id	sid	tid	token	lemma	pos
ejpam-3743	1	1	european	european	PROPN
ejpam-3743	1	2	journal	journal	PROPN
ejpam-3743	1	3	of	of	ADP
ejpam-3743	1	4	pure	pure	ADJ
ejpam-3743	1	5	and	and	CCONJ
ejpam-3743	1	6	applied	apply	VERB
ejpam-3743	1	7	mathematics	mathematic	NOUN
ejpam-3743	1	8	vol	vol	NOUN
ejpam-3743	1	9	.	.	PROPN
ejpam-3743	2	1	13	13	NUM
ejpam-3743	2	2	,	,	PUNCT
ejpam-3743	2	3	no	no	INTJ
ejpam-3743	2	4	.	.	NOUN
ejpam-3743	2	5	3	3	NUM
ejpam-3743	2	6	,	,	PUNCT
ejpam-3743	2	7	2020	2020	NUM
ejpam-3743	2	8	,	,	PUNCT
ejpam-3743	2	9	427	427	NUM
ejpam-3743	2	10	-	-	SYM
ejpam-3743	2	11	443	443	NUM
ejpam-3743	2	12	issn	issn	PROPN
ejpam-3743	2	13	1307	1307	NUM
ejpam-3743	2	14	-	-	SYM
ejpam-3743	2	15	5543	5543	NUM
ejpam-3743	2	16	–	–	PUNCT
ejpam-3743	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3743	2	18	published	publish	VERB
ejpam-3743	2	19	by	by	ADP
ejpam-3743	2	20	new	new	PROPN
ejpam-3743	2	21	york	york	PROPN
ejpam-3743	2	22	business	business	PROPN
ejpam-3743	2	23	global	global	ADJ
ejpam-3743	2	24	limit	limit	NOUN
ejpam-3743	2	25	points	point	NOUN
ejpam-3743	2	26	and	and	CCONJ
ejpam-3743	2	27	separation	separation	NOUN
ejpam-3743	2	28	axioms	axiom	NOUN
ejpam-3743	2	29	with	with	ADP
ejpam-3743	2	30	respect	respect	NOUN
ejpam-3743	2	31	to	to	ADP
ejpam-3743	2	32	supra	supra	NOUN
ejpam-3743	2	33	semi	semi	ADJ
ejpam-3743	2	34	-	-	ADJ
ejpam-3743	2	35	open	open	ADJ
ejpam-3743	2	36	sets	set	NOUN
ejpam-3743	2	37	t.	t.	PROPN
ejpam-3743	2	38	m.	m.	PROPN
ejpam-3743	2	39	al	al	PROPN
ejpam-3743	2	40	-	-	PUNCT
ejpam-3743	2	41	shami1,∗	shami1,∗	PROPN
ejpam-3743	2	42	,	,	PUNCT
ejpam-3743	2	43	e.	e.	PROPN
ejpam-3743	2	44	a.	a.	PROPN
ejpam-3743	2	45	abo	abo	PROPN
ejpam-3743	2	46	-	-	PUNCT
ejpam-3743	2	47	tabl2,3	tabl2,3	PROPN
ejpam-3743	2	48	,	,	PUNCT
ejpam-3743	2	49	b.	b.	PROPN
ejpam-3743	2	50	a.	a.	PROPN
ejpam-3743	2	51	asaad4,5	asaad4,5	PROPN
ejpam-3743	2	52	,	,	PUNCT
ejpam-3743	2	53	m.	m.	NOUN
ejpam-3743	2	54	a.	a.	NOUN
ejpam-3743	2	55	arahet6	arahet6	PROPN
ejpam-3743	2	56	1	1	NUM
ejpam-3743	2	57	department	department	NOUN
ejpam-3743	2	58	of	of	ADP
ejpam-3743	2	59	mathematics	mathematic	NOUN
ejpam-3743	2	60	,	,	PUNCT
ejpam-3743	2	61	sana’a	sana’a	NOUN
ejpam-3743	2	62	university	university	NOUN
ejpam-3743	2	63	,	,	PUNCT
ejpam-3743	2	64	sana’a	sana’a	NOUN
ejpam-3743	2	65	,	,	PUNCT
ejpam-3743	2	66	yemen	yemen	PROPN
ejpam-3743	2	67	2	2	NUM
ejpam-3743	2	68	department	department	NOUN
ejpam-3743	2	69	of	of	ADP
ejpam-3743	2	70	mathematics	mathematic	NOUN
ejpam-3743	2	71	,	,	PUNCT
ejpam-3743	2	72	college	college	NOUN
ejpam-3743	2	73	of	of	ADP
ejpam-3743	2	74	arts	art	NOUN
ejpam-3743	2	75	and	and	CCONJ
ejpam-3743	2	76	sciences	science	NOUN
ejpam-3743	2	77	,	,	PUNCT
ejpam-3743	2	78	methnab	methnab	NOUN
ejpam-3743	2	79	,	,	PUNCT
ejpam-3743	2	80	qassim	qassim	PROPN
ejpam-3743	2	81	university	university	PROPN
ejpam-3743	2	82	,	,	PUNCT
ejpam-3743	3	1	p.	p.	PROPN
ejpam-3743	3	2	o.	o.	PROPN
ejpam-3743	3	3	box	box	PROPN
ejpam-3743	3	4	931	931	NUM
ejpam-3743	3	5	,	,	PUNCT
ejpam-3743	3	6	buridah	buridah	NOUN
ejpam-3743	3	7	51931	51931	NUM
ejpam-3743	3	8	,	,	PUNCT
ejpam-3743	3	9	methnab	methnab	PROPN
ejpam-3743	3	10	,	,	PUNCT
ejpam-3743	3	11	saudia	saudia	PROPN
ejpam-3743	3	12	arabia	arabia	PROPN
ejpam-3743	3	13	3	3	NUM
ejpam-3743	3	14	department	department	NOUN
ejpam-3743	3	15	of	of	ADP
ejpam-3743	3	16	mathematics	mathematic	NOUN
ejpam-3743	3	17	,	,	PUNCT
ejpam-3743	3	18	faculty	faculty	NOUN
ejpam-3743	3	19	of	of	ADP
ejpam-3743	3	20	science	science	NOUN
ejpam-3743	3	21	,	,	PUNCT
ejpam-3743	3	22	assiut	assiut	PROPN
ejpam-3743	3	23	university	university	PROPN
ejpam-3743	3	24	,	,	PUNCT
ejpam-3743	3	25	assiut	assiut	PROPN
ejpam-3743	3	26	,	,	PUNCT
ejpam-3743	3	27	egypt	egypt	PROPN
ejpam-3743	3	28	4	4	NUM
ejpam-3743	3	29	department	department	NOUN
ejpam-3743	3	30	of	of	ADP
ejpam-3743	3	31	computer	computer	NOUN
ejpam-3743	3	32	science	science	NOUN
ejpam-3743	3	33	,	,	PUNCT
ejpam-3743	3	34	college	college	NOUN
ejpam-3743	3	35	of	of	ADP
ejpam-3743	3	36	science	science	NOUN
ejpam-3743	3	37	,	,	PUNCT
ejpam-3743	3	38	cihan	cihan	VERB
ejpam-3743	3	39	university	university	NOUN
ejpam-3743	3	40	-	-	PUNCT
ejpam-3743	3	41	duhok	duhok	NOUN
ejpam-3743	3	42	,	,	PUNCT
ejpam-3743	3	43	kurdistan	kurdistan	ADJ
ejpam-3743	3	44	region	region	NOUN
ejpam-3743	3	45	,	,	PUNCT
ejpam-3743	3	46	iraq	iraq	PROPN
ejpam-3743	3	47	5	5	NUM
ejpam-3743	3	48	department	department	NOUN
ejpam-3743	3	49	of	of	ADP
ejpam-3743	3	50	mathematics	mathematic	NOUN
ejpam-3743	3	51	,	,	PUNCT
ejpam-3743	3	52	faculty	faculty	NOUN
ejpam-3743	3	53	of	of	ADP
ejpam-3743	3	54	science	science	NOUN
ejpam-3743	3	55	,	,	PUNCT
ejpam-3743	3	56	university	university	NOUN
ejpam-3743	3	57	of	of	ADP
ejpam-3743	3	58	zakho	zakho	PROPN
ejpam-3743	3	59	,	,	PUNCT
ejpam-3743	3	60	kurdistan	kurdistan	ADJ
ejpam-3743	3	61	region	region	NOUN
ejpam-3743	3	62	,	,	PUNCT
ejpam-3743	3	63	iraq	iraq	PROPN
ejpam-3743	3	64	6	6	NUM
ejpam-3743	3	65	department	department	NOUN
ejpam-3743	3	66	of	of	ADP
ejpam-3743	3	67	mathematics	mathematic	NOUN
ejpam-3743	3	68	,	,	PUNCT
ejpam-3743	3	69	amran	amran	ADJ
ejpam-3743	3	70	university	university	NOUN
ejpam-3743	3	71	,	,	PUNCT
ejpam-3743	3	72	amran	amran	PROPN
ejpam-3743	3	73	,	,	PUNCT
ejpam-3743	3	74	yemen	yemen	PROPN
ejpam-3743	3	75	abstract	abstract	NOUN
ejpam-3743	3	76	.	.	PUNCT
ejpam-3743	4	1	sometimes	sometimes	ADV
ejpam-3743	4	2	we	we	PRON
ejpam-3743	4	3	need	need	VERB
ejpam-3743	4	4	to	to	PART
ejpam-3743	4	5	minimize	minimize	VERB
ejpam-3743	4	6	the	the	DET
ejpam-3743	4	7	conditions	condition	NOUN
ejpam-3743	4	8	of	of	ADP
ejpam-3743	4	9	topology	topology	NOUN
ejpam-3743	4	10	for	for	ADP
ejpam-3743	4	11	different	different	ADJ
ejpam-3743	4	12	reasons	reason	NOUN
ejpam-3743	4	13	such	such	ADJ
ejpam-3743	4	14	as	as	ADP
ejpam-3743	4	15	obtaining	obtain	VERB
ejpam-3743	4	16	more	more	ADV
ejpam-3743	4	17	convenient	convenient	ADJ
ejpam-3743	4	18	structures	structure	NOUN
ejpam-3743	4	19	to	to	PART
ejpam-3743	4	20	describe	describe	VERB
ejpam-3743	4	21	some	some	DET
ejpam-3743	4	22	real	real	ADJ
ejpam-3743	4	23	-	-	PUNCT
ejpam-3743	4	24	life	life	NOUN
ejpam-3743	4	25	problems	problem	NOUN
ejpam-3743	4	26	,	,	PUNCT
ejpam-3743	4	27	or	or	CCONJ
ejpam-3743	4	28	constructing	construct	VERB
ejpam-3743	4	29	some	some	DET
ejpam-3743	4	30	counterexamples	counterexample	NOUN
ejpam-3743	4	31	whom	whom	PRON
ejpam-3743	4	32	show	show	VERB
ejpam-3743	4	33	the	the	DET
ejpam-3743	4	34	interrelations	interrelation	NOUN
ejpam-3743	4	35	between	between	ADP
ejpam-3743	4	36	certain	certain	ADJ
ejpam-3743	4	37	topological	topological	ADJ
ejpam-3743	4	38	concepts	concept	NOUN
ejpam-3743	4	39	,	,	PUNCT
ejpam-3743	4	40	or	or	CCONJ
ejpam-3743	4	41	preserving	preserve	VERB
ejpam-3743	4	42	some	some	DET
ejpam-3743	4	43	properties	property	NOUN
ejpam-3743	4	44	under	under	ADP
ejpam-3743	4	45	fewer	few	ADJ
ejpam-3743	4	46	conditions	condition	NOUN
ejpam-3743	4	47	of	of	ADP
ejpam-3743	4	48	those	those	PRON
ejpam-3743	4	49	on	on	ADP
ejpam-3743	4	50	topology	topology	NOUN
ejpam-3743	4	51	.	.	PUNCT
ejpam-3743	5	1	to	to	PART
ejpam-3743	5	2	contribute	contribute	VERB
ejpam-3743	5	3	this	this	DET
ejpam-3743	5	4	research	research	NOUN
ejpam-3743	5	5	area	area	NOUN
ejpam-3743	5	6	,	,	PUNCT
ejpam-3743	5	7	in	in	ADP
ejpam-3743	5	8	this	this	DET
ejpam-3743	5	9	paper	paper	NOUN
ejpam-3743	5	10	,	,	PUNCT
ejpam-3743	5	11	we	we	PRON
ejpam-3743	5	12	establish	establish	VERB
ejpam-3743	5	13	some	some	DET
ejpam-3743	5	14	new	new	ADJ
ejpam-3743	5	15	concepts	concept	NOUN
ejpam-3743	5	16	on	on	ADP
ejpam-3743	5	17	supra	supra	PROPN
ejpam-3743	5	18	topological	topological	ADJ
ejpam-3743	5	19	spaces	space	NOUN
ejpam-3743	5	20	using	use	VERB
ejpam-3743	5	21	supra	supra	PROPN
ejpam-3743	5	22	semi	semi	ADJ
ejpam-3743	5	23	-	-	ADJ
ejpam-3743	5	24	open	open	ADJ
ejpam-3743	5	25	sets	set	NOUN
ejpam-3743	5	26	and	and	CCONJ
ejpam-3743	5	27	give	give	VERB
ejpam-3743	5	28	some	some	DET
ejpam-3743	5	29	characterizations	characterization	NOUN
ejpam-3743	5	30	of	of	ADP
ejpam-3743	5	31	them	they	PRON
ejpam-3743	5	32	.	.	PUNCT
ejpam-3743	6	1	first	first	ADV
ejpam-3743	6	2	,	,	PUNCT
ejpam-3743	6	3	we	we	PRON
ejpam-3743	6	4	introduce	introduce	VERB
ejpam-3743	6	5	a	a	DET
ejpam-3743	6	6	concept	concept	NOUN
ejpam-3743	6	7	of	of	ADP
ejpam-3743	6	8	supra	supra	PROPN
ejpam-3743	6	9	semi	semi	NOUN
ejpam-3743	6	10	limit	limit	NOUN
ejpam-3743	6	11	points	point	NOUN
ejpam-3743	6	12	of	of	ADP
ejpam-3743	6	13	a	a	DET
ejpam-3743	6	14	set	set	NOUN
ejpam-3743	6	15	and	and	CCONJ
ejpam-3743	6	16	study	study	VERB
ejpam-3743	6	17	main	main	ADJ
ejpam-3743	6	18	properties	property	NOUN
ejpam-3743	6	19	,	,	PUNCT
ejpam-3743	6	20	in	in	ADP
ejpam-3743	6	21	particular	particular	ADJ
ejpam-3743	6	22	,	,	PUNCT
ejpam-3743	6	23	on	on	ADP
ejpam-3743	6	24	the	the	DET
ejpam-3743	6	25	spaces	space	NOUN
ejpam-3743	6	26	that	that	PRON
ejpam-3743	6	27	possess	possess	VERB
ejpam-3743	6	28	the	the	DET
ejpam-3743	6	29	difference	difference	NOUN
ejpam-3743	6	30	property	property	NOUN
ejpam-3743	6	31	.	.	PUNCT
ejpam-3743	7	1	second	second	ADJ
ejpam-3743	7	2	,	,	PUNCT
ejpam-3743	7	3	we	we	PRON
ejpam-3743	7	4	define	define	VERB
ejpam-3743	7	5	and	and	CCONJ
ejpam-3743	7	6	investigate	investigate	VERB
ejpam-3743	7	7	new	new	ADJ
ejpam-3743	7	8	separation	separation	NOUN
ejpam-3743	7	9	axioms	axiom	NOUN
ejpam-3743	7	10	,	,	PUNCT
ejpam-3743	7	11	namely	namely	ADV
ejpam-3743	7	12	supra	supra	ADJ
ejpam-3743	7	13	semi	semi	ADV
ejpam-3743	7	14	ti	ti	NOUN
ejpam-3743	7	15	-	-	NOUN
ejpam-3743	7	16	spaces	space	NOUN
ejpam-3743	7	17	(	(	PUNCT
ejpam-3743	7	18	i	i	NOUN
ejpam-3743	7	19	=	=	NOUN
ejpam-3743	7	20	0	0	NUM
ejpam-3743	7	21	,	,	PUNCT
ejpam-3743	7	22	1	1	NUM
ejpam-3743	7	23	,	,	PUNCT
ejpam-3743	7	24	2	2	NUM
ejpam-3743	7	25	,	,	PUNCT
ejpam-3743	7	26	3	3	NUM
ejpam-3743	7	27	,	,	PUNCT
ejpam-3743	7	28	4	4	NUM
ejpam-3743	7	29	)	)	PUNCT
ejpam-3743	7	30	and	and	CCONJ
ejpam-3743	7	31	give	give	VERB
ejpam-3743	7	32	complete	complete	ADJ
ejpam-3743	7	33	descriptions	description	NOUN
ejpam-3743	7	34	for	for	ADP
ejpam-3743	7	35	each	each	DET
ejpam-3743	7	36	one	one	NUM
ejpam-3743	7	37	of	of	ADP
ejpam-3743	7	38	them	they	PRON
ejpam-3743	7	39	.	.	PUNCT
ejpam-3743	8	1	we	we	PRON
ejpam-3743	8	2	provide	provide	VERB
ejpam-3743	8	3	some	some	DET
ejpam-3743	8	4	examples	example	NOUN
ejpam-3743	8	5	to	to	PART
ejpam-3743	8	6	show	show	VERB
ejpam-3743	8	7	the	the	DET
ejpam-3743	8	8	relationships	relationship	NOUN
ejpam-3743	8	9	between	between	ADP
ejpam-3743	8	10	them	they	PRON
ejpam-3743	8	11	as	as	ADV
ejpam-3743	8	12	well	well	ADV
ejpam-3743	8	13	as	as	ADP
ejpam-3743	8	14	with	with	ADP
ejpam-3743	8	15	sti	sti	NOUN
ejpam-3743	8	16	-	-	NOUN
ejpam-3743	8	17	space	space	NOUN
ejpam-3743	8	18	.	.	PUNCT
ejpam-3743	9	1	2020	2020	NUM
ejpam-3743	9	2	mathematics	mathematic	NOUN
ejpam-3743	9	3	subject	subject	NOUN
ejpam-3743	9	4	classifications	classification	NOUN
ejpam-3743	9	5	:	:	PUNCT
ejpam-3743	9	6	54a05	54a05	NUM
ejpam-3743	9	7	,	,	PUNCT
ejpam-3743	9	8	54c10	54c10	NUM
ejpam-3743	9	9	,	,	PUNCT
ejpam-3743	9	10	54d10	54d10	NUM
ejpam-3743	9	11	,	,	PUNCT
ejpam-3743	9	12	54d15	54d15	PRON
ejpam-3743	9	13	key	key	ADJ
ejpam-3743	9	14	words	word	NOUN
ejpam-3743	9	15	and	and	CCONJ
ejpam-3743	9	16	phrases	phrase	NOUN
ejpam-3743	9	17	:	:	PUNCT
ejpam-3743	9	18	supra	supra	ADJ
ejpam-3743	9	19	semi	semi	ADJ
ejpam-3743	9	20	-	-	ADJ
ejpam-3743	9	21	open	open	ADJ
ejpam-3743	9	22	set	set	NOUN
ejpam-3743	9	23	,	,	PUNCT
ejpam-3743	9	24	supra	supra	PROPN
ejpam-3743	9	25	semi	semi	NOUN
ejpam-3743	9	26	limit	limit	NOUN
ejpam-3743	9	27	point	point	NOUN
ejpam-3743	9	28	,	,	PUNCT
ejpam-3743	9	29	ssti	ssti	NOUN
ejpam-3743	9	30	-	-	PUNCT
ejpam-3743	9	31	space	space	NOUN
ejpam-3743	9	32	(	(	PUNCT
ejpam-3743	9	33	i	i	NOUN
ejpam-3743	9	34	=	=	NOUN
ejpam-3743	9	35	0	0	NUM
ejpam-3743	9	36	,	,	PUNCT
ejpam-3743	9	37	1	1	NUM
ejpam-3743	9	38	,	,	PUNCT
ejpam-3743	9	39	2	2	NUM
ejpam-3743	9	40	,	,	PUNCT
ejpam-3743	9	41	3	3	NUM
ejpam-3743	9	42	,	,	PUNCT
ejpam-3743	9	43	4	4	NUM
ejpam-3743	9	44	)	)	PUNCT
ejpam-3743	9	45	1	1	NUM
ejpam-3743	9	46	.	.	PUNCT
ejpam-3743	10	1	introduction	introduction	NOUN
ejpam-3743	10	2	and	and	CCONJ
ejpam-3743	10	3	preliminaries	preliminary	NOUN
ejpam-3743	10	4	a	a	DET
ejpam-3743	10	5	structure	structure	NOUN
ejpam-3743	10	6	on	on	ADP
ejpam-3743	10	7	a	a	DET
ejpam-3743	10	8	nonempty	nonempty	ADV
ejpam-3743	10	9	set	set	VERB
ejpam-3743	10	10	x	x	PUNCT
ejpam-3743	10	11	is	be	AUX
ejpam-3743	10	12	a	a	DET
ejpam-3743	10	13	subset	subset	NOUN
ejpam-3743	10	14	of	of	ADP
ejpam-3743	10	15	its	its	PRON
ejpam-3743	10	16	power	power	NOUN
ejpam-3743	10	17	set	set	NOUN
ejpam-3743	10	18	p	p	PROPN
ejpam-3743	10	19	(	(	PUNCT
ejpam-3743	10	20	x	x	NOUN
ejpam-3743	10	21	)	)	PUNCT
ejpam-3743	10	22	,	,	PUNCT
ejpam-3743	10	23	topological	topological	ADJ
ejpam-3743	10	24	spaces	space	NOUN
ejpam-3743	10	25	is	be	AUX
ejpam-3743	10	26	an	an	DET
ejpam-3743	10	27	example	example	NOUN
ejpam-3743	10	28	of	of	ADP
ejpam-3743	10	29	structure	structure	NOUN
ejpam-3743	10	30	satisfying	satisfy	VERB
ejpam-3743	10	31	three	three	NUM
ejpam-3743	10	32	conditions	condition	NOUN
ejpam-3743	10	33	.	.	PUNCT
ejpam-3743	11	1	in	in	ADP
ejpam-3743	11	2	fact	fact	NOUN
ejpam-3743	11	3	,	,	PUNCT
ejpam-3743	11	4	topological	topological	ADJ
ejpam-3743	11	5	spaces	space	NOUN
ejpam-3743	11	6	have	have	AUX
ejpam-3743	11	7	been	be	AUX
ejpam-3743	11	8	generalized	generalize	VERB
ejpam-3743	11	9	in	in	ADP
ejpam-3743	11	10	many	many	ADJ
ejpam-3743	11	11	ways	way	NOUN
ejpam-3743	11	12	.	.	PUNCT
ejpam-3743	12	1	alexendroff	alexendroff	NOUN
ejpam-3743	13	1	[	[	X
ejpam-3743	13	2	12	12	NUM
ejpam-3743	13	3	]	]	PUNCT
ejpam-3743	13	4	,	,	PUNCT
ejpam-3743	13	5	in	in	ADP
ejpam-3743	13	6	1940	1940	NUM
ejpam-3743	13	7	,	,	PUNCT
ejpam-3743	13	8	developed	develop	VERB
ejpam-3743	13	9	abstract	abstract	ADJ
ejpam-3743	13	10	spaces	space	NOUN
ejpam-3743	13	11	where	where	SCONJ
ejpam-3743	13	12	∗corresponding	∗corresponde	VERB
ejpam-3743	13	13	author	author	NOUN
ejpam-3743	13	14	.	.	PUNCT
ejpam-3743	14	1	doi	doi	NOUN
ejpam-3743	14	2	:	:	PUNCT
ejpam-3743	14	3	https://doi.org/10.29020/nybg.ejpam.v13i3.3743	https://doi.org/10.29020/nybg.ejpam.v13i3.3743	PROPN
ejpam-3743	14	4	email	email	NOUN
ejpam-3743	14	5	addresses	address	VERB
ejpam-3743	14	6	:	:	PUNCT
ejpam-3743	14	7	tareqalshami83@gmail.com	tareqalshami83@gmail.com	X
ejpam-3743	14	8	(	(	PUNCT
ejpam-3743	14	9	t.	t.	PROPN
ejpam-3743	14	10	m.	m.	PROPN
ejpam-3743	14	11	al	al	PROPN
ejpam-3743	14	12	-	-	PUNCT
ejpam-3743	14	13	shami	shami	PROPN
ejpam-3743	14	14	)	)	PUNCT
ejpam-3743	14	15	,	,	PUNCT
ejpam-3743	14	16	a.adotabl@qu.edu.sa	a.adotabl@qu.edu.sa	PROPN
ejpam-3743	14	17	(	(	PUNCT
ejpam-3743	14	18	e.	e.	PROPN
ejpam-3743	14	19	a.	a.	PROPN
ejpam-3743	14	20	abo	abo	PROPN
ejpam-3743	14	21	-	-	PUNCT
ejpam-3743	14	22	tabl	tabl	NOUN
ejpam-3743	14	23	)	)	PUNCT
ejpam-3743	14	24	,	,	PUNCT
ejpam-3743	14	25	baravan.asaad@uoz.edu.krd	baravan.asaad@uoz.edu.krd	PROPN
ejpam-3743	14	26	(	(	PUNCT
ejpam-3743	14	27	b.	b.	PROPN
ejpam-3743	14	28	a.	a.	PROPN
ejpam-3743	14	29	asaad	asaad	PROPN
ejpam-3743	14	30	)	)	PUNCT
ejpam-3743	14	31	,	,	PUNCT
ejpam-3743	14	32	malroheet@yahoo.com	malroheet@yahoo.com	X
ejpam-3743	14	33	(	(	PUNCT
ejpam-3743	14	34	m.	m.	NOUN
ejpam-3743	14	35	a.	a.	PROPN
ejpam-3743	14	36	arahet	arahet	PROPN
ejpam-3743	14	37	)	)	PUNCT
ejpam-3743	14	38	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-3743	15	1	427	427	NUM
ejpam-3743	16	1	c	c	NOUN
ejpam-3743	16	2	©	©	NOUN
ejpam-3743	16	3	2020	2020	NUM
ejpam-3743	16	4	ejpam	ejpam	VERB
ejpam-3743	16	5	all	all	DET
ejpam-3743	16	6	rights	right	NOUN
ejpam-3743	16	7	reserved	reserve	VERB
ejpam-3743	16	8	.	.	PUNCT
ejpam-3743	17	1	t.	t.	PROPN
ejpam-3743	17	2	m.	m.	PROPN
ejpam-3743	17	3	al	al	PROPN
ejpam-3743	17	4	-	-	PUNCT
ejpam-3743	17	5	shami	shami	PROPN
ejpam-3743	17	6	et	et	PROPN
ejpam-3743	17	7	al	al	PROPN
ejpam-3743	17	8	.	.	PUNCT
ejpam-3743	17	9	/	/	SYM
ejpam-3743	17	10	eur	eur	PROPN
ejpam-3743	17	11	.	.	PUNCT
ejpam-3743	18	1	j.	j.	PROPN
ejpam-3743	18	2	pure	pure	PROPN
ejpam-3743	18	3	appl	appl	PROPN
ejpam-3743	18	4	.	.	PROPN
ejpam-3743	18	5	math	math	PROPN
ejpam-3743	18	6	,	,	PUNCT
ejpam-3743	18	7	13	13	NUM
ejpam-3743	18	8	(	(	PUNCT
ejpam-3743	18	9	3	3	NUM
ejpam-3743	18	10	)	)	PUNCT
ejpam-3743	18	11	(	(	PUNCT
ejpam-3743	18	12	2020	2020	NUM
ejpam-3743	18	13	)	)	PUNCT
ejpam-3743	18	14	,	,	PUNCT
ejpam-3743	18	15	427	427	NUM
ejpam-3743	18	16	-	-	SYM
ejpam-3743	18	17	443	443	NUM
ejpam-3743	18	18	428	428	NUM
ejpam-3743	18	19	he	he	PRON
ejpam-3743	18	20	strengthened	strengthen	VERB
ejpam-3743	18	21	the	the	DET
ejpam-3743	18	22	intersection	intersection	NOUN
ejpam-3743	18	23	condition	condition	NOUN
ejpam-3743	18	24	.	.	PUNCT
ejpam-3743	19	1	mashhour	mashhour	INTJ
ejpam-3743	19	2	et	et	PROPN
ejpam-3743	19	3	al	al	PROPN
ejpam-3743	19	4	.	.	PUNCT
ejpam-3743	20	1	[	[	X
ejpam-3743	20	2	21	21	NUM
ejpam-3743	20	3	]	]	X
ejpam-3743	20	4	,	,	PUNCT
ejpam-3743	20	5	in	in	ADP
ejpam-3743	20	6	1983	1983	NUM
ejpam-3743	20	7	,	,	PUNCT
ejpam-3743	20	8	considered	consider	VERB
ejpam-3743	20	9	supra	supra	PROPN
ejpam-3743	20	10	topological	topological	ADJ
ejpam-3743	20	11	spaces	space	NOUN
ejpam-3743	20	12	by	by	ADP
ejpam-3743	20	13	neglecting	neglect	VERB
ejpam-3743	20	14	the	the	DET
ejpam-3743	20	15	intersection	intersection	NOUN
ejpam-3743	20	16	condition	condition	NOUN
ejpam-3743	20	17	.	.	PUNCT
ejpam-3743	21	1	maki	maki	NOUN
ejpam-3743	21	2	et	et	PROPN
ejpam-3743	21	3	al	al	PROPN
ejpam-3743	21	4	.	.	PUNCT
ejpam-3743	22	1	[	[	X
ejpam-3743	22	2	20	20	NUM
ejpam-3743	22	3	]	]	PUNCT
ejpam-3743	22	4	,	,	PUNCT
ejpam-3743	22	5	in	in	ADP
ejpam-3743	22	6	1996	1996	NUM
ejpam-3743	22	7	,	,	PUNCT
ejpam-3743	22	8	presented	present	VERB
ejpam-3743	22	9	a	a	DET
ejpam-3743	22	10	minimal	minimal	ADJ
ejpam-3743	22	11	structure	structure	NOUN
ejpam-3743	22	12	as	as	ADP
ejpam-3743	22	13	a	a	DET
ejpam-3743	22	14	collection	collection	NOUN
ejpam-3743	22	15	contains	contain	VERB
ejpam-3743	22	16	the	the	DET
ejpam-3743	22	17	empty	empty	ADJ
ejpam-3743	22	18	and	and	CCONJ
ejpam-3743	22	19	universal	universal	ADJ
ejpam-3743	22	20	sets	set	NOUN
ejpam-3743	22	21	.	.	PUNCT
ejpam-3743	23	1	császár	császár	NOUN
ejpam-3743	24	1	[	[	X
ejpam-3743	24	2	13	13	NUM
ejpam-3743	24	3	]	]	PUNCT
ejpam-3743	24	4	,	,	PUNCT
ejpam-3743	24	5	in	in	ADP
ejpam-3743	24	6	2002	2002	NUM
ejpam-3743	24	7	,	,	PUNCT
ejpam-3743	24	8	introduced	introduce	VERB
ejpam-3743	24	9	generalized	generalized	ADJ
ejpam-3743	24	10	topological	topological	ADJ
ejpam-3743	24	11	spaces	space	NOUN
ejpam-3743	24	12	if	if	SCONJ
ejpam-3743	24	13	it	it	PRON
ejpam-3743	24	14	contains	contain	VERB
ejpam-3743	24	15	the	the	DET
ejpam-3743	24	16	empty	empty	ADJ
ejpam-3743	24	17	set	set	NOUN
ejpam-3743	24	18	and	and	CCONJ
ejpam-3743	24	19	is	be	AUX
ejpam-3743	24	20	closed	close	VERB
ejpam-3743	24	21	under	under	ADP
ejpam-3743	24	22	a	a	DET
ejpam-3743	24	23	nonempty	nonempty	ADJ
ejpam-3743	24	24	union	union	NOUN
ejpam-3743	24	25	;	;	PUNCT
ejpam-3743	24	26	and	and	CCONJ
ejpam-3743	24	27	in	in	ADP
ejpam-3743	24	28	2011	2011	NUM
ejpam-3743	24	29	,	,	PUNCT
ejpam-3743	24	30	he	he	PRON
ejpam-3743	25	1	[	[	X
ejpam-3743	25	2	14	14	NUM
ejpam-3743	25	3	]	]	PUNCT
ejpam-3743	25	4	studied	study	VERB
ejpam-3743	25	5	a	a	DET
ejpam-3743	25	6	weak	weak	ADJ
ejpam-3743	25	7	structure	structure	NOUN
ejpam-3743	25	8	as	as	SCONJ
ejpam-3743	25	9	a	a	DET
ejpam-3743	25	10	collection	collection	NOUN
ejpam-3743	25	11	contains	contain	VERB
ejpam-3743	25	12	the	the	DET
ejpam-3743	25	13	empty	empty	ADJ
ejpam-3743	25	14	set	set	NOUN
ejpam-3743	25	15	.	.	PUNCT
ejpam-3743	26	1	al	al	PROPN
ejpam-3743	26	2	-	-	PUNCT
ejpam-3743	26	3	odhari	odhari	ADJ
ejpam-3743	26	4	[	[	X
ejpam-3743	26	5	1	1	NUM
ejpam-3743	26	6	]	]	PUNCT
ejpam-3743	26	7	,	,	PUNCT
ejpam-3743	26	8	in	in	ADP
ejpam-3743	26	9	2015	2015	NUM
ejpam-3743	26	10	,	,	PUNCT
ejpam-3743	26	11	defined	define	VERB
ejpam-3743	26	12	infra	infra	NOUN
ejpam-3743	26	13	topological	topological	ADJ
ejpam-3743	26	14	spaces	space	NOUN
ejpam-3743	26	15	by	by	ADP
ejpam-3743	26	16	dropping	drop	VERB
ejpam-3743	26	17	only	only	ADV
ejpam-3743	26	18	the	the	DET
ejpam-3743	26	19	union	union	NOUN
ejpam-3743	26	20	condition	condition	NOUN
ejpam-3743	26	21	.	.	PUNCT
ejpam-3743	27	1	many	many	ADJ
ejpam-3743	27	2	aspects	aspect	NOUN
ejpam-3743	27	3	of	of	ADP
ejpam-3743	27	4	such	such	ADJ
ejpam-3743	27	5	spaces	space	NOUN
ejpam-3743	27	6	have	have	AUX
ejpam-3743	27	7	already	already	ADV
ejpam-3743	27	8	been	be	AUX
ejpam-3743	27	9	studied	study	VERB
ejpam-3743	27	10	.	.	PUNCT
ejpam-3743	28	1	supra	supra	PROPN
ejpam-3743	28	2	topological	topological	ADJ
ejpam-3743	28	3	spaces	space	NOUN
ejpam-3743	28	4	is	be	AUX
ejpam-3743	28	5	one	one	NUM
ejpam-3743	28	6	of	of	ADP
ejpam-3743	28	7	the	the	DET
ejpam-3743	28	8	most	most	ADV
ejpam-3743	28	9	important	important	ADJ
ejpam-3743	28	10	developments	development	NOUN
ejpam-3743	28	11	of	of	ADP
ejpam-3743	28	12	general	general	ADJ
ejpam-3743	28	13	topology	topology	NOUN
ejpam-3743	28	14	in	in	ADP
ejpam-3743	28	15	recent	recent	ADJ
ejpam-3743	28	16	years	year	NOUN
ejpam-3743	28	17	.	.	PUNCT
ejpam-3743	29	1	a	a	DET
ejpam-3743	29	2	family	family	NOUN
ejpam-3743	29	3	µ	µ	X
ejpam-3743	29	4	of	of	ADP
ejpam-3743	29	5	subsets	subset	NOUN
ejpam-3743	29	6	of	of	ADP
ejpam-3743	29	7	a	a	DET
ejpam-3743	29	8	nonempty	nonempty	ADV
ejpam-3743	29	9	set	set	VERB
ejpam-3743	29	10	x	x	PUNCT
ejpam-3743	29	11	is	be	AUX
ejpam-3743	29	12	called	call	VERB
ejpam-3743	29	13	a	a	DET
ejpam-3743	29	14	supra	supra	ADJ
ejpam-3743	29	15	topology	topology	NOUN
ejpam-3743	29	16	if	if	SCONJ
ejpam-3743	29	17	it	it	PRON
ejpam-3743	29	18	satisfies	satisfy	VERB
ejpam-3743	29	19	two	two	NUM
ejpam-3743	29	20	conditions	condition	NOUN
ejpam-3743	29	21	:	:	PUNCT
ejpam-3743	29	22	the	the	DET
ejpam-3743	29	23	first	first	ADJ
ejpam-3743	29	24	one	one	NOUN
ejpam-3743	29	25	is	be	AUX
ejpam-3743	29	26	the	the	DET
ejpam-3743	29	27	empty	empty	ADJ
ejpam-3743	29	28	and	and	CCONJ
ejpam-3743	29	29	universal	universal	ADJ
ejpam-3743	29	30	sets	set	NOUN
ejpam-3743	29	31	belong	belong	VERB
ejpam-3743	29	32	to	to	ADP
ejpam-3743	29	33	µ	µ	NUM
ejpam-3743	29	34	;	;	PUNCT
ejpam-3743	29	35	and	and	CCONJ
ejpam-3743	29	36	the	the	DET
ejpam-3743	29	37	second	second	ADJ
ejpam-3743	29	38	one	one	NOUN
ejpam-3743	29	39	is	be	AUX
ejpam-3743	29	40	it	it	PRON
ejpam-3743	29	41	is	be	AUX
ejpam-3743	29	42	closed	close	VERB
ejpam-3743	29	43	under	under	ADP
ejpam-3743	29	44	arbitrary	arbitrary	ADJ
ejpam-3743	29	45	union	union	NOUN
ejpam-3743	29	46	.	.	PUNCT
ejpam-3743	30	1	some	some	DET
ejpam-3743	30	2	authors	author	NOUN
ejpam-3743	30	3	remove	remove	VERB
ejpam-3743	30	4	the	the	DET
ejpam-3743	30	5	empty	empty	ADJ
ejpam-3743	30	6	set	set	NOUN
ejpam-3743	30	7	from	from	ADP
ejpam-3743	30	8	the	the	DET
ejpam-3743	30	9	first	first	ADJ
ejpam-3743	30	10	condition	condition	NOUN
ejpam-3743	30	11	of	of	ADP
ejpam-3743	30	12	a	a	DET
ejpam-3743	30	13	supra	supra	ADJ
ejpam-3743	30	14	topology	topology	NOUN
ejpam-3743	30	15	because	because	SCONJ
ejpam-3743	30	16	it	it	PRON
ejpam-3743	30	17	is	be	AUX
ejpam-3743	30	18	obtained	obtain	VERB
ejpam-3743	30	19	from	from	ADP
ejpam-3743	30	20	the	the	DET
ejpam-3743	30	21	second	second	ADJ
ejpam-3743	30	22	condition	condition	NOUN
ejpam-3743	30	23	as	as	ADP
ejpam-3743	30	24	the	the	DET
ejpam-3743	30	25	union	union	NOUN
ejpam-3743	30	26	of	of	ADP
ejpam-3743	30	27	an	an	DET
ejpam-3743	30	28	empty	empty	ADJ
ejpam-3743	30	29	collection	collection	NOUN
ejpam-3743	30	30	of	of	ADP
ejpam-3743	30	31	sets	set	NOUN
ejpam-3743	30	32	.	.	PUNCT
ejpam-3743	31	1	mashhour	mashhour	INTJ
ejpam-3743	31	2	et	et	PROPN
ejpam-3743	31	3	al	al	PROPN
ejpam-3743	31	4	.	.	PUNCT
ejpam-3743	32	1	[	[	X
ejpam-3743	32	2	21	21	NUM
ejpam-3743	32	3	]	]	PUNCT
ejpam-3743	32	4	studied	study	VERB
ejpam-3743	32	5	some	some	DET
ejpam-3743	32	6	basic	basic	ADJ
ejpam-3743	32	7	operators	operator	NOUN
ejpam-3743	32	8	,	,	PUNCT
ejpam-3743	32	9	continuity	continuity	NOUN
ejpam-3743	32	10	and	and	CCONJ
ejpam-3743	32	11	separation	separation	NOUN
ejpam-3743	32	12	axioms	axiom	NOUN
ejpam-3743	32	13	on	on	ADP
ejpam-3743	32	14	supra	supra	PROPN
ejpam-3743	32	15	topological	topological	ADJ
ejpam-3743	32	16	spaces	space	NOUN
ejpam-3743	32	17	.	.	PUNCT
ejpam-3743	33	1	al	al	PROPN
ejpam-3743	33	2	-	-	PUNCT
ejpam-3743	33	3	shami	shami	PROPN
ejpam-3743	34	1	[	[	X
ejpam-3743	34	2	2	2	NUM
ejpam-3743	34	3	]	]	PUNCT
ejpam-3743	34	4	investigated	investigate	VERB
ejpam-3743	34	5	the	the	DET
ejpam-3743	34	6	classical	classical	ADJ
ejpam-3743	34	7	topological	topological	ADJ
ejpam-3743	34	8	notions	notion	NOUN
ejpam-3743	34	9	such	such	ADJ
ejpam-3743	34	10	as	as	ADP
ejpam-3743	34	11	limit	limit	NOUN
ejpam-3743	34	12	points	point	NOUN
ejpam-3743	34	13	of	of	ADP
ejpam-3743	34	14	a	a	DET
ejpam-3743	34	15	set	set	NOUN
ejpam-3743	34	16	,	,	PUNCT
ejpam-3743	34	17	compactness	compactness	NOUN
ejpam-3743	34	18	,	,	PUNCT
ejpam-3743	34	19	and	and	CCONJ
ejpam-3743	34	20	separation	separation	NOUN
ejpam-3743	34	21	axioms	axiom	NOUN
ejpam-3743	34	22	on	on	ADP
ejpam-3743	34	23	the	the	DET
ejpam-3743	34	24	supra	supra	PROPN
ejpam-3743	34	25	topological	topological	ADJ
ejpam-3743	34	26	spaces	space	NOUN
ejpam-3743	34	27	.	.	PUNCT
ejpam-3743	35	1	he	he	PRON
ejpam-3743	36	1	[	[	X
ejpam-3743	36	2	7	7	X
ejpam-3743	36	3	]	]	PUNCT
ejpam-3743	36	4	also	also	ADV
ejpam-3743	36	5	studied	study	VERB
ejpam-3743	36	6	paracompactness	paracompactness	NOUN
ejpam-3743	36	7	on	on	ADP
ejpam-3743	36	8	supra	supra	PROPN
ejpam-3743	36	9	topological	topological	ADJ
ejpam-3743	36	10	spaces	space	NOUN
ejpam-3743	36	11	.	.	PUNCT
ejpam-3743	37	1	it	it	PRON
ejpam-3743	37	2	should	should	AUX
ejpam-3743	37	3	be	be	AUX
ejpam-3743	37	4	noted	note	VERB
ejpam-3743	37	5	that	that	SCONJ
ejpam-3743	37	6	the	the	DET
ejpam-3743	37	7	supra	supra	PROPN
ejpam-3743	37	8	topological	topological	ADJ
ejpam-3743	37	9	frame	frame	NOUN
ejpam-3743	37	10	can	can	AUX
ejpam-3743	37	11	be	be	AUX
ejpam-3743	37	12	more	more	ADV
ejpam-3743	37	13	convenient	convenient	ADJ
ejpam-3743	37	14	to	to	PART
ejpam-3743	37	15	solve	solve	VERB
ejpam-3743	37	16	some	some	DET
ejpam-3743	37	17	practical	practical	ADJ
ejpam-3743	37	18	problems	problem	NOUN
ejpam-3743	37	19	and	and	CCONJ
ejpam-3743	37	20	to	to	PART
ejpam-3743	37	21	model	model	VERB
ejpam-3743	37	22	some	some	DET
ejpam-3743	37	23	phenomena	phenomenon	NOUN
ejpam-3743	37	24	as	as	SCONJ
ejpam-3743	37	25	pointed	point	VERB
ejpam-3743	37	26	out	out	ADP
ejpam-3743	37	27	in	in	ADP
ejpam-3743	37	28	[	[	X
ejpam-3743	37	29	19	19	NUM
ejpam-3743	37	30	]	]	PUNCT
ejpam-3743	37	31	.	.	PUNCT
ejpam-3743	38	1	some	some	DET
ejpam-3743	38	2	results	result	NOUN
ejpam-3743	38	3	via	via	ADP
ejpam-3743	38	4	topology	topology	NOUN
ejpam-3743	38	5	do	do	AUX
ejpam-3743	38	6	not	not	PART
ejpam-3743	38	7	still	still	ADV
ejpam-3743	38	8	valid	valid	ADJ
ejpam-3743	38	9	via	via	ADP
ejpam-3743	38	10	supra	supra	PROPN
ejpam-3743	38	11	topology	topology	NOUN
ejpam-3743	38	12	such	such	ADJ
ejpam-3743	38	13	as	as	ADP
ejpam-3743	38	14	the	the	DET
ejpam-3743	38	15	distribution	distribution	NOUN
ejpam-3743	38	16	of	of	ADP
ejpam-3743	38	17	the	the	DET
ejpam-3743	38	18	closure	closure	NOUN
ejpam-3743	38	19	operator	operator	NOUN
ejpam-3743	38	20	between	between	ADP
ejpam-3743	38	21	the	the	DET
ejpam-3743	38	22	union	union	NOUN
ejpam-3743	38	23	of	of	ADP
ejpam-3743	38	24	two	two	NUM
ejpam-3743	38	25	sets	set	NOUN
ejpam-3743	38	26	and	and	CCONJ
ejpam-3743	38	27	the	the	DET
ejpam-3743	38	28	distribution	distribution	NOUN
ejpam-3743	38	29	of	of	ADP
ejpam-3743	38	30	the	the	DET
ejpam-3743	38	31	interior	interior	ADJ
ejpam-3743	38	32	operator	operator	NOUN
ejpam-3743	38	33	between	between	ADP
ejpam-3743	38	34	the	the	DET
ejpam-3743	38	35	intersection	intersection	NOUN
ejpam-3743	38	36	of	of	ADP
ejpam-3743	38	37	two	two	NUM
ejpam-3743	38	38	sets	set	NOUN
ejpam-3743	38	39	.	.	PUNCT
ejpam-3743	39	1	also	also	ADV
ejpam-3743	39	2	,	,	PUNCT
ejpam-3743	39	3	the	the	DET
ejpam-3743	39	4	property	property	NOUN
ejpam-3743	39	5	of	of	ADP
ejpam-3743	39	6	a	a	DET
ejpam-3743	39	7	compact	compact	ADJ
ejpam-3743	39	8	subset	subset	NOUN
ejpam-3743	39	9	of	of	ADP
ejpam-3743	39	10	a	a	DET
ejpam-3743	39	11	t2	t2	NOUN
ejpam-3743	39	12	-	-	PUNCT
ejpam-3743	39	13	space	space	NOUN
ejpam-3743	39	14	is	be	AUX
ejpam-3743	39	15	closed	close	VERB
ejpam-3743	39	16	is	be	AUX
ejpam-3743	39	17	invalid	invalid	ADJ
ejpam-3743	39	18	on	on	ADP
ejpam-3743	39	19	the	the	DET
ejpam-3743	39	20	supra	supra	PROPN
ejpam-3743	39	21	topologies	topology	NOUN
ejpam-3743	39	22	.	.	PUNCT
ejpam-3743	40	1	to	to	PART
ejpam-3743	40	2	extend	extend	VERB
ejpam-3743	40	3	a	a	DET
ejpam-3743	40	4	class	class	NOUN
ejpam-3743	40	5	of	of	ADP
ejpam-3743	40	6	supra	supra	PROPN
ejpam-3743	40	7	open	open	ADJ
ejpam-3743	40	8	sets	set	NOUN
ejpam-3743	40	9	,	,	PUNCT
ejpam-3743	40	10	the	the	DET
ejpam-3743	40	11	notion	notion	NOUN
ejpam-3743	40	12	of	of	ADP
ejpam-3743	40	13	supra	supra	PROPN
ejpam-3743	40	14	α	α	PROPN
ejpam-3743	40	15	-	-	NOUN
ejpam-3743	40	16	open	open	ADJ
ejpam-3743	40	17	[	[	X
ejpam-3743	40	18	15	15	NUM
ejpam-3743	40	19	]	]	X
ejpam-3743	40	20	,	,	PUNCT
ejpam-3743	40	21	supra	supra	ADJ
ejpam-3743	40	22	pre	pre	ADJ
ejpam-3743	40	23	-	-	ADJ
ejpam-3743	40	24	open	open	ADJ
ejpam-3743	40	25	[	[	X
ejpam-3743	40	26	24	24	NUM
ejpam-3743	40	27	]	]	PUNCT
ejpam-3743	40	28	,	,	PUNCT
ejpam-3743	40	29	supra	supra	PROPN
ejpam-3743	40	30	b	b	X
ejpam-3743	40	31	-	-	PUNCT
ejpam-3743	40	32	open	open	ADJ
ejpam-3743	40	33	[	[	X
ejpam-3743	40	34	26	26	NUM
ejpam-3743	40	35	]	]	X
ejpam-3743	40	36	,	,	PUNCT
ejpam-3743	40	37	supra	supra	PROPN
ejpam-3743	40	38	β	β	NOUN
ejpam-3743	40	39	-	-	VERB
ejpam-3743	40	40	open	open	ADJ
ejpam-3743	40	41	[	[	X
ejpam-3743	40	42	18	18	NUM
ejpam-3743	40	43	]	]	PUNCT
ejpam-3743	40	44	,	,	PUNCT
ejpam-3743	40	45	supra	supra	ADJ
ejpam-3743	40	46	r	r	NOUN
ejpam-3743	40	47	-	-	NOUN
ejpam-3743	40	48	open	open	ADJ
ejpam-3743	40	49	[	[	X
ejpam-3743	40	50	16	16	NUM
ejpam-3743	40	51	]	]	PUNCT
ejpam-3743	40	52	and	and	CCONJ
ejpam-3743	40	53	supra	supra	ADJ
ejpam-3743	40	54	semi	semi	ADJ
ejpam-3743	40	55	-	-	ADJ
ejpam-3743	40	56	open	open	ADJ
ejpam-3743	40	57	sets	set	NOUN
ejpam-3743	40	58	[	[	X
ejpam-3743	40	59	3	3	X
ejpam-3743	40	60	]	]	PUNCT
ejpam-3743	40	61	have	have	AUX
ejpam-3743	40	62	been	be	AUX
ejpam-3743	40	63	introduced	introduce	VERB
ejpam-3743	40	64	and	and	CCONJ
ejpam-3743	40	65	their	their	PRON
ejpam-3743	40	66	main	main	ADJ
ejpam-3743	40	67	properties	property	NOUN
ejpam-3743	40	68	have	have	AUX
ejpam-3743	40	69	been	be	AUX
ejpam-3743	40	70	discussed	discuss	VERB
ejpam-3743	40	71	.	.	PUNCT
ejpam-3743	41	1	these	these	DET
ejpam-3743	41	2	generalizations	generalization	NOUN
ejpam-3743	41	3	of	of	ADP
ejpam-3743	41	4	supra	supra	ADJ
ejpam-3743	41	5	open	open	ADJ
ejpam-3743	41	6	sets	set	NOUN
ejpam-3743	41	7	were	be	AUX
ejpam-3743	41	8	defined	define	VERB
ejpam-3743	41	9	in	in	ADP
ejpam-3743	41	10	a	a	DET
ejpam-3743	41	11	similar	similar	ADJ
ejpam-3743	41	12	way	way	NOUN
ejpam-3743	41	13	of	of	ADP
ejpam-3743	41	14	defining	define	VERB
ejpam-3743	41	15	them	they	PRON
ejpam-3743	41	16	on	on	ADP
ejpam-3743	41	17	general	general	ADJ
ejpam-3743	41	18	topology	topology	NOUN
ejpam-3743	41	19	.	.	PUNCT
ejpam-3743	42	1	in	in	ADP
ejpam-3743	42	2	other	other	ADJ
ejpam-3743	42	3	words	word	NOUN
ejpam-3743	42	4	,	,	PUNCT
ejpam-3743	42	5	their	their	PRON
ejpam-3743	42	6	definitions	definition	NOUN
ejpam-3743	42	7	were	be	AUX
ejpam-3743	42	8	formulated	formulate	VERB
ejpam-3743	42	9	using	use	VERB
ejpam-3743	42	10	supra	supra	ADJ
ejpam-3743	42	11	interior	interior	PROPN
ejpam-3743	42	12	and	and	CCONJ
ejpam-3743	42	13	supra	supra	ADJ
ejpam-3743	42	14	closure	closure	NOUN
ejpam-3743	42	15	operators	operator	NOUN
ejpam-3743	42	16	instead	instead	ADV
ejpam-3743	42	17	of	of	ADP
ejpam-3743	42	18	interior	interior	ADJ
ejpam-3743	42	19	and	and	CCONJ
ejpam-3743	42	20	closure	closure	NOUN
ejpam-3743	42	21	operators	operator	NOUN
ejpam-3743	42	22	.	.	PUNCT
ejpam-3743	43	1	these	these	DET
ejpam-3743	43	2	generalizations	generalization	NOUN
ejpam-3743	43	3	have	have	AUX
ejpam-3743	43	4	been	be	AUX
ejpam-3743	43	5	utilized	utilize	VERB
ejpam-3743	43	6	to	to	PART
ejpam-3743	43	7	define	define	VERB
ejpam-3743	43	8	new	new	ADJ
ejpam-3743	43	9	versions	version	NOUN
ejpam-3743	43	10	of	of	ADP
ejpam-3743	43	11	compactness	compactness	NOUN
ejpam-3743	43	12	,	,	PUNCT
ejpam-3743	43	13	connectedness	connectedness	NOUN
ejpam-3743	43	14	and	and	CCONJ
ejpam-3743	43	15	separation	separation	NOUN
ejpam-3743	43	16	axioms	axiom	NOUN
ejpam-3743	43	17	,	,	PUNCT
ejpam-3743	43	18	see	see	VERB
ejpam-3743	43	19	,	,	PUNCT
ejpam-3743	43	20	for	for	ADP
ejpam-3743	43	21	example	example	NOUN
ejpam-3743	43	22	[	[	X
ejpam-3743	43	23	5	5	NUM
ejpam-3743	43	24	,	,	PUNCT
ejpam-3743	43	25	6	6	NUM
ejpam-3743	43	26	,	,	PUNCT
ejpam-3743	43	27	17	17	NUM
ejpam-3743	43	28	,	,	PUNCT
ejpam-3743	43	29	22	22	NUM
ejpam-3743	43	30	,	,	PUNCT
ejpam-3743	43	31	25	25	NUM
ejpam-3743	43	32	]	]	PUNCT
ejpam-3743	43	33	.	.	PUNCT
ejpam-3743	44	1	the	the	DET
ejpam-3743	44	2	class	class	NOUN
ejpam-3743	44	3	of	of	ADP
ejpam-3743	44	4	supra	supra	ADJ
ejpam-3743	44	5	r	r	NOUN
ejpam-3743	44	6	-	-	PUNCT
ejpam-3743	44	7	open	open	ADJ
ejpam-3743	44	8	sets	set	NOUN
ejpam-3743	44	9	has	have	AUX
ejpam-3743	44	10	been	be	AUX
ejpam-3743	44	11	studied	study	VERB
ejpam-3743	44	12	in	in	ADP
ejpam-3743	44	13	[	[	X
ejpam-3743	44	14	4	4	NUM
ejpam-3743	44	15	,	,	PUNCT
ejpam-3743	44	16	11	11	NUM
ejpam-3743	44	17	]	]	PUNCT
ejpam-3743	44	18	under	under	ADP
ejpam-3743	44	19	the	the	DET
ejpam-3743	44	20	name	name	NOUN
ejpam-3743	44	21	of	of	ADP
ejpam-3743	44	22	somewhere	somewhere	ADJ
ejpam-3743	44	23	dense	dense	ADJ
ejpam-3743	44	24	sets	set	NOUN
ejpam-3743	44	25	.	.	PUNCT
ejpam-3743	45	1	mustafa	mustafa	PROPN
ejpam-3743	45	2	and	and	CCONJ
ejpam-3743	45	3	qoqazeh	qoqazeh	NOUN
ejpam-3743	46	1	[	[	X
ejpam-3743	46	2	23	23	NUM
ejpam-3743	46	3	]	]	PUNCT
ejpam-3743	46	4	took	take	VERB
ejpam-3743	46	5	advantage	advantage	NOUN
ejpam-3743	46	6	of	of	ADP
ejpam-3743	46	7	supra	supra	ADJ
ejpam-3743	46	8	d	d	NOUN
ejpam-3743	46	9	-	-	PUNCT
ejpam-3743	46	10	sets	set	VERB
ejpam-3743	46	11	to	to	PART
ejpam-3743	46	12	define	define	VERB
ejpam-3743	46	13	separation	separation	NOUN
ejpam-3743	46	14	axioms	axiom	NOUN
ejpam-3743	46	15	on	on	ADP
ejpam-3743	46	16	supra	supra	PROPN
ejpam-3743	46	17	topological	topological	ADJ
ejpam-3743	46	18	spaces	space	NOUN
ejpam-3743	46	19	.	.	PUNCT
ejpam-3743	47	1	recently	recently	ADV
ejpam-3743	47	2	,	,	PUNCT
ejpam-3743	47	3	al	al	PROPN
ejpam-3743	47	4	-	-	PUNCT
ejpam-3743	47	5	shami	shami	PROPN
ejpam-3743	47	6	and	and	CCONJ
ejpam-3743	47	7	el	el	PROPN
ejpam-3743	47	8	-	-	PROPN
ejpam-3743	47	9	shafei	shafei	NOUN
ejpam-3743	47	10	[	[	X
ejpam-3743	47	11	9	9	NUM
ejpam-3743	47	12	,	,	PUNCT
ejpam-3743	47	13	10	10	NUM
ejpam-3743	47	14	]	]	PUNCT
ejpam-3743	47	15	have	have	AUX
ejpam-3743	47	16	studied	study	VERB
ejpam-3743	47	17	separation	separation	NOUN
ejpam-3743	47	18	axioms	axiom	NOUN
ejpam-3743	47	19	on	on	ADP
ejpam-3743	47	20	supra	supra	PROPN
ejpam-3743	47	21	soft	soft	ADJ
ejpam-3743	47	22	topological	topological	ADJ
ejpam-3743	47	23	spaces	space	NOUN
ejpam-3743	47	24	and	and	CCONJ
ejpam-3743	47	25	supra	supra	PROPN
ejpam-3743	47	26	soft	soft	ADJ
ejpam-3743	47	27	topological	topological	ADJ
ejpam-3743	47	28	ordered	order	VERB
ejpam-3743	47	29	spaces	space	NOUN
ejpam-3743	47	30	.	.	PUNCT
ejpam-3743	48	1	the	the	DET
ejpam-3743	48	2	layout	layout	NOUN
ejpam-3743	48	3	of	of	ADP
ejpam-3743	48	4	the	the	DET
ejpam-3743	48	5	paper	paper	NOUN
ejpam-3743	48	6	is	be	AUX
ejpam-3743	48	7	as	as	ADP
ejpam-3743	48	8	following	follow	VERB
ejpam-3743	48	9	:	:	PUNCT
ejpam-3743	48	10	in	in	ADP
ejpam-3743	48	11	section	section	NOUN
ejpam-3743	48	12	(	(	PUNCT
ejpam-3743	48	13	2	2	NUM
ejpam-3743	48	14	)	)	PUNCT
ejpam-3743	48	15	,	,	PUNCT
ejpam-3743	48	16	we	we	PRON
ejpam-3743	48	17	explore	explore	VERB
ejpam-3743	48	18	a	a	DET
ejpam-3743	48	19	concept	concept	NOUN
ejpam-3743	48	20	of	of	ADP
ejpam-3743	48	21	supra	supra	PROPN
ejpam-3743	48	22	semi	semi	NOUN
ejpam-3743	48	23	limit	limit	NOUN
ejpam-3743	48	24	points	point	NOUN
ejpam-3743	48	25	of	of	ADP
ejpam-3743	48	26	a	a	DET
ejpam-3743	48	27	set	set	NOUN
ejpam-3743	48	28	.	.	PUNCT
ejpam-3743	49	1	in	in	ADP
ejpam-3743	49	2	section	section	NOUN
ejpam-3743	49	3	(	(	PUNCT
ejpam-3743	49	4	3	3	NUM
ejpam-3743	49	5	)	)	PUNCT
ejpam-3743	49	6	,	,	PUNCT
ejpam-3743	49	7	we	we	PRON
ejpam-3743	49	8	initiate	initiate	VERB
ejpam-3743	49	9	new	new	ADJ
ejpam-3743	49	10	types	type	NOUN
ejpam-3743	49	11	of	of	ADP
ejpam-3743	49	12	separation	separation	NOUN
ejpam-3743	49	13	axioms	axiom	NOUN
ejpam-3743	49	14	using	use	VERB
ejpam-3743	49	15	supra	supra	PROPN
ejpam-3743	49	16	semi	semi	ADJ
ejpam-3743	49	17	-	-	ADJ
ejpam-3743	49	18	open	open	ADJ
ejpam-3743	49	19	sets	set	NOUN
ejpam-3743	49	20	and	and	CCONJ
ejpam-3743	49	21	illustrate	illustrate	VERB
ejpam-3743	49	22	the	the	DET
ejpam-3743	49	23	relationships	relationship	NOUN
ejpam-3743	49	24	between	between	ADP
ejpam-3743	49	25	them	they	PRON
ejpam-3743	49	26	with	with	ADP
ejpam-3743	49	27	the	the	DET
ejpam-3743	49	28	help	help	NOUN
ejpam-3743	49	29	of	of	ADP
ejpam-3743	49	30	examples	example	NOUN
ejpam-3743	49	31	.	.	PUNCT
ejpam-3743	50	1	section	section	NOUN
ejpam-3743	50	2	(	(	PUNCT
ejpam-3743	50	3	4	4	X
ejpam-3743	50	4	)	)	PUNCT
ejpam-3743	50	5	concludes	conclude	VERB
ejpam-3743	50	6	the	the	DET
ejpam-3743	50	7	paper	paper	NOUN
ejpam-3743	50	8	with	with	ADP
ejpam-3743	50	9	summary	summary	NOUN
ejpam-3743	50	10	and	and	CCONJ
ejpam-3743	50	11	further	further	ADJ
ejpam-3743	50	12	works	work	NOUN
ejpam-3743	50	13	.	.	PUNCT
ejpam-3743	51	1	in	in	ADP
ejpam-3743	51	2	the	the	DET
ejpam-3743	51	3	rest	rest	NOUN
ejpam-3743	51	4	of	of	ADP
ejpam-3743	51	5	this	this	DET
ejpam-3743	51	6	section	section	NOUN
ejpam-3743	51	7	,	,	PUNCT
ejpam-3743	51	8	we	we	PRON
ejpam-3743	51	9	mention	mention	VERB
ejpam-3743	51	10	some	some	DET
ejpam-3743	51	11	definitions	definition	NOUN
ejpam-3743	51	12	and	and	CCONJ
ejpam-3743	51	13	results	result	NOUN
ejpam-3743	51	14	of	of	ADP
ejpam-3743	51	15	supra	supra	ADJ
ejpam-3743	51	16	topology	topology	NOUN
ejpam-3743	51	17	and	and	CCONJ
ejpam-3743	51	18	supra	supra	NOUN
ejpam-3743	51	19	semi	semi	ADJ
ejpam-3743	51	20	-	-	ADJ
ejpam-3743	51	21	open	open	ADJ
ejpam-3743	51	22	sets	set	NOUN
ejpam-3743	51	23	that	that	PRON
ejpam-3743	51	24	make	make	VERB
ejpam-3743	51	25	this	this	DET
ejpam-3743	51	26	study	study	NOUN
ejpam-3743	51	27	self	self	NOUN
ejpam-3743	51	28	-	-	PUNCT
ejpam-3743	51	29	contained	contain	VERB
ejpam-3743	51	30	and	and	CCONJ
ejpam-3743	51	31	easy	easy	ADJ
ejpam-3743	51	32	to	to	PART
ejpam-3743	51	33	read	read	VERB
ejpam-3743	51	34	.	.	PUNCT
ejpam-3743	52	1	t.	t.	PROPN
ejpam-3743	52	2	m.	m.	PROPN
ejpam-3743	52	3	al	al	PROPN
ejpam-3743	52	4	-	-	PUNCT
ejpam-3743	52	5	shami	shami	PROPN
ejpam-3743	52	6	et	et	PROPN
ejpam-3743	52	7	al	al	PROPN
ejpam-3743	52	8	.	.	PUNCT
ejpam-3743	52	9	/	/	SYM
ejpam-3743	52	10	eur	eur	PROPN
ejpam-3743	52	11	.	.	PUNCT
ejpam-3743	53	1	j.	j.	PROPN
ejpam-3743	53	2	pure	pure	PROPN
ejpam-3743	53	3	appl	appl	PROPN
ejpam-3743	53	4	.	.	PROPN
ejpam-3743	53	5	math	math	PROPN
ejpam-3743	53	6	,	,	PUNCT
ejpam-3743	53	7	13	13	NUM
ejpam-3743	53	8	(	(	PUNCT
ejpam-3743	53	9	3	3	NUM
ejpam-3743	53	10	)	)	PUNCT
ejpam-3743	53	11	(	(	PUNCT
ejpam-3743	53	12	2020	2020	NUM
ejpam-3743	53	13	)	)	PUNCT
ejpam-3743	53	14	,	,	PUNCT
ejpam-3743	53	15	427	427	NUM
ejpam-3743	53	16	-	-	SYM
ejpam-3743	53	17	443	443	NUM
ejpam-3743	53	18	429	429	NUM
ejpam-3743	53	19	definition	definition	NOUN
ejpam-3743	53	20	1	1	NUM
ejpam-3743	53	21	.	.	PUNCT
ejpam-3743	54	1	[	[	X
ejpam-3743	54	2	21	21	NUM
ejpam-3743	54	3	]	]	PUNCT
ejpam-3743	54	4	a	a	DET
ejpam-3743	54	5	family	family	NOUN
ejpam-3743	54	6	µ	µ	X
ejpam-3743	54	7	of	of	ADP
ejpam-3743	54	8	subsets	subset	NOUN
ejpam-3743	54	9	of	of	ADP
ejpam-3743	54	10	a	a	DET
ejpam-3743	54	11	nonempty	nonempty	ADV
ejpam-3743	54	12	set	set	VERB
ejpam-3743	54	13	x	x	PUNCT
ejpam-3743	54	14	is	be	AUX
ejpam-3743	54	15	called	call	VERB
ejpam-3743	54	16	a	a	DET
ejpam-3743	54	17	supra	supra	ADJ
ejpam-3743	54	18	topology	topology	NOUN
ejpam-3743	54	19	provided	provide	VERB
ejpam-3743	54	20	that	that	SCONJ
ejpam-3743	54	21	the	the	DET
ejpam-3743	54	22	following	follow	VERB
ejpam-3743	54	23	two	two	NUM
ejpam-3743	54	24	conditions	condition	NOUN
ejpam-3743	54	25	hold	hold	VERB
ejpam-3743	54	26	.	.	PUNCT
ejpam-3743	55	1	(	(	PUNCT
ejpam-3743	55	2	i	i	NOUN
ejpam-3743	55	3	)	)	PUNCT
ejpam-3743	55	4	x	x	PUNCT
ejpam-3743	55	5	and	and	CCONJ
ejpam-3743	55	6	∅	∅	NOUN
ejpam-3743	55	7	∈	∈	PROPN
ejpam-3743	55	8	µ.	µ.	NOUN
ejpam-3743	55	9	(	(	PUNCT
ejpam-3743	55	10	ii	ii	NOUN
ejpam-3743	55	11	)	)	PUNCT
ejpam-3743	55	12	µ	µ	PROPN
ejpam-3743	55	13	is	be	AUX
ejpam-3743	55	14	closed	close	VERB
ejpam-3743	55	15	under	under	ADP
ejpam-3743	55	16	arbitrary	arbitrary	ADJ
ejpam-3743	55	17	union	union	NOUN
ejpam-3743	55	18	.	.	PUNCT
ejpam-3743	56	1	then	then	ADV
ejpam-3743	56	2	the	the	DET
ejpam-3743	56	3	pair	pair	NOUN
ejpam-3743	56	4	(	(	PUNCT
ejpam-3743	56	5	x,µ	x,µ	NOUN
ejpam-3743	56	6	)	)	PUNCT
ejpam-3743	56	7	is	be	AUX
ejpam-3743	56	8	called	call	VERB
ejpam-3743	56	9	a	a	DET
ejpam-3743	56	10	supra	supra	ADJ
ejpam-3743	56	11	topological	topological	ADJ
ejpam-3743	56	12	space	space	NOUN
ejpam-3743	56	13	.	.	PUNCT
ejpam-3743	57	1	every	every	DET
ejpam-3743	57	2	element	element	NOUN
ejpam-3743	57	3	of	of	ADP
ejpam-3743	57	4	µ	µ	PROPN
ejpam-3743	57	5	is	be	AUX
ejpam-3743	57	6	called	call	VERB
ejpam-3743	57	7	a	a	DET
ejpam-3743	57	8	supra	supra	PROPN
ejpam-3743	57	9	open	open	ADJ
ejpam-3743	57	10	set	set	NOUN
ejpam-3743	57	11	and	and	CCONJ
ejpam-3743	57	12	its	its	PRON
ejpam-3743	57	13	complement	complement	NOUN
ejpam-3743	57	14	is	be	AUX
ejpam-3743	57	15	called	call	VERB
ejpam-3743	57	16	a	a	DET
ejpam-3743	57	17	supra	supra	NOUN
ejpam-3743	57	18	closed	close	VERB
ejpam-3743	57	19	set	set	NOUN
ejpam-3743	57	20	.	.	PUNCT
ejpam-3743	58	1	remark	remark	PROPN
ejpam-3743	58	2	1	1	NUM
ejpam-3743	58	3	.	.	PUNCT
ejpam-3743	59	1	(	(	PUNCT
ejpam-3743	59	2	i	i	NOUN
ejpam-3743	59	3	)	)	PUNCT
ejpam-3743	59	4	µ	µ	PROPN
ejpam-3743	59	5	is	be	AUX
ejpam-3743	59	6	called	call	VERB
ejpam-3743	59	7	an	an	DET
ejpam-3743	59	8	associated	associated	ADJ
ejpam-3743	59	9	supra	supra	NOUN
ejpam-3743	59	10	topology	topology	NOUN
ejpam-3743	59	11	with	with	ADP
ejpam-3743	59	12	a	a	DET
ejpam-3743	59	13	topology	topology	NOUN
ejpam-3743	59	14	τ	τ	X
ejpam-3743	59	15	if	if	SCONJ
ejpam-3743	59	16	τ	τ	PROPN
ejpam-3743	59	17	⊆	⊆	NUM
ejpam-3743	59	18	µ.	µ.	NOUN
ejpam-3743	59	19	(	(	PUNCT
ejpam-3743	59	20	ii	ii	NOUN
ejpam-3743	59	21	)	)	PUNCT
ejpam-3743	59	22	through	through	ADP
ejpam-3743	59	23	this	this	DET
ejpam-3743	59	24	paper	paper	NOUN
ejpam-3743	59	25	,	,	PUNCT
ejpam-3743	59	26	we	we	PRON
ejpam-3743	59	27	consider	consider	VERB
ejpam-3743	59	28	(	(	PUNCT
ejpam-3743	59	29	x,µ	x,µ	NOUN
ejpam-3743	59	30	)	)	PUNCT
ejpam-3743	59	31	and	and	CCONJ
ejpam-3743	59	32	(	(	PUNCT
ejpam-3743	59	33	y	y	PROPN
ejpam-3743	59	34	,	,	PUNCT
ejpam-3743	59	35	ν	ν	NOUN
ejpam-3743	59	36	)	)	PUNCT
ejpam-3743	59	37	are	be	AUX
ejpam-3743	59	38	associated	associate	VERB
ejpam-3743	59	39	supra	supra	PROPN
ejpam-3743	59	40	topological	topological	ADJ
ejpam-3743	59	41	spaces	space	NOUN
ejpam-3743	59	42	with	with	ADP
ejpam-3743	59	43	the	the	DET
ejpam-3743	59	44	topological	topological	ADJ
ejpam-3743	59	45	spaces	space	NOUN
ejpam-3743	59	46	(	(	PUNCT
ejpam-3743	59	47	x	x	X
ejpam-3743	59	48	,	,	PUNCT
ejpam-3743	59	49	τ	τ	X
ejpam-3743	59	50	)	)	PUNCT
ejpam-3743	59	51	and	and	CCONJ
ejpam-3743	59	52	(	(	PUNCT
ejpam-3743	59	53	y	y	PROPN
ejpam-3743	59	54	,	,	PUNCT
ejpam-3743	59	55	θ	θ	PROPN
ejpam-3743	59	56	)	)	PUNCT
ejpam-3743	59	57	,	,	PUNCT
ejpam-3743	59	58	respectively	respectively	ADV
ejpam-3743	59	59	.	.	PUNCT
ejpam-3743	60	1	definition	definition	NOUN
ejpam-3743	60	2	2	2	NUM
ejpam-3743	60	3	.	.	PUNCT
ejpam-3743	61	1	[	[	X
ejpam-3743	61	2	21	21	NUM
ejpam-3743	61	3	]	]	PUNCT
ejpam-3743	61	4	let	let	VERB
ejpam-3743	61	5	a	a	PRON
ejpam-3743	61	6	be	be	AUX
ejpam-3743	61	7	a	a	DET
ejpam-3743	61	8	subset	subset	NOUN
ejpam-3743	61	9	of	of	ADP
ejpam-3743	61	10	(	(	PUNCT
ejpam-3743	61	11	x,µ	x,µ	NOUN
ejpam-3743	61	12	)	)	PUNCT
ejpam-3743	61	13	.	.	PUNCT
ejpam-3743	62	1	then	then	ADV
ejpam-3743	62	2	intµ(a	intµ(a	PROPN
ejpam-3743	62	3	)	)	PUNCT
ejpam-3743	62	4	is	be	AUX
ejpam-3743	62	5	the	the	DET
ejpam-3743	62	6	union	union	NOUN
ejpam-3743	62	7	of	of	ADP
ejpam-3743	62	8	all	all	DET
ejpam-3743	62	9	supra	supra	PROPN
ejpam-3743	62	10	open	open	ADJ
ejpam-3743	62	11	sets	set	NOUN
ejpam-3743	62	12	contained	contain	VERB
ejpam-3743	62	13	in	in	ADP
ejpam-3743	62	14	a	a	PRON
ejpam-3743	62	15	and	and	CCONJ
ejpam-3743	62	16	clµ(a	clµ(a	ADJ
ejpam-3743	62	17	)	)	PUNCT
ejpam-3743	62	18	is	be	AUX
ejpam-3743	62	19	the	the	DET
ejpam-3743	62	20	intersection	intersection	NOUN
ejpam-3743	62	21	of	of	ADP
ejpam-3743	62	22	all	all	DET
ejpam-3743	62	23	supra	supra	PROPN
ejpam-3743	62	24	closed	close	VERB
ejpam-3743	62	25	sets	set	NOUN
ejpam-3743	62	26	containing	contain	VERB
ejpam-3743	62	27	a.	a.	NOUN
ejpam-3743	62	28	if	if	SCONJ
ejpam-3743	62	29	there	there	PRON
ejpam-3743	62	30	is	be	VERB
ejpam-3743	62	31	no	no	DET
ejpam-3743	62	32	confusion	confusion	NOUN
ejpam-3743	62	33	,	,	PUNCT
ejpam-3743	62	34	we	we	PRON
ejpam-3743	62	35	write	write	VERB
ejpam-3743	62	36	int(a	int(a	PROPN
ejpam-3743	62	37	)	)	PUNCT
ejpam-3743	62	38	and	and	CCONJ
ejpam-3743	62	39	cl(a	cl(a	NUM
ejpam-3743	62	40	)	)	PUNCT
ejpam-3743	62	41	in	in	ADP
ejpam-3743	62	42	the	the	DET
ejpam-3743	62	43	places	place	NOUN
ejpam-3743	62	44	of	of	ADP
ejpam-3743	62	45	intµ(a	intµ(a	NOUN
ejpam-3743	62	46	)	)	PUNCT
ejpam-3743	62	47	and	and	CCONJ
ejpam-3743	62	48	clµ(a	clµ(a	PROPN
ejpam-3743	62	49	)	)	PUNCT
ejpam-3743	62	50	,	,	PUNCT
ejpam-3743	62	51	respectively	respectively	ADV
ejpam-3743	62	52	.	.	PUNCT
ejpam-3743	63	1	definition	definition	NOUN
ejpam-3743	63	2	3	3	NUM
ejpam-3743	63	3	.	.	PUNCT
ejpam-3743	64	1	[	[	X
ejpam-3743	64	2	3	3	X
ejpam-3743	64	3	]	]	PUNCT
ejpam-3743	64	4	a	a	DET
ejpam-3743	64	5	subset	subset	NOUN
ejpam-3743	64	6	a	a	DET
ejpam-3743	64	7	of	of	ADP
ejpam-3743	64	8	(	(	PUNCT
ejpam-3743	64	9	x,µ	x,µ	NOUN
ejpam-3743	64	10	)	)	PUNCT
ejpam-3743	64	11	is	be	AUX
ejpam-3743	64	12	said	say	VERB
ejpam-3743	64	13	to	to	PART
ejpam-3743	64	14	be	be	AUX
ejpam-3743	64	15	supra	supra	ADJ
ejpam-3743	64	16	semi	semi	ADJ
ejpam-3743	64	17	-	-	ADJ
ejpam-3743	64	18	open	open	ADJ
ejpam-3743	64	19	if	if	SCONJ
ejpam-3743	64	20	a	a	DET
ejpam-3743	64	21	⊆	⊆	NUM
ejpam-3743	64	22	cl(int(a	cl(int(a	NOUN
ejpam-3743	64	23	)	)	PUNCT
ejpam-3743	64	24	)	)	PUNCT
ejpam-3743	64	25	.	.	PUNCT
ejpam-3743	65	1	definition	definition	NOUN
ejpam-3743	65	2	4	4	NUM
ejpam-3743	65	3	.	.	PUNCT
ejpam-3743	66	1	[	[	X
ejpam-3743	66	2	3	3	X
ejpam-3743	66	3	]	]	PUNCT
ejpam-3743	66	4	for	for	ADP
ejpam-3743	66	5	a	a	DET
ejpam-3743	66	6	subset	subset	NOUN
ejpam-3743	66	7	a	a	PRON
ejpam-3743	66	8	of	of	ADP
ejpam-3743	66	9	(	(	PUNCT
ejpam-3743	66	10	x,µ	x,µ	NOUN
ejpam-3743	66	11	)	)	PUNCT
ejpam-3743	66	12	,	,	PUNCT
ejpam-3743	66	13	sintµ(a	sintµ(a	NOUN
ejpam-3743	66	14	)	)	PUNCT
ejpam-3743	66	15	is	be	AUX
ejpam-3743	66	16	the	the	DET
ejpam-3743	66	17	union	union	NOUN
ejpam-3743	66	18	of	of	ADP
ejpam-3743	66	19	all	all	DET
ejpam-3743	66	20	supra	supra	ADJ
ejpam-3743	66	21	semi	semi	ADJ
ejpam-3743	66	22	-	-	ADJ
ejpam-3743	66	23	open	open	ADJ
ejpam-3743	66	24	sets	set	NOUN
ejpam-3743	66	25	contained	contain	VERB
ejpam-3743	66	26	in	in	ADP
ejpam-3743	66	27	a	a	PRON
ejpam-3743	66	28	and	and	CCONJ
ejpam-3743	66	29	sclµ(a	sclµ(a	ADJ
ejpam-3743	66	30	)	)	PUNCT
ejpam-3743	66	31	is	be	AUX
ejpam-3743	66	32	the	the	DET
ejpam-3743	66	33	intersection	intersection	NOUN
ejpam-3743	66	34	of	of	ADP
ejpam-3743	66	35	all	all	DET
ejpam-3743	66	36	supra	supra	ADJ
ejpam-3743	66	37	semi	semi	ADJ
ejpam-3743	66	38	-	-	ADJ
ejpam-3743	66	39	closed	closed	ADJ
ejpam-3743	66	40	sets	set	NOUN
ejpam-3743	66	41	containing	contain	VERB
ejpam-3743	66	42	a.	a.	NOUN
ejpam-3743	66	43	if	if	SCONJ
ejpam-3743	66	44	there	there	PRON
ejpam-3743	66	45	is	be	VERB
ejpam-3743	66	46	no	no	DET
ejpam-3743	66	47	confusion	confusion	NOUN
ejpam-3743	66	48	,	,	PUNCT
ejpam-3743	66	49	we	we	PRON
ejpam-3743	66	50	write	write	VERB
ejpam-3743	66	51	sint(a	sint(a	PROPN
ejpam-3743	66	52	)	)	PUNCT
ejpam-3743	66	53	and	and	CCONJ
ejpam-3743	66	54	scl(a	scl(a	NUM
ejpam-3743	66	55	)	)	PUNCT
ejpam-3743	66	56	in	in	ADP
ejpam-3743	66	57	the	the	DET
ejpam-3743	66	58	places	place	NOUN
ejpam-3743	66	59	of	of	ADP
ejpam-3743	66	60	sintµ(a	sintµ(a	NOUN
ejpam-3743	66	61	)	)	PUNCT
ejpam-3743	66	62	and	and	CCONJ
ejpam-3743	66	63	sclµ(a	sclµ(a	NOUN
ejpam-3743	66	64	)	)	PUNCT
ejpam-3743	66	65	,	,	PUNCT
ejpam-3743	66	66	respectively	respectively	ADV
ejpam-3743	66	67	.	.	PUNCT
ejpam-3743	67	1	definition	definition	NOUN
ejpam-3743	67	2	5	5	NUM
ejpam-3743	67	3	.	.	PUNCT
ejpam-3743	68	1	[	[	X
ejpam-3743	68	2	3	3	X
ejpam-3743	68	3	]	]	PUNCT
ejpam-3743	68	4	a	a	DET
ejpam-3743	68	5	map	map	NOUN
ejpam-3743	68	6	g	g	NOUN
ejpam-3743	68	7	:	:	PUNCT
ejpam-3743	68	8	(	(	PUNCT
ejpam-3743	68	9	x,µ)→	x,µ)→	X
ejpam-3743	68	10	(	(	PUNCT
ejpam-3743	68	11	y	y	PROPN
ejpam-3743	68	12	,	,	PUNCT
ejpam-3743	68	13	ν	ν	NOUN
ejpam-3743	68	14	)	)	PUNCT
ejpam-3743	68	15	is	be	AUX
ejpam-3743	68	16	said	say	VERB
ejpam-3743	68	17	to	to	PART
ejpam-3743	68	18	be	be	AUX
ejpam-3743	68	19	:	:	PUNCT
ejpam-3743	68	20	(	(	PUNCT
ejpam-3743	68	21	i	i	NOUN
ejpam-3743	68	22	)	)	PUNCT
ejpam-3743	68	23	supra	supra	PROPN
ejpam-3743	68	24	semi	semi	ADV
ejpam-3743	68	25	-	-	ADJ
ejpam-3743	68	26	continuous	continuous	ADJ
ejpam-3743	68	27	if	if	SCONJ
ejpam-3743	68	28	the	the	DET
ejpam-3743	68	29	inverse	inverse	ADJ
ejpam-3743	68	30	image	image	NOUN
ejpam-3743	68	31	of	of	ADP
ejpam-3743	68	32	each	each	DET
ejpam-3743	68	33	open	open	ADJ
ejpam-3743	68	34	subset	subset	NOUN
ejpam-3743	68	35	of	of	ADP
ejpam-3743	68	36	y	y	PROPN
ejpam-3743	68	37	is	be	AUX
ejpam-3743	68	38	a	a	DET
ejpam-3743	68	39	supra	supra	PROPN
ejpam-3743	68	40	semiopen	semiopen	PROPN
ejpam-3743	68	41	subset	subset	NOUN
ejpam-3743	68	42	of	of	ADP
ejpam-3743	68	43	x.	x.	PROPN
ejpam-3743	68	44	(	(	PUNCT
ejpam-3743	68	45	ii	ii	PROPN
ejpam-3743	68	46	)	)	PUNCT
ejpam-3743	68	47	supra	supra	PROPN
ejpam-3743	68	48	semi	semi	ADJ
ejpam-3743	68	49	-	-	ADJ
ejpam-3743	68	50	open	open	ADJ
ejpam-3743	68	51	(	(	PUNCT
ejpam-3743	68	52	resp	resp	NOUN
ejpam-3743	68	53	.	.	PUNCT
ejpam-3743	69	1	supra	supra	PROPN
ejpam-3743	69	2	semi	semi	ADJ
ejpam-3743	69	3	-	-	ADJ
ejpam-3743	69	4	closed	closed	ADJ
ejpam-3743	69	5	)	)	PUNCT
ejpam-3743	69	6	if	if	SCONJ
ejpam-3743	69	7	the	the	DET
ejpam-3743	69	8	image	image	NOUN
ejpam-3743	69	9	of	of	ADP
ejpam-3743	69	10	each	each	PRON
ejpam-3743	69	11	open	open	ADJ
ejpam-3743	69	12	(	(	PUNCT
ejpam-3743	69	13	resp	resp	NOUN
ejpam-3743	69	14	.	.	PUNCT
ejpam-3743	70	1	closed	closed	ADJ
ejpam-3743	70	2	)	)	PUNCT
ejpam-3743	70	3	subset	subset	NOUN
ejpam-3743	70	4	of	of	ADP
ejpam-3743	70	5	x	x	PUNCT
ejpam-3743	70	6	is	be	AUX
ejpam-3743	70	7	a	a	DET
ejpam-3743	70	8	supra	supra	NOUN
ejpam-3743	70	9	semi	semi	ADJ
ejpam-3743	70	10	-	-	ADJ
ejpam-3743	70	11	open	open	ADJ
ejpam-3743	70	12	(	(	PUNCT
ejpam-3743	70	13	resp	resp	NOUN
ejpam-3743	70	14	.	.	PUNCT
ejpam-3743	71	1	supra	supra	PROPN
ejpam-3743	71	2	semi	semi	ADJ
ejpam-3743	71	3	-	-	ADJ
ejpam-3743	71	4	closed	closed	ADJ
ejpam-3743	71	5	)	)	PUNCT
ejpam-3743	71	6	subset	subset	NOUN
ejpam-3743	71	7	of	of	ADP
ejpam-3743	71	8	y	y	PROPN
ejpam-3743	71	9	.	.	PUNCT
ejpam-3743	72	1	definition	definition	NOUN
ejpam-3743	72	2	6	6	NUM
ejpam-3743	72	3	.	.	PUNCT
ejpam-3743	73	1	[	[	X
ejpam-3743	73	2	2	2	X
ejpam-3743	73	3	]	]	PUNCT
ejpam-3743	73	4	let	let	VERB
ejpam-3743	73	5	a	a	PRON
ejpam-3743	73	6	be	be	AUX
ejpam-3743	73	7	a	a	DET
ejpam-3743	73	8	subset	subset	NOUN
ejpam-3743	73	9	of	of	ADP
ejpam-3743	73	10	(	(	PUNCT
ejpam-3743	73	11	x,µ	x,µ	NOUN
ejpam-3743	73	12	)	)	PUNCT
ejpam-3743	73	13	.	.	PUNCT
ejpam-3743	74	1	the	the	DET
ejpam-3743	74	2	family	family	NOUN
ejpam-3743	74	3	µa	µa	NOUN
ejpam-3743	74	4	=	=	PUNCT
ejpam-3743	74	5	{	{	PUNCT
ejpam-3743	74	6	a	a	DET
ejpam-3743	74	7	⋂	⋂	PROPN
ejpam-3743	74	8	g	g	NOUN
ejpam-3743	74	9	:	:	PUNCT
ejpam-3743	74	10	g	g	PROPN
ejpam-3743	74	11	∈	∈	PROPN
ejpam-3743	74	12	µ	µ	X
ejpam-3743	74	13	}	}	PUNCT
ejpam-3743	74	14	is	be	AUX
ejpam-3743	74	15	called	call	VERB
ejpam-3743	74	16	a	a	DET
ejpam-3743	74	17	supra	supra	ADJ
ejpam-3743	74	18	relative	relative	ADJ
ejpam-3743	74	19	topology	topology	NOUN
ejpam-3743	74	20	on	on	ADP
ejpam-3743	74	21	a.	a.	NOUN
ejpam-3743	74	22	a	a	DET
ejpam-3743	74	23	pair	pair	NOUN
ejpam-3743	74	24	(	(	PUNCT
ejpam-3743	74	25	a,µa	a,µa	NUM
ejpam-3743	74	26	)	)	PUNCT
ejpam-3743	74	27	is	be	AUX
ejpam-3743	74	28	called	call	VERB
ejpam-3743	74	29	a	a	DET
ejpam-3743	74	30	supra	supra	ADJ
ejpam-3743	74	31	subspace	subspace	NOUN
ejpam-3743	74	32	of	of	ADP
ejpam-3743	74	33	(	(	PUNCT
ejpam-3743	74	34	x,µ	x,µ	NOUN
ejpam-3743	74	35	)	)	PUNCT
ejpam-3743	74	36	.	.	PUNCT
ejpam-3743	75	1	definition	definition	NOUN
ejpam-3743	75	2	7	7	NUM
ejpam-3743	75	3	.	.	PUNCT
ejpam-3743	76	1	[	[	X
ejpam-3743	76	2	8	8	NUM
ejpam-3743	76	3	]	]	X
ejpam-3743	76	4	β	β	X
ejpam-3743	76	5	is	be	AUX
ejpam-3743	76	6	called	call	VERB
ejpam-3743	76	7	a	a	DET
ejpam-3743	76	8	basis	basis	NOUN
ejpam-3743	76	9	for	for	ADP
ejpam-3743	76	10	a	a	DET
ejpam-3743	76	11	supra	supra	ADJ
ejpam-3743	76	12	topology	topology	NOUN
ejpam-3743	76	13	(	(	PUNCT
ejpam-3743	76	14	x,µ	x,µ	NOUN
ejpam-3743	76	15	)	)	PUNCT
ejpam-3743	76	16	if	if	SCONJ
ejpam-3743	76	17	every	every	DET
ejpam-3743	76	18	member	member	NOUN
ejpam-3743	76	19	of	of	ADP
ejpam-3743	76	20	µ	µ	PROPN
ejpam-3743	76	21	can	can	AUX
ejpam-3743	76	22	be	be	AUX
ejpam-3743	76	23	expressed	express	VERB
ejpam-3743	76	24	as	as	ADP
ejpam-3743	76	25	a	a	DET
ejpam-3743	76	26	union	union	NOUN
ejpam-3743	76	27	of	of	ADP
ejpam-3743	76	28	elements	element	NOUN
ejpam-3743	76	29	of	of	ADP
ejpam-3743	76	30	β	β	X
ejpam-3743	76	31	.	.	PUNCT
ejpam-3743	77	1	definition	definition	NOUN
ejpam-3743	77	2	8	8	NUM
ejpam-3743	77	3	.	.	PUNCT
ejpam-3743	78	1	[	[	X
ejpam-3743	78	2	8	8	NUM
ejpam-3743	78	3	]	]	X
ejpam-3743	78	4	let	let	VERB
ejpam-3743	78	5	{	{	PUNCT
ejpam-3743	78	6	(	(	PUNCT
ejpam-3743	78	7	xi	xi	PROPN
ejpam-3743	78	8	,	,	PUNCT
ejpam-3743	78	9	µi	µi	PROPN
ejpam-3743	78	10	)	)	PUNCT
ejpam-3743	78	11	:	:	PUNCT
ejpam-3743	79	1	i	i	PRON
ejpam-3743	79	2	=	=	NOUN
ejpam-3743	79	3	1	1	NUM
ejpam-3743	79	4	,	,	PUNCT
ejpam-3743	79	5	2	2	NUM
ejpam-3743	79	6	,	,	PUNCT
ejpam-3743	79	7	...	...	PUNCT
ejpam-3743	79	8	,	,	PUNCT
ejpam-3743	79	9	n	n	CCONJ
ejpam-3743	79	10	}	}	PUNCT
ejpam-3743	79	11	be	be	AUX
ejpam-3743	79	12	the	the	DET
ejpam-3743	79	13	collection	collection	NOUN
ejpam-3743	79	14	of	of	ADP
ejpam-3743	79	15	supra	supra	PROPN
ejpam-3743	79	16	topological	topological	ADJ
ejpam-3743	79	17	spaces	space	NOUN
ejpam-3743	79	18	.	.	PUNCT
ejpam-3743	80	1	then	then	ADV
ejpam-3743	80	2	β	β	X
ejpam-3743	80	3	=	=	SYM
ejpam-3743	80	4	∏n	∏n	ADJ
ejpam-3743	80	5	i=1	i=1	PRON
ejpam-3743	80	6	µi	µi	PROPN
ejpam-3743	80	7	=	=	PUNCT
ejpam-3743	80	8	{	{	PUNCT
ejpam-3743	80	9	∏n	∏n	ADJ
ejpam-3743	80	10	i=1gi	i=1gi	X
ejpam-3743	80	11	:	:	PUNCT
ejpam-3743	80	12	gi	gi	VERB
ejpam-3743	80	13	∈	∈	PROPN
ejpam-3743	80	14	µi	µi	ADP
ejpam-3743	80	15	}	}	PUNCT
ejpam-3743	80	16	defines	define	VERB
ejpam-3743	80	17	a	a	DET
ejpam-3743	80	18	basis	basis	NOUN
ejpam-3743	80	19	for	for	ADP
ejpam-3743	80	20	a	a	DET
ejpam-3743	80	21	supra	supra	PROPN
ejpam-3743	80	22	topology	topology	NOUN
ejpam-3743	80	23	t	t	PROPN
ejpam-3743	80	24	on	on	ADP
ejpam-3743	80	25	x	x	X
ejpam-3743	80	26	=	=	VERB
ejpam-3743	80	27	∏n	∏n	PROPN
ejpam-3743	80	28	i=1xi	i=1xi	NOUN
ejpam-3743	80	29	.	.	PUNCT
ejpam-3743	81	1	the	the	DET
ejpam-3743	81	2	pair	pair	NOUN
ejpam-3743	81	3	(	(	PUNCT
ejpam-3743	81	4	x	x	X
ejpam-3743	81	5	,	,	PUNCT
ejpam-3743	81	6	t	t	PROPN
ejpam-3743	81	7	)	)	PUNCT
ejpam-3743	81	8	is	be	AUX
ejpam-3743	81	9	called	call	VERB
ejpam-3743	81	10	a	a	DET
ejpam-3743	81	11	finite	finite	ADJ
ejpam-3743	81	12	product	product	NOUN
ejpam-3743	81	13	supra	supra	NOUN
ejpam-3743	81	14	spaces	space	VERB
ejpam-3743	81	15	.	.	PUNCT
ejpam-3743	82	1	proposition	proposition	NOUN
ejpam-3743	82	2	1	1	NUM
ejpam-3743	82	3	.	.	PUNCT
ejpam-3743	83	1	[	[	X
ejpam-3743	83	2	8	8	NUM
ejpam-3743	83	3	]	]	PUNCT
ejpam-3743	83	4	let	let	VERB
ejpam-3743	83	5	a	a	PRON
ejpam-3743	83	6	and	and	CCONJ
ejpam-3743	83	7	b	b	NOUN
ejpam-3743	83	8	be	be	AUX
ejpam-3743	83	9	two	two	NUM
ejpam-3743	83	10	subsets	subset	NOUN
ejpam-3743	83	11	of	of	ADP
ejpam-3743	83	12	(	(	PUNCT
ejpam-3743	83	13	x,µ	x,µ	NOUN
ejpam-3743	83	14	)	)	PUNCT
ejpam-3743	83	15	and	and	CCONJ
ejpam-3743	83	16	(	(	PUNCT
ejpam-3743	83	17	y	y	PROPN
ejpam-3743	83	18	,	,	PUNCT
ejpam-3743	83	19	ν	ν	NOUN
ejpam-3743	83	20	)	)	PUNCT
ejpam-3743	83	21	,	,	PUNCT
ejpam-3743	83	22	respectively	respectively	ADV
ejpam-3743	83	23	.	.	PUNCT
ejpam-3743	84	1	then	then	ADV
ejpam-3743	84	2	:	:	PUNCT
ejpam-3743	84	3	(	(	PUNCT
ejpam-3743	84	4	i	i	NOUN
ejpam-3743	84	5	)	)	PUNCT
ejpam-3743	84	6	cl(a)×	cl(a)×	PROPN
ejpam-3743	84	7	cl(b	cl(b	NOUN
ejpam-3743	84	8	)	)	PUNCT
ejpam-3743	84	9	=	=	SYM
ejpam-3743	84	10	cl(a×b	cl(a×b	PROPN
ejpam-3743	84	11	)	)	PUNCT
ejpam-3743	84	12	.	.	PUNCT
ejpam-3743	85	1	(	(	PUNCT
ejpam-3743	85	2	ii	ii	X
ejpam-3743	85	3	)	)	PUNCT
ejpam-3743	85	4	int(a)×	int(a)×	NOUN
ejpam-3743	85	5	int(b	int(b	PART
ejpam-3743	85	6	)	)	PUNCT
ejpam-3743	85	7	=	=	SYM
ejpam-3743	85	8	int(a×b	int(a×b	PROPN
ejpam-3743	85	9	)	)	PUNCT
ejpam-3743	85	10	.	.	PUNCT
ejpam-3743	86	1	t.	t.	PROPN
ejpam-3743	86	2	m.	m.	PROPN
ejpam-3743	86	3	al	al	PROPN
ejpam-3743	86	4	-	-	PUNCT
ejpam-3743	86	5	shami	shami	PROPN
ejpam-3743	86	6	et	et	PROPN
ejpam-3743	86	7	al	al	PROPN
ejpam-3743	86	8	.	.	PUNCT
ejpam-3743	86	9	/	/	SYM
ejpam-3743	86	10	eur	eur	PROPN
ejpam-3743	86	11	.	.	PUNCT
ejpam-3743	87	1	j.	j.	PROPN
ejpam-3743	87	2	pure	pure	PROPN
ejpam-3743	87	3	appl	appl	PROPN
ejpam-3743	87	4	.	.	PROPN
ejpam-3743	87	5	math	math	PROPN
ejpam-3743	87	6	,	,	PUNCT
ejpam-3743	87	7	13	13	NUM
ejpam-3743	87	8	(	(	PUNCT
ejpam-3743	87	9	3	3	NUM
ejpam-3743	87	10	)	)	PUNCT
ejpam-3743	87	11	(	(	PUNCT
ejpam-3743	87	12	2020	2020	NUM
ejpam-3743	87	13	)	)	PUNCT
ejpam-3743	87	14	,	,	PUNCT
ejpam-3743	87	15	427	427	NUM
ejpam-3743	87	16	-	-	SYM
ejpam-3743	87	17	443	443	NUM
ejpam-3743	87	18	430	430	NUM
ejpam-3743	87	19	2	2	NUM
ejpam-3743	87	20	.	.	PUNCT
ejpam-3743	88	1	limit	limit	NOUN
ejpam-3743	88	2	points	point	NOUN
ejpam-3743	88	3	of	of	ADP
ejpam-3743	88	4	a	a	DET
ejpam-3743	88	5	set	set	NOUN
ejpam-3743	88	6	with	with	ADP
ejpam-3743	88	7	respect	respect	NOUN
ejpam-3743	88	8	to	to	ADP
ejpam-3743	88	9	supra	supra	PROPN
ejpam-3743	88	10	semi	semi	ADJ
ejpam-3743	88	11	-	-	ADJ
ejpam-3743	88	12	open	open	ADJ
ejpam-3743	88	13	sets	set	NOUN
ejpam-3743	88	14	in	in	ADP
ejpam-3743	88	15	this	this	DET
ejpam-3743	88	16	section	section	NOUN
ejpam-3743	88	17	,	,	PUNCT
ejpam-3743	88	18	we	we	PRON
ejpam-3743	88	19	introduce	introduce	VERB
ejpam-3743	88	20	and	and	CCONJ
ejpam-3743	88	21	study	study	VERB
ejpam-3743	88	22	supra	supra	PROPN
ejpam-3743	88	23	semi	semi	NOUN
ejpam-3743	88	24	limit	limit	VERB
ejpam-3743	88	25	points	point	NOUN
ejpam-3743	88	26	of	of	ADP
ejpam-3743	88	27	a	a	DET
ejpam-3743	88	28	set	set	NOUN
ejpam-3743	88	29	.	.	PUNCT
ejpam-3743	89	1	we	we	PRON
ejpam-3743	89	2	explore	explore	VERB
ejpam-3743	89	3	many	many	ADJ
ejpam-3743	89	4	properties	property	NOUN
ejpam-3743	89	5	of	of	ADP
ejpam-3743	89	6	them	they	PRON
ejpam-3743	89	7	and	and	CCONJ
ejpam-3743	89	8	discuss	discuss	VERB
ejpam-3743	89	9	their	their	PRON
ejpam-3743	89	10	behaviour	behaviour	NOUN
ejpam-3743	89	11	on	on	ADP
ejpam-3743	89	12	the	the	DET
ejpam-3743	89	13	spaces	space	NOUN
ejpam-3743	89	14	that	that	PRON
ejpam-3743	89	15	possess	possess	VERB
ejpam-3743	89	16	the	the	DET
ejpam-3743	89	17	difference	difference	NOUN
ejpam-3743	89	18	property	property	NOUN
ejpam-3743	89	19	.	.	PUNCT
ejpam-3743	90	1	for	for	ADP
ejpam-3743	90	2	more	more	ADJ
ejpam-3743	90	3	illustration	illustration	NOUN
ejpam-3743	90	4	of	of	ADP
ejpam-3743	90	5	the	the	DET
ejpam-3743	90	6	presented	present	VERB
ejpam-3743	90	7	findings	finding	NOUN
ejpam-3743	90	8	,	,	PUNCT
ejpam-3743	90	9	some	some	DET
ejpam-3743	90	10	interesting	interesting	ADJ
ejpam-3743	90	11	examples	example	NOUN
ejpam-3743	90	12	are	be	AUX
ejpam-3743	90	13	given	give	VERB
ejpam-3743	90	14	.	.	PUNCT
ejpam-3743	91	1	definition	definition	NOUN
ejpam-3743	91	2	9	9	NUM
ejpam-3743	91	3	.	.	PUNCT
ejpam-3743	92	1	a	a	DET
ejpam-3743	92	2	subset	subset	NOUN
ejpam-3743	92	3	a	a	DET
ejpam-3743	92	4	of	of	ADP
ejpam-3743	92	5	(	(	PUNCT
ejpam-3743	92	6	x,µ	x,µ	NOUN
ejpam-3743	92	7	)	)	PUNCT
ejpam-3743	92	8	is	be	AUX
ejpam-3743	92	9	said	say	VERB
ejpam-3743	92	10	to	to	PART
ejpam-3743	92	11	be	be	AUX
ejpam-3743	92	12	a	a	DET
ejpam-3743	92	13	supra	supra	ADJ
ejpam-3743	92	14	semi	semi	ADJ
ejpam-3743	92	15	neighbourhood	neighbourhood	NOUN
ejpam-3743	92	16	of	of	ADP
ejpam-3743	92	17	x	x	SYM
ejpam-3743	92	18	∈	∈	PROPN
ejpam-3743	92	19	x	x	PUNCT
ejpam-3743	92	20	provided	provide	VERB
ejpam-3743	92	21	that	that	SCONJ
ejpam-3743	92	22	there	there	PRON
ejpam-3743	92	23	is	be	VERB
ejpam-3743	92	24	a	a	DET
ejpam-3743	92	25	supra	supra	NOUN
ejpam-3743	92	26	semi	semi	ADV
ejpam-3743	92	27	open	open	ADJ
ejpam-3743	92	28	set	set	VERB
ejpam-3743	92	29	f	f	PROPN
ejpam-3743	92	30	containing	contain	VERB
ejpam-3743	92	31	x	x	PUNCT
ejpam-3743	92	32	such	such	ADJ
ejpam-3743	92	33	that	that	SCONJ
ejpam-3743	92	34	x	x	SYM
ejpam-3743	92	35	∈	∈	NOUN
ejpam-3743	92	36	f	f	NOUN
ejpam-3743	92	37	⊆	⊆	NUM
ejpam-3743	92	38	a.	a.	NOUN
ejpam-3743	92	39	definition	definition	NOUN
ejpam-3743	92	40	10	10	NUM
ejpam-3743	92	41	.	.	PUNCT
ejpam-3743	93	1	a	a	DET
ejpam-3743	93	2	point	point	NOUN
ejpam-3743	93	3	x	x	X
ejpam-3743	93	4	∈	∈	NOUN
ejpam-3743	93	5	x	x	PUNCT
ejpam-3743	93	6	is	be	AUX
ejpam-3743	93	7	said	say	VERB
ejpam-3743	93	8	to	to	PART
ejpam-3743	93	9	be	be	AUX
ejpam-3743	93	10	a	a	DET
ejpam-3743	93	11	supra	supra	NOUN
ejpam-3743	93	12	semi	semi	ADJ
ejpam-3743	93	13	limit	limit	NOUN
ejpam-3743	93	14	point	point	NOUN
ejpam-3743	93	15	of	of	ADP
ejpam-3743	93	16	a	a	DET
ejpam-3743	93	17	subset	subset	NOUN
ejpam-3743	93	18	a	a	DET
ejpam-3743	93	19	of	of	ADP
ejpam-3743	93	20	(	(	PUNCT
ejpam-3743	93	21	x,µ	x,µ	NOUN
ejpam-3743	93	22	)	)	PUNCT
ejpam-3743	93	23	provided	provide	VERB
ejpam-3743	93	24	that	that	SCONJ
ejpam-3743	93	25	every	every	DET
ejpam-3743	93	26	supra	supra	NOUN
ejpam-3743	93	27	semi	semi	ADJ
ejpam-3743	93	28	neighborhood	neighborhood	NOUN
ejpam-3743	93	29	of	of	ADP
ejpam-3743	93	30	x	x	PUNCT
ejpam-3743	93	31	contains	contain	VERB
ejpam-3743	93	32	at	at	ADV
ejpam-3743	93	33	least	least	ADV
ejpam-3743	93	34	one	one	NUM
ejpam-3743	93	35	point	point	NOUN
ejpam-3743	93	36	of	of	ADP
ejpam-3743	93	37	a	a	DET
ejpam-3743	93	38	other	other	ADJ
ejpam-3743	93	39	than	than	ADP
ejpam-3743	93	40	x	x	PRON
ejpam-3743	93	41	itself	itself	PRON
ejpam-3743	93	42	.	.	PUNCT
ejpam-3743	94	1	all	all	DET
ejpam-3743	94	2	supra	supra	PROPN
ejpam-3743	94	3	semi	semi	ADV
ejpam-3743	94	4	limit	limit	VERB
ejpam-3743	94	5	points	point	NOUN
ejpam-3743	94	6	of	of	ADP
ejpam-3743	94	7	a	a	PRON
ejpam-3743	94	8	is	be	AUX
ejpam-3743	94	9	said	say	VERB
ejpam-3743	94	10	to	to	PART
ejpam-3743	94	11	be	be	AUX
ejpam-3743	94	12	a	a	DET
ejpam-3743	94	13	supra	supra	NOUN
ejpam-3743	94	14	semi	semi	ADV
ejpam-3743	94	15	derived	derive	VERB
ejpam-3743	94	16	set	set	NOUN
ejpam-3743	94	17	of	of	ADP
ejpam-3743	94	18	a	a	PRON
ejpam-3743	94	19	and	and	CCONJ
ejpam-3743	94	20	is	be	AUX
ejpam-3743	94	21	denoted	denote	VERB
ejpam-3743	94	22	by	by	ADP
ejpam-3743	94	23	as′.	as′.	PROPN
ejpam-3743	94	24	proposition	proposition	PROPN
ejpam-3743	95	1	2	2	X
ejpam-3743	95	2	.	.	PUNCT
ejpam-3743	96	1	if	if	SCONJ
ejpam-3743	96	2	a	a	DET
ejpam-3743	96	3	⊆	⊆	NUM
ejpam-3743	96	4	b	b	NOUN
ejpam-3743	96	5	,	,	PUNCT
ejpam-3743	96	6	then	then	ADV
ejpam-3743	96	7	as′	as′	VERB
ejpam-3743	96	8	⊆	⊆	NUM
ejpam-3743	96	9	bs′	bs′	NOUN
ejpam-3743	96	10	for	for	ADP
ejpam-3743	96	11	every	every	DET
ejpam-3743	96	12	a	a	PROPN
ejpam-3743	96	13	,	,	PUNCT
ejpam-3743	96	14	b	b	NOUN
ejpam-3743	96	15	⊆	⊆	NUM
ejpam-3743	96	16	(	(	PUNCT
ejpam-3743	96	17	x,µ	x,µ	NOUN
ejpam-3743	96	18	)	)	PUNCT
ejpam-3743	96	19	.	.	PUNCT
ejpam-3743	97	1	proof	proof	NOUN
ejpam-3743	97	2	.	.	PUNCT
ejpam-3743	98	1	straightforward	straightforward	ADJ
ejpam-3743	98	2	.	.	PUNCT
ejpam-3743	99	1	corollary	corollary	ADJ
ejpam-3743	99	2	1	1	NUM
ejpam-3743	99	3	.	.	PUNCT
ejpam-3743	100	1	we	we	PRON
ejpam-3743	100	2	have	have	VERB
ejpam-3743	100	3	the	the	DET
ejpam-3743	100	4	following	follow	VERB
ejpam-3743	100	5	results	result	NOUN
ejpam-3743	100	6	for	for	ADP
ejpam-3743	100	7	every	every	DET
ejpam-3743	100	8	a	a	DET
ejpam-3743	100	9	,	,	PUNCT
ejpam-3743	100	10	b	b	NOUN
ejpam-3743	100	11	⊆	⊆	NUM
ejpam-3743	100	12	(	(	PUNCT
ejpam-3743	100	13	x,µ	x,µ	NOUN
ejpam-3743	100	14	)	)	PUNCT
ejpam-3743	100	15	.	.	PUNCT
ejpam-3743	101	1	(	(	PUNCT
ejpam-3743	101	2	i	i	NOUN
ejpam-3743	101	3	)	)	PUNCT
ejpam-3743	101	4	as′	as′	NOUN
ejpam-3743	101	5	⋃	⋃	NOUN
ejpam-3743	101	6	bs′	bs′	NOUN
ejpam-3743	101	7	⊆	⊆	NUM
ejpam-3743	101	8	(	(	PUNCT
ejpam-3743	101	9	a	a	DET
ejpam-3743	101	10	⋃	⋃	PROPN
ejpam-3743	101	11	b)s′.	b)s′.	PROPN
ejpam-3743	101	12	(	(	PUNCT
ejpam-3743	101	13	ii	ii	PROPN
ejpam-3743	101	14	)	)	PUNCT
ejpam-3743	101	15	(	(	PUNCT
ejpam-3743	101	16	a	a	DET
ejpam-3743	101	17	⋂	⋂	PROPN
ejpam-3743	101	18	b)s′	b)s′	VERB
ejpam-3743	101	19	⊆	⊆	NUM
ejpam-3743	101	20	as′	as′	NOUN
ejpam-3743	101	21	⋂	⋂	PROPN
ejpam-3743	101	22	bs′.	bs′.	NOUN
ejpam-3743	101	23	the	the	DET
ejpam-3743	101	24	following	follow	VERB
ejpam-3743	101	25	example	example	NOUN
ejpam-3743	101	26	illustrates	illustrate	VERB
ejpam-3743	101	27	that	that	SCONJ
ejpam-3743	101	28	the	the	DET
ejpam-3743	101	29	converse	converse	NOUN
ejpam-3743	101	30	of	of	ADP
ejpam-3743	101	31	the	the	DET
ejpam-3743	101	32	above	above	ADJ
ejpam-3743	101	33	proposition	proposition	NOUN
ejpam-3743	101	34	and	and	CCONJ
ejpam-3743	101	35	corollary	corollary	ADJ
ejpam-3743	101	36	fails	fail	NOUN
ejpam-3743	101	37	.	.	PUNCT
ejpam-3743	102	1	example	example	NOUN
ejpam-3743	103	1	1	1	NUM
ejpam-3743	103	2	.	.	PUNCT
ejpam-3743	103	3	let	let	VERB
ejpam-3743	103	4	µ	µ	X
ejpam-3743	103	5	=	=	SYM
ejpam-3743	103	6	{	{	PUNCT
ejpam-3743	103	7	∅	∅	NOUN
ejpam-3743	103	8	,	,	PUNCT
ejpam-3743	103	9	x	x	X
ejpam-3743	103	10	,	,	PUNCT
ejpam-3743	103	11	{	{	PUNCT
ejpam-3743	103	12	1	1	NUM
ejpam-3743	103	13	,	,	PUNCT
ejpam-3743	103	14	2	2	NUM
ejpam-3743	103	15	}	}	PUNCT
ejpam-3743	103	16	,	,	PUNCT
ejpam-3743	103	17	{	{	PUNCT
ejpam-3743	103	18	2	2	NUM
ejpam-3743	103	19	,	,	PUNCT
ejpam-3743	103	20	3	3	NUM
ejpam-3743	103	21	}	}	PUNCT
ejpam-3743	103	22	,	,	PUNCT
ejpam-3743	103	23	{	{	PUNCT
ejpam-3743	103	24	1	1	NUM
ejpam-3743	103	25	,	,	PUNCT
ejpam-3743	103	26	2	2	NUM
ejpam-3743	103	27	,	,	PUNCT
ejpam-3743	103	28	3	3	NUM
ejpam-3743	103	29	}	}	PUNCT
ejpam-3743	103	30	}	}	PUNCT
ejpam-3743	103	31	be	be	AUX
ejpam-3743	103	32	a	a	DET
ejpam-3743	103	33	supra	supra	ADJ
ejpam-3743	103	34	topology	topology	NOUN
ejpam-3743	103	35	on	on	ADP
ejpam-3743	103	36	x	x	X
ejpam-3743	103	37	=	=	SYM
ejpam-3743	103	38	{	{	PUNCT
ejpam-3743	103	39	1	1	NUM
ejpam-3743	103	40	,	,	PUNCT
ejpam-3743	103	41	2	2	NUM
ejpam-3743	103	42	,	,	PUNCT
ejpam-3743	103	43	3	3	NUM
ejpam-3743	103	44	,	,	PUNCT
ejpam-3743	103	45	4	4	NUM
ejpam-3743	103	46	}	}	PUNCT
ejpam-3743	103	47	.	.	PUNCT
ejpam-3743	104	1	then	then	ADV
ejpam-3743	104	2	{	{	PUNCT
ejpam-3743	104	3	∅	∅	NOUN
ejpam-3743	104	4	,	,	PUNCT
ejpam-3743	104	5	x	x	X
ejpam-3743	104	6	,	,	PUNCT
ejpam-3743	104	7	{	{	PUNCT
ejpam-3743	104	8	1	1	NUM
ejpam-3743	104	9	,	,	PUNCT
ejpam-3743	104	10	2	2	NUM
ejpam-3743	104	11	}	}	PUNCT
ejpam-3743	104	12	,	,	PUNCT
ejpam-3743	104	13	{	{	PUNCT
ejpam-3743	104	14	2	2	NUM
ejpam-3743	104	15	,	,	PUNCT
ejpam-3743	104	16	3	3	NUM
ejpam-3743	104	17	}	}	PUNCT
ejpam-3743	104	18	,	,	PUNCT
ejpam-3743	104	19	{	{	PUNCT
ejpam-3743	104	20	1	1	NUM
ejpam-3743	104	21	,	,	PUNCT
ejpam-3743	104	22	2	2	NUM
ejpam-3743	104	23	,	,	PUNCT
ejpam-3743	104	24	3	3	NUM
ejpam-3743	104	25	}	}	PUNCT
ejpam-3743	104	26	,	,	PUNCT
ejpam-3743	104	27	{	{	PUNCT
ejpam-3743	104	28	1	1	NUM
ejpam-3743	104	29	,	,	PUNCT
ejpam-3743	104	30	2	2	NUM
ejpam-3743	104	31	,	,	PUNCT
ejpam-3743	104	32	4	4	NUM
ejpam-3743	104	33	}	}	PUNCT
ejpam-3743	104	34	,	,	PUNCT
ejpam-3743	104	35	{	{	PUNCT
ejpam-3743	104	36	2	2	NUM
ejpam-3743	104	37	,	,	PUNCT
ejpam-3743	104	38	3	3	NUM
ejpam-3743	104	39	,	,	PUNCT
ejpam-3743	104	40	4	4	NUM
ejpam-3743	104	41	}	}	PUNCT
ejpam-3743	104	42	}	}	PUNCT
ejpam-3743	104	43	is	be	AUX
ejpam-3743	104	44	the	the	DET
ejpam-3743	104	45	collection	collection	NOUN
ejpam-3743	104	46	of	of	ADP
ejpam-3743	104	47	all	all	DET
ejpam-3743	104	48	supra	supra	PROPN
ejpam-3743	104	49	semiopen	semiopen	VERB
ejpam-3743	104	50	subsets	subset	NOUN
ejpam-3743	104	51	of	of	ADP
ejpam-3743	104	52	(	(	PUNCT
ejpam-3743	104	53	x,µ	x,µ	NOUN
ejpam-3743	104	54	)	)	PUNCT
ejpam-3743	104	55	.	.	PUNCT
ejpam-3743	105	1	if	if	SCONJ
ejpam-3743	105	2	a	a	PRON
ejpam-3743	105	3	=	=	X
ejpam-3743	105	4	{	{	PUNCT
ejpam-3743	105	5	2	2	NUM
ejpam-3743	105	6	}	}	PUNCT
ejpam-3743	105	7	,	,	PUNCT
ejpam-3743	105	8	b	b	X
ejpam-3743	105	9	=	=	SYM
ejpam-3743	105	10	{	{	PUNCT
ejpam-3743	105	11	2	2	NUM
ejpam-3743	105	12	,	,	PUNCT
ejpam-3743	105	13	4	4	NUM
ejpam-3743	105	14	}	}	PUNCT
ejpam-3743	105	15	,	,	PUNCT
ejpam-3743	105	16	c	c	X
ejpam-3743	105	17	=	=	SYM
ejpam-3743	105	18	{	{	PUNCT
ejpam-3743	105	19	1	1	NUM
ejpam-3743	105	20	,	,	PUNCT
ejpam-3743	105	21	3	3	NUM
ejpam-3743	105	22	,	,	PUNCT
ejpam-3743	105	23	4	4	NUM
ejpam-3743	105	24	}	}	PUNCT
ejpam-3743	105	25	and	and	CCONJ
ejpam-3743	105	26	d	d	NOUN
ejpam-3743	105	27	=	=	PUNCT
ejpam-3743	105	28	{	{	PUNCT
ejpam-3743	105	29	2	2	NUM
ejpam-3743	105	30	,	,	PUNCT
ejpam-3743	105	31	3	3	NUM
ejpam-3743	105	32	,	,	PUNCT
ejpam-3743	105	33	4	4	NUM
ejpam-3743	105	34	}	}	PUNCT
ejpam-3743	105	35	,	,	PUNCT
ejpam-3743	105	36	then	then	ADV
ejpam-3743	105	37	as′	as′	X
ejpam-3743	105	38	=	=	PUNCT
ejpam-3743	105	39	{	{	PUNCT
ejpam-3743	105	40	1	1	NUM
ejpam-3743	105	41	,	,	PUNCT
ejpam-3743	105	42	3	3	NUM
ejpam-3743	105	43	,	,	PUNCT
ejpam-3743	105	44	4	4	NUM
ejpam-3743	105	45	}	}	PUNCT
ejpam-3743	105	46	,	,	PUNCT
ejpam-3743	105	47	bs′	bs′	PROPN
ejpam-3743	106	1	=	=	SYM
ejpam-3743	106	2	{	{	PUNCT
ejpam-3743	106	3	1	1	NUM
ejpam-3743	106	4	,	,	PUNCT
ejpam-3743	106	5	3	3	NUM
ejpam-3743	106	6	,	,	PUNCT
ejpam-3743	106	7	4	4	NUM
ejpam-3743	106	8	}	}	PUNCT
ejpam-3743	106	9	,	,	PUNCT
ejpam-3743	106	10	cs′	cs′	X
ejpam-3743	106	11	=	=	PUNCT
ejpam-3743	106	12	{	{	PUNCT
ejpam-3743	106	13	2	2	NUM
ejpam-3743	106	14	,	,	PUNCT
ejpam-3743	106	15	4	4	NUM
ejpam-3743	106	16	}	}	PUNCT
ejpam-3743	106	17	and	and	CCONJ
ejpam-3743	106	18	ds′	ds′	VERB
ejpam-3743	106	19	=	=	SYM
ejpam-3743	106	20	{	{	PUNCT
ejpam-3743	106	21	1	1	NUM
ejpam-3743	106	22	,	,	PUNCT
ejpam-3743	106	23	3	3	NUM
ejpam-3743	106	24	,	,	PUNCT
ejpam-3743	106	25	4	4	NUM
ejpam-3743	106	26	}	}	PUNCT
ejpam-3743	106	27	.	.	PUNCT
ejpam-3743	107	1	now	now	ADV
ejpam-3743	107	2	,	,	PUNCT
ejpam-3743	107	3	one	one	NUM
ejpam-3743	107	4	readily	readily	ADV
ejpam-3743	107	5	checks	check	VERB
ejpam-3743	107	6	the	the	DET
ejpam-3743	107	7	following	following	NOUN
ejpam-3743	107	8	:	:	PUNCT
ejpam-3743	107	9	(	(	PUNCT
ejpam-3743	107	10	i	i	NOUN
ejpam-3743	107	11	)	)	PUNCT
ejpam-3743	107	12	bs′	bs′	PROPN
ejpam-3743	108	1	⊆	⊆	NUM
ejpam-3743	108	2	as′	as′	NOUN
ejpam-3743	108	3	,	,	PUNCT
ejpam-3743	108	4	but	but	CCONJ
ejpam-3743	108	5	b	b	X
ejpam-3743	108	6	6⊆	6⊆	NUM
ejpam-3743	108	7	a.	a.	NOUN
ejpam-3743	108	8	(	(	PUNCT
ejpam-3743	108	9	ii	ii	NOUN
ejpam-3743	108	10	)	)	PUNCT
ejpam-3743	108	11	bs′⋃ds′	bs′⋃ds′	PROPN
ejpam-3743	108	12	=	=	PUNCT
ejpam-3743	108	13	{	{	PUNCT
ejpam-3743	108	14	1	1	NUM
ejpam-3743	108	15	,	,	PUNCT
ejpam-3743	108	16	3	3	NUM
ejpam-3743	108	17	,	,	PUNCT
ejpam-3743	108	18	4	4	NUM
ejpam-3743	108	19	}	}	PUNCT
ejpam-3743	108	20	and	and	CCONJ
ejpam-3743	108	21	(	(	PUNCT
ejpam-3743	108	22	b	b	NOUN
ejpam-3743	108	23	⋃	⋃	NOUN
ejpam-3743	108	24	d)s′	d)s′	NOUN
ejpam-3743	108	25	=	=	SYM
ejpam-3743	108	26	xs′	xs′	PROPN
ejpam-3743	109	1	=	=	PUNCT
ejpam-3743	109	2	x.	x.	NOUN
ejpam-3743	109	3	(	(	PUNCT
ejpam-3743	109	4	iii	iii	X
ejpam-3743	109	5	)	)	PUNCT
ejpam-3743	109	6	bs′⋂cs′	bs′⋂cs′	X
ejpam-3743	110	1	=	=	NOUN
ejpam-3743	110	2	{	{	PUNCT
ejpam-3743	110	3	4	4	NUM
ejpam-3743	110	4	}	}	PUNCT
ejpam-3743	110	5	and	and	CCONJ
ejpam-3743	110	6	(	(	PUNCT
ejpam-3743	110	7	b	b	NOUN
ejpam-3743	110	8	⋂	⋂	NUM
ejpam-3743	110	9	c)s′	c)s′	ADJ
ejpam-3743	110	10	=	=	PUNCT
ejpam-3743	110	11	{	{	PUNCT
ejpam-3743	110	12	4}s′	4}s′	NOUN
ejpam-3743	110	13	=	=	PUNCT
ejpam-3743	110	14	∅.	∅.	NOUN
ejpam-3743	110	15	proposition	proposition	NOUN
ejpam-3743	110	16	3	3	NUM
ejpam-3743	110	17	.	.	PUNCT
ejpam-3743	110	18	let	let	VERB
ejpam-3743	110	19	a	a	DET
ejpam-3743	110	20	be	be	AUX
ejpam-3743	110	21	a	a	DET
ejpam-3743	110	22	subset	subset	NOUN
ejpam-3743	110	23	of	of	ADP
ejpam-3743	110	24	(	(	PUNCT
ejpam-3743	110	25	x,µ	x,µ	NOUN
ejpam-3743	110	26	)	)	PUNCT
ejpam-3743	110	27	and	and	CCONJ
ejpam-3743	110	28	x	x	PUNCT
ejpam-3743	110	29	∈	∈	NOUN
ejpam-3743	110	30	x.	x.	NOUN
ejpam-3743	110	31	then	then	ADV
ejpam-3743	110	32	x	x	SYM
ejpam-3743	110	33	∈	∈	PROPN
ejpam-3743	110	34	as′	as′	NOUN
ejpam-3743	110	35	if	if	SCONJ
ejpam-3743	110	36	and	and	CCONJ
ejpam-3743	110	37	only	only	ADV
ejpam-3743	110	38	if	if	SCONJ
ejpam-3743	110	39	x	x	SYM
ejpam-3743	110	40	∈	∈	PROPN
ejpam-3743	110	41	(	(	PUNCT
ejpam-3743	110	42	a	a	DET
ejpam-3743	110	43	\	\	PROPN
ejpam-3743	110	44	{	{	PUNCT
ejpam-3743	110	45	x})s′.	x})s′.	PROPN
ejpam-3743	110	46	proof	proof	NOUN
ejpam-3743	110	47	.	.	PUNCT
ejpam-3743	111	1	necessity	necessity	NOUN
ejpam-3743	111	2	:	:	PUNCT
ejpam-3743	111	3	let	let	VERB
ejpam-3743	111	4	x	x	X
ejpam-3743	111	5	∈	∈	PROPN
ejpam-3743	111	6	as′.	as′.	PROPN
ejpam-3743	111	7	then	then	ADV
ejpam-3743	111	8	for	for	ADP
ejpam-3743	111	9	every	every	DET
ejpam-3743	111	10	supra	supra	NOUN
ejpam-3743	111	11	semi	semi	ADV
ejpam-3743	111	12	open	open	ADJ
ejpam-3743	111	13	set	set	VERB
ejpam-3743	111	14	g	g	NOUN
ejpam-3743	111	15	containing	contain	VERB
ejpam-3743	111	16	x	x	SYM
ejpam-3743	111	17	,	,	PUNCT
ejpam-3743	111	18	we	we	PRON
ejpam-3743	111	19	have	have	VERB
ejpam-3743	111	20	(	(	PUNCT
ejpam-3743	111	21	g	g	NOUN
ejpam-3743	111	22	\	\	PROPN
ejpam-3743	111	23	{	{	PUNCT
ejpam-3743	111	24	x	x	NOUN
ejpam-3743	111	25	}	}	PUNCT
ejpam-3743	111	26	)	)	PUNCT
ejpam-3743	112	1	⋂	⋂	PROPN
ejpam-3743	112	2	a	a	PRON
ejpam-3743	112	3	6=	6=	NUM
ejpam-3743	112	4	∅.	∅.	NOUN
ejpam-3743	112	5	therefore	therefore	ADV
ejpam-3743	112	6	(	(	PUNCT
ejpam-3743	112	7	g	g	PROPN
ejpam-3743	112	8	\	\	PROPN
ejpam-3743	112	9	{	{	PUNCT
ejpam-3743	112	10	x	x	NOUN
ejpam-3743	112	11	}	}	PUNCT
ejpam-3743	112	12	)	)	PUNCT
ejpam-3743	112	13	⋂	⋂	PROPN
ejpam-3743	112	14	(	(	PUNCT
ejpam-3743	112	15	a	a	DET
ejpam-3743	112	16	\	\	PROPN
ejpam-3743	112	17	{	{	PUNCT
ejpam-3743	112	18	x	x	NOUN
ejpam-3743	112	19	}	}	PUNCT
ejpam-3743	112	20	)	)	PUNCT
ejpam-3743	112	21	6=	6=	ADP
ejpam-3743	112	22	∅.	∅.	VERB
ejpam-3743	112	23	thus	thus	ADV
ejpam-3743	112	24	x	x	SYM
ejpam-3743	112	25	∈	∈	PROPN
ejpam-3743	112	26	(	(	PUNCT
ejpam-3743	112	27	a	a	DET
ejpam-3743	112	28	\	\	PROPN
ejpam-3743	112	29	{	{	PUNCT
ejpam-3743	112	30	x})s′.	x})s′.	PROPN
ejpam-3743	112	31	sufficiency	sufficiency	NOUN
ejpam-3743	112	32	:	:	PUNCT
ejpam-3743	112	33	it	it	PRON
ejpam-3743	112	34	follows	follow	VERB
ejpam-3743	112	35	from	from	ADP
ejpam-3743	112	36	proposition	proposition	NOUN
ejpam-3743	112	37	(	(	PUNCT
ejpam-3743	112	38	2	2	NUM
ejpam-3743	112	39	)	)	PUNCT
ejpam-3743	112	40	.	.	PUNCT
ejpam-3743	113	1	t.	t.	PROPN
ejpam-3743	113	2	m.	m.	PROPN
ejpam-3743	113	3	al	al	PROPN
ejpam-3743	113	4	-	-	PUNCT
ejpam-3743	113	5	shami	shami	PROPN
ejpam-3743	113	6	et	et	PROPN
ejpam-3743	113	7	al	al	PROPN
ejpam-3743	113	8	.	.	PUNCT
ejpam-3743	113	9	/	/	SYM
ejpam-3743	113	10	eur	eur	PROPN
ejpam-3743	113	11	.	.	PUNCT
ejpam-3743	114	1	j.	j.	PROPN
ejpam-3743	114	2	pure	pure	PROPN
ejpam-3743	114	3	appl	appl	PROPN
ejpam-3743	114	4	.	.	PROPN
ejpam-3743	114	5	math	math	PROPN
ejpam-3743	114	6	,	,	PUNCT
ejpam-3743	114	7	13	13	NUM
ejpam-3743	114	8	(	(	PUNCT
ejpam-3743	114	9	3	3	NUM
ejpam-3743	114	10	)	)	PUNCT
ejpam-3743	114	11	(	(	PUNCT
ejpam-3743	114	12	2020	2020	NUM
ejpam-3743	114	13	)	)	PUNCT
ejpam-3743	114	14	,	,	PUNCT
ejpam-3743	114	15	427	427	NUM
ejpam-3743	114	16	-	-	SYM
ejpam-3743	114	17	443	443	NUM
ejpam-3743	114	18	431	431	NUM
ejpam-3743	114	19	theorem	theorem	NOUN
ejpam-3743	114	20	1	1	NUM
ejpam-3743	114	21	.	.	PUNCT
ejpam-3743	115	1	let	let	VERB
ejpam-3743	115	2	a	a	DET
ejpam-3743	115	3	be	be	AUX
ejpam-3743	115	4	a	a	DET
ejpam-3743	115	5	subset	subset	NOUN
ejpam-3743	115	6	of	of	ADP
ejpam-3743	115	7	(	(	PUNCT
ejpam-3743	115	8	x,µ	x,µ	NOUN
ejpam-3743	115	9	)	)	PUNCT
ejpam-3743	115	10	.	.	PUNCT
ejpam-3743	116	1	then	then	ADV
ejpam-3743	116	2	the	the	DET
ejpam-3743	116	3	following	following	ADJ
ejpam-3743	116	4	results	result	NOUN
ejpam-3743	116	5	hold	hold	VERB
ejpam-3743	116	6	.	.	PUNCT
ejpam-3743	117	1	(	(	PUNCT
ejpam-3743	117	2	i	i	NOUN
ejpam-3743	117	3	)	)	PUNCT
ejpam-3743	117	4	a	a	PRON
ejpam-3743	117	5	is	be	AUX
ejpam-3743	117	6	a	a	DET
ejpam-3743	117	7	supra	supra	ADJ
ejpam-3743	117	8	semi	semi	ADJ
ejpam-3743	117	9	-	-	ADJ
ejpam-3743	117	10	closed	closed	ADJ
ejpam-3743	117	11	set	set	ADJ
ejpam-3743	117	12	iff	iff	PROPN
ejpam-3743	117	13	as′	as′	NOUN
ejpam-3743	117	14	⊆	⊆	NUM
ejpam-3743	117	15	a.	a.	NOUN
ejpam-3743	117	16	(	(	PUNCT
ejpam-3743	117	17	ii	ii	PROPN
ejpam-3743	117	18	)	)	PUNCT
ejpam-3743	117	19	a	a	DET
ejpam-3743	117	20	⋃	⋃	NOUN
ejpam-3743	117	21	as′	as′	NOUN
ejpam-3743	117	22	is	be	AUX
ejpam-3743	117	23	a	a	DET
ejpam-3743	117	24	supra	supra	ADJ
ejpam-3743	117	25	semi	semi	ADJ
ejpam-3743	117	26	-	-	ADJ
ejpam-3743	117	27	closed	closed	ADJ
ejpam-3743	117	28	set	set	NOUN
ejpam-3743	117	29	.	.	PUNCT
ejpam-3743	118	1	(	(	PUNCT
ejpam-3743	118	2	iii	iii	X
ejpam-3743	118	3	)	)	PUNCT
ejpam-3743	118	4	scl(a	scl(a	PROPN
ejpam-3743	118	5	)	)	PUNCT
ejpam-3743	118	6	=	=	PUNCT
ejpam-3743	119	1	a	a	DET
ejpam-3743	119	2	⋃	⋃	ADV
ejpam-3743	119	3	as′.	as′.	PROPN
ejpam-3743	119	4	proof	proof	NOUN
ejpam-3743	119	5	.	.	PUNCT
ejpam-3743	120	1	(	(	PUNCT
ejpam-3743	120	2	i	i	NOUN
ejpam-3743	120	3	)	)	PUNCT
ejpam-3743	120	4	suppose	suppose	VERB
ejpam-3743	120	5	that	that	SCONJ
ejpam-3743	120	6	a	a	PRON
ejpam-3743	120	7	is	be	AUX
ejpam-3743	120	8	a	a	DET
ejpam-3743	120	9	supra	supra	ADJ
ejpam-3743	120	10	semi	semi	ADJ
ejpam-3743	120	11	-	-	ADJ
ejpam-3743	120	12	closed	closed	ADJ
ejpam-3743	120	13	set	set	NOUN
ejpam-3743	120	14	and	and	CCONJ
ejpam-3743	120	15	x	x	SYM
ejpam-3743	120	16	6∈	6∈	PROPN
ejpam-3743	120	17	a.	a.	NOUN
ejpam-3743	120	18	then	then	ADV
ejpam-3743	120	19	ac	ac	PROPN
ejpam-3743	120	20	is	be	AUX
ejpam-3743	120	21	a	a	DET
ejpam-3743	120	22	supra	supra	ADJ
ejpam-3743	120	23	semi	semi	ADJ
ejpam-3743	120	24	-	-	ADJ
ejpam-3743	120	25	open	open	ADJ
ejpam-3743	120	26	set	set	NOUN
ejpam-3743	120	27	containing	contain	VERB
ejpam-3743	120	28	x.	x.	NOUN
ejpam-3743	120	29	in	in	ADP
ejpam-3743	120	30	this	this	DET
ejpam-3743	120	31	case	case	NOUN
ejpam-3743	120	32	ac	ac	ADV
ejpam-3743	120	33	⋂	⋂	PROPN
ejpam-3743	120	34	a	a	DET
ejpam-3743	120	35	=	=	PUNCT
ejpam-3743	120	36	∅	∅	NOUN
ejpam-3743	120	37	leads	lead	VERB
ejpam-3743	120	38	to	to	ADP
ejpam-3743	120	39	x	x	PROPN
ejpam-3743	120	40	6∈	6∈	PROPN
ejpam-3743	120	41	as′.	as′.	PROPN
ejpam-3743	120	42	therefore	therefore	ADV
ejpam-3743	120	43	as′	as′	VERB
ejpam-3743	120	44	⊆	⊆	NUM
ejpam-3743	120	45	a.	a.	NOUN
ejpam-3743	120	46	conversely	conversely	ADV
ejpam-3743	120	47	,	,	PUNCT
ejpam-3743	120	48	let	let	VERB
ejpam-3743	120	49	x	x	X
ejpam-3743	120	50	∈	∈	NOUN
ejpam-3743	120	51	ac	ac	NOUN
ejpam-3743	120	52	and	and	CCONJ
ejpam-3743	120	53	let	let	VERB
ejpam-3743	120	54	as′	as′	NOUN
ejpam-3743	120	55	⊆	⊆	NUM
ejpam-3743	120	56	a.	a.	NOUN
ejpam-3743	120	57	then	then	ADV
ejpam-3743	121	1	x	x	SYM
ejpam-3743	121	2	6∈	6∈	PROPN
ejpam-3743	121	3	as′.	as′.	PROPN
ejpam-3743	121	4	therefore	therefore	ADV
ejpam-3743	121	5	there	there	PRON
ejpam-3743	121	6	is	be	VERB
ejpam-3743	121	7	a	a	DET
ejpam-3743	121	8	supra	supra	ADJ
ejpam-3743	121	9	semi	semi	ADJ
ejpam-3743	121	10	-	-	ADJ
ejpam-3743	121	11	open	open	ADJ
ejpam-3743	121	12	set	set	ADJ
ejpam-3743	121	13	gx	gx	PROPN
ejpam-3743	121	14	such	such	ADJ
ejpam-3743	121	15	that	that	SCONJ
ejpam-3743	121	16	gx	gx	PROPN
ejpam-3743	121	17	\{x	\{x	PROPN
ejpam-3743	121	18	}	}	PUNCT
ejpam-3743	121	19	⋂	⋂	PROPN
ejpam-3743	121	20	a	a	DET
ejpam-3743	121	21	=	=	X
ejpam-3743	121	22	∅.	∅.	NOUN
ejpam-3743	121	23	since	since	SCONJ
ejpam-3743	121	24	x	x	PROPN
ejpam-3743	121	25	∈	∈	PROPN
ejpam-3743	121	26	ac	ac	PROPN
ejpam-3743	121	27	,	,	PUNCT
ejpam-3743	121	28	then	then	ADV
ejpam-3743	121	29	gx	gx	PROPN
ejpam-3743	121	30	⋂	⋂	PROPN
ejpam-3743	121	31	a	a	DET
ejpam-3743	121	32	=	=	X
ejpam-3743	121	33	∅.	∅.	NOUN
ejpam-3743	121	34	now	now	ADV
ejpam-3743	121	35	,	,	PUNCT
ejpam-3743	121	36	gx	gx	PROPN
ejpam-3743	121	37	⊆	⊆	NUM
ejpam-3743	121	38	ac	ac	PROPN
ejpam-3743	121	39	.	.	PUNCT
ejpam-3743	122	1	therefore	therefore	ADV
ejpam-3743	122	2	ac	ac	PROPN
ejpam-3743	123	1	=	=	PUNCT
ejpam-3743	123	2	⋃	⋃	PROPN
ejpam-3743	123	3	{	{	PUNCT
ejpam-3743	123	4	gx	gx	PROPN
ejpam-3743	123	5	:	:	PUNCT
ejpam-3743	123	6	x	x	SYM
ejpam-3743	123	7	∈	∈	NOUN
ejpam-3743	123	8	ac	ac	PROPN
ejpam-3743	123	9	}	}	PUNCT
ejpam-3743	123	10	.	.	PUNCT
ejpam-3743	124	1	thus	thus	ADV
ejpam-3743	124	2	a	a	PRON
ejpam-3743	124	3	is	be	AUX
ejpam-3743	124	4	supra	supra	ADJ
ejpam-3743	124	5	semi	semi	ADJ
ejpam-3743	124	6	-	-	ADJ
ejpam-3743	124	7	closed	closed	ADJ
ejpam-3743	124	8	.	.	PUNCT
ejpam-3743	125	1	(	(	PUNCT
ejpam-3743	125	2	ii	ii	NOUN
ejpam-3743	125	3	)	)	PUNCT
ejpam-3743	125	4	let	let	VERB
ejpam-3743	125	5	x	x	SYM
ejpam-3743	125	6	6∈	6∈	PROPN
ejpam-3743	125	7	(	(	PUNCT
ejpam-3743	125	8	a	a	DET
ejpam-3743	125	9	⋃	⋃	NOUN
ejpam-3743	125	10	as′	as′	NOUN
ejpam-3743	125	11	)	)	PUNCT
ejpam-3743	125	12	.	.	PUNCT
ejpam-3743	126	1	then	then	ADV
ejpam-3743	126	2	x	x	X
ejpam-3743	126	3	6∈	6∈	PROPN
ejpam-3743	126	4	a	a	PROPN
ejpam-3743	126	5	and	and	CCONJ
ejpam-3743	126	6	x	x	SYM
ejpam-3743	126	7	6∈	6∈	PROPN
ejpam-3743	126	8	as′.	as′.	PROPN
ejpam-3743	127	1	therefore	therefore	ADV
ejpam-3743	127	2	there	there	PRON
ejpam-3743	127	3	is	be	VERB
ejpam-3743	127	4	a	a	DET
ejpam-3743	127	5	supra	supra	ADJ
ejpam-3743	127	6	semi	semi	ADJ
ejpam-3743	127	7	-	-	ADJ
ejpam-3743	127	8	open	open	ADJ
ejpam-3743	127	9	set	set	NOUN
ejpam-3743	127	10	g	g	PROPN
ejpam-3743	127	11	such	such	ADJ
ejpam-3743	127	12	that	that	SCONJ
ejpam-3743	127	13	g	g	PROPN
ejpam-3743	127	14	⋂	⋂	PROPN
ejpam-3743	127	15	a	a	DET
ejpam-3743	127	16	=	=	PUNCT
ejpam-3743	127	17	∅	∅	NOUN
ejpam-3743	127	18	(	(	PUNCT
ejpam-3743	127	19	1	1	X
ejpam-3743	127	20	)	)	PUNCT
ejpam-3743	127	21	now	now	ADV
ejpam-3743	127	22	,	,	PUNCT
ejpam-3743	127	23	for	for	ADP
ejpam-3743	127	24	each	each	DET
ejpam-3743	127	25	x	x	SYM
ejpam-3743	127	26	∈	∈	PROPN
ejpam-3743	127	27	g	g	PROPN
ejpam-3743	127	28	,	,	PUNCT
ejpam-3743	127	29	we	we	PRON
ejpam-3743	127	30	have	have	VERB
ejpam-3743	127	31	x	x	PART
ejpam-3743	127	32	6∈	6∈	PROPN
ejpam-3743	127	33	as′.	as′.	PROPN
ejpam-3743	127	34	this	this	PRON
ejpam-3743	127	35	means	mean	VERB
ejpam-3743	127	36	that	that	SCONJ
ejpam-3743	127	37	g	g	PROPN
ejpam-3743	127	38	⋂	⋂	PROPN
ejpam-3743	127	39	as′	as′	NOUN
ejpam-3743	127	40	=	=	NOUN
ejpam-3743	127	41	∅	∅	NOUN
ejpam-3743	127	42	(	(	PUNCT
ejpam-3743	127	43	2	2	NUM
ejpam-3743	127	44	)	)	PUNCT
ejpam-3743	127	45	from	from	ADP
ejpam-3743	127	46	(	(	PUNCT
ejpam-3743	127	47	1	1	NUM
ejpam-3743	127	48	)	)	PUNCT
ejpam-3743	127	49	and	and	CCONJ
ejpam-3743	127	50	(	(	PUNCT
ejpam-3743	127	51	2	2	NUM
ejpam-3743	127	52	)	)	PUNCT
ejpam-3743	127	53	,	,	PUNCT
ejpam-3743	127	54	we	we	PRON
ejpam-3743	127	55	obtain	obtain	VERB
ejpam-3743	127	56	g	g	PROPN
ejpam-3743	127	57	⋂	⋂	PROPN
ejpam-3743	127	58	(	(	PUNCT
ejpam-3743	127	59	a	a	DET
ejpam-3743	127	60	⋃	⋃	NOUN
ejpam-3743	127	61	as′	as′	NOUN
ejpam-3743	127	62	)	)	PUNCT
ejpam-3743	127	63	=	=	PUNCT
ejpam-3743	128	1	∅.	∅.	ADP
ejpam-3743	128	2	this	this	PRON
ejpam-3743	128	3	implies	imply	VERB
ejpam-3743	128	4	that	that	SCONJ
ejpam-3743	128	5	x	x	SYM
ejpam-3743	128	6	6∈	6∈	NOUN
ejpam-3743	128	7	(	(	PUNCT
ejpam-3743	128	8	a	a	DET
ejpam-3743	128	9	⋃	⋃	NOUN
ejpam-3743	128	10	as′)s′.	as′)s′.	PUNCT
ejpam-3743	128	11	hence	hence	ADV
ejpam-3743	128	12	(	(	PUNCT
ejpam-3743	128	13	a	a	DET
ejpam-3743	128	14	⋃	⋃	NOUN
ejpam-3743	128	15	as′)s′	as′)s′	ADP
ejpam-3743	128	16	⊆	⊆	NUM
ejpam-3743	128	17	(	(	PUNCT
ejpam-3743	128	18	a	a	DET
ejpam-3743	128	19	⋃	⋃	NOUN
ejpam-3743	128	20	as′	as′	NOUN
ejpam-3743	128	21	)	)	PUNCT
ejpam-3743	128	22	.	.	PUNCT
ejpam-3743	129	1	by	by	ADP
ejpam-3743	129	2	(	(	PUNCT
ejpam-3743	129	3	i	i	NOUN
ejpam-3743	129	4	)	)	PUNCT
ejpam-3743	129	5	,	,	PUNCT
ejpam-3743	129	6	a	a	DET
ejpam-3743	129	7	⋃	⋃	NOUN
ejpam-3743	129	8	as′	as′	NOUN
ejpam-3743	129	9	is	be	AUX
ejpam-3743	129	10	a	a	DET
ejpam-3743	129	11	supra	supra	ADJ
ejpam-3743	129	12	semi	semi	ADJ
ejpam-3743	129	13	-	-	ADJ
ejpam-3743	129	14	closed	closed	ADJ
ejpam-3743	129	15	set	set	NOUN
ejpam-3743	129	16	,	,	PUNCT
ejpam-3743	129	17	as	as	SCONJ
ejpam-3743	129	18	required	require	VERB
ejpam-3743	129	19	.	.	PUNCT
ejpam-3743	130	1	(	(	PUNCT
ejpam-3743	130	2	iii	iii	X
ejpam-3743	130	3	)	)	PUNCT
ejpam-3743	130	4	since	since	SCONJ
ejpam-3743	130	5	a	a	DET
ejpam-3743	130	6	⊆	⊆	NUM
ejpam-3743	130	7	scl(a	scl(a	NOUN
ejpam-3743	130	8	)	)	PUNCT
ejpam-3743	130	9	and	and	CCONJ
ejpam-3743	130	10	as′	as′	NOUN
ejpam-3743	130	11	⊆	⊆	NUM
ejpam-3743	130	12	(	(	PUNCT
ejpam-3743	130	13	scl(a))s′	scl(a))s′	NOUN
ejpam-3743	130	14	⊆	⊆	NUM
ejpam-3743	130	15	scl(a	scl(a	PROPN
ejpam-3743	130	16	)	)	PUNCT
ejpam-3743	130	17	,	,	PUNCT
ejpam-3743	130	18	then	then	ADV
ejpam-3743	130	19	a	a	DET
ejpam-3743	130	20	⋃	⋃	PROPN
ejpam-3743	130	21	as′	as′	NOUN
ejpam-3743	130	22	⊆	⊆	NUM
ejpam-3743	130	23	scl(a	scl(a	NOUN
ejpam-3743	130	24	)	)	PUNCT
ejpam-3743	130	25	.	.	PUNCT
ejpam-3743	131	1	since	since	SCONJ
ejpam-3743	131	2	a	a	DET
ejpam-3743	131	3	⋃	⋃	NOUN
ejpam-3743	131	4	as′	as′	NOUN
ejpam-3743	131	5	is	be	AUX
ejpam-3743	131	6	a	a	DET
ejpam-3743	131	7	supra	supra	ADJ
ejpam-3743	131	8	semi	semi	ADJ
ejpam-3743	131	9	-	-	ADJ
ejpam-3743	131	10	closed	closed	ADJ
ejpam-3743	131	11	set	set	NOUN
ejpam-3743	131	12	containing	contain	VERB
ejpam-3743	131	13	a	a	PRON
ejpam-3743	131	14	and	and	CCONJ
ejpam-3743	131	15	scl(a	scl(a	NUM
ejpam-3743	131	16	)	)	PUNCT
ejpam-3743	131	17	is	be	AUX
ejpam-3743	131	18	the	the	DET
ejpam-3743	131	19	smallest	small	ADJ
ejpam-3743	131	20	supra	supra	NOUN
ejpam-3743	131	21	semi	semi	ADJ
ejpam-3743	131	22	-	-	ADJ
ejpam-3743	131	23	closed	closed	ADJ
ejpam-3743	131	24	set	set	NOUN
ejpam-3743	131	25	containing	contain	VERB
ejpam-3743	131	26	a	a	DET
ejpam-3743	131	27	,	,	PUNCT
ejpam-3743	131	28	then	then	ADV
ejpam-3743	131	29	scl(a	scl(a	PROPN
ejpam-3743	131	30	)	)	PUNCT
ejpam-3743	131	31	⊆	⊆	NUM
ejpam-3743	131	32	a	a	DET
ejpam-3743	131	33	⋃	⋃	PROPN
ejpam-3743	131	34	as′.	as′.	PROPN
ejpam-3743	131	35	therefore	therefore	ADV
ejpam-3743	131	36	scl(a	scl(a	PROPN
ejpam-3743	131	37	)	)	PUNCT
ejpam-3743	131	38	=	=	PUNCT
ejpam-3743	131	39	a	a	DET
ejpam-3743	131	40	⋃	⋃	PROPN
ejpam-3743	131	41	as′.	as′.	PROPN
ejpam-3743	131	42	corollary	corollary	NOUN
ejpam-3743	131	43	2	2	NUM
ejpam-3743	131	44	.	.	PUNCT
ejpam-3743	132	1	if	if	SCONJ
ejpam-3743	132	2	a	a	PRON
ejpam-3743	132	3	is	be	AUX
ejpam-3743	132	4	a	a	DET
ejpam-3743	132	5	supra	supra	ADJ
ejpam-3743	132	6	semi	semi	ADJ
ejpam-3743	132	7	-	-	ADJ
ejpam-3743	132	8	closed	closed	ADJ
ejpam-3743	132	9	subset	subset	NOUN
ejpam-3743	132	10	of	of	ADP
ejpam-3743	132	11	(	(	PUNCT
ejpam-3743	132	12	x,µ	x,µ	NOUN
ejpam-3743	132	13	)	)	PUNCT
ejpam-3743	132	14	,	,	PUNCT
ejpam-3743	132	15	then	then	ADV
ejpam-3743	132	16	as′	as′	NOUN
ejpam-3743	132	17	,	,	PUNCT
ejpam-3743	132	18	(	(	PUNCT
ejpam-3743	132	19	as′)s′	as′)s′	PROPN
ejpam-3743	132	20	,	,	PUNCT
ejpam-3743	132	21	(	(	PUNCT
ejpam-3743	132	22	(	(	PUNCT
ejpam-3743	132	23	as′)s′)s′	as′)s′)s′	INTJ
ejpam-3743	132	24	,	,	PUNCT
ejpam-3743	132	25	...	...	PUNCT
ejpam-3743	132	26	are	be	AUX
ejpam-3743	132	27	supra	supra	ADJ
ejpam-3743	132	28	semi	semi	ADJ
ejpam-3743	132	29	-	-	ADJ
ejpam-3743	132	30	closed	closed	ADJ
ejpam-3743	132	31	sets	set	NOUN
ejpam-3743	132	32	.	.	PUNCT
ejpam-3743	133	1	definition	definition	NOUN
ejpam-3743	133	2	11	11	NUM
ejpam-3743	133	3	.	.	PUNCT
ejpam-3743	134	1	a	a	DET
ejpam-3743	134	2	map	map	NOUN
ejpam-3743	134	3	g	g	NOUN
ejpam-3743	134	4	:	:	PUNCT
ejpam-3743	134	5	(	(	PUNCT
ejpam-3743	134	6	x,µ)→	x,µ)→	X
ejpam-3743	134	7	(	(	PUNCT
ejpam-3743	134	8	y	y	PROPN
ejpam-3743	134	9	,	,	PUNCT
ejpam-3743	134	10	ν	ν	NOUN
ejpam-3743	134	11	)	)	PUNCT
ejpam-3743	134	12	is	be	AUX
ejpam-3743	134	13	said	say	VERB
ejpam-3743	134	14	to	to	PART
ejpam-3743	134	15	be	be	AUX
ejpam-3743	134	16	:	:	PUNCT
ejpam-3743	134	17	(	(	PUNCT
ejpam-3743	134	18	i	i	NOUN
ejpam-3743	134	19	)	)	PUNCT
ejpam-3743	134	20	supra	supra	PROPN
ejpam-3743	134	21	semi?-continuous	semi?-continuous	PROPN
ejpam-3743	134	22	if	if	SCONJ
ejpam-3743	134	23	g−1(h	g−1(h	PROPN
ejpam-3743	134	24	)	)	PUNCT
ejpam-3743	134	25	is	be	AUX
ejpam-3743	134	26	a	a	DET
ejpam-3743	134	27	supra	supra	ADJ
ejpam-3743	134	28	semi	semi	ADJ
ejpam-3743	134	29	-	-	ADJ
ejpam-3743	134	30	open	open	ADJ
ejpam-3743	134	31	set	set	NOUN
ejpam-3743	134	32	in	in	ADP
ejpam-3743	134	33	x	x	PUNCT
ejpam-3743	134	34	for	for	ADP
ejpam-3743	134	35	every	every	DET
ejpam-3743	134	36	supra	supra	NOUN
ejpam-3743	134	37	semi	semi	ADJ
ejpam-3743	134	38	-	-	ADJ
ejpam-3743	134	39	open	open	ADJ
ejpam-3743	134	40	set	set	NOUN
ejpam-3743	134	41	in	in	ADP
ejpam-3743	134	42	y	y	PROPN
ejpam-3743	134	43	.	.	PUNCT
ejpam-3743	135	1	(	(	PUNCT
ejpam-3743	135	2	ii	ii	NOUN
ejpam-3743	135	3	)	)	PUNCT
ejpam-3743	135	4	supra	supra	PROPN
ejpam-3743	135	5	semi?-open	semi?-open	PROPN
ejpam-3743	135	6	(	(	PUNCT
ejpam-3743	135	7	resp	resp	NOUN
ejpam-3743	135	8	.	.	PUNCT
ejpam-3743	136	1	supra	supra	PROPN
ejpam-3743	136	2	semi?-closed	semi?-close	VERB
ejpam-3743	136	3	)	)	PUNCT
ejpam-3743	136	4	if	if	SCONJ
ejpam-3743	136	5	g(h	g(h	NUM
ejpam-3743	136	6	)	)	PUNCT
ejpam-3743	136	7	is	be	AUX
ejpam-3743	136	8	a	a	DET
ejpam-3743	136	9	supra	supra	NOUN
ejpam-3743	136	10	semi	semi	ADJ
ejpam-3743	136	11	-	-	ADJ
ejpam-3743	136	12	open	open	ADJ
ejpam-3743	136	13	(	(	PUNCT
ejpam-3743	136	14	resp	resp	NOUN
ejpam-3743	136	15	.	.	PUNCT
ejpam-3743	137	1	supra	supra	PROPN
ejpam-3743	137	2	semi	semi	ADJ
ejpam-3743	137	3	-	-	ADJ
ejpam-3743	137	4	closed	closed	ADJ
ejpam-3743	137	5	)	)	PUNCT
ejpam-3743	137	6	set	set	VERB
ejpam-3743	137	7	in	in	ADP
ejpam-3743	137	8	y	y	PROPN
ejpam-3743	137	9	for	for	ADP
ejpam-3743	137	10	every	every	DET
ejpam-3743	137	11	supra	supra	NOUN
ejpam-3743	137	12	semi	semi	ADJ
ejpam-3743	137	13	-	-	ADJ
ejpam-3743	137	14	open	open	ADJ
ejpam-3743	137	15	(	(	PUNCT
ejpam-3743	137	16	resp	resp	NOUN
ejpam-3743	137	17	.	.	PUNCT
ejpam-3743	138	1	supra	supra	PROPN
ejpam-3743	138	2	semi	semi	ADJ
ejpam-3743	138	3	-	-	ADJ
ejpam-3743	138	4	closed	closed	ADJ
ejpam-3743	138	5	)	)	PUNCT
ejpam-3743	138	6	set	set	VERB
ejpam-3743	138	7	in	in	ADP
ejpam-3743	138	8	x.	x.	PROPN
ejpam-3743	138	9	(	(	PUNCT
ejpam-3743	138	10	iii	iii	NOUN
ejpam-3743	138	11	)	)	PUNCT
ejpam-3743	138	12	supra	supra	NOUN
ejpam-3743	138	13	semi?-homeomorphism	semi?-homeomorphism	PROPN
ejpam-3743	138	14	if	if	SCONJ
ejpam-3743	138	15	it	it	PRON
ejpam-3743	138	16	is	be	AUX
ejpam-3743	138	17	bijective	bijective	ADJ
ejpam-3743	138	18	,	,	PUNCT
ejpam-3743	138	19	supra	supra	PROPN
ejpam-3743	138	20	semi?-continuous	semi?-continuous	ADJ
ejpam-3743	138	21	and	and	CCONJ
ejpam-3743	138	22	supra	supra	PROPN
ejpam-3743	138	23	semi?-open	semi?-open	PROPN
ejpam-3743	138	24	.	.	PUNCT
ejpam-3743	139	1	theorem	theorem	NOUN
ejpam-3743	139	2	2	2	NUM
ejpam-3743	139	3	.	.	PUNCT
ejpam-3743	140	1	if	if	SCONJ
ejpam-3743	140	2	g	g	NOUN
ejpam-3743	140	3	:	:	PUNCT
ejpam-3743	140	4	(	(	PUNCT
ejpam-3743	140	5	x,µ)→	x,µ)→	X
ejpam-3743	140	6	(	(	PUNCT
ejpam-3743	140	7	y	y	PROPN
ejpam-3743	140	8	,	,	PUNCT
ejpam-3743	140	9	ν	ν	NOUN
ejpam-3743	140	10	)	)	PUNCT
ejpam-3743	140	11	is	be	AUX
ejpam-3743	140	12	a	a	DET
ejpam-3743	140	13	supra	supra	ADJ
ejpam-3743	140	14	semi?-homeomorphism	semi?-homeomorphism	NOUN
ejpam-3743	140	15	map	map	NOUN
ejpam-3743	140	16	,	,	PUNCT
ejpam-3743	140	17	then	then	ADV
ejpam-3743	140	18	g(as′	g(as′	X
ejpam-3743	140	19	)	)	PUNCT
ejpam-3743	141	1	=	=	SYM
ejpam-3743	141	2	(	(	PUNCT
ejpam-3743	141	3	g(a))s′	g(a))s′	NOUN
ejpam-3743	141	4	for	for	ADP
ejpam-3743	141	5	each	each	PRON
ejpam-3743	141	6	a	a	DET
ejpam-3743	141	7	⊆	⊆	NUM
ejpam-3743	141	8	x.	x.	NOUN
ejpam-3743	142	1	t.	t.	PROPN
ejpam-3743	142	2	m.	m.	PROPN
ejpam-3743	142	3	al	al	PROPN
ejpam-3743	142	4	-	-	PUNCT
ejpam-3743	142	5	shami	shami	PROPN
ejpam-3743	142	6	et	et	PROPN
ejpam-3743	142	7	al	al	PROPN
ejpam-3743	142	8	.	.	PUNCT
ejpam-3743	142	9	/	/	SYM
ejpam-3743	142	10	eur	eur	PROPN
ejpam-3743	142	11	.	.	PUNCT
ejpam-3743	143	1	j.	j.	PROPN
ejpam-3743	143	2	pure	pure	PROPN
ejpam-3743	143	3	appl	appl	PROPN
ejpam-3743	143	4	.	.	PROPN
ejpam-3743	143	5	math	math	PROPN
ejpam-3743	143	6	,	,	PUNCT
ejpam-3743	143	7	13	13	NUM
ejpam-3743	143	8	(	(	PUNCT
ejpam-3743	143	9	3	3	NUM
ejpam-3743	143	10	)	)	PUNCT
ejpam-3743	143	11	(	(	PUNCT
ejpam-3743	143	12	2020	2020	NUM
ejpam-3743	143	13	)	)	PUNCT
ejpam-3743	143	14	,	,	PUNCT
ejpam-3743	143	15	427	427	NUM
ejpam-3743	143	16	-	-	SYM
ejpam-3743	143	17	443	443	NUM
ejpam-3743	143	18	432	432	NUM
ejpam-3743	143	19	proof	proof	NOUN
ejpam-3743	143	20	.	.	PUNCT
ejpam-3743	144	1	let	let	VERB
ejpam-3743	144	2	a	a	DET
ejpam-3743	144	3	6∈	6∈	NOUN
ejpam-3743	144	4	(	(	PUNCT
ejpam-3743	144	5	g(a))s′.	g(a))s′.	X
ejpam-3743	144	6	then	then	ADV
ejpam-3743	144	7	there	there	PRON
ejpam-3743	144	8	is	be	VERB
ejpam-3743	144	9	a	a	DET
ejpam-3743	144	10	supra	supra	ADJ
ejpam-3743	144	11	semi	semi	ADJ
ejpam-3743	144	12	-	-	ADJ
ejpam-3743	144	13	open	open	ADJ
ejpam-3743	144	14	set	set	ADJ
ejpam-3743	144	15	h	h	NOUN
ejpam-3743	144	16	containing	contain	VERB
ejpam-3743	144	17	a	a	DET
ejpam-3743	144	18	such	such	ADJ
ejpam-3743	144	19	that	that	PRON
ejpam-3743	144	20	(	(	PUNCT
ejpam-3743	144	21	h	h	NOUN
ejpam-3743	144	22	\	\	PROPN
ejpam-3743	144	23	{	{	PUNCT
ejpam-3743	144	24	a	a	NOUN
ejpam-3743	144	25	}	}	PUNCT
ejpam-3743	144	26	)	)	PUNCT
ejpam-3743	144	27	⋂	⋂	PROPN
ejpam-3743	144	28	g(a	g(a	PROPN
ejpam-3743	144	29	)	)	PUNCT
ejpam-3743	145	1	=	=	PUNCT
ejpam-3743	145	2	∅.	∅.	PRON
ejpam-3743	145	3	so	so	ADV
ejpam-3743	145	4	g−1[(h	g−1[(h	ADP
ejpam-3743	145	5	\	\	NOUN
ejpam-3743	145	6	{	{	PUNCT
ejpam-3743	145	7	a	a	NOUN
ejpam-3743	145	8	}	}	PUNCT
ejpam-3743	145	9	)	)	PUNCT
ejpam-3743	145	10	⋂	⋂	PROPN
ejpam-3743	145	11	g(a	g(a	PROPN
ejpam-3743	145	12	)	)	PUNCT
ejpam-3743	145	13	]	]	PUNCT
ejpam-3743	146	1	=	=	PUNCT
ejpam-3743	146	2	g−1(∅	g−1(∅	PROPN
ejpam-3743	146	3	)	)	PUNCT
ejpam-3743	146	4	.	.	PUNCT
ejpam-3743	147	1	this	this	PRON
ejpam-3743	147	2	implies	imply	VERB
ejpam-3743	147	3	that	that	SCONJ
ejpam-3743	147	4	(	(	PUNCT
ejpam-3743	147	5	g−1(h	g−1(h	PROPN
ejpam-3743	147	6	)	)	PUNCT
ejpam-3743	147	7	\	\	PROPN
ejpam-3743	147	8	g−1(a	g−1(a	NOUN
ejpam-3743	147	9	)	)	PUNCT
ejpam-3743	147	10	)	)	PUNCT
ejpam-3743	148	1	⋂	⋂	PROPN
ejpam-3743	148	2	a	a	DET
ejpam-3743	148	3	=	=	X
ejpam-3743	148	4	∅.	∅.	X
ejpam-3743	148	5	thus	thus	ADV
ejpam-3743	148	6	g−1(a	g−1(a	PROPN
ejpam-3743	148	7	)	)	PUNCT
ejpam-3743	148	8	6∈	6∈	PROPN
ejpam-3743	148	9	as′.	as′.	PROPN
ejpam-3743	148	10	since	since	SCONJ
ejpam-3743	148	11	g	g	PROPN
ejpam-3743	148	12	is	be	AUX
ejpam-3743	148	13	bijective	bijective	ADJ
ejpam-3743	148	14	,	,	PUNCT
ejpam-3743	148	15	then	then	ADV
ejpam-3743	148	16	a	a	DET
ejpam-3743	148	17	6∈	6∈	NOUN
ejpam-3743	148	18	g(as′	g(as′	PROPN
ejpam-3743	148	19	)	)	PUNCT
ejpam-3743	148	20	.	.	PUNCT
ejpam-3743	149	1	therefore	therefore	ADV
ejpam-3743	149	2	g(as′	g(as′	X
ejpam-3743	149	3	)	)	PUNCT
ejpam-3743	150	1	⊆	⊆	NUM
ejpam-3743	150	2	(	(	PUNCT
ejpam-3743	150	3	g(a))s′.	g(a))s′.	NOUN
ejpam-3743	150	4	by	by	ADP
ejpam-3743	150	5	reversing	reverse	VERB
ejpam-3743	150	6	the	the	DET
ejpam-3743	150	7	preceding	precede	VERB
ejpam-3743	150	8	steps	step	NOUN
ejpam-3743	150	9	,	,	PUNCT
ejpam-3743	150	10	we	we	PRON
ejpam-3743	150	11	find	find	VERB
ejpam-3743	150	12	that	that	SCONJ
ejpam-3743	150	13	(	(	PUNCT
ejpam-3743	150	14	g(a))s′	g(a))s′	NOUN
ejpam-3743	150	15	⊆	⊆	NUM
ejpam-3743	150	16	g(as′	g(as′	NOUN
ejpam-3743	150	17	)	)	PUNCT
ejpam-3743	150	18	.	.	PUNCT
ejpam-3743	151	1	hence	hence	ADV
ejpam-3743	151	2	,	,	PUNCT
ejpam-3743	151	3	the	the	DET
ejpam-3743	151	4	proof	proof	NOUN
ejpam-3743	151	5	is	be	AUX
ejpam-3743	151	6	complete	complete	ADJ
ejpam-3743	151	7	.	.	PUNCT
ejpam-3743	152	1	definition	definition	NOUN
ejpam-3743	152	2	12	12	NUM
ejpam-3743	152	3	.	.	PUNCT
ejpam-3743	153	1	for	for	ADP
ejpam-3743	153	2	a	a	DET
ejpam-3743	153	3	nonempty	nonempty	ADJ
ejpam-3743	153	4	set	set	VERB
ejpam-3743	153	5	x	x	NOUN
ejpam-3743	153	6	,	,	PUNCT
ejpam-3743	153	7	a	a	DET
ejpam-3743	153	8	sub	sub	NOUN
ejpam-3743	153	9	collection	collection	NOUN
ejpam-3743	153	10	λ	λ	PROPN
ejpam-3743	153	11	of	of	ADP
ejpam-3743	153	12	2x	2x	NUM
ejpam-3743	153	13	is	be	AUX
ejpam-3743	153	14	said	say	VERB
ejpam-3743	153	15	to	to	PART
ejpam-3743	153	16	have	have	VERB
ejpam-3743	153	17	the	the	DET
ejpam-3743	153	18	difference	difference	NOUN
ejpam-3743	153	19	property	property	NOUN
ejpam-3743	153	20	provided	provide	VERB
ejpam-3743	153	21	that	that	SCONJ
ejpam-3743	153	22	g	g	PROPN
ejpam-3743	153	23	∈	∈	PROPN
ejpam-3743	153	24	λ	λ	PROPN
ejpam-3743	153	25	implies	imply	VERB
ejpam-3743	153	26	that	that	SCONJ
ejpam-3743	153	27	g	g	PROPN
ejpam-3743	153	28	\	\	PROPN
ejpam-3743	153	29	{	{	PUNCT
ejpam-3743	153	30	x	x	NOUN
ejpam-3743	153	31	}	}	PUNCT
ejpam-3743	153	32	∈	∈	PROPN
ejpam-3743	153	33	λ	λ	NOUN
ejpam-3743	153	34	.	.	PUNCT
ejpam-3743	154	1	the	the	DET
ejpam-3743	154	2	following	follow	VERB
ejpam-3743	154	3	two	two	NUM
ejpam-3743	154	4	examples	example	NOUN
ejpam-3743	154	5	illustrate	illustrate	VERB
ejpam-3743	154	6	the	the	DET
ejpam-3743	154	7	existence	existence	NOUN
ejpam-3743	154	8	and	and	CCONJ
ejpam-3743	154	9	uniqueness	uniqueness	NOUN
ejpam-3743	154	10	of	of	ADP
ejpam-3743	154	11	the	the	DET
ejpam-3743	154	12	difference	difference	NOUN
ejpam-3743	154	13	property	property	NOUN
ejpam-3743	154	14	.	.	PUNCT
ejpam-3743	155	1	example	example	NOUN
ejpam-3743	156	1	2	2	NUM
ejpam-3743	156	2	.	.	X
ejpam-3743	156	3	let	let	VERB
ejpam-3743	156	4	µ	µ	X
ejpam-3743	156	5	=	=	SYM
ejpam-3743	156	6	{	{	PUNCT
ejpam-3743	156	7	∅	∅	NOUN
ejpam-3743	156	8	,	,	PUNCT
ejpam-3743	156	9	g	g	PROPN
ejpam-3743	156	10	⊆	⊆	NUM
ejpam-3743	156	11	n	n	NOUN
ejpam-3743	156	12	:	:	PUNCT
ejpam-3743	156	13	g	g	NOUN
ejpam-3743	156	14	is	be	AUX
ejpam-3743	156	15	infinite	infinite	ADJ
ejpam-3743	156	16	}	}	PUNCT
ejpam-3743	156	17	be	be	AUX
ejpam-3743	156	18	a	a	DET
ejpam-3743	156	19	supra	supra	ADJ
ejpam-3743	156	20	topology	topology	NOUN
ejpam-3743	156	21	on	on	ADP
ejpam-3743	156	22	the	the	DET
ejpam-3743	156	23	set	set	NOUN
ejpam-3743	156	24	of	of	ADP
ejpam-3743	156	25	natural	natural	ADJ
ejpam-3743	156	26	numbers	number	NOUN
ejpam-3743	156	27	n	n	ADV
ejpam-3743	156	28	.	.	PUNCT
ejpam-3743	157	1	it	it	PRON
ejpam-3743	157	2	is	be	AUX
ejpam-3743	157	3	clear	clear	ADJ
ejpam-3743	157	4	that	that	SCONJ
ejpam-3743	157	5	the	the	DET
ejpam-3743	157	6	infinity	infinity	NOUN
ejpam-3743	157	7	of	of	ADP
ejpam-3743	157	8	g	g	PROPN
ejpam-3743	157	9	implies	imply	VERB
ejpam-3743	157	10	the	the	DET
ejpam-3743	157	11	infinity	infinity	NOUN
ejpam-3743	157	12	of	of	ADP
ejpam-3743	157	13	g\{x	g\{x	PROPN
ejpam-3743	157	14	}	}	PUNCT
ejpam-3743	157	15	.	.	PUNCT
ejpam-3743	158	1	that	that	PRON
ejpam-3743	158	2	is	be	AUX
ejpam-3743	158	3	,	,	PUNCT
ejpam-3743	158	4	g	g	PROPN
ejpam-3743	158	5	∈	∈	PROPN
ejpam-3743	158	6	µ	µ	PRON
ejpam-3743	158	7	implies	imply	VERB
ejpam-3743	158	8	g	g	PROPN
ejpam-3743	158	9	\	\	PROPN
ejpam-3743	158	10	{	{	PUNCT
ejpam-3743	158	11	x	x	NOUN
ejpam-3743	158	12	}	}	PUNCT
ejpam-3743	158	13	∈	∈	PROPN
ejpam-3743	158	14	µ.	µ.	NOUN
ejpam-3743	158	15	then	then	ADV
ejpam-3743	158	16	(	(	PUNCT
ejpam-3743	158	17	n	n	X
ejpam-3743	158	18	,	,	PUNCT
ejpam-3743	158	19	µ	µ	X
ejpam-3743	158	20	)	)	PUNCT
ejpam-3743	158	21	has	have	VERB
ejpam-3743	158	22	the	the	DET
ejpam-3743	158	23	difference	difference	NOUN
ejpam-3743	158	24	property	property	NOUN
ejpam-3743	158	25	.	.	PUNCT
ejpam-3743	159	1	also	also	ADV
ejpam-3743	159	2	,	,	PUNCT
ejpam-3743	159	3	it	it	PRON
ejpam-3743	159	4	can	can	AUX
ejpam-3743	159	5	be	be	AUX
ejpam-3743	159	6	seen	see	VERB
ejpam-3743	159	7	that	that	SCONJ
ejpam-3743	159	8	the	the	DET
ejpam-3743	159	9	collection	collection	NOUN
ejpam-3743	159	10	of	of	ADP
ejpam-3743	159	11	supra	supra	PROPN
ejpam-3743	159	12	semi	semi	ADJ
ejpam-3743	159	13	-	-	ADJ
ejpam-3743	159	14	open	open	ADJ
ejpam-3743	159	15	subsets	subset	NOUN
ejpam-3743	159	16	of	of	ADP
ejpam-3743	159	17	(	(	PUNCT
ejpam-3743	159	18	n	n	X
ejpam-3743	159	19	,	,	PUNCT
ejpam-3743	159	20	µ	µ	X
ejpam-3743	159	21	)	)	PUNCT
ejpam-3743	159	22	coincides	coincide	VERB
ejpam-3743	159	23	with	with	ADP
ejpam-3743	159	24	the	the	DET
ejpam-3743	159	25	collection	collection	NOUN
ejpam-3743	159	26	of	of	ADP
ejpam-3743	159	27	supra	supra	PROPN
ejpam-3743	159	28	open	open	ADJ
ejpam-3743	159	29	sets	set	NOUN
ejpam-3743	159	30	.	.	PUNCT
ejpam-3743	160	1	hence	hence	ADV
ejpam-3743	160	2	,	,	PUNCT
ejpam-3743	160	3	(	(	PUNCT
ejpam-3743	160	4	n	n	X
ejpam-3743	160	5	,	,	PUNCT
ejpam-3743	160	6	µ	µ	X
ejpam-3743	160	7	)	)	PUNCT
ejpam-3743	160	8	has	have	VERB
ejpam-3743	160	9	the	the	DET
ejpam-3743	160	10	difference	difference	NOUN
ejpam-3743	160	11	property	property	NOUN
ejpam-3743	160	12	for	for	ADP
ejpam-3743	160	13	the	the	DET
ejpam-3743	160	14	collection	collection	NOUN
ejpam-3743	160	15	of	of	ADP
ejpam-3743	160	16	supra	supra	PROPN
ejpam-3743	160	17	semi	semi	ADJ
ejpam-3743	160	18	-	-	ADJ
ejpam-3743	160	19	open	open	ADJ
ejpam-3743	160	20	sets	set	NOUN
ejpam-3743	160	21	.	.	PUNCT
ejpam-3743	161	1	example	example	NOUN
ejpam-3743	162	1	3	3	X
ejpam-3743	162	2	.	.	PUNCT
ejpam-3743	162	3	let	let	VERB
ejpam-3743	162	4	µ	µ	X
ejpam-3743	162	5	=	=	SYM
ejpam-3743	162	6	{	{	PUNCT
ejpam-3743	162	7	∅	∅	NOUN
ejpam-3743	162	8	,	,	PUNCT
ejpam-3743	162	9	g	g	PROPN
ejpam-3743	162	10	⊆	⊆	NUM
ejpam-3743	162	11	n	n	NOUN
ejpam-3743	162	12	:	:	PUNCT
ejpam-3743	162	13	g	g	ADP
ejpam-3743	162	14	such	such	ADJ
ejpam-3743	162	15	that	that	SCONJ
ejpam-3743	162	16	{	{	PUNCT
ejpam-3743	162	17	1	1	NUM
ejpam-3743	162	18	,	,	PUNCT
ejpam-3743	162	19	2	2	NUM
ejpam-3743	162	20	}	}	SYM
ejpam-3743	162	21	⊆	⊆	NUM
ejpam-3743	162	22	g	g	NOUN
ejpam-3743	162	23	or	or	CCONJ
ejpam-3743	162	24	{	{	PUNCT
ejpam-3743	162	25	2	2	NUM
ejpam-3743	162	26	,	,	PUNCT
ejpam-3743	162	27	3	3	NUM
ejpam-3743	162	28	}	}	SYM
ejpam-3743	162	29	⊆	⊆	NUM
ejpam-3743	162	30	g	g	NOUN
ejpam-3743	162	31	}	}	PUNCT
ejpam-3743	162	32	be	be	AUX
ejpam-3743	162	33	a	a	DET
ejpam-3743	162	34	supra	supra	ADJ
ejpam-3743	162	35	topology	topology	NOUN
ejpam-3743	162	36	on	on	ADP
ejpam-3743	162	37	the	the	DET
ejpam-3743	162	38	set	set	NOUN
ejpam-3743	162	39	of	of	ADP
ejpam-3743	162	40	natural	natural	ADJ
ejpam-3743	162	41	numbers	number	NOUN
ejpam-3743	162	42	n	n	ADV
ejpam-3743	162	43	.	.	PUNCT
ejpam-3743	163	1	then	then	ADV
ejpam-3743	163	2	{	{	PUNCT
ejpam-3743	163	3	1	1	NUM
ejpam-3743	163	4	,	,	PUNCT
ejpam-3743	163	5	2	2	NUM
ejpam-3743	163	6	}	}	PUNCT
ejpam-3743	163	7	∈	∈	PROPN
ejpam-3743	163	8	µ	µ	NOUN
ejpam-3743	163	9	,	,	PUNCT
ejpam-3743	163	10	but	but	CCONJ
ejpam-3743	163	11	{	{	PUNCT
ejpam-3743	163	12	1	1	NUM
ejpam-3743	163	13	,	,	PUNCT
ejpam-3743	163	14	2	2	NUM
ejpam-3743	163	15	}	}	PUNCT
ejpam-3743	163	16	\	\	NOUN
ejpam-3743	163	17	{	{	PUNCT
ejpam-3743	163	18	2	2	NUM
ejpam-3743	163	19	}	}	PUNCT
ejpam-3743	163	20	=	=	NOUN
ejpam-3743	163	21	{	{	PUNCT
ejpam-3743	163	22	1	1	NUM
ejpam-3743	163	23	}	}	PUNCT
ejpam-3743	163	24	6∈	6∈	PROPN
ejpam-3743	163	25	µ.	µ.	NOUN
ejpam-3743	163	26	therefore	therefore	ADV
ejpam-3743	163	27	(	(	PUNCT
ejpam-3743	163	28	x,µ	x,µ	NOUN
ejpam-3743	163	29	)	)	PUNCT
ejpam-3743	163	30	does	do	AUX
ejpam-3743	163	31	not	not	PART
ejpam-3743	163	32	have	have	VERB
ejpam-3743	163	33	the	the	DET
ejpam-3743	163	34	difference	difference	NOUN
ejpam-3743	163	35	property	property	NOUN
ejpam-3743	163	36	.	.	PUNCT
ejpam-3743	164	1	theorem	theorem	NOUN
ejpam-3743	164	2	3	3	NUM
ejpam-3743	164	3	.	.	PUNCT
ejpam-3743	165	1	if	if	SCONJ
ejpam-3743	165	2	(	(	PUNCT
ejpam-3743	165	3	x,µ	x,µ	NOUN
ejpam-3743	165	4	)	)	PUNCT
ejpam-3743	165	5	has	have	VERB
ejpam-3743	165	6	the	the	DET
ejpam-3743	165	7	difference	difference	NOUN
ejpam-3743	165	8	property	property	NOUN
ejpam-3743	165	9	for	for	ADP
ejpam-3743	165	10	the	the	DET
ejpam-3743	165	11	collection	collection	NOUN
ejpam-3743	165	12	of	of	ADP
ejpam-3743	165	13	supra	supra	PROPN
ejpam-3743	165	14	semi	semi	ADJ
ejpam-3743	165	15	-	-	ADJ
ejpam-3743	165	16	open	open	ADJ
ejpam-3743	165	17	sets	set	NOUN
ejpam-3743	165	18	,	,	PUNCT
ejpam-3743	165	19	then	then	ADV
ejpam-3743	165	20	the	the	DET
ejpam-3743	165	21	following	follow	VERB
ejpam-3743	165	22	properties	property	NOUN
ejpam-3743	165	23	hold	hold	VERB
ejpam-3743	165	24	for	for	ADP
ejpam-3743	165	25	a	a	DET
ejpam-3743	165	26	⊆	⊆	NUM
ejpam-3743	165	27	x.	x.	NOUN
ejpam-3743	165	28	(	(	PUNCT
ejpam-3743	165	29	i	i	NOUN
ejpam-3743	165	30	)	)	PUNCT
ejpam-3743	165	31	(	(	PUNCT
ejpam-3743	165	32	as′)s′	as′)s′	PROPN
ejpam-3743	165	33	⊆	⊆	NUM
ejpam-3743	165	34	as′.	as′.	PROPN
ejpam-3743	165	35	(	(	PUNCT
ejpam-3743	165	36	ii	ii	NOUN
ejpam-3743	165	37	)	)	PUNCT
ejpam-3743	165	38	scl(as′	scl(as′	PROPN
ejpam-3743	165	39	)	)	PUNCT
ejpam-3743	165	40	=	=	SYM
ejpam-3743	165	41	as′	as′	NOUN
ejpam-3743	165	42	=	=	SYM
ejpam-3743	165	43	(	(	PUNCT
ejpam-3743	165	44	scl(a))s′.	scl(a))s′.	PROPN
ejpam-3743	165	45	(	(	PUNCT
ejpam-3743	165	46	iii	iii	NOUN
ejpam-3743	165	47	)	)	PUNCT
ejpam-3743	165	48	as′	as′	NOUN
ejpam-3743	165	49	=	=	NOUN
ejpam-3743	165	50	∅	∅	NOUN
ejpam-3743	165	51	if	if	SCONJ
ejpam-3743	165	52	a	a	PRON
ejpam-3743	165	53	is	be	AUX
ejpam-3743	165	54	finite	finite	ADJ
ejpam-3743	165	55	.	.	PUNCT
ejpam-3743	166	1	proof	proof	NOUN
ejpam-3743	166	2	.	.	PUNCT
ejpam-3743	167	1	(	(	PUNCT
ejpam-3743	167	2	i	i	NOUN
ejpam-3743	167	3	)	)	PUNCT
ejpam-3743	167	4	let	let	VERB
ejpam-3743	167	5	x	x	SYM
ejpam-3743	167	6	6∈	6∈	PROPN
ejpam-3743	167	7	as′.	as′.	PROPN
ejpam-3743	167	8	then	then	ADV
ejpam-3743	167	9	there	there	PRON
ejpam-3743	167	10	is	be	VERB
ejpam-3743	167	11	a	a	DET
ejpam-3743	167	12	supra	supra	ADJ
ejpam-3743	167	13	semi	semi	ADJ
ejpam-3743	167	14	-	-	ADJ
ejpam-3743	167	15	open	open	ADJ
ejpam-3743	167	16	set	set	NOUN
ejpam-3743	167	17	g	g	NOUN
ejpam-3743	167	18	containing	contain	VERB
ejpam-3743	167	19	x	x	PUNCT
ejpam-3743	167	20	such	such	ADJ
ejpam-3743	167	21	that	that	SCONJ
ejpam-3743	167	22	g	g	PROPN
ejpam-3743	167	23	\	\	PROPN
ejpam-3743	167	24	{	{	PUNCT
ejpam-3743	167	25	x	x	NOUN
ejpam-3743	167	26	}	}	PUNCT
ejpam-3743	167	27	⋂	⋂	PROPN
ejpam-3743	167	28	a	a	DET
ejpam-3743	167	29	=	=	X
ejpam-3743	167	30	∅.	∅.	NOUN
ejpam-3743	167	31	since	since	SCONJ
ejpam-3743	167	32	(	(	PUNCT
ejpam-3743	167	33	x,µ	x,µ	NOUN
ejpam-3743	167	34	)	)	PUNCT
ejpam-3743	167	35	has	have	VERB
ejpam-3743	167	36	the	the	DET
ejpam-3743	167	37	difference	difference	NOUN
ejpam-3743	167	38	property	property	NOUN
ejpam-3743	167	39	for	for	ADP
ejpam-3743	167	40	the	the	DET
ejpam-3743	167	41	collection	collection	NOUN
ejpam-3743	167	42	of	of	ADP
ejpam-3743	167	43	supra	supra	PROPN
ejpam-3743	167	44	semi	semi	ADJ
ejpam-3743	167	45	-	-	ADJ
ejpam-3743	167	46	open	open	ADJ
ejpam-3743	167	47	sets	set	NOUN
ejpam-3743	167	48	,	,	PUNCT
ejpam-3743	167	49	then	then	ADV
ejpam-3743	167	50	g	g	PROPN
ejpam-3743	167	51	\	\	PROPN
ejpam-3743	167	52	{	{	PUNCT
ejpam-3743	167	53	x	x	X
ejpam-3743	167	54	}	}	PUNCT
ejpam-3743	167	55	is	be	AUX
ejpam-3743	167	56	a	a	DET
ejpam-3743	167	57	supra	supra	ADJ
ejpam-3743	167	58	semi	semi	ADJ
ejpam-3743	167	59	-	-	ADJ
ejpam-3743	167	60	open	open	ADJ
ejpam-3743	167	61	set	set	NOUN
ejpam-3743	167	62	.	.	PUNCT
ejpam-3743	168	1	therefore	therefore	ADV
ejpam-3743	168	2	g	g	PROPN
ejpam-3743	168	3	\	\	PROPN
ejpam-3743	168	4	{	{	PUNCT
ejpam-3743	168	5	x	x	NOUN
ejpam-3743	168	6	}	}	PUNCT
ejpam-3743	168	7	⋂	⋂	PROPN
ejpam-3743	168	8	as′	as′	NOUN
ejpam-3743	168	9	=	=	PUNCT
ejpam-3743	168	10	∅.	∅.	NOUN
ejpam-3743	168	11	since	since	SCONJ
ejpam-3743	168	12	x	x	PROPN
ejpam-3743	168	13	6∈	6∈	PROPN
ejpam-3743	168	14	as′	as′	NOUN
ejpam-3743	168	15	,	,	PUNCT
ejpam-3743	168	16	then	then	ADV
ejpam-3743	168	17	g	g	PROPN
ejpam-3743	168	18	⋂	⋂	PROPN
ejpam-3743	168	19	(	(	PUNCT
ejpam-3743	168	20	as′)s′	as′)s′	NOUN
ejpam-3743	168	21	=	=	PRON
ejpam-3743	168	22	∅.	∅.	VERB
ejpam-3743	168	23	thus	thus	ADV
ejpam-3743	168	24	x	x	SYM
ejpam-3743	168	25	6∈	6∈	NOUN
ejpam-3743	168	26	(	(	PUNCT
ejpam-3743	168	27	as′)s′.	as′)s′.	X
ejpam-3743	168	28	hence	hence	ADV
ejpam-3743	168	29	,	,	PUNCT
ejpam-3743	168	30	(	(	PUNCT
ejpam-3743	168	31	as′)s′	as′)s′	PROPN
ejpam-3743	168	32	⊆	⊆	NUM
ejpam-3743	168	33	as′.	as′.	PROPN
ejpam-3743	168	34	(	(	PUNCT
ejpam-3743	168	35	ii	ii	PROPN
ejpam-3743	168	36	)	)	PUNCT
ejpam-3743	168	37	since	since	SCONJ
ejpam-3743	168	38	(	(	PUNCT
ejpam-3743	168	39	as′)s′	as′)s′	PROPN
ejpam-3743	168	40	⊆	⊆	NUM
ejpam-3743	168	41	as′	as′	NOUN
ejpam-3743	168	42	,	,	PUNCT
ejpam-3743	168	43	then	then	ADV
ejpam-3743	168	44	it	it	PRON
ejpam-3743	168	45	follows	follow	VERB
ejpam-3743	168	46	from	from	ADP
ejpam-3743	168	47	theorem	theorem	ADJ
ejpam-3743	168	48	(	(	PUNCT
ejpam-3743	168	49	1	1	NUM
ejpam-3743	168	50	)	)	PUNCT
ejpam-3743	168	51	that	that	PRON
ejpam-3743	168	52	as′	as′	PROPN
ejpam-3743	168	53	is	be	AUX
ejpam-3743	168	54	a	a	DET
ejpam-3743	168	55	supra	supra	ADJ
ejpam-3743	168	56	semi	semi	ADJ
ejpam-3743	168	57	-	-	ADJ
ejpam-3743	168	58	closed	closed	ADJ
ejpam-3743	168	59	set	set	NOUN
ejpam-3743	168	60	.	.	PUNCT
ejpam-3743	169	1	therefore	therefore	ADV
ejpam-3743	169	2	scl(as′	scl(as′	PROPN
ejpam-3743	169	3	)	)	PUNCT
ejpam-3743	169	4	=	=	SYM
ejpam-3743	169	5	as′	as′	NOUN
ejpam-3743	169	6	(	(	PUNCT
ejpam-3743	169	7	3	3	NUM
ejpam-3743	169	8	)	)	PUNCT
ejpam-3743	169	9	also	also	ADV
ejpam-3743	169	10	,	,	PUNCT
ejpam-3743	169	11	(	(	PUNCT
ejpam-3743	169	12	a)s′	a)s′	VERB
ejpam-3743	169	13	⊆	⊆	NUM
ejpam-3743	169	14	(	(	PUNCT
ejpam-3743	169	15	scl(a))s′	scl(a))s′	NOUN
ejpam-3743	169	16	because	because	SCONJ
ejpam-3743	169	17	a	a	DET
ejpam-3743	169	18	⊆	⊆	NUM
ejpam-3743	169	19	scl(a	scl(a	NOUN
ejpam-3743	169	20	)	)	PUNCT
ejpam-3743	169	21	.	.	PUNCT
ejpam-3743	170	1	on	on	ADP
ejpam-3743	170	2	the	the	DET
ejpam-3743	170	3	other	other	ADJ
ejpam-3743	170	4	hand	hand	NOUN
ejpam-3743	170	5	,	,	PUNCT
ejpam-3743	170	6	let	let	VERB
ejpam-3743	170	7	x	x	PRON
ejpam-3743	170	8	6∈	6∈	PROPN
ejpam-3743	170	9	(	(	PUNCT
ejpam-3743	170	10	a)s′.	a)s′.	INTJ
ejpam-3743	170	11	then	then	ADV
ejpam-3743	170	12	it	it	PRON
ejpam-3743	170	13	follows	follow	VERB
ejpam-3743	170	14	from	from	ADP
ejpam-3743	170	15	1	1	NUM
ejpam-3743	170	16	above	above	ADP
ejpam-3743	170	17	that	that	PRON
ejpam-3743	170	18	g	g	NOUN
ejpam-3743	170	19	\	\	PROPN
ejpam-3743	170	20	{	{	PUNCT
ejpam-3743	170	21	x	x	NOUN
ejpam-3743	170	22	}	}	PUNCT
ejpam-3743	170	23	⋂	⋂	PROPN
ejpam-3743	170	24	a	a	DET
ejpam-3743	170	25	=	=	PUNCT
ejpam-3743	170	26	∅	∅	NOUN
ejpam-3743	170	27	and	and	CCONJ
ejpam-3743	170	28	g	g	PROPN
ejpam-3743	170	29	\	\	PUNCT
ejpam-3743	170	30	{	{	PUNCT
ejpam-3743	170	31	x	x	NOUN
ejpam-3743	170	32	}	}	PUNCT
ejpam-3743	170	33	⋂	⋂	PROPN
ejpam-3743	170	34	as′	as′	NOUN
ejpam-3743	170	35	=	=	PUNCT
ejpam-3743	170	36	∅.	∅.	X
ejpam-3743	170	37	this	this	PRON
ejpam-3743	170	38	means	mean	VERB
ejpam-3743	170	39	that	that	SCONJ
ejpam-3743	170	40	g	g	PROPN
ejpam-3743	170	41	\	\	PROPN
ejpam-3743	170	42	{	{	PUNCT
ejpam-3743	170	43	x	x	NOUN
ejpam-3743	170	44	}	}	PUNCT
ejpam-3743	170	45	⋂	⋂	PROPN
ejpam-3743	170	46	scl(a	scl(a	PROPN
ejpam-3743	170	47	)	)	PUNCT
ejpam-3743	170	48	=	=	PUNCT
ejpam-3743	170	49	∅.	∅.	VERB
ejpam-3743	170	50	therefore	therefore	ADV
ejpam-3743	170	51	x	x	PROPN
ejpam-3743	170	52	6∈	6∈	PROPN
ejpam-3743	170	53	(	(	PUNCT
ejpam-3743	170	54	scl(a))s′.	scl(a))s′.	PROPN
ejpam-3743	170	55	thus	thus	ADV
ejpam-3743	170	56	(	(	PUNCT
ejpam-3743	170	57	scl(a))s′	scl(a))s′	NOUN
ejpam-3743	170	58	⊆	⊆	NUM
ejpam-3743	170	59	(	(	PUNCT
ejpam-3743	170	60	a)s′.	a)s′.	INTJ
ejpam-3743	170	61	hence	hence	ADV
ejpam-3743	170	62	(	(	PUNCT
ejpam-3743	170	63	scl(a))s′	scl(a))s′	NOUN
ejpam-3743	170	64	=	=	SYM
ejpam-3743	170	65	(	(	PUNCT
ejpam-3743	170	66	a)s′	a)s′	X
ejpam-3743	170	67	(	(	PUNCT
ejpam-3743	170	68	4	4	NUM
ejpam-3743	170	69	)	)	PUNCT
ejpam-3743	170	70	from	from	ADP
ejpam-3743	170	71	(	(	PUNCT
ejpam-3743	170	72	3	3	NUM
ejpam-3743	170	73	)	)	PUNCT
ejpam-3743	170	74	and	and	CCONJ
ejpam-3743	170	75	(	(	PUNCT
ejpam-3743	170	76	4	4	NUM
ejpam-3743	170	77	)	)	PUNCT
ejpam-3743	170	78	,	,	PUNCT
ejpam-3743	170	79	the	the	DET
ejpam-3743	170	80	desired	desire	VERB
ejpam-3743	170	81	result	result	NOUN
ejpam-3743	170	82	is	be	AUX
ejpam-3743	170	83	proved	prove	VERB
ejpam-3743	170	84	.	.	PUNCT
ejpam-3743	171	1	t.	t.	PROPN
ejpam-3743	171	2	m.	m.	PROPN
ejpam-3743	171	3	al	al	PROPN
ejpam-3743	171	4	-	-	PUNCT
ejpam-3743	171	5	shami	shami	PROPN
ejpam-3743	171	6	et	et	PROPN
ejpam-3743	171	7	al	al	PROPN
ejpam-3743	171	8	.	.	PUNCT
ejpam-3743	171	9	/	/	SYM
ejpam-3743	171	10	eur	eur	PROPN
ejpam-3743	171	11	.	.	PUNCT
ejpam-3743	172	1	j.	j.	PROPN
ejpam-3743	172	2	pure	pure	PROPN
ejpam-3743	172	3	appl	appl	PROPN
ejpam-3743	172	4	.	.	PROPN
ejpam-3743	172	5	math	math	PROPN
ejpam-3743	172	6	,	,	PUNCT
ejpam-3743	172	7	13	13	NUM
ejpam-3743	172	8	(	(	PUNCT
ejpam-3743	172	9	3	3	NUM
ejpam-3743	172	10	)	)	PUNCT
ejpam-3743	172	11	(	(	PUNCT
ejpam-3743	172	12	2020	2020	NUM
ejpam-3743	172	13	)	)	PUNCT
ejpam-3743	172	14	,	,	PUNCT
ejpam-3743	172	15	427	427	NUM
ejpam-3743	172	16	-	-	SYM
ejpam-3743	172	17	443	443	NUM
ejpam-3743	172	18	433	433	NUM
ejpam-3743	172	19	(	(	PUNCT
ejpam-3743	172	20	iii	iii	NOUN
ejpam-3743	172	21	)	)	PUNCT
ejpam-3743	172	22	let	let	VERB
ejpam-3743	172	23	a	a	PRON
ejpam-3743	172	24	be	be	AUX
ejpam-3743	172	25	a	a	DET
ejpam-3743	172	26	finite	finite	NOUN
ejpam-3743	172	27	subset	subset	NOUN
ejpam-3743	172	28	of	of	ADP
ejpam-3743	172	29	x.	x.	PROPN
ejpam-3743	172	30	suppose	suppose	VERB
ejpam-3743	172	31	that	that	SCONJ
ejpam-3743	172	32	there	there	PRON
ejpam-3743	172	33	exists	exist	VERB
ejpam-3743	172	34	an	an	DET
ejpam-3743	172	35	element	element	NOUN
ejpam-3743	172	36	x	x	SYM
ejpam-3743	172	37	∈	∈	PROPN
ejpam-3743	172	38	x	x	X
ejpam-3743	172	39	such	such	ADJ
ejpam-3743	172	40	that	that	SCONJ
ejpam-3743	172	41	x	x	SYM
ejpam-3743	172	42	∈	∈	PROPN
ejpam-3743	172	43	as′.	as′.	PROPN
ejpam-3743	172	44	then	then	ADV
ejpam-3743	172	45	for	for	ADP
ejpam-3743	172	46	every	every	DET
ejpam-3743	172	47	supra	supra	NOUN
ejpam-3743	172	48	semi	semi	ADJ
ejpam-3743	172	49	-	-	ADJ
ejpam-3743	172	50	open	open	ADJ
ejpam-3743	172	51	set	set	NOUN
ejpam-3743	172	52	g	g	NOUN
ejpam-3743	172	53	containing	contain	VERB
ejpam-3743	172	54	x	x	SYM
ejpam-3743	172	55	,	,	PUNCT
ejpam-3743	172	56	we	we	PRON
ejpam-3743	172	57	have	have	VERB
ejpam-3743	172	58	g\{x	g\{x	NOUN
ejpam-3743	172	59	}	}	PUNCT
ejpam-3743	172	60	⋂	⋂	PROPN
ejpam-3743	172	61	a	a	PRON
ejpam-3743	172	62	6=	6=	NUM
ejpam-3743	172	63	∅.	∅.	NOUN
ejpam-3743	172	64	therefore	therefore	ADV
ejpam-3743	172	65	for	for	ADP
ejpam-3743	172	66	every	every	DET
ejpam-3743	172	67	y	y	PROPN
ejpam-3743	172	68	∈	∈	PROPN
ejpam-3743	172	69	a	a	DET
ejpam-3743	172	70	such	such	ADJ
ejpam-3743	172	71	that	that	SCONJ
ejpam-3743	172	72	y	y	PROPN
ejpam-3743	172	73	6=	6=	PROPN
ejpam-3743	172	74	x	x	SYM
ejpam-3743	172	75	,	,	PUNCT
ejpam-3743	172	76	we	we	PRON
ejpam-3743	172	77	have	have	VERB
ejpam-3743	172	78	g	g	PROPN
ejpam-3743	172	79	\	\	X
ejpam-3743	172	80	{	{	PUNCT
ejpam-3743	172	81	x	x	NOUN
ejpam-3743	172	82	,	,	PUNCT
ejpam-3743	172	83	y	y	PRON
ejpam-3743	172	84	}	}	PUNCT
ejpam-3743	172	85	is	be	AUX
ejpam-3743	172	86	a	a	DET
ejpam-3743	172	87	supra	supra	ADJ
ejpam-3743	172	88	semi	semi	ADJ
ejpam-3743	172	89	-	-	ADJ
ejpam-3743	172	90	open	open	ADJ
ejpam-3743	172	91	set	set	NOUN
ejpam-3743	172	92	.	.	PUNCT
ejpam-3743	173	1	thus	thus	ADV
ejpam-3743	173	2	g\[a	g\[a	PROPN
ejpam-3743	173	3	⋃	⋃	PROPN
ejpam-3743	173	4	{	{	PUNCT
ejpam-3743	173	5	x	x	NOUN
ejpam-3743	173	6	}	}	PUNCT
ejpam-3743	173	7	]	]	PUNCT
ejpam-3743	173	8	is	be	AUX
ejpam-3743	173	9	a	a	DET
ejpam-3743	173	10	supra	supra	ADJ
ejpam-3743	173	11	semi	semi	ADJ
ejpam-3743	173	12	-	-	ADJ
ejpam-3743	173	13	open	open	ADJ
ejpam-3743	173	14	set	set	VERB
ejpam-3743	173	15	such	such	ADJ
ejpam-3743	173	16	that	that	DET
ejpam-3743	173	17	g\[a	g\[a	PROPN
ejpam-3743	173	18	⋃	⋃	NOUN
ejpam-3743	173	19	{	{	PUNCT
ejpam-3743	173	20	x	x	NOUN
ejpam-3743	173	21	}	}	PUNCT
ejpam-3743	173	22	]	]	PUNCT
ejpam-3743	174	1	⋂	⋂	PROPN
ejpam-3743	174	2	a	a	DET
ejpam-3743	174	3	=	=	PUNCT
ejpam-3743	174	4	∅.	∅.	NOUN
ejpam-3743	174	5	this	this	PRON
ejpam-3743	174	6	implies	imply	VERB
ejpam-3743	174	7	that	that	SCONJ
ejpam-3743	174	8	x	x	SYM
ejpam-3743	174	9	6∈	6∈	NOUN
ejpam-3743	174	10	as′.	as′.	PROPN
ejpam-3743	175	1	but	but	CCONJ
ejpam-3743	175	2	this	this	PRON
ejpam-3743	175	3	is	be	AUX
ejpam-3743	175	4	a	a	DET
ejpam-3743	175	5	contradiction	contradiction	NOUN
ejpam-3743	175	6	.	.	PUNCT
ejpam-3743	176	1	hence	hence	ADV
ejpam-3743	176	2	,	,	PUNCT
ejpam-3743	176	3	it	it	PRON
ejpam-3743	176	4	must	must	AUX
ejpam-3743	176	5	be	be	AUX
ejpam-3743	176	6	that	that	DET
ejpam-3743	176	7	as′	as′	NOUN
ejpam-3743	176	8	=	=	PUNCT
ejpam-3743	176	9	∅.	∅.	ADJ
ejpam-3743	176	10	we	we	PRON
ejpam-3743	176	11	explain	explain	VERB
ejpam-3743	176	12	that	that	SCONJ
ejpam-3743	176	13	the	the	DET
ejpam-3743	176	14	three	three	NUM
ejpam-3743	176	15	properties	property	NOUN
ejpam-3743	176	16	mentioned	mention	VERB
ejpam-3743	176	17	in	in	ADP
ejpam-3743	176	18	the	the	DET
ejpam-3743	176	19	above	above	ADJ
ejpam-3743	176	20	theorem	theorem	NOUN
ejpam-3743	176	21	need	need	AUX
ejpam-3743	176	22	not	not	PART
ejpam-3743	176	23	be	be	AUX
ejpam-3743	176	24	true	true	ADJ
ejpam-3743	176	25	if	if	SCONJ
ejpam-3743	176	26	(	(	PUNCT
ejpam-3743	176	27	x,µ	x,µ	NOUN
ejpam-3743	176	28	)	)	PUNCT
ejpam-3743	176	29	does	do	AUX
ejpam-3743	176	30	not	not	PART
ejpam-3743	176	31	have	have	VERB
ejpam-3743	176	32	the	the	DET
ejpam-3743	176	33	difference	difference	NOUN
ejpam-3743	176	34	property	property	NOUN
ejpam-3743	176	35	for	for	ADP
ejpam-3743	176	36	the	the	DET
ejpam-3743	176	37	collection	collection	NOUN
ejpam-3743	176	38	of	of	ADP
ejpam-3743	176	39	supra	supra	PROPN
ejpam-3743	176	40	semi	semi	ADJ
ejpam-3743	176	41	-	-	ADJ
ejpam-3743	176	42	open	open	ADJ
ejpam-3743	176	43	sets	set	NOUN
ejpam-3743	176	44	.	.	PUNCT
ejpam-3743	177	1	let	let	VERB
ejpam-3743	177	2	a	a	PRON
ejpam-3743	177	3	=	=	PUNCT
ejpam-3743	177	4	{	{	PUNCT
ejpam-3743	177	5	1	1	NUM
ejpam-3743	177	6	,	,	PUNCT
ejpam-3743	177	7	3	3	NUM
ejpam-3743	177	8	}	}	PUNCT
ejpam-3743	177	9	be	be	AUX
ejpam-3743	177	10	a	a	DET
ejpam-3743	177	11	subset	subset	NOUN
ejpam-3743	177	12	of	of	ADP
ejpam-3743	177	13	supra	supra	PROPN
ejpam-3743	177	14	topological	topological	ADJ
ejpam-3743	177	15	space	space	NOUN
ejpam-3743	177	16	given	give	VERB
ejpam-3743	177	17	in	in	ADP
ejpam-3743	177	18	example	example	NOUN
ejpam-3743	177	19	(	(	PUNCT
ejpam-3743	177	20	3	3	NUM
ejpam-3743	177	21	)	)	PUNCT
ejpam-3743	177	22	.	.	PUNCT
ejpam-3743	178	1	then	then	ADV
ejpam-3743	178	2	as′	as′	X
ejpam-3743	178	3	=	=	SYM
ejpam-3743	178	4	n	n	CCONJ
ejpam-3743	178	5	\	\	NOUN
ejpam-3743	178	6	{	{	PUNCT
ejpam-3743	178	7	1	1	NUM
ejpam-3743	178	8	,	,	PUNCT
ejpam-3743	178	9	3	3	NUM
ejpam-3743	178	10	}	}	PUNCT
ejpam-3743	178	11	,	,	PUNCT
ejpam-3743	178	12	(	(	PUNCT
ejpam-3743	178	13	as′)s′	as′)s′	X
ejpam-3743	178	14	=	=	SYM
ejpam-3743	178	15	n	n	NOUN
ejpam-3743	178	16	and	and	CCONJ
ejpam-3743	178	17	scl(as′	scl(as′	NOUN
ejpam-3743	178	18	)	)	PUNCT
ejpam-3743	178	19	=	=	SYM
ejpam-3743	178	20	n	n	PROPN
ejpam-3743	178	21	.	.	PUNCT
ejpam-3743	179	1	this	this	PRON
ejpam-3743	179	2	leads	lead	VERB
ejpam-3743	179	3	to	to	ADP
ejpam-3743	179	4	the	the	DET
ejpam-3743	179	5	following	follow	VERB
ejpam-3743	179	6	three	three	NUM
ejpam-3743	179	7	properties	property	NOUN
ejpam-3743	179	8	.	.	PUNCT
ejpam-3743	180	1	(	(	PUNCT
ejpam-3743	180	2	i	i	NOUN
ejpam-3743	180	3	)	)	PUNCT
ejpam-3743	180	4	(	(	PUNCT
ejpam-3743	180	5	as′)s′	as′)s′	PROPN
ejpam-3743	180	6	6⊆	6⊆	PROPN
ejpam-3743	180	7	as′.	as′.	PROPN
ejpam-3743	180	8	(	(	PUNCT
ejpam-3743	180	9	ii	ii	PROPN
ejpam-3743	180	10	)	)	PUNCT
ejpam-3743	180	11	scl(as′	scl(as′	PROPN
ejpam-3743	180	12	)	)	PUNCT
ejpam-3743	180	13	6=	6=	NUM
ejpam-3743	180	14	as′.	as′.	PROPN
ejpam-3743	180	15	(	(	PUNCT
ejpam-3743	180	16	iii	iii	NOUN
ejpam-3743	180	17	)	)	PUNCT
ejpam-3743	180	18	as′	as′	NOUN
ejpam-3743	180	19	6=	6=	NOUN
ejpam-3743	180	20	∅	∅	NOUN
ejpam-3743	180	21	in	in	ADP
ejpam-3743	180	22	spite	spite	NOUN
ejpam-3743	180	23	of	of	ADP
ejpam-3743	180	24	a	a	PRON
ejpam-3743	180	25	is	be	AUX
ejpam-3743	180	26	finite	finite	ADJ
ejpam-3743	180	27	.	.	PUNCT
ejpam-3743	181	1	3	3	X
ejpam-3743	181	2	.	.	NOUN
ejpam-3743	181	3	separation	separation	NOUN
ejpam-3743	181	4	axioms	axiom	NOUN
ejpam-3743	181	5	with	with	ADP
ejpam-3743	181	6	respect	respect	NOUN
ejpam-3743	181	7	to	to	ADP
ejpam-3743	181	8	supra	supra	NOUN
ejpam-3743	181	9	semi	semi	ADJ
ejpam-3743	181	10	-	-	ADJ
ejpam-3743	181	11	open	open	ADJ
ejpam-3743	181	12	sets	set	NOUN
ejpam-3743	181	13	in	in	ADP
ejpam-3743	181	14	this	this	DET
ejpam-3743	181	15	section	section	NOUN
ejpam-3743	181	16	,	,	PUNCT
ejpam-3743	181	17	we	we	PRON
ejpam-3743	181	18	utilize	utilize	VERB
ejpam-3743	181	19	supra	supra	NOUN
ejpam-3743	181	20	semi	semi	ADJ
ejpam-3743	181	21	-	-	ADJ
ejpam-3743	181	22	open	open	ADJ
ejpam-3743	181	23	sets	set	NOUN
ejpam-3743	181	24	to	to	PART
ejpam-3743	181	25	introduce	introduce	VERB
ejpam-3743	181	26	the	the	DET
ejpam-3743	181	27	concepts	concept	NOUN
ejpam-3743	181	28	of	of	ADP
ejpam-3743	181	29	supra	supra	PROPN
ejpam-3743	181	30	semi	semi	ADV
ejpam-3743	181	31	regular	regular	ADJ
ejpam-3743	181	32	,	,	PUNCT
ejpam-3743	181	33	supra	supra	PROPN
ejpam-3743	181	34	semi	semi	ADV
ejpam-3743	181	35	normal	normal	ADJ
ejpam-3743	181	36	and	and	CCONJ
ejpam-3743	181	37	ssti	ssti	NOUN
ejpam-3743	181	38	-	-	PUNCT
ejpam-3743	181	39	spaces	space	NOUN
ejpam-3743	181	40	(	(	PUNCT
ejpam-3743	181	41	i	i	NOUN
ejpam-3743	181	42	=	=	NOUN
ejpam-3743	181	43	0	0	NUM
ejpam-3743	181	44	,	,	PUNCT
ejpam-3743	181	45	1	1	NUM
ejpam-3743	181	46	,	,	PUNCT
ejpam-3743	181	47	2	2	NUM
ejpam-3743	181	48	,	,	PUNCT
ejpam-3743	181	49	3	3	NUM
ejpam-3743	181	50	,	,	PUNCT
ejpam-3743	181	51	4	4	NUM
ejpam-3743	181	52	)	)	PUNCT
ejpam-3743	181	53	.	.	PUNCT
ejpam-3743	182	1	we	we	PRON
ejpam-3743	182	2	give	give	VERB
ejpam-3743	182	3	some	some	DET
ejpam-3743	182	4	characterizations	characterization	NOUN
ejpam-3743	182	5	for	for	ADP
ejpam-3743	182	6	each	each	DET
ejpam-3743	182	7	one	one	NUM
ejpam-3743	182	8	of	of	ADP
ejpam-3743	182	9	them	they	PRON
ejpam-3743	182	10	and	and	CCONJ
ejpam-3743	182	11	elucidate	elucidate	VERB
ejpam-3743	182	12	the	the	DET
ejpam-3743	182	13	relationships	relationship	NOUN
ejpam-3743	182	14	among	among	ADP
ejpam-3743	182	15	themselves	themselves	PRON
ejpam-3743	182	16	as	as	ADV
ejpam-3743	182	17	well	well	ADV
ejpam-3743	182	18	as	as	ADP
ejpam-3743	182	19	with	with	ADP
ejpam-3743	182	20	sti	sti	NOUN
ejpam-3743	182	21	-	-	NOUN
ejpam-3743	182	22	space	space	NOUN
ejpam-3743	182	23	.	.	PUNCT
ejpam-3743	183	1	definition	definition	NOUN
ejpam-3743	183	2	13	13	NUM
ejpam-3743	183	3	.	.	PUNCT
ejpam-3743	184	1	a	a	DET
ejpam-3743	184	2	supra	supra	PROPN
ejpam-3743	184	3	topological	topological	ADJ
ejpam-3743	184	4	space	space	NOUN
ejpam-3743	184	5	(	(	PUNCT
ejpam-3743	184	6	x,µ	x,µ	NOUN
ejpam-3743	184	7	)	)	PUNCT
ejpam-3743	184	8	is	be	AUX
ejpam-3743	184	9	said	say	VERB
ejpam-3743	184	10	to	to	PART
ejpam-3743	184	11	be	be	AUX
ejpam-3743	184	12	:	:	PUNCT
ejpam-3743	184	13	(	(	PUNCT
ejpam-3743	184	14	i	i	NOUN
ejpam-3743	184	15	)	)	PUNCT
ejpam-3743	184	16	sst0	sst0	PROPN
ejpam-3743	184	17	if	if	SCONJ
ejpam-3743	184	18	for	for	ADP
ejpam-3743	184	19	every	every	DET
ejpam-3743	184	20	a	a	DET
ejpam-3743	184	21	6=	6=	NUM
ejpam-3743	184	22	b	b	PROPN
ejpam-3743	184	23	∈	∈	PROPN
ejpam-3743	184	24	x	x	NOUN
ejpam-3743	184	25	,	,	PUNCT
ejpam-3743	184	26	there	there	PRON
ejpam-3743	184	27	exists	exist	VERB
ejpam-3743	184	28	a	a	DET
ejpam-3743	184	29	supra	supra	NOUN
ejpam-3743	184	30	semi	semi	ADJ
ejpam-3743	184	31	-	-	ADJ
ejpam-3743	184	32	open	open	ADJ
ejpam-3743	184	33	set	set	NOUN
ejpam-3743	184	34	containing	contain	VERB
ejpam-3743	184	35	only	only	ADV
ejpam-3743	184	36	one	one	NUM
ejpam-3743	184	37	of	of	ADP
ejpam-3743	184	38	them	they	PRON
ejpam-3743	184	39	.	.	PUNCT
ejpam-3743	185	1	(	(	PUNCT
ejpam-3743	185	2	ii	ii	NOUN
ejpam-3743	185	3	)	)	PUNCT
ejpam-3743	185	4	sst1	sst1	NOUN
ejpam-3743	185	5	if	if	SCONJ
ejpam-3743	185	6	for	for	ADP
ejpam-3743	185	7	every	every	DET
ejpam-3743	185	8	a	a	PRON
ejpam-3743	185	9	6=	6=	NUM
ejpam-3743	185	10	b	b	PROPN
ejpam-3743	185	11	∈	∈	PROPN
ejpam-3743	185	12	x	x	NOUN
ejpam-3743	185	13	,	,	PUNCT
ejpam-3743	185	14	there	there	PRON
ejpam-3743	185	15	exist	exist	VERB
ejpam-3743	185	16	two	two	NUM
ejpam-3743	185	17	supra	supra	ADJ
ejpam-3743	185	18	semi	semi	ADJ
ejpam-3743	185	19	-	-	ADJ
ejpam-3743	185	20	open	open	ADJ
ejpam-3743	185	21	sets	set	VERB
ejpam-3743	185	22	one	one	NUM
ejpam-3743	185	23	of	of	ADP
ejpam-3743	185	24	them	they	PRON
ejpam-3743	185	25	contains	contain	VERB
ejpam-3743	185	26	a	a	DET
ejpam-3743	185	27	but	but	CCONJ
ejpam-3743	185	28	not	not	PART
ejpam-3743	185	29	b	b	NOUN
ejpam-3743	185	30	and	and	CCONJ
ejpam-3743	185	31	the	the	DET
ejpam-3743	185	32	other	other	ADJ
ejpam-3743	185	33	contains	contain	VERB
ejpam-3743	185	34	b	b	NOUN
ejpam-3743	185	35	but	but	CCONJ
ejpam-3743	185	36	not	not	PART
ejpam-3743	185	37	a.	a.	NOUN
ejpam-3743	185	38	(	(	PUNCT
ejpam-3743	185	39	iii	iii	NOUN
ejpam-3743	185	40	)	)	PUNCT
ejpam-3743	185	41	supra	supra	PROPN
ejpam-3743	185	42	semi	semi	ADJ
ejpam-3743	185	43	hausdorff	hausdorff	PROPN
ejpam-3743	185	44	(	(	PUNCT
ejpam-3743	185	45	or	or	CCONJ
ejpam-3743	185	46	sst2	sst2	NOUN
ejpam-3743	185	47	)	)	PUNCT
ejpam-3743	185	48	if	if	SCONJ
ejpam-3743	185	49	for	for	ADP
ejpam-3743	185	50	every	every	DET
ejpam-3743	185	51	a	a	PRON
ejpam-3743	185	52	6=	6=	NUM
ejpam-3743	185	53	b	b	PROPN
ejpam-3743	185	54	∈	∈	PROPN
ejpam-3743	185	55	x	x	NOUN
ejpam-3743	185	56	,	,	PUNCT
ejpam-3743	185	57	there	there	PRON
ejpam-3743	185	58	exist	exist	VERB
ejpam-3743	185	59	two	two	NUM
ejpam-3743	185	60	disjoint	disjoint	ADJ
ejpam-3743	185	61	supra	supra	PROPN
ejpam-3743	185	62	semi	semi	ADJ
ejpam-3743	185	63	-	-	ADJ
ejpam-3743	185	64	open	open	ADJ
ejpam-3743	185	65	sets	set	NOUN
ejpam-3743	185	66	u	u	NOUN
ejpam-3743	185	67	and	and	CCONJ
ejpam-3743	185	68	v	v	NOUN
ejpam-3743	185	69	containing	contain	VERB
ejpam-3743	185	70	a	a	PRON
ejpam-3743	185	71	and	and	CCONJ
ejpam-3743	185	72	b	b	NOUN
ejpam-3743	185	73	,	,	PUNCT
ejpam-3743	185	74	respectively	respectively	ADV
ejpam-3743	185	75	.	.	PUNCT
ejpam-3743	186	1	(	(	PUNCT
ejpam-3743	186	2	iv	iv	X
ejpam-3743	186	3	)	)	PUNCT
ejpam-3743	186	4	supra	supra	NOUN
ejpam-3743	186	5	semi	semi	ADV
ejpam-3743	186	6	regular	regular	ADV
ejpam-3743	186	7	if	if	SCONJ
ejpam-3743	186	8	for	for	ADP
ejpam-3743	186	9	every	every	DET
ejpam-3743	186	10	supra	supra	NOUN
ejpam-3743	186	11	semi	semi	ADJ
ejpam-3743	186	12	-	-	ADJ
ejpam-3743	186	13	closed	closed	ADJ
ejpam-3743	186	14	set	set	VERB
ejpam-3743	186	15	f	f	PROPN
ejpam-3743	186	16	and	and	CCONJ
ejpam-3743	186	17	each	each	DET
ejpam-3743	186	18	a	a	DET
ejpam-3743	186	19	6∈	6∈	NOUN
ejpam-3743	186	20	f	f	NOUN
ejpam-3743	186	21	,	,	PUNCT
ejpam-3743	186	22	there	there	PRON
ejpam-3743	186	23	exist	exist	VERB
ejpam-3743	186	24	disjoint	disjoint	ADJ
ejpam-3743	186	25	supra	supra	PROPN
ejpam-3743	186	26	semi	semi	ADJ
ejpam-3743	186	27	-	-	ADJ
ejpam-3743	186	28	open	open	ADJ
ejpam-3743	186	29	sets	set	NOUN
ejpam-3743	186	30	u	u	NOUN
ejpam-3743	186	31	and	and	CCONJ
ejpam-3743	186	32	v	v	ADP
ejpam-3743	186	33	containing	contain	VERB
ejpam-3743	186	34	f	f	PROPN
ejpam-3743	186	35	and	and	CCONJ
ejpam-3743	186	36	a	a	PRON
ejpam-3743	186	37	,	,	PUNCT
ejpam-3743	186	38	respectively	respectively	ADV
ejpam-3743	186	39	.	.	PUNCT
ejpam-3743	187	1	(	(	PUNCT
ejpam-3743	187	2	v	v	NOUN
ejpam-3743	187	3	)	)	PUNCT
ejpam-3743	187	4	supra	supra	NOUN
ejpam-3743	187	5	semi	semi	ADV
ejpam-3743	187	6	normal	normal	ADJ
ejpam-3743	187	7	if	if	SCONJ
ejpam-3743	187	8	for	for	ADP
ejpam-3743	187	9	every	every	DET
ejpam-3743	187	10	disjoint	disjoint	ADJ
ejpam-3743	187	11	supra	supra	PROPN
ejpam-3743	188	1	semi	semi	ADJ
ejpam-3743	188	2	-	-	ADJ
ejpam-3743	188	3	closed	closed	ADJ
ejpam-3743	188	4	sets	set	NOUN
ejpam-3743	188	5	f	f	PROPN
ejpam-3743	188	6	and	and	CCONJ
ejpam-3743	188	7	h	h	NOUN
ejpam-3743	188	8	,	,	PUNCT
ejpam-3743	188	9	there	there	PRON
ejpam-3743	188	10	exist	exist	VERB
ejpam-3743	188	11	disjoint	disjoint	ADJ
ejpam-3743	188	12	supra	supra	PROPN
ejpam-3743	188	13	semi	semi	ADJ
ejpam-3743	188	14	-	-	ADJ
ejpam-3743	188	15	open	open	ADJ
ejpam-3743	188	16	sets	set	NOUN
ejpam-3743	188	17	u	u	NOUN
ejpam-3743	188	18	and	and	CCONJ
ejpam-3743	188	19	v	v	ADP
ejpam-3743	188	20	containing	contain	VERB
ejpam-3743	188	21	f	f	PROPN
ejpam-3743	188	22	and	and	CCONJ
ejpam-3743	188	23	h	h	NOUN
ejpam-3743	188	24	,	,	PUNCT
ejpam-3743	188	25	respectively	respectively	ADV
ejpam-3743	188	26	.	.	PUNCT
ejpam-3743	189	1	(	(	PUNCT
ejpam-3743	189	2	vi	vi	NOUN
ejpam-3743	189	3	)	)	PUNCT
ejpam-3743	189	4	sst3	sst3	NOUN
ejpam-3743	189	5	(	(	PUNCT
ejpam-3743	189	6	resp	resp	NOUN
ejpam-3743	189	7	.	.	PUNCT
ejpam-3743	190	1	sst4	sst4	PROPN
ejpam-3743	190	2	)	)	PUNCT
ejpam-3743	191	1	if	if	SCONJ
ejpam-3743	191	2	it	it	PRON
ejpam-3743	191	3	is	be	AUX
ejpam-3743	191	4	both	both	DET
ejpam-3743	191	5	supra	supra	ADJ
ejpam-3743	191	6	semi	semi	ADV
ejpam-3743	191	7	regular	regular	ADJ
ejpam-3743	191	8	(	(	PUNCT
ejpam-3743	191	9	resp	resp	NOUN
ejpam-3743	191	10	.	.	PUNCT
ejpam-3743	192	1	supra	supra	PROPN
ejpam-3743	192	2	semi	semi	ADJ
ejpam-3743	192	3	normal	normal	ADJ
ejpam-3743	192	4	)	)	PUNCT
ejpam-3743	192	5	and	and	CCONJ
ejpam-3743	192	6	sst1	sst1	PROPN
ejpam-3743	192	7	.	.	PUNCT
ejpam-3743	193	1	theorem	theorem	VERB
ejpam-3743	193	2	4	4	NUM
ejpam-3743	193	3	.	.	PUNCT
ejpam-3743	194	1	the	the	DET
ejpam-3743	194	2	following	follow	VERB
ejpam-3743	194	3	three	three	NUM
ejpam-3743	194	4	statements	statement	NOUN
ejpam-3743	194	5	are	be	AUX
ejpam-3743	194	6	equivalent	equivalent	ADJ
ejpam-3743	194	7	:	:	PUNCT
ejpam-3743	194	8	(	(	PUNCT
ejpam-3743	194	9	i	i	NOUN
ejpam-3743	194	10	)	)	PUNCT
ejpam-3743	194	11	(	(	PUNCT
ejpam-3743	194	12	x,µ	x,µ	NOUN
ejpam-3743	194	13	)	)	PUNCT
ejpam-3743	194	14	is	be	AUX
ejpam-3743	194	15	an	an	DET
ejpam-3743	194	16	sst0	sst0	NOUN
ejpam-3743	194	17	-	-	PUNCT
ejpam-3743	194	18	space	space	NOUN
ejpam-3743	194	19	;	;	PUNCT
ejpam-3743	194	20	t.	t.	PROPN
ejpam-3743	194	21	m.	m.	PROPN
ejpam-3743	194	22	al	al	PROPN
ejpam-3743	194	23	-	-	PUNCT
ejpam-3743	194	24	shami	shami	PROPN
ejpam-3743	194	25	et	et	PROPN
ejpam-3743	194	26	al	al	PROPN
ejpam-3743	194	27	.	.	PUNCT
ejpam-3743	194	28	/	/	SYM
ejpam-3743	194	29	eur	eur	PROPN
ejpam-3743	194	30	.	.	PUNCT
ejpam-3743	195	1	j.	j.	PROPN
ejpam-3743	195	2	pure	pure	PROPN
ejpam-3743	195	3	appl	appl	PROPN
ejpam-3743	195	4	.	.	PROPN
ejpam-3743	195	5	math	math	PROPN
ejpam-3743	195	6	,	,	PUNCT
ejpam-3743	195	7	13	13	NUM
ejpam-3743	195	8	(	(	PUNCT
ejpam-3743	195	9	3	3	NUM
ejpam-3743	195	10	)	)	PUNCT
ejpam-3743	195	11	(	(	PUNCT
ejpam-3743	195	12	2020	2020	NUM
ejpam-3743	195	13	)	)	PUNCT
ejpam-3743	195	14	,	,	PUNCT
ejpam-3743	195	15	427	427	NUM
ejpam-3743	195	16	-	-	SYM
ejpam-3743	195	17	443	443	NUM
ejpam-3743	195	18	434	434	NUM
ejpam-3743	195	19	(	(	PUNCT
ejpam-3743	195	20	ii	ii	NOUN
ejpam-3743	195	21	)	)	PUNCT
ejpam-3743	195	22	scl({a	scl({a	NOUN
ejpam-3743	195	23	}	}	PUNCT
ejpam-3743	195	24	)	)	PUNCT
ejpam-3743	195	25	6=	6=	X
ejpam-3743	195	26	scl({b	scl({b	PROPN
ejpam-3743	195	27	}	}	PUNCT
ejpam-3743	195	28	)	)	PUNCT
ejpam-3743	195	29	for	for	ADP
ejpam-3743	195	30	each	each	DET
ejpam-3743	195	31	a	a	DET
ejpam-3743	195	32	6=	6=	SYM
ejpam-3743	195	33	b	b	PROPN
ejpam-3743	195	34	∈	∈	PROPN
ejpam-3743	195	35	x	x	X
ejpam-3743	195	36	;	;	PUNCT
ejpam-3743	195	37	(	(	PUNCT
ejpam-3743	195	38	iii	iii	NOUN
ejpam-3743	195	39	)	)	PUNCT
ejpam-3743	195	40	for	for	ADP
ejpam-3743	195	41	each	each	PRON
ejpam-3743	195	42	a	a	DET
ejpam-3743	195	43	∈	∈	PROPN
ejpam-3743	195	44	x	x	NOUN
ejpam-3743	195	45	,	,	PUNCT
ejpam-3743	195	46	we	we	PRON
ejpam-3743	195	47	have	have	AUX
ejpam-3743	195	48	{	{	PUNCT
ejpam-3743	195	49	a}s′	a}s′	PROPN
ejpam-3743	195	50	is	be	AUX
ejpam-3743	195	51	a	a	DET
ejpam-3743	195	52	union	union	NOUN
ejpam-3743	195	53	of	of	ADP
ejpam-3743	195	54	supra	supra	PROPN
ejpam-3743	195	55	semi	semi	ADJ
ejpam-3743	195	56	-	-	ADJ
ejpam-3743	195	57	closed	closed	ADJ
ejpam-3743	195	58	sets	set	NOUN
ejpam-3743	195	59	.	.	PUNCT
ejpam-3743	196	1	proof	proof	NOUN
ejpam-3743	196	2	.	.	PUNCT
ejpam-3743	197	1	1→	1→	NUM
ejpam-3743	197	2	2	2	NUM
ejpam-3743	197	3	:	:	PUNCT
ejpam-3743	197	4	for	for	ADP
ejpam-3743	197	5	each	each	DET
ejpam-3743	197	6	a	a	DET
ejpam-3743	197	7	6=	6=	SYM
ejpam-3743	197	8	b	b	PROPN
ejpam-3743	197	9	∈	∈	PROPN
ejpam-3743	197	10	x	x	NOUN
ejpam-3743	197	11	,	,	PUNCT
ejpam-3743	197	12	there	there	PRON
ejpam-3743	197	13	exists	exist	VERB
ejpam-3743	197	14	a	a	DET
ejpam-3743	197	15	supra	supra	NOUN
ejpam-3743	197	16	semi	semi	ADJ
ejpam-3743	197	17	-	-	ADJ
ejpam-3743	197	18	open	open	ADJ
ejpam-3743	197	19	set	set	NOUN
ejpam-3743	197	20	g	g	NOUN
ejpam-3743	197	21	containing	contain	VERB
ejpam-3743	197	22	a	a	PRON
ejpam-3743	197	23	but	but	CCONJ
ejpam-3743	197	24	not	not	PART
ejpam-3743	197	25	b	b	NOUN
ejpam-3743	197	26	,	,	PUNCT
ejpam-3743	197	27	or	or	CCONJ
ejpam-3743	197	28	containing	contain	VERB
ejpam-3743	197	29	b	b	PROPN
ejpam-3743	197	30	but	but	CCONJ
ejpam-3743	197	31	not	not	PART
ejpam-3743	198	1	a.	a.	NOUN
ejpam-3743	198	2	say	say	VERB
ejpam-3743	198	3	a	a	DET
ejpam-3743	198	4	∈	∈	PROPN
ejpam-3743	198	5	g	g	NOUN
ejpam-3743	198	6	and	and	CCONJ
ejpam-3743	198	7	b	b	PROPN
ejpam-3743	198	8	6∈	6∈	PROPN
ejpam-3743	198	9	g.	g.	NOUN
ejpam-3743	198	10	then	then	ADV
ejpam-3743	198	11	a	a	DET
ejpam-3743	198	12	6∈	6∈	PROPN
ejpam-3743	198	13	scl({b	scl({b	PROPN
ejpam-3743	198	14	}	}	PUNCT
ejpam-3743	198	15	)	)	PUNCT
ejpam-3743	198	16	because	because	SCONJ
ejpam-3743	198	17	g	g	PROPN
ejpam-3743	198	18	is	be	AUX
ejpam-3743	198	19	a	a	DET
ejpam-3743	198	20	supra	supra	ADJ
ejpam-3743	198	21	semi	semi	ADJ
ejpam-3743	198	22	-	-	ADJ
ejpam-3743	198	23	open	open	ADJ
ejpam-3743	198	24	set	set	NOUN
ejpam-3743	198	25	containing	contain	VERB
ejpam-3743	198	26	a	a	DET
ejpam-3743	198	27	such	such	ADJ
ejpam-3743	198	28	that	that	SCONJ
ejpam-3743	198	29	g	g	PROPN
ejpam-3743	198	30	⋂	⋂	PROPN
ejpam-3743	198	31	{	{	PUNCT
ejpam-3743	198	32	b	b	NOUN
ejpam-3743	198	33	}	}	PUNCT
ejpam-3743	198	34	=	=	PUNCT
ejpam-3743	198	35	∅.	∅.	NOUN
ejpam-3743	198	36	since	since	SCONJ
ejpam-3743	198	37	a	a	DET
ejpam-3743	198	38	∈	∈	PROPN
ejpam-3743	198	39	scl({a	scl({a	NOUN
ejpam-3743	198	40	}	}	PUNCT
ejpam-3743	198	41	)	)	PUNCT
ejpam-3743	198	42	,	,	PUNCT
ejpam-3743	198	43	then	then	ADV
ejpam-3743	198	44	scl({a	scl({a	PROPN
ejpam-3743	198	45	}	}	PUNCT
ejpam-3743	198	46	)	)	PUNCT
ejpam-3743	198	47	6=	6=	X
ejpam-3743	198	48	scl({b	scl({b	PROPN
ejpam-3743	198	49	}	}	PUNCT
ejpam-3743	198	50	)	)	PUNCT
ejpam-3743	198	51	.	.	PUNCT
ejpam-3743	199	1	2	2	NUM
ejpam-3743	199	2	→	→	SYM
ejpam-3743	199	3	3	3	NUM
ejpam-3743	199	4	:	:	PUNCT
ejpam-3743	199	5	let	let	VERB
ejpam-3743	199	6	b	b	X
ejpam-3743	199	7	∈	∈	PROPN
ejpam-3743	199	8	{	{	PUNCT
ejpam-3743	199	9	a}s′.	a}s′.	PROPN
ejpam-3743	199	10	then	then	ADV
ejpam-3743	199	11	b	b	PROPN
ejpam-3743	199	12	6=	6=	ADP
ejpam-3743	199	13	a	a	PRON
ejpam-3743	199	14	and	and	CCONJ
ejpam-3743	199	15	b	b	NOUN
ejpam-3743	199	16	∈	∈	PROPN
ejpam-3743	199	17	{	{	PUNCT
ejpam-3743	199	18	a	a	NOUN
ejpam-3743	199	19	}	}	PUNCT
ejpam-3743	199	20	⋃	⋃	NOUN
ejpam-3743	199	21	{	{	PUNCT
ejpam-3743	199	22	a}s′	a}s′	PROPN
ejpam-3743	199	23	=	=	SYM
ejpam-3743	199	24	scl({a	scl({a	PROPN
ejpam-3743	199	25	}	}	PUNCT
ejpam-3743	199	26	)	)	PUNCT
ejpam-3743	199	27	.	.	PUNCT
ejpam-3743	200	1	therefore	therefore	ADV
ejpam-3743	200	2	scl(b	scl(b	PROPN
ejpam-3743	200	3	)	)	PUNCT
ejpam-3743	200	4	⊆	⊆	NUM
ejpam-3743	200	5	scl({a	scl({a	NOUN
ejpam-3743	200	6	}	}	PUNCT
ejpam-3743	200	7	)	)	PUNCT
ejpam-3743	200	8	.	.	PUNCT
ejpam-3743	201	1	thus	thus	ADV
ejpam-3743	201	2	b	b	X
ejpam-3743	201	3	∈	∈	PROPN
ejpam-3743	201	4	scl(b	scl(b	PROPN
ejpam-3743	201	5	)	)	PUNCT
ejpam-3743	201	6	⊆	⊆	NUM
ejpam-3743	201	7	{	{	PUNCT
ejpam-3743	201	8	a}s′.	a}s′.	PROPN
ejpam-3743	201	9	hence	hence	ADV
ejpam-3743	201	10	,	,	PUNCT
ejpam-3743	201	11	{	{	PUNCT
ejpam-3743	201	12	a}s′	a}s′	PROPN
ejpam-3743	201	13	=	=	SYM
ejpam-3743	201	14	⋃	⋃	NOUN
ejpam-3743	201	15	{	{	PUNCT
ejpam-3743	201	16	scl(b	scl(b	NOUN
ejpam-3743	201	17	):	):	PUNCT
ejpam-3743	201	18	for	for	ADP
ejpam-3743	201	19	each	each	DET
ejpam-3743	201	20	b	b	PROPN
ejpam-3743	201	21	∈	∈	PROPN
ejpam-3743	201	22	{	{	PUNCT
ejpam-3743	201	23	a}s′	a}s′	PROPN
ejpam-3743	201	24	}	}	PUNCT
ejpam-3743	201	25	.	.	PUNCT
ejpam-3743	202	1	3→	3→	NUM
ejpam-3743	202	2	1	1	NUM
ejpam-3743	202	3	:	:	PUNCT
ejpam-3743	202	4	let	let	VERB
ejpam-3743	202	5	a	a	DET
ejpam-3743	202	6	6=	6=	PROPN
ejpam-3743	202	7	b.	b.	PROPN
ejpam-3743	203	1	then	then	ADV
ejpam-3743	203	2	we	we	PRON
ejpam-3743	203	3	have	have	VERB
ejpam-3743	203	4	two	two	NUM
ejpam-3743	203	5	cases	case	NOUN
ejpam-3743	203	6	:	:	PUNCT
ejpam-3743	203	7	(	(	PUNCT
ejpam-3743	203	8	i	i	NOUN
ejpam-3743	203	9	)	)	PUNCT
ejpam-3743	203	10	either	either	CCONJ
ejpam-3743	203	11	b	b	X
ejpam-3743	203	12	∈	∈	PROPN
ejpam-3743	203	13	{	{	PUNCT
ejpam-3743	203	14	a}s′.	a}s′.	PROPN
ejpam-3743	203	15	then	then	ADV
ejpam-3743	203	16	there	there	PRON
ejpam-3743	203	17	is	be	VERB
ejpam-3743	203	18	a	a	DET
ejpam-3743	203	19	supra	supra	ADJ
ejpam-3743	203	20	semi	semi	ADJ
ejpam-3743	203	21	-	-	ADJ
ejpam-3743	203	22	closed	closed	ADJ
ejpam-3743	203	23	set	set	ADJ
ejpam-3743	203	24	f	f	PROPN
ejpam-3743	203	25	such	such	ADJ
ejpam-3743	203	26	that	that	DET
ejpam-3743	203	27	b	b	X
ejpam-3743	203	28	∈	∈	NOUN
ejpam-3743	203	29	f	f	PROPN
ejpam-3743	203	30	⊆	⊆	NUM
ejpam-3743	203	31	{	{	PUNCT
ejpam-3743	203	32	a}s′.	a}s′.	PROPN
ejpam-3743	203	33	since	since	SCONJ
ejpam-3743	203	34	a	a	DET
ejpam-3743	203	35	6∈	6∈	NOUN
ejpam-3743	203	36	{	{	PUNCT
ejpam-3743	203	37	a}s′	a}s′	PROPN
ejpam-3743	203	38	,	,	PUNCT
ejpam-3743	203	39	then	then	ADV
ejpam-3743	203	40	a	a	DET
ejpam-3743	203	41	6∈	6∈	NOUN
ejpam-3743	203	42	f	f	X
ejpam-3743	203	43	.	.	PUNCT
ejpam-3743	204	1	therefore	therefore	ADV
ejpam-3743	204	2	f	f	PROPN
ejpam-3743	204	3	c	c	PROPN
ejpam-3743	204	4	is	be	AUX
ejpam-3743	204	5	a	a	DET
ejpam-3743	204	6	supra	supra	ADJ
ejpam-3743	204	7	semi	semi	ADJ
ejpam-3743	204	8	-	-	ADJ
ejpam-3743	204	9	open	open	ADJ
ejpam-3743	204	10	set	set	NOUN
ejpam-3743	204	11	containing	contain	VERB
ejpam-3743	204	12	a	a	DET
ejpam-3743	204	13	such	such	ADJ
ejpam-3743	204	14	that	that	DET
ejpam-3743	204	15	b	b	PROPN
ejpam-3743	204	16	6∈	6∈	PROPN
ejpam-3743	205	1	f	f	PROPN
ejpam-3743	205	2	c.	c.	PROPN
ejpam-3743	205	3	(	(	PUNCT
ejpam-3743	205	4	ii	ii	PROPN
ejpam-3743	205	5	)	)	PUNCT
ejpam-3743	205	6	or	or	CCONJ
ejpam-3743	205	7	b	b	X
ejpam-3743	205	8	6∈	6∈	NOUN
ejpam-3743	205	9	{	{	PUNCT
ejpam-3743	205	10	a}s′.	a}s′.	PROPN
ejpam-3743	205	11	then	then	ADV
ejpam-3743	205	12	there	there	PRON
ejpam-3743	205	13	is	be	VERB
ejpam-3743	205	14	a	a	DET
ejpam-3743	205	15	supra	supra	ADJ
ejpam-3743	205	16	semi	semi	ADJ
ejpam-3743	205	17	-	-	ADJ
ejpam-3743	205	18	open	open	ADJ
ejpam-3743	205	19	set	set	NOUN
ejpam-3743	205	20	g	g	NOUN
ejpam-3743	205	21	containing	contain	VERB
ejpam-3743	205	22	b	b	NOUN
ejpam-3743	205	23	such	such	ADJ
ejpam-3743	205	24	that	that	SCONJ
ejpam-3743	205	25	a	a	DET
ejpam-3743	205	26	6∈	6∈	NOUN
ejpam-3743	205	27	g.	g.	NOUN
ejpam-3743	205	28	in	in	ADP
ejpam-3743	205	29	the	the	DET
ejpam-3743	205	30	both	both	DET
ejpam-3743	205	31	cases	case	NOUN
ejpam-3743	205	32	above	above	ADV
ejpam-3743	205	33	,	,	PUNCT
ejpam-3743	205	34	we	we	PRON
ejpam-3743	205	35	infer	infer	VERB
ejpam-3743	205	36	that	that	SCONJ
ejpam-3743	205	37	(	(	PUNCT
ejpam-3743	205	38	x,µ	x,µ	NOUN
ejpam-3743	205	39	)	)	PUNCT
ejpam-3743	205	40	is	be	AUX
ejpam-3743	205	41	an	an	DET
ejpam-3743	205	42	sst0	sst0	NOUN
ejpam-3743	205	43	-	-	PUNCT
ejpam-3743	205	44	space	space	NOUN
ejpam-3743	205	45	.	.	PUNCT
ejpam-3743	206	1	corollary	corollary	ADJ
ejpam-3743	206	2	3	3	NUM
ejpam-3743	206	3	.	.	PUNCT
ejpam-3743	207	1	an	an	DET
ejpam-3743	207	2	sst0	sst0	NOUN
ejpam-3743	207	3	-	-	PUNCT
ejpam-3743	207	4	space	space	NOUN
ejpam-3743	207	5	(	(	PUNCT
ejpam-3743	207	6	x,µ	x,µ	NOUN
ejpam-3743	207	7	)	)	PUNCT
ejpam-3743	207	8	contains	contain	VERB
ejpam-3743	207	9	at	at	ADP
ejpam-3743	207	10	most	most	ADJ
ejpam-3743	207	11	a	a	DET
ejpam-3743	207	12	supra	supra	NOUN
ejpam-3743	207	13	semi	semi	ADV
ejpam-3743	207	14	dense	dense	ADJ
ejpam-3743	207	15	singleton	singleton	PROPN
ejpam-3743	207	16	set	set	NOUN
ejpam-3743	207	17	(	(	PUNCT
ejpam-3743	207	18	{	{	PUNCT
ejpam-3743	207	19	a	a	PRON
ejpam-3743	207	20	}	}	PUNCT
ejpam-3743	207	21	is	be	AUX
ejpam-3743	207	22	a	a	DET
ejpam-3743	207	23	supra	supra	NOUN
ejpam-3743	207	24	semi	semi	ADV
ejpam-3743	207	25	dense	dense	ADJ
ejpam-3743	207	26	set	set	NOUN
ejpam-3743	207	27	if	if	SCONJ
ejpam-3743	207	28	scl{a	scl{a	NOUN
ejpam-3743	207	29	}	}	PUNCT
ejpam-3743	207	30	=	=	SYM
ejpam-3743	207	31	x	x	X
ejpam-3743	207	32	)	)	PUNCT
ejpam-3743	207	33	.	.	PUNCT
ejpam-3743	208	1	proof	proof	NOUN
ejpam-3743	208	2	.	.	PUNCT
ejpam-3743	209	1	let	let	VERB
ejpam-3743	209	2	(	(	PUNCT
ejpam-3743	209	3	x,µ	x,µ	NOUN
ejpam-3743	209	4	)	)	PUNCT
ejpam-3743	209	5	be	be	VERB
ejpam-3743	209	6	an	an	DET
ejpam-3743	209	7	sst0	sst0	NOUN
ejpam-3743	209	8	-	-	PUNCT
ejpam-3743	209	9	space	space	NOUN
ejpam-3743	209	10	.	.	PUNCT
ejpam-3743	210	1	suppose	suppose	VERB
ejpam-3743	210	2	that	that	SCONJ
ejpam-3743	210	3	there	there	PRON
ejpam-3743	210	4	are	be	VERB
ejpam-3743	210	5	two	two	NUM
ejpam-3743	210	6	distinct	distinct	ADJ
ejpam-3743	210	7	singleton	singleton	NOUN
ejpam-3743	210	8	set	set	NOUN
ejpam-3743	210	9	{	{	PUNCT
ejpam-3743	210	10	a	a	NOUN
ejpam-3743	210	11	}	}	PUNCT
ejpam-3743	210	12	and	and	CCONJ
ejpam-3743	210	13	{	{	PUNCT
ejpam-3743	210	14	b	b	NOUN
ejpam-3743	210	15	}	}	PUNCT
ejpam-3743	210	16	such	such	ADJ
ejpam-3743	210	17	that	that	SCONJ
ejpam-3743	210	18	scl({a	scl({a	NOUN
ejpam-3743	210	19	}	}	PUNCT
ejpam-3743	210	20	)	)	PUNCT
ejpam-3743	211	1	=	=	SYM
ejpam-3743	211	2	scl({b	scl({b	PROPN
ejpam-3743	211	3	}	}	PUNCT
ejpam-3743	211	4	)	)	PUNCT
ejpam-3743	212	1	=	=	PUNCT
ejpam-3743	212	2	x.	x.	NOUN
ejpam-3743	212	3	then	then	ADV
ejpam-3743	212	4	(	(	PUNCT
ejpam-3743	212	5	x,µ	x,µ	NOUN
ejpam-3743	212	6	)	)	PUNCT
ejpam-3743	212	7	is	be	AUX
ejpam-3743	212	8	not	not	PART
ejpam-3743	212	9	an	an	DET
ejpam-3743	212	10	sst0	sst0	NOUN
ejpam-3743	212	11	-	-	PUNCT
ejpam-3743	212	12	space	space	NOUN
ejpam-3743	212	13	,	,	PUNCT
ejpam-3743	212	14	a	a	DET
ejpam-3743	212	15	contradiction	contradiction	NOUN
ejpam-3743	212	16	.	.	PUNCT
ejpam-3743	213	1	hence	hence	ADV
ejpam-3743	213	2	,	,	PUNCT
ejpam-3743	213	3	(	(	PUNCT
ejpam-3743	213	4	x,µ	x,µ	NOUN
ejpam-3743	213	5	)	)	PUNCT
ejpam-3743	213	6	contains	contain	VERB
ejpam-3743	213	7	at	at	ADP
ejpam-3743	213	8	most	most	ADJ
ejpam-3743	213	9	a	a	DET
ejpam-3743	213	10	supra	supra	NOUN
ejpam-3743	213	11	semi	semi	ADV
ejpam-3743	213	12	dense	dense	ADJ
ejpam-3743	213	13	singleton	singleton	PROPN
ejpam-3743	213	14	set	set	NOUN
ejpam-3743	213	15	.	.	PUNCT
ejpam-3743	214	1	theorem	theorem	VERB
ejpam-3743	214	2	5	5	NUM
ejpam-3743	214	3	.	.	PUNCT
ejpam-3743	215	1	the	the	DET
ejpam-3743	215	2	following	follow	VERB
ejpam-3743	215	3	four	four	NUM
ejpam-3743	215	4	statements	statement	NOUN
ejpam-3743	215	5	are	be	AUX
ejpam-3743	215	6	equivalent	equivalent	ADJ
ejpam-3743	215	7	:	:	PUNCT
ejpam-3743	215	8	(	(	PUNCT
ejpam-3743	215	9	i	i	NOUN
ejpam-3743	215	10	)	)	PUNCT
ejpam-3743	215	11	(	(	PUNCT
ejpam-3743	215	12	x,µ	x,µ	NOUN
ejpam-3743	215	13	)	)	PUNCT
ejpam-3743	215	14	is	be	AUX
ejpam-3743	215	15	an	an	DET
ejpam-3743	215	16	sst1	sst1	NOUN
ejpam-3743	215	17	-	-	PUNCT
ejpam-3743	215	18	space	space	NOUN
ejpam-3743	215	19	;	;	PUNCT
ejpam-3743	215	20	(	(	PUNCT
ejpam-3743	215	21	ii	ii	NOUN
ejpam-3743	215	22	)	)	PUNCT
ejpam-3743	215	23	every	every	DET
ejpam-3743	215	24	singleton	singleton	NOUN
ejpam-3743	215	25	subset	subset	NOUN
ejpam-3743	215	26	of	of	ADP
ejpam-3743	215	27	(	(	PUNCT
ejpam-3743	215	28	x,µ	x,µ	NOUN
ejpam-3743	215	29	)	)	PUNCT
ejpam-3743	215	30	is	be	AUX
ejpam-3743	215	31	supra	supra	ADJ
ejpam-3743	215	32	semi	semi	ADV
ejpam-3743	215	33	-	-	ADJ
ejpam-3743	215	34	closed	closed	ADJ
ejpam-3743	215	35	;	;	PUNCT
ejpam-3743	215	36	(	(	PUNCT
ejpam-3743	215	37	iii	iii	X
ejpam-3743	215	38	)	)	PUNCT
ejpam-3743	215	39	the	the	DET
ejpam-3743	215	40	intersection	intersection	NOUN
ejpam-3743	215	41	of	of	ADP
ejpam-3743	215	42	all	all	DET
ejpam-3743	215	43	supra	supra	ADJ
ejpam-3743	215	44	semi	semi	ADJ
ejpam-3743	215	45	-	-	ADJ
ejpam-3743	215	46	open	open	ADJ
ejpam-3743	215	47	sets	set	NOUN
ejpam-3743	215	48	containing	contain	VERB
ejpam-3743	215	49	a	a	DET
ejpam-3743	215	50	set	set	NOUN
ejpam-3743	215	51	a	a	PRON
ejpam-3743	215	52	is	be	AUX
ejpam-3743	215	53	exactly	exactly	ADV
ejpam-3743	215	54	a	a	PRON
ejpam-3743	215	55	;	;	PUNCT
ejpam-3743	215	56	(	(	PUNCT
ejpam-3743	215	57	iv	iv	X
ejpam-3743	215	58	)	)	PUNCT
ejpam-3743	215	59	{	{	PUNCT
ejpam-3743	215	60	a}s′	a}s′	PROPN
ejpam-3743	215	61	=	=	SYM
ejpam-3743	215	62	∅	∅	NOUN
ejpam-3743	215	63	for	for	ADP
ejpam-3743	215	64	each	each	DET
ejpam-3743	215	65	a	a	DET
ejpam-3743	215	66	∈	∈	NOUN
ejpam-3743	215	67	x.	x.	NOUN
ejpam-3743	215	68	proof	proof	NOUN
ejpam-3743	215	69	.	.	PUNCT
ejpam-3743	216	1	1	1	NUM
ejpam-3743	216	2	→	→	SYM
ejpam-3743	216	3	2	2	NUM
ejpam-3743	216	4	:	:	PUNCT
ejpam-3743	216	5	consider	consider	VERB
ejpam-3743	216	6	(	(	PUNCT
ejpam-3743	216	7	x,µ	x,µ	NOUN
ejpam-3743	216	8	)	)	PUNCT
ejpam-3743	216	9	is	be	AUX
ejpam-3743	216	10	an	an	DET
ejpam-3743	216	11	sst1	sst1	NOUN
ejpam-3743	216	12	-	-	PUNCT
ejpam-3743	216	13	space	space	NOUN
ejpam-3743	216	14	and	and	CCONJ
ejpam-3743	216	15	let	let	VERB
ejpam-3743	216	16	{	{	PUNCT
ejpam-3743	216	17	a	a	NOUN
ejpam-3743	216	18	}	}	PUNCT
ejpam-3743	216	19	⊆	⊆	NUM
ejpam-3743	216	20	x.	x.	NOUN
ejpam-3743	216	21	for	for	ADP
ejpam-3743	216	22	all	all	DET
ejpam-3743	216	23	b	b	NOUN
ejpam-3743	216	24	∈	∈	NOUN
ejpam-3743	216	25	x	x	PUNCT
ejpam-3743	216	26	such	such	ADJ
ejpam-3743	216	27	that	that	SCONJ
ejpam-3743	216	28	a	a	DET
ejpam-3743	216	29	6=	6=	PROPN
ejpam-3743	216	30	b	b	PROPN
ejpam-3743	216	31	,	,	PUNCT
ejpam-3743	216	32	there	there	PRON
ejpam-3743	216	33	exists	exist	VERB
ejpam-3743	216	34	a	a	DET
ejpam-3743	216	35	supra	supra	NOUN
ejpam-3743	216	36	semi	semi	ADJ
ejpam-3743	216	37	-	-	ADJ
ejpam-3743	216	38	open	open	ADJ
ejpam-3743	216	39	set	set	NOUN
ejpam-3743	216	40	g	g	NOUN
ejpam-3743	216	41	containing	contain	VERB
ejpam-3743	216	42	b	b	NOUN
ejpam-3743	216	43	such	such	ADJ
ejpam-3743	216	44	that	that	SCONJ
ejpam-3743	216	45	g	g	PROPN
ejpam-3743	216	46	⋂	⋂	PROPN
ejpam-3743	216	47	{	{	PUNCT
ejpam-3743	216	48	a	a	NOUN
ejpam-3743	216	49	}	}	PUNCT
ejpam-3743	216	50	=	=	PUNCT
ejpam-3743	216	51	∅.	∅.	NOUN
ejpam-3743	216	52	then	then	ADV
ejpam-3743	216	53	b	b	PROPN
ejpam-3743	216	54	6∈	6∈	PROPN
ejpam-3743	216	55	scl({a	scl({a	PROPN
ejpam-3743	216	56	}	}	PUNCT
ejpam-3743	216	57	)	)	PUNCT
ejpam-3743	216	58	.	.	PUNCT
ejpam-3743	217	1	therefore	therefore	ADV
ejpam-3743	217	2	,	,	PUNCT
ejpam-3743	217	3	scl({a	scl({a	PROPN
ejpam-3743	217	4	}	}	PUNCT
ejpam-3743	217	5	)	)	PUNCT
ejpam-3743	218	1	=	=	PRON
ejpam-3743	218	2	{	{	PUNCT
ejpam-3743	218	3	a	a	X
ejpam-3743	218	4	}	}	PUNCT
ejpam-3743	218	5	.	.	PUNCT
ejpam-3743	219	1	thus	thus	ADV
ejpam-3743	219	2	,	,	PUNCT
ejpam-3743	219	3	{	{	PUNCT
ejpam-3743	219	4	a	a	PRON
ejpam-3743	219	5	}	}	PUNCT
ejpam-3743	219	6	is	be	AUX
ejpam-3743	219	7	a	a	DET
ejpam-3743	219	8	supra	supra	ADJ
ejpam-3743	219	9	semi	semi	ADJ
ejpam-3743	219	10	-	-	ADJ
ejpam-3743	219	11	closed	closed	ADJ
ejpam-3743	219	12	set	set	NOUN
ejpam-3743	219	13	.	.	PUNCT
ejpam-3743	220	1	2	2	NUM
ejpam-3743	220	2	→	→	SYM
ejpam-3743	220	3	3	3	NUM
ejpam-3743	220	4	:	:	PUNCT
ejpam-3743	220	5	let	let	VERB
ejpam-3743	220	6	a	a	PRON
ejpam-3743	220	7	be	be	AUX
ejpam-3743	220	8	a	a	DET
ejpam-3743	220	9	subset	subset	NOUN
ejpam-3743	220	10	of	of	ADP
ejpam-3743	220	11	(	(	PUNCT
ejpam-3743	220	12	x,µ	x,µ	NOUN
ejpam-3743	220	13	)	)	PUNCT
ejpam-3743	220	14	.	.	PUNCT
ejpam-3743	221	1	then	then	ADV
ejpam-3743	221	2	for	for	ADP
ejpam-3743	221	3	each	each	DET
ejpam-3743	221	4	a	a	DET
ejpam-3743	221	5	∈	∈	PROPN
ejpam-3743	221	6	ac	ac	NOUN
ejpam-3743	221	7	,	,	PUNCT
ejpam-3743	221	8	we	we	PRON
ejpam-3743	221	9	have	have	AUX
ejpam-3743	221	10	{	{	PUNCT
ejpam-3743	221	11	a}c	a}c	PROPN
ejpam-3743	221	12	is	be	AUX
ejpam-3743	221	13	a	a	DET
ejpam-3743	221	14	supra	supra	ADJ
ejpam-3743	221	15	semi	semi	ADJ
ejpam-3743	221	16	-	-	ADJ
ejpam-3743	221	17	open	open	ADJ
ejpam-3743	221	18	set	set	NOUN
ejpam-3743	221	19	containing	contain	VERB
ejpam-3743	221	20	a.	a.	NOUN
ejpam-3743	221	21	now	now	ADV
ejpam-3743	221	22	,	,	PUNCT
ejpam-3743	221	23	a	a	DET
ejpam-3743	221	24	⊆	⊆	NUM
ejpam-3743	221	25	{	{	PUNCT
ejpam-3743	221	26	g	g	NOUN
ejpam-3743	221	27	:	:	PUNCT
ejpam-3743	221	28	g	g	PROPN
ejpam-3743	221	29	is	be	AUX
ejpam-3743	221	30	a	a	DET
ejpam-3743	221	31	supra	supra	ADJ
ejpam-3743	221	32	semi	semi	ADJ
ejpam-3743	221	33	-	-	ADJ
ejpam-3743	221	34	open	open	ADJ
ejpam-3743	221	35	set	set	NOUN
ejpam-3743	221	36	containing	contain	VERB
ejpam-3743	221	37	a	a	PRON
ejpam-3743	221	38	}	}	PUNCT
ejpam-3743	221	39	⊆	⊆	NUM
ejpam-3743	221	40	{	{	PUNCT
ejpam-3743	221	41	{	{	PUNCT
ejpam-3743	221	42	a}c	a}c	NOUN
ejpam-3743	221	43	:	:	PUNCT
ejpam-3743	221	44	a	a	DET
ejpam-3743	221	45	∈	∈	PROPN
ejpam-3743	221	46	ac	ac	PROPN
ejpam-3743	221	47	}	}	PUNCT
ejpam-3743	221	48	⊆	⊆	NUM
ejpam-3743	221	49	a.	a.	NOUN
ejpam-3743	221	50	thus	thus	ADV
ejpam-3743	221	51	,	,	PUNCT
ejpam-3743	221	52	a	a	DET
ejpam-3743	221	53	=	=	X
ejpam-3743	221	54	{	{	PUNCT
ejpam-3743	221	55	g	g	NOUN
ejpam-3743	221	56	:	:	PUNCT
ejpam-3743	221	57	g	g	PROPN
ejpam-3743	221	58	is	be	AUX
ejpam-3743	221	59	a	a	DET
ejpam-3743	221	60	supra	supra	ADJ
ejpam-3743	221	61	semi	semi	ADJ
ejpam-3743	221	62	-	-	ADJ
ejpam-3743	221	63	open	open	ADJ
ejpam-3743	221	64	set	set	NOUN
ejpam-3743	221	65	containing	contain	VERB
ejpam-3743	221	66	a	a	PRON
ejpam-3743	221	67	}	}	PUNCT
ejpam-3743	221	68	,	,	PUNCT
ejpam-3743	221	69	as	as	SCONJ
ejpam-3743	221	70	required	require	VERB
ejpam-3743	221	71	.	.	PUNCT
ejpam-3743	222	1	3	3	NUM
ejpam-3743	222	2	→	→	SYM
ejpam-3743	222	3	4	4	NUM
ejpam-3743	222	4	:	:	PUNCT
ejpam-3743	222	5	suppose	suppose	VERB
ejpam-3743	222	6	that	that	SCONJ
ejpam-3743	222	7	there	there	PRON
ejpam-3743	222	8	exists	exist	VERB
ejpam-3743	222	9	a	a	DET
ejpam-3743	222	10	∈	∈	NOUN
ejpam-3743	222	11	x	x	PUNCT
ejpam-3743	222	12	such	such	ADJ
ejpam-3743	222	13	that	that	SCONJ
ejpam-3743	222	14	{	{	PUNCT
ejpam-3743	222	15	a}s′	a}s′	PROPN
ejpam-3743	222	16	6=	6=	ADP
ejpam-3743	222	17	∅.	∅.	VERB
ejpam-3743	222	18	then	then	ADV
ejpam-3743	222	19	there	there	PRON
ejpam-3743	222	20	exists	exist	VERB
ejpam-3743	222	21	b	b	PROPN
ejpam-3743	222	22	6=	6=	ADP
ejpam-3743	222	23	a	a	DET
ejpam-3743	222	24	such	such	ADJ
ejpam-3743	222	25	that	that	DET
ejpam-3743	222	26	b	b	X
ejpam-3743	222	27	∈	∈	PROPN
ejpam-3743	222	28	{	{	PUNCT
ejpam-3743	222	29	a}s′.	a}s′.	PROPN
ejpam-3743	222	30	therefore	therefore	ADV
ejpam-3743	222	31	g\{b	g\{b	PROPN
ejpam-3743	222	32	}	}	PUNCT
ejpam-3743	222	33	⋂	⋂	PROPN
ejpam-3743	222	34	{	{	PUNCT
ejpam-3743	222	35	a	a	NOUN
ejpam-3743	222	36	}	}	PUNCT
ejpam-3743	222	37	6=	6=	NOUN
ejpam-3743	222	38	∅	∅	NOUN
ejpam-3743	222	39	for	for	ADP
ejpam-3743	222	40	every	every	DET
ejpam-3743	222	41	supra	supra	NOUN
ejpam-3743	222	42	semi	semi	ADJ
ejpam-3743	222	43	-	-	ADJ
ejpam-3743	222	44	open	open	ADJ
ejpam-3743	222	45	set	set	NOUN
ejpam-3743	222	46	g	g	NOUN
ejpam-3743	222	47	containing	contain	VERB
ejpam-3743	222	48	b.	b.	PROPN
ejpam-3743	222	49	this	this	PRON
ejpam-3743	222	50	implies	imply	VERB
ejpam-3743	222	51	that	that	SCONJ
ejpam-3743	222	52	any	any	DET
ejpam-3743	222	53	supra	supra	NOUN
ejpam-3743	222	54	semi	semi	ADJ
ejpam-3743	222	55	-	-	ADJ
ejpam-3743	222	56	open	open	ADJ
ejpam-3743	222	57	set	set	NOUN
ejpam-3743	222	58	containing	contain	VERB
ejpam-3743	222	59	b	b	PROPN
ejpam-3743	222	60	contains	contain	VERB
ejpam-3743	222	61	a	a	DET
ejpam-3743	222	62	as	as	ADV
ejpam-3743	222	63	well	well	ADV
ejpam-3743	222	64	.	.	PUNCT
ejpam-3743	223	1	thus	thus	ADV
ejpam-3743	223	2	the	the	DET
ejpam-3743	223	3	t.	t.	PROPN
ejpam-3743	223	4	m.	m.	PROPN
ejpam-3743	223	5	al	al	PROPN
ejpam-3743	223	6	-	-	PUNCT
ejpam-3743	223	7	shami	shami	PROPN
ejpam-3743	223	8	et	et	PROPN
ejpam-3743	223	9	al	al	PROPN
ejpam-3743	223	10	.	.	PUNCT
ejpam-3743	223	11	/	/	SYM
ejpam-3743	223	12	eur	eur	PROPN
ejpam-3743	223	13	.	.	PUNCT
ejpam-3743	224	1	j.	j.	PROPN
ejpam-3743	224	2	pure	pure	PROPN
ejpam-3743	224	3	appl	appl	PROPN
ejpam-3743	224	4	.	.	PROPN
ejpam-3743	224	5	math	math	PROPN
ejpam-3743	224	6	,	,	PUNCT
ejpam-3743	224	7	13	13	NUM
ejpam-3743	224	8	(	(	PUNCT
ejpam-3743	224	9	3	3	NUM
ejpam-3743	224	10	)	)	PUNCT
ejpam-3743	224	11	(	(	PUNCT
ejpam-3743	224	12	2020	2020	NUM
ejpam-3743	224	13	)	)	PUNCT
ejpam-3743	224	14	,	,	PUNCT
ejpam-3743	224	15	427	427	NUM
ejpam-3743	224	16	-	-	SYM
ejpam-3743	224	17	443	443	NUM
ejpam-3743	224	18	435	435	NUM
ejpam-3743	224	19	intersection	intersection	NOUN
ejpam-3743	224	20	of	of	ADP
ejpam-3743	224	21	all	all	DET
ejpam-3743	224	22	supra	supra	ADJ
ejpam-3743	224	23	semi	semi	ADJ
ejpam-3743	224	24	-	-	ADJ
ejpam-3743	224	25	open	open	ADJ
ejpam-3743	224	26	sets	set	NOUN
ejpam-3743	224	27	containing	contain	VERB
ejpam-3743	224	28	b	b	NOUN
ejpam-3743	224	29	is	be	AUX
ejpam-3743	224	30	not	not	PART
ejpam-3743	224	31	equal	equal	ADJ
ejpam-3743	224	32	{	{	PUNCT
ejpam-3743	224	33	b	b	NOUN
ejpam-3743	224	34	}	}	PUNCT
ejpam-3743	224	35	.	.	PUNCT
ejpam-3743	225	1	but	but	CCONJ
ejpam-3743	225	2	this	this	PRON
ejpam-3743	225	3	contradicts	contradict	VERB
ejpam-3743	225	4	3	3	NUM
ejpam-3743	225	5	.	.	PUNCT
ejpam-3743	226	1	hence	hence	ADV
ejpam-3743	226	2	,	,	PUNCT
ejpam-3743	226	3	it	it	PRON
ejpam-3743	226	4	must	must	AUX
ejpam-3743	226	5	be	be	AUX
ejpam-3743	226	6	{	{	PUNCT
ejpam-3743	226	7	a}s′	a}s′	X
ejpam-3743	226	8	=	=	PROPN
ejpam-3743	226	9	∅.	∅.	VERB
ejpam-3743	226	10	4	4	NUM
ejpam-3743	226	11	→	→	SYM
ejpam-3743	226	12	1	1	NUM
ejpam-3743	226	13	:	:	PUNCT
ejpam-3743	226	14	let	let	VERB
ejpam-3743	226	15	a	a	DET
ejpam-3743	226	16	6=	6=	ADP
ejpam-3743	226	17	b.	b.	PROPN
ejpam-3743	226	18	since	since	SCONJ
ejpam-3743	226	19	{	{	PUNCT
ejpam-3743	226	20	a}s′	a}s′	PROPN
ejpam-3743	226	21	=	=	SYM
ejpam-3743	226	22	∅	∅	NOUN
ejpam-3743	226	23	and	and	CCONJ
ejpam-3743	226	24	{	{	PUNCT
ejpam-3743	226	25	b}s′	b}s′	NOUN
ejpam-3743	226	26	=	=	SYM
ejpam-3743	226	27	∅	∅	NOUN
ejpam-3743	226	28	,	,	PUNCT
ejpam-3743	226	29	then	then	ADV
ejpam-3743	226	30	{	{	PUNCT
ejpam-3743	226	31	a	a	NOUN
ejpam-3743	226	32	}	}	PUNCT
ejpam-3743	226	33	and	and	CCONJ
ejpam-3743	226	34	{	{	PUNCT
ejpam-3743	226	35	b	b	NOUN
ejpam-3743	226	36	}	}	PUNCT
ejpam-3743	226	37	are	be	AUX
ejpam-3743	226	38	supra	supra	ADJ
ejpam-3743	226	39	semiclosed	semiclose	VERB
ejpam-3743	226	40	sets	set	NOUN
ejpam-3743	226	41	.	.	PUNCT
ejpam-3743	227	1	therefore	therefore	ADV
ejpam-3743	227	2	{	{	PUNCT
ejpam-3743	227	3	a}c	a}c	PROPN
ejpam-3743	227	4	and	and	CCONJ
ejpam-3743	227	5	{	{	PUNCT
ejpam-3743	227	6	b}c	b}c	NOUN
ejpam-3743	227	7	are	be	AUX
ejpam-3743	227	8	supra	supra	ADJ
ejpam-3743	227	9	semi	semi	ADJ
ejpam-3743	227	10	-	-	ADJ
ejpam-3743	227	11	open	open	ADJ
ejpam-3743	227	12	sets	set	NOUN
ejpam-3743	227	13	containing	contain	VERB
ejpam-3743	227	14	{	{	PUNCT
ejpam-3743	227	15	b	b	NOUN
ejpam-3743	227	16	}	}	PUNCT
ejpam-3743	227	17	and	and	CCONJ
ejpam-3743	227	18	{	{	PUNCT
ejpam-3743	227	19	a	a	PRON
ejpam-3743	227	20	}	}	PUNCT
ejpam-3743	227	21	,	,	PUNCT
ejpam-3743	227	22	respectively	respectively	ADV
ejpam-3743	227	23	.	.	PUNCT
ejpam-3743	228	1	thus	thus	ADV
ejpam-3743	228	2	,	,	PUNCT
ejpam-3743	228	3	(	(	PUNCT
ejpam-3743	228	4	x,µ	x,µ	NOUN
ejpam-3743	228	5	)	)	PUNCT
ejpam-3743	228	6	is	be	AUX
ejpam-3743	228	7	an	an	DET
ejpam-3743	228	8	sst1	sst1	NOUN
ejpam-3743	228	9	-	-	PUNCT
ejpam-3743	228	10	space	space	NOUN
ejpam-3743	228	11	.	.	PUNCT
ejpam-3743	229	1	proposition	proposition	NOUN
ejpam-3743	229	2	4	4	NUM
ejpam-3743	229	3	.	.	PUNCT
ejpam-3743	230	1	every	every	DET
ejpam-3743	230	2	(	(	PUNCT
ejpam-3743	230	3	x,µ	x,µ	NOUN
ejpam-3743	230	4	)	)	PUNCT
ejpam-3743	230	5	satisfying	satisfy	VERB
ejpam-3743	230	6	the	the	DET
ejpam-3743	230	7	difference	difference	NOUN
ejpam-3743	230	8	property	property	NOUN
ejpam-3743	230	9	for	for	ADP
ejpam-3743	230	10	the	the	DET
ejpam-3743	230	11	collection	collection	NOUN
ejpam-3743	230	12	of	of	ADP
ejpam-3743	230	13	supra	supra	PROPN
ejpam-3743	230	14	semi	semi	ADJ
ejpam-3743	230	15	-	-	ADJ
ejpam-3743	230	16	open	open	ADJ
ejpam-3743	230	17	sets	set	NOUN
ejpam-3743	230	18	is	be	AUX
ejpam-3743	230	19	an	an	DET
ejpam-3743	230	20	sst1	sst1	NOUN
ejpam-3743	230	21	-	-	PUNCT
ejpam-3743	230	22	space	space	NOUN
ejpam-3743	230	23	.	.	PUNCT
ejpam-3743	231	1	proof	proof	NOUN
ejpam-3743	231	2	.	.	PUNCT
ejpam-3743	232	1	let	let	VERB
ejpam-3743	232	2	a	a	DET
ejpam-3743	232	3	6=	6=	NUM
ejpam-3743	232	4	b	b	PROPN
ejpam-3743	232	5	∈	∈	PROPN
ejpam-3743	232	6	x.	x.	NOUN
ejpam-3743	233	1	since	since	SCONJ
ejpam-3743	233	2	x	x	PRON
ejpam-3743	233	3	is	be	AUX
ejpam-3743	233	4	a	a	DET
ejpam-3743	233	5	supra	supra	ADJ
ejpam-3743	233	6	semi	semi	ADJ
ejpam-3743	233	7	-	-	ADJ
ejpam-3743	233	8	open	open	ADJ
ejpam-3743	233	9	set	set	NOUN
ejpam-3743	233	10	and	and	CCONJ
ejpam-3743	233	11	(	(	PUNCT
ejpam-3743	233	12	x,µ	x,µ	NOUN
ejpam-3743	233	13	)	)	PUNCT
ejpam-3743	233	14	satisfies	satisfy	VERB
ejpam-3743	233	15	the	the	DET
ejpam-3743	233	16	difference	difference	NOUN
ejpam-3743	233	17	property	property	NOUN
ejpam-3743	233	18	for	for	ADP
ejpam-3743	233	19	the	the	DET
ejpam-3743	233	20	collection	collection	NOUN
ejpam-3743	233	21	of	of	ADP
ejpam-3743	233	22	supra	supra	PROPN
ejpam-3743	233	23	semi	semi	ADJ
ejpam-3743	233	24	-	-	ADJ
ejpam-3743	233	25	open	open	ADJ
ejpam-3743	233	26	sets	set	NOUN
ejpam-3743	233	27	,	,	PUNCT
ejpam-3743	233	28	then	then	ADV
ejpam-3743	233	29	x	x	SYM
ejpam-3743	233	30	\	\	PROPN
ejpam-3743	233	31	{	{	PUNCT
ejpam-3743	233	32	a	a	NOUN
ejpam-3743	233	33	}	}	PUNCT
ejpam-3743	233	34	and	and	CCONJ
ejpam-3743	233	35	x	x	SYM
ejpam-3743	233	36	\	\	PROPN
ejpam-3743	233	37	{	{	PUNCT
ejpam-3743	233	38	b	b	NOUN
ejpam-3743	233	39	}	}	PUNCT
ejpam-3743	233	40	are	be	AUX
ejpam-3743	233	41	supra	supra	ADJ
ejpam-3743	233	42	semi	semi	ADJ
ejpam-3743	233	43	-	-	ADJ
ejpam-3743	233	44	open	open	ADJ
ejpam-3743	233	45	sets	set	NOUN
ejpam-3743	233	46	containing	contain	VERB
ejpam-3743	233	47	b	b	PROPN
ejpam-3743	233	48	and	and	CCONJ
ejpam-3743	233	49	a	a	PRON
ejpam-3743	233	50	,	,	PUNCT
ejpam-3743	233	51	respectively	respectively	ADV
ejpam-3743	233	52	,	,	PUNCT
ejpam-3743	233	53	such	such	ADJ
ejpam-3743	233	54	that	that	SCONJ
ejpam-3743	233	55	a	a	DET
ejpam-3743	233	56	6∈	6∈	NOUN
ejpam-3743	233	57	x	x	SYM
ejpam-3743	233	58	\	\	X
ejpam-3743	233	59	{	{	PUNCT
ejpam-3743	233	60	a	a	NOUN
ejpam-3743	233	61	}	}	PUNCT
ejpam-3743	233	62	and	and	CCONJ
ejpam-3743	233	63	b	b	X
ejpam-3743	233	64	6∈	6∈	NOUN
ejpam-3743	233	65	x	x	SYM
ejpam-3743	233	66	\	\	X
ejpam-3743	233	67	{	{	PUNCT
ejpam-3743	233	68	b	b	NOUN
ejpam-3743	233	69	}	}	PUNCT
ejpam-3743	233	70	.	.	PUNCT
ejpam-3743	234	1	hence	hence	ADV
ejpam-3743	234	2	,	,	PUNCT
ejpam-3743	234	3	(	(	PUNCT
ejpam-3743	234	4	x,µ	x,µ	NOUN
ejpam-3743	234	5	)	)	PUNCT
ejpam-3743	234	6	is	be	AUX
ejpam-3743	234	7	an	an	DET
ejpam-3743	234	8	sst1	sst1	NOUN
ejpam-3743	234	9	-	-	PUNCT
ejpam-3743	234	10	space	space	NOUN
ejpam-3743	234	11	.	.	PUNCT
ejpam-3743	235	1	we	we	PRON
ejpam-3743	235	2	show	show	VERB
ejpam-3743	235	3	by	by	ADP
ejpam-3743	235	4	the	the	DET
ejpam-3743	235	5	following	following	ADJ
ejpam-3743	235	6	example	example	NOUN
ejpam-3743	235	7	that	that	SCONJ
ejpam-3743	235	8	the	the	DET
ejpam-3743	235	9	converse	converse	NOUN
ejpam-3743	235	10	of	of	ADP
ejpam-3743	235	11	the	the	DET
ejpam-3743	235	12	above	above	ADJ
ejpam-3743	235	13	proposition	proposition	NOUN
ejpam-3743	235	14	is	be	AUX
ejpam-3743	235	15	not	not	PART
ejpam-3743	235	16	always	always	ADV
ejpam-3743	235	17	true	true	ADJ
ejpam-3743	235	18	.	.	PUNCT
ejpam-3743	236	1	example	example	NOUN
ejpam-3743	237	1	4	4	X
ejpam-3743	237	2	.	.	PUNCT
ejpam-3743	237	3	let	let	VERB
ejpam-3743	237	4	µ	µ	X
ejpam-3743	237	5	=	=	SYM
ejpam-3743	237	6	{	{	PUNCT
ejpam-3743	237	7	∅	∅	NOUN
ejpam-3743	237	8	,	,	PUNCT
ejpam-3743	237	9	g	g	PROPN
ejpam-3743	237	10	⊆	⊆	NUM
ejpam-3743	237	11	n	n	NUM
ejpam-3743	237	12	:	:	PUNCT
ejpam-3743	237	13	1	1	NUM
ejpam-3743	237	14	∈	∈	NOUN
ejpam-3743	237	15	g	g	NOUN
ejpam-3743	237	16	,	,	PUNCT
ejpam-3743	237	17	or	or	CCONJ
ejpam-3743	237	18	1	1	NUM
ejpam-3743	237	19	6∈	6∈	NOUN
ejpam-3743	237	20	g	g	PROPN
ejpam-3743	237	21	and	and	CCONJ
ejpam-3743	237	22	gc	gc	PROPN
ejpam-3743	237	23	is	be	AUX
ejpam-3743	237	24	finite	finite	PROPN
ejpam-3743	237	25	}	}	PUNCT
ejpam-3743	237	26	be	be	VERB
ejpam-3743	237	27	a	a	DET
ejpam-3743	237	28	supra	supra	ADJ
ejpam-3743	237	29	topology	topology	NOUN
ejpam-3743	237	30	on	on	ADP
ejpam-3743	237	31	the	the	DET
ejpam-3743	237	32	natural	natural	ADJ
ejpam-3743	237	33	numbers	number	NOUN
ejpam-3743	237	34	set	set	VERB
ejpam-3743	237	35	n	n	PROPN
ejpam-3743	237	36	.	.	PUNCT
ejpam-3743	238	1	note	note	VERB
ejpam-3743	238	2	that	that	SCONJ
ejpam-3743	238	3	(	(	PUNCT
ejpam-3743	238	4	n	n	X
ejpam-3743	238	5	,	,	PUNCT
ejpam-3743	238	6	µ	µ	X
ejpam-3743	238	7	)	)	PUNCT
ejpam-3743	238	8	is	be	AUX
ejpam-3743	238	9	not	not	PART
ejpam-3743	238	10	a	a	DET
ejpam-3743	238	11	topological	topological	ADJ
ejpam-3743	238	12	space	space	NOUN
ejpam-3743	238	13	.	.	PUNCT
ejpam-3743	239	1	then	then	ADV
ejpam-3743	239	2	the	the	DET
ejpam-3743	239	3	collection	collection	NOUN
ejpam-3743	239	4	of	of	ADP
ejpam-3743	239	5	all	all	DET
ejpam-3743	239	6	supra	supra	ADJ
ejpam-3743	239	7	semi	semi	ADJ
ejpam-3743	239	8	-	-	ADJ
ejpam-3743	239	9	open	open	ADJ
ejpam-3743	239	10	subsets	subset	NOUN
ejpam-3743	239	11	of	of	ADP
ejpam-3743	239	12	(	(	PUNCT
ejpam-3743	239	13	n	n	X
ejpam-3743	239	14	,	,	PUNCT
ejpam-3743	239	15	µ	µ	X
ejpam-3743	239	16	)	)	PUNCT
ejpam-3743	239	17	coincides	coincide	VERB
ejpam-3743	239	18	with	with	ADP
ejpam-3743	239	19	the	the	DET
ejpam-3743	239	20	collection	collection	NOUN
ejpam-3743	239	21	of	of	ADP
ejpam-3743	239	22	supra	supra	PROPN
ejpam-3743	239	23	open	open	ADJ
ejpam-3743	239	24	sets	set	NOUN
ejpam-3743	239	25	.	.	PUNCT
ejpam-3743	240	1	it	it	PRON
ejpam-3743	240	2	is	be	AUX
ejpam-3743	240	3	clear	clear	ADJ
ejpam-3743	240	4	that	that	SCONJ
ejpam-3743	240	5	(	(	PUNCT
ejpam-3743	240	6	n	n	X
ejpam-3743	240	7	,	,	PUNCT
ejpam-3743	240	8	µ	µ	X
ejpam-3743	240	9	)	)	PUNCT
ejpam-3743	240	10	is	be	AUX
ejpam-3743	240	11	not	not	PART
ejpam-3743	240	12	an	an	DET
ejpam-3743	240	13	sst1	sst1	NOUN
ejpam-3743	240	14	-	-	PUNCT
ejpam-3743	240	15	space	space	NOUN
ejpam-3743	240	16	.	.	PUNCT
ejpam-3743	241	1	on	on	ADP
ejpam-3743	241	2	the	the	DET
ejpam-3743	241	3	other	other	ADJ
ejpam-3743	241	4	hand	hand	NOUN
ejpam-3743	241	5	,	,	PUNCT
ejpam-3743	241	6	(	(	PUNCT
ejpam-3743	241	7	n	n	X
ejpam-3743	241	8	,	,	PUNCT
ejpam-3743	241	9	µ	µ	X
ejpam-3743	241	10	)	)	PUNCT
ejpam-3743	241	11	does	do	AUX
ejpam-3743	241	12	not	not	PART
ejpam-3743	241	13	satisfy	satisfy	VERB
ejpam-3743	241	14	the	the	DET
ejpam-3743	241	15	difference	difference	NOUN
ejpam-3743	241	16	property	property	NOUN
ejpam-3743	241	17	for	for	ADP
ejpam-3743	241	18	the	the	DET
ejpam-3743	241	19	collection	collection	NOUN
ejpam-3743	241	20	of	of	ADP
ejpam-3743	241	21	supra	supra	PROPN
ejpam-3743	241	22	semi	semi	ADJ
ejpam-3743	241	23	-	-	ADJ
ejpam-3743	241	24	open	open	ADJ
ejpam-3743	241	25	sets	set	NOUN
ejpam-3743	241	26	because	because	SCONJ
ejpam-3743	241	27	{	{	PUNCT
ejpam-3743	241	28	1	1	NUM
ejpam-3743	241	29	,	,	PUNCT
ejpam-3743	241	30	2	2	NUM
ejpam-3743	241	31	,	,	PUNCT
ejpam-3743	241	32	3	3	NUM
ejpam-3743	241	33	}	}	PUNCT
ejpam-3743	241	34	is	be	AUX
ejpam-3743	241	35	a	a	DET
ejpam-3743	241	36	supra	supra	ADJ
ejpam-3743	241	37	semi	semi	ADJ
ejpam-3743	241	38	-	-	ADJ
ejpam-3743	241	39	open	open	ADJ
ejpam-3743	241	40	set	set	NOUN
ejpam-3743	241	41	,	,	PUNCT
ejpam-3743	241	42	but	but	CCONJ
ejpam-3743	241	43	{	{	PUNCT
ejpam-3743	241	44	1	1	NUM
ejpam-3743	241	45	,	,	PUNCT
ejpam-3743	241	46	2	2	NUM
ejpam-3743	241	47	,	,	PUNCT
ejpam-3743	241	48	3	3	NUM
ejpam-3743	241	49	}	}	PUNCT
ejpam-3743	241	50	\	\	NOUN
ejpam-3743	241	51	{	{	PUNCT
ejpam-3743	241	52	1	1	NUM
ejpam-3743	241	53	}	}	PUNCT
ejpam-3743	241	54	is	be	AUX
ejpam-3743	241	55	not	not	PART
ejpam-3743	241	56	supra	supra	ADJ
ejpam-3743	241	57	semi	semi	ADJ
ejpam-3743	241	58	-	-	ADJ
ejpam-3743	241	59	open	open	ADJ
ejpam-3743	241	60	.	.	PUNCT
ejpam-3743	242	1	we	we	PRON
ejpam-3743	242	2	need	need	VERB
ejpam-3743	242	3	the	the	DET
ejpam-3743	242	4	following	follow	VERB
ejpam-3743	242	5	definition	definition	NOUN
ejpam-3743	242	6	to	to	PART
ejpam-3743	242	7	obtain	obtain	VERB
ejpam-3743	242	8	the	the	DET
ejpam-3743	242	9	equivalence	equivalence	NOUN
ejpam-3743	242	10	between	between	ADP
ejpam-3743	242	11	sst0	sst0	PROPN
ejpam-3743	242	12	and	and	CCONJ
ejpam-3743	242	13	sst1	sst1	PROPN
ejpam-3743	242	14	.	.	PUNCT
ejpam-3743	243	1	definition	definition	NOUN
ejpam-3743	243	2	14	14	NUM
ejpam-3743	243	3	.	.	PUNCT
ejpam-3743	244	1	(	(	PUNCT
ejpam-3743	244	2	x,µ	x,µ	NOUN
ejpam-3743	244	3	)	)	PUNCT
ejpam-3743	244	4	is	be	AUX
ejpam-3743	244	5	is	be	AUX
ejpam-3743	244	6	called	call	VERB
ejpam-3743	244	7	a	a	DET
ejpam-3743	244	8	supra	supra	PROPN
ejpam-3743	244	9	semi	semi	ADJ
ejpam-3743	244	10	symmetric	symmetric	ADJ
ejpam-3743	244	11	space	space	NOUN
ejpam-3743	244	12	if	if	SCONJ
ejpam-3743	244	13	a	a	DET
ejpam-3743	244	14	∈	∈	PROPN
ejpam-3743	244	15	scl{b	scl{b	NOUN
ejpam-3743	244	16	}	}	PUNCT
ejpam-3743	244	17	implies	imply	VERB
ejpam-3743	244	18	that	that	SCONJ
ejpam-3743	244	19	b	b	PROPN
ejpam-3743	244	20	∈	∈	PROPN
ejpam-3743	244	21	scl{a	scl{a	PROPN
ejpam-3743	244	22	}	}	PUNCT
ejpam-3743	244	23	for	for	ADP
ejpam-3743	244	24	a	a	DET
ejpam-3743	244	25	6=	6=	NUM
ejpam-3743	244	26	b	b	PROPN
ejpam-3743	244	27	∈	∈	PROPN
ejpam-3743	244	28	x.	x.	NOUN
ejpam-3743	244	29	theorem	theorem	VERB
ejpam-3743	244	30	6	6	NUM
ejpam-3743	244	31	.	.	PUNCT
ejpam-3743	245	1	let	let	VERB
ejpam-3743	245	2	(	(	PUNCT
ejpam-3743	245	3	x,µ	x,µ	NOUN
ejpam-3743	245	4	)	)	PUNCT
ejpam-3743	245	5	be	be	VERB
ejpam-3743	245	6	a	a	DET
ejpam-3743	245	7	supra	supra	ADJ
ejpam-3743	245	8	semi	semi	ADJ
ejpam-3743	245	9	symmetric	symmetric	ADJ
ejpam-3743	245	10	space	space	NOUN
ejpam-3743	245	11	.	.	PUNCT
ejpam-3743	246	1	then	then	ADV
ejpam-3743	246	2	it	it	PRON
ejpam-3743	246	3	is	be	AUX
ejpam-3743	246	4	sst1	sst1	PROPN
ejpam-3743	246	5	iff	iff	PROPN
ejpam-3743	246	6	it	it	PRON
ejpam-3743	246	7	is	be	AUX
ejpam-3743	246	8	sst0	sst0	PROPN
ejpam-3743	246	9	.	.	PUNCT
ejpam-3743	247	1	proof	proof	NOUN
ejpam-3743	247	2	.	.	PUNCT
ejpam-3743	248	1	the	the	DET
ejpam-3743	248	2	necessary	necessary	ADJ
ejpam-3743	248	3	condition	condition	NOUN
ejpam-3743	248	4	is	be	AUX
ejpam-3743	248	5	obvious	obvious	ADJ
ejpam-3743	248	6	.	.	PUNCT
ejpam-3743	249	1	to	to	PART
ejpam-3743	249	2	prove	prove	VERB
ejpam-3743	249	3	the	the	DET
ejpam-3743	249	4	sufficient	sufficient	ADJ
ejpam-3743	249	5	condition	condition	NOUN
ejpam-3743	249	6	,	,	PUNCT
ejpam-3743	249	7	let	let	VERB
ejpam-3743	249	8	a	a	DET
ejpam-3743	249	9	6=	6=	ADP
ejpam-3743	249	10	b.	b.	PROPN
ejpam-3743	249	11	then	then	ADV
ejpam-3743	249	12	there	there	PRON
ejpam-3743	249	13	exist	exist	VERB
ejpam-3743	249	14	a	a	DET
ejpam-3743	249	15	supra	supra	NOUN
ejpam-3743	249	16	semi	semi	ADJ
ejpam-3743	249	17	-	-	ADJ
ejpam-3743	249	18	open	open	ADJ
ejpam-3743	249	19	set	set	NOUN
ejpam-3743	249	20	g	g	NOUN
ejpam-3743	249	21	containing	contain	VERB
ejpam-3743	249	22	only	only	ADV
ejpam-3743	249	23	one	one	NUM
ejpam-3743	249	24	of	of	ADP
ejpam-3743	249	25	them	they	PRON
ejpam-3743	249	26	.	.	PUNCT
ejpam-3743	250	1	say	say	VERB
ejpam-3743	250	2	,	,	PUNCT
ejpam-3743	250	3	a	a	DET
ejpam-3743	250	4	∈	∈	PROPN
ejpam-3743	250	5	g	g	NOUN
ejpam-3743	250	6	and	and	CCONJ
ejpam-3743	250	7	b	b	PROPN
ejpam-3743	250	8	6∈	6∈	PROPN
ejpam-3743	250	9	g.	g.	PROPN
ejpam-3743	250	10	therefore	therefore	ADV
ejpam-3743	250	11	a	a	DET
ejpam-3743	250	12	6∈	6∈	NOUN
ejpam-3743	250	13	scl{b	scl{b	NOUN
ejpam-3743	250	14	}	}	PUNCT
ejpam-3743	250	15	.	.	PUNCT
ejpam-3743	251	1	by	by	ADP
ejpam-3743	251	2	the	the	DET
ejpam-3743	251	3	supra	supra	PROPN
ejpam-3743	251	4	semi	semi	PROPN
ejpam-3743	251	5	symmetry	symmetry	PROPN
ejpam-3743	251	6	of	of	ADP
ejpam-3743	251	7	(	(	PUNCT
ejpam-3743	251	8	x,µ	x,µ	NOUN
ejpam-3743	251	9	)	)	PUNCT
ejpam-3743	251	10	,	,	PUNCT
ejpam-3743	251	11	we	we	PRON
ejpam-3743	251	12	have	have	VERB
ejpam-3743	251	13	b	b	NUM
ejpam-3743	251	14	6∈	6∈	PROPN
ejpam-3743	251	15	scl{a	scl{a	PRON
ejpam-3743	251	16	}	}	PUNCT
ejpam-3743	251	17	.	.	PUNCT
ejpam-3743	252	1	thus	thus	ADV
ejpam-3743	252	2	(	(	PUNCT
ejpam-3743	252	3	scl{a})c	scl{a})c	PROPN
ejpam-3743	252	4	is	be	AUX
ejpam-3743	252	5	a	a	DET
ejpam-3743	252	6	supra	supra	NOUN
ejpam-3743	252	7	semi	semi	ADJ
ejpam-3743	252	8	-	-	ADJ
ejpam-3743	252	9	open	open	ADJ
ejpam-3743	252	10	set	set	NOUN
ejpam-3743	252	11	containing	contain	VERB
ejpam-3743	252	12	b.	b.	PROPN
ejpam-3743	252	13	hence	hence	ADV
ejpam-3743	252	14	,	,	PUNCT
ejpam-3743	252	15	(	(	PUNCT
ejpam-3743	252	16	x,µ	x,µ	NOUN
ejpam-3743	252	17	)	)	PUNCT
ejpam-3743	252	18	is	be	AUX
ejpam-3743	252	19	sst1	sst1	PROPN
ejpam-3743	252	20	.	.	PUNCT
ejpam-3743	253	1	theorem	theorem	VERB
ejpam-3743	253	2	7	7	NUM
ejpam-3743	253	3	.	.	PUNCT
ejpam-3743	254	1	the	the	DET
ejpam-3743	254	2	following	follow	VERB
ejpam-3743	254	3	three	three	NUM
ejpam-3743	254	4	statements	statement	NOUN
ejpam-3743	254	5	are	be	AUX
ejpam-3743	254	6	equivalent	equivalent	ADJ
ejpam-3743	254	7	:	:	PUNCT
ejpam-3743	254	8	(	(	PUNCT
ejpam-3743	254	9	i	i	NOUN
ejpam-3743	254	10	)	)	PUNCT
ejpam-3743	254	11	(	(	PUNCT
ejpam-3743	254	12	x,µ	x,µ	NOUN
ejpam-3743	254	13	)	)	PUNCT
ejpam-3743	254	14	is	be	AUX
ejpam-3743	254	15	an	an	DET
ejpam-3743	254	16	sst2	sst2	NOUN
ejpam-3743	254	17	-	-	PUNCT
ejpam-3743	254	18	space	space	NOUN
ejpam-3743	254	19	;	;	PUNCT
ejpam-3743	254	20	(	(	PUNCT
ejpam-3743	254	21	ii	ii	NOUN
ejpam-3743	254	22	)	)	PUNCT
ejpam-3743	254	23	{	{	PUNCT
ejpam-3743	254	24	a	a	X
ejpam-3743	254	25	}	}	PUNCT
ejpam-3743	254	26	=	=	SYM
ejpam-3743	254	27	⋂	⋂	PROPN
ejpam-3743	254	28	{	{	PUNCT
ejpam-3743	254	29	fi	fi	NOUN
ejpam-3743	254	30	:	:	PUNCT
ejpam-3743	254	31	fi	fi	NOUN
ejpam-3743	254	32	is	be	AUX
ejpam-3743	254	33	a	a	DET
ejpam-3743	254	34	supra	supra	ADJ
ejpam-3743	254	35	semi	semi	ADJ
ejpam-3743	254	36	-	-	ADJ
ejpam-3743	254	37	closed	closed	ADJ
ejpam-3743	254	38	neighborhood	neighborhood	NOUN
ejpam-3743	254	39	of	of	ADP
ejpam-3743	254	40	a	a	PRON
ejpam-3743	254	41	}	}	PUNCT
ejpam-3743	254	42	for	for	ADP
ejpam-3743	254	43	each	each	DET
ejpam-3743	254	44	a	a	DET
ejpam-3743	254	45	∈	∈	PROPN
ejpam-3743	254	46	x	x	X
ejpam-3743	254	47	;	;	PUNCT
ejpam-3743	254	48	(	(	PUNCT
ejpam-3743	254	49	iii	iii	X
ejpam-3743	254	50	)	)	PUNCT
ejpam-3743	254	51	the	the	DET
ejpam-3743	254	52	diagonal	diagonal	ADJ
ejpam-3743	254	53	4	4	NUM
ejpam-3743	254	54	=	=	SYM
ejpam-3743	254	55	{	{	PUNCT
ejpam-3743	254	56	(	(	PUNCT
ejpam-3743	254	57	a	a	PRON
ejpam-3743	254	58	,	,	PUNCT
ejpam-3743	254	59	a	a	NOUN
ejpam-3743	254	60	)	)	PUNCT
ejpam-3743	254	61	:	:	PUNCT
ejpam-3743	254	62	a	a	DET
ejpam-3743	254	63	∈	∈	PROPN
ejpam-3743	254	64	x	x	PRON
ejpam-3743	254	65	}	}	PUNCT
ejpam-3743	254	66	is	be	AUX
ejpam-3743	254	67	supra	supra	ADJ
ejpam-3743	254	68	semi	semi	ADV
ejpam-3743	254	69	-	-	ADJ
ejpam-3743	254	70	closed	closed	ADJ
ejpam-3743	254	71	in	in	ADP
ejpam-3743	254	72	the	the	DET
ejpam-3743	254	73	product	product	NOUN
ejpam-3743	254	74	supra	supra	PROPN
ejpam-3743	254	75	space	space	NOUN
ejpam-3743	254	76	x	x	X
ejpam-3743	254	77	×x	×x	X
ejpam-3743	254	78	.	.	PUNCT
ejpam-3743	255	1	t.	t.	PROPN
ejpam-3743	255	2	m.	m.	PROPN
ejpam-3743	255	3	al	al	PROPN
ejpam-3743	255	4	-	-	PUNCT
ejpam-3743	255	5	shami	shami	PROPN
ejpam-3743	255	6	et	et	PROPN
ejpam-3743	255	7	al	al	PROPN
ejpam-3743	255	8	.	.	PUNCT
ejpam-3743	255	9	/	/	SYM
ejpam-3743	255	10	eur	eur	PROPN
ejpam-3743	255	11	.	.	PUNCT
ejpam-3743	256	1	j.	j.	PROPN
ejpam-3743	256	2	pure	pure	PROPN
ejpam-3743	256	3	appl	appl	PROPN
ejpam-3743	256	4	.	.	PROPN
ejpam-3743	256	5	math	math	PROPN
ejpam-3743	256	6	,	,	PUNCT
ejpam-3743	256	7	13	13	NUM
ejpam-3743	256	8	(	(	PUNCT
ejpam-3743	256	9	3	3	NUM
ejpam-3743	256	10	)	)	PUNCT
ejpam-3743	256	11	(	(	PUNCT
ejpam-3743	256	12	2020	2020	NUM
ejpam-3743	256	13	)	)	PUNCT
ejpam-3743	256	14	,	,	PUNCT
ejpam-3743	256	15	427	427	NUM
ejpam-3743	256	16	-	-	SYM
ejpam-3743	256	17	443	443	NUM
ejpam-3743	256	18	436	436	NUM
ejpam-3743	256	19	proof	proof	NOUN
ejpam-3743	256	20	.	.	PUNCT
ejpam-3743	257	1	1	1	NUM
ejpam-3743	257	2	→	→	SYM
ejpam-3743	257	3	2	2	NUM
ejpam-3743	257	4	:	:	PUNCT
ejpam-3743	257	5	consider	consider	VERB
ejpam-3743	257	6	(	(	PUNCT
ejpam-3743	257	7	x,µ	x,µ	NOUN
ejpam-3743	257	8	)	)	PUNCT
ejpam-3743	257	9	is	be	AUX
ejpam-3743	257	10	an	an	DET
ejpam-3743	257	11	sst2	sst2	NOUN
ejpam-3743	257	12	-	-	PUNCT
ejpam-3743	257	13	space	space	NOUN
ejpam-3743	257	14	.	.	PUNCT
ejpam-3743	258	1	then	then	ADV
ejpam-3743	258	2	for	for	ADP
ejpam-3743	258	3	a	a	DET
ejpam-3743	258	4	6=	6=	PROPN
ejpam-3743	258	5	b	b	PROPN
ejpam-3743	258	6	,	,	PUNCT
ejpam-3743	258	7	there	there	PRON
ejpam-3743	258	8	exist	exist	VERB
ejpam-3743	258	9	two	two	NUM
ejpam-3743	258	10	disjoint	disjoint	ADJ
ejpam-3743	258	11	supra	supra	PROPN
ejpam-3743	258	12	semi	semi	ADJ
ejpam-3743	258	13	-	-	ADJ
ejpam-3743	258	14	open	open	ADJ
ejpam-3743	258	15	sets	set	NOUN
ejpam-3743	258	16	gi	gi	VERB
ejpam-3743	258	17	and	and	CCONJ
ejpam-3743	258	18	hi	hi	INTJ
ejpam-3743	258	19	such	such	ADJ
ejpam-3743	258	20	that	that	SCONJ
ejpam-3743	258	21	a	a	DET
ejpam-3743	258	22	∈	∈	NOUN
ejpam-3743	258	23	gi	gi	NOUN
ejpam-3743	258	24	and	and	CCONJ
ejpam-3743	258	25	b	b	X
ejpam-3743	258	26	∈	∈	PROPN
ejpam-3743	258	27	hi	hi	INTJ
ejpam-3743	258	28	.	.	PUNCT
ejpam-3743	259	1	obviously	obviously	ADV
ejpam-3743	259	2	,	,	PUNCT
ejpam-3743	259	3	gi	gi	VERB
ejpam-3743	259	4	⊆	⊆	NUM
ejpam-3743	259	5	hc	hc	PROPN
ejpam-3743	259	6	i	i	PRON
ejpam-3743	259	7	.	.	PUNCT
ejpam-3743	260	1	therefore	therefore	ADV
ejpam-3743	260	2	a	a	DET
ejpam-3743	260	3	∈	∈	PROPN
ejpam-3743	260	4	scl(gi	scl(gi	NOUN
ejpam-3743	260	5	)	)	PUNCT
ejpam-3743	261	1	⊆	⊆	NUM
ejpam-3743	261	2	hc	hc	PART
ejpam-3743	261	3	i	i	NOUN
ejpam-3743	261	4	=	=	SYM
ejpam-3743	261	5	fi	fi	NOUN
ejpam-3743	261	6	.	.	PUNCT
ejpam-3743	262	1	thus	thus	ADV
ejpam-3743	262	2	,	,	PUNCT
ejpam-3743	262	3	fi	fi	NOUN
ejpam-3743	262	4	is	be	AUX
ejpam-3743	262	5	a	a	DET
ejpam-3743	262	6	supra	supra	ADJ
ejpam-3743	262	7	semi	semi	ADJ
ejpam-3743	262	8	-	-	ADJ
ejpam-3743	262	9	closed	closed	ADJ
ejpam-3743	262	10	neighborhood	neighborhood	NOUN
ejpam-3743	262	11	of	of	ADP
ejpam-3743	262	12	a	a	DET
ejpam-3743	262	13	such	such	ADJ
ejpam-3743	262	14	that	that	DET
ejpam-3743	262	15	b	b	PROPN
ejpam-3743	262	16	6∈	6∈	PROPN
ejpam-3743	262	17	fi	fi	NOUN
ejpam-3743	262	18	.	.	PUNCT
ejpam-3743	263	1	hence	hence	ADV
ejpam-3743	263	2	,	,	PUNCT
ejpam-3743	263	3	{	{	PUNCT
ejpam-3743	263	4	a	a	X
ejpam-3743	263	5	}	}	PUNCT
ejpam-3743	263	6	=	=	SYM
ejpam-3743	263	7	⋂	⋂	PROPN
ejpam-3743	263	8	{	{	PUNCT
ejpam-3743	263	9	fi	fi	NOUN
ejpam-3743	263	10	:	:	PUNCT
ejpam-3743	263	11	fi	fi	NOUN
ejpam-3743	263	12	is	be	AUX
ejpam-3743	263	13	a	a	DET
ejpam-3743	263	14	supra	supra	ADJ
ejpam-3743	263	15	semi	semi	ADJ
ejpam-3743	263	16	-	-	ADJ
ejpam-3743	263	17	closed	closed	ADJ
ejpam-3743	263	18	neighborhood	neighborhood	NOUN
ejpam-3743	263	19	of	of	ADP
ejpam-3743	263	20	a	a	PRON
ejpam-3743	263	21	}	}	PUNCT
ejpam-3743	263	22	.	.	PUNCT
ejpam-3743	264	1	2	2	NUM
ejpam-3743	264	2	→	→	SYM
ejpam-3743	264	3	1	1	NUM
ejpam-3743	264	4	:	:	PUNCT
ejpam-3743	264	5	to	to	PART
ejpam-3743	264	6	prove	prove	VERB
ejpam-3743	264	7	that	that	SCONJ
ejpam-3743	264	8	(	(	PUNCT
ejpam-3743	264	9	x,µ	x,µ	NOUN
ejpam-3743	264	10	)	)	PUNCT
ejpam-3743	264	11	is	be	AUX
ejpam-3743	264	12	an	an	DET
ejpam-3743	264	13	sst2	sst2	NOUN
ejpam-3743	264	14	-	-	PUNCT
ejpam-3743	264	15	space	space	NOUN
ejpam-3743	264	16	,	,	PUNCT
ejpam-3743	264	17	let	let	VERB
ejpam-3743	264	18	a	a	DET
ejpam-3743	264	19	6=	6=	ADP
ejpam-3743	264	20	b.	b.	PROPN
ejpam-3743	264	21	since	since	SCONJ
ejpam-3743	264	22	{	{	PUNCT
ejpam-3743	264	23	a	a	X
ejpam-3743	264	24	}	}	PUNCT
ejpam-3743	264	25	=	=	SYM
ejpam-3743	264	26	⋂	⋂	PROPN
ejpam-3743	264	27	{	{	PUNCT
ejpam-3743	264	28	fi	fi	NOUN
ejpam-3743	264	29	:	:	PUNCT
ejpam-3743	264	30	fi	fi	NOUN
ejpam-3743	264	31	is	be	AUX
ejpam-3743	264	32	a	a	DET
ejpam-3743	264	33	supra	supra	ADJ
ejpam-3743	264	34	semi	semi	ADJ
ejpam-3743	264	35	-	-	ADJ
ejpam-3743	264	36	closed	closed	ADJ
ejpam-3743	264	37	neighborhood	neighborhood	NOUN
ejpam-3743	264	38	of	of	ADP
ejpam-3743	264	39	a	a	PRON
ejpam-3743	264	40	}	}	PUNCT
ejpam-3743	264	41	,	,	PUNCT
ejpam-3743	264	42	then	then	ADV
ejpam-3743	264	43	there	there	PRON
ejpam-3743	264	44	exists	exist	VERB
ejpam-3743	264	45	a	a	DET
ejpam-3743	264	46	supra	supra	NOUN
ejpam-3743	264	47	semi	semi	ADJ
ejpam-3743	264	48	-	-	ADJ
ejpam-3743	264	49	closed	closed	ADJ
ejpam-3743	264	50	neighborhood	neighborhood	NOUN
ejpam-3743	264	51	fi0	fi0	NOUN
ejpam-3743	264	52	of	of	ADP
ejpam-3743	264	53	a	a	DET
ejpam-3743	264	54	such	such	ADJ
ejpam-3743	264	55	that	that	DET
ejpam-3743	264	56	b	b	PROPN
ejpam-3743	264	57	6∈	6∈	NOUN
ejpam-3743	264	58	fi0	fi0	ADV
ejpam-3743	264	59	.	.	PUNCT
ejpam-3743	265	1	therefore	therefore	ADV
ejpam-3743	265	2	there	there	PRON
ejpam-3743	265	3	exists	exist	VERB
ejpam-3743	265	4	a	a	DET
ejpam-3743	265	5	supra	supra	NOUN
ejpam-3743	265	6	semi	semi	ADJ
ejpam-3743	265	7	-	-	ADJ
ejpam-3743	265	8	open	open	ADJ
ejpam-3743	265	9	set	set	NOUN
ejpam-3743	265	10	g	g	NOUN
ejpam-3743	265	11	containing	contain	VERB
ejpam-3743	265	12	a	a	DET
ejpam-3743	265	13	such	such	ADJ
ejpam-3743	265	14	that	that	SCONJ
ejpam-3743	265	15	a	a	DET
ejpam-3743	265	16	∈	∈	PROPN
ejpam-3743	265	17	scl(g	scl(g	NOUN
ejpam-3743	265	18	)	)	PUNCT
ejpam-3743	265	19	⊆	⊆	NUM
ejpam-3743	265	20	fi0	fi0	NOUN
ejpam-3743	265	21	.	.	PUNCT
ejpam-3743	266	1	it	it	PRON
ejpam-3743	266	2	is	be	AUX
ejpam-3743	266	3	clear	clear	ADJ
ejpam-3743	266	4	that	that	SCONJ
ejpam-3743	266	5	(	(	PUNCT
ejpam-3743	266	6	scl(g))c	scl(g))c	PROPN
ejpam-3743	266	7	is	be	AUX
ejpam-3743	266	8	a	a	DET
ejpam-3743	266	9	supra	supra	NOUN
ejpam-3743	266	10	semi	semi	ADJ
ejpam-3743	266	11	-	-	ADJ
ejpam-3743	266	12	open	open	ADJ
ejpam-3743	266	13	set	set	NOUN
ejpam-3743	266	14	containing	contain	VERB
ejpam-3743	266	15	b	b	PROPN
ejpam-3743	266	16	and	and	CCONJ
ejpam-3743	266	17	g	g	PROPN
ejpam-3743	266	18	⋂	⋂	PROPN
ejpam-3743	266	19	(	(	PUNCT
ejpam-3743	266	20	scl(g))c	scl(g))c	PROPN
ejpam-3743	266	21	=	=	PROPN
ejpam-3743	266	22	∅.	∅.	NOUN
ejpam-3743	266	23	hence	hence	ADV
ejpam-3743	266	24	,	,	PUNCT
ejpam-3743	266	25	(	(	PUNCT
ejpam-3743	266	26	x,µ	x,µ	NOUN
ejpam-3743	266	27	)	)	PUNCT
ejpam-3743	266	28	is	be	AUX
ejpam-3743	266	29	an	an	DET
ejpam-3743	266	30	sst2	sst2	NOUN
ejpam-3743	266	31	-	-	PUNCT
ejpam-3743	266	32	space	space	NOUN
ejpam-3743	266	33	.	.	PUNCT
ejpam-3743	267	1	1→	1→	NUM
ejpam-3743	267	2	3	3	NUM
ejpam-3743	267	3	:	:	PUNCT
ejpam-3743	267	4	suppose	suppose	VERB
ejpam-3743	267	5	that	that	SCONJ
ejpam-3743	267	6	(	(	PUNCT
ejpam-3743	267	7	x,µ	x,µ	NOUN
ejpam-3743	267	8	)	)	PUNCT
ejpam-3743	267	9	is	be	AUX
ejpam-3743	267	10	sst2	sst2	ADJ
ejpam-3743	267	11	and	and	CCONJ
ejpam-3743	267	12	let	let	VERB
ejpam-3743	267	13	(	(	PUNCT
ejpam-3743	267	14	a	a	PRON
ejpam-3743	267	15	,	,	PUNCT
ejpam-3743	267	16	b	b	NOUN
ejpam-3743	267	17	)	)	PUNCT
ejpam-3743	267	18	∈	∈	PROPN
ejpam-3743	267	19	x×x−4	x×x−4	PROPN
ejpam-3743	267	20	.	.	PUNCT
ejpam-3743	268	1	then	then	ADV
ejpam-3743	268	2	a	a	DET
ejpam-3743	268	3	6=	6=	PROPN
ejpam-3743	268	4	b.	b.	PROPN
ejpam-3743	268	5	therefore	therefore	ADV
ejpam-3743	268	6	there	there	PRON
ejpam-3743	268	7	exist	exist	VERB
ejpam-3743	268	8	two	two	NUM
ejpam-3743	268	9	disjoint	disjoint	ADJ
ejpam-3743	268	10	supra	supra	PROPN
ejpam-3743	268	11	semi	semi	ADJ
ejpam-3743	268	12	-	-	ADJ
ejpam-3743	268	13	open	open	ADJ
ejpam-3743	268	14	sets	set	NOUN
ejpam-3743	268	15	g	g	NOUN
ejpam-3743	268	16	and	and	CCONJ
ejpam-3743	268	17	h	h	NOUN
ejpam-3743	268	18	containing	contain	VERB
ejpam-3743	268	19	a	a	PRON
ejpam-3743	268	20	and	and	CCONJ
ejpam-3743	268	21	b	b	NOUN
ejpam-3743	268	22	,	,	PUNCT
ejpam-3743	268	23	respectively	respectively	ADV
ejpam-3743	268	24	.	.	PUNCT
ejpam-3743	269	1	thus	thus	ADV
ejpam-3743	269	2	,	,	PUNCT
ejpam-3743	269	3	(	(	PUNCT
ejpam-3743	269	4	a	a	PRON
ejpam-3743	269	5	,	,	PUNCT
ejpam-3743	269	6	b	b	NOUN
ejpam-3743	269	7	)	)	PUNCT
ejpam-3743	269	8	∈	∈	NOUN
ejpam-3743	269	9	g×h	g×h	PROPN
ejpam-3743	269	10	⊆	⊆	NUM
ejpam-3743	269	11	x×x−4	x×x−4	NOUN
ejpam-3743	269	12	,	,	PUNCT
ejpam-3743	269	13	proving	prove	VERB
ejpam-3743	269	14	that	that	SCONJ
ejpam-3743	269	15	x×x−4	x×x−4	PROPN
ejpam-3743	269	16	is	be	AUX
ejpam-3743	269	17	a	a	DET
ejpam-3743	269	18	supra	supra	ADJ
ejpam-3743	269	19	semi	semi	ADJ
ejpam-3743	269	20	neighbourhood	neighbourhood	NOUN
ejpam-3743	269	21	of	of	ADP
ejpam-3743	269	22	any	any	PRON
ejpam-3743	269	23	of	of	ADP
ejpam-3743	269	24	its	its	PRON
ejpam-3743	269	25	points	point	NOUN
ejpam-3743	269	26	.	.	PUNCT
ejpam-3743	270	1	hence	hence	ADV
ejpam-3743	270	2	,	,	PUNCT
ejpam-3743	270	3	4	4	NUM
ejpam-3743	270	4	is	be	AUX
ejpam-3743	270	5	supra	supra	ADJ
ejpam-3743	270	6	semi	semi	ADV
ejpam-3743	270	7	-	-	ADJ
ejpam-3743	270	8	closed	closed	ADJ
ejpam-3743	270	9	.	.	PUNCT
ejpam-3743	271	1	3	3	NUM
ejpam-3743	271	2	→	→	SYM
ejpam-3743	271	3	1	1	NUM
ejpam-3743	271	4	:	:	PUNCT
ejpam-3743	271	5	suppose	suppose	VERB
ejpam-3743	271	6	that	that	SCONJ
ejpam-3743	271	7	4	4	NUM
ejpam-3743	271	8	is	be	AUX
ejpam-3743	271	9	a	a	DET
ejpam-3743	271	10	supra	supra	ADJ
ejpam-3743	271	11	semi	semi	ADJ
ejpam-3743	271	12	-	-	ADJ
ejpam-3743	271	13	closed	closed	ADJ
ejpam-3743	271	14	subset	subset	NOUN
ejpam-3743	271	15	of	of	ADP
ejpam-3743	271	16	x	x	SYM
ejpam-3743	271	17	×	×	NOUN
ejpam-3743	271	18	x	x	PUNCT
ejpam-3743	271	19	and	and	CCONJ
ejpam-3743	271	20	let	let	VERB
ejpam-3743	271	21	a	a	PRON
ejpam-3743	271	22	6=	6=	NUM
ejpam-3743	271	23	b	b	PROPN
ejpam-3743	271	24	∈	∈	PROPN
ejpam-3743	271	25	x.	x.	NOUN
ejpam-3743	272	1	then	then	ADV
ejpam-3743	272	2	x	x	SYM
ejpam-3743	272	3	×	×	NOUN
ejpam-3743	272	4	x	x	PUNCT
ejpam-3743	272	5	−	−	PROPN
ejpam-3743	272	6	4	4	NUM
ejpam-3743	272	7	is	be	AUX
ejpam-3743	272	8	a	a	DET
ejpam-3743	272	9	supra	supra	ADJ
ejpam-3743	272	10	semi	semi	ADJ
ejpam-3743	272	11	-	-	ADJ
ejpam-3743	272	12	open	open	ADJ
ejpam-3743	272	13	set	set	NOUN
ejpam-3743	272	14	containing	contain	VERB
ejpam-3743	272	15	(	(	PUNCT
ejpam-3743	272	16	a	a	DET
ejpam-3743	272	17	,	,	PUNCT
ejpam-3743	272	18	b	b	NOUN
ejpam-3743	272	19	)	)	PUNCT
ejpam-3743	272	20	.	.	PUNCT
ejpam-3743	273	1	therefore	therefore	ADV
ejpam-3743	273	2	there	there	PRON
ejpam-3743	273	3	exist	exist	VERB
ejpam-3743	273	4	two	two	NUM
ejpam-3743	273	5	supra	supra	ADJ
ejpam-3743	273	6	semi	semi	ADJ
ejpam-3743	273	7	-	-	ADJ
ejpam-3743	273	8	open	open	ADJ
ejpam-3743	273	9	subsets	subset	NOUN
ejpam-3743	273	10	g	g	PROPN
ejpam-3743	273	11	and	and	CCONJ
ejpam-3743	273	12	h	h	PROPN
ejpam-3743	273	13	of	of	ADP
ejpam-3743	273	14	(	(	PUNCT
ejpam-3743	273	15	x,µ	x,µ	NOUN
ejpam-3743	273	16	)	)	PUNCT
ejpam-3743	273	17	such	such	ADJ
ejpam-3743	273	18	that	that	SCONJ
ejpam-3743	273	19	(	(	PUNCT
ejpam-3743	273	20	a	a	PRON
ejpam-3743	273	21	,	,	PUNCT
ejpam-3743	273	22	b	b	NOUN
ejpam-3743	273	23	)	)	PUNCT
ejpam-3743	273	24	∈	∈	PROPN
ejpam-3743	274	1	g	g	ADP
ejpam-3743	274	2	×	×	PROPN
ejpam-3743	274	3	h	h	NOUN
ejpam-3743	274	4	⊆	⊆	NUM
ejpam-3743	274	5	x	x	SYM
ejpam-3743	274	6	×	×	NOUN
ejpam-3743	274	7	x	x	SYM
ejpam-3743	274	8	−	−	PROPN
ejpam-3743	274	9	4	4	NUM
ejpam-3743	274	10	.	.	PUNCT
ejpam-3743	275	1	this	this	PRON
ejpam-3743	275	2	implies	imply	VERB
ejpam-3743	275	3	that	that	SCONJ
ejpam-3743	275	4	g	g	PROPN
ejpam-3743	275	5	and	and	CCONJ
ejpam-3743	275	6	h	h	NOUN
ejpam-3743	275	7	are	be	AUX
ejpam-3743	275	8	two	two	NUM
ejpam-3743	275	9	disjoint	disjoint	ADJ
ejpam-3743	275	10	supra	supra	NOUN
ejpam-3743	275	11	semi	semi	ADJ
ejpam-3743	275	12	-	-	ADJ
ejpam-3743	275	13	open	open	ADJ
ejpam-3743	275	14	sets	set	NOUN
ejpam-3743	275	15	containing	contain	VERB
ejpam-3743	275	16	a	a	PRON
ejpam-3743	275	17	and	and	CCONJ
ejpam-3743	275	18	b	b	NOUN
ejpam-3743	275	19	,	,	PUNCT
ejpam-3743	275	20	respectively	respectively	ADV
ejpam-3743	275	21	.	.	PUNCT
ejpam-3743	276	1	hence	hence	ADV
ejpam-3743	276	2	,	,	PUNCT
ejpam-3743	276	3	(	(	PUNCT
ejpam-3743	276	4	x,µ	x,µ	NOUN
ejpam-3743	276	5	)	)	PUNCT
ejpam-3743	276	6	is	be	AUX
ejpam-3743	276	7	sst2	sst2	PROPN
ejpam-3743	276	8	.	.	PUNCT
ejpam-3743	277	1	theorem	theorem	VERB
ejpam-3743	277	2	8	8	NUM
ejpam-3743	277	3	.	.	PUNCT
ejpam-3743	278	1	the	the	DET
ejpam-3743	278	2	the	the	DET
ejpam-3743	278	3	following	following	ADJ
ejpam-3743	278	4	three	three	NUM
ejpam-3743	278	5	statements	statement	NOUN
ejpam-3743	278	6	are	be	AUX
ejpam-3743	278	7	equivalent	equivalent	ADJ
ejpam-3743	278	8	:	:	PUNCT
ejpam-3743	278	9	(	(	PUNCT
ejpam-3743	278	10	i	i	NOUN
ejpam-3743	278	11	)	)	PUNCT
ejpam-3743	278	12	(	(	PUNCT
ejpam-3743	278	13	x,µ	x,µ	NOUN
ejpam-3743	278	14	)	)	PUNCT
ejpam-3743	278	15	is	be	AUX
ejpam-3743	278	16	supra	supra	ADJ
ejpam-3743	278	17	semi	semi	ADV
ejpam-3743	278	18	regular	regular	ADJ
ejpam-3743	278	19	;	;	PUNCT
ejpam-3743	278	20	(	(	PUNCT
ejpam-3743	278	21	ii	ii	NOUN
ejpam-3743	278	22	)	)	PUNCT
ejpam-3743	278	23	for	for	ADP
ejpam-3743	278	24	each	each	DET
ejpam-3743	278	25	supra	supra	NOUN
ejpam-3743	278	26	semi	semi	ADJ
ejpam-3743	278	27	-	-	ADJ
ejpam-3743	278	28	open	open	ADJ
ejpam-3743	278	29	subset	subset	ADJ
ejpam-3743	278	30	u	u	PROPN
ejpam-3743	278	31	of	of	ADP
ejpam-3743	278	32	(	(	PUNCT
ejpam-3743	278	33	x,µ	x,µ	NOUN
ejpam-3743	278	34	)	)	PUNCT
ejpam-3743	278	35	containing	contain	VERB
ejpam-3743	278	36	a	a	PRON
ejpam-3743	278	37	,	,	PUNCT
ejpam-3743	278	38	there	there	PRON
ejpam-3743	278	39	exists	exist	VERB
ejpam-3743	278	40	a	a	DET
ejpam-3743	278	41	supra	supra	PROPN
ejpam-3743	278	42	semiopen	semiopen	PROPN
ejpam-3743	278	43	subset	subset	VERB
ejpam-3743	278	44	v	v	ADP
ejpam-3743	278	45	of	of	ADP
ejpam-3743	278	46	(	(	PUNCT
ejpam-3743	278	47	x,µ	x,µ	NOUN
ejpam-3743	278	48	)	)	PUNCT
ejpam-3743	278	49	such	such	ADJ
ejpam-3743	278	50	that	that	SCONJ
ejpam-3743	278	51	a	a	DET
ejpam-3743	278	52	∈	∈	NOUN
ejpam-3743	278	53	v	v	ADP
ejpam-3743	278	54	⊆	⊆	NUM
ejpam-3743	278	55	scl(v	scl(v	PROPN
ejpam-3743	278	56	)	)	PUNCT
ejpam-3743	278	57	⊆	⊆	NUM
ejpam-3743	278	58	u	u	NOUN
ejpam-3743	278	59	;	;	PUNCT
ejpam-3743	278	60	(	(	PUNCT
ejpam-3743	278	61	iii	iii	X
ejpam-3743	278	62	)	)	PUNCT
ejpam-3743	278	63	every	every	DET
ejpam-3743	278	64	supra	supra	NOUN
ejpam-3743	278	65	semi	semi	ADJ
ejpam-3743	278	66	-	-	ADJ
ejpam-3743	278	67	open	open	ADJ
ejpam-3743	278	68	subset	subset	ADJ
ejpam-3743	278	69	u	u	PROPN
ejpam-3743	278	70	of	of	ADP
ejpam-3743	278	71	(	(	PUNCT
ejpam-3743	278	72	x,µ	x,µ	NOUN
ejpam-3743	278	73	)	)	PUNCT
ejpam-3743	278	74	can	can	AUX
ejpam-3743	278	75	be	be	AUX
ejpam-3743	278	76	represented	represent	VERB
ejpam-3743	278	77	as	as	SCONJ
ejpam-3743	278	78	follows	follow	VERB
ejpam-3743	278	79	:	:	PUNCT
ejpam-3743	278	80	u	u	NOUN
ejpam-3743	278	81	=	=	PUNCT
ejpam-3743	278	82	⋃	⋃	NOUN
ejpam-3743	278	83	{	{	PUNCT
ejpam-3743	278	84	h	h	NOUN
ejpam-3743	278	85	:	:	PUNCT
ejpam-3743	278	86	h	h	NOUN
ejpam-3743	278	87	is	be	AUX
ejpam-3743	278	88	a	a	DET
ejpam-3743	278	89	supra	supra	ADJ
ejpam-3743	278	90	semi	semi	ADJ
ejpam-3743	278	91	-	-	ADJ
ejpam-3743	278	92	open	open	ADJ
ejpam-3743	278	93	subset	subset	NOUN
ejpam-3743	278	94	of	of	ADP
ejpam-3743	278	95	(	(	PUNCT
ejpam-3743	278	96	x,µ	x,µ	NOUN
ejpam-3743	278	97	)	)	PUNCT
ejpam-3743	278	98	and	and	CCONJ
ejpam-3743	278	99	scl(h	scl(h	PROPN
ejpam-3743	278	100	)	)	PUNCT
ejpam-3743	278	101	⊆	⊆	NUM
ejpam-3743	278	102	u	u	NOUN
ejpam-3743	278	103	}	}	PUNCT
ejpam-3743	278	104	.	.	PUNCT
ejpam-3743	279	1	proof	proof	NOUN
ejpam-3743	279	2	.	.	PUNCT
ejpam-3743	280	1	1	1	NUM
ejpam-3743	280	2	→	→	SYM
ejpam-3743	280	3	2	2	NUM
ejpam-3743	280	4	:	:	PUNCT
ejpam-3743	280	5	let	let	VERB
ejpam-3743	280	6	(	(	PUNCT
ejpam-3743	280	7	x,µ	x,µ	NOUN
ejpam-3743	280	8	)	)	PUNCT
ejpam-3743	280	9	be	be	VERB
ejpam-3743	280	10	a	a	DET
ejpam-3743	280	11	supra	supra	NOUN
ejpam-3743	280	12	semi	semi	ADJ
ejpam-3743	280	13	regular	regular	ADJ
ejpam-3743	280	14	space	space	NOUN
ejpam-3743	280	15	and	and	CCONJ
ejpam-3743	280	16	u	u	NOUN
ejpam-3743	280	17	be	be	VERB
ejpam-3743	280	18	a	a	DET
ejpam-3743	280	19	supra	supra	NOUN
ejpam-3743	280	20	semi	semi	ADJ
ejpam-3743	280	21	-	-	ADJ
ejpam-3743	280	22	open	open	ADJ
ejpam-3743	280	23	set	set	NOUN
ejpam-3743	280	24	such	such	ADJ
ejpam-3743	280	25	that	that	SCONJ
ejpam-3743	280	26	a	a	DET
ejpam-3743	280	27	∈	∈	PROPN
ejpam-3743	280	28	u	u	NOUN
ejpam-3743	280	29	.	.	PUNCT
ejpam-3743	281	1	then	then	ADV
ejpam-3743	281	2	there	there	PRON
ejpam-3743	281	3	exist	exist	VERB
ejpam-3743	281	4	disjoint	disjoint	ADJ
ejpam-3743	281	5	supra	supra	PROPN
ejpam-3743	281	6	semi	semi	ADJ
ejpam-3743	281	7	-	-	ADJ
ejpam-3743	281	8	open	open	ADJ
ejpam-3743	281	9	sets	set	NOUN
ejpam-3743	281	10	v	v	ADP
ejpam-3743	281	11	and	and	CCONJ
ejpam-3743	281	12	w	w	NOUN
ejpam-3743	281	13	containing	contain	VERB
ejpam-3743	281	14	a	a	DET
ejpam-3743	281	15	and	and	CCONJ
ejpam-3743	281	16	u	u	NOUN
ejpam-3743	281	17	c	c	NOUN
ejpam-3743	281	18	,	,	PUNCT
ejpam-3743	281	19	respectively	respectively	ADV
ejpam-3743	281	20	.	.	PUNCT
ejpam-3743	282	1	therefore	therefore	ADV
ejpam-3743	282	2	a	a	DET
ejpam-3743	282	3	∈	∈	NOUN
ejpam-3743	282	4	v	v	ADP
ejpam-3743	282	5	⊆w	⊆w	NOUN
ejpam-3743	282	6	c	c	NOUN
ejpam-3743	282	7	⊆	⊆	NUM
ejpam-3743	282	8	u	u	NOUN
ejpam-3743	282	9	.	.	PUNCT
ejpam-3743	283	1	thus	thus	ADV
ejpam-3743	283	2	a	a	DET
ejpam-3743	283	3	∈	∈	NOUN
ejpam-3743	283	4	v	v	ADP
ejpam-3743	283	5	⊆	⊆	NUM
ejpam-3743	283	6	scl(v	scl(v	PROPN
ejpam-3743	283	7	)	)	PUNCT
ejpam-3743	283	8	⊆	⊆	NUM
ejpam-3743	283	9	u	u	NOUN
ejpam-3743	283	10	.	.	PUNCT
ejpam-3743	284	1	2→	2→	NUM
ejpam-3743	284	2	3	3	NUM
ejpam-3743	284	3	:	:	PUNCT
ejpam-3743	284	4	suppose	suppose	VERB
ejpam-3743	284	5	that	that	SCONJ
ejpam-3743	284	6	u	u	PROPN
ejpam-3743	284	7	is	be	AUX
ejpam-3743	284	8	a	a	DET
ejpam-3743	284	9	supra	supra	ADJ
ejpam-3743	284	10	semi	semi	ADJ
ejpam-3743	284	11	-	-	ADJ
ejpam-3743	284	12	open	open	ADJ
ejpam-3743	284	13	set	set	NOUN
ejpam-3743	284	14	.	.	PUNCT
ejpam-3743	285	1	by	by	ADP
ejpam-3743	285	2	hypothesise	hypothesise	NOUN
ejpam-3743	285	3	,	,	PUNCT
ejpam-3743	285	4	for	for	ADP
ejpam-3743	285	5	each	each	DET
ejpam-3743	285	6	a	a	DET
ejpam-3743	285	7	∈	∈	PROPN
ejpam-3743	285	8	u	u	NOUN
ejpam-3743	285	9	,	,	PUNCT
ejpam-3743	285	10	there	there	PRON
ejpam-3743	285	11	exists	exist	VERB
ejpam-3743	285	12	a	a	DET
ejpam-3743	285	13	supra	supra	NOUN
ejpam-3743	285	14	semi	semi	ADJ
ejpam-3743	285	15	-	-	ADJ
ejpam-3743	285	16	open	open	ADJ
ejpam-3743	285	17	set	set	ADJ
ejpam-3743	285	18	h	h	NOUN
ejpam-3743	285	19	such	such	ADJ
ejpam-3743	285	20	that	that	SCONJ
ejpam-3743	285	21	a	a	DET
ejpam-3743	285	22	∈	∈	PROPN
ejpam-3743	285	23	h	h	NOUN
ejpam-3743	285	24	⊆	⊆	NUM
ejpam-3743	285	25	scl(h	scl(h	PROPN
ejpam-3743	285	26	)	)	PUNCT
ejpam-3743	285	27	⊆	⊆	NUM
ejpam-3743	285	28	u	u	NOUN
ejpam-3743	285	29	.	.	PUNCT
ejpam-3743	286	1	then	then	ADV
ejpam-3743	286	2	u	u	X
ejpam-3743	287	1	=	=	PUNCT
ejpam-3743	287	2	⋃	⋃	NOUN
ejpam-3743	287	3	{	{	PUNCT
ejpam-3743	287	4	h	h	NOUN
ejpam-3743	287	5	:	:	PUNCT
ejpam-3743	287	6	h	h	PROPN
ejpam-3743	287	7	is	be	AUX
ejpam-3743	287	8	supra	supra	ADJ
ejpam-3743	287	9	semi	semi	ADJ
ejpam-3743	287	10	-	-	ADJ
ejpam-3743	287	11	open	open	ADJ
ejpam-3743	287	12	and	and	CCONJ
ejpam-3743	287	13	scl(h	scl(h	PROPN
ejpam-3743	287	14	)	)	PUNCT
ejpam-3743	287	15	⊆	⊆	NUM
ejpam-3743	287	16	u	u	NOUN
ejpam-3743	287	17	}	}	PUNCT
ejpam-3743	287	18	.	.	PUNCT
ejpam-3743	288	1	3	3	NUM
ejpam-3743	288	2	→	→	SYM
ejpam-3743	288	3	1	1	NUM
ejpam-3743	288	4	:	:	PUNCT
ejpam-3743	288	5	let	let	VERB
ejpam-3743	288	6	f	f	PRON
ejpam-3743	288	7	be	be	AUX
ejpam-3743	288	8	a	a	DET
ejpam-3743	288	9	supra	supra	ADJ
ejpam-3743	288	10	semi	semi	ADJ
ejpam-3743	288	11	-	-	ADJ
ejpam-3743	288	12	closed	closed	ADJ
ejpam-3743	288	13	set	set	NOUN
ejpam-3743	288	14	such	such	ADJ
ejpam-3743	288	15	that	that	SCONJ
ejpam-3743	288	16	a	a	DET
ejpam-3743	288	17	6∈	6∈	NOUN
ejpam-3743	288	18	f	f	X
ejpam-3743	288	19	.	.	PUNCT
ejpam-3743	289	1	then	then	ADV
ejpam-3743	289	2	f	f	PROPN
ejpam-3743	289	3	c	c	PROPN
ejpam-3743	289	4	=	=	PUNCT
ejpam-3743	289	5	⋃	⋃	NOUN
ejpam-3743	289	6	{	{	PUNCT
ejpam-3743	289	7	h	h	NOUN
ejpam-3743	289	8	:	:	PUNCT
ejpam-3743	289	9	h	h	PROPN
ejpam-3743	289	10	is	be	AUX
ejpam-3743	289	11	supra	supra	ADJ
ejpam-3743	289	12	semi	semi	ADJ
ejpam-3743	289	13	-	-	ADJ
ejpam-3743	289	14	open	open	ADJ
ejpam-3743	289	15	and	and	CCONJ
ejpam-3743	289	16	scl(h	scl(h	PROPN
ejpam-3743	289	17	)	)	PUNCT
ejpam-3743	289	18	⊆	⊆	NUM
ejpam-3743	289	19	f	f	NOUN
ejpam-3743	289	20	c	c	NOUN
ejpam-3743	289	21	}	}	PUNCT
ejpam-3743	289	22	.	.	PUNCT
ejpam-3743	290	1	since	since	SCONJ
ejpam-3743	290	2	a	a	DET
ejpam-3743	290	3	∈	∈	PROPN
ejpam-3743	290	4	f	f	NOUN
ejpam-3743	290	5	c	c	NOUN
ejpam-3743	290	6	,	,	PUNCT
ejpam-3743	290	7	then	then	ADV
ejpam-3743	290	8	there	there	PRON
ejpam-3743	290	9	exists	exist	VERB
ejpam-3743	290	10	a	a	DET
ejpam-3743	290	11	supra	supra	NOUN
ejpam-3743	290	12	semi	semi	ADJ
ejpam-3743	290	13	-	-	ADJ
ejpam-3743	290	14	open	open	ADJ
ejpam-3743	290	15	set	set	NOUN
ejpam-3743	290	16	ha	ha	INTJ
ejpam-3743	290	17	containing	contain	VERB
ejpam-3743	290	18	a	a	DET
ejpam-3743	290	19	such	such	ADJ
ejpam-3743	290	20	that	that	DET
ejpam-3743	290	21	scl(ha	scl(ha	NOUN
ejpam-3743	290	22	)	)	PUNCT
ejpam-3743	290	23	⊆	⊆	NUM
ejpam-3743	290	24	f	f	PROPN
ejpam-3743	290	25	c.	c.	NOUN
ejpam-3743	290	26	take	take	VERB
ejpam-3743	290	27	v	v	NOUN
ejpam-3743	290	28	=	=	SYM
ejpam-3743	290	29	(	(	PUNCT
ejpam-3743	290	30	scl(ha	scl(ha	X
ejpam-3743	290	31	)	)	PUNCT
ejpam-3743	290	32	)	)	PUNCT
ejpam-3743	291	1	c.	c.	NOUN
ejpam-3743	291	2	then	then	ADV
ejpam-3743	291	3	v	v	NOUN
ejpam-3743	291	4	is	be	AUX
ejpam-3743	291	5	a	a	DET
ejpam-3743	291	6	supra	supra	ADJ
ejpam-3743	291	7	semi	semi	ADJ
ejpam-3743	291	8	-	-	ADJ
ejpam-3743	291	9	open	open	ADJ
ejpam-3743	291	10	set	set	NOUN
ejpam-3743	291	11	containing	contain	VERB
ejpam-3743	291	12	f	f	PROPN
ejpam-3743	291	13	and	and	CCONJ
ejpam-3743	291	14	v	v	ADP
ejpam-3743	291	15	⋂	⋂	PROPN
ejpam-3743	291	16	ha	ha	INTJ
ejpam-3743	291	17	=	=	PUNCT
ejpam-3743	291	18	∅.	∅.	NOUN
ejpam-3743	291	19	this	this	PRON
ejpam-3743	291	20	completes	complete	VERB
ejpam-3743	291	21	the	the	DET
ejpam-3743	291	22	proof	proof	NOUN
ejpam-3743	291	23	.	.	PUNCT
ejpam-3743	292	1	theorem	theorem	ADJ
ejpam-3743	292	2	9	9	NUM
ejpam-3743	292	3	.	.	X
ejpam-3743	293	1	consider	consider	VERB
ejpam-3743	293	2	(	(	PUNCT
ejpam-3743	293	3	x,µ	x,µ	NOUN
ejpam-3743	293	4	)	)	PUNCT
ejpam-3743	293	5	is	be	AUX
ejpam-3743	293	6	a	a	DET
ejpam-3743	293	7	supra	supra	NOUN
ejpam-3743	293	8	semi	semi	ADJ
ejpam-3743	293	9	regular	regular	ADJ
ejpam-3743	293	10	space	space	NOUN
ejpam-3743	293	11	.	.	PUNCT
ejpam-3743	294	1	then	then	ADV
ejpam-3743	294	2	the	the	DET
ejpam-3743	294	3	following	follow	VERB
ejpam-3743	294	4	concepts	concept	NOUN
ejpam-3743	294	5	are	be	AUX
ejpam-3743	294	6	equivalent	equivalent	ADJ
ejpam-3743	294	7	:	:	PUNCT
ejpam-3743	294	8	(	(	PUNCT
ejpam-3743	294	9	i	i	NOUN
ejpam-3743	294	10	)	)	PUNCT
ejpam-3743	294	11	(	(	PUNCT
ejpam-3743	294	12	x,µ	x,µ	NOUN
ejpam-3743	294	13	)	)	PUNCT
ejpam-3743	294	14	is	be	AUX
ejpam-3743	294	15	an	an	DET
ejpam-3743	294	16	sst2	sst2	NOUN
ejpam-3743	294	17	-	-	PUNCT
ejpam-3743	294	18	space	space	NOUN
ejpam-3743	294	19	;	;	PUNCT
ejpam-3743	294	20	t.	t.	PROPN
ejpam-3743	294	21	m.	m.	PROPN
ejpam-3743	294	22	al	al	PROPN
ejpam-3743	294	23	-	-	PUNCT
ejpam-3743	294	24	shami	shami	PROPN
ejpam-3743	294	25	et	et	PROPN
ejpam-3743	294	26	al	al	PROPN
ejpam-3743	294	27	.	.	PUNCT
ejpam-3743	294	28	/	/	SYM
ejpam-3743	294	29	eur	eur	PROPN
ejpam-3743	294	30	.	.	PUNCT
ejpam-3743	295	1	j.	j.	PROPN
ejpam-3743	295	2	pure	pure	PROPN
ejpam-3743	295	3	appl	appl	PROPN
ejpam-3743	295	4	.	.	PROPN
ejpam-3743	295	5	math	math	PROPN
ejpam-3743	295	6	,	,	PUNCT
ejpam-3743	295	7	13	13	NUM
ejpam-3743	295	8	(	(	PUNCT
ejpam-3743	295	9	3	3	NUM
ejpam-3743	295	10	)	)	PUNCT
ejpam-3743	295	11	(	(	PUNCT
ejpam-3743	295	12	2020	2020	NUM
ejpam-3743	295	13	)	)	PUNCT
ejpam-3743	295	14	,	,	PUNCT
ejpam-3743	295	15	427	427	NUM
ejpam-3743	295	16	-	-	SYM
ejpam-3743	295	17	443	443	NUM
ejpam-3743	295	18	437	437	NUM
ejpam-3743	295	19	(	(	PUNCT
ejpam-3743	295	20	ii	ii	NOUN
ejpam-3743	295	21	)	)	PUNCT
ejpam-3743	295	22	(	(	PUNCT
ejpam-3743	295	23	x,µ	x,µ	NOUN
ejpam-3743	295	24	)	)	PUNCT
ejpam-3743	295	25	is	be	AUX
ejpam-3743	295	26	an	an	DET
ejpam-3743	295	27	sst1	sst1	NOUN
ejpam-3743	295	28	-	-	PUNCT
ejpam-3743	295	29	space	space	NOUN
ejpam-3743	295	30	;	;	PUNCT
ejpam-3743	295	31	(	(	PUNCT
ejpam-3743	295	32	iii	iii	X
ejpam-3743	295	33	)	)	PUNCT
ejpam-3743	295	34	(	(	PUNCT
ejpam-3743	295	35	x,µ	x,µ	NOUN
ejpam-3743	295	36	)	)	PUNCT
ejpam-3743	295	37	is	be	AUX
ejpam-3743	295	38	an	an	DET
ejpam-3743	295	39	sst0	sst0	NOUN
ejpam-3743	295	40	-	-	PUNCT
ejpam-3743	295	41	space	space	NOUN
ejpam-3743	295	42	.	.	PUNCT
ejpam-3743	296	1	proof	proof	NOUN
ejpam-3743	296	2	.	.	PUNCT
ejpam-3743	297	1	the	the	DET
ejpam-3743	297	2	implications	implication	NOUN
ejpam-3743	297	3	1→	1→	NUM
ejpam-3743	297	4	2→	2→	NUM
ejpam-3743	297	5	3	3	NUM
ejpam-3743	297	6	are	be	AUX
ejpam-3743	297	7	obvious	obvious	ADJ
ejpam-3743	297	8	.	.	PUNCT
ejpam-3743	298	1	3	3	NUM
ejpam-3743	298	2	→	→	SYM
ejpam-3743	298	3	1	1	NUM
ejpam-3743	298	4	:	:	PUNCT
ejpam-3743	298	5	let	let	VERB
ejpam-3743	298	6	a	a	DET
ejpam-3743	298	7	,	,	PUNCT
ejpam-3743	298	8	b	b	X
ejpam-3743	298	9	∈	∈	PROPN
ejpam-3743	298	10	x	x	PUNCT
ejpam-3743	298	11	such	such	ADJ
ejpam-3743	298	12	that	that	SCONJ
ejpam-3743	298	13	a	a	DET
ejpam-3743	298	14	6=	6=	ADP
ejpam-3743	298	15	b.	b.	PROPN
ejpam-3743	298	16	since	since	SCONJ
ejpam-3743	298	17	(	(	PUNCT
ejpam-3743	298	18	x,µ	x,µ	NOUN
ejpam-3743	298	19	)	)	PUNCT
ejpam-3743	298	20	is	be	AUX
ejpam-3743	298	21	an	an	DET
ejpam-3743	298	22	sst0	sst0	NOUN
ejpam-3743	298	23	-	-	PUNCT
ejpam-3743	298	24	space	space	NOUN
ejpam-3743	298	25	,	,	PUNCT
ejpam-3743	298	26	then	then	ADV
ejpam-3743	298	27	from	from	ADP
ejpam-3743	298	28	theorem	theorem	NOUN
ejpam-3743	298	29	(	(	PUNCT
ejpam-3743	298	30	4	4	NUM
ejpam-3743	298	31	)	)	PUNCT
ejpam-3743	298	32	,	,	PUNCT
ejpam-3743	298	33	we	we	PRON
ejpam-3743	298	34	get	get	VERB
ejpam-3743	298	35	scl{a	scl{a	PRON
ejpam-3743	298	36	}	}	PUNCT
ejpam-3743	298	37	6=	6=	NOUN
ejpam-3743	298	38	scl{b	scl{b	NOUN
ejpam-3743	298	39	}	}	PUNCT
ejpam-3743	298	40	.	.	PUNCT
ejpam-3743	299	1	therefore	therefore	ADV
ejpam-3743	299	2	a	a	DET
ejpam-3743	299	3	6∈	6∈	NOUN
ejpam-3743	299	4	scl{b	scl{b	NOUN
ejpam-3743	299	5	}	}	PUNCT
ejpam-3743	299	6	or	or	CCONJ
ejpam-3743	299	7	b	b	X
ejpam-3743	299	8	6∈	6∈	NOUN
ejpam-3743	299	9	scl{a	scl{a	PROPN
ejpam-3743	299	10	}	}	PUNCT
ejpam-3743	299	11	.	.	PUNCT
ejpam-3743	300	1	say	say	VERB
ejpam-3743	300	2	,	,	PUNCT
ejpam-3743	300	3	a	a	DET
ejpam-3743	300	4	6∈	6∈	NOUN
ejpam-3743	300	5	scl{b	scl{b	NOUN
ejpam-3743	300	6	}	}	PUNCT
ejpam-3743	300	7	.	.	PUNCT
ejpam-3743	301	1	since	since	SCONJ
ejpam-3743	301	2	(	(	PUNCT
ejpam-3743	301	3	x,µ	x,µ	NOUN
ejpam-3743	301	4	)	)	PUNCT
ejpam-3743	301	5	is	be	AUX
ejpam-3743	301	6	supra	supra	ADJ
ejpam-3743	301	7	semi	semi	ADV
ejpam-3743	301	8	regular	regular	ADJ
ejpam-3743	301	9	,	,	PUNCT
ejpam-3743	301	10	then	then	ADV
ejpam-3743	301	11	there	there	PRON
ejpam-3743	301	12	exist	exist	VERB
ejpam-3743	301	13	disjoint	disjoint	ADJ
ejpam-3743	301	14	supra	supra	PROPN
ejpam-3743	301	15	semi	semi	ADJ
ejpam-3743	301	16	-	-	ADJ
ejpam-3743	301	17	open	open	ADJ
ejpam-3743	301	18	sets	set	NOUN
ejpam-3743	301	19	g	g	NOUN
ejpam-3743	301	20	and	and	CCONJ
ejpam-3743	301	21	h	h	NOUN
ejpam-3743	301	22	containing	contain	VERB
ejpam-3743	301	23	a	a	DET
ejpam-3743	301	24	and	and	CCONJ
ejpam-3743	301	25	scl{b	scl{b	NOUN
ejpam-3743	301	26	}	}	PUNCT
ejpam-3743	301	27	,	,	PUNCT
ejpam-3743	301	28	respectively	respectively	ADV
ejpam-3743	301	29	.	.	PUNCT
ejpam-3743	302	1	thus	thus	ADV
ejpam-3743	302	2	(	(	PUNCT
ejpam-3743	302	3	x,µ	x,µ	NOUN
ejpam-3743	302	4	)	)	PUNCT
ejpam-3743	302	5	is	be	AUX
ejpam-3743	302	6	an	an	DET
ejpam-3743	302	7	sst2	sst2	NOUN
ejpam-3743	302	8	-	-	PUNCT
ejpam-3743	302	9	space	space	NOUN
ejpam-3743	302	10	.	.	PUNCT
ejpam-3743	303	1	theorem	theorem	ADJ
ejpam-3743	303	2	10	10	NUM
ejpam-3743	303	3	.	.	PUNCT
ejpam-3743	304	1	the	the	DET
ejpam-3743	304	2	following	follow	VERB
ejpam-3743	304	3	statements	statement	NOUN
ejpam-3743	304	4	are	be	AUX
ejpam-3743	304	5	equivalent	equivalent	ADJ
ejpam-3743	304	6	:	:	PUNCT
ejpam-3743	304	7	(	(	PUNCT
ejpam-3743	304	8	i	i	NOUN
ejpam-3743	304	9	)	)	PUNCT
ejpam-3743	304	10	(	(	PUNCT
ejpam-3743	304	11	x,µ	x,µ	NOUN
ejpam-3743	304	12	)	)	PUNCT
ejpam-3743	304	13	is	be	AUX
ejpam-3743	304	14	supra	supra	ADJ
ejpam-3743	304	15	semi	semi	ADV
ejpam-3743	304	16	normal	normal	ADJ
ejpam-3743	304	17	;	;	PUNCT
ejpam-3743	304	18	(	(	PUNCT
ejpam-3743	304	19	ii	ii	NOUN
ejpam-3743	304	20	)	)	PUNCT
ejpam-3743	304	21	for	for	ADP
ejpam-3743	304	22	each	each	DET
ejpam-3743	304	23	supra	supra	PROPN
ejpam-3743	304	24	semi	semi	ADJ
ejpam-3743	304	25	-	-	ADJ
ejpam-3743	304	26	closed	closed	ADJ
ejpam-3743	304	27	set	set	VERB
ejpam-3743	304	28	f	f	NOUN
ejpam-3743	304	29	and	and	CCONJ
ejpam-3743	304	30	each	each	DET
ejpam-3743	304	31	supra	supra	PROPN
ejpam-3743	304	32	semi	semi	ADJ
ejpam-3743	304	33	-	-	ADJ
ejpam-3743	304	34	open	open	ADJ
ejpam-3743	304	35	set	set	NOUN
ejpam-3743	304	36	u	u	NOUN
ejpam-3743	304	37	containing	contain	VERB
ejpam-3743	304	38	f	f	NOUN
ejpam-3743	304	39	,	,	PUNCT
ejpam-3743	304	40	there	there	PRON
ejpam-3743	304	41	exists	exist	VERB
ejpam-3743	304	42	a	a	DET
ejpam-3743	304	43	supra	supra	NOUN
ejpam-3743	304	44	semi	semi	ADJ
ejpam-3743	304	45	-	-	ADJ
ejpam-3743	304	46	open	open	ADJ
ejpam-3743	304	47	set	set	VERB
ejpam-3743	304	48	v	v	ADP
ejpam-3743	304	49	such	such	ADJ
ejpam-3743	304	50	that	that	SCONJ
ejpam-3743	304	51	f	f	PROPN
ejpam-3743	305	1	⊆	⊆	NUM
ejpam-3743	305	2	v	v	ADP
ejpam-3743	305	3	⊆	⊆	NUM
ejpam-3743	305	4	scl(v	scl(v	NUM
ejpam-3743	305	5	)	)	PUNCT
ejpam-3743	305	6	⊆	⊆	NUM
ejpam-3743	305	7	u	u	NOUN
ejpam-3743	305	8	;	;	PUNCT
ejpam-3743	305	9	(	(	PUNCT
ejpam-3743	305	10	iii	iii	NOUN
ejpam-3743	305	11	)	)	PUNCT
ejpam-3743	305	12	for	for	ADP
ejpam-3743	305	13	every	every	DET
ejpam-3743	305	14	supra	supra	NOUN
ejpam-3743	305	15	semi	semi	ADJ
ejpam-3743	305	16	-	-	ADJ
ejpam-3743	305	17	open	open	ADJ
ejpam-3743	305	18	sets	set	NOUN
ejpam-3743	305	19	u	u	NOUN
ejpam-3743	305	20	and	and	CCONJ
ejpam-3743	305	21	v	v	ADP
ejpam-3743	305	22	such	such	ADJ
ejpam-3743	305	23	that	that	DET
ejpam-3743	305	24	u	u	NOUN
ejpam-3743	305	25	⋃	⋃	NOUN
ejpam-3743	305	26	v	v	NOUN
ejpam-3743	305	27	=	=	SYM
ejpam-3743	305	28	x	x	NOUN
ejpam-3743	305	29	,	,	PUNCT
ejpam-3743	305	30	there	there	PRON
ejpam-3743	305	31	are	be	VERB
ejpam-3743	305	32	two	two	NUM
ejpam-3743	305	33	supra	supra	ADJ
ejpam-3743	305	34	semi	semi	ADJ
ejpam-3743	305	35	-	-	ADJ
ejpam-3743	305	36	closed	closed	ADJ
ejpam-3743	305	37	sets	set	NOUN
ejpam-3743	305	38	f	f	PROPN
ejpam-3743	305	39	and	and	CCONJ
ejpam-3743	305	40	h	h	PROPN
ejpam-3743	305	41	contained	contain	VERB
ejpam-3743	305	42	in	in	ADP
ejpam-3743	305	43	u	u	NOUN
ejpam-3743	305	44	and	and	CCONJ
ejpam-3743	305	45	v	v	NOUN
ejpam-3743	305	46	,	,	PUNCT
ejpam-3743	305	47	respectively	respectively	ADV
ejpam-3743	305	48	,	,	PUNCT
ejpam-3743	305	49	such	such	ADJ
ejpam-3743	305	50	that	that	SCONJ
ejpam-3743	305	51	f	f	PROPN
ejpam-3743	305	52	⋃	⋃	NOUN
ejpam-3743	305	53	h	h	NOUN
ejpam-3743	305	54	=	=	PUNCT
ejpam-3743	305	55	x.	x.	NOUN
ejpam-3743	305	56	proof	proof	NOUN
ejpam-3743	305	57	.	.	PUNCT
ejpam-3743	306	1	1	1	NUM
ejpam-3743	306	2	→	→	SYM
ejpam-3743	306	3	2	2	NUM
ejpam-3743	306	4	:	:	PUNCT
ejpam-3743	306	5	consider	consider	VERB
ejpam-3743	306	6	(	(	PUNCT
ejpam-3743	306	7	x,µ	x,µ	NOUN
ejpam-3743	306	8	)	)	PUNCT
ejpam-3743	306	9	is	be	AUX
ejpam-3743	306	10	supra	supra	ADJ
ejpam-3743	306	11	semi	semi	ADV
ejpam-3743	306	12	normal	normal	ADJ
ejpam-3743	306	13	and	and	CCONJ
ejpam-3743	306	14	f	f	PROPN
ejpam-3743	306	15	is	be	AUX
ejpam-3743	306	16	a	a	DET
ejpam-3743	306	17	supra	supra	ADJ
ejpam-3743	306	18	semi	semi	ADJ
ejpam-3743	306	19	-	-	ADJ
ejpam-3743	306	20	closed	closed	ADJ
ejpam-3743	306	21	subset	subset	NOUN
ejpam-3743	306	22	of	of	ADP
ejpam-3743	306	23	a	a	DET
ejpam-3743	306	24	supra	supra	NOUN
ejpam-3743	306	25	semi	semi	ADJ
ejpam-3743	306	26	-	-	ADJ
ejpam-3743	306	27	open	open	ADJ
ejpam-3743	306	28	set	set	NOUN
ejpam-3743	306	29	u	u	NOUN
ejpam-3743	306	30	.	.	PUNCT
ejpam-3743	307	1	then	then	ADV
ejpam-3743	307	2	u	u	PROPN
ejpam-3743	307	3	c	c	PROPN
ejpam-3743	307	4	and	and	CCONJ
ejpam-3743	307	5	f	f	PROPN
ejpam-3743	307	6	are	be	AUX
ejpam-3743	307	7	disjoint	disjoint	PROPN
ejpam-3743	307	8	supra	supra	PROPN
ejpam-3743	307	9	semi	semi	ADJ
ejpam-3743	307	10	-	-	ADJ
ejpam-3743	307	11	closed	closed	ADJ
ejpam-3743	307	12	sets	set	NOUN
ejpam-3743	307	13	.	.	PUNCT
ejpam-3743	308	1	therefor	therefor	ADP
ejpam-3743	308	2	there	there	PRON
ejpam-3743	308	3	exist	exist	VERB
ejpam-3743	308	4	two	two	NUM
ejpam-3743	308	5	disjoint	disjoint	ADJ
ejpam-3743	308	6	supra	supra	PROPN
ejpam-3743	308	7	semi	semi	ADJ
ejpam-3743	308	8	-	-	ADJ
ejpam-3743	308	9	open	open	ADJ
ejpam-3743	308	10	sets	set	NOUN
ejpam-3743	308	11	w	w	VERB
ejpam-3743	308	12	and	and	CCONJ
ejpam-3743	308	13	v	v	ADP
ejpam-3743	308	14	containing	contain	VERB
ejpam-3743	308	15	u	u	PROPN
ejpam-3743	308	16	c	c	PROPN
ejpam-3743	308	17	and	and	CCONJ
ejpam-3743	308	18	f	f	PROPN
ejpam-3743	308	19	,	,	PUNCT
ejpam-3743	308	20	respectively	respectively	ADV
ejpam-3743	308	21	.	.	PUNCT
ejpam-3743	309	1	thus	thus	ADV
ejpam-3743	309	2	f	f	PROPN
ejpam-3743	309	3	⊆	⊆	NUM
ejpam-3743	309	4	v	v	ADP
ejpam-3743	309	5	⊆w	⊆w	NOUN
ejpam-3743	309	6	c	c	NOUN
ejpam-3743	309	7	=	=	SYM
ejpam-3743	309	8	scl(w	scl(w	PROPN
ejpam-3743	309	9	c	c	NOUN
ejpam-3743	309	10	)	)	PUNCT
ejpam-3743	309	11	⊆	⊆	NUM
ejpam-3743	309	12	u	u	NOUN
ejpam-3743	309	13	.	.	PUNCT
ejpam-3743	310	1	hence	hence	ADV
ejpam-3743	310	2	,	,	PUNCT
ejpam-3743	310	3	f	f	PROPN
ejpam-3743	310	4	⊆	⊆	NUM
ejpam-3743	310	5	v	v	ADP
ejpam-3743	310	6	⊆	⊆	NUM
ejpam-3743	310	7	scl(v	scl(v	PROPN
ejpam-3743	310	8	)	)	PUNCT
ejpam-3743	310	9	⊆	⊆	NUM
ejpam-3743	310	10	u	u	NOUN
ejpam-3743	310	11	.	.	PUNCT
ejpam-3743	311	1	2→	2→	NUM
ejpam-3743	311	2	3	3	NUM
ejpam-3743	311	3	:	:	PUNCT
ejpam-3743	311	4	consider	consider	VERB
ejpam-3743	311	5	u	u	NOUN
ejpam-3743	311	6	and	and	CCONJ
ejpam-3743	311	7	v	v	NOUN
ejpam-3743	311	8	are	be	AUX
ejpam-3743	311	9	supra	supra	ADJ
ejpam-3743	311	10	semi	semi	ADJ
ejpam-3743	311	11	-	-	ADJ
ejpam-3743	311	12	open	open	ADJ
ejpam-3743	311	13	sets	set	NOUN
ejpam-3743	311	14	such	such	ADJ
ejpam-3743	311	15	that	that	DET
ejpam-3743	311	16	u	u	NOUN
ejpam-3743	311	17	⋃	⋃	NOUN
ejpam-3743	311	18	v	v	NOUN
ejpam-3743	311	19	=	=	PUNCT
ejpam-3743	311	20	x.	x.	NOUN
ejpam-3743	311	21	then	then	ADV
ejpam-3743	311	22	u	u	X
ejpam-3743	311	23	c	c	PROPN
ejpam-3743	311	24	is	be	AUX
ejpam-3743	311	25	a	a	DET
ejpam-3743	311	26	supra	supra	ADJ
ejpam-3743	311	27	semi	semi	ADJ
ejpam-3743	311	28	-	-	ADJ
ejpam-3743	311	29	closed	closed	ADJ
ejpam-3743	311	30	sets	set	NOUN
ejpam-3743	311	31	such	such	ADJ
ejpam-3743	311	32	that	that	DET
ejpam-3743	311	33	u	u	NOUN
ejpam-3743	311	34	c	c	PROPN
ejpam-3743	311	35	⊆	⊆	NUM
ejpam-3743	311	36	v	v	NOUN
ejpam-3743	311	37	.	.	PUNCT
ejpam-3743	312	1	by	by	ADP
ejpam-3743	312	2	2	2	NUM
ejpam-3743	312	3	,	,	PUNCT
ejpam-3743	312	4	there	there	PRON
ejpam-3743	312	5	is	be	VERB
ejpam-3743	312	6	a	a	DET
ejpam-3743	312	7	supra	supra	ADJ
ejpam-3743	312	8	semi	semi	ADJ
ejpam-3743	312	9	-	-	ADJ
ejpam-3743	312	10	open	open	ADJ
ejpam-3743	312	11	set	set	NOUN
ejpam-3743	312	12	g	g	PROPN
ejpam-3743	312	13	such	such	ADJ
ejpam-3743	312	14	that	that	DET
ejpam-3743	312	15	u	u	NOUN
ejpam-3743	312	16	c	c	PROPN
ejpam-3743	312	17	⊆	⊆	NUM
ejpam-3743	312	18	g	g	NOUN
ejpam-3743	312	19	⊆	⊆	NUM
ejpam-3743	312	20	scl(g	scl(g	NOUN
ejpam-3743	312	21	)	)	PUNCT
ejpam-3743	312	22	⊆	⊆	NUM
ejpam-3743	312	23	v	v	NOUN
ejpam-3743	312	24	.	.	PUNCT
ejpam-3743	313	1	thus	thus	ADV
ejpam-3743	313	2	gc	gc	PROPN
ejpam-3743	313	3	⊆	⊆	NUM
ejpam-3743	313	4	u	u	NOUN
ejpam-3743	313	5	and	and	CCONJ
ejpam-3743	313	6	scl(g	scl(g	PROPN
ejpam-3743	313	7	)	)	PUNCT
ejpam-3743	313	8	⊆	⊆	NUM
ejpam-3743	313	9	v	v	NOUN
ejpam-3743	313	10	are	be	AUX
ejpam-3743	313	11	supra	supra	ADJ
ejpam-3743	313	12	semi	semi	ADJ
ejpam-3743	313	13	-	-	ADJ
ejpam-3743	313	14	closed	closed	ADJ
ejpam-3743	313	15	sets	set	NOUN
ejpam-3743	313	16	such	such	ADJ
ejpam-3743	313	17	that	that	DET
ejpam-3743	313	18	gc	gc	PROPN
ejpam-3743	313	19	⋃	⋃	PROPN
ejpam-3743	313	20	scl(g	scl(g	NOUN
ejpam-3743	313	21	)	)	PUNCT
ejpam-3743	313	22	=	=	PUNCT
ejpam-3743	313	23	x.	x.	NOUN
ejpam-3743	313	24	3	3	NUM
ejpam-3743	313	25	→	→	SYM
ejpam-3743	313	26	1	1	NUM
ejpam-3743	313	27	:	:	PUNCT
ejpam-3743	313	28	consider	consider	VERB
ejpam-3743	313	29	f	f	PROPN
ejpam-3743	313	30	and	and	CCONJ
ejpam-3743	313	31	h	h	PROPN
ejpam-3743	313	32	are	be	AUX
ejpam-3743	313	33	disjoint	disjoint	ADJ
ejpam-3743	313	34	supra	supra	PROPN
ejpam-3743	313	35	semi	semi	ADJ
ejpam-3743	313	36	-	-	ADJ
ejpam-3743	313	37	closed	closed	ADJ
ejpam-3743	313	38	sets	set	NOUN
ejpam-3743	313	39	.	.	PUNCT
ejpam-3743	314	1	since	since	SCONJ
ejpam-3743	314	2	f	f	PROPN
ejpam-3743	314	3	c	c	PROPN
ejpam-3743	314	4	and	and	CCONJ
ejpam-3743	314	5	hc	hc	PROPN
ejpam-3743	314	6	are	be	AUX
ejpam-3743	314	7	supra	supra	ADJ
ejpam-3743	314	8	open	open	ADJ
ejpam-3743	314	9	sets	set	NOUN
ejpam-3743	314	10	such	such	ADJ
ejpam-3743	314	11	that	that	SCONJ
ejpam-3743	314	12	f	f	PROPN
ejpam-3743	314	13	c	c	PROPN
ejpam-3743	314	14	⋃	⋃	NOUN
ejpam-3743	314	15	hc	hc	NOUN
ejpam-3743	314	16	=	=	SYM
ejpam-3743	314	17	x	x	NOUN
ejpam-3743	314	18	,	,	PUNCT
ejpam-3743	314	19	then	then	ADV
ejpam-3743	314	20	there	there	PRON
ejpam-3743	314	21	are	be	VERB
ejpam-3743	314	22	two	two	NUM
ejpam-3743	314	23	supra	supra	ADJ
ejpam-3743	314	24	semi	semi	ADJ
ejpam-3743	314	25	-	-	ADJ
ejpam-3743	314	26	closed	closed	ADJ
ejpam-3743	314	27	sets	set	NOUN
ejpam-3743	314	28	m	m	VERB
ejpam-3743	314	29	and	and	CCONJ
ejpam-3743	314	30	n	n	CCONJ
ejpam-3743	314	31	such	such	ADJ
ejpam-3743	314	32	that	that	SCONJ
ejpam-3743	314	33	m	m	PROPN
ejpam-3743	314	34	⊆	⊆	NUM
ejpam-3743	314	35	f	f	PROPN
ejpam-3743	314	36	c	c	NOUN
ejpam-3743	314	37	,	,	PUNCT
ejpam-3743	314	38	n	n	PROPN
ejpam-3743	314	39	⊆	⊆	NUM
ejpam-3743	314	40	hc	hc	NOUN
ejpam-3743	314	41	and	and	CCONJ
ejpam-3743	314	42	m	m	PROPN
ejpam-3743	314	43	⋃	⋃	NOUN
ejpam-3743	314	44	n	n	NOUN
ejpam-3743	314	45	=	=	PUNCT
ejpam-3743	314	46	x.	x.	NOUN
ejpam-3743	315	1	thus	thus	ADV
ejpam-3743	315	2	m	m	PROPN
ejpam-3743	315	3	c	c	NOUN
ejpam-3743	315	4	and	and	CCONJ
ejpam-3743	315	5	n	n	PROPN
ejpam-3743	315	6	c	c	NOUN
ejpam-3743	315	7	are	be	AUX
ejpam-3743	315	8	two	two	NUM
ejpam-3743	315	9	disjoint	disjoint	ADJ
ejpam-3743	315	10	supra	supra	NOUN
ejpam-3743	315	11	semi	semi	ADJ
ejpam-3743	315	12	-	-	ADJ
ejpam-3743	315	13	open	open	ADJ
ejpam-3743	315	14	sets	set	NOUN
ejpam-3743	315	15	containing	contain	VERB
ejpam-3743	315	16	f	f	PROPN
ejpam-3743	315	17	and	and	CCONJ
ejpam-3743	315	18	h	h	NOUN
ejpam-3743	315	19	,	,	PUNCT
ejpam-3743	315	20	respectively	respectively	ADV
ejpam-3743	315	21	.	.	PUNCT
ejpam-3743	316	1	hence	hence	ADV
ejpam-3743	316	2	,	,	PUNCT
ejpam-3743	316	3	(	(	PUNCT
ejpam-3743	316	4	x,µ	x,µ	NOUN
ejpam-3743	316	5	)	)	PUNCT
ejpam-3743	316	6	is	be	AUX
ejpam-3743	316	7	supra	supra	ADJ
ejpam-3743	316	8	semi	semi	ADV
ejpam-3743	316	9	normal	normal	ADJ
ejpam-3743	316	10	.	.	PUNCT
ejpam-3743	317	1	now	now	ADV
ejpam-3743	317	2	,	,	PUNCT
ejpam-3743	317	3	we	we	PRON
ejpam-3743	317	4	show	show	VERB
ejpam-3743	317	5	the	the	DET
ejpam-3743	317	6	implications	implication	NOUN
ejpam-3743	317	7	of	of	ADP
ejpam-3743	317	8	these	these	DET
ejpam-3743	317	9	separation	separation	NOUN
ejpam-3743	317	10	axioms	axiom	NOUN
ejpam-3743	317	11	among	among	ADP
ejpam-3743	317	12	themselves	themselves	PRON
ejpam-3743	317	13	as	as	ADV
ejpam-3743	317	14	well	well	ADV
ejpam-3743	317	15	as	as	ADP
ejpam-3743	317	16	with	with	ADP
ejpam-3743	317	17	sti	sti	NOUN
ejpam-3743	317	18	-	-	NOUN
ejpam-3743	317	19	space	space	NOUN
ejpam-3743	317	20	.	.	PUNCT
ejpam-3743	318	1	it	it	PRON
ejpam-3743	318	2	should	should	AUX
ejpam-3743	318	3	be	be	AUX
ejpam-3743	318	4	noted	note	VERB
ejpam-3743	318	5	that	that	SCONJ
ejpam-3743	318	6	the	the	DET
ejpam-3743	318	7	concepts	concept	NOUN
ejpam-3743	318	8	of	of	ADP
ejpam-3743	318	9	sti	sti	PROPN
ejpam-3743	318	10	-	-	PUNCT
ejpam-3743	318	11	space	space	NOUN
ejpam-3743	318	12	which	which	PRON
ejpam-3743	318	13	were	be	AUX
ejpam-3743	318	14	defined	define	VERB
ejpam-3743	318	15	by	by	ADP
ejpam-3743	318	16	replacing	replace	VERB
ejpam-3743	318	17	’	'	PUNCT
ejpam-3743	318	18	supra	supra	ADJ
ejpam-3743	318	19	semi	semi	ADJ
ejpam-3743	318	20	-	-	ADJ
ejpam-3743	318	21	open	open	ADJ
ejpam-3743	318	22	’	'	PUNCT
ejpam-3743	318	23	by	by	ADP
ejpam-3743	318	24	’	'	PUNCT
ejpam-3743	318	25	supra	supra	ADJ
ejpam-3743	318	26	open	open	NOUN
ejpam-3743	318	27	’	'	PUNCT
ejpam-3743	318	28	in	in	ADP
ejpam-3743	318	29	definition	definition	NOUN
ejpam-3743	318	30	(	(	PUNCT
ejpam-3743	318	31	13	13	NUM
ejpam-3743	318	32	)	)	PUNCT
ejpam-3743	318	33	,	,	PUNCT
ejpam-3743	318	34	see	see	VERB
ejpam-3743	318	35	,	,	PUNCT
ejpam-3743	318	36	[	[	X
ejpam-3743	318	37	2	2	NUM
ejpam-3743	318	38	,	,	PUNCT
ejpam-3743	318	39	21	21	NUM
ejpam-3743	318	40	]	]	PUNCT
ejpam-3743	318	41	.	.	PUNCT
ejpam-3743	319	1	theorem	theorem	VERB
ejpam-3743	319	2	11	11	NUM
ejpam-3743	319	3	.	.	PUNCT
ejpam-3743	320	1	every	every	DET
ejpam-3743	320	2	ssti	ssti	NOUN
ejpam-3743	320	3	-	-	PUNCT
ejpam-3743	320	4	space	space	NOUN
ejpam-3743	320	5	is	be	AUX
ejpam-3743	320	6	ssti−1	ssti−1	PROPN
ejpam-3743	320	7	for	for	ADP
ejpam-3743	320	8	i	i	PRON
ejpam-3743	320	9	=	=	SYM
ejpam-3743	320	10	1	1	NUM
ejpam-3743	320	11	,	,	PUNCT
ejpam-3743	320	12	2	2	NUM
ejpam-3743	320	13	,	,	PUNCT
ejpam-3743	320	14	3	3	NUM
ejpam-3743	320	15	,	,	PUNCT
ejpam-3743	320	16	4	4	NUM
ejpam-3743	320	17	.	.	X
ejpam-3743	320	18	converse	converse	NOUN
ejpam-3743	320	19	of	of	ADP
ejpam-3743	320	20	this	this	DET
ejpam-3743	320	21	theorem	theorem	NOUN
ejpam-3743	320	22	is	be	AUX
ejpam-3743	320	23	not	not	PART
ejpam-3743	320	24	necessary	necessary	ADJ
ejpam-3743	320	25	true	true	ADJ
ejpam-3743	320	26	as	as	SCONJ
ejpam-3743	320	27	it	it	PRON
ejpam-3743	320	28	is	be	AUX
ejpam-3743	320	29	seen	see	VERB
ejpam-3743	320	30	in	in	ADP
ejpam-3743	320	31	the	the	DET
ejpam-3743	320	32	following	follow	VERB
ejpam-3743	320	33	examples	example	NOUN
ejpam-3743	320	34	.	.	PUNCT
ejpam-3743	321	1	example	example	NOUN
ejpam-3743	321	2	5	5	NUM
ejpam-3743	321	3	.	.	PUNCT
ejpam-3743	322	1	let	let	VERB
ejpam-3743	322	2	µ	µ	X
ejpam-3743	322	3	=	=	SYM
ejpam-3743	322	4	{	{	PUNCT
ejpam-3743	322	5	∅	∅	NOUN
ejpam-3743	322	6	,	,	PUNCT
ejpam-3743	322	7	x	x	X
ejpam-3743	322	8	,	,	PUNCT
ejpam-3743	322	9	{	{	PUNCT
ejpam-3743	322	10	1	1	NUM
ejpam-3743	322	11	}	}	PUNCT
ejpam-3743	322	12	}	}	PUNCT
ejpam-3743	322	13	be	be	AUX
ejpam-3743	322	14	a	a	DET
ejpam-3743	322	15	supra	supra	ADJ
ejpam-3743	322	16	topology	topology	NOUN
ejpam-3743	322	17	on	on	ADP
ejpam-3743	322	18	x	x	X
ejpam-3743	322	19	=	=	SYM
ejpam-3743	322	20	{	{	PUNCT
ejpam-3743	322	21	1	1	NUM
ejpam-3743	322	22	,	,	PUNCT
ejpam-3743	322	23	2	2	NUM
ejpam-3743	322	24	,	,	PUNCT
ejpam-3743	322	25	3	3	NUM
ejpam-3743	322	26	}	}	PUNCT
ejpam-3743	322	27	.	.	PUNCT
ejpam-3743	323	1	then	then	ADV
ejpam-3743	323	2	the	the	DET
ejpam-3743	323	3	collection	collection	NOUN
ejpam-3743	323	4	of	of	ADP
ejpam-3743	323	5	all	all	DET
ejpam-3743	323	6	supra	supra	ADJ
ejpam-3743	323	7	semi	semi	ADJ
ejpam-3743	323	8	-	-	ADJ
ejpam-3743	323	9	open	open	ADJ
ejpam-3743	323	10	subsets	subset	NOUN
ejpam-3743	323	11	of	of	ADP
ejpam-3743	323	12	(	(	PUNCT
ejpam-3743	323	13	x,µ	x,µ	NOUN
ejpam-3743	323	14	)	)	PUNCT
ejpam-3743	323	15	is	be	AUX
ejpam-3743	323	16	{	{	PUNCT
ejpam-3743	323	17	∅	∅	NOUN
ejpam-3743	323	18	,	,	PUNCT
ejpam-3743	323	19	x	x	X
ejpam-3743	323	20	,	,	PUNCT
ejpam-3743	323	21	{	{	PUNCT
ejpam-3743	323	22	1	1	NUM
ejpam-3743	323	23	}	}	PUNCT
ejpam-3743	323	24	,	,	PUNCT
ejpam-3743	323	25	{	{	PUNCT
ejpam-3743	323	26	1	1	NUM
ejpam-3743	323	27	,	,	PUNCT
ejpam-3743	323	28	2	2	NUM
ejpam-3743	323	29	}	}	PUNCT
ejpam-3743	323	30	,	,	PUNCT
ejpam-3743	323	31	{	{	PUNCT
ejpam-3743	323	32	1	1	NUM
ejpam-3743	323	33	,	,	PUNCT
ejpam-3743	323	34	3	3	NUM
ejpam-3743	323	35	}	}	PUNCT
ejpam-3743	323	36	}	}	PUNCT
ejpam-3743	323	37	.	.	PUNCT
ejpam-3743	324	1	therefore	therefore	ADV
ejpam-3743	324	2	(	(	PUNCT
ejpam-3743	324	3	x,µ	x,µ	NOUN
ejpam-3743	324	4	)	)	PUNCT
ejpam-3743	324	5	is	be	AUX
ejpam-3743	324	6	not	not	PART
ejpam-3743	324	7	an	an	DET
ejpam-3743	324	8	sst1	sst1	NOUN
ejpam-3743	324	9	-	-	PUNCT
ejpam-3743	324	10	space	space	NOUN
ejpam-3743	324	11	,	,	PUNCT
ejpam-3743	324	12	because	because	SCONJ
ejpam-3743	324	13	1	1	NUM
ejpam-3743	324	14	6=	6=	SYM
ejpam-3743	324	15	2	2	NUM
ejpam-3743	324	16	and	and	CCONJ
ejpam-3743	324	17	every	every	DET
ejpam-3743	324	18	supra	supra	NOUN
ejpam-3743	324	19	semi	semi	ADJ
ejpam-3743	324	20	-	-	ADJ
ejpam-3743	324	21	open	open	ADJ
ejpam-3743	324	22	set	set	NOUN
ejpam-3743	324	23	containing	contain	VERB
ejpam-3743	324	24	2	2	NUM
ejpam-3743	324	25	contains	contain	VERB
ejpam-3743	324	26	1	1	NUM
ejpam-3743	324	27	as	as	ADV
ejpam-3743	324	28	well	well	ADV
ejpam-3743	324	29	.	.	PUNCT
ejpam-3743	325	1	on	on	ADP
ejpam-3743	325	2	the	the	DET
ejpam-3743	325	3	other	other	ADJ
ejpam-3743	325	4	hand	hand	NOUN
ejpam-3743	325	5	,	,	PUNCT
ejpam-3743	325	6	it	it	PRON
ejpam-3743	325	7	can	can	AUX
ejpam-3743	325	8	be	be	AUX
ejpam-3743	325	9	checked	check	VERB
ejpam-3743	325	10	that	that	SCONJ
ejpam-3743	325	11	(	(	PUNCT
ejpam-3743	325	12	x,µ	x,µ	NOUN
ejpam-3743	325	13	)	)	PUNCT
ejpam-3743	325	14	is	be	AUX
ejpam-3743	325	15	sst0	sst0	PROPN
ejpam-3743	325	16	.	.	PUNCT
ejpam-3743	326	1	t.	t.	PROPN
ejpam-3743	326	2	m.	m.	PROPN
ejpam-3743	326	3	al	al	PROPN
ejpam-3743	326	4	-	-	PUNCT
ejpam-3743	326	5	shami	shami	PROPN
ejpam-3743	326	6	et	et	PROPN
ejpam-3743	326	7	al	al	PROPN
ejpam-3743	326	8	.	.	PUNCT
ejpam-3743	326	9	/	/	SYM
ejpam-3743	326	10	eur	eur	PROPN
ejpam-3743	326	11	.	.	PUNCT
ejpam-3743	327	1	j.	j.	PROPN
ejpam-3743	327	2	pure	pure	PROPN
ejpam-3743	327	3	appl	appl	PROPN
ejpam-3743	327	4	.	.	PROPN
ejpam-3743	327	5	math	math	PROPN
ejpam-3743	327	6	,	,	PUNCT
ejpam-3743	327	7	13	13	NUM
ejpam-3743	327	8	(	(	PUNCT
ejpam-3743	327	9	3	3	NUM
ejpam-3743	327	10	)	)	PUNCT
ejpam-3743	327	11	(	(	PUNCT
ejpam-3743	327	12	2020	2020	NUM
ejpam-3743	327	13	)	)	PUNCT
ejpam-3743	327	14	,	,	PUNCT
ejpam-3743	327	15	427	427	NUM
ejpam-3743	327	16	-	-	SYM
ejpam-3743	327	17	443	443	NUM
ejpam-3743	327	18	438	438	NUM
ejpam-3743	327	19	example	example	NOUN
ejpam-3743	327	20	6	6	NUM
ejpam-3743	327	21	.	.	PUNCT
ejpam-3743	328	1	let	let	VERB
ejpam-3743	328	2	µ	µ	X
ejpam-3743	328	3	=	=	SYM
ejpam-3743	328	4	{	{	PUNCT
ejpam-3743	328	5	∅	∅	NOUN
ejpam-3743	328	6	,	,	PUNCT
ejpam-3743	328	7	x	x	X
ejpam-3743	328	8	,	,	PUNCT
ejpam-3743	328	9	{	{	PUNCT
ejpam-3743	328	10	1	1	NUM
ejpam-3743	328	11	,	,	PUNCT
ejpam-3743	328	12	2	2	NUM
ejpam-3743	328	13	}	}	PUNCT
ejpam-3743	328	14	,	,	PUNCT
ejpam-3743	328	15	{	{	PUNCT
ejpam-3743	328	16	1	1	NUM
ejpam-3743	328	17	,	,	PUNCT
ejpam-3743	328	18	3	3	NUM
ejpam-3743	328	19	}	}	PUNCT
ejpam-3743	328	20	,	,	PUNCT
ejpam-3743	328	21	{	{	PUNCT
ejpam-3743	328	22	2	2	NUM
ejpam-3743	328	23	,	,	PUNCT
ejpam-3743	328	24	3	3	NUM
ejpam-3743	328	25	}	}	PUNCT
ejpam-3743	328	26	,	,	PUNCT
ejpam-3743	328	27	{	{	PUNCT
ejpam-3743	328	28	1	1	NUM
ejpam-3743	328	29	,	,	PUNCT
ejpam-3743	328	30	2	2	NUM
ejpam-3743	328	31	,	,	PUNCT
ejpam-3743	328	32	3	3	NUM
ejpam-3743	328	33	}	}	PUNCT
ejpam-3743	328	34	}	}	PUNCT
ejpam-3743	328	35	be	be	AUX
ejpam-3743	328	36	a	a	DET
ejpam-3743	328	37	supra	supra	ADJ
ejpam-3743	328	38	topology	topology	NOUN
ejpam-3743	328	39	on	on	ADP
ejpam-3743	328	40	x	x	X
ejpam-3743	328	41	=	=	SYM
ejpam-3743	328	42	{	{	PUNCT
ejpam-3743	328	43	1	1	NUM
ejpam-3743	328	44	,	,	PUNCT
ejpam-3743	328	45	2	2	NUM
ejpam-3743	328	46	,	,	PUNCT
ejpam-3743	328	47	3	3	NUM
ejpam-3743	328	48	,	,	PUNCT
ejpam-3743	328	49	4	4	NUM
ejpam-3743	328	50	}	}	PUNCT
ejpam-3743	328	51	.	.	PUNCT
ejpam-3743	329	1	then	then	ADV
ejpam-3743	329	2	the	the	DET
ejpam-3743	329	3	collection	collection	NOUN
ejpam-3743	329	4	of	of	ADP
ejpam-3743	329	5	all	all	DET
ejpam-3743	329	6	supra	supra	ADJ
ejpam-3743	329	7	semi	semi	ADJ
ejpam-3743	329	8	-	-	ADJ
ejpam-3743	329	9	open	open	ADJ
ejpam-3743	329	10	subsets	subset	NOUN
ejpam-3743	329	11	of	of	ADP
ejpam-3743	329	12	(	(	PUNCT
ejpam-3743	329	13	x,µ	x,µ	NOUN
ejpam-3743	329	14	)	)	PUNCT
ejpam-3743	329	15	is	be	AUX
ejpam-3743	329	16	{	{	PUNCT
ejpam-3743	329	17	∅	∅	NOUN
ejpam-3743	329	18	,	,	PUNCT
ejpam-3743	329	19	x	x	X
ejpam-3743	329	20	,	,	PUNCT
ejpam-3743	329	21	{	{	PUNCT
ejpam-3743	329	22	1	1	NUM
ejpam-3743	329	23	,	,	PUNCT
ejpam-3743	329	24	2	2	NUM
ejpam-3743	329	25	}	}	PUNCT
ejpam-3743	329	26	,	,	PUNCT
ejpam-3743	329	27	{	{	PUNCT
ejpam-3743	329	28	1	1	NUM
ejpam-3743	329	29	,	,	PUNCT
ejpam-3743	329	30	3	3	NUM
ejpam-3743	329	31	}	}	PUNCT
ejpam-3743	329	32	,	,	PUNCT
ejpam-3743	329	33	{	{	PUNCT
ejpam-3743	329	34	2	2	NUM
ejpam-3743	329	35	,	,	PUNCT
ejpam-3743	329	36	3	3	NUM
ejpam-3743	329	37	}	}	PUNCT
ejpam-3743	329	38	,	,	PUNCT
ejpam-3743	329	39	{	{	PUNCT
ejpam-3743	329	40	1	1	NUM
ejpam-3743	329	41	,	,	PUNCT
ejpam-3743	329	42	2	2	NUM
ejpam-3743	329	43	,	,	PUNCT
ejpam-3743	329	44	3	3	NUM
ejpam-3743	329	45	}	}	PUNCT
ejpam-3743	329	46	,	,	PUNCT
ejpam-3743	329	47	{	{	PUNCT
ejpam-3743	329	48	1	1	NUM
ejpam-3743	329	49	,	,	PUNCT
ejpam-3743	329	50	2	2	NUM
ejpam-3743	329	51	,	,	PUNCT
ejpam-3743	329	52	4	4	NUM
ejpam-3743	329	53	}	}	PUNCT
ejpam-3743	329	54	,	,	PUNCT
ejpam-3743	329	55	{	{	PUNCT
ejpam-3743	329	56	1	1	NUM
ejpam-3743	329	57	,	,	PUNCT
ejpam-3743	329	58	3	3	NUM
ejpam-3743	329	59	,	,	PUNCT
ejpam-3743	329	60	4	4	NUM
ejpam-3743	329	61	}	}	PUNCT
ejpam-3743	329	62	,	,	PUNCT
ejpam-3743	329	63	{	{	PUNCT
ejpam-3743	329	64	2	2	NUM
ejpam-3743	329	65	,	,	PUNCT
ejpam-3743	329	66	3	3	NUM
ejpam-3743	329	67	,	,	PUNCT
ejpam-3743	329	68	4	4	NUM
ejpam-3743	329	69	}	}	PUNCT
ejpam-3743	329	70	}	}	PUNCT
ejpam-3743	329	71	.	.	PUNCT
ejpam-3743	330	1	therefore	therefore	ADV
ejpam-3743	330	2	(	(	PUNCT
ejpam-3743	330	3	x,µ	x,µ	NOUN
ejpam-3743	330	4	)	)	PUNCT
ejpam-3743	330	5	is	be	AUX
ejpam-3743	330	6	not	not	PART
ejpam-3743	330	7	an	an	DET
ejpam-3743	330	8	sst2	sst2	NOUN
ejpam-3743	330	9	-	-	PUNCT
ejpam-3743	330	10	space	space	NOUN
ejpam-3743	330	11	,	,	PUNCT
ejpam-3743	330	12	because	because	SCONJ
ejpam-3743	330	13	3	3	NUM
ejpam-3743	330	14	6=	6=	SYM
ejpam-3743	330	15	4	4	NUM
ejpam-3743	330	16	and	and	CCONJ
ejpam-3743	330	17	there	there	PRON
ejpam-3743	330	18	do	do	AUX
ejpam-3743	330	19	not	not	PART
ejpam-3743	330	20	exist	exist	VERB
ejpam-3743	330	21	disjoint	disjoint	ADJ
ejpam-3743	330	22	supra	supra	NOUN
ejpam-3743	330	23	semi	semi	ADJ
ejpam-3743	330	24	-	-	ADJ
ejpam-3743	330	25	open	open	ADJ
ejpam-3743	330	26	sets	set	NOUN
ejpam-3743	330	27	such	such	ADJ
ejpam-3743	330	28	that	that	PRON
ejpam-3743	330	29	one	one	NUM
ejpam-3743	330	30	of	of	ADP
ejpam-3743	330	31	them	they	PRON
ejpam-3743	330	32	contains	contain	VERB
ejpam-3743	330	33	3	3	NUM
ejpam-3743	330	34	and	and	CCONJ
ejpam-3743	330	35	the	the	DET
ejpam-3743	330	36	other	other	ADJ
ejpam-3743	330	37	contains	contain	VERB
ejpam-3743	330	38	4	4	NUM
ejpam-3743	330	39	.	.	PUNCT
ejpam-3743	331	1	on	on	ADP
ejpam-3743	331	2	the	the	DET
ejpam-3743	331	3	other	other	ADJ
ejpam-3743	331	4	hand	hand	NOUN
ejpam-3743	331	5	,	,	PUNCT
ejpam-3743	331	6	it	it	PRON
ejpam-3743	331	7	can	can	AUX
ejpam-3743	331	8	be	be	AUX
ejpam-3743	331	9	checked	check	VERB
ejpam-3743	331	10	that	that	SCONJ
ejpam-3743	331	11	(	(	PUNCT
ejpam-3743	331	12	x,µ	x,µ	NOUN
ejpam-3743	331	13	)	)	PUNCT
ejpam-3743	331	14	is	be	AUX
ejpam-3743	331	15	sst1	sst1	PROPN
ejpam-3743	331	16	.	.	PUNCT
ejpam-3743	332	1	example	example	NOUN
ejpam-3743	333	1	7	7	NUM
ejpam-3743	333	2	.	.	PUNCT
ejpam-3743	333	3	let	let	VERB
ejpam-3743	333	4	µ	µ	X
ejpam-3743	333	5	=	=	SYM
ejpam-3743	333	6	{	{	PUNCT
ejpam-3743	333	7	∅	∅	NOUN
ejpam-3743	333	8	,	,	PUNCT
ejpam-3743	333	9	x	x	X
ejpam-3743	333	10	,	,	PUNCT
ejpam-3743	333	11	{	{	PUNCT
ejpam-3743	333	12	1	1	NUM
ejpam-3743	333	13	,	,	PUNCT
ejpam-3743	333	14	2	2	NUM
ejpam-3743	333	15	}	}	PUNCT
ejpam-3743	333	16	,	,	PUNCT
ejpam-3743	333	17	{	{	PUNCT
ejpam-3743	333	18	3	3	NUM
ejpam-3743	333	19	,	,	PUNCT
ejpam-3743	333	20	4	4	NUM
ejpam-3743	333	21	}	}	PUNCT
ejpam-3743	333	22	,	,	PUNCT
ejpam-3743	333	23	{	{	PUNCT
ejpam-3743	333	24	1	1	NUM
ejpam-3743	333	25	,	,	PUNCT
ejpam-3743	333	26	3	3	NUM
ejpam-3743	333	27	}	}	PUNCT
ejpam-3743	333	28	,	,	PUNCT
ejpam-3743	333	29	{	{	PUNCT
ejpam-3743	333	30	2	2	NUM
ejpam-3743	333	31	,	,	PUNCT
ejpam-3743	333	32	4	4	NUM
ejpam-3743	333	33	}	}	PUNCT
ejpam-3743	333	34	,	,	PUNCT
ejpam-3743	333	35	{	{	PUNCT
ejpam-3743	333	36	2	2	NUM
ejpam-3743	333	37	,	,	PUNCT
ejpam-3743	333	38	3	3	NUM
ejpam-3743	333	39	}	}	PUNCT
ejpam-3743	333	40	,	,	PUNCT
ejpam-3743	333	41	{	{	PUNCT
ejpam-3743	333	42	1	1	NUM
ejpam-3743	333	43	,	,	PUNCT
ejpam-3743	333	44	2	2	NUM
ejpam-3743	333	45	,	,	PUNCT
ejpam-3743	333	46	3	3	NUM
ejpam-3743	333	47	}	}	PUNCT
ejpam-3743	333	48	,	,	PUNCT
ejpam-3743	333	49	{	{	PUNCT
ejpam-3743	333	50	1	1	NUM
ejpam-3743	333	51	,	,	PUNCT
ejpam-3743	333	52	2	2	NUM
ejpam-3743	333	53	,	,	PUNCT
ejpam-3743	333	54	4	4	NUM
ejpam-3743	333	55	}	}	PUNCT
ejpam-3743	333	56	,	,	PUNCT
ejpam-3743	333	57	{	{	PUNCT
ejpam-3743	333	58	1	1	NUM
ejpam-3743	333	59	,	,	PUNCT
ejpam-3743	333	60	3	3	NUM
ejpam-3743	333	61	,	,	PUNCT
ejpam-3743	333	62	4	4	NUM
ejpam-3743	333	63	}	}	PUNCT
ejpam-3743	333	64	,	,	PUNCT
ejpam-3743	333	65	{	{	PUNCT
ejpam-3743	333	66	2	2	NUM
ejpam-3743	333	67	,	,	PUNCT
ejpam-3743	333	68	3	3	NUM
ejpam-3743	333	69	,	,	PUNCT
ejpam-3743	333	70	4	4	NUM
ejpam-3743	333	71	}	}	PUNCT
ejpam-3743	333	72	}	}	PUNCT
ejpam-3743	333	73	be	be	AUX
ejpam-3743	333	74	a	a	DET
ejpam-3743	333	75	supra	supra	ADJ
ejpam-3743	333	76	topology	topology	NOUN
ejpam-3743	333	77	on	on	ADP
ejpam-3743	333	78	x	x	X
ejpam-3743	333	79	=	=	SYM
ejpam-3743	333	80	{	{	PUNCT
ejpam-3743	333	81	1	1	NUM
ejpam-3743	333	82	,	,	PUNCT
ejpam-3743	333	83	2	2	NUM
ejpam-3743	333	84	,	,	PUNCT
ejpam-3743	333	85	3	3	NUM
ejpam-3743	333	86	,	,	PUNCT
ejpam-3743	333	87	4	4	NUM
ejpam-3743	333	88	}	}	PUNCT
ejpam-3743	333	89	.	.	PUNCT
ejpam-3743	334	1	in	in	ADP
ejpam-3743	334	2	(	(	PUNCT
ejpam-3743	334	3	x,µ	x,µ	NOUN
ejpam-3743	334	4	)	)	PUNCT
ejpam-3743	334	5	,	,	PUNCT
ejpam-3743	334	6	every	every	DET
ejpam-3743	334	7	set	set	NOUN
ejpam-3743	334	8	is	be	AUX
ejpam-3743	334	9	supra	supra	PROPN
ejpam-3743	334	10	open	open	ADJ
ejpam-3743	334	11	iff	iff	PROPN
ejpam-3743	334	12	it	it	PRON
ejpam-3743	334	13	is	be	AUX
ejpam-3743	334	14	supra	supra	ADJ
ejpam-3743	334	15	semi	semi	ADJ
ejpam-3743	334	16	-	-	ADJ
ejpam-3743	334	17	open	open	ADJ
ejpam-3743	334	18	.	.	PUNCT
ejpam-3743	335	1	now	now	ADV
ejpam-3743	335	2	,	,	PUNCT
ejpam-3743	335	3	{	{	PUNCT
ejpam-3743	335	4	1	1	NUM
ejpam-3743	335	5	,	,	PUNCT
ejpam-3743	335	6	4	4	NUM
ejpam-3743	335	7	}	}	PUNCT
ejpam-3743	335	8	is	be	AUX
ejpam-3743	335	9	a	a	DET
ejpam-3743	335	10	supra	supra	ADJ
ejpam-3743	335	11	semi	semi	ADJ
ejpam-3743	335	12	-	-	ADJ
ejpam-3743	335	13	closed	closed	ADJ
ejpam-3743	335	14	set	set	NOUN
ejpam-3743	335	15	and	and	CCONJ
ejpam-3743	335	16	2	2	NUM
ejpam-3743	335	17	6∈	6∈	NOUN
ejpam-3743	335	18	{	{	PUNCT
ejpam-3743	335	19	1	1	NUM
ejpam-3743	335	20	,	,	PUNCT
ejpam-3743	335	21	4	4	NUM
ejpam-3743	335	22	}	}	PUNCT
ejpam-3743	335	23	.	.	PUNCT
ejpam-3743	336	1	since	since	SCONJ
ejpam-3743	336	2	there	there	PRON
ejpam-3743	336	3	do	do	AUX
ejpam-3743	336	4	not	not	PART
ejpam-3743	336	5	exist	exist	VERB
ejpam-3743	336	6	two	two	NUM
ejpam-3743	336	7	disjoint	disjoint	ADJ
ejpam-3743	336	8	supra	supra	PROPN
ejpam-3743	336	9	semi	semi	ADJ
ejpam-3743	336	10	-	-	ADJ
ejpam-3743	336	11	open	open	ADJ
ejpam-3743	336	12	sets	set	NOUN
ejpam-3743	336	13	such	such	ADJ
ejpam-3743	336	14	that	that	PRON
ejpam-3743	336	15	one	one	NUM
ejpam-3743	336	16	of	of	ADP
ejpam-3743	336	17	them	they	PRON
ejpam-3743	336	18	contains	contain	VERB
ejpam-3743	336	19	2	2	NUM
ejpam-3743	336	20	and	and	CCONJ
ejpam-3743	336	21	the	the	DET
ejpam-3743	336	22	other	other	ADJ
ejpam-3743	336	23	contains	contain	VERB
ejpam-3743	336	24	{	{	PUNCT
ejpam-3743	336	25	1	1	NUM
ejpam-3743	336	26	,	,	PUNCT
ejpam-3743	336	27	4	4	NUM
ejpam-3743	336	28	}	}	PUNCT
ejpam-3743	336	29	,	,	PUNCT
ejpam-3743	336	30	then	then	ADV
ejpam-3743	336	31	(	(	PUNCT
ejpam-3743	336	32	x,µ	x,µ	NOUN
ejpam-3743	336	33	)	)	PUNCT
ejpam-3743	336	34	is	be	AUX
ejpam-3743	336	35	not	not	PART
ejpam-3743	336	36	supra	supra	ADJ
ejpam-3743	336	37	sst3	sst3	PROPN
ejpam-3743	336	38	.	.	PUNCT
ejpam-3743	337	1	on	on	ADP
ejpam-3743	337	2	the	the	DET
ejpam-3743	337	3	other	other	ADJ
ejpam-3743	337	4	hand	hand	NOUN
ejpam-3743	337	5	,	,	PUNCT
ejpam-3743	337	6	it	it	PRON
ejpam-3743	337	7	can	can	AUX
ejpam-3743	337	8	be	be	AUX
ejpam-3743	337	9	checked	check	VERB
ejpam-3743	337	10	that	that	SCONJ
ejpam-3743	337	11	(	(	PUNCT
ejpam-3743	337	12	x,µ	x,µ	NOUN
ejpam-3743	337	13	)	)	PUNCT
ejpam-3743	337	14	is	be	AUX
ejpam-3743	337	15	sst2	sst2	PROPN
ejpam-3743	337	16	.	.	PUNCT
ejpam-3743	337	17	example	example	NOUN
ejpam-3743	338	1	8	8	NUM
ejpam-3743	338	2	.	.	PUNCT
ejpam-3743	338	3	assume	assume	VERB
ejpam-3743	338	4	that	that	SCONJ
ejpam-3743	338	5	(	(	PUNCT
ejpam-3743	338	6	n	n	X
ejpam-3743	338	7	,	,	PUNCT
ejpam-3743	338	8	µ	µ	X
ejpam-3743	338	9	)	)	PUNCT
ejpam-3743	338	10	is	be	AUX
ejpam-3743	338	11	the	the	DET
ejpam-3743	338	12	same	same	ADJ
ejpam-3743	338	13	as	as	ADP
ejpam-3743	338	14	in	in	ADP
ejpam-3743	338	15	example	example	NOUN
ejpam-3743	338	16	(	(	PUNCT
ejpam-3743	338	17	4	4	NUM
ejpam-3743	338	18	)	)	PUNCT
ejpam-3743	338	19	.	.	PUNCT
ejpam-3743	339	1	then	then	ADV
ejpam-3743	339	2	{	{	PUNCT
ejpam-3743	339	3	2n	2n	NUM
ejpam-3743	339	4	:	:	PUNCT
ejpam-3743	339	5	n	n	CCONJ
ejpam-3743	339	6	∈	∈	PROPN
ejpam-3743	339	7	n	n	CCONJ
ejpam-3743	339	8	}	}	PUNCT
ejpam-3743	339	9	and	and	CCONJ
ejpam-3743	339	10	{	{	PUNCT
ejpam-3743	339	11	2n+	2n+	NUM
ejpam-3743	339	12	3	3	NUM
ejpam-3743	339	13	:	:	PUNCT
ejpam-3743	339	14	n	n	CCONJ
ejpam-3743	339	15	∈	∈	PROPN
ejpam-3743	339	16	n	n	CCONJ
ejpam-3743	339	17	}	}	PUNCT
ejpam-3743	339	18	are	be	AUX
ejpam-3743	339	19	disjoint	disjoint	NOUN
ejpam-3743	339	20	supra	supra	PROPN
ejpam-3743	339	21	semi	semi	ADJ
ejpam-3743	339	22	-	-	ADJ
ejpam-3743	339	23	closed	closed	ADJ
ejpam-3743	339	24	subsets	subset	NOUN
ejpam-3743	339	25	of	of	ADP
ejpam-3743	339	26	(	(	PUNCT
ejpam-3743	339	27	n	n	X
ejpam-3743	339	28	,	,	PUNCT
ejpam-3743	339	29	µ	µ	NOUN
ejpam-3743	339	30	)	)	PUNCT
ejpam-3743	339	31	.	.	PUNCT
ejpam-3743	340	1	since	since	SCONJ
ejpam-3743	340	2	there	there	PRON
ejpam-3743	340	3	do	do	AUX
ejpam-3743	340	4	not	not	PART
ejpam-3743	340	5	exist	exist	VERB
ejpam-3743	340	6	two	two	NUM
ejpam-3743	340	7	disjoint	disjoint	ADJ
ejpam-3743	340	8	supra	supra	PROPN
ejpam-3743	340	9	semi	semi	ADJ
ejpam-3743	340	10	-	-	ADJ
ejpam-3743	340	11	open	open	ADJ
ejpam-3743	340	12	sets	set	NOUN
ejpam-3743	340	13	such	such	ADJ
ejpam-3743	340	14	that	that	PRON
ejpam-3743	340	15	one	one	NUM
ejpam-3743	340	16	of	of	ADP
ejpam-3743	340	17	them	they	PRON
ejpam-3743	340	18	contains	contain	VERB
ejpam-3743	340	19	{	{	PUNCT
ejpam-3743	340	20	2n	2n	NUM
ejpam-3743	340	21	:	:	PUNCT
ejpam-3743	340	22	n	n	CCONJ
ejpam-3743	340	23	∈	∈	PROPN
ejpam-3743	340	24	n	n	CCONJ
ejpam-3743	340	25	}	}	PUNCT
ejpam-3743	340	26	and	and	CCONJ
ejpam-3743	340	27	the	the	DET
ejpam-3743	340	28	other	other	ADJ
ejpam-3743	340	29	contains	contain	VERB
ejpam-3743	340	30	{	{	PUNCT
ejpam-3743	340	31	2n	2n	NUM
ejpam-3743	341	1	+	+	CCONJ
ejpam-3743	341	2	3	3	NUM
ejpam-3743	341	3	:	:	PUNCT
ejpam-3743	341	4	n	n	CCONJ
ejpam-3743	341	5	∈	∈	PROPN
ejpam-3743	341	6	n	n	CCONJ
ejpam-3743	341	7	}	}	PUNCT
ejpam-3743	341	8	,	,	PUNCT
ejpam-3743	341	9	then	then	ADV
ejpam-3743	341	10	(	(	PUNCT
ejpam-3743	341	11	n	n	X
ejpam-3743	341	12	,	,	PUNCT
ejpam-3743	341	13	µ	µ	X
ejpam-3743	341	14	)	)	PUNCT
ejpam-3743	341	15	is	be	AUX
ejpam-3743	341	16	not	not	PART
ejpam-3743	341	17	supra	supra	ADJ
ejpam-3743	341	18	semi	semi	ADV
ejpam-3743	341	19	normal	normal	ADJ
ejpam-3743	341	20	.	.	PUNCT
ejpam-3743	342	1	therefore	therefore	ADV
ejpam-3743	342	2	it	it	PRON
ejpam-3743	342	3	is	be	AUX
ejpam-3743	342	4	not	not	PART
ejpam-3743	342	5	sst4	sst4	ADJ
ejpam-3743	342	6	.	.	PUNCT
ejpam-3743	343	1	on	on	ADP
ejpam-3743	343	2	the	the	DET
ejpam-3743	343	3	other	other	ADJ
ejpam-3743	343	4	hand	hand	NOUN
ejpam-3743	343	5	,	,	PUNCT
ejpam-3743	343	6	it	it	PRON
ejpam-3743	343	7	can	can	AUX
ejpam-3743	343	8	be	be	AUX
ejpam-3743	343	9	checked	check	VERB
ejpam-3743	343	10	that	that	PRON
ejpam-3743	343	11	(	(	PUNCT
ejpam-3743	343	12	n	n	X
ejpam-3743	343	13	,	,	PUNCT
ejpam-3743	343	14	µ	µ	X
ejpam-3743	343	15	)	)	PUNCT
ejpam-3743	343	16	is	be	AUX
ejpam-3743	343	17	sst3	sst3	PROPN
ejpam-3743	343	18	.	.	PUNCT
ejpam-3743	344	1	theorem	theorem	ADJ
ejpam-3743	344	2	12	12	NUM
ejpam-3743	344	3	.	.	PUNCT
ejpam-3743	345	1	every	every	DET
ejpam-3743	345	2	sti	sti	PROPN
ejpam-3743	345	3	-	-	PUNCT
ejpam-3743	345	4	space	space	NOUN
ejpam-3743	345	5	(	(	PUNCT
ejpam-3743	345	6	x,µ	x,µ	NOUN
ejpam-3743	345	7	)	)	PUNCT
ejpam-3743	345	8	is	be	AUX
ejpam-3743	345	9	ssti	ssti	ADJ
ejpam-3743	345	10	for	for	ADP
ejpam-3743	345	11	i	i	PROPN
ejpam-3743	345	12	=	=	SYM
ejpam-3743	345	13	0	0	NUM
ejpam-3743	345	14	,	,	PUNCT
ejpam-3743	345	15	1	1	NUM
ejpam-3743	345	16	,	,	PUNCT
ejpam-3743	345	17	2	2	NUM
ejpam-3743	345	18	.	.	PUNCT
ejpam-3743	345	19	proof	proof	NOUN
ejpam-3743	345	20	.	.	PUNCT
ejpam-3743	346	1	it	it	PRON
ejpam-3743	346	2	follows	follow	VERB
ejpam-3743	346	3	from	from	ADP
ejpam-3743	346	4	the	the	DET
ejpam-3743	346	5	fact	fact	NOUN
ejpam-3743	346	6	that	that	SCONJ
ejpam-3743	346	7	every	every	DET
ejpam-3743	346	8	supra	supra	PROPN
ejpam-3743	346	9	open	open	ADJ
ejpam-3743	346	10	set	set	NOUN
ejpam-3743	346	11	is	be	AUX
ejpam-3743	346	12	supra	supra	ADJ
ejpam-3743	346	13	semi	semi	ADJ
ejpam-3743	346	14	-	-	ADJ
ejpam-3743	346	15	open	open	ADJ
ejpam-3743	346	16	.	.	PUNCT
ejpam-3743	347	1	converse	converse	NOUN
ejpam-3743	347	2	of	of	ADP
ejpam-3743	347	3	this	this	DET
ejpam-3743	347	4	theorem	theorem	NOUN
ejpam-3743	347	5	is	be	AUX
ejpam-3743	347	6	not	not	PART
ejpam-3743	347	7	necessary	necessary	ADJ
ejpam-3743	347	8	true	true	ADJ
ejpam-3743	347	9	as	as	SCONJ
ejpam-3743	347	10	it	it	PRON
ejpam-3743	347	11	is	be	AUX
ejpam-3743	347	12	seen	see	VERB
ejpam-3743	347	13	in	in	ADP
ejpam-3743	347	14	the	the	DET
ejpam-3743	347	15	following	follow	VERB
ejpam-3743	347	16	examples	example	NOUN
ejpam-3743	347	17	.	.	PUNCT
ejpam-3743	348	1	example	example	NOUN
ejpam-3743	348	2	9	9	NUM
ejpam-3743	348	3	.	.	X
ejpam-3743	348	4	assume	assume	VERB
ejpam-3743	348	5	that	that	SCONJ
ejpam-3743	348	6	(	(	PUNCT
ejpam-3743	348	7	x,µ	x,µ	NOUN
ejpam-3743	348	8	)	)	PUNCT
ejpam-3743	348	9	is	be	AUX
ejpam-3743	348	10	the	the	DET
ejpam-3743	348	11	same	same	ADJ
ejpam-3743	348	12	as	as	ADP
ejpam-3743	348	13	in	in	ADP
ejpam-3743	348	14	example	example	NOUN
ejpam-3743	348	15	(	(	PUNCT
ejpam-3743	348	16	5	5	NUM
ejpam-3743	348	17	)	)	PUNCT
ejpam-3743	348	18	.	.	PUNCT
ejpam-3743	349	1	then	then	ADV
ejpam-3743	349	2	(	(	PUNCT
ejpam-3743	349	3	x,µ	x,µ	NOUN
ejpam-3743	349	4	)	)	PUNCT
ejpam-3743	349	5	is	be	AUX
ejpam-3743	349	6	not	not	PART
ejpam-3743	349	7	an	an	DET
ejpam-3743	349	8	st0	st0	NOUN
ejpam-3743	349	9	-	-	NOUN
ejpam-3743	349	10	space	space	NOUN
ejpam-3743	349	11	.	.	PUNCT
ejpam-3743	350	1	on	on	ADP
ejpam-3743	350	2	the	the	DET
ejpam-3743	350	3	other	other	ADJ
ejpam-3743	350	4	hand	hand	NOUN
ejpam-3743	350	5	,	,	PUNCT
ejpam-3743	350	6	the	the	DET
ejpam-3743	350	7	collection	collection	NOUN
ejpam-3743	350	8	of	of	ADP
ejpam-3743	350	9	all	all	DET
ejpam-3743	350	10	supra	supra	ADJ
ejpam-3743	350	11	semi	semi	ADJ
ejpam-3743	350	12	-	-	ADJ
ejpam-3743	350	13	open	open	ADJ
ejpam-3743	350	14	subsets	subset	NOUN
ejpam-3743	350	15	of	of	ADP
ejpam-3743	350	16	(	(	PUNCT
ejpam-3743	350	17	x,µ	x,µ	NOUN
ejpam-3743	350	18	)	)	PUNCT
ejpam-3743	350	19	is	be	AUX
ejpam-3743	350	20	{	{	PUNCT
ejpam-3743	350	21	∅	∅	NOUN
ejpam-3743	350	22	,	,	PUNCT
ejpam-3743	350	23	x	x	X
ejpam-3743	350	24	,	,	PUNCT
ejpam-3743	350	25	{	{	PUNCT
ejpam-3743	350	26	1	1	NUM
ejpam-3743	350	27	}	}	PUNCT
ejpam-3743	350	28	,	,	PUNCT
ejpam-3743	350	29	{	{	PUNCT
ejpam-3743	350	30	1	1	NUM
ejpam-3743	350	31	,	,	PUNCT
ejpam-3743	350	32	2	2	NUM
ejpam-3743	350	33	}	}	PUNCT
ejpam-3743	350	34	,	,	PUNCT
ejpam-3743	350	35	{	{	PUNCT
ejpam-3743	350	36	1	1	NUM
ejpam-3743	350	37	,	,	PUNCT
ejpam-3743	350	38	3	3	NUM
ejpam-3743	350	39	}	}	PUNCT
ejpam-3743	350	40	}	}	PUNCT
ejpam-3743	350	41	.	.	PUNCT
ejpam-3743	351	1	hence	hence	ADV
ejpam-3743	351	2	,	,	PUNCT
ejpam-3743	351	3	(	(	PUNCT
ejpam-3743	351	4	x,µ	x,µ	NOUN
ejpam-3743	351	5	)	)	PUNCT
ejpam-3743	351	6	is	be	AUX
ejpam-3743	351	7	sst0	sst0	PROPN
ejpam-3743	351	8	.	.	PUNCT
ejpam-3743	351	9	example	example	NOUN
ejpam-3743	352	1	10	10	NUM
ejpam-3743	352	2	.	.	PUNCT
ejpam-3743	353	1	let	let	VERB
ejpam-3743	353	2	µ	µ	X
ejpam-3743	353	3	=	=	SYM
ejpam-3743	353	4	{	{	PUNCT
ejpam-3743	353	5	∅	∅	NOUN
ejpam-3743	353	6	,	,	PUNCT
ejpam-3743	353	7	x	x	X
ejpam-3743	353	8	,	,	PUNCT
ejpam-3743	353	9	{	{	PUNCT
ejpam-3743	353	10	1	1	NUM
ejpam-3743	353	11	}	}	PUNCT
ejpam-3743	353	12	,	,	PUNCT
ejpam-3743	353	13	{	{	PUNCT
ejpam-3743	353	14	2	2	NUM
ejpam-3743	353	15	}	}	PUNCT
ejpam-3743	353	16	,	,	PUNCT
ejpam-3743	353	17	{	{	PUNCT
ejpam-3743	353	18	1	1	NUM
ejpam-3743	353	19	,	,	PUNCT
ejpam-3743	353	20	2	2	NUM
ejpam-3743	353	21	}	}	PUNCT
ejpam-3743	353	22	}	}	PUNCT
ejpam-3743	353	23	be	be	AUX
ejpam-3743	353	24	a	a	DET
ejpam-3743	353	25	supra	supra	ADJ
ejpam-3743	353	26	topology	topology	NOUN
ejpam-3743	353	27	on	on	ADP
ejpam-3743	353	28	x	x	X
ejpam-3743	353	29	=	=	SYM
ejpam-3743	353	30	{	{	PUNCT
ejpam-3743	353	31	1	1	NUM
ejpam-3743	353	32	,	,	PUNCT
ejpam-3743	353	33	2	2	NUM
ejpam-3743	353	34	,	,	PUNCT
ejpam-3743	353	35	3	3	NUM
ejpam-3743	353	36	}	}	PUNCT
ejpam-3743	353	37	.	.	PUNCT
ejpam-3743	354	1	then	then	ADV
ejpam-3743	354	2	(	(	PUNCT
ejpam-3743	354	3	x,µ	x,µ	NOUN
ejpam-3743	354	4	)	)	PUNCT
ejpam-3743	354	5	is	be	AUX
ejpam-3743	354	6	not	not	PART
ejpam-3743	354	7	an	an	DET
ejpam-3743	354	8	st1	st1	PROPN
ejpam-3743	354	9	-	-	PUNCT
ejpam-3743	354	10	space	space	NOUN
ejpam-3743	354	11	.	.	PUNCT
ejpam-3743	355	1	on	on	ADP
ejpam-3743	355	2	the	the	DET
ejpam-3743	355	3	other	other	ADJ
ejpam-3743	355	4	hand	hand	NOUN
ejpam-3743	355	5	,	,	PUNCT
ejpam-3743	355	6	the	the	DET
ejpam-3743	355	7	collection	collection	NOUN
ejpam-3743	355	8	of	of	ADP
ejpam-3743	355	9	all	all	DET
ejpam-3743	355	10	supra	supra	ADJ
ejpam-3743	355	11	semi	semi	ADJ
ejpam-3743	355	12	-	-	ADJ
ejpam-3743	355	13	open	open	ADJ
ejpam-3743	355	14	subsets	subset	NOUN
ejpam-3743	355	15	of	of	ADP
ejpam-3743	355	16	(	(	PUNCT
ejpam-3743	355	17	x,µ	x,µ	NOUN
ejpam-3743	355	18	)	)	PUNCT
ejpam-3743	355	19	is	be	AUX
ejpam-3743	355	20	{	{	PUNCT
ejpam-3743	355	21	∅	∅	NOUN
ejpam-3743	355	22	,	,	PUNCT
ejpam-3743	355	23	x	x	X
ejpam-3743	355	24	,	,	PUNCT
ejpam-3743	355	25	{	{	PUNCT
ejpam-3743	355	26	1	1	NUM
ejpam-3743	355	27	}	}	PUNCT
ejpam-3743	355	28	,	,	PUNCT
ejpam-3743	355	29	{	{	PUNCT
ejpam-3743	355	30	2	2	NUM
ejpam-3743	355	31	}	}	PUNCT
ejpam-3743	355	32	,	,	PUNCT
ejpam-3743	355	33	{	{	PUNCT
ejpam-3743	355	34	1	1	NUM
ejpam-3743	355	35	,	,	PUNCT
ejpam-3743	355	36	2	2	NUM
ejpam-3743	355	37	}	}	PUNCT
ejpam-3743	355	38	,	,	PUNCT
ejpam-3743	355	39	{	{	PUNCT
ejpam-3743	355	40	1	1	NUM
ejpam-3743	355	41	,	,	PUNCT
ejpam-3743	355	42	3	3	NUM
ejpam-3743	355	43	}	}	PUNCT
ejpam-3743	355	44	,	,	PUNCT
ejpam-3743	355	45	{	{	PUNCT
ejpam-3743	355	46	2	2	NUM
ejpam-3743	355	47	,	,	PUNCT
ejpam-3743	355	48	3	3	NUM
ejpam-3743	355	49	}	}	PUNCT
ejpam-3743	355	50	}	}	PUNCT
ejpam-3743	355	51	.	.	PUNCT
ejpam-3743	356	1	now	now	ADV
ejpam-3743	356	2	,	,	PUNCT
ejpam-3743	356	3	it	it	PRON
ejpam-3743	356	4	can	can	AUX
ejpam-3743	356	5	be	be	AUX
ejpam-3743	356	6	checked	check	VERB
ejpam-3743	356	7	that	that	SCONJ
ejpam-3743	356	8	(	(	PUNCT
ejpam-3743	356	9	x,µ	x,µ	NOUN
ejpam-3743	356	10	)	)	PUNCT
ejpam-3743	356	11	is	be	AUX
ejpam-3743	356	12	sst4	sst4	NOUN
ejpam-3743	356	13	.	.	PUNCT
ejpam-3743	357	1	we	we	PRON
ejpam-3743	357	2	complete	complete	VERB
ejpam-3743	357	3	this	this	DET
ejpam-3743	357	4	section	section	NOUN
ejpam-3743	357	5	by	by	ADP
ejpam-3743	357	6	discussing	discuss	VERB
ejpam-3743	357	7	these	these	DET
ejpam-3743	357	8	separation	separation	NOUN
ejpam-3743	357	9	axioms	axiom	NOUN
ejpam-3743	357	10	in	in	ADP
ejpam-3743	357	11	terms	term	NOUN
ejpam-3743	357	12	of	of	ADP
ejpam-3743	357	13	hereditary	hereditary	ADJ
ejpam-3743	357	14	and	and	CCONJ
ejpam-3743	357	15	topological	topological	ADJ
ejpam-3743	357	16	properties	property	NOUN
ejpam-3743	357	17	and	and	CCONJ
ejpam-3743	357	18	finite	finite	ADJ
ejpam-3743	357	19	product	product	NOUN
ejpam-3743	357	20	space	space	NOUN
ejpam-3743	357	21	.	.	PUNCT
ejpam-3743	358	1	definition	definition	NOUN
ejpam-3743	358	2	15	15	NUM
ejpam-3743	358	3	.	.	PUNCT
ejpam-3743	359	1	for	for	ADP
ejpam-3743	359	2	a	a	DET
ejpam-3743	359	3	nonempty	nonempty	NOUN
ejpam-3743	359	4	subset	subset	VERB
ejpam-3743	359	5	a	a	DET
ejpam-3743	359	6	of	of	ADP
ejpam-3743	359	7	(	(	PUNCT
ejpam-3743	359	8	x,µ	x,µ	NOUN
ejpam-3743	359	9	)	)	PUNCT
ejpam-3743	359	10	,	,	PUNCT
ejpam-3743	359	11	the	the	DET
ejpam-3743	359	12	family	family	NOUN
ejpam-3743	359	13	µa	µa	NOUN
ejpam-3743	359	14	=	=	PUNCT
ejpam-3743	359	15	{	{	PUNCT
ejpam-3743	359	16	a	a	DET
ejpam-3743	359	17	⋂	⋂	PROPN
ejpam-3743	359	18	g	g	NOUN
ejpam-3743	359	19	:	:	PUNCT
ejpam-3743	359	20	g	g	PROPN
ejpam-3743	359	21	is	be	AUX
ejpam-3743	359	22	a	a	DET
ejpam-3743	359	23	supra	supra	ADJ
ejpam-3743	359	24	semi	semi	ADJ
ejpam-3743	359	25	-	-	ADJ
ejpam-3743	359	26	open	open	ADJ
ejpam-3743	359	27	subset	subset	NOUN
ejpam-3743	359	28	of	of	ADP
ejpam-3743	359	29	(	(	PUNCT
ejpam-3743	359	30	x,µ	x,µ	NOUN
ejpam-3743	359	31	)	)	PUNCT
ejpam-3743	359	32	}	}	PUNCT
ejpam-3743	359	33	is	be	AUX
ejpam-3743	359	34	called	call	VERB
ejpam-3743	359	35	a	a	DET
ejpam-3743	359	36	relative	relative	ADJ
ejpam-3743	359	37	semi	semi	NOUN
ejpam-3743	359	38	-	-	NOUN
ejpam-3743	359	39	topology	topology	NOUN
ejpam-3743	359	40	on	on	ADP
ejpam-3743	359	41	a.	a.	NOUN
ejpam-3743	359	42	a	a	DET
ejpam-3743	359	43	pair	pair	NOUN
ejpam-3743	359	44	(	(	PUNCT
ejpam-3743	359	45	a,µa	a,µa	NUM
ejpam-3743	359	46	)	)	PUNCT
ejpam-3743	359	47	is	be	AUX
ejpam-3743	359	48	called	call	VERB
ejpam-3743	359	49	a	a	DET
ejpam-3743	359	50	semi	semi	NOUN
ejpam-3743	359	51	-	-	NOUN
ejpam-3743	359	52	subspace	subspace	NOUN
ejpam-3743	359	53	of	of	ADP
ejpam-3743	359	54	(	(	PUNCT
ejpam-3743	359	55	x,µ	x,µ	NOUN
ejpam-3743	359	56	)	)	PUNCT
ejpam-3743	359	57	.	.	PUNCT
ejpam-3743	360	1	one	one	PRON
ejpam-3743	360	2	can	can	AUX
ejpam-3743	360	3	easily	easily	ADV
ejpam-3743	360	4	prove	prove	VERB
ejpam-3743	360	5	that	that	SCONJ
ejpam-3743	360	6	a	a	DET
ejpam-3743	360	7	semi	semi	NOUN
ejpam-3743	360	8	-	-	NOUN
ejpam-3743	360	9	subspace	subspace	ADJ
ejpam-3743	360	10	(	(	PUNCT
ejpam-3743	360	11	a,µa	a,µa	NUM
ejpam-3743	360	12	)	)	PUNCT
ejpam-3743	360	13	of	of	ADP
ejpam-3743	360	14	(	(	PUNCT
ejpam-3743	360	15	x,µ	x,µ	NOUN
ejpam-3743	360	16	)	)	PUNCT
ejpam-3743	360	17	is	be	AUX
ejpam-3743	360	18	a	a	DET
ejpam-3743	360	19	supra	supra	ADJ
ejpam-3743	360	20	topological	topological	ADJ
ejpam-3743	360	21	space	space	NOUN
ejpam-3743	360	22	.	.	PUNCT
ejpam-3743	361	1	proposition	proposition	NOUN
ejpam-3743	361	2	5	5	NUM
ejpam-3743	361	3	.	.	PUNCT
ejpam-3743	362	1	let	let	AUX
ejpam-3743	362	2	(	(	PUNCT
ejpam-3743	362	3	y	y	NOUN
ejpam-3743	362	4	,	,	PUNCT
ejpam-3743	362	5	µy	µy	X
ejpam-3743	362	6	)	)	PUNCT
ejpam-3743	362	7	be	be	AUX
ejpam-3743	362	8	a	a	DET
ejpam-3743	362	9	semi	semi	NOUN
ejpam-3743	362	10	-	-	NOUN
ejpam-3743	362	11	subspace	subspace	NOUN
ejpam-3743	362	12	of	of	ADP
ejpam-3743	362	13	(	(	PUNCT
ejpam-3743	362	14	x,µ	x,µ	NOUN
ejpam-3743	362	15	)	)	PUNCT
ejpam-3743	362	16	.	.	PUNCT
ejpam-3743	363	1	a	a	DET
ejpam-3743	363	2	subset	subset	ADJ
ejpam-3743	363	3	h	h	NOUN
ejpam-3743	363	4	of	of	ADP
ejpam-3743	363	5	y	y	PROPN
ejpam-3743	363	6	is	be	AUX
ejpam-3743	363	7	supra	supra	ADJ
ejpam-3743	363	8	semi	semi	ADV
ejpam-3743	363	9	-	-	ADJ
ejpam-3743	363	10	closed	closed	ADJ
ejpam-3743	363	11	in	in	ADP
ejpam-3743	363	12	(	(	PUNCT
ejpam-3743	363	13	y	y	PROPN
ejpam-3743	363	14	,	,	PUNCT
ejpam-3743	363	15	µy	µy	ADV
ejpam-3743	363	16	)	)	PUNCT
ejpam-3743	364	1	iff	iff	PROPN
ejpam-3743	364	2	there	there	PRON
ejpam-3743	364	3	exists	exist	VERB
ejpam-3743	364	4	a	a	DET
ejpam-3743	364	5	supra	supra	NOUN
ejpam-3743	364	6	semi	semi	ADJ
ejpam-3743	364	7	-	-	ADJ
ejpam-3743	364	8	closed	closed	ADJ
ejpam-3743	364	9	subset	subset	ADJ
ejpam-3743	364	10	f	f	PROPN
ejpam-3743	364	11	of	of	ADP
ejpam-3743	364	12	(	(	PUNCT
ejpam-3743	364	13	x,µ	x,µ	NOUN
ejpam-3743	364	14	)	)	PUNCT
ejpam-3743	364	15	such	such	ADJ
ejpam-3743	364	16	that	that	DET
ejpam-3743	364	17	h	h	NOUN
ejpam-3743	365	1	=	=	SYM
ejpam-3743	365	2	y	y	PROPN
ejpam-3743	365	3	⋂	⋂	PROPN
ejpam-3743	365	4	f	f	PROPN
ejpam-3743	365	5	.	.	PUNCT
ejpam-3743	366	1	t.	t.	PROPN
ejpam-3743	366	2	m.	m.	PROPN
ejpam-3743	366	3	al	al	PROPN
ejpam-3743	366	4	-	-	PUNCT
ejpam-3743	366	5	shami	shami	PROPN
ejpam-3743	366	6	et	et	PROPN
ejpam-3743	366	7	al	al	PROPN
ejpam-3743	366	8	.	.	PUNCT
ejpam-3743	366	9	/	/	SYM
ejpam-3743	366	10	eur	eur	PROPN
ejpam-3743	366	11	.	.	PUNCT
ejpam-3743	367	1	j.	j.	PROPN
ejpam-3743	367	2	pure	pure	PROPN
ejpam-3743	367	3	appl	appl	PROPN
ejpam-3743	367	4	.	.	PROPN
ejpam-3743	367	5	math	math	PROPN
ejpam-3743	367	6	,	,	PUNCT
ejpam-3743	367	7	13	13	NUM
ejpam-3743	367	8	(	(	PUNCT
ejpam-3743	367	9	3	3	NUM
ejpam-3743	367	10	)	)	PUNCT
ejpam-3743	367	11	(	(	PUNCT
ejpam-3743	367	12	2020	2020	NUM
ejpam-3743	367	13	)	)	PUNCT
ejpam-3743	367	14	,	,	PUNCT
ejpam-3743	367	15	427	427	NUM
ejpam-3743	367	16	-	-	SYM
ejpam-3743	367	17	443	443	NUM
ejpam-3743	367	18	439	439	NUM
ejpam-3743	367	19	proof	proof	NOUN
ejpam-3743	367	20	.	.	PUNCT
ejpam-3743	368	1	necessity	necessity	NOUN
ejpam-3743	368	2	:	:	PUNCT
ejpam-3743	368	3	let	let	VERB
ejpam-3743	368	4	h	h	NOUN
ejpam-3743	368	5	be	be	AUX
ejpam-3743	368	6	a	a	DET
ejpam-3743	368	7	supra	supra	ADJ
ejpam-3743	368	8	semi	semi	ADJ
ejpam-3743	368	9	-	-	ADJ
ejpam-3743	368	10	closed	closed	ADJ
ejpam-3743	368	11	subset	subset	NOUN
ejpam-3743	368	12	of	of	ADP
ejpam-3743	368	13	(	(	PUNCT
ejpam-3743	368	14	y	y	PROPN
ejpam-3743	368	15	,	,	PUNCT
ejpam-3743	368	16	µy	µy	ADV
ejpam-3743	368	17	)	)	PUNCT
ejpam-3743	368	18	.	.	PUNCT
ejpam-3743	369	1	then	then	ADV
ejpam-3743	369	2	there	there	PRON
ejpam-3743	369	3	exists	exist	VERB
ejpam-3743	369	4	a	a	DET
ejpam-3743	369	5	supra	supra	NOUN
ejpam-3743	369	6	semi	semi	ADJ
ejpam-3743	369	7	-	-	ADJ
ejpam-3743	369	8	open	open	ADJ
ejpam-3743	369	9	subset	subset	NOUN
ejpam-3743	369	10	w	w	PROPN
ejpam-3743	369	11	of	of	ADP
ejpam-3743	369	12	(	(	PUNCT
ejpam-3743	369	13	y	y	PROPN
ejpam-3743	369	14	,	,	PUNCT
ejpam-3743	369	15	µy	µy	ADV
ejpam-3743	369	16	)	)	PUNCT
ejpam-3743	369	17	such	such	ADJ
ejpam-3743	369	18	that	that	DET
ejpam-3743	369	19	h	h	NOUN
ejpam-3743	369	20	=	=	SYM
ejpam-3743	369	21	y	y	PROPN
ejpam-3743	369	22	\w	\w	ADJ
ejpam-3743	369	23	.	.	PUNCT
ejpam-3743	370	1	now	now	ADV
ejpam-3743	370	2	,	,	PUNCT
ejpam-3743	370	3	there	there	PRON
ejpam-3743	370	4	exists	exist	VERB
ejpam-3743	370	5	a	a	DET
ejpam-3743	370	6	supra	supra	PROPN
ejpam-3743	370	7	semiopen	semiopen	PROPN
ejpam-3743	370	8	subset	subset	VERB
ejpam-3743	370	9	v	v	ADP
ejpam-3743	370	10	of	of	ADP
ejpam-3743	370	11	(	(	PUNCT
ejpam-3743	370	12	x,µ	x,µ	NOUN
ejpam-3743	370	13	)	)	PUNCT
ejpam-3743	370	14	such	such	ADJ
ejpam-3743	370	15	that	that	DET
ejpam-3743	370	16	w	w	PROPN
ejpam-3743	370	17	=	=	SYM
ejpam-3743	370	18	y	y	PROPN
ejpam-3743	370	19	⋂	⋂	PROPN
ejpam-3743	370	20	v	v	NOUN
ejpam-3743	370	21	.	.	PUNCT
ejpam-3743	371	1	therefore	therefore	ADV
ejpam-3743	371	2	h	h	NOUN
ejpam-3743	371	3	=	=	SYM
ejpam-3743	371	4	y	y	PROPN
ejpam-3743	371	5	\	\	PROPN
ejpam-3743	372	1	(	(	PUNCT
ejpam-3743	372	2	y	y	PROPN
ejpam-3743	372	3	⋂	⋂	PROPN
ejpam-3743	372	4	v	v	NOUN
ejpam-3743	372	5	)	)	PUNCT
ejpam-3743	373	1	=	=	PUNCT
ejpam-3743	373	2	y	y	PROPN
ejpam-3743	373	3	⋂	⋂	PROPN
ejpam-3743	373	4	v	v	ADP
ejpam-3743	373	5	c.	c.	NOUN
ejpam-3743	373	6	by	by	ADP
ejpam-3743	373	7	taking	take	VERB
ejpam-3743	373	8	f	f	PROPN
ejpam-3743	373	9	=	=	X
ejpam-3743	373	10	v	v	PROPN
ejpam-3743	373	11	c	c	NOUN
ejpam-3743	373	12	,	,	PUNCT
ejpam-3743	373	13	the	the	DET
ejpam-3743	373	14	proof	proof	NOUN
ejpam-3743	373	15	of	of	ADP
ejpam-3743	373	16	the	the	DET
ejpam-3743	373	17	necessary	necessary	ADJ
ejpam-3743	373	18	part	part	NOUN
ejpam-3743	373	19	is	be	AUX
ejpam-3743	373	20	complete	complete	ADJ
ejpam-3743	373	21	.	.	PUNCT
ejpam-3743	374	1	sufficiency	sufficiency	NOUN
ejpam-3743	374	2	:	:	PUNCT
ejpam-3743	374	3	let	let	VERB
ejpam-3743	374	4	h	h	NOUN
ejpam-3743	374	5	=	=	PUNCT
ejpam-3743	375	1	y	y	PROPN
ejpam-3743	375	2	⋂	⋂	PROPN
ejpam-3743	375	3	f	f	PROPN
ejpam-3743	375	4	such	such	ADJ
ejpam-3743	375	5	that	that	SCONJ
ejpam-3743	375	6	f	f	PROPN
ejpam-3743	375	7	is	be	AUX
ejpam-3743	375	8	a	a	DET
ejpam-3743	375	9	supra	supra	ADJ
ejpam-3743	375	10	semi	semi	ADJ
ejpam-3743	375	11	-	-	ADJ
ejpam-3743	375	12	closed	closed	ADJ
ejpam-3743	375	13	subset	subset	NOUN
ejpam-3743	375	14	of	of	ADP
ejpam-3743	375	15	(	(	PUNCT
ejpam-3743	375	16	x,µ	x,µ	NOUN
ejpam-3743	375	17	)	)	PUNCT
ejpam-3743	375	18	.	.	PUNCT
ejpam-3743	376	1	then	then	ADV
ejpam-3743	376	2	y	y	PROPN
ejpam-3743	376	3	\h	\h	PUNCT
ejpam-3743	377	1	=	=	PUNCT
ejpam-3743	378	1	y	y	PROPN
ejpam-3743	378	2	\(y	\(y	NUM
ejpam-3743	378	3	⋂	⋂	PROPN
ejpam-3743	378	4	f	f	PROPN
ejpam-3743	378	5	)	)	PUNCT
ejpam-3743	379	1	=	=	PUNCT
ejpam-3743	379	2	(	(	PUNCT
ejpam-3743	379	3	y	y	PROPN
ejpam-3743	379	4	⋂	⋂	PROPN
ejpam-3743	380	1	x)\(y	x)\(y	PROPN
ejpam-3743	380	2	⋂	⋂	PROPN
ejpam-3743	380	3	f	f	PROPN
ejpam-3743	380	4	)	)	PUNCT
ejpam-3743	381	1	=	=	PUNCT
ejpam-3743	381	2	y	y	PROPN
ejpam-3743	381	3	⋂	⋂	PROPN
ejpam-3743	381	4	(	(	PUNCT
ejpam-3743	381	5	x	x	X
ejpam-3743	381	6	\f	\f	X
ejpam-3743	381	7	)	)	PUNCT
ejpam-3743	381	8	.	.	PUNCT
ejpam-3743	382	1	since	since	SCONJ
ejpam-3743	382	2	x	x	PRON
ejpam-3743	382	3	\f	\f	X
ejpam-3743	382	4	is	be	AUX
ejpam-3743	382	5	a	a	DET
ejpam-3743	382	6	supra	supra	ADJ
ejpam-3743	382	7	semi	semi	ADJ
ejpam-3743	382	8	-	-	ADJ
ejpam-3743	382	9	open	open	ADJ
ejpam-3743	382	10	subset	subset	NOUN
ejpam-3743	382	11	of	of	ADP
ejpam-3743	382	12	(	(	PUNCT
ejpam-3743	382	13	x,µ	x,µ	NOUN
ejpam-3743	382	14	)	)	PUNCT
ejpam-3743	382	15	,	,	PUNCT
ejpam-3743	382	16	then	then	ADV
ejpam-3743	382	17	y	y	PROPN
ejpam-3743	382	18	\	\	PROPN
ejpam-3743	382	19	h	h	NOUN
ejpam-3743	382	20	is	be	AUX
ejpam-3743	382	21	a	a	DET
ejpam-3743	382	22	supra	supra	ADJ
ejpam-3743	382	23	semi	semi	ADJ
ejpam-3743	382	24	-	-	ADJ
ejpam-3743	382	25	open	open	ADJ
ejpam-3743	382	26	subset	subset	NOUN
ejpam-3743	382	27	of	of	ADP
ejpam-3743	382	28	(	(	PUNCT
ejpam-3743	382	29	y	y	PROPN
ejpam-3743	382	30	,	,	PUNCT
ejpam-3743	382	31	µy	µy	ADV
ejpam-3743	382	32	)	)	PUNCT
ejpam-3743	382	33	.	.	PUNCT
ejpam-3743	383	1	thus	thus	ADV
ejpam-3743	383	2	h	h	NOUN
ejpam-3743	383	3	is	be	AUX
ejpam-3743	383	4	a	a	DET
ejpam-3743	383	5	supra	supra	ADJ
ejpam-3743	383	6	semi	semi	ADJ
ejpam-3743	383	7	-	-	ADJ
ejpam-3743	383	8	closed	closed	ADJ
ejpam-3743	383	9	subset	subset	NOUN
ejpam-3743	383	10	of	of	ADP
ejpam-3743	383	11	(	(	PUNCT
ejpam-3743	383	12	y	y	PROPN
ejpam-3743	383	13	,	,	PUNCT
ejpam-3743	383	14	µy	µy	ADV
ejpam-3743	383	15	)	)	PUNCT
ejpam-3743	383	16	.	.	PUNCT
ejpam-3743	384	1	definition	definition	NOUN
ejpam-3743	384	2	16	16	NUM
ejpam-3743	384	3	.	.	PUNCT
ejpam-3743	385	1	a	a	DET
ejpam-3743	385	2	property	property	NOUN
ejpam-3743	385	3	is	be	AUX
ejpam-3743	385	4	said	say	VERB
ejpam-3743	385	5	to	to	PART
ejpam-3743	385	6	be	be	AUX
ejpam-3743	385	7	a	a	DET
ejpam-3743	385	8	relative	relative	ADJ
ejpam-3743	385	9	semi	semi	ADJ
ejpam-3743	385	10	-	-	ADJ
ejpam-3743	385	11	hereditary	hereditary	ADJ
ejpam-3743	385	12	property	property	NOUN
ejpam-3743	385	13	if	if	SCONJ
ejpam-3743	385	14	the	the	DET
ejpam-3743	385	15	property	property	NOUN
ejpam-3743	385	16	passes	pass	VERB
ejpam-3743	385	17	from	from	ADP
ejpam-3743	385	18	a	a	DET
ejpam-3743	385	19	supra	supra	ADJ
ejpam-3743	385	20	topological	topological	ADJ
ejpam-3743	385	21	space	space	NOUN
ejpam-3743	385	22	to	to	ADP
ejpam-3743	385	23	every	every	DET
ejpam-3743	385	24	relative	relative	ADJ
ejpam-3743	385	25	semi	semi	NOUN
ejpam-3743	385	26	-	-	NOUN
ejpam-3743	385	27	subspace	subspace	NOUN
ejpam-3743	385	28	.	.	PUNCT
ejpam-3743	386	1	theorem	theorem	VERB
ejpam-3743	386	2	13	13	NUM
ejpam-3743	386	3	.	.	PUNCT
ejpam-3743	387	1	a	a	DET
ejpam-3743	387	2	property	property	NOUN
ejpam-3743	387	3	of	of	ADP
ejpam-3743	387	4	being	be	AUX
ejpam-3743	387	5	an	an	DET
ejpam-3743	387	6	ssti	ssti	NOUN
ejpam-3743	387	7	-	-	PUNCT
ejpam-3743	387	8	space	space	NOUN
ejpam-3743	387	9	is	be	AUX
ejpam-3743	387	10	a	a	DET
ejpam-3743	387	11	relative	relative	ADJ
ejpam-3743	387	12	semi	semi	NOUN
ejpam-3743	387	13	-	-	ADJ
ejpam-3743	387	14	hereditary	hereditary	ADJ
ejpam-3743	387	15	for	for	ADP
ejpam-3743	387	16	i	i	PROPN
ejpam-3743	387	17	=	=	NOUN
ejpam-3743	387	18	0	0	NUM
ejpam-3743	387	19	,	,	PUNCT
ejpam-3743	387	20	1	1	NUM
ejpam-3743	387	21	,	,	PUNCT
ejpam-3743	387	22	2	2	NUM
ejpam-3743	387	23	,	,	PUNCT
ejpam-3743	387	24	3	3	NUM
ejpam-3743	387	25	.	.	PUNCT
ejpam-3743	387	26	proof	proof	NOUN
ejpam-3743	387	27	.	.	PUNCT
ejpam-3743	388	1	we	we	PRON
ejpam-3743	388	2	shall	shall	AUX
ejpam-3743	388	3	suffice	suffice	VERB
ejpam-3743	388	4	with	with	ADP
ejpam-3743	388	5	proof	proof	NOUN
ejpam-3743	388	6	of	of	ADP
ejpam-3743	388	7	case	case	NOUN
ejpam-3743	388	8	i	i	PRON
ejpam-3743	388	9	=	=	NOUN
ejpam-3743	388	10	3	3	NUM
ejpam-3743	388	11	which	which	PRON
ejpam-3743	388	12	directly	directly	ADV
ejpam-3743	388	13	contains	contain	VERB
ejpam-3743	388	14	the	the	DET
ejpam-3743	388	15	case	case	NOUN
ejpam-3743	388	16	i	i	PRON
ejpam-3743	388	17	=	=	NOUN
ejpam-3743	389	1	1	1	X
ejpam-3743	389	2	.	.	PUNCT
ejpam-3743	389	3	in	in	ADP
ejpam-3743	389	4	a	a	DET
ejpam-3743	389	5	similar	similar	ADJ
ejpam-3743	389	6	way	way	NOUN
ejpam-3743	389	7	,	,	PUNCT
ejpam-3743	389	8	one	one	PRON
ejpam-3743	389	9	can	can	AUX
ejpam-3743	389	10	prove	prove	VERB
ejpam-3743	389	11	the	the	DET
ejpam-3743	389	12	cases	case	NOUN
ejpam-3743	389	13	i	i	PRON
ejpam-3743	389	14	=	=	NOUN
ejpam-3743	389	15	0	0	NUM
ejpam-3743	389	16	,	,	PUNCT
ejpam-3743	389	17	2	2	NUM
ejpam-3743	389	18	.	.	PUNCT
ejpam-3743	389	19	suppose	suppose	VERB
ejpam-3743	389	20	that	that	SCONJ
ejpam-3743	389	21	(	(	PUNCT
ejpam-3743	389	22	a,µa	a,µa	NUM
ejpam-3743	389	23	)	)	PUNCT
ejpam-3743	389	24	is	be	AUX
ejpam-3743	389	25	a	a	DET
ejpam-3743	389	26	relative	relative	ADJ
ejpam-3743	389	27	semi	semi	NOUN
ejpam-3743	389	28	-	-	NOUN
ejpam-3743	389	29	subspace	subspace	NOUN
ejpam-3743	389	30	of	of	ADP
ejpam-3743	389	31	an	an	DET
ejpam-3743	389	32	sst3	sst3	NOUN
ejpam-3743	389	33	-	-	PUNCT
ejpam-3743	389	34	space	space	NOUN
ejpam-3743	389	35	(	(	PUNCT
ejpam-3743	389	36	x,µ	x,µ	NOUN
ejpam-3743	389	37	)	)	PUNCT
ejpam-3743	389	38	.	.	PUNCT
ejpam-3743	390	1	we	we	PRON
ejpam-3743	390	2	first	first	ADV
ejpam-3743	390	3	show	show	VERB
ejpam-3743	390	4	that	that	SCONJ
ejpam-3743	390	5	(	(	PUNCT
ejpam-3743	390	6	a,µa	a,µa	NUM
ejpam-3743	390	7	)	)	PUNCT
ejpam-3743	390	8	is	be	AUX
ejpam-3743	390	9	an	an	DET
ejpam-3743	390	10	sst1	sst1	NOUN
ejpam-3743	390	11	-	-	PUNCT
ejpam-3743	390	12	space	space	NOUN
ejpam-3743	390	13	.	.	PUNCT
ejpam-3743	391	1	let	let	VERB
ejpam-3743	391	2	x	x	PRON
ejpam-3743	391	3	6=	6=	ADP
ejpam-3743	391	4	y	y	PROPN
ejpam-3743	391	5	∈	∈	PROPN
ejpam-3743	391	6	a	a	DET
ejpam-3743	391	7	⊆	⊆	NUM
ejpam-3743	391	8	x.	x.	NOUN
ejpam-3743	391	9	then	then	ADV
ejpam-3743	391	10	there	there	PRON
ejpam-3743	391	11	are	be	VERB
ejpam-3743	391	12	two	two	NUM
ejpam-3743	391	13	supra	supra	ADJ
ejpam-3743	391	14	semi	semi	ADJ
ejpam-3743	391	15	-	-	ADJ
ejpam-3743	391	16	open	open	ADJ
ejpam-3743	391	17	subsets	subset	NOUN
ejpam-3743	391	18	u	u	NOUN
ejpam-3743	391	19	and	and	CCONJ
ejpam-3743	391	20	v	v	X
ejpam-3743	391	21	of	of	ADP
ejpam-3743	391	22	(	(	PUNCT
ejpam-3743	391	23	x,µ	x,µ	NOUN
ejpam-3743	391	24	)	)	PUNCT
ejpam-3743	391	25	containing	contain	VERB
ejpam-3743	391	26	x	x	PROPN
ejpam-3743	391	27	and	and	CCONJ
ejpam-3743	391	28	y	y	PROPN
ejpam-3743	391	29	,	,	PUNCT
ejpam-3743	391	30	respectively	respectively	ADV
ejpam-3743	391	31	,	,	PUNCT
ejpam-3743	392	1	such	such	ADJ
ejpam-3743	392	2	that	that	SCONJ
ejpam-3743	392	3	x	x	PROPN
ejpam-3743	392	4	6∈	6∈	NUM
ejpam-3743	392	5	v	v	NOUN
ejpam-3743	392	6	and	and	CCONJ
ejpam-3743	392	7	y	y	PROPN
ejpam-3743	392	8	6∈	6∈	PROPN
ejpam-3743	392	9	u	u	PROPN
ejpam-3743	392	10	.	.	PUNCT
ejpam-3743	393	1	now	now	ADV
ejpam-3743	393	2	,	,	PUNCT
ejpam-3743	393	3	g	g	PROPN
ejpam-3743	393	4	=	=	PUNCT
ejpam-3743	393	5	a	a	DET
ejpam-3743	393	6	⋂	⋂	PROPN
ejpam-3743	393	7	u	u	NOUN
ejpam-3743	393	8	and	and	CCONJ
ejpam-3743	393	9	h	h	NOUN
ejpam-3743	393	10	=	=	NOUN
ejpam-3743	394	1	a	a	DET
ejpam-3743	394	2	⋂	⋂	PROPN
ejpam-3743	394	3	v	v	NOUN
ejpam-3743	394	4	are	be	AUX
ejpam-3743	394	5	two	two	NUM
ejpam-3743	394	6	supra	supra	ADJ
ejpam-3743	394	7	semi	semi	ADJ
ejpam-3743	394	8	-	-	ADJ
ejpam-3743	394	9	open	open	ADJ
ejpam-3743	394	10	subsets	subset	NOUN
ejpam-3743	394	11	of	of	ADP
ejpam-3743	394	12	(	(	PUNCT
ejpam-3743	394	13	a,µa	a,µa	PROPN
ejpam-3743	394	14	)	)	PUNCT
ejpam-3743	394	15	containing	contain	VERB
ejpam-3743	394	16	x	x	PROPN
ejpam-3743	394	17	and	and	CCONJ
ejpam-3743	394	18	y	y	PROPN
ejpam-3743	394	19	,	,	PUNCT
ejpam-3743	394	20	respectively	respectively	ADV
ejpam-3743	394	21	,	,	PUNCT
ejpam-3743	394	22	such	such	ADJ
ejpam-3743	394	23	that	that	SCONJ
ejpam-3743	394	24	x	x	SYM
ejpam-3743	394	25	6∈	6∈	NOUN
ejpam-3743	394	26	h	h	NOUN
ejpam-3743	394	27	and	and	CCONJ
ejpam-3743	394	28	y	y	PROPN
ejpam-3743	394	29	6∈	6∈	PROPN
ejpam-3743	394	30	g.	g.	PROPN
ejpam-3743	394	31	thus	thus	ADV
ejpam-3743	394	32	,	,	PUNCT
ejpam-3743	394	33	(	(	PUNCT
ejpam-3743	394	34	a,µa	a,µa	NUM
ejpam-3743	394	35	)	)	PUNCT
ejpam-3743	394	36	is	be	AUX
ejpam-3743	394	37	sst1	sst1	PROPN
ejpam-3743	394	38	.	.	PUNCT
ejpam-3743	395	1	second	second	ADJ
ejpam-3743	395	2	,	,	PUNCT
ejpam-3743	395	3	we	we	PRON
ejpam-3743	395	4	show	show	VERB
ejpam-3743	395	5	that	that	SCONJ
ejpam-3743	395	6	(	(	PUNCT
ejpam-3743	395	7	a,µa	a,µa	NUM
ejpam-3743	395	8	)	)	PUNCT
ejpam-3743	395	9	is	be	AUX
ejpam-3743	395	10	supra	supra	ADJ
ejpam-3743	395	11	semi	semi	ADV
ejpam-3743	395	12	regular	regular	ADJ
ejpam-3743	395	13	.	.	PUNCT
ejpam-3743	396	1	let	let	VERB
ejpam-3743	396	2	h	h	PRON
ejpam-3743	396	3	be	be	AUX
ejpam-3743	396	4	a	a	DET
ejpam-3743	396	5	supra	supra	ADJ
ejpam-3743	396	6	semi	semi	ADJ
ejpam-3743	396	7	-	-	ADJ
ejpam-3743	396	8	closed	closed	ADJ
ejpam-3743	396	9	subset	subset	NOUN
ejpam-3743	396	10	of	of	ADP
ejpam-3743	396	11	(	(	PUNCT
ejpam-3743	396	12	a,µa	a,µa	NUM
ejpam-3743	396	13	)	)	PUNCT
ejpam-3743	396	14	and	and	CCONJ
ejpam-3743	396	15	a	a	DET
ejpam-3743	396	16	∈	∈	PROPN
ejpam-3743	396	17	a	a	DET
ejpam-3743	396	18	such	such	ADJ
ejpam-3743	396	19	that	that	SCONJ
ejpam-3743	396	20	a	a	DET
ejpam-3743	396	21	6∈	6∈	PROPN
ejpam-3743	396	22	h.	h.	NOUN
ejpam-3743	397	1	it	it	PRON
ejpam-3743	397	2	follows	follow	VERB
ejpam-3743	397	3	from	from	ADP
ejpam-3743	397	4	proposition	proposition	NOUN
ejpam-3743	397	5	(	(	PUNCT
ejpam-3743	397	6	5	5	NUM
ejpam-3743	397	7	)	)	PUNCT
ejpam-3743	397	8	that	that	SCONJ
ejpam-3743	397	9	there	there	PRON
ejpam-3743	397	10	is	be	VERB
ejpam-3743	397	11	a	a	DET
ejpam-3743	397	12	supra	supra	ADJ
ejpam-3743	397	13	semi	semi	ADJ
ejpam-3743	397	14	-	-	ADJ
ejpam-3743	397	15	closed	closed	ADJ
ejpam-3743	397	16	subset	subset	ADJ
ejpam-3743	397	17	f	f	PROPN
ejpam-3743	397	18	of	of	ADP
ejpam-3743	397	19	(	(	PUNCT
ejpam-3743	397	20	x,µ	x,µ	NOUN
ejpam-3743	397	21	)	)	PUNCT
ejpam-3743	397	22	such	such	ADJ
ejpam-3743	397	23	that	that	DET
ejpam-3743	397	24	h	h	NOUN
ejpam-3743	397	25	=	=	SYM
ejpam-3743	397	26	f	f	PROPN
ejpam-3743	397	27	⋂	⋂	PROPN
ejpam-3743	397	28	a.	a.	NOUN
ejpam-3743	397	29	since	since	SCONJ
ejpam-3743	397	30	a	a	DET
ejpam-3743	397	31	6∈	6∈	NOUN
ejpam-3743	397	32	f	f	NOUN
ejpam-3743	397	33	,	,	PUNCT
ejpam-3743	397	34	then	then	ADV
ejpam-3743	397	35	there	there	PRON
ejpam-3743	397	36	exist	exist	VERB
ejpam-3743	397	37	disjoint	disjoint	ADJ
ejpam-3743	397	38	supra	supra	PROPN
ejpam-3743	397	39	semi	semi	ADJ
ejpam-3743	397	40	-	-	ADJ
ejpam-3743	397	41	open	open	ADJ
ejpam-3743	397	42	subsets	subset	NOUN
ejpam-3743	397	43	u	u	NOUN
ejpam-3743	397	44	and	and	CCONJ
ejpam-3743	397	45	v	v	X
ejpam-3743	397	46	of	of	ADP
ejpam-3743	397	47	(	(	PUNCT
ejpam-3743	397	48	x,µ	x,µ	NOUN
ejpam-3743	397	49	)	)	PUNCT
ejpam-3743	397	50	containing	contain	VERB
ejpam-3743	397	51	f	f	PROPN
ejpam-3743	397	52	and	and	CCONJ
ejpam-3743	397	53	a	a	PRON
ejpam-3743	397	54	,	,	PUNCT
ejpam-3743	397	55	respectively	respectively	ADV
ejpam-3743	397	56	.	.	PUNCT
ejpam-3743	398	1	now	now	ADV
ejpam-3743	398	2	,	,	PUNCT
ejpam-3743	398	3	m	m	VERB
ejpam-3743	398	4	=	=	VERB
ejpam-3743	398	5	u	u	PROPN
ejpam-3743	398	6	⋂	⋂	PROPN
ejpam-3743	398	7	a	a	PRON
ejpam-3743	398	8	and	and	CCONJ
ejpam-3743	398	9	n	n	NOUN
ejpam-3743	398	10	=	=	PROPN
ejpam-3743	398	11	v	v	ADP
ejpam-3743	398	12	⋂	⋂	PROPN
ejpam-3743	398	13	a	a	PRON
ejpam-3743	398	14	are	be	AUX
ejpam-3743	398	15	disjoint	disjoint	NOUN
ejpam-3743	398	16	supra	supra	NOUN
ejpam-3743	398	17	semi	semi	ADJ
ejpam-3743	398	18	-	-	ADJ
ejpam-3743	398	19	open	open	ADJ
ejpam-3743	398	20	subsets	subset	NOUN
ejpam-3743	398	21	of	of	ADP
ejpam-3743	398	22	(	(	PUNCT
ejpam-3743	398	23	a,µa	a,µa	PROPN
ejpam-3743	398	24	)	)	PUNCT
ejpam-3743	398	25	containing	contain	VERB
ejpam-3743	398	26	h	h	NOUN
ejpam-3743	398	27	and	and	CCONJ
ejpam-3743	398	28	a	a	PRON
ejpam-3743	398	29	,	,	PUNCT
ejpam-3743	398	30	respectively	respectively	ADV
ejpam-3743	398	31	.	.	PUNCT
ejpam-3743	399	1	thus	thus	ADV
ejpam-3743	399	2	(	(	PUNCT
ejpam-3743	399	3	a,µa	a,µa	NUM
ejpam-3743	399	4	)	)	PUNCT
ejpam-3743	399	5	is	be	AUX
ejpam-3743	399	6	supra	supra	ADJ
ejpam-3743	399	7	semi	semi	ADV
ejpam-3743	399	8	regular	regular	ADJ
ejpam-3743	399	9	.	.	PUNCT
ejpam-3743	400	1	hence	hence	ADV
ejpam-3743	400	2	,	,	PUNCT
ejpam-3743	400	3	the	the	DET
ejpam-3743	400	4	proof	proof	NOUN
ejpam-3743	400	5	is	be	AUX
ejpam-3743	400	6	complete	complete	ADJ
ejpam-3743	400	7	.	.	PUNCT
ejpam-3743	401	1	proposition	proposition	NOUN
ejpam-3743	401	2	6	6	NUM
ejpam-3743	401	3	.	.	PUNCT
ejpam-3743	402	1	let	let	VERB
ejpam-3743	402	2	g	g	NOUN
ejpam-3743	402	3	:	:	PUNCT
ejpam-3743	402	4	(	(	PUNCT
ejpam-3743	402	5	x,µ	x,µ	NOUN
ejpam-3743	402	6	)	)	PUNCT
ejpam-3743	402	7	→	→	SYM
ejpam-3743	402	8	(	(	PUNCT
ejpam-3743	402	9	y	y	PROPN
ejpam-3743	402	10	,	,	PUNCT
ejpam-3743	402	11	θ	θ	PROPN
ejpam-3743	402	12	)	)	PUNCT
ejpam-3743	402	13	be	be	VERB
ejpam-3743	402	14	an	an	DET
ejpam-3743	402	15	injective	injective	ADJ
ejpam-3743	402	16	supra	supra	NOUN
ejpam-3743	402	17	semi	semi	ADJ
ejpam-3743	402	18	-	-	ADJ
ejpam-3743	402	19	continuous	continuous	ADJ
ejpam-3743	402	20	map	map	NOUN
ejpam-3743	402	21	.	.	PUNCT
ejpam-3743	403	1	if	if	SCONJ
ejpam-3743	403	2	(	(	PUNCT
ejpam-3743	403	3	y	y	PROPN
ejpam-3743	403	4	,	,	PUNCT
ejpam-3743	403	5	θ	θ	PROPN
ejpam-3743	403	6	)	)	PUNCT
ejpam-3743	403	7	is	be	AUX
ejpam-3743	403	8	ti	ti	NOUN
ejpam-3743	403	9	,	,	PUNCT
ejpam-3743	403	10	then	then	ADV
ejpam-3743	403	11	(	(	PUNCT
ejpam-3743	403	12	x,µ	x,µ	NOUN
ejpam-3743	403	13	)	)	PUNCT
ejpam-3743	404	1	is	be	AUX
ejpam-3743	404	2	ssti	ssti	ADJ
ejpam-3743	404	3	for	for	ADP
ejpam-3743	404	4	i	i	PROPN
ejpam-3743	404	5	=	=	SYM
ejpam-3743	404	6	0	0	NUM
ejpam-3743	404	7	,	,	PUNCT
ejpam-3743	404	8	1	1	NUM
ejpam-3743	404	9	,	,	PUNCT
ejpam-3743	404	10	2	2	NUM
ejpam-3743	404	11	.	.	PUNCT
ejpam-3743	404	12	proof	proof	NOUN
ejpam-3743	404	13	.	.	PUNCT
ejpam-3743	405	1	we	we	PRON
ejpam-3743	405	2	only	only	ADV
ejpam-3743	405	3	prove	prove	VERB
ejpam-3743	405	4	the	the	DET
ejpam-3743	405	5	proposition	proposition	NOUN
ejpam-3743	405	6	in	in	ADP
ejpam-3743	405	7	the	the	DET
ejpam-3743	405	8	case	case	NOUN
ejpam-3743	405	9	of	of	ADP
ejpam-3743	405	10	i	i	PRON
ejpam-3743	405	11	=	=	PROPN
ejpam-3743	405	12	2	2	NUM
ejpam-3743	405	13	and	and	CCONJ
ejpam-3743	405	14	the	the	DET
ejpam-3743	405	15	other	other	ADJ
ejpam-3743	405	16	cases	case	NOUN
ejpam-3743	405	17	can	can	AUX
ejpam-3743	405	18	be	be	AUX
ejpam-3743	405	19	made	make	VERB
ejpam-3743	405	20	similarly	similarly	ADV
ejpam-3743	405	21	.	.	PUNCT
ejpam-3743	406	1	let	let	VERB
ejpam-3743	406	2	a	a	DET
ejpam-3743	406	3	6=	6=	NUM
ejpam-3743	406	4	b	b	PROPN
ejpam-3743	406	5	∈	∈	PROPN
ejpam-3743	406	6	x.	x.	NOUN
ejpam-3743	406	7	then	then	ADV
ejpam-3743	406	8	,	,	PUNCT
ejpam-3743	406	9	it	it	PRON
ejpam-3743	406	10	follows	follow	VERB
ejpam-3743	406	11	from	from	ADP
ejpam-3743	406	12	the	the	DET
ejpam-3743	406	13	injectivity	injectivity	NOUN
ejpam-3743	406	14	of	of	ADP
ejpam-3743	406	15	g	g	NOUN
ejpam-3743	406	16	,	,	PUNCT
ejpam-3743	406	17	that	that	SCONJ
ejpam-3743	406	18	there	there	PRON
ejpam-3743	406	19	are	be	VERB
ejpam-3743	406	20	x	x	X
ejpam-3743	406	21	6=	6=	NUM
ejpam-3743	406	22	y	y	PROPN
ejpam-3743	406	23	∈	∈	PROPN
ejpam-3743	406	24	y	y	PROPN
ejpam-3743	406	25	such	such	ADJ
ejpam-3743	406	26	that	that	SCONJ
ejpam-3743	406	27	x	x	X
ejpam-3743	406	28	=	=	SYM
ejpam-3743	406	29	f(a	f(a	PROPN
ejpam-3743	406	30	)	)	PUNCT
ejpam-3743	406	31	and	and	CCONJ
ejpam-3743	406	32	y	y	PROPN
ejpam-3743	406	33	=	=	SYM
ejpam-3743	406	34	f(b	f(b	PROPN
ejpam-3743	406	35	)	)	PUNCT
ejpam-3743	406	36	.	.	PUNCT
ejpam-3743	407	1	since	since	SCONJ
ejpam-3743	407	2	(	(	PUNCT
ejpam-3743	407	3	y	y	PROPN
ejpam-3743	407	4	,	,	PUNCT
ejpam-3743	407	5	θ	θ	PROPN
ejpam-3743	407	6	)	)	PUNCT
ejpam-3743	407	7	is	be	AUX
ejpam-3743	407	8	t2	t2	NOUN
ejpam-3743	407	9	,	,	PUNCT
ejpam-3743	407	10	then	then	ADV
ejpam-3743	407	11	there	there	PRON
ejpam-3743	407	12	are	be	VERB
ejpam-3743	407	13	two	two	NUM
ejpam-3743	407	14	disjoint	disjoint	ADJ
ejpam-3743	407	15	open	open	ADJ
ejpam-3743	407	16	subsets	subset	NOUN
ejpam-3743	407	17	u	u	NOUN
ejpam-3743	407	18	and	and	CCONJ
ejpam-3743	407	19	v	v	NOUN
ejpam-3743	407	20	of	of	ADP
ejpam-3743	407	21	(	(	PUNCT
ejpam-3743	407	22	y	y	PROPN
ejpam-3743	407	23	,	,	PUNCT
ejpam-3743	407	24	θ	θ	NOUN
ejpam-3743	407	25	)	)	PUNCT
ejpam-3743	407	26	containing	contain	VERB
ejpam-3743	407	27	a	a	PRON
ejpam-3743	407	28	and	and	CCONJ
ejpam-3743	407	29	b	b	NOUN
ejpam-3743	407	30	,	,	PUNCT
ejpam-3743	407	31	respectively	respectively	ADV
ejpam-3743	407	32	.	.	PUNCT
ejpam-3743	408	1	now	now	ADV
ejpam-3743	408	2	,	,	PUNCT
ejpam-3743	408	3	g−1(u	g−1(u	PROPN
ejpam-3743	408	4	)	)	PUNCT
ejpam-3743	408	5	and	and	CCONJ
ejpam-3743	408	6	g−1(v	g−1(v	NOUN
ejpam-3743	408	7	)	)	PUNCT
ejpam-3743	408	8	are	be	AUX
ejpam-3743	408	9	disjoint	disjoint	NOUN
ejpam-3743	408	10	supra	supra	PROPN
ejpam-3743	408	11	semi	semi	ADJ
ejpam-3743	408	12	-	-	ADJ
ejpam-3743	408	13	open	open	ADJ
ejpam-3743	408	14	subsets	subset	NOUN
ejpam-3743	408	15	of	of	ADP
ejpam-3743	408	16	(	(	PUNCT
ejpam-3743	408	17	x,µ	x,µ	NOUN
ejpam-3743	408	18	)	)	PUNCT
ejpam-3743	408	19	containing	contain	VERB
ejpam-3743	408	20	a	a	PRON
ejpam-3743	408	21	and	and	CCONJ
ejpam-3743	408	22	b	b	NOUN
ejpam-3743	408	23	,	,	PUNCT
ejpam-3743	408	24	respectively	respectively	ADV
ejpam-3743	408	25	.	.	PUNCT
ejpam-3743	409	1	hence	hence	ADV
ejpam-3743	409	2	,	,	PUNCT
ejpam-3743	409	3	(	(	PUNCT
ejpam-3743	409	4	x,µ	x,µ	NOUN
ejpam-3743	409	5	)	)	PUNCT
ejpam-3743	409	6	is	be	AUX
ejpam-3743	409	7	sst2	sst2	ADJ
ejpam-3743	409	8	,	,	PUNCT
ejpam-3743	409	9	as	as	SCONJ
ejpam-3743	409	10	required	require	VERB
ejpam-3743	409	11	.	.	PUNCT
ejpam-3743	410	1	in	in	ADP
ejpam-3743	410	2	a	a	DET
ejpam-3743	410	3	similar	similar	ADJ
ejpam-3743	410	4	way	way	NOUN
ejpam-3743	410	5	,	,	PUNCT
ejpam-3743	410	6	one	one	PRON
ejpam-3743	410	7	can	can	AUX
ejpam-3743	410	8	prove	prove	VERB
ejpam-3743	410	9	the	the	DET
ejpam-3743	410	10	following	follow	VERB
ejpam-3743	410	11	results	result	NOUN
ejpam-3743	410	12	.	.	PUNCT
ejpam-3743	411	1	proposition	proposition	NOUN
ejpam-3743	411	2	7	7	NUM
ejpam-3743	411	3	.	.	PUNCT
ejpam-3743	412	1	let	let	VERB
ejpam-3743	412	2	g	g	NOUN
ejpam-3743	412	3	:	:	PUNCT
ejpam-3743	412	4	(	(	PUNCT
ejpam-3743	412	5	x	x	X
ejpam-3743	412	6	,	,	PUNCT
ejpam-3743	412	7	τ	τ	X
ejpam-3743	412	8	)	)	PUNCT
ejpam-3743	412	9	→	→	SYM
ejpam-3743	412	10	(	(	PUNCT
ejpam-3743	412	11	y	y	PROPN
ejpam-3743	412	12	,	,	PUNCT
ejpam-3743	412	13	ν	ν	NOUN
ejpam-3743	412	14	)	)	PUNCT
ejpam-3743	412	15	be	be	AUX
ejpam-3743	412	16	a	a	DET
ejpam-3743	412	17	bijective	bijective	ADJ
ejpam-3743	412	18	supra	supra	NOUN
ejpam-3743	412	19	semi	semi	ADJ
ejpam-3743	412	20	-	-	ADJ
ejpam-3743	412	21	open	open	ADJ
ejpam-3743	412	22	map	map	NOUN
ejpam-3743	412	23	.	.	PUNCT
ejpam-3743	413	1	if	if	SCONJ
ejpam-3743	413	2	(	(	PUNCT
ejpam-3743	413	3	x	x	NOUN
ejpam-3743	413	4	,	,	PUNCT
ejpam-3743	413	5	τ	τ	X
ejpam-3743	413	6	)	)	PUNCT
ejpam-3743	413	7	is	be	AUX
ejpam-3743	413	8	ti	ti	NOUN
ejpam-3743	413	9	,	,	PUNCT
ejpam-3743	413	10	then	then	ADV
ejpam-3743	413	11	(	(	PUNCT
ejpam-3743	413	12	y	y	PROPN
ejpam-3743	413	13	,	,	PUNCT
ejpam-3743	413	14	ν	ν	NOUN
ejpam-3743	413	15	)	)	PUNCT
ejpam-3743	413	16	is	be	AUX
ejpam-3743	413	17	ssti	ssti	ADJ
ejpam-3743	413	18	for	for	ADP
ejpam-3743	413	19	i	i	PROPN
ejpam-3743	413	20	=	=	SYM
ejpam-3743	413	21	0	0	NUM
ejpam-3743	413	22	,	,	PUNCT
ejpam-3743	413	23	1	1	NUM
ejpam-3743	413	24	,	,	PUNCT
ejpam-3743	413	25	2	2	NUM
ejpam-3743	413	26	.	.	PUNCT
ejpam-3743	414	1	t.	t.	PROPN
ejpam-3743	414	2	m.	m.	PROPN
ejpam-3743	414	3	al	al	PROPN
ejpam-3743	414	4	-	-	PUNCT
ejpam-3743	414	5	shami	shami	PROPN
ejpam-3743	414	6	et	et	PROPN
ejpam-3743	414	7	al	al	PROPN
ejpam-3743	414	8	.	.	PUNCT
ejpam-3743	414	9	/	/	SYM
ejpam-3743	414	10	eur	eur	PROPN
ejpam-3743	414	11	.	.	PUNCT
ejpam-3743	415	1	j.	j.	PROPN
ejpam-3743	415	2	pure	pure	PROPN
ejpam-3743	415	3	appl	appl	PROPN
ejpam-3743	415	4	.	.	PROPN
ejpam-3743	415	5	math	math	PROPN
ejpam-3743	415	6	,	,	PUNCT
ejpam-3743	415	7	13	13	NUM
ejpam-3743	415	8	(	(	PUNCT
ejpam-3743	415	9	3	3	NUM
ejpam-3743	415	10	)	)	PUNCT
ejpam-3743	415	11	(	(	PUNCT
ejpam-3743	415	12	2020	2020	NUM
ejpam-3743	415	13	)	)	PUNCT
ejpam-3743	415	14	,	,	PUNCT
ejpam-3743	415	15	427	427	NUM
ejpam-3743	415	16	-	-	SYM
ejpam-3743	415	17	443	443	NUM
ejpam-3743	415	18	440	440	NUM
ejpam-3743	415	19	proposition	proposition	NOUN
ejpam-3743	415	20	8	8	NUM
ejpam-3743	415	21	.	.	PUNCT
ejpam-3743	416	1	let	let	VERB
ejpam-3743	416	2	g	g	NOUN
ejpam-3743	416	3	:	:	PUNCT
ejpam-3743	416	4	(	(	PUNCT
ejpam-3743	416	5	x	x	X
ejpam-3743	416	6	,	,	PUNCT
ejpam-3743	416	7	τ	τ	X
ejpam-3743	416	8	)	)	PUNCT
ejpam-3743	416	9	→	→	SYM
ejpam-3743	416	10	(	(	PUNCT
ejpam-3743	416	11	y	y	PROPN
ejpam-3743	416	12	,	,	PUNCT
ejpam-3743	416	13	ν	ν	NOUN
ejpam-3743	416	14	)	)	PUNCT
ejpam-3743	416	15	be	be	AUX
ejpam-3743	416	16	an	an	DET
ejpam-3743	416	17	injective	injective	ADJ
ejpam-3743	416	18	supra	supra	ADJ
ejpam-3743	416	19	semi?-continuous	semi?-continuous	ADJ
ejpam-3743	416	20	map	map	NOUN
ejpam-3743	416	21	.	.	PUNCT
ejpam-3743	417	1	if	if	SCONJ
ejpam-3743	417	2	(	(	PUNCT
ejpam-3743	417	3	x	x	NOUN
ejpam-3743	417	4	,	,	PUNCT
ejpam-3743	417	5	τ	τ	X
ejpam-3743	417	6	)	)	PUNCT
ejpam-3743	417	7	is	be	AUX
ejpam-3743	417	8	ssti	ssti	NOUN
ejpam-3743	417	9	,	,	PUNCT
ejpam-3743	417	10	then	then	ADV
ejpam-3743	417	11	(	(	PUNCT
ejpam-3743	417	12	y	y	NOUN
ejpam-3743	417	13	,	,	PUNCT
ejpam-3743	417	14	ν	ν	NOUN
ejpam-3743	417	15	)	)	PUNCT
ejpam-3743	417	16	is	be	AUX
ejpam-3743	417	17	ssti	ssti	ADJ
ejpam-3743	417	18	for	for	ADP
ejpam-3743	417	19	i	i	PROPN
ejpam-3743	417	20	=	=	SYM
ejpam-3743	417	21	0	0	NUM
ejpam-3743	417	22	,	,	PUNCT
ejpam-3743	417	23	1	1	NUM
ejpam-3743	417	24	,	,	PUNCT
ejpam-3743	417	25	2	2	NUM
ejpam-3743	417	26	.	.	X
ejpam-3743	417	27	proposition	proposition	NOUN
ejpam-3743	417	28	9	9	NUM
ejpam-3743	417	29	.	.	PUNCT
ejpam-3743	418	1	let	let	VERB
ejpam-3743	418	2	g	g	NOUN
ejpam-3743	418	3	:	:	PUNCT
ejpam-3743	418	4	(	(	PUNCT
ejpam-3743	418	5	x	x	X
ejpam-3743	418	6	,	,	PUNCT
ejpam-3743	418	7	τ)→	τ)→	PROPN
ejpam-3743	418	8	(	(	PUNCT
ejpam-3743	418	9	y	y	PROPN
ejpam-3743	418	10	,	,	PUNCT
ejpam-3743	418	11	ν	ν	NOUN
ejpam-3743	418	12	)	)	PUNCT
ejpam-3743	418	13	be	be	AUX
ejpam-3743	418	14	a	a	DET
ejpam-3743	418	15	bijective	bijective	ADJ
ejpam-3743	418	16	supra	supra	NOUN
ejpam-3743	418	17	semi?-open	semi?-open	PROPN
ejpam-3743	418	18	map	map	NOUN
ejpam-3743	418	19	.	.	PUNCT
ejpam-3743	419	1	if	if	SCONJ
ejpam-3743	419	2	(	(	PUNCT
ejpam-3743	419	3	x	x	NOUN
ejpam-3743	419	4	,	,	PUNCT
ejpam-3743	419	5	τ	τ	X
ejpam-3743	419	6	)	)	PUNCT
ejpam-3743	419	7	is	be	AUX
ejpam-3743	419	8	ssti	ssti	NOUN
ejpam-3743	419	9	,	,	PUNCT
ejpam-3743	419	10	then	then	ADV
ejpam-3743	419	11	(	(	PUNCT
ejpam-3743	419	12	y	y	NOUN
ejpam-3743	419	13	,	,	PUNCT
ejpam-3743	419	14	ν	ν	NOUN
ejpam-3743	419	15	)	)	PUNCT
ejpam-3743	419	16	is	be	AUX
ejpam-3743	419	17	ssti	ssti	ADJ
ejpam-3743	419	18	for	for	ADP
ejpam-3743	419	19	i	i	PROPN
ejpam-3743	419	20	=	=	SYM
ejpam-3743	419	21	0	0	NUM
ejpam-3743	419	22	,	,	PUNCT
ejpam-3743	419	23	1	1	NUM
ejpam-3743	419	24	,	,	PUNCT
ejpam-3743	419	25	2	2	NUM
ejpam-3743	419	26	.	.	X
ejpam-3743	419	27	proposition	proposition	NOUN
ejpam-3743	419	28	10	10	NUM
ejpam-3743	419	29	.	.	PUNCT
ejpam-3743	420	1	let	let	VERB
ejpam-3743	420	2	g	g	NOUN
ejpam-3743	420	3	:	:	PUNCT
ejpam-3743	420	4	(	(	PUNCT
ejpam-3743	420	5	x	x	X
ejpam-3743	420	6	,	,	PUNCT
ejpam-3743	420	7	τ	τ	X
ejpam-3743	420	8	)	)	PUNCT
ejpam-3743	420	9	→	→	SYM
ejpam-3743	420	10	(	(	PUNCT
ejpam-3743	420	11	y	y	PROPN
ejpam-3743	420	12	,	,	PUNCT
ejpam-3743	420	13	ν	ν	NOUN
ejpam-3743	420	14	)	)	PUNCT
ejpam-3743	420	15	be	be	AUX
ejpam-3743	420	16	a	a	DET
ejpam-3743	420	17	supra	supra	ADJ
ejpam-3743	420	18	semi?-homeomorphism	semi?-homeomorphism	NOUN
ejpam-3743	420	19	map	map	NOUN
ejpam-3743	420	20	.	.	PUNCT
ejpam-3743	421	1	then	then	ADV
ejpam-3743	421	2	(	(	PUNCT
ejpam-3743	421	3	x	x	X
ejpam-3743	421	4	,	,	PUNCT
ejpam-3743	421	5	τ	τ	X
ejpam-3743	421	6	)	)	PUNCT
ejpam-3743	421	7	is	be	AUX
ejpam-3743	421	8	ssti	ssti	ADJ
ejpam-3743	421	9	iff	iff	PROPN
ejpam-3743	421	10	(	(	PUNCT
ejpam-3743	421	11	y	y	PROPN
ejpam-3743	421	12	,	,	PUNCT
ejpam-3743	421	13	ν	ν	NOUN
ejpam-3743	421	14	)	)	PUNCT
ejpam-3743	421	15	is	be	AUX
ejpam-3743	421	16	ssti	ssti	ADJ
ejpam-3743	421	17	for	for	ADP
ejpam-3743	421	18	i	i	PROPN
ejpam-3743	421	19	=	=	SYM
ejpam-3743	421	20	0	0	NUM
ejpam-3743	421	21	,	,	PUNCT
ejpam-3743	421	22	1	1	NUM
ejpam-3743	421	23	,	,	PUNCT
ejpam-3743	421	24	2	2	NUM
ejpam-3743	421	25	,	,	PUNCT
ejpam-3743	421	26	3	3	NUM
ejpam-3743	421	27	,	,	PUNCT
ejpam-3743	421	28	4	4	NUM
ejpam-3743	421	29	.	.	PUNCT
ejpam-3743	421	30	theorem	theorem	VERB
ejpam-3743	421	31	14	14	NUM
ejpam-3743	421	32	.	.	PUNCT
ejpam-3743	422	1	a	a	PRON
ejpam-3743	422	2	and	and	CCONJ
ejpam-3743	422	3	b	b	NOUN
ejpam-3743	422	4	are	be	AUX
ejpam-3743	422	5	supra	supra	ADJ
ejpam-3743	422	6	semi	semi	ADJ
ejpam-3743	422	7	-	-	ADJ
ejpam-3743	422	8	open	open	ADJ
ejpam-3743	422	9	sets	set	NOUN
ejpam-3743	422	10	iff	iff	VERB
ejpam-3743	422	11	the	the	DET
ejpam-3743	422	12	product	product	NOUN
ejpam-3743	422	13	of	of	ADP
ejpam-3743	422	14	them	they	PRON
ejpam-3743	422	15	is	be	AUX
ejpam-3743	422	16	supra	supra	PROPN
ejpam-3743	422	17	semiopen	semiopen	ADJ
ejpam-3743	422	18	.	.	PUNCT
ejpam-3743	423	1	proof	proof	NOUN
ejpam-3743	423	2	.	.	PUNCT
ejpam-3743	424	1	let	let	VERB
ejpam-3743	424	2	a	a	PRON
ejpam-3743	424	3	and	and	CCONJ
ejpam-3743	424	4	b	b	NOUN
ejpam-3743	424	5	be	be	AUX
ejpam-3743	424	6	two	two	NUM
ejpam-3743	424	7	supra	supra	ADJ
ejpam-3743	424	8	semi	semi	ADJ
ejpam-3743	424	9	-	-	ADJ
ejpam-3743	424	10	open	open	ADJ
ejpam-3743	424	11	sets	set	NOUN
ejpam-3743	424	12	.	.	PUNCT
ejpam-3743	425	1	then	then	ADV
ejpam-3743	425	2	a	a	DET
ejpam-3743	425	3	⊆	⊆	NUM
ejpam-3743	425	4	cl(int(a	cl(int(a	NOUN
ejpam-3743	425	5	)	)	PUNCT
ejpam-3743	425	6	)	)	PUNCT
ejpam-3743	426	1	and	and	CCONJ
ejpam-3743	426	2	b	b	NOUN
ejpam-3743	426	3	⊆	⊆	NUM
ejpam-3743	426	4	cl(int(b	cl(int(b	NOUN
ejpam-3743	426	5	)	)	PUNCT
ejpam-3743	426	6	)	)	PUNCT
ejpam-3743	426	7	.	.	PUNCT
ejpam-3743	427	1	so	so	ADV
ejpam-3743	427	2	a	a	DET
ejpam-3743	427	3	×	×	PROPN
ejpam-3743	427	4	b	b	PROPN
ejpam-3743	427	5	⊆	⊆	NUM
ejpam-3743	427	6	cl(int(a	cl(int(a	NOUN
ejpam-3743	427	7	)	)	PUNCT
ejpam-3743	427	8	)	)	PUNCT
ejpam-3743	428	1	×	×	NOUN
ejpam-3743	428	2	cl(int(b	cl(int(b	NOUN
ejpam-3743	428	3	)	)	PUNCT
ejpam-3743	428	4	)	)	PUNCT
ejpam-3743	429	1	=	=	SYM
ejpam-3743	429	2	cl(int(a	cl(int(a	PROPN
ejpam-3743	429	3	×	×	PROPN
ejpam-3743	429	4	b	b	NOUN
ejpam-3743	429	5	)	)	PUNCT
ejpam-3743	429	6	)	)	PUNCT
ejpam-3743	429	7	.	.	PUNCT
ejpam-3743	430	1	thus	thus	ADV
ejpam-3743	430	2	a	a	DET
ejpam-3743	430	3	×	×	PROPN
ejpam-3743	430	4	b	b	NOUN
ejpam-3743	430	5	is	be	AUX
ejpam-3743	430	6	a	a	DET
ejpam-3743	430	7	supra	supra	ADJ
ejpam-3743	430	8	semi	semi	ADJ
ejpam-3743	430	9	-	-	ADJ
ejpam-3743	430	10	open	open	ADJ
ejpam-3743	430	11	set	set	NOUN
ejpam-3743	430	12	.	.	PUNCT
ejpam-3743	431	1	conversely	conversely	ADV
ejpam-3743	431	2	,	,	PUNCT
ejpam-3743	431	3	let	let	VERB
ejpam-3743	431	4	a	a	DET
ejpam-3743	431	5	×	×	PROPN
ejpam-3743	431	6	b	b	NOUN
ejpam-3743	431	7	be	be	AUX
ejpam-3743	431	8	a	a	DET
ejpam-3743	431	9	supra	supra	NOUN
ejpam-3743	431	10	semi	semi	ADJ
ejpam-3743	431	11	-	-	ADJ
ejpam-3743	431	12	open	open	ADJ
ejpam-3743	431	13	set	set	NOUN
ejpam-3743	431	14	.	.	PUNCT
ejpam-3743	432	1	then	then	ADV
ejpam-3743	432	2	a	a	DET
ejpam-3743	432	3	×	×	PROPN
ejpam-3743	432	4	b	b	NOUN
ejpam-3743	432	5	⊆	⊆	NUM
ejpam-3743	432	6	cl(int(a×	cl(int(a×	NUM
ejpam-3743	432	7	b	b	NOUN
ejpam-3743	432	8	)	)	PUNCT
ejpam-3743	432	9	)	)	PUNCT
ejpam-3743	433	1	=	=	SYM
ejpam-3743	433	2	cl(int(a))×	cl(int(a))×	PROPN
ejpam-3743	433	3	cl(int(b	cl(int(b	NOUN
ejpam-3743	433	4	)	)	PUNCT
ejpam-3743	433	5	)	)	PUNCT
ejpam-3743	433	6	.	.	PUNCT
ejpam-3743	434	1	so	so	ADV
ejpam-3743	434	2	a	a	DET
ejpam-3743	434	3	⊆	⊆	NUM
ejpam-3743	434	4	cl(int(a	cl(int(a	NOUN
ejpam-3743	434	5	)	)	PUNCT
ejpam-3743	434	6	)	)	PUNCT
ejpam-3743	435	1	and	and	CCONJ
ejpam-3743	435	2	b	b	NOUN
ejpam-3743	435	3	⊆	⊆	NUM
ejpam-3743	435	4	cl(int(b	cl(int(b	NOUN
ejpam-3743	435	5	)	)	PUNCT
ejpam-3743	435	6	)	)	PUNCT
ejpam-3743	435	7	.	.	PUNCT
ejpam-3743	436	1	hence	hence	ADV
ejpam-3743	436	2	,	,	PUNCT
ejpam-3743	436	3	the	the	DET
ejpam-3743	436	4	proof	proof	NOUN
ejpam-3743	436	5	is	be	AUX
ejpam-3743	436	6	complete	complete	ADJ
ejpam-3743	436	7	.	.	PUNCT
ejpam-3743	437	1	theorem	theorem	ADJ
ejpam-3743	437	2	15	15	NUM
ejpam-3743	437	3	.	.	PUNCT
ejpam-3743	438	1	the	the	DET
ejpam-3743	438	2	finite	finite	ADJ
ejpam-3743	438	3	product	product	NOUN
ejpam-3743	438	4	of	of	ADP
ejpam-3743	438	5	ssti	ssti	NOUN
ejpam-3743	438	6	-	-	PUNCT
ejpam-3743	438	7	spaces	space	NOUN
ejpam-3743	438	8	is	be	AUX
ejpam-3743	438	9	ssti	ssti	ADJ
ejpam-3743	438	10	for	for	ADP
ejpam-3743	438	11	i	i	PROPN
ejpam-3743	438	12	=	=	SYM
ejpam-3743	438	13	0	0	NUM
ejpam-3743	438	14	,	,	PUNCT
ejpam-3743	438	15	1	1	NUM
ejpam-3743	438	16	,	,	PUNCT
ejpam-3743	438	17	2	2	NUM
ejpam-3743	438	18	.	.	PUNCT
ejpam-3743	438	19	proof	proof	NOUN
ejpam-3743	438	20	.	.	PUNCT
ejpam-3743	439	1	we	we	PRON
ejpam-3743	439	2	shall	shall	AUX
ejpam-3743	439	3	suffice	suffice	VERB
ejpam-3743	439	4	with	with	ADP
ejpam-3743	439	5	proof	proof	NOUN
ejpam-3743	439	6	of	of	ADP
ejpam-3743	439	7	case	case	NOUN
ejpam-3743	439	8	i	i	PRON
ejpam-3743	439	9	=	=	NOUN
ejpam-3743	439	10	3	3	NUM
ejpam-3743	439	11	which	which	PRON
ejpam-3743	439	12	directly	directly	ADV
ejpam-3743	439	13	contains	contain	VERB
ejpam-3743	439	14	the	the	DET
ejpam-3743	439	15	case	case	NOUN
ejpam-3743	439	16	i	i	PRON
ejpam-3743	439	17	=	=	NOUN
ejpam-3743	440	1	1	1	X
ejpam-3743	440	2	.	.	PUNCT
ejpam-3743	440	3	in	in	ADP
ejpam-3743	440	4	a	a	DET
ejpam-3743	440	5	similar	similar	ADJ
ejpam-3743	440	6	way	way	NOUN
ejpam-3743	440	7	,	,	PUNCT
ejpam-3743	440	8	one	one	PRON
ejpam-3743	440	9	can	can	AUX
ejpam-3743	440	10	prove	prove	VERB
ejpam-3743	440	11	the	the	DET
ejpam-3743	440	12	cases	case	NOUN
ejpam-3743	440	13	i	i	PRON
ejpam-3743	440	14	=	=	NOUN
ejpam-3743	440	15	0	0	NUM
ejpam-3743	440	16	,	,	PUNCT
ejpam-3743	440	17	2	2	NUM
ejpam-3743	440	18	.	.	X
ejpam-3743	440	19	for	for	ADP
ejpam-3743	440	20	simplicity	simplicity	NOUN
ejpam-3743	440	21	,	,	PUNCT
ejpam-3743	440	22	the	the	DET
ejpam-3743	440	23	proof	proof	NOUN
ejpam-3743	440	24	is	be	AUX
ejpam-3743	440	25	given	give	VERB
ejpam-3743	440	26	for	for	ADP
ejpam-3743	440	27	two	two	NUM
ejpam-3743	440	28	supra	supra	ADJ
ejpam-3743	440	29	topological	topological	ADJ
ejpam-3743	440	30	spaces	space	NOUN
ejpam-3743	440	31	(	(	PUNCT
ejpam-3743	440	32	x,µ	x,µ	NOUN
ejpam-3743	440	33	)	)	PUNCT
ejpam-3743	440	34	and	and	CCONJ
ejpam-3743	440	35	(	(	PUNCT
ejpam-3743	440	36	y	y	PROPN
ejpam-3743	440	37	,	,	PUNCT
ejpam-3743	440	38	ν	ν	NOUN
ejpam-3743	440	39	)	)	PUNCT
ejpam-3743	440	40	.	.	PUNCT
ejpam-3743	441	1	let	let	AUX
ejpam-3743	441	2	(	(	PUNCT
ejpam-3743	441	3	x×y	x×y	PROPN
ejpam-3743	441	4	,	,	PUNCT
ejpam-3743	441	5	t	t	PROPN
ejpam-3743	441	6	)	)	PUNCT
ejpam-3743	441	7	be	be	AUX
ejpam-3743	441	8	the	the	DET
ejpam-3743	441	9	product	product	NOUN
ejpam-3743	441	10	supra	supra	ADJ
ejpam-3743	441	11	space	space	NOUN
ejpam-3743	441	12	of	of	ADP
ejpam-3743	441	13	(	(	PUNCT
ejpam-3743	441	14	x,µ	x,µ	NOUN
ejpam-3743	441	15	)	)	PUNCT
ejpam-3743	441	16	and	and	CCONJ
ejpam-3743	441	17	(	(	PUNCT
ejpam-3743	441	18	y	y	PROPN
ejpam-3743	441	19	,	,	PUNCT
ejpam-3743	441	20	ν	ν	NOUN
ejpam-3743	441	21	)	)	PUNCT
ejpam-3743	441	22	.	.	PUNCT
ejpam-3743	442	1	suppose	suppose	VERB
ejpam-3743	442	2	that	that	SCONJ
ejpam-3743	442	3	(	(	PUNCT
ejpam-3743	442	4	x1	x1	PROPN
ejpam-3743	442	5	,	,	PUNCT
ejpam-3743	442	6	y1	y1	PROPN
ejpam-3743	442	7	)	)	PUNCT
ejpam-3743	442	8	6=	6=	X
ejpam-3743	442	9	(	(	PUNCT
ejpam-3743	442	10	x2	x2	PROPN
ejpam-3743	442	11	,	,	PUNCT
ejpam-3743	442	12	y2	y2	PROPN
ejpam-3743	442	13	)	)	PUNCT
ejpam-3743	442	14	.	.	PUNCT
ejpam-3743	443	1	then	then	ADV
ejpam-3743	443	2	either	either	CCONJ
ejpam-3743	443	3	x1	x1	PROPN
ejpam-3743	443	4	6=	6=	NUM
ejpam-3743	443	5	x2	x2	PROPN
ejpam-3743	443	6	or	or	CCONJ
ejpam-3743	443	7	y1	y1	INTJ
ejpam-3743	443	8	6=	6=	NUM
ejpam-3743	443	9	y2	y2	PROPN
ejpam-3743	443	10	.	.	PUNCT
ejpam-3743	444	1	without	without	ADP
ejpam-3743	444	2	loss	loss	NOUN
ejpam-3743	444	3	of	of	ADP
ejpam-3743	444	4	generality	generality	NOUN
ejpam-3743	444	5	,	,	PUNCT
ejpam-3743	444	6	suppose	suppose	VERB
ejpam-3743	444	7	that	that	SCONJ
ejpam-3743	444	8	x1	x1	PROPN
ejpam-3743	444	9	6=	6=	NUM
ejpam-3743	444	10	x2	x2	PROPN
ejpam-3743	444	11	.	.	PUNCT
ejpam-3743	445	1	therefore	therefore	ADV
ejpam-3743	445	2	there	there	PRON
ejpam-3743	445	3	exist	exist	VERB
ejpam-3743	445	4	two	two	NUM
ejpam-3743	445	5	disjoint	disjoint	ADJ
ejpam-3743	445	6	supra	supra	PROPN
ejpam-3743	445	7	semi	semi	ADJ
ejpam-3743	445	8	-	-	ADJ
ejpam-3743	445	9	open	open	ADJ
ejpam-3743	445	10	subsets	subset	NOUN
ejpam-3743	445	11	u	u	NOUN
ejpam-3743	445	12	and	and	CCONJ
ejpam-3743	445	13	v	v	X
ejpam-3743	445	14	of	of	ADP
ejpam-3743	445	15	(	(	PUNCT
ejpam-3743	445	16	x,µ	x,µ	NOUN
ejpam-3743	445	17	)	)	PUNCT
ejpam-3743	445	18	containing	contain	VERB
ejpam-3743	445	19	x1	x1	PROPN
ejpam-3743	445	20	and	and	CCONJ
ejpam-3743	445	21	x2	x2	PROPN
ejpam-3743	445	22	,	,	PUNCT
ejpam-3743	445	23	respectively	respectively	ADV
ejpam-3743	445	24	.	.	PUNCT
ejpam-3743	446	1	it	it	PRON
ejpam-3743	446	2	follows	follow	VERB
ejpam-3743	446	3	from	from	ADP
ejpam-3743	446	4	theorem	theorem	ADJ
ejpam-3743	446	5	(	(	PUNCT
ejpam-3743	446	6	14	14	NUM
ejpam-3743	446	7	)	)	PUNCT
ejpam-3743	446	8	that	that	SCONJ
ejpam-3743	447	1	u	u	PRON
ejpam-3743	447	2	×	×	NOUN
ejpam-3743	447	3	y	y	PROPN
ejpam-3743	447	4	and	and	CCONJ
ejpam-3743	447	5	v	v	PRON
ejpam-3743	447	6	×	×	PROPN
ejpam-3743	447	7	y	y	PROPN
ejpam-3743	447	8	are	be	AUX
ejpam-3743	447	9	two	two	NUM
ejpam-3743	447	10	supra	supra	ADJ
ejpam-3743	447	11	semi	semi	ADJ
ejpam-3743	447	12	-	-	ADJ
ejpam-3743	447	13	open	open	ADJ
ejpam-3743	447	14	subsets	subset	NOUN
ejpam-3743	447	15	of	of	ADP
ejpam-3743	447	16	(	(	PUNCT
ejpam-3743	447	17	x	x	PROPN
ejpam-3743	447	18	×	×	PROPN
ejpam-3743	447	19	y	y	PROPN
ejpam-3743	447	20	,	,	PUNCT
ejpam-3743	447	21	t	t	NOUN
ejpam-3743	447	22	)	)	PUNCT
ejpam-3743	447	23	containing	contain	VERB
ejpam-3743	447	24	(	(	PUNCT
ejpam-3743	447	25	x1	x1	PROPN
ejpam-3743	447	26	,	,	PUNCT
ejpam-3743	447	27	y1	y1	PROPN
ejpam-3743	447	28	)	)	PUNCT
ejpam-3743	447	29	and	and	CCONJ
ejpam-3743	447	30	(	(	PUNCT
ejpam-3743	447	31	x2	x2	PROPN
ejpam-3743	447	32	,	,	PUNCT
ejpam-3743	447	33	y2	y2	PROPN
ejpam-3743	447	34	)	)	PUNCT
ejpam-3743	447	35	,	,	PUNCT
ejpam-3743	447	36	respectively	respectively	ADV
ejpam-3743	447	37	,	,	PUNCT
ejpam-3743	447	38	such	such	ADJ
ejpam-3743	447	39	that	that	SCONJ
ejpam-3743	447	40	(	(	PUNCT
ejpam-3743	447	41	u	u	NOUN
ejpam-3743	447	42	×	×	PROPN
ejpam-3743	447	43	y	y	PROPN
ejpam-3743	447	44	)	)	PUNCT
ejpam-3743	447	45	⋂̃	⋂̃	NOUN
ejpam-3743	447	46	(	(	PUNCT
ejpam-3743	447	47	v	v	NUM
ejpam-3743	447	48	×	×	PROPN
ejpam-3743	447	49	y	y	PROPN
ejpam-3743	447	50	)	)	PUNCT
ejpam-3743	448	1	=	=	PUNCT
ejpam-3743	448	2	∅.	∅.	VERB
ejpam-3743	448	3	hence	hence	ADV
ejpam-3743	448	4	,	,	PUNCT
ejpam-3743	448	5	(	(	PUNCT
ejpam-3743	448	6	x	x	SYM
ejpam-3743	448	7	×	×	PROPN
ejpam-3743	448	8	y	y	PROPN
ejpam-3743	448	9	,	,	PUNCT
ejpam-3743	448	10	t	t	PROPN
ejpam-3743	448	11	)	)	PUNCT
ejpam-3743	448	12	is	be	AUX
ejpam-3743	448	13	sst2	sst2	NOUN
ejpam-3743	448	14	.	.	PUNCT
ejpam-3743	449	1	definition	definition	NOUN
ejpam-3743	449	2	17	17	NUM
ejpam-3743	449	3	.	.	PUNCT
ejpam-3743	450	1	let	let	VERB
ejpam-3743	450	2	(	(	PUNCT
ejpam-3743	450	3	x,µ	x,µ	NOUN
ejpam-3743	450	4	)	)	PUNCT
ejpam-3743	450	5	and	and	CCONJ
ejpam-3743	450	6	(	(	PUNCT
ejpam-3743	450	7	y	y	PROPN
ejpam-3743	450	8	,	,	PUNCT
ejpam-3743	450	9	ν	ν	NOUN
ejpam-3743	450	10	)	)	PUNCT
ejpam-3743	450	11	be	be	VERB
ejpam-3743	450	12	two	two	NUM
ejpam-3743	450	13	supra	supra	ADJ
ejpam-3743	450	14	topological	topological	ADJ
ejpam-3743	450	15	spaces	space	NOUN
ejpam-3743	450	16	and	and	CCONJ
ejpam-3743	450	17	(	(	PUNCT
ejpam-3743	450	18	x	x	SYM
ejpam-3743	450	19	×	×	PROPN
ejpam-3743	450	20	y	y	PROPN
ejpam-3743	450	21	,	,	PUNCT
ejpam-3743	450	22	t	t	PROPN
ejpam-3743	450	23	)	)	PUNCT
ejpam-3743	450	24	be	be	AUX
ejpam-3743	450	25	their	their	PRON
ejpam-3743	450	26	product	product	NOUN
ejpam-3743	450	27	supra	supra	ADJ
ejpam-3743	450	28	space	space	NOUN
ejpam-3743	450	29	such	such	ADJ
ejpam-3743	450	30	that	that	DET
ejpam-3743	450	31	c1	c1	PROPN
ejpam-3743	450	32	and	and	CCONJ
ejpam-3743	450	33	c2	c2	PROPN
ejpam-3743	450	34	are	be	AUX
ejpam-3743	450	35	the	the	DET
ejpam-3743	450	36	collections	collection	NOUN
ejpam-3743	450	37	of	of	ADP
ejpam-3743	450	38	all	all	DET
ejpam-3743	450	39	supra	supra	ADJ
ejpam-3743	450	40	semi	semi	ADJ
ejpam-3743	450	41	-	-	ADJ
ejpam-3743	450	42	open	open	ADJ
ejpam-3743	450	43	subsets	subset	NOUN
ejpam-3743	450	44	of	of	ADP
ejpam-3743	450	45	(	(	PUNCT
ejpam-3743	450	46	x,µ	x,µ	NOUN
ejpam-3743	450	47	)	)	PUNCT
ejpam-3743	450	48	and	and	CCONJ
ejpam-3743	450	49	(	(	PUNCT
ejpam-3743	450	50	y	y	PROPN
ejpam-3743	450	51	,	,	PUNCT
ejpam-3743	450	52	ν	ν	NOUN
ejpam-3743	450	53	)	)	PUNCT
ejpam-3743	450	54	,	,	PUNCT
ejpam-3743	450	55	respectively	respectively	ADV
ejpam-3743	450	56	.	.	PUNCT
ejpam-3743	451	1	then	then	ADV
ejpam-3743	451	2	β	β	X
ejpam-3743	451	3	=	=	PUNCT
ejpam-3743	451	4	{	{	PUNCT
ejpam-3743	451	5	g×h	g×h	PROPN
ejpam-3743	451	6	:	:	PUNCT
ejpam-3743	451	7	g	g	PROPN
ejpam-3743	451	8	∈	∈	PROPN
ejpam-3743	451	9	c1	c1	PROPN
ejpam-3743	451	10	and	and	CCONJ
ejpam-3743	451	11	h	h	NOUN
ejpam-3743	451	12	∈	∈	PROPN
ejpam-3743	451	13	c2	c2	PROPN
ejpam-3743	451	14	}	}	PUNCT
ejpam-3743	451	15	defines	define	VERB
ejpam-3743	451	16	a	a	DET
ejpam-3743	451	17	basis	basis	NOUN
ejpam-3743	451	18	for	for	SCONJ
ejpam-3743	451	19	a	a	DET
ejpam-3743	451	20	supra	supra	ADJ
ejpam-3743	451	21	topology	topology	NOUN
ejpam-3743	451	22	c	c	NOUN
ejpam-3743	451	23	on	on	ADP
ejpam-3743	451	24	x	x	PUNCT
ejpam-3743	451	25	×y	×y	ADV
ejpam-3743	451	26	.	.	PUNCT
ejpam-3743	452	1	we	we	PRON
ejpam-3743	452	2	called	call	VERB
ejpam-3743	452	3	(	(	PUNCT
ejpam-3743	452	4	x	x	X
ejpam-3743	452	5	×y	×y	ADV
ejpam-3743	452	6	,	,	PUNCT
ejpam-3743	452	7	c	c	NOUN
ejpam-3743	452	8	)	)	PUNCT
ejpam-3743	452	9	a	a	DET
ejpam-3743	452	10	semi	semi	ADJ
ejpam-3743	452	11	-	-	ADJ
ejpam-3743	452	12	finite	finite	ADJ
ejpam-3743	452	13	product	product	NOUN
ejpam-3743	452	14	supra	supra	PROPN
ejpam-3743	452	15	space	space	NOUN
ejpam-3743	452	16	.	.	PUNCT
ejpam-3743	453	1	lemma	lemma	PROPN
ejpam-3743	453	2	1	1	X
ejpam-3743	453	3	.	.	PUNCT
ejpam-3743	454	1	let	let	VERB
ejpam-3743	454	2	(	(	PUNCT
ejpam-3743	454	3	x,µ	x,µ	NOUN
ejpam-3743	454	4	)	)	PUNCT
ejpam-3743	454	5	and	and	CCONJ
ejpam-3743	454	6	(	(	PUNCT
ejpam-3743	454	7	y	y	PROPN
ejpam-3743	454	8	,	,	PUNCT
ejpam-3743	454	9	ν	ν	NOUN
ejpam-3743	454	10	)	)	PUNCT
ejpam-3743	454	11	be	be	VERB
ejpam-3743	454	12	two	two	NUM
ejpam-3743	454	13	supra	supra	ADJ
ejpam-3743	454	14	topological	topological	ADJ
ejpam-3743	454	15	spaces	space	NOUN
ejpam-3743	454	16	and	and	CCONJ
ejpam-3743	454	17	(	(	PUNCT
ejpam-3743	454	18	x	x	SYM
ejpam-3743	454	19	×	×	PROPN
ejpam-3743	454	20	y	y	PROPN
ejpam-3743	454	21	,	,	PUNCT
ejpam-3743	454	22	c	c	AUX
ejpam-3743	454	23	)	)	PUNCT
ejpam-3743	454	24	be	be	VERB
ejpam-3743	454	25	their	their	PRON
ejpam-3743	454	26	semi	semi	ADJ
ejpam-3743	454	27	-	-	ADJ
ejpam-3743	454	28	product	product	ADJ
ejpam-3743	454	29	supra	supra	ADJ
ejpam-3743	454	30	space	space	NOUN
ejpam-3743	454	31	.	.	PUNCT
ejpam-3743	455	1	if	if	SCONJ
ejpam-3743	455	2	e	e	PROPN
ejpam-3743	455	3	is	be	AUX
ejpam-3743	455	4	a	a	DET
ejpam-3743	455	5	supra	supra	NOUN
ejpam-3743	455	6	closed	close	VERB
ejpam-3743	455	7	subset	subset	NOUN
ejpam-3743	455	8	of	of	ADP
ejpam-3743	455	9	(	(	PUNCT
ejpam-3743	455	10	x	x	PROPN
ejpam-3743	455	11	×	×	PROPN
ejpam-3743	455	12	y	y	PROPN
ejpam-3743	455	13	,	,	PUNCT
ejpam-3743	455	14	c	c	NOUN
ejpam-3743	455	15	)	)	PUNCT
ejpam-3743	455	16	,	,	PUNCT
ejpam-3743	455	17	then	then	ADV
ejpam-3743	455	18	e	e	PROPN
ejpam-3743	456	1	=	=	SYM
ejpam-3743	456	2	⋂	⋂	PROPN
ejpam-3743	456	3	i∈i	i∈i	ADJ
ejpam-3743	456	4	[	[	X
ejpam-3743	456	5	(	(	PUNCT
ejpam-3743	456	6	fi	fi	INTJ
ejpam-3743	456	7	×	×	PROPN
ejpam-3743	456	8	y	y	PROPN
ejpam-3743	456	9	)	)	PUNCT
ejpam-3743	457	1	⋃	⋃	PROPN
ejpam-3743	457	2	(	(	PUNCT
ejpam-3743	457	3	x	x	SYM
ejpam-3743	457	4	×	×	NOUN
ejpam-3743	457	5	hi	hi	INTJ
ejpam-3743	457	6	)	)	PUNCT
ejpam-3743	457	7	]	]	PUNCT
ejpam-3743	457	8	,	,	PUNCT
ejpam-3743	457	9	where	where	SCONJ
ejpam-3743	457	10	fi	fi	NOUN
ejpam-3743	457	11	and	and	CCONJ
ejpam-3743	457	12	hi	hi	INTJ
ejpam-3743	457	13	are	be	AUX
ejpam-3743	457	14	supra	supra	ADJ
ejpam-3743	457	15	semi	semi	ADJ
ejpam-3743	457	16	-	-	ADJ
ejpam-3743	457	17	closed	closed	ADJ
ejpam-3743	457	18	subsets	subset	NOUN
ejpam-3743	457	19	of	of	ADP
ejpam-3743	457	20	(	(	PUNCT
ejpam-3743	457	21	x,µ	x,µ	NOUN
ejpam-3743	457	22	)	)	PUNCT
ejpam-3743	457	23	and	and	CCONJ
ejpam-3743	457	24	(	(	PUNCT
ejpam-3743	457	25	y	y	PROPN
ejpam-3743	457	26	,	,	PUNCT
ejpam-3743	457	27	ν	ν	NOUN
ejpam-3743	457	28	)	)	PUNCT
ejpam-3743	457	29	,	,	PUNCT
ejpam-3743	457	30	respectively	respectively	ADV
ejpam-3743	457	31	.	.	PUNCT
ejpam-3743	458	1	theorem	theorem	VERB
ejpam-3743	458	2	16	16	NUM
ejpam-3743	458	3	.	.	PUNCT
ejpam-3743	459	1	the	the	DET
ejpam-3743	459	2	semi	semi	ADJ
ejpam-3743	459	3	-	-	ADJ
ejpam-3743	459	4	finite	finite	ADJ
ejpam-3743	459	5	product	product	NOUN
ejpam-3743	459	6	of	of	ADP
ejpam-3743	459	7	ssti	ssti	NOUN
ejpam-3743	459	8	-	-	PUNCT
ejpam-3743	459	9	spaces	space	NOUN
ejpam-3743	459	10	is	be	AUX
ejpam-3743	459	11	sti	sti	PROPN
ejpam-3743	459	12	for	for	ADP
ejpam-3743	459	13	i	i	PROPN
ejpam-3743	459	14	=	=	SYM
ejpam-3743	459	15	0	0	NUM
ejpam-3743	459	16	,	,	PUNCT
ejpam-3743	459	17	1	1	NUM
ejpam-3743	459	18	,	,	PUNCT
ejpam-3743	459	19	2	2	NUM
ejpam-3743	459	20	,	,	PUNCT
ejpam-3743	459	21	3	3	NUM
ejpam-3743	459	22	.	.	PUNCT
ejpam-3743	460	1	proof	proof	NOUN
ejpam-3743	460	2	.	.	PUNCT
ejpam-3743	461	1	we	we	PRON
ejpam-3743	461	2	shall	shall	AUX
ejpam-3743	461	3	suffice	suffice	VERB
ejpam-3743	461	4	with	with	ADP
ejpam-3743	461	5	proof	proof	NOUN
ejpam-3743	461	6	of	of	ADP
ejpam-3743	461	7	case	case	NOUN
ejpam-3743	461	8	i	i	PRON
ejpam-3743	461	9	=	=	NOUN
ejpam-3743	461	10	3	3	NUM
ejpam-3743	461	11	which	which	PRON
ejpam-3743	461	12	directly	directly	ADV
ejpam-3743	461	13	contains	contain	VERB
ejpam-3743	461	14	the	the	DET
ejpam-3743	461	15	case	case	NOUN
ejpam-3743	461	16	i	i	PRON
ejpam-3743	461	17	=	=	NOUN
ejpam-3743	462	1	1	1	X
ejpam-3743	462	2	.	.	PUNCT
ejpam-3743	462	3	in	in	ADP
ejpam-3743	462	4	a	a	DET
ejpam-3743	462	5	similar	similar	ADJ
ejpam-3743	462	6	way	way	NOUN
ejpam-3743	462	7	,	,	PUNCT
ejpam-3743	462	8	one	one	PRON
ejpam-3743	462	9	can	can	AUX
ejpam-3743	462	10	prove	prove	VERB
ejpam-3743	462	11	the	the	DET
ejpam-3743	462	12	cases	case	NOUN
ejpam-3743	462	13	i	i	PRON
ejpam-3743	462	14	=	=	NOUN
ejpam-3743	462	15	0	0	NUM
ejpam-3743	462	16	,	,	PUNCT
ejpam-3743	462	17	2	2	NUM
ejpam-3743	462	18	.	.	X
ejpam-3743	462	19	for	for	ADP
ejpam-3743	462	20	simplicity	simplicity	NOUN
ejpam-3743	462	21	,	,	PUNCT
ejpam-3743	462	22	the	the	DET
ejpam-3743	462	23	proof	proof	NOUN
ejpam-3743	462	24	is	be	AUX
ejpam-3743	462	25	given	give	VERB
ejpam-3743	462	26	for	for	ADP
ejpam-3743	462	27	two	two	NUM
ejpam-3743	462	28	supra	supra	ADJ
ejpam-3743	462	29	topological	topological	ADJ
ejpam-3743	462	30	spaces	space	NOUN
ejpam-3743	462	31	(	(	PUNCT
ejpam-3743	462	32	x,µ	x,µ	NOUN
ejpam-3743	462	33	)	)	PUNCT
ejpam-3743	462	34	and	and	CCONJ
ejpam-3743	462	35	(	(	PUNCT
ejpam-3743	462	36	y	y	PROPN
ejpam-3743	462	37	,	,	PUNCT
ejpam-3743	462	38	ν	ν	NOUN
ejpam-3743	462	39	)	)	PUNCT
ejpam-3743	462	40	.	.	PUNCT
ejpam-3743	463	1	t.	t.	PROPN
ejpam-3743	463	2	m.	m.	PROPN
ejpam-3743	463	3	al	al	PROPN
ejpam-3743	463	4	-	-	PUNCT
ejpam-3743	463	5	shami	shami	PROPN
ejpam-3743	463	6	et	et	PROPN
ejpam-3743	463	7	al	al	PROPN
ejpam-3743	463	8	.	.	PUNCT
ejpam-3743	463	9	/	/	SYM
ejpam-3743	463	10	eur	eur	PROPN
ejpam-3743	463	11	.	.	PUNCT
ejpam-3743	464	1	j.	j.	PROPN
ejpam-3743	464	2	pure	pure	PROPN
ejpam-3743	464	3	appl	appl	PROPN
ejpam-3743	464	4	.	.	PROPN
ejpam-3743	464	5	math	math	PROPN
ejpam-3743	464	6	,	,	PUNCT
ejpam-3743	464	7	13	13	NUM
ejpam-3743	464	8	(	(	PUNCT
ejpam-3743	464	9	3	3	NUM
ejpam-3743	464	10	)	)	PUNCT
ejpam-3743	464	11	(	(	PUNCT
ejpam-3743	464	12	2020	2020	NUM
ejpam-3743	464	13	)	)	PUNCT
ejpam-3743	464	14	,	,	PUNCT
ejpam-3743	464	15	427	427	NUM
ejpam-3743	464	16	-	-	SYM
ejpam-3743	464	17	443	443	NUM
ejpam-3743	464	18	441	441	NUM
ejpam-3743	464	19	let	let	VERB
ejpam-3743	464	20	(	(	PUNCT
ejpam-3743	464	21	x	x	SYM
ejpam-3743	464	22	×	×	PROPN
ejpam-3743	464	23	y	y	PROPN
ejpam-3743	464	24	,	,	PUNCT
ejpam-3743	464	25	c	c	AUX
ejpam-3743	464	26	)	)	PUNCT
ejpam-3743	464	27	be	be	AUX
ejpam-3743	464	28	the	the	DET
ejpam-3743	464	29	semi	semi	ADJ
ejpam-3743	464	30	-	-	ADJ
ejpam-3743	464	31	product	product	ADJ
ejpam-3743	464	32	supra	supra	ADJ
ejpam-3743	464	33	space	space	NOUN
ejpam-3743	464	34	of	of	ADP
ejpam-3743	464	35	(	(	PUNCT
ejpam-3743	464	36	x,µ	x,µ	NOUN
ejpam-3743	464	37	)	)	PUNCT
ejpam-3743	464	38	and	and	CCONJ
ejpam-3743	464	39	(	(	PUNCT
ejpam-3743	464	40	y	y	PROPN
ejpam-3743	464	41	,	,	PUNCT
ejpam-3743	464	42	ν	ν	NOUN
ejpam-3743	464	43	)	)	PUNCT
ejpam-3743	464	44	.	.	PUNCT
ejpam-3743	465	1	we	we	PRON
ejpam-3743	465	2	first	first	ADV
ejpam-3743	465	3	prove	prove	VERB
ejpam-3743	465	4	that	that	SCONJ
ejpam-3743	465	5	(	(	PUNCT
ejpam-3743	465	6	x	x	SYM
ejpam-3743	465	7	×	×	PROPN
ejpam-3743	465	8	y	y	PROPN
ejpam-3743	465	9	,	,	PUNCT
ejpam-3743	465	10	c	c	NOUN
ejpam-3743	465	11	)	)	PUNCT
ejpam-3743	465	12	is	be	AUX
ejpam-3743	465	13	st1	st1	PROPN
ejpam-3743	465	14	.	.	PROPN
ejpam-3743	465	15	suppose	suppose	VERB
ejpam-3743	465	16	that	that	SCONJ
ejpam-3743	465	17	(	(	PUNCT
ejpam-3743	465	18	x1	x1	PROPN
ejpam-3743	465	19	,	,	PUNCT
ejpam-3743	465	20	y1	y1	PROPN
ejpam-3743	465	21	)	)	PUNCT
ejpam-3743	465	22	6=	6=	X
ejpam-3743	465	23	(	(	PUNCT
ejpam-3743	465	24	x2	x2	PROPN
ejpam-3743	465	25	,	,	PUNCT
ejpam-3743	465	26	y2	y2	PROPN
ejpam-3743	465	27	)	)	PUNCT
ejpam-3743	465	28	.	.	PUNCT
ejpam-3743	466	1	then	then	ADV
ejpam-3743	466	2	either	either	CCONJ
ejpam-3743	466	3	x1	x1	PROPN
ejpam-3743	466	4	6=	6=	NUM
ejpam-3743	466	5	x2	x2	PROPN
ejpam-3743	466	6	or	or	CCONJ
ejpam-3743	466	7	y1	y1	INTJ
ejpam-3743	466	8	6=	6=	NUM
ejpam-3743	466	9	y2	y2	PROPN
ejpam-3743	466	10	.	.	PUNCT
ejpam-3743	467	1	without	without	ADP
ejpam-3743	467	2	loss	loss	NOUN
ejpam-3743	467	3	of	of	ADP
ejpam-3743	467	4	generality	generality	NOUN
ejpam-3743	467	5	,	,	PUNCT
ejpam-3743	467	6	suppose	suppose	VERB
ejpam-3743	467	7	that	that	SCONJ
ejpam-3743	467	8	x1	x1	PROPN
ejpam-3743	467	9	6=	6=	NUM
ejpam-3743	467	10	x2	x2	PROPN
ejpam-3743	467	11	.	.	PUNCT
ejpam-3743	468	1	therefore	therefore	ADV
ejpam-3743	468	2	there	there	PRON
ejpam-3743	468	3	exist	exist	VERB
ejpam-3743	468	4	two	two	NUM
ejpam-3743	468	5	supra	supra	ADJ
ejpam-3743	468	6	semi	semi	ADJ
ejpam-3743	468	7	-	-	ADJ
ejpam-3743	468	8	open	open	ADJ
ejpam-3743	468	9	subsets	subset	NOUN
ejpam-3743	468	10	u	u	NOUN
ejpam-3743	468	11	and	and	CCONJ
ejpam-3743	468	12	v	v	X
ejpam-3743	468	13	of	of	ADP
ejpam-3743	468	14	(	(	PUNCT
ejpam-3743	468	15	x,µ	x,µ	NOUN
ejpam-3743	468	16	)	)	PUNCT
ejpam-3743	468	17	containing	contain	VERB
ejpam-3743	468	18	x1	x1	PROPN
ejpam-3743	468	19	and	and	CCONJ
ejpam-3743	468	20	x2	x2	PROPN
ejpam-3743	468	21	,	,	PUNCT
ejpam-3743	468	22	respectively	respectively	ADV
ejpam-3743	468	23	.	.	PUNCT
ejpam-3743	469	1	according	accord	VERB
ejpam-3743	469	2	to	to	ADP
ejpam-3743	469	3	definition(17	definition(17	NOUN
ejpam-3743	469	4	)	)	PUNCT
ejpam-3743	469	5	,	,	PUNCT
ejpam-3743	469	6	u	u	PROPN
ejpam-3743	469	7	×	×	PROPN
ejpam-3743	469	8	y	y	PROPN
ejpam-3743	469	9	and	and	CCONJ
ejpam-3743	469	10	v	v	PRON
ejpam-3743	469	11	×	×	PROPN
ejpam-3743	469	12	y	y	PROPN
ejpam-3743	469	13	are	be	AUX
ejpam-3743	469	14	two	two	NUM
ejpam-3743	469	15	supra	supra	ADJ
ejpam-3743	469	16	open	open	ADJ
ejpam-3743	469	17	subsets	subset	NOUN
ejpam-3743	469	18	of	of	ADP
ejpam-3743	469	19	(	(	PUNCT
ejpam-3743	469	20	x	x	PROPN
ejpam-3743	469	21	×	×	PROPN
ejpam-3743	469	22	y	y	PROPN
ejpam-3743	469	23	,	,	PUNCT
ejpam-3743	469	24	c	c	NOUN
ejpam-3743	469	25	)	)	PUNCT
ejpam-3743	469	26	containing	contain	VERB
ejpam-3743	469	27	(	(	PUNCT
ejpam-3743	469	28	x1	x1	PROPN
ejpam-3743	469	29	,	,	PUNCT
ejpam-3743	469	30	y1	y1	PROPN
ejpam-3743	469	31	)	)	PUNCT
ejpam-3743	469	32	and	and	CCONJ
ejpam-3743	469	33	(	(	PUNCT
ejpam-3743	469	34	x2	x2	PROPN
ejpam-3743	469	35	,	,	PUNCT
ejpam-3743	469	36	y2	y2	PROPN
ejpam-3743	469	37	)	)	PUNCT
ejpam-3743	469	38	such	such	ADJ
ejpam-3743	469	39	that	that	SCONJ
ejpam-3743	469	40	(	(	PUNCT
ejpam-3743	469	41	x1	x1	PROPN
ejpam-3743	469	42	,	,	PUNCT
ejpam-3743	469	43	y1	y1	PROPN
ejpam-3743	469	44	)	)	PUNCT
ejpam-3743	469	45	6∈	6∈	NOUN
ejpam-3743	469	46	v	v	ADP
ejpam-3743	469	47	×y	×y	PUNCT
ejpam-3743	469	48	and	and	CCONJ
ejpam-3743	469	49	(	(	PUNCT
ejpam-3743	469	50	x2	x2	PROPN
ejpam-3743	469	51	,	,	PUNCT
ejpam-3743	469	52	y2	y2	PROPN
ejpam-3743	469	53	)	)	PUNCT
ejpam-3743	469	54	6∈	6∈	NOUN
ejpam-3743	469	55	u	u	PROPN
ejpam-3743	469	56	×y	×y	PUNCT
ejpam-3743	469	57	.	.	PUNCT
ejpam-3743	470	1	hence	hence	ADV
ejpam-3743	470	2	,	,	PUNCT
ejpam-3743	470	3	(	(	PUNCT
ejpam-3743	470	4	x	x	X
ejpam-3743	470	5	×y	×y	ADV
ejpam-3743	470	6	,	,	PUNCT
ejpam-3743	470	7	c	c	NOUN
ejpam-3743	470	8	)	)	PUNCT
ejpam-3743	470	9	is	be	AUX
ejpam-3743	470	10	st1	st1	PROPN
ejpam-3743	470	11	.	.	PROPN
ejpam-3743	471	1	second	second	PROPN
ejpam-3743	471	2	,	,	PUNCT
ejpam-3743	471	3	we	we	PRON
ejpam-3743	471	4	prove	prove	VERB
ejpam-3743	471	5	that	that	SCONJ
ejpam-3743	471	6	(	(	PUNCT
ejpam-3743	471	7	x	x	SYM
ejpam-3743	471	8	×	×	PROPN
ejpam-3743	471	9	y	y	PROPN
ejpam-3743	471	10	,	,	PUNCT
ejpam-3743	471	11	c	c	NOUN
ejpam-3743	471	12	)	)	PUNCT
ejpam-3743	471	13	is	be	AUX
ejpam-3743	471	14	supra	supra	ADJ
ejpam-3743	471	15	regular	regular	ADJ
ejpam-3743	471	16	.	.	PUNCT
ejpam-3743	472	1	suppose	suppose	VERB
ejpam-3743	472	2	that	that	SCONJ
ejpam-3743	472	3	(	(	PUNCT
ejpam-3743	472	4	x	x	X
ejpam-3743	472	5	,	,	PUNCT
ejpam-3743	472	6	y	y	NOUN
ejpam-3743	472	7	)	)	PUNCT
ejpam-3743	472	8	∈	∈	PROPN
ejpam-3743	472	9	x	x	SYM
ejpam-3743	472	10	×	×	PROPN
ejpam-3743	472	11	y	y	PROPN
ejpam-3743	472	12	and	and	CCONJ
ejpam-3743	472	13	e	e	PROPN
ejpam-3743	472	14	is	be	AUX
ejpam-3743	472	15	a	a	DET
ejpam-3743	472	16	supra	supra	NOUN
ejpam-3743	472	17	closed	close	VERB
ejpam-3743	472	18	subset	subset	NOUN
ejpam-3743	472	19	of	of	ADP
ejpam-3743	472	20	(	(	PUNCT
ejpam-3743	472	21	x	x	PROPN
ejpam-3743	472	22	×	×	PROPN
ejpam-3743	472	23	y	y	PROPN
ejpam-3743	472	24	,	,	PUNCT
ejpam-3743	472	25	c	c	NOUN
ejpam-3743	472	26	)	)	PUNCT
ejpam-3743	472	27	such	such	ADJ
ejpam-3743	472	28	that	that	SCONJ
ejpam-3743	472	29	(	(	PUNCT
ejpam-3743	472	30	x	x	NOUN
ejpam-3743	472	31	,	,	PUNCT
ejpam-3743	472	32	y	y	PROPN
ejpam-3743	472	33	)	)	PUNCT
ejpam-3743	472	34	6∈	6∈	NOUN
ejpam-3743	472	35	e	e	NOUN
ejpam-3743	472	36	=	=	SYM
ejpam-3743	472	37	⋂	⋂	PROPN
ejpam-3743	472	38	i∈i	i∈i	ADJ
ejpam-3743	472	39	[	[	X
ejpam-3743	472	40	(	(	PUNCT
ejpam-3743	472	41	fi	fi	INTJ
ejpam-3743	472	42	×	×	PROPN
ejpam-3743	472	43	y	y	PROPN
ejpam-3743	472	44	)	)	PUNCT
ejpam-3743	473	1	⋃	⋃	PROPN
ejpam-3743	473	2	(	(	PUNCT
ejpam-3743	473	3	x	x	SYM
ejpam-3743	473	4	×hi	×hi	NOUN
ejpam-3743	473	5	)	)	PUNCT
ejpam-3743	473	6	]	]	PUNCT
ejpam-3743	473	7	,	,	PUNCT
ejpam-3743	473	8	where	where	SCONJ
ejpam-3743	473	9	fi	fi	NOUN
ejpam-3743	473	10	and	and	CCONJ
ejpam-3743	473	11	hi	hi	INTJ
ejpam-3743	473	12	are	be	AUX
ejpam-3743	473	13	supra	supra	ADJ
ejpam-3743	473	14	semi	semi	ADJ
ejpam-3743	473	15	-	-	ADJ
ejpam-3743	473	16	closed	closed	ADJ
ejpam-3743	473	17	subsets	subset	NOUN
ejpam-3743	473	18	of	of	ADP
ejpam-3743	473	19	(	(	PUNCT
ejpam-3743	473	20	x,µ	x,µ	NOUN
ejpam-3743	473	21	)	)	PUNCT
ejpam-3743	473	22	and	and	CCONJ
ejpam-3743	473	23	(	(	PUNCT
ejpam-3743	473	24	y	y	PROPN
ejpam-3743	473	25	,	,	PUNCT
ejpam-3743	473	26	ν	ν	NOUN
ejpam-3743	473	27	)	)	PUNCT
ejpam-3743	473	28	,	,	PUNCT
ejpam-3743	473	29	respectively	respectively	ADV
ejpam-3743	473	30	.	.	PUNCT
ejpam-3743	474	1	then	then	ADV
ejpam-3743	474	2	there	there	PRON
ejpam-3743	474	3	exists	exist	VERB
ejpam-3743	474	4	j	j	PROPN
ejpam-3743	474	5	∈	∈	PROPN
ejpam-3743	475	1	i	i	PRON
ejpam-3743	475	2	such	such	ADJ
ejpam-3743	475	3	that	that	SCONJ
ejpam-3743	475	4	(	(	PUNCT
ejpam-3743	475	5	x	x	NOUN
ejpam-3743	475	6	,	,	PUNCT
ejpam-3743	475	7	y	y	PROPN
ejpam-3743	475	8	)	)	PUNCT
ejpam-3743	475	9	6∈	6∈	NOUN
ejpam-3743	476	1	[	[	X
ejpam-3743	476	2	(	(	PUNCT
ejpam-3743	476	3	fj	fj	INTJ
ejpam-3743	476	4	×	×	PROPN
ejpam-3743	476	5	y	y	PROPN
ejpam-3743	476	6	)	)	PUNCT
ejpam-3743	477	1	⋃	⋃	PROPN
ejpam-3743	477	2	(	(	PUNCT
ejpam-3743	477	3	x	x	SYM
ejpam-3743	477	4	×hj	×hj	PROPN
ejpam-3743	477	5	)	)	PUNCT
ejpam-3743	477	6	]	]	PUNCT
ejpam-3743	477	7	.	.	PUNCT
ejpam-3743	478	1	this	this	PRON
ejpam-3743	478	2	means	mean	VERB
ejpam-3743	478	3	that	that	SCONJ
ejpam-3743	478	4	x	x	SYM
ejpam-3743	478	5	6∈	6∈	NOUN
ejpam-3743	478	6	fj	fj	PROPN
ejpam-3743	478	7	and	and	CCONJ
ejpam-3743	478	8	y	y	PROPN
ejpam-3743	478	9	6∈	6∈	PROPN
ejpam-3743	478	10	hj	hj	X
ejpam-3743	478	11	.	.	PUNCT
ejpam-3743	479	1	since	since	SCONJ
ejpam-3743	479	2	(	(	PUNCT
ejpam-3743	479	3	x,µ	x,µ	NOUN
ejpam-3743	479	4	)	)	PUNCT
ejpam-3743	479	5	and	and	CCONJ
ejpam-3743	479	6	(	(	PUNCT
ejpam-3743	479	7	y	y	PROPN
ejpam-3743	479	8	,	,	PUNCT
ejpam-3743	479	9	ν	ν	NOUN
ejpam-3743	479	10	)	)	PUNCT
ejpam-3743	479	11	are	be	AUX
ejpam-3743	479	12	supra	supra	ADJ
ejpam-3743	479	13	semi	semi	ADV
ejpam-3743	479	14	regular	regular	ADJ
ejpam-3743	479	15	,	,	PUNCT
ejpam-3743	479	16	then	then	ADV
ejpam-3743	479	17	there	there	PRON
ejpam-3743	479	18	exist	exist	VERB
ejpam-3743	479	19	disjoint	disjoint	ADJ
ejpam-3743	479	20	supra	supra	PROPN
ejpam-3743	479	21	semiopen	semiopen	PROPN
ejpam-3743	479	22	subsets	subset	NOUN
ejpam-3743	479	23	u	u	PROPN
ejpam-3743	479	24	and	and	CCONJ
ejpam-3743	479	25	v	v	X
ejpam-3743	479	26	of	of	ADP
ejpam-3743	479	27	(	(	PUNCT
ejpam-3743	479	28	x,µ	x,µ	NOUN
ejpam-3743	479	29	)	)	PUNCT
ejpam-3743	479	30	containing	contain	VERB
ejpam-3743	479	31	x	x	PROPN
ejpam-3743	479	32	and	and	CCONJ
ejpam-3743	479	33	fj	fj	PROPN
ejpam-3743	479	34	,	,	PUNCT
ejpam-3743	479	35	respectively	respectively	ADV
ejpam-3743	479	36	,	,	PUNCT
ejpam-3743	479	37	and	and	CCONJ
ejpam-3743	479	38	there	there	PRON
ejpam-3743	479	39	exist	exist	VERB
ejpam-3743	479	40	disjoint	disjoint	ADJ
ejpam-3743	479	41	supra	supra	PROPN
ejpam-3743	479	42	semi	semi	ADJ
ejpam-3743	479	43	-	-	ADJ
ejpam-3743	479	44	open	open	ADJ
ejpam-3743	479	45	subsets	subset	NOUN
ejpam-3743	479	46	m	m	VERB
ejpam-3743	479	47	and	and	CCONJ
ejpam-3743	479	48	n	n	PROPN
ejpam-3743	479	49	of	of	ADP
ejpam-3743	479	50	(	(	PUNCT
ejpam-3743	479	51	y	y	PROPN
ejpam-3743	479	52	,	,	PUNCT
ejpam-3743	479	53	ν	ν	NOUN
ejpam-3743	479	54	)	)	PUNCT
ejpam-3743	479	55	containing	contain	VERB
ejpam-3743	479	56	y	y	PROPN
ejpam-3743	479	57	and	and	CCONJ
ejpam-3743	479	58	hj	hj	PROPN
ejpam-3743	479	59	,	,	PUNCT
ejpam-3743	479	60	respectively	respectively	ADV
ejpam-3743	479	61	.	.	PUNCT
ejpam-3743	480	1	therefore	therefore	ADV
ejpam-3743	480	2	u	u	NOUN
ejpam-3743	480	3	×m	×m	NOUN
ejpam-3743	480	4	and	and	CCONJ
ejpam-3743	480	5	[	[	X
ejpam-3743	480	6	(	(	PUNCT
ejpam-3743	480	7	v	v	NUM
ejpam-3743	480	8	×	×	PROPN
ejpam-3743	480	9	y	y	PROPN
ejpam-3743	480	10	)	)	PUNCT
ejpam-3743	480	11	⋃	⋃	PROPN
ejpam-3743	480	12	(	(	PUNCT
ejpam-3743	480	13	x	x	SYM
ejpam-3743	480	14	×	×	NOUN
ejpam-3743	480	15	n	n	CCONJ
ejpam-3743	480	16	)	)	PUNCT
ejpam-3743	480	17	]	]	PUNCT
ejpam-3743	480	18	are	be	AUX
ejpam-3743	480	19	two	two	NUM
ejpam-3743	480	20	supra	supra	ADJ
ejpam-3743	480	21	open	open	ADJ
ejpam-3743	480	22	subsets	subset	NOUN
ejpam-3743	480	23	of	of	ADP
ejpam-3743	480	24	(	(	PUNCT
ejpam-3743	480	25	x	x	PROPN
ejpam-3743	480	26	×	×	PROPN
ejpam-3743	480	27	y	y	PROPN
ejpam-3743	480	28	,	,	PUNCT
ejpam-3743	480	29	c	c	NOUN
ejpam-3743	480	30	)	)	PUNCT
ejpam-3743	480	31	containing	contain	VERB
ejpam-3743	480	32	(	(	PUNCT
ejpam-3743	480	33	x	x	NOUN
ejpam-3743	480	34	,	,	PUNCT
ejpam-3743	480	35	y	y	PROPN
ejpam-3743	480	36	)	)	PUNCT
ejpam-3743	480	37	and	and	CCONJ
ejpam-3743	480	38	[	[	X
ejpam-3743	480	39	(	(	PUNCT
ejpam-3743	480	40	fj	fj	INTJ
ejpam-3743	480	41	×	×	PROPN
ejpam-3743	480	42	y	y	PROPN
ejpam-3743	480	43	)	)	PUNCT
ejpam-3743	481	1	⋃	⋃	PROPN
ejpam-3743	481	2	(	(	PUNCT
ejpam-3743	481	3	x	x	SYM
ejpam-3743	481	4	×hj	×hj	PROPN
ejpam-3743	481	5	)	)	PUNCT
ejpam-3743	481	6	]	]	PUNCT
ejpam-3743	481	7	,	,	PUNCT
ejpam-3743	481	8	respectively	respectively	ADV
ejpam-3743	481	9	.	.	PUNCT
ejpam-3743	482	1	obviously	obviously	ADV
ejpam-3743	482	2	,	,	PUNCT
ejpam-3743	482	3	e	e	PROPN
ejpam-3743	482	4	⊆	⊆	NUM
ejpam-3743	482	5	[	[	X
ejpam-3743	482	6	(	(	PUNCT
ejpam-3743	482	7	fj	fj	INTJ
ejpam-3743	482	8	×	×	PROPN
ejpam-3743	482	9	y	y	PROPN
ejpam-3743	482	10	)	)	PUNCT
ejpam-3743	482	11	⋃	⋃	PROPN
ejpam-3743	482	12	(	(	PUNCT
ejpam-3743	482	13	x	x	SYM
ejpam-3743	482	14	×hj	×hj	PROPN
ejpam-3743	482	15	)	)	PUNCT
ejpam-3743	482	16	]	]	PUNCT
ejpam-3743	482	17	and	and	CCONJ
ejpam-3743	482	18	(	(	PUNCT
ejpam-3743	482	19	u	u	NOUN
ejpam-3743	482	20	×m	×m	NOUN
ejpam-3743	482	21	)	)	PUNCT
ejpam-3743	482	22	⋂	⋂	PROPN
ejpam-3743	483	1	[	[	X
ejpam-3743	483	2	(	(	PUNCT
ejpam-3743	483	3	v	v	NUM
ejpam-3743	483	4	×	×	PROPN
ejpam-3743	483	5	y	y	PROPN
ejpam-3743	483	6	)	)	PUNCT
ejpam-3743	484	1	⋃	⋃	PROPN
ejpam-3743	484	2	(	(	PUNCT
ejpam-3743	484	3	x	x	X
ejpam-3743	484	4	×n	×n	PROPN
ejpam-3743	484	5	)	)	PUNCT
ejpam-3743	484	6	]	]	PUNCT
ejpam-3743	485	1	=	=	PUNCT
ejpam-3743	485	2	∅.	∅.	VERB
ejpam-3743	485	3	thus	thus	ADV
ejpam-3743	485	4	,	,	PUNCT
ejpam-3743	485	5	(	(	PUNCT
ejpam-3743	485	6	x	x	SYM
ejpam-3743	485	7	×	×	PROPN
ejpam-3743	485	8	y	y	PROPN
ejpam-3743	485	9	,	,	PUNCT
ejpam-3743	485	10	t	t	PROPN
ejpam-3743	485	11	)	)	PUNCT
ejpam-3743	485	12	is	be	AUX
ejpam-3743	485	13	supra	supra	ADJ
ejpam-3743	485	14	regular	regular	ADJ
ejpam-3743	485	15	.	.	PUNCT
ejpam-3743	486	1	hence	hence	ADV
ejpam-3743	486	2	,	,	PUNCT
ejpam-3743	486	3	the	the	DET
ejpam-3743	486	4	proof	proof	NOUN
ejpam-3743	486	5	is	be	AUX
ejpam-3743	486	6	complete	complete	ADJ
ejpam-3743	486	7	.	.	PUNCT
ejpam-3743	487	1	4	4	X
ejpam-3743	487	2	.	.	X
ejpam-3743	487	3	conclusion	conclusion	NOUN
ejpam-3743	487	4	there	there	PRON
ejpam-3743	487	5	are	be	VERB
ejpam-3743	487	6	many	many	ADJ
ejpam-3743	487	7	generalizations	generalization	NOUN
ejpam-3743	487	8	of	of	ADP
ejpam-3743	487	9	topological	topological	ADJ
ejpam-3743	487	10	spaces	space	NOUN
ejpam-3743	487	11	which	which	PRON
ejpam-3743	487	12	help	help	VERB
ejpam-3743	487	13	us	we	PRON
ejpam-3743	487	14	to	to	AUX
ejpam-3743	487	15	picture	picture	NOUN
ejpam-3743	487	16	and	and	CCONJ
ejpam-3743	487	17	satisfy	satisfy	VERB
ejpam-3743	487	18	many	many	ADJ
ejpam-3743	487	19	topological	topological	ADJ
ejpam-3743	487	20	properties	property	NOUN
ejpam-3743	487	21	under	under	ADP
ejpam-3743	487	22	fewer	few	ADJ
ejpam-3743	487	23	conditions	condition	NOUN
ejpam-3743	487	24	such	such	ADJ
ejpam-3743	487	25	as	as	ADP
ejpam-3743	487	26	supra	supra	PROPN
ejpam-3743	487	27	topology	topology	NOUN
ejpam-3743	487	28	,	,	PUNCT
ejpam-3743	487	29	minimal	minimal	ADJ
ejpam-3743	487	30	structure	structure	NOUN
ejpam-3743	487	31	and	and	CCONJ
ejpam-3743	487	32	generalized	generalized	ADJ
ejpam-3743	487	33	topology	topology	NOUN
ejpam-3743	487	34	.	.	PUNCT
ejpam-3743	488	1	this	this	DET
ejpam-3743	488	2	work	work	NOUN
ejpam-3743	488	3	is	be	AUX
ejpam-3743	488	4	devoted	devote	VERB
ejpam-3743	488	5	to	to	ADP
ejpam-3743	488	6	introducing	introduce	VERB
ejpam-3743	488	7	and	and	CCONJ
ejpam-3743	488	8	discussing	discuss	VERB
ejpam-3743	488	9	the	the	DET
ejpam-3743	488	10	concepts	concept	NOUN
ejpam-3743	488	11	of	of	ADP
ejpam-3743	488	12	limits	limit	NOUN
ejpam-3743	488	13	points	point	NOUN
ejpam-3743	488	14	of	of	ADP
ejpam-3743	488	15	a	a	DET
ejpam-3743	488	16	set	set	NOUN
ejpam-3743	488	17	and	and	CCONJ
ejpam-3743	488	18	separation	separation	NOUN
ejpam-3743	488	19	axioms	axiom	NOUN
ejpam-3743	488	20	with	with	ADP
ejpam-3743	488	21	respect	respect	NOUN
ejpam-3743	488	22	to	to	ADP
ejpam-3743	488	23	semi	semi	ADJ
ejpam-3743	488	24	-	-	ADJ
ejpam-3743	488	25	open	open	ADJ
ejpam-3743	488	26	sets	set	NOUN
ejpam-3743	488	27	.	.	PUNCT
ejpam-3743	489	1	we	we	PRON
ejpam-3743	489	2	have	have	AUX
ejpam-3743	489	3	established	establish	VERB
ejpam-3743	489	4	their	their	PRON
ejpam-3743	489	5	main	main	ADJ
ejpam-3743	489	6	properties	property	NOUN
ejpam-3743	489	7	and	and	CCONJ
ejpam-3743	489	8	provided	provide	VERB
ejpam-3743	489	9	some	some	DET
ejpam-3743	489	10	examples	example	NOUN
ejpam-3743	489	11	to	to	PART
ejpam-3743	489	12	show	show	VERB
ejpam-3743	489	13	the	the	DET
ejpam-3743	489	14	obtained	obtain	VERB
ejpam-3743	489	15	results	result	NOUN
ejpam-3743	489	16	.	.	PUNCT
ejpam-3743	490	1	from	from	ADP
ejpam-3743	490	2	the	the	DET
ejpam-3743	490	3	concrete	concrete	ADJ
ejpam-3743	490	4	thoughts	thought	NOUN
ejpam-3743	490	5	given	give	VERB
ejpam-3743	490	6	in	in	ADP
ejpam-3743	490	7	this	this	DET
ejpam-3743	490	8	work	work	NOUN
ejpam-3743	490	9	,	,	PUNCT
ejpam-3743	490	10	it	it	PRON
ejpam-3743	490	11	can	can	AUX
ejpam-3743	490	12	be	be	AUX
ejpam-3743	490	13	done	do	VERB
ejpam-3743	490	14	more	more	ADJ
ejpam-3743	490	15	investigations	investigation	NOUN
ejpam-3743	490	16	on	on	ADP
ejpam-3743	490	17	the	the	DET
ejpam-3743	490	18	theoretical	theoretical	ADJ
ejpam-3743	490	19	parts	part	NOUN
ejpam-3743	490	20	of	of	ADP
ejpam-3743	490	21	these	these	DET
ejpam-3743	490	22	generalized	generalize	VERB
ejpam-3743	490	23	ideas	idea	NOUN
ejpam-3743	490	24	which	which	PRON
ejpam-3743	490	25	is	be	AUX
ejpam-3743	490	26	valuable	valuable	ADJ
ejpam-3743	490	27	by	by	ADP
ejpam-3743	490	28	studying	study	VERB
ejpam-3743	490	29	the	the	DET
ejpam-3743	490	30	following	follow	VERB
ejpam-3743	490	31	themes	theme	NOUN
ejpam-3743	490	32	:	:	PUNCT
ejpam-3743	490	33	(	(	PUNCT
ejpam-3743	490	34	i	i	NOUN
ejpam-3743	490	35	)	)	PUNCT
ejpam-3743	490	36	define	define	VERB
ejpam-3743	490	37	weak	weak	ADJ
ejpam-3743	490	38	types	type	NOUN
ejpam-3743	490	39	of	of	ADP
ejpam-3743	490	40	supra	supra	PROPN
ejpam-3743	490	41	semi	semi	ADV
ejpam-3743	490	42	regular	regular	ADJ
ejpam-3743	490	43	and	and	CCONJ
ejpam-3743	490	44	supra	supra	ADJ
ejpam-3743	490	45	semi	semi	ADJ
ejpam-3743	490	46	normal	normal	ADJ
ejpam-3743	490	47	spaces	space	NOUN
ejpam-3743	490	48	.	.	PUNCT
ejpam-3743	491	1	(	(	PUNCT
ejpam-3743	491	2	ii	ii	NOUN
ejpam-3743	491	3	)	)	PUNCT
ejpam-3743	491	4	study	study	NOUN
ejpam-3743	491	5	ssti	ssti	NOUN
ejpam-3743	491	6	-	-	PUNCT
ejpam-3743	491	7	spaces	space	NOUN
ejpam-3743	491	8	for	for	ADP
ejpam-3743	491	9	(	(	PUNCT
ejpam-3743	491	10	i	i	NOUN
ejpam-3743	491	11	=	=	NOUN
ejpam-3743	491	12	1	1	NUM
ejpam-3743	491	13	2	2	NUM
ejpam-3743	491	14	,	,	PUNCT
ejpam-3743	491	15	2	2	NUM
ejpam-3743	491	16	1	1	NUM
ejpam-3743	491	17	2	2	NUM
ejpam-3743	491	18	,	,	PUNCT
ejpam-3743	491	19	3	3	NUM
ejpam-3743	491	20	1	1	NUM
ejpam-3743	491	21	2	2	NUM
ejpam-3743	491	22	,	,	PUNCT
ejpam-3743	491	23	5	5	NUM
ejpam-3743	491	24	)	)	PUNCT
ejpam-3743	491	25	(	(	PUNCT
ejpam-3743	491	26	iii	iii	X
ejpam-3743	491	27	)	)	PUNCT
ejpam-3743	491	28	explore	explore	VERB
ejpam-3743	491	29	the	the	DET
ejpam-3743	491	30	concepts	concept	NOUN
ejpam-3743	491	31	introduced	introduce	VERB
ejpam-3743	491	32	herein	herein	NOUN
ejpam-3743	491	33	using	use	VERB
ejpam-3743	491	34	the	the	DET
ejpam-3743	491	35	classes	class	NOUN
ejpam-3743	491	36	of	of	ADP
ejpam-3743	491	37	supra	supra	PROPN
ejpam-3743	491	38	α	α	PROPN
ejpam-3743	491	39	-	-	ADJ
ejpam-3743	491	40	open	open	ADJ
ejpam-3743	491	41	sets	set	NOUN
ejpam-3743	491	42	,	,	PUNCT
ejpam-3743	491	43	supra	supra	PROPN
ejpam-3743	491	44	b	b	NOUN
ejpam-3743	491	45	-	-	PUNCT
ejpam-3743	491	46	open	open	ADJ
ejpam-3743	491	47	sets	set	NOUN
ejpam-3743	491	48	and	and	CCONJ
ejpam-3743	491	49	supra	supra	PROPN
ejpam-3743	491	50	β	β	NOUN
ejpam-3743	491	51	-	-	ADJ
ejpam-3743	491	52	open	open	ADJ
ejpam-3743	491	53	sets	set	NOUN
ejpam-3743	491	54	.	.	PUNCT
ejpam-3743	492	1	(	(	PUNCT
ejpam-3743	492	2	iv	iv	X
ejpam-3743	492	3	)	)	PUNCT
ejpam-3743	492	4	investigate	investigate	NOUN
ejpam-3743	492	5	of	of	ADP
ejpam-3743	492	6	the	the	DET
ejpam-3743	492	7	possibility	possibility	NOUN
ejpam-3743	492	8	of	of	ADP
ejpam-3743	492	9	applying	apply	VERB
ejpam-3743	492	10	these	these	DET
ejpam-3743	492	11	concepts	concept	NOUN
ejpam-3743	492	12	on	on	ADP
ejpam-3743	492	13	information	information	NOUN
ejpam-3743	492	14	system	system	NOUN
ejpam-3743	492	15	,	,	PUNCT
ejpam-3743	492	16	especially	especially	ADV
ejpam-3743	492	17	,	,	PUNCT
ejpam-3743	492	18	separation	separation	NOUN
ejpam-3743	492	19	axioms	axiom	VERB
ejpam-3743	492	20	.	.	PUNCT
ejpam-3743	493	1	conflict	conflict	NOUN
ejpam-3743	493	2	of	of	ADP
ejpam-3743	493	3	interest	interest	NOUN
ejpam-3743	493	4	the	the	DET
ejpam-3743	493	5	authors	author	NOUN
ejpam-3743	493	6	declare	declare	VERB
ejpam-3743	493	7	that	that	SCONJ
ejpam-3743	493	8	there	there	PRON
ejpam-3743	493	9	is	be	VERB
ejpam-3743	493	10	no	no	DET
ejpam-3743	493	11	conflict	conflict	NOUN
ejpam-3743	493	12	of	of	ADP
ejpam-3743	493	13	interest	interest	NOUN
ejpam-3743	493	14	regarding	regard	VERB
ejpam-3743	493	15	the	the	DET
ejpam-3743	493	16	publication	publication	NOUN
ejpam-3743	493	17	of	of	ADP
ejpam-3743	493	18	this	this	DET
ejpam-3743	493	19	paper	paper	NOUN
ejpam-3743	493	20	.	.	PUNCT
ejpam-3743	494	1	references	reference	NOUN
ejpam-3743	494	2	442	442	NUM
ejpam-3743	494	3	acknowledgements	acknowledgement	NOUN
ejpam-3743	494	4	the	the	DET
ejpam-3743	494	5	authors	author	NOUN
ejpam-3743	494	6	would	would	AUX
ejpam-3743	494	7	like	like	VERB
ejpam-3743	494	8	to	to	PART
ejpam-3743	494	9	thank	thank	VERB
ejpam-3743	494	10	the	the	DET
ejpam-3743	494	11	reviewers	reviewer	NOUN
ejpam-3743	494	12	for	for	ADP
ejpam-3743	494	13	their	their	PRON
ejpam-3743	494	14	valuable	valuable	ADJ
ejpam-3743	494	15	comments	comment	NOUN
ejpam-3743	494	16	which	which	PRON
ejpam-3743	494	17	improved	improve	VERB
ejpam-3743	494	18	the	the	DET
ejpam-3743	494	19	presentation	presentation	NOUN
ejpam-3743	494	20	of	of	ADP
ejpam-3743	494	21	this	this	DET
ejpam-3743	494	22	paper	paper	NOUN
ejpam-3743	494	23	.	.	PUNCT
ejpam-3743	495	1	references	reference	NOUN
ejpam-3743	495	2	[	[	X
ejpam-3743	495	3	1	1	X
ejpam-3743	495	4	]	]	PUNCT
ejpam-3743	495	5	a	a	DET
ejpam-3743	495	6	m	m	NOUN
ejpam-3743	495	7	al	al	NOUN
ejpam-3743	495	8	-	-	PUNCT
ejpam-3743	495	9	odhari	odhari	ADJ
ejpam-3743	495	10	.	.	PUNCT
ejpam-3743	496	1	on	on	ADP
ejpam-3743	496	2	infra	infra	NOUN
ejpam-3743	496	3	topological	topological	ADJ
ejpam-3743	496	4	spaces	space	NOUN
ejpam-3743	496	5	.	.	PUNCT
ejpam-3743	497	1	international	international	ADJ
ejpam-3743	497	2	journal	journal	PROPN
ejpam-3743	497	3	of	of	ADP
ejpam-3743	497	4	mathematical	mathematical	ADJ
ejpam-3743	497	5	archive	archive	NOUN
ejpam-3743	497	6	,	,	PUNCT
ejpam-3743	497	7	6(11):179–184	6(11):179–184	NOUN
ejpam-3743	497	8	,	,	PUNCT
ejpam-3743	497	9	2015	2015	NUM
ejpam-3743	497	10	.	.	PUNCT
ejpam-3743	498	1	[	[	X
ejpam-3743	498	2	2	2	NUM
ejpam-3743	498	3	]	]	PUNCT
ejpam-3743	498	4	t	t	PROPN
ejpam-3743	498	5	m	m	PROPN
ejpam-3743	498	6	al	al	PROPN
ejpam-3743	498	7	-	-	PUNCT
ejpam-3743	498	8	shami	shami	PROPN
ejpam-3743	498	9	.	.	PUNCT
ejpam-3743	499	1	some	some	DET
ejpam-3743	499	2	results	result	NOUN
ejpam-3743	499	3	related	relate	VERB
ejpam-3743	499	4	to	to	ADP
ejpam-3743	499	5	supra	supra	PROPN
ejpam-3743	499	6	topological	topological	ADJ
ejpam-3743	499	7	spaces	space	NOUN
ejpam-3743	499	8	.	.	PUNCT
ejpam-3743	500	1	journal	journal	NOUN
ejpam-3743	500	2	of	of	ADP
ejpam-3743	500	3	advanced	advanced	ADJ
ejpam-3743	500	4	studies	study	NOUN
ejpam-3743	500	5	in	in	ADP
ejpam-3743	500	6	topology	topology	NOUN
ejpam-3743	500	7	,	,	PUNCT
ejpam-3743	500	8	4(7):283–294	4(7):283–294	NUM
ejpam-3743	500	9	,	,	PUNCT
ejpam-3743	500	10	2016	2016	NUM
ejpam-3743	500	11	.	.	PUNCT
ejpam-3743	501	1	[	[	X
ejpam-3743	501	2	3	3	X
ejpam-3743	501	3	]	]	X
ejpam-3743	501	4	t	t	PROPN
ejpam-3743	501	5	m	m	PROPN
ejpam-3743	501	6	al	al	PROPN
ejpam-3743	501	7	-	-	PUNCT
ejpam-3743	501	8	shami	shami	PROPN
ejpam-3743	501	9	.	.	PUNCT
ejpam-3743	502	1	on	on	ADP
ejpam-3743	502	2	supra	supra	PROPN
ejpam-3743	502	3	semi	semi	ADV
ejpam-3743	502	4	open	open	ADJ
ejpam-3743	502	5	sets	set	NOUN
ejpam-3743	502	6	and	and	CCONJ
ejpam-3743	502	7	some	some	DET
ejpam-3743	502	8	applications	application	NOUN
ejpam-3743	502	9	on	on	ADP
ejpam-3743	502	10	topological	topological	ADJ
ejpam-3743	502	11	spaces	space	NOUN
ejpam-3743	502	12	.	.	PUNCT
ejpam-3743	503	1	journal	journal	NOUN
ejpam-3743	503	2	of	of	ADP
ejpam-3743	503	3	advanced	advanced	ADJ
ejpam-3743	503	4	studies	study	NOUN
ejpam-3743	503	5	in	in	ADP
ejpam-3743	503	6	topology	topology	NOUN
ejpam-3743	503	7	,	,	PUNCT
ejpam-3743	503	8	8(2):144–153	8(2):144–153	NOUN
ejpam-3743	503	9	,	,	PUNCT
ejpam-3743	503	10	2017	2017	NUM
ejpam-3743	503	11	.	.	PUNCT
ejpam-3743	504	1	[	[	X
ejpam-3743	504	2	4	4	X
ejpam-3743	504	3	]	]	X
ejpam-3743	504	4	t	t	PROPN
ejpam-3743	504	5	m	m	PROPN
ejpam-3743	504	6	al	al	PROPN
ejpam-3743	504	7	-	-	PUNCT
ejpam-3743	504	8	shami	shami	PROPN
ejpam-3743	504	9	.	.	PUNCT
ejpam-3743	505	1	somewhere	somewhere	ADV
ejpam-3743	505	2	dense	dense	ADJ
ejpam-3743	505	3	sets	set	NOUN
ejpam-3743	505	4	and	and	CCONJ
ejpam-3743	505	5	st1	st1	PROPN
ejpam-3743	505	6	-	-	PUNCT
ejpam-3743	505	7	spaces	spaces	PROPN
ejpam-3743	505	8	.	.	PUNCT
ejpam-3743	506	1	punjab	punjab	PROPN
ejpam-3743	506	2	university	university	PROPN
ejpam-3743	506	3	journal	journal	NOUN
ejpam-3743	506	4	of	of	ADP
ejpam-3743	506	5	mathematics	mathematic	NOUN
ejpam-3743	506	6	,	,	PUNCT
ejpam-3743	506	7	49(2):101–111	49(2):101–111	PROPN
ejpam-3743	506	8	,	,	PUNCT
ejpam-3743	506	9	2017	2017	NUM
ejpam-3743	506	10	.	.	PUNCT
ejpam-3743	507	1	[	[	X
ejpam-3743	507	2	5	5	NUM
ejpam-3743	507	3	]	]	PUNCT
ejpam-3743	507	4	t	t	PROPN
ejpam-3743	507	5	m	m	PROPN
ejpam-3743	507	6	al	al	PROPN
ejpam-3743	507	7	-	-	PUNCT
ejpam-3743	507	8	shami	shami	PROPN
ejpam-3743	507	9	.	.	PUNCT
ejpam-3743	508	1	utilizing	utilize	VERB
ejpam-3743	508	2	supra	supra	PROPN
ejpam-3743	508	3	α	α	PROPN
ejpam-3743	508	4	-	-	ADJ
ejpam-3743	508	5	open	open	ADJ
ejpam-3743	508	6	sets	set	NOUN
ejpam-3743	508	7	to	to	PART
ejpam-3743	508	8	generate	generate	VERB
ejpam-3743	508	9	new	new	ADJ
ejpam-3743	508	10	types	type	NOUN
ejpam-3743	508	11	of	of	ADP
ejpam-3743	508	12	supra	supra	ADJ
ejpam-3743	508	13	compact	compact	ADJ
ejpam-3743	508	14	and	and	CCONJ
ejpam-3743	508	15	supra	supra	ADJ
ejpam-3743	508	16	lindelöf	lindelöf	NOUN
ejpam-3743	508	17	spaces	space	VERB
ejpam-3743	508	18	.	.	PUNCT
ejpam-3743	509	1	facta	facta	PROPN
ejpam-3743	509	2	universitatis	universitatis	PROPN
ejpam-3743	509	3	,	,	PUNCT
ejpam-3743	509	4	series	series	NOUN
ejpam-3743	509	5	:	:	PUNCT
ejpam-3743	509	6	mathematics	mathematic	NOUN
ejpam-3743	509	7	and	and	CCONJ
ejpam-3743	509	8	informatics	informatic	NOUN
ejpam-3743	509	9	,	,	PUNCT
ejpam-3743	509	10	32(1):151–162	32(1):151–162	PROPN
ejpam-3743	509	11	,	,	PUNCT
ejpam-3743	509	12	2017	2017	NUM
ejpam-3743	509	13	.	.	PUNCT
ejpam-3743	510	1	[	[	X
ejpam-3743	510	2	6	6	NUM
ejpam-3743	510	3	]	]	PUNCT
ejpam-3743	510	4	t	t	PROPN
ejpam-3743	510	5	m	m	PROPN
ejpam-3743	510	6	al	al	PROPN
ejpam-3743	510	7	-	-	PUNCT
ejpam-3743	510	8	shami	shami	PROPN
ejpam-3743	510	9	.	.	PUNCT
ejpam-3743	511	1	supra	supra	ADJ
ejpam-3743	511	2	semi	semi	NOUN
ejpam-3743	511	3	-	-	NOUN
ejpam-3743	511	4	compactness	compactness	NOUN
ejpam-3743	511	5	via	via	ADP
ejpam-3743	511	6	supra	supra	PROPN
ejpam-3743	511	7	topological	topological	PROPN
ejpam-3743	511	8	spaces	space	NOUN
ejpam-3743	511	9	.	.	PUNCT
ejpam-3743	512	1	journal	journal	PROPN
ejpam-3743	512	2	of	of	ADP
ejpam-3743	512	3	taibah	taibah	PROPN
ejpam-3743	512	4	university	university	PROPN
ejpam-3743	512	5	for	for	ADP
ejpam-3743	512	6	science	science	NOUN
ejpam-3743	512	7	,	,	PUNCT
ejpam-3743	512	8	12(3):338–343	12(3):338–343	PROPN
ejpam-3743	512	9	,	,	PUNCT
ejpam-3743	512	10	2018	2018	NUM
ejpam-3743	512	11	.	.	PUNCT
ejpam-3743	513	1	[	[	X
ejpam-3743	513	2	7	7	X
ejpam-3743	513	3	]	]	X
ejpam-3743	513	4	t	t	PROPN
ejpam-3743	513	5	m	m	PROPN
ejpam-3743	513	6	al	al	PROPN
ejpam-3743	513	7	-	-	PUNCT
ejpam-3743	513	8	shami	shami	PROPN
ejpam-3743	513	9	.	.	PUNCT
ejpam-3743	514	1	paracompactness	paracompactness	NOUN
ejpam-3743	514	2	on	on	ADP
ejpam-3743	514	3	supra	supra	PROPN
ejpam-3743	514	4	topological	topological	ADJ
ejpam-3743	514	5	spaces	space	NOUN
ejpam-3743	514	6	.	.	PUNCT
ejpam-3743	515	1	journal	journal	NOUN
ejpam-3743	515	2	of	of	ADP
ejpam-3743	515	3	linear	linear	PROPN
ejpam-3743	515	4	and	and	CCONJ
ejpam-3743	515	5	topological	topological	ADJ
ejpam-3743	515	6	algebra	algebra	NOUN
ejpam-3743	515	7	,	,	PUNCT
ejpam-3743	515	8	9(2):121–127	9(2):121–127	NUM
ejpam-3743	515	9	,	,	PUNCT
ejpam-3743	515	10	2020	2020	NUM
ejpam-3743	515	11	.	.	PUNCT
ejpam-3743	516	1	[	[	X
ejpam-3743	516	2	8	8	NUM
ejpam-3743	516	3	]	]	X
ejpam-3743	516	4	t	t	PROPN
ejpam-3743	516	5	m	m	PROPN
ejpam-3743	516	6	al	al	PROPN
ejpam-3743	516	7	-	-	PUNCT
ejpam-3743	516	8	shami	shami	PROPN
ejpam-3743	516	9	,	,	PUNCT
ejpam-3743	516	10	b	b	PROPN
ejpam-3743	516	11	a	a	DET
ejpam-3743	516	12	asaad	asaad	NOUN
ejpam-3743	516	13	,	,	PUNCT
ejpam-3743	516	14	and	and	CCONJ
ejpam-3743	516	15	m	m	PROPN
ejpam-3743	516	16	a	a	DET
ejpam-3743	516	17	el	el	PROPN
ejpam-3743	516	18	-	-	NOUN
ejpam-3743	516	19	gayar	gayar	NOUN
ejpam-3743	516	20	.	.	PUNCT
ejpam-3743	517	1	various	various	ADJ
ejpam-3743	517	2	types	type	NOUN
ejpam-3743	517	3	of	of	ADP
ejpam-3743	517	4	supra	supra	ADJ
ejpam-3743	517	5	pre	pre	ADJ
ejpam-3743	517	6	-	-	ADJ
ejpam-3743	517	7	compact	compact	ADJ
ejpam-3743	517	8	and	and	CCONJ
ejpam-3743	517	9	supra	supra	ADJ
ejpam-3743	517	10	pre	pre	PROPN
ejpam-3743	517	11	-	-	NOUN
ejpam-3743	517	12	lindelöf	lindelöf	NOUN
ejpam-3743	517	13	spaces	space	NOUN
ejpam-3743	517	14	.	.	PUNCT
ejpam-3743	518	1	missouri	missouri	PROPN
ejpam-3743	518	2	journal	journal	PROPN
ejpam-3743	518	3	of	of	ADP
ejpam-3743	518	4	mathematical	mathematical	ADJ
ejpam-3743	518	5	science	science	NOUN
ejpam-3743	518	6	,	,	PUNCT
ejpam-3743	518	7	32(1):1–20	32(1):1–20	NUM
ejpam-3743	518	8	,	,	PUNCT
ejpam-3743	518	9	2020	2020	NUM
ejpam-3743	518	10	.	.	PUNCT
ejpam-3743	519	1	[	[	X
ejpam-3743	519	2	9	9	NUM
ejpam-3743	519	3	]	]	X
ejpam-3743	519	4	t	t	PROPN
ejpam-3743	519	5	m	m	PROPN
ejpam-3743	519	6	al	al	PROPN
ejpam-3743	519	7	-	-	PUNCT
ejpam-3743	519	8	shami	shami	PROPN
ejpam-3743	519	9	and	and	CCONJ
ejpam-3743	519	10	m	m	PROPN
ejpam-3743	519	11	e	e	PROPN
ejpam-3743	519	12	el	el	PROPN
ejpam-3743	519	13	-	-	PUNCT
ejpam-3743	519	14	shafei	shafei	NOUN
ejpam-3743	519	15	.	.	PUNCT
ejpam-3743	520	1	on	on	ADP
ejpam-3743	520	2	supra	supra	PROPN
ejpam-3743	520	3	soft	soft	ADJ
ejpam-3743	520	4	topological	topological	ADJ
ejpam-3743	520	5	ordered	order	VERB
ejpam-3743	520	6	spaces	space	NOUN
ejpam-3743	520	7	.	.	PUNCT
ejpam-3743	521	1	arab	arab	PROPN
ejpam-3743	521	2	journal	journal	PROPN
ejpam-3743	521	3	of	of	ADP
ejpam-3743	521	4	basic	basic	ADJ
ejpam-3743	521	5	and	and	CCONJ
ejpam-3743	521	6	applied	applied	ADJ
ejpam-3743	521	7	sciences	science	NOUN
ejpam-3743	521	8	,	,	PUNCT
ejpam-3743	521	9	26(1):433–445	26(1):433–445	NOUN
ejpam-3743	521	10	,	,	PUNCT
ejpam-3743	521	11	2019	2019	NUM
ejpam-3743	521	12	.	.	PUNCT
ejpam-3743	522	1	[	[	X
ejpam-3743	522	2	10	10	NUM
ejpam-3743	522	3	]	]	X
ejpam-3743	522	4	t	t	PROPN
ejpam-3743	522	5	m	m	PROPN
ejpam-3743	522	6	al	al	PROPN
ejpam-3743	522	7	-	-	PUNCT
ejpam-3743	522	8	shami	shami	PROPN
ejpam-3743	522	9	and	and	CCONJ
ejpam-3743	522	10	m	m	PROPN
ejpam-3743	522	11	e	e	PROPN
ejpam-3743	522	12	el	el	PROPN
ejpam-3743	522	13	-	-	PUNCT
ejpam-3743	522	14	shafei	shafei	NOUN
ejpam-3743	522	15	.	.	PUNCT
ejpam-3743	523	1	two	two	NUM
ejpam-3743	523	2	types	type	NOUN
ejpam-3743	523	3	of	of	ADP
ejpam-3743	523	4	separation	separation	NOUN
ejpam-3743	523	5	axioms	axiom	NOUN
ejpam-3743	523	6	on	on	ADP
ejpam-3743	523	7	supra	supra	PROPN
ejpam-3743	523	8	soft	soft	ADJ
ejpam-3743	523	9	topological	topological	ADJ
ejpam-3743	523	10	spaces	space	NOUN
ejpam-3743	523	11	.	.	PUNCT
ejpam-3743	524	1	demonstratio	demonstratio	PROPN
ejpam-3743	524	2	mathematica	mathematica	PROPN
ejpam-3743	524	3	,	,	PUNCT
ejpam-3743	524	4	52(1):147–165	52(1):147–165	PROPN
ejpam-3743	524	5	,	,	PUNCT
ejpam-3743	524	6	2019	2019	NUM
ejpam-3743	524	7	.	.	PUNCT
ejpam-3743	525	1	[	[	X
ejpam-3743	525	2	11	11	NUM
ejpam-3743	525	3	]	]	X
ejpam-3743	525	4	t	t	PROPN
ejpam-3743	525	5	m	m	PROPN
ejpam-3743	525	6	al	al	PROPN
ejpam-3743	525	7	-	-	PUNCT
ejpam-3743	525	8	shami	shami	PROPN
ejpam-3743	525	9	and	and	CCONJ
ejpam-3743	525	10	t	t	PROPN
ejpam-3743	525	11	noiri	noiri	PROPN
ejpam-3743	525	12	.	.	PUNCT
ejpam-3743	526	1	more	more	ADJ
ejpam-3743	526	2	notions	notion	NOUN
ejpam-3743	526	3	and	and	CCONJ
ejpam-3743	526	4	mappings	mapping	NOUN
ejpam-3743	526	5	via	via	ADP
ejpam-3743	526	6	somewhere	somewhere	ADJ
ejpam-3743	526	7	dense	dense	ADJ
ejpam-3743	526	8	sets	set	NOUN
ejpam-3743	526	9	.	.	PUNCT
ejpam-3743	527	1	afrika	afrika	ADJ
ejpam-3743	527	2	matematika	matematika	PROPN
ejpam-3743	527	3	,	,	PUNCT
ejpam-3743	527	4	30(7):1011–1024	30(7):1011–1024	PROPN
ejpam-3743	527	5	,	,	PUNCT
ejpam-3743	527	6	2019	2019	NUM
ejpam-3743	527	7	.	.	PUNCT
ejpam-3743	528	1	[	[	X
ejpam-3743	528	2	12	12	NUM
ejpam-3743	528	3	]	]	X
ejpam-3743	528	4	p	p	NOUN
ejpam-3743	528	5	alexandroff	alexandroff	NOUN
ejpam-3743	528	6	.	.	PUNCT
ejpam-3743	529	1	diskrete	diskrete	PROPN
ejpam-3743	529	2	räume	räume	PROPN
ejpam-3743	529	3	.	.	PUNCT
ejpam-3743	530	1	rec	rec	PROPN
ejpam-3743	530	2	.	.	PROPN
ejpam-3743	530	3	math	math	NOUN
ejpam-3743	530	4	.	.	PUNCT
ejpam-3743	531	1	[	[	X
ejpam-3743	531	2	mat	mat	NOUN
ejpam-3743	531	3	.	.	INTJ
ejpam-3743	531	4	sbornik	sbornik	PROPN
ejpam-3743	531	5	]	]	X
ejpam-3743	531	6	n.s	n.s	PROPN
ejpam-3743	531	7	.	.	PROPN
ejpam-3743	531	8	,	,	PUNCT
ejpam-3743	531	9	2(44):501–519	2(44):501–519	NUM
ejpam-3743	531	10	,	,	PUNCT
ejpam-3743	531	11	1937	1937	NUM
ejpam-3743	531	12	.	.	PUNCT
ejpam-3743	532	1	[	[	X
ejpam-3743	532	2	13	13	NUM
ejpam-3743	532	3	]	]	PUNCT
ejpam-3743	532	4	á	á	NOUN
ejpam-3743	532	5	császár	császár	NOUN
ejpam-3743	532	6	.	.	PUNCT
ejpam-3743	533	1	generalized	generalize	VERB
ejpam-3743	533	2	topology	topology	NOUN
ejpam-3743	533	3	,	,	PUNCT
ejpam-3743	533	4	generalized	generalize	VERB
ejpam-3743	533	5	continuity	continuity	NOUN
ejpam-3743	533	6	.	.	PUNCT
ejpam-3743	534	1	acta	acta	PROPN
ejpam-3743	534	2	mathematica	mathematica	PROPN
ejpam-3743	534	3	hungarica	hungarica	PROPN
ejpam-3743	534	4	,	,	PUNCT
ejpam-3743	534	5	96:351–357	96:351–357	PROPN
ejpam-3743	534	6	,	,	PUNCT
ejpam-3743	534	7	2002	2002	NUM
ejpam-3743	534	8	.	.	PUNCT
ejpam-3743	535	1	[	[	X
ejpam-3743	535	2	14	14	NUM
ejpam-3743	535	3	]	]	PUNCT
ejpam-3743	535	4	á	á	NOUN
ejpam-3743	535	5	császár	császár	NOUN
ejpam-3743	535	6	.	.	PUNCT
ejpam-3743	536	1	weak	weak	ADJ
ejpam-3743	536	2	structure	structure	NOUN
ejpam-3743	536	3	.	.	PUNCT
ejpam-3743	537	1	acta	acta	PROPN
ejpam-3743	537	2	mathematica	mathematica	PROPN
ejpam-3743	537	3	hungarica	hungarica	PROPN
ejpam-3743	537	4	,	,	PUNCT
ejpam-3743	537	5	131(11):193–195	131(11):193–195	NUM
ejpam-3743	537	6	,	,	PUNCT
ejpam-3743	537	7	2011	2011	NUM
ejpam-3743	537	8	.	.	PUNCT
ejpam-3743	538	1	references	reference	NOUN
ejpam-3743	538	2	443	443	NUM
ejpam-3743	539	1	[	[	X
ejpam-3743	539	2	15	15	NUM
ejpam-3743	539	3	]	]	X
ejpam-3743	539	4	r	r	NOUN
ejpam-3743	539	5	devi	devi	X
ejpam-3743	539	6	,	,	PUNCT
ejpam-3743	539	7	s	s	PART
ejpam-3743	539	8	sampathkumar	sampathkumar	NOUN
ejpam-3743	539	9	,	,	PUNCT
ejpam-3743	539	10	and	and	CCONJ
ejpam-3743	539	11	m	m	PROPN
ejpam-3743	539	12	caldas	caldas	PROPN
ejpam-3743	539	13	.	.	PUNCT
ejpam-3743	540	1	on	on	ADP
ejpam-3743	540	2	α	α	NOUN
ejpam-3743	540	3	-	-	ADJ
ejpam-3743	540	4	open	open	ADJ
ejpam-3743	540	5	sets	set	NOUN
ejpam-3743	540	6	and	and	CCONJ
ejpam-3743	540	7	sα	sα	ADJ
ejpam-3743	540	8	-	-	ADJ
ejpam-3743	540	9	continuous	continuous	ADJ
ejpam-3743	540	10	maps	map	NOUN
ejpam-3743	540	11	.	.	PUNCT
ejpam-3743	541	1	general	general	ADJ
ejpam-3743	541	2	mathematics	mathematics	PROPN
ejpam-3743	541	3	,	,	PUNCT
ejpam-3743	541	4	16:77–84	16:77–84	NOUN
ejpam-3743	541	5	,	,	PUNCT
ejpam-3743	541	6	2008	2008	NUM
ejpam-3743	541	7	.	.	PUNCT
ejpam-3743	542	1	[	[	X
ejpam-3743	542	2	16	16	NUM
ejpam-3743	542	3	]	]	X
ejpam-3743	542	4	m	m	PROPN
ejpam-3743	542	5	e	e	NOUN
ejpam-3743	542	6	el	el	PROPN
ejpam-3743	542	7	-	-	PUNCT
ejpam-3743	542	8	shafei	shafei	PROPN
ejpam-3743	542	9	,	,	PUNCT
ejpam-3743	542	10	m	m	NOUN
ejpam-3743	542	11	abo	abo	NOUN
ejpam-3743	542	12	-	-	PUNCT
ejpam-3743	542	13	elhamayel	elhamayel	NOUN
ejpam-3743	542	14	,	,	PUNCT
ejpam-3743	542	15	and	and	CCONJ
ejpam-3743	542	16	t	t	PROPN
ejpam-3743	542	17	m	m	PROPN
ejpam-3743	542	18	al	al	PROPN
ejpam-3743	542	19	-	-	PUNCT
ejpam-3743	542	20	shami	shami	PROPN
ejpam-3743	542	21	.	.	PUNCT
ejpam-3743	543	1	on	on	ADP
ejpam-3743	543	2	supra	supra	PROPN
ejpam-3743	543	3	r	r	NOUN
ejpam-3743	543	4	-	-	PUNCT
ejpam-3743	543	5	open	open	ADJ
ejpam-3743	543	6	sets	set	NOUN
ejpam-3743	543	7	and	and	CCONJ
ejpam-3743	543	8	some	some	DET
ejpam-3743	543	9	applications	application	NOUN
ejpam-3743	543	10	on	on	ADP
ejpam-3743	543	11	topological	topological	ADJ
ejpam-3743	543	12	spaces	space	NOUN
ejpam-3743	543	13	.	.	PUNCT
ejpam-3743	544	1	journal	journal	NOUN
ejpam-3743	544	2	of	of	ADP
ejpam-3743	544	3	progressive	progressive	ADJ
ejpam-3743	544	4	research	research	NOUN
ejpam-3743	544	5	in	in	ADP
ejpam-3743	544	6	mathematics	mathematic	NOUN
ejpam-3743	544	7	,	,	PUNCT
ejpam-3743	544	8	8(2):1237–1248	8(2):1237–1248	NUM
ejpam-3743	544	9	,	,	PUNCT
ejpam-3743	544	10	2016	2016	NUM
ejpam-3743	544	11	.	.	PUNCT
ejpam-3743	545	1	[	[	X
ejpam-3743	545	2	17	17	NUM
ejpam-3743	545	3	]	]	X
ejpam-3743	545	4	m	m	PROPN
ejpam-3743	545	5	e	e	NOUN
ejpam-3743	545	6	el	el	PROPN
ejpam-3743	545	7	-	-	PUNCT
ejpam-3743	545	8	shafei	shafei	PROPN
ejpam-3743	545	9	,	,	PUNCT
ejpam-3743	545	10	a	a	DET
ejpam-3743	545	11	h	h	NOUN
ejpam-3743	545	12	zakari	zakari	NOUN
ejpam-3743	545	13	,	,	PUNCT
ejpam-3743	545	14	and	and	CCONJ
ejpam-3743	545	15	t	t	PROPN
ejpam-3743	545	16	m	m	PROPN
ejpam-3743	545	17	al	al	PROPN
ejpam-3743	545	18	-	-	PUNCT
ejpam-3743	545	19	shami	shami	PROPN
ejpam-3743	545	20	.	.	PUNCT
ejpam-3743	546	1	some	some	DET
ejpam-3743	546	2	applications	application	NOUN
ejpam-3743	546	3	of	of	ADP
ejpam-3743	546	4	supra	supra	ADJ
ejpam-3743	546	5	preopen	preopen	ADJ
ejpam-3743	546	6	sets	set	NOUN
ejpam-3743	546	7	.	.	PUNCT
ejpam-3743	547	1	journal	journal	NOUN
ejpam-3743	547	2	of	of	ADP
ejpam-3743	547	3	mathematics	mathematic	NOUN
ejpam-3743	547	4	,	,	PUNCT
ejpam-3743	547	5	volume	volume	NOUN
ejpam-3743	547	6	2020	2020	NUM
ejpam-3743	547	7	,	,	PUNCT
ejpam-3743	547	8	article	article	NOUN
ejpam-3743	547	9	i	i	PROPN
ejpam-3743	547	10	d	d	PROPN
ejpam-3743	547	11	9634206:11	9634206:11	NUM
ejpam-3743	547	12	pages	page	NOUN
ejpam-3743	547	13	,	,	PUNCT
ejpam-3743	547	14	2020	2020	NUM
ejpam-3743	547	15	.	.	PUNCT
ejpam-3743	548	1	[	[	X
ejpam-3743	548	2	18	18	NUM
ejpam-3743	548	3	]	]	X
ejpam-3743	548	4	s	s	VERB
ejpam-3743	548	5	jafari	jafari	ADJ
ejpam-3743	548	6	and	and	CCONJ
ejpam-3743	548	7	s	s	NOUN
ejpam-3743	548	8	tahiliani	tahiliani	NOUN
ejpam-3743	548	9	.	.	PUNCT
ejpam-3743	549	1	supra	supra	PROPN
ejpam-3743	549	2	β	β	X
ejpam-3743	549	3	-	-	ADJ
ejpam-3743	549	4	open	open	ADJ
ejpam-3743	549	5	sets	set	NOUN
ejpam-3743	549	6	and	and	CCONJ
ejpam-3743	549	7	supra	supra	ADJ
ejpam-3743	549	8	β	β	NOUN
ejpam-3743	549	9	-	-	NOUN
ejpam-3743	549	10	continuity	continuity	NOUN
ejpam-3743	549	11	on	on	ADP
ejpam-3743	549	12	topological	topological	ADJ
ejpam-3743	549	13	spaces	space	NOUN
ejpam-3743	549	14	.	.	PUNCT
ejpam-3743	550	1	annales	annales	PROPN
ejpam-3743	550	2	univ	univ	PROPN
ejpam-3743	550	3	.	.	PUNCT
ejpam-3743	551	1	sci	sci	PROPN
ejpam-3743	551	2	.	.	PUNCT
ejpam-3743	551	3	budapest	budapest	PROPN
ejpam-3743	551	4	.	.	PUNCT
ejpam-3743	552	1	,	,	PUNCT
ejpam-3743	552	2	56:1–9	56:1–9	NUM
ejpam-3743	552	3	,	,	PUNCT
ejpam-3743	552	4	2013	2013	NUM
ejpam-3743	552	5	.	.	PUNCT
ejpam-3743	553	1	[	[	X
ejpam-3743	553	2	19	19	NUM
ejpam-3743	553	3	]	]	PUNCT
ejpam-3743	553	4	a	a	DET
ejpam-3743	553	5	m	m	NOUN
ejpam-3743	553	6	kozae	kozae	NOUN
ejpam-3743	553	7	,	,	PUNCT
ejpam-3743	553	8	m	m	NOUN
ejpam-3743	553	9	shokry	shokry	NOUN
ejpam-3743	553	10	,	,	PUNCT
ejpam-3743	553	11	and	and	CCONJ
ejpam-3743	553	12	m	m	PROPN
ejpam-3743	553	13	zidan	zidan	PROPN
ejpam-3743	553	14	.	.	PUNCT
ejpam-3743	554	1	supra	supra	PROPN
ejpam-3743	554	2	topologies	topology	NOUN
ejpam-3743	554	3	for	for	ADP
ejpam-3743	554	4	digital	digital	ADJ
ejpam-3743	554	5	plane	plane	NOUN
ejpam-3743	554	6	.	.	PUNCT
ejpam-3743	555	1	aascit	aascit	PROPN
ejpam-3743	555	2	communications	communication	NOUN
ejpam-3743	555	3	,	,	PUNCT
ejpam-3743	555	4	3(1):1–10	3(1):1–10	NUM
ejpam-3743	555	5	,	,	PUNCT
ejpam-3743	555	6	2016	2016	NUM
ejpam-3743	555	7	.	.	PUNCT
ejpam-3743	556	1	[	[	X
ejpam-3743	556	2	20	20	NUM
ejpam-3743	556	3	]	]	X
ejpam-3743	556	4	h	h	NOUN
ejpam-3743	556	5	maki	maki	NOUN
ejpam-3743	556	6	,	,	PUNCT
ejpam-3743	556	7	j	j	PROPN
ejpam-3743	556	8	umehara	umehara	NOUN
ejpam-3743	556	9	,	,	PUNCT
ejpam-3743	556	10	and	and	CCONJ
ejpam-3743	556	11	t	t	PROPN
ejpam-3743	556	12	noiri	noiri	PROPN
ejpam-3743	556	13	.	.	PUNCT
ejpam-3743	557	1	every	every	DET
ejpam-3743	557	2	topological	topological	ADJ
ejpam-3743	557	3	space	space	NOUN
ejpam-3743	557	4	is	be	AUX
ejpam-3743	557	5	pret	pret	PROPN
ejpam-3743	557	6	1	1	NUM
ejpam-3743	557	7	2	2	NUM
ejpam-3743	557	8	.	.	PUNCT
ejpam-3743	558	1	mem	mem	PROPN
ejpam-3743	558	2	.	.	PUNCT
ejpam-3743	559	1	fac	fac	PROPN
ejpam-3743	559	2	.	.	PUNCT
ejpam-3743	560	1	sci	sci	PROPN
ejpam-3743	560	2	.	.	PROPN
ejpam-3743	560	3	kochi	kochi	PROPN
ejpam-3743	560	4	.	.	PUNCT
ejpam-3743	561	1	univ	univ	PROPN
ejpam-3743	561	2	.	.	PUNCT
ejpam-3743	561	3	ser	ser	PROPN
ejpam-3743	561	4	.	.	PUNCT
ejpam-3743	562	1	a	a	DET
ejpam-3743	562	2	math	math	NOUN
ejpam-3743	562	3	.	.	PUNCT
ejpam-3743	562	4	,	,	PUNCT
ejpam-3743	562	5	17:33–42	17:33–42	PROPN
ejpam-3743	562	6	,	,	PUNCT
ejpam-3743	562	7	1996	1996	NUM
ejpam-3743	562	8	.	.	PUNCT
ejpam-3743	563	1	[	[	X
ejpam-3743	563	2	21	21	NUM
ejpam-3743	563	3	]	]	X
ejpam-3743	563	4	a	a	DET
ejpam-3743	563	5	s	s	X
ejpam-3743	563	6	mashhour	mashhour	NOUN
ejpam-3743	563	7	,	,	PUNCT
ejpam-3743	563	8	a	a	DET
ejpam-3743	563	9	a	a	DET
ejpam-3743	563	10	allam	allam	PROPN
ejpam-3743	563	11	,	,	PUNCT
ejpam-3743	563	12	f	f	PROPN
ejpam-3743	563	13	s	s	PROPN
ejpam-3743	563	14	mahmoud	mahmoud	PROPN
ejpam-3743	563	15	,	,	PUNCT
ejpam-3743	563	16	and	and	CCONJ
ejpam-3743	563	17	f	f	PROPN
ejpam-3743	563	18	h	h	PROPN
ejpam-3743	563	19	kheder	kheder	PROPN
ejpam-3743	563	20	.	.	PUNCT
ejpam-3743	564	1	on	on	ADP
ejpam-3743	564	2	supra	supra	PROPN
ejpam-3743	564	3	topological	topological	ADJ
ejpam-3743	564	4	spaces	space	NOUN
ejpam-3743	564	5	.	.	PUNCT
ejpam-3743	565	1	indian	indian	ADJ
ejpam-3743	565	2	journal	journal	PROPN
ejpam-3743	565	3	of	of	ADP
ejpam-3743	565	4	pure	pure	ADJ
ejpam-3743	565	5	and	and	CCONJ
ejpam-3743	565	6	applied	applied	ADJ
ejpam-3743	565	7	mathematics	mathematic	NOUN
ejpam-3743	565	8	,	,	PUNCT
ejpam-3743	565	9	14(4):502–510	14(4):502–510	PROPN
ejpam-3743	565	10	,	,	PUNCT
ejpam-3743	565	11	1983	1983	NUM
ejpam-3743	565	12	.	.	PUNCT
ejpam-3743	566	1	[	[	X
ejpam-3743	566	2	22	22	NUM
ejpam-3743	566	3	]	]	X
ejpam-3743	566	4	j	j	PROPN
ejpam-3743	566	5	m	m	PROPN
ejpam-3743	566	6	mustafa	mustafa	PROPN
ejpam-3743	566	7	.	.	PUNCT
ejpam-3743	567	1	supra	supra	PROPN
ejpam-3743	567	2	b	b	PROPN
ejpam-3743	567	3	-	-	PUNCT
ejpam-3743	567	4	compact	compact	ADJ
ejpam-3743	567	5	and	and	CCONJ
ejpam-3743	567	6	supra	supra	ADJ
ejpam-3743	567	7	b	b	PROPN
ejpam-3743	567	8	-	-	PUNCT
ejpam-3743	567	9	lindelof	lindelof	PROPN
ejpam-3743	567	10	spaces	space	NOUN
ejpam-3743	567	11	.	.	PUNCT
ejpam-3743	568	1	journal	journal	NOUN
ejpam-3743	568	2	of	of	ADP
ejpam-3743	568	3	mathematics	mathematic	NOUN
ejpam-3743	568	4	and	and	CCONJ
ejpam-3743	568	5	applictions	appliction	NOUN
ejpam-3743	568	6	,	,	PUNCT
ejpam-3743	568	7	36:79–83	36:79–83	NUM
ejpam-3743	568	8	,	,	PUNCT
ejpam-3743	568	9	2013	2013	NUM
ejpam-3743	568	10	.	.	PUNCT
ejpam-3743	569	1	[	[	X
ejpam-3743	569	2	23	23	NUM
ejpam-3743	569	3	]	]	X
ejpam-3743	569	4	j	j	PROPN
ejpam-3743	569	5	m	m	PROPN
ejpam-3743	569	6	mustafa	mustafa	PROPN
ejpam-3743	569	7	and	and	CCONJ
ejpam-3743	569	8	h	h	DET
ejpam-3743	569	9	a	a	DET
ejpam-3743	569	10	qoqazeh	qoqazeh	NOUN
ejpam-3743	569	11	.	.	PUNCT
ejpam-3743	570	1	supra	supra	PROPN
ejpam-3743	570	2	d	d	NOUN
ejpam-3743	570	3	-	-	PUNCT
ejpam-3743	570	4	sets	set	NOUN
ejpam-3743	570	5	and	and	CCONJ
ejpam-3743	570	6	associated	associated	ADJ
ejpam-3743	570	7	separation	separation	NOUN
ejpam-3743	570	8	axioms	axiom	NOUN
ejpam-3743	570	9	.	.	PUNCT
ejpam-3743	571	1	international	international	ADJ
ejpam-3743	571	2	journal	journal	NOUN
ejpam-3743	571	3	of	of	ADP
ejpam-3743	571	4	pure	pure	ADJ
ejpam-3743	571	5	and	and	CCONJ
ejpam-3743	571	6	applied	applied	ADJ
ejpam-3743	571	7	mathematics	mathematic	NOUN
ejpam-3743	571	8	,	,	PUNCT
ejpam-3743	571	9	80(5):657–663	80(5):657–663	NUM
ejpam-3743	571	10	,	,	PUNCT
ejpam-3743	571	11	2012	2012	NUM
ejpam-3743	571	12	.	.	PUNCT
ejpam-3743	572	1	[	[	X
ejpam-3743	572	2	24	24	NUM
ejpam-3743	572	3	]	]	X
ejpam-3743	572	4	o	o	X
ejpam-3743	572	5	r	r	NOUN
ejpam-3743	572	6	sayed	say	VERB
ejpam-3743	572	7	.	.	PUNCT
ejpam-3743	573	1	supra	supra	PROPN
ejpam-3743	573	2	pre	pre	ADJ
ejpam-3743	573	3	-	-	ADJ
ejpam-3743	573	4	open	open	ADJ
ejpam-3743	573	5	sets	set	NOUN
ejpam-3743	573	6	and	and	CCONJ
ejpam-3743	573	7	supra	supra	NOUN
ejpam-3743	573	8	pre	pre	ADJ
ejpam-3743	573	9	-	-	ADJ
ejpam-3743	573	10	continuous	continuous	ADJ
ejpam-3743	573	11	on	on	ADP
ejpam-3743	573	12	topological	topological	ADJ
ejpam-3743	573	13	spaces	space	NOUN
ejpam-3743	573	14	.	.	PUNCT
ejpam-3743	574	1	series	series	PROPN
ejpam-3743	574	2	mathematics	mathematics	PROPN
ejpam-3743	574	3	and	and	CCONJ
ejpam-3743	574	4	information	information	NOUN
ejpam-3743	574	5	,	,	PUNCT
ejpam-3743	574	6	20(2):79–88	20(2):79–88	NUM
ejpam-3743	574	7	,	,	PUNCT
ejpam-3743	574	8	2010	2010	NUM
ejpam-3743	574	9	.	.	PUNCT
ejpam-3743	575	1	[	[	X
ejpam-3743	575	2	25	25	NUM
ejpam-3743	575	3	]	]	X
ejpam-3743	575	4	o	o	X
ejpam-3743	575	5	r	r	NOUN
ejpam-3743	575	6	sayed	say	VERB
ejpam-3743	575	7	.	.	PUNCT
ejpam-3743	576	1	supra	supra	PROPN
ejpam-3743	576	2	β	β	NOUN
ejpam-3743	576	3	-	-	NOUN
ejpam-3743	576	4	connectedness	connectedness	NOUN
ejpam-3743	576	5	on	on	ADP
ejpam-3743	576	6	topological	topological	ADJ
ejpam-3743	576	7	spaces	space	NOUN
ejpam-3743	576	8	.	.	PUNCT
ejpam-3743	577	1	proceedings	proceeding	NOUN
ejpam-3743	577	2	of	of	ADP
ejpam-3743	577	3	the	the	DET
ejpam-3743	577	4	pakistan	pakistan	PROPN
ejpam-3743	577	5	academy	academy	PROPN
ejpam-3743	577	6	of	of	ADP
ejpam-3743	577	7	sciences	sciences	PROPN
ejpam-3743	577	8	,	,	PUNCT
ejpam-3743	577	9	49(1):19–23	49(1):19–23	PRON
ejpam-3743	577	10	,	,	PUNCT
ejpam-3743	577	11	2012	2012	NUM
ejpam-3743	577	12	.	.	PUNCT
ejpam-3743	578	1	[	[	X
ejpam-3743	578	2	26	26	NUM
ejpam-3743	578	3	]	]	X
ejpam-3743	578	4	o	o	NOUN
ejpam-3743	578	5	r	r	NOUN
ejpam-3743	578	6	sayed	say	VERB
ejpam-3743	578	7	and	and	CCONJ
ejpam-3743	578	8	t	t	PROPN
ejpam-3743	578	9	noiri	noiri	PROPN
ejpam-3743	578	10	.	.	PUNCT
ejpam-3743	579	1	on	on	ADP
ejpam-3743	579	2	supra	supra	PROPN
ejpam-3743	579	3	b	b	PROPN
ejpam-3743	579	4	-	-	PUNCT
ejpam-3743	579	5	open	open	ADJ
ejpam-3743	579	6	sets	set	NOUN
ejpam-3743	579	7	and	and	CCONJ
ejpam-3743	579	8	supra	supra	PROPN
ejpam-3743	579	9	b	b	NOUN
ejpam-3743	579	10	-	-	PUNCT
ejpam-3743	579	11	continuity	continuity	NOUN
ejpam-3743	579	12	on	on	ADP
ejpam-3743	579	13	topological	topological	ADJ
ejpam-3743	579	14	spaces	space	NOUN
ejpam-3743	579	15	.	.	PUNCT
ejpam-3743	580	1	european	european	ADJ
ejpam-3743	580	2	journal	journal	PROPN
ejpam-3743	580	3	of	of	ADP
ejpam-3743	580	4	pure	pure	ADJ
ejpam-3743	580	5	and	and	CCONJ
ejpam-3743	580	6	applied	applied	ADJ
ejpam-3743	580	7	mathematics	mathematic	NOUN
ejpam-3743	580	8	,	,	PUNCT
ejpam-3743	580	9	3:295–302	3:295–302	NUM
ejpam-3743	580	10	,	,	PUNCT
ejpam-3743	580	11	2010	2010	NUM
ejpam-3743	580	12	.	.	PUNCT