT
ejpam-1068	188	14	.	.	PUNCT
ejpam-1068	189	1	then	then	ADV
ejpam-1068	189	2	every	every	DET
ejpam-1068	189	3	ψg	ψg	NOUN
ejpam-1068	189	4	-regular	-regular	ADJ
ejpam-1068	189	5	space	space	NOUN
ejpam-1068	189	6	reduces	reduce	VERB
ejpam-1068	189	7	to	to	ADP
ejpam-1068	189	8	a	a	DET
ejpam-1068	189	9	regular	regular	ADJ
ejpam-1068	189	10	[	[	X
ejpam-1068	189	11	5	5	NUM
ejpam-1068	189	12	]	]	PUNCT
ejpam-1068	189	13	(	(	PUNCT
ejpam-1068	189	14	resp	resp	NOUN
ejpam-1068	189	15	.	.	PUNCT
ejpam-1068	190	1	p	p	X
ejpam-1068	190	2	-	-	PUNCT
ejpam-1068	190	3	regular	regular	ADJ
ejpam-1068	190	4	[	[	X
ejpam-1068	190	5	7	7	NUM
ejpam-1068	190	6	]	]	PUNCT
ejpam-1068	190	7	,	,	PUNCT
ejpam-1068	190	8	s	s	NOUN
ejpam-1068	190	9	-	-	ADJ
ejpam-1068	190	10	regular	regular	ADJ
ejpam-1068	191	1	[	[	X
ejpam-1068	191	2	10	10	NUM
ejpam-1068	191	3	]	]	PUNCT
ejpam-1068	191	4	,	,	PUNCT
ejpam-1068	191	5	β	β	X
ejpam-1068	191	6	-regular	-regular	ADJ
ejpam-1068	191	7	[	[	X
ejpam-1068	191	8	1	1	NUM
ejpam-1068	191	9	]	]	SYM
ejpam-1068	191	10	)	)	PUNCT
ejpam-1068	191	11	space	space	NOUN
ejpam-1068	191	12	if	if	SCONJ
ejpam-1068	191	13	one	one	PRON
ejpam-1068	191	14	takes	take	VERB
ejpam-1068	191	15	ψ	ψ	NOUN
ejpam-1068	191	16	to	to	PART
ejpam-1068	191	17	be	be	AUX
ejpam-1068	191	18	int	int	NOUN
ejpam-1068	191	19	(	(	PUNCT
ejpam-1068	191	20	resp	resp	NOUN
ejpam-1068	191	21	.	.	PUNCT
ejpam-1068	191	22	intcl	intcl	PROPN
ejpam-1068	191	23	,	,	PUNCT
ejpam-1068	191	24	cl	cl	NOUN
ejpam-1068	191	25	int	int	NOUN
ejpam-1068	191	26	,	,	PUNCT
ejpam-1068	191	27	cl	cl	NOUN
ejpam-1068	191	28	intcl	intcl	NOUN
ejpam-1068	191	29	)	)	PUNCT
ejpam-1068	191	30	.	.	PUNCT
ejpam-1068	192	1	theorem	theorem	VERB
ejpam-1068	192	2	9	9	NUM
ejpam-1068	192	3	.	.	PUNCT
ejpam-1068	193	1	let	let	VERB
ejpam-1068	193	2	ψ	ψ	PART
ejpam-1068	193	3	be	be	AUX
ejpam-1068	193	4	an	an	DET
ejpam-1068	193	5	operation	operation	NOUN
ejpam-1068	193	6	on	on	ADP
ejpam-1068	193	7	a	a	DET
ejpam-1068	193	8	topological	topological	ADJ
ejpam-1068	193	9	space	space	NOUN
ejpam-1068	193	10	(	(	PUNCT
ejpam-1068	193	11	x	x	X
ejpam-1068	193	12	,	,	PUNCT
ejpam-1068	193	13	τ	τ	PROPN
ejpam-1068	193	14	)	)	PUNCT
ejpam-1068	193	15	.	.	PUNCT
ejpam-1068	194	1	then	then	ADV
ejpam-1068	194	2	the	the	DET
ejpam-1068	194	3	following	follow	VERB
ejpam-1068	194	4	statements	statement	NOUN
ejpam-1068	194	5	are	be	AUX
ejpam-1068	194	6	equivalent	equivalent	ADJ
ejpam-1068	194	7	:	:	PUNCT
ejpam-1068	194	8	(	(	PUNCT
ejpam-1068	194	9	i	i	NOUN
ejpam-1068	194	10	)	)	PUNCT
ejpam-1068	194	11	x	x	PRON
ejpam-1068	194	12	is	be	AUX
ejpam-1068	194	13	ψg	ψg	NOUN
ejpam-1068	194	14	-regular	-regular	ADJ
ejpam-1068	194	15	.	.	PUNCT
ejpam-1068	195	1	(	(	PUNCT
ejpam-1068	195	2	ii	ii	NOUN
ejpam-1068	195	3	)	)	PUNCT
ejpam-1068	195	4	for	for	ADP
ejpam-1068	195	5	each	each	DET
ejpam-1068	195	6	x	x	SYM
ejpam-1068	195	7	∈	∈	PROPN
ejpam-1068	195	8	x	x	X
ejpam-1068	195	9	and	and	CCONJ
ejpam-1068	195	10	each	each	DET
ejpam-1068	195	11	u	u	PROPN
ejpam-1068	195	12	∈	∈	PROPN
ejpam-1068	195	13	τ	τ	X
ejpam-1068	195	14	with	with	ADP
ejpam-1068	195	15	x	x	PROPN
ejpam-1068	195	16	∈	∈	PROPN
ejpam-1068	195	17	u	u	NOUN
ejpam-1068	195	18	,	,	PUNCT
ejpam-1068	195	19	there	there	PRON
ejpam-1068	195	20	exists	exist	VERB
ejpam-1068	195	21	v	v	ADP
ejpam-1068	195	22	∈ψo	∈ψo	PROPN
ejpam-1068	195	23	(	(	PUNCT
ejpam-1068	195	24	x	x	X
ejpam-1068	195	25	)	)	PUNCT
ejpam-1068	195	26	such	such	ADJ
ejpam-1068	195	27	that	that	SCONJ
ejpam-1068	195	28	x	x	SYM
ejpam-1068	195	29	∈	∈	PROPN
ejpam-1068	195	30	v	v	NUM
ejpam-1068	195	31	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	195	32	cl(v	cl(v	NOUN
ejpam-1068	195	33	)	)	PUNCT
ejpam-1068	195	34	⊆	⊆	NUM
ejpam-1068	195	35	u.	u.	NOUN
ejpam-1068	195	36	(	(	PUNCT
ejpam-1068	195	37	iii	iii	NOUN
ejpam-1068	195	38	)	)	PUNCT
ejpam-1068	195	39	for	for	ADP
ejpam-1068	195	40	each	each	DET
ejpam-1068	195	41	closed	close	VERB
ejpam-1068	195	42	set	set	VERB
ejpam-1068	195	43	f	f	PROPN
ejpam-1068	195	44	of	of	ADP
ejpam-1068	195	45	x	x	PROPN
ejpam-1068	195	46	,	,	PUNCT
ejpam-1068	195	47	∩{ψ−	∩{ψ−	PROPN
ejpam-1068	195	48	cl(v	cl(v	NOUN
ejpam-1068	195	49	)	)	PUNCT
ejpam-1068	195	50	:	:	PUNCT
ejpam-1068	195	51	f	f	PROPN
ejpam-1068	195	52	⊆	⊆	NUM
ejpam-1068	195	53	v	v	ADP
ejpam-1068	195	54	∈ψo	∈ψo	PROPN
ejpam-1068	195	55	(	(	PUNCT
ejpam-1068	195	56	x	x	NOUN
ejpam-1068	195	57	)	)	PUNCT
ejpam-1068	195	58	}	}	PUNCT
ejpam-1068	196	1	=	=	SYM
ejpam-1068	196	2	f.	f.	PROPN
ejpam-1068	196	3	(	(	PUNCT
ejpam-1068	196	4	iv	iv	X
ejpam-1068	196	5	)	)	PUNCT
ejpam-1068	196	6	for	for	ADP
ejpam-1068	196	7	each	each	DET
ejpam-1068	196	8	a	a	DET
ejpam-1068	196	9	⊆	⊆	NUM
ejpam-1068	196	10	x	x	SYM
ejpam-1068	196	11	and	and	CCONJ
ejpam-1068	196	12	each	each	DET
ejpam-1068	196	13	u	u	PROPN
ejpam-1068	196	14	∈	∈	PROPN
ejpam-1068	196	15	τ	τ	X
ejpam-1068	196	16	with	with	ADP
ejpam-1068	196	17	a	a	DET
ejpam-1068	196	18	∩	∩	ADJ
ejpam-1068	196	19	u	u	NOUN
ejpam-1068	196	20	6=	6=	NOUN
ejpam-1068	196	21	∅	∅	NOUN
ejpam-1068	196	22	,	,	PUNCT
ejpam-1068	196	23	there	there	PRON
ejpam-1068	196	24	exists	exist	VERB
ejpam-1068	196	25	v	v	ADP
ejpam-1068	196	26	∈	∈	PROPN
ejpam-1068	196	27	ψo	ψo	PRON
ejpam-1068	196	28	(	(	PUNCT
ejpam-1068	196	29	x	x	X
ejpam-1068	196	30	)	)	PUNCT
ejpam-1068	197	1	such	such	ADJ
ejpam-1068	197	2	that	that	SCONJ
ejpam-1068	197	3	a∩	a∩	PROPN
ejpam-1068	197	4	v	v	ADP
ejpam-1068	197	5	6=	6=	NOUN
ejpam-1068	197	6	∅	∅	NOUN
ejpam-1068	197	7	and	and	CCONJ
ejpam-1068	197	8	ψ−	ψ−	VERB
ejpam-1068	197	9	cl(v	cl(v	NOUN
ejpam-1068	197	10	)	)	PUNCT
ejpam-1068	197	11	⊆	⊆	X
ejpam-1068	197	12	u.	u.	NOUN
ejpam-1068	197	13	(	(	PUNCT
ejpam-1068	197	14	v	v	NOUN
ejpam-1068	197	15	)	)	PUNCT
ejpam-1068	197	16	for	for	ADP
ejpam-1068	197	17	each	each	DET
ejpam-1068	197	18	non	non	ADJ
ejpam-1068	197	19	-	-	ADJ
ejpam-1068	197	20	empty	empty	ADJ
ejpam-1068	197	21	subset	subset	NOUN
ejpam-1068	197	22	a	a	PRON
ejpam-1068	197	23	of	of	ADP
ejpam-1068	197	24	x	x	X
ejpam-1068	197	25	and	and	CCONJ
ejpam-1068	197	26	each	each	DET
ejpam-1068	197	27	closed	close	VERB
ejpam-1068	197	28	subset	subset	VERB
ejpam-1068	197	29	f	f	PROPN
ejpam-1068	197	30	of	of	ADP
ejpam-1068	197	31	x	x	PUNCT
ejpam-1068	197	32	with	with	ADP
ejpam-1068	197	33	a∩	a∩	PROPN
ejpam-1068	197	34	f	f	NOUN
ejpam-1068	197	35	=	=	PUNCT
ejpam-1068	197	36	∅	∅	NOUN
ejpam-1068	197	37	,	,	PUNCT
ejpam-1068	197	38	there	there	PRON
ejpam-1068	197	39	exist	exist	VERB
ejpam-1068	197	40	v	v	ADP
ejpam-1068	197	41	,	,	PUNCT
ejpam-1068	197	42	w	w	NOUN
ejpam-1068	197	43	∈ψo	∈ψo	PROPN
ejpam-1068	197	44	(	(	PUNCT
ejpam-1068	197	45	x	x	X
ejpam-1068	197	46	)	)	PUNCT
ejpam-1068	197	47	such	such	ADJ
ejpam-1068	197	48	that	that	SCONJ
ejpam-1068	197	49	a∩	a∩	PROPN
ejpam-1068	197	50	v	v	ADP
ejpam-1068	197	51	6=	6=	PROPN
ejpam-1068	197	52	∅	∅	NOUN
ejpam-1068	197	53	,	,	PUNCT
ejpam-1068	197	54	f	f	PROPN
ejpam-1068	197	55	⊆w	⊆w	NOUN
ejpam-1068	197	56	and	and	CCONJ
ejpam-1068	197	57	w	w	PROPN
ejpam-1068	197	58	∩	∩	ADJ
ejpam-1068	197	59	v	v	NOUN
ejpam-1068	197	60	=	=	SYM
ejpam-1068	197	61	∅.	∅.	X
ejpam-1068	197	62	(	(	PUNCT
ejpam-1068	197	63	vi	vi	NOUN
ejpam-1068	197	64	)	)	PUNCT
ejpam-1068	197	65	for	for	ADP
ejpam-1068	197	66	each	each	DET
ejpam-1068	197	67	closed	close	VERB
ejpam-1068	197	68	set	set	VERB
ejpam-1068	197	69	f	f	PROPN
ejpam-1068	197	70	and	and	CCONJ
ejpam-1068	197	71	x	x	PROPN
ejpam-1068	197	72	6∈	6∈	NOUN
ejpam-1068	198	1	f	f	NOUN
ejpam-1068	198	2	,	,	PUNCT
ejpam-1068	198	3	there	there	PRON
ejpam-1068	198	4	exist	exist	VERB
ejpam-1068	198	5	u	u	PRON
ejpam-1068	198	6	∈	∈	PROPN
ejpam-1068	198	7	ψo	ψo	PRON
ejpam-1068	198	8	(	(	PUNCT
ejpam-1068	198	9	x	x	X
ejpam-1068	198	10	)	)	PUNCT
ejpam-1068	198	11	and	and	CCONJ
ejpam-1068	198	12	a	a	DET
ejpam-1068	198	13	gψ	gψ	ADV
ejpam-1068	198	14	-	-	PUNCT
ejpam-1068	198	15	open	open	ADJ
ejpam-1068	198	16	set	set	VERB
ejpam-1068	198	17	v	v	ADP
ejpam-1068	198	18	such	such	ADJ
ejpam-1068	198	19	that	that	SCONJ
ejpam-1068	198	20	x	x	SYM
ejpam-1068	198	21	∈	∈	PROPN
ejpam-1068	198	22	u	u	PROPN
ejpam-1068	198	23	,	,	PUNCT
ejpam-1068	198	24	f	f	PROPN
ejpam-1068	198	25	⊆	⊆	NUM
ejpam-1068	198	26	v	v	NOUN
ejpam-1068	198	27	and	and	CCONJ
ejpam-1068	198	28	u	u	NOUN
ejpam-1068	198	29	∩	∩	NOUN
ejpam-1068	198	30	v	v	NOUN
ejpam-1068	198	31	=	=	PUNCT
ejpam-1068	198	32	∅.	∅.	PROPN
ejpam-1068	198	33	b.	b.	PROPN
ejpam-1068	198	34	roy	roy	PROPN
ejpam-1068	198	35	,	,	PUNCT
ejpam-1068	198	36	r.	r.	PROPN
ejpam-1068	198	37	sen	sen	PROPN
ejpam-1068	198	38	,	,	PUNCT
ejpam-1068	198	39	t.	t.	PROPN
ejpam-1068	198	40	noiri	noiri	PROPN
ejpam-1068	198	41	/	/	SYM
ejpam-1068	198	42	eur	eur	PROPN
ejpam-1068	198	43	.	.	PUNCT
ejpam-1068	199	1	j.	j.	PROPN
ejpam-1068	199	2	pure	pure	PROPN
ejpam-1068	199	3	appl	appl	PROPN
ejpam-1068	199	4	.	.	PROPN
ejpam-1068	199	5	math	math	PROPN
ejpam-1068	199	6	,	,	PUNCT
ejpam-1068	199	7	6	6	NUM
ejpam-1068	199	8	(	(	PUNCT
ejpam-1068	199	9	2013	2013	NUM
ejpam-1068	199	10	)	)	PUNCT
ejpam-1068	199	11	,	,	PUNCT
ejpam-1068	199	12	44	44	NUM
ejpam-1068	199	13	-	-	SYM
ejpam-1068	199	14	52	52	NUM
ejpam-1068	199	15	49	49	NUM
ejpam-1068	199	16	(	(	PUNCT
ejpam-1068	199	17	vii	vii	PROPN
ejpam-1068	199	18	)	)	PUNCT
ejpam-1068	199	19	for	for	ADP
ejpam-1068	199	20	each	each	DET
ejpam-1068	199	21	a	a	DET
ejpam-1068	199	22	⊆	⊆	NUM
ejpam-1068	199	23	x	x	SYM
ejpam-1068	199	24	and	and	CCONJ
ejpam-1068	199	25	each	each	DET
ejpam-1068	199	26	closed	close	VERB
ejpam-1068	199	27	set	set	VERB
ejpam-1068	199	28	f	f	PROPN
ejpam-1068	199	29	with	with	ADP
ejpam-1068	199	30	a	a	DET
ejpam-1068	199	31	∩	∩	ADJ
ejpam-1068	199	32	f	f	NOUN
ejpam-1068	199	33	=	=	NOUN
ejpam-1068	199	34	∅	∅	NOUN
ejpam-1068	199	35	,	,	PUNCT
ejpam-1068	199	36	there	there	PRON
ejpam-1068	199	37	exist	exist	VERB
ejpam-1068	199	38	u	u	PRON
ejpam-1068	199	39	∈	∈	PROPN
ejpam-1068	199	40	ψo	ψo	PRON
ejpam-1068	199	41	(	(	PUNCT
ejpam-1068	199	42	x	x	X
ejpam-1068	199	43	)	)	PUNCT
ejpam-1068	199	44	and	and	CCONJ
ejpam-1068	199	45	a	a	DET
ejpam-1068	199	46	gψ	gψ	ADV
ejpam-1068	199	47	-	-	PUNCT
ejpam-1068	199	48	open	open	ADJ
ejpam-1068	199	49	set	set	VERB
ejpam-1068	199	50	v	v	ADP
ejpam-1068	199	51	such	such	ADJ
ejpam-1068	199	52	that	that	SCONJ
ejpam-1068	199	53	a∩	a∩	PROPN
ejpam-1068	199	54	u	u	PROPN
ejpam-1068	199	55	6=	6=	PROPN
ejpam-1068	199	56	∅	∅	NOUN
ejpam-1068	199	57	,	,	PUNCT
ejpam-1068	199	58	f	f	PROPN
ejpam-1068	199	59	⊆	⊆	PROPN
ejpam-1068	199	60	v	v	NOUN
ejpam-1068	199	61	and	and	CCONJ
ejpam-1068	199	62	u	u	NOUN
ejpam-1068	199	63	∩	∩	NOUN
ejpam-1068	199	64	v	v	NOUN
ejpam-1068	199	65	=	=	PUNCT
ejpam-1068	199	66	∅.	∅.	NOUN
ejpam-1068	199	67	proof	proof	NOUN
ejpam-1068	199	68	.	.	PUNCT
ejpam-1068	200	1	(	(	PUNCT
ejpam-1068	200	2	i	i	NOUN
ejpam-1068	200	3	)	)	PUNCT
ejpam-1068	200	4	⇒	⇒	PROPN
ejpam-1068	200	5	(	(	PUNCT
ejpam-1068	200	6	ii	ii	PROPN
ejpam-1068	200	7	)	)	PUNCT
ejpam-1068	200	8	:	:	PUNCT
ejpam-1068	200	9	let	let	VERB
ejpam-1068	200	10	x	x	SYM
ejpam-1068	200	11	6∈	6∈	PROPN
ejpam-1068	200	12	(	(	PUNCT
ejpam-1068	200	13	x	x	SYM
ejpam-1068	200	14	\	\	PROPN
ejpam-1068	200	15	u	u	NOUN
ejpam-1068	200	16	)	)	PUNCT
ejpam-1068	200	17	,	,	PUNCT
ejpam-1068	200	18	where	where	SCONJ
ejpam-1068	200	19	u	u	PROPN
ejpam-1068	200	20	∈	∈	PROPN
ejpam-1068	200	21	τ	τ	PROPN
ejpam-1068	200	22	.	.	PUNCT
ejpam-1068	200	23	then	then	ADV
ejpam-1068	200	24	there	there	PRON
ejpam-1068	200	25	exist	exist	VERB
ejpam-1068	200	26	disjoint	disjoint	NOUN
ejpam-1068	200	27	g	g	NOUN
ejpam-1068	200	28	,	,	PUNCT
ejpam-1068	200	29	v	v	PROPN
ejpam-1068	200	30	∈	∈	NOUN
ejpam-1068	200	31	ψo	ψo	PRON
ejpam-1068	200	32	(	(	PUNCT
ejpam-1068	200	33	x	x	X
ejpam-1068	200	34	)	)	PUNCT
ejpam-1068	200	35	such	such	ADJ
ejpam-1068	200	36	that	that	SCONJ
ejpam-1068	200	37	(	(	PUNCT
ejpam-1068	200	38	x	x	SYM
ejpam-1068	200	39	\	\	PROPN
ejpam-1068	200	40	u)⊆	u)⊆	NUM
ejpam-1068	200	41	g	g	NOUN
ejpam-1068	200	42	and	and	CCONJ
ejpam-1068	200	43	x	x	SYM
ejpam-1068	200	44	∈	∈	PROPN
ejpam-1068	200	45	v	v	NOUN
ejpam-1068	200	46	.	.	PUNCT
ejpam-1068	201	1	thus	thus	ADV
ejpam-1068	201	2	v	v	ADP
ejpam-1068	201	3	⊆	⊆	NUM
ejpam-1068	201	4	x	x	SYM
ejpam-1068	201	5	\	\	PROPN
ejpam-1068	201	6	g	g	PROPN
ejpam-1068	201	7	and	and	CCONJ
ejpam-1068	201	8	so	so	ADV
ejpam-1068	201	9	x	x	SYM
ejpam-1068	201	10	∈	∈	PROPN
ejpam-1068	201	11	v	v	NUM
ejpam-1068	201	12	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	201	13	cl(v	cl(v	NOUN
ejpam-1068	201	14	)	)	PUNCT
ejpam-1068	201	15	⊆	⊆	NUM
ejpam-1068	201	16	x	x	SYM
ejpam-1068	201	17	\	\	PROPN
ejpam-1068	201	18	g	g	PROPN
ejpam-1068	201	19	⊆	⊆	NUM
ejpam-1068	201	20	u	u	NOUN
ejpam-1068	201	21	.	.	PUNCT
ejpam-1068	202	1	(	(	PUNCT
ejpam-1068	202	2	ii	ii	NOUN
ejpam-1068	202	3	)	)	PUNCT
ejpam-1068	202	4	⇒	⇒	NOUN
ejpam-1068	202	5	(	(	PUNCT
ejpam-1068	202	6	iii	iii	NOUN
ejpam-1068	202	7	)	)	PUNCT
ejpam-1068	202	8	:	:	PUNCT
ejpam-1068	202	9	let	let	VERB
ejpam-1068	202	10	x	x	PUNCT
ejpam-1068	202	11	\	\	PROPN
ejpam-1068	202	12	f	f	PROPN
ejpam-1068	202	13	∈	∈	PROPN
ejpam-1068	202	14	τ	τ	X
ejpam-1068	202	15	with	with	ADP
ejpam-1068	202	16	x	x	PROPN
ejpam-1068	202	17	∈	∈	PROPN
ejpam-1068	202	18	x	x	PUNCT
ejpam-1068	202	19	\	\	PROPN
ejpam-1068	203	1	f	f	PROPN
ejpam-1068	203	2	.	.	PUNCT
ejpam-1068	204	1	then	then	ADV
ejpam-1068	204	2	by	by	ADP
ejpam-1068	204	3	(	(	PUNCT
ejpam-1068	204	4	ii	ii	NOUN
ejpam-1068	204	5	)	)	PUNCT
ejpam-1068	204	6	,	,	PUNCT
ejpam-1068	204	7	there	there	PRON
ejpam-1068	204	8	exists	exist	VERB
ejpam-1068	204	9	u	u	PRON
ejpam-1068	204	10	∈ψo	∈ψo	X
ejpam-1068	204	11	(	(	PUNCT
ejpam-1068	204	12	x	x	X
ejpam-1068	204	13	)	)	PUNCT
ejpam-1068	204	14	such	such	ADJ
ejpam-1068	204	15	that	that	SCONJ
ejpam-1068	204	16	x	x	SYM
ejpam-1068	204	17	∈	∈	PROPN
ejpam-1068	204	18	u	u	NOUN
ejpam-1068	204	19	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	204	20	cl(u	cl(u	PROPN
ejpam-1068	204	21	)	)	PUNCT
ejpam-1068	204	22	⊆	⊆	NUM
ejpam-1068	204	23	(	(	PUNCT
ejpam-1068	204	24	x	x	SYM
ejpam-1068	204	25	\	\	PROPN
ejpam-1068	204	26	f	f	X
ejpam-1068	204	27	)	)	PUNCT
ejpam-1068	204	28	.	.	PUNCT
ejpam-1068	205	1	so	so	ADV
ejpam-1068	205	2	f	f	PROPN
ejpam-1068	205	3	⊆	⊆	NUM
ejpam-1068	205	4	x	x	SYM
ejpam-1068	205	5	\ψ−	\ψ−	ADJ
ejpam-1068	205	6	cl(u	cl(u	NOUN
ejpam-1068	205	7	)	)	PUNCT
ejpam-1068	205	8	=	=	SYM
ejpam-1068	205	9	v	v	X
ejpam-1068	205	10	(	(	PUNCT
ejpam-1068	205	11	say	say	INTJ
ejpam-1068	205	12	)	)	PUNCT
ejpam-1068	205	13	∈ψo	∈ψo	PROPN
ejpam-1068	205	14	(	(	PUNCT
ejpam-1068	205	15	x	x	SYM
ejpam-1068	205	16	)	)	PUNCT
ejpam-1068	205	17	and	and	CCONJ
ejpam-1068	205	18	u	u	NOUN
ejpam-1068	205	19	∩v	∩v	NOUN
ejpam-1068	205	20	=	=	PUNCT
ejpam-1068	205	21	∅.	∅.	VERB
ejpam-1068	205	22	then	then	ADV
ejpam-1068	205	23	x	x	X
ejpam-1068	205	24	6∈ψ−	6∈ψ−	NUM
ejpam-1068	205	25	cl(v	cl(v	NOUN
ejpam-1068	205	26	)	)	PUNCT
ejpam-1068	205	27	.	.	PUNCT
ejpam-1068	206	1	thus	thus	ADV
ejpam-1068	206	2	f	f	PROPN
ejpam-1068	206	3	⊇	⊇	PROPN
ejpam-1068	206	4	∩{ψ−	∩{ψ−	PROPN
ejpam-1068	206	5	cl(v	cl(v	NOUN
ejpam-1068	206	6	)	)	PUNCT
ejpam-1068	206	7	:	:	PUNCT
ejpam-1068	207	1	f	f	PROPN
ejpam-1068	207	2	⊆	⊆	NUM
ejpam-1068	207	3	v	v	ADP
ejpam-1068	207	4	∈ψo	∈ψo	PROPN
ejpam-1068	207	5	(	(	PUNCT
ejpam-1068	207	6	x	x	NOUN
ejpam-1068	207	7	)	)	PUNCT
ejpam-1068	207	8	}	}	PUNCT
ejpam-1068	207	9	.	.	PUNCT
ejpam-1068	208	1	(	(	PUNCT
ejpam-1068	208	2	iii	iii	X
ejpam-1068	208	3	)	)	PUNCT
ejpam-1068	208	4	⇒	⇒	NOUN
ejpam-1068	208	5	(	(	PUNCT
ejpam-1068	208	6	iv	iv	NUM
ejpam-1068	208	7	)	)	PUNCT
ejpam-1068	208	8	:	:	PUNCT
ejpam-1068	208	9	let	let	VERB
ejpam-1068	208	10	a	a	PRON
ejpam-1068	208	11	be	be	AUX
ejpam-1068	208	12	a	a	DET
ejpam-1068	208	13	subset	subset	NOUN
ejpam-1068	208	14	of	of	ADP
ejpam-1068	208	15	x	x	SYM
ejpam-1068	208	16	such	such	ADJ
ejpam-1068	208	17	that	that	SCONJ
ejpam-1068	208	18	u	u	PROPN
ejpam-1068	208	19	∈	∈	PROPN
ejpam-1068	208	20	τ	τ	X
ejpam-1068	208	21	with	with	ADP
ejpam-1068	208	22	a∩	a∩	PROPN
ejpam-1068	208	23	u	u	PROPN
ejpam-1068	208	24	6=	6=	AUX
ejpam-1068	208	25	∅.	∅.	ADV
ejpam-1068	208	26	let	let	VERB
ejpam-1068	208	27	x	x	X
ejpam-1068	208	28	∈	∈	PROPN
ejpam-1068	208	29	a∩	a∩	PROPN
ejpam-1068	208	30	u	u	NOUN
ejpam-1068	208	31	.	.	PUNCT
ejpam-1068	209	1	then	then	ADV
ejpam-1068	209	2	x	x	X
ejpam-1068	209	3	6∈	6∈	PROPN
ejpam-1068	209	4	(	(	PUNCT
ejpam-1068	209	5	x	x	X
ejpam-1068	209	6	\u	\u	X
ejpam-1068	209	7	)	)	PUNCT
ejpam-1068	209	8	.	.	PUNCT
ejpam-1068	210	1	hence	hence	ADV
ejpam-1068	210	2	by	by	ADP
ejpam-1068	210	3	(	(	PUNCT
ejpam-1068	210	4	iii	iii	NOUN
ejpam-1068	210	5	)	)	PUNCT
ejpam-1068	210	6	,	,	PUNCT
ejpam-1068	210	7	there	there	PRON
ejpam-1068	210	8	exists	exist	VERB
ejpam-1068	210	9	w	w	PROPN
ejpam-1068	210	10	∈ψo	∈ψo	PROPN
ejpam-1068	210	11	(	(	PUNCT
ejpam-1068	210	12	x	x	X
ejpam-1068	210	13	)	)	PUNCT
ejpam-1068	210	14	such	such	ADJ
ejpam-1068	210	15	that	that	SCONJ
ejpam-1068	210	16	x	x	PUNCT
ejpam-1068	210	17	\u	\u	PUNCT
ejpam-1068	210	18	⊆w	⊆w	NOUN
ejpam-1068	210	19	and	and	CCONJ
ejpam-1068	210	20	x	x	SYM
ejpam-1068	210	21	6∈ψ−	6∈ψ−	NUM
ejpam-1068	210	22	cl(w	cl(w	NOUN
ejpam-1068	210	23	)	)	PUNCT
ejpam-1068	210	24	.	.	PUNCT
ejpam-1068	211	1	put	put	VERB
ejpam-1068	211	2	v	v	NUM
ejpam-1068	211	3	=	=	NOUN
ejpam-1068	211	4	x	x	SYM
ejpam-1068	211	5	\	\	PROPN
ejpam-1068	211	6	ψ	ψ	X
ejpam-1068	211	7	−	−	PROPN
ejpam-1068	211	8	cl(w	cl(w	NOUN
ejpam-1068	211	9	)	)	PUNCT
ejpam-1068	211	10	which	which	PRON
ejpam-1068	211	11	is	be	AUX
ejpam-1068	211	12	a	a	DET
ejpam-1068	211	13	ψ	ψ	NOUN
ejpam-1068	211	14	-	-	ADJ
ejpam-1068	211	15	open	open	ADJ
ejpam-1068	211	16	set	set	NOUN
ejpam-1068	211	17	containing	contain	VERB
ejpam-1068	211	18	x	x	PUNCT
ejpam-1068	211	19	and	and	CCONJ
ejpam-1068	211	20	hence	hence	ADV
ejpam-1068	211	21	a	a	DET
ejpam-1068	211	22	∩	∩	ADJ
ejpam-1068	211	23	v	v	ADP
ejpam-1068	211	24	6=	6=	ADP
ejpam-1068	211	25	∅.	∅.	NOUN
ejpam-1068	211	26	now	now	ADV
ejpam-1068	211	27	v	v	ADP
ejpam-1068	211	28	⊆	⊆	NUM
ejpam-1068	211	29	x	x	X
ejpam-1068	211	30	\w	\w	ADJ
ejpam-1068	211	31	and	and	CCONJ
ejpam-1068	211	32	so	so	ADV
ejpam-1068	211	33	ψ−	ψ−	VERB
ejpam-1068	211	34	cl(v	cl(v	NOUN
ejpam-1068	211	35	)	)	PUNCT
ejpam-1068	211	36	⊆	⊆	X
ejpam-1068	211	37	x	x	X
ejpam-1068	211	38	\w	\w	VERB
ejpam-1068	211	39	⊆	⊆	NUM
ejpam-1068	211	40	u	u	NOUN
ejpam-1068	211	41	.	.	PUNCT
ejpam-1068	212	1	(	(	PUNCT
ejpam-1068	212	2	iv)⇒	iv)⇒	X
ejpam-1068	212	3	(	(	PUNCT
ejpam-1068	212	4	v	v	NOUN
ejpam-1068	212	5	)	)	PUNCT
ejpam-1068	212	6	:	:	PUNCT
ejpam-1068	212	7	let	let	VERB
ejpam-1068	212	8	f	f	PRON
ejpam-1068	212	9	be	be	AUX
ejpam-1068	212	10	a	a	DET
ejpam-1068	212	11	set	set	NOUN
ejpam-1068	212	12	as	as	ADP
ejpam-1068	212	13	in	in	ADP
ejpam-1068	212	14	the	the	DET
ejpam-1068	212	15	hypothesis	hypothesis	NOUN
ejpam-1068	212	16	of	of	ADP
ejpam-1068	212	17	(	(	PUNCT
ejpam-1068	212	18	v	v	NOUN
ejpam-1068	212	19	)	)	PUNCT
ejpam-1068	212	20	.	.	PUNCT
ejpam-1068	213	1	then	then	ADV
ejpam-1068	213	2	x	x	SYM
ejpam-1068	213	3	\	\	PROPN
ejpam-1068	213	4	f	f	PROPN
ejpam-1068	213	5	∈	∈	PROPN
ejpam-1068	213	6	τ	τ	PROPN
ejpam-1068	213	7	with	with	ADP
ejpam-1068	213	8	a∩	a∩	PROPN
ejpam-1068	213	9	(	(	PUNCT
ejpam-1068	213	10	x	x	SYM
ejpam-1068	213	11	\	\	PROPN
ejpam-1068	213	12	f	f	X
ejpam-1068	213	13	)	)	PUNCT
ejpam-1068	213	14	6=	6=	ADP
ejpam-1068	213	15	∅	∅	NOUN
ejpam-1068	213	16	and	and	CCONJ
ejpam-1068	213	17	hence	hence	ADV
ejpam-1068	213	18	by	by	ADP
ejpam-1068	213	19	(	(	PUNCT
ejpam-1068	213	20	iv	iv	X
ejpam-1068	213	21	)	)	PUNCT
ejpam-1068	213	22	,	,	PUNCT
ejpam-1068	213	23	there	there	PRON
ejpam-1068	213	24	exists	exist	VERB
ejpam-1068	213	25	v	v	ADP
ejpam-1068	213	26	∈ψo	∈ψo	PROPN
ejpam-1068	213	27	(	(	PUNCT
ejpam-1068	213	28	x	x	X
ejpam-1068	213	29	)	)	PUNCT
ejpam-1068	213	30	such	such	ADJ
ejpam-1068	213	31	that	that	SCONJ
ejpam-1068	213	32	a∩	a∩	PROPN
ejpam-1068	213	33	v	v	ADP
ejpam-1068	213	34	6=	6=	NOUN
ejpam-1068	213	35	∅	∅	NOUN
ejpam-1068	213	36	and	and	CCONJ
ejpam-1068	213	37	ψ−	ψ−	VERB
ejpam-1068	213	38	cl(v	cl(v	NOUN
ejpam-1068	213	39	)	)	PUNCT
ejpam-1068	214	1	⊆	⊆	NUM
ejpam-1068	214	2	x	x	SYM
ejpam-1068	214	3	\	\	PROPN
ejpam-1068	214	4	f	f	X
ejpam-1068	214	5	.	.	PUNCT
ejpam-1068	215	1	if	if	SCONJ
ejpam-1068	215	2	we	we	PRON
ejpam-1068	215	3	put	put	VERB
ejpam-1068	215	4	w	w	NOUN
ejpam-1068	215	5	=	=	NOUN
ejpam-1068	215	6	x	x	NOUN
ejpam-1068	215	7	\ψ−	\ψ−	NOUN
ejpam-1068	215	8	cl(v	cl(v	PRON
ejpam-1068	215	9	)	)	PUNCT
ejpam-1068	215	10	,	,	PUNCT
ejpam-1068	215	11	then	then	ADV
ejpam-1068	215	12	f	f	PROPN
ejpam-1068	215	13	⊆w	⊆w	NOUN
ejpam-1068	215	14	and	and	CCONJ
ejpam-1068	215	15	w	w	PROPN
ejpam-1068	215	16	∩	∩	ADJ
ejpam-1068	215	17	v	v	NOUN
ejpam-1068	215	18	=	=	SYM
ejpam-1068	215	19	∅.	∅.	X
ejpam-1068	215	20	(	(	PUNCT
ejpam-1068	215	21	v	v	NOUN
ejpam-1068	215	22	)	)	PUNCT
ejpam-1068	215	23	⇒	⇒	NOUN
ejpam-1068	215	24	(	(	PUNCT
ejpam-1068	215	25	i	i	NOUN
ejpam-1068	215	26	)	)	PUNCT
ejpam-1068	215	27	:	:	PUNCT
ejpam-1068	215	28	let	let	VERB
ejpam-1068	215	29	f	f	PRON
ejpam-1068	215	30	be	be	AUX
ejpam-1068	215	31	a	a	DET
ejpam-1068	215	32	closed	closed	ADJ
ejpam-1068	215	33	set	set	VERB
ejpam-1068	215	34	not	not	PART
ejpam-1068	215	35	containing	contain	VERB
ejpam-1068	215	36	x	x	X
ejpam-1068	215	37	.	.	PUNCT
ejpam-1068	216	1	then	then	ADV
ejpam-1068	216	2	f	f	PROPN
ejpam-1068	216	3	∩	∩	X
ejpam-1068	216	4	{	{	PUNCT
ejpam-1068	216	5	x	x	NOUN
ejpam-1068	216	6	}	}	PUNCT
ejpam-1068	216	7	=	=	PUNCT
ejpam-1068	216	8	∅.	∅.	VERB
ejpam-1068	216	9	thus	thus	ADV
ejpam-1068	216	10	by	by	ADP
ejpam-1068	216	11	(	(	PUNCT
ejpam-1068	216	12	v	v	NOUN
ejpam-1068	216	13	)	)	PUNCT
ejpam-1068	216	14	,	,	PUNCT
ejpam-1068	216	15	there	there	PRON
ejpam-1068	216	16	exist	exist	VERB
ejpam-1068	216	17	v	v	ADP
ejpam-1068	216	18	,	,	PUNCT
ejpam-1068	216	19	w	w	NOUN
ejpam-1068	216	20	∈ψo	∈ψo	PROPN
ejpam-1068	216	21	(	(	PUNCT
ejpam-1068	216	22	x	x	X
ejpam-1068	216	23	)	)	PUNCT
ejpam-1068	216	24	such	such	ADJ
ejpam-1068	216	25	that	that	SCONJ
ejpam-1068	216	26	x	x	SYM
ejpam-1068	216	27	∈	∈	NOUN
ejpam-1068	216	28	v	v	NOUN
ejpam-1068	216	29	,	,	PUNCT
ejpam-1068	216	30	f	f	PROPN
ejpam-1068	216	31	⊆w	⊆w	NOUN
ejpam-1068	216	32	and	and	CCONJ
ejpam-1068	216	33	w	w	PROPN
ejpam-1068	216	34	∩	∩	ADJ
ejpam-1068	216	35	v	v	NOUN
ejpam-1068	216	36	=	=	SYM
ejpam-1068	216	37	∅.	∅.	X
ejpam-1068	216	38	(	(	PUNCT
ejpam-1068	216	39	i)⇒	i)⇒	PROPN
ejpam-1068	216	40	(	(	PUNCT
ejpam-1068	216	41	vi	vi	NOUN
ejpam-1068	216	42	)	)	PUNCT
ejpam-1068	216	43	:	:	PUNCT
ejpam-1068	216	44	trivial	trivial	ADJ
ejpam-1068	216	45	.	.	PUNCT
ejpam-1068	217	1	(	(	PUNCT
ejpam-1068	217	2	vi	vi	NOUN
ejpam-1068	217	3	)	)	PUNCT
ejpam-1068	217	4	⇒	⇒	NOUN
ejpam-1068	217	5	(	(	PUNCT
ejpam-1068	217	6	vii	vii	PROPN
ejpam-1068	217	7	)	)	PUNCT
ejpam-1068	217	8	:	:	PUNCT
ejpam-1068	217	9	let	let	VERB
ejpam-1068	217	10	a	a	DET
ejpam-1068	217	11	⊆	⊆	NUM
ejpam-1068	217	12	x	x	PUNCT
ejpam-1068	217	13	and	and	CCONJ
ejpam-1068	217	14	f	f	PROPN
ejpam-1068	217	15	be	be	AUX
ejpam-1068	217	16	a	a	DET
ejpam-1068	217	17	closed	closed	ADJ
ejpam-1068	217	18	set	set	NOUN
ejpam-1068	217	19	with	with	ADP
ejpam-1068	217	20	a∩	a∩	PROPN
ejpam-1068	217	21	f	f	PROPN
ejpam-1068	218	1	=	=	PUNCT
ejpam-1068	218	2	∅.	∅.	NOUN
ejpam-1068	218	3	then	then	ADV
ejpam-1068	218	4	for	for	ADP
ejpam-1068	218	5	a	a	DET
ejpam-1068	218	6	∈	∈	PROPN
ejpam-1068	218	7	a	a	PRON
ejpam-1068	218	8	,	,	PUNCT
ejpam-1068	218	9	a	a	DET
ejpam-1068	218	10	6∈	6∈	NOUN
ejpam-1068	218	11	f	f	X
ejpam-1068	218	12	,	,	PUNCT
ejpam-1068	218	13	and	and	CCONJ
ejpam-1068	218	14	hence	hence	ADV
ejpam-1068	218	15	by	by	ADP
ejpam-1068	218	16	(	(	PUNCT
ejpam-1068	218	17	vi	vi	NOUN
ejpam-1068	218	18	)	)	PUNCT
ejpam-1068	218	19	,	,	PUNCT
ejpam-1068	218	20	there	there	PRON
ejpam-1068	218	21	exist	exist	VERB
ejpam-1068	218	22	u	u	PRON
ejpam-1068	218	23	∈	∈	PROPN
ejpam-1068	218	24	ψo	ψo	PRON
ejpam-1068	218	25	(	(	PUNCT
ejpam-1068	218	26	x	x	X
ejpam-1068	218	27	)	)	PUNCT
ejpam-1068	218	28	and	and	CCONJ
ejpam-1068	218	29	a	a	DET
ejpam-1068	218	30	gψ	gψ	ADV
ejpam-1068	218	31	-	-	PUNCT
ejpam-1068	218	32	open	open	ADJ
ejpam-1068	218	33	set	set	VERB
ejpam-1068	218	34	v	v	ADP
ejpam-1068	218	35	such	such	DET
ejpam-1068	218	36	that	that	SCONJ
ejpam-1068	218	37	a	a	DET
ejpam-1068	218	38	∈	∈	PROPN
ejpam-1068	218	39	u	u	NOUN
ejpam-1068	218	40	,	,	PUNCT
ejpam-1068	218	41	f	f	PROPN
ejpam-1068	218	42	⊆	⊆	PROPN
ejpam-1068	218	43	v	v	NOUN
ejpam-1068	218	44	and	and	CCONJ
ejpam-1068	218	45	u	u	NOUN
ejpam-1068	218	46	∩	∩	NOUN
ejpam-1068	218	47	v	v	NOUN
ejpam-1068	218	48	=	=	PUNCT
ejpam-1068	218	49	∅.	∅.	VERB
ejpam-1068	218	50	so	so	ADV
ejpam-1068	218	51	a∩	a∩	PROPN
ejpam-1068	218	52	u	u	PROPN
ejpam-1068	218	53	6=	6=	PROPN
ejpam-1068	218	54	∅	∅	NOUN
ejpam-1068	218	55	,	,	PUNCT
ejpam-1068	218	56	f	f	PROPN
ejpam-1068	218	57	⊆	⊆	PROPN
ejpam-1068	218	58	v	v	NOUN
ejpam-1068	218	59	and	and	CCONJ
ejpam-1068	218	60	u	u	NOUN
ejpam-1068	218	61	∩	∩	NOUN
ejpam-1068	218	62	v	v	NOUN
ejpam-1068	218	63	=	=	SYM
ejpam-1068	218	64	∅.	∅.	X
ejpam-1068	218	65	(	(	PUNCT
ejpam-1068	218	66	vii	vii	PROPN
ejpam-1068	218	67	)	)	PUNCT
ejpam-1068	218	68	⇒	⇒	NOUN
ejpam-1068	218	69	(	(	PUNCT
ejpam-1068	218	70	i	i	NOUN
ejpam-1068	218	71	)	)	PUNCT
ejpam-1068	218	72	:	:	PUNCT
ejpam-1068	218	73	let	let	VERB
ejpam-1068	218	74	x	x	SYM
ejpam-1068	218	75	6∈	6∈	NOUN
ejpam-1068	218	76	f	f	X
ejpam-1068	218	77	,	,	PUNCT
ejpam-1068	218	78	where	where	SCONJ
ejpam-1068	218	79	f	f	PROPN
ejpam-1068	218	80	is	be	AUX
ejpam-1068	218	81	closed	close	VERB
ejpam-1068	218	82	in	in	ADP
ejpam-1068	218	83	x	x	X
ejpam-1068	218	84	.	.	PUNCT
ejpam-1068	219	1	since	since	SCONJ
ejpam-1068	219	2	{	{	PUNCT
ejpam-1068	219	3	x	x	NOUN
ejpam-1068	219	4	}	}	PUNCT
ejpam-1068	219	5	∩	∩	ADJ
ejpam-1068	219	6	f	f	NOUN
ejpam-1068	219	7	=	=	NOUN
ejpam-1068	219	8	∅	∅	NOUN
ejpam-1068	219	9	,	,	PUNCT
ejpam-1068	219	10	by	by	ADP
ejpam-1068	219	11	(	(	PUNCT
ejpam-1068	219	12	vii	vii	PROPN
ejpam-1068	219	13	)	)	PUNCT
ejpam-1068	219	14	there	there	PRON
ejpam-1068	219	15	exist	exist	VERB
ejpam-1068	219	16	u	u	PRON
ejpam-1068	219	17	∈	∈	PROPN
ejpam-1068	219	18	ψo	ψo	PRON
ejpam-1068	219	19	(	(	PUNCT
ejpam-1068	219	20	x	x	X
ejpam-1068	219	21	)	)	PUNCT
ejpam-1068	219	22	and	and	CCONJ
ejpam-1068	219	23	a	a	DET
ejpam-1068	219	24	gψ	gψ	ADV
ejpam-1068	219	25	-	-	PUNCT
ejpam-1068	219	26	open	open	ADJ
ejpam-1068	219	27	set	set	NOUN
ejpam-1068	219	28	w	w	ADP
ejpam-1068	219	29	such	such	ADJ
ejpam-1068	219	30	that	that	SCONJ
ejpam-1068	219	31	x	x	SYM
ejpam-1068	219	32	∈	∈	PROPN
ejpam-1068	219	33	u	u	PROPN
ejpam-1068	219	34	,	,	PUNCT
ejpam-1068	219	35	f	f	PROPN
ejpam-1068	219	36	⊆	⊆	NUM
ejpam-1068	219	37	w	w	PROPN
ejpam-1068	219	38	and	and	CCONJ
ejpam-1068	219	39	u	u	NOUN
ejpam-1068	219	40	∩w	∩w	NOUN
ejpam-1068	219	41	=	=	PUNCT
ejpam-1068	220	1	∅.	∅.	VERB
ejpam-1068	220	2	then	then	ADV
ejpam-1068	220	3	f	f	PROPN
ejpam-1068	220	4	⊆ψ−	⊆ψ−	PROPN
ejpam-1068	220	5	int(w	int(w	NOUN
ejpam-1068	220	6	)	)	PUNCT
ejpam-1068	220	7	=	=	SYM
ejpam-1068	220	8	v	v	X
ejpam-1068	220	9	(	(	PUNCT
ejpam-1068	220	10	say	say	INTJ
ejpam-1068	220	11	)	)	PUNCT
ejpam-1068	220	12	(	(	PUNCT
ejpam-1068	220	13	by	by	ADP
ejpam-1068	220	14	theorem	theorem	NOUN
ejpam-1068	220	15	4	4	NUM
ejpam-1068	220	16	)	)	PUNCT
ejpam-1068	220	17	and	and	CCONJ
ejpam-1068	220	18	hence	hence	ADV
ejpam-1068	220	19	v	v	ADP
ejpam-1068	220	20	∩	∩	ADJ
ejpam-1068	220	21	u	u	NOUN
ejpam-1068	220	22	=	=	X
ejpam-1068	220	23	∅.	∅.	NOUN
ejpam-1068	220	24	definition	definition	NOUN
ejpam-1068	220	25	6	6	NUM
ejpam-1068	220	26	.	.	PUNCT
ejpam-1068	221	1	let	let	VERB
ejpam-1068	221	2	ψ	ψ	PART
ejpam-1068	221	3	be	be	AUX
ejpam-1068	221	4	an	an	DET
ejpam-1068	221	5	operation	operation	NOUN
ejpam-1068	221	6	on	on	ADP
ejpam-1068	221	7	a	a	DET
ejpam-1068	221	8	topological	topological	ADJ
ejpam-1068	221	9	space	space	NOUN
ejpam-1068	221	10	(	(	PUNCT
ejpam-1068	221	11	x	x	X
ejpam-1068	221	12	,	,	PUNCT
ejpam-1068	221	13	τ	τ	PROPN
ejpam-1068	221	14	)	)	PUNCT
ejpam-1068	221	15	.	.	PUNCT
ejpam-1068	222	1	then	then	ADV
ejpam-1068	222	2	(	(	PUNCT
ejpam-1068	222	3	x	x	X
ejpam-1068	222	4	,	,	PUNCT
ejpam-1068	222	5	τ	τ	X
ejpam-1068	222	6	)	)	PUNCT
ejpam-1068	222	7	is	be	AUX
ejpam-1068	222	8	said	say	VERB
ejpam-1068	222	9	to	to	PART
ejpam-1068	222	10	be	be	AUX
ejpam-1068	222	11	ψg	ψg	NOUN
ejpam-1068	222	12	-	-	NOUN
ejpam-1068	222	13	normal	normal	ADJ
ejpam-1068	222	14	if	if	SCONJ
ejpam-1068	222	15	for	for	ADP
ejpam-1068	222	16	any	any	DET
ejpam-1068	222	17	two	two	NUM
ejpam-1068	222	18	disjoint	disjoint	NOUN
ejpam-1068	222	19	closed	closed	ADJ
ejpam-1068	222	20	sets	set	NOUN
ejpam-1068	222	21	a	a	PRON
ejpam-1068	222	22	and	and	CCONJ
ejpam-1068	222	23	b	b	NOUN
ejpam-1068	222	24	there	there	PRON
ejpam-1068	222	25	exist	exist	VERB
ejpam-1068	222	26	two	two	NUM
ejpam-1068	222	27	disjoint	disjoint	NOUN
ejpam-1068	222	28	ψ	ψ	ADJ
ejpam-1068	222	29	-	-	ADJ
ejpam-1068	222	30	open	open	ADJ
ejpam-1068	222	31	sets	set	NOUN
ejpam-1068	222	32	u	u	NOUN
ejpam-1068	222	33	and	and	CCONJ
ejpam-1068	222	34	v	v	ADP
ejpam-1068	222	35	such	such	ADJ
ejpam-1068	222	36	that	that	PRON
ejpam-1068	222	37	a⊆	a⊆	PROPN
ejpam-1068	222	38	u	u	NOUN
ejpam-1068	222	39	and	and	CCONJ
ejpam-1068	222	40	b	b	NOUN
ejpam-1068	222	41	⊆	⊆	NUM
ejpam-1068	222	42	v	v	NOUN
ejpam-1068	222	43	.	.	PUNCT
ejpam-1068	223	1	remark	remark	PROPN
ejpam-1068	223	2	6	6	NUM
ejpam-1068	223	3	.	.	PUNCT
ejpam-1068	224	1	let	let	VERB
ejpam-1068	224	2	ψ	ψ	PART
ejpam-1068	224	3	be	be	AUX
ejpam-1068	224	4	an	an	DET
ejpam-1068	224	5	operation	operation	NOUN
ejpam-1068	224	6	on	on	ADP
ejpam-1068	224	7	a	a	DET
ejpam-1068	224	8	space	space	NOUN
ejpam-1068	224	9	(	(	PUNCT
ejpam-1068	224	10	x	x	X
ejpam-1068	224	11	,	,	PUNCT
ejpam-1068	224	12	τ	τ	PROPN
ejpam-1068	224	13	)	)	PUNCT
ejpam-1068	224	14	.	.	PUNCT
ejpam-1068	225	1	then	then	ADV
ejpam-1068	225	2	every	every	DET
ejpam-1068	225	3	ψg	ψg	NOUN
ejpam-1068	225	4	-	-	ADJ
ejpam-1068	225	5	normal	normal	ADJ
ejpam-1068	225	6	space	space	NOUN
ejpam-1068	225	7	reduces	reduce	VERB
ejpam-1068	225	8	to	to	ADP
ejpam-1068	225	9	a	a	DET
ejpam-1068	225	10	normal	normal	ADJ
ejpam-1068	225	11	[	[	X
ejpam-1068	225	12	5	5	NUM
ejpam-1068	225	13	]	]	PUNCT
ejpam-1068	225	14	(	(	PUNCT
ejpam-1068	225	15	resp	resp	NOUN
ejpam-1068	225	16	.	.	PUNCT
ejpam-1068	226	1	pre	pre	ADJ
ejpam-1068	226	2	-	-	ADJ
ejpam-1068	226	3	normal	normal	ADJ
ejpam-1068	226	4	[	[	X
ejpam-1068	226	5	16	16	NUM
ejpam-1068	226	6	]	]	PUNCT
ejpam-1068	226	7	or	or	CCONJ
ejpam-1068	226	8	p	p	NOUN
ejpam-1068	226	9	-	-	PUNCT
ejpam-1068	226	10	normal	normal	ADJ
ejpam-1068	227	1	[	[	X
ejpam-1068	227	2	18	18	NUM
ejpam-1068	227	3	]	]	PUNCT
ejpam-1068	227	4	,	,	PUNCT
ejpam-1068	227	5	s	s	NOUN
ejpam-1068	227	6	-	-	ADJ
ejpam-1068	227	7	normal	normal	ADJ
ejpam-1068	227	8	[	[	X
ejpam-1068	227	9	11	11	NUM
ejpam-1068	227	10	]	]	PUNCT
ejpam-1068	227	11	,	,	PUNCT
ejpam-1068	227	12	δp	δp	ADV
ejpam-1068	227	13	-	-	ADJ
ejpam-1068	227	14	normal	normal	ADJ
ejpam-1068	227	15	[	[	X
ejpam-1068	227	16	6	6	NUM
ejpam-1068	227	17	]	]	PUNCT
ejpam-1068	227	18	,	,	PUNCT
ejpam-1068	227	19	β	β	X
ejpam-1068	227	20	-normal	-normal	ADJ
ejpam-1068	227	21	[	[	X
ejpam-1068	227	22	12	12	NUM
ejpam-1068	227	23	]	]	SYM
ejpam-1068	227	24	)	)	PUNCT
ejpam-1068	227	25	space	space	NOUN
ejpam-1068	227	26	if	if	SCONJ
ejpam-1068	227	27	one	one	PRON
ejpam-1068	227	28	takes	take	VERB
ejpam-1068	227	29	ψ	ψ	NOUN
ejpam-1068	227	30	to	to	PART
ejpam-1068	227	31	be	be	AUX
ejpam-1068	227	32	int	int	NOUN
ejpam-1068	227	33	(	(	PUNCT
ejpam-1068	227	34	resp	resp	NOUN
ejpam-1068	227	35	.	.	PUNCT
ejpam-1068	227	36	intcl	intcl	PROPN
ejpam-1068	227	37	,	,	PUNCT
ejpam-1068	227	38	cl	cl	NOUN
ejpam-1068	227	39	int	int	NOUN
ejpam-1068	227	40	,	,	PUNCT
ejpam-1068	227	41	intclδ	intclδ	NOUN
ejpam-1068	227	42	,	,	PUNCT
ejpam-1068	227	43	cl	cl	NOUN
ejpam-1068	227	44	intcl	intcl	NOUN
ejpam-1068	227	45	)	)	PUNCT
ejpam-1068	227	46	.	.	PUNCT
ejpam-1068	228	1	theorem	theorem	ADJ
ejpam-1068	228	2	10	10	NUM
ejpam-1068	228	3	.	.	PUNCT
ejpam-1068	229	1	letψ	letψ	NOUN
ejpam-1068	229	2	be	be	AUX
ejpam-1068	229	3	an	an	DET
ejpam-1068	229	4	operation	operation	NOUN
ejpam-1068	229	5	on	on	ADP
ejpam-1068	229	6	a	a	DET
ejpam-1068	229	7	topological	topological	ADJ
ejpam-1068	229	8	space	space	NOUN
ejpam-1068	229	9	(	(	PUNCT
ejpam-1068	229	10	x	x	X
ejpam-1068	229	11	,	,	PUNCT
ejpam-1068	229	12	τ	τ	PROPN
ejpam-1068	229	13	)	)	PUNCT
ejpam-1068	229	14	.	.	PUNCT
ejpam-1068	230	1	then	then	ADV
ejpam-1068	230	2	the	the	DET
ejpam-1068	230	3	following	follow	VERB
ejpam-1068	230	4	statements	statement	NOUN
ejpam-1068	230	5	are	be	AUX
ejpam-1068	230	6	equivalent	equivalent	ADJ
ejpam-1068	230	7	:	:	PUNCT
ejpam-1068	230	8	(	(	PUNCT
ejpam-1068	230	9	i	i	NOUN
ejpam-1068	230	10	)	)	PUNCT
ejpam-1068	230	11	x	x	PRON
ejpam-1068	230	12	is	be	AUX
ejpam-1068	230	13	ψg	ψg	NOUN
ejpam-1068	230	14	-normal	-normal	NOUN
ejpam-1068	230	15	.	.	PUNCT
ejpam-1068	231	1	(	(	PUNCT
ejpam-1068	231	2	ii	ii	NOUN
ejpam-1068	231	3	)	)	PUNCT
ejpam-1068	231	4	for	for	ADP
ejpam-1068	231	5	any	any	DET
ejpam-1068	231	6	pair	pair	NOUN
ejpam-1068	231	7	of	of	ADP
ejpam-1068	231	8	disjoint	disjoint	NOUN
ejpam-1068	231	9	closed	closed	ADJ
ejpam-1068	231	10	sets	set	NOUN
ejpam-1068	231	11	a	a	PRON
ejpam-1068	231	12	and	and	CCONJ
ejpam-1068	231	13	b	b	NOUN
ejpam-1068	231	14	of	of	ADP
ejpam-1068	231	15	x	x	SYM
ejpam-1068	231	16	,	,	PUNCT
ejpam-1068	231	17	there	there	PRON
ejpam-1068	231	18	exist	exist	VERB
ejpam-1068	231	19	disjoint	disjoint	ADJ
ejpam-1068	231	20	gψ	gψ	ADJ
ejpam-1068	231	21	-	-	PUNCT
ejpam-1068	231	22	open	open	ADJ
ejpam-1068	231	23	sets	set	NOUN
ejpam-1068	231	24	u	u	NOUN
ejpam-1068	231	25	and	and	CCONJ
ejpam-1068	231	26	v	v	NOUN
ejpam-1068	231	27	of	of	ADP
ejpam-1068	231	28	x	x	PUNCT
ejpam-1068	231	29	such	such	ADJ
ejpam-1068	231	30	that	that	PRON
ejpam-1068	231	31	a⊆	a⊆	PROPN
ejpam-1068	231	32	u	u	NOUN
ejpam-1068	231	33	and	and	CCONJ
ejpam-1068	231	34	b	b	NOUN
ejpam-1068	231	35	⊆	⊆	NUM
ejpam-1068	231	36	v	v	NOUN
ejpam-1068	231	37	.	.	PUNCT
ejpam-1068	232	1	(	(	PUNCT
ejpam-1068	232	2	iii	iii	NOUN
ejpam-1068	232	3	)	)	PUNCT
ejpam-1068	232	4	for	for	ADP
ejpam-1068	232	5	each	each	DET
ejpam-1068	232	6	closed	close	VERB
ejpam-1068	232	7	set	set	VERB
ejpam-1068	232	8	a	a	PRON
ejpam-1068	232	9	and	and	CCONJ
ejpam-1068	232	10	each	each	DET
ejpam-1068	232	11	open	open	ADJ
ejpam-1068	232	12	set	set	VERB
ejpam-1068	232	13	b	b	NOUN
ejpam-1068	232	14	containing	contain	VERB
ejpam-1068	232	15	a	a	PRON
ejpam-1068	232	16	,	,	PUNCT
ejpam-1068	232	17	there	there	PRON
ejpam-1068	232	18	exists	exist	VERB
ejpam-1068	232	19	a	a	DET
ejpam-1068	232	20	gψ	gψ	ADV
ejpam-1068	232	21	-	-	PUNCT
ejpam-1068	232	22	open	open	ADJ
ejpam-1068	232	23	set	set	NOUN
ejpam-1068	232	24	u	u	NOUN
ejpam-1068	232	25	such	such	ADJ
ejpam-1068	232	26	that	that	PRON
ejpam-1068	232	27	a⊆	a⊆	PROPN
ejpam-1068	232	28	u	u	NOUN
ejpam-1068	232	29	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	232	30	cl(u	cl(u	NOUN
ejpam-1068	232	31	)	)	PUNCT
ejpam-1068	233	1	⊆	⊆	NUM
ejpam-1068	233	2	b.	b.	PROPN
ejpam-1068	233	3	(	(	PUNCT
ejpam-1068	233	4	iv	iv	X
ejpam-1068	233	5	)	)	PUNCT
ejpam-1068	233	6	for	for	ADP
ejpam-1068	233	7	each	each	DET
ejpam-1068	233	8	closed	close	VERB
ejpam-1068	233	9	set	set	VERB
ejpam-1068	233	10	a	a	PRON
ejpam-1068	233	11	and	and	CCONJ
ejpam-1068	233	12	each	each	DET
ejpam-1068	233	13	g	g	NOUN
ejpam-1068	233	14	-	-	PUNCT
ejpam-1068	233	15	open	open	ADJ
ejpam-1068	233	16	set	set	NOUN
ejpam-1068	233	17	b	b	PROPN
ejpam-1068	233	18	containing	contain	VERB
ejpam-1068	233	19	a	a	PRON
ejpam-1068	233	20	,	,	PUNCT
ejpam-1068	233	21	there	there	PRON
ejpam-1068	233	22	exists	exist	VERB
ejpam-1068	233	23	a	a	DET
ejpam-1068	233	24	ψ	ψ	NOUN
ejpam-1068	233	25	-	-	ADJ
ejpam-1068	233	26	open	open	ADJ
ejpam-1068	233	27	set	set	NOUN
ejpam-1068	233	28	u	u	NOUN
ejpam-1068	233	29	such	such	ADJ
ejpam-1068	233	30	that	that	PRON
ejpam-1068	233	31	a⊆	a⊆	PROPN
ejpam-1068	233	32	u	u	NOUN
ejpam-1068	233	33	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	233	34	cl(u	cl(u	NOUN
ejpam-1068	233	35	)	)	PUNCT
ejpam-1068	233	36	⊆	⊆	NUM
ejpam-1068	233	37	int(b	int(b	NUM
ejpam-1068	233	38	)	)	PUNCT
ejpam-1068	233	39	.	.	PUNCT
ejpam-1068	234	1	references	reference	NOUN
ejpam-1068	234	2	50	50	NUM
ejpam-1068	234	3	(	(	PUNCT
ejpam-1068	234	4	v	v	NOUN
ejpam-1068	234	5	)	)	PUNCT
ejpam-1068	234	6	for	for	ADP
ejpam-1068	234	7	each	each	DET
ejpam-1068	234	8	closed	close	VERB
ejpam-1068	234	9	set	set	VERB
ejpam-1068	234	10	a	a	PRON
ejpam-1068	234	11	and	and	CCONJ
ejpam-1068	234	12	each	each	DET
ejpam-1068	234	13	g	g	NOUN
ejpam-1068	234	14	-	-	PUNCT
ejpam-1068	234	15	open	open	ADJ
ejpam-1068	234	16	set	set	NOUN
ejpam-1068	234	17	b	b	PROPN
ejpam-1068	234	18	containing	contain	VERB
ejpam-1068	234	19	a	a	PRON
ejpam-1068	234	20	,	,	PUNCT
ejpam-1068	234	21	there	there	PRON
ejpam-1068	234	22	exists	exist	VERB
ejpam-1068	234	23	a	a	DET
ejpam-1068	234	24	gψ	gψ	ADV
ejpam-1068	234	25	-	-	PUNCT
ejpam-1068	234	26	open	open	ADJ
ejpam-1068	234	27	set	set	NOUN
ejpam-1068	234	28	g	g	PROPN
ejpam-1068	234	29	such	such	ADJ
ejpam-1068	234	30	that	that	PRON
ejpam-1068	234	31	a⊆	a⊆	VERB
ejpam-1068	234	32	g	g	ADP
ejpam-1068	234	33	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	234	34	cl(g	cl(g	NOUN
ejpam-1068	234	35	)	)	PUNCT
ejpam-1068	234	36	⊆	⊆	NUM
ejpam-1068	234	37	int(b	int(b	NOUN
ejpam-1068	234	38	)	)	PUNCT
ejpam-1068	234	39	.	.	PUNCT
ejpam-1068	235	1	(	(	PUNCT
ejpam-1068	235	2	vi	vi	X
ejpam-1068	235	3	)	)	PUNCT
ejpam-1068	235	4	for	for	ADP
ejpam-1068	235	5	each	each	PRON
ejpam-1068	235	6	g	g	NOUN
ejpam-1068	235	7	-	-	PUNCT
ejpam-1068	235	8	closed	closed	ADJ
ejpam-1068	235	9	set	set	NOUN
ejpam-1068	235	10	a	a	PRON
ejpam-1068	235	11	and	and	CCONJ
ejpam-1068	235	12	each	each	DET
ejpam-1068	235	13	open	open	ADJ
ejpam-1068	235	14	set	set	VERB
ejpam-1068	235	15	b	b	NOUN
ejpam-1068	235	16	containing	contain	VERB
ejpam-1068	235	17	a	a	PRON
ejpam-1068	235	18	,	,	PUNCT
ejpam-1068	235	19	there	there	PRON
ejpam-1068	235	20	exists	exist	VERB
ejpam-1068	235	21	a	a	DET
ejpam-1068	235	22	ψ	ψ	NOUN
ejpam-1068	235	23	-	-	ADJ
ejpam-1068	235	24	open	open	ADJ
ejpam-1068	235	25	set	set	NOUN
ejpam-1068	235	26	u	u	PRON
ejpam-1068	235	27	such	such	ADJ
ejpam-1068	235	28	that	that	PRON
ejpam-1068	235	29	cl(a	cl(a	PUNCT
ejpam-1068	235	30	)	)	PUNCT
ejpam-1068	235	31	⊆	⊆	NUM
ejpam-1068	235	32	u	u	NOUN
ejpam-1068	235	33	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	235	34	cl(u	cl(u	NOUN
ejpam-1068	235	35	)	)	PUNCT
ejpam-1068	235	36	⊆	⊆	NUM
ejpam-1068	235	37	b.	b.	PROPN
ejpam-1068	235	38	(	(	PUNCT
ejpam-1068	235	39	vii	vii	PROPN
ejpam-1068	235	40	)	)	PUNCT
ejpam-1068	235	41	for	for	ADP
ejpam-1068	235	42	each	each	DET
ejpam-1068	235	43	g	g	NOUN
ejpam-1068	235	44	-	-	PUNCT
ejpam-1068	235	45	closed	closed	ADJ
ejpam-1068	235	46	set	set	NOUN
ejpam-1068	235	47	a	a	PRON
ejpam-1068	235	48	and	and	CCONJ
ejpam-1068	235	49	each	each	DET
ejpam-1068	235	50	open	open	ADJ
ejpam-1068	235	51	set	set	VERB
ejpam-1068	235	52	b	b	NOUN
ejpam-1068	235	53	containing	contain	VERB
ejpam-1068	235	54	a	a	PRON
ejpam-1068	235	55	,	,	PUNCT
ejpam-1068	235	56	there	there	PRON
ejpam-1068	235	57	exists	exist	VERB
ejpam-1068	235	58	a	a	DET
ejpam-1068	235	59	gψ	gψ	ADV
ejpam-1068	235	60	-	-	PUNCT
ejpam-1068	235	61	open	open	ADJ
ejpam-1068	235	62	set	set	NOUN
ejpam-1068	235	63	g	g	PROPN
ejpam-1068	235	64	such	such	ADJ
ejpam-1068	235	65	that	that	PRON
ejpam-1068	235	66	cl(a	cl(a	PUNCT
ejpam-1068	235	67	)	)	PUNCT
ejpam-1068	235	68	⊆	⊆	NUM
ejpam-1068	235	69	g	g	NOUN
ejpam-1068	235	70	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	235	71	cl(g	cl(g	NOUN
ejpam-1068	235	72	)	)	PUNCT
ejpam-1068	235	73	⊆	⊆	NUM
ejpam-1068	235	74	b.	b.	NOUN
ejpam-1068	235	75	proof	proof	NOUN
ejpam-1068	235	76	.	.	PUNCT
ejpam-1068	236	1	(	(	PUNCT
ejpam-1068	236	2	i)⇒	i)⇒	PROPN
ejpam-1068	236	3	(	(	PUNCT
ejpam-1068	236	4	ii	ii	NOUN
ejpam-1068	236	5	)	)	PUNCT
ejpam-1068	236	6	:	:	PUNCT
ejpam-1068	236	7	let	let	VERB
ejpam-1068	236	8	a	a	PRON
ejpam-1068	236	9	and	and	CCONJ
ejpam-1068	236	10	b	b	NOUN
ejpam-1068	236	11	be	be	AUX
ejpam-1068	236	12	a	a	DET
ejpam-1068	236	13	pair	pair	NOUN
ejpam-1068	236	14	of	of	ADP
ejpam-1068	236	15	disjoint	disjoint	NOUN
ejpam-1068	236	16	closed	close	VERB
ejpam-1068	236	17	sets	set	NOUN
ejpam-1068	236	18	of	of	ADP
ejpam-1068	236	19	x	x	X
ejpam-1068	236	20	.	.	PUNCT
ejpam-1068	237	1	then	then	ADV
ejpam-1068	237	2	by	by	ADP
ejpam-1068	237	3	(	(	PUNCT
ejpam-1068	237	4	i	i	NOUN
ejpam-1068	237	5	)	)	PUNCT
ejpam-1068	237	6	there	there	PRON
ejpam-1068	237	7	exist	exist	VERB
ejpam-1068	237	8	disjoint	disjoint	NOUN
ejpam-1068	237	9	ψ	ψ	ADJ
ejpam-1068	237	10	-	-	ADJ
ejpam-1068	237	11	open	open	ADJ
ejpam-1068	237	12	sets	set	NOUN
ejpam-1068	237	13	u	u	NOUN
ejpam-1068	237	14	and	and	CCONJ
ejpam-1068	237	15	v	v	NOUN
ejpam-1068	237	16	of	of	ADP
ejpam-1068	237	17	x	x	PUNCT
ejpam-1068	237	18	such	such	ADJ
ejpam-1068	237	19	that	that	SCONJ
ejpam-1068	237	20	a	a	DET
ejpam-1068	237	21	⊆	⊆	NUM
ejpam-1068	237	22	u	u	NOUN
ejpam-1068	237	23	and	and	CCONJ
ejpam-1068	237	24	b	b	NOUN
ejpam-1068	237	25	⊆	⊆	NUM
ejpam-1068	237	26	v	v	NOUN
ejpam-1068	237	27	.	.	PUNCT
ejpam-1068	238	1	then	then	ADV
ejpam-1068	238	2	the	the	DET
ejpam-1068	238	3	rest	rest	NOUN
ejpam-1068	238	4	follows	follow	VERB
ejpam-1068	238	5	from	from	ADP
ejpam-1068	238	6	remark	remark	NOUN
ejpam-1068	238	7	4(ii	4(ii	PROPN
ejpam-1068	238	8	)	)	PUNCT
ejpam-1068	238	9	.	.	PUNCT
ejpam-1068	239	1	(	(	PUNCT
ejpam-1068	239	2	ii	ii	NOUN
ejpam-1068	239	3	)	)	PUNCT
ejpam-1068	239	4	⇒	⇒	NOUN
ejpam-1068	239	5	(	(	PUNCT
ejpam-1068	239	6	iii	iii	NOUN
ejpam-1068	239	7	)	)	PUNCT
ejpam-1068	239	8	:	:	PUNCT
ejpam-1068	239	9	let	let	VERB
ejpam-1068	239	10	a	a	PRON
ejpam-1068	239	11	be	be	AUX
ejpam-1068	239	12	a	a	DET
ejpam-1068	239	13	closed	closed	ADJ
ejpam-1068	239	14	set	set	NOUN
ejpam-1068	239	15	and	and	CCONJ
ejpam-1068	239	16	b	b	NOUN
ejpam-1068	239	17	be	be	AUX
ejpam-1068	239	18	an	an	DET
ejpam-1068	239	19	open	open	ADJ
ejpam-1068	239	20	set	set	NOUN
ejpam-1068	239	21	containing	contain	VERB
ejpam-1068	239	22	a.	a.	NOUN
ejpam-1068	239	23	then	then	ADV
ejpam-1068	239	24	a	a	PRON
ejpam-1068	239	25	and	and	CCONJ
ejpam-1068	239	26	x	x	SYM
ejpam-1068	239	27	\	\	PROPN
ejpam-1068	239	28	b	b	PROPN
ejpam-1068	239	29	are	be	AUX
ejpam-1068	239	30	two	two	NUM
ejpam-1068	239	31	disjoint	disjoint	ADJ
ejpam-1068	239	32	closed	close	VERB
ejpam-1068	239	33	sets	set	NOUN
ejpam-1068	239	34	.	.	PUNCT
ejpam-1068	240	1	hence	hence	ADV
ejpam-1068	240	2	by	by	ADP
ejpam-1068	240	3	(	(	PUNCT
ejpam-1068	240	4	ii	ii	NOUN
ejpam-1068	240	5	)	)	PUNCT
ejpam-1068	240	6	there	there	PRON
ejpam-1068	240	7	exist	exist	VERB
ejpam-1068	240	8	disjoint	disjoint	NOUN
ejpam-1068	240	9	gψ	gψ	ADJ
ejpam-1068	240	10	-	-	PUNCT
ejpam-1068	240	11	open	open	ADJ
ejpam-1068	240	12	sets	set	NOUN
ejpam-1068	240	13	u	u	NOUN
ejpam-1068	240	14	and	and	CCONJ
ejpam-1068	240	15	v	v	NOUN
ejpam-1068	240	16	of	of	ADP
ejpam-1068	240	17	x	x	PUNCT
ejpam-1068	240	18	such	such	ADJ
ejpam-1068	240	19	that	that	SCONJ
ejpam-1068	240	20	a	a	DET
ejpam-1068	240	21	⊆	⊆	NUM
ejpam-1068	240	22	u	u	NOUN
ejpam-1068	240	23	and	and	CCONJ
ejpam-1068	240	24	bc	bc	VERB
ejpam-1068	240	25	⊆	⊆	NUM
ejpam-1068	240	26	v	v	NOUN
ejpam-1068	240	27	.	.	PUNCT
ejpam-1068	241	1	since	since	SCONJ
ejpam-1068	241	2	v	v	NOUN
ejpam-1068	241	3	is	be	AUX
ejpam-1068	241	4	gψ	gψ	ADJ
ejpam-1068	241	5	-	-	PUNCT
ejpam-1068	241	6	open	open	ADJ
ejpam-1068	241	7	and	and	CCONJ
ejpam-1068	241	8	x	x	SYM
ejpam-1068	241	9	\	\	PROPN
ejpam-1068	241	10	b	b	PROPN
ejpam-1068	241	11	is	be	AUX
ejpam-1068	241	12	a	a	DET
ejpam-1068	241	13	closed	closed	ADJ
ejpam-1068	241	14	set	set	NOUN
ejpam-1068	241	15	with	with	ADP
ejpam-1068	241	16	x	x	SYM
ejpam-1068	241	17	\	\	PROPN
ejpam-1068	241	18	b	b	PROPN
ejpam-1068	241	19	⊆	⊆	NUM
ejpam-1068	241	20	v	v	NOUN
ejpam-1068	241	21	,	,	PUNCT
ejpam-1068	241	22	by	by	ADP
ejpam-1068	241	23	theorem	theorem	NOUN
ejpam-1068	241	24	4	4	NUM
ejpam-1068	241	25	,	,	PUNCT
ejpam-1068	241	26	x	x	SYM
ejpam-1068	241	27	\	\	PROPN
ejpam-1068	241	28	b	b	PROPN
ejpam-1068	242	1	⊆	⊆	NUM
ejpam-1068	242	2	ψ	ψ	NOUN
ejpam-1068	242	3	−	−	PROPN
ejpam-1068	242	4	int(v	int(v	PROPN
ejpam-1068	242	5	)	)	PUNCT
ejpam-1068	242	6	.	.	PUNCT
ejpam-1068	243	1	hence	hence	ADV
ejpam-1068	243	2	ψ	ψ	X
ejpam-1068	243	3	−	−	PROPN
ejpam-1068	243	4	cl(x	cl(x	SYM
ejpam-1068	243	5	\	\	PROPN
ejpam-1068	243	6	v	v	NOUN
ejpam-1068	243	7	)	)	PUNCT
ejpam-1068	243	8	=	=	PUNCT
ejpam-1068	244	1	x	x	SYM
ejpam-1068	244	2	\	\	PROPN
ejpam-1068	245	1	ψ	ψ	X
ejpam-1068	245	2	−	−	PROPN
ejpam-1068	245	3	int(v	int(v	PROPN
ejpam-1068	245	4	)	)	PUNCT
ejpam-1068	245	5	⊆	⊆	NUM
ejpam-1068	245	6	b.	b.	NOUN
ejpam-1068	245	7	thus	thus	ADV
ejpam-1068	245	8	a⊆	a⊆	VERB
ejpam-1068	245	9	u	u	NOUN
ejpam-1068	245	10	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	245	11	cl(u	cl(u	NOUN
ejpam-1068	245	12	)	)	PUNCT
ejpam-1068	245	13	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	245	14	cl(x	cl(x	X
ejpam-1068	245	15	\	\	PROPN
ejpam-1068	245	16	v	v	NOUN
ejpam-1068	245	17	)	)	PUNCT
ejpam-1068	245	18	⊆	⊆	NUM
ejpam-1068	245	19	b.	b.	X
ejpam-1068	245	20	(	(	PUNCT
ejpam-1068	245	21	iii	iii	NOUN
ejpam-1068	245	22	)	)	PUNCT
ejpam-1068	245	23	⇒	⇒	NOUN
ejpam-1068	245	24	(	(	PUNCT
ejpam-1068	245	25	i	i	NOUN
ejpam-1068	245	26	)	)	PUNCT
ejpam-1068	245	27	:	:	PUNCT
ejpam-1068	245	28	let	let	VERB
ejpam-1068	245	29	a	a	PRON
ejpam-1068	245	30	and	and	CCONJ
ejpam-1068	245	31	b	b	NOUN
ejpam-1068	245	32	be	be	AUX
ejpam-1068	245	33	two	two	NUM
ejpam-1068	245	34	disjoint	disjoint	ADJ
ejpam-1068	245	35	closed	close	VERB
ejpam-1068	245	36	subsets	subset	NOUN
ejpam-1068	245	37	of	of	ADP
ejpam-1068	245	38	x	x	X
ejpam-1068	245	39	.	.	PUNCT
ejpam-1068	246	1	then	then	ADV
ejpam-1068	246	2	a	a	PRON
ejpam-1068	246	3	is	be	AUX
ejpam-1068	246	4	a	a	DET
ejpam-1068	246	5	closed	closed	ADJ
ejpam-1068	246	6	set	set	NOUN
ejpam-1068	246	7	and	and	CCONJ
ejpam-1068	246	8	bc	bc	PROPN
ejpam-1068	246	9	is	be	AUX
ejpam-1068	246	10	an	an	DET
ejpam-1068	246	11	open	open	ADJ
ejpam-1068	246	12	set	set	NOUN
ejpam-1068	246	13	containing	contain	VERB
ejpam-1068	246	14	a.	a.	NOUN
ejpam-1068	246	15	thus	thus	ADV
ejpam-1068	246	16	by	by	ADP
ejpam-1068	246	17	(	(	PUNCT
ejpam-1068	246	18	iii	iii	NOUN
ejpam-1068	246	19	)	)	PUNCT
ejpam-1068	246	20	,	,	PUNCT
ejpam-1068	246	21	there	there	PRON
ejpam-1068	246	22	exists	exist	VERB
ejpam-1068	246	23	a	a	DET
ejpam-1068	246	24	gψ	gψ	ADV
ejpam-1068	246	25	-	-	PUNCT
ejpam-1068	246	26	open	open	ADJ
ejpam-1068	246	27	set	set	NOUN
ejpam-1068	246	28	u	u	PRON
ejpam-1068	246	29	such	such	ADJ
ejpam-1068	246	30	that	that	SCONJ
ejpam-1068	246	31	a	a	DET
ejpam-1068	246	32	⊆	⊆	NUM
ejpam-1068	246	33	u	u	NOUN
ejpam-1068	246	34	⊆	⊆	NUM
ejpam-1068	246	35	ψ−	ψ−	ADJ
ejpam-1068	246	36	cl(u	cl(u	NOUN
ejpam-1068	246	37	)	)	PUNCT
ejpam-1068	246	38	⊆	⊆	NUM
ejpam-1068	246	39	bc	bc	PROPN
ejpam-1068	246	40	.	.	PUNCT
ejpam-1068	247	1	thus	thus	ADV
ejpam-1068	247	2	by	by	ADP
ejpam-1068	247	3	theorem	theorem	NOUN
ejpam-1068	247	4	4	4	NUM
ejpam-1068	247	5	,	,	PUNCT
ejpam-1068	247	6	a	a	DET
ejpam-1068	247	7	⊆	⊆	NUM
ejpam-1068	247	8	ψ−	ψ−	PROPN
ejpam-1068	247	9	int(u	int(u	PROPN
ejpam-1068	247	10	)	)	PUNCT
ejpam-1068	247	11	,	,	PUNCT
ejpam-1068	247	12	b	b	X
ejpam-1068	247	13	⊆	⊆	NUM
ejpam-1068	247	14	x	x	SYM
ejpam-1068	247	15	\ψ−	\ψ−	ADJ
ejpam-1068	247	16	cl(u	cl(u	NOUN
ejpam-1068	247	17	)	)	PUNCT
ejpam-1068	247	18	,	,	PUNCT
ejpam-1068	247	19	where	where	SCONJ
ejpam-1068	247	20	ψ−	ψ−	VERB
ejpam-1068	247	21	int(u	int(u	PROPN
ejpam-1068	247	22	)	)	PUNCT
ejpam-1068	247	23	and	and	CCONJ
ejpam-1068	247	24	x	x	ADP
ejpam-1068	247	25	\ψ−	\ψ−	ADJ
ejpam-1068	247	26	cl(u	cl(u	NOUN
ejpam-1068	247	27	)	)	PUNCT
ejpam-1068	247	28	are	be	AUX
ejpam-1068	247	29	two	two	NUM
ejpam-1068	247	30	disjoint	disjoint	NOUN
ejpam-1068	247	31	ψ	ψ	ADJ
ejpam-1068	247	32	-	-	ADJ
ejpam-1068	247	33	open	open	ADJ
ejpam-1068	247	34	sets	set	NOUN
ejpam-1068	247	35	.	.	PUNCT
ejpam-1068	248	1	(	(	PUNCT
ejpam-1068	248	2	iv)⇒	iv)⇒	X
ejpam-1068	248	3	(	(	PUNCT
ejpam-1068	248	4	v)⇒	v)⇒	PROPN
ejpam-1068	248	5	(	(	PUNCT
ejpam-1068	248	6	ii	ii	NOUN
ejpam-1068	248	7	)	)	PUNCT
ejpam-1068	248	8	:	:	PUNCT
ejpam-1068	248	9	obvious	obvious	ADJ
ejpam-1068	248	10	.	.	PUNCT
ejpam-1068	249	1	(	(	PUNCT
ejpam-1068	249	2	vi)⇒	vi)⇒	NUM
ejpam-1068	249	3	(	(	PUNCT
ejpam-1068	249	4	vii	vii	PROPN
ejpam-1068	249	5	)	)	PUNCT
ejpam-1068	249	6	⇒	⇒	PROPN
ejpam-1068	249	7	(	(	PUNCT
ejpam-1068	249	8	iii	iii	NOUN
ejpam-1068	249	9	)	)	PUNCT
ejpam-1068	249	10	:	:	PUNCT
ejpam-1068	249	11	obvious	obvious	ADJ
ejpam-1068	249	12	.	.	PUNCT
ejpam-1068	250	1	(	(	PUNCT
ejpam-1068	250	2	iii	iii	X
ejpam-1068	250	3	)	)	PUNCT
ejpam-1068	250	4	⇒	⇒	NOUN
ejpam-1068	250	5	(	(	PUNCT
ejpam-1068	250	6	v	v	NOUN
ejpam-1068	250	7	)	)	PUNCT
ejpam-1068	250	8	:	:	PUNCT
ejpam-1068	250	9	let	let	VERB
ejpam-1068	250	10	a	a	PRON
ejpam-1068	250	11	be	be	AUX
ejpam-1068	250	12	a	a	DET
ejpam-1068	250	13	closed	closed	ADJ
ejpam-1068	250	14	set	set	NOUN
ejpam-1068	250	15	and	and	CCONJ
ejpam-1068	250	16	b	b	NOUN
ejpam-1068	250	17	be	be	AUX
ejpam-1068	250	18	a	a	DET
ejpam-1068	250	19	g	g	NOUN
ejpam-1068	250	20	-	-	PUNCT
ejpam-1068	250	21	open	open	ADJ
ejpam-1068	250	22	set	set	NOUN
ejpam-1068	250	23	c	c	PROPN
ejpam-1068	250	24	ontaining	ontaine	VERB
ejpam-1068	250	25	a.	a.	NOUN
ejpam-1068	250	26	since	since	SCONJ
ejpam-1068	250	27	b	b	PROPN
ejpam-1068	250	28	is	be	AUX
ejpam-1068	250	29	g	g	NOUN
ejpam-1068	250	30	-	-	PUNCT
ejpam-1068	250	31	open	open	ADJ
ejpam-1068	250	32	and	and	CCONJ
ejpam-1068	250	33	a	a	PRON
ejpam-1068	250	34	is	be	AUX
ejpam-1068	250	35	closed	closed	ADJ
ejpam-1068	250	36	,	,	PUNCT
ejpam-1068	250	37	by	by	ADP
ejpam-1068	250	38	theorem	theorem	VERB
ejpam-1068	250	39	4.2	4.2	NUM
ejpam-1068	250	40	of	of	ADP
ejpam-1068	250	41	[	[	X
ejpam-1068	250	42	9	9	NUM
ejpam-1068	250	43	]	]	PUNCT
ejpam-1068	250	44	a	a	DET
ejpam-1068	250	45	⊆	⊆	NUM
ejpam-1068	250	46	int(b	int(b	NOUN
ejpam-1068	250	47	)	)	PUNCT
ejpam-1068	250	48	.	.	PUNCT
ejpam-1068	251	1	thus	thus	ADV
ejpam-1068	251	2	by	by	ADP
ejpam-1068	251	3	(	(	PUNCT
ejpam-1068	251	4	iii	iii	NOUN
ejpam-1068	251	5	)	)	PUNCT
ejpam-1068	251	6	,	,	PUNCT
ejpam-1068	251	7	there	there	PRON
ejpam-1068	251	8	exists	exist	VERB
ejpam-1068	251	9	a	a	DET
ejpam-1068	251	10	gψ	gψ	ADV
ejpam-1068	251	11	-	-	PUNCT
ejpam-1068	251	12	open	open	ADJ
ejpam-1068	251	13	set	set	NOUN
ejpam-1068	251	14	g	g	PROPN
ejpam-1068	251	15	such	such	ADJ
ejpam-1068	251	16	that	that	PRON
ejpam-1068	251	17	a⊆	a⊆	VERB
ejpam-1068	251	18	g	g	ADP
ejpam-1068	251	19	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	251	20	cl(g	cl(g	NOUN
ejpam-1068	251	21	)	)	PUNCT
ejpam-1068	251	22	⊆	⊆	NUM
ejpam-1068	251	23	int(b	int(b	NOUN
ejpam-1068	251	24	)	)	PUNCT
ejpam-1068	251	25	.	.	PUNCT
ejpam-1068	252	1	(	(	PUNCT
ejpam-1068	252	2	v	v	NOUN
ejpam-1068	252	3	)	)	PUNCT
ejpam-1068	252	4	⇒	⇒	NOUN
ejpam-1068	252	5	(	(	PUNCT
ejpam-1068	252	6	vi	vi	NOUN
ejpam-1068	252	7	)	)	PUNCT
ejpam-1068	252	8	:	:	PUNCT
ejpam-1068	252	9	let	let	VERB
ejpam-1068	252	10	a	a	PRON
ejpam-1068	252	11	be	be	AUX
ejpam-1068	252	12	a	a	DET
ejpam-1068	252	13	g	g	NOUN
ejpam-1068	252	14	-	-	PUNCT
ejpam-1068	252	15	closed	close	VERB
ejpam-1068	252	16	subset	subset	NOUN
ejpam-1068	252	17	of	of	ADP
ejpam-1068	252	18	x	x	PROPN
ejpam-1068	252	19	and	and	CCONJ
ejpam-1068	252	20	b	b	NOUN
ejpam-1068	252	21	be	be	AUX
ejpam-1068	252	22	an	an	DET
ejpam-1068	252	23	open	open	ADJ
ejpam-1068	252	24	set	set	NOUN
ejpam-1068	252	25	containing	contain	VERB
ejpam-1068	252	26	a.	a.	NOUN
ejpam-1068	252	27	then	then	ADV
ejpam-1068	252	28	cl(a	cl(a	PUNCT
ejpam-1068	252	29	)	)	PUNCT
ejpam-1068	252	30	⊆	⊆	NUM
ejpam-1068	252	31	b	b	NOUN
ejpam-1068	252	32	,	,	PUNCT
ejpam-1068	252	33	where	where	SCONJ
ejpam-1068	252	34	b	b	NOUN
ejpam-1068	252	35	is	be	AUX
ejpam-1068	252	36	g	g	NOUN
ejpam-1068	252	37	-	-	PUNCT
ejpam-1068	252	38	open	open	ADJ
ejpam-1068	252	39	.	.	PUNCT
ejpam-1068	253	1	thus	thus	ADV
ejpam-1068	253	2	there	there	PRON
ejpam-1068	253	3	exists	exist	VERB
ejpam-1068	253	4	a	a	DET
ejpam-1068	253	5	gψ	gψ	ADV
ejpam-1068	253	6	-	-	PUNCT
ejpam-1068	253	7	open	open	ADJ
ejpam-1068	253	8	set	set	NOUN
ejpam-1068	253	9	g	g	PROPN
ejpam-1068	253	10	such	such	ADJ
ejpam-1068	253	11	that	that	PRON
ejpam-1068	253	12	cl(a	cl(a	PUNCT
ejpam-1068	253	13	)	)	PUNCT
ejpam-1068	253	14	⊆	⊆	NUM
ejpam-1068	253	15	g	g	NOUN
ejpam-1068	253	16	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	253	17	cl(g	cl(g	NOUN
ejpam-1068	253	18	)	)	PUNCT
ejpam-1068	253	19	⊆	⊆	NUM
ejpam-1068	253	20	b.	b.	NOUN
ejpam-1068	253	21	since	since	SCONJ
ejpam-1068	253	22	g	g	PROPN
ejpam-1068	253	23	is	be	AUX
ejpam-1068	253	24	gψ	gψ	ADJ
ejpam-1068	253	25	-	-	PUNCT
ejpam-1068	253	26	open	open	ADJ
ejpam-1068	253	27	and	and	CCONJ
ejpam-1068	253	28	cl(a	cl(a	NUM
ejpam-1068	253	29	)	)	PUNCT
ejpam-1068	253	30	⊆	⊆	NUM
ejpam-1068	253	31	g	g	NOUN
ejpam-1068	253	32	,	,	PUNCT
ejpam-1068	253	33	by	by	ADP
ejpam-1068	253	34	theorem	theorem	NOUN
ejpam-1068	253	35	4	4	NUM
ejpam-1068	253	36	,	,	PUNCT
ejpam-1068	253	37	cl(a	cl(a	NUM
ejpam-1068	253	38	)	)	PUNCT
ejpam-1068	253	39	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	253	40	int(g	int(g	NOUN
ejpam-1068	253	41	)	)	PUNCT
ejpam-1068	253	42	.	.	PUNCT
ejpam-1068	254	1	put	put	VERB
ejpam-1068	254	2	u	u	NOUN
ejpam-1068	254	3	=	=	NOUN
ejpam-1068	254	4	ψ−	ψ−	PROPN
ejpam-1068	254	5	int(g	int(g	NOUN
ejpam-1068	254	6	)	)	PUNCT
ejpam-1068	254	7	.	.	PUNCT
ejpam-1068	255	1	then	then	ADV
ejpam-1068	255	2	u	u	PROPN
ejpam-1068	255	3	is	be	AUX
ejpam-1068	255	4	ψ	ψ	VERB
ejpam-1068	255	5	-	-	ADJ
ejpam-1068	255	6	open	open	ADJ
ejpam-1068	255	7	and	and	CCONJ
ejpam-1068	255	8	cl(a	cl(a	NUM
ejpam-1068	255	9	)	)	PUNCT
ejpam-1068	255	10	⊆	⊆	NUM
ejpam-1068	255	11	u	u	NOUN
ejpam-1068	255	12	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	255	13	cl(u	cl(u	NOUN
ejpam-1068	255	14	)	)	PUNCT
ejpam-1068	256	1	=	=	X
ejpam-1068	256	2	ψ−	ψ−	VERB
ejpam-1068	256	3	cl(ψ−	cl(ψ−	PROPN
ejpam-1068	256	4	int(g	int(g	PROPN
ejpam-1068	256	5	)	)	PUNCT
ejpam-1068	256	6	)	)	PUNCT
ejpam-1068	256	7	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	256	8	cl(g	cl(g	NOUN
ejpam-1068	256	9	)	)	PUNCT
ejpam-1068	256	10	⊆	⊆	NUM
ejpam-1068	256	11	b.	b.	PROPN
ejpam-1068	256	12	(	(	PUNCT
ejpam-1068	256	13	vi)⇒	vi)⇒	NUM
ejpam-1068	256	14	(	(	PUNCT
ejpam-1068	256	15	iv	iv	NUM
ejpam-1068	256	16	)	)	PUNCT
ejpam-1068	256	17	:	:	PUNCT
ejpam-1068	256	18	let	let	VERB
ejpam-1068	256	19	a	a	PRON
ejpam-1068	256	20	be	be	AUX
ejpam-1068	256	21	a	a	DET
ejpam-1068	256	22	closed	closed	ADJ
ejpam-1068	256	23	set	set	NOUN
ejpam-1068	256	24	and	and	CCONJ
ejpam-1068	256	25	b	b	NOUN
ejpam-1068	256	26	be	be	AUX
ejpam-1068	256	27	a	a	DET
ejpam-1068	256	28	g	g	NOUN
ejpam-1068	256	29	-	-	PUNCT
ejpam-1068	256	30	open	open	ADJ
ejpam-1068	256	31	set	set	NOUN
ejpam-1068	256	32	containing	contain	VERB
ejpam-1068	256	33	a.	a.	NOUN
ejpam-1068	256	34	then	then	ADV
ejpam-1068	256	35	by	by	ADP
ejpam-1068	256	36	theorem	theorem	VERB
ejpam-1068	256	37	4.2	4.2	NUM
ejpam-1068	256	38	of	of	ADP
ejpam-1068	256	39	[	[	X
ejpam-1068	256	40	9	9	NUM
ejpam-1068	256	41	]	]	PUNCT
ejpam-1068	256	42	,	,	PUNCT
ejpam-1068	256	43	cl(a	cl(a	X
ejpam-1068	256	44	)	)	PUNCT
ejpam-1068	256	45	=	=	PUNCT
ejpam-1068	256	46	a	a	DET
ejpam-1068	256	47	⊆	⊆	NUM
ejpam-1068	256	48	int(b	int(b	NOUN
ejpam-1068	256	49	)	)	PUNCT
ejpam-1068	256	50	,	,	PUNCT
ejpam-1068	256	51	where	where	SCONJ
ejpam-1068	256	52	a	a	PRON
ejpam-1068	256	53	is	be	AUX
ejpam-1068	256	54	g	g	NOUN
ejpam-1068	256	55	-	-	PUNCT
ejpam-1068	256	56	closed	closed	ADJ
ejpam-1068	256	57	(	(	PUNCT
ejpam-1068	256	58	as	as	ADP
ejpam-1068	256	59	a	a	PRON
ejpam-1068	256	60	is	be	AUX
ejpam-1068	256	61	closed	closed	ADJ
ejpam-1068	256	62	)	)	PUNCT
ejpam-1068	256	63	and	and	CCONJ
ejpam-1068	256	64	int(b	int(b	NOUN
ejpam-1068	256	65	)	)	PUNCT
ejpam-1068	256	66	is	be	AUX
ejpam-1068	256	67	open	open	ADJ
ejpam-1068	256	68	.	.	PUNCT
ejpam-1068	257	1	thus	thus	ADV
ejpam-1068	257	2	by	by	ADP
ejpam-1068	257	3	(	(	PUNCT
ejpam-1068	257	4	vi	vi	NOUN
ejpam-1068	257	5	)	)	PUNCT
ejpam-1068	257	6	,	,	PUNCT
ejpam-1068	257	7	there	there	PRON
ejpam-1068	257	8	exists	exist	VERB
ejpam-1068	257	9	a	a	DET
ejpam-1068	257	10	ψ	ψ	NOUN
ejpam-1068	257	11	-	-	ADJ
ejpam-1068	257	12	open	open	ADJ
ejpam-1068	257	13	set	set	NOUN
ejpam-1068	257	14	u	u	PRON
ejpam-1068	257	15	such	such	ADJ
ejpam-1068	257	16	that	that	PRON
ejpam-1068	257	17	cl(a	cl(a	PUNCT
ejpam-1068	257	18	)	)	PUNCT
ejpam-1068	257	19	=	=	PUNCT
ejpam-1068	257	20	a⊆	a⊆	PROPN
ejpam-1068	257	21	u	u	NOUN
ejpam-1068	257	22	⊆ψ−	⊆ψ−	NOUN
ejpam-1068	257	23	cl(u	cl(u	NOUN
ejpam-1068	257	24	)	)	PUNCT
ejpam-1068	257	25	⊆	⊆	NUM
ejpam-1068	257	26	int(b	int(b	NUM
ejpam-1068	257	27	)	)	PUNCT
ejpam-1068	257	28	.	.	PUNCT
ejpam-1068	258	1	acknowledgements	acknowledgement	VERB
ejpam-1068	258	2	the	the	DET
ejpam-1068	258	3	first	first	ADJ
ejpam-1068	258	4	two	two	NUM
ejpam-1068	258	5	authors	author	NOUN
ejpam-1068	258	6	acknowledge	acknowledge	VERB
ejpam-1068	258	7	the	the	DET
ejpam-1068	258	8	financial	financial	ADJ
ejpam-1068	258	9	support	support	NOUN
ejpam-1068	258	10	from	from	ADP
ejpam-1068	258	11	ugc	ugc	PROPN
ejpam-1068	258	12	,	,	PUNCT
ejpam-1068	258	13	new	new	ADJ
ejpam-1068	258	14	delhi	delhi	PROPN
ejpam-1068	258	15	.	.	PUNCT
ejpam-1068	259	1	references	reference	NOUN
ejpam-1068	259	2	[	[	X
ejpam-1068	259	3	1	1	NUM
ejpam-1068	259	4	]	]	X
ejpam-1068	259	5	m	m	VERB
ejpam-1068	259	6	e	e	PROPN
ejpam-1068	259	7	abd	abd	PROPN
ejpam-1068	259	8	el	el	PROPN
ejpam-1068	259	9	-	-	PROPN
ejpam-1068	259	10	monsef	monsef	ADJ
ejpam-1068	259	11	,	,	PUNCT
ejpam-1068	259	12	a	a	DET
ejpam-1068	259	13	n	n	X
ejpam-1068	259	14	geaisa	geaisa	NOUN
ejpam-1068	259	15	,	,	PUNCT
ejpam-1068	259	16	and	and	CCONJ
ejpam-1068	259	17	r	r	X
ejpam-1068	259	18	a	a	DET
ejpam-1068	259	19	mahmoud	mahmoud	NOUN
ejpam-1068	259	20	.	.	PUNCT
ejpam-1068	260	1	β	β	NOUN
ejpam-1068	260	2	-regular	-regular	ADJ
ejpam-1068	260	3	spaces	space	NOUN
ejpam-1068	260	4	.	.	PUNCT
ejpam-1068	261	1	proceedings	proceeding	NOUN
ejpam-1068	261	2	of	of	ADP
ejpam-1068	261	3	the	the	DET
ejpam-1068	261	4	mathematical	mathematical	ADJ
ejpam-1068	261	5	and	and	CCONJ
ejpam-1068	261	6	physical	physical	ADJ
ejpam-1068	261	7	society	society	NOUN
ejpam-1068	261	8	of	of	ADP
ejpam-1068	261	9	egypt	egypt	PROPN
ejpam-1068	261	10	,	,	PUNCT
ejpam-1068	261	11	60:47–52	60:47–52	NUM
ejpam-1068	261	12	,	,	PUNCT
ejpam-1068	261	13	1985	1985	NUM
ejpam-1068	261	14	.	.	PUNCT
ejpam-1068	262	1	references	reference	NOUN
ejpam-1068	262	2	51	51	NUM
ejpam-1068	263	1	[	[	X
ejpam-1068	263	2	2	2	NUM
ejpam-1068	263	3	]	]	X
ejpam-1068	263	4	s	s	X
ejpam-1068	263	5	p	p	NOUN
ejpam-1068	263	6	arya	arya	NOUN
ejpam-1068	263	7	and	and	CCONJ
ejpam-1068	263	8	t	t	PROPN
ejpam-1068	263	9	nour	nour	PROPN
ejpam-1068	263	10	.	.	PUNCT
ejpam-1068	264	1	characterizations	characterization	NOUN
ejpam-1068	264	2	of	of	ADP
ejpam-1068	264	3	s	s	NOUN
ejpam-1068	264	4	-	-	ADJ
ejpam-1068	264	5	normal	normal	ADJ
ejpam-1068	264	6	spaces	space	NOUN
ejpam-1068	264	7	.	.	PUNCT
ejpam-1068	265	1	indian	indian	ADJ
ejpam-1068	265	2	journal	journal	PROPN
ejpam-1068	265	3	of	of	ADP
ejpam-1068	265	4	pure	pure	ADJ
ejpam-1068	265	5	and	and	CCONJ
ejpam-1068	265	6	applied	applied	ADJ
ejpam-1068	265	7	mathematics	mathematic	NOUN
ejpam-1068	265	8	,	,	PUNCT
ejpam-1068	265	9	21:717–719	21:717–719	NUM
ejpam-1068	265	10	,	,	PUNCT
ejpam-1068	265	11	1990	1990	NUM
ejpam-1068	265	12	.	.	PUNCT
ejpam-1068	266	1	[	[	X
ejpam-1068	266	2	3	3	NUM
ejpam-1068	266	3	]	]	PUNCT
ejpam-1068	266	4	á	á	X
ejpam-1068	266	5	császár	császár	NOUN
ejpam-1068	266	6	.	.	PUNCT
ejpam-1068	267	1	generalized	generalize	VERB
ejpam-1068	267	2	open	open	ADJ
ejpam-1068	267	3	sets	set	NOUN
ejpam-1068	267	4	.	.	PUNCT
ejpam-1068	268	1	acta	acta	PROPN
ejpam-1068	268	2	mathematica	mathematica	PROPN
ejpam-1068	268	3	hungarica	hungarica	PROPN
ejpam-1068	268	4	,	,	PUNCT
ejpam-1068	268	5	75(1	75(1	NOUN
ejpam-1068	268	6	-	-	PUNCT
ejpam-1068	268	7	2):65–87	2):65–87	NUM
ejpam-1068	268	8	,	,	PUNCT
ejpam-1068	268	9	1997	1997	NUM
ejpam-1068	268	10	.	.	PUNCT
ejpam-1068	269	1	[	[	X
ejpam-1068	269	2	4	4	NUM
ejpam-1068	269	3	]	]	X
ejpam-1068	269	4	j	j	PROPN
ejpam-1068	269	5	dontchev	dontchev	NOUN
ejpam-1068	269	6	.	.	PUNCT
ejpam-1068	270	1	on	on	ADP
ejpam-1068	270	2	generalizing	generalize	VERB
ejpam-1068	270	3	semi	semi	ADJ
ejpam-1068	270	4	-	-	ADJ
ejpam-1068	270	5	preopen	preopen	ADJ
ejpam-1068	270	6	sets	set	NOUN
ejpam-1068	270	7	.	.	PUNCT
ejpam-1068	271	1	memoirs	memoir	NOUN
ejpam-1068	271	2	of	of	ADP
ejpam-1068	271	3	the	the	DET
ejpam-1068	271	4	faculty	faculty	NOUN
ejpam-1068	271	5	of	of	ADP
ejpam-1068	271	6	science	science	NOUN
ejpam-1068	271	7	.	.	PUNCT
ejpam-1068	272	1	kochi	kochi	PROPN
ejpam-1068	272	2	university	university	PROPN
ejpam-1068	272	3	(	(	PUNCT
ejpam-1068	272	4	series	series	VERB
ejpam-1068	272	5	a	a	DET
ejpam-1068	272	6	mathematics	mathematic	NOUN
ejpam-1068	272	7	)	)	PUNCT
ejpam-1068	272	8	,	,	PUNCT
ejpam-1068	272	9	16:35–48	16:35–48	NUM
ejpam-1068	272	10	,	,	PUNCT
ejpam-1068	272	11	1995	1995	NUM
ejpam-1068	272	12	.	.	PUNCT
ejpam-1068	273	1	[	[	X
ejpam-1068	273	2	5	5	NUM
ejpam-1068	273	3	]	]	PUNCT
ejpam-1068	273	4	j	j	PROPN
ejpam-1068	273	5	dugunji	dugunji	PROPN
ejpam-1068	273	6	.	.	PUNCT
ejpam-1068	274	1	topology	topology	PROPN
ejpam-1068	274	2	.	.	PUNCT
ejpam-1068	275	1	allyn	allyn	PROPN
ejpam-1068	275	2	and	and	CCONJ
ejpam-1068	275	3	bacon	bacon	PROPN
ejpam-1068	275	4	,	,	PUNCT
ejpam-1068	275	5	boston	boston	PROPN
ejpam-1068	275	6	,	,	PUNCT
ejpam-1068	275	7	1966	1966	NUM
ejpam-1068	275	8	.	.	PUNCT
ejpam-1068	276	1	[	[	X
ejpam-1068	276	2	6	6	NUM
ejpam-1068	276	3	]	]	PUNCT
ejpam-1068	276	4	e	e	NOUN
ejpam-1068	276	5	ekici	ekici	NOUN
ejpam-1068	276	6	and	and	CCONJ
ejpam-1068	276	7	t	t	PROPN
ejpam-1068	276	8	noiri	noiri	PROPN
ejpam-1068	276	9	.	.	PUNCT
ejpam-1068	277	1	on	on	ADP
ejpam-1068	277	2	a	a	DET
ejpam-1068	277	3	generalization	generalization	NOUN
ejpam-1068	277	4	of	of	ADP
ejpam-1068	277	5	normal	normal	ADJ
ejpam-1068	277	6	,	,	PUNCT
ejpam-1068	277	7	almost	almost	ADV
ejpam-1068	277	8	normal	normal	ADJ
ejpam-1068	277	9	and	and	CCONJ
ejpam-1068	277	10	mildly	mildly	ADV
ejpam-1068	277	11	normal	normal	ADJ
ejpam-1068	277	12	spaces	space	NOUN
ejpam-1068	277	13	-	-	PUNCT
ejpam-1068	277	14	i.	i.	PROPN
ejpam-1068	277	15	mathematica	mathematica	PROPN
ejpam-1068	277	16	moravica	moravica	PROPN
ejpam-1068	277	17	,	,	PUNCT
ejpam-1068	277	18	10:9–20	10:9–20	NUM
ejpam-1068	277	19	,	,	PUNCT
ejpam-1068	277	20	2006	2006	NUM
ejpam-1068	277	21	.	.	PUNCT
ejpam-1068	278	1	[	[	X
ejpam-1068	278	2	7	7	NUM
ejpam-1068	278	3	]	]	SYM
ejpam-1068	278	4	s	s	X
ejpam-1068	278	5	n	n	PRON
ejpam-1068	278	6	el	el	PROPN
ejpam-1068	278	7	-	-	PUNCT
ejpam-1068	278	8	deeb	deeb	PROPN
ejpam-1068	278	9	,	,	PUNCT
ejpam-1068	278	10	i	i	PRON
ejpam-1068	278	11	a	a	DET
ejpam-1068	278	12	hasanein	hasanein	NOUN
ejpam-1068	278	13	,	,	PUNCT
ejpam-1068	278	14	a	a	PRON
ejpam-1068	278	15	s	s	X
ejpam-1068	278	16	mashhour	mashhour	NOUN
ejpam-1068	278	17	,	,	PUNCT
ejpam-1068	278	18	and	and	CCONJ
ejpam-1068	278	19	t	t	PROPN
ejpam-1068	278	20	noiri	noiri	PROPN
ejpam-1068	278	21	.	.	PUNCT
ejpam-1068	279	1	on	on	ADP
ejpam-1068	279	2	p	p	NOUN
ejpam-1068	279	3	-	-	PUNCT
ejpam-1068	279	4	regular	regular	ADJ
ejpam-1068	279	5	spaces	space	NOUN
ejpam-1068	279	6	.	.	PUNCT
ejpam-1068	280	1	bulletin	bulletin	PROPN
ejpam-1068	280	2	mathématique	mathématique	PROPN
ejpam-1068	280	3	de	de	X
ejpam-1068	280	4	la	la	PROPN
ejpam-1068	280	5	société	société	PROPN
ejpam-1068	280	6	des	des	PROPN
ejpam-1068	280	7	sciences	sciences	PROPN
ejpam-1068	280	8	mathématiques	mathématiques	PROPN
ejpam-1068	280	9	de	de	PROPN
ejpam-1068	280	10	roumanie	roumanie	PROPN
ejpam-1068	280	11	,	,	PUNCT
ejpam-1068	280	12	75(27):311–315	75(27):311–315	PROPN
ejpam-1068	280	13	,	,	PUNCT
ejpam-1068	280	14	1983	1983	NUM
ejpam-1068	280	15	.	.	PUNCT
ejpam-1068	281	1	[	[	X
ejpam-1068	281	2	8	8	NUM
ejpam-1068	281	3	]	]	X
ejpam-1068	281	4	m	m	VERB
ejpam-1068	281	5	kücük	kücük	NOUN
ejpam-1068	281	6	and	and	CCONJ
ejpam-1068	281	7	i̇	i̇	PROPN
ejpam-1068	281	8	zorlutuna	zorlutuna	NOUN
ejpam-1068	281	9	.	.	PUNCT
ejpam-1068	282	1	a	a	DET
ejpam-1068	282	2	unified	unified	ADJ
ejpam-1068	282	3	theory	theory	NOUN
ejpam-1068	282	4	for	for	ADP
ejpam-1068	282	5	weak	weak	ADJ
ejpam-1068	282	6	separation	separation	NOUN
ejpam-1068	282	7	properties	property	NOUN
ejpam-1068	282	8	.	.	PUNCT
ejpam-1068	283	1	international	international	ADJ
ejpam-1068	283	2	journal	journal	PROPN
ejpam-1068	283	3	of	of	ADP
ejpam-1068	283	4	mathematics	mathematics	PROPN
ejpam-1068	283	5	and	and	CCONJ
ejpam-1068	283	6	mathematical	mathematical	ADJ
ejpam-1068	283	7	sciences	science	NOUN
ejpam-1068	283	8	,	,	PUNCT
ejpam-1068	283	9	24(11):765–772	24(11):765–772	NUM
ejpam-1068	283	10	,	,	PUNCT
ejpam-1068	283	11	2000	2000	NUM
ejpam-1068	283	12	.	.	PUNCT
ejpam-1068	284	1	[	[	X
ejpam-1068	284	2	9	9	NUM
ejpam-1068	284	3	]	]	PUNCT
ejpam-1068	284	4	n	n	DET
ejpam-1068	284	5	levine	levine	PROPN
ejpam-1068	284	6	.	.	PUNCT
ejpam-1068	285	1	generalized	generalize	VERB
ejpam-1068	285	2	closed	closed	ADJ
ejpam-1068	285	3	sets	set	NOUN
ejpam-1068	285	4	in	in	ADP
ejpam-1068	285	5	topology	topology	NOUN
ejpam-1068	285	6	.	.	PUNCT
ejpam-1068	286	1	rendicondi	rendicondi	VERB
ejpam-1068	286	2	del	del	PROPN
ejpam-1068	286	3	circolo	circolo	PROPN
ejpam-1068	286	4	matematico	matematico	NOUN
ejpam-1068	286	5	di	di	NOUN
ejpam-1068	286	6	palermo	palermo	NOUN
ejpam-1068	286	7	,	,	PUNCT
ejpam-1068	286	8	19(2):89–96	19(2):89–96	NUM
ejpam-1068	286	9	,	,	PUNCT
ejpam-1068	286	10	1970	1970	NUM
ejpam-1068	286	11	.	.	PUNCT
ejpam-1068	287	1	[	[	X
ejpam-1068	287	2	10	10	NUM
ejpam-1068	287	3	]	]	SYM
ejpam-1068	287	4	s	s	PART
ejpam-1068	287	5	n	n	X
ejpam-1068	287	6	maheshwari	maheshwari	NOUN
ejpam-1068	287	7	and	and	CCONJ
ejpam-1068	287	8	r	r	NOUN
ejpam-1068	287	9	prasad	prasad	NOUN
ejpam-1068	287	10	.	.	PUNCT
ejpam-1068	288	1	on	on	ADP
ejpam-1068	288	2	s	s	NOUN
ejpam-1068	288	3	-	-	ADJ
ejpam-1068	288	4	regular	regular	ADJ
ejpam-1068	288	5	spaces	space	NOUN
ejpam-1068	288	6	.	.	PUNCT
ejpam-1068	289	1	glasnik	glasnik	PROPN
ejpam-1068	289	2	matematicki	matematicki	PROPN
ejpam-1068	289	3	series	series	PROPN
ejpam-1068	289	4	iii	iii	PROPN
ejpam-1068	289	5	,	,	PUNCT
ejpam-1068	289	6	30(10):347–350	30(10):347–350	NUM
ejpam-1068	289	7	,	,	PUNCT
ejpam-1068	289	8	1975	1975	NUM
ejpam-1068	289	9	.	.	PUNCT
ejpam-1068	290	1	[	[	X
ejpam-1068	290	2	11	11	NUM
ejpam-1068	290	3	]	]	SYM
ejpam-1068	290	4	s	s	VERB
ejpam-1068	290	5	n	n	X
ejpam-1068	290	6	maheshwari	maheshwari	NOUN
ejpam-1068	290	7	and	and	CCONJ
ejpam-1068	290	8	r	r	NOUN
ejpam-1068	290	9	prasad	prasad	NOUN
ejpam-1068	290	10	.	.	PUNCT
ejpam-1068	291	1	on	on	ADP
ejpam-1068	291	2	s	s	NOUN
ejpam-1068	291	3	-	-	ADJ
ejpam-1068	291	4	normal	normal	ADJ
ejpam-1068	291	5	spaces	space	NOUN
ejpam-1068	291	6	.	.	PUNCT
ejpam-1068	292	1	bulletin	bulletin	PROPN
ejpam-1068	292	2	mathématique	mathématique	PROPN
ejpam-1068	292	3	de	de	X
ejpam-1068	292	4	la	la	PROPN
ejpam-1068	292	5	société	société	PROPN
ejpam-1068	292	6	des	des	PROPN
ejpam-1068	292	7	sciences	sciences	PROPN
ejpam-1068	292	8	mathématiques	mathématiques	PROPN
ejpam-1068	292	9	de	de	PROPN
ejpam-1068	292	10	roumanie	roumanie	PROPN
ejpam-1068	292	11	,	,	PUNCT
ejpam-1068	292	12	70(22):27–29	70(22):27–29	NUM
ejpam-1068	292	13	,	,	PUNCT
ejpam-1068	292	14	1978	1978	NUM
ejpam-1068	292	15	.	.	PUNCT
ejpam-1068	293	1	[	[	X
ejpam-1068	293	2	12	12	NUM
ejpam-1068	293	3	]	]	X
ejpam-1068	293	4	r	r	NOUN
ejpam-1068	293	5	a	a	DET
ejpam-1068	293	6	mahmoud	mahmoud	PROPN
ejpam-1068	293	7	and	and	CCONJ
ejpam-1068	293	8	m	m	PROPN
ejpam-1068	293	9	e	e	PROPN
ejpam-1068	293	10	abd	abd	PROPN
ejpam-1068	293	11	el	el	PROPN
ejpam-1068	293	12	-	-	PROPN
ejpam-1068	293	13	monsef	monsef	ADJ
ejpam-1068	293	14	.	.	PUNCT
ejpam-1068	294	1	β	β	NOUN
ejpam-1068	294	2	-irresolute	-irresolute	PROPN
ejpam-1068	294	3	and	and	CCONJ
ejpam-1068	294	4	β	β	X
ejpam-1068	294	5	-topological	-topological	ADJ
ejpam-1068	294	6	invariants	invariant	NOUN
ejpam-1068	294	7	.	.	PUNCT
ejpam-1068	295	1	proceedings	proceeding	NOUN
ejpam-1068	295	2	of	of	ADP
ejpam-1068	295	3	the	the	DET
ejpam-1068	295	4	pakistan	pakistan	PROPN
ejpam-1068	295	5	academy	academy	PROPN
ejpam-1068	295	6	of	of	ADP
ejpam-1068	295	7	sciences	sciences	PROPN
ejpam-1068	295	8	,	,	PUNCT
ejpam-1068	295	9	27(3):285–296	27(3):285–296	NUM
ejpam-1068	295	10	,	,	PUNCT
ejpam-1068	295	11	1990	1990	NUM
ejpam-1068	295	12	.	.	PUNCT
ejpam-1068	296	1	[	[	X
ejpam-1068	296	2	13	13	NUM
ejpam-1068	296	3	]	]	SYM
ejpam-1068	296	4	h	h	NOUN
ejpam-1068	296	5	maki	maki	NOUN
ejpam-1068	296	6	,	,	PUNCT
ejpam-1068	296	7	r	r	NOUN
ejpam-1068	296	8	devi	devi	PROPN
ejpam-1068	296	9	,	,	PUNCT
ejpam-1068	296	10	and	and	CCONJ
ejpam-1068	296	11	k	k	PROPN
ejpam-1068	296	12	balachandran	balachandran	PROPN
ejpam-1068	296	13	.	.	PUNCT
ejpam-1068	297	1	associated	associated	ADJ
ejpam-1068	297	2	topologies	topology	NOUN
ejpam-1068	297	3	of	of	ADP
ejpam-1068	297	4	generalized	generalized	ADJ
ejpam-1068	297	5	α	α	NOUN
ejpam-1068	297	6	-	-	PUNCT
ejpam-1068	297	7	closed	closed	ADJ
ejpam-1068	297	8	sets	set	NOUN
ejpam-1068	297	9	and	and	CCONJ
ejpam-1068	297	10	α	α	DET
ejpam-1068	297	11	generalized	generalize	VERB
ejpam-1068	297	12	closed	close	VERB
ejpam-1068	297	13	sets	set	NOUN
ejpam-1068	297	14	.	.	PUNCT
ejpam-1068	298	1	memoirs	memoir	NOUN
ejpam-1068	298	2	of	of	ADP
ejpam-1068	298	3	the	the	DET
ejpam-1068	298	4	faculty	faculty	NOUN
ejpam-1068	298	5	of	of	ADP
ejpam-1068	298	6	science	science	NOUN
ejpam-1068	298	7	.	.	PUNCT
ejpam-1068	299	1	kochi	kochi	PROPN
ejpam-1068	299	2	university	university	PROPN
ejpam-1068	299	3	(	(	PUNCT
ejpam-1068	299	4	series	series	VERB
ejpam-1068	299	5	a	a	DET
ejpam-1068	299	6	mathematics	mathematic	NOUN
ejpam-1068	299	7	)	)	PUNCT
ejpam-1068	299	8	,	,	PUNCT
ejpam-1068	299	9	15(3):51–63	15(3):51–63	NUM
ejpam-1068	299	10	,	,	PUNCT
ejpam-1068	299	11	1994	1994	NUM
ejpam-1068	299	12	.	.	PUNCT
ejpam-1068	300	1	[	[	X
ejpam-1068	300	2	14	14	NUM
ejpam-1068	300	3	]	]	X
ejpam-1068	300	4	a	a	DET
ejpam-1068	300	5	s	s	X
ejpam-1068	300	6	mashhour	mashhour	NOUN
ejpam-1068	300	7	,	,	PUNCT
ejpam-1068	300	8	m	m	VERB
ejpam-1068	300	9	e	e	PROPN
ejpam-1068	300	10	abd	abd	PROPN
ejpam-1068	300	11	el	el	PROPN
ejpam-1068	300	12	-	-	PROPN
ejpam-1068	300	13	monsef	monsef	ADJ
ejpam-1068	300	14	,	,	PUNCT
ejpam-1068	300	15	and	and	CCONJ
ejpam-1068	300	16	s	s	PROPN
ejpam-1068	300	17	n	n	PRON
ejpam-1068	300	18	el	el	PROPN
ejpam-1068	300	19	-	-	PUNCT
ejpam-1068	300	20	deeb	deeb	PROPN
ejpam-1068	300	21	.	.	PUNCT
ejpam-1068	301	1	on	on	ADP
ejpam-1068	301	2	precontinuous	precontinuous	ADJ
ejpam-1068	301	3	and	and	CCONJ
ejpam-1068	301	4	weak	weak	ADJ
ejpam-1068	301	5	precontinuous	precontinuous	ADJ
ejpam-1068	301	6	mappings	mapping	NOUN
ejpam-1068	301	7	.	.	PUNCT
ejpam-1068	302	1	proceedings	proceeding	NOUN
ejpam-1068	302	2	of	of	ADP
ejpam-1068	302	3	the	the	DET
ejpam-1068	302	4	mathematical	mathematical	ADJ
ejpam-1068	302	5	and	and	CCONJ
ejpam-1068	302	6	physical	physical	ADJ
ejpam-1068	302	7	society	society	NOUN
ejpam-1068	302	8	of	of	ADP
ejpam-1068	302	9	egypt	egypt	PROPN
ejpam-1068	302	10	,	,	PUNCT
ejpam-1068	302	11	53:47–53	53:47–53	NUM
ejpam-1068	302	12	,	,	PUNCT
ejpam-1068	302	13	1982	1982	NUM
ejpam-1068	302	14	.	.	PUNCT
ejpam-1068	303	1	[	[	X
ejpam-1068	303	2	15	15	NUM
ejpam-1068	303	3	]	]	X
ejpam-1068	303	4	t	t	PROPN
ejpam-1068	303	5	noiri	noiri	PROPN
ejpam-1068	303	6	and	and	CCONJ
ejpam-1068	303	7	b	b	PROPN
ejpam-1068	303	8	roy	roy	PROPN
ejpam-1068	303	9	.	.	PROPN
ejpam-1068	303	10	unification	unification	NOUN
ejpam-1068	303	11	of	of	ADP
ejpam-1068	303	12	generalized	generalized	ADJ
ejpam-1068	303	13	open	open	ADJ
ejpam-1068	303	14	sets	set	NOUN
ejpam-1068	303	15	in	in	ADP
ejpam-1068	303	16	topological	topological	ADJ
ejpam-1068	303	17	spaces	space	NOUN
ejpam-1068	303	18	.	.	PUNCT
ejpam-1068	304	1	acta	acta	PROPN
ejpam-1068	304	2	mathematica	mathematica	PROPN
ejpam-1068	304	3	hungarica	hungarica	PROPN
ejpam-1068	304	4	,	,	PUNCT
ejpam-1068	304	5	130:349–357	130:349–357	NUM
ejpam-1068	304	6	,	,	PUNCT
ejpam-1068	304	7	2011	2011	NUM
ejpam-1068	304	8	.	.	PUNCT
ejpam-1068	305	1	[	[	X
ejpam-1068	305	2	16	16	NUM
ejpam-1068	305	3	]	]	X
ejpam-1068	306	1	t	t	PROPN
ejpam-1068	306	2	m	m	PROPN
ejpam-1068	306	3	nour	nour	PROPN
ejpam-1068	306	4	.	.	PUNCT
ejpam-1068	307	1	contributions	contribution	NOUN
ejpam-1068	307	2	to	to	ADP
ejpam-1068	307	3	the	the	DET
ejpam-1068	307	4	theory	theory	NOUN
ejpam-1068	307	5	of	of	ADP
ejpam-1068	307	6	bitopological	bitopological	ADJ
ejpam-1068	307	7	spaces	space	NOUN
ejpam-1068	307	8	.	.	PUNCT
ejpam-1068	308	1	phd	phd	NOUN
ejpam-1068	308	2	thesis	thesis	PROPN
ejpam-1068	308	3	,	,	PUNCT
ejpam-1068	308	4	delhi	delhi	PROPN
ejpam-1068	308	5	university	university	PROPN
ejpam-1068	308	6	,	,	PUNCT
ejpam-1068	308	7	1989	1989	NUM
ejpam-1068	308	8	.	.	PUNCT
ejpam-1068	309	1	[	[	X
ejpam-1068	309	2	17	17	NUM
ejpam-1068	309	3	]	]	X
ejpam-1068	309	4	j	j	PROPN
ejpam-1068	309	5	h	h	PROPN
ejpam-1068	309	6	park	park	PROPN
ejpam-1068	309	7	,	,	PUNCT
ejpam-1068	309	8	y	y	PROPN
ejpam-1068	309	9	b	b	PROPN
ejpam-1068	309	10	park	park	NOUN
ejpam-1068	309	11	,	,	PUNCT
ejpam-1068	309	12	and	and	CCONJ
ejpam-1068	309	13	b	b	X
ejpam-1068	309	14	y	y	PROPN
ejpam-1068	309	15	lee	lee	PROPN
ejpam-1068	309	16	.	.	PUNCT
ejpam-1068	310	1	on	on	ADP
ejpam-1068	310	2	gp	gp	ADJ
ejpam-1068	310	3	-	-	ADJ
ejpam-1068	310	4	closed	closed	ADJ
ejpam-1068	310	5	sets	set	NOUN
ejpam-1068	310	6	and	and	CCONJ
ejpam-1068	310	7	pre	pre	VERB
ejpam-1068	310	8	gp	gp	ADJ
ejpam-1068	310	9	-	-	ADJ
ejpam-1068	310	10	continuous	continuous	ADJ
ejpam-1068	310	11	functions	function	NOUN
ejpam-1068	310	12	.	.	PUNCT
ejpam-1068	311	1	indian	indian	ADJ
ejpam-1068	311	2	journal	journal	PROPN
ejpam-1068	311	3	of	of	ADP
ejpam-1068	311	4	pure	pure	ADJ
ejpam-1068	311	5	and	and	CCONJ
ejpam-1068	311	6	applied	applied	ADJ
ejpam-1068	311	7	mathematics	mathematic	NOUN
ejpam-1068	311	8	,	,	PUNCT
ejpam-1068	311	9	33(1):3–12	33(1):3–12	NUM
ejpam-1068	311	10	,	,	PUNCT
ejpam-1068	311	11	2002	2002	NUM
ejpam-1068	311	12	.	.	PUNCT
ejpam-1068	312	1	references	reference	NOUN
ejpam-1068	312	2	52	52	NUM
ejpam-1068	313	1	[	[	X
ejpam-1068	313	2	18	18	NUM
ejpam-1068	313	3	]	]	X
ejpam-1068	313	4	m	m	VERB
ejpam-1068	313	5	c	c	NOUN
ejpam-1068	313	6	paul	paul	PROPN
ejpam-1068	313	7	and	and	CCONJ
ejpam-1068	313	8	p	p	NOUN
ejpam-1068	313	9	bhattacharyya	bhattacharyya	ADJ
ejpam-1068	313	10	.	.	PUNCT
ejpam-1068	314	1	on	on	ADP
ejpam-1068	314	2	p	p	ADJ
ejpam-1068	314	3	-	-	PUNCT
ejpam-1068	314	4	normal	normal	ADJ
ejpam-1068	314	5	spaces	space	NOUN
ejpam-1068	314	6	.	.	PUNCT
ejpam-1068	315	1	soochow	soochow	PROPN
ejpam-1068	315	2	journal	journal	PROPN
ejpam-1068	315	3	of	of	ADP
ejpam-1068	315	4	mathematics	mathematic	NOUN
ejpam-1068	315	5	,	,	PUNCT
ejpam-1068	315	6	21(3):273–289	21(3):273–289	PROPN
ejpam-1068	315	7	,	,	PUNCT
ejpam-1068	315	8	1995	1995	NUM
ejpam-1068	315	9	.	.	PUNCT
ejpam-1068	316	1	[	[	X
ejpam-1068	316	2	19	19	NUM
ejpam-1068	316	3	]	]	SYM
ejpam-1068	316	4	s	s	X
ejpam-1068	316	5	raychaudhuri	raychaudhuri	ADJ
ejpam-1068	316	6	and	and	CCONJ
ejpam-1068	316	7	m	m	PROPN
ejpam-1068	316	8	n	n	PRON
ejpam-1068	316	9	mukherjee	mukherjee	NOUN
ejpam-1068	316	10	.	.	PUNCT
ejpam-1068	317	1	on	on	ADP
ejpam-1068	317	2	δ	δ	PROPN
ejpam-1068	317	3	-	-	PUNCT
ejpam-1068	317	4	almost	almost	ADV
ejpam-1068	317	5	continuity	continuity	NOUN
ejpam-1068	317	6	and	and	CCONJ
ejpam-1068	317	7	δ	δ	NOUN
ejpam-1068	317	8	-	-	PUNCT
ejpam-1068	317	9	preopen	preopen	ADJ
ejpam-1068	317	10	sets	set	NOUN
ejpam-1068	317	11	.	.	PUNCT
ejpam-1068	318	1	bulletin	bulletin	NOUN
ejpam-1068	318	2	of	of	ADP
ejpam-1068	318	3	the	the	DET
ejpam-1068	318	4	institute	institute	PROPN
ejpam-1068	318	5	of	of	ADP
ejpam-1068	318	6	mathematics	mathematics	PROPN
ejpam-1068	318	7	academia	academia	PROPN
ejpam-1068	318	8	sinica	sinica	PROPN
ejpam-1068	318	9	,	,	PUNCT
ejpam-1068	318	10	21:357–366	21:357–366	PROPN
ejpam-1068	318	11	,	,	PUNCT
ejpam-1068	318	12	1993	1993	NUM
ejpam-1068	318	13	.	.	PUNCT