id	sid	tid	token	lemma	pos
ejpam-678	1	1	4_678_das.dvi	4_678_das.dvi	NUM
ejpam-678	1	2	european	european	ADJ
ejpam-678	1	3	journal	journal	NOUN
ejpam-678	1	4	of	of	ADP
ejpam-678	1	5	pure	pure	ADJ
ejpam-678	1	6	and	and	CCONJ
ejpam-678	1	7	applied	apply	VERB
ejpam-678	1	8	mathematics	mathematic	NOUN
ejpam-678	1	9	vol	vol	NOUN
ejpam-678	1	10	.	.	PROPN
ejpam-678	2	1	4	4	NUM
ejpam-678	2	2	,	,	PUNCT
ejpam-678	2	3	no	no	INTJ
ejpam-678	2	4	.	.	NOUN
ejpam-678	2	5	1	1	NUM
ejpam-678	2	6	,	,	PUNCT
ejpam-678	2	7	2011	2011	NUM
ejpam-678	2	8	,	,	PUNCT
ejpam-678	2	9	34	34	NUM
ejpam-678	2	10	-	-	SYM
ejpam-678	2	11	41	41	NUM
ejpam-678	2	12	issn	issn	PROPN
ejpam-678	2	13	1307	1307	NUM
ejpam-678	2	14	-	-	SYM
ejpam-678	2	15	5543	5543	NUM
ejpam-678	2	16	–	–	PUNCT
ejpam-678	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-678	2	18	simultaneous	simultaneous	ADJ
ejpam-678	2	19	generalizations	generalization	NOUN
ejpam-678	2	20	of	of	ADP
ejpam-678	2	21	regularity	regularity	NOUN
ejpam-678	2	22	and	and	CCONJ
ejpam-678	2	23	normality	normality	NOUN
ejpam-678	2	24	a.	a.	PROPN
ejpam-678	2	25	k.	k.	PROPN
ejpam-678	3	1	das	das	PROPN
ejpam-678	3	2	school	school	NOUN
ejpam-678	3	3	of	of	ADP
ejpam-678	3	4	mathematics	mathematic	NOUN
ejpam-678	3	5	,	,	PUNCT
ejpam-678	3	6	shri	shri	PROPN
ejpam-678	3	7	mata	mata	PROPN
ejpam-678	3	8	vaishno	vaishno	PROPN
ejpam-678	3	9	devi	devi	PROPN
ejpam-678	3	10	university	university	PROPN
ejpam-678	3	11	,	,	PUNCT
ejpam-678	3	12	katra-182320	katra-182320	NOUN
ejpam-678	3	13	,	,	PUNCT
ejpam-678	3	14	j&k	j&k	PROPN
ejpam-678	3	15	,	,	PUNCT
ejpam-678	3	16	india	india	PROPN
ejpam-678	3	17	abstract	abstract	PROPN
ejpam-678	3	18	.	.	PUNCT
ejpam-678	4	1	a	a	DET
ejpam-678	4	2	generalization	generalization	NOUN
ejpam-678	4	3	of	of	ADP
ejpam-678	4	4	regularity	regularity	NOUN
ejpam-678	4	5	called	call	VERB
ejpam-678	4	6	θ	θ	PROPN
ejpam-678	4	7	-regularity	-regularity	PROPN
ejpam-678	4	8	was	be	AUX
ejpam-678	4	9	earlier	early	ADV
ejpam-678	4	10	introduced	introduce	VERB
ejpam-678	4	11	to	to	PART
ejpam-678	4	12	decompose	decompose	VERB
ejpam-678	4	13	normality	normality	NOUN
ejpam-678	4	14	and	and	CCONJ
ejpam-678	4	15	also	also	ADV
ejpam-678	4	16	utilised	utilise	VERB
ejpam-678	4	17	to	to	PART
ejpam-678	4	18	factorize	factorize	VERB
ejpam-678	4	19	regularity	regularity	NOUN
ejpam-678	4	20	.	.	PUNCT
ejpam-678	5	1	every	every	DET
ejpam-678	5	2	normal	normal	ADJ
ejpam-678	5	3	space	space	NOUN
ejpam-678	5	4	need	need	AUX
ejpam-678	5	5	not	not	PART
ejpam-678	5	6	be	be	AUX
ejpam-678	5	7	regular	regular	ADJ
ejpam-678	5	8	,	,	PUNCT
ejpam-678	5	9	but	but	CCONJ
ejpam-678	5	10	every	every	DET
ejpam-678	5	11	normal	normal	ADJ
ejpam-678	5	12	space	space	NOUN
ejpam-678	5	13	is	be	AUX
ejpam-678	5	14	θ	θ	NOUN
ejpam-678	5	15	-regular	-regular	ADJ
ejpam-678	5	16	.	.	PUNCT
ejpam-678	6	1	in	in	ADP
ejpam-678	6	2	this	this	DET
ejpam-678	6	3	paper	paper	NOUN
ejpam-678	6	4	three	three	NUM
ejpam-678	6	5	variants	variant	NOUN
ejpam-678	6	6	of	of	ADP
ejpam-678	6	7	θ	θ	PROPN
ejpam-678	6	8	-regular	-regular	ADJ
ejpam-678	6	9	spaces	space	NOUN
ejpam-678	6	10	is	be	AUX
ejpam-678	6	11	introduced	introduce	VERB
ejpam-678	6	12	and	and	CCONJ
ejpam-678	6	13	studied	study	VERB
ejpam-678	6	14	.	.	PUNCT
ejpam-678	7	1	2000	2000	NUM
ejpam-678	7	2	mathematics	mathematic	NOUN
ejpam-678	7	3	subject	subject	NOUN
ejpam-678	7	4	classifications	classification	NOUN
ejpam-678	7	5	:	:	PUNCT
ejpam-678	7	6	54d10	54d10	NUM
ejpam-678	7	7	,	,	PUNCT
ejpam-678	7	8	54d15	54d15	NUM
ejpam-678	7	9	key	key	ADJ
ejpam-678	7	10	words	word	NOUN
ejpam-678	7	11	and	and	CCONJ
ejpam-678	7	12	phrases	phrase	NOUN
ejpam-678	7	13	:	:	PUNCT
ejpam-678	7	14	θ	θ	NOUN
ejpam-678	7	15	-open	-open	NOUN
ejpam-678	7	16	sets	set	NOUN
ejpam-678	7	17	,	,	PUNCT
ejpam-678	7	18	θ	θ	PROPN
ejpam-678	7	19	-closed	-close	VERB
ejpam-678	7	20	sets	set	NOUN
ejpam-678	7	21	,	,	PUNCT
ejpam-678	7	22	almost	almost	ADV
ejpam-678	7	23	normal	normal	ADJ
ejpam-678	7	24	space	space	NOUN
ejpam-678	7	25	,	,	PUNCT
ejpam-678	7	26	(	(	PUNCT
ejpam-678	7	27	weakly)(functionally	weakly)(functionally	ADV
ejpam-678	7	28	)	)	PUNCT
ejpam-678	7	29	θ	θ	PROPN
ejpam-678	7	30	-normal	-normal	ADJ
ejpam-678	7	31	space	space	NOUN
ejpam-678	7	32	,	,	PUNCT
ejpam-678	7	33	(	(	PUNCT
ejpam-678	7	34	weakly	weakly	ADJ
ejpam-678	7	35	)	)	PUNCT
ejpam-678	7	36	θ	θ	SYM
ejpam-678	7	37	-regular	-regular	ADJ
ejpam-678	7	38	,	,	PUNCT
ejpam-678	7	39	point	point	NOUN
ejpam-678	7	40	(	(	PUNCT
ejpam-678	7	41	weakly	weakly	ADJ
ejpam-678	7	42	)	)	PUNCT
ejpam-678	7	43	θ	θ	SYM
ejpam-678	7	44	-regular	-regular	ADJ
ejpam-678	7	45	.	.	PUNCT
ejpam-678	8	1	1	1	X
ejpam-678	8	2	.	.	X
ejpam-678	8	3	introduction	introduction	NOUN
ejpam-678	8	4	and	and	CCONJ
ejpam-678	8	5	preliminaries	preliminary	NOUN
ejpam-678	8	6	many	many	ADJ
ejpam-678	8	7	generalizations	generalization	NOUN
ejpam-678	8	8	of	of	ADP
ejpam-678	8	9	regularity	regularity	NOUN
ejpam-678	8	10	that	that	PRON
ejpam-678	8	11	exists	exist	VERB
ejpam-678	8	12	in	in	ADP
ejpam-678	8	13	the	the	DET
ejpam-678	8	14	mathematical	mathematical	ADJ
ejpam-678	8	15	literature	literature	NOUN
ejpam-678	8	16	fails	fail	VERB
ejpam-678	8	17	to	to	PART
ejpam-678	8	18	be	be	AUX
ejpam-678	8	19	a	a	DET
ejpam-678	8	20	generalization	generalization	NOUN
ejpam-678	8	21	of	of	ADP
ejpam-678	8	22	normality	normality	NOUN
ejpam-678	8	23	.	.	PUNCT
ejpam-678	9	1	but	but	CCONJ
ejpam-678	9	2	in	in	ADP
ejpam-678	9	3	order	order	NOUN
ejpam-678	9	4	to	to	PART
ejpam-678	9	5	obtain	obtain	VERB
ejpam-678	9	6	a	a	DET
ejpam-678	9	7	decomposition	decomposition	NOUN
ejpam-678	9	8	of	of	ADP
ejpam-678	9	9	normality	normality	NOUN
ejpam-678	9	10	,	,	PUNCT
ejpam-678	9	11	the	the	DET
ejpam-678	9	12	notion	notion	NOUN
ejpam-678	9	13	of	of	ADP
ejpam-678	9	14	θ	θ	PROPN
ejpam-678	9	15	-regularity	-regularity	PROPN
ejpam-678	9	16	was	be	AUX
ejpam-678	9	17	introduced	introduce	VERB
ejpam-678	9	18	in	in	ADP
ejpam-678	9	19	[	[	X
ejpam-678	9	20	6	6	NUM
ejpam-678	9	21	]	]	PUNCT
ejpam-678	9	22	which	which	PRON
ejpam-678	9	23	is	be	AUX
ejpam-678	9	24	a	a	DET
ejpam-678	9	25	simultaneous	simultaneous	ADJ
ejpam-678	9	26	generalization	generalization	NOUN
ejpam-678	9	27	of	of	ADP
ejpam-678	9	28	regularity	regularity	NOUN
ejpam-678	9	29	as	as	ADV
ejpam-678	9	30	well	well	ADV
ejpam-678	9	31	as	as	ADP
ejpam-678	9	32	normality	normality	NOUN
ejpam-678	9	33	.	.	PUNCT
ejpam-678	10	1	it	it	PRON
ejpam-678	10	2	is	be	AUX
ejpam-678	10	3	obvious	obvious	ADJ
ejpam-678	10	4	from	from	ADP
ejpam-678	10	5	the	the	DET
ejpam-678	10	6	definition	definition	NOUN
ejpam-678	10	7	that	that	SCONJ
ejpam-678	10	8	every	every	DET
ejpam-678	10	9	regular	regular	ADJ
ejpam-678	10	10	space	space	NOUN
ejpam-678	10	11	is	be	AUX
ejpam-678	10	12	θ	θ	NOUN
ejpam-678	10	13	-regular	-regular	ADJ
ejpam-678	10	14	as	as	ADP
ejpam-678	10	15	in	in	ADP
ejpam-678	10	16	a	a	DET
ejpam-678	10	17	regular	regular	ADJ
ejpam-678	10	18	space	space	NOUN
ejpam-678	10	19	every	every	DET
ejpam-678	10	20	closed	closed	ADJ
ejpam-678	10	21	set	set	NOUN
ejpam-678	10	22	is	be	AUX
ejpam-678	10	23	θ	θ	PROPN
ejpam-678	10	24	-closed	-close	VERB
ejpam-678	10	25	[	[	X
ejpam-678	10	26	14	14	NUM
ejpam-678	10	27	]	]	PUNCT
ejpam-678	10	28	.	.	PUNCT
ejpam-678	11	1	in	in	ADP
ejpam-678	11	2	general	general	ADJ
ejpam-678	11	3	a	a	DET
ejpam-678	11	4	normal	normal	ADJ
ejpam-678	11	5	space	space	NOUN
ejpam-678	11	6	need	need	AUX
ejpam-678	11	7	not	not	PART
ejpam-678	11	8	be	be	AUX
ejpam-678	11	9	regular	regular	ADJ
ejpam-678	11	10	,	,	PUNCT
ejpam-678	11	11	but	but	CCONJ
ejpam-678	11	12	in	in	ADP
ejpam-678	11	13	contrast	contrast	NOUN
ejpam-678	11	14	every	every	DET
ejpam-678	11	15	normal	normal	ADJ
ejpam-678	11	16	space	space	NOUN
ejpam-678	11	17	is	be	AUX
ejpam-678	11	18	θ	θ	PROPN
ejpam-678	11	19	-regular	-regular	ADJ
ejpam-678	11	20	[	[	X
ejpam-678	11	21	6	6	NUM
ejpam-678	11	22	]	]	PUNCT
ejpam-678	11	23	.	.	PUNCT
ejpam-678	12	1	also	also	ADV
ejpam-678	12	2	it	it	PRON
ejpam-678	12	3	is	be	AUX
ejpam-678	12	4	observed	observe	VERB
ejpam-678	12	5	in	in	ADP
ejpam-678	12	6	[	[	X
ejpam-678	12	7	5	5	NUM
ejpam-678	12	8	]	]	PUNCT
ejpam-678	12	9	that	that	SCONJ
ejpam-678	12	10	the	the	DET
ejpam-678	12	11	notion	notion	NOUN
ejpam-678	12	12	of	of	ADP
ejpam-678	12	13	θ	θ	PROPN
ejpam-678	12	14	-regularity	-regularity	PROPN
ejpam-678	12	15	serves	serve	VERB
ejpam-678	12	16	as	as	ADP
ejpam-678	12	17	a	a	DET
ejpam-678	12	18	decomposition	decomposition	NOUN
ejpam-678	12	19	of	of	ADP
ejpam-678	12	20	regularity	regularity	NOUN
ejpam-678	12	21	in	in	ADP
ejpam-678	12	22	terms	term	NOUN
ejpam-678	12	23	of	of	ADP
ejpam-678	12	24	r0	r0	NOUN
ejpam-678	12	25	and	and	CCONJ
ejpam-678	12	26	r1	r1	NOUN
ejpam-678	12	27	spaces	space	NOUN
ejpam-678	12	28	.	.	PUNCT
ejpam-678	13	1	in	in	ADP
ejpam-678	13	2	this	this	DET
ejpam-678	13	3	paper	paper	NOUN
ejpam-678	13	4	we	we	PRON
ejpam-678	13	5	introduced	introduce	VERB
ejpam-678	13	6	three	three	NUM
ejpam-678	13	7	more	more	ADJ
ejpam-678	13	8	variants	variant	NOUN
ejpam-678	13	9	of	of	ADP
ejpam-678	13	10	θ	θ	NOUN
ejpam-678	13	11	-regular	-regular	ADJ
ejpam-678	13	12	spaces	space	NOUN
ejpam-678	13	13	and	and	CCONJ
ejpam-678	13	14	studied	study	VERB
ejpam-678	13	15	their	their	PRON
ejpam-678	13	16	properties	property	NOUN
ejpam-678	13	17	.	.	PUNCT
ejpam-678	14	1	let	let	VERB
ejpam-678	14	2	x	x	PRON
ejpam-678	14	3	be	be	AUX
ejpam-678	14	4	a	a	DET
ejpam-678	14	5	topological	topological	ADJ
ejpam-678	14	6	space	space	NOUN
ejpam-678	14	7	and	and	CCONJ
ejpam-678	14	8	let	let	VERB
ejpam-678	14	9	a⊂	a⊂	NOUN
ejpam-678	14	10	x	x	SYM
ejpam-678	14	11	.	.	PUNCT
ejpam-678	15	1	throughout	throughout	ADP
ejpam-678	15	2	the	the	DET
ejpam-678	15	3	present	present	ADJ
ejpam-678	15	4	paper	paper	NOUN
ejpam-678	15	5	,	,	PUNCT
ejpam-678	15	6	the	the	DET
ejpam-678	15	7	closure	closure	NOUN
ejpam-678	15	8	of	of	ADP
ejpam-678	15	9	a	a	DET
ejpam-678	15	10	set	set	NOUN
ejpam-678	15	11	a	a	PRON
ejpam-678	15	12	will	will	AUX
ejpam-678	15	13	be	be	AUX
ejpam-678	15	14	denoted	denote	VERB
ejpam-678	15	15	by	by	ADP
ejpam-678	15	16	a	a	PRON
ejpam-678	15	17	or	or	CCONJ
ejpam-678	15	18	cla	cla	NOUN
ejpam-678	15	19	and	and	CCONJ
ejpam-678	15	20	the	the	DET
ejpam-678	15	21	interior	interior	NOUN
ejpam-678	15	22	by	by	ADP
ejpam-678	15	23	inta	inta	PROPN
ejpam-678	15	24	.	.	PUNCT
ejpam-678	16	1	a	a	DET
ejpam-678	16	2	set	set	NOUN
ejpam-678	16	3	u	u	NOUN
ejpam-678	16	4	⊂	⊂	PROPN
ejpam-678	16	5	x	x	PROPN
ejpam-678	16	6	is	be	AUX
ejpam-678	16	7	said	say	VERB
ejpam-678	16	8	to	to	PART
ejpam-678	16	9	be	be	AUX
ejpam-678	16	10	regularly	regularly	ADV
ejpam-678	16	11	open	open	ADJ
ejpam-678	16	12	if	if	SCONJ
ejpam-678	16	13	u	u	NOUN
ejpam-678	16	14	=	=	NOUN
ejpam-678	16	15	intu	intu	VERB
ejpam-678	16	16	.	.	PUNCT
ejpam-678	17	1	the	the	DET
ejpam-678	17	2	complement	complement	NOUN
ejpam-678	17	3	of	of	ADP
ejpam-678	17	4	a	a	DET
ejpam-678	17	5	regularly	regularly	ADV
ejpam-678	17	6	open	open	ADJ
ejpam-678	17	7	set	set	NOUN
ejpam-678	17	8	is	be	AUX
ejpam-678	17	9	called	call	VERB
ejpam-678	17	10	regularly	regularly	ADV
ejpam-678	17	11	closed	closed	ADJ
ejpam-678	17	12	.	.	PUNCT
ejpam-678	18	1	a	a	DET
ejpam-678	18	2	point	point	NOUN
ejpam-678	18	3	x	x	X
ejpam-678	18	4	∈	∈	NOUN
ejpam-678	18	5	x	x	PUNCT
ejpam-678	18	6	is	be	AUX
ejpam-678	18	7	called	call	VERB
ejpam-678	18	8	a	a	DET
ejpam-678	18	9	θ	θ	PROPN
ejpam-678	18	10	-limit	-limit	NOUN
ejpam-678	18	11	point	point	NOUN
ejpam-678	18	12	[	[	X
ejpam-678	18	13	14	14	NUM
ejpam-678	18	14	]	]	PUNCT
ejpam-678	18	15	of	of	ADP
ejpam-678	18	16	a	a	PRON
ejpam-678	18	17	if	if	SCONJ
ejpam-678	18	18	every	every	DET
ejpam-678	18	19	closed	closed	ADJ
ejpam-678	18	20	neighbourhood	neighbourhood	NOUN
ejpam-678	18	21	of	of	ADP
ejpam-678	18	22	x	x	PUNCT
ejpam-678	18	23	intersects	intersect	NOUN
ejpam-678	18	24	a.	a.	NOUN
ejpam-678	18	25	let	let	VERB
ejpam-678	18	26	clθa	clθa	NOUN
ejpam-678	18	27	denotes	denote	NOUN
ejpam-678	18	28	the	the	DET
ejpam-678	18	29	set	set	NOUN
ejpam-678	18	30	of	of	ADP
ejpam-678	18	31	all	all	DET
ejpam-678	18	32	θ	θ	PROPN
ejpam-678	18	33	-limit	-limit	NOUN
ejpam-678	18	34	point	point	NOUN
ejpam-678	18	35	of	of	ADP
ejpam-678	18	36	a.	a.	NOUN
ejpam-678	18	37	the	the	DET
ejpam-678	18	38	set	set	NOUN
ejpam-678	18	39	a	a	PRON
ejpam-678	18	40	is	be	AUX
ejpam-678	18	41	called	call	VERB
ejpam-678	18	42	θ	θ	NOUN
ejpam-678	18	43	-closed	-close	VERB
ejpam-678	18	44	if	if	SCONJ
ejpam-678	18	45	a	a	DET
ejpam-678	18	46	=	=	NOUN
ejpam-678	18	47	clθa	clθa	NOUN
ejpam-678	18	48	.	.	PUNCT
ejpam-678	19	1	the	the	DET
ejpam-678	19	2	complement	complement	NOUN
ejpam-678	19	3	of	of	ADP
ejpam-678	19	4	a	a	DET
ejpam-678	19	5	θ	θ	PROPN
ejpam-678	19	6	-closed	-close	VERB
ejpam-678	19	7	set	set	NOUN
ejpam-678	19	8	will	will	AUX
ejpam-678	19	9	be	be	AUX
ejpam-678	19	10	referred	refer	VERB
ejpam-678	19	11	to	to	ADP
ejpam-678	19	12	as	as	ADP
ejpam-678	19	13	a	a	DET
ejpam-678	19	14	θ	θ	PROPN
ejpam-678	19	15	-open	-open	NOUN
ejpam-678	19	16	set	set	NOUN
ejpam-678	19	17	.	.	PUNCT
ejpam-678	20	1	the	the	DET
ejpam-678	20	2	family	family	NOUN
ejpam-678	20	3	of	of	ADP
ejpam-678	20	4	θ	θ	PROPN
ejpam-678	20	5	-open	-open	PROPN
ejpam-678	20	6	sets	set	NOUN
ejpam-678	20	7	forms	form	VERB
ejpam-678	20	8	a	a	DET
ejpam-678	20	9	topology	topology	NOUN
ejpam-678	20	10	on	on	ADP
ejpam-678	20	11	x	x	X
ejpam-678	20	12	.	.	PUNCT
ejpam-678	21	1	a	a	DET
ejpam-678	21	2	space	space	NOUN
ejpam-678	21	3	x	x	PUNCT
ejpam-678	21	4	is	be	AUX
ejpam-678	21	5	said	say	VERB
ejpam-678	21	6	to	to	PART
ejpam-678	21	7	be	be	AUX
ejpam-678	21	8	almost	almost	ADV
ejpam-678	21	9	regular	regular	ADJ
ejpam-678	21	10	[	[	X
ejpam-678	21	11	9	9	NUM
ejpam-678	21	12	]	]	X
ejpam-678	21	13	if	if	SCONJ
ejpam-678	21	14	every	every	DET
ejpam-678	21	15	regularly	regularly	ADV
ejpam-678	21	16	closed	close	VERB
ejpam-678	21	17	set	set	VERB
ejpam-678	21	18	and	and	CCONJ
ejpam-678	21	19	a	a	DET
ejpam-678	21	20	point	point	NOUN
ejpam-678	21	21	not	not	PART
ejpam-678	21	22	in	in	ADP
ejpam-678	21	23	it	it	PRON
ejpam-678	21	24	are	be	AUX
ejpam-678	21	25	contained	contain	VERB
ejpam-678	21	26	in	in	ADP
ejpam-678	21	27	disjoint	disjoint	ADJ
ejpam-678	21	28	open	open	ADJ
ejpam-678	21	29	sets	set	NOUN
ejpam-678	21	30	.	.	PUNCT
ejpam-678	22	1	a	a	DET
ejpam-678	22	2	space	space	NOUN
ejpam-678	22	3	is	be	AUX
ejpam-678	22	4	called	call	VERB
ejpam-678	22	5	almost	almost	ADV
ejpam-678	22	6	normal	normal	ADJ
ejpam-678	22	7	[	[	X
ejpam-678	22	8	10	10	NUM
ejpam-678	22	9	]	]	X
ejpam-678	22	10	if	if	SCONJ
ejpam-678	22	11	every	every	DET
ejpam-678	22	12	pair	pair	NOUN
ejpam-678	22	13	of	of	ADP
ejpam-678	22	14	disjoint	disjoint	NOUN
ejpam-678	22	15	closed	close	VERB
ejpam-678	22	16	sets	set	NOUN
ejpam-678	22	17	,	,	PUNCT
ejpam-678	22	18	one	one	NUM
ejpam-678	22	19	of	of	ADP
ejpam-678	22	20	which	which	PRON
ejpam-678	22	21	is	be	AUX
ejpam-678	22	22	regularly	regularly	ADV
ejpam-678	22	23	closed	close	VERB
ejpam-678	22	24	,	,	PUNCT
ejpam-678	22	25	are	be	AUX
ejpam-678	22	26	contained	contain	VERB
ejpam-678	22	27	in	in	ADP
ejpam-678	22	28	disjoint	disjoint	ADJ
ejpam-678	22	29	open	open	ADJ
ejpam-678	22	30	sets	set	NOUN
ejpam-678	22	31	and	and	CCONJ
ejpam-678	22	32	a	a	DET
ejpam-678	22	33	space	space	NOUN
ejpam-678	22	34	x	x	PUNCT
ejpam-678	22	35	is	be	AUX
ejpam-678	22	36	said	say	VERB
ejpam-678	22	37	to	to	PART
ejpam-678	22	38	be	be	AUX
ejpam-678	22	39	mildly	mildly	ADV
ejpam-678	22	40	normal	normal	ADJ
ejpam-678	22	41	[	[	X
ejpam-678	22	42	12	12	NUM
ejpam-678	22	43	]	]	X
ejpam-678	22	44	(	(	PUNCT
ejpam-678	22	45	or	or	CCONJ
ejpam-678	22	46	κ	κ	NOUN
ejpam-678	22	47	-	-	ADJ
ejpam-678	22	48	normal	normal	ADJ
ejpam-678	22	49	[	[	X
ejpam-678	22	50	13	13	NUM
ejpam-678	22	51	]	]	SYM
ejpam-678	22	52	)	)	PUNCT
ejpam-678	22	53	if	if	SCONJ
ejpam-678	22	54	every	every	DET
ejpam-678	22	55	pair	pair	NOUN
ejpam-678	22	56	of	of	ADP
ejpam-678	22	57	disjoint	disjoint	NOUN
ejpam-678	22	58	regularly	regularly	ADV
ejpam-678	22	59	closed	close	VERB
ejpam-678	22	60	sets	set	NOUN
ejpam-678	22	61	are	be	AUX
ejpam-678	22	62	contained	contain	VERB
ejpam-678	22	63	in	in	ADP
ejpam-678	22	64	disjoint	disjoint	ADJ
ejpam-678	22	65	open	open	ADJ
ejpam-678	22	66	sets	set	NOUN
ejpam-678	22	67	.	.	PUNCT
ejpam-678	23	1	a	a	DET
ejpam-678	23	2	space	space	NOUN
ejpam-678	23	3	x	x	PUNCT
ejpam-678	23	4	is	be	AUX
ejpam-678	23	5	said	say	VERB
ejpam-678	23	6	to	to	PART
ejpam-678	23	7	be	be	AUX
ejpam-678	23	8	email	email	NOUN
ejpam-678	23	9	addresses	address	NOUN
ejpam-678	23	10	:	:	PUNCT
ejpam-678	24	1	ak.das	ak.das	PROPN
ejpam-678	24	2	�	�	PROPN
ejpam-678	24	3	smvdu.a	smvdu.a	PROPN
ejpam-678	24	4	.in	.in	ADV
ejpam-678	24	5	,	,	PUNCT
ejpam-678	24	6	akdasdu	akdasdu	PROPN
ejpam-678	24	7	�	�	PROPN
ejpam-678	24	8	yahoo	yahoo	PROPN
ejpam-678	24	9	.	.	PUNCT
ejpam-678	25	1	o.in	o.in	PROPN
ejpam-678	25	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-678	25	3	34	34	NUM
ejpam-678	25	4	c	c	NOUN
ejpam-678	25	5	©	©	PROPN
ejpam-678	25	6	2010	2010	NUM
ejpam-678	25	7	ejpam	ejpam	NOUN
ejpam-678	25	8	all	all	DET
ejpam-678	25	9	rights	right	NOUN
ejpam-678	25	10	reserved	reserve	VERB
ejpam-678	25	11	.	.	PUNCT
ejpam-678	26	1	a.	a.	PROPN
ejpam-678	26	2	das	das	PROPN
ejpam-678	26	3	/	/	SYM
ejpam-678	26	4	eur	eur	PROPN
ejpam-678	26	5	.	.	PUNCT
ejpam-678	27	1	j.	j.	PROPN
ejpam-678	27	2	pure	pure	PROPN
ejpam-678	27	3	appl	appl	PROPN
ejpam-678	27	4	.	.	PROPN
ejpam-678	27	5	math	math	PROPN
ejpam-678	27	6	,	,	PUNCT
ejpam-678	27	7	4	4	NUM
ejpam-678	27	8	(	(	PUNCT
ejpam-678	27	9	2011	2011	NUM
ejpam-678	27	10	)	)	PUNCT
ejpam-678	27	11	,	,	PUNCT
ejpam-678	27	12	34	34	NUM
ejpam-678	27	13	-	-	SYM
ejpam-678	27	14	41	41	NUM
ejpam-678	27	15	35	35	NUM
ejpam-678	27	16	nearly	nearly	ADV
ejpam-678	27	17	compact[11	compact[11	NOUN
ejpam-678	27	18	]	]	PUNCT
ejpam-678	27	19	if	if	SCONJ
ejpam-678	27	20	every	every	DET
ejpam-678	27	21	open	open	ADJ
ejpam-678	27	22	covering	covering	NOUN
ejpam-678	27	23	of	of	ADP
ejpam-678	27	24	x	x	PUNCT
ejpam-678	27	25	admits	admit	VERB
ejpam-678	27	26	a	a	DET
ejpam-678	27	27	finite	finite	ADJ
ejpam-678	27	28	subcollection	subcollection	NOUN
ejpam-678	27	29	the	the	DET
ejpam-678	27	30	interiors	interior	NOUN
ejpam-678	27	31	of	of	ADP
ejpam-678	27	32	the	the	DET
ejpam-678	27	33	closures	closure	NOUN
ejpam-678	27	34	of	of	ADP
ejpam-678	27	35	whose	whose	DET
ejpam-678	27	36	members	member	NOUN
ejpam-678	27	37	cover	cover	VERB
ejpam-678	27	38	x	x	X
ejpam-678	27	39	.	.	PUNCT
ejpam-678	28	1	definition	definition	NOUN
ejpam-678	28	2	1	1	NUM
ejpam-678	28	3	.	.	PUNCT
ejpam-678	29	1	a	a	DET
ejpam-678	29	2	topological	topological	ADJ
ejpam-678	29	3	space	space	NOUN
ejpam-678	29	4	x	x	PRON
ejpam-678	29	5	is	be	AUX
ejpam-678	29	6	said	say	VERB
ejpam-678	29	7	to	to	PART
ejpam-678	29	8	be	be	AUX
ejpam-678	29	9	(	(	PUNCT
ejpam-678	29	10	i	i	NOUN
ejpam-678	29	11	)	)	PUNCT
ejpam-678	30	1	θ	θ	PROPN
ejpam-678	30	2	-normal[6	-normal[6	PROPN
ejpam-678	30	3	]	]	X
ejpam-678	30	4	if	if	SCONJ
ejpam-678	30	5	every	every	DET
ejpam-678	30	6	pair	pair	NOUN
ejpam-678	30	7	of	of	ADP
ejpam-678	30	8	disjoint	disjoint	NOUN
ejpam-678	30	9	closed	closed	ADJ
ejpam-678	30	10	sets	set	NOUN
ejpam-678	30	11	one	one	NUM
ejpam-678	30	12	of	of	ADP
ejpam-678	30	13	which	which	PRON
ejpam-678	30	14	is	be	AUX
ejpam-678	30	15	θ	θ	PROPN
ejpam-678	30	16	-closed	-close	VERB
ejpam-678	30	17	are	be	AUX
ejpam-678	30	18	contained	contain	VERB
ejpam-678	30	19	in	in	ADP
ejpam-678	30	20	disjoint	disjoint	ADJ
ejpam-678	30	21	open	open	ADJ
ejpam-678	30	22	sets	set	NOUN
ejpam-678	30	23	;	;	PUNCT
ejpam-678	30	24	(	(	PUNCT
ejpam-678	30	25	ii	ii	NOUN
ejpam-678	30	26	)	)	PUNCT
ejpam-678	30	27	weakly	weakly	ADV
ejpam-678	30	28	θ	θ	PROPN
ejpam-678	30	29	-normal[6	-normal[6	PROPN
ejpam-678	30	30	]	]	X
ejpam-678	30	31	if	if	SCONJ
ejpam-678	30	32	every	every	DET
ejpam-678	30	33	pair	pair	NOUN
ejpam-678	30	34	of	of	ADP
ejpam-678	30	35	disjoint	disjoint	NOUN
ejpam-678	30	36	θ	θ	PROPN
ejpam-678	30	37	-closed	-close	VERB
ejpam-678	30	38	sets	set	NOUN
ejpam-678	30	39	are	be	AUX
ejpam-678	30	40	contained	contain	VERB
ejpam-678	30	41	in	in	ADP
ejpam-678	30	42	disjoint	disjoint	ADJ
ejpam-678	30	43	open	open	ADJ
ejpam-678	30	44	sets	set	NOUN
ejpam-678	30	45	;	;	PUNCT
ejpam-678	31	1	(	(	PUNCT
ejpam-678	31	2	iii	iii	NOUN
ejpam-678	31	3	)	)	PUNCT
ejpam-678	31	4	functionally	functionally	ADV
ejpam-678	31	5	θ	θ	PROPN
ejpam-678	31	6	-normal	-normal	NOUN
ejpam-678	31	7	(	(	PUNCT
ejpam-678	31	8	[	[	X
ejpam-678	31	9	4	4	NUM
ejpam-678	31	10	,	,	PUNCT
ejpam-678	31	11	6	6	NUM
ejpam-678	31	12	]	]	PUNCT
ejpam-678	31	13	)	)	PUNCT
ejpam-678	31	14	if	if	SCONJ
ejpam-678	31	15	for	for	ADP
ejpam-678	31	16	every	every	DET
ejpam-678	31	17	pair	pair	NOUN
ejpam-678	31	18	of	of	ADP
ejpam-678	31	19	disjoint	disjoint	NOUN
ejpam-678	31	20	closed	closed	ADJ
ejpam-678	31	21	sets	set	NOUN
ejpam-678	31	22	a	a	DET
ejpam-678	31	23	and	and	CCONJ
ejpam-678	31	24	b	b	NOUN
ejpam-678	31	25	one	one	NUM
ejpam-678	31	26	of	of	ADP
ejpam-678	31	27	which	which	PRON
ejpam-678	31	28	is	be	AUX
ejpam-678	31	29	θ	θ	PROPN
ejpam-678	31	30	-closed	-close	VERB
ejpam-678	31	31	there	there	PRON
ejpam-678	31	32	exists	exist	VERB
ejpam-678	31	33	a	a	DET
ejpam-678	31	34	continuous	continuous	ADJ
ejpam-678	31	35	function	function	NOUN
ejpam-678	31	36	f	f	NOUN
ejpam-678	31	37	:	:	PUNCT
ejpam-678	31	38	x	x	SYM
ejpam-678	31	39	→[0,1	→[0,1	NOUN
ejpam-678	31	40	]	]	PUNCT
ejpam-678	32	1	such	such	ADJ
ejpam-678	32	2	that	that	SCONJ
ejpam-678	32	3	f	f	PROPN
ejpam-678	32	4	(	(	PUNCT
ejpam-678	32	5	a	a	X
ejpam-678	32	6	)	)	PUNCT
ejpam-678	32	7	=	=	SYM
ejpam-678	32	8	0	0	NUM
ejpam-678	32	9	and	and	CCONJ
ejpam-678	32	10	f	f	PROPN
ejpam-678	32	11	(	(	PUNCT
ejpam-678	32	12	b)=1	b)=1	VERB
ejpam-678	32	13	;	;	PUNCT
ejpam-678	32	14	(	(	PUNCT
ejpam-678	32	15	iv	iv	X
ejpam-678	32	16	)	)	PUNCT
ejpam-678	32	17	weakly	weakly	ADV
ejpam-678	32	18	functionally	functionally	ADV
ejpam-678	32	19	θ	θ	X
ejpam-678	32	20	-normal	-normal	ADJ
ejpam-678	32	21	(	(	PUNCT
ejpam-678	32	22	wf	wf	PROPN
ejpam-678	32	23	θ	θ	PROPN
ejpam-678	32	24	-normal)([4	-normal)([4	ADJ
ejpam-678	32	25	,	,	PUNCT
ejpam-678	32	26	6	6	NUM
ejpam-678	32	27	]	]	PUNCT
ejpam-678	32	28	)	)	PUNCT
ejpam-678	32	29	if	if	SCONJ
ejpam-678	32	30	for	for	ADP
ejpam-678	32	31	every	every	DET
ejpam-678	32	32	pair	pair	NOUN
ejpam-678	32	33	of	of	ADP
ejpam-678	32	34	disjoint	disjoint	NOUN
ejpam-678	32	35	θ	θ	PROPN
ejpam-678	32	36	closed	close	VERB
ejpam-678	32	37	sets	set	NOUN
ejpam-678	32	38	a	a	PRON
ejpam-678	32	39	and	and	CCONJ
ejpam-678	32	40	b	b	NOUN
ejpam-678	32	41	there	there	PRON
ejpam-678	32	42	exists	exist	VERB
ejpam-678	32	43	a	a	DET
ejpam-678	32	44	continuous	continuous	ADJ
ejpam-678	32	45	function	function	NOUN
ejpam-678	32	46	f	f	NOUN
ejpam-678	32	47	:	:	PUNCT
ejpam-678	32	48	x	x	X
ejpam-678	32	49	→	→	PUNCT
ejpam-678	33	1	[	[	X
ejpam-678	33	2	0,1	0,1	NUM
ejpam-678	33	3	]	]	PUNCT
ejpam-678	33	4	such	such	ADJ
ejpam-678	33	5	that	that	SCONJ
ejpam-678	33	6	f	f	PROPN
ejpam-678	33	7	(	(	PUNCT
ejpam-678	33	8	a	a	X
ejpam-678	33	9	)	)	PUNCT
ejpam-678	33	10	=	=	SYM
ejpam-678	33	11	0	0	NUM
ejpam-678	33	12	and	and	CCONJ
ejpam-678	33	13	f	f	PROPN
ejpam-678	33	14	(	(	PUNCT
ejpam-678	33	15	b)=	b)=	X
ejpam-678	33	16	1	1	NUM
ejpam-678	33	17	;	;	PUNCT
ejpam-678	33	18	and	and	CCONJ
ejpam-678	33	19	(	(	PUNCT
ejpam-678	33	20	v	v	NOUN
ejpam-678	33	21	)	)	PUNCT
ejpam-678	33	22	σ	σ	PROPN
ejpam-678	33	23	-	-	PUNCT
ejpam-678	33	24	normal[7	normal[7	NOUN
ejpam-678	33	25	]	]	PUNCT
ejpam-678	33	26	if	if	SCONJ
ejpam-678	33	27	for	for	ADP
ejpam-678	33	28	each	each	DET
ejpam-678	33	29	closed	close	VERB
ejpam-678	33	30	set	set	VERB
ejpam-678	33	31	f	f	NOUN
ejpam-678	33	32	and	and	CCONJ
ejpam-678	33	33	each	each	DET
ejpam-678	33	34	open	open	ADJ
ejpam-678	33	35	set	set	VERB
ejpam-678	33	36	u	u	NOUN
ejpam-678	33	37	containing	contain	VERB
ejpam-678	33	38	f	f	X
ejpam-678	33	39	,	,	PUNCT
ejpam-678	33	40	there	there	PRON
ejpam-678	33	41	exists	exist	VERB
ejpam-678	33	42	a	a	DET
ejpam-678	33	43	regular	regular	ADJ
ejpam-678	33	44	fσ	fσ	NOUN
ejpam-678	33	45	set	set	VERB
ejpam-678	33	46	v	v	ADP
ejpam-678	33	47	such	such	DET
ejpam-678	33	48	that	that	SCONJ
ejpam-678	33	49	f	f	PROPN
ejpam-678	33	50	⊂	⊂	PROPN
ejpam-678	33	51	v	v	PROPN
ejpam-678	33	52	⊂	⊂	PROPN
ejpam-678	33	53	u.	u.	PROPN
ejpam-678	33	54	2	2	X
ejpam-678	33	55	.	.	PUNCT
ejpam-678	34	1	variants	variant	NOUN
ejpam-678	34	2	of	of	ADP
ejpam-678	34	3	θ	θ	PROPN
ejpam-678	34	4	-regular	-regular	NOUN
ejpam-678	34	5	spaces	space	NOUN
ejpam-678	34	6	definition	definition	NOUN
ejpam-678	34	7	2	2	NUM
ejpam-678	34	8	.	.	PUNCT
ejpam-678	35	1	a	a	DET
ejpam-678	35	2	topological	topological	ADJ
ejpam-678	35	3	space	space	NOUN
ejpam-678	35	4	x	x	PRON
ejpam-678	35	5	is	be	AUX
ejpam-678	35	6	said	say	VERB
ejpam-678	35	7	to	to	PART
ejpam-678	35	8	be	be	AUX
ejpam-678	35	9	(	(	PUNCT
ejpam-678	35	10	i	i	NOUN
ejpam-678	35	11	)	)	PUNCT
ejpam-678	35	12	θ	θ	PROPN
ejpam-678	36	1	-regular[6	-regular[6	PUNCT
ejpam-678	36	2	]	]	X
ejpam-678	36	3	if	if	SCONJ
ejpam-678	36	4	for	for	ADP
ejpam-678	36	5	each	each	DET
ejpam-678	36	6	closed	close	VERB
ejpam-678	36	7	set	set	VERB
ejpam-678	36	8	f	f	NOUN
ejpam-678	36	9	and	and	CCONJ
ejpam-678	36	10	each	each	DET
ejpam-678	36	11	open	open	ADJ
ejpam-678	36	12	set	set	VERB
ejpam-678	36	13	u	u	NOUN
ejpam-678	36	14	containing	contain	VERB
ejpam-678	36	15	f	f	X
ejpam-678	36	16	,	,	PUNCT
ejpam-678	36	17	there	there	PRON
ejpam-678	36	18	exists	exist	VERB
ejpam-678	36	19	a	a	DET
ejpam-678	36	20	θ	θ	PROPN
ejpam-678	36	21	-open	-open	NOUN
ejpam-678	36	22	set	set	VERB
ejpam-678	36	23	v	v	ADP
ejpam-678	36	24	such	such	DET
ejpam-678	36	25	that	that	SCONJ
ejpam-678	36	26	f	f	PROPN
ejpam-678	36	27	⊂	⊂	PROPN
ejpam-678	36	28	v	v	PROPN
ejpam-678	36	29	⊂	⊂	PROPN
ejpam-678	36	30	u.	u.	PROPN
ejpam-678	36	31	(	(	PUNCT
ejpam-678	36	32	ii	ii	NOUN
ejpam-678	36	33	)	)	PUNCT
ejpam-678	36	34	weakly	weakly	ADJ
ejpam-678	36	35	θ	θ	NOUN
ejpam-678	36	36	-regular	-regular	ADJ
ejpam-678	36	37	if	if	SCONJ
ejpam-678	36	38	for	for	ADP
ejpam-678	36	39	each	each	PRON
ejpam-678	36	40	θ	θ	PROPN
ejpam-678	36	41	-closed	-close	VERB
ejpam-678	36	42	set	set	VERB
ejpam-678	36	43	f	f	NOUN
ejpam-678	36	44	and	and	CCONJ
ejpam-678	36	45	each	each	DET
ejpam-678	36	46	open	open	ADJ
ejpam-678	36	47	set	set	VERB
ejpam-678	36	48	u	u	NOUN
ejpam-678	36	49	containing	contain	VERB
ejpam-678	36	50	f	f	X
ejpam-678	36	51	,	,	PUNCT
ejpam-678	36	52	there	there	PRON
ejpam-678	36	53	exists	exist	VERB
ejpam-678	36	54	a	a	DET
ejpam-678	36	55	θ	θ	PROPN
ejpam-678	36	56	-open	-open	NOUN
ejpam-678	36	57	set	set	VERB
ejpam-678	36	58	v	v	ADP
ejpam-678	36	59	such	such	DET
ejpam-678	36	60	that	that	SCONJ
ejpam-678	36	61	f	f	PROPN
ejpam-678	36	62	⊂	⊂	PROPN
ejpam-678	36	63	v	v	PROPN
ejpam-678	36	64	⊂	⊂	PROPN
ejpam-678	36	65	u.	u.	PROPN
ejpam-678	36	66	(	(	PUNCT
ejpam-678	36	67	iii	iii	NOUN
ejpam-678	36	68	)	)	PUNCT
ejpam-678	36	69	point	point	NOUN
ejpam-678	36	70	θ	θ	NOUN
ejpam-678	36	71	-regular	-regular	ADJ
ejpam-678	36	72	if	if	SCONJ
ejpam-678	36	73	for	for	ADP
ejpam-678	36	74	each	each	DET
ejpam-678	36	75	closed	closed	ADJ
ejpam-678	36	76	singleton	singleton	NOUN
ejpam-678	36	77	{	{	PUNCT
ejpam-678	36	78	x	x	NOUN
ejpam-678	36	79	}	}	PUNCT
ejpam-678	36	80	and	and	CCONJ
ejpam-678	36	81	each	each	DET
ejpam-678	36	82	open	open	ADJ
ejpam-678	36	83	set	set	VERB
ejpam-678	36	84	u	u	NOUN
ejpam-678	36	85	containing	contain	VERB
ejpam-678	36	86	x	x	PRON
ejpam-678	36	87	,	,	PUNCT
ejpam-678	36	88	there	there	PRON
ejpam-678	36	89	exists	exist	VERB
ejpam-678	36	90	a	a	DET
ejpam-678	36	91	θ	θ	PROPN
ejpam-678	36	92	-open	-open	NOUN
ejpam-678	36	93	set	set	VERB
ejpam-678	36	94	v	v	ADP
ejpam-678	36	95	such	such	ADJ
ejpam-678	36	96	that	that	SCONJ
ejpam-678	36	97	x	x	SYM
ejpam-678	36	98	∈	∈	PROPN
ejpam-678	36	99	v	v	ADP
ejpam-678	36	100	⊂	⊂	PROPN
ejpam-678	36	101	u.	u.	PROPN
ejpam-678	36	102	(	(	PUNCT
ejpam-678	36	103	iv	iv	X
ejpam-678	36	104	)	)	PUNCT
ejpam-678	36	105	point	point	NOUN
ejpam-678	36	106	weakly	weakly	ADJ
ejpam-678	36	107	θ	θ	NOUN
ejpam-678	36	108	-regular	-regular	ADJ
ejpam-678	36	109	if	if	SCONJ
ejpam-678	36	110	for	for	ADP
ejpam-678	36	111	each	each	DET
ejpam-678	36	112	θ	θ	PROPN
ejpam-678	36	113	-closed	-close	VERB
ejpam-678	36	114	singleton	singleton	PROPN
ejpam-678	36	115	{	{	PUNCT
ejpam-678	36	116	x	x	NOUN
ejpam-678	36	117	}	}	PUNCT
ejpam-678	36	118	and	and	CCONJ
ejpam-678	36	119	each	each	DET
ejpam-678	36	120	open	open	ADJ
ejpam-678	36	121	set	set	VERB
ejpam-678	36	122	u	u	NOUN
ejpam-678	36	123	containing	contain	VERB
ejpam-678	36	124	x	x	PRON
ejpam-678	36	125	,	,	PUNCT
ejpam-678	36	126	there	there	PRON
ejpam-678	36	127	exists	exist	VERB
ejpam-678	36	128	a	a	DET
ejpam-678	36	129	θ	θ	PROPN
ejpam-678	36	130	-open	-open	NOUN
ejpam-678	36	131	set	set	VERB
ejpam-678	36	132	v	v	ADP
ejpam-678	36	133	such	such	ADJ
ejpam-678	36	134	that	that	SCONJ
ejpam-678	36	135	x	x	SYM
ejpam-678	36	136	∈	∈	PROPN
ejpam-678	36	137	v	v	ADP
ejpam-678	36	138	⊂	⊂	PROPN
ejpam-678	36	139	u.	u.	VERB
ejpam-678	36	140	the	the	DET
ejpam-678	36	141	above	above	ADP
ejpam-678	36	142	notion	notion	NOUN
ejpam-678	36	143	of	of	ADP
ejpam-678	36	144	θ	θ	PROPN
ejpam-678	36	145	-regularity	-regularity	PROPN
ejpam-678	36	146	is	be	AUX
ejpam-678	36	147	exclusively	exclusively	ADV
ejpam-678	36	148	different	different	ADJ
ejpam-678	36	149	from	from	ADP
ejpam-678	36	150	the	the	DET
ejpam-678	36	151	concept	concept	NOUN
ejpam-678	36	152	of	of	ADP
ejpam-678	36	153	θ	θ	PROPN
ejpam-678	36	154	-regularity	-regularity	NOUN
ejpam-678	36	155	introduced	introduce	VERB
ejpam-678	36	156	by	by	ADP
ejpam-678	36	157	jankovic	jankovic	PROPN
ejpam-678	37	1	[	[	X
ejpam-678	37	2	3	3	X
ejpam-678	37	3	]	]	PUNCT
ejpam-678	37	4	which	which	PRON
ejpam-678	37	5	was	be	AUX
ejpam-678	37	6	utilized	utilize	VERB
ejpam-678	37	7	by	by	ADP
ejpam-678	37	8	kovar	kovar	PROPN
ejpam-678	37	9	[	[	X
ejpam-678	37	10	8	8	NUM
ejpam-678	37	11	]	]	PUNCT
ejpam-678	37	12	to	to	PART
ejpam-678	37	13	study	study	VERB
ejpam-678	37	14	covering	cover	VERB
ejpam-678	37	15	axioms	axiom	NOUN
ejpam-678	37	16	including	include	VERB
ejpam-678	37	17	compactness	compactness	NOUN
ejpam-678	37	18	and	and	CCONJ
ejpam-678	37	19	paracompactness	paracompactness	NOUN
ejpam-678	37	20	.	.	PUNCT
ejpam-678	38	1	in	in	ADP
ejpam-678	38	2	[	[	X
ejpam-678	38	3	8	8	NUM
ejpam-678	38	4	]	]	PUNCT
ejpam-678	38	5	,	,	PUNCT
ejpam-678	38	6	kovar	kovar	PROPN
ejpam-678	38	7	proved	prove	VERB
ejpam-678	38	8	that	that	SCONJ
ejpam-678	38	9	jankovic	jankovic	PROPN
ejpam-678	38	10	’s	’s	PROPN
ejpam-678	38	11	θ	θ	PROPN
ejpam-678	38	12	-regularity	-regularity	PROPN
ejpam-678	38	13	coincides	coincide	VERB
ejpam-678	38	14	with	with	ADP
ejpam-678	38	15	the	the	DET
ejpam-678	38	16	notion	notion	NOUN
ejpam-678	38	17	of	of	ADP
ejpam-678	38	18	point	point	NOUN
ejpam-678	38	19	paracompactness	paracompactness	PROPN
ejpam-678	38	20	introduced	introduce	VERB
ejpam-678	38	21	by	by	ADP
ejpam-678	38	22	boyte	boyte	NOUN
ejpam-678	39	1	[	[	X
ejpam-678	39	2	1	1	NUM
ejpam-678	39	3	]	]	PUNCT
ejpam-678	39	4	.	.	PUNCT
ejpam-678	40	1	from	from	ADP
ejpam-678	40	2	here	here	ADV
ejpam-678	40	3	onward	onward	ADV
ejpam-678	40	4	the	the	DET
ejpam-678	40	5	term	term	NOUN
ejpam-678	40	6	“	"	PUNCT
ejpam-678	40	7	θ	θ	PROPN
ejpam-678	40	8	-regularity	-regularity	NOUN
ejpam-678	40	9	”	"	PUNCT
ejpam-678	40	10	will	will	AUX
ejpam-678	40	11	always	always	ADV
ejpam-678	40	12	be	be	AUX
ejpam-678	40	13	meant	mean	VERB
ejpam-678	40	14	in	in	ADP
ejpam-678	40	15	the	the	DET
ejpam-678	40	16	sense	sense	NOUN
ejpam-678	40	17	of	of	ADP
ejpam-678	40	18	definition	definition	NOUN
ejpam-678	40	19	2	2	NUM
ejpam-678	40	20	.	.	PUNCT
ejpam-678	41	1	the	the	DET
ejpam-678	41	2	following	follow	VERB
ejpam-678	41	3	implications	implication	NOUN
ejpam-678	41	4	are	be	AUX
ejpam-678	41	5	obvious	obvious	ADJ
ejpam-678	41	6	,	,	PUNCT
ejpam-678	41	7	but	but	CCONJ
ejpam-678	41	8	none	none	NOUN
ejpam-678	41	9	of	of	ADP
ejpam-678	41	10	them	they	PRON
ejpam-678	41	11	are	be	AUX
ejpam-678	41	12	reversible	reversible	ADJ
ejpam-678	41	13	.	.	PUNCT
ejpam-678	42	1	a.	a.	PROPN
ejpam-678	42	2	das	das	PROPN
ejpam-678	42	3	/	/	SYM
ejpam-678	42	4	eur	eur	PROPN
ejpam-678	42	5	.	.	PUNCT
ejpam-678	43	1	j.	j.	PROPN
ejpam-678	43	2	pure	pure	PROPN
ejpam-678	43	3	appl	appl	PROPN
ejpam-678	43	4	.	.	PROPN
ejpam-678	43	5	math	math	PROPN
ejpam-678	43	6	,	,	PUNCT
ejpam-678	43	7	4	4	NUM
ejpam-678	43	8	(	(	PUNCT
ejpam-678	43	9	2011	2011	NUM
ejpam-678	43	10	)	)	PUNCT
ejpam-678	43	11	,	,	PUNCT
ejpam-678	43	12	34	34	NUM
ejpam-678	43	13	-	-	SYM
ejpam-678	43	14	41	41	NUM
ejpam-678	43	15	36	36	NUM
ejpam-678	43	16	example	example	NOUN
ejpam-678	43	17	1	1	NUM
ejpam-678	43	18	(	(	PUNCT
ejpam-678	43	19	a	a	DET
ejpam-678	43	20	point	point	NOUN
ejpam-678	43	21	θ	θ	NOUN
ejpam-678	43	22	-regular	-regular	ADJ
ejpam-678	43	23	space	space	NOUN
ejpam-678	43	24	which	which	PRON
ejpam-678	43	25	is	be	AUX
ejpam-678	43	26	not	not	PART
ejpam-678	43	27	θ	θ	NOUN
ejpam-678	43	28	-regular	-regular	ADJ
ejpam-678	43	29	.	.	PUNCT
ejpam-678	43	30	)	)	PUNCT
ejpam-678	43	31	.	.	PUNCT
ejpam-678	44	1	let	let	VERB
ejpam-678	44	2	x	x	PUNCT
ejpam-678	44	3	=	=	PRON
ejpam-678	44	4	{	{	PUNCT
ejpam-678	44	5	a	a	PRON
ejpam-678	44	6	,	,	PUNCT
ejpam-678	44	7	b	b	NOUN
ejpam-678	44	8	,	,	PUNCT
ejpam-678	44	9	c	c	NOUN
ejpam-678	44	10	,	,	PUNCT
ejpam-678	44	11	d	d	X
ejpam-678	44	12	,	,	PUNCT
ejpam-678	44	13	e	e	NOUN
ejpam-678	44	14	}	}	PUNCT
ejpam-678	44	15	and	and	CCONJ
ejpam-678	44	16	t	t	NOUN
ejpam-678	44	17	=	=	SYM
ejpam-678	44	18	{	{	PUNCT
ejpam-678	44	19	{	{	PUNCT
ejpam-678	44	20	a	a	PROPN
ejpam-678	44	21	,	,	PUNCT
ejpam-678	44	22	b	b	NOUN
ejpam-678	44	23	,	,	PUNCT
ejpam-678	44	24	c	c	NOUN
ejpam-678	44	25	}	}	PUNCT
ejpam-678	44	26	,	,	PUNCT
ejpam-678	44	27	{	{	PUNCT
ejpam-678	44	28	c	c	X
ejpam-678	44	29	,	,	PUNCT
ejpam-678	44	30	d	d	X
ejpam-678	44	31	,	,	PUNCT
ejpam-678	44	32	e	e	NOUN
ejpam-678	44	33	}	}	PUNCT
ejpam-678	44	34	,	,	PUNCT
ejpam-678	44	35	{	{	PUNCT
ejpam-678	44	36	c},ϕ	c},ϕ	NOUN
ejpam-678	44	37	,	,	PUNCT
ejpam-678	44	38	x	x	SYM
ejpam-678	44	39	}	}	PUNCT
ejpam-678	44	40	.	.	PUNCT
ejpam-678	45	1	here	here	ADV
ejpam-678	45	2	x	x	PUNCT
ejpam-678	45	3	is	be	AUX
ejpam-678	45	4	vacuously	vacuously	ADV
ejpam-678	45	5	point	point	NOUN
ejpam-678	45	6	θ	θ	NOUN
ejpam-678	45	7	-regular	-regular	ADJ
ejpam-678	45	8	,	,	PUNCT
ejpam-678	45	9	but	but	CCONJ
ejpam-678	45	10	not	not	PART
ejpam-678	45	11	θ	θ	NOUN
ejpam-678	45	12	-regular	-regular	ADJ
ejpam-678	45	13	as	as	ADP
ejpam-678	45	14	{	{	PUNCT
ejpam-678	45	15	a	a	PRON
ejpam-678	45	16	,	,	PUNCT
ejpam-678	45	17	b	b	NOUN
ejpam-678	45	18	}	}	PUNCT
ejpam-678	45	19	⊂	⊂	PRON
ejpam-678	45	20	{	{	PUNCT
ejpam-678	45	21	a	a	PRON
ejpam-678	45	22	,	,	PUNCT
ejpam-678	45	23	b	b	NOUN
ejpam-678	45	24	,	,	PUNCT
ejpam-678	45	25	c	c	NOUN
ejpam-678	45	26	}	}	PUNCT
ejpam-678	45	27	but	but	CCONJ
ejpam-678	45	28	there	there	PRON
ejpam-678	45	29	is	be	VERB
ejpam-678	45	30	no	no	DET
ejpam-678	45	31	θ	θ	PROPN
ejpam-678	45	32	-open	-open	NOUN
ejpam-678	45	33	set	set	NOUN
ejpam-678	45	34	containing	contain	VERB
ejpam-678	45	35	{	{	PUNCT
ejpam-678	45	36	a	a	DET
ejpam-678	45	37	,	,	PUNCT
ejpam-678	45	38	b	b	NOUN
ejpam-678	45	39	}	}	PUNCT
ejpam-678	45	40	and	and	CCONJ
ejpam-678	45	41	contained	contain	VERB
ejpam-678	45	42	in	in	ADP
ejpam-678	45	43	{	{	PUNCT
ejpam-678	45	44	a	a	PRON
ejpam-678	45	45	,	,	PUNCT
ejpam-678	45	46	b	b	NOUN
ejpam-678	45	47	,	,	PUNCT
ejpam-678	45	48	c	c	NOUN
ejpam-678	45	49	}	}	PUNCT
ejpam-678	45	50	.	.	PUNCT
ejpam-678	46	1	example	example	NOUN
ejpam-678	46	2	2	2	NUM
ejpam-678	46	3	(	(	PUNCT
ejpam-678	46	4	a	a	DET
ejpam-678	46	5	point	point	NOUN
ejpam-678	46	6	weakly	weakly	ADJ
ejpam-678	46	7	θ	θ	NOUN
ejpam-678	46	8	-regular	-regular	ADJ
ejpam-678	46	9	space	space	NOUN
ejpam-678	46	10	which	which	PRON
ejpam-678	46	11	is	be	AUX
ejpam-678	46	12	not	not	PART
ejpam-678	46	13	point	point	NOUN
ejpam-678	46	14	θ	θ	NOUN
ejpam-678	46	15	-regular	-regular	ADJ
ejpam-678	46	16	.	.	PUNCT
ejpam-678	46	17	)	)	PUNCT
ejpam-678	46	18	.	.	PUNCT
ejpam-678	47	1	co	co	VERB
ejpam-678	47	2	-	-	ADJ
ejpam-678	47	3	finite	finite	ADJ
ejpam-678	47	4	topology	topology	NOUN
ejpam-678	47	5	is	be	AUX
ejpam-678	47	6	point	point	NOUN
ejpam-678	47	7	weakly	weakly	ADJ
ejpam-678	47	8	θ	θ	NOUN
ejpam-678	47	9	-regular	-regular	ADJ
ejpam-678	47	10	but	but	CCONJ
ejpam-678	47	11	not	not	PART
ejpam-678	47	12	point	point	NOUN
ejpam-678	47	13	θ	θ	NOUN
ejpam-678	47	14	-regular	-regular	ADJ
ejpam-678	47	15	.	.	PUNCT
ejpam-678	48	1	example	example	NOUN
ejpam-678	48	2	3	3	NUM
ejpam-678	48	3	(	(	PUNCT
ejpam-678	48	4	a	a	DET
ejpam-678	48	5	point	point	NOUN
ejpam-678	48	6	weakly	weakly	ADJ
ejpam-678	48	7	θ	θ	NOUN
ejpam-678	48	8	-regular	-regular	ADJ
ejpam-678	48	9	space	space	NOUN
ejpam-678	48	10	which	which	PRON
ejpam-678	48	11	is	be	AUX
ejpam-678	48	12	not	not	PART
ejpam-678	48	13	point	point	NOUN
ejpam-678	48	14	θ	θ	NOUN
ejpam-678	48	15	-regular	-regular	ADJ
ejpam-678	48	16	.	.	PUNCT
ejpam-678	48	17	)	)	PUNCT
ejpam-678	48	18	.	.	PUNCT
ejpam-678	49	1	let	let	VERB
ejpam-678	49	2	x	x	PUNCT
ejpam-678	49	3	=	=	PRON
ejpam-678	49	4	{	{	PUNCT
ejpam-678	49	5	a	a	PRON
ejpam-678	49	6	,	,	PUNCT
ejpam-678	49	7	b	b	NOUN
ejpam-678	49	8	,	,	PUNCT
ejpam-678	49	9	c	c	NOUN
ejpam-678	49	10	}	}	PUNCT
ejpam-678	49	11	and	and	CCONJ
ejpam-678	49	12	t	t	NOUN
ejpam-678	49	13	=	=	SYM
ejpam-678	49	14	{	{	PUNCT
ejpam-678	49	15	{	{	PUNCT
ejpam-678	49	16	a	a	PROPN
ejpam-678	49	17	,	,	PUNCT
ejpam-678	49	18	b	b	NOUN
ejpam-678	49	19	}	}	PUNCT
ejpam-678	49	20	,	,	PUNCT
ejpam-678	49	21	{	{	PUNCT
ejpam-678	49	22	b	b	X
ejpam-678	49	23	,	,	PUNCT
ejpam-678	49	24	c	c	NOUN
ejpam-678	49	25	}	}	PUNCT
ejpam-678	49	26	,	,	PUNCT
ejpam-678	49	27	{	{	PUNCT
ejpam-678	49	28	b},ϕ	b},ϕ	NOUN
ejpam-678	49	29	,	,	PUNCT
ejpam-678	49	30	x	x	PUNCT
ejpam-678	49	31	}	}	PUNCT
ejpam-678	49	32	.	.	PUNCT
ejpam-678	50	1	here	here	ADV
ejpam-678	50	2	x	x	PUNCT
ejpam-678	50	3	is	be	AUX
ejpam-678	50	4	vacuously	vacuously	ADV
ejpam-678	50	5	point	point	VERB
ejpam-678	50	6	weakly	weakly	ADJ
ejpam-678	50	7	θ	θ	NOUN
ejpam-678	50	8	-regular	-regular	ADJ
ejpam-678	50	9	,	,	PUNCT
ejpam-678	50	10	but	but	CCONJ
ejpam-678	50	11	not	not	PART
ejpam-678	50	12	point	point	VERB
ejpam-678	50	13	θ	θ	NOUN
ejpam-678	50	14	-regular	-regular	ADJ
ejpam-678	50	15	as	as	ADP
ejpam-678	50	16	{	{	PUNCT
ejpam-678	50	17	a	a	NOUN
ejpam-678	50	18	}	}	PUNCT
ejpam-678	50	19	⊂	⊂	PROPN
ejpam-678	50	20	{	{	PUNCT
ejpam-678	50	21	a	a	DET
ejpam-678	50	22	,	,	PUNCT
ejpam-678	50	23	b	b	NOUN
ejpam-678	50	24	}	}	PUNCT
ejpam-678	50	25	but	but	CCONJ
ejpam-678	50	26	there	there	PRON
ejpam-678	50	27	is	be	VERB
ejpam-678	50	28	no	no	DET
ejpam-678	50	29	θ	θ	PROPN
ejpam-678	50	30	-open	-open	NOUN
ejpam-678	50	31	set	set	NOUN
ejpam-678	50	32	containing	contain	VERB
ejpam-678	50	33	{	{	PUNCT
ejpam-678	50	34	a	a	NOUN
ejpam-678	50	35	}	}	PUNCT
ejpam-678	50	36	and	and	CCONJ
ejpam-678	50	37	contained	contain	VERB
ejpam-678	50	38	in	in	ADP
ejpam-678	50	39	{	{	PUNCT
ejpam-678	50	40	a	a	DET
ejpam-678	50	41	,	,	PUNCT
ejpam-678	50	42	b	b	NOUN
ejpam-678	50	43	}	}	PUNCT
ejpam-678	50	44	.	.	PUNCT
ejpam-678	51	1	question	question	NOUN
ejpam-678	51	2	1	1	NUM
ejpam-678	51	3	.	.	PUNCT
ejpam-678	52	1	does	do	AUX
ejpam-678	52	2	there	there	PRON
ejpam-678	52	3	exists	exist	VERB
ejpam-678	52	4	a	a	DET
ejpam-678	52	5	point	point	NOUN
ejpam-678	52	6	weakly	weakly	ADJ
ejpam-678	52	7	θ	θ	NOUN
ejpam-678	52	8	-regular	-regular	ADJ
ejpam-678	52	9	space	space	NOUN
ejpam-678	52	10	which	which	PRON
ejpam-678	52	11	is	be	AUX
ejpam-678	52	12	not	not	PART
ejpam-678	52	13	weakly	weakly	ADJ
ejpam-678	52	14	θ	θ	NOUN
ejpam-678	52	15	-regular	-regular	ADJ
ejpam-678	52	16	?	?	PUNCT
ejpam-678	53	1	it	it	PRON
ejpam-678	53	2	is	be	AUX
ejpam-678	53	3	obvious	obvious	ADJ
ejpam-678	53	4	from	from	ADP
ejpam-678	53	5	the	the	DET
ejpam-678	53	6	definitions	definition	NOUN
ejpam-678	53	7	that	that	PRON
ejpam-678	53	8	,	,	PUNCT
ejpam-678	53	9	a	a	DET
ejpam-678	53	10	r0	r0	NOUN
ejpam-678	53	11	-	-	PUNCT
ejpam-678	53	12	space	space	NOUN
ejpam-678	53	13	is	be	AUX
ejpam-678	53	14	regular	regular	ADJ
ejpam-678	53	15	if	if	SCONJ
ejpam-678	53	16	and	and	CCONJ
ejpam-678	53	17	only	only	ADV
ejpam-678	53	18	if	if	SCONJ
ejpam-678	53	19	it	it	PRON
ejpam-678	53	20	is	be	AUX
ejpam-678	53	21	θ	θ	NOUN
ejpam-678	53	22	-regular	-regular	ADJ
ejpam-678	53	23	and	and	CCONJ
ejpam-678	53	24	a	a	DET
ejpam-678	53	25	t1	t1	NOUN
ejpam-678	53	26	-	-	PUNCT
ejpam-678	53	27	space	space	NOUN
ejpam-678	53	28	is	be	AUX
ejpam-678	53	29	t3	t3	PROPN
ejpam-678	53	30	if	if	SCONJ
ejpam-678	53	31	and	and	CCONJ
ejpam-678	53	32	only	only	ADV
ejpam-678	53	33	if	if	SCONJ
ejpam-678	53	34	it	it	PRON
ejpam-678	53	35	is	be	AUX
ejpam-678	53	36	point	point	NOUN
ejpam-678	53	37	θ	θ	NOUN
ejpam-678	53	38	-regular	-regular	ADJ
ejpam-678	53	39	.	.	PUNCT
ejpam-678	54	1	similarly	similarly	ADV
ejpam-678	54	2	,	,	PUNCT
ejpam-678	54	3	a	a	DET
ejpam-678	54	4	hausdroff	hausdroff	NOUN
ejpam-678	54	5	space	space	NOUN
ejpam-678	54	6	is	be	AUX
ejpam-678	54	7	t3	t3	PROPN
ejpam-678	54	8	if	if	SCONJ
ejpam-678	55	1	and	and	CCONJ
ejpam-678	55	2	only	only	ADV
ejpam-678	55	3	if	if	SCONJ
ejpam-678	55	4	it	it	PRON
ejpam-678	55	5	is	be	AUX
ejpam-678	55	6	point	point	NOUN
ejpam-678	55	7	weakly	weakly	ADJ
ejpam-678	55	8	θ	θ	NOUN
ejpam-678	55	9	-regular	-regular	ADJ
ejpam-678	55	10	.	.	PUNCT
ejpam-678	56	1	theorem	theorem	NOUN
ejpam-678	56	2	1	1	NUM
ejpam-678	56	3	.	.	X
ejpam-678	57	1	for	for	ADP
ejpam-678	57	2	a	a	DET
ejpam-678	57	3	point	point	NOUN
ejpam-678	57	4	θ	θ	NOUN
ejpam-678	57	5	-regular	-regular	ADJ
ejpam-678	57	6	space	space	NOUN
ejpam-678	57	7	,	,	PUNCT
ejpam-678	57	8	the	the	DET
ejpam-678	57	9	following	follow	VERB
ejpam-678	57	10	statements	statement	NOUN
ejpam-678	57	11	are	be	AUX
ejpam-678	57	12	equivalent	equivalent	ADJ
ejpam-678	57	13	.	.	PUNCT
ejpam-678	58	1	(	(	PUNCT
ejpam-678	58	2	i	i	NOUN
ejpam-678	58	3	)	)	PUNCT
ejpam-678	58	4	for	for	ADP
ejpam-678	58	5	every	every	DET
ejpam-678	58	6	pair	pair	NOUN
ejpam-678	58	7	of	of	ADP
ejpam-678	58	8	distinct	distinct	ADJ
ejpam-678	58	9	points	point	NOUN
ejpam-678	58	10	x	x	PUNCT
ejpam-678	58	11	and	and	CCONJ
ejpam-678	58	12	y	y	PROPN
ejpam-678	58	13	in	in	ADP
ejpam-678	58	14	x	x	SYM
ejpam-678	58	15	,	,	PUNCT
ejpam-678	58	16	there	there	PRON
ejpam-678	58	17	exist	exist	VERB
ejpam-678	58	18	θ	θ	PROPN
ejpam-678	58	19	-open	-open	NOUN
ejpam-678	58	20	sets	set	NOUN
ejpam-678	58	21	p	p	NOUN
ejpam-678	58	22	and	and	CCONJ
ejpam-678	58	23	q	q	NOUN
ejpam-678	58	24	such	such	ADJ
ejpam-678	58	25	that	that	SCONJ
ejpam-678	58	26	x	x	SYM
ejpam-678	58	27	∈	∈	PROPN
ejpam-678	58	28	u	u	NOUN
ejpam-678	58	29	,	,	PUNCT
ejpam-678	58	30	y	y	PROPN
ejpam-678	58	31	∈	∈	PROPN
ejpam-678	58	32	v	v	NOUN
ejpam-678	58	33	and	and	CCONJ
ejpam-678	58	34	p	p	NOUN
ejpam-678	58	35	∩q	∩q	PROPN
ejpam-678	59	1	=	=	PUNCT
ejpam-678	59	2	ϕ.	ϕ.	PROPN
ejpam-678	59	3	(	(	PUNCT
ejpam-678	59	4	ii	ii	PROPN
ejpam-678	59	5	)	)	PUNCT
ejpam-678	59	6	x	x	PUNCT
ejpam-678	59	7	is	be	AUX
ejpam-678	59	8	θt2	θt2	PROPN
ejpam-678	59	9	.	.	PUNCT
ejpam-678	60	1	(	(	PUNCT
ejpam-678	60	2	iii	iii	X
ejpam-678	60	3	)	)	PUNCT
ejpam-678	60	4	x	x	PRON
ejpam-678	60	5	is	be	AUX
ejpam-678	60	6	urysohn	urysohn	ADJ
ejpam-678	60	7	.	.	PUNCT
ejpam-678	61	1	(	(	PUNCT
ejpam-678	61	2	iv	iv	X
ejpam-678	61	3	)	)	PUNCT
ejpam-678	61	4	x	x	X
ejpam-678	61	5	is	be	AUX
ejpam-678	61	6	t2	t2	NOUN
ejpam-678	61	7	.	.	PUNCT
ejpam-678	62	1	(	(	PUNCT
ejpam-678	62	2	v	v	NOUN
ejpam-678	62	3	)	)	PUNCT
ejpam-678	62	4	x	x	PUNCT
ejpam-678	62	5	is	be	AUX
ejpam-678	62	6	t1	t1	NOUN
ejpam-678	62	7	.	.	PUNCT
ejpam-678	63	1	proof	proof	NOUN
ejpam-678	63	2	.	.	PUNCT
ejpam-678	64	1	let	let	VERB
ejpam-678	64	2	x	x	PRON
ejpam-678	64	3	and	and	CCONJ
ejpam-678	64	4	y	y	PROPN
ejpam-678	64	5	be	be	AUX
ejpam-678	64	6	two	two	NUM
ejpam-678	64	7	disjoint	disjoint	ADJ
ejpam-678	64	8	points	point	NOUN
ejpam-678	64	9	in	in	ADP
ejpam-678	64	10	x	x	X
ejpam-678	64	11	.	.	PUNCT
ejpam-678	65	1	since	since	SCONJ
ejpam-678	65	2	x	x	PROPN
ejpam-678	65	3	is	be	AUX
ejpam-678	65	4	t1	t1	PROPN
ejpam-678	65	5	,	,	PUNCT
ejpam-678	65	6	the	the	DET
ejpam-678	65	7	closed	closed	ADJ
ejpam-678	65	8	set	set	NOUN
ejpam-678	65	9	{	{	PUNCT
ejpam-678	65	10	x	x	NOUN
ejpam-678	65	11	}	}	PUNCT
ejpam-678	65	12	is	be	AUX
ejpam-678	65	13	contained	contain	VERB
ejpam-678	65	14	in	in	ADP
ejpam-678	65	15	an	an	DET
ejpam-678	65	16	open	open	ADJ
ejpam-678	65	17	set	set	NOUN
ejpam-678	65	18	x	x	X
ejpam-678	65	19	−	−	PROPN
ejpam-678	65	20	{	{	PUNCT
ejpam-678	65	21	y	y	NOUN
ejpam-678	65	22	}	}	PUNCT
ejpam-678	65	23	.	.	PUNCT
ejpam-678	66	1	thus	thus	ADV
ejpam-678	66	2	by	by	ADP
ejpam-678	66	3	point	point	NOUN
ejpam-678	66	4	θ	θ	PROPN
ejpam-678	66	5	-regularity	-regularity	NOUN
ejpam-678	66	6	of	of	ADP
ejpam-678	66	7	x	x	SYM
ejpam-678	66	8	,	,	PUNCT
ejpam-678	66	9	there	there	PRON
ejpam-678	66	10	exists	exist	VERB
ejpam-678	66	11	a	a	DET
ejpam-678	66	12	θ	θ	PROPN
ejpam-678	66	13	-open	-open	NOUN
ejpam-678	66	14	set	set	VERB
ejpam-678	66	15	v	v	ADP
ejpam-678	66	16	such	such	ADJ
ejpam-678	66	17	that	that	SCONJ
ejpam-678	66	18	x	x	SYM
ejpam-678	66	19	∈	∈	PROPN
ejpam-678	66	20	v	v	ADP
ejpam-678	66	21	⊂	⊂	PROPN
ejpam-678	66	22	x	x	PUNCT
ejpam-678	66	23	−	−	PROPN
ejpam-678	66	24	{	{	PUNCT
ejpam-678	66	25	y	y	NOUN
ejpam-678	66	26	}	}	PUNCT
ejpam-678	66	27	.	.	PUNCT
ejpam-678	67	1	since	since	SCONJ
ejpam-678	67	2	v	v	NOUN
ejpam-678	67	3	is	be	AUX
ejpam-678	67	4	θ	θ	PROPN
ejpam-678	67	5	-open	-open	PROPN
ejpam-678	67	6	there	there	PRON
ejpam-678	67	7	exists	exist	VERB
ejpam-678	67	8	a	a	DET
ejpam-678	67	9	open	open	ADJ
ejpam-678	67	10	set	set	NOUN
ejpam-678	67	11	u	u	PRON
ejpam-678	67	12	such	such	ADJ
ejpam-678	67	13	that	that	SCONJ
ejpam-678	67	14	x	x	SYM
ejpam-678	67	15	∈	∈	PROPN
ejpam-678	67	16	u	u	NOUN
ejpam-678	67	17	⊂	⊂	PROPN
ejpam-678	67	18	u	u	X
ejpam-678	67	19	⊂	⊂	PROPN
ejpam-678	67	20	v	v	ADP
ejpam-678	67	21	⊂	⊂	PROPN
ejpam-678	67	22	x	x	PUNCT
ejpam-678	67	23	−{y	−{y	NOUN
ejpam-678	67	24	}	}	PUNCT
ejpam-678	67	25	.	.	PUNCT
ejpam-678	68	1	i.e.	i.e.	X
ejpam-678	68	2	;	;	PUNCT
ejpam-678	68	3	x	x	X
ejpam-678	68	4	∈	∈	PROPN
ejpam-678	68	5	u	u	NOUN
ejpam-678	68	6	and	and	CCONJ
ejpam-678	68	7	y	y	PROPN
ejpam-678	68	8	∈	∈	PROPN
ejpam-678	68	9	x	x	PUNCT
ejpam-678	69	1	−	−	PROPN
ejpam-678	69	2	u	u	NOUN
ejpam-678	69	3	.	.	PUNCT
ejpam-678	70	1	again	again	ADV
ejpam-678	70	2	by	by	ADP
ejpam-678	70	3	point	point	NOUN
ejpam-678	70	4	θ	θ	PROPN
ejpam-678	70	5	-regularity	-regularity	NOUN
ejpam-678	70	6	,	,	PUNCT
ejpam-678	70	7	there	there	PRON
ejpam-678	70	8	exist	exist	VERB
ejpam-678	70	9	θ	θ	PROPN
ejpam-678	70	10	-open	-open	NOUN
ejpam-678	70	11	sets	set	NOUN
ejpam-678	70	12	p	p	NOUN
ejpam-678	70	13	and	and	CCONJ
ejpam-678	70	14	q	q	NOUN
ejpam-678	70	15	such	such	ADJ
ejpam-678	70	16	that	that	SCONJ
ejpam-678	70	17	x	x	SYM
ejpam-678	70	18	∈	∈	PROPN
ejpam-678	70	19	p	p	X
ejpam-678	70	20	,	,	PUNCT
ejpam-678	70	21	y	y	PROPN
ejpam-678	70	22	∈	∈	PROPN
ejpam-678	70	23	q	q	NOUN
ejpam-678	70	24	and	and	CCONJ
ejpam-678	70	25	p	p	NOUN
ejpam-678	70	26	∩q	∩q	PROPN
ejpam-678	70	27	=	=	PUNCT
ejpam-678	70	28	ϕ.	ϕ.	PROPN
ejpam-678	70	29	a.	a.	PROPN
ejpam-678	70	30	das	das	PROPN
ejpam-678	70	31	/	/	SYM
ejpam-678	70	32	eur	eur	PROPN
ejpam-678	70	33	.	.	PUNCT
ejpam-678	71	1	j.	j.	PROPN
ejpam-678	71	2	pure	pure	PROPN
ejpam-678	71	3	appl	appl	PROPN
ejpam-678	71	4	.	.	PROPN
ejpam-678	71	5	math	math	PROPN
ejpam-678	71	6	,	,	PUNCT
ejpam-678	71	7	4	4	NUM
ejpam-678	71	8	(	(	PUNCT
ejpam-678	71	9	2011	2011	NUM
ejpam-678	71	10	)	)	PUNCT
ejpam-678	71	11	,	,	PUNCT
ejpam-678	71	12	34	34	NUM
ejpam-678	71	13	-	-	SYM
ejpam-678	71	14	41	41	NUM
ejpam-678	71	15	37	37	NUM
ejpam-678	71	16	theorem	theorem	NOUN
ejpam-678	71	17	2	2	NUM
ejpam-678	71	18	.	.	X
ejpam-678	71	19	for	for	ADP
ejpam-678	71	20	a	a	DET
ejpam-678	71	21	t1	t1	NOUN
ejpam-678	71	22	space	space	NOUN
ejpam-678	71	23	,	,	PUNCT
ejpam-678	71	24	the	the	DET
ejpam-678	71	25	following	follow	VERB
ejpam-678	71	26	statements	statement	NOUN
ejpam-678	71	27	are	be	AUX
ejpam-678	71	28	equivalent	equivalent	ADJ
ejpam-678	71	29	.	.	PUNCT
ejpam-678	72	1	(	(	PUNCT
ejpam-678	72	2	i	i	NOUN
ejpam-678	72	3	)	)	PUNCT
ejpam-678	72	4	x	x	PRON
ejpam-678	72	5	is	be	AUX
ejpam-678	72	6	t3	t3	PROPN
ejpam-678	72	7	.	.	PUNCT
ejpam-678	73	1	(	(	PUNCT
ejpam-678	73	2	ii	ii	NOUN
ejpam-678	73	3	)	)	PUNCT
ejpam-678	73	4	x	x	PUNCT
ejpam-678	73	5	is	be	AUX
ejpam-678	73	6	regular	regular	ADJ
ejpam-678	73	7	.	.	PUNCT
ejpam-678	74	1	(	(	PUNCT
ejpam-678	74	2	iii	iii	X
ejpam-678	74	3	)	)	PUNCT
ejpam-678	74	4	x	x	PUNCT
ejpam-678	74	5	is	be	AUX
ejpam-678	74	6	θ	θ	NOUN
ejpam-678	74	7	-regular	-regular	ADJ
ejpam-678	74	8	.	.	PUNCT
ejpam-678	75	1	(	(	PUNCT
ejpam-678	75	2	iv	iv	X
ejpam-678	75	3	)	)	PUNCT
ejpam-678	75	4	x	x	X
ejpam-678	75	5	is	be	AUX
ejpam-678	75	6	point	point	NOUN
ejpam-678	75	7	θ	θ	NOUN
ejpam-678	75	8	-regular	-regular	ADJ
ejpam-678	75	9	.	.	PUNCT
ejpam-678	76	1	proof	proof	NOUN
ejpam-678	76	2	.	.	PUNCT
ejpam-678	77	1	let	let	VERB
ejpam-678	77	2	x	x	PRON
ejpam-678	77	3	be	be	AUX
ejpam-678	77	4	a	a	DET
ejpam-678	77	5	t1	t1	NOUN
ejpam-678	77	6	point	point	NOUN
ejpam-678	77	7	θ	θ	NOUN
ejpam-678	77	8	-regular	-regular	ADJ
ejpam-678	77	9	space	space	NOUN
ejpam-678	77	10	.	.	PUNCT
ejpam-678	78	1	let	let	VERB
ejpam-678	78	2	x	x	X
ejpam-678	78	3	/∈	/∈	VERB
ejpam-678	79	1	a	a	INTJ
ejpam-678	79	2	,	,	PUNCT
ejpam-678	79	3	where	where	SCONJ
ejpam-678	79	4	a	a	PRON
ejpam-678	79	5	is	be	AUX
ejpam-678	79	6	a	a	DET
ejpam-678	79	7	closed	closed	ADJ
ejpam-678	79	8	set	set	NOUN
ejpam-678	79	9	in	in	ADP
ejpam-678	79	10	x	x	X
ejpam-678	79	11	.	.	PUNCT
ejpam-678	80	1	since	since	SCONJ
ejpam-678	80	2	x	x	PRON
ejpam-678	80	3	is	be	AUX
ejpam-678	80	4	a	a	DET
ejpam-678	80	5	t1	t1	NOUN
ejpam-678	80	6	space	space	NOUN
ejpam-678	80	7	,	,	PUNCT
ejpam-678	80	8	the	the	DET
ejpam-678	80	9	singleton	singleton	NOUN
ejpam-678	80	10	{	{	PUNCT
ejpam-678	80	11	x	x	NOUN
ejpam-678	80	12	}	}	PUNCT
ejpam-678	80	13	is	be	AUX
ejpam-678	80	14	closed	close	VERB
ejpam-678	80	15	and	and	CCONJ
ejpam-678	80	16	contained	contain	VERB
ejpam-678	80	17	in	in	ADP
ejpam-678	80	18	x	x	X
ejpam-678	80	19	−	−	NOUN
ejpam-678	80	20	a.	a.	NOUN
ejpam-678	80	21	by	by	ADP
ejpam-678	80	22	point	point	NOUN
ejpam-678	80	23	θ	θ	PROPN
ejpam-678	80	24	-regularity	-regularity	NOUN
ejpam-678	80	25	of	of	ADP
ejpam-678	80	26	x	x	SYM
ejpam-678	80	27	,	,	PUNCT
ejpam-678	80	28	there	there	PRON
ejpam-678	80	29	exists	exist	VERB
ejpam-678	80	30	a	a	DET
ejpam-678	80	31	θ	θ	PROPN
ejpam-678	80	32	-open	-open	NOUN
ejpam-678	80	33	set	set	VERB
ejpam-678	80	34	v	v	ADP
ejpam-678	80	35	such	such	ADJ
ejpam-678	80	36	that	that	SCONJ
ejpam-678	80	37	x	x	SYM
ejpam-678	80	38	∈	∈	PROPN
ejpam-678	80	39	v	v	ADP
ejpam-678	80	40	⊂	⊂	PROPN
ejpam-678	80	41	x	x	PUNCT
ejpam-678	80	42	−	−	VERB
ejpam-678	80	43	a.	a.	NOUN
ejpam-678	80	44	since	since	SCONJ
ejpam-678	80	45	v	v	NUM
ejpam-678	80	46	is	be	AUX
ejpam-678	80	47	θ	θ	PROPN
ejpam-678	80	48	-open	-open	PROPN
ejpam-678	80	49	there	there	PRON
ejpam-678	80	50	exists	exist	VERB
ejpam-678	80	51	an	an	DET
ejpam-678	80	52	open	open	ADJ
ejpam-678	80	53	set	set	NOUN
ejpam-678	80	54	u	u	PRON
ejpam-678	80	55	such	such	ADJ
ejpam-678	80	56	that	that	SCONJ
ejpam-678	80	57	x	x	SYM
ejpam-678	80	58	∈	∈	PROPN
ejpam-678	80	59	u	u	NOUN
ejpam-678	80	60	⊂	⊂	PROPN
ejpam-678	80	61	u	u	X
ejpam-678	80	62	⊂	⊂	PROPN
ejpam-678	80	63	v	v	ADP
ejpam-678	80	64	⊂	⊂	PROPN
ejpam-678	80	65	x	x	X
ejpam-678	80	66	−	−	VERB
ejpam-678	80	67	a.	a.	NOUN
ejpam-678	80	68	therefore	therefore	ADV
ejpam-678	80	69	x	x	X
ejpam-678	80	70	is	be	AUX
ejpam-678	80	71	regular	regular	ADJ
ejpam-678	80	72	and	and	CCONJ
ejpam-678	80	73	thus	thus	ADV
ejpam-678	80	74	t3	t3	PROPN
ejpam-678	80	75	.	.	PUNCT
ejpam-678	81	1	theorem	theorem	VERB
ejpam-678	81	2	3	3	NUM
ejpam-678	81	3	.	.	PUNCT
ejpam-678	82	1	every	every	DET
ejpam-678	82	2	t1	t1	NOUN
ejpam-678	82	3	point	point	NOUN
ejpam-678	82	4	θ	θ	NOUN
ejpam-678	82	5	-regular	-regular	ADJ
ejpam-678	82	6	space	space	NOUN
ejpam-678	82	7	is	be	AUX
ejpam-678	82	8	hausdorff	hausdorff	NOUN
ejpam-678	82	9	.	.	PUNCT
ejpam-678	83	1	proof	proof	NOUN
ejpam-678	83	2	.	.	PUNCT
ejpam-678	84	1	let	let	VERB
ejpam-678	84	2	x	x	PRON
ejpam-678	84	3	be	be	AUX
ejpam-678	84	4	a	a	DET
ejpam-678	84	5	t1	t1	NOUN
ejpam-678	84	6	point	point	NOUN
ejpam-678	84	7	θ	θ	NOUN
ejpam-678	84	8	-regular	-regular	ADJ
ejpam-678	84	9	space	space	NOUN
ejpam-678	84	10	and	and	CCONJ
ejpam-678	84	11	let	let	VERB
ejpam-678	84	12	x	x	PRON
ejpam-678	84	13	,	,	PUNCT
ejpam-678	84	14	y	y	PROPN
ejpam-678	84	15	be	be	VERB
ejpam-678	84	16	two	two	NUM
ejpam-678	84	17	distinct	distinct	ADJ
ejpam-678	84	18	points	point	NOUN
ejpam-678	84	19	in	in	ADP
ejpam-678	84	20	x	x	X
ejpam-678	84	21	.	.	PUNCT
ejpam-678	85	1	since	since	SCONJ
ejpam-678	85	2	x	x	PROPN
ejpam-678	85	3	is	be	AUX
ejpam-678	85	4	t1	t1	NOUN
ejpam-678	85	5	,	,	PUNCT
ejpam-678	85	6	{	{	PUNCT
ejpam-678	85	7	x	x	X
ejpam-678	85	8	}	}	PUNCT
ejpam-678	85	9	is	be	AUX
ejpam-678	85	10	a	a	DET
ejpam-678	85	11	closed	closed	ADJ
ejpam-678	85	12	singleton	singleton	NOUN
ejpam-678	85	13	contained	contain	VERB
ejpam-678	85	14	in	in	ADP
ejpam-678	85	15	the	the	DET
ejpam-678	85	16	open	open	ADJ
ejpam-678	85	17	set	set	NOUN
ejpam-678	85	18	x	x	X
ejpam-678	85	19	−	−	PROPN
ejpam-678	85	20	{	{	PUNCT
ejpam-678	85	21	y	y	NOUN
ejpam-678	85	22	}	}	PUNCT
ejpam-678	85	23	.	.	PUNCT
ejpam-678	86	1	by	by	ADP
ejpam-678	86	2	point	point	NOUN
ejpam-678	86	3	θ	θ	PROPN
ejpam-678	86	4	-regularity	-regularity	NOUN
ejpam-678	86	5	of	of	ADP
ejpam-678	86	6	x	x	SYM
ejpam-678	86	7	,	,	PUNCT
ejpam-678	86	8	there	there	PRON
ejpam-678	86	9	exists	exist	VERB
ejpam-678	86	10	a	a	DET
ejpam-678	86	11	θ	θ	PROPN
ejpam-678	86	12	-open	-open	NOUN
ejpam-678	86	13	set	set	VERB
ejpam-678	86	14	u	u	PRON
ejpam-678	86	15	such	such	ADJ
ejpam-678	86	16	that	that	SCONJ
ejpam-678	86	17	x	x	SYM
ejpam-678	86	18	∈	∈	PROPN
ejpam-678	86	19	u	u	NOUN
ejpam-678	86	20	⊂	⊂	PROPN
ejpam-678	86	21	x	x	PUNCT
ejpam-678	86	22	−	−	X
ejpam-678	86	23	{	{	PUNCT
ejpam-678	86	24	y	y	NOUN
ejpam-678	86	25	}	}	PUNCT
ejpam-678	86	26	.	.	PUNCT
ejpam-678	87	1	thus	thus	ADV
ejpam-678	87	2	there	there	PRON
ejpam-678	87	3	exists	exist	VERB
ejpam-678	87	4	an	an	DET
ejpam-678	87	5	open	open	ADJ
ejpam-678	87	6	set	set	NOUN
ejpam-678	87	7	v	v	ADP
ejpam-678	87	8	such	such	ADJ
ejpam-678	87	9	that	that	SCONJ
ejpam-678	87	10	x	x	SYM
ejpam-678	87	11	∈	∈	PROPN
ejpam-678	87	12	v	v	ADP
ejpam-678	87	13	⊂	⊂	PROPN
ejpam-678	87	14	v	v	X
ejpam-678	87	15	⊂	⊂	PROPN
ejpam-678	87	16	u	u	X
ejpam-678	87	17	⊂	⊂	PROPN
ejpam-678	87	18	x	x	PUNCT
ejpam-678	87	19	−	−	X
ejpam-678	87	20	{	{	PUNCT
ejpam-678	87	21	y	y	NOUN
ejpam-678	87	22	}	}	PUNCT
ejpam-678	87	23	.	.	PUNCT
ejpam-678	88	1	so	so	ADV
ejpam-678	88	2	v	v	NOUN
ejpam-678	88	3	and	and	CCONJ
ejpam-678	88	4	x	x	NOUN
ejpam-678	88	5	−	−	NOUN
ejpam-678	88	6	v	v	NOUN
ejpam-678	88	7	are	be	AUX
ejpam-678	88	8	two	two	NUM
ejpam-678	88	9	disjoint	disjoint	ADJ
ejpam-678	88	10	open	open	ADJ
ejpam-678	88	11	sets	set	NOUN
ejpam-678	88	12	containing	contain	VERB
ejpam-678	88	13	x	x	X
ejpam-678	88	14	and	and	CCONJ
ejpam-678	88	15	y	y	PROPN
ejpam-678	88	16	respectively	respectively	ADV
ejpam-678	88	17	.	.	PUNCT
ejpam-678	89	1	theorem	theorem	VERB
ejpam-678	89	2	4	4	NUM
ejpam-678	89	3	.	.	X
ejpam-678	90	1	for	for	ADP
ejpam-678	90	2	a	a	DET
ejpam-678	90	3	t2	t2	NOUN
ejpam-678	90	4	space	space	NOUN
ejpam-678	90	5	,	,	PUNCT
ejpam-678	90	6	the	the	DET
ejpam-678	90	7	following	follow	VERB
ejpam-678	90	8	statements	statement	NOUN
ejpam-678	90	9	are	be	AUX
ejpam-678	90	10	equivalent	equivalent	ADJ
ejpam-678	90	11	.	.	PUNCT
ejpam-678	91	1	(	(	PUNCT
ejpam-678	91	2	i	i	NOUN
ejpam-678	91	3	)	)	PUNCT
ejpam-678	91	4	x	x	PRON
ejpam-678	91	5	is	be	AUX
ejpam-678	91	6	t3	t3	PROPN
ejpam-678	91	7	.	.	PUNCT
ejpam-678	92	1	(	(	PUNCT
ejpam-678	92	2	ii	ii	NOUN
ejpam-678	92	3	)	)	PUNCT
ejpam-678	92	4	x	x	PUNCT
ejpam-678	92	5	is	be	AUX
ejpam-678	92	6	regular	regular	ADJ
ejpam-678	92	7	(	(	PUNCT
ejpam-678	92	8	iii	iii	NOUN
ejpam-678	92	9	)	)	PUNCT
ejpam-678	92	10	x	x	PUNCT
ejpam-678	92	11	is	be	AUX
ejpam-678	92	12	θ	θ	PROPN
ejpam-678	92	13	-regular	-regular	ADJ
ejpam-678	92	14	(	(	PUNCT
ejpam-678	92	15	iv	iv	X
ejpam-678	92	16	)	)	PUNCT
ejpam-678	92	17	x	x	X
ejpam-678	92	18	is	be	AUX
ejpam-678	92	19	weakly	weakly	ADJ
ejpam-678	92	20	θ	θ	NOUN
ejpam-678	92	21	-regular	-regular	ADJ
ejpam-678	92	22	(	(	PUNCT
ejpam-678	92	23	v	v	NOUN
ejpam-678	92	24	)	)	PUNCT
ejpam-678	92	25	x	x	X
ejpam-678	92	26	is	be	AUX
ejpam-678	92	27	point	point	NOUN
ejpam-678	92	28	θ	θ	NOUN
ejpam-678	92	29	-regular	-regular	ADJ
ejpam-678	92	30	(	(	PUNCT
ejpam-678	92	31	vi	vi	NOUN
ejpam-678	92	32	)	)	PUNCT
ejpam-678	92	33	x	x	X
ejpam-678	92	34	is	be	AUX
ejpam-678	92	35	point	point	NOUN
ejpam-678	92	36	weakly	weakly	ADJ
ejpam-678	92	37	θ	θ	NOUN
ejpam-678	92	38	-regular	-regular	ADJ
ejpam-678	92	39	proof	proof	NOUN
ejpam-678	92	40	.	.	PUNCT
ejpam-678	93	1	obvious	obvious	ADJ
ejpam-678	93	2	.	.	PUNCT
ejpam-678	94	1	theorem	theorem	VERB
ejpam-678	94	2	5	5	NUM
ejpam-678	94	3	.	.	PUNCT
ejpam-678	95	1	every	every	DET
ejpam-678	95	2	functionally	functionally	ADV
ejpam-678	95	3	θ	θ	PROPN
ejpam-678	95	4	-normal	-normal	ADJ
ejpam-678	95	5	space	space	NOUN
ejpam-678	95	6	is	be	AUX
ejpam-678	95	7	weakly	weakly	ADJ
ejpam-678	95	8	θ	θ	NOUN
ejpam-678	95	9	-regular	-regular	ADJ
ejpam-678	95	10	.	.	PUNCT
ejpam-678	96	1	proof	proof	NOUN
ejpam-678	96	2	.	.	PUNCT
ejpam-678	97	1	let	let	VERB
ejpam-678	97	2	a	a	DET
ejpam-678	97	3	be	be	AUX
ejpam-678	97	4	a	a	DET
ejpam-678	97	5	θ	θ	NOUN
ejpam-678	97	6	-closed	-close	VERB
ejpam-678	97	7	set	set	NOUN
ejpam-678	97	8	contained	contain	VERB
ejpam-678	97	9	in	in	ADP
ejpam-678	97	10	an	an	DET
ejpam-678	97	11	open	open	ADJ
ejpam-678	97	12	set	set	NOUN
ejpam-678	97	13	u	u	NOUN
ejpam-678	97	14	.	.	PUNCT
ejpam-678	98	1	let	let	VERB
ejpam-678	98	2	b	b	NOUN
ejpam-678	98	3	=	=	SYM
ejpam-678	98	4	x	x	SYM
ejpam-678	99	1	−	−	PROPN
ejpam-678	99	2	u	u	NOUN
ejpam-678	99	3	.	.	PUNCT
ejpam-678	100	1	then	then	ADV
ejpam-678	100	2	a	a	PRON
ejpam-678	100	3	and	and	CCONJ
ejpam-678	100	4	b	b	NOUN
ejpam-678	100	5	are	be	AUX
ejpam-678	100	6	disjoint	disjoint	ADJ
ejpam-678	100	7	closed	close	VERB
ejpam-678	100	8	sets	set	NOUN
ejpam-678	100	9	in	in	ADP
ejpam-678	100	10	x	x	X
ejpam-678	100	11	.	.	PUNCT
ejpam-678	101	1	by	by	ADP
ejpam-678	101	2	functional	functional	ADJ
ejpam-678	101	3	θ	θ	PROPN
ejpam-678	101	4	-normality	-normality	NOUN
ejpam-678	101	5	of	of	ADP
ejpam-678	101	6	x	x	PRON
ejpam-678	101	7	,	,	PUNCT
ejpam-678	101	8	there	there	PRON
ejpam-678	101	9	exists	exist	VERB
ejpam-678	101	10	a	a	DET
ejpam-678	101	11	continuous	continuous	ADJ
ejpam-678	101	12	function	function	NOUN
ejpam-678	101	13	f	f	NOUN
ejpam-678	101	14	:	:	PUNCT
ejpam-678	101	15	x	x	X
ejpam-678	101	16	→	→	PUNCT
ejpam-678	102	1	[	[	X
ejpam-678	102	2	0,1	0,1	NUM
ejpam-678	102	3	]	]	PUNCT
ejpam-678	102	4	such	such	ADJ
ejpam-678	102	5	that	that	SCONJ
ejpam-678	102	6	f	f	PROPN
ejpam-678	102	7	(	(	PUNCT
ejpam-678	102	8	a	a	X
ejpam-678	102	9	)	)	PUNCT
ejpam-678	102	10	=	=	SYM
ejpam-678	102	11	0	0	NUM
ejpam-678	102	12	and	and	CCONJ
ejpam-678	102	13	f	f	PROPN
ejpam-678	102	14	(	(	PUNCT
ejpam-678	102	15	b	b	NOUN
ejpam-678	102	16	)	)	PUNCT
ejpam-678	102	17	=	=	SYM
ejpam-678	102	18	1	1	X
ejpam-678	102	19	.	.	PUNCT
ejpam-678	102	20	let	let	VERB
ejpam-678	102	21	v	v	VERB
ejpam-678	102	22	=	=	SYM
ejpam-678	102	23	f	f	NOUN
ejpam-678	102	24	−1[0,1/2	−1[0,1/2	PROPN
ejpam-678	102	25	)	)	PUNCT
ejpam-678	102	26	.	.	PUNCT
ejpam-678	103	1	then	then	ADV
ejpam-678	103	2	a⊂	a⊂	VERB
ejpam-678	103	3	v	v	ADP
ejpam-678	103	4	⊂	⊂	PROPN
ejpam-678	103	5	u	u	NOUN
ejpam-678	103	6	.	.	PUNCT
ejpam-678	104	1	we	we	PRON
ejpam-678	104	2	claim	claim	VERB
ejpam-678	104	3	that	that	SCONJ
ejpam-678	104	4	v	v	NOUN
ejpam-678	104	5	is	be	AUX
ejpam-678	104	6	a	a	DET
ejpam-678	104	7	θ	θ	PROPN
ejpam-678	104	8	-open	-open	NOUN
ejpam-678	104	9	set	set	NOUN
ejpam-678	104	10	.	.	PUNCT
ejpam-678	105	1	let	let	VERB
ejpam-678	105	2	x	x	SYM
ejpam-678	105	3	∈	∈	NOUN
ejpam-678	105	4	v	v	NOUN
ejpam-678	105	5	.	.	PUNCT
ejpam-678	106	1	then	then	ADV
ejpam-678	106	2	f	f	X
ejpam-678	106	3	(	(	PUNCT
ejpam-678	106	4	x	x	X
ejpam-678	106	5	)	)	PUNCT
ejpam-678	106	6	∈	∈	PROPN
ejpam-678	107	1	[	[	X
ejpam-678	107	2	0,1/2	0,1/2	NUM
ejpam-678	107	3	)	)	PUNCT
ejpam-678	107	4	.	.	PUNCT
ejpam-678	108	1	so	so	ADV
ejpam-678	108	2	there	there	PRON
ejpam-678	108	3	is	be	VERB
ejpam-678	108	4	a	a	DET
ejpam-678	108	5	closed	closed	ADJ
ejpam-678	108	6	neighbourhood	neighbourhood	NOUN
ejpam-678	108	7	n	n	NOUN
ejpam-678	108	8	of	of	ADP
ejpam-678	108	9	f	f	PROPN
ejpam-678	108	10	(	(	PUNCT
ejpam-678	108	11	x	x	NOUN
ejpam-678	108	12	)	)	PUNCT
ejpam-678	108	13	contained	contain	VERB
ejpam-678	108	14	in	in	ADP
ejpam-678	108	15	[	[	X
ejpam-678	108	16	0,1/2	0,1/2	NUM
ejpam-678	108	17	)	)	PUNCT
ejpam-678	108	18	⊂	⊂	PROPN
ejpam-678	109	1	[	[	X
ejpam-678	109	2	0,1	0,1	NUM
ejpam-678	109	3	]	]	PUNCT
ejpam-678	109	4	.	.	PUNCT
ejpam-678	110	1	let	let	VERB
ejpam-678	110	2	ux	ux	INTJ
ejpam-678	110	3	=	=	PUNCT
ejpam-678	110	4	int	int	PROPN
ejpam-678	110	5	f	f	PROPN
ejpam-678	110	6	−1(n	−1(n	NOUN
ejpam-678	110	7	)	)	PUNCT
ejpam-678	110	8	.	.	PUNCT
ejpam-678	111	1	then	then	ADV
ejpam-678	111	2	x	x	SYM
ejpam-678	111	3	∈	∈	PROPN
ejpam-678	111	4	ux	ux	PROPN
ejpam-678	111	5	⊂	⊂	X
ejpam-678	111	6	u	u	PROPN
ejpam-678	111	7	x	x	X
ejpam-678	111	8	⊂	⊂	PROPN
ejpam-678	111	9	f	f	X
ejpam-678	111	10	−1(n)⊂	−1(n)⊂	X
ejpam-678	111	11	v	v	NOUN
ejpam-678	111	12	.	.	PUNCT
ejpam-678	112	1	hence	hence	ADV
ejpam-678	112	2	v	v	NOUN
ejpam-678	112	3	is	be	AUX
ejpam-678	112	4	θ	θ	PROPN
ejpam-678	112	5	-open	-open	NOUN
ejpam-678	112	6	.	.	PUNCT
ejpam-678	113	1	therefore	therefore	ADV
ejpam-678	113	2	x	x	X
ejpam-678	113	3	is	be	AUX
ejpam-678	113	4	θ	θ	NOUN
ejpam-678	113	5	-regular	-regular	ADJ
ejpam-678	113	6	.	.	PUNCT
ejpam-678	114	1	a.	a.	PROPN
ejpam-678	114	2	das	das	PROPN
ejpam-678	114	3	/	/	SYM
ejpam-678	114	4	eur	eur	PROPN
ejpam-678	114	5	.	.	PUNCT
ejpam-678	115	1	j.	j.	PROPN
ejpam-678	115	2	pure	pure	PROPN
ejpam-678	115	3	appl	appl	PROPN
ejpam-678	115	4	.	.	PROPN
ejpam-678	115	5	math	math	PROPN
ejpam-678	115	6	,	,	PUNCT
ejpam-678	115	7	4	4	NUM
ejpam-678	115	8	(	(	PUNCT
ejpam-678	115	9	2011	2011	NUM
ejpam-678	115	10	)	)	PUNCT
ejpam-678	115	11	,	,	PUNCT
ejpam-678	115	12	34	34	NUM
ejpam-678	115	13	-	-	SYM
ejpam-678	115	14	41	41	NUM
ejpam-678	115	15	38	38	NUM
ejpam-678	115	16	remark	remark	NOUN
ejpam-678	115	17	1	1	NUM
ejpam-678	115	18	.	.	PUNCT
ejpam-678	116	1	functionally	functionally	ADV
ejpam-678	116	2	θ	θ	PROPN
ejpam-678	116	3	-normal	-normal	ADJ
ejpam-678	116	4	spaces	space	NOUN
ejpam-678	116	5	need	need	AUX
ejpam-678	116	6	not	not	PART
ejpam-678	116	7	be	be	AUX
ejpam-678	116	8	θ	θ	NOUN
ejpam-678	116	9	-regular	-regular	ADJ
ejpam-678	116	10	.	.	PUNCT
ejpam-678	117	1	i.e.	i.e.	X
ejpam-678	117	2	;	;	PUNCT
ejpam-678	117	3	let	let	VERB
ejpam-678	117	4	x	x	PUNCT
ejpam-678	117	5	=	=	PRON
ejpam-678	117	6	{	{	PUNCT
ejpam-678	117	7	a	a	DET
ejpam-678	117	8	,	,	PUNCT
ejpam-678	117	9	b	b	NOUN
ejpam-678	117	10	,	,	PUNCT
ejpam-678	117	11	c	c	NOUN
ejpam-678	117	12	}	}	PUNCT
ejpam-678	117	13	,	,	PUNCT
ejpam-678	117	14	τ	τ	X
ejpam-678	117	15	=	=	PUNCT
ejpam-678	117	16	{	{	PUNCT
ejpam-678	117	17	{	{	PUNCT
ejpam-678	117	18	a	a	PROPN
ejpam-678	117	19	,	,	PUNCT
ejpam-678	117	20	b	b	NOUN
ejpam-678	117	21	}	}	PUNCT
ejpam-678	117	22	,	,	PUNCT
ejpam-678	117	23	{	{	PUNCT
ejpam-678	117	24	b	b	X
ejpam-678	117	25	}	}	PUNCT
ejpam-678	117	26	,	,	PUNCT
ejpam-678	117	27	{	{	PUNCT
ejpam-678	117	28	b	b	NOUN
ejpam-678	117	29	,	,	PUNCT
ejpam-678	117	30	c},φ	c},φ	ADV
ejpam-678	117	31	,	,	PUNCT
ejpam-678	117	32	x	x	PUNCT
ejpam-678	117	33	}	}	PUNCT
ejpam-678	117	34	is	be	AUX
ejpam-678	117	35	a	a	DET
ejpam-678	117	36	functionally	functionally	ADV
ejpam-678	117	37	θ	θ	PROPN
ejpam-678	117	38	-normal	-normal	ADJ
ejpam-678	117	39	space	space	NOUN
ejpam-678	117	40	which	which	PRON
ejpam-678	117	41	is	be	AUX
ejpam-678	117	42	not	not	PART
ejpam-678	117	43	θ	θ	NOUN
ejpam-678	117	44	-regular	-regular	ADJ
ejpam-678	117	45	.	.	PUNCT
ejpam-678	118	1	theorem	theorem	VERB
ejpam-678	118	2	6	6	NUM
ejpam-678	118	3	.	.	PUNCT
ejpam-678	119	1	every	every	PRON
ejpam-678	119	2	nearly	nearly	ADV
ejpam-678	119	3	compact	compact	ADJ
ejpam-678	119	4	weakly	weakly	ADJ
ejpam-678	119	5	θ	θ	NOUN
ejpam-678	119	6	-regular	-regular	ADJ
ejpam-678	119	7	space	space	NOUN
ejpam-678	119	8	is	be	AUX
ejpam-678	119	9	θ	θ	NOUN
ejpam-678	119	10	-normal	-normal	NOUN
ejpam-678	119	11	.	.	PUNCT
ejpam-678	120	1	proof	proof	NOUN
ejpam-678	120	2	.	.	PUNCT
ejpam-678	121	1	let	let	VERB
ejpam-678	121	2	a	a	PRON
ejpam-678	121	3	and	and	CCONJ
ejpam-678	121	4	b	b	NOUN
ejpam-678	121	5	be	be	AUX
ejpam-678	121	6	two	two	NUM
ejpam-678	121	7	disjoint	disjoint	ADJ
ejpam-678	121	8	closed	close	VERB
ejpam-678	121	9	sets	set	NOUN
ejpam-678	121	10	of	of	ADP
ejpam-678	121	11	x	x	PUNCT
ejpam-678	121	12	where	where	SCONJ
ejpam-678	121	13	a	a	PRON
ejpam-678	121	14	is	be	AUX
ejpam-678	121	15	θ	θ	PROPN
ejpam-678	121	16	-closed	-close	VERB
ejpam-678	121	17	.	.	PUNCT
ejpam-678	122	1	then	then	ADV
ejpam-678	122	2	a⊂	a⊂	VERB
ejpam-678	122	3	x	x	X
ejpam-678	122	4	−	−	PROPN
ejpam-678	122	5	b.	b.	NOUN
ejpam-678	122	6	thus	thus	ADV
ejpam-678	122	7	by	by	ADP
ejpam-678	122	8	θ	θ	PROPN
ejpam-678	122	9	-regularity	-regularity	PROPN
ejpam-678	122	10	of	of	ADP
ejpam-678	122	11	x	x	SYM
ejpam-678	122	12	there	there	PRON
ejpam-678	122	13	exist	exist	VERB
ejpam-678	122	14	an	an	DET
ejpam-678	122	15	θ	θ	PROPN
ejpam-678	122	16	-open	-open	NOUN
ejpam-678	122	17	set	set	VERB
ejpam-678	122	18	v	v	ADP
ejpam-678	122	19	such	such	DET
ejpam-678	122	20	that	that	SCONJ
ejpam-678	122	21	a	a	DET
ejpam-678	122	22	⊂	⊂	X
ejpam-678	122	23	v	v	X
ejpam-678	122	24	⊂	⊂	PROPN
ejpam-678	122	25	x	x	X
ejpam-678	122	26	−	−	PROPN
ejpam-678	122	27	b.	b.	NOUN
ejpam-678	122	28	since	since	SCONJ
ejpam-678	122	29	v	v	NUM
ejpam-678	122	30	is	be	AUX
ejpam-678	122	31	θ	θ	PROPN
ejpam-678	122	32	-open	-open	NOUN
ejpam-678	122	33	,	,	PUNCT
ejpam-678	122	34	for	for	ADP
ejpam-678	122	35	every	every	DET
ejpam-678	122	36	x	x	SYM
ejpam-678	122	37	∈	∈	PROPN
ejpam-678	122	38	a	a	PRON
ejpam-678	122	39	there	there	PRON
ejpam-678	122	40	exist	exist	VERB
ejpam-678	122	41	an	an	DET
ejpam-678	122	42	open	open	ADJ
ejpam-678	122	43	set	set	NOUN
ejpam-678	122	44	ux	ux	ADP
ejpam-678	122	45	such	such	ADJ
ejpam-678	122	46	that	that	SCONJ
ejpam-678	122	47	x	x	SYM
ejpam-678	122	48	∈	∈	PROPN
ejpam-678	122	49	ux	ux	NOUN
ejpam-678	122	50	⊂	⊂	X
ejpam-678	122	51	u	u	PROPN
ejpam-678	122	52	x	x	X
ejpam-678	122	53	⊂	⊂	PROPN
ejpam-678	122	54	v	v	ADP
ejpam-678	122	55	⊂	⊂	PROPN
ejpam-678	122	56	x	x	PUNCT
ejpam-678	122	57	−	−	PROPN
ejpam-678	122	58	b.	b.	NOUN
ejpam-678	122	59	then	then	ADV
ejpam-678	122	60	u	u	X
ejpam-678	122	61	=	=	PUNCT
ejpam-678	122	62	{	{	PUNCT
ejpam-678	122	63	ux	ux	INTJ
ejpam-678	122	64	:	:	PUNCT
ejpam-678	122	65	x	x	X
ejpam-678	122	66	∈	∈	PROPN
ejpam-678	122	67	a	a	PRON
ejpam-678	122	68	}	}	PUNCT
ejpam-678	122	69	is	be	AUX
ejpam-678	122	70	an	an	DET
ejpam-678	122	71	open	open	ADJ
ejpam-678	122	72	cover	cover	NOUN
ejpam-678	122	73	of	of	ADP
ejpam-678	122	74	a.	a.	NOUN
ejpam-678	122	75	since	since	SCONJ
ejpam-678	122	76	a	a	PRON
ejpam-678	122	77	is	be	AUX
ejpam-678	122	78	θ	θ	NOUN
ejpam-678	122	79	-closed	-close	VERB
ejpam-678	122	80	,	,	PUNCT
ejpam-678	122	81	by	by	ADP
ejpam-678	122	82	[	[	X
ejpam-678	122	83	2	2	NUM
ejpam-678	122	84	,	,	PUNCT
ejpam-678	122	85	proposition	proposition	NOUN
ejpam-678	122	86	2.1	2.1	NUM
ejpam-678	122	87	]	]	PUNCT
ejpam-678	122	88	,	,	PUNCT
ejpam-678	122	89	a	a	PRON
ejpam-678	122	90	is	be	AUX
ejpam-678	122	91	n	n	PRON
ejpam-678	122	92	-closed	-close	VERB
ejpam-678	122	93	relative	relative	ADJ
ejpam-678	122	94	to	to	ADP
ejpam-678	122	95	x	x	X
ejpam-678	122	96	.	.	PUNCT
ejpam-678	123	1	hence	hence	ADV
ejpam-678	123	2	u	u	NOUN
ejpam-678	123	3	has	have	VERB
ejpam-678	123	4	finite	finite	ADJ
ejpam-678	123	5	subcollection	subcollection	NOUN
ejpam-678	123	6	such	such	ADJ
ejpam-678	123	7	that	that	SCONJ
ejpam-678	123	8	a	a	DET
ejpam-678	123	9	⊂	⊂	PROPN
ejpam-678	123	10	n⋃	n⋃	PROPN
ejpam-678	123	11	i=1	i=1	PROPN
ejpam-678	123	12	intuxi	intuxi	NOUN
ejpam-678	123	13	.	.	PUNCT
ejpam-678	124	1	thus	thus	ADV
ejpam-678	124	2	b	b	X
ejpam-678	124	3	⊂	⊂	PROPN
ejpam-678	124	4	n⋂	n⋂	VERB
ejpam-678	124	5	i=1	i=1	PROPN
ejpam-678	125	1	(	(	PUNCT
ejpam-678	125	2	x	x	SYM
ejpam-678	125	3	−	−	PROPN
ejpam-678	125	4	uxi	uxi	NOUN
ejpam-678	125	5	)	)	PUNCT
ejpam-678	125	6	.	.	PUNCT
ejpam-678	126	1	therefore	therefore	ADV
ejpam-678	126	2	x	x	X
ejpam-678	126	3	is	be	AUX
ejpam-678	126	4	θ	θ	NOUN
ejpam-678	126	5	-normal	-normal	ADJ
ejpam-678	126	6	.	.	PUNCT
ejpam-678	127	1	corollary	corollary	ADJ
ejpam-678	127	2	1	1	NUM
ejpam-678	127	3	.	.	PUNCT
ejpam-678	128	1	every	every	PRON
ejpam-678	128	2	nearly	nearly	ADV
ejpam-678	128	3	compact	compact	ADJ
ejpam-678	128	4	θ	θ	NOUN
ejpam-678	128	5	-regular	-regular	ADJ
ejpam-678	128	6	space	space	NOUN
ejpam-678	128	7	is	be	AUX
ejpam-678	128	8	normal	normal	ADJ
ejpam-678	128	9	.	.	PUNCT
ejpam-678	129	1	proof	proof	NOUN
ejpam-678	129	2	.	.	PUNCT
ejpam-678	130	1	the	the	DET
ejpam-678	130	2	above	above	ADJ
ejpam-678	130	3	result	result	NOUN
ejpam-678	130	4	is	be	AUX
ejpam-678	130	5	obvious	obvious	ADJ
ejpam-678	130	6	,	,	PUNCT
ejpam-678	130	7	since	since	SCONJ
ejpam-678	130	8	every	every	PRON
ejpam-678	130	9	θ	θ	NOUN
ejpam-678	130	10	-regular	-regular	ADJ
ejpam-678	130	11	θ	θ	NOUN
ejpam-678	130	12	-normal	-normal	ADJ
ejpam-678	130	13	space	space	NOUN
ejpam-678	130	14	is	be	AUX
ejpam-678	130	15	normal	normal	ADJ
ejpam-678	130	16	.	.	PUNCT
ejpam-678	131	1	remark	remark	NOUN
ejpam-678	131	2	2	2	NUM
ejpam-678	131	3	.	.	PUNCT
ejpam-678	132	1	the	the	DET
ejpam-678	132	2	following	follow	VERB
ejpam-678	132	3	example	example	NOUN
ejpam-678	132	4	shows	show	VERB
ejpam-678	132	5	that	that	SCONJ
ejpam-678	132	6	the	the	DET
ejpam-678	132	7	hypothesis	hypothesis	NOUN
ejpam-678	132	8	of	of	ADP
ejpam-678	132	9	θ	θ	PROPN
ejpam-678	132	10	-regularity	-regularity	NOUN
ejpam-678	132	11	in	in	ADP
ejpam-678	132	12	the	the	DET
ejpam-678	132	13	above	above	ADJ
ejpam-678	132	14	corollary	corollary	NOUN
ejpam-678	132	15	can	can	AUX
ejpam-678	132	16	not	not	PART
ejpam-678	132	17	be	be	AUX
ejpam-678	132	18	weakened	weaken	VERB
ejpam-678	132	19	to	to	ADP
ejpam-678	132	20	“	"	PUNCT
ejpam-678	132	21	weak	weak	ADJ
ejpam-678	132	22	θ	θ	PROPN
ejpam-678	132	23	-regularity	-regularity	NOUN
ejpam-678	132	24	”	"	PUNCT
ejpam-678	132	25	as	as	SCONJ
ejpam-678	132	26	nearly	nearly	ADV
ejpam-678	132	27	compact	compact	ADJ
ejpam-678	132	28	weakly	weakly	ADJ
ejpam-678	132	29	θ	θ	NOUN
ejpam-678	132	30	-regular	-regular	ADJ
ejpam-678	132	31	spaces	space	NOUN
ejpam-678	132	32	need	need	AUX
ejpam-678	132	33	not	not	PART
ejpam-678	132	34	be	be	AUX
ejpam-678	132	35	almost	almost	ADV
ejpam-678	132	36	normal	normal	ADJ
ejpam-678	132	37	.	.	PUNCT
ejpam-678	133	1	e.g.	e.g.	ADV
ejpam-678	133	2	;	;	PUNCT
ejpam-678	133	3	the	the	DET
ejpam-678	133	4	set	set	NOUN
ejpam-678	133	5	x	x	X
ejpam-678	133	6	=	=	X
ejpam-678	133	7	{	{	PUNCT
ejpam-678	133	8	a	a	PRON
ejpam-678	133	9	,	,	PUNCT
ejpam-678	133	10	b	b	NOUN
ejpam-678	133	11	,	,	PUNCT
ejpam-678	133	12	c	c	NOUN
ejpam-678	133	13	,	,	PUNCT
ejpam-678	133	14	d	d	NOUN
ejpam-678	133	15	}	}	PUNCT
ejpam-678	133	16	with	with	ADP
ejpam-678	133	17	topology	topology	NOUN
ejpam-678	133	18	τ	τ	X
ejpam-678	133	19	=	=	SYM
ejpam-678	133	20	{	{	PUNCT
ejpam-678	133	21	{	{	PUNCT
ejpam-678	133	22	a	a	PROPN
ejpam-678	133	23	,	,	PUNCT
ejpam-678	133	24	b	b	NOUN
ejpam-678	133	25	}	}	PUNCT
ejpam-678	133	26	,	,	PUNCT
ejpam-678	133	27	{	{	PUNCT
ejpam-678	133	28	b	b	X
ejpam-678	133	29	}	}	PUNCT
ejpam-678	133	30	,	,	PUNCT
ejpam-678	133	31	{	{	PUNCT
ejpam-678	133	32	b	b	X
ejpam-678	133	33	,	,	PUNCT
ejpam-678	133	34	c	c	NOUN
ejpam-678	133	35	}	}	PUNCT
ejpam-678	133	36	,	,	PUNCT
ejpam-678	133	37	{	{	PUNCT
ejpam-678	133	38	c	c	X
ejpam-678	133	39	}	}	PUNCT
ejpam-678	133	40	,	,	PUNCT
ejpam-678	133	41	{	{	PUNCT
ejpam-678	133	42	b	b	X
ejpam-678	133	43	,	,	PUNCT
ejpam-678	133	44	c	c	NOUN
ejpam-678	133	45	,	,	PUNCT
ejpam-678	133	46	d	d	NOUN
ejpam-678	133	47	}	}	PUNCT
ejpam-678	133	48	,	,	PUNCT
ejpam-678	133	49	{	{	PUNCT
ejpam-678	133	50	a	a	DET
ejpam-678	133	51	,	,	PUNCT
ejpam-678	133	52	b	b	NOUN
ejpam-678	133	53	,	,	PUNCT
ejpam-678	133	54	c	c	NOUN
ejpam-678	133	55	}	}	PUNCT
ejpam-678	133	56	,	,	PUNCT
ejpam-678	133	57	x	x	X
ejpam-678	133	58	,	,	PUNCT
ejpam-678	133	59	;	;	PUNCT
ejpam-678	133	60	}	}	PUNCT
ejpam-678	133	61	is	be	AUX
ejpam-678	133	62	compact	compact	ADJ
ejpam-678	133	63	and	and	CCONJ
ejpam-678	133	64	weakly	weakly	ADJ
ejpam-678	134	1	θ	θ	NOUN
ejpam-678	134	2	-regular	-regular	ADJ
ejpam-678	134	3	but	but	CCONJ
ejpam-678	134	4	not	not	PART
ejpam-678	134	5	almost	almost	ADV
ejpam-678	134	6	normal	normal	ADJ
ejpam-678	134	7	as	as	ADP
ejpam-678	134	8	the	the	DET
ejpam-678	134	9	regularly	regularly	ADV
ejpam-678	134	10	closed	closed	ADJ
ejpam-678	134	11	set	set	ADJ
ejpam-678	134	12	{	{	PUNCT
ejpam-678	134	13	c	c	NOUN
ejpam-678	134	14	,	,	PUNCT
ejpam-678	134	15	d	d	NOUN
ejpam-678	134	16	}	}	PUNCT
ejpam-678	134	17	and	and	CCONJ
ejpam-678	134	18	closed	close	VERB
ejpam-678	134	19	set	set	VERB
ejpam-678	134	20	{	{	PUNCT
ejpam-678	134	21	a	a	PRON
ejpam-678	134	22	}	}	PUNCT
ejpam-678	134	23	can	can	AUX
ejpam-678	134	24	not	not	PART
ejpam-678	134	25	be	be	AUX
ejpam-678	134	26	separated	separate	VERB
ejpam-678	134	27	by	by	ADP
ejpam-678	134	28	disjoint	disjoint	ADJ
ejpam-678	134	29	open	open	ADJ
ejpam-678	134	30	sets	set	NOUN
ejpam-678	134	31	.	.	PUNCT
ejpam-678	135	1	it	it	PRON
ejpam-678	135	2	is	be	AUX
ejpam-678	135	3	well	well	ADV
ejpam-678	135	4	known	know	VERB
ejpam-678	135	5	that	that	SCONJ
ejpam-678	135	6	every	every	DET
ejpam-678	135	7	compact	compact	ADJ
ejpam-678	135	8	hausdorff	hausdorff	NOUN
ejpam-678	135	9	space	space	NOUN
ejpam-678	135	10	is	be	AUX
ejpam-678	135	11	normal	normal	ADJ
ejpam-678	135	12	.	.	PUNCT
ejpam-678	136	1	however	however	ADV
ejpam-678	136	2	,	,	PUNCT
ejpam-678	136	3	in	in	ADP
ejpam-678	136	4	the	the	DET
ejpam-678	136	5	absence	absence	NOUN
ejpam-678	136	6	of	of	ADP
ejpam-678	136	7	hausdorffness	hausdorffness	NOUN
ejpam-678	136	8	or	or	CCONJ
ejpam-678	136	9	regularity	regularity	NOUN
ejpam-678	136	10	a	a	DET
ejpam-678	136	11	compact	compact	ADJ
ejpam-678	136	12	space	space	NOUN
ejpam-678	136	13	may	may	AUX
ejpam-678	136	14	fail	fail	VERB
ejpam-678	136	15	to	to	PART
ejpam-678	136	16	be	be	AUX
ejpam-678	136	17	normal	normal	ADJ
ejpam-678	136	18	.	.	PUNCT
ejpam-678	137	1	thus	thus	ADV
ejpam-678	137	2	it	it	PRON
ejpam-678	137	3	is	be	AUX
ejpam-678	137	4	useful	useful	ADJ
ejpam-678	137	5	to	to	PART
ejpam-678	137	6	know	know	VERB
ejpam-678	137	7	which	which	DET
ejpam-678	137	8	topological	topological	ADJ
ejpam-678	137	9	property	property	NOUN
ejpam-678	137	10	weaker	weak	ADJ
ejpam-678	137	11	than	than	ADP
ejpam-678	137	12	hausdorffness	hausdorffness	NOUN
ejpam-678	137	13	with	with	ADP
ejpam-678	137	14	compactness	compactness	NOUN
ejpam-678	137	15	implies	imply	VERB
ejpam-678	137	16	normality	normality	NOUN
ejpam-678	137	17	.	.	PUNCT
ejpam-678	138	1	the	the	DET
ejpam-678	138	2	property	property	NOUN
ejpam-678	138	3	of	of	ADP
ejpam-678	138	4	being	be	AUX
ejpam-678	138	5	a	a	DET
ejpam-678	138	6	t1	t1	NOUN
ejpam-678	138	7	-	-	PUNCT
ejpam-678	138	8	space	space	NOUN
ejpam-678	138	9	fails	fail	VERB
ejpam-678	138	10	to	to	PART
ejpam-678	138	11	do	do	VERB
ejpam-678	138	12	the	the	DET
ejpam-678	138	13	job	job	NOUN
ejpam-678	138	14	since	since	SCONJ
ejpam-678	138	15	the	the	DET
ejpam-678	138	16	cofinite	cofinite	NOUN
ejpam-678	138	17	topology	topology	NOUN
ejpam-678	138	18	on	on	ADP
ejpam-678	138	19	an	an	DET
ejpam-678	138	20	infinite	infinite	ADJ
ejpam-678	138	21	set	set	NOUN
ejpam-678	138	22	is	be	AUX
ejpam-678	138	23	a	a	DET
ejpam-678	138	24	compact	compact	ADJ
ejpam-678	138	25	t1	t1	NOUN
ejpam-678	138	26	space	space	NOUN
ejpam-678	138	27	which	which	PRON
ejpam-678	138	28	is	be	AUX
ejpam-678	138	29	not	not	PART
ejpam-678	138	30	normal	normal	ADJ
ejpam-678	138	31	.	.	PUNCT
ejpam-678	139	1	however	however	ADV
ejpam-678	139	2	,	,	PUNCT
ejpam-678	139	3	it	it	PRON
ejpam-678	139	4	is	be	AUX
ejpam-678	139	5	well	well	ADV
ejpam-678	139	6	known	know	VERB
ejpam-678	139	7	that	that	SCONJ
ejpam-678	139	8	every	every	DET
ejpam-678	139	9	compact	compact	ADJ
ejpam-678	139	10	r1	r1	NOUN
ejpam-678	139	11	-	-	PUNCT
ejpam-678	139	12	space	space	NOUN
ejpam-678	139	13	is	be	AUX
ejpam-678	139	14	normal	normal	ADJ
ejpam-678	139	15	the	the	DET
ejpam-678	139	16	following	following	ADJ
ejpam-678	139	17	result	result	NOUN
ejpam-678	139	18	of	of	ADP
ejpam-678	139	19	[	[	X
ejpam-678	139	20	6	6	NUM
ejpam-678	139	21	]	]	PUNCT
ejpam-678	139	22	is	be	AUX
ejpam-678	139	23	an	an	DET
ejpam-678	139	24	improvement	improvement	NOUN
ejpam-678	139	25	of	of	ADP
ejpam-678	139	26	well	well	ADV
ejpam-678	139	27	known	know	VERB
ejpam-678	139	28	results	result	NOUN
ejpam-678	139	29	such	such	ADJ
ejpam-678	139	30	as	as	ADP
ejpam-678	139	31	every	every	DET
ejpam-678	139	32	compact	compact	ADJ
ejpam-678	139	33	hausdorff	hausdorff	NOUN
ejpam-678	139	34	space	space	NOUN
ejpam-678	139	35	is	be	AUX
ejpam-678	139	36	normal	normal	ADJ
ejpam-678	139	37	and	and	CCONJ
ejpam-678	139	38	every	every	DET
ejpam-678	139	39	compact	compact	ADJ
ejpam-678	139	40	(	(	PUNCT
ejpam-678	139	41	or	or	CCONJ
ejpam-678	139	42	lindelöf	lindelöf	NOUN
ejpam-678	139	43	)	)	PUNCT
ejpam-678	139	44	regular	regular	ADJ
ejpam-678	139	45	space	space	NOUN
ejpam-678	139	46	is	be	AUX
ejpam-678	139	47	normal	normal	ADJ
ejpam-678	139	48	.	.	PUNCT
ejpam-678	140	1	theorem	theorem	VERB
ejpam-678	140	2	7	7	NUM
ejpam-678	140	3	.	.	PUNCT
ejpam-678	141	1	every	every	DET
ejpam-678	141	2	paracompact	paracompact	ADJ
ejpam-678	141	3	θ	θ	NOUN
ejpam-678	141	4	-regular	-regular	ADJ
ejpam-678	141	5	space	space	NOUN
ejpam-678	141	6	is	be	AUX
ejpam-678	141	7	normal	normal	ADJ
ejpam-678	141	8	.	.	PUNCT
ejpam-678	142	1	theorem	theorem	VERB
ejpam-678	142	2	8	8	NUM
ejpam-678	142	3	.	.	PUNCT
ejpam-678	143	1	every	every	DET
ejpam-678	143	2	lindelöf	lindelöf	NOUN
ejpam-678	143	3	θ	θ	NOUN
ejpam-678	143	4	-regular	-regular	ADJ
ejpam-678	143	5	space	space	NOUN
ejpam-678	143	6	is	be	AUX
ejpam-678	143	7	normal	normal	ADJ
ejpam-678	143	8	.	.	PUNCT
ejpam-678	144	1	remark	remark	NOUN
ejpam-678	144	2	3	3	NUM
ejpam-678	144	3	.	.	PUNCT
ejpam-678	145	1	the	the	DET
ejpam-678	145	2	condition	condition	NOUN
ejpam-678	145	3	of	of	ADP
ejpam-678	145	4	θ	θ	PROPN
ejpam-678	145	5	-regularity	-regularity	NOUN
ejpam-678	145	6	in	in	ADP
ejpam-678	145	7	the	the	DET
ejpam-678	145	8	above	above	ADJ
ejpam-678	145	9	theorem	theorem	NOUN
ejpam-678	145	10	can	can	AUX
ejpam-678	145	11	not	not	PART
ejpam-678	145	12	be	be	AUX
ejpam-678	145	13	weakened	weaken	VERB
ejpam-678	145	14	as	as	SCONJ
ejpam-678	145	15	the	the	DET
ejpam-678	145	16	example	example	NOUN
ejpam-678	145	17	cited	cite	VERB
ejpam-678	145	18	in	in	ADP
ejpam-678	145	19	remark	remark	NOUN
ejpam-678	145	20	2	2	NUM
ejpam-678	145	21	is	be	AUX
ejpam-678	145	22	a	a	DET
ejpam-678	145	23	paracompact	paracompact	ADJ
ejpam-678	145	24	weakly	weakly	ADJ
ejpam-678	145	25	θ	θ	NOUN
ejpam-678	145	26	-regular	-regular	ADJ
ejpam-678	145	27	space	space	NOUN
ejpam-678	145	28	which	which	PRON
ejpam-678	145	29	fails	fail	VERB
ejpam-678	145	30	to	to	PART
ejpam-678	145	31	be	be	AUX
ejpam-678	145	32	almost	almost	ADV
ejpam-678	145	33	normal	normal	ADJ
ejpam-678	145	34	.	.	PUNCT
ejpam-678	146	1	although	although	SCONJ
ejpam-678	146	2	every	every	DET
ejpam-678	146	3	compact	compact	ADJ
ejpam-678	146	4	θ	θ	NOUN
ejpam-678	146	5	-regular	-regular	ADJ
ejpam-678	146	6	space	space	NOUN
ejpam-678	146	7	is	be	AUX
ejpam-678	146	8	normal	normal	ADJ
ejpam-678	146	9	,	,	PUNCT
ejpam-678	146	10	but	but	CCONJ
ejpam-678	146	11	it	it	PRON
ejpam-678	146	12	is	be	AUX
ejpam-678	146	13	in	in	ADP
ejpam-678	146	14	the	the	DET
ejpam-678	146	15	absence	absence	NOUN
ejpam-678	146	16	of	of	ADP
ejpam-678	146	17	t1	t1	NOUN
ejpam-678	146	18	property	property	NOUN
ejpam-678	146	19	,	,	PUNCT
ejpam-678	146	20	as	as	SCONJ
ejpam-678	146	21	every	every	DET
ejpam-678	146	22	t1	t1	NOUN
ejpam-678	146	23	θ	θ	NOUN
ejpam-678	146	24	-regular	-regular	ADJ
ejpam-678	146	25	space	space	NOUN
ejpam-678	146	26	is	be	AUX
ejpam-678	146	27	regular	regular	ADJ
ejpam-678	146	28	.	.	PUNCT
ejpam-678	147	1	thus	thus	ADV
ejpam-678	147	2	it	it	PRON
ejpam-678	147	3	is	be	AUX
ejpam-678	147	4	very	very	ADV
ejpam-678	147	5	natural	natural	ADJ
ejpam-678	147	6	to	to	PART
ejpam-678	147	7	ask	ask	VERB
ejpam-678	147	8	the	the	DET
ejpam-678	147	9	following	follow	VERB
ejpam-678	147	10	question	question	NOUN
ejpam-678	147	11	.	.	PUNCT
ejpam-678	148	1	question	question	NOUN
ejpam-678	148	2	2	2	NUM
ejpam-678	148	3	.	.	NOUN
ejpam-678	148	4	which	which	PRON
ejpam-678	148	5	non	non	ADJ
ejpam-678	148	6	-	-	ADJ
ejpam-678	148	7	regular	regular	ADJ
ejpam-678	148	8	,	,	PUNCT
ejpam-678	148	9	non	non	ADJ
ejpam-678	148	10	-	-	ADJ
ejpam-678	148	11	hausdorff	hausdorff	ADJ
ejpam-678	148	12	,	,	PUNCT
ejpam-678	148	13	t1	t1	ADJ
ejpam-678	148	14	-	-	ADJ
ejpam-678	148	15	compact	compact	ADJ
ejpam-678	148	16	spaces	space	NOUN
ejpam-678	148	17	are	be	AUX
ejpam-678	148	18	normal	normal	ADJ
ejpam-678	148	19	?	?	PUNCT
ejpam-678	149	1	a.	a.	NOUN
ejpam-678	149	2	das	das	PROPN
ejpam-678	149	3	/	/	SYM
ejpam-678	149	4	eur	eur	PROPN
ejpam-678	149	5	.	.	PUNCT
ejpam-678	150	1	j.	j.	PROPN
ejpam-678	150	2	pure	pure	PROPN
ejpam-678	150	3	appl	appl	PROPN
ejpam-678	150	4	.	.	PROPN
ejpam-678	150	5	math	math	PROPN
ejpam-678	150	6	,	,	PUNCT
ejpam-678	150	7	4	4	NUM
ejpam-678	150	8	(	(	PUNCT
ejpam-678	150	9	2011	2011	NUM
ejpam-678	150	10	)	)	PUNCT
ejpam-678	150	11	,	,	PUNCT
ejpam-678	150	12	34	34	NUM
ejpam-678	150	13	-	-	SYM
ejpam-678	150	14	41	41	NUM
ejpam-678	150	15	39	39	NUM
ejpam-678	150	16	let	let	VERB
ejpam-678	150	17	us	we	PRON
ejpam-678	150	18	recall	recall	VERB
ejpam-678	150	19	that	that	SCONJ
ejpam-678	150	20	a	a	DET
ejpam-678	150	21	space	space	NOUN
ejpam-678	150	22	x	x	PUNCT
ejpam-678	150	23	is	be	AUX
ejpam-678	150	24	seminormal	seminormal	ADJ
ejpam-678	150	25	if	if	SCONJ
ejpam-678	150	26	for	for	SCONJ
ejpam-678	150	27	every	every	DET
ejpam-678	150	28	closed	close	VERB
ejpam-678	150	29	set	set	VERB
ejpam-678	150	30	f	f	PROPN
ejpam-678	150	31	contained	contain	VERB
ejpam-678	150	32	in	in	ADP
ejpam-678	150	33	an	an	DET
ejpam-678	150	34	open	open	ADJ
ejpam-678	150	35	set	set	NOUN
ejpam-678	150	36	u	u	NOUN
ejpam-678	150	37	there	there	PRON
ejpam-678	150	38	exists	exist	VERB
ejpam-678	150	39	a	a	DET
ejpam-678	150	40	regularly	regularly	ADV
ejpam-678	150	41	open	open	ADJ
ejpam-678	150	42	set	set	VERB
ejpam-678	150	43	v	v	ADP
ejpam-678	150	44	such	such	DET
ejpam-678	150	45	that	that	SCONJ
ejpam-678	150	46	f	f	PROPN
ejpam-678	150	47	⊂	⊂	PROPN
ejpam-678	150	48	v	v	ADP
ejpam-678	150	49	⊂	⊂	PROPN
ejpam-678	150	50	u	u	PROPN
ejpam-678	150	51	.	.	PUNCT
ejpam-678	151	1	a	a	DET
ejpam-678	151	2	space	space	NOUN
ejpam-678	151	3	is	be	AUX
ejpam-678	151	4	said	say	VERB
ejpam-678	151	5	to	to	PART
ejpam-678	151	6	be	be	AUX
ejpam-678	151	7	θ	θ	PROPN
ejpam-678	151	8	-seminormal	-seminormal	PROPN
ejpam-678	151	9	[	[	X
ejpam-678	151	10	15	15	NUM
ejpam-678	151	11	]	]	X
ejpam-678	151	12	if	if	SCONJ
ejpam-678	151	13	for	for	SCONJ
ejpam-678	151	14	every	every	DET
ejpam-678	151	15	θ	θ	PROPN
ejpam-678	151	16	-closed	-close	VERB
ejpam-678	151	17	set	set	NOUN
ejpam-678	151	18	f	f	PROPN
ejpam-678	151	19	contained	contain	VERB
ejpam-678	151	20	in	in	ADP
ejpam-678	151	21	an	an	DET
ejpam-678	151	22	open	open	ADJ
ejpam-678	151	23	set	set	NOUN
ejpam-678	151	24	u	u	NOUN
ejpam-678	151	25	there	there	PRON
ejpam-678	151	26	exists	exist	VERB
ejpam-678	151	27	a	a	DET
ejpam-678	151	28	regularly	regularly	ADV
ejpam-678	151	29	open	open	ADJ
ejpam-678	151	30	set	set	VERB
ejpam-678	151	31	v	v	ADP
ejpam-678	152	1	such	such	DET
ejpam-678	152	2	that	that	SCONJ
ejpam-678	152	3	f	f	PROPN
ejpam-678	152	4	⊂	⊂	PROPN
ejpam-678	152	5	v	v	ADP
ejpam-678	152	6	⊂	⊂	PROPN
ejpam-678	152	7	u	u	PROPN
ejpam-678	152	8	.	.	PUNCT
ejpam-678	152	9	example	example	NOUN
ejpam-678	153	1	4	4	NUM
ejpam-678	153	2	.	.	PUNCT
ejpam-678	153	3	a	a	DET
ejpam-678	153	4	seminormal	seminormal	ADJ
ejpam-678	153	5	space	space	NOUN
ejpam-678	153	6	which	which	PRON
ejpam-678	153	7	is	be	AUX
ejpam-678	153	8	not	not	PART
ejpam-678	153	9	θ	θ	NOUN
ejpam-678	153	10	-regular	-regular	ADJ
ejpam-678	153	11	.	.	PUNCT
ejpam-678	154	1	let	let	VERB
ejpam-678	154	2	x	x	PRON
ejpam-678	154	3	be	be	AUX
ejpam-678	154	4	the	the	DET
ejpam-678	154	5	set	set	NOUN
ejpam-678	154	6	of	of	ADP
ejpam-678	154	7	positive	positive	ADJ
ejpam-678	154	8	integers	integer	NOUN
ejpam-678	154	9	.	.	PUNCT
ejpam-678	155	1	define	define	VERB
ejpam-678	155	2	a	a	DET
ejpam-678	155	3	topology	topology	NOUN
ejpam-678	155	4	on	on	ADP
ejpam-678	155	5	x	x	PUNCT
ejpam-678	155	6	by	by	ADP
ejpam-678	155	7	taking	take	VERB
ejpam-678	155	8	every	every	DET
ejpam-678	155	9	odd	odd	ADJ
ejpam-678	155	10	integer	integer	NOUN
ejpam-678	155	11	to	to	PART
ejpam-678	155	12	be	be	AUX
ejpam-678	155	13	open	open	ADJ
ejpam-678	155	14	and	and	CCONJ
ejpam-678	155	15	a	a	DET
ejpam-678	155	16	set	set	NOUN
ejpam-678	155	17	u	u	X
ejpam-678	155	18	⊂	⊂	PROPN
ejpam-678	155	19	x	x	X
ejpam-678	155	20	is	be	AUX
ejpam-678	155	21	open	open	ADJ
ejpam-678	155	22	if	if	SCONJ
ejpam-678	155	23	for	for	ADP
ejpam-678	155	24	every	every	DET
ejpam-678	155	25	even	even	ADV
ejpam-678	155	26	integer	integer	NOUN
ejpam-678	155	27	p	p	PROPN
ejpam-678	155	28	∈	∈	PROPN
ejpam-678	155	29	u	u	NOUN
ejpam-678	155	30	,	,	PUNCT
ejpam-678	155	31	the	the	DET
ejpam-678	155	32	predecessor	predecessor	NOUN
ejpam-678	155	33	and	and	CCONJ
ejpam-678	155	34	the	the	DET
ejpam-678	155	35	successor	successor	NOUN
ejpam-678	155	36	of	of	ADP
ejpam-678	155	37	p	p	NOUN
ejpam-678	155	38	are	be	AUX
ejpam-678	155	39	also	also	ADV
ejpam-678	155	40	in	in	ADP
ejpam-678	155	41	u.	u.	NOUN
ejpam-678	155	42	since	since	SCONJ
ejpam-678	155	43	every	every	DET
ejpam-678	155	44	open	open	ADJ
ejpam-678	155	45	set	set	NOUN
ejpam-678	155	46	is	be	AUX
ejpam-678	155	47	regularly	regularly	ADV
ejpam-678	155	48	open	open	ADJ
ejpam-678	155	49	in	in	ADP
ejpam-678	155	50	this	this	DET
ejpam-678	155	51	topology	topology	NOUN
ejpam-678	155	52	,	,	PUNCT
ejpam-678	155	53	the	the	DET
ejpam-678	155	54	space	space	NOUN
ejpam-678	155	55	is	be	AUX
ejpam-678	155	56	seminormal	seminormal	ADJ
ejpam-678	155	57	but	but	CCONJ
ejpam-678	155	58	the	the	DET
ejpam-678	155	59	space	space	NOUN
ejpam-678	155	60	is	be	AUX
ejpam-678	155	61	not	not	PART
ejpam-678	155	62	θ	θ	NOUN
ejpam-678	155	63	-regular	-regular	ADJ
ejpam-678	155	64	.	.	PUNCT
ejpam-678	156	1	theorem	theorem	NOUN
ejpam-678	156	2	9	9	NUM
ejpam-678	156	3	.	.	PUNCT
ejpam-678	157	1	every	every	DET
ejpam-678	157	2	almost	almost	ADV
ejpam-678	157	3	regular	regular	ADJ
ejpam-678	157	4	seminormal	seminormal	ADJ
ejpam-678	157	5	space	space	NOUN
ejpam-678	157	6	is	be	AUX
ejpam-678	157	7	θ	θ	NOUN
ejpam-678	157	8	-regular	-regular	ADJ
ejpam-678	157	9	.	.	PUNCT
ejpam-678	158	1	proof	proof	NOUN
ejpam-678	158	2	.	.	PUNCT
ejpam-678	159	1	let	let	VERB
ejpam-678	159	2	f	f	PRON
ejpam-678	159	3	be	be	AUX
ejpam-678	159	4	a	a	DET
ejpam-678	159	5	closed	closed	ADJ
ejpam-678	159	6	set	set	NOUN
ejpam-678	159	7	contained	contain	VERB
ejpam-678	159	8	in	in	ADP
ejpam-678	159	9	an	an	DET
ejpam-678	159	10	open	open	ADJ
ejpam-678	159	11	set	set	NOUN
ejpam-678	159	12	u	u	NOUN
ejpam-678	159	13	.	.	PUNCT
ejpam-678	160	1	since	since	SCONJ
ejpam-678	160	2	x	x	PRON
ejpam-678	160	3	is	be	AUX
ejpam-678	160	4	seminormal	seminormal	ADJ
ejpam-678	160	5	there	there	PRON
ejpam-678	160	6	exists	exist	VERB
ejpam-678	160	7	a	a	DET
ejpam-678	160	8	regularly	regularly	ADV
ejpam-678	160	9	open	open	ADJ
ejpam-678	160	10	set	set	VERB
ejpam-678	160	11	v	v	ADP
ejpam-678	160	12	such	such	DET
ejpam-678	160	13	that	that	SCONJ
ejpam-678	160	14	f	f	PROPN
ejpam-678	160	15	⊂	⊂	PROPN
ejpam-678	160	16	v	v	ADP
ejpam-678	160	17	⊂	⊂	PROPN
ejpam-678	160	18	u	u	PROPN
ejpam-678	160	19	.	.	PUNCT
ejpam-678	161	1	since	since	SCONJ
ejpam-678	161	2	in	in	ADP
ejpam-678	161	3	an	an	DET
ejpam-678	161	4	almost	almost	ADV
ejpam-678	161	5	regular	regular	ADJ
ejpam-678	161	6	space	space	NOUN
ejpam-678	161	7	every	every	PRON
ejpam-678	161	8	regularly	regularly	ADV
ejpam-678	161	9	open	open	ADJ
ejpam-678	161	10	set	set	NOUN
ejpam-678	161	11	is	be	AUX
ejpam-678	161	12	θ	θ	PROPN
ejpam-678	161	13	-open	-open	PROPN
ejpam-678	161	14	,	,	PUNCT
ejpam-678	161	15	the	the	DET
ejpam-678	161	16	space	space	NOUN
ejpam-678	161	17	is	be	AUX
ejpam-678	161	18	θ	θ	NOUN
ejpam-678	161	19	-regular	-regular	ADJ
ejpam-678	161	20	.	.	PUNCT
ejpam-678	162	1	corollary	corollary	ADJ
ejpam-678	162	2	2	2	NUM
ejpam-678	162	3	.	.	PUNCT
ejpam-678	163	1	an	an	DET
ejpam-678	163	2	almost	almost	ADV
ejpam-678	163	3	regular	regular	ADJ
ejpam-678	163	4	space	space	NOUN
ejpam-678	163	5	is	be	AUX
ejpam-678	163	6	normal	normal	ADJ
ejpam-678	163	7	if	if	SCONJ
ejpam-678	163	8	and	and	CCONJ
ejpam-678	163	9	only	only	ADV
ejpam-678	163	10	if	if	SCONJ
ejpam-678	163	11	it	it	PRON
ejpam-678	163	12	is	be	AUX
ejpam-678	163	13	seminormal	seminormal	ADJ
ejpam-678	163	14	and	and	CCONJ
ejpam-678	163	15	weakly	weakly	ADJ
ejpam-678	163	16	θ	θ	NOUN
ejpam-678	163	17	normal	normal	ADJ
ejpam-678	163	18	.	.	PUNCT
ejpam-678	164	1	proof	proof	NOUN
ejpam-678	164	2	.	.	PUNCT
ejpam-678	165	1	proof	proof	NOUN
ejpam-678	165	2	is	be	AUX
ejpam-678	165	3	obvious	obvious	ADJ
ejpam-678	165	4	,	,	PUNCT
ejpam-678	165	5	since	since	SCONJ
ejpam-678	165	6	every	every	DET
ejpam-678	165	7	θ	θ	NOUN
ejpam-678	165	8	-regular	-regular	ADJ
ejpam-678	165	9	weakly	weakly	ADJ
ejpam-678	165	10	θ	θ	NOUN
ejpam-678	165	11	-normal	-normal	ADJ
ejpam-678	165	12	space	space	NOUN
ejpam-678	165	13	is	be	AUX
ejpam-678	165	14	normal	normal	ADJ
ejpam-678	165	15	.	.	PUNCT
ejpam-678	166	1	theorem	theorem	ADJ
ejpam-678	166	2	10	10	NUM
ejpam-678	166	3	.	.	PUNCT
ejpam-678	167	1	every	every	PRON
ejpam-678	167	2	almost	almost	ADV
ejpam-678	167	3	regular	regular	ADJ
ejpam-678	167	4	θ	θ	NOUN
ejpam-678	167	5	-seminormal	-seminormal	ADJ
ejpam-678	167	6	space	space	NOUN
ejpam-678	167	7	is	be	AUX
ejpam-678	167	8	weakly	weakly	ADJ
ejpam-678	167	9	θ	θ	NOUN
ejpam-678	167	10	-regular	-regular	ADJ
ejpam-678	167	11	.	.	PUNCT
ejpam-678	168	1	3	3	X
ejpam-678	168	2	.	.	NOUN
ejpam-678	168	3	subspaces	subspace	NOUN
ejpam-678	168	4	lemma	lemma	PROPN
ejpam-678	168	5	1	1	NUM
ejpam-678	168	6	.	.	PUNCT
ejpam-678	169	1	if	if	SCONJ
ejpam-678	169	2	y	y	PROPN
ejpam-678	169	3	⊂	⊂	PROPN
ejpam-678	169	4	x	x	X
ejpam-678	169	5	and	and	CCONJ
ejpam-678	169	6	a	a	PRON
ejpam-678	169	7	is	be	AUX
ejpam-678	169	8	any	any	DET
ejpam-678	169	9	θ	θ	PROPN
ejpam-678	169	10	-open	-open	NOUN
ejpam-678	169	11	set	set	VERB
ejpam-678	169	12	in	in	ADP
ejpam-678	169	13	x	x	PUNCT
ejpam-678	169	14	then	then	ADV
ejpam-678	169	15	a∩	a∩	PROPN
ejpam-678	169	16	y	y	PROPN
ejpam-678	169	17	is	be	AUX
ejpam-678	169	18	θ	θ	PROPN
ejpam-678	169	19	-open	-open	PROPN
ejpam-678	169	20	in	in	ADP
ejpam-678	169	21	y	y	PROPN
ejpam-678	169	22	.	.	PUNCT
ejpam-678	170	1	theorem	theorem	VERB
ejpam-678	170	2	11	11	NUM
ejpam-678	170	3	.	.	PUNCT
ejpam-678	171	1	if	if	SCONJ
ejpam-678	171	2	y	y	PROPN
ejpam-678	171	3	is	be	AUX
ejpam-678	171	4	a	a	DET
ejpam-678	171	5	closed	closed	ADJ
ejpam-678	171	6	subspace	subspace	NOUN
ejpam-678	171	7	of	of	ADP
ejpam-678	171	8	x	x	PUNCT
ejpam-678	171	9	and	and	CCONJ
ejpam-678	171	10	x	x	X
ejpam-678	171	11	is	be	AUX
ejpam-678	171	12	θ	θ	NOUN
ejpam-678	171	13	-regular	-regular	ADJ
ejpam-678	171	14	then	then	ADV
ejpam-678	171	15	y	y	PROPN
ejpam-678	171	16	is	be	AUX
ejpam-678	171	17	θ	θ	PROPN
ejpam-678	171	18	-regular	-regular	ADJ
ejpam-678	171	19	.	.	PUNCT
ejpam-678	172	1	proof	proof	NOUN
ejpam-678	172	2	.	.	PUNCT
ejpam-678	173	1	let	let	VERB
ejpam-678	173	2	x	x	PRON
ejpam-678	173	3	be	be	AUX
ejpam-678	173	4	a	a	DET
ejpam-678	173	5	θ	θ	NOUN
ejpam-678	173	6	-regular	-regular	ADJ
ejpam-678	173	7	space	space	NOUN
ejpam-678	173	8	and	and	CCONJ
ejpam-678	173	9	y	y	NOUN
ejpam-678	173	10	⊂	⊂	PROPN
ejpam-678	173	11	x	x	X
ejpam-678	173	12	.	.	PUNCT
ejpam-678	174	1	let	let	VERB
ejpam-678	174	2	f	f	PRON
ejpam-678	174	3	be	be	AUX
ejpam-678	174	4	a	a	DET
ejpam-678	174	5	closed	closed	ADJ
ejpam-678	174	6	set	set	NOUN
ejpam-678	174	7	in	in	ADP
ejpam-678	174	8	y	y	PROPN
ejpam-678	174	9	which	which	PRON
ejpam-678	174	10	is	be	AUX
ejpam-678	174	11	contained	contain	VERB
ejpam-678	174	12	in	in	ADP
ejpam-678	174	13	an	an	DET
ejpam-678	174	14	open	open	ADJ
ejpam-678	174	15	set	set	NOUN
ejpam-678	174	16	u	u	NOUN
ejpam-678	174	17	of	of	ADP
ejpam-678	174	18	y	y	PROPN
ejpam-678	174	19	.	.	PUNCT
ejpam-678	175	1	since	since	SCONJ
ejpam-678	175	2	f	f	PROPN
ejpam-678	175	3	is	be	AUX
ejpam-678	175	4	closed	close	VERB
ejpam-678	175	5	in	in	ADP
ejpam-678	175	6	y	y	PROPN
ejpam-678	175	7	and	and	CCONJ
ejpam-678	175	8	y	y	PROPN
ejpam-678	175	9	is	be	AUX
ejpam-678	175	10	a	a	DET
ejpam-678	175	11	closed	closed	ADJ
ejpam-678	175	12	subspace	subspace	NOUN
ejpam-678	175	13	of	of	ADP
ejpam-678	175	14	x	x	X
ejpam-678	175	15	,	,	PUNCT
ejpam-678	175	16	f	f	PROPN
ejpam-678	175	17	is	be	AUX
ejpam-678	175	18	closed	close	VERB
ejpam-678	175	19	in	in	ADP
ejpam-678	175	20	x	x	X
ejpam-678	175	21	.	.	PUNCT
ejpam-678	176	1	since	since	SCONJ
ejpam-678	176	2	u	u	NOUN
ejpam-678	176	3	is	be	AUX
ejpam-678	176	4	open	open	ADJ
ejpam-678	176	5	in	in	ADP
ejpam-678	176	6	y	y	PROPN
ejpam-678	176	7	,	,	PUNCT
ejpam-678	176	8	there	there	PRON
ejpam-678	176	9	exists	exist	VERB
ejpam-678	176	10	an	an	DET
ejpam-678	176	11	open	open	ADJ
ejpam-678	176	12	set	set	NOUN
ejpam-678	176	13	v	v	NOUN
ejpam-678	176	14	in	in	ADP
ejpam-678	176	15	x	x	PUNCT
ejpam-678	176	16	such	such	ADJ
ejpam-678	176	17	that	that	PRON
ejpam-678	176	18	u	u	NOUN
ejpam-678	176	19	=	=	SYM
ejpam-678	176	20	v	v	PROPN
ejpam-678	176	21	∩	∩	X
ejpam-678	176	22	y	y	PROPN
ejpam-678	176	23	.	.	PUNCT
ejpam-678	177	1	thus	thus	ADV
ejpam-678	177	2	f	f	PROPN
ejpam-678	177	3	⊂	⊂	PROPN
ejpam-678	177	4	v	v	PROPN
ejpam-678	177	5	.	.	PUNCT
ejpam-678	178	1	by	by	ADP
ejpam-678	178	2	θ	θ	PROPN
ejpam-678	178	3	-regularity	-regularity	NOUN
ejpam-678	178	4	of	of	ADP
ejpam-678	178	5	x	x	SYM
ejpam-678	178	6	,	,	PUNCT
ejpam-678	178	7	there	there	PRON
ejpam-678	178	8	exists	exist	VERB
ejpam-678	178	9	a	a	DET
ejpam-678	178	10	θ	θ	PROPN
ejpam-678	178	11	-open	-open	NOUN
ejpam-678	178	12	set	set	VERB
ejpam-678	178	13	w	w	NOUN
ejpam-678	178	14	in	in	ADP
ejpam-678	178	15	x	x	PROPN
ejpam-678	178	16	such	such	ADJ
ejpam-678	178	17	that	that	SCONJ
ejpam-678	178	18	f	f	PROPN
ejpam-678	178	19	⊂w	⊂w	PROPN
ejpam-678	178	20	⊂	⊂	PROPN
ejpam-678	178	21	v	v	PROPN
ejpam-678	178	22	,	,	PUNCT
ejpam-678	178	23	i.e	i.e	PROPN
ejpam-678	178	24	,	,	PUNCT
ejpam-678	178	25	;	;	PUNCT
ejpam-678	178	26	f	f	PROPN
ejpam-678	178	27	∩	∩	PROPN
ejpam-678	178	28	y	y	PROPN
ejpam-678	178	29	⊂w	⊂w	PROPN
ejpam-678	178	30	∩	∩	PROPN
ejpam-678	178	31	y	y	PROPN
ejpam-678	178	32	⊂	⊂	PROPN
ejpam-678	178	33	v	v	ADP
ejpam-678	178	34	∩	∩	ADJ
ejpam-678	178	35	y	y	PROPN
ejpam-678	178	36	⇒	⇒	X
ejpam-678	178	37	f	f	PROPN
ejpam-678	178	38	⊂w	⊂w	PROPN
ejpam-678	178	39	∩	∩	PROPN
ejpam-678	178	40	y	y	PROPN
ejpam-678	178	41	⊂	⊂	PROPN
ejpam-678	178	42	u	u	PROPN
ejpam-678	178	43	.	.	PUNCT
ejpam-678	179	1	by	by	ADP
ejpam-678	179	2	the	the	DET
ejpam-678	179	3	previous	previous	ADJ
ejpam-678	179	4	lemma	lemma	PROPN
ejpam-678	179	5	w	w	PROPN
ejpam-678	179	6	∩	∩	PROPN
ejpam-678	179	7	y	y	PROPN
ejpam-678	179	8	is	be	AUX
ejpam-678	179	9	θ	θ	PROPN
ejpam-678	179	10	-open	-open	PROPN
ejpam-678	179	11	in	in	ADP
ejpam-678	179	12	y	y	PROPN
ejpam-678	179	13	.	.	PUNCT
ejpam-678	180	1	hence	hence	ADV
ejpam-678	180	2	y	y	PROPN
ejpam-678	180	3	is	be	AUX
ejpam-678	180	4	θ	θ	PROPN
ejpam-678	180	5	-regular	-regular	ADJ
ejpam-678	180	6	.	.	PUNCT
ejpam-678	181	1	theorem	theorem	NOUN
ejpam-678	181	2	12	12	NUM
ejpam-678	181	3	.	.	PUNCT
ejpam-678	182	1	if	if	SCONJ
ejpam-678	182	2	y	y	PROPN
ejpam-678	182	3	is	be	AUX
ejpam-678	182	4	a	a	DET
ejpam-678	182	5	closed	closed	ADJ
ejpam-678	182	6	subspace	subspace	NOUN
ejpam-678	182	7	of	of	ADP
ejpam-678	182	8	x	x	PUNCT
ejpam-678	182	9	and	and	CCONJ
ejpam-678	182	10	x	x	ADJ
ejpam-678	182	11	is	be	AUX
ejpam-678	182	12	point	point	NOUN
ejpam-678	182	13	θ	θ	NOUN
ejpam-678	182	14	-regular	-regular	ADJ
ejpam-678	182	15	,	,	PUNCT
ejpam-678	182	16	then	then	ADV
ejpam-678	182	17	y	y	PROPN
ejpam-678	182	18	is	be	AUX
ejpam-678	182	19	point	point	NOUN
ejpam-678	182	20	θ	θ	NOUN
ejpam-678	182	21	-regular	-regular	ADJ
ejpam-678	182	22	.	.	PUNCT
ejpam-678	183	1	lemma	lemma	PROPN
ejpam-678	183	2	2	2	NUM
ejpam-678	183	3	.	.	PUNCT
ejpam-678	184	1	if	if	SCONJ
ejpam-678	184	2	y	y	PROPN
ejpam-678	184	3	is	be	AUX
ejpam-678	184	4	θ	θ	PROPN
ejpam-678	184	5	-open	-open	PROPN
ejpam-678	184	6	in	in	ADP
ejpam-678	184	7	x	x	X
ejpam-678	184	8	and	and	CCONJ
ejpam-678	184	9	a	a	PRON
ejpam-678	184	10	is	be	AUX
ejpam-678	184	11	θ	θ	PROPN
ejpam-678	184	12	-open	-open	PROPN
ejpam-678	184	13	in	in	ADP
ejpam-678	184	14	y	y	PROPN
ejpam-678	184	15	,	,	PUNCT
ejpam-678	184	16	then	then	ADV
ejpam-678	184	17	a	a	PRON
ejpam-678	184	18	is	be	AUX
ejpam-678	184	19	θ	θ	NOUN
ejpam-678	184	20	-open	-open	ADJ
ejpam-678	184	21	in	in	ADP
ejpam-678	184	22	x	x	X
ejpam-678	184	23	.	.	PUNCT
ejpam-678	185	1	lemma	lemma	PROPN
ejpam-678	186	1	3	3	X
ejpam-678	186	2	.	.	PUNCT
ejpam-678	187	1	if	if	SCONJ
ejpam-678	187	2	y	y	PROPN
ejpam-678	187	3	is	be	AUX
ejpam-678	187	4	θ	θ	PROPN
ejpam-678	187	5	-open	-open	PROPN
ejpam-678	187	6	in	in	ADP
ejpam-678	187	7	x	x	X
ejpam-678	187	8	and	and	CCONJ
ejpam-678	187	9	a	a	PRON
ejpam-678	187	10	is	be	AUX
ejpam-678	187	11	θ	θ	NOUN
ejpam-678	187	12	-closed	-close	VERB
ejpam-678	187	13	in	in	ADP
ejpam-678	187	14	y	y	PROPN
ejpam-678	187	15	then	then	ADV
ejpam-678	187	16	a	a	PRON
ejpam-678	187	17	is	be	AUX
ejpam-678	187	18	θ	θ	NOUN
ejpam-678	187	19	-closed	-close	VERB
ejpam-678	187	20	in	in	ADP
ejpam-678	187	21	x	x	X
ejpam-678	187	22	.	.	PUNCT
ejpam-678	188	1	proof	proof	NOUN
ejpam-678	188	2	.	.	PUNCT
ejpam-678	189	1	let	let	VERB
ejpam-678	189	2	y	y	PRON
ejpam-678	189	3	be	be	AUX
ejpam-678	189	4	a	a	DET
ejpam-678	189	5	θ	θ	PROPN
ejpam-678	189	6	-open	-open	NOUN
ejpam-678	189	7	set	set	VERB
ejpam-678	189	8	in	in	ADP
ejpam-678	189	9	x	x	PUNCT
ejpam-678	189	10	and	and	CCONJ
ejpam-678	189	11	let	let	VERB
ejpam-678	189	12	a	a	DET
ejpam-678	189	13	be	be	AUX
ejpam-678	189	14	θ	θ	NOUN
ejpam-678	189	15	-closed	-close	VERB
ejpam-678	189	16	in	in	ADP
ejpam-678	189	17	y	y	PROPN
ejpam-678	189	18	.	.	PUNCT
ejpam-678	190	1	then	then	ADV
ejpam-678	190	2	(	(	PUNCT
ejpam-678	190	3	y	y	PROPN
ejpam-678	190	4	−	−	PROPN
ejpam-678	190	5	a	a	X
ejpam-678	190	6	)	)	PUNCT
ejpam-678	190	7	is	be	AUX
ejpam-678	190	8	θ	θ	PROPN
ejpam-678	190	9	-open	-open	PROPN
ejpam-678	190	10	in	in	ADP
ejpam-678	190	11	y	y	PROPN
ejpam-678	190	12	.thus	.thus	ADV
ejpam-678	190	13	by	by	ADP
ejpam-678	190	14	previous	previous	ADJ
ejpam-678	190	15	lemma	lemma	PROPN
ejpam-678	190	16	(	(	PUNCT
ejpam-678	190	17	y	y	PROPN
ejpam-678	190	18	−	−	PROPN
ejpam-678	190	19	a	a	NOUN
ejpam-678	190	20	)	)	PUNCT
ejpam-678	190	21	is	be	AUX
ejpam-678	190	22	θ	θ	PROPN
ejpam-678	190	23	-open	-open	ADJ
ejpam-678	190	24	in	in	ADP
ejpam-678	190	25	x	x	X
ejpam-678	190	26	.	.	PUNCT
ejpam-678	191	1	therefore	therefore	ADV
ejpam-678	191	2	x	x	X
ejpam-678	191	3	−	−	PROPN
ejpam-678	191	4	(	(	PUNCT
ejpam-678	191	5	y	y	PROPN
ejpam-678	191	6	−	−	PROPN
ejpam-678	191	7	a	a	NOUN
ejpam-678	191	8	)	)	PUNCT
ejpam-678	191	9	is	be	AUX
ejpam-678	191	10	θ	θ	PROPN
ejpam-678	191	11	-closed	-close	VERB
ejpam-678	191	12	in	in	ADP
ejpam-678	191	13	x	x	X
ejpam-678	191	14	.	.	PUNCT
ejpam-678	192	1	hence	hence	ADV
ejpam-678	192	2	a	a	PRON
ejpam-678	192	3	is	be	AUX
ejpam-678	192	4	θ	θ	NOUN
ejpam-678	192	5	-closed	-close	VERB
ejpam-678	192	6	in	in	ADP
ejpam-678	192	7	x	x	X
ejpam-678	192	8	.	.	PUNCT
ejpam-678	193	1	references	reference	NOUN
ejpam-678	193	2	40	40	NUM
ejpam-678	193	3	theorem	theorem	VERB
ejpam-678	193	4	13	13	NUM
ejpam-678	193	5	.	.	PUNCT
ejpam-678	194	1	if	if	SCONJ
ejpam-678	194	2	y	y	PROPN
ejpam-678	194	3	is	be	AUX
ejpam-678	194	4	a	a	DET
ejpam-678	194	5	θ	θ	PROPN
ejpam-678	194	6	-open	-open	NOUN
ejpam-678	194	7	subspace	subspace	NOUN
ejpam-678	194	8	of	of	ADP
ejpam-678	194	9	x	x	PUNCT
ejpam-678	194	10	and	and	CCONJ
ejpam-678	194	11	x	x	X
ejpam-678	194	12	is	be	AUX
ejpam-678	194	13	weakly	weakly	ADJ
ejpam-678	194	14	θ	θ	NOUN
ejpam-678	194	15	-regular	-regular	ADJ
ejpam-678	194	16	,	,	PUNCT
ejpam-678	194	17	then	then	ADV
ejpam-678	194	18	y	y	PROPN
ejpam-678	194	19	is	be	AUX
ejpam-678	194	20	weakly	weakly	ADJ
ejpam-678	194	21	θ	θ	NOUN
ejpam-678	194	22	-regular	-regular	ADJ
ejpam-678	194	23	.	.	PUNCT
ejpam-678	195	1	proof	proof	NOUN
ejpam-678	195	2	.	.	PUNCT
ejpam-678	196	1	let	let	VERB
ejpam-678	196	2	y	y	PRON
ejpam-678	196	3	be	be	AUX
ejpam-678	196	4	a	a	DET
ejpam-678	196	5	θ	θ	PROPN
ejpam-678	196	6	-open	-open	NOUN
ejpam-678	196	7	subspace	subspace	NOUN
ejpam-678	196	8	of	of	ADP
ejpam-678	196	9	x	x	PUNCT
ejpam-678	196	10	and	and	CCONJ
ejpam-678	196	11	x	x	X
ejpam-678	196	12	is	be	AUX
ejpam-678	196	13	weakly	weakly	ADJ
ejpam-678	196	14	θ	θ	NOUN
ejpam-678	196	15	-regular	-regular	ADJ
ejpam-678	196	16	.	.	PUNCT
ejpam-678	197	1	let	let	VERB
ejpam-678	197	2	f	f	PRON
ejpam-678	197	3	be	be	AUX
ejpam-678	197	4	a	a	DET
ejpam-678	197	5	θ	θ	NOUN
ejpam-678	197	6	-closed	-close	VERB
ejpam-678	197	7	set	set	NOUN
ejpam-678	197	8	in	in	ADP
ejpam-678	197	9	y	y	PROPN
ejpam-678	197	10	and	and	CCONJ
ejpam-678	197	11	contained	contain	VERB
ejpam-678	197	12	in	in	ADP
ejpam-678	197	13	an	an	DET
ejpam-678	197	14	open	open	ADJ
ejpam-678	197	15	set	set	NOUN
ejpam-678	197	16	u	u	NOUN
ejpam-678	197	17	of	of	ADP
ejpam-678	197	18	y	y	PROPN
ejpam-678	197	19	.	.	PUNCT
ejpam-678	198	1	since	since	SCONJ
ejpam-678	198	2	y	y	PROPN
ejpam-678	198	3	is	be	AUX
ejpam-678	198	4	θ	θ	PROPN
ejpam-678	198	5	-open	-open	PROPN
ejpam-678	198	6	in	in	ADP
ejpam-678	198	7	x	x	SYM
ejpam-678	198	8	,	,	PUNCT
ejpam-678	198	9	f	f	PROPN
ejpam-678	198	10	is	be	AUX
ejpam-678	198	11	θ	θ	PROPN
ejpam-678	198	12	-closed	-close	VERB
ejpam-678	198	13	in	in	ADP
ejpam-678	198	14	x	x	X
ejpam-678	198	15	.	.	PUNCT
ejpam-678	199	1	since	since	SCONJ
ejpam-678	199	2	u	u	NOUN
ejpam-678	199	3	is	be	AUX
ejpam-678	199	4	open	open	ADJ
ejpam-678	199	5	in	in	ADP
ejpam-678	199	6	y	y	PROPN
ejpam-678	199	7	,	,	PUNCT
ejpam-678	199	8	there	there	PRON
ejpam-678	199	9	exists	exist	VERB
ejpam-678	199	10	a	a	DET
ejpam-678	199	11	open	open	ADJ
ejpam-678	199	12	set	set	NOUN
ejpam-678	199	13	v	v	NOUN
ejpam-678	199	14	in	in	ADP
ejpam-678	199	15	x	x	PUNCT
ejpam-678	199	16	such	such	ADJ
ejpam-678	199	17	that	that	PRON
ejpam-678	199	18	u	u	NOUN
ejpam-678	199	19	=	=	SYM
ejpam-678	199	20	v	v	PROPN
ejpam-678	199	21	∩	∩	X
ejpam-678	199	22	y	y	PROPN
ejpam-678	199	23	.	.	PUNCT
ejpam-678	200	1	so	so	ADV
ejpam-678	200	2	f	f	PROPN
ejpam-678	201	1	⊂	⊂	PROPN
ejpam-678	201	2	v	v	PROPN
ejpam-678	201	3	.	.	PUNCT
ejpam-678	202	1	by	by	ADP
ejpam-678	202	2	weak	weak	ADJ
ejpam-678	202	3	θ	θ	PROPN
ejpam-678	202	4	-regularity	-regularity	NOUN
ejpam-678	202	5	of	of	ADP
ejpam-678	202	6	x	x	SYM
ejpam-678	202	7	,	,	PUNCT
ejpam-678	202	8	there	there	PRON
ejpam-678	202	9	exists	exist	VERB
ejpam-678	202	10	a	a	DET
ejpam-678	202	11	θ	θ	PROPN
ejpam-678	202	12	-open	-open	NOUN
ejpam-678	202	13	set	set	VERB
ejpam-678	202	14	w	w	NOUN
ejpam-678	202	15	in	in	ADP
ejpam-678	202	16	x	x	PROPN
ejpam-678	202	17	such	such	ADJ
ejpam-678	202	18	that	that	SCONJ
ejpam-678	202	19	f	f	PROPN
ejpam-678	202	20	⊂w	⊂w	PROPN
ejpam-678	202	21	⊂	⊂	PROPN
ejpam-678	202	22	v	v	PROPN
ejpam-678	202	23	.	.	PUNCT
ejpam-678	203	1	thus	thus	ADV
ejpam-678	203	2	f	f	PROPN
ejpam-678	203	3	⊂w∩y	⊂w∩y	PROPN
ejpam-678	203	4	⊂	⊂	PROPN
ejpam-678	203	5	v	v	PROPN
ejpam-678	203	6	,	,	PUNCT
ejpam-678	203	7	where	where	SCONJ
ejpam-678	203	8	w	w	PROPN
ejpam-678	203	9	∩	∩	NOUN
ejpam-678	203	10	y	y	PROPN
ejpam-678	203	11	is	be	AUX
ejpam-678	203	12	θ	θ	PROPN
ejpam-678	203	13	-open	-open	PROPN
ejpam-678	203	14	in	in	ADP
ejpam-678	203	15	y	y	PROPN
ejpam-678	203	16	.	.	PUNCT
ejpam-678	204	1	hence	hence	ADV
ejpam-678	204	2	y	y	PROPN
ejpam-678	204	3	is	be	AUX
ejpam-678	204	4	weakly	weakly	ADJ
ejpam-678	204	5	θ	θ	NOUN
ejpam-678	204	6	-regular	-regular	ADJ
ejpam-678	204	7	.	.	PUNCT
ejpam-678	205	1	theorem	theorem	VERB
ejpam-678	205	2	14	14	NUM
ejpam-678	205	3	.	.	PUNCT
ejpam-678	206	1	if	if	SCONJ
ejpam-678	206	2	y	y	PROPN
ejpam-678	206	3	is	be	AUX
ejpam-678	206	4	a	a	DET
ejpam-678	206	5	θ	θ	PROPN
ejpam-678	206	6	-open	-open	NOUN
ejpam-678	206	7	subspace	subspace	NOUN
ejpam-678	206	8	of	of	ADP
ejpam-678	206	9	x	x	PUNCT
ejpam-678	206	10	and	and	CCONJ
ejpam-678	206	11	x	x	ADJ
ejpam-678	206	12	is	be	AUX
ejpam-678	206	13	point	point	NOUN
ejpam-678	206	14	weakly	weakly	ADJ
ejpam-678	206	15	θ	θ	NOUN
ejpam-678	206	16	-regular	-regular	ADJ
ejpam-678	206	17	,	,	PUNCT
ejpam-678	206	18	then	then	ADV
ejpam-678	206	19	y	y	PROPN
ejpam-678	206	20	is	be	AUX
ejpam-678	206	21	point	point	NOUN
ejpam-678	206	22	weakly	weakly	ADJ
ejpam-678	206	23	θ	θ	NOUN
ejpam-678	206	24	-regular	-regular	ADJ
ejpam-678	206	25	.	.	PUNCT
ejpam-678	207	1	references	reference	NOUN
ejpam-678	207	2	[	[	X
ejpam-678	207	3	1	1	X
ejpam-678	207	4	]	]	PUNCT
ejpam-678	207	5	j.	j.	PROPN
ejpam-678	207	6	m.	m.	PROPN
ejpam-678	207	7	boyte	boyte	PROPN
ejpam-678	207	8	,	,	PUNCT
ejpam-678	207	9	point	point	NOUN
ejpam-678	207	10	(	(	PUNCT
ejpam-678	207	11	countable	countable	ADJ
ejpam-678	207	12	)	)	PUNCT
ejpam-678	207	13	paracompactness	paracompactness	NOUN
ejpam-678	207	14	,	,	PUNCT
ejpam-678	207	15	j.	j.	PROPN
ejpam-678	207	16	austr	austr	PROPN
ejpam-678	207	17	.	.	PUNCT
ejpam-678	208	1	math	math	PROPN
ejpam-678	208	2	.	.	PUNCT
ejpam-678	209	1	soc	soc	PROPN
ejpam-678	209	2	.	.	PUNCT
ejpam-678	210	1	15	15	NUM
ejpam-678	210	2	,	,	PUNCT
ejpam-678	210	3	138	138	NUM
ejpam-678	210	4	-	-	SYM
ejpam-678	210	5	144	144	NUM
ejpam-678	210	6	.	.	PUNCT
ejpam-678	210	7	1973	1973	NUM
ejpam-678	210	8	.	.	PUNCT
ejpam-678	211	1	[	[	X
ejpam-678	211	2	2	2	X
ejpam-678	211	3	]	]	PUNCT
ejpam-678	211	4	j.	j.	PROPN
ejpam-678	211	5	dontchev	dontchev	PROPN
ejpam-678	211	6	and	and	CCONJ
ejpam-678	211	7	t.	t.	PROPN
ejpam-678	211	8	noiri	noiri	PROPN
ejpam-678	211	9	,	,	PUNCT
ejpam-678	211	10	n	n	CCONJ
ejpam-678	211	11	-	-	PUNCT
ejpam-678	211	12	closed	closed	ADJ
ejpam-678	211	13	subsets	subset	NOUN
ejpam-678	211	14	of	of	ADP
ejpam-678	211	15	nearly	nearly	ADV
ejpam-678	211	16	compact	compact	ADJ
ejpam-678	211	17	spaces	space	NOUN
ejpam-678	211	18	,	,	PUNCT
ejpam-678	211	19	acta	acta	PROPN
ejpam-678	211	20	.	.	PUNCT
ejpam-678	211	21	math	math	NOUN
ejpam-678	211	22	.	.	PUNCT
ejpam-678	212	1	hungar	hungar	PROPN
ejpam-678	212	2	.	.	PUNCT
ejpam-678	212	3	,	,	PUNCT
ejpam-678	212	4	86(1	86(1	PROPN
ejpam-678	212	5	-	-	PUNCT
ejpam-678	212	6	2	2	NUM
ejpam-678	212	7	)	)	PUNCT
ejpam-678	212	8	,	,	PUNCT
ejpam-678	212	9	117–125	117–125	NUM
ejpam-678	212	10	.	.	PUNCT
ejpam-678	212	11	2000	2000	NUM
ejpam-678	212	12	.	.	PUNCT
ejpam-678	213	1	[	[	X
ejpam-678	213	2	3	3	X
ejpam-678	213	3	]	]	X
ejpam-678	213	4	d.	d.	PROPN
ejpam-678	213	5	jankovic	jankovic	PROPN
ejpam-678	213	6	,	,	PUNCT
ejpam-678	213	7	θ	θ	PROPN
ejpam-678	213	8	-regular	-regular	NOUN
ejpam-678	213	9	spaces	space	NOUN
ejpam-678	213	10	,	,	PUNCT
ejpam-678	213	11	inter	inter	PROPN
ejpam-678	213	12	.	.	PUNCT
ejpam-678	214	1	j.	j.	PROPN
ejpam-678	214	2	math	math	PROPN
ejpam-678	214	3	.	.	PUNCT
ejpam-678	215	1	math	math	NOUN
ejpam-678	215	2	.	.	PUNCT
ejpam-678	216	1	sc	sc	PROPN
ejpam-678	216	2	.	.	PROPN
ejpam-678	216	3	,	,	PUNCT
ejpam-678	216	4	8	8	NUM
ejpam-678	216	5	,	,	PUNCT
ejpam-678	216	6	no.3	no.3	VERB
ejpam-678	216	7	,	,	PUNCT
ejpam-678	216	8	615	615	NUM
ejpam-678	216	9	-	-	SYM
ejpam-678	216	10	619	619	NUM
ejpam-678	216	11	.	.	PUNCT
ejpam-678	217	1	1985	1985	NUM
ejpam-678	217	2	.	.	PUNCT
ejpam-678	218	1	[	[	X
ejpam-678	218	2	4	4	NUM
ejpam-678	218	3	]	]	X
ejpam-678	218	4	j.k	j.k	PROPN
ejpam-678	218	5	.	.	PROPN
ejpam-678	218	6	kohli	kohli	PROPN
ejpam-678	218	7	and	and	CCONJ
ejpam-678	218	8	a.k	a.k	PROPN
ejpam-678	218	9	.	.	PUNCT
ejpam-678	218	10	das	das	PROPN
ejpam-678	218	11	,	,	PUNCT
ejpam-678	218	12	on	on	ADP
ejpam-678	218	13	functionally	functionally	ADV
ejpam-678	218	14	θ	θ	ADJ
ejpam-678	218	15	-normal	-normal	ADJ
ejpam-678	218	16	spaces	space	NOUN
ejpam-678	218	17	,	,	PUNCT
ejpam-678	218	18	appl	appl	PROPN
ejpam-678	218	19	.	.	PUNCT
ejpam-678	219	1	gen	gen	PROPN
ejpam-678	219	2	.	.	PROPN
ejpam-678	219	3	topol	topol	PROPN
ejpam-678	219	4	.	.	PROPN
ejpam-678	219	5	,	,	PUNCT
ejpam-678	219	6	6(1	6(1	NUM
ejpam-678	219	7	)	)	PUNCT
ejpam-678	219	8	,	,	PUNCT
ejpam-678	219	9	1–14	1–14	PROPN
ejpam-678	219	10	.	.	PROPN
ejpam-678	219	11	2005	2005	NUM
ejpam-678	219	12	.	.	PUNCT
ejpam-678	220	1	[	[	X
ejpam-678	220	2	5	5	X
ejpam-678	220	3	]	]	PUNCT
ejpam-678	220	4	j.	j.	PROPN
ejpam-678	220	5	k.	k.	PROPN
ejpam-678	220	6	kohli	kohli	PROPN
ejpam-678	220	7	and	and	CCONJ
ejpam-678	220	8	a.	a.	PROPN
ejpam-678	220	9	k.	k.	PROPN
ejpam-678	220	10	das	das	PROPN
ejpam-678	220	11	,	,	PUNCT
ejpam-678	220	12	characterizations	characterization	NOUN
ejpam-678	220	13	of	of	ADP
ejpam-678	220	14	certain	certain	ADJ
ejpam-678	220	15	sub(super)-classes	sub(super)-classe	NOUN
ejpam-678	220	16	of	of	ADP
ejpam-678	220	17	hausdorff	hausdorff	NOUN
ejpam-678	220	18	spaces	space	NOUN
ejpam-678	220	19	and	and	CCONJ
ejpam-678	220	20	a	a	DET
ejpam-678	220	21	factorization	factorization	NOUN
ejpam-678	220	22	of	of	ADP
ejpam-678	220	23	regularity	regularity	NOUN
ejpam-678	220	24	,	,	PUNCT
ejpam-678	220	25	indian	indian	ADJ
ejpam-678	220	26	j.	j.	PROPN
ejpam-678	220	27	pure	pure	PROPN
ejpam-678	220	28	appl	appl	PROPN
ejpam-678	220	29	.	.	PUNCT
ejpam-678	220	30	math	math	PROPN
ejpam-678	220	31	.	.	PUNCT
ejpam-678	220	32	,	,	PUNCT
ejpam-678	220	33	35(4	35(4	NUM
ejpam-678	220	34	)	)	PUNCT
ejpam-678	220	35	,	,	PUNCT
ejpam-678	220	36	463	463	NUM
ejpam-678	220	37	-	-	SYM
ejpam-678	220	38	470	470	NUM
ejpam-678	220	39	.	.	PUNCT
ejpam-678	221	1	2004	2004	NUM
ejpam-678	221	2	.	.	PUNCT
ejpam-678	222	1	[	[	X
ejpam-678	222	2	6	6	NUM
ejpam-678	222	3	]	]	X
ejpam-678	222	4	j.k	j.k	PROPN
ejpam-678	222	5	.	.	PROPN
ejpam-678	222	6	kohli	kohli	PROPN
ejpam-678	222	7	and	and	CCONJ
ejpam-678	222	8	a.k	a.k	PROPN
ejpam-678	222	9	.	.	PUNCT
ejpam-678	222	10	das	das	PROPN
ejpam-678	222	11	,	,	PUNCT
ejpam-678	222	12	new	new	ADJ
ejpam-678	222	13	normality	normality	NOUN
ejpam-678	222	14	axioms	axiom	NOUN
ejpam-678	222	15	and	and	CCONJ
ejpam-678	222	16	decompositions	decomposition	NOUN
ejpam-678	222	17	of	of	ADP
ejpam-678	222	18	normality	normality	NOUN
ejpam-678	222	19	,	,	PUNCT
ejpam-678	222	20	glas	glas	PROPN
ejpam-678	222	21	.	.	PUNCT
ejpam-678	222	22	mat	mat	PROPN
ejpam-678	222	23	.	.	PUNCT
ejpam-678	222	24	ser	ser	PROPN
ejpam-678	222	25	.	.	PUNCT
ejpam-678	222	26	iii	iii	PROPN
ejpam-678	222	27	37(57	37(57	NUM
ejpam-678	222	28	)	)	PUNCT
ejpam-678	222	29	,	,	PUNCT
ejpam-678	222	30	no1	no1	NOUN
ejpam-678	222	31	,	,	PUNCT
ejpam-678	222	32	163–173	163–173	NUM
ejpam-678	222	33	.	.	PUNCT
ejpam-678	222	34	2002	2002	NUM
ejpam-678	222	35	.	.	PUNCT
ejpam-678	223	1	[	[	X
ejpam-678	223	2	7	7	X
ejpam-678	223	3	]	]	X
ejpam-678	223	4	j.k	j.k	PROPN
ejpam-678	223	5	.	.	PROPN
ejpam-678	223	6	kohli	kohli	PROPN
ejpam-678	223	7	and	and	CCONJ
ejpam-678	223	8	d.	d.	PROPN
ejpam-678	223	9	singh	singh	PROPN
ejpam-678	223	10	,	,	PUNCT
ejpam-678	223	11	weak	weak	ADJ
ejpam-678	223	12	normality	normality	NOUN
ejpam-678	223	13	properties	property	NOUN
ejpam-678	223	14	and	and	CCONJ
ejpam-678	223	15	factorizations	factorization	NOUN
ejpam-678	223	16	of	of	ADP
ejpam-678	223	17	normality	normality	NOUN
ejpam-678	223	18	,	,	PUNCT
ejpam-678	223	19	acta	acta	PROPN
ejpam-678	223	20	.	.	PUNCT
ejpam-678	224	1	math	math	NOUN
ejpam-678	224	2	.	.	PUNCT
ejpam-678	225	1	hungar	hungar	NOUN
ejpam-678	225	2	.	.	PUNCT
ejpam-678	226	1	110(1	110(1	NUM
ejpam-678	226	2	-	-	SYM
ejpam-678	226	3	2	2	NUM
ejpam-678	226	4	)	)	PUNCT
ejpam-678	226	5	,	,	PUNCT
ejpam-678	226	6	67–80	67–80	PROPN
ejpam-678	226	7	.	.	PUNCT
ejpam-678	226	8	2006	2006	NUM
ejpam-678	226	9	.	.	PUNCT
ejpam-678	227	1	[	[	X
ejpam-678	227	2	8	8	NUM
ejpam-678	227	3	]	]	X
ejpam-678	227	4	m.m	m.m	PROPN
ejpam-678	227	5	.	.	PROPN
ejpam-678	227	6	kovar	kovar	PROPN
ejpam-678	227	7	,	,	PUNCT
ejpam-678	227	8	on	on	ADP
ejpam-678	227	9	θ	θ	PROPN
ejpam-678	227	10	-regular	-regular	ADJ
ejpam-678	227	11	spaces	space	NOUN
ejpam-678	227	12	,	,	PUNCT
ejpam-678	227	13	inter	inter	PROPN
ejpam-678	227	14	.	.	PUNCT
ejpam-678	228	1	j.	j.	PROPN
ejpam-678	228	2	math	math	PROPN
ejpam-678	228	3	.	.	PUNCT
ejpam-678	229	1	math	math	NOUN
ejpam-678	229	2	.	.	PUNCT
ejpam-678	230	1	sc	sc	PROPN
ejpam-678	230	2	.	.	PROPN
ejpam-678	230	3	,	,	PUNCT
ejpam-678	230	4	17	17	NUM
ejpam-678	230	5	(	(	PUNCT
ejpam-678	230	6	4	4	NUM
ejpam-678	230	7	)	)	PUNCT
ejpam-678	230	8	687	687	NUM
ejpam-678	230	9	-	-	SYM
ejpam-678	230	10	692	692	NUM
ejpam-678	230	11	.	.	NUM
ejpam-678	230	12	1994	1994	NUM
ejpam-678	230	13	.	.	PUNCT
ejpam-678	231	1	[	[	X
ejpam-678	231	2	9	9	NUM
ejpam-678	231	3	]	]	X
ejpam-678	231	4	m.k	m.k	PROPN
ejpam-678	231	5	.	.	PROPN
ejpam-678	231	6	singal	singal	PROPN
ejpam-678	231	7	and	and	CCONJ
ejpam-678	231	8	s.p	s.p	PROPN
ejpam-678	231	9	.	.	PROPN
ejpam-678	231	10	arya	arya	PROPN
ejpam-678	231	11	,	,	PUNCT
ejpam-678	231	12	on	on	ADP
ejpam-678	231	13	almost	almost	ADV
ejpam-678	231	14	regular	regular	ADJ
ejpam-678	231	15	spaces	space	NOUN
ejpam-678	231	16	,	,	PUNCT
ejpam-678	231	17	glasnik	glasnik	PROPN
ejpam-678	231	18	mat	mat	PROPN
ejpam-678	231	19	.	.	PROPN
ejpam-678	231	20	4(24	4(24	NUM
ejpam-678	231	21	)	)	PUNCT
ejpam-678	231	22	,	,	PUNCT
ejpam-678	231	23	89–99	89–99	NUM
ejpam-678	231	24	.	.	PUNCT
ejpam-678	231	25	1969	1969	NUM
ejpam-678	231	26	.	.	PUNCT
ejpam-678	232	1	[	[	X
ejpam-678	232	2	10	10	NUM
ejpam-678	232	3	]	]	X
ejpam-678	232	4	m.k	m.k	PROPN
ejpam-678	232	5	.	.	PROPN
ejpam-678	232	6	singal	singal	PROPN
ejpam-678	232	7	and	and	CCONJ
ejpam-678	232	8	s.p	s.p	PROPN
ejpam-678	232	9	.	.	PROPN
ejpam-678	232	10	arya	arya	PROPN
ejpam-678	232	11	,	,	PUNCT
ejpam-678	232	12	on	on	ADP
ejpam-678	232	13	almost	almost	ADV
ejpam-678	232	14	normal	normal	ADJ
ejpam-678	232	15	and	and	CCONJ
ejpam-678	232	16	almost	almost	ADV
ejpam-678	232	17	completely	completely	ADV
ejpam-678	232	18	regular	regular	ADJ
ejpam-678	232	19	spaces	space	NOUN
ejpam-678	232	20	,	,	PUNCT
ejpam-678	232	21	glasnik	glasnik	PROPN
ejpam-678	232	22	mat	mat	PROPN
ejpam-678	232	23	.	.	PROPN
ejpam-678	232	24	5(25	5(25	NUM
ejpam-678	232	25	)	)	PUNCT
ejpam-678	232	26	,	,	PUNCT
ejpam-678	232	27	141–152	141–152	NUM
ejpam-678	232	28	.	.	PUNCT
ejpam-678	232	29	1970	1970	NUM
ejpam-678	232	30	.	.	PUNCT
ejpam-678	233	1	[	[	X
ejpam-678	233	2	11	11	NUM
ejpam-678	233	3	]	]	X
ejpam-678	233	4	m.k.singal	m.k.singal	ADJ
ejpam-678	233	5	and	and	CCONJ
ejpam-678	233	6	a.	a.	PROPN
ejpam-678	233	7	mathur	mathur	PROPN
ejpam-678	233	8	,	,	PUNCT
ejpam-678	233	9	on	on	ADP
ejpam-678	233	10	nearly	nearly	ADV
ejpam-678	233	11	compact	compact	ADJ
ejpam-678	233	12	spaces	space	NOUN
ejpam-678	233	13	,	,	PUNCT
ejpam-678	233	14	boll	boll	NOUN
ejpam-678	233	15	.	.	PUNCT
ejpam-678	234	1	u.m.i	u.m.i	PROPN
ejpam-678	234	2	.	.	PROPN
ejpam-678	235	1	4	4	NUM
ejpam-678	235	2	,	,	PUNCT
ejpam-678	235	3	702–710	702–710	NUM
ejpam-678	235	4	.	.	PUNCT
ejpam-678	236	1	1969	1969	NUM
ejpam-678	236	2	.	.	PUNCT
ejpam-678	237	1	[	[	X
ejpam-678	237	2	12	12	NUM
ejpam-678	237	3	]	]	X
ejpam-678	237	4	m.k.singal	m.k.singal	PROPN
ejpam-678	237	5	and	and	CCONJ
ejpam-678	237	6	a.r	a.r	PROPN
ejpam-678	237	7	.	.	PROPN
ejpam-678	237	8	singal	singal	PROPN
ejpam-678	237	9	,	,	PUNCT
ejpam-678	237	10	mildly	mildly	ADV
ejpam-678	237	11	normal	normal	ADJ
ejpam-678	237	12	spaces	space	NOUN
ejpam-678	237	13	,	,	PUNCT
ejpam-678	237	14	kyungpook	kyungpook	PROPN
ejpam-678	237	15	math	math	NOUN
ejpam-678	237	16	j.	j.	PROPN
ejpam-678	237	17	13	13	NUM
ejpam-678	237	18	,	,	PUNCT
ejpam-678	237	19	27–31	27–31	PROPN
ejpam-678	237	20	.	.	NOUN
ejpam-678	237	21	1973	1973	NUM
ejpam-678	237	22	.	.	PUNCT
ejpam-678	238	1	[	[	X
ejpam-678	238	2	13	13	NUM
ejpam-678	238	3	]	]	X
ejpam-678	238	4	e.v	e.v	PROPN
ejpam-678	238	5	.	.	PUNCT
ejpam-678	238	6	stchepin	stchepin	NOUN
ejpam-678	238	7	,	,	PUNCT
ejpam-678	238	8	real	real	ADV
ejpam-678	238	9	valued	value	VERB
ejpam-678	238	10	functions	function	NOUN
ejpam-678	238	11	and	and	CCONJ
ejpam-678	238	12	spaces	space	NOUN
ejpam-678	238	13	close	close	ADV
ejpam-678	238	14	to	to	ADP
ejpam-678	238	15	normal	normal	ADJ
ejpam-678	238	16	,	,	PUNCT
ejpam-678	238	17	sib	sib	PROPN
ejpam-678	238	18	.	.	PUNCT
ejpam-678	239	1	j.	j.	PROPN
ejpam-678	239	2	math	math	PROPN
ejpam-678	239	3	.	.	PUNCT
ejpam-678	240	1	13:5	13:5	NUM
ejpam-678	240	2	,	,	PUNCT
ejpam-678	240	3	1182	1182	NUM
ejpam-678	240	4	–	–	PUNCT
ejpam-678	240	5	1196	1196	NUM
ejpam-678	240	6	.	.	PUNCT
ejpam-678	241	1	1972	1972	NUM
ejpam-678	241	2	references	reference	NOUN
ejpam-678	241	3	41	41	NUM
ejpam-678	242	1	[	[	X
ejpam-678	242	2	14	14	NUM
ejpam-678	242	3	]	]	X
ejpam-678	242	4	n.v	n.v	PROPN
ejpam-678	242	5	.	.	PROPN
ejpam-678	242	6	veličko	veličko	PROPN
ejpam-678	242	7	h	h	NOUN
ejpam-678	242	8	-	-	PUNCT
ejpam-678	242	9	closed	close	VERB
ejpam-678	242	10	topological	topological	ADJ
ejpam-678	242	11	spaces	space	NOUN
ejpam-678	242	12	,	,	PUNCT
ejpam-678	242	13	amer	amer	PROPN
ejpam-678	242	14	.	.	PROPN
ejpam-678	242	15	math	math	PROPN
ejpam-678	242	16	.	.	PUNCT
ejpam-678	243	1	soc	soc	PROPN
ejpam-678	243	2	.	.	PUNCT
ejpam-678	244	1	transl	transl	PROPN
ejpam-678	244	2	.	.	PUNCT
ejpam-678	245	1	78(2	78(2	X
ejpam-678	245	2	)	)	PUNCT
ejpam-678	245	3	„	„	PUNCT
ejpam-678	245	4	103–118	103–118	NUM
ejpam-678	245	5	.	.	PUNCT
ejpam-678	245	6	1968	1968	NUM
ejpam-678	245	7	.	.	PUNCT
ejpam-678	246	1	[	[	X
ejpam-678	246	2	15	15	NUM
ejpam-678	246	3	]	]	X
ejpam-678	246	4	g.	g.	PROPN
ejpam-678	246	5	vigilino	vigilino	PROPN
ejpam-678	246	6	,	,	PUNCT
ejpam-678	246	7	seminormal	seminormal	ADJ
ejpam-678	246	8	and	and	CCONJ
ejpam-678	246	9	c	c	NOUN
ejpam-678	246	10	-	-	ADJ
ejpam-678	246	11	compact	compact	ADJ
ejpam-678	246	12	spaces	space	NOUN
ejpam-678	246	13	,	,	PUNCT
ejpam-678	246	14	duke	duke	PROPN
ejpam-678	246	15	j.	j.	PROPN
ejpam-678	246	16	math	math	PROPN
ejpam-678	246	17	.	.	PUNCT
ejpam-678	247	1	38	38	NUM
ejpam-678	247	2	,	,	PUNCT
ejpam-678	247	3	57–61	57–61	NUM
ejpam-678	247	4	.	.	PUNCT
ejpam-678	247	5	1971	1971	NUM
ejpam-678	247	6	.	.	PUNCT