id	sid	tid	token	lemma	pos
ejpam-5161	1	1	european	european	PROPN
ejpam-5161	1	2	journal	journal	PROPN
ejpam-5161	1	3	of	of	ADP
ejpam-5161	1	4	pure	pure	ADJ
ejpam-5161	1	5	and	and	CCONJ
ejpam-5161	1	6	applied	apply	VERB
ejpam-5161	1	7	mathematics	mathematic	NOUN
ejpam-5161	1	8	vol	vol	NOUN
ejpam-5161	1	9	.	.	PROPN
ejpam-5161	2	1	17	17	NUM
ejpam-5161	2	2	,	,	PUNCT
ejpam-5161	2	3	no	no	INTJ
ejpam-5161	2	4	.	.	NOUN
ejpam-5161	2	5	2	2	NUM
ejpam-5161	2	6	,	,	PUNCT
ejpam-5161	2	7	2024	2024	NUM
ejpam-5161	2	8	,	,	PUNCT
ejpam-5161	2	9	1168	1168	NUM
ejpam-5161	2	10	-	-	SYM
ejpam-5161	2	11	1182	1182	NUM
ejpam-5161	2	12	issn	issn	PROPN
ejpam-5161	2	13	1307	1307	NUM
ejpam-5161	2	14	-	-	SYM
ejpam-5161	2	15	5543	5543	NUM
ejpam-5161	2	16	–	–	PUNCT
ejpam-5161	2	17	ejpam.com	ejpam.com	X
ejpam-5161	2	18	published	publish	VERB
ejpam-5161	2	19	by	by	ADP
ejpam-5161	2	20	new	new	PROPN
ejpam-5161	2	21	york	york	PROPN
ejpam-5161	2	22	business	business	PROPN
ejpam-5161	2	23	global	global	ADJ
ejpam-5161	2	24	methods	method	NOUN
ejpam-5161	2	25	of	of	ADP
ejpam-5161	2	26	generating	generate	VERB
ejpam-5161	2	27	soft	soft	ADJ
ejpam-5161	2	28	topologies	topology	NOUN
ejpam-5161	2	29	and	and	CCONJ
ejpam-5161	3	1	soft	soft	ADJ
ejpam-5161	3	2	separation	separation	NOUN
ejpam-5161	3	3	axioms	axiom	NOUN
ejpam-5161	3	4	zanyar	zanyar	PROPN
ejpam-5161	3	5	a.	a.	NOUN
ejpam-5161	3	6	ameen1,∗	ameen1,∗	PROPN
ejpam-5161	3	7	,	,	PUNCT
ejpam-5161	3	8	ohud	ohud	PROPN
ejpam-5161	3	9	f.	f.	PROPN
ejpam-5161	3	10	alghamdi2	alghamdi2	PROPN
ejpam-5161	3	11	,	,	PUNCT
ejpam-5161	3	12	baravan	baravan	ADJ
ejpam-5161	3	13	a.	a.	PROPN
ejpam-5161	3	14	asaad3,4	asaad3,4	PROPN
ejpam-5161	3	15	,	,	PUNCT
ejpam-5161	3	16	ramadhan	ramadhan	PROPN
ejpam-5161	3	17	a.	a.	NOUN
ejpam-5161	3	18	mohammed5	mohammed5	PROPN
ejpam-5161	3	19	1	1	NUM
ejpam-5161	3	20	department	department	NOUN
ejpam-5161	3	21	of	of	ADP
ejpam-5161	3	22	mathematics	mathematic	NOUN
ejpam-5161	3	23	,	,	PUNCT
ejpam-5161	3	24	college	college	NOUN
ejpam-5161	3	25	of	of	ADP
ejpam-5161	3	26	science	science	NOUN
ejpam-5161	3	27	,	,	PUNCT
ejpam-5161	3	28	university	university	NOUN
ejpam-5161	3	29	of	of	ADP
ejpam-5161	3	30	duhok	duhok	NOUN
ejpam-5161	3	31	,	,	PUNCT
ejpam-5161	3	32	duhok	duhok	NOUN
ejpam-5161	3	33	42001	42001	NUM
ejpam-5161	3	34	,	,	PUNCT
ejpam-5161	3	35	iraq	iraq	PROPN
ejpam-5161	3	36	2	2	NUM
ejpam-5161	3	37	department	department	NOUN
ejpam-5161	3	38	of	of	ADP
ejpam-5161	3	39	mathematics	mathematic	NOUN
ejpam-5161	3	40	,	,	PUNCT
ejpam-5161	3	41	faculty	faculty	NOUN
ejpam-5161	3	42	of	of	ADP
ejpam-5161	3	43	science	science	NOUN
ejpam-5161	3	44	,	,	PUNCT
ejpam-5161	3	45	al	al	PROPN
ejpam-5161	3	46	-	-	PUNCT
ejpam-5161	3	47	baha	baha	PROPN
ejpam-5161	3	48	university	university	PROPN
ejpam-5161	3	49	,	,	PUNCT
ejpam-5161	3	50	al	al	PROPN
ejpam-5161	3	51	-	-	PUNCT
ejpam-5161	3	52	baha	baha	PROPN
ejpam-5161	3	53	,	,	PUNCT
ejpam-5161	3	54	saudi	saudi	PROPN
ejpam-5161	3	55	arabia	arabia	PROPN
ejpam-5161	3	56	3	3	NUM
ejpam-5161	3	57	department	department	NOUN
ejpam-5161	3	58	of	of	ADP
ejpam-5161	3	59	mathematics	mathematic	NOUN
ejpam-5161	3	60	,	,	PUNCT
ejpam-5161	3	61	faculty	faculty	NOUN
ejpam-5161	3	62	of	of	ADP
ejpam-5161	3	63	science	science	NOUN
ejpam-5161	3	64	,	,	PUNCT
ejpam-5161	3	65	university	university	NOUN
ejpam-5161	3	66	of	of	ADP
ejpam-5161	3	67	zakho	zakho	PROPN
ejpam-5161	3	68	,	,	PUNCT
ejpam-5161	3	69	zakho	zakho	PROPN
ejpam-5161	3	70	42002	42002	NUM
ejpam-5161	3	71	,	,	PUNCT
ejpam-5161	3	72	iraq	iraq	PROPN
ejpam-5161	3	73	4	4	NUM
ejpam-5161	3	74	department	department	NOUN
ejpam-5161	3	75	of	of	ADP
ejpam-5161	3	76	computer	computer	NOUN
ejpam-5161	3	77	science	science	NOUN
ejpam-5161	3	78	,	,	PUNCT
ejpam-5161	3	79	college	college	NOUN
ejpam-5161	3	80	of	of	ADP
ejpam-5161	3	81	science	science	NOUN
ejpam-5161	3	82	,	,	PUNCT
ejpam-5161	3	83	cihan	cihan	VERB
ejpam-5161	3	84	university	university	NOUN
ejpam-5161	3	85	-	-	PUNCT
ejpam-5161	3	86	duhok	duhok	NOUN
ejpam-5161	3	87	,	,	PUNCT
ejpam-5161	3	88	duhok	duhok	NOUN
ejpam-5161	3	89	42001	42001	NUM
ejpam-5161	3	90	,	,	PUNCT
ejpam-5161	3	91	iraq	iraq	PROPN
ejpam-5161	3	92	5	5	NUM
ejpam-5161	3	93	department	department	NOUN
ejpam-5161	3	94	of	of	ADP
ejpam-5161	3	95	mathematics	mathematic	NOUN
ejpam-5161	3	96	,	,	PUNCT
ejpam-5161	3	97	college	college	NOUN
ejpam-5161	3	98	of	of	ADP
ejpam-5161	3	99	basic	basic	ADJ
ejpam-5161	3	100	education	education	NOUN
ejpam-5161	3	101	,	,	PUNCT
ejpam-5161	3	102	university	university	NOUN
ejpam-5161	3	103	of	of	ADP
ejpam-5161	3	104	duhok	duhok	NOUN
ejpam-5161	3	105	,	,	PUNCT
ejpam-5161	3	106	duhok	duhok	NOUN
ejpam-5161	3	107	42001	42001	NUM
ejpam-5161	3	108	,	,	PUNCT
ejpam-5161	3	109	iraq	iraq	PROPN
ejpam-5161	3	110	abstract	abstract	NOUN
ejpam-5161	3	111	.	.	PUNCT
ejpam-5161	4	1	the	the	DET
ejpam-5161	4	2	paper	paper	NOUN
ejpam-5161	4	3	develops	develop	VERB
ejpam-5161	4	4	a	a	DET
ejpam-5161	4	5	novel	novel	ADJ
ejpam-5161	4	6	analysis	analysis	NOUN
ejpam-5161	4	7	of	of	ADP
ejpam-5161	4	8	mutual	mutual	ADJ
ejpam-5161	4	9	interactions	interaction	NOUN
ejpam-5161	4	10	between	between	ADP
ejpam-5161	4	11	topology	topology	NOUN
ejpam-5161	4	12	and	and	CCONJ
ejpam-5161	4	13	soft	soft	ADJ
ejpam-5161	4	14	topology	topology	NOUN
ejpam-5161	4	15	.	.	PUNCT
ejpam-5161	5	1	it	it	PRON
ejpam-5161	5	2	is	be	AUX
ejpam-5161	5	3	known	know	VERB
ejpam-5161	5	4	that	that	SCONJ
ejpam-5161	5	5	each	each	DET
ejpam-5161	5	6	soft	soft	ADJ
ejpam-5161	5	7	topology	topology	NOUN
ejpam-5161	5	8	produces	produce	VERB
ejpam-5161	5	9	a	a	DET
ejpam-5161	5	10	system	system	NOUN
ejpam-5161	5	11	of	of	ADP
ejpam-5161	5	12	crisp	crisp	ADJ
ejpam-5161	5	13	(	(	PUNCT
ejpam-5161	5	14	parameterized	parameterized	ADJ
ejpam-5161	5	15	)	)	PUNCT
ejpam-5161	5	16	topologies	topology	NOUN
ejpam-5161	5	17	.	.	PUNCT
ejpam-5161	6	1	the	the	DET
ejpam-5161	6	2	other	other	ADJ
ejpam-5161	6	3	way	way	NOUN
ejpam-5161	6	4	round	round	ADV
ejpam-5161	6	5	is	be	AUX
ejpam-5161	6	6	also	also	ADV
ejpam-5161	6	7	possible	possible	ADJ
ejpam-5161	6	8	.	.	PUNCT
ejpam-5161	7	1	namely	namely	ADV
ejpam-5161	7	2	,	,	PUNCT
ejpam-5161	7	3	one	one	PRON
ejpam-5161	7	4	can	can	AUX
ejpam-5161	7	5	generate	generate	VERB
ejpam-5161	7	6	a	a	DET
ejpam-5161	7	7	soft	soft	ADJ
ejpam-5161	7	8	topology	topology	NOUN
ejpam-5161	7	9	from	from	ADP
ejpam-5161	7	10	a	a	DET
ejpam-5161	7	11	system	system	NOUN
ejpam-5161	7	12	of	of	ADP
ejpam-5161	7	13	crisp	crisp	ADJ
ejpam-5161	7	14	topologies	topology	NOUN
ejpam-5161	7	15	.	.	PUNCT
ejpam-5161	8	1	different	different	ADJ
ejpam-5161	8	2	methods	method	NOUN
ejpam-5161	8	3	of	of	ADP
ejpam-5161	8	4	producing	produce	VERB
ejpam-5161	8	5	soft	soft	ADJ
ejpam-5161	8	6	topologies	topology	NOUN
ejpam-5161	8	7	are	be	AUX
ejpam-5161	8	8	discussed	discuss	VERB
ejpam-5161	8	9	by	by	ADP
ejpam-5161	8	10	implementing	implement	VERB
ejpam-5161	8	11	two	two	NUM
ejpam-5161	8	12	formulas	formula	NOUN
ejpam-5161	8	13	.	.	PUNCT
ejpam-5161	9	1	then	then	ADV
ejpam-5161	9	2	,	,	PUNCT
ejpam-5161	9	3	the	the	DET
ejpam-5161	9	4	relationships	relationship	NOUN
ejpam-5161	9	5	between	between	ADP
ejpam-5161	9	6	the	the	DET
ejpam-5161	9	7	resulting	result	VERB
ejpam-5161	9	8	soft	soft	ADJ
ejpam-5161	9	9	topologies	topology	NOUN
ejpam-5161	9	10	are	be	AUX
ejpam-5161	9	11	obtained	obtain	VERB
ejpam-5161	9	12	.	.	PUNCT
ejpam-5161	10	1	with	with	ADP
ejpam-5161	10	2	the	the	DET
ejpam-5161	10	3	help	help	NOUN
ejpam-5161	10	4	of	of	ADP
ejpam-5161	10	5	an	an	DET
ejpam-5161	10	6	example	example	NOUN
ejpam-5161	10	7	,	,	PUNCT
ejpam-5161	10	8	it	it	PRON
ejpam-5161	10	9	is	be	AUX
ejpam-5161	10	10	demonstrated	demonstrate	VERB
ejpam-5161	10	11	that	that	SCONJ
ejpam-5161	10	12	one	one	NUM
ejpam-5161	10	13	formula	formula	NOUN
ejpam-5161	10	14	is	be	AUX
ejpam-5161	10	15	more	more	ADV
ejpam-5161	10	16	constructible	constructible	ADJ
ejpam-5161	10	17	than	than	ADP
ejpam-5161	10	18	the	the	DET
ejpam-5161	10	19	other	other	ADJ
ejpam-5161	10	20	.	.	PUNCT
ejpam-5161	11	1	now	now	ADV
ejpam-5161	11	2	,	,	PUNCT
ejpam-5161	11	3	it	it	PRON
ejpam-5161	11	4	is	be	AUX
ejpam-5161	11	5	reasonable	reasonable	ADJ
ejpam-5161	11	6	to	to	PART
ejpam-5161	11	7	ask	ask	VERB
ejpam-5161	11	8	which	which	DET
ejpam-5161	11	9	(	(	PUNCT
ejpam-5161	11	10	topological	topological	ADJ
ejpam-5161	11	11	)	)	PUNCT
ejpam-5161	11	12	properties	property	NOUN
ejpam-5161	11	13	of	of	ADP
ejpam-5161	11	14	a	a	DET
ejpam-5161	11	15	soft	soft	ADJ
ejpam-5161	11	16	topology	topology	NOUN
ejpam-5161	11	17	can	can	AUX
ejpam-5161	11	18	be	be	AUX
ejpam-5161	11	19	transferred	transfer	VERB
ejpam-5161	11	20	to	to	ADP
ejpam-5161	11	21	the	the	DET
ejpam-5161	11	22	set	set	NOUN
ejpam-5161	11	23	of	of	ADP
ejpam-5161	11	24	crisp	crisp	ADJ
ejpam-5161	11	25	topologies	topology	NOUN
ejpam-5161	11	26	,	,	PUNCT
ejpam-5161	11	27	or	or	CCONJ
ejpam-5161	11	28	the	the	DET
ejpam-5161	11	29	opposite	opposite	NOUN
ejpam-5161	11	30	.	.	PUNCT
ejpam-5161	12	1	to	to	PART
ejpam-5161	12	2	address	address	VERB
ejpam-5161	12	3	this	this	DET
ejpam-5161	12	4	question	question	NOUN
ejpam-5161	12	5	,	,	PUNCT
ejpam-5161	12	6	we	we	PRON
ejpam-5161	12	7	consider	consider	VERB
ejpam-5161	12	8	the	the	DET
ejpam-5161	12	9	standard	standard	ADJ
ejpam-5161	12	10	separation	separation	NOUN
ejpam-5161	12	11	axioms	axiom	NOUN
ejpam-5161	12	12	and	and	CCONJ
ejpam-5161	12	13	show	show	VERB
ejpam-5161	12	14	how	how	SCONJ
ejpam-5161	12	15	well	well	ADV
ejpam-5161	12	16	these	these	DET
ejpam-5161	12	17	axioms	axiom	NOUN
ejpam-5161	12	18	can	can	AUX
ejpam-5161	12	19	be	be	AUX
ejpam-5161	12	20	preserved	preserve	VERB
ejpam-5161	12	21	when	when	SCONJ
ejpam-5161	12	22	moving	move	VERB
ejpam-5161	12	23	from	from	ADP
ejpam-5161	12	24	a	a	DET
ejpam-5161	12	25	system	system	NOUN
ejpam-5161	12	26	of	of	ADP
ejpam-5161	12	27	crisp	crisp	ADJ
ejpam-5161	12	28	topologies	topology	NOUN
ejpam-5161	12	29	to	to	ADP
ejpam-5161	12	30	the	the	DET
ejpam-5161	12	31	soft	soft	ADJ
ejpam-5161	12	32	topology	topology	NOUN
ejpam-5161	12	33	generated	generate	VERB
ejpam-5161	12	34	by	by	ADP
ejpam-5161	12	35	it	it	PRON
ejpam-5161	12	36	and	and	CCONJ
ejpam-5161	12	37	contrariwise	contrariwise	ADV
ejpam-5161	12	38	.	.	PUNCT
ejpam-5161	13	1	additionally	additionally	ADV
ejpam-5161	13	2	,	,	PUNCT
ejpam-5161	13	3	our	our	PRON
ejpam-5161	13	4	findings	finding	NOUN
ejpam-5161	13	5	extend	extend	VERB
ejpam-5161	13	6	and	and	CCONJ
ejpam-5161	13	7	disprove	disprove	VERB
ejpam-5161	13	8	some	some	DET
ejpam-5161	13	9	results	result	NOUN
ejpam-5161	13	10	from	from	ADP
ejpam-5161	13	11	the	the	DET
ejpam-5161	13	12	literature	literature	NOUN
ejpam-5161	13	13	.	.	PUNCT
ejpam-5161	14	1	2020	2020	NUM
ejpam-5161	14	2	mathematics	mathematics	PROPN
ejpam-5161	14	3	subject	subject	NOUN
ejpam-5161	14	4	classifications	classification	NOUN
ejpam-5161	14	5	:	:	PUNCT
ejpam-5161	14	6	54a05	54a05	NUM
ejpam-5161	14	7	,	,	PUNCT
ejpam-5161	14	8	54h99	54h99	NUM
ejpam-5161	14	9	key	key	ADJ
ejpam-5161	14	10	words	word	NOUN
ejpam-5161	14	11	and	and	CCONJ
ejpam-5161	14	12	phrases	phrase	NOUN
ejpam-5161	14	13	:	:	PUNCT
ejpam-5161	14	14	soft	soft	ADJ
ejpam-5161	14	15	topology	topology	NOUN
ejpam-5161	14	16	,	,	PUNCT
ejpam-5161	14	17	soft	soft	ADJ
ejpam-5161	14	18	t0	t0	NOUN
ejpam-5161	14	19	,	,	PUNCT
ejpam-5161	14	20	soft	soft	ADJ
ejpam-5161	14	21	t1	t1	NOUN
ejpam-5161	14	22	,	,	PUNCT
ejpam-5161	14	23	soft	soft	ADJ
ejpam-5161	14	24	t2	t2	NOUN
ejpam-5161	14	25	,	,	PUNCT
ejpam-5161	14	26	soft	soft	ADJ
ejpam-5161	14	27	regular	regular	ADJ
ejpam-5161	14	28	,	,	PUNCT
ejpam-5161	14	29	soft	soft	ADJ
ejpam-5161	14	30	normal	normal	ADJ
ejpam-5161	14	31	,	,	PUNCT
ejpam-5161	14	32	soft	soft	ADJ
ejpam-5161	14	33	t3	t3	NOUN
ejpam-5161	14	34	,	,	PUNCT
ejpam-5161	14	35	soft	soft	ADJ
ejpam-5161	14	36	t4	t4	PROPN
ejpam-5161	14	37	1	1	NUM
ejpam-5161	14	38	.	.	PUNCT
ejpam-5161	14	39	introduction	introduction	NOUN
ejpam-5161	14	40	in	in	ADP
ejpam-5161	14	41	its	its	PRON
ejpam-5161	14	42	modern	modern	ADJ
ejpam-5161	14	43	version	version	NOUN
ejpam-5161	14	44	,	,	PUNCT
ejpam-5161	14	45	the	the	DET
ejpam-5161	14	46	weierstrass	weierstrass	NOUN
ejpam-5161	14	47	extreme	extreme	ADJ
ejpam-5161	14	48	value	value	NOUN
ejpam-5161	14	49	theorem	theorem	NOUN
ejpam-5161	14	50	demonstrates	demonstrate	VERB
ejpam-5161	14	51	that	that	SCONJ
ejpam-5161	14	52	topological	topological	ADJ
ejpam-5161	14	53	considerations	consideration	NOUN
ejpam-5161	14	54	can	can	AUX
ejpam-5161	14	55	be	be	AUX
ejpam-5161	14	56	useful	useful	ADJ
ejpam-5161	14	57	in	in	ADP
ejpam-5161	14	58	decision	decision	NOUN
ejpam-5161	14	59	-	-	PUNCT
ejpam-5161	14	60	making	make	VERB
ejpam-5161	14	61	theory	theory	NOUN
ejpam-5161	14	62	and	and	CCONJ
ejpam-5161	14	63	economics	economic	NOUN
ejpam-5161	14	64	,	,	PUNCT
ejpam-5161	14	65	(	(	PUNCT
ejpam-5161	14	66	see	see	VERB
ejpam-5161	14	67	,	,	PUNCT
ejpam-5161	14	68	[	[	X
ejpam-5161	14	69	4	4	NUM
ejpam-5161	14	70	]	]	NUM
ejpam-5161	14	71	)	)	PUNCT
ejpam-5161	14	72	.	.	PUNCT
ejpam-5161	15	1	indeed	indeed	ADV
ejpam-5161	15	2	,	,	PUNCT
ejpam-5161	15	3	the	the	DET
ejpam-5161	15	4	development	development	NOUN
ejpam-5161	15	5	of	of	ADP
ejpam-5161	15	6	topological	topological	ADJ
ejpam-5161	15	7	structures	structure	NOUN
ejpam-5161	15	8	helps	help	VERB
ejpam-5161	15	9	to	to	PART
ejpam-5161	15	10	enhance	enhance	VERB
ejpam-5161	15	11	other	other	ADJ
ejpam-5161	15	12	disciplines	discipline	NOUN
ejpam-5161	15	13	.	.	PUNCT
ejpam-5161	16	1	∗corresponding	∗corresponde	VERB
ejpam-5161	16	2	author	author	NOUN
ejpam-5161	16	3	.	.	PUNCT
ejpam-5161	17	1	doi	doi	NOUN
ejpam-5161	17	2	:	:	PUNCT
ejpam-5161	17	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5161	https://doi.org/10.29020/nybg.ejpam.v17i2.5161	ADJ
ejpam-5161	17	4	email	email	NOUN
ejpam-5161	17	5	addresses	address	NOUN
ejpam-5161	17	6	:	:	PUNCT
ejpam-5161	17	7	zanyar@uod.ac	zanyar@uod.ac	X
ejpam-5161	17	8	(	(	PUNCT
ejpam-5161	17	9	z.	z.	PROPN
ejpam-5161	17	10	a.	a.	NOUN
ejpam-5161	17	11	ameen	ameen	PROPN
ejpam-5161	17	12	)	)	PUNCT
ejpam-5161	17	13	,	,	PUNCT
ejpam-5161	17	14	ofalghamdi@bu.edu.sa	ofalghamdi@bu.edu.sa	PROPN
ejpam-5161	17	15	(	(	PUNCT
ejpam-5161	17	16	o.	o.	PROPN
ejpam-5161	17	17	f.	f.	PROPN
ejpam-5161	17	18	alghamdi	alghamdi	PROPN
ejpam-5161	17	19	)	)	PUNCT
ejpam-5161	17	20	,	,	PUNCT
ejpam-5161	17	21	baravan.asaad@uoz.edu.kr	baravan.asaad@uoz.edu.kr	X
ejpam-5161	17	22	(	(	PUNCT
ejpam-5161	17	23	b.	b.	PROPN
ejpam-5161	17	24	a.	a.	NOUN
ejpam-5161	17	25	asaad	asaad	PROPN
ejpam-5161	17	26	)	)	PUNCT
ejpam-5161	17	27	,	,	PUNCT
ejpam-5161	17	28	ramadhan.hajani@uod.ac	ramadhan.hajani@uod.ac	PROPN
ejpam-5161	17	29	(	(	PUNCT
ejpam-5161	17	30	r.	r.	PROPN
ejpam-5161	17	31	a.	a.	PROPN
ejpam-5161	17	32	mohammed	mohammed	PROPN
ejpam-5161	17	33	)	)	PUNCT
ejpam-5161	17	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5161	17	35	1168	1168	NUM
ejpam-5161	17	36	©	©	ADP
ejpam-5161	17	37	2024	2024	NUM
ejpam-5161	17	38	ejpam	ejpam	NOUN
ejpam-5161	17	39	all	all	DET
ejpam-5161	17	40	rights	right	NOUN
ejpam-5161	17	41	reserved	reserve	VERB
ejpam-5161	17	42	.	.	PUNCT
ejpam-5161	18	1	z.	z.	PROPN
ejpam-5161	18	2	a.	a.	PROPN
ejpam-5161	18	3	ameen	ameen	PROPN
ejpam-5161	18	4	et	et	PROPN
ejpam-5161	18	5	al	al	PROPN
ejpam-5161	18	6	.	.	PUNCT
ejpam-5161	18	7	/	/	SYM
ejpam-5161	18	8	eur	eur	PROPN
ejpam-5161	18	9	.	.	PUNCT
ejpam-5161	19	1	j.	j.	PROPN
ejpam-5161	19	2	pure	pure	PROPN
ejpam-5161	19	3	appl	appl	PROPN
ejpam-5161	19	4	.	.	PROPN
ejpam-5161	19	5	math	math	PROPN
ejpam-5161	19	6	,	,	PUNCT
ejpam-5161	19	7	17	17	NUM
ejpam-5161	19	8	(	(	PUNCT
ejpam-5161	19	9	2	2	NUM
ejpam-5161	19	10	)	)	PUNCT
ejpam-5161	19	11	(	(	PUNCT
ejpam-5161	19	12	2024	2024	NUM
ejpam-5161	19	13	)	)	PUNCT
ejpam-5161	19	14	,	,	PUNCT
ejpam-5161	19	15	1168	1168	NUM
ejpam-5161	19	16	-	-	SYM
ejpam-5161	19	17	1182	1182	NUM
ejpam-5161	19	18	1169	1169	NUM
ejpam-5161	19	19	general	general	ADJ
ejpam-5161	19	20	topology	topology	NOUN
ejpam-5161	19	21	is	be	AUX
ejpam-5161	19	22	the	the	DET
ejpam-5161	19	23	mathematical	mathematical	ADJ
ejpam-5161	19	24	branch	branch	NOUN
ejpam-5161	19	25	of	of	ADP
ejpam-5161	19	26	topology	topology	NOUN
ejpam-5161	19	27	that	that	PRON
ejpam-5161	19	28	concerns	concern	VERB
ejpam-5161	19	29	itself	itself	PRON
ejpam-5161	19	30	with	with	ADP
ejpam-5161	19	31	the	the	DET
ejpam-5161	19	32	foundational	foundational	ADJ
ejpam-5161	19	33	set	set	NOUN
ejpam-5161	19	34	-	-	PUNCT
ejpam-5161	19	35	theoretic	theoretic	NOUN
ejpam-5161	19	36	notions	notion	NOUN
ejpam-5161	19	37	and	and	CCONJ
ejpam-5161	19	38	constructions	construction	NOUN
ejpam-5161	19	39	.	.	PUNCT
ejpam-5161	20	1	motivated	motivate	VERB
ejpam-5161	20	2	by	by	ADP
ejpam-5161	20	3	the	the	DET
ejpam-5161	20	4	standard	standard	ADJ
ejpam-5161	20	5	axioms	axiom	NOUN
ejpam-5161	20	6	of	of	ADP
ejpam-5161	20	7	classical	classical	ADJ
ejpam-5161	20	8	topological	topological	ADJ
ejpam-5161	20	9	space	space	NOUN
ejpam-5161	20	10	,	,	PUNCT
ejpam-5161	20	11	shabir	shabir	NOUN
ejpam-5161	20	12	and	and	CCONJ
ejpam-5161	20	13	naz	naz	PROPN
ejpam-5161	21	1	[	[	X
ejpam-5161	21	2	28	28	NUM
ejpam-5161	21	3	]	]	PUNCT
ejpam-5161	21	4	,	,	PUNCT
ejpam-5161	21	5	and	and	CCONJ
ejpam-5161	21	6	çağman	çağman	NOUN
ejpam-5161	21	7	et	et	NOUN
ejpam-5161	21	8	al	al	PROPN
ejpam-5161	21	9	.	.	PUNCT
ejpam-5161	22	1	[	[	X
ejpam-5161	22	2	15	15	NUM
ejpam-5161	22	3	]	]	PUNCT
ejpam-5161	22	4	,	,	PUNCT
ejpam-5161	22	5	separately	separately	ADV
ejpam-5161	22	6	,	,	PUNCT
ejpam-5161	22	7	introduced	introduce	VERB
ejpam-5161	22	8	another	another	DET
ejpam-5161	22	9	branch	branch	NOUN
ejpam-5161	22	10	of	of	ADP
ejpam-5161	22	11	topology	topology	NOUN
ejpam-5161	22	12	named	name	VERB
ejpam-5161	22	13	“	"	PUNCT
ejpam-5161	22	14	soft	soft	ADJ
ejpam-5161	22	15	topology	topology	NOUN
ejpam-5161	22	16	.	.	PUNCT
ejpam-5161	22	17	”	"	PUNCT
ejpam-5161	22	18	soft	soft	ADJ
ejpam-5161	22	19	topology	topology	NOUN
ejpam-5161	22	20	is	be	AUX
ejpam-5161	22	21	a	a	DET
ejpam-5161	22	22	combination	combination	NOUN
ejpam-5161	22	23	of	of	ADP
ejpam-5161	22	24	soft	soft	ADJ
ejpam-5161	22	25	set	set	NOUN
ejpam-5161	22	26	theory	theory	NOUN
ejpam-5161	22	27	and	and	CCONJ
ejpam-5161	22	28	topology	topology	NOUN
ejpam-5161	22	29	.	.	PUNCT
ejpam-5161	23	1	it	it	PRON
ejpam-5161	23	2	is	be	AUX
ejpam-5161	23	3	focused	focus	VERB
ejpam-5161	23	4	on	on	ADP
ejpam-5161	23	5	the	the	DET
ejpam-5161	23	6	construction	construction	NOUN
ejpam-5161	23	7	of	of	ADP
ejpam-5161	23	8	the	the	DET
ejpam-5161	23	9	system	system	NOUN
ejpam-5161	23	10	of	of	ADP
ejpam-5161	23	11	all	all	DET
ejpam-5161	23	12	soft	soft	ADJ
ejpam-5161	23	13	sets	set	NOUN
ejpam-5161	23	14	.	.	PUNCT
ejpam-5161	24	1	soft	soft	ADJ
ejpam-5161	24	2	sets	set	NOUN
ejpam-5161	24	3	were	be	AUX
ejpam-5161	24	4	presented	present	VERB
ejpam-5161	24	5	as	as	ADP
ejpam-5161	24	6	a	a	DET
ejpam-5161	24	7	collection	collection	NOUN
ejpam-5161	24	8	of	of	ADP
ejpam-5161	24	9	relevant	relevant	ADJ
ejpam-5161	24	10	parameters	parameter	NOUN
ejpam-5161	24	11	to	to	PART
ejpam-5161	24	12	characterize	characterize	VERB
ejpam-5161	24	13	a	a	DET
ejpam-5161	24	14	universe	universe	NOUN
ejpam-5161	24	15	of	of	ADP
ejpam-5161	24	16	possibilities	possibility	NOUN
ejpam-5161	24	17	.	.	PUNCT
ejpam-5161	25	1	soft	soft	ADJ
ejpam-5161	25	2	set	set	NOUN
ejpam-5161	25	3	theory	theory	NOUN
ejpam-5161	25	4	has	have	AUX
ejpam-5161	25	5	been	be	AUX
ejpam-5161	25	6	a	a	DET
ejpam-5161	25	7	fruitful	fruitful	ADJ
ejpam-5161	25	8	area	area	NOUN
ejpam-5161	25	9	of	of	ADP
ejpam-5161	25	10	study	study	NOUN
ejpam-5161	25	11	and	and	CCONJ
ejpam-5161	25	12	connection	connection	NOUN
ejpam-5161	25	13	with	with	ADP
ejpam-5161	25	14	various	various	ADJ
ejpam-5161	25	15	disciplines	discipline	NOUN
ejpam-5161	25	16	since	since	SCONJ
ejpam-5161	25	17	its	its	PRON
ejpam-5161	25	18	establishment	establishment	NOUN
ejpam-5161	25	19	.	.	PUNCT
ejpam-5161	26	1	molodtsov	molodtsov	PROPN
ejpam-5161	27	1	[	[	X
ejpam-5161	27	2	24	24	NUM
ejpam-5161	27	3	]	]	PUNCT
ejpam-5161	27	4	,	,	PUNCT
ejpam-5161	27	5	in	in	ADP
ejpam-5161	27	6	1999	1999	NUM
ejpam-5161	27	7	,	,	PUNCT
ejpam-5161	27	8	originated	originate	VERB
ejpam-5161	27	9	the	the	DET
ejpam-5161	27	10	soft	soft	ADJ
ejpam-5161	27	11	set	set	NOUN
ejpam-5161	27	12	theory	theory	NOUN
ejpam-5161	27	13	as	as	ADP
ejpam-5161	27	14	a	a	DET
ejpam-5161	27	15	mathematical	mathematical	ADJ
ejpam-5161	27	16	tool	tool	NOUN
ejpam-5161	27	17	for	for	ADP
ejpam-5161	27	18	dealing	deal	VERB
ejpam-5161	27	19	with	with	ADP
ejpam-5161	27	20	uncertainty	uncertainty	NOUN
ejpam-5161	27	21	which	which	PRON
ejpam-5161	27	22	is	be	AUX
ejpam-5161	27	23	free	free	ADJ
ejpam-5161	27	24	of	of	ADP
ejpam-5161	27	25	the	the	DET
ejpam-5161	27	26	challenges	challenge	NOUN
ejpam-5161	27	27	related	relate	VERB
ejpam-5161	27	28	with	with	ADP
ejpam-5161	27	29	other	other	ADJ
ejpam-5161	27	30	theories	theory	NOUN
ejpam-5161	27	31	such	such	ADJ
ejpam-5161	27	32	as	as	ADP
ejpam-5161	27	33	fuzzy	fuzzy	ADJ
ejpam-5161	27	34	set	set	NOUN
ejpam-5161	27	35	theory	theory	NOUN
ejpam-5161	27	36	[	[	X
ejpam-5161	27	37	32	32	NUM
ejpam-5161	27	38	]	]	PUNCT
ejpam-5161	27	39	,	,	PUNCT
ejpam-5161	27	40	rough	rough	ADJ
ejpam-5161	27	41	set	set	NOUN
ejpam-5161	27	42	theory	theory	NOUN
ejpam-5161	27	43	[	[	X
ejpam-5161	27	44	26	26	NUM
ejpam-5161	27	45	]	]	PUNCT
ejpam-5161	27	46	,	,	PUNCT
ejpam-5161	27	47	and	and	CCONJ
ejpam-5161	27	48	so	so	ADV
ejpam-5161	27	49	on	on	ADV
ejpam-5161	27	50	.	.	PUNCT
ejpam-5161	28	1	in	in	ADP
ejpam-5161	28	2	particular	particular	ADJ
ejpam-5161	28	3	,	,	PUNCT
ejpam-5161	28	4	the	the	DET
ejpam-5161	28	5	nature	nature	NOUN
ejpam-5161	28	6	of	of	ADP
ejpam-5161	28	7	parameter	parameter	NOUN
ejpam-5161	28	8	sets	set	NOUN
ejpam-5161	28	9	associated	associate	VERB
ejpam-5161	28	10	with	with	ADP
ejpam-5161	28	11	soft	soft	ADJ
ejpam-5161	28	12	sets	set	NOUN
ejpam-5161	28	13	provides	provide	VERB
ejpam-5161	28	14	a	a	DET
ejpam-5161	28	15	standardized	standardized	ADJ
ejpam-5161	28	16	foundation	foundation	NOUN
ejpam-5161	28	17	for	for	ADP
ejpam-5161	28	18	modeling	model	VERB
ejpam-5161	28	19	uncertain	uncertain	ADJ
ejpam-5161	28	20	data	datum	NOUN
ejpam-5161	28	21	.	.	PUNCT
ejpam-5161	29	1	this	this	PRON
ejpam-5161	29	2	leads	lead	VERB
ejpam-5161	29	3	to	to	ADP
ejpam-5161	29	4	the	the	DET
ejpam-5161	29	5	rapid	rapid	ADJ
ejpam-5161	29	6	growth	growth	NOUN
ejpam-5161	29	7	of	of	ADP
ejpam-5161	29	8	soft	soft	ADJ
ejpam-5161	29	9	set	set	NOUN
ejpam-5161	29	10	theory	theory	NOUN
ejpam-5161	29	11	and	and	CCONJ
ejpam-5161	29	12	soft	soft	ADJ
ejpam-5161	29	13	topology	topology	NOUN
ejpam-5161	29	14	in	in	ADP
ejpam-5161	29	15	a	a	DET
ejpam-5161	29	16	short	short	ADJ
ejpam-5161	29	17	amount	amount	NOUN
ejpam-5161	29	18	of	of	ADP
ejpam-5161	29	19	time	time	NOUN
ejpam-5161	29	20	and	and	CCONJ
ejpam-5161	29	21	provides	provide	VERB
ejpam-5161	29	22	various	various	ADJ
ejpam-5161	29	23	applications	application	NOUN
ejpam-5161	29	24	of	of	ADP
ejpam-5161	29	25	soft	soft	ADJ
ejpam-5161	29	26	sets	set	NOUN
ejpam-5161	29	27	in	in	ADP
ejpam-5161	29	28	real	real	ADJ
ejpam-5161	29	29	life	life	NOUN
ejpam-5161	29	30	see	see	VERB
ejpam-5161	29	31	[	[	X
ejpam-5161	29	32	16	16	NUM
ejpam-5161	29	33	,	,	PUNCT
ejpam-5161	29	34	17	17	NUM
ejpam-5161	29	35	,	,	PUNCT
ejpam-5161	29	36	27	27	NUM
ejpam-5161	29	37	,	,	PUNCT
ejpam-5161	29	38	30	30	NUM
ejpam-5161	29	39	]	]	PUNCT
ejpam-5161	29	40	)	)	PUNCT
ejpam-5161	29	41	.	.	PUNCT
ejpam-5161	30	1	there	there	PRON
ejpam-5161	30	2	are	be	VERB
ejpam-5161	30	3	various	various	ADJ
ejpam-5161	30	4	studies	study	NOUN
ejpam-5161	30	5	that	that	PRON
ejpam-5161	30	6	have	have	AUX
ejpam-5161	30	7	made	make	VERB
ejpam-5161	30	8	significant	significant	ADJ
ejpam-5161	30	9	contributions	contribution	NOUN
ejpam-5161	30	10	to	to	ADP
ejpam-5161	30	11	the	the	DET
ejpam-5161	30	12	development	development	NOUN
ejpam-5161	30	13	of	of	ADP
ejpam-5161	30	14	soft	soft	ADJ
ejpam-5161	30	15	topology	topology	NOUN
ejpam-5161	30	16	since	since	SCONJ
ejpam-5161	30	17	its	its	PRON
ejpam-5161	30	18	foundation	foundation	NOUN
ejpam-5161	30	19	in	in	ADP
ejpam-5161	30	20	[	[	X
ejpam-5161	30	21	15	15	NUM
ejpam-5161	30	22	,	,	PUNCT
ejpam-5161	30	23	28	28	NUM
ejpam-5161	30	24	]	]	PUNCT
ejpam-5161	30	25	.	.	PUNCT
ejpam-5161	31	1	a	a	DET
ejpam-5161	31	2	soft	soft	ADJ
ejpam-5161	31	3	topological	topological	ADJ
ejpam-5161	31	4	approach	approach	NOUN
ejpam-5161	31	5	was	be	AUX
ejpam-5161	31	6	then	then	ADV
ejpam-5161	31	7	used	use	VERB
ejpam-5161	31	8	to	to	PART
ejpam-5161	31	9	interpret	interpret	VERB
ejpam-5161	31	10	the	the	DET
ejpam-5161	31	11	behavior	behavior	NOUN
ejpam-5161	31	12	of	of	ADP
ejpam-5161	31	13	the	the	DET
ejpam-5161	31	14	most	most	ADV
ejpam-5161	31	15	fundamental	fundamental	ADJ
ejpam-5161	31	16	concepts	concept	NOUN
ejpam-5161	31	17	in	in	ADP
ejpam-5161	31	18	(	(	PUNCT
ejpam-5161	31	19	general	general	ADJ
ejpam-5161	31	20	)	)	PUNCT
ejpam-5161	31	21	topology	topology	NOUN
ejpam-5161	31	22	.	.	PUNCT
ejpam-5161	32	1	to	to	PART
ejpam-5161	32	2	be	be	AUX
ejpam-5161	32	3	specific	specific	ADJ
ejpam-5161	32	4	,	,	PUNCT
ejpam-5161	32	5	soft	soft	ADJ
ejpam-5161	32	6	compactness	compactness	NOUN
ejpam-5161	33	1	[	[	X
ejpam-5161	33	2	14	14	NUM
ejpam-5161	33	3	]	]	X
ejpam-5161	33	4	,	,	PUNCT
ejpam-5161	33	5	soft	soft	ADJ
ejpam-5161	33	6	connectedness	connectedness	NOUN
ejpam-5161	33	7	[	[	X
ejpam-5161	33	8	20	20	NUM
ejpam-5161	33	9	]	]	PUNCT
ejpam-5161	33	10	,	,	PUNCT
ejpam-5161	33	11	soft	soft	ADJ
ejpam-5161	33	12	submaximality	submaximality	NOUN
ejpam-5161	33	13	[	[	X
ejpam-5161	33	14	2	2	NUM
ejpam-5161	33	15	]	]	PUNCT
ejpam-5161	33	16	,	,	PUNCT
ejpam-5161	33	17	soft	soft	ADJ
ejpam-5161	33	18	extremal	extremal	ADJ
ejpam-5161	33	19	disconnectedness	disconnectedness	NOUN
ejpam-5161	34	1	[	[	X
ejpam-5161	34	2	13	13	NUM
ejpam-5161	34	3	]	]	PUNCT
ejpam-5161	34	4	,	,	PUNCT
ejpam-5161	34	5	soft	soft	ADJ
ejpam-5161	34	6	clustering	clustering	NOUN
ejpam-5161	34	7	[	[	X
ejpam-5161	34	8	9	9	NUM
ejpam-5161	34	9	]	]	PUNCT
ejpam-5161	34	10	,	,	PUNCT
ejpam-5161	34	11	soft	soft	ADJ
ejpam-5161	34	12	simple	simple	ADJ
ejpam-5161	34	13	extendedness	extendedness	NOUN
ejpam-5161	34	14	[	[	X
ejpam-5161	34	15	8	8	NUM
ejpam-5161	34	16	]	]	PUNCT
ejpam-5161	34	17	,	,	PUNCT
ejpam-5161	34	18	and	and	CCONJ
ejpam-5161	34	19	soft	soft	ADJ
ejpam-5161	34	20	nodecness	nodecness	NOUN
ejpam-5161	35	1	[	[	X
ejpam-5161	35	2	6	6	NUM
ejpam-5161	35	3	]	]	PUNCT
ejpam-5161	35	4	,	,	PUNCT
ejpam-5161	35	5	and	and	CCONJ
ejpam-5161	35	6	congruence	congruence	VERB
ejpam-5161	35	7	representations	representation	NOUN
ejpam-5161	36	1	[	[	X
ejpam-5161	36	2	11	11	NUM
ejpam-5161	36	3	]	]	PUNCT
ejpam-5161	36	4	of	of	ADP
ejpam-5161	36	5	soft	soft	ADJ
ejpam-5161	36	6	spaces	space	NOUN
ejpam-5161	36	7	.	.	PUNCT
ejpam-5161	37	1	different	different	ADJ
ejpam-5161	37	2	methods	method	NOUN
ejpam-5161	37	3	of	of	ADP
ejpam-5161	37	4	generating	generate	VERB
ejpam-5161	37	5	soft	soft	ADJ
ejpam-5161	37	6	topologies	topology	NOUN
ejpam-5161	37	7	on	on	ADP
ejpam-5161	37	8	a	a	DET
ejpam-5161	37	9	common	common	ADJ
ejpam-5161	37	10	universal	universal	ADJ
ejpam-5161	37	11	set	set	NOUN
ejpam-5161	37	12	were	be	AUX
ejpam-5161	37	13	discussed	discuss	VERB
ejpam-5161	37	14	in	in	ADP
ejpam-5161	37	15	[	[	X
ejpam-5161	37	16	3	3	NUM
ejpam-5161	37	17	,	,	PUNCT
ejpam-5161	37	18	4	4	NUM
ejpam-5161	37	19	,	,	PUNCT
ejpam-5161	37	20	19	19	NUM
ejpam-5161	37	21	,	,	PUNCT
ejpam-5161	37	22	25	25	NUM
ejpam-5161	37	23	,	,	PUNCT
ejpam-5161	37	24	29	29	NUM
ejpam-5161	37	25	,	,	PUNCT
ejpam-5161	37	26	33	33	NUM
ejpam-5161	37	27	]	]	PUNCT
ejpam-5161	37	28	.	.	PUNCT
ejpam-5161	38	1	soft	soft	ADJ
ejpam-5161	38	2	continuity	continuity	NOUN
ejpam-5161	38	3	of	of	ADP
ejpam-5161	38	4	mappings	mapping	NOUN
ejpam-5161	38	5	has	have	AUX
ejpam-5161	38	6	been	be	AUX
ejpam-5161	38	7	widely	widely	ADV
ejpam-5161	38	8	generalized	generalize	VERB
ejpam-5161	38	9	to	to	ADP
ejpam-5161	38	10	diverse	diverse	ADJ
ejpam-5161	38	11	classes	class	NOUN
ejpam-5161	38	12	,	,	PUNCT
ejpam-5161	38	13	including	include	VERB
ejpam-5161	38	14	soft	soft	ADJ
ejpam-5161	38	15	semi	semi	NOUN
ejpam-5161	38	16	-	-	NOUN
ejpam-5161	38	17	continuity	continuity	NOUN
ejpam-5161	38	18	[	[	X
ejpam-5161	38	19	21	21	NUM
ejpam-5161	38	20	]	]	X
ejpam-5161	38	21	,	,	PUNCT
ejpam-5161	38	22	soft	soft	ADJ
ejpam-5161	38	23	β	β	NOUN
ejpam-5161	38	24	-	-	NOUN
ejpam-5161	38	25	continuity	continuity	NOUN
ejpam-5161	38	26	[	[	X
ejpam-5161	38	27	31	31	NUM
ejpam-5161	38	28	]	]	PUNCT
ejpam-5161	38	29	,	,	PUNCT
ejpam-5161	38	30	soft	soft	ADJ
ejpam-5161	38	31	u	u	NOUN
ejpam-5161	38	32	-	-	NOUN
ejpam-5161	38	33	continuity	continuity	NOUN
ejpam-5161	38	34	[	[	X
ejpam-5161	38	35	7	7	NUM
ejpam-5161	38	36	]	]	PUNCT
ejpam-5161	38	37	,	,	PUNCT
ejpam-5161	38	38	soft	soft	ADJ
ejpam-5161	38	39	sd	sd	NOUN
ejpam-5161	38	40	-	-	PUNCT
ejpam-5161	38	41	continuity	continuity	NOUN
ejpam-5161	38	42	[	[	X
ejpam-5161	38	43	10	10	NUM
ejpam-5161	38	44	]	]	PUNCT
ejpam-5161	38	45	,	,	PUNCT
ejpam-5161	38	46	and	and	CCONJ
ejpam-5161	38	47	mappings	mapping	NOUN
ejpam-5161	38	48	of	of	ADP
ejpam-5161	38	49	the	the	DET
ejpam-5161	38	50	baire	baire	NOUN
ejpam-5161	38	51	property	property	NOUN
ejpam-5161	38	52	[	[	X
ejpam-5161	38	53	12	12	NUM
ejpam-5161	38	54	]	]	PUNCT
ejpam-5161	38	55	.	.	PUNCT
ejpam-5161	39	1	soft	soft	ADJ
ejpam-5161	39	2	separation	separation	NOUN
ejpam-5161	39	3	axioms	axiom	NOUN
ejpam-5161	39	4	are	be	AUX
ejpam-5161	39	5	another	another	DET
ejpam-5161	39	6	significant	significant	ADJ
ejpam-5161	39	7	aspect	aspect	NOUN
ejpam-5161	39	8	in	in	ADP
ejpam-5161	39	9	the	the	DET
ejpam-5161	39	10	late	late	ADJ
ejpam-5161	39	11	development	development	NOUN
ejpam-5161	39	12	of	of	ADP
ejpam-5161	39	13	soft	soft	ADJ
ejpam-5161	39	14	topology	topology	NOUN
ejpam-5161	39	15	;	;	PUNCT
ejpam-5161	39	16	see	see	VERB
ejpam-5161	39	17	for	for	ADP
ejpam-5161	39	18	example	example	NOUN
ejpam-5161	39	19	[	[	X
ejpam-5161	39	20	1	1	NUM
ejpam-5161	39	21	,	,	PUNCT
ejpam-5161	39	22	23	23	NUM
ejpam-5161	39	23	,	,	PUNCT
ejpam-5161	39	24	28	28	NUM
ejpam-5161	39	25	]	]	PUNCT
ejpam-5161	39	26	.	.	PUNCT
ejpam-5161	40	1	two	two	NUM
ejpam-5161	40	2	remarkable	remarkable	ADJ
ejpam-5161	40	3	formulas	formula	NOUN
ejpam-5161	40	4	for	for	ADP
ejpam-5161	40	5	generating	generate	VERB
ejpam-5161	40	6	soft	soft	ADJ
ejpam-5161	40	7	topologies	topology	NOUN
ejpam-5161	40	8	from	from	ADP
ejpam-5161	40	9	a	a	DET
ejpam-5161	40	10	system	system	NOUN
ejpam-5161	40	11	of	of	ADP
ejpam-5161	40	12	crisp	crisp	ADJ
ejpam-5161	40	13	topologies	topology	NOUN
ejpam-5161	40	14	have	have	AUX
ejpam-5161	40	15	been	be	AUX
ejpam-5161	40	16	given	give	VERB
ejpam-5161	40	17	by	by	ADP
ejpam-5161	40	18	terepeta	terepeta	NOUN
ejpam-5161	40	19	[	[	X
ejpam-5161	40	20	29	29	NUM
ejpam-5161	40	21	]	]	PUNCT
ejpam-5161	40	22	.	.	PUNCT
ejpam-5161	41	1	one	one	NUM
ejpam-5161	41	2	of	of	ADP
ejpam-5161	41	3	the	the	DET
ejpam-5161	41	4	formulas	formula	NOUN
ejpam-5161	41	5	(	(	PUNCT
ejpam-5161	41	6	formula	formula	NOUN
ejpam-5161	41	7	2	2	NUM
ejpam-5161	41	8	)	)	PUNCT
ejpam-5161	41	9	is	be	AUX
ejpam-5161	41	10	said	say	VERB
ejpam-5161	41	11	to	to	PART
ejpam-5161	41	12	generate	generate	VERB
ejpam-5161	41	13	a	a	DET
ejpam-5161	41	14	single	single	ADJ
ejpam-5161	41	15	set	set	VERB
ejpam-5161	41	16	soft	soft	ADJ
ejpam-5161	41	17	topology	topology	NOUN
ejpam-5161	41	18	,	,	PUNCT
ejpam-5161	41	19	while	while	SCONJ
ejpam-5161	41	20	the	the	DET
ejpam-5161	41	21	other	other	ADJ
ejpam-5161	41	22	one	one	NOUN
ejpam-5161	41	23	generates	generate	VERB
ejpam-5161	41	24	a	a	DET
ejpam-5161	41	25	more	more	ADV
ejpam-5161	41	26	general	general	ADJ
ejpam-5161	41	27	soft	soft	ADJ
ejpam-5161	41	28	topology	topology	NOUN
ejpam-5161	41	29	(	(	PUNCT
ejpam-5161	41	30	formula	formula	NOUN
ejpam-5161	41	31	1	1	NUM
ejpam-5161	41	32	)	)	PUNCT
ejpam-5161	41	33	.	.	PUNCT
ejpam-5161	42	1	terepeta	terepeta	NOUN
ejpam-5161	42	2	mainly	mainly	ADV
ejpam-5161	42	3	applied	apply	VERB
ejpam-5161	42	4	formula	formula	NOUN
ejpam-5161	42	5	2	2	NUM
ejpam-5161	42	6	to	to	PART
ejpam-5161	42	7	study	study	VERB
ejpam-5161	42	8	the	the	DET
ejpam-5161	42	9	inheritance	inheritance	NOUN
ejpam-5161	42	10	of	of	ADP
ejpam-5161	42	11	soft	soft	ADJ
ejpam-5161	42	12	separation	separation	NOUN
ejpam-5161	42	13	axioms	axiom	NOUN
ejpam-5161	42	14	after	after	ADP
ejpam-5161	42	15	the	the	DET
ejpam-5161	42	16	system	system	NOUN
ejpam-5161	42	17	of	of	ADP
ejpam-5161	42	18	crisp	crisp	ADJ
ejpam-5161	42	19	topologies	topology	NOUN
ejpam-5161	42	20	.	.	PUNCT
ejpam-5161	43	1	recently	recently	ADV
ejpam-5161	43	2	,	,	PUNCT
ejpam-5161	43	3	alcantud	alcantud	PROPN
ejpam-5161	43	4	[	[	X
ejpam-5161	43	5	3	3	NUM
ejpam-5161	43	6	]	]	PUNCT
ejpam-5161	43	7	proposed	propose	VERB
ejpam-5161	43	8	a	a	DET
ejpam-5161	43	9	slight	slight	ADJ
ejpam-5161	43	10	extension	extension	NOUN
ejpam-5161	43	11	of	of	ADP
ejpam-5161	43	12	formula	formula	NOUN
ejpam-5161	43	13	1	1	NUM
ejpam-5161	43	14	(	(	PUNCT
ejpam-5161	43	15	we	we	PRON
ejpam-5161	43	16	also	also	ADV
ejpam-5161	43	17	call	call	VERB
ejpam-5161	43	18	it	it	PRON
ejpam-5161	43	19	formula	formula	NOUN
ejpam-5161	43	20	1	1	NUM
ejpam-5161	43	21	)	)	PUNCT
ejpam-5161	43	22	.	.	PUNCT
ejpam-5161	44	1	he	he	PRON
ejpam-5161	44	2	then	then	ADV
ejpam-5161	44	3	employed	employ	VERB
ejpam-5161	44	4	such	such	DET
ejpam-5161	44	5	a	a	DET
ejpam-5161	44	6	formula	formula	NOUN
ejpam-5161	44	7	to	to	PART
ejpam-5161	44	8	investigate	investigate	VERB
ejpam-5161	44	9	the	the	DET
ejpam-5161	44	10	behavior	behavior	NOUN
ejpam-5161	44	11	of	of	ADP
ejpam-5161	44	12	separability	separability	NOUN
ejpam-5161	44	13	and	and	CCONJ
ejpam-5161	44	14	second	second	ADJ
ejpam-5161	44	15	countability	countability	NOUN
ejpam-5161	44	16	axioms	axiom	NOUN
ejpam-5161	44	17	between	between	ADP
ejpam-5161	44	18	a	a	DET
ejpam-5161	44	19	system	system	NOUN
ejpam-5161	44	20	of	of	ADP
ejpam-5161	44	21	crisp	crisp	ADJ
ejpam-5161	44	22	topologies	topology	NOUN
ejpam-5161	44	23	and	and	CCONJ
ejpam-5161	44	24	the	the	DET
ejpam-5161	44	25	soft	soft	ADJ
ejpam-5161	44	26	topology	topology	NOUN
ejpam-5161	44	27	generated	generate	VERB
ejpam-5161	44	28	by	by	ADP
ejpam-5161	44	29	it	it	PRON
ejpam-5161	44	30	.	.	PUNCT
ejpam-5161	45	1	recently	recently	ADV
ejpam-5161	45	2	,	,	PUNCT
ejpam-5161	45	3	alcantud	alcantud	X
ejpam-5161	45	4	[	[	X
ejpam-5161	45	5	4	4	NUM
ejpam-5161	45	6	]	]	PUNCT
ejpam-5161	45	7	established	establish	VERB
ejpam-5161	45	8	crucial	crucial	ADJ
ejpam-5161	45	9	relationships	relationship	NOUN
ejpam-5161	45	10	between	between	ADP
ejpam-5161	45	11	soft	soft	ADJ
ejpam-5161	45	12	and	and	CCONJ
ejpam-5161	45	13	fuzzy	fuzzy	ADJ
ejpam-5161	45	14	soft	soft	ADJ
ejpam-5161	45	15	topologies	topology	NOUN
ejpam-5161	45	16	.	.	PUNCT
ejpam-5161	46	1	the	the	DET
ejpam-5161	46	2	work	work	NOUN
ejpam-5161	46	3	of	of	ADP
ejpam-5161	46	4	terepeta	terepeta	NOUN
ejpam-5161	46	5	and	and	CCONJ
ejpam-5161	46	6	alcantud	alcantud	PROPN
ejpam-5161	46	7	inspired	inspire	VERB
ejpam-5161	46	8	us	we	PRON
ejpam-5161	46	9	to	to	PART
ejpam-5161	46	10	attempt	attempt	VERB
ejpam-5161	46	11	this	this	DET
ejpam-5161	46	12	research	research	NOUN
ejpam-5161	46	13	.	.	PUNCT
ejpam-5161	47	1	following	follow	VERB
ejpam-5161	47	2	their	their	PRON
ejpam-5161	47	3	direction	direction	NOUN
ejpam-5161	47	4	,	,	PUNCT
ejpam-5161	47	5	we	we	PRON
ejpam-5161	47	6	first	first	ADV
ejpam-5161	47	7	apply	apply	VERB
ejpam-5161	47	8	the	the	DET
ejpam-5161	47	9	formulas	formula	NOUN
ejpam-5161	47	10	to	to	ADP
ejpam-5161	47	11	the	the	DET
ejpam-5161	47	12	system	system	NOUN
ejpam-5161	47	13	of	of	ADP
ejpam-5161	47	14	crisp	crisp	ADJ
ejpam-5161	47	15	topologies	topology	NOUN
ejpam-5161	47	16	taken	take	VERB
ejpam-5161	47	17	from	from	ADP
ejpam-5161	47	18	a	a	DET
ejpam-5161	47	19	soft	soft	ADJ
ejpam-5161	47	20	topology	topology	NOUN
ejpam-5161	47	21	in	in	ADP
ejpam-5161	47	22	order	order	NOUN
ejpam-5161	47	23	to	to	PART
ejpam-5161	47	24	determine	determine	VERB
ejpam-5161	47	25	the	the	DET
ejpam-5161	47	26	connections	connection	NOUN
ejpam-5161	47	27	between	between	ADP
ejpam-5161	47	28	the	the	DET
ejpam-5161	47	29	obtained	obtain	VERB
ejpam-5161	47	30	soft	soft	ADJ
ejpam-5161	47	31	topologies	topology	NOUN
ejpam-5161	47	32	and	and	CCONJ
ejpam-5161	47	33	the	the	DET
ejpam-5161	47	34	original	original	ADJ
ejpam-5161	47	35	one	one	NOUN
ejpam-5161	47	36	.	.	PUNCT
ejpam-5161	48	1	in	in	ADP
ejpam-5161	48	2	addition	addition	NOUN
ejpam-5161	48	3	,	,	PUNCT
ejpam-5161	48	4	we	we	PRON
ejpam-5161	48	5	use	use	VERB
ejpam-5161	48	6	formula	formula	NOUN
ejpam-5161	48	7	1	1	NUM
ejpam-5161	48	8	to	to	PART
ejpam-5161	48	9	verify	verify	VERB
ejpam-5161	48	10	how	how	SCONJ
ejpam-5161	48	11	well	well	ADV
ejpam-5161	48	12	the	the	DET
ejpam-5161	48	13	separation	separation	NOUN
ejpam-5161	48	14	axioms	axiom	NOUN
ejpam-5161	48	15	are	be	AUX
ejpam-5161	48	16	transferred	transfer	VERB
ejpam-5161	48	17	between	between	ADP
ejpam-5161	48	18	a	a	DET
ejpam-5161	48	19	system	system	NOUN
ejpam-5161	48	20	of	of	ADP
ejpam-5161	48	21	crisp	crisp	ADJ
ejpam-5161	48	22	topologies	topology	NOUN
ejpam-5161	48	23	and	and	CCONJ
ejpam-5161	48	24	the	the	DET
ejpam-5161	48	25	soft	soft	ADJ
ejpam-5161	48	26	topology	topology	NOUN
ejpam-5161	48	27	generated	generate	VERB
ejpam-5161	48	28	by	by	ADP
ejpam-5161	48	29	it	it	PRON
ejpam-5161	48	30	.	.	PUNCT
ejpam-5161	49	1	the	the	DET
ejpam-5161	49	2	latter	latter	ADJ
ejpam-5161	49	3	statement	statement	NOUN
ejpam-5161	49	4	extends	extend	VERB
ejpam-5161	49	5	the	the	DET
ejpam-5161	49	6	work	work	NOUN
ejpam-5161	49	7	of	of	ADP
ejpam-5161	49	8	terepeta	terepeta	NOUN
ejpam-5161	49	9	(	(	PUNCT
ejpam-5161	49	10	see	see	VERB
ejpam-5161	49	11	,	,	PUNCT
ejpam-5161	49	12	section	section	NOUN
ejpam-5161	49	13	2.1	2.1	NUM
ejpam-5161	49	14	in	in	ADP
ejpam-5161	49	15	[	[	X
ejpam-5161	49	16	29	29	NUM
ejpam-5161	49	17	]	]	NUM
ejpam-5161	49	18	)	)	PUNCT
ejpam-5161	49	19	,	,	PUNCT
ejpam-5161	49	20	which	which	PRON
ejpam-5161	49	21	is	be	AUX
ejpam-5161	49	22	the	the	DET
ejpam-5161	49	23	main	main	ADJ
ejpam-5161	49	24	objective	objective	NOUN
ejpam-5161	49	25	of	of	ADP
ejpam-5161	49	26	this	this	DET
ejpam-5161	49	27	research	research	NOUN
ejpam-5161	49	28	.	.	PUNCT
ejpam-5161	50	1	z.	z.	PROPN
ejpam-5161	50	2	a.	a.	PROPN
ejpam-5161	50	3	ameen	ameen	PROPN
ejpam-5161	50	4	et	et	PROPN
ejpam-5161	50	5	al	al	PROPN
ejpam-5161	50	6	.	.	PUNCT
ejpam-5161	50	7	/	/	SYM
ejpam-5161	50	8	eur	eur	PROPN
ejpam-5161	50	9	.	.	PUNCT
ejpam-5161	51	1	j.	j.	PROPN
ejpam-5161	51	2	pure	pure	PROPN
ejpam-5161	51	3	appl	appl	PROPN
ejpam-5161	51	4	.	.	PROPN
ejpam-5161	51	5	math	math	PROPN
ejpam-5161	51	6	,	,	PUNCT
ejpam-5161	51	7	17	17	NUM
ejpam-5161	51	8	(	(	PUNCT
ejpam-5161	51	9	2	2	NUM
ejpam-5161	51	10	)	)	PUNCT
ejpam-5161	51	11	(	(	PUNCT
ejpam-5161	51	12	2024	2024	NUM
ejpam-5161	51	13	)	)	PUNCT
ejpam-5161	51	14	,	,	PUNCT
ejpam-5161	51	15	1168	1168	NUM
ejpam-5161	51	16	-	-	SYM
ejpam-5161	51	17	1182	1182	NUM
ejpam-5161	51	18	1170	1170	NUM
ejpam-5161	51	19	2	2	NUM
ejpam-5161	51	20	.	.	PUNCT
ejpam-5161	52	1	preliminaries	preliminary	NOUN
ejpam-5161	52	2	let	let	VERB
ejpam-5161	52	3	x	x	PRON
ejpam-5161	52	4	be	be	AUX
ejpam-5161	52	5	an	an	DET
ejpam-5161	52	6	initial	initial	ADJ
ejpam-5161	52	7	universe	universe	NOUN
ejpam-5161	52	8	,	,	PUNCT
ejpam-5161	52	9	p(x	p(x	PROPN
ejpam-5161	52	10	)	)	PUNCT
ejpam-5161	52	11	be	be	VERB
ejpam-5161	52	12	all	all	DET
ejpam-5161	52	13	subsets	subset	NOUN
ejpam-5161	52	14	of	of	ADP
ejpam-5161	52	15	x	x	PUNCT
ejpam-5161	52	16	and	and	CCONJ
ejpam-5161	52	17	ω	ω	NUM
ejpam-5161	52	18	be	be	AUX
ejpam-5161	52	19	a	a	DET
ejpam-5161	52	20	set	set	NOUN
ejpam-5161	52	21	of	of	ADP
ejpam-5161	52	22	parameters	parameter	NOUN
ejpam-5161	52	23	.	.	PUNCT
ejpam-5161	53	1	an	an	DET
ejpam-5161	53	2	ordered	order	VERB
ejpam-5161	53	3	pair	pair	NOUN
ejpam-5161	53	4	(	(	PUNCT
ejpam-5161	53	5	f	f	X
ejpam-5161	53	6	,	,	PUNCT
ejpam-5161	53	7	ω	ω	NOUN
ejpam-5161	53	8	)	)	PUNCT
ejpam-5161	53	9	=	=	PRON
ejpam-5161	53	10	{	{	PUNCT
ejpam-5161	53	11	(	(	PUNCT
ejpam-5161	53	12	ω	ω	PROPN
ejpam-5161	53	13	,	,	PUNCT
ejpam-5161	53	14	f	f	PROPN
ejpam-5161	53	15	(	(	PUNCT
ejpam-5161	53	16	ω	ω	NOUN
ejpam-5161	53	17	)	)	PUNCT
ejpam-5161	53	18	)	)	PUNCT
ejpam-5161	53	19	:	:	PUNCT
ejpam-5161	54	1	ω	ω	X
ejpam-5161	54	2	∈	∈	PROPN
ejpam-5161	54	3	ω	ω	PROPN
ejpam-5161	54	4	}	}	PUNCT
ejpam-5161	54	5	is	be	AUX
ejpam-5161	54	6	said	say	VERB
ejpam-5161	54	7	to	to	PART
ejpam-5161	54	8	be	be	AUX
ejpam-5161	54	9	a	a	DET
ejpam-5161	54	10	soft	soft	ADJ
ejpam-5161	54	11	set	set	NOUN
ejpam-5161	54	12	over	over	ADP
ejpam-5161	54	13	x	x	NOUN
ejpam-5161	54	14	,	,	PUNCT
ejpam-5161	54	15	where	where	SCONJ
ejpam-5161	54	16	f	f	X
ejpam-5161	54	17	:	:	PUNCT
ejpam-5161	54	18	ω	ω	PROPN
ejpam-5161	54	19	→	→	SYM
ejpam-5161	54	20	p(x	p(x	PROPN
ejpam-5161	54	21	)	)	PUNCT
ejpam-5161	54	22	is	be	AUX
ejpam-5161	54	23	a	a	DET
ejpam-5161	54	24	set	set	ADJ
ejpam-5161	54	25	value	value	NOUN
ejpam-5161	54	26	mapping	mapping	NOUN
ejpam-5161	54	27	.	.	PUNCT
ejpam-5161	55	1	the	the	DET
ejpam-5161	55	2	family	family	NOUN
ejpam-5161	55	3	of	of	ADP
ejpam-5161	55	4	all	all	DET
ejpam-5161	55	5	soft	soft	ADJ
ejpam-5161	55	6	sets	set	NOUN
ejpam-5161	55	7	on	on	ADP
ejpam-5161	55	8	x	x	VERB
ejpam-5161	55	9	is	be	AUX
ejpam-5161	55	10	represented	represent	VERB
ejpam-5161	55	11	by	by	ADP
ejpam-5161	55	12	sω(x	sω(x	NOUN
ejpam-5161	55	13	)	)	PUNCT
ejpam-5161	55	14	.	.	PUNCT
ejpam-5161	56	1	the	the	DET
ejpam-5161	56	2	soft	soft	ADJ
ejpam-5161	56	3	set	set	NOUN
ejpam-5161	56	4	(	(	PUNCT
ejpam-5161	56	5	x	x	NOUN
ejpam-5161	56	6	,	,	PUNCT
ejpam-5161	56	7	ω)\(f	ω)\(f	PROPN
ejpam-5161	56	8	,	,	PUNCT
ejpam-5161	56	9	ω	ω	NUM
ejpam-5161	56	10	)	)	PUNCT
ejpam-5161	56	11	(	(	PUNCT
ejpam-5161	56	12	or	or	CCONJ
ejpam-5161	56	13	simply	simply	ADV
ejpam-5161	56	14	(	(	PUNCT
ejpam-5161	56	15	f	f	X
ejpam-5161	56	16	,	,	PUNCT
ejpam-5161	56	17	ω)c	ω)c	NOUN
ejpam-5161	56	18	=	=	SYM
ejpam-5161	56	19	(	(	PUNCT
ejpam-5161	56	20	f	f	PROPN
ejpam-5161	56	21	c	c	PROPN
ejpam-5161	56	22	,	,	PUNCT
ejpam-5161	56	23	ω	ω	NOUN
ejpam-5161	56	24	)	)	PUNCT
ejpam-5161	56	25	)	)	PUNCT
ejpam-5161	56	26	is	be	AUX
ejpam-5161	56	27	the	the	DET
ejpam-5161	56	28	complement	complement	NOUN
ejpam-5161	56	29	of	of	ADP
ejpam-5161	56	30	(	(	PUNCT
ejpam-5161	56	31	f	f	PROPN
ejpam-5161	56	32	,	,	PUNCT
ejpam-5161	56	33	ω	ω	PROPN
ejpam-5161	56	34	)	)	PUNCT
ejpam-5161	56	35	,	,	PUNCT
ejpam-5161	56	36	where	where	SCONJ
ejpam-5161	56	37	f	f	PROPN
ejpam-5161	56	38	c	c	X
ejpam-5161	56	39	:	:	PUNCT
ejpam-5161	56	40	ω	ω	PROPN
ejpam-5161	56	41	→	→	SYM
ejpam-5161	56	42	p(x	p(x	PROPN
ejpam-5161	56	43	)	)	PUNCT
ejpam-5161	56	44	is	be	AUX
ejpam-5161	56	45	given	give	VERB
ejpam-5161	56	46	by	by	ADP
ejpam-5161	56	47	f	f	PROPN
ejpam-5161	56	48	c(ω	c(ω	PROPN
ejpam-5161	56	49	)	)	PUNCT
ejpam-5161	57	1	=	=	SYM
ejpam-5161	58	1	x\f	x\f	PROPN
ejpam-5161	58	2	(	(	PUNCT
ejpam-5161	58	3	ω	ω	NOUN
ejpam-5161	58	4	)	)	PUNCT
ejpam-5161	58	5	for	for	ADP
ejpam-5161	58	6	each	each	DET
ejpam-5161	58	7	ω	ω	PROPN
ejpam-5161	58	8	∈	∈	PROPN
ejpam-5161	58	9	ω	ω	PROPN
ejpam-5161	58	10	.	.	PUNCT
ejpam-5161	59	1	a	a	DET
ejpam-5161	59	2	soft	soft	ADJ
ejpam-5161	59	3	subset	subset	NOUN
ejpam-5161	59	4	(	(	PUNCT
ejpam-5161	59	5	f	f	X
ejpam-5161	59	6	,	,	PUNCT
ejpam-5161	59	7	ω	ω	NOUN
ejpam-5161	59	8	)	)	PUNCT
ejpam-5161	59	9	over	over	ADV
ejpam-5161	59	10	x	x	VERB
ejpam-5161	59	11	is	be	AUX
ejpam-5161	59	12	called	call	VERB
ejpam-5161	59	13	null	null	ADJ
ejpam-5161	59	14	,	,	PUNCT
ejpam-5161	59	15	denoted	denote	VERB
ejpam-5161	59	16	by	by	ADP
ejpam-5161	59	17	φ̃	φ̃	PROPN
ejpam-5161	59	18	,	,	PUNCT
ejpam-5161	59	19	if	if	SCONJ
ejpam-5161	59	20	f	f	PROPN
ejpam-5161	59	21	(	(	PUNCT
ejpam-5161	59	22	ω	ω	NOUN
ejpam-5161	59	23	)	)	PUNCT
ejpam-5161	59	24	=	=	NOUN
ejpam-5161	59	25	∅	∅	NOUN
ejpam-5161	59	26	for	for	ADP
ejpam-5161	59	27	each	each	DET
ejpam-5161	59	28	ω	ω	PROPN
ejpam-5161	59	29	∈	∈	PROPN
ejpam-5161	59	30	ω	ω	NOUN
ejpam-5161	59	31	and	and	CCONJ
ejpam-5161	59	32	is	be	AUX
ejpam-5161	59	33	called	call	VERB
ejpam-5161	59	34	absolute	absolute	ADJ
ejpam-5161	59	35	,	,	PUNCT
ejpam-5161	59	36	denoted	denote	VERB
ejpam-5161	59	37	by	by	ADP
ejpam-5161	59	38	x̃	x̃	PROPN
ejpam-5161	59	39	,	,	PUNCT
ejpam-5161	59	40	if	if	SCONJ
ejpam-5161	59	41	f	f	PROPN
ejpam-5161	59	42	(	(	PUNCT
ejpam-5161	59	43	ω	ω	NOUN
ejpam-5161	59	44	)	)	PUNCT
ejpam-5161	59	45	=	=	SYM
ejpam-5161	60	1	x	x	PUNCT
ejpam-5161	60	2	for	for	ADP
ejpam-5161	60	3	each	each	DET
ejpam-5161	60	4	ω	ω	PROPN
ejpam-5161	60	5	∈	∈	PROPN
ejpam-5161	60	6	ω	ω	PROPN
ejpam-5161	60	7	.	.	PUNCT
ejpam-5161	60	8	notice	notice	VERB
ejpam-5161	60	9	that	that	SCONJ
ejpam-5161	60	10	x̃c	x̃c	PROPN
ejpam-5161	60	11	=	=	PUNCT
ejpam-5161	61	1	φ̃	φ̃	PROPN
ejpam-5161	61	2	and	and	CCONJ
ejpam-5161	61	3	φ̃c	φ̃c	X
ejpam-5161	62	1	=	=	PUNCT
ejpam-5161	62	2	x̃.	x̃.	ADV
ejpam-5161	62	3	it	it	PRON
ejpam-5161	62	4	is	be	AUX
ejpam-5161	62	5	said	say	VERB
ejpam-5161	62	6	that	that	SCONJ
ejpam-5161	62	7	(	(	PUNCT
ejpam-5161	62	8	a	a	DET
ejpam-5161	62	9	,	,	PUNCT
ejpam-5161	62	10	ω	ω	NOUN
ejpam-5161	62	11	)	)	PUNCT
ejpam-5161	62	12	is	be	AUX
ejpam-5161	62	13	a	a	DET
ejpam-5161	62	14	soft	soft	ADJ
ejpam-5161	62	15	subset	subset	NOUN
ejpam-5161	62	16	of	of	ADP
ejpam-5161	62	17	(	(	PUNCT
ejpam-5161	62	18	b	b	PROPN
ejpam-5161	62	19	,	,	PUNCT
ejpam-5161	62	20	ω	ω	NOUN
ejpam-5161	62	21	)	)	PUNCT
ejpam-5161	62	22	(	(	PUNCT
ejpam-5161	62	23	written	write	VERB
ejpam-5161	62	24	by	by	ADP
ejpam-5161	62	25	(	(	PUNCT
ejpam-5161	62	26	a	a	DET
ejpam-5161	62	27	,	,	PUNCT
ejpam-5161	62	28	ω)⊆̃(b	ω)⊆̃(b	PROPN
ejpam-5161	62	29	,	,	PUNCT
ejpam-5161	62	30	ω	ω	NOUN
ejpam-5161	62	31	)	)	PUNCT
ejpam-5161	62	32	,	,	PUNCT
ejpam-5161	63	1	[	[	X
ejpam-5161	63	2	22	22	NUM
ejpam-5161	63	3	]	]	SYM
ejpam-5161	63	4	)	)	PUNCT
ejpam-5161	63	5	if	if	SCONJ
ejpam-5161	63	6	a(ω	a(ω	PROPN
ejpam-5161	63	7	)	)	PUNCT
ejpam-5161	63	8	⊆	⊆	NUM
ejpam-5161	63	9	b(ω	b(ω	ADV
ejpam-5161	63	10	)	)	PUNCT
ejpam-5161	63	11	for	for	ADP
ejpam-5161	63	12	each	each	DET
ejpam-5161	63	13	ω	ω	PROPN
ejpam-5161	63	14	∈	∈	PROPN
ejpam-5161	63	15	ω	ω	PROPN
ejpam-5161	63	16	,	,	PUNCT
ejpam-5161	63	17	and	and	CCONJ
ejpam-5161	63	18	(	(	PUNCT
ejpam-5161	63	19	a	a	DET
ejpam-5161	63	20	,	,	PUNCT
ejpam-5161	63	21	ω	ω	NOUN
ejpam-5161	63	22	)	)	PUNCT
ejpam-5161	63	23	=	=	SYM
ejpam-5161	63	24	(	(	PUNCT
ejpam-5161	63	25	b	b	PROPN
ejpam-5161	63	26	,	,	PUNCT
ejpam-5161	63	27	ω	ω	NOUN
ejpam-5161	63	28	)	)	PUNCT
ejpam-5161	63	29	if	if	SCONJ
ejpam-5161	63	30	(	(	PUNCT
ejpam-5161	63	31	a	a	DET
ejpam-5161	63	32	,	,	PUNCT
ejpam-5161	63	33	ω)⊆̃(b	ω)⊆̃(b	PROPN
ejpam-5161	63	34	,	,	PUNCT
ejpam-5161	63	35	ω	ω	NOUN
ejpam-5161	63	36	)	)	PUNCT
ejpam-5161	63	37	and	and	CCONJ
ejpam-5161	63	38	(	(	PUNCT
ejpam-5161	63	39	b	b	X
ejpam-5161	63	40	,	,	PUNCT
ejpam-5161	63	41	ω)⊆̃(a	ω)⊆̃(a	PROPN
ejpam-5161	63	42	,	,	PUNCT
ejpam-5161	63	43	ω	ω	NOUN
ejpam-5161	63	44	)	)	PUNCT
ejpam-5161	63	45	.	.	PUNCT
ejpam-5161	64	1	the	the	DET
ejpam-5161	64	2	union	union	NOUN
ejpam-5161	64	3	of	of	ADP
ejpam-5161	64	4	soft	soft	ADJ
ejpam-5161	64	5	sets	set	NOUN
ejpam-5161	64	6	(	(	PUNCT
ejpam-5161	64	7	a	a	DET
ejpam-5161	64	8	,	,	PUNCT
ejpam-5161	64	9	ω	ω	NOUN
ejpam-5161	64	10	)	)	PUNCT
ejpam-5161	64	11	,	,	PUNCT
ejpam-5161	64	12	(	(	PUNCT
ejpam-5161	64	13	b	b	X
ejpam-5161	64	14	,	,	PUNCT
ejpam-5161	64	15	ω	ω	NUM
ejpam-5161	64	16	)	)	PUNCT
ejpam-5161	64	17	is	be	AUX
ejpam-5161	64	18	represented	represent	VERB
ejpam-5161	64	19	by	by	ADP
ejpam-5161	64	20	(	(	PUNCT
ejpam-5161	64	21	f	f	X
ejpam-5161	64	22	,	,	PUNCT
ejpam-5161	64	23	ω	ω	NOUN
ejpam-5161	64	24	)	)	PUNCT
ejpam-5161	64	25	=	=	SYM
ejpam-5161	64	26	(	(	PUNCT
ejpam-5161	64	27	a	a	DET
ejpam-5161	64	28	,	,	PUNCT
ejpam-5161	64	29	ω)∪̃(b	ω)∪̃(b	NOUN
ejpam-5161	64	30	,	,	PUNCT
ejpam-5161	64	31	ω	ω	NOUN
ejpam-5161	64	32	)	)	PUNCT
ejpam-5161	64	33	,	,	PUNCT
ejpam-5161	64	34	where	where	SCONJ
ejpam-5161	64	35	f	f	PROPN
ejpam-5161	64	36	(	(	PUNCT
ejpam-5161	64	37	ω	ω	NOUN
ejpam-5161	64	38	)	)	PUNCT
ejpam-5161	64	39	=	=	PUNCT
ejpam-5161	64	40	a(ω)∪b(ω	a(ω)∪b(ω	NOUN
ejpam-5161	64	41	)	)	PUNCT
ejpam-5161	64	42	for	for	ADP
ejpam-5161	64	43	each	each	DET
ejpam-5161	64	44	ω	ω	PROPN
ejpam-5161	64	45	∈	∈	PROPN
ejpam-5161	64	46	ω	ω	PROPN
ejpam-5161	64	47	,	,	PUNCT
ejpam-5161	64	48	and	and	CCONJ
ejpam-5161	64	49	intersection	intersection	NOUN
ejpam-5161	64	50	of	of	ADP
ejpam-5161	64	51	soft	soft	ADJ
ejpam-5161	64	52	sets	set	NOUN
ejpam-5161	64	53	(	(	PUNCT
ejpam-5161	64	54	a	a	DET
ejpam-5161	64	55	,	,	PUNCT
ejpam-5161	64	56	ω	ω	NOUN
ejpam-5161	64	57	)	)	PUNCT
ejpam-5161	64	58	,	,	PUNCT
ejpam-5161	64	59	(	(	PUNCT
ejpam-5161	64	60	b	b	X
ejpam-5161	64	61	,	,	PUNCT
ejpam-5161	64	62	ω	ω	NOUN
ejpam-5161	64	63	)	)	PUNCT
ejpam-5161	64	64	is	be	AUX
ejpam-5161	64	65	given	give	VERB
ejpam-5161	64	66	by	by	ADP
ejpam-5161	64	67	(	(	PUNCT
ejpam-5161	64	68	f	f	PROPN
ejpam-5161	64	69	,	,	PUNCT
ejpam-5161	64	70	ω	ω	NOUN
ejpam-5161	64	71	)	)	PUNCT
ejpam-5161	65	1	=	=	SYM
ejpam-5161	65	2	(	(	PUNCT
ejpam-5161	65	3	a	a	PRON
ejpam-5161	65	4	,	,	PUNCT
ejpam-5161	65	5	ω)∩̃(b	ω)∩̃(b	PROPN
ejpam-5161	65	6	,	,	PUNCT
ejpam-5161	65	7	ω	ω	NOUN
ejpam-5161	65	8	)	)	PUNCT
ejpam-5161	65	9	,	,	PUNCT
ejpam-5161	65	10	where	where	SCONJ
ejpam-5161	65	11	f	f	PROPN
ejpam-5161	65	12	(	(	PUNCT
ejpam-5161	65	13	ω	ω	NOUN
ejpam-5161	65	14	)	)	PUNCT
ejpam-5161	65	15	=	=	SYM
ejpam-5161	65	16	a(ω	a(ω	PROPN
ejpam-5161	65	17	)	)	PUNCT
ejpam-5161	65	18	∩	∩	NOUN
ejpam-5161	65	19	b(ω	b(ω	ADV
ejpam-5161	65	20	)	)	PUNCT
ejpam-5161	65	21	for	for	ADP
ejpam-5161	65	22	each	each	DET
ejpam-5161	65	23	ω	ω	PROPN
ejpam-5161	65	24	∈	∈	PROPN
ejpam-5161	65	25	ω	ω	PROPN
ejpam-5161	65	26	,	,	PUNCT
ejpam-5161	65	27	see	see	VERB
ejpam-5161	65	28	[	[	X
ejpam-5161	65	29	5	5	NUM
ejpam-5161	65	30	]	]	PUNCT
ejpam-5161	65	31	.	.	PUNCT
ejpam-5161	66	1	a	a	DET
ejpam-5161	66	2	soft	soft	ADJ
ejpam-5161	66	3	point	point	NOUN
ejpam-5161	66	4	[	[	X
ejpam-5161	66	5	28	28	NUM
ejpam-5161	66	6	]	]	X
ejpam-5161	66	7	is	be	AUX
ejpam-5161	66	8	a	a	DET
ejpam-5161	66	9	soft	soft	ADJ
ejpam-5161	66	10	set	set	NOUN
ejpam-5161	66	11	(	(	PUNCT
ejpam-5161	66	12	f	f	X
ejpam-5161	66	13	,	,	PUNCT
ejpam-5161	66	14	ω	ω	NOUN
ejpam-5161	66	15	)	)	PUNCT
ejpam-5161	66	16	over	over	ADP
ejpam-5161	66	17	x	x	PUNCT
ejpam-5161	66	18	in	in	ADP
ejpam-5161	66	19	which	which	PRON
ejpam-5161	66	20	f	f	PROPN
ejpam-5161	66	21	(	(	PUNCT
ejpam-5161	66	22	ω	ω	NOUN
ejpam-5161	66	23	)	)	PUNCT
ejpam-5161	66	24	=	=	PRON
ejpam-5161	66	25	{	{	PUNCT
ejpam-5161	66	26	x	x	NOUN
ejpam-5161	66	27	}	}	PUNCT
ejpam-5161	66	28	for	for	ADP
ejpam-5161	66	29	each	each	DET
ejpam-5161	66	30	ω	ω	PROPN
ejpam-5161	66	31	∈	∈	PROPN
ejpam-5161	66	32	ω	ω	PROPN
ejpam-5161	66	33	,	,	PUNCT
ejpam-5161	66	34	where	where	SCONJ
ejpam-5161	66	35	x	x	PUNCT
ejpam-5161	66	36	∈	∈	NOUN
ejpam-5161	66	37	x	x	NOUN
ejpam-5161	66	38	,	,	PUNCT
ejpam-5161	66	39	and	and	CCONJ
ejpam-5161	66	40	is	be	AUX
ejpam-5161	66	41	denoted	denote	VERB
ejpam-5161	66	42	by	by	ADP
ejpam-5161	66	43	(	(	PUNCT
ejpam-5161	66	44	{	{	PUNCT
ejpam-5161	66	45	x},ω	x},ω	PROPN
ejpam-5161	66	46	)	)	PUNCT
ejpam-5161	66	47	.	.	PUNCT
ejpam-5161	67	1	it	it	PRON
ejpam-5161	67	2	is	be	AUX
ejpam-5161	67	3	said	say	VERB
ejpam-5161	67	4	that	that	SCONJ
ejpam-5161	67	5	a	a	DET
ejpam-5161	67	6	soft	soft	ADJ
ejpam-5161	67	7	point	point	NOUN
ejpam-5161	67	8	(	(	PUNCT
ejpam-5161	67	9	{	{	PUNCT
ejpam-5161	67	10	x},ω	x},ω	X
ejpam-5161	67	11	)	)	PUNCT
ejpam-5161	67	12	is	be	AUX
ejpam-5161	67	13	in	in	ADP
ejpam-5161	67	14	(	(	PUNCT
ejpam-5161	67	15	f	f	X
ejpam-5161	67	16	,	,	PUNCT
ejpam-5161	67	17	ω	ω	NUM
ejpam-5161	67	18	)	)	PUNCT
ejpam-5161	67	19	(	(	PUNCT
ejpam-5161	68	1	briefly	briefly	ADV
ejpam-5161	68	2	,	,	PUNCT
ejpam-5161	68	3	x	x	SYM
ejpam-5161	68	4	∈	∈	PROPN
ejpam-5161	68	5	(	(	PUNCT
ejpam-5161	68	6	f	f	PROPN
ejpam-5161	68	7	,	,	PUNCT
ejpam-5161	68	8	ω	ω	NOUN
ejpam-5161	68	9	)	)	PUNCT
ejpam-5161	68	10	)	)	PUNCT
ejpam-5161	69	1	if	if	SCONJ
ejpam-5161	69	2	x	x	SYM
ejpam-5161	69	3	∈	∈	PROPN
ejpam-5161	69	4	f	f	X
ejpam-5161	69	5	(	(	PUNCT
ejpam-5161	69	6	ω	ω	NOUN
ejpam-5161	69	7	)	)	PUNCT
ejpam-5161	69	8	for	for	ADP
ejpam-5161	69	9	each	each	DET
ejpam-5161	69	10	ω	ω	PROPN
ejpam-5161	69	11	∈	∈	PROPN
ejpam-5161	69	12	ω	ω	PROPN
ejpam-5161	69	13	.	.	PUNCT
ejpam-5161	70	1	on	on	ADP
ejpam-5161	70	2	the	the	DET
ejpam-5161	70	3	other	other	ADJ
ejpam-5161	70	4	hand	hand	NOUN
ejpam-5161	70	5	,	,	PUNCT
ejpam-5161	70	6	x	x	X
ejpam-5161	70	7	/∈	/∈	PUNCT
ejpam-5161	71	1	(	(	PUNCT
ejpam-5161	71	2	f	f	X
ejpam-5161	71	3	,	,	PUNCT
ejpam-5161	71	4	ω	ω	NOUN
ejpam-5161	71	5	)	)	PUNCT
ejpam-5161	71	6	if	if	SCONJ
ejpam-5161	71	7	x	x	PROPN
ejpam-5161	71	8	/∈	/∈	PROPN
ejpam-5161	71	9	f	f	PROPN
ejpam-5161	71	10	(	(	PUNCT
ejpam-5161	71	11	ω	ω	NOUN
ejpam-5161	71	12	)	)	PUNCT
ejpam-5161	71	13	for	for	ADP
ejpam-5161	71	14	some	some	DET
ejpam-5161	71	15	ω	ω	NUM
ejpam-5161	71	16	∈	∈	PROPN
ejpam-5161	71	17	ω	ω	PROPN
ejpam-5161	71	18	.	.	PUNCT
ejpam-5161	72	1	this	this	PRON
ejpam-5161	72	2	implies	imply	VERB
ejpam-5161	72	3	that	that	SCONJ
ejpam-5161	72	4	if	if	SCONJ
ejpam-5161	72	5	(	(	PUNCT
ejpam-5161	72	6	{	{	PUNCT
ejpam-5161	72	7	x},ω	x},ω	X
ejpam-5161	72	8	)	)	PUNCT
ejpam-5161	72	9	⋂̃	⋂̃	NOUN
ejpam-5161	72	10	(	(	PUNCT
ejpam-5161	72	11	f	f	PROPN
ejpam-5161	72	12	,	,	PUNCT
ejpam-5161	72	13	ω	ω	NOUN
ejpam-5161	72	14	)	)	PUNCT
ejpam-5161	72	15	=	=	PUNCT
ejpam-5161	73	1	φ̃	φ̃	PROPN
ejpam-5161	73	2	,	,	PUNCT
ejpam-5161	73	3	then	then	ADV
ejpam-5161	73	4	x	x	X
ejpam-5161	73	5	/∈	/∈	PUNCT
ejpam-5161	73	6	(	(	PUNCT
ejpam-5161	73	7	f	f	X
ejpam-5161	73	8	,	,	PUNCT
ejpam-5161	73	9	ω	ω	NOUN
ejpam-5161	73	10	)	)	PUNCT
ejpam-5161	73	11	.	.	PUNCT
ejpam-5161	74	1	definition	definition	NOUN
ejpam-5161	74	2	1	1	NUM
ejpam-5161	74	3	.	.	PUNCT
ejpam-5161	75	1	[	[	X
ejpam-5161	75	2	28	28	NUM
ejpam-5161	75	3	]	]	X
ejpam-5161	75	4	a	a	DET
ejpam-5161	75	5	collection	collection	NOUN
ejpam-5161	75	6	σ	σ	NOUN
ejpam-5161	75	7	of	of	ADP
ejpam-5161	75	8	sω(x	sω(x	NUM
ejpam-5161	75	9	)	)	PUNCT
ejpam-5161	75	10	is	be	AUX
ejpam-5161	75	11	said	say	VERB
ejpam-5161	75	12	to	to	PART
ejpam-5161	75	13	be	be	AUX
ejpam-5161	75	14	a	a	DET
ejpam-5161	75	15	soft	soft	ADJ
ejpam-5161	75	16	topology	topology	NOUN
ejpam-5161	75	17	on	on	ADP
ejpam-5161	75	18	x	x	SYM
ejpam-5161	75	19	if	if	SCONJ
ejpam-5161	75	20	the	the	DET
ejpam-5161	75	21	following	follow	VERB
ejpam-5161	75	22	conditions	condition	NOUN
ejpam-5161	75	23	are	be	AUX
ejpam-5161	75	24	satisfied	satisfied	ADJ
ejpam-5161	75	25	:	:	PUNCT
ejpam-5161	75	26	(	(	PUNCT
ejpam-5161	75	27	i	i	NOUN
ejpam-5161	75	28	)	)	PUNCT
ejpam-5161	75	29	φ̃	φ̃	PROPN
ejpam-5161	75	30	,	,	PUNCT
ejpam-5161	75	31	x̃	x̃	PROPN
ejpam-5161	75	32	∈	∈	PROPN
ejpam-5161	75	33	σ	σ	PROPN
ejpam-5161	75	34	;	;	PUNCT
ejpam-5161	75	35	(	(	PUNCT
ejpam-5161	75	36	ii	ii	NOUN
ejpam-5161	75	37	)	)	PUNCT
ejpam-5161	75	38	if	if	SCONJ
ejpam-5161	75	39	(	(	PUNCT
ejpam-5161	75	40	f1,ω	f1,ω	PROPN
ejpam-5161	75	41	)	)	PUNCT
ejpam-5161	75	42	,	,	PUNCT
ejpam-5161	75	43	(	(	PUNCT
ejpam-5161	75	44	f2,ω	f2,ω	NOUN
ejpam-5161	75	45	)	)	PUNCT
ejpam-5161	75	46	∈	∈	PROPN
ejpam-5161	75	47	σ	σ	PROPN
ejpam-5161	75	48	,	,	PUNCT
ejpam-5161	75	49	then	then	ADV
ejpam-5161	75	50	(	(	PUNCT
ejpam-5161	75	51	f1,ω)∩̃(f2,ω	f1,ω)∩̃(f2,ω	NOUN
ejpam-5161	75	52	)	)	PUNCT
ejpam-5161	75	53	∈	∈	PROPN
ejpam-5161	75	54	σ	σ	PROPN
ejpam-5161	75	55	;	;	PUNCT
ejpam-5161	75	56	and	and	CCONJ
ejpam-5161	75	57	(	(	PUNCT
ejpam-5161	75	58	iii	iii	X
ejpam-5161	75	59	)	)	PUNCT
ejpam-5161	75	60	if	if	SCONJ
ejpam-5161	75	61	each	each	PRON
ejpam-5161	75	62	{	{	PUNCT
ejpam-5161	75	63	(	(	PUNCT
ejpam-5161	75	64	fi	fi	NOUN
ejpam-5161	75	65	,	,	PUNCT
ejpam-5161	75	66	ω	ω	NUM
ejpam-5161	75	67	)	)	PUNCT
ejpam-5161	75	68	:	:	PUNCT
ejpam-5161	76	1	i	i	PRON
ejpam-5161	76	2	∈	∈	PROPN
ejpam-5161	76	3	i}⊆̃σ	i}⊆̃σ	PROPN
ejpam-5161	76	4	,	,	PUNCT
ejpam-5161	76	5	then	then	ADV
ejpam-5161	76	6	⋃̃	⋃̃	PROPN
ejpam-5161	76	7	i∈i(fi	i∈i(fi	PROPN
ejpam-5161	76	8	,	,	PUNCT
ejpam-5161	76	9	ω	ω	NOUN
ejpam-5161	76	10	)	)	PUNCT
ejpam-5161	76	11	∈	∈	PROPN
ejpam-5161	76	12	σ	σ	PROPN
ejpam-5161	76	13	.	.	PUNCT
ejpam-5161	76	14	terminologically	terminologically	PROPN
ejpam-5161	76	15	,	,	PUNCT
ejpam-5161	76	16	we	we	PRON
ejpam-5161	76	17	call	call	VERB
ejpam-5161	76	18	(	(	PUNCT
ejpam-5161	76	19	x	x	NOUN
ejpam-5161	76	20	,	,	PUNCT
ejpam-5161	76	21	σ	σ	PROPN
ejpam-5161	76	22	,	,	PUNCT
ejpam-5161	76	23	ω	ω	PROPN
ejpam-5161	76	24	)	)	PUNCT
ejpam-5161	76	25	a	a	DET
ejpam-5161	76	26	soft	soft	ADJ
ejpam-5161	76	27	topological	topological	ADJ
ejpam-5161	76	28	space	space	NOUN
ejpam-5161	76	29	on	on	ADP
ejpam-5161	76	30	x.	x.	NOUN
ejpam-5161	76	31	the	the	DET
ejpam-5161	76	32	elements	element	NOUN
ejpam-5161	76	33	of	of	ADP
ejpam-5161	76	34	σ	σ	PROPN
ejpam-5161	76	35	are	be	AUX
ejpam-5161	76	36	called	call	VERB
ejpam-5161	76	37	soft	soft	ADJ
ejpam-5161	76	38	open	open	ADJ
ejpam-5161	76	39	sets	set	NOUN
ejpam-5161	76	40	in	in	ADP
ejpam-5161	76	41	σ	σ	PROPN
ejpam-5161	76	42	(	(	PUNCT
ejpam-5161	76	43	or	or	CCONJ
ejpam-5161	76	44	simply	simply	ADV
ejpam-5161	76	45	,	,	PUNCT
ejpam-5161	76	46	soft	soft	ADJ
ejpam-5161	76	47	open	open	ADJ
ejpam-5161	76	48	sets	set	NOUN
ejpam-5161	76	49	when	when	SCONJ
ejpam-5161	76	50	no	no	DET
ejpam-5161	76	51	confusion	confusion	NOUN
ejpam-5161	76	52	arises	arise	VERB
ejpam-5161	76	53	)	)	PUNCT
ejpam-5161	76	54	,	,	PUNCT
ejpam-5161	76	55	and	and	CCONJ
ejpam-5161	76	56	their	their	PRON
ejpam-5161	76	57	complements	complement	NOUN
ejpam-5161	76	58	are	be	AUX
ejpam-5161	76	59	called	call	VERB
ejpam-5161	76	60	soft	soft	ADJ
ejpam-5161	76	61	closed	closed	ADJ
ejpam-5161	76	62	sets	set	NOUN
ejpam-5161	76	63	in	in	ADP
ejpam-5161	76	64	σ	σ	PROPN
ejpam-5161	76	65	(	(	PUNCT
ejpam-5161	76	66	or	or	CCONJ
ejpam-5161	76	67	shortly	shortly	ADV
ejpam-5161	76	68	,	,	PUNCT
ejpam-5161	76	69	soft	soft	ADJ
ejpam-5161	76	70	closed	closed	ADJ
ejpam-5161	76	71	sets	set	NOUN
ejpam-5161	76	72	)	)	PUNCT
ejpam-5161	76	73	.	.	PUNCT
ejpam-5161	77	1	we	we	PRON
ejpam-5161	77	2	use	use	VERB
ejpam-5161	77	3	(	(	PUNCT
ejpam-5161	77	4	x	x	X
ejpam-5161	77	5	,	,	PUNCT
ejpam-5161	77	6	σ	σ	PROPN
ejpam-5161	77	7	,	,	PUNCT
ejpam-5161	77	8	ω	ω	NOUN
ejpam-5161	77	9	)	)	PUNCT
ejpam-5161	77	10	to	to	PART
ejpam-5161	77	11	mention	mention	VERB
ejpam-5161	77	12	a	a	DET
ejpam-5161	77	13	soft	soft	ADJ
ejpam-5161	77	14	topological	topological	ADJ
ejpam-5161	77	15	space	space	NOUN
ejpam-5161	77	16	.	.	PUNCT
ejpam-5161	78	1	in	in	ADP
ejpam-5161	78	2	addition	addition	NOUN
ejpam-5161	78	3	,	,	PUNCT
ejpam-5161	78	4	(	(	PUNCT
ejpam-5161	78	5	f	f	X
ejpam-5161	78	6	,	,	PUNCT
ejpam-5161	78	7	ω	ω	NOUN
ejpam-5161	78	8	)	)	PUNCT
ejpam-5161	78	9	and	and	CCONJ
ejpam-5161	78	10	(	(	PUNCT
ejpam-5161	78	11	g	g	PROPN
ejpam-5161	78	12	,	,	PUNCT
ejpam-5161	78	13	ω	ω	NOUN
ejpam-5161	78	14	)	)	PUNCT
ejpam-5161	78	15	are	be	AUX
ejpam-5161	78	16	disjoint	disjoint	ADJ
ejpam-5161	78	17	soft	soft	ADJ
ejpam-5161	78	18	sets	set	NOUN
ejpam-5161	78	19	over	over	ADP
ejpam-5161	78	20	x	x	PUNCT
ejpam-5161	78	21	if	if	SCONJ
ejpam-5161	78	22	(	(	PUNCT
ejpam-5161	78	23	f	f	X
ejpam-5161	78	24	,	,	PUNCT
ejpam-5161	78	25	ω)∩̃(g	ω)∩̃(g	PROPN
ejpam-5161	78	26	,	,	PUNCT
ejpam-5161	78	27	ω	ω	NOUN
ejpam-5161	78	28	)	)	PUNCT
ejpam-5161	78	29	=	=	SYM
ejpam-5161	78	30	φ̃.	φ̃.	ADJ
ejpam-5161	78	31	definition	definition	NOUN
ejpam-5161	78	32	2	2	NUM
ejpam-5161	78	33	.	.	PUNCT
ejpam-5161	79	1	[	[	X
ejpam-5161	79	2	15	15	NUM
ejpam-5161	79	3	]	]	X
ejpam-5161	79	4	a	a	DET
ejpam-5161	79	5	subcollection	subcollection	NOUN
ejpam-5161	79	6	b	b	NOUN
ejpam-5161	79	7	⊆	⊆	NUM
ejpam-5161	79	8	σ	σ	PROPN
ejpam-5161	79	9	is	be	AUX
ejpam-5161	79	10	called	call	VERB
ejpam-5161	79	11	a	a	DET
ejpam-5161	79	12	soft	soft	ADJ
ejpam-5161	79	13	base	base	NOUN
ejpam-5161	79	14	for	for	ADP
ejpam-5161	79	15	the	the	DET
ejpam-5161	79	16	soft	soft	ADJ
ejpam-5161	79	17	topology	topology	NOUN
ejpam-5161	79	18	σ	σ	NOUN
ejpam-5161	79	19	if	if	SCONJ
ejpam-5161	79	20	each	each	DET
ejpam-5161	79	21	element	element	NOUN
ejpam-5161	79	22	of	of	ADP
ejpam-5161	79	23	σ	σ	PROPN
ejpam-5161	79	24	is	be	AUX
ejpam-5161	79	25	a	a	DET
ejpam-5161	79	26	union	union	NOUN
ejpam-5161	79	27	of	of	ADP
ejpam-5161	79	28	elements	element	NOUN
ejpam-5161	79	29	of	of	ADP
ejpam-5161	79	30	b.	b.	PROPN
ejpam-5161	79	31	definition	definition	NOUN
ejpam-5161	79	32	3	3	NUM
ejpam-5161	79	33	.	.	PUNCT
ejpam-5161	80	1	[	[	X
ejpam-5161	80	2	15	15	NUM
ejpam-5161	80	3	]	]	X
ejpam-5161	80	4	let	let	VERB
ejpam-5161	80	5	σ1,σ2	σ1,σ2	PROPN
ejpam-5161	80	6	be	be	AUX
ejpam-5161	80	7	two	two	NUM
ejpam-5161	80	8	soft	soft	ADJ
ejpam-5161	80	9	topologies	topology	NOUN
ejpam-5161	80	10	on	on	ADP
ejpam-5161	80	11	x.	x.	NOUN
ejpam-5161	81	1	it	it	PRON
ejpam-5161	81	2	is	be	AUX
ejpam-5161	81	3	said	say	VERB
ejpam-5161	81	4	that	that	SCONJ
ejpam-5161	81	5	σ2	σ2	PROPN
ejpam-5161	81	6	is	be	AUX
ejpam-5161	81	7	finer	fine	ADJ
ejpam-5161	81	8	than	than	ADP
ejpam-5161	81	9	σ1	σ1	PROPN
ejpam-5161	81	10	(	(	PUNCT
ejpam-5161	81	11	or	or	CCONJ
ejpam-5161	81	12	σ1	σ1	NOUN
ejpam-5161	81	13	is	be	AUX
ejpam-5161	81	14	coarser	coarse	ADJ
ejpam-5161	81	15	than	than	ADP
ejpam-5161	81	16	σ2	σ2	PROPN
ejpam-5161	81	17	)	)	PUNCT
ejpam-5161	81	18	if	if	SCONJ
ejpam-5161	81	19	σ1⊆̃σ2	σ1⊆̃σ2	VERB
ejpam-5161	81	20	.	.	PUNCT
ejpam-5161	82	1	lemma	lemma	PROPN
ejpam-5161	82	2	1	1	NUM
ejpam-5161	82	3	.	.	PUNCT
ejpam-5161	83	1	[	[	X
ejpam-5161	83	2	28	28	NUM
ejpam-5161	83	3	]	]	X
ejpam-5161	83	4	let	let	VERB
ejpam-5161	83	5	(	(	PUNCT
ejpam-5161	83	6	x	x	NOUN
ejpam-5161	83	7	,	,	PUNCT
ejpam-5161	83	8	σ	σ	PROPN
ejpam-5161	83	9	,	,	PUNCT
ejpam-5161	83	10	ω	ω	PROPN
ejpam-5161	83	11	)	)	PUNCT
ejpam-5161	83	12	be	be	AUX
ejpam-5161	83	13	a	a	DET
ejpam-5161	83	14	soft	soft	ADJ
ejpam-5161	83	15	topology	topology	NOUN
ejpam-5161	83	16	on	on	ADP
ejpam-5161	83	17	x.	x.	NOUN
ejpam-5161	83	18	for	for	ADP
ejpam-5161	83	19	each	each	DET
ejpam-5161	83	20	ω	ω	PROPN
ejpam-5161	83	21	∈	∈	PROPN
ejpam-5161	83	22	ω	ω	PROPN
ejpam-5161	83	23	,	,	PUNCT
ejpam-5161	83	24	σω	σω	X
ejpam-5161	83	25	=	=	SYM
ejpam-5161	83	26	{	{	PUNCT
ejpam-5161	83	27	f	f	PROPN
ejpam-5161	83	28	(	(	PUNCT
ejpam-5161	83	29	ω	ω	PROPN
ejpam-5161	83	30	)	)	PUNCT
ejpam-5161	83	31	:	:	PUNCT
ejpam-5161	83	32	(	(	PUNCT
ejpam-5161	83	33	f	f	X
ejpam-5161	83	34	,	,	PUNCT
ejpam-5161	83	35	ω	ω	NUM
ejpam-5161	83	36	)	)	PUNCT
ejpam-5161	83	37	∈	∈	PROPN
ejpam-5161	83	38	σ	σ	PROPN
ejpam-5161	83	39	}	}	PUNCT
ejpam-5161	83	40	is	be	AUX
ejpam-5161	83	41	a	a	DET
ejpam-5161	83	42	crisp	crisp	ADJ
ejpam-5161	83	43	topology	topology	NOUN
ejpam-5161	83	44	on	on	ADP
ejpam-5161	83	45	x.	x.	NOUN
ejpam-5161	83	46	definition	definition	NOUN
ejpam-5161	83	47	4	4	NUM
ejpam-5161	83	48	.	.	PUNCT
ejpam-5161	84	1	[	[	X
ejpam-5161	84	2	2	2	NUM
ejpam-5161	84	3	]	]	X
ejpam-5161	84	4	let	let	VERB
ejpam-5161	84	5	f⊆̃sω(x	f⊆̃sω(x	NOUN
ejpam-5161	84	6	)	)	PUNCT
ejpam-5161	84	7	.	.	PUNCT
ejpam-5161	85	1	the	the	DET
ejpam-5161	85	2	intersection	intersection	NOUN
ejpam-5161	85	3	of	of	ADP
ejpam-5161	85	4	all	all	DET
ejpam-5161	85	5	soft	soft	ADJ
ejpam-5161	85	6	topologies	topology	NOUN
ejpam-5161	85	7	on	on	ADP
ejpam-5161	85	8	x	x	PUNCT
ejpam-5161	85	9	including	include	VERB
ejpam-5161	85	10	f	f	PROPN
ejpam-5161	85	11	is	be	AUX
ejpam-5161	85	12	called	call	VERB
ejpam-5161	85	13	a	a	DET
ejpam-5161	85	14	soft	soft	ADJ
ejpam-5161	85	15	topology	topology	NOUN
ejpam-5161	85	16	generated	generate	VERB
ejpam-5161	85	17	by	by	ADP
ejpam-5161	85	18	f	f	PROPN
ejpam-5161	85	19	and	and	CCONJ
ejpam-5161	85	20	is	be	AUX
ejpam-5161	85	21	referred	refer	VERB
ejpam-5161	85	22	to	to	ADP
ejpam-5161	85	23	t	t	PROPN
ejpam-5161	85	24	(	(	PUNCT
ejpam-5161	85	25	f	f	NOUN
ejpam-5161	85	26	)	)	PUNCT
ejpam-5161	85	27	.	.	PUNCT
ejpam-5161	86	1	z.	z.	PROPN
ejpam-5161	86	2	a.	a.	PROPN
ejpam-5161	86	3	ameen	ameen	PROPN
ejpam-5161	86	4	et	et	PROPN
ejpam-5161	86	5	al	al	PROPN
ejpam-5161	86	6	.	.	PUNCT
ejpam-5161	86	7	/	/	SYM
ejpam-5161	86	8	eur	eur	PROPN
ejpam-5161	86	9	.	.	PUNCT
ejpam-5161	87	1	j.	j.	PROPN
ejpam-5161	87	2	pure	pure	PROPN
ejpam-5161	87	3	appl	appl	PROPN
ejpam-5161	87	4	.	.	PROPN
ejpam-5161	87	5	math	math	PROPN
ejpam-5161	87	6	,	,	PUNCT
ejpam-5161	87	7	17	17	NUM
ejpam-5161	87	8	(	(	PUNCT
ejpam-5161	87	9	2	2	NUM
ejpam-5161	87	10	)	)	PUNCT
ejpam-5161	87	11	(	(	PUNCT
ejpam-5161	87	12	2024	2024	NUM
ejpam-5161	87	13	)	)	PUNCT
ejpam-5161	87	14	,	,	PUNCT
ejpam-5161	87	15	1168	1168	NUM
ejpam-5161	87	16	-	-	SYM
ejpam-5161	87	17	1182	1182	NUM
ejpam-5161	87	18	1171	1171	NUM
ejpam-5161	87	19	lemma	lemma	PROPN
ejpam-5161	87	20	2	2	NUM
ejpam-5161	87	21	.	.	PUNCT
ejpam-5161	88	1	[	[	X
ejpam-5161	88	2	2	2	NUM
ejpam-5161	88	3	,	,	PUNCT
ejpam-5161	88	4	lemma	lemma	PROPN
ejpam-5161	88	5	3.5	3.5	NUM
ejpam-5161	88	6	]	]	PUNCT
ejpam-5161	88	7	let	let	VERB
ejpam-5161	88	8	σ1,σ2	σ1,σ2	PROPN
ejpam-5161	88	9	be	be	AUX
ejpam-5161	88	10	two	two	NUM
ejpam-5161	88	11	soft	soft	ADJ
ejpam-5161	88	12	topologies	topology	NOUN
ejpam-5161	88	13	on	on	ADP
ejpam-5161	88	14	x.	x.	NOUN
ejpam-5161	88	15	the	the	DET
ejpam-5161	88	16	resulting	result	VERB
ejpam-5161	88	17	soft	soft	ADJ
ejpam-5161	88	18	topology	topology	NOUN
ejpam-5161	88	19	t	t	NOUN
ejpam-5161	88	20	(	(	PUNCT
ejpam-5161	88	21	σ1∪̃σ2	σ1∪̃σ2	PROPN
ejpam-5161	88	22	)	)	PUNCT
ejpam-5161	88	23	is	be	AUX
ejpam-5161	88	24	identical	identical	ADJ
ejpam-5161	88	25	to	to	ADP
ejpam-5161	88	26	the	the	DET
ejpam-5161	88	27	soft	soft	ADJ
ejpam-5161	88	28	topology	topology	NOUN
ejpam-5161	88	29	t	t	NOUN
ejpam-5161	88	30	(	(	PUNCT
ejpam-5161	88	31	f	f	X
ejpam-5161	88	32	)	)	PUNCT
ejpam-5161	88	33	generated	generate	VERB
ejpam-5161	88	34	by	by	ADP
ejpam-5161	88	35	f	f	PROPN
ejpam-5161	88	36	=	=	PRON
ejpam-5161	88	37	{	{	PUNCT
ejpam-5161	88	38	(	(	PUNCT
ejpam-5161	88	39	f1,ω)∩̃(f2,ω	f1,ω)∩̃(f2,ω	NOUN
ejpam-5161	88	40	)	)	PUNCT
ejpam-5161	88	41	:	:	PUNCT
ejpam-5161	88	42	(	(	PUNCT
ejpam-5161	88	43	f1,ω	f1,ω	PROPN
ejpam-5161	88	44	)	)	PUNCT
ejpam-5161	88	45	∈	∈	PROPN
ejpam-5161	88	46	σ1	σ1	PROPN
ejpam-5161	88	47	,	,	PUNCT
ejpam-5161	88	48	(	(	PUNCT
ejpam-5161	88	49	f2,ω	f2,ω	PROPN
ejpam-5161	88	50	)	)	PUNCT
ejpam-5161	88	51	∈	∈	PROPN
ejpam-5161	88	52	σ2	σ2	PROPN
ejpam-5161	88	53	}	}	PUNCT
ejpam-5161	88	54	.	.	PUNCT
ejpam-5161	89	1	definition	definition	NOUN
ejpam-5161	89	2	5	5	NUM
ejpam-5161	89	3	.	.	PUNCT
ejpam-5161	90	1	[	[	X
ejpam-5161	90	2	28	28	NUM
ejpam-5161	90	3	]	]	X
ejpam-5161	90	4	a	a	DET
ejpam-5161	90	5	soft	soft	ADJ
ejpam-5161	90	6	space	space	NOUN
ejpam-5161	90	7	(	(	PUNCT
ejpam-5161	90	8	x	x	X
ejpam-5161	90	9	,	,	PUNCT
ejpam-5161	90	10	σ	σ	PROPN
ejpam-5161	90	11	,	,	PUNCT
ejpam-5161	90	12	ω	ω	NOUN
ejpam-5161	90	13	)	)	PUNCT
ejpam-5161	90	14	is	be	AUX
ejpam-5161	90	15	called	call	VERB
ejpam-5161	90	16	(	(	PUNCT
ejpam-5161	90	17	i	i	NOUN
ejpam-5161	90	18	)	)	PUNCT
ejpam-5161	90	19	soft	soft	ADJ
ejpam-5161	90	20	t0	t0	PROPN
ejpam-5161	90	21	if	if	SCONJ
ejpam-5161	90	22	for	for	ADP
ejpam-5161	90	23	each	each	DET
ejpam-5161	90	24	x	x	NOUN
ejpam-5161	90	25	,	,	PUNCT
ejpam-5161	90	26	y	y	PROPN
ejpam-5161	90	27	∈	∈	PROPN
ejpam-5161	90	28	x	x	PUNCT
ejpam-5161	90	29	with	with	ADP
ejpam-5161	90	30	x	x	PUNCT
ejpam-5161	90	31	̸=	̸=	PROPN
ejpam-5161	90	32	y	y	NUM
ejpam-5161	90	33	,	,	PUNCT
ejpam-5161	90	34	there	there	PRON
ejpam-5161	90	35	exist	exist	VERB
ejpam-5161	90	36	soft	soft	ADJ
ejpam-5161	90	37	open	open	ADJ
ejpam-5161	90	38	sets	set	NOUN
ejpam-5161	90	39	(	(	PUNCT
ejpam-5161	90	40	u	u	NOUN
ejpam-5161	90	41	,	,	PUNCT
ejpam-5161	90	42	ω	ω	NOUN
ejpam-5161	90	43	)	)	PUNCT
ejpam-5161	90	44	,	,	PUNCT
ejpam-5161	90	45	(	(	PUNCT
ejpam-5161	90	46	v	v	NOUN
ejpam-5161	90	47	,	,	PUNCT
ejpam-5161	90	48	ω	ω	NOUN
ejpam-5161	90	49	)	)	PUNCT
ejpam-5161	91	1	such	such	ADJ
ejpam-5161	91	2	that	that	SCONJ
ejpam-5161	91	3	x	x	SYM
ejpam-5161	91	4	∈	∈	PROPN
ejpam-5161	91	5	(	(	PUNCT
ejpam-5161	91	6	u	u	NOUN
ejpam-5161	91	7	,	,	PUNCT
ejpam-5161	91	8	ω	ω	PROPN
ejpam-5161	91	9	)	)	PUNCT
ejpam-5161	91	10	,	,	PUNCT
ejpam-5161	91	11	y	y	PROPN
ejpam-5161	91	12	/∈	/∈	PUNCT
ejpam-5161	91	13	(	(	PUNCT
ejpam-5161	91	14	u	u	NOUN
ejpam-5161	91	15	,	,	PUNCT
ejpam-5161	91	16	ω	ω	NOUN
ejpam-5161	91	17	)	)	PUNCT
ejpam-5161	91	18	or	or	CCONJ
ejpam-5161	91	19	x	x	ADJ
ejpam-5161	91	20	/∈	/∈	PUNCT
ejpam-5161	91	21	(	(	PUNCT
ejpam-5161	91	22	v	v	NOUN
ejpam-5161	91	23	,	,	PUNCT
ejpam-5161	91	24	ω	ω	NOUN
ejpam-5161	91	25	)	)	PUNCT
ejpam-5161	91	26	,	,	PUNCT
ejpam-5161	91	27	y	y	PROPN
ejpam-5161	91	28	∈	∈	PROPN
ejpam-5161	91	29	(	(	PUNCT
ejpam-5161	91	30	v	v	NOUN
ejpam-5161	91	31	,	,	PUNCT
ejpam-5161	91	32	ω	ω	NOUN
ejpam-5161	91	33	)	)	PUNCT
ejpam-5161	91	34	,	,	PUNCT
ejpam-5161	91	35	(	(	PUNCT
ejpam-5161	91	36	ii	ii	NOUN
ejpam-5161	91	37	)	)	PUNCT
ejpam-5161	91	38	soft	soft	ADJ
ejpam-5161	91	39	t1	t1	NOUN
ejpam-5161	91	40	if	if	SCONJ
ejpam-5161	91	41	for	for	ADP
ejpam-5161	91	42	each	each	DET
ejpam-5161	91	43	x	x	NOUN
ejpam-5161	91	44	,	,	PUNCT
ejpam-5161	91	45	y	y	PROPN
ejpam-5161	91	46	∈	∈	PROPN
ejpam-5161	91	47	x	x	PUNCT
ejpam-5161	91	48	with	with	ADP
ejpam-5161	91	49	x	x	PUNCT
ejpam-5161	91	50	̸=	̸=	PROPN
ejpam-5161	91	51	y	y	NUM
ejpam-5161	91	52	,	,	PUNCT
ejpam-5161	91	53	there	there	PRON
ejpam-5161	91	54	exist	exist	VERB
ejpam-5161	91	55	soft	soft	ADJ
ejpam-5161	91	56	open	open	ADJ
ejpam-5161	91	57	sets	set	NOUN
ejpam-5161	91	58	(	(	PUNCT
ejpam-5161	91	59	u	u	NOUN
ejpam-5161	91	60	,	,	PUNCT
ejpam-5161	91	61	ω	ω	NOUN
ejpam-5161	91	62	)	)	PUNCT
ejpam-5161	91	63	,	,	PUNCT
ejpam-5161	91	64	(	(	PUNCT
ejpam-5161	91	65	v	v	NOUN
ejpam-5161	91	66	,	,	PUNCT
ejpam-5161	91	67	ω	ω	NOUN
ejpam-5161	91	68	)	)	PUNCT
ejpam-5161	91	69	such	such	ADJ
ejpam-5161	91	70	that	that	SCONJ
ejpam-5161	91	71	x	x	SYM
ejpam-5161	91	72	∈	∈	PROPN
ejpam-5161	91	73	(	(	PUNCT
ejpam-5161	91	74	u	u	NOUN
ejpam-5161	91	75	,	,	PUNCT
ejpam-5161	91	76	ω	ω	PROPN
ejpam-5161	91	77	)	)	PUNCT
ejpam-5161	91	78	,	,	PUNCT
ejpam-5161	91	79	y	y	PROPN
ejpam-5161	91	80	/∈	/∈	PUNCT
ejpam-5161	91	81	(	(	PUNCT
ejpam-5161	91	82	u	u	NOUN
ejpam-5161	91	83	,	,	PUNCT
ejpam-5161	91	84	ω	ω	NOUN
ejpam-5161	91	85	)	)	PUNCT
ejpam-5161	91	86	and	and	CCONJ
ejpam-5161	91	87	x	x	X
ejpam-5161	91	88	/∈	/∈	PUNCT
ejpam-5161	91	89	(	(	PUNCT
ejpam-5161	91	90	v	v	NOUN
ejpam-5161	91	91	,	,	PUNCT
ejpam-5161	91	92	ω	ω	NOUN
ejpam-5161	91	93	)	)	PUNCT
ejpam-5161	91	94	,	,	PUNCT
ejpam-5161	91	95	y	y	PROPN
ejpam-5161	91	96	∈	∈	PROPN
ejpam-5161	91	97	(	(	PUNCT
ejpam-5161	91	98	v	v	NOUN
ejpam-5161	91	99	,	,	PUNCT
ejpam-5161	91	100	ω	ω	NOUN
ejpam-5161	91	101	)	)	PUNCT
ejpam-5161	91	102	,	,	PUNCT
ejpam-5161	91	103	(	(	PUNCT
ejpam-5161	91	104	iii	iii	X
ejpam-5161	91	105	)	)	PUNCT
ejpam-5161	91	106	soft	soft	ADJ
ejpam-5161	91	107	t2	t2	NOUN
ejpam-5161	91	108	(	(	PUNCT
ejpam-5161	91	109	soft	soft	ADJ
ejpam-5161	91	110	hausdorff	hausdorff	NOUN
ejpam-5161	91	111	)	)	PUNCT
ejpam-5161	91	112	if	if	SCONJ
ejpam-5161	91	113	for	for	ADP
ejpam-5161	91	114	each	each	DET
ejpam-5161	91	115	x	x	NOUN
ejpam-5161	91	116	,	,	PUNCT
ejpam-5161	91	117	y	y	PROPN
ejpam-5161	91	118	∈	∈	PROPN
ejpam-5161	91	119	x	x	PUNCT
ejpam-5161	91	120	with	with	ADP
ejpam-5161	91	121	x	x	PUNCT
ejpam-5161	91	122	̸=	̸=	PROPN
ejpam-5161	91	123	y	y	NUM
ejpam-5161	91	124	,	,	PUNCT
ejpam-5161	91	125	there	there	PRON
ejpam-5161	91	126	exist	exist	VERB
ejpam-5161	91	127	soft	soft	ADJ
ejpam-5161	91	128	open	open	ADJ
ejpam-5161	91	129	sets	set	NOUN
ejpam-5161	91	130	(	(	PUNCT
ejpam-5161	91	131	u	u	NOUN
ejpam-5161	91	132	,	,	PUNCT
ejpam-5161	91	133	ω	ω	NOUN
ejpam-5161	91	134	)	)	PUNCT
ejpam-5161	91	135	,	,	PUNCT
ejpam-5161	91	136	(	(	PUNCT
ejpam-5161	91	137	v	v	NOUN
ejpam-5161	91	138	,	,	PUNCT
ejpam-5161	91	139	ω	ω	NOUN
ejpam-5161	91	140	)	)	PUNCT
ejpam-5161	91	141	containing	contain	VERB
ejpam-5161	91	142	x	x	PROPN
ejpam-5161	91	143	,	,	PUNCT
ejpam-5161	91	144	y	y	PROPN
ejpam-5161	91	145	respectively	respectively	ADV
ejpam-5161	91	146	such	such	ADJ
ejpam-5161	91	147	that	that	SCONJ
ejpam-5161	91	148	(	(	PUNCT
ejpam-5161	91	149	u	u	NOUN
ejpam-5161	91	150	,	,	PUNCT
ejpam-5161	91	151	ω	ω	NOUN
ejpam-5161	91	152	)	)	PUNCT
ejpam-5161	91	153	⋂̃	⋂̃	NOUN
ejpam-5161	91	154	(	(	PUNCT
ejpam-5161	91	155	v	v	NOUN
ejpam-5161	91	156	,	,	PUNCT
ejpam-5161	91	157	ω	ω	NOUN
ejpam-5161	91	158	)	)	PUNCT
ejpam-5161	91	159	=	=	SYM
ejpam-5161	91	160	φ̃.	φ̃.	PROPN
ejpam-5161	91	161	(	(	PUNCT
ejpam-5161	91	162	iv	iv	NOUN
ejpam-5161	91	163	)	)	PUNCT
ejpam-5161	91	164	soft	soft	ADJ
ejpam-5161	91	165	regular	regular	ADV
ejpam-5161	91	166	if	if	SCONJ
ejpam-5161	91	167	for	for	ADP
ejpam-5161	91	168	each	each	DET
ejpam-5161	91	169	soft	soft	ADJ
ejpam-5161	91	170	closed	closed	ADJ
ejpam-5161	91	171	set	set	NOUN
ejpam-5161	91	172	(	(	PUNCT
ejpam-5161	91	173	f	f	NUM
ejpam-5161	91	174	,	,	PUNCT
ejpam-5161	91	175	ω	ω	NOUN
ejpam-5161	91	176	)	)	PUNCT
ejpam-5161	91	177	and	and	CCONJ
ejpam-5161	91	178	each	each	DET
ejpam-5161	91	179	soft	soft	ADJ
ejpam-5161	91	180	point	point	NOUN
ejpam-5161	91	181	x	x	PUNCT
ejpam-5161	91	182	with	with	ADP
ejpam-5161	91	183	x	x	PROPN
ejpam-5161	91	184	/∈	/∈	PUNCT
ejpam-5161	91	185	(	(	PUNCT
ejpam-5161	91	186	f	f	X
ejpam-5161	91	187	,	,	PUNCT
ejpam-5161	91	188	ω	ω	PROPN
ejpam-5161	91	189	)	)	PUNCT
ejpam-5161	91	190	,	,	PUNCT
ejpam-5161	91	191	there	there	PRON
ejpam-5161	91	192	exist	exist	VERB
ejpam-5161	91	193	soft	soft	ADJ
ejpam-5161	91	194	open	open	ADJ
ejpam-5161	91	195	sets	set	NOUN
ejpam-5161	91	196	(	(	PUNCT
ejpam-5161	91	197	u	u	NOUN
ejpam-5161	91	198	,	,	PUNCT
ejpam-5161	91	199	ω	ω	NOUN
ejpam-5161	91	200	)	)	PUNCT
ejpam-5161	91	201	,	,	PUNCT
ejpam-5161	91	202	(	(	PUNCT
ejpam-5161	91	203	v	v	NOUN
ejpam-5161	91	204	,	,	PUNCT
ejpam-5161	91	205	ω	ω	NOUN
ejpam-5161	91	206	)	)	PUNCT
ejpam-5161	92	1	such	such	ADJ
ejpam-5161	92	2	that	that	SCONJ
ejpam-5161	92	3	x	x	SYM
ejpam-5161	92	4	∈	∈	PROPN
ejpam-5161	92	5	(	(	PUNCT
ejpam-5161	92	6	u	u	NOUN
ejpam-5161	92	7	,	,	PUNCT
ejpam-5161	92	8	ω	ω	NOUN
ejpam-5161	92	9	)	)	PUNCT
ejpam-5161	92	10	,	,	PUNCT
ejpam-5161	92	11	(	(	PUNCT
ejpam-5161	92	12	f	f	X
ejpam-5161	92	13	,	,	PUNCT
ejpam-5161	92	14	ω)⊆̃(v	ω)⊆̃(v	PROPN
ejpam-5161	92	15	,	,	PUNCT
ejpam-5161	92	16	ω	ω	NOUN
ejpam-5161	92	17	)	)	PUNCT
ejpam-5161	92	18	and	and	CCONJ
ejpam-5161	92	19	(	(	PUNCT
ejpam-5161	92	20	u	u	NOUN
ejpam-5161	92	21	,	,	PUNCT
ejpam-5161	92	22	ω	ω	NOUN
ejpam-5161	92	23	)	)	PUNCT
ejpam-5161	92	24	⋂̃	⋂̃	NOUN
ejpam-5161	92	25	(	(	PUNCT
ejpam-5161	92	26	v	v	NOUN
ejpam-5161	92	27	,	,	PUNCT
ejpam-5161	92	28	ω	ω	NOUN
ejpam-5161	92	29	)	)	PUNCT
ejpam-5161	92	30	=	=	SYM
ejpam-5161	92	31	φ̃.	φ̃.	PROPN
ejpam-5161	92	32	(	(	PUNCT
ejpam-5161	92	33	v	v	NOUN
ejpam-5161	92	34	)	)	PUNCT
ejpam-5161	92	35	soft	soft	ADJ
ejpam-5161	92	36	normal	normal	ADJ
ejpam-5161	92	37	if	if	SCONJ
ejpam-5161	92	38	for	for	ADP
ejpam-5161	92	39	each	each	DET
ejpam-5161	92	40	soft	soft	ADJ
ejpam-5161	92	41	closed	closed	ADJ
ejpam-5161	92	42	sets	set	NOUN
ejpam-5161	92	43	(	(	PUNCT
ejpam-5161	92	44	f	f	X
ejpam-5161	92	45	,	,	PUNCT
ejpam-5161	92	46	ω	ω	PROPN
ejpam-5161	92	47	)	)	PUNCT
ejpam-5161	92	48	,	,	PUNCT
ejpam-5161	92	49	(	(	PUNCT
ejpam-5161	92	50	d	d	X
ejpam-5161	92	51	,	,	PUNCT
ejpam-5161	92	52	ω	ω	NOUN
ejpam-5161	92	53	)	)	PUNCT
ejpam-5161	92	54	with	with	ADP
ejpam-5161	92	55	(	(	PUNCT
ejpam-5161	92	56	f	f	X
ejpam-5161	92	57	,	,	PUNCT
ejpam-5161	92	58	ω	ω	NOUN
ejpam-5161	92	59	)	)	PUNCT
ejpam-5161	92	60	⋂̃	⋂̃	NOUN
ejpam-5161	92	61	(	(	PUNCT
ejpam-5161	92	62	d	d	PROPN
ejpam-5161	92	63	,	,	PUNCT
ejpam-5161	92	64	ω	ω	NOUN
ejpam-5161	92	65	)	)	PUNCT
ejpam-5161	92	66	=	=	PUNCT
ejpam-5161	92	67	φ̃	φ̃	PROPN
ejpam-5161	92	68	,	,	PUNCT
ejpam-5161	92	69	there	there	PRON
ejpam-5161	92	70	exist	exist	VERB
ejpam-5161	92	71	soft	soft	ADJ
ejpam-5161	92	72	open	open	ADJ
ejpam-5161	92	73	sets	set	NOUN
ejpam-5161	92	74	(	(	PUNCT
ejpam-5161	92	75	u	u	NOUN
ejpam-5161	92	76	,	,	PUNCT
ejpam-5161	92	77	ω	ω	NOUN
ejpam-5161	92	78	)	)	PUNCT
ejpam-5161	92	79	,	,	PUNCT
ejpam-5161	92	80	(	(	PUNCT
ejpam-5161	92	81	v	v	NOUN
ejpam-5161	92	82	,	,	PUNCT
ejpam-5161	92	83	ω	ω	NOUN
ejpam-5161	92	84	)	)	PUNCT
ejpam-5161	92	85	such	such	ADJ
ejpam-5161	92	86	that	that	SCONJ
ejpam-5161	92	87	(	(	PUNCT
ejpam-5161	92	88	f	f	X
ejpam-5161	92	89	,	,	PUNCT
ejpam-5161	92	90	ω)⊆̃(u	ω)⊆̃(u	PROPN
ejpam-5161	92	91	,	,	PUNCT
ejpam-5161	92	92	ω	ω	NOUN
ejpam-5161	92	93	)	)	PUNCT
ejpam-5161	92	94	,	,	PUNCT
ejpam-5161	92	95	(	(	PUNCT
ejpam-5161	92	96	d	d	X
ejpam-5161	92	97	,	,	PUNCT
ejpam-5161	92	98	ω)⊆̃(v	ω)⊆̃(v	PROPN
ejpam-5161	92	99	,	,	PUNCT
ejpam-5161	92	100	ω	ω	NOUN
ejpam-5161	92	101	)	)	PUNCT
ejpam-5161	92	102	and	and	CCONJ
ejpam-5161	92	103	(	(	PUNCT
ejpam-5161	92	104	u	u	NOUN
ejpam-5161	92	105	,	,	PUNCT
ejpam-5161	92	106	ω	ω	NOUN
ejpam-5161	92	107	)	)	PUNCT
ejpam-5161	92	108	⋂̃	⋂̃	NOUN
ejpam-5161	92	109	(	(	PUNCT
ejpam-5161	92	110	v	v	NOUN
ejpam-5161	92	111	,	,	PUNCT
ejpam-5161	92	112	ω	ω	NOUN
ejpam-5161	92	113	)	)	PUNCT
ejpam-5161	92	114	=	=	SYM
ejpam-5161	92	115	φ̃.	φ̃.	PROPN
ejpam-5161	92	116	(	(	PUNCT
ejpam-5161	92	117	vi	vi	NOUN
ejpam-5161	92	118	)	)	PUNCT
ejpam-5161	92	119	soft	soft	ADJ
ejpam-5161	92	120	t3	t3	NOUN
ejpam-5161	92	121	if	if	SCONJ
ejpam-5161	92	122	it	it	PRON
ejpam-5161	92	123	is	be	AUX
ejpam-5161	92	124	soft	soft	ADJ
ejpam-5161	92	125	t1	t1	NOUN
ejpam-5161	92	126	and	and	CCONJ
ejpam-5161	92	127	soft	soft	ADJ
ejpam-5161	92	128	regular	regular	ADJ
ejpam-5161	92	129	.	.	PUNCT
ejpam-5161	93	1	(	(	PUNCT
ejpam-5161	93	2	vii	vii	PROPN
ejpam-5161	93	3	)	)	PUNCT
ejpam-5161	93	4	soft	soft	ADJ
ejpam-5161	93	5	t4	t4	PROPN
ejpam-5161	93	6	if	if	SCONJ
ejpam-5161	93	7	it	it	PRON
ejpam-5161	93	8	is	be	AUX
ejpam-5161	93	9	soft	soft	ADJ
ejpam-5161	93	10	t1	t1	NOUN
ejpam-5161	93	11	and	and	CCONJ
ejpam-5161	93	12	soft	soft	ADJ
ejpam-5161	93	13	normal	normal	ADJ
ejpam-5161	93	14	.	.	PUNCT
ejpam-5161	94	1	lemma	lemma	PROPN
ejpam-5161	94	2	3	3	X
ejpam-5161	94	3	.	.	PUNCT
ejpam-5161	95	1	[	[	X
ejpam-5161	95	2	23	23	NUM
ejpam-5161	95	3	,	,	PUNCT
ejpam-5161	95	4	theorem	theorem	VERB
ejpam-5161	95	5	3.18	3.18	NUM
ejpam-5161	95	6	]	]	PUNCT
ejpam-5161	95	7	if	if	SCONJ
ejpam-5161	95	8	(	(	PUNCT
ejpam-5161	95	9	x	x	X
ejpam-5161	95	10	,	,	PUNCT
ejpam-5161	95	11	σ	σ	PROPN
ejpam-5161	95	12	,	,	PUNCT
ejpam-5161	95	13	ω	ω	NOUN
ejpam-5161	95	14	)	)	PUNCT
ejpam-5161	95	15	is	be	AUX
ejpam-5161	95	16	a	a	DET
ejpam-5161	95	17	soft	soft	ADJ
ejpam-5161	95	18	regular	regular	ADJ
ejpam-5161	95	19	space	space	NOUN
ejpam-5161	95	20	,	,	PUNCT
ejpam-5161	95	21	then	then	ADV
ejpam-5161	95	22	σω	σω	VERB
ejpam-5161	95	23	=	=	SYM
ejpam-5161	95	24	σω′	σω′	X
ejpam-5161	95	25	for	for	ADP
ejpam-5161	95	26	each	each	DET
ejpam-5161	95	27	ω	ω	NOUN
ejpam-5161	95	28	,	,	PUNCT
ejpam-5161	95	29	ω′	ω′	PROPN
ejpam-5161	95	30	∈	∈	PROPN
ejpam-5161	95	31	ω	ω	PROPN
ejpam-5161	95	32	.	.	PROPN
ejpam-5161	96	1	3	3	NUM
ejpam-5161	96	2	.	.	X
ejpam-5161	96	3	methods	method	NOUN
ejpam-5161	96	4	of	of	ADP
ejpam-5161	96	5	generating	generate	VERB
ejpam-5161	96	6	soft	soft	ADJ
ejpam-5161	96	7	topologies	topology	NOUN
ejpam-5161	96	8	and	and	CCONJ
ejpam-5161	96	9	their	their	PRON
ejpam-5161	96	10	relationships	relationship	NOUN
ejpam-5161	96	11	this	this	DET
ejpam-5161	96	12	section	section	NOUN
ejpam-5161	96	13	provides	provide	VERB
ejpam-5161	96	14	different	different	ADJ
ejpam-5161	96	15	methods	method	NOUN
ejpam-5161	96	16	of	of	ADP
ejpam-5161	96	17	producing	produce	VERB
ejpam-5161	96	18	soft	soft	ADJ
ejpam-5161	96	19	topologies	topology	NOUN
ejpam-5161	96	20	via	via	ADP
ejpam-5161	96	21	formulas	formula	NOUN
ejpam-5161	96	22	1	1	NUM
ejpam-5161	96	23	&	&	CCONJ
ejpam-5161	96	24	2	2	NUM
ejpam-5161	96	25	.	.	PUNCT
ejpam-5161	97	1	an	an	DET
ejpam-5161	97	2	example	example	NOUN
ejpam-5161	97	3	is	be	AUX
ejpam-5161	97	4	given	give	VERB
ejpam-5161	97	5	which	which	PRON
ejpam-5161	97	6	discusses	discuss	VERB
ejpam-5161	97	7	the	the	DET
ejpam-5161	97	8	implementation	implementation	NOUN
ejpam-5161	97	9	of	of	ADP
ejpam-5161	97	10	these	these	DET
ejpam-5161	97	11	formulas	formula	NOUN
ejpam-5161	97	12	in	in	ADP
ejpam-5161	97	13	detail	detail	NOUN
ejpam-5161	97	14	.	.	PUNCT
ejpam-5161	98	1	the	the	DET
ejpam-5161	98	2	relationships	relationship	NOUN
ejpam-5161	98	3	between	between	ADP
ejpam-5161	98	4	the	the	DET
ejpam-5161	98	5	original	original	ADJ
ejpam-5161	98	6	soft	soft	ADJ
ejpam-5161	98	7	topology	topology	NOUN
ejpam-5161	98	8	and	and	CCONJ
ejpam-5161	98	9	the	the	DET
ejpam-5161	98	10	soft	soft	ADJ
ejpam-5161	98	11	topologies	topology	NOUN
ejpam-5161	98	12	that	that	PRON
ejpam-5161	98	13	are	be	AUX
ejpam-5161	98	14	produced	produce	VERB
ejpam-5161	98	15	by	by	ADP
ejpam-5161	98	16	formulas	formula	NOUN
ejpam-5161	98	17	1	1	NUM
ejpam-5161	98	18	&	&	CCONJ
ejpam-5161	98	19	2	2	NUM
ejpam-5161	98	20	.	.	PUNCT
ejpam-5161	98	21	definition	definition	NOUN
ejpam-5161	98	22	6	6	NUM
ejpam-5161	98	23	.	.	PUNCT
ejpam-5161	99	1	[	[	X
ejpam-5161	99	2	3	3	NUM
ejpam-5161	99	3	,	,	PUNCT
ejpam-5161	99	4	29	29	NUM
ejpam-5161	99	5	]	]	PUNCT
ejpam-5161	99	6	let	let	VERB
ejpam-5161	99	7	σ	σ	X
ejpam-5161	99	8	=	=	PUNCT
ejpam-5161	99	9	{	{	PUNCT
ejpam-5161	99	10	σω	σω	NOUN
ejpam-5161	99	11	:	:	PUNCT
ejpam-5161	99	12	ω	ω	PROPN
ejpam-5161	99	13	∈	∈	PROPN
ejpam-5161	99	14	ω	ω	PROPN
ejpam-5161	99	15	}	}	PUNCT
ejpam-5161	99	16	be	be	AUX
ejpam-5161	99	17	a	a	DET
ejpam-5161	99	18	family	family	NOUN
ejpam-5161	99	19	of	of	ADP
ejpam-5161	99	20	(	(	PUNCT
ejpam-5161	99	21	crisp	crisp	ADJ
ejpam-5161	99	22	)	)	PUNCT
ejpam-5161	99	23	topologies	topology	NOUN
ejpam-5161	99	24	on	on	ADP
ejpam-5161	99	25	a	a	DET
ejpam-5161	99	26	set	set	NOUN
ejpam-5161	99	27	x	x	PUNCT
ejpam-5161	99	28	for	for	ADP
ejpam-5161	99	29	some	some	DET
ejpam-5161	99	30	index	index	NOUN
ejpam-5161	99	31	set	set	VERB
ejpam-5161	99	32	ω	ω	PROPN
ejpam-5161	99	33	.	.	PUNCT
ejpam-5161	100	1	then	then	ADV
ejpam-5161	100	2	following	follow	VERB
ejpam-5161	100	3	procedures	procedure	NOUN
ejpam-5161	100	4	produce	produce	VERB
ejpam-5161	100	5	different	different	ADJ
ejpam-5161	100	6	soft	soft	ADJ
ejpam-5161	100	7	topologies	topology	NOUN
ejpam-5161	100	8	on	on	ADP
ejpam-5161	100	9	x	x	NOUN
ejpam-5161	100	10	:	:	PUNCT
ejpam-5161	100	11	(	(	PUNCT
ejpam-5161	100	12	formula	formula	NOUN
ejpam-5161	100	13	1	1	NUM
ejpam-5161	100	14	)	)	PUNCT
ejpam-5161	100	15	t	t	PROPN
ejpam-5161	100	16	(	(	PUNCT
ejpam-5161	100	17	σ	σ	NOUN
ejpam-5161	100	18	)	)	PUNCT
ejpam-5161	100	19	=	=	PRON
ejpam-5161	100	20	{	{	PUNCT
ejpam-5161	100	21	{	{	PUNCT
ejpam-5161	100	22	(	(	PUNCT
ejpam-5161	100	23	ω	ω	PROPN
ejpam-5161	100	24	,	,	PUNCT
ejpam-5161	100	25	f	f	PROPN
ejpam-5161	100	26	(	(	PUNCT
ejpam-5161	100	27	ω	ω	NOUN
ejpam-5161	100	28	)	)	PUNCT
ejpam-5161	100	29	)	)	PUNCT
ejpam-5161	100	30	:	:	PUNCT
ejpam-5161	101	1	ω	ω	X
ejpam-5161	101	2	∈	∈	PROPN
ejpam-5161	101	3	ω	ω	PROPN
ejpam-5161	101	4	}	}	PUNCT
ejpam-5161	101	5	∈	∈	PROPN
ejpam-5161	101	6	sω(x	sω(x	NOUN
ejpam-5161	101	7	)	)	PUNCT
ejpam-5161	101	8	:	:	PUNCT
ejpam-5161	102	1	f	f	PROPN
ejpam-5161	102	2	(	(	PUNCT
ejpam-5161	102	3	ω	ω	NOUN
ejpam-5161	102	4	)	)	PUNCT
ejpam-5161	102	5	∈	∈	PROPN
ejpam-5161	102	6	σω	σω	NOUN
ejpam-5161	102	7	,	,	PUNCT
ejpam-5161	102	8	∀ω	∀ω	PUNCT
ejpam-5161	102	9	∈	∈	PROPN
ejpam-5161	102	10	ω	ω	PROPN
ejpam-5161	102	11	}	}	PUNCT
ejpam-5161	102	12	,	,	PUNCT
ejpam-5161	102	13	t	t	PROPN
ejpam-5161	102	14	(	(	PUNCT
ejpam-5161	102	15	σ	σ	NOUN
ejpam-5161	102	16	)	)	PUNCT
ejpam-5161	102	17	is	be	AUX
ejpam-5161	102	18	called	call	VERB
ejpam-5161	102	19	a	a	DET
ejpam-5161	102	20	soft	soft	ADJ
ejpam-5161	102	21	topology	topology	NOUN
ejpam-5161	102	22	generated	generate	VERB
ejpam-5161	102	23	by	by	ADP
ejpam-5161	102	24	σ	σ	PROPN
ejpam-5161	102	25	.	.	PUNCT
ejpam-5161	103	1	if	if	SCONJ
ejpam-5161	103	2	for	for	ADP
ejpam-5161	103	3	each	each	DET
ejpam-5161	103	4	ω	ω	NOUN
ejpam-5161	103	5	,	,	PUNCT
ejpam-5161	103	6	ω′	ω′	PROPN
ejpam-5161	103	7	∈	∈	PROPN
ejpam-5161	103	8	ω	ω	PROPN
ejpam-5161	103	9	,	,	PUNCT
ejpam-5161	103	10	σω	σω	ADJ
ejpam-5161	103	11	=	=	SYM
ejpam-5161	103	12	σω′	σω′	PROPN
ejpam-5161	103	13	=	=	SYM
ejpam-5161	103	14	σ	σ	PROPN
ejpam-5161	103	15	,	,	PUNCT
ejpam-5161	103	16	then	then	ADV
ejpam-5161	103	17	t	t	PROPN
ejpam-5161	103	18	(	(	PUNCT
ejpam-5161	103	19	σ	σ	PROPN
ejpam-5161	103	20	)	)	PUNCT
ejpam-5161	103	21	=	=	SYM
ejpam-5161	103	22	t	t	PROPN
ejpam-5161	103	23	(	(	PUNCT
ejpam-5161	103	24	σ	σ	PROPN
ejpam-5161	103	25	)	)	PUNCT
ejpam-5161	103	26	.	.	PUNCT
ejpam-5161	104	1	(	(	PUNCT
ejpam-5161	104	2	formula	formula	NOUN
ejpam-5161	104	3	2	2	NUM
ejpam-5161	104	4	)	)	PUNCT
ejpam-5161	104	5	t̂	t̂	NUM
ejpam-5161	104	6	(	(	PUNCT
ejpam-5161	104	7	σω	σω	NOUN
ejpam-5161	104	8	)	)	PUNCT
ejpam-5161	104	9	=	=	PRON
ejpam-5161	104	10	{	{	PUNCT
ejpam-5161	104	11	{	{	PUNCT
ejpam-5161	104	12	(	(	PUNCT
ejpam-5161	104	13	ω	ω	PROPN
ejpam-5161	104	14	,	,	PUNCT
ejpam-5161	104	15	f	f	PROPN
ejpam-5161	104	16	(	(	PUNCT
ejpam-5161	104	17	ω	ω	NOUN
ejpam-5161	104	18	)	)	PUNCT
ejpam-5161	104	19	)	)	PUNCT
ejpam-5161	104	20	:	:	PUNCT
ejpam-5161	105	1	ω	ω	X
ejpam-5161	105	2	∈	∈	PROPN
ejpam-5161	105	3	ω	ω	PROPN
ejpam-5161	105	4	}	}	PUNCT
ejpam-5161	105	5	∈	∈	PROPN
ejpam-5161	105	6	sω(x	sω(x	NOUN
ejpam-5161	105	7	)	)	PUNCT
ejpam-5161	105	8	:	:	PUNCT
ejpam-5161	106	1	f	f	PROPN
ejpam-5161	106	2	(	(	PUNCT
ejpam-5161	106	3	ω	ω	NOUN
ejpam-5161	106	4	)	)	PUNCT
ejpam-5161	106	5	=	=	SYM
ejpam-5161	106	6	f	f	PROPN
ejpam-5161	106	7	(	(	PUNCT
ejpam-5161	106	8	ω′	ω′	X
ejpam-5161	106	9	)	)	PUNCT
ejpam-5161	106	10	∈	∈	PROPN
ejpam-5161	106	11	σω,∀ω	σω,∀ω	PROPN
ejpam-5161	106	12	,	,	PUNCT
ejpam-5161	106	13	ω′	ω′	X
ejpam-5161	106	14	∈	∈	PROPN
ejpam-5161	106	15	ω	ω	PROPN
ejpam-5161	106	16	}	}	PUNCT
ejpam-5161	106	17	,	,	PUNCT
ejpam-5161	106	18	t̂	t̂	NUM
ejpam-5161	106	19	(	(	PUNCT
ejpam-5161	106	20	σω	σω	NOUN
ejpam-5161	106	21	)	)	PUNCT
ejpam-5161	106	22	is	be	AUX
ejpam-5161	106	23	called	call	VERB
ejpam-5161	106	24	a	a	DET
ejpam-5161	106	25	single	single	ADJ
ejpam-5161	106	26	set	set	VERB
ejpam-5161	106	27	soft	soft	ADJ
ejpam-5161	106	28	topology	topology	NOUN
ejpam-5161	106	29	generated	generate	VERB
ejpam-5161	106	30	by	by	ADP
ejpam-5161	106	31	σω	σω	PROPN
ejpam-5161	106	32	.	.	PUNCT
ejpam-5161	106	33	z.	z.	PROPN
ejpam-5161	106	34	a.	a.	PROPN
ejpam-5161	106	35	ameen	ameen	PROPN
ejpam-5161	106	36	et	et	PROPN
ejpam-5161	106	37	al	al	PROPN
ejpam-5161	106	38	.	.	PUNCT
ejpam-5161	106	39	/	/	SYM
ejpam-5161	106	40	eur	eur	PROPN
ejpam-5161	106	41	.	.	PUNCT
ejpam-5161	107	1	j.	j.	PROPN
ejpam-5161	107	2	pure	pure	PROPN
ejpam-5161	107	3	appl	appl	PROPN
ejpam-5161	107	4	.	.	PROPN
ejpam-5161	107	5	math	math	PROPN
ejpam-5161	107	6	,	,	PUNCT
ejpam-5161	107	7	17	17	NUM
ejpam-5161	107	8	(	(	PUNCT
ejpam-5161	107	9	2	2	NUM
ejpam-5161	107	10	)	)	PUNCT
ejpam-5161	107	11	(	(	PUNCT
ejpam-5161	107	12	2024	2024	NUM
ejpam-5161	107	13	)	)	PUNCT
ejpam-5161	107	14	,	,	PUNCT
ejpam-5161	107	15	1168	1168	NUM
ejpam-5161	107	16	-	-	SYM
ejpam-5161	107	17	1182	1182	NUM
ejpam-5161	107	18	1172	1172	NUM
ejpam-5161	107	19	definition	definition	NOUN
ejpam-5161	107	20	7	7	NUM
ejpam-5161	107	21	.	.	PUNCT
ejpam-5161	108	1	let	let	VERB
ejpam-5161	108	2	(	(	PUNCT
ejpam-5161	108	3	x	x	NOUN
ejpam-5161	108	4	,	,	PUNCT
ejpam-5161	108	5	σ	σ	PROPN
ejpam-5161	108	6	,	,	PUNCT
ejpam-5161	108	7	ω	ω	PROPN
ejpam-5161	108	8	)	)	PUNCT
ejpam-5161	108	9	be	be	VERB
ejpam-5161	108	10	a	a	DET
ejpam-5161	108	11	soft	soft	ADJ
ejpam-5161	108	12	topological	topological	ADJ
ejpam-5161	108	13	space	space	NOUN
ejpam-5161	108	14	.	.	PUNCT
ejpam-5161	109	1	if	if	SCONJ
ejpam-5161	109	2	σ	σ	NUM
ejpam-5161	109	3	=	=	PUNCT
ejpam-5161	109	4	{	{	PUNCT
ejpam-5161	109	5	σω	σω	NOUN
ejpam-5161	109	6	:	:	PUNCT
ejpam-5161	109	7	ω	ω	PROPN
ejpam-5161	109	8	∈	∈	PROPN
ejpam-5161	109	9	ω	ω	PROPN
ejpam-5161	109	10	}	}	PUNCT
ejpam-5161	109	11	is	be	AUX
ejpam-5161	109	12	the	the	DET
ejpam-5161	109	13	family	family	NOUN
ejpam-5161	109	14	of	of	ADP
ejpam-5161	109	15	all	all	DET
ejpam-5161	109	16	crisp	crisp	ADJ
ejpam-5161	109	17	topologies	topology	NOUN
ejpam-5161	109	18	from	from	ADP
ejpam-5161	109	19	σ	σ	PROPN
ejpam-5161	109	20	,	,	PUNCT
ejpam-5161	109	21	then	then	ADV
ejpam-5161	109	22	t	t	PROPN
ejpam-5161	109	23	(	(	PUNCT
ejpam-5161	109	24	σ	σ	PROPN
ejpam-5161	109	25	)	)	PUNCT
ejpam-5161	109	26	is	be	AUX
ejpam-5161	109	27	called	call	VERB
ejpam-5161	109	28	the	the	DET
ejpam-5161	109	29	soft	soft	ADJ
ejpam-5161	109	30	topology	topology	NOUN
ejpam-5161	109	31	associated	associate	VERB
ejpam-5161	109	32	with	with	ADP
ejpam-5161	109	33	σ	σ	PROPN
ejpam-5161	109	34	.	.	PROPN
ejpam-5161	109	35	note	note	NOUN
ejpam-5161	109	36	that	that	SCONJ
ejpam-5161	109	37	t	t	PROPN
ejpam-5161	109	38	(	(	PUNCT
ejpam-5161	109	39	σ	σ	PROPN
ejpam-5161	109	40	)	)	PUNCT
ejpam-5161	109	41	is	be	AUX
ejpam-5161	109	42	called	call	VERB
ejpam-5161	109	43	an	an	DET
ejpam-5161	109	44	extended	extended	ADJ
ejpam-5161	109	45	soft	soft	ADJ
ejpam-5161	109	46	topology	topology	NOUN
ejpam-5161	109	47	in	in	ADP
ejpam-5161	109	48	[	[	X
ejpam-5161	109	49	25	25	NUM
ejpam-5161	109	50	]	]	PUNCT
ejpam-5161	109	51	.	.	PUNCT
ejpam-5161	110	1	lemma	lemma	PROPN
ejpam-5161	110	2	4	4	X
ejpam-5161	110	3	.	.	PUNCT
ejpam-5161	111	1	let	let	VERB
ejpam-5161	111	2	σ	σ	NOUN
ejpam-5161	111	3	=	=	PUNCT
ejpam-5161	111	4	{	{	PUNCT
ejpam-5161	111	5	σω	σω	NOUN
ejpam-5161	111	6	:	:	PUNCT
ejpam-5161	111	7	ω	ω	PROPN
ejpam-5161	111	8	∈	∈	PROPN
ejpam-5161	111	9	ω	ω	PROPN
ejpam-5161	111	10	}	}	PUNCT
ejpam-5161	111	11	be	be	VERB
ejpam-5161	111	12	the	the	DET
ejpam-5161	111	13	family	family	NOUN
ejpam-5161	111	14	of	of	ADP
ejpam-5161	111	15	all	all	DET
ejpam-5161	111	16	crisp	crisp	ADJ
ejpam-5161	111	17	topologies	topology	NOUN
ejpam-5161	111	18	from	from	ADP
ejpam-5161	111	19	(	(	PUNCT
ejpam-5161	111	20	x	x	NOUN
ejpam-5161	111	21	,	,	PUNCT
ejpam-5161	111	22	σ	σ	PROPN
ejpam-5161	111	23	,	,	PUNCT
ejpam-5161	111	24	ω	ω	PROPN
ejpam-5161	111	25	)	)	PUNCT
ejpam-5161	111	26	.	.	PUNCT
ejpam-5161	112	1	then	then	ADV
ejpam-5161	112	2	σ⊆̃t	σ⊆̃t	PROPN
ejpam-5161	112	3	(	(	PUNCT
ejpam-5161	112	4	σ	σ	PROPN
ejpam-5161	112	5	)	)	PUNCT
ejpam-5161	112	6	.	.	PUNCT
ejpam-5161	113	1	proof	proof	NOUN
ejpam-5161	113	2	.	.	PUNCT
ejpam-5161	114	1	it	it	PRON
ejpam-5161	114	2	can	can	AUX
ejpam-5161	114	3	be	be	AUX
ejpam-5161	114	4	concluded	conclude	VERB
ejpam-5161	114	5	from	from	ADP
ejpam-5161	114	6	the	the	DET
ejpam-5161	114	7	definition	definition	NOUN
ejpam-5161	114	8	of	of	ADP
ejpam-5161	114	9	soft	soft	ADJ
ejpam-5161	114	10	sets	set	NOUN
ejpam-5161	114	11	and	and	CCONJ
ejpam-5161	114	12	the	the	DET
ejpam-5161	114	13	soft	soft	ADJ
ejpam-5161	114	14	topology	topology	NOUN
ejpam-5161	114	15	generated	generate	VERB
ejpam-5161	114	16	by	by	ADP
ejpam-5161	114	17	σ	σ	PROPN
ejpam-5161	114	18	.	.	PUNCT
ejpam-5161	115	1	lemma	lemma	PROPN
ejpam-5161	115	2	5	5	X
ejpam-5161	115	3	.	.	PUNCT
ejpam-5161	116	1	let	let	VERB
ejpam-5161	116	2	β̄	β̄	NOUN
ejpam-5161	117	1	=	=	PRON
ejpam-5161	117	2	{	{	PUNCT
ejpam-5161	117	3	βω	βω	NOUN
ejpam-5161	117	4	:	:	PUNCT
ejpam-5161	117	5	ω	ω	PROPN
ejpam-5161	117	6	∈	∈	PROPN
ejpam-5161	117	7	ω	ω	PROPN
ejpam-5161	117	8	}	}	PUNCT
ejpam-5161	117	9	be	be	AUX
ejpam-5161	117	10	a	a	DET
ejpam-5161	117	11	family	family	NOUN
ejpam-5161	117	12	of	of	ADP
ejpam-5161	117	13	bases	basis	NOUN
ejpam-5161	117	14	for	for	ADP
ejpam-5161	117	15	the	the	DET
ejpam-5161	117	16	topologies	topology	NOUN
ejpam-5161	117	17	σω	σω	VERB
ejpam-5161	117	18	on	on	ADP
ejpam-5161	117	19	x.	x.	NOUN
ejpam-5161	117	20	then	then	ADV
ejpam-5161	117	21	b(β̄	b(β̄	VERB
ejpam-5161	117	22	)	)	PUNCT
ejpam-5161	117	23	=	=	PRON
ejpam-5161	117	24	{	{	PUNCT
ejpam-5161	117	25	{	{	PUNCT
ejpam-5161	117	26	(	(	PUNCT
ejpam-5161	117	27	ω	ω	PROPN
ejpam-5161	117	28	,	,	PUNCT
ejpam-5161	117	29	f	f	PROPN
ejpam-5161	117	30	(	(	PUNCT
ejpam-5161	117	31	ω	ω	NOUN
ejpam-5161	117	32	)	)	PUNCT
ejpam-5161	117	33	)	)	PUNCT
ejpam-5161	117	34	:	:	PUNCT
ejpam-5161	118	1	ω	ω	X
ejpam-5161	118	2	∈	∈	PROPN
ejpam-5161	118	3	ω	ω	PROPN
ejpam-5161	118	4	}	}	PUNCT
ejpam-5161	118	5	∈	∈	PROPN
ejpam-5161	118	6	sω(x	sω(x	NOUN
ejpam-5161	118	7	)	)	PUNCT
ejpam-5161	118	8	:	:	PUNCT
ejpam-5161	119	1	f	f	PROPN
ejpam-5161	119	2	(	(	PUNCT
ejpam-5161	119	3	ω	ω	NOUN
ejpam-5161	119	4	)	)	PUNCT
ejpam-5161	119	5	∈	∈	PROPN
ejpam-5161	119	6	βω	βω	NOUN
ejpam-5161	119	7	∪	∪	PROPN
ejpam-5161	119	8	{	{	PUNCT
ejpam-5161	119	9	∅},∀ω	∅},∀ω	PROPN
ejpam-5161	119	10	∈	∈	PROPN
ejpam-5161	119	11	ω	ω	PROPN
ejpam-5161	119	12	}	}	PUNCT
ejpam-5161	119	13	is	be	AUX
ejpam-5161	119	14	a	a	DET
ejpam-5161	119	15	base	base	NOUN
ejpam-5161	119	16	for	for	ADP
ejpam-5161	119	17	a	a	DET
ejpam-5161	119	18	soft	soft	ADJ
ejpam-5161	119	19	topology	topology	NOUN
ejpam-5161	119	20	on	on	ADP
ejpam-5161	119	21	x	x	PUNCT
ejpam-5161	119	22	and	and	CCONJ
ejpam-5161	119	23	t	t	PROPN
ejpam-5161	119	24	(	(	PUNCT
ejpam-5161	119	25	σ	σ	PROPN
ejpam-5161	119	26	)	)	PUNCT
ejpam-5161	119	27	=	=	SYM
ejpam-5161	119	28	t	t	PROPN
ejpam-5161	119	29	(	(	PUNCT
ejpam-5161	119	30	b(β̄	b(β̄	PROPN
ejpam-5161	119	31	)	)	PUNCT
ejpam-5161	119	32	)	)	PUNCT
ejpam-5161	119	33	.	.	PUNCT
ejpam-5161	120	1	proof	proof	NOUN
ejpam-5161	120	2	.	.	PUNCT
ejpam-5161	121	1	by	by	ADP
ejpam-5161	121	2	using	use	VERB
ejpam-5161	121	3	corollary	corollary	ADJ
ejpam-5161	121	4	3	3	NUM
ejpam-5161	121	5	in	in	ADP
ejpam-5161	121	6	[	[	X
ejpam-5161	121	7	3	3	NUM
ejpam-5161	121	8	]	]	PUNCT
ejpam-5161	121	9	and	and	CCONJ
ejpam-5161	121	10	simple	simple	ADJ
ejpam-5161	121	11	modifications	modification	NOUN
ejpam-5161	121	12	to	to	ADP
ejpam-5161	121	13	the	the	DET
ejpam-5161	121	14	proof	proof	NOUN
ejpam-5161	121	15	of	of	ADP
ejpam-5161	121	16	theorem	theorem	NOUN
ejpam-5161	121	17	3	3	NUM
ejpam-5161	121	18	in	in	ADP
ejpam-5161	121	19	[	[	X
ejpam-5161	121	20	3	3	NUM
ejpam-5161	121	21	]	]	PUNCT
ejpam-5161	121	22	,	,	PUNCT
ejpam-5161	121	23	we	we	PRON
ejpam-5161	121	24	can	can	AUX
ejpam-5161	121	25	conclude	conclude	VERB
ejpam-5161	121	26	the	the	DET
ejpam-5161	121	27	proof	proof	NOUN
ejpam-5161	121	28	.	.	PUNCT
ejpam-5161	122	1	the	the	DET
ejpam-5161	122	2	following	following	ADJ
ejpam-5161	122	3	result	result	NOUN
ejpam-5161	122	4	is	be	AUX
ejpam-5161	122	5	a	a	DET
ejpam-5161	122	6	straightforward	straightforward	ADJ
ejpam-5161	122	7	generalization	generalization	NOUN
ejpam-5161	122	8	of	of	ADP
ejpam-5161	122	9	lemma	lemma	PROPN
ejpam-5161	122	10	2	2	NUM
ejpam-5161	122	11	,	,	PUNCT
ejpam-5161	122	12	so	so	ADV
ejpam-5161	122	13	the	the	DET
ejpam-5161	122	14	proof	proof	NOUN
ejpam-5161	122	15	is	be	AUX
ejpam-5161	122	16	omitted	omit	VERB
ejpam-5161	122	17	.	.	PUNCT
ejpam-5161	123	1	lemma	lemma	PROPN
ejpam-5161	123	2	6	6	NUM
ejpam-5161	123	3	.	.	PUNCT
ejpam-5161	124	1	let	let	AUX
ejpam-5161	124	2	{	{	PUNCT
ejpam-5161	124	3	σω	σω	VERB
ejpam-5161	124	4	:	:	PUNCT
ejpam-5161	124	5	ω	ω	PROPN
ejpam-5161	124	6	∈	∈	PROPN
ejpam-5161	124	7	ω	ω	PROPN
ejpam-5161	124	8	}	}	PUNCT
ejpam-5161	124	9	be	be	AUX
ejpam-5161	124	10	a	a	DET
ejpam-5161	124	11	family	family	NOUN
ejpam-5161	124	12	of	of	ADP
ejpam-5161	124	13	soft	soft	ADJ
ejpam-5161	124	14	topologies	topology	NOUN
ejpam-5161	124	15	on	on	ADP
ejpam-5161	124	16	x.	x.	NOUN
ejpam-5161	124	17	the	the	DET
ejpam-5161	124	18	resulting	result	VERB
ejpam-5161	124	19	soft	soft	ADJ
ejpam-5161	124	20	topology	topology	NOUN
ejpam-5161	124	21	t	t	NOUN
ejpam-5161	124	22	(	(	PUNCT
ejpam-5161	124	23	⋃̃	⋃̃	PROPN
ejpam-5161	124	24	ω∈ωσω	ω∈ωσω	PROPN
ejpam-5161	124	25	)	)	PUNCT
ejpam-5161	124	26	is	be	AUX
ejpam-5161	124	27	identical	identical	ADJ
ejpam-5161	124	28	to	to	ADP
ejpam-5161	124	29	the	the	DET
ejpam-5161	124	30	soft	soft	ADJ
ejpam-5161	124	31	topology	topology	NOUN
ejpam-5161	124	32	t	t	NOUN
ejpam-5161	124	33	(	(	PUNCT
ejpam-5161	124	34	f	f	X
ejpam-5161	124	35	)	)	PUNCT
ejpam-5161	124	36	generated	generate	VERB
ejpam-5161	124	37	by	by	ADP
ejpam-5161	124	38	f	f	PROPN
ejpam-5161	124	39	=	=	PROPN
ejpam-5161	124	40	{	{	PUNCT
ejpam-5161	124	41	⋂̃n	⋂̃n	ADJ
ejpam-5161	124	42	ωi=1(fωi	ωi=1(fωi	NOUN
ejpam-5161	124	43	,	,	PUNCT
ejpam-5161	124	44	ω	ω	PROPN
ejpam-5161	124	45	)	)	PUNCT
ejpam-5161	124	46	:	:	PUNCT
ejpam-5161	124	47	(	(	PUNCT
ejpam-5161	124	48	fωi	fωi	NOUN
ejpam-5161	124	49	,	,	PUNCT
ejpam-5161	124	50	ω	ω	NUM
ejpam-5161	124	51	)	)	PUNCT
ejpam-5161	124	52	∈	∈	PROPN
ejpam-5161	124	53	⋃̃	⋃̃	PROPN
ejpam-5161	124	54	ωi∈ωσωi	ωi∈ωσωi	NOUN
ejpam-5161	124	55	}	}	PUNCT
ejpam-5161	124	56	.	.	PUNCT
ejpam-5161	125	1	lemma	lemma	PROPN
ejpam-5161	125	2	7	7	X
ejpam-5161	125	3	.	.	PUNCT
ejpam-5161	126	1	let	let	VERB
ejpam-5161	126	2	σ	σ	NOUN
ejpam-5161	126	3	=	=	PUNCT
ejpam-5161	126	4	{	{	PUNCT
ejpam-5161	126	5	σω	σω	NOUN
ejpam-5161	126	6	:	:	PUNCT
ejpam-5161	126	7	ω	ω	PROPN
ejpam-5161	126	8	∈	∈	PROPN
ejpam-5161	126	9	ω	ω	PROPN
ejpam-5161	126	10	}	}	PUNCT
ejpam-5161	126	11	be	be	AUX
ejpam-5161	126	12	a	a	DET
ejpam-5161	126	13	family	family	NOUN
ejpam-5161	126	14	of	of	ADP
ejpam-5161	126	15	crisp	crisp	ADJ
ejpam-5161	126	16	topologies	topology	NOUN
ejpam-5161	126	17	on	on	ADP
ejpam-5161	126	18	x.	x.	NOUN
ejpam-5161	127	1	then	then	ADV
ejpam-5161	127	2	t	t	PROPN
ejpam-5161	127	3	(	(	PUNCT
ejpam-5161	127	4	⋃̃	⋃̃	PROPN
ejpam-5161	127	5	ω∈ω	ω∈ω	NUM
ejpam-5161	127	6	t̂	t̂	NUM
ejpam-5161	127	7	(	(	PUNCT
ejpam-5161	127	8	σω	σω	NOUN
ejpam-5161	127	9	)	)	PUNCT
ejpam-5161	127	10	)	)	PUNCT
ejpam-5161	128	1	=	=	SYM
ejpam-5161	128	2	t̂	t̂	PROPN
ejpam-5161	128	3	(	(	PUNCT
ejpam-5161	128	4	t	t	PROPN
ejpam-5161	128	5	(	(	PUNCT
ejpam-5161	128	6	⋃	⋃	PROPN
ejpam-5161	128	7	ω∈ω	ω∈ω	X
ejpam-5161	128	8	σω	σω	NOUN
ejpam-5161	128	9	)	)	PUNCT
ejpam-5161	128	10	)	)	PUNCT
ejpam-5161	128	11	.	.	PUNCT
ejpam-5161	129	1	proof	proof	NOUN
ejpam-5161	129	2	.	.	PUNCT
ejpam-5161	130	1	the	the	DET
ejpam-5161	130	2	lemma	lemma	PROPN
ejpam-5161	130	3	5	5	NUM
ejpam-5161	130	4	reduces	reduce	VERB
ejpam-5161	130	5	the	the	DET
ejpam-5161	130	6	task	task	NOUN
ejpam-5161	130	7	of	of	ADP
ejpam-5161	130	8	working	work	VERB
ejpam-5161	130	9	with	with	ADP
ejpam-5161	130	10	basic	basic	ADJ
ejpam-5161	130	11	soft	soft	ADJ
ejpam-5161	130	12	open	open	ADJ
ejpam-5161	130	13	sets	set	NOUN
ejpam-5161	130	14	rather	rather	ADV
ejpam-5161	130	15	than	than	ADP
ejpam-5161	130	16	soft	soft	ADJ
ejpam-5161	130	17	open	open	ADJ
ejpam-5161	130	18	sets	set	NOUN
ejpam-5161	130	19	.	.	PUNCT
ejpam-5161	131	1	let	let	VERB
ejpam-5161	131	2	(	(	PUNCT
ejpam-5161	131	3	b0,ω	b0,ω	SYM
ejpam-5161	131	4	)	)	PUNCT
ejpam-5161	131	5	∈	∈	PROPN
ejpam-5161	131	6	t	t	PROPN
ejpam-5161	131	7	(	(	PUNCT
ejpam-5161	131	8	⋃̃	⋃̃	PROPN
ejpam-5161	131	9	ω∈ωt̂	ω∈ωt̂	NUM
ejpam-5161	131	10	(	(	PUNCT
ejpam-5161	131	11	σω	σω	NOUN
ejpam-5161	131	12	)	)	PUNCT
ejpam-5161	131	13	)	)	PUNCT
ejpam-5161	131	14	.	.	PUNCT
ejpam-5161	132	1	then	then	ADV
ejpam-5161	132	2	(	(	PUNCT
ejpam-5161	132	3	b0,ω	b0,ω	X
ejpam-5161	132	4	)	)	PUNCT
ejpam-5161	132	5	=	=	PUNCT
ejpam-5161	132	6	⋂̃n	⋂̃n	ADJ
ejpam-5161	132	7	i=1(bi	i=1(bi	PROPN
ejpam-5161	132	8	,	,	PUNCT
ejpam-5161	132	9	ω	ω	NOUN
ejpam-5161	132	10	)	)	PUNCT
ejpam-5161	132	11	for	for	ADP
ejpam-5161	132	12	(	(	PUNCT
ejpam-5161	132	13	bi	bi	PROPN
ejpam-5161	132	14	,	,	PUNCT
ejpam-5161	132	15	ω	ω	NOUN
ejpam-5161	132	16	)	)	PUNCT
ejpam-5161	132	17	∈⋃̃	∈⋃̃	NUM
ejpam-5161	132	18	t̂	t̂	NUM
ejpam-5161	132	19	(	(	PUNCT
ejpam-5161	132	20	σω	σω	NOUN
ejpam-5161	132	21	)	)	PUNCT
ejpam-5161	132	22	,	,	PUNCT
ejpam-5161	132	23	and	and	CCONJ
ejpam-5161	132	24	so	so	ADV
ejpam-5161	132	25	(	(	PUNCT
ejpam-5161	132	26	b0,ω	b0,ω	PROPN
ejpam-5161	132	27	)	)	PUNCT
ejpam-5161	132	28	=	=	PUNCT
ejpam-5161	132	29	⋂̃n	⋂̃n	ADJ
ejpam-5161	132	30	i=1(bi	i=1(bi	PROPN
ejpam-5161	132	31	,	,	PUNCT
ejpam-5161	132	32	ω	ω	NOUN
ejpam-5161	132	33	)	)	PUNCT
ejpam-5161	132	34	such	such	ADJ
ejpam-5161	132	35	that	that	SCONJ
ejpam-5161	132	36	(	(	PUNCT
ejpam-5161	132	37	bi	bi	NOUN
ejpam-5161	132	38	,	,	PUNCT
ejpam-5161	132	39	ω	ω	NOUN
ejpam-5161	132	40	)	)	PUNCT
ejpam-5161	132	41	∈	∈	PROPN
ejpam-5161	132	42	t̂	t̂	NUM
ejpam-5161	132	43	(	(	PUNCT
ejpam-5161	132	44	σω	σω	NOUN
ejpam-5161	132	45	)	)	PUNCT
ejpam-5161	132	46	for	for	ADP
ejpam-5161	132	47	some	some	DET
ejpam-5161	132	48	ω	ω	NUM
ejpam-5161	132	49	∈	∈	PROPN
ejpam-5161	132	50	ω	ω	PROPN
ejpam-5161	132	51	.	.	PUNCT
ejpam-5161	133	1	by	by	ADP
ejpam-5161	133	2	formula	formula	NOUN
ejpam-5161	133	3	2	2	NUM
ejpam-5161	133	4	,	,	PUNCT
ejpam-5161	133	5	one	one	PRON
ejpam-5161	133	6	can	can	AUX
ejpam-5161	133	7	detach	detach	VERB
ejpam-5161	133	8	ω	ω	PROPN
ejpam-5161	133	9	from	from	ADP
ejpam-5161	133	10	(	(	PUNCT
ejpam-5161	133	11	bi	bi	PROPN
ejpam-5161	133	12	,	,	PUNCT
ejpam-5161	133	13	ω	ω	NOUN
ejpam-5161	133	14	)	)	PUNCT
ejpam-5161	133	15	for	for	ADP
ejpam-5161	133	16	i	i	PROPN
ejpam-5161	133	17	=	=	SYM
ejpam-5161	133	18	0	0	NUM
ejpam-5161	133	19	,	,	PUNCT
ejpam-5161	133	20	1	1	NUM
ejpam-5161	133	21	,	,	PUNCT
ejpam-5161	133	22	·	·	PUNCT
ejpam-5161	133	23	·	·	PUNCT
ejpam-5161	133	24	·	·	PUNCT
ejpam-5161	133	25	,	,	PUNCT
ejpam-5161	133	26	n	n	CCONJ
ejpam-5161	133	27	,	,	PUNCT
ejpam-5161	133	28	and	and	CCONJ
ejpam-5161	133	29	get	get	VERB
ejpam-5161	133	30	b0	b0	NOUN
ejpam-5161	133	31	=	=	PUNCT
ejpam-5161	133	32	⋂n	⋂n	PROPN
ejpam-5161	133	33	i=1bi	i=1bi	ADJ
ejpam-5161	133	34	,	,	PUNCT
ejpam-5161	133	35	where	where	SCONJ
ejpam-5161	133	36	bi	bi	PROPN
ejpam-5161	133	37	∈	∈	PROPN
ejpam-5161	133	38	σω	σω	VERB
ejpam-5161	133	39	for	for	ADP
ejpam-5161	133	40	some	some	DET
ejpam-5161	133	41	ω	ω	NUM
ejpam-5161	133	42	∈	∈	PROPN
ejpam-5161	133	43	ω	ω	PROPN
ejpam-5161	133	44	.	.	PUNCT
ejpam-5161	134	1	this	this	PRON
ejpam-5161	134	2	implies	imply	VERB
ejpam-5161	134	3	that	that	SCONJ
ejpam-5161	134	4	b0	b0	NOUN
ejpam-5161	134	5	=	=	PUNCT
ejpam-5161	134	6	⋂n	⋂n	NOUN
ejpam-5161	134	7	i=1bi	i=1bi	NUM
ejpam-5161	134	8	for	for	ADP
ejpam-5161	134	9	bi	bi	PROPN
ejpam-5161	134	10	∈	∈	PROPN
ejpam-5161	134	11	⋃	⋃	PROPN
ejpam-5161	134	12	σω	σω	NOUN
ejpam-5161	134	13	.	.	PUNCT
ejpam-5161	135	1	therefore	therefore	ADV
ejpam-5161	135	2	,	,	PUNCT
ejpam-5161	135	3	by	by	ADP
ejpam-5161	135	4	formula	formula	NOUN
ejpam-5161	135	5	2	2	NUM
ejpam-5161	135	6	,	,	PUNCT
ejpam-5161	135	7	(	(	PUNCT
ejpam-5161	135	8	b0,ω	b0,ω	PROPN
ejpam-5161	135	9	)	)	PUNCT
ejpam-5161	135	10	∈	∈	NOUN
ejpam-5161	135	11	t̂	t̂	NUM
ejpam-5161	135	12	(	(	PUNCT
ejpam-5161	135	13	t	t	PROPN
ejpam-5161	135	14	(	(	PUNCT
ejpam-5161	135	15	⋃̃	⋃̃	PROPN
ejpam-5161	135	16	σω	σω	NUM
ejpam-5161	135	17	)	)	PUNCT
ejpam-5161	135	18	)	)	PUNCT
ejpam-5161	135	19	.	.	PUNCT
ejpam-5161	136	1	the	the	DET
ejpam-5161	136	2	reverse	reverse	NOUN
ejpam-5161	136	3	of	of	ADP
ejpam-5161	136	4	the	the	DET
ejpam-5161	136	5	inclusion	inclusion	NOUN
ejpam-5161	136	6	can	can	AUX
ejpam-5161	136	7	be	be	AUX
ejpam-5161	136	8	proved	prove	VERB
ejpam-5161	136	9	by	by	ADP
ejpam-5161	136	10	a	a	DET
ejpam-5161	136	11	similar	similar	ADJ
ejpam-5161	136	12	technique	technique	NOUN
ejpam-5161	136	13	.	.	PUNCT
ejpam-5161	137	1	the	the	DET
ejpam-5161	137	2	following	follow	VERB
ejpam-5161	137	3	example	example	NOUN
ejpam-5161	137	4	shows	show	VERB
ejpam-5161	137	5	how	how	SCONJ
ejpam-5161	137	6	the	the	DET
ejpam-5161	137	7	techniques	technique	NOUN
ejpam-5161	137	8	in	in	ADP
ejpam-5161	137	9	definition	definition	NOUN
ejpam-5161	137	10	1	1	NUM
ejpam-5161	137	11	and	and	CCONJ
ejpam-5161	137	12	the	the	DET
ejpam-5161	137	13	relations	relation	NOUN
ejpam-5161	137	14	in	in	ADP
ejpam-5161	137	15	lemmas	lemmas	PROPN
ejpam-5161	137	16	4−7	4−7	PROPN
ejpam-5161	137	17	can	can	AUX
ejpam-5161	137	18	be	be	AUX
ejpam-5161	137	19	used	use	VERB
ejpam-5161	137	20	in	in	ADP
ejpam-5161	137	21	practice	practice	NOUN
ejpam-5161	137	22	:	:	PUNCT
ejpam-5161	137	23	example	example	NOUN
ejpam-5161	138	1	1	1	X
ejpam-5161	138	2	.	.	PUNCT
ejpam-5161	139	1	let	let	VERB
ejpam-5161	139	2	x	x	PUNCT
ejpam-5161	139	3	=	=	PRON
ejpam-5161	139	4	{	{	PUNCT
ejpam-5161	139	5	x1	x1	PROPN
ejpam-5161	139	6	,	,	PUNCT
ejpam-5161	139	7	x2	x2	PROPN
ejpam-5161	139	8	,	,	PUNCT
ejpam-5161	139	9	x3	x3	ADJ
ejpam-5161	139	10	}	}	PUNCT
ejpam-5161	139	11	,	,	PUNCT
ejpam-5161	139	12	ω	ω	PROPN
ejpam-5161	139	13	=	=	SYM
ejpam-5161	139	14	{	{	PUNCT
ejpam-5161	139	15	ω1	ω1	PROPN
ejpam-5161	139	16	,	,	PUNCT
ejpam-5161	139	17	ω2	ω2	ADJ
ejpam-5161	139	18	}	}	PUNCT
ejpam-5161	139	19	.	.	PUNCT
ejpam-5161	140	1	consider	consider	VERB
ejpam-5161	140	2	the	the	DET
ejpam-5161	140	3	soft	soft	ADJ
ejpam-5161	140	4	topology	topology	NOUN
ejpam-5161	140	5	on	on	ADP
ejpam-5161	140	6	x	x	PROPN
ejpam-5161	140	7	,	,	PUNCT
ejpam-5161	140	8	σ	σ	X
ejpam-5161	140	9	=	=	SYM
ejpam-5161	140	10	{	{	PUNCT
ejpam-5161	140	11	φ̃	φ̃	PROPN
ejpam-5161	140	12	,	,	PUNCT
ejpam-5161	140	13	(	(	PUNCT
ejpam-5161	140	14	f1,ω	f1,ω	PROPN
ejpam-5161	140	15	)	)	PUNCT
ejpam-5161	140	16	,	,	PUNCT
ejpam-5161	140	17	(	(	PUNCT
ejpam-5161	140	18	f2,ω	f2,ω	PROPN
ejpam-5161	140	19	)	)	PUNCT
ejpam-5161	140	20	,	,	PUNCT
ejpam-5161	140	21	(	(	PUNCT
ejpam-5161	140	22	f3,ω	f3,ω	PROPN
ejpam-5161	140	23	)	)	PUNCT
ejpam-5161	140	24	,	,	PUNCT
ejpam-5161	140	25	(	(	PUNCT
ejpam-5161	140	26	f4,ω	f4,ω	PROPN
ejpam-5161	140	27	)	)	PUNCT
ejpam-5161	140	28	,	,	PUNCT
ejpam-5161	140	29	x̃	x̃	PROPN
ejpam-5161	140	30	}	}	PUNCT
ejpam-5161	140	31	,	,	PUNCT
ejpam-5161	140	32	where	where	SCONJ
ejpam-5161	140	33	(	(	PUNCT
ejpam-5161	140	34	f1,ω	f1,ω	PROPN
ejpam-5161	140	35	)	)	PUNCT
ejpam-5161	140	36	=	=	PRON
ejpam-5161	141	1	{	{	PUNCT
ejpam-5161	141	2	(	(	PUNCT
ejpam-5161	141	3	ω1	ω1	PROPN
ejpam-5161	141	4	,	,	PUNCT
ejpam-5161	141	5	{	{	PUNCT
ejpam-5161	141	6	x1	x1	ADJ
ejpam-5161	141	7	}	}	PUNCT
ejpam-5161	141	8	)	)	PUNCT
ejpam-5161	141	9	,	,	PUNCT
ejpam-5161	141	10	(	(	PUNCT
ejpam-5161	141	11	ω2	ω2	ADJ
ejpam-5161	141	12	,	,	PUNCT
ejpam-5161	141	13	∅	∅	NOUN
ejpam-5161	141	14	)	)	PUNCT
ejpam-5161	141	15	}	}	PUNCT
ejpam-5161	141	16	,	,	PUNCT
ejpam-5161	141	17	z.	z.	PROPN
ejpam-5161	141	18	a.	a.	PROPN
ejpam-5161	141	19	ameen	ameen	PROPN
ejpam-5161	141	20	et	et	PROPN
ejpam-5161	141	21	al	al	PROPN
ejpam-5161	141	22	.	.	PUNCT
ejpam-5161	141	23	/	/	SYM
ejpam-5161	141	24	eur	eur	PROPN
ejpam-5161	141	25	.	.	PUNCT
ejpam-5161	142	1	j.	j.	PROPN
ejpam-5161	142	2	pure	pure	PROPN
ejpam-5161	142	3	appl	appl	PROPN
ejpam-5161	142	4	.	.	PROPN
ejpam-5161	142	5	math	math	PROPN
ejpam-5161	142	6	,	,	PUNCT
ejpam-5161	142	7	17	17	NUM
ejpam-5161	142	8	(	(	PUNCT
ejpam-5161	142	9	2	2	NUM
ejpam-5161	142	10	)	)	PUNCT
ejpam-5161	142	11	(	(	PUNCT
ejpam-5161	142	12	2024	2024	NUM
ejpam-5161	142	13	)	)	PUNCT
ejpam-5161	142	14	,	,	PUNCT
ejpam-5161	142	15	1168	1168	NUM
ejpam-5161	142	16	-	-	SYM
ejpam-5161	142	17	1182	1182	NUM
ejpam-5161	142	18	1173	1173	NUM
ejpam-5161	142	19	(	(	PUNCT
ejpam-5161	142	20	f2,ω	f2,ω	PROPN
ejpam-5161	142	21	)	)	PUNCT
ejpam-5161	142	22	=	=	SYM
ejpam-5161	142	23	{	{	PUNCT
ejpam-5161	142	24	(	(	PUNCT
ejpam-5161	142	25	ω1	ω1	PROPN
ejpam-5161	142	26	,	,	PUNCT
ejpam-5161	142	27	{	{	PUNCT
ejpam-5161	142	28	x1	x1	PROPN
ejpam-5161	142	29	,	,	PUNCT
ejpam-5161	142	30	x2	x2	PROPN
ejpam-5161	142	31	}	}	PUNCT
ejpam-5161	142	32	)	)	PUNCT
ejpam-5161	142	33	,	,	PUNCT
ejpam-5161	142	34	(	(	PUNCT
ejpam-5161	142	35	ω2	ω2	ADJ
ejpam-5161	142	36	,	,	PUNCT
ejpam-5161	142	37	x	x	NOUN
ejpam-5161	142	38	)	)	PUNCT
ejpam-5161	142	39	}	}	PUNCT
ejpam-5161	142	40	,	,	PUNCT
ejpam-5161	142	41	(	(	PUNCT
ejpam-5161	142	42	f3,ω	f3,ω	PROPN
ejpam-5161	142	43	)	)	PUNCT
ejpam-5161	142	44	=	=	SYM
ejpam-5161	142	45	{	{	PUNCT
ejpam-5161	142	46	(	(	PUNCT
ejpam-5161	142	47	ω1	ω1	PROPN
ejpam-5161	142	48	,	,	PUNCT
ejpam-5161	142	49	∅	∅	NOUN
ejpam-5161	142	50	)	)	PUNCT
ejpam-5161	142	51	,	,	PUNCT
ejpam-5161	142	52	(	(	PUNCT
ejpam-5161	142	53	ω2	ω2	ADV
ejpam-5161	142	54	,	,	PUNCT
ejpam-5161	142	55	{	{	PUNCT
ejpam-5161	142	56	x3	x3	ADJ
ejpam-5161	142	57	}	}	PUNCT
ejpam-5161	142	58	)	)	PUNCT
ejpam-5161	142	59	}	}	PUNCT
ejpam-5161	142	60	,	,	PUNCT
ejpam-5161	142	61	and	and	CCONJ
ejpam-5161	142	62	(	(	PUNCT
ejpam-5161	142	63	f4,ω	f4,ω	PROPN
ejpam-5161	142	64	)	)	PUNCT
ejpam-5161	142	65	=	=	PRON
ejpam-5161	142	66	{	{	PUNCT
ejpam-5161	142	67	(	(	PUNCT
ejpam-5161	142	68	ω1	ω1	PROPN
ejpam-5161	142	69	,	,	PUNCT
ejpam-5161	142	70	{	{	PUNCT
ejpam-5161	142	71	x1	x1	ADJ
ejpam-5161	142	72	}	}	PUNCT
ejpam-5161	142	73	)	)	PUNCT
ejpam-5161	142	74	,	,	PUNCT
ejpam-5161	142	75	(	(	PUNCT
ejpam-5161	142	76	ω2	ω2	ADV
ejpam-5161	142	77	,	,	PUNCT
ejpam-5161	142	78	{	{	PUNCT
ejpam-5161	142	79	x3	x3	ADJ
ejpam-5161	142	80	}	}	PUNCT
ejpam-5161	142	81	)	)	PUNCT
ejpam-5161	142	82	}	}	PUNCT
ejpam-5161	142	83	.	.	PUNCT
ejpam-5161	143	1	the	the	DET
ejpam-5161	143	2	crisp	crisp	ADJ
ejpam-5161	143	3	topologies	topology	NOUN
ejpam-5161	143	4	from	from	ADP
ejpam-5161	143	5	σ	σ	PROPN
ejpam-5161	143	6	are	be	AUX
ejpam-5161	143	7	σω1	σω1	NOUN
ejpam-5161	143	8	=	=	SYM
ejpam-5161	143	9	{	{	PUNCT
ejpam-5161	143	10	∅	∅	NOUN
ejpam-5161	143	11	,	,	PUNCT
ejpam-5161	143	12	{	{	PUNCT
ejpam-5161	143	13	x1	x1	PROPN
ejpam-5161	143	14	}	}	PUNCT
ejpam-5161	143	15	,	,	PUNCT
ejpam-5161	143	16	{	{	PUNCT
ejpam-5161	143	17	x1	x1	PROPN
ejpam-5161	143	18	,	,	PUNCT
ejpam-5161	143	19	x2	x2	PROPN
ejpam-5161	143	20	}	}	PUNCT
ejpam-5161	143	21	,	,	PUNCT
ejpam-5161	143	22	x	x	NOUN
ejpam-5161	143	23	}	}	PUNCT
ejpam-5161	143	24	and	and	CCONJ
ejpam-5161	143	25	σω2	σω2	ADP
ejpam-5161	143	26	=	=	SYM
ejpam-5161	143	27	{	{	PUNCT
ejpam-5161	143	28	∅	∅	NOUN
ejpam-5161	143	29	,	,	PUNCT
ejpam-5161	143	30	{	{	PUNCT
ejpam-5161	143	31	x3	x3	ADJ
ejpam-5161	143	32	}	}	PUNCT
ejpam-5161	143	33	,	,	PUNCT
ejpam-5161	143	34	x	x	NOUN
ejpam-5161	143	35	}	}	PUNCT
ejpam-5161	143	36	.	.	PUNCT
ejpam-5161	144	1	applying	apply	VERB
ejpam-5161	144	2	the	the	DET
ejpam-5161	144	3	formula	formula	NOUN
ejpam-5161	144	4	2	2	NUM
ejpam-5161	144	5	,	,	PUNCT
ejpam-5161	144	6	we	we	PRON
ejpam-5161	144	7	obtain	obtain	VERB
ejpam-5161	144	8	the	the	DET
ejpam-5161	144	9	following	follow	VERB
ejpam-5161	144	10	two	two	NUM
ejpam-5161	144	11	soft	soft	ADJ
ejpam-5161	144	12	topologies	topology	NOUN
ejpam-5161	144	13	on	on	ADP
ejpam-5161	144	14	x	x	NOUN
ejpam-5161	144	15	:	:	PUNCT
ejpam-5161	144	16	t̂	t̂	NUM
ejpam-5161	144	17	(	(	PUNCT
ejpam-5161	144	18	σω1	σω1	NOUN
ejpam-5161	144	19	)	)	PUNCT
ejpam-5161	144	20	=	=	PRON
ejpam-5161	145	1	{	{	PUNCT
ejpam-5161	145	2	φ̃	φ̃	PROPN
ejpam-5161	145	3	,	,	PUNCT
ejpam-5161	145	4	{	{	PUNCT
ejpam-5161	145	5	(	(	PUNCT
ejpam-5161	145	6	ω1	ω1	PROPN
ejpam-5161	145	7	,	,	PUNCT
ejpam-5161	145	8	{	{	PUNCT
ejpam-5161	145	9	x1	x1	ADJ
ejpam-5161	145	10	}	}	PUNCT
ejpam-5161	145	11	)	)	PUNCT
ejpam-5161	145	12	,	,	PUNCT
ejpam-5161	145	13	(	(	PUNCT
ejpam-5161	145	14	ω2	ω2	ADV
ejpam-5161	145	15	,	,	PUNCT
ejpam-5161	145	16	{	{	PUNCT
ejpam-5161	145	17	x1	x1	ADJ
ejpam-5161	145	18	}	}	PUNCT
ejpam-5161	145	19	)	)	PUNCT
ejpam-5161	145	20	}	}	PUNCT
ejpam-5161	145	21	,	,	PUNCT
ejpam-5161	145	22	{	{	PUNCT
ejpam-5161	145	23	(	(	PUNCT
ejpam-5161	145	24	ω1	ω1	PROPN
ejpam-5161	145	25	,	,	PUNCT
ejpam-5161	145	26	{	{	PUNCT
ejpam-5161	145	27	x1	x1	PROPN
ejpam-5161	145	28	,	,	PUNCT
ejpam-5161	145	29	x2	x2	PROPN
ejpam-5161	145	30	}	}	PUNCT
ejpam-5161	145	31	)	)	PUNCT
ejpam-5161	145	32	,	,	PUNCT
ejpam-5161	145	33	(	(	PUNCT
ejpam-5161	145	34	ω2	ω2	ADV
ejpam-5161	145	35	,	,	PUNCT
ejpam-5161	145	36	{	{	PUNCT
ejpam-5161	145	37	x1	x1	PROPN
ejpam-5161	145	38	,	,	PUNCT
ejpam-5161	145	39	x2	x2	PROPN
ejpam-5161	145	40	}	}	PUNCT
ejpam-5161	145	41	)	)	PUNCT
ejpam-5161	145	42	}	}	PUNCT
ejpam-5161	145	43	,	,	PUNCT
ejpam-5161	145	44	x̃	x̃	PROPN
ejpam-5161	145	45	}	}	PUNCT
ejpam-5161	145	46	=	=	SYM
ejpam-5161	145	47	{	{	PUNCT
ejpam-5161	145	48	φ̃	φ̃	PROPN
ejpam-5161	145	49	,	,	PUNCT
ejpam-5161	145	50	(	(	PUNCT
ejpam-5161	145	51	{	{	PUNCT
ejpam-5161	145	52	x1},ω	x1},ω	PROPN
ejpam-5161	145	53	)	)	PUNCT
ejpam-5161	145	54	,	,	PUNCT
ejpam-5161	145	55	(	(	PUNCT
ejpam-5161	145	56	{	{	PUNCT
ejpam-5161	145	57	x1	x1	PROPN
ejpam-5161	145	58	,	,	PUNCT
ejpam-5161	145	59	x2},ω	x2},ω	PROPN
ejpam-5161	145	60	)	)	PUNCT
ejpam-5161	145	61	,	,	PUNCT
ejpam-5161	145	62	x̃	x̃	PROPN
ejpam-5161	145	63	}	}	PUNCT
ejpam-5161	145	64	(	(	PUNCT
ejpam-5161	145	65	more	more	ADV
ejpam-5161	145	66	compactly	compactly	ADV
ejpam-5161	145	67	)	)	PUNCT
ejpam-5161	145	68	and	and	CCONJ
ejpam-5161	145	69	t̂	t̂	NUM
ejpam-5161	145	70	(	(	PUNCT
ejpam-5161	145	71	σω2	σω2	ADP
ejpam-5161	145	72	)	)	PUNCT
ejpam-5161	145	73	=	=	PRON
ejpam-5161	145	74	{	{	PUNCT
ejpam-5161	145	75	φ̃	φ̃	PROPN
ejpam-5161	145	76	,	,	PUNCT
ejpam-5161	145	77	{	{	PUNCT
ejpam-5161	145	78	(	(	PUNCT
ejpam-5161	145	79	ω1	ω1	PROPN
ejpam-5161	145	80	,	,	PUNCT
ejpam-5161	145	81	{	{	PUNCT
ejpam-5161	145	82	x3	x3	ADJ
ejpam-5161	145	83	}	}	PUNCT
ejpam-5161	145	84	)	)	PUNCT
ejpam-5161	145	85	,	,	PUNCT
ejpam-5161	145	86	(	(	PUNCT
ejpam-5161	145	87	ω2	ω2	ADV
ejpam-5161	145	88	,	,	PUNCT
ejpam-5161	145	89	{	{	PUNCT
ejpam-5161	145	90	x3	x3	ADJ
ejpam-5161	145	91	}	}	PUNCT
ejpam-5161	145	92	)	)	PUNCT
ejpam-5161	145	93	}	}	PUNCT
ejpam-5161	145	94	,	,	PUNCT
ejpam-5161	145	95	x̃	x̃	PROPN
ejpam-5161	145	96	}	}	PUNCT
ejpam-5161	145	97	=	=	SYM
ejpam-5161	145	98	{	{	PUNCT
ejpam-5161	145	99	φ̃	φ̃	PROPN
ejpam-5161	145	100	,	,	PUNCT
ejpam-5161	145	101	(	(	PUNCT
ejpam-5161	145	102	ω	ω	NOUN
ejpam-5161	145	103	,	,	PUNCT
ejpam-5161	145	104	{	{	PUNCT
ejpam-5161	145	105	x3	x3	ADJ
ejpam-5161	145	106	}	}	PUNCT
ejpam-5161	145	107	)	)	PUNCT
ejpam-5161	145	108	,	,	PUNCT
ejpam-5161	145	109	x̃	x̃	PROPN
ejpam-5161	145	110	)	)	PUNCT
ejpam-5161	145	111	}	}	PUNCT
ejpam-5161	145	112	.	.	PUNCT
ejpam-5161	146	1	from	from	ADP
ejpam-5161	146	2	lemma	lemma	PROPN
ejpam-5161	146	3	6	6	NUM
ejpam-5161	146	4	,	,	PUNCT
ejpam-5161	146	5	we	we	PRON
ejpam-5161	146	6	can	can	AUX
ejpam-5161	146	7	naturally	naturally	ADV
ejpam-5161	146	8	generate	generate	VERB
ejpam-5161	146	9	a	a	DET
ejpam-5161	146	10	soft	soft	ADJ
ejpam-5161	146	11	topology	topology	NOUN
ejpam-5161	146	12	t	t	NOUN
ejpam-5161	146	13	on	on	ADP
ejpam-5161	146	14	x	x	PUNCT
ejpam-5161	146	15	by	by	ADP
ejpam-5161	146	16	the	the	DET
ejpam-5161	146	17	union	union	NOUN
ejpam-5161	146	18	of	of	ADP
ejpam-5161	146	19	t̂	t̂	PROPN
ejpam-5161	146	20	(	(	PUNCT
ejpam-5161	146	21	σω1	σω1	NOUN
ejpam-5161	146	22	)	)	PUNCT
ejpam-5161	146	23	and	and	CCONJ
ejpam-5161	146	24	t̂	t̂	NUM
ejpam-5161	146	25	(	(	PUNCT
ejpam-5161	146	26	σω2	σω2	NOUN
ejpam-5161	146	27	)	)	PUNCT
ejpam-5161	146	28	.	.	PUNCT
ejpam-5161	147	1	that	that	PRON
ejpam-5161	147	2	is	be	AUX
ejpam-5161	147	3	,	,	PUNCT
ejpam-5161	147	4	t	t	PROPN
ejpam-5161	147	5	(	(	PUNCT
ejpam-5161	147	6	⋃̃2	⋃̃2	PROPN
ejpam-5161	147	7	i=1	i=1	PROPN
ejpam-5161	147	8	t̂	t̂	PROPN
ejpam-5161	147	9	(	(	PUNCT
ejpam-5161	147	10	σωi	σωi	PROPN
ejpam-5161	147	11	)	)	PUNCT
ejpam-5161	147	12	)	)	PUNCT
ejpam-5161	148	1	=	=	PRON
ejpam-5161	148	2	{	{	PUNCT
ejpam-5161	148	3	φ̃	φ̃	PROPN
ejpam-5161	148	4	,	,	PUNCT
ejpam-5161	148	5	(	(	PUNCT
ejpam-5161	148	6	g1,ω	g1,ω	PROPN
ejpam-5161	148	7	)	)	PUNCT
ejpam-5161	148	8	,	,	PUNCT
ejpam-5161	148	9	(	(	PUNCT
ejpam-5161	148	10	g2,ω	g2,ω	PROPN
ejpam-5161	148	11	)	)	PUNCT
ejpam-5161	148	12	,	,	PUNCT
ejpam-5161	148	13	(	(	PUNCT
ejpam-5161	148	14	g3,ω	g3,ω	PROPN
ejpam-5161	148	15	)	)	PUNCT
ejpam-5161	148	16	,	,	PUNCT
ejpam-5161	148	17	(	(	PUNCT
ejpam-5161	148	18	g4,ω	g4,ω	PROPN
ejpam-5161	148	19	)	)	PUNCT
ejpam-5161	148	20	,	,	PUNCT
ejpam-5161	148	21	x̃	x̃	PROPN
ejpam-5161	148	22	}	}	PUNCT
ejpam-5161	148	23	,	,	PUNCT
ejpam-5161	148	24	where	where	SCONJ
ejpam-5161	148	25	(	(	PUNCT
ejpam-5161	148	26	g1,ω	g1,ω	PROPN
ejpam-5161	148	27	)	)	PUNCT
ejpam-5161	148	28	=	=	PRON
ejpam-5161	148	29	{	{	PUNCT
ejpam-5161	148	30	(	(	PUNCT
ejpam-5161	148	31	ω1	ω1	PROPN
ejpam-5161	148	32	,	,	PUNCT
ejpam-5161	148	33	{	{	PUNCT
ejpam-5161	148	34	x1	x1	ADJ
ejpam-5161	148	35	}	}	PUNCT
ejpam-5161	148	36	)	)	PUNCT
ejpam-5161	148	37	,	,	PUNCT
ejpam-5161	148	38	(	(	PUNCT
ejpam-5161	148	39	ω2	ω2	ADV
ejpam-5161	148	40	,	,	PUNCT
ejpam-5161	148	41	{	{	PUNCT
ejpam-5161	148	42	x1	x1	ADJ
ejpam-5161	148	43	}	}	PUNCT
ejpam-5161	148	44	)	)	PUNCT
ejpam-5161	148	45	}	}	PUNCT
ejpam-5161	148	46	,	,	PUNCT
ejpam-5161	148	47	(	(	PUNCT
ejpam-5161	148	48	g2,ω	g2,ω	PROPN
ejpam-5161	148	49	)	)	PUNCT
ejpam-5161	148	50	=	=	PRON
ejpam-5161	148	51	{	{	PUNCT
ejpam-5161	148	52	(	(	PUNCT
ejpam-5161	148	53	ω1	ω1	PROPN
ejpam-5161	148	54	,	,	PUNCT
ejpam-5161	148	55	{	{	PUNCT
ejpam-5161	148	56	x3	x3	ADJ
ejpam-5161	148	57	}	}	PUNCT
ejpam-5161	148	58	)	)	PUNCT
ejpam-5161	148	59	,	,	PUNCT
ejpam-5161	148	60	(	(	PUNCT
ejpam-5161	148	61	ω2	ω2	ADV
ejpam-5161	148	62	,	,	PUNCT
ejpam-5161	148	63	{	{	PUNCT
ejpam-5161	148	64	x3	x3	ADJ
ejpam-5161	148	65	}	}	PUNCT
ejpam-5161	148	66	)	)	PUNCT
ejpam-5161	148	67	}	}	PUNCT
ejpam-5161	148	68	,	,	PUNCT
ejpam-5161	148	69	(	(	PUNCT
ejpam-5161	148	70	g3,ω	g3,ω	X
ejpam-5161	148	71	)	)	PUNCT
ejpam-5161	148	72	=	=	PRON
ejpam-5161	148	73	{	{	PUNCT
ejpam-5161	148	74	(	(	PUNCT
ejpam-5161	148	75	ω1	ω1	PROPN
ejpam-5161	148	76	,	,	PUNCT
ejpam-5161	148	77	{	{	PUNCT
ejpam-5161	148	78	x1	x1	PROPN
ejpam-5161	148	79	,	,	PUNCT
ejpam-5161	148	80	x2	x2	PROPN
ejpam-5161	148	81	}	}	PUNCT
ejpam-5161	148	82	)	)	PUNCT
ejpam-5161	148	83	,	,	PUNCT
ejpam-5161	148	84	(	(	PUNCT
ejpam-5161	148	85	ω2	ω2	ADV
ejpam-5161	148	86	,	,	PUNCT
ejpam-5161	148	87	{	{	PUNCT
ejpam-5161	148	88	x1	x1	PROPN
ejpam-5161	148	89	,	,	PUNCT
ejpam-5161	148	90	x2	x2	PROPN
ejpam-5161	148	91	}	}	PUNCT
ejpam-5161	148	92	)	)	PUNCT
ejpam-5161	148	93	}	}	PUNCT
ejpam-5161	148	94	,	,	PUNCT
ejpam-5161	148	95	and	and	CCONJ
ejpam-5161	148	96	(	(	PUNCT
ejpam-5161	148	97	g4,ω	g4,ω	PROPN
ejpam-5161	148	98	)	)	PUNCT
ejpam-5161	148	99	=	=	PRON
ejpam-5161	148	100	{	{	PUNCT
ejpam-5161	148	101	(	(	PUNCT
ejpam-5161	148	102	ω1	ω1	PROPN
ejpam-5161	148	103	,	,	PUNCT
ejpam-5161	148	104	{	{	PUNCT
ejpam-5161	148	105	x1	x1	PROPN
ejpam-5161	148	106	,	,	PUNCT
ejpam-5161	148	107	x3	x3	ADJ
ejpam-5161	148	108	}	}	PUNCT
ejpam-5161	148	109	)	)	PUNCT
ejpam-5161	148	110	,	,	PUNCT
ejpam-5161	148	111	(	(	PUNCT
ejpam-5161	148	112	ω2	ω2	ADV
ejpam-5161	148	113	,	,	PUNCT
ejpam-5161	148	114	{	{	PUNCT
ejpam-5161	148	115	x1	x1	ADJ
ejpam-5161	148	116	,	,	PUNCT
ejpam-5161	148	117	x3	x3	ADJ
ejpam-5161	148	118	}	}	PUNCT
ejpam-5161	148	119	)	)	PUNCT
ejpam-5161	148	120	}	}	PUNCT
ejpam-5161	148	121	.	.	PUNCT
ejpam-5161	149	1	the	the	DET
ejpam-5161	149	2	compact	compact	ADJ
ejpam-5161	149	3	form	form	NOUN
ejpam-5161	149	4	of	of	ADP
ejpam-5161	149	5	the	the	DET
ejpam-5161	149	6	above	above	ADJ
ejpam-5161	149	7	conclusion	conclusion	NOUN
ejpam-5161	149	8	is	be	AUX
ejpam-5161	149	9	t	t	PROPN
ejpam-5161	149	10	(	(	PUNCT
ejpam-5161	149	11	⋃̃2	⋃̃2	PROPN
ejpam-5161	149	12	i=1	i=1	PROPN
ejpam-5161	149	13	t̂	t̂	PROPN
ejpam-5161	149	14	(	(	PUNCT
ejpam-5161	149	15	σωi	σωi	PROPN
ejpam-5161	149	16	)	)	PUNCT
ejpam-5161	149	17	)	)	PUNCT
ejpam-5161	150	1	=	=	PRON
ejpam-5161	150	2	{	{	PUNCT
ejpam-5161	150	3	φ̃	φ̃	PROPN
ejpam-5161	150	4	,	,	PUNCT
ejpam-5161	150	5	(	(	PUNCT
ejpam-5161	150	6	{	{	PUNCT
ejpam-5161	150	7	x1},ω	x1},ω	PROPN
ejpam-5161	150	8	)	)	PUNCT
ejpam-5161	150	9	,	,	PUNCT
ejpam-5161	150	10	(	(	PUNCT
ejpam-5161	150	11	{	{	PUNCT
ejpam-5161	150	12	x3},ω	x3},ω	PROPN
ejpam-5161	150	13	)	)	PUNCT
ejpam-5161	150	14	,	,	PUNCT
ejpam-5161	150	15	(	(	PUNCT
ejpam-5161	150	16	{	{	PUNCT
ejpam-5161	150	17	x1	x1	PROPN
ejpam-5161	150	18	,	,	PUNCT
ejpam-5161	150	19	x2},ω	x2},ω	PROPN
ejpam-5161	150	20	)	)	PUNCT
ejpam-5161	150	21	,	,	PUNCT
ejpam-5161	150	22	(	(	PUNCT
ejpam-5161	150	23	{	{	PUNCT
ejpam-5161	150	24	x1	x1	PROPN
ejpam-5161	150	25	,	,	PUNCT
ejpam-5161	150	26	x3},ω	x3},ω	PROPN
ejpam-5161	150	27	)	)	PUNCT
ejpam-5161	150	28	,	,	PUNCT
ejpam-5161	150	29	x̃	x̃	PROPN
ejpam-5161	150	30	}	}	PUNCT
ejpam-5161	150	31	.	.	PUNCT
ejpam-5161	151	1	by	by	ADP
ejpam-5161	151	2	applying	apply	VERB
ejpam-5161	151	3	the	the	DET
ejpam-5161	151	4	formula	formula	NOUN
ejpam-5161	151	5	1	1	NUM
ejpam-5161	151	6	,	,	PUNCT
ejpam-5161	151	7	the	the	DET
ejpam-5161	151	8	next	next	ADJ
ejpam-5161	151	9	soft	soft	ADJ
ejpam-5161	151	10	topology	topology	NOUN
ejpam-5161	151	11	on	on	ADP
ejpam-5161	151	12	x	x	PUNCT
ejpam-5161	151	13	will	will	AUX
ejpam-5161	151	14	be	be	AUX
ejpam-5161	151	15	obtained	obtain	VERB
ejpam-5161	151	16	.	.	PUNCT
ejpam-5161	152	1	t	t	PROPN
ejpam-5161	152	2	(	(	PUNCT
ejpam-5161	152	3	σ	σ	PROPN
ejpam-5161	152	4	)	)	PUNCT
ejpam-5161	152	5	=	=	SYM
ejpam-5161	152	6	t	t	PROPN
ejpam-5161	152	7	(	(	PUNCT
ejpam-5161	152	8	{	{	PUNCT
ejpam-5161	152	9	σω1	σω1	NOUN
ejpam-5161	152	10	,	,	PUNCT
ejpam-5161	152	11	σω2	σω2	ADP
ejpam-5161	152	12	}	}	PUNCT
ejpam-5161	152	13	)	)	PUNCT
ejpam-5161	152	14	=	=	PRON
ejpam-5161	152	15	{	{	PUNCT
ejpam-5161	152	16	φ̃	φ̃	PROPN
ejpam-5161	152	17	,	,	PUNCT
ejpam-5161	152	18	(	(	PUNCT
ejpam-5161	152	19	h1,ω	h1,ω	PROPN
ejpam-5161	152	20	)	)	PUNCT
ejpam-5161	152	21	,	,	PUNCT
ejpam-5161	152	22	(	(	PUNCT
ejpam-5161	152	23	h2,ω	h2,ω	PROPN
ejpam-5161	152	24	)	)	PUNCT
ejpam-5161	152	25	,	,	PUNCT
ejpam-5161	152	26	·	·	PUNCT
ejpam-5161	152	27	·	·	PUNCT
ejpam-5161	152	28	·	·	PUNCT
ejpam-5161	152	29	,	,	PUNCT
ejpam-5161	152	30	(	(	PUNCT
ejpam-5161	152	31	h10,ω	h10,ω	NUM
ejpam-5161	152	32	)	)	PUNCT
ejpam-5161	152	33	,	,	PUNCT
ejpam-5161	152	34	x̃	x̃	PROPN
ejpam-5161	152	35	}	}	PUNCT
ejpam-5161	152	36	,	,	PUNCT
ejpam-5161	152	37	where	where	SCONJ
ejpam-5161	152	38	(	(	PUNCT
ejpam-5161	152	39	h1,ω	h1,ω	NOUN
ejpam-5161	152	40	)	)	PUNCT
ejpam-5161	152	41	=	=	PRON
ejpam-5161	152	42	{	{	PUNCT
ejpam-5161	152	43	(	(	PUNCT
ejpam-5161	152	44	ω1	ω1	PROPN
ejpam-5161	152	45	,	,	PUNCT
ejpam-5161	152	46	∅	∅	NOUN
ejpam-5161	152	47	)	)	PUNCT
ejpam-5161	152	48	,	,	PUNCT
ejpam-5161	152	49	(	(	PUNCT
ejpam-5161	152	50	ω2	ω2	ADJ
ejpam-5161	152	51	,	,	PUNCT
ejpam-5161	152	52	x	x	NOUN
ejpam-5161	152	53	)	)	PUNCT
ejpam-5161	152	54	}	}	PUNCT
ejpam-5161	152	55	,	,	PUNCT
ejpam-5161	152	56	(	(	PUNCT
ejpam-5161	152	57	h2,ω	h2,ω	PROPN
ejpam-5161	152	58	)	)	PUNCT
ejpam-5161	152	59	=	=	PRON
ejpam-5161	152	60	{	{	PUNCT
ejpam-5161	152	61	(	(	PUNCT
ejpam-5161	152	62	ω1	ω1	PROPN
ejpam-5161	152	63	,	,	PUNCT
ejpam-5161	152	64	∅	∅	NOUN
ejpam-5161	152	65	)	)	PUNCT
ejpam-5161	152	66	,	,	PUNCT
ejpam-5161	152	67	(	(	PUNCT
ejpam-5161	152	68	ω2	ω2	ADV
ejpam-5161	152	69	,	,	PUNCT
ejpam-5161	152	70	{	{	PUNCT
ejpam-5161	152	71	x3	x3	ADJ
ejpam-5161	152	72	}	}	PUNCT
ejpam-5161	152	73	)	)	PUNCT
ejpam-5161	152	74	}	}	PUNCT
ejpam-5161	152	75	,	,	PUNCT
ejpam-5161	152	76	(	(	PUNCT
ejpam-5161	152	77	h3,ω	h3,ω	PROPN
ejpam-5161	152	78	)	)	PUNCT
ejpam-5161	152	79	=	=	PRON
ejpam-5161	152	80	{	{	PUNCT
ejpam-5161	152	81	(	(	PUNCT
ejpam-5161	152	82	ω1	ω1	PROPN
ejpam-5161	152	83	,	,	PUNCT
ejpam-5161	152	84	x	x	NOUN
ejpam-5161	152	85	)	)	PUNCT
ejpam-5161	152	86	,	,	PUNCT
ejpam-5161	152	87	(	(	PUNCT
ejpam-5161	152	88	ω2	ω2	ADJ
ejpam-5161	152	89	,	,	PUNCT
ejpam-5161	152	90	∅	∅	NOUN
ejpam-5161	152	91	)	)	PUNCT
ejpam-5161	152	92	}	}	PUNCT
ejpam-5161	152	93	,	,	PUNCT
ejpam-5161	152	94	(	(	PUNCT
ejpam-5161	152	95	h4,ω	h4,ω	PROPN
ejpam-5161	152	96	)	)	PUNCT
ejpam-5161	152	97	=	=	SYM
ejpam-5161	152	98	{	{	PUNCT
ejpam-5161	152	99	(	(	PUNCT
ejpam-5161	152	100	ω1	ω1	PROPN
ejpam-5161	152	101	,	,	PUNCT
ejpam-5161	152	102	x	x	NOUN
ejpam-5161	152	103	)	)	PUNCT
ejpam-5161	152	104	,	,	PUNCT
ejpam-5161	152	105	(	(	PUNCT
ejpam-5161	152	106	ω2	ω2	ADV
ejpam-5161	152	107	,	,	PUNCT
ejpam-5161	152	108	{	{	PUNCT
ejpam-5161	152	109	x3	x3	ADJ
ejpam-5161	152	110	}	}	PUNCT
ejpam-5161	152	111	)	)	PUNCT
ejpam-5161	152	112	}	}	PUNCT
ejpam-5161	152	113	,	,	PUNCT
ejpam-5161	152	114	(	(	PUNCT
ejpam-5161	152	115	h5,ω	h5,ω	PROPN
ejpam-5161	152	116	)	)	PUNCT
ejpam-5161	152	117	=	=	PRON
ejpam-5161	152	118	{	{	PUNCT
ejpam-5161	152	119	(	(	PUNCT
ejpam-5161	152	120	ω1	ω1	PROPN
ejpam-5161	152	121	,	,	PUNCT
ejpam-5161	152	122	{	{	PUNCT
ejpam-5161	152	123	x1	x1	ADJ
ejpam-5161	152	124	}	}	PUNCT
ejpam-5161	152	125	)	)	PUNCT
ejpam-5161	152	126	,	,	PUNCT
ejpam-5161	152	127	(	(	PUNCT
ejpam-5161	152	128	ω2	ω2	ADJ
ejpam-5161	152	129	,	,	PUNCT
ejpam-5161	152	130	∅	∅	NOUN
ejpam-5161	152	131	)	)	PUNCT
ejpam-5161	152	132	}	}	PUNCT
ejpam-5161	152	133	,	,	PUNCT
ejpam-5161	152	134	(	(	PUNCT
ejpam-5161	152	135	h6,ω	h6,ω	PROPN
ejpam-5161	152	136	)	)	PUNCT
ejpam-5161	152	137	=	=	PRON
ejpam-5161	152	138	{	{	PUNCT
ejpam-5161	152	139	(	(	PUNCT
ejpam-5161	152	140	ω1	ω1	PROPN
ejpam-5161	152	141	,	,	PUNCT
ejpam-5161	152	142	{	{	PUNCT
ejpam-5161	152	143	x1	x1	ADJ
ejpam-5161	152	144	}	}	PUNCT
ejpam-5161	152	145	)	)	PUNCT
ejpam-5161	152	146	,	,	PUNCT
ejpam-5161	152	147	(	(	PUNCT
ejpam-5161	152	148	ω2	ω2	ADJ
ejpam-5161	152	149	,	,	PUNCT
ejpam-5161	152	150	x	x	NOUN
ejpam-5161	152	151	)	)	PUNCT
ejpam-5161	152	152	}	}	PUNCT
ejpam-5161	152	153	,	,	PUNCT
ejpam-5161	152	154	z.	z.	PROPN
ejpam-5161	152	155	a.	a.	PROPN
ejpam-5161	152	156	ameen	ameen	PROPN
ejpam-5161	152	157	et	et	PROPN
ejpam-5161	152	158	al	al	PROPN
ejpam-5161	152	159	.	.	PUNCT
ejpam-5161	152	160	/	/	SYM
ejpam-5161	152	161	eur	eur	PROPN
ejpam-5161	152	162	.	.	PUNCT
ejpam-5161	153	1	j.	j.	PROPN
ejpam-5161	153	2	pure	pure	PROPN
ejpam-5161	153	3	appl	appl	PROPN
ejpam-5161	153	4	.	.	PROPN
ejpam-5161	153	5	math	math	PROPN
ejpam-5161	153	6	,	,	PUNCT
ejpam-5161	153	7	17	17	NUM
ejpam-5161	153	8	(	(	PUNCT
ejpam-5161	153	9	2	2	NUM
ejpam-5161	153	10	)	)	PUNCT
ejpam-5161	153	11	(	(	PUNCT
ejpam-5161	153	12	2024	2024	NUM
ejpam-5161	153	13	)	)	PUNCT
ejpam-5161	153	14	,	,	PUNCT
ejpam-5161	153	15	1168	1168	NUM
ejpam-5161	153	16	-	-	SYM
ejpam-5161	153	17	1182	1182	NUM
ejpam-5161	153	18	1174	1174	NUM
ejpam-5161	153	19	(	(	PUNCT
ejpam-5161	153	20	h7,ω	h7,ω	PROPN
ejpam-5161	153	21	)	)	PUNCT
ejpam-5161	153	22	=	=	SYM
ejpam-5161	153	23	{	{	PUNCT
ejpam-5161	153	24	(	(	PUNCT
ejpam-5161	153	25	ω1	ω1	PROPN
ejpam-5161	153	26	,	,	PUNCT
ejpam-5161	153	27	{	{	PUNCT
ejpam-5161	153	28	x1	x1	ADJ
ejpam-5161	153	29	}	}	PUNCT
ejpam-5161	153	30	)	)	PUNCT
ejpam-5161	153	31	,	,	PUNCT
ejpam-5161	153	32	(	(	PUNCT
ejpam-5161	153	33	ω2	ω2	ADV
ejpam-5161	153	34	,	,	PUNCT
ejpam-5161	153	35	{	{	PUNCT
ejpam-5161	153	36	x3	x3	ADJ
ejpam-5161	153	37	}	}	PUNCT
ejpam-5161	153	38	)	)	PUNCT
ejpam-5161	153	39	}	}	PUNCT
ejpam-5161	153	40	,	,	PUNCT
ejpam-5161	153	41	(	(	PUNCT
ejpam-5161	153	42	h8,ω	h8,ω	PROPN
ejpam-5161	153	43	)	)	PUNCT
ejpam-5161	153	44	=	=	SYM
ejpam-5161	153	45	{	{	PUNCT
ejpam-5161	153	46	(	(	PUNCT
ejpam-5161	153	47	ω1	ω1	PROPN
ejpam-5161	153	48	,	,	PUNCT
ejpam-5161	153	49	{	{	PUNCT
ejpam-5161	153	50	x1	x1	PROPN
ejpam-5161	153	51	,	,	PUNCT
ejpam-5161	153	52	x2	x2	PROPN
ejpam-5161	153	53	}	}	PUNCT
ejpam-5161	153	54	)	)	PUNCT
ejpam-5161	153	55	,	,	PUNCT
ejpam-5161	153	56	(	(	PUNCT
ejpam-5161	153	57	ω2	ω2	ADJ
ejpam-5161	153	58	,	,	PUNCT
ejpam-5161	153	59	∅	∅	NOUN
ejpam-5161	153	60	)	)	PUNCT
ejpam-5161	153	61	}	}	PUNCT
ejpam-5161	153	62	,	,	PUNCT
ejpam-5161	153	63	(	(	PUNCT
ejpam-5161	153	64	h9,ω	h9,ω	PROPN
ejpam-5161	153	65	)	)	PUNCT
ejpam-5161	153	66	=	=	PRON
ejpam-5161	153	67	{	{	PUNCT
ejpam-5161	153	68	(	(	PUNCT
ejpam-5161	153	69	ω1	ω1	PROPN
ejpam-5161	153	70	,	,	PUNCT
ejpam-5161	153	71	{	{	PUNCT
ejpam-5161	153	72	x1	x1	PROPN
ejpam-5161	153	73	,	,	PUNCT
ejpam-5161	153	74	x2	x2	PROPN
ejpam-5161	153	75	}	}	PUNCT
ejpam-5161	153	76	)	)	PUNCT
ejpam-5161	153	77	,	,	PUNCT
ejpam-5161	153	78	(	(	PUNCT
ejpam-5161	153	79	ω2	ω2	ADJ
ejpam-5161	153	80	,	,	PUNCT
ejpam-5161	153	81	x	x	NOUN
ejpam-5161	153	82	)	)	PUNCT
ejpam-5161	153	83	}	}	PUNCT
ejpam-5161	153	84	,	,	PUNCT
ejpam-5161	153	85	and	and	CCONJ
ejpam-5161	153	86	(	(	PUNCT
ejpam-5161	153	87	h10,ω	h10,ω	ADJ
ejpam-5161	153	88	)	)	PUNCT
ejpam-5161	153	89	=	=	PRON
ejpam-5161	153	90	{	{	PUNCT
ejpam-5161	153	91	(	(	PUNCT
ejpam-5161	153	92	ω1	ω1	PROPN
ejpam-5161	153	93	,	,	PUNCT
ejpam-5161	153	94	{	{	PUNCT
ejpam-5161	153	95	x1	x1	PROPN
ejpam-5161	153	96	,	,	PUNCT
ejpam-5161	153	97	x2	x2	PROPN
ejpam-5161	153	98	}	}	PUNCT
ejpam-5161	153	99	)	)	PUNCT
ejpam-5161	153	100	,	,	PUNCT
ejpam-5161	153	101	(	(	PUNCT
ejpam-5161	153	102	ω2	ω2	ADV
ejpam-5161	153	103	,	,	PUNCT
ejpam-5161	153	104	{	{	PUNCT
ejpam-5161	153	105	x3	x3	ADJ
ejpam-5161	153	106	}	}	PUNCT
ejpam-5161	153	107	)	)	PUNCT
ejpam-5161	153	108	}	}	PUNCT
ejpam-5161	153	109	.	.	PUNCT
ejpam-5161	154	1	one	one	PRON
ejpam-5161	154	2	can	can	AUX
ejpam-5161	154	3	easily	easily	ADV
ejpam-5161	154	4	check	check	VERB
ejpam-5161	154	5	that	that	SCONJ
ejpam-5161	154	6	the	the	DET
ejpam-5161	154	7	above	above	ADJ
ejpam-5161	154	8	computations	computation	NOUN
ejpam-5161	154	9	lead	lead	VERB
ejpam-5161	154	10	to	to	ADP
ejpam-5161	154	11	the	the	DET
ejpam-5161	154	12	following	follow	VERB
ejpam-5161	154	13	observations	observation	NOUN
ejpam-5161	154	14	:	:	PUNCT
ejpam-5161	154	15	•	•	NUM
ejpam-5161	154	16	σ	σ	NOUN
ejpam-5161	154	17	is	be	AUX
ejpam-5161	154	18	a	a	DET
ejpam-5161	154	19	subcollection	subcollection	NOUN
ejpam-5161	154	20	of	of	ADP
ejpam-5161	154	21	t	t	PROPN
ejpam-5161	154	22	(	(	PUNCT
ejpam-5161	154	23	σ	σ	PROPN
ejpam-5161	154	24	)	)	PUNCT
ejpam-5161	154	25	.	.	PUNCT
ejpam-5161	155	1	•	•	NUM
ejpam-5161	155	2	σ	σ	PROPN
ejpam-5161	155	3	is	be	AUX
ejpam-5161	155	4	independent	independent	ADJ
ejpam-5161	155	5	of	of	ADP
ejpam-5161	155	6	t	t	PROPN
ejpam-5161	155	7	(	(	PUNCT
ejpam-5161	155	8	⋃̃2	⋃̃2	PROPN
ejpam-5161	155	9	i=1t̂	i=1t̂	PROPN
ejpam-5161	155	10	(	(	PUNCT
ejpam-5161	155	11	σωi	σωi	PROPN
ejpam-5161	155	12	)	)	PUNCT
ejpam-5161	155	13	)	)	PUNCT
ejpam-5161	155	14	.	.	PUNCT
ejpam-5161	156	1	•	•	NUM
ejpam-5161	156	2	t	t	PROPN
ejpam-5161	156	3	(	(	PUNCT
ejpam-5161	156	4	⋃̃2	⋃̃2	PROPN
ejpam-5161	156	5	i=1t̂	i=1t̂	PROPN
ejpam-5161	156	6	(	(	PUNCT
ejpam-5161	156	7	σωi	σωi	PROPN
ejpam-5161	156	8	)	)	PUNCT
ejpam-5161	156	9	)	)	PUNCT
ejpam-5161	156	10	is	be	AUX
ejpam-5161	156	11	independent	independent	ADJ
ejpam-5161	156	12	of	of	ADP
ejpam-5161	156	13	t	t	PROPN
ejpam-5161	156	14	(	(	PUNCT
ejpam-5161	156	15	σ	σ	PROPN
ejpam-5161	156	16	)	)	PUNCT
ejpam-5161	156	17	.	.	PUNCT
ejpam-5161	157	1	the	the	DET
ejpam-5161	157	2	relationships	relationship	NOUN
ejpam-5161	157	3	between	between	ADP
ejpam-5161	157	4	the	the	DET
ejpam-5161	157	5	soft	soft	ADJ
ejpam-5161	157	6	topologies	topology	NOUN
ejpam-5161	157	7	on	on	ADP
ejpam-5161	157	8	a	a	DET
ejpam-5161	157	9	common	common	ADJ
ejpam-5161	157	10	universe	universe	NOUN
ejpam-5161	157	11	obtained	obtain	VERB
ejpam-5161	157	12	by	by	ADP
ejpam-5161	157	13	the	the	DET
ejpam-5161	157	14	methods	method	NOUN
ejpam-5161	157	15	described	describe	VERB
ejpam-5161	157	16	in	in	ADP
ejpam-5161	157	17	this	this	DET
ejpam-5161	157	18	section	section	NOUN
ejpam-5161	157	19	is	be	AUX
ejpam-5161	157	20	summarized	summarize	VERB
ejpam-5161	157	21	in	in	ADP
ejpam-5161	157	22	diagram	diagram	NOUN
ejpam-5161	157	23	1	1	NUM
ejpam-5161	157	24	.	.	PUNCT
ejpam-5161	158	1	σ	σ	PROPN
ejpam-5161	158	2	t	t	PROPN
ejpam-5161	158	3	(	(	PUNCT
ejpam-5161	158	4	σ	σ	PROPN
ejpam-5161	158	5	)	)	PUNCT
ejpam-5161	158	6	σ	σ	PROPN
ejpam-5161	158	7	=	=	PUNCT
ejpam-5161	158	8	{	{	PUNCT
ejpam-5161	158	9	σω	σω	NOUN
ejpam-5161	158	10	:	:	PUNCT
ejpam-5161	158	11	ω	ω	PROPN
ejpam-5161	158	12	∈	∈	PROPN
ejpam-5161	158	13	ω	ω	PROPN
ejpam-5161	158	14	}	}	PUNCT
ejpam-5161	158	15	t̂	t̂	NUM
ejpam-5161	158	16	(	(	PUNCT
ejpam-5161	158	17	t	t	PROPN
ejpam-5161	158	18	(	(	PUNCT
ejpam-5161	158	19	⋃̃	⋃̃	PROPN
ejpam-5161	158	20	σ	σ	PROPN
ejpam-5161	158	21	)	)	PUNCT
ejpam-5161	158	22	)	)	PUNCT
ejpam-5161	159	1	p	p	NOUN
ejpam-5161	160	1	ro	ro	X
ejpam-5161	160	2	d	d	X
ejpam-5161	160	3	u	u	X
ejpam-5161	160	4	ces	ces	X
ejpam-5161	160	5	⊇̃	⊇̃	X
ejpam-5161	160	6	independent	independent	ADJ
ejpam-5161	160	7	generates	generate	NOUN
ejpam-5161	160	8	generates	generate	VERB
ejpam-5161	160	9	figure	figure	NOUN
ejpam-5161	160	10	1	1	NUM
ejpam-5161	160	11	:	:	PUNCT
ejpam-5161	160	12	relationships	relationship	NOUN
ejpam-5161	160	13	between	between	ADP
ejpam-5161	160	14	different	different	ADJ
ejpam-5161	160	15	soft	soft	ADJ
ejpam-5161	160	16	topologies	topology	NOUN
ejpam-5161	160	17	4	4	NUM
ejpam-5161	160	18	.	.	PUNCT
ejpam-5161	161	1	non	non	ADJ
ejpam-5161	161	2	-	-	ADJ
ejpam-5161	161	3	uniqueness	uniqueness	NOUN
ejpam-5161	161	4	of	of	ADP
ejpam-5161	161	5	soft	soft	ADJ
ejpam-5161	161	6	topology	topology	NOUN
ejpam-5161	161	7	t	t	NOUN
ejpam-5161	161	8	(	(	PUNCT
ejpam-5161	161	9	σ	σ	PROPN
ejpam-5161	161	10	)	)	PUNCT
ejpam-5161	161	11	associated	associate	VERB
ejpam-5161	161	12	with	with	ADP
ejpam-5161	161	13	σ	σ	PROPN
ejpam-5161	161	14	in	in	ADP
ejpam-5161	161	15	this	this	DET
ejpam-5161	161	16	short	short	ADJ
ejpam-5161	161	17	section	section	NOUN
ejpam-5161	161	18	,	,	PUNCT
ejpam-5161	161	19	we	we	PRON
ejpam-5161	161	20	provide	provide	VERB
ejpam-5161	161	21	an	an	DET
ejpam-5161	161	22	example	example	NOUN
ejpam-5161	161	23	to	to	PART
ejpam-5161	161	24	witness	witness	VERB
ejpam-5161	161	25	that	that	SCONJ
ejpam-5161	161	26	two	two	NUM
ejpam-5161	161	27	different	different	ADJ
ejpam-5161	161	28	(	(	PUNCT
ejpam-5161	161	29	even	even	ADV
ejpam-5161	161	30	incomparable	incomparable	ADJ
ejpam-5161	161	31	)	)	PUNCT
ejpam-5161	161	32	soft	soft	ADJ
ejpam-5161	161	33	topologies	topology	NOUN
ejpam-5161	161	34	may	may	AUX
ejpam-5161	161	35	have	have	VERB
ejpam-5161	161	36	a	a	DET
ejpam-5161	161	37	common	common	ADJ
ejpam-5161	161	38	associated	associated	ADJ
ejpam-5161	161	39	soft	soft	ADJ
ejpam-5161	161	40	topology	topology	NOUN
ejpam-5161	161	41	.	.	PUNCT
ejpam-5161	162	1	example	example	NOUN
ejpam-5161	163	1	2	2	NUM
ejpam-5161	163	2	.	.	X
ejpam-5161	163	3	consider	consider	VERB
ejpam-5161	163	4	the	the	DET
ejpam-5161	163	5	soft	soft	ADJ
ejpam-5161	163	6	topology	topology	NOUN
ejpam-5161	163	7	on	on	ADP
ejpam-5161	163	8	x	x	PROPN
ejpam-5161	163	9	,	,	PUNCT
ejpam-5161	163	10	σ	σ	X
ejpam-5161	163	11	=	=	SYM
ejpam-5161	163	12	{	{	PUNCT
ejpam-5161	163	13	φ̃	φ̃	PROPN
ejpam-5161	163	14	,	,	PUNCT
ejpam-5161	163	15	(	(	PUNCT
ejpam-5161	163	16	f1,ω	f1,ω	PROPN
ejpam-5161	163	17	)	)	PUNCT
ejpam-5161	163	18	,	,	PUNCT
ejpam-5161	163	19	(	(	PUNCT
ejpam-5161	163	20	f2,ω	f2,ω	PROPN
ejpam-5161	163	21	)	)	PUNCT
ejpam-5161	163	22	,	,	PUNCT
ejpam-5161	163	23	(	(	PUNCT
ejpam-5161	163	24	f3,ω	f3,ω	PROPN
ejpam-5161	163	25	)	)	PUNCT
ejpam-5161	163	26	,	,	PUNCT
ejpam-5161	163	27	(	(	PUNCT
ejpam-5161	163	28	f4,ω	f4,ω	PROPN
ejpam-5161	163	29	)	)	PUNCT
ejpam-5161	163	30	,	,	PUNCT
ejpam-5161	163	31	x̃	x̃	PROPN
ejpam-5161	163	32	}	}	PUNCT
ejpam-5161	163	33	given	give	VERB
ejpam-5161	163	34	in	in	ADP
ejpam-5161	163	35	example	example	NOUN
ejpam-5161	163	36	1	1	NUM
ejpam-5161	163	37	,	,	PUNCT
ejpam-5161	163	38	there	there	ADV
ejpam-5161	163	39	x	x	X
ejpam-5161	163	40	=	=	PUNCT
ejpam-5161	163	41	{	{	PUNCT
ejpam-5161	163	42	x1	x1	PROPN
ejpam-5161	163	43	,	,	PUNCT
ejpam-5161	163	44	x2	x2	PROPN
ejpam-5161	163	45	,	,	PUNCT
ejpam-5161	163	46	x3	x3	ADJ
ejpam-5161	163	47	}	}	PUNCT
ejpam-5161	163	48	,	,	PUNCT
ejpam-5161	163	49	ω	ω	PROPN
ejpam-5161	163	50	=	=	SYM
ejpam-5161	163	51	{	{	PUNCT
ejpam-5161	163	52	ω1	ω1	PROPN
ejpam-5161	163	53	,	,	PUNCT
ejpam-5161	163	54	ω2	ω2	ADJ
ejpam-5161	163	55	}	}	PUNCT
ejpam-5161	163	56	.	.	PUNCT
ejpam-5161	164	1	let	let	VERB
ejpam-5161	164	2	σ′	σ′	VERB
ejpam-5161	164	3	=	=	PUNCT
ejpam-5161	164	4	{	{	PUNCT
ejpam-5161	164	5	φ̃	φ̃	PROPN
ejpam-5161	164	6	,	,	PUNCT
ejpam-5161	164	7	(	(	PUNCT
ejpam-5161	164	8	r1,ω	r1,ω	PROPN
ejpam-5161	164	9	)	)	PUNCT
ejpam-5161	164	10	,	,	PUNCT
ejpam-5161	164	11	(	(	PUNCT
ejpam-5161	164	12	r2,ω	r2,ω	NOUN
ejpam-5161	164	13	)	)	PUNCT
ejpam-5161	164	14	,	,	PUNCT
ejpam-5161	164	15	(	(	PUNCT
ejpam-5161	164	16	r3,ω	r3,ω	PROPN
ejpam-5161	164	17	)	)	PUNCT
ejpam-5161	164	18	,	,	PUNCT
ejpam-5161	164	19	(	(	PUNCT
ejpam-5161	164	20	r4,ω	r4,ω	PROPN
ejpam-5161	164	21	)	)	PUNCT
ejpam-5161	164	22	,	,	PUNCT
ejpam-5161	164	23	x̃	x̃	PROPN
ejpam-5161	164	24	}	}	PUNCT
ejpam-5161	164	25	be	be	VERB
ejpam-5161	164	26	another	another	DET
ejpam-5161	164	27	soft	soft	ADJ
ejpam-5161	164	28	topology	topology	NOUN
ejpam-5161	164	29	on	on	ADP
ejpam-5161	164	30	x	x	NOUN
ejpam-5161	164	31	,	,	PUNCT
ejpam-5161	164	32	where	where	SCONJ
ejpam-5161	164	33	(	(	PUNCT
ejpam-5161	164	34	r1,ω	r1,ω	PROPN
ejpam-5161	164	35	)	)	PUNCT
ejpam-5161	164	36	=	=	PRON
ejpam-5161	164	37	{	{	PUNCT
ejpam-5161	164	38	(	(	PUNCT
ejpam-5161	164	39	ω1	ω1	PROPN
ejpam-5161	164	40	,	,	PUNCT
ejpam-5161	164	41	{	{	PUNCT
ejpam-5161	164	42	x1	x1	ADJ
ejpam-5161	164	43	}	}	PUNCT
ejpam-5161	164	44	)	)	PUNCT
ejpam-5161	164	45	,	,	PUNCT
ejpam-5161	164	46	(	(	PUNCT
ejpam-5161	164	47	ω2	ω2	ADJ
ejpam-5161	164	48	,	,	PUNCT
ejpam-5161	164	49	∅	∅	NOUN
ejpam-5161	164	50	)	)	PUNCT
ejpam-5161	164	51	}	}	PUNCT
ejpam-5161	164	52	,	,	PUNCT
ejpam-5161	164	53	(	(	PUNCT
ejpam-5161	164	54	r2,ω	r2,ω	NOUN
ejpam-5161	164	55	)	)	PUNCT
ejpam-5161	164	56	=	=	PRON
ejpam-5161	165	1	{	{	PUNCT
ejpam-5161	165	2	(	(	PUNCT
ejpam-5161	165	3	ω1	ω1	PROPN
ejpam-5161	165	4	,	,	PUNCT
ejpam-5161	165	5	{	{	PUNCT
ejpam-5161	165	6	x1	x1	PROPN
ejpam-5161	165	7	,	,	PUNCT
ejpam-5161	165	8	x2	x2	PROPN
ejpam-5161	165	9	}	}	PUNCT
ejpam-5161	165	10	)	)	PUNCT
ejpam-5161	165	11	,	,	PUNCT
ejpam-5161	165	12	(	(	PUNCT
ejpam-5161	165	13	ω2	ω2	ADJ
ejpam-5161	165	14	,	,	PUNCT
ejpam-5161	165	15	x	x	NOUN
ejpam-5161	165	16	)	)	PUNCT
ejpam-5161	165	17	}	}	PUNCT
ejpam-5161	165	18	,	,	PUNCT
ejpam-5161	165	19	(	(	PUNCT
ejpam-5161	165	20	r3,ω	r3,ω	PROPN
ejpam-5161	165	21	)	)	PUNCT
ejpam-5161	165	22	=	=	PRON
ejpam-5161	165	23	{	{	PUNCT
ejpam-5161	165	24	(	(	PUNCT
ejpam-5161	165	25	ω1	ω1	PROPN
ejpam-5161	165	26	,	,	PUNCT
ejpam-5161	165	27	x	x	NOUN
ejpam-5161	165	28	)	)	PUNCT
ejpam-5161	165	29	,	,	PUNCT
ejpam-5161	165	30	(	(	PUNCT
ejpam-5161	165	31	ω2	ω2	ADV
ejpam-5161	165	32	,	,	PUNCT
ejpam-5161	165	33	{	{	PUNCT
ejpam-5161	165	34	x3	x3	ADJ
ejpam-5161	165	35	}	}	PUNCT
ejpam-5161	165	36	)	)	PUNCT
ejpam-5161	165	37	}	}	PUNCT
ejpam-5161	165	38	,	,	PUNCT
ejpam-5161	165	39	and	and	CCONJ
ejpam-5161	165	40	(	(	PUNCT
ejpam-5161	165	41	r4,ω	r4,ω	PROPN
ejpam-5161	165	42	)	)	PUNCT
ejpam-5161	165	43	=	=	SYM
ejpam-5161	165	44	{	{	PUNCT
ejpam-5161	165	45	(	(	PUNCT
ejpam-5161	165	46	ω1	ω1	PROPN
ejpam-5161	165	47	,	,	PUNCT
ejpam-5161	165	48	{	{	PUNCT
ejpam-5161	165	49	x1	x1	PROPN
ejpam-5161	165	50	,	,	PUNCT
ejpam-5161	165	51	x2	x2	PROPN
ejpam-5161	165	52	}	}	PUNCT
ejpam-5161	165	53	)	)	PUNCT
ejpam-5161	165	54	,	,	PUNCT
ejpam-5161	165	55	(	(	PUNCT
ejpam-5161	165	56	ω2	ω2	ADV
ejpam-5161	165	57	,	,	PUNCT
ejpam-5161	165	58	{	{	PUNCT
ejpam-5161	165	59	x3	x3	ADJ
ejpam-5161	165	60	}	}	PUNCT
ejpam-5161	165	61	)	)	PUNCT
ejpam-5161	165	62	}	}	PUNCT
ejpam-5161	165	63	.	.	PUNCT
ejpam-5161	166	1	then	then	ADV
ejpam-5161	166	2	σ	σ	PROPN
ejpam-5161	166	3	and	and	CCONJ
ejpam-5161	166	4	σ′	σ′	PROPN
ejpam-5161	166	5	are	be	AUX
ejpam-5161	166	6	incomparable	incomparable	ADJ
ejpam-5161	166	7	.	.	PUNCT
ejpam-5161	167	1	set	set	VERB
ejpam-5161	167	2	σ̂	σ̂	X
ejpam-5161	167	3	=	=	SYM
ejpam-5161	167	4	σ	σ	PROPN
ejpam-5161	167	5	⋃̃	⋃̃	PROPN
ejpam-5161	167	6	σ′.	σ′.	NOUN
ejpam-5161	167	7	therefore	therefore	ADV
ejpam-5161	167	8	,	,	PUNCT
ejpam-5161	167	9	σ̂	σ̂	X
ejpam-5161	167	10	is	be	AUX
ejpam-5161	167	11	finer	fine	ADJ
ejpam-5161	167	12	than	than	ADP
ejpam-5161	167	13	both	both	DET
ejpam-5161	167	14	σ	σ	PROPN
ejpam-5161	167	15	and	and	CCONJ
ejpam-5161	167	16	σ′.	σ′.	PROPN
ejpam-5161	167	17	on	on	ADP
ejpam-5161	167	18	the	the	DET
ejpam-5161	167	19	other	other	ADJ
ejpam-5161	167	20	hand	hand	NOUN
ejpam-5161	167	21	,	,	PUNCT
ejpam-5161	167	22	σ	σ	PROPN
ejpam-5161	167	23	,	,	PUNCT
ejpam-5161	167	24	σ′	σ′	PROPN
ejpam-5161	167	25	and	and	CCONJ
ejpam-5161	167	26	σ̂	σ̂	PROPN
ejpam-5161	167	27	have	have	VERB
ejpam-5161	167	28	the	the	DET
ejpam-5161	167	29	same	same	ADJ
ejpam-5161	167	30	family	family	NOUN
ejpam-5161	167	31	of	of	ADP
ejpam-5161	167	32	crisp	crisp	ADJ
ejpam-5161	167	33	topologies	topology	NOUN
ejpam-5161	167	34	σ	σ	NOUN
ejpam-5161	167	35	=	=	SYM
ejpam-5161	167	36	{	{	PUNCT
ejpam-5161	167	37	σω1	σω1	NOUN
ejpam-5161	167	38	,	,	PUNCT
ejpam-5161	167	39	σω2	σω2	ADP
ejpam-5161	167	40	}	}	PUNCT
ejpam-5161	167	41	,	,	PUNCT
ejpam-5161	167	42	and	and	CCONJ
ejpam-5161	167	43	thus	thus	ADV
ejpam-5161	167	44	they	they	PRON
ejpam-5161	167	45	generate	generate	VERB
ejpam-5161	167	46	only	only	ADV
ejpam-5161	167	47	one	one	NUM
ejpam-5161	167	48	t	t	NOUN
ejpam-5161	167	49	(	(	PUNCT
ejpam-5161	167	50	σ	σ	PROPN
ejpam-5161	167	51	)	)	PUNCT
ejpam-5161	167	52	.	.	PUNCT
ejpam-5161	168	1	z.	z.	PROPN
ejpam-5161	168	2	a.	a.	PROPN
ejpam-5161	168	3	ameen	ameen	PROPN
ejpam-5161	168	4	et	et	PROPN
ejpam-5161	168	5	al	al	PROPN
ejpam-5161	168	6	.	.	PUNCT
ejpam-5161	168	7	/	/	SYM
ejpam-5161	168	8	eur	eur	PROPN
ejpam-5161	168	9	.	.	PUNCT
ejpam-5161	169	1	j.	j.	PROPN
ejpam-5161	169	2	pure	pure	PROPN
ejpam-5161	169	3	appl	appl	PROPN
ejpam-5161	169	4	.	.	PROPN
ejpam-5161	169	5	math	math	PROPN
ejpam-5161	169	6	,	,	PUNCT
ejpam-5161	169	7	17	17	NUM
ejpam-5161	169	8	(	(	PUNCT
ejpam-5161	169	9	2	2	NUM
ejpam-5161	169	10	)	)	PUNCT
ejpam-5161	169	11	(	(	PUNCT
ejpam-5161	169	12	2024	2024	NUM
ejpam-5161	169	13	)	)	PUNCT
ejpam-5161	169	14	,	,	PUNCT
ejpam-5161	169	15	1168	1168	NUM
ejpam-5161	169	16	-	-	SYM
ejpam-5161	169	17	1182	1182	NUM
ejpam-5161	169	18	1175	1175	NUM
ejpam-5161	169	19	5	5	NUM
ejpam-5161	169	20	.	.	PUNCT
ejpam-5161	169	21	separation	separation	NOUN
ejpam-5161	169	22	axioms	axiom	NOUN
ejpam-5161	169	23	preservation	preservation	NOUN
ejpam-5161	169	24	between	between	ADP
ejpam-5161	169	25	σ	σ	PROPN
ejpam-5161	169	26	and	and	CCONJ
ejpam-5161	169	27	t	t	PROPN
ejpam-5161	169	28	(	(	PUNCT
ejpam-5161	169	29	σ	σ	PROPN
ejpam-5161	169	30	)	)	PUNCT
ejpam-5161	169	31	with	with	ADP
ejpam-5161	169	32	the	the	DET
ejpam-5161	169	33	exception	exception	NOUN
ejpam-5161	169	34	of	of	ADP
ejpam-5161	169	35	t	t	PROPN
ejpam-5161	169	36	(	(	PUNCT
ejpam-5161	169	37	σ	σ	PROPN
ejpam-5161	169	38	)	)	PUNCT
ejpam-5161	169	39	,	,	PUNCT
ejpam-5161	169	40	a	a	DET
ejpam-5161	169	41	single	single	ADJ
ejpam-5161	169	42	set	set	VERB
ejpam-5161	169	43	soft	soft	ADJ
ejpam-5161	169	44	topology	topology	NOUN
ejpam-5161	169	45	t̂	t̂	PRON
ejpam-5161	169	46	(	(	PUNCT
ejpam-5161	169	47	σ	σ	NOUN
ejpam-5161	169	48	)	)	PUNCT
ejpam-5161	169	49	generated	generate	VERB
ejpam-5161	169	50	by	by	ADP
ejpam-5161	169	51	σ	σ	PROPN
ejpam-5161	169	52	inherits	inherit	VERB
ejpam-5161	169	53	soft	soft	ADJ
ejpam-5161	169	54	separation	separation	NOUN
ejpam-5161	169	55	axioms	axiom	NOUN
ejpam-5161	169	56	after	after	ADP
ejpam-5161	169	57	σ	σ	PROPN
ejpam-5161	169	58	,	,	PUNCT
ejpam-5161	169	59	according	accord	VERB
ejpam-5161	169	60	to	to	ADP
ejpam-5161	169	61	terepeta	terepeta	NOUN
ejpam-5161	169	62	[	[	X
ejpam-5161	169	63	29	29	NUM
ejpam-5161	169	64	]	]	PUNCT
ejpam-5161	169	65	.	.	PUNCT
ejpam-5161	170	1	in	in	ADP
ejpam-5161	170	2	this	this	DET
ejpam-5161	170	3	section	section	NOUN
ejpam-5161	170	4	,	,	PUNCT
ejpam-5161	170	5	we	we	PRON
ejpam-5161	170	6	use	use	VERB
ejpam-5161	170	7	t	t	PROPN
ejpam-5161	170	8	(	(	PUNCT
ejpam-5161	170	9	σ	σ	PROPN
ejpam-5161	170	10	)	)	PUNCT
ejpam-5161	170	11	to	to	PART
ejpam-5161	170	12	see	see	VERB
ejpam-5161	170	13	how	how	SCONJ
ejpam-5161	170	14	well	well	ADV
ejpam-5161	170	15	separation	separation	NOUN
ejpam-5161	170	16	axioms	axiom	NOUN
ejpam-5161	170	17	are	be	AUX
ejpam-5161	170	18	preserved	preserve	VERB
ejpam-5161	170	19	when	when	SCONJ
ejpam-5161	170	20	moving	move	VERB
ejpam-5161	170	21	from	from	ADP
ejpam-5161	170	22	σ	σ	PROPN
ejpam-5161	170	23	to	to	ADP
ejpam-5161	170	24	t	t	PROPN
ejpam-5161	170	25	(	(	PUNCT
ejpam-5161	170	26	σ	σ	PROPN
ejpam-5161	170	27	)	)	PUNCT
ejpam-5161	170	28	and	and	CCONJ
ejpam-5161	170	29	vice	vice	ADV
ejpam-5161	170	30	versa	versa	ADV
ejpam-5161	170	31	.	.	PUNCT
ejpam-5161	171	1	here	here	ADV
ejpam-5161	171	2	,	,	PUNCT
ejpam-5161	171	3	we	we	PRON
ejpam-5161	171	4	start	start	VERB
ejpam-5161	171	5	defining	define	VERB
ejpam-5161	171	6	special	special	ADJ
ejpam-5161	171	7	types	type	NOUN
ejpam-5161	171	8	of	of	ADP
ejpam-5161	171	9	soft	soft	ADJ
ejpam-5161	171	10	sets	set	NOUN
ejpam-5161	171	11	that	that	PRON
ejpam-5161	171	12	exist	exist	VERB
ejpam-5161	171	13	when	when	SCONJ
ejpam-5161	171	14	constructing	construct	VERB
ejpam-5161	171	15	a	a	DET
ejpam-5161	171	16	soft	soft	ADJ
ejpam-5161	171	17	topology	topology	NOUN
ejpam-5161	171	18	by	by	ADP
ejpam-5161	171	19	using	use	VERB
ejpam-5161	171	20	t	t	PROPN
ejpam-5161	171	21	(	(	PUNCT
ejpam-5161	171	22	σ	σ	PROPN
ejpam-5161	171	23	)	)	PUNCT
ejpam-5161	171	24	for	for	ADP
ejpam-5161	171	25	future	future	ADJ
ejpam-5161	171	26	usage	usage	NOUN
ejpam-5161	171	27	.	.	PUNCT
ejpam-5161	172	1	definition	definition	NOUN
ejpam-5161	172	2	8	8	NUM
ejpam-5161	172	3	.	.	PUNCT
ejpam-5161	173	1	let	let	VERB
ejpam-5161	173	2	g	g	NOUN
ejpam-5161	173	3	,	,	PUNCT
ejpam-5161	173	4	h	h	NOUN
ejpam-5161	173	5	⊂	⊂	PROPN
ejpam-5161	173	6	x	x	X
ejpam-5161	173	7	and	and	CCONJ
ejpam-5161	173	8	let	let	VERB
ejpam-5161	173	9	ω	ω	NUM
ejpam-5161	173	10	∈	∈	PROPN
ejpam-5161	173	11	ω	ω	PROPN
ejpam-5161	173	12	,	,	PUNCT
ejpam-5161	173	13	we	we	PRON
ejpam-5161	173	14	define	define	VERB
ejpam-5161	173	15	(	(	PUNCT
ejpam-5161	173	16	i	i	NOUN
ejpam-5161	173	17	)	)	PUNCT
ejpam-5161	173	18	(	(	PUNCT
ejpam-5161	173	19	fg	fg	PROPN
ejpam-5161	173	20	ω	ω	PROPN
ejpam-5161	173	21	,	,	PUNCT
ejpam-5161	173	22	ω	ω	NOUN
ejpam-5161	173	23	)	)	PUNCT
ejpam-5161	173	24	to	to	PART
ejpam-5161	173	25	be	be	AUX
ejpam-5161	173	26	a	a	DET
ejpam-5161	173	27	soft	soft	ADJ
ejpam-5161	173	28	set	set	NOUN
ejpam-5161	173	29	over	over	ADP
ejpam-5161	173	30	x	x	NOUN
ejpam-5161	173	31	such	such	ADJ
ejpam-5161	173	32	that	that	SCONJ
ejpam-5161	173	33	fg	fg	PROPN
ejpam-5161	173	34	ω	ω	PROPN
ejpam-5161	173	35	(	(	PUNCT
ejpam-5161	173	36	ω	ω	NOUN
ejpam-5161	173	37	)	)	PUNCT
ejpam-5161	173	38	=	=	SYM
ejpam-5161	173	39	g	g	PROPN
ejpam-5161	173	40	and	and	CCONJ
ejpam-5161	173	41	fg	fg	PROPN
ejpam-5161	173	42	ω	ω	PROPN
ejpam-5161	173	43	(	(	PUNCT
ejpam-5161	173	44	ω′	ω′	X
ejpam-5161	173	45	)	)	PUNCT
ejpam-5161	173	46	=	=	SYM
ejpam-5161	174	1	x	x	X
ejpam-5161	174	2	for	for	ADP
ejpam-5161	174	3	each	each	DET
ejpam-5161	174	4	ω′	ω′	NUM
ejpam-5161	174	5	̸=	̸=	PROPN
ejpam-5161	174	6	ω	ω	PROPN
ejpam-5161	174	7	.	.	PUNCT
ejpam-5161	174	8	(	(	PUNCT
ejpam-5161	174	9	ii	ii	NOUN
ejpam-5161	174	10	)	)	PUNCT
ejpam-5161	174	11	(	(	PUNCT
ejpam-5161	174	12	fω	fω	PROPN
ejpam-5161	174	13	h	h	NOUN
ejpam-5161	174	14	,	,	PUNCT
ejpam-5161	174	15	ω	ω	PROPN
ejpam-5161	174	16	)	)	PUNCT
ejpam-5161	174	17	to	to	PART
ejpam-5161	174	18	be	be	AUX
ejpam-5161	174	19	a	a	DET
ejpam-5161	174	20	soft	soft	ADJ
ejpam-5161	174	21	set	set	NOUN
ejpam-5161	174	22	over	over	ADP
ejpam-5161	174	23	x	x	NOUN
ejpam-5161	174	24	such	such	ADJ
ejpam-5161	174	25	that	that	SCONJ
ejpam-5161	174	26	fω	fω	PROPN
ejpam-5161	174	27	h(ω	h(ω	PROPN
ejpam-5161	174	28	)	)	PUNCT
ejpam-5161	174	29	=	=	SYM
ejpam-5161	174	30	h	h	NOUN
ejpam-5161	174	31	and	and	CCONJ
ejpam-5161	174	32	fω	fω	ADP
ejpam-5161	174	33	h(ω′	h(ω′	PROPN
ejpam-5161	174	34	)	)	PUNCT
ejpam-5161	175	1	=	=	NOUN
ejpam-5161	175	2	∅	∅	NOUN
ejpam-5161	175	3	for	for	ADP
ejpam-5161	175	4	each	each	DET
ejpam-5161	175	5	ω′	ω′	NUM
ejpam-5161	175	6	̸=	̸=	PROPN
ejpam-5161	175	7	ω	ω	NUM
ejpam-5161	175	8	,	,	PUNCT
ejpam-5161	175	9	(	(	PUNCT
ejpam-5161	175	10	see	see	VERB
ejpam-5161	175	11	,	,	PUNCT
ejpam-5161	175	12	[	[	X
ejpam-5161	175	13	3	3	NUM
ejpam-5161	175	14	,	,	PUNCT
ejpam-5161	175	15	definition	definition	NOUN
ejpam-5161	175	16	5	5	NUM
ejpam-5161	175	17	]	]	PUNCT
ejpam-5161	175	18	)	)	PUNCT
ejpam-5161	175	19	.	.	PUNCT
ejpam-5161	176	1	note	note	VERB
ejpam-5161	176	2	that	that	SCONJ
ejpam-5161	176	3	(	(	PUNCT
ejpam-5161	176	4	fg	fg	PROPN
ejpam-5161	176	5	ω	ω	PROPN
ejpam-5161	176	6	,	,	PUNCT
ejpam-5161	176	7	ω)c	ω)c	NOUN
ejpam-5161	176	8	=	=	SYM
ejpam-5161	176	9	(	(	PUNCT
ejpam-5161	176	10	fω	fω	PROPN
ejpam-5161	176	11	h	h	PROPN
ejpam-5161	176	12	,	,	PUNCT
ejpam-5161	176	13	ω	ω	PROPN
ejpam-5161	176	14	)	)	PUNCT
ejpam-5161	176	15	if	if	SCONJ
ejpam-5161	176	16	and	and	CCONJ
ejpam-5161	176	17	only	only	ADV
ejpam-5161	176	18	if	if	SCONJ
ejpam-5161	176	19	gc	gc	PROPN
ejpam-5161	176	20	=	=	PROPN
ejpam-5161	176	21	h.	h.	PROPN
ejpam-5161	176	22	theorem	theorem	VERB
ejpam-5161	176	23	1	1	X
ejpam-5161	176	24	.	.	PUNCT
ejpam-5161	177	1	let	let	VERB
ejpam-5161	177	2	σ	σ	NOUN
ejpam-5161	177	3	=	=	PUNCT
ejpam-5161	177	4	{	{	PUNCT
ejpam-5161	177	5	σω	σω	NOUN
ejpam-5161	177	6	:	:	PUNCT
ejpam-5161	177	7	ω	ω	PROPN
ejpam-5161	177	8	∈	∈	PROPN
ejpam-5161	177	9	ω	ω	PROPN
ejpam-5161	177	10	}	}	PUNCT
ejpam-5161	177	11	be	be	AUX
ejpam-5161	177	12	a	a	DET
ejpam-5161	177	13	family	family	NOUN
ejpam-5161	177	14	of	of	ADP
ejpam-5161	177	15	crisp	crisp	ADJ
ejpam-5161	177	16	topologies	topology	NOUN
ejpam-5161	177	17	on	on	ADP
ejpam-5161	177	18	x.	x.	NOUN
ejpam-5161	177	19	if	if	SCONJ
ejpam-5161	177	20	σω	σω	VERB
ejpam-5161	177	21	is	be	AUX
ejpam-5161	177	22	a	a	DET
ejpam-5161	177	23	t0	t0	NOUN
ejpam-5161	177	24	-	-	NOUN
ejpam-5161	177	25	space	space	NOUN
ejpam-5161	177	26	for	for	ADP
ejpam-5161	177	27	some	some	DET
ejpam-5161	177	28	ω	ω	NUM
ejpam-5161	177	29	∈	∈	PROPN
ejpam-5161	177	30	ω	ω	NOUN
ejpam-5161	177	31	then	then	ADV
ejpam-5161	177	32	t	t	PROPN
ejpam-5161	177	33	(	(	PUNCT
ejpam-5161	177	34	σ	σ	PROPN
ejpam-5161	177	35	)	)	PUNCT
ejpam-5161	177	36	is	be	AUX
ejpam-5161	177	37	a	a	DET
ejpam-5161	177	38	soft	soft	ADJ
ejpam-5161	177	39	t0	t0	NOUN
ejpam-5161	177	40	-	-	NOUN
ejpam-5161	177	41	space	space	NOUN
ejpam-5161	177	42	.	.	PUNCT
ejpam-5161	178	1	proof	proof	NOUN
ejpam-5161	178	2	.	.	PUNCT
ejpam-5161	179	1	suppose	suppose	VERB
ejpam-5161	179	2	that	that	SCONJ
ejpam-5161	179	3	σω	σω	PROPN
ejpam-5161	179	4	is	be	AUX
ejpam-5161	179	5	a	a	DET
ejpam-5161	179	6	t0	t0	NOUN
ejpam-5161	179	7	-	-	NOUN
ejpam-5161	179	8	space	space	NOUN
ejpam-5161	179	9	for	for	ADP
ejpam-5161	179	10	some	some	DET
ejpam-5161	179	11	ω	ω	NUM
ejpam-5161	179	12	∈	∈	PROPN
ejpam-5161	179	13	ω	ω	PROPN
ejpam-5161	179	14	.	.	PUNCT
ejpam-5161	180	1	let	let	VERB
ejpam-5161	180	2	x	x	PRON
ejpam-5161	180	3	,	,	PUNCT
ejpam-5161	180	4	y	y	PROPN
ejpam-5161	180	5	∈	∈	PROPN
ejpam-5161	180	6	x	x	PUNCT
ejpam-5161	180	7	with	with	ADP
ejpam-5161	180	8	x	x	PUNCT
ejpam-5161	180	9	̸=	̸=	PROPN
ejpam-5161	180	10	y.	y.	NOUN
ejpam-5161	180	11	then	then	ADV
ejpam-5161	180	12	there	there	PRON
ejpam-5161	180	13	exist	exist	VERB
ejpam-5161	180	14	open	open	ADJ
ejpam-5161	180	15	sets	set	NOUN
ejpam-5161	180	16	u	u	NOUN
ejpam-5161	180	17	,	,	PUNCT
ejpam-5161	180	18	v	v	PROPN
ejpam-5161	180	19	∈	∈	NOUN
ejpam-5161	180	20	σω	σω	VERB
ejpam-5161	180	21	such	such	ADJ
ejpam-5161	180	22	that	that	SCONJ
ejpam-5161	180	23	x	x	SYM
ejpam-5161	180	24	∈	∈	PROPN
ejpam-5161	180	25	u	u	NOUN
ejpam-5161	180	26	,	,	PUNCT
ejpam-5161	180	27	y	y	PROPN
ejpam-5161	180	28	/∈	/∈	PUNCT
ejpam-5161	180	29	u	u	NOUN
ejpam-5161	180	30	or	or	CCONJ
ejpam-5161	180	31	x	x	NOUN
ejpam-5161	180	32	/∈	/∈	PROPN
ejpam-5161	180	33	v	v	INTJ
ejpam-5161	180	34	,	,	PUNCT
ejpam-5161	180	35	y	y	PROPN
ejpam-5161	180	36	∈	∈	PROPN
ejpam-5161	180	37	v	v	NOUN
ejpam-5161	180	38	.	.	PUNCT
ejpam-5161	181	1	by	by	ADP
ejpam-5161	181	2	definition	definition	NOUN
ejpam-5161	181	3	8	8	NUM
ejpam-5161	181	4	,	,	PUNCT
ejpam-5161	181	5	there	there	PRON
ejpam-5161	181	6	exist	exist	VERB
ejpam-5161	181	7	two	two	NUM
ejpam-5161	181	8	corresponding	corresponding	ADJ
ejpam-5161	181	9	soft	soft	ADJ
ejpam-5161	181	10	sets	set	NOUN
ejpam-5161	181	11	(	(	PUNCT
ejpam-5161	181	12	fu	fu	PROPN
ejpam-5161	181	13	ω	ω	PROPN
ejpam-5161	181	14	,	,	PUNCT
ejpam-5161	181	15	ω	ω	PROPN
ejpam-5161	181	16	)	)	PUNCT
ejpam-5161	181	17	,	,	PUNCT
ejpam-5161	181	18	(	(	PUNCT
ejpam-5161	181	19	f	f	PROPN
ejpam-5161	181	20	v	v	X
ejpam-5161	181	21	ω	ω	PROPN
ejpam-5161	181	22	,	,	PUNCT
ejpam-5161	181	23	ω	ω	NUM
ejpam-5161	181	24	)	)	PUNCT
ejpam-5161	181	25	∈	∈	PROPN
ejpam-5161	181	26	t	t	PROPN
ejpam-5161	181	27	(	(	PUNCT
ejpam-5161	181	28	σ	σ	PROPN
ejpam-5161	181	29	)	)	PUNCT
ejpam-5161	181	30	for	for	ADP
ejpam-5161	181	31	which	which	PRON
ejpam-5161	181	32	x	x	SYM
ejpam-5161	181	33	∈	∈	PROPN
ejpam-5161	181	34	(	(	PUNCT
ejpam-5161	181	35	fu	fu	PROPN
ejpam-5161	181	36	ω	ω	PROPN
ejpam-5161	181	37	,	,	PUNCT
ejpam-5161	181	38	ω	ω	PROPN
ejpam-5161	181	39	)	)	PUNCT
ejpam-5161	181	40	,	,	PUNCT
ejpam-5161	181	41	y	y	PROPN
ejpam-5161	181	42	/∈	/∈	PUNCT
ejpam-5161	181	43	(	(	PUNCT
ejpam-5161	181	44	fu	fu	PROPN
ejpam-5161	181	45	ω	ω	PROPN
ejpam-5161	181	46	,	,	PUNCT
ejpam-5161	181	47	ω	ω	NOUN
ejpam-5161	181	48	)	)	PUNCT
ejpam-5161	181	49	or	or	CCONJ
ejpam-5161	181	50	x	x	PUNCT
ejpam-5161	181	51	/∈	/∈	PUNCT
ejpam-5161	182	1	(	(	PUNCT
ejpam-5161	182	2	f	f	PROPN
ejpam-5161	182	3	v	v	PROPN
ejpam-5161	182	4	ω	ω	PROPN
ejpam-5161	182	5	,	,	PUNCT
ejpam-5161	182	6	ω	ω	PROPN
ejpam-5161	182	7	)	)	PUNCT
ejpam-5161	182	8	,	,	PUNCT
ejpam-5161	182	9	y	y	PROPN
ejpam-5161	182	10	∈	∈	PROPN
ejpam-5161	182	11	(	(	PUNCT
ejpam-5161	182	12	f	f	PROPN
ejpam-5161	182	13	v	v	PROPN
ejpam-5161	182	14	ω	ω	PROPN
ejpam-5161	182	15	,	,	PUNCT
ejpam-5161	182	16	ω	ω	PROPN
ejpam-5161	182	17	)	)	PUNCT
ejpam-5161	182	18	.	.	PUNCT
ejpam-5161	183	1	thus	thus	ADV
ejpam-5161	183	2	,	,	PUNCT
ejpam-5161	183	3	t	t	PROPN
ejpam-5161	183	4	(	(	PUNCT
ejpam-5161	183	5	σ	σ	PROPN
ejpam-5161	183	6	)	)	PUNCT
ejpam-5161	183	7	is	be	AUX
ejpam-5161	183	8	soft	soft	ADJ
ejpam-5161	183	9	t0	t0	NOUN
ejpam-5161	183	10	.	.	PUNCT
ejpam-5161	184	1	the	the	DET
ejpam-5161	184	2	following	follow	VERB
ejpam-5161	184	3	example	example	NOUN
ejpam-5161	184	4	shows	show	VERB
ejpam-5161	184	5	that	that	SCONJ
ejpam-5161	184	6	the	the	DET
ejpam-5161	184	7	converse	converse	NOUN
ejpam-5161	184	8	of	of	ADP
ejpam-5161	184	9	theorem	theorem	NOUN
ejpam-5161	184	10	1	1	NUM
ejpam-5161	184	11	is	be	AUX
ejpam-5161	184	12	not	not	PART
ejpam-5161	184	13	true	true	ADJ
ejpam-5161	184	14	in	in	ADP
ejpam-5161	184	15	general	general	ADJ
ejpam-5161	184	16	.	.	PUNCT
ejpam-5161	185	1	example	example	NOUN
ejpam-5161	186	1	3	3	X
ejpam-5161	186	2	.	.	PUNCT
ejpam-5161	186	3	let	let	VERB
ejpam-5161	186	4	x	x	PUNCT
ejpam-5161	186	5	=	=	PRON
ejpam-5161	186	6	{	{	PUNCT
ejpam-5161	186	7	x1	x1	PROPN
ejpam-5161	186	8	,	,	PUNCT
ejpam-5161	186	9	x2	x2	PROPN
ejpam-5161	186	10	,	,	PUNCT
ejpam-5161	186	11	x3	x3	ADJ
ejpam-5161	186	12	}	}	PUNCT
ejpam-5161	186	13	and	and	CCONJ
ejpam-5161	186	14	let	let	VERB
ejpam-5161	186	15	σω1	σω1	NOUN
ejpam-5161	186	16	=	=	SYM
ejpam-5161	186	17	{	{	PUNCT
ejpam-5161	186	18	∅	∅	NOUN
ejpam-5161	186	19	,	,	PUNCT
ejpam-5161	186	20	{	{	PUNCT
ejpam-5161	186	21	x1	x1	PROPN
ejpam-5161	186	22	}	}	PUNCT
ejpam-5161	186	23	,	,	PUNCT
ejpam-5161	186	24	{	{	PUNCT
ejpam-5161	186	25	x2	x2	ADJ
ejpam-5161	186	26	,	,	PUNCT
ejpam-5161	186	27	x3	x3	ADJ
ejpam-5161	186	28	}	}	PUNCT
ejpam-5161	186	29	,	,	PUNCT
ejpam-5161	186	30	x	x	NOUN
ejpam-5161	186	31	}	}	PUNCT
ejpam-5161	186	32	and	and	CCONJ
ejpam-5161	186	33	σω2	σω2	ADP
ejpam-5161	186	34	=	=	SYM
ejpam-5161	186	35	{	{	PUNCT
ejpam-5161	186	36	∅	∅	NOUN
ejpam-5161	186	37	,	,	PUNCT
ejpam-5161	186	38	{	{	PUNCT
ejpam-5161	186	39	x3	x3	ADJ
ejpam-5161	186	40	}	}	PUNCT
ejpam-5161	186	41	,	,	PUNCT
ejpam-5161	186	42	{	{	PUNCT
ejpam-5161	186	43	x1	x1	PROPN
ejpam-5161	186	44	,	,	PUNCT
ejpam-5161	186	45	x2	x2	PROPN
ejpam-5161	186	46	}	}	PUNCT
ejpam-5161	186	47	,	,	PUNCT
ejpam-5161	186	48	x	x	X
ejpam-5161	186	49	}	}	PUNCT
ejpam-5161	186	50	be	be	AUX
ejpam-5161	186	51	crisp	crisp	ADJ
ejpam-5161	186	52	topologies	topology	NOUN
ejpam-5161	186	53	on	on	ADP
ejpam-5161	186	54	x	x	PUNCT
ejpam-5161	186	55	indexed	index	VERB
ejpam-5161	186	56	by	by	ADP
ejpam-5161	186	57	ω	ω	PROPN
ejpam-5161	186	58	=	=	SYM
ejpam-5161	186	59	{	{	PUNCT
ejpam-5161	186	60	ω1	ω1	PROPN
ejpam-5161	186	61	,	,	PUNCT
ejpam-5161	186	62	ω2	ω2	ADJ
ejpam-5161	186	63	}	}	PUNCT
ejpam-5161	186	64	.	.	PUNCT
ejpam-5161	187	1	by	by	ADP
ejpam-5161	187	2	using	use	VERB
ejpam-5161	187	3	the	the	DET
ejpam-5161	187	4	formula	formula	NOUN
ejpam-5161	187	5	1	1	NUM
ejpam-5161	187	6	,	,	PUNCT
ejpam-5161	187	7	the	the	DET
ejpam-5161	187	8	following	follow	VERB
ejpam-5161	187	9	soft	soft	ADJ
ejpam-5161	187	10	topology	topology	NOUN
ejpam-5161	187	11	on	on	ADP
ejpam-5161	187	12	x	x	PUNCT
ejpam-5161	187	13	will	will	AUX
ejpam-5161	187	14	be	be	AUX
ejpam-5161	187	15	obtained	obtain	VERB
ejpam-5161	187	16	:	:	PUNCT
ejpam-5161	187	17	t	t	PROPN
ejpam-5161	187	18	(	(	PUNCT
ejpam-5161	187	19	σ	σ	PROPN
ejpam-5161	187	20	)	)	PUNCT
ejpam-5161	187	21	=	=	SYM
ejpam-5161	187	22	t	t	PROPN
ejpam-5161	187	23	(	(	PUNCT
ejpam-5161	187	24	{	{	PUNCT
ejpam-5161	187	25	σω1	σω1	NOUN
ejpam-5161	187	26	,	,	PUNCT
ejpam-5161	187	27	σω2	σω2	ADP
ejpam-5161	187	28	}	}	PUNCT
ejpam-5161	187	29	)	)	PUNCT
ejpam-5161	187	30	=	=	PRON
ejpam-5161	187	31	{	{	PUNCT
ejpam-5161	187	32	φ̃	φ̃	PROPN
ejpam-5161	187	33	,	,	PUNCT
ejpam-5161	187	34	(	(	PUNCT
ejpam-5161	187	35	h1,ω	h1,ω	PROPN
ejpam-5161	187	36	)	)	PUNCT
ejpam-5161	187	37	,	,	PUNCT
ejpam-5161	187	38	(	(	PUNCT
ejpam-5161	187	39	h2,ω	h2,ω	PROPN
ejpam-5161	187	40	)	)	PUNCT
ejpam-5161	187	41	,	,	PUNCT
ejpam-5161	187	42	(	(	PUNCT
ejpam-5161	187	43	h3,ω	h3,ω	PROPN
ejpam-5161	187	44	)	)	PUNCT
ejpam-5161	187	45	,	,	PUNCT
ejpam-5161	187	46	·	·	PUNCT
ejpam-5161	187	47	·	·	PUNCT
ejpam-5161	187	48	·	·	PUNCT
ejpam-5161	187	49	,	,	PUNCT
ejpam-5161	187	50	(	(	PUNCT
ejpam-5161	187	51	h14,ω	h14,ω	ADJ
ejpam-5161	187	52	)	)	PUNCT
ejpam-5161	187	53	,	,	PUNCT
ejpam-5161	187	54	x̃	x̃	PROPN
ejpam-5161	187	55	}	}	PUNCT
ejpam-5161	187	56	,	,	PUNCT
ejpam-5161	187	57	where	where	SCONJ
ejpam-5161	187	58	(	(	PUNCT
ejpam-5161	187	59	h1,ω	h1,ω	NOUN
ejpam-5161	187	60	)	)	PUNCT
ejpam-5161	187	61	=	=	PRON
ejpam-5161	187	62	{	{	PUNCT
ejpam-5161	187	63	(	(	PUNCT
ejpam-5161	187	64	ω1	ω1	PROPN
ejpam-5161	187	65	,	,	PUNCT
ejpam-5161	187	66	x	x	NOUN
ejpam-5161	187	67	)	)	PUNCT
ejpam-5161	187	68	,	,	PUNCT
ejpam-5161	187	69	(	(	PUNCT
ejpam-5161	187	70	ω2	ω2	ADJ
ejpam-5161	187	71	,	,	PUNCT
ejpam-5161	187	72	∅	∅	NOUN
ejpam-5161	187	73	)	)	PUNCT
ejpam-5161	187	74	}	}	PUNCT
ejpam-5161	187	75	,	,	PUNCT
ejpam-5161	187	76	(	(	PUNCT
ejpam-5161	187	77	h2,ω	h2,ω	PROPN
ejpam-5161	187	78	)	)	PUNCT
ejpam-5161	187	79	=	=	PRON
ejpam-5161	187	80	{	{	PUNCT
ejpam-5161	187	81	(	(	PUNCT
ejpam-5161	187	82	ω1	ω1	PROPN
ejpam-5161	187	83	,	,	PUNCT
ejpam-5161	187	84	{	{	PUNCT
ejpam-5161	187	85	x1	x1	ADJ
ejpam-5161	187	86	}	}	PUNCT
ejpam-5161	187	87	)	)	PUNCT
ejpam-5161	187	88	,	,	PUNCT
ejpam-5161	187	89	(	(	PUNCT
ejpam-5161	187	90	ω2	ω2	ADJ
ejpam-5161	187	91	,	,	PUNCT
ejpam-5161	187	92	∅	∅	NOUN
ejpam-5161	187	93	)	)	PUNCT
ejpam-5161	187	94	}	}	PUNCT
ejpam-5161	187	95	,	,	PUNCT
ejpam-5161	187	96	(	(	PUNCT
ejpam-5161	187	97	h3,ω	h3,ω	PROPN
ejpam-5161	187	98	)	)	PUNCT
ejpam-5161	187	99	=	=	PRON
ejpam-5161	187	100	{	{	PUNCT
ejpam-5161	187	101	(	(	PUNCT
ejpam-5161	187	102	ω1	ω1	PROPN
ejpam-5161	187	103	,	,	PUNCT
ejpam-5161	187	104	{	{	PUNCT
ejpam-5161	187	105	x2	x2	ADJ
ejpam-5161	187	106	,	,	PUNCT
ejpam-5161	187	107	x3	x3	ADJ
ejpam-5161	187	108	}	}	PUNCT
ejpam-5161	187	109	)	)	PUNCT
ejpam-5161	187	110	,	,	PUNCT
ejpam-5161	187	111	(	(	PUNCT
ejpam-5161	187	112	ω2	ω2	ADJ
ejpam-5161	187	113	,	,	PUNCT
ejpam-5161	187	114	∅	∅	NOUN
ejpam-5161	187	115	)	)	PUNCT
ejpam-5161	187	116	}	}	PUNCT
ejpam-5161	187	117	,	,	PUNCT
ejpam-5161	187	118	(	(	PUNCT
ejpam-5161	187	119	h4,ω	h4,ω	PROPN
ejpam-5161	187	120	)	)	PUNCT
ejpam-5161	187	121	=	=	SYM
ejpam-5161	187	122	{	{	PUNCT
ejpam-5161	187	123	(	(	PUNCT
ejpam-5161	187	124	ω1	ω1	PROPN
ejpam-5161	187	125	,	,	PUNCT
ejpam-5161	187	126	∅	∅	NOUN
ejpam-5161	187	127	)	)	PUNCT
ejpam-5161	187	128	,	,	PUNCT
ejpam-5161	187	129	(	(	PUNCT
ejpam-5161	187	130	ω2	ω2	ADJ
ejpam-5161	187	131	,	,	PUNCT
ejpam-5161	187	132	x	x	NOUN
ejpam-5161	187	133	)	)	PUNCT
ejpam-5161	187	134	}	}	PUNCT
ejpam-5161	187	135	,	,	PUNCT
ejpam-5161	187	136	(	(	PUNCT
ejpam-5161	187	137	h5,ω	h5,ω	PROPN
ejpam-5161	187	138	)	)	PUNCT
ejpam-5161	187	139	=	=	PRON
ejpam-5161	187	140	{	{	PUNCT
ejpam-5161	187	141	(	(	PUNCT
ejpam-5161	187	142	ω1	ω1	PROPN
ejpam-5161	187	143	,	,	PUNCT
ejpam-5161	187	144	{	{	PUNCT
ejpam-5161	187	145	x1	x1	ADJ
ejpam-5161	187	146	}	}	PUNCT
ejpam-5161	187	147	)	)	PUNCT
ejpam-5161	187	148	,	,	PUNCT
ejpam-5161	187	149	(	(	PUNCT
ejpam-5161	187	150	ω2	ω2	ADJ
ejpam-5161	187	151	,	,	PUNCT
ejpam-5161	187	152	x	x	NOUN
ejpam-5161	187	153	)	)	PUNCT
ejpam-5161	187	154	}	}	PUNCT
ejpam-5161	187	155	,	,	PUNCT
ejpam-5161	187	156	(	(	PUNCT
ejpam-5161	187	157	h6,ω	h6,ω	PROPN
ejpam-5161	187	158	)	)	PUNCT
ejpam-5161	187	159	=	=	PRON
ejpam-5161	187	160	{	{	PUNCT
ejpam-5161	187	161	(	(	PUNCT
ejpam-5161	187	162	ω1	ω1	PROPN
ejpam-5161	187	163	,	,	PUNCT
ejpam-5161	187	164	{	{	PUNCT
ejpam-5161	187	165	x2	x2	ADJ
ejpam-5161	187	166	,	,	PUNCT
ejpam-5161	187	167	x3	x3	ADJ
ejpam-5161	187	168	}	}	PUNCT
ejpam-5161	187	169	)	)	PUNCT
ejpam-5161	187	170	,	,	PUNCT
ejpam-5161	187	171	(	(	PUNCT
ejpam-5161	187	172	ω2	ω2	ADJ
ejpam-5161	187	173	,	,	PUNCT
ejpam-5161	187	174	x	x	NOUN
ejpam-5161	187	175	)	)	PUNCT
ejpam-5161	187	176	}	}	PUNCT
ejpam-5161	187	177	,	,	PUNCT
ejpam-5161	187	178	(	(	PUNCT
ejpam-5161	187	179	h7,ω	h7,ω	PROPN
ejpam-5161	187	180	)	)	PUNCT
ejpam-5161	187	181	=	=	SYM
ejpam-5161	187	182	{	{	PUNCT
ejpam-5161	187	183	(	(	PUNCT
ejpam-5161	187	184	ω1	ω1	PROPN
ejpam-5161	187	185	,	,	PUNCT
ejpam-5161	187	186	∅	∅	NOUN
ejpam-5161	187	187	)	)	PUNCT
ejpam-5161	187	188	,	,	PUNCT
ejpam-5161	187	189	(	(	PUNCT
ejpam-5161	187	190	ω2	ω2	ADV
ejpam-5161	187	191	,	,	PUNCT
ejpam-5161	187	192	{	{	PUNCT
ejpam-5161	187	193	x1	x1	PROPN
ejpam-5161	187	194	,	,	PUNCT
ejpam-5161	187	195	x2	x2	PROPN
ejpam-5161	187	196	}	}	PUNCT
ejpam-5161	187	197	)	)	PUNCT
ejpam-5161	187	198	}	}	PUNCT
ejpam-5161	187	199	,	,	PUNCT
ejpam-5161	187	200	(	(	PUNCT
ejpam-5161	187	201	h8,ω	h8,ω	PROPN
ejpam-5161	187	202	)	)	PUNCT
ejpam-5161	187	203	=	=	SYM
ejpam-5161	187	204	{	{	PUNCT
ejpam-5161	187	205	(	(	PUNCT
ejpam-5161	187	206	ω1	ω1	PROPN
ejpam-5161	187	207	,	,	PUNCT
ejpam-5161	187	208	x	x	NOUN
ejpam-5161	187	209	)	)	PUNCT
ejpam-5161	187	210	,	,	PUNCT
ejpam-5161	187	211	(	(	PUNCT
ejpam-5161	187	212	ω2	ω2	ADV
ejpam-5161	187	213	,	,	PUNCT
ejpam-5161	187	214	{	{	PUNCT
ejpam-5161	187	215	x1	x1	PROPN
ejpam-5161	187	216	,	,	PUNCT
ejpam-5161	187	217	x2	x2	PROPN
ejpam-5161	187	218	}	}	PUNCT
ejpam-5161	187	219	)	)	PUNCT
ejpam-5161	187	220	}	}	PUNCT
ejpam-5161	187	221	,	,	PUNCT
ejpam-5161	187	222	(	(	PUNCT
ejpam-5161	187	223	h9,ω	h9,ω	PROPN
ejpam-5161	187	224	)	)	PUNCT
ejpam-5161	187	225	=	=	PRON
ejpam-5161	187	226	{	{	PUNCT
ejpam-5161	187	227	(	(	PUNCT
ejpam-5161	187	228	ω1	ω1	PROPN
ejpam-5161	187	229	,	,	PUNCT
ejpam-5161	187	230	{	{	PUNCT
ejpam-5161	187	231	x1	x1	ADJ
ejpam-5161	187	232	}	}	PUNCT
ejpam-5161	187	233	)	)	PUNCT
ejpam-5161	187	234	,	,	PUNCT
ejpam-5161	187	235	(	(	PUNCT
ejpam-5161	187	236	ω2	ω2	ADV
ejpam-5161	187	237	,	,	PUNCT
ejpam-5161	187	238	{	{	PUNCT
ejpam-5161	187	239	x1	x1	PROPN
ejpam-5161	187	240	,	,	PUNCT
ejpam-5161	187	241	x2	x2	PROPN
ejpam-5161	187	242	}	}	PUNCT
ejpam-5161	187	243	)	)	PUNCT
ejpam-5161	187	244	}	}	PUNCT
ejpam-5161	187	245	,	,	PUNCT
ejpam-5161	187	246	z.	z.	PROPN
ejpam-5161	187	247	a.	a.	PROPN
ejpam-5161	187	248	ameen	ameen	PROPN
ejpam-5161	187	249	et	et	PROPN
ejpam-5161	187	250	al	al	PROPN
ejpam-5161	187	251	.	.	PUNCT
ejpam-5161	187	252	/	/	SYM
ejpam-5161	187	253	eur	eur	PROPN
ejpam-5161	187	254	.	.	PUNCT
ejpam-5161	188	1	j.	j.	PROPN
ejpam-5161	188	2	pure	pure	PROPN
ejpam-5161	188	3	appl	appl	PROPN
ejpam-5161	188	4	.	.	PROPN
ejpam-5161	188	5	math	math	PROPN
ejpam-5161	188	6	,	,	PUNCT
ejpam-5161	188	7	17	17	NUM
ejpam-5161	188	8	(	(	PUNCT
ejpam-5161	188	9	2	2	NUM
ejpam-5161	188	10	)	)	PUNCT
ejpam-5161	188	11	(	(	PUNCT
ejpam-5161	188	12	2024	2024	NUM
ejpam-5161	188	13	)	)	PUNCT
ejpam-5161	188	14	,	,	PUNCT
ejpam-5161	188	15	1168	1168	NUM
ejpam-5161	188	16	-	-	SYM
ejpam-5161	188	17	1182	1182	NUM
ejpam-5161	188	18	1176	1176	NUM
ejpam-5161	188	19	(	(	PUNCT
ejpam-5161	188	20	h10,ω	h10,ω	ADJ
ejpam-5161	188	21	)	)	PUNCT
ejpam-5161	188	22	=	=	PRON
ejpam-5161	188	23	{	{	PUNCT
ejpam-5161	188	24	(	(	PUNCT
ejpam-5161	188	25	ω1	ω1	PROPN
ejpam-5161	188	26	,	,	PUNCT
ejpam-5161	188	27	{	{	PUNCT
ejpam-5161	188	28	x2	x2	ADJ
ejpam-5161	188	29	,	,	PUNCT
ejpam-5161	188	30	x3	x3	ADJ
ejpam-5161	188	31	}	}	PUNCT
ejpam-5161	188	32	)	)	PUNCT
ejpam-5161	188	33	,	,	PUNCT
ejpam-5161	188	34	(	(	PUNCT
ejpam-5161	188	35	ω2	ω2	ADV
ejpam-5161	188	36	,	,	PUNCT
ejpam-5161	188	37	{	{	PUNCT
ejpam-5161	188	38	x1	x1	PROPN
ejpam-5161	188	39	,	,	PUNCT
ejpam-5161	188	40	x2	x2	PROPN
ejpam-5161	188	41	}	}	PUNCT
ejpam-5161	188	42	)	)	PUNCT
ejpam-5161	188	43	}	}	PUNCT
ejpam-5161	188	44	,	,	PUNCT
ejpam-5161	188	45	(	(	PUNCT
ejpam-5161	188	46	h11,ω	h11,ω	NOUN
ejpam-5161	188	47	)	)	PUNCT
ejpam-5161	188	48	=	=	PRON
ejpam-5161	188	49	{	{	PUNCT
ejpam-5161	188	50	(	(	PUNCT
ejpam-5161	188	51	ω1	ω1	PROPN
ejpam-5161	188	52	,	,	PUNCT
ejpam-5161	188	53	∅	∅	NOUN
ejpam-5161	188	54	)	)	PUNCT
ejpam-5161	188	55	,	,	PUNCT
ejpam-5161	188	56	(	(	PUNCT
ejpam-5161	188	57	ω2	ω2	ADV
ejpam-5161	188	58	,	,	PUNCT
ejpam-5161	188	59	{	{	PUNCT
ejpam-5161	188	60	x3	x3	ADJ
ejpam-5161	188	61	}	}	PUNCT
ejpam-5161	188	62	)	)	PUNCT
ejpam-5161	188	63	}	}	PUNCT
ejpam-5161	188	64	,	,	PUNCT
ejpam-5161	188	65	(	(	PUNCT
ejpam-5161	188	66	h12,ω	h12,ω	NOUN
ejpam-5161	188	67	)	)	PUNCT
ejpam-5161	188	68	=	=	PRON
ejpam-5161	188	69	{	{	PUNCT
ejpam-5161	188	70	(	(	PUNCT
ejpam-5161	188	71	ω1	ω1	PROPN
ejpam-5161	188	72	,	,	PUNCT
ejpam-5161	188	73	x	x	NOUN
ejpam-5161	188	74	)	)	PUNCT
ejpam-5161	188	75	,	,	PUNCT
ejpam-5161	188	76	(	(	PUNCT
ejpam-5161	188	77	ω2	ω2	ADV
ejpam-5161	188	78	,	,	PUNCT
ejpam-5161	188	79	{	{	PUNCT
ejpam-5161	188	80	x3	x3	ADJ
ejpam-5161	188	81	}	}	PUNCT
ejpam-5161	188	82	)	)	PUNCT
ejpam-5161	188	83	}	}	PUNCT
ejpam-5161	188	84	,	,	PUNCT
ejpam-5161	188	85	(	(	PUNCT
ejpam-5161	188	86	h13,ω	h13,ω	X
ejpam-5161	188	87	)	)	PUNCT
ejpam-5161	188	88	=	=	SYM
ejpam-5161	188	89	{	{	PUNCT
ejpam-5161	188	90	(	(	PUNCT
ejpam-5161	188	91	ω1	ω1	PROPN
ejpam-5161	188	92	,	,	PUNCT
ejpam-5161	188	93	{	{	PUNCT
ejpam-5161	188	94	x1	x1	ADJ
ejpam-5161	188	95	}	}	PUNCT
ejpam-5161	188	96	)	)	PUNCT
ejpam-5161	188	97	,	,	PUNCT
ejpam-5161	188	98	(	(	PUNCT
ejpam-5161	188	99	ω2	ω2	ADV
ejpam-5161	188	100	,	,	PUNCT
ejpam-5161	188	101	{	{	PUNCT
ejpam-5161	188	102	x3	x3	ADJ
ejpam-5161	188	103	}	}	PUNCT
ejpam-5161	188	104	)	)	PUNCT
ejpam-5161	188	105	}	}	PUNCT
ejpam-5161	188	106	,	,	PUNCT
ejpam-5161	188	107	and	and	CCONJ
ejpam-5161	188	108	(	(	PUNCT
ejpam-5161	188	109	h14,ω	h14,ω	ADJ
ejpam-5161	188	110	)	)	PUNCT
ejpam-5161	188	111	=	=	PRON
ejpam-5161	188	112	{	{	PUNCT
ejpam-5161	188	113	(	(	PUNCT
ejpam-5161	188	114	ω1	ω1	PROPN
ejpam-5161	188	115	,	,	PUNCT
ejpam-5161	188	116	{	{	PUNCT
ejpam-5161	188	117	x2	x2	ADJ
ejpam-5161	188	118	,	,	PUNCT
ejpam-5161	188	119	x3	x3	ADJ
ejpam-5161	188	120	}	}	PUNCT
ejpam-5161	188	121	)	)	PUNCT
ejpam-5161	188	122	,	,	PUNCT
ejpam-5161	188	123	(	(	PUNCT
ejpam-5161	188	124	ω2	ω2	ADV
ejpam-5161	188	125	,	,	PUNCT
ejpam-5161	188	126	{	{	PUNCT
ejpam-5161	188	127	x3	x3	ADJ
ejpam-5161	188	128	}	}	PUNCT
ejpam-5161	188	129	)	)	PUNCT
ejpam-5161	188	130	}	}	PUNCT
ejpam-5161	188	131	.	.	PUNCT
ejpam-5161	189	1	since	since	SCONJ
ejpam-5161	189	2	x1	x1	PROPN
ejpam-5161	189	3	∈	∈	PROPN
ejpam-5161	189	4	(	(	PUNCT
ejpam-5161	189	5	h5,ω	h5,ω	PROPN
ejpam-5161	189	6	)	)	PUNCT
ejpam-5161	189	7	,	,	PUNCT
ejpam-5161	189	8	x2	x2	PROPN
ejpam-5161	189	9	,	,	PUNCT
ejpam-5161	189	10	x3	x3	PROPN
ejpam-5161	189	11	̸∈	̸∈	PROPN
ejpam-5161	189	12	(	(	PUNCT
ejpam-5161	189	13	h5,ω	h5,ω	PROPN
ejpam-5161	189	14	)	)	PUNCT
ejpam-5161	189	15	and	and	CCONJ
ejpam-5161	189	16	x3	x3	PROPN
ejpam-5161	189	17	∈	∈	PROPN
ejpam-5161	189	18	(	(	PUNCT
ejpam-5161	189	19	h14,ω	h14,ω	ADJ
ejpam-5161	189	20	)	)	PUNCT
ejpam-5161	189	21	,	,	PUNCT
ejpam-5161	189	22	x2	x2	PROPN
ejpam-5161	189	23	̸∈	̸∈	PROPN
ejpam-5161	189	24	(	(	PUNCT
ejpam-5161	189	25	h14,ω	h14,ω	PROPN
ejpam-5161	189	26	)	)	PUNCT
ejpam-5161	189	27	,	,	PUNCT
ejpam-5161	189	28	then	then	ADV
ejpam-5161	189	29	t	t	PROPN
ejpam-5161	189	30	(	(	PUNCT
ejpam-5161	189	31	σ	σ	PROPN
ejpam-5161	189	32	)	)	PUNCT
ejpam-5161	189	33	is	be	AUX
ejpam-5161	189	34	soft	soft	ADJ
ejpam-5161	189	35	t0	t0	NOUN
ejpam-5161	189	36	.	.	PUNCT
ejpam-5161	190	1	on	on	ADP
ejpam-5161	190	2	the	the	DET
ejpam-5161	190	3	other	other	ADJ
ejpam-5161	190	4	hand	hand	NOUN
ejpam-5161	190	5	,	,	PUNCT
ejpam-5161	190	6	neither	neither	PRON
ejpam-5161	190	7	of	of	ADP
ejpam-5161	190	8	σω1	σω1	NOUN
ejpam-5161	190	9	nor	nor	CCONJ
ejpam-5161	190	10	σω2	σω2	ADP
ejpam-5161	190	11	is	be	AUX
ejpam-5161	190	12	t0	t0	NOUN
ejpam-5161	190	13	.	.	PUNCT
ejpam-5161	191	1	theorem	theorem	NOUN
ejpam-5161	191	2	2	2	NUM
ejpam-5161	191	3	.	.	PUNCT
ejpam-5161	192	1	let	let	VERB
ejpam-5161	192	2	σ	σ	NOUN
ejpam-5161	192	3	=	=	PUNCT
ejpam-5161	192	4	{	{	PUNCT
ejpam-5161	192	5	σω	σω	NOUN
ejpam-5161	192	6	:	:	PUNCT
ejpam-5161	192	7	ω	ω	PROPN
ejpam-5161	192	8	∈	∈	PROPN
ejpam-5161	192	9	ω	ω	PROPN
ejpam-5161	192	10	}	}	PUNCT
ejpam-5161	192	11	be	be	AUX
ejpam-5161	192	12	a	a	DET
ejpam-5161	192	13	family	family	NOUN
ejpam-5161	192	14	of	of	ADP
ejpam-5161	192	15	crisp	crisp	ADJ
ejpam-5161	192	16	topologies	topology	NOUN
ejpam-5161	192	17	on	on	ADP
ejpam-5161	192	18	x.	x.	NOUN
ejpam-5161	192	19	if	if	SCONJ
ejpam-5161	192	20	σω	σω	VERB
ejpam-5161	192	21	is	be	AUX
ejpam-5161	192	22	a	a	DET
ejpam-5161	192	23	t1	t1	NOUN
ejpam-5161	192	24	-	-	PUNCT
ejpam-5161	192	25	space	space	NOUN
ejpam-5161	192	26	for	for	ADP
ejpam-5161	192	27	some	some	DET
ejpam-5161	192	28	ω	ω	NUM
ejpam-5161	192	29	∈	∈	PROPN
ejpam-5161	192	30	ω	ω	PROPN
ejpam-5161	192	31	,	,	PUNCT
ejpam-5161	192	32	then	then	ADV
ejpam-5161	192	33	t	t	PROPN
ejpam-5161	192	34	(	(	PUNCT
ejpam-5161	192	35	σ	σ	PROPN
ejpam-5161	192	36	)	)	PUNCT
ejpam-5161	192	37	is	be	AUX
ejpam-5161	192	38	a	a	DET
ejpam-5161	192	39	soft	soft	ADJ
ejpam-5161	192	40	t1	t1	NOUN
ejpam-5161	192	41	-	-	PUNCT
ejpam-5161	192	42	space	space	NOUN
ejpam-5161	192	43	.	.	PUNCT
ejpam-5161	193	1	proof	proof	NOUN
ejpam-5161	193	2	.	.	PUNCT
ejpam-5161	194	1	it	it	PRON
ejpam-5161	194	2	is	be	AUX
ejpam-5161	194	3	entirely	entirely	ADV
ejpam-5161	194	4	analogous	analogous	ADJ
ejpam-5161	194	5	to	to	ADP
ejpam-5161	194	6	the	the	DET
ejpam-5161	194	7	first	first	ADJ
ejpam-5161	194	8	part	part	NOUN
ejpam-5161	194	9	of	of	ADP
ejpam-5161	194	10	the	the	DET
ejpam-5161	194	11	proof	proof	NOUN
ejpam-5161	194	12	of	of	ADP
ejpam-5161	194	13	theorem	theorem	NOUN
ejpam-5161	194	14	1	1	NUM
ejpam-5161	194	15	.	.	PUNCT
ejpam-5161	195	1	the	the	DET
ejpam-5161	195	2	following	follow	VERB
ejpam-5161	195	3	example	example	NOUN
ejpam-5161	195	4	shows	show	VERB
ejpam-5161	195	5	that	that	SCONJ
ejpam-5161	195	6	the	the	DET
ejpam-5161	195	7	converse	converse	NOUN
ejpam-5161	195	8	of	of	ADP
ejpam-5161	195	9	theorem	theorem	ADJ
ejpam-5161	195	10	2	2	NUM
ejpam-5161	195	11	is	be	AUX
ejpam-5161	195	12	not	not	PART
ejpam-5161	195	13	true	true	ADJ
ejpam-5161	195	14	in	in	ADP
ejpam-5161	195	15	general	general	ADJ
ejpam-5161	195	16	.	.	PUNCT
ejpam-5161	196	1	it	it	PRON
ejpam-5161	196	2	also	also	ADV
ejpam-5161	196	3	refutes	refute	VERB
ejpam-5161	196	4	theorem	theorem	VERB
ejpam-5161	196	5	3.5	3.5	NUM
ejpam-5161	196	6	in	in	ADP
ejpam-5161	196	7	[	[	X
ejpam-5161	196	8	18	18	NUM
ejpam-5161	196	9	]	]	SYM
ejpam-5161	196	10	:	:	PUNCT
ejpam-5161	196	11	example	example	NOUN
ejpam-5161	197	1	4	4	X
ejpam-5161	197	2	.	.	PUNCT
ejpam-5161	198	1	let	let	VERB
ejpam-5161	198	2	x	x	PUNCT
ejpam-5161	198	3	=	=	PRON
ejpam-5161	198	4	{	{	PUNCT
ejpam-5161	198	5	x1	x1	PROPN
ejpam-5161	198	6	,	,	PUNCT
ejpam-5161	198	7	x2	x2	PROPN
ejpam-5161	198	8	}	}	PUNCT
ejpam-5161	198	9	and	and	CCONJ
ejpam-5161	198	10	let	let	VERB
ejpam-5161	198	11	σω1	σω1	NOUN
ejpam-5161	198	12	=	=	SYM
ejpam-5161	198	13	{	{	PUNCT
ejpam-5161	198	14	∅	∅	NOUN
ejpam-5161	198	15	,	,	PUNCT
ejpam-5161	198	16	{	{	PUNCT
ejpam-5161	198	17	x1	x1	PROPN
ejpam-5161	198	18	}	}	PUNCT
ejpam-5161	198	19	,	,	PUNCT
ejpam-5161	198	20	x	x	NOUN
ejpam-5161	198	21	}	}	PUNCT
ejpam-5161	198	22	and	and	CCONJ
ejpam-5161	198	23	σω2	σω2	ADP
ejpam-5161	198	24	=	=	SYM
ejpam-5161	198	25	{	{	PUNCT
ejpam-5161	198	26	∅	∅	NOUN
ejpam-5161	198	27	,	,	PUNCT
ejpam-5161	198	28	{	{	PUNCT
ejpam-5161	198	29	x2	x2	ADJ
ejpam-5161	198	30	}	}	PUNCT
ejpam-5161	198	31	,	,	PUNCT
ejpam-5161	198	32	x	x	X
ejpam-5161	198	33	}	}	PUNCT
ejpam-5161	198	34	be	be	AUX
ejpam-5161	198	35	crisp	crisp	ADJ
ejpam-5161	198	36	topologies	topology	NOUN
ejpam-5161	198	37	on	on	ADP
ejpam-5161	198	38	x	x	PUNCT
ejpam-5161	198	39	indexed	index	VERB
ejpam-5161	198	40	by	by	ADP
ejpam-5161	198	41	ω	ω	PROPN
ejpam-5161	198	42	=	=	SYM
ejpam-5161	198	43	{	{	PUNCT
ejpam-5161	198	44	ω1	ω1	PROPN
ejpam-5161	198	45	,	,	PUNCT
ejpam-5161	198	46	ω2	ω2	ADJ
ejpam-5161	198	47	}	}	PUNCT
ejpam-5161	198	48	.	.	PUNCT
ejpam-5161	199	1	by	by	ADP
ejpam-5161	199	2	using	use	VERB
ejpam-5161	199	3	the	the	DET
ejpam-5161	199	4	formula	formula	NOUN
ejpam-5161	199	5	1	1	NUM
ejpam-5161	199	6	,	,	PUNCT
ejpam-5161	199	7	the	the	DET
ejpam-5161	199	8	following	follow	VERB
ejpam-5161	199	9	soft	soft	ADJ
ejpam-5161	199	10	topology	topology	NOUN
ejpam-5161	199	11	on	on	ADP
ejpam-5161	199	12	x	x	PUNCT
ejpam-5161	199	13	will	will	AUX
ejpam-5161	199	14	be	be	AUX
ejpam-5161	199	15	obtained	obtain	VERB
ejpam-5161	199	16	:	:	PUNCT
ejpam-5161	199	17	t	t	PROPN
ejpam-5161	199	18	(	(	PUNCT
ejpam-5161	199	19	σ	σ	PROPN
ejpam-5161	199	20	)	)	PUNCT
ejpam-5161	199	21	=	=	SYM
ejpam-5161	199	22	t	t	PROPN
ejpam-5161	199	23	(	(	PUNCT
ejpam-5161	199	24	{	{	PUNCT
ejpam-5161	199	25	σω1	σω1	NOUN
ejpam-5161	199	26	,	,	PUNCT
ejpam-5161	199	27	σω2	σω2	ADP
ejpam-5161	199	28	}	}	PUNCT
ejpam-5161	199	29	)	)	PUNCT
ejpam-5161	200	1	=	=	NOUN
ejpam-5161	200	2	{	{	PUNCT
ejpam-5161	200	3	φ̃	φ̃	PROPN
ejpam-5161	200	4	,	,	PUNCT
ejpam-5161	200	5	(	(	PUNCT
ejpam-5161	200	6	h1,ω	h1,ω	PROPN
ejpam-5161	200	7	)	)	PUNCT
ejpam-5161	200	8	,	,	PUNCT
ejpam-5161	200	9	(	(	PUNCT
ejpam-5161	200	10	h2,ω	h2,ω	PROPN
ejpam-5161	200	11	)	)	PUNCT
ejpam-5161	200	12	,	,	PUNCT
ejpam-5161	200	13	(	(	PUNCT
ejpam-5161	200	14	h3,ω	h3,ω	PROPN
ejpam-5161	200	15	)	)	PUNCT
ejpam-5161	200	16	,	,	PUNCT
ejpam-5161	200	17	(	(	PUNCT
ejpam-5161	200	18	h4,ω	h4,ω	PROPN
ejpam-5161	200	19	)	)	PUNCT
ejpam-5161	200	20	,	,	PUNCT
ejpam-5161	200	21	(	(	PUNCT
ejpam-5161	200	22	h5,ω	h5,ω	PROPN
ejpam-5161	200	23	)	)	PUNCT
ejpam-5161	200	24	,	,	PUNCT
ejpam-5161	200	25	(	(	PUNCT
ejpam-5161	200	26	h6,ω	h6,ω	PROPN
ejpam-5161	200	27	)	)	PUNCT
ejpam-5161	200	28	,	,	PUNCT
ejpam-5161	200	29	(	(	PUNCT
ejpam-5161	200	30	h7,ω	h7,ω	PROPN
ejpam-5161	200	31	)	)	PUNCT
ejpam-5161	200	32	,	,	PUNCT
ejpam-5161	200	33	x̃	x̃	PROPN
ejpam-5161	200	34	}	}	PUNCT
ejpam-5161	200	35	,	,	PUNCT
ejpam-5161	200	36	where	where	SCONJ
ejpam-5161	200	37	(	(	PUNCT
ejpam-5161	200	38	h1,ω	h1,ω	NOUN
ejpam-5161	200	39	)	)	PUNCT
ejpam-5161	200	40	=	=	PRON
ejpam-5161	200	41	{	{	PUNCT
ejpam-5161	200	42	(	(	PUNCT
ejpam-5161	200	43	ω1	ω1	PROPN
ejpam-5161	200	44	,	,	PUNCT
ejpam-5161	200	45	∅	∅	NOUN
ejpam-5161	200	46	)	)	PUNCT
ejpam-5161	200	47	,	,	PUNCT
ejpam-5161	200	48	(	(	PUNCT
ejpam-5161	200	49	ω2	ω2	ADJ
ejpam-5161	200	50	,	,	PUNCT
ejpam-5161	200	51	x	x	NOUN
ejpam-5161	200	52	)	)	PUNCT
ejpam-5161	200	53	}	}	PUNCT
ejpam-5161	200	54	,	,	PUNCT
ejpam-5161	200	55	(	(	PUNCT
ejpam-5161	200	56	h2,ω	h2,ω	PROPN
ejpam-5161	200	57	)	)	PUNCT
ejpam-5161	200	58	=	=	PRON
ejpam-5161	200	59	{	{	PUNCT
ejpam-5161	200	60	(	(	PUNCT
ejpam-5161	200	61	ω1	ω1	PROPN
ejpam-5161	200	62	,	,	PUNCT
ejpam-5161	200	63	x	x	NOUN
ejpam-5161	200	64	)	)	PUNCT
ejpam-5161	200	65	,	,	PUNCT
ejpam-5161	200	66	(	(	PUNCT
ejpam-5161	200	67	ω2	ω2	ADJ
ejpam-5161	200	68	,	,	PUNCT
ejpam-5161	200	69	∅	∅	NOUN
ejpam-5161	200	70	)	)	PUNCT
ejpam-5161	200	71	}	}	PUNCT
ejpam-5161	200	72	,	,	PUNCT
ejpam-5161	200	73	(	(	PUNCT
ejpam-5161	200	74	h3,ω	h3,ω	PROPN
ejpam-5161	200	75	)	)	PUNCT
ejpam-5161	200	76	=	=	PRON
ejpam-5161	200	77	{	{	PUNCT
ejpam-5161	200	78	(	(	PUNCT
ejpam-5161	200	79	ω1	ω1	PROPN
ejpam-5161	200	80	,	,	PUNCT
ejpam-5161	200	81	∅	∅	NOUN
ejpam-5161	200	82	)	)	PUNCT
ejpam-5161	200	83	,	,	PUNCT
ejpam-5161	200	84	(	(	PUNCT
ejpam-5161	200	85	ω2	ω2	ADV
ejpam-5161	200	86	,	,	PUNCT
ejpam-5161	200	87	{	{	PUNCT
ejpam-5161	200	88	x2	x2	ADJ
ejpam-5161	200	89	}	}	PUNCT
ejpam-5161	200	90	)	)	PUNCT
ejpam-5161	200	91	}	}	PUNCT
ejpam-5161	200	92	,	,	PUNCT
ejpam-5161	200	93	(	(	PUNCT
ejpam-5161	200	94	h4,ω	h4,ω	PROPN
ejpam-5161	200	95	)	)	PUNCT
ejpam-5161	200	96	=	=	SYM
ejpam-5161	200	97	{	{	PUNCT
ejpam-5161	200	98	(	(	PUNCT
ejpam-5161	200	99	ω1	ω1	PROPN
ejpam-5161	200	100	,	,	PUNCT
ejpam-5161	200	101	x	x	NOUN
ejpam-5161	200	102	)	)	PUNCT
ejpam-5161	200	103	,	,	PUNCT
ejpam-5161	200	104	(	(	PUNCT
ejpam-5161	200	105	ω2	ω2	ADV
ejpam-5161	200	106	,	,	PUNCT
ejpam-5161	200	107	{	{	PUNCT
ejpam-5161	200	108	x2	x2	ADJ
ejpam-5161	200	109	}	}	PUNCT
ejpam-5161	200	110	)	)	PUNCT
ejpam-5161	200	111	}	}	PUNCT
ejpam-5161	200	112	,	,	PUNCT
ejpam-5161	200	113	(	(	PUNCT
ejpam-5161	200	114	h5,ω	h5,ω	PROPN
ejpam-5161	200	115	)	)	PUNCT
ejpam-5161	200	116	=	=	PRON
ejpam-5161	200	117	{	{	PUNCT
ejpam-5161	200	118	(	(	PUNCT
ejpam-5161	200	119	ω1	ω1	PROPN
ejpam-5161	200	120	,	,	PUNCT
ejpam-5161	200	121	{	{	PUNCT
ejpam-5161	200	122	x1	x1	ADJ
ejpam-5161	200	123	}	}	PUNCT
ejpam-5161	200	124	)	)	PUNCT
ejpam-5161	200	125	,	,	PUNCT
ejpam-5161	200	126	(	(	PUNCT
ejpam-5161	200	127	ω2	ω2	ADJ
ejpam-5161	200	128	,	,	PUNCT
ejpam-5161	200	129	∅	∅	NOUN
ejpam-5161	200	130	)	)	PUNCT
ejpam-5161	200	131	}	}	PUNCT
ejpam-5161	200	132	,	,	PUNCT
ejpam-5161	200	133	(	(	PUNCT
ejpam-5161	200	134	h6,ω	h6,ω	PROPN
ejpam-5161	200	135	)	)	PUNCT
ejpam-5161	200	136	=	=	PRON
ejpam-5161	200	137	{	{	PUNCT
ejpam-5161	200	138	(	(	PUNCT
ejpam-5161	200	139	ω1	ω1	PROPN
ejpam-5161	200	140	,	,	PUNCT
ejpam-5161	200	141	{	{	PUNCT
ejpam-5161	200	142	x1	x1	ADJ
ejpam-5161	200	143	}	}	PUNCT
ejpam-5161	200	144	)	)	PUNCT
ejpam-5161	200	145	,	,	PUNCT
ejpam-5161	200	146	(	(	PUNCT
ejpam-5161	200	147	ω2	ω2	ADJ
ejpam-5161	200	148	,	,	PUNCT
ejpam-5161	200	149	x	x	NOUN
ejpam-5161	200	150	)	)	PUNCT
ejpam-5161	200	151	}	}	PUNCT
ejpam-5161	200	152	,	,	PUNCT
ejpam-5161	200	153	and	and	CCONJ
ejpam-5161	200	154	(	(	PUNCT
ejpam-5161	200	155	h7,ω	h7,ω	PROPN
ejpam-5161	200	156	)	)	PUNCT
ejpam-5161	200	157	=	=	SYM
ejpam-5161	200	158	{	{	PUNCT
ejpam-5161	200	159	(	(	PUNCT
ejpam-5161	200	160	ω1	ω1	PROPN
ejpam-5161	200	161	,	,	PUNCT
ejpam-5161	200	162	{	{	PUNCT
ejpam-5161	200	163	x1	x1	ADJ
ejpam-5161	200	164	}	}	PUNCT
ejpam-5161	200	165	)	)	PUNCT
ejpam-5161	200	166	,	,	PUNCT
ejpam-5161	200	167	(	(	PUNCT
ejpam-5161	200	168	ω2	ω2	ADV
ejpam-5161	200	169	,	,	PUNCT
ejpam-5161	200	170	{	{	PUNCT
ejpam-5161	200	171	x2	x2	ADJ
ejpam-5161	200	172	}	}	PUNCT
ejpam-5161	200	173	)	)	PUNCT
ejpam-5161	200	174	}	}	PUNCT
ejpam-5161	200	175	.	.	PUNCT
ejpam-5161	201	1	then	then	ADV
ejpam-5161	201	2	(	(	PUNCT
ejpam-5161	201	3	h4,ω	h4,ω	PROPN
ejpam-5161	201	4	)	)	PUNCT
ejpam-5161	201	5	and	and	CCONJ
ejpam-5161	201	6	(	(	PUNCT
ejpam-5161	201	7	h6,ω	h6,ω	PROPN
ejpam-5161	201	8	)	)	PUNCT
ejpam-5161	201	9	are	be	AUX
ejpam-5161	201	10	soft	soft	ADJ
ejpam-5161	201	11	open	open	ADJ
ejpam-5161	201	12	sets	set	NOUN
ejpam-5161	201	13	in	in	ADP
ejpam-5161	201	14	t	t	PROPN
ejpam-5161	201	15	(	(	PUNCT
ejpam-5161	201	16	σ	σ	PROPN
ejpam-5161	201	17	)	)	PUNCT
ejpam-5161	201	18	such	such	ADJ
ejpam-5161	201	19	that	that	SCONJ
ejpam-5161	201	20	x1	x1	PROPN
ejpam-5161	201	21	∈	∈	PROPN
ejpam-5161	201	22	(	(	PUNCT
ejpam-5161	201	23	h6,ω	h6,ω	PROPN
ejpam-5161	201	24	)	)	PUNCT
ejpam-5161	201	25	,	,	PUNCT
ejpam-5161	201	26	x2	x2	PROPN
ejpam-5161	201	27	/∈	/∈	PUNCT
ejpam-5161	201	28	(	(	PUNCT
ejpam-5161	201	29	h6,ω	h6,ω	PROPN
ejpam-5161	201	30	)	)	PUNCT
ejpam-5161	201	31	and	and	CCONJ
ejpam-5161	201	32	x2	x2	PROPN
ejpam-5161	201	33	∈	∈	PROPN
ejpam-5161	201	34	(	(	PUNCT
ejpam-5161	201	35	h4,ω	h4,ω	PROPN
ejpam-5161	201	36	)	)	PUNCT
ejpam-5161	201	37	,	,	PUNCT
ejpam-5161	201	38	x1	x1	PROPN
ejpam-5161	201	39	/∈	/∈	PUNCT
ejpam-5161	201	40	(	(	PUNCT
ejpam-5161	201	41	h4,ω	h4,ω	PROPN
ejpam-5161	201	42	)	)	PUNCT
ejpam-5161	201	43	.	.	PUNCT
ejpam-5161	202	1	thus	thus	ADV
ejpam-5161	202	2	,	,	PUNCT
ejpam-5161	202	3	t	t	PROPN
ejpam-5161	202	4	(	(	PUNCT
ejpam-5161	202	5	σ	σ	NOUN
ejpam-5161	202	6	)	)	PUNCT
ejpam-5161	202	7	is	be	AUX
ejpam-5161	202	8	soft	soft	ADJ
ejpam-5161	202	9	t1	t1	NOUN
ejpam-5161	202	10	.	.	PUNCT
ejpam-5161	203	1	on	on	ADP
ejpam-5161	203	2	the	the	DET
ejpam-5161	203	3	other	other	ADJ
ejpam-5161	203	4	hand	hand	NOUN
ejpam-5161	203	5	,	,	PUNCT
ejpam-5161	203	6	neither	neither	PRON
ejpam-5161	203	7	of	of	ADP
ejpam-5161	203	8	σω1	σω1	NOUN
ejpam-5161	203	9	nor	nor	CCONJ
ejpam-5161	203	10	σω2	σω2	NOUN
ejpam-5161	203	11	is	be	AUX
ejpam-5161	203	12	t1	t1	NOUN
ejpam-5161	203	13	.	.	PUNCT
ejpam-5161	204	1	theorem	theorem	NOUN
ejpam-5161	204	2	3	3	X
ejpam-5161	204	3	.	.	PUNCT
ejpam-5161	205	1	let	let	VERB
ejpam-5161	205	2	σ	σ	NOUN
ejpam-5161	205	3	=	=	PUNCT
ejpam-5161	205	4	{	{	PUNCT
ejpam-5161	205	5	σω	σω	NOUN
ejpam-5161	205	6	:	:	PUNCT
ejpam-5161	205	7	ω	ω	PROPN
ejpam-5161	205	8	∈	∈	PROPN
ejpam-5161	205	9	ω	ω	PROPN
ejpam-5161	205	10	}	}	PUNCT
ejpam-5161	205	11	be	be	AUX
ejpam-5161	205	12	a	a	DET
ejpam-5161	205	13	family	family	NOUN
ejpam-5161	205	14	of	of	ADP
ejpam-5161	205	15	crisp	crisp	ADJ
ejpam-5161	205	16	topologies	topology	NOUN
ejpam-5161	205	17	on	on	ADP
ejpam-5161	205	18	x.	x.	NOUN
ejpam-5161	205	19	then	then	ADV
ejpam-5161	205	20	σω	σω	VERB
ejpam-5161	205	21	is	be	AUX
ejpam-5161	205	22	a	a	DET
ejpam-5161	205	23	t2	t2	NOUN
ejpam-5161	205	24	-	-	PUNCT
ejpam-5161	205	25	space	space	NOUN
ejpam-5161	205	26	for	for	ADP
ejpam-5161	205	27	each	each	DET
ejpam-5161	205	28	ω	ω	PROPN
ejpam-5161	205	29	∈	∈	PROPN
ejpam-5161	205	30	ω	ω	NOUN
ejpam-5161	206	1	if	if	SCONJ
ejpam-5161	206	2	and	and	CCONJ
ejpam-5161	206	3	only	only	ADV
ejpam-5161	206	4	if	if	SCONJ
ejpam-5161	206	5	t	t	PROPN
ejpam-5161	206	6	(	(	PUNCT
ejpam-5161	206	7	σ	σ	PROPN
ejpam-5161	206	8	)	)	PUNCT
ejpam-5161	206	9	is	be	AUX
ejpam-5161	206	10	a	a	DET
ejpam-5161	206	11	soft	soft	ADJ
ejpam-5161	206	12	t2	t2	NOUN
ejpam-5161	206	13	-	-	PUNCT
ejpam-5161	206	14	space	space	NOUN
ejpam-5161	206	15	.	.	PUNCT
ejpam-5161	207	1	proof	proof	NOUN
ejpam-5161	207	2	.	.	PUNCT
ejpam-5161	208	1	assume	assume	VERB
ejpam-5161	208	2	that	that	SCONJ
ejpam-5161	208	3	σω	σω	VERB
ejpam-5161	208	4	is	be	AUX
ejpam-5161	208	5	t2	t2	NOUN
ejpam-5161	208	6	for	for	ADP
ejpam-5161	208	7	each	each	DET
ejpam-5161	208	8	ω	ω	PROPN
ejpam-5161	208	9	∈	∈	PROPN
ejpam-5161	208	10	ω	ω	PROPN
ejpam-5161	208	11	.	.	PUNCT
ejpam-5161	209	1	let	let	VERB
ejpam-5161	209	2	x	x	PRON
ejpam-5161	209	3	,	,	PUNCT
ejpam-5161	209	4	y	y	PROPN
ejpam-5161	209	5	∈	∈	PROPN
ejpam-5161	209	6	x	x	PUNCT
ejpam-5161	209	7	with	with	ADP
ejpam-5161	209	8	x	x	PUNCT
ejpam-5161	209	9	̸=	̸=	PROPN
ejpam-5161	209	10	y.	y.	NOUN
ejpam-5161	209	11	then	then	ADV
ejpam-5161	209	12	,	,	PUNCT
ejpam-5161	209	13	for	for	ADP
ejpam-5161	209	14	each	each	DET
ejpam-5161	209	15	ω	ω	NOUN
ejpam-5161	209	16	,	,	PUNCT
ejpam-5161	209	17	there	there	PRON
ejpam-5161	209	18	exist	exist	VERB
ejpam-5161	209	19	open	open	ADJ
ejpam-5161	209	20	sets	set	NOUN
ejpam-5161	209	21	u(ω	u(ω	PROPN
ejpam-5161	209	22	)	)	PUNCT
ejpam-5161	209	23	,	,	PUNCT
ejpam-5161	209	24	v	v	X
ejpam-5161	209	25	(	(	PUNCT
ejpam-5161	209	26	ω	ω	NOUN
ejpam-5161	209	27	)	)	PUNCT
ejpam-5161	209	28	∈	∈	PROPN
ejpam-5161	209	29	σω	σω	VERB
ejpam-5161	209	30	such	such	ADJ
ejpam-5161	209	31	that	that	SCONJ
ejpam-5161	209	32	x	x	SYM
ejpam-5161	209	33	∈	∈	PROPN
ejpam-5161	209	34	u(ω	u(ω	PROPN
ejpam-5161	209	35	)	)	PUNCT
ejpam-5161	209	36	,	,	PUNCT
ejpam-5161	209	37	y	y	PROPN
ejpam-5161	209	38	∈	∈	PROPN
ejpam-5161	209	39	v	v	PROPN
ejpam-5161	209	40	(	(	PUNCT
ejpam-5161	209	41	ω	ω	NOUN
ejpam-5161	209	42	)	)	PUNCT
ejpam-5161	209	43	and	and	CCONJ
ejpam-5161	209	44	u(ω	u(ω	PROPN
ejpam-5161	209	45	)	)	PUNCT
ejpam-5161	209	46	∩	∩	PROPN
ejpam-5161	209	47	v	v	X
ejpam-5161	209	48	(	(	PUNCT
ejpam-5161	209	49	ω	ω	NOUN
ejpam-5161	209	50	)	)	PUNCT
ejpam-5161	209	51	=	=	PUNCT
ejpam-5161	209	52	∅.	∅.	PRON
ejpam-5161	209	53	set	set	VERB
ejpam-5161	209	54	(	(	PUNCT
ejpam-5161	209	55	u	u	NOUN
ejpam-5161	209	56	,	,	PUNCT
ejpam-5161	209	57	ω	ω	NOUN
ejpam-5161	209	58	)	)	PUNCT
ejpam-5161	210	1	=	=	PRON
ejpam-5161	210	2	{	{	PUNCT
ejpam-5161	210	3	(	(	PUNCT
ejpam-5161	210	4	ω	ω	PROPN
ejpam-5161	210	5	,	,	PUNCT
ejpam-5161	210	6	u(ω	u(ω	PROPN
ejpam-5161	210	7	)	)	PUNCT
ejpam-5161	210	8	)	)	PUNCT
ejpam-5161	210	9	:	:	PUNCT
ejpam-5161	211	1	ω	ω	X
ejpam-5161	211	2	∈	∈	PROPN
ejpam-5161	211	3	ω	ω	PROPN
ejpam-5161	211	4	}	}	PUNCT
ejpam-5161	211	5	and	and	CCONJ
ejpam-5161	211	6	(	(	PUNCT
ejpam-5161	211	7	v	v	NOUN
ejpam-5161	211	8	,	,	PUNCT
ejpam-5161	211	9	ω	ω	NOUN
ejpam-5161	211	10	)	)	PUNCT
ejpam-5161	211	11	=	=	PRON
ejpam-5161	211	12	{	{	PUNCT
ejpam-5161	211	13	(	(	PUNCT
ejpam-5161	211	14	ω	ω	PROPN
ejpam-5161	211	15	,	,	PUNCT
ejpam-5161	211	16	v	v	PROPN
ejpam-5161	211	17	(	(	PUNCT
ejpam-5161	211	18	ω	ω	NOUN
ejpam-5161	211	19	)	)	PUNCT
ejpam-5161	211	20	)	)	PUNCT
ejpam-5161	211	21	:	:	PUNCT
ejpam-5161	212	1	ω	ω	X
ejpam-5161	212	2	∈	∈	PROPN
ejpam-5161	212	3	z.	z.	PROPN
ejpam-5161	212	4	a.	a.	NOUN
ejpam-5161	212	5	ameen	ameen	PROPN
ejpam-5161	212	6	et	et	PROPN
ejpam-5161	212	7	al	al	PROPN
ejpam-5161	212	8	.	.	PUNCT
ejpam-5161	212	9	/	/	SYM
ejpam-5161	212	10	eur	eur	PROPN
ejpam-5161	212	11	.	.	PUNCT
ejpam-5161	213	1	j.	j.	PROPN
ejpam-5161	213	2	pure	pure	PROPN
ejpam-5161	213	3	appl	appl	PROPN
ejpam-5161	213	4	.	.	PROPN
ejpam-5161	213	5	math	math	PROPN
ejpam-5161	213	6	,	,	PUNCT
ejpam-5161	213	7	17	17	NUM
ejpam-5161	213	8	(	(	PUNCT
ejpam-5161	213	9	2	2	NUM
ejpam-5161	213	10	)	)	PUNCT
ejpam-5161	213	11	(	(	PUNCT
ejpam-5161	213	12	2024	2024	NUM
ejpam-5161	213	13	)	)	PUNCT
ejpam-5161	213	14	,	,	PUNCT
ejpam-5161	213	15	1168	1168	NUM
ejpam-5161	213	16	-	-	SYM
ejpam-5161	213	17	1182	1182	NUM
ejpam-5161	213	18	1177	1177	NUM
ejpam-5161	213	19	ω	ω	NOUN
ejpam-5161	213	20	}	}	PUNCT
ejpam-5161	213	21	.	.	PUNCT
ejpam-5161	214	1	then	then	ADV
ejpam-5161	214	2	,	,	PUNCT
ejpam-5161	214	3	(	(	PUNCT
ejpam-5161	214	4	u	u	NOUN
ejpam-5161	214	5	,	,	PUNCT
ejpam-5161	214	6	ω	ω	NOUN
ejpam-5161	214	7	)	)	PUNCT
ejpam-5161	214	8	,	,	PUNCT
ejpam-5161	214	9	(	(	PUNCT
ejpam-5161	214	10	v	v	NOUN
ejpam-5161	214	11	,	,	PUNCT
ejpam-5161	214	12	ω	ω	NOUN
ejpam-5161	214	13	)	)	PUNCT
ejpam-5161	214	14	∈	∈	PROPN
ejpam-5161	214	15	t	t	PROPN
ejpam-5161	214	16	(	(	PUNCT
ejpam-5161	214	17	σ	σ	PROPN
ejpam-5161	214	18	)	)	PUNCT
ejpam-5161	214	19	such	such	ADJ
ejpam-5161	214	20	that	that	SCONJ
ejpam-5161	214	21	x	x	SYM
ejpam-5161	214	22	∈	∈	PROPN
ejpam-5161	214	23	(	(	PUNCT
ejpam-5161	214	24	u	u	NOUN
ejpam-5161	214	25	,	,	PUNCT
ejpam-5161	214	26	ω	ω	PROPN
ejpam-5161	214	27	)	)	PUNCT
ejpam-5161	214	28	,	,	PUNCT
ejpam-5161	214	29	y	y	PROPN
ejpam-5161	214	30	∈	∈	PROPN
ejpam-5161	214	31	(	(	PUNCT
ejpam-5161	214	32	v	v	NOUN
ejpam-5161	214	33	,	,	PUNCT
ejpam-5161	214	34	ω	ω	NOUN
ejpam-5161	214	35	)	)	PUNCT
ejpam-5161	214	36	and	and	CCONJ
ejpam-5161	214	37	(	(	PUNCT
ejpam-5161	214	38	u	u	NOUN
ejpam-5161	214	39	,	,	PUNCT
ejpam-5161	214	40	ω	ω	NOUN
ejpam-5161	214	41	)	)	PUNCT
ejpam-5161	214	42	⋂̃	⋂̃	NOUN
ejpam-5161	214	43	(	(	PUNCT
ejpam-5161	214	44	v	v	NOUN
ejpam-5161	214	45	,	,	PUNCT
ejpam-5161	214	46	ω	ω	NOUN
ejpam-5161	214	47	)	)	PUNCT
ejpam-5161	214	48	=	=	PRON
ejpam-5161	214	49	{	{	PUNCT
ejpam-5161	214	50	(	(	PUNCT
ejpam-5161	214	51	ω	ω	PROPN
ejpam-5161	214	52	,	,	PUNCT
ejpam-5161	214	53	u(ω	u(ω	PROPN
ejpam-5161	214	54	)	)	PUNCT
ejpam-5161	214	55	∩	∩	PROPN
ejpam-5161	214	56	v	v	X
ejpam-5161	214	57	(	(	PUNCT
ejpam-5161	214	58	ω	ω	NOUN
ejpam-5161	214	59	)	)	PUNCT
ejpam-5161	214	60	)	)	PUNCT
ejpam-5161	214	61	:	:	PUNCT
ejpam-5161	215	1	ω	ω	X
ejpam-5161	215	2	∈	∈	PROPN
ejpam-5161	215	3	ω	ω	NOUN
ejpam-5161	215	4	}	}	PUNCT
ejpam-5161	215	5	=	=	SYM
ejpam-5161	215	6	φ̃.	φ̃.	PROPN
ejpam-5161	215	7	hence	hence	ADV
ejpam-5161	215	8	,	,	PUNCT
ejpam-5161	215	9	t	t	PROPN
ejpam-5161	215	10	(	(	PUNCT
ejpam-5161	215	11	σ	σ	NOUN
ejpam-5161	215	12	)	)	PUNCT
ejpam-5161	215	13	is	be	AUX
ejpam-5161	215	14	soft	soft	ADJ
ejpam-5161	215	15	t2	t2	NOUN
ejpam-5161	215	16	.	.	PUNCT
ejpam-5161	216	1	conversely	conversely	ADV
ejpam-5161	216	2	,	,	PUNCT
ejpam-5161	216	3	let	let	VERB
ejpam-5161	216	4	x	x	PRON
ejpam-5161	216	5	,	,	PUNCT
ejpam-5161	216	6	y	y	PROPN
ejpam-5161	216	7	∈	∈	PROPN
ejpam-5161	216	8	x	x	PUNCT
ejpam-5161	216	9	with	with	ADP
ejpam-5161	216	10	x	x	PUNCT
ejpam-5161	216	11	̸=	̸=	PROPN
ejpam-5161	216	12	y.	y.	NOUN
ejpam-5161	216	13	suppose	suppose	VERB
ejpam-5161	216	14	that	that	SCONJ
ejpam-5161	216	15	t	t	PROPN
ejpam-5161	216	16	(	(	PUNCT
ejpam-5161	216	17	σ	σ	PROPN
ejpam-5161	216	18	)	)	PUNCT
ejpam-5161	216	19	is	be	AUX
ejpam-5161	216	20	soft	soft	ADJ
ejpam-5161	216	21	t2	t2	NOUN
ejpam-5161	216	22	.	.	PUNCT
ejpam-5161	217	1	then	then	ADV
ejpam-5161	217	2	,	,	PUNCT
ejpam-5161	217	3	there	there	PRON
ejpam-5161	217	4	exist	exist	VERB
ejpam-5161	217	5	soft	soft	ADJ
ejpam-5161	217	6	open	open	ADJ
ejpam-5161	217	7	sets	set	NOUN
ejpam-5161	217	8	(	(	PUNCT
ejpam-5161	217	9	g	g	PROPN
ejpam-5161	217	10	,	,	PUNCT
ejpam-5161	217	11	ω	ω	NOUN
ejpam-5161	217	12	)	)	PUNCT
ejpam-5161	217	13	,	,	PUNCT
ejpam-5161	217	14	(	(	PUNCT
ejpam-5161	217	15	h	h	NOUN
ejpam-5161	217	16	,	,	PUNCT
ejpam-5161	217	17	ω	ω	NOUN
ejpam-5161	217	18	)	)	PUNCT
ejpam-5161	218	1	such	such	ADJ
ejpam-5161	218	2	that	that	SCONJ
ejpam-5161	218	3	x	x	SYM
ejpam-5161	218	4	∈	∈	PROPN
ejpam-5161	218	5	(	(	PUNCT
ejpam-5161	218	6	g	g	PROPN
ejpam-5161	218	7	,	,	PUNCT
ejpam-5161	218	8	ω	ω	NOUN
ejpam-5161	218	9	)	)	PUNCT
ejpam-5161	218	10	,	,	PUNCT
ejpam-5161	218	11	y	y	PROPN
ejpam-5161	218	12	∈	∈	PROPN
ejpam-5161	218	13	(	(	PUNCT
ejpam-5161	218	14	h	h	NOUN
ejpam-5161	218	15	,	,	PUNCT
ejpam-5161	218	16	ω	ω	NOUN
ejpam-5161	218	17	)	)	PUNCT
ejpam-5161	218	18	and	and	CCONJ
ejpam-5161	218	19	(	(	PUNCT
ejpam-5161	218	20	g	g	PROPN
ejpam-5161	218	21	,	,	PUNCT
ejpam-5161	218	22	ω	ω	NOUN
ejpam-5161	218	23	)	)	PUNCT
ejpam-5161	218	24	⋂̃	⋂̃	NOUN
ejpam-5161	218	25	(	(	PUNCT
ejpam-5161	218	26	h	h	NOUN
ejpam-5161	218	27	,	,	PUNCT
ejpam-5161	218	28	ω	ω	NOUN
ejpam-5161	218	29	)	)	PUNCT
ejpam-5161	218	30	=	=	SYM
ejpam-5161	218	31	φ̃.	φ̃.	NOUN
ejpam-5161	218	32	this	this	PRON
ejpam-5161	218	33	means	mean	VERB
ejpam-5161	218	34	that	that	SCONJ
ejpam-5161	218	35	for	for	ADP
ejpam-5161	218	36	each	each	DET
ejpam-5161	218	37	ω	ω	PROPN
ejpam-5161	218	38	∈	∈	PROPN
ejpam-5161	218	39	ω	ω	PROPN
ejpam-5161	218	40	,	,	PUNCT
ejpam-5161	218	41	x	x	PROPN
ejpam-5161	218	42	∈	∈	PROPN
ejpam-5161	218	43	g(ω	g(ω	PROPN
ejpam-5161	218	44	)	)	PUNCT
ejpam-5161	218	45	,	,	PUNCT
ejpam-5161	218	46	y	y	PROPN
ejpam-5161	218	47	∈	∈	PROPN
ejpam-5161	218	48	h(ω	h(ω	PROPN
ejpam-5161	218	49	)	)	PUNCT
ejpam-5161	218	50	and	and	CCONJ
ejpam-5161	218	51	g(ω	g(ω	NOUN
ejpam-5161	218	52	)	)	PUNCT
ejpam-5161	218	53	∩h(ω	∩h(ω	PROPN
ejpam-5161	218	54	)	)	PUNCT
ejpam-5161	218	55	=	=	PUNCT
ejpam-5161	218	56	∅.	∅.	ADP
ejpam-5161	218	57	thus	thus	ADV
ejpam-5161	218	58	,	,	PUNCT
ejpam-5161	218	59	σω	σω	VERB
ejpam-5161	218	60	is	be	AUX
ejpam-5161	218	61	t2	t2	NOUN
ejpam-5161	218	62	for	for	ADP
ejpam-5161	218	63	each	each	DET
ejpam-5161	218	64	ω	ω	PROPN
ejpam-5161	218	65	∈	∈	PROPN
ejpam-5161	218	66	ω	ω	PROPN
ejpam-5161	218	67	.	.	PUNCT
ejpam-5161	219	1	corollary	corollary	ADJ
ejpam-5161	219	2	1	1	NUM
ejpam-5161	219	3	.	.	PUNCT
ejpam-5161	220	1	if	if	SCONJ
ejpam-5161	220	2	(	(	PUNCT
ejpam-5161	220	3	x	x	X
ejpam-5161	220	4	,	,	PUNCT
ejpam-5161	220	5	σ	σ	PROPN
ejpam-5161	220	6	,	,	PUNCT
ejpam-5161	220	7	ω	ω	NOUN
ejpam-5161	220	8	)	)	PUNCT
ejpam-5161	220	9	is	be	AUX
ejpam-5161	220	10	a	a	DET
ejpam-5161	220	11	soft	soft	ADJ
ejpam-5161	220	12	t2	t2	NOUN
ejpam-5161	220	13	-	-	PUNCT
ejpam-5161	220	14	space	space	NOUN
ejpam-5161	220	15	,	,	PUNCT
ejpam-5161	220	16	then	then	ADV
ejpam-5161	220	17	σω	σω	VERB
ejpam-5161	220	18	is	be	AUX
ejpam-5161	220	19	t2	t2	NOUN
ejpam-5161	220	20	for	for	ADP
ejpam-5161	220	21	each	each	DET
ejpam-5161	220	22	ω	ω	PROPN
ejpam-5161	220	23	∈	∈	PROPN
ejpam-5161	220	24	ω	ω	PROPN
ejpam-5161	220	25	.	.	PUNCT
ejpam-5161	221	1	proof	proof	NOUN
ejpam-5161	221	2	.	.	PUNCT
ejpam-5161	222	1	it	it	PRON
ejpam-5161	222	2	is	be	AUX
ejpam-5161	222	3	an	an	DET
ejpam-5161	222	4	immediate	immediate	ADJ
ejpam-5161	222	5	consequence	consequence	NOUN
ejpam-5161	222	6	of	of	ADP
ejpam-5161	222	7	lemma	lemma	PROPN
ejpam-5161	222	8	4	4	NUM
ejpam-5161	222	9	and	and	CCONJ
ejpam-5161	222	10	theorem	theorem	VERB
ejpam-5161	222	11	3	3	NUM
ejpam-5161	222	12	.	.	NOUN
ejpam-5161	222	13	notice	notice	NOUN
ejpam-5161	222	14	that	that	SCONJ
ejpam-5161	222	15	theorem	theorem	VERB
ejpam-5161	222	16	3	3	NUM
ejpam-5161	222	17	and	and	CCONJ
ejpam-5161	222	18	corollary	corollary	ADJ
ejpam-5161	222	19	1	1	NUM
ejpam-5161	222	20	generalize	generalize	NOUN
ejpam-5161	222	21	(	(	PUNCT
ejpam-5161	222	22	part	part	NOUN
ejpam-5161	222	23	of	of	ADP
ejpam-5161	222	24	)	)	PUNCT
ejpam-5161	222	25	theorem	theorem	VERB
ejpam-5161	222	26	4	4	NUM
ejpam-5161	222	27	in	in	ADP
ejpam-5161	222	28	[	[	X
ejpam-5161	222	29	29	29	NUM
ejpam-5161	222	30	]	]	PUNCT
ejpam-5161	222	31	and	and	CCONJ
ejpam-5161	222	32	proposition	proposition	NOUN
ejpam-5161	222	33	17	17	NUM
ejpam-5161	222	34	in	in	ADP
ejpam-5161	222	35	[	[	X
ejpam-5161	222	36	28	28	NUM
ejpam-5161	222	37	]	]	PUNCT
ejpam-5161	222	38	,	,	PUNCT
ejpam-5161	222	39	respectively	respectively	ADV
ejpam-5161	222	40	.	.	PUNCT
ejpam-5161	223	1	lemma	lemma	PROPN
ejpam-5161	223	2	8	8	NUM
ejpam-5161	223	3	.	.	PUNCT
ejpam-5161	224	1	[	[	X
ejpam-5161	224	2	29	29	NUM
ejpam-5161	224	3	,	,	PUNCT
ejpam-5161	224	4	theorem	theorem	VERB
ejpam-5161	224	5	3	3	NUM
ejpam-5161	224	6	]	]	PUNCT
ejpam-5161	224	7	let	let	VERB
ejpam-5161	224	8	σ	σ	NOUN
ejpam-5161	224	9	be	be	AUX
ejpam-5161	224	10	a	a	DET
ejpam-5161	224	11	(	(	PUNCT
ejpam-5161	224	12	crisp	crisp	ADJ
ejpam-5161	224	13	)	)	PUNCT
ejpam-5161	224	14	topology	topology	NOUN
ejpam-5161	224	15	on	on	ADP
ejpam-5161	224	16	a	a	DET
ejpam-5161	224	17	set	set	NOUN
ejpam-5161	224	18	x.	x.	NOUN
ejpam-5161	224	19	a	a	DET
ejpam-5161	224	20	soft	soft	ADJ
ejpam-5161	224	21	set	set	NOUN
ejpam-5161	224	22	(	(	PUNCT
ejpam-5161	224	23	f	f	X
ejpam-5161	224	24	,	,	PUNCT
ejpam-5161	224	25	ω	ω	NUM
ejpam-5161	224	26	)	)	PUNCT
ejpam-5161	224	27	is	be	AUX
ejpam-5161	224	28	soft	soft	ADJ
ejpam-5161	224	29	closed	closed	ADJ
ejpam-5161	224	30	in	in	ADP
ejpam-5161	224	31	t	t	PROPN
ejpam-5161	224	32	(	(	PUNCT
ejpam-5161	224	33	σ	σ	PROPN
ejpam-5161	224	34	)	)	PUNCT
ejpam-5161	225	1	if	if	SCONJ
ejpam-5161	225	2	and	and	CCONJ
ejpam-5161	225	3	only	only	ADV
ejpam-5161	225	4	if	if	SCONJ
ejpam-5161	225	5	(	(	PUNCT
ejpam-5161	225	6	f	f	X
ejpam-5161	225	7	,	,	PUNCT
ejpam-5161	225	8	ω	ω	NOUN
ejpam-5161	225	9	)	)	PUNCT
ejpam-5161	225	10	=	=	PRON
ejpam-5161	225	11	{	{	PUNCT
ejpam-5161	225	12	(	(	PUNCT
ejpam-5161	225	13	ω	ω	PROPN
ejpam-5161	225	14	,	,	PUNCT
ejpam-5161	225	15	f	f	PROPN
ejpam-5161	225	16	(	(	PUNCT
ejpam-5161	225	17	ω	ω	NOUN
ejpam-5161	225	18	)	)	PUNCT
ejpam-5161	225	19	)	)	PUNCT
ejpam-5161	225	20	:	:	PUNCT
ejpam-5161	225	21	f	f	PROPN
ejpam-5161	225	22	c(ω	c(ω	X
ejpam-5161	225	23	)	)	PUNCT
ejpam-5161	225	24	∈	∈	PROPN
ejpam-5161	225	25	σ	σ	PROPN
ejpam-5161	225	26	}	}	PUNCT
ejpam-5161	225	27	.	.	PUNCT
ejpam-5161	226	1	theorem	theorem	ADJ
ejpam-5161	226	2	4	4	NUM
ejpam-5161	226	3	.	.	PUNCT
ejpam-5161	227	1	let	let	VERB
ejpam-5161	227	2	σ	σ	NOUN
ejpam-5161	227	3	=	=	PUNCT
ejpam-5161	227	4	{	{	PUNCT
ejpam-5161	227	5	σω	σω	NOUN
ejpam-5161	227	6	:	:	PUNCT
ejpam-5161	227	7	ω	ω	PROPN
ejpam-5161	227	8	∈	∈	PROPN
ejpam-5161	227	9	ω	ω	PROPN
ejpam-5161	227	10	}	}	PUNCT
ejpam-5161	227	11	be	be	AUX
ejpam-5161	227	12	a	a	DET
ejpam-5161	227	13	family	family	NOUN
ejpam-5161	227	14	of	of	ADP
ejpam-5161	227	15	crisp	crisp	ADJ
ejpam-5161	227	16	topologies	topology	NOUN
ejpam-5161	227	17	on	on	ADP
ejpam-5161	227	18	x.	x.	NOUN
ejpam-5161	227	19	if	if	SCONJ
ejpam-5161	227	20	t	t	PROPN
ejpam-5161	227	21	(	(	PUNCT
ejpam-5161	227	22	σ	σ	PROPN
ejpam-5161	227	23	)	)	PUNCT
ejpam-5161	227	24	is	be	AUX
ejpam-5161	227	25	a	a	DET
ejpam-5161	227	26	soft	soft	ADJ
ejpam-5161	227	27	regular	regular	ADJ
ejpam-5161	227	28	space	space	NOUN
ejpam-5161	227	29	,	,	PUNCT
ejpam-5161	227	30	then	then	ADV
ejpam-5161	227	31	σω	σω	VERB
ejpam-5161	227	32	is	be	AUX
ejpam-5161	227	33	a	a	DET
ejpam-5161	227	34	regular	regular	ADJ
ejpam-5161	227	35	space	space	NOUN
ejpam-5161	227	36	for	for	ADP
ejpam-5161	227	37	each	each	DET
ejpam-5161	227	38	ω	ω	PROPN
ejpam-5161	227	39	∈	∈	PROPN
ejpam-5161	227	40	ω	ω	PROPN
ejpam-5161	227	41	.	.	PUNCT
ejpam-5161	228	1	proof	proof	NOUN
ejpam-5161	228	2	.	.	PUNCT
ejpam-5161	229	1	let	let	VERB
ejpam-5161	229	2	ω	ω	NUM
ejpam-5161	229	3	∈	∈	PROPN
ejpam-5161	229	4	ω	ω	X
ejpam-5161	229	5	.	.	PUNCT
ejpam-5161	230	1	take	take	VERB
ejpam-5161	230	2	x	x	PUNCT
ejpam-5161	230	3	∈	∈	NOUN
ejpam-5161	230	4	x	x	X
ejpam-5161	230	5	and	and	CCONJ
ejpam-5161	230	6	f	f	PROPN
ejpam-5161	230	7	(	(	PUNCT
ejpam-5161	230	8	ω	ω	NOUN
ejpam-5161	230	9	)	)	PUNCT
ejpam-5161	230	10	be	be	VERB
ejpam-5161	230	11	a	a	DET
ejpam-5161	230	12	closed	closed	ADJ
ejpam-5161	230	13	set	set	NOUN
ejpam-5161	230	14	in	in	ADP
ejpam-5161	230	15	(	(	PUNCT
ejpam-5161	230	16	x	x	NOUN
ejpam-5161	230	17	,	,	PUNCT
ejpam-5161	230	18	σω	σω	VERB
ejpam-5161	230	19	)	)	PUNCT
ejpam-5161	230	20	such	such	ADJ
ejpam-5161	230	21	that	that	PRON
ejpam-5161	230	22	x	x	X
ejpam-5161	230	23	/∈	/∈	PUNCT
ejpam-5161	231	1	f	f	PROPN
ejpam-5161	231	2	(	(	PUNCT
ejpam-5161	231	3	ω	ω	NOUN
ejpam-5161	231	4	)	)	PUNCT
ejpam-5161	231	5	.	.	PUNCT
ejpam-5161	232	1	the	the	DET
ejpam-5161	232	2	definition	definition	NOUN
ejpam-5161	232	3	6	6	NUM
ejpam-5161	232	4	and	and	CCONJ
ejpam-5161	232	5	lemma	lemma	PROPN
ejpam-5161	232	6	3	3	NUM
ejpam-5161	232	7	tell	tell	VERB
ejpam-5161	232	8	us	we	PRON
ejpam-5161	232	9	that	that	DET
ejpam-5161	232	10	soft	soft	ADJ
ejpam-5161	232	11	regularity	regularity	NOUN
ejpam-5161	232	12	of	of	ADP
ejpam-5161	232	13	t	t	PROPN
ejpam-5161	232	14	(	(	PUNCT
ejpam-5161	232	15	σ	σ	PROPN
ejpam-5161	232	16	)	)	PUNCT
ejpam-5161	232	17	guarantees	guarantee	VERB
ejpam-5161	232	18	the	the	DET
ejpam-5161	232	19	equality	equality	NOUN
ejpam-5161	232	20	of	of	ADP
ejpam-5161	232	21	t	t	PROPN
ejpam-5161	232	22	(	(	PUNCT
ejpam-5161	232	23	σ	σ	PROPN
ejpam-5161	232	24	)	)	PUNCT
ejpam-5161	232	25	=	=	SYM
ejpam-5161	232	26	t	t	PROPN
ejpam-5161	232	27	(	(	PUNCT
ejpam-5161	232	28	σ	σ	PROPN
ejpam-5161	232	29	)	)	PUNCT
ejpam-5161	232	30	.	.	PUNCT
ejpam-5161	233	1	set	set	NOUN
ejpam-5161	233	2	(	(	PUNCT
ejpam-5161	233	3	f	f	PROPN
ejpam-5161	233	4	,	,	PUNCT
ejpam-5161	233	5	ω	ω	NOUN
ejpam-5161	233	6	)	)	PUNCT
ejpam-5161	233	7	=	=	PRON
ejpam-5161	233	8	{	{	PUNCT
ejpam-5161	233	9	(	(	PUNCT
ejpam-5161	233	10	ω	ω	PROPN
ejpam-5161	233	11	,	,	PUNCT
ejpam-5161	233	12	f	f	PROPN
ejpam-5161	233	13	(	(	PUNCT
ejpam-5161	233	14	ω	ω	NOUN
ejpam-5161	233	15	)	)	PUNCT
ejpam-5161	233	16	)	)	PUNCT
ejpam-5161	233	17	:	:	PUNCT
ejpam-5161	234	1	f	f	PROPN
ejpam-5161	234	2	c(ω	c(ω	X
ejpam-5161	234	3	)	)	PUNCT
ejpam-5161	234	4	∈	∈	PROPN
ejpam-5161	234	5	σ	σ	PROPN
ejpam-5161	234	6	}	}	PUNCT
ejpam-5161	234	7	.	.	PUNCT
ejpam-5161	235	1	by	by	ADP
ejpam-5161	235	2	lemma	lemma	PROPN
ejpam-5161	235	3	8	8	NUM
ejpam-5161	235	4	,	,	PUNCT
ejpam-5161	235	5	(	(	PUNCT
ejpam-5161	235	6	f	f	X
ejpam-5161	235	7	,	,	PUNCT
ejpam-5161	235	8	ω	ω	NOUN
ejpam-5161	235	9	)	)	PUNCT
ejpam-5161	235	10	is	be	AUX
ejpam-5161	235	11	soft	soft	ADJ
ejpam-5161	235	12	closed	closed	ADJ
ejpam-5161	235	13	in	in	ADP
ejpam-5161	235	14	t	t	PROPN
ejpam-5161	235	15	(	(	PUNCT
ejpam-5161	235	16	σ	σ	PROPN
ejpam-5161	235	17	)	)	PUNCT
ejpam-5161	235	18	along	along	ADP
ejpam-5161	235	19	with	with	ADP
ejpam-5161	235	20	x	x	X
ejpam-5161	235	21	/∈	/∈	PUNCT
ejpam-5161	236	1	(	(	PUNCT
ejpam-5161	236	2	f	f	X
ejpam-5161	236	3	,	,	PUNCT
ejpam-5161	236	4	ω	ω	NOUN
ejpam-5161	236	5	)	)	PUNCT
ejpam-5161	236	6	.	.	PUNCT
ejpam-5161	237	1	since	since	SCONJ
ejpam-5161	237	2	t	t	PROPN
ejpam-5161	237	3	(	(	PUNCT
ejpam-5161	237	4	σ	σ	NOUN
ejpam-5161	237	5	)	)	PUNCT
ejpam-5161	237	6	is	be	AUX
ejpam-5161	237	7	soft	soft	ADJ
ejpam-5161	237	8	regular	regular	ADJ
ejpam-5161	237	9	,	,	PUNCT
ejpam-5161	237	10	then	then	ADV
ejpam-5161	237	11	there	there	PRON
ejpam-5161	237	12	exist	exist	VERB
ejpam-5161	237	13	soft	soft	ADJ
ejpam-5161	237	14	open	open	ADJ
ejpam-5161	237	15	sets	set	NOUN
ejpam-5161	237	16	(	(	PUNCT
ejpam-5161	237	17	u	u	NOUN
ejpam-5161	237	18	,	,	PUNCT
ejpam-5161	237	19	ω	ω	NOUN
ejpam-5161	237	20	)	)	PUNCT
ejpam-5161	237	21	,	,	PUNCT
ejpam-5161	237	22	(	(	PUNCT
ejpam-5161	237	23	v	v	NOUN
ejpam-5161	237	24	,	,	PUNCT
ejpam-5161	237	25	ω	ω	NOUN
ejpam-5161	237	26	)	)	PUNCT
ejpam-5161	237	27	in	in	ADP
ejpam-5161	237	28	t	t	PROPN
ejpam-5161	237	29	(	(	PUNCT
ejpam-5161	237	30	σ	σ	PROPN
ejpam-5161	237	31	)	)	PUNCT
ejpam-5161	237	32	such	such	ADJ
ejpam-5161	237	33	that	that	SCONJ
ejpam-5161	237	34	x	x	SYM
ejpam-5161	237	35	∈	∈	PROPN
ejpam-5161	237	36	(	(	PUNCT
ejpam-5161	237	37	u	u	NOUN
ejpam-5161	237	38	,	,	PUNCT
ejpam-5161	237	39	ω	ω	NOUN
ejpam-5161	237	40	)	)	PUNCT
ejpam-5161	237	41	,	,	PUNCT
ejpam-5161	237	42	(	(	PUNCT
ejpam-5161	237	43	f	f	X
ejpam-5161	237	44	,	,	PUNCT
ejpam-5161	237	45	ω)⊆̃(v	ω)⊆̃(v	PROPN
ejpam-5161	237	46	,	,	PUNCT
ejpam-5161	237	47	ω	ω	NOUN
ejpam-5161	237	48	)	)	PUNCT
ejpam-5161	237	49	and	and	CCONJ
ejpam-5161	237	50	φ̃	φ̃	PROPN
ejpam-5161	237	51	=	=	SYM
ejpam-5161	237	52	(	(	PUNCT
ejpam-5161	237	53	u	u	NOUN
ejpam-5161	237	54	,	,	PUNCT
ejpam-5161	237	55	ω	ω	NOUN
ejpam-5161	237	56	)	)	PUNCT
ejpam-5161	237	57	⋂̃	⋂̃	NOUN
ejpam-5161	237	58	(	(	PUNCT
ejpam-5161	237	59	v	v	NOUN
ejpam-5161	237	60	,	,	PUNCT
ejpam-5161	237	61	ω	ω	NOUN
ejpam-5161	237	62	)	)	PUNCT
ejpam-5161	237	63	=	=	PRON
ejpam-5161	237	64	{	{	PUNCT
ejpam-5161	237	65	(	(	PUNCT
ejpam-5161	237	66	ω	ω	PROPN
ejpam-5161	237	67	,	,	PUNCT
ejpam-5161	237	68	u(ω	u(ω	PROPN
ejpam-5161	237	69	)	)	PUNCT
ejpam-5161	237	70	∩	∩	PROPN
ejpam-5161	237	71	v	v	X
ejpam-5161	237	72	(	(	PUNCT
ejpam-5161	237	73	ω	ω	NOUN
ejpam-5161	237	74	)	)	PUNCT
ejpam-5161	237	75	)	)	PUNCT
ejpam-5161	237	76	:	:	PUNCT
ejpam-5161	238	1	ω	ω	X
ejpam-5161	238	2	∈	∈	PROPN
ejpam-5161	238	3	ω	ω	PROPN
ejpam-5161	238	4	}	}	PUNCT
ejpam-5161	238	5	.	.	PUNCT
ejpam-5161	239	1	this	this	PRON
ejpam-5161	239	2	implies	imply	VERB
ejpam-5161	239	3	that	that	SCONJ
ejpam-5161	239	4	x	x	SYM
ejpam-5161	239	5	∈	∈	PROPN
ejpam-5161	239	6	u(ω	u(ω	PROPN
ejpam-5161	239	7	)	)	PUNCT
ejpam-5161	239	8	,	,	PUNCT
ejpam-5161	239	9	f	f	PROPN
ejpam-5161	239	10	(	(	PUNCT
ejpam-5161	239	11	ω	ω	PROPN
ejpam-5161	239	12	)	)	PUNCT
ejpam-5161	239	13	⊆	⊆	NUM
ejpam-5161	239	14	v	v	NOUN
ejpam-5161	239	15	(	(	PUNCT
ejpam-5161	239	16	ω	ω	NOUN
ejpam-5161	239	17	)	)	PUNCT
ejpam-5161	239	18	and	and	CCONJ
ejpam-5161	239	19	u(ω	u(ω	PROPN
ejpam-5161	239	20	)	)	PUNCT
ejpam-5161	239	21	∩	∩	PROPN
ejpam-5161	239	22	v	v	X
ejpam-5161	239	23	(	(	PUNCT
ejpam-5161	239	24	ω	ω	NOUN
ejpam-5161	239	25	)	)	PUNCT
ejpam-5161	239	26	=	=	NOUN
ejpam-5161	239	27	∅	∅	NOUN
ejpam-5161	239	28	for	for	ADP
ejpam-5161	239	29	each	each	DET
ejpam-5161	239	30	ω	ω	PROPN
ejpam-5161	239	31	∈	∈	PROPN
ejpam-5161	239	32	ω	ω	PROPN
ejpam-5161	239	33	.	.	PUNCT
ejpam-5161	240	1	since	since	SCONJ
ejpam-5161	240	2	u(ω	u(ω	PROPN
ejpam-5161	240	3	)	)	PUNCT
ejpam-5161	240	4	,	,	PUNCT
ejpam-5161	240	5	v	v	X
ejpam-5161	240	6	(	(	PUNCT
ejpam-5161	240	7	ω	ω	NOUN
ejpam-5161	240	8	)	)	PUNCT
ejpam-5161	240	9	∈	∈	PROPN
ejpam-5161	240	10	σω	σω	NOUN
ejpam-5161	240	11	,	,	PUNCT
ejpam-5161	240	12	then	then	ADV
ejpam-5161	240	13	σω	σω	VERB
ejpam-5161	240	14	is	be	AUX
ejpam-5161	240	15	regular	regular	ADJ
ejpam-5161	240	16	for	for	ADP
ejpam-5161	240	17	each	each	DET
ejpam-5161	240	18	ω	ω	PROPN
ejpam-5161	240	19	∈	∈	PROPN
ejpam-5161	240	20	ω	ω	PROPN
ejpam-5161	240	21	.	.	PUNCT
ejpam-5161	240	22	corollary	corollary	ADJ
ejpam-5161	240	23	2	2	NUM
ejpam-5161	240	24	.	.	PUNCT
ejpam-5161	241	1	if	if	SCONJ
ejpam-5161	241	2	(	(	PUNCT
ejpam-5161	241	3	x	x	X
ejpam-5161	241	4	,	,	PUNCT
ejpam-5161	241	5	σ	σ	PROPN
ejpam-5161	241	6	,	,	PUNCT
ejpam-5161	241	7	ω	ω	NOUN
ejpam-5161	241	8	)	)	PUNCT
ejpam-5161	241	9	is	be	AUX
ejpam-5161	241	10	a	a	DET
ejpam-5161	241	11	soft	soft	ADJ
ejpam-5161	241	12	regular	regular	ADJ
ejpam-5161	241	13	space	space	NOUN
ejpam-5161	241	14	,	,	PUNCT
ejpam-5161	241	15	then	then	ADV
ejpam-5161	241	16	σω	σω	VERB
ejpam-5161	241	17	is	be	AUX
ejpam-5161	241	18	regular	regular	ADJ
ejpam-5161	241	19	for	for	ADP
ejpam-5161	241	20	each	each	DET
ejpam-5161	241	21	ω	ω	PROPN
ejpam-5161	241	22	∈	∈	PROPN
ejpam-5161	241	23	ω	ω	PROPN
ejpam-5161	241	24	.	.	PUNCT
ejpam-5161	242	1	proof	proof	NOUN
ejpam-5161	242	2	.	.	PUNCT
ejpam-5161	243	1	it	it	PRON
ejpam-5161	243	2	can	can	AUX
ejpam-5161	243	3	be	be	AUX
ejpam-5161	243	4	concluded	conclude	VERB
ejpam-5161	243	5	from	from	ADP
ejpam-5161	243	6	lemma	lemma	PROPN
ejpam-5161	243	7	4	4	NUM
ejpam-5161	243	8	and	and	CCONJ
ejpam-5161	243	9	theorem	theorem	VERB
ejpam-5161	243	10	4	4	NUM
ejpam-5161	243	11	.	.	NOUN
ejpam-5161	243	12	remark	remark	NOUN
ejpam-5161	243	13	1	1	NUM
ejpam-5161	243	14	.	.	PUNCT
ejpam-5161	244	1	we	we	PRON
ejpam-5161	244	2	shall	shall	AUX
ejpam-5161	244	3	mention	mention	VERB
ejpam-5161	244	4	that	that	SCONJ
ejpam-5161	244	5	it	it	PRON
ejpam-5161	244	6	is	be	AUX
ejpam-5161	244	7	observed	observe	VERB
ejpam-5161	244	8	in	in	ADP
ejpam-5161	244	9	remark	remark	NOUN
ejpam-5161	244	10	3.23	3.23	NUM
ejpam-5161	244	11	(	(	PUNCT
ejpam-5161	244	12	2	2	NUM
ejpam-5161	244	13	’	'	PUNCT
ejpam-5161	244	14	)	)	PUNCT
ejpam-5161	245	1	[	[	X
ejpam-5161	245	2	23	23	NUM
ejpam-5161	245	3	]	]	PUNCT
ejpam-5161	245	4	that	that	SCONJ
ejpam-5161	245	5	if	if	SCONJ
ejpam-5161	245	6	(	(	PUNCT
ejpam-5161	245	7	x	x	X
ejpam-5161	245	8	,	,	PUNCT
ejpam-5161	245	9	σ	σ	PROPN
ejpam-5161	245	10	,	,	PUNCT
ejpam-5161	245	11	ω	ω	NOUN
ejpam-5161	245	12	)	)	PUNCT
ejpam-5161	245	13	is	be	AUX
ejpam-5161	245	14	a	a	DET
ejpam-5161	245	15	soft	soft	ADJ
ejpam-5161	245	16	t3	t3	NOUN
ejpam-5161	245	17	space	space	NOUN
ejpam-5161	245	18	,	,	PUNCT
ejpam-5161	245	19	then	then	ADV
ejpam-5161	245	20	σω	σω	VERB
ejpam-5161	245	21	is	be	AUX
ejpam-5161	245	22	t3	t3	NOUN
ejpam-5161	245	23	for	for	ADP
ejpam-5161	245	24	each	each	DET
ejpam-5161	245	25	ω	ω	PROPN
ejpam-5161	245	26	∈	∈	PROPN
ejpam-5161	245	27	ω	ω	NOUN
ejpam-5161	245	28	.	.	PUNCT
ejpam-5161	246	1	this	this	DET
ejpam-5161	246	2	conclusion	conclusion	NOUN
ejpam-5161	246	3	is	be	AUX
ejpam-5161	246	4	more	more	ADV
ejpam-5161	246	5	general	general	ADJ
ejpam-5161	246	6	than	than	ADP
ejpam-5161	246	7	corollary	corollary	ADJ
ejpam-5161	246	8	2	2	NUM
ejpam-5161	246	9	,	,	PUNCT
ejpam-5161	246	10	but	but	CCONJ
ejpam-5161	246	11	it	it	PRON
ejpam-5161	246	12	can	can	AUX
ejpam-5161	246	13	not	not	PART
ejpam-5161	246	14	be	be	AUX
ejpam-5161	246	15	followed	follow	VERB
ejpam-5161	246	16	from	from	ADP
ejpam-5161	246	17	any	any	PRON
ejpam-5161	246	18	of	of	ADP
ejpam-5161	246	19	our	our	PRON
ejpam-5161	246	20	results	result	NOUN
ejpam-5161	246	21	due	due	ADP
ejpam-5161	246	22	to	to	PART
ejpam-5161	246	23	example	example	NOUN
ejpam-5161	246	24	4	4	NUM
ejpam-5161	246	25	.	.	PUNCT
ejpam-5161	247	1	the	the	DET
ejpam-5161	247	2	examples	example	NOUN
ejpam-5161	247	3	given	give	VERB
ejpam-5161	247	4	below	below	ADV
ejpam-5161	247	5	disprove	disprove	VERB
ejpam-5161	247	6	the	the	DET
ejpam-5161	247	7	reverse	reverse	NOUN
ejpam-5161	247	8	of	of	ADP
ejpam-5161	247	9	theorem	theorem	ADJ
ejpam-5161	247	10	4	4	NUM
ejpam-5161	247	11	:	:	PUNCT
ejpam-5161	247	12	example	example	NOUN
ejpam-5161	247	13	5	5	X
ejpam-5161	247	14	.	.	PUNCT
ejpam-5161	248	1	let	let	VERB
ejpam-5161	248	2	x	x	PUNCT
ejpam-5161	248	3	=	=	PRON
ejpam-5161	248	4	{	{	PUNCT
ejpam-5161	248	5	x	x	NOUN
ejpam-5161	248	6	}	}	PUNCT
ejpam-5161	248	7	,	,	PUNCT
ejpam-5161	248	8	let	let	VERB
ejpam-5161	248	9	ω	ω	NOUN
ejpam-5161	248	10	=	=	SYM
ejpam-5161	248	11	{	{	PUNCT
ejpam-5161	248	12	ω1	ω1	PROPN
ejpam-5161	248	13	,	,	PUNCT
ejpam-5161	248	14	ω2	ω2	ADJ
ejpam-5161	248	15	}	}	PUNCT
ejpam-5161	248	16	,	,	PUNCT
ejpam-5161	248	17	and	and	CCONJ
ejpam-5161	248	18	let	let	VERB
ejpam-5161	248	19	σ	σ	NOUN
ejpam-5161	248	20	=	=	PRON
ejpam-5161	248	21	{	{	PUNCT
ejpam-5161	248	22	σω1	σω1	NOUN
ejpam-5161	248	23	,	,	PUNCT
ejpam-5161	248	24	σω2	σω2	ADP
ejpam-5161	248	25	}	}	PUNCT
ejpam-5161	248	26	,	,	PUNCT
ejpam-5161	248	27	where	where	SCONJ
ejpam-5161	248	28	σω1	σω1	NOUN
ejpam-5161	248	29	=	=	SYM
ejpam-5161	248	30	σω2	σω2	ADP
ejpam-5161	248	31	=	=	SYM
ejpam-5161	248	32	{	{	PUNCT
ejpam-5161	248	33	∅	∅	NOUN
ejpam-5161	248	34	,	,	PUNCT
ejpam-5161	248	35	x	x	NOUN
ejpam-5161	248	36	}	}	PUNCT
ejpam-5161	248	37	.	.	PUNCT
ejpam-5161	249	1	one	one	PRON
ejpam-5161	249	2	can	can	AUX
ejpam-5161	249	3	check	check	VERB
ejpam-5161	249	4	that	that	SCONJ
ejpam-5161	249	5	each	each	DET
ejpam-5161	249	6	σωi	σωi	NOUN
ejpam-5161	249	7	is	be	AUX
ejpam-5161	249	8	trivially	trivially	ADV
ejpam-5161	249	9	a	a	DET
ejpam-5161	249	10	regular	regular	ADJ
ejpam-5161	249	11	space	space	NOUN
ejpam-5161	249	12	.	.	PUNCT
ejpam-5161	250	1	on	on	ADP
ejpam-5161	250	2	the	the	DET
ejpam-5161	250	3	other	other	ADJ
ejpam-5161	250	4	hand	hand	NOUN
ejpam-5161	250	5	,	,	PUNCT
ejpam-5161	250	6	the	the	DET
ejpam-5161	250	7	soft	soft	ADJ
ejpam-5161	250	8	topology	topology	NOUN
ejpam-5161	250	9	t	t	NOUN
ejpam-5161	250	10	(	(	PUNCT
ejpam-5161	250	11	σ	σ	NOUN
ejpam-5161	250	12	)	)	PUNCT
ejpam-5161	250	13	=	=	PRON
ejpam-5161	250	14	{	{	PUNCT
ejpam-5161	250	15	φ̃	φ̃	PROPN
ejpam-5161	250	16	,	,	PUNCT
ejpam-5161	250	17	(	(	PUNCT
ejpam-5161	250	18	f1,ω	f1,ω	PROPN
ejpam-5161	250	19	)	)	PUNCT
ejpam-5161	250	20	,	,	PUNCT
ejpam-5161	250	21	(	(	PUNCT
ejpam-5161	250	22	f2,ω	f2,ω	PROPN
ejpam-5161	250	23	)	)	PUNCT
ejpam-5161	250	24	,	,	PUNCT
ejpam-5161	250	25	x̃	x̃	PROPN
ejpam-5161	250	26	}	}	PUNCT
ejpam-5161	250	27	is	be	AUX
ejpam-5161	250	28	not	not	PART
ejpam-5161	250	29	soft	soft	ADJ
ejpam-5161	250	30	regular	regular	ADJ
ejpam-5161	250	31	,	,	PUNCT
ejpam-5161	250	32	where	where	SCONJ
ejpam-5161	250	33	(	(	PUNCT
ejpam-5161	250	34	f1,ω	f1,ω	PROPN
ejpam-5161	250	35	)	)	PUNCT
ejpam-5161	250	36	=	=	PRON
ejpam-5161	251	1	{	{	PUNCT
ejpam-5161	251	2	(	(	PUNCT
ejpam-5161	251	3	ω1	ω1	PROPN
ejpam-5161	251	4	,	,	PUNCT
ejpam-5161	251	5	∅	∅	NOUN
ejpam-5161	251	6	)	)	PUNCT
ejpam-5161	251	7	,	,	PUNCT
ejpam-5161	251	8	(	(	PUNCT
ejpam-5161	251	9	ω2	ω2	ADJ
ejpam-5161	251	10	,	,	PUNCT
ejpam-5161	251	11	x	x	NOUN
ejpam-5161	251	12	)	)	PUNCT
ejpam-5161	251	13	}	}	PUNCT
ejpam-5161	251	14	and	and	CCONJ
ejpam-5161	251	15	(	(	PUNCT
ejpam-5161	251	16	f2,ω	f2,ω	PROPN
ejpam-5161	251	17	)	)	PUNCT
ejpam-5161	251	18	=	=	SYM
ejpam-5161	251	19	{	{	PUNCT
ejpam-5161	251	20	(	(	PUNCT
ejpam-5161	251	21	ω1	ω1	PROPN
ejpam-5161	251	22	,	,	PUNCT
ejpam-5161	251	23	x	x	NOUN
ejpam-5161	251	24	)	)	PUNCT
ejpam-5161	251	25	,	,	PUNCT
ejpam-5161	251	26	(	(	PUNCT
ejpam-5161	251	27	ω2	ω2	ADJ
ejpam-5161	251	28	,	,	PUNCT
ejpam-5161	251	29	∅	∅	NOUN
ejpam-5161	251	30	)	)	PUNCT
ejpam-5161	251	31	}	}	PUNCT
ejpam-5161	251	32	.	.	PUNCT
ejpam-5161	252	1	indeed	indeed	ADV
ejpam-5161	252	2	,	,	PUNCT
ejpam-5161	252	3	x	x	PROPN
ejpam-5161	252	4	/∈	/∈	PUNCT
ejpam-5161	252	5	(	(	PUNCT
ejpam-5161	252	6	fi	fi	NOUN
ejpam-5161	252	7	,	,	PUNCT
ejpam-5161	252	8	ω)c	ω)c	NOUN
ejpam-5161	252	9	for	for	ADP
ejpam-5161	252	10	each	each	DET
ejpam-5161	252	11	i	i	NOUN
ejpam-5161	252	12	,	,	PUNCT
ejpam-5161	252	13	but	but	CCONJ
ejpam-5161	252	14	no	no	DET
ejpam-5161	252	15	soft	soft	ADJ
ejpam-5161	252	16	open	open	ADJ
ejpam-5161	252	17	sets	set	NOUN
ejpam-5161	252	18	in	in	ADP
ejpam-5161	252	19	t	t	PROPN
ejpam-5161	252	20	(	(	PUNCT
ejpam-5161	252	21	σ	σ	NOUN
ejpam-5161	252	22	)	)	PUNCT
ejpam-5161	252	23	can	can	AUX
ejpam-5161	252	24	separate	separate	VERB
ejpam-5161	252	25	them	they	PRON
ejpam-5161	252	26	.	.	PUNCT
ejpam-5161	253	1	z.	z.	PROPN
ejpam-5161	253	2	a.	a.	PROPN
ejpam-5161	253	3	ameen	ameen	PROPN
ejpam-5161	253	4	et	et	PROPN
ejpam-5161	253	5	al	al	PROPN
ejpam-5161	253	6	.	.	PUNCT
ejpam-5161	253	7	/	/	SYM
ejpam-5161	253	8	eur	eur	PROPN
ejpam-5161	253	9	.	.	PUNCT
ejpam-5161	254	1	j.	j.	PROPN
ejpam-5161	254	2	pure	pure	PROPN
ejpam-5161	254	3	appl	appl	PROPN
ejpam-5161	254	4	.	.	PROPN
ejpam-5161	254	5	math	math	PROPN
ejpam-5161	254	6	,	,	PUNCT
ejpam-5161	254	7	17	17	NUM
ejpam-5161	254	8	(	(	PUNCT
ejpam-5161	254	9	2	2	NUM
ejpam-5161	254	10	)	)	PUNCT
ejpam-5161	254	11	(	(	PUNCT
ejpam-5161	254	12	2024	2024	NUM
ejpam-5161	254	13	)	)	PUNCT
ejpam-5161	254	14	,	,	PUNCT
ejpam-5161	254	15	1168	1168	NUM
ejpam-5161	254	16	-	-	SYM
ejpam-5161	254	17	1182	1182	NUM
ejpam-5161	254	18	1178	1178	NUM
ejpam-5161	254	19	example	example	NOUN
ejpam-5161	254	20	6	6	NUM
ejpam-5161	254	21	.	.	X
ejpam-5161	255	1	consider	consider	VERB
ejpam-5161	255	2	(	(	PUNCT
ejpam-5161	255	3	r	r	NOUN
ejpam-5161	255	4	,	,	PUNCT
ejpam-5161	255	5	u	u	NOUN
ejpam-5161	255	6	)	)	PUNCT
ejpam-5161	255	7	,	,	PUNCT
ejpam-5161	255	8	the	the	DET
ejpam-5161	255	9	natural	natural	ADJ
ejpam-5161	255	10	topology	topology	NOUN
ejpam-5161	255	11	on	on	ADP
ejpam-5161	255	12	r.	r.	PROPN
ejpam-5161	255	13	let	let	VERB
ejpam-5161	255	14	ω	ω	PROPN
ejpam-5161	255	15	=	=	SYM
ejpam-5161	255	16	{	{	PUNCT
ejpam-5161	255	17	ω1	ω1	PROPN
ejpam-5161	255	18	,	,	PUNCT
ejpam-5161	255	19	ω2	ω2	ADJ
ejpam-5161	255	20	}	}	PUNCT
ejpam-5161	255	21	.	.	PUNCT
ejpam-5161	256	1	it	it	PRON
ejpam-5161	256	2	is	be	AUX
ejpam-5161	256	3	well	well	ADV
ejpam-5161	256	4	known	know	VERB
ejpam-5161	256	5	that	that	SCONJ
ejpam-5161	256	6	the	the	DET
ejpam-5161	256	7	natural	natural	ADJ
ejpam-5161	256	8	topology	topology	NOUN
ejpam-5161	256	9	is	be	AUX
ejpam-5161	256	10	t3	t3	NOUN
ejpam-5161	256	11	space	space	NOUN
ejpam-5161	256	12	.	.	PUNCT
ejpam-5161	257	1	we	we	PRON
ejpam-5161	257	2	will	will	AUX
ejpam-5161	257	3	prove	prove	VERB
ejpam-5161	257	4	that	that	SCONJ
ejpam-5161	257	5	t	t	PROPN
ejpam-5161	257	6	(	(	PUNCT
ejpam-5161	257	7	u	u	NOUN
ejpam-5161	257	8	)	)	PUNCT
ejpam-5161	257	9	is	be	AUX
ejpam-5161	257	10	not	not	PART
ejpam-5161	257	11	t3	t3	NOUN
ejpam-5161	257	12	,	,	PUNCT
ejpam-5161	257	13	where	where	SCONJ
ejpam-5161	257	14	t	t	PROPN
ejpam-5161	257	15	(	(	PUNCT
ejpam-5161	257	16	u	u	NOUN
ejpam-5161	257	17	)	)	PUNCT
ejpam-5161	257	18	=	=	SYM
ejpam-5161	257	19	t	t	PROPN
ejpam-5161	257	20	(	(	PUNCT
ejpam-5161	257	21	b(β̄	b(β̄	PROPN
ejpam-5161	257	22	)	)	PUNCT
ejpam-5161	257	23	)	)	PUNCT
ejpam-5161	257	24	which	which	PRON
ejpam-5161	257	25	is	be	AUX
ejpam-5161	257	26	defined	define	VERB
ejpam-5161	257	27	in	in	ADP
ejpam-5161	257	28	lemma	lemma	PROPN
ejpam-5161	257	29	5	5	NUM
ejpam-5161	257	30	.	.	PUNCT
ejpam-5161	257	31	pick	pick	VERB
ejpam-5161	257	32	the	the	DET
ejpam-5161	257	33	point	point	NOUN
ejpam-5161	257	34	0	0	PUNCT
ejpam-5161	258	1	and	and	CCONJ
ejpam-5161	258	2	(	(	PUNCT
ejpam-5161	258	3	f	f	X
ejpam-5161	258	4	,	,	PUNCT
ejpam-5161	258	5	ω	ω	NOUN
ejpam-5161	258	6	)	)	PUNCT
ejpam-5161	258	7	=	=	PRON
ejpam-5161	258	8	{	{	PUNCT
ejpam-5161	258	9	(	(	PUNCT
ejpam-5161	258	10	ω1	ω1	PROPN
ejpam-5161	258	11	,	,	PUNCT
ejpam-5161	258	12	[	[	X
ejpam-5161	258	13	−1	−1	NOUN
ejpam-5161	258	14	,	,	PUNCT
ejpam-5161	258	15	1	1	NUM
ejpam-5161	258	16	]	]	NUM
ejpam-5161	258	17	)	)	PUNCT
ejpam-5161	258	18	,	,	PUNCT
ejpam-5161	258	19	(	(	PUNCT
ejpam-5161	258	20	ω2	ω2	ADV
ejpam-5161	258	21	,	,	PUNCT
ejpam-5161	258	22	[	[	X
ejpam-5161	258	23	2	2	NUM
ejpam-5161	258	24	,	,	PUNCT
ejpam-5161	258	25	3	3	NUM
ejpam-5161	258	26	]	]	PUNCT
ejpam-5161	258	27	)	)	PUNCT
ejpam-5161	258	28	}	}	PUNCT
ejpam-5161	258	29	.	.	PUNCT
ejpam-5161	259	1	hence	hence	ADV
ejpam-5161	259	2	,	,	PUNCT
ejpam-5161	259	3	0	0	NUM
ejpam-5161	259	4	̸∈	̸∈	PROPN
ejpam-5161	259	5	(	(	PUNCT
ejpam-5161	259	6	f	f	PROPN
ejpam-5161	259	7	,	,	PUNCT
ejpam-5161	259	8	ω	ω	NOUN
ejpam-5161	259	9	)	)	PUNCT
ejpam-5161	259	10	and	and	CCONJ
ejpam-5161	259	11	(	(	PUNCT
ejpam-5161	259	12	f	f	X
ejpam-5161	259	13	,	,	PUNCT
ejpam-5161	259	14	ω	ω	NOUN
ejpam-5161	259	15	)	)	PUNCT
ejpam-5161	259	16	is	be	AUX
ejpam-5161	259	17	a	a	DET
ejpam-5161	259	18	closed	closed	ADJ
ejpam-5161	259	19	soft	soft	ADJ
ejpam-5161	259	20	set	set	NOUN
ejpam-5161	259	21	.	.	PUNCT
ejpam-5161	260	1	let	let	VERB
ejpam-5161	260	2	(	(	PUNCT
ejpam-5161	260	3	w1,ω	w1,ω	PROPN
ejpam-5161	260	4	)	)	PUNCT
ejpam-5161	260	5	and	and	CCONJ
ejpam-5161	260	6	(	(	PUNCT
ejpam-5161	260	7	w2,ω	w2,ω	PROPN
ejpam-5161	260	8	)	)	PUNCT
ejpam-5161	260	9	be	be	VERB
ejpam-5161	260	10	any	any	DET
ejpam-5161	260	11	two	two	NUM
ejpam-5161	260	12	basic	basic	ADJ
ejpam-5161	260	13	open	open	ADJ
ejpam-5161	260	14	soft	soft	ADJ
ejpam-5161	260	15	sets	set	NOUN
ejpam-5161	260	16	such	such	ADJ
ejpam-5161	260	17	that	that	DET
ejpam-5161	260	18	0	0	NUM
ejpam-5161	260	19	∈	∈	PROPN
ejpam-5161	260	20	(	(	PUNCT
ejpam-5161	260	21	w1,ω	w1,ω	PROPN
ejpam-5161	260	22	)	)	PUNCT
ejpam-5161	260	23	and	and	CCONJ
ejpam-5161	260	24	(	(	PUNCT
ejpam-5161	260	25	f	f	X
ejpam-5161	260	26	,	,	PUNCT
ejpam-5161	260	27	ω)⊆̃(w2,ω	ω)⊆̃(w2,ω	PROPN
ejpam-5161	260	28	)	)	PUNCT
ejpam-5161	260	29	.	.	PUNCT
ejpam-5161	261	1	then	then	ADV
ejpam-5161	261	2	,	,	PUNCT
ejpam-5161	261	3	(	(	PUNCT
ejpam-5161	261	4	w1,ω	w1,ω	PROPN
ejpam-5161	261	5	)	)	PUNCT
ejpam-5161	261	6	=	=	PRON
ejpam-5161	261	7	{	{	PUNCT
ejpam-5161	261	8	(	(	PUNCT
ejpam-5161	261	9	ω1	ω1	PROPN
ejpam-5161	261	10	,	,	PUNCT
ejpam-5161	261	11	(	(	PUNCT
ejpam-5161	261	12	a	a	DET
ejpam-5161	261	13	,	,	PUNCT
ejpam-5161	261	14	b	b	NOUN
ejpam-5161	261	15	)	)	PUNCT
ejpam-5161	261	16	)	)	PUNCT
ejpam-5161	261	17	,	,	PUNCT
ejpam-5161	261	18	(	(	PUNCT
ejpam-5161	261	19	ω2	ω2	ADV
ejpam-5161	261	20	,	,	PUNCT
ejpam-5161	261	21	(	(	PUNCT
ejpam-5161	261	22	c	c	X
ejpam-5161	261	23	,	,	PUNCT
ejpam-5161	261	24	d	d	NOUN
ejpam-5161	261	25	)	)	PUNCT
ejpam-5161	261	26	}	}	PUNCT
ejpam-5161	261	27	such	such	ADJ
ejpam-5161	261	28	that	that	SCONJ
ejpam-5161	261	29	0	0	NUM
ejpam-5161	261	30	∈	∈	NOUN
ejpam-5161	261	31	(	(	PUNCT
ejpam-5161	261	32	a	a	DET
ejpam-5161	261	33	,	,	PUNCT
ejpam-5161	261	34	b	b	NOUN
ejpam-5161	261	35	)	)	PUNCT
ejpam-5161	261	36	,	,	PUNCT
ejpam-5161	261	37	0	0	NUM
ejpam-5161	261	38	∈	∈	PROPN
ejpam-5161	261	39	(	(	PUNCT
ejpam-5161	261	40	c	c	NOUN
ejpam-5161	261	41	,	,	PUNCT
ejpam-5161	261	42	d	d	NOUN
ejpam-5161	261	43	)	)	PUNCT
ejpam-5161	261	44	and	and	CCONJ
ejpam-5161	261	45	(	(	PUNCT
ejpam-5161	261	46	w2,ω	w2,ω	PROPN
ejpam-5161	261	47	)	)	PUNCT
ejpam-5161	261	48	=	=	SYM
ejpam-5161	261	49	{	{	PUNCT
ejpam-5161	261	50	(	(	PUNCT
ejpam-5161	261	51	ω1	ω1	PROPN
ejpam-5161	261	52	,	,	PUNCT
ejpam-5161	261	53	(	(	PUNCT
ejpam-5161	261	54	r	r	NOUN
ejpam-5161	261	55	,	,	PUNCT
ejpam-5161	261	56	t	t	PROPN
ejpam-5161	261	57	)	)	PUNCT
ejpam-5161	261	58	)	)	PUNCT
ejpam-5161	261	59	,	,	PUNCT
ejpam-5161	261	60	(	(	PUNCT
ejpam-5161	261	61	ω2	ω2	ADV
ejpam-5161	261	62	,	,	PUNCT
ejpam-5161	261	63	(	(	PUNCT
ejpam-5161	261	64	s	s	X
ejpam-5161	261	65	,	,	PUNCT
ejpam-5161	261	66	k	k	NOUN
ejpam-5161	261	67	)	)	PUNCT
ejpam-5161	261	68	}	}	PUNCT
ejpam-5161	261	69	.	.	PUNCT
ejpam-5161	262	1	since	since	SCONJ
ejpam-5161	262	2	0	0	NUM
ejpam-5161	262	3	∈	∈	PROPN
ejpam-5161	262	4	f	f	PROPN
ejpam-5161	262	5	(	(	PUNCT
ejpam-5161	262	6	ω1	ω1	PROPN
ejpam-5161	262	7	)	)	PUNCT
ejpam-5161	262	8	=	=	PUNCT
ejpam-5161	263	1	[	[	X
ejpam-5161	263	2	−1	−1	NOUN
ejpam-5161	263	3	,	,	PUNCT
ejpam-5161	263	4	1	1	NUM
ejpam-5161	263	5	]	]	PUNCT
ejpam-5161	263	6	⊂	⊂	PUNCT
ejpam-5161	263	7	w2(ω1	w2(ω1	NOUN
ejpam-5161	263	8	)	)	PUNCT
ejpam-5161	263	9	,	,	PUNCT
ejpam-5161	263	10	then	then	ADV
ejpam-5161	263	11	0	0	NUM
ejpam-5161	263	12	∈	∈	NOUN
ejpam-5161	263	13	(	(	PUNCT
ejpam-5161	263	14	r	r	NOUN
ejpam-5161	263	15	,	,	PUNCT
ejpam-5161	263	16	t	t	PROPN
ejpam-5161	263	17	)	)	PUNCT
ejpam-5161	263	18	which	which	PRON
ejpam-5161	263	19	implies	imply	VERB
ejpam-5161	263	20	that	that	SCONJ
ejpam-5161	263	21	(	(	PUNCT
ejpam-5161	263	22	w1,ω	w1,ω	PROPN
ejpam-5161	263	23	)	)	PUNCT
ejpam-5161	263	24	⋂̃	⋂̃	NOUN
ejpam-5161	263	25	(	(	PUNCT
ejpam-5161	263	26	w2,ω	w2,ω	PROPN
ejpam-5161	263	27	)	)	PUNCT
ejpam-5161	263	28	̸=	̸=	PROPN
ejpam-5161	263	29	φ̃.	φ̃.	PROPN
ejpam-5161	263	30	theorem	theorem	VERB
ejpam-5161	263	31	5	5	NUM
ejpam-5161	263	32	.	.	PUNCT
ejpam-5161	264	1	let	let	VERB
ejpam-5161	264	2	σ	σ	NOUN
ejpam-5161	264	3	=	=	PUNCT
ejpam-5161	264	4	{	{	PUNCT
ejpam-5161	264	5	σω	σω	NOUN
ejpam-5161	264	6	:	:	PUNCT
ejpam-5161	264	7	ω	ω	PROPN
ejpam-5161	264	8	∈	∈	PROPN
ejpam-5161	264	9	ω	ω	PROPN
ejpam-5161	264	10	}	}	PUNCT
ejpam-5161	264	11	be	be	AUX
ejpam-5161	264	12	a	a	DET
ejpam-5161	264	13	family	family	NOUN
ejpam-5161	264	14	of	of	ADP
ejpam-5161	264	15	crisp	crisp	ADJ
ejpam-5161	264	16	topologies	topology	NOUN
ejpam-5161	264	17	on	on	ADP
ejpam-5161	264	18	x.	x.	NOUN
ejpam-5161	264	19	then	then	ADV
ejpam-5161	264	20	σω	σω	VERB
ejpam-5161	264	21	is	be	AUX
ejpam-5161	264	22	a	a	DET
ejpam-5161	264	23	normal	normal	ADJ
ejpam-5161	264	24	space	space	NOUN
ejpam-5161	264	25	for	for	ADP
ejpam-5161	264	26	each	each	DET
ejpam-5161	264	27	ω	ω	PROPN
ejpam-5161	264	28	∈	∈	PROPN
ejpam-5161	264	29	ω	ω	NOUN
ejpam-5161	265	1	if	if	SCONJ
ejpam-5161	265	2	and	and	CCONJ
ejpam-5161	265	3	only	only	ADV
ejpam-5161	265	4	if	if	SCONJ
ejpam-5161	265	5	t	t	PROPN
ejpam-5161	265	6	(	(	PUNCT
ejpam-5161	265	7	σ	σ	PROPN
ejpam-5161	265	8	)	)	PUNCT
ejpam-5161	265	9	is	be	AUX
ejpam-5161	265	10	a	a	DET
ejpam-5161	265	11	soft	soft	ADJ
ejpam-5161	265	12	normal	normal	ADJ
ejpam-5161	265	13	space	space	NOUN
ejpam-5161	265	14	.	.	PUNCT
ejpam-5161	266	1	proof	proof	NOUN
ejpam-5161	266	2	.	.	PUNCT
ejpam-5161	267	1	let	let	VERB
ejpam-5161	267	2	σω	σω	AUX
ejpam-5161	267	3	be	be	AUX
ejpam-5161	267	4	normal	normal	ADJ
ejpam-5161	267	5	for	for	ADP
ejpam-5161	267	6	each	each	DET
ejpam-5161	267	7	ω	ω	PROPN
ejpam-5161	267	8	∈	∈	PROPN
ejpam-5161	267	9	ω	ω	PROPN
ejpam-5161	267	10	.	.	PUNCT
ejpam-5161	268	1	suppose	suppose	VERB
ejpam-5161	268	2	(	(	PUNCT
ejpam-5161	268	3	a	a	DET
ejpam-5161	268	4	,	,	PUNCT
ejpam-5161	268	5	ω	ω	NOUN
ejpam-5161	268	6	)	)	PUNCT
ejpam-5161	268	7	,	,	PUNCT
ejpam-5161	268	8	(	(	PUNCT
ejpam-5161	268	9	b	b	X
ejpam-5161	268	10	,	,	PUNCT
ejpam-5161	268	11	ω	ω	NUM
ejpam-5161	268	12	)	)	PUNCT
ejpam-5161	268	13	are	be	AUX
ejpam-5161	268	14	disjoint	disjoint	ADJ
ejpam-5161	268	15	soft	soft	ADJ
ejpam-5161	268	16	closed	closed	ADJ
ejpam-5161	268	17	sets	set	NOUN
ejpam-5161	268	18	in	in	ADP
ejpam-5161	268	19	t	t	PROPN
ejpam-5161	268	20	(	(	PUNCT
ejpam-5161	268	21	σ	σ	PROPN
ejpam-5161	268	22	)	)	PUNCT
ejpam-5161	268	23	.	.	PUNCT
ejpam-5161	269	1	then	then	ADV
ejpam-5161	269	2	(	(	PUNCT
ejpam-5161	269	3	a	a	DET
ejpam-5161	269	4	,	,	PUNCT
ejpam-5161	269	5	ω	ω	NOUN
ejpam-5161	269	6	)	)	PUNCT
ejpam-5161	269	7	=	=	PRON
ejpam-5161	269	8	{	{	PUNCT
ejpam-5161	269	9	(	(	PUNCT
ejpam-5161	269	10	ω	ω	NOUN
ejpam-5161	269	11	,	,	PUNCT
ejpam-5161	269	12	a(ω	a(ω	PROPN
ejpam-5161	269	13	)	)	PUNCT
ejpam-5161	269	14	)	)	PUNCT
ejpam-5161	269	15	:	:	PUNCT
ejpam-5161	269	16	ac(ω	ac(ω	X
ejpam-5161	269	17	)	)	PUNCT
ejpam-5161	269	18	∈	∈	PROPN
ejpam-5161	269	19	σω	σω	NOUN
ejpam-5161	269	20	,	,	PUNCT
ejpam-5161	269	21	ω	ω	PROPN
ejpam-5161	269	22	∈	∈	PROPN
ejpam-5161	269	23	ω	ω	PROPN
ejpam-5161	269	24	}	}	PUNCT
ejpam-5161	269	25	and	and	CCONJ
ejpam-5161	269	26	(	(	PUNCT
ejpam-5161	269	27	b	b	PROPN
ejpam-5161	269	28	,	,	PUNCT
ejpam-5161	269	29	ω	ω	NOUN
ejpam-5161	269	30	)	)	PUNCT
ejpam-5161	269	31	=	=	PRON
ejpam-5161	269	32	{	{	PUNCT
ejpam-5161	269	33	(	(	PUNCT
ejpam-5161	269	34	ω	ω	NOUN
ejpam-5161	269	35	,	,	PUNCT
ejpam-5161	269	36	b(ω	b(ω	NOUN
ejpam-5161	269	37	)	)	PUNCT
ejpam-5161	269	38	)	)	PUNCT
ejpam-5161	269	39	:	:	PUNCT
ejpam-5161	269	40	bc(ω	bc(ω	X
ejpam-5161	269	41	)	)	PUNCT
ejpam-5161	269	42	∈	∈	PROPN
ejpam-5161	269	43	σω	σω	NOUN
ejpam-5161	269	44	,	,	PUNCT
ejpam-5161	269	45	ω	ω	PROPN
ejpam-5161	269	46	∈	∈	PROPN
ejpam-5161	269	47	ω	ω	PROPN
ejpam-5161	269	48	}	}	PUNCT
ejpam-5161	269	49	.	.	PUNCT
ejpam-5161	270	1	therefore	therefore	ADV
ejpam-5161	270	2	φ̃	φ̃	PROPN
ejpam-5161	270	3	=	=	SYM
ejpam-5161	270	4	(	(	PUNCT
ejpam-5161	270	5	a	a	PRON
ejpam-5161	270	6	,	,	PUNCT
ejpam-5161	270	7	ω	ω	NOUN
ejpam-5161	270	8	)	)	PUNCT
ejpam-5161	270	9	⋂̃	⋂̃	NOUN
ejpam-5161	270	10	(	(	PUNCT
ejpam-5161	270	11	b	b	PROPN
ejpam-5161	270	12	,	,	PUNCT
ejpam-5161	270	13	ω	ω	NOUN
ejpam-5161	270	14	)	)	PUNCT
ejpam-5161	270	15	=	=	PRON
ejpam-5161	270	16	{	{	PUNCT
ejpam-5161	270	17	(	(	PUNCT
ejpam-5161	270	18	ω	ω	NOUN
ejpam-5161	270	19	,	,	PUNCT
ejpam-5161	270	20	a(ω	a(ω	PROPN
ejpam-5161	270	21	)	)	PUNCT
ejpam-5161	270	22	∩b(ω	∩b(ω	PROPN
ejpam-5161	270	23	)	)	PUNCT
ejpam-5161	270	24	)	)	PUNCT
ejpam-5161	270	25	:	:	PUNCT
ejpam-5161	270	26	ac(ω	ac(ω	X
ejpam-5161	270	27	)	)	PUNCT
ejpam-5161	270	28	,	,	PUNCT
ejpam-5161	270	29	bc(ω	bc(ω	NUM
ejpam-5161	270	30	)	)	PUNCT
ejpam-5161	270	31	∈	∈	PROPN
ejpam-5161	270	32	σω	σω	NOUN
ejpam-5161	270	33	,	,	PUNCT
ejpam-5161	270	34	ω	ω	PROPN
ejpam-5161	270	35	∈	∈	PROPN
ejpam-5161	270	36	ω	ω	PROPN
ejpam-5161	270	37	}	}	PUNCT
ejpam-5161	270	38	.	.	PUNCT
ejpam-5161	271	1	we	we	PRON
ejpam-5161	271	2	obtain	obtain	VERB
ejpam-5161	271	3	that	that	SCONJ
ejpam-5161	271	4	a(ω	a(ω	PROPN
ejpam-5161	271	5	)	)	PUNCT
ejpam-5161	271	6	∩	∩	NOUN
ejpam-5161	271	7	b(ω	b(ω	ADV
ejpam-5161	271	8	)	)	PUNCT
ejpam-5161	271	9	=	=	PUNCT
ejpam-5161	271	10	∅.	∅.	NOUN
ejpam-5161	271	11	since	since	SCONJ
ejpam-5161	271	12	σω	σω	PROPN
ejpam-5161	271	13	is	be	AUX
ejpam-5161	271	14	a	a	DET
ejpam-5161	271	15	normal	normal	ADJ
ejpam-5161	271	16	space	space	NOUN
ejpam-5161	271	17	for	for	ADP
ejpam-5161	271	18	each	each	DET
ejpam-5161	271	19	ω	ω	PROPN
ejpam-5161	271	20	∈	∈	PROPN
ejpam-5161	271	21	ω	ω	NOUN
ejpam-5161	271	22	,	,	PUNCT
ejpam-5161	271	23	there	there	PRON
ejpam-5161	271	24	exist	exist	VERB
ejpam-5161	271	25	open	open	ADJ
ejpam-5161	271	26	sets	set	NOUN
ejpam-5161	271	27	g(ω	g(ω	PROPN
ejpam-5161	271	28	)	)	PUNCT
ejpam-5161	271	29	,	,	PUNCT
ejpam-5161	271	30	h(ω	h(ω	PROPN
ejpam-5161	271	31	)	)	PUNCT
ejpam-5161	271	32	such	such	ADJ
ejpam-5161	271	33	that	that	SCONJ
ejpam-5161	271	34	a(ω	a(ω	PROPN
ejpam-5161	271	35	)	)	PUNCT
ejpam-5161	271	36	⊆	⊆	NUM
ejpam-5161	271	37	g(ω	g(ω	NOUN
ejpam-5161	271	38	)	)	PUNCT
ejpam-5161	271	39	,	,	PUNCT
ejpam-5161	271	40	b(ω	b(ω	ADV
ejpam-5161	271	41	)	)	PUNCT
ejpam-5161	271	42	⊆	⊆	NUM
ejpam-5161	271	43	h(ω	h(ω	PROPN
ejpam-5161	271	44	)	)	PUNCT
ejpam-5161	271	45	and	and	CCONJ
ejpam-5161	271	46	g(ω	g(ω	NOUN
ejpam-5161	271	47	)	)	PUNCT
ejpam-5161	271	48	∩h(ω	∩h(ω	PROPN
ejpam-5161	271	49	)	)	PUNCT
ejpam-5161	271	50	=	=	PUNCT
ejpam-5161	271	51	∅.	∅.	NOUN
ejpam-5161	271	52	set	set	VERB
ejpam-5161	271	53	(	(	PUNCT
ejpam-5161	271	54	g	g	PROPN
ejpam-5161	271	55	,	,	PUNCT
ejpam-5161	271	56	ω	ω	NOUN
ejpam-5161	271	57	)	)	PUNCT
ejpam-5161	271	58	=	=	PRON
ejpam-5161	271	59	{	{	PUNCT
ejpam-5161	271	60	(	(	PUNCT
ejpam-5161	271	61	ω	ω	PROPN
ejpam-5161	271	62	,	,	PUNCT
ejpam-5161	271	63	g(ω	g(ω	PROPN
ejpam-5161	271	64	)	)	PUNCT
ejpam-5161	271	65	)	)	PUNCT
ejpam-5161	271	66	:	:	PUNCT
ejpam-5161	272	1	ω	ω	X
ejpam-5161	272	2	∈	∈	PROPN
ejpam-5161	272	3	ω	ω	PROPN
ejpam-5161	272	4	}	}	PUNCT
ejpam-5161	272	5	and	and	CCONJ
ejpam-5161	272	6	(	(	PUNCT
ejpam-5161	272	7	h	h	NOUN
ejpam-5161	272	8	,	,	PUNCT
ejpam-5161	272	9	ω	ω	NOUN
ejpam-5161	272	10	)	)	PUNCT
ejpam-5161	272	11	=	=	PRON
ejpam-5161	272	12	{	{	PUNCT
ejpam-5161	272	13	(	(	PUNCT
ejpam-5161	272	14	ω	ω	NOUN
ejpam-5161	272	15	,	,	PUNCT
ejpam-5161	272	16	h(ω	h(ω	PROPN
ejpam-5161	272	17	)	)	PUNCT
ejpam-5161	272	18	)	)	PUNCT
ejpam-5161	272	19	:	:	PUNCT
ejpam-5161	273	1	ω	ω	X
ejpam-5161	273	2	∈	∈	PROPN
ejpam-5161	273	3	ω	ω	PROPN
ejpam-5161	273	4	}	}	PUNCT
ejpam-5161	273	5	.	.	PUNCT
ejpam-5161	274	1	then	then	ADV
ejpam-5161	274	2	(	(	PUNCT
ejpam-5161	274	3	g	g	PROPN
ejpam-5161	274	4	,	,	PUNCT
ejpam-5161	274	5	ω	ω	NOUN
ejpam-5161	274	6	)	)	PUNCT
ejpam-5161	274	7	,	,	PUNCT
ejpam-5161	274	8	(	(	PUNCT
ejpam-5161	274	9	h	h	NOUN
ejpam-5161	274	10	,	,	PUNCT
ejpam-5161	274	11	ω	ω	NUM
ejpam-5161	274	12	)	)	PUNCT
ejpam-5161	274	13	∈	∈	PROPN
ejpam-5161	274	14	t	t	PROPN
ejpam-5161	274	15	(	(	PUNCT
ejpam-5161	274	16	σ	σ	PROPN
ejpam-5161	274	17	)	)	PUNCT
ejpam-5161	274	18	such	such	ADJ
ejpam-5161	274	19	that	that	SCONJ
ejpam-5161	274	20	(	(	PUNCT
ejpam-5161	274	21	a	a	PRON
ejpam-5161	274	22	,	,	PUNCT
ejpam-5161	274	23	ω)⊆̃(g	ω)⊆̃(g	PROPN
ejpam-5161	274	24	,	,	PUNCT
ejpam-5161	274	25	ω	ω	NOUN
ejpam-5161	274	26	)	)	PUNCT
ejpam-5161	274	27	and	and	CCONJ
ejpam-5161	274	28	(	(	PUNCT
ejpam-5161	274	29	b	b	NOUN
ejpam-5161	274	30	,	,	PUNCT
ejpam-5161	274	31	ω)⊆̃(h	ω)⊆̃(h	PROPN
ejpam-5161	274	32	,	,	PUNCT
ejpam-5161	274	33	ω	ω	NOUN
ejpam-5161	274	34	)	)	PUNCT
ejpam-5161	274	35	.	.	PUNCT
ejpam-5161	275	1	furthermore	furthermore	ADV
ejpam-5161	275	2	,	,	PUNCT
ejpam-5161	275	3	(	(	PUNCT
ejpam-5161	275	4	g	g	NOUN
ejpam-5161	275	5	,	,	PUNCT
ejpam-5161	275	6	ω	ω	NOUN
ejpam-5161	275	7	)	)	PUNCT
ejpam-5161	275	8	⋂̃	⋂̃	NOUN
ejpam-5161	275	9	(	(	PUNCT
ejpam-5161	275	10	h	h	NOUN
ejpam-5161	275	11	,	,	PUNCT
ejpam-5161	275	12	ω	ω	NOUN
ejpam-5161	275	13	)	)	PUNCT
ejpam-5161	275	14	=	=	PRON
ejpam-5161	275	15	{	{	PUNCT
ejpam-5161	275	16	(	(	PUNCT
ejpam-5161	275	17	ω	ω	PROPN
ejpam-5161	275	18	,	,	PUNCT
ejpam-5161	275	19	g(ω	g(ω	NOUN
ejpam-5161	275	20	)	)	PUNCT
ejpam-5161	275	21	∩h(ω	∩h(ω	PROPN
ejpam-5161	275	22	)	)	PUNCT
ejpam-5161	275	23	)	)	PUNCT
ejpam-5161	275	24	:	:	PUNCT
ejpam-5161	275	25	ω	ω	X
ejpam-5161	275	26	∈	∈	PROPN
ejpam-5161	275	27	ω	ω	NOUN
ejpam-5161	275	28	}	}	PUNCT
ejpam-5161	275	29	=	=	SYM
ejpam-5161	275	30	φ̃.	φ̃.	NOUN
ejpam-5161	275	31	this	this	PRON
ejpam-5161	275	32	shows	show	VERB
ejpam-5161	275	33	that	that	SCONJ
ejpam-5161	275	34	t	t	PROPN
ejpam-5161	275	35	(	(	PUNCT
ejpam-5161	275	36	σ	σ	NOUN
ejpam-5161	275	37	)	)	PUNCT
ejpam-5161	275	38	is	be	AUX
ejpam-5161	275	39	soft	soft	ADJ
ejpam-5161	275	40	normal	normal	ADJ
ejpam-5161	275	41	.	.	PUNCT
ejpam-5161	276	1	conversely	conversely	ADV
ejpam-5161	276	2	,	,	PUNCT
ejpam-5161	276	3	for	for	ADP
ejpam-5161	276	4	each	each	DET
ejpam-5161	276	5	ω	ω	PROPN
ejpam-5161	276	6	∈	∈	PROPN
ejpam-5161	276	7	ω	ω	NOUN
ejpam-5161	276	8	,	,	PUNCT
ejpam-5161	276	9	we	we	PRON
ejpam-5161	276	10	let	let	VERB
ejpam-5161	276	11	c(ω	c(ω	NOUN
ejpam-5161	276	12	)	)	PUNCT
ejpam-5161	276	13	,	,	PUNCT
ejpam-5161	276	14	d(ω	d(ω	PROPN
ejpam-5161	276	15	)	)	PUNCT
ejpam-5161	276	16	be	be	AUX
ejpam-5161	276	17	disjoint	disjoint	NOUN
ejpam-5161	276	18	closed	close	VERB
ejpam-5161	276	19	sets	set	NOUN
ejpam-5161	276	20	in	in	ADP
ejpam-5161	276	21	σω	σω	PROPN
ejpam-5161	276	22	.	.	PUNCT
ejpam-5161	277	1	by	by	ADP
ejpam-5161	277	2	lemma	lemma	PROPN
ejpam-5161	277	3	8	8	NUM
ejpam-5161	277	4	,	,	PUNCT
ejpam-5161	277	5	(	(	PUNCT
ejpam-5161	277	6	c	c	X
ejpam-5161	277	7	,	,	PUNCT
ejpam-5161	277	8	ω	ω	NOUN
ejpam-5161	277	9	)	)	PUNCT
ejpam-5161	277	10	=	=	PRON
ejpam-5161	277	11	{	{	PUNCT
ejpam-5161	277	12	(	(	PUNCT
ejpam-5161	277	13	ω	ω	NOUN
ejpam-5161	277	14	,	,	PUNCT
ejpam-5161	277	15	c(ω	c(ω	PROPN
ejpam-5161	277	16	)	)	PUNCT
ejpam-5161	277	17	)	)	PUNCT
ejpam-5161	277	18	:	:	PUNCT
ejpam-5161	277	19	cc(ω	cc(ω	X
ejpam-5161	277	20	)	)	PUNCT
ejpam-5161	277	21	∈	∈	PROPN
ejpam-5161	277	22	σω	σω	NOUN
ejpam-5161	277	23	,	,	PUNCT
ejpam-5161	277	24	ω	ω	PROPN
ejpam-5161	277	25	∈	∈	PROPN
ejpam-5161	277	26	ω	ω	PROPN
ejpam-5161	277	27	}	}	PUNCT
ejpam-5161	277	28	and	and	CCONJ
ejpam-5161	277	29	(	(	PUNCT
ejpam-5161	277	30	d	d	PROPN
ejpam-5161	277	31	,	,	PUNCT
ejpam-5161	277	32	ω	ω	NOUN
ejpam-5161	277	33	)	)	PUNCT
ejpam-5161	277	34	=	=	PRON
ejpam-5161	277	35	{	{	PUNCT
ejpam-5161	277	36	(	(	PUNCT
ejpam-5161	277	37	ω	ω	PROPN
ejpam-5161	277	38	,	,	PUNCT
ejpam-5161	277	39	d(ω	d(ω	PROPN
ejpam-5161	277	40	)	)	PUNCT
ejpam-5161	277	41	)	)	PUNCT
ejpam-5161	277	42	:	:	PUNCT
ejpam-5161	277	43	dc(ω	dc(ω	X
ejpam-5161	277	44	)	)	PUNCT
ejpam-5161	277	45	∈	∈	PROPN
ejpam-5161	277	46	σω	σω	NOUN
ejpam-5161	277	47	,	,	PUNCT
ejpam-5161	277	48	ω	ω	PROPN
ejpam-5161	277	49	∈	∈	PROPN
ejpam-5161	277	50	ω	ω	PROPN
ejpam-5161	277	51	}	}	PUNCT
ejpam-5161	277	52	are	be	AUX
ejpam-5161	277	53	soft	soft	ADJ
ejpam-5161	277	54	closed	closed	ADJ
ejpam-5161	277	55	sets	set	NOUN
ejpam-5161	277	56	in	in	ADP
ejpam-5161	277	57	t	t	PROPN
ejpam-5161	277	58	(	(	PUNCT
ejpam-5161	277	59	σ	σ	PROPN
ejpam-5161	277	60	)	)	PUNCT
ejpam-5161	277	61	and	and	CCONJ
ejpam-5161	277	62	(	(	PUNCT
ejpam-5161	277	63	c	c	X
ejpam-5161	277	64	,	,	PUNCT
ejpam-5161	277	65	ω	ω	NOUN
ejpam-5161	277	66	)	)	PUNCT
ejpam-5161	277	67	⋂̃	⋂̃	NOUN
ejpam-5161	277	68	(	(	PUNCT
ejpam-5161	277	69	d	d	PROPN
ejpam-5161	277	70	,	,	PUNCT
ejpam-5161	277	71	ω	ω	NOUN
ejpam-5161	277	72	)	)	PUNCT
ejpam-5161	277	73	=	=	PRON
ejpam-5161	277	74	{	{	PUNCT
ejpam-5161	277	75	(	(	PUNCT
ejpam-5161	277	76	ω	ω	NOUN
ejpam-5161	277	77	,	,	PUNCT
ejpam-5161	277	78	c(ω	c(ω	PROPN
ejpam-5161	277	79	)	)	PUNCT
ejpam-5161	277	80	∩	∩	NOUN
ejpam-5161	277	81	d(ω	d(ω	PROPN
ejpam-5161	277	82	)	)	PUNCT
ejpam-5161	277	83	)	)	PUNCT
ejpam-5161	277	84	:	:	PUNCT
ejpam-5161	278	1	ω	ω	X
ejpam-5161	278	2	∈	∈	PROPN
ejpam-5161	278	3	ω	ω	NOUN
ejpam-5161	278	4	}	}	PUNCT
ejpam-5161	278	5	=	=	SYM
ejpam-5161	278	6	φ̃.	φ̃.	PROPN
ejpam-5161	278	7	since	since	SCONJ
ejpam-5161	278	8	t	t	PROPN
ejpam-5161	278	9	(	(	PUNCT
ejpam-5161	278	10	σ	σ	PROPN
ejpam-5161	278	11	)	)	PUNCT
ejpam-5161	278	12	is	be	AUX
ejpam-5161	278	13	soft	soft	ADJ
ejpam-5161	278	14	normal	normal	ADJ
ejpam-5161	278	15	,	,	PUNCT
ejpam-5161	278	16	then	then	ADV
ejpam-5161	278	17	there	there	PRON
ejpam-5161	278	18	exist	exist	VERB
ejpam-5161	278	19	disjoint	disjoint	ADJ
ejpam-5161	278	20	soft	soft	ADJ
ejpam-5161	278	21	open	open	ADJ
ejpam-5161	278	22	sets	set	NOUN
ejpam-5161	278	23	(	(	PUNCT
ejpam-5161	278	24	u	u	NOUN
ejpam-5161	278	25	,	,	PUNCT
ejpam-5161	278	26	ω	ω	NOUN
ejpam-5161	278	27	)	)	PUNCT
ejpam-5161	278	28	,	,	PUNCT
ejpam-5161	278	29	(	(	PUNCT
ejpam-5161	278	30	v	v	NOUN
ejpam-5161	278	31	,	,	PUNCT
ejpam-5161	278	32	ω	ω	NOUN
ejpam-5161	278	33	)	)	PUNCT
ejpam-5161	278	34	such	such	ADJ
ejpam-5161	278	35	that	that	SCONJ
ejpam-5161	278	36	(	(	PUNCT
ejpam-5161	278	37	c	c	X
ejpam-5161	278	38	,	,	PUNCT
ejpam-5161	278	39	ω)⊆̃(u	ω)⊆̃(u	PROPN
ejpam-5161	278	40	,	,	PUNCT
ejpam-5161	278	41	ω	ω	NOUN
ejpam-5161	278	42	)	)	PUNCT
ejpam-5161	278	43	and	and	CCONJ
ejpam-5161	278	44	(	(	PUNCT
ejpam-5161	278	45	d	d	NOUN
ejpam-5161	278	46	,	,	PUNCT
ejpam-5161	278	47	ω)⊆̃(v	ω)⊆̃(v	PROPN
ejpam-5161	278	48	,	,	PUNCT
ejpam-5161	278	49	ω	ω	NOUN
ejpam-5161	278	50	)	)	PUNCT
ejpam-5161	278	51	.	.	PUNCT
ejpam-5161	279	1	this	this	PRON
ejpam-5161	279	2	implies	imply	VERB
ejpam-5161	279	3	that	that	SCONJ
ejpam-5161	279	4	c(ω	c(ω	NOUN
ejpam-5161	279	5	)	)	PUNCT
ejpam-5161	279	6	⊆	⊆	NUM
ejpam-5161	279	7	u(ω	u(ω	PROPN
ejpam-5161	279	8	)	)	PUNCT
ejpam-5161	279	9	,	,	PUNCT
ejpam-5161	279	10	d(ω	d(ω	PROPN
ejpam-5161	279	11	)	)	PUNCT
ejpam-5161	279	12	⊆	⊆	NUM
ejpam-5161	279	13	v	v	X
ejpam-5161	279	14	(	(	PUNCT
ejpam-5161	279	15	ω	ω	NOUN
ejpam-5161	279	16	)	)	PUNCT
ejpam-5161	279	17	and	and	CCONJ
ejpam-5161	279	18	u(ω	u(ω	PROPN
ejpam-5161	279	19	)	)	PUNCT
ejpam-5161	279	20	∩	∩	PROPN
ejpam-5161	279	21	v	v	X
ejpam-5161	279	22	(	(	PUNCT
ejpam-5161	279	23	ω	ω	NOUN
ejpam-5161	279	24	)	)	PUNCT
ejpam-5161	279	25	=	=	NOUN
ejpam-5161	279	26	∅	∅	NOUN
ejpam-5161	279	27	for	for	ADP
ejpam-5161	279	28	each	each	DET
ejpam-5161	279	29	ω	ω	PROPN
ejpam-5161	279	30	∈	∈	PROPN
ejpam-5161	279	31	ω	ω	PROPN
ejpam-5161	279	32	.	.	PUNCT
ejpam-5161	280	1	thus	thus	ADV
ejpam-5161	280	2	,	,	PUNCT
ejpam-5161	280	3	σω	σω	VERB
ejpam-5161	280	4	is	be	AUX
ejpam-5161	280	5	normal	normal	ADJ
ejpam-5161	280	6	for	for	ADP
ejpam-5161	280	7	each	each	DET
ejpam-5161	280	8	ω	ω	PROPN
ejpam-5161	280	9	∈	∈	PROPN
ejpam-5161	280	10	ω	ω	NOUN
ejpam-5161	280	11	.	.	PUNCT
ejpam-5161	281	1	we	we	PRON
ejpam-5161	281	2	shall	shall	AUX
ejpam-5161	281	3	remark	remark	VERB
ejpam-5161	281	4	that	that	SCONJ
ejpam-5161	281	5	if	if	SCONJ
ejpam-5161	281	6	(	(	PUNCT
ejpam-5161	281	7	x	x	X
ejpam-5161	281	8	,	,	PUNCT
ejpam-5161	281	9	σ	σ	PROPN
ejpam-5161	281	10	,	,	PUNCT
ejpam-5161	281	11	ω	ω	NOUN
ejpam-5161	281	12	)	)	PUNCT
ejpam-5161	281	13	is	be	AUX
ejpam-5161	281	14	a	a	DET
ejpam-5161	281	15	soft	soft	ADJ
ejpam-5161	281	16	normal	normal	ADJ
ejpam-5161	281	17	space	space	NOUN
ejpam-5161	281	18	,	,	PUNCT
ejpam-5161	281	19	then	then	ADV
ejpam-5161	281	20	σω	σω	AUX
ejpam-5161	281	21	need	need	AUX
ejpam-5161	281	22	not	not	PART
ejpam-5161	281	23	be	be	AUX
ejpam-5161	281	24	a	a	DET
ejpam-5161	281	25	normal	normal	ADJ
ejpam-5161	281	26	space	space	NOUN
ejpam-5161	281	27	for	for	ADP
ejpam-5161	281	28	each	each	DET
ejpam-5161	281	29	ω	ω	PROPN
ejpam-5161	281	30	∈	∈	PROPN
ejpam-5161	281	31	ω	ω	PROPN
ejpam-5161	281	32	.	.	PUNCT
ejpam-5161	281	33	example	example	NOUN
ejpam-5161	282	1	7	7	NUM
ejpam-5161	282	2	.	.	PUNCT
ejpam-5161	283	1	let	let	VERB
ejpam-5161	283	2	x	x	PUNCT
ejpam-5161	283	3	=	=	PRON
ejpam-5161	283	4	{	{	PUNCT
ejpam-5161	283	5	x1	x1	PROPN
ejpam-5161	283	6	,	,	PUNCT
ejpam-5161	283	7	x2	x2	PROPN
ejpam-5161	283	8	,	,	PUNCT
ejpam-5161	283	9	x3	x3	ADJ
ejpam-5161	283	10	}	}	PUNCT
ejpam-5161	283	11	and	and	CCONJ
ejpam-5161	283	12	ω	ω	NUM
ejpam-5161	283	13	=	=	SYM
ejpam-5161	283	14	{	{	PUNCT
ejpam-5161	283	15	ω1	ω1	PROPN
ejpam-5161	283	16	,	,	PUNCT
ejpam-5161	283	17	ω2	ω2	ADJ
ejpam-5161	283	18	}	}	PUNCT
ejpam-5161	283	19	.	.	PUNCT
ejpam-5161	284	1	suppose	suppose	VERB
ejpam-5161	285	1	σ	σ	NOUN
ejpam-5161	285	2	=	=	X
ejpam-5161	285	3	{	{	PUNCT
ejpam-5161	285	4	φ̃	φ̃	PROPN
ejpam-5161	285	5	,	,	PUNCT
ejpam-5161	285	6	(	(	PUNCT
ejpam-5161	285	7	h1,ω	h1,ω	PROPN
ejpam-5161	285	8	)	)	PUNCT
ejpam-5161	285	9	,	,	PUNCT
ejpam-5161	285	10	(	(	PUNCT
ejpam-5161	285	11	h2,ω	h2,ω	PROPN
ejpam-5161	285	12	)	)	PUNCT
ejpam-5161	285	13	,	,	PUNCT
ejpam-5161	285	14	·	·	PUNCT
ejpam-5161	285	15	·	·	PUNCT
ejpam-5161	285	16	·	·	PUNCT
ejpam-5161	285	17	,	,	PUNCT
ejpam-5161	285	18	(	(	PUNCT
ejpam-5161	285	19	h9,ω	h9,ω	PROPN
ejpam-5161	285	20	)	)	PUNCT
ejpam-5161	285	21	,	,	PUNCT
ejpam-5161	285	22	x̃	x̃	PROPN
ejpam-5161	285	23	}	}	PUNCT
ejpam-5161	285	24	,	,	PUNCT
ejpam-5161	285	25	where	where	SCONJ
ejpam-5161	285	26	(	(	PUNCT
ejpam-5161	285	27	h1,ω	h1,ω	NOUN
ejpam-5161	285	28	)	)	PUNCT
ejpam-5161	285	29	=	=	PRON
ejpam-5161	285	30	{	{	PUNCT
ejpam-5161	285	31	(	(	PUNCT
ejpam-5161	285	32	ω1	ω1	PROPN
ejpam-5161	285	33	,	,	PUNCT
ejpam-5161	285	34	∅	∅	NOUN
ejpam-5161	285	35	)	)	PUNCT
ejpam-5161	285	36	,	,	PUNCT
ejpam-5161	285	37	(	(	PUNCT
ejpam-5161	285	38	ω2	ω2	ADV
ejpam-5161	285	39	,	,	PUNCT
ejpam-5161	285	40	{	{	PUNCT
ejpam-5161	285	41	x3	x3	ADJ
ejpam-5161	285	42	}	}	PUNCT
ejpam-5161	285	43	)	)	PUNCT
ejpam-5161	285	44	}	}	PUNCT
ejpam-5161	285	45	,	,	PUNCT
ejpam-5161	285	46	(	(	PUNCT
ejpam-5161	285	47	h2,ω	h2,ω	PROPN
ejpam-5161	285	48	)	)	PUNCT
ejpam-5161	285	49	=	=	PRON
ejpam-5161	285	50	{	{	PUNCT
ejpam-5161	285	51	(	(	PUNCT
ejpam-5161	285	52	ω1	ω1	PROPN
ejpam-5161	285	53	,	,	PUNCT
ejpam-5161	285	54	{	{	PUNCT
ejpam-5161	285	55	x3	x3	ADJ
ejpam-5161	285	56	}	}	PUNCT
ejpam-5161	285	57	)	)	PUNCT
ejpam-5161	285	58	,	,	PUNCT
ejpam-5161	285	59	(	(	PUNCT
ejpam-5161	285	60	ω2	ω2	ADJ
ejpam-5161	285	61	,	,	PUNCT
ejpam-5161	285	62	∅	∅	NOUN
ejpam-5161	285	63	)	)	PUNCT
ejpam-5161	285	64	}	}	PUNCT
ejpam-5161	285	65	,	,	PUNCT
ejpam-5161	285	66	(	(	PUNCT
ejpam-5161	285	67	h3,ω	h3,ω	PROPN
ejpam-5161	285	68	)	)	PUNCT
ejpam-5161	285	69	=	=	PRON
ejpam-5161	285	70	{	{	PUNCT
ejpam-5161	285	71	(	(	PUNCT
ejpam-5161	285	72	ω1	ω1	PROPN
ejpam-5161	285	73	,	,	PUNCT
ejpam-5161	285	74	{	{	PUNCT
ejpam-5161	285	75	x2	x2	ADJ
ejpam-5161	285	76	,	,	PUNCT
ejpam-5161	285	77	x3	x3	ADJ
ejpam-5161	285	78	}	}	PUNCT
ejpam-5161	285	79	)	)	PUNCT
ejpam-5161	285	80	,	,	PUNCT
ejpam-5161	285	81	(	(	PUNCT
ejpam-5161	285	82	ω2	ω2	ADJ
ejpam-5161	285	83	,	,	PUNCT
ejpam-5161	285	84	∅	∅	NOUN
ejpam-5161	285	85	)	)	PUNCT
ejpam-5161	285	86	}	}	PUNCT
ejpam-5161	285	87	,	,	PUNCT
ejpam-5161	285	88	(	(	PUNCT
ejpam-5161	285	89	h4,ω	h4,ω	PROPN
ejpam-5161	285	90	)	)	PUNCT
ejpam-5161	285	91	=	=	SYM
ejpam-5161	285	92	{	{	PUNCT
ejpam-5161	285	93	(	(	PUNCT
ejpam-5161	285	94	ω1	ω1	PROPN
ejpam-5161	285	95	,	,	PUNCT
ejpam-5161	285	96	x	x	NOUN
ejpam-5161	285	97	)	)	PUNCT
ejpam-5161	285	98	,	,	PUNCT
ejpam-5161	285	99	(	(	PUNCT
ejpam-5161	285	100	ω2	ω2	ADJ
ejpam-5161	285	101	,	,	PUNCT
ejpam-5161	285	102	∅	∅	NOUN
ejpam-5161	285	103	)	)	PUNCT
ejpam-5161	285	104	}	}	PUNCT
ejpam-5161	285	105	,	,	PUNCT
ejpam-5161	285	106	(	(	PUNCT
ejpam-5161	285	107	h5,ω	h5,ω	PROPN
ejpam-5161	285	108	)	)	PUNCT
ejpam-5161	285	109	=	=	PRON
ejpam-5161	285	110	{	{	PUNCT
ejpam-5161	285	111	(	(	PUNCT
ejpam-5161	285	112	ω1	ω1	PROPN
ejpam-5161	285	113	,	,	PUNCT
ejpam-5161	285	114	{	{	PUNCT
ejpam-5161	285	115	x1	x1	PROPN
ejpam-5161	285	116	,	,	PUNCT
ejpam-5161	285	117	x3	x3	ADJ
ejpam-5161	285	118	}	}	PUNCT
ejpam-5161	285	119	)	)	PUNCT
ejpam-5161	285	120	,	,	PUNCT
ejpam-5161	285	121	(	(	PUNCT
ejpam-5161	285	122	ω2	ω2	ADJ
ejpam-5161	285	123	,	,	PUNCT
ejpam-5161	285	124	∅	∅	NOUN
ejpam-5161	285	125	)	)	PUNCT
ejpam-5161	285	126	}	}	PUNCT
ejpam-5161	285	127	,	,	PUNCT
ejpam-5161	285	128	(	(	PUNCT
ejpam-5161	285	129	h6,ω	h6,ω	PROPN
ejpam-5161	285	130	)	)	PUNCT
ejpam-5161	285	131	=	=	PRON
ejpam-5161	285	132	{	{	PUNCT
ejpam-5161	285	133	(	(	PUNCT
ejpam-5161	285	134	ω1	ω1	PROPN
ejpam-5161	285	135	,	,	PUNCT
ejpam-5161	285	136	{	{	PUNCT
ejpam-5161	285	137	x3	x3	ADJ
ejpam-5161	285	138	}	}	PUNCT
ejpam-5161	285	139	)	)	PUNCT
ejpam-5161	285	140	,	,	PUNCT
ejpam-5161	285	141	(	(	PUNCT
ejpam-5161	285	142	ω2	ω2	ADV
ejpam-5161	285	143	,	,	PUNCT
ejpam-5161	285	144	{	{	PUNCT
ejpam-5161	285	145	x3	x3	ADJ
ejpam-5161	285	146	}	}	PUNCT
ejpam-5161	285	147	)	)	PUNCT
ejpam-5161	285	148	}	}	PUNCT
ejpam-5161	285	149	,	,	PUNCT
ejpam-5161	285	150	(	(	PUNCT
ejpam-5161	285	151	h7,ω	h7,ω	PROPN
ejpam-5161	285	152	)	)	PUNCT
ejpam-5161	285	153	=	=	SYM
ejpam-5161	285	154	{	{	PUNCT
ejpam-5161	285	155	(	(	PUNCT
ejpam-5161	285	156	ω1	ω1	PROPN
ejpam-5161	285	157	,	,	PUNCT
ejpam-5161	285	158	{	{	PUNCT
ejpam-5161	285	159	x2	x2	ADJ
ejpam-5161	285	160	,	,	PUNCT
ejpam-5161	285	161	x3	x3	ADJ
ejpam-5161	285	162	}	}	PUNCT
ejpam-5161	285	163	)	)	PUNCT
ejpam-5161	285	164	,	,	PUNCT
ejpam-5161	285	165	(	(	PUNCT
ejpam-5161	285	166	ω2	ω2	ADV
ejpam-5161	285	167	,	,	PUNCT
ejpam-5161	285	168	{	{	PUNCT
ejpam-5161	285	169	x3	x3	ADJ
ejpam-5161	285	170	}	}	PUNCT
ejpam-5161	285	171	)	)	PUNCT
ejpam-5161	285	172	}	}	PUNCT
ejpam-5161	285	173	,	,	PUNCT
ejpam-5161	285	174	(	(	PUNCT
ejpam-5161	285	175	h8,ω	h8,ω	PROPN
ejpam-5161	285	176	)	)	PUNCT
ejpam-5161	285	177	=	=	SYM
ejpam-5161	285	178	{	{	PUNCT
ejpam-5161	285	179	(	(	PUNCT
ejpam-5161	285	180	ω1	ω1	PROPN
ejpam-5161	285	181	,	,	PUNCT
ejpam-5161	285	182	x	x	NOUN
ejpam-5161	285	183	)	)	PUNCT
ejpam-5161	285	184	,	,	PUNCT
ejpam-5161	285	185	(	(	PUNCT
ejpam-5161	285	186	ω2	ω2	ADV
ejpam-5161	285	187	,	,	PUNCT
ejpam-5161	285	188	{	{	PUNCT
ejpam-5161	285	189	x3	x3	ADJ
ejpam-5161	285	190	}	}	PUNCT
ejpam-5161	285	191	)	)	PUNCT
ejpam-5161	285	192	}	}	PUNCT
ejpam-5161	285	193	,	,	PUNCT
ejpam-5161	285	194	and	and	CCONJ
ejpam-5161	285	195	z.	z.	PROPN
ejpam-5161	285	196	a.	a.	PROPN
ejpam-5161	285	197	ameen	ameen	PROPN
ejpam-5161	285	198	et	et	PROPN
ejpam-5161	285	199	al	al	PROPN
ejpam-5161	285	200	.	.	PUNCT
ejpam-5161	285	201	/	/	SYM
ejpam-5161	285	202	eur	eur	PROPN
ejpam-5161	285	203	.	.	PUNCT
ejpam-5161	286	1	j.	j.	PROPN
ejpam-5161	286	2	pure	pure	PROPN
ejpam-5161	286	3	appl	appl	PROPN
ejpam-5161	286	4	.	.	PROPN
ejpam-5161	286	5	math	math	PROPN
ejpam-5161	286	6	,	,	PUNCT
ejpam-5161	286	7	17	17	NUM
ejpam-5161	286	8	(	(	PUNCT
ejpam-5161	286	9	2	2	NUM
ejpam-5161	286	10	)	)	PUNCT
ejpam-5161	286	11	(	(	PUNCT
ejpam-5161	286	12	2024	2024	NUM
ejpam-5161	286	13	)	)	PUNCT
ejpam-5161	286	14	,	,	PUNCT
ejpam-5161	286	15	1168	1168	NUM
ejpam-5161	286	16	-	-	SYM
ejpam-5161	286	17	1182	1182	NUM
ejpam-5161	286	18	1179	1179	NUM
ejpam-5161	286	19	(	(	PUNCT
ejpam-5161	286	20	h9,ω	h9,ω	PROPN
ejpam-5161	286	21	)	)	PUNCT
ejpam-5161	286	22	=	=	PRON
ejpam-5161	286	23	{	{	PUNCT
ejpam-5161	286	24	(	(	PUNCT
ejpam-5161	286	25	ω1	ω1	PROPN
ejpam-5161	286	26	,	,	PUNCT
ejpam-5161	286	27	{	{	PUNCT
ejpam-5161	286	28	x1	x1	PROPN
ejpam-5161	286	29	,	,	PUNCT
ejpam-5161	286	30	x3	x3	ADJ
ejpam-5161	286	31	}	}	PUNCT
ejpam-5161	286	32	)	)	PUNCT
ejpam-5161	286	33	,	,	PUNCT
ejpam-5161	286	34	(	(	PUNCT
ejpam-5161	286	35	ω2	ω2	ADV
ejpam-5161	286	36	,	,	PUNCT
ejpam-5161	286	37	{	{	PUNCT
ejpam-5161	286	38	x3	x3	ADJ
ejpam-5161	286	39	}	}	PUNCT
ejpam-5161	286	40	)	)	PUNCT
ejpam-5161	286	41	}	}	PUNCT
ejpam-5161	286	42	.	.	PUNCT
ejpam-5161	287	1	then	then	ADV
ejpam-5161	287	2	σ	σ	PROPN
ejpam-5161	287	3	is	be	AUX
ejpam-5161	287	4	a	a	DET
ejpam-5161	287	5	soft	soft	ADJ
ejpam-5161	287	6	normal	normal	ADJ
ejpam-5161	287	7	space	space	NOUN
ejpam-5161	287	8	as	as	SCONJ
ejpam-5161	287	9	each	each	DET
ejpam-5161	287	10	pair	pair	NOUN
ejpam-5161	287	11	of	of	ADP
ejpam-5161	287	12	non	non	ADJ
ejpam-5161	287	13	-	-	ADJ
ejpam-5161	287	14	null	null	ADJ
ejpam-5161	287	15	soft	soft	ADJ
ejpam-5161	287	16	closed	closed	ADJ
ejpam-5161	287	17	sets	set	NOUN
ejpam-5161	287	18	intersects	intersect	NOUN
ejpam-5161	287	19	each	each	DET
ejpam-5161	287	20	other	other	ADJ
ejpam-5161	287	21	.	.	PUNCT
ejpam-5161	288	1	on	on	ADP
ejpam-5161	288	2	the	the	DET
ejpam-5161	288	3	other	other	ADJ
ejpam-5161	288	4	hand	hand	NOUN
ejpam-5161	288	5	,	,	PUNCT
ejpam-5161	288	6	σω1	σω1	NOUN
ejpam-5161	288	7	=	=	SYM
ejpam-5161	288	8	{	{	PUNCT
ejpam-5161	288	9	x	x	NOUN
ejpam-5161	288	10	,	,	PUNCT
ejpam-5161	288	11	∅	∅	NOUN
ejpam-5161	288	12	,	,	PUNCT
ejpam-5161	288	13	{	{	PUNCT
ejpam-5161	288	14	x3	x3	ADJ
ejpam-5161	288	15	}	}	PUNCT
ejpam-5161	288	16	,	,	PUNCT
ejpam-5161	288	17	{	{	PUNCT
ejpam-5161	288	18	x2	x2	ADJ
ejpam-5161	288	19	,	,	PUNCT
ejpam-5161	288	20	x3	x3	ADJ
ejpam-5161	288	21	}	}	PUNCT
ejpam-5161	288	22	,	,	PUNCT
ejpam-5161	288	23	{	{	PUNCT
ejpam-5161	288	24	x1	x1	ADJ
ejpam-5161	288	25	,	,	PUNCT
ejpam-5161	288	26	x3	x3	ADJ
ejpam-5161	288	27	}	}	PUNCT
ejpam-5161	288	28	}	}	PUNCT
ejpam-5161	288	29	is	be	AUX
ejpam-5161	288	30	not	not	PART
ejpam-5161	288	31	normal	normal	ADJ
ejpam-5161	288	32	.	.	PUNCT
ejpam-5161	289	1	indeed	indeed	ADV
ejpam-5161	289	2	,	,	PUNCT
ejpam-5161	289	3	x3	x3	ADJ
ejpam-5161	289	4	/∈	/∈	PUNCT
ejpam-5161	290	1	{	{	PUNCT
ejpam-5161	290	2	x1	x1	PROPN
ejpam-5161	290	3	}	}	PUNCT
ejpam-5161	290	4	and	and	CCONJ
ejpam-5161	290	5	{	{	PUNCT
ejpam-5161	290	6	x1	x1	PROPN
ejpam-5161	290	7	}	}	PUNCT
ejpam-5161	290	8	is	be	AUX
ejpam-5161	290	9	a	a	DET
ejpam-5161	290	10	closed	closed	ADJ
ejpam-5161	290	11	set	set	NOUN
ejpam-5161	290	12	in	in	ADP
ejpam-5161	290	13	σω1	σω1	NOUN
ejpam-5161	290	14	.	.	PUNCT
ejpam-5161	291	1	let	let	VERB
ejpam-5161	291	2	u	u	NOUN
ejpam-5161	291	3	,	,	PUNCT
ejpam-5161	291	4	v	v	PROPN
ejpam-5161	291	5	∈	∈	NOUN
ejpam-5161	291	6	σω1	σω1	NOUN
ejpam-5161	291	7	such	such	ADJ
ejpam-5161	291	8	that	that	SCONJ
ejpam-5161	291	9	x3	x3	PROPN
ejpam-5161	291	10	∈	∈	PROPN
ejpam-5161	291	11	u	u	NOUN
ejpam-5161	291	12	and	and	CCONJ
ejpam-5161	291	13	{	{	PUNCT
ejpam-5161	291	14	x1	x1	PROPN
ejpam-5161	291	15	}	}	PUNCT
ejpam-5161	291	16	⊆	⊆	NUM
ejpam-5161	291	17	v	v	NOUN
ejpam-5161	291	18	.	.	PUNCT
ejpam-5161	292	1	hence	hence	ADV
ejpam-5161	292	2	,	,	PUNCT
ejpam-5161	292	3	by	by	ADP
ejpam-5161	292	4	the	the	DET
ejpam-5161	292	5	definition	definition	NOUN
ejpam-5161	292	6	of	of	ADP
ejpam-5161	292	7	σω1	σω1	NOUN
ejpam-5161	292	8	,	,	PUNCT
ejpam-5161	292	9	we	we	PRON
ejpam-5161	292	10	know	know	VERB
ejpam-5161	292	11	that	that	SCONJ
ejpam-5161	292	12	{	{	PUNCT
ejpam-5161	292	13	x3	x3	ADJ
ejpam-5161	292	14	}	}	PUNCT
ejpam-5161	292	15	⊆	⊆	NUM
ejpam-5161	292	16	u	u	NOUN
ejpam-5161	292	17	and	and	CCONJ
ejpam-5161	292	18	{	{	PUNCT
ejpam-5161	292	19	x1	x1	PROPN
ejpam-5161	292	20	,	,	PUNCT
ejpam-5161	292	21	x3	x3	ADJ
ejpam-5161	292	22	}	}	PUNCT
ejpam-5161	292	23	⊆	⊆	NUM
ejpam-5161	292	24	v	v	NOUN
ejpam-5161	292	25	.	.	PUNCT
ejpam-5161	293	1	therefore	therefore	ADV
ejpam-5161	293	2	,	,	PUNCT
ejpam-5161	293	3	u	u	PROPN
ejpam-5161	293	4	∩	∩	NOUN
ejpam-5161	293	5	v	v	ADP
ejpam-5161	293	6	̸=	̸=	PROPN
ejpam-5161	293	7	∅.	∅.	ADP
ejpam-5161	293	8	the	the	DET
ejpam-5161	293	9	following	following	ADJ
ejpam-5161	293	10	example	example	NOUN
ejpam-5161	293	11	demonstrates	demonstrate	VERB
ejpam-5161	293	12	that	that	SCONJ
ejpam-5161	293	13	t	t	PROPN
ejpam-5161	293	14	(	(	PUNCT
ejpam-5161	293	15	σ	σ	NOUN
ejpam-5161	293	16	)	)	PUNCT
ejpam-5161	293	17	needs	need	VERB
ejpam-5161	293	18	not	not	PART
ejpam-5161	293	19	to	to	PART
ejpam-5161	293	20	be	be	AUX
ejpam-5161	293	21	soft	soft	ADJ
ejpam-5161	293	22	normal	normal	ADJ
ejpam-5161	293	23	if	if	SCONJ
ejpam-5161	293	24	σω	σω	ADJ
ejpam-5161	293	25	is	be	AUX
ejpam-5161	293	26	not	not	PART
ejpam-5161	293	27	normal	normal	ADJ
ejpam-5161	293	28	for	for	ADP
ejpam-5161	293	29	some	some	DET
ejpam-5161	293	30	ω	ω	NUM
ejpam-5161	293	31	∈	∈	PROPN
ejpam-5161	293	32	ω	ω	PROPN
ejpam-5161	293	33	.	.	PROPN
ejpam-5161	293	34	example	example	NOUN
ejpam-5161	293	35	8	8	NUM
ejpam-5161	293	36	.	.	PUNCT
ejpam-5161	294	1	let	let	VERB
ejpam-5161	294	2	x	x	PUNCT
ejpam-5161	294	3	=	=	PRON
ejpam-5161	294	4	{	{	PUNCT
ejpam-5161	294	5	x1	x1	PROPN
ejpam-5161	294	6	,	,	PUNCT
ejpam-5161	294	7	x2	x2	PROPN
ejpam-5161	294	8	,	,	PUNCT
ejpam-5161	294	9	x3	x3	ADJ
ejpam-5161	294	10	}	}	PUNCT
ejpam-5161	294	11	and	and	CCONJ
ejpam-5161	294	12	ω	ω	NUM
ejpam-5161	294	13	=	=	SYM
ejpam-5161	294	14	{	{	PUNCT
ejpam-5161	294	15	ω1	ω1	PROPN
ejpam-5161	294	16	,	,	PUNCT
ejpam-5161	294	17	ω2	ω2	ADJ
ejpam-5161	294	18	}	}	PUNCT
ejpam-5161	294	19	.	.	PUNCT
ejpam-5161	295	1	take	take	VERB
ejpam-5161	295	2	σω1	σω1	NOUN
ejpam-5161	295	3	=	=	SYM
ejpam-5161	295	4	{	{	PUNCT
ejpam-5161	295	5	∅	∅	NOUN
ejpam-5161	295	6	,	,	PUNCT
ejpam-5161	295	7	x	x	NOUN
ejpam-5161	295	8	}	}	PUNCT
ejpam-5161	295	9	and	and	CCONJ
ejpam-5161	295	10	σω2	σω2	ADP
ejpam-5161	295	11	=	=	SYM
ejpam-5161	295	12	{	{	PUNCT
ejpam-5161	295	13	∅	∅	NOUN
ejpam-5161	295	14	,	,	PUNCT
ejpam-5161	295	15	{	{	PUNCT
ejpam-5161	295	16	x1	x1	PROPN
ejpam-5161	295	17	}	}	PUNCT
ejpam-5161	295	18	,	,	PUNCT
ejpam-5161	295	19	{	{	PUNCT
ejpam-5161	295	20	x1	x1	PROPN
ejpam-5161	295	21	,	,	PUNCT
ejpam-5161	295	22	x2	x2	PROPN
ejpam-5161	295	23	}	}	PUNCT
ejpam-5161	295	24	,	,	PUNCT
ejpam-5161	295	25	{	{	PUNCT
ejpam-5161	295	26	x1	x1	ADJ
ejpam-5161	295	27	,	,	PUNCT
ejpam-5161	295	28	x3	x3	ADJ
ejpam-5161	295	29	}	}	PUNCT
ejpam-5161	295	30	,	,	PUNCT
ejpam-5161	295	31	x	x	NOUN
ejpam-5161	295	32	}	}	PUNCT
ejpam-5161	295	33	.	.	PUNCT
ejpam-5161	296	1	one	one	PRON
ejpam-5161	296	2	can	can	AUX
ejpam-5161	296	3	easily	easily	ADV
ejpam-5161	296	4	verify	verify	VERB
ejpam-5161	296	5	that	that	SCONJ
ejpam-5161	296	6	σω1	σω1	NOUN
ejpam-5161	296	7	is	be	AUX
ejpam-5161	296	8	normal	normal	ADJ
ejpam-5161	296	9	.	.	PUNCT
ejpam-5161	297	1	however	however	ADV
ejpam-5161	297	2	,	,	PUNCT
ejpam-5161	297	3	σω2	σω2	ADV
ejpam-5161	297	4	is	be	AUX
ejpam-5161	297	5	not	not	PART
ejpam-5161	297	6	normal	normal	ADJ
ejpam-5161	297	7	since	since	SCONJ
ejpam-5161	297	8	{	{	PUNCT
ejpam-5161	297	9	x2	x2	PROPN
ejpam-5161	297	10	}	}	PUNCT
ejpam-5161	297	11	,	,	PUNCT
ejpam-5161	297	12	{	{	PUNCT
ejpam-5161	297	13	x3	x3	ADJ
ejpam-5161	297	14	}	}	PUNCT
ejpam-5161	297	15	are	be	AUX
ejpam-5161	297	16	disjoint	disjoint	NOUN
ejpam-5161	297	17	closed	close	VERB
ejpam-5161	297	18	sets	set	NOUN
ejpam-5161	297	19	in	in	ADP
ejpam-5161	297	20	σω2	σω2	ADP
ejpam-5161	297	21	that	that	PRON
ejpam-5161	297	22	can	can	AUX
ejpam-5161	297	23	not	not	PART
ejpam-5161	297	24	be	be	AUX
ejpam-5161	297	25	separated	separate	VERB
ejpam-5161	297	26	by	by	ADP
ejpam-5161	297	27	two	two	NUM
ejpam-5161	297	28	disjoint	disjoint	ADJ
ejpam-5161	297	29	open	open	ADJ
ejpam-5161	297	30	sets	set	NOUN
ejpam-5161	297	31	.	.	PUNCT
ejpam-5161	298	1	the	the	DET
ejpam-5161	298	2	soft	soft	ADJ
ejpam-5161	298	3	topology	topology	NOUN
ejpam-5161	298	4	:	:	PUNCT
ejpam-5161	298	5	t	t	PROPN
ejpam-5161	298	6	(	(	PUNCT
ejpam-5161	298	7	σ	σ	PROPN
ejpam-5161	298	8	)	)	PUNCT
ejpam-5161	298	9	=	=	PRON
ejpam-5161	298	10	{	{	PUNCT
ejpam-5161	298	11	φ̃	φ̃	PROPN
ejpam-5161	298	12	,	,	PUNCT
ejpam-5161	298	13	(	(	PUNCT
ejpam-5161	298	14	f1,ω	f1,ω	PROPN
ejpam-5161	298	15	)	)	PUNCT
ejpam-5161	298	16	,	,	PUNCT
ejpam-5161	298	17	(	(	PUNCT
ejpam-5161	298	18	f2,ω	f2,ω	PROPN
ejpam-5161	298	19	)	)	PUNCT
ejpam-5161	298	20	,	,	PUNCT
ejpam-5161	298	21	(	(	PUNCT
ejpam-5161	298	22	f3,ω	f3,ω	PROPN
ejpam-5161	298	23	)	)	PUNCT
ejpam-5161	298	24	,	,	PUNCT
ejpam-5161	298	25	(	(	PUNCT
ejpam-5161	298	26	f4,ω	f4,ω	PROPN
ejpam-5161	298	27	)	)	PUNCT
ejpam-5161	298	28	,	,	PUNCT
ejpam-5161	298	29	(	(	PUNCT
ejpam-5161	298	30	f5,ω	f5,ω	PROPN
ejpam-5161	298	31	)	)	PUNCT
ejpam-5161	298	32	,	,	PUNCT
ejpam-5161	298	33	(	(	PUNCT
ejpam-5161	298	34	f6,ω	f6,ω	NOUN
ejpam-5161	298	35	)	)	PUNCT
ejpam-5161	298	36	,	,	PUNCT
ejpam-5161	298	37	(	(	PUNCT
ejpam-5161	298	38	f7,ω	f7,ω	PROPN
ejpam-5161	298	39	)	)	PUNCT
ejpam-5161	298	40	,	,	PUNCT
ejpam-5161	298	41	(	(	PUNCT
ejpam-5161	298	42	f8,ω	f8,ω	PROPN
ejpam-5161	298	43	)	)	PUNCT
ejpam-5161	298	44	,	,	PUNCT
ejpam-5161	298	45	x̃	x̃	PROPN
ejpam-5161	298	46	}	}	PUNCT
ejpam-5161	298	47	,	,	PUNCT
ejpam-5161	298	48	where	where	SCONJ
ejpam-5161	298	49	(	(	PUNCT
ejpam-5161	298	50	f1,ω	f1,ω	PROPN
ejpam-5161	298	51	)	)	PUNCT
ejpam-5161	298	52	=	=	PRON
ejpam-5161	298	53	{	{	PUNCT
ejpam-5161	298	54	(	(	PUNCT
ejpam-5161	298	55	ω1	ω1	PROPN
ejpam-5161	298	56	,	,	PUNCT
ejpam-5161	298	57	∅	∅	NOUN
ejpam-5161	298	58	)	)	PUNCT
ejpam-5161	298	59	,	,	PUNCT
ejpam-5161	298	60	(	(	PUNCT
ejpam-5161	298	61	ω2	ω2	ADV
ejpam-5161	298	62	,	,	PUNCT
ejpam-5161	298	63	{	{	PUNCT
ejpam-5161	298	64	x1	x1	ADJ
ejpam-5161	298	65	}	}	PUNCT
ejpam-5161	298	66	)	)	PUNCT
ejpam-5161	298	67	}	}	PUNCT
ejpam-5161	298	68	,	,	PUNCT
ejpam-5161	298	69	(	(	PUNCT
ejpam-5161	298	70	f2,ω	f2,ω	PROPN
ejpam-5161	298	71	)	)	PUNCT
ejpam-5161	298	72	=	=	SYM
ejpam-5161	298	73	{	{	PUNCT
ejpam-5161	298	74	(	(	PUNCT
ejpam-5161	298	75	ω1	ω1	PROPN
ejpam-5161	298	76	,	,	PUNCT
ejpam-5161	298	77	∅	∅	NOUN
ejpam-5161	298	78	)	)	PUNCT
ejpam-5161	298	79	,	,	PUNCT
ejpam-5161	298	80	(	(	PUNCT
ejpam-5161	298	81	ω2	ω2	ADV
ejpam-5161	298	82	,	,	PUNCT
ejpam-5161	298	83	{	{	PUNCT
ejpam-5161	298	84	x1	x1	PROPN
ejpam-5161	298	85	,	,	PUNCT
ejpam-5161	298	86	x2	x2	PROPN
ejpam-5161	298	87	}	}	PUNCT
ejpam-5161	298	88	)	)	PUNCT
ejpam-5161	298	89	}	}	PUNCT
ejpam-5161	298	90	,	,	PUNCT
ejpam-5161	298	91	(	(	PUNCT
ejpam-5161	298	92	f3,ω	f3,ω	PROPN
ejpam-5161	298	93	)	)	PUNCT
ejpam-5161	298	94	=	=	SYM
ejpam-5161	298	95	{	{	PUNCT
ejpam-5161	298	96	(	(	PUNCT
ejpam-5161	298	97	ω1	ω1	PROPN
ejpam-5161	298	98	,	,	PUNCT
ejpam-5161	298	99	∅	∅	NOUN
ejpam-5161	298	100	)	)	PUNCT
ejpam-5161	298	101	,	,	PUNCT
ejpam-5161	298	102	(	(	PUNCT
ejpam-5161	298	103	ω2	ω2	ADV
ejpam-5161	298	104	,	,	PUNCT
ejpam-5161	298	105	{	{	PUNCT
ejpam-5161	298	106	x1	x1	ADJ
ejpam-5161	298	107	,	,	PUNCT
ejpam-5161	298	108	x3	x3	ADJ
ejpam-5161	298	109	}	}	PUNCT
ejpam-5161	298	110	)	)	PUNCT
ejpam-5161	298	111	}	}	PUNCT
ejpam-5161	298	112	,	,	PUNCT
ejpam-5161	298	113	(	(	PUNCT
ejpam-5161	298	114	f4,ω	f4,ω	PROPN
ejpam-5161	298	115	)	)	PUNCT
ejpam-5161	298	116	=	=	PRON
ejpam-5161	298	117	{	{	PUNCT
ejpam-5161	298	118	(	(	PUNCT
ejpam-5161	298	119	ω1	ω1	PROPN
ejpam-5161	298	120	,	,	PUNCT
ejpam-5161	298	121	∅	∅	NOUN
ejpam-5161	298	122	)	)	PUNCT
ejpam-5161	298	123	,	,	PUNCT
ejpam-5161	298	124	(	(	PUNCT
ejpam-5161	298	125	ω2	ω2	ADJ
ejpam-5161	298	126	,	,	PUNCT
ejpam-5161	298	127	x	x	NOUN
ejpam-5161	298	128	)	)	PUNCT
ejpam-5161	298	129	}	}	PUNCT
ejpam-5161	298	130	,	,	PUNCT
ejpam-5161	298	131	(	(	PUNCT
ejpam-5161	298	132	f5,ω	f5,ω	PROPN
ejpam-5161	298	133	)	)	PUNCT
ejpam-5161	298	134	=	=	PRON
ejpam-5161	298	135	{	{	PUNCT
ejpam-5161	298	136	(	(	PUNCT
ejpam-5161	298	137	ω1	ω1	PROPN
ejpam-5161	298	138	,	,	PUNCT
ejpam-5161	298	139	x	x	NOUN
ejpam-5161	298	140	)	)	PUNCT
ejpam-5161	298	141	,	,	PUNCT
ejpam-5161	298	142	(	(	PUNCT
ejpam-5161	298	143	ω2	ω2	ADJ
ejpam-5161	298	144	,	,	PUNCT
ejpam-5161	298	145	∅	∅	NOUN
ejpam-5161	298	146	)	)	PUNCT
ejpam-5161	298	147	}	}	PUNCT
ejpam-5161	298	148	,	,	PUNCT
ejpam-5161	298	149	(	(	PUNCT
ejpam-5161	298	150	f6,ω	f6,ω	NOUN
ejpam-5161	298	151	)	)	PUNCT
ejpam-5161	298	152	=	=	PRON
ejpam-5161	298	153	{	{	PUNCT
ejpam-5161	298	154	(	(	PUNCT
ejpam-5161	298	155	ω1	ω1	PROPN
ejpam-5161	298	156	,	,	PUNCT
ejpam-5161	298	157	x	x	NOUN
ejpam-5161	298	158	)	)	PUNCT
ejpam-5161	298	159	,	,	PUNCT
ejpam-5161	298	160	(	(	PUNCT
ejpam-5161	298	161	ω2	ω2	ADV
ejpam-5161	298	162	,	,	PUNCT
ejpam-5161	298	163	{	{	PUNCT
ejpam-5161	298	164	x1	x1	ADJ
ejpam-5161	298	165	}	}	PUNCT
ejpam-5161	298	166	)	)	PUNCT
ejpam-5161	298	167	}	}	PUNCT
ejpam-5161	298	168	,	,	PUNCT
ejpam-5161	298	169	(	(	PUNCT
ejpam-5161	298	170	f7,ω	f7,ω	PROPN
ejpam-5161	298	171	)	)	PUNCT
ejpam-5161	298	172	=	=	SYM
ejpam-5161	298	173	{	{	PUNCT
ejpam-5161	298	174	(	(	PUNCT
ejpam-5161	298	175	ω1	ω1	PROPN
ejpam-5161	298	176	,	,	PUNCT
ejpam-5161	298	177	x	x	NOUN
ejpam-5161	298	178	)	)	PUNCT
ejpam-5161	298	179	,	,	PUNCT
ejpam-5161	298	180	(	(	PUNCT
ejpam-5161	298	181	ω2	ω2	ADV
ejpam-5161	298	182	,	,	PUNCT
ejpam-5161	298	183	{	{	PUNCT
ejpam-5161	298	184	x1	x1	PROPN
ejpam-5161	298	185	,	,	PUNCT
ejpam-5161	298	186	x2	x2	PROPN
ejpam-5161	298	187	}	}	PUNCT
ejpam-5161	298	188	)	)	PUNCT
ejpam-5161	298	189	}	}	PUNCT
ejpam-5161	298	190	,	,	PUNCT
ejpam-5161	298	191	and	and	CCONJ
ejpam-5161	298	192	(	(	PUNCT
ejpam-5161	298	193	f8,ω	f8,ω	PROPN
ejpam-5161	298	194	)	)	PUNCT
ejpam-5161	298	195	=	=	SYM
ejpam-5161	298	196	{	{	PUNCT
ejpam-5161	298	197	(	(	PUNCT
ejpam-5161	298	198	ω1	ω1	PROPN
ejpam-5161	298	199	,	,	PUNCT
ejpam-5161	298	200	x	x	NOUN
ejpam-5161	298	201	)	)	PUNCT
ejpam-5161	298	202	,	,	PUNCT
ejpam-5161	298	203	(	(	PUNCT
ejpam-5161	298	204	ω2	ω2	ADV
ejpam-5161	298	205	,	,	PUNCT
ejpam-5161	298	206	{	{	PUNCT
ejpam-5161	298	207	x1	x1	ADJ
ejpam-5161	298	208	,	,	PUNCT
ejpam-5161	298	209	x3	x3	ADJ
ejpam-5161	298	210	}	}	PUNCT
ejpam-5161	298	211	)	)	PUNCT
ejpam-5161	298	212	}	}	PUNCT
ejpam-5161	298	213	,	,	PUNCT
ejpam-5161	298	214	is	be	AUX
ejpam-5161	298	215	not	not	PART
ejpam-5161	298	216	a	a	DET
ejpam-5161	298	217	soft	soft	ADJ
ejpam-5161	298	218	normal	normal	ADJ
ejpam-5161	298	219	space	space	NOUN
ejpam-5161	298	220	.	.	PUNCT
ejpam-5161	299	1	indeed	indeed	ADV
ejpam-5161	299	2	,	,	PUNCT
ejpam-5161	299	3	since	since	SCONJ
ejpam-5161	299	4	{	{	PUNCT
ejpam-5161	299	5	(	(	PUNCT
ejpam-5161	299	6	ω1	ω1	PROPN
ejpam-5161	299	7	,	,	PUNCT
ejpam-5161	299	8	∅	∅	NOUN
ejpam-5161	299	9	)	)	PUNCT
ejpam-5161	299	10	,	,	PUNCT
ejpam-5161	299	11	(	(	PUNCT
ejpam-5161	299	12	ω2	ω2	ADV
ejpam-5161	299	13	,	,	PUNCT
ejpam-5161	299	14	{	{	PUNCT
ejpam-5161	299	15	x3	x3	ADJ
ejpam-5161	299	16	}	}	PUNCT
ejpam-5161	299	17	)	)	PUNCT
ejpam-5161	299	18	}	}	PUNCT
ejpam-5161	299	19	and	and	CCONJ
ejpam-5161	299	20	{	{	PUNCT
ejpam-5161	299	21	(	(	PUNCT
ejpam-5161	299	22	ω1	ω1	PROPN
ejpam-5161	299	23	,	,	PUNCT
ejpam-5161	299	24	x	x	NOUN
ejpam-5161	299	25	)	)	PUNCT
ejpam-5161	299	26	,	,	PUNCT
ejpam-5161	299	27	(	(	PUNCT
ejpam-5161	299	28	ω2	ω2	ADV
ejpam-5161	299	29	,	,	PUNCT
ejpam-5161	299	30	{	{	PUNCT
ejpam-5161	299	31	x2	x2	ADJ
ejpam-5161	299	32	}	}	PUNCT
ejpam-5161	299	33	)	)	PUNCT
ejpam-5161	299	34	}	}	PUNCT
ejpam-5161	299	35	are	be	AUX
ejpam-5161	299	36	disjoint	disjoint	ADJ
ejpam-5161	299	37	soft	soft	ADJ
ejpam-5161	299	38	closed	closed	ADJ
ejpam-5161	299	39	sets	set	NOUN
ejpam-5161	299	40	in	in	ADP
ejpam-5161	299	41	t	t	PROPN
ejpam-5161	299	42	(	(	PUNCT
ejpam-5161	299	43	σ	σ	PROPN
ejpam-5161	299	44	)	)	PUNCT
ejpam-5161	299	45	but	but	CCONJ
ejpam-5161	299	46	there	there	PRON
ejpam-5161	299	47	are	be	VERB
ejpam-5161	299	48	no	no	DET
ejpam-5161	299	49	disjoint	disjoint	ADJ
ejpam-5161	299	50	soft	soft	ADJ
ejpam-5161	299	51	open	open	ADJ
ejpam-5161	299	52	sets	set	NOUN
ejpam-5161	299	53	can	can	AUX
ejpam-5161	299	54	separate	separate	VERB
ejpam-5161	299	55	them	they	PRON
ejpam-5161	299	56	.	.	PUNCT
ejpam-5161	300	1	remark	remark	PROPN
ejpam-5161	300	2	2	2	NUM
ejpam-5161	300	3	.	.	PUNCT
ejpam-5161	300	4	notice	notice	VERB
ejpam-5161	300	5	that	that	SCONJ
ejpam-5161	300	6	we	we	PRON
ejpam-5161	300	7	can	can	AUX
ejpam-5161	300	8	provide	provide	VERB
ejpam-5161	300	9	a	a	DET
ejpam-5161	300	10	more	more	ADV
ejpam-5161	300	11	general	general	ADJ
ejpam-5161	300	12	proof	proof	NOUN
ejpam-5161	300	13	sketch	sketch	NOUN
ejpam-5161	300	14	that	that	PRON
ejpam-5161	300	15	proves	prove	VERB
ejpam-5161	300	16	the	the	DET
ejpam-5161	300	17	above	above	ADJ
ejpam-5161	300	18	claim	claim	NOUN
ejpam-5161	300	19	,	,	PUNCT
ejpam-5161	300	20	which	which	PRON
ejpam-5161	300	21	is	be	AUX
ejpam-5161	300	22	another	another	DET
ejpam-5161	300	23	proof	proof	NOUN
ejpam-5161	300	24	to	to	ADP
ejpam-5161	300	25	the	the	DET
ejpam-5161	300	26	part	part	NOUN
ejpam-5161	300	27	one	one	NUM
ejpam-5161	300	28	of	of	ADP
ejpam-5161	300	29	theorem	theorem	NOUN
ejpam-5161	300	30	5	5	NUM
ejpam-5161	300	31	.	.	PUNCT
ejpam-5161	301	1	if	if	SCONJ
ejpam-5161	301	2	σ	σ	NUM
ejpam-5161	301	3	=	=	PUNCT
ejpam-5161	301	4	{	{	PUNCT
ejpam-5161	301	5	σω	σω	NOUN
ejpam-5161	301	6	:	:	PUNCT
ejpam-5161	301	7	ω	ω	PROPN
ejpam-5161	301	8	∈	∈	PROPN
ejpam-5161	301	9	ω	ω	PROPN
ejpam-5161	301	10	}	}	PUNCT
ejpam-5161	301	11	is	be	AUX
ejpam-5161	301	12	not	not	PART
ejpam-5161	301	13	a	a	DET
ejpam-5161	301	14	normal	normal	ADJ
ejpam-5161	301	15	topology	topology	NOUN
ejpam-5161	301	16	for	for	ADP
ejpam-5161	301	17	some	some	DET
ejpam-5161	301	18	ω̄	ω̄	ADJ
ejpam-5161	301	19	∈	∈	PROPN
ejpam-5161	301	20	ω	ω	NOUN
ejpam-5161	301	21	,	,	PUNCT
ejpam-5161	301	22	then	then	ADV
ejpam-5161	301	23	there	there	PRON
ejpam-5161	301	24	are	be	VERB
ejpam-5161	301	25	closed	closed	ADJ
ejpam-5161	301	26	sets	set	NOUN
ejpam-5161	301	27	a	a	DET
ejpam-5161	301	28	,	,	PUNCT
ejpam-5161	301	29	b	b	NOUN
ejpam-5161	301	30	in	in	ADP
ejpam-5161	301	31	σω̄	σω̄	NOUN
ejpam-5161	301	32	which	which	PRON
ejpam-5161	301	33	can	can	AUX
ejpam-5161	301	34	not	not	PART
ejpam-5161	301	35	be	be	AUX
ejpam-5161	301	36	separated	separate	VERB
ejpam-5161	301	37	by	by	ADP
ejpam-5161	301	38	any	any	DET
ejpam-5161	301	39	open	open	ADJ
ejpam-5161	301	40	sets	set	NOUN
ejpam-5161	301	41	.	.	PUNCT
ejpam-5161	302	1	the	the	DET
ejpam-5161	302	2	soft	soft	ADJ
ejpam-5161	302	3	sets	set	NOUN
ejpam-5161	302	4	(	(	PUNCT
ejpam-5161	302	5	f	f	X
ejpam-5161	302	6	ω̄	ω̄	ADP
ejpam-5161	302	7	a	a	DET
ejpam-5161	302	8	,	,	PUNCT
ejpam-5161	302	9	ω	ω	NOUN
ejpam-5161	302	10	)	)	PUNCT
ejpam-5161	302	11	,	,	PUNCT
ejpam-5161	302	12	(	(	PUNCT
ejpam-5161	302	13	fb	fb	INTJ
ejpam-5161	302	14	ω̄	ω̄	ADP
ejpam-5161	302	15	,	,	PUNCT
ejpam-5161	302	16	ω	ω	NOUN
ejpam-5161	302	17	)	)	PUNCT
ejpam-5161	302	18	are	be	AUX
ejpam-5161	302	19	closed	close	VERB
ejpam-5161	302	20	and	and	CCONJ
ejpam-5161	302	21	disjoint	disjoint	VERB
ejpam-5161	302	22	in	in	ADP
ejpam-5161	302	23	t	t	PROPN
ejpam-5161	302	24	(	(	PUNCT
ejpam-5161	302	25	σ	σ	PROPN
ejpam-5161	302	26	)	)	PUNCT
ejpam-5161	302	27	.	.	PUNCT
ejpam-5161	303	1	if	if	SCONJ
ejpam-5161	303	2	there	there	PRON
ejpam-5161	303	3	exist	exist	VERB
ejpam-5161	303	4	soft	soft	ADJ
ejpam-5161	303	5	open	open	ADJ
ejpam-5161	303	6	sets	set	NOUN
ejpam-5161	303	7	(	(	PUNCT
ejpam-5161	303	8	g	g	PROPN
ejpam-5161	303	9	,	,	PUNCT
ejpam-5161	303	10	ω	ω	NOUN
ejpam-5161	303	11	)	)	PUNCT
ejpam-5161	303	12	,	,	PUNCT
ejpam-5161	303	13	(	(	PUNCT
ejpam-5161	303	14	h	h	NOUN
ejpam-5161	303	15	,	,	PUNCT
ejpam-5161	303	16	ω	ω	NOUN
ejpam-5161	303	17	)	)	PUNCT
ejpam-5161	303	18	in	in	ADP
ejpam-5161	303	19	t	t	PROPN
ejpam-5161	303	20	(	(	PUNCT
ejpam-5161	303	21	σ	σ	PROPN
ejpam-5161	303	22	)	)	PUNCT
ejpam-5161	303	23	such	such	ADJ
ejpam-5161	303	24	that	that	SCONJ
ejpam-5161	303	25	(	(	PUNCT
ejpam-5161	303	26	f	f	X
ejpam-5161	303	27	ω̄	ω̄	ADP
ejpam-5161	303	28	a	a	DET
ejpam-5161	303	29	,	,	PUNCT
ejpam-5161	303	30	ω)⊆̃(g	ω)⊆̃(g	PROPN
ejpam-5161	303	31	,	,	PUNCT
ejpam-5161	303	32	ω	ω	NOUN
ejpam-5161	303	33	)	)	PUNCT
ejpam-5161	303	34	,	,	PUNCT
ejpam-5161	303	35	(	(	PUNCT
ejpam-5161	303	36	fb	fb	INTJ
ejpam-5161	303	37	ω̄	ω̄	ADV
ejpam-5161	303	38	,	,	PUNCT
ejpam-5161	303	39	ω)⊆̃(h	ω)⊆̃(h	PROPN
ejpam-5161	303	40	,	,	PUNCT
ejpam-5161	303	41	ω	ω	NOUN
ejpam-5161	303	42	)	)	PUNCT
ejpam-5161	303	43	and	and	CCONJ
ejpam-5161	303	44	(	(	PUNCT
ejpam-5161	303	45	g	g	PROPN
ejpam-5161	303	46	,	,	PUNCT
ejpam-5161	303	47	ω	ω	NOUN
ejpam-5161	303	48	)	)	PUNCT
ejpam-5161	303	49	⋂̃	⋂̃	NOUN
ejpam-5161	303	50	(	(	PUNCT
ejpam-5161	303	51	h	h	NOUN
ejpam-5161	303	52	,	,	PUNCT
ejpam-5161	303	53	ω	ω	NOUN
ejpam-5161	303	54	)	)	PUNCT
ejpam-5161	303	55	=	=	PUNCT
ejpam-5161	304	1	φ̃	φ̃	PROPN
ejpam-5161	304	2	,	,	PUNCT
ejpam-5161	304	3	then	then	ADV
ejpam-5161	304	4	a	a	DET
ejpam-5161	304	5	⊆	⊆	NUM
ejpam-5161	304	6	g(ω̄	g(ω̄	NOUN
ejpam-5161	304	7	)	)	PUNCT
ejpam-5161	304	8	,	,	PUNCT
ejpam-5161	304	9	b	b	X
ejpam-5161	304	10	⊆	⊆	NUM
ejpam-5161	304	11	h(ω̄	h(ω̄	NUM
ejpam-5161	304	12	)	)	PUNCT
ejpam-5161	304	13	and	and	CCONJ
ejpam-5161	304	14	g(ω̄	g(ω̄	NOUN
ejpam-5161	304	15	)	)	PUNCT
ejpam-5161	304	16	∩h(ω̄	∩h(ω̄	NUM
ejpam-5161	304	17	)	)	PUNCT
ejpam-5161	304	18	=	=	NOUN
ejpam-5161	304	19	∅	∅	NOUN
ejpam-5161	304	20	,	,	PUNCT
ejpam-5161	304	21	which	which	PRON
ejpam-5161	304	22	is	be	AUX
ejpam-5161	304	23	a	a	DET
ejpam-5161	304	24	contradiction	contradiction	NOUN
ejpam-5161	304	25	.	.	PUNCT
ejpam-5161	305	1	6	6	X
ejpam-5161	305	2	.	.	X
ejpam-5161	305	3	conclusion	conclusion	NOUN
ejpam-5161	305	4	this	this	DET
ejpam-5161	305	5	study	study	NOUN
ejpam-5161	305	6	develops	develop	VERB
ejpam-5161	305	7	a	a	DET
ejpam-5161	305	8	methodical	methodical	ADJ
ejpam-5161	305	9	understanding	understanding	NOUN
ejpam-5161	305	10	of	of	ADP
ejpam-5161	305	11	the	the	DET
ejpam-5161	305	12	connections	connection	NOUN
ejpam-5161	305	13	between	between	ADP
ejpam-5161	305	14	a	a	DET
ejpam-5161	305	15	system	system	NOUN
ejpam-5161	305	16	of	of	ADP
ejpam-5161	305	17	crisp	crisp	ADJ
ejpam-5161	305	18	topologies	topology	NOUN
ejpam-5161	305	19	and	and	CCONJ
ejpam-5161	305	20	the	the	DET
ejpam-5161	305	21	soft	soft	ADJ
ejpam-5161	305	22	topology	topology	NOUN
ejpam-5161	305	23	produced	produce	VERB
ejpam-5161	305	24	by	by	ADP
ejpam-5161	305	25	it	it	PRON
ejpam-5161	305	26	.	.	PUNCT
ejpam-5161	306	1	the	the	DET
ejpam-5161	306	2	procedure	procedure	NOUN
ejpam-5161	306	3	is	be	AUX
ejpam-5161	306	4	carried	carry	VERB
ejpam-5161	306	5	out	out	ADP
ejpam-5161	306	6	with	with	ADP
ejpam-5161	306	7	the	the	DET
ejpam-5161	306	8	references	reference	NOUN
ejpam-5161	306	9	1180	1180	NUM
ejpam-5161	306	10	help	help	NOUN
ejpam-5161	306	11	of	of	ADP
ejpam-5161	306	12	two	two	NUM
ejpam-5161	306	13	formulas	formula	NOUN
ejpam-5161	306	14	.	.	PUNCT
ejpam-5161	307	1	if	if	SCONJ
ejpam-5161	307	2	we	we	PRON
ejpam-5161	307	3	start	start	VERB
ejpam-5161	307	4	from	from	ADP
ejpam-5161	307	5	an	an	DET
ejpam-5161	307	6	original	original	ADJ
ejpam-5161	307	7	soft	soft	ADJ
ejpam-5161	307	8	topology	topology	NOUN
ejpam-5161	307	9	,	,	PUNCT
ejpam-5161	307	10	then	then	ADV
ejpam-5161	307	11	it	it	PRON
ejpam-5161	307	12	produces	produce	VERB
ejpam-5161	307	13	a	a	DET
ejpam-5161	307	14	system	system	NOUN
ejpam-5161	307	15	of	of	ADP
ejpam-5161	307	16	crisp	crisp	ADJ
ejpam-5161	307	17	topologies	topology	NOUN
ejpam-5161	307	18	.	.	PUNCT
ejpam-5161	308	1	with	with	ADP
ejpam-5161	308	2	our	our	PRON
ejpam-5161	308	3	formulas	formula	NOUN
ejpam-5161	308	4	,	,	PUNCT
ejpam-5161	308	5	we	we	PRON
ejpam-5161	308	6	can	can	AUX
ejpam-5161	308	7	generate	generate	VERB
ejpam-5161	308	8	two	two	NUM
ejpam-5161	308	9	different	different	ADJ
ejpam-5161	308	10	new	new	ADJ
ejpam-5161	308	11	soft	soft	ADJ
ejpam-5161	308	12	topologies	topology	NOUN
ejpam-5161	308	13	.	.	PUNCT
ejpam-5161	309	1	we	we	PRON
ejpam-5161	309	2	have	have	AUX
ejpam-5161	309	3	discussed	discuss	VERB
ejpam-5161	309	4	the	the	DET
ejpam-5161	309	5	relationships	relationship	NOUN
ejpam-5161	309	6	between	between	ADP
ejpam-5161	309	7	these	these	DET
ejpam-5161	309	8	soft	soft	ADJ
ejpam-5161	309	9	topologies	topology	NOUN
ejpam-5161	309	10	.	.	PUNCT
ejpam-5161	310	1	moreover	moreover	ADV
ejpam-5161	310	2	,	,	PUNCT
ejpam-5161	310	3	we	we	PRON
ejpam-5161	310	4	show	show	VERB
ejpam-5161	310	5	that	that	SCONJ
ejpam-5161	310	6	the	the	DET
ejpam-5161	310	7	resulting	result	VERB
ejpam-5161	310	8	soft	soft	ADJ
ejpam-5161	310	9	topology	topology	NOUN
ejpam-5161	310	10	via	via	ADP
ejpam-5161	310	11	formula	formula	NOUN
ejpam-5161	310	12	1	1	NUM
ejpam-5161	310	13	is	be	AUX
ejpam-5161	310	14	always	always	ADV
ejpam-5161	310	15	finer	fine	ADJ
ejpam-5161	310	16	than	than	ADP
ejpam-5161	310	17	the	the	DET
ejpam-5161	310	18	original	original	ADJ
ejpam-5161	310	19	one	one	NOUN
ejpam-5161	310	20	,	,	PUNCT
ejpam-5161	310	21	while	while	SCONJ
ejpam-5161	310	22	the	the	DET
ejpam-5161	310	23	soft	soft	ADJ
ejpam-5161	310	24	topology	topology	NOUN
ejpam-5161	310	25	generated	generate	VERB
ejpam-5161	310	26	by	by	ADP
ejpam-5161	310	27	formula	formula	NOUN
ejpam-5161	310	28	2	2	NUM
ejpam-5161	310	29	is	be	AUX
ejpam-5161	310	30	incomparable	incomparable	ADJ
ejpam-5161	310	31	.	.	PUNCT
ejpam-5161	311	1	we	we	PRON
ejpam-5161	311	2	see	see	VERB
ejpam-5161	311	3	that	that	SCONJ
ejpam-5161	311	4	two	two	NUM
ejpam-5161	311	5	different	different	ADJ
ejpam-5161	311	6	original	original	ADJ
ejpam-5161	311	7	soft	soft	ADJ
ejpam-5161	311	8	topologies	topology	NOUN
ejpam-5161	311	9	may	may	AUX
ejpam-5161	311	10	generate	generate	VERB
ejpam-5161	311	11	a	a	DET
ejpam-5161	311	12	single	single	ADJ
ejpam-5161	311	13	soft	soft	ADJ
ejpam-5161	311	14	topology	topology	NOUN
ejpam-5161	311	15	by	by	ADP
ejpam-5161	311	16	either	either	PRON
ejpam-5161	311	17	of	of	ADP
ejpam-5161	311	18	the	the	DET
ejpam-5161	311	19	formulas	formula	NOUN
ejpam-5161	311	20	.	.	PUNCT
ejpam-5161	312	1	furthermore	furthermore	ADV
ejpam-5161	312	2	,	,	PUNCT
ejpam-5161	312	3	we	we	PRON
ejpam-5161	312	4	study	study	VERB
ejpam-5161	312	5	the	the	DET
ejpam-5161	312	6	preservation	preservation	NOUN
ejpam-5161	312	7	of	of	ADP
ejpam-5161	312	8	separation	separation	NOUN
ejpam-5161	312	9	axioms	axiom	NOUN
ejpam-5161	312	10	between	between	ADP
ejpam-5161	312	11	the	the	DET
ejpam-5161	312	12	system	system	NOUN
ejpam-5161	312	13	of	of	ADP
ejpam-5161	312	14	crisp	crisp	ADJ
ejpam-5161	312	15	topologies	topology	NOUN
ejpam-5161	312	16	and	and	CCONJ
ejpam-5161	312	17	the	the	DET
ejpam-5161	312	18	soft	soft	ADJ
ejpam-5161	312	19	topology	topology	NOUN
ejpam-5161	312	20	generated	generate	VERB
ejpam-5161	312	21	by	by	ADP
ejpam-5161	312	22	it	it	PRON
ejpam-5161	312	23	.	.	PUNCT
ejpam-5161	313	1	more	more	ADV
ejpam-5161	313	2	precisely	precisely	ADV
ejpam-5161	313	3	,	,	PUNCT
ejpam-5161	313	4	we	we	PRON
ejpam-5161	313	5	show	show	VERB
ejpam-5161	313	6	that	that	SCONJ
ejpam-5161	313	7	hausdorffness	hausdorffness	NOUN
ejpam-5161	313	8	and	and	CCONJ
ejpam-5161	313	9	normality	normality	NOUN
ejpam-5161	313	10	behave	behave	VERB
ejpam-5161	313	11	better	well	ADV
ejpam-5161	313	12	in	in	ADP
ejpam-5161	313	13	transforming	transform	VERB
ejpam-5161	313	14	to	to	ADP
ejpam-5161	313	15	soft	soft	ADJ
ejpam-5161	313	16	topologies	topology	NOUN
ejpam-5161	313	17	and	and	CCONJ
ejpam-5161	313	18	conversely	conversely	ADV
ejpam-5161	313	19	.	.	PUNCT
ejpam-5161	314	1	on	on	ADP
ejpam-5161	314	2	the	the	DET
ejpam-5161	314	3	other	other	ADJ
ejpam-5161	314	4	hand	hand	NOUN
ejpam-5161	314	5	,	,	PUNCT
ejpam-5161	314	6	other	other	ADJ
ejpam-5161	314	7	separation	separation	NOUN
ejpam-5161	314	8	axioms	axiom	NOUN
ejpam-5161	314	9	act	act	VERB
ejpam-5161	314	10	differently	differently	ADV
ejpam-5161	314	11	.	.	PUNCT
ejpam-5161	315	1	if	if	SCONJ
ejpam-5161	315	2	one	one	NUM
ejpam-5161	315	3	of	of	ADP
ejpam-5161	315	4	the	the	DET
ejpam-5161	315	5	crisp	crisp	ADJ
ejpam-5161	315	6	topologies	topology	NOUN
ejpam-5161	315	7	is	be	AUX
ejpam-5161	315	8	respectively	respectively	ADV
ejpam-5161	315	9	t0	t0	NOUN
ejpam-5161	315	10	,	,	PUNCT
ejpam-5161	315	11	t1	t1	PROPN
ejpam-5161	315	12	,	,	PUNCT
ejpam-5161	315	13	then	then	ADV
ejpam-5161	315	14	it	it	PRON
ejpam-5161	315	15	guarantees	guarantee	VERB
ejpam-5161	315	16	that	that	SCONJ
ejpam-5161	315	17	the	the	DET
ejpam-5161	315	18	resulting	result	VERB
ejpam-5161	315	19	soft	soft	ADJ
ejpam-5161	315	20	topology	topology	NOUN
ejpam-5161	315	21	is	be	AUX
ejpam-5161	315	22	soft	soft	ADJ
ejpam-5161	315	23	t0	t0	NOUN
ejpam-5161	315	24	,	,	PUNCT
ejpam-5161	315	25	t1	t1	PROPN
ejpam-5161	315	26	.	.	PUNCT
ejpam-5161	316	1	the	the	DET
ejpam-5161	316	2	converse	converse	NOUN
ejpam-5161	316	3	may	may	AUX
ejpam-5161	316	4	not	not	PART
ejpam-5161	316	5	be	be	AUX
ejpam-5161	316	6	true	true	ADJ
ejpam-5161	316	7	.	.	PUNCT
ejpam-5161	317	1	all	all	PRON
ejpam-5161	317	2	of	of	ADP
ejpam-5161	317	3	the	the	DET
ejpam-5161	317	4	crisp	crisp	ADJ
ejpam-5161	317	5	topologies	topology	NOUN
ejpam-5161	317	6	are	be	AUX
ejpam-5161	317	7	regular	regular	ADJ
ejpam-5161	317	8	when	when	SCONJ
ejpam-5161	317	9	the	the	DET
ejpam-5161	317	10	soft	soft	ADJ
ejpam-5161	317	11	topology	topology	NOUN
ejpam-5161	317	12	generated	generate	VERB
ejpam-5161	317	13	by	by	ADP
ejpam-5161	317	14	them	they	PRON
ejpam-5161	317	15	is	be	AUX
ejpam-5161	317	16	a	a	DET
ejpam-5161	317	17	soft	soft	ADJ
ejpam-5161	317	18	regular	regular	NOUN
ejpam-5161	317	19	.	.	PUNCT
ejpam-5161	318	1	references	reference	NOUN
ejpam-5161	318	2	[	[	X
ejpam-5161	318	3	1	1	X
ejpam-5161	318	4	]	]	X
ejpam-5161	318	5	dina	dina	PROPN
ejpam-5161	318	6	abuzaid	abuzaid	PROPN
ejpam-5161	318	7	and	and	CCONJ
ejpam-5161	318	8	samer	samer	PROPN
ejpam-5161	318	9	al	al	PROPN
ejpam-5161	318	10	ghour	ghour	PROPN
ejpam-5161	318	11	.	.	PUNCT
ejpam-5161	319	1	three	three	NUM
ejpam-5161	319	2	new	new	ADJ
ejpam-5161	319	3	soft	soft	ADJ
ejpam-5161	319	4	separation	separation	NOUN
ejpam-5161	319	5	axioms	axiom	NOUN
ejpam-5161	319	6	in	in	ADP
ejpam-5161	319	7	soft	soft	ADJ
ejpam-5161	319	8	topological	topological	ADJ
ejpam-5161	319	9	spaces	space	NOUN
ejpam-5161	319	10	.	.	PUNCT
ejpam-5161	320	1	aims	aim	VERB
ejpam-5161	320	2	mathematics	mathematic	NOUN
ejpam-5161	320	3	,	,	PUNCT
ejpam-5161	320	4	9(2):4632–4648	9(2):4632–4648	NOUN
ejpam-5161	320	5	,	,	PUNCT
ejpam-5161	320	6	2024	2024	NUM
ejpam-5161	320	7	.	.	PUNCT
ejpam-5161	321	1	[	[	X
ejpam-5161	321	2	2	2	NUM
ejpam-5161	321	3	]	]	PUNCT
ejpam-5161	321	4	samer	samer	PROPN
ejpam-5161	321	5	al	al	PROPN
ejpam-5161	321	6	ghour	ghour	PROPN
ejpam-5161	321	7	and	and	CCONJ
ejpam-5161	321	8	zanyar	zanyar	X
ejpam-5161	321	9	a	a	DET
ejpam-5161	321	10	ameen	ameen	NOUN
ejpam-5161	321	11	.	.	PUNCT
ejpam-5161	322	1	maximal	maximal	ADJ
ejpam-5161	322	2	soft	soft	ADJ
ejpam-5161	322	3	compact	compact	ADJ
ejpam-5161	322	4	and	and	CCONJ
ejpam-5161	322	5	maximal	maximal	ADJ
ejpam-5161	322	6	soft	soft	ADJ
ejpam-5161	322	7	connected	connected	ADJ
ejpam-5161	322	8	topologies	topology	NOUN
ejpam-5161	322	9	.	.	PUNCT
ejpam-5161	323	1	applied	apply	VERB
ejpam-5161	323	2	computational	computational	ADJ
ejpam-5161	323	3	intelligence	intelligence	NOUN
ejpam-5161	323	4	and	and	CCONJ
ejpam-5161	323	5	soft	soft	ADJ
ejpam-5161	323	6	computing	computing	NOUN
ejpam-5161	323	7	,	,	PUNCT
ejpam-5161	323	8	2022	2022	NUM
ejpam-5161	323	9	:	:	PUNCT
ejpam-5161	323	10	article	article	NOUN
ejpam-5161	323	11	i	i	PROPN
ejpam-5161	323	12	d	d	PROPN
ejpam-5161	323	13	9860015	9860015	NUM
ejpam-5161	323	14	,	,	PUNCT
ejpam-5161	323	15	7	7	NUM
ejpam-5161	323	16	pages	page	NOUN
ejpam-5161	323	17	.	.	PUNCT
ejpam-5161	324	1	[	[	X
ejpam-5161	324	2	3	3	X
ejpam-5161	324	3	]	]	X
ejpam-5161	324	4	jose	jose	NOUN
ejpam-5161	324	5	carlos	carlos	PROPN
ejpam-5161	324	6	r	r	PROPN
ejpam-5161	324	7	alcantud	alcantud	PROPN
ejpam-5161	324	8	.	.	PUNCT
ejpam-5161	324	9	soft	soft	ADJ
ejpam-5161	324	10	open	open	ADJ
ejpam-5161	324	11	bases	basis	NOUN
ejpam-5161	324	12	and	and	CCONJ
ejpam-5161	324	13	a	a	DET
ejpam-5161	324	14	novel	novel	ADJ
ejpam-5161	324	15	construction	construction	NOUN
ejpam-5161	324	16	of	of	ADP
ejpam-5161	324	17	soft	soft	ADJ
ejpam-5161	324	18	topologies	topology	NOUN
ejpam-5161	324	19	from	from	ADP
ejpam-5161	324	20	bases	basis	NOUN
ejpam-5161	324	21	for	for	ADP
ejpam-5161	324	22	topologies	topology	NOUN
ejpam-5161	324	23	.	.	PUNCT
ejpam-5161	325	1	mathematics	mathematic	NOUN
ejpam-5161	325	2	,	,	PUNCT
ejpam-5161	325	3	8(5):672	8(5):672	NUM
ejpam-5161	325	4	,	,	PUNCT
ejpam-5161	325	5	2020	2020	NUM
ejpam-5161	325	6	.	.	PUNCT
ejpam-5161	326	1	[	[	X
ejpam-5161	326	2	4	4	NUM
ejpam-5161	326	3	]	]	X
ejpam-5161	326	4	josé	josé	PROPN
ejpam-5161	326	5	carlos	carlos	PROPN
ejpam-5161	326	6	r	r	PROPN
ejpam-5161	326	7	alcantud	alcantud	PROPN
ejpam-5161	326	8	.	.	PUNCT
ejpam-5161	327	1	the	the	DET
ejpam-5161	327	2	relationship	relationship	NOUN
ejpam-5161	327	3	between	between	ADP
ejpam-5161	327	4	fuzzy	fuzzy	ADJ
ejpam-5161	327	5	soft	soft	ADJ
ejpam-5161	327	6	and	and	CCONJ
ejpam-5161	327	7	soft	soft	ADJ
ejpam-5161	327	8	topologies	topology	NOUN
ejpam-5161	327	9	.	.	PUNCT
ejpam-5161	328	1	international	international	ADJ
ejpam-5161	328	2	journal	journal	NOUN
ejpam-5161	328	3	of	of	ADP
ejpam-5161	328	4	fuzzy	fuzzy	ADJ
ejpam-5161	328	5	systems	system	NOUN
ejpam-5161	328	6	,	,	PUNCT
ejpam-5161	328	7	24(3):1653–1668	24(3):1653–1668	NUM
ejpam-5161	328	8	,	,	PUNCT
ejpam-5161	328	9	2022	2022	NUM
ejpam-5161	328	10	.	.	PUNCT
ejpam-5161	329	1	[	[	X
ejpam-5161	329	2	5	5	NUM
ejpam-5161	329	3	]	]	X
ejpam-5161	329	4	m	m	PROPN
ejpam-5161	329	5	irfan	irfan	PROPN
ejpam-5161	329	6	ali	ali	PROPN
ejpam-5161	329	7	,	,	PUNCT
ejpam-5161	329	8	feng	feng	PROPN
ejpam-5161	329	9	feng	feng	PROPN
ejpam-5161	329	10	,	,	PUNCT
ejpam-5161	329	11	xiaoyan	xiaoyan	PROPN
ejpam-5161	329	12	liu	liu	PROPN
ejpam-5161	329	13	,	,	PUNCT
ejpam-5161	329	14	won	win	VERB
ejpam-5161	329	15	keun	keun	PROPN
ejpam-5161	329	16	min	min	PROPN
ejpam-5161	329	17	,	,	PUNCT
ejpam-5161	329	18	and	and	CCONJ
ejpam-5161	329	19	muhammad	muhammad	PROPN
ejpam-5161	329	20	shabir	shabir	PROPN
ejpam-5161	329	21	.	.	PUNCT
ejpam-5161	330	1	on	on	ADP
ejpam-5161	330	2	some	some	DET
ejpam-5161	330	3	new	new	ADJ
ejpam-5161	330	4	operations	operation	NOUN
ejpam-5161	330	5	in	in	ADP
ejpam-5161	330	6	soft	soft	ADJ
ejpam-5161	330	7	set	set	NOUN
ejpam-5161	330	8	theory	theory	NOUN
ejpam-5161	330	9	.	.	PUNCT
ejpam-5161	331	1	computers	computer	NOUN
ejpam-5161	331	2	&	&	CCONJ
ejpam-5161	331	3	mathematics	mathematics	PROPN
ejpam-5161	331	4	with	with	ADP
ejpam-5161	331	5	applications	application	NOUN
ejpam-5161	331	6	,	,	PUNCT
ejpam-5161	331	7	57(9):1547–1553	57(9):1547–1553	NUM
ejpam-5161	331	8	,	,	PUNCT
ejpam-5161	331	9	2009	2009	NUM
ejpam-5161	331	10	.	.	PUNCT
ejpam-5161	332	1	[	[	X
ejpam-5161	332	2	6	6	NUM
ejpam-5161	332	3	]	]	SYM
ejpam-5161	332	4	mesfer	mesfer	NOUN
ejpam-5161	332	5	h	h	NOUN
ejpam-5161	332	6	alqahtani	alqahtani	PROPN
ejpam-5161	332	7	and	and	CCONJ
ejpam-5161	332	8	zanyar	zanyar	X
ejpam-5161	332	9	a	a	DET
ejpam-5161	332	10	ameen	ameen	NOUN
ejpam-5161	332	11	.	.	PUNCT
ejpam-5161	333	1	soft	soft	ADJ
ejpam-5161	333	2	nodec	nodec	ADJ
ejpam-5161	333	3	spaces	space	NOUN
ejpam-5161	333	4	.	.	PUNCT
ejpam-5161	334	1	aims	aim	VERB
ejpam-5161	334	2	mathematics	mathematic	NOUN
ejpam-5161	334	3	,	,	PUNCT
ejpam-5161	334	4	9:3289–3302	9:3289–3302	NUM
ejpam-5161	334	5	,	,	PUNCT
ejpam-5161	334	6	2024	2024	NUM
ejpam-5161	334	7	.	.	PUNCT
ejpam-5161	335	1	[	[	X
ejpam-5161	335	2	7	7	NUM
ejpam-5161	335	3	]	]	PUNCT
ejpam-5161	335	4	zanyar	zanyar	PROPN
ejpam-5161	335	5	ameen	ameen	PROPN
ejpam-5161	335	6	.	.	PUNCT
ejpam-5161	336	1	a	a	DET
ejpam-5161	336	2	non	non	ADJ
ejpam-5161	336	3	-	-	ADJ
ejpam-5161	336	4	continuous	continuous	ADJ
ejpam-5161	336	5	soft	soft	ADJ
ejpam-5161	336	6	mapping	mapping	NOUN
ejpam-5161	336	7	that	that	PRON
ejpam-5161	336	8	preserves	preserve	VERB
ejpam-5161	336	9	some	some	DET
ejpam-5161	336	10	structural	structural	ADJ
ejpam-5161	336	11	soft	soft	ADJ
ejpam-5161	336	12	sets	set	NOUN
ejpam-5161	336	13	.	.	PUNCT
ejpam-5161	337	1	journal	journal	NOUN
ejpam-5161	337	2	of	of	ADP
ejpam-5161	337	3	intelligent	intelligent	ADJ
ejpam-5161	337	4	&	&	CCONJ
ejpam-5161	337	5	fuzzy	fuzzy	ADJ
ejpam-5161	337	6	systems	system	NOUN
ejpam-5161	337	7	,	,	PUNCT
ejpam-5161	337	8	42(6):5839–5845	42(6):5839–5845	NUM
ejpam-5161	337	9	,	,	PUNCT
ejpam-5161	337	10	2022	2022	NUM
ejpam-5161	337	11	.	.	PUNCT
ejpam-5161	338	1	[	[	X
ejpam-5161	338	2	8	8	NUM
ejpam-5161	338	3	]	]	PUNCT
ejpam-5161	338	4	zanyar	zanyar	PROPN
ejpam-5161	338	5	a	a	DET
ejpam-5161	338	6	ameen	ameen	PROPN
ejpam-5161	338	7	and	and	CCONJ
ejpam-5161	338	8	samer	samer	PROPN
ejpam-5161	338	9	al	al	PROPN
ejpam-5161	338	10	ghour	ghour	PROPN
ejpam-5161	338	11	.	.	PUNCT
ejpam-5161	339	1	extensions	extension	NOUN
ejpam-5161	339	2	of	of	ADP
ejpam-5161	339	3	soft	soft	ADJ
ejpam-5161	339	4	topologies	topology	NOUN
ejpam-5161	339	5	.	.	PUNCT
ejpam-5161	340	1	filomat	filomat	NOUN
ejpam-5161	340	2	,	,	PUNCT
ejpam-5161	340	3	36(15):5279–5287	36(15):5279–5287	NUM
ejpam-5161	340	4	,	,	PUNCT
ejpam-5161	340	5	2022	2022	NUM
ejpam-5161	340	6	.	.	PUNCT
ejpam-5161	341	1	[	[	X
ejpam-5161	341	2	9	9	NUM
ejpam-5161	341	3	]	]	PUNCT
ejpam-5161	341	4	zanyar	zanyar	PROPN
ejpam-5161	341	5	a	a	DET
ejpam-5161	341	6	ameen	ameen	PROPN
ejpam-5161	341	7	and	and	CCONJ
ejpam-5161	341	8	samer	samer	PROPN
ejpam-5161	341	9	al	al	PROPN
ejpam-5161	341	10	ghour	ghour	PROPN
ejpam-5161	341	11	.	.	PUNCT
ejpam-5161	342	1	cluster	cluster	NOUN
ejpam-5161	342	2	soft	soft	ADJ
ejpam-5161	342	3	sets	set	NOUN
ejpam-5161	342	4	and	and	CCONJ
ejpam-5161	342	5	cluster	cluster	NOUN
ejpam-5161	342	6	soft	soft	ADJ
ejpam-5161	342	7	topologies	topology	NOUN
ejpam-5161	342	8	.	.	PUNCT
ejpam-5161	343	1	computational	computational	ADJ
ejpam-5161	343	2	and	and	CCONJ
ejpam-5161	343	3	applied	applied	ADJ
ejpam-5161	343	4	mathematics	mathematic	NOUN
ejpam-5161	343	5	,	,	PUNCT
ejpam-5161	343	6	42(8):337	42(8):337	NOUN
ejpam-5161	343	7	,	,	PUNCT
ejpam-5161	343	8	2023	2023	NUM
ejpam-5161	343	9	.	.	PUNCT
ejpam-5161	344	1	references	reference	NOUN
ejpam-5161	344	2	1181	1181	NUM
ejpam-5161	345	1	[	[	X
ejpam-5161	345	2	10	10	NUM
ejpam-5161	345	3	]	]	PUNCT
ejpam-5161	345	4	zanyar	zanyar	PROPN
ejpam-5161	345	5	a	a	DET
ejpam-5161	345	6	ameen	ameen	PROPN
ejpam-5161	345	7	,	,	PUNCT
ejpam-5161	345	8	tareq	tareq	PROPN
ejpam-5161	345	9	m	m	PROPN
ejpam-5161	345	10	al	al	PROPN
ejpam-5161	345	11	-	-	PUNCT
ejpam-5161	345	12	shami	shami	PROPN
ejpam-5161	345	13	,	,	PUNCT
ejpam-5161	345	14	and	and	CCONJ
ejpam-5161	345	15	baracan	baracan	VERB
ejpam-5161	345	16	a	a	DET
ejpam-5161	345	17	asaad	asaad	NOUN
ejpam-5161	345	18	.	.	PUNCT
ejpam-5161	346	1	further	further	ADJ
ejpam-5161	346	2	properties	property	NOUN
ejpam-5161	346	3	of	of	ADP
ejpam-5161	346	4	soft	soft	ADJ
ejpam-5161	346	5	somewhere	somewhere	ADV
ejpam-5161	346	6	dense	dense	ADJ
ejpam-5161	346	7	continuous	continuous	ADJ
ejpam-5161	346	8	functions	function	NOUN
ejpam-5161	346	9	and	and	CCONJ
ejpam-5161	346	10	soft	soft	ADJ
ejpam-5161	346	11	baire	baire	NOUN
ejpam-5161	346	12	spaces	space	NOUN
ejpam-5161	346	13	.	.	PUNCT
ejpam-5161	347	1	j.	j.	PROPN
ejpam-5161	347	2	math	math	PROPN
ejpam-5161	347	3	.	.	PUNCT
ejpam-5161	348	1	comput	comput	NOUN
ejpam-5161	348	2	.	.	PUNCT
ejpam-5161	349	1	sci	sci	PROPN
ejpam-5161	349	2	,	,	PUNCT
ejpam-5161	349	3	32:54–63	32:54–63	NUM
ejpam-5161	349	4	,	,	PUNCT
ejpam-5161	349	5	2024	2024	NUM
ejpam-5161	349	6	.	.	PUNCT
ejpam-5161	350	1	[	[	X
ejpam-5161	350	2	11	11	NUM
ejpam-5161	350	3	]	]	PUNCT
ejpam-5161	350	4	zanyar	zanyar	PROPN
ejpam-5161	350	5	a	a	DET
ejpam-5161	350	6	ameen	ameen	NOUN
ejpam-5161	350	7	and	and	CCONJ
ejpam-5161	350	8	mesfer	mesfer	VERB
ejpam-5161	350	9	h	h	PROPN
ejpam-5161	350	10	alqahtani	alqahtani	PROPN
ejpam-5161	350	11	.	.	PUNCT
ejpam-5161	351	1	congruence	congruence	NOUN
ejpam-5161	351	2	representations	representation	NOUN
ejpam-5161	351	3	via	via	ADP
ejpam-5161	351	4	soft	soft	ADJ
ejpam-5161	351	5	ideals	ideal	NOUN
ejpam-5161	351	6	in	in	ADP
ejpam-5161	351	7	soft	soft	ADJ
ejpam-5161	351	8	topological	topological	ADJ
ejpam-5161	351	9	spaces	space	NOUN
ejpam-5161	351	10	.	.	PUNCT
ejpam-5161	352	1	axioms	axiom	NOUN
ejpam-5161	352	2	,	,	PUNCT
ejpam-5161	352	3	12(11):1015	12(11):1015	NUM
ejpam-5161	352	4	,	,	PUNCT
ejpam-5161	352	5	2023	2023	NUM
ejpam-5161	352	6	.	.	PUNCT
ejpam-5161	353	1	[	[	X
ejpam-5161	353	2	12	12	NUM
ejpam-5161	353	3	]	]	PUNCT
ejpam-5161	353	4	zanyar	zanyar	PROPN
ejpam-5161	353	5	a	a	DET
ejpam-5161	353	6	ameen	ameen	NOUN
ejpam-5161	353	7	and	and	CCONJ
ejpam-5161	353	8	mesfer	mesfer	VERB
ejpam-5161	353	9	h	h	PROPN
ejpam-5161	353	10	alqahtani	alqahtani	ADJ
ejpam-5161	353	11	.	.	PUNCT
ejpam-5161	354	1	some	some	DET
ejpam-5161	354	2	classes	class	NOUN
ejpam-5161	354	3	of	of	ADP
ejpam-5161	354	4	soft	soft	ADJ
ejpam-5161	354	5	functions	function	NOUN
ejpam-5161	354	6	defined	define	VERB
ejpam-5161	354	7	by	by	ADP
ejpam-5161	354	8	soft	soft	ADJ
ejpam-5161	354	9	open	open	ADJ
ejpam-5161	354	10	sets	set	NOUN
ejpam-5161	354	11	modulo	modulo	VERB
ejpam-5161	354	12	soft	soft	ADJ
ejpam-5161	354	13	sets	set	NOUN
ejpam-5161	354	14	of	of	ADP
ejpam-5161	354	15	the	the	DET
ejpam-5161	354	16	first	first	ADJ
ejpam-5161	354	17	category	category	NOUN
ejpam-5161	354	18	.	.	PUNCT
ejpam-5161	355	1	mathematics	mathematic	NOUN
ejpam-5161	355	2	,	,	PUNCT
ejpam-5161	355	3	11(20):4368	11(20):4368	NUM
ejpam-5161	355	4	,	,	PUNCT
ejpam-5161	355	5	2023	2023	NUM
ejpam-5161	355	6	.	.	PUNCT
ejpam-5161	356	1	[	[	X
ejpam-5161	356	2	13	13	NUM
ejpam-5161	356	3	]	]	PUNCT
ejpam-5161	356	4	baravan	baravan	NOUN
ejpam-5161	356	5	a	a	DET
ejpam-5161	356	6	asaad	asaad	NOUN
ejpam-5161	356	7	.	.	PUNCT
ejpam-5161	357	1	results	result	NOUN
ejpam-5161	357	2	on	on	ADP
ejpam-5161	357	3	soft	soft	ADJ
ejpam-5161	357	4	extremally	extremally	ADV
ejpam-5161	357	5	disconnectedness	disconnectedness	NOUN
ejpam-5161	357	6	of	of	ADP
ejpam-5161	357	7	soft	soft	ADJ
ejpam-5161	357	8	topological	topological	ADJ
ejpam-5161	357	9	spaces	space	NOUN
ejpam-5161	357	10	.	.	PUNCT
ejpam-5161	358	1	j.	j.	PROPN
ejpam-5161	358	2	math	math	PROPN
ejpam-5161	358	3	.	.	PUNCT
ejpam-5161	359	1	computer	computer	PROPN
ejpam-5161	359	2	sci	sci	PROPN
ejpam-5161	359	3	,	,	PUNCT
ejpam-5161	359	4	17:448–464	17:448–464	NUM
ejpam-5161	359	5	,	,	PUNCT
ejpam-5161	359	6	2017	2017	NUM
ejpam-5161	359	7	.	.	PUNCT
ejpam-5161	360	1	[	[	X
ejpam-5161	360	2	14	14	NUM
ejpam-5161	360	3	]	]	PUNCT
ejpam-5161	360	4	abdülkadir	abdülkadir	NOUN
ejpam-5161	360	5	aygünoğlu	aygünoğlu	PROPN
ejpam-5161	360	6	and	and	CCONJ
ejpam-5161	360	7	halis	halis	ADJ
ejpam-5161	360	8	aygün	aygün	NOUN
ejpam-5161	360	9	.	.	PUNCT
ejpam-5161	361	1	some	some	DET
ejpam-5161	361	2	notes	note	NOUN
ejpam-5161	361	3	on	on	ADP
ejpam-5161	361	4	soft	soft	ADJ
ejpam-5161	361	5	topological	topological	ADJ
ejpam-5161	361	6	spaces	space	NOUN
ejpam-5161	361	7	.	.	PUNCT
ejpam-5161	362	1	neural	neural	ADJ
ejpam-5161	362	2	computing	computing	NOUN
ejpam-5161	362	3	and	and	CCONJ
ejpam-5161	362	4	applications	application	NOUN
ejpam-5161	362	5	,	,	PUNCT
ejpam-5161	362	6	21(1):113–119	21(1):113–119	NUM
ejpam-5161	362	7	,	,	PUNCT
ejpam-5161	362	8	2012	2012	NUM
ejpam-5161	362	9	.	.	PUNCT
ejpam-5161	363	1	[	[	X
ejpam-5161	363	2	15	15	NUM
ejpam-5161	363	3	]	]	X
ejpam-5161	363	4	naim	naim	PROPN
ejpam-5161	363	5	çağman	çağman	PROPN
ejpam-5161	363	6	,	,	PUNCT
ejpam-5161	363	7	serkan	serkan	PROPN
ejpam-5161	363	8	karataş	karataş	PROPN
ejpam-5161	363	9	,	,	PUNCT
ejpam-5161	363	10	and	and	CCONJ
ejpam-5161	363	11	serdar	serdar	PROPN
ejpam-5161	363	12	enginoglu	enginoglu	PROPN
ejpam-5161	363	13	.	.	PUNCT
ejpam-5161	363	14	soft	soft	ADJ
ejpam-5161	363	15	topology	topology	NOUN
ejpam-5161	363	16	.	.	PUNCT
ejpam-5161	364	1	computers	computer	NOUN
ejpam-5161	364	2	&	&	CCONJ
ejpam-5161	364	3	mathematics	mathematics	PROPN
ejpam-5161	364	4	with	with	ADP
ejpam-5161	364	5	applications	application	NOUN
ejpam-5161	364	6	,	,	PUNCT
ejpam-5161	364	7	62(1):351–358	62(1):351–358	PROPN
ejpam-5161	364	8	,	,	PUNCT
ejpam-5161	364	9	2011	2011	NUM
ejpam-5161	364	10	.	.	PUNCT
ejpam-5161	365	1	[	[	X
ejpam-5161	365	2	16	16	NUM
ejpam-5161	365	3	]	]	PUNCT
ejpam-5161	365	4	orhan	orhan	PROPN
ejpam-5161	365	5	dalkılıç	dalkılıç	PROPN
ejpam-5161	365	6	and	and	CCONJ
ejpam-5161	365	7	naime	naime	PROPN
ejpam-5161	365	8	demirtaş.	demirtaş.	PROPN
ejpam-5161	365	9	algorithms	algorithm	NOUN
ejpam-5161	365	10	for	for	ADP
ejpam-5161	365	11	covid-19	covid-19	PROPN
ejpam-5161	365	12	outbreak	outbreak	NOUN
ejpam-5161	365	13	using	use	VERB
ejpam-5161	365	14	soft	soft	ADJ
ejpam-5161	365	15	set	set	NOUN
ejpam-5161	365	16	theory	theory	NOUN
ejpam-5161	365	17	:	:	PUNCT
ejpam-5161	365	18	estimation	estimation	NOUN
ejpam-5161	365	19	and	and	CCONJ
ejpam-5161	365	20	application	application	NOUN
ejpam-5161	365	21	.	.	PUNCT
ejpam-5161	366	1	soft	soft	ADJ
ejpam-5161	366	2	computing	computing	NOUN
ejpam-5161	366	3	,	,	PUNCT
ejpam-5161	366	4	27:3203–3211	27:3203–3211	NUM
ejpam-5161	366	5	,	,	PUNCT
ejpam-5161	366	6	2023	2023	NUM
ejpam-5161	366	7	.	.	PUNCT
ejpam-5161	367	1	[	[	X
ejpam-5161	367	2	17	17	NUM
ejpam-5161	367	3	]	]	X
ejpam-5161	367	4	mostafa	mostafa	PROPN
ejpam-5161	367	5	k	k	PROPN
ejpam-5161	367	6	el	el	PROPN
ejpam-5161	367	7	-	-	PROPN
ejpam-5161	367	8	bably	bably	ADV
ejpam-5161	367	9	,	,	PUNCT
ejpam-5161	367	10	radwan	radwan	VERB
ejpam-5161	367	11	abu	abu	PROPN
ejpam-5161	367	12	-	-	PUNCT
ejpam-5161	367	13	gdairi	gdairi	PROPN
ejpam-5161	367	14	,	,	PUNCT
ejpam-5161	367	15	and	and	CCONJ
ejpam-5161	367	16	mostafa	mostafa	PROPN
ejpam-5161	367	17	a	a	DET
ejpam-5161	367	18	el	el	PROPN
ejpam-5161	367	19	-	-	NOUN
ejpam-5161	367	20	gayar	gayar	NOUN
ejpam-5161	367	21	.	.	PUNCT
ejpam-5161	368	1	medical	medical	ADJ
ejpam-5161	368	2	diagnosis	diagnosis	NOUN
ejpam-5161	368	3	for	for	ADP
ejpam-5161	368	4	the	the	DET
ejpam-5161	368	5	problem	problem	NOUN
ejpam-5161	368	6	of	of	ADP
ejpam-5161	368	7	chikungunya	chikungunya	NOUN
ejpam-5161	368	8	disease	disease	NOUN
ejpam-5161	368	9	using	use	VERB
ejpam-5161	368	10	soft	soft	ADJ
ejpam-5161	368	11	rough	rough	ADJ
ejpam-5161	368	12	sets	set	NOUN
ejpam-5161	368	13	.	.	PUNCT
ejpam-5161	369	1	aims	aim	VERB
ejpam-5161	369	2	mathematics	mathematics	PROPN
ejpam-5161	369	3	,	,	PUNCT
ejpam-5161	369	4	8(4):9082–9105	8(4):9082–9105	NOUN
ejpam-5161	369	5	,	,	PUNCT
ejpam-5161	369	6	2023	2023	NUM
ejpam-5161	369	7	.	.	PUNCT
ejpam-5161	370	1	[	[	X
ejpam-5161	370	2	18	18	NUM
ejpam-5161	370	3	]	]	PUNCT
ejpam-5161	370	4	orhan	orhan	PROPN
ejpam-5161	370	5	göçür	göçür	PROPN
ejpam-5161	370	6	and	and	CCONJ
ejpam-5161	370	7	abdullah	abdullah	PROPN
ejpam-5161	370	8	kopuzlu	kopuzlu	PROPN
ejpam-5161	370	9	.	.	PUNCT
ejpam-5161	371	1	on	on	ADP
ejpam-5161	371	2	soft	soft	ADJ
ejpam-5161	371	3	separation	separation	NOUN
ejpam-5161	371	4	axioms	axiom	NOUN
ejpam-5161	371	5	.	.	PUNCT
ejpam-5161	372	1	ann	ann	PROPN
ejpam-5161	372	2	.	.	PUNCT
ejpam-5161	372	3	fuzzy	fuzzy	ADJ
ejpam-5161	372	4	math	math	PROPN
ejpam-5161	372	5	.	.	PUNCT
ejpam-5161	373	1	inform	inform	NOUN
ejpam-5161	373	2	,	,	PUNCT
ejpam-5161	373	3	9(5):817–822	9(5):817–822	NOUN
ejpam-5161	373	4	,	,	PUNCT
ejpam-5161	373	5	2015	2015	NUM
ejpam-5161	373	6	.	.	PUNCT
ejpam-5161	374	1	[	[	X
ejpam-5161	374	2	19	19	NUM
ejpam-5161	374	3	]	]	X
ejpam-5161	374	4	saeid	saeid	PROPN
ejpam-5161	374	5	jafari	jafari	PROPN
ejpam-5161	374	6	,	,	PUNCT
ejpam-5161	374	7	aa	aa	PROPN
ejpam-5161	374	8	el	el	PROPN
ejpam-5161	374	9	-	-	PUNCT
ejpam-5161	374	10	atik	atik	PROPN
ejpam-5161	374	11	,	,	PUNCT
ejpam-5161	374	12	raja	raja	PROPN
ejpam-5161	374	13	mohammad	mohammad	PROPN
ejpam-5161	374	14	latif	latif	PROPN
ejpam-5161	374	15	,	,	PUNCT
ejpam-5161	374	16	and	and	CCONJ
ejpam-5161	374	17	mk	mk	PROPN
ejpam-5161	374	18	el	el	PROPN
ejpam-5161	374	19	-	-	PROPN
ejpam-5161	374	20	bably	bably	PROPN
ejpam-5161	374	21	.	.	PUNCT
ejpam-5161	375	1	soft	soft	ADJ
ejpam-5161	375	2	topological	topological	ADJ
ejpam-5161	375	3	spaces	space	NOUN
ejpam-5161	375	4	induced	induce	VERB
ejpam-5161	375	5	via	via	ADP
ejpam-5161	375	6	soft	soft	ADJ
ejpam-5161	375	7	relations	relation	NOUN
ejpam-5161	375	8	.	.	PUNCT
ejpam-5161	376	1	wseas	wseas	PROPN
ejpam-5161	376	2	trans	trans	PROPN
ejpam-5161	376	3	.	.	PROPN
ejpam-5161	376	4	math	math	PROPN
ejpam-5161	376	5	,	,	PUNCT
ejpam-5161	376	6	20:1–8	20:1–8	NUM
ejpam-5161	376	7	,	,	PUNCT
ejpam-5161	376	8	2021	2021	NUM
ejpam-5161	376	9	.	.	PUNCT
ejpam-5161	377	1	[	[	X
ejpam-5161	377	2	20	20	NUM
ejpam-5161	377	3	]	]	PUNCT
ejpam-5161	377	4	fucai	fucai	PROPN
ejpam-5161	377	5	lin	lin	PROPN
ejpam-5161	377	6	.	.	PUNCT
ejpam-5161	378	1	soft	soft	ADJ
ejpam-5161	378	2	connected	connect	VERB
ejpam-5161	378	3	spaces	space	NOUN
ejpam-5161	378	4	and	and	CCONJ
ejpam-5161	378	5	soft	soft	ADJ
ejpam-5161	378	6	paracompact	paracompact	ADJ
ejpam-5161	378	7	spaces	space	NOUN
ejpam-5161	378	8	.	.	PUNCT
ejpam-5161	379	1	international	international	ADJ
ejpam-5161	379	2	journal	journal	PROPN
ejpam-5161	379	3	of	of	ADP
ejpam-5161	379	4	mathematical	mathematical	ADJ
ejpam-5161	379	5	and	and	CCONJ
ejpam-5161	379	6	computational	computational	ADJ
ejpam-5161	379	7	sciences	science	NOUN
ejpam-5161	379	8	,	,	PUNCT
ejpam-5161	379	9	7(2):277–283	7(2):277–283	NUM
ejpam-5161	379	10	,	,	PUNCT
ejpam-5161	379	11	2013	2013	NUM
ejpam-5161	379	12	.	.	PUNCT
ejpam-5161	380	1	[	[	X
ejpam-5161	380	2	21	21	NUM
ejpam-5161	380	3	]	]	X
ejpam-5161	380	4	juthika	juthika	PROPN
ejpam-5161	380	5	mahanta	mahanta	PROPN
ejpam-5161	380	6	and	and	CCONJ
ejpam-5161	380	7	pramod	pramod	PROPN
ejpam-5161	380	8	kumar	kumar	PROPN
ejpam-5161	380	9	das	das	PROPN
ejpam-5161	380	10	.	.	PUNCT
ejpam-5161	381	1	on	on	ADP
ejpam-5161	381	2	soft	soft	ADJ
ejpam-5161	381	3	topological	topological	ADJ
ejpam-5161	381	4	space	space	NOUN
ejpam-5161	381	5	via	via	ADP
ejpam-5161	381	6	semiopen	semiopen	VERB
ejpam-5161	381	7	and	and	CCONJ
ejpam-5161	381	8	semiclosed	semiclose	VERB
ejpam-5161	381	9	soft	soft	ADJ
ejpam-5161	381	10	sets	set	NOUN
ejpam-5161	381	11	.	.	PUNCT
ejpam-5161	382	1	kyungpook	kyungpook	PROPN
ejpam-5161	382	2	math	math	PROPN
ejpam-5161	382	3	j.	j.	PROPN
ejpam-5161	382	4	,	,	PUNCT
ejpam-5161	382	5	54:221–236	54:221–236	PROPN
ejpam-5161	382	6	,	,	PUNCT
ejpam-5161	382	7	2014	2014	NUM
ejpam-5161	382	8	.	.	PUNCT
ejpam-5161	383	1	[	[	X
ejpam-5161	383	2	22	22	NUM
ejpam-5161	383	3	]	]	X
ejpam-5161	383	4	pabitra	pabitra	PROPN
ejpam-5161	383	5	kumar	kumar	PROPN
ejpam-5161	383	6	maji	maji	PROPN
ejpam-5161	383	7	,	,	PUNCT
ejpam-5161	383	8	ranjit	ranjit	PROPN
ejpam-5161	383	9	biswas	biswas	PROPN
ejpam-5161	383	10	,	,	PUNCT
ejpam-5161	383	11	and	and	CCONJ
ejpam-5161	383	12	a	a	DET
ejpam-5161	383	13	ranjan	ranjan	PROPN
ejpam-5161	383	14	roy	roy	PROPN
ejpam-5161	383	15	.	.	PROPN
ejpam-5161	383	16	soft	soft	ADJ
ejpam-5161	383	17	set	set	NOUN
ejpam-5161	383	18	theory	theory	NOUN
ejpam-5161	383	19	.	.	PUNCT
ejpam-5161	384	1	computers	computer	NOUN
ejpam-5161	384	2	&	&	CCONJ
ejpam-5161	384	3	mathematics	mathematics	PROPN
ejpam-5161	384	4	with	with	ADP
ejpam-5161	384	5	applications	application	NOUN
ejpam-5161	384	6	,	,	PUNCT
ejpam-5161	384	7	45(4	45(4	NOUN
ejpam-5161	384	8	-	-	PUNCT
ejpam-5161	384	9	5):555–562	5):555–562	NUM
ejpam-5161	384	10	,	,	PUNCT
ejpam-5161	384	11	2003	2003	NUM
ejpam-5161	384	12	.	.	PUNCT
ejpam-5161	385	1	[	[	X
ejpam-5161	385	2	23	23	NUM
ejpam-5161	385	3	]	]	PUNCT
ejpam-5161	385	4	won	win	VERB
ejpam-5161	385	5	keun	keun	PROPN
ejpam-5161	385	6	min	min	PROPN
ejpam-5161	385	7	.	.	PROPN
ejpam-5161	386	1	a	a	DET
ejpam-5161	386	2	note	note	NOUN
ejpam-5161	386	3	on	on	ADP
ejpam-5161	386	4	soft	soft	ADJ
ejpam-5161	386	5	topological	topological	ADJ
ejpam-5161	386	6	spaces	space	NOUN
ejpam-5161	386	7	.	.	PUNCT
ejpam-5161	387	1	computers	computer	NOUN
ejpam-5161	387	2	&	&	CCONJ
ejpam-5161	387	3	mathematics	mathematics	PROPN
ejpam-5161	387	4	with	with	ADP
ejpam-5161	387	5	applications	application	NOUN
ejpam-5161	387	6	,	,	PUNCT
ejpam-5161	387	7	62(9):3524–3528	62(9):3524–3528	NUM
ejpam-5161	387	8	,	,	PUNCT
ejpam-5161	387	9	2011	2011	NUM
ejpam-5161	387	10	.	.	PUNCT
ejpam-5161	388	1	[	[	X
ejpam-5161	388	2	24	24	NUM
ejpam-5161	388	3	]	]	X
ejpam-5161	388	4	dmitriy	dmitriy	PROPN
ejpam-5161	388	5	molodtsov	molodtsov	PROPN
ejpam-5161	388	6	.	.	PUNCT
ejpam-5161	389	1	soft	soft	ADJ
ejpam-5161	389	2	set	set	VERB
ejpam-5161	389	3	theory	theory	NOUN
ejpam-5161	389	4	—	—	PUNCT
ejpam-5161	389	5	first	first	ADJ
ejpam-5161	389	6	results	result	NOUN
ejpam-5161	389	7	.	.	PUNCT
ejpam-5161	390	1	computers	computer	NOUN
ejpam-5161	390	2	&	&	CCONJ
ejpam-5161	390	3	mathematics	mathematics	PROPN
ejpam-5161	390	4	with	with	ADP
ejpam-5161	390	5	applications	application	NOUN
ejpam-5161	390	6	,	,	PUNCT
ejpam-5161	390	7	37(4	37(4	PROPN
ejpam-5161	390	8	-	-	PUNCT
ejpam-5161	390	9	5):19–31	5):19–31	NUM
ejpam-5161	390	10	,	,	PUNCT
ejpam-5161	390	11	1999	1999	NUM
ejpam-5161	390	12	.	.	PUNCT
ejpam-5161	391	1	[	[	X
ejpam-5161	391	2	25	25	NUM
ejpam-5161	391	3	]	]	PUNCT
ejpam-5161	391	4	sk	sk	X
ejpam-5161	391	5	nazmul	nazmul	PROPN
ejpam-5161	391	6	and	and	CCONJ
ejpam-5161	391	7	sk	sk	ADP
ejpam-5161	391	8	samanta	samanta	PROPN
ejpam-5161	391	9	.	.	PUNCT
ejpam-5161	392	1	neighbourhood	neighbourhood	NOUN
ejpam-5161	392	2	properties	property	NOUN
ejpam-5161	392	3	of	of	ADP
ejpam-5161	392	4	soft	soft	ADJ
ejpam-5161	392	5	topological	topological	ADJ
ejpam-5161	392	6	spaces	space	NOUN
ejpam-5161	392	7	.	.	PUNCT
ejpam-5161	393	1	ann	ann	PROPN
ejpam-5161	393	2	.	.	PUNCT
ejpam-5161	393	3	fuzzy	fuzzy	ADJ
ejpam-5161	393	4	math	math	PROPN
ejpam-5161	393	5	.	.	PUNCT
ejpam-5161	394	1	inform	inform	NOUN
ejpam-5161	394	2	,	,	PUNCT
ejpam-5161	394	3	6(1):1–15	6(1):1–15	NUM
ejpam-5161	394	4	,	,	PUNCT
ejpam-5161	394	5	2013	2013	NUM
ejpam-5161	394	6	.	.	PUNCT
ejpam-5161	395	1	references	reference	NOUN
ejpam-5161	395	2	1182	1182	NUM
ejpam-5161	395	3	[	[	X
ejpam-5161	395	4	26	26	NUM
ejpam-5161	395	5	]	]	PUNCT
ejpam-5161	395	6	zdzis	zdzis	NOUN
ejpam-5161	395	7	law	law	NOUN
ejpam-5161	395	8	pawlak	pawlak	NOUN
ejpam-5161	395	9	.	.	PUNCT
ejpam-5161	396	1	rough	rough	ADJ
ejpam-5161	396	2	sets	set	NOUN
ejpam-5161	396	3	.	.	PUNCT
ejpam-5161	397	1	international	international	ADJ
ejpam-5161	397	2	journal	journal	PROPN
ejpam-5161	397	3	of	of	ADP
ejpam-5161	397	4	computer	computer	PROPN
ejpam-5161	397	5	&	&	CCONJ
ejpam-5161	397	6	information	information	PROPN
ejpam-5161	397	7	sciences	sciences	PROPN
ejpam-5161	397	8	,	,	PUNCT
ejpam-5161	397	9	11(5):341–356	11(5):341–356	NUM
ejpam-5161	397	10	,	,	PUNCT
ejpam-5161	397	11	1982	1982	NUM
ejpam-5161	397	12	.	.	PUNCT
ejpam-5161	398	1	[	[	X
ejpam-5161	398	2	27	27	NUM
ejpam-5161	398	3	]	]	PUNCT
ejpam-5161	398	4	daowu	daowu	NOUN
ejpam-5161	398	5	pei	pei	PROPN
ejpam-5161	398	6	and	and	CCONJ
ejpam-5161	398	7	duoqian	duoqian	PROPN
ejpam-5161	398	8	miao	miao	PROPN
ejpam-5161	398	9	.	.	PUNCT
ejpam-5161	399	1	from	from	ADP
ejpam-5161	399	2	soft	soft	ADJ
ejpam-5161	399	3	sets	set	NOUN
ejpam-5161	399	4	to	to	ADP
ejpam-5161	399	5	information	information	NOUN
ejpam-5161	399	6	systems	system	NOUN
ejpam-5161	399	7	.	.	PUNCT
ejpam-5161	400	1	in	in	ADP
ejpam-5161	400	2	2005	2005	NUM
ejpam-5161	400	3	ieee	ieee	NOUN
ejpam-5161	400	4	international	international	ADJ
ejpam-5161	400	5	conference	conference	NOUN
ejpam-5161	400	6	on	on	ADP
ejpam-5161	400	7	granular	granular	ADJ
ejpam-5161	400	8	computing	computing	NOUN
ejpam-5161	400	9	,	,	PUNCT
ejpam-5161	400	10	volume	volume	NOUN
ejpam-5161	400	11	2	2	NUM
ejpam-5161	400	12	,	,	PUNCT
ejpam-5161	400	13	pages	page	NOUN
ejpam-5161	400	14	617–621	617–621	NUM
ejpam-5161	400	15	.	.	PUNCT
ejpam-5161	400	16	ieee	ieee	PROPN
ejpam-5161	400	17	,	,	PUNCT
ejpam-5161	400	18	2005	2005	NUM
ejpam-5161	400	19	.	.	PUNCT
ejpam-5161	401	1	[	[	X
ejpam-5161	401	2	28	28	NUM
ejpam-5161	401	3	]	]	X
ejpam-5161	401	4	muhammad	muhammad	PROPN
ejpam-5161	401	5	shabir	shabir	PROPN
ejpam-5161	401	6	and	and	CCONJ
ejpam-5161	401	7	munazza	munazza	PROPN
ejpam-5161	401	8	naz	naz	PROPN
ejpam-5161	401	9	.	.	PUNCT
ejpam-5161	402	1	on	on	ADP
ejpam-5161	402	2	soft	soft	ADJ
ejpam-5161	402	3	topological	topological	ADJ
ejpam-5161	402	4	spaces	space	NOUN
ejpam-5161	402	5	.	.	PUNCT
ejpam-5161	403	1	computers	computer	NOUN
ejpam-5161	403	2	&	&	CCONJ
ejpam-5161	403	3	mathematics	mathematics	PROPN
ejpam-5161	403	4	with	with	ADP
ejpam-5161	403	5	applications	application	NOUN
ejpam-5161	403	6	,	,	PUNCT
ejpam-5161	403	7	61(7):1786–1799	61(7):1786–1799	NUM
ejpam-5161	403	8	,	,	PUNCT
ejpam-5161	403	9	2011	2011	NUM
ejpam-5161	403	10	.	.	PUNCT
ejpam-5161	404	1	[	[	X
ejpam-5161	404	2	29	29	NUM
ejpam-5161	404	3	]	]	X
ejpam-5161	404	4	ma	ma	PROPN
ejpam-5161	404	5	lgorzata	lgorzata	PROPN
ejpam-5161	404	6	terepeta	terepeta	PROPN
ejpam-5161	404	7	.	.	PUNCT
ejpam-5161	405	1	on	on	ADP
ejpam-5161	405	2	separating	separate	VERB
ejpam-5161	405	3	axioms	axiom	NOUN
ejpam-5161	405	4	and	and	CCONJ
ejpam-5161	405	5	similarity	similarity	NOUN
ejpam-5161	405	6	of	of	ADP
ejpam-5161	405	7	soft	soft	ADJ
ejpam-5161	405	8	topological	topological	ADJ
ejpam-5161	405	9	spaces	space	NOUN
ejpam-5161	405	10	.	.	PUNCT
ejpam-5161	406	1	soft	soft	ADJ
ejpam-5161	406	2	computing	computing	NOUN
ejpam-5161	406	3	,	,	PUNCT
ejpam-5161	406	4	23(3):1049–1057	23(3):1049–1057	NUM
ejpam-5161	406	5	,	,	PUNCT
ejpam-5161	406	6	2019	2019	NUM
ejpam-5161	406	7	.	.	PUNCT
ejpam-5161	407	1	[	[	X
ejpam-5161	407	2	30	30	NUM
ejpam-5161	407	3	]	]	X
ejpam-5161	407	4	saziye	saziye	NOUN
ejpam-5161	407	5	yuksel	yuksel	PROPN
ejpam-5161	407	6	,	,	PUNCT
ejpam-5161	407	7	tugbahan	tugbahan	PROPN
ejpam-5161	407	8	dizman	dizman	NOUN
ejpam-5161	407	9	,	,	PUNCT
ejpam-5161	407	10	gulnur	gulnur	NOUN
ejpam-5161	407	11	yildizdan	yildizdan	NOUN
ejpam-5161	407	12	,	,	PUNCT
ejpam-5161	407	13	and	and	CCONJ
ejpam-5161	407	14	unal	unal	ADJ
ejpam-5161	407	15	sert	sert	NOUN
ejpam-5161	407	16	.	.	PUNCT
ejpam-5161	408	1	application	application	NOUN
ejpam-5161	408	2	of	of	ADP
ejpam-5161	408	3	soft	soft	ADJ
ejpam-5161	408	4	sets	set	NOUN
ejpam-5161	408	5	to	to	PART
ejpam-5161	408	6	diagnose	diagnose	VERB
ejpam-5161	408	7	the	the	DET
ejpam-5161	408	8	prostate	prostate	NOUN
ejpam-5161	408	9	cancer	cancer	NOUN
ejpam-5161	408	10	risk	risk	NOUN
ejpam-5161	408	11	.	.	PUNCT
ejpam-5161	409	1	journal	journal	NOUN
ejpam-5161	409	2	of	of	ADP
ejpam-5161	409	3	inequalities	inequality	NOUN
ejpam-5161	409	4	and	and	CCONJ
ejpam-5161	409	5	applications	application	NOUN
ejpam-5161	409	6	,	,	PUNCT
ejpam-5161	409	7	2013(1):1–11	2013(1):1–11	PROPN
ejpam-5161	409	8	,	,	PUNCT
ejpam-5161	409	9	2013	2013	NUM
ejpam-5161	409	10	.	.	PUNCT
ejpam-5161	410	1	[	[	X
ejpam-5161	410	2	31	31	NUM
ejpam-5161	410	3	]	]	X
ejpam-5161	410	4	yunus	yunus	PROPN
ejpam-5161	410	5	yumak	yumak	PROPN
ejpam-5161	410	6	and	and	CCONJ
ejpam-5161	410	7	aynur	aynur	ADV
ejpam-5161	410	8	keskin	keskin	PROPN
ejpam-5161	410	9	kaymarkci	kaymarkci	PROPN
ejpam-5161	410	10	.	.	PUNCT
ejpam-5161	411	1	soft	soft	ADJ
ejpam-5161	411	2	β	β	ADJ
ejpam-5161	411	3	-	-	ADJ
ejpam-5161	411	4	open	open	ADJ
ejpam-5161	411	5	sets	set	NOUN
ejpam-5161	411	6	and	and	CCONJ
ejpam-5161	411	7	their	their	PRON
ejpam-5161	411	8	applications	application	NOUN
ejpam-5161	411	9	.	.	PUNCT
ejpam-5161	412	1	journal	journal	NOUN
ejpam-5161	412	2	of	of	ADP
ejpam-5161	412	3	new	new	ADJ
ejpam-5161	412	4	theory	theory	NOUN
ejpam-5161	412	5	,	,	PUNCT
ejpam-5161	412	6	(	(	PUNCT
ejpam-5161	412	7	4):80–89	4):80–89	NUM
ejpam-5161	412	8	,	,	PUNCT
ejpam-5161	412	9	2015	2015	NUM
ejpam-5161	412	10	.	.	PUNCT
ejpam-5161	413	1	[	[	X
ejpam-5161	413	2	32	32	NUM
ejpam-5161	413	3	]	]	SYM
ejpam-5161	413	4	l.a	l.a	PROPN
ejpam-5161	413	5	.	.	PROPN
ejpam-5161	413	6	zadeh	zadeh	PROPN
ejpam-5161	413	7	.	.	PUNCT
ejpam-5161	413	8	fuzzy	fuzzy	ADJ
ejpam-5161	413	9	sets	set	NOUN
ejpam-5161	413	10	.	.	PUNCT
ejpam-5161	414	1	information	information	NOUN
ejpam-5161	414	2	and	and	CCONJ
ejpam-5161	414	3	control	control	NOUN
ejpam-5161	414	4	,	,	PUNCT
ejpam-5161	414	5	8(3):338–353	8(3):338–353	NUM
ejpam-5161	414	6	,	,	PUNCT
ejpam-5161	414	7	1965	1965	NUM
ejpam-5161	414	8	.	.	PUNCT
ejpam-5161	415	1	[	[	X
ejpam-5161	415	2	33	33	NUM
ejpam-5161	415	3	]	]	PUNCT
ejpam-5161	415	4	i̇dris	i̇dris	PROPN
ejpam-5161	415	5	zorlutuna	zorlutuna	PROPN
ejpam-5161	415	6	,	,	PUNCT
ejpam-5161	415	7	m	m	PROPN
ejpam-5161	415	8	akdag	akdag	PROPN
ejpam-5161	415	9	,	,	PUNCT
ejpam-5161	415	10	wk	wk	X
ejpam-5161	415	11	min	min	NOUN
ejpam-5161	415	12	,	,	PUNCT
ejpam-5161	415	13	and	and	CCONJ
ejpam-5161	415	14	s	s	VERB
ejpam-5161	415	15	atmaca	atmaca	NOUN
ejpam-5161	415	16	.	.	PUNCT
ejpam-5161	416	1	remarks	remark	NOUN
ejpam-5161	416	2	on	on	ADP
ejpam-5161	416	3	soft	soft	ADJ
ejpam-5161	416	4	topological	topological	ADJ
ejpam-5161	416	5	spaces	space	NOUN
ejpam-5161	416	6	.	.	PUNCT
ejpam-5161	417	1	annals	annal	NOUN
ejpam-5161	417	2	of	of	ADP
ejpam-5161	417	3	fuzzy	fuzzy	ADJ
ejpam-5161	417	4	mathematics	mathematic	NOUN
ejpam-5161	417	5	and	and	CCONJ
ejpam-5161	417	6	informatics	informatic	NOUN
ejpam-5161	417	7	,	,	PUNCT
ejpam-5161	417	8	3(2):171–185	3(2):171–185	NUM
ejpam-5161	417	9	,	,	PUNCT
ejpam-5161	417	10	2012	2012	NUM
ejpam-5161	417	11	.	.	PUNCT
ejpam-5161	418	1	introduction	introduction	NOUN
ejpam-5161	418	2	preliminaries	preliminary	NOUN
ejpam-5161	418	3	methods	method	NOUN
ejpam-5161	418	4	of	of	ADP
ejpam-5161	418	5	generating	generate	VERB
ejpam-5161	418	6	soft	soft	ADJ
ejpam-5161	418	7	topologies	topology	NOUN
ejpam-5161	418	8	and	and	CCONJ
ejpam-5161	418	9	their	their	PRON
ejpam-5161	418	10	relationships	relationship	NOUN
ejpam-5161	418	11	non	non	ADJ
ejpam-5161	418	12	-	-	ADJ
ejpam-5161	418	13	uniqueness	uniqueness	NOUN
ejpam-5161	418	14	of	of	ADP
ejpam-5161	418	15	soft	soft	ADJ
ejpam-5161	418	16	topology	topology	NOUN
ejpam-5161	418	17	t	t	PROPN
ejpam-5161	418	18	(	(	PUNCT
ejpam-5161	418	19	)	)	PUNCT
ejpam-5161	418	20	associated	associate	VERB
ejpam-5161	418	21	with	with	ADP
ejpam-5161	418	22	separation	separation	NOUN
ejpam-5161	418	23	axioms	axiom	NOUN
ejpam-5161	418	24	preservation	preservation	NOUN
ejpam-5161	418	25	between	between	ADP
ejpam-5161	418	26	and	and	CCONJ
ejpam-5161	418	27	t	t	PROPN
ejpam-5161	418	28	(	(	PUNCT
ejpam-5161	418	29	)	)	PUNCT
ejpam-5161	418	30	conclusion	conclusion	NOUN