id	sid	tid	token	lemma	pos
ejpam-6597	1	1	european	european	PROPN
ejpam-6597	1	2	journal	journal	PROPN
ejpam-6597	1	3	of	of	ADP
ejpam-6597	1	4	pure	pure	ADJ
ejpam-6597	1	5	and	and	CCONJ
ejpam-6597	1	6	applied	applied	ADJ
ejpam-6597	1	7	mathematics	mathematic	NOUN
ejpam-6597	1	8	2025	2025	NUM
ejpam-6597	1	9	,	,	PUNCT
ejpam-6597	1	10	vol	vol	NOUN
ejpam-6597	1	11	.	.	PROPN
ejpam-6597	1	12	18	18	NUM
ejpam-6597	1	13	,	,	PUNCT
ejpam-6597	1	14	issue	issue	NOUN
ejpam-6597	1	15	4	4	NUM
ejpam-6597	1	16	,	,	PUNCT
ejpam-6597	1	17	article	article	NOUN
ejpam-6597	1	18	number	number	NOUN
ejpam-6597	1	19	6597	6597	NUM
ejpam-6597	1	20	issn	issn	PROPN
ejpam-6597	1	21	1307	1307	NUM
ejpam-6597	1	22	-	-	SYM
ejpam-6597	1	23	5543	5543	NUM
ejpam-6597	1	24	–	–	PUNCT
ejpam-6597	1	25	ejpam.com	ejpam.com	X
ejpam-6597	1	26	published	publish	VERB
ejpam-6597	1	27	by	by	ADP
ejpam-6597	1	28	new	new	PROPN
ejpam-6597	1	29	york	york	PROPN
ejpam-6597	1	30	business	business	PROPN
ejpam-6597	1	31	global	global	PROPN
ejpam-6597	1	32	collectionwise	collectionwise	PROPN
ejpam-6597	1	33	pre	pre	PROPN
ejpam-6597	1	34	-	-	NOUN
ejpam-6597	1	35	normality	normality	ADJ
ejpam-6597	1	36	in	in	ADP
ejpam-6597	1	37	topological	topological	ADJ
ejpam-6597	1	38	spaces	space	NOUN
ejpam-6597	1	39	sadeq	sadeq	VERB
ejpam-6597	1	40	ali	ali	PROPN
ejpam-6597	1	41	thabit1,∗	thabit1,∗	PROPN
ejpam-6597	1	42	,	,	PUNCT
ejpam-6597	1	43	alyaa	alyaa	PROPN
ejpam-6597	1	44	al	al	PROPN
ejpam-6597	1	45	-	-	PUNCT
ejpam-6597	1	46	awadi2,3,∗	awadi2,3,∗	PROPN
ejpam-6597	1	47	,	,	PUNCT
ejpam-6597	1	48	rafiqa	rafiqa	VERB
ejpam-6597	1	49	noaman1	noaman1	ADV
ejpam-6597	1	50	1	1	NUM
ejpam-6597	1	51	department	department	NOUN
ejpam-6597	1	52	of	of	ADP
ejpam-6597	1	53	mathematics	mathematic	NOUN
ejpam-6597	1	54	,	,	PUNCT
ejpam-6597	1	55	faculty	faculty	NOUN
ejpam-6597	1	56	of	of	ADP
ejpam-6597	1	57	applied	apply	VERB
ejpam-6597	1	58	and	and	CCONJ
ejpam-6597	1	59	health	health	NOUN
ejpam-6597	1	60	sciences	sciences	PROPN
ejpam-6597	1	61	,	,	PUNCT
ejpam-6597	1	62	mahrah	mahrah	PROPN
ejpam-6597	1	63	university	university	PROPN
ejpam-6597	1	64	,	,	PUNCT
ejpam-6597	1	65	yemen	yemen	PROPN
ejpam-6597	1	66	2	2	NUM
ejpam-6597	1	67	department	department	NOUN
ejpam-6597	1	68	of	of	ADP
ejpam-6597	1	69	mathematics	mathematic	NOUN
ejpam-6597	1	70	and	and	CCONJ
ejpam-6597	1	71	statistics	statistic	NOUN
ejpam-6597	1	72	,	,	PUNCT
ejpam-6597	1	73	faculty	faculty	NOUN
ejpam-6597	1	74	of	of	ADP
ejpam-6597	1	75	science	science	NOUN
ejpam-6597	1	76	,	,	PUNCT
ejpam-6597	1	77	university	university	NOUN
ejpam-6597	1	78	of	of	ADP
ejpam-6597	1	79	jeddah	jeddah	PROPN
ejpam-6597	1	80	,	,	PUNCT
ejpam-6597	1	81	jeddah	jeddah	PROPN
ejpam-6597	1	82	,	,	PUNCT
ejpam-6597	1	83	saudi	saudi	PROPN
ejpam-6597	1	84	arabia	arabia	PROPN
ejpam-6597	1	85	3	3	NUM
ejpam-6597	1	86	department	department	NOUN
ejpam-6597	1	87	of	of	ADP
ejpam-6597	1	88	mathematics	mathematic	NOUN
ejpam-6597	1	89	,	,	PUNCT
ejpam-6597	1	90	faculty	faculty	NOUN
ejpam-6597	1	91	of	of	ADP
ejpam-6597	1	92	education	education	NOUN
ejpam-6597	1	93	,	,	PUNCT
ejpam-6597	1	94	mahrah	mahrah	PROPN
ejpam-6597	1	95	university	university	PROPN
ejpam-6597	1	96	,	,	PUNCT
ejpam-6597	1	97	yemen	yemen	PROPN
ejpam-6597	1	98	abstract	abstract	NOUN
ejpam-6597	1	99	.	.	PUNCT
ejpam-6597	2	1	this	this	DET
ejpam-6597	2	2	paper	paper	NOUN
ejpam-6597	2	3	introduces	introduce	NOUN
ejpam-6597	2	4	and	and	CCONJ
ejpam-6597	2	5	studies	study	NOUN
ejpam-6597	2	6	a	a	DET
ejpam-6597	2	7	new	new	ADJ
ejpam-6597	2	8	topological	topological	ADJ
ejpam-6597	2	9	property	property	NOUN
ejpam-6597	2	10	called	call	VERB
ejpam-6597	2	11	collectionwise	collectionwise	PROPN
ejpam-6597	2	12	prenormality	prenormality	NOUN
ejpam-6597	2	13	.	.	PUNCT
ejpam-6597	3	1	a	a	DET
ejpam-6597	3	2	space	space	NOUN
ejpam-6597	3	3	x	x	PUNCT
ejpam-6597	3	4	is	be	AUX
ejpam-6597	3	5	said	say	VERB
ejpam-6597	3	6	to	to	PART
ejpam-6597	3	7	be	be	AUX
ejpam-6597	3	8	collectionwise	collectionwise	ADV
ejpam-6597	3	9	pre	pre	ADJ
ejpam-6597	3	10	-	-	ADJ
ejpam-6597	3	11	normal	normal	ADJ
ejpam-6597	3	12	if	if	SCONJ
ejpam-6597	3	13	and	and	CCONJ
ejpam-6597	3	14	only	only	ADV
ejpam-6597	3	15	if	if	SCONJ
ejpam-6597	3	16	x	x	PRON
ejpam-6597	3	17	is	be	AUX
ejpam-6597	3	18	t1	t1	NOUN
ejpam-6597	3	19	and	and	CCONJ
ejpam-6597	3	20	for	for	ADP
ejpam-6597	3	21	every	every	DET
ejpam-6597	3	22	discrete	discrete	ADJ
ejpam-6597	3	23	family	family	NOUN
ejpam-6597	3	24	f	f	PROPN
ejpam-6597	4	1	=	=	PRON
ejpam-6597	4	2	{	{	PUNCT
ejpam-6597	4	3	fs}s∈s	fs}s∈s	X
ejpam-6597	4	4	of	of	ADP
ejpam-6597	4	5	closed	closed	ADJ
ejpam-6597	4	6	subsets	subset	NOUN
ejpam-6597	4	7	of	of	ADP
ejpam-6597	4	8	x	x	PRON
ejpam-6597	4	9	,	,	PUNCT
ejpam-6597	4	10	there	there	PRON
ejpam-6597	4	11	exists	exist	VERB
ejpam-6597	4	12	a	a	DET
ejpam-6597	4	13	discrete	discrete	ADJ
ejpam-6597	4	14	family	family	NOUN
ejpam-6597	4	15	u	u	NOUN
ejpam-6597	4	16	=	=	PUNCT
ejpam-6597	4	17	{	{	PUNCT
ejpam-6597	4	18	us}s∈s	us}s∈s	PROPN
ejpam-6597	4	19	of	of	ADP
ejpam-6597	4	20	pre	pre	ADJ
ejpam-6597	4	21	-	-	ADJ
ejpam-6597	4	22	open	open	ADJ
ejpam-6597	4	23	subsets	subset	NOUN
ejpam-6597	4	24	of	of	ADP
ejpam-6597	4	25	x	x	SYM
ejpam-6597	4	26	such	such	ADJ
ejpam-6597	4	27	that	that	PRON
ejpam-6597	4	28	fs	fs	ADP
ejpam-6597	4	29	⊆	⊆	NUM
ejpam-6597	4	30	us	we	PRON
ejpam-6597	4	31	for	for	ADP
ejpam-6597	4	32	each	each	DET
ejpam-6597	4	33	s	s	PART
ejpam-6597	4	34	∈	∈	PROPN
ejpam-6597	4	35	s.	s.	PROPN
ejpam-6597	4	36	we	we	PRON
ejpam-6597	4	37	investigate	investigate	VERB
ejpam-6597	4	38	this	this	DET
ejpam-6597	4	39	property	property	NOUN
ejpam-6597	4	40	and	and	CCONJ
ejpam-6597	4	41	present	present	ADJ
ejpam-6597	4	42	examples	example	NOUN
ejpam-6597	4	43	that	that	PRON
ejpam-6597	4	44	illustrate	illustrate	VERB
ejpam-6597	4	45	its	its	PRON
ejpam-6597	4	46	relationship	relationship	NOUN
ejpam-6597	4	47	with	with	ADP
ejpam-6597	4	48	other	other	ADJ
ejpam-6597	4	49	known	know	VERB
ejpam-6597	4	50	topological	topological	ADJ
ejpam-6597	4	51	properties	property	NOUN
ejpam-6597	4	52	.	.	PUNCT
ejpam-6597	5	1	2020	2020	NUM
ejpam-6597	5	2	mathematics	mathematic	NOUN
ejpam-6597	5	3	subject	subject	NOUN
ejpam-6597	5	4	classifications	classification	NOUN
ejpam-6597	5	5	:	:	PUNCT
ejpam-6597	5	6	54c10	54c10	NUM
ejpam-6597	5	7	,	,	PUNCT
ejpam-6597	5	8	54d10	54d10	NUM
ejpam-6597	5	9	,	,	PUNCT
ejpam-6597	5	10	54d20	54d20	NUM
ejpam-6597	5	11	,	,	PUNCT
ejpam-6597	5	12	54d15	54d15	NUM
ejpam-6597	5	13	,	,	PUNCT
ejpam-6597	5	14	54d70	54d70	NUM
ejpam-6597	5	15	key	key	ADJ
ejpam-6597	5	16	words	word	NOUN
ejpam-6597	5	17	and	and	CCONJ
ejpam-6597	5	18	phrases	phrase	NOUN
ejpam-6597	5	19	:	:	PUNCT
ejpam-6597	5	20	normal	normal	ADJ
ejpam-6597	5	21	,	,	PUNCT
ejpam-6597	5	22	collectionwise	collectionwise	ADV
ejpam-6597	5	23	normal	normal	ADJ
ejpam-6597	5	24	,	,	PUNCT
ejpam-6597	5	25	paracompact	paracompact	ADJ
ejpam-6597	5	26	,	,	PUNCT
ejpam-6597	5	27	pre	pre	ADJ
ejpam-6597	5	28	-	-	ADJ
ejpam-6597	5	29	normal	normal	ADJ
ejpam-6597	5	30	,	,	PUNCT
ejpam-6597	5	31	discrete	discrete	ADJ
ejpam-6597	5	32	family	family	NOUN
ejpam-6597	5	33	,	,	PUNCT
ejpam-6597	5	34	p1	p1	NOUN
ejpam-6597	5	35	-	-	PUNCT
ejpam-6597	5	36	paracompact	paracompact	ADJ
ejpam-6597	5	37	,	,	PUNCT
ejpam-6597	5	38	sub	sub	ADJ
ejpam-6597	5	39	-	-	ADJ
ejpam-6597	5	40	maximal	maximal	ADJ
ejpam-6597	5	41	1	1	NUM
ejpam-6597	5	42	.	.	PUNCT
ejpam-6597	5	43	introduction	introduction	NOUN
ejpam-6597	5	44	in	in	ADP
ejpam-6597	5	45	this	this	DET
ejpam-6597	5	46	paper	paper	NOUN
ejpam-6597	5	47	,	,	PUNCT
ejpam-6597	5	48	we	we	PRON
ejpam-6597	5	49	introduce	introduce	VERB
ejpam-6597	5	50	and	and	CCONJ
ejpam-6597	5	51	study	study	VERB
ejpam-6597	5	52	a	a	DET
ejpam-6597	5	53	weak	weak	ADJ
ejpam-6597	5	54	version	version	NOUN
ejpam-6597	5	55	of	of	ADP
ejpam-6597	5	56	collectionwise	collectionwise	PROPN
ejpam-6597	5	57	normality	normality	NOUN
ejpam-6597	5	58	called	call	VERB
ejpam-6597	5	59	collectionwise	collectionwise	PROPN
ejpam-6597	5	60	pre	pre	NOUN
ejpam-6597	5	61	-	-	NOUN
ejpam-6597	5	62	normality	normality	ADJ
ejpam-6597	5	63	,	,	PUNCT
ejpam-6597	5	64	which	which	PRON
ejpam-6597	5	65	is	be	AUX
ejpam-6597	5	66	a	a	DET
ejpam-6597	5	67	generalization	generalization	NOUN
ejpam-6597	5	68	of	of	ADP
ejpam-6597	5	69	collectionwise	collectionwise	PROPN
ejpam-6597	5	70	normality	normality	NOUN
ejpam-6597	5	71	.	.	PUNCT
ejpam-6597	6	1	the	the	DET
ejpam-6597	6	2	space	space	NOUN
ejpam-6597	6	3	x	x	PRON
ejpam-6597	6	4	means	mean	VERB
ejpam-6597	6	5	a	a	DET
ejpam-6597	6	6	topological	topological	ADJ
ejpam-6597	6	7	space	space	NOUN
ejpam-6597	6	8	in	in	ADP
ejpam-6597	6	9	whole	whole	ADJ
ejpam-6597	6	10	paper	paper	NOUN
ejpam-6597	6	11	.	.	PUNCT
ejpam-6597	7	1	we	we	PRON
ejpam-6597	7	2	need	need	VERB
ejpam-6597	7	3	to	to	PART
ejpam-6597	7	4	recall	recall	VERB
ejpam-6597	7	5	that	that	PRON
ejpam-6597	7	6	:	:	PUNCT
ejpam-6597	7	7	a	a	DET
ejpam-6597	7	8	subset	subset	NOUN
ejpam-6597	7	9	a	a	PRON
ejpam-6597	7	10	of	of	ADP
ejpam-6597	7	11	a	a	DET
ejpam-6597	7	12	space	space	NOUN
ejpam-6597	7	13	x	x	PUNCT
ejpam-6597	7	14	is	be	AUX
ejpam-6597	7	15	said	say	VERB
ejpam-6597	7	16	to	to	PART
ejpam-6597	7	17	be	be	AUX
ejpam-6597	7	18	a	a	DET
ejpam-6597	7	19	closed	closed	ADJ
ejpam-6597	7	20	domain	domain	NOUN
ejpam-6597	7	21	subset	subset	NOUN
ejpam-6597	7	22	if	if	SCONJ
ejpam-6597	7	23	it	it	PRON
ejpam-6597	7	24	is	be	AUX
ejpam-6597	7	25	the	the	DET
ejpam-6597	7	26	closure	closure	NOUN
ejpam-6597	7	27	of	of	ADP
ejpam-6597	7	28	its	its	PRON
ejpam-6597	7	29	own	own	ADJ
ejpam-6597	7	30	interior	interior	NOUN
ejpam-6597	7	31	[	[	X
ejpam-6597	7	32	1	1	NUM
ejpam-6597	7	33	]	]	PUNCT
ejpam-6597	7	34	.	.	PUNCT
ejpam-6597	8	1	the	the	DET
ejpam-6597	8	2	complement	complement	NOUN
ejpam-6597	8	3	of	of	ADP
ejpam-6597	8	4	a	a	DET
ejpam-6597	8	5	closed	closed	ADJ
ejpam-6597	8	6	domain	domain	NOUN
ejpam-6597	8	7	subset	subset	NOUN
ejpam-6597	8	8	is	be	AUX
ejpam-6597	8	9	called	call	VERB
ejpam-6597	8	10	open	open	ADJ
ejpam-6597	8	11	domain	domain	NOUN
ejpam-6597	8	12	.	.	PUNCT
ejpam-6597	9	1	a	a	DET
ejpam-6597	9	2	subset	subset	NOUN
ejpam-6597	9	3	a	a	PRON
ejpam-6597	9	4	of	of	ADP
ejpam-6597	9	5	a	a	DET
ejpam-6597	9	6	space	space	NOUN
ejpam-6597	9	7	x	x	PUNCT
ejpam-6597	9	8	is	be	AUX
ejpam-6597	9	9	called	call	VERB
ejpam-6597	9	10	π	π	PROPN
ejpam-6597	9	11	-	-	VERB
ejpam-6597	9	12	closed	closed	ADJ
ejpam-6597	9	13	if	if	SCONJ
ejpam-6597	9	14	it	it	PRON
ejpam-6597	9	15	is	be	AUX
ejpam-6597	9	16	a	a	DET
ejpam-6597	9	17	finite	finite	ADJ
ejpam-6597	9	18	intersection	intersection	NOUN
ejpam-6597	9	19	of	of	ADP
ejpam-6597	9	20	closed	closed	ADJ
ejpam-6597	9	21	domain	domain	NOUN
ejpam-6597	9	22	subsets	subset	NOUN
ejpam-6597	10	1	[	[	X
ejpam-6597	10	2	2	2	NUM
ejpam-6597	10	3	]	]	PUNCT
ejpam-6597	10	4	.	.	PUNCT
ejpam-6597	11	1	the	the	DET
ejpam-6597	11	2	complement	complement	NOUN
ejpam-6597	11	3	of	of	ADP
ejpam-6597	11	4	a	a	DET
ejpam-6597	11	5	π	π	PROPN
ejpam-6597	11	6	-	-	ADJ
ejpam-6597	11	7	closed	closed	ADJ
ejpam-6597	11	8	subset	subset	NOUN
ejpam-6597	11	9	is	be	AUX
ejpam-6597	11	10	called	call	VERB
ejpam-6597	11	11	π	π	PROPN
ejpam-6597	11	12	-	-	NOUN
ejpam-6597	11	13	open	open	ADJ
ejpam-6597	11	14	.	.	PUNCT
ejpam-6597	12	1	a	a	DET
ejpam-6597	12	2	subset	subset	NOUN
ejpam-6597	12	3	a	a	PRON
ejpam-6597	12	4	of	of	ADP
ejpam-6597	12	5	x	x	SYM
ejpam-6597	12	6	is	be	AUX
ejpam-6597	12	7	said	say	VERB
ejpam-6597	12	8	to	to	PART
ejpam-6597	12	9	be	be	AUX
ejpam-6597	12	10	pre	pre	ADJ
ejpam-6597	12	11	-	-	ADJ
ejpam-6597	12	12	open	open	ADJ
ejpam-6597	12	13	[	[	X
ejpam-6597	12	14	3	3	NUM
ejpam-6597	12	15	]	]	PUNCT
ejpam-6597	12	16	,	,	PUNCT
ejpam-6597	12	17	if	if	SCONJ
ejpam-6597	12	18	a	a	DET
ejpam-6597	12	19	⊆	⊆	NUM
ejpam-6597	12	20	int(a	int(a	NOUN
ejpam-6597	12	21	)	)	PUNCT
ejpam-6597	12	22	.	.	PUNCT
ejpam-6597	13	1	the	the	DET
ejpam-6597	13	2	complement	complement	NOUN
ejpam-6597	13	3	of	of	ADP
ejpam-6597	13	4	a	a	DET
ejpam-6597	13	5	pre	pre	ADJ
ejpam-6597	13	6	-	-	ADJ
ejpam-6597	13	7	open	open	ADJ
ejpam-6597	13	8	set	set	NOUN
ejpam-6597	13	9	is	be	AUX
ejpam-6597	13	10	called	call	VERB
ejpam-6597	13	11	pre	pre	ADJ
ejpam-6597	13	12	-	-	VERB
ejpam-6597	13	13	closed	closed	ADJ
ejpam-6597	13	14	.	.	PUNCT
ejpam-6597	14	1	the	the	DET
ejpam-6597	14	2	intersection	intersection	NOUN
ejpam-6597	14	3	of	of	ADP
ejpam-6597	14	4	all	all	DET
ejpam-6597	14	5	pre	pre	ADJ
ejpam-6597	14	6	-	-	ADJ
ejpam-6597	14	7	closed	closed	ADJ
ejpam-6597	14	8	sets	set	NOUN
ejpam-6597	14	9	containing	contain	VERB
ejpam-6597	14	10	a	a	PRON
ejpam-6597	14	11	is	be	AUX
ejpam-6597	14	12	called	call	VERB
ejpam-6597	14	13	a	a	DET
ejpam-6597	14	14	pre	pre	NOUN
ejpam-6597	14	15	-	-	NOUN
ejpam-6597	14	16	closure	closure	NOUN
ejpam-6597	14	17	of	of	ADP
ejpam-6597	14	18	a	a	PRON
ejpam-6597	14	19	[	[	X
ejpam-6597	14	20	4	4	NUM
ejpam-6597	14	21	,	,	PUNCT
ejpam-6597	14	22	5	5	NUM
ejpam-6597	14	23	]	]	PUNCT
ejpam-6597	14	24	,	,	PUNCT
ejpam-6597	14	25	and	and	CCONJ
ejpam-6597	14	26	denoted	denote	VERB
ejpam-6597	14	27	by	by	ADP
ejpam-6597	14	28	p	p	NOUN
ejpam-6597	14	29	cl(a	cl(a	NUM
ejpam-6597	14	30	)	)	PUNCT
ejpam-6597	14	31	.	.	PUNCT
ejpam-6597	15	1	the	the	DET
ejpam-6597	15	2	pre	pre	NOUN
ejpam-6597	15	3	-	-	NOUN
ejpam-6597	15	4	interior	interior	ADJ
ejpam-6597	15	5	of	of	ADP
ejpam-6597	15	6	a	a	PRON
ejpam-6597	15	7	,	,	PUNCT
ejpam-6597	15	8	denoted	denote	VERB
ejpam-6597	15	9	by	by	ADP
ejpam-6597	15	10	p	p	PROPN
ejpam-6597	15	11	int(a	int(a	PROPN
ejpam-6597	15	12	)	)	PUNCT
ejpam-6597	15	13	,	,	PUNCT
ejpam-6597	15	14	is	be	AUX
ejpam-6597	15	15	defined	define	VERB
ejpam-6597	15	16	to	to	PART
ejpam-6597	15	17	be	be	AUX
ejpam-6597	15	18	the	the	DET
ejpam-6597	15	19	union	union	NOUN
ejpam-6597	15	20	of	of	ADP
ejpam-6597	15	21	all	all	DET
ejpam-6597	15	22	pre	pre	ADJ
ejpam-6597	15	23	-	-	ADJ
ejpam-6597	15	24	open	open	ADJ
ejpam-6597	15	25	sets	set	NOUN
ejpam-6597	15	26	contained	contain	VERB
ejpam-6597	15	27	in	in	ADP
ejpam-6597	15	28	a.	a.	NOUN
ejpam-6597	15	29	a	a	DET
ejpam-6597	15	30	subset	subset	NOUN
ejpam-6597	15	31	a	a	PRON
ejpam-6597	15	32	is	be	AUX
ejpam-6597	15	33	said	say	VERB
ejpam-6597	15	34	to	to	PART
ejpam-6597	15	35	be	be	AUX
ejpam-6597	15	36	a	a	DET
ejpam-6597	15	37	pre	pre	ADJ
ejpam-6597	15	38	-	-	ADJ
ejpam-6597	15	39	neighborhood	neighborhood	NOUN
ejpam-6597	15	40	of	of	ADP
ejpam-6597	15	41	x	x	PRON
ejpam-6597	15	42	,	,	PUNCT
ejpam-6597	15	43	[	[	X
ejpam-6597	15	44	5	5	NUM
ejpam-6597	15	45	]	]	PUNCT
ejpam-6597	15	46	,	,	PUNCT
ejpam-6597	15	47	if	if	SCONJ
ejpam-6597	15	48	there	there	PRON
ejpam-6597	15	49	exists	exist	VERB
ejpam-6597	15	50	a	a	DET
ejpam-6597	15	51	∗corresponding	∗corresponding	NOUN
ejpam-6597	15	52	author	author	NOUN
ejpam-6597	15	53	.	.	PUNCT
ejpam-6597	16	1	∗corresponding	∗corresponde	VERB
ejpam-6597	16	2	author	author	NOUN
ejpam-6597	16	3	.	.	PUNCT
ejpam-6597	17	1	doi	doi	NOUN
ejpam-6597	17	2	:	:	PUNCT
ejpam-6597	17	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6597	https://doi.org/10.29020/nybg.ejpam.v18i4.6597	ADJ
ejpam-6597	17	4	email	email	NOUN
ejpam-6597	17	5	addresses	address	NOUN
ejpam-6597	17	6	:	:	PUNCT
ejpam-6597	17	7	sthabit1975@gmail.com	sthabit1975@gmail.com	X
ejpam-6597	17	8	,	,	PUNCT
ejpam-6597	17	9	s.thabit@mhru.edu.ye	s.thabit@mhru.edu.ye	PROPN
ejpam-6597	17	10	(	(	PUNCT
ejpam-6597	17	11	s.	s.	PROPN
ejpam-6597	17	12	a.	a.	PROPN
ejpam-6597	17	13	thabit	thabit	PROPN
ejpam-6597	17	14	)	)	PUNCT
ejpam-6597	17	15	,	,	PUNCT
ejpam-6597	17	16	aaalawadi@uj.edu.sa	aaalawadi@uj.edu.sa	PROPN
ejpam-6597	17	17	(	(	PUNCT
ejpam-6597	17	18	a.	a.	PROPN
ejpam-6597	17	19	al	al	PROPN
ejpam-6597	17	20	-	-	PUNCT
ejpam-6597	17	21	awadi	awadi	NOUN
ejpam-6597	17	22	)	)	PUNCT
ejpam-6597	17	23	,	,	PUNCT
ejpam-6597	17	24	rafiqa7757@gmail.com	rafiqa7757@gmail.com	X
ejpam-6597	18	1	(	(	PUNCT
ejpam-6597	18	2	r.	r.	PROPN
ejpam-6597	18	3	noaman	noaman	PROPN
ejpam-6597	18	4	)	)	PUNCT
ejpam-6597	18	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6597	19	1	1	1	NUM
ejpam-6597	19	2	copyright	copyright	NOUN
ejpam-6597	19	3	:	:	PUNCT
ejpam-6597	19	4	©	©	PROPN
ejpam-6597	19	5	2025	2025	NUM
ejpam-6597	19	6	the	the	DET
ejpam-6597	19	7	author(s	author(s	NOUN
ejpam-6597	19	8	)	)	PUNCT
ejpam-6597	19	9	.	.	PUNCT
ejpam-6597	20	1	(	(	PUNCT
ejpam-6597	20	2	cc	cc	NOUN
ejpam-6597	20	3	by	by	ADP
ejpam-6597	20	4	-	-	PUNCT
ejpam-6597	20	5	nc	nc	PROPN
ejpam-6597	20	6	4.0	4.0	NUM
ejpam-6597	20	7	)	)	PUNCT
ejpam-6597	20	8	s.	s.	PROPN
ejpam-6597	20	9	a.	a.	PROPN
ejpam-6597	20	10	thabit	thabit	PROPN
ejpam-6597	20	11	,	,	PUNCT
ejpam-6597	20	12	a.	a.	PROPN
ejpam-6597	20	13	al	al	PROPN
ejpam-6597	20	14	-	-	PUNCT
ejpam-6597	20	15	awadi	awadi	PROPN
ejpam-6597	20	16	,	,	PUNCT
ejpam-6597	20	17	r.	r.	PROPN
ejpam-6597	20	18	noaman	noaman	PROPN
ejpam-6597	20	19	/	/	SYM
ejpam-6597	20	20	eur	eur	PROPN
ejpam-6597	20	21	.	.	PUNCT
ejpam-6597	21	1	j.	j.	PROPN
ejpam-6597	21	2	pure	pure	PROPN
ejpam-6597	21	3	appl	appl	PROPN
ejpam-6597	21	4	.	.	PROPN
ejpam-6597	21	5	math	math	PROPN
ejpam-6597	21	6	,	,	PUNCT
ejpam-6597	21	7	18	18	NUM
ejpam-6597	21	8	(	(	PUNCT
ejpam-6597	21	9	4	4	NUM
ejpam-6597	21	10	)	)	PUNCT
ejpam-6597	21	11	(	(	PUNCT
ejpam-6597	21	12	2025	2025	NUM
ejpam-6597	21	13	)	)	PUNCT
ejpam-6597	21	14	,	,	PUNCT
ejpam-6597	21	15	6597	6597	NUM
ejpam-6597	21	16	2	2	NUM
ejpam-6597	21	17	of	of	ADP
ejpam-6597	21	18	15	15	NUM
ejpam-6597	21	19	pre	pre	ADJ
ejpam-6597	21	20	-	-	ADJ
ejpam-6597	21	21	open	open	ADJ
ejpam-6597	21	22	set	set	ADJ
ejpam-6597	21	23	u	u	PRON
ejpam-6597	21	24	such	such	ADJ
ejpam-6597	21	25	that	that	SCONJ
ejpam-6597	21	26	x	x	SYM
ejpam-6597	21	27	∈	∈	NOUN
ejpam-6597	21	28	u	u	NOUN
ejpam-6597	21	29	⊆	⊆	NUM
ejpam-6597	21	30	a.	a.	NOUN
ejpam-6597	21	31	the	the	DET
ejpam-6597	21	32	family	family	NOUN
ejpam-6597	21	33	of	of	ADP
ejpam-6597	21	34	all	all	DET
ejpam-6597	21	35	pre	pre	ADJ
ejpam-6597	21	36	-	-	ADJ
ejpam-6597	21	37	open	open	ADJ
ejpam-6597	21	38	subsets	subset	NOUN
ejpam-6597	21	39	of	of	ADP
ejpam-6597	21	40	x	x	PROPN
ejpam-6597	21	41	is	be	AUX
ejpam-6597	21	42	denoted	denote	VERB
ejpam-6597	21	43	by	by	ADP
ejpam-6597	21	44	po(x	po(x	NOUN
ejpam-6597	21	45	)	)	PUNCT
ejpam-6597	21	46	and	and	CCONJ
ejpam-6597	21	47	the	the	DET
ejpam-6597	21	48	family	family	NOUN
ejpam-6597	21	49	of	of	ADP
ejpam-6597	21	50	all	all	DET
ejpam-6597	21	51	pre	pre	ADJ
ejpam-6597	21	52	-	-	ADJ
ejpam-6597	21	53	closed	closed	ADJ
ejpam-6597	21	54	subsets	subset	NOUN
ejpam-6597	21	55	is	be	AUX
ejpam-6597	21	56	denoted	denote	VERB
ejpam-6597	21	57	by	by	ADP
ejpam-6597	21	58	pc(x).observe	pc(x).observe	NOUN
ejpam-6597	21	59	that	that	SCONJ
ejpam-6597	21	60	:	:	PUNCT
ejpam-6597	21	61	closed	closed	ADJ
ejpam-6597	21	62	domain	domain	NOUN
ejpam-6597	21	63	=	=	NOUN
ejpam-6597	21	64	⇒	⇒	X
ejpam-6597	21	65	π	π	PROPN
ejpam-6597	21	66	-	-	ADJ
ejpam-6597	21	67	closed	closed	ADJ
ejpam-6597	21	68	=	=	NOUN
ejpam-6597	21	69	⇒	⇒	NOUN
ejpam-6597	21	70	closed	close	VERB
ejpam-6597	21	71	=	=	NOUN
ejpam-6597	21	72	⇒	⇒	NOUN
ejpam-6597	21	73	pre	pre	ADJ
ejpam-6597	21	74	-	-	ADJ
ejpam-6597	21	75	closed	closed	ADJ
ejpam-6597	21	76	open	open	ADJ
ejpam-6597	21	77	domain	domain	NOUN
ejpam-6597	21	78	=	=	NOUN
ejpam-6597	21	79	⇒	⇒	X
ejpam-6597	21	80	π	π	ADJ
ejpam-6597	21	81	-	-	ADJ
ejpam-6597	21	82	open	open	ADJ
ejpam-6597	21	83	=	=	NOUN
ejpam-6597	21	84	⇒	⇒	NOUN
ejpam-6597	21	85	open	open	ADJ
ejpam-6597	21	86	=	=	NOUN
ejpam-6597	21	87	⇒	⇒	NOUN
ejpam-6597	21	88	pre	pre	ADJ
ejpam-6597	21	89	-	-	ADJ
ejpam-6597	21	90	open	open	VERB
ejpam-6597	21	91	a	a	DET
ejpam-6597	21	92	space	space	NOUN
ejpam-6597	21	93	x	x	PUNCT
ejpam-6597	21	94	is	be	AUX
ejpam-6597	21	95	called	call	VERB
ejpam-6597	21	96	pre	pre	ADJ
ejpam-6597	21	97	-	-	ADJ
ejpam-6597	21	98	normal	normal	ADJ
ejpam-6597	21	99	if	if	SCONJ
ejpam-6597	21	100	for	for	ADP
ejpam-6597	21	101	every	every	DET
ejpam-6597	21	102	pair	pair	NOUN
ejpam-6597	21	103	of	of	ADP
ejpam-6597	21	104	disjoint	disjoint	NOUN
ejpam-6597	21	105	closed	closed	ADJ
ejpam-6597	21	106	subsets	subset	NOUN
ejpam-6597	21	107	a	a	PRON
ejpam-6597	21	108	and	and	CCONJ
ejpam-6597	21	109	b	b	NOUN
ejpam-6597	21	110	,	,	PUNCT
ejpam-6597	21	111	there	there	PRON
ejpam-6597	21	112	exist	exist	VERB
ejpam-6597	21	113	disjoint	disjoint	ADJ
ejpam-6597	21	114	pre	pre	ADJ
ejpam-6597	21	115	-	-	ADJ
ejpam-6597	21	116	open	open	ADJ
ejpam-6597	21	117	subsets	subset	NOUN
ejpam-6597	21	118	u	u	NOUN
ejpam-6597	21	119	and	and	CCONJ
ejpam-6597	21	120	v	v	ADP
ejpam-6597	21	121	such	such	ADJ
ejpam-6597	21	122	that	that	SCONJ
ejpam-6597	21	123	a	a	DET
ejpam-6597	21	124	⊆	⊆	NUM
ejpam-6597	21	125	u	u	NOUN
ejpam-6597	21	126	and	and	CCONJ
ejpam-6597	21	127	b	b	NOUN
ejpam-6597	21	128	⊆	⊆	NUM
ejpam-6597	21	129	v	v	ADP
ejpam-6597	21	130	[	[	X
ejpam-6597	21	131	6	6	NUM
ejpam-6597	21	132	]	]	PUNCT
ejpam-6597	21	133	.	.	PUNCT
ejpam-6597	22	1	a	a	DET
ejpam-6597	22	2	space	space	NOUN
ejpam-6597	22	3	x	x	PUNCT
ejpam-6597	22	4	is	be	AUX
ejpam-6597	22	5	said	say	VERB
ejpam-6597	22	6	to	to	PART
ejpam-6597	22	7	be	be	AUX
ejpam-6597	22	8	a	a	DET
ejpam-6597	22	9	sub	sub	ADJ
ejpam-6597	22	10	-	-	ADJ
ejpam-6597	22	11	maximal	maximal	ADJ
ejpam-6597	22	12	if	if	SCONJ
ejpam-6597	22	13	every	every	DET
ejpam-6597	22	14	dense	dense	ADJ
ejpam-6597	22	15	subset	subset	NOUN
ejpam-6597	22	16	of	of	ADP
ejpam-6597	22	17	x	x	PUNCT
ejpam-6597	22	18	is	be	AUX
ejpam-6597	22	19	an	an	DET
ejpam-6597	22	20	open	open	ADJ
ejpam-6597	22	21	[	[	X
ejpam-6597	22	22	6	6	NUM
ejpam-6597	22	23	]	]	PUNCT
ejpam-6597	22	24	.	.	PUNCT
ejpam-6597	23	1	a	a	DET
ejpam-6597	23	2	space	space	NOUN
ejpam-6597	23	3	x	x	PUNCT
ejpam-6597	23	4	is	be	AUX
ejpam-6597	23	5	called	call	VERB
ejpam-6597	23	6	an	an	DET
ejpam-6597	23	7	pre	pre	NOUN
ejpam-6597	23	8	-	-	ADJ
ejpam-6597	23	9	regular	regular	ADJ
ejpam-6597	23	10	if	if	SCONJ
ejpam-6597	23	11	for	for	ADP
ejpam-6597	23	12	each	each	DET
ejpam-6597	23	13	closed	close	VERB
ejpam-6597	23	14	set	set	VERB
ejpam-6597	23	15	f	f	NOUN
ejpam-6597	23	16	and	and	CCONJ
ejpam-6597	23	17	each	each	DET
ejpam-6597	23	18	x	x	PROPN
ejpam-6597	23	19	̸∈	̸∈	PROPN
ejpam-6597	23	20	f	f	PROPN
ejpam-6597	23	21	,	,	PUNCT
ejpam-6597	23	22	there	there	PRON
ejpam-6597	23	23	exist	exist	VERB
ejpam-6597	23	24	disjoint	disjoint	ADJ
ejpam-6597	23	25	pre	pre	ADJ
ejpam-6597	23	26	-	-	ADJ
ejpam-6597	23	27	open	open	ADJ
ejpam-6597	23	28	sets	set	NOUN
ejpam-6597	23	29	u	u	NOUN
ejpam-6597	23	30	and	and	CCONJ
ejpam-6597	23	31	v	v	ADP
ejpam-6597	23	32	such	such	ADJ
ejpam-6597	23	33	that	that	SCONJ
ejpam-6597	23	34	x	x	SYM
ejpam-6597	23	35	∈	∈	PROPN
ejpam-6597	23	36	u	u	NOUN
ejpam-6597	23	37	and	and	CCONJ
ejpam-6597	23	38	f	f	PROPN
ejpam-6597	24	1	⊆	⊆	NUM
ejpam-6597	24	2	v	v	ADP
ejpam-6597	24	3	[	[	X
ejpam-6597	24	4	3	3	NUM
ejpam-6597	24	5	,	,	PUNCT
ejpam-6597	24	6	7	7	NUM
ejpam-6597	24	7	]	]	PUNCT
ejpam-6597	24	8	.	.	PUNCT
ejpam-6597	25	1	a	a	DET
ejpam-6597	25	2	space	space	NOUN
ejpam-6597	25	3	x	x	PUNCT
ejpam-6597	25	4	is	be	AUX
ejpam-6597	25	5	called	call	VERB
ejpam-6597	25	6	a	a	DET
ejpam-6597	25	7	pre	pre	NOUN
ejpam-6597	25	8	-	-	NOUN
ejpam-6597	25	9	t2	t2	ADJ
ejpam-6597	25	10	,	,	PUNCT
ejpam-6597	25	11	if	if	SCONJ
ejpam-6597	25	12	for	for	ADP
ejpam-6597	25	13	any	any	DET
ejpam-6597	25	14	distinct	distinct	ADJ
ejpam-6597	25	15	two	two	NUM
ejpam-6597	25	16	points	point	NOUN
ejpam-6597	25	17	x	x	X
ejpam-6597	25	18	̸=	̸=	PROPN
ejpam-6597	25	19	y	y	PROPN
ejpam-6597	25	20	,	,	PUNCT
ejpam-6597	25	21	there	there	PRON
ejpam-6597	25	22	exist	exist	VERB
ejpam-6597	25	23	two	two	NUM
ejpam-6597	25	24	disjoint	disjoint	ADJ
ejpam-6597	25	25	pre	pre	ADJ
ejpam-6597	25	26	-	-	ADJ
ejpam-6597	25	27	open	open	ADJ
ejpam-6597	25	28	sets	set	NOUN
ejpam-6597	25	29	u	u	NOUN
ejpam-6597	25	30	and	and	CCONJ
ejpam-6597	25	31	v	v	NOUN
ejpam-6597	25	32	in	in	ADP
ejpam-6597	25	33	x	x	PUNCT
ejpam-6597	25	34	such	such	ADJ
ejpam-6597	25	35	that	that	SCONJ
ejpam-6597	25	36	x	x	SYM
ejpam-6597	25	37	∈	∈	PROPN
ejpam-6597	25	38	u	u	NOUN
ejpam-6597	25	39	and	and	CCONJ
ejpam-6597	25	40	y	y	PROPN
ejpam-6597	25	41	∈	∈	PROPN
ejpam-6597	25	42	v	v	NOUN
ejpam-6597	25	43	.	.	PUNCT
ejpam-6597	26	1	a	a	DET
ejpam-6597	26	2	space	space	NOUN
ejpam-6597	26	3	x	x	PUNCT
ejpam-6597	26	4	is	be	AUX
ejpam-6597	26	5	called	call	VERB
ejpam-6597	26	6	a	a	DET
ejpam-6597	26	7	pre	pre	ADJ
ejpam-6597	26	8	-	-	ADJ
ejpam-6597	26	9	t1	t1	ADJ
ejpam-6597	26	10	-	-	PUNCT
ejpam-6597	26	11	space	space	NOUN
ejpam-6597	26	12	if	if	SCONJ
ejpam-6597	26	13	for	for	ADP
ejpam-6597	26	14	each	each	DET
ejpam-6597	26	15	x	x	NOUN
ejpam-6597	26	16	,	,	PUNCT
ejpam-6597	26	17	y	y	PROPN
ejpam-6597	26	18	∈	∈	PROPN
ejpam-6597	26	19	x	x	PUNCT
ejpam-6597	26	20	with	with	ADP
ejpam-6597	26	21	x	x	PUNCT
ejpam-6597	26	22	̸=	̸=	PROPN
ejpam-6597	26	23	y	y	NUM
ejpam-6597	26	24	,	,	PUNCT
ejpam-6597	26	25	there	there	PRON
ejpam-6597	26	26	exist	exist	VERB
ejpam-6597	26	27	pre	pre	ADJ
ejpam-6597	26	28	-	-	ADJ
ejpam-6597	26	29	open	open	ADJ
ejpam-6597	26	30	sets	set	NOUN
ejpam-6597	26	31	u	u	NOUN
ejpam-6597	26	32	and	and	CCONJ
ejpam-6597	26	33	v	v	ADP
ejpam-6597	26	34	such	such	ADJ
ejpam-6597	26	35	that	that	SCONJ
ejpam-6597	26	36	x	x	SYM
ejpam-6597	26	37	∈	∈	PROPN
ejpam-6597	26	38	u	u	NOUN
ejpam-6597	26	39	,	,	PUNCT
ejpam-6597	26	40	y	y	PROPN
ejpam-6597	26	41	∈	∈	PROPN
ejpam-6597	26	42	v	v	NOUN
ejpam-6597	26	43	and	and	CCONJ
ejpam-6597	26	44	x	x	PART
ejpam-6597	26	45	̸∈	̸∈	PROPN
ejpam-6597	26	46	v	v	PROPN
ejpam-6597	26	47	,	,	PUNCT
ejpam-6597	26	48	y	y	PROPN
ejpam-6597	26	49	̸∈	̸∈	PROPN
ejpam-6597	26	50	u	u	PROPN
ejpam-6597	26	51	.	.	PUNCT
ejpam-6597	27	1	a	a	DET
ejpam-6597	27	2	space	space	NOUN
ejpam-6597	27	3	x	x	PUNCT
ejpam-6597	27	4	is	be	AUX
ejpam-6597	27	5	called	call	VERB
ejpam-6597	27	6	a	a	DET
ejpam-6597	27	7	p1	p1	NOUN
ejpam-6597	27	8	-	-	PUNCT
ejpam-6597	27	9	paracompact	paracompact	NOUN
ejpam-6597	27	10	if	if	SCONJ
ejpam-6597	27	11	every	every	DET
ejpam-6597	27	12	pre	pre	ADJ
ejpam-6597	27	13	-	-	ADJ
ejpam-6597	27	14	open	open	ADJ
ejpam-6597	27	15	cover	cover	NOUN
ejpam-6597	27	16	of	of	ADP
ejpam-6597	27	17	x	x	PUNCT
ejpam-6597	27	18	has	have	VERB
ejpam-6597	27	19	a	a	DET
ejpam-6597	27	20	locally	locally	ADV
ejpam-6597	27	21	finite	finite	ADJ
ejpam-6597	27	22	open	open	ADJ
ejpam-6597	27	23	refinement	refinement	NOUN
ejpam-6597	28	1	[	[	X
ejpam-6597	28	2	3	3	NUM
ejpam-6597	28	3	]	]	PUNCT
ejpam-6597	28	4	.	.	PUNCT
ejpam-6597	29	1	a	a	DET
ejpam-6597	29	2	space	space	NOUN
ejpam-6597	29	3	x	x	PUNCT
ejpam-6597	29	4	is	be	AUX
ejpam-6597	29	5	called	call	VERB
ejpam-6597	29	6	a	a	DET
ejpam-6597	29	7	pre	pre	ADJ
ejpam-6597	29	8	-	-	ADJ
ejpam-6597	29	9	compact	compact	ADJ
ejpam-6597	29	10	space	space	NOUN
ejpam-6597	29	11	if	if	SCONJ
ejpam-6597	29	12	every	every	DET
ejpam-6597	29	13	pre	pre	ADJ
ejpam-6597	29	14	-	-	ADJ
ejpam-6597	29	15	open	open	ADJ
ejpam-6597	29	16	cover	cover	NOUN
ejpam-6597	29	17	of	of	ADP
ejpam-6597	29	18	x	x	PUNCT
ejpam-6597	29	19	has	have	VERB
ejpam-6597	29	20	a	a	DET
ejpam-6597	29	21	finite	finite	ADJ
ejpam-6597	29	22	subcover	subcover	PROPN
ejpam-6597	29	23	.	.	PUNCT
ejpam-6597	30	1	a	a	DET
ejpam-6597	30	2	space	space	NOUN
ejpam-6597	30	3	x	x	PUNCT
ejpam-6597	30	4	is	be	AUX
ejpam-6597	30	5	called	call	VERB
ejpam-6597	30	6	a	a	DET
ejpam-6597	30	7	pre	pre	NOUN
ejpam-6597	30	8	-	-	NOUN
ejpam-6597	30	9	lindelöf	lindelöf	ADJ
ejpam-6597	30	10	space	space	NOUN
ejpam-6597	30	11	if	if	SCONJ
ejpam-6597	30	12	every	every	DET
ejpam-6597	30	13	pre	pre	ADJ
ejpam-6597	30	14	-	-	ADJ
ejpam-6597	30	15	open	open	ADJ
ejpam-6597	30	16	cover	cover	NOUN
ejpam-6597	30	17	of	of	ADP
ejpam-6597	30	18	x	x	PUNCT
ejpam-6597	30	19	has	have	VERB
ejpam-6597	30	20	a	a	DET
ejpam-6597	30	21	countable	countable	ADJ
ejpam-6597	30	22	subcover	subcover	NOUN
ejpam-6597	30	23	.	.	PUNCT
ejpam-6597	31	1	a	a	DET
ejpam-6597	31	2	family	family	NOUN
ejpam-6597	31	3	u	u	NOUN
ejpam-6597	31	4	=	=	PUNCT
ejpam-6597	31	5	{	{	PUNCT
ejpam-6597	31	6	as}s∈s	as}s∈s	NOUN
ejpam-6597	31	7	of	of	ADP
ejpam-6597	31	8	subsets	subset	NOUN
ejpam-6597	31	9	of	of	ADP
ejpam-6597	31	10	a	a	DET
ejpam-6597	31	11	space	space	NOUN
ejpam-6597	31	12	x	x	PUNCT
ejpam-6597	31	13	is	be	AUX
ejpam-6597	31	14	called	call	VERB
ejpam-6597	31	15	a	a	DET
ejpam-6597	31	16	discrete	discrete	ADJ
ejpam-6597	31	17	family	family	NOUN
ejpam-6597	31	18	if	if	SCONJ
ejpam-6597	31	19	every	every	DET
ejpam-6597	31	20	point	point	NOUN
ejpam-6597	31	21	x	x	PUNCT
ejpam-6597	31	22	of	of	ADP
ejpam-6597	31	23	x	x	PUNCT
ejpam-6597	31	24	has	have	VERB
ejpam-6597	31	25	a	a	DET
ejpam-6597	31	26	neighborhood	neighborhood	NOUN
ejpam-6597	31	27	that	that	PRON
ejpam-6597	31	28	intersects	intersect	VERB
ejpam-6597	31	29	at	at	ADP
ejpam-6597	31	30	most	most	ADV
ejpam-6597	31	31	one	one	NUM
ejpam-6597	31	32	element	element	NOUN
ejpam-6597	31	33	of	of	ADP
ejpam-6597	31	34	u	u	NOUN
ejpam-6597	31	35	[	[	X
ejpam-6597	31	36	8	8	NUM
ejpam-6597	31	37	]	]	PUNCT
ejpam-6597	31	38	.	.	PUNCT
ejpam-6597	32	1	a	a	DET
ejpam-6597	32	2	space	space	NOUN
ejpam-6597	32	3	x	x	PUNCT
ejpam-6597	32	4	is	be	AUX
ejpam-6597	32	5	paracompact	paracompact	ADJ
ejpam-6597	32	6	if	if	SCONJ
ejpam-6597	32	7	every	every	DET
ejpam-6597	32	8	open	open	ADJ
ejpam-6597	32	9	cover	cover	NOUN
ejpam-6597	32	10	of	of	ADP
ejpam-6597	32	11	x	x	PUNCT
ejpam-6597	32	12	has	have	VERB
ejpam-6597	32	13	a	a	DET
ejpam-6597	32	14	locally	locally	ADV
ejpam-6597	32	15	finite	finite	ADJ
ejpam-6597	32	16	open	open	ADJ
ejpam-6597	32	17	refinement	refinement	NOUN
ejpam-6597	33	1	[	[	X
ejpam-6597	33	2	8–10	8–10	NOUN
ejpam-6597	33	3	]	]	PUNCT
ejpam-6597	33	4	.	.	PUNCT
ejpam-6597	34	1	a	a	DET
ejpam-6597	34	2	space	space	NOUN
ejpam-6597	34	3	x	x	PUNCT
ejpam-6597	34	4	is	be	AUX
ejpam-6597	34	5	called	call	VERB
ejpam-6597	34	6	countably	countably	ADV
ejpam-6597	34	7	paracompact	paracompact	ADJ
ejpam-6597	34	8	if	if	SCONJ
ejpam-6597	34	9	every	every	DET
ejpam-6597	34	10	countable	countable	ADJ
ejpam-6597	34	11	open	open	ADJ
ejpam-6597	34	12	cover	cover	NOUN
ejpam-6597	34	13	for	for	ADP
ejpam-6597	34	14	x	x	PUNCT
ejpam-6597	34	15	has	have	VERB
ejpam-6597	34	16	a	a	DET
ejpam-6597	34	17	locally	locally	ADV
ejpam-6597	34	18	finite	finite	ADJ
ejpam-6597	34	19	open	open	ADJ
ejpam-6597	34	20	-	-	PUNCT
ejpam-6597	34	21	refinement	refinement	NOUN
ejpam-6597	34	22	,	,	PUNCT
ejpam-6597	34	23	[	[	X
ejpam-6597	34	24	8	8	NUM
ejpam-6597	34	25	,	,	PUNCT
ejpam-6597	34	26	9	9	NUM
ejpam-6597	34	27	]	]	PUNCT
ejpam-6597	34	28	.	.	PUNCT
ejpam-6597	35	1	a	a	DET
ejpam-6597	35	2	space	space	NOUN
ejpam-6597	35	3	x	x	PUNCT
ejpam-6597	35	4	is	be	AUX
ejpam-6597	35	5	called	call	VERB
ejpam-6597	35	6	a	a	DET
ejpam-6597	35	7	collectionwise	collectionwise	ADV
ejpam-6597	35	8	normal	normal	ADJ
ejpam-6597	35	9	space	space	NOUN
ejpam-6597	35	10	if	if	SCONJ
ejpam-6597	35	11	and	and	CCONJ
ejpam-6597	35	12	only	only	ADV
ejpam-6597	35	13	if	if	SCONJ
ejpam-6597	35	14	x	x	PRON
ejpam-6597	35	15	is	be	AUX
ejpam-6597	35	16	a	a	DET
ejpam-6597	35	17	t1	t1	NOUN
ejpam-6597	35	18	-	-	PUNCT
ejpam-6597	35	19	space	space	NOUN
ejpam-6597	35	20	and	and	CCONJ
ejpam-6597	35	21	for	for	ADP
ejpam-6597	35	22	every	every	DET
ejpam-6597	35	23	discrete	discrete	ADJ
ejpam-6597	35	24	family	family	NOUN
ejpam-6597	35	25	f	f	PROPN
ejpam-6597	36	1	=	=	PRON
ejpam-6597	36	2	{	{	PUNCT
ejpam-6597	36	3	fs}s∈s	fs}s∈s	X
ejpam-6597	36	4	of	of	ADP
ejpam-6597	36	5	closed	closed	ADJ
ejpam-6597	36	6	subsets	subset	NOUN
ejpam-6597	36	7	of	of	ADP
ejpam-6597	36	8	x	x	PRON
ejpam-6597	36	9	,	,	PUNCT
ejpam-6597	36	10	there	there	PRON
ejpam-6597	36	11	exits	exit	VERB
ejpam-6597	36	12	a	a	DET
ejpam-6597	36	13	discrete	discrete	ADJ
ejpam-6597	36	14	family	family	NOUN
ejpam-6597	36	15	u	u	NOUN
ejpam-6597	36	16	=	=	PUNCT
ejpam-6597	36	17	{	{	PUNCT
ejpam-6597	36	18	us}s∈s	us}s∈s	NOUN
ejpam-6597	36	19	of	of	ADP
ejpam-6597	36	20	open	open	ADJ
ejpam-6597	36	21	subsets	subset	NOUN
ejpam-6597	36	22	of	of	ADP
ejpam-6597	36	23	x	x	SYM
ejpam-6597	36	24	such	such	ADJ
ejpam-6597	36	25	that	that	PRON
ejpam-6597	36	26	fs	fs	ADP
ejpam-6597	36	27	⊆	⊆	NUM
ejpam-6597	36	28	us	we	PRON
ejpam-6597	36	29	for	for	ADP
ejpam-6597	36	30	each	each	DET
ejpam-6597	36	31	s	s	X
ejpam-6597	36	32	∈	∈	ADJ
ejpam-6597	36	33	s	s	PART
ejpam-6597	36	34	[	[	X
ejpam-6597	36	35	9	9	NUM
ejpam-6597	36	36	]	]	PUNCT
ejpam-6597	36	37	.	.	PUNCT
ejpam-6597	37	1	observe	observe	VERB
ejpam-6597	37	2	that	that	SCONJ
ejpam-6597	37	3	:	:	PUNCT
ejpam-6597	37	4	every	every	DET
ejpam-6597	37	5	normal	normal	ADJ
ejpam-6597	37	6	space	space	NOUN
ejpam-6597	37	7	is	be	AUX
ejpam-6597	37	8	pre	pre	ADJ
ejpam-6597	37	9	-	-	ADJ
ejpam-6597	37	10	normal	normal	ADJ
ejpam-6597	37	11	.	.	PUNCT
ejpam-6597	37	12	.	.	PUNCT
ejpam-6597	38	1	2	2	X
ejpam-6597	38	2	.	.	X
ejpam-6597	38	3	preliminaries	preliminary	NOUN
ejpam-6597	38	4	first	first	ADV
ejpam-6597	38	5	,	,	PUNCT
ejpam-6597	38	6	we	we	PRON
ejpam-6597	38	7	present	present	VERB
ejpam-6597	38	8	the	the	DET
ejpam-6597	38	9	main	main	ADJ
ejpam-6597	38	10	definitions	definition	NOUN
ejpam-6597	38	11	of	of	ADP
ejpam-6597	38	12	this	this	DET
ejpam-6597	38	13	work	work	NOUN
ejpam-6597	38	14	.	.	PUNCT
ejpam-6597	39	1	definition	definition	NOUN
ejpam-6597	39	2	1	1	NUM
ejpam-6597	39	3	.	.	PUNCT
ejpam-6597	40	1	a	a	DET
ejpam-6597	40	2	space	space	NOUN
ejpam-6597	40	3	x	x	PUNCT
ejpam-6597	40	4	is	be	AUX
ejpam-6597	40	5	called	call	VERB
ejpam-6597	40	6	a	a	DET
ejpam-6597	40	7	collectionwise	collectionwise	ADV
ejpam-6597	40	8	pre	pre	ADJ
ejpam-6597	40	9	-	-	ADJ
ejpam-6597	40	10	normal	normal	ADJ
ejpam-6597	40	11	space	space	NOUN
ejpam-6597	40	12	if	if	SCONJ
ejpam-6597	40	13	and	and	CCONJ
ejpam-6597	40	14	only	only	ADV
ejpam-6597	40	15	if	if	SCONJ
ejpam-6597	40	16	x	x	PRON
ejpam-6597	40	17	is	be	AUX
ejpam-6597	40	18	t1	t1	NOUN
ejpam-6597	40	19	and	and	CCONJ
ejpam-6597	40	20	for	for	ADP
ejpam-6597	40	21	every	every	DET
ejpam-6597	40	22	discrete	discrete	ADJ
ejpam-6597	40	23	family	family	NOUN
ejpam-6597	40	24	f	f	PROPN
ejpam-6597	41	1	=	=	PRON
ejpam-6597	41	2	{	{	PUNCT
ejpam-6597	41	3	fs}s∈s	fs}s∈s	X
ejpam-6597	41	4	of	of	ADP
ejpam-6597	41	5	closed	closed	ADJ
ejpam-6597	41	6	subsets	subset	NOUN
ejpam-6597	41	7	of	of	ADP
ejpam-6597	41	8	x	x	PRON
ejpam-6597	41	9	,	,	PUNCT
ejpam-6597	41	10	there	there	PRON
ejpam-6597	41	11	exits	exit	VERB
ejpam-6597	41	12	a	a	DET
ejpam-6597	41	13	discrete	discrete	ADJ
ejpam-6597	41	14	family	family	NOUN
ejpam-6597	41	15	u	u	NOUN
ejpam-6597	41	16	=	=	PUNCT
ejpam-6597	41	17	{	{	PUNCT
ejpam-6597	41	18	us}s∈s	us}s∈s	PROPN
ejpam-6597	41	19	of	of	ADP
ejpam-6597	41	20	pre	pre	ADJ
ejpam-6597	41	21	-	-	ADJ
ejpam-6597	41	22	open	open	ADJ
ejpam-6597	41	23	subsets	subset	NOUN
ejpam-6597	41	24	of	of	ADP
ejpam-6597	41	25	x	x	SYM
ejpam-6597	41	26	such	such	ADJ
ejpam-6597	41	27	that	that	PRON
ejpam-6597	41	28	fs	fs	ADP
ejpam-6597	41	29	⊆	⊆	NUM
ejpam-6597	41	30	us	we	PRON
ejpam-6597	41	31	for	for	ADP
ejpam-6597	41	32	each	each	DET
ejpam-6597	41	33	s	s	PROPN
ejpam-6597	41	34	∈	∈	PROPN
ejpam-6597	41	35	s.	s.	PROPN
ejpam-6597	41	36	from	from	ADP
ejpam-6597	41	37	definition	definition	NOUN
ejpam-6597	41	38	1	1	NUM
ejpam-6597	41	39	,	,	PUNCT
ejpam-6597	41	40	clearly	clearly	ADV
ejpam-6597	41	41	that	that	SCONJ
ejpam-6597	41	42	:	:	PUNCT
ejpam-6597	41	43	every	every	DET
ejpam-6597	41	44	collectionwise	collectionwise	ADJ
ejpam-6597	41	45	pre	pre	ADJ
ejpam-6597	41	46	-	-	ADJ
ejpam-6597	41	47	normal	normal	ADJ
ejpam-6597	41	48	space	space	NOUN
ejpam-6597	41	49	is	be	AUX
ejpam-6597	41	50	t1	t1	NOUN
ejpam-6597	41	51	and	and	CCONJ
ejpam-6597	41	52	any	any	DET
ejpam-6597	41	53	non	non	ADJ
ejpam-6597	41	54	t1	t1	NOUN
ejpam-6597	41	55	-	-	PUNCT
ejpam-6597	41	56	space	space	NOUN
ejpam-6597	41	57	can	can	AUX
ejpam-6597	41	58	not	not	PART
ejpam-6597	41	59	be	be	AUX
ejpam-6597	41	60	collectionwise	collectionwise	ADV
ejpam-6597	41	61	pre	pre	ADJ
ejpam-6597	41	62	-	-	ADJ
ejpam-6597	41	63	normal	normal	ADJ
ejpam-6597	41	64	.	.	PUNCT
ejpam-6597	42	1	first	first	ADV
ejpam-6597	42	2	,	,	PUNCT
ejpam-6597	42	3	we	we	PRON
ejpam-6597	42	4	give	give	VERB
ejpam-6597	42	5	the	the	DET
ejpam-6597	42	6	following	following	ADJ
ejpam-6597	42	7	basic	basic	ADJ
ejpam-6597	42	8	results	result	NOUN
ejpam-6597	42	9	:	:	PUNCT
ejpam-6597	42	10	theorem	theorem	NOUN
ejpam-6597	42	11	1	1	NUM
ejpam-6597	42	12	.	.	PUNCT
ejpam-6597	43	1	every	every	DET
ejpam-6597	43	2	collectionwise	collectionwise	ADV
ejpam-6597	43	3	normal	normal	ADJ
ejpam-6597	43	4	space	space	NOUN
ejpam-6597	43	5	is	be	AUX
ejpam-6597	43	6	collectionwise	collectionwise	ADV
ejpam-6597	43	7	pre	pre	ADJ
ejpam-6597	43	8	-	-	ADJ
ejpam-6597	43	9	normal	normal	ADJ
ejpam-6597	43	10	.	.	PUNCT
ejpam-6597	44	1	proof	proof	NOUN
ejpam-6597	44	2	.	.	PUNCT
ejpam-6597	45	1	let	let	VERB
ejpam-6597	45	2	x	x	PRON
ejpam-6597	45	3	be	be	AUX
ejpam-6597	45	4	a	a	DET
ejpam-6597	45	5	collectionwise	collectionwise	ADV
ejpam-6597	45	6	normal	normal	ADJ
ejpam-6597	45	7	space	space	NOUN
ejpam-6597	45	8	.	.	PUNCT
ejpam-6597	46	1	we	we	PRON
ejpam-6597	46	2	show	show	VERB
ejpam-6597	46	3	that	that	SCONJ
ejpam-6597	46	4	x	x	PRON
ejpam-6597	46	5	is	be	AUX
ejpam-6597	46	6	collectionwise	collectionwise	ADV
ejpam-6597	46	7	pre	pre	ADJ
ejpam-6597	46	8	-	-	ADJ
ejpam-6597	46	9	normal	normal	ADJ
ejpam-6597	46	10	.	.	PUNCT
ejpam-6597	47	1	for	for	ADP
ejpam-6597	47	2	that	that	PRON
ejpam-6597	47	3	,	,	PUNCT
ejpam-6597	47	4	let	let	VERB
ejpam-6597	47	5	{	{	PUNCT
ejpam-6597	47	6	fs}s∈s	fs}s∈s	PART
ejpam-6597	47	7	be	be	AUX
ejpam-6597	47	8	a	a	DET
ejpam-6597	47	9	discrete	discrete	ADJ
ejpam-6597	47	10	family	family	NOUN
ejpam-6597	47	11	of	of	ADP
ejpam-6597	47	12	closed	closed	ADJ
ejpam-6597	47	13	subsets	subset	NOUN
ejpam-6597	47	14	of	of	ADP
ejpam-6597	47	15	x.	x.	NOUN
ejpam-6597	47	16	since	since	SCONJ
ejpam-6597	47	17	x	x	PRON
ejpam-6597	47	18	is	be	AUX
ejpam-6597	47	19	collectionwise	collectionwise	ADV
ejpam-6597	47	20	normal	normal	ADJ
ejpam-6597	47	21	,	,	PUNCT
ejpam-6597	47	22	there	there	PRON
ejpam-6597	47	23	exists	exist	VERB
ejpam-6597	47	24	a	a	DET
ejpam-6597	47	25	discrete	discrete	ADJ
ejpam-6597	47	26	family	family	NOUN
ejpam-6597	47	27	{	{	PUNCT
ejpam-6597	47	28	us}s∈s	us}s∈s	NOUN
ejpam-6597	47	29	of	of	ADP
ejpam-6597	47	30	open	open	ADJ
ejpam-6597	47	31	subsets	subset	NOUN
ejpam-6597	47	32	of	of	ADP
ejpam-6597	47	33	x	x	SYM
ejpam-6597	47	34	such	such	ADJ
ejpam-6597	47	35	that	that	PRON
ejpam-6597	47	36	fs	fs	ADP
ejpam-6597	47	37	⊆	⊆	NUM
ejpam-6597	47	38	us	we	PRON
ejpam-6597	47	39	for	for	ADP
ejpam-6597	47	40	each	each	DET
ejpam-6597	47	41	s	s	PROPN
ejpam-6597	47	42	∈	∈	PROPN
ejpam-6597	47	43	s.	s.	PROPN
ejpam-6597	47	44	since	since	SCONJ
ejpam-6597	47	45	every	every	DET
ejpam-6597	47	46	open	open	ADJ
ejpam-6597	47	47	set	set	NOUN
ejpam-6597	47	48	is	be	AUX
ejpam-6597	47	49	pre	pre	ADJ
ejpam-6597	47	50	-	-	ADJ
ejpam-6597	47	51	open	open	ADJ
ejpam-6597	47	52	,	,	PUNCT
ejpam-6597	47	53	{	{	PUNCT
ejpam-6597	47	54	us}s∈s	us}s∈s	NOUN
ejpam-6597	47	55	is	be	AUX
ejpam-6597	47	56	a	a	DET
ejpam-6597	47	57	discrete	discrete	ADJ
ejpam-6597	47	58	family	family	NOUN
ejpam-6597	47	59	of	of	ADP
ejpam-6597	47	60	pre	pre	ADJ
ejpam-6597	47	61	-	-	ADJ
ejpam-6597	47	62	open	open	ADJ
ejpam-6597	47	63	subsets	subset	NOUN
ejpam-6597	47	64	of	of	ADP
ejpam-6597	47	65	x	x	SYM
ejpam-6597	47	66	such	such	ADJ
ejpam-6597	47	67	that	that	PRON
ejpam-6597	47	68	fs	fs	ADP
ejpam-6597	47	69	⊆	⊆	NUM
ejpam-6597	47	70	us	we	PRON
ejpam-6597	47	71	for	for	ADP
ejpam-6597	47	72	each	each	DET
ejpam-6597	47	73	s	s	PROPN
ejpam-6597	47	74	∈	∈	PROPN
ejpam-6597	47	75	s.	s.	PROPN
ejpam-6597	47	76	therefore	therefore	ADV
ejpam-6597	47	77	,	,	PUNCT
ejpam-6597	47	78	x	x	PUNCT
ejpam-6597	47	79	is	be	AUX
ejpam-6597	47	80	collectionwise	collectionwise	ADV
ejpam-6597	47	81	pre	pre	ADJ
ejpam-6597	47	82	-	-	ADJ
ejpam-6597	47	83	normal	normal	ADJ
ejpam-6597	47	84	.	.	PUNCT
ejpam-6597	48	1	the	the	DET
ejpam-6597	48	2	converse	converse	NOUN
ejpam-6597	48	3	of	of	ADP
ejpam-6597	48	4	theorem	theorem	NOUN
ejpam-6597	48	5	1	1	NUM
ejpam-6597	48	6	is	be	AUX
ejpam-6597	48	7	not	not	PART
ejpam-6597	48	8	true	true	ADJ
ejpam-6597	48	9	in	in	ADP
ejpam-6597	48	10	general	general	ADJ
ejpam-6597	48	11	.	.	PUNCT
ejpam-6597	49	1	here	here	ADV
ejpam-6597	49	2	is	be	AUX
ejpam-6597	49	3	an	an	DET
ejpam-6597	49	4	example	example	NOUN
ejpam-6597	49	5	of	of	ADP
ejpam-6597	49	6	a	a	DET
ejpam-6597	49	7	collectionwise	collectionwise	ADV
ejpam-6597	49	8	pre	pre	ADJ
ejpam-6597	49	9	-	-	ADJ
ejpam-6597	49	10	normal	normal	ADJ
ejpam-6597	49	11	space	space	NOUN
ejpam-6597	49	12	which	which	PRON
ejpam-6597	49	13	is	be	AUX
ejpam-6597	49	14	not	not	PART
ejpam-6597	49	15	collectionwise	collectionwise	ADV
ejpam-6597	49	16	normal	normal	ADJ
ejpam-6597	49	17	:	:	PUNCT
ejpam-6597	49	18	s.	s.	PROPN
ejpam-6597	49	19	a.	a.	PROPN
ejpam-6597	49	20	thabit	thabit	PROPN
ejpam-6597	49	21	,	,	PUNCT
ejpam-6597	49	22	a.	a.	PROPN
ejpam-6597	49	23	al	al	PROPN
ejpam-6597	49	24	-	-	PUNCT
ejpam-6597	49	25	awadi	awadi	PROPN
ejpam-6597	49	26	,	,	PUNCT
ejpam-6597	49	27	r.	r.	PROPN
ejpam-6597	49	28	noaman	noaman	PROPN
ejpam-6597	49	29	/	/	SYM
ejpam-6597	49	30	eur	eur	PROPN
ejpam-6597	49	31	.	.	PUNCT
ejpam-6597	50	1	j.	j.	PROPN
ejpam-6597	50	2	pure	pure	PROPN
ejpam-6597	50	3	appl	appl	PROPN
ejpam-6597	50	4	.	.	PROPN
ejpam-6597	50	5	math	math	PROPN
ejpam-6597	50	6	,	,	PUNCT
ejpam-6597	50	7	18	18	NUM
ejpam-6597	50	8	(	(	PUNCT
ejpam-6597	50	9	4	4	NUM
ejpam-6597	50	10	)	)	PUNCT
ejpam-6597	50	11	(	(	PUNCT
ejpam-6597	50	12	2025	2025	NUM
ejpam-6597	50	13	)	)	PUNCT
ejpam-6597	50	14	,	,	PUNCT
ejpam-6597	50	15	6597	6597	NUM
ejpam-6597	50	16	3	3	NUM
ejpam-6597	50	17	of	of	ADP
ejpam-6597	50	18	15	15	NUM
ejpam-6597	50	19	example	example	NOUN
ejpam-6597	50	20	1	1	NUM
ejpam-6597	50	21	.	.	PUNCT
ejpam-6597	51	1	the	the	DET
ejpam-6597	51	2	finite	finite	PROPN
ejpam-6597	51	3	complement	complement	NOUN
ejpam-6597	51	4	topology	topology	NOUN
ejpam-6597	51	5	:	:	PUNCT
ejpam-6597	51	6	[	[	X
ejpam-6597	51	7	10	10	NUM
ejpam-6597	51	8	,	,	PUNCT
ejpam-6597	51	9	example	example	NOUN
ejpam-6597	51	10	19	19	NUM
ejpam-6597	51	11	]	]	PUNCT
ejpam-6597	51	12	,	,	PUNCT
ejpam-6597	51	13	(	(	PUNCT
ejpam-6597	51	14	r	r	NOUN
ejpam-6597	51	15	,	,	PUNCT
ejpam-6597	51	16	cf	cf	NOUN
ejpam-6597	51	17	)	)	PUNCT
ejpam-6597	51	18	is	be	AUX
ejpam-6597	51	19	a	a	DET
ejpam-6597	51	20	t1	t1	NOUN
ejpam-6597	51	21	,	,	PUNCT
ejpam-6597	51	22	compact	compact	ADJ
ejpam-6597	51	23	,	,	PUNCT
ejpam-6597	51	24	countably	countably	ADV
ejpam-6597	51	25	compact	compact	ADJ
ejpam-6597	51	26	,	,	PUNCT
ejpam-6597	51	27	lindelöf	lindelöf	PROPN
ejpam-6597	51	28	,	,	PUNCT
ejpam-6597	51	29	separable	separable	ADJ
ejpam-6597	51	30	and	and	CCONJ
ejpam-6597	51	31	paracompact	paracompact	ADJ
ejpam-6597	51	32	space	space	NOUN
ejpam-6597	51	33	which	which	PRON
ejpam-6597	51	34	is	be	AUX
ejpam-6597	51	35	neither	neither	CCONJ
ejpam-6597	51	36	regular	regular	ADJ
ejpam-6597	51	37	,	,	PUNCT
ejpam-6597	51	38	normal	normal	ADJ
ejpam-6597	51	39	,	,	PUNCT
ejpam-6597	51	40	first	first	ADV
ejpam-6597	51	41	countable	countable	ADJ
ejpam-6597	51	42	nor	nor	CCONJ
ejpam-6597	51	43	second	second	ADJ
ejpam-6597	51	44	countable	countable	ADJ
ejpam-6597	51	45	[	[	X
ejpam-6597	51	46	10	10	NUM
ejpam-6597	51	47	]	]	PUNCT
ejpam-6597	51	48	.	.	PUNCT
ejpam-6597	52	1	the	the	DET
ejpam-6597	52	2	finite	finite	PROPN
ejpam-6597	52	3	complement	complement	NOUN
ejpam-6597	52	4	topology	topology	NOUN
ejpam-6597	52	5	is	be	AUX
ejpam-6597	52	6	a	a	DET
ejpam-6597	52	7	pre	pre	ADJ
ejpam-6597	52	8	-	-	ADJ
ejpam-6597	52	9	normal	normal	ADJ
ejpam-6597	52	10	space	space	NOUN
ejpam-6597	52	11	which	which	PRON
ejpam-6597	52	12	is	be	AUX
ejpam-6597	52	13	not	not	PART
ejpam-6597	52	14	normal	normal	ADJ
ejpam-6597	52	15	[	[	X
ejpam-6597	52	16	11	11	NUM
ejpam-6597	52	17	]	]	PUNCT
ejpam-6597	52	18	.	.	PUNCT
ejpam-6597	53	1	hence	hence	ADV
ejpam-6597	53	2	,	,	PUNCT
ejpam-6597	53	3	the	the	DET
ejpam-6597	53	4	finite	finite	ADJ
ejpam-6597	53	5	complement	complement	NOUN
ejpam-6597	53	6	topology	topology	NOUN
ejpam-6597	53	7	is	be	AUX
ejpam-6597	53	8	not	not	PART
ejpam-6597	53	9	collectionwise	collectionwise	ADV
ejpam-6597	53	10	normal	normal	ADJ
ejpam-6597	53	11	.	.	PUNCT
ejpam-6597	54	1	since	since	SCONJ
ejpam-6597	54	2	x	x	PRON
ejpam-6597	54	3	is	be	AUX
ejpam-6597	54	4	t1	t1	NOUN
ejpam-6597	54	5	countably	countably	ADV
ejpam-6597	54	6	compact	compact	ADJ
ejpam-6597	54	7	pre	pre	ADJ
ejpam-6597	54	8	-	-	ADJ
ejpam-6597	54	9	normal	normal	ADJ
ejpam-6597	54	10	space	space	NOUN
ejpam-6597	54	11	,	,	PUNCT
ejpam-6597	54	12	by	by	ADP
ejpam-6597	54	13	theorem	theorem	VERB
ejpam-6597	54	14	11	11	NUM
ejpam-6597	54	15	the	the	DET
ejpam-6597	54	16	finite	finite	PROPN
ejpam-6597	54	17	complement	complement	NOUN
ejpam-6597	54	18	topology	topology	NOUN
ejpam-6597	54	19	is	be	AUX
ejpam-6597	54	20	collectionwise	collectionwise	ADV
ejpam-6597	54	21	pre	pre	ADJ
ejpam-6597	54	22	-	-	ADJ
ejpam-6597	54	23	normal	normal	ADJ
ejpam-6597	54	24	.	.	PUNCT
ejpam-6597	55	1	theorem	theorem	NOUN
ejpam-6597	55	2	2	2	NUM
ejpam-6597	55	3	.	.	PUNCT
ejpam-6597	56	1	every	every	DET
ejpam-6597	56	2	collectionwise	collectionwise	ADV
ejpam-6597	56	3	pre	pre	ADJ
ejpam-6597	56	4	-	-	ADJ
ejpam-6597	56	5	normal	normal	ADJ
ejpam-6597	56	6	space	space	NOUN
ejpam-6597	56	7	is	be	AUX
ejpam-6597	56	8	pre	pre	ADJ
ejpam-6597	56	9	-	-	ADJ
ejpam-6597	56	10	normal	normal	ADJ
ejpam-6597	56	11	.	.	PUNCT
ejpam-6597	57	1	proof	proof	NOUN
ejpam-6597	57	2	.	.	PUNCT
ejpam-6597	58	1	let	let	VERB
ejpam-6597	58	2	fr	fr	PROPN
ejpam-6597	58	3	and	and	CCONJ
ejpam-6597	58	4	ft	ft	PROPN
ejpam-6597	58	5	be	be	AUX
ejpam-6597	58	6	any	any	DET
ejpam-6597	58	7	two	two	NUM
ejpam-6597	58	8	disjoint	disjoint	NOUN
ejpam-6597	58	9	closed	closed	ADJ
ejpam-6597	58	10	subsets	subset	NOUN
ejpam-6597	58	11	of	of	ADP
ejpam-6597	58	12	x.	x.	NOUN
ejpam-6597	58	13	consider	consider	VERB
ejpam-6597	58	14	f	f	NOUN
ejpam-6597	58	15	=	=	PRON
ejpam-6597	58	16	{	{	PUNCT
ejpam-6597	58	17	fs	fs	X
ejpam-6597	58	18	:	:	PUNCT
ejpam-6597	58	19	s	s	VERB
ejpam-6597	58	20	∈	∈	PROPN
ejpam-6597	58	21	s	s	AUX
ejpam-6597	58	22	}	}	PUNCT
ejpam-6597	58	23	be	be	AUX
ejpam-6597	58	24	a	a	DET
ejpam-6597	58	25	discrete	discrete	ADJ
ejpam-6597	58	26	family	family	NOUN
ejpam-6597	58	27	of	of	ADP
ejpam-6597	58	28	all	all	DET
ejpam-6597	58	29	pairwise	pairwise	NOUN
ejpam-6597	58	30	disjoint	disjoint	NOUN
ejpam-6597	58	31	closed	close	VERB
ejpam-6597	58	32	subsets	subset	NOUN
ejpam-6597	58	33	of	of	ADP
ejpam-6597	58	34	a	a	DET
ejpam-6597	58	35	collectionwise	collectionwise	PROPN
ejpam-6597	58	36	prenormal	prenormal	NOUN
ejpam-6597	58	37	space	space	NOUN
ejpam-6597	58	38	x.	x.	NOUN
ejpam-6597	58	39	by	by	ADP
ejpam-6597	58	40	collectionwise	collectionwise	PROPN
ejpam-6597	58	41	pre	pre	PROPN
ejpam-6597	58	42	-	-	NOUN
ejpam-6597	58	43	normality	normality	NOUN
ejpam-6597	58	44	of	of	ADP
ejpam-6597	58	45	x	x	NOUN
ejpam-6597	58	46	,	,	PUNCT
ejpam-6597	58	47	there	there	PRON
ejpam-6597	58	48	exists	exist	VERB
ejpam-6597	58	49	a	a	DET
ejpam-6597	58	50	discrete	discrete	ADJ
ejpam-6597	58	51	family	family	NOUN
ejpam-6597	58	52	v	v	NOUN
ejpam-6597	58	53	=	=	PUNCT
ejpam-6597	58	54	{	{	PUNCT
ejpam-6597	58	55	vs	vs	ADP
ejpam-6597	58	56	:	:	PUNCT
ejpam-6597	58	57	s	s	X
ejpam-6597	58	58	∈	∈	PROPN
ejpam-6597	58	59	s	s	PART
ejpam-6597	58	60	}	}	PUNCT
ejpam-6597	58	61	of	of	ADP
ejpam-6597	58	62	pre	pre	ADJ
ejpam-6597	58	63	-	-	ADJ
ejpam-6597	58	64	open	open	ADJ
ejpam-6597	58	65	subsets	subset	NOUN
ejpam-6597	58	66	of	of	ADP
ejpam-6597	58	67	x	x	SYM
ejpam-6597	58	68	such	such	ADJ
ejpam-6597	58	69	that	that	PRON
ejpam-6597	58	70	fs	fs	ADP
ejpam-6597	58	71	⊆	⊆	NUM
ejpam-6597	58	72	vs	vs	ADP
ejpam-6597	58	73	for	for	ADP
ejpam-6597	58	74	each	each	DET
ejpam-6597	58	75	s	s	PROPN
ejpam-6597	58	76	∈	∈	PROPN
ejpam-6597	58	77	s.	s.	PROPN
ejpam-6597	58	78	thus	thus	ADV
ejpam-6597	58	79	,	,	PUNCT
ejpam-6597	58	80	there	there	PRON
ejpam-6597	58	81	exist	exist	VERB
ejpam-6597	58	82	vr	vr	PROPN
ejpam-6597	58	83	,	,	PUNCT
ejpam-6597	58	84	vt	vt	PROPN
ejpam-6597	58	85	∈	∈	PROPN
ejpam-6597	58	86	v	v	ADP
ejpam-6597	58	87	such	such	ADJ
ejpam-6597	58	88	that	that	SCONJ
ejpam-6597	58	89	fr	fr	PROPN
ejpam-6597	58	90	⊆	⊆	NUM
ejpam-6597	58	91	vr	vr	NOUN
ejpam-6597	58	92	,	,	PUNCT
ejpam-6597	58	93	ft	ft	PROPN
ejpam-6597	58	94	⊆	⊆	NUM
ejpam-6597	58	95	vt	vt	PROPN
ejpam-6597	58	96	and	and	CCONJ
ejpam-6597	58	97	vr	vr	PROPN
ejpam-6597	58	98	∩	∩	PROPN
ejpam-6597	58	99	vt	vt	NOUN
ejpam-6597	58	100	=	=	PROPN
ejpam-6597	58	101	∅.	∅.	VERB
ejpam-6597	58	102	hence	hence	ADV
ejpam-6597	58	103	,	,	PUNCT
ejpam-6597	58	104	x	x	X
ejpam-6597	58	105	is	be	AUX
ejpam-6597	58	106	pre	pre	ADJ
ejpam-6597	58	107	-	-	ADJ
ejpam-6597	58	108	normal	normal	ADJ
ejpam-6597	58	109	.	.	PUNCT
ejpam-6597	59	1	the	the	DET
ejpam-6597	59	2	converse	converse	NOUN
ejpam-6597	59	3	of	of	ADP
ejpam-6597	59	4	theorem	theorem	ADJ
ejpam-6597	59	5	2	2	NUM
ejpam-6597	59	6	is	be	AUX
ejpam-6597	59	7	not	not	PART
ejpam-6597	59	8	true	true	ADJ
ejpam-6597	59	9	in	in	ADP
ejpam-6597	59	10	general	general	ADJ
ejpam-6597	59	11	.	.	PUNCT
ejpam-6597	60	1	here	here	ADV
ejpam-6597	60	2	is	be	AUX
ejpam-6597	60	3	an	an	DET
ejpam-6597	60	4	example	example	NOUN
ejpam-6597	60	5	of	of	ADP
ejpam-6597	60	6	a	a	DET
ejpam-6597	60	7	pre	pre	ADJ
ejpam-6597	60	8	-	-	ADJ
ejpam-6597	60	9	normal	normal	ADJ
ejpam-6597	60	10	space	space	NOUN
ejpam-6597	60	11	which	which	PRON
ejpam-6597	60	12	is	be	AUX
ejpam-6597	60	13	not	not	PART
ejpam-6597	60	14	collectionwise	collectionwise	ADV
ejpam-6597	60	15	pre	pre	ADJ
ejpam-6597	60	16	-	-	ADJ
ejpam-6597	60	17	normal	normal	ADJ
ejpam-6597	60	18	:	:	PUNCT
ejpam-6597	60	19	example	example	NOUN
ejpam-6597	61	1	2	2	NUM
ejpam-6597	61	2	.	.	X
ejpam-6597	62	1	the	the	DET
ejpam-6597	62	2	left	left	ADJ
ejpam-6597	62	3	ray	ray	NOUN
ejpam-6597	62	4	topology	topology	NOUN
ejpam-6597	62	5	(	(	PUNCT
ejpam-6597	62	6	r	r	NOUN
ejpam-6597	62	7	,	,	PUNCT
ejpam-6597	62	8	l	l	NOUN
ejpam-6597	62	9	)	)	PUNCT
ejpam-6597	62	10	and	and	CCONJ
ejpam-6597	62	11	the	the	DET
ejpam-6597	62	12	right	right	ADJ
ejpam-6597	62	13	ray	ray	NOUN
ejpam-6597	62	14	topology	topology	NOUN
ejpam-6597	62	15	(	(	PUNCT
ejpam-6597	62	16	r	r	NOUN
ejpam-6597	62	17	,	,	PUNCT
ejpam-6597	62	18	r	r	NOUN
ejpam-6597	62	19	)	)	PUNCT
ejpam-6597	62	20	are	be	AUX
ejpam-6597	62	21	normal	normal	ADJ
ejpam-6597	62	22	and	and	CCONJ
ejpam-6597	62	23	almost	almost	ADV
ejpam-6597	62	24	completely	completely	ADV
ejpam-6597	62	25	regular	regular	ADJ
ejpam-6597	62	26	spaces	space	NOUN
ejpam-6597	62	27	.	.	PUNCT
ejpam-6597	63	1	since	since	SCONJ
ejpam-6597	63	2	the	the	DET
ejpam-6597	63	3	two	two	NUM
ejpam-6597	63	4	spaces	space	NOUN
ejpam-6597	63	5	are	be	AUX
ejpam-6597	63	6	normal	normal	ADJ
ejpam-6597	63	7	,	,	PUNCT
ejpam-6597	63	8	we	we	PRON
ejpam-6597	63	9	conclude	conclude	VERB
ejpam-6597	63	10	(	(	PUNCT
ejpam-6597	63	11	r	r	NOUN
ejpam-6597	63	12	,	,	PUNCT
ejpam-6597	63	13	l	l	NOUN
ejpam-6597	63	14	)	)	PUNCT
ejpam-6597	63	15	and	and	CCONJ
ejpam-6597	63	16	(	(	PUNCT
ejpam-6597	63	17	r	r	NOUN
ejpam-6597	63	18	,	,	PUNCT
ejpam-6597	63	19	r	r	NOUN
ejpam-6597	63	20	)	)	PUNCT
ejpam-6597	63	21	are	be	AUX
ejpam-6597	63	22	pre	pre	ADJ
ejpam-6597	63	23	-	-	ADJ
ejpam-6597	63	24	normal	normal	ADJ
ejpam-6597	63	25	.	.	PUNCT
ejpam-6597	64	1	since	since	SCONJ
ejpam-6597	64	2	the	the	DET
ejpam-6597	64	3	two	two	NUM
ejpam-6597	64	4	spaces	space	NOUN
ejpam-6597	64	5	are	be	AUX
ejpam-6597	64	6	not	not	PART
ejpam-6597	64	7	t1	t1	ADJ
ejpam-6597	64	8	,	,	PUNCT
ejpam-6597	64	9	we	we	PRON
ejpam-6597	64	10	get	get	VERB
ejpam-6597	64	11	(	(	PUNCT
ejpam-6597	64	12	r	r	NOUN
ejpam-6597	64	13	,	,	PUNCT
ejpam-6597	64	14	l	l	NOUN
ejpam-6597	64	15	)	)	PUNCT
ejpam-6597	64	16	and	and	CCONJ
ejpam-6597	64	17	(	(	PUNCT
ejpam-6597	64	18	r	r	NOUN
ejpam-6597	64	19	,	,	PUNCT
ejpam-6597	64	20	r	r	NOUN
ejpam-6597	64	21	)	)	PUNCT
ejpam-6597	64	22	are	be	AUX
ejpam-6597	64	23	not	not	PART
ejpam-6597	64	24	collectionwise	collectionwise	ADV
ejpam-6597	64	25	pre	pre	ADJ
ejpam-6597	64	26	-	-	ADJ
ejpam-6597	64	27	normal	normal	ADJ
ejpam-6597	64	28	.	.	PUNCT
ejpam-6597	65	1	therefore	therefore	ADV
ejpam-6597	65	2	,	,	PUNCT
ejpam-6597	65	3	(	(	PUNCT
ejpam-6597	65	4	r	r	NOUN
ejpam-6597	65	5	,	,	PUNCT
ejpam-6597	65	6	l	l	NOUN
ejpam-6597	65	7	)	)	PUNCT
ejpam-6597	65	8	and	and	CCONJ
ejpam-6597	65	9	(	(	PUNCT
ejpam-6597	65	10	r	r	NOUN
ejpam-6597	65	11	,	,	PUNCT
ejpam-6597	65	12	r	r	NOUN
ejpam-6597	65	13	)	)	PUNCT
ejpam-6597	65	14	are	be	AUX
ejpam-6597	65	15	examples	example	NOUN
ejpam-6597	65	16	of	of	ADP
ejpam-6597	65	17	pre	pre	ADJ
ejpam-6597	65	18	-	-	ADJ
ejpam-6597	65	19	normal	normal	ADJ
ejpam-6597	65	20	spaces	space	NOUN
ejpam-6597	65	21	which	which	PRON
ejpam-6597	65	22	are	be	AUX
ejpam-6597	65	23	not	not	PART
ejpam-6597	65	24	collectionwise	collectionwise	ADV
ejpam-6597	65	25	pre	pre	ADJ
ejpam-6597	65	26	-	-	ADJ
ejpam-6597	65	27	normal	normal	ADJ
ejpam-6597	65	28	.	.	PUNCT
ejpam-6597	66	1	since	since	SCONJ
ejpam-6597	66	2	every	every	DET
ejpam-6597	66	3	hausdorff	hausdorff	NOUN
ejpam-6597	66	4	paracompact	paracompact	NOUN
ejpam-6597	66	5	space	space	NOUN
ejpam-6597	66	6	is	be	AUX
ejpam-6597	66	7	collectionwise	collectionwise	ADV
ejpam-6597	66	8	normal	normal	ADJ
ejpam-6597	66	9	[	[	X
ejpam-6597	66	10	9	9	NUM
ejpam-6597	66	11	]	]	PUNCT
ejpam-6597	66	12	,	,	PUNCT
ejpam-6597	66	13	and	and	CCONJ
ejpam-6597	66	14	every	every	DET
ejpam-6597	66	15	collectionwise	collectionwise	ADV
ejpam-6597	66	16	normal	normal	ADJ
ejpam-6597	66	17	is	be	AUX
ejpam-6597	66	18	collectionwise	collectionwise	ADV
ejpam-6597	66	19	pre	pre	ADJ
ejpam-6597	66	20	-	-	ADJ
ejpam-6597	66	21	normal	normal	ADJ
ejpam-6597	66	22	,	,	PUNCT
ejpam-6597	66	23	we	we	PRON
ejpam-6597	66	24	conclude	conclude	VERB
ejpam-6597	66	25	the	the	DET
ejpam-6597	66	26	next	next	ADJ
ejpam-6597	66	27	corollary	corollary	NOUN
ejpam-6597	66	28	:	:	PUNCT
ejpam-6597	66	29	corollary	corollary	ADJ
ejpam-6597	66	30	1	1	NUM
ejpam-6597	66	31	.	.	PUNCT
ejpam-6597	67	1	every	every	DET
ejpam-6597	67	2	hausdorff	hausdorff	NOUN
ejpam-6597	67	3	paracompact	paracompact	NOUN
ejpam-6597	67	4	space	space	NOUN
ejpam-6597	67	5	is	be	AUX
ejpam-6597	67	6	collectionwise	collectionwise	ADV
ejpam-6597	67	7	pre	pre	ADJ
ejpam-6597	67	8	-	-	ADJ
ejpam-6597	67	9	normal	normal	ADJ
ejpam-6597	67	10	.	.	PUNCT
ejpam-6597	68	1	observe	observe	VERB
ejpam-6597	68	2	that	that	SCONJ
ejpam-6597	68	3	:	:	PUNCT
ejpam-6597	68	4	every	every	DET
ejpam-6597	68	5	p1	p1	NOUN
ejpam-6597	68	6	-	-	PUNCT
ejpam-6597	68	7	paracompact	paracompact	ADJ
ejpam-6597	68	8	space	space	NOUN
ejpam-6597	68	9	is	be	AUX
ejpam-6597	68	10	paracompact	paracompact	ADJ
ejpam-6597	68	11	[	[	X
ejpam-6597	68	12	11	11	NUM
ejpam-6597	68	13	,	,	PUNCT
ejpam-6597	68	14	12	12	NUM
ejpam-6597	68	15	]	]	PUNCT
ejpam-6597	68	16	,	,	PUNCT
ejpam-6597	68	17	we	we	PRON
ejpam-6597	68	18	get	get	VERB
ejpam-6597	68	19	:	:	PUNCT
ejpam-6597	68	20	corollary	corollary	ADJ
ejpam-6597	68	21	2	2	NUM
ejpam-6597	68	22	.	.	PUNCT
ejpam-6597	69	1	every	every	DET
ejpam-6597	69	2	regular	regular	ADJ
ejpam-6597	69	3	p1	p1	NOUN
ejpam-6597	69	4	-	-	PUNCT
ejpam-6597	69	5	paracompact	paracompact	ADJ
ejpam-6597	69	6	t1	t1	NOUN
ejpam-6597	69	7	-	-	PUNCT
ejpam-6597	69	8	space	space	NOUN
ejpam-6597	69	9	is	be	AUX
ejpam-6597	69	10	collectionwise	collectionwise	ADV
ejpam-6597	69	11	pre	pre	ADJ
ejpam-6597	69	12	-	-	ADJ
ejpam-6597	69	13	normal	normal	ADJ
ejpam-6597	69	14	.	.	PUNCT
ejpam-6597	70	1	theorem	theorem	NOUN
ejpam-6597	70	2	3	3	NUM
ejpam-6597	70	3	.	.	PUNCT
ejpam-6597	71	1	every	every	DET
ejpam-6597	71	2	t1	t1	NOUN
ejpam-6597	71	3	pre	pre	ADJ
ejpam-6597	71	4	-	-	ADJ
ejpam-6597	71	5	regular	regular	ADJ
ejpam-6597	71	6	p1	p1	NOUN
ejpam-6597	71	7	-	-	PUNCT
ejpam-6597	71	8	paracompact	paracompact	ADJ
ejpam-6597	71	9	space	space	NOUN
ejpam-6597	71	10	is	be	AUX
ejpam-6597	71	11	pre	pre	ADJ
ejpam-6597	71	12	-	-	ADJ
ejpam-6597	71	13	normal	normal	ADJ
ejpam-6597	71	14	.	.	PUNCT
ejpam-6597	72	1	proof	proof	NOUN
ejpam-6597	72	2	.	.	PUNCT
ejpam-6597	73	1	let	let	VERB
ejpam-6597	73	2	x	x	PRON
ejpam-6597	73	3	be	be	AUX
ejpam-6597	73	4	a	a	DET
ejpam-6597	73	5	pre	pre	ADJ
ejpam-6597	73	6	-	-	ADJ
ejpam-6597	73	7	regular	regular	ADJ
ejpam-6597	73	8	paracompact	paracompact	ADJ
ejpam-6597	73	9	space	space	NOUN
ejpam-6597	73	10	.	.	PUNCT
ejpam-6597	74	1	we	we	PRON
ejpam-6597	74	2	show	show	VERB
ejpam-6597	74	3	that	that	SCONJ
ejpam-6597	74	4	x	x	PRON
ejpam-6597	74	5	is	be	AUX
ejpam-6597	74	6	pre	pre	ADJ
ejpam-6597	74	7	-	-	ADJ
ejpam-6597	74	8	normal	normal	ADJ
ejpam-6597	74	9	.	.	PUNCT
ejpam-6597	75	1	let	let	VERB
ejpam-6597	75	2	a	a	PRON
ejpam-6597	75	3	and	and	CCONJ
ejpam-6597	75	4	b	b	NOUN
ejpam-6597	75	5	be	be	AUX
ejpam-6597	75	6	any	any	DET
ejpam-6597	75	7	disjoint	disjoint	NOUN
ejpam-6597	75	8	closed	close	VERB
ejpam-6597	75	9	sets	set	NOUN
ejpam-6597	75	10	in	in	ADP
ejpam-6597	75	11	x	x	NOUN
ejpam-6597	75	12	,	,	PUNCT
ejpam-6597	75	13	i.e.	i.e.	X
ejpam-6597	75	14	a	a	DET
ejpam-6597	75	15	∩	∩	ADJ
ejpam-6597	75	16	b	b	NOUN
ejpam-6597	75	17	=	=	SYM
ejpam-6597	75	18	∅.	∅.	NOUN
ejpam-6597	75	19	then	then	ADV
ejpam-6597	75	20	for	for	ADP
ejpam-6597	75	21	each	each	DET
ejpam-6597	75	22	x	x	SYM
ejpam-6597	75	23	∈	∈	PROPN
ejpam-6597	75	24	a	a	X
ejpam-6597	75	25	,	,	PUNCT
ejpam-6597	75	26	we	we	PRON
ejpam-6597	75	27	have	have	VERB
ejpam-6597	75	28	x	x	PROPN
ejpam-6597	75	29	̸∈	̸∈	PROPN
ejpam-6597	75	30	b.	b.	PROPN
ejpam-6597	75	31	therefore	therefore	ADV
ejpam-6597	75	32	,	,	PUNCT
ejpam-6597	75	33	x	x	SYM
ejpam-6597	75	34	\	\	PROPN
ejpam-6597	75	35	b	b	NOUN
ejpam-6597	75	36	is	be	AUX
ejpam-6597	75	37	an	an	DET
ejpam-6597	75	38	open	open	ADJ
ejpam-6597	75	39	containing	contain	VERB
ejpam-6597	75	40	x	x	NOUN
ejpam-6597	75	41	and	and	CCONJ
ejpam-6597	75	42	hence	hence	ADV
ejpam-6597	75	43	x	x	ADP
ejpam-6597	75	44	\	\	PROPN
ejpam-6597	75	45	b	b	NOUN
ejpam-6597	75	46	is	be	AUX
ejpam-6597	75	47	pre	pre	ADJ
ejpam-6597	75	48	-	-	ADJ
ejpam-6597	75	49	open	open	ADJ
ejpam-6597	75	50	.	.	PUNCT
ejpam-6597	76	1	by	by	ADP
ejpam-6597	76	2	pre	pre	VERB
ejpam-6597	76	3	-	-	NOUN
ejpam-6597	76	4	regularity	regularity	NOUN
ejpam-6597	76	5	of	of	ADP
ejpam-6597	76	6	x	x	NOUN
ejpam-6597	76	7	,	,	PUNCT
ejpam-6597	76	8	there	there	PRON
ejpam-6597	76	9	exists	exist	VERB
ejpam-6597	76	10	a	a	DET
ejpam-6597	76	11	pre	pre	ADJ
ejpam-6597	76	12	-	-	ADJ
ejpam-6597	76	13	open	open	ADJ
ejpam-6597	76	14	set	set	NOUN
ejpam-6597	76	15	ux	ux	ADP
ejpam-6597	76	16	such	such	ADJ
ejpam-6597	76	17	that	that	SCONJ
ejpam-6597	76	18	x	x	SYM
ejpam-6597	76	19	∈	∈	NOUN
ejpam-6597	76	20	ux	ux	NOUN
ejpam-6597	76	21	and	and	CCONJ
ejpam-6597	76	22	cl(ux	cl(ux	NOUN
ejpam-6597	76	23	)	)	PUNCT
ejpam-6597	76	24	∩	∩	NOUN
ejpam-6597	76	25	b	b	X
ejpam-6597	76	26	=	=	PUNCT
ejpam-6597	76	27	∅.	∅.	NOUN
ejpam-6597	76	28	so	so	ADV
ejpam-6597	76	29	,	,	PUNCT
ejpam-6597	76	30	the	the	DET
ejpam-6597	76	31	family	family	NOUN
ejpam-6597	76	32	{	{	PUNCT
ejpam-6597	76	33	ux	ux	NOUN
ejpam-6597	76	34	:	:	PUNCT
ejpam-6597	76	35	x	x	SYM
ejpam-6597	76	36	∈	∈	NOUN
ejpam-6597	76	37	a}∪{x	a}∪{x	NOUN
ejpam-6597	76	38	\b	\b	PROPN
ejpam-6597	76	39	}	}	PUNCT
ejpam-6597	76	40	is	be	AUX
ejpam-6597	76	41	pre	pre	ADJ
ejpam-6597	76	42	-	-	ADJ
ejpam-6597	76	43	open	open	ADJ
ejpam-6597	76	44	cover	cover	NOUN
ejpam-6597	76	45	of	of	ADP
ejpam-6597	76	46	x.	x.	NOUN
ejpam-6597	76	47	since	since	SCONJ
ejpam-6597	76	48	x	x	PROPN
ejpam-6597	76	49	is	be	AUX
ejpam-6597	76	50	p1	p1	NOUN
ejpam-6597	76	51	-	-	NOUN
ejpam-6597	76	52	paracompact	paracompact	ADJ
ejpam-6597	76	53	,	,	PUNCT
ejpam-6597	76	54	there	there	PRON
ejpam-6597	76	55	exists	exist	VERB
ejpam-6597	76	56	a	a	DET
ejpam-6597	76	57	locally	locally	ADV
ejpam-6597	76	58	finite	finite	ADJ
ejpam-6597	76	59	pre	pre	ADJ
ejpam-6597	76	60	-	-	ADJ
ejpam-6597	76	61	open	open	ADJ
ejpam-6597	76	62	refinement	refinement	NOUN
ejpam-6597	76	63	of	of	ADP
ejpam-6597	76	64	it	it	PRON
ejpam-6597	76	65	.	.	PUNCT
ejpam-6597	77	1	let	let	VERB
ejpam-6597	77	2	u	u	PRON
ejpam-6597	77	3	=	=	X
ejpam-6597	77	4	{	{	PUNCT
ejpam-6597	77	5	uα	uα	X
ejpam-6597	77	6	:	:	PUNCT
ejpam-6597	77	7	α	α	PROPN
ejpam-6597	77	8	∈	∈	PROPN
ejpam-6597	77	9	λ	λ	NOUN
ejpam-6597	77	10	}	}	PUNCT
ejpam-6597	77	11	denotes	denote	NOUN
ejpam-6597	77	12	to	to	ADP
ejpam-6597	77	13	the	the	DET
ejpam-6597	77	14	members	member	NOUN
ejpam-6597	77	15	of	of	ADP
ejpam-6597	77	16	the	the	DET
ejpam-6597	77	17	family	family	NOUN
ejpam-6597	77	18	which	which	PRON
ejpam-6597	77	19	have	have	VERB
ejpam-6597	77	20	a	a	DET
ejpam-6597	77	21	non	non	ADJ
ejpam-6597	77	22	-	-	ADJ
ejpam-6597	77	23	empty	empty	ADJ
ejpam-6597	77	24	intersection	intersection	NOUN
ejpam-6597	77	25	with	with	ADP
ejpam-6597	77	26	a.	a.	NOUN
ejpam-6597	77	27	let	let	VERB
ejpam-6597	77	28	v1	v1	NOUN
ejpam-6597	77	29	=	=	SYM
ejpam-6597	77	30	∪α∈λuα	∪α∈λuα	PROPN
ejpam-6597	77	31	.	.	PUNCT
ejpam-6597	78	1	then	then	ADV
ejpam-6597	78	2	,	,	PUNCT
ejpam-6597	78	3	v1	v1	PROPN
ejpam-6597	78	4	is	be	AUX
ejpam-6597	78	5	pre	pre	ADJ
ejpam-6597	78	6	-	-	ADJ
ejpam-6597	78	7	open	open	ADJ
ejpam-6597	78	8	such	such	ADJ
ejpam-6597	78	9	that	that	SCONJ
ejpam-6597	78	10	a	a	DET
ejpam-6597	78	11	⊆	⊆	NUM
ejpam-6597	78	12	v1	v1	NOUN
ejpam-6597	78	13	.	.	PUNCT
ejpam-6597	79	1	let	let	VERB
ejpam-6597	79	2	v2	v2	VERB
ejpam-6597	79	3	=	=	PUNCT
ejpam-6597	79	4	x	x	SYM
ejpam-6597	79	5	\	\	X
ejpam-6597	79	6	∪α∈λcl(uα	∪α∈λcl(uα	NOUN
ejpam-6597	79	7	)	)	PUNCT
ejpam-6597	79	8	.	.	PUNCT
ejpam-6597	80	1	then	then	ADV
ejpam-6597	80	2	,	,	PUNCT
ejpam-6597	80	3	v2	v2	PROPN
ejpam-6597	80	4	is	be	AUX
ejpam-6597	80	5	pre	pre	ADJ
ejpam-6597	80	6	-	-	ADJ
ejpam-6597	80	7	open	open	ADJ
ejpam-6597	80	8	because	because	SCONJ
ejpam-6597	80	9	{	{	PUNCT
ejpam-6597	80	10	uα	uα	X
ejpam-6597	80	11	:	:	PUNCT
ejpam-6597	80	12	α	α	PROPN
ejpam-6597	80	13	∈	∈	PROPN
ejpam-6597	80	14	λ	λ	PROPN
ejpam-6597	80	15	}	}	PUNCT
ejpam-6597	80	16	is	be	AUX
ejpam-6597	80	17	locally	locally	ADV
ejpam-6597	80	18	finite	finite	NOUN
ejpam-6597	80	19	and	and	CCONJ
ejpam-6597	80	20	cl(∪α∈λuα	cl(∪α∈λuα	NOUN
ejpam-6597	80	21	)	)	PUNCT
ejpam-6597	80	22	=	=	PUNCT
ejpam-6597	80	23	∪α∈λcl(uα	∪α∈λcl(uα	NOUN
ejpam-6597	80	24	)	)	PUNCT
ejpam-6597	80	25	.	.	PUNCT
ejpam-6597	81	1	thus	thus	ADV
ejpam-6597	81	2	,	,	PUNCT
ejpam-6597	81	3	v1	v1	NOUN
ejpam-6597	81	4	∩	∩	ADJ
ejpam-6597	81	5	v2	v2	NOUN
ejpam-6597	81	6	=	=	PUNCT
ejpam-6597	81	7	∅.	∅.	NOUN
ejpam-6597	81	8	since	since	SCONJ
ejpam-6597	81	9	u	u	NOUN
ejpam-6597	81	10	is	be	AUX
ejpam-6597	81	11	refinement	refinement	NOUN
ejpam-6597	81	12	and	and	CCONJ
ejpam-6597	81	13	each	each	DET
ejpam-6597	81	14	member	member	NOUN
ejpam-6597	81	15	of	of	ADP
ejpam-6597	81	16	it	it	PRON
ejpam-6597	81	17	intersects	intersect	VERB
ejpam-6597	81	18	a	a	PRON
ejpam-6597	81	19	,	,	PUNCT
ejpam-6597	81	20	for	for	SCONJ
ejpam-6597	81	21	each	each	DET
ejpam-6597	81	22	uα	uα	PROPN
ejpam-6597	81	23	∈	∈	PROPN
ejpam-6597	81	24	u	u	NOUN
ejpam-6597	81	25	there	there	PRON
ejpam-6597	81	26	exists	exist	VERB
ejpam-6597	81	27	x	x	X
ejpam-6597	81	28	∈	∈	PROPN
ejpam-6597	81	29	a	a	DET
ejpam-6597	81	30	such	such	ADJ
ejpam-6597	81	31	that	that	SCONJ
ejpam-6597	81	32	uα	uα	PROPN
ejpam-6597	81	33	⊆	⊆	NUM
ejpam-6597	81	34	cl(ux	cl(ux	NOUN
ejpam-6597	81	35	)	)	PUNCT
ejpam-6597	81	36	.	.	PUNCT
ejpam-6597	82	1	now	now	ADV
ejpam-6597	82	2	,	,	PUNCT
ejpam-6597	82	3	cl(uα	cl(uα	PROPN
ejpam-6597	82	4	)	)	PUNCT
ejpam-6597	83	1	⊆	⊆	NUM
ejpam-6597	83	2	x	x	SYM
ejpam-6597	83	3	\	\	PROPN
ejpam-6597	83	4	b.	b.	PROPN
ejpam-6597	83	5	thus	thus	ADV
ejpam-6597	83	6	,	,	PUNCT
ejpam-6597	83	7	b	b	PROPN
ejpam-6597	83	8	⊆	⊆	NUM
ejpam-6597	83	9	x	x	SYM
ejpam-6597	83	10	\	\	PROPN
ejpam-6597	83	11	cl(uα	cl(uα	NOUN
ejpam-6597	83	12	)	)	PUNCT
ejpam-6597	83	13	for	for	ADP
ejpam-6597	83	14	each	each	DET
ejpam-6597	83	15	uα	uα	PROPN
ejpam-6597	83	16	∈	∈	PROPN
ejpam-6597	83	17	u	u	PROPN
ejpam-6597	83	18	.	.	PUNCT
ejpam-6597	84	1	so	so	ADV
ejpam-6597	84	2	,	,	PUNCT
ejpam-6597	84	3	b	b	PROPN
ejpam-6597	84	4	⊆	⊆	NUM
ejpam-6597	84	5	∩α∈λ(x	∩α∈λ(x	PROPN
ejpam-6597	84	6	\	\	PROPN
ejpam-6597	84	7	cl(uα	cl(uα	NOUN
ejpam-6597	84	8	)	)	PUNCT
ejpam-6597	84	9	)	)	PUNCT
ejpam-6597	85	1	=	=	PUNCT
ejpam-6597	85	2	x	x	SYM
ejpam-6597	85	3	\	\	X
ejpam-6597	85	4	∪α∈λcl(uα	∪α∈λcl(uα	PROPN
ejpam-6597	85	5	)	)	PUNCT
ejpam-6597	85	6	=	=	SYM
ejpam-6597	85	7	v2	v2	PROPN
ejpam-6597	85	8	.	.	PUNCT
ejpam-6597	86	1	thus	thus	ADV
ejpam-6597	86	2	,	,	PUNCT
ejpam-6597	86	3	b	b	PROPN
ejpam-6597	86	4	⊆	⊆	NUM
ejpam-6597	86	5	v2	v2	NOUN
ejpam-6597	86	6	.	.	PUNCT
ejpam-6597	87	1	therefore	therefore	ADV
ejpam-6597	87	2	,	,	PUNCT
ejpam-6597	87	3	v1	v1	VERB
ejpam-6597	87	4	and	and	CCONJ
ejpam-6597	87	5	v2	v2	PROPN
ejpam-6597	87	6	are	be	AUX
ejpam-6597	87	7	disjoint	disjoint	ADJ
ejpam-6597	87	8	pre	pre	ADJ
ejpam-6597	87	9	-	-	ADJ
ejpam-6597	87	10	open	open	ADJ
ejpam-6597	87	11	subsets	subset	NOUN
ejpam-6597	87	12	of	of	ADP
ejpam-6597	87	13	x	x	SYM
ejpam-6597	87	14	such	such	ADJ
ejpam-6597	87	15	that	that	SCONJ
ejpam-6597	87	16	a	a	DET
ejpam-6597	87	17	⊆	⊆	NUM
ejpam-6597	87	18	v1	v1	NOUN
ejpam-6597	87	19	and	and	CCONJ
ejpam-6597	87	20	b	b	NOUN
ejpam-6597	87	21	⊆	⊆	NUM
ejpam-6597	87	22	v2	v2	NOUN
ejpam-6597	87	23	.	.	PUNCT
ejpam-6597	88	1	hence	hence	ADV
ejpam-6597	88	2	,	,	PUNCT
ejpam-6597	88	3	x	x	X
ejpam-6597	88	4	is	be	AUX
ejpam-6597	88	5	pre	pre	ADJ
ejpam-6597	88	6	-	-	ADJ
ejpam-6597	88	7	normal	normal	ADJ
ejpam-6597	88	8	.	.	PUNCT
ejpam-6597	89	1	s.	s.	PROPN
ejpam-6597	89	2	a.	a.	PROPN
ejpam-6597	89	3	thabit	thabit	PROPN
ejpam-6597	89	4	,	,	PUNCT
ejpam-6597	89	5	a.	a.	PROPN
ejpam-6597	89	6	al	al	PROPN
ejpam-6597	89	7	-	-	PUNCT
ejpam-6597	89	8	awadi	awadi	PROPN
ejpam-6597	89	9	,	,	PUNCT
ejpam-6597	89	10	r.	r.	PROPN
ejpam-6597	89	11	noaman	noaman	PROPN
ejpam-6597	89	12	/	/	SYM
ejpam-6597	89	13	eur	eur	PROPN
ejpam-6597	89	14	.	.	PUNCT
ejpam-6597	90	1	j.	j.	PROPN
ejpam-6597	90	2	pure	pure	PROPN
ejpam-6597	90	3	appl	appl	PROPN
ejpam-6597	90	4	.	.	PROPN
ejpam-6597	90	5	math	math	PROPN
ejpam-6597	90	6	,	,	PUNCT
ejpam-6597	90	7	18	18	NUM
ejpam-6597	90	8	(	(	PUNCT
ejpam-6597	90	9	4	4	NUM
ejpam-6597	90	10	)	)	PUNCT
ejpam-6597	90	11	(	(	PUNCT
ejpam-6597	90	12	2025	2025	NUM
ejpam-6597	90	13	)	)	PUNCT
ejpam-6597	90	14	,	,	PUNCT
ejpam-6597	90	15	6597	6597	NUM
ejpam-6597	90	16	4	4	NUM
ejpam-6597	90	17	of	of	ADP
ejpam-6597	90	18	15	15	NUM
ejpam-6597	90	19	theorem	theorem	NOUN
ejpam-6597	90	20	4	4	NUM
ejpam-6597	90	21	.	.	PUNCT
ejpam-6597	91	1	every	every	DET
ejpam-6597	91	2	t1	t1	NOUN
ejpam-6597	91	3	pre	pre	ADJ
ejpam-6597	91	4	-	-	ADJ
ejpam-6597	91	5	regular	regular	ADJ
ejpam-6597	91	6	space	space	NOUN
ejpam-6597	91	7	is	be	AUX
ejpam-6597	91	8	pre	pre	ADJ
ejpam-6597	91	9	-	-	NOUN
ejpam-6597	91	10	t2	t2	ADJ
ejpam-6597	91	11	.	.	PUNCT
ejpam-6597	92	1	proof	proof	NOUN
ejpam-6597	92	2	.	.	PUNCT
ejpam-6597	93	1	let	let	VERB
ejpam-6597	93	2	x	x	PRON
ejpam-6597	93	3	be	be	AUX
ejpam-6597	93	4	a	a	DET
ejpam-6597	93	5	t1	t1	NOUN
ejpam-6597	93	6	pre	pre	ADJ
ejpam-6597	93	7	-	-	ADJ
ejpam-6597	93	8	regular	regular	ADJ
ejpam-6597	93	9	space	space	NOUN
ejpam-6597	93	10	.	.	PUNCT
ejpam-6597	94	1	let	let	VERB
ejpam-6597	94	2	x	x	PRON
ejpam-6597	94	3	,	,	PUNCT
ejpam-6597	94	4	y	y	PROPN
ejpam-6597	94	5	∈	∈	PROPN
ejpam-6597	94	6	x	x	PUNCT
ejpam-6597	94	7	such	such	ADJ
ejpam-6597	94	8	that	that	SCONJ
ejpam-6597	94	9	x	x	SYM
ejpam-6597	94	10	̸=	̸=	PROPN
ejpam-6597	94	11	y.	y.	NOUN
ejpam-6597	94	12	since	since	SCONJ
ejpam-6597	94	13	x	x	PROPN
ejpam-6597	94	14	is	be	AUX
ejpam-6597	94	15	t1	t1	NOUN
ejpam-6597	94	16	,	,	PUNCT
ejpam-6597	94	17	{	{	PUNCT
ejpam-6597	94	18	x	x	X
ejpam-6597	94	19	}	}	PUNCT
ejpam-6597	94	20	and	and	CCONJ
ejpam-6597	94	21	{	{	PUNCT
ejpam-6597	94	22	y	y	NOUN
ejpam-6597	94	23	}	}	PUNCT
ejpam-6597	94	24	are	be	AUX
ejpam-6597	94	25	closed	close	VERB
ejpam-6597	94	26	sets	set	NOUN
ejpam-6597	94	27	in	in	ADP
ejpam-6597	94	28	x	x	SYM
ejpam-6597	95	1	such	such	ADJ
ejpam-6597	95	2	that	that	SCONJ
ejpam-6597	95	3	x	x	SYM
ejpam-6597	95	4	̸∈	̸∈	PROPN
ejpam-6597	95	5	{	{	PUNCT
ejpam-6597	95	6	y	y	PROPN
ejpam-6597	95	7	}	}	PUNCT
ejpam-6597	95	8	.	.	PUNCT
ejpam-6597	96	1	by	by	ADP
ejpam-6597	96	2	pre	pre	VERB
ejpam-6597	96	3	-	-	NOUN
ejpam-6597	96	4	regularity	regularity	NOUN
ejpam-6597	96	5	of	of	ADP
ejpam-6597	96	6	x	x	NOUN
ejpam-6597	96	7	,	,	PUNCT
ejpam-6597	96	8	there	there	PRON
ejpam-6597	96	9	exist	exist	VERB
ejpam-6597	96	10	two	two	NUM
ejpam-6597	96	11	pre	pre	ADJ
ejpam-6597	96	12	-	-	ADJ
ejpam-6597	96	13	open	open	ADJ
ejpam-6597	96	14	sets	set	NOUN
ejpam-6597	96	15	u	u	NOUN
ejpam-6597	96	16	and	and	CCONJ
ejpam-6597	96	17	v	v	NOUN
ejpam-6597	96	18	in	in	ADP
ejpam-6597	96	19	x	x	PUNCT
ejpam-6597	96	20	such	such	ADJ
ejpam-6597	96	21	that	that	SCONJ
ejpam-6597	96	22	x	x	SYM
ejpam-6597	96	23	∈	∈	PROPN
ejpam-6597	96	24	u	u	NOUN
ejpam-6597	96	25	,	,	PUNCT
ejpam-6597	96	26	{	{	PUNCT
ejpam-6597	96	27	y	y	NOUN
ejpam-6597	96	28	}	}	PUNCT
ejpam-6597	96	29	⊆	⊆	NUM
ejpam-6597	96	30	v	v	NOUN
ejpam-6597	96	31	and	and	CCONJ
ejpam-6597	96	32	u	u	NOUN
ejpam-6597	96	33	∩	∩	NOUN
ejpam-6597	96	34	v	v	NOUN
ejpam-6597	96	35	=	=	PUNCT
ejpam-6597	96	36	∅.	∅.	VERB
ejpam-6597	96	37	thus	thus	ADV
ejpam-6597	96	38	,	,	PUNCT
ejpam-6597	96	39	there	there	PRON
ejpam-6597	96	40	exist	exist	VERB
ejpam-6597	96	41	two	two	NUM
ejpam-6597	96	42	pre	pre	ADJ
ejpam-6597	96	43	-	-	ADJ
ejpam-6597	96	44	open	open	ADJ
ejpam-6597	96	45	sets	set	NOUN
ejpam-6597	96	46	u	u	NOUN
ejpam-6597	96	47	and	and	CCONJ
ejpam-6597	96	48	v	v	NOUN
ejpam-6597	96	49	in	in	ADP
ejpam-6597	96	50	x	x	PUNCT
ejpam-6597	96	51	such	such	ADJ
ejpam-6597	96	52	that	that	SCONJ
ejpam-6597	96	53	x	x	SYM
ejpam-6597	96	54	∈	∈	PROPN
ejpam-6597	96	55	u	u	NOUN
ejpam-6597	96	56	,	,	PUNCT
ejpam-6597	96	57	y	y	PROPN
ejpam-6597	96	58	∈	∈	PROPN
ejpam-6597	96	59	v	v	NOUN
ejpam-6597	96	60	and	and	CCONJ
ejpam-6597	96	61	u	u	NOUN
ejpam-6597	96	62	∩	∩	NOUN
ejpam-6597	96	63	v	v	NOUN
ejpam-6597	96	64	=	=	PUNCT
ejpam-6597	96	65	∅.	∅.	VERB
ejpam-6597	96	66	therefore	therefore	ADV
ejpam-6597	96	67	,	,	PUNCT
ejpam-6597	96	68	x	x	X
ejpam-6597	96	69	is	be	AUX
ejpam-6597	96	70	pre	pre	ADJ
ejpam-6597	96	71	-	-	NOUN
ejpam-6597	96	72	t2	t2	ADJ
ejpam-6597	96	73	.	.	PUNCT
ejpam-6597	97	1	theorem	theorem	NOUN
ejpam-6597	97	2	5	5	NUM
ejpam-6597	97	3	.	.	PUNCT
ejpam-6597	98	1	every	every	DET
ejpam-6597	98	2	pre	pre	ADJ
ejpam-6597	98	3	-	-	ADJ
ejpam-6597	98	4	t2	t2	ADJ
ejpam-6597	98	5	p1	p1	NOUN
ejpam-6597	98	6	-	-	PUNCT
ejpam-6597	98	7	paracompact	paracompact	ADJ
ejpam-6597	98	8	space	space	NOUN
ejpam-6597	98	9	is	be	AUX
ejpam-6597	98	10	collectionwise	collectionwise	ADV
ejpam-6597	98	11	pre	pre	ADJ
ejpam-6597	98	12	-	-	ADJ
ejpam-6597	98	13	normal	normal	ADJ
ejpam-6597	98	14	.	.	PUNCT
ejpam-6597	99	1	proof	proof	NOUN
ejpam-6597	99	2	.	.	PUNCT
ejpam-6597	100	1	let	let	VERB
ejpam-6597	100	2	f	f	NOUN
ejpam-6597	100	3	=	=	PRON
ejpam-6597	100	4	{	{	PUNCT
ejpam-6597	100	5	bs	bs	X
ejpam-6597	100	6	:	:	PUNCT
ejpam-6597	100	7	s	s	X
ejpam-6597	100	8	∈	∈	PROPN
ejpam-6597	100	9	s	s	AUX
ejpam-6597	100	10	}	}	PUNCT
ejpam-6597	100	11	be	be	AUX
ejpam-6597	100	12	a	a	DET
ejpam-6597	100	13	discrete	discrete	ADJ
ejpam-6597	100	14	family	family	NOUN
ejpam-6597	100	15	of	of	ADP
ejpam-6597	100	16	closed	closed	ADJ
ejpam-6597	100	17	subsets	subset	NOUN
ejpam-6597	100	18	of	of	ADP
ejpam-6597	100	19	a	a	DET
ejpam-6597	100	20	p1	p1	NOUN
ejpam-6597	100	21	-	-	PUNCT
ejpam-6597	100	22	paracompact	paracompact	ADJ
ejpam-6597	100	23	space	space	NOUN
ejpam-6597	100	24	x.	x.	NOUN
ejpam-6597	100	25	then	then	ADV
ejpam-6597	100	26	,	,	PUNCT
ejpam-6597	100	27	for	for	SCONJ
ejpam-6597	100	28	each	each	DET
ejpam-6597	100	29	x	x	SYM
ejpam-6597	100	30	∈	∈	PROPN
ejpam-6597	100	31	x	x	X
ejpam-6597	100	32	,	,	PUNCT
ejpam-6597	100	33	choose	choose	VERB
ejpam-6597	100	34	a	a	DET
ejpam-6597	100	35	pre	pre	ADJ
ejpam-6597	100	36	-	-	ADJ
ejpam-6597	100	37	open	open	ADJ
ejpam-6597	100	38	neighborhood	neighborhood	NOUN
ejpam-6597	100	39	hx	hx	NOUN
ejpam-6597	100	40	of	of	ADP
ejpam-6597	100	41	a	a	DET
ejpam-6597	100	42	point	point	NOUN
ejpam-6597	100	43	x	x	PUNCT
ejpam-6597	100	44	whose	whose	DET
ejpam-6597	100	45	closure	closure	NOUN
ejpam-6597	100	46	meets	meet	VERB
ejpam-6597	100	47	at	at	ADP
ejpam-6597	100	48	most	most	ADV
ejpam-6597	100	49	one	one	NUM
ejpam-6597	100	50	set	set	VERB
ejpam-6597	100	51	bs	bs	NOUN
ejpam-6597	100	52	.	.	PUNCT
ejpam-6597	101	1	thus	thus	ADV
ejpam-6597	101	2	,	,	PUNCT
ejpam-6597	101	3	{	{	PUNCT
ejpam-6597	101	4	hx	hx	NOUN
ejpam-6597	101	5	:	:	PUNCT
ejpam-6597	101	6	x	x	SYM
ejpam-6597	101	7	∈	∈	PROPN
ejpam-6597	101	8	x	x	PRON
ejpam-6597	101	9	}	}	PUNCT
ejpam-6597	101	10	is	be	AUX
ejpam-6597	101	11	a	a	DET
ejpam-6597	101	12	pre	pre	ADJ
ejpam-6597	101	13	-	-	ADJ
ejpam-6597	101	14	open	open	ADJ
ejpam-6597	101	15	cover	cover	NOUN
ejpam-6597	101	16	for	for	ADP
ejpam-6597	101	17	x.	x.	NOUN
ejpam-6597	101	18	by	by	ADP
ejpam-6597	101	19	p1paracompactness	p1paracompactness	ADJ
ejpam-6597	101	20	ofx	ofx	NOUN
ejpam-6597	101	21	,	,	PUNCT
ejpam-6597	101	22	there	there	PRON
ejpam-6597	101	23	exists	exist	VERB
ejpam-6597	101	24	a	a	DET
ejpam-6597	101	25	locally	locally	ADV
ejpam-6597	101	26	finite	finite	ADJ
ejpam-6597	101	27	pre	pre	ADJ
ejpam-6597	101	28	-	-	ADJ
ejpam-6597	101	29	open	open	ADJ
ejpam-6597	101	30	refinementw	refinementw	NOUN
ejpam-6597	101	31	of	of	ADP
ejpam-6597	101	32	{	{	PUNCT
ejpam-6597	101	33	hx	hx	PROPN
ejpam-6597	101	34	:	:	PUNCT
ejpam-6597	101	35	x	x	SYM
ejpam-6597	101	36	∈	∈	NOUN
ejpam-6597	101	37	x	x	NOUN
ejpam-6597	101	38	}	}	PUNCT
ejpam-6597	101	39	.	.	PUNCT
ejpam-6597	102	1	now	now	ADV
ejpam-6597	102	2	,	,	PUNCT
ejpam-6597	102	3	for	for	ADP
ejpam-6597	102	4	each	each	DET
ejpam-6597	102	5	s	s	X
ejpam-6597	102	6	∈	∈	PROPN
ejpam-6597	102	7	s	s	NOUN
ejpam-6597	102	8	,	,	PUNCT
ejpam-6597	102	9	let	let	VERB
ejpam-6597	102	10	vs	vs	ADP
ejpam-6597	102	11	=	=	PUNCT
ejpam-6597	102	12	x	x	SYM
ejpam-6597	102	13	\	\	PROPN
ejpam-6597	102	14	⋃	⋃	PUNCT
ejpam-6597	102	15	{	{	PUNCT
ejpam-6597	102	16	cl(w	cl(w	NOUN
ejpam-6597	102	17	)	)	PUNCT
ejpam-6597	102	18	:	:	PUNCT
ejpam-6597	103	1	w	w	X
ejpam-6597	103	2	∈	∈	PROPN
ejpam-6597	103	3	w	w	PROPN
ejpam-6597	103	4	and	and	CCONJ
ejpam-6597	103	5	cl(w	cl(w	NOUN
ejpam-6597	103	6	)	)	PUNCT
ejpam-6597	103	7	∩	∩	NOUN
ejpam-6597	103	8	bs	bs	ADP
ejpam-6597	103	9	=	=	VERB
ejpam-6597	103	10	∅	∅	NOUN
ejpam-6597	103	11	}	}	PUNCT
ejpam-6597	103	12	,	,	PUNCT
ejpam-6597	103	13	which	which	PRON
ejpam-6597	103	14	is	be	AUX
ejpam-6597	103	15	pre	pre	ADJ
ejpam-6597	103	16	-	-	ADJ
ejpam-6597	103	17	open	open	ADJ
ejpam-6597	103	18	in	in	ADP
ejpam-6597	103	19	x	x	PUNCT
ejpam-6597	103	20	for	for	SCONJ
ejpam-6597	103	21	each	each	DET
ejpam-6597	103	22	s	s	X
ejpam-6597	103	23	∈	∈	NOUN
ejpam-6597	103	24	s	s	VERB
ejpam-6597	103	25	such	such	ADJ
ejpam-6597	103	26	that	that	SCONJ
ejpam-6597	103	27	bs	bs	PROPN
ejpam-6597	103	28	⊆	⊆	NUM
ejpam-6597	103	29	vs.	vs.	ADP
ejpam-6597	103	30	since	since	SCONJ
ejpam-6597	103	31	for	for	ADP
ejpam-6597	103	32	each	each	DET
ejpam-6597	103	33	w	w	PROPN
ejpam-6597	103	34	∈	∈	PROPN
ejpam-6597	103	35	w	w	PROPN
ejpam-6597	103	36	,	,	PUNCT
ejpam-6597	103	37	cl(w	cl(w	NOUN
ejpam-6597	103	38	)	)	PUNCT
ejpam-6597	103	39	meets	meet	VERB
ejpam-6597	103	40	at	at	ADP
ejpam-6597	103	41	most	most	ADV
ejpam-6597	103	42	one	one	NUM
ejpam-6597	103	43	set	set	VERB
ejpam-6597	103	44	bs	bs	NOUN
ejpam-6597	103	45	.	.	PUNCT
ejpam-6597	104	1	then	then	ADV
ejpam-6597	104	2	,	,	PUNCT
ejpam-6597	104	3	w	w	NOUN
ejpam-6597	104	4	meets	meet	VERB
ejpam-6597	104	5	at	at	ADP
ejpam-6597	104	6	most	most	ADV
ejpam-6597	104	7	one	one	NUM
ejpam-6597	104	8	set	set	VERB
ejpam-6597	104	9	bs	bs	NOUN
ejpam-6597	104	10	.	.	PUNCT
ejpam-6597	105	1	so	so	ADV
ejpam-6597	105	2	,	,	PUNCT
ejpam-6597	105	3	{	{	PUNCT
ejpam-6597	105	4	vs	vs	ADP
ejpam-6597	105	5	:	:	PUNCT
ejpam-6597	105	6	s	s	X
ejpam-6597	105	7	∈	∈	PROPN
ejpam-6597	105	8	s	s	AUX
ejpam-6597	105	9	}	}	PUNCT
ejpam-6597	105	10	is	be	AUX
ejpam-6597	105	11	a	a	DET
ejpam-6597	105	12	discrete	discrete	ADJ
ejpam-6597	105	13	family	family	NOUN
ejpam-6597	105	14	of	of	ADP
ejpam-6597	105	15	pre	pre	ADJ
ejpam-6597	105	16	-	-	ADJ
ejpam-6597	105	17	open	open	ADJ
ejpam-6597	105	18	subsets	subset	NOUN
ejpam-6597	105	19	of	of	ADP
ejpam-6597	105	20	x	x	SYM
ejpam-6597	105	21	such	such	ADJ
ejpam-6597	105	22	that	that	SCONJ
ejpam-6597	105	23	bs	bs	NOUN
ejpam-6597	105	24	⊆	⊆	NUM
ejpam-6597	105	25	vs	vs	ADP
ejpam-6597	105	26	for	for	ADP
ejpam-6597	105	27	each	each	DET
ejpam-6597	105	28	s	s	PROPN
ejpam-6597	105	29	∈	∈	PROPN
ejpam-6597	105	30	s.	s.	PROPN
ejpam-6597	105	31	since	since	SCONJ
ejpam-6597	105	32	x	x	PROPN
ejpam-6597	105	33	is	be	AUX
ejpam-6597	105	34	t1	t1	NOUN
ejpam-6597	105	35	,	,	PUNCT
ejpam-6597	105	36	we	we	PRON
ejpam-6597	105	37	get	get	VERB
ejpam-6597	105	38	x	x	SYM
ejpam-6597	105	39	is	be	AUX
ejpam-6597	105	40	collectionwise	collectionwise	ADV
ejpam-6597	105	41	pre	pre	ADJ
ejpam-6597	105	42	-	-	ADJ
ejpam-6597	105	43	normal	normal	ADJ
ejpam-6597	105	44	.	.	PUNCT
ejpam-6597	106	1	since	since	SCONJ
ejpam-6597	106	2	every	every	DET
ejpam-6597	106	3	t2	t2	NOUN
ejpam-6597	106	4	-	-	PUNCT
ejpam-6597	106	5	space	space	NOUN
ejpam-6597	106	6	is	be	AUX
ejpam-6597	106	7	pre	pre	ADJ
ejpam-6597	106	8	-	-	ADJ
ejpam-6597	106	9	t2	t2	ADJ
ejpam-6597	106	10	-	-	PUNCT
ejpam-6597	106	11	space	space	NOUN
ejpam-6597	106	12	,	,	PUNCT
ejpam-6597	106	13	we	we	PRON
ejpam-6597	106	14	conclude	conclude	VERB
ejpam-6597	106	15	:	:	PUNCT
ejpam-6597	106	16	corollary	corollary	ADJ
ejpam-6597	106	17	3	3	X
ejpam-6597	106	18	.	.	PUNCT
ejpam-6597	107	1	every	every	DET
ejpam-6597	107	2	t2	t2	NOUN
ejpam-6597	107	3	p1	p1	NOUN
ejpam-6597	107	4	-	-	PUNCT
ejpam-6597	107	5	paracompact	paracompact	ADJ
ejpam-6597	107	6	space	space	NOUN
ejpam-6597	107	7	is	be	AUX
ejpam-6597	107	8	collectionwise	collectionwise	ADV
ejpam-6597	107	9	pre	pre	ADJ
ejpam-6597	107	10	-	-	ADJ
ejpam-6597	107	11	normal	normal	ADJ
ejpam-6597	107	12	.	.	PUNCT
ejpam-6597	108	1	since	since	SCONJ
ejpam-6597	108	2	every	every	DET
ejpam-6597	108	3	pre	pre	ADJ
ejpam-6597	108	4	-	-	ADJ
ejpam-6597	108	5	compact	compact	ADJ
ejpam-6597	108	6	space	space	NOUN
ejpam-6597	108	7	is	be	AUX
ejpam-6597	108	8	p1	p1	NOUN
ejpam-6597	108	9	-	-	PUNCT
ejpam-6597	108	10	paracompact	paracompact	ADJ
ejpam-6597	108	11	,	,	PUNCT
ejpam-6597	108	12	we	we	PRON
ejpam-6597	108	13	get	get	VERB
ejpam-6597	108	14	:	:	PUNCT
ejpam-6597	108	15	corollary	corollary	ADJ
ejpam-6597	108	16	4	4	NUM
ejpam-6597	108	17	.	.	PUNCT
ejpam-6597	109	1	every	every	DET
ejpam-6597	109	2	pre	pre	ADJ
ejpam-6597	109	3	-	-	ADJ
ejpam-6597	109	4	t2	t2	ADJ
ejpam-6597	109	5	pre	pre	ADJ
ejpam-6597	109	6	-	-	ADJ
ejpam-6597	109	7	compact	compact	ADJ
ejpam-6597	109	8	space	space	NOUN
ejpam-6597	109	9	is	be	AUX
ejpam-6597	109	10	collectionwise	collectionwise	ADV
ejpam-6597	109	11	pre	pre	ADJ
ejpam-6597	109	12	-	-	ADJ
ejpam-6597	109	13	normal	normal	ADJ
ejpam-6597	109	14	.	.	PUNCT
ejpam-6597	110	1	corollary	corollary	ADJ
ejpam-6597	110	2	5	5	NUM
ejpam-6597	110	3	.	.	PUNCT
ejpam-6597	111	1	every	every	DET
ejpam-6597	111	2	pre	pre	ADJ
ejpam-6597	111	3	-	-	ADJ
ejpam-6597	111	4	regular	regular	ADJ
ejpam-6597	111	5	pre	pre	ADJ
ejpam-6597	111	6	-	-	ADJ
ejpam-6597	111	7	compact	compact	ADJ
ejpam-6597	111	8	t1	t1	NOUN
ejpam-6597	111	9	-	-	PUNCT
ejpam-6597	111	10	space	space	NOUN
ejpam-6597	111	11	is	be	AUX
ejpam-6597	111	12	collectionwise	collectionwise	ADV
ejpam-6597	111	13	pre	pre	ADJ
ejpam-6597	111	14	-	-	ADJ
ejpam-6597	111	15	normal	normal	ADJ
ejpam-6597	111	16	.	.	PUNCT
ejpam-6597	112	1	the	the	DET
ejpam-6597	112	2	proofs	proof	NOUN
ejpam-6597	112	3	of	of	ADP
ejpam-6597	112	4	the	the	DET
ejpam-6597	112	5	next	next	ADJ
ejpam-6597	112	6	results	result	NOUN
ejpam-6597	112	7	is	be	AUX
ejpam-6597	112	8	similar	similar	ADJ
ejpam-6597	112	9	to	to	ADP
ejpam-6597	112	10	that	that	PRON
ejpam-6597	112	11	of	of	ADP
ejpam-6597	112	12	the	the	DET
ejpam-6597	112	13	corresponding	corresponding	ADJ
ejpam-6597	112	14	results	result	NOUN
ejpam-6597	112	15	for	for	ADP
ejpam-6597	112	16	normality	normality	NOUN
ejpam-6597	112	17	.	.	PUNCT
ejpam-6597	113	1	theorem	theorem	VERB
ejpam-6597	113	2	6	6	NUM
ejpam-6597	113	3	.	.	PUNCT
ejpam-6597	114	1	every	every	DET
ejpam-6597	114	2	t1	t1	NOUN
ejpam-6597	114	3	-	-	PUNCT
ejpam-6597	114	4	pre	pre	ADJ
ejpam-6597	114	5	-	-	ADJ
ejpam-6597	114	6	normal	normal	ADJ
ejpam-6597	114	7	space	space	NOUN
ejpam-6597	114	8	is	be	AUX
ejpam-6597	114	9	pre	pre	ADJ
ejpam-6597	114	10	-	-	ADJ
ejpam-6597	114	11	regular	regular	ADJ
ejpam-6597	114	12	.	.	PUNCT
ejpam-6597	115	1	proof	proof	NOUN
ejpam-6597	115	2	.	.	PUNCT
ejpam-6597	116	1	let	let	VERB
ejpam-6597	116	2	x	x	PRON
ejpam-6597	116	3	be	be	AUX
ejpam-6597	116	4	a	a	DET
ejpam-6597	116	5	t1	t1	NOUN
ejpam-6597	116	6	pre	pre	ADJ
ejpam-6597	116	7	-	-	ADJ
ejpam-6597	116	8	normal	normal	ADJ
ejpam-6597	116	9	space	space	NOUN
ejpam-6597	116	10	.	.	PUNCT
ejpam-6597	117	1	let	let	VERB
ejpam-6597	117	2	x	x	PUNCT
ejpam-6597	117	3	∈	∈	PROPN
ejpam-6597	117	4	x	x	X
ejpam-6597	117	5	and	and	CCONJ
ejpam-6597	117	6	f	f	PROPN
ejpam-6597	117	7	be	be	AUX
ejpam-6597	117	8	any	any	DET
ejpam-6597	117	9	closed	closed	ADJ
ejpam-6597	117	10	set	set	VERB
ejpam-6597	117	11	in	in	ADP
ejpam-6597	117	12	x	x	INTJ
ejpam-6597	117	13	such	such	ADJ
ejpam-6597	117	14	that	that	SCONJ
ejpam-6597	117	15	x	x	X
ejpam-6597	117	16	̸∈	̸∈	PROPN
ejpam-6597	117	17	f	f	PROPN
ejpam-6597	117	18	.	.	PUNCT
ejpam-6597	118	1	since	since	SCONJ
ejpam-6597	118	2	x	x	PROPN
ejpam-6597	118	3	is	be	AUX
ejpam-6597	118	4	t1	t1	NOUN
ejpam-6597	118	5	,	,	PUNCT
ejpam-6597	118	6	we	we	PRON
ejpam-6597	118	7	have	have	VERB
ejpam-6597	118	8	{	{	PUNCT
ejpam-6597	118	9	x	x	NOUN
ejpam-6597	118	10	}	}	PUNCT
ejpam-6597	118	11	is	be	AUX
ejpam-6597	118	12	closed	close	VERB
ejpam-6597	118	13	set	set	VERB
ejpam-6597	118	14	in	in	ADP
ejpam-6597	118	15	x	x	PUNCT
ejpam-6597	118	16	and	and	CCONJ
ejpam-6597	118	17	{	{	PUNCT
ejpam-6597	118	18	x	x	NOUN
ejpam-6597	118	19	}	}	PUNCT
ejpam-6597	118	20	∩	∩	ADJ
ejpam-6597	118	21	f	f	X
ejpam-6597	118	22	=	=	PUNCT
ejpam-6597	118	23	∅.	∅.	X
ejpam-6597	118	24	by	by	ADP
ejpam-6597	118	25	pre	pre	ADJ
ejpam-6597	118	26	-	-	NOUN
ejpam-6597	118	27	normality	normality	NOUN
ejpam-6597	118	28	of	of	ADP
ejpam-6597	118	29	x	x	NOUN
ejpam-6597	118	30	,	,	PUNCT
ejpam-6597	118	31	there	there	PRON
ejpam-6597	118	32	exist	exist	VERB
ejpam-6597	118	33	two	two	NUM
ejpam-6597	118	34	disjoint	disjoint	ADJ
ejpam-6597	118	35	pre	pre	ADJ
ejpam-6597	118	36	-	-	ADJ
ejpam-6597	118	37	open	open	ADJ
ejpam-6597	118	38	sets	set	NOUN
ejpam-6597	118	39	u	u	NOUN
ejpam-6597	118	40	and	and	CCONJ
ejpam-6597	118	41	v	v	NOUN
ejpam-6597	118	42	in	in	ADP
ejpam-6597	118	43	x	x	INTJ
ejpam-6597	118	44	such	such	ADJ
ejpam-6597	118	45	that	that	SCONJ
ejpam-6597	118	46	{	{	PUNCT
ejpam-6597	118	47	x	x	NOUN
ejpam-6597	118	48	}	}	PUNCT
ejpam-6597	118	49	⊆	⊆	NUM
ejpam-6597	118	50	u	u	NOUN
ejpam-6597	118	51	and	and	CCONJ
ejpam-6597	118	52	f	f	PROPN
ejpam-6597	118	53	⊆	⊆	NUM
ejpam-6597	118	54	v	v	NOUN
ejpam-6597	118	55	.	.	PUNCT
ejpam-6597	119	1	hence	hence	ADV
ejpam-6597	119	2	,	,	PUNCT
ejpam-6597	119	3	x	x	PUNCT
ejpam-6597	119	4	∈	∈	PROPN
ejpam-6597	119	5	u	u	PROPN
ejpam-6597	119	6	,	,	PUNCT
ejpam-6597	119	7	f	f	PROPN
ejpam-6597	119	8	⊆	⊆	PROPN
ejpam-6597	119	9	v	v	NOUN
ejpam-6597	119	10	and	and	CCONJ
ejpam-6597	119	11	u	u	NOUN
ejpam-6597	119	12	∩	∩	NOUN
ejpam-6597	119	13	v	v	NOUN
ejpam-6597	119	14	=	=	PUNCT
ejpam-6597	119	15	∅.	∅.	VERB
ejpam-6597	119	16	therefore	therefore	ADV
ejpam-6597	119	17	,	,	PUNCT
ejpam-6597	119	18	x	x	X
ejpam-6597	119	19	is	be	AUX
ejpam-6597	119	20	pre	pre	ADJ
ejpam-6597	119	21	-	-	ADJ
ejpam-6597	119	22	regular	regular	ADJ
ejpam-6597	119	23	.	.	PUNCT
ejpam-6597	120	1	since	since	SCONJ
ejpam-6597	120	2	every	every	DET
ejpam-6597	120	3	collectionwise	collectionwise	ADV
ejpam-6597	120	4	pre	pre	ADJ
ejpam-6597	120	5	-	-	ADJ
ejpam-6597	120	6	normal	normal	ADJ
ejpam-6597	120	7	space	space	NOUN
ejpam-6597	120	8	is	be	AUX
ejpam-6597	120	9	t1	t1	NOUN
ejpam-6597	120	10	,	,	PUNCT
ejpam-6597	120	11	we	we	PRON
ejpam-6597	120	12	get	get	VERB
ejpam-6597	120	13	:	:	PUNCT
ejpam-6597	120	14	corollary	corollary	ADJ
ejpam-6597	120	15	6	6	NUM
ejpam-6597	120	16	.	.	PUNCT
ejpam-6597	121	1	every	every	DET
ejpam-6597	121	2	collectionwise	collectionwise	ADV
ejpam-6597	121	3	pre	pre	ADJ
ejpam-6597	121	4	-	-	ADJ
ejpam-6597	121	5	normal	normal	ADJ
ejpam-6597	121	6	space	space	NOUN
ejpam-6597	121	7	is	be	AUX
ejpam-6597	121	8	pre	pre	ADJ
ejpam-6597	121	9	-	-	ADJ
ejpam-6597	121	10	regular	regular	ADJ
ejpam-6597	121	11	.	.	PUNCT
ejpam-6597	122	1	theorem	theorem	VERB
ejpam-6597	122	2	7	7	NUM
ejpam-6597	122	3	.	.	PUNCT
ejpam-6597	123	1	every	every	DET
ejpam-6597	123	2	pre	pre	ADJ
ejpam-6597	123	3	-	-	ADJ
ejpam-6597	123	4	regular	regular	ADJ
ejpam-6597	123	5	pre	pre	ADJ
ejpam-6597	123	6	-	-	NOUN
ejpam-6597	123	7	lindelöf	lindelöf	ADJ
ejpam-6597	123	8	space	space	NOUN
ejpam-6597	123	9	is	be	AUX
ejpam-6597	123	10	pre	pre	ADJ
ejpam-6597	123	11	-	-	ADJ
ejpam-6597	123	12	normal	normal	ADJ
ejpam-6597	123	13	.	.	PUNCT
ejpam-6597	124	1	s.	s.	PROPN
ejpam-6597	124	2	a.	a.	PROPN
ejpam-6597	124	3	thabit	thabit	PROPN
ejpam-6597	124	4	,	,	PUNCT
ejpam-6597	124	5	a.	a.	PROPN
ejpam-6597	124	6	al	al	PROPN
ejpam-6597	124	7	-	-	PUNCT
ejpam-6597	124	8	awadi	awadi	PROPN
ejpam-6597	124	9	,	,	PUNCT
ejpam-6597	124	10	r.	r.	PROPN
ejpam-6597	124	11	noaman	noaman	PROPN
ejpam-6597	124	12	/	/	SYM
ejpam-6597	124	13	eur	eur	PROPN
ejpam-6597	124	14	.	.	PUNCT
ejpam-6597	125	1	j.	j.	PROPN
ejpam-6597	125	2	pure	pure	PROPN
ejpam-6597	125	3	appl	appl	PROPN
ejpam-6597	125	4	.	.	PROPN
ejpam-6597	125	5	math	math	PROPN
ejpam-6597	125	6	,	,	PUNCT
ejpam-6597	125	7	18	18	NUM
ejpam-6597	125	8	(	(	PUNCT
ejpam-6597	125	9	4	4	NUM
ejpam-6597	125	10	)	)	PUNCT
ejpam-6597	125	11	(	(	PUNCT
ejpam-6597	125	12	2025	2025	NUM
ejpam-6597	125	13	)	)	PUNCT
ejpam-6597	125	14	,	,	PUNCT
ejpam-6597	125	15	6597	6597	NUM
ejpam-6597	125	16	5	5	NUM
ejpam-6597	125	17	of	of	ADP
ejpam-6597	125	18	15	15	NUM
ejpam-6597	125	19	proof	proof	NOUN
ejpam-6597	125	20	.	.	PUNCT
ejpam-6597	126	1	let	let	VERB
ejpam-6597	126	2	x	x	PRON
ejpam-6597	126	3	be	be	AUX
ejpam-6597	126	4	a	a	DET
ejpam-6597	126	5	pre	pre	ADJ
ejpam-6597	126	6	-	-	ADJ
ejpam-6597	126	7	regular	regular	ADJ
ejpam-6597	126	8	pre	pre	ADJ
ejpam-6597	126	9	-	-	ADJ
ejpam-6597	126	10	lindelöf	lindelöf	ADJ
ejpam-6597	126	11	space	space	NOUN
ejpam-6597	126	12	.	.	PUNCT
ejpam-6597	127	1	let	let	VERB
ejpam-6597	127	2	a	a	PRON
ejpam-6597	127	3	and	and	CCONJ
ejpam-6597	127	4	b	b	NOUN
ejpam-6597	127	5	be	be	AUX
ejpam-6597	127	6	any	any	DET
ejpam-6597	127	7	disjoint	disjoint	NOUN
ejpam-6597	127	8	closed	close	VERB
ejpam-6597	127	9	subsets	subset	NOUN
ejpam-6597	127	10	of	of	ADP
ejpam-6597	127	11	x	x	NOUN
ejpam-6597	127	12	,	,	PUNCT
ejpam-6597	127	13	i.e.	i.e.	X
ejpam-6597	127	14	a	a	DET
ejpam-6597	127	15	∩	∩	ADJ
ejpam-6597	127	16	b	b	NOUN
ejpam-6597	127	17	=	=	SYM
ejpam-6597	127	18	∅.	∅.	NOUN
ejpam-6597	127	19	then	then	ADV
ejpam-6597	127	20	for	for	ADP
ejpam-6597	127	21	each	each	DET
ejpam-6597	127	22	x	x	SYM
ejpam-6597	127	23	∈	∈	PROPN
ejpam-6597	127	24	a	a	X
ejpam-6597	127	25	,	,	PUNCT
ejpam-6597	127	26	we	we	PRON
ejpam-6597	127	27	have	have	VERB
ejpam-6597	127	28	x	x	PROPN
ejpam-6597	127	29	̸∈	̸∈	PROPN
ejpam-6597	127	30	b.	b.	PROPN
ejpam-6597	127	31	therefore	therefore	ADV
ejpam-6597	127	32	,	,	PUNCT
ejpam-6597	127	33	x	x	SYM
ejpam-6597	127	34	\	\	PROPN
ejpam-6597	127	35	b	b	NOUN
ejpam-6597	127	36	is	be	AUX
ejpam-6597	127	37	an	an	DET
ejpam-6597	127	38	open	open	ADJ
ejpam-6597	127	39	containing	contain	VERB
ejpam-6597	127	40	x	x	PUNCT
ejpam-6597	127	41	and	and	CCONJ
ejpam-6597	127	42	hence	hence	ADV
ejpam-6597	127	43	b	b	PROPN
ejpam-6597	127	44	is	be	AUX
ejpam-6597	127	45	pre	pre	ADJ
ejpam-6597	127	46	-	-	ADJ
ejpam-6597	127	47	open	open	ADJ
ejpam-6597	127	48	.	.	PUNCT
ejpam-6597	128	1	by	by	ADP
ejpam-6597	128	2	pre	pre	VERB
ejpam-6597	128	3	-	-	NOUN
ejpam-6597	128	4	regularity	regularity	NOUN
ejpam-6597	128	5	of	of	ADP
ejpam-6597	128	6	x	x	NOUN
ejpam-6597	128	7	,	,	PUNCT
ejpam-6597	128	8	there	there	PRON
ejpam-6597	128	9	exists	exist	VERB
ejpam-6597	128	10	a	a	DET
ejpam-6597	128	11	pre	pre	ADJ
ejpam-6597	128	12	-	-	ADJ
ejpam-6597	128	13	open	open	ADJ
ejpam-6597	128	14	set	set	NOUN
ejpam-6597	128	15	ux	ux	ADP
ejpam-6597	128	16	such	such	ADJ
ejpam-6597	128	17	that	that	SCONJ
ejpam-6597	128	18	x	x	SYM
ejpam-6597	128	19	∈	∈	PROPN
ejpam-6597	128	20	ux	ux	PROPN
ejpam-6597	128	21	,	,	PUNCT
ejpam-6597	128	22	ux	ux	PROPN
ejpam-6597	128	23	∩	∩	PROPN
ejpam-6597	128	24	b	b	NOUN
ejpam-6597	128	25	=	=	NOUN
ejpam-6597	128	26	∅	∅	NOUN
ejpam-6597	128	27	and	and	CCONJ
ejpam-6597	128	28	cl(ux	cl(ux	NOUN
ejpam-6597	128	29	)	)	PUNCT
ejpam-6597	128	30	∩	∩	NOUN
ejpam-6597	128	31	b	b	X
ejpam-6597	128	32	=	=	PUNCT
ejpam-6597	128	33	∅.	∅.	NOUN
ejpam-6597	128	34	so	so	ADV
ejpam-6597	128	35	,	,	PUNCT
ejpam-6597	128	36	the	the	DET
ejpam-6597	128	37	family	family	NOUN
ejpam-6597	128	38	{	{	PUNCT
ejpam-6597	128	39	ux	ux	NOUN
ejpam-6597	128	40	:	:	PUNCT
ejpam-6597	128	41	x	x	SYM
ejpam-6597	128	42	∈	∈	NOUN
ejpam-6597	128	43	a}∪{x	a}∪{x	NOUN
ejpam-6597	128	44	\b	\b	PROPN
ejpam-6597	128	45	}	}	PUNCT
ejpam-6597	128	46	is	be	AUX
ejpam-6597	128	47	pre	pre	ADJ
ejpam-6597	128	48	-	-	ADJ
ejpam-6597	128	49	open	open	ADJ
ejpam-6597	128	50	cover	cover	NOUN
ejpam-6597	128	51	of	of	ADP
ejpam-6597	128	52	x.	x.	NOUN
ejpam-6597	128	53	since	since	SCONJ
ejpam-6597	128	54	x	x	PROPN
ejpam-6597	128	55	is	be	AUX
ejpam-6597	128	56	pre	pre	NOUN
ejpam-6597	128	57	-	-	NOUN
ejpam-6597	128	58	lindelöf	lindelöf	NOUN
ejpam-6597	128	59	,	,	PUNCT
ejpam-6597	128	60	x	x	PRON
ejpam-6597	128	61	has	have	VERB
ejpam-6597	128	62	a	a	DET
ejpam-6597	128	63	countable	countable	ADJ
ejpam-6597	128	64	subcover	subcover	NOUN
ejpam-6597	128	65	say	say	VERB
ejpam-6597	128	66	{	{	PUNCT
ejpam-6597	128	67	uxi	uxi	NOUN
ejpam-6597	128	68	:	:	PUNCT
ejpam-6597	128	69	i	i	PRON
ejpam-6597	128	70	∈	∈	PROPN
ejpam-6597	128	71	n	n	CCONJ
ejpam-6597	128	72	}	}	PUNCT
ejpam-6597	128	73	.	.	PUNCT
ejpam-6597	129	1	observe	observe	VERB
ejpam-6597	129	2	that	that	SCONJ
ejpam-6597	129	3	a	a	DET
ejpam-6597	129	4	⊆	⊆	NUM
ejpam-6597	129	5	∞	∞	NUM
ejpam-6597	129	6	∪	∪	NOUN
ejpam-6597	129	7	i=1	i=1	PROPN
ejpam-6597	129	8	uxi	uxi	NOUN
ejpam-6597	129	9	and	and	CCONJ
ejpam-6597	129	10	b	b	X
ejpam-6597	129	11	⊆	⊆	NUM
ejpam-6597	129	12	x	x	SYM
ejpam-6597	129	13	\	\	NOUN
ejpam-6597	129	14	cl	cl	NOUN
ejpam-6597	129	15	(	(	PUNCT
ejpam-6597	129	16	∞	∞	PROPN
ejpam-6597	129	17	∪	∪	VERB
ejpam-6597	129	18	i=1	i=1	PROPN
ejpam-6597	129	19	uxi	uxi	NOUN
ejpam-6597	129	20	)	)	PUNCT
ejpam-6597	129	21	.	.	PUNCT
ejpam-6597	130	1	let	let	VERB
ejpam-6597	130	2	u	u	PRON
ejpam-6597	130	3	=	=	NOUN
ejpam-6597	130	4	∞	∞	NUM
ejpam-6597	130	5	∪	∪	VERB
ejpam-6597	130	6	i=1	i=1	PRON
ejpam-6597	130	7	uxi	uxi	NOUN
ejpam-6597	130	8	and	and	CCONJ
ejpam-6597	130	9	v	v	X
ejpam-6597	130	10	=	=	SYM
ejpam-6597	130	11	x	x	SYM
ejpam-6597	130	12	\	\	NOUN
ejpam-6597	130	13	cl	cl	NOUN
ejpam-6597	130	14	(	(	PUNCT
ejpam-6597	130	15	∞	∞	PROPN
ejpam-6597	130	16	∪	∪	VERB
ejpam-6597	130	17	i=1	i=1	PROPN
ejpam-6597	130	18	uxi	uxi	NOUN
ejpam-6597	130	19	)	)	PUNCT
ejpam-6597	130	20	.	.	PUNCT
ejpam-6597	131	1	then	then	ADV
ejpam-6597	131	2	,	,	PUNCT
ejpam-6597	131	3	u	u	NOUN
ejpam-6597	131	4	and	and	CCONJ
ejpam-6597	131	5	v	v	NOUN
ejpam-6597	131	6	are	be	AUX
ejpam-6597	131	7	disjoint	disjoint	ADJ
ejpam-6597	131	8	pre	pre	ADJ
ejpam-6597	131	9	-	-	ADJ
ejpam-6597	131	10	open	open	ADJ
ejpam-6597	131	11	sets	set	NOUN
ejpam-6597	131	12	in	in	ADP
ejpam-6597	131	13	x	x	SYM
ejpam-6597	131	14	such	such	ADJ
ejpam-6597	131	15	that	that	SCONJ
ejpam-6597	131	16	a	a	DET
ejpam-6597	131	17	⊆	⊆	NUM
ejpam-6597	131	18	u	u	NOUN
ejpam-6597	131	19	and	and	CCONJ
ejpam-6597	131	20	b	b	NOUN
ejpam-6597	131	21	⊆	⊆	NUM
ejpam-6597	131	22	v	v	NOUN
ejpam-6597	131	23	.	.	PUNCT
ejpam-6597	132	1	therefore	therefore	ADV
ejpam-6597	132	2	,	,	PUNCT
ejpam-6597	132	3	x	x	X
ejpam-6597	132	4	is	be	AUX
ejpam-6597	132	5	pre	pre	ADJ
ejpam-6597	132	6	-	-	ADJ
ejpam-6597	132	7	normal	normal	ADJ
ejpam-6597	132	8	.	.	PUNCT
ejpam-6597	133	1	theorem	theorem	VERB
ejpam-6597	133	2	8	8	NUM
ejpam-6597	133	3	.	.	PUNCT
ejpam-6597	134	1	every	every	DET
ejpam-6597	134	2	t1	t1	NOUN
ejpam-6597	134	3	pre	pre	ADJ
ejpam-6597	134	4	-	-	ADJ
ejpam-6597	134	5	regular	regular	ADJ
ejpam-6597	134	6	pre	pre	ADJ
ejpam-6597	134	7	-	-	NOUN
ejpam-6597	134	8	lindelöf	lindelöf	ADJ
ejpam-6597	134	9	space	space	NOUN
ejpam-6597	134	10	is	be	AUX
ejpam-6597	134	11	collectionwise	collectionwise	ADV
ejpam-6597	134	12	pre	pre	ADJ
ejpam-6597	134	13	-	-	ADJ
ejpam-6597	134	14	normal	normal	ADJ
ejpam-6597	134	15	.	.	PUNCT
ejpam-6597	135	1	proof	proof	NOUN
ejpam-6597	135	2	.	.	PUNCT
ejpam-6597	136	1	let	let	VERB
ejpam-6597	136	2	x	x	PRON
ejpam-6597	136	3	be	be	AUX
ejpam-6597	136	4	a	a	DET
ejpam-6597	136	5	pre	pre	ADJ
ejpam-6597	136	6	-	-	ADJ
ejpam-6597	136	7	regular	regular	ADJ
ejpam-6597	136	8	pre	pre	ADJ
ejpam-6597	136	9	-	-	ADJ
ejpam-6597	136	10	lindelöf	lindelöf	ADJ
ejpam-6597	136	11	space	space	NOUN
ejpam-6597	136	12	.	.	PUNCT
ejpam-6597	137	1	by	by	ADP
ejpam-6597	137	2	theorem	theorem	NOUN
ejpam-6597	137	3	7	7	NUM
ejpam-6597	137	4	x	x	VERB
ejpam-6597	137	5	is	be	AUX
ejpam-6597	137	6	pre	pre	ADJ
ejpam-6597	137	7	-	-	ADJ
ejpam-6597	137	8	normal	normal	ADJ
ejpam-6597	137	9	.	.	PUNCT
ejpam-6597	138	1	let	let	VERB
ejpam-6597	138	2	f	f	NOUN
ejpam-6597	138	3	=	=	PRON
ejpam-6597	138	4	{	{	PUNCT
ejpam-6597	138	5	fs	fs	X
ejpam-6597	138	6	:	:	PUNCT
ejpam-6597	138	7	s	s	VERB
ejpam-6597	138	8	∈	∈	PROPN
ejpam-6597	138	9	s	s	AUX
ejpam-6597	138	10	}	}	PUNCT
ejpam-6597	138	11	be	be	AUX
ejpam-6597	138	12	a	a	DET
ejpam-6597	138	13	discrete	discrete	ADJ
ejpam-6597	138	14	family	family	NOUN
ejpam-6597	138	15	of	of	ADP
ejpam-6597	138	16	pairwise	pairwise	PROPN
ejpam-6597	138	17	disjoint	disjoint	NOUN
ejpam-6597	138	18	closed	close	VERB
ejpam-6597	138	19	subsets	subset	NOUN
ejpam-6597	138	20	of	of	ADP
ejpam-6597	138	21	x.	x.	NOUN
ejpam-6597	138	22	then	then	ADV
ejpam-6597	138	23	,	,	PUNCT
ejpam-6597	138	24	fs	fs	ADP
ejpam-6597	138	25	∩	∩	NOUN
ejpam-6597	139	1	ft	ft	NOUN
ejpam-6597	139	2	=	=	NOUN
ejpam-6597	139	3	∅	∅	NOUN
ejpam-6597	139	4	for	for	ADP
ejpam-6597	139	5	each	each	PRON
ejpam-6597	139	6	s	s	PART
ejpam-6597	139	7	̸=	̸=	PROPN
ejpam-6597	139	8	t.	t.	NOUN
ejpam-6597	139	9	by	by	ADP
ejpam-6597	139	10	pre	pre	ADJ
ejpam-6597	139	11	-	-	NOUN
ejpam-6597	139	12	normality	normality	NOUN
ejpam-6597	139	13	of	of	ADP
ejpam-6597	139	14	x	x	NOUN
ejpam-6597	139	15	,	,	PUNCT
ejpam-6597	139	16	there	there	PRON
ejpam-6597	139	17	exist	exist	VERB
ejpam-6597	139	18	two	two	NUM
ejpam-6597	139	19	disjoint	disjoint	ADJ
ejpam-6597	139	20	pre	pre	ADJ
ejpam-6597	139	21	-	-	ADJ
ejpam-6597	139	22	open	open	ADJ
ejpam-6597	139	23	sets	set	VERB
ejpam-6597	139	24	us	we	PRON
ejpam-6597	139	25	and	and	CCONJ
ejpam-6597	139	26	ut	ut	PROPN
ejpam-6597	139	27	in	in	ADP
ejpam-6597	139	28	x	x	SYM
ejpam-6597	139	29	such	such	ADJ
ejpam-6597	139	30	that	that	PRON
ejpam-6597	139	31	fs	fs	ADP
ejpam-6597	139	32	⊆	⊆	NUM
ejpam-6597	139	33	us	we	PRON
ejpam-6597	139	34	,	,	PUNCT
ejpam-6597	139	35	ft	ft	PROPN
ejpam-6597	139	36	⊆	⊆	NUM
ejpam-6597	139	37	ut	ut	PROPN
ejpam-6597	139	38	and	and	CCONJ
ejpam-6597	139	39	cl(us	cl(us	PROPN
ejpam-6597	139	40	)	)	PUNCT
ejpam-6597	139	41	∩	∩	ADJ
ejpam-6597	139	42	cl(ut	cl(ut	PROPN
ejpam-6597	139	43	)	)	PUNCT
ejpam-6597	140	1	=	=	NOUN
ejpam-6597	140	2	∅	∅	NOUN
ejpam-6597	140	3	where	where	SCONJ
ejpam-6597	140	4	s	s	VERB
ejpam-6597	140	5	̸=	̸=	PROPN
ejpam-6597	140	6	t.	t.	NOUN
ejpam-6597	140	7	then	then	ADV
ejpam-6597	140	8	,	,	PUNCT
ejpam-6597	140	9	the	the	DET
ejpam-6597	140	10	family	family	NOUN
ejpam-6597	140	11	{	{	PUNCT
ejpam-6597	140	12	us}s∈s	us}s∈s	PROPN
ejpam-6597	140	13	is	be	AUX
ejpam-6597	140	14	a	a	DET
ejpam-6597	140	15	family	family	NOUN
ejpam-6597	140	16	of	of	ADP
ejpam-6597	140	17	pre	pre	ADJ
ejpam-6597	140	18	-	-	ADJ
ejpam-6597	140	19	open	open	ADJ
ejpam-6597	140	20	sets	set	NOUN
ejpam-6597	140	21	in	in	ADP
ejpam-6597	140	22	x.	x.	NOUN
ejpam-6597	140	23	now	now	ADV
ejpam-6597	140	24	,	,	PUNCT
ejpam-6597	140	25	we	we	PRON
ejpam-6597	140	26	show	show	VERB
ejpam-6597	140	27	that	that	SCONJ
ejpam-6597	140	28	{	{	PUNCT
ejpam-6597	140	29	us}s∈s	us}s∈s	NOUN
ejpam-6597	140	30	is	be	AUX
ejpam-6597	140	31	discrete	discrete	ADJ
ejpam-6597	140	32	.	.	PUNCT
ejpam-6597	141	1	if	if	SCONJ
ejpam-6597	141	2	not	not	PART
ejpam-6597	141	3	,	,	PUNCT
ejpam-6597	141	4	there	there	PRON
ejpam-6597	141	5	exists	exist	VERB
ejpam-6597	141	6	x	x	X
ejpam-6597	141	7	∈	∈	PROPN
ejpam-6597	141	8	x	x	X
ejpam-6597	141	9	such	such	ADJ
ejpam-6597	141	10	that	that	PRON
ejpam-6597	141	11	for	for	ADP
ejpam-6597	141	12	any	any	DET
ejpam-6597	141	13	pre	pre	ADJ
ejpam-6597	141	14	-	-	ADJ
ejpam-6597	141	15	open	open	ADJ
ejpam-6597	141	16	neighborhood	neighborhood	NOUN
ejpam-6597	141	17	wx	wx	NOUN
ejpam-6597	141	18	of	of	ADP
ejpam-6597	141	19	x	x	INTJ
ejpam-6597	141	20	we	we	PRON
ejpam-6597	141	21	have	have	VERB
ejpam-6597	141	22	wx	wx	PROPN
ejpam-6597	141	23	∩	∩	NOUN
ejpam-6597	141	24	us	us	PROPN
ejpam-6597	141	25	̸=	̸=	PROPN
ejpam-6597	141	26	∅	∅	NOUN
ejpam-6597	141	27	=	=	NOUN
ejpam-6597	141	28	̸	̸	ADV
ejpam-6597	141	29	wx	wx	PROPN
ejpam-6597	141	30	∩	∩	X
ejpam-6597	141	31	ut	ut	PROPN
ejpam-6597	141	32	with	with	ADP
ejpam-6597	141	33	s	s	PRON
ejpam-6597	141	34	̸=	̸=	PROPN
ejpam-6597	141	35	t.	t.	PROPN
ejpam-6597	141	36	thus	thus	ADV
ejpam-6597	141	37	,	,	PUNCT
ejpam-6597	141	38	x	x	PROPN
ejpam-6597	141	39	∈	∈	PROPN
ejpam-6597	141	40	cl(us	cl(us	PROPN
ejpam-6597	141	41	)	)	PUNCT
ejpam-6597	141	42	and	and	CCONJ
ejpam-6597	141	43	x	x	PROPN
ejpam-6597	141	44	∈	∈	PROPN
ejpam-6597	141	45	cl(ut	cl(ut	PROPN
ejpam-6597	141	46	)	)	PUNCT
ejpam-6597	141	47	.	.	PUNCT
ejpam-6597	142	1	hence	hence	ADV
ejpam-6597	142	2	,	,	PUNCT
ejpam-6597	142	3	x	x	PROPN
ejpam-6597	142	4	∈	∈	PROPN
ejpam-6597	142	5	cl(us)∩cl(ut	cl(us)∩cl(ut	PROPN
ejpam-6597	142	6	)	)	PUNCT
ejpam-6597	142	7	,	,	PUNCT
ejpam-6597	142	8	which	which	PRON
ejpam-6597	142	9	is	be	AUX
ejpam-6597	142	10	a	a	DET
ejpam-6597	142	11	contradiction	contradiction	NOUN
ejpam-6597	142	12	.	.	PUNCT
ejpam-6597	143	1	hence	hence	ADV
ejpam-6597	143	2	,	,	PUNCT
ejpam-6597	143	3	the	the	DET
ejpam-6597	143	4	family	family	NOUN
ejpam-6597	143	5	{	{	PUNCT
ejpam-6597	143	6	us}s∈s	us}s∈s	PROPN
ejpam-6597	143	7	must	must	AUX
ejpam-6597	143	8	be	be	AUX
ejpam-6597	143	9	a	a	DET
ejpam-6597	143	10	discrete	discrete	ADJ
ejpam-6597	143	11	family	family	NOUN
ejpam-6597	143	12	of	of	ADP
ejpam-6597	143	13	pre	pre	ADJ
ejpam-6597	143	14	-	-	ADJ
ejpam-6597	143	15	open	open	ADJ
ejpam-6597	143	16	sets	set	NOUN
ejpam-6597	143	17	in	in	ADP
ejpam-6597	143	18	x	x	SYM
ejpam-6597	143	19	such	such	ADJ
ejpam-6597	143	20	that	that	PRON
ejpam-6597	143	21	fs	fs	ADP
ejpam-6597	143	22	⊆	⊆	NUM
ejpam-6597	143	23	us	we	PRON
ejpam-6597	143	24	for	for	ADP
ejpam-6597	143	25	each	each	DET
ejpam-6597	143	26	s	s	PROPN
ejpam-6597	143	27	∈	∈	PROPN
ejpam-6597	143	28	s.	s.	PROPN
ejpam-6597	143	29	since	since	SCONJ
ejpam-6597	143	30	x	x	PROPN
ejpam-6597	143	31	is	be	AUX
ejpam-6597	143	32	t1	t1	NOUN
ejpam-6597	143	33	,	,	PUNCT
ejpam-6597	143	34	we	we	PRON
ejpam-6597	143	35	obtain	obtain	VERB
ejpam-6597	143	36	x	x	VERB
ejpam-6597	143	37	is	be	AUX
ejpam-6597	143	38	collectionwise	collectionwise	ADV
ejpam-6597	143	39	pre	pre	ADJ
ejpam-6597	143	40	-	-	ADJ
ejpam-6597	143	41	normal	normal	ADJ
ejpam-6597	143	42	.	.	PUNCT
ejpam-6597	144	1	recall	recall	VERB
ejpam-6597	144	2	that	that	PRON
ejpam-6597	144	3	:	:	PUNCT
ejpam-6597	144	4	a	a	DET
ejpam-6597	144	5	space	space	NOUN
ejpam-6597	144	6	x	x	PUNCT
ejpam-6597	144	7	is	be	AUX
ejpam-6597	144	8	called	call	VERB
ejpam-6597	144	9	collectionwise	collectionwise	PROPN
ejpam-6597	144	10	hausdorff	hausdorff	NOUN
ejpam-6597	144	11	if	if	SCONJ
ejpam-6597	144	12	x	x	PRON
ejpam-6597	144	13	is	be	AUX
ejpam-6597	144	14	t1	t1	NOUN
ejpam-6597	144	15	and	and	CCONJ
ejpam-6597	144	16	for	for	ADP
ejpam-6597	144	17	every	every	DET
ejpam-6597	144	18	discrete	discrete	ADJ
ejpam-6597	144	19	collection	collection	NOUN
ejpam-6597	144	20	{	{	PUNCT
ejpam-6597	144	21	xs}s∈s	xs}s∈s	NOUN
ejpam-6597	144	22	of	of	ADP
ejpam-6597	144	23	points	point	NOUN
ejpam-6597	144	24	of	of	ADP
ejpam-6597	144	25	x	x	PRON
ejpam-6597	144	26	,	,	PUNCT
ejpam-6597	144	27	there	there	PRON
ejpam-6597	144	28	exists	exist	VERB
ejpam-6597	144	29	a	a	DET
ejpam-6597	144	30	disjoint	disjoint	ADJ
ejpam-6597	144	31	collection	collection	NOUN
ejpam-6597	144	32	{	{	PUNCT
ejpam-6597	144	33	vs}s∈s	vs}s∈s	NOUN
ejpam-6597	144	34	of	of	ADP
ejpam-6597	144	35	open	open	ADJ
ejpam-6597	144	36	subsets	subset	NOUN
ejpam-6597	144	37	of	of	ADP
ejpam-6597	144	38	x	x	SYM
ejpam-6597	144	39	such	such	ADJ
ejpam-6597	144	40	that	that	SCONJ
ejpam-6597	144	41	xs	xs	PROPN
ejpam-6597	144	42	∈	∈	PROPN
ejpam-6597	144	43	vs	vs	ADP
ejpam-6597	144	44	for	for	ADP
ejpam-6597	144	45	each	each	DET
ejpam-6597	144	46	s	s	X
ejpam-6597	144	47	∈	∈	ADJ
ejpam-6597	144	48	s	s	PART
ejpam-6597	144	49	[	[	X
ejpam-6597	144	50	13	13	NUM
ejpam-6597	144	51	]	]	PUNCT
ejpam-6597	144	52	.	.	PUNCT
ejpam-6597	145	1	since	since	SCONJ
ejpam-6597	145	2	every	every	DET
ejpam-6597	145	3	collectionwise	collectionwise	PROPN
ejpam-6597	145	4	hausdorff	hausdorff	PROPN
ejpam-6597	145	5	p1	p1	PROPN
ejpam-6597	145	6	-	-	PUNCT
ejpam-6597	145	7	paracompact	paracompact	ADJ
ejpam-6597	145	8	space	space	NOUN
ejpam-6597	145	9	is	be	AUX
ejpam-6597	145	10	hausdorff	hausdorff	NOUN
ejpam-6597	145	11	paracompact	paracompact	NOUN
ejpam-6597	145	12	,	,	PUNCT
ejpam-6597	145	13	and	and	CCONJ
ejpam-6597	145	14	every	every	DET
ejpam-6597	145	15	pre	pre	ADJ
ejpam-6597	145	16	-	-	ADJ
ejpam-6597	145	17	compact	compact	ADJ
ejpam-6597	145	18	space	space	NOUN
ejpam-6597	145	19	is	be	AUX
ejpam-6597	145	20	p1	p1	NOUN
ejpam-6597	145	21	-	-	PUNCT
ejpam-6597	145	22	paracompact	paracompact	ADJ
ejpam-6597	145	23	,	,	PUNCT
ejpam-6597	145	24	we	we	PRON
ejpam-6597	145	25	conclude	conclude	VERB
ejpam-6597	145	26	:	:	PUNCT
ejpam-6597	145	27	corollary	corollary	ADJ
ejpam-6597	145	28	7	7	NUM
ejpam-6597	145	29	.	.	PUNCT
ejpam-6597	146	1	every	every	DET
ejpam-6597	146	2	collectionwise	collectionwise	PROPN
ejpam-6597	146	3	hausdorff	hausdorff	PROPN
ejpam-6597	146	4	p1	p1	PROPN
ejpam-6597	146	5	-	-	PUNCT
ejpam-6597	146	6	paracompact	paracompact	ADJ
ejpam-6597	146	7	space	space	NOUN
ejpam-6597	146	8	is	be	AUX
ejpam-6597	146	9	collectionwise	collectionwise	ADV
ejpam-6597	146	10	prenormal	prenormal	ADJ
ejpam-6597	146	11	.	.	PUNCT
ejpam-6597	147	1	observe	observe	VERB
ejpam-6597	147	2	that	that	SCONJ
ejpam-6597	147	3	:	:	PUNCT
ejpam-6597	147	4	every	every	DET
ejpam-6597	147	5	p1	p1	NOUN
ejpam-6597	147	6	-	-	PUNCT
ejpam-6597	147	7	paracompact	paracompact	ADJ
ejpam-6597	147	8	space	space	NOUN
ejpam-6597	147	9	is	be	AUX
ejpam-6597	147	10	paracompact	paracompact	ADJ
ejpam-6597	147	11	,	,	PUNCT
ejpam-6597	147	12	every	every	DET
ejpam-6597	147	13	pre	pre	NOUN
ejpam-6597	147	14	-	-	NOUN
ejpam-6597	147	15	lindelöf	lindelöf	ADJ
ejpam-6597	147	16	space	space	NOUN
ejpam-6597	147	17	is	be	AUX
ejpam-6597	147	18	lindelöf	lindelöf	NOUN
ejpam-6597	147	19	,	,	PUNCT
ejpam-6597	147	20	every	every	DET
ejpam-6597	147	21	pre	pre	ADJ
ejpam-6597	147	22	-	-	ADJ
ejpam-6597	147	23	compact	compact	ADJ
ejpam-6597	147	24	space	space	NOUN
ejpam-6597	147	25	is	be	AUX
ejpam-6597	147	26	compact	compact	ADJ
ejpam-6597	147	27	,	,	PUNCT
ejpam-6597	147	28	every	every	DET
ejpam-6597	147	29	p1	p1	NOUN
ejpam-6597	147	30	-	-	PUNCT
ejpam-6597	147	31	paracompact	paracompact	ADJ
ejpam-6597	147	32	space	space	NOUN
ejpam-6597	147	33	is	be	AUX
ejpam-6597	147	34	submaximal	submaximal	ADJ
ejpam-6597	147	35	[	[	X
ejpam-6597	147	36	12	12	NUM
ejpam-6597	147	37	]	]	PUNCT
ejpam-6597	147	38	,	,	PUNCT
ejpam-6597	147	39	every	every	DET
ejpam-6597	147	40	sub	sub	ADJ
ejpam-6597	147	41	-	-	ADJ
ejpam-6597	147	42	maximal	maximal	ADJ
ejpam-6597	147	43	pre	pre	ADJ
ejpam-6597	147	44	-	-	ADJ
ejpam-6597	147	45	regular	regular	ADJ
ejpam-6597	147	46	space	space	NOUN
ejpam-6597	147	47	is	be	AUX
ejpam-6597	147	48	regular	regular	ADJ
ejpam-6597	147	49	[	[	X
ejpam-6597	147	50	12	12	NUM
ejpam-6597	147	51	]	]	PUNCT
ejpam-6597	147	52	,	,	PUNCT
ejpam-6597	147	53	int(a	int(a	PROPN
ejpam-6597	147	54	)	)	PUNCT
ejpam-6597	147	55	⊆	⊆	NUM
ejpam-6597	147	56	p	p	NOUN
ejpam-6597	147	57	int(a	int(a	PROPN
ejpam-6597	147	58	)	)	PUNCT
ejpam-6597	147	59	⊆	⊆	NUM
ejpam-6597	147	60	a	a	DET
ejpam-6597	147	61	⊆	⊆	NUM
ejpam-6597	147	62	p	p	NOUN
ejpam-6597	147	63	cl(a	cl(a	X
ejpam-6597	147	64	)	)	PUNCT
ejpam-6597	147	65	⊆	⊆	NUM
ejpam-6597	147	66	a	a	PRON
ejpam-6597	147	67	for	for	ADP
ejpam-6597	147	68	each	each	DET
ejpam-6597	147	69	a	a	DET
ejpam-6597	147	70	⊆	⊆	NUM
ejpam-6597	147	71	x	x	SYM
ejpam-6597	148	1	[	[	X
ejpam-6597	148	2	11	11	NUM
ejpam-6597	148	3	]	]	PUNCT
ejpam-6597	148	4	,	,	PUNCT
ejpam-6597	148	5	and	and	CCONJ
ejpam-6597	148	6	if	if	SCONJ
ejpam-6597	148	7	x	x	PRON
ejpam-6597	148	8	is	be	AUX
ejpam-6597	148	9	sub	sub	ADJ
ejpam-6597	148	10	-	-	ADJ
ejpam-6597	148	11	maximal	maximal	ADJ
ejpam-6597	148	12	space	space	NOUN
ejpam-6597	148	13	,	,	PUNCT
ejpam-6597	148	14	then	then	ADV
ejpam-6597	148	15	p	p	NOUN
ejpam-6597	148	16	cl(a	cl(a	PUNCT
ejpam-6597	148	17	)	)	PUNCT
ejpam-6597	148	18	=	=	SYM
ejpam-6597	148	19	a	a	DET
ejpam-6597	148	20	for	for	ADP
ejpam-6597	148	21	each	each	DET
ejpam-6597	148	22	a	a	DET
ejpam-6597	148	23	⊆	⊆	NUM
ejpam-6597	148	24	x.	x.	NOUN
ejpam-6597	148	25	lemma	lemma	PROPN
ejpam-6597	148	26	1	1	NUM
ejpam-6597	148	27	.	.	PUNCT
ejpam-6597	149	1	[	[	X
ejpam-6597	149	2	11	11	NUM
ejpam-6597	149	3	]	]	PUNCT
ejpam-6597	149	4	,	,	PUNCT
ejpam-6597	149	5	let	let	VERB
ejpam-6597	149	6	x	x	PRON
ejpam-6597	149	7	be	be	AUX
ejpam-6597	149	8	a	a	DET
ejpam-6597	149	9	space	space	NOUN
ejpam-6597	149	10	.	.	PUNCT
ejpam-6597	150	1	then	then	ADV
ejpam-6597	150	2	:	:	PUNCT
ejpam-6597	150	3	(	(	PUNCT
ejpam-6597	150	4	1	1	X
ejpam-6597	150	5	)	)	PUNCT
ejpam-6597	150	6	any	any	DET
ejpam-6597	150	7	dense	dense	ADJ
ejpam-6597	150	8	subset	subset	NOUN
ejpam-6597	150	9	of	of	ADP
ejpam-6597	150	10	x	x	PUNCT
ejpam-6597	150	11	is	be	AUX
ejpam-6597	150	12	pre	pre	ADJ
ejpam-6597	150	13	-	-	ADJ
ejpam-6597	150	14	open	open	ADJ
ejpam-6597	150	15	.	.	PUNCT
ejpam-6597	151	1	if	if	SCONJ
ejpam-6597	151	2	d	d	NOUN
ejpam-6597	151	3	is	be	AUX
ejpam-6597	151	4	dense	dense	ADJ
ejpam-6597	151	5	subset	subset	NOUN
ejpam-6597	151	6	of	of	ADP
ejpam-6597	151	7	x	x	PUNCT
ejpam-6597	151	8	and	and	CCONJ
ejpam-6597	151	9	a	a	PRON
ejpam-6597	151	10	is	be	AUX
ejpam-6597	151	11	closed	close	VERB
ejpam-6597	151	12	subset	subset	NOUN
ejpam-6597	151	13	of	of	ADP
ejpam-6597	151	14	x	x	PRON
ejpam-6597	151	15	,	,	PUNCT
ejpam-6597	151	16	then	then	ADV
ejpam-6597	151	17	d	d	X
ejpam-6597	151	18	∪a	∪a	NUM
ejpam-6597	151	19	and	and	CCONJ
ejpam-6597	151	20	d	d	PROPN
ejpam-6597	151	21	\a	\a	ADJ
ejpam-6597	151	22	are	be	AUX
ejpam-6597	151	23	pre	pre	ADJ
ejpam-6597	151	24	-	-	ADJ
ejpam-6597	151	25	open	open	ADJ
ejpam-6597	151	26	.	.	PUNCT
ejpam-6597	152	1	(	(	PUNCT
ejpam-6597	152	2	2	2	X
ejpam-6597	152	3	)	)	PUNCT
ejpam-6597	152	4	let	let	VERB
ejpam-6597	152	5	d	d	PRON
ejpam-6597	152	6	be	be	AUX
ejpam-6597	152	7	a	a	DET
ejpam-6597	152	8	dense	dense	ADJ
ejpam-6597	152	9	subset	subset	NOUN
ejpam-6597	152	10	of	of	ADP
ejpam-6597	152	11	x.	x.	NOUN
ejpam-6597	152	12	for	for	ADP
ejpam-6597	152	13	any	any	DET
ejpam-6597	152	14	two	two	NUM
ejpam-6597	152	15	disjoint	disjoint	NOUN
ejpam-6597	152	16	closed	closed	ADJ
ejpam-6597	152	17	subsets	subset	NOUN
ejpam-6597	152	18	a	a	PRON
ejpam-6597	152	19	and	and	CCONJ
ejpam-6597	152	20	b	b	NOUN
ejpam-6597	152	21	,	,	PUNCT
ejpam-6597	152	22	the	the	DET
ejpam-6597	152	23	sets	set	NOUN
ejpam-6597	152	24	u	u	NOUN
ejpam-6597	152	25	=	=	PUNCT
ejpam-6597	152	26	(	(	PUNCT
ejpam-6597	152	27	d	d	NOUN
ejpam-6597	152	28	\a	\a	NUM
ejpam-6597	152	29	)	)	PUNCT
ejpam-6597	152	30	⋃	⋃	NOUN
ejpam-6597	152	31	b	b	NOUN
ejpam-6597	152	32	and	and	CCONJ
ejpam-6597	152	33	v	v	NOUN
ejpam-6597	152	34	=	=	SYM
ejpam-6597	152	35	(	(	PUNCT
ejpam-6597	152	36	d	d	NOUN
ejpam-6597	152	37	\b	\b	NOUN
ejpam-6597	152	38	)	)	PUNCT
ejpam-6597	152	39	⋃	⋃	SCONJ
ejpam-6597	152	40	a	a	PRON
ejpam-6597	152	41	are	be	AUX
ejpam-6597	152	42	pre	pre	ADJ
ejpam-6597	152	43	-	-	ADJ
ejpam-6597	152	44	open	open	ADJ
ejpam-6597	152	45	subsets	subset	NOUN
ejpam-6597	152	46	.	.	PUNCT
ejpam-6597	153	1	s.	s.	PROPN
ejpam-6597	153	2	a.	a.	PROPN
ejpam-6597	153	3	thabit	thabit	PROPN
ejpam-6597	153	4	,	,	PUNCT
ejpam-6597	153	5	a.	a.	PROPN
ejpam-6597	153	6	al	al	PROPN
ejpam-6597	153	7	-	-	PUNCT
ejpam-6597	153	8	awadi	awadi	PROPN
ejpam-6597	153	9	,	,	PUNCT
ejpam-6597	153	10	r.	r.	PROPN
ejpam-6597	153	11	noaman	noaman	PROPN
ejpam-6597	153	12	/	/	SYM
ejpam-6597	153	13	eur	eur	PROPN
ejpam-6597	153	14	.	.	PUNCT
ejpam-6597	154	1	j.	j.	PROPN
ejpam-6597	154	2	pure	pure	PROPN
ejpam-6597	154	3	appl	appl	PROPN
ejpam-6597	154	4	.	.	PROPN
ejpam-6597	154	5	math	math	PROPN
ejpam-6597	154	6	,	,	PUNCT
ejpam-6597	154	7	18	18	NUM
ejpam-6597	154	8	(	(	PUNCT
ejpam-6597	154	9	4	4	NUM
ejpam-6597	154	10	)	)	PUNCT
ejpam-6597	154	11	(	(	PUNCT
ejpam-6597	154	12	2025	2025	NUM
ejpam-6597	154	13	)	)	PUNCT
ejpam-6597	154	14	,	,	PUNCT
ejpam-6597	154	15	6597	6597	NUM
ejpam-6597	154	16	6	6	NUM
ejpam-6597	154	17	of	of	ADP
ejpam-6597	154	18	15	15	NUM
ejpam-6597	154	19	(	(	PUNCT
ejpam-6597	154	20	3	3	NUM
ejpam-6597	154	21	)	)	PUNCT
ejpam-6597	154	22	if	if	SCONJ
ejpam-6597	154	23	x	x	PRON
ejpam-6597	154	24	has	have	VERB
ejpam-6597	154	25	two	two	NUM
ejpam-6597	154	26	disjoint	disjoint	ADJ
ejpam-6597	154	27	dense	dense	ADJ
ejpam-6597	154	28	subsets	subset	NOUN
ejpam-6597	154	29	,	,	PUNCT
ejpam-6597	154	30	then	then	ADV
ejpam-6597	154	31	x	x	PUNCT
ejpam-6597	154	32	is	be	AUX
ejpam-6597	154	33	pre	pre	ADJ
ejpam-6597	154	34	-	-	ADJ
ejpam-6597	154	35	normal	normal	ADJ
ejpam-6597	154	36	.	.	PUNCT
ejpam-6597	155	1	theorem	theorem	VERB
ejpam-6597	155	2	9	9	NUM
ejpam-6597	155	3	.	.	PUNCT
ejpam-6597	156	1	[	[	X
ejpam-6597	156	2	11	11	NUM
ejpam-6597	156	3	]	]	PUNCT
ejpam-6597	156	4	,	,	PUNCT
ejpam-6597	156	5	let	let	VERB
ejpam-6597	156	6	x	x	PRON
ejpam-6597	156	7	be	be	AUX
ejpam-6597	156	8	a	a	DET
ejpam-6597	156	9	sub	sub	ADJ
ejpam-6597	156	10	-	-	ADJ
ejpam-6597	156	11	maximal	maximal	ADJ
ejpam-6597	156	12	space	space	NOUN
ejpam-6597	156	13	.	.	PUNCT
ejpam-6597	157	1	fix	fix	VERB
ejpam-6597	157	2	a	a	DET
ejpam-6597	157	3	point	point	NOUN
ejpam-6597	157	4	p	p	X
ejpam-6597	157	5	∈	∈	PROPN
ejpam-6597	157	6	x	x	PUNCT
ejpam-6597	157	7	and	and	CCONJ
ejpam-6597	157	8	let	let	VERB
ejpam-6597	157	9	m	m	VERB
ejpam-6597	157	10	=	=	VERB
ejpam-6597	157	11	x	x	SYM
ejpam-6597	157	12	\{p	\{p	NOUN
ejpam-6597	157	13	}	}	PUNCT
ejpam-6597	157	14	.	.	PUNCT
ejpam-6597	158	1	then	then	ADV
ejpam-6597	158	2	,	,	PUNCT
ejpam-6597	158	3	m	m	PROPN
ejpam-6597	158	4	is	be	AUX
ejpam-6597	158	5	a	a	DET
ejpam-6597	158	6	sub	sub	ADJ
ejpam-6597	158	7	-	-	ADJ
ejpam-6597	158	8	maximal	maximal	ADJ
ejpam-6597	158	9	subspace	subspace	NOUN
ejpam-6597	158	10	of	of	ADP
ejpam-6597	158	11	x.	x.	NOUN
ejpam-6597	158	12	observe	observe	VERB
ejpam-6597	158	13	that	that	SCONJ
ejpam-6597	158	14	:	:	PUNCT
ejpam-6597	158	15	the	the	DET
ejpam-6597	158	16	product	product	NOUN
ejpam-6597	158	17	space	space	NOUN
ejpam-6597	158	18	ω1	ω1	PROPN
ejpam-6597	158	19	×	×	PROPN
ejpam-6597	158	20	ω1	ω1	PROPN
ejpam-6597	158	21	+	+	CCONJ
ejpam-6597	158	22	1	1	NUM
ejpam-6597	158	23	is	be	AUX
ejpam-6597	158	24	not	not	PART
ejpam-6597	158	25	pre	pre	ADJ
ejpam-6597	158	26	-	-	ADJ
ejpam-6597	158	27	normal	normal	ADJ
ejpam-6597	158	28	,	,	PUNCT
ejpam-6597	158	29	the	the	DET
ejpam-6597	158	30	product	product	NOUN
ejpam-6597	158	31	space	space	NOUN
ejpam-6597	158	32	x	x	PUNCT
ejpam-6597	158	33	=	=	SYM
ejpam-6597	158	34	(	(	PUNCT
ejpam-6597	158	35	ω0	ω0	ADV
ejpam-6597	158	36	+	+	CCONJ
ejpam-6597	158	37	1	1	X
ejpam-6597	158	38	)	)	PUNCT
ejpam-6597	158	39	×	×	NOUN
ejpam-6597	158	40	(	(	PUNCT
ejpam-6597	158	41	ω1	ω1	PROPN
ejpam-6597	158	42	+	+	CCONJ
ejpam-6597	158	43	1	1	NUM
ejpam-6597	158	44	)	)	PUNCT
ejpam-6597	158	45	is	be	AUX
ejpam-6597	158	46	pre	pre	ADJ
ejpam-6597	158	47	-	-	ADJ
ejpam-6597	158	48	normal	normal	ADJ
ejpam-6597	158	49	sub	sub	ADJ
ejpam-6597	158	50	-	-	ADJ
ejpam-6597	158	51	maximal	maximal	ADJ
ejpam-6597	158	52	space	space	NOUN
ejpam-6597	158	53	and	and	CCONJ
ejpam-6597	158	54	hence	hence	ADV
ejpam-6597	158	55	x	x	VERB
ejpam-6597	158	56	is	be	AUX
ejpam-6597	158	57	collectionwise	collectionwise	ADV
ejpam-6597	158	58	pre	pre	ADJ
ejpam-6597	158	59	-	-	ADJ
ejpam-6597	158	60	normal	normal	ADJ
ejpam-6597	158	61	,	,	PUNCT
ejpam-6597	158	62	the	the	DET
ejpam-6597	158	63	tychonoff	tychonoff	NOUN
ejpam-6597	158	64	plank	plank	NOUN
ejpam-6597	158	65	m	m	PROPN
ejpam-6597	158	66	=	=	SYM
ejpam-6597	158	67	(	(	PUNCT
ejpam-6597	158	68	ω0	ω0	ADV
ejpam-6597	158	69	+	+	NOUN
ejpam-6597	158	70	1)×(ω1	1)×(ω1	NUM
ejpam-6597	158	71	+	+	NOUN
ejpam-6597	158	72	1)\{(ω0	1)\{(ω0	NUM
ejpam-6597	158	73	,	,	PUNCT
ejpam-6597	158	74	ω1	ω1	PROPN
ejpam-6597	158	75	)	)	PUNCT
ejpam-6597	158	76	}	}	PUNCT
ejpam-6597	158	77	is	be	AUX
ejpam-6597	158	78	dense	dense	ADJ
ejpam-6597	158	79	sub	sub	ADJ
ejpam-6597	158	80	-	-	ADJ
ejpam-6597	158	81	maximal	maximal	ADJ
ejpam-6597	158	82	subspace	subspace	NOUN
ejpam-6597	158	83	of	of	ADP
ejpam-6597	158	84	x	x	PRON
ejpam-6597	158	85	,	,	PUNCT
ejpam-6597	158	86	which	which	PRON
ejpam-6597	158	87	is	be	AUX
ejpam-6597	158	88	not	not	PART
ejpam-6597	158	89	collectionwise	collectionwise	ADV
ejpam-6597	158	90	pre	pre	ADJ
ejpam-6597	158	91	-	-	ADJ
ejpam-6597	158	92	normal	normal	ADJ
ejpam-6597	158	93	,	,	PUNCT
ejpam-6597	158	94	every	every	DET
ejpam-6597	158	95	pre	pre	ADJ
ejpam-6597	158	96	-	-	ADJ
ejpam-6597	158	97	normal	normal	ADJ
ejpam-6597	158	98	sub	sub	ADJ
ejpam-6597	158	99	-	-	ADJ
ejpam-6597	158	100	maximal	maximal	ADJ
ejpam-6597	158	101	space	space	NOUN
ejpam-6597	158	102	is	be	AUX
ejpam-6597	158	103	normal	normal	ADJ
ejpam-6597	158	104	,	,	PUNCT
ejpam-6597	158	105	the	the	DET
ejpam-6597	158	106	product	product	NOUN
ejpam-6597	158	107	of	of	ADP
ejpam-6597	158	108	two	two	NUM
ejpam-6597	158	109	sub	sub	ADJ
ejpam-6597	158	110	-	-	ADJ
ejpam-6597	158	111	maximal	maximal	ADJ
ejpam-6597	158	112	spaces	space	NOUN
ejpam-6597	158	113	is	be	AUX
ejpam-6597	158	114	sub	sub	ADJ
ejpam-6597	158	115	-	-	ADJ
ejpam-6597	158	116	maximal	maximal	ADJ
ejpam-6597	158	117	[	[	X
ejpam-6597	158	118	11	11	NUM
ejpam-6597	158	119	]	]	PUNCT
ejpam-6597	158	120	and	and	CCONJ
ejpam-6597	158	121	every	every	DET
ejpam-6597	158	122	p1	p1	NOUN
ejpam-6597	158	123	-	-	PUNCT
ejpam-6597	158	124	paracompact	paracompact	ADJ
ejpam-6597	158	125	space	space	NOUN
ejpam-6597	158	126	is	be	AUX
ejpam-6597	158	127	sub	sub	ADJ
ejpam-6597	158	128	-	-	ADJ
ejpam-6597	158	129	maximal	maximal	ADJ
ejpam-6597	158	130	and	and	CCONJ
ejpam-6597	158	131	paracompact	paracompact	ADJ
ejpam-6597	158	132	[	[	X
ejpam-6597	158	133	12	12	NUM
ejpam-6597	158	134	]	]	PUNCT
ejpam-6597	158	135	.	.	PUNCT
ejpam-6597	159	1	theorem	theorem	ADJ
ejpam-6597	159	2	10	10	NUM
ejpam-6597	159	3	.	.	PUNCT
ejpam-6597	160	1	every	every	DET
ejpam-6597	160	2	collectionwise	collectionwise	ADV
ejpam-6597	160	3	pre	pre	ADJ
ejpam-6597	160	4	-	-	ADJ
ejpam-6597	160	5	normal	normal	ADJ
ejpam-6597	160	6	sub	sub	ADJ
ejpam-6597	160	7	-	-	ADJ
ejpam-6597	160	8	maximal	maximal	ADJ
ejpam-6597	160	9	space	space	NOUN
ejpam-6597	160	10	is	be	AUX
ejpam-6597	160	11	collectionwise	collectionwise	ADV
ejpam-6597	160	12	normal	normal	ADJ
ejpam-6597	160	13	.	.	PUNCT
ejpam-6597	161	1	proof	proof	NOUN
ejpam-6597	161	2	.	.	PUNCT
ejpam-6597	162	1	let	let	VERB
ejpam-6597	162	2	{	{	PUNCT
ejpam-6597	162	3	fs}s∈s	fs}s∈s	PART
ejpam-6597	162	4	be	be	AUX
ejpam-6597	162	5	a	a	DET
ejpam-6597	162	6	discrete	discrete	ADJ
ejpam-6597	162	7	family	family	NOUN
ejpam-6597	162	8	of	of	ADP
ejpam-6597	162	9	closed	closed	ADJ
ejpam-6597	162	10	subsets	subset	NOUN
ejpam-6597	162	11	ofx	ofx	NOUN
ejpam-6597	162	12	.	.	PUNCT
ejpam-6597	163	1	sincex	sincex	PROPN
ejpam-6597	163	2	is	be	AUX
ejpam-6597	163	3	collectionwise	collectionwise	ADV
ejpam-6597	163	4	pre	pre	ADJ
ejpam-6597	163	5	-	-	ADJ
ejpam-6597	163	6	normal	normal	ADJ
ejpam-6597	163	7	,	,	PUNCT
ejpam-6597	163	8	there	there	PRON
ejpam-6597	163	9	exists	exist	VERB
ejpam-6597	163	10	a	a	DET
ejpam-6597	163	11	discrete	discrete	ADJ
ejpam-6597	163	12	family	family	NOUN
ejpam-6597	163	13	{	{	PUNCT
ejpam-6597	163	14	us}s∈s	us}s∈s	PROPN
ejpam-6597	163	15	of	of	ADP
ejpam-6597	163	16	pre	pre	ADJ
ejpam-6597	163	17	-	-	ADJ
ejpam-6597	163	18	open	open	ADJ
ejpam-6597	163	19	subsets	subset	NOUN
ejpam-6597	163	20	of	of	ADP
ejpam-6597	163	21	x	x	SYM
ejpam-6597	163	22	such	such	ADJ
ejpam-6597	163	23	that	that	PRON
ejpam-6597	163	24	fs	fs	ADP
ejpam-6597	163	25	⊆	⊆	NUM
ejpam-6597	163	26	us	we	PRON
ejpam-6597	163	27	for	for	ADP
ejpam-6597	163	28	each	each	DET
ejpam-6597	163	29	s	s	PROPN
ejpam-6597	163	30	∈	∈	PROPN
ejpam-6597	163	31	s.	s.	PROPN
ejpam-6597	163	32	since	since	SCONJ
ejpam-6597	163	33	x	x	PROPN
ejpam-6597	163	34	is	be	AUX
ejpam-6597	163	35	sub	sub	ADJ
ejpam-6597	163	36	-	-	ADJ
ejpam-6597	163	37	maximal	maximal	ADJ
ejpam-6597	163	38	,	,	PUNCT
ejpam-6597	163	39	every	every	DET
ejpam-6597	163	40	pre	pre	ADJ
ejpam-6597	163	41	-	-	ADJ
ejpam-6597	163	42	open	open	ADJ
ejpam-6597	163	43	set	set	NOUN
ejpam-6597	163	44	in	in	ADP
ejpam-6597	163	45	x	x	PUNCT
ejpam-6597	163	46	is	be	AUX
ejpam-6597	163	47	open	open	ADJ
ejpam-6597	163	48	.	.	PUNCT
ejpam-6597	164	1	therefore	therefore	ADV
ejpam-6597	164	2	,	,	PUNCT
ejpam-6597	164	3	{	{	PUNCT
ejpam-6597	164	4	us}s∈s	us}s∈s	NOUN
ejpam-6597	164	5	is	be	AUX
ejpam-6597	164	6	a	a	DET
ejpam-6597	164	7	discrete	discrete	ADJ
ejpam-6597	164	8	family	family	NOUN
ejpam-6597	164	9	of	of	ADP
ejpam-6597	164	10	open	open	ADJ
ejpam-6597	164	11	subsets	subset	NOUN
ejpam-6597	164	12	of	of	ADP
ejpam-6597	164	13	x	x	SYM
ejpam-6597	164	14	such	such	ADJ
ejpam-6597	164	15	that	that	PRON
ejpam-6597	164	16	fs	fs	ADP
ejpam-6597	164	17	⊆	⊆	NUM
ejpam-6597	164	18	us	we	PRON
ejpam-6597	164	19	for	for	ADP
ejpam-6597	164	20	each	each	DET
ejpam-6597	164	21	s	s	PROPN
ejpam-6597	164	22	∈	∈	PROPN
ejpam-6597	164	23	s.	s.	PROPN
ejpam-6597	164	24	hence	hence	ADV
ejpam-6597	164	25	,	,	PUNCT
ejpam-6597	164	26	x	x	PRON
ejpam-6597	164	27	is	be	AUX
ejpam-6597	164	28	collectionwise	collectionwise	ADV
ejpam-6597	164	29	normal	normal	ADJ
ejpam-6597	164	30	.	.	PUNCT
ejpam-6597	165	1	since	since	SCONJ
ejpam-6597	165	2	every	every	DET
ejpam-6597	165	3	hausdorff	hausdorff	NOUN
ejpam-6597	165	4	p1	p1	NOUN
ejpam-6597	165	5	-	-	PUNCT
ejpam-6597	165	6	paracompact	paracompact	ADJ
ejpam-6597	165	7	space	space	NOUN
ejpam-6597	165	8	is	be	AUX
ejpam-6597	165	9	hausdorff	hausdorff	NOUN
ejpam-6597	165	10	paracompact	paracompact	PROPN
ejpam-6597	165	11	,	,	PUNCT
ejpam-6597	165	12	we	we	PRON
ejpam-6597	165	13	get	get	VERB
ejpam-6597	165	14	:	:	PUNCT
ejpam-6597	165	15	corollary	corollary	ADJ
ejpam-6597	165	16	8	8	NUM
ejpam-6597	165	17	.	.	PUNCT
ejpam-6597	166	1	every	every	DET
ejpam-6597	166	2	hausdorff	hausdorff	NOUN
ejpam-6597	166	3	p1	p1	NOUN
ejpam-6597	166	4	-	-	PUNCT
ejpam-6597	166	5	paracompact	paracompact	ADJ
ejpam-6597	166	6	space	space	NOUN
ejpam-6597	166	7	is	be	AUX
ejpam-6597	166	8	collectionwise	collectionwise	ADV
ejpam-6597	166	9	normal	normal	ADJ
ejpam-6597	166	10	and	and	CCONJ
ejpam-6597	166	11	hence	hence	ADV
ejpam-6597	166	12	collectionwise	collectionwise	ADV
ejpam-6597	166	13	pre	pre	ADJ
ejpam-6597	166	14	-	-	ADJ
ejpam-6597	166	15	normal	normal	ADJ
ejpam-6597	166	16	.	.	PUNCT
ejpam-6597	167	1	note	note	VERB
ejpam-6597	167	2	that	that	SCONJ
ejpam-6597	167	3	:	:	PUNCT
ejpam-6597	167	4	every	every	DET
ejpam-6597	167	5	hausdorff	hausdorff	NOUN
ejpam-6597	167	6	countably	countably	ADV
ejpam-6597	167	7	compact	compact	ADJ
ejpam-6597	167	8	normal	normal	ADJ
ejpam-6597	167	9	space	space	NOUN
ejpam-6597	167	10	is	be	AUX
ejpam-6597	167	11	collectionwise	collectionwise	ADV
ejpam-6597	167	12	normal	normal	ADJ
ejpam-6597	168	1	[	[	X
ejpam-6597	168	2	9	9	NUM
ejpam-6597	168	3	]	]	PUNCT
ejpam-6597	168	4	,	,	PUNCT
ejpam-6597	168	5	thus	thus	ADV
ejpam-6597	168	6	we	we	PRON
ejpam-6597	168	7	get	get	VERB
ejpam-6597	168	8	the	the	DET
ejpam-6597	168	9	following	follow	VERB
ejpam-6597	168	10	results	result	NOUN
ejpam-6597	168	11	:	:	PUNCT
ejpam-6597	168	12	theorem	theorem	VERB
ejpam-6597	168	13	11	11	NUM
ejpam-6597	168	14	.	.	PUNCT
ejpam-6597	169	1	every	every	DET
ejpam-6597	169	2	t1	t1	NOUN
ejpam-6597	169	3	countably	countably	ADV
ejpam-6597	169	4	compact	compact	ADJ
ejpam-6597	169	5	pre	pre	ADJ
ejpam-6597	169	6	-	-	ADJ
ejpam-6597	169	7	normal	normal	ADJ
ejpam-6597	169	8	space	space	NOUN
ejpam-6597	169	9	is	be	AUX
ejpam-6597	169	10	collectionwise	collectionwise	ADV
ejpam-6597	169	11	pre	pre	ADJ
ejpam-6597	169	12	-	-	ADJ
ejpam-6597	169	13	normal	normal	ADJ
ejpam-6597	169	14	.	.	PUNCT
ejpam-6597	170	1	proof	proof	NOUN
ejpam-6597	170	2	.	.	PUNCT
ejpam-6597	171	1	let	let	VERB
ejpam-6597	171	2	{	{	PUNCT
ejpam-6597	171	3	fs}s∈s	fs}s∈s	X
ejpam-6597	171	4	be	be	AUX
ejpam-6597	171	5	any	any	DET
ejpam-6597	171	6	discrete	discrete	ADJ
ejpam-6597	171	7	family	family	NOUN
ejpam-6597	171	8	of	of	ADP
ejpam-6597	171	9	closed	closed	ADJ
ejpam-6597	171	10	subsets	subset	NOUN
ejpam-6597	171	11	of	of	ADP
ejpam-6597	171	12	x.	x.	NOUN
ejpam-6597	171	13	since	since	SCONJ
ejpam-6597	171	14	every	every	DET
ejpam-6597	171	15	discrete	discrete	ADJ
ejpam-6597	171	16	family	family	NOUN
ejpam-6597	171	17	is	be	AUX
ejpam-6597	171	18	locally	locally	ADV
ejpam-6597	171	19	finite	finite	ADJ
ejpam-6597	171	20	family	family	NOUN
ejpam-6597	171	21	,	,	PUNCT
ejpam-6597	171	22	the	the	DET
ejpam-6597	171	23	family	family	NOUN
ejpam-6597	171	24	{	{	PUNCT
ejpam-6597	171	25	fs}s∈s	fs}s∈s	X
ejpam-6597	171	26	is	be	AUX
ejpam-6597	171	27	locally	locally	ADV
ejpam-6597	171	28	finite	finite	ADJ
ejpam-6597	171	29	family	family	NOUN
ejpam-6597	171	30	of	of	ADP
ejpam-6597	171	31	closed	closed	ADJ
ejpam-6597	171	32	subsets	subset	NOUN
ejpam-6597	171	33	of	of	ADP
ejpam-6597	171	34	x.	x.	NOUN
ejpam-6597	171	35	since	since	SCONJ
ejpam-6597	171	36	x	x	PRON
ejpam-6597	171	37	is	be	AUX
ejpam-6597	171	38	countably	countably	ADV
ejpam-6597	171	39	compact	compact	ADJ
ejpam-6597	171	40	,	,	PUNCT
ejpam-6597	171	41	the	the	DET
ejpam-6597	171	42	family	family	NOUN
ejpam-6597	171	43	{	{	PUNCT
ejpam-6597	171	44	fs}s∈s	fs}s∈s	X
ejpam-6597	171	45	is	be	AUX
ejpam-6597	171	46	finite	finite	ADJ
ejpam-6597	171	47	family	family	NOUN
ejpam-6597	171	48	of	of	ADP
ejpam-6597	171	49	pairwise	pairwise	PROPN
ejpam-6597	171	50	disjoint	disjoint	NOUN
ejpam-6597	171	51	closed	close	VERB
ejpam-6597	171	52	subsets	subset	NOUN
ejpam-6597	171	53	of	of	ADP
ejpam-6597	171	54	x.	x.	NOUN
ejpam-6597	171	55	then	then	ADV
ejpam-6597	171	56	,	,	PUNCT
ejpam-6597	171	57	the	the	DET
ejpam-6597	171	58	family	family	NOUN
ejpam-6597	171	59	can	can	AUX
ejpam-6597	171	60	be	be	AUX
ejpam-6597	171	61	rewritten	rewrite	VERB
ejpam-6597	171	62	as	as	ADP
ejpam-6597	171	63	{	{	PUNCT
ejpam-6597	171	64	fsi}ni=1	fsi}ni=1	PROPN
ejpam-6597	171	65	,	,	PUNCT
ejpam-6597	171	66	for	for	ADP
ejpam-6597	171	67	some	some	DET
ejpam-6597	171	68	n	n	PRON
ejpam-6597	171	69	∈	∈	NOUN
ejpam-6597	171	70	n.	n.	NOUN
ejpam-6597	171	71	by	by	ADP
ejpam-6597	171	72	pre	pre	VERB
ejpam-6597	171	73	-	-	NOUN
ejpam-6597	171	74	normality	normality	NOUN
ejpam-6597	171	75	of	of	ADP
ejpam-6597	171	76	x	x	PRON
ejpam-6597	171	77	,	,	PUNCT
ejpam-6597	171	78	for	for	ADP
ejpam-6597	171	79	any	any	DET
ejpam-6597	171	80	disjoint	disjoint	NOUN
ejpam-6597	171	81	closed	close	VERB
ejpam-6597	171	82	sets	set	NOUN
ejpam-6597	171	83	fsi	fsi	PROPN
ejpam-6597	171	84	and	and	CCONJ
ejpam-6597	171	85	fsj	fsj	PROPN
ejpam-6597	171	86	,	,	PUNCT
ejpam-6597	171	87	there	there	PRON
ejpam-6597	171	88	exist	exist	VERB
ejpam-6597	171	89	two	two	NUM
ejpam-6597	171	90	disjoint	disjoint	ADJ
ejpam-6597	171	91	pre	pre	ADJ
ejpam-6597	171	92	-	-	ADJ
ejpam-6597	171	93	open	open	ADJ
ejpam-6597	171	94	sets	set	NOUN
ejpam-6597	171	95	usi	usi	NOUN
ejpam-6597	171	96	and	and	CCONJ
ejpam-6597	171	97	usj	usj	VERB
ejpam-6597	171	98	in	in	ADP
ejpam-6597	171	99	x	x	SYM
ejpam-6597	171	100	such	such	ADJ
ejpam-6597	171	101	that	that	SCONJ
ejpam-6597	171	102	fsi	fsi	PROPN
ejpam-6597	171	103	⊆	⊆	NUM
ejpam-6597	171	104	usi	usi	PROPN
ejpam-6597	171	105	and	and	CCONJ
ejpam-6597	171	106	fsj	fsj	PROPN
ejpam-6597	171	107	⊆	⊆	NUM
ejpam-6597	171	108	usj	usj	PROPN
ejpam-6597	171	109	,	,	PUNCT
ejpam-6597	171	110	usi	usi	PROPN
ejpam-6597	171	111	∩usj	∩usj	NOUN
ejpam-6597	171	112	=	=	PUNCT
ejpam-6597	171	113	∅	∅	NOUN
ejpam-6597	171	114	and	and	CCONJ
ejpam-6597	171	115	thus	thus	ADV
ejpam-6597	171	116	cl(usi)∩	cl(usi)∩	NUM
ejpam-6597	171	117	cl(usj	cl(usj	NOUN
ejpam-6597	171	118	)	)	PUNCT
ejpam-6597	172	1	=	=	NOUN
ejpam-6597	172	2	∅	∅	NOUN
ejpam-6597	172	3	for	for	ADP
ejpam-6597	172	4	each	each	DET
ejpam-6597	172	5	i	i	PRON
ejpam-6597	172	6	̸=	̸=	PROPN
ejpam-6597	172	7	j.	j.	PROPN
ejpam-6597	172	8	then	then	ADV
ejpam-6597	172	9	,	,	PUNCT
ejpam-6597	172	10	the	the	DET
ejpam-6597	172	11	family	family	NOUN
ejpam-6597	172	12	{	{	PUNCT
ejpam-6597	172	13	usi}ni=1	usi}ni=1	PROPN
ejpam-6597	172	14	is	be	AUX
ejpam-6597	172	15	a	a	DET
ejpam-6597	172	16	family	family	NOUN
ejpam-6597	172	17	of	of	ADP
ejpam-6597	172	18	pre	pre	ADJ
ejpam-6597	172	19	-	-	ADJ
ejpam-6597	172	20	open	open	ADJ
ejpam-6597	172	21	sets	set	NOUN
ejpam-6597	172	22	in	in	ADP
ejpam-6597	172	23	x	x	SYM
ejpam-6597	172	24	such	such	ADJ
ejpam-6597	172	25	that	that	SCONJ
ejpam-6597	172	26	fsi	fsi	PROPN
ejpam-6597	172	27	⊆	⊆	NUM
ejpam-6597	172	28	usi	usi	NOUN
ejpam-6597	172	29	for	for	ADP
ejpam-6597	172	30	each	each	DET
ejpam-6597	172	31	i	i	NOUN
ejpam-6597	172	32	=	=	NOUN
ejpam-6597	172	33	1	1	NUM
ejpam-6597	172	34	,	,	PUNCT
ejpam-6597	172	35	2	2	NUM
ejpam-6597	172	36	,	,	PUNCT
ejpam-6597	172	37	3	3	NUM
ejpam-6597	172	38	,	,	PUNCT
ejpam-6597	172	39	.	.	PUNCT
ejpam-6597	172	40	.	.	PUNCT
ejpam-6597	173	1	.	.	PUNCT
ejpam-6597	174	1	,	,	PUNCT
ejpam-6597	174	2	n.	n.	NOUN
ejpam-6597	174	3	it	it	PRON
ejpam-6597	174	4	can	can	AUX
ejpam-6597	174	5	be	be	AUX
ejpam-6597	174	6	observed	observe	VERB
ejpam-6597	174	7	that	that	SCONJ
ejpam-6597	174	8	the	the	DET
ejpam-6597	174	9	family	family	NOUN
ejpam-6597	174	10	{	{	PUNCT
ejpam-6597	174	11	usi}ni=1	usi}ni=1	PROPN
ejpam-6597	174	12	is	be	AUX
ejpam-6597	174	13	discrete	discrete	ADJ
ejpam-6597	174	14	.	.	PUNCT
ejpam-6597	175	1	therefore	therefore	ADV
ejpam-6597	175	2	,	,	PUNCT
ejpam-6597	175	3	the	the	DET
ejpam-6597	175	4	family	family	NOUN
ejpam-6597	175	5	{	{	PUNCT
ejpam-6597	175	6	usi}ni=1	usi}ni=1	PROPN
ejpam-6597	175	7	is	be	AUX
ejpam-6597	175	8	discrete	discrete	ADJ
ejpam-6597	175	9	family	family	NOUN
ejpam-6597	175	10	of	of	ADP
ejpam-6597	175	11	pre	pre	ADJ
ejpam-6597	175	12	-	-	ADJ
ejpam-6597	175	13	open	open	ADJ
ejpam-6597	175	14	sets	set	NOUN
ejpam-6597	175	15	in	in	ADP
ejpam-6597	175	16	x	x	SYM
ejpam-6597	175	17	such	such	ADJ
ejpam-6597	175	18	that	that	SCONJ
ejpam-6597	175	19	fsi	fsi	PROPN
ejpam-6597	175	20	⊆	⊆	NUM
ejpam-6597	175	21	usi	usi	NOUN
ejpam-6597	175	22	for	for	ADP
ejpam-6597	175	23	each	each	DET
ejpam-6597	175	24	i	i	NOUN
ejpam-6597	175	25	=	=	NOUN
ejpam-6597	175	26	1	1	NUM
ejpam-6597	175	27	,	,	PUNCT
ejpam-6597	175	28	2	2	NUM
ejpam-6597	175	29	,	,	PUNCT
ejpam-6597	175	30	3	3	NUM
ejpam-6597	175	31	,	,	PUNCT
ejpam-6597	175	32	.	.	PUNCT
ejpam-6597	175	33	.	.	PUNCT
ejpam-6597	176	1	.	.	PUNCT
ejpam-6597	177	1	,	,	PUNCT
ejpam-6597	177	2	n.	n.	PROPN
ejpam-6597	177	3	hence	hence	ADV
ejpam-6597	177	4	,	,	PUNCT
ejpam-6597	177	5	x	x	PRON
ejpam-6597	177	6	is	be	AUX
ejpam-6597	177	7	collectionwise	collectionwise	ADV
ejpam-6597	177	8	pre	pre	ADJ
ejpam-6597	177	9	-	-	ADJ
ejpam-6597	177	10	normal	normal	ADJ
ejpam-6597	177	11	.	.	PUNCT
ejpam-6597	178	1	since	since	SCONJ
ejpam-6597	178	2	every	every	DET
ejpam-6597	178	3	countable	countable	ADJ
ejpam-6597	178	4	countably	countably	ADV
ejpam-6597	178	5	-	-	ADJ
ejpam-6597	178	6	compact	compact	ADJ
ejpam-6597	178	7	space	space	NOUN
ejpam-6597	178	8	is	be	AUX
ejpam-6597	178	9	separable	separable	ADJ
ejpam-6597	178	10	compact	compact	ADJ
ejpam-6597	179	1	[	[	X
ejpam-6597	179	2	9	9	NUM
ejpam-6597	179	3	]	]	PUNCT
ejpam-6597	179	4	,	,	PUNCT
ejpam-6597	179	5	we	we	PRON
ejpam-6597	179	6	obtain	obtain	VERB
ejpam-6597	179	7	:	:	PUNCT
ejpam-6597	179	8	corollary	corollary	ADJ
ejpam-6597	179	9	9	9	NUM
ejpam-6597	179	10	.	.	PUNCT
ejpam-6597	180	1	every	every	DET
ejpam-6597	180	2	countable	countable	ADJ
ejpam-6597	180	3	hausdorff	hausdorff	NOUN
ejpam-6597	180	4	countably	countably	ADV
ejpam-6597	180	5	compact	compact	ADJ
ejpam-6597	180	6	space	space	NOUN
ejpam-6597	180	7	is	be	AUX
ejpam-6597	180	8	collectionwise	collectionwise	ADV
ejpam-6597	180	9	prenormal	prenormal	ADJ
ejpam-6597	180	10	.	.	PUNCT
ejpam-6597	181	1	since	since	SCONJ
ejpam-6597	181	2	every	every	DET
ejpam-6597	181	3	collectionwise	collectionwise	ADV
ejpam-6597	181	4	pre	pre	ADJ
ejpam-6597	181	5	-	-	ADJ
ejpam-6597	181	6	normal	normal	ADJ
ejpam-6597	181	7	space	space	NOUN
ejpam-6597	181	8	is	be	AUX
ejpam-6597	181	9	t1	t1	NOUN
ejpam-6597	181	10	and	and	CCONJ
ejpam-6597	181	11	every	every	DET
ejpam-6597	181	12	finite	finite	ADJ
ejpam-6597	181	13	t1	t1	NOUN
ejpam-6597	181	14	-	-	PUNCT
ejpam-6597	181	15	space	space	NOUN
ejpam-6597	181	16	is	be	AUX
ejpam-6597	181	17	discrete	discrete	ADJ
ejpam-6597	181	18	,	,	PUNCT
ejpam-6597	181	19	we	we	PRON
ejpam-6597	181	20	get	get	VERB
ejpam-6597	181	21	the	the	DET
ejpam-6597	181	22	following	follow	VERB
ejpam-6597	181	23	corollary	corollary	NOUN
ejpam-6597	181	24	:	:	PUNCT
ejpam-6597	181	25	s.	s.	PROPN
ejpam-6597	181	26	a.	a.	PROPN
ejpam-6597	181	27	thabit	thabit	PROPN
ejpam-6597	181	28	,	,	PUNCT
ejpam-6597	181	29	a.	a.	PROPN
ejpam-6597	181	30	al	al	PROPN
ejpam-6597	181	31	-	-	PUNCT
ejpam-6597	181	32	awadi	awadi	PROPN
ejpam-6597	181	33	,	,	PUNCT
ejpam-6597	181	34	r.	r.	PROPN
ejpam-6597	181	35	noaman	noaman	PROPN
ejpam-6597	181	36	/	/	SYM
ejpam-6597	181	37	eur	eur	PROPN
ejpam-6597	181	38	.	.	PUNCT
ejpam-6597	182	1	j.	j.	PROPN
ejpam-6597	182	2	pure	pure	PROPN
ejpam-6597	182	3	appl	appl	PROPN
ejpam-6597	182	4	.	.	PROPN
ejpam-6597	182	5	math	math	PROPN
ejpam-6597	182	6	,	,	PUNCT
ejpam-6597	182	7	18	18	NUM
ejpam-6597	182	8	(	(	PUNCT
ejpam-6597	182	9	4	4	NUM
ejpam-6597	182	10	)	)	PUNCT
ejpam-6597	182	11	(	(	PUNCT
ejpam-6597	182	12	2025	2025	NUM
ejpam-6597	182	13	)	)	PUNCT
ejpam-6597	182	14	,	,	PUNCT
ejpam-6597	182	15	6597	6597	NUM
ejpam-6597	182	16	7	7	NUM
ejpam-6597	182	17	of	of	ADP
ejpam-6597	182	18	15	15	NUM
ejpam-6597	182	19	corollary	corollary	ADJ
ejpam-6597	182	20	10	10	NUM
ejpam-6597	182	21	.	.	PUNCT
ejpam-6597	183	1	every	every	DET
ejpam-6597	183	2	finite	finite	PROPN
ejpam-6597	183	3	collectionwise	collectionwise	PROPN
ejpam-6597	183	4	pre	pre	ADJ
ejpam-6597	183	5	-	-	ADJ
ejpam-6597	183	6	normal	normal	ADJ
ejpam-6597	183	7	space	space	NOUN
ejpam-6597	183	8	is	be	AUX
ejpam-6597	183	9	discrete	discrete	ADJ
ejpam-6597	183	10	and	and	CCONJ
ejpam-6597	183	11	hence	hence	ADV
ejpam-6597	183	12	it	it	PRON
ejpam-6597	183	13	is	be	AUX
ejpam-6597	183	14	collectionwise	collectionwise	ADV
ejpam-6597	183	15	normal	normal	ADJ
ejpam-6597	183	16	.	.	PUNCT
ejpam-6597	184	1	theorem	theorem	NOUN
ejpam-6597	184	2	12	12	NUM
ejpam-6597	184	3	.	.	PUNCT
ejpam-6597	185	1	collectionwise	collectionwise	PROPN
ejpam-6597	185	2	pre	pre	ADJ
ejpam-6597	185	3	-	-	ADJ
ejpam-6597	185	4	normality	normality	ADJ
ejpam-6597	185	5	is	be	AUX
ejpam-6597	185	6	a	a	DET
ejpam-6597	185	7	topological	topological	ADJ
ejpam-6597	185	8	property	property	NOUN
ejpam-6597	185	9	.	.	PUNCT
ejpam-6597	186	1	proof	proof	NOUN
ejpam-6597	186	2	.	.	PUNCT
ejpam-6597	187	1	let	let	VERB
ejpam-6597	187	2	x	x	PART
ejpam-6597	187	3	∼=	∼=	VERB
ejpam-6597	187	4	y	y	PROPN
ejpam-6597	187	5	and	and	CCONJ
ejpam-6597	187	6	x	x	AUX
ejpam-6597	187	7	be	be	AUX
ejpam-6597	187	8	a	a	DET
ejpam-6597	187	9	collectionwise	collectionwise	ADV
ejpam-6597	187	10	pre	pre	ADJ
ejpam-6597	187	11	-	-	ADJ
ejpam-6597	187	12	normal	normal	ADJ
ejpam-6597	187	13	space	space	NOUN
ejpam-6597	187	14	.	.	PUNCT
ejpam-6597	188	1	then	then	ADV
ejpam-6597	188	2	,	,	PUNCT
ejpam-6597	188	3	there	there	PRON
ejpam-6597	188	4	exists	exist	VERB
ejpam-6597	188	5	a	a	DET
ejpam-6597	188	6	function	function	NOUN
ejpam-6597	188	7	f	f	NOUN
ejpam-6597	188	8	:	:	PUNCT
ejpam-6597	188	9	x	x	X
ejpam-6597	188	10	→	→	PUNCT
ejpam-6597	188	11	y	y	NUM
ejpam-6597	188	12	such	such	ADJ
ejpam-6597	188	13	that	that	SCONJ
ejpam-6597	188	14	f	f	PROPN
ejpam-6597	188	15	is	be	AUX
ejpam-6597	188	16	1	1	NUM
ejpam-6597	188	17	-	-	SYM
ejpam-6597	188	18	1	1	NUM
ejpam-6597	188	19	,	,	PUNCT
ejpam-6597	188	20	onto	onto	ADP
ejpam-6597	188	21	,	,	PUNCT
ejpam-6597	188	22	continuous	continuous	ADJ
ejpam-6597	188	23	and	and	CCONJ
ejpam-6597	188	24	f−1	f−1	PROPN
ejpam-6597	188	25	is	be	AUX
ejpam-6597	188	26	continuous	continuous	ADJ
ejpam-6597	188	27	.	.	PUNCT
ejpam-6597	189	1	we	we	PRON
ejpam-6597	189	2	show	show	VERB
ejpam-6597	189	3	that	that	SCONJ
ejpam-6597	189	4	y	y	PROPN
ejpam-6597	189	5	is	be	AUX
ejpam-6597	189	6	collectionwise	collectionwise	ADV
ejpam-6597	189	7	pre	pre	ADJ
ejpam-6597	189	8	-	-	ADJ
ejpam-6597	189	9	normal	normal	ADJ
ejpam-6597	189	10	.	.	PUNCT
ejpam-6597	190	1	let	let	VERB
ejpam-6597	190	2	f	f	NOUN
ejpam-6597	190	3	=	=	PRON
ejpam-6597	190	4	{	{	PUNCT
ejpam-6597	190	5	fs	fs	X
ejpam-6597	190	6	:	:	PUNCT
ejpam-6597	190	7	s	s	VERB
ejpam-6597	190	8	∈	∈	PROPN
ejpam-6597	190	9	s	s	AUX
ejpam-6597	190	10	}	}	PUNCT
ejpam-6597	190	11	be	be	AUX
ejpam-6597	190	12	any	any	DET
ejpam-6597	190	13	discrete	discrete	ADJ
ejpam-6597	190	14	family	family	NOUN
ejpam-6597	190	15	of	of	ADP
ejpam-6597	190	16	closed	closed	ADJ
ejpam-6597	190	17	subsets	subset	NOUN
ejpam-6597	190	18	of	of	ADP
ejpam-6597	190	19	y	y	PROPN
ejpam-6597	190	20	.	.	PUNCT
ejpam-6597	191	1	then	then	ADV
ejpam-6597	191	2	,	,	PUNCT
ejpam-6597	191	3	fs	fs	X
ejpam-6597	191	4	is	be	AUX
ejpam-6597	191	5	closed	close	VERB
ejpam-6597	191	6	in	in	ADP
ejpam-6597	191	7	y	y	PROPN
ejpam-6597	191	8	for	for	ADP
ejpam-6597	191	9	each	each	DET
ejpam-6597	191	10	s	s	PROPN
ejpam-6597	191	11	∈	∈	PROPN
ejpam-6597	191	12	s.	s.	PROPN
ejpam-6597	191	13	since	since	SCONJ
ejpam-6597	191	14	f	f	PROPN
ejpam-6597	191	15	is	be	AUX
ejpam-6597	191	16	continuous	continuous	ADJ
ejpam-6597	191	17	,	,	PUNCT
ejpam-6597	191	18	f−1(fs	f−1(fs	PROPN
ejpam-6597	191	19	)	)	PUNCT
ejpam-6597	191	20	is	be	AUX
ejpam-6597	191	21	a	a	DET
ejpam-6597	191	22	closed	closed	ADJ
ejpam-6597	191	23	subset	subset	NOUN
ejpam-6597	191	24	of	of	ADP
ejpam-6597	191	25	x	x	PUNCT
ejpam-6597	191	26	for	for	ADP
ejpam-6597	191	27	each	each	DET
ejpam-6597	191	28	s	s	PROPN
ejpam-6597	191	29	∈	∈	PROPN
ejpam-6597	191	30	s.	s.	PROPN
ejpam-6597	191	31	note	note	VERB
ejpam-6597	191	32	that	that	SCONJ
ejpam-6597	191	33	:	:	PUNCT
ejpam-6597	191	34	{	{	PUNCT
ejpam-6597	191	35	f−1(fs	f−1(fs	X
ejpam-6597	191	36	)	)	PUNCT
ejpam-6597	191	37	:	:	PUNCT
ejpam-6597	191	38	s	s	VERB
ejpam-6597	191	39	∈	∈	PROPN
ejpam-6597	191	40	s	s	AUX
ejpam-6597	191	41	}	}	PUNCT
ejpam-6597	191	42	is	be	AUX
ejpam-6597	191	43	a	a	DET
ejpam-6597	191	44	discrete	discrete	ADJ
ejpam-6597	191	45	family	family	NOUN
ejpam-6597	191	46	of	of	ADP
ejpam-6597	191	47	closed	closed	ADJ
ejpam-6597	191	48	subsets	subset	NOUN
ejpam-6597	191	49	of	of	ADP
ejpam-6597	191	50	x.	x.	NOUN
ejpam-6597	191	51	since	since	SCONJ
ejpam-6597	191	52	x	x	PRON
ejpam-6597	191	53	is	be	AUX
ejpam-6597	191	54	collectionwise	collectionwise	ADV
ejpam-6597	191	55	pre	pre	ADJ
ejpam-6597	191	56	-	-	ADJ
ejpam-6597	191	57	normal	normal	ADJ
ejpam-6597	191	58	,	,	PUNCT
ejpam-6597	191	59	there	there	PRON
ejpam-6597	191	60	is	be	VERB
ejpam-6597	191	61	a	a	DET
ejpam-6597	191	62	discrete	discrete	ADJ
ejpam-6597	191	63	family	family	NOUN
ejpam-6597	191	64	{	{	PUNCT
ejpam-6597	191	65	vs	vs	ADP
ejpam-6597	191	66	:	:	PUNCT
ejpam-6597	191	67	s	s	X
ejpam-6597	191	68	∈	∈	PROPN
ejpam-6597	191	69	s	s	PART
ejpam-6597	191	70	}	}	PUNCT
ejpam-6597	191	71	of	of	ADP
ejpam-6597	191	72	pre	pre	ADJ
ejpam-6597	191	73	-	-	ADJ
ejpam-6597	191	74	open	open	ADJ
ejpam-6597	191	75	subsets	subset	NOUN
ejpam-6597	191	76	of	of	ADP
ejpam-6597	191	77	x	x	SYM
ejpam-6597	191	78	such	such	ADJ
ejpam-6597	191	79	that	that	DET
ejpam-6597	191	80	f−1(fs	f−1(fs	PROPN
ejpam-6597	191	81	)	)	PUNCT
ejpam-6597	191	82	⊆	⊆	NUM
ejpam-6597	191	83	vs	vs	ADP
ejpam-6597	191	84	for	for	ADP
ejpam-6597	191	85	each	each	DET
ejpam-6597	191	86	s	s	X
ejpam-6597	191	87	∈	∈	PROPN
ejpam-6597	191	88	s.	s.	PROPN
ejpam-6597	192	1	so	so	ADV
ejpam-6597	192	2	,	,	PUNCT
ejpam-6597	192	3	fs	fs	ADP
ejpam-6597	192	4	⊆	⊆	NUM
ejpam-6597	192	5	f(vs	f(v	NOUN
ejpam-6597	192	6	)	)	PUNCT
ejpam-6597	192	7	for	for	ADP
ejpam-6597	192	8	each	each	DET
ejpam-6597	192	9	s	s	PROPN
ejpam-6597	192	10	∈	∈	PROPN
ejpam-6597	192	11	s.	s.	PROPN
ejpam-6597	192	12	since	since	SCONJ
ejpam-6597	192	13	f	f	PROPN
ejpam-6597	192	14	is	be	AUX
ejpam-6597	192	15	homeomorphism	homeomorphism	PROPN
ejpam-6597	192	16	,	,	PUNCT
ejpam-6597	192	17	we	we	PRON
ejpam-6597	192	18	have	have	VERB
ejpam-6597	192	19	f(vs	f(v	NOUN
ejpam-6597	192	20	)	)	PUNCT
ejpam-6597	192	21	is	be	AUX
ejpam-6597	192	22	a	a	DET
ejpam-6597	192	23	pre	pre	ADJ
ejpam-6597	192	24	-	-	ADJ
ejpam-6597	192	25	open	open	ADJ
ejpam-6597	192	26	subset	subset	NOUN
ejpam-6597	192	27	of	of	ADP
ejpam-6597	192	28	y	y	PROPN
ejpam-6597	192	29	for	for	ADP
ejpam-6597	192	30	each	each	DET
ejpam-6597	192	31	s	s	PROPN
ejpam-6597	192	32	∈	∈	PROPN
ejpam-6597	192	33	s.	s.	PROPN
ejpam-6597	193	1	thus	thus	ADV
ejpam-6597	193	2	,	,	PUNCT
ejpam-6597	193	3	we	we	PRON
ejpam-6597	193	4	have	have	VERB
ejpam-6597	193	5	{	{	PUNCT
ejpam-6597	193	6	f(vs)}s∈s	f(vs)}s∈s	NOUN
ejpam-6597	193	7	is	be	AUX
ejpam-6597	193	8	a	a	DET
ejpam-6597	193	9	discrete	discrete	ADJ
ejpam-6597	193	10	family	family	NOUN
ejpam-6597	193	11	of	of	ADP
ejpam-6597	193	12	pre	pre	ADJ
ejpam-6597	193	13	-	-	ADJ
ejpam-6597	193	14	open	open	ADJ
ejpam-6597	193	15	subsets	subset	NOUN
ejpam-6597	193	16	of	of	ADP
ejpam-6597	193	17	y	y	PRON
ejpam-6597	193	18	such	such	ADJ
ejpam-6597	193	19	that	that	SCONJ
ejpam-6597	193	20	fs	fs	ADP
ejpam-6597	193	21	⊆	⊆	NUM
ejpam-6597	193	22	f(vs	f(v	NOUN
ejpam-6597	193	23	)	)	PUNCT
ejpam-6597	193	24	for	for	ADP
ejpam-6597	193	25	each	each	DET
ejpam-6597	193	26	s	s	PROPN
ejpam-6597	193	27	∈	∈	PROPN
ejpam-6597	193	28	s.	s.	PROPN
ejpam-6597	193	29	therefore	therefore	ADV
ejpam-6597	193	30	,	,	PUNCT
ejpam-6597	193	31	y	y	PROPN
ejpam-6597	193	32	is	be	AUX
ejpam-6597	193	33	collectionwise	collectionwise	ADV
ejpam-6597	193	34	pre	pre	ADJ
ejpam-6597	193	35	-	-	ADJ
ejpam-6597	193	36	normal	normal	ADJ
ejpam-6597	193	37	.	.	PUNCT
ejpam-6597	194	1	theorem	theorem	VERB
ejpam-6597	194	2	13	13	NUM
ejpam-6597	194	3	.	.	PUNCT
ejpam-6597	195	1	the	the	DET
ejpam-6597	195	2	sum	sum	NOUN
ejpam-6597	195	3	x	x	PUNCT
ejpam-6597	195	4	=	=	SYM
ejpam-6597	195	5	⊕s∈sxs	⊕s∈sxs	PROPN
ejpam-6597	195	6	,	,	PUNCT
ejpam-6597	195	7	xs	xs	PROPN
ejpam-6597	195	8	̸=	̸=	PROPN
ejpam-6597	195	9	∅	∅	NOUN
ejpam-6597	195	10	for	for	ADP
ejpam-6597	195	11	each	each	DET
ejpam-6597	195	12	s	s	X
ejpam-6597	195	13	∈	∈	PROPN
ejpam-6597	195	14	s	s	NOUN
ejpam-6597	195	15	,	,	PUNCT
ejpam-6597	195	16	is	be	AUX
ejpam-6597	195	17	collectionwise	collectionwise	ADV
ejpam-6597	195	18	pre	pre	ADJ
ejpam-6597	195	19	-	-	ADJ
ejpam-6597	195	20	normal	normal	ADJ
ejpam-6597	195	21	if	if	SCONJ
ejpam-6597	195	22	and	and	CCONJ
ejpam-6597	195	23	only	only	ADV
ejpam-6597	195	24	if	if	SCONJ
ejpam-6597	195	25	each	each	DET
ejpam-6597	195	26	xs	xs	PROPN
ejpam-6597	195	27	is	be	AUX
ejpam-6597	195	28	collectionwise	collectionwise	ADV
ejpam-6597	195	29	pre	pre	ADJ
ejpam-6597	195	30	-	-	ADJ
ejpam-6597	195	31	normal	normal	ADJ
ejpam-6597	195	32	.	.	PUNCT
ejpam-6597	196	1	proof	proof	NOUN
ejpam-6597	196	2	.	.	PUNCT
ejpam-6597	197	1	let	let	VERB
ejpam-6597	197	2	x	x	SYM
ejpam-6597	197	3	=	=	SYM
ejpam-6597	197	4	⊕	⊕	PROPN
ejpam-6597	197	5	s∈s	s∈s	NOUN
ejpam-6597	197	6	xs	xs	PROPN
ejpam-6597	197	7	be	be	AUX
ejpam-6597	197	8	a	a	DET
ejpam-6597	197	9	collectionwise	collectionwise	ADV
ejpam-6597	197	10	pre	pre	ADJ
ejpam-6597	197	11	-	-	ADJ
ejpam-6597	197	12	normal	normal	ADJ
ejpam-6597	197	13	space	space	NOUN
ejpam-6597	197	14	.	.	PUNCT
ejpam-6597	198	1	since	since	SCONJ
ejpam-6597	198	2	xs	xs	PROPN
ejpam-6597	198	3	⊆	⊆	NUM
ejpam-6597	198	4	x	x	X
ejpam-6597	198	5	is	be	AUX
ejpam-6597	198	6	a	a	DET
ejpam-6597	198	7	clopen	clopen	ADJ
ejpam-6597	198	8	subspace	subspace	NOUN
ejpam-6597	198	9	of	of	ADP
ejpam-6597	198	10	a	a	DET
ejpam-6597	198	11	collectionwise	collectionwise	ADV
ejpam-6597	198	12	pre	pre	ADJ
ejpam-6597	198	13	-	-	ADJ
ejpam-6597	198	14	normal	normal	ADJ
ejpam-6597	198	15	space	space	NOUN
ejpam-6597	198	16	x	x	PUNCT
ejpam-6597	198	17	and	and	CCONJ
ejpam-6597	198	18	a	a	DET
ejpam-6597	198	19	clopen	clopen	ADJ
ejpam-6597	198	20	subspace	subspace	NOUN
ejpam-6597	198	21	of	of	ADP
ejpam-6597	198	22	a	a	DET
ejpam-6597	198	23	collectionwise	collectionwise	ADV
ejpam-6597	198	24	pre	pre	ADJ
ejpam-6597	198	25	-	-	ADJ
ejpam-6597	198	26	normal	normal	ADJ
ejpam-6597	198	27	space	space	NOUN
ejpam-6597	198	28	is	be	AUX
ejpam-6597	198	29	collectionwise	collectionwise	ADV
ejpam-6597	198	30	pre	pre	ADJ
ejpam-6597	198	31	-	-	ADJ
ejpam-6597	198	32	normal	normal	ADJ
ejpam-6597	198	33	(	(	PUNCT
ejpam-6597	198	34	corollary	corollary	ADJ
ejpam-6597	198	35	12	12	NUM
ejpam-6597	198	36	)	)	PUNCT
ejpam-6597	198	37	,	,	PUNCT
ejpam-6597	198	38	we	we	PRON
ejpam-6597	198	39	have	have	VERB
ejpam-6597	198	40	xs	xs	PROPN
ejpam-6597	198	41	is	be	AUX
ejpam-6597	198	42	collectionwise	collectionwise	ADV
ejpam-6597	198	43	pre	pre	ADJ
ejpam-6597	198	44	-	-	ADJ
ejpam-6597	198	45	normal	normal	ADJ
ejpam-6597	198	46	for	for	ADP
ejpam-6597	198	47	each	each	DET
ejpam-6597	198	48	s	s	PROPN
ejpam-6597	198	49	∈	∈	PROPN
ejpam-6597	198	50	s.	s.	PROPN
ejpam-6597	198	51	now	now	ADV
ejpam-6597	198	52	,	,	PUNCT
ejpam-6597	198	53	let	let	VERB
ejpam-6597	198	54	xs	xs	PRON
ejpam-6597	198	55	be	be	AUX
ejpam-6597	198	56	a	a	DET
ejpam-6597	198	57	collectionwise	collectionwise	ADV
ejpam-6597	198	58	pre	pre	ADJ
ejpam-6597	198	59	-	-	ADJ
ejpam-6597	198	60	normal	normal	ADJ
ejpam-6597	198	61	space	space	NOUN
ejpam-6597	198	62	for	for	ADP
ejpam-6597	198	63	each	each	DET
ejpam-6597	198	64	s	s	PART
ejpam-6597	198	65	∈	∈	PROPN
ejpam-6597	198	66	s.	s.	PROPN
ejpam-6597	198	67	we	we	PRON
ejpam-6597	198	68	show	show	VERB
ejpam-6597	198	69	that	that	SCONJ
ejpam-6597	198	70	x	x	NOUN
ejpam-6597	198	71	=	=	SYM
ejpam-6597	198	72	⊕	⊕	PROPN
ejpam-6597	198	73	s∈s	s∈s	NOUN
ejpam-6597	198	74	xs	xs	PROPN
ejpam-6597	198	75	is	be	AUX
ejpam-6597	198	76	collectionwise	collectionwise	ADV
ejpam-6597	198	77	pre	pre	ADJ
ejpam-6597	198	78	-	-	ADJ
ejpam-6597	198	79	normal	normal	ADJ
ejpam-6597	198	80	.	.	PUNCT
ejpam-6597	199	1	let	let	VERB
ejpam-6597	199	2	{	{	PUNCT
ejpam-6597	199	3	fi	fi	NOUN
ejpam-6597	199	4	:	:	PUNCT
ejpam-6597	200	1	i	i	PRON
ejpam-6597	200	2	∈	∈	VERB
ejpam-6597	200	3	i	i	PRON
ejpam-6597	200	4	}	}	PUNCT
ejpam-6597	200	5	be	be	AUX
ejpam-6597	200	6	a	a	DET
ejpam-6597	200	7	discrete	discrete	ADJ
ejpam-6597	200	8	family	family	NOUN
ejpam-6597	200	9	of	of	ADP
ejpam-6597	200	10	closed	closed	ADJ
ejpam-6597	200	11	subsets	subset	NOUN
ejpam-6597	200	12	of	of	ADP
ejpam-6597	200	13	x.	x.	NOUN
ejpam-6597	200	14	then	then	ADV
ejpam-6597	200	15	,	,	PUNCT
ejpam-6597	200	16	{	{	PUNCT
ejpam-6597	200	17	fi	fi	NOUN
ejpam-6597	200	18	∩	∩	ADJ
ejpam-6597	200	19	xs	xs	NOUN
ejpam-6597	200	20	:	:	PUNCT
ejpam-6597	201	1	i	i	PRON
ejpam-6597	201	2	∈	∈	VERB
ejpam-6597	201	3	i	i	PRON
ejpam-6597	201	4	}	}	PUNCT
ejpam-6597	201	5	is	be	AUX
ejpam-6597	201	6	a	a	DET
ejpam-6597	201	7	discrete	discrete	ADJ
ejpam-6597	201	8	family	family	NOUN
ejpam-6597	201	9	of	of	ADP
ejpam-6597	201	10	closed	closed	ADJ
ejpam-6597	201	11	subsets	subset	NOUN
ejpam-6597	201	12	of	of	ADP
ejpam-6597	201	13	xs	xs	PROPN
ejpam-6597	201	14	for	for	ADP
ejpam-6597	201	15	each	each	DET
ejpam-6597	201	16	s	s	PROPN
ejpam-6597	201	17	∈	∈	PROPN
ejpam-6597	201	18	s.	s.	PROPN
ejpam-6597	201	19	by	by	ADP
ejpam-6597	201	20	collectionwise	collectionwise	PROPN
ejpam-6597	201	21	pre	pre	PROPN
ejpam-6597	201	22	-	-	NOUN
ejpam-6597	201	23	normality	normality	NOUN
ejpam-6597	201	24	of	of	ADP
ejpam-6597	201	25	xs	xs	PROPN
ejpam-6597	201	26	,	,	PUNCT
ejpam-6597	201	27	there	there	PRON
ejpam-6597	201	28	exists	exist	VERB
ejpam-6597	201	29	a	a	DET
ejpam-6597	201	30	discrete	discrete	ADJ
ejpam-6597	201	31	family	family	NOUN
ejpam-6597	201	32	{	{	PUNCT
ejpam-6597	201	33	uis	uis	PROPN
ejpam-6597	201	34	:	:	PUNCT
ejpam-6597	201	35	i	i	PROPN
ejpam-6597	201	36	∈	∈	VERB
ejpam-6597	202	1	i	i	X
ejpam-6597	202	2	}	}	PUNCT
ejpam-6597	202	3	of	of	ADP
ejpam-6597	202	4	pre	pre	ADJ
ejpam-6597	202	5	-	-	ADJ
ejpam-6597	202	6	open	open	ADJ
ejpam-6597	202	7	subsets	subset	NOUN
ejpam-6597	202	8	of	of	ADP
ejpam-6597	202	9	xs	xs	PROPN
ejpam-6597	202	10	such	such	ADJ
ejpam-6597	202	11	that	that	DET
ejpam-6597	202	12	fi	fi	NOUN
ejpam-6597	202	13	∩xs	∩xs	NOUN
ejpam-6597	202	14	⊆	⊆	NUM
ejpam-6597	202	15	uis	uis	PROPN
ejpam-6597	202	16	for	for	ADP
ejpam-6597	202	17	each	each	DET
ejpam-6597	202	18	s	s	PROPN
ejpam-6597	202	19	∈	∈	PROPN
ejpam-6597	202	20	s.	s.	PROPN
ejpam-6597	202	21	thus	thus	ADV
ejpam-6597	202	22	,	,	PUNCT
ejpam-6597	202	23	∪	∪	ADP
ejpam-6597	202	24	s∈s	s∈s	NOUN
ejpam-6597	202	25	(	(	PUNCT
ejpam-6597	202	26	fi	fi	NOUN
ejpam-6597	202	27	∩xs	∩xs	NOUN
ejpam-6597	202	28	)	)	PUNCT
ejpam-6597	202	29	⊆	⊆	NUM
ejpam-6597	202	30	∪	∪	ADP
ejpam-6597	202	31	s∈s	s∈s	NOUN
ejpam-6597	202	32	uis	uis	PROPN
ejpam-6597	202	33	.	.	PROPN
ejpam-6597	203	1	put	put	VERB
ejpam-6597	203	2	ui	ui	NOUN
ejpam-6597	203	3	=	=	PUNCT
ejpam-6597	203	4	∪	∪	ADP
ejpam-6597	203	5	s∈s	s∈s	NOUN
ejpam-6597	203	6	uis	uis	PROPN
ejpam-6597	203	7	,	,	PUNCT
ejpam-6597	203	8	which	which	PRON
ejpam-6597	203	9	is	be	AUX
ejpam-6597	203	10	a	a	DET
ejpam-6597	203	11	pre	pre	ADJ
ejpam-6597	203	12	-	-	ADJ
ejpam-6597	203	13	open	open	ADJ
ejpam-6597	203	14	set	set	NOUN
ejpam-6597	203	15	in	in	ADP
ejpam-6597	203	16	x	x	PUNCT
ejpam-6597	203	17	for	for	ADP
ejpam-6597	203	18	each	each	DET
ejpam-6597	203	19	i	i	PROPN
ejpam-6597	203	20	∈	∈	PROPN
ejpam-6597	203	21	i.	i.	NOUN
ejpam-6597	204	1	so	so	ADV
ejpam-6597	204	2	,	,	PUNCT
ejpam-6597	204	3	we	we	PRON
ejpam-6597	204	4	have	have	VERB
ejpam-6597	204	5	fi	fi	NOUN
ejpam-6597	204	6	⊆	⊆	NUM
ejpam-6597	204	7	ui	ui	NOUN
ejpam-6597	204	8	for	for	ADP
ejpam-6597	204	9	each	each	DET
ejpam-6597	204	10	i	i	PROPN
ejpam-6597	204	11	∈	∈	PROPN
ejpam-6597	204	12	i.	i.	NOUN
ejpam-6597	204	13	hence	hence	ADV
ejpam-6597	204	14	,	,	PUNCT
ejpam-6597	204	15	{	{	PUNCT
ejpam-6597	204	16	ui	ui	NOUN
ejpam-6597	204	17	:	:	PUNCT
ejpam-6597	204	18	i	i	PRON
ejpam-6597	204	19	∈	∈	VERB
ejpam-6597	205	1	i	i	PRON
ejpam-6597	205	2	}	}	PUNCT
ejpam-6597	205	3	is	be	AUX
ejpam-6597	205	4	a	a	DET
ejpam-6597	205	5	discrete	discrete	ADJ
ejpam-6597	205	6	family	family	NOUN
ejpam-6597	205	7	of	of	ADP
ejpam-6597	205	8	pre	pre	ADJ
ejpam-6597	205	9	-	-	ADJ
ejpam-6597	205	10	open	open	ADJ
ejpam-6597	205	11	subsets	subset	NOUN
ejpam-6597	205	12	of	of	ADP
ejpam-6597	205	13	x	x	PUNCT
ejpam-6597	205	14	such	such	ADJ
ejpam-6597	205	15	that	that	DET
ejpam-6597	205	16	fi	fi	NOUN
ejpam-6597	205	17	⊆	⊆	NUM
ejpam-6597	205	18	ui	ui	NOUN
ejpam-6597	205	19	for	for	ADP
ejpam-6597	205	20	each	each	DET
ejpam-6597	205	21	i	i	PROPN
ejpam-6597	205	22	∈	∈	PROPN
ejpam-6597	205	23	i.	i.	NOUN
ejpam-6597	205	24	therefore	therefore	ADV
ejpam-6597	205	25	,	,	PUNCT
ejpam-6597	205	26	x	x	SYM
ejpam-6597	205	27	=	=	SYM
ejpam-6597	205	28	⊕	⊕	PROPN
ejpam-6597	205	29	s∈s	s∈s	NOUN
ejpam-6597	205	30	xs	xs	PROPN
ejpam-6597	205	31	is	be	AUX
ejpam-6597	205	32	collectionwise	collectionwise	ADV
ejpam-6597	205	33	pre	pre	ADJ
ejpam-6597	205	34	-	-	ADJ
ejpam-6597	205	35	normal	normal	ADJ
ejpam-6597	205	36	.	.	PUNCT
ejpam-6597	206	1	corollary	corollary	ADJ
ejpam-6597	206	2	11	11	NUM
ejpam-6597	206	3	.	.	PUNCT
ejpam-6597	207	1	collectionwise	collectionwise	PROPN
ejpam-6597	207	2	pre	pre	ADJ
ejpam-6597	207	3	-	-	ADJ
ejpam-6597	207	4	normality	normality	ADJ
ejpam-6597	207	5	is	be	AUX
ejpam-6597	207	6	an	an	DET
ejpam-6597	207	7	additive	additive	ADJ
ejpam-6597	207	8	property	property	NOUN
ejpam-6597	207	9	.	.	PUNCT
ejpam-6597	208	1	3	3	X
ejpam-6597	208	2	.	.	X
ejpam-6597	208	3	characterizations	characterization	NOUN
ejpam-6597	208	4	of	of	ADP
ejpam-6597	208	5	collectionwise	collectionwise	PROPN
ejpam-6597	208	6	pre	pre	NOUN
ejpam-6597	208	7	-	-	NOUN
ejpam-6597	208	8	normality	normality	ADJ
ejpam-6597	208	9	now	now	ADV
ejpam-6597	208	10	,	,	PUNCT
ejpam-6597	208	11	we	we	PRON
ejpam-6597	208	12	give	give	VERB
ejpam-6597	208	13	some	some	DET
ejpam-6597	208	14	characterizations	characterization	NOUN
ejpam-6597	208	15	of	of	ADP
ejpam-6597	208	16	collectionwise	collectionwise	PROPN
ejpam-6597	208	17	pre	pre	ADJ
ejpam-6597	208	18	-	-	ADJ
ejpam-6597	208	19	normal	normal	ADJ
ejpam-6597	208	20	spaces	space	NOUN
ejpam-6597	208	21	.	.	PUNCT
ejpam-6597	209	1	first	first	ADV
ejpam-6597	209	2	,	,	PUNCT
ejpam-6597	209	3	we	we	PRON
ejpam-6597	209	4	need	need	VERB
ejpam-6597	209	5	to	to	PART
ejpam-6597	209	6	recall	recall	VERB
ejpam-6597	209	7	the	the	DET
ejpam-6597	209	8	next	next	ADJ
ejpam-6597	209	9	definitions	definition	NOUN
ejpam-6597	209	10	:	:	PUNCT
ejpam-6597	209	11	definition	definition	NOUN
ejpam-6597	209	12	2	2	NUM
ejpam-6597	209	13	.	.	PUNCT
ejpam-6597	209	14	a	a	DET
ejpam-6597	209	15	subset	subset	NOUN
ejpam-6597	209	16	a	a	PRON
ejpam-6597	209	17	of	of	ADP
ejpam-6597	209	18	x	x	PRON
ejpam-6597	209	19	is	be	AUX
ejpam-6597	209	20	called	call	VERB
ejpam-6597	209	21	:	:	PUNCT
ejpam-6597	209	22	•	•	ADV
ejpam-6597	209	23	generalized	generalize	VERB
ejpam-6597	209	24	closed	close	VERB
ejpam-6597	209	25	(	(	PUNCT
ejpam-6597	209	26	briefly	briefly	ADV
ejpam-6597	209	27	;	;	PUNCT
ejpam-6597	209	28	g	g	NOUN
ejpam-6597	209	29	-	-	PUNCT
ejpam-6597	209	30	closed	closed	ADJ
ejpam-6597	209	31	)	)	PUNCT
ejpam-6597	209	32	if	if	SCONJ
ejpam-6597	209	33	a	a	DET
ejpam-6597	209	34	⊆	⊆	NUM
ejpam-6597	209	35	u	u	NOUN
ejpam-6597	209	36	whenever	whenever	SCONJ
ejpam-6597	209	37	a	a	DET
ejpam-6597	209	38	⊆	⊆	NUM
ejpam-6597	209	39	u	u	NOUN
ejpam-6597	209	40	and	and	CCONJ
ejpam-6597	209	41	u	u	NOUN
ejpam-6597	209	42	is	be	AUX
ejpam-6597	209	43	open	open	ADJ
ejpam-6597	209	44	[	[	X
ejpam-6597	209	45	14	14	NUM
ejpam-6597	209	46	]	]	PUNCT
ejpam-6597	209	47	.	.	PUNCT
ejpam-6597	210	1	•	•	NUM
ejpam-6597	210	2	generalized	generalized	ADJ
ejpam-6597	210	3	pre	pre	ADJ
ejpam-6597	210	4	-	-	ADJ
ejpam-6597	210	5	open	open	ADJ
ejpam-6597	210	6	(	(	PUNCT
ejpam-6597	210	7	briefly	briefly	ADV
ejpam-6597	210	8	;	;	PUNCT
ejpam-6597	210	9	g	g	NOUN
ejpam-6597	210	10	-	-	PUNCT
ejpam-6597	210	11	pre	pre	NOUN
ejpam-6597	210	12	-	-	ADJ
ejpam-6597	210	13	open	open	ADJ
ejpam-6597	210	14	)	)	PUNCT
ejpam-6597	211	1	if	if	SCONJ
ejpam-6597	211	2	f	f	PROPN
ejpam-6597	211	3	⊆	⊆	NUM
ejpam-6597	211	4	p	p	NOUN
ejpam-6597	211	5	int(a	int(a	PROPN
ejpam-6597	211	6	)	)	PUNCT
ejpam-6597	211	7	whenever	whenever	SCONJ
ejpam-6597	211	8	f	f	PROPN
ejpam-6597	211	9	⊆	⊆	PROPN
ejpam-6597	211	10	a	a	PRON
ejpam-6597	211	11	and	and	CCONJ
ejpam-6597	211	12	f	f	PROPN
ejpam-6597	211	13	is	be	AUX
ejpam-6597	211	14	closed[15	closed[15	NOUN
ejpam-6597	211	15	]	]	X
ejpam-6597	211	16	.	.	PUNCT
ejpam-6597	212	1	s.	s.	PROPN
ejpam-6597	212	2	a.	a.	PROPN
ejpam-6597	212	3	thabit	thabit	PROPN
ejpam-6597	212	4	,	,	PUNCT
ejpam-6597	212	5	a.	a.	PROPN
ejpam-6597	212	6	al	al	PROPN
ejpam-6597	212	7	-	-	PUNCT
ejpam-6597	212	8	awadi	awadi	PROPN
ejpam-6597	212	9	,	,	PUNCT
ejpam-6597	212	10	r.	r.	PROPN
ejpam-6597	212	11	noaman	noaman	PROPN
ejpam-6597	212	12	/	/	SYM
ejpam-6597	212	13	eur	eur	PROPN
ejpam-6597	212	14	.	.	PUNCT
ejpam-6597	213	1	j.	j.	PROPN
ejpam-6597	213	2	pure	pure	PROPN
ejpam-6597	213	3	appl	appl	PROPN
ejpam-6597	213	4	.	.	PROPN
ejpam-6597	213	5	math	math	PROPN
ejpam-6597	213	6	,	,	PUNCT
ejpam-6597	213	7	18	18	NUM
ejpam-6597	213	8	(	(	PUNCT
ejpam-6597	213	9	4	4	NUM
ejpam-6597	213	10	)	)	PUNCT
ejpam-6597	213	11	(	(	PUNCT
ejpam-6597	213	12	2025	2025	NUM
ejpam-6597	213	13	)	)	PUNCT
ejpam-6597	213	14	,	,	PUNCT
ejpam-6597	213	15	6597	6597	NUM
ejpam-6597	213	16	8	8	NUM
ejpam-6597	213	17	of	of	ADP
ejpam-6597	213	18	15	15	NUM
ejpam-6597	213	19	•	•	NOUN
ejpam-6597	213	20	strongly	strongly	ADV
ejpam-6597	213	21	generalized	generalize	VERB
ejpam-6597	213	22	pre	pre	ADJ
ejpam-6597	213	23	-	-	ADJ
ejpam-6597	213	24	open	open	ADJ
ejpam-6597	213	25	(	(	PUNCT
ejpam-6597	213	26	briefly	briefly	ADV
ejpam-6597	213	27	;	;	PUNCT
ejpam-6597	213	28	g∗-pre	g∗-pre	NOUN
ejpam-6597	213	29	-	-	PUNCT
ejpam-6597	213	30	open	open	ADJ
ejpam-6597	213	31	)	)	PUNCT
ejpam-6597	213	32	if	if	SCONJ
ejpam-6597	213	33	f	f	PROPN
ejpam-6597	213	34	⊆	⊆	NUM
ejpam-6597	213	35	p	p	NOUN
ejpam-6597	213	36	int(a	int(a	PROPN
ejpam-6597	213	37	)	)	PUNCT
ejpam-6597	213	38	whenever	whenever	SCONJ
ejpam-6597	213	39	f	f	PROPN
ejpam-6597	213	40	⊆	⊆	PROPN
ejpam-6597	213	41	a	a	PRON
ejpam-6597	213	42	and	and	CCONJ
ejpam-6597	213	43	f	f	PROPN
ejpam-6597	213	44	is	be	AUX
ejpam-6597	213	45	g	g	NOUN
ejpam-6597	213	46	-	-	PUNCT
ejpam-6597	213	47	closed	closed	ADJ
ejpam-6597	214	1	[	[	X
ejpam-6597	214	2	16	16	NUM
ejpam-6597	214	3	]	]	PUNCT
ejpam-6597	214	4	.	.	PUNCT
ejpam-6597	215	1	•	•	NUM
ejpam-6597	215	2	π	π	X
ejpam-6597	215	3	-	-	ADJ
ejpam-6597	215	4	generalized	generalized	ADJ
ejpam-6597	215	5	pre	pre	ADJ
ejpam-6597	215	6	-	-	ADJ
ejpam-6597	215	7	open	open	ADJ
ejpam-6597	215	8	,	,	PUNCT
ejpam-6597	215	9	(	(	PUNCT
ejpam-6597	215	10	briefly	briefly	ADV
ejpam-6597	215	11	;	;	PUNCT
ejpam-6597	215	12	πg	πg	DET
ejpam-6597	215	13	-	-	PUNCT
ejpam-6597	215	14	pre	pre	ADJ
ejpam-6597	215	15	-	-	ADJ
ejpam-6597	215	16	open	open	ADJ
ejpam-6597	215	17	)	)	PUNCT
ejpam-6597	215	18	if	if	SCONJ
ejpam-6597	215	19	f	f	PROPN
ejpam-6597	215	20	⊆	⊆	NUM
ejpam-6597	215	21	p	p	NOUN
ejpam-6597	215	22	int(a	int(a	PROPN
ejpam-6597	215	23	)	)	PUNCT
ejpam-6597	215	24	whenever	whenever	SCONJ
ejpam-6597	215	25	f	f	PROPN
ejpam-6597	215	26	⊆	⊆	PROPN
ejpam-6597	215	27	a	a	PRON
ejpam-6597	215	28	and	and	CCONJ
ejpam-6597	215	29	f	f	PROPN
ejpam-6597	215	30	is	be	AUX
ejpam-6597	215	31	π	π	PROPN
ejpam-6597	215	32	-	-	VERB
ejpam-6597	215	33	closed.[17	closed.[17	ADJ
ejpam-6597	215	34	]	]	PUNCT
ejpam-6597	215	35	observe	observe	VERB
ejpam-6597	215	36	that	that	SCONJ
ejpam-6597	215	37	:	:	PUNCT
ejpam-6597	215	38	every	every	DET
ejpam-6597	215	39	open	open	ADJ
ejpam-6597	215	40	set	set	NOUN
ejpam-6597	215	41	is	be	AUX
ejpam-6597	215	42	pre	pre	ADJ
ejpam-6597	215	43	-	-	ADJ
ejpam-6597	215	44	open	open	ADJ
ejpam-6597	215	45	and	and	CCONJ
ejpam-6597	215	46	every	every	DET
ejpam-6597	215	47	closed	close	VERB
ejpam-6597	215	48	set	set	NOUN
ejpam-6597	215	49	is	be	AUX
ejpam-6597	215	50	pre	pre	ADJ
ejpam-6597	215	51	-	-	ADJ
ejpam-6597	215	52	closed	closed	ADJ
ejpam-6597	215	53	.	.	PUNCT
ejpam-6597	216	1	from	from	ADP
ejpam-6597	216	2	the	the	DET
ejpam-6597	216	3	definition	definition	NOUN
ejpam-6597	216	4	2	2	NUM
ejpam-6597	216	5	,	,	PUNCT
ejpam-6597	216	6	we	we	PRON
ejpam-6597	216	7	have	have	AUX
ejpam-6597	216	8	:	:	PUNCT
ejpam-6597	216	9	pre	pre	ADJ
ejpam-6597	216	10	-	-	ADJ
ejpam-6597	216	11	open	open	ADJ
ejpam-6597	216	12	=	=	NOUN
ejpam-6597	216	13	⇒	⇒	NOUN
ejpam-6597	216	14	g∗-pre	g∗-pre	NOUN
ejpam-6597	216	15	-	-	PUNCT
ejpam-6597	216	16	open	open	ADJ
ejpam-6597	216	17	=	=	NOUN
ejpam-6597	216	18	⇒	⇒	NOUN
ejpam-6597	216	19	g	g	NOUN
ejpam-6597	216	20	-	-	PUNCT
ejpam-6597	216	21	pre	pre	ADJ
ejpam-6597	216	22	-	-	ADJ
ejpam-6597	216	23	open	open	ADJ
ejpam-6597	216	24	=	=	NOUN
ejpam-6597	216	25	⇒	⇒	NOUN
ejpam-6597	216	26	πg	πg	PRON
ejpam-6597	216	27	-	-	PUNCT
ejpam-6597	216	28	pre	pre	ADJ
ejpam-6597	216	29	-	-	ADJ
ejpam-6597	216	30	open	open	ADJ
ejpam-6597	216	31	g∗-closed	g∗-close	VERB
ejpam-6597	216	32	(	(	PUNCT
ejpam-6597	216	33	g	g	NOUN
ejpam-6597	216	34	-	-	PUNCT
ejpam-6597	216	35	closed	closed	ADJ
ejpam-6597	216	36	,	,	PUNCT
ejpam-6597	216	37	πg	πg	PRON
ejpam-6597	216	38	-	-	PUNCT
ejpam-6597	216	39	closed	closed	ADJ
ejpam-6597	216	40	)	)	PUNCT
ejpam-6597	217	1	=	=	VERB
ejpam-6597	217	2	⇒	⇒	NOUN
ejpam-6597	217	3	g∗-pre	g∗-pre	NOUN
ejpam-6597	217	4	-	-	PUNCT
ejpam-6597	217	5	closed	closed	ADJ
ejpam-6597	217	6	(	(	PUNCT
ejpam-6597	217	7	g	g	NOUN
ejpam-6597	217	8	-	-	PUNCT
ejpam-6597	217	9	pre	pre	NOUN
ejpam-6597	217	10	-	-	ADJ
ejpam-6597	217	11	closed	closed	ADJ
ejpam-6597	217	12	,	,	PUNCT
ejpam-6597	217	13	πg	πg	PRON
ejpam-6597	217	14	-	-	PUNCT
ejpam-6597	217	15	pre	pre	ADJ
ejpam-6597	217	16	-	-	ADJ
ejpam-6597	217	17	closed	closed	ADJ
ejpam-6597	217	18	)	)	PUNCT
ejpam-6597	217	19	now	now	ADV
ejpam-6597	217	20	,	,	PUNCT
ejpam-6597	217	21	we	we	PRON
ejpam-6597	217	22	give	give	VERB
ejpam-6597	217	23	the	the	DET
ejpam-6597	217	24	following	following	NOUN
ejpam-6597	217	25	theorem	theorem	VERB
ejpam-6597	217	26	,	,	PUNCT
ejpam-6597	217	27	which	which	PRON
ejpam-6597	217	28	is	be	AUX
ejpam-6597	217	29	useful	useful	ADJ
ejpam-6597	217	30	for	for	ADP
ejpam-6597	217	31	giving	give	VERB
ejpam-6597	217	32	some	some	DET
ejpam-6597	217	33	characterizations	characterization	NOUN
ejpam-6597	217	34	of	of	ADP
ejpam-6597	217	35	collectionwise	collectionwise	PROPN
ejpam-6597	217	36	pre	pre	ADJ
ejpam-6597	217	37	-	-	ADJ
ejpam-6597	217	38	normal	normal	ADJ
ejpam-6597	217	39	spaces	space	NOUN
ejpam-6597	217	40	.	.	PUNCT
ejpam-6597	218	1	theorem	theorem	NOUN
ejpam-6597	218	2	14	14	NUM
ejpam-6597	218	3	.	.	PUNCT
ejpam-6597	219	1	let	let	VERB
ejpam-6597	219	2	x	x	PRON
ejpam-6597	219	3	be	be	AUX
ejpam-6597	219	4	a	a	DET
ejpam-6597	219	5	space	space	NOUN
ejpam-6597	219	6	.	.	PUNCT
ejpam-6597	220	1	the	the	DET
ejpam-6597	220	2	following	follow	VERB
ejpam-6597	220	3	statements	statement	NOUN
ejpam-6597	220	4	are	be	AUX
ejpam-6597	220	5	equivalent	equivalent	ADJ
ejpam-6597	220	6	:	:	PUNCT
ejpam-6597	220	7	(	(	PUNCT
ejpam-6597	220	8	1	1	X
ejpam-6597	220	9	)	)	PUNCT
ejpam-6597	220	10	x	x	PUNCT
ejpam-6597	220	11	is	be	AUX
ejpam-6597	220	12	collectionwise	collectionwise	ADV
ejpam-6597	220	13	pre	pre	ADJ
ejpam-6597	220	14	-	-	ADJ
ejpam-6597	220	15	normal	normal	ADJ
ejpam-6597	220	16	.	.	PUNCT
ejpam-6597	221	1	(	(	PUNCT
ejpam-6597	221	2	2	2	X
ejpam-6597	221	3	)	)	PUNCT
ejpam-6597	221	4	for	for	ADP
ejpam-6597	221	5	any	any	DET
ejpam-6597	221	6	discrete	discrete	ADJ
ejpam-6597	221	7	family	family	NOUN
ejpam-6597	221	8	{	{	PUNCT
ejpam-6597	221	9	fs}s∈s	fs}s∈s	X
ejpam-6597	221	10	of	of	ADP
ejpam-6597	221	11	closed	closed	ADJ
ejpam-6597	221	12	sets	set	NOUN
ejpam-6597	221	13	in	in	ADP
ejpam-6597	221	14	x	x	NOUN
ejpam-6597	221	15	,	,	PUNCT
ejpam-6597	221	16	there	there	PRON
ejpam-6597	221	17	exists	exist	VERB
ejpam-6597	221	18	a	a	DET
ejpam-6597	221	19	discrete	discrete	ADJ
ejpam-6597	221	20	family	family	NOUN
ejpam-6597	221	21	{	{	PUNCT
ejpam-6597	221	22	us}s∈s	us}s∈s	PROPN
ejpam-6597	221	23	of	of	ADP
ejpam-6597	221	24	g⋆-pre	g⋆-pre	NOUN
ejpam-6597	221	25	-	-	PUNCT
ejpam-6597	221	26	open	open	ADJ
ejpam-6597	221	27	sets	set	NOUN
ejpam-6597	221	28	in	in	ADP
ejpam-6597	221	29	x	x	SYM
ejpam-6597	221	30	such	such	ADJ
ejpam-6597	221	31	that	that	PRON
ejpam-6597	221	32	fs	fs	ADP
ejpam-6597	221	33	⊆	⊆	NUM
ejpam-6597	221	34	p	p	NOUN
ejpam-6597	221	35	int(us	int(us	NOUN
ejpam-6597	221	36	)	)	PUNCT
ejpam-6597	221	37	for	for	ADP
ejpam-6597	221	38	each	each	DET
ejpam-6597	221	39	s	s	PROPN
ejpam-6597	221	40	∈	∈	PROPN
ejpam-6597	221	41	s.	s.	PROPN
ejpam-6597	221	42	(	(	PUNCT
ejpam-6597	221	43	3	3	X
ejpam-6597	221	44	)	)	PUNCT
ejpam-6597	221	45	for	for	ADP
ejpam-6597	221	46	any	any	DET
ejpam-6597	221	47	discrete	discrete	ADJ
ejpam-6597	221	48	family	family	NOUN
ejpam-6597	221	49	{	{	PUNCT
ejpam-6597	221	50	fs}s∈s	fs}s∈s	X
ejpam-6597	221	51	of	of	ADP
ejpam-6597	221	52	closed	closed	ADJ
ejpam-6597	221	53	sets	set	NOUN
ejpam-6597	221	54	in	in	ADP
ejpam-6597	221	55	x	x	NOUN
ejpam-6597	221	56	,	,	PUNCT
ejpam-6597	221	57	there	there	PRON
ejpam-6597	221	58	exists	exist	VERB
ejpam-6597	221	59	a	a	DET
ejpam-6597	221	60	discrete	discrete	ADJ
ejpam-6597	221	61	family	family	NOUN
ejpam-6597	221	62	{	{	PUNCT
ejpam-6597	221	63	us}s∈s	us}s∈s	PROPN
ejpam-6597	221	64	of	of	ADP
ejpam-6597	221	65	g	g	NOUN
ejpam-6597	221	66	-	-	PUNCT
ejpam-6597	221	67	pre	pre	ADJ
ejpam-6597	221	68	-	-	ADJ
ejpam-6597	221	69	open	open	ADJ
ejpam-6597	221	70	sets	set	NOUN
ejpam-6597	221	71	in	in	ADP
ejpam-6597	221	72	x	x	SYM
ejpam-6597	221	73	such	such	ADJ
ejpam-6597	221	74	that	that	PRON
ejpam-6597	221	75	fs	fs	ADP
ejpam-6597	221	76	⊆	⊆	NUM
ejpam-6597	221	77	p	p	NOUN
ejpam-6597	221	78	int(us	int(us	NOUN
ejpam-6597	221	79	)	)	PUNCT
ejpam-6597	221	80	for	for	ADP
ejpam-6597	221	81	each	each	DET
ejpam-6597	221	82	s	s	PROPN
ejpam-6597	221	83	∈	∈	PROPN
ejpam-6597	221	84	s.	s.	PROPN
ejpam-6597	221	85	(	(	PUNCT
ejpam-6597	221	86	4	4	NUM
ejpam-6597	221	87	)	)	PUNCT
ejpam-6597	221	88	for	for	ADP
ejpam-6597	221	89	any	any	DET
ejpam-6597	221	90	discrete	discrete	ADJ
ejpam-6597	221	91	family	family	NOUN
ejpam-6597	221	92	{	{	PUNCT
ejpam-6597	221	93	fs}s∈s	fs}s∈s	X
ejpam-6597	221	94	of	of	ADP
ejpam-6597	221	95	closed	closed	ADJ
ejpam-6597	221	96	sets	set	NOUN
ejpam-6597	221	97	in	in	ADP
ejpam-6597	221	98	x	x	NOUN
ejpam-6597	221	99	,	,	PUNCT
ejpam-6597	221	100	there	there	PRON
ejpam-6597	221	101	exists	exist	VERB
ejpam-6597	221	102	a	a	DET
ejpam-6597	221	103	discrete	discrete	ADJ
ejpam-6597	221	104	family	family	NOUN
ejpam-6597	221	105	{	{	PUNCT
ejpam-6597	221	106	us}s∈s	us}s∈s	PROPN
ejpam-6597	221	107	of	of	ADP
ejpam-6597	221	108	πg	πg	PRON
ejpam-6597	221	109	-	-	PUNCT
ejpam-6597	221	110	pre	pre	ADJ
ejpam-6597	221	111	-	-	ADJ
ejpam-6597	221	112	open	open	ADJ
ejpam-6597	221	113	sets	set	NOUN
ejpam-6597	221	114	in	in	ADP
ejpam-6597	221	115	x	x	SYM
ejpam-6597	221	116	such	such	ADJ
ejpam-6597	221	117	that	that	PRON
ejpam-6597	221	118	fs	fs	ADP
ejpam-6597	221	119	⊆	⊆	NUM
ejpam-6597	221	120	p	p	NOUN
ejpam-6597	221	121	int(us	int(us	NOUN
ejpam-6597	221	122	)	)	PUNCT
ejpam-6597	221	123	for	for	ADP
ejpam-6597	221	124	each	each	DET
ejpam-6597	221	125	s	s	PROPN
ejpam-6597	221	126	∈	∈	PROPN
ejpam-6597	221	127	s.	s.	PROPN
ejpam-6597	221	128	proof	proof	PROPN
ejpam-6597	221	129	.	.	PUNCT
ejpam-6597	222	1	(	(	PUNCT
ejpam-6597	222	2	1	1	X
ejpam-6597	222	3	)	)	PUNCT
ejpam-6597	222	4	=	=	NOUN
ejpam-6597	222	5	⇒	⇒	NOUN
ejpam-6597	222	6	(	(	PUNCT
ejpam-6597	222	7	2	2	NUM
ejpam-6597	222	8	):	):	PUNCT
ejpam-6597	222	9	let	let	VERB
ejpam-6597	222	10	x	x	PRON
ejpam-6597	222	11	be	be	AUX
ejpam-6597	222	12	collectionwise	collectionwise	ADV
ejpam-6597	222	13	pre	pre	ADJ
ejpam-6597	222	14	-	-	ADJ
ejpam-6597	222	15	normal	normal	ADJ
ejpam-6597	222	16	.	.	PUNCT
ejpam-6597	223	1	let	let	VERB
ejpam-6597	223	2	{	{	PUNCT
ejpam-6597	223	3	fs}s∈s	fs}s∈s	PART
ejpam-6597	223	4	be	be	AUX
ejpam-6597	223	5	a	a	DET
ejpam-6597	223	6	discrete	discrete	ADJ
ejpam-6597	223	7	family	family	NOUN
ejpam-6597	223	8	of	of	ADP
ejpam-6597	223	9	closed	closed	ADJ
ejpam-6597	223	10	subsets	subset	NOUN
ejpam-6597	223	11	of	of	ADP
ejpam-6597	223	12	x.	x.	NOUN
ejpam-6597	223	13	by	by	ADP
ejpam-6597	223	14	collectionwise	collectionwise	PROPN
ejpam-6597	223	15	pre	pre	PROPN
ejpam-6597	223	16	-	-	NOUN
ejpam-6597	223	17	normality	normality	NOUN
ejpam-6597	223	18	of	of	ADP
ejpam-6597	223	19	x	x	NOUN
ejpam-6597	223	20	,	,	PUNCT
ejpam-6597	223	21	there	there	PRON
ejpam-6597	223	22	exists	exist	VERB
ejpam-6597	223	23	a	a	DET
ejpam-6597	223	24	discrete	discrete	ADJ
ejpam-6597	223	25	family	family	NOUN
ejpam-6597	223	26	{	{	PUNCT
ejpam-6597	223	27	us}s∈s	us}s∈s	PROPN
ejpam-6597	223	28	of	of	ADP
ejpam-6597	223	29	pre	pre	ADJ
ejpam-6597	223	30	-	-	ADJ
ejpam-6597	223	31	open	open	ADJ
ejpam-6597	223	32	sets	set	NOUN
ejpam-6597	223	33	in	in	ADP
ejpam-6597	223	34	x	x	SYM
ejpam-6597	223	35	such	such	ADJ
ejpam-6597	223	36	that	that	PRON
ejpam-6597	223	37	fs	fs	ADP
ejpam-6597	223	38	⊆	⊆	NUM
ejpam-6597	223	39	us	we	PRON
ejpam-6597	223	40	for	for	ADP
ejpam-6597	223	41	each	each	DET
ejpam-6597	223	42	s	s	PROPN
ejpam-6597	223	43	∈	∈	PROPN
ejpam-6597	223	44	s.	s.	PROPN
ejpam-6597	223	45	since	since	SCONJ
ejpam-6597	223	46	every	every	DET
ejpam-6597	223	47	pre	pre	ADJ
ejpam-6597	223	48	-	-	ADJ
ejpam-6597	223	49	open	open	ADJ
ejpam-6597	223	50	set	set	NOUN
ejpam-6597	223	51	is	be	AUX
ejpam-6597	223	52	g⋆-pre	g⋆-pre	NOUN
ejpam-6597	223	53	-	-	PUNCT
ejpam-6597	223	54	open	open	ADJ
ejpam-6597	223	55	,	,	PUNCT
ejpam-6597	223	56	we	we	PRON
ejpam-6597	223	57	have	have	VERB
ejpam-6597	223	58	{	{	PUNCT
ejpam-6597	223	59	us}s∈s	us}s∈s	NOUN
ejpam-6597	223	60	is	be	AUX
ejpam-6597	223	61	a	a	DET
ejpam-6597	223	62	discrete	discrete	ADJ
ejpam-6597	223	63	family	family	NOUN
ejpam-6597	223	64	of	of	ADP
ejpam-6597	223	65	g⋆-pre	g⋆-pre	NOUN
ejpam-6597	223	66	-	-	PUNCT
ejpam-6597	223	67	open	open	ADJ
ejpam-6597	223	68	sets	set	NOUN
ejpam-6597	223	69	in	in	ADP
ejpam-6597	223	70	x	x	SYM
ejpam-6597	223	71	such	such	ADJ
ejpam-6597	223	72	that	that	PRON
ejpam-6597	223	73	fs	fs	ADP
ejpam-6597	223	74	⊆	⊆	NUM
ejpam-6597	223	75	us	we	PRON
ejpam-6597	223	76	for	for	ADP
ejpam-6597	223	77	each	each	DET
ejpam-6597	223	78	s	s	PROPN
ejpam-6597	223	79	∈	∈	PROPN
ejpam-6597	223	80	s.	s.	PROPN
ejpam-6597	223	81	since	since	SCONJ
ejpam-6597	223	82	us	we	PRON
ejpam-6597	223	83	is	be	AUX
ejpam-6597	223	84	g	g	NOUN
ejpam-6597	223	85	-	-	PUNCT
ejpam-6597	223	86	pre	pre	NOUN
ejpam-6597	223	87	-	-	ADJ
ejpam-6597	223	88	open	open	ADJ
ejpam-6597	223	89	as	as	SCONJ
ejpam-6597	223	90	every	every	DET
ejpam-6597	223	91	pre	pre	ADJ
ejpam-6597	223	92	-	-	ADJ
ejpam-6597	223	93	open	open	ADJ
ejpam-6597	223	94	set	set	NOUN
ejpam-6597	223	95	is	be	AUX
ejpam-6597	223	96	g	g	NOUN
ejpam-6597	223	97	-	-	PUNCT
ejpam-6597	223	98	pre	pre	NOUN
ejpam-6597	223	99	-	-	ADJ
ejpam-6597	223	100	open	open	ADJ
ejpam-6597	223	101	,	,	PUNCT
ejpam-6597	223	102	and	and	CCONJ
ejpam-6597	223	103	fs	fs	ADP
ejpam-6597	223	104	⊆	⊆	NUM
ejpam-6597	223	105	us	we	PRON
ejpam-6597	223	106	we	we	PRON
ejpam-6597	223	107	have	have	VERB
ejpam-6597	223	108	fs	fs	ADP
ejpam-6597	223	109	⊆	⊆	NUM
ejpam-6597	223	110	p	p	NOUN
ejpam-6597	223	111	int(us	int(us	NOUN
ejpam-6597	223	112	)	)	PUNCT
ejpam-6597	223	113	for	for	ADP
ejpam-6597	223	114	each	each	DET
ejpam-6597	223	115	s	s	PROPN
ejpam-6597	223	116	∈	∈	PROPN
ejpam-6597	223	117	s.	s.	PROPN
ejpam-6597	223	118	(	(	PUNCT
ejpam-6597	223	119	2	2	X
ejpam-6597	223	120	)	)	PUNCT
ejpam-6597	224	1	=	=	NOUN
ejpam-6597	224	2	⇒	⇒	NOUN
ejpam-6597	224	3	(	(	PUNCT
ejpam-6597	224	4	3	3	X
ejpam-6597	224	5	)	)	PUNCT
ejpam-6597	225	1	=	=	NOUN
ejpam-6597	225	2	⇒	⇒	NOUN
ejpam-6597	225	3	(	(	PUNCT
ejpam-6597	225	4	4	4	X
ejpam-6597	225	5	)	)	PUNCT
ejpam-6597	225	6	are	be	AUX
ejpam-6597	225	7	obvious	obvious	ADJ
ejpam-6597	225	8	.	.	PUNCT
ejpam-6597	226	1	(	(	PUNCT
ejpam-6597	226	2	4	4	X
ejpam-6597	226	3	)	)	PUNCT
ejpam-6597	226	4	=	=	NOUN
ejpam-6597	226	5	⇒	⇒	NOUN
ejpam-6597	226	6	(	(	PUNCT
ejpam-6597	226	7	1	1	NUM
ejpam-6597	226	8	):	):	PUNCT
ejpam-6597	226	9	suppose	suppose	VERB
ejpam-6597	226	10	(	(	PUNCT
ejpam-6597	226	11	4	4	NUM
ejpam-6597	226	12	)	)	PUNCT
ejpam-6597	226	13	holds	hold	VERB
ejpam-6597	226	14	.	.	PUNCT
ejpam-6597	227	1	we	we	PRON
ejpam-6597	227	2	show	show	VERB
ejpam-6597	227	3	that	that	SCONJ
ejpam-6597	227	4	x	x	PRON
ejpam-6597	227	5	is	be	AUX
ejpam-6597	227	6	collectionwise	collectionwise	ADV
ejpam-6597	227	7	pre	pre	ADJ
ejpam-6597	227	8	-	-	ADJ
ejpam-6597	227	9	normal	normal	ADJ
ejpam-6597	227	10	.	.	PUNCT
ejpam-6597	228	1	let	let	VERB
ejpam-6597	228	2	{	{	PUNCT
ejpam-6597	228	3	fs}s∈s	fs}s∈s	PART
ejpam-6597	228	4	be	be	AUX
ejpam-6597	228	5	a	a	DET
ejpam-6597	228	6	discrete	discrete	ADJ
ejpam-6597	228	7	family	family	NOUN
ejpam-6597	228	8	of	of	ADP
ejpam-6597	228	9	closed	closed	ADJ
ejpam-6597	228	10	subsets	subset	NOUN
ejpam-6597	228	11	of	of	ADP
ejpam-6597	228	12	x.	x.	NOUN
ejpam-6597	228	13	by	by	ADP
ejpam-6597	228	14	(	(	PUNCT
ejpam-6597	228	15	4	4	NUM
ejpam-6597	228	16	)	)	PUNCT
ejpam-6597	228	17	,	,	PUNCT
ejpam-6597	228	18	there	there	PRON
ejpam-6597	228	19	exists	exist	VERB
ejpam-6597	228	20	a	a	DET
ejpam-6597	228	21	discrete	discrete	ADJ
ejpam-6597	228	22	family	family	NOUN
ejpam-6597	228	23	{	{	PUNCT
ejpam-6597	228	24	us}s∈s	us}s∈s	PROPN
ejpam-6597	228	25	of	of	ADP
ejpam-6597	228	26	πg	πg	PRON
ejpam-6597	228	27	-	-	PUNCT
ejpam-6597	228	28	pre	pre	ADJ
ejpam-6597	228	29	-	-	ADJ
ejpam-6597	228	30	open	open	ADJ
ejpam-6597	228	31	sets	set	NOUN
ejpam-6597	228	32	in	in	ADP
ejpam-6597	228	33	x	x	SYM
ejpam-6597	228	34	such	such	ADJ
ejpam-6597	228	35	that	that	PRON
ejpam-6597	228	36	fs	fs	ADP
ejpam-6597	228	37	⊆	⊆	NUM
ejpam-6597	228	38	p	p	NOUN
ejpam-6597	228	39	int(us	int(us	NOUN
ejpam-6597	228	40	)	)	PUNCT
ejpam-6597	228	41	for	for	SCONJ
ejpam-6597	228	42	each	each	DET
ejpam-6597	228	43	s	s	PROPN
ejpam-6597	228	44	∈	∈	PROPN
ejpam-6597	228	45	s.	s.	PROPN
ejpam-6597	228	46	put	put	VERB
ejpam-6597	228	47	vs	vs	ADP
ejpam-6597	228	48	=	=	X
ejpam-6597	228	49	p	p	NOUN
ejpam-6597	228	50	int(us	int(us	NOUN
ejpam-6597	228	51	)	)	PUNCT
ejpam-6597	228	52	for	for	ADP
ejpam-6597	228	53	each	each	DET
ejpam-6597	228	54	s	s	PROPN
ejpam-6597	228	55	∈	∈	PROPN
ejpam-6597	228	56	s.	s.	PROPN
ejpam-6597	228	57	then	then	ADV
ejpam-6597	228	58	,	,	PUNCT
ejpam-6597	228	59	vs	vs	ADP
ejpam-6597	228	60	is	be	AUX
ejpam-6597	228	61	pre	pre	ADJ
ejpam-6597	228	62	-	-	ADJ
ejpam-6597	228	63	open	open	ADJ
ejpam-6597	228	64	subset	subset	NOUN
ejpam-6597	228	65	of	of	ADP
ejpam-6597	228	66	x	x	PUNCT
ejpam-6597	228	67	for	for	ADP
ejpam-6597	228	68	each	each	DET
ejpam-6597	228	69	s	s	PROPN
ejpam-6597	228	70	∈	∈	PROPN
ejpam-6597	228	71	s.	s.	PROPN
ejpam-6597	228	72	since	since	SCONJ
ejpam-6597	228	73	{	{	PUNCT
ejpam-6597	228	74	us}s∈s	us}s∈s	NOUN
ejpam-6597	228	75	is	be	AUX
ejpam-6597	228	76	discrete	discrete	ADJ
ejpam-6597	228	77	family	family	NOUN
ejpam-6597	228	78	and	and	CCONJ
ejpam-6597	228	79	vs	vs	ADP
ejpam-6597	228	80	⊆	⊆	NUM
ejpam-6597	228	81	us	we	PRON
ejpam-6597	228	82	for	for	ADP
ejpam-6597	228	83	each	each	DET
ejpam-6597	228	84	s	s	X
ejpam-6597	228	85	∈	∈	PROPN
ejpam-6597	228	86	s	s	NOUN
ejpam-6597	228	87	,	,	PUNCT
ejpam-6597	228	88	we	we	PRON
ejpam-6597	228	89	obtain	obtain	VERB
ejpam-6597	228	90	{	{	PUNCT
ejpam-6597	228	91	vs}s∈s	vs}s∈s	NOUN
ejpam-6597	228	92	is	be	AUX
ejpam-6597	228	93	a	a	DET
ejpam-6597	228	94	discrete	discrete	ADJ
ejpam-6597	228	95	family	family	NOUN
ejpam-6597	228	96	of	of	ADP
ejpam-6597	228	97	pre	pre	ADJ
ejpam-6597	228	98	-	-	ADJ
ejpam-6597	228	99	open	open	ADJ
ejpam-6597	228	100	subsets	subset	NOUN
ejpam-6597	228	101	of	of	ADP
ejpam-6597	228	102	x	x	SYM
ejpam-6597	228	103	such	such	ADJ
ejpam-6597	228	104	that	that	PRON
ejpam-6597	228	105	fs	fs	ADP
ejpam-6597	228	106	⊆	⊆	NUM
ejpam-6597	228	107	vs	vs	ADP
ejpam-6597	228	108	for	for	ADP
ejpam-6597	228	109	each	each	DET
ejpam-6597	228	110	s	s	PART
ejpam-6597	228	111	∈	∈	PROPN
ejpam-6597	228	112	s.	s.	PROPN
ejpam-6597	228	113	therefore	therefore	ADV
ejpam-6597	228	114	,	,	PUNCT
ejpam-6597	228	115	x	x	PUNCT
ejpam-6597	228	116	is	be	AUX
ejpam-6597	228	117	collectionwise	collectionwise	ADV
ejpam-6597	228	118	pre	pre	ADJ
ejpam-6597	228	119	-	-	ADJ
ejpam-6597	228	120	normal	normal	ADJ
ejpam-6597	228	121	.	.	PUNCT
ejpam-6597	229	1	theorem	theorem	VERB
ejpam-6597	229	2	15	15	NUM
ejpam-6597	229	3	.	.	PUNCT
ejpam-6597	230	1	a	a	DET
ejpam-6597	230	2	space	space	NOUN
ejpam-6597	230	3	x	x	PUNCT
ejpam-6597	230	4	is	be	AUX
ejpam-6597	230	5	collectionwise	collectionwise	ADV
ejpam-6597	230	6	pre	pre	ADJ
ejpam-6597	230	7	-	-	ADJ
ejpam-6597	230	8	normal	normal	ADJ
ejpam-6597	230	9	if	if	SCONJ
ejpam-6597	230	10	one	one	NUM
ejpam-6597	230	11	of	of	ADP
ejpam-6597	230	12	the	the	DET
ejpam-6597	230	13	next	next	ADJ
ejpam-6597	230	14	equivalent	equivalent	ADJ
ejpam-6597	230	15	statements	statement	NOUN
ejpam-6597	230	16	holds	hold	VERB
ejpam-6597	230	17	:	:	PUNCT
ejpam-6597	230	18	(	(	PUNCT
ejpam-6597	230	19	1	1	X
ejpam-6597	230	20	)	)	PUNCT
ejpam-6597	230	21	for	for	ADP
ejpam-6597	230	22	any	any	DET
ejpam-6597	230	23	discrete	discrete	ADJ
ejpam-6597	230	24	family	family	NOUN
ejpam-6597	230	25	{	{	PUNCT
ejpam-6597	230	26	fs}s∈s	fs}s∈s	X
ejpam-6597	230	27	of	of	ADP
ejpam-6597	230	28	g	g	NOUN
ejpam-6597	230	29	-	-	PUNCT
ejpam-6597	230	30	closed	close	VERB
ejpam-6597	230	31	sets	set	NOUN
ejpam-6597	230	32	in	in	ADP
ejpam-6597	230	33	x	x	NOUN
ejpam-6597	230	34	,	,	PUNCT
ejpam-6597	230	35	there	there	PRON
ejpam-6597	230	36	exists	exist	VERB
ejpam-6597	230	37	a	a	DET
ejpam-6597	230	38	discrete	discrete	ADJ
ejpam-6597	230	39	family	family	NOUN
ejpam-6597	230	40	{	{	PUNCT
ejpam-6597	230	41	us}s∈s	us}s∈s	PROPN
ejpam-6597	230	42	of	of	ADP
ejpam-6597	230	43	π	π	PROPN
ejpam-6597	230	44	-	-	ADJ
ejpam-6597	230	45	pre	pre	ADJ
ejpam-6597	230	46	-	-	ADJ
ejpam-6597	230	47	open	open	ADJ
ejpam-6597	230	48	sets	set	NOUN
ejpam-6597	230	49	in	in	ADP
ejpam-6597	230	50	x	x	SYM
ejpam-6597	230	51	such	such	ADJ
ejpam-6597	230	52	that	that	SCONJ
ejpam-6597	230	53	p	p	PROPN
ejpam-6597	230	54	cl(fs	cl(fs	PROPN
ejpam-6597	230	55	)	)	PUNCT
ejpam-6597	230	56	⊆	⊆	NUM
ejpam-6597	230	57	us	we	PRON
ejpam-6597	230	58	for	for	ADP
ejpam-6597	230	59	each	each	DET
ejpam-6597	230	60	s	s	PROPN
ejpam-6597	230	61	∈	∈	PROPN
ejpam-6597	230	62	s.	s.	PROPN
ejpam-6597	230	63	s.	s.	PROPN
ejpam-6597	230	64	a.	a.	PROPN
ejpam-6597	230	65	thabit	thabit	PROPN
ejpam-6597	230	66	,	,	PUNCT
ejpam-6597	230	67	a.	a.	PROPN
ejpam-6597	230	68	al	al	PROPN
ejpam-6597	230	69	-	-	PUNCT
ejpam-6597	230	70	awadi	awadi	PROPN
ejpam-6597	230	71	,	,	PUNCT
ejpam-6597	230	72	r.	r.	PROPN
ejpam-6597	230	73	noaman	noaman	PROPN
ejpam-6597	230	74	/	/	SYM
ejpam-6597	230	75	eur	eur	PROPN
ejpam-6597	230	76	.	.	PUNCT
ejpam-6597	231	1	j.	j.	PROPN
ejpam-6597	231	2	pure	pure	PROPN
ejpam-6597	231	3	appl	appl	PROPN
ejpam-6597	231	4	.	.	PROPN
ejpam-6597	231	5	math	math	PROPN
ejpam-6597	231	6	,	,	PUNCT
ejpam-6597	231	7	18	18	NUM
ejpam-6597	231	8	(	(	PUNCT
ejpam-6597	231	9	4	4	NUM
ejpam-6597	231	10	)	)	PUNCT
ejpam-6597	231	11	(	(	PUNCT
ejpam-6597	231	12	2025	2025	NUM
ejpam-6597	231	13	)	)	PUNCT
ejpam-6597	231	14	,	,	PUNCT
ejpam-6597	231	15	6597	6597	NUM
ejpam-6597	231	16	9	9	NUM
ejpam-6597	231	17	of	of	ADP
ejpam-6597	231	18	15	15	NUM
ejpam-6597	231	19	(	(	PUNCT
ejpam-6597	231	20	2	2	NUM
ejpam-6597	231	21	)	)	PUNCT
ejpam-6597	231	22	for	for	ADP
ejpam-6597	231	23	any	any	DET
ejpam-6597	231	24	discrete	discrete	ADJ
ejpam-6597	231	25	family	family	NOUN
ejpam-6597	231	26	{	{	PUNCT
ejpam-6597	231	27	fs}s∈s	fs}s∈s	X
ejpam-6597	231	28	of	of	ADP
ejpam-6597	231	29	g	g	NOUN
ejpam-6597	231	30	-	-	PUNCT
ejpam-6597	231	31	closed	close	VERB
ejpam-6597	231	32	sets	set	NOUN
ejpam-6597	231	33	in	in	ADP
ejpam-6597	231	34	x	x	NOUN
ejpam-6597	231	35	,	,	PUNCT
ejpam-6597	231	36	there	there	PRON
ejpam-6597	231	37	exists	exist	VERB
ejpam-6597	231	38	a	a	DET
ejpam-6597	231	39	discrete	discrete	ADJ
ejpam-6597	231	40	family	family	NOUN
ejpam-6597	231	41	{	{	PUNCT
ejpam-6597	231	42	us}s∈s	us}s∈s	PROPN
ejpam-6597	231	43	of	of	ADP
ejpam-6597	231	44	pre	pre	ADJ
ejpam-6597	231	45	-	-	ADJ
ejpam-6597	231	46	open	open	ADJ
ejpam-6597	231	47	sets	set	NOUN
ejpam-6597	231	48	in	in	ADP
ejpam-6597	231	49	x	x	SYM
ejpam-6597	231	50	such	such	ADJ
ejpam-6597	231	51	that	that	SCONJ
ejpam-6597	231	52	p	p	PROPN
ejpam-6597	231	53	cl(fs	cl(fs	PROPN
ejpam-6597	231	54	)	)	PUNCT
ejpam-6597	231	55	⊆	⊆	NUM
ejpam-6597	231	56	us	we	PRON
ejpam-6597	231	57	for	for	ADP
ejpam-6597	231	58	each	each	DET
ejpam-6597	231	59	s	s	PROPN
ejpam-6597	231	60	∈	∈	PROPN
ejpam-6597	231	61	s.	s.	PROPN
ejpam-6597	231	62	(	(	PUNCT
ejpam-6597	231	63	3	3	X
ejpam-6597	231	64	)	)	PUNCT
ejpam-6597	231	65	for	for	ADP
ejpam-6597	231	66	any	any	DET
ejpam-6597	231	67	discrete	discrete	ADJ
ejpam-6597	231	68	family	family	NOUN
ejpam-6597	231	69	{	{	PUNCT
ejpam-6597	231	70	fs}s∈s	fs}s∈s	X
ejpam-6597	231	71	of	of	ADP
ejpam-6597	231	72	g	g	NOUN
ejpam-6597	231	73	-	-	PUNCT
ejpam-6597	231	74	closed	close	VERB
ejpam-6597	231	75	sets	set	NOUN
ejpam-6597	231	76	in	in	ADP
ejpam-6597	231	77	x	x	NOUN
ejpam-6597	231	78	,	,	PUNCT
ejpam-6597	231	79	there	there	PRON
ejpam-6597	231	80	exists	exist	VERB
ejpam-6597	231	81	a	a	DET
ejpam-6597	231	82	discrete	discrete	ADJ
ejpam-6597	231	83	family	family	NOUN
ejpam-6597	231	84	{	{	PUNCT
ejpam-6597	231	85	us}s∈s	us}s∈s	PROPN
ejpam-6597	231	86	of	of	ADP
ejpam-6597	231	87	g⋆-pre	g⋆-pre	NOUN
ejpam-6597	231	88	-	-	PUNCT
ejpam-6597	231	89	open	open	ADJ
ejpam-6597	231	90	sets	set	NOUN
ejpam-6597	231	91	in	in	ADP
ejpam-6597	231	92	x	x	SYM
ejpam-6597	231	93	such	such	ADJ
ejpam-6597	231	94	that	that	SCONJ
ejpam-6597	231	95	p	p	PROPN
ejpam-6597	231	96	cl(fs	cl(fs	PROPN
ejpam-6597	231	97	)	)	PUNCT
ejpam-6597	231	98	⊆	⊆	NUM
ejpam-6597	231	99	p	p	NOUN
ejpam-6597	231	100	int(us	int(us	NOUN
ejpam-6597	231	101	)	)	PUNCT
ejpam-6597	231	102	for	for	ADP
ejpam-6597	231	103	each	each	DET
ejpam-6597	231	104	s	s	PROPN
ejpam-6597	231	105	∈	∈	PROPN
ejpam-6597	231	106	s.	s.	PROPN
ejpam-6597	231	107	(	(	PUNCT
ejpam-6597	231	108	4	4	NUM
ejpam-6597	231	109	)	)	PUNCT
ejpam-6597	231	110	for	for	ADP
ejpam-6597	231	111	any	any	DET
ejpam-6597	231	112	discrete	discrete	ADJ
ejpam-6597	231	113	family	family	NOUN
ejpam-6597	231	114	{	{	PUNCT
ejpam-6597	231	115	fs}s∈s	fs}s∈s	X
ejpam-6597	231	116	of	of	ADP
ejpam-6597	231	117	g	g	NOUN
ejpam-6597	231	118	-	-	PUNCT
ejpam-6597	231	119	closed	close	VERB
ejpam-6597	231	120	sets	set	NOUN
ejpam-6597	231	121	in	in	ADP
ejpam-6597	231	122	x	x	NOUN
ejpam-6597	231	123	,	,	PUNCT
ejpam-6597	231	124	there	there	PRON
ejpam-6597	231	125	exists	exist	VERB
ejpam-6597	231	126	a	a	DET
ejpam-6597	231	127	discrete	discrete	ADJ
ejpam-6597	231	128	family	family	NOUN
ejpam-6597	231	129	{	{	PUNCT
ejpam-6597	231	130	us}s∈s	us}s∈s	PROPN
ejpam-6597	231	131	of	of	ADP
ejpam-6597	231	132	g	g	NOUN
ejpam-6597	231	133	-	-	PUNCT
ejpam-6597	231	134	pre	pre	ADJ
ejpam-6597	231	135	-	-	ADJ
ejpam-6597	231	136	open	open	ADJ
ejpam-6597	231	137	sets	set	NOUN
ejpam-6597	231	138	in	in	ADP
ejpam-6597	231	139	x	x	SYM
ejpam-6597	231	140	such	such	ADJ
ejpam-6597	231	141	that	that	SCONJ
ejpam-6597	231	142	p	p	PROPN
ejpam-6597	231	143	cl(fs	cl(fs	PROPN
ejpam-6597	231	144	)	)	PUNCT
ejpam-6597	231	145	⊆	⊆	NUM
ejpam-6597	231	146	p	p	NOUN
ejpam-6597	231	147	int(us	int(us	NOUN
ejpam-6597	231	148	)	)	PUNCT
ejpam-6597	231	149	for	for	ADP
ejpam-6597	231	150	each	each	DET
ejpam-6597	231	151	s	s	PROPN
ejpam-6597	231	152	∈	∈	PROPN
ejpam-6597	231	153	s.	s.	PROPN
ejpam-6597	231	154	(	(	PUNCT
ejpam-6597	231	155	5	5	NUM
ejpam-6597	231	156	)	)	PUNCT
ejpam-6597	231	157	for	for	ADP
ejpam-6597	231	158	any	any	DET
ejpam-6597	231	159	discrete	discrete	ADJ
ejpam-6597	231	160	family	family	NOUN
ejpam-6597	231	161	{	{	PUNCT
ejpam-6597	231	162	fs}s∈s	fs}s∈s	X
ejpam-6597	231	163	of	of	ADP
ejpam-6597	231	164	g	g	NOUN
ejpam-6597	231	165	-	-	PUNCT
ejpam-6597	231	166	closed	close	VERB
ejpam-6597	231	167	sets	set	NOUN
ejpam-6597	231	168	in	in	ADP
ejpam-6597	231	169	x	x	NOUN
ejpam-6597	231	170	,	,	PUNCT
ejpam-6597	231	171	there	there	PRON
ejpam-6597	231	172	exists	exist	VERB
ejpam-6597	231	173	a	a	DET
ejpam-6597	231	174	discrete	discrete	ADJ
ejpam-6597	231	175	family	family	NOUN
ejpam-6597	231	176	{	{	PUNCT
ejpam-6597	231	177	us}s∈s	us}s∈s	PROPN
ejpam-6597	231	178	of	of	ADP
ejpam-6597	231	179	πg	πg	PRON
ejpam-6597	231	180	-	-	PUNCT
ejpam-6597	231	181	pre	pre	ADJ
ejpam-6597	231	182	-	-	ADJ
ejpam-6597	231	183	open	open	ADJ
ejpam-6597	231	184	sets	set	NOUN
ejpam-6597	231	185	in	in	ADP
ejpam-6597	231	186	x	x	SYM
ejpam-6597	231	187	such	such	ADJ
ejpam-6597	231	188	that	that	SCONJ
ejpam-6597	231	189	p	p	PROPN
ejpam-6597	231	190	cl(fs	cl(fs	PROPN
ejpam-6597	231	191	)	)	PUNCT
ejpam-6597	231	192	⊆	⊆	NUM
ejpam-6597	231	193	p	p	NOUN
ejpam-6597	231	194	int(us	int(us	NOUN
ejpam-6597	231	195	)	)	PUNCT
ejpam-6597	231	196	for	for	ADP
ejpam-6597	231	197	each	each	DET
ejpam-6597	231	198	s	s	PROPN
ejpam-6597	231	199	∈	∈	PROPN
ejpam-6597	231	200	s.	s.	PROPN
ejpam-6597	231	201	proof	proof	PROPN
ejpam-6597	231	202	.	.	PUNCT
ejpam-6597	232	1	(	(	PUNCT
ejpam-6597	232	2	1	1	X
ejpam-6597	232	3	)	)	PUNCT
ejpam-6597	232	4	=	=	NOUN
ejpam-6597	232	5	⇒	⇒	NOUN
ejpam-6597	232	6	(	(	PUNCT
ejpam-6597	232	7	2	2	NUM
ejpam-6597	232	8	)	)	PUNCT
ejpam-6597	233	1	=	=	NOUN
ejpam-6597	233	2	⇒	⇒	NOUN
ejpam-6597	233	3	(	(	PUNCT
ejpam-6597	233	4	3	3	X
ejpam-6597	233	5	)	)	PUNCT
ejpam-6597	234	1	=	=	NOUN
ejpam-6597	234	2	⇒	⇒	NOUN
ejpam-6597	234	3	(	(	PUNCT
ejpam-6597	234	4	4	4	NUM
ejpam-6597	234	5	)	)	PUNCT
ejpam-6597	234	6	=	=	NOUN
ejpam-6597	234	7	⇒	⇒	NOUN
ejpam-6597	234	8	(	(	PUNCT
ejpam-6597	234	9	5	5	X
ejpam-6597	234	10	)	)	PUNCT
ejpam-6597	234	11	are	be	AUX
ejpam-6597	234	12	obvious	obvious	ADJ
ejpam-6597	234	13	.	.	PUNCT
ejpam-6597	235	1	now	now	ADV
ejpam-6597	235	2	,	,	PUNCT
ejpam-6597	235	3	we	we	PRON
ejpam-6597	235	4	show	show	VERB
ejpam-6597	235	5	that	that	SCONJ
ejpam-6597	235	6	:	:	PUNCT
ejpam-6597	235	7	(	(	PUNCT
ejpam-6597	235	8	5	5	X
ejpam-6597	235	9	)	)	PUNCT
ejpam-6597	235	10	=	=	NOUN
ejpam-6597	235	11	⇒	⇒	NOUN
ejpam-6597	235	12	collectionwise	collectionwise	ADV
ejpam-6597	235	13	pre	pre	VERB
ejpam-6597	235	14	−	−	PROPN
ejpam-6597	235	15	normality	normality	NOUN
ejpam-6597	235	16	:	:	PUNCT
ejpam-6597	235	17	suppose	suppose	VERB
ejpam-6597	235	18	(	(	PUNCT
ejpam-6597	235	19	5	5	NUM
ejpam-6597	235	20	)	)	PUNCT
ejpam-6597	235	21	holds	hold	VERB
ejpam-6597	235	22	.	.	PUNCT
ejpam-6597	236	1	let	let	VERB
ejpam-6597	236	2	{	{	PUNCT
ejpam-6597	236	3	fs}s∈s	fs}s∈s	PART
ejpam-6597	236	4	be	be	AUX
ejpam-6597	236	5	a	a	DET
ejpam-6597	236	6	discrete	discrete	ADJ
ejpam-6597	236	7	family	family	NOUN
ejpam-6597	236	8	of	of	ADP
ejpam-6597	236	9	closed	closed	ADJ
ejpam-6597	236	10	subsets	subset	NOUN
ejpam-6597	236	11	of	of	ADP
ejpam-6597	236	12	x.	x.	NOUN
ejpam-6597	236	13	since	since	SCONJ
ejpam-6597	236	14	every	every	DET
ejpam-6597	236	15	closed	close	VERB
ejpam-6597	236	16	set	set	NOUN
ejpam-6597	236	17	is	be	AUX
ejpam-6597	236	18	g	g	NOUN
ejpam-6597	236	19	-	-	PUNCT
ejpam-6597	236	20	closed	closed	ADJ
ejpam-6597	236	21	,	,	PUNCT
ejpam-6597	237	1	the	the	DET
ejpam-6597	237	2	family	family	NOUN
ejpam-6597	237	3	{	{	PUNCT
ejpam-6597	237	4	fs}s∈s	fs}s∈s	X
ejpam-6597	237	5	is	be	AUX
ejpam-6597	237	6	a	a	DET
ejpam-6597	237	7	discrete	discrete	ADJ
ejpam-6597	237	8	family	family	NOUN
ejpam-6597	237	9	of	of	ADP
ejpam-6597	237	10	g	g	NOUN
ejpam-6597	237	11	-	-	PUNCT
ejpam-6597	237	12	closed	closed	ADJ
ejpam-6597	237	13	subsets	subset	NOUN
ejpam-6597	237	14	of	of	ADP
ejpam-6597	237	15	x.	x.	NOUN
ejpam-6597	237	16	by	by	ADP
ejpam-6597	237	17	(	(	PUNCT
ejpam-6597	237	18	5	5	NUM
ejpam-6597	237	19	)	)	PUNCT
ejpam-6597	237	20	,	,	PUNCT
ejpam-6597	237	21	there	there	PRON
ejpam-6597	237	22	exists	exist	VERB
ejpam-6597	237	23	a	a	DET
ejpam-6597	237	24	discrete	discrete	ADJ
ejpam-6597	237	25	family	family	NOUN
ejpam-6597	237	26	{	{	PUNCT
ejpam-6597	237	27	us}s∈s	us}s∈s	PROPN
ejpam-6597	237	28	of	of	ADP
ejpam-6597	237	29	πg	πg	PRON
ejpam-6597	237	30	-	-	PUNCT
ejpam-6597	237	31	pre	pre	ADJ
ejpam-6597	237	32	-	-	ADJ
ejpam-6597	237	33	open	open	ADJ
ejpam-6597	237	34	sets	set	NOUN
ejpam-6597	237	35	in	in	ADP
ejpam-6597	237	36	x	x	SYM
ejpam-6597	237	37	such	such	ADJ
ejpam-6597	237	38	that	that	SCONJ
ejpam-6597	237	39	p	p	PROPN
ejpam-6597	237	40	cl(fs	cl(fs	PROPN
ejpam-6597	237	41	)	)	PUNCT
ejpam-6597	237	42	⊆	⊆	NUM
ejpam-6597	237	43	p	p	NOUN
ejpam-6597	237	44	int(us	int(us	NOUN
ejpam-6597	237	45	)	)	PUNCT
ejpam-6597	237	46	for	for	ADP
ejpam-6597	237	47	each	each	DET
ejpam-6597	237	48	s	s	PROPN
ejpam-6597	237	49	∈	∈	PROPN
ejpam-6597	237	50	s.	s.	PROPN
ejpam-6597	237	51	since	since	SCONJ
ejpam-6597	237	52	fs	fs	PROPN
ejpam-6597	237	53	is	be	AUX
ejpam-6597	237	54	pre	pre	ADJ
ejpam-6597	237	55	-	-	VERB
ejpam-6597	237	56	closed	closed	ADJ
ejpam-6597	237	57	for	for	ADP
ejpam-6597	237	58	each	each	DET
ejpam-6597	237	59	s	s	X
ejpam-6597	237	60	∈	∈	PROPN
ejpam-6597	237	61	s	s	PART
ejpam-6597	237	62	,	,	PUNCT
ejpam-6597	237	63	we	we	PRON
ejpam-6597	237	64	get	get	VERB
ejpam-6597	237	65	fs	fs	ADP
ejpam-6597	237	66	⊆	⊆	NUM
ejpam-6597	237	67	p	p	NOUN
ejpam-6597	237	68	int(us	int(us	NOUN
ejpam-6597	237	69	)	)	PUNCT
ejpam-6597	237	70	for	for	ADP
ejpam-6597	237	71	each	each	DET
ejpam-6597	237	72	s	s	PROPN
ejpam-6597	237	73	∈	∈	PROPN
ejpam-6597	237	74	s.	s.	PROPN
ejpam-6597	237	75	let	let	VERB
ejpam-6597	237	76	vs	vs	ADP
ejpam-6597	237	77	=	=	PUNCT
ejpam-6597	237	78	p	p	NOUN
ejpam-6597	237	79	int(us	int(us	NOUN
ejpam-6597	237	80	)	)	PUNCT
ejpam-6597	237	81	for	for	ADP
ejpam-6597	237	82	each	each	DET
ejpam-6597	237	83	s	s	PROPN
ejpam-6597	237	84	∈	∈	PROPN
ejpam-6597	237	85	s.	s.	PROPN
ejpam-6597	237	86	then	then	ADV
ejpam-6597	237	87	,	,	PUNCT
ejpam-6597	237	88	vs	vs	ADP
ejpam-6597	237	89	is	be	AUX
ejpam-6597	237	90	pre	pre	ADJ
ejpam-6597	237	91	-	-	ADJ
ejpam-6597	237	92	open	open	ADJ
ejpam-6597	237	93	set	set	NOUN
ejpam-6597	237	94	in	in	ADP
ejpam-6597	237	95	x	x	PUNCT
ejpam-6597	237	96	for	for	ADP
ejpam-6597	237	97	each	each	DET
ejpam-6597	237	98	s	s	PROPN
ejpam-6597	237	99	∈	∈	PROPN
ejpam-6597	237	100	s.	s.	PROPN
ejpam-6597	237	101	since	since	SCONJ
ejpam-6597	237	102	vs	vs	ADP
ejpam-6597	237	103	⊆	⊆	NUM
ejpam-6597	237	104	us	we	PRON
ejpam-6597	237	105	for	for	ADP
ejpam-6597	237	106	each	each	DET
ejpam-6597	237	107	s	s	X
ejpam-6597	237	108	∈	∈	PROPN
ejpam-6597	237	109	s	s	PART
ejpam-6597	237	110	and	and	CCONJ
ejpam-6597	237	111	{	{	PUNCT
ejpam-6597	237	112	us}s∈s	us}s∈s	NOUN
ejpam-6597	237	113	is	be	AUX
ejpam-6597	237	114	discrete	discrete	ADJ
ejpam-6597	237	115	,	,	PUNCT
ejpam-6597	237	116	we	we	PRON
ejpam-6597	237	117	conclude	conclude	VERB
ejpam-6597	237	118	that	that	SCONJ
ejpam-6597	237	119	{	{	PUNCT
ejpam-6597	237	120	vs}s∈s	vs}s∈s	NOUN
ejpam-6597	237	121	is	be	AUX
ejpam-6597	237	122	a	a	DET
ejpam-6597	237	123	discrete	discrete	ADJ
ejpam-6597	237	124	family	family	NOUN
ejpam-6597	237	125	of	of	ADP
ejpam-6597	237	126	pre	pre	ADJ
ejpam-6597	237	127	-	-	ADJ
ejpam-6597	237	128	open	open	ADJ
ejpam-6597	237	129	sets	set	NOUN
ejpam-6597	237	130	in	in	ADP
ejpam-6597	237	131	x	x	SYM
ejpam-6597	237	132	such	such	ADJ
ejpam-6597	237	133	that	that	PRON
ejpam-6597	237	134	fs	fs	ADP
ejpam-6597	237	135	⊆	⊆	NUM
ejpam-6597	237	136	vs	vs	ADP
ejpam-6597	237	137	for	for	ADP
ejpam-6597	237	138	each	each	DET
ejpam-6597	237	139	s	s	PART
ejpam-6597	237	140	∈	∈	PROPN
ejpam-6597	237	141	s.	s.	PROPN
ejpam-6597	237	142	therefore	therefore	ADV
ejpam-6597	237	143	,	,	PUNCT
ejpam-6597	237	144	x	x	PUNCT
ejpam-6597	237	145	is	be	AUX
ejpam-6597	237	146	collectionwise	collectionwise	ADV
ejpam-6597	237	147	pre	pre	ADJ
ejpam-6597	237	148	-	-	ADJ
ejpam-6597	237	149	normal	normal	ADJ
ejpam-6597	237	150	.	.	PUNCT
ejpam-6597	238	1	4	4	X
ejpam-6597	238	2	.	.	X
ejpam-6597	238	3	collectionwise	collectionwise	PROPN
ejpam-6597	238	4	pre	pre	NOUN
ejpam-6597	238	5	-	-	NOUN
ejpam-6597	238	6	normality	normality	ADJ
ejpam-6597	238	7	in	in	ADP
ejpam-6597	238	8	subspaces	subspace	NOUN
ejpam-6597	238	9	now	now	ADV
ejpam-6597	238	10	,	,	PUNCT
ejpam-6597	238	11	we	we	PRON
ejpam-6597	238	12	study	study	VERB
ejpam-6597	238	13	collectionwise	collectionwise	ADV
ejpam-6597	238	14	pre	pre	NOUN
ejpam-6597	238	15	-	-	NOUN
ejpam-6597	238	16	normality	normality	ADJ
ejpam-6597	238	17	in	in	ADP
ejpam-6597	238	18	subspaces	subspace	NOUN
ejpam-6597	238	19	.	.	PUNCT
ejpam-6597	239	1	the	the	DET
ejpam-6597	239	2	next	next	ADJ
ejpam-6597	239	3	example	example	NOUN
ejpam-6597	239	4	shows	show	VERB
ejpam-6597	239	5	that	that	SCONJ
ejpam-6597	239	6	collectionwise	collectionwise	PROPN
ejpam-6597	239	7	pre	pre	NOUN
ejpam-6597	239	8	-	-	ADJ
ejpam-6597	239	9	normality	normality	NOUN
ejpam-6597	239	10	is	be	AUX
ejpam-6597	239	11	not	not	PART
ejpam-6597	239	12	a	a	DET
ejpam-6597	239	13	hereditary	hereditary	ADJ
ejpam-6597	239	14	property	property	NOUN
ejpam-6597	239	15	in	in	ADP
ejpam-6597	239	16	general	general	ADJ
ejpam-6597	239	17	.	.	PUNCT
ejpam-6597	240	1	example	example	NOUN
ejpam-6597	241	1	3	3	X
ejpam-6597	241	2	.	.	X
ejpam-6597	241	3	consider	consider	VERB
ejpam-6597	241	4	the	the	DET
ejpam-6597	241	5	product	product	NOUN
ejpam-6597	241	6	space	space	NOUN
ejpam-6597	241	7	x	x	PUNCT
ejpam-6597	241	8	=	=	SYM
ejpam-6597	241	9	(	(	PUNCT
ejpam-6597	241	10	ω0	ω0	ADV
ejpam-6597	241	11	+	+	NOUN
ejpam-6597	241	12	1)×(ω1	1)×(ω1	NUM
ejpam-6597	241	13	+	+	ADJ
ejpam-6597	241	14	1	1	NUM
ejpam-6597	241	15	)	)	PUNCT
ejpam-6597	241	16	,	,	PUNCT
ejpam-6597	241	17	which	which	PRON
ejpam-6597	241	18	is	be	AUX
ejpam-6597	241	19	pre	pre	ADJ
ejpam-6597	241	20	-	-	ADJ
ejpam-6597	241	21	normal	normal	ADJ
ejpam-6597	241	22	,	,	PUNCT
ejpam-6597	241	23	but	but	CCONJ
ejpam-6597	241	24	the	the	DET
ejpam-6597	241	25	subspace	subspace	NOUN
ejpam-6597	241	26	m	m	VERB
ejpam-6597	241	27	=	=	SYM
ejpam-6597	241	28	x	x	SYM
ejpam-6597	241	29	\	\	X
ejpam-6597	241	30	{	{	PUNCT
ejpam-6597	241	31	⟨ω0	⟨ω0	PROPN
ejpam-6597	241	32	,	,	PUNCT
ejpam-6597	241	33	ω1⟩	ω1⟩	NOUN
ejpam-6597	241	34	}	}	PUNCT
ejpam-6597	241	35	is	be	AUX
ejpam-6597	241	36	not	not	PART
ejpam-6597	241	37	pre	pre	ADJ
ejpam-6597	241	38	-	-	ADJ
ejpam-6597	241	39	normal	normal	ADJ
ejpam-6597	241	40	[	[	X
ejpam-6597	241	41	11	11	NUM
ejpam-6597	241	42	]	]	PUNCT
ejpam-6597	241	43	.	.	PUNCT
ejpam-6597	242	1	since	since	SCONJ
ejpam-6597	242	2	x	x	PROPN
ejpam-6597	242	3	=	=	SYM
ejpam-6597	242	4	(	(	PUNCT
ejpam-6597	242	5	ω0	ω0	ADV
ejpam-6597	242	6	+	+	ADJ
ejpam-6597	242	7	1)×	1)×	NUM
ejpam-6597	242	8	(	(	PUNCT
ejpam-6597	242	9	ω1	ω1	PROPN
ejpam-6597	242	10	+	+	CCONJ
ejpam-6597	242	11	1	1	NUM
ejpam-6597	242	12	)	)	PUNCT
ejpam-6597	242	13	is	be	AUX
ejpam-6597	242	14	normal	normal	ADJ
ejpam-6597	242	15	,	,	PUNCT
ejpam-6597	242	16	it	it	PRON
ejpam-6597	242	17	is	be	AUX
ejpam-6597	242	18	pre	pre	ADJ
ejpam-6597	242	19	-	-	ADJ
ejpam-6597	242	20	normal	normal	ADJ
ejpam-6597	242	21	.	.	PUNCT
ejpam-6597	243	1	the	the	DET
ejpam-6597	243	2	tychonoff	tychonoff	NOUN
ejpam-6597	243	3	plank	plank	NOUN
ejpam-6597	243	4	m	m	NOUN
ejpam-6597	243	5	=	=	PUNCT
ejpam-6597	243	6	x	x	PUNCT
ejpam-6597	243	7	\{⟨ω0	\{⟨ω0	ADV
ejpam-6597	243	8	,	,	PUNCT
ejpam-6597	243	9	ω1⟩	ω1⟩	NOUN
ejpam-6597	243	10	}	}	PUNCT
ejpam-6597	243	11	is	be	AUX
ejpam-6597	243	12	dense	dense	ADJ
ejpam-6597	243	13	subspace	subspace	NOUN
ejpam-6597	243	14	of	of	ADP
ejpam-6597	243	15	x.	x.	NOUN
ejpam-6597	243	16	since	since	SCONJ
ejpam-6597	243	17	both	both	DET
ejpam-6597	243	18	ω0	ω0	PROPN
ejpam-6597	243	19	+	+	PROPN
ejpam-6597	243	20	1	1	NUM
ejpam-6597	243	21	and	and	CCONJ
ejpam-6597	243	22	ω1	ω1	PROPN
ejpam-6597	243	23	+	+	PROPN
ejpam-6597	243	24	1	1	NUM
ejpam-6597	243	25	are	be	AUX
ejpam-6597	243	26	sub	sub	ADJ
ejpam-6597	243	27	-	-	ADJ
ejpam-6597	243	28	maximal	maximal	ADJ
ejpam-6597	243	29	spaces	space	NOUN
ejpam-6597	243	30	and	and	CCONJ
ejpam-6597	243	31	the	the	DET
ejpam-6597	243	32	product	product	NOUN
ejpam-6597	243	33	of	of	ADP
ejpam-6597	243	34	two	two	NUM
ejpam-6597	243	35	sub	sub	ADJ
ejpam-6597	243	36	-	-	ADJ
ejpam-6597	243	37	maximal	maximal	ADJ
ejpam-6597	243	38	spaces	space	NOUN
ejpam-6597	243	39	is	be	AUX
ejpam-6597	243	40	sub	sub	ADJ
ejpam-6597	243	41	-	-	ADJ
ejpam-6597	243	42	maximal	maximal	ADJ
ejpam-6597	243	43	,	,	PUNCT
ejpam-6597	243	44	we	we	PRON
ejpam-6597	243	45	obtain	obtain	VERB
ejpam-6597	243	46	the	the	DET
ejpam-6597	243	47	space	space	NOUN
ejpam-6597	243	48	x	x	PUNCT
ejpam-6597	244	1	=	=	SYM
ejpam-6597	244	2	(	(	PUNCT
ejpam-6597	244	3	ω0	ω0	ADV
ejpam-6597	244	4	+	+	ADJ
ejpam-6597	244	5	1)×	1)×	NUM
ejpam-6597	244	6	(	(	PUNCT
ejpam-6597	244	7	ω1	ω1	PROPN
ejpam-6597	244	8	+	+	CCONJ
ejpam-6597	244	9	1	1	NUM
ejpam-6597	244	10	)	)	PUNCT
ejpam-6597	244	11	is	be	AUX
ejpam-6597	244	12	sub	sub	ADJ
ejpam-6597	244	13	-	-	ADJ
ejpam-6597	244	14	maximal	maximal	ADJ
ejpam-6597	244	15	.	.	PUNCT
ejpam-6597	245	1	by	by	ADP
ejpam-6597	245	2	theorem	theorem	NOUN
ejpam-6597	245	3	9	9	NUM
ejpam-6597	245	4	,	,	PUNCT
ejpam-6597	245	5	m	m	VERB
ejpam-6597	245	6	=	=	NOUN
ejpam-6597	245	7	x	x	SYM
ejpam-6597	245	8	\	\	X
ejpam-6597	245	9	{	{	PUNCT
ejpam-6597	245	10	⟨ω0	⟨ω0	PROPN
ejpam-6597	245	11	,	,	PUNCT
ejpam-6597	245	12	ω1⟩	ω1⟩	NOUN
ejpam-6597	245	13	}	}	PUNCT
ejpam-6597	245	14	is	be	AUX
ejpam-6597	245	15	sub	sub	ADJ
ejpam-6597	245	16	-	-	ADJ
ejpam-6597	245	17	maximal	maximal	ADJ
ejpam-6597	245	18	subspace	subspace	NOUN
ejpam-6597	245	19	of	of	ADP
ejpam-6597	245	20	x.	x.	NOUN
ejpam-6597	245	21	since	since	SCONJ
ejpam-6597	245	22	the	the	DET
ejpam-6597	245	23	subspace	subspace	NOUN
ejpam-6597	245	24	m	m	VERB
ejpam-6597	245	25	is	be	AUX
ejpam-6597	245	26	not	not	PART
ejpam-6597	245	27	normal	normal	ADJ
ejpam-6597	245	28	,	,	PUNCT
ejpam-6597	245	29	we	we	PRON
ejpam-6597	245	30	obtain	obtain	VERB
ejpam-6597	245	31	m	m	VERB
ejpam-6597	245	32	is	be	AUX
ejpam-6597	245	33	not	not	PART
ejpam-6597	245	34	pre	pre	ADJ
ejpam-6597	245	35	-	-	ADJ
ejpam-6597	245	36	normal	normal	ADJ
ejpam-6597	245	37	.	.	PUNCT
ejpam-6597	246	1	since	since	SCONJ
ejpam-6597	246	2	m	m	PROPN
ejpam-6597	246	3	=	=	NOUN
ejpam-6597	246	4	x	x	PUNCT
ejpam-6597	246	5	\{⟨ω0	\{⟨ω0	ADV
ejpam-6597	246	6	,	,	PUNCT
ejpam-6597	246	7	ω1⟩	ω1⟩	NOUN
ejpam-6597	246	8	}	}	PUNCT
ejpam-6597	246	9	is	be	AUX
ejpam-6597	246	10	not	not	PART
ejpam-6597	246	11	collectionwise	collectionwise	ADV
ejpam-6597	246	12	normal	normal	ADJ
ejpam-6597	246	13	,	,	PUNCT
ejpam-6597	246	14	we	we	PRON
ejpam-6597	246	15	get	get	VERB
ejpam-6597	246	16	m	m	VERB
ejpam-6597	246	17	=	=	PUNCT
ejpam-6597	246	18	x	x	SYM
ejpam-6597	246	19	\	\	NOUN
ejpam-6597	246	20	{	{	PUNCT
ejpam-6597	246	21	⟨ω0	⟨ω0	PROPN
ejpam-6597	246	22	,	,	PUNCT
ejpam-6597	246	23	ω1⟩	ω1⟩	NOUN
ejpam-6597	246	24	}	}	PUNCT
ejpam-6597	246	25	is	be	AUX
ejpam-6597	246	26	not	not	PART
ejpam-6597	246	27	collectionwise	collectionwise	ADV
ejpam-6597	246	28	pre	pre	ADJ
ejpam-6597	246	29	-	-	ADJ
ejpam-6597	246	30	normal	normal	ADJ
ejpam-6597	246	31	.	.	PUNCT
ejpam-6597	247	1	lemma	lemma	PROPN
ejpam-6597	247	2	2	2	NUM
ejpam-6597	247	3	.	.	PUNCT
ejpam-6597	248	1	[	[	X
ejpam-6597	248	2	11	11	NUM
ejpam-6597	248	3	]	]	PUNCT
ejpam-6597	248	4	,	,	PUNCT
ejpam-6597	248	5	let	let	VERB
ejpam-6597	248	6	m	m	PRON
ejpam-6597	248	7	be	be	AUX
ejpam-6597	248	8	a	a	DET
ejpam-6597	248	9	closed	closed	ADJ
ejpam-6597	248	10	domain	domain	NOUN
ejpam-6597	248	11	subspace	subspace	NOUN
ejpam-6597	248	12	of	of	ADP
ejpam-6597	248	13	x	x	PROPN
ejpam-6597	248	14	and	and	CCONJ
ejpam-6597	248	15	a	a	DET
ejpam-6597	248	16	⊆	⊆	NUM
ejpam-6597	248	17	m	m	NOUN
ejpam-6597	248	18	.	.	PUNCT
ejpam-6597	249	1	a	a	PRON
ejpam-6597	249	2	is	be	AUX
ejpam-6597	249	3	pre	pre	ADJ
ejpam-6597	249	4	-	-	ADJ
ejpam-6597	249	5	closed	closed	ADJ
ejpam-6597	249	6	(	(	PUNCT
ejpam-6597	249	7	pre	pre	ADJ
ejpam-6597	249	8	-	-	ADJ
ejpam-6597	249	9	open	open	ADJ
ejpam-6597	249	10	)	)	PUNCT
ejpam-6597	249	11	in	in	ADP
ejpam-6597	249	12	m	m	PROPN
ejpam-6597	249	13	,	,	PUNCT
ejpam-6597	249	14	if	if	SCONJ
ejpam-6597	249	15	and	and	CCONJ
ejpam-6597	249	16	only	only	ADV
ejpam-6597	249	17	if	if	SCONJ
ejpam-6597	249	18	a	a	PRON
ejpam-6597	249	19	is	be	AUX
ejpam-6597	249	20	pre	pre	ADJ
ejpam-6597	249	21	-	-	ADJ
ejpam-6597	249	22	closed	closed	ADJ
ejpam-6597	249	23	(	(	PUNCT
ejpam-6597	249	24	pre	pre	ADJ
ejpam-6597	249	25	-	-	ADJ
ejpam-6597	249	26	open	open	ADJ
ejpam-6597	249	27	)	)	PUNCT
ejpam-6597	249	28	in	in	ADP
ejpam-6597	249	29	x.	x.	PROPN
ejpam-6597	249	30	theorem	theorem	VERB
ejpam-6597	249	31	16	16	NUM
ejpam-6597	249	32	.	.	PUNCT
ejpam-6597	250	1	let	let	VERB
ejpam-6597	250	2	m	m	PRON
ejpam-6597	250	3	be	be	AUX
ejpam-6597	250	4	a	a	DET
ejpam-6597	250	5	closed	closed	ADJ
ejpam-6597	250	6	domain	domain	NOUN
ejpam-6597	250	7	subspace	subspace	NOUN
ejpam-6597	250	8	of	of	ADP
ejpam-6597	250	9	x.	x.	NOUN
ejpam-6597	250	10	then	then	ADV
ejpam-6597	250	11	:	:	PUNCT
ejpam-6597	250	12	(	(	PUNCT
ejpam-6597	250	13	1	1	X
ejpam-6597	250	14	)	)	PUNCT
ejpam-6597	250	15	a	a	DET
ejpam-6597	250	16	family	family	NOUN
ejpam-6597	250	17	{	{	PUNCT
ejpam-6597	250	18	fs}s∈s	fs}s∈s	X
ejpam-6597	250	19	is	be	AUX
ejpam-6597	250	20	discrete	discrete	ADJ
ejpam-6597	250	21	family	family	NOUN
ejpam-6597	250	22	of	of	ADP
ejpam-6597	250	23	closed	closed	ADJ
ejpam-6597	250	24	sets	set	NOUN
ejpam-6597	250	25	in	in	ADP
ejpam-6597	250	26	m	m	PROPN
ejpam-6597	250	27	if	if	SCONJ
ejpam-6597	251	1	and	and	CCONJ
ejpam-6597	251	2	only	only	ADV
ejpam-6597	251	3	if	if	SCONJ
ejpam-6597	251	4	{	{	PUNCT
ejpam-6597	251	5	fs}s∈s	fs}s∈s	NOUN
ejpam-6597	251	6	is	be	AUX
ejpam-6597	251	7	discrete	discrete	ADJ
ejpam-6597	251	8	family	family	NOUN
ejpam-6597	251	9	of	of	ADP
ejpam-6597	251	10	closed	closed	ADJ
ejpam-6597	251	11	sets	set	NOUN
ejpam-6597	251	12	in	in	ADP
ejpam-6597	251	13	x	x	NOUN
ejpam-6597	251	14	,	,	PUNCT
ejpam-6597	251	15	where	where	SCONJ
ejpam-6597	251	16	fs	fs	ADP
ejpam-6597	251	17	⊆	⊆	NUM
ejpam-6597	251	18	m	m	NOUN
ejpam-6597	251	19	for	for	ADP
ejpam-6597	251	20	each	each	DET
ejpam-6597	251	21	s	s	PROPN
ejpam-6597	251	22	∈	∈	PROPN
ejpam-6597	251	23	s.	s.	PROPN
ejpam-6597	251	24	s.	s.	PROPN
ejpam-6597	251	25	a.	a.	PROPN
ejpam-6597	251	26	thabit	thabit	PROPN
ejpam-6597	251	27	,	,	PUNCT
ejpam-6597	251	28	a.	a.	PROPN
ejpam-6597	251	29	al	al	PROPN
ejpam-6597	251	30	-	-	PUNCT
ejpam-6597	251	31	awadi	awadi	PROPN
ejpam-6597	251	32	,	,	PUNCT
ejpam-6597	251	33	r.	r.	PROPN
ejpam-6597	251	34	noaman	noaman	PROPN
ejpam-6597	251	35	/	/	SYM
ejpam-6597	251	36	eur	eur	PROPN
ejpam-6597	251	37	.	.	PUNCT
ejpam-6597	252	1	j.	j.	PROPN
ejpam-6597	252	2	pure	pure	PROPN
ejpam-6597	252	3	appl	appl	PROPN
ejpam-6597	252	4	.	.	PROPN
ejpam-6597	252	5	math	math	PROPN
ejpam-6597	252	6	,	,	PUNCT
ejpam-6597	252	7	18	18	NUM
ejpam-6597	252	8	(	(	PUNCT
ejpam-6597	252	9	4	4	NUM
ejpam-6597	252	10	)	)	PUNCT
ejpam-6597	252	11	(	(	PUNCT
ejpam-6597	252	12	2025	2025	NUM
ejpam-6597	252	13	)	)	PUNCT
ejpam-6597	252	14	,	,	PUNCT
ejpam-6597	252	15	6597	6597	NUM
ejpam-6597	252	16	10	10	NUM
ejpam-6597	252	17	of	of	ADP
ejpam-6597	252	18	15	15	NUM
ejpam-6597	252	19	(	(	PUNCT
ejpam-6597	252	20	2	2	NUM
ejpam-6597	252	21	)	)	PUNCT
ejpam-6597	252	22	a	a	DET
ejpam-6597	252	23	family	family	NOUN
ejpam-6597	252	24	{	{	PUNCT
ejpam-6597	252	25	fs}s∈s	fs}s∈s	X
ejpam-6597	252	26	is	be	AUX
ejpam-6597	252	27	discrete	discrete	ADJ
ejpam-6597	252	28	family	family	NOUN
ejpam-6597	252	29	of	of	ADP
ejpam-6597	252	30	pre	pre	ADJ
ejpam-6597	252	31	-	-	ADJ
ejpam-6597	252	32	open	open	ADJ
ejpam-6597	252	33	sets	set	NOUN
ejpam-6597	252	34	in	in	ADP
ejpam-6597	252	35	m	m	PROPN
ejpam-6597	252	36	if	if	SCONJ
ejpam-6597	252	37	and	and	CCONJ
ejpam-6597	252	38	only	only	ADV
ejpam-6597	252	39	if	if	SCONJ
ejpam-6597	252	40	{	{	PUNCT
ejpam-6597	252	41	fs}s∈s	fs}s∈s	NOUN
ejpam-6597	252	42	is	be	AUX
ejpam-6597	252	43	discrete	discrete	ADJ
ejpam-6597	252	44	family	family	NOUN
ejpam-6597	252	45	of	of	ADP
ejpam-6597	252	46	pre	pre	ADJ
ejpam-6597	252	47	-	-	ADJ
ejpam-6597	252	48	open	open	ADJ
ejpam-6597	252	49	sets	set	NOUN
ejpam-6597	252	50	in	in	ADP
ejpam-6597	252	51	x	x	NOUN
ejpam-6597	252	52	,	,	PUNCT
ejpam-6597	252	53	where	where	SCONJ
ejpam-6597	252	54	fs	fs	ADP
ejpam-6597	252	55	⊆	⊆	NUM
ejpam-6597	252	56	m	m	NOUN
ejpam-6597	252	57	for	for	ADP
ejpam-6597	252	58	each	each	DET
ejpam-6597	252	59	s	s	PROPN
ejpam-6597	252	60	∈	∈	PROPN
ejpam-6597	252	61	s.	s.	PROPN
ejpam-6597	252	62	proof	proof	PROPN
ejpam-6597	252	63	.	.	PUNCT
ejpam-6597	253	1	let	let	VERB
ejpam-6597	253	2	m	m	PRON
ejpam-6597	253	3	be	be	AUX
ejpam-6597	253	4	a	a	DET
ejpam-6597	253	5	closed	closed	ADJ
ejpam-6597	253	6	domain	domain	NOUN
ejpam-6597	253	7	subspace	subspace	NOUN
ejpam-6597	253	8	of	of	ADP
ejpam-6597	253	9	x.	x.	NOUN
ejpam-6597	253	10	then	then	ADV
ejpam-6597	253	11	:	:	PUNCT
ejpam-6597	253	12	(	(	PUNCT
ejpam-6597	253	13	1	1	NUM
ejpam-6597	253	14	):	):	PUNCT
ejpam-6597	253	15	let	let	VERB
ejpam-6597	253	16	{	{	PUNCT
ejpam-6597	253	17	fs}s∈s	fs}s∈s	PART
ejpam-6597	253	18	be	be	AUX
ejpam-6597	253	19	a	a	DET
ejpam-6597	253	20	discrete	discrete	ADJ
ejpam-6597	253	21	family	family	NOUN
ejpam-6597	253	22	of	of	ADP
ejpam-6597	253	23	closed	closed	ADJ
ejpam-6597	253	24	sets	set	NOUN
ejpam-6597	253	25	in	in	ADP
ejpam-6597	253	26	m	m	PROPN
ejpam-6597	253	27	.	.	PUNCT
ejpam-6597	254	1	then	then	ADV
ejpam-6597	254	2	,	,	PUNCT
ejpam-6597	254	3	fs	fs	X
ejpam-6597	254	4	is	be	AUX
ejpam-6597	254	5	closed	close	VERB
ejpam-6597	254	6	subset	subset	NOUN
ejpam-6597	254	7	of	of	ADP
ejpam-6597	254	8	m	m	PROPN
ejpam-6597	254	9	for	for	ADP
ejpam-6597	254	10	each	each	DET
ejpam-6597	254	11	s	s	PROPN
ejpam-6597	254	12	∈	∈	PROPN
ejpam-6597	254	13	s.	s.	PROPN
ejpam-6597	254	14	since	since	SCONJ
ejpam-6597	254	15	m	m	PROPN
ejpam-6597	254	16	is	be	AUX
ejpam-6597	254	17	closed	close	VERB
ejpam-6597	254	18	subset	subset	NOUN
ejpam-6597	254	19	of	of	ADP
ejpam-6597	254	20	x	x	PRON
ejpam-6597	254	21	,	,	PUNCT
ejpam-6597	254	22	we	we	PRON
ejpam-6597	254	23	have	have	VERB
ejpam-6597	254	24	fs	fs	INTJ
ejpam-6597	254	25	is	be	AUX
ejpam-6597	254	26	closed	close	VERB
ejpam-6597	254	27	set	set	VERB
ejpam-6597	254	28	in	in	ADP
ejpam-6597	254	29	x	x	PUNCT
ejpam-6597	254	30	for	for	ADP
ejpam-6597	254	31	each	each	DET
ejpam-6597	254	32	s	s	PROPN
ejpam-6597	254	33	∈	∈	PROPN
ejpam-6597	254	34	s.	s.	PROPN
ejpam-6597	254	35	hence	hence	ADV
ejpam-6597	254	36	,	,	PUNCT
ejpam-6597	254	37	{	{	PUNCT
ejpam-6597	254	38	fs}s∈s	fs}s∈s	X
ejpam-6597	254	39	is	be	AUX
ejpam-6597	254	40	discrete	discrete	ADJ
ejpam-6597	254	41	family	family	NOUN
ejpam-6597	254	42	of	of	ADP
ejpam-6597	254	43	closed	closed	ADJ
ejpam-6597	254	44	sets	set	NOUN
ejpam-6597	254	45	in	in	ADP
ejpam-6597	254	46	x	x	NOUN
ejpam-6597	254	47	,	,	PUNCT
ejpam-6597	254	48	where	where	SCONJ
ejpam-6597	254	49	fs	fs	ADP
ejpam-6597	254	50	⊆	⊆	NUM
ejpam-6597	254	51	m	m	NOUN
ejpam-6597	254	52	for	for	ADP
ejpam-6597	254	53	each	each	DET
ejpam-6597	254	54	s	s	PART
ejpam-6597	254	55	∈	∈	PROPN
ejpam-6597	254	56	s.	s.	PROPN
ejpam-6597	254	57	conversely	conversely	ADV
ejpam-6597	254	58	,	,	PUNCT
ejpam-6597	254	59	let	let	VERB
ejpam-6597	254	60	{	{	PUNCT
ejpam-6597	254	61	fs}s∈s	fs}s∈s	PART
ejpam-6597	254	62	be	be	AUX
ejpam-6597	254	63	a	a	DET
ejpam-6597	254	64	discrete	discrete	ADJ
ejpam-6597	254	65	family	family	NOUN
ejpam-6597	254	66	of	of	ADP
ejpam-6597	254	67	closed	closed	ADJ
ejpam-6597	254	68	sets	set	NOUN
ejpam-6597	254	69	in	in	ADP
ejpam-6597	254	70	x	x	NOUN
ejpam-6597	254	71	,	,	PUNCT
ejpam-6597	254	72	where	where	SCONJ
ejpam-6597	254	73	fs	fs	ADP
ejpam-6597	254	74	⊆	⊆	NUM
ejpam-6597	254	75	m	m	NOUN
ejpam-6597	254	76	for	for	ADP
ejpam-6597	254	77	each	each	DET
ejpam-6597	254	78	s	s	PROPN
ejpam-6597	254	79	∈	∈	PROPN
ejpam-6597	254	80	s.	s.	PROPN
ejpam-6597	254	81	then	then	ADV
ejpam-6597	254	82	,	,	PUNCT
ejpam-6597	254	83	fs	fs	X
ejpam-6597	254	84	is	be	AUX
ejpam-6597	254	85	closed	close	VERB
ejpam-6597	254	86	in	in	ADP
ejpam-6597	254	87	x	x	PUNCT
ejpam-6597	254	88	for	for	ADP
ejpam-6597	254	89	each	each	DET
ejpam-6597	254	90	s	s	PROPN
ejpam-6597	254	91	∈	∈	PROPN
ejpam-6597	254	92	s.	s.	PROPN
ejpam-6597	254	93	since	since	SCONJ
ejpam-6597	254	94	m	m	PROPN
ejpam-6597	254	95	is	be	AUX
ejpam-6597	254	96	closed	close	VERB
ejpam-6597	254	97	in	in	ADP
ejpam-6597	254	98	x	x	NOUN
ejpam-6597	254	99	,	,	PUNCT
ejpam-6597	254	100	we	we	PRON
ejpam-6597	254	101	have	have	VERB
ejpam-6597	254	102	fs∩m	fs∩m	NOUN
ejpam-6597	254	103	=	=	PUNCT
ejpam-6597	254	104	fs	fs	PROPN
ejpam-6597	254	105	is	be	AUX
ejpam-6597	254	106	closed	close	VERB
ejpam-6597	254	107	set	set	VERB
ejpam-6597	254	108	in	in	ADP
ejpam-6597	254	109	m	m	PROPN
ejpam-6597	254	110	for	for	ADP
ejpam-6597	254	111	each	each	DET
ejpam-6597	254	112	s	s	PROPN
ejpam-6597	254	113	∈	∈	PROPN
ejpam-6597	254	114	s.	s.	PROPN
ejpam-6597	254	115	then	then	ADV
ejpam-6597	254	116	,	,	PUNCT
ejpam-6597	254	117	{	{	PUNCT
ejpam-6597	254	118	fs}s∈s	fs}s∈s	X
ejpam-6597	254	119	is	be	AUX
ejpam-6597	254	120	a	a	DET
ejpam-6597	254	121	discrete	discrete	ADJ
ejpam-6597	254	122	family	family	NOUN
ejpam-6597	254	123	of	of	ADP
ejpam-6597	254	124	closed	closed	ADJ
ejpam-6597	254	125	sets	set	NOUN
ejpam-6597	254	126	in	in	ADP
ejpam-6597	254	127	m	m	PROPN
ejpam-6597	254	128	.	.	PUNCT
ejpam-6597	255	1	(	(	PUNCT
ejpam-6597	255	2	2	2	NUM
ejpam-6597	255	3	):	):	PUNCT
ejpam-6597	255	4	let	let	VERB
ejpam-6597	255	5	{	{	PUNCT
ejpam-6597	255	6	fs}s∈s	fs}s∈s	PART
ejpam-6597	255	7	be	be	AUX
ejpam-6597	255	8	a	a	DET
ejpam-6597	255	9	discrete	discrete	ADJ
ejpam-6597	255	10	family	family	NOUN
ejpam-6597	255	11	of	of	ADP
ejpam-6597	255	12	pre	pre	ADJ
ejpam-6597	255	13	-	-	ADJ
ejpam-6597	255	14	open	open	ADJ
ejpam-6597	255	15	sets	set	NOUN
ejpam-6597	255	16	in	in	ADP
ejpam-6597	255	17	m	m	PROPN
ejpam-6597	255	18	.	.	PUNCT
ejpam-6597	256	1	then	then	ADV
ejpam-6597	256	2	,	,	PUNCT
ejpam-6597	256	3	fs	fs	X
ejpam-6597	256	4	is	be	AUX
ejpam-6597	256	5	pre	pre	ADJ
ejpam-6597	256	6	-	-	ADJ
ejpam-6597	256	7	open	open	ADJ
ejpam-6597	256	8	set	set	NOUN
ejpam-6597	256	9	in	in	ADP
ejpam-6597	256	10	m	m	PROPN
ejpam-6597	256	11	for	for	ADP
ejpam-6597	256	12	each	each	DET
ejpam-6597	256	13	s	s	PROPN
ejpam-6597	256	14	∈	∈	PROPN
ejpam-6597	256	15	s.	s.	PROPN
ejpam-6597	256	16	since	since	SCONJ
ejpam-6597	256	17	m	m	PROPN
ejpam-6597	256	18	is	be	AUX
ejpam-6597	256	19	closed	closed	ADJ
ejpam-6597	256	20	domain	domain	NOUN
ejpam-6597	256	21	set	set	VERB
ejpam-6597	256	22	in	in	ADP
ejpam-6597	256	23	x	x	PROPN
ejpam-6597	256	24	,	,	PUNCT
ejpam-6597	256	25	by	by	ADP
ejpam-6597	256	26	lemma	lemma	PROPN
ejpam-6597	256	27	2	2	NUM
ejpam-6597	256	28	fs	fs	NOUN
ejpam-6597	256	29	is	be	AUX
ejpam-6597	256	30	pre	pre	ADJ
ejpam-6597	256	31	-	-	ADJ
ejpam-6597	256	32	open	open	ADJ
ejpam-6597	256	33	set	set	NOUN
ejpam-6597	256	34	in	in	ADP
ejpam-6597	256	35	x	x	PUNCT
ejpam-6597	256	36	for	for	ADP
ejpam-6597	256	37	each	each	DET
ejpam-6597	256	38	s	s	PROPN
ejpam-6597	256	39	∈	∈	PROPN
ejpam-6597	256	40	s.	s.	PROPN
ejpam-6597	256	41	hence	hence	ADV
ejpam-6597	256	42	,	,	PUNCT
ejpam-6597	256	43	{	{	PUNCT
ejpam-6597	256	44	fs}s∈s	fs}s∈s	X
ejpam-6597	256	45	is	be	AUX
ejpam-6597	256	46	a	a	DET
ejpam-6597	256	47	discrete	discrete	ADJ
ejpam-6597	256	48	family	family	NOUN
ejpam-6597	256	49	of	of	ADP
ejpam-6597	256	50	pre	pre	ADJ
ejpam-6597	256	51	-	-	ADJ
ejpam-6597	256	52	open	open	ADJ
ejpam-6597	256	53	sets	set	NOUN
ejpam-6597	256	54	in	in	ADP
ejpam-6597	256	55	x	x	NOUN
ejpam-6597	256	56	,	,	PUNCT
ejpam-6597	256	57	where	where	SCONJ
ejpam-6597	256	58	fs	fs	ADP
ejpam-6597	256	59	⊆	⊆	NUM
ejpam-6597	256	60	m	m	NOUN
ejpam-6597	256	61	for	for	ADP
ejpam-6597	256	62	each	each	DET
ejpam-6597	256	63	s	s	PART
ejpam-6597	256	64	∈	∈	PROPN
ejpam-6597	256	65	s.	s.	PROPN
ejpam-6597	256	66	conversely	conversely	ADV
ejpam-6597	256	67	,	,	PUNCT
ejpam-6597	256	68	let	let	VERB
ejpam-6597	256	69	{	{	PUNCT
ejpam-6597	256	70	fs}s∈s	fs}s∈s	PART
ejpam-6597	256	71	be	be	AUX
ejpam-6597	256	72	a	a	DET
ejpam-6597	256	73	discrete	discrete	ADJ
ejpam-6597	256	74	family	family	NOUN
ejpam-6597	256	75	of	of	ADP
ejpam-6597	256	76	pre	pre	ADJ
ejpam-6597	256	77	-	-	ADJ
ejpam-6597	256	78	open	open	ADJ
ejpam-6597	256	79	sets	set	NOUN
ejpam-6597	256	80	in	in	ADP
ejpam-6597	256	81	x	x	NOUN
ejpam-6597	256	82	,	,	PUNCT
ejpam-6597	256	83	where	where	SCONJ
ejpam-6597	256	84	fs	fs	ADP
ejpam-6597	256	85	⊆	⊆	NUM
ejpam-6597	256	86	m	m	NOUN
ejpam-6597	256	87	for	for	ADP
ejpam-6597	256	88	each	each	DET
ejpam-6597	256	89	s	s	PROPN
ejpam-6597	256	90	∈	∈	PROPN
ejpam-6597	256	91	s.	s.	PROPN
ejpam-6597	256	92	then	then	ADV
ejpam-6597	256	93	,	,	PUNCT
ejpam-6597	256	94	fs	fs	X
ejpam-6597	256	95	is	be	AUX
ejpam-6597	256	96	pre	pre	ADJ
ejpam-6597	256	97	-	-	ADJ
ejpam-6597	256	98	open	open	ADJ
ejpam-6597	256	99	set	set	NOUN
ejpam-6597	256	100	in	in	ADP
ejpam-6597	256	101	x	x	PUNCT
ejpam-6597	256	102	for	for	ADP
ejpam-6597	256	103	each	each	DET
ejpam-6597	256	104	s	s	PROPN
ejpam-6597	256	105	∈	∈	PROPN
ejpam-6597	256	106	s.	s.	PROPN
ejpam-6597	256	107	since	since	SCONJ
ejpam-6597	256	108	m	m	PROPN
ejpam-6597	256	109	is	be	AUX
ejpam-6597	256	110	closed	closed	ADJ
ejpam-6597	256	111	domain	domain	NOUN
ejpam-6597	256	112	in	in	ADP
ejpam-6597	256	113	x	x	PROPN
ejpam-6597	256	114	,	,	PUNCT
ejpam-6597	256	115	by	by	ADP
ejpam-6597	256	116	lemma	lemma	PROPN
ejpam-6597	256	117	2	2	NUM
ejpam-6597	256	118	we	we	PRON
ejpam-6597	256	119	have	have	VERB
ejpam-6597	256	120	fs	fs	INTJ
ejpam-6597	256	121	is	be	AUX
ejpam-6597	256	122	pre	pre	ADJ
ejpam-6597	256	123	-	-	ADJ
ejpam-6597	256	124	open	open	ADJ
ejpam-6597	256	125	set	set	NOUN
ejpam-6597	256	126	in	in	ADP
ejpam-6597	256	127	m	m	PROPN
ejpam-6597	256	128	for	for	ADP
ejpam-6597	256	129	each	each	DET
ejpam-6597	256	130	s	s	PROPN
ejpam-6597	256	131	∈	∈	PROPN
ejpam-6597	256	132	s.	s.	PROPN
ejpam-6597	256	133	then	then	ADV
ejpam-6597	256	134	,	,	PUNCT
ejpam-6597	256	135	{	{	PUNCT
ejpam-6597	256	136	fs}s∈s	fs}s∈s	X
ejpam-6597	256	137	is	be	AUX
ejpam-6597	256	138	a	a	DET
ejpam-6597	256	139	discrete	discrete	ADJ
ejpam-6597	256	140	family	family	NOUN
ejpam-6597	256	141	of	of	ADP
ejpam-6597	256	142	pre	pre	ADJ
ejpam-6597	256	143	-	-	ADJ
ejpam-6597	256	144	open	open	ADJ
ejpam-6597	256	145	sets	set	NOUN
ejpam-6597	256	146	in	in	ADP
ejpam-6597	256	147	m	m	PROPN
ejpam-6597	256	148	.	.	PUNCT
ejpam-6597	257	1	lemma	lemma	PROPN
ejpam-6597	257	2	3	3	NUM
ejpam-6597	257	3	.	.	PUNCT
ejpam-6597	258	1	[	[	X
ejpam-6597	258	2	11	11	NUM
ejpam-6597	258	3	]	]	PUNCT
ejpam-6597	258	4	,	,	PUNCT
ejpam-6597	258	5	let	let	VERB
ejpam-6597	258	6	m	m	PRON
ejpam-6597	258	7	be	be	AUX
ejpam-6597	258	8	a	a	DET
ejpam-6597	258	9	closed	closed	ADJ
ejpam-6597	258	10	domain	domain	NOUN
ejpam-6597	258	11	subspace	subspace	NOUN
ejpam-6597	258	12	of	of	ADP
ejpam-6597	258	13	x	x	PROPN
ejpam-6597	258	14	and	and	CCONJ
ejpam-6597	258	15	a	a	DET
ejpam-6597	258	16	⊆	⊆	NUM
ejpam-6597	258	17	m	m	NOUN
ejpam-6597	258	18	.	.	PUNCT
ejpam-6597	259	1	then	then	ADV
ejpam-6597	259	2	:	:	PUNCT
ejpam-6597	259	3	(	(	PUNCT
ejpam-6597	259	4	1	1	X
ejpam-6597	259	5	)	)	PUNCT
ejpam-6597	259	6	a	a	PRON
ejpam-6597	259	7	is	be	AUX
ejpam-6597	259	8	pre	pre	ADJ
ejpam-6597	259	9	-	-	ADJ
ejpam-6597	259	10	closed	closed	ADJ
ejpam-6597	259	11	(	(	PUNCT
ejpam-6597	259	12	pre	pre	ADJ
ejpam-6597	259	13	-	-	ADJ
ejpam-6597	259	14	open	open	ADJ
ejpam-6597	259	15	)	)	PUNCT
ejpam-6597	259	16	in	in	ADP
ejpam-6597	259	17	m	m	PROPN
ejpam-6597	259	18	if	if	SCONJ
ejpam-6597	260	1	and	and	CCONJ
ejpam-6597	260	2	only	only	ADV
ejpam-6597	260	3	if	if	SCONJ
ejpam-6597	260	4	a	a	PRON
ejpam-6597	260	5	is	be	AUX
ejpam-6597	260	6	pre	pre	ADJ
ejpam-6597	260	7	-	-	ADJ
ejpam-6597	260	8	closed	closed	ADJ
ejpam-6597	260	9	(	(	PUNCT
ejpam-6597	260	10	pre	pre	ADJ
ejpam-6597	260	11	-	-	ADJ
ejpam-6597	260	12	open	open	ADJ
ejpam-6597	260	13	)	)	PUNCT
ejpam-6597	260	14	in	in	ADP
ejpam-6597	260	15	x.	x.	PROPN
ejpam-6597	260	16	(	(	PUNCT
ejpam-6597	260	17	2	2	NUM
ejpam-6597	260	18	)	)	PUNCT
ejpam-6597	260	19	if	if	SCONJ
ejpam-6597	260	20	a	a	DET
ejpam-6597	260	21	⊆	⊆	NUM
ejpam-6597	260	22	x	x	NOUN
ejpam-6597	260	23	and	and	CCONJ
ejpam-6597	260	24	a	a	PRON
ejpam-6597	260	25	is	be	AUX
ejpam-6597	260	26	pre	pre	ADJ
ejpam-6597	260	27	-	-	ADJ
ejpam-6597	260	28	closed	closed	ADJ
ejpam-6597	260	29	(	(	PUNCT
ejpam-6597	260	30	pre	pre	ADJ
ejpam-6597	260	31	-	-	ADJ
ejpam-6597	260	32	open	open	ADJ
ejpam-6597	260	33	)	)	PUNCT
ejpam-6597	260	34	in	in	ADP
ejpam-6597	260	35	x	x	NOUN
ejpam-6597	260	36	,	,	PUNCT
ejpam-6597	260	37	then	then	ADV
ejpam-6597	260	38	a	a	DET
ejpam-6597	260	39	∩m	∩m	PROPN
ejpam-6597	260	40	is	be	AUX
ejpam-6597	260	41	pre	pre	ADJ
ejpam-6597	260	42	-	-	ADJ
ejpam-6597	260	43	closed	closed	ADJ
ejpam-6597	260	44	(	(	PUNCT
ejpam-6597	260	45	pre	pre	ADJ
ejpam-6597	260	46	-	-	ADJ
ejpam-6597	260	47	open	open	ADJ
ejpam-6597	260	48	)	)	PUNCT
ejpam-6597	260	49	in	in	ADP
ejpam-6597	260	50	m	m	PROPN
ejpam-6597	260	51	.	.	PUNCT
ejpam-6597	261	1	theorem	theorem	ADJ
ejpam-6597	261	2	17	17	NUM
ejpam-6597	261	3	.	.	PUNCT
ejpam-6597	262	1	a	a	DET
ejpam-6597	262	2	closed	closed	ADJ
ejpam-6597	262	3	domain	domain	NOUN
ejpam-6597	262	4	subspace	subspace	NOUN
ejpam-6597	262	5	of	of	ADP
ejpam-6597	262	6	a	a	DET
ejpam-6597	262	7	collectionwise	collectionwise	ADV
ejpam-6597	262	8	pre	pre	ADJ
ejpam-6597	262	9	-	-	ADJ
ejpam-6597	262	10	normal	normal	ADJ
ejpam-6597	262	11	space	space	NOUN
ejpam-6597	262	12	is	be	AUX
ejpam-6597	262	13	collectionwise	collectionwise	ADV
ejpam-6597	262	14	pre	pre	ADJ
ejpam-6597	262	15	-	-	ADJ
ejpam-6597	262	16	normal	normal	ADJ
ejpam-6597	262	17	.	.	PUNCT
ejpam-6597	263	1	proof	proof	NOUN
ejpam-6597	263	2	.	.	PUNCT
ejpam-6597	264	1	let	let	VERB
ejpam-6597	264	2	{	{	PUNCT
ejpam-6597	264	3	fs	fs	VERB
ejpam-6597	264	4	:	:	PUNCT
ejpam-6597	264	5	s	s	PART
ejpam-6597	264	6	∈	∈	PROPN
ejpam-6597	264	7	s	s	AUX
ejpam-6597	264	8	}	}	PUNCT
ejpam-6597	264	9	be	be	AUX
ejpam-6597	264	10	a	a	DET
ejpam-6597	264	11	discrete	discrete	ADJ
ejpam-6597	264	12	family	family	NOUN
ejpam-6597	264	13	of	of	ADP
ejpam-6597	264	14	closed	closed	ADJ
ejpam-6597	264	15	subsets	subset	NOUN
ejpam-6597	264	16	of	of	ADP
ejpam-6597	264	17	m	m	PRON
ejpam-6597	264	18	.	.	PUNCT
ejpam-6597	265	1	by	by	ADP
ejpam-6597	265	2	theorem	theorem	NOUN
ejpam-6597	265	3	16	16	NUM
ejpam-6597	265	4	,	,	PUNCT
ejpam-6597	265	5	{	{	PUNCT
ejpam-6597	265	6	fs	fs	X
ejpam-6597	265	7	:	:	PUNCT
ejpam-6597	265	8	s	s	PART
ejpam-6597	265	9	∈	∈	PROPN
ejpam-6597	265	10	s	s	AUX
ejpam-6597	265	11	}	}	PUNCT
ejpam-6597	265	12	is	be	AUX
ejpam-6597	265	13	a	a	DET
ejpam-6597	265	14	discrete	discrete	ADJ
ejpam-6597	265	15	family	family	NOUN
ejpam-6597	265	16	of	of	ADP
ejpam-6597	265	17	closed	closed	ADJ
ejpam-6597	265	18	subsets	subset	NOUN
ejpam-6597	265	19	of	of	ADP
ejpam-6597	265	20	x.	x.	NOUN
ejpam-6597	265	21	since	since	SCONJ
ejpam-6597	265	22	x	x	PRON
ejpam-6597	265	23	is	be	AUX
ejpam-6597	265	24	collectionwise	collectionwise	ADV
ejpam-6597	265	25	pre	pre	ADJ
ejpam-6597	265	26	-	-	ADJ
ejpam-6597	265	27	normal	normal	ADJ
ejpam-6597	265	28	,	,	PUNCT
ejpam-6597	265	29	there	there	PRON
ejpam-6597	265	30	exists	exist	VERB
ejpam-6597	265	31	a	a	DET
ejpam-6597	265	32	family	family	NOUN
ejpam-6597	265	33	{	{	PUNCT
ejpam-6597	265	34	us	we	PRON
ejpam-6597	265	35	:	:	PUNCT
ejpam-6597	265	36	s	s	VERB
ejpam-6597	265	37	∈	∈	PROPN
ejpam-6597	265	38	s	s	PART
ejpam-6597	265	39	}	}	PUNCT
ejpam-6597	265	40	of	of	ADP
ejpam-6597	265	41	pre	pre	ADJ
ejpam-6597	265	42	-	-	ADJ
ejpam-6597	265	43	open	open	ADJ
ejpam-6597	265	44	subsets	subset	NOUN
ejpam-6597	265	45	of	of	ADP
ejpam-6597	265	46	x	x	SYM
ejpam-6597	265	47	such	such	ADJ
ejpam-6597	265	48	that	that	PRON
ejpam-6597	265	49	fs	fs	ADP
ejpam-6597	265	50	⊆	⊆	NUM
ejpam-6597	265	51	us	we	PRON
ejpam-6597	265	52	for	for	ADP
ejpam-6597	265	53	each	each	DET
ejpam-6597	265	54	s	s	PROPN
ejpam-6597	265	55	∈	∈	PROPN
ejpam-6597	265	56	s.	s.	PROPN
ejpam-6597	265	57	thus	thus	ADV
ejpam-6597	265	58	,	,	PUNCT
ejpam-6597	265	59	fs∩m	fs∩m	NOUN
ejpam-6597	265	60	⊆	⊆	NUM
ejpam-6597	265	61	us∩m	us∩m	NOUN
ejpam-6597	265	62	and	and	CCONJ
ejpam-6597	265	63	so	so	ADV
ejpam-6597	265	64	fs	fs	ADP
ejpam-6597	265	65	⊆	⊆	NUM
ejpam-6597	265	66	us∩m	us∩m	NOUN
ejpam-6597	265	67	for	for	ADP
ejpam-6597	265	68	each	each	DET
ejpam-6597	265	69	s	s	PROPN
ejpam-6597	265	70	∈	∈	PROPN
ejpam-6597	265	71	s.	s.	PROPN
ejpam-6597	265	72	by	by	ADP
ejpam-6597	265	73	lemma	lemma	PROPN
ejpam-6597	265	74	3	3	NUM
ejpam-6597	265	75	,	,	PUNCT
ejpam-6597	265	76	we	we	PRON
ejpam-6597	265	77	have	have	VERB
ejpam-6597	265	78	us∩m	us∩m	NOUN
ejpam-6597	265	79	is	be	AUX
ejpam-6597	265	80	pre	pre	ADJ
ejpam-6597	265	81	-	-	ADJ
ejpam-6597	265	82	open	open	ADJ
ejpam-6597	265	83	set	set	NOUN
ejpam-6597	265	84	in	in	ADP
ejpam-6597	265	85	m	m	PROPN
ejpam-6597	265	86	for	for	ADP
ejpam-6597	265	87	each	each	DET
ejpam-6597	265	88	s	s	PROPN
ejpam-6597	265	89	∈	∈	PROPN
ejpam-6597	265	90	s.	s.	PROPN
ejpam-6597	265	91	hence	hence	ADV
ejpam-6597	265	92	,	,	PUNCT
ejpam-6597	265	93	{	{	PUNCT
ejpam-6597	265	94	us∩m	us∩m	NOUN
ejpam-6597	265	95	:	:	PUNCT
ejpam-6597	265	96	s	s	VERB
ejpam-6597	265	97	∈	∈	PROPN
ejpam-6597	265	98	s	s	AUX
ejpam-6597	265	99	}	}	PUNCT
ejpam-6597	265	100	is	be	AUX
ejpam-6597	265	101	a	a	DET
ejpam-6597	265	102	discrete	discrete	ADJ
ejpam-6597	265	103	family	family	NOUN
ejpam-6597	265	104	of	of	ADP
ejpam-6597	265	105	pre	pre	ADJ
ejpam-6597	265	106	-	-	ADJ
ejpam-6597	265	107	open	open	ADJ
ejpam-6597	265	108	subsets	subset	NOUN
ejpam-6597	265	109	of	of	ADP
ejpam-6597	265	110	m	m	PRON
ejpam-6597	265	111	such	such	ADJ
ejpam-6597	265	112	that	that	SCONJ
ejpam-6597	265	113	fs	fs	ADP
ejpam-6597	265	114	⊆	⊆	NUM
ejpam-6597	265	115	us	we	PRON
ejpam-6597	265	116	∩m	∩m	PROPN
ejpam-6597	265	117	for	for	ADP
ejpam-6597	265	118	each	each	DET
ejpam-6597	265	119	s	s	PROPN
ejpam-6597	265	120	∈	∈	PROPN
ejpam-6597	265	121	s.	s.	PROPN
ejpam-6597	265	122	therefore	therefore	ADV
ejpam-6597	265	123	,	,	PUNCT
ejpam-6597	265	124	m	m	VERB
ejpam-6597	265	125	is	be	AUX
ejpam-6597	265	126	collectionwise	collectionwise	ADV
ejpam-6597	265	127	pre	pre	ADJ
ejpam-6597	265	128	-	-	ADJ
ejpam-6597	265	129	normal	normal	ADJ
ejpam-6597	265	130	.	.	PUNCT
ejpam-6597	266	1	since	since	SCONJ
ejpam-6597	266	2	every	every	DET
ejpam-6597	266	3	clopen	clopen	ADJ
ejpam-6597	266	4	subset	subset	NOUN
ejpam-6597	266	5	of	of	ADP
ejpam-6597	266	6	a	a	DET
ejpam-6597	266	7	spacex	spacex	NOUN
ejpam-6597	266	8	is	be	AUX
ejpam-6597	266	9	closed	closed	ADJ
ejpam-6597	266	10	domain	domain	NOUN
ejpam-6597	266	11	,	,	PUNCT
ejpam-6597	266	12	we	we	PRON
ejpam-6597	266	13	conclude	conclude	VERB
ejpam-6597	266	14	the	the	DET
ejpam-6597	266	15	next	next	ADJ
ejpam-6597	266	16	corollary	corollary	NOUN
ejpam-6597	266	17	:	:	PUNCT
ejpam-6597	266	18	corollary	corollary	ADJ
ejpam-6597	266	19	12	12	NUM
ejpam-6597	266	20	.	.	PUNCT
ejpam-6597	267	1	a	a	DET
ejpam-6597	267	2	clopen	clopen	ADJ
ejpam-6597	267	3	subspace	subspace	NOUN
ejpam-6597	267	4	of	of	ADP
ejpam-6597	267	5	a	a	DET
ejpam-6597	267	6	collectionwise	collectionwise	ADV
ejpam-6597	267	7	pre	pre	ADJ
ejpam-6597	267	8	-	-	ADJ
ejpam-6597	267	9	normal	normal	ADJ
ejpam-6597	267	10	space	space	NOUN
ejpam-6597	267	11	is	be	AUX
ejpam-6597	267	12	collectionwise	collectionwise	ADV
ejpam-6597	267	13	pre	pre	ADJ
ejpam-6597	267	14	-	-	ADJ
ejpam-6597	267	15	normal	normal	ADJ
ejpam-6597	267	16	.	.	PUNCT
ejpam-6597	268	1	5	5	X
ejpam-6597	268	2	.	.	X
ejpam-6597	268	3	the	the	DET
ejpam-6597	268	4	product	product	NOUN
ejpam-6597	268	5	of	of	ADP
ejpam-6597	268	6	collectionwise	collectionwise	PROPN
ejpam-6597	268	7	pre	pre	NOUN
ejpam-6597	268	8	-	-	NOUN
ejpam-6597	268	9	normality	normality	ADJ
ejpam-6597	268	10	in	in	ADP
ejpam-6597	268	11	this	this	DET
ejpam-6597	268	12	section	section	NOUN
ejpam-6597	268	13	,	,	PUNCT
ejpam-6597	268	14	we	we	PRON
ejpam-6597	268	15	study	study	VERB
ejpam-6597	268	16	the	the	DET
ejpam-6597	268	17	product	product	NOUN
ejpam-6597	268	18	of	of	ADP
ejpam-6597	268	19	collectionwise	collectionwise	PROPN
ejpam-6597	268	20	pre	pre	NOUN
ejpam-6597	268	21	-	-	NOUN
ejpam-6597	268	22	normality	normality	NOUN
ejpam-6597	268	23	as	as	SCONJ
ejpam-6597	268	24	follows	follow	VERB
ejpam-6597	268	25	:	:	PUNCT
ejpam-6597	268	26	s.	s.	PROPN
ejpam-6597	268	27	a.	a.	PROPN
ejpam-6597	268	28	thabit	thabit	PROPN
ejpam-6597	268	29	,	,	PUNCT
ejpam-6597	268	30	a.	a.	PROPN
ejpam-6597	268	31	al	al	PROPN
ejpam-6597	268	32	-	-	PUNCT
ejpam-6597	268	33	awadi	awadi	PROPN
ejpam-6597	268	34	,	,	PUNCT
ejpam-6597	268	35	r.	r.	PROPN
ejpam-6597	268	36	noaman	noaman	PROPN
ejpam-6597	268	37	/	/	SYM
ejpam-6597	268	38	eur	eur	PROPN
ejpam-6597	268	39	.	.	PUNCT
ejpam-6597	269	1	j.	j.	PROPN
ejpam-6597	269	2	pure	pure	PROPN
ejpam-6597	269	3	appl	appl	PROPN
ejpam-6597	269	4	.	.	PROPN
ejpam-6597	269	5	math	math	PROPN
ejpam-6597	269	6	,	,	PUNCT
ejpam-6597	269	7	18	18	NUM
ejpam-6597	269	8	(	(	PUNCT
ejpam-6597	269	9	4	4	NUM
ejpam-6597	269	10	)	)	PUNCT
ejpam-6597	269	11	(	(	PUNCT
ejpam-6597	269	12	2025	2025	NUM
ejpam-6597	269	13	)	)	PUNCT
ejpam-6597	269	14	,	,	PUNCT
ejpam-6597	269	15	6597	6597	NUM
ejpam-6597	269	16	11	11	NUM
ejpam-6597	269	17	of	of	ADP
ejpam-6597	269	18	15	15	NUM
ejpam-6597	269	19	theorem	theorem	NOUN
ejpam-6597	269	20	18	18	NUM
ejpam-6597	269	21	.	.	PUNCT
ejpam-6597	270	1	let	let	AUX
ejpam-6597	270	2	(	(	PUNCT
ejpam-6597	270	3	xi	xi	NOUN
ejpam-6597	270	4	,	,	PUNCT
ejpam-6597	270	5	ti	ti	NOUN
ejpam-6597	270	6	)	)	PUNCT
ejpam-6597	270	7	be	be	VERB
ejpam-6597	270	8	a	a	DET
ejpam-6597	270	9	topological	topological	ADJ
ejpam-6597	270	10	space	space	NOUN
ejpam-6597	270	11	for	for	ADP
ejpam-6597	270	12	each	each	DET
ejpam-6597	270	13	i	i	PRON
ejpam-6597	270	14	∈	∈	PROPN
ejpam-6597	270	15	{	{	PUNCT
ejpam-6597	270	16	1	1	NUM
ejpam-6597	270	17	,	,	PUNCT
ejpam-6597	270	18	2	2	NUM
ejpam-6597	270	19	,	,	PUNCT
ejpam-6597	270	20	3	3	NUM
ejpam-6597	270	21	,	,	PUNCT
ejpam-6597	270	22	...	...	PUNCT
ejpam-6597	270	23	,	,	PUNCT
ejpam-6597	270	24	n	n	CCONJ
ejpam-6597	270	25	}	}	PUNCT
ejpam-6597	270	26	,	,	PUNCT
ejpam-6597	270	27	n	n	PROPN
ejpam-6597	270	28	∈	∈	PROPN
ejpam-6597	270	29	n.	n.	NOUN
ejpam-6597	270	30	let	let	VERB
ejpam-6597	270	31	t	t	NOUN
ejpam-6597	270	32	be	be	AUX
ejpam-6597	270	33	the	the	DET
ejpam-6597	270	34	product	product	NOUN
ejpam-6597	270	35	topology	topology	NOUN
ejpam-6597	270	36	on	on	ADP
ejpam-6597	270	37	x	x	X
ejpam-6597	270	38	=	=	VERB
ejpam-6597	270	39	∏n	∏n	PROPN
ejpam-6597	270	40	i=1xi	i=1xi	NOUN
ejpam-6597	270	41	.	.	PUNCT
ejpam-6597	271	1	if	if	SCONJ
ejpam-6597	271	2	(	(	PUNCT
ejpam-6597	271	3	x	x	X
ejpam-6597	271	4	,	,	PUNCT
ejpam-6597	271	5	t	t	PROPN
ejpam-6597	271	6	)	)	PUNCT
ejpam-6597	271	7	is	be	AUX
ejpam-6597	271	8	collectionwise	collectionwise	ADV
ejpam-6597	271	9	pre	pre	ADJ
ejpam-6597	271	10	-	-	ADJ
ejpam-6597	271	11	normal	normal	ADJ
ejpam-6597	271	12	,	,	PUNCT
ejpam-6597	271	13	then	then	ADV
ejpam-6597	271	14	(	(	PUNCT
ejpam-6597	271	15	xi	xi	X
ejpam-6597	271	16	,	,	PUNCT
ejpam-6597	271	17	ti	ti	NOUN
ejpam-6597	271	18	)	)	PUNCT
ejpam-6597	271	19	is	be	AUX
ejpam-6597	271	20	collectionwise	collectionwise	ADV
ejpam-6597	271	21	pre	pre	ADJ
ejpam-6597	271	22	-	-	ADJ
ejpam-6597	271	23	normal	normal	ADJ
ejpam-6597	271	24	for	for	ADP
ejpam-6597	271	25	each	each	DET
ejpam-6597	271	26	i	i	PRON
ejpam-6597	271	27	∈	∈	PROPN
ejpam-6597	271	28	{	{	PUNCT
ejpam-6597	271	29	1	1	NUM
ejpam-6597	271	30	,	,	PUNCT
ejpam-6597	271	31	2	2	NUM
ejpam-6597	271	32	,	,	PUNCT
ejpam-6597	271	33	3	3	NUM
ejpam-6597	271	34	,	,	PUNCT
ejpam-6597	271	35	...	...	PUNCT
ejpam-6597	271	36	,	,	PUNCT
ejpam-6597	271	37	n	n	CCONJ
ejpam-6597	271	38	}	}	PUNCT
ejpam-6597	271	39	.	.	PUNCT
ejpam-6597	272	1	proof	proof	NOUN
ejpam-6597	272	2	.	.	PUNCT
ejpam-6597	273	1	let	let	VERB
ejpam-6597	273	2	x	x	PUNCT
ejpam-6597	273	3	=	=	PUNCT
ejpam-6597	273	4	n∏	n∏	PROPN
ejpam-6597	273	5	i=1	i=1	PROPN
ejpam-6597	273	6	xi	xi	AUX
ejpam-6597	273	7	be	be	AUX
ejpam-6597	273	8	a	a	DET
ejpam-6597	273	9	collectionwise	collectionwise	ADV
ejpam-6597	273	10	pre	pre	ADJ
ejpam-6597	273	11	-	-	ADJ
ejpam-6597	273	12	normal	normal	ADJ
ejpam-6597	273	13	space	space	NOUN
ejpam-6597	273	14	.	.	PUNCT
ejpam-6597	274	1	let	let	VERB
ejpam-6597	274	2	m	m	PRON
ejpam-6597	274	3	∈	∈	VERB
ejpam-6597	274	4	{	{	PUNCT
ejpam-6597	274	5	1	1	NUM
ejpam-6597	274	6	,	,	PUNCT
ejpam-6597	274	7	2	2	NUM
ejpam-6597	274	8	,	,	PUNCT
ejpam-6597	274	9	3	3	NUM
ejpam-6597	274	10	,	,	PUNCT
ejpam-6597	274	11	...	...	PUNCT
ejpam-6597	274	12	,	,	PUNCT
ejpam-6597	274	13	n	n	CCONJ
ejpam-6597	274	14	}	}	PUNCT
ejpam-6597	274	15	be	be	AUX
ejpam-6597	274	16	arbitrary	arbitrary	ADJ
ejpam-6597	274	17	.	.	PUNCT
ejpam-6597	275	1	let	let	VERB
ejpam-6597	275	2	{	{	PUNCT
ejpam-6597	275	3	fsm}s∈s	fsm}s∈s	NOUN
ejpam-6597	275	4	be	be	AUX
ejpam-6597	275	5	any	any	DET
ejpam-6597	275	6	discrete	discrete	ADJ
ejpam-6597	275	7	family	family	NOUN
ejpam-6597	275	8	of	of	ADP
ejpam-6597	275	9	closed	closed	ADJ
ejpam-6597	275	10	subsets	subset	NOUN
ejpam-6597	275	11	of	of	ADP
ejpam-6597	275	12	xm	xm	PROPN
ejpam-6597	275	13	.	.	PUNCT
ejpam-6597	276	1	let	let	VERB
ejpam-6597	276	2	πm	πm	INTJ
ejpam-6597	276	3	:	:	PUNCT
ejpam-6597	276	4	n∏	n∏	PROPN
ejpam-6597	276	5	i=1	i=1	PROPN
ejpam-6597	277	1	xi	xi	X
ejpam-6597	277	2	−→	−→	NOUN
ejpam-6597	277	3	xm	xm	PROPN
ejpam-6597	277	4	be	be	AUX
ejpam-6597	277	5	the	the	DET
ejpam-6597	277	6	natural	natural	ADJ
ejpam-6597	277	7	projection	projection	NOUN
ejpam-6597	277	8	map	map	NOUN
ejpam-6597	277	9	from	from	ADP
ejpam-6597	277	10	x	x	PUNCT
ejpam-6597	277	11	onto	onto	ADP
ejpam-6597	277	12	xm	xm	PROPN
ejpam-6597	277	13	.	.	PUNCT
ejpam-6597	278	1	now	now	ADV
ejpam-6597	278	2	,	,	PUNCT
ejpam-6597	278	3	π−1	π−1	PROPN
ejpam-6597	278	4	m	m	PROPN
ejpam-6597	278	5	(	(	PUNCT
ejpam-6597	278	6	fsm	fsm	PROPN
ejpam-6597	278	7	)	)	PUNCT
ejpam-6597	278	8	=	=	PUNCT
ejpam-6597	278	9	n∏	n∏	PROPN
ejpam-6597	278	10	i=1	i=1	PROPN
ejpam-6597	278	11	wi	wi	PROPN
ejpam-6597	278	12	,	,	PUNCT
ejpam-6597	278	13	(	(	PUNCT
ejpam-6597	278	14	where	where	SCONJ
ejpam-6597	278	15	wi	wi	PROPN
ejpam-6597	278	16	=	=	SYM
ejpam-6597	278	17	xi	xi	PROPN
ejpam-6597	278	18	for	for	ADP
ejpam-6597	278	19	each	each	DET
ejpam-6597	278	20	i	i	PRON
ejpam-6597	278	21	̸=	̸=	PROPN
ejpam-6597	278	22	m	m	VERB
ejpam-6597	278	23	)	)	PUNCT
ejpam-6597	278	24	is	be	AUX
ejpam-6597	278	25	closed	close	VERB
ejpam-6597	278	26	in	in	ADP
ejpam-6597	278	27	x.	x.	NOUN
ejpam-6597	278	28	then	then	ADV
ejpam-6597	278	29	,	,	PUNCT
ejpam-6597	278	30	{	{	PUNCT
ejpam-6597	278	31	π−1	π−1	PROPN
ejpam-6597	278	32	m	m	VERB
ejpam-6597	278	33	(	(	PUNCT
ejpam-6597	278	34	fsm)}s∈s	fsm)}s∈s	NOUN
ejpam-6597	278	35	is	be	AUX
ejpam-6597	278	36	a	a	DET
ejpam-6597	278	37	discrete	discrete	ADJ
ejpam-6597	278	38	family	family	NOUN
ejpam-6597	278	39	of	of	ADP
ejpam-6597	278	40	closed	closed	ADJ
ejpam-6597	278	41	sets	set	NOUN
ejpam-6597	278	42	in	in	ADP
ejpam-6597	278	43	x.	x.	NOUN
ejpam-6597	278	44	since	since	SCONJ
ejpam-6597	278	45	x	x	PRON
ejpam-6597	278	46	is	be	AUX
ejpam-6597	278	47	collectionwise	collectionwise	ADV
ejpam-6597	278	48	pre	pre	ADJ
ejpam-6597	278	49	-	-	ADJ
ejpam-6597	278	50	normal	normal	ADJ
ejpam-6597	278	51	,	,	PUNCT
ejpam-6597	278	52	there	there	PRON
ejpam-6597	278	53	exists	exist	VERB
ejpam-6597	278	54	a	a	DET
ejpam-6597	278	55	discrete	discrete	ADJ
ejpam-6597	278	56	family	family	NOUN
ejpam-6597	278	57	{	{	PUNCT
ejpam-6597	278	58	us}s∈s	us}s∈s	PROPN
ejpam-6597	278	59	of	of	ADP
ejpam-6597	278	60	pre	pre	ADJ
ejpam-6597	278	61	-	-	ADJ
ejpam-6597	278	62	open	open	ADJ
ejpam-6597	278	63	sets	set	NOUN
ejpam-6597	278	64	in	in	ADP
ejpam-6597	278	65	x	x	SYM
ejpam-6597	278	66	such	such	ADJ
ejpam-6597	278	67	that	that	SCONJ
ejpam-6597	278	68	π−1	π−1	PROPN
ejpam-6597	278	69	m	m	PROPN
ejpam-6597	278	70	(	(	PUNCT
ejpam-6597	278	71	fsm	fsm	PROPN
ejpam-6597	278	72	)	)	PUNCT
ejpam-6597	278	73	⊆	⊆	NUM
ejpam-6597	278	74	us	we	PRON
ejpam-6597	278	75	for	for	ADP
ejpam-6597	278	76	each	each	DET
ejpam-6597	278	77	s	s	PROPN
ejpam-6597	278	78	∈	∈	PROPN
ejpam-6597	278	79	s.	s.	PROPN
ejpam-6597	278	80	then	then	ADV
ejpam-6597	278	81	,	,	PUNCT
ejpam-6597	278	82	we	we	PRON
ejpam-6597	278	83	have	have	VERB
ejpam-6597	278	84	fsm	fsm	PROPN
ejpam-6597	278	85	⊆	⊆	NUM
ejpam-6597	278	86	πm(us	πm(us	PROPN
ejpam-6597	278	87	)	)	PUNCT
ejpam-6597	278	88	for	for	ADP
ejpam-6597	278	89	each	each	DET
ejpam-6597	278	90	s	s	PROPN
ejpam-6597	278	91	∈	∈	PROPN
ejpam-6597	278	92	s.	s.	PROPN
ejpam-6597	278	93	since	since	SCONJ
ejpam-6597	278	94	πm	πm	ADV
ejpam-6597	278	95	is	be	AUX
ejpam-6597	278	96	a	a	DET
ejpam-6597	278	97	clopen	clopen	ADJ
ejpam-6597	278	98	onto	onto	ADP
ejpam-6597	278	99	continuous	continuous	ADJ
ejpam-6597	278	100	function	function	NOUN
ejpam-6597	278	101	,	,	PUNCT
ejpam-6597	278	102	then	then	ADV
ejpam-6597	278	103	πm(us	πm(us	PROPN
ejpam-6597	278	104	)	)	PUNCT
ejpam-6597	278	105	is	be	AUX
ejpam-6597	278	106	pre	pre	ADJ
ejpam-6597	278	107	-	-	ADJ
ejpam-6597	278	108	open	open	ADJ
ejpam-6597	278	109	set	set	NOUN
ejpam-6597	278	110	in	in	ADP
ejpam-6597	278	111	xm	xm	PROPN
ejpam-6597	278	112	for	for	ADP
ejpam-6597	278	113	each	each	DET
ejpam-6597	278	114	s	s	PROPN
ejpam-6597	278	115	∈	∈	PROPN
ejpam-6597	278	116	s.	s.	PROPN
ejpam-6597	278	117	thus	thus	ADV
ejpam-6597	278	118	,	,	PUNCT
ejpam-6597	278	119	{	{	PUNCT
ejpam-6597	278	120	πm(us)}s∈s	πm(us)}s∈s	NOUN
ejpam-6597	278	121	is	be	AUX
ejpam-6597	278	122	a	a	DET
ejpam-6597	278	123	discrete	discrete	ADJ
ejpam-6597	278	124	family	family	NOUN
ejpam-6597	278	125	of	of	ADP
ejpam-6597	278	126	preopen	preopen	ADJ
ejpam-6597	278	127	sets	set	NOUN
ejpam-6597	278	128	in	in	ADP
ejpam-6597	278	129	xm	xm	PROPN
ejpam-6597	278	130	such	such	ADJ
ejpam-6597	278	131	that	that	SCONJ
ejpam-6597	278	132	fsm	fsm	PROPN
ejpam-6597	278	133	⊆	⊆	NUM
ejpam-6597	278	134	πm(us	πm(us	PROPN
ejpam-6597	278	135	)	)	PUNCT
ejpam-6597	278	136	for	for	ADP
ejpam-6597	278	137	each	each	DET
ejpam-6597	278	138	s	s	PROPN
ejpam-6597	278	139	∈	∈	PROPN
ejpam-6597	278	140	s.	s.	PROPN
ejpam-6597	278	141	hence	hence	ADV
ejpam-6597	278	142	,	,	PUNCT
ejpam-6597	278	143	xm	xm	PROPN
ejpam-6597	278	144	is	be	AUX
ejpam-6597	278	145	collectionwise	collectionwise	ADV
ejpam-6597	278	146	pre	pre	ADJ
ejpam-6597	278	147	-	-	ADJ
ejpam-6597	278	148	normal	normal	ADJ
ejpam-6597	278	149	.	.	PUNCT
ejpam-6597	279	1	since	since	SCONJ
ejpam-6597	279	2	m	m	PROPN
ejpam-6597	279	3	was	be	AUX
ejpam-6597	279	4	arbitrary	arbitrary	ADJ
ejpam-6597	279	5	,	,	PUNCT
ejpam-6597	279	6	then	then	ADV
ejpam-6597	279	7	(	(	PUNCT
ejpam-6597	279	8	xi	xi	X
ejpam-6597	279	9	,	,	PUNCT
ejpam-6597	279	10	ti	ti	NOUN
ejpam-6597	279	11	)	)	PUNCT
ejpam-6597	279	12	is	be	AUX
ejpam-6597	279	13	collectionwise	collectionwise	ADV
ejpam-6597	279	14	pre	pre	ADJ
ejpam-6597	279	15	-	-	ADJ
ejpam-6597	279	16	normal	normal	ADJ
ejpam-6597	279	17	for	for	ADP
ejpam-6597	279	18	each	each	DET
ejpam-6597	279	19	i	i	PRON
ejpam-6597	279	20	∈	∈	PROPN
ejpam-6597	279	21	{	{	PUNCT
ejpam-6597	279	22	1	1	NUM
ejpam-6597	279	23	,	,	PUNCT
ejpam-6597	279	24	2	2	NUM
ejpam-6597	279	25	,	,	PUNCT
ejpam-6597	279	26	3	3	NUM
ejpam-6597	279	27	,	,	PUNCT
ejpam-6597	279	28	...	...	PUNCT
ejpam-6597	279	29	,	,	PUNCT
ejpam-6597	279	30	n	n	CCONJ
ejpam-6597	279	31	}	}	PUNCT
ejpam-6597	279	32	.	.	PUNCT
ejpam-6597	280	1	corollary	corollary	ADJ
ejpam-6597	280	2	13	13	NUM
ejpam-6597	280	3	.	.	PUNCT
ejpam-6597	281	1	•	•	NOUN
ejpam-6597	281	2	if	if	SCONJ
ejpam-6597	281	3	the	the	DET
ejpam-6597	281	4	product	product	NOUN
ejpam-6597	281	5	space	space	NOUN
ejpam-6597	281	6	x	x	X
ejpam-6597	281	7	×	×	NOUN
ejpam-6597	281	8	y	y	PROPN
ejpam-6597	281	9	is	be	AUX
ejpam-6597	281	10	collectionwise	collectionwise	ADV
ejpam-6597	281	11	pre	pre	ADJ
ejpam-6597	281	12	-	-	ADJ
ejpam-6597	281	13	normal	normal	ADJ
ejpam-6597	281	14	,	,	PUNCT
ejpam-6597	281	15	then	then	ADV
ejpam-6597	281	16	both	both	DET
ejpam-6597	281	17	x	x	X
ejpam-6597	281	18	and	and	CCONJ
ejpam-6597	281	19	y	y	PROPN
ejpam-6597	281	20	are	be	AUX
ejpam-6597	281	21	collectionwise	collectionwise	ADV
ejpam-6597	281	22	pre	pre	ADJ
ejpam-6597	281	23	-	-	ADJ
ejpam-6597	281	24	normal	normal	ADJ
ejpam-6597	281	25	.	.	PUNCT
ejpam-6597	282	1	•	•	INTJ
ejpam-6597	283	1	if	if	SCONJ
ejpam-6597	283	2	x	x	PRON
ejpam-6597	283	3	×	×	NOUN
ejpam-6597	283	4	i	i	PRON
ejpam-6597	283	5	is	be	AUX
ejpam-6597	283	6	collectionwise	collectionwise	ADV
ejpam-6597	283	7	pre	pre	ADJ
ejpam-6597	283	8	-	-	ADJ
ejpam-6597	283	9	normal	normal	ADJ
ejpam-6597	283	10	,	,	PUNCT
ejpam-6597	283	11	then	then	ADV
ejpam-6597	283	12	x	x	PUNCT
ejpam-6597	283	13	is	be	AUX
ejpam-6597	283	14	collectionwise	collectionwise	ADV
ejpam-6597	283	15	pre	pre	ADJ
ejpam-6597	283	16	-	-	ADJ
ejpam-6597	283	17	normal	normal	ADJ
ejpam-6597	283	18	.	.	PUNCT
ejpam-6597	284	1	•	•	NUM
ejpam-6597	284	2	a	a	DET
ejpam-6597	284	3	space	space	NOUN
ejpam-6597	284	4	x	x	PUNCT
ejpam-6597	284	5	is	be	AUX
ejpam-6597	284	6	collectionwise	collectionwise	ADV
ejpam-6597	284	7	pre	pre	ADJ
ejpam-6597	284	8	-	-	ADJ
ejpam-6597	284	9	normal	normal	ADJ
ejpam-6597	284	10	if	if	SCONJ
ejpam-6597	284	11	and	and	CCONJ
ejpam-6597	284	12	only	only	ADV
ejpam-6597	284	13	if	if	SCONJ
ejpam-6597	284	14	x	x	X
ejpam-6597	284	15	×	×	NOUN
ejpam-6597	284	16	{	{	PUNCT
ejpam-6597	284	17	0	0	NUM
ejpam-6597	284	18	}	}	PUNCT
ejpam-6597	284	19	is	be	AUX
ejpam-6597	284	20	collectionwise	collectionwise	ADV
ejpam-6597	284	21	prenormal	prenormal	ADJ
ejpam-6597	284	22	.	.	PUNCT
ejpam-6597	285	1	note	note	VERB
ejpam-6597	285	2	that	that	SCONJ
ejpam-6597	285	3	:	:	PUNCT
ejpam-6597	285	4	collectionwise	collectionwise	ADV
ejpam-6597	285	5	pre	pre	ADJ
ejpam-6597	285	6	-	-	ADJ
ejpam-6597	285	7	normality	normality	NOUN
ejpam-6597	285	8	is	be	AUX
ejpam-6597	285	9	not	not	PART
ejpam-6597	285	10	productive	productive	ADJ
ejpam-6597	285	11	in	in	ADP
ejpam-6597	285	12	general	general	ADJ
ejpam-6597	285	13	.	.	PUNCT
ejpam-6597	286	1	here	here	ADV
ejpam-6597	286	2	is	be	AUX
ejpam-6597	286	3	an	an	DET
ejpam-6597	286	4	example	example	NOUN
ejpam-6597	286	5	:	:	PUNCT
ejpam-6597	286	6	example	example	NOUN
ejpam-6597	286	7	4	4	NUM
ejpam-6597	286	8	.	.	PUNCT
ejpam-6597	287	1	the	the	DET
ejpam-6597	287	2	space	space	NOUN
ejpam-6597	287	3	ω1×(ω1	ω1×(ω1	PUNCT
ejpam-6597	287	4	+	+	NOUN
ejpam-6597	287	5	1	1	NUM
ejpam-6597	287	6	)	)	PUNCT
ejpam-6597	287	7	,	,	PUNCT
ejpam-6597	287	8	[	[	X
ejpam-6597	287	9	10	10	NUM
ejpam-6597	287	10	]	]	PUNCT
ejpam-6597	287	11	,	,	PUNCT
ejpam-6597	287	12	is	be	AUX
ejpam-6597	287	13	tychonoff	tychonoff	NOUN
ejpam-6597	287	14	,	,	PUNCT
ejpam-6597	287	15	mildly	mildly	ADV
ejpam-6597	287	16	normal	normal	ADJ
ejpam-6597	287	17	,	,	PUNCT
ejpam-6597	287	18	locally	locally	ADV
ejpam-6597	287	19	compact	compact	ADJ
ejpam-6597	287	20	and	and	CCONJ
ejpam-6597	287	21	countably	countably	ADV
ejpam-6597	287	22	compact	compact	ADJ
ejpam-6597	287	23	space	space	NOUN
ejpam-6597	287	24	which	which	PRON
ejpam-6597	287	25	is	be	AUX
ejpam-6597	287	26	neither	neither	CCONJ
ejpam-6597	287	27	almost	almost	ADV
ejpam-6597	287	28	normal	normal	ADJ
ejpam-6597	287	29	,	,	PUNCT
ejpam-6597	287	30	normal	normal	ADJ
ejpam-6597	287	31	,	,	PUNCT
ejpam-6597	287	32	compact	compact	ADJ
ejpam-6597	287	33	nor	nor	CCONJ
ejpam-6597	287	34	lindelöf	lindelöf	NOUN
ejpam-6597	287	35	.	.	PUNCT
ejpam-6597	288	1	since	since	SCONJ
ejpam-6597	288	2	x	x	PRON
ejpam-6597	288	3	is	be	AUX
ejpam-6597	288	4	not	not	PART
ejpam-6597	288	5	normal	normal	ADJ
ejpam-6597	288	6	,	,	PUNCT
ejpam-6597	288	7	the	the	DET
ejpam-6597	288	8	space	space	NOUN
ejpam-6597	288	9	ω1	ω1	PROPN
ejpam-6597	288	10	×	×	PROPN
ejpam-6597	288	11	(	(	PUNCT
ejpam-6597	288	12	ω1	ω1	PROPN
ejpam-6597	288	13	+	+	CCONJ
ejpam-6597	288	14	1	1	NUM
ejpam-6597	288	15	)	)	PUNCT
ejpam-6597	288	16	is	be	AUX
ejpam-6597	288	17	not	not	PART
ejpam-6597	288	18	collectionwise	collectionwise	ADV
ejpam-6597	288	19	normal	normal	ADJ
ejpam-6597	288	20	.	.	PUNCT
ejpam-6597	289	1	since	since	SCONJ
ejpam-6597	289	2	ω1	ω1	PROPN
ejpam-6597	289	3	and	and	CCONJ
ejpam-6597	289	4	ω1	ω1	PROPN
ejpam-6597	289	5	+	+	PROPN
ejpam-6597	289	6	1	1	NUM
ejpam-6597	289	7	are	be	AUX
ejpam-6597	289	8	sub	sub	ADJ
ejpam-6597	289	9	-	-	ADJ
ejpam-6597	289	10	maximal	maximal	ADJ
ejpam-6597	289	11	spaces	space	NOUN
ejpam-6597	289	12	[	[	X
ejpam-6597	289	13	11	11	NUM
ejpam-6597	289	14	]	]	PUNCT
ejpam-6597	289	15	,	,	PUNCT
ejpam-6597	289	16	we	we	PRON
ejpam-6597	289	17	get	get	VERB
ejpam-6597	289	18	ω1×(ω1	ω1×(ω1	ADV
ejpam-6597	289	19	+	+	NOUN
ejpam-6597	289	20	1	1	NUM
ejpam-6597	289	21	)	)	PUNCT
ejpam-6597	289	22	is	be	AUX
ejpam-6597	289	23	sub	sub	ADJ
ejpam-6597	289	24	-	-	ADJ
ejpam-6597	289	25	maximal	maximal	ADJ
ejpam-6597	289	26	.	.	PUNCT
ejpam-6597	290	1	since	since	SCONJ
ejpam-6597	290	2	ω1×(ω1	ω1×(ω1	NUM
ejpam-6597	290	3	+	+	NOUN
ejpam-6597	290	4	1	1	NUM
ejpam-6597	290	5	)	)	PUNCT
ejpam-6597	290	6	is	be	AUX
ejpam-6597	290	7	not	not	PART
ejpam-6597	290	8	normal	normal	ADJ
ejpam-6597	290	9	,	,	PUNCT
ejpam-6597	290	10	we	we	PRON
ejpam-6597	290	11	conclude	conclude	VERB
ejpam-6597	290	12	that	that	SCONJ
ejpam-6597	290	13	ω1×	ω1×	PROPN
ejpam-6597	290	14	(	(	PUNCT
ejpam-6597	290	15	ω1	ω1	PROPN
ejpam-6597	290	16	+	+	PROPN
ejpam-6597	290	17	1	1	NUM
ejpam-6597	290	18	)	)	PUNCT
ejpam-6597	290	19	is	be	AUX
ejpam-6597	290	20	not	not	PART
ejpam-6597	290	21	pre	pre	ADJ
ejpam-6597	290	22	-	-	ADJ
ejpam-6597	290	23	normal	normal	ADJ
ejpam-6597	290	24	.	.	PUNCT
ejpam-6597	291	1	therefore	therefore	ADV
ejpam-6597	291	2	,	,	PUNCT
ejpam-6597	291	3	ω1×	ω1×	PROPN
ejpam-6597	291	4	(	(	PUNCT
ejpam-6597	291	5	ω1	ω1	PROPN
ejpam-6597	291	6	+	+	PROPN
ejpam-6597	291	7	1	1	NUM
ejpam-6597	291	8	)	)	PUNCT
ejpam-6597	291	9	is	be	AUX
ejpam-6597	291	10	not	not	PART
ejpam-6597	291	11	collectionwise	collectionwise	ADV
ejpam-6597	291	12	pre	pre	ADJ
ejpam-6597	291	13	-	-	ADJ
ejpam-6597	291	14	normal	normal	ADJ
ejpam-6597	291	15	.	.	PUNCT
ejpam-6597	292	1	this	this	DET
ejpam-6597	292	2	example	example	NOUN
ejpam-6597	292	3	shows	show	VERB
ejpam-6597	292	4	that	that	SCONJ
ejpam-6597	292	5	the	the	DET
ejpam-6597	292	6	product	product	NOUN
ejpam-6597	292	7	of	of	ADP
ejpam-6597	292	8	two	two	NUM
ejpam-6597	292	9	collectionwise	collectionwise	ADV
ejpam-6597	292	10	pre	pre	ADJ
ejpam-6597	292	11	-	-	ADJ
ejpam-6597	292	12	normal	normal	ADJ
ejpam-6597	292	13	spaces	space	NOUN
ejpam-6597	292	14	can	can	AUX
ejpam-6597	292	15	not	not	PART
ejpam-6597	292	16	be	be	AUX
ejpam-6597	292	17	collectionwise	collectionwise	ADV
ejpam-6597	292	18	pre	pre	ADJ
ejpam-6597	292	19	-	-	ADJ
ejpam-6597	292	20	normal	normal	ADJ
ejpam-6597	292	21	.	.	PUNCT
ejpam-6597	293	1	observe	observe	VERB
ejpam-6597	293	2	that	that	SCONJ
ejpam-6597	293	3	:	:	PUNCT
ejpam-6597	293	4	any	any	DET
ejpam-6597	293	5	tychonoff	tychonoff	NOUN
ejpam-6597	293	6	space	space	NOUN
ejpam-6597	293	7	y	y	PROPN
ejpam-6597	293	8	has	have	VERB
ejpam-6597	293	9	a	a	DET
ejpam-6597	293	10	one	one	NUM
ejpam-6597	293	11	-	-	PUNCT
ejpam-6597	293	12	point	point	NOUN
ejpam-6597	293	13	compactification	compactification	NOUN
ejpam-6597	293	14	x	x	PUNCT
ejpam-6597	293	15	=	=	PUNCT
ejpam-6597	293	16	y	y	PROPN
ejpam-6597	293	17	∪	∪	VERB
ejpam-6597	293	18	{	{	PUNCT
ejpam-6597	293	19	p	p	NOUN
ejpam-6597	293	20	}	}	PUNCT
ejpam-6597	293	21	,	,	PUNCT
ejpam-6597	293	22	p	p	PROPN
ejpam-6597	293	23	̸∈	̸∈	PROPN
ejpam-6597	293	24	y	y	PROPN
ejpam-6597	293	25	and	and	CCONJ
ejpam-6597	293	26	x	x	PRON
ejpam-6597	293	27	is	be	AUX
ejpam-6597	293	28	a	a	DET
ejpam-6597	293	29	hausdorff	hausdorff	ADJ
ejpam-6597	293	30	compact	compact	ADJ
ejpam-6597	293	31	space	space	NOUN
ejpam-6597	294	1	[	[	X
ejpam-6597	294	2	18	18	NUM
ejpam-6597	294	3	]	]	PUNCT
ejpam-6597	294	4	,	,	PUNCT
ejpam-6597	294	5	we	we	PRON
ejpam-6597	294	6	get	get	VERB
ejpam-6597	294	7	:	:	PUNCT
ejpam-6597	294	8	corollary	corollary	ADJ
ejpam-6597	294	9	14	14	NUM
ejpam-6597	294	10	.	.	PUNCT
ejpam-6597	295	1	any	any	DET
ejpam-6597	295	2	compactification	compactification	NOUN
ejpam-6597	295	3	x	x	PUNCT
ejpam-6597	295	4	of	of	ADP
ejpam-6597	295	5	a	a	DET
ejpam-6597	295	6	tychonoff	tychonoff	NOUN
ejpam-6597	295	7	space	space	NOUN
ejpam-6597	295	8	y	y	PROPN
ejpam-6597	295	9	is	be	AUX
ejpam-6597	295	10	collectionwise	collectionwise	ADV
ejpam-6597	295	11	prenormal	prenormal	ADJ
ejpam-6597	295	12	.	.	PUNCT
ejpam-6597	296	1	in	in	ADP
ejpam-6597	296	2	particular	particular	ADJ
ejpam-6597	296	3	,	,	PUNCT
ejpam-6597	296	4	any	any	DET
ejpam-6597	296	5	tychonoff	tychonoff	NOUN
ejpam-6597	296	6	space	space	NOUN
ejpam-6597	296	7	y	y	PROPN
ejpam-6597	296	8	has	have	VERB
ejpam-6597	296	9	a	a	DET
ejpam-6597	296	10	one	one	NUM
ejpam-6597	296	11	-	-	PUNCT
ejpam-6597	296	12	point	point	NOUN
ejpam-6597	296	13	compactification	compactification	NOUN
ejpam-6597	296	14	x	x	PUNCT
ejpam-6597	297	1	=	=	PUNCT
ejpam-6597	297	2	y	y	PROPN
ejpam-6597	297	3	∪	∪	VERB
ejpam-6597	297	4	{	{	PUNCT
ejpam-6597	297	5	p	p	NOUN
ejpam-6597	297	6	}	}	PUNCT
ejpam-6597	297	7	,	,	PUNCT
ejpam-6597	297	8	p	p	PROPN
ejpam-6597	297	9	̸∈	̸∈	PROPN
ejpam-6597	297	10	y	y	PROPN
ejpam-6597	297	11	and	and	CCONJ
ejpam-6597	297	12	x	x	X
ejpam-6597	297	13	is	be	AUX
ejpam-6597	297	14	collectionwise	collectionwise	ADV
ejpam-6597	297	15	pre	pre	ADJ
ejpam-6597	297	16	-	-	ADJ
ejpam-6597	297	17	normal	normal	ADJ
ejpam-6597	297	18	.	.	PUNCT
ejpam-6597	298	1	s.	s.	PROPN
ejpam-6597	298	2	a.	a.	PROPN
ejpam-6597	298	3	thabit	thabit	PROPN
ejpam-6597	298	4	,	,	PUNCT
ejpam-6597	298	5	a.	a.	PROPN
ejpam-6597	298	6	al	al	PROPN
ejpam-6597	298	7	-	-	PUNCT
ejpam-6597	298	8	awadi	awadi	PROPN
ejpam-6597	298	9	,	,	PUNCT
ejpam-6597	298	10	r.	r.	PROPN
ejpam-6597	298	11	noaman	noaman	PROPN
ejpam-6597	298	12	/	/	SYM
ejpam-6597	298	13	eur	eur	PROPN
ejpam-6597	298	14	.	.	PUNCT
ejpam-6597	299	1	j.	j.	PROPN
ejpam-6597	299	2	pure	pure	PROPN
ejpam-6597	299	3	appl	appl	PROPN
ejpam-6597	299	4	.	.	PROPN
ejpam-6597	299	5	math	math	PROPN
ejpam-6597	299	6	,	,	PUNCT
ejpam-6597	299	7	18	18	NUM
ejpam-6597	299	8	(	(	PUNCT
ejpam-6597	299	9	4	4	NUM
ejpam-6597	299	10	)	)	PUNCT
ejpam-6597	299	11	(	(	PUNCT
ejpam-6597	299	12	2025	2025	NUM
ejpam-6597	299	13	)	)	PUNCT
ejpam-6597	299	14	,	,	PUNCT
ejpam-6597	299	15	6597	6597	NUM
ejpam-6597	299	16	12	12	NUM
ejpam-6597	299	17	of	of	ADP
ejpam-6597	299	18	15	15	NUM
ejpam-6597	299	19	6	6	NUM
ejpam-6597	299	20	.	.	PUNCT
ejpam-6597	300	1	the	the	DET
ejpam-6597	300	2	closed	closed	ADJ
ejpam-6597	300	3	extension	extension	NOUN
ejpam-6597	300	4	and	and	CCONJ
ejpam-6597	300	5	the	the	DET
ejpam-6597	300	6	discrete	discrete	ADJ
ejpam-6597	300	7	extension	extension	NOUN
ejpam-6597	300	8	spaces	space	NOUN
ejpam-6597	300	9	of	of	ADP
ejpam-6597	300	10	collectionwise	collectionwise	PROPN
ejpam-6597	300	11	pre	pre	NOUN
ejpam-6597	300	12	-	-	NOUN
ejpam-6597	300	13	normality	normality	ADJ
ejpam-6597	300	14	now	now	ADV
ejpam-6597	300	15	,	,	PUNCT
ejpam-6597	300	16	we	we	PRON
ejpam-6597	300	17	study	study	VERB
ejpam-6597	300	18	the	the	DET
ejpam-6597	300	19	closed	closed	ADJ
ejpam-6597	300	20	extension	extension	NOUN
ejpam-6597	300	21	and	and	CCONJ
ejpam-6597	300	22	the	the	DET
ejpam-6597	300	23	discrete	discrete	ADJ
ejpam-6597	300	24	extension	extension	NOUN
ejpam-6597	300	25	spaces	space	NOUN
ejpam-6597	300	26	of	of	ADP
ejpam-6597	300	27	collectionwise	collectionwise	PROPN
ejpam-6597	300	28	pre	pre	NOUN
ejpam-6597	300	29	-	-	NOUN
ejpam-6597	300	30	normality	normality	ADJ
ejpam-6597	300	31	.	.	PUNCT
ejpam-6597	301	1	in	in	ADP
ejpam-6597	301	2	fact	fact	NOUN
ejpam-6597	301	3	,	,	PUNCT
ejpam-6597	301	4	collectionwise	collectionwise	ADV
ejpam-6597	301	5	pre	pre	ADJ
ejpam-6597	301	6	-	-	ADJ
ejpam-6597	301	7	normality	normality	ADJ
ejpam-6597	301	8	is	be	AUX
ejpam-6597	301	9	not	not	PART
ejpam-6597	301	10	preserved	preserve	VERB
ejpam-6597	301	11	by	by	ADP
ejpam-6597	301	12	the	the	DET
ejpam-6597	301	13	discrete	discrete	ADJ
ejpam-6597	301	14	extension	extension	NOUN
ejpam-6597	301	15	space	space	NOUN
ejpam-6597	301	16	xm	xm	PROPN
ejpam-6597	301	17	in	in	ADP
ejpam-6597	301	18	general	general	ADJ
ejpam-6597	301	19	.	.	PUNCT
ejpam-6597	302	1	here	here	ADV
ejpam-6597	302	2	is	be	AUX
ejpam-6597	302	3	a	a	DET
ejpam-6597	302	4	counterexample	counterexample	NOUN
ejpam-6597	302	5	:	:	PUNCT
ejpam-6597	302	6	example	example	NOUN
ejpam-6597	302	7	5	5	NUM
ejpam-6597	302	8	.	.	PUNCT
ejpam-6597	303	1	[	[	X
ejpam-6597	303	2	18	18	NUM
ejpam-6597	303	3	,	,	PUNCT
ejpam-6597	303	4	example	example	NOUN
ejpam-6597	303	5	8	8	NUM
ejpam-6597	303	6	]	]	PUNCT
ejpam-6597	303	7	,	,	PUNCT
ejpam-6597	303	8	the	the	DET
ejpam-6597	303	9	rational	rational	ADJ
ejpam-6597	303	10	sequence	sequence	NOUN
ejpam-6597	303	11	topology	topology	NOUN
ejpam-6597	303	12	[	[	X
ejpam-6597	303	13	10	10	NUM
ejpam-6597	303	14	,	,	PUNCT
ejpam-6597	303	15	example	example	NOUN
ejpam-6597	303	16	65	65	NUM
ejpam-6597	303	17	]	]	PUNCT
ejpam-6597	303	18	,	,	PUNCT
ejpam-6597	303	19	is	be	AUX
ejpam-6597	303	20	a	a	DET
ejpam-6597	303	21	first	first	ADJ
ejpam-6597	303	22	countable	countable	ADJ
ejpam-6597	303	23	,	,	PUNCT
ejpam-6597	303	24	zero	zero	NUM
ejpam-6597	303	25	-	-	PUNCT
ejpam-6597	303	26	dimensional	dimensional	ADJ
ejpam-6597	303	27	,	,	PUNCT
ejpam-6597	303	28	tychonoff	tychonoff	NOUN
ejpam-6597	303	29	,	,	PUNCT
ejpam-6597	303	30	locally	locally	ADV
ejpam-6597	303	31	compact	compact	ADJ
ejpam-6597	303	32	,	,	PUNCT
ejpam-6597	303	33	separable	separable	ADJ
ejpam-6597	303	34	space	space	NOUN
ejpam-6597	303	35	which	which	PRON
ejpam-6597	303	36	is	be	AUX
ejpam-6597	303	37	neither	neither	CCONJ
ejpam-6597	303	38	paracompact	paracompact	ADJ
ejpam-6597	303	39	,	,	PUNCT
ejpam-6597	303	40	normal	normal	ADJ
ejpam-6597	303	41	nor	nor	CCONJ
ejpam-6597	303	42	lindelöf	lindelöf	NOUN
ejpam-6597	303	43	[	[	X
ejpam-6597	303	44	10	10	NUM
ejpam-6597	303	45	]	]	PUNCT
ejpam-6597	303	46	.	.	PUNCT
ejpam-6597	304	1	by	by	ADP
ejpam-6597	304	2	corollary	corollary	ADJ
ejpam-6597	304	3	14	14	NUM
ejpam-6597	304	4	,	,	PUNCT
ejpam-6597	304	5	r	r	NOUN
ejpam-6597	304	6	with	with	ADP
ejpam-6597	304	7	the	the	DET
ejpam-6597	304	8	rational	rational	ADJ
ejpam-6597	304	9	sequence	sequence	NOUN
ejpam-6597	304	10	topology	topology	NOUN
ejpam-6597	304	11	has	have	VERB
ejpam-6597	304	12	a	a	DET
ejpam-6597	304	13	one	one	NUM
ejpam-6597	304	14	-	-	PUNCT
ejpam-6597	304	15	point	point	NOUN
ejpam-6597	304	16	compactification	compactification	NOUN
ejpam-6597	304	17	.	.	PUNCT
ejpam-6597	305	1	let	let	VERB
ejpam-6597	305	2	x	x	PUNCT
ejpam-6597	305	3	=	=	PUNCT
ejpam-6597	305	4	r	r	NOUN
ejpam-6597	305	5	∪	∪	X
ejpam-6597	305	6	{	{	PUNCT
ejpam-6597	305	7	p	p	NOUN
ejpam-6597	305	8	}	}	PUNCT
ejpam-6597	305	9	,	,	PUNCT
ejpam-6597	305	10	p	p	PROPN
ejpam-6597	305	11	̸∈	̸∈	PROPN
ejpam-6597	305	12	r	r	PROPN
ejpam-6597	305	13	,	,	PUNCT
ejpam-6597	305	14	be	be	AUX
ejpam-6597	305	15	a	a	DET
ejpam-6597	305	16	one	one	NUM
ejpam-6597	305	17	-	-	PUNCT
ejpam-6597	305	18	point	point	NOUN
ejpam-6597	305	19	compactification	compactification	NOUN
ejpam-6597	305	20	of	of	ADP
ejpam-6597	305	21	r.	r.	PROPN
ejpam-6597	305	22	by	by	ADP
ejpam-6597	305	23	corollary	corollary	ADJ
ejpam-6597	305	24	14	14	NUM
ejpam-6597	305	25	,	,	PUNCT
ejpam-6597	305	26	x	x	X
ejpam-6597	305	27	is	be	AUX
ejpam-6597	305	28	hausdorff	hausdorff	NOUN
ejpam-6597	305	29	compact	compact	ADJ
ejpam-6597	305	30	.	.	PUNCT
ejpam-6597	306	1	hence	hence	ADV
ejpam-6597	306	2	,	,	PUNCT
ejpam-6597	306	3	x	x	PRON
ejpam-6597	306	4	is	be	AUX
ejpam-6597	306	5	collectionwise	collectionwise	ADV
ejpam-6597	306	6	pre	pre	ADJ
ejpam-6597	306	7	-	-	ADJ
ejpam-6597	306	8	normal	normal	ADJ
ejpam-6597	306	9	.	.	PUNCT
ejpam-6597	307	1	now	now	ADV
ejpam-6597	307	2	,	,	PUNCT
ejpam-6597	307	3	let	let	VERB
ejpam-6597	307	4	xr	xr	PROPN
ejpam-6597	307	5	=	=	PUNCT
ejpam-6597	307	6	r∪{p	r∪{p	PROPN
ejpam-6597	307	7	}	}	PUNCT
ejpam-6597	307	8	.	.	PUNCT
ejpam-6597	308	1	then	then	ADV
ejpam-6597	308	2	,	,	PUNCT
ejpam-6597	308	3	xr	xr	PROPN
ejpam-6597	308	4	is	be	AUX
ejpam-6597	308	5	first	first	ADV
ejpam-6597	308	6	countable	countable	ADJ
ejpam-6597	308	7	,	,	PUNCT
ejpam-6597	308	8	separable	separable	ADJ
ejpam-6597	308	9	and	and	CCONJ
ejpam-6597	308	10	tychonoff	tychonoff	NOUN
ejpam-6597	308	11	space	space	NOUN
ejpam-6597	308	12	which	which	PRON
ejpam-6597	308	13	is	be	AUX
ejpam-6597	308	14	not	not	PART
ejpam-6597	308	15	normal	normal	ADJ
ejpam-6597	308	16	and	and	CCONJ
ejpam-6597	308	17	{	{	PUNCT
ejpam-6597	308	18	p	p	X
ejpam-6597	308	19	}	}	PUNCT
ejpam-6597	308	20	is	be	AUX
ejpam-6597	308	21	clopen	clopen	ADJ
ejpam-6597	308	22	subset	subset	NOUN
ejpam-6597	309	1	[	[	X
ejpam-6597	309	2	18	18	NUM
ejpam-6597	309	3	]	]	PUNCT
ejpam-6597	309	4	.	.	PUNCT
ejpam-6597	310	1	since	since	SCONJ
ejpam-6597	310	2	r	r	NOUN
ejpam-6597	310	3	is	be	AUX
ejpam-6597	310	4	clopen	clopen	ADJ
ejpam-6597	310	5	subspace	subspace	NOUN
ejpam-6597	310	6	in	in	ADP
ejpam-6597	310	7	xr	xr	PROPN
ejpam-6597	310	8	and	and	CCONJ
ejpam-6597	310	9	r	r	NOUN
ejpam-6597	310	10	is	be	AUX
ejpam-6597	310	11	not	not	PART
ejpam-6597	310	12	pre	pre	ADJ
ejpam-6597	310	13	-	-	ADJ
ejpam-6597	310	14	normal	normal	ADJ
ejpam-6597	310	15	,	,	PUNCT
ejpam-6597	310	16	we	we	PRON
ejpam-6597	310	17	conclude	conclude	VERB
ejpam-6597	310	18	that	that	SCONJ
ejpam-6597	310	19	xr	xr	PROPN
ejpam-6597	310	20	is	be	AUX
ejpam-6597	310	21	not	not	PART
ejpam-6597	310	22	pre	pre	ADJ
ejpam-6597	310	23	-	-	ADJ
ejpam-6597	310	24	normal	normal	ADJ
ejpam-6597	310	25	.	.	PUNCT
ejpam-6597	311	1	therefore	therefore	ADV
ejpam-6597	311	2	,	,	PUNCT
ejpam-6597	311	3	xr	xr	PROPN
ejpam-6597	311	4	is	be	AUX
ejpam-6597	311	5	neither	neither	CCONJ
ejpam-6597	311	6	collectionwise	collectionwise	ADV
ejpam-6597	311	7	normal	normal	ADJ
ejpam-6597	311	8	nor	nor	CCONJ
ejpam-6597	311	9	collectionwise	collectionwise	ADV
ejpam-6597	311	10	pre	pre	ADJ
ejpam-6597	311	11	-	-	ADJ
ejpam-6597	311	12	normal	normal	ADJ
ejpam-6597	311	13	because	because	SCONJ
ejpam-6597	311	14	r	r	NOUN
ejpam-6597	311	15	with	with	ADP
ejpam-6597	311	16	the	the	DET
ejpam-6597	311	17	rational	rational	ADJ
ejpam-6597	311	18	sequence	sequence	NOUN
ejpam-6597	311	19	topology	topology	NOUN
ejpam-6597	311	20	is	be	AUX
ejpam-6597	311	21	sub	sub	ADJ
ejpam-6597	311	22	-	-	ADJ
ejpam-6597	311	23	maximal	maximal	ADJ
ejpam-6597	311	24	[	[	X
ejpam-6597	311	25	11	11	NUM
ejpam-6597	311	26	]	]	PUNCT
ejpam-6597	311	27	.	.	PUNCT
ejpam-6597	312	1	hence	hence	ADV
ejpam-6597	312	2	,	,	PUNCT
ejpam-6597	312	3	xr	xr	PROPN
ejpam-6597	312	4	is	be	AUX
ejpam-6597	312	5	a	a	DET
ejpam-6597	312	6	discrete	discrete	ADJ
ejpam-6597	312	7	extension	extension	NOUN
ejpam-6597	312	8	space	space	NOUN
ejpam-6597	312	9	of	of	ADP
ejpam-6597	312	10	a	a	DET
ejpam-6597	312	11	collectionwise	collectionwise	ADV
ejpam-6597	312	12	pre	pre	ADJ
ejpam-6597	312	13	-	-	ADJ
ejpam-6597	312	14	normal	normal	ADJ
ejpam-6597	312	15	space	space	NOUN
ejpam-6597	312	16	x	x	PUNCT
ejpam-6597	313	1	=	=	PUNCT
ejpam-6597	313	2	r	r	NOUN
ejpam-6597	313	3	∪	∪	X
ejpam-6597	313	4	{	{	PUNCT
ejpam-6597	313	5	p	p	NOUN
ejpam-6597	313	6	}	}	PUNCT
ejpam-6597	313	7	which	which	PRON
ejpam-6597	313	8	is	be	AUX
ejpam-6597	313	9	not	not	PART
ejpam-6597	313	10	collectionwise	collectionwise	ADV
ejpam-6597	313	11	pre	pre	ADJ
ejpam-6597	313	12	-	-	ADJ
ejpam-6597	313	13	normal	normal	ADJ
ejpam-6597	313	14	.	.	PUNCT
ejpam-6597	314	1	now	now	ADV
ejpam-6597	314	2	,	,	PUNCT
ejpam-6597	314	3	we	we	PRON
ejpam-6597	314	4	give	give	VERB
ejpam-6597	314	5	the	the	DET
ejpam-6597	314	6	following	follow	VERB
ejpam-6597	314	7	results	result	NOUN
ejpam-6597	314	8	:	:	PUNCT
ejpam-6597	314	9	lemma	lemma	PROPN
ejpam-6597	314	10	4	4	X
ejpam-6597	314	11	.	.	PUNCT
ejpam-6597	315	1	[	[	X
ejpam-6597	315	2	11	11	NUM
ejpam-6597	315	3	]	]	PUNCT
ejpam-6597	315	4	,	,	PUNCT
ejpam-6597	315	5	let	let	VERB
ejpam-6597	315	6	m	m	PRON
ejpam-6597	315	7	be	be	AUX
ejpam-6597	315	8	a	a	DET
ejpam-6597	315	9	closed	closed	ADJ
ejpam-6597	315	10	subspace	subspace	NOUN
ejpam-6597	315	11	of	of	ADP
ejpam-6597	315	12	x	x	X
ejpam-6597	315	13	and	and	CCONJ
ejpam-6597	315	14	a	a	DET
ejpam-6597	315	15	⊆	⊆	NUM
ejpam-6597	315	16	m	m	NOUN
ejpam-6597	315	17	.	.	PUNCT
ejpam-6597	316	1	then	then	ADV
ejpam-6597	316	2	:	:	PUNCT
ejpam-6597	316	3	if	if	SCONJ
ejpam-6597	316	4	a	a	PRON
ejpam-6597	316	5	is	be	AUX
ejpam-6597	316	6	pre	pre	ADJ
ejpam-6597	316	7	-	-	ADJ
ejpam-6597	316	8	closed	closed	ADJ
ejpam-6597	316	9	(	(	PUNCT
ejpam-6597	316	10	pre	pre	ADJ
ejpam-6597	316	11	-	-	ADJ
ejpam-6597	316	12	open	open	ADJ
ejpam-6597	316	13	)	)	PUNCT
ejpam-6597	316	14	in	in	ADP
ejpam-6597	316	15	m	m	PROPN
ejpam-6597	316	16	,	,	PUNCT
ejpam-6597	316	17	then	then	ADV
ejpam-6597	316	18	a	a	PRON
ejpam-6597	316	19	is	be	AUX
ejpam-6597	316	20	pre	pre	ADJ
ejpam-6597	316	21	-	-	ADJ
ejpam-6597	316	22	closed	closed	ADJ
ejpam-6597	316	23	(	(	PUNCT
ejpam-6597	316	24	pre	pre	ADJ
ejpam-6597	316	25	-	-	ADJ
ejpam-6597	316	26	open	open	ADJ
ejpam-6597	316	27	)	)	PUNCT
ejpam-6597	316	28	in	in	ADP
ejpam-6597	316	29	x.	x.	PROPN
ejpam-6597	316	30	lemma	lemma	PROPN
ejpam-6597	317	1	5	5	X
ejpam-6597	317	2	.	.	PUNCT
ejpam-6597	318	1	let	let	AUX
ejpam-6597	318	2	m	m	PRON
ejpam-6597	318	3	be	be	AUX
ejpam-6597	318	4	a	a	DET
ejpam-6597	318	5	closed	closed	ADJ
ejpam-6597	318	6	subspace	subspace	NOUN
ejpam-6597	318	7	of	of	ADP
ejpam-6597	318	8	x.	x.	NOUN
ejpam-6597	318	9	then	then	ADV
ejpam-6597	318	10	:	:	PUNCT
ejpam-6597	318	11	(	(	PUNCT
ejpam-6597	318	12	1	1	X
ejpam-6597	318	13	)	)	PUNCT
ejpam-6597	318	14	if	if	SCONJ
ejpam-6597	318	15	a	a	PRON
ejpam-6597	318	16	is	be	AUX
ejpam-6597	318	17	a	a	DET
ejpam-6597	318	18	pre	pre	ADJ
ejpam-6597	318	19	-	-	ADJ
ejpam-6597	318	20	closed	closed	ADJ
ejpam-6597	318	21	(	(	PUNCT
ejpam-6597	318	22	pre	pre	ADJ
ejpam-6597	318	23	-	-	ADJ
ejpam-6597	318	24	open	open	ADJ
ejpam-6597	318	25	)	)	PUNCT
ejpam-6597	318	26	set	set	VERB
ejpam-6597	318	27	in	in	ADP
ejpam-6597	318	28	x	x	NOUN
ejpam-6597	318	29	,	,	PUNCT
ejpam-6597	318	30	then	then	ADV
ejpam-6597	318	31	a	a	PRON
ejpam-6597	318	32	is	be	AUX
ejpam-6597	318	33	pre	pre	ADJ
ejpam-6597	318	34	-	-	ADJ
ejpam-6597	318	35	closed	closed	ADJ
ejpam-6597	318	36	(	(	PUNCT
ejpam-6597	318	37	pre	pre	ADJ
ejpam-6597	318	38	-	-	ADJ
ejpam-6597	318	39	open	open	ADJ
ejpam-6597	318	40	)	)	PUNCT
ejpam-6597	318	41	set	set	VERB
ejpam-6597	318	42	in	in	ADP
ejpam-6597	318	43	xm	xm	PROPN
ejpam-6597	318	44	.	.	PUNCT
ejpam-6597	319	1	(	(	PUNCT
ejpam-6597	319	2	2	2	X
ejpam-6597	319	3	)	)	PUNCT
ejpam-6597	319	4	if	if	SCONJ
ejpam-6597	319	5	a	a	PRON
ejpam-6597	319	6	is	be	AUX
ejpam-6597	319	7	a	a	DET
ejpam-6597	319	8	closed	closed	ADJ
ejpam-6597	319	9	set	set	NOUN
ejpam-6597	319	10	in	in	ADP
ejpam-6597	319	11	xm	xm	PROPN
ejpam-6597	319	12	,	,	PUNCT
ejpam-6597	319	13	then	then	ADV
ejpam-6597	319	14	a	a	DET
ejpam-6597	319	15	∩m	∩m	PROPN
ejpam-6597	319	16	is	be	AUX
ejpam-6597	319	17	closed	close	VERB
ejpam-6597	319	18	subset	subset	NOUN
ejpam-6597	319	19	of	of	ADP
ejpam-6597	319	20	a	a	DET
ejpam-6597	319	21	subspace	subspace	NOUN
ejpam-6597	319	22	m	m	VERB
ejpam-6597	319	23	in	in	ADP
ejpam-6597	319	24	x.	x.	PROPN
ejpam-6597	319	25	(	(	PUNCT
ejpam-6597	319	26	3	3	NUM
ejpam-6597	319	27	)	)	PUNCT
ejpam-6597	319	28	if	if	SCONJ
ejpam-6597	319	29	a	a	PRON
ejpam-6597	319	30	is	be	AUX
ejpam-6597	319	31	a	a	DET
ejpam-6597	319	32	closed	closed	ADJ
ejpam-6597	319	33	set	set	NOUN
ejpam-6597	319	34	in	in	ADP
ejpam-6597	319	35	xm	xm	PROPN
ejpam-6597	319	36	,	,	PUNCT
ejpam-6597	319	37	then	then	ADV
ejpam-6597	319	38	a1	a1	VERB
ejpam-6597	319	39	=	=	PUNCT
ejpam-6597	320	1	a	a	DET
ejpam-6597	320	2	∩m	∩m	NOUN
ejpam-6597	320	3	is	be	AUX
ejpam-6597	320	4	a	a	DET
ejpam-6597	320	5	closed	closed	ADJ
ejpam-6597	320	6	set	set	NOUN
ejpam-6597	320	7	in	in	ADP
ejpam-6597	320	8	x.	x.	NOUN
ejpam-6597	320	9	proof	proof	NOUN
ejpam-6597	320	10	.	.	PUNCT
ejpam-6597	321	1	let	let	VERB
ejpam-6597	321	2	m	m	PRON
ejpam-6597	321	3	be	be	AUX
ejpam-6597	321	4	a	a	DET
ejpam-6597	321	5	closed	closed	ADJ
ejpam-6597	321	6	subspace	subspace	NOUN
ejpam-6597	321	7	of	of	ADP
ejpam-6597	321	8	x.	x.	PROPN
ejpam-6597	321	9	(	(	PUNCT
ejpam-6597	321	10	1	1	X
ejpam-6597	321	11	)	)	PUNCT
ejpam-6597	321	12	let	let	VERB
ejpam-6597	321	13	a	a	PRON
ejpam-6597	321	14	be	be	AUX
ejpam-6597	321	15	a	a	DET
ejpam-6597	321	16	pre	pre	ADJ
ejpam-6597	321	17	-	-	ADJ
ejpam-6597	321	18	closed	closed	ADJ
ejpam-6597	321	19	(	(	PUNCT
ejpam-6597	321	20	pre	pre	ADJ
ejpam-6597	321	21	-	-	ADJ
ejpam-6597	321	22	open	open	ADJ
ejpam-6597	321	23	)	)	PUNCT
ejpam-6597	321	24	set	set	VERB
ejpam-6597	321	25	in	in	ADP
ejpam-6597	321	26	x.	x.	NOUN
ejpam-6597	321	27	since	since	SCONJ
ejpam-6597	321	28	x	x	PROPN
ejpam-6597	321	29	⊂	⊂	PROPN
ejpam-6597	321	30	xm	xm	PROPN
ejpam-6597	321	31	is	be	AUX
ejpam-6597	321	32	a	a	DET
ejpam-6597	321	33	closed	closed	ADJ
ejpam-6597	321	34	subspace	subspace	NOUN
ejpam-6597	321	35	of	of	ADP
ejpam-6597	321	36	xm	xm	PROPN
ejpam-6597	322	1	[	[	X
ejpam-6597	322	2	18	18	NUM
ejpam-6597	322	3	]	]	PUNCT
ejpam-6597	322	4	,	,	PUNCT
ejpam-6597	322	5	and	and	CCONJ
ejpam-6597	322	6	a	a	PRON
ejpam-6597	322	7	is	be	AUX
ejpam-6597	322	8	pre	pre	ADJ
ejpam-6597	322	9	-	-	ADJ
ejpam-6597	322	10	closed	closed	ADJ
ejpam-6597	322	11	(	(	PUNCT
ejpam-6597	322	12	pre	pre	ADJ
ejpam-6597	322	13	-	-	ADJ
ejpam-6597	322	14	open	open	ADJ
ejpam-6597	322	15	)	)	PUNCT
ejpam-6597	322	16	in	in	ADP
ejpam-6597	322	17	x	x	NOUN
ejpam-6597	322	18	,	,	PUNCT
ejpam-6597	322	19	by	by	ADP
ejpam-6597	322	20	lemma	lemma	PROPN
ejpam-6597	322	21	4	4	NUM
ejpam-6597	322	22	we	we	PRON
ejpam-6597	322	23	conclude	conclude	VERB
ejpam-6597	322	24	that	that	SCONJ
ejpam-6597	322	25	a	a	PRON
ejpam-6597	322	26	is	be	AUX
ejpam-6597	322	27	pre	pre	ADJ
ejpam-6597	322	28	-	-	ADJ
ejpam-6597	322	29	closed	closed	ADJ
ejpam-6597	322	30	(	(	PUNCT
ejpam-6597	322	31	pre	pre	ADJ
ejpam-6597	322	32	-	-	ADJ
ejpam-6597	322	33	open	open	ADJ
ejpam-6597	322	34	)	)	PUNCT
ejpam-6597	322	35	in	in	ADP
ejpam-6597	322	36	xm	xm	PROPN
ejpam-6597	322	37	.	.	PUNCT
ejpam-6597	323	1	(	(	PUNCT
ejpam-6597	323	2	2	2	X
ejpam-6597	323	3	)	)	PUNCT
ejpam-6597	323	4	let	let	VERB
ejpam-6597	323	5	a	a	DET
ejpam-6597	323	6	be	be	AUX
ejpam-6597	323	7	a	a	DET
ejpam-6597	323	8	closed	closed	ADJ
ejpam-6597	323	9	set	set	NOUN
ejpam-6597	323	10	in	in	ADP
ejpam-6597	323	11	xm	xm	PROPN
ejpam-6597	323	12	.	.	PUNCT
ejpam-6597	324	1	since	since	SCONJ
ejpam-6597	324	2	m	m	PROPN
ejpam-6597	324	3	⊂	⊂	PROPN
ejpam-6597	324	4	xm	xm	PROPN
ejpam-6597	324	5	is	be	AUX
ejpam-6597	324	6	closed	close	VERB
ejpam-6597	324	7	in	in	ADP
ejpam-6597	324	8	both	both	PRON
ejpam-6597	324	9	x	x	X
ejpam-6597	324	10	and	and	CCONJ
ejpam-6597	324	11	xm	xm	PROPN
ejpam-6597	324	12	and	and	CCONJ
ejpam-6597	324	13	its	its	PRON
ejpam-6597	324	14	topology	topology	NOUN
ejpam-6597	324	15	coincides	coincide	VERB
ejpam-6597	324	16	with	with	ADP
ejpam-6597	324	17	the	the	DET
ejpam-6597	324	18	topology	topology	NOUN
ejpam-6597	324	19	on	on	ADP
ejpam-6597	324	20	m	m	NOUN
ejpam-6597	324	21	by	by	ADP
ejpam-6597	324	22	the	the	DET
ejpam-6597	324	23	topology	topology	NOUN
ejpam-6597	324	24	on	on	ADP
ejpam-6597	324	25	x	x	SYM
ejpam-6597	324	26	,	,	PUNCT
ejpam-6597	324	27	i.e.	i.e.	X
ejpam-6597	324	28	tm	tm	X
ejpam-6597	324	29	=	=	PROPN
ejpam-6597	324	30	t(m)m	t(m)m	PROPN
ejpam-6597	325	1	[	[	X
ejpam-6597	325	2	18	18	NUM
ejpam-6597	325	3	]	]	PUNCT
ejpam-6597	325	4	,	,	PUNCT
ejpam-6597	325	5	we	we	PRON
ejpam-6597	325	6	get	get	VERB
ejpam-6597	325	7	a	a	DET
ejpam-6597	325	8	∩m	∩m	NOUN
ejpam-6597	325	9	is	be	AUX
ejpam-6597	325	10	a	a	DET
ejpam-6597	325	11	closed	closed	ADJ
ejpam-6597	325	12	subset	subset	NOUN
ejpam-6597	325	13	of	of	ADP
ejpam-6597	325	14	a	a	DET
ejpam-6597	325	15	subspace	subspace	NOUN
ejpam-6597	325	16	m	m	VERB
ejpam-6597	325	17	in	in	ADP
ejpam-6597	325	18	xm	xm	PROPN
ejpam-6597	325	19	.	.	PUNCT
ejpam-6597	326	1	since	since	SCONJ
ejpam-6597	326	2	tm	tm	PROPN
ejpam-6597	326	3	=	=	PROPN
ejpam-6597	326	4	t(m)m	t(m)m	PROPN
ejpam-6597	326	5	,	,	PUNCT
ejpam-6597	326	6	a	a	DET
ejpam-6597	326	7	∩m	∩m	PROPN
ejpam-6597	326	8	is	be	AUX
ejpam-6597	326	9	a	a	DET
ejpam-6597	326	10	closed	closed	ADJ
ejpam-6597	326	11	subset	subset	NOUN
ejpam-6597	326	12	of	of	ADP
ejpam-6597	326	13	a	a	DET
ejpam-6597	326	14	subspace	subspace	NOUN
ejpam-6597	326	15	m	m	VERB
ejpam-6597	326	16	in	in	ADP
ejpam-6597	326	17	x.	x.	PROPN
ejpam-6597	326	18	(	(	PUNCT
ejpam-6597	326	19	3	3	X
ejpam-6597	326	20	)	)	PUNCT
ejpam-6597	326	21	let	let	VERB
ejpam-6597	326	22	a	a	DET
ejpam-6597	326	23	be	be	AUX
ejpam-6597	326	24	a	a	DET
ejpam-6597	326	25	closed	closed	ADJ
ejpam-6597	326	26	set	set	NOUN
ejpam-6597	326	27	in	in	ADP
ejpam-6597	326	28	xm	xm	PROPN
ejpam-6597	326	29	.	.	PUNCT
ejpam-6597	327	1	by	by	ADP
ejpam-6597	327	2	part	part	NOUN
ejpam-6597	327	3	(	(	PUNCT
ejpam-6597	327	4	2	2	NUM
ejpam-6597	327	5	)	)	PUNCT
ejpam-6597	327	6	,	,	PUNCT
ejpam-6597	327	7	a1	a1	NOUN
ejpam-6597	327	8	=	=	PUNCT
ejpam-6597	327	9	a	a	DET
ejpam-6597	327	10	∩	∩	NOUN
ejpam-6597	327	11	m	m	VERB
ejpam-6597	327	12	is	be	AUX
ejpam-6597	327	13	a	a	DET
ejpam-6597	327	14	closed	closed	ADJ
ejpam-6597	327	15	subset	subset	NOUN
ejpam-6597	327	16	of	of	ADP
ejpam-6597	327	17	a	a	DET
ejpam-6597	327	18	subspace	subspace	NOUN
ejpam-6597	327	19	m	m	VERB
ejpam-6597	327	20	in	in	ADP
ejpam-6597	327	21	x.	x.	NOUN
ejpam-6597	327	22	since	since	SCONJ
ejpam-6597	327	23	m	m	PROPN
ejpam-6597	327	24	is	be	AUX
ejpam-6597	327	25	closed	close	VERB
ejpam-6597	327	26	subspace	subspace	NOUN
ejpam-6597	327	27	of	of	ADP
ejpam-6597	327	28	x	x	PUNCT
ejpam-6597	327	29	and	and	CCONJ
ejpam-6597	327	30	a	a	DET
ejpam-6597	327	31	∩m	∩m	NOUN
ejpam-6597	327	32	is	be	AUX
ejpam-6597	327	33	closed	close	VERB
ejpam-6597	327	34	subset	subset	NOUN
ejpam-6597	327	35	of	of	ADP
ejpam-6597	327	36	m	m	PROPN
ejpam-6597	327	37	in	in	ADP
ejpam-6597	327	38	x	x	PRON
ejpam-6597	327	39	,	,	PUNCT
ejpam-6597	327	40	we	we	PRON
ejpam-6597	327	41	have	have	VERB
ejpam-6597	327	42	a1	a1	NOUN
ejpam-6597	327	43	=	=	PUNCT
ejpam-6597	327	44	a	a	DET
ejpam-6597	327	45	∩m	∩m	NOUN
ejpam-6597	327	46	is	be	AUX
ejpam-6597	327	47	a	a	DET
ejpam-6597	327	48	closed	closed	ADJ
ejpam-6597	327	49	set	set	NOUN
ejpam-6597	327	50	in	in	ADP
ejpam-6597	327	51	x.	x.	PROPN
ejpam-6597	327	52	s.	s.	PROPN
ejpam-6597	327	53	a.	a.	PROPN
ejpam-6597	327	54	thabit	thabit	PROPN
ejpam-6597	327	55	,	,	PUNCT
ejpam-6597	327	56	a.	a.	PROPN
ejpam-6597	327	57	al	al	PROPN
ejpam-6597	327	58	-	-	PUNCT
ejpam-6597	327	59	awadi	awadi	PROPN
ejpam-6597	327	60	,	,	PUNCT
ejpam-6597	327	61	r.	r.	PROPN
ejpam-6597	327	62	noaman	noaman	PROPN
ejpam-6597	327	63	/	/	SYM
ejpam-6597	327	64	eur	eur	PROPN
ejpam-6597	327	65	.	.	PUNCT
ejpam-6597	328	1	j.	j.	PROPN
ejpam-6597	328	2	pure	pure	PROPN
ejpam-6597	328	3	appl	appl	PROPN
ejpam-6597	328	4	.	.	PROPN
ejpam-6597	328	5	math	math	PROPN
ejpam-6597	328	6	,	,	PUNCT
ejpam-6597	328	7	18	18	NUM
ejpam-6597	328	8	(	(	PUNCT
ejpam-6597	328	9	4	4	NUM
ejpam-6597	328	10	)	)	PUNCT
ejpam-6597	328	11	(	(	PUNCT
ejpam-6597	328	12	2025	2025	NUM
ejpam-6597	328	13	)	)	PUNCT
ejpam-6597	328	14	,	,	PUNCT
ejpam-6597	328	15	6597	6597	NUM
ejpam-6597	328	16	13	13	NUM
ejpam-6597	328	17	of	of	ADP
ejpam-6597	328	18	15	15	NUM
ejpam-6597	328	19	lemma	lemma	PROPN
ejpam-6597	328	20	6	6	NUM
ejpam-6597	328	21	.	.	PUNCT
ejpam-6597	329	1	let	let	VERB
ejpam-6597	329	2	m	m	PRON
ejpam-6597	329	3	be	be	AUX
ejpam-6597	329	4	a	a	DET
ejpam-6597	329	5	closed	closed	ADJ
ejpam-6597	329	6	subspace	subspace	NOUN
ejpam-6597	329	7	of	of	ADP
ejpam-6597	329	8	a	a	DET
ejpam-6597	329	9	space	space	NOUN
ejpam-6597	329	10	x.	x.	NOUN
ejpam-6597	329	11	then	then	ADV
ejpam-6597	329	12	:	:	PUNCT
ejpam-6597	329	13	if	if	SCONJ
ejpam-6597	329	14	{	{	PUNCT
ejpam-6597	329	15	fs}s∈s	fs}s∈s	X
ejpam-6597	329	16	is	be	AUX
ejpam-6597	329	17	a	a	DET
ejpam-6597	329	18	discrete	discrete	ADJ
ejpam-6597	329	19	family	family	NOUN
ejpam-6597	329	20	of	of	ADP
ejpam-6597	329	21	closed	closed	ADJ
ejpam-6597	329	22	sets	set	NOUN
ejpam-6597	329	23	in	in	ADP
ejpam-6597	329	24	xm	xm	PROPN
ejpam-6597	329	25	,	,	PUNCT
ejpam-6597	329	26	then	then	ADV
ejpam-6597	329	27	{	{	PUNCT
ejpam-6597	329	28	fs	fs	ADP
ejpam-6597	329	29	∩m}s∈s	∩m}s∈s	PROPN
ejpam-6597	329	30	is	be	AUX
ejpam-6597	329	31	a	a	DET
ejpam-6597	329	32	discrete	discrete	ADJ
ejpam-6597	329	33	family	family	NOUN
ejpam-6597	329	34	of	of	ADP
ejpam-6597	329	35	closed	closed	ADJ
ejpam-6597	329	36	sets	set	NOUN
ejpam-6597	329	37	in	in	ADP
ejpam-6597	329	38	x.	x.	NOUN
ejpam-6597	329	39	proof	proof	NOUN
ejpam-6597	329	40	.	.	PUNCT
ejpam-6597	330	1	let	let	VERB
ejpam-6597	330	2	m	m	PRON
ejpam-6597	330	3	be	be	AUX
ejpam-6597	330	4	a	a	DET
ejpam-6597	330	5	closed	closed	ADJ
ejpam-6597	330	6	subspace	subspace	NOUN
ejpam-6597	330	7	of	of	ADP
ejpam-6597	330	8	x	x	PUNCT
ejpam-6597	330	9	and	and	CCONJ
ejpam-6597	330	10	{	{	PUNCT
ejpam-6597	330	11	fs}s∈s	fs}s∈s	X
ejpam-6597	330	12	be	be	AUX
ejpam-6597	330	13	a	a	DET
ejpam-6597	330	14	discrete	discrete	ADJ
ejpam-6597	330	15	family	family	NOUN
ejpam-6597	330	16	of	of	ADP
ejpam-6597	330	17	closed	closed	ADJ
ejpam-6597	330	18	sets	set	NOUN
ejpam-6597	330	19	in	in	ADP
ejpam-6597	330	20	xm	xm	PROPN
ejpam-6597	330	21	.	.	PUNCT
ejpam-6597	331	1	then	then	ADV
ejpam-6597	331	2	,	,	PUNCT
ejpam-6597	331	3	fs	fs	X
ejpam-6597	331	4	is	be	AUX
ejpam-6597	331	5	closed	close	VERB
ejpam-6597	331	6	set	set	VERB
ejpam-6597	331	7	in	in	ADP
ejpam-6597	331	8	xm	xm	PROPN
ejpam-6597	331	9	for	for	ADP
ejpam-6597	331	10	each	each	DET
ejpam-6597	331	11	s	s	PROPN
ejpam-6597	331	12	∈	∈	PROPN
ejpam-6597	331	13	s.	s.	PROPN
ejpam-6597	331	14	by	by	ADP
ejpam-6597	331	15	lemma	lemma	PROPN
ejpam-6597	331	16	5	5	NUM
ejpam-6597	331	17	,	,	PUNCT
ejpam-6597	331	18	we	we	PRON
ejpam-6597	331	19	get	get	VERB
ejpam-6597	331	20	fs∩m	fs∩m	NOUN
ejpam-6597	332	1	is	be	AUX
ejpam-6597	332	2	closed	close	VERB
ejpam-6597	332	3	subset	subset	NOUN
ejpam-6597	332	4	of	of	ADP
ejpam-6597	332	5	a	a	DET
ejpam-6597	332	6	subspace	subspace	NOUN
ejpam-6597	332	7	m	m	VERB
ejpam-6597	332	8	in	in	ADP
ejpam-6597	332	9	x	x	PUNCT
ejpam-6597	332	10	for	for	SCONJ
ejpam-6597	332	11	each	each	DET
ejpam-6597	332	12	s	s	PROPN
ejpam-6597	332	13	∈	∈	PROPN
ejpam-6597	332	14	s.	s.	PROPN
ejpam-6597	332	15	put	put	VERB
ejpam-6597	332	16	gs	gs	NOUN
ejpam-6597	332	17	=	=	PUNCT
ejpam-6597	332	18	fs	fs	X
ejpam-6597	332	19	∩	∩	NOUN
ejpam-6597	332	20	m	m	VERB
ejpam-6597	332	21	for	for	ADP
ejpam-6597	332	22	each	each	DET
ejpam-6597	332	23	s	s	PROPN
ejpam-6597	332	24	∈	∈	PROPN
ejpam-6597	332	25	s.	s.	PROPN
ejpam-6597	332	26	then	then	ADV
ejpam-6597	332	27	,	,	PUNCT
ejpam-6597	332	28	{	{	PUNCT
ejpam-6597	332	29	gs}s∈s	gs}s∈s	NOUN
ejpam-6597	332	30	is	be	AUX
ejpam-6597	332	31	a	a	DET
ejpam-6597	332	32	family	family	NOUN
ejpam-6597	332	33	of	of	ADP
ejpam-6597	332	34	closed	closed	ADJ
ejpam-6597	332	35	subsets	subset	NOUN
ejpam-6597	332	36	of	of	ADP
ejpam-6597	332	37	x.	x.	NOUN
ejpam-6597	332	38	since	since	SCONJ
ejpam-6597	332	39	{	{	PUNCT
ejpam-6597	332	40	fs}s∈s	fs}s∈s	X
ejpam-6597	332	41	is	be	AUX
ejpam-6597	332	42	a	a	DET
ejpam-6597	332	43	discrete	discrete	ADJ
ejpam-6597	332	44	family	family	NOUN
ejpam-6597	332	45	,	,	PUNCT
ejpam-6597	332	46	x	x	PROPN
ejpam-6597	332	47	=	=	PUNCT
ejpam-6597	332	48	xm	xm	PROPN
ejpam-6597	332	49	,	,	PUNCT
ejpam-6597	332	50	t	t	PROPN
ejpam-6597	332	51	⊆	⊆	NUM
ejpam-6597	332	52	t(m	t(m	PROPN
ejpam-6597	332	53	)	)	PUNCT
ejpam-6597	332	54	and	and	CCONJ
ejpam-6597	332	55	gs	gs	INTJ
ejpam-6597	332	56	⊆	⊆	NUM
ejpam-6597	332	57	fs	f	NOUN
ejpam-6597	332	58	for	for	ADP
ejpam-6597	332	59	each	each	DET
ejpam-6597	332	60	s	s	X
ejpam-6597	332	61	∈	∈	PROPN
ejpam-6597	332	62	s	s	NOUN
ejpam-6597	332	63	,	,	PUNCT
ejpam-6597	332	64	we	we	PRON
ejpam-6597	332	65	obtain	obtain	AUX
ejpam-6597	332	66	{	{	PUNCT
ejpam-6597	332	67	gs}s∈s	gs}s∈s	VERB
ejpam-6597	332	68	is	be	AUX
ejpam-6597	332	69	a	a	DET
ejpam-6597	332	70	discrete	discrete	ADJ
ejpam-6597	332	71	family	family	NOUN
ejpam-6597	332	72	of	of	ADP
ejpam-6597	332	73	closed	closed	ADJ
ejpam-6597	332	74	subsets	subset	NOUN
ejpam-6597	332	75	of	of	ADP
ejpam-6597	332	76	x.	x.	NOUN
ejpam-6597	332	77	hence	hence	ADV
ejpam-6597	332	78	,	,	PUNCT
ejpam-6597	332	79	{	{	PUNCT
ejpam-6597	332	80	fs	fs	ADP
ejpam-6597	332	81	∩m}s∈s	∩m}s∈s	PROPN
ejpam-6597	332	82	is	be	AUX
ejpam-6597	332	83	a	a	DET
ejpam-6597	332	84	discrete	discrete	ADJ
ejpam-6597	332	85	family	family	NOUN
ejpam-6597	332	86	of	of	ADP
ejpam-6597	332	87	closed	closed	ADJ
ejpam-6597	332	88	sets	set	NOUN
ejpam-6597	332	89	in	in	ADP
ejpam-6597	332	90	x.	x.	NOUN
ejpam-6597	332	91	theorem	theorem	VERB
ejpam-6597	332	92	19	19	NUM
ejpam-6597	332	93	.	.	PUNCT
ejpam-6597	333	1	if	if	SCONJ
ejpam-6597	333	2	x	x	PRON
ejpam-6597	333	3	is	be	AUX
ejpam-6597	333	4	collectionwise	collectionwise	ADV
ejpam-6597	333	5	pre	pre	ADJ
ejpam-6597	333	6	-	-	ADJ
ejpam-6597	333	7	normal	normal	ADJ
ejpam-6597	333	8	and	and	CCONJ
ejpam-6597	333	9	m	m	VERB
ejpam-6597	333	10	is	be	AUX
ejpam-6597	333	11	a	a	DET
ejpam-6597	333	12	closed	closed	ADJ
ejpam-6597	333	13	subspace	subspace	NOUN
ejpam-6597	333	14	of	of	ADP
ejpam-6597	333	15	x	x	PRON
ejpam-6597	333	16	,	,	PUNCT
ejpam-6597	333	17	then	then	ADV
ejpam-6597	333	18	xm	xm	PROPN
ejpam-6597	333	19	is	be	AUX
ejpam-6597	333	20	collectionwise	collectionwise	ADV
ejpam-6597	333	21	pre	pre	ADJ
ejpam-6597	333	22	-	-	ADJ
ejpam-6597	333	23	normal	normal	ADJ
ejpam-6597	333	24	.	.	PUNCT
ejpam-6597	334	1	proof	proof	NOUN
ejpam-6597	334	2	.	.	PUNCT
ejpam-6597	335	1	let	let	VERB
ejpam-6597	335	2	{	{	PUNCT
ejpam-6597	335	3	fs}s∈s	fs}s∈s	PART
ejpam-6597	335	4	be	be	AUX
ejpam-6597	335	5	a	a	DET
ejpam-6597	335	6	discrete	discrete	ADJ
ejpam-6597	335	7	family	family	NOUN
ejpam-6597	335	8	of	of	ADP
ejpam-6597	335	9	closed	closed	ADJ
ejpam-6597	335	10	sets	set	NOUN
ejpam-6597	335	11	in	in	ADP
ejpam-6597	335	12	xm	xm	PROPN
ejpam-6597	335	13	.	.	PUNCT
ejpam-6597	336	1	since	since	SCONJ
ejpam-6597	336	2	m	m	PROPN
ejpam-6597	336	3	is	be	AUX
ejpam-6597	336	4	closed	close	VERB
ejpam-6597	336	5	in	in	ADP
ejpam-6597	336	6	x	x	NOUN
ejpam-6597	336	7	,	,	PUNCT
ejpam-6597	336	8	by	by	ADP
ejpam-6597	336	9	lemma	lemma	PROPN
ejpam-6597	336	10	6	6	NUM
ejpam-6597	336	11	we	we	PRON
ejpam-6597	336	12	get	get	VERB
ejpam-6597	336	13	{	{	PUNCT
ejpam-6597	336	14	fs∩m}s∈s	fs∩m}s∈s	PROPN
ejpam-6597	336	15	is	be	AUX
ejpam-6597	336	16	a	a	DET
ejpam-6597	336	17	discrete	discrete	ADJ
ejpam-6597	336	18	family	family	NOUN
ejpam-6597	336	19	of	of	ADP
ejpam-6597	336	20	closed	closed	ADJ
ejpam-6597	336	21	sets	set	NOUN
ejpam-6597	336	22	in	in	ADP
ejpam-6597	336	23	x.	x.	NOUN
ejpam-6597	336	24	by	by	ADP
ejpam-6597	336	25	collectionwise	collectionwise	PROPN
ejpam-6597	336	26	pre	pre	PROPN
ejpam-6597	336	27	-	-	NOUN
ejpam-6597	336	28	normality	normality	NOUN
ejpam-6597	336	29	of	of	ADP
ejpam-6597	336	30	x	x	NOUN
ejpam-6597	336	31	,	,	PUNCT
ejpam-6597	336	32	there	there	PRON
ejpam-6597	336	33	exists	exist	VERB
ejpam-6597	336	34	a	a	DET
ejpam-6597	336	35	discrete	discrete	ADJ
ejpam-6597	336	36	family	family	NOUN
ejpam-6597	336	37	{	{	PUNCT
ejpam-6597	336	38	us}s∈s	us}s∈s	PROPN
ejpam-6597	336	39	of	of	ADP
ejpam-6597	336	40	pre	pre	ADJ
ejpam-6597	336	41	-	-	ADJ
ejpam-6597	336	42	open	open	ADJ
ejpam-6597	336	43	sets	set	NOUN
ejpam-6597	336	44	in	in	ADP
ejpam-6597	336	45	x	x	SYM
ejpam-6597	336	46	such	such	ADJ
ejpam-6597	336	47	that	that	DET
ejpam-6597	336	48	fs∩m	fs∩m	NOUN
ejpam-6597	336	49	⊆	⊆	NUM
ejpam-6597	336	50	us	we	PRON
ejpam-6597	336	51	for	for	ADP
ejpam-6597	336	52	each	each	DET
ejpam-6597	336	53	s	s	PROPN
ejpam-6597	336	54	∈	∈	PROPN
ejpam-6597	336	55	s.	s.	PROPN
ejpam-6597	336	56	let	let	VERB
ejpam-6597	336	57	vs	vs	ADP
ejpam-6597	336	58	=	=	PUNCT
ejpam-6597	336	59	us∪fs	us∪fs	PROPN
ejpam-6597	336	60	\m	\m	NOUN
ejpam-6597	336	61	for	for	ADP
ejpam-6597	336	62	each	each	DET
ejpam-6597	336	63	s	s	PROPN
ejpam-6597	336	64	∈	∈	PROPN
ejpam-6597	336	65	s.	s.	PROPN
ejpam-6597	336	66	then	then	ADV
ejpam-6597	336	67	,	,	PUNCT
ejpam-6597	336	68	vs	vs	ADP
ejpam-6597	336	69	is	be	AUX
ejpam-6597	336	70	pre	pre	ADJ
ejpam-6597	336	71	-	-	ADJ
ejpam-6597	336	72	open	open	ADJ
ejpam-6597	336	73	set	set	NOUN
ejpam-6597	336	74	in	in	ADP
ejpam-6597	336	75	xm	xm	PROPN
ejpam-6597	336	76	and	and	CCONJ
ejpam-6597	336	77	fs	fs	ADP
ejpam-6597	336	78	⊆	⊆	NUM
ejpam-6597	336	79	vs	vs	ADP
ejpam-6597	336	80	for	for	ADP
ejpam-6597	336	81	each	each	DET
ejpam-6597	336	82	s	s	PROPN
ejpam-6597	336	83	∈	∈	PROPN
ejpam-6597	336	84	s.	s.	PROPN
ejpam-6597	336	85	observe	observe	VERB
ejpam-6597	336	86	that	that	SCONJ
ejpam-6597	336	87	{	{	PUNCT
ejpam-6597	336	88	vs	vs	ADP
ejpam-6597	336	89	:	:	PUNCT
ejpam-6597	336	90	s	s	X
ejpam-6597	336	91	∈	∈	PROPN
ejpam-6597	336	92	s	s	AUX
ejpam-6597	336	93	}	}	PUNCT
ejpam-6597	336	94	is	be	AUX
ejpam-6597	336	95	discrete	discrete	ADJ
ejpam-6597	336	96	.	.	PUNCT
ejpam-6597	337	1	hence	hence	ADV
ejpam-6597	337	2	,	,	PUNCT
ejpam-6597	337	3	{	{	PUNCT
ejpam-6597	337	4	vs}s∈s	vs}s∈s	NOUN
ejpam-6597	337	5	is	be	AUX
ejpam-6597	337	6	a	a	DET
ejpam-6597	337	7	discrete	discrete	ADJ
ejpam-6597	337	8	family	family	NOUN
ejpam-6597	337	9	of	of	ADP
ejpam-6597	337	10	pre	pre	ADJ
ejpam-6597	337	11	-	-	ADJ
ejpam-6597	337	12	open	open	ADJ
ejpam-6597	337	13	sets	set	NOUN
ejpam-6597	337	14	in	in	ADP
ejpam-6597	337	15	xm	xm	PROPN
ejpam-6597	337	16	such	such	ADJ
ejpam-6597	337	17	that	that	SCONJ
ejpam-6597	337	18	fs	fs	ADP
ejpam-6597	337	19	⊆	⊆	NUM
ejpam-6597	337	20	vs	vs	ADP
ejpam-6597	337	21	for	for	ADP
ejpam-6597	337	22	each	each	DET
ejpam-6597	337	23	s	s	PART
ejpam-6597	337	24	∈	∈	PROPN
ejpam-6597	337	25	s.	s.	PROPN
ejpam-6597	337	26	therefore	therefore	ADV
ejpam-6597	337	27	,	,	PUNCT
ejpam-6597	337	28	xm	xm	PROPN
ejpam-6597	337	29	is	be	AUX
ejpam-6597	337	30	collectionwise	collectionwise	ADV
ejpam-6597	337	31	pre	pre	ADJ
ejpam-6597	337	32	-	-	ADJ
ejpam-6597	337	33	normal	normal	ADJ
ejpam-6597	337	34	.	.	PUNCT
ejpam-6597	338	1	since	since	SCONJ
ejpam-6597	338	2	the	the	DET
ejpam-6597	338	3	closed	closed	ADJ
ejpam-6597	338	4	extension	extension	NOUN
ejpam-6597	338	5	space	space	NOUN
ejpam-6597	338	6	(	(	PUNCT
ejpam-6597	338	7	xp	xp	INTJ
ejpam-6597	338	8	,	,	PUNCT
ejpam-6597	338	9	t	t	PROPN
ejpam-6597	338	10	∗	∗	NOUN
ejpam-6597	338	11	)	)	PUNCT
ejpam-6597	338	12	of	of	ADP
ejpam-6597	338	13	a	a	DET
ejpam-6597	338	14	space	space	NOUN
ejpam-6597	338	15	(	(	PUNCT
ejpam-6597	338	16	x	x	X
ejpam-6597	338	17	,	,	PUNCT
ejpam-6597	338	18	t	t	PROPN
ejpam-6597	338	19	)	)	PUNCT
ejpam-6597	338	20	is	be	AUX
ejpam-6597	338	21	separable	separable	ADJ
ejpam-6597	338	22	,	,	PUNCT
ejpam-6597	338	23	first	first	ADV
ejpam-6597	338	24	countable	countable	ADJ
ejpam-6597	338	25	,	,	PUNCT
ejpam-6597	338	26	second	second	ADV
ejpam-6597	338	27	countable	countable	ADJ
ejpam-6597	338	28	and	and	CCONJ
ejpam-6597	338	29	t0	t0	NOUN
ejpam-6597	338	30	-	-	NOUN
ejpam-6597	338	31	space	space	NOUN
ejpam-6597	338	32	which	which	PRON
ejpam-6597	338	33	is	be	AUX
ejpam-6597	338	34	neither	neither	CCONJ
ejpam-6597	338	35	t1	t1	NOUN
ejpam-6597	338	36	,	,	PUNCT
ejpam-6597	338	37	hausdorff	hausdorff	NOUN
ejpam-6597	338	38	,	,	PUNCT
ejpam-6597	338	39	regular	regular	ADJ
ejpam-6597	338	40	nor	nor	CCONJ
ejpam-6597	338	41	normal	normal	ADJ
ejpam-6597	338	42	[	[	X
ejpam-6597	338	43	19	19	NUM
ejpam-6597	338	44	]	]	PUNCT
ejpam-6597	338	45	,	,	PUNCT
ejpam-6597	338	46	we	we	PRON
ejpam-6597	338	47	get	get	VERB
ejpam-6597	338	48	the	the	DET
ejpam-6597	338	49	next	next	ADJ
ejpam-6597	338	50	corollary	corollary	NOUN
ejpam-6597	338	51	:	:	PUNCT
ejpam-6597	338	52	corollary	corollary	ADJ
ejpam-6597	338	53	15	15	NUM
ejpam-6597	338	54	.	.	PUNCT
ejpam-6597	339	1	any	any	DET
ejpam-6597	339	2	closed	close	VERB
ejpam-6597	339	3	extension	extension	NOUN
ejpam-6597	339	4	space	space	NOUN
ejpam-6597	339	5	(	(	PUNCT
ejpam-6597	339	6	xp	xp	INTJ
ejpam-6597	339	7	,	,	PUNCT
ejpam-6597	339	8	t	t	PROPN
ejpam-6597	339	9	∗	∗	NOUN
ejpam-6597	339	10	)	)	PUNCT
ejpam-6597	339	11	of	of	ADP
ejpam-6597	339	12	a	a	DET
ejpam-6597	339	13	collectionwise	collectionwise	ADV
ejpam-6597	339	14	pre	pre	ADJ
ejpam-6597	339	15	-	-	ADJ
ejpam-6597	339	16	normal	normal	ADJ
ejpam-6597	339	17	space	space	NOUN
ejpam-6597	339	18	(	(	PUNCT
ejpam-6597	339	19	x	x	X
ejpam-6597	339	20	,	,	PUNCT
ejpam-6597	339	21	t	t	PROPN
ejpam-6597	339	22	)	)	PUNCT
ejpam-6597	339	23	can	can	AUX
ejpam-6597	339	24	not	not	PART
ejpam-6597	339	25	be	be	AUX
ejpam-6597	339	26	collectionwise	collectionwise	ADV
ejpam-6597	339	27	pre	pre	ADJ
ejpam-6597	339	28	-	-	ADJ
ejpam-6597	339	29	normal	normal	ADJ
ejpam-6597	339	30	.	.	PUNCT
ejpam-6597	340	1	that	that	PRON
ejpam-6597	340	2	is	be	AUX
ejpam-6597	340	3	:	:	PUNCT
ejpam-6597	340	4	collectionwise	collectionwise	ADV
ejpam-6597	340	5	pre	pre	ADJ
ejpam-6597	340	6	-	-	ADJ
ejpam-6597	340	7	normality	normality	ADJ
ejpam-6597	340	8	is	be	AUX
ejpam-6597	340	9	not	not	PART
ejpam-6597	340	10	preserved	preserve	VERB
ejpam-6597	340	11	by	by	ADP
ejpam-6597	340	12	the	the	DET
ejpam-6597	340	13	closed	closed	ADJ
ejpam-6597	340	14	extension	extension	NOUN
ejpam-6597	340	15	spaces	space	NOUN
ejpam-6597	340	16	.	.	PUNCT
ejpam-6597	341	1	proof	proof	NOUN
ejpam-6597	341	2	.	.	PUNCT
ejpam-6597	342	1	since	since	SCONJ
ejpam-6597	342	2	the	the	DET
ejpam-6597	342	3	closed	closed	ADJ
ejpam-6597	342	4	extension	extension	NOUN
ejpam-6597	342	5	space	space	NOUN
ejpam-6597	342	6	(	(	PUNCT
ejpam-6597	342	7	xp	xp	INTJ
ejpam-6597	342	8	,	,	PUNCT
ejpam-6597	342	9	t	t	PROPN
ejpam-6597	342	10	∗	∗	NOUN
ejpam-6597	342	11	)	)	PUNCT
ejpam-6597	342	12	of	of	ADP
ejpam-6597	342	13	a	a	DET
ejpam-6597	342	14	space	space	NOUN
ejpam-6597	342	15	(	(	PUNCT
ejpam-6597	342	16	x	x	X
ejpam-6597	342	17	,	,	PUNCT
ejpam-6597	342	18	t	t	PROPN
ejpam-6597	342	19	)	)	PUNCT
ejpam-6597	342	20	is	be	AUX
ejpam-6597	342	21	not	not	PART
ejpam-6597	342	22	t1	t1	NOUN
ejpam-6597	342	23	-	-	NOUN
ejpam-6597	342	24	space	space	NOUN
ejpam-6597	342	25	,	,	PUNCT
ejpam-6597	342	26	and	and	CCONJ
ejpam-6597	342	27	every	every	DET
ejpam-6597	342	28	collectionwise	collectionwise	ADJ
ejpam-6597	342	29	pre	pre	ADJ
ejpam-6597	342	30	-	-	ADJ
ejpam-6597	342	31	normal	normal	ADJ
ejpam-6597	342	32	space	space	NOUN
ejpam-6597	342	33	is	be	AUX
ejpam-6597	342	34	t1	t1	NOUN
ejpam-6597	342	35	,	,	PUNCT
ejpam-6597	342	36	we	we	PRON
ejpam-6597	342	37	conclude	conclude	VERB
ejpam-6597	342	38	that	that	SCONJ
ejpam-6597	342	39	any	any	DET
ejpam-6597	342	40	closed	closed	ADJ
ejpam-6597	342	41	extension	extension	NOUN
ejpam-6597	342	42	space	space	NOUN
ejpam-6597	342	43	(	(	PUNCT
ejpam-6597	342	44	xp	xp	INTJ
ejpam-6597	342	45	,	,	PUNCT
ejpam-6597	342	46	t	t	PROPN
ejpam-6597	342	47	∗	∗	NOUN
ejpam-6597	342	48	)	)	PUNCT
ejpam-6597	342	49	of	of	ADP
ejpam-6597	342	50	a	a	DET
ejpam-6597	342	51	collectionwise	collectionwise	ADV
ejpam-6597	342	52	pre	pre	ADJ
ejpam-6597	342	53	-	-	ADJ
ejpam-6597	342	54	normal	normal	ADJ
ejpam-6597	342	55	space	space	NOUN
ejpam-6597	342	56	(	(	PUNCT
ejpam-6597	342	57	x	x	X
ejpam-6597	342	58	,	,	PUNCT
ejpam-6597	342	59	t	t	PROPN
ejpam-6597	342	60	)	)	PUNCT
ejpam-6597	342	61	is	be	AUX
ejpam-6597	342	62	not	not	PART
ejpam-6597	342	63	collectionwise	collectionwise	ADV
ejpam-6597	342	64	pre	pre	ADJ
ejpam-6597	342	65	-	-	ADJ
ejpam-6597	342	66	normal	normal	ADJ
ejpam-6597	342	67	.	.	PUNCT
ejpam-6597	343	1	now	now	ADV
ejpam-6597	343	2	,	,	PUNCT
ejpam-6597	343	3	we	we	PRON
ejpam-6597	343	4	present	present	VERB
ejpam-6597	343	5	the	the	DET
ejpam-6597	343	6	next	next	ADJ
ejpam-6597	343	7	examples	example	NOUN
ejpam-6597	343	8	.	.	PUNCT
ejpam-6597	344	1	here	here	ADV
ejpam-6597	344	2	is	be	AUX
ejpam-6597	344	3	a	a	DET
ejpam-6597	344	4	tychonoff	tychonoff	NOUN
ejpam-6597	344	5	space	space	NOUN
ejpam-6597	344	6	which	which	PRON
ejpam-6597	344	7	is	be	AUX
ejpam-6597	344	8	not	not	PART
ejpam-6597	344	9	collectionwise	collectionwise	ADV
ejpam-6597	344	10	pre	pre	ADJ
ejpam-6597	344	11	-	-	ADJ
ejpam-6597	344	12	normal	normal	ADJ
ejpam-6597	344	13	:	:	PUNCT
ejpam-6597	344	14	example	example	NOUN
ejpam-6597	344	15	6	6	NUM
ejpam-6597	344	16	.	.	PUNCT
ejpam-6597	345	1	the	the	DET
ejpam-6597	345	2	rational	rational	ADJ
ejpam-6597	345	3	sequence	sequence	NOUN
ejpam-6597	345	4	topology	topology	NOUN
ejpam-6597	345	5	[	[	X
ejpam-6597	345	6	10	10	NUM
ejpam-6597	345	7	,	,	PUNCT
ejpam-6597	345	8	example	example	NOUN
ejpam-6597	345	9	65	65	NUM
ejpam-6597	345	10	]	]	PUNCT
ejpam-6597	345	11	,	,	PUNCT
ejpam-6597	345	12	(	(	PUNCT
ejpam-6597	345	13	r	r	NOUN
ejpam-6597	345	14	,	,	PUNCT
ejpam-6597	345	15	rs	rs	NOUN
ejpam-6597	345	16	)	)	PUNCT
ejpam-6597	345	17	is	be	AUX
ejpam-6597	345	18	a	a	DET
ejpam-6597	345	19	tychonoff	tychonoff	NOUN
ejpam-6597	345	20	first	first	ADV
ejpam-6597	345	21	countable	countable	ADJ
ejpam-6597	345	22	,	,	PUNCT
ejpam-6597	345	23	zero	zero	NUM
ejpam-6597	345	24	-	-	PUNCT
ejpam-6597	345	25	dimensional	dimensional	ADJ
ejpam-6597	345	26	,	,	PUNCT
ejpam-6597	345	27	locally	locally	ADV
ejpam-6597	345	28	compact	compact	ADJ
ejpam-6597	345	29	,	,	PUNCT
ejpam-6597	345	30	separable	separable	ADJ
ejpam-6597	345	31	and	and	CCONJ
ejpam-6597	345	32	almost	almost	ADV
ejpam-6597	345	33	normal	normal	ADJ
ejpam-6597	345	34	space	space	NOUN
ejpam-6597	345	35	which	which	PRON
ejpam-6597	345	36	is	be	AUX
ejpam-6597	345	37	neither	neither	CCONJ
ejpam-6597	345	38	paracompact	paracompact	ADJ
ejpam-6597	345	39	,	,	PUNCT
ejpam-6597	345	40	normal	normal	ADJ
ejpam-6597	345	41	,	,	PUNCT
ejpam-6597	345	42	extremally	extremally	ADV
ejpam-6597	345	43	disconnected	disconnect	VERB
ejpam-6597	345	44	,	,	PUNCT
ejpam-6597	345	45	π	π	PROPN
ejpam-6597	345	46	-	-	ADJ
ejpam-6597	345	47	normal	normal	ADJ
ejpam-6597	345	48	nor	nor	CCONJ
ejpam-6597	345	49	lindelöf	lindelöf	NOUN
ejpam-6597	345	50	[	[	X
ejpam-6597	345	51	10	10	NUM
ejpam-6597	345	52	,	,	PUNCT
ejpam-6597	345	53	11	11	NUM
ejpam-6597	345	54	]	]	PUNCT
ejpam-6597	345	55	.	.	PUNCT
ejpam-6597	346	1	observe	observe	VERB
ejpam-6597	346	2	that	that	SCONJ
ejpam-6597	346	3	:	:	PUNCT
ejpam-6597	346	4	the	the	DET
ejpam-6597	346	5	rational	rational	ADJ
ejpam-6597	346	6	sequence	sequence	NOUN
ejpam-6597	346	7	topology	topology	NOUN
ejpam-6597	346	8	is	be	AUX
ejpam-6597	346	9	an	an	DET
ejpam-6597	346	10	example	example	NOUN
ejpam-6597	346	11	of	of	ADP
ejpam-6597	346	12	a	a	DET
ejpam-6597	346	13	tychonoff	tychonoff	NOUN
ejpam-6597	346	14	space	space	NOUN
ejpam-6597	346	15	which	which	PRON
ejpam-6597	346	16	is	be	AUX
ejpam-6597	346	17	neither	neither	PRON
ejpam-6597	346	18	pre	pre	ADJ
ejpam-6597	346	19	-	-	ADJ
ejpam-6597	346	20	normal	normal	ADJ
ejpam-6597	346	21	nor	nor	CCONJ
ejpam-6597	346	22	normal	normal	ADJ
ejpam-6597	346	23	being	be	AUX
ejpam-6597	346	24	sub	sub	ADJ
ejpam-6597	346	25	-	-	ADJ
ejpam-6597	346	26	maximal	maximal	ADJ
ejpam-6597	346	27	space	space	NOUN
ejpam-6597	346	28	[	[	X
ejpam-6597	346	29	11	11	NUM
ejpam-6597	346	30	]	]	PUNCT
ejpam-6597	346	31	.	.	PUNCT
ejpam-6597	347	1	therefore	therefore	ADV
ejpam-6597	347	2	,	,	PUNCT
ejpam-6597	347	3	the	the	DET
ejpam-6597	347	4	rational	rational	ADJ
ejpam-6597	347	5	sequence	sequence	NOUN
ejpam-6597	347	6	topology	topology	NOUN
ejpam-6597	347	7	is	be	AUX
ejpam-6597	347	8	neither	neither	CCONJ
ejpam-6597	347	9	collectionwise	collectionwise	ADV
ejpam-6597	347	10	pre	pre	ADJ
ejpam-6597	347	11	-	-	ADJ
ejpam-6597	347	12	normal	normal	ADJ
ejpam-6597	347	13	nor	nor	CCONJ
ejpam-6597	347	14	collectionwise	collectionwise	ADV
ejpam-6597	347	15	normal	normal	ADJ
ejpam-6597	347	16	the	the	DET
ejpam-6597	347	17	following	follow	VERB
ejpam-6597	347	18	problems	problem	NOUN
ejpam-6597	347	19	are	be	AUX
ejpam-6597	347	20	still	still	ADV
ejpam-6597	347	21	open	open	ADJ
ejpam-6597	347	22	in	in	ADP
ejpam-6597	347	23	this	this	DET
ejpam-6597	347	24	research	research	NOUN
ejpam-6597	347	25	:	:	PUNCT
ejpam-6597	347	26	is	be	AUX
ejpam-6597	347	27	there	there	PRON
ejpam-6597	347	28	an	an	DET
ejpam-6597	347	29	example	example	NOUN
ejpam-6597	347	30	of	of	ADP
ejpam-6597	347	31	a	a	DET
ejpam-6597	347	32	t1	t1	NOUN
ejpam-6597	347	33	prenormal	prenormal	NOUN
ejpam-6597	347	34	space	space	NOUN
ejpam-6597	347	35	which	which	PRON
ejpam-6597	347	36	is	be	AUX
ejpam-6597	347	37	not	not	PART
ejpam-6597	347	38	collectionwise	collectionwise	ADV
ejpam-6597	347	39	pre	pre	ADJ
ejpam-6597	347	40	-	-	ADJ
ejpam-6597	347	41	normal	normal	ADJ
ejpam-6597	347	42	?	?	PUNCT
ejpam-6597	347	43	,	,	PUNCT
ejpam-6597	347	44	is	be	AUX
ejpam-6597	347	45	there	there	PRON
ejpam-6597	347	46	a	a	DET
ejpam-6597	347	47	tychonoff	tychonoff	NOUN
ejpam-6597	347	48	collectionwise	collectionwise	ADV
ejpam-6597	347	49	pre	pre	ADJ
ejpam-6597	347	50	-	-	ADJ
ejpam-6597	347	51	normal	normal	ADJ
ejpam-6597	347	52	space	space	NOUN
ejpam-6597	347	53	which	which	PRON
ejpam-6597	347	54	is	be	AUX
ejpam-6597	347	55	not	not	PART
ejpam-6597	347	56	collectionwise	collectionwise	ADV
ejpam-6597	347	57	normal	normal	ADJ
ejpam-6597	347	58	?	?	PUNCT
ejpam-6597	347	59	,	,	PUNCT
ejpam-6597	347	60	is	be	AUX
ejpam-6597	347	61	a	a	DET
ejpam-6597	347	62	closed	closed	ADJ
ejpam-6597	347	63	subspace	subspace	NOUN
ejpam-6597	347	64	of	of	ADP
ejpam-6597	347	65	a	a	DET
ejpam-6597	347	66	collectionwise	collectionwise	ADV
ejpam-6597	347	67	pre	pre	ADJ
ejpam-6597	347	68	-	-	ADJ
ejpam-6597	347	69	normal	normal	ADJ
ejpam-6597	347	70	space	space	NOUN
ejpam-6597	347	71	,	,	PUNCT
ejpam-6597	347	72	collectionwise	collectionwise	ADV
ejpam-6597	347	73	pre	pre	ADJ
ejpam-6597	347	74	-	-	ADJ
ejpam-6597	347	75	normal	normal	ADJ
ejpam-6597	347	76	?	?	PUNCT
ejpam-6597	347	77	,	,	PUNCT
ejpam-6597	347	78	are	be	AUX
ejpam-6597	347	79	the	the	DET
ejpam-6597	347	80	niemytzki	niemytzki	ADJ
ejpam-6597	347	81	plane	plane	NOUN
ejpam-6597	347	82	topology	topology	NOUN
ejpam-6597	347	83	and	and	CCONJ
ejpam-6597	347	84	the	the	DET
ejpam-6597	347	85	countable	countable	ADJ
ejpam-6597	347	86	complement	complement	NOUN
ejpam-6597	347	87	topology	topology	NOUN
ejpam-6597	347	88	(	(	PUNCT
ejpam-6597	347	89	r	r	NOUN
ejpam-6597	347	90	,	,	PUNCT
ejpam-6597	347	91	cc	cc	NOUN
ejpam-6597	347	92	)	)	PUNCT
ejpam-6597	347	93	,	,	PUNCT
ejpam-6597	347	94	collectionwise	collectionwise	ADV
ejpam-6597	347	95	pre	pre	ADJ
ejpam-6597	347	96	-	-	ADJ
ejpam-6597	347	97	normal	normal	ADJ
ejpam-6597	347	98	?	?	PUNCT
ejpam-6597	347	99	,	,	PUNCT
ejpam-6597	347	100	and	and	CCONJ
ejpam-6597	347	101	is	be	AUX
ejpam-6597	347	102	a	a	DET
ejpam-6597	347	103	quotient	quotient	NOUN
ejpam-6597	347	104	space	space	NOUN
ejpam-6597	347	105	of	of	ADP
ejpam-6597	347	106	a	a	DET
ejpam-6597	347	107	collectionwise	collectionwise	ADV
ejpam-6597	347	108	pre	pre	ADJ
ejpam-6597	347	109	-	-	ADJ
ejpam-6597	347	110	normal	normal	ADJ
ejpam-6597	347	111	space	space	NOUN
ejpam-6597	347	112	,	,	PUNCT
ejpam-6597	347	113	collectionwise	collectionwise	ADV
ejpam-6597	347	114	pre	pre	ADJ
ejpam-6597	347	115	-	-	ADJ
ejpam-6597	347	116	normal	normal	ADJ
ejpam-6597	347	117	?	?	PUNCT
ejpam-6597	347	118	.	.	PUNCT
ejpam-6597	348	1	s.	s.	PROPN
ejpam-6597	348	2	a.	a.	PROPN
ejpam-6597	348	3	thabit	thabit	PROPN
ejpam-6597	348	4	,	,	PUNCT
ejpam-6597	348	5	a.	a.	PROPN
ejpam-6597	348	6	al	al	PROPN
ejpam-6597	348	7	-	-	PUNCT
ejpam-6597	348	8	awadi	awadi	PROPN
ejpam-6597	348	9	,	,	PUNCT
ejpam-6597	348	10	r.	r.	PROPN
ejpam-6597	348	11	noaman	noaman	PROPN
ejpam-6597	348	12	/	/	SYM
ejpam-6597	348	13	eur	eur	PROPN
ejpam-6597	348	14	.	.	PUNCT
ejpam-6597	349	1	j.	j.	PROPN
ejpam-6597	349	2	pure	pure	PROPN
ejpam-6597	349	3	appl	appl	PROPN
ejpam-6597	349	4	.	.	PROPN
ejpam-6597	349	5	math	math	PROPN
ejpam-6597	349	6	,	,	PUNCT
ejpam-6597	349	7	18	18	NUM
ejpam-6597	349	8	(	(	PUNCT
ejpam-6597	349	9	4	4	NUM
ejpam-6597	349	10	)	)	PUNCT
ejpam-6597	349	11	(	(	PUNCT
ejpam-6597	349	12	2025	2025	NUM
ejpam-6597	349	13	)	)	PUNCT
ejpam-6597	349	14	,	,	PUNCT
ejpam-6597	349	15	6597	6597	NUM
ejpam-6597	349	16	14	14	NUM
ejpam-6597	349	17	of	of	ADP
ejpam-6597	349	18	15	15	NUM
ejpam-6597	349	19	7	7	NUM
ejpam-6597	349	20	.	.	PUNCT
ejpam-6597	349	21	conclusion	conclusion	VERB
ejpam-6597	349	22	new	new	ADJ
ejpam-6597	349	23	topological	topological	ADJ
ejpam-6597	349	24	property	property	NOUN
ejpam-6597	349	25	,	,	PUNCT
ejpam-6597	349	26	called	call	VERB
ejpam-6597	349	27	collectionwise	collectionwise	PROPN
ejpam-6597	349	28	pre	pre	ADJ
ejpam-6597	349	29	-	-	ADJ
ejpam-6597	349	30	normality	normality	NOUN
ejpam-6597	349	31	has	have	AUX
ejpam-6597	349	32	been	be	AUX
ejpam-6597	349	33	studied	study	VERB
ejpam-6597	349	34	in	in	ADP
ejpam-6597	349	35	this	this	DET
ejpam-6597	349	36	work	work	NOUN
ejpam-6597	349	37	.	.	PUNCT
ejpam-6597	350	1	some	some	DET
ejpam-6597	350	2	results	result	NOUN
ejpam-6597	350	3	,	,	PUNCT
ejpam-6597	350	4	properties	property	NOUN
ejpam-6597	350	5	,	,	PUNCT
ejpam-6597	350	6	relationships	relationship	NOUN
ejpam-6597	350	7	,	,	PUNCT
ejpam-6597	350	8	characterizations	characterization	NOUN
ejpam-6597	350	9	and	and	CCONJ
ejpam-6597	350	10	counterexamples	counterexample	NOUN
ejpam-6597	350	11	were	be	AUX
ejpam-6597	350	12	given	give	VERB
ejpam-6597	350	13	and	and	CCONJ
ejpam-6597	350	14	discussed	discuss	VERB
ejpam-6597	350	15	.	.	PUNCT
ejpam-6597	351	1	the	the	DET
ejpam-6597	351	2	importance	importance	NOUN
ejpam-6597	351	3	of	of	ADP
ejpam-6597	351	4	this	this	DET
ejpam-6597	351	5	study	study	NOUN
ejpam-6597	351	6	is	be	AUX
ejpam-6597	351	7	to	to	PART
ejpam-6597	351	8	open	open	VERB
ejpam-6597	351	9	a	a	DET
ejpam-6597	351	10	window	window	NOUN
ejpam-6597	351	11	for	for	ADP
ejpam-6597	351	12	future	future	ADJ
ejpam-6597	351	13	studies	study	NOUN
ejpam-6597	351	14	and	and	CCONJ
ejpam-6597	351	15	to	to	PART
ejpam-6597	351	16	help	help	VERB
ejpam-6597	351	17	us	we	PRON
ejpam-6597	351	18	for	for	ADP
ejpam-6597	351	19	obtaining	obtain	VERB
ejpam-6597	351	20	some	some	DET
ejpam-6597	351	21	new	new	ADJ
ejpam-6597	351	22	results	result	NOUN
ejpam-6597	351	23	of	of	ADP
ejpam-6597	351	24	several	several	ADJ
ejpam-6597	351	25	weak	weak	ADJ
ejpam-6597	351	26	versions	version	NOUN
ejpam-6597	351	27	of	of	ADP
ejpam-6597	351	28	collectionwise	collectionwise	ADJ
ejpam-6597	351	29	normality	normality	NOUN
ejpam-6597	351	30	in	in	ADP
ejpam-6597	351	31	the	the	DET
ejpam-6597	351	32	future	future	ADJ
ejpam-6597	351	33	researches	research	NOUN
ejpam-6597	351	34	.	.	PUNCT
ejpam-6597	352	1	acknowledgements	acknowledgement	NOUN
ejpam-6597	352	2	the	the	DET
ejpam-6597	352	3	authors	author	NOUN
ejpam-6597	352	4	would	would	AUX
ejpam-6597	352	5	like	like	VERB
ejpam-6597	352	6	to	to	PART
ejpam-6597	352	7	thank	thank	VERB
ejpam-6597	352	8	the	the	DET
ejpam-6597	352	9	anonymous	anonymous	ADJ
ejpam-6597	352	10	referee	referee	NOUN
ejpam-6597	352	11	for	for	ADP
ejpam-6597	352	12	his	his	PRON
ejpam-6597	352	13	/	/	SYM
ejpam-6597	352	14	her	her	PRON
ejpam-6597	352	15	comments	comment	NOUN
ejpam-6597	352	16	that	that	PRON
ejpam-6597	352	17	will	will	AUX
ejpam-6597	352	18	help	help	VERB
ejpam-6597	352	19	us	we	PRON
ejpam-6597	352	20	improve	improve	VERB
ejpam-6597	352	21	this	this	DET
ejpam-6597	352	22	article	article	NOUN
ejpam-6597	352	23	.	.	PUNCT
ejpam-6597	353	1	references	reference	NOUN
ejpam-6597	353	2	[	[	X
ejpam-6597	353	3	1	1	NUM
ejpam-6597	353	4	]	]	PUNCT
ejpam-6597	353	5	c.	c.	PROPN
ejpam-6597	353	6	kuratowski	kuratowski	PROPN
ejpam-6597	353	7	.	.	PUNCT
ejpam-6597	354	1	topology	topology	PROPN
ejpam-6597	354	2	i.	i.	PROPN
ejpam-6597	354	3	hafner	hafner	PROPN
ejpam-6597	354	4	,	,	PUNCT
ejpam-6597	354	5	new	new	PROPN
ejpam-6597	354	6	york	york	PROPN
ejpam-6597	354	7	,	,	PUNCT
ejpam-6597	354	8	4	4	NUM
ejpam-6597	354	9	edition	edition	NOUN
ejpam-6597	354	10	,	,	PUNCT
ejpam-6597	354	11	1958	1958	NUM
ejpam-6597	354	12	.	.	PUNCT
ejpam-6597	355	1	[	[	X
ejpam-6597	355	2	2	2	X
ejpam-6597	355	3	]	]	PUNCT
ejpam-6597	355	4	v.	v.	CCONJ
ejpam-6597	355	5	zaitsev	zaitsev	NOUN
ejpam-6597	355	6	.	.	PUNCT
ejpam-6597	356	1	on	on	ADP
ejpam-6597	356	2	certain	certain	ADJ
ejpam-6597	356	3	classes	class	NOUN
ejpam-6597	356	4	of	of	ADP
ejpam-6597	356	5	topological	topological	ADJ
ejpam-6597	356	6	spaces	space	NOUN
ejpam-6597	356	7	and	and	CCONJ
ejpam-6597	356	8	their	their	PRON
ejpam-6597	356	9	bicompactifications	bicompactification	NOUN
ejpam-6597	356	10	.	.	PUNCT
ejpam-6597	357	1	doklady	doklady	PROPN
ejpam-6597	357	2	akademii	akademii	NOUN
ejpam-6597	357	3	nauk	nauk	NOUN
ejpam-6597	357	4	sssr	sssr	NOUN
ejpam-6597	357	5	,	,	PUNCT
ejpam-6597	357	6	178:778–779	178:778–779	NUM
ejpam-6597	357	7	,	,	PUNCT
ejpam-6597	357	8	1968	1968	NUM
ejpam-6597	357	9	.	.	PUNCT
ejpam-6597	358	1	[	[	X
ejpam-6597	358	2	3	3	NUM
ejpam-6597	358	3	]	]	PUNCT
ejpam-6597	358	4	a.	a.	NOUN
ejpam-6597	358	5	s.	s.	PROPN
ejpam-6597	358	6	mashhour	mashhour	PROPN
ejpam-6597	358	7	,	,	PUNCT
ejpam-6597	358	8	m.	m.	PROPN
ejpam-6597	358	9	e.	e.	PROPN
ejpam-6597	358	10	abd	abd	PROPN
ejpam-6597	359	1	el	el	PROPN
ejpam-6597	359	2	-	-	PROPN
ejpam-6597	359	3	monsef	monsef	ADJ
ejpam-6597	359	4	,	,	PUNCT
ejpam-6597	359	5	and	and	CCONJ
ejpam-6597	359	6	i.	i.	PROPN
ejpam-6597	359	7	a.	a.	PROPN
ejpam-6597	359	8	hasanein	hasanein	PROPN
ejpam-6597	359	9	.	.	PUNCT
ejpam-6597	360	1	on	on	ADP
ejpam-6597	360	2	pretopological	pretopological	ADJ
ejpam-6597	360	3	spaces	space	NOUN
ejpam-6597	360	4	.	.	PUNCT
ejpam-6597	361	1	bulletin	bulletin	PROPN
ejpam-6597	361	2	mathématique	mathématique	PROPN
ejpam-6597	361	3	de	de	X
ejpam-6597	361	4	la	la	PROPN
ejpam-6597	361	5	société	société	PROPN
ejpam-6597	361	6	des	des	PROPN
ejpam-6597	361	7	sciences	science	NOUN
ejpam-6597	361	8	mathématiques	mathématiques	PROPN
ejpam-6597	361	9	de	de	X
ejpam-6597	361	10	la	la	X
ejpam-6597	361	11	république	république	PROPN
ejpam-6597	361	12	socialiste	socialiste	PROPN
ejpam-6597	361	13	de	de	PROPN
ejpam-6597	361	14	roumanie	roumanie	PROPN
ejpam-6597	361	15	,	,	PUNCT
ejpam-6597	361	16	28(76):39–45	28(76):39–45	NUM
ejpam-6597	361	17	,	,	PUNCT
ejpam-6597	361	18	1984	1984	NUM
ejpam-6597	361	19	.	.	PUNCT
ejpam-6597	362	1	[	[	X
ejpam-6597	362	2	4	4	X
ejpam-6597	362	3	]	]	PUNCT
ejpam-6597	362	4	s.	s.	PROPN
ejpam-6597	362	5	r.	r.	PROPN
ejpam-6597	362	6	malghan	malghan	PROPN
ejpam-6597	362	7	and	and	CCONJ
ejpam-6597	362	8	g.	g.	PROPN
ejpam-6597	362	9	b.	b.	PROPN
ejpam-6597	362	10	navalagi	navalagi	PROPN
ejpam-6597	362	11	.	.	PUNCT
ejpam-6597	363	1	almost	almost	ADV
ejpam-6597	363	2	p	p	NOUN
ejpam-6597	363	3	-	-	PUNCT
ejpam-6597	363	4	regular	regular	ADJ
ejpam-6597	363	5	,	,	PUNCT
ejpam-6597	363	6	p	p	NOUN
ejpam-6597	363	7	-	-	PUNCT
ejpam-6597	363	8	completely	completely	ADV
ejpam-6597	363	9	regular	regular	ADJ
ejpam-6597	363	10	and	and	CCONJ
ejpam-6597	363	11	almost	almost	ADV
ejpam-6597	363	12	p	p	NOUN
ejpam-6597	363	13	-	-	PUNCT
ejpam-6597	363	14	completely	completely	ADV
ejpam-6597	363	15	regular	regular	ADJ
ejpam-6597	363	16	spaces	space	NOUN
ejpam-6597	363	17	.	.	PUNCT
ejpam-6597	364	1	bulletin	bulletin	PROPN
ejpam-6597	364	2	mathématique	mathématique	PROPN
ejpam-6597	364	3	de	de	X
ejpam-6597	364	4	la	la	PROPN
ejpam-6597	364	5	société	société	PROPN
ejpam-6597	364	6	des	des	PROPN
ejpam-6597	364	7	sciences	science	NOUN
ejpam-6597	364	8	mathématiques	mathématiques	PROPN
ejpam-6597	364	9	de	de	X
ejpam-6597	364	10	la	la	X
ejpam-6597	364	11	république	république	PROPN
ejpam-6597	364	12	socialiste	socialiste	PROPN
ejpam-6597	364	13	de	de	PROPN
ejpam-6597	364	14	roumanie	roumanie	PROPN
ejpam-6597	364	15	,	,	PUNCT
ejpam-6597	364	16	34(82):317–326	34(82):317–326	NUM
ejpam-6597	364	17	,	,	PUNCT
ejpam-6597	364	18	1990	1990	NUM
ejpam-6597	364	19	.	.	PUNCT
ejpam-6597	365	1	[	[	X
ejpam-6597	365	2	5	5	X
ejpam-6597	365	3	]	]	PUNCT
ejpam-6597	365	4	g.	g.	PROPN
ejpam-6597	365	5	b.	b.	PROPN
ejpam-6597	365	6	navalagi	navalagi	PROPN
ejpam-6597	365	7	.	.	PUNCT
ejpam-6597	366	1	pre	pre	VERB
ejpam-6597	366	2	-	-	NOUN
ejpam-6597	366	3	neighbourhoods	neighbourhood	NOUN
ejpam-6597	366	4	.	.	PUNCT
ejpam-6597	367	1	the	the	DET
ejpam-6597	367	2	mathematics	mathematics	PROPN
ejpam-6597	367	3	education	education	NOUN
ejpam-6597	367	4	,	,	PUNCT
ejpam-6597	367	5	32(4):201–206	32(4):201–206	NOUN
ejpam-6597	367	6	,	,	PUNCT
ejpam-6597	367	7	1998	1998	NUM
ejpam-6597	367	8	.	.	PUNCT
ejpam-6597	368	1	[	[	X
ejpam-6597	368	2	6	6	X
ejpam-6597	368	3	]	]	PUNCT
ejpam-6597	368	4	j.	j.	PROPN
ejpam-6597	368	5	h.	h.	PROPN
ejpam-6597	368	6	park	park	PROPN
ejpam-6597	368	7	.	.	PUNCT
ejpam-6597	369	1	almost	almost	ADV
ejpam-6597	369	2	p	p	ADJ
ejpam-6597	369	3	-	-	PUNCT
ejpam-6597	369	4	normal	normal	ADJ
ejpam-6597	369	5	,	,	PUNCT
ejpam-6597	369	6	mildly	mildly	ADV
ejpam-6597	369	7	p	p	NOUN
ejpam-6597	369	8	-	-	PUNCT
ejpam-6597	369	9	normal	normal	ADJ
ejpam-6597	369	10	spaces	space	NOUN
ejpam-6597	369	11	and	and	CCONJ
ejpam-6597	369	12	some	some	DET
ejpam-6597	369	13	functions	function	NOUN
ejpam-6597	369	14	.	.	PUNCT
ejpam-6597	370	1	chaos	chaos	NOUN
ejpam-6597	370	2	,	,	PUNCT
ejpam-6597	370	3	solitons	soliton	NOUN
ejpam-6597	370	4	and	and	CCONJ
ejpam-6597	370	5	fractals	fractal	NOUN
ejpam-6597	370	6	,	,	PUNCT
ejpam-6597	370	7	18:267–274	18:267–274	PROPN
ejpam-6597	370	8	,	,	PUNCT
ejpam-6597	370	9	2003	2003	NUM
ejpam-6597	370	10	.	.	PUNCT
ejpam-6597	371	1	[	[	X
ejpam-6597	371	2	7	7	X
ejpam-6597	371	3	]	]	PUNCT
ejpam-6597	371	4	a.	a.	NOUN
ejpam-6597	371	5	s.	s.	PROPN
ejpam-6597	371	6	mashhour	mashhour	PROPN
ejpam-6597	371	7	,	,	PUNCT
ejpam-6597	371	8	m.	m.	PROPN
ejpam-6597	371	9	e.	e.	PROPN
ejpam-6597	371	10	abd	abd	PROPN
ejpam-6597	371	11	el	el	PROPN
ejpam-6597	371	12	-	-	PROPN
ejpam-6597	371	13	monsef	monsef	ADJ
ejpam-6597	371	14	,	,	PUNCT
ejpam-6597	371	15	and	and	CCONJ
ejpam-6597	371	16	s.	s.	PROPN
ejpam-6597	371	17	n.	n.	PROPN
ejpam-6597	371	18	el	el	PROPN
ejpam-6597	371	19	-	-	PROPN
ejpam-6597	371	20	deeb	deeb	PROPN
ejpam-6597	371	21	.	.	PUNCT
ejpam-6597	372	1	on	on	ADP
ejpam-6597	372	2	precontinuous	precontinuous	ADJ
ejpam-6597	372	3	and	and	CCONJ
ejpam-6597	372	4	weak	weak	ADJ
ejpam-6597	372	5	precontinuous	precontinuous	ADJ
ejpam-6597	372	6	mappings	mapping	NOUN
ejpam-6597	372	7	.	.	PUNCT
ejpam-6597	373	1	proceedings	proceeding	NOUN
ejpam-6597	373	2	of	of	ADP
ejpam-6597	373	3	the	the	DET
ejpam-6597	373	4	mathematical	mathematical	ADJ
ejpam-6597	373	5	and	and	CCONJ
ejpam-6597	373	6	physical	physical	ADJ
ejpam-6597	373	7	society	society	NOUN
ejpam-6597	373	8	of	of	ADP
ejpam-6597	373	9	egypt	egypt	PROPN
ejpam-6597	373	10	,	,	PUNCT
ejpam-6597	373	11	53:47–53	53:47–53	NUM
ejpam-6597	373	12	,	,	PUNCT
ejpam-6597	373	13	1982	1982	NUM
ejpam-6597	373	14	.	.	PUNCT
ejpam-6597	374	1	[	[	X
ejpam-6597	374	2	8	8	NUM
ejpam-6597	374	3	]	]	X
ejpam-6597	374	4	c.	c.	PROPN
ejpam-6597	374	5	patty	patty	PROPN
ejpam-6597	374	6	.	.	PUNCT
ejpam-6597	375	1	foundations	foundation	NOUN
ejpam-6597	375	2	of	of	ADP
ejpam-6597	375	3	topology	topology	NOUN
ejpam-6597	375	4	.	.	PUNCT
ejpam-6597	376	1	pws	pws	PROPN
ejpam-6597	376	2	-	-	PUNCT
ejpam-6597	376	3	kent	kent	PROPN
ejpam-6597	376	4	publishing	publishing	PROPN
ejpam-6597	376	5	company	company	NOUN
ejpam-6597	376	6	,	,	PUNCT
ejpam-6597	376	7	boston	boston	PROPN
ejpam-6597	376	8	,	,	PUNCT
ejpam-6597	376	9	1993	1993	NUM
ejpam-6597	376	10	.	.	PUNCT
ejpam-6597	377	1	[	[	X
ejpam-6597	377	2	9	9	NUM
ejpam-6597	377	3	]	]	X
ejpam-6597	377	4	r.	r.	PROPN
ejpam-6597	377	5	engelking	engelke	VERB
ejpam-6597	377	6	.	.	PUNCT
ejpam-6597	378	1	general	general	ADJ
ejpam-6597	378	2	topology	topology	NOUN
ejpam-6597	378	3	,	,	PUNCT
ejpam-6597	378	4	volume	volume	NOUN
ejpam-6597	378	5	6	6	NUM
ejpam-6597	378	6	of	of	ADP
ejpam-6597	378	7	sigma	sigma	PROPN
ejpam-6597	378	8	series	series	PROPN
ejpam-6597	378	9	in	in	ADP
ejpam-6597	378	10	pure	pure	ADJ
ejpam-6597	378	11	mathematics	mathematic	NOUN
ejpam-6597	378	12	.	.	PUNCT
ejpam-6597	379	1	heldermann	heldermann	PROPN
ejpam-6597	379	2	,	,	PUNCT
ejpam-6597	379	3	berlin	berlin	PROPN
ejpam-6597	379	4	,	,	PUNCT
ejpam-6597	379	5	1989	1989	NUM
ejpam-6597	379	6	.	.	PUNCT
ejpam-6597	380	1	[	[	X
ejpam-6597	380	2	10	10	NUM
ejpam-6597	380	3	]	]	X
ejpam-6597	380	4	l.	l.	PROPN
ejpam-6597	380	5	a.	a.	PROPN
ejpam-6597	380	6	steen	steen	PROPN
ejpam-6597	380	7	and	and	CCONJ
ejpam-6597	380	8	j.	j.	PROPN
ejpam-6597	380	9	a.	a.	PROPN
ejpam-6597	380	10	seebach	seebach	PROPN
ejpam-6597	380	11	.	.	PUNCT
ejpam-6597	381	1	counterexamples	counterexample	NOUN
ejpam-6597	381	2	in	in	ADP
ejpam-6597	381	3	topology	topology	NOUN
ejpam-6597	381	4	.	.	PUNCT
ejpam-6597	382	1	dover	dover	PROPN
ejpam-6597	382	2	publications	publications	PROPN
ejpam-6597	382	3	,	,	PUNCT
ejpam-6597	382	4	inc	inc	PROPN
ejpam-6597	382	5	.	.	PROPN
ejpam-6597	382	6	,	,	PUNCT
ejpam-6597	382	7	new	new	PROPN
ejpam-6597	382	8	york	york	PROPN
ejpam-6597	382	9	,	,	PUNCT
ejpam-6597	382	10	1995	1995	NUM
ejpam-6597	382	11	.	.	PUNCT
ejpam-6597	383	1	[	[	X
ejpam-6597	383	2	11	11	NUM
ejpam-6597	383	3	]	]	PUNCT
ejpam-6597	383	4	s.	s.	PROPN
ejpam-6597	383	5	a.	a.	PROPN
ejpam-6597	383	6	s.	s.	PROPN
ejpam-6597	383	7	thabit	thabit	PROPN
ejpam-6597	383	8	.	.	PUNCT
ejpam-6597	384	1	π	π	X
ejpam-6597	384	2	-	-	NOUN
ejpam-6597	384	3	normality	normality	NOUN
ejpam-6597	384	4	in	in	ADP
ejpam-6597	384	5	topological	topological	ADJ
ejpam-6597	384	6	spaces	space	NOUN
ejpam-6597	384	7	and	and	CCONJ
ejpam-6597	384	8	its	its	PRON
ejpam-6597	384	9	generalization	generalization	NOUN
ejpam-6597	384	10	.	.	PUNCT
ejpam-6597	385	1	malaysia	malaysia	PROPN
ejpam-6597	385	2	,	,	PUNCT
ejpam-6597	385	3	2013	2013	NUM
ejpam-6597	385	4	.	.	PUNCT
ejpam-6597	386	1	[	[	X
ejpam-6597	386	2	12	12	NUM
ejpam-6597	386	3	]	]	X
ejpam-6597	386	4	g.	g.	PROPN
ejpam-6597	386	5	b.	b.	PROPN
ejpam-6597	386	6	navalagi	navalagi	PROPN
ejpam-6597	386	7	.	.	PUNCT
ejpam-6597	387	1	p	p	X
ejpam-6597	387	2	-	-	PUNCT
ejpam-6597	387	3	normal	normal	ADJ
ejpam-6597	387	4	,	,	PUNCT
ejpam-6597	387	5	almost	almost	ADV
ejpam-6597	387	6	p	p	ADJ
ejpam-6597	387	7	-	-	PUNCT
ejpam-6597	387	8	normal	normal	ADJ
ejpam-6597	387	9	and	and	CCONJ
ejpam-6597	387	10	mildly	mildly	ADV
ejpam-6597	387	11	p	p	ADJ
ejpam-6597	387	12	-	-	PUNCT
ejpam-6597	387	13	normal	normal	ADJ
ejpam-6597	387	14	spaces	space	NOUN
ejpam-6597	387	15	.	.	PUNCT
ejpam-6597	388	1	2000	2000	NUM
ejpam-6597	388	2	.	.	PUNCT
ejpam-6597	389	1	topology	topology	NOUN
ejpam-6597	389	2	atlas	atlas	PROPN
ejpam-6597	389	3	preprint	preprint	VERB
ejpam-6597	389	4	427	427	NUM
ejpam-6597	389	5	.	.	PUNCT
ejpam-6597	390	1	[	[	X
ejpam-6597	390	2	13	13	NUM
ejpam-6597	390	3	]	]	PUNCT
ejpam-6597	390	4	t.	t.	NOUN
ejpam-6597	390	5	przymusinski	przymusinski	PROPN
ejpam-6597	390	6	.	.	PUNCT
ejpam-6597	391	1	a	a	DET
ejpam-6597	391	2	note	note	NOUN
ejpam-6597	391	3	on	on	ADP
ejpam-6597	391	4	collectionwise	collectionwise	ADJ
ejpam-6597	391	5	normality	normality	NOUN
ejpam-6597	391	6	of	of	ADP
ejpam-6597	391	7	product	product	NOUN
ejpam-6597	391	8	spaces	space	NOUN
ejpam-6597	391	9	.	.	PUNCT
ejpam-6597	392	1	in	in	ADP
ejpam-6597	392	2	colloquium	colloquium	NOUN
ejpam-6597	392	3	mathematicum	mathematicum	NOUN
ejpam-6597	392	4	,	,	PUNCT
ejpam-6597	392	5	volume	volume	NOUN
ejpam-6597	392	6	xxxiii	xxxiii	NOUN
ejpam-6597	392	7	,	,	PUNCT
ejpam-6597	392	8	pages	page	NOUN
ejpam-6597	392	9	65–70	65–70	NUM
ejpam-6597	392	10	,	,	PUNCT
ejpam-6597	392	11	1975	1975	NUM
ejpam-6597	392	12	.	.	PUNCT
ejpam-6597	393	1	s.	s.	PROPN
ejpam-6597	393	2	a.	a.	PROPN
ejpam-6597	393	3	thabit	thabit	PROPN
ejpam-6597	393	4	,	,	PUNCT
ejpam-6597	393	5	a.	a.	PROPN
ejpam-6597	393	6	al	al	PROPN
ejpam-6597	393	7	-	-	PUNCT
ejpam-6597	393	8	awadi	awadi	PROPN
ejpam-6597	393	9	,	,	PUNCT
ejpam-6597	393	10	r.	r.	PROPN
ejpam-6597	393	11	noaman	noaman	PROPN
ejpam-6597	393	12	/	/	SYM
ejpam-6597	393	13	eur	eur	PROPN
ejpam-6597	393	14	.	.	PUNCT
ejpam-6597	394	1	j.	j.	PROPN
ejpam-6597	394	2	pure	pure	PROPN
ejpam-6597	394	3	appl	appl	PROPN
ejpam-6597	394	4	.	.	PROPN
ejpam-6597	394	5	math	math	PROPN
ejpam-6597	394	6	,	,	PUNCT
ejpam-6597	394	7	18	18	NUM
ejpam-6597	394	8	(	(	PUNCT
ejpam-6597	394	9	4	4	NUM
ejpam-6597	394	10	)	)	PUNCT
ejpam-6597	394	11	(	(	PUNCT
ejpam-6597	394	12	2025	2025	NUM
ejpam-6597	394	13	)	)	PUNCT
ejpam-6597	394	14	,	,	PUNCT
ejpam-6597	394	15	6597	6597	NUM
ejpam-6597	394	16	15	15	NUM
ejpam-6597	394	17	of	of	ADP
ejpam-6597	394	18	15	15	NUM
ejpam-6597	394	19	[	[	SYM
ejpam-6597	394	20	14	14	NUM
ejpam-6597	394	21	]	]	X
ejpam-6597	394	22	n.	n.	PROPN
ejpam-6597	394	23	levine	levine	PROPN
ejpam-6597	394	24	.	.	PUNCT
ejpam-6597	395	1	generalized	generalize	VERB
ejpam-6597	395	2	closed	closed	ADJ
ejpam-6597	395	3	sets	set	NOUN
ejpam-6597	395	4	in	in	ADP
ejpam-6597	395	5	topology	topology	NOUN
ejpam-6597	395	6	.	.	PUNCT
ejpam-6597	396	1	rendiconti	rendiconti	VERB
ejpam-6597	396	2	del	del	PROPN
ejpam-6597	396	3	circolo	circolo	PROPN
ejpam-6597	396	4	matematico	matematico	NOUN
ejpam-6597	396	5	di	di	NOUN
ejpam-6597	396	6	palermo	palermo	NOUN
ejpam-6597	396	7	,	,	PUNCT
ejpam-6597	396	8	19:89–96	19:89–96	NUM
ejpam-6597	396	9	,	,	PUNCT
ejpam-6597	396	10	1970	1970	NUM
ejpam-6597	396	11	.	.	PUNCT
ejpam-6597	397	1	[	[	X
ejpam-6597	397	2	15	15	NUM
ejpam-6597	397	3	]	]	X
ejpam-6597	397	4	h.	h.	PROPN
ejpam-6597	397	5	maki	maki	PROPN
ejpam-6597	397	6	,	,	PUNCT
ejpam-6597	397	7	j.	j.	PROPN
ejpam-6597	397	8	umbehara	umbehara	PROPN
ejpam-6597	397	9	,	,	PUNCT
ejpam-6597	397	10	and	and	CCONJ
ejpam-6597	397	11	t.	t.	PROPN
ejpam-6597	397	12	noiri	noiri	PROPN
ejpam-6597	397	13	.	.	PUNCT
ejpam-6597	398	1	every	every	DET
ejpam-6597	398	2	topological	topological	ADJ
ejpam-6597	398	3	space	space	NOUN
ejpam-6597	398	4	is	be	AUX
ejpam-6597	398	5	pre	pre	ADJ
ejpam-6597	398	6	-	-	ADJ
ejpam-6597	398	7	t	t	ADJ
ejpam-6597	398	8	1	1	NUM
ejpam-6597	398	9	2	2	NUM
ejpam-6597	398	10	.	.	PUNCT
ejpam-6597	399	1	memoirs	memoir	NOUN
ejpam-6597	399	2	of	of	ADP
ejpam-6597	399	3	the	the	DET
ejpam-6597	399	4	faculty	faculty	NOUN
ejpam-6597	399	5	of	of	ADP
ejpam-6597	399	6	science	science	PROPN
ejpam-6597	399	7	kochi	kochi	PROPN
ejpam-6597	399	8	university	university	PROPN
ejpam-6597	399	9	series	series	PROPN
ejpam-6597	399	10	a	a	PRON
ejpam-6597	399	11	(	(	PUNCT
ejpam-6597	399	12	mathematics	mathematic	NOUN
ejpam-6597	399	13	)	)	PUNCT
ejpam-6597	399	14	,	,	PUNCT
ejpam-6597	399	15	17:33–42	17:33–42	NUM
ejpam-6597	399	16	,	,	PUNCT
ejpam-6597	399	17	1996	1996	NUM
ejpam-6597	399	18	.	.	PUNCT
ejpam-6597	400	1	[	[	X
ejpam-6597	400	2	16	16	NUM
ejpam-6597	400	3	]	]	PUNCT
ejpam-6597	400	4	m.	m.	PROPN
ejpam-6597	400	5	k.	k.	PROPN
ejpam-6597	400	6	r.	r.	PROPN
ejpam-6597	400	7	s.	s.	PROPN
ejpam-6597	400	8	veerakumar	veerakumar	PROPN
ejpam-6597	400	9	.	.	PROPN
ejpam-6597	401	1	g∗-preclosed	g∗-preclose	VERB
ejpam-6597	401	2	sets	set	NOUN
ejpam-6597	401	3	.	.	PUNCT
ejpam-6597	402	1	acta	acta	PROPN
ejpam-6597	402	2	ciencia	ciencia	PROPN
ejpam-6597	402	3	indica	indica	PROPN
ejpam-6597	402	4	,	,	PUNCT
ejpam-6597	402	5	28(1):51–60	28(1):51–60	NUM
ejpam-6597	402	6	,	,	PUNCT
ejpam-6597	402	7	2002	2002	NUM
ejpam-6597	402	8	.	.	PUNCT
ejpam-6597	403	1	[	[	X
ejpam-6597	403	2	17	17	NUM
ejpam-6597	403	3	]	]	PUNCT
ejpam-6597	403	4	m.	m.	NOUN
ejpam-6597	403	5	s.	s.	PROPN
ejpam-6597	403	6	sarsak	sarsak	PROPN
ejpam-6597	403	7	and	and	CCONJ
ejpam-6597	403	8	n.	n.	PROPN
ejpam-6597	403	9	rajesh	rajesh	PROPN
ejpam-6597	403	10	.	.	PUNCT
ejpam-6597	404	1	π	π	PROPN
ejpam-6597	404	2	-	-	PUNCT
ejpam-6597	404	3	generalized	generalized	ADJ
ejpam-6597	404	4	semi	semi	ADJ
ejpam-6597	404	5	-	-	ADJ
ejpam-6597	404	6	preclosed	preclose	VERB
ejpam-6597	404	7	sets	set	NOUN
ejpam-6597	404	8	.	.	PUNCT
ejpam-6597	405	1	international	international	ADJ
ejpam-6597	405	2	mathematical	mathematical	PROPN
ejpam-6597	405	3	forum	forum	PROPN
ejpam-6597	405	4	,	,	PUNCT
ejpam-6597	405	5	5(12):573–578	5(12):573–578	NUM
ejpam-6597	405	6	,	,	PUNCT
ejpam-6597	405	7	2010	2010	NUM
ejpam-6597	405	8	.	.	PUNCT
ejpam-6597	406	1	[	[	X
ejpam-6597	406	2	18	18	NUM
ejpam-6597	406	3	]	]	SYM
ejpam-6597	406	4	alyaa	alyaa	NOUN
ejpam-6597	406	5	alawadi	alawadi	NOUN
ejpam-6597	406	6	,	,	PUNCT
ejpam-6597	406	7	lutfi	lutfi	PROPN
ejpam-6597	406	8	kalantan	kalantan	PROPN
ejpam-6597	406	9	,	,	PUNCT
ejpam-6597	406	10	and	and	CCONJ
ejpam-6597	406	11	maha	maha	PROPN
ejpam-6597	406	12	mohammed	mohammed	PROPN
ejpam-6597	406	13	saeed	saeed	PROPN
ejpam-6597	406	14	.	.	PUNCT
ejpam-6597	407	1	on	on	ADP
ejpam-6597	407	2	the	the	DET
ejpam-6597	407	3	discrete	discrete	ADJ
ejpam-6597	407	4	extension	extension	NOUN
ejpam-6597	407	5	spaces	space	NOUN
ejpam-6597	407	6	.	.	PUNCT
ejpam-6597	408	1	journal	journal	PROPN
ejpam-6597	408	2	of	of	ADP
ejpam-6597	408	3	mathematical	mathematical	ADJ
ejpam-6597	408	4	analysis	analysis	NOUN
ejpam-6597	408	5	,	,	PUNCT
ejpam-6597	408	6	9(2):150–157	9(2):150–157	NOUN
ejpam-6597	408	7	,	,	PUNCT
ejpam-6597	408	8	2018	2018	NUM
ejpam-6597	408	9	.	.	PUNCT
ejpam-6597	409	1	[	[	X
ejpam-6597	409	2	19	19	NUM
ejpam-6597	409	3	]	]	X
ejpam-6597	409	4	dina	dina	PROPN
ejpam-6597	409	5	abuzaid	abuzaid	PROPN
ejpam-6597	409	6	,	,	PUNCT
ejpam-6597	409	7	suad	suad	PROPN
ejpam-6597	409	8	al	al	PROPN
ejpam-6597	409	9	-	-	PUNCT
ejpam-6597	409	10	qarhi	qarhi	PROPN
ejpam-6597	409	11	,	,	PUNCT
ejpam-6597	409	12	and	and	CCONJ
ejpam-6597	409	13	lutfi	lutfi	PROPN
ejpam-6597	409	14	kalantan	kalantan	PROPN
ejpam-6597	409	15	.	.	PUNCT
ejpam-6597	410	1	closed	close	VERB
ejpam-6597	410	2	extension	extension	NOUN
ejpam-6597	410	3	topological	topological	ADJ
ejpam-6597	410	4	spaces	space	NOUN
ejpam-6597	410	5	.	.	PUNCT
ejpam-6597	411	1	european	european	ADJ
ejpam-6597	411	2	journal	journal	PROPN
ejpam-6597	411	3	of	of	ADP
ejpam-6597	411	4	pure	pure	ADJ
ejpam-6597	411	5	and	and	CCONJ
ejpam-6597	411	6	applied	applied	ADJ
ejpam-6597	411	7	mathematics	mathematic	NOUN
ejpam-6597	411	8	,	,	PUNCT
ejpam-6597	411	9	15(2):672–680	15(2):672–680	NUM
ejpam-6597	411	10	,	,	PUNCT
ejpam-6597	411	11	2022	2022	NUM
ejpam-6597	411	12	.	.	PUNCT