id	sid	tid	token	lemma	pos
ejpam-110	1	1	9_breuckmann.dvi	9_breuckmann.dvi	NUM
ejpam-110	1	2	european	european	ADJ
ejpam-110	1	3	journal	journal	NOUN
ejpam-110	1	4	of	of	ADP
ejpam-110	1	5	pure	pure	ADJ
ejpam-110	1	6	and	and	CCONJ
ejpam-110	1	7	applied	apply	VERB
ejpam-110	1	8	mathematics	mathematic	NOUN
ejpam-110	1	9	vol	vol	NOUN
ejpam-110	1	10	.	.	PROPN
ejpam-110	2	1	2	2	NUM
ejpam-110	2	2	,	,	PUNCT
ejpam-110	2	3	no	no	INTJ
ejpam-110	2	4	.	.	NOUN
ejpam-110	2	5	1	1	NUM
ejpam-110	2	6	,	,	PUNCT
ejpam-110	2	7	2009	2009	NUM
ejpam-110	2	8	,	,	PUNCT
ejpam-110	2	9	(	(	PUNCT
ejpam-110	2	10	147	147	NUM
ejpam-110	2	11	-	-	SYM
ejpam-110	2	12	161	161	NUM
ejpam-110	2	13	)	)	PUNCT
ejpam-110	2	14	issn	issn	PROPN
ejpam-110	2	15	1307	1307	NUM
ejpam-110	2	16	-	-	SYM
ejpam-110	2	17	5543	5543	NUM
ejpam-110	2	18	–	–	PUNCT
ejpam-110	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-110	2	20	local	local	ADJ
ejpam-110	2	21	compactness	compactness	NOUN
ejpam-110	2	22	in	in	ADP
ejpam-110	2	23	l	l	ADJ
ejpam-110	2	24	-	-	ADJ
ejpam-110	2	25	fuzzy	fuzzy	ADJ
ejpam-110	2	26	spaces	space	NOUN
ejpam-110	2	27	t.k	t.k	PROPN
ejpam-110	2	28	.	.	PROPN
ejpam-110	2	29	breuckmann1	breuckmann1	PROPN
ejpam-110	2	30	,	,	PUNCT
ejpam-110	2	31	s.r.t	s.r.t	NOUN
ejpam-110	2	32	.	.	PUNCT
ejpam-110	3	1	kudri1	kudri1	PROPN
ejpam-110	3	2	,	,	PUNCT
ejpam-110	3	3	and	and	CCONJ
ejpam-110	3	4	h.	h.	PROPN
ejpam-110	3	5	aygün2∗	aygün2∗	PROPN
ejpam-110	3	6	1	1	NUM
ejpam-110	3	7	department	department	NOUN
ejpam-110	3	8	of	of	ADP
ejpam-110	3	9	mathematics	mathematic	NOUN
ejpam-110	3	10	,	,	PUNCT
ejpam-110	3	11	federal	federal	ADJ
ejpam-110	3	12	university	university	PROPN
ejpam-110	3	13	of	of	ADP
ejpam-110	3	14	paraná	paraná	PROPN
ejpam-110	3	15	,	,	PUNCT
ejpam-110	3	16	p.	p.	PROPN
ejpam-110	3	17	o.	o.	PROPN
ejpam-110	3	18	box	box	PROPN
ejpam-110	3	19	019081	019081	NUM
ejpam-110	3	20	,	,	PUNCT
ejpam-110	3	21	curitiba	curitiba	PROPN
ejpam-110	3	22	,	,	PUNCT
ejpam-110	3	23	pr	pr	NOUN
ejpam-110	3	24	,	,	PUNCT
ejpam-110	3	25	81531990	81531990	NUM
ejpam-110	3	26	,	,	PUNCT
ejpam-110	3	27	brazil	brazil	PROPN
ejpam-110	3	28	2	2	NUM
ejpam-110	3	29	department	department	NOUN
ejpam-110	3	30	of	of	ADP
ejpam-110	3	31	mathematics	mathematic	NOUN
ejpam-110	3	32	,	,	PUNCT
ejpam-110	3	33	kocaeli	kocaeli	PROPN
ejpam-110	3	34	university	university	PROPN
ejpam-110	3	35	,	,	PUNCT
ejpam-110	3	36	41380	41380	NUM
ejpam-110	3	37	,	,	PUNCT
ejpam-110	3	38	izmit	izmit	NOUN
ejpam-110	3	39	,	,	PUNCT
ejpam-110	3	40	turkey	turkey	NOUN
ejpam-110	3	41	,	,	PUNCT
ejpam-110	3	42	fax	fax	NOUN
ejpam-110	3	43	:	:	PUNCT
ejpam-110	3	44	+90	+90	NUM
ejpam-110	3	45	-	-	PUNCT
ejpam-110	3	46	262	262	NUM
ejpam-110	3	47	-	-	PUNCT
ejpam-110	3	48	3032003	3032003	NUM
ejpam-110	3	49	abstract	abstract	NOUN
ejpam-110	3	50	.	.	PUNCT
ejpam-110	4	1	in	in	ADP
ejpam-110	4	2	an	an	DET
ejpam-110	4	3	l	l	ADJ
ejpam-110	4	4	-	-	ADJ
ejpam-110	4	5	topological	topological	ADJ
ejpam-110	4	6	space	space	NOUN
ejpam-110	4	7	we	we	PRON
ejpam-110	4	8	present	present	VERB
ejpam-110	4	9	good	good	ADJ
ejpam-110	4	10	definitions	definition	NOUN
ejpam-110	4	11	for	for	ADP
ejpam-110	4	12	local	local	ADJ
ejpam-110	4	13	compactness	compactness	NOUN
ejpam-110	4	14	,	,	PUNCT
ejpam-110	4	15	weak	weak	ADJ
ejpam-110	4	16	local	local	ADJ
ejpam-110	4	17	compactness	compactness	NOUN
ejpam-110	4	18	and	and	CCONJ
ejpam-110	4	19	relative	relative	ADJ
ejpam-110	4	20	local	local	ADJ
ejpam-110	4	21	compactness	compactness	NOUN
ejpam-110	4	22	.	.	PUNCT
ejpam-110	5	1	we	we	PRON
ejpam-110	5	2	obtain	obtain	VERB
ejpam-110	5	3	the	the	DET
ejpam-110	5	4	equivalence	equivalence	NOUN
ejpam-110	5	5	of	of	ADP
ejpam-110	5	6	these	these	DET
ejpam-110	5	7	properties	property	NOUN
ejpam-110	5	8	in	in	ADP
ejpam-110	5	9	a	a	DET
ejpam-110	5	10	hausdorff	hausdorff	NOUN
ejpam-110	5	11	space	space	NOUN
ejpam-110	5	12	and	and	CCONJ
ejpam-110	5	13	we	we	PRON
ejpam-110	5	14	also	also	ADV
ejpam-110	5	15	obtain	obtain	VERB
ejpam-110	5	16	a	a	DET
ejpam-110	5	17	one	one	NUM
ejpam-110	5	18	point	point	NOUN
ejpam-110	5	19	compactification	compactification	NOUN
ejpam-110	5	20	theorem	theorem	NOUN
ejpam-110	5	21	.	.	PUNCT
ejpam-110	6	1	key	key	ADJ
ejpam-110	6	2	words	word	NOUN
ejpam-110	6	3	:	:	PUNCT
ejpam-110	6	4	fuzzy	fuzzy	ADJ
ejpam-110	6	5	lattice	lattice	NOUN
ejpam-110	6	6	,	,	PUNCT
ejpam-110	6	7	l	l	NOUN
ejpam-110	6	8	-	-	NOUN
ejpam-110	6	9	topology	topology	NOUN
ejpam-110	6	10	,	,	PUNCT
ejpam-110	6	11	local	local	ADJ
ejpam-110	6	12	compactness	compactness	NOUN
ejpam-110	6	13	,	,	PUNCT
ejpam-110	6	14	weak	weak	ADJ
ejpam-110	6	15	local	local	ADJ
ejpam-110	6	16	compactness	compactness	NOUN
ejpam-110	6	17	,	,	PUNCT
ejpam-110	6	18	relative	relative	ADJ
ejpam-110	6	19	local	local	ADJ
ejpam-110	6	20	compactness	compactness	NOUN
ejpam-110	6	21	1	1	NUM
ejpam-110	6	22	.	.	PUNCT
ejpam-110	6	23	introduction	introduction	NOUN
ejpam-110	6	24	in	in	ADP
ejpam-110	6	25	general	general	ADJ
ejpam-110	6	26	topology	topology	NOUN
ejpam-110	6	27	there	there	PRON
ejpam-110	6	28	are	be	VERB
ejpam-110	6	29	three	three	NUM
ejpam-110	6	30	usual	usual	ADJ
ejpam-110	6	31	ways	way	NOUN
ejpam-110	6	32	to	to	PART
ejpam-110	6	33	define	define	VERB
ejpam-110	6	34	local	local	ADJ
ejpam-110	6	35	compactness	compactness	NOUN
ejpam-110	6	36	,	,	PUNCT
ejpam-110	6	37	which	which	DET
ejpam-110	6	38	ones	one	NOUN
ejpam-110	6	39	we	we	PRON
ejpam-110	6	40	call	call	VERB
ejpam-110	6	41	here	here	ADV
ejpam-110	6	42	local	local	ADJ
ejpam-110	6	43	compactness	compactness	NOUN
ejpam-110	6	44	,	,	PUNCT
ejpam-110	6	45	weak	weak	ADJ
ejpam-110	6	46	local	local	ADJ
ejpam-110	6	47	compactness	compactness	NOUN
ejpam-110	6	48	and	and	CCONJ
ejpam-110	6	49	relative	relative	ADJ
ejpam-110	6	50	local	local	ADJ
ejpam-110	6	51	compactness	compactness	NOUN
ejpam-110	6	52	.	.	PUNCT
ejpam-110	7	1	definition	definition	NOUN
ejpam-110	7	2	1.1	1.1	NUM
ejpam-110	7	3	.	.	PUNCT
ejpam-110	8	1	let	let	VERB
ejpam-110	8	2	〈	〈	PROPN
ejpam-110	8	3	x	x	SYM
ejpam-110	8	4	,	,	PUNCT
ejpam-110	8	5	δ	δ	PROPN
ejpam-110	8	6	〉	〉	NOUN
ejpam-110	8	7	be	be	VERB
ejpam-110	8	8	a	a	DET
ejpam-110	8	9	topological	topological	ADJ
ejpam-110	8	10	space	space	NOUN
ejpam-110	8	11	.	.	PUNCT
ejpam-110	9	1	we	we	PRON
ejpam-110	9	2	say	say	VERB
ejpam-110	9	3	that	that	SCONJ
ejpam-110	9	4	〈	〈	PROPN
ejpam-110	9	5	x	x	SYM
ejpam-110	9	6	,	,	PUNCT
ejpam-110	9	7	δ	δ	PROPN
ejpam-110	9	8	〉	〉	NOUN
ejpam-110	9	9	is	be	AUX
ejpam-110	9	10	:	:	PUNCT
ejpam-110	9	11	(	(	PUNCT
ejpam-110	9	12	i	i	NOUN
ejpam-110	9	13	)	)	PUNCT
ejpam-110	9	14	locally	locally	ADV
ejpam-110	9	15	compact	compact	ADJ
ejpam-110	9	16	if	if	SCONJ
ejpam-110	9	17	and	and	CCONJ
ejpam-110	9	18	only	only	ADV
ejpam-110	9	19	if	if	SCONJ
ejpam-110	9	20	for	for	ADP
ejpam-110	9	21	each	each	DET
ejpam-110	9	22	x	x	SYM
ejpam-110	9	23	∈	∈	PROPN
ejpam-110	9	24	x	x	X
ejpam-110	9	25	and	and	CCONJ
ejpam-110	9	26	v	v	ADP
ejpam-110	9	27	∈	∈	PROPN
ejpam-110	9	28	δ	δ	NOUN
ejpam-110	9	29	with	with	ADP
ejpam-110	9	30	x	x	PROPN
ejpam-110	9	31	∈	∈	PROPN
ejpam-110	9	32	v	v	NOUN
ejpam-110	9	33	there	there	PRON
ejpam-110	9	34	exist	exist	VERB
ejpam-110	9	35	u	u	PROPN
ejpam-110	9	36	∈	∈	PROPN
ejpam-110	9	37	δ	δ	PROPN
ejpam-110	9	38	and	and	CCONJ
ejpam-110	9	39	a	a	DET
ejpam-110	9	40	compact	compact	ADJ
ejpam-110	9	41	subset	subset	NOUN
ejpam-110	9	42	k	k	PROPN
ejpam-110	9	43	of	of	ADP
ejpam-110	9	44	x	x	PUNCT
ejpam-110	9	45	with	with	ADP
ejpam-110	9	46	x	x	PROPN
ejpam-110	9	47	∈	∈	PROPN
ejpam-110	9	48	u	u	NOUN
ejpam-110	9	49	and	and	CCONJ
ejpam-110	9	50	u	u	NOUN
ejpam-110	9	51	⊂	⊂	PROPN
ejpam-110	9	52	k	k	PROPN
ejpam-110	10	1	⊂	⊂	PROPN
ejpam-110	10	2	v	v	PROPN
ejpam-110	10	3	.	.	PUNCT
ejpam-110	11	1	(	(	PUNCT
ejpam-110	11	2	ii	ii	NOUN
ejpam-110	11	3	)	)	PUNCT
ejpam-110	11	4	weakly	weakly	ADV
ejpam-110	11	5	locally	locally	ADV
ejpam-110	11	6	compact	compact	ADJ
ejpam-110	11	7	if	if	SCONJ
ejpam-110	12	1	and	and	CCONJ
ejpam-110	12	2	only	only	ADV
ejpam-110	12	3	if	if	SCONJ
ejpam-110	12	4	for	for	ADP
ejpam-110	12	5	each	each	DET
ejpam-110	12	6	x	x	SYM
ejpam-110	12	7	∈	∈	PROPN
ejpam-110	12	8	x	x	PUNCT
ejpam-110	12	9	there	there	PRON
ejpam-110	12	10	exist	exist	VERB
ejpam-110	12	11	u	u	PROPN
ejpam-110	12	12	∈	∈	PROPN
ejpam-110	12	13	δ	δ	PROPN
ejpam-110	12	14	and	and	CCONJ
ejpam-110	12	15	a	a	DET
ejpam-110	12	16	compact	compact	ADJ
ejpam-110	12	17	subset	subset	NOUN
ejpam-110	12	18	k	k	PROPN
ejpam-110	12	19	of	of	ADP
ejpam-110	12	20	x	x	PUNCT
ejpam-110	12	21	with	with	ADP
ejpam-110	12	22	x	x	PROPN
ejpam-110	12	23	∈	∈	PROPN
ejpam-110	12	24	u	u	NOUN
ejpam-110	12	25	and	and	CCONJ
ejpam-110	12	26	u	u	PROPN
ejpam-110	13	1	⊂	⊂	PROPN
ejpam-110	13	2	k.	k.	PROPN
ejpam-110	13	3	∗corresponding	∗corresponding	PROPN
ejpam-110	13	4	author	author	NOUN
ejpam-110	13	5	.	.	PUNCT
ejpam-110	14	1	email	email	NOUN
ejpam-110	14	2	address	address	PROPN
ejpam-110	14	3	:	:	PUNCT
ejpam-110	15	1	halis	halis	PROPN
ejpam-110	15	2	�	�	VERB
ejpam-110	15	3	ko	ko	PROPN
ejpam-110	15	4	aeli.edu.tr	aeli.edu.tr	PROPN
ejpam-110	15	5	(	(	PUNCT
ejpam-110	15	6	h.	h.	PROPN
ejpam-110	15	7	aygün	aygün	PROPN
ejpam-110	15	8	)	)	PUNCT
ejpam-110	15	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-110	16	1	147	147	NUM
ejpam-110	16	2	c	c	X
ejpam-110	16	3	©	©	PROPN
ejpam-110	16	4	2009	2009	NUM
ejpam-110	16	5	ejpam	ejpam	NOUN
ejpam-110	16	6	all	all	DET
ejpam-110	16	7	rights	right	NOUN
ejpam-110	16	8	reserved	reserve	VERB
ejpam-110	16	9	.	.	PUNCT
ejpam-110	17	1	t.	t.	PROPN
ejpam-110	17	2	breuckmann	breuckmann	PROPN
ejpam-110	17	3	,	,	PUNCT
ejpam-110	17	4	s.	s.	PROPN
ejpam-110	17	5	kudri	kudri	PROPN
ejpam-110	17	6	,	,	PUNCT
ejpam-110	17	7	and	and	CCONJ
ejpam-110	17	8	h.	h.	PROPN
ejpam-110	17	9	aygün	aygün	PROPN
ejpam-110	17	10	/	/	SYM
ejpam-110	17	11	eur	eur	PROPN
ejpam-110	17	12	.	.	PUNCT
ejpam-110	18	1	j.	j.	PROPN
ejpam-110	18	2	pure	pure	PROPN
ejpam-110	18	3	appl	appl	PROPN
ejpam-110	18	4	.	.	PROPN
ejpam-110	18	5	math	math	PROPN
ejpam-110	18	6	,	,	PUNCT
ejpam-110	18	7	2	2	NUM
ejpam-110	18	8	(	(	PUNCT
ejpam-110	18	9	2009	2009	NUM
ejpam-110	18	10	)	)	PUNCT
ejpam-110	18	11	,	,	PUNCT
ejpam-110	18	12	(	(	PUNCT
ejpam-110	18	13	147	147	NUM
ejpam-110	18	14	-	-	SYM
ejpam-110	18	15	161	161	NUM
ejpam-110	18	16	)	)	PUNCT
ejpam-110	18	17	148	148	NUM
ejpam-110	18	18	(	(	PUNCT
ejpam-110	18	19	iii	iii	NOUN
ejpam-110	18	20	)	)	PUNCT
ejpam-110	18	21	relatively	relatively	ADV
ejpam-110	18	22	locally	locally	ADV
ejpam-110	18	23	compact	compact	ADJ
ejpam-110	18	24	if	if	SCONJ
ejpam-110	18	25	and	and	CCONJ
ejpam-110	18	26	only	only	ADV
ejpam-110	18	27	if	if	SCONJ
ejpam-110	18	28	for	for	ADP
ejpam-110	18	29	each	each	DET
ejpam-110	18	30	x	x	SYM
ejpam-110	18	31	∈	∈	PROPN
ejpam-110	18	32	x	x	PUNCT
ejpam-110	18	33	there	there	PRON
ejpam-110	18	34	exist	exist	VERB
ejpam-110	18	35	u	u	PROPN
ejpam-110	18	36	∈	∈	PROPN
ejpam-110	18	37	δ	δ	NOUN
ejpam-110	18	38	with	with	ADP
ejpam-110	18	39	x	x	PROPN
ejpam-110	18	40	∈	∈	PROPN
ejpam-110	18	41	u	u	NOUN
ejpam-110	18	42	and	and	CCONJ
ejpam-110	18	43	u	u	NOUN
ejpam-110	18	44	compact	compact	ADJ
ejpam-110	18	45	.	.	PUNCT
ejpam-110	19	1	in	in	ADP
ejpam-110	19	2	this	this	DET
ejpam-110	19	3	paper	paper	NOUN
ejpam-110	19	4	we	we	PRON
ejpam-110	19	5	present	present	VERB
ejpam-110	19	6	a	a	DET
ejpam-110	19	7	generalization	generalization	NOUN
ejpam-110	19	8	for	for	ADP
ejpam-110	19	9	an	an	DET
ejpam-110	19	10	l	l	NOUN
ejpam-110	19	11	topological	topological	ADJ
ejpam-110	19	12	spaces	space	NOUN
ejpam-110	19	13	of	of	ADP
ejpam-110	19	14	these	these	DET
ejpam-110	19	15	three	three	NUM
ejpam-110	19	16	properties	property	NOUN
ejpam-110	19	17	.	.	PUNCT
ejpam-110	20	1	we	we	PRON
ejpam-110	20	2	show	show	VERB
ejpam-110	20	3	the	the	DET
ejpam-110	20	4	goodness	goodness	NOUN
ejpam-110	20	5	of	of	ADP
ejpam-110	20	6	the	the	DET
ejpam-110	20	7	proposed	propose	VERB
ejpam-110	20	8	definitions	definition	NOUN
ejpam-110	20	9	,	,	PUNCT
ejpam-110	20	10	the	the	DET
ejpam-110	20	11	equivalence	equivalence	NOUN
ejpam-110	20	12	in	in	ADP
ejpam-110	20	13	hausdorff	hausdorff	NOUN
ejpam-110	20	14	spaces	space	NOUN
ejpam-110	20	15	and	and	CCONJ
ejpam-110	20	16	present	present	VERB
ejpam-110	20	17	a	a	DET
ejpam-110	20	18	one	one	NUM
ejpam-110	20	19	point	point	NOUN
ejpam-110	20	20	compactification	compactification	NOUN
ejpam-110	20	21	theorem	theorem	NOUN
ejpam-110	20	22	.	.	PROPN
ejpam-110	20	23	2	2	X
ejpam-110	20	24	.	.	NUM
ejpam-110	20	25	preliminaries	preliminary	NOUN
ejpam-110	20	26	throughout	throughout	ADP
ejpam-110	20	27	this	this	DET
ejpam-110	20	28	paper	paper	NOUN
ejpam-110	20	29	x	x	PUNCT
ejpam-110	20	30	and	and	CCONJ
ejpam-110	20	31	y	y	PROPN
ejpam-110	20	32	are	be	AUX
ejpam-110	20	33	assumed	assume	VERB
ejpam-110	20	34	nonempty	nonempty	ADJ
ejpam-110	20	35	ordinary	ordinary	ADJ
ejpam-110	20	36	sets	set	NOUN
ejpam-110	20	37	,	,	PUNCT
ejpam-110	20	38	and	and	CCONJ
ejpam-110	20	39	l	l	NOUN
ejpam-110	20	40	=	=	SYM
ejpam-110	20	41	l	l	NOUN
ejpam-110	20	42	≤,∨,∧,′	≤,∨,∧,′	X
ejpam-110	20	43	�	�	PROPN
ejpam-110	20	44	always	always	ADV
ejpam-110	20	45	will	will	AUX
ejpam-110	20	46	denote	denote	VERB
ejpam-110	20	47	a	a	DET
ejpam-110	20	48	fuzzy	fuzzy	ADJ
ejpam-110	20	49	lattice	lattice	NOUN
ejpam-110	20	50	with	with	ADP
ejpam-110	20	51	its	its	PRON
ejpam-110	20	52	scott	scott	PROPN
ejpam-110	20	53	topology	topology	NOUN
ejpam-110	20	54	,	,	PUNCT
ejpam-110	20	55	i.e.	i.e.	X
ejpam-110	20	56	,	,	PUNCT
ejpam-110	20	57	a	a	DET
ejpam-110	20	58	complete	complete	ADJ
ejpam-110	20	59	completely	completely	ADV
ejpam-110	20	60	distributive	distributive	ADJ
ejpam-110	20	61	lattice	lattice	NOUN
ejpam-110	20	62	with	with	ADP
ejpam-110	20	63	a	a	DET
ejpam-110	20	64	smallest	small	ADJ
ejpam-110	20	65	element	element	NOUN
ejpam-110	20	66	0	0	PUNCT
ejpam-110	20	67	and	and	CCONJ
ejpam-110	20	68	a	a	DET
ejpam-110	20	69	greatest	great	ADJ
ejpam-110	20	70	element	element	NOUN
ejpam-110	20	71	1	1	NUM
ejpam-110	20	72	(	(	PUNCT
ejpam-110	20	73	0	0	NUM
ejpam-110	20	74	6=	6=	NUM
ejpam-110	20	75	1	1	NUM
ejpam-110	20	76	)	)	PUNCT
ejpam-110	20	77	,	,	PUNCT
ejpam-110	20	78	with	with	ADP
ejpam-110	20	79	an	an	DET
ejpam-110	20	80	order	order	NOUN
ejpam-110	20	81	reversing	reverse	VERB
ejpam-110	20	82	involution	involution	NOUN
ejpam-110	20	83	a→	a→	NUM
ejpam-110	20	84	a′	a′	PROPN
ejpam-110	20	85	,	,	PUNCT
ejpam-110	20	86	and	and	CCONJ
ejpam-110	20	87	the	the	DET
ejpam-110	20	88	topology	topology	NOUN
ejpam-110	20	89	is	be	AUX
ejpam-110	20	90	generated	generate	VERB
ejpam-110	20	91	by	by	ADP
ejpam-110	20	92	the	the	DET
ejpam-110	20	93	sets	set	NOUN
ejpam-110	20	94	�	�	PROPN
ejpam-110	20	95	x	x	SYM
ejpam-110	20	96	∈	∈	PROPN
ejpam-110	20	97	l	l	NOUN
ejpam-110	20	98	;	;	PUNCT
ejpam-110	20	99	x	x	PUNCT
ejpam-110	20	100	�	�	PROPN
ejpam-110	20	101	p	p	NOUN
ejpam-110	20	102	where	where	SCONJ
ejpam-110	20	103	p	p	PROPN
ejpam-110	20	104	∈	∈	PROPN
ejpam-110	20	105	pr(l	pr(l	NOUN
ejpam-110	20	106	)	)	PUNCT
ejpam-110	20	107	is	be	AUX
ejpam-110	20	108	a	a	DET
ejpam-110	20	109	prime	prime	ADJ
ejpam-110	20	110	element	element	NOUN
ejpam-110	20	111	of	of	ADP
ejpam-110	20	112	l	l	PROPN
ejpam-110	20	113	,	,	PUNCT
ejpam-110	20	114	details	detail	NOUN
ejpam-110	20	115	in	in	ADP
ejpam-110	20	116	[	[	X
ejpam-110	20	117	1	1	NUM
ejpam-110	20	118	]	]	PUNCT
ejpam-110	20	119	.	.	PUNCT
ejpam-110	21	1	if	if	SCONJ
ejpam-110	21	2	a⊂	a⊂	PRON
ejpam-110	21	3	x	x	NOUN
ejpam-110	21	4	we	we	PRON
ejpam-110	21	5	denote	denote	VERB
ejpam-110	21	6	by	by	ADP
ejpam-110	21	7	χa	χa	PRON
ejpam-110	21	8	the	the	DET
ejpam-110	21	9	characteristic	characteristic	ADJ
ejpam-110	21	10	function	function	NOUN
ejpam-110	21	11	of	of	ADP
ejpam-110	21	12	a	a	PRON
ejpam-110	21	13	in	in	ADP
ejpam-110	21	14	x	x	X
ejpam-110	21	15	.	.	PUNCT
ejpam-110	22	1	we	we	PRON
ejpam-110	22	2	denote	denote	VERB
ejpam-110	22	3	by	by	ADP
ejpam-110	22	4	lx	lx	ADP
ejpam-110	22	5	the	the	DET
ejpam-110	22	6	set	set	NOUN
ejpam-110	22	7	of	of	ADP
ejpam-110	22	8	functions	function	NOUN
ejpam-110	22	9	f	f	NOUN
ejpam-110	22	10	:	:	PUNCT
ejpam-110	22	11	x	x	X
ejpam-110	22	12	→	→	PUNCT
ejpam-110	22	13	l	l	NOUN
ejpam-110	22	14	called	call	VERB
ejpam-110	22	15	l	l	NOUN
ejpam-110	22	16	-	-	PUNCT
ejpam-110	22	17	sets	set	NOUN
ejpam-110	22	18	.	.	PUNCT
ejpam-110	23	1	an	an	DET
ejpam-110	23	2	l	l	NOUN
ejpam-110	23	3	-	-	NOUN
ejpam-110	23	4	point	point	NOUN
ejpam-110	23	5	in	in	ADP
ejpam-110	23	6	x	x	PROPN
ejpam-110	23	7	is	be	AUX
ejpam-110	23	8	an	an	DET
ejpam-110	23	9	l	l	NOUN
ejpam-110	23	10	-	-	ADJ
ejpam-110	23	11	set	set	VERB
ejpam-110	23	12	xp	xp	NOUN
ejpam-110	23	13	:	:	PUNCT
ejpam-110	23	14	x	x	X
ejpam-110	23	15	→	→	SYM
ejpam-110	23	16	l	l	NOUN
ejpam-110	23	17	,	,	PUNCT
ejpam-110	23	18	where	where	SCONJ
ejpam-110	23	19	x	x	SYM
ejpam-110	23	20	∈	∈	PROPN
ejpam-110	23	21	x	x	X
ejpam-110	23	22	and	and	CCONJ
ejpam-110	23	23	p	p	PROPN
ejpam-110	23	24	∈	∈	PROPN
ejpam-110	23	25	pr(l	pr(l	NOUN
ejpam-110	23	26	)	)	PUNCT
ejpam-110	23	27	,	,	PUNCT
ejpam-110	23	28	defined	define	VERB
ejpam-110	23	29	by	by	ADP
ejpam-110	23	30	:	:	PUNCT
ejpam-110	23	31	xp(y	xp(y	X
ejpam-110	23	32	)	)	PUNCT
ejpam-110	24	1	=	=	SYM
ejpam-110	24	2	p	p	X
ejpam-110	25	1	if	if	SCONJ
ejpam-110	25	2	y	y	PROPN
ejpam-110	25	3	=	=	PUNCT
ejpam-110	25	4	x	x	X
ejpam-110	25	5	,	,	PUNCT
ejpam-110	25	6	and	and	CCONJ
ejpam-110	25	7	xp(y	xp(y	X
ejpam-110	25	8	)	)	PUNCT
ejpam-110	25	9	=	=	SYM
ejpam-110	25	10	1	1	NUM
ejpam-110	25	11	otherwise	otherwise	ADV
ejpam-110	25	12	.	.	PUNCT
ejpam-110	26	1	we	we	PRON
ejpam-110	26	2	say	say	VERB
ejpam-110	26	3	that	that	SCONJ
ejpam-110	26	4	xp	xp	INTJ
ejpam-110	27	1	∈	∈	PROPN
ejpam-110	27	2	f	f	PROPN
ejpam-110	28	1	if	if	SCONJ
ejpam-110	28	2	and	and	CCONJ
ejpam-110	28	3	only	only	ADV
ejpam-110	28	4	if	if	SCONJ
ejpam-110	28	5	f	f	PROPN
ejpam-110	28	6	(	(	PUNCT
ejpam-110	28	7	x	x	NOUN
ejpam-110	28	8	)	)	PUNCT
ejpam-110	28	9	�	�	PROPN
ejpam-110	28	10	p	p	NOUN
ejpam-110	28	11	,	,	PUNCT
ejpam-110	28	12	see	see	VERB
ejpam-110	28	13	[	[	X
ejpam-110	28	14	6	6	NUM
ejpam-110	28	15	]	]	PUNCT
ejpam-110	28	16	.	.	PUNCT
ejpam-110	29	1	let	let	VERB
ejpam-110	29	2	〈	〈	PROPN
ejpam-110	29	3	x	x	PROPN
ejpam-110	29	4	,	,	PUNCT
ejpam-110	29	5	δ	δ	PROPN
ejpam-110	29	6	〉	〉	NOUN
ejpam-110	29	7	be	be	VERB
ejpam-110	29	8	a	a	DET
ejpam-110	29	9	topological	topological	ADJ
ejpam-110	29	10	space	space	NOUN
ejpam-110	29	11	.	.	PUNCT
ejpam-110	30	1	in	in	ADP
ejpam-110	30	2	[	[	X
ejpam-110	30	3	7	7	NUM
ejpam-110	30	4	]	]	PUNCT
ejpam-110	30	5	,	,	PUNCT
ejpam-110	30	6	warner	warner	PROPN
ejpam-110	30	7	proved	prove	VERB
ejpam-110	30	8	that	that	SCONJ
ejpam-110	30	9	the	the	DET
ejpam-110	30	10	set	set	NOUN
ejpam-110	30	11	ω(δ	ω(δ	NOUN
ejpam-110	30	12	)	)	PUNCT
ejpam-110	30	13	formed	form	VERB
ejpam-110	30	14	by	by	ADP
ejpam-110	30	15	the	the	DET
ejpam-110	30	16	continuous	continuous	ADJ
ejpam-110	30	17	functions	function	NOUN
ejpam-110	30	18	f	f	NOUN
ejpam-110	30	19	:	:	PUNCT
ejpam-110	30	20	x	x	X
ejpam-110	30	21	→	→	PUNCT
ejpam-110	30	22	l	l	NOUN
ejpam-110	30	23	is	be	AUX
ejpam-110	30	24	an	an	DET
ejpam-110	30	25	l	l	NOUN
ejpam-110	30	26	-	-	NOUN
ejpam-110	30	27	topology	topology	NOUN
ejpam-110	30	28	.	.	PUNCT
ejpam-110	31	1	the	the	DET
ejpam-110	31	2	base	base	NOUN
ejpam-110	31	3	for	for	ADP
ejpam-110	31	4	the	the	DET
ejpam-110	31	5	space	space	NOUN
ejpam-110	31	6	ω(δ	ω(δ	PROPN
ejpam-110	31	7	)	)	PUNCT
ejpam-110	31	8	is	be	AUX
ejpam-110	31	9	formed	form	VERB
ejpam-110	31	10	by	by	ADP
ejpam-110	31	11	the	the	DET
ejpam-110	31	12	functions	function	NOUN
ejpam-110	31	13	f	f	X
ejpam-110	31	14	(	(	PUNCT
ejpam-110	31	15	x	x	X
ejpam-110	31	16	)	)	PUNCT
ejpam-110	31	17	=	=	PUNCT
ejpam-110	31	18			PROPN
ejpam-110	31	19			X
ejpam-110	31	20			PROPN
ejpam-110	31	21	b	b	PROPN
ejpam-110	31	22	if	if	SCONJ
ejpam-110	31	23	x	x	PROPN
ejpam-110	31	24	∈	∈	PROPN
ejpam-110	31	25	v	v	ADP
ejpam-110	31	26	∈	∈	PROPN
ejpam-110	31	27	δ	δ	NOUN
ejpam-110	31	28	0	0	PUNCT
ejpam-110	32	1	if	if	SCONJ
ejpam-110	32	2	x	x	X
ejpam-110	32	3	/∈	/∈	NOUN
ejpam-110	32	4	v	v	ADP
ejpam-110	32	5	this	this	PRON
ejpam-110	32	6	provides	provide	VERB
ejpam-110	32	7	a	a	DET
ejpam-110	32	8	”	"	PUNCT
ejpam-110	32	9	goodness	goodness	NOUN
ejpam-110	32	10	of	of	ADP
ejpam-110	32	11	extension	extension	NOUN
ejpam-110	32	12	”	"	PUNCT
ejpam-110	32	13	criterion	criterion	NOUN
ejpam-110	32	14	for	for	ADP
ejpam-110	32	15	l	l	ADJ
ejpam-110	32	16	-	-	ADJ
ejpam-110	32	17	topological	topological	ADJ
ejpam-110	32	18	spaces	space	NOUN
ejpam-110	32	19	.	.	PUNCT
ejpam-110	33	1	definition	definition	NOUN
ejpam-110	33	2	2.1	2.1	NUM
ejpam-110	33	3	.	.	PUNCT
ejpam-110	34	1	[	[	X
ejpam-110	34	2	4	4	NUM
ejpam-110	34	3	,	,	PUNCT
ejpam-110	34	4	pu	pu	PROPN
ejpam-110	34	5	and	and	CCONJ
ejpam-110	34	6	liu	liu	PROPN
ejpam-110	34	7	]	]	X
ejpam-110	34	8	let	let	VERB
ejpam-110	34	9	〈	〈	PROPN
ejpam-110	34	10	x	x	PROPN
ejpam-110	34	11	,	,	PUNCT
ejpam-110	34	12	t	t	PROPN
ejpam-110	34	13	〉	〉	NOUN
ejpam-110	34	14	be	be	VERB
ejpam-110	34	15	an	an	DET
ejpam-110	34	16	l	l	NOUN
ejpam-110	34	17	topological	topological	ADJ
ejpam-110	34	18	space	space	NOUN
ejpam-110	34	19	and	and	CCONJ
ejpam-110	34	20	let	let	VERB
ejpam-110	34	21	f	f	PROPN
ejpam-110	34	22	∈	∈	PROPN
ejpam-110	34	23	lx	lx	NOUN
ejpam-110	34	24	.	.	PUNCT
ejpam-110	35	1	the	the	DET
ejpam-110	35	2	closure	closure	NOUN
ejpam-110	35	3	of	of	ADP
ejpam-110	35	4	f	f	PROPN
ejpam-110	35	5	,	,	PUNCT
ejpam-110	35	6	cl	cl	PROPN
ejpam-110	35	7	(	(	PUNCT
ejpam-110	35	8	f	f	PROPN
ejpam-110	35	9	)	)	PUNCT
ejpam-110	35	10	or	or	CCONJ
ejpam-110	35	11	f	f	PROPN
ejpam-110	35	12	,	,	PUNCT
ejpam-110	35	13	is	be	AUX
ejpam-110	35	14	the	the	DET
ejpam-110	35	15	l	l	NOUN
ejpam-110	35	16	-	-	ADJ
ejpam-110	35	17	set	set	NOUN
ejpam-110	35	18	defined	define	VERB
ejpam-110	35	19	by	by	ADP
ejpam-110	35	20	:	:	PUNCT
ejpam-110	35	21	cl	cl	NOUN
ejpam-110	35	22	(	(	PUNCT
ejpam-110	35	23	f	f	X
ejpam-110	35	24	)	)	PUNCT
ejpam-110	36	1	=	=	PUNCT
ejpam-110	36	2	∧	∧	NOUN
ejpam-110	36	3	¦	¦	PROPN
ejpam-110	36	4	g	g	PROPN
ejpam-110	36	5	∈	∈	PROPN
ejpam-110	36	6	lx	lx	NOUN
ejpam-110	36	7	;	;	PUNCT
ejpam-110	36	8	f	f	PROPN
ejpam-110	36	9	≤	≤	ADV
ejpam-110	36	10	g	g	PROPN
ejpam-110	36	11	,	,	PUNCT
ejpam-110	36	12	g′	g′	PROPN
ejpam-110	36	13	∈	∈	PROPN
ejpam-110	36	14	t	t	PROPN
ejpam-110	36	15	©	©	PROPN
ejpam-110	36	16	t.	t.	PROPN
ejpam-110	36	17	breuckmann	breuckmann	PROPN
ejpam-110	36	18	,	,	PUNCT
ejpam-110	36	19	s.	s.	PROPN
ejpam-110	36	20	kudri	kudri	PROPN
ejpam-110	36	21	,	,	PUNCT
ejpam-110	36	22	and	and	CCONJ
ejpam-110	36	23	h.	h.	PROPN
ejpam-110	36	24	aygün	aygün	PROPN
ejpam-110	36	25	/	/	SYM
ejpam-110	36	26	eur	eur	PROPN
ejpam-110	36	27	.	.	PUNCT
ejpam-110	37	1	j.	j.	PROPN
ejpam-110	37	2	pure	pure	PROPN
ejpam-110	37	3	appl	appl	PROPN
ejpam-110	37	4	.	.	PROPN
ejpam-110	37	5	math	math	PROPN
ejpam-110	37	6	,	,	PUNCT
ejpam-110	37	7	2	2	NUM
ejpam-110	37	8	(	(	PUNCT
ejpam-110	37	9	2009	2009	NUM
ejpam-110	37	10	)	)	PUNCT
ejpam-110	37	11	,	,	PUNCT
ejpam-110	37	12	(	(	PUNCT
ejpam-110	37	13	147	147	NUM
ejpam-110	37	14	-	-	SYM
ejpam-110	37	15	161	161	NUM
ejpam-110	37	16	)	)	PUNCT
ejpam-110	37	17	149	149	NUM
ejpam-110	37	18	definition	definition	NOUN
ejpam-110	37	19	2.2	2.2	NUM
ejpam-110	37	20	.	.	PUNCT
ejpam-110	38	1	[	[	X
ejpam-110	38	2	2	2	NUM
ejpam-110	38	3	,	,	PUNCT
ejpam-110	38	4	kudri	kudri	NOUN
ejpam-110	38	5	]	]	PUNCT
ejpam-110	38	6	let	let	VERB
ejpam-110	38	7	〈	〈	PROPN
ejpam-110	38	8	x	x	PROPN
ejpam-110	38	9	,	,	PUNCT
ejpam-110	38	10	t	t	PROPN
ejpam-110	38	11	〉	〉	NOUN
ejpam-110	38	12	be	be	VERB
ejpam-110	38	13	an	an	DET
ejpam-110	38	14	l	l	ADJ
ejpam-110	38	15	-	-	ADJ
ejpam-110	38	16	topological	topological	ADJ
ejpam-110	38	17	space	space	NOUN
ejpam-110	38	18	and	and	CCONJ
ejpam-110	38	19	let	let	VERB
ejpam-110	38	20	g	g	PROPN
ejpam-110	38	21	∈	∈	PROPN
ejpam-110	38	22	lx	lx	NOUN
ejpam-110	38	23	.	.	PUNCT
ejpam-110	39	1	we	we	PRON
ejpam-110	39	2	say	say	VERB
ejpam-110	39	3	that	that	SCONJ
ejpam-110	39	4	g	g	PROPN
ejpam-110	39	5	is	be	AUX
ejpam-110	39	6	compact	compact	ADJ
ejpam-110	39	7	if	if	SCONJ
ejpam-110	39	8	and	and	CCONJ
ejpam-110	39	9	only	only	ADV
ejpam-110	39	10	if	if	SCONJ
ejpam-110	39	11	for	for	ADP
ejpam-110	39	12	each	each	DET
ejpam-110	39	13	p	p	PROPN
ejpam-110	39	14	∈	∈	PROPN
ejpam-110	39	15	pr(l	pr(l	NOUN
ejpam-110	39	16	)	)	PUNCT
ejpam-110	39	17	and	and	CCONJ
ejpam-110	39	18	each	each	DET
ejpam-110	39	19	family	family	NOUN
ejpam-110	39	20	¦	¦	PROPN
ejpam-110	39	21	f	f	PROPN
ejpam-110	39	22	j	j	PROPN
ejpam-110	39	23	©	©	PROPN
ejpam-110	39	24	j∈j	j∈j	NOUN
ejpam-110	39	25	of	of	ADP
ejpam-110	39	26	open	open	ADJ
ejpam-110	39	27	l	l	NOUN
ejpam-110	39	28	-	-	NOUN
ejpam-110	39	29	sets	set	VERB
ejpam-110	39	30	such	such	ADJ
ejpam-110	39	31	that	that	DET
ejpam-110	39	32	�	�	PROPN
ejpam-110	39	33	∨	∨	NUM
ejpam-110	39	34	j∈j	j∈j	PROPN
ejpam-110	39	35	f	f	PROPN
ejpam-110	39	36	j	j	PROPN
ejpam-110	39	37	�	�	PROPN
ejpam-110	39	38	(	(	PUNCT
ejpam-110	39	39	x	x	NOUN
ejpam-110	39	40	)	)	PUNCT
ejpam-110	39	41	�	�	PROPN
ejpam-110	39	42	p	p	NOUN
ejpam-110	39	43	for	for	ADP
ejpam-110	39	44	all	all	DET
ejpam-110	39	45	x	x	SYM
ejpam-110	39	46	∈	∈	PROPN
ejpam-110	39	47	x	x	PUNCT
ejpam-110	39	48	with	with	ADP
ejpam-110	39	49	g(x	g(x	NOUN
ejpam-110	39	50	)	)	PUNCT
ejpam-110	39	51	≥	≥	NOUN
ejpam-110	39	52	p′	p′	NOUN
ejpam-110	39	53	,	,	PUNCT
ejpam-110	39	54	there	there	PRON
ejpam-110	39	55	exist	exist	VERB
ejpam-110	39	56	a	a	DET
ejpam-110	39	57	finite	finite	NOUN
ejpam-110	39	58	set	set	VERB
ejpam-110	39	59	j1	j1	PROPN
ejpam-110	39	60	of	of	ADP
ejpam-110	39	61	j	j	PROPN
ejpam-110	39	62	such	such	ADJ
ejpam-110	39	63	that	that	DET
ejpam-110	39	64	�	�	PROPN
ejpam-110	39	65	∨	∨	NUM
ejpam-110	39	66	j∈j1	j∈j1	PROPN
ejpam-110	39	67	f	f	PROPN
ejpam-110	39	68	j	j	PROPN
ejpam-110	39	69	�	�	PROPN
ejpam-110	39	70	(	(	PUNCT
ejpam-110	39	71	x	x	NOUN
ejpam-110	39	72	)	)	PUNCT
ejpam-110	39	73	�	�	PROPN
ejpam-110	39	74	p	p	NOUN
ejpam-110	39	75	for	for	ADP
ejpam-110	39	76	all	all	DET
ejpam-110	39	77	x	x	SYM
ejpam-110	39	78	∈	∈	PROPN
ejpam-110	39	79	x	x	PUNCT
ejpam-110	39	80	with	with	SCONJ
ejpam-110	39	81	g(x)≥	g(x)≥	NOUN
ejpam-110	39	82	p′.	p′.	NOUN
ejpam-110	39	83	theorem	theorem	VERB
ejpam-110	39	84	2.1	2.1	NUM
ejpam-110	39	85	.	.	PUNCT
ejpam-110	40	1	[	[	X
ejpam-110	40	2	5	5	NUM
ejpam-110	40	3	,	,	PUNCT
ejpam-110	40	4	warner	warner	PROPN
ejpam-110	40	5	and	and	CCONJ
ejpam-110	40	6	mclean	mclean	PROPN
ejpam-110	40	7	]	]	PUNCT
ejpam-110	40	8	let	let	VERB
ejpam-110	40	9	〈	〈	PROPN
ejpam-110	40	10	x	x	SYM
ejpam-110	40	11	,	,	PUNCT
ejpam-110	40	12	δ	δ	PROPN
ejpam-110	40	13	〉	〉	NOUN
ejpam-110	40	14	be	be	VERB
ejpam-110	40	15	a	a	DET
ejpam-110	40	16	topological	topological	ADJ
ejpam-110	40	17	space	space	NOUN
ejpam-110	40	18	.	.	PUNCT
ejpam-110	41	1	then	then	ADV
ejpam-110	41	2	:	:	PUNCT
ejpam-110	41	3	〈	〈	PROPN
ejpam-110	41	4	x	x	SYM
ejpam-110	41	5	,	,	PUNCT
ejpam-110	41	6	δ	δ	PROPN
ejpam-110	41	7	〉	〉	NOUN
ejpam-110	41	8	is	be	AUX
ejpam-110	41	9	compact	compact	ADJ
ejpam-110	41	10	if	if	SCONJ
ejpam-110	42	1	and	and	CCONJ
ejpam-110	42	2	only	only	ADV
ejpam-110	42	3	if	if	SCONJ
ejpam-110	42	4	〈	〈	PROPN
ejpam-110	42	5	x	x	SYM
ejpam-110	42	6	,	,	PUNCT
ejpam-110	42	7	ω(δ	ω(δ	PROPN
ejpam-110	42	8	)	)	PUNCT
ejpam-110	42	9	〉	〉	NOUN
ejpam-110	42	10	is	be	AUX
ejpam-110	42	11	compact	compact	ADJ
ejpam-110	42	12	.	.	PUNCT
ejpam-110	43	1	proposition	proposition	NOUN
ejpam-110	43	2	2.1	2.1	NUM
ejpam-110	43	3	.	.	PUNCT
ejpam-110	44	1	[	[	X
ejpam-110	44	2	2	2	NUM
ejpam-110	44	3	,	,	PUNCT
ejpam-110	44	4	kudri	kudri	NOUN
ejpam-110	44	5	]	]	PUNCT
ejpam-110	44	6	let	let	VERB
ejpam-110	44	7	〈	〈	PROPN
ejpam-110	44	8	x	x	PROPN
ejpam-110	44	9	,	,	PUNCT
ejpam-110	44	10	t	t	PROPN
ejpam-110	44	11	〉	〉	NOUN
ejpam-110	44	12	be	be	VERB
ejpam-110	44	13	an	an	DET
ejpam-110	44	14	hausdorff	hausdorff	NOUN
ejpam-110	44	15	l	l	ADJ
ejpam-110	44	16	-	-	ADJ
ejpam-110	44	17	topological	topological	ADJ
ejpam-110	44	18	space	space	NOUN
ejpam-110	44	19	and	and	CCONJ
ejpam-110	44	20	f	f	NOUN
ejpam-110	44	21	⊂	⊂	PROPN
ejpam-110	44	22	x	x	X
ejpam-110	44	23	.	.	PUNCT
ejpam-110	45	1	if	if	SCONJ
ejpam-110	45	2	χf	χf	NOUN
ejpam-110	45	3	is	be	AUX
ejpam-110	45	4	compact	compact	ADJ
ejpam-110	45	5	in	in	ADP
ejpam-110	45	6	〈	〈	PROPN
ejpam-110	45	7	x	x	X
ejpam-110	45	8	,	,	PUNCT
ejpam-110	45	9	t	t	PROPN
ejpam-110	45	10	〉	〉	NOUN
ejpam-110	45	11	then	then	ADV
ejpam-110	45	12	χf	χf	VERB
ejpam-110	45	13	is	be	AUX
ejpam-110	45	14	closed	closed	ADJ
ejpam-110	45	15	.	.	PUNCT
ejpam-110	46	1	proposition	proposition	NOUN
ejpam-110	46	2	2.2	2.2	NUM
ejpam-110	46	3	.	.	PUNCT
ejpam-110	47	1	[	[	X
ejpam-110	47	2	2	2	NUM
ejpam-110	47	3	,	,	PUNCT
ejpam-110	47	4	kudri	kudri	NOUN
ejpam-110	47	5	]	]	PUNCT
ejpam-110	47	6	let	let	VERB
ejpam-110	47	7	〈	〈	PROPN
ejpam-110	47	8	x	x	PROPN
ejpam-110	47	9	,	,	PUNCT
ejpam-110	47	10	t	t	PROPN
ejpam-110	47	11	〉	〉	NOUN
ejpam-110	47	12	be	be	VERB
ejpam-110	47	13	an	an	DET
ejpam-110	47	14	l	l	ADJ
ejpam-110	47	15	-	-	ADJ
ejpam-110	47	16	topological	topological	ADJ
ejpam-110	47	17	space	space	NOUN
ejpam-110	47	18	.	.	PUNCT
ejpam-110	48	1	if	if	SCONJ
ejpam-110	48	2	g	g	PROPN
ejpam-110	48	3	∈	∈	PROPN
ejpam-110	48	4	lx	lx	NOUN
ejpam-110	48	5	is	be	AUX
ejpam-110	48	6	a	a	DET
ejpam-110	48	7	compact	compact	ADJ
ejpam-110	48	8	l	l	NOUN
ejpam-110	48	9	-	-	NOUN
ejpam-110	48	10	set	set	ADJ
ejpam-110	48	11	,	,	PUNCT
ejpam-110	48	12	then	then	ADV
ejpam-110	48	13	for	for	ADP
ejpam-110	48	14	each	each	DET
ejpam-110	48	15	closed	closed	ADJ
ejpam-110	48	16	l	l	NOUN
ejpam-110	48	17	-	-	ADJ
ejpam-110	48	18	set	set	VERB
ejpam-110	48	19	h	h	NOUN
ejpam-110	48	20	∈	∈	NOUN
ejpam-110	48	21	lx	lx	NOUN
ejpam-110	48	22	,	,	PUNCT
ejpam-110	48	23	h∧	h∧	PROPN
ejpam-110	48	24	g	g	PROPN
ejpam-110	48	25	is	be	AUX
ejpam-110	48	26	a	a	DET
ejpam-110	48	27	compact	compact	ADJ
ejpam-110	48	28	l	l	NOUN
ejpam-110	48	29	-	-	NOUN
ejpam-110	48	30	set	set	NOUN
ejpam-110	48	31	.	.	PUNCT
ejpam-110	49	1	proposition	proposition	NOUN
ejpam-110	49	2	2.3	2.3	NUM
ejpam-110	49	3	.	.	PUNCT
ejpam-110	50	1	[	[	X
ejpam-110	50	2	2	2	NUM
ejpam-110	50	3	,	,	PUNCT
ejpam-110	50	4	kudri	kudri	NOUN
ejpam-110	50	5	]	]	PUNCT
ejpam-110	50	6	let	let	VERB
ejpam-110	50	7	x	x	PRON
ejpam-110	50	8	,	,	PUNCT
ejpam-110	50	9	tx	tx	PROPN
ejpam-110	50	10	�	�	PROPN
ejpam-110	50	11	and	and	CCONJ
ejpam-110	50	12	y	y	PROPN
ejpam-110	50	13	,	,	PUNCT
ejpam-110	50	14	ty	ty	PRON
ejpam-110	50	15	�	�	PROPN
ejpam-110	50	16	be	be	AUX
ejpam-110	50	17	l	l	ADJ
ejpam-110	50	18	-	-	ADJ
ejpam-110	50	19	topological	topological	ADJ
ejpam-110	50	20	spaces	space	NOUN
ejpam-110	50	21	and	and	CCONJ
ejpam-110	50	22	let	let	VERB
ejpam-110	50	23	f	f	NOUN
ejpam-110	50	24	:	:	PUNCT
ejpam-110	50	25	x	x	X
ejpam-110	50	26	→	→	SYM
ejpam-110	50	27	y	y	X
ejpam-110	50	28	be	be	AUX
ejpam-110	50	29	a	a	DET
ejpam-110	50	30	continuous	continuous	ADJ
ejpam-110	50	31	mapping	mapping	NOUN
ejpam-110	50	32	.	.	PUNCT
ejpam-110	51	1	if	if	SCONJ
ejpam-110	51	2	g	g	PROPN
ejpam-110	51	3	∈	∈	PROPN
ejpam-110	51	4	lx	lx	NOUN
ejpam-110	51	5	is	be	AUX
ejpam-110	51	6	a	a	DET
ejpam-110	51	7	compact	compact	ADJ
ejpam-110	51	8	l	l	NOUN
ejpam-110	51	9	-	-	NOUN
ejpam-110	51	10	set	set	NOUN
ejpam-110	51	11	,	,	PUNCT
ejpam-110	51	12	then	then	ADV
ejpam-110	51	13	f	f	PROPN
ejpam-110	51	14	(	(	PUNCT
ejpam-110	51	15	g	g	NOUN
ejpam-110	51	16	)	)	PUNCT
ejpam-110	51	17	∈	∈	NOUN
ejpam-110	51	18	ly	ly	X
ejpam-110	51	19	is	be	AUX
ejpam-110	51	20	a	a	DET
ejpam-110	51	21	compact	compact	ADJ
ejpam-110	51	22	l	l	NOUN
ejpam-110	51	23	-	-	NOUN
ejpam-110	51	24	set	set	NOUN
ejpam-110	51	25	.	.	PUNCT
ejpam-110	52	1	proposition	proposition	NOUN
ejpam-110	52	2	2.4	2.4	NUM
ejpam-110	52	3	.	.	PUNCT
ejpam-110	53	1	[	[	X
ejpam-110	53	2	2	2	NUM
ejpam-110	53	3	,	,	PUNCT
ejpam-110	53	4	kudri	kudri	NOUN
ejpam-110	53	5	]	]	PUNCT
ejpam-110	53	6	let	let	VERB
ejpam-110	53	7	¦	¦	X
ejpam-110	53	8	¬	¬	PROPN
ejpam-110	53	9	x	x	SYM
ejpam-110	53	10	j	j	PROPN
ejpam-110	53	11	,	,	PUNCT
ejpam-110	53	12	t	t	PROPN
ejpam-110	53	13	j	j	PROPN
ejpam-110	53	14	¶	¶	PROPN
ejpam-110	53	15	©	©	PROPN
ejpam-110	53	16	j∈j	j∈j	NOUN
ejpam-110	53	17	be	be	AUX
ejpam-110	53	18	a	a	DET
ejpam-110	53	19	family	family	NOUN
ejpam-110	53	20	of	of	ADP
ejpam-110	53	21	l	l	ADJ
ejpam-110	53	22	-	-	ADJ
ejpam-110	53	23	topological	topological	ADJ
ejpam-110	53	24	spaces	space	NOUN
ejpam-110	53	25	and	and	CCONJ
ejpam-110	53	26	g	g	NOUN
ejpam-110	53	27	j	j	PROPN
ejpam-110	53	28	∈	∈	PROPN
ejpam-110	54	1	lx	lx	ADP
ejpam-110	54	2	j	j	PROPN
ejpam-110	54	3	be	be	VERB
ejpam-110	54	4	a	a	DET
ejpam-110	54	5	compact	compact	ADJ
ejpam-110	54	6	l	l	NOUN
ejpam-110	54	7	-	-	NOUN
ejpam-110	54	8	set	set	NOUN
ejpam-110	54	9	for	for	ADP
ejpam-110	54	10	each	each	DET
ejpam-110	54	11	j	j	PROPN
ejpam-110	54	12	∈	∈	PROPN
ejpam-110	54	13	j.	j.	PROPN
ejpam-110	54	14	then	then	ADV
ejpam-110	54	15	the	the	DET
ejpam-110	54	16	product	product	NOUN
ejpam-110	54	17	set	set	VERB
ejpam-110	54	18	g	g	PROPN
ejpam-110	54	19	=	=	PUNCT
ejpam-110	54	20	∧	∧	PROPN
ejpam-110	54	21	j∈jπ	j∈jπ	PROPN
ejpam-110	54	22	−1	−1	PROPN
ejpam-110	54	23	j	j	PROPN
ejpam-110	54	24	(	(	PUNCT
ejpam-110	54	25	g	g	PROPN
ejpam-110	54	26	j	j	PROPN
ejpam-110	54	27	)	)	PUNCT
ejpam-110	54	28	is	be	AUX
ejpam-110	54	29	a	a	DET
ejpam-110	54	30	compact	compact	ADJ
ejpam-110	54	31	l	l	NOUN
ejpam-110	54	32	-	-	NOUN
ejpam-110	54	33	set	set	VERB
ejpam-110	54	34	in	in	ADP
ejpam-110	54	35	the	the	DET
ejpam-110	54	36	product	product	NOUN
ejpam-110	54	37	space	space	NOUN
ejpam-110	54	38	.	.	PUNCT
ejpam-110	55	1	proposition	proposition	NOUN
ejpam-110	55	2	2.5	2.5	NUM
ejpam-110	55	3	.	.	PUNCT
ejpam-110	56	1	[	[	X
ejpam-110	56	2	2	2	NUM
ejpam-110	56	3	,	,	PUNCT
ejpam-110	56	4	kudri	kudri	NOUN
ejpam-110	56	5	]	]	PUNCT
ejpam-110	56	6	let	let	VERB
ejpam-110	56	7	s	s	PRON
ejpam-110	56	8	be	be	AUX
ejpam-110	56	9	a	a	DET
ejpam-110	56	10	subbase	subbase	NOUN
ejpam-110	56	11	for	for	ADP
ejpam-110	56	12	the	the	DET
ejpam-110	56	13	l	l	NOUN
ejpam-110	56	14	-	-	NOUN
ejpam-110	56	15	topology	topology	NOUN
ejpam-110	56	16	t	t	NOUN
ejpam-110	56	17	in	in	ADP
ejpam-110	56	18	x	x	PUNCT
ejpam-110	56	19	and	and	CCONJ
ejpam-110	56	20	let	let	VERB
ejpam-110	56	21	g	g	PROPN
ejpam-110	56	22	∈	∈	PROPN
ejpam-110	56	23	lx	lx	NOUN
ejpam-110	56	24	.	.	PUNCT
ejpam-110	57	1	if	if	SCONJ
ejpam-110	57	2	for	for	ADP
ejpam-110	57	3	each	each	DET
ejpam-110	57	4	p	p	PROPN
ejpam-110	57	5	∈	∈	PROPN
ejpam-110	57	6	pr(l	pr(l	NOUN
ejpam-110	57	7	)	)	PUNCT
ejpam-110	57	8	and	and	CCONJ
ejpam-110	57	9	each	each	DET
ejpam-110	57	10	family	family	NOUN
ejpam-110	57	11	¦	¦	PROPN
ejpam-110	57	12	f	f	PROPN
ejpam-110	57	13	j	j	PROPN
ejpam-110	57	14	©	©	PROPN
ejpam-110	57	15	j∈j	j∈j	NOUN
ejpam-110	57	16	of	of	ADP
ejpam-110	57	17	sub	sub	NOUN
ejpam-110	57	18	basis	basis	NOUN
ejpam-110	57	19	open	open	ADJ
ejpam-110	57	20	l	l	NOUN
ejpam-110	57	21	-	-	NOUN
ejpam-110	57	22	sets	set	NOUN
ejpam-110	57	23	with	with	ADP
ejpam-110	57	24	�	�	PROPN
ejpam-110	57	25	∨	∨	NUM
ejpam-110	57	26	j∈j	j∈j	PROPN
ejpam-110	57	27	f	f	PROPN
ejpam-110	57	28	j	j	PROPN
ejpam-110	57	29	�	�	PROPN
ejpam-110	57	30	(	(	PUNCT
ejpam-110	57	31	x	x	NOUN
ejpam-110	57	32	)	)	PUNCT
ejpam-110	57	33	�	�	PROPN
ejpam-110	57	34	p	p	NOUN
ejpam-110	57	35	for	for	ADP
ejpam-110	57	36	all	all	DET
ejpam-110	57	37	x	x	SYM
ejpam-110	57	38	∈	∈	PROPN
ejpam-110	57	39	x	x	PUNCT
ejpam-110	57	40	with	with	ADP
ejpam-110	57	41	g(x)≥	g(x)≥	PROPN
ejpam-110	57	42	p′	p′	NOUN
ejpam-110	57	43	there	there	PRON
ejpam-110	57	44	exists	exist	VERB
ejpam-110	57	45	a	a	DET
ejpam-110	57	46	finite	finite	NOUN
ejpam-110	57	47	subset	subset	VERB
ejpam-110	57	48	f	f	PROPN
ejpam-110	57	49	of	of	ADP
ejpam-110	57	50	j	j	PROPN
ejpam-110	57	51	with	with	ADP
ejpam-110	57	52	�	�	PROPN
ejpam-110	57	53	∨	∨	NUM
ejpam-110	57	54	j∈f	j∈f	PROPN
ejpam-110	57	55	f	f	PROPN
ejpam-110	57	56	j	j	PROPN
ejpam-110	57	57	�	�	PROPN
ejpam-110	57	58	(	(	PUNCT
ejpam-110	57	59	x	x	NOUN
ejpam-110	57	60	)	)	PUNCT
ejpam-110	57	61	�	�	PROPN
ejpam-110	57	62	p	p	NOUN
ejpam-110	57	63	for	for	ADP
ejpam-110	57	64	all	all	DET
ejpam-110	57	65	x	x	SYM
ejpam-110	57	66	∈	∈	PROPN
ejpam-110	57	67	x	x	PUNCT
ejpam-110	57	68	with	with	ADP
ejpam-110	57	69	g(x)≥	g(x)≥	PROPN
ejpam-110	57	70	p′	p′	PROPN
ejpam-110	57	71	,	,	PUNCT
ejpam-110	57	72	then	then	ADV
ejpam-110	57	73	,	,	PUNCT
ejpam-110	57	74	g	g	PROPN
ejpam-110	57	75	is	be	AUX
ejpam-110	57	76	compact	compact	ADJ
ejpam-110	57	77	in	in	ADP
ejpam-110	57	78	〈	〈	PROPN
ejpam-110	57	79	x	x	SYM
ejpam-110	57	80	,	,	PUNCT
ejpam-110	57	81	t	t	PROPN
ejpam-110	57	82	〉	〉	NOUN
ejpam-110	57	83	.	.	PUNCT
ejpam-110	58	1	definition	definition	NOUN
ejpam-110	58	2	2.3	2.3	NUM
ejpam-110	58	3	.	.	PUNCT
ejpam-110	59	1	[	[	X
ejpam-110	59	2	5	5	NUM
ejpam-110	59	3	,	,	PUNCT
ejpam-110	59	4	warner	warner	PROPN
ejpam-110	59	5	and	and	CCONJ
ejpam-110	59	6	mclean	mclean	PROPN
ejpam-110	59	7	]	]	PUNCT
ejpam-110	59	8	an	an	DET
ejpam-110	59	9	l	l	ADJ
ejpam-110	59	10	-	-	ADJ
ejpam-110	59	11	topological	topological	ADJ
ejpam-110	59	12	space	space	NOUN
ejpam-110	59	13	〈	〈	PROPN
ejpam-110	59	14	x	x	X
ejpam-110	59	15	,	,	PUNCT
ejpam-110	59	16	t	t	PROPN
ejpam-110	59	17	〉	〉	NOUN
ejpam-110	59	18	is	be	AUX
ejpam-110	59	19	hausdorff	hausdorff	NOUN
ejpam-110	59	20	if	if	SCONJ
ejpam-110	59	21	and	and	CCONJ
ejpam-110	59	22	only	only	ADV
ejpam-110	59	23	if	if	SCONJ
ejpam-110	59	24	for	for	ADP
ejpam-110	59	25	every	every	DET
ejpam-110	59	26	p	p	X
ejpam-110	59	27	,	,	PUNCT
ejpam-110	59	28	q	q	NOUN
ejpam-110	59	29	∈	∈	NOUN
ejpam-110	59	30	pr(l	pr(l	NOUN
ejpam-110	59	31	)	)	PUNCT
ejpam-110	59	32	and	and	CCONJ
ejpam-110	59	33	every	every	DET
ejpam-110	59	34	x	x	X
ejpam-110	59	35	6=	6=	ADP
ejpam-110	59	36	y	y	NOUN
ejpam-110	59	37	in	in	ADP
ejpam-110	59	38	x	x	SYM
ejpam-110	59	39	there	there	PRON
ejpam-110	59	40	exist	exist	VERB
ejpam-110	59	41	f	f	NOUN
ejpam-110	59	42	,	,	PUNCT
ejpam-110	59	43	g	g	PROPN
ejpam-110	59	44	∈	∈	PROPN
ejpam-110	59	45	t	t	NOUN
ejpam-110	59	46	such	such	ADJ
ejpam-110	59	47	that	that	SCONJ
ejpam-110	59	48	f	f	PROPN
ejpam-110	59	49	(	(	PUNCT
ejpam-110	59	50	x	x	X
ejpam-110	59	51	)	)	PUNCT
ejpam-110	59	52	�	�	PROPN
ejpam-110	59	53	p	p	PROPN
ejpam-110	59	54	,	,	PUNCT
ejpam-110	59	55	g(y	g(y	PROPN
ejpam-110	59	56	)	)	PUNCT
ejpam-110	59	57	�	�	PROPN
ejpam-110	59	58	q	q	PROPN
ejpam-110	60	1	and	and	CCONJ
ejpam-110	60	2	,	,	PUNCT
ejpam-110	60	3	f	f	PROPN
ejpam-110	60	4	(	(	PUNCT
ejpam-110	60	5	z	z	NOUN
ejpam-110	60	6	)	)	PUNCT
ejpam-110	60	7	=	=	SYM
ejpam-110	60	8	0	0	NUM
ejpam-110	60	9	or	or	CCONJ
ejpam-110	60	10	g(z	g(z	ADJ
ejpam-110	60	11	)	)	PUNCT
ejpam-110	61	1	=	=	SYM
ejpam-110	61	2	0	0	NUM
ejpam-110	61	3	for	for	ADP
ejpam-110	61	4	all	all	DET
ejpam-110	61	5	z	z	NOUN
ejpam-110	61	6	∈	∈	PROPN
ejpam-110	61	7	x	x	X
ejpam-110	61	8	.	.	PUNCT
ejpam-110	62	1	theorem	theorem	VERB
ejpam-110	62	2	2.2	2.2	NUM
ejpam-110	62	3	.	.	PUNCT
ejpam-110	63	1	[	[	X
ejpam-110	63	2	5	5	NUM
ejpam-110	63	3	,	,	PUNCT
ejpam-110	63	4	warner	warner	PROPN
ejpam-110	63	5	and	and	CCONJ
ejpam-110	63	6	mclean	mclean	PROPN
ejpam-110	63	7	]	]	PUNCT
ejpam-110	63	8	let	let	VERB
ejpam-110	63	9	〈	〈	PROPN
ejpam-110	63	10	x	x	SYM
ejpam-110	63	11	,	,	PUNCT
ejpam-110	63	12	δ	δ	PROPN
ejpam-110	63	13	〉	〉	NOUN
ejpam-110	63	14	be	be	VERB
ejpam-110	63	15	a	a	DET
ejpam-110	63	16	topological	topological	ADJ
ejpam-110	63	17	space	space	NOUN
ejpam-110	63	18	.	.	PUNCT
ejpam-110	64	1	then	then	ADV
ejpam-110	64	2	:	:	PUNCT
ejpam-110	64	3	〈	〈	PROPN
ejpam-110	64	4	x	x	SYM
ejpam-110	64	5	,	,	PUNCT
ejpam-110	64	6	δ	δ	PROPN
ejpam-110	64	7	〉	〉	NOUN
ejpam-110	64	8	is	be	AUX
ejpam-110	64	9	hausdorff	hausdorff	NOUN
ejpam-110	64	10	if	if	SCONJ
ejpam-110	64	11	and	and	CCONJ
ejpam-110	64	12	only	only	ADV
ejpam-110	64	13	if	if	SCONJ
ejpam-110	64	14	〈	〈	PROPN
ejpam-110	64	15	x	x	SYM
ejpam-110	64	16	,	,	PUNCT
ejpam-110	64	17	ω(δ	ω(δ	PROPN
ejpam-110	64	18	)	)	PUNCT
ejpam-110	64	19	〉	〉	NOUN
ejpam-110	64	20	is	be	AUX
ejpam-110	64	21	hausdorff	hausdorff	NOUN
ejpam-110	64	22	.	.	PUNCT
ejpam-110	65	1	theorem	theorem	VERB
ejpam-110	65	2	2.3	2.3	NUM
ejpam-110	65	3	.	.	PUNCT
ejpam-110	66	1	[	[	X
ejpam-110	66	2	5	5	NUM
ejpam-110	66	3	,	,	PUNCT
ejpam-110	66	4	warner	warner	NOUN
ejpam-110	66	5	and	and	CCONJ
ejpam-110	66	6	mclean	mclean	PROPN
ejpam-110	66	7	]	]	PUNCT
ejpam-110	66	8	if	if	SCONJ
ejpam-110	66	9	〈	〈	PROPN
ejpam-110	66	10	x	x	X
ejpam-110	66	11	,	,	PUNCT
ejpam-110	66	12	t	t	PROPN
ejpam-110	66	13	〉	〉	NOUN
ejpam-110	66	14	is	be	AUX
ejpam-110	66	15	a	a	DET
ejpam-110	66	16	compact	compact	ADJ
ejpam-110	66	17	hausdorff	hausdorff	NOUN
ejpam-110	66	18	fully	fully	ADV
ejpam-110	66	19	stratified	stratify	VERB
ejpam-110	66	20	ltopological	ltopological	ADJ
ejpam-110	66	21	space	space	NOUN
ejpam-110	66	22	then	then	ADV
ejpam-110	66	23	it	it	PRON
ejpam-110	66	24	’s	’	VERB
ejpam-110	66	25	topological	topological	ADJ
ejpam-110	66	26	,	,	PUNCT
ejpam-110	66	27	that	that	PRON
ejpam-110	66	28	s	s	VERB
ejpam-110	66	29	it	it	PRON
ejpam-110	66	30	,	,	PUNCT
ejpam-110	66	31	there	there	PRON
ejpam-110	66	32	is	be	VERB
ejpam-110	66	33	a	a	DET
ejpam-110	66	34	topology	topology	NOUN
ejpam-110	66	35	δ	δ	NOUN
ejpam-110	66	36	∈	∈	PROPN
ejpam-110	66	37	x	x	PUNCT
ejpam-110	66	38	such	such	ADJ
ejpam-110	66	39	that	that	SCONJ
ejpam-110	66	40	t	t	NOUN
ejpam-110	66	41	=	=	NOUN
ejpam-110	66	42	ω(δ	ω(δ	PROPN
ejpam-110	66	43	)	)	PUNCT
ejpam-110	66	44	.	.	PUNCT
ejpam-110	67	1	t.	t.	PROPN
ejpam-110	67	2	breuckmann	breuckmann	PROPN
ejpam-110	67	3	,	,	PUNCT
ejpam-110	67	4	s.	s.	PROPN
ejpam-110	67	5	kudri	kudri	PROPN
ejpam-110	67	6	,	,	PUNCT
ejpam-110	67	7	and	and	CCONJ
ejpam-110	67	8	h.	h.	PROPN
ejpam-110	67	9	aygün	aygün	PROPN
ejpam-110	67	10	/	/	SYM
ejpam-110	67	11	eur	eur	PROPN
ejpam-110	67	12	.	.	PUNCT
ejpam-110	68	1	j.	j.	PROPN
ejpam-110	68	2	pure	pure	PROPN
ejpam-110	68	3	appl	appl	PROPN
ejpam-110	68	4	.	.	PROPN
ejpam-110	68	5	math	math	PROPN
ejpam-110	68	6	,	,	PUNCT
ejpam-110	68	7	2	2	NUM
ejpam-110	68	8	(	(	PUNCT
ejpam-110	68	9	2009	2009	NUM
ejpam-110	68	10	)	)	PUNCT
ejpam-110	68	11	,	,	PUNCT
ejpam-110	68	12	(	(	PUNCT
ejpam-110	68	13	147	147	NUM
ejpam-110	68	14	-	-	SYM
ejpam-110	68	15	161	161	NUM
ejpam-110	68	16	)	)	PUNCT
ejpam-110	68	17	150	150	NUM
ejpam-110	68	18	definition	definition	NOUN
ejpam-110	68	19	2.4	2.4	NUM
ejpam-110	68	20	.	.	PUNCT
ejpam-110	69	1	[	[	X
ejpam-110	69	2	5	5	NUM
ejpam-110	69	3	,	,	PUNCT
ejpam-110	69	4	warner	warner	PROPN
ejpam-110	69	5	and	and	CCONJ
ejpam-110	69	6	mclean	mclean	PROPN
ejpam-110	69	7	]	]	PUNCT
ejpam-110	69	8	an	an	DET
ejpam-110	69	9	l	l	ADJ
ejpam-110	69	10	-	-	ADJ
ejpam-110	69	11	topological	topological	ADJ
ejpam-110	69	12	space	space	NOUN
ejpam-110	69	13	〈	〈	PROPN
ejpam-110	69	14	x	x	X
ejpam-110	69	15	,	,	PUNCT
ejpam-110	69	16	t	t	PROPN
ejpam-110	69	17	〉	〉	NOUN
ejpam-110	69	18	is	be	AUX
ejpam-110	69	19	regular	regular	ADJ
ejpam-110	69	20	if	if	SCONJ
ejpam-110	69	21	and	and	CCONJ
ejpam-110	69	22	only	only	ADV
ejpam-110	69	23	if	if	SCONJ
ejpam-110	69	24	for	for	ADP
ejpam-110	69	25	every	every	DET
ejpam-110	69	26	p	p	PROPN
ejpam-110	69	27	∈	∈	PROPN
ejpam-110	69	28	pr(l	pr(l	NOUN
ejpam-110	69	29	)	)	PUNCT
ejpam-110	69	30	,	,	PUNCT
ejpam-110	69	31	for	for	ADP
ejpam-110	69	32	each	each	DET
ejpam-110	69	33	x	x	SYM
ejpam-110	69	34	∈	∈	PROPN
ejpam-110	69	35	x	x	X
ejpam-110	69	36	and	and	CCONJ
ejpam-110	69	37	each	each	DET
ejpam-110	69	38	closed	closed	ADJ
ejpam-110	69	39	l	l	NOUN
ejpam-110	69	40	-	-	ADJ
ejpam-110	69	41	set	set	VERB
ejpam-110	69	42	f	f	NOUN
ejpam-110	69	43	such	such	ADJ
ejpam-110	69	44	that	that	SCONJ
ejpam-110	69	45	there	there	PRON
ejpam-110	69	46	is	be	VERB
ejpam-110	69	47	y	y	PROPN
ejpam-110	69	48	∈	∈	PROPN
ejpam-110	69	49	x	x	PUNCT
ejpam-110	69	50	with	with	ADP
ejpam-110	69	51	f	f	PROPN
ejpam-110	69	52	(	(	PUNCT
ejpam-110	69	53	y	y	PROPN
ejpam-110	69	54	)	)	PUNCT
ejpam-110	69	55	≥	≥	NOUN
ejpam-110	69	56	p′	p′	NOUN
ejpam-110	69	57	and	and	CCONJ
ejpam-110	69	58	f	f	PROPN
ejpam-110	69	59	(	(	PUNCT
ejpam-110	69	60	x	x	X
ejpam-110	69	61	)	)	PUNCT
ejpam-110	69	62	=	=	SYM
ejpam-110	69	63	0	0	NUM
ejpam-110	69	64	,	,	PUNCT
ejpam-110	69	65	there	there	PRON
ejpam-110	69	66	are	be	VERB
ejpam-110	69	67	u	u	NOUN
ejpam-110	69	68	,	,	PUNCT
ejpam-110	69	69	v	v	PROPN
ejpam-110	69	70	∈	∈	PROPN
ejpam-110	69	71	t	t	NOUN
ejpam-110	69	72	with	with	ADP
ejpam-110	69	73	u(x	u(x	NOUN
ejpam-110	69	74	)	)	PUNCT
ejpam-110	69	75	�	�	PROPN
ejpam-110	69	76	p	p	NOUN
ejpam-110	69	77	,	,	PUNCT
ejpam-110	69	78	v(z	v(z	PROPN
ejpam-110	69	79	)	)	PUNCT
ejpam-110	69	80	�	�	PROPN
ejpam-110	69	81	p	p	NOUN
ejpam-110	69	82	for	for	ADP
ejpam-110	69	83	each	each	DET
ejpam-110	69	84	z	z	NOUN
ejpam-110	69	85	∈	∈	PROPN
ejpam-110	69	86	x	x	PUNCT
ejpam-110	69	87	with	with	ADP
ejpam-110	69	88	f	f	PROPN
ejpam-110	69	89	(	(	PUNCT
ejpam-110	69	90	z	z	NOUN
ejpam-110	69	91	)	)	PUNCT
ejpam-110	69	92	≥	≥	NOUN
ejpam-110	69	93	p′	p′	NOUN
ejpam-110	69	94	,	,	PUNCT
ejpam-110	69	95	and	and	CCONJ
ejpam-110	69	96	,	,	PUNCT
ejpam-110	69	97	u(z	u(z	PROPN
ejpam-110	69	98	)	)	PUNCT
ejpam-110	69	99	=	=	SYM
ejpam-110	69	100	0	0	NUM
ejpam-110	69	101	or	or	CCONJ
ejpam-110	69	102	v(z	v(z	NOUN
ejpam-110	69	103	)	)	PUNCT
ejpam-110	70	1	=	=	SYM
ejpam-110	70	2	0	0	NUM
ejpam-110	71	1	for	for	ADP
ejpam-110	71	2	each	each	DET
ejpam-110	71	3	z	z	NOUN
ejpam-110	71	4	∈	∈	PROPN
ejpam-110	71	5	x	x	X
ejpam-110	71	6	.	.	PUNCT
ejpam-110	71	7	theorem	theorem	VERB
ejpam-110	71	8	2.4	2.4	NUM
ejpam-110	71	9	.	.	PUNCT
ejpam-110	72	1	[	[	X
ejpam-110	72	2	2	2	NUM
ejpam-110	72	3	,	,	PUNCT
ejpam-110	72	4	kudri	kudri	NOUN
ejpam-110	72	5	]	]	PUNCT
ejpam-110	72	6	if	if	SCONJ
ejpam-110	72	7	〈	〈	PROPN
ejpam-110	72	8	x	x	SYM
ejpam-110	72	9	,	,	PUNCT
ejpam-110	72	10	δ	δ	PROPN
ejpam-110	72	11	〉	〉	NOUN
ejpam-110	72	12	is	be	AUX
ejpam-110	72	13	a	a	DET
ejpam-110	72	14	compact	compact	ADJ
ejpam-110	72	15	hausdorff	hausdorff	NOUN
ejpam-110	72	16	l	l	ADJ
ejpam-110	72	17	-	-	ADJ
ejpam-110	72	18	topological	topological	ADJ
ejpam-110	72	19	space	space	NOUN
ejpam-110	72	20	then	then	ADV
ejpam-110	72	21	〈	〈	PROPN
ejpam-110	72	22	x	x	X
ejpam-110	72	23	,	,	PUNCT
ejpam-110	72	24	t	t	PROPN
ejpam-110	72	25	〉	〉	NOUN
ejpam-110	72	26	is	be	AUX
ejpam-110	72	27	regular	regular	ADJ
ejpam-110	72	28	.	.	PUNCT
ejpam-110	73	1	3	3	X
ejpam-110	73	2	.	.	NUM
ejpam-110	73	3	proposed	propose	VERB
ejpam-110	73	4	definitions	definition	NOUN
ejpam-110	73	5	and	and	CCONJ
ejpam-110	73	6	their	their	PRON
ejpam-110	73	7	goodness	goodness	NOUN
ejpam-110	73	8	theorems	theorem	NOUN
ejpam-110	73	9	definition	definition	NOUN
ejpam-110	73	10	3.1	3.1	NUM
ejpam-110	73	11	.	.	PUNCT
ejpam-110	74	1	an	an	DET
ejpam-110	74	2	l	l	ADJ
ejpam-110	74	3	-	-	ADJ
ejpam-110	74	4	topological	topological	ADJ
ejpam-110	74	5	space	space	NOUN
ejpam-110	74	6	〈	〈	PROPN
ejpam-110	74	7	x	x	X
ejpam-110	74	8	,	,	PUNCT
ejpam-110	74	9	t	t	PROPN
ejpam-110	74	10	〉	〉	NOUN
ejpam-110	74	11	is	be	AUX
ejpam-110	74	12	locally	locally	ADV
ejpam-110	74	13	compact	compact	ADJ
ejpam-110	74	14	if	if	SCONJ
ejpam-110	74	15	and	and	CCONJ
ejpam-110	74	16	only	only	ADV
ejpam-110	74	17	if	if	SCONJ
ejpam-110	74	18	for	for	ADP
ejpam-110	74	19	each	each	DET
ejpam-110	74	20	x	x	SYM
ejpam-110	74	21	∈	∈	PROPN
ejpam-110	74	22	x	x	X
ejpam-110	74	23	,	,	PUNCT
ejpam-110	74	24	p	p	PROPN
ejpam-110	74	25	∈	∈	PROPN
ejpam-110	74	26	pr(l	pr(l	NOUN
ejpam-110	74	27	)	)	PUNCT
ejpam-110	74	28	and	and	CCONJ
ejpam-110	74	29	f	f	PROPN
ejpam-110	74	30	∈	∈	PROPN
ejpam-110	74	31	t	t	PROPN
ejpam-110	74	32	with	with	ADP
ejpam-110	74	33	f	f	PROPN
ejpam-110	74	34	(	(	PUNCT
ejpam-110	74	35	x	x	NOUN
ejpam-110	74	36	)	)	PUNCT
ejpam-110	74	37	�	�	PROPN
ejpam-110	74	38	p	p	NOUN
ejpam-110	74	39	there	there	PRON
ejpam-110	74	40	exist	exist	VERB
ejpam-110	74	41	g	g	PROPN
ejpam-110	74	42	∈	∈	PROPN
ejpam-110	74	43	t	t	PROPN
ejpam-110	74	44	and	and	CCONJ
ejpam-110	74	45	k	k	PROPN
ejpam-110	74	46	∈	∈	PROPN
ejpam-110	75	1	lx	lx	ADV
ejpam-110	75	2	,	,	PUNCT
ejpam-110	75	3	with	with	ADP
ejpam-110	75	4	χsupp(k	χsupp(k	PROPN
ejpam-110	75	5	)	)	PUNCT
ejpam-110	75	6	compact	compact	ADJ
ejpam-110	75	7	,	,	PUNCT
ejpam-110	75	8	such	such	ADJ
ejpam-110	75	9	that	that	SCONJ
ejpam-110	75	10	f	f	PROPN
ejpam-110	75	11	(	(	PUNCT
ejpam-110	75	12	x	x	X
ejpam-110	75	13	)	)	PUNCT
ejpam-110	75	14	�	�	PROPN
ejpam-110	75	15	p	p	NOUN
ejpam-110	75	16	and	and	CCONJ
ejpam-110	75	17	g	g	NOUN
ejpam-110	75	18	≤	≤	NUM
ejpam-110	75	19	k	k	NOUN
ejpam-110	75	20	≤	≤	PROPN
ejpam-110	75	21	f	f	PROPN
ejpam-110	75	22	.	.	PUNCT
ejpam-110	76	1	theorem	theorem	VERB
ejpam-110	76	2	3.1	3.1	NUM
ejpam-110	76	3	.	.	PUNCT
ejpam-110	77	1	(	(	PUNCT
ejpam-110	77	2	the	the	DET
ejpam-110	77	3	goodness	goodness	NOUN
ejpam-110	77	4	of	of	ADP
ejpam-110	77	5	local	local	ADJ
ejpam-110	77	6	compactness	compactness	NOUN
ejpam-110	77	7	)	)	PUNCT
ejpam-110	77	8	let	let	VERB
ejpam-110	77	9	〈	〈	PROPN
ejpam-110	77	10	x	x	PROPN
ejpam-110	77	11	,	,	PUNCT
ejpam-110	77	12	δ	δ	PROPN
ejpam-110	77	13	〉	〉	NOUN
ejpam-110	77	14	be	be	VERB
ejpam-110	77	15	an	an	DET
ejpam-110	77	16	topological	topological	ADJ
ejpam-110	77	17	space	space	NOUN
ejpam-110	77	18	.	.	PUNCT
ejpam-110	78	1	then	then	ADV
ejpam-110	78	2	:	:	PUNCT
ejpam-110	78	3	〈	〈	PROPN
ejpam-110	78	4	x	x	SYM
ejpam-110	78	5	,	,	PUNCT
ejpam-110	78	6	δ	δ	PROPN
ejpam-110	78	7	〉	〉	NOUN
ejpam-110	78	8	is	be	AUX
ejpam-110	78	9	locally	locally	ADV
ejpam-110	78	10	compact	compact	ADJ
ejpam-110	78	11	if	if	SCONJ
ejpam-110	79	1	and	and	CCONJ
ejpam-110	79	2	only	only	ADV
ejpam-110	79	3	if	if	SCONJ
ejpam-110	79	4	〈	〈	PROPN
ejpam-110	79	5	x	x	SYM
ejpam-110	79	6	,	,	PUNCT
ejpam-110	79	7	ω(δ	ω(δ	PROPN
ejpam-110	79	8	)	)	PUNCT
ejpam-110	79	9	〉	〉	NOUN
ejpam-110	79	10	is	be	AUX
ejpam-110	79	11	locally	locally	ADV
ejpam-110	79	12	compact	compact	ADJ
ejpam-110	79	13	.	.	PUNCT
ejpam-110	80	1	proof	proof	NOUN
ejpam-110	80	2	.	.	PUNCT
ejpam-110	81	1	necessity	necessity	NOUN
ejpam-110	81	2	:	:	PUNCT
ejpam-110	81	3	let	let	VERB
ejpam-110	81	4	x	x	PUNCT
ejpam-110	81	5	∈	∈	PROPN
ejpam-110	81	6	x	x	X
ejpam-110	81	7	,	,	PUNCT
ejpam-110	81	8	let	let	VERB
ejpam-110	81	9	p	p	PRON
ejpam-110	81	10	∈	∈	NOUN
ejpam-110	81	11	pr(l	pr(l	NOUN
ejpam-110	81	12	)	)	PUNCT
ejpam-110	81	13	and	and	CCONJ
ejpam-110	81	14	let	let	VERB
ejpam-110	81	15	f	f	PROPN
ejpam-110	81	16	∈	∈	PROPN
ejpam-110	81	17	ω(δ	ω(δ	PROPN
ejpam-110	81	18	)	)	PUNCT
ejpam-110	81	19	such	such	ADJ
ejpam-110	81	20	that	that	SCONJ
ejpam-110	81	21	f	f	PROPN
ejpam-110	81	22	(	(	PUNCT
ejpam-110	81	23	x	x	NOUN
ejpam-110	81	24	)	)	PUNCT
ejpam-110	81	25	�	�	PROPN
ejpam-110	81	26	p.	p.	NOUN
ejpam-110	81	27	let	let	VERB
ejpam-110	81	28	h	h	PROPN
ejpam-110	81	29	∈ω(δ	∈ω(δ	PROPN
ejpam-110	81	30	)	)	PUNCT
ejpam-110	81	31	be	be	VERB
ejpam-110	81	32	an	an	DET
ejpam-110	81	33	basic	basic	ADJ
ejpam-110	81	34	open	open	ADJ
ejpam-110	81	35	l	l	NOUN
ejpam-110	81	36	-	-	NOUN
ejpam-110	81	37	set	set	VERB
ejpam-110	81	38	with	with	ADP
ejpam-110	81	39	h(x	h(x	PROPN
ejpam-110	81	40	)	)	PUNCT
ejpam-110	81	41	�	�	PROPN
ejpam-110	81	42	p	p	PROPN
ejpam-110	81	43	and	and	CCONJ
ejpam-110	81	44	h≤	h≤	PROPN
ejpam-110	81	45	f	f	NOUN
ejpam-110	81	46	defined	define	VERB
ejpam-110	81	47	by	by	ADP
ejpam-110	81	48	h(y	h(y	NOUN
ejpam-110	81	49	)	)	PUNCT
ejpam-110	81	50	=	=	PUNCT
ejpam-110	82	1			PROPN
ejpam-110	82	2			X
ejpam-110	82	3			ADJ
ejpam-110	82	4	e	e	NOUN
ejpam-110	82	5	if	if	SCONJ
ejpam-110	82	6	y	y	PROPN
ejpam-110	82	7	∈	∈	PROPN
ejpam-110	82	8	v	v	ADP
ejpam-110	82	9	∈	∈	PROPN
ejpam-110	82	10	δ	δ	NOUN
ejpam-110	82	11	0	0	PUNCT
ejpam-110	82	12	if	if	SCONJ
ejpam-110	82	13	y	y	PROPN
ejpam-110	82	14	/∈	/∈	VERB
ejpam-110	82	15	v	v	NOUN
ejpam-110	82	16	since	since	SCONJ
ejpam-110	82	17	〈	〈	NOUN
ejpam-110	82	18	x	x	SYM
ejpam-110	82	19	,	,	PUNCT
ejpam-110	82	20	δ	δ	PROPN
ejpam-110	82	21	〉	〉	NOUN
ejpam-110	82	22	is	be	AUX
ejpam-110	82	23	locally	locally	ADV
ejpam-110	82	24	compact	compact	ADJ
ejpam-110	82	25	,	,	PUNCT
ejpam-110	82	26	there	there	PRON
ejpam-110	82	27	exist	exist	VERB
ejpam-110	82	28	u	u	PROPN
ejpam-110	82	29	∈	∈	PROPN
ejpam-110	82	30	δ	δ	PROPN
ejpam-110	82	31	and	and	CCONJ
ejpam-110	82	32	a	a	DET
ejpam-110	82	33	compact	compact	ADJ
ejpam-110	82	34	subset	subset	NOUN
ejpam-110	82	35	j	j	PROPN
ejpam-110	82	36	of	of	ADP
ejpam-110	82	37	x	x	SYM
ejpam-110	82	38	such	such	ADJ
ejpam-110	82	39	that	that	SCONJ
ejpam-110	82	40	x	x	SYM
ejpam-110	82	41	∈	∈	PROPN
ejpam-110	82	42	u	u	NOUN
ejpam-110	82	43	and	and	CCONJ
ejpam-110	82	44	u	u	NOUN
ejpam-110	82	45	⊂	⊂	PROPN
ejpam-110	82	46	j	j	PROPN
ejpam-110	83	1	⊂	⊂	PROPN
ejpam-110	83	2	v	v	PROPN
ejpam-110	83	3	.	.	PUNCT
ejpam-110	84	1	let	let	VERB
ejpam-110	84	2	g	g	PROPN
ejpam-110	84	3	∈ω(δ	∈ω(δ	PROPN
ejpam-110	84	4	)	)	PUNCT
ejpam-110	84	5	and	and	CCONJ
ejpam-110	84	6	k	k	PROPN
ejpam-110	84	7	∈	∈	PROPN
ejpam-110	84	8	lx	lx	ADV
ejpam-110	84	9	defined	define	VERB
ejpam-110	84	10	by	by	ADP
ejpam-110	84	11	:	:	PUNCT
ejpam-110	84	12	g(y	g(y	X
ejpam-110	84	13	)	)	PUNCT
ejpam-110	84	14	=	=	PUNCT
ejpam-110	85	1			PROPN
ejpam-110	85	2			X
ejpam-110	85	3			ADJ
ejpam-110	85	4	e	e	NOUN
ejpam-110	85	5	if	if	SCONJ
ejpam-110	85	6	y	y	PROPN
ejpam-110	85	7	∈	∈	PROPN
ejpam-110	85	8	u	u	NOUN
ejpam-110	85	9	∈	∈	PROPN
ejpam-110	85	10	δ	δ	PROPN
ejpam-110	85	11	0	0	PUNCT
ejpam-110	85	12	if	if	SCONJ
ejpam-110	85	13	y	y	PROPN
ejpam-110	85	14	/∈	/∈	PUNCT
ejpam-110	85	15	u	u	NOUN
ejpam-110	85	16	k(y	k(y	PROPN
ejpam-110	85	17	)	)	PUNCT
ejpam-110	85	18	=	=	PUNCT
ejpam-110	85	19			PROPN
ejpam-110	85	20			X
ejpam-110	85	21			ADJ
ejpam-110	85	22	e	e	NOUN
ejpam-110	86	1	if	if	SCONJ
ejpam-110	86	2	y	y	PROPN
ejpam-110	86	3	∈	∈	PROPN
ejpam-110	86	4	j	j	PROPN
ejpam-110	86	5	∈	∈	PROPN
ejpam-110	86	6	δ	δ	PROPN
ejpam-110	86	7	0	0	PUNCT
ejpam-110	87	1	if	if	SCONJ
ejpam-110	87	2	y	y	PROPN
ejpam-110	87	3	/∈	/∈	PUNCT
ejpam-110	88	1	j	j	PROPN
ejpam-110	88	2	then	then	ADV
ejpam-110	88	3	g(x	g(x	PROPN
ejpam-110	88	4	)	)	PUNCT
ejpam-110	88	5	�	�	PROPN
ejpam-110	88	6	p	p	NOUN
ejpam-110	88	7	,	,	PUNCT
ejpam-110	88	8	g	g	PROPN
ejpam-110	88	9	≤	≤	PROPN
ejpam-110	88	10	k	k	X
ejpam-110	88	11	≤	≤	NUM
ejpam-110	88	12	h	h	NOUN
ejpam-110	88	13	≤	≤	NUM
ejpam-110	88	14	f	f	PROPN
ejpam-110	88	15	and	and	CCONJ
ejpam-110	88	16	χsupp(k	χsupp(k	PROPN
ejpam-110	88	17	)	)	PUNCT
ejpam-110	88	18	=	=	PRON
ejpam-110	88	19	χj	χj	PROPN
ejpam-110	88	20	is	be	AUX
ejpam-110	88	21	compact	compact	ADJ
ejpam-110	88	22	since	since	SCONJ
ejpam-110	88	23	j	j	PROPN
ejpam-110	88	24	is	be	AUX
ejpam-110	88	25	compact	compact	ADJ
ejpam-110	88	26	.	.	PUNCT
ejpam-110	89	1	hence	hence	ADV
ejpam-110	89	2	,	,	PUNCT
ejpam-110	89	3	〈	〈	PROPN
ejpam-110	89	4	x	x	SYM
ejpam-110	89	5	,	,	PUNCT
ejpam-110	89	6	ω(δ	ω(δ	PROPN
ejpam-110	89	7	)	)	PUNCT
ejpam-110	89	8	〉	〉	NOUN
ejpam-110	89	9	is	be	AUX
ejpam-110	89	10	locally	locally	ADV
ejpam-110	89	11	compact	compact	ADJ
ejpam-110	89	12	.	.	PUNCT
ejpam-110	90	1	t.	t.	PROPN
ejpam-110	90	2	breuckmann	breuckmann	PROPN
ejpam-110	90	3	,	,	PUNCT
ejpam-110	90	4	s.	s.	PROPN
ejpam-110	90	5	kudri	kudri	PROPN
ejpam-110	90	6	,	,	PUNCT
ejpam-110	90	7	and	and	CCONJ
ejpam-110	90	8	h.	h.	PROPN
ejpam-110	90	9	aygün	aygün	PROPN
ejpam-110	90	10	/	/	SYM
ejpam-110	90	11	eur	eur	PROPN
ejpam-110	90	12	.	.	PUNCT
ejpam-110	91	1	j.	j.	PROPN
ejpam-110	91	2	pure	pure	PROPN
ejpam-110	91	3	appl	appl	PROPN
ejpam-110	91	4	.	.	PROPN
ejpam-110	91	5	math	math	PROPN
ejpam-110	91	6	,	,	PUNCT
ejpam-110	91	7	2	2	NUM
ejpam-110	91	8	(	(	PUNCT
ejpam-110	91	9	2009	2009	NUM
ejpam-110	91	10	)	)	PUNCT
ejpam-110	91	11	,	,	PUNCT
ejpam-110	91	12	(	(	PUNCT
ejpam-110	91	13	147	147	NUM
ejpam-110	91	14	-	-	SYM
ejpam-110	91	15	161	161	NUM
ejpam-110	91	16	)	)	PUNCT
ejpam-110	91	17	151	151	NUM
ejpam-110	91	18	suficiency	suficiency	NOUN
ejpam-110	91	19	:	:	PUNCT
ejpam-110	91	20	let	let	VERB
ejpam-110	91	21	x	x	X
ejpam-110	91	22	∈	∈	PROPN
ejpam-110	91	23	x	x	X
ejpam-110	91	24	and	and	CCONJ
ejpam-110	91	25	v	v	ADP
ejpam-110	91	26	∈	∈	PROPN
ejpam-110	91	27	δ	δ	NOUN
ejpam-110	91	28	such	such	ADJ
ejpam-110	91	29	that	that	SCONJ
ejpam-110	91	30	x	x	SYM
ejpam-110	91	31	∈	∈	NOUN
ejpam-110	91	32	v	v	NOUN
ejpam-110	91	33	.	.	PUNCT
ejpam-110	92	1	fix	fix	VERB
ejpam-110	92	2	p	p	NOUN
ejpam-110	92	3	∈	∈	PROPN
ejpam-110	92	4	pr(l	pr(l	NOUN
ejpam-110	92	5	)	)	PUNCT
ejpam-110	92	6	.	.	PUNCT
ejpam-110	93	1	since	since	SCONJ
ejpam-110	93	2	〈	〈	PROPN
ejpam-110	93	3	x	x	SYM
ejpam-110	93	4	,	,	PUNCT
ejpam-110	93	5	ω(δ	ω(δ	PROPN
ejpam-110	93	6	)	)	PUNCT
ejpam-110	93	7	〉	〉	NOUN
ejpam-110	93	8	is	be	AUX
ejpam-110	93	9	locally	locally	ADV
ejpam-110	93	10	compact	compact	ADJ
ejpam-110	93	11	,	,	PUNCT
ejpam-110	93	12	for	for	ADP
ejpam-110	93	13	f	f	PROPN
ejpam-110	93	14	=	=	SYM
ejpam-110	93	15	χv	χv	PROPN
ejpam-110	93	16	,	,	PUNCT
ejpam-110	93	17	there	there	PRON
ejpam-110	93	18	exist	exist	VERB
ejpam-110	93	19	g	g	PROPN
ejpam-110	93	20	∈	∈	PROPN
ejpam-110	93	21	ω(δ	ω(δ	PROPN
ejpam-110	93	22	)	)	PUNCT
ejpam-110	93	23	and	and	CCONJ
ejpam-110	93	24	k	k	PROPN
ejpam-110	93	25	∈	∈	PROPN
ejpam-110	93	26	lx	lx	ADV
ejpam-110	93	27	,	,	PUNCT
ejpam-110	93	28	with	with	ADP
ejpam-110	93	29	χsupp(k	χsupp(k	PROPN
ejpam-110	93	30	)	)	PUNCT
ejpam-110	93	31	compact	compact	ADJ
ejpam-110	93	32	,	,	PUNCT
ejpam-110	93	33	such	such	ADJ
ejpam-110	93	34	that	that	SCONJ
ejpam-110	93	35	g(x	g(x	NOUN
ejpam-110	93	36	)	)	PUNCT
ejpam-110	93	37	�	�	PROPN
ejpam-110	93	38	p	p	NOUN
ejpam-110	93	39	and	and	CCONJ
ejpam-110	93	40	g	g	NOUN
ejpam-110	93	41	≤	≤	NUM
ejpam-110	94	1	k	k	NOUN
ejpam-110	94	2	≤	≤	PROPN
ejpam-110	94	3	f	f	X
ejpam-110	94	4	.	.	PUNCT
ejpam-110	95	1	let	let	VERB
ejpam-110	95	2	u	u	PRON
ejpam-110	95	3	=	=	PROPN
ejpam-110	95	4	g−1	g−1	PROPN
ejpam-110	95	5	�	�	PROPN
ejpam-110	95	6	t	t	PROPN
ejpam-110	95	7	∈	∈	PROPN
ejpam-110	95	8	l	l	NOUN
ejpam-110	95	9	;	;	PUNCT
ejpam-110	95	10	t	t	PROPN
ejpam-110	95	11	�	�	PROPN
ejpam-110	95	12	p	p	PROPN
ejpam-110	95	13	and	and	CCONJ
ejpam-110	95	14	let	let	VERB
ejpam-110	95	15	k	k	PROPN
ejpam-110	95	16	=	=	SYM
ejpam-110	95	17	supp(k	supp(k	PROPN
ejpam-110	95	18	)	)	PUNCT
ejpam-110	95	19	,	,	PUNCT
ejpam-110	95	20	then	then	ADV
ejpam-110	95	21	,	,	PUNCT
ejpam-110	95	22	u	u	PROPN
ejpam-110	95	23	∈	∈	PROPN
ejpam-110	95	24	δ	δ	PROPN
ejpam-110	95	25	,	,	PUNCT
ejpam-110	95	26	x	x	PUNCT
ejpam-110	95	27	∈	∈	PROPN
ejpam-110	95	28	u	u	NOUN
ejpam-110	95	29	,	,	PUNCT
ejpam-110	95	30	k	k	PROPN
ejpam-110	95	31	is	be	AUX
ejpam-110	95	32	a	a	DET
ejpam-110	95	33	compact	compact	ADJ
ejpam-110	95	34	subset	subset	NOUN
ejpam-110	95	35	of	of	ADP
ejpam-110	95	36	x	x	PRON
ejpam-110	95	37	since	since	SCONJ
ejpam-110	95	38	χsupp(k	χsupp(k	NOUN
ejpam-110	95	39	)	)	PUNCT
ejpam-110	95	40	is	be	AUX
ejpam-110	95	41	compact	compact	ADJ
ejpam-110	95	42	and	and	CCONJ
ejpam-110	95	43	u	u	X
ejpam-110	96	1	⊂	⊂	PROPN
ejpam-110	96	2	k	k	PROPN
ejpam-110	96	3	⊂	⊂	PROPN
ejpam-110	96	4	v	v	PROPN
ejpam-110	96	5	.	.	PUNCT
ejpam-110	97	1	hence	hence	ADV
ejpam-110	97	2	,	,	PUNCT
ejpam-110	97	3	〈	〈	PROPN
ejpam-110	97	4	x	x	SYM
ejpam-110	97	5	,	,	PUNCT
ejpam-110	97	6	δ	δ	PROPN
ejpam-110	97	7	〉	〉	NOUN
ejpam-110	97	8	is	be	AUX
ejpam-110	97	9	locally	locally	ADV
ejpam-110	97	10	compact	compact	ADJ
ejpam-110	97	11	.	.	PUNCT
ejpam-110	98	1	definition	definition	NOUN
ejpam-110	98	2	3.2	3.2	NUM
ejpam-110	98	3	.	.	PUNCT
ejpam-110	99	1	an	an	DET
ejpam-110	99	2	l	l	ADJ
ejpam-110	99	3	-	-	ADJ
ejpam-110	99	4	topological	topological	ADJ
ejpam-110	99	5	space	space	NOUN
ejpam-110	99	6	〈	〈	PROPN
ejpam-110	99	7	x	x	X
ejpam-110	99	8	,	,	PUNCT
ejpam-110	99	9	t	t	PROPN
ejpam-110	99	10	〉	〉	NOUN
ejpam-110	99	11	is	be	AUX
ejpam-110	99	12	weakly	weakly	ADV
ejpam-110	99	13	locally	locally	ADV
ejpam-110	99	14	compact	compact	ADJ
ejpam-110	99	15	if	if	SCONJ
ejpam-110	99	16	and	and	CCONJ
ejpam-110	99	17	only	only	ADV
ejpam-110	99	18	if	if	SCONJ
ejpam-110	99	19	for	for	ADP
ejpam-110	99	20	each	each	DET
ejpam-110	99	21	x	x	SYM
ejpam-110	99	22	∈	∈	PROPN
ejpam-110	99	23	x	x	X
ejpam-110	99	24	and	and	CCONJ
ejpam-110	99	25	p	p	PROPN
ejpam-110	99	26	∈	∈	PROPN
ejpam-110	99	27	pr(l	pr(l	NOUN
ejpam-110	99	28	)	)	PUNCT
ejpam-110	99	29	there	there	PRON
ejpam-110	99	30	exist	exist	VERB
ejpam-110	99	31	f	f	PROPN
ejpam-110	99	32	∈	∈	PROPN
ejpam-110	99	33	t	t	PROPN
ejpam-110	99	34	and	and	CCONJ
ejpam-110	99	35	k	k	PROPN
ejpam-110	99	36	∈	∈	PROPN
ejpam-110	100	1	lx	lx	ADV
ejpam-110	100	2	,	,	PUNCT
ejpam-110	100	3	with	with	ADP
ejpam-110	100	4	χsupp(k	χsupp(k	PROPN
ejpam-110	100	5	)	)	PUNCT
ejpam-110	100	6	compact	compact	ADJ
ejpam-110	100	7	,	,	PUNCT
ejpam-110	100	8	such	such	ADJ
ejpam-110	100	9	that	that	SCONJ
ejpam-110	100	10	f	f	PROPN
ejpam-110	100	11	(	(	PUNCT
ejpam-110	100	12	x	x	X
ejpam-110	100	13	)	)	PUNCT
ejpam-110	100	14	�	�	PROPN
ejpam-110	100	15	p	p	PROPN
ejpam-110	100	16	and	and	CCONJ
ejpam-110	100	17	f	f	PROPN
ejpam-110	100	18	≤	≤	PROPN
ejpam-110	100	19	k.	k.	PROPN
ejpam-110	100	20	theorem	theorem	VERB
ejpam-110	100	21	3.2	3.2	NUM
ejpam-110	100	22	.	.	PUNCT
ejpam-110	101	1	(	(	PUNCT
ejpam-110	101	2	the	the	DET
ejpam-110	101	3	goodness	goodness	NOUN
ejpam-110	101	4	of	of	ADP
ejpam-110	101	5	weak	weak	ADJ
ejpam-110	101	6	local	local	ADJ
ejpam-110	101	7	compactness	compactness	NOUN
ejpam-110	101	8	)	)	PUNCT
ejpam-110	101	9	let	let	VERB
ejpam-110	101	10	〈	〈	PROPN
ejpam-110	101	11	x	x	PROPN
ejpam-110	101	12	,	,	PUNCT
ejpam-110	101	13	δ	δ	PROPN
ejpam-110	101	14	〉	〉	NOUN
ejpam-110	101	15	be	be	VERB
ejpam-110	101	16	an	an	DET
ejpam-110	101	17	topological	topological	ADJ
ejpam-110	101	18	space	space	NOUN
ejpam-110	101	19	.	.	PUNCT
ejpam-110	102	1	then	then	ADV
ejpam-110	102	2	:	:	PUNCT
ejpam-110	102	3	〈	〈	PROPN
ejpam-110	102	4	x	x	SYM
ejpam-110	102	5	,	,	PUNCT
ejpam-110	102	6	δ	δ	PROPN
ejpam-110	102	7	〉	〉	NOUN
ejpam-110	102	8	is	be	AUX
ejpam-110	102	9	weakly	weakly	ADV
ejpam-110	102	10	locally	locally	ADV
ejpam-110	102	11	compact	compact	ADJ
ejpam-110	102	12	if	if	SCONJ
ejpam-110	103	1	and	and	CCONJ
ejpam-110	103	2	only	only	ADV
ejpam-110	103	3	if	if	SCONJ
ejpam-110	103	4	〈	〈	PROPN
ejpam-110	103	5	x	x	SYM
ejpam-110	103	6	,	,	PUNCT
ejpam-110	103	7	ω(δ	ω(δ	PROPN
ejpam-110	103	8	)	)	PUNCT
ejpam-110	103	9	〉	〉	NOUN
ejpam-110	103	10	is	be	AUX
ejpam-110	103	11	weakly	weakly	ADV
ejpam-110	103	12	locally	locally	ADV
ejpam-110	103	13	compact	compact	ADJ
ejpam-110	103	14	.	.	PUNCT
ejpam-110	104	1	proof	proof	NOUN
ejpam-110	104	2	.	.	PUNCT
ejpam-110	105	1	necessity	necessity	NOUN
ejpam-110	105	2	:	:	PUNCT
ejpam-110	105	3	let	let	VERB
ejpam-110	105	4	x	x	X
ejpam-110	105	5	∈	∈	PROPN
ejpam-110	105	6	x	x	PUNCT
ejpam-110	105	7	and	and	CCONJ
ejpam-110	105	8	let	let	VERB
ejpam-110	105	9	p	p	PRON
ejpam-110	105	10	∈	∈	PROPN
ejpam-110	105	11	pr(l	pr(l	NOUN
ejpam-110	105	12	)	)	PUNCT
ejpam-110	105	13	.	.	PUNCT
ejpam-110	106	1	since	since	SCONJ
ejpam-110	106	2	〈	〈	PROPN
ejpam-110	106	3	x	x	SYM
ejpam-110	106	4	,	,	PUNCT
ejpam-110	106	5	δ	δ	PROPN
ejpam-110	106	6	〉	〉	NOUN
ejpam-110	106	7	is	be	AUX
ejpam-110	106	8	weakly	weakly	ADV
ejpam-110	106	9	locally	locally	ADV
ejpam-110	106	10	compact	compact	ADJ
ejpam-110	106	11	,	,	PUNCT
ejpam-110	106	12	there	there	PRON
ejpam-110	106	13	exist	exist	VERB
ejpam-110	106	14	u	u	PROPN
ejpam-110	106	15	∈	∈	PROPN
ejpam-110	106	16	δ	δ	PROPN
ejpam-110	106	17	and	and	CCONJ
ejpam-110	106	18	a	a	DET
ejpam-110	106	19	compact	compact	ADJ
ejpam-110	106	20	subset	subset	NOUN
ejpam-110	106	21	j	j	PROPN
ejpam-110	106	22	of	of	ADP
ejpam-110	106	23	x	x	SYM
ejpam-110	106	24	such	such	ADJ
ejpam-110	106	25	that	that	SCONJ
ejpam-110	106	26	x	x	SYM
ejpam-110	106	27	∈	∈	PROPN
ejpam-110	106	28	u	u	NOUN
ejpam-110	106	29	and	and	CCONJ
ejpam-110	106	30	u	u	NOUN
ejpam-110	106	31	⊂	⊂	PROPN
ejpam-110	106	32	j	j	PROPN
ejpam-110	106	33	.	.	PUNCT
ejpam-110	107	1	let	let	VERB
ejpam-110	107	2	g	g	NOUN
ejpam-110	107	3	=	=	PUNCT
ejpam-110	107	4	χu	χu	NOUN
ejpam-110	107	5	and	and	CCONJ
ejpam-110	107	6	let	let	VERB
ejpam-110	107	7	k	k	PROPN
ejpam-110	107	8	=	=	PUNCT
ejpam-110	107	9	χj	χj	PROPN
ejpam-110	107	10	,	,	PUNCT
ejpam-110	107	11	then	then	ADV
ejpam-110	107	12	g	g	PROPN
ejpam-110	107	13	∈	∈	PROPN
ejpam-110	107	14	ω(δ	ω(δ	PROPN
ejpam-110	107	15	)	)	PUNCT
ejpam-110	107	16	,	,	PUNCT
ejpam-110	108	1	g(x	g(x	NOUN
ejpam-110	108	2	)	)	PUNCT
ejpam-110	108	3	�	�	PROPN
ejpam-110	108	4	p	p	NOUN
ejpam-110	108	5	,	,	PUNCT
ejpam-110	108	6	g	g	PROPN
ejpam-110	108	7	≤	≤	PROPN
ejpam-110	108	8	k	k	PROPN
ejpam-110	108	9	and	and	CCONJ
ejpam-110	108	10	χsupp(k	χsupp(k	PROPN
ejpam-110	108	11	)	)	PUNCT
ejpam-110	108	12	=	=	PRON
ejpam-110	108	13	χj	χj	PROPN
ejpam-110	108	14	is	be	AUX
ejpam-110	108	15	compact	compact	ADJ
ejpam-110	108	16	since	since	SCONJ
ejpam-110	108	17	j	j	PROPN
ejpam-110	108	18	is	be	AUX
ejpam-110	108	19	compact	compact	ADJ
ejpam-110	108	20	.	.	PUNCT
ejpam-110	109	1	hence	hence	ADV
ejpam-110	109	2	,	,	PUNCT
ejpam-110	109	3	〈	〈	PROPN
ejpam-110	109	4	x	x	SYM
ejpam-110	109	5	,	,	PUNCT
ejpam-110	109	6	ω(δ	ω(δ	PROPN
ejpam-110	109	7	)	)	PUNCT
ejpam-110	109	8	〉	〉	NOUN
ejpam-110	109	9	is	be	AUX
ejpam-110	109	10	weakly	weakly	ADV
ejpam-110	109	11	locally	locally	ADV
ejpam-110	109	12	compact	compact	ADJ
ejpam-110	109	13	.	.	PUNCT
ejpam-110	110	1	suficiency	suficiency	NOUN
ejpam-110	110	2	:	:	PUNCT
ejpam-110	110	3	let	let	VERB
ejpam-110	110	4	x	x	X
ejpam-110	110	5	∈	∈	PROPN
ejpam-110	110	6	x	x	X
ejpam-110	110	7	and	and	CCONJ
ejpam-110	110	8	fix	fix	VERB
ejpam-110	110	9	p	p	NOUN
ejpam-110	110	10	∈	∈	PROPN
ejpam-110	110	11	pr(l	pr(l	NOUN
ejpam-110	110	12	)	)	PUNCT
ejpam-110	110	13	.	.	PUNCT
ejpam-110	111	1	since	since	SCONJ
ejpam-110	111	2	〈	〈	PROPN
ejpam-110	111	3	x	x	SYM
ejpam-110	111	4	,	,	PUNCT
ejpam-110	111	5	ω(δ	ω(δ	PROPN
ejpam-110	111	6	)	)	PUNCT
ejpam-110	111	7	〉	〉	NOUN
ejpam-110	111	8	is	be	AUX
ejpam-110	111	9	locally	locally	ADV
ejpam-110	111	10	compact	compact	ADJ
ejpam-110	111	11	there	there	ADV
ejpam-110	111	12	exist	exist	VERB
ejpam-110	111	13	g	g	PROPN
ejpam-110	111	14	∈ω(δ	∈ω(δ	PROPN
ejpam-110	111	15	)	)	PUNCT
ejpam-110	111	16	and	and	CCONJ
ejpam-110	111	17	k	k	PROPN
ejpam-110	111	18	∈	∈	PROPN
ejpam-110	112	1	lx	lx	ADV
ejpam-110	112	2	,	,	PUNCT
ejpam-110	112	3	with	with	ADP
ejpam-110	112	4	χsupp(k	χsupp(k	PROPN
ejpam-110	112	5	)	)	PUNCT
ejpam-110	112	6	compact	compact	ADJ
ejpam-110	112	7	,	,	PUNCT
ejpam-110	112	8	such	such	ADJ
ejpam-110	112	9	that	that	SCONJ
ejpam-110	112	10	g(x	g(x	NOUN
ejpam-110	112	11	)	)	PUNCT
ejpam-110	112	12	�	�	PROPN
ejpam-110	112	13	p	p	NOUN
ejpam-110	112	14	and	and	CCONJ
ejpam-110	112	15	g	g	PROPN
ejpam-110	112	16	≤	≤	PROPN
ejpam-110	112	17	k.	k.	PROPN
ejpam-110	113	1	let	let	VERB
ejpam-110	113	2	v	v	NOUN
ejpam-110	113	3	=	=	SYM
ejpam-110	113	4	g−1	g−1	PROPN
ejpam-110	113	5	�	�	PROPN
ejpam-110	113	6	t	t	PROPN
ejpam-110	113	7	∈	∈	PROPN
ejpam-110	113	8	l	l	NOUN
ejpam-110	113	9	;	;	PUNCT
ejpam-110	113	10	t	t	PROPN
ejpam-110	113	11	�	�	PROPN
ejpam-110	113	12	p	p	PROPN
ejpam-110	113	13	and	and	CCONJ
ejpam-110	113	14	let	let	VERB
ejpam-110	113	15	k	k	PROPN
ejpam-110	113	16	=	=	SYM
ejpam-110	113	17	supp(k	supp(k	PROPN
ejpam-110	113	18	)	)	PUNCT
ejpam-110	113	19	,	,	PUNCT
ejpam-110	113	20	then	then	ADV
ejpam-110	113	21	,	,	PUNCT
ejpam-110	113	22	v	v	PROPN
ejpam-110	113	23	∈	∈	PROPN
ejpam-110	113	24	δ	δ	PROPN
ejpam-110	113	25	,	,	PUNCT
ejpam-110	113	26	x	x	PROPN
ejpam-110	113	27	∈	∈	PROPN
ejpam-110	113	28	v	v	NOUN
ejpam-110	113	29	,	,	PUNCT
ejpam-110	113	30	k	k	PROPN
ejpam-110	113	31	is	be	AUX
ejpam-110	113	32	a	a	DET
ejpam-110	113	33	compact	compact	ADJ
ejpam-110	113	34	subset	subset	NOUN
ejpam-110	113	35	of	of	ADP
ejpam-110	113	36	x	x	PRON
ejpam-110	113	37	since	since	SCONJ
ejpam-110	113	38	χsupp(k	χsupp(k	NOUN
ejpam-110	113	39	)	)	PUNCT
ejpam-110	113	40	is	be	AUX
ejpam-110	113	41	compact	compact	ADJ
ejpam-110	113	42	and	and	CCONJ
ejpam-110	113	43	v	v	ADP
ejpam-110	113	44	⊂	⊂	PROPN
ejpam-110	113	45	k	k	X
ejpam-110	113	46	.	.	PUNCT
ejpam-110	114	1	hence	hence	ADV
ejpam-110	114	2	,	,	PUNCT
ejpam-110	114	3	〈	〈	PROPN
ejpam-110	114	4	x	x	SYM
ejpam-110	114	5	,	,	PUNCT
ejpam-110	114	6	δ	δ	PROPN
ejpam-110	114	7	〉	〉	NOUN
ejpam-110	114	8	is	be	AUX
ejpam-110	114	9	weakly	weakly	ADV
ejpam-110	114	10	locally	locally	ADV
ejpam-110	114	11	compact	compact	ADJ
ejpam-110	114	12	.	.	PUNCT
ejpam-110	115	1	definition	definition	NOUN
ejpam-110	115	2	3.3	3.3	NUM
ejpam-110	115	3	.	.	PUNCT
ejpam-110	116	1	an	an	DET
ejpam-110	116	2	l	l	ADJ
ejpam-110	116	3	-	-	ADJ
ejpam-110	116	4	topological	topological	ADJ
ejpam-110	116	5	space	space	NOUN
ejpam-110	116	6	〈	〈	PROPN
ejpam-110	116	7	x	x	X
ejpam-110	116	8	,	,	PUNCT
ejpam-110	116	9	t	t	PROPN
ejpam-110	116	10	〉	〉	NOUN
ejpam-110	116	11	is	be	AUX
ejpam-110	116	12	relatively	relatively	ADV
ejpam-110	116	13	locally	locally	ADV
ejpam-110	116	14	compact	compact	ADJ
ejpam-110	116	15	if	if	SCONJ
ejpam-110	116	16	and	and	CCONJ
ejpam-110	116	17	only	only	ADV
ejpam-110	116	18	if	if	SCONJ
ejpam-110	116	19	for	for	ADP
ejpam-110	116	20	each	each	DET
ejpam-110	116	21	x	x	SYM
ejpam-110	116	22	∈	∈	PROPN
ejpam-110	116	23	x	x	X
ejpam-110	116	24	and	and	CCONJ
ejpam-110	116	25	p	p	PROPN
ejpam-110	116	26	∈	∈	PROPN
ejpam-110	116	27	pr(l	pr(l	NOUN
ejpam-110	116	28	)	)	PUNCT
ejpam-110	116	29	there	there	PRON
ejpam-110	116	30	exists	exist	VERB
ejpam-110	116	31	f	f	PROPN
ejpam-110	116	32	∈	∈	PROPN
ejpam-110	116	33	t	t	PROPN
ejpam-110	116	34	,	,	PUNCT
ejpam-110	116	35	with	with	ADP
ejpam-110	116	36	χ	χ	DET
ejpam-110	116	37	supp	supp	PROPN
ejpam-110	116	38	(	(	PUNCT
ejpam-110	116	39	f	f	PROPN
ejpam-110	116	40	)	)	PUNCT
ejpam-110	116	41	compact	compact	ADJ
ejpam-110	116	42	,	,	PUNCT
ejpam-110	116	43	such	such	ADJ
ejpam-110	116	44	that	that	SCONJ
ejpam-110	116	45	f	f	PROPN
ejpam-110	116	46	(	(	PUNCT
ejpam-110	116	47	x	x	NOUN
ejpam-110	116	48	)	)	PUNCT
ejpam-110	116	49	�	�	PROPN
ejpam-110	116	50	p.	p.	NOUN
ejpam-110	116	51	theorem	theorem	VERB
ejpam-110	116	52	3.3	3.3	NUM
ejpam-110	116	53	.	.	PUNCT
ejpam-110	117	1	(	(	PUNCT
ejpam-110	117	2	the	the	DET
ejpam-110	117	3	goodness	goodness	NOUN
ejpam-110	117	4	of	of	ADP
ejpam-110	117	5	relative	relative	ADJ
ejpam-110	117	6	local	local	ADJ
ejpam-110	117	7	compactness	compactness	NOUN
ejpam-110	117	8	)	)	PUNCT
ejpam-110	117	9	let	let	VERB
ejpam-110	117	10	〈	〈	PROPN
ejpam-110	117	11	x	x	PROPN
ejpam-110	117	12	,	,	PUNCT
ejpam-110	117	13	δ	δ	PROPN
ejpam-110	117	14	〉	〉	NOUN
ejpam-110	117	15	be	be	VERB
ejpam-110	117	16	an	an	DET
ejpam-110	117	17	topological	topological	ADJ
ejpam-110	117	18	space	space	NOUN
ejpam-110	117	19	.	.	PUNCT
ejpam-110	118	1	then	then	ADV
ejpam-110	118	2	:	:	PUNCT
ejpam-110	118	3	〈	〈	PROPN
ejpam-110	118	4	x	x	SYM
ejpam-110	118	5	,	,	PUNCT
ejpam-110	118	6	δ	δ	PROPN
ejpam-110	118	7	〉	〉	NOUN
ejpam-110	118	8	is	be	AUX
ejpam-110	118	9	relatively	relatively	ADV
ejpam-110	118	10	locally	locally	ADV
ejpam-110	118	11	compact	compact	ADJ
ejpam-110	118	12	if	if	SCONJ
ejpam-110	119	1	and	and	CCONJ
ejpam-110	119	2	only	only	ADV
ejpam-110	119	3	if	if	SCONJ
ejpam-110	119	4	〈	〈	PROPN
ejpam-110	119	5	x	x	SYM
ejpam-110	119	6	,	,	PUNCT
ejpam-110	119	7	ω(δ	ω(δ	PROPN
ejpam-110	119	8	)	)	PUNCT
ejpam-110	119	9	〉	〉	NOUN
ejpam-110	119	10	is	be	AUX
ejpam-110	119	11	relatively	relatively	ADV
ejpam-110	119	12	locally	locally	ADV
ejpam-110	119	13	compact	compact	ADJ
ejpam-110	119	14	.	.	PUNCT
ejpam-110	120	1	proof	proof	NOUN
ejpam-110	120	2	.	.	PUNCT
ejpam-110	121	1	necessity	necessity	NOUN
ejpam-110	121	2	:	:	PUNCT
ejpam-110	121	3	let	let	VERB
ejpam-110	121	4	x	x	PUNCT
ejpam-110	121	5	∈	∈	PROPN
ejpam-110	121	6	x	x	X
ejpam-110	121	7	an	an	DET
ejpam-110	121	8	let	let	NOUN
ejpam-110	121	9	p	p	X
ejpam-110	121	10	∈	∈	PROPN
ejpam-110	121	11	pr(l	pr(l	NOUN
ejpam-110	121	12	)	)	PUNCT
ejpam-110	121	13	.	.	PUNCT
ejpam-110	122	1	since	since	SCONJ
ejpam-110	122	2	〈	〈	PROPN
ejpam-110	122	3	x	x	SYM
ejpam-110	122	4	,	,	PUNCT
ejpam-110	122	5	δ	δ	PROPN
ejpam-110	122	6	〉	〉	NOUN
ejpam-110	122	7	is	be	AUX
ejpam-110	122	8	relatively	relatively	ADV
ejpam-110	122	9	locally	locally	ADV
ejpam-110	122	10	compact	compact	ADJ
ejpam-110	122	11	there	there	PRON
ejpam-110	122	12	is	be	VERB
ejpam-110	122	13	v	v	ADP
ejpam-110	122	14	∈	∈	PROPN
ejpam-110	122	15	δ	δ	NOUN
ejpam-110	122	16	with	with	ADP
ejpam-110	122	17	x	x	PROPN
ejpam-110	122	18	∈	∈	PROPN
ejpam-110	122	19	v	v	NOUN
ejpam-110	122	20	and	and	CCONJ
ejpam-110	122	21	v	v	NOUN
ejpam-110	122	22	compact	compact	ADJ
ejpam-110	122	23	.	.	PUNCT
ejpam-110	123	1	let	let	VERB
ejpam-110	123	2	f	f	NOUN
ejpam-110	123	3	=	=	PUNCT
ejpam-110	123	4	χv	χv	PROPN
ejpam-110	123	5	,	,	PUNCT
ejpam-110	123	6	then	then	ADV
ejpam-110	123	7	f	f	X
ejpam-110	123	8	(	(	PUNCT
ejpam-110	123	9	x	x	X
ejpam-110	123	10	)	)	PUNCT
ejpam-110	123	11	=	=	SYM
ejpam-110	123	12	1	1	NUM
ejpam-110	123	13	�	�	PROPN
ejpam-110	123	14	p.	p.	NOUN
ejpam-110	123	15	we	we	PRON
ejpam-110	123	16	also	also	ADV
ejpam-110	123	17	have	have	VERB
ejpam-110	123	18	that	that	DET
ejpam-110	123	19	f	f	PROPN
ejpam-110	123	20	=	=	SYM
ejpam-110	123	21	χv	χv	PROPN
ejpam-110	123	22	,	,	PUNCT
ejpam-110	123	23	hence	hence	ADV
ejpam-110	123	24	supp	supp	PROPN
ejpam-110	123	25	(	(	PUNCT
ejpam-110	123	26	f	f	NOUN
ejpam-110	123	27	)	)	PUNCT
ejpam-110	124	1	=	=	SYM
ejpam-110	124	2	v	v	NOUN
ejpam-110	124	3	is	be	AUX
ejpam-110	124	4	compact	compact	ADJ
ejpam-110	124	5	,	,	PUNCT
ejpam-110	124	6	therefore	therefore	ADV
ejpam-110	124	7	χ	χ	DET
ejpam-110	124	8	supp	supp	NOUN
ejpam-110	124	9	(	(	PUNCT
ejpam-110	124	10	f	f	PROPN
ejpam-110	124	11	)	)	PUNCT
ejpam-110	124	12	is	be	AUX
ejpam-110	124	13	compact	compact	ADJ
ejpam-110	124	14	.	.	PUNCT
ejpam-110	125	1	t.	t.	PROPN
ejpam-110	125	2	breuckmann	breuckmann	PROPN
ejpam-110	125	3	,	,	PUNCT
ejpam-110	125	4	s.	s.	PROPN
ejpam-110	125	5	kudri	kudri	PROPN
ejpam-110	125	6	,	,	PUNCT
ejpam-110	125	7	and	and	CCONJ
ejpam-110	125	8	h.	h.	PROPN
ejpam-110	125	9	aygün	aygün	PROPN
ejpam-110	125	10	/	/	SYM
ejpam-110	125	11	eur	eur	PROPN
ejpam-110	125	12	.	.	PUNCT
ejpam-110	126	1	j.	j.	PROPN
ejpam-110	126	2	pure	pure	PROPN
ejpam-110	126	3	appl	appl	PROPN
ejpam-110	126	4	.	.	PROPN
ejpam-110	126	5	math	math	PROPN
ejpam-110	126	6	,	,	PUNCT
ejpam-110	126	7	2	2	NUM
ejpam-110	126	8	(	(	PUNCT
ejpam-110	126	9	2009	2009	NUM
ejpam-110	126	10	)	)	PUNCT
ejpam-110	126	11	,	,	PUNCT
ejpam-110	126	12	(	(	PUNCT
ejpam-110	126	13	147	147	NUM
ejpam-110	126	14	-	-	SYM
ejpam-110	126	15	161	161	NUM
ejpam-110	126	16	)	)	PUNCT
ejpam-110	126	17	152	152	NUM
ejpam-110	126	18	suficiency	suficiency	NOUN
ejpam-110	126	19	:	:	PUNCT
ejpam-110	126	20	let	let	VERB
ejpam-110	126	21	x	x	X
ejpam-110	126	22	∈	∈	PROPN
ejpam-110	126	23	x	x	PUNCT
ejpam-110	126	24	and	and	CCONJ
ejpam-110	126	25	let	let	VERB
ejpam-110	126	26	p	p	PRON
ejpam-110	126	27	∈	∈	PROPN
ejpam-110	126	28	pr(l	pr(l	X
ejpam-110	126	29	)	)	PUNCT
ejpam-110	126	30	be	be	AUX
ejpam-110	126	31	fixed	fix	VERB
ejpam-110	126	32	.	.	PUNCT
ejpam-110	127	1	since	since	SCONJ
ejpam-110	127	2	〈	〈	PROPN
ejpam-110	127	3	x	x	SYM
ejpam-110	127	4	,	,	PUNCT
ejpam-110	127	5	ω(δ	ω(δ	PROPN
ejpam-110	127	6	)	)	PUNCT
ejpam-110	127	7	〉	〉	NOUN
ejpam-110	127	8	is	be	AUX
ejpam-110	127	9	relatively	relatively	ADV
ejpam-110	127	10	locally	locally	ADV
ejpam-110	127	11	compact	compact	ADJ
ejpam-110	127	12	there	there	PRON
ejpam-110	127	13	is	be	VERB
ejpam-110	127	14	f	f	PROPN
ejpam-110	127	15	∈	∈	PROPN
ejpam-110	127	16	ω(δ	ω(δ	PROPN
ejpam-110	127	17	)	)	PUNCT
ejpam-110	127	18	,	,	PUNCT
ejpam-110	127	19	with	with	ADP
ejpam-110	127	20	χ	χ	DET
ejpam-110	127	21	supp	supp	PROPN
ejpam-110	127	22	(	(	PUNCT
ejpam-110	127	23	f	f	PROPN
ejpam-110	127	24	)	)	PUNCT
ejpam-110	127	25	compact	compact	ADJ
ejpam-110	127	26	,	,	PUNCT
ejpam-110	127	27	such	such	ADJ
ejpam-110	127	28	that	that	SCONJ
ejpam-110	127	29	f	f	PROPN
ejpam-110	127	30	(	(	PUNCT
ejpam-110	127	31	x	x	X
ejpam-110	127	32	)	)	PUNCT
ejpam-110	127	33	�	�	PROPN
ejpam-110	127	34	p	p	NOUN
ejpam-110	127	35	,	,	PUNCT
ejpam-110	127	36	hence	hence	ADV
ejpam-110	127	37	supp	supp	NOUN
ejpam-110	127	38	(	(	PUNCT
ejpam-110	127	39	f	f	PROPN
ejpam-110	127	40	)	)	PUNCT
ejpam-110	127	41	is	be	AUX
ejpam-110	127	42	compact	compact	ADJ
ejpam-110	127	43	.	.	PUNCT
ejpam-110	128	1	let	let	VERB
ejpam-110	128	2	g	g	PROPN
ejpam-110	128	3	∈	∈	PROPN
ejpam-110	128	4	lx	lx	ADP
ejpam-110	128	5	a	a	DET
ejpam-110	128	6	basic	basic	ADJ
ejpam-110	128	7	open	open	ADJ
ejpam-110	128	8	l	l	NOUN
ejpam-110	128	9	-	-	ADJ
ejpam-110	128	10	set	set	ADJ
ejpam-110	128	11	,	,	PUNCT
ejpam-110	128	12	g(x	g(x	NOUN
ejpam-110	128	13	)	)	PUNCT
ejpam-110	128	14	�	�	PROPN
ejpam-110	128	15	p	p	NOUN
ejpam-110	128	16	and	and	CCONJ
ejpam-110	128	17	g	g	NOUN
ejpam-110	128	18	≤	≤	PROPN
ejpam-110	128	19	f	f	NOUN
ejpam-110	128	20	,	,	PUNCT
ejpam-110	128	21	defined	define	VERB
ejpam-110	128	22	by	by	ADP
ejpam-110	128	23	g(y	g(y	NOUN
ejpam-110	128	24	)	)	PUNCT
ejpam-110	128	25	=	=	PUNCT
ejpam-110	129	1			PROPN
ejpam-110	129	2			X
ejpam-110	129	3			ADJ
ejpam-110	129	4	e	e	NOUN
ejpam-110	129	5	if	if	SCONJ
ejpam-110	129	6	y	y	PROPN
ejpam-110	129	7	∈	∈	PROPN
ejpam-110	129	8	v	v	ADP
ejpam-110	129	9	∈	∈	PROPN
ejpam-110	129	10	δ	δ	NOUN
ejpam-110	129	11	0	0	PUNCT
ejpam-110	130	1	if	if	SCONJ
ejpam-110	130	2	y	y	PROPN
ejpam-110	130	3	/∈	/∈	VERB
ejpam-110	130	4	v	v	NOUN
ejpam-110	130	5	since	since	SCONJ
ejpam-110	130	6	g	g	NOUN
ejpam-110	130	7	≤	≤	NUM
ejpam-110	130	8	f	f	PROPN
ejpam-110	130	9	and	and	CCONJ
ejpam-110	130	10	g(y	g(y	PROPN
ejpam-110	130	11	)	)	PUNCT
ejpam-110	130	12	=	=	PUNCT
ejpam-110	131	1			PROPN
ejpam-110	131	2			X
ejpam-110	131	3			ADJ
ejpam-110	131	4	e	e	PROPN
ejpam-110	131	5	se	se	X
ejpam-110	131	6	y	y	PROPN
ejpam-110	131	7	∈	∈	PROPN
ejpam-110	131	8	v	v	ADP
ejpam-110	131	9	∈	∈	PROPN
ejpam-110	131	10	δ	δ	NOUN
ejpam-110	131	11	0	0	PUNCT
ejpam-110	131	12	se	se	PROPN
ejpam-110	131	13	y	y	PROPN
ejpam-110	131	14	/∈	/∈	PUNCT
ejpam-110	132	1	v	v	INTJ
ejpam-110	132	2	we	we	PRON
ejpam-110	132	3	have	have	VERB
ejpam-110	132	4	g	g	NOUN
ejpam-110	132	5	≤	≤	NUM
ejpam-110	132	6	f	f	NOUN
ejpam-110	132	7	and	and	CCONJ
ejpam-110	132	8	v	v	NOUN
ejpam-110	132	9	=	=	SYM
ejpam-110	132	10	supp(g)⊂	supp(g)⊂	NOUN
ejpam-110	132	11	supp	supp	PROPN
ejpam-110	132	12	(	(	PUNCT
ejpam-110	132	13	f	f	PROPN
ejpam-110	132	14	)	)	PUNCT
ejpam-110	132	15	,	,	PUNCT
ejpam-110	132	16	thus	thus	ADV
ejpam-110	132	17	,	,	PUNCT
ejpam-110	132	18	v	v	NOUN
ejpam-110	132	19	is	be	AUX
ejpam-110	132	20	compact	compact	ADJ
ejpam-110	132	21	since	since	SCONJ
ejpam-110	132	22	it	it	PRON
ejpam-110	132	23	is	be	AUX
ejpam-110	132	24	closed	closed	ADJ
ejpam-110	132	25	and	and	CCONJ
ejpam-110	132	26	supp	supp	PROPN
ejpam-110	132	27	(	(	PUNCT
ejpam-110	132	28	f	f	PROPN
ejpam-110	132	29	)	)	PUNCT
ejpam-110	132	30	is	be	AUX
ejpam-110	132	31	compact	compact	ADJ
ejpam-110	132	32	.	.	PUNCT
ejpam-110	133	1	4	4	X
ejpam-110	133	2	.	.	X
ejpam-110	133	3	some	some	DET
ejpam-110	133	4	properties	property	NOUN
ejpam-110	133	5	and	and	CCONJ
ejpam-110	133	6	comparison	comparison	NOUN
ejpam-110	133	7	theorem	theorem	VERB
ejpam-110	133	8	4.1	4.1	NUM
ejpam-110	133	9	.	.	PUNCT
ejpam-110	134	1	let	let	VERB
ejpam-110	134	2	x	x	PRON
ejpam-110	134	3	,	,	PUNCT
ejpam-110	134	4	tx	tx	PROPN
ejpam-110	134	5	�	�	PROPN
ejpam-110	134	6	be	be	AUX
ejpam-110	134	7	a	a	DET
ejpam-110	134	8	locally	locally	ADV
ejpam-110	134	9	compact	compact	ADJ
ejpam-110	134	10	l	l	ADJ
ejpam-110	134	11	-	-	ADJ
ejpam-110	134	12	topological	topological	ADJ
ejpam-110	134	13	space	space	NOUN
ejpam-110	134	14	and	and	CCONJ
ejpam-110	134	15	let	let	VERB
ejpam-110	134	16	y	y	PRON
ejpam-110	134	17	,	,	PUNCT
ejpam-110	134	18	ty	ty	PRON
ejpam-110	134	19	�	�	PROPN
ejpam-110	134	20	be	be	AUX
ejpam-110	134	21	an	an	DET
ejpam-110	134	22	ltopological	ltopological	ADJ
ejpam-110	134	23	space	space	NOUN
ejpam-110	134	24	.	.	PUNCT
ejpam-110	135	1	if	if	SCONJ
ejpam-110	135	2	h	h	PRON
ejpam-110	135	3	:	:	PUNCT
ejpam-110	135	4	x	x	X
ejpam-110	135	5	→	→	SYM
ejpam-110	135	6	y	y	PROPN
ejpam-110	135	7	is	be	AUX
ejpam-110	135	8	a	a	DET
ejpam-110	135	9	continuous	continuous	ADJ
ejpam-110	135	10	open	open	ADJ
ejpam-110	135	11	surjection	surjection	NOUN
ejpam-110	135	12	then	then	ADV
ejpam-110	135	13	y	y	PROPN
ejpam-110	135	14	,	,	PUNCT
ejpam-110	135	15	ty	ty	PRON
ejpam-110	135	16	�	�	PROPN
ejpam-110	135	17	is	be	AUX
ejpam-110	135	18	locally	locally	ADV
ejpam-110	135	19	compact	compact	ADJ
ejpam-110	135	20	.	.	PUNCT
ejpam-110	136	1	proof	proof	NOUN
ejpam-110	136	2	.	.	PUNCT
ejpam-110	137	1	let	let	VERB
ejpam-110	137	2	y	y	PROPN
ejpam-110	137	3	∈	∈	PROPN
ejpam-110	137	4	y	y	PROPN
ejpam-110	137	5	with	with	ADP
ejpam-110	137	6	y	y	PROPN
ejpam-110	137	7	=	=	SYM
ejpam-110	137	8	h(x	h(x	PROPN
ejpam-110	137	9	)	)	PUNCT
ejpam-110	137	10	,	,	PUNCT
ejpam-110	137	11	let	let	VERB
ejpam-110	137	12	p	p	PRON
ejpam-110	137	13	∈	∈	PROPN
ejpam-110	137	14	pr(l	pr(l	NOUN
ejpam-110	137	15	)	)	PUNCT
ejpam-110	137	16	and	and	CCONJ
ejpam-110	137	17	f	f	PROPN
ejpam-110	137	18	∈	∈	PROPN
ejpam-110	137	19	ty	ty	INTJ
ejpam-110	137	20	with	with	ADP
ejpam-110	137	21	f	f	PROPN
ejpam-110	137	22	(	(	PUNCT
ejpam-110	137	23	y	y	PROPN
ejpam-110	137	24	)	)	PUNCT
ejpam-110	137	25	�	�	PROPN
ejpam-110	138	1	p.	p.	NOUN
ejpam-110	138	2	let	let	VERB
ejpam-110	139	1	j	j	PROPN
ejpam-110	139	2	=	=	SYM
ejpam-110	139	3	h−1	h−1	PROPN
ejpam-110	139	4	(	(	PUNCT
ejpam-110	139	5	f	f	PROPN
ejpam-110	139	6	)	)	PUNCT
ejpam-110	139	7	,	,	PUNCT
ejpam-110	139	8	then	then	ADV
ejpam-110	139	9	j	j	PROPN
ejpam-110	139	10	∈	∈	PROPN
ejpam-110	139	11	tx	tx	PROPN
ejpam-110	139	12	since	since	SCONJ
ejpam-110	139	13	h	h	NOUN
ejpam-110	139	14	is	be	AUX
ejpam-110	139	15	continuous	continuous	ADJ
ejpam-110	139	16	and	and	CCONJ
ejpam-110	139	17	j(x	j(x	NOUN
ejpam-110	139	18	)	)	PUNCT
ejpam-110	140	1	=	=	SYM
ejpam-110	140	2	f	f	PROPN
ejpam-110	140	3	(	(	PUNCT
ejpam-110	140	4	y	y	PROPN
ejpam-110	140	5	)	)	PUNCT
ejpam-110	140	6	�	�	PROPN
ejpam-110	140	7	p.	p.	NOUN
ejpam-110	140	8	since	since	SCONJ
ejpam-110	140	9	x	x	PRON
ejpam-110	140	10	,	,	PUNCT
ejpam-110	140	11	tx	tx	PROPN
ejpam-110	140	12	�	�	PROPN
ejpam-110	140	13	is	be	AUX
ejpam-110	140	14	locally	locally	ADV
ejpam-110	140	15	compact	compact	ADJ
ejpam-110	140	16	there	there	ADV
ejpam-110	140	17	exist	exist	VERB
ejpam-110	140	18	i	i	PRON
ejpam-110	140	19	∈	∈	PROPN
ejpam-110	140	20	tx	tx	PROPN
ejpam-110	140	21	and	and	CCONJ
ejpam-110	140	22	c	c	NOUN
ejpam-110	140	23	∈	∈	PROPN
ejpam-110	141	1	lx	lx	NOUN
ejpam-110	141	2	,	,	PUNCT
ejpam-110	141	3	withχsupp(c	withχsupp(c	NOUN
ejpam-110	141	4	)	)	PUNCT
ejpam-110	141	5	compact	compact	ADJ
ejpam-110	141	6	,	,	PUNCT
ejpam-110	141	7	such	such	ADJ
ejpam-110	141	8	that	that	DET
ejpam-110	141	9	i(x	i(x	NOUN
ejpam-110	141	10	)	)	PUNCT
ejpam-110	141	11	�	�	PROPN
ejpam-110	141	12	p	p	NOUN
ejpam-110	142	1	and	and	CCONJ
ejpam-110	142	2	i	i	PRON
ejpam-110	142	3	�	�	PROPN
ejpam-110	142	4	c	c	PROPN
ejpam-110	142	5	�	�	PROPN
ejpam-110	142	6	j.	j.	PROPN
ejpam-110	142	7	let	let	VERB
ejpam-110	142	8	g	g	PROPN
ejpam-110	142	9	=	=	SYM
ejpam-110	142	10	h	h	PROPN
ejpam-110	142	11	(	(	PUNCT
ejpam-110	142	12	j	j	NOUN
ejpam-110	142	13	)	)	PUNCT
ejpam-110	142	14	and	and	CCONJ
ejpam-110	142	15	let	let	VERB
ejpam-110	142	16	k	k	PROPN
ejpam-110	142	17	=	=	SYM
ejpam-110	142	18	h(c	h(c	PROPN
ejpam-110	142	19	)	)	PUNCT
ejpam-110	142	20	.	.	PUNCT
ejpam-110	143	1	then	then	ADV
ejpam-110	143	2	g	g	PROPN
ejpam-110	143	3	∈	∈	PROPN
ejpam-110	143	4	ty	ty	INTJ
ejpam-110	143	5	since	since	SCONJ
ejpam-110	143	6	h	h	NOUN
ejpam-110	143	7	is	be	AUX
ejpam-110	143	8	open	open	ADJ
ejpam-110	143	9	and	and	CCONJ
ejpam-110	143	10	g	g	NOUN
ejpam-110	143	11	≤	≤	NOUN
ejpam-110	143	12	k	k	X
ejpam-110	143	13	≤	≤	PROPN
ejpam-110	143	14	f	f	PROPN
ejpam-110	143	15	since	since	SCONJ
ejpam-110	143	16	i	i	PRON
ejpam-110	143	17	�	�	PROPN
ejpam-110	143	18	c	c	PROPN
ejpam-110	143	19	�	�	PROPN
ejpam-110	143	20	j.	j.	PROPN
ejpam-110	143	21	since	since	SCONJ
ejpam-110	143	22	h	h	PROPN
ejpam-110	143	23	is	be	AUX
ejpam-110	143	24	continuous	continuous	ADJ
ejpam-110	143	25	and	and	CCONJ
ejpam-110	143	26	χsupp(c	χsupp(c	NUM
ejpam-110	143	27	)	)	PUNCT
ejpam-110	143	28	is	be	AUX
ejpam-110	143	29	compact	compact	ADJ
ejpam-110	143	30	we	we	PRON
ejpam-110	143	31	have	have	VERB
ejpam-110	143	32	h(χsupp(c	h(χsupp(c	NUM
ejpam-110	143	33	)	)	PUNCT
ejpam-110	143	34	)	)	PUNCT
ejpam-110	143	35	,	,	PUNCT
ejpam-110	143	36	but	but	CCONJ
ejpam-110	143	37	:	:	PUNCT
ejpam-110	143	38	h(χsupp(c	h(χsupp(c	X
ejpam-110	143	39	)	)	PUNCT
ejpam-110	143	40	)	)	PUNCT
ejpam-110	144	1	=	=	SYM
ejpam-110	144	2	χh(supp(c	χh(supp(c	NUM
ejpam-110	144	3	)	)	PUNCT
ejpam-110	144	4	)	)	PUNCT
ejpam-110	145	1	=	=	SYM
ejpam-110	145	2	χsupp(h(c	χsupp(h(c	PROPN
ejpam-110	145	3	)	)	PUNCT
ejpam-110	145	4	)	)	PUNCT
ejpam-110	146	1	=	=	SYM
ejpam-110	146	2	χsupp(k	χsupp(k	PROPN
ejpam-110	146	3	)	)	PUNCT
ejpam-110	146	4	hence	hence	ADV
ejpam-110	146	5	,	,	PUNCT
ejpam-110	146	6	y	y	PROPN
ejpam-110	146	7	,	,	PUNCT
ejpam-110	146	8	ty	ty	PRON
ejpam-110	146	9	�	�	PROPN
ejpam-110	146	10	is	be	AUX
ejpam-110	146	11	locally	locally	ADV
ejpam-110	146	12	compact	compact	ADJ
ejpam-110	146	13	.	.	PUNCT
ejpam-110	147	1	theorem	theorem	VERB
ejpam-110	147	2	4.2	4.2	NUM
ejpam-110	147	3	.	.	PUNCT
ejpam-110	148	1	let	let	VERB
ejpam-110	148	2	x	x	PRON
ejpam-110	148	3	,	,	PUNCT
ejpam-110	148	4	tx	tx	PROPN
ejpam-110	148	5	�	�	PROPN
ejpam-110	148	6	be	be	AUX
ejpam-110	148	7	a	a	DET
ejpam-110	148	8	weakly	weakly	ADJ
ejpam-110	148	9	locally	locally	ADV
ejpam-110	148	10	compact	compact	ADJ
ejpam-110	148	11	l	l	ADJ
ejpam-110	148	12	-	-	ADJ
ejpam-110	148	13	topological	topological	ADJ
ejpam-110	148	14	space	space	NOUN
ejpam-110	148	15	and	and	CCONJ
ejpam-110	148	16	let	let	VERB
ejpam-110	148	17	y	y	PRON
ejpam-110	148	18	,	,	PUNCT
ejpam-110	148	19	ty	ty	PRON
ejpam-110	148	20	�	�	PROPN
ejpam-110	148	21	be	be	AUX
ejpam-110	148	22	an	an	DET
ejpam-110	148	23	l	l	ADJ
ejpam-110	148	24	-	-	ADJ
ejpam-110	148	25	topological	topological	ADJ
ejpam-110	148	26	space	space	NOUN
ejpam-110	148	27	.	.	PUNCT
ejpam-110	149	1	if	if	SCONJ
ejpam-110	149	2	h	h	PRON
ejpam-110	149	3	:	:	PUNCT
ejpam-110	149	4	x	x	X
ejpam-110	149	5	→	→	SYM
ejpam-110	149	6	y	y	PROPN
ejpam-110	149	7	is	be	AUX
ejpam-110	149	8	a	a	DET
ejpam-110	149	9	continuous	continuous	ADJ
ejpam-110	149	10	open	open	ADJ
ejpam-110	149	11	surjection	surjection	NOUN
ejpam-110	149	12	then	then	ADV
ejpam-110	149	13	y	y	PROPN
ejpam-110	149	14	,	,	PUNCT
ejpam-110	149	15	ty	ty	PRON
ejpam-110	149	16	�	�	PROPN
ejpam-110	149	17	is	be	AUX
ejpam-110	149	18	weakly	weakly	ADV
ejpam-110	149	19	locally	locally	ADV
ejpam-110	149	20	compact	compact	ADJ
ejpam-110	149	21	.	.	PUNCT
ejpam-110	150	1	t.	t.	PROPN
ejpam-110	150	2	breuckmann	breuckmann	PROPN
ejpam-110	150	3	,	,	PUNCT
ejpam-110	150	4	s.	s.	PROPN
ejpam-110	150	5	kudri	kudri	PROPN
ejpam-110	150	6	,	,	PUNCT
ejpam-110	150	7	and	and	CCONJ
ejpam-110	150	8	h.	h.	PROPN
ejpam-110	150	9	aygün	aygün	PROPN
ejpam-110	150	10	/	/	SYM
ejpam-110	150	11	eur	eur	PROPN
ejpam-110	150	12	.	.	PUNCT
ejpam-110	151	1	j.	j.	PROPN
ejpam-110	151	2	pure	pure	PROPN
ejpam-110	151	3	appl	appl	PROPN
ejpam-110	151	4	.	.	PROPN
ejpam-110	151	5	math	math	PROPN
ejpam-110	151	6	,	,	PUNCT
ejpam-110	151	7	2	2	NUM
ejpam-110	151	8	(	(	PUNCT
ejpam-110	151	9	2009	2009	NUM
ejpam-110	151	10	)	)	PUNCT
ejpam-110	151	11	,	,	PUNCT
ejpam-110	151	12	(	(	PUNCT
ejpam-110	151	13	147	147	NUM
ejpam-110	151	14	-	-	SYM
ejpam-110	151	15	161	161	NUM
ejpam-110	151	16	)	)	PUNCT
ejpam-110	151	17	153	153	NUM
ejpam-110	151	18	proof	proof	NOUN
ejpam-110	151	19	.	.	PUNCT
ejpam-110	152	1	let	let	VERB
ejpam-110	152	2	y	y	PROPN
ejpam-110	152	3	∈	∈	PROPN
ejpam-110	152	4	y	y	PROPN
ejpam-110	152	5	with	with	ADP
ejpam-110	152	6	y	y	PROPN
ejpam-110	152	7	=	=	SYM
ejpam-110	152	8	h(x	h(x	PROPN
ejpam-110	152	9	)	)	PUNCT
ejpam-110	152	10	and	and	CCONJ
ejpam-110	152	11	let	let	VERB
ejpam-110	152	12	p	p	PRON
ejpam-110	152	13	∈	∈	PROPN
ejpam-110	152	14	pr(l	pr(l	NOUN
ejpam-110	152	15	)	)	PUNCT
ejpam-110	152	16	.	.	PUNCT
ejpam-110	153	1	since	since	SCONJ
ejpam-110	153	2	x	x	X
ejpam-110	153	3	,	,	PUNCT
ejpam-110	153	4	tx	tx	PROPN
ejpam-110	153	5	�	�	PROPN
ejpam-110	153	6	is	be	AUX
ejpam-110	153	7	weakly	weakly	ADV
ejpam-110	153	8	locally	locally	ADV
ejpam-110	153	9	compact	compact	ADJ
ejpam-110	153	10	there	there	PRON
ejpam-110	153	11	exist	exist	VERB
ejpam-110	153	12	i	i	PRON
ejpam-110	153	13	∈	∈	PROPN
ejpam-110	153	14	tx	tx	PROPN
ejpam-110	153	15	and	and	CCONJ
ejpam-110	153	16	c	c	NOUN
ejpam-110	153	17	∈	∈	PROPN
ejpam-110	153	18	lx	lx	ADV
ejpam-110	153	19	,	,	PUNCT
ejpam-110	153	20	with	with	ADP
ejpam-110	153	21	χsupp(c	χsupp(c	NOUN
ejpam-110	153	22	)	)	PUNCT
ejpam-110	153	23	compact	compact	ADJ
ejpam-110	153	24	,	,	PUNCT
ejpam-110	154	1	such	such	ADJ
ejpam-110	154	2	that	that	DET
ejpam-110	154	3	i(x	i(x	NOUN
ejpam-110	154	4	)	)	PUNCT
ejpam-110	154	5	�	�	PROPN
ejpam-110	154	6	p	p	NOUN
ejpam-110	154	7	and	and	CCONJ
ejpam-110	154	8	i	i	PRON
ejpam-110	154	9	�	�	PROPN
ejpam-110	154	10	c.	c.	PROPN
ejpam-110	154	11	let	let	VERB
ejpam-110	154	12	g	g	PROPN
ejpam-110	154	13	=	=	SYM
ejpam-110	154	14	h	h	PROPN
ejpam-110	154	15	(	(	PUNCT
ejpam-110	154	16	j	j	NOUN
ejpam-110	154	17	)	)	PUNCT
ejpam-110	154	18	and	and	CCONJ
ejpam-110	154	19	let	let	VERB
ejpam-110	154	20	k	k	PROPN
ejpam-110	154	21	=	=	SYM
ejpam-110	154	22	h(c	h(c	PROPN
ejpam-110	154	23	)	)	PUNCT
ejpam-110	154	24	.	.	PUNCT
ejpam-110	155	1	then	then	ADV
ejpam-110	155	2	g	g	PROPN
ejpam-110	155	3	∈	∈	PROPN
ejpam-110	155	4	ty	ty	INTJ
ejpam-110	155	5	since	since	SCONJ
ejpam-110	155	6	h	h	NOUN
ejpam-110	155	7	is	be	AUX
ejpam-110	155	8	open	open	ADJ
ejpam-110	155	9	and	and	CCONJ
ejpam-110	155	10	g	g	NOUN
ejpam-110	155	11	≤	≤	PROPN
ejpam-110	156	1	k	k	NOUN
ejpam-110	157	1	since	since	SCONJ
ejpam-110	157	2	i	i	PRON
ejpam-110	157	3	�	�	PROPN
ejpam-110	157	4	c.	c.	PROPN
ejpam-110	157	5	since	since	SCONJ
ejpam-110	157	6	h	h	PROPN
ejpam-110	157	7	is	be	AUX
ejpam-110	157	8	continuous	continuous	ADJ
ejpam-110	157	9	and	and	CCONJ
ejpam-110	157	10	χsupp(c	χsupp(c	NUM
ejpam-110	157	11	)	)	PUNCT
ejpam-110	157	12	is	be	AUX
ejpam-110	157	13	compact	compact	ADJ
ejpam-110	157	14	we	we	PRON
ejpam-110	157	15	have	have	VERB
ejpam-110	157	16	h(χsupp(c	h(χsupp(c	NUM
ejpam-110	157	17	)	)	PUNCT
ejpam-110	157	18	)	)	PUNCT
ejpam-110	157	19	,	,	PUNCT
ejpam-110	157	20	but	but	CCONJ
ejpam-110	157	21	:	:	PUNCT
ejpam-110	157	22	h(χsupp(c	h(χsupp(c	X
ejpam-110	157	23	)	)	PUNCT
ejpam-110	157	24	)	)	PUNCT
ejpam-110	158	1	=	=	SYM
ejpam-110	158	2	χh(supp(c	χh(supp(c	NUM
ejpam-110	158	3	)	)	PUNCT
ejpam-110	158	4	)	)	PUNCT
ejpam-110	159	1	=	=	SYM
ejpam-110	159	2	χsupp(h(c	χsupp(h(c	PROPN
ejpam-110	159	3	)	)	PUNCT
ejpam-110	159	4	)	)	PUNCT
ejpam-110	160	1	=	=	SYM
ejpam-110	160	2	χsupp(k	χsupp(k	PROPN
ejpam-110	160	3	)	)	PUNCT
ejpam-110	160	4	hence	hence	ADV
ejpam-110	160	5	,	,	PUNCT
ejpam-110	160	6	y	y	PROPN
ejpam-110	160	7	,	,	PUNCT
ejpam-110	160	8	ty	ty	PRON
ejpam-110	160	9	�	�	PROPN
ejpam-110	160	10	is	be	AUX
ejpam-110	160	11	weakly	weakly	ADV
ejpam-110	160	12	locally	locally	ADV
ejpam-110	160	13	compact	compact	ADJ
ejpam-110	160	14	.	.	PUNCT
ejpam-110	161	1	theorem	theorem	VERB
ejpam-110	161	2	4.3	4.3	NUM
ejpam-110	161	3	.	.	PUNCT
ejpam-110	162	1	let	let	VERB
ejpam-110	162	2	x	x	PRON
ejpam-110	162	3	,	,	PUNCT
ejpam-110	162	4	tx	tx	PROPN
ejpam-110	162	5	�	�	PROPN
ejpam-110	162	6	be	be	AUX
ejpam-110	162	7	a	a	DET
ejpam-110	162	8	relatively	relatively	ADV
ejpam-110	162	9	locally	locally	ADV
ejpam-110	162	10	compact	compact	ADJ
ejpam-110	162	11	l	l	ADJ
ejpam-110	162	12	-	-	ADJ
ejpam-110	162	13	topological	topological	ADJ
ejpam-110	162	14	space	space	NOUN
ejpam-110	162	15	and	and	CCONJ
ejpam-110	162	16	let	let	VERB
ejpam-110	162	17	y	y	PRON
ejpam-110	162	18	,	,	PUNCT
ejpam-110	162	19	ty	ty	PRON
ejpam-110	162	20	�	�	PROPN
ejpam-110	162	21	be	be	AUX
ejpam-110	162	22	an	an	DET
ejpam-110	162	23	l	l	ADJ
ejpam-110	162	24	-	-	ADJ
ejpam-110	162	25	topological	topological	ADJ
ejpam-110	162	26	space	space	NOUN
ejpam-110	162	27	.	.	PUNCT
ejpam-110	163	1	if	if	SCONJ
ejpam-110	163	2	h	h	PRON
ejpam-110	163	3	:	:	PUNCT
ejpam-110	163	4	x	x	X
ejpam-110	163	5	→	→	SYM
ejpam-110	163	6	y	y	PROPN
ejpam-110	163	7	is	be	AUX
ejpam-110	163	8	a	a	DET
ejpam-110	163	9	continuous	continuous	ADJ
ejpam-110	163	10	open	open	ADJ
ejpam-110	163	11	surjection	surjection	NOUN
ejpam-110	163	12	with	with	ADP
ejpam-110	163	13	h(g	h(g	NOUN
ejpam-110	163	14	)	)	PUNCT
ejpam-110	163	15	≤	≤	NUM
ejpam-110	163	16	h(g	h(g	NOUN
ejpam-110	163	17	)	)	PUNCT
ejpam-110	163	18	for	for	ADP
ejpam-110	163	19	every	every	DET
ejpam-110	163	20	g	g	PROPN
ejpam-110	163	21	∈	∈	PROPN
ejpam-110	163	22	lx	lx	NOUN
ejpam-110	163	23	,	,	PUNCT
ejpam-110	163	24	then	then	ADV
ejpam-110	163	25	,	,	PUNCT
ejpam-110	163	26	y	y	PROPN
ejpam-110	163	27	,	,	PUNCT
ejpam-110	163	28	ty	ty	PRON
ejpam-110	163	29	�	�	PROPN
ejpam-110	163	30	is	be	AUX
ejpam-110	163	31	relatively	relatively	ADV
ejpam-110	163	32	locally	locally	ADV
ejpam-110	163	33	compact	compact	ADJ
ejpam-110	163	34	.	.	PUNCT
ejpam-110	164	1	proof	proof	NOUN
ejpam-110	164	2	.	.	PUNCT
ejpam-110	165	1	let	let	VERB
ejpam-110	165	2	y	y	PROPN
ejpam-110	165	3	∈	∈	PROPN
ejpam-110	165	4	y	y	PROPN
ejpam-110	165	5	with	with	ADP
ejpam-110	165	6	y	y	PROPN
ejpam-110	165	7	=	=	SYM
ejpam-110	165	8	h(x	h(x	PROPN
ejpam-110	165	9	)	)	PUNCT
ejpam-110	165	10	and	and	CCONJ
ejpam-110	165	11	let	let	VERB
ejpam-110	165	12	p	p	PRON
ejpam-110	165	13	∈	∈	PROPN
ejpam-110	165	14	pr(l	pr(l	NOUN
ejpam-110	165	15	)	)	PUNCT
ejpam-110	165	16	.	.	PUNCT
ejpam-110	166	1	since	since	SCONJ
ejpam-110	166	2	x	x	X
ejpam-110	166	3	,	,	PUNCT
ejpam-110	166	4	tx	tx	PROPN
ejpam-110	166	5	�	�	PROPN
ejpam-110	166	6	is	be	AUX
ejpam-110	166	7	relatively	relatively	ADV
ejpam-110	166	8	locally	locally	ADV
ejpam-110	166	9	compact	compact	ADJ
ejpam-110	166	10	there	there	PRON
ejpam-110	166	11	is	be	VERB
ejpam-110	166	12	g	g	PROPN
ejpam-110	166	13	∈	∈	PROPN
ejpam-110	166	14	tx	tx	PROPN
ejpam-110	166	15	,	,	PUNCT
ejpam-110	166	16	with	with	ADP
ejpam-110	166	17	χsupp(g	χsupp(g	NOUN
ejpam-110	166	18	)	)	PUNCT
ejpam-110	166	19	compact	compact	ADJ
ejpam-110	166	20	,	,	PUNCT
ejpam-110	167	1	such	such	ADJ
ejpam-110	167	2	that	that	DET
ejpam-110	167	3	g(x)≤	g(x)≤	PROPN
ejpam-110	167	4	p.	p.	NOUN
ejpam-110	167	5	let	let	VERB
ejpam-110	167	6	f	f	PROPN
ejpam-110	167	7	=	=	PUNCT
ejpam-110	167	8	h(g	h(g	PROPN
ejpam-110	167	9	)	)	PUNCT
ejpam-110	167	10	,	,	PUNCT
ejpam-110	167	11	then	then	ADV
ejpam-110	167	12	:	:	PUNCT
ejpam-110	167	13	f	f	PROPN
ejpam-110	167	14	(	(	PUNCT
ejpam-110	167	15	x	x	X
ejpam-110	167	16	)	)	PUNCT
ejpam-110	167	17	�	�	PROPN
ejpam-110	167	18	p	p	PROPN
ejpam-110	167	19	,	,	PUNCT
ejpam-110	167	20	f	f	PROPN
ejpam-110	167	21	∈	∈	PROPN
ejpam-110	168	1	ty	ty	INTJ
ejpam-110	168	2	since	since	SCONJ
ejpam-110	168	3	h	h	NOUN
ejpam-110	168	4	is	be	AUX
ejpam-110	168	5	open	open	ADJ
ejpam-110	168	6	,	,	PUNCT
ejpam-110	168	7	and	and	CCONJ
ejpam-110	168	8	h(χsupp(g	h(χsupp(g	NUM
ejpam-110	168	9	)	)	PUNCT
ejpam-110	168	10	)	)	PUNCT
ejpam-110	168	11	is	be	AUX
ejpam-110	168	12	a	a	DET
ejpam-110	168	13	compact	compact	ADJ
ejpam-110	168	14	l	l	NOUN
ejpam-110	168	15	-	-	NOUN
ejpam-110	168	16	set	set	NOUN
ejpam-110	168	17	in	in	ADP
ejpam-110	168	18	ly	ly	ADP
ejpam-110	168	19	since	since	SCONJ
ejpam-110	168	20	h	h	NOUN
ejpam-110	168	21	ï£	ï£	NOUN
ejpam-110	168	22	¡	¡	PROPN
ejpam-110	168	23	continuous	continuous	ADJ
ejpam-110	168	24	.	.	PUNCT
ejpam-110	169	1	but	but	CCONJ
ejpam-110	169	2	:	:	PUNCT
ejpam-110	169	3	h(χsupp(g	h(χsupp(g	X
ejpam-110	169	4	)	)	PUNCT
ejpam-110	169	5	)	)	PUNCT
ejpam-110	170	1	=	=	SYM
ejpam-110	170	2	χh(supp(g	χh(supp(g	NOUN
ejpam-110	170	3	)	)	PUNCT
ejpam-110	170	4	)	)	PUNCT
ejpam-110	171	1	=	=	SYM
ejpam-110	171	2	χsupp(h(g	χsupp(h(g	NOUN
ejpam-110	171	3	)	)	PUNCT
ejpam-110	171	4	)	)	PUNCT
ejpam-110	172	1	=	=	SYM
ejpam-110	172	2	χsupp(h(g	χsupp(h(g	NOUN
ejpam-110	172	3	)	)	PUNCT
ejpam-110	172	4	)	)	PUNCT
ejpam-110	173	1	=	=	PUNCT
ejpam-110	173	2	χ	χ	DET
ejpam-110	173	3	supp	supp	NOUN
ejpam-110	173	4	(	(	PUNCT
ejpam-110	173	5	f	f	PROPN
ejpam-110	173	6	)	)	PUNCT
ejpam-110	173	7	)	)	PUNCT
ejpam-110	173	8	where	where	SCONJ
ejpam-110	173	9	the	the	DET
ejpam-110	173	10	last	last	ADJ
ejpam-110	173	11	equality	equality	NOUN
ejpam-110	173	12	is	be	AUX
ejpam-110	173	13	due	due	ADJ
ejpam-110	173	14	to	to	ADP
ejpam-110	173	15	the	the	DET
ejpam-110	173	16	continuity	continuity	NOUN
ejpam-110	173	17	of	of	ADP
ejpam-110	173	18	h	h	NOUN
ejpam-110	173	19	and	and	CCONJ
ejpam-110	173	20	the	the	DET
ejpam-110	173	21	condition	condition	NOUN
ejpam-110	173	22	mention	mention	VERB
ejpam-110	173	23	in	in	ADP
ejpam-110	173	24	theorem	theorem	NOUN
ejpam-110	173	25	.	.	PUNCT
ejpam-110	174	1	hence	hence	ADV
ejpam-110	174	2	,	,	PUNCT
ejpam-110	174	3	y	y	PROPN
ejpam-110	174	4	,	,	PUNCT
ejpam-110	174	5	ty	ty	PRON
ejpam-110	174	6	�	�	PROPN
ejpam-110	174	7	is	be	AUX
ejpam-110	174	8	relatively	relatively	ADV
ejpam-110	174	9	locally	locally	ADV
ejpam-110	174	10	compact	compact	ADJ
ejpam-110	174	11	.	.	PUNCT
ejpam-110	175	1	theorem	theorem	VERB
ejpam-110	175	2	4.4	4.4	NUM
ejpam-110	175	3	.	.	PUNCT
ejpam-110	176	1	let	let	VERB
ejpam-110	176	2	〈	〈	PROPN
ejpam-110	176	3	x	x	PROPN
ejpam-110	176	4	,	,	PUNCT
ejpam-110	176	5	t	t	PROPN
ejpam-110	176	6	〉	〉	NOUN
ejpam-110	176	7	be	be	VERB
ejpam-110	176	8	a	a	DET
ejpam-110	176	9	locally	locally	ADV
ejpam-110	176	10	compact	compact	ADJ
ejpam-110	176	11	l	l	ADJ
ejpam-110	176	12	-	-	ADJ
ejpam-110	176	13	topological	topological	ADJ
ejpam-110	176	14	space	space	NOUN
ejpam-110	176	15	,	,	PUNCT
ejpam-110	176	16	then	then	ADV
ejpam-110	176	17	〈	〈	PROPN
ejpam-110	176	18	x	x	X
ejpam-110	176	19	,	,	PUNCT
ejpam-110	176	20	t	t	PROPN
ejpam-110	176	21	〉	〉	NOUN
ejpam-110	176	22	is	be	AUX
ejpam-110	176	23	weakly	weakly	ADV
ejpam-110	176	24	locally	locally	ADV
ejpam-110	176	25	compact	compact	ADJ
ejpam-110	176	26	.	.	PUNCT
ejpam-110	177	1	proof	proof	NOUN
ejpam-110	177	2	.	.	PUNCT
ejpam-110	178	1	let	let	VERB
ejpam-110	178	2	x	x	PUNCT
ejpam-110	178	3	∈	∈	PROPN
ejpam-110	178	4	x	x	PUNCT
ejpam-110	178	5	and	and	CCONJ
ejpam-110	178	6	let	let	VERB
ejpam-110	178	7	p	p	PRON
ejpam-110	178	8	∈	∈	PROPN
ejpam-110	178	9	pr(l	pr(l	NOUN
ejpam-110	178	10	)	)	PUNCT
ejpam-110	178	11	.	.	PUNCT
ejpam-110	179	1	since	since	SCONJ
ejpam-110	179	2	〈	〈	PROPN
ejpam-110	179	3	x	x	X
ejpam-110	179	4	,	,	PUNCT
ejpam-110	179	5	t	t	PROPN
ejpam-110	179	6	〉	〉	NOUN
ejpam-110	179	7	is	be	AUX
ejpam-110	179	8	locally	locally	ADV
ejpam-110	179	9	compact	compact	ADJ
ejpam-110	179	10	,	,	PUNCT
ejpam-110	179	11	for	for	ADP
ejpam-110	179	12	f	f	PROPN
ejpam-110	179	13	=	=	SYM
ejpam-110	179	14	x	x	NOUN
ejpam-110	179	15	,	,	PUNCT
ejpam-110	179	16	there	there	PRON
ejpam-110	179	17	exist	exist	VERB
ejpam-110	179	18	g	g	PROPN
ejpam-110	179	19	∈	∈	PROPN
ejpam-110	179	20	t	t	PROPN
ejpam-110	179	21	and	and	CCONJ
ejpam-110	179	22	k	k	PROPN
ejpam-110	179	23	∈	∈	PROPN
ejpam-110	179	24	lx	lx	ADV
ejpam-110	179	25	,	,	PUNCT
ejpam-110	179	26	with	with	ADP
ejpam-110	179	27	χsupp(k	χsupp(k	PROPN
ejpam-110	179	28	)	)	PUNCT
ejpam-110	179	29	compact	compact	ADJ
ejpam-110	179	30	,	,	PUNCT
ejpam-110	179	31	such	such	ADJ
ejpam-110	179	32	that	that	SCONJ
ejpam-110	179	33	g(x	g(x	NOUN
ejpam-110	179	34	)	)	PUNCT
ejpam-110	179	35	�	�	PROPN
ejpam-110	179	36	p	p	NOUN
ejpam-110	179	37	and	and	CCONJ
ejpam-110	179	38	g	g	NOUN
ejpam-110	179	39	≤	≤	NUM
ejpam-110	180	1	k	k	NOUN
ejpam-110	180	2	≤	≤	PROPN
ejpam-110	180	3	f	f	X
ejpam-110	180	4	.	.	PUNCT
ejpam-110	181	1	so	so	ADV
ejpam-110	181	2	〈	〈	PROPN
ejpam-110	181	3	x	x	X
ejpam-110	181	4	,	,	PUNCT
ejpam-110	181	5	t	t	PROPN
ejpam-110	181	6	〉	〉	NOUN
ejpam-110	181	7	is	be	AUX
ejpam-110	181	8	weakly	weakly	ADV
ejpam-110	181	9	locally	locally	ADV
ejpam-110	181	10	compact	compact	ADJ
ejpam-110	181	11	.	.	PUNCT
ejpam-110	182	1	theorem	theorem	VERB
ejpam-110	182	2	4.5	4.5	NUM
ejpam-110	182	3	.	.	PUNCT
ejpam-110	183	1	if	if	SCONJ
ejpam-110	183	2	〈	〈	PROPN
ejpam-110	183	3	x	x	X
ejpam-110	183	4	,	,	PUNCT
ejpam-110	183	5	t	t	PROPN
ejpam-110	183	6	〉	〉	NOUN
ejpam-110	183	7	is	be	AUX
ejpam-110	183	8	a	a	DET
ejpam-110	183	9	compact	compact	ADJ
ejpam-110	183	10	hausdorff	hausdorff	NOUN
ejpam-110	183	11	fully	fully	ADV
ejpam-110	183	12	stratified	stratify	VERB
ejpam-110	183	13	l	l	ADJ
ejpam-110	183	14	-	-	ADJ
ejpam-110	183	15	topological	topological	ADJ
ejpam-110	183	16	space	space	NOUN
ejpam-110	183	17	then	then	ADV
ejpam-110	183	18	〈	〈	PROPN
ejpam-110	183	19	x	x	X
ejpam-110	183	20	,	,	PUNCT
ejpam-110	183	21	t	t	PROPN
ejpam-110	183	22	〉	〉	NOUN
ejpam-110	183	23	is	be	AUX
ejpam-110	183	24	locally	locally	ADV
ejpam-110	183	25	compact	compact	ADJ
ejpam-110	183	26	.	.	PUNCT
ejpam-110	184	1	proof	proof	NOUN
ejpam-110	184	2	.	.	PUNCT
ejpam-110	185	1	since	since	SCONJ
ejpam-110	185	2	〈	〈	PROPN
ejpam-110	185	3	x	x	X
ejpam-110	185	4	,	,	PUNCT
ejpam-110	185	5	t	t	PROPN
ejpam-110	185	6	〉	〉	NOUN
ejpam-110	185	7	a	a	DET
ejpam-110	185	8	compact	compact	ADJ
ejpam-110	185	9	hausdorff	hausdorff	NOUN
ejpam-110	185	10	fully	fully	ADV
ejpam-110	185	11	stratified	stratify	VERB
ejpam-110	185	12	l	l	ADJ
ejpam-110	185	13	-	-	ADJ
ejpam-110	185	14	topological	topological	ADJ
ejpam-110	185	15	space	space	NOUN
ejpam-110	185	16	there	there	PRON
ejpam-110	185	17	is	be	VERB
ejpam-110	185	18	a	a	DET
ejpam-110	185	19	topology	topology	NOUN
ejpam-110	185	20	δ	δ	NOUN
ejpam-110	185	21	in	in	ADP
ejpam-110	185	22	x	x	PROPN
ejpam-110	185	23	such	such	ADJ
ejpam-110	185	24	that	that	DET
ejpam-110	185	25	t	t	NOUN
ejpam-110	185	26	=	=	PUNCT
ejpam-110	185	27	ω(δ	ω(δ	PROPN
ejpam-110	185	28	)	)	PUNCT
ejpam-110	185	29	.	.	PUNCT
ejpam-110	186	1	by	by	ADP
ejpam-110	186	2	theorems	theorem	NOUN
ejpam-110	186	3	2.1	2.1	NUM
ejpam-110	186	4	and	and	CCONJ
ejpam-110	186	5	2.2	2.2	NUM
ejpam-110	186	6	we	we	PRON
ejpam-110	186	7	have	have	VERB
ejpam-110	186	8	that	that	PRON
ejpam-110	186	9	〈	〈	PROPN
ejpam-110	186	10	x	x	SYM
ejpam-110	186	11	,	,	PUNCT
ejpam-110	186	12	δ	δ	PROPN
ejpam-110	186	13	〉	〉	NOUN
ejpam-110	186	14	is	be	AUX
ejpam-110	186	15	a	a	DET
ejpam-110	186	16	t.	t.	NOUN
ejpam-110	186	17	breuckmann	breuckmann	PROPN
ejpam-110	186	18	,	,	PUNCT
ejpam-110	186	19	s.	s.	PROPN
ejpam-110	186	20	kudri	kudri	PROPN
ejpam-110	186	21	,	,	PUNCT
ejpam-110	186	22	and	and	CCONJ
ejpam-110	186	23	h.	h.	PROPN
ejpam-110	186	24	aygün	aygün	PROPN
ejpam-110	186	25	/	/	SYM
ejpam-110	186	26	eur	eur	PROPN
ejpam-110	186	27	.	.	PUNCT
ejpam-110	187	1	j.	j.	PROPN
ejpam-110	187	2	pure	pure	PROPN
ejpam-110	187	3	appl	appl	PROPN
ejpam-110	187	4	.	.	PROPN
ejpam-110	187	5	math	math	PROPN
ejpam-110	187	6	,	,	PUNCT
ejpam-110	187	7	2	2	NUM
ejpam-110	187	8	(	(	PUNCT
ejpam-110	187	9	2009	2009	NUM
ejpam-110	187	10	)	)	PUNCT
ejpam-110	187	11	,	,	PUNCT
ejpam-110	187	12	(	(	PUNCT
ejpam-110	187	13	147	147	NUM
ejpam-110	187	14	-	-	SYM
ejpam-110	187	15	161	161	NUM
ejpam-110	187	16	)	)	PUNCT
ejpam-110	187	17	154	154	NUM
ejpam-110	187	18	compact	compact	ADJ
ejpam-110	187	19	hausdorff	hausdorff	NOUN
ejpam-110	187	20	topological	topological	ADJ
ejpam-110	187	21	space	space	NOUN
ejpam-110	187	22	,	,	PUNCT
ejpam-110	187	23	hence	hence	ADV
ejpam-110	187	24	it	it	PRON
ejpam-110	187	25	’s	’	VERB
ejpam-110	187	26	locally	locally	ADV
ejpam-110	187	27	compact	compact	ADJ
ejpam-110	187	28	.	.	PUNCT
ejpam-110	188	1	by	by	ADP
ejpam-110	188	2	theorem	theorem	ADJ
ejpam-110	188	3	3.1	3.1	NUM
ejpam-110	188	4	,	,	PUNCT
ejpam-110	188	5	〈	〈	PROPN
ejpam-110	188	6	x	x	X
ejpam-110	188	7	,	,	PUNCT
ejpam-110	188	8	t	t	PROPN
ejpam-110	188	9	〉	〉	NOUN
ejpam-110	188	10	is	be	AUX
ejpam-110	188	11	locally	locally	ADV
ejpam-110	188	12	compact	compact	ADJ
ejpam-110	188	13	.	.	PUNCT
ejpam-110	189	1	theorem	theorem	VERB
ejpam-110	189	2	4.6	4.6	NUM
ejpam-110	189	3	.	.	PUNCT
ejpam-110	190	1	let	let	VERB
ejpam-110	190	2	〈	〈	PROPN
ejpam-110	190	3	x	x	PROPN
ejpam-110	190	4	,	,	PUNCT
ejpam-110	190	5	t	t	PROPN
ejpam-110	190	6	〉	〉	NOUN
ejpam-110	190	7	be	be	VERB
ejpam-110	190	8	a	a	DET
ejpam-110	190	9	weakly	weakly	ADV
ejpam-110	190	10	locally	locally	ADV
ejpam-110	190	11	compact	compact	ADJ
ejpam-110	190	12	hausdorff	hausdorff	NOUN
ejpam-110	190	13	fully	fully	ADV
ejpam-110	190	14	stratified	stratify	VERB
ejpam-110	190	15	l	l	ADJ
ejpam-110	190	16	-	-	ADJ
ejpam-110	190	17	topological	topological	ADJ
ejpam-110	190	18	space	space	NOUN
ejpam-110	190	19	,	,	PUNCT
ejpam-110	190	20	then	then	ADV
ejpam-110	190	21	〈	〈	PROPN
ejpam-110	190	22	x	x	X
ejpam-110	190	23	,	,	PUNCT
ejpam-110	190	24	t	t	PROPN
ejpam-110	190	25	〉	〉	NOUN
ejpam-110	190	26	is	be	AUX
ejpam-110	190	27	locally	locally	ADV
ejpam-110	190	28	compact	compact	ADJ
ejpam-110	190	29	.	.	PUNCT
ejpam-110	191	1	proof	proof	NOUN
ejpam-110	191	2	.	.	PUNCT
ejpam-110	192	1	let	let	VERB
ejpam-110	192	2	x	x	SYM
ejpam-110	192	3	∈	∈	PROPN
ejpam-110	192	4	x	x	X
ejpam-110	192	5	,	,	PUNCT
ejpam-110	192	6	let	let	VERB
ejpam-110	192	7	p	p	PRON
ejpam-110	192	8	∈	∈	NOUN
ejpam-110	192	9	pr(l	pr(l	NOUN
ejpam-110	192	10	)	)	PUNCT
ejpam-110	192	11	and	and	CCONJ
ejpam-110	192	12	let	let	VERB
ejpam-110	192	13	f	f	PROPN
ejpam-110	192	14	∈	∈	PROPN
ejpam-110	192	15	t	t	PROPN
ejpam-110	192	16	such	such	ADJ
ejpam-110	192	17	that	that	SCONJ
ejpam-110	192	18	f	f	PROPN
ejpam-110	192	19	(	(	PUNCT
ejpam-110	192	20	x	x	NOUN
ejpam-110	192	21	)	)	PUNCT
ejpam-110	192	22	�	�	PROPN
ejpam-110	192	23	p.	p.	NOUN
ejpam-110	192	24	we	we	PRON
ejpam-110	192	25	must	must	AUX
ejpam-110	192	26	show	show	VERB
ejpam-110	192	27	that	that	SCONJ
ejpam-110	192	28	there	there	PRON
ejpam-110	192	29	exist	exist	VERB
ejpam-110	192	30	g	g	PROPN
ejpam-110	192	31	∈	∈	PROPN
ejpam-110	192	32	t	t	PROPN
ejpam-110	192	33	and	and	CCONJ
ejpam-110	192	34	k	k	PROPN
ejpam-110	192	35	∈	∈	PROPN
ejpam-110	193	1	lx	lx	ADV
ejpam-110	193	2	,	,	PUNCT
ejpam-110	193	3	with	with	ADP
ejpam-110	193	4	χsupp(k	χsupp(k	PROPN
ejpam-110	193	5	)	)	PUNCT
ejpam-110	193	6	compact	compact	ADJ
ejpam-110	193	7	,	,	PUNCT
ejpam-110	193	8	such	such	ADJ
ejpam-110	193	9	that	that	SCONJ
ejpam-110	193	10	g(x	g(x	NOUN
ejpam-110	193	11	)	)	PUNCT
ejpam-110	193	12	�	�	PROPN
ejpam-110	193	13	p	p	NOUN
ejpam-110	193	14	and	and	CCONJ
ejpam-110	193	15	g	g	NOUN
ejpam-110	193	16	≤	≤	NUM
ejpam-110	193	17	k	k	NOUN
ejpam-110	193	18	≤	≤	PROPN
ejpam-110	193	19	f	f	PROPN
ejpam-110	193	20	.	.	PUNCT
ejpam-110	194	1	since	since	SCONJ
ejpam-110	194	2	〈	〈	PROPN
ejpam-110	194	3	x	x	X
ejpam-110	194	4	,	,	PUNCT
ejpam-110	194	5	t	t	PROPN
ejpam-110	194	6	〉	〉	NOUN
ejpam-110	194	7	is	be	AUX
ejpam-110	194	8	weakly	weakly	ADV
ejpam-110	194	9	locally	locally	ADV
ejpam-110	194	10	compact	compact	ADJ
ejpam-110	194	11	there	there	PRON
ejpam-110	194	12	exist	exist	VERB
ejpam-110	194	13	i	i	PRON
ejpam-110	194	14	∈	∈	PROPN
ejpam-110	194	15	t	t	PROPN
ejpam-110	194	16	and	and	CCONJ
ejpam-110	194	17	j	j	PROPN
ejpam-110	194	18	∈	∈	PROPN
ejpam-110	194	19	lx	lx	ADV
ejpam-110	194	20	,	,	PUNCT
ejpam-110	194	21	with	with	ADP
ejpam-110	194	22	χsupp	χsupp	PROPN
ejpam-110	194	23	(	(	PUNCT
ejpam-110	194	24	j	j	NOUN
ejpam-110	194	25	)	)	PUNCT
ejpam-110	194	26	compact	compact	ADJ
ejpam-110	194	27	,	,	PUNCT
ejpam-110	194	28	such	such	ADJ
ejpam-110	194	29	that	that	DET
ejpam-110	194	30	i(x	i(x	PROPN
ejpam-110	194	31	)	)	PUNCT
ejpam-110	194	32	�	�	PROPN
ejpam-110	194	33	p	p	NOUN
ejpam-110	194	34	and	and	CCONJ
ejpam-110	194	35	i	i	PRON
ejpam-110	194	36	≤	≤	PROPN
ejpam-110	194	37	j.	j.	PROPN
ejpam-110	194	38	let	let	VERB
ejpam-110	194	39	d	d	NOUN
ejpam-110	194	40	=	=	SYM
ejpam-110	194	41	supp	supp	PROPN
ejpam-110	194	42	(	(	PUNCT
ejpam-110	194	43	j	j	NOUN
ejpam-110	194	44	)	)	PUNCT
ejpam-110	194	45	.	.	PUNCT
ejpam-110	195	1	since	since	SCONJ
ejpam-110	195	2	χsupp	χsupp	PROPN
ejpam-110	195	3	(	(	PUNCT
ejpam-110	195	4	j	j	NOUN
ejpam-110	195	5	)	)	PUNCT
ejpam-110	195	6	is	be	AUX
ejpam-110	195	7	compact	compact	ADJ
ejpam-110	195	8	and	and	CCONJ
ejpam-110	195	9	〈	〈	NOUN
ejpam-110	195	10	x	x	NOUN
ejpam-110	195	11	,	,	PUNCT
ejpam-110	195	12	t	t	PROPN
ejpam-110	195	13	〉	〉	NOUN
ejpam-110	195	14	is	be	AUX
ejpam-110	195	15	hausdorff	hausdorff	NOUN
ejpam-110	195	16	fully	fully	ADV
ejpam-110	195	17	stratified	stratify	VERB
ejpam-110	195	18	,	,	PUNCT
ejpam-110	195	19	the	the	DET
ejpam-110	195	20	subspace	subspace	NOUN
ejpam-110	195	21	d	d	NOUN
ejpam-110	195	22	,	,	PUNCT
ejpam-110	195	23	td	td	PROPN
ejpam-110	195	24	�	�	PROPN
ejpam-110	195	25	is	be	AUX
ejpam-110	195	26	a	a	DET
ejpam-110	195	27	compact	compact	ADJ
ejpam-110	195	28	hausdorff	hausdorff	NOUN
ejpam-110	195	29	fully	fully	ADV
ejpam-110	195	30	stratified	stratify	VERB
ejpam-110	195	31	l	l	ADJ
ejpam-110	195	32	-	-	ADJ
ejpam-110	195	33	topological	topological	ADJ
ejpam-110	195	34	space	space	NOUN
ejpam-110	195	35	,	,	PUNCT
ejpam-110	195	36	then	then	ADV
ejpam-110	195	37	,	,	PUNCT
ejpam-110	195	38	by	by	ADP
ejpam-110	195	39	theorem	theorem	NOUN
ejpam-110	195	40	4.5	4.5	NUM
ejpam-110	196	1	it	it	PRON
ejpam-110	196	2	’s	’	VERB
ejpam-110	196	3	locally	locally	ADV
ejpam-110	196	4	compact	compact	ADJ
ejpam-110	196	5	,	,	PUNCT
ejpam-110	196	6	hence	hence	ADV
ejpam-110	196	7	for	for	ADP
ejpam-110	196	8	fd	fd	PROPN
ejpam-110	196	9	=	=	SYM
ejpam-110	196	10	f	f	PROPN
ejpam-110	196	11	|d	|d	NOUN
ejpam-110	196	12	there	there	PRON
ejpam-110	196	13	exist	exist	VERB
ejpam-110	196	14	hd	hd	NOUN
ejpam-110	196	15	∈	∈	NOUN
ejpam-110	196	16	td	td	NOUN
ejpam-110	196	17	and	and	CCONJ
ejpam-110	196	18	c	c	NOUN
ejpam-110	196	19	∈	∈	PROPN
ejpam-110	196	20	ld	ld	PROPN
ejpam-110	196	21	,	,	PUNCT
ejpam-110	196	22	with	with	ADP
ejpam-110	196	23	χsupp(c	χsupp(c	NOUN
ejpam-110	196	24	)	)	PUNCT
ejpam-110	196	25	compact	compact	ADJ
ejpam-110	196	26	,	,	PUNCT
ejpam-110	196	27	such	such	ADJ
ejpam-110	196	28	that	that	PRON
ejpam-110	196	29	hd	hd	VERB
ejpam-110	196	30	≤	≤	PROPN
ejpam-110	196	31	cd	cd	PROPN
ejpam-110	196	32	≤	≤	NUM
ejpam-110	196	33	fd	fd	PROPN
ejpam-110	196	34	and	and	CCONJ
ejpam-110	196	35	hd(x	hd(x	NOUN
ejpam-110	196	36	)	)	PUNCT
ejpam-110	197	1	�	�	PROPN
ejpam-110	197	2	p.	p.	NOUN
ejpam-110	197	3	let	let	VERB
ejpam-110	197	4	h	h	PROPN
ejpam-110	197	5	∈	∈	PROPN
ejpam-110	197	6	t	t	PROPN
ejpam-110	197	7	such	such	ADJ
ejpam-110	197	8	that	that	SCONJ
ejpam-110	197	9	h|d	h|d	NOUN
ejpam-110	197	10	=	=	PUNCT
ejpam-110	197	11	hd	hd	NOUN
ejpam-110	197	12	and	and	CCONJ
ejpam-110	197	13	define	define	VERB
ejpam-110	197	14	k	k	PROPN
ejpam-110	197	15	∈	∈	PROPN
ejpam-110	197	16	lx	lx	NOUN
ejpam-110	197	17	by	by	ADP
ejpam-110	197	18	k(y	k(y	NOUN
ejpam-110	197	19	)	)	PUNCT
ejpam-110	197	20	=	=	PUNCT
ejpam-110	197	21			PROPN
ejpam-110	197	22			ADJ
ejpam-110	197	23			NOUN
ejpam-110	197	24	cd(y	cd(y	PUNCT
ejpam-110	197	25	)	)	PUNCT
ejpam-110	198	1	if	if	SCONJ
ejpam-110	198	2	y	y	PROPN
ejpam-110	198	3	∈	∈	PROPN
ejpam-110	198	4	d	d	NOUN
ejpam-110	198	5	0	0	PUNCT
ejpam-110	198	6	if	if	SCONJ
ejpam-110	198	7	y	y	PROPN
ejpam-110	198	8	/∈	/∈	PUNCT
ejpam-110	199	1	d	d	NOUN
ejpam-110	199	2	then	then	ADV
ejpam-110	199	3	,	,	PUNCT
ejpam-110	199	4	h(x	h(x	PROPN
ejpam-110	199	5	)	)	PUNCT
ejpam-110	199	6	�	�	PROPN
ejpam-110	199	7	p	p	NOUN
ejpam-110	199	8	and	and	CCONJ
ejpam-110	199	9	χsupp(k	χsupp(k	PROPN
ejpam-110	199	10	)	)	PUNCT
ejpam-110	199	11	is	be	AUX
ejpam-110	199	12	compact	compact	ADJ
ejpam-110	199	13	since	since	SCONJ
ejpam-110	199	14	supp(k	supp(k	PROPN
ejpam-110	199	15	)	)	PUNCT
ejpam-110	199	16	=	=	SYM
ejpam-110	199	17	supp(cd	supp(cd	NOUN
ejpam-110	199	18	)	)	PUNCT
ejpam-110	199	19	.	.	PUNCT
ejpam-110	200	1	let	let	VERB
ejpam-110	200	2	g	g	PROPN
ejpam-110	200	3	=	=	VERB
ejpam-110	200	4	h∧	h∧	PROPN
ejpam-110	200	5	j	j	PROPN
ejpam-110	200	6	,	,	PUNCT
ejpam-110	200	7	then	then	ADV
ejpam-110	200	8	g	g	PROPN
ejpam-110	200	9	∈	∈	PROPN
ejpam-110	200	10	t	t	PROPN
ejpam-110	200	11	and	and	CCONJ
ejpam-110	200	12	g(x	g(x	NOUN
ejpam-110	201	1	)	)	PUNCT
ejpam-110	201	2	�	�	PROPN
ejpam-110	201	3	p.	p.	NOUN
ejpam-110	201	4	we	we	PRON
ejpam-110	201	5	proof	proof	VERB
ejpam-110	201	6	now	now	ADV
ejpam-110	201	7	that	that	SCONJ
ejpam-110	201	8	g	g	PROPN
ejpam-110	201	9	≤	≤	X
ejpam-110	201	10	k	k	NOUN
ejpam-110	201	11	≤	≤	PROPN
ejpam-110	201	12	f	f	PROPN
ejpam-110	201	13	,	,	PUNCT
ejpam-110	201	14	in	in	ADP
ejpam-110	201	15	fact	fact	NOUN
ejpam-110	201	16	,	,	PUNCT
ejpam-110	202	1	if	if	SCONJ
ejpam-110	202	2	y	y	PROPN
ejpam-110	202	3	∈	∈	PROPN
ejpam-110	202	4	d	d	X
ejpam-110	202	5	then	then	ADV
ejpam-110	202	6	g(y	g(y	NOUN
ejpam-110	202	7	)	)	PUNCT
ejpam-110	202	8	≤	≤	NOUN
ejpam-110	202	9	h(y	h(y	ADV
ejpam-110	202	10	)	)	PUNCT
ejpam-110	202	11	≤	≤	NUM
ejpam-110	202	12	k(y	k(y	PROPN
ejpam-110	202	13	)	)	PUNCT
ejpam-110	202	14	≤	≤	NUM
ejpam-110	202	15	f	f	X
ejpam-110	202	16	(	(	PUNCT
ejpam-110	202	17	y	y	NOUN
ejpam-110	202	18	)	)	PUNCT
ejpam-110	202	19	since	since	SCONJ
ejpam-110	202	20	hd	hd	NOUN
ejpam-110	202	21	≤	≤	PROPN
ejpam-110	202	22	cd	cd	PROPN
ejpam-110	202	23	≤	≤	PROPN
ejpam-110	202	24	fd	fd	PROPN
ejpam-110	202	25	,	,	PUNCT
ejpam-110	202	26	and	and	CCONJ
ejpam-110	202	27	if	if	SCONJ
ejpam-110	202	28	y	y	PROPN
ejpam-110	202	29	/∈	/∈	PUNCT
ejpam-110	203	1	d	d	NOUN
ejpam-110	203	2	then	then	ADV
ejpam-110	203	3	j(y	j(y	PROPN
ejpam-110	203	4	)	)	PUNCT
ejpam-110	203	5	=	=	SYM
ejpam-110	203	6	0	0	NUM
ejpam-110	203	7	and	and	CCONJ
ejpam-110	203	8	k(y	k(y	PROPN
ejpam-110	203	9	)	)	PUNCT
ejpam-110	204	1	=	=	SYM
ejpam-110	204	2	0	0	NUM
ejpam-110	204	3	,	,	PUNCT
ejpam-110	204	4	so	so	ADV
ejpam-110	204	5	g(y	g(y	NOUN
ejpam-110	204	6	)	)	PUNCT
ejpam-110	204	7	=	=	PUNCT
ejpam-110	205	1	0=	0=	NUM
ejpam-110	205	2	k(y	k(y	PROPN
ejpam-110	205	3	)	)	PUNCT
ejpam-110	206	1	≤	≤	NUM
ejpam-110	206	2	f	f	X
ejpam-110	206	3	(	(	PUNCT
ejpam-110	206	4	y	y	PROPN
ejpam-110	206	5	)	)	PUNCT
ejpam-110	206	6	.	.	PUNCT
ejpam-110	207	1	theorem	theorem	NOUN
ejpam-110	207	2	4.7	4.7	NUM
ejpam-110	207	3	.	.	PUNCT
ejpam-110	208	1	let	let	VERB
ejpam-110	208	2	〈	〈	PROPN
ejpam-110	208	3	x	x	PROPN
ejpam-110	208	4	,	,	PUNCT
ejpam-110	208	5	t	t	PROPN
ejpam-110	208	6	〉	〉	NOUN
ejpam-110	208	7	be	be	VERB
ejpam-110	208	8	a	a	DET
ejpam-110	208	9	relatively	relatively	ADV
ejpam-110	208	10	locally	locally	ADV
ejpam-110	208	11	compact	compact	ADJ
ejpam-110	208	12	l	l	ADJ
ejpam-110	208	13	-	-	ADJ
ejpam-110	208	14	topological	topological	ADJ
ejpam-110	208	15	space	space	NOUN
ejpam-110	208	16	,	,	PUNCT
ejpam-110	208	17	then	then	ADV
ejpam-110	208	18	〈	〈	PROPN
ejpam-110	208	19	x	x	X
ejpam-110	208	20	,	,	PUNCT
ejpam-110	208	21	t	t	PROPN
ejpam-110	208	22	〉	〉	NOUN
ejpam-110	208	23	is	be	AUX
ejpam-110	208	24	weakly	weakly	ADV
ejpam-110	208	25	locally	locally	ADV
ejpam-110	208	26	compact	compact	ADJ
ejpam-110	208	27	.	.	PUNCT
ejpam-110	209	1	proof	proof	NOUN
ejpam-110	209	2	.	.	PUNCT
ejpam-110	210	1	let	let	VERB
ejpam-110	210	2	x	x	PUNCT
ejpam-110	210	3	∈	∈	PROPN
ejpam-110	210	4	x	x	PUNCT
ejpam-110	210	5	and	and	CCONJ
ejpam-110	210	6	let	let	VERB
ejpam-110	210	7	p	p	PRON
ejpam-110	210	8	∈	∈	PROPN
ejpam-110	210	9	pr(l	pr(l	NOUN
ejpam-110	210	10	)	)	PUNCT
ejpam-110	210	11	.	.	PUNCT
ejpam-110	211	1	since	since	SCONJ
ejpam-110	211	2	〈	〈	PROPN
ejpam-110	211	3	x	x	X
ejpam-110	211	4	,	,	PUNCT
ejpam-110	211	5	t	t	PROPN
ejpam-110	211	6	〉	〉	NOUN
ejpam-110	211	7	is	be	AUX
ejpam-110	211	8	relatively	relatively	ADV
ejpam-110	211	9	locally	locally	ADV
ejpam-110	211	10	compact	compact	ADJ
ejpam-110	211	11	there	there	PRON
ejpam-110	211	12	exists	exist	VERB
ejpam-110	211	13	g	g	PROPN
ejpam-110	211	14	∈	∈	PROPN
ejpam-110	211	15	t	t	PROPN
ejpam-110	211	16	,	,	PUNCT
ejpam-110	211	17	with	with	ADP
ejpam-110	211	18	χsupp(g	χsupp(g	NOUN
ejpam-110	211	19	)	)	PUNCT
ejpam-110	211	20	compact	compact	ADJ
ejpam-110	211	21	,	,	PUNCT
ejpam-110	212	1	such	such	ADJ
ejpam-110	212	2	that	that	SCONJ
ejpam-110	212	3	g(x	g(x	NOUN
ejpam-110	212	4	)	)	PUNCT
ejpam-110	212	5	�	�	PROPN
ejpam-110	212	6	p.	p.	NOUN
ejpam-110	212	7	since	since	SCONJ
ejpam-110	212	8	g	g	PROPN
ejpam-110	212	9	≤	≤	NUM
ejpam-110	212	10	g	g	NOUN
ejpam-110	212	11	,	,	PUNCT
ejpam-110	212	12	〈	〈	PROPN
ejpam-110	212	13	x	x	X
ejpam-110	212	14	,	,	PUNCT
ejpam-110	212	15	t	t	PROPN
ejpam-110	212	16	〉	〉	NOUN
ejpam-110	212	17	is	be	AUX
ejpam-110	212	18	weakly	weakly	ADV
ejpam-110	212	19	locally	locally	ADV
ejpam-110	212	20	compact	compact	ADJ
ejpam-110	212	21	.	.	PUNCT
ejpam-110	213	1	theorem	theorem	NOUN
ejpam-110	213	2	4.8	4.8	NUM
ejpam-110	213	3	.	.	PUNCT
ejpam-110	214	1	let	let	VERB
ejpam-110	214	2	〈	〈	PROPN
ejpam-110	214	3	x	x	PROPN
ejpam-110	214	4	,	,	PUNCT
ejpam-110	214	5	t	t	PROPN
ejpam-110	214	6	〉	〉	NOUN
ejpam-110	214	7	be	be	VERB
ejpam-110	214	8	a	a	DET
ejpam-110	214	9	weakly	weakly	ADV
ejpam-110	214	10	locally	locally	ADV
ejpam-110	214	11	compact	compact	ADJ
ejpam-110	214	12	hausdorff	hausdorff	NOUN
ejpam-110	214	13	fully	fully	ADV
ejpam-110	214	14	stratified	stratify	VERB
ejpam-110	214	15	l	l	ADJ
ejpam-110	214	16	-	-	ADJ
ejpam-110	214	17	topological	topological	ADJ
ejpam-110	214	18	space	space	NOUN
ejpam-110	214	19	such	such	ADJ
ejpam-110	214	20	that	that	SCONJ
ejpam-110	214	21	χ	χ	DET
ejpam-110	214	22	supp	supp	NOUN
ejpam-110	214	23	(	(	PUNCT
ejpam-110	214	24	f	f	PROPN
ejpam-110	214	25	)	)	PUNCT
ejpam-110	214	26	=	=	SYM
ejpam-110	214	27	χsupp	χsupp	PROPN
ejpam-110	214	28	(	(	PUNCT
ejpam-110	214	29	f	f	PROPN
ejpam-110	214	30	)	)	PUNCT
ejpam-110	214	31	,	,	PUNCT
ejpam-110	214	32	then	then	ADV
ejpam-110	214	33	it	it	PRON
ejpam-110	214	34	’s	’	VERB
ejpam-110	214	35	relatively	relatively	ADV
ejpam-110	214	36	locally	locally	ADV
ejpam-110	214	37	compact	compact	ADJ
ejpam-110	214	38	.	.	PUNCT
ejpam-110	215	1	t.	t.	PROPN
ejpam-110	215	2	breuckmann	breuckmann	PROPN
ejpam-110	215	3	,	,	PUNCT
ejpam-110	215	4	s.	s.	PROPN
ejpam-110	215	5	kudri	kudri	PROPN
ejpam-110	215	6	,	,	PUNCT
ejpam-110	215	7	and	and	CCONJ
ejpam-110	215	8	h.	h.	PROPN
ejpam-110	215	9	aygün	aygün	PROPN
ejpam-110	215	10	/	/	SYM
ejpam-110	215	11	eur	eur	PROPN
ejpam-110	215	12	.	.	PUNCT
ejpam-110	216	1	j.	j.	PROPN
ejpam-110	216	2	pure	pure	PROPN
ejpam-110	216	3	appl	appl	PROPN
ejpam-110	216	4	.	.	PROPN
ejpam-110	216	5	math	math	PROPN
ejpam-110	216	6	,	,	PUNCT
ejpam-110	216	7	2	2	NUM
ejpam-110	216	8	(	(	PUNCT
ejpam-110	216	9	2009	2009	NUM
ejpam-110	216	10	)	)	PUNCT
ejpam-110	216	11	,	,	PUNCT
ejpam-110	216	12	(	(	PUNCT
ejpam-110	216	13	147	147	NUM
ejpam-110	216	14	-	-	SYM
ejpam-110	216	15	161	161	NUM
ejpam-110	216	16	)	)	PUNCT
ejpam-110	216	17	155	155	NUM
ejpam-110	216	18	proof	proof	NOUN
ejpam-110	216	19	.	.	PUNCT
ejpam-110	217	1	let	let	VERB
ejpam-110	217	2	x	x	PUNCT
ejpam-110	217	3	∈	∈	PROPN
ejpam-110	217	4	x	x	PUNCT
ejpam-110	217	5	and	and	CCONJ
ejpam-110	217	6	let	let	VERB
ejpam-110	217	7	p	p	PRON
ejpam-110	217	8	∈	∈	PROPN
ejpam-110	217	9	pr(l	pr(l	NOUN
ejpam-110	217	10	)	)	PUNCT
ejpam-110	217	11	.	.	PUNCT
ejpam-110	218	1	since	since	SCONJ
ejpam-110	218	2	〈	〈	PROPN
ejpam-110	218	3	x	x	X
ejpam-110	218	4	,	,	PUNCT
ejpam-110	218	5	t	t	PROPN
ejpam-110	218	6	〉	〉	NOUN
ejpam-110	218	7	is	be	AUX
ejpam-110	218	8	weakly	weakly	ADV
ejpam-110	218	9	locally	locally	ADV
ejpam-110	218	10	compact	compact	ADJ
ejpam-110	218	11	there	there	ADV
ejpam-110	218	12	exist	exist	VERB
ejpam-110	218	13	f	f	PROPN
ejpam-110	218	14	∈	∈	PROPN
ejpam-110	218	15	t	t	PROPN
ejpam-110	218	16	and	and	CCONJ
ejpam-110	218	17	k	k	PROPN
ejpam-110	218	18	∈	∈	PROPN
ejpam-110	219	1	lx	lx	ADV
ejpam-110	219	2	,	,	PUNCT
ejpam-110	219	3	with	with	ADP
ejpam-110	219	4	χsupp(k	χsupp(k	PROPN
ejpam-110	219	5	)	)	PUNCT
ejpam-110	219	6	compact	compact	ADJ
ejpam-110	219	7	,	,	PUNCT
ejpam-110	219	8	such	such	ADJ
ejpam-110	219	9	that	that	SCONJ
ejpam-110	219	10	f	f	PROPN
ejpam-110	219	11	(	(	PUNCT
ejpam-110	219	12	x	x	X
ejpam-110	219	13	)	)	PUNCT
ejpam-110	219	14	�	�	PROPN
ejpam-110	219	15	p	p	PROPN
ejpam-110	219	16	and	and	CCONJ
ejpam-110	219	17	f	f	PROPN
ejpam-110	219	18	≤	≤	PROPN
ejpam-110	219	19	k.	k.	PROPN
ejpam-110	219	20	since	since	SCONJ
ejpam-110	219	21	χsupp(k	χsupp(k	PROPN
ejpam-110	219	22	)	)	PUNCT
ejpam-110	219	23	is	be	AUX
ejpam-110	219	24	a	a	DET
ejpam-110	219	25	compact	compact	ADJ
ejpam-110	219	26	l	l	NOUN
ejpam-110	219	27	-	-	NOUN
ejpam-110	219	28	set	set	VERB
ejpam-110	219	29	in	in	ADP
ejpam-110	219	30	a	a	DET
ejpam-110	219	31	hausdorff	hausdorff	NOUN
ejpam-110	219	32	space	space	NOUN
ejpam-110	219	33	,	,	PUNCT
ejpam-110	219	34	it	it	PRON
ejpam-110	219	35	’s	’	VERB
ejpam-110	219	36	closed	close	VERB
ejpam-110	219	37	,	,	PUNCT
ejpam-110	219	38	by	by	ADP
ejpam-110	219	39	proposition	proposition	NOUN
ejpam-110	219	40	2.1	2.1	NUM
ejpam-110	219	41	,	,	PUNCT
ejpam-110	219	42	so	so	ADV
ejpam-110	219	43	,	,	PUNCT
ejpam-110	219	44	χsupp(k	χsupp(k	PROPN
ejpam-110	219	45	)	)	PUNCT
ejpam-110	220	1	=	=	SYM
ejpam-110	220	2	χsupp(k	χsupp(k	PROPN
ejpam-110	220	3	)	)	PUNCT
ejpam-110	220	4	.	.	PUNCT
ejpam-110	221	1	since	since	SCONJ
ejpam-110	221	2	f	f	PROPN
ejpam-110	221	3	≤	≤	PROPN
ejpam-110	221	4	k	k	PROPN
ejpam-110	221	5	,	,	PUNCT
ejpam-110	221	6	χsupp	χsupp	PROPN
ejpam-110	221	7	(	(	PUNCT
ejpam-110	221	8	f	f	PROPN
ejpam-110	221	9	)	)	PUNCT
ejpam-110	221	10	≤	≤	NUM
ejpam-110	221	11	χsupp(k	χsupp(k	PROPN
ejpam-110	221	12	)	)	PUNCT
ejpam-110	221	13	then	then	ADV
ejpam-110	221	14	χsupp	χsupp	PROPN
ejpam-110	221	15	(	(	PUNCT
ejpam-110	221	16	f	f	PROPN
ejpam-110	221	17	)	)	PUNCT
ejpam-110	221	18	≤	≤	NUM
ejpam-110	222	1	χsupp(k	χsupp(k	PROPN
ejpam-110	222	2	)	)	PUNCT
ejpam-110	222	3	,	,	PUNCT
ejpam-110	222	4	hence	hence	ADV
ejpam-110	222	5	χsupp	χsupp	VERB
ejpam-110	222	6	(	(	PUNCT
ejpam-110	222	7	f	f	PROPN
ejpam-110	222	8	)	)	PUNCT
ejpam-110	222	9	is	be	AUX
ejpam-110	222	10	a	a	DET
ejpam-110	222	11	compact	compact	ADJ
ejpam-110	222	12	l	l	NOUN
ejpam-110	222	13	-	-	NOUN
ejpam-110	222	14	set	set	NOUN
ejpam-110	222	15	since	since	SCONJ
ejpam-110	222	16	it	it	PRON
ejpam-110	222	17	’s	’	VERB
ejpam-110	222	18	closed	closed	ADJ
ejpam-110	222	19	and	and	CCONJ
ejpam-110	222	20	χsupp(k	χsupp(k	NOUN
ejpam-110	222	21	)	)	PUNCT
ejpam-110	222	22	is	be	AUX
ejpam-110	222	23	compact	compact	ADJ
ejpam-110	222	24	,	,	PUNCT
ejpam-110	222	25	by	by	ADP
ejpam-110	222	26	proposition	proposition	NOUN
ejpam-110	222	27	2.2	2.2	NUM
ejpam-110	222	28	.	.	PUNCT
ejpam-110	223	1	but	but	CCONJ
ejpam-110	223	2	χsupp	χsupp	PROPN
ejpam-110	223	3	(	(	PUNCT
ejpam-110	223	4	f	f	PROPN
ejpam-110	223	5	)	)	PUNCT
ejpam-110	223	6	=	=	SYM
ejpam-110	223	7	χsupp	χsupp	PROPN
ejpam-110	223	8	(	(	PUNCT
ejpam-110	223	9	f	f	PROPN
ejpam-110	223	10	)	)	PUNCT
ejpam-110	223	11	,	,	PUNCT
ejpam-110	223	12	then	then	ADV
ejpam-110	223	13	χ	χ	DET
ejpam-110	223	14	supp	supp	PROPN
ejpam-110	223	15	(	(	PUNCT
ejpam-110	223	16	f	f	PROPN
ejpam-110	223	17	)	)	PUNCT
ejpam-110	223	18	is	be	AUX
ejpam-110	223	19	a	a	DET
ejpam-110	223	20	compact	compact	ADJ
ejpam-110	223	21	l	l	NOUN
ejpam-110	223	22	-	-	NOUN
ejpam-110	223	23	set	set	NOUN
ejpam-110	223	24	.	.	PUNCT
ejpam-110	224	1	therefore	therefore	ADV
ejpam-110	224	2	〈	〈	PROPN
ejpam-110	224	3	x	x	X
ejpam-110	224	4	,	,	PUNCT
ejpam-110	224	5	t	t	PROPN
ejpam-110	224	6	〉	〉	NOUN
ejpam-110	224	7	is	be	AUX
ejpam-110	224	8	relatively	relatively	ADV
ejpam-110	224	9	locally	locally	ADV
ejpam-110	224	10	compact	compact	ADJ
ejpam-110	224	11	.	.	PUNCT
ejpam-110	225	1	theorem	theorem	VERB
ejpam-110	225	2	4.9	4.9	NUM
ejpam-110	225	3	.	.	PUNCT
ejpam-110	226	1	let	let	VERB
ejpam-110	226	2	�	�	PROPN
ejpam-110	226	3	xλ	xλ	PROPN
ejpam-110	226	4	λ∈j	λ∈j	PROPN
ejpam-110	226	5	be	be	AUX
ejpam-110	226	6	a	a	DET
ejpam-110	226	7	family	family	NOUN
ejpam-110	226	8	of	of	ADP
ejpam-110	226	9	nonempty	nonempty	ADV
ejpam-110	226	10	fully	fully	ADV
ejpam-110	226	11	stratified	stratify	VERB
ejpam-110	226	12	l	l	ADJ
ejpam-110	226	13	-	-	ADJ
ejpam-110	226	14	topological	topological	ADJ
ejpam-110	226	15	spaces	space	NOUN
ejpam-110	226	16	.	.	PUNCT
ejpam-110	227	1	then	then	ADV
ejpam-110	227	2	:	:	PUNCT
ejpam-110	227	3	the	the	DET
ejpam-110	227	4	product	product	NOUN
ejpam-110	227	5	l	l	ADJ
ejpam-110	227	6	-	-	ADJ
ejpam-110	227	7	topological	topological	ADJ
ejpam-110	227	8	space	space	NOUN
ejpam-110	227	9	∏	∏	PROPN
ejpam-110	227	10	λ∈j	λ∈j	ADV
ejpam-110	227	11	xλ	xλ	PROPN
ejpam-110	227	12	is	be	AUX
ejpam-110	227	13	locally	locally	ADV
ejpam-110	227	14	compact	compact	ADJ
ejpam-110	227	15	if	if	SCONJ
ejpam-110	228	1	and	and	CCONJ
ejpam-110	228	2	only	only	ADV
ejpam-110	228	3	if	if	SCONJ
ejpam-110	228	4	each	each	DET
ejpam-110	228	5	xλ	xλ	PROPN
ejpam-110	228	6	is	be	AUX
ejpam-110	228	7	locally	locally	ADV
ejpam-110	228	8	compact	compact	ADJ
ejpam-110	228	9	and	and	CCONJ
ejpam-110	228	10	all	all	PRON
ejpam-110	228	11	but	but	ADV
ejpam-110	228	12	finitely	finitely	ADV
ejpam-110	228	13	many	many	ADJ
ejpam-110	228	14	xλ	xλ	NOUN
ejpam-110	228	15	are	be	AUX
ejpam-110	228	16	compact	compact	ADJ
ejpam-110	228	17	.	.	PUNCT
ejpam-110	229	1	proof	proof	NOUN
ejpam-110	229	2	.	.	PUNCT
ejpam-110	230	1	necessity	necessity	NOUN
ejpam-110	230	2	:	:	PUNCT
ejpam-110	230	3	since	since	SCONJ
ejpam-110	230	4	the	the	DET
ejpam-110	230	5	λth	λth	PROPN
ejpam-110	230	6	projection	projection	NOUN
ejpam-110	230	7	,	,	PUNCT
ejpam-110	230	8	πλ	πλ	X
ejpam-110	230	9	:	:	PUNCT
ejpam-110	230	10	∏	∏	NUM
ejpam-110	230	11	λ∈j	λ∈j	NOUN
ejpam-110	230	12	xλ	xλ	PROPN
ejpam-110	230	13	→	→	SYM
ejpam-110	230	14	xλ	xλ	NOUN
ejpam-110	230	15	,	,	PUNCT
ejpam-110	230	16	is	be	AUX
ejpam-110	230	17	a	a	DET
ejpam-110	230	18	continuous	continuous	ADJ
ejpam-110	230	19	open	open	ADJ
ejpam-110	230	20	surjection	surjection	NOUN
ejpam-110	230	21	and	and	CCONJ
ejpam-110	230	22	∏	∏	PROPN
ejpam-110	230	23	λ∈j	λ∈j	X
ejpam-110	230	24	xλ	xλ	PROPN
ejpam-110	230	25	is	be	AUX
ejpam-110	230	26	locally	locally	ADV
ejpam-110	230	27	compact	compact	ADJ
ejpam-110	230	28	,	,	PUNCT
ejpam-110	230	29	by	by	ADP
ejpam-110	230	30	theorem	theorem	NOUN
ejpam-110	230	31	4.1	4.1	NUM
ejpam-110	230	32	,	,	PUNCT
ejpam-110	230	33	xλ	xλ	PROPN
ejpam-110	230	34	is	be	AUX
ejpam-110	230	35	locally	locally	ADV
ejpam-110	230	36	compact	compact	ADJ
ejpam-110	230	37	for	for	ADP
ejpam-110	230	38	each	each	DET
ejpam-110	230	39	λ	λ	PROPN
ejpam-110	230	40	∈	∈	PROPN
ejpam-110	230	41	j	j	PROPN
ejpam-110	230	42	.	.	PUNCT
ejpam-110	231	1	now	now	ADV
ejpam-110	231	2	,	,	PUNCT
ejpam-110	231	3	let	let	VERB
ejpam-110	231	4	p	p	PRON
ejpam-110	231	5	∈	∈	PROPN
ejpam-110	231	6	pr(l	pr(l	NOUN
ejpam-110	231	7	)	)	PUNCT
ejpam-110	231	8	,	,	PUNCT
ejpam-110	231	9	x	x	PUNCT
ejpam-110	231	10	∈	∈	NOUN
ejpam-110	231	11	∏	∏	X
ejpam-110	231	12	λ∈j	λ∈j	X
ejpam-110	231	13	xλ	xλ	PROPN
ejpam-110	231	14	and	and	CCONJ
ejpam-110	231	15	let	let	VERB
ejpam-110	231	16	f	f	PRON
ejpam-110	231	17	be	be	AUX
ejpam-110	231	18	an	an	DET
ejpam-110	231	19	open	open	ADJ
ejpam-110	231	20	l	l	NOUN
ejpam-110	231	21	-	-	NOUN
ejpam-110	231	22	set	set	VERB
ejpam-110	231	23	in	in	ADP
ejpam-110	231	24	∏	∏	PROPN
ejpam-110	231	25	λ∈j	λ∈j	X
ejpam-110	231	26	xλ	xλ	NOUN
ejpam-110	231	27	with	with	ADP
ejpam-110	231	28	f	f	PROPN
ejpam-110	231	29	(	(	PUNCT
ejpam-110	231	30	x	x	NOUN
ejpam-110	231	31	)	)	PUNCT
ejpam-110	231	32	�	�	PROPN
ejpam-110	231	33	p.	p.	NOUN
ejpam-110	231	34	then	then	ADV
ejpam-110	231	35	by	by	ADP
ejpam-110	231	36	the	the	DET
ejpam-110	231	37	local	local	ADJ
ejpam-110	231	38	compactness	compactness	NOUN
ejpam-110	231	39	of	of	ADP
ejpam-110	231	40	∏	∏	PROPN
ejpam-110	231	41	λ∈j	λ∈j	X
ejpam-110	231	42	xλ	xλ	NOUN
ejpam-110	231	43	,	,	PUNCT
ejpam-110	231	44	there	there	PRON
ejpam-110	231	45	are	be	VERB
ejpam-110	231	46	an	an	DET
ejpam-110	231	47	open	open	ADJ
ejpam-110	231	48	l	l	NOUN
ejpam-110	231	49	-	-	ADJ
ejpam-110	231	50	set	set	VERB
ejpam-110	231	51	g	g	NOUN
ejpam-110	231	52	in	in	ADP
ejpam-110	231	53	∏	∏	PROPN
ejpam-110	231	54	λ∈j	λ∈j	X
ejpam-110	231	55	xλ	xλ	NOUN
ejpam-110	231	56	with	with	ADP
ejpam-110	231	57	g(x	g(x	NOUN
ejpam-110	231	58	)	)	PUNCT
ejpam-110	231	59	�	�	PROPN
ejpam-110	231	60	p	p	PROPN
ejpam-110	231	61	and	and	CCONJ
ejpam-110	231	62	an	an	DET
ejpam-110	231	63	l	l	NOUN
ejpam-110	231	64	-	-	ADJ
ejpam-110	231	65	set	set	ADJ
ejpam-110	231	66	k	k	PROPN
ejpam-110	231	67	in	in	ADP
ejpam-110	231	68	∏	∏	PROPN
ejpam-110	231	69	λ∈j	λ∈j	X
ejpam-110	231	70	xλ	xλ	NOUN
ejpam-110	231	71	with	with	ADP
ejpam-110	231	72	χsupp(k	χsupp(k	PROPN
ejpam-110	231	73	)	)	PUNCT
ejpam-110	231	74	compact	compact	ADJ
ejpam-110	231	75	such	such	ADJ
ejpam-110	231	76	that	that	SCONJ
ejpam-110	231	77	g	g	PROPN
ejpam-110	232	1	≤	≤	NOUN
ejpam-110	232	2	k	k	NOUN
ejpam-110	232	3	≤	≤	PROPN
ejpam-110	232	4	f	f	X
ejpam-110	232	5	.	.	PUNCT
ejpam-110	233	1	let	let	VERB
ejpam-110	233	2	∧m	∧m	PROPN
ejpam-110	233	3	i=1π	i=1π	ADV
ejpam-110	233	4	−1	−1	NOUN
ejpam-110	233	5	λi	λi	PROPN
ejpam-110	233	6	(	(	PUNCT
ejpam-110	233	7	gλi	gλi	NOUN
ejpam-110	233	8	)	)	PUNCT
ejpam-110	233	9	be	be	AUX
ejpam-110	233	10	a	a	DET
ejpam-110	233	11	basic	basic	ADJ
ejpam-110	233	12	open	open	ADJ
ejpam-110	233	13	l	l	NOUN
ejpam-110	233	14	-	-	NOUN
ejpam-110	233	15	set	set	VERB
ejpam-110	233	16	such	such	ADJ
ejpam-110	233	17	that	that	SCONJ
ejpam-110	233	18	∧m	∧m	PROPN
ejpam-110	233	19	i=1π	i=1π	ADV
ejpam-110	233	20	−1	−1	NOUN
ejpam-110	233	21	λi	λi	NOUN
ejpam-110	233	22	(	(	PUNCT
ejpam-110	233	23	gλi	gλi	NOUN
ejpam-110	233	24	)	)	PUNCT
ejpam-110	233	25	≤	≤	NOUN
ejpam-110	233	26	g	g	ADP
ejpam-110	234	1	≤	≤	NUM
ejpam-110	234	2	k	k	NOUN
ejpam-110	234	3	≤	≤	PROPN
ejpam-110	234	4	f	f	PROPN
ejpam-110	234	5	.	.	PUNCT
ejpam-110	235	1	then	then	ADV
ejpam-110	235	2	χsupp(k	χsupp(k	PROPN
ejpam-110	235	3	)	)	PUNCT
ejpam-110	235	4	≥	≥	NOUN
ejpam-110	236	1	χsupp(∧m	χsupp(∧m	PROPN
ejpam-110	236	2	i=1	i=1	PROPN
ejpam-110	236	3	π−1	π−1	PROPN
ejpam-110	236	4	λi	λi	ADP
ejpam-110	236	5	(	(	PUNCT
ejpam-110	236	6	gλi	gλi	NOUN
ejpam-110	236	7	)	)	PUNCT
ejpam-110	236	8	)	)	PUNCT
ejpam-110	237	1	=	=	PUNCT
ejpam-110	238	1	χ∩m	χ∩m	PROPN
ejpam-110	238	2	i=1	i=1	PROPN
ejpam-110	238	3	supp(π−1	supp(π−1	PROPN
ejpam-110	238	4	λi	λi	ADP
ejpam-110	238	5	(	(	PUNCT
ejpam-110	238	6	gλi	gλi	NOUN
ejpam-110	238	7	)	)	PUNCT
ejpam-110	238	8	)	)	PUNCT
ejpam-110	239	1	=	=	PUNCT
ejpam-110	239	2	∧	∧	NOUN
ejpam-110	239	3	m	m	NOUN
ejpam-110	239	4	i=1χsupp(π−1	i=1χsupp(π−1	PROPN
ejpam-110	239	5	λi	λi	NOUN
ejpam-110	239	6	(	(	PUNCT
ejpam-110	239	7	gλi	gλi	NOUN
ejpam-110	239	8	)	)	PUNCT
ejpam-110	239	9	)	)	PUNCT
ejpam-110	240	1	=	=	SYM
ejpam-110	240	2	∧m	∧m	ADJ
ejpam-110	240	3	i=1π	i=1π	ADV
ejpam-110	240	4	−1	−1	NOUN
ejpam-110	240	5	λi	λi	INTJ
ejpam-110	240	6	(	(	PUNCT
ejpam-110	240	7	χsupp(gλi	χsupp(gλi	PROPN
ejpam-110	240	8	)	)	PUNCT
ejpam-110	240	9	)	)	PUNCT
ejpam-110	240	10	thus	thus	ADV
ejpam-110	240	11	πλ(supp(k	πλ(supp(k	NOUN
ejpam-110	240	12	)	)	PUNCT
ejpam-110	240	13	)	)	PUNCT
ejpam-110	240	14	≥	≥	NOUN
ejpam-110	241	1	πλ(∧	πλ(∧	VERB
ejpam-110	241	2	m	m	VERB
ejpam-110	241	3	i=1	i=1	PROPN
ejpam-110	241	4	π−1	π−1	PROPN
ejpam-110	241	5	λi	λi	ADP
ejpam-110	241	6	(	(	PUNCT
ejpam-110	241	7	χsupp(gλi	χsupp(gλi	PROPN
ejpam-110	241	8	)	)	PUNCT
ejpam-110	241	9	)	)	PUNCT
ejpam-110	241	10	)	)	PUNCT
ejpam-110	242	1	=	=	PUNCT
ejpam-110	242	2	xλ	xλ	NOUN
ejpam-110	242	3	for	for	ADP
ejpam-110	242	4	all	all	DET
ejpam-110	242	5	λ	λ	PROPN
ejpam-110	242	6	/∈	/∈	PROPN
ejpam-110	242	7	�	�	PROPN
ejpam-110	242	8	λ1	λ1	PROPN
ejpam-110	242	9	,	,	PUNCT
ejpam-110	242	10	·	·	PUNCT
ejpam-110	242	11	·	·	PUNCT
ejpam-110	242	12	·	·	PUNCT
ejpam-110	242	13	,	,	PUNCT
ejpam-110	242	14	λm	λm	X
ejpam-110	242	15	.	.	PUNCT
ejpam-110	243	1	since	since	SCONJ
ejpam-110	243	2	πλ	πλ	PROPN
ejpam-110	243	3	is	be	AUX
ejpam-110	243	4	continuous	continuous	ADJ
ejpam-110	243	5	,	,	PUNCT
ejpam-110	243	6	χsupp(k	χsupp(k	PROPN
ejpam-110	243	7	)	)	PUNCT
ejpam-110	243	8	is	be	AUX
ejpam-110	243	9	compact	compact	ADJ
ejpam-110	243	10	in	in	ADP
ejpam-110	243	11	∏	∏	PROPN
ejpam-110	243	12	λ∈j	λ∈j	NOUN
ejpam-110	243	13	xλ	xλ	PROPN
ejpam-110	243	14	and	and	CCONJ
ejpam-110	243	15	πλ(χsupp(k	πλ(χsupp(k	PROPN
ejpam-110	243	16	)	)	PUNCT
ejpam-110	243	17	)	)	PUNCT
ejpam-110	244	1	=	=	SYM
ejpam-110	244	2	xλ	xλ	NOUN
ejpam-110	244	3	,	,	PUNCT
ejpam-110	244	4	we	we	PRON
ejpam-110	244	5	have	have	VERB
ejpam-110	244	6	by	by	ADP
ejpam-110	244	7	proposition	proposition	NOUN
ejpam-110	244	8	2.3	2.3	NUM
ejpam-110	244	9	that	that	PRON
ejpam-110	244	10	xλ	xλ	PROPN
ejpam-110	244	11	is	be	AUX
ejpam-110	244	12	compact	compact	ADJ
ejpam-110	244	13	for	for	ADP
ejpam-110	244	14	each	each	DET
ejpam-110	244	15	λ	λ	NOUN
ejpam-110	244	16	except	except	SCONJ
ejpam-110	244	17	possibly	possibly	ADV
ejpam-110	244	18	λ	λ	PROPN
ejpam-110	244	19	∈	∈	PROPN
ejpam-110	244	20	�	�	PROPN
ejpam-110	244	21	λ1	λ1	PROPN
ejpam-110	244	22	,	,	PUNCT
ejpam-110	244	23	·	·	PUNCT
ejpam-110	244	24	·	·	PUNCT
ejpam-110	244	25	·	·	PUNCT
ejpam-110	244	26	,	,	PUNCT
ejpam-110	244	27	λm	λm	X
ejpam-110	244	28	.	.	PUNCT
ejpam-110	245	1	sufficiency	sufficiency	NOUN
ejpam-110	245	2	:	:	PUNCT
ejpam-110	245	3	let	let	VERB
ejpam-110	245	4	p	p	X
ejpam-110	245	5	∈	∈	PROPN
ejpam-110	245	6	pr(l	pr(l	NOUN
ejpam-110	245	7	)	)	PUNCT
ejpam-110	245	8	,	,	PUNCT
ejpam-110	245	9	x	x	PUNCT
ejpam-110	245	10	∈	∈	NOUN
ejpam-110	245	11	∏	∏	X
ejpam-110	245	12	λ∈j	λ∈j	X
ejpam-110	245	13	xλ	xλ	PROPN
ejpam-110	245	14	and	and	CCONJ
ejpam-110	245	15	f	f	PROPN
ejpam-110	245	16	∧m	∧m	PROPN
ejpam-110	246	1	λ=1	λ=1	PUNCT
ejpam-110	246	2	π−1	π−1	PROPN
ejpam-110	246	3	λi	λi	ADP
ejpam-110	246	4	(	(	PUNCT
ejpam-110	246	5	fλi	fλi	PROPN
ejpam-110	246	6	)	)	PUNCT
ejpam-110	246	7	be	be	AUX
ejpam-110	246	8	a	a	DET
ejpam-110	246	9	basic	basic	ADJ
ejpam-110	246	10	open	open	ADJ
ejpam-110	246	11	l	l	NOUN
ejpam-110	246	12	-	-	NOUN
ejpam-110	246	13	set	set	VERB
ejpam-110	246	14	in	in	ADP
ejpam-110	246	15	the	the	DET
ejpam-110	246	16	product	product	NOUN
ejpam-110	246	17	l	l	ADJ
ejpam-110	246	18	-	-	ADJ
ejpam-110	246	19	topological	topological	ADJ
ejpam-110	246	20	space	space	NOUN
ejpam-110	246	21	∏	∏	PROPN
ejpam-110	246	22	λ∈j	λ∈j	ADV
ejpam-110	246	23	xλ	xλ	ADP
ejpam-110	246	24	such	such	ADJ
ejpam-110	246	25	that	that	SCONJ
ejpam-110	246	26	f	f	PROPN
ejpam-110	246	27	(	(	PUNCT
ejpam-110	246	28	x	x	X
ejpam-110	246	29	)	)	PUNCT
ejpam-110	246	30	�	�	PROPN
ejpam-110	246	31	p	p	NOUN
ejpam-110	246	32	where	where	SCONJ
ejpam-110	246	33	fλi	fλi	NOUN
ejpam-110	246	34	is	be	AUX
ejpam-110	246	35	an	an	DET
ejpam-110	246	36	open	open	ADJ
ejpam-110	246	37	l	l	NOUN
ejpam-110	246	38	-	-	NOUN
ejpam-110	246	39	set	set	NOUN
ejpam-110	246	40	in	in	ADP
ejpam-110	246	41	xλi	xλi	PROPN
ejpam-110	246	42	.	.	PUNCT
ejpam-110	247	1	we	we	PRON
ejpam-110	247	2	assume	assume	VERB
ejpam-110	247	3	that	that	SCONJ
ejpam-110	247	4	�	�	PROPN
ejpam-110	247	5	λ1	λ1	PROPN
ejpam-110	247	6	,	,	PUNCT
ejpam-110	247	7	·	·	PUNCT
ejpam-110	247	8	·	·	PUNCT
ejpam-110	247	9	·	·	PUNCT
ejpam-110	247	10	,	,	PUNCT
ejpam-110	247	11	λm	λm	ADP
ejpam-110	247	12	is	be	AUX
ejpam-110	247	13	expanded	expand	VERB
ejpam-110	247	14	to	to	PART
ejpam-110	247	15	include	include	VERB
ejpam-110	247	16	all	all	DET
ejpam-110	247	17	λ	λ	PROPN
ejpam-110	247	18	for	for	ADP
ejpam-110	247	19	which	which	PRON
ejpam-110	247	20	xλ	xλ	PROPN
ejpam-110	247	21	is	be	AUX
ejpam-110	247	22	not	not	PART
ejpam-110	247	23	compact	compact	ADJ
ejpam-110	247	24	.	.	PUNCT
ejpam-110	248	1	we	we	PRON
ejpam-110	248	2	have	have	VERB
ejpam-110	248	3	that	that	DET
ejpam-110	248	4	f	f	PROPN
ejpam-110	248	5	(	(	PUNCT
ejpam-110	248	6	x	x	X
ejpam-110	248	7	)	)	PUNCT
ejpam-110	248	8	�	�	PROPN
ejpam-110	248	9	p	p	PROPN
ejpam-110	248	10	implies	imply	VERB
ejpam-110	248	11	fλi	fλi	PROPN
ejpam-110	249	1	(	(	PUNCT
ejpam-110	249	2	xλi	xλi	PROPN
ejpam-110	249	3	)	)	PUNCT
ejpam-110	249	4	�	�	PROPN
ejpam-110	249	5	p	p	PROPN
ejpam-110	249	6	for	for	ADP
ejpam-110	249	7	all	all	PRON
ejpam-110	249	8	i	i	PRON
ejpam-110	249	9	∈	∈	PROPN
ejpam-110	249	10	{	{	PUNCT
ejpam-110	249	11	1	1	NUM
ejpam-110	249	12	,	,	PUNCT
ejpam-110	249	13	·	·	PUNCT
ejpam-110	249	14	·	·	PUNCT
ejpam-110	249	15	·	·	PUNCT
ejpam-110	249	16	,	,	PUNCT
ejpam-110	249	17	m	m	PROPN
ejpam-110	249	18	}	}	PUNCT
ejpam-110	249	19	.	.	PUNCT
ejpam-110	250	1	from	from	ADP
ejpam-110	250	2	the	the	DET
ejpam-110	250	3	local	local	ADJ
ejpam-110	250	4	compactness	compactness	NOUN
ejpam-110	250	5	of	of	ADP
ejpam-110	250	6	each	each	DET
ejpam-110	250	7	xλi	xλi	PROPN
ejpam-110	250	8	,	,	PUNCT
ejpam-110	250	9	there	there	PRON
ejpam-110	250	10	are	be	VERB
ejpam-110	250	11	an	an	DET
ejpam-110	250	12	open	open	ADJ
ejpam-110	250	13	l	l	NOUN
ejpam-110	250	14	-	-	ADJ
ejpam-110	250	15	set	set	VERB
ejpam-110	250	16	gλi	gλi	NOUN
ejpam-110	250	17	in	in	ADP
ejpam-110	250	18	xλi	xλi	PROPN
ejpam-110	250	19	and	and	CCONJ
ejpam-110	250	20	an	an	DET
ejpam-110	250	21	l	l	NOUN
ejpam-110	250	22	-	-	ADJ
ejpam-110	250	23	set	set	VERB
ejpam-110	250	24	kλi	kλi	NOUN
ejpam-110	250	25	in	in	ADP
ejpam-110	250	26	xλi	xλi	PROPN
ejpam-110	250	27	,	,	PUNCT
ejpam-110	250	28	with	with	ADP
ejpam-110	250	29	χsupp(kλi	χsupp(kλi	NOUN
ejpam-110	250	30	)	)	PUNCT
ejpam-110	250	31	compact	compact	ADJ
ejpam-110	250	32	,	,	PUNCT
ejpam-110	250	33	such	such	ADJ
ejpam-110	250	34	that	that	DET
ejpam-110	250	35	gλi	gλi	NOUN
ejpam-110	250	36	(	(	PUNCT
ejpam-110	250	37	xλi	xλi	PROPN
ejpam-110	250	38	)	)	PUNCT
ejpam-110	250	39	�	�	PROPN
ejpam-110	250	40	p	p	NOUN
ejpam-110	250	41	and	and	CCONJ
ejpam-110	250	42	gλi	gλi	VERB
ejpam-110	250	43	≤	≤	NUM
ejpam-110	250	44	kλi	kλi	PROPN
ejpam-110	250	45	≤	≤	ADJ
ejpam-110	250	46	fλi	fλi	NOUN
ejpam-110	250	47	.	.	PUNCT
ejpam-110	251	1	t.	t.	PROPN
ejpam-110	251	2	breuckmann	breuckmann	PROPN
ejpam-110	251	3	,	,	PUNCT
ejpam-110	251	4	s.	s.	PROPN
ejpam-110	251	5	kudri	kudri	PROPN
ejpam-110	251	6	,	,	PUNCT
ejpam-110	251	7	and	and	CCONJ
ejpam-110	251	8	h.	h.	PROPN
ejpam-110	251	9	aygün	aygün	PROPN
ejpam-110	251	10	/	/	SYM
ejpam-110	251	11	eur	eur	PROPN
ejpam-110	251	12	.	.	PUNCT
ejpam-110	252	1	j.	j.	PROPN
ejpam-110	252	2	pure	pure	PROPN
ejpam-110	252	3	appl	appl	PROPN
ejpam-110	252	4	.	.	PROPN
ejpam-110	252	5	math	math	PROPN
ejpam-110	252	6	,	,	PUNCT
ejpam-110	252	7	2	2	NUM
ejpam-110	252	8	(	(	PUNCT
ejpam-110	252	9	2009	2009	NUM
ejpam-110	252	10	)	)	PUNCT
ejpam-110	252	11	,	,	PUNCT
ejpam-110	252	12	(	(	PUNCT
ejpam-110	252	13	147	147	NUM
ejpam-110	252	14	-	-	SYM
ejpam-110	252	15	161	161	NUM
ejpam-110	252	16	)	)	PUNCT
ejpam-110	252	17	156	156	NUM
ejpam-110	252	18	let	let	VERB
ejpam-110	252	19	g	g	NOUN
ejpam-110	252	20	=	=	PUNCT
ejpam-110	252	21	∧m	∧m	PROPN
ejpam-110	252	22	i=1	i=1	PROPN
ejpam-110	252	23	π−1	π−1	PROPN
ejpam-110	252	24	λi	λi	ADP
ejpam-110	252	25	(	(	PUNCT
ejpam-110	252	26	gλi	gλi	NOUN
ejpam-110	252	27	)	)	PUNCT
ejpam-110	252	28	and	and	CCONJ
ejpam-110	252	29	k	k	X
ejpam-110	252	30	=	=	PUNCT
ejpam-110	252	31	∧m	∧m	PROPN
ejpam-110	252	32	i=1	i=1	PROPN
ejpam-110	253	1	π−1	π−1	PROPN
ejpam-110	253	2	λi	λi	ADP
ejpam-110	253	3	(	(	PUNCT
ejpam-110	253	4	kλi	kλi	NOUN
ejpam-110	253	5	)	)	PUNCT
ejpam-110	253	6	,	,	PUNCT
ejpam-110	253	7	then	then	ADV
ejpam-110	253	8	,	,	PUNCT
ejpam-110	253	9	g	g	PROPN
ejpam-110	253	10	is	be	AUX
ejpam-110	253	11	an	an	DET
ejpam-110	253	12	open	open	ADJ
ejpam-110	253	13	l	l	NOUN
ejpam-110	253	14	-	-	NOUN
ejpam-110	253	15	set	set	VERB
ejpam-110	253	16	in	in	ADP
ejpam-110	253	17	∏	∏	PROPN
ejpam-110	253	18	λ∈j	λ∈j	X
ejpam-110	253	19	xλ	xλ	NOUN
ejpam-110	253	20	,	,	PUNCT
ejpam-110	253	21	g	g	PROPN
ejpam-110	253	22	≤	≤	NOUN
ejpam-110	253	23	k	k	NOUN
ejpam-110	253	24	≤	≤	PROPN
ejpam-110	253	25	f	f	PROPN
ejpam-110	253	26	and	and	CCONJ
ejpam-110	253	27	g(x	g(x	NOUN
ejpam-110	253	28	)	)	PUNCT
ejpam-110	254	1	=	=	SYM
ejpam-110	254	2	∧m	∧m	ADJ
ejpam-110	254	3	i=1π	i=1π	ADV
ejpam-110	254	4	−1	−1	NOUN
ejpam-110	254	5	λi	λi	NOUN
ejpam-110	254	6	(	(	PUNCT
ejpam-110	254	7	gλi	gλi	NOUN
ejpam-110	254	8	)	)	PUNCT
ejpam-110	254	9	(	(	PUNCT
ejpam-110	254	10	x	x	X
ejpam-110	254	11	)	)	PUNCT
ejpam-110	254	12	=	=	SYM
ejpam-110	254	13	∧m	∧m	PROPN
ejpam-110	254	14	i=1	i=1	PROPN
ejpam-110	254	15	gλi	gλi	PROPN
ejpam-110	254	16	(	(	PUNCT
ejpam-110	254	17	xλi	xλi	PROPN
ejpam-110	254	18	)	)	PUNCT
ejpam-110	254	19	�	�	PROPN
ejpam-110	255	1	p	p	X
ejpam-110	255	2	we	we	PRON
ejpam-110	255	3	also	also	ADV
ejpam-110	255	4	have	have	VERB
ejpam-110	255	5	χsupp(k	χsupp(k	NOUN
ejpam-110	255	6	)	)	PUNCT
ejpam-110	255	7	=	=	PUNCT
ejpam-110	256	1	χsupp(∧m	χsupp(∧m	PROPN
ejpam-110	256	2	i=1	i=1	X
ejpam-110	256	3	π−1	π−1	PROPN
ejpam-110	256	4	λi	λi	NOUN
ejpam-110	256	5	(	(	PUNCT
ejpam-110	256	6	kλi	kλi	NOUN
ejpam-110	256	7	)	)	PUNCT
ejpam-110	256	8	)	)	PUNCT
ejpam-110	257	1	=	=	PUNCT
ejpam-110	257	2	∧	∧	NOUN
ejpam-110	257	3	m	m	VERB
ejpam-110	257	4	i=1π	i=1π	ADJ
ejpam-110	257	5	−1	−1	ADV
ejpam-110	257	6	λi	λi	INTJ
ejpam-110	257	7	(	(	PUNCT
ejpam-110	257	8	χsupp(kλi	χsupp(kλi	NOUN
ejpam-110	257	9	)	)	PUNCT
ejpam-110	257	10	)	)	PUNCT
ejpam-110	258	1	=	=	PUNCT
ejpam-110	258	2	∧λ∈j	∧λ∈j	PROPN
ejpam-110	258	3	wλ	wλ	VERB
ejpam-110	258	4	where	where	SCONJ
ejpam-110	258	5	wλi	wλi	NOUN
ejpam-110	258	6	=	=	SYM
ejpam-110	258	7	π−1	π−1	PROPN
ejpam-110	258	8	λi	λi	ADP
ejpam-110	258	9	(	(	PUNCT
ejpam-110	258	10	χsupp(kλi	χsupp(kλi	NOUN
ejpam-110	258	11	)	)	PUNCT
ejpam-110	258	12	)	)	PUNCT
ejpam-110	258	13	for	for	ADP
ejpam-110	258	14	i	i	PROPN
ejpam-110	258	15	∈	∈	PROPN
ejpam-110	258	16	{	{	PUNCT
ejpam-110	258	17	1	1	NUM
ejpam-110	258	18	,	,	PUNCT
ejpam-110	258	19	·	·	PUNCT
ejpam-110	258	20	·	·	PUNCT
ejpam-110	258	21	·	·	PUNCT
ejpam-110	258	22	,	,	PUNCT
ejpam-110	258	23	m	m	VERB
ejpam-110	258	24	}	}	PUNCT
ejpam-110	258	25	and	and	CCONJ
ejpam-110	258	26	wλ	wλ	NOUN
ejpam-110	258	27	=	=	NOUN
ejpam-110	258	28	xλ	xλ	PROPN
ejpam-110	258	29	for	for	ADP
ejpam-110	258	30	λ	λ	PROPN
ejpam-110	258	31	/∈	/∈	PUNCT
ejpam-110	258	32	{	{	PUNCT
ejpam-110	258	33	1	1	NUM
ejpam-110	258	34	,	,	PUNCT
ejpam-110	258	35	·	·	PUNCT
ejpam-110	258	36	·	·	PUNCT
ejpam-110	258	37	·	·	PUNCT
ejpam-110	258	38	,	,	PUNCT
ejpam-110	258	39	m	m	NOUN
ejpam-110	258	40	}	}	PUNCT
ejpam-110	258	41	.	.	PUNCT
ejpam-110	259	1	then	then	ADV
ejpam-110	259	2	χsupp(k	χsupp(k	PROPN
ejpam-110	259	3	)	)	PUNCT
ejpam-110	259	4	is	be	AUX
ejpam-110	259	5	a	a	DET
ejpam-110	259	6	compact	compact	ADJ
ejpam-110	259	7	l	l	NOUN
ejpam-110	259	8	-	-	NOUN
ejpam-110	259	9	set	set	VERB
ejpam-110	259	10	in	in	ADP
ejpam-110	259	11	∏	∏	NUM
ejpam-110	259	12	λßj	λßj	NOUN
ejpam-110	259	13	xλ	xλ	NOUN
ejpam-110	259	14	by	by	ADP
ejpam-110	259	15	proposition	proposition	NOUN
ejpam-110	259	16	2.4	2.4	NUM
ejpam-110	259	17	since	since	SCONJ
ejpam-110	259	18	χsupp(kλi	χsupp(kλi	NOUN
ejpam-110	259	19	)	)	PUNCT
ejpam-110	259	20	is	be	AUX
ejpam-110	259	21	compact	compact	ADJ
ejpam-110	259	22	for	for	ADP
ejpam-110	259	23	each	each	DET
ejpam-110	259	24	i	i	PRON
ejpam-110	259	25	∈	∈	PROPN
ejpam-110	259	26	{	{	PUNCT
ejpam-110	259	27	1	1	NUM
ejpam-110	259	28	,	,	PUNCT
ejpam-110	259	29	·	·	PUNCT
ejpam-110	259	30	·	·	PUNCT
ejpam-110	259	31	·	·	PUNCT
ejpam-110	259	32	,	,	PUNCT
ejpam-110	259	33	m	m	VERB
ejpam-110	259	34	}	}	PUNCT
ejpam-110	259	35	and	and	CCONJ
ejpam-110	259	36	xλ	xλ	PROPN
ejpam-110	259	37	is	be	AUX
ejpam-110	259	38	compact	compact	ADJ
ejpam-110	259	39	for	for	ADP
ejpam-110	259	40	each	each	DET
ejpam-110	259	41	λ	λ	PROPN
ejpam-110	259	42	/∈	/∈	PUNCT
ejpam-110	259	43	{	{	PUNCT
ejpam-110	259	44	1	1	NUM
ejpam-110	259	45	,	,	PUNCT
ejpam-110	259	46	·	·	PUNCT
ejpam-110	259	47	·	·	PUNCT
ejpam-110	259	48	·	·	PUNCT
ejpam-110	259	49	,	,	PUNCT
ejpam-110	259	50	m	m	VERB
ejpam-110	259	51	}	}	PUNCT
ejpam-110	259	52	.	.	PUNCT
ejpam-110	260	1	theorem	theorem	VERB
ejpam-110	260	2	4.10	4.10	NUM
ejpam-110	260	3	.	.	PUNCT
ejpam-110	261	1	let	let	VERB
ejpam-110	261	2	�	�	PROPN
ejpam-110	261	3	xλ	xλ	PROPN
ejpam-110	261	4	λ∈j	λ∈j	PROPN
ejpam-110	261	5	be	be	AUX
ejpam-110	261	6	a	a	DET
ejpam-110	261	7	family	family	NOUN
ejpam-110	261	8	of	of	ADP
ejpam-110	261	9	nonempty	nonempty	ADV
ejpam-110	261	10	fully	fully	ADV
ejpam-110	261	11	stratified	stratify	VERB
ejpam-110	261	12	l	l	ADJ
ejpam-110	261	13	-	-	ADJ
ejpam-110	261	14	topological	topological	ADJ
ejpam-110	261	15	spaces	space	NOUN
ejpam-110	261	16	.	.	PUNCT
ejpam-110	262	1	then	then	ADV
ejpam-110	262	2	:	:	PUNCT
ejpam-110	262	3	the	the	DET
ejpam-110	262	4	product	product	NOUN
ejpam-110	262	5	l	l	ADJ
ejpam-110	262	6	-	-	ADJ
ejpam-110	262	7	topological	topological	ADJ
ejpam-110	262	8	space	space	NOUN
ejpam-110	262	9	∏	∏	PROPN
ejpam-110	262	10	λ∈j	λ∈j	ADV
ejpam-110	262	11	xλ	xλ	PROPN
ejpam-110	262	12	is	be	AUX
ejpam-110	262	13	weakly	weakly	ADV
ejpam-110	262	14	locally	locally	ADV
ejpam-110	262	15	compact	compact	ADJ
ejpam-110	262	16	if	if	SCONJ
ejpam-110	263	1	and	and	CCONJ
ejpam-110	263	2	only	only	ADV
ejpam-110	263	3	if	if	SCONJ
ejpam-110	263	4	each	each	DET
ejpam-110	263	5	xλ	xλ	NOUN
ejpam-110	263	6	is	be	AUX
ejpam-110	263	7	weakly	weakly	ADV
ejpam-110	263	8	locally	locally	ADV
ejpam-110	263	9	compact	compact	ADJ
ejpam-110	263	10	and	and	CCONJ
ejpam-110	263	11	all	all	PRON
ejpam-110	263	12	but	but	ADV
ejpam-110	263	13	finitely	finitely	ADV
ejpam-110	263	14	many	many	ADJ
ejpam-110	263	15	xλ	xλ	NOUN
ejpam-110	263	16	are	be	AUX
ejpam-110	263	17	compact	compact	ADJ
ejpam-110	263	18	.	.	PUNCT
ejpam-110	264	1	proof	proof	NOUN
ejpam-110	264	2	.	.	PUNCT
ejpam-110	265	1	the	the	DET
ejpam-110	265	2	proof	proof	NOUN
ejpam-110	265	3	is	be	AUX
ejpam-110	265	4	analogous	analogous	ADJ
ejpam-110	265	5	to	to	ADP
ejpam-110	265	6	the	the	DET
ejpam-110	265	7	theorem	theorem	ADJ
ejpam-110	265	8	4.9	4.9	NUM
ejpam-110	265	9	,	,	PUNCT
ejpam-110	265	10	so	so	SCONJ
ejpam-110	265	11	we	we	PRON
ejpam-110	265	12	just	just	ADV
ejpam-110	265	13	give	give	VERB
ejpam-110	265	14	the	the	DET
ejpam-110	265	15	outline	outline	NOUN
ejpam-110	265	16	for	for	ADP
ejpam-110	265	17	the	the	DET
ejpam-110	265	18	proof	proof	NOUN
ejpam-110	265	19	.	.	PUNCT
ejpam-110	266	1	necessity	necessity	NOUN
ejpam-110	266	2	:	:	PUNCT
ejpam-110	266	3	the	the	DET
ejpam-110	266	4	weak	weak	ADJ
ejpam-110	266	5	local	local	ADJ
ejpam-110	266	6	compactness	compactness	NOUN
ejpam-110	266	7	of	of	ADP
ejpam-110	266	8	x	x	PUNCT
ejpam-110	266	9	j	j	PROPN
ejpam-110	266	10	is	be	AUX
ejpam-110	266	11	by	by	ADP
ejpam-110	266	12	theorem	theorem	NOUN
ejpam-110	266	13	4.2	4.2	NUM
ejpam-110	266	14	.	.	PUNCT
ejpam-110	267	1	for	for	ADP
ejpam-110	267	2	the	the	DET
ejpam-110	267	3	rest	rest	NOUN
ejpam-110	267	4	,	,	PUNCT
ejpam-110	267	5	use	use	VERB
ejpam-110	267	6	the	the	DET
ejpam-110	267	7	weak	weak	ADJ
ejpam-110	267	8	local	local	ADJ
ejpam-110	267	9	compactness	compactness	NOUN
ejpam-110	267	10	to	to	PART
ejpam-110	267	11	obtain	obtain	VERB
ejpam-110	267	12	an	an	DET
ejpam-110	267	13	open	open	ADJ
ejpam-110	267	14	l	l	NOUN
ejpam-110	267	15	-	-	ADJ
ejpam-110	267	16	set	set	VERB
ejpam-110	267	17	g	g	NOUN
ejpam-110	267	18	in	in	ADP
ejpam-110	267	19	∏	∏	PROPN
ejpam-110	267	20	j∈j	j∈j	NOUN
ejpam-110	267	21	x	x	X
ejpam-110	267	22	j	j	PROPN
ejpam-110	267	23	and	and	CCONJ
ejpam-110	267	24	an	an	DET
ejpam-110	267	25	l	l	NOUN
ejpam-110	267	26	-	-	ADJ
ejpam-110	267	27	set	set	ADJ
ejpam-110	267	28	k	k	PROPN
ejpam-110	267	29	in	in	ADP
ejpam-110	267	30	∏	∏	PROPN
ejpam-110	267	31	j∈j	j∈j	NOUN
ejpam-110	267	32	x	x	SYM
ejpam-110	267	33	j	j	PROPN
ejpam-110	267	34	,	,	PUNCT
ejpam-110	267	35	with	with	ADP
ejpam-110	267	36	χsupp(k	χsupp(k	PROPN
ejpam-110	267	37	)	)	PUNCT
ejpam-110	267	38	compact	compact	ADJ
ejpam-110	267	39	,	,	PUNCT
ejpam-110	267	40	such	such	ADJ
ejpam-110	267	41	that	that	SCONJ
ejpam-110	267	42	g(x	g(x	NOUN
ejpam-110	267	43	)	)	PUNCT
ejpam-110	267	44	�	�	PROPN
ejpam-110	267	45	p	p	NOUN
ejpam-110	267	46	and	and	CCONJ
ejpam-110	267	47	g	g	PROPN
ejpam-110	267	48	≤	≤	PROPN
ejpam-110	267	49	k.	k.	PROPN
ejpam-110	267	50	sufficiency	sufficiency	PROPN
ejpam-110	267	51	:	:	PUNCT
ejpam-110	267	52	for	for	ADP
ejpam-110	267	53	p	p	PROPN
ejpam-110	267	54	∈	∈	PROPN
ejpam-110	267	55	pr(l	pr(l	NOUN
ejpam-110	267	56	)	)	PUNCT
ejpam-110	267	57	and	and	CCONJ
ejpam-110	267	58	x	x	PUNCT
ejpam-110	267	59	∈	∈	NOUN
ejpam-110	267	60	∏	∏	PROPN
ejpam-110	267	61	j∈j	j∈j	NOUN
ejpam-110	267	62	x	x	X
ejpam-110	267	63	j	j	PROPN
ejpam-110	267	64	use	use	VERB
ejpam-110	267	65	the	the	DET
ejpam-110	267	66	weak	weak	ADJ
ejpam-110	267	67	local	local	ADJ
ejpam-110	267	68	compactness	compactness	NOUN
ejpam-110	267	69	of	of	ADP
ejpam-110	267	70	x	x	PROPN
ejpam-110	267	71	j	j	PROPN
ejpam-110	267	72	,	,	PUNCT
ejpam-110	267	73	j	j	PROPN
ejpam-110	267	74	/∈	/∈	PUNCT
ejpam-110	267	75	�	�	PROPN
ejpam-110	267	76	j1	j1	PROPN
ejpam-110	267	77	,	,	PUNCT
ejpam-110	267	78	·	·	PUNCT
ejpam-110	267	79	·	·	PUNCT
ejpam-110	267	80	·	·	PUNCT
ejpam-110	268	1	jm	jm	NOUN
ejpam-110	268	2	where	where	SCONJ
ejpam-110	268	3	the	the	DET
ejpam-110	268	4	set	set	NOUN
ejpam-110	268	5	is	be	AUX
ejpam-110	268	6	the	the	DET
ejpam-110	268	7	index	index	NOUN
ejpam-110	268	8	where	where	SCONJ
ejpam-110	268	9	x	x	X
ejpam-110	268	10	j	j	PROPN
ejpam-110	268	11	is	be	AUX
ejpam-110	268	12	not	not	PART
ejpam-110	268	13	compact	compact	ADJ
ejpam-110	268	14	,	,	PUNCT
ejpam-110	268	15	to	to	PART
ejpam-110	268	16	obtain	obtain	VERB
ejpam-110	268	17	g	g	PROPN
ejpam-110	268	18	ji	ji	PROPN
ejpam-110	268	19	in	in	ADP
ejpam-110	268	20	∏	∏	PROPN
ejpam-110	268	21	j∈j	j∈j	NOUN
ejpam-110	268	22	x	x	X
ejpam-110	268	23	j	j	PROPN
ejpam-110	268	24	and	and	CCONJ
ejpam-110	268	25	an	an	DET
ejpam-110	268	26	l	l	NOUN
ejpam-110	268	27	-	-	ADJ
ejpam-110	268	28	set	set	VERB
ejpam-110	268	29	k	k	PROPN
ejpam-110	268	30	ji	ji	PROPN
ejpam-110	268	31	in	in	ADP
ejpam-110	268	32	∏	∏	PROPN
ejpam-110	268	33	j∈j	j∈j	NOUN
ejpam-110	268	34	x	x	SYM
ejpam-110	268	35	j	j	PROPN
ejpam-110	268	36	,	,	PUNCT
ejpam-110	268	37	with	with	ADP
ejpam-110	268	38	χsupp(k	χsupp(k	PROPN
ejpam-110	268	39	ji	ji	PROPN
ejpam-110	268	40	)	)	PUNCT
ejpam-110	268	41	compact	compact	ADJ
ejpam-110	268	42	,	,	PUNCT
ejpam-110	268	43	such	such	ADJ
ejpam-110	268	44	that	that	SCONJ
ejpam-110	268	45	g	g	PROPN
ejpam-110	268	46	ji	ji	PROPN
ejpam-110	268	47	(	(	PUNCT
ejpam-110	268	48	x	x	NOUN
ejpam-110	268	49	)	)	PUNCT
ejpam-110	268	50	�	�	PROPN
ejpam-110	268	51	p	p	PROPN
ejpam-110	268	52	and	and	CCONJ
ejpam-110	268	53	g	g	PROPN
ejpam-110	268	54	ji	ji	PROPN
ejpam-110	268	55	≤	≤	PROPN
ejpam-110	268	56	k	k	PROPN
ejpam-110	268	57	ji	ji	PROPN
ejpam-110	268	58	.	.	PUNCT
ejpam-110	269	1	for	for	ADP
ejpam-110	269	2	the	the	DET
ejpam-110	269	3	rest	rest	NOUN
ejpam-110	269	4	just	just	ADV
ejpam-110	269	5	take	take	VERB
ejpam-110	269	6	g	g	NOUN
ejpam-110	269	7	=	=	PUNCT
ejpam-110	269	8	∧m	∧m	PROPN
ejpam-110	269	9	i=1π	i=1π	ADV
ejpam-110	269	10	−1	−1	NOUN
ejpam-110	269	11	λi	λi	NOUN
ejpam-110	269	12	(	(	PUNCT
ejpam-110	269	13	gλi	gλi	NOUN
ejpam-110	269	14	)	)	PUNCT
ejpam-110	269	15	and	and	CCONJ
ejpam-110	269	16	k	k	X
ejpam-110	270	1	=	=	PUNCT
ejpam-110	270	2	∧m	∧m	ADJ
ejpam-110	270	3	i=1π	i=1π	ADV
ejpam-110	270	4	−1	−1	NOUN
ejpam-110	270	5	λi	λi	INTJ
ejpam-110	270	6	(	(	PUNCT
ejpam-110	270	7	kλi	kλi	PROPN
ejpam-110	270	8	)	)	PUNCT
ejpam-110	270	9	.	.	PUNCT
ejpam-110	271	1	theorem	theorem	VERB
ejpam-110	271	2	4.11	4.11	NUM
ejpam-110	271	3	.	.	PUNCT
ejpam-110	272	1	if	if	SCONJ
ejpam-110	272	2	〈	〈	PROPN
ejpam-110	272	3	x	x	X
ejpam-110	272	4	,	,	PUNCT
ejpam-110	272	5	t	t	PROPN
ejpam-110	272	6	〉	〉	NOUN
ejpam-110	272	7	is	be	AUX
ejpam-110	272	8	a	a	DET
ejpam-110	272	9	hausdorff	hausdorff	NOUN
ejpam-110	272	10	weakly	weakly	ADV
ejpam-110	272	11	locally	locally	ADV
ejpam-110	272	12	compact	compact	ADJ
ejpam-110	272	13	l	l	ADJ
ejpam-110	272	14	-	-	ADJ
ejpam-110	272	15	topological	topological	ADJ
ejpam-110	272	16	space	space	NOUN
ejpam-110	272	17	then	then	ADV
ejpam-110	272	18	〈	〈	PROPN
ejpam-110	272	19	x	x	X
ejpam-110	272	20	,	,	PUNCT
ejpam-110	272	21	t	t	PROPN
ejpam-110	272	22	〉	〉	NOUN
ejpam-110	272	23	is	be	AUX
ejpam-110	272	24	regular	regular	ADJ
ejpam-110	272	25	.	.	PUNCT
ejpam-110	273	1	proof	proof	NOUN
ejpam-110	273	2	.	.	PUNCT
ejpam-110	274	1	let	let	VERB
ejpam-110	274	2	x	x	SYM
ejpam-110	274	3	∈	∈	PROPN
ejpam-110	274	4	x	x	X
ejpam-110	274	5	,	,	PUNCT
ejpam-110	274	6	let	let	VERB
ejpam-110	274	7	p	p	PRON
ejpam-110	274	8	∈	∈	NOUN
ejpam-110	274	9	pr(l	pr(l	NOUN
ejpam-110	274	10	)	)	PUNCT
ejpam-110	274	11	and	and	CCONJ
ejpam-110	274	12	let	let	VERB
ejpam-110	274	13	h	h	PRON
ejpam-110	274	14	be	be	AUX
ejpam-110	274	15	a	a	DET
ejpam-110	274	16	closed	closed	ADJ
ejpam-110	274	17	l	l	NOUN
ejpam-110	274	18	-	-	NOUN
ejpam-110	274	19	set	set	VERB
ejpam-110	274	20	such	such	ADJ
ejpam-110	274	21	that	that	SCONJ
ejpam-110	274	22	h(x	h(x	PROPN
ejpam-110	274	23	)	)	PUNCT
ejpam-110	275	1	=	=	SYM
ejpam-110	275	2	0	0	PUNCT
ejpam-110	276	1	and	and	CCONJ
ejpam-110	276	2	there	there	PRON
ejpam-110	276	3	exists	exist	VERB
ejpam-110	276	4	y0	y0	PROPN
ejpam-110	276	5	∈	∈	NOUN
ejpam-110	276	6	x	x	PUNCT
ejpam-110	276	7	with	with	ADP
ejpam-110	276	8	h(y0)≥	h(y0)≥	NOUN
ejpam-110	276	9	p′.	p′.	NOUN
ejpam-110	276	10	let	let	VERB
ejpam-110	276	11	’s	’s	NOUN
ejpam-110	276	12	show	show	VERB
ejpam-110	276	13	that	that	SCONJ
ejpam-110	276	14	there	there	PRON
ejpam-110	276	15	are	be	VERB
ejpam-110	276	16	u	u	NOUN
ejpam-110	276	17	,	,	PUNCT
ejpam-110	276	18	v	v	PROPN
ejpam-110	276	19	∈	∈	PROPN
ejpam-110	276	20	t	t	NOUN
ejpam-110	276	21	such	such	ADJ
ejpam-110	276	22	that	that	SCONJ
ejpam-110	276	23	u(x	u(x	PROPN
ejpam-110	276	24	)	)	PUNCT
ejpam-110	276	25	�	�	PROPN
ejpam-110	276	26	p	p	NOUN
ejpam-110	276	27	,	,	PUNCT
ejpam-110	276	28	v(y	v(y	PROPN
ejpam-110	276	29	)	)	PUNCT
ejpam-110	276	30	�	�	PROPN
ejpam-110	276	31	p	p	PROPN
ejpam-110	276	32	for	for	ADP
ejpam-110	276	33	each	each	DET
ejpam-110	276	34	y	y	PROPN
ejpam-110	276	35	∈	∈	PROPN
ejpam-110	276	36	x	x	PUNCT
ejpam-110	276	37	with	with	ADP
ejpam-110	276	38	h(y)≥	h(y)≥	ADJ
ejpam-110	276	39	p′	p′	NOUN
ejpam-110	276	40	,	,	PUNCT
ejpam-110	276	41	and	and	CCONJ
ejpam-110	276	42	,	,	PUNCT
ejpam-110	276	43	u(z	u(z	PROPN
ejpam-110	276	44	)	)	PUNCT
ejpam-110	276	45	=	=	SYM
ejpam-110	276	46	0	0	NUM
ejpam-110	276	47	or	or	CCONJ
ejpam-110	276	48	v(z	v(z	NOUN
ejpam-110	276	49	)	)	PUNCT
ejpam-110	276	50	=	=	SYM
ejpam-110	276	51	0	0	NUM
ejpam-110	277	1	for	for	ADP
ejpam-110	277	2	each	each	DET
ejpam-110	277	3	z	z	NOUN
ejpam-110	277	4	∈	∈	PROPN
ejpam-110	277	5	x	x	X
ejpam-110	277	6	.	.	PUNCT
ejpam-110	277	7	t.	t.	PROPN
ejpam-110	277	8	breuckmann	breuckmann	PROPN
ejpam-110	277	9	,	,	PUNCT
ejpam-110	277	10	s.	s.	PROPN
ejpam-110	277	11	kudri	kudri	PROPN
ejpam-110	277	12	,	,	PUNCT
ejpam-110	277	13	and	and	CCONJ
ejpam-110	277	14	h.	h.	PROPN
ejpam-110	277	15	aygün	aygün	PROPN
ejpam-110	277	16	/	/	SYM
ejpam-110	277	17	eur	eur	PROPN
ejpam-110	277	18	.	.	PUNCT
ejpam-110	278	1	j.	j.	PROPN
ejpam-110	278	2	pure	pure	PROPN
ejpam-110	278	3	appl	appl	PROPN
ejpam-110	278	4	.	.	PROPN
ejpam-110	278	5	math	math	PROPN
ejpam-110	278	6	,	,	PUNCT
ejpam-110	278	7	2	2	NUM
ejpam-110	278	8	(	(	PUNCT
ejpam-110	278	9	2009	2009	NUM
ejpam-110	278	10	)	)	PUNCT
ejpam-110	278	11	,	,	PUNCT
ejpam-110	278	12	(	(	PUNCT
ejpam-110	278	13	147	147	NUM
ejpam-110	278	14	-	-	SYM
ejpam-110	278	15	161	161	NUM
ejpam-110	278	16	)	)	PUNCT
ejpam-110	278	17	157	157	NUM
ejpam-110	278	18	since	since	SCONJ
ejpam-110	278	19	〈	〈	PROPN
ejpam-110	278	20	x	x	PROPN
ejpam-110	278	21	,	,	PUNCT
ejpam-110	278	22	t	t	PROPN
ejpam-110	278	23	〉	〉	NOUN
ejpam-110	278	24	is	be	AUX
ejpam-110	278	25	weakly	weakly	ADV
ejpam-110	278	26	locally	locally	ADV
ejpam-110	278	27	compact	compact	ADJ
ejpam-110	278	28	there	there	PRON
ejpam-110	278	29	are	be	VERB
ejpam-110	278	30	f	f	PROPN
ejpam-110	278	31	∈	∈	PROPN
ejpam-110	278	32	t	t	PROPN
ejpam-110	278	33	and	and	CCONJ
ejpam-110	278	34	h	h	NOUN
ejpam-110	278	35	∈	∈	PROPN
ejpam-110	279	1	lx	lx	ADV
ejpam-110	279	2	,	,	PUNCT
ejpam-110	279	3	with	with	ADP
ejpam-110	279	4	χ	χ	PRON
ejpam-110	279	5	supp(k	supp(k	PROPN
ejpam-110	279	6	)	)	PUNCT
ejpam-110	279	7	compact	compact	ADJ
ejpam-110	279	8	,	,	PUNCT
ejpam-110	279	9	such	such	ADJ
ejpam-110	279	10	that	that	SCONJ
ejpam-110	279	11	f	f	PROPN
ejpam-110	279	12	(	(	PUNCT
ejpam-110	279	13	x	x	X
ejpam-110	279	14	)	)	PUNCT
ejpam-110	279	15	�	�	PROPN
ejpam-110	279	16	p	p	PROPN
ejpam-110	279	17	and	and	CCONJ
ejpam-110	279	18	f	f	PROPN
ejpam-110	279	19	≤	≤	PROPN
ejpam-110	279	20	k.	k.	PROPN
ejpam-110	279	21	let	let	VERB
ejpam-110	279	22	d	d	NOUN
ejpam-110	279	23	=	=	SYM
ejpam-110	279	24	supp(k	supp(k	PROPN
ejpam-110	279	25	)	)	PUNCT
ejpam-110	279	26	,	,	PUNCT
ejpam-110	279	27	then	then	ADV
ejpam-110	279	28	:	:	PUNCT
ejpam-110	279	29	(	(	PUNCT
ejpam-110	279	30	1	1	X
ejpam-110	279	31	)	)	PUNCT
ejpam-110	279	32	x	x	SYM
ejpam-110	280	1	∈	∈	PROPN
ejpam-110	280	2	d	d	X
ejpam-110	280	3	since	since	SCONJ
ejpam-110	280	4	f	f	PROPN
ejpam-110	280	5	(	(	PUNCT
ejpam-110	280	6	x	x	NOUN
ejpam-110	280	7	)	)	PUNCT
ejpam-110	280	8	�	�	PROPN
ejpam-110	280	9	p	p	PROPN
ejpam-110	280	10	and	and	CCONJ
ejpam-110	280	11	f	f	PROPN
ejpam-110	280	12	≤	≤	PROPN
ejpam-110	280	13	k.	k.	PROPN
ejpam-110	280	14	(	(	PUNCT
ejpam-110	280	15	2	2	NUM
ejpam-110	280	16	)	)	PUNCT
ejpam-110	280	17	f	f	NOUN
ejpam-110	280	18	(	(	PUNCT
ejpam-110	280	19	z	z	NOUN
ejpam-110	280	20	)	)	PUNCT
ejpam-110	280	21	=	=	SYM
ejpam-110	280	22	0	0	NUM
ejpam-110	280	23	for	for	ADP
ejpam-110	280	24	each	each	DET
ejpam-110	280	25	z	z	PROPN
ejpam-110	280	26	∈	∈	PROPN
ejpam-110	280	27	dc	dc	PROPN
ejpam-110	280	28	since	since	SCONJ
ejpam-110	280	29	f	f	PROPN
ejpam-110	280	30	≤	≤	PROPN
ejpam-110	280	31	k	k	PROPN
ejpam-110	280	32	and	and	CCONJ
ejpam-110	280	33	k(z	k(z	PROPN
ejpam-110	280	34	)	)	PUNCT
ejpam-110	281	1	=	=	SYM
ejpam-110	281	2	0	0	NUM
ejpam-110	282	1	for	for	ADP
ejpam-110	282	2	each	each	DET
ejpam-110	282	3	z	z	PROPN
ejpam-110	282	4	∈	∈	PROPN
ejpam-110	282	5	dc	dc	PROPN
ejpam-110	282	6	.	.	PUNCT
ejpam-110	283	1	(	(	PUNCT
ejpam-110	283	2	3	3	X
ejpam-110	283	3	)	)	PUNCT
ejpam-110	283	4	since	since	SCONJ
ejpam-110	283	5	χd	χd	PROPN
ejpam-110	283	6	is	be	AUX
ejpam-110	283	7	a	a	DET
ejpam-110	283	8	compact	compact	ADJ
ejpam-110	283	9	l	l	NOUN
ejpam-110	283	10	-	-	ADJ
ejpam-110	283	11	set	set	ADJ
ejpam-110	283	12	and	and	CCONJ
ejpam-110	283	13	〈	〈	NOUN
ejpam-110	283	14	x	x	PROPN
ejpam-110	283	15	,	,	PUNCT
ejpam-110	283	16	t	t	PROPN
ejpam-110	283	17	〉	〉	NOUN
ejpam-110	283	18	is	be	AUX
ejpam-110	283	19	hausdorff	hausdorff	NOUN
ejpam-110	283	20	we	we	PRON
ejpam-110	283	21	have	have	VERB
ejpam-110	283	22	that	that	SCONJ
ejpam-110	283	23	χd	χd	PROPN
ejpam-110	283	24	is	be	AUX
ejpam-110	283	25	a	a	DET
ejpam-110	283	26	closed	closed	ADJ
ejpam-110	283	27	l	l	NOUN
ejpam-110	283	28	-	-	NOUN
ejpam-110	283	29	set	set	NOUN
ejpam-110	283	30	,	,	PUNCT
ejpam-110	283	31	then	then	ADV
ejpam-110	283	32	χ	χ	X
ejpam-110	283	33	′d	′d	NOUN
ejpam-110	283	34	=	=	SYM
ejpam-110	283	35	χdc	χdc	PROPN
ejpam-110	283	36	∈	∈	PROPN
ejpam-110	283	37	t	t	PROPN
ejpam-110	283	38	is	be	AUX
ejpam-110	283	39	an	an	DET
ejpam-110	283	40	open	open	ADJ
ejpam-110	283	41	l	l	NOUN
ejpam-110	283	42	-	-	NOUN
ejpam-110	283	43	set	set	NOUN
ejpam-110	283	44	.	.	PUNCT
ejpam-110	284	1	since	since	SCONJ
ejpam-110	284	2	χd	χd	PROPN
ejpam-110	284	3	is	be	AUX
ejpam-110	284	4	compact	compact	ADJ
ejpam-110	284	5	and	and	CCONJ
ejpam-110	284	6	〈	〈	NOUN
ejpam-110	284	7	x	x	NOUN
ejpam-110	284	8	,	,	PUNCT
ejpam-110	284	9	t	t	PROPN
ejpam-110	284	10	〉	〉	NOUN
ejpam-110	284	11	is	be	AUX
ejpam-110	284	12	hausdorff	hausdorff	NOUN
ejpam-110	284	13	,	,	PUNCT
ejpam-110	284	14	the	the	DET
ejpam-110	284	15	l	l	ADJ
ejpam-110	284	16	-	-	ADJ
ejpam-110	284	17	topological	topological	ADJ
ejpam-110	284	18	space	space	NOUN
ejpam-110	284	19	d	d	NOUN
ejpam-110	284	20	,	,	PUNCT
ejpam-110	284	21	td	td	PROPN
ejpam-110	284	22	�	�	PROPN
ejpam-110	284	23	is	be	AUX
ejpam-110	284	24	compact	compact	ADJ
ejpam-110	284	25	and	and	CCONJ
ejpam-110	284	26	hausdorff	hausdorff	NOUN
ejpam-110	284	27	,	,	PUNCT
ejpam-110	284	28	hence	hence	ADV
ejpam-110	284	29	d	d	NOUN
ejpam-110	284	30	,	,	PUNCT
ejpam-110	284	31	td	td	PROPN
ejpam-110	284	32	�	�	PROPN
ejpam-110	284	33	is	be	AUX
ejpam-110	284	34	regular	regular	ADJ
ejpam-110	284	35	by	by	ADP
ejpam-110	284	36	theorem	theorem	ADJ
ejpam-110	284	37	2.4	2.4	NUM
ejpam-110	284	38	.	.	PUNCT
ejpam-110	285	1	case	case	NOUN
ejpam-110	285	2	1	1	NUM
ejpam-110	285	3	:	:	PUNCT
ejpam-110	285	4	there	there	PRON
ejpam-110	285	5	exist	exist	VERB
ejpam-110	285	6	y	y	PROPN
ejpam-110	285	7	∈	∈	PROPN
ejpam-110	286	1	d	d	ADP
ejpam-110	286	2	such	such	ADJ
ejpam-110	286	3	that	that	SCONJ
ejpam-110	286	4	h(y	h(y	NOUN
ejpam-110	286	5	)	)	PUNCT
ejpam-110	286	6	≥	≥	NOUN
ejpam-110	286	7	p′.	p′.	NOUN
ejpam-110	286	8	in	in	ADP
ejpam-110	286	9	this	this	DET
ejpam-110	286	10	case	case	NOUN
ejpam-110	286	11	,	,	PUNCT
ejpam-110	286	12	by	by	ADP
ejpam-110	286	13	(	(	PUNCT
ejpam-110	286	14	1	1	NUM
ejpam-110	286	15	)	)	PUNCT
ejpam-110	286	16	and	and	CCONJ
ejpam-110	286	17	by	by	ADP
ejpam-110	286	18	regularity	regularity	NOUN
ejpam-110	286	19	of	of	ADP
ejpam-110	286	20	d	d	NOUN
ejpam-110	286	21	,	,	PUNCT
ejpam-110	286	22	td	td	PROPN
ejpam-110	286	23	�	�	PROPN
ejpam-110	286	24	,	,	PUNCT
ejpam-110	286	25	there	there	PRON
ejpam-110	286	26	are	be	VERB
ejpam-110	286	27	ud	ud	ADP
ejpam-110	286	28	,	,	PUNCT
ejpam-110	286	29	vd	vd	NOUN
ejpam-110	286	30	∈	∈	NOUN
ejpam-110	286	31	td	td	NOUN
ejpam-110	286	32	such	such	ADJ
ejpam-110	286	33	that	that	PRON
ejpam-110	286	34	ud(x	ud(x	NOUN
ejpam-110	286	35	)	)	PUNCT
ejpam-110	286	36	�	�	PROPN
ejpam-110	286	37	p	p	NOUN
ejpam-110	286	38	,	,	PUNCT
ejpam-110	286	39	vd(z	vd(z	NUM
ejpam-110	286	40	)	)	PUNCT
ejpam-110	286	41	�	�	PROPN
ejpam-110	286	42	p	p	PROPN
ejpam-110	286	43	for	for	ADP
ejpam-110	286	44	each	each	DET
ejpam-110	286	45	z	z	NOUN
ejpam-110	286	46	∈	∈	PROPN
ejpam-110	286	47	d	d	NOUN
ejpam-110	286	48	with	with	ADP
ejpam-110	286	49	h(z	h(z	NOUN
ejpam-110	286	50	)	)	PUNCT
ejpam-110	286	51	≤	≤	NOUN
ejpam-110	286	52	p	p	X
ejpam-110	286	53	,	,	PUNCT
ejpam-110	286	54	and	and	CCONJ
ejpam-110	286	55	,	,	PUNCT
ejpam-110	286	56	ud(z	ud(z	X
ejpam-110	286	57	)	)	PUNCT
ejpam-110	286	58	=	=	SYM
ejpam-110	286	59	0	0	NUM
ejpam-110	286	60	or	or	CCONJ
ejpam-110	286	61	vd(z	vd(z	NOUN
ejpam-110	286	62	)	)	PUNCT
ejpam-110	286	63	=	=	SYM
ejpam-110	286	64	0	0	NUM
ejpam-110	286	65	for	for	ADP
ejpam-110	286	66	each	each	DET
ejpam-110	286	67	z	z	PROPN
ejpam-110	286	68	∈	∈	PROPN
ejpam-110	286	69	d.	d.	NOUN
ejpam-110	286	70	let	let	VERB
ejpam-110	286	71	u∗	u∗	ADV
ejpam-110	286	72	,	,	PUNCT
ejpam-110	286	73	v∗	v∗	PROPN
ejpam-110	286	74	∈	∈	PROPN
ejpam-110	286	75	t	t	NOUN
ejpam-110	286	76	such	such	ADJ
ejpam-110	286	77	that	that	SCONJ
ejpam-110	286	78	u∗|d	u∗|d	PROPN
ejpam-110	287	1	=	=	PUNCT
ejpam-110	287	2	ud	ud	INTJ
ejpam-110	287	3	and	and	CCONJ
ejpam-110	287	4	v∗|d	v∗|d	NOUN
ejpam-110	287	5	=	=	SYM
ejpam-110	287	6	vd	vd	NOUN
ejpam-110	287	7	,	,	PUNCT
ejpam-110	287	8	and	and	CCONJ
ejpam-110	287	9	define	define	VERB
ejpam-110	287	10	u	u	NOUN
ejpam-110	287	11	=	=	PROPN
ejpam-110	287	12	u∗∨	u∗∨	PROPN
ejpam-110	287	13	f	f	PROPN
ejpam-110	287	14	and	and	CCONJ
ejpam-110	287	15	v	v	NOUN
ejpam-110	287	16	=	=	SYM
ejpam-110	287	17	v∗∧χdc	v∗∧χdc	X
ejpam-110	287	18	.	.	PUNCT
ejpam-110	288	1	then	then	ADV
ejpam-110	288	2	we	we	PRON
ejpam-110	288	3	have	have	VERB
ejpam-110	288	4	:	:	PUNCT
ejpam-110	288	5	(	(	PUNCT
ejpam-110	288	6	a	a	X
ejpam-110	288	7	)	)	PUNCT
ejpam-110	288	8	u	u	PROPN
ejpam-110	288	9	∈	∈	PROPN
ejpam-110	288	10	t	t	PROPN
ejpam-110	288	11	since	since	SCONJ
ejpam-110	288	12	u∗	u∗	PROPN
ejpam-110	288	13	,	,	PUNCT
ejpam-110	288	14	f	f	PROPN
ejpam-110	288	15	∈	∈	PROPN
ejpam-110	288	16	t	t	PROPN
ejpam-110	288	17	,	,	PUNCT
ejpam-110	288	18	and	and	CCONJ
ejpam-110	288	19	v	v	ADP
ejpam-110	288	20	∈	∈	PROPN
ejpam-110	288	21	t	t	NOUN
ejpam-110	288	22	since	since	SCONJ
ejpam-110	288	23	v∗	v∗	PROPN
ejpam-110	288	24	∈	∈	PROPN
ejpam-110	288	25	t	t	X
ejpam-110	288	26	an	an	DET
ejpam-110	288	27	by	by	ADP
ejpam-110	288	28	(	(	PUNCT
ejpam-110	288	29	3	3	NUM
ejpam-110	288	30	)	)	PUNCT
ejpam-110	288	31	.	.	PUNCT
ejpam-110	289	1	(	(	PUNCT
ejpam-110	289	2	b	b	X
ejpam-110	289	3	)	)	PUNCT
ejpam-110	289	4	since	since	SCONJ
ejpam-110	289	5	x	x	PROPN
ejpam-110	289	6	∈	∈	PROPN
ejpam-110	289	7	d	d	PROPN
ejpam-110	289	8	,	,	PUNCT
ejpam-110	289	9	u∗(x	u∗(x	PROPN
ejpam-110	289	10	)	)	PUNCT
ejpam-110	289	11	=	=	PUNCT
ejpam-110	289	12	ud(x	ud(x	X
ejpam-110	289	13	)	)	PUNCT
ejpam-110	289	14	�	�	PROPN
ejpam-110	289	15	p	p	NOUN
ejpam-110	289	16	,	,	PUNCT
ejpam-110	289	17	then	then	ADV
ejpam-110	289	18	u(x	u(x	PROPN
ejpam-110	289	19	)	)	PUNCT
ejpam-110	289	20	�	�	PROPN
ejpam-110	289	21	p	p	PROPN
ejpam-110	289	22	since	since	SCONJ
ejpam-110	289	23	f	f	PROPN
ejpam-110	289	24	(	(	PUNCT
ejpam-110	289	25	x	x	NOUN
ejpam-110	289	26	)	)	PUNCT
ejpam-110	289	27	�	�	PROPN
ejpam-110	289	28	p	p	NOUN
ejpam-110	289	29	and	and	CCONJ
ejpam-110	289	30	p	p	NOUN
ejpam-110	289	31	∈	∈	PROPN
ejpam-110	289	32	pr(l	pr(l	NOUN
ejpam-110	289	33	)	)	PUNCT
ejpam-110	289	34	.	.	PUNCT
ejpam-110	290	1	(	(	PUNCT
ejpam-110	290	2	c	c	X
ejpam-110	290	3	)	)	PUNCT
ejpam-110	290	4	let	let	VERB
ejpam-110	290	5	z	z	NOUN
ejpam-110	290	6	∈	∈	PROPN
ejpam-110	290	7	x	x	PUNCT
ejpam-110	290	8	such	such	ADJ
ejpam-110	290	9	that	that	SCONJ
ejpam-110	290	10	h(z	h(z	NOUN
ejpam-110	290	11	)	)	PUNCT
ejpam-110	290	12	≥	≥	NOUN
ejpam-110	290	13	p′.	p′.	X
ejpam-110	290	14	z	z	PROPN
ejpam-110	290	15	∈	∈	PROPN
ejpam-110	290	16	d	d	X
ejpam-110	290	17	⇒	⇒	NOUN
ejpam-110	290	18	v(z	v(z	PROPN
ejpam-110	290	19	)	)	PUNCT
ejpam-110	291	1	=	=	SYM
ejpam-110	291	2	v∗(z	v∗(z	NOUN
ejpam-110	291	3	)	)	PUNCT
ejpam-110	291	4	=	=	NOUN
ejpam-110	291	5	vd(z	vd(z	NOUN
ejpam-110	291	6	)	)	PUNCT
ejpam-110	291	7	�	�	PROPN
ejpam-110	292	1	p	p	NOUN
ejpam-110	292	2	z	z	PROPN
ejpam-110	292	3	∈	∈	PROPN
ejpam-110	292	4	dc	dc	PROPN
ejpam-110	292	5	⇒	⇒	PROPN
ejpam-110	292	6	χdc(z	χdc(z	PROPN
ejpam-110	292	7	)	)	PUNCT
ejpam-110	292	8	=	=	SYM
ejpam-110	292	9	1	1	NUM
ejpam-110	292	10	�	�	PROPN
ejpam-110	292	11	p⇒	p⇒	PROPN
ejpam-110	292	12	v(z	v(z	PROPN
ejpam-110	292	13	)	)	PUNCT
ejpam-110	293	1	=	=	SYM
ejpam-110	293	2	χdc	χdc	X
ejpam-110	293	3	(	(	PUNCT
ejpam-110	293	4	z	z	NOUN
ejpam-110	293	5	)	)	PUNCT
ejpam-110	293	6	�	�	PROPN
ejpam-110	293	7	p	p	PROPN
ejpam-110	293	8	(	(	PUNCT
ejpam-110	293	9	d	d	NOUN
ejpam-110	293	10	)	)	PUNCT
ejpam-110	293	11	let	let	VERB
ejpam-110	293	12	z	z	NOUN
ejpam-110	293	13	∈	∈	PROPN
ejpam-110	293	14	x	x	PUNCT
ejpam-110	293	15	such	such	ADJ
ejpam-110	293	16	that	that	DET
ejpam-110	293	17	u(z	u(z	NOUN
ejpam-110	293	18	)	)	PUNCT
ejpam-110	293	19	6=	6=	ADP
ejpam-110	293	20	0	0	NUM
ejpam-110	293	21	,	,	PUNCT
ejpam-110	293	22	then	then	ADV
ejpam-110	293	23	,	,	PUNCT
ejpam-110	293	24	u∗(z	u∗(z	NOUN
ejpam-110	293	25	)	)	PUNCT
ejpam-110	293	26	6=	6=	SYM
ejpam-110	293	27	0	0	NUM
ejpam-110	293	28	and	and	CCONJ
ejpam-110	293	29	f	f	PROPN
ejpam-110	293	30	(	(	PUNCT
ejpam-110	293	31	z	z	NOUN
ejpam-110	293	32	)	)	PUNCT
ejpam-110	293	33	6=	6=	ADP
ejpam-110	293	34	0	0	X
ejpam-110	293	35	.	.	PUNCT
ejpam-110	294	1	by	by	ADP
ejpam-110	294	2	(	(	PUNCT
ejpam-110	294	3	2	2	NUM
ejpam-110	294	4	)	)	PUNCT
ejpam-110	294	5	,	,	PUNCT
ejpam-110	294	6	z	z	PROPN
ejpam-110	294	7	∈	∈	PROPN
ejpam-110	295	1	d	d	NOUN
ejpam-110	295	2	,	,	PUNCT
ejpam-110	295	3	then	then	ADV
ejpam-110	295	4	ud(z	ud(z	X
ejpam-110	295	5	)	)	PUNCT
ejpam-110	295	6	=	=	SYM
ejpam-110	295	7	u∗(z	u∗(z	NOUN
ejpam-110	295	8	)	)	PUNCT
ejpam-110	295	9	6=	6=	ADP
ejpam-110	295	10	0	0	NUM
ejpam-110	295	11	,	,	PUNCT
ejpam-110	295	12	hence	hence	ADV
ejpam-110	295	13	v∗(z	v∗(z	NOUN
ejpam-110	295	14	)	)	PUNCT
ejpam-110	295	15	=	=	NOUN
ejpam-110	295	16	vd(z	vd(z	NOUN
ejpam-110	295	17	)	)	PUNCT
ejpam-110	295	18	=	=	SYM
ejpam-110	295	19	0	0	NUM
ejpam-110	295	20	,	,	PUNCT
ejpam-110	295	21	so	so	ADV
ejpam-110	295	22	v(z	v(z	NOUN
ejpam-110	295	23	)	)	PUNCT
ejpam-110	295	24	=	=	SYM
ejpam-110	295	25	v∗(z)∧χdc	v∗(z)∧χdc	NOUN
ejpam-110	295	26	(	(	PUNCT
ejpam-110	295	27	z	z	NOUN
ejpam-110	295	28	)	)	PUNCT
ejpam-110	295	29	=	=	SYM
ejpam-110	295	30	0∧	0∧	NOUN
ejpam-110	295	31	0=	0=	NOUN
ejpam-110	295	32	0	0	NUM
ejpam-110	295	33	case	case	NOUN
ejpam-110	295	34	2	2	NUM
ejpam-110	295	35	:	:	PUNCT
ejpam-110	295	36	there	there	PRON
ejpam-110	295	37	is	be	VERB
ejpam-110	295	38	not	not	PART
ejpam-110	295	39	y	y	PROPN
ejpam-110	295	40	∈	∈	PROPN
ejpam-110	296	1	d	d	ADP
ejpam-110	296	2	such	such	ADJ
ejpam-110	296	3	that	that	DET
ejpam-110	296	4	h(y)≥	h(y)≥	ADJ
ejpam-110	296	5	p′.	p′.	NOUN
ejpam-110	296	6	let	let	VERB
ejpam-110	296	7	u=	u=	NOUN
ejpam-110	296	8	f	f	NOUN
ejpam-110	296	9	and	and	CCONJ
ejpam-110	296	10	v	v	NOUN
ejpam-110	296	11	=	=	ADJ
ejpam-110	296	12	χdc	χdc	NOUN
ejpam-110	296	13	,	,	PUNCT
ejpam-110	296	14	then	then	ADV
ejpam-110	296	15	u	u	NOUN
ejpam-110	296	16	,	,	PUNCT
ejpam-110	296	17	v	v	PROPN
ejpam-110	296	18	∈	∈	PROPN
ejpam-110	296	19	t	t	NOUN
ejpam-110	296	20	and	and	CCONJ
ejpam-110	296	21	:	:	PUNCT
ejpam-110	296	22	t.	t.	PROPN
ejpam-110	296	23	breuckmann	breuckmann	PROPN
ejpam-110	296	24	,	,	PUNCT
ejpam-110	296	25	s.	s.	PROPN
ejpam-110	296	26	kudri	kudri	PROPN
ejpam-110	296	27	,	,	PUNCT
ejpam-110	296	28	and	and	CCONJ
ejpam-110	296	29	h.	h.	PROPN
ejpam-110	296	30	aygün	aygün	PROPN
ejpam-110	296	31	/	/	SYM
ejpam-110	296	32	eur	eur	PROPN
ejpam-110	296	33	.	.	PUNCT
ejpam-110	297	1	j.	j.	PROPN
ejpam-110	297	2	pure	pure	PROPN
ejpam-110	297	3	appl	appl	PROPN
ejpam-110	297	4	.	.	PROPN
ejpam-110	297	5	math	math	PROPN
ejpam-110	297	6	,	,	PUNCT
ejpam-110	297	7	2	2	NUM
ejpam-110	297	8	(	(	PUNCT
ejpam-110	297	9	2009	2009	NUM
ejpam-110	297	10	)	)	PUNCT
ejpam-110	297	11	,	,	PUNCT
ejpam-110	297	12	(	(	PUNCT
ejpam-110	297	13	147	147	NUM
ejpam-110	297	14	-	-	SYM
ejpam-110	297	15	161	161	NUM
ejpam-110	297	16	)	)	PUNCT
ejpam-110	297	17	158	158	NUM
ejpam-110	297	18	(	(	PUNCT
ejpam-110	297	19	a	a	NOUN
ejpam-110	297	20	)	)	PUNCT
ejpam-110	297	21	u(x	u(x	PROPN
ejpam-110	297	22	)	)	PUNCT
ejpam-110	298	1	=	=	SYM
ejpam-110	298	2	f	f	X
ejpam-110	298	3	(	(	PUNCT
ejpam-110	298	4	x	x	NOUN
ejpam-110	298	5	)	)	PUNCT
ejpam-110	298	6	�	�	PROPN
ejpam-110	298	7	p	p	PROPN
ejpam-110	298	8	(	(	PUNCT
ejpam-110	298	9	b	b	NOUN
ejpam-110	298	10	)	)	PUNCT
ejpam-110	298	11	let	let	VERB
ejpam-110	298	12	z	z	NOUN
ejpam-110	298	13	∈	∈	PROPN
ejpam-110	298	14	x	x	PUNCT
ejpam-110	298	15	such	such	ADJ
ejpam-110	298	16	that	that	SCONJ
ejpam-110	298	17	h(z	h(z	NOUN
ejpam-110	298	18	)	)	PUNCT
ejpam-110	298	19	≥	≥	NOUN
ejpam-110	298	20	p′	p′	NOUN
ejpam-110	298	21	,	,	PUNCT
ejpam-110	298	22	then	then	ADV
ejpam-110	298	23	z	z	PROPN
ejpam-110	298	24	∈	∈	PROPN
ejpam-110	298	25	dc	dc	PROPN
ejpam-110	298	26	since	since	SCONJ
ejpam-110	298	27	in	in	ADP
ejpam-110	298	28	this	this	DET
ejpam-110	298	29	case	case	NOUN
ejpam-110	298	30	there	there	PRON
ejpam-110	298	31	is	be	VERB
ejpam-110	298	32	not	not	PART
ejpam-110	298	33	z	z	NOUN
ejpam-110	298	34	∈	∈	PROPN
ejpam-110	298	35	d	d	NOUN
ejpam-110	298	36	with	with	ADP
ejpam-110	298	37	h(z	h(z	NOUN
ejpam-110	298	38	)	)	PUNCT
ejpam-110	298	39	≥	≥	NOUN
ejpam-110	298	40	p′	p′	NOUN
ejpam-110	298	41	,	,	PUNCT
ejpam-110	298	42	hence	hence	ADV
ejpam-110	298	43	χdc(z	χdc(z	PROPN
ejpam-110	298	44	)	)	PUNCT
ejpam-110	298	45	=	=	SYM
ejpam-110	299	1	1	1	NUM
ejpam-110	299	2	,	,	PUNCT
ejpam-110	299	3	so	so	ADV
ejpam-110	299	4	v(z	v(z	NOUN
ejpam-110	299	5	)	)	PUNCT
ejpam-110	299	6	=	=	SYM
ejpam-110	300	1	1	1	NUM
ejpam-110	300	2	�	�	PROPN
ejpam-110	300	3	p.	p.	NOUN
ejpam-110	300	4	(	(	PUNCT
ejpam-110	300	5	c	c	X
ejpam-110	300	6	)	)	PUNCT
ejpam-110	300	7	let	let	VERB
ejpam-110	300	8	z	z	NOUN
ejpam-110	300	9	∈	∈	PROPN
ejpam-110	300	10	x	x	PUNCT
ejpam-110	300	11	such	such	ADJ
ejpam-110	300	12	that	that	SCONJ
ejpam-110	300	13	u(z	u(z	NOUN
ejpam-110	300	14	)	)	PUNCT
ejpam-110	301	1	=	=	SYM
ejpam-110	301	2	f	f	X
ejpam-110	301	3	(	(	PUNCT
ejpam-110	301	4	z	z	NOUN
ejpam-110	301	5	)	)	PUNCT
ejpam-110	301	6	6=	6=	ADP
ejpam-110	301	7	0	0	NUM
ejpam-110	301	8	,	,	PUNCT
ejpam-110	301	9	then	then	ADV
ejpam-110	301	10	by	by	ADP
ejpam-110	301	11	(	(	PUNCT
ejpam-110	301	12	2	2	NUM
ejpam-110	301	13	)	)	PUNCT
ejpam-110	301	14	,	,	PUNCT
ejpam-110	302	1	z	z	PROPN
ejpam-110	302	2	∈	∈	PROPN
ejpam-110	302	3	d	d	NOUN
ejpam-110	302	4	,	,	PUNCT
ejpam-110	302	5	hence	hence	ADV
ejpam-110	302	6	v(z	v(z	NOUN
ejpam-110	302	7	)	)	PUNCT
ejpam-110	303	1	=	=	SYM
ejpam-110	303	2	χdc	χdc	X
ejpam-110	303	3	(	(	PUNCT
ejpam-110	303	4	z	z	NOUN
ejpam-110	303	5	)	)	PUNCT
ejpam-110	303	6	=	=	SYM
ejpam-110	303	7	0	0	X
ejpam-110	303	8	.	.	PUNCT
ejpam-110	304	1	therefore	therefore	ADV
ejpam-110	304	2	〈	〈	PROPN
ejpam-110	304	3	x	x	X
ejpam-110	304	4	,	,	PUNCT
ejpam-110	304	5	t	t	PROPN
ejpam-110	304	6	〉	〉	NOUN
ejpam-110	304	7	is	be	AUX
ejpam-110	304	8	regular	regular	ADJ
ejpam-110	304	9	.	.	PUNCT
ejpam-110	305	1	it	it	PRON
ejpam-110	305	2	’s	’	VERB
ejpam-110	305	3	immediate	immediate	ADJ
ejpam-110	305	4	that	that	SCONJ
ejpam-110	305	5	locally	locally	ADV
ejpam-110	305	6	compact	compact	ADJ
ejpam-110	305	7	and	and	CCONJ
ejpam-110	305	8	relatively	relatively	ADV
ejpam-110	305	9	locally	locally	ADV
ejpam-110	305	10	compact	compact	ADJ
ejpam-110	305	11	hausdorff	hausdorff	NOUN
ejpam-110	305	12	spaces	space	NOUN
ejpam-110	305	13	are	be	AUX
ejpam-110	305	14	regular	regular	ADJ
ejpam-110	305	15	since	since	SCONJ
ejpam-110	305	16	these	these	DET
ejpam-110	305	17	spaces	space	NOUN
ejpam-110	305	18	are	be	AUX
ejpam-110	305	19	weakly	weakly	ADV
ejpam-110	305	20	locally	locally	ADV
ejpam-110	305	21	compact	compact	ADJ
ejpam-110	305	22	by	by	ADP
ejpam-110	305	23	theorems	theorem	NOUN
ejpam-110	305	24	4.4	4.4	NUM
ejpam-110	305	25	and	and	CCONJ
ejpam-110	305	26	4.7	4.7	NUM
ejpam-110	305	27	.	.	NOUN
ejpam-110	306	1	5	5	NUM
ejpam-110	306	2	.	.	PUNCT
ejpam-110	307	1	the	the	DET
ejpam-110	307	2	one	one	NUM
ejpam-110	307	3	point	point	NOUN
ejpam-110	307	4	compactification	compactification	NOUN
ejpam-110	307	5	the	the	DET
ejpam-110	307	6	following	follow	VERB
ejpam-110	307	7	is	be	AUX
ejpam-110	307	8	based	base	VERB
ejpam-110	307	9	on	on	ADP
ejpam-110	307	10	[	[	X
ejpam-110	307	11	3	3	NUM
ejpam-110	307	12	]	]	PUNCT
ejpam-110	307	13	.	.	PUNCT
ejpam-110	308	1	let	let	VERB
ejpam-110	308	2	x	x	PRON
ejpam-110	308	3	,	,	PUNCT
ejpam-110	308	4	tx	tx	PROPN
ejpam-110	308	5	�	�	PROPN
ejpam-110	308	6	be	be	AUX
ejpam-110	308	7	a	a	DET
ejpam-110	308	8	hausdorff	hausdorff	NOUN
ejpam-110	308	9	l	l	NOUN
ejpam-110	308	10	topologiacal	topologiacal	ADJ
ejpam-110	308	11	space	space	NOUN
ejpam-110	308	12	which	which	PRON
ejpam-110	308	13	is	be	AUX
ejpam-110	308	14	not	not	PART
ejpam-110	308	15	compact	compact	ADJ
ejpam-110	308	16	,	,	PUNCT
ejpam-110	308	17	but	but	CCONJ
ejpam-110	308	18	weakly	weakly	ADV
ejpam-110	308	19	locally	locally	ADV
ejpam-110	308	20	compact	compact	ADJ
ejpam-110	308	21	.	.	PUNCT
ejpam-110	309	1	let	let	VERB
ejpam-110	309	2	y	y	NOUN
ejpam-110	309	3	=	=	PUNCT
ejpam-110	309	4	x∪{∞}with	x∪{∞}with	PROPN
ejpam-110	309	5	l	l	NOUN
ejpam-110	309	6	topology	topology	NOUN
ejpam-110	309	7	ty	ty	INTJ
ejpam-110	309	8	generated	generate	VERB
ejpam-110	309	9	by	by	ADP
ejpam-110	309	10	the	the	DET
ejpam-110	309	11	subbase	subbase	NOUN
ejpam-110	309	12	s=	s=	NOUN
ejpam-110	309	13	¦	¦	PROPN
ejpam-110	309	14	f1	f1	PROPN
ejpam-110	309	15	∈	∈	PROPN
ejpam-110	309	16	ly	ly	X
ejpam-110	309	17	;	;	PUNCT
ejpam-110	309	18	f	f	PROPN
ejpam-110	309	19	∈	∈	PROPN
ejpam-110	309	20	tx	tx	VERB
ejpam-110	309	21	©	©	PROPN
ejpam-110	309	22	∪	∪	X
ejpam-110	309	23	¦	¦	PROPN
ejpam-110	309	24	χb∞	χb∞	PROPN
ejpam-110	309	25	∈	∈	PROPN
ejpam-110	309	26	ly	ly	ADP
ejpam-110	309	27	;	;	PUNCT
ejpam-110	309	28	χb	χb	PROPN
ejpam-110	309	29	∈	∈	PROPN
ejpam-110	309	30	c	c	PUNCT
ejpam-110	310	1	©	©	NOUN
ejpam-110	310	2	,	,	PUNCT
ejpam-110	310	3	where	where	SCONJ
ejpam-110	310	4	:	:	PUNCT
ejpam-110	310	5	(	(	PUNCT
ejpam-110	310	6	i	i	NOUN
ejpam-110	310	7	)	)	PUNCT
ejpam-110	310	8	f1	f1	PROPN
ejpam-110	310	9	∈	∈	PROPN
ejpam-110	310	10	lx	lx	NOUN
ejpam-110	310	11	is	be	AUX
ejpam-110	310	12	defined	define	VERB
ejpam-110	310	13	by	by	ADP
ejpam-110	310	14	:	:	PUNCT
ejpam-110	310	15	f1(y	f1(y	NUM
ejpam-110	310	16	)	)	PUNCT
ejpam-110	310	17	=	=	PUNCT
ejpam-110	311	1			PROPN
ejpam-110	311	2			X
ejpam-110	311	3			ADJ
ejpam-110	311	4	f	f	PROPN
ejpam-110	311	5	(	(	PUNCT
ejpam-110	311	6	y	y	PROPN
ejpam-110	311	7	)	)	PUNCT
ejpam-110	311	8	if	if	SCONJ
ejpam-110	311	9	y	y	PROPN
ejpam-110	311	10	∈	∈	PROPN
ejpam-110	311	11	x	x	X
ejpam-110	311	12	0	0	PUNCT
ejpam-110	311	13	if	if	SCONJ
ejpam-110	311	14	y	y	PROPN
ejpam-110	311	15	=	=	AUX
ejpam-110	311	16	∞	∞	PROPN
ejpam-110	311	17	(	(	PUNCT
ejpam-110	311	18	ii	ii	NOUN
ejpam-110	311	19	)	)	PUNCT
ejpam-110	311	20	c	c	NOUN
ejpam-110	312	1	=	=	PUNCT
ejpam-110	312	2	¦	¦	X
ejpam-110	312	3	χb	χb	PROPN
ejpam-110	312	4	∈	∈	PROPN
ejpam-110	312	5	lx	lx	ADV
ejpam-110	312	6	;	;	PUNCT
ejpam-110	312	7	b	b	X
ejpam-110	312	8	⊂	⊂	PROPN
ejpam-110	312	9	x	x	X
ejpam-110	312	10	,	,	PUNCT
ejpam-110	312	11	χb	χb	PROPN
ejpam-110	312	12	compacto	compacto	VERB
ejpam-110	312	13	©	©	PROPN
ejpam-110	312	14	(	(	PUNCT
ejpam-110	312	15	iii	iii	NOUN
ejpam-110	312	16	)	)	PUNCT
ejpam-110	312	17	for	for	ADP
ejpam-110	312	18	χb	χb	PROPN
ejpam-110	312	19	∈	∈	PROPN
ejpam-110	312	20	c	c	AUX
ejpam-110	312	21	,	,	PUNCT
ejpam-110	312	22	define	define	VERB
ejpam-110	312	23	b∞	b∞	PROPN
ejpam-110	312	24	=	=	SYM
ejpam-110	312	25	{	{	PUNCT
ejpam-110	312	26	∞	∞	NOUN
ejpam-110	312	27	}	}	PUNCT
ejpam-110	312	28	∪	∪	NOUN
ejpam-110	312	29	(	(	PUNCT
ejpam-110	312	30	x	x	NOUN
ejpam-110	312	31	−	−	PROPN
ejpam-110	312	32	b	b	NOUN
ejpam-110	312	33	)	)	PUNCT
ejpam-110	312	34	and	and	CCONJ
ejpam-110	312	35	:	:	PUNCT
ejpam-110	312	36	χb∞	χb∞	PROPN
ejpam-110	312	37	(	(	PUNCT
ejpam-110	312	38	y	y	NOUN
ejpam-110	312	39	)	)	PUNCT
ejpam-110	312	40	=	=	PUNCT
ejpam-110	313	1			PROPN
ejpam-110	313	2			X
ejpam-110	313	3			NOUN
ejpam-110	313	4	1	1	NUM
ejpam-110	313	5	if	if	SCONJ
ejpam-110	313	6	y	y	PROPN
ejpam-110	313	7	∈	∈	PROPN
ejpam-110	313	8	b∞	b∞	X
ejpam-110	313	9	0	0	PUNCT
ejpam-110	313	10	if	if	SCONJ
ejpam-110	313	11	y	y	PROPN
ejpam-110	313	12	∈	∈	PROPN
ejpam-110	313	13	b.	b.	PROPN
ejpam-110	314	1	the	the	DET
ejpam-110	314	2	l	l	PROPN
ejpam-110	314	3	topological	topological	ADJ
ejpam-110	314	4	space	space	PROPN
ejpam-110	314	5	y	y	PROPN
ejpam-110	314	6	,	,	PUNCT
ejpam-110	314	7	ty	ty	PRON
ejpam-110	314	8	�	�	PROPN
ejpam-110	314	9	is	be	AUX
ejpam-110	314	10	called	call	VERB
ejpam-110	314	11	the	the	DET
ejpam-110	314	12	one	one	NUM
ejpam-110	314	13	point	point	NOUN
ejpam-110	314	14	compactification	compactification	NOUN
ejpam-110	314	15	of	of	ADP
ejpam-110	314	16	x	x	SYM
ejpam-110	314	17	,	,	PUNCT
ejpam-110	314	18	tx	tx	PROPN
ejpam-110	314	19	�	�	PROPN
ejpam-110	314	20	.	.	PUNCT
ejpam-110	315	1	theorem	theorem	VERB
ejpam-110	315	2	5.1	5.1	NUM
ejpam-110	315	3	.	.	PUNCT
ejpam-110	316	1	let	let	VERB
ejpam-110	316	2	x	x	PRON
ejpam-110	316	3	,	,	PUNCT
ejpam-110	316	4	tx	tx	PROPN
ejpam-110	316	5	�	�	PROPN
ejpam-110	316	6	be	be	AUX
ejpam-110	316	7	a	a	DET
ejpam-110	316	8	weakly	weakly	ADV
ejpam-110	316	9	locally	locally	ADV
ejpam-110	316	10	compact	compact	ADJ
ejpam-110	316	11	hausdorff	hausdorff	NOUN
ejpam-110	316	12	l	l	ADJ
ejpam-110	316	13	-	-	ADJ
ejpam-110	316	14	topological	topological	ADJ
ejpam-110	316	15	space	space	NOUN
ejpam-110	316	16	which	which	PRON
ejpam-110	316	17	is	be	AUX
ejpam-110	316	18	not	not	PART
ejpam-110	316	19	compact	compact	ADJ
ejpam-110	316	20	,	,	PUNCT
ejpam-110	316	21	and	and	CCONJ
ejpam-110	316	22	let	let	VERB
ejpam-110	316	23	y	y	PRON
ejpam-110	316	24	,	,	PUNCT
ejpam-110	316	25	ty	ty	PRON
ejpam-110	316	26	�	�	PROPN
ejpam-110	316	27	be	be	AUX
ejpam-110	316	28	their	their	PRON
ejpam-110	316	29	one	one	NUM
ejpam-110	316	30	point	point	NOUN
ejpam-110	316	31	compactification	compactification	NOUN
ejpam-110	316	32	.	.	PUNCT
ejpam-110	317	1	then	then	ADV
ejpam-110	317	2	,	,	PUNCT
ejpam-110	317	3	y	y	PROPN
ejpam-110	317	4	,	,	PUNCT
ejpam-110	317	5	ty	ty	PRON
ejpam-110	317	6	�	�	PROPN
ejpam-110	317	7	is	be	AUX
ejpam-110	317	8	a	a	DET
ejpam-110	317	9	compact	compact	ADJ
ejpam-110	317	10	hausdorff	hausdorff	NOUN
ejpam-110	317	11	l	l	ADJ
ejpam-110	317	12	-	-	ADJ
ejpam-110	317	13	topological	topological	ADJ
ejpam-110	317	14	space	space	NOUN
ejpam-110	317	15	,	,	PUNCT
ejpam-110	317	16	cl(x	cl(x	X
ejpam-110	317	17	)	)	PUNCT
ejpam-110	318	1	=	=	SYM
ejpam-110	318	2	y	y	PROPN
ejpam-110	318	3	and	and	CCONJ
ejpam-110	318	4	x	x	INTJ
ejpam-110	318	5	,	,	PUNCT
ejpam-110	318	6	tx	tx	PROPN
ejpam-110	318	7	�	�	PROPN
ejpam-110	318	8	is	be	AUX
ejpam-110	318	9	a	a	DET
ejpam-110	318	10	subspace	subspace	NOUN
ejpam-110	318	11	of	of	ADP
ejpam-110	318	12	y	y	PROPN
ejpam-110	318	13	,	,	PUNCT
ejpam-110	318	14	ty	ty	PROPN
ejpam-110	318	15	�	�	PROPN
ejpam-110	318	16	.	.	PUNCT
ejpam-110	319	1	t.	t.	PROPN
ejpam-110	319	2	breuckmann	breuckmann	PROPN
ejpam-110	319	3	,	,	PUNCT
ejpam-110	319	4	s.	s.	PROPN
ejpam-110	319	5	kudri	kudri	PROPN
ejpam-110	319	6	,	,	PUNCT
ejpam-110	319	7	and	and	CCONJ
ejpam-110	319	8	h.	h.	PROPN
ejpam-110	319	9	aygün	aygün	PROPN
ejpam-110	319	10	/	/	SYM
ejpam-110	319	11	eur	eur	PROPN
ejpam-110	319	12	.	.	PUNCT
ejpam-110	320	1	j.	j.	PROPN
ejpam-110	320	2	pure	pure	PROPN
ejpam-110	320	3	appl	appl	PROPN
ejpam-110	320	4	.	.	PROPN
ejpam-110	320	5	math	math	PROPN
ejpam-110	320	6	,	,	PUNCT
ejpam-110	320	7	2	2	NUM
ejpam-110	320	8	(	(	PUNCT
ejpam-110	320	9	2009	2009	NUM
ejpam-110	320	10	)	)	PUNCT
ejpam-110	320	11	,	,	PUNCT
ejpam-110	320	12	(	(	PUNCT
ejpam-110	320	13	147	147	NUM
ejpam-110	320	14	-	-	SYM
ejpam-110	320	15	161	161	NUM
ejpam-110	320	16	)	)	PUNCT
ejpam-110	320	17	159	159	NUM
ejpam-110	320	18	proof	proof	NOUN
ejpam-110	320	19	.	.	PUNCT
ejpam-110	321	1	(	(	PUNCT
ejpam-110	321	2	i	i	NOUN
ejpam-110	321	3	)	)	PUNCT
ejpam-110	321	4	x	x	SYM
ejpam-110	321	5	,	,	PUNCT
ejpam-110	321	6	tx	tx	PROPN
ejpam-110	321	7	�	�	PROPN
ejpam-110	321	8	is	be	AUX
ejpam-110	321	9	a	a	DET
ejpam-110	321	10	subspace	subspace	NOUN
ejpam-110	321	11	of	of	ADP
ejpam-110	321	12	y	y	PROPN
ejpam-110	321	13	,	,	PUNCT
ejpam-110	321	14	ty	ty	PROPN
ejpam-110	321	15	�	�	PROPN
ejpam-110	321	16	.	.	PUNCT
ejpam-110	322	1	in	in	ADP
ejpam-110	322	2	fact	fact	NOUN
ejpam-110	322	3	,	,	PUNCT
ejpam-110	322	4	given	give	VERB
ejpam-110	322	5	g	g	PROPN
ejpam-110	322	6	∈	∈	PROPN
ejpam-110	322	7	ty	ty	INTJ
ejpam-110	322	8	,	,	PUNCT
ejpam-110	322	9	g|x	g|x	PROPN
ejpam-110	322	10	∈	∈	PROPN
ejpam-110	322	11	tx	tx	PROPN
ejpam-110	322	12	.	.	PUNCT
ejpam-110	323	1	(	(	PUNCT
ejpam-110	323	2	ii	ii	NOUN
ejpam-110	323	3	)	)	PUNCT
ejpam-110	323	4	cl(x	cl(x	X
ejpam-110	323	5	)	)	PUNCT
ejpam-110	324	1	=	=	PUNCT
ejpam-110	324	2	y	y	PROPN
ejpam-110	324	3	.	.	PUNCT
ejpam-110	325	1	in	in	ADP
ejpam-110	325	2	fact	fact	NOUN
ejpam-110	325	3	,	,	PUNCT
ejpam-110	325	4	if	if	SCONJ
ejpam-110	325	5	cl(x	cl(x	NOUN
ejpam-110	325	6	)	)	PUNCT
ejpam-110	325	7	6=	6=	ADP
ejpam-110	325	8	y	y	PROPN
ejpam-110	325	9	,	,	PUNCT
ejpam-110	325	10	then	then	ADV
ejpam-110	325	11	cl(x	cl(x	PUNCT
ejpam-110	325	12	)	)	PUNCT
ejpam-110	325	13	is	be	AUX
ejpam-110	325	14	an	an	DET
ejpam-110	325	15	l	l	NOUN
ejpam-110	325	16	-	-	NOUN
ejpam-110	325	17	set	set	NOUN
ejpam-110	325	18	of	of	ADP
ejpam-110	325	19	the	the	DET
ejpam-110	325	20	form	form	NOUN
ejpam-110	325	21	cl(x	cl(x	PUNCT
ejpam-110	325	22	)	)	PUNCT
ejpam-110	325	23	(	(	PUNCT
ejpam-110	325	24	y	y	NOUN
ejpam-110	325	25	)	)	PUNCT
ejpam-110	325	26	=	=	PUNCT
ejpam-110	326	1			PROPN
ejpam-110	326	2			X
ejpam-110	326	3			NOUN
ejpam-110	326	4	1	1	NUM
ejpam-110	326	5	if	if	SCONJ
ejpam-110	326	6	y	y	PROPN
ejpam-110	326	7	∈	∈	PROPN
ejpam-110	326	8	x	x	X
ejpam-110	326	9	l	l	NOUN
ejpam-110	326	10	6=	6=	NUM
ejpam-110	326	11	1	1	NUM
ejpam-110	326	12	if	if	SCONJ
ejpam-110	326	13	y	y	PROPN
ejpam-110	326	14	=	=	NOUN
ejpam-110	326	15	∞	∞	PROPN
ejpam-110	326	16	the	the	DET
ejpam-110	326	17	complement	complement	NOUN
ejpam-110	326	18	of	of	ADP
ejpam-110	326	19	cl(x	cl(x	NOUN
ejpam-110	326	20	)	)	PUNCT
ejpam-110	326	21	is	be	AUX
ejpam-110	326	22	the	the	DET
ejpam-110	326	23	open	open	ADJ
ejpam-110	326	24	l	l	NOUN
ejpam-110	326	25	-	-	ADJ
ejpam-110	326	26	set	set	VERB
ejpam-110	326	27	cl(x	cl(x	X
ejpam-110	326	28	)	)	PUNCT
ejpam-110	326	29	′(y	′(y	NOUN
ejpam-110	326	30	)	)	PUNCT
ejpam-110	326	31	=	=	PUNCT
ejpam-110	327	1			PROPN
ejpam-110	327	2			PRON
ejpam-110	327	3			NOUN
ejpam-110	327	4	0	0	PUNCT
ejpam-110	328	1	if	if	SCONJ
ejpam-110	328	2	y	y	PROPN
ejpam-110	328	3	∈	∈	PROPN
ejpam-110	328	4	x	x	X
ejpam-110	328	5	l′	l′	X
ejpam-110	328	6	6=	6=	NUM
ejpam-110	328	7	0	0	PUNCT
ejpam-110	329	1	if	if	SCONJ
ejpam-110	329	2	y	y	PROPN
ejpam-110	329	3	=	=	AUX
ejpam-110	329	4	∞	∞	PROPN
ejpam-110	329	5	let	let	VERB
ejpam-110	329	6	f	f	PROPN
ejpam-110	329	7	=	=	SYM
ejpam-110	329	8	χb1∞	χb1∞	PROPN
ejpam-110	329	9	∧	∧	PROPN
ejpam-110	329	10	·	·	PUNCT
ejpam-110	329	11	·	·	PUNCT
ejpam-110	329	12	·	·	PUNCT
ejpam-110	330	1	∧	∧	NOUN
ejpam-110	330	2	χbn∞	χbn∞	NOUN
ejpam-110	330	3	be	be	AUX
ejpam-110	330	4	a	a	DET
ejpam-110	330	5	basic	basic	ADJ
ejpam-110	330	6	open	open	ADJ
ejpam-110	330	7	l	l	NOUN
ejpam-110	330	8	-	-	NOUN
ejpam-110	330	9	set	set	VERB
ejpam-110	330	10	such	such	ADJ
ejpam-110	330	11	that	that	SCONJ
ejpam-110	330	12	f	f	PROPN
ejpam-110	330	13	≤	≤	PROPN
ejpam-110	330	14	cl(x	cl(x	PUNCT
ejpam-110	330	15	)	)	PUNCT
ejpam-110	331	1	′	′	ADP
ejpam-110	331	2	where	where	SCONJ
ejpam-110	331	3	b1	b1	NOUN
ejpam-110	331	4	,	,	PUNCT
ejpam-110	331	5	·	·	PUNCT
ejpam-110	331	6	·	·	PUNCT
ejpam-110	331	7	·	·	PUNCT
ejpam-110	331	8	,	,	PUNCT
ejpam-110	331	9	bn	bn	X
ejpam-110	331	10	are	be	AUX
ejpam-110	331	11	subsets	subset	NOUN
ejpam-110	331	12	of	of	ADP
ejpam-110	331	13	x	x	PUNCT
ejpam-110	331	14	with	with	ADP
ejpam-110	331	15	the	the	DET
ejpam-110	331	16	l	l	NOUN
ejpam-110	331	17	-	-	PUNCT
ejpam-110	331	18	sets	set	NOUN
ejpam-110	331	19	χb1	χb1	NOUN
ejpam-110	331	20	,	,	PUNCT
ejpam-110	331	21	·	·	PUNCT
ejpam-110	331	22	·	·	PUNCT
ejpam-110	331	23	·	·	PUNCT
ejpam-110	331	24	,	,	PUNCT
ejpam-110	331	25	χb1	χb1	PROPN
ejpam-110	331	26	compacts	compact	NOUN
ejpam-110	331	27	.	.	PUNCT
ejpam-110	332	1	we	we	PRON
ejpam-110	332	2	have	have	VERB
ejpam-110	332	3	for	for	ADP
ejpam-110	332	4	y	y	PROPN
ejpam-110	332	5	=	=	NOUN
ejpam-110	332	6	∞	∞	PROPN
ejpam-110	332	7	that	that	PRON
ejpam-110	333	1	f	f	PROPN
ejpam-110	333	2	(	(	PUNCT
ejpam-110	333	3	y	y	NOUN
ejpam-110	333	4	)	)	PUNCT
ejpam-110	333	5	=	=	SYM
ejpam-110	333	6	1≤	1≤	NUM
ejpam-110	333	7	l′	l′	NOUN
ejpam-110	333	8	,	,	PUNCT
ejpam-110	333	9	then	then	ADV
ejpam-110	333	10	l′	l′	VERB
ejpam-110	333	11	=	=	SYM
ejpam-110	333	12	1	1	NUM
ejpam-110	333	13	,	,	PUNCT
ejpam-110	333	14	so	so	ADV
ejpam-110	333	15	l	l	NOUN
ejpam-110	333	16	=	=	SYM
ejpam-110	334	1	0	0	X
ejpam-110	334	2	.	.	PUNCT
ejpam-110	335	1	we	we	PRON
ejpam-110	335	2	also	also	ADV
ejpam-110	335	3	have	have	VERB
ejpam-110	335	4	:	:	PUNCT
ejpam-110	335	5	f	f	PROPN
ejpam-110	335	6	≤	≤	PROPN
ejpam-110	335	7	cl(x	cl(x	PUNCT
ejpam-110	335	8	)	)	PUNCT
ejpam-110	336	1	′	′	NUM
ejpam-110	336	2	⇒	⇒	NOUN
ejpam-110	336	3	χb1∞	χb1∞	NOUN
ejpam-110	336	4	∧	∧	PROPN
ejpam-110	336	5	·	·	PUNCT
ejpam-110	336	6	·	·	PUNCT
ejpam-110	336	7	·	·	PUNCT
ejpam-110	336	8	∧χbn∞	∧χbn∞	VERB
ejpam-110	336	9	≤	≤	NOUN
ejpam-110	336	10	cl(x	cl(x	PUNCT
ejpam-110	336	11	)	)	PUNCT
ejpam-110	336	12	′	′	NUM
ejpam-110	336	13	⇒	⇒	NOUN
ejpam-110	336	14	cl(x	cl(x	PUNCT
ejpam-110	336	15	)	)	PUNCT
ejpam-110	336	16	≤	≤	PUNCT
ejpam-110	337	1	χ	χ	DET
ejpam-110	337	2	′b1∞	′b1∞	NOUN
ejpam-110	337	3	∨	∨	NUM
ejpam-110	337	4	·	·	PUNCT
ejpam-110	337	5	·	·	PUNCT
ejpam-110	337	6	·	·	PUNCT
ejpam-110	337	7	∨χ	∨χ	VERB
ejpam-110	337	8	′bn∞	′bn∞	PROPN
ejpam-110	337	9	.	.	PUNCT
ejpam-110	338	1	since	since	SCONJ
ejpam-110	338	2	x	x	PROPN
ejpam-110	338	3	≤	≤	X
ejpam-110	338	4	cl(x	cl(x	X
ejpam-110	338	5	)	)	PUNCT
ejpam-110	338	6	and	and	CCONJ
ejpam-110	338	7	χ	χ	X
ejpam-110	338	8	′bi∞	′bi∞	PROPN
ejpam-110	338	9	|x	|x	NOUN
ejpam-110	338	10	=	=	PUNCT
ejpam-110	338	11	χbi	χbi	NOUN
ejpam-110	338	12	we	we	PRON
ejpam-110	338	13	have	have	VERB
ejpam-110	338	14	x	x	NOUN
ejpam-110	338	15	≤	≤	X
ejpam-110	338	16	χb1	χb1	NOUN
ejpam-110	338	17	∨	∨	NUM
ejpam-110	338	18	·	·	PUNCT
ejpam-110	338	19	·	·	PUNCT
ejpam-110	338	20	·	·	PUNCT
ejpam-110	338	21	∨χbn	∨χbn	PROPN
ejpam-110	338	22	,	,	PUNCT
ejpam-110	338	23	thus	thus	ADV
ejpam-110	338	24	,	,	PUNCT
ejpam-110	338	25	x	x	SYM
ejpam-110	338	26	=	=	PRON
ejpam-110	338	27	χb1	χb1	PROPN
ejpam-110	338	28	∨	∨	NUM
ejpam-110	338	29	·	·	PUNCT
ejpam-110	338	30	·	·	PUNCT
ejpam-110	338	31	·	·	PUNCT
ejpam-110	338	32	∨χbn	∨χbn	ADJ
ejpam-110	338	33	.	.	PUNCT
ejpam-110	339	1	hence	hence	ADV
ejpam-110	339	2	,	,	PUNCT
ejpam-110	339	3	x	x	PRON
ejpam-110	339	4	is	be	AUX
ejpam-110	339	5	compact	compact	ADJ
ejpam-110	339	6	which	which	PRON
ejpam-110	339	7	leads	lead	VERB
ejpam-110	339	8	to	to	ADP
ejpam-110	339	9	a	a	DET
ejpam-110	339	10	contradiction	contradiction	NOUN
ejpam-110	339	11	.	.	PUNCT
ejpam-110	340	1	(	(	PUNCT
ejpam-110	340	2	iii	iii	X
ejpam-110	340	3	)	)	PUNCT
ejpam-110	340	4	y	y	PROPN
ejpam-110	340	5	,	,	PUNCT
ejpam-110	340	6	ty	ty	PRON
ejpam-110	340	7	�	�	PROPN
ejpam-110	340	8	is	be	AUX
ejpam-110	340	9	compact	compact	ADJ
ejpam-110	340	10	.	.	PUNCT
ejpam-110	341	1	in	in	ADP
ejpam-110	341	2	fact	fact	NOUN
ejpam-110	341	3	,	,	PUNCT
ejpam-110	341	4	let	let	VERB
ejpam-110	341	5	p	p	PRON
ejpam-110	341	6	∈	∈	NOUN
ejpam-110	341	7	pr(l	pr(l	NOUN
ejpam-110	341	8	)	)	PUNCT
ejpam-110	341	9	and	and	CCONJ
ejpam-110	341	10	b	b	X
ejpam-110	341	11	=	=	SYM
ejpam-110	341	12	¦	¦	PROPN
ejpam-110	341	13	f	f	PROPN
ejpam-110	341	14	j	j	PROPN
ejpam-110	341	15	©	©	PROPN
ejpam-110	341	16	j∈j	j∈j	PROPN
ejpam-110	341	17	be	be	AUX
ejpam-110	341	18	a	a	DET
ejpam-110	341	19	family	family	NOUN
ejpam-110	341	20	of	of	ADP
ejpam-110	341	21	subbasis	subbasis	VERB
ejpam-110	341	22	open	open	ADJ
ejpam-110	341	23	l	l	NOUN
ejpam-110	341	24	-	-	NOUN
ejpam-110	341	25	sets	set	NOUN
ejpam-110	341	26	with	with	ADP
ejpam-110	341	27	�	�	PROPN
ejpam-110	341	28	∨	∨	NUM
ejpam-110	341	29	j∈j	j∈j	PROPN
ejpam-110	341	30	f	f	PROPN
ejpam-110	341	31	j	j	PROPN
ejpam-110	341	32	�	�	PROPN
ejpam-110	341	33	(	(	PUNCT
ejpam-110	341	34	y	y	PROPN
ejpam-110	341	35	)	)	PUNCT
ejpam-110	341	36	�	�	PROPN
ejpam-110	341	37	p	p	PROPN
ejpam-110	341	38	for	for	ADP
ejpam-110	341	39	each	each	DET
ejpam-110	341	40	y	y	PROPN
ejpam-110	341	41	∈	∈	PROPN
ejpam-110	341	42	y	y	PROPN
ejpam-110	341	43	.	.	PUNCT
ejpam-110	342	1	then	then	ADV
ejpam-110	342	2	there	there	PRON
ejpam-110	342	3	is	be	VERB
ejpam-110	342	4	j	j	PROPN
ejpam-110	342	5	∈	∈	PROPN
ejpam-110	342	6	j	j	PROPN
ejpam-110	342	7	such	such	ADJ
ejpam-110	342	8	that	that	SCONJ
ejpam-110	342	9	f	f	PROPN
ejpam-110	342	10	j	j	PROPN
ejpam-110	342	11	=	=	SYM
ejpam-110	342	12	χb∞	χb∞	PROPN
ejpam-110	342	13	with	with	ADP
ejpam-110	342	14	b	b	PROPN
ejpam-110	342	15	⊂	⊂	PROPN
ejpam-110	342	16	x	x	X
ejpam-110	342	17	and	and	CCONJ
ejpam-110	342	18	χb	χb	ADP
ejpam-110	342	19	compact	compact	ADJ
ejpam-110	342	20	,	,	PUNCT
ejpam-110	342	21	since	since	SCONJ
ejpam-110	342	22	in	in	ADP
ejpam-110	342	23	the	the	DET
ejpam-110	342	24	other	other	ADJ
ejpam-110	342	25	side	side	NOUN
ejpam-110	342	26	,	,	PUNCT
ejpam-110	342	27	�	�	PROPN
ejpam-110	342	28	∨	∨	NUM
ejpam-110	342	29	j∈j	j∈j	PROPN
ejpam-110	342	30	f	f	PROPN
ejpam-110	342	31	j	j	PROPN
ejpam-110	342	32	�	�	PROPN
ejpam-110	342	33	(	(	PUNCT
ejpam-110	342	34	∞	∞	PROPN
ejpam-110	342	35	)	)	PUNCT
ejpam-110	343	1	=	=	PUNCT
ejpam-110	343	2	0≤	0≤	NUM
ejpam-110	344	1	p.	p.	NOUN
ejpam-110	344	2	let	let	VERB
ejpam-110	344	3	b1	b1	NOUN
ejpam-110	344	4	=	=	SYM
ejpam-110	344	5	¦	¦	PROPN
ejpam-110	344	6	f	f	PROPN
ejpam-110	344	7	j	j	PROPN
ejpam-110	344	8	|x	|x	PROPN
ejpam-110	344	9	©	©	PROPN
ejpam-110	344	10	j∈j1	j∈j1	PROPN
ejpam-110	344	11	where	where	SCONJ
ejpam-110	344	12	j1	j1	PROPN
ejpam-110	344	13	=	=	SYM
ejpam-110	344	14	¦	¦	PROPN
ejpam-110	344	15	j	j	PROPN
ejpam-110	344	16	∈	∈	PROPN
ejpam-110	344	17	j	j	PROPN
ejpam-110	344	18	;	;	PUNCT
ejpam-110	344	19	f	f	PROPN
ejpam-110	344	20	j	j	PROPN
ejpam-110	344	21	6=	6=	PROPN
ejpam-110	345	1	χb∞	χb∞	PROPN
ejpam-110	345	2	©	©	PROPN
ejpam-110	345	3	,	,	PUNCT
ejpam-110	345	4	then	then	ADV
ejpam-110	345	5	b1	b1	NOUN
ejpam-110	345	6	is	be	AUX
ejpam-110	345	7	such	such	ADJ
ejpam-110	345	8	that	that	SCONJ
ejpam-110	345	9	�	�	PROPN
ejpam-110	345	10	∨	∨	NUM
ejpam-110	345	11	j∈j1	j∈j1	PROPN
ejpam-110	345	12	f	f	PROPN
ejpam-110	345	13	j	j	PROPN
ejpam-110	345	14	|x	|x	PROPN
ejpam-110	345	15	�	�	PROPN
ejpam-110	345	16	(	(	PUNCT
ejpam-110	345	17	x	x	NOUN
ejpam-110	345	18	)	)	PUNCT
ejpam-110	345	19	�	�	PROPN
ejpam-110	345	20	p	p	PROPN
ejpam-110	345	21	for	for	ADP
ejpam-110	345	22	each	each	DET
ejpam-110	345	23	x	x	SYM
ejpam-110	345	24	∈	∈	PROPN
ejpam-110	345	25	x	x	PUNCT
ejpam-110	345	26	with	with	ADP
ejpam-110	345	27	χb(x)≥	χb(x)≥	NOUN
ejpam-110	345	28	p′.	p′.	NOUN
ejpam-110	345	29	since	since	SCONJ
ejpam-110	345	30	χb	χb	PRON
ejpam-110	345	31	is	be	AUX
ejpam-110	345	32	compact	compact	ADJ
ejpam-110	345	33	there	there	PRON
ejpam-110	345	34	is	be	VERB
ejpam-110	345	35	a	a	DET
ejpam-110	345	36	finite	finite	NOUN
ejpam-110	345	37	subset	subset	VERB
ejpam-110	345	38	j2	j2	PROPN
ejpam-110	345	39	of	of	ADP
ejpam-110	345	40	j1	j1	PROPN
ejpam-110	345	41	such	such	ADJ
ejpam-110	345	42	that	that	SCONJ
ejpam-110	345	43	�	�	PROPN
ejpam-110	345	44	∨	∨	NUM
ejpam-110	345	45	j∈j2	j∈j2	PROPN
ejpam-110	345	46	f	f	PROPN
ejpam-110	345	47	j	j	PROPN
ejpam-110	345	48	|x	|x	PROPN
ejpam-110	345	49	�	�	PROPN
ejpam-110	345	50	(	(	PUNCT
ejpam-110	345	51	x	x	NOUN
ejpam-110	345	52	)	)	PUNCT
ejpam-110	345	53	�	�	PROPN
ejpam-110	345	54	p	p	NOUN
ejpam-110	345	55	for	for	ADP
ejpam-110	345	56	each	each	DET
ejpam-110	345	57	x	x	SYM
ejpam-110	345	58	∈	∈	PROPN
ejpam-110	345	59	x	x	PUNCT
ejpam-110	345	60	with	with	ADP
ejpam-110	345	61	χb(x	χb(x	ADJ
ejpam-110	345	62	)	)	PUNCT
ejpam-110	345	63	≥	≥	NOUN
ejpam-110	345	64	p′.	p′.	NOUN
ejpam-110	345	65	then	then	ADV
ejpam-110	345	66	,	,	PUNCT
ejpam-110	345	67	�	�	PROPN
ejpam-110	345	68	χb∞	χb∞	PROPN
ejpam-110	345	69	∨∨	∨∨	ADJ
ejpam-110	345	70	j∈j2	j∈j2	PROPN
ejpam-110	345	71	f	f	PROPN
ejpam-110	345	72	j	j	PROPN
ejpam-110	345	73	�	�	PROPN
ejpam-110	345	74	(	(	PUNCT
ejpam-110	345	75	y	y	PROPN
ejpam-110	345	76	)	)	PUNCT
ejpam-110	345	77	�	�	PROPN
ejpam-110	345	78	p	p	PROPN
ejpam-110	345	79	for	for	ADP
ejpam-110	345	80	each	each	DET
ejpam-110	345	81	y	y	PROPN
ejpam-110	345	82	∈	∈	PROPN
ejpam-110	345	83	y	y	PROPN
ejpam-110	345	84	.	.	PUNCT
ejpam-110	346	1	hence	hence	ADV
ejpam-110	346	2	by	by	ADP
ejpam-110	346	3	proposition	proposition	NOUN
ejpam-110	346	4	2.5	2.5	NUM
ejpam-110	346	5	y	y	NOUN
ejpam-110	346	6	,	,	PUNCT
ejpam-110	346	7	ty	ty	PRON
ejpam-110	346	8	�	�	PROPN
ejpam-110	346	9	is	be	AUX
ejpam-110	346	10	compact	compact	ADJ
ejpam-110	346	11	.	.	PUNCT
ejpam-110	347	1	references	reference	NOUN
ejpam-110	347	2	160	160	NUM
ejpam-110	347	3	(	(	PUNCT
ejpam-110	347	4	iv	iv	X
ejpam-110	347	5	)	)	PUNCT
ejpam-110	347	6	y	y	PROPN
ejpam-110	347	7	,	,	PUNCT
ejpam-110	347	8	ty	ty	NUM
ejpam-110	347	9	�	�	PROPN
ejpam-110	347	10	ï£	ï£	ADJ
ejpam-110	347	11	¡	¡	PROPN
ejpam-110	347	12	hausdorff	hausdorff	NOUN
ejpam-110	347	13	.	.	PUNCT
ejpam-110	348	1	in	in	ADP
ejpam-110	348	2	fact	fact	NOUN
ejpam-110	348	3	,	,	PUNCT
ejpam-110	348	4	let	let	VERB
ejpam-110	348	5	x	x	PART
ejpam-110	348	6	�	�	PROPN
ejpam-110	348	7	y	y	PROPN
ejpam-110	348	8	in	in	ADP
ejpam-110	348	9	y	y	PROPN
ejpam-110	348	10	and	and	CCONJ
ejpam-110	348	11	p	p	X
ejpam-110	348	12	,	,	PUNCT
ejpam-110	348	13	q	q	NOUN
ejpam-110	348	14	∈	∈	NOUN
ejpam-110	348	15	pr(l	pr(l	NOUN
ejpam-110	348	16	)	)	PUNCT
ejpam-110	348	17	.	.	PUNCT
ejpam-110	349	1	if	if	SCONJ
ejpam-110	349	2	x	x	PRON
ejpam-110	349	3	,	,	PUNCT
ejpam-110	349	4	y	y	PROPN
ejpam-110	349	5	∈	∈	PROPN
ejpam-110	349	6	x	x	INTJ
ejpam-110	349	7	,	,	PUNCT
ejpam-110	349	8	since	since	SCONJ
ejpam-110	349	9	x	x	PRON
ejpam-110	349	10	is	be	AUX
ejpam-110	349	11	hausdorff	hausdorff	NOUN
ejpam-110	349	12	,	,	PUNCT
ejpam-110	349	13	there	there	PRON
ejpam-110	349	14	exist	exist	VERB
ejpam-110	349	15	f	f	NOUN
ejpam-110	349	16	,	,	PUNCT
ejpam-110	349	17	g	g	PROPN
ejpam-110	349	18	∈	∈	PROPN
ejpam-110	349	19	tx	tx	PROPN
ejpam-110	349	20	with	with	ADP
ejpam-110	349	21	f	f	PROPN
ejpam-110	349	22	(	(	PUNCT
ejpam-110	349	23	x	x	NOUN
ejpam-110	349	24	)	)	PUNCT
ejpam-110	349	25	�	�	PROPN
ejpam-110	349	26	p	p	PROPN
ejpam-110	349	27	,	,	PUNCT
ejpam-110	349	28	g(y	g(y	PROPN
ejpam-110	349	29	)	)	PUNCT
ejpam-110	349	30	�	�	PROPN
ejpam-110	349	31	q	q	PROPN
ejpam-110	349	32	,	,	PUNCT
ejpam-110	349	33	and	and	CCONJ
ejpam-110	349	34	,	,	PUNCT
ejpam-110	349	35	f	f	PROPN
ejpam-110	349	36	(	(	PUNCT
ejpam-110	349	37	z	z	NOUN
ejpam-110	349	38	)	)	PUNCT
ejpam-110	349	39	=	=	SYM
ejpam-110	349	40	0	0	NUM
ejpam-110	349	41	or	or	CCONJ
ejpam-110	349	42	g(z	g(z	ADJ
ejpam-110	349	43	)	)	PUNCT
ejpam-110	350	1	=	=	SYM
ejpam-110	350	2	0	0	NUM
ejpam-110	351	1	for	for	ADP
ejpam-110	351	2	each	each	DET
ejpam-110	351	3	z	z	NOUN
ejpam-110	351	4	∈	∈	PROPN
ejpam-110	351	5	x	x	X
ejpam-110	351	6	.	.	PUNCT
ejpam-110	352	1	then	then	ADV
ejpam-110	352	2	f1	f1	PROPN
ejpam-110	352	3	∈	∈	PROPN
ejpam-110	352	4	ty	ty	INTJ
ejpam-110	352	5	,	,	PUNCT
ejpam-110	352	6	g1	g1	PROPN
ejpam-110	352	7	∈	∈	PROPN
ejpam-110	352	8	ty	ty	INTJ
ejpam-110	352	9	,	,	PUNCT
ejpam-110	352	10	f1(x	f1(x	PROPN
ejpam-110	352	11	)	)	PUNCT
ejpam-110	352	12	=	=	SYM
ejpam-110	353	1	f	f	X
ejpam-110	353	2	(	(	PUNCT
ejpam-110	353	3	x	x	NOUN
ejpam-110	353	4	)	)	PUNCT
ejpam-110	353	5	�	�	PROPN
ejpam-110	353	6	p	p	PROPN
ejpam-110	353	7	,	,	PUNCT
ejpam-110	353	8	g1(y	g1(y	PROPN
ejpam-110	353	9	)	)	PUNCT
ejpam-110	353	10	=	=	SYM
ejpam-110	353	11	g(y	g(y	NOUN
ejpam-110	353	12	)	)	PUNCT
ejpam-110	353	13	�	�	PROPN
ejpam-110	353	14	q	q	PROPN
ejpam-110	353	15	,	,	PUNCT
ejpam-110	353	16	and	and	CCONJ
ejpam-110	353	17	,	,	PUNCT
ejpam-110	353	18	f1(z	f1(z	PROPN
ejpam-110	353	19	)	)	PUNCT
ejpam-110	353	20	=	=	SYM
ejpam-110	353	21	0	0	NUM
ejpam-110	353	22	or	or	CCONJ
ejpam-110	353	23	g1(z	g1(z	PROPN
ejpam-110	353	24	)	)	PUNCT
ejpam-110	353	25	=	=	SYM
ejpam-110	353	26	0	0	NUM
ejpam-110	353	27	for	for	ADP
ejpam-110	353	28	each	each	DET
ejpam-110	353	29	z	z	NOUN
ejpam-110	353	30	∈	∈	PROPN
ejpam-110	353	31	y	y	PROPN
ejpam-110	353	32	.	.	PUNCT
ejpam-110	354	1	if	if	SCONJ
ejpam-110	354	2	x	x	SYM
ejpam-110	354	3	∈	∈	PROPN
ejpam-110	354	4	x	x	X
ejpam-110	354	5	and	and	CCONJ
ejpam-110	354	6	y	y	PROPN
ejpam-110	354	7	=	=	SYM
ejpam-110	354	8	∞	∞	PROPN
ejpam-110	354	9	,	,	PUNCT
ejpam-110	354	10	since	since	SCONJ
ejpam-110	354	11	x	x	PRON
ejpam-110	354	12	is	be	AUX
ejpam-110	354	13	weakly	weakly	ADV
ejpam-110	354	14	locally	locally	ADV
ejpam-110	354	15	compact	compact	ADJ
ejpam-110	354	16	there	there	PRON
ejpam-110	354	17	are	be	VERB
ejpam-110	354	18	f	f	PROPN
ejpam-110	354	19	∈	∈	PROPN
ejpam-110	354	20	tx	tx	PROPN
ejpam-110	354	21	and	and	CCONJ
ejpam-110	354	22	k	k	PROPN
ejpam-110	354	23	∈	∈	PROPN
ejpam-110	355	1	lx	lx	ADV
ejpam-110	355	2	,	,	PUNCT
ejpam-110	355	3	with	with	ADP
ejpam-110	355	4	χsupp(k	χsupp(k	PROPN
ejpam-110	355	5	)	)	PUNCT
ejpam-110	355	6	compact	compact	ADJ
ejpam-110	355	7	,	,	PUNCT
ejpam-110	355	8	such	such	ADJ
ejpam-110	355	9	that	that	SCONJ
ejpam-110	355	10	f	f	PROPN
ejpam-110	355	11	(	(	PUNCT
ejpam-110	355	12	x	x	X
ejpam-110	355	13	)	)	PUNCT
ejpam-110	355	14	�	�	PROPN
ejpam-110	355	15	p	p	PROPN
ejpam-110	355	16	and	and	CCONJ
ejpam-110	355	17	f	f	PROPN
ejpam-110	355	18	≤	≤	PROPN
ejpam-110	355	19	k.	k.	PROPN
ejpam-110	355	20	let	let	VERB
ejpam-110	355	21	b	b	NOUN
ejpam-110	355	22	=	=	SYM
ejpam-110	355	23	supp(k	supp(k	PROPN
ejpam-110	355	24	)	)	PUNCT
ejpam-110	355	25	and	and	CCONJ
ejpam-110	355	26	f1(y	f1(y	NUM
ejpam-110	355	27	)	)	PUNCT
ejpam-110	355	28	=	=	PUNCT
ejpam-110	356	1			PROPN
ejpam-110	356	2			X
ejpam-110	356	3			ADJ
ejpam-110	356	4	f	f	PROPN
ejpam-110	356	5	(	(	PUNCT
ejpam-110	356	6	y	y	PROPN
ejpam-110	356	7	)	)	PUNCT
ejpam-110	356	8	if	if	SCONJ
ejpam-110	356	9	y	y	PROPN
ejpam-110	356	10	∈	∈	PROPN
ejpam-110	356	11	x	x	X
ejpam-110	356	12	0	0	PUNCT
ejpam-110	357	1	if	if	SCONJ
ejpam-110	357	2	y	y	PROPN
ejpam-110	357	3	=	=	NOUN
ejpam-110	357	4	∞	∞	PROPN
ejpam-110	357	5	then	then	ADV
ejpam-110	357	6	f1	f1	PROPN
ejpam-110	357	7	∈	∈	PROPN
ejpam-110	357	8	ty	ty	INTJ
ejpam-110	357	9	and	and	CCONJ
ejpam-110	357	10	χb∞	χb∞	PROPN
ejpam-110	357	11	∈	∈	PROPN
ejpam-110	358	1	ty	ty	INTJ
ejpam-110	358	2	.	.	PUNCT
ejpam-110	359	1	it	it	PRON
ejpam-110	359	2	follow	follow	VERB
ejpam-110	359	3	that	that	PRON
ejpam-110	359	4	f1(x	f1(x	NOUN
ejpam-110	359	5	)	)	PUNCT
ejpam-110	360	1	=	=	SYM
ejpam-110	360	2	f	f	X
ejpam-110	360	3	(	(	PUNCT
ejpam-110	360	4	x	x	NOUN
ejpam-110	360	5	)	)	PUNCT
ejpam-110	360	6	�	�	PROPN
ejpam-110	360	7	p	p	PROPN
ejpam-110	360	8	and	and	CCONJ
ejpam-110	360	9	χb∞	χb∞	PROPN
ejpam-110	360	10	(	(	PUNCT
ejpam-110	360	11	y	y	NOUN
ejpam-110	360	12	)	)	PUNCT
ejpam-110	360	13	=	=	SYM
ejpam-110	360	14	1	1	NUM
ejpam-110	360	15	�	�	PROPN
ejpam-110	360	16	q.	q.	PROPN
ejpam-110	360	17	also	also	ADV
ejpam-110	360	18	:	:	PUNCT
ejpam-110	360	19	(	(	PUNCT
ejpam-110	360	20	a	a	X
ejpam-110	360	21	)	)	PUNCT
ejpam-110	360	22	z	z	NOUN
ejpam-110	360	23	∈	∈	PROPN
ejpam-110	361	1	b⇒	b⇒	PROPN
ejpam-110	361	2	χb∞	χb∞	PROPN
ejpam-110	362	1	(	(	PUNCT
ejpam-110	362	2	z	z	NOUN
ejpam-110	362	3	)	)	PUNCT
ejpam-110	362	4	=	=	SYM
ejpam-110	362	5	0	0	PUNCT
ejpam-110	362	6	(	(	PUNCT
ejpam-110	362	7	b	b	NOUN
ejpam-110	362	8	)	)	PUNCT
ejpam-110	362	9	z	z	NOUN
ejpam-110	362	10	∈	∈	PROPN
ejpam-110	362	11	x	x	X
ejpam-110	363	1	−	−	NOUN
ejpam-110	363	2	b	b	X
ejpam-110	363	3	=	=	SYM
ejpam-110	363	4	x	x	SYM
ejpam-110	363	5	−	−	NOUN
ejpam-110	363	6	supp	supp	NOUN
ejpam-110	363	7	(	(	PUNCT
ejpam-110	363	8	f	f	NOUN
ejpam-110	363	9	)	)	PUNCT
ejpam-110	363	10	⇒	⇒	PROPN
ejpam-110	363	11	f	f	PROPN
ejpam-110	363	12	(	(	PUNCT
ejpam-110	363	13	z	z	NOUN
ejpam-110	363	14	)	)	PUNCT
ejpam-110	363	15	=	=	SYM
ejpam-110	363	16	0⇒	0⇒	NUM
ejpam-110	363	17	f1(z	f1(z	PROPN
ejpam-110	363	18	)	)	PUNCT
ejpam-110	363	19	=	=	SYM
ejpam-110	363	20	f	f	X
ejpam-110	363	21	(	(	PUNCT
ejpam-110	363	22	z	z	NOUN
ejpam-110	363	23	)	)	PUNCT
ejpam-110	363	24	=	=	SYM
ejpam-110	363	25	0	0	PUNCT
ejpam-110	363	26	(	(	PUNCT
ejpam-110	363	27	c	c	NOUN
ejpam-110	363	28	)	)	PUNCT
ejpam-110	363	29	z	z	NOUN
ejpam-110	364	1	=	=	SYM
ejpam-110	364	2	∞⇒	∞⇒	PROPN
ejpam-110	364	3	f1(z	f1(z	PROPN
ejpam-110	364	4	)	)	PUNCT
ejpam-110	364	5	=	=	SYM
ejpam-110	364	6	0	0	PUNCT
ejpam-110	364	7	hence	hence	ADV
ejpam-110	364	8	for	for	ADP
ejpam-110	364	9	each	each	DET
ejpam-110	364	10	z	z	NOUN
ejpam-110	364	11	∈	∈	PROPN
ejpam-110	364	12	y	y	PROPN
ejpam-110	364	13	,	,	PUNCT
ejpam-110	364	14	f1(z	f1(z	PROPN
ejpam-110	364	15	)	)	PUNCT
ejpam-110	364	16	=	=	SYM
ejpam-110	364	17	0	0	NUM
ejpam-110	364	18	or	or	CCONJ
ejpam-110	364	19	χb∞	χb∞	PROPN
ejpam-110	364	20	(	(	PUNCT
ejpam-110	364	21	z	z	NOUN
ejpam-110	364	22	)	)	PUNCT
ejpam-110	365	1	=	=	SYM
ejpam-110	365	2	0	0	X
ejpam-110	365	3	.	.	PUNCT
ejpam-110	366	1	these	these	DET
ejpam-110	366	2	conditions	condition	NOUN
ejpam-110	366	3	proof	proof	VERB
ejpam-110	366	4	the	the	DET
ejpam-110	366	5	theorem	theorem	NOUN
ejpam-110	366	6	.	.	PUNCT
ejpam-110	367	1	by	by	ADP
ejpam-110	367	2	an	an	DET
ejpam-110	367	3	analogous	analogous	ADJ
ejpam-110	367	4	way	way	NOUN
ejpam-110	367	5	we	we	PRON
ejpam-110	367	6	can	can	AUX
ejpam-110	367	7	obtain	obtain	VERB
ejpam-110	367	8	one	one	NUM
ejpam-110	367	9	point	point	NOUN
ejpam-110	367	10	compactification	compactification	NOUN
ejpam-110	367	11	theorems	theorem	VERB
ejpam-110	367	12	for	for	ADP
ejpam-110	367	13	locally	locally	ADV
ejpam-110	367	14	compact	compact	ADJ
ejpam-110	367	15	an	an	DET
ejpam-110	367	16	relatively	relatively	ADV
ejpam-110	367	17	locally	locally	ADV
ejpam-110	367	18	compact	compact	ADJ
ejpam-110	367	19	spaces	space	NOUN
ejpam-110	367	20	since	since	SCONJ
ejpam-110	367	21	by	by	ADP
ejpam-110	367	22	theorems	theorem	NOUN
ejpam-110	367	23	4.4	4.4	NUM
ejpam-110	367	24	and	and	CCONJ
ejpam-110	367	25	4.7	4.7	NUM
ejpam-110	367	26	these	these	DET
ejpam-110	367	27	space	space	NOUN
ejpam-110	367	28	are	be	AUX
ejpam-110	367	29	weakly	weakly	ADV
ejpam-110	367	30	locally	locally	ADV
ejpam-110	367	31	compact	compact	ADJ
ejpam-110	367	32	.	.	PUNCT
ejpam-110	368	1	references	reference	NOUN
ejpam-110	368	2	[	[	X
ejpam-110	368	3	1	1	NUM
ejpam-110	368	4	]	]	PUNCT
ejpam-110	368	5	g.	g.	PROPN
ejpam-110	368	6	gierz	gierz	PROPN
ejpam-110	368	7	et	et	PROPN
ejpam-110	368	8	al	al	PROPN
ejpam-110	368	9	.	.	PROPN
ejpam-110	368	10	,	,	PUNCT
ejpam-110	368	11	a	a	DET
ejpam-110	368	12	compendium	compendium	NOUN
ejpam-110	368	13	of	of	ADP
ejpam-110	368	14	continuous	continuous	ADJ
ejpam-110	368	15	lattices	lattice	NOUN
ejpam-110	368	16	,	,	PUNCT
ejpam-110	368	17	springer	springer	NOUN
ejpam-110	368	18	-	-	PUNCT
ejpam-110	368	19	verlag	verlag	PROPN
ejpam-110	368	20	,	,	PUNCT
ejpam-110	368	21	1980	1980	NUM
ejpam-110	368	22	.	.	PUNCT
ejpam-110	369	1	[	[	X
ejpam-110	369	2	2	2	NUM
ejpam-110	369	3	]	]	PUNCT
ejpam-110	369	4	s.r.t	s.r.t	PROPN
ejpam-110	369	5	.	.	PUNCT
ejpam-110	369	6	kudri	kudri	PROPN
ejpam-110	369	7	.	.	PUNCT
ejpam-110	370	1	“	"	PUNCT
ejpam-110	370	2	compacness	compacness	NOUN
ejpam-110	370	3	in	in	ADP
ejpam-110	370	4	l	l	ADJ
ejpam-110	370	5	-	-	ADJ
ejpam-110	370	6	fuzzy	fuzzy	ADJ
ejpam-110	370	7	topological	topological	ADJ
ejpam-110	370	8	spaces	space	NOUN
ejpam-110	370	9	”	"	PUNCT
ejpam-110	370	10	,	,	PUNCT
ejpam-110	370	11	fuzzy	fuzzy	ADJ
ejpam-110	370	12	sets	set	NOUN
ejpam-110	370	13	and	and	CCONJ
ejpam-110	370	14	systems	system	NOUN
ejpam-110	370	15	67	67	NUM
ejpam-110	370	16	,	,	PUNCT
ejpam-110	370	17	(	(	PUNCT
ejpam-110	370	18	1994	1994	NUM
ejpam-110	370	19	)	)	PUNCT
ejpam-110	370	20	329	329	NUM
ejpam-110	370	21	-	-	SYM
ejpam-110	370	22	446	446	NUM
ejpam-110	370	23	.	.	PUNCT
ejpam-110	371	1	[	[	X
ejpam-110	371	2	3	3	NUM
ejpam-110	371	3	]	]	X
ejpam-110	371	4	s.r.t	s.r.t	PROPN
ejpam-110	371	5	.	.	PUNCT
ejpam-110	371	6	kudri	kudri	PROPN
ejpam-110	371	7	.	.	PUNCT
ejpam-110	372	1	“	"	PUNCT
ejpam-110	372	2	l	l	ADJ
ejpam-110	372	3	-	-	ADJ
ejpam-110	372	4	fuzzy	fuzzy	ADJ
ejpam-110	372	5	local	local	ADJ
ejpam-110	372	6	compactness	compactness	NOUN
ejpam-110	372	7	”	"	PUNCT
ejpam-110	372	8	,	,	PUNCT
ejpam-110	372	9	fuzzy	fuzzy	ADJ
ejpam-110	372	10	sets	set	NOUN
ejpam-110	372	11	and	and	CCONJ
ejpam-110	372	12	systems	system	NOUN
ejpam-110	372	13	67	67	NUM
ejpam-110	372	14	,	,	PUNCT
ejpam-110	372	15	(	(	PUNCT
ejpam-110	372	16	1994	1994	NUM
ejpam-110	372	17	)	)	PUNCT
ejpam-110	372	18	337	337	NUM
ejpam-110	372	19	-	-	SYM
ejpam-110	372	20	345	345	NUM
ejpam-110	372	21	.	.	PUNCT
ejpam-110	373	1	[	[	X
ejpam-110	373	2	4	4	NUM
ejpam-110	373	3	]	]	SYM
ejpam-110	373	4	p.m.	p.m.	NOUN
ejpam-110	373	5	piu	piu	PROPN
ejpam-110	373	6	,	,	PUNCT
ejpam-110	373	7	y.m	y.m	PROPN
ejpam-110	373	8	.	.	PROPN
ejpam-110	373	9	liu	liu	PROPN
ejpam-110	373	10	,	,	PUNCT
ejpam-110	373	11	“	"	PUNCT
ejpam-110	373	12	fuzzy	fuzzy	ADJ
ejpam-110	373	13	topology	topology	NOUN
ejpam-110	373	14	i	i	NOUN
ejpam-110	373	15	,	,	PUNCT
ejpam-110	373	16	neighbourhood	neighbourhood	NOUN
ejpam-110	373	17	structure	structure	NOUN
ejpam-110	373	18	of	of	ADP
ejpam-110	373	19	a	a	DET
ejpam-110	373	20	fuzzy	fuzzy	ADJ
ejpam-110	373	21	point	point	NOUN
ejpam-110	373	22	and	and	CCONJ
ejpam-110	373	23	moore	moore	PROPN
ejpam-110	373	24	-	-	PUNCT
ejpam-110	373	25	smith	smith	PROPN
ejpam-110	373	26	convergence	convergence	NOUN
ejpam-110	373	27	”	"	PUNCT
ejpam-110	373	28	,	,	PUNCT
ejpam-110	373	29	j.math.anal.appl	j.math.anal.appl	NOUN
ejpam-110	373	30	.	.	PUNCT
ejpam-110	374	1	76	76	NUM
ejpam-110	374	2	,	,	PUNCT
ejpam-110	374	3	(	(	PUNCT
ejpam-110	374	4	1980	1980	NUM
ejpam-110	374	5	)	)	PUNCT
ejpam-110	374	6	references	reference	NOUN
ejpam-110	374	7	161	161	NUM
ejpam-110	374	8	[	[	SYM
ejpam-110	374	9	5	5	NUM
ejpam-110	374	10	]	]	PUNCT
ejpam-110	374	11	m.	m.	NOUN
ejpam-110	374	12	w.	w.	PROPN
ejpam-110	374	13	warner	warner	PROPN
ejpam-110	374	14	and	and	CCONJ
ejpam-110	374	15	r.	r.	PROPN
ejpam-110	374	16	g.	g.	PROPN
ejpam-110	374	17	mclean	mclean	PROPN
ejpam-110	374	18	,	,	PUNCT
ejpam-110	374	19	“	"	PUNCT
ejpam-110	374	20	on	on	ADP
ejpam-110	374	21	compact	compact	ADJ
ejpam-110	374	22	hausdorff	hausdorff	NOUN
ejpam-110	374	23	l	l	ADJ
ejpam-110	374	24	-	-	ADJ
ejpam-110	374	25	fuzzy	fuzzy	ADJ
ejpam-110	374	26	spaces	space	NOUN
ejpam-110	374	27	”	"	PUNCT
ejpam-110	374	28	,	,	PUNCT
ejpam-110	374	29	fuzzy	fuzzy	ADJ
ejpam-110	374	30	sets	set	NOUN
ejpam-110	374	31	and	and	CCONJ
ejpam-110	374	32	systems	system	NOUN
ejpam-110	374	33	56	56	NUM
ejpam-110	374	34	,	,	PUNCT
ejpam-110	374	35	(	(	PUNCT
ejpam-110	374	36	1993	1993	NUM
ejpam-110	374	37	)	)	PUNCT
ejpam-110	374	38	103	103	NUM
ejpam-110	374	39	-	-	SYM
ejpam-110	374	40	110	110	NUM
ejpam-110	374	41	.	.	PUNCT
ejpam-110	375	1	[	[	X
ejpam-110	375	2	6	6	NUM
ejpam-110	375	3	]	]	X
ejpam-110	375	4	m.w	m.w	PROPN
ejpam-110	375	5	.	.	PUNCT
ejpam-110	375	6	warner	warner	PROPN
ejpam-110	375	7	,	,	PUNCT
ejpam-110	375	8	frame	frame	NOUN
ejpam-110	375	9	-	-	PUNCT
ejpam-110	375	10	fuzzy	fuzzy	ADJ
ejpam-110	375	11	points	point	NOUN
ejpam-110	375	12	and	and	CCONJ
ejpam-110	375	13	memberschip	memberschip	NOUN
ejpam-110	375	14	,	,	PUNCT
ejpam-110	375	15	fuzzy	fuzzy	ADJ
ejpam-110	375	16	sets	set	NOUN
ejpam-110	375	17	and	and	CCONJ
ejpam-110	375	18	systems	system	NOUN
ejpam-110	375	19	42	42	NUM
ejpam-110	375	20	(	(	PUNCT
ejpam-110	375	21	1991	1991	NUM
ejpam-110	375	22	)	)	PUNCT
ejpam-110	375	23	335	335	NUM
ejpam-110	375	24	-	-	SYM
ejpam-110	375	25	344	344	NUM
ejpam-110	375	26	.	.	PUNCT
ejpam-110	376	1	[	[	X
ejpam-110	376	2	7	7	X
ejpam-110	376	3	]	]	X
ejpam-110	376	4	m.w	m.w	PROPN
ejpam-110	376	5	.	.	PUNCT
ejpam-110	376	6	warner	warner	PROPN
ejpam-110	376	7	,	,	PUNCT
ejpam-110	376	8	fuzzy	fuzzy	ADJ
ejpam-110	376	9	topology	topology	NOUN
ejpam-110	376	10	with	with	ADP
ejpam-110	376	11	respect	respect	NOUN
ejpam-110	376	12	to	to	ADP
ejpam-110	376	13	continuous	continuous	ADJ
ejpam-110	376	14	lattices	lattice	NOUN
ejpam-110	376	15	,	,	PUNCT
ejpam-110	376	16	fuzzy	fuzzy	ADJ
ejpam-110	376	17	sets	set	NOUN
ejpam-110	376	18	and	and	CCONJ
ejpam-110	376	19	systems	system	NOUN
ejpam-110	376	20	35	35	NUM
ejpam-110	376	21	(	(	PUNCT
ejpam-110	376	22	1990	1990	NUM
ejpam-110	376	23	)	)	PUNCT
ejpam-110	376	24	85	85	NUM
ejpam-110	376	25	-	-	SYM
ejpam-110	376	26	91	91	NUM
ejpam-110	376	27	.	.	PUNCT