id	sid	tid	token	lemma	pos
ejpam-4497	1	1	european	european	PROPN
ejpam-4497	1	2	journal	journal	PROPN
ejpam-4497	1	3	of	of	ADP
ejpam-4497	1	4	pure	pure	ADJ
ejpam-4497	1	5	and	and	CCONJ
ejpam-4497	1	6	applied	apply	VERB
ejpam-4497	1	7	mathematics	mathematic	NOUN
ejpam-4497	1	8	vol	vol	NOUN
ejpam-4497	1	9	.	.	PROPN
ejpam-4497	2	1	15	15	NUM
ejpam-4497	2	2	,	,	PUNCT
ejpam-4497	2	3	no	no	INTJ
ejpam-4497	2	4	.	.	NOUN
ejpam-4497	2	5	4	4	NUM
ejpam-4497	2	6	,	,	PUNCT
ejpam-4497	2	7	2022	2022	NUM
ejpam-4497	2	8	,	,	PUNCT
ejpam-4497	2	9	1455	1455	NUM
ejpam-4497	2	10	-	-	SYM
ejpam-4497	2	11	1471	1471	NUM
ejpam-4497	2	12	issn	issn	PROPN
ejpam-4497	2	13	1307	1307	NUM
ejpam-4497	2	14	-	-	SYM
ejpam-4497	2	15	5543	5543	NUM
ejpam-4497	2	16	–	–	PUNCT
ejpam-4497	2	17	ejpam.com	ejpam.com	X
ejpam-4497	2	18	published	publish	VERB
ejpam-4497	2	19	by	by	ADP
ejpam-4497	2	20	new	new	PROPN
ejpam-4497	2	21	york	york	PROPN
ejpam-4497	2	22	business	business	PROPN
ejpam-4497	2	23	global	global	PROPN
ejpam-4497	2	24	on	on	ADP
ejpam-4497	2	25	b	b	X
ejpam-4497	2	26	-	-	PUNCT
ejpam-4497	2	27	open	open	ADJ
ejpam-4497	2	28	sets	set	NOUN
ejpam-4497	2	29	via	via	ADP
ejpam-4497	2	30	infra	infra	NOUN
ejpam-4497	2	31	soft	soft	ADJ
ejpam-4497	2	32	topological	topological	ADJ
ejpam-4497	2	33	spaces	space	NOUN
ejpam-4497	2	34	radwan	radwan	VERB
ejpam-4497	2	35	abu	abu	NOUN
ejpam-4497	2	36	-	-	PUNCT
ejpam-4497	2	37	gdairi1	gdairi1	PROPN
ejpam-4497	2	38	,	,	PUNCT
ejpam-4497	2	39	mohammed	mohammed	PROPN
ejpam-4497	2	40	m.	m.	PROPN
ejpam-4497	2	41	ali	ali	PROPN
ejpam-4497	2	42	al	al	PROPN
ejpam-4497	2	43	-	-	PUNCT
ejpam-4497	2	44	shamiri2,3	shamiri2,3	PROPN
ejpam-4497	2	45	,	,	PUNCT
ejpam-4497	2	46	s.	s.	PROPN
ejpam-4497	2	47	saleh4,5	saleh4,5	PROPN
ejpam-4497	2	48	,	,	PUNCT
ejpam-4497	2	49	t.	t.	PROPN
ejpam-4497	2	50	m.	m.	PROPN
ejpam-4497	2	51	al	al	PROPN
ejpam-4497	2	52	-	-	PUNCT
ejpam-4497	2	53	shami6,7,∗	shami6,7,∗	PROPN
ejpam-4497	2	54	1	1	NUM
ejpam-4497	2	55	department	department	NOUN
ejpam-4497	2	56	of	of	ADP
ejpam-4497	2	57	mathematics	mathematic	NOUN
ejpam-4497	2	58	,	,	PUNCT
ejpam-4497	2	59	faculty	faculty	NOUN
ejpam-4497	2	60	of	of	ADP
ejpam-4497	2	61	science	science	NOUN
ejpam-4497	2	62	,	,	PUNCT
ejpam-4497	2	63	zarqa	zarqa	PROPN
ejpam-4497	2	64	university	university	PROPN
ejpam-4497	2	65	,	,	PUNCT
ejpam-4497	2	66	p.o	p.o	PROPN
ejpam-4497	2	67	.	.	PROPN
ejpam-4497	2	68	box	box	PROPN
ejpam-4497	2	69	13110	13110	NUM
ejpam-4497	2	70	zarqa	zarqa	PROPN
ejpam-4497	2	71	,	,	PUNCT
ejpam-4497	2	72	jordan	jordan	PROPN
ejpam-4497	2	73	2	2	NUM
ejpam-4497	2	74	department	department	NOUN
ejpam-4497	2	75	of	of	ADP
ejpam-4497	2	76	mathematics	mathematic	NOUN
ejpam-4497	2	77	,	,	PUNCT
ejpam-4497	2	78	faculty	faculty	NOUN
ejpam-4497	2	79	of	of	ADP
ejpam-4497	2	80	science	science	NOUN
ejpam-4497	2	81	and	and	CCONJ
ejpam-4497	2	82	arts	art	NOUN
ejpam-4497	2	83	,	,	PUNCT
ejpam-4497	2	84	king	king	PROPN
ejpam-4497	2	85	khalid	khalid	PROPN
ejpam-4497	2	86	university	university	PROPN
ejpam-4497	2	87	,	,	PUNCT
ejpam-4497	2	88	muhayl	muhayl	PROPN
ejpam-4497	2	89	assir	assir	PROPN
ejpam-4497	2	90	,	,	PUNCT
ejpam-4497	2	91	saudy	saudy	PROPN
ejpam-4497	2	92	arabia	arabia	PROPN
ejpam-4497	2	93	3	3	NUM
ejpam-4497	2	94	department	department	NOUN
ejpam-4497	2	95	of	of	ADP
ejpam-4497	2	96	mathematics	mathematic	NOUN
ejpam-4497	2	97	and	and	CCONJ
ejpam-4497	2	98	computer	computer	NOUN
ejpam-4497	2	99	,	,	PUNCT
ejpam-4497	2	100	faculty	faculty	NOUN
ejpam-4497	2	101	of	of	ADP
ejpam-4497	2	102	science	science	NOUN
ejpam-4497	2	103	,	,	PUNCT
ejpam-4497	2	104	ibb	ibb	PROPN
ejpam-4497	2	105	university	university	NOUN
ejpam-4497	2	106	,	,	PUNCT
ejpam-4497	2	107	ibb	ibb	NOUN
ejpam-4497	2	108	,	,	PUNCT
ejpam-4497	2	109	yemen	yemen	PROPN
ejpam-4497	2	110	4	4	NUM
ejpam-4497	2	111	computer	computer	NOUN
ejpam-4497	2	112	science	science	NOUN
ejpam-4497	2	113	department	department	PROPN
ejpam-4497	2	114	,	,	PUNCT
ejpam-4497	2	115	cihan	cihan	VERB
ejpam-4497	2	116	university	university	NOUN
ejpam-4497	2	117	-	-	PUNCT
ejpam-4497	2	118	erbil	erbil	PROPN
ejpam-4497	2	119	,	,	PUNCT
ejpam-4497	2	120	kurdistan	kurdistan	ADJ
ejpam-4497	2	121	region	region	NOUN
ejpam-4497	2	122	,	,	PUNCT
ejpam-4497	2	123	iraq	iraq	PROPN
ejpam-4497	2	124	5	5	NUM
ejpam-4497	2	125	department	department	NOUN
ejpam-4497	2	126	of	of	ADP
ejpam-4497	2	127	mathematics	mathematic	NOUN
ejpam-4497	2	128	,	,	PUNCT
ejpam-4497	2	129	hodeidah	hodeidah	PROPN
ejpam-4497	2	130	university	university	NOUN
ejpam-4497	2	131	,	,	PUNCT
ejpam-4497	2	132	hodeidah	hodeidah	PROPN
ejpam-4497	2	133	,	,	PUNCT
ejpam-4497	2	134	yemen	yemen	PROPN
ejpam-4497	2	135	6	6	NUM
ejpam-4497	2	136	department	department	NOUN
ejpam-4497	2	137	of	of	ADP
ejpam-4497	2	138	mathematics	mathematic	NOUN
ejpam-4497	2	139	,	,	PUNCT
ejpam-4497	2	140	sana’a	sana’a	NOUN
ejpam-4497	2	141	university	university	NOUN
ejpam-4497	2	142	,	,	PUNCT
ejpam-4497	2	143	sana’a	sana’a	NOUN
ejpam-4497	2	144	,	,	PUNCT
ejpam-4497	2	145	yemen	yemen	PROPN
ejpam-4497	2	146	7	7	NUM
ejpam-4497	2	147	future	future	PROPN
ejpam-4497	2	148	university	university	NOUN
ejpam-4497	2	149	,	,	PUNCT
ejpam-4497	2	150	egypt	egypt	PROPN
ejpam-4497	2	151	abstract	abstract	PROPN
ejpam-4497	2	152	.	.	PUNCT
ejpam-4497	3	1	this	this	DET
ejpam-4497	3	2	work	work	NOUN
ejpam-4497	3	3	aims	aim	VERB
ejpam-4497	3	4	to	to	PART
ejpam-4497	3	5	present	present	VERB
ejpam-4497	3	6	the	the	DET
ejpam-4497	3	7	concept	concept	NOUN
ejpam-4497	3	8	of	of	ADP
ejpam-4497	3	9	infra	infra	NOUN
ejpam-4497	3	10	soft	soft	ADJ
ejpam-4497	3	11	b	b	NOUN
ejpam-4497	3	12	-	-	PUNCT
ejpam-4497	3	13	open	open	ADJ
ejpam-4497	3	14	sets	set	NOUN
ejpam-4497	3	15	(	(	PUNCT
ejpam-4497	3	16	is	be	AUX
ejpam-4497	3	17	-	-	PUNCT
ejpam-4497	3	18	b	b	NOUN
ejpam-4497	3	19	-	-	PUNCT
ejpam-4497	3	20	open	open	ADJ
ejpam-4497	3	21	sets	set	NOUN
ejpam-4497	3	22	)	)	PUNCT
ejpam-4497	3	23	as	as	ADP
ejpam-4497	3	24	a	a	DET
ejpam-4497	3	25	generalized	generalized	ADJ
ejpam-4497	3	26	new	new	ADJ
ejpam-4497	3	27	class	class	NOUN
ejpam-4497	3	28	of	of	ADP
ejpam-4497	3	29	infra	infra	NOUN
ejpam-4497	3	30	open	open	ADJ
ejpam-4497	3	31	sets	set	NOUN
ejpam-4497	3	32	(	(	PUNCT
ejpam-4497	3	33	is	be	AUX
ejpam-4497	3	34	-	-	PUNCT
ejpam-4497	3	35	open	open	ADJ
ejpam-4497	3	36	sets	set	NOUN
ejpam-4497	3	37	)	)	PUNCT
ejpam-4497	3	38	.	.	PUNCT
ejpam-4497	4	1	we	we	PRON
ejpam-4497	4	2	first	first	ADV
ejpam-4497	4	3	investigate	investigate	VERB
ejpam-4497	4	4	their	their	PRON
ejpam-4497	4	5	basic	basic	ADJ
ejpam-4497	4	6	properties	property	NOUN
ejpam-4497	4	7	and	and	CCONJ
ejpam-4497	4	8	study	study	VERB
ejpam-4497	4	9	their	their	PRON
ejpam-4497	4	10	behaviours	behaviour	NOUN
ejpam-4497	4	11	under	under	ADP
ejpam-4497	4	12	infra	infra	NOUN
ejpam-4497	4	13	soft	soft	ADJ
ejpam-4497	4	14	homeomorphism	homeomorphism	NOUN
ejpam-4497	4	15	maps	map	NOUN
ejpam-4497	4	16	.	.	PUNCT
ejpam-4497	5	1	then	then	ADV
ejpam-4497	5	2	,	,	PUNCT
ejpam-4497	5	3	we	we	PRON
ejpam-4497	5	4	establish	establish	VERB
ejpam-4497	5	5	some	some	DET
ejpam-4497	5	6	soft	soft	ADJ
ejpam-4497	5	7	operators	operator	NOUN
ejpam-4497	5	8	such	such	ADJ
ejpam-4497	5	9	as	as	ADP
ejpam-4497	5	10	interior	interior	ADJ
ejpam-4497	5	11	,	,	PUNCT
ejpam-4497	5	12	closure	closure	NOUN
ejpam-4497	5	13	,	,	PUNCT
ejpam-4497	5	14	limit	limit	NOUN
ejpam-4497	5	15	and	and	CCONJ
ejpam-4497	5	16	boundary	boundary	ADJ
ejpam-4497	5	17	using	use	VERB
ejpam-4497	5	18	is	be	AUX
ejpam-4497	5	19	-	-	PUNCT
ejpam-4497	5	20	b	b	NOUN
ejpam-4497	5	21	-	-	PUNCT
ejpam-4497	5	22	open	open	ADJ
ejpam-4497	5	23	sets	set	NOUN
ejpam-4497	5	24	and	and	CCONJ
ejpam-4497	5	25	is	be	AUX
ejpam-4497	5	26	-	-	PUNCT
ejpam-4497	5	27	b	b	NOUN
ejpam-4497	5	28	-	-	PUNCT
ejpam-4497	5	29	closed	closed	ADJ
ejpam-4497	5	30	sets	set	NOUN
ejpam-4497	5	31	.	.	PUNCT
ejpam-4497	6	1	the	the	DET
ejpam-4497	6	2	relationships	relationship	NOUN
ejpam-4497	6	3	between	between	ADP
ejpam-4497	6	4	them	they	PRON
ejpam-4497	6	5	are	be	AUX
ejpam-4497	6	6	illustrated	illustrate	VERB
ejpam-4497	6	7	and	and	CCONJ
ejpam-4497	6	8	discussed	discuss	VERB
ejpam-4497	6	9	.	.	PUNCT
ejpam-4497	7	1	finally	finally	ADV
ejpam-4497	7	2	,	,	PUNCT
ejpam-4497	7	3	we	we	PRON
ejpam-4497	7	4	display	display	VERB
ejpam-4497	7	5	some	some	DET
ejpam-4497	7	6	soft	soft	ADJ
ejpam-4497	7	7	maps	map	NOUN
ejpam-4497	7	8	(	(	PUNCT
ejpam-4497	7	9	s	s	NOUN
ejpam-4497	7	10	-	-	PUNCT
ejpam-4497	7	11	map	map	NOUN
ejpam-4497	7	12	)	)	PUNCT
ejpam-4497	7	13	defined	define	VERB
ejpam-4497	7	14	using	use	VERB
ejpam-4497	7	15	is	be	AUX
ejpam-4497	7	16	-	-	PUNCT
ejpam-4497	7	17	b	b	NOUN
ejpam-4497	7	18	-	-	PUNCT
ejpam-4497	7	19	open	open	ADJ
ejpam-4497	7	20	and	and	CCONJ
ejpam-4497	7	21	is	be	AUX
ejpam-4497	7	22	-	-	PUNCT
ejpam-4497	7	23	b	b	NOUN
ejpam-4497	7	24	-	-	PUNCT
ejpam-4497	7	25	closed	closed	ADJ
ejpam-4497	7	26	sets	set	NOUN
ejpam-4497	7	27	and	and	CCONJ
ejpam-4497	7	28	scrutinize	scrutinize	VERB
ejpam-4497	7	29	their	their	PRON
ejpam-4497	7	30	master	master	NOUN
ejpam-4497	7	31	properties	property	NOUN
ejpam-4497	7	32	.	.	PUNCT
ejpam-4497	8	1	2020	2020	NUM
ejpam-4497	8	2	mathematics	mathematic	NOUN
ejpam-4497	8	3	subject	subject	NOUN
ejpam-4497	8	4	classifications	classification	NOUN
ejpam-4497	8	5	:	:	PUNCT
ejpam-4497	8	6	54a40	54a40	NUM
ejpam-4497	8	7	,	,	PUNCT
ejpam-4497	8	8	54c08	54c08	NUM
ejpam-4497	8	9	,	,	PUNCT
ejpam-4497	8	10	54c99	54c99	DET
ejpam-4497	8	11	key	key	ADJ
ejpam-4497	8	12	words	word	NOUN
ejpam-4497	8	13	and	and	CCONJ
ejpam-4497	8	14	phrases	phrase	NOUN
ejpam-4497	8	15	:	:	PUNCT
ejpam-4497	8	16	infra	infra	NOUN
ejpam-4497	8	17	soft	soft	ADJ
ejpam-4497	8	18	b	b	NOUN
ejpam-4497	8	19	-	-	PUNCT
ejpam-4497	8	20	open	open	ADJ
ejpam-4497	8	21	set	set	NOUN
ejpam-4497	8	22	,	,	PUNCT
ejpam-4497	8	23	infra	infra	NOUN
ejpam-4497	8	24	soft	soft	ADJ
ejpam-4497	8	25	b	b	NOUN
ejpam-4497	8	26	-	-	ADJ
ejpam-4497	8	27	interior	interior	ADJ
ejpam-4497	8	28	points	point	NOUN
ejpam-4497	8	29	,	,	PUNCT
ejpam-4497	8	30	infra	infra	NOUN
ejpam-4497	8	31	soft	soft	ADJ
ejpam-4497	8	32	b	b	NOUN
ejpam-4497	8	33	-	-	PUNCT
ejpam-4497	8	34	closure	closure	NOUN
ejpam-4497	8	35	points	point	NOUN
ejpam-4497	8	36	,	,	PUNCT
ejpam-4497	8	37	infra	infra	NOUN
ejpam-4497	8	38	soft	soft	ADJ
ejpam-4497	8	39	b	b	NOUN
ejpam-4497	8	40	-	-	PUNCT
ejpam-4497	8	41	continuity	continuity	NOUN
ejpam-4497	8	42	1	1	NUM
ejpam-4497	8	43	.	.	PUNCT
ejpam-4497	9	1	introduction	introduction	NOUN
ejpam-4497	9	2	molodtsov	molodtsov	NOUN
ejpam-4497	9	3	[	[	X
ejpam-4497	9	4	62	62	NUM
ejpam-4497	9	5	]	]	PUNCT
ejpam-4497	9	6	proposed	propose	VERB
ejpam-4497	9	7	the	the	DET
ejpam-4497	9	8	idea	idea	NOUN
ejpam-4497	9	9	of	of	ADP
ejpam-4497	9	10	soft	soft	ADJ
ejpam-4497	9	11	set	set	NOUN
ejpam-4497	9	12	(	(	PUNCT
ejpam-4497	9	13	s	s	NOUN
ejpam-4497	9	14	-	-	PUNCT
ejpam-4497	9	15	set	set	NOUN
ejpam-4497	9	16	)	)	PUNCT
ejpam-4497	9	17	as	as	ADP
ejpam-4497	9	18	a	a	DET
ejpam-4497	9	19	new	new	ADJ
ejpam-4497	9	20	mathematical	mathematical	ADJ
ejpam-4497	9	21	tool	tool	NOUN
ejpam-4497	9	22	to	to	PART
ejpam-4497	9	23	deal	deal	VERB
ejpam-4497	9	24	with	with	ADP
ejpam-4497	9	25	vagueness	vagueness	NOUN
ejpam-4497	9	26	.	.	PUNCT
ejpam-4497	10	1	he	he	PRON
ejpam-4497	10	2	presented	present	VERB
ejpam-4497	10	3	some	some	PRON
ejpam-4497	10	4	of	of	ADP
ejpam-4497	10	5	its	its	PRON
ejpam-4497	10	6	applications	application	NOUN
ejpam-4497	10	7	to	to	ADP
ejpam-4497	10	8	some	some	DET
ejpam-4497	10	9	areas	area	NOUN
ejpam-4497	10	10	.	.	PUNCT
ejpam-4497	11	1	since	since	SCONJ
ejpam-4497	11	2	the	the	DET
ejpam-4497	11	3	advent	advent	NOUN
ejpam-4497	11	4	of	of	ADP
ejpam-4497	11	5	s	s	NOUN
ejpam-4497	11	6	-	-	PUNCT
ejpam-4497	11	7	set	set	NOUN
ejpam-4497	11	8	,	,	PUNCT
ejpam-4497	11	9	they	they	PRON
ejpam-4497	11	10	have	have	AUX
ejpam-4497	11	11	been	be	AUX
ejpam-4497	11	12	applied	apply	VERB
ejpam-4497	11	13	to	to	PART
ejpam-4497	11	14	address	address	VERB
ejpam-4497	11	15	some	some	DET
ejpam-4497	11	16	problems	problem	NOUN
ejpam-4497	11	17	and	and	CCONJ
ejpam-4497	11	18	phenomena	phenomenon	NOUN
ejpam-4497	11	19	in	in	ADP
ejpam-4497	11	20	different	different	ADJ
ejpam-4497	11	21	disciplines	discipline	NOUN
ejpam-4497	11	22	such	such	ADJ
ejpam-4497	11	23	as	as	ADP
ejpam-4497	11	24	information	information	NOUN
ejpam-4497	11	25	system	system	NOUN
ejpam-4497	12	1	[	[	X
ejpam-4497	12	2	9	9	NUM
ejpam-4497	12	3	]	]	PUNCT
ejpam-4497	12	4	,	,	PUNCT
ejpam-4497	12	5	economy	economy	NOUN
ejpam-4497	12	6	[	[	X
ejpam-4497	12	7	14	14	NUM
ejpam-4497	12	8	]	]	PUNCT
ejpam-4497	12	9	,	,	PUNCT
ejpam-4497	12	10	linear	linear	ADJ
ejpam-4497	12	11	equations	equation	NOUN
ejpam-4497	12	12	[	[	X
ejpam-4497	12	13	27	27	NUM
ejpam-4497	12	14	]	]	PUNCT
ejpam-4497	12	15	,	,	PUNCT
ejpam-4497	12	16	computer	computer	NOUN
ejpam-4497	12	17	science	science	NOUN
ejpam-4497	12	18	[	[	X
ejpam-4497	12	19	50	50	NUM
ejpam-4497	12	20	]	]	PUNCT
ejpam-4497	12	21	and	and	CCONJ
ejpam-4497	12	22	decision	decision	NOUN
ejpam-4497	12	23	-	-	PUNCT
ejpam-4497	12	24	making	make	VERB
ejpam-4497	12	25	problems	problem	NOUN
ejpam-4497	12	26	[	[	X
ejpam-4497	12	27	53	53	NUM
ejpam-4497	12	28	]	]	PUNCT
ejpam-4497	12	29	.	.	PUNCT
ejpam-4497	13	1	the	the	DET
ejpam-4497	13	2	main	main	ADJ
ejpam-4497	13	3	operations	operation	NOUN
ejpam-4497	13	4	and	and	CCONJ
ejpam-4497	13	5	operators	operator	NOUN
ejpam-4497	13	6	via	via	ADP
ejpam-4497	13	7	s	s	ADV
ejpam-4497	13	8	-	-	PUNCT
ejpam-4497	13	9	set	set	VERB
ejpam-4497	13	10	theory	theory	NOUN
ejpam-4497	13	11	such	such	ADJ
ejpam-4497	13	12	as	as	ADP
ejpam-4497	13	13	the	the	DET
ejpam-4497	13	14	difference	difference	NOUN
ejpam-4497	13	15	,	,	PUNCT
ejpam-4497	13	16	intersection	intersection	NOUN
ejpam-4497	13	17	,	,	PUNCT
ejpam-4497	13	18	and	and	CCONJ
ejpam-4497	13	19	union	union	NOUN
ejpam-4497	13	20	between	between	ADP
ejpam-4497	13	21	two	two	NUM
ejpam-4497	13	22	s	s	NOUN
ejpam-4497	13	23	-	-	PUNCT
ejpam-4497	13	24	sets	set	NOUN
ejpam-4497	13	25	,	,	PUNCT
ejpam-4497	13	26	and	and	CCONJ
ejpam-4497	13	27	a	a	DET
ejpam-4497	13	28	complement	complement	NOUN
ejpam-4497	13	29	of	of	ADP
ejpam-4497	13	30	an	an	DET
ejpam-4497	13	31	s	s	NOUN
ejpam-4497	13	32	-	-	PUNCT
ejpam-4497	13	33	set	set	ADJ
ejpam-4497	13	34	were	be	AUX
ejpam-4497	13	35	introduced	introduce	VERB
ejpam-4497	13	36	by	by	ADP
ejpam-4497	13	37	maji	maji	PROPN
ejpam-4497	13	38	et	et	NOUN
ejpam-4497	13	39	∗corresponding	∗corresponde	VERB
ejpam-4497	13	40	author	author	NOUN
ejpam-4497	13	41	.	.	PUNCT
ejpam-4497	14	1	doi	doi	NOUN
ejpam-4497	14	2	:	:	PUNCT
ejpam-4497	14	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4497	https://doi.org/10.29020/nybg.ejpam.v15i4.4497	PROPN
ejpam-4497	14	4	email	email	NOUN
ejpam-4497	14	5	addresses	address	NOUN
ejpam-4497	14	6	:	:	PUNCT
ejpam-4497	14	7	rgdairi@zu.edu.jo	rgdairi@zu.edu.jo	PROPN
ejpam-4497	14	8	(	(	PUNCT
ejpam-4497	14	9	r.	r.	PROPN
ejpam-4497	14	10	abu	abu	PROPN
ejpam-4497	14	11	-	-	PUNCT
ejpam-4497	14	12	gdairi	gdairi	PROPN
ejpam-4497	14	13	)	)	PUNCT
ejpam-4497	14	14	,	,	PUNCT
ejpam-4497	14	15	mal-shamiri@kkul.edu.sa	mal-shamiri@kkul.edu.sa	PROPN
ejpam-4497	14	16	(	(	PUNCT
ejpam-4497	14	17	m.m.a	m.m.a	NOUN
ejpam-4497	14	18	.	.	PUNCT
ejpam-4497	15	1	al	al	PROPN
ejpam-4497	15	2	-	-	PUNCT
ejpam-4497	15	3	shamiri	shamiri	PROPN
ejpam-4497	15	4	)	)	PUNCT
ejpam-4497	15	5	,	,	PUNCT
ejpam-4497	16	1	salem.saleh@cihanuniversity.edu.iq	salem.saleh@cihanuniversity.edu.iq	NOUN
ejpam-4497	16	2	(	(	PUNCT
ejpam-4497	16	3	s.	s.	PROPN
ejpam-4497	16	4	saleh	saleh	PROPN
ejpam-4497	16	5	)	)	PUNCT
ejpam-4497	16	6	,	,	PUNCT
ejpam-4497	16	7	tareqalshami83@gmail.com	tareqalshami83@gmail.com	X
ejpam-4497	16	8	(	(	PUNCT
ejpam-4497	16	9	t.m	t.m	PROPN
ejpam-4497	16	10	.	.	PROPN
ejpam-4497	16	11	al	al	PROPN
ejpam-4497	16	12	-	-	PUNCT
ejpam-4497	16	13	shami	shami	PROPN
ejpam-4497	16	14	)	)	PUNCT
ejpam-4497	16	15	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4497	17	1	1455	1455	NUM
ejpam-4497	17	2	©	©	PROPN
ejpam-4497	17	3	2022	2022	NUM
ejpam-4497	17	4	ejpam	ejpam	VERB
ejpam-4497	17	5	all	all	DET
ejpam-4497	17	6	rights	right	NOUN
ejpam-4497	17	7	reserved	reserve	VERB
ejpam-4497	17	8	.	.	PUNCT
ejpam-4497	18	1	t.m	t.m	X
ejpam-4497	18	2	.	.	PUNCT
ejpam-4497	18	3	al	al	PROPN
ejpam-4497	18	4	-	-	PUNCT
ejpam-4497	18	5	shami	shami	PROPN
ejpam-4497	18	6	et	et	PROPN
ejpam-4497	18	7	al	al	PROPN
ejpam-4497	18	8	.	.	PUNCT
ejpam-4497	18	9	/	/	SYM
ejpam-4497	18	10	eur	eur	PROPN
ejpam-4497	18	11	.	.	PUNCT
ejpam-4497	19	1	j.	j.	PROPN
ejpam-4497	19	2	pure	pure	PROPN
ejpam-4497	19	3	appl	appl	PROPN
ejpam-4497	19	4	.	.	PROPN
ejpam-4497	19	5	math	math	PROPN
ejpam-4497	19	6	,	,	PUNCT
ejpam-4497	19	7	15	15	NUM
ejpam-4497	19	8	(	(	PUNCT
ejpam-4497	19	9	4	4	NUM
ejpam-4497	19	10	)	)	PUNCT
ejpam-4497	19	11	(	(	PUNCT
ejpam-4497	19	12	2022	2022	NUM
ejpam-4497	19	13	)	)	PUNCT
ejpam-4497	19	14	,	,	PUNCT
ejpam-4497	19	15	1455	1455	NUM
ejpam-4497	19	16	-	-	SYM
ejpam-4497	19	17	1471	1471	NUM
ejpam-4497	19	18	1456	1456	NUM
ejpam-4497	19	19	al	al	PROPN
ejpam-4497	19	20	.	.	PUNCT
ejpam-4497	20	1	[	[	X
ejpam-4497	20	2	61	61	NUM
ejpam-4497	20	3	]	]	PUNCT
ejpam-4497	20	4	.	.	PUNCT
ejpam-4497	21	1	then	then	ADV
ejpam-4497	21	2	,	,	PUNCT
ejpam-4497	21	3	new	new	ADJ
ejpam-4497	21	4	operations	operation	NOUN
ejpam-4497	21	5	and	and	CCONJ
ejpam-4497	21	6	operators	operator	NOUN
ejpam-4497	21	7	between	between	ADP
ejpam-4497	21	8	s	s	NOUN
ejpam-4497	21	9	-	-	PUNCT
ejpam-4497	21	10	sets	set	NOUN
ejpam-4497	21	11	were	be	AUX
ejpam-4497	21	12	presented	present	VERB
ejpam-4497	21	13	in	in	ADP
ejpam-4497	21	14	[	[	X
ejpam-4497	21	15	27	27	NUM
ejpam-4497	21	16	,	,	PUNCT
ejpam-4497	21	17	44	44	NUM
ejpam-4497	21	18	]	]	PUNCT
ejpam-4497	21	19	.	.	PUNCT
ejpam-4497	22	1	some	some	DET
ejpam-4497	22	2	extensions	extension	NOUN
ejpam-4497	22	3	of	of	ADP
ejpam-4497	22	4	s	s	NOUN
ejpam-4497	22	5	-	-	PUNCT
ejpam-4497	22	6	sets	set	NOUN
ejpam-4497	22	7	were	be	AUX
ejpam-4497	22	8	proposed	propose	VERB
ejpam-4497	22	9	with	with	ADP
ejpam-4497	22	10	the	the	DET
ejpam-4497	22	11	goal	goal	NOUN
ejpam-4497	22	12	of	of	ADP
ejpam-4497	22	13	expanding	expand	VERB
ejpam-4497	22	14	the	the	DET
ejpam-4497	22	15	applications	application	NOUN
ejpam-4497	22	16	of	of	ADP
ejpam-4497	22	17	s	s	NOUN
ejpam-4497	22	18	-	-	PUNCT
ejpam-4497	22	19	sets	set	NOUN
ejpam-4497	22	20	such	such	ADJ
ejpam-4497	22	21	as	as	ADP
ejpam-4497	22	22	bipolar	bipolar	ADJ
ejpam-4497	22	23	s	s	NOUN
ejpam-4497	22	24	-	-	PUNCT
ejpam-4497	22	25	sets	set	NOUN
ejpam-4497	22	26	[	[	X
ejpam-4497	22	27	8	8	NUM
ejpam-4497	22	28	]	]	PUNCT
ejpam-4497	22	29	and	and	CCONJ
ejpam-4497	22	30	double	double	ADJ
ejpam-4497	22	31	-	-	PUNCT
ejpam-4497	22	32	framed	frame	VERB
ejpam-4497	22	33	s	s	NOUN
ejpam-4497	22	34	-	-	PUNCT
ejpam-4497	22	35	sets	set	NOUN
ejpam-4497	22	36	[	[	X
ejpam-4497	22	37	38	38	NUM
ejpam-4497	22	38	]	]	PUNCT
ejpam-4497	22	39	.	.	PUNCT
ejpam-4497	23	1	recently	recently	ADV
ejpam-4497	23	2	,	,	PUNCT
ejpam-4497	23	3	topology	topology	NOUN
ejpam-4497	23	4	has	have	AUX
ejpam-4497	23	5	been	be	AUX
ejpam-4497	23	6	applied	apply	VERB
ejpam-4497	23	7	to	to	PART
ejpam-4497	23	8	model	model	VERB
ejpam-4497	23	9	some	some	DET
ejpam-4497	23	10	real	real	ADJ
ejpam-4497	23	11	-	-	PUNCT
ejpam-4497	23	12	life	life	NOUN
ejpam-4497	23	13	issues	issue	NOUN
ejpam-4497	23	14	as	as	SCONJ
ejpam-4497	23	15	showed	show	VERB
ejpam-4497	23	16	in	in	ADP
ejpam-4497	23	17	[	[	X
ejpam-4497	23	18	1	1	NUM
ejpam-4497	23	19	,	,	PUNCT
ejpam-4497	23	20	11	11	NUM
ejpam-4497	23	21	,	,	PUNCT
ejpam-4497	23	22	15	15	NUM
ejpam-4497	23	23	,	,	PUNCT
ejpam-4497	23	24	16	16	NUM
ejpam-4497	23	25	,	,	PUNCT
ejpam-4497	23	26	32	32	NUM
ejpam-4497	23	27	,	,	PUNCT
ejpam-4497	23	28	46	46	NUM
ejpam-4497	23	29	,	,	PUNCT
ejpam-4497	23	30	56	56	NUM
ejpam-4497	23	31	,	,	PUNCT
ejpam-4497	23	32	64	64	NUM
ejpam-4497	23	33	]	]	PUNCT
ejpam-4497	23	34	.	.	PUNCT
ejpam-4497	24	1	to	to	PART
ejpam-4497	24	2	study	study	VERB
ejpam-4497	24	3	topology	topology	NOUN
ejpam-4497	24	4	via	via	ADP
ejpam-4497	24	5	s	s	NOUN
ejpam-4497	24	6	-	-	PUNCT
ejpam-4497	24	7	set	set	ADJ
ejpam-4497	24	8	theory	theory	NOUN
ejpam-4497	24	9	,	,	PUNCT
ejpam-4497	24	10	çaǧman	çaǧman	PROPN
ejpam-4497	24	11	et	et	PROPN
ejpam-4497	24	12	al	al	PROPN
ejpam-4497	24	13	.	.	PUNCT
ejpam-4497	25	1	[	[	X
ejpam-4497	25	2	51	51	NUM
ejpam-4497	25	3	]	]	PUNCT
ejpam-4497	25	4	and	and	CCONJ
ejpam-4497	25	5	shabir	shabir	PROPN
ejpam-4497	25	6	and	and	CCONJ
ejpam-4497	25	7	naz	naz	PROPN
ejpam-4497	25	8	[	[	X
ejpam-4497	25	9	65	65	NUM
ejpam-4497	25	10	]	]	PUNCT
ejpam-4497	25	11	,	,	PUNCT
ejpam-4497	25	12	in	in	ADP
ejpam-4497	25	13	2011	2011	NUM
ejpam-4497	25	14	,	,	PUNCT
ejpam-4497	25	15	introduced	introduce	VERB
ejpam-4497	25	16	the	the	DET
ejpam-4497	25	17	concept	concept	NOUN
ejpam-4497	25	18	of	of	ADP
ejpam-4497	25	19	soft	soft	ADJ
ejpam-4497	25	20	topology(st	topology(st	NOUN
ejpam-4497	25	21	)	)	PUNCT
ejpam-4497	25	22	.	.	PUNCT
ejpam-4497	26	1	they	they	PRON
ejpam-4497	26	2	followed	follow	VERB
ejpam-4497	26	3	different	different	ADJ
ejpam-4497	26	4	techniques	technique	NOUN
ejpam-4497	26	5	for	for	ADP
ejpam-4497	26	6	studying	study	VERB
ejpam-4497	26	7	st	st	PROPN
ejpam-4497	26	8	.	.	PROPN
ejpam-4497	27	1	this	this	DET
ejpam-4497	27	2	article	article	NOUN
ejpam-4497	27	3	follows	follow	VERB
ejpam-4497	27	4	shabir	shabir	PROPN
ejpam-4497	27	5	and	and	CCONJ
ejpam-4497	27	6	naz	naz	PROPN
ejpam-4497	27	7	’	'	PUNCT
ejpam-4497	27	8	technique	technique	NOUN
ejpam-4497	27	9	which	which	PRON
ejpam-4497	27	10	is	be	AUX
ejpam-4497	27	11	defined	define	VERB
ejpam-4497	27	12	an	an	DET
ejpam-4497	27	13	st	st	NOUN
ejpam-4497	27	14	over	over	ADP
ejpam-4497	27	15	a	a	DET
ejpam-4497	27	16	fixed	fix	VERB
ejpam-4497	27	17	set	set	NOUN
ejpam-4497	27	18	of	of	ADP
ejpam-4497	27	19	universe	universe	NOUN
ejpam-4497	27	20	and	and	CCONJ
ejpam-4497	27	21	a	a	DET
ejpam-4497	27	22	fixed	fix	VERB
ejpam-4497	27	23	set	set	NOUN
ejpam-4497	27	24	of	of	ADP
ejpam-4497	27	25	parameters	parameter	NOUN
ejpam-4497	27	26	.	.	PUNCT
ejpam-4497	28	1	the	the	DET
ejpam-4497	28	2	basic	basic	ADJ
ejpam-4497	28	3	concepts	concept	NOUN
ejpam-4497	28	4	and	and	CCONJ
ejpam-4497	28	5	notions	notion	NOUN
ejpam-4497	28	6	of	of	ADP
ejpam-4497	28	7	classical	classical	ADJ
ejpam-4497	28	8	topology	topology	NOUN
ejpam-4497	28	9	have	have	AUX
ejpam-4497	28	10	been	be	AUX
ejpam-4497	28	11	studied	study	VERB
ejpam-4497	28	12	in	in	ADP
ejpam-4497	28	13	st	st	PROPN
ejpam-4497	28	14	such	such	ADJ
ejpam-4497	28	15	as	as	ADP
ejpam-4497	28	16	caliber	caliber	NOUN
ejpam-4497	28	17	and	and	CCONJ
ejpam-4497	28	18	chain	chain	NOUN
ejpam-4497	28	19	conditions	condition	NOUN
ejpam-4497	28	20	[	[	X
ejpam-4497	28	21	43	43	NUM
ejpam-4497	28	22	]	]	PUNCT
ejpam-4497	28	23	,	,	PUNCT
ejpam-4497	28	24	compactness	compactness	NOUN
ejpam-4497	28	25	[	[	X
ejpam-4497	28	26	2	2	NUM
ejpam-4497	28	27	,	,	PUNCT
ejpam-4497	28	28	26	26	NUM
ejpam-4497	28	29	,	,	PUNCT
ejpam-4497	28	30	28	28	NUM
ejpam-4497	28	31	,	,	PUNCT
ejpam-4497	28	32	29	29	NUM
ejpam-4497	28	33	,	,	PUNCT
ejpam-4497	28	34	40	40	NUM
ejpam-4497	28	35	,	,	PUNCT
ejpam-4497	28	36	49	49	NUM
ejpam-4497	28	37	]	]	PUNCT
ejpam-4497	28	38	,	,	PUNCT
ejpam-4497	29	1	local	local	ADJ
ejpam-4497	29	2	compactness	compactness	NOUN
ejpam-4497	29	3	[	[	X
ejpam-4497	29	4	47	47	NUM
ejpam-4497	29	5	]	]	PUNCT
ejpam-4497	29	6	separation	separation	NOUN
ejpam-4497	29	7	axioms	axiom	NOUN
ejpam-4497	29	8	[	[	X
ejpam-4497	29	9	18	18	NUM
ejpam-4497	29	10	,	,	PUNCT
ejpam-4497	29	11	21	21	NUM
ejpam-4497	29	12	,	,	PUNCT
ejpam-4497	29	13	22	22	NUM
ejpam-4497	29	14	,	,	PUNCT
ejpam-4497	29	15	42	42	NUM
ejpam-4497	29	16	,	,	PUNCT
ejpam-4497	29	17	45	45	NUM
ejpam-4497	29	18	,	,	PUNCT
ejpam-4497	29	19	52	52	NUM
ejpam-4497	29	20	]	]	PUNCT
ejpam-4497	29	21	,	,	PUNCT
ejpam-4497	29	22	fixed	fix	VERB
ejpam-4497	29	23	point	point	NOUN
ejpam-4497	29	24	theorem	theorem	VERB
ejpam-4497	29	25	[	[	X
ejpam-4497	29	26	7	7	NUM
ejpam-4497	29	27	,	,	PUNCT
ejpam-4497	29	28	19	19	NUM
ejpam-4497	29	29	]	]	PUNCT
ejpam-4497	29	30	,	,	PUNCT
ejpam-4497	29	31	connectedness	connectedness	NOUN
ejpam-4497	29	32	[	[	X
ejpam-4497	29	33	54	54	NUM
ejpam-4497	29	34	,	,	PUNCT
ejpam-4497	29	35	57	57	NUM
ejpam-4497	29	36	,	,	PUNCT
ejpam-4497	29	37	60	60	NUM
ejpam-4497	29	38	]	]	PUNCT
ejpam-4497	29	39	,	,	PUNCT
ejpam-4497	29	40	mappings	mapping	NOUN
ejpam-4497	29	41	[	[	X
ejpam-4497	29	42	20	20	NUM
ejpam-4497	29	43	,	,	PUNCT
ejpam-4497	29	44	25	25	NUM
ejpam-4497	29	45	,	,	PUNCT
ejpam-4497	29	46	30	30	NUM
ejpam-4497	29	47	,	,	PUNCT
ejpam-4497	29	48	58	58	NUM
ejpam-4497	29	49	]	]	PUNCT
ejpam-4497	29	50	,	,	PUNCT
ejpam-4497	29	51	bioperators	bioperator	NOUN
ejpam-4497	30	1	[	[	X
ejpam-4497	30	2	48	48	NUM
ejpam-4497	30	3	]	]	PUNCT
ejpam-4497	30	4	,	,	PUNCT
ejpam-4497	30	5	covering	cover	VERB
ejpam-4497	30	6	properties	property	NOUN
ejpam-4497	30	7	[	[	X
ejpam-4497	30	8	34	34	NUM
ejpam-4497	30	9	,	,	PUNCT
ejpam-4497	30	10	35	35	NUM
ejpam-4497	30	11	,	,	PUNCT
ejpam-4497	30	12	59	59	NUM
ejpam-4497	30	13	]	]	PUNCT
ejpam-4497	30	14	,	,	PUNCT
ejpam-4497	30	15	sum	sum	NOUN
ejpam-4497	30	16	of	of	ADP
ejpam-4497	30	17	topologies	topology	NOUN
ejpam-4497	30	18	[	[	X
ejpam-4497	30	19	31	31	NUM
ejpam-4497	30	20	,	,	PUNCT
ejpam-4497	30	21	36	36	NUM
ejpam-4497	30	22	]	]	PUNCT
ejpam-4497	30	23	and	and	CCONJ
ejpam-4497	30	24	generalized	generalize	VERB
ejpam-4497	30	25	open	open	ADJ
ejpam-4497	30	26	sets	set	NOUN
ejpam-4497	30	27	[	[	X
ejpam-4497	30	28	3	3	NUM
ejpam-4497	30	29	]	]	PUNCT
ejpam-4497	30	30	.	.	PUNCT
ejpam-4497	31	1	additionally	additionally	ADV
ejpam-4497	31	2	,	,	PUNCT
ejpam-4497	31	3	sts	st	NOUN
ejpam-4497	31	4	and	and	CCONJ
ejpam-4497	31	5	supra	supra	PROPN
ejpam-4497	31	6	sts	st	NOUN
ejpam-4497	31	7	were	be	AUX
ejpam-4497	31	8	discussed	discuss	VERB
ejpam-4497	31	9	in	in	ADP
ejpam-4497	31	10	ordered	order	VERB
ejpam-4497	31	11	settings	setting	NOUN
ejpam-4497	31	12	as	as	SCONJ
ejpam-4497	31	13	given	give	VERB
ejpam-4497	31	14	in	in	ADP
ejpam-4497	31	15	[	[	X
ejpam-4497	31	16	24	24	NUM
ejpam-4497	31	17	]	]	PUNCT
ejpam-4497	31	18	.	.	PUNCT
ejpam-4497	32	1	al	al	PROPN
ejpam-4497	32	2	-	-	PUNCT
ejpam-4497	32	3	shami	shami	PROPN
ejpam-4497	32	4	and	and	CCONJ
ejpam-4497	32	5	kočinac	kočinac	PROPN
ejpam-4497	32	6	[	[	X
ejpam-4497	32	7	33	33	NUM
ejpam-4497	32	8	]	]	PUNCT
ejpam-4497	32	9	elucidated	elucidate	VERB
ejpam-4497	32	10	the	the	DET
ejpam-4497	32	11	conditions	condition	NOUN
ejpam-4497	32	12	under	under	ADP
ejpam-4497	32	13	which	which	PRON
ejpam-4497	32	14	the	the	DET
ejpam-4497	32	15	soft	soft	ADJ
ejpam-4497	32	16	operators	operator	NOUN
ejpam-4497	32	17	and	and	CCONJ
ejpam-4497	32	18	classical	classical	ADJ
ejpam-4497	32	19	operators	operator	NOUN
ejpam-4497	32	20	of	of	ADP
ejpam-4497	32	21	interior	interior	ADJ
ejpam-4497	32	22	and	and	CCONJ
ejpam-4497	32	23	closure	closure	NOUN
ejpam-4497	32	24	are	be	AUX
ejpam-4497	32	25	interchangeable	interchangeable	ADJ
ejpam-4497	32	26	.	.	PUNCT
ejpam-4497	33	1	it	it	PRON
ejpam-4497	33	2	should	should	AUX
ejpam-4497	33	3	be	be	AUX
ejpam-4497	33	4	noted	note	VERB
ejpam-4497	33	5	that	that	SCONJ
ejpam-4497	33	6	some	some	DET
ejpam-4497	33	7	classical	classical	ADJ
ejpam-4497	33	8	topological	topological	ADJ
ejpam-4497	33	9	properties	property	NOUN
ejpam-4497	33	10	were	be	AUX
ejpam-4497	33	11	generalized	generalize	VERB
ejpam-4497	33	12	to	to	PART
ejpam-4497	33	13	sts	st	NOUN
ejpam-4497	33	14	without	without	ADP
ejpam-4497	33	15	consideration	consideration	NOUN
ejpam-4497	33	16	for	for	ADP
ejpam-4497	33	17	the	the	DET
ejpam-4497	33	18	divergences	divergence	NOUN
ejpam-4497	33	19	between	between	ADP
ejpam-4497	33	20	sts	st	NOUN
ejpam-4497	33	21	and	and	CCONJ
ejpam-4497	33	22	classical	classical	ADJ
ejpam-4497	33	23	topologies	topology	NOUN
ejpam-4497	33	24	,	,	PUNCT
ejpam-4497	33	25	which	which	PRON
ejpam-4497	33	26	causes	cause	VERB
ejpam-4497	33	27	some	some	DET
ejpam-4497	33	28	incorrect	incorrect	ADJ
ejpam-4497	33	29	forms	form	NOUN
ejpam-4497	33	30	of	of	ADP
ejpam-4497	33	31	some	some	DET
ejpam-4497	33	32	results	result	NOUN
ejpam-4497	33	33	;	;	PUNCT
ejpam-4497	33	34	so	so	CCONJ
ejpam-4497	33	35	some	some	DET
ejpam-4497	33	36	articles	article	NOUN
ejpam-4497	33	37	were	be	AUX
ejpam-4497	33	38	conducted	conduct	VERB
ejpam-4497	33	39	to	to	PART
ejpam-4497	33	40	put	put	VERB
ejpam-4497	33	41	forward	forward	ADP
ejpam-4497	33	42	the	the	DET
ejpam-4497	33	43	correct	correct	ADJ
ejpam-4497	33	44	frame	frame	NOUN
ejpam-4497	33	45	of	of	ADP
ejpam-4497	33	46	these	these	DET
ejpam-4497	33	47	results	result	NOUN
ejpam-4497	33	48	via	via	ADP
ejpam-4497	33	49	soft	soft	ADJ
ejpam-4497	33	50	structures	structure	NOUN
ejpam-4497	33	51	;	;	PUNCT
ejpam-4497	33	52	see	see	VERB
ejpam-4497	33	53	[	[	X
ejpam-4497	33	54	4–6	4–6	X
ejpam-4497	33	55	]	]	X
ejpam-4497	33	56	.	.	PUNCT
ejpam-4497	34	1	in	in	ADP
ejpam-4497	34	2	2021	2021	NUM
ejpam-4497	34	3	,	,	PUNCT
ejpam-4497	34	4	al	al	PROPN
ejpam-4497	34	5	-	-	PUNCT
ejpam-4497	34	6	shami	shami	PROPN
ejpam-4497	34	7	[	[	X
ejpam-4497	34	8	13	13	NUM
ejpam-4497	34	9	]	]	PUNCT
ejpam-4497	34	10	familiarized	familiarize	VERB
ejpam-4497	34	11	the	the	DET
ejpam-4497	34	12	structure	structure	NOUN
ejpam-4497	34	13	of	of	ADP
ejpam-4497	34	14	infra	infra	NOUN
ejpam-4497	34	15	soft	soft	ADJ
ejpam-4497	34	16	topologies(ists	topologies(ist	NOUN
ejpam-4497	34	17	)	)	PUNCT
ejpam-4497	35	1	[	[	X
ejpam-4497	35	2	13	13	NUM
ejpam-4497	35	3	]	]	PUNCT
ejpam-4497	35	4	and	and	CCONJ
ejpam-4497	35	5	showed	show	VERB
ejpam-4497	35	6	the	the	DET
ejpam-4497	35	7	motivations	motivation	NOUN
ejpam-4497	35	8	for	for	ADP
ejpam-4497	35	9	studying	study	VERB
ejpam-4497	35	10	this	this	DET
ejpam-4497	35	11	structure	structure	NOUN
ejpam-4497	35	12	.	.	PUNCT
ejpam-4497	36	1	he	he	PRON
ejpam-4497	36	2	with	with	ADP
ejpam-4497	36	3	his	his	PRON
ejpam-4497	36	4	coauthors	coauthor	NOUN
ejpam-4497	36	5	continued	continue	VERB
ejpam-4497	36	6	investigating	investigate	VERB
ejpam-4497	36	7	several	several	ADJ
ejpam-4497	36	8	topological	topological	ADJ
ejpam-4497	36	9	concepts	concept	NOUN
ejpam-4497	36	10	and	and	CCONJ
ejpam-4497	36	11	properties	property	NOUN
ejpam-4497	36	12	via	via	ADP
ejpam-4497	36	13	this	this	DET
ejpam-4497	36	14	structure	structure	NOUN
ejpam-4497	36	15	such	such	ADJ
ejpam-4497	36	16	as	as	ADP
ejpam-4497	36	17	compactness	compactness	NOUN
ejpam-4497	36	18	[	[	X
ejpam-4497	36	19	12	12	NUM
ejpam-4497	36	20	]	]	PUNCT
ejpam-4497	36	21	,	,	PUNCT
ejpam-4497	36	22	homeomorphisms	homeomorphism	VERB
ejpam-4497	37	1	[	[	X
ejpam-4497	37	2	10	10	NUM
ejpam-4497	37	3	]	]	PUNCT
ejpam-4497	37	4	,	,	PUNCT
ejpam-4497	37	5	connectedness	connectedness	NOUN
ejpam-4497	37	6	[	[	X
ejpam-4497	37	7	17	17	NUM
ejpam-4497	37	8	]	]	PUNCT
ejpam-4497	37	9	,	,	PUNCT
ejpam-4497	37	10	separation	separation	NOUN
ejpam-4497	37	11	axioms	axiom	VERB
ejpam-4497	37	12	[	[	X
ejpam-4497	37	13	37	37	NUM
ejpam-4497	37	14	,	,	PUNCT
ejpam-4497	37	15	39	39	NUM
ejpam-4497	37	16	]	]	PUNCT
ejpam-4497	37	17	,	,	PUNCT
ejpam-4497	37	18	infra	infra	NOUN
ejpam-4497	37	19	soft	soft	ADJ
ejpam-4497	37	20	semi	semi	ADJ
ejpam-4497	37	21	-	-	ADJ
ejpam-4497	37	22	open	open	ADJ
ejpam-4497	37	23	(	(	PUNCT
ejpam-4497	37	24	is	be	AUX
ejpam-4497	37	25	-	-	PUNCT
ejpam-4497	37	26	semi	semi	ADV
ejpam-4497	37	27	-	-	ADJ
ejpam-4497	37	28	open	open	ADJ
ejpam-4497	37	29	)	)	PUNCT
ejpam-4497	38	1	[	[	X
ejpam-4497	38	2	23	23	NUM
ejpam-4497	38	3	]	]	PUNCT
ejpam-4497	38	4	and	and	CCONJ
ejpam-4497	38	5	infra	infra	NOUN
ejpam-4497	38	6	soft	soft	ADJ
ejpam-4497	38	7	pre	pre	ADJ
ejpam-4497	38	8	-	-	ADJ
ejpam-4497	38	9	open	open	ADJ
ejpam-4497	38	10	(	(	PUNCT
ejpam-4497	38	11	is	be	AUX
ejpam-4497	38	12	-	-	PUNCT
ejpam-4497	38	13	pre	pre	ADJ
ejpam-4497	38	14	-	-	ADJ
ejpam-4497	38	15	open	open	ADJ
ejpam-4497	38	16	)	)	PUNCT
ejpam-4497	38	17	sets	set	VERB
ejpam-4497	38	18	[	[	X
ejpam-4497	38	19	41	41	NUM
ejpam-4497	38	20	]	]	PUNCT
ejpam-4497	38	21	.	.	PUNCT
ejpam-4497	39	1	in	in	ADP
ejpam-4497	39	2	this	this	DET
ejpam-4497	39	3	article	article	NOUN
ejpam-4497	39	4	,	,	PUNCT
ejpam-4497	39	5	we	we	PRON
ejpam-4497	39	6	display	display	VERB
ejpam-4497	39	7	the	the	DET
ejpam-4497	39	8	notion	notion	NOUN
ejpam-4497	39	9	of	of	ADP
ejpam-4497	39	10	soft	soft	ADJ
ejpam-4497	39	11	b	b	NOUN
ejpam-4497	39	12	-	-	PUNCT
ejpam-4497	39	13	open	open	ADJ
ejpam-4497	39	14	sets	set	NOUN
ejpam-4497	39	15	(	(	PUNCT
ejpam-4497	39	16	s	s	NOUN
ejpam-4497	39	17	-	-	PUNCT
ejpam-4497	39	18	b	b	NOUN
ejpam-4497	39	19	-	-	PUNCT
ejpam-4497	39	20	open	open	ADJ
ejpam-4497	39	21	sets	set	NOUN
ejpam-4497	39	22	)	)	PUNCT
ejpam-4497	39	23	and	and	CCONJ
ejpam-4497	39	24	applied	apply	VERB
ejpam-4497	39	25	to	to	PART
ejpam-4497	39	26	initiate	initiate	VERB
ejpam-4497	39	27	new	new	ADJ
ejpam-4497	39	28	operators	operator	NOUN
ejpam-4497	39	29	and	and	CCONJ
ejpam-4497	39	30	mappings	mapping	NOUN
ejpam-4497	39	31	via	via	ADP
ejpam-4497	39	32	infra	infra	NOUN
ejpam-4497	39	33	soft	soft	ADJ
ejpam-4497	39	34	structures	structure	NOUN
ejpam-4497	39	35	.	.	PUNCT
ejpam-4497	40	1	the	the	DET
ejpam-4497	40	2	structure	structure	NOUN
ejpam-4497	40	3	of	of	ADP
ejpam-4497	40	4	this	this	DET
ejpam-4497	40	5	article	article	NOUN
ejpam-4497	40	6	is	be	AUX
ejpam-4497	40	7	designed	design	VERB
ejpam-4497	40	8	as	as	SCONJ
ejpam-4497	40	9	follows	follow	VERB
ejpam-4497	40	10	.	.	PUNCT
ejpam-4497	41	1	in	in	ADP
ejpam-4497	41	2	sect	sect	NOUN
ejpam-4497	41	3	.	.	PUNCT
ejpam-4497	42	1	2	2	NUM
ejpam-4497	42	2	,	,	PUNCT
ejpam-4497	42	3	we	we	PRON
ejpam-4497	42	4	recall	recall	VERB
ejpam-4497	42	5	the	the	DET
ejpam-4497	42	6	main	main	ADJ
ejpam-4497	42	7	ideas	idea	NOUN
ejpam-4497	42	8	and	and	CCONJ
ejpam-4497	42	9	findings	finding	NOUN
ejpam-4497	42	10	that	that	PRON
ejpam-4497	42	11	make	make	VERB
ejpam-4497	42	12	this	this	DET
ejpam-4497	42	13	work	work	NOUN
ejpam-4497	42	14	self	self	NOUN
ejpam-4497	42	15	-	-	PUNCT
ejpam-4497	42	16	contained	contain	VERB
ejpam-4497	42	17	.	.	PUNCT
ejpam-4497	43	1	in	in	ADP
ejpam-4497	43	2	sect	sect	NOUN
ejpam-4497	43	3	.	.	PUNCT
ejpam-4497	44	1	3	3	X
ejpam-4497	44	2	,	,	PUNCT
ejpam-4497	44	3	we	we	PRON
ejpam-4497	44	4	introduce	introduce	VERB
ejpam-4497	44	5	the	the	DET
ejpam-4497	44	6	notion	notion	NOUN
ejpam-4497	44	7	of	of	ADP
ejpam-4497	44	8	infra	infra	NOUN
ejpam-4497	44	9	soft	soft	ADJ
ejpam-4497	44	10	b	b	NOUN
ejpam-4497	44	11	-	-	PUNCT
ejpam-4497	44	12	open	open	ADJ
ejpam-4497	44	13	sets(is	sets(is	PROPN
ejpam-4497	44	14	-	-	PUNCT
ejpam-4497	44	15	b	b	NOUN
ejpam-4497	44	16	-	-	PUNCT
ejpam-4497	44	17	open	open	ADJ
ejpam-4497	44	18	sets	set	NOUN
ejpam-4497	44	19	)	)	PUNCT
ejpam-4497	44	20	and	and	CCONJ
ejpam-4497	44	21	establish	establish	VERB
ejpam-4497	44	22	its	its	PRON
ejpam-4497	44	23	master	master	NOUN
ejpam-4497	44	24	characterizations	characterization	NOUN
ejpam-4497	44	25	.	.	PUNCT
ejpam-4497	45	1	in	in	ADP
ejpam-4497	45	2	sect	sect	NOUN
ejpam-4497	45	3	.	.	PUNCT
ejpam-4497	46	1	4	4	X
ejpam-4497	46	2	,	,	PUNCT
ejpam-4497	46	3	we	we	PRON
ejpam-4497	46	4	define	define	VERB
ejpam-4497	46	5	new	new	ADJ
ejpam-4497	46	6	operators	operator	NOUN
ejpam-4497	46	7	and	and	CCONJ
ejpam-4497	46	8	discuss	discuss	VERB
ejpam-4497	46	9	their	their	PRON
ejpam-4497	46	10	main	main	ADJ
ejpam-4497	46	11	properties	property	NOUN
ejpam-4497	46	12	.	.	PUNCT
ejpam-4497	47	1	in	in	ADP
ejpam-4497	47	2	sect	sect	NOUN
ejpam-4497	47	3	.	.	PUNCT
ejpam-4497	48	1	5	5	NUM
ejpam-4497	48	2	,	,	PUNCT
ejpam-4497	48	3	we	we	PRON
ejpam-4497	48	4	explore	explore	VERB
ejpam-4497	48	5	novel	novel	ADJ
ejpam-4497	48	6	kinds	kind	NOUN
ejpam-4497	48	7	of	of	ADP
ejpam-4497	48	8	mappings	mapping	NOUN
ejpam-4497	48	9	and	and	CCONJ
ejpam-4497	48	10	demonstrated	demonstrate	VERB
ejpam-4497	48	11	their	their	PRON
ejpam-4497	48	12	features	feature	NOUN
ejpam-4497	48	13	.	.	PUNCT
ejpam-4497	49	1	ultimately	ultimately	ADV
ejpam-4497	49	2	,	,	PUNCT
ejpam-4497	49	3	we	we	PRON
ejpam-4497	49	4	give	give	VERB
ejpam-4497	49	5	the	the	DET
ejpam-4497	49	6	main	main	ADJ
ejpam-4497	49	7	contributions	contribution	NOUN
ejpam-4497	49	8	of	of	ADP
ejpam-4497	49	9	the	the	DET
ejpam-4497	49	10	article	article	NOUN
ejpam-4497	49	11	and	and	CCONJ
ejpam-4497	49	12	propose	propose	VERB
ejpam-4497	49	13	some	some	DET
ejpam-4497	49	14	future	future	ADJ
ejpam-4497	49	15	works	work	NOUN
ejpam-4497	49	16	.	.	PUNCT
ejpam-4497	50	1	2	2	X
ejpam-4497	50	2	.	.	NUM
ejpam-4497	50	3	preliminaries	preliminary	NOUN
ejpam-4497	50	4	2.1	2.1	NUM
ejpam-4497	50	5	.	.	PUNCT
ejpam-4497	51	1	soft	soft	ADJ
ejpam-4497	51	2	set	set	ADJ
ejpam-4497	51	3	theory	theory	NOUN
ejpam-4497	51	4	definition	definition	NOUN
ejpam-4497	51	5	1	1	NUM
ejpam-4497	51	6	.	.	PUNCT
ejpam-4497	52	1	[	[	X
ejpam-4497	52	2	62	62	NUM
ejpam-4497	52	3	]	]	PUNCT
ejpam-4497	52	4	a	a	DET
ejpam-4497	52	5	mapping	mapping	NOUN
ejpam-4497	52	6	h	h	NOUN
ejpam-4497	52	7	from	from	ADP
ejpam-4497	52	8	a	a	DET
ejpam-4497	52	9	set	set	NOUN
ejpam-4497	52	10	of	of	ADP
ejpam-4497	52	11	parameters	parameter	NOUN
ejpam-4497	52	12	o	o	INTJ
ejpam-4497	52	13	into	into	ADP
ejpam-4497	52	14	2x	2x	NUM
ejpam-4497	52	15	,	,	PUNCT
ejpam-4497	52	16	where	where	SCONJ
ejpam-4497	52	17	2x	2x	NUM
ejpam-4497	52	18	is	be	AUX
ejpam-4497	52	19	the	the	DET
ejpam-4497	52	20	power	power	NOUN
ejpam-4497	52	21	set	set	NOUN
ejpam-4497	52	22	of	of	ADP
ejpam-4497	52	23	x	x	PRON
ejpam-4497	52	24	,	,	PUNCT
ejpam-4497	52	25	is	be	AUX
ejpam-4497	52	26	called	call	VERB
ejpam-4497	52	27	an	an	DET
ejpam-4497	52	28	s	s	NOUN
ejpam-4497	52	29	-	-	PUNCT
ejpam-4497	52	30	set	set	NOUN
ejpam-4497	52	31	denoted	denote	VERB
ejpam-4497	52	32	by	by	ADP
ejpam-4497	52	33	(	(	PUNCT
ejpam-4497	52	34	h	h	NOUN
ejpam-4497	52	35	,	,	PUNCT
ejpam-4497	52	36	o	o	NOUN
ejpam-4497	52	37	)	)	PUNCT
ejpam-4497	52	38	,	,	PUNCT
ejpam-4497	52	39	and	and	CCONJ
ejpam-4497	52	40	it	it	PRON
ejpam-4497	52	41	can	can	AUX
ejpam-4497	52	42	written	write	VERB
ejpam-4497	52	43	as	as	SCONJ
ejpam-4497	52	44	follows	follow	VERB
ejpam-4497	52	45	(	(	PUNCT
ejpam-4497	52	46	h	h	NOUN
ejpam-4497	52	47	,	,	PUNCT
ejpam-4497	52	48	o	o	NOUN
ejpam-4497	52	49	)	)	PUNCT
ejpam-4497	52	50	=	=	SYM
ejpam-4497	52	51	{	{	PUNCT
ejpam-4497	52	52	(	(	PUNCT
ejpam-4497	52	53	o	o	NOUN
ejpam-4497	52	54	,	,	PUNCT
ejpam-4497	52	55	h(o	h(o	PROPN
ejpam-4497	52	56	)	)	PUNCT
ejpam-4497	52	57	)	)	PUNCT
ejpam-4497	52	58	:	:	PUNCT
ejpam-4497	53	1	o	o	X
ejpam-4497	53	2	∈	∈	NOUN
ejpam-4497	53	3	o	o	X
ejpam-4497	53	4	and	and	CCONJ
ejpam-4497	53	5	h(o	h(o	PROPN
ejpam-4497	53	6	)	)	PUNCT
ejpam-4497	53	7	∈	∈	PROPN
ejpam-4497	53	8	2x	2x	NUM
ejpam-4497	53	9	}	}	PUNCT
ejpam-4497	53	10	.	.	PUNCT
ejpam-4497	54	1	c(xo	c(xo	NOUN
ejpam-4497	54	2	)	)	PUNCT
ejpam-4497	54	3	refers	refer	VERB
ejpam-4497	54	4	to	to	ADP
ejpam-4497	54	5	the	the	DET
ejpam-4497	54	6	class	class	NOUN
ejpam-4497	54	7	of	of	ADP
ejpam-4497	54	8	all	all	DET
ejpam-4497	54	9	s	s	NOUN
ejpam-4497	54	10	-	-	NOUN
ejpam-4497	54	11	sets	set	NOUN
ejpam-4497	54	12	over	over	ADP
ejpam-4497	54	13	x	x	PUNCT
ejpam-4497	54	14	with	with	ADP
ejpam-4497	54	15	the	the	DET
ejpam-4497	54	16	set	set	NOUN
ejpam-4497	54	17	of	of	ADP
ejpam-4497	54	18	parameters	parameter	NOUN
ejpam-4497	55	1	o.	o.	PROPN
ejpam-4497	55	2	t.m	t.m	PROPN
ejpam-4497	55	3	.	.	PROPN
ejpam-4497	55	4	al	al	PROPN
ejpam-4497	55	5	-	-	PUNCT
ejpam-4497	55	6	shami	shami	PROPN
ejpam-4497	55	7	et	et	PROPN
ejpam-4497	55	8	al	al	PROPN
ejpam-4497	55	9	.	.	PUNCT
ejpam-4497	55	10	/	/	SYM
ejpam-4497	55	11	eur	eur	PROPN
ejpam-4497	55	12	.	.	PUNCT
ejpam-4497	56	1	j.	j.	PROPN
ejpam-4497	56	2	pure	pure	PROPN
ejpam-4497	56	3	appl	appl	PROPN
ejpam-4497	56	4	.	.	PROPN
ejpam-4497	56	5	math	math	PROPN
ejpam-4497	56	6	,	,	PUNCT
ejpam-4497	56	7	15	15	NUM
ejpam-4497	56	8	(	(	PUNCT
ejpam-4497	56	9	4	4	NUM
ejpam-4497	56	10	)	)	PUNCT
ejpam-4497	56	11	(	(	PUNCT
ejpam-4497	56	12	2022	2022	NUM
ejpam-4497	56	13	)	)	PUNCT
ejpam-4497	56	14	,	,	PUNCT
ejpam-4497	56	15	1455	1455	NUM
ejpam-4497	56	16	-	-	SYM
ejpam-4497	56	17	1471	1471	NUM
ejpam-4497	56	18	1457	1457	NUM
ejpam-4497	56	19	definition	definition	NOUN
ejpam-4497	56	20	2	2	NUM
ejpam-4497	56	21	.	.	PUNCT
ejpam-4497	57	1	[	[	X
ejpam-4497	57	2	44	44	NUM
ejpam-4497	57	3	]	]	PUNCT
ejpam-4497	57	4	a	a	DET
ejpam-4497	57	5	complement	complement	NOUN
ejpam-4497	57	6	of	of	ADP
ejpam-4497	57	7	an	an	DET
ejpam-4497	57	8	s	s	NOUN
ejpam-4497	57	9	-	-	PUNCT
ejpam-4497	57	10	set	set	VERB
ejpam-4497	57	11	(	(	PUNCT
ejpam-4497	57	12	h	h	NOUN
ejpam-4497	57	13	,	,	PUNCT
ejpam-4497	57	14	o	o	NOUN
ejpam-4497	57	15	)	)	PUNCT
ejpam-4497	57	16	,	,	PUNCT
ejpam-4497	57	17	denoted	denote	VERB
ejpam-4497	57	18	by	by	ADP
ejpam-4497	57	19	(	(	PUNCT
ejpam-4497	57	20	hc	hc	PROPN
ejpam-4497	57	21	,	,	PUNCT
ejpam-4497	57	22	o	o	NOUN
ejpam-4497	57	23	)	)	PUNCT
ejpam-4497	57	24	,	,	PUNCT
ejpam-4497	57	25	provided	provide	VERB
ejpam-4497	57	26	that	that	SCONJ
ejpam-4497	57	27	a	a	DET
ejpam-4497	57	28	map	map	NOUN
ejpam-4497	57	29	hc	hc	INTJ
ejpam-4497	57	30	:	:	PUNCT
ejpam-4497	57	31	o	o	X
ejpam-4497	57	32	→	→	PUNCT
ejpam-4497	57	33	2x	2x	NUM
ejpam-4497	57	34	is	be	AUX
ejpam-4497	57	35	given	give	VERB
ejpam-4497	57	36	by	by	ADP
ejpam-4497	57	37	hc(o	hc(o	NOUN
ejpam-4497	57	38	)	)	PUNCT
ejpam-4497	57	39	=	=	PUNCT
ejpam-4497	58	1	x	x	SYM
ejpam-4497	58	2	\	\	X
ejpam-4497	58	3	h(o	h(o	PROPN
ejpam-4497	58	4	)	)	PUNCT
ejpam-4497	58	5	for	for	ADP
ejpam-4497	58	6	each	each	DET
ejpam-4497	58	7	o	o	NOUN
ejpam-4497	58	8	∈	∈	PROPN
ejpam-4497	58	9	o.	o.	NOUN
ejpam-4497	58	10	definition	definition	NOUN
ejpam-4497	58	11	3	3	NUM
ejpam-4497	58	12	.	.	PUNCT
ejpam-4497	59	1	[	[	X
ejpam-4497	59	2	61	61	NUM
ejpam-4497	59	3	]	]	X
ejpam-4497	59	4	if	if	SCONJ
ejpam-4497	59	5	h(o	h(o	PROPN
ejpam-4497	59	6	)	)	PUNCT
ejpam-4497	60	1	=	=	NOUN
ejpam-4497	60	2	∅	∅	NOUN
ejpam-4497	60	3	(	(	PUNCT
ejpam-4497	60	4	resp	resp	NOUN
ejpam-4497	60	5	.	.	PUNCT
ejpam-4497	60	6	,	,	PUNCT
ejpam-4497	60	7	h(o	h(o	PROPN
ejpam-4497	60	8	)	)	PUNCT
ejpam-4497	60	9	=	=	SYM
ejpam-4497	61	1	x	x	X
ejpam-4497	61	2	)	)	PUNCT
ejpam-4497	61	3	for	for	ADP
ejpam-4497	61	4	all	all	DET
ejpam-4497	61	5	o	o	NOUN
ejpam-4497	61	6	∈	∈	X
ejpam-4497	61	7	o	o	NOUN
ejpam-4497	61	8	,	,	PUNCT
ejpam-4497	61	9	then	then	ADV
ejpam-4497	61	10	(	(	PUNCT
ejpam-4497	61	11	h	h	NOUN
ejpam-4497	61	12	,	,	PUNCT
ejpam-4497	61	13	o	o	NOUN
ejpam-4497	61	14	)	)	PUNCT
ejpam-4497	61	15	is	be	AUX
ejpam-4497	61	16	called	call	VERB
ejpam-4497	61	17	a	a	DET
ejpam-4497	61	18	null	null	ADJ
ejpam-4497	61	19	s	s	NOUN
ejpam-4497	61	20	-	-	PUNCT
ejpam-4497	61	21	set	set	ADJ
ejpam-4497	61	22	(	(	PUNCT
ejpam-4497	61	23	resp	resp	NOUN
ejpam-4497	61	24	.	.	PROPN
ejpam-4497	62	1	,	,	PUNCT
ejpam-4497	62	2	an	an	DET
ejpam-4497	62	3	absolute	absolute	ADJ
ejpam-4497	62	4	)	)	PUNCT
ejpam-4497	62	5	s	s	NOUN
ejpam-4497	62	6	-	-	PUNCT
ejpam-4497	62	7	set	set	VERB
ejpam-4497	62	8	over	over	ADP
ejpam-4497	62	9	x.	x.	PROPN
ejpam-4497	62	10	φ	φ	PROPN
ejpam-4497	62	11	and	and	CCONJ
ejpam-4497	62	12	x̃	x̃	PROPN
ejpam-4497	62	13	are	be	AUX
ejpam-4497	62	14	the	the	DET
ejpam-4497	62	15	symbols	symbol	NOUN
ejpam-4497	62	16	of	of	ADP
ejpam-4497	62	17	null	null	NOUN
ejpam-4497	62	18	s	s	PART
ejpam-4497	62	19	-	-	PUNCT
ejpam-4497	62	20	set	set	VERB
ejpam-4497	62	21	and	and	CCONJ
ejpam-4497	62	22	absolute	absolute	ADJ
ejpam-4497	62	23	s	s	NOUN
ejpam-4497	62	24	-	-	PUNCT
ejpam-4497	62	25	set	set	ADJ
ejpam-4497	62	26	,	,	PUNCT
ejpam-4497	62	27	respectively	respectively	ADV
ejpam-4497	62	28	.	.	PUNCT
ejpam-4497	63	1	definition	definition	NOUN
ejpam-4497	63	2	4	4	NUM
ejpam-4497	63	3	.	.	PUNCT
ejpam-4497	64	1	[	[	X
ejpam-4497	64	2	63	63	NUM
ejpam-4497	64	3	]	]	PUNCT
ejpam-4497	64	4	(	(	PUNCT
ejpam-4497	64	5	h	h	NOUN
ejpam-4497	64	6	,	,	PUNCT
ejpam-4497	64	7	o	o	NOUN
ejpam-4497	64	8	)	)	PUNCT
ejpam-4497	64	9	is	be	AUX
ejpam-4497	64	10	called	call	VERB
ejpam-4497	64	11	a	a	DET
ejpam-4497	64	12	soft	soft	ADJ
ejpam-4497	64	13	point	point	NOUN
ejpam-4497	64	14	(	(	PUNCT
ejpam-4497	64	15	s	s	NOUN
ejpam-4497	64	16	-	-	NOUN
ejpam-4497	64	17	point	point	NOUN
ejpam-4497	64	18	)	)	PUNCT
ejpam-4497	64	19	on	on	ADP
ejpam-4497	64	20	x	x	SYM
ejpam-4497	64	21	if	if	SCONJ
ejpam-4497	64	22	there	there	PRON
ejpam-4497	64	23	is	be	VERB
ejpam-4497	64	24	o	o	PROPN
ejpam-4497	64	25	∈	∈	NOUN
ejpam-4497	64	26	o	o	NOUN
ejpam-4497	64	27	such	such	ADJ
ejpam-4497	64	28	that	that	SCONJ
ejpam-4497	64	29	h(o	h(o	PROPN
ejpam-4497	64	30	)	)	PUNCT
ejpam-4497	65	1	=	=	PUNCT
ejpam-4497	65	2	x	x	PUNCT
ejpam-4497	65	3	∈	∈	PROPN
ejpam-4497	65	4	x	x	X
ejpam-4497	65	5	and	and	CCONJ
ejpam-4497	65	6	h(o′	h(o′	NUM
ejpam-4497	65	7	)	)	PUNCT
ejpam-4497	66	1	=	=	NOUN
ejpam-4497	66	2	∅	∅	NOUN
ejpam-4497	66	3	for	for	ADP
ejpam-4497	66	4	each	each	DET
ejpam-4497	66	5	o′	o′	NUM
ejpam-4497	66	6	̸=	̸=	PROPN
ejpam-4497	66	7	o.	o.	VERB
ejpam-4497	66	8	the	the	DET
ejpam-4497	66	9	symbol	symbol	NOUN
ejpam-4497	66	10	of	of	ADP
ejpam-4497	66	11	an	an	DET
ejpam-4497	66	12	s	s	NOUN
ejpam-4497	66	13	-	-	PUNCT
ejpam-4497	66	14	point	point	NOUN
ejpam-4497	66	15	will	will	AUX
ejpam-4497	66	16	be	be	AUX
ejpam-4497	66	17	δxo	δxo	NOUN
ejpam-4497	66	18	.	.	PUNCT
ejpam-4497	67	1	definition	definition	NOUN
ejpam-4497	67	2	5	5	NUM
ejpam-4497	67	3	.	.	PUNCT
ejpam-4497	68	1	[	[	X
ejpam-4497	68	2	44	44	NUM
ejpam-4497	68	3	]	]	PUNCT
ejpam-4497	68	4	the	the	DET
ejpam-4497	68	5	intersection	intersection	NOUN
ejpam-4497	68	6	of	of	ADP
ejpam-4497	68	7	s	s	NOUN
ejpam-4497	68	8	-	-	PUNCT
ejpam-4497	68	9	sets	set	NOUN
ejpam-4497	68	10	(	(	PUNCT
ejpam-4497	68	11	h	h	NOUN
ejpam-4497	68	12	,	,	PUNCT
ejpam-4497	68	13	o	o	NOUN
ejpam-4497	68	14	)	)	PUNCT
ejpam-4497	68	15	and	and	CCONJ
ejpam-4497	68	16	(	(	PUNCT
ejpam-4497	68	17	f	f	PROPN
ejpam-4497	68	18	,	,	PUNCT
ejpam-4497	68	19	∆	∆	PROPN
ejpam-4497	68	20	)	)	PUNCT
ejpam-4497	68	21	on	on	ADP
ejpam-4497	68	22	x	x	SYM
ejpam-4497	68	23	,	,	PUNCT
ejpam-4497	68	24	symbolized	symbolize	VERB
ejpam-4497	68	25	by	by	ADP
ejpam-4497	68	26	(	(	PUNCT
ejpam-4497	68	27	h	h	NOUN
ejpam-4497	68	28	,	,	PUNCT
ejpam-4497	68	29	o)∩̃(f	o)∩̃(f	ADV
ejpam-4497	68	30	,	,	PUNCT
ejpam-4497	68	31	∆	∆	PROPN
ejpam-4497	68	32	)	)	PUNCT
ejpam-4497	68	33	,	,	PUNCT
ejpam-4497	68	34	is	be	AUX
ejpam-4497	68	35	an	an	DET
ejpam-4497	68	36	s	s	NOUN
ejpam-4497	68	37	-	-	PUNCT
ejpam-4497	68	38	set	set	ADJ
ejpam-4497	68	39	(	(	PUNCT
ejpam-4497	68	40	g	g	PROPN
ejpam-4497	68	41	,	,	PUNCT
ejpam-4497	68	42	t	t	PROPN
ejpam-4497	68	43	)	)	PUNCT
ejpam-4497	68	44	,	,	PUNCT
ejpam-4497	68	45	where	where	SCONJ
ejpam-4497	68	46	t	t	NOUN
ejpam-4497	68	47	=	=	PUNCT
ejpam-4497	68	48	o	o	PROPN
ejpam-4497	68	49	∩∆	∩∆	X
ejpam-4497	68	50	̸=	̸=	PROPN
ejpam-4497	68	51	∅	∅	NOUN
ejpam-4497	68	52	,	,	PUNCT
ejpam-4497	68	53	and	and	CCONJ
ejpam-4497	68	54	a	a	DET
ejpam-4497	68	55	map	map	NOUN
ejpam-4497	68	56	g	g	NOUN
ejpam-4497	68	57	:	:	PUNCT
ejpam-4497	68	58	t	t	PROPN
ejpam-4497	68	59	→	→	SYM
ejpam-4497	68	60	2x	2x	NUM
ejpam-4497	68	61	is	be	AUX
ejpam-4497	68	62	given	give	VERB
ejpam-4497	68	63	by	by	ADP
ejpam-4497	68	64	g(o	g(o	PROPN
ejpam-4497	68	65	)	)	PUNCT
ejpam-4497	68	66	=	=	SYM
ejpam-4497	69	1	h(o	h(o	X
ejpam-4497	69	2	)	)	PUNCT
ejpam-4497	69	3	∩	∩	NOUN
ejpam-4497	69	4	f(o	f(o	NOUN
ejpam-4497	69	5	)	)	PUNCT
ejpam-4497	69	6	for	for	ADP
ejpam-4497	69	7	each	each	DET
ejpam-4497	69	8	o	o	NOUN
ejpam-4497	69	9	∈	∈	PROPN
ejpam-4497	69	10	t	t	PROPN
ejpam-4497	69	11	.	.	PUNCT
ejpam-4497	70	1	definition	definition	NOUN
ejpam-4497	70	2	6	6	NUM
ejpam-4497	70	3	.	.	PUNCT
ejpam-4497	71	1	[	[	X
ejpam-4497	71	2	61	61	NUM
ejpam-4497	71	3	]	]	PUNCT
ejpam-4497	71	4	the	the	DET
ejpam-4497	71	5	union	union	NOUN
ejpam-4497	71	6	of	of	ADP
ejpam-4497	71	7	s	s	NOUN
ejpam-4497	71	8	-	-	PUNCT
ejpam-4497	71	9	sets	set	NOUN
ejpam-4497	71	10	(	(	PUNCT
ejpam-4497	71	11	h	h	NOUN
ejpam-4497	71	12	,	,	PUNCT
ejpam-4497	71	13	o	o	NOUN
ejpam-4497	71	14	)	)	PUNCT
ejpam-4497	71	15	and	and	CCONJ
ejpam-4497	71	16	(	(	PUNCT
ejpam-4497	71	17	f	f	PROPN
ejpam-4497	71	18	,	,	PUNCT
ejpam-4497	71	19	∆	∆	PROPN
ejpam-4497	71	20	)	)	PUNCT
ejpam-4497	71	21	on	on	ADP
ejpam-4497	71	22	x	x	SYM
ejpam-4497	71	23	,	,	PUNCT
ejpam-4497	71	24	symbolized	symbolize	VERB
ejpam-4497	71	25	by	by	ADP
ejpam-4497	71	26	(	(	PUNCT
ejpam-4497	71	27	h	h	NOUN
ejpam-4497	71	28	,	,	PUNCT
ejpam-4497	71	29	o)∪̃(f	o)∪̃(f	PRON
ejpam-4497	71	30	,	,	PUNCT
ejpam-4497	71	31	∆	∆	PROPN
ejpam-4497	71	32	)	)	PUNCT
ejpam-4497	71	33	,	,	PUNCT
ejpam-4497	71	34	is	be	AUX
ejpam-4497	71	35	an	an	DET
ejpam-4497	71	36	s	s	NOUN
ejpam-4497	71	37	-	-	PUNCT
ejpam-4497	71	38	set	set	ADJ
ejpam-4497	71	39	(	(	PUNCT
ejpam-4497	71	40	g	g	PROPN
ejpam-4497	71	41	,	,	PUNCT
ejpam-4497	71	42	t	t	PROPN
ejpam-4497	71	43	)	)	PUNCT
ejpam-4497	71	44	,	,	PUNCT
ejpam-4497	71	45	where	where	SCONJ
ejpam-4497	71	46	t	t	NOUN
ejpam-4497	71	47	=	=	SYM
ejpam-4497	71	48	o	o	PROPN
ejpam-4497	71	49	∪∆	∪∆	NOUN
ejpam-4497	71	50	and	and	CCONJ
ejpam-4497	71	51	a	a	DET
ejpam-4497	71	52	map	map	NOUN
ejpam-4497	71	53	t	t	NOUN
ejpam-4497	71	54	:	:	PUNCT
ejpam-4497	71	55	o	o	X
ejpam-4497	71	56	→	→	PUNCT
ejpam-4497	71	57	2x	2x	NUM
ejpam-4497	71	58	is	be	AUX
ejpam-4497	71	59	given	give	VERB
ejpam-4497	71	60	as	as	SCONJ
ejpam-4497	71	61	follows	follow	VERB
ejpam-4497	71	62	:	:	PUNCT
ejpam-4497	71	63	g(o	g(o	PROPN
ejpam-4497	71	64	)	)	PUNCT
ejpam-4497	71	65	=	=	PUNCT
ejpam-4497	71	66			PUNCT
ejpam-4497	71	67	h(o	h(o	PROPN
ejpam-4497	71	68	)	)	PUNCT
ejpam-4497	71	69	:	:	PUNCT
ejpam-4497	72	1	o	o	X
ejpam-4497	72	2	∈	∈	X
ejpam-4497	72	3	o	o	X
ejpam-4497	72	4	\∆	\∆	ADP
ejpam-4497	72	5	f(o	f(o	NOUN
ejpam-4497	72	6	)	)	PUNCT
ejpam-4497	72	7	:	:	PUNCT
ejpam-4497	72	8	o	o	X
ejpam-4497	72	9	∈	∈	PROPN
ejpam-4497	72	10	∆	∆	X
ejpam-4497	72	11	\	\	X
ejpam-4497	73	1	o	o	X
ejpam-4497	73	2	h(o	h(o	PROPN
ejpam-4497	73	3	)	)	PUNCT
ejpam-4497	73	4	∪	∪	ADP
ejpam-4497	73	5	f(o	f(o	NOUN
ejpam-4497	73	6	)	)	PUNCT
ejpam-4497	73	7	:	:	PUNCT
ejpam-4497	74	1	o	o	X
ejpam-4497	74	2	∈	∈	NOUN
ejpam-4497	74	3	o	o	X
ejpam-4497	74	4	∩∆	∩∆	PROPN
ejpam-4497	74	5	definition	definition	NOUN
ejpam-4497	74	6	7	7	NUM
ejpam-4497	74	7	.	.	PUNCT
ejpam-4497	75	1	[	[	X
ejpam-4497	75	2	55	55	NUM
ejpam-4497	75	3	]	]	PUNCT
ejpam-4497	75	4	a	a	DET
ejpam-4497	75	5	s	s	X
ejpam-4497	75	6	-	-	PUNCT
ejpam-4497	75	7	set	set	ADJ
ejpam-4497	75	8	(	(	PUNCT
ejpam-4497	75	9	h	h	NOUN
ejpam-4497	75	10	,	,	PUNCT
ejpam-4497	75	11	o	o	NOUN
ejpam-4497	75	12	)	)	PUNCT
ejpam-4497	75	13	is	be	AUX
ejpam-4497	75	14	a	a	DET
ejpam-4497	75	15	subset	subset	NOUN
ejpam-4497	75	16	of	of	ADP
ejpam-4497	75	17	an	an	DET
ejpam-4497	75	18	s	s	NOUN
ejpam-4497	75	19	-	-	PUNCT
ejpam-4497	75	20	set	set	VERB
ejpam-4497	75	21	(	(	PUNCT
ejpam-4497	75	22	f	f	X
ejpam-4497	75	23	,	,	PUNCT
ejpam-4497	75	24	∆	∆	PROPN
ejpam-4497	75	25	)	)	PUNCT
ejpam-4497	75	26	,	,	PUNCT
ejpam-4497	75	27	symbolized	symbolize	VERB
ejpam-4497	75	28	by	by	ADP
ejpam-4497	75	29	(	(	PUNCT
ejpam-4497	75	30	h	h	NOUN
ejpam-4497	75	31	,	,	PUNCT
ejpam-4497	75	32	o)⊆̃(f	o)⊆̃(f	PROPN
ejpam-4497	75	33	,	,	PUNCT
ejpam-4497	75	34	∆	∆	PROPN
ejpam-4497	75	35	)	)	PUNCT
ejpam-4497	75	36	,	,	PUNCT
ejpam-4497	75	37	if	if	SCONJ
ejpam-4497	75	38	o	o	PROPN
ejpam-4497	75	39	⊆	⊆	NUM
ejpam-4497	75	40	∆	∆	PROPN
ejpam-4497	75	41	and	and	CCONJ
ejpam-4497	75	42	h(o	h(o	PROPN
ejpam-4497	75	43	)	)	PUNCT
ejpam-4497	76	1	⊆	⊆	NUM
ejpam-4497	76	2	f(o	f(o	NOUN
ejpam-4497	76	3	)	)	PUNCT
ejpam-4497	76	4	for	for	ADP
ejpam-4497	76	5	all	all	DET
ejpam-4497	76	6	o	o	NOUN
ejpam-4497	76	7	∈	∈	ADJ
ejpam-4497	76	8	o.	o.	NOUN
ejpam-4497	77	1	if	if	SCONJ
ejpam-4497	77	2	(	(	PUNCT
ejpam-4497	77	3	h	h	NOUN
ejpam-4497	77	4	,	,	PUNCT
ejpam-4497	77	5	o)⊆̃(f	o)⊆̃(f	PROPN
ejpam-4497	77	6	,	,	PUNCT
ejpam-4497	77	7	∆	∆	PROPN
ejpam-4497	77	8	)	)	PUNCT
ejpam-4497	77	9	and	and	CCONJ
ejpam-4497	77	10	(	(	PUNCT
ejpam-4497	77	11	f	f	PROPN
ejpam-4497	77	12	,	,	PUNCT
ejpam-4497	77	13	∆)⊆̃(h	∆)⊆̃(h	PROPN
ejpam-4497	77	14	,	,	PUNCT
ejpam-4497	77	15	o	o	NOUN
ejpam-4497	77	16	)	)	PUNCT
ejpam-4497	77	17	,	,	PUNCT
ejpam-4497	77	18	then	then	ADV
ejpam-4497	77	19	(	(	PUNCT
ejpam-4497	77	20	h	h	NOUN
ejpam-4497	77	21	,	,	PUNCT
ejpam-4497	77	22	o	o	NOUN
ejpam-4497	77	23	)	)	PUNCT
ejpam-4497	77	24	and	and	CCONJ
ejpam-4497	77	25	(	(	PUNCT
ejpam-4497	77	26	f	f	PROPN
ejpam-4497	77	27	,	,	PUNCT
ejpam-4497	77	28	∆	∆	PROPN
ejpam-4497	77	29	)	)	PUNCT
ejpam-4497	77	30	are	be	AUX
ejpam-4497	77	31	called	call	VERB
ejpam-4497	77	32	soft	soft	ADJ
ejpam-4497	77	33	equal	equal	ADJ
ejpam-4497	77	34	.	.	PUNCT
ejpam-4497	78	1	the	the	DET
ejpam-4497	78	2	definition	definition	NOUN
ejpam-4497	78	3	of	of	ADP
ejpam-4497	78	4	soft	soft	ADJ
ejpam-4497	78	5	maps(s	maps(s	NOUN
ejpam-4497	78	6	-	-	PUNCT
ejpam-4497	78	7	map	map	NOUN
ejpam-4497	78	8	)	)	PUNCT
ejpam-4497	78	9	in	in	ADP
ejpam-4497	78	10	[	[	X
ejpam-4497	78	11	58	58	NUM
ejpam-4497	78	12	]	]	PUNCT
ejpam-4497	78	13	was	be	AUX
ejpam-4497	78	14	adjusted	adjust	VERB
ejpam-4497	78	15	as	as	SCONJ
ejpam-4497	78	16	follows	follow	VERB
ejpam-4497	78	17	.	.	PUNCT
ejpam-4497	79	1	definition	definition	NOUN
ejpam-4497	79	2	8	8	NUM
ejpam-4497	79	3	.	.	PUNCT
ejpam-4497	80	1	[	[	X
ejpam-4497	80	2	10	10	NUM
ejpam-4497	80	3	]	]	PUNCT
ejpam-4497	80	4	let	let	VERB
ejpam-4497	80	5	f	f	PRON
ejpam-4497	80	6	:	:	PUNCT
ejpam-4497	80	7	x	x	X
ejpam-4497	80	8	→	→	SYM
ejpam-4497	80	9	s	s	X
ejpam-4497	80	10	and	and	CCONJ
ejpam-4497	80	11	ψ	ψ	NOUN
ejpam-4497	80	12	:	:	PUNCT
ejpam-4497	80	13	o	o	X
ejpam-4497	80	14	→	→	PUNCT
ejpam-4497	80	15	∆	∆	X
ejpam-4497	80	16	be	be	VERB
ejpam-4497	80	17	two	two	NUM
ejpam-4497	80	18	maps	map	NOUN
ejpam-4497	80	19	.	.	PUNCT
ejpam-4497	81	1	a	a	DET
ejpam-4497	81	2	s	s	NOUN
ejpam-4497	81	3	-	-	PUNCT
ejpam-4497	81	4	map	map	NOUN
ejpam-4497	81	5	fψ	fψ	NOUN
ejpam-4497	81	6	of	of	ADP
ejpam-4497	81	7	c(xo	c(xo	NOUN
ejpam-4497	81	8	)	)	PUNCT
ejpam-4497	81	9	into	into	ADP
ejpam-4497	81	10	c(s∆	c(s∆	PROPN
ejpam-4497	81	11	)	)	PUNCT
ejpam-4497	81	12	is	be	AUX
ejpam-4497	81	13	a	a	DET
ejpam-4497	81	14	relation	relation	NOUN
ejpam-4497	81	15	such	such	ADJ
ejpam-4497	81	16	that	that	SCONJ
ejpam-4497	81	17	any	any	DET
ejpam-4497	81	18	s	s	NOUN
ejpam-4497	81	19	-	-	PUNCT
ejpam-4497	81	20	point	point	NOUN
ejpam-4497	81	21	in	in	ADP
ejpam-4497	81	22	c(xo	c(xo	NOUN
ejpam-4497	81	23	)	)	PUNCT
ejpam-4497	81	24	is	be	AUX
ejpam-4497	81	25	related	relate	VERB
ejpam-4497	81	26	to	to	ADP
ejpam-4497	81	27	one	one	NUM
ejpam-4497	81	28	and	and	CCONJ
ejpam-4497	81	29	only	only	ADV
ejpam-4497	81	30	one	one	NUM
ejpam-4497	81	31	s	s	NOUN
ejpam-4497	81	32	-	-	NOUN
ejpam-4497	81	33	point	point	NOUN
ejpam-4497	81	34	in	in	ADP
ejpam-4497	81	35	c(s∆	c(s∆	PROPN
ejpam-4497	81	36	)	)	PUNCT
ejpam-4497	81	37	such	such	ADJ
ejpam-4497	81	38	that	that	PRON
ejpam-4497	81	39	fψ(δ	fψ(δ	NOUN
ejpam-4497	82	1	x	x	SYM
ejpam-4497	82	2	o	o	NOUN
ejpam-4497	82	3	)	)	PUNCT
ejpam-4497	82	4	=	=	SYM
ejpam-4497	82	5	δ	δ	PROPN
ejpam-4497	82	6	f(x	f(x	PROPN
ejpam-4497	82	7	)	)	PUNCT
ejpam-4497	82	8	ψ(o	ψ(o	PROPN
ejpam-4497	82	9	)	)	PUNCT
ejpam-4497	82	10	for	for	ADP
ejpam-4497	82	11	any	any	DET
ejpam-4497	82	12	δxo	δxo	NOUN
ejpam-4497	82	13	∈	∈	PROPN
ejpam-4497	82	14	c(xo	c(xo	PROPN
ejpam-4497	82	15	)	)	PUNCT
ejpam-4497	82	16	.	.	PUNCT
ejpam-4497	83	1	in	in	ADP
ejpam-4497	83	2	addition	addition	NOUN
ejpam-4497	83	3	,	,	PUNCT
ejpam-4497	83	4	f−1	f−1	PROPN
ejpam-4497	83	5	ψ	ψ	X
ejpam-4497	83	6	(	(	PUNCT
ejpam-4497	83	7	δyγ	δyγ	NOUN
ejpam-4497	83	8	)	)	PUNCT
ejpam-4497	83	9	=	=	SYM
ejpam-4497	83	10	⊔	⊔	PROPN
ejpam-4497	83	11	λ∈ψ−1(γ	λ∈ψ−1(γ	NOUN
ejpam-4497	83	12	)	)	PUNCT
ejpam-4497	83	13	x∈f−1(y	x∈f−1(y	PROPN
ejpam-4497	83	14	)	)	PUNCT
ejpam-4497	83	15	δxλ	δxλ	VERB
ejpam-4497	83	16	for	for	ADP
ejpam-4497	83	17	any	any	DET
ejpam-4497	83	18	δyγ	δyγ	NOUN
ejpam-4497	83	19	∈	∈	PROPN
ejpam-4497	83	20	c(s∆	c(s∆	PROPN
ejpam-4497	83	21	)	)	PUNCT
ejpam-4497	83	22	.	.	PUNCT
ejpam-4497	84	1	definition	definition	NOUN
ejpam-4497	84	2	9	9	NUM
ejpam-4497	84	3	.	.	PUNCT
ejpam-4497	85	1	[	[	X
ejpam-4497	85	2	63	63	NUM
ejpam-4497	85	3	]	]	PUNCT
ejpam-4497	85	4	for	for	ADP
ejpam-4497	85	5	an	an	DET
ejpam-4497	85	6	s	s	NOUN
ejpam-4497	85	7	-	-	PUNCT
ejpam-4497	85	8	map	map	NOUN
ejpam-4497	85	9	fψ	fψ	NOUN
ejpam-4497	85	10	:	:	PUNCT
ejpam-4497	85	11	c(xo	c(xo	NUM
ejpam-4497	85	12	)	)	PUNCT
ejpam-4497	85	13	→	→	SYM
ejpam-4497	85	14	c(s∆	c(s∆	PROPN
ejpam-4497	85	15	)	)	PUNCT
ejpam-4497	85	16	,	,	PUNCT
ejpam-4497	85	17	if	if	SCONJ
ejpam-4497	85	18	f	f	PROPN
ejpam-4497	85	19	and	and	CCONJ
ejpam-4497	85	20	ψ	ψ	PROPN
ejpam-4497	85	21	are	be	AUX
ejpam-4497	85	22	injective	injective	ADJ
ejpam-4497	85	23	(	(	PUNCT
ejpam-4497	85	24	resp	resp	NOUN
ejpam-4497	85	25	.	.	PUNCT
ejpam-4497	85	26	,	,	PUNCT
ejpam-4497	85	27	surjective	surjective	ADJ
ejpam-4497	85	28	,	,	PUNCT
ejpam-4497	85	29	bijective	bijective	ADJ
ejpam-4497	85	30	)	)	PUNCT
ejpam-4497	85	31	,	,	PUNCT
ejpam-4497	85	32	then	then	ADV
ejpam-4497	85	33	fψ	fψ	PROPN
ejpam-4497	85	34	is	be	AUX
ejpam-4497	85	35	called	call	VERB
ejpam-4497	85	36	injective	injective	ADJ
ejpam-4497	85	37	(	(	PUNCT
ejpam-4497	85	38	resp	resp	NOUN
ejpam-4497	85	39	.	.	PUNCT
ejpam-4497	85	40	,	,	PUNCT
ejpam-4497	85	41	surjective	surjective	ADJ
ejpam-4497	85	42	,	,	PUNCT
ejpam-4497	85	43	bijective	bijective	ADJ
ejpam-4497	85	44	)	)	PUNCT
ejpam-4497	85	45	.	.	PUNCT
ejpam-4497	86	1	2.2	2.2	NUM
ejpam-4497	86	2	.	.	PUNCT
ejpam-4497	87	1	infra	infra	NOUN
ejpam-4497	87	2	soft	soft	ADJ
ejpam-4497	87	3	topological	topological	ADJ
ejpam-4497	87	4	spaces	space	NOUN
ejpam-4497	87	5	definition	definition	NOUN
ejpam-4497	87	6	10	10	NUM
ejpam-4497	87	7	.	.	PUNCT
ejpam-4497	88	1	[	[	X
ejpam-4497	88	2	13	13	NUM
ejpam-4497	88	3	]	]	PUNCT
ejpam-4497	88	4	a	a	DET
ejpam-4497	88	5	subfamily	subfamily	ADV
ejpam-4497	88	6	µ	µ	X
ejpam-4497	88	7	of	of	ADP
ejpam-4497	88	8	c(xo	c(xo	PROPN
ejpam-4497	88	9	)	)	PUNCT
ejpam-4497	88	10	is	be	AUX
ejpam-4497	88	11	called	call	VERB
ejpam-4497	88	12	an	an	DET
ejpam-4497	88	13	infra	infra	NOUN
ejpam-4497	88	14	soft	soft	ADJ
ejpam-4497	88	15	topology(ist	topology(ist	NOUN
ejpam-4497	88	16	)	)	PUNCT
ejpam-4497	88	17	on	on	ADP
ejpam-4497	88	18	x	x	SYM
ejpam-4497	88	19	if	if	SCONJ
ejpam-4497	88	20	it	it	PRON
ejpam-4497	88	21	contains	contain	VERB
ejpam-4497	88	22	φ	φ	PROPN
ejpam-4497	88	23	and	and	CCONJ
ejpam-4497	88	24	it	it	PRON
ejpam-4497	88	25	is	be	AUX
ejpam-4497	88	26	closed	close	VERB
ejpam-4497	88	27	under	under	ADP
ejpam-4497	88	28	finite	finite	ADJ
ejpam-4497	88	29	intersection	intersection	NOUN
ejpam-4497	88	30	.	.	PUNCT
ejpam-4497	89	1	the	the	DET
ejpam-4497	89	2	triple	triple	ADJ
ejpam-4497	89	3	(	(	PUNCT
ejpam-4497	89	4	x,µ,o	x,µ,o	PROPN
ejpam-4497	89	5	)	)	PUNCT
ejpam-4497	89	6	is	be	AUX
ejpam-4497	89	7	called	call	VERB
ejpam-4497	89	8	an	an	DET
ejpam-4497	89	9	ists	ist	NOUN
ejpam-4497	89	10	.	.	PUNCT
ejpam-4497	90	1	the	the	DET
ejpam-4497	90	2	elements	element	NOUN
ejpam-4497	90	3	of	of	ADP
ejpam-4497	90	4	µ	µ	NOUN
ejpam-4497	90	5	are	be	AUX
ejpam-4497	90	6	called	call	VERB
ejpam-4497	90	7	is	be	AUX
ejpam-4497	90	8	-	-	PUNCT
ejpam-4497	90	9	open	open	ADJ
ejpam-4497	90	10	sets	set	NOUN
ejpam-4497	90	11	and	and	CCONJ
ejpam-4497	90	12	their	their	PRON
ejpam-4497	90	13	complements	complement	NOUN
ejpam-4497	90	14	are	be	AUX
ejpam-4497	90	15	called	call	VERB
ejpam-4497	90	16	is	be	AUX
ejpam-4497	90	17	-	-	PUNCT
ejpam-4497	90	18	closed	closed	ADJ
ejpam-4497	90	19	sets	set	NOUN
ejpam-4497	90	20	.	.	PUNCT
ejpam-4497	91	1	definition	definition	NOUN
ejpam-4497	91	2	11	11	NUM
ejpam-4497	91	3	.	.	PUNCT
ejpam-4497	92	1	[	[	X
ejpam-4497	92	2	13	13	NUM
ejpam-4497	92	3	]	]	PUNCT
ejpam-4497	92	4	let	let	VERB
ejpam-4497	92	5	(	(	PUNCT
ejpam-4497	92	6	h	h	NOUN
ejpam-4497	92	7	,	,	PUNCT
ejpam-4497	92	8	o	o	NOUN
ejpam-4497	92	9	)	)	PUNCT
ejpam-4497	92	10	be	be	AUX
ejpam-4497	92	11	a	a	DET
ejpam-4497	92	12	subset	subset	NOUN
ejpam-4497	92	13	of	of	ADP
ejpam-4497	92	14	(	(	PUNCT
ejpam-4497	92	15	x,µ,o	x,µ,o	PROPN
ejpam-4497	92	16	)	)	PUNCT
ejpam-4497	92	17	.	.	PUNCT
ejpam-4497	93	1	t.m	t.m	PROPN
ejpam-4497	93	2	.	.	PUNCT
ejpam-4497	93	3	al	al	PROPN
ejpam-4497	93	4	-	-	PUNCT
ejpam-4497	93	5	shami	shami	PROPN
ejpam-4497	93	6	et	et	PROPN
ejpam-4497	93	7	al	al	PROPN
ejpam-4497	93	8	.	.	PUNCT
ejpam-4497	93	9	/	/	SYM
ejpam-4497	93	10	eur	eur	PROPN
ejpam-4497	93	11	.	.	PUNCT
ejpam-4497	94	1	j.	j.	PROPN
ejpam-4497	94	2	pure	pure	PROPN
ejpam-4497	94	3	appl	appl	PROPN
ejpam-4497	94	4	.	.	PROPN
ejpam-4497	94	5	math	math	PROPN
ejpam-4497	94	6	,	,	PUNCT
ejpam-4497	94	7	15	15	NUM
ejpam-4497	94	8	(	(	PUNCT
ejpam-4497	94	9	4	4	NUM
ejpam-4497	94	10	)	)	PUNCT
ejpam-4497	94	11	(	(	PUNCT
ejpam-4497	94	12	2022	2022	NUM
ejpam-4497	94	13	)	)	PUNCT
ejpam-4497	94	14	,	,	PUNCT
ejpam-4497	94	15	1455	1455	NUM
ejpam-4497	94	16	-	-	SYM
ejpam-4497	94	17	1471	1471	NUM
ejpam-4497	94	18	1458	1458	NUM
ejpam-4497	94	19	(	(	PUNCT
ejpam-4497	94	20	i	i	NOUN
ejpam-4497	94	21	)	)	PUNCT
ejpam-4497	94	22	the	the	DET
ejpam-4497	94	23	is	be	AUX
ejpam-4497	94	24	-	-	PUNCT
ejpam-4497	94	25	closure	closure	NOUN
ejpam-4497	94	26	points	point	NOUN
ejpam-4497	94	27	of	of	ADP
ejpam-4497	94	28	(	(	PUNCT
ejpam-4497	94	29	h	h	NOUN
ejpam-4497	94	30	,	,	PUNCT
ejpam-4497	94	31	o	o	NOUN
ejpam-4497	94	32	)	)	PUNCT
ejpam-4497	94	33	,	,	PUNCT
ejpam-4497	94	34	denoted	denote	VERB
ejpam-4497	94	35	by	by	ADP
ejpam-4497	94	36	cl(h	cl(h	X
ejpam-4497	94	37	,	,	PUNCT
ejpam-4497	94	38	o	o	NOUN
ejpam-4497	94	39	)	)	PUNCT
ejpam-4497	94	40	,	,	PUNCT
ejpam-4497	94	41	is	be	AUX
ejpam-4497	94	42	the	the	DET
ejpam-4497	94	43	intersection	intersection	NOUN
ejpam-4497	94	44	of	of	ADP
ejpam-4497	94	45	all	all	DET
ejpam-4497	94	46	is	be	AUX
ejpam-4497	94	47	-	-	PUNCT
ejpam-4497	94	48	closed	closed	ADJ
ejpam-4497	94	49	subsets	subset	NOUN
ejpam-4497	94	50	of	of	ADP
ejpam-4497	94	51	(	(	PUNCT
ejpam-4497	94	52	x,µ,o	x,µ,o	PROPN
ejpam-4497	94	53	)	)	PUNCT
ejpam-4497	94	54	containing	contain	VERB
ejpam-4497	94	55	(	(	PUNCT
ejpam-4497	94	56	h	h	NOUN
ejpam-4497	94	57	,	,	PUNCT
ejpam-4497	94	58	o	o	NOUN
ejpam-4497	94	59	)	)	PUNCT
ejpam-4497	94	60	.	.	PUNCT
ejpam-4497	95	1	(	(	PUNCT
ejpam-4497	95	2	ii	ii	X
ejpam-4497	95	3	)	)	PUNCT
ejpam-4497	95	4	the	the	DET
ejpam-4497	95	5	is	be	AUX
ejpam-4497	95	6	-	-	PUNCT
ejpam-4497	95	7	interior	interior	ADJ
ejpam-4497	95	8	points	point	NOUN
ejpam-4497	95	9	of	of	ADP
ejpam-4497	95	10	(	(	PUNCT
ejpam-4497	95	11	h	h	NOUN
ejpam-4497	95	12	,	,	PUNCT
ejpam-4497	95	13	o	o	NOUN
ejpam-4497	95	14	)	)	PUNCT
ejpam-4497	95	15	,	,	PUNCT
ejpam-4497	95	16	denoted	denote	VERB
ejpam-4497	95	17	by	by	ADP
ejpam-4497	95	18	int(h	int(h	PROPN
ejpam-4497	95	19	,	,	PUNCT
ejpam-4497	95	20	o	o	NOUN
ejpam-4497	95	21	)	)	PUNCT
ejpam-4497	95	22	is	be	AUX
ejpam-4497	95	23	the	the	DET
ejpam-4497	95	24	union	union	NOUN
ejpam-4497	95	25	of	of	ADP
ejpam-4497	95	26	all	all	PRON
ejpam-4497	95	27	is	be	AUX
ejpam-4497	95	28	-	-	PUNCT
ejpam-4497	95	29	open	open	ADJ
ejpam-4497	95	30	subsets	subset	NOUN
ejpam-4497	95	31	of	of	ADP
ejpam-4497	95	32	(	(	PUNCT
ejpam-4497	95	33	x,µ,o	x,µ,o	PROPN
ejpam-4497	95	34	)	)	PUNCT
ejpam-4497	95	35	which	which	PRON
ejpam-4497	95	36	are	be	AUX
ejpam-4497	95	37	contained	contain	VERB
ejpam-4497	95	38	in	in	ADP
ejpam-4497	95	39	(	(	PUNCT
ejpam-4497	95	40	h	h	NOUN
ejpam-4497	95	41	,	,	PUNCT
ejpam-4497	95	42	o	o	NOUN
ejpam-4497	95	43	)	)	PUNCT
ejpam-4497	95	44	.	.	PUNCT
ejpam-4497	96	1	proposition	proposition	NOUN
ejpam-4497	96	2	1	1	NUM
ejpam-4497	96	3	.	.	PUNCT
ejpam-4497	97	1	[	[	X
ejpam-4497	97	2	13	13	NUM
ejpam-4497	97	3	]	]	PUNCT
ejpam-4497	97	4	let	let	VERB
ejpam-4497	97	5	(	(	PUNCT
ejpam-4497	97	6	h	h	NOUN
ejpam-4497	97	7	,	,	PUNCT
ejpam-4497	97	8	o	o	NOUN
ejpam-4497	97	9	)	)	PUNCT
ejpam-4497	97	10	and	and	CCONJ
ejpam-4497	97	11	(	(	PUNCT
ejpam-4497	97	12	f	f	X
ejpam-4497	97	13	,	,	PUNCT
ejpam-4497	97	14	o	o	NOUN
ejpam-4497	97	15	)	)	PUNCT
ejpam-4497	97	16	subsets	subset	NOUN
ejpam-4497	97	17	of	of	ADP
ejpam-4497	97	18	an	an	DET
ejpam-4497	97	19	ists	ist	NOUN
ejpam-4497	97	20	(	(	PUNCT
ejpam-4497	97	21	x,µ,o	x,µ,o	PROPN
ejpam-4497	97	22	)	)	PUNCT
ejpam-4497	97	23	.	.	PUNCT
ejpam-4497	98	1	then	then	ADV
ejpam-4497	98	2	(	(	PUNCT
ejpam-4497	98	3	i	i	NOUN
ejpam-4497	98	4	)	)	PUNCT
ejpam-4497	98	5	cl[(h	cl[(h	PROPN
ejpam-4497	98	6	,	,	PUNCT
ejpam-4497	98	7	o)∪̃(f	o)∪̃(f	PROPN
ejpam-4497	98	8	,	,	PUNCT
ejpam-4497	98	9	o	o	NOUN
ejpam-4497	98	10	)	)	PUNCT
ejpam-4497	98	11	]	]	PUNCT
ejpam-4497	99	1	=	=	PUNCT
ejpam-4497	99	2	cl(h	cl(h	X
ejpam-4497	99	3	,	,	PUNCT
ejpam-4497	99	4	o)∪̃cl(f	o)∪̃cl(f	PROPN
ejpam-4497	99	5	,	,	PUNCT
ejpam-4497	99	6	o	o	NOUN
ejpam-4497	99	7	)	)	PUNCT
ejpam-4497	99	8	,	,	PUNCT
ejpam-4497	99	9	and	and	CCONJ
ejpam-4497	99	10	(	(	PUNCT
ejpam-4497	99	11	ii	ii	NOUN
ejpam-4497	99	12	)	)	PUNCT
ejpam-4497	99	13	int[(h	int[(h	PROPN
ejpam-4497	99	14	,	,	PUNCT
ejpam-4497	99	15	o)∩̃(f	o)∩̃(f	PROPN
ejpam-4497	99	16	,	,	PUNCT
ejpam-4497	99	17	o	o	NOUN
ejpam-4497	99	18	)	)	PUNCT
ejpam-4497	99	19	]	]	PUNCT
ejpam-4497	100	1	=	=	PUNCT
ejpam-4497	100	2	int(h	int(h	PROPN
ejpam-4497	100	3	,	,	PUNCT
ejpam-4497	100	4	o)∩̃int(f	o)∩̃int(f	X
ejpam-4497	100	5	,	,	PUNCT
ejpam-4497	100	6	o	o	NOUN
ejpam-4497	100	7	)	)	PUNCT
ejpam-4497	100	8	.	.	PUNCT
ejpam-4497	101	1	proposition	proposition	NOUN
ejpam-4497	101	2	2	2	NUM
ejpam-4497	101	3	.	.	PUNCT
ejpam-4497	102	1	[	[	X
ejpam-4497	102	2	13	13	NUM
ejpam-4497	102	3	]	]	PUNCT
ejpam-4497	102	4	let	let	VERB
ejpam-4497	102	5	(	(	PUNCT
ejpam-4497	102	6	h	h	NOUN
ejpam-4497	102	7	,	,	PUNCT
ejpam-4497	102	8	o	o	NOUN
ejpam-4497	102	9	)	)	PUNCT
ejpam-4497	102	10	be	be	VERB
ejpam-4497	102	11	an	an	DET
ejpam-4497	102	12	is	is	NOUN
ejpam-4497	102	13	-	-	PUNCT
ejpam-4497	102	14	open	open	ADJ
ejpam-4497	102	15	set	set	NOUN
ejpam-4497	102	16	.	.	PUNCT
ejpam-4497	103	1	then	then	ADV
ejpam-4497	103	2	(	(	PUNCT
ejpam-4497	103	3	h	h	NOUN
ejpam-4497	103	4	,	,	PUNCT
ejpam-4497	103	5	o)∩̃cl(f	o)∩̃cl(f	NUM
ejpam-4497	103	6	,	,	PUNCT
ejpam-4497	103	7	o)⊆̃cl[(h	o)⊆̃cl[(h	PROPN
ejpam-4497	103	8	,	,	PUNCT
ejpam-4497	103	9	o)∪̃(f	o)∪̃(f	PROPN
ejpam-4497	103	10	,	,	PUNCT
ejpam-4497	103	11	o	o	NOUN
ejpam-4497	103	12	)	)	PUNCT
ejpam-4497	103	13	]	]	PUNCT
ejpam-4497	103	14	for	for	ADP
ejpam-4497	103	15	any	any	PRON
ejpam-4497	103	16	(	(	PUNCT
ejpam-4497	103	17	f	f	PROPN
ejpam-4497	103	18	,	,	PUNCT
ejpam-4497	103	19	o	o	NOUN
ejpam-4497	103	20	)	)	PUNCT
ejpam-4497	103	21	in	in	ADP
ejpam-4497	103	22	(	(	PUNCT
ejpam-4497	103	23	x,µ,o	x,µ,o	PROPN
ejpam-4497	103	24	)	)	PUNCT
ejpam-4497	103	25	.	.	PUNCT
ejpam-4497	104	1	proposition	proposition	NOUN
ejpam-4497	104	2	3	3	NUM
ejpam-4497	104	3	.	.	PUNCT
ejpam-4497	105	1	[	[	X
ejpam-4497	105	2	13	13	NUM
ejpam-4497	105	3	]	]	PUNCT
ejpam-4497	105	4	let	let	VERB
ejpam-4497	105	5	(	(	PUNCT
ejpam-4497	105	6	h	h	NOUN
ejpam-4497	105	7	,	,	PUNCT
ejpam-4497	105	8	o	o	NOUN
ejpam-4497	105	9	)	)	PUNCT
ejpam-4497	105	10	be	be	VERB
ejpam-4497	105	11	an	an	DET
ejpam-4497	105	12	is	is	NOUN
ejpam-4497	105	13	-	-	PUNCT
ejpam-4497	105	14	closed	closed	ADJ
ejpam-4497	105	15	set	set	NOUN
ejpam-4497	105	16	.	.	PUNCT
ejpam-4497	106	1	then	then	ADV
ejpam-4497	106	2	int[(h	int[(h	PROPN
ejpam-4497	106	3	,	,	PUNCT
ejpam-4497	106	4	o)∪̃(f	o)∪̃(f	PROPN
ejpam-4497	106	5	,	,	PUNCT
ejpam-4497	106	6	o)]⊆̃(h	o)]⊆̃(h	ADV
ejpam-4497	106	7	,	,	PUNCT
ejpam-4497	106	8	o)∪̃int(f	o)∪̃int(f	X
ejpam-4497	106	9	,	,	PUNCT
ejpam-4497	106	10	o	o	NOUN
ejpam-4497	106	11	)	)	PUNCT
ejpam-4497	106	12	for	for	ADP
ejpam-4497	106	13	any	any	DET
ejpam-4497	106	14	(	(	PUNCT
ejpam-4497	106	15	h	h	NOUN
ejpam-4497	106	16	,	,	PUNCT
ejpam-4497	106	17	o	o	NOUN
ejpam-4497	106	18	)	)	PUNCT
ejpam-4497	106	19	in	in	ADP
ejpam-4497	106	20	(	(	PUNCT
ejpam-4497	106	21	x,µ,o	x,µ,o	PROPN
ejpam-4497	106	22	)	)	PUNCT
ejpam-4497	106	23	.	.	PUNCT
ejpam-4497	107	1	definition	definition	NOUN
ejpam-4497	107	2	12	12	NUM
ejpam-4497	107	3	.	.	PUNCT
ejpam-4497	108	1	[	[	X
ejpam-4497	108	2	10	10	NUM
ejpam-4497	108	3	]	]	X
ejpam-4497	108	4	a	a	DET
ejpam-4497	108	5	bijective	bijective	ADJ
ejpam-4497	108	6	s	s	NOUN
ejpam-4497	108	7	-	-	PUNCT
ejpam-4497	108	8	map	map	NOUN
ejpam-4497	108	9	fψ	fψ	NOUN
ejpam-4497	108	10	:	:	PUNCT
ejpam-4497	108	11	(	(	PUNCT
ejpam-4497	108	12	x,µ,o	x,µ,o	NOUN
ejpam-4497	108	13	)	)	PUNCT
ejpam-4497	108	14	→	→	PUNCT
ejpam-4497	108	15	(	(	PUNCT
ejpam-4497	108	16	s	s	PROPN
ejpam-4497	108	17	,	,	PUNCT
ejpam-4497	108	18	ν,∆	ν,∆	NUM
ejpam-4497	108	19	)	)	PUNCT
ejpam-4497	108	20	is	be	AUX
ejpam-4497	108	21	said	say	VERB
ejpam-4497	108	22	to	to	PART
ejpam-4497	108	23	be	be	AUX
ejpam-4497	108	24	an	an	DET
ejpam-4497	108	25	ishomeomorphism	ishomeomorphism	NOUN
ejpam-4497	108	26	if	if	SCONJ
ejpam-4497	108	27	it	it	PRON
ejpam-4497	108	28	is	be	AUX
ejpam-4497	108	29	is	be	AUX
ejpam-4497	108	30	-	-	PUNCT
ejpam-4497	108	31	open	open	ADJ
ejpam-4497	108	32	(	(	PUNCT
ejpam-4497	108	33	i.e	i.e	NOUN
ejpam-4497	108	34	,	,	PUNCT
ejpam-4497	108	35	the	the	DET
ejpam-4497	108	36	image	image	NOUN
ejpam-4497	108	37	of	of	ADP
ejpam-4497	108	38	any	any	PRON
ejpam-4497	108	39	is	be	AUX
ejpam-4497	108	40	-	-	PUNCT
ejpam-4497	108	41	open	open	ADJ
ejpam-4497	108	42	set	set	NOUN
ejpam-4497	108	43	is	be	AUX
ejpam-4497	108	44	is	be	AUX
ejpam-4497	108	45	-	-	PUNCT
ejpam-4497	108	46	open	open	ADJ
ejpam-4497	108	47	)	)	PUNCT
ejpam-4497	108	48	,	,	PUNCT
ejpam-4497	108	49	and	and	CCONJ
ejpam-4497	108	50	iscontinuous	iscontinuous	ADJ
ejpam-4497	108	51	(	(	PUNCT
ejpam-4497	108	52	i.e	i.e	PROPN
ejpam-4497	108	53	,	,	PUNCT
ejpam-4497	108	54	the	the	DET
ejpam-4497	108	55	pre	pre	NOUN
ejpam-4497	108	56	-	-	NOUN
ejpam-4497	108	57	image	image	NOUN
ejpam-4497	108	58	of	of	ADP
ejpam-4497	108	59	any	any	PRON
ejpam-4497	108	60	is	be	AUX
ejpam-4497	108	61	-	-	PUNCT
ejpam-4497	108	62	open	open	ADJ
ejpam-4497	108	63	set	set	NOUN
ejpam-4497	108	64	is	be	AUX
ejpam-4497	108	65	is	be	AUX
ejpam-4497	108	66	-	-	PUNCT
ejpam-4497	108	67	open	open	ADJ
ejpam-4497	108	68	)	)	PUNCT
ejpam-4497	108	69	.	.	PUNCT
ejpam-4497	109	1	we	we	PRON
ejpam-4497	109	2	call	call	VERB
ejpam-4497	109	3	a	a	DET
ejpam-4497	109	4	property	property	NOUN
ejpam-4497	109	5	which	which	PRON
ejpam-4497	109	6	is	be	AUX
ejpam-4497	109	7	kept	keep	VERB
ejpam-4497	109	8	by	by	ADP
ejpam-4497	109	9	any	any	PRON
ejpam-4497	109	10	is	be	AUX
ejpam-4497	109	11	-	-	PUNCT
ejpam-4497	109	12	homeomorphism	homeomorphism	NOUN
ejpam-4497	109	13	an	an	DET
ejpam-4497	109	14	is	be	AUX
ejpam-4497	109	15	-	-	PUNCT
ejpam-4497	109	16	topological	topological	ADJ
ejpam-4497	109	17	property	property	NOUN
ejpam-4497	109	18	.	.	PUNCT
ejpam-4497	110	1	definition	definition	NOUN
ejpam-4497	110	2	13	13	NUM
ejpam-4497	110	3	.	.	PUNCT
ejpam-4497	111	1	[	[	X
ejpam-4497	111	2	10	10	NUM
ejpam-4497	111	3	]	]	PUNCT
ejpam-4497	111	4	let	let	AUX
ejpam-4497	111	5	fψ	fψ	VERB
ejpam-4497	111	6	:	:	PUNCT
ejpam-4497	111	7	(	(	PUNCT
ejpam-4497	111	8	x,µ,o	x,µ,o	NOUN
ejpam-4497	111	9	)	)	PUNCT
ejpam-4497	111	10	→	→	PUNCT
ejpam-4497	111	11	(	(	PUNCT
ejpam-4497	111	12	s	s	PROPN
ejpam-4497	111	13	,	,	PUNCT
ejpam-4497	111	14	ν,∆	ν,∆	NUM
ejpam-4497	111	15	)	)	PUNCT
ejpam-4497	111	16	be	be	VERB
ejpam-4497	111	17	an	an	DET
ejpam-4497	111	18	s	s	NOUN
ejpam-4497	111	19	-	-	PUNCT
ejpam-4497	111	20	map	map	NOUN
ejpam-4497	111	21	and	and	CCONJ
ejpam-4497	111	22	m	m	VERB
ejpam-4497	111	23	=	=	NOUN
ejpam-4497	111	24	̸	̸	VERB
ejpam-4497	111	25	∅	∅	NOUN
ejpam-4497	111	26	be	be	AUX
ejpam-4497	111	27	a	a	DET
ejpam-4497	111	28	subset	subset	NOUN
ejpam-4497	111	29	of	of	ADP
ejpam-4497	111	30	x.	x.	NOUN
ejpam-4497	111	31	a	a	DET
ejpam-4497	111	32	s	s	NOUN
ejpam-4497	111	33	-	-	PUNCT
ejpam-4497	111	34	map	map	NOUN
ejpam-4497	111	35	fψ|m	fψ|m	NOUN
ejpam-4497	111	36	:	:	PUNCT
ejpam-4497	111	37	(	(	PUNCT
ejpam-4497	111	38	m	m	PROPN
ejpam-4497	111	39	,	,	PUNCT
ejpam-4497	111	40	µm	µm	NOUN
ejpam-4497	111	41	,	,	PUNCT
ejpam-4497	111	42	o	o	NOUN
ejpam-4497	111	43	)	)	PUNCT
ejpam-4497	111	44	→	→	SYM
ejpam-4497	111	45	(	(	PUNCT
ejpam-4497	111	46	s	s	PROPN
ejpam-4497	111	47	,	,	PUNCT
ejpam-4497	111	48	ν,∆	ν,∆	NOUN
ejpam-4497	111	49	)	)	PUNCT
ejpam-4497	111	50	which	which	PRON
ejpam-4497	111	51	given	give	VERB
ejpam-4497	111	52	by	by	ADP
ejpam-4497	111	53	fψ|m(δmo	fψ|m(δmo	ADJ
ejpam-4497	111	54	)	)	PUNCT
ejpam-4497	111	55	=	=	SYM
ejpam-4497	112	1	fψ(δ	fψ(δ	NUM
ejpam-4497	112	2	m	m	VERB
ejpam-4497	112	3	o	o	NOUN
ejpam-4497	112	4	)	)	PUNCT
ejpam-4497	112	5	for	for	ADP
ejpam-4497	112	6	every	every	DET
ejpam-4497	112	7	δmo	δmo	PROPN
ejpam-4497	112	8	∈	∈	PROPN
ejpam-4497	112	9	m̃	m̃	PROPN
ejpam-4497	112	10	is	be	AUX
ejpam-4497	112	11	called	call	VERB
ejpam-4497	112	12	a	a	DET
ejpam-4497	112	13	restriction	restriction	NOUN
ejpam-4497	112	14	s	s	NOUN
ejpam-4497	112	15	-	-	NOUN
ejpam-4497	112	16	map	map	NOUN
ejpam-4497	112	17	of	of	ADP
ejpam-4497	112	18	fψ	fψ	NOUN
ejpam-4497	112	19	on	on	ADP
ejpam-4497	112	20	m.	m.	NOUN
ejpam-4497	112	21	lemma	lemma	PROPN
ejpam-4497	112	22	1	1	NUM
ejpam-4497	112	23	.	.	PUNCT
ejpam-4497	113	1	[	[	X
ejpam-4497	113	2	23	23	NUM
ejpam-4497	113	3	,	,	PUNCT
ejpam-4497	113	4	41	41	NUM
ejpam-4497	113	5	]	]	PUNCT
ejpam-4497	113	6	let	let	AUX
ejpam-4497	113	7	fψ	fψ	VERB
ejpam-4497	113	8	:	:	PUNCT
ejpam-4497	113	9	(	(	PUNCT
ejpam-4497	113	10	x1	x1	PROPN
ejpam-4497	113	11	,	,	PUNCT
ejpam-4497	113	12	µ1,o1	µ1,o1	PROPN
ejpam-4497	113	13	)	)	PUNCT
ejpam-4497	113	14	→	→	SYM
ejpam-4497	113	15	(	(	PUNCT
ejpam-4497	113	16	x2	x2	PROPN
ejpam-4497	113	17	,	,	PUNCT
ejpam-4497	113	18	µ2,o2	µ2,o2	PROPN
ejpam-4497	113	19	)	)	PUNCT
ejpam-4497	113	20	be	be	AUX
ejpam-4497	113	21	an	an	DET
ejpam-4497	113	22	is	is	NOUN
ejpam-4497	113	23	-	-	PUNCT
ejpam-4497	113	24	homeomorphism	homeomorphism	NOUN
ejpam-4497	113	25	map	map	NOUN
ejpam-4497	113	26	.	.	PUNCT
ejpam-4497	114	1	then	then	ADV
ejpam-4497	114	2	for	for	ADP
ejpam-4497	114	3	any	any	DET
ejpam-4497	114	4	(	(	PUNCT
ejpam-4497	114	5	h	h	NOUN
ejpam-4497	114	6	,	,	PUNCT
ejpam-4497	114	7	o1	o1	NOUN
ejpam-4497	114	8	)	)	PUNCT
ejpam-4497	114	9	we	we	PRON
ejpam-4497	114	10	have	have	VERB
ejpam-4497	114	11	:	:	PUNCT
ejpam-4497	114	12	(	(	PUNCT
ejpam-4497	114	13	i	i	NOUN
ejpam-4497	114	14	)	)	PUNCT
ejpam-4497	114	15	fψ(int(h	fψ(int(h	PROPN
ejpam-4497	114	16	,	,	PUNCT
ejpam-4497	114	17	o1	o1	NOUN
ejpam-4497	114	18	)	)	PUNCT
ejpam-4497	114	19	)	)	PUNCT
ejpam-4497	115	1	=	=	SYM
ejpam-4497	115	2	int(fψ(h	int(fψ(h	PROPN
ejpam-4497	115	3	,	,	PUNCT
ejpam-4497	115	4	o1	o1	NOUN
ejpam-4497	115	5	)	)	PUNCT
ejpam-4497	115	6	)	)	PUNCT
ejpam-4497	115	7	.	.	PUNCT
ejpam-4497	116	1	(	(	PUNCT
ejpam-4497	116	2	ii	ii	NOUN
ejpam-4497	116	3	)	)	PUNCT
ejpam-4497	116	4	fψ(cl(h	fψ(cl(h	PROPN
ejpam-4497	116	5	,	,	PUNCT
ejpam-4497	116	6	o1	o1	NOUN
ejpam-4497	116	7	)	)	PUNCT
ejpam-4497	116	8	)	)	PUNCT
ejpam-4497	117	1	=	=	SYM
ejpam-4497	117	2	cl(fψ(h	cl(fψ(h	NOUN
ejpam-4497	117	3	,	,	PUNCT
ejpam-4497	117	4	o1	o1	NOUN
ejpam-4497	117	5	)	)	PUNCT
ejpam-4497	117	6	)	)	PUNCT
ejpam-4497	117	7	.	.	PUNCT
ejpam-4497	118	1	3	3	X
ejpam-4497	118	2	.	.	X
ejpam-4497	118	3	main	main	ADJ
ejpam-4497	118	4	properties	property	NOUN
ejpam-4497	118	5	of	of	ADP
ejpam-4497	118	6	infra	infra	NOUN
ejpam-4497	118	7	soft	soft	ADJ
ejpam-4497	118	8	b	b	NOUN
ejpam-4497	118	9	-	-	PUNCT
ejpam-4497	118	10	open	open	ADJ
ejpam-4497	118	11	sets	set	NOUN
ejpam-4497	118	12	definition	definition	NOUN
ejpam-4497	118	13	14	14	NUM
ejpam-4497	118	14	.	.	PUNCT
ejpam-4497	119	1	a	a	DET
ejpam-4497	119	2	s	s	NOUN
ejpam-4497	119	3	-	-	PUNCT
ejpam-4497	119	4	set	set	ADJ
ejpam-4497	119	5	(	(	PUNCT
ejpam-4497	119	6	h	h	NOUN
ejpam-4497	119	7	,	,	PUNCT
ejpam-4497	119	8	o	o	NOUN
ejpam-4497	119	9	)	)	PUNCT
ejpam-4497	119	10	in	in	ADP
ejpam-4497	119	11	an	an	DET
ejpam-4497	119	12	ists	ist	NOUN
ejpam-4497	119	13	(	(	PUNCT
ejpam-4497	119	14	x,µ,o	x,µ,o	PROPN
ejpam-4497	119	15	)	)	PUNCT
ejpam-4497	119	16	is	be	AUX
ejpam-4497	119	17	said	say	VERB
ejpam-4497	119	18	to	to	PART
ejpam-4497	119	19	be	be	AUX
ejpam-4497	119	20	is	be	AUX
ejpam-4497	119	21	-	-	PUNCT
ejpam-4497	119	22	b	b	NOUN
ejpam-4497	119	23	-	-	PUNCT
ejpam-4497	119	24	open	open	ADJ
ejpam-4497	119	25	if	if	SCONJ
ejpam-4497	119	26	(	(	PUNCT
ejpam-4497	119	27	h	h	NOUN
ejpam-4497	119	28	,	,	PUNCT
ejpam-4497	119	29	o)⊆̃	o)⊆̃	INTJ
ejpam-4497	119	30	int(cl(h	int(cl(h	PROPN
ejpam-4497	119	31	,	,	PUNCT
ejpam-4497	119	32	o))∪̃cl(int(h	o))∪̃cl(int(h	ADJ
ejpam-4497	119	33	,	,	PUNCT
ejpam-4497	119	34	o	o	NOUN
ejpam-4497	119	35	)	)	PUNCT
ejpam-4497	119	36	)	)	PUNCT
ejpam-4497	119	37	.	.	PUNCT
ejpam-4497	120	1	its	its	PRON
ejpam-4497	120	2	complement	complement	NOUN
ejpam-4497	120	3	is	be	AUX
ejpam-4497	120	4	said	say	VERB
ejpam-4497	120	5	to	to	PART
ejpam-4497	120	6	be	be	AUX
ejpam-4497	120	7	an	an	DET
ejpam-4497	120	8	is	is	NOUN
ejpam-4497	120	9	-	-	PUNCT
ejpam-4497	120	10	b	b	NOUN
ejpam-4497	120	11	-	-	PUNCT
ejpam-4497	120	12	closed	closed	ADJ
ejpam-4497	120	13	set	set	NOUN
ejpam-4497	120	14	.	.	PUNCT
ejpam-4497	121	1	proposition	proposition	NOUN
ejpam-4497	121	2	4	4	NUM
ejpam-4497	121	3	.	.	PUNCT
ejpam-4497	122	1	every	every	PRON
ejpam-4497	122	2	is	be	AUX
ejpam-4497	122	3	-	-	PUNCT
ejpam-4497	122	4	semi	semi	ADJ
ejpam-4497	122	5	-	-	ADJ
ejpam-4497	122	6	open	open	ADJ
ejpam-4497	122	7	(	(	PUNCT
ejpam-4497	122	8	is	be	AUX
ejpam-4497	122	9	-	-	PUNCT
ejpam-4497	122	10	pre	pre	ADJ
ejpam-4497	122	11	-	-	ADJ
ejpam-4497	122	12	open	open	ADJ
ejpam-4497	122	13	)	)	PUNCT
ejpam-4497	122	14	set	set	NOUN
ejpam-4497	122	15	is	be	AUX
ejpam-4497	122	16	is	be	AUX
ejpam-4497	122	17	-	-	PUNCT
ejpam-4497	122	18	b	b	NOUN
ejpam-4497	122	19	-	-	PUNCT
ejpam-4497	122	20	open	open	ADJ
ejpam-4497	122	21	.	.	PUNCT
ejpam-4497	123	1	proof	proof	NOUN
ejpam-4497	123	2	.	.	PUNCT
ejpam-4497	124	1	let	let	VERB
ejpam-4497	124	2	(	(	PUNCT
ejpam-4497	124	3	h	h	NOUN
ejpam-4497	124	4	,	,	PUNCT
ejpam-4497	124	5	o	o	NOUN
ejpam-4497	124	6	)	)	PUNCT
ejpam-4497	124	7	be	be	VERB
ejpam-4497	124	8	an	an	DET
ejpam-4497	124	9	is	is	NOUN
ejpam-4497	124	10	-	-	PUNCT
ejpam-4497	124	11	semi	semi	ADJ
ejpam-4497	124	12	-	-	ADJ
ejpam-4497	124	13	open	open	ADJ
ejpam-4497	124	14	(	(	PUNCT
ejpam-4497	124	15	resp	resp	NOUN
ejpam-4497	124	16	.	.	PUNCT
ejpam-4497	125	1	is	be	AUX
ejpam-4497	125	2	-	-	PUNCT
ejpam-4497	125	3	pre	pre	ADJ
ejpam-4497	125	4	-	-	ADJ
ejpam-4497	125	5	open	open	ADJ
ejpam-4497	125	6	)	)	PUNCT
ejpam-4497	125	7	set	set	NOUN
ejpam-4497	125	8	.	.	PUNCT
ejpam-4497	126	1	then	then	ADV
ejpam-4497	126	2	,	,	PUNCT
ejpam-4497	126	3	(	(	PUNCT
ejpam-4497	126	4	h	h	NOUN
ejpam-4497	126	5	,	,	PUNCT
ejpam-4497	126	6	o)⊆̃cl(int(h	o)⊆̃cl(int(h	NOUN
ejpam-4497	126	7	,	,	PUNCT
ejpam-4497	126	8	o	o	NOUN
ejpam-4497	126	9	)	)	PUNCT
ejpam-4497	126	10	)	)	PUNCT
ejpam-4497	126	11	(	(	PUNCT
ejpam-4497	126	12	resp	resp	NOUN
ejpam-4497	126	13	.	.	PUNCT
ejpam-4497	127	1	(	(	PUNCT
ejpam-4497	127	2	h	h	NOUN
ejpam-4497	127	3	,	,	PUNCT
ejpam-4497	127	4	o)⊆̃int(cl(h	o)⊆̃int(cl(h	PROPN
ejpam-4497	127	5	,	,	PUNCT
ejpam-4497	127	6	o	o	NOUN
ejpam-4497	127	7	)	)	PUNCT
ejpam-4497	127	8	)	)	PUNCT
ejpam-4497	127	9	)	)	PUNCT
ejpam-4497	127	10	.	.	PUNCT
ejpam-4497	128	1	automatically	automatically	ADV
ejpam-4497	128	2	,	,	PUNCT
ejpam-4497	128	3	we	we	PRON
ejpam-4497	128	4	obtain	obtain	VERB
ejpam-4497	128	5	(	(	PUNCT
ejpam-4497	128	6	h	h	NOUN
ejpam-4497	128	7	,	,	PUNCT
ejpam-4497	128	8	o)⊆̃int(cl(h	o)⊆̃int(cl(h	PROPN
ejpam-4497	128	9	,	,	PUNCT
ejpam-4497	128	10	o))∪̃cl(int(h	o))∪̃cl(int(h	ADJ
ejpam-4497	128	11	,	,	PUNCT
ejpam-4497	128	12	o	o	NOUN
ejpam-4497	128	13	)	)	PUNCT
ejpam-4497	128	14	)	)	PUNCT
ejpam-4497	128	15	,	,	PUNCT
ejpam-4497	128	16	which	which	PRON
ejpam-4497	128	17	means	mean	VERB
ejpam-4497	128	18	that	that	SCONJ
ejpam-4497	128	19	(	(	PUNCT
ejpam-4497	128	20	h	h	NOUN
ejpam-4497	128	21	,	,	PUNCT
ejpam-4497	128	22	o	o	NOUN
ejpam-4497	128	23	)	)	PUNCT
ejpam-4497	128	24	is	be	AUX
ejpam-4497	128	25	is	be	AUX
ejpam-4497	128	26	-	-	PUNCT
ejpam-4497	128	27	b	b	NOUN
ejpam-4497	128	28	-	-	PUNCT
ejpam-4497	128	29	open	open	ADJ
ejpam-4497	128	30	.	.	PUNCT
ejpam-4497	129	1	the	the	DET
ejpam-4497	129	2	converse	converse	NOUN
ejpam-4497	129	3	of	of	ADP
ejpam-4497	129	4	the	the	DET
ejpam-4497	129	5	above	above	ADJ
ejpam-4497	129	6	proposition	proposition	NOUN
ejpam-4497	129	7	fails	fail	VERB
ejpam-4497	129	8	as	as	SCONJ
ejpam-4497	129	9	the	the	DET
ejpam-4497	129	10	next	next	ADJ
ejpam-4497	129	11	example	example	NOUN
ejpam-4497	129	12	shows	show	VERB
ejpam-4497	129	13	.	.	PUNCT
ejpam-4497	130	1	t.m	t.m	PROPN
ejpam-4497	130	2	.	.	PUNCT
ejpam-4497	130	3	al	al	PROPN
ejpam-4497	130	4	-	-	PUNCT
ejpam-4497	130	5	shami	shami	PROPN
ejpam-4497	130	6	et	et	PROPN
ejpam-4497	130	7	al	al	PROPN
ejpam-4497	130	8	.	.	PUNCT
ejpam-4497	130	9	/	/	SYM
ejpam-4497	130	10	eur	eur	PROPN
ejpam-4497	130	11	.	.	PUNCT
ejpam-4497	131	1	j.	j.	PROPN
ejpam-4497	131	2	pure	pure	PROPN
ejpam-4497	131	3	appl	appl	PROPN
ejpam-4497	131	4	.	.	PROPN
ejpam-4497	131	5	math	math	PROPN
ejpam-4497	131	6	,	,	PUNCT
ejpam-4497	131	7	15	15	NUM
ejpam-4497	131	8	(	(	PUNCT
ejpam-4497	131	9	4	4	NUM
ejpam-4497	131	10	)	)	PUNCT
ejpam-4497	131	11	(	(	PUNCT
ejpam-4497	131	12	2022	2022	NUM
ejpam-4497	131	13	)	)	PUNCT
ejpam-4497	131	14	,	,	PUNCT
ejpam-4497	131	15	1455	1455	NUM
ejpam-4497	131	16	-	-	SYM
ejpam-4497	131	17	1471	1471	NUM
ejpam-4497	131	18	1459	1459	NUM
ejpam-4497	131	19	example	example	NOUN
ejpam-4497	131	20	1	1	NUM
ejpam-4497	131	21	.	.	PUNCT
ejpam-4497	132	1	let	let	VERB
ejpam-4497	132	2	x	x	PUNCT
ejpam-4497	132	3	=	=	PRON
ejpam-4497	132	4	{	{	PUNCT
ejpam-4497	132	5	x1	x1	PROPN
ejpam-4497	132	6	,	,	PUNCT
ejpam-4497	132	7	x2	x2	PROPN
ejpam-4497	132	8	,	,	PUNCT
ejpam-4497	132	9	x3	x3	ADJ
ejpam-4497	132	10	}	}	PUNCT
ejpam-4497	132	11	and	and	CCONJ
ejpam-4497	132	12	o	o	NOUN
ejpam-4497	132	13	=	=	PUNCT
ejpam-4497	132	14	{	{	PUNCT
ejpam-4497	132	15	o1	o1	PROPN
ejpam-4497	132	16	,	,	PUNCT
ejpam-4497	132	17	o2	o2	PROPN
ejpam-4497	132	18	}	}	PUNCT
ejpam-4497	132	19	.	.	PUNCT
ejpam-4497	133	1	then	then	ADV
ejpam-4497	133	2	µ	µ	X
ejpam-4497	133	3	=	=	SYM
ejpam-4497	133	4	{	{	PUNCT
ejpam-4497	133	5	φ	φ	PROPN
ejpam-4497	133	6	,	,	PUNCT
ejpam-4497	133	7	x̃	x̃	PROPN
ejpam-4497	133	8	,	,	PUNCT
ejpam-4497	133	9	(	(	PUNCT
ejpam-4497	133	10	h1,o	h1,o	NOUN
ejpam-4497	133	11	)	)	PUNCT
ejpam-4497	133	12	,	,	PUNCT
ejpam-4497	133	13	(	(	PUNCT
ejpam-4497	133	14	h2,o	h2,o	NOUN
ejpam-4497	133	15	)	)	PUNCT
ejpam-4497	133	16	}	}	PUNCT
ejpam-4497	133	17	is	be	AUX
ejpam-4497	133	18	an	an	DET
ejpam-4497	133	19	ist	ist	NOUN
ejpam-4497	133	20	on	on	ADP
ejpam-4497	133	21	x	x	X
ejpam-4497	133	22	,	,	PUNCT
ejpam-4497	133	23	where	where	SCONJ
ejpam-4497	133	24	(	(	PUNCT
ejpam-4497	133	25	h1,o	h1,o	NOUN
ejpam-4497	133	26	)	)	PUNCT
ejpam-4497	133	27	=	=	PRON
ejpam-4497	133	28	{	{	PUNCT
ejpam-4497	133	29	(	(	PUNCT
ejpam-4497	133	30	o1	o1	NOUN
ejpam-4497	133	31	,	,	PUNCT
ejpam-4497	133	32	{	{	PUNCT
ejpam-4497	133	33	x1	x1	ADJ
ejpam-4497	133	34	}	}	PUNCT
ejpam-4497	133	35	)	)	PUNCT
ejpam-4497	133	36	,	,	PUNCT
ejpam-4497	133	37	(	(	PUNCT
ejpam-4497	133	38	o2	o2	PROPN
ejpam-4497	133	39	,	,	PUNCT
ejpam-4497	133	40	{	{	PUNCT
ejpam-4497	133	41	x2	x2	ADJ
ejpam-4497	133	42	,	,	PUNCT
ejpam-4497	133	43	x3	x3	ADJ
ejpam-4497	133	44	}	}	PUNCT
ejpam-4497	133	45	)	)	PUNCT
ejpam-4497	133	46	}	}	PUNCT
ejpam-4497	133	47	and	and	CCONJ
ejpam-4497	133	48	(	(	PUNCT
ejpam-4497	133	49	h2,o	h2,o	PROPN
ejpam-4497	133	50	)	)	PUNCT
ejpam-4497	133	51	=	=	SYM
ejpam-4497	133	52	{	{	PUNCT
ejpam-4497	133	53	(	(	PUNCT
ejpam-4497	133	54	o1	o1	NOUN
ejpam-4497	133	55	,	,	PUNCT
ejpam-4497	133	56	{	{	PUNCT
ejpam-4497	133	57	x3	x3	ADJ
ejpam-4497	133	58	}	}	PUNCT
ejpam-4497	133	59	)	)	PUNCT
ejpam-4497	133	60	,	,	PUNCT
ejpam-4497	133	61	(	(	PUNCT
ejpam-4497	133	62	o2	o2	PROPN
ejpam-4497	133	63	,	,	PUNCT
ejpam-4497	133	64	{	{	PUNCT
ejpam-4497	133	65	x1	x1	NOUN
ejpam-4497	133	66	}	}	PUNCT
ejpam-4497	133	67	)	)	PUNCT
ejpam-4497	133	68	}	}	PUNCT
ejpam-4497	133	69	.	.	PUNCT
ejpam-4497	134	1	let	let	VERB
ejpam-4497	134	2	(	(	PUNCT
ejpam-4497	134	3	h5,o	h5,o	PROPN
ejpam-4497	134	4	)	)	PUNCT
ejpam-4497	134	5	=	=	SYM
ejpam-4497	134	6	{	{	PUNCT
ejpam-4497	134	7	(	(	PUNCT
ejpam-4497	134	8	o1	o1	NOUN
ejpam-4497	134	9	,	,	PUNCT
ejpam-4497	134	10	{	{	PUNCT
ejpam-4497	134	11	x3	x3	ADJ
ejpam-4497	134	12	}	}	PUNCT
ejpam-4497	134	13	)	)	PUNCT
ejpam-4497	134	14	,	,	PUNCT
ejpam-4497	134	15	(	(	PUNCT
ejpam-4497	134	16	o2	o2	PROPN
ejpam-4497	134	17	,	,	PUNCT
ejpam-4497	134	18	{	{	PUNCT
ejpam-4497	134	19	x3	x3	ADJ
ejpam-4497	134	20	}	}	PUNCT
ejpam-4497	134	21	)	)	PUNCT
ejpam-4497	134	22	}	}	PUNCT
ejpam-4497	134	23	and	and	CCONJ
ejpam-4497	134	24	(	(	PUNCT
ejpam-4497	134	25	h6,o	h6,o	PROPN
ejpam-4497	134	26	)	)	PUNCT
ejpam-4497	134	27	=	=	PRON
ejpam-4497	134	28	{	{	PUNCT
ejpam-4497	134	29	(	(	PUNCT
ejpam-4497	134	30	o1	o1	NOUN
ejpam-4497	134	31	,	,	PUNCT
ejpam-4497	134	32	{	{	PUNCT
ejpam-4497	134	33	x1	x1	PROPN
ejpam-4497	134	34	,	,	PUNCT
ejpam-4497	134	35	x2	x2	PROPN
ejpam-4497	134	36	}	}	PUNCT
ejpam-4497	134	37	)	)	PUNCT
ejpam-4497	134	38	,	,	PUNCT
ejpam-4497	134	39	(	(	PUNCT
ejpam-4497	134	40	o2	o2	PROPN
ejpam-4497	134	41	,	,	PUNCT
ejpam-4497	134	42	{	{	PUNCT
ejpam-4497	134	43	x2	x2	ADJ
ejpam-4497	134	44	,	,	PUNCT
ejpam-4497	134	45	x3	x3	ADJ
ejpam-4497	134	46	}	}	PUNCT
ejpam-4497	134	47	)	)	PUNCT
ejpam-4497	134	48	}	}	PUNCT
ejpam-4497	134	49	.	.	PUNCT
ejpam-4497	135	1	then	then	ADV
ejpam-4497	135	2	(	(	PUNCT
ejpam-4497	135	3	h5,o	h5,o	PROPN
ejpam-4497	135	4	)	)	PUNCT
ejpam-4497	135	5	and	and	CCONJ
ejpam-4497	135	6	(	(	PUNCT
ejpam-4497	135	7	h6,o	h6,o	PROPN
ejpam-4497	135	8	)	)	PUNCT
ejpam-4497	135	9	are	be	AUX
ejpam-4497	135	10	is	be	AUX
ejpam-4497	135	11	-	-	PUNCT
ejpam-4497	135	12	b	b	NOUN
ejpam-4497	135	13	-	-	PUNCT
ejpam-4497	135	14	open	open	ADJ
ejpam-4497	135	15	sets	set	NOUN
ejpam-4497	135	16	because	because	SCONJ
ejpam-4497	135	17	cl(h5,o	cl(h5,o	PROPN
ejpam-4497	135	18	)	)	PUNCT
ejpam-4497	136	1	=	=	PUNCT
ejpam-4497	136	2	x̃	x̃	PROPN
ejpam-4497	136	3	and	and	CCONJ
ejpam-4497	136	4	cl(int(h6,o	cl(int(h6,o	NOUN
ejpam-4497	136	5	)	)	PUNCT
ejpam-4497	136	6	)	)	PUNCT
ejpam-4497	137	1	=	=	PRON
ejpam-4497	137	2	(	(	PUNCT
ejpam-4497	137	3	h6,o	h6,o	PROPN
ejpam-4497	137	4	)	)	PUNCT
ejpam-4497	137	5	.	.	PUNCT
ejpam-4497	138	1	but	but	CCONJ
ejpam-4497	138	2	(	(	PUNCT
ejpam-4497	138	3	h5,o	h5,o	PROPN
ejpam-4497	138	4	)	)	PUNCT
ejpam-4497	138	5	is	be	AUX
ejpam-4497	138	6	not	not	PART
ejpam-4497	138	7	is	be	AUX
ejpam-4497	138	8	-	-	PUNCT
ejpam-4497	138	9	semi	semi	ADV
ejpam-4497	138	10	-	-	ADJ
ejpam-4497	138	11	open	open	ADJ
ejpam-4497	138	12	because	because	SCONJ
ejpam-4497	138	13	int(h5,o	int(h5,o	PROPN
ejpam-4497	138	14	)	)	PUNCT
ejpam-4497	138	15	=	=	SYM
ejpam-4497	138	16	φ	φ	PROPN
ejpam-4497	138	17	,	,	PUNCT
ejpam-4497	138	18	and	and	CCONJ
ejpam-4497	138	19	(	(	PUNCT
ejpam-4497	138	20	h6,o	h6,o	PROPN
ejpam-4497	138	21	)	)	PUNCT
ejpam-4497	138	22	is	be	AUX
ejpam-4497	138	23	not	not	PART
ejpam-4497	138	24	is	be	AUX
ejpam-4497	138	25	-	-	PUNCT
ejpam-4497	138	26	pre	pre	ADJ
ejpam-4497	138	27	-	-	ADJ
ejpam-4497	138	28	open	open	ADJ
ejpam-4497	138	29	because	because	SCONJ
ejpam-4497	138	30	int(cl(h5,o	int(cl(h5,o	NUM
ejpam-4497	138	31	)	)	PUNCT
ejpam-4497	138	32	)	)	PUNCT
ejpam-4497	139	1	=	=	PRON
ejpam-4497	139	2	{	{	PUNCT
ejpam-4497	139	3	(	(	PUNCT
ejpam-4497	139	4	o1	o1	NOUN
ejpam-4497	139	5	,	,	PUNCT
ejpam-4497	139	6	{	{	PUNCT
ejpam-4497	139	7	x1	x1	ADJ
ejpam-4497	139	8	}	}	PUNCT
ejpam-4497	139	9	)	)	PUNCT
ejpam-4497	139	10	,	,	PUNCT
ejpam-4497	139	11	(	(	PUNCT
ejpam-4497	139	12	o2	o2	PROPN
ejpam-4497	139	13	,	,	PUNCT
ejpam-4497	139	14	{	{	PUNCT
ejpam-4497	139	15	x2	x2	PROPN
ejpam-4497	139	16	,	,	PUNCT
ejpam-4497	139	17	x3})}⊉̃(h6,o	x3})}⊉̃(h6,o	PROPN
ejpam-4497	139	18	)	)	PUNCT
ejpam-4497	139	19	.	.	PUNCT
ejpam-4497	140	1	proposition	proposition	NOUN
ejpam-4497	140	2	5	5	NUM
ejpam-4497	140	3	.	.	PUNCT
ejpam-4497	141	1	the	the	DET
ejpam-4497	141	2	unions	union	NOUN
ejpam-4497	141	3	of	of	ADP
ejpam-4497	141	4	is	be	AUX
ejpam-4497	141	5	-	-	PUNCT
ejpam-4497	141	6	b	b	NOUN
ejpam-4497	141	7	-	-	PUNCT
ejpam-4497	141	8	open	open	ADJ
ejpam-4497	141	9	sets	set	NOUN
ejpam-4497	141	10	is	be	AUX
ejpam-4497	141	11	is	be	AUX
ejpam-4497	141	12	-	-	PUNCT
ejpam-4497	141	13	b	b	NOUN
ejpam-4497	141	14	-	-	PUNCT
ejpam-4497	141	15	open	open	ADJ
ejpam-4497	141	16	.	.	PUNCT
ejpam-4497	142	1	proof	proof	NOUN
ejpam-4497	142	2	.	.	PUNCT
ejpam-4497	143	1	consider	consider	VERB
ejpam-4497	143	2	{	{	PUNCT
ejpam-4497	143	3	(	(	PUNCT
ejpam-4497	143	4	hj	hj	PROPN
ejpam-4497	143	5	,	,	PUNCT
ejpam-4497	143	6	o	o	NOUN
ejpam-4497	143	7	)	)	PUNCT
ejpam-4497	143	8	:	:	PUNCT
ejpam-4497	144	1	j	j	PROPN
ejpam-4497	144	2	∈	∈	PROPN
ejpam-4497	144	3	j	j	PROPN
ejpam-4497	144	4	}	}	PUNCT
ejpam-4497	144	5	as	as	ADP
ejpam-4497	144	6	a	a	DET
ejpam-4497	144	7	family	family	NOUN
ejpam-4497	144	8	of	of	ADP
ejpam-4497	144	9	is	be	AUX
ejpam-4497	144	10	-	-	PUNCT
ejpam-4497	144	11	b	b	NOUN
ejpam-4497	144	12	-	-	PUNCT
ejpam-4497	144	13	open	open	ADJ
ejpam-4497	144	14	sets	set	NOUN
ejpam-4497	144	15	.	.	PUNCT
ejpam-4497	144	16	suppose	suppose	VERB
ejpam-4497	144	17	j	j	PROPN
ejpam-4497	144	18	̸=	̸=	PROPN
ejpam-4497	144	19	∅.	∅.	NOUN
ejpam-4497	144	20	then	then	ADV
ejpam-4497	144	21	(	(	PUNCT
ejpam-4497	144	22	hj	hj	PROPN
ejpam-4497	144	23	,	,	PUNCT
ejpam-4497	144	24	o)⊆̃int(cl(h	o)⊆̃int(cl(h	PROPN
ejpam-4497	144	25	,	,	PUNCT
ejpam-4497	144	26	o))∪̃cl(int(h	o))∪̃cl(int(h	ADJ
ejpam-4497	144	27	,	,	PUNCT
ejpam-4497	144	28	o	o	NOUN
ejpam-4497	144	29	)	)	PUNCT
ejpam-4497	144	30	)	)	PUNCT
ejpam-4497	144	31	for	for	ADP
ejpam-4497	144	32	each	each	DET
ejpam-4497	144	33	j	j	PROPN
ejpam-4497	144	34	∈	∈	PROPN
ejpam-4497	144	35	j	j	PROPN
ejpam-4497	144	36	.	.	PUNCT
ejpam-4497	145	1	thus	thus	ADV
ejpam-4497	145	2	,	,	PUNCT
ejpam-4497	145	3	∪̃j∈j(hj	∪̃j∈j(hj	VERB
ejpam-4497	145	4	,	,	PUNCT
ejpam-4497	145	5	o)⊆̃∪̃j∈j	o)⊆̃∪̃j∈j	PROPN
ejpam-4497	146	1	[	[	X
ejpam-4497	146	2	int(cl(h	int(cl(h	PROPN
ejpam-4497	146	3	,	,	PUNCT
ejpam-4497	146	4	o	o	NOUN
ejpam-4497	146	5	)	)	PUNCT
ejpam-4497	146	6	)	)	PUNCT
ejpam-4497	147	1	∪̃cl(int(h	∪̃cl(int(h	ADJ
ejpam-4497	147	2	,	,	PUNCT
ejpam-4497	147	3	o	o	NOUN
ejpam-4497	147	4	)	)	PUNCT
ejpam-4497	147	5	)	)	PUNCT
ejpam-4497	147	6	]	]	PUNCT
ejpam-4497	148	1	⊆̃int(cl(∪̃j∈j(hj	⊆̃int(cl(∪̃j∈j(hj	NOUN
ejpam-4497	148	2	,	,	PUNCT
ejpam-4497	148	3	o)))∪̃	o)))∪̃	VERB
ejpam-4497	148	4	cl(int(∪̃j∈j(hj	cl(int(∪̃j∈j(hj	NOUN
ejpam-4497	148	5	,	,	PUNCT
ejpam-4497	148	6	o	o	NOUN
ejpam-4497	148	7	)	)	PUNCT
ejpam-4497	148	8	)	)	PUNCT
ejpam-4497	148	9	)	)	PUNCT
ejpam-4497	148	10	.	.	PUNCT
ejpam-4497	149	1	hence	hence	ADV
ejpam-4497	149	2	,	,	PUNCT
ejpam-4497	149	3	∪̃j∈j(hj	∪̃j∈j(hj	VERB
ejpam-4497	149	4	,	,	PUNCT
ejpam-4497	149	5	o	o	NOUN
ejpam-4497	149	6	)	)	PUNCT
ejpam-4497	149	7	is	be	AUX
ejpam-4497	149	8	isb	isb	NOUN
ejpam-4497	149	9	-	-	PUNCT
ejpam-4497	149	10	open	open	ADJ
ejpam-4497	149	11	.	.	PUNCT
ejpam-4497	150	1	corollary	corollary	ADJ
ejpam-4497	150	2	1	1	NUM
ejpam-4497	150	3	.	.	PUNCT
ejpam-4497	151	1	the	the	DET
ejpam-4497	151	2	intersections	intersection	NOUN
ejpam-4497	151	3	of	of	ADP
ejpam-4497	151	4	is	is	NOUN
ejpam-4497	151	5	-	-	PUNCT
ejpam-4497	151	6	b	b	NOUN
ejpam-4497	151	7	-	-	PUNCT
ejpam-4497	151	8	closed	closed	ADJ
ejpam-4497	151	9	sets	set	NOUN
ejpam-4497	151	10	is	be	AUX
ejpam-4497	151	11	is	be	AUX
ejpam-4497	151	12	-	-	PUNCT
ejpam-4497	151	13	b	b	NOUN
ejpam-4497	151	14	-	-	PUNCT
ejpam-4497	151	15	closed	closed	ADJ
ejpam-4497	151	16	.	.	PUNCT
ejpam-4497	152	1	proposition	proposition	NOUN
ejpam-4497	152	2	6	6	NUM
ejpam-4497	152	3	.	.	PUNCT
ejpam-4497	153	1	if	if	SCONJ
ejpam-4497	153	2	(	(	PUNCT
ejpam-4497	153	3	h1,o	h1,o	NOUN
ejpam-4497	153	4	)	)	PUNCT
ejpam-4497	153	5	is	be	AUX
ejpam-4497	153	6	is	be	AUX
ejpam-4497	153	7	-	-	PUNCT
ejpam-4497	153	8	open	open	ADJ
ejpam-4497	153	9	and	and	CCONJ
ejpam-4497	154	1	(	(	PUNCT
ejpam-4497	154	2	h2,o	h2,o	PROPN
ejpam-4497	154	3	)	)	PUNCT
ejpam-4497	154	4	is	be	AUX
ejpam-4497	154	5	is	be	AUX
ejpam-4497	154	6	-	-	PUNCT
ejpam-4497	154	7	b	b	NOUN
ejpam-4497	154	8	-	-	PUNCT
ejpam-4497	154	9	open	open	ADJ
ejpam-4497	154	10	,	,	PUNCT
ejpam-4497	154	11	then	then	ADV
ejpam-4497	154	12	(	(	PUNCT
ejpam-4497	154	13	h1,o)∩̃(h2,o	h1,o)∩̃(h2,o	NOUN
ejpam-4497	154	14	)	)	PUNCT
ejpam-4497	154	15	is	be	AUX
ejpam-4497	154	16	is	be	AUX
ejpam-4497	154	17	-	-	PUNCT
ejpam-4497	154	18	b	b	NOUN
ejpam-4497	154	19	-	-	PUNCT
ejpam-4497	154	20	open	open	ADJ
ejpam-4497	154	21	.	.	PUNCT
ejpam-4497	155	1	proof	proof	NOUN
ejpam-4497	155	2	.	.	PUNCT
ejpam-4497	156	1	let	let	AUX
ejpam-4497	156	2	(	(	PUNCT
ejpam-4497	156	3	h1,o	h1,o	NOUN
ejpam-4497	156	4	)	)	PUNCT
ejpam-4497	156	5	and	and	CCONJ
ejpam-4497	156	6	(	(	PUNCT
ejpam-4497	156	7	h2,o	h2,o	PROPN
ejpam-4497	156	8	)	)	PUNCT
ejpam-4497	156	9	be	be	AUX
ejpam-4497	156	10	as	as	SCONJ
ejpam-4497	156	11	given	give	VERB
ejpam-4497	156	12	in	in	ADP
ejpam-4497	156	13	the	the	DET
ejpam-4497	156	14	proposition	proposition	NOUN
ejpam-4497	156	15	.	.	PUNCT
ejpam-4497	157	1	then	then	ADV
ejpam-4497	157	2	(	(	PUNCT
ejpam-4497	157	3	h1,o)∩̃(h2,o)⊆̃	h1,o)∩̃(h2,o)⊆̃	INTJ
ejpam-4497	157	4	(	(	PUNCT
ejpam-4497	157	5	h1,o)∩̃[int(cl(h2,o))∪̃cl(int(h2,o	h1,o)∩̃[int(cl(h2,o))∪̃cl(int(h2,o	NOUN
ejpam-4497	157	6	)	)	PUNCT
ejpam-4497	157	7	)	)	PUNCT
ejpam-4497	157	8	]	]	PUNCT
ejpam-4497	158	1	=	=	PUNCT
ejpam-4497	159	1	[	[	X
ejpam-4497	159	2	(	(	PUNCT
ejpam-4497	159	3	h1,o)∩̃int(cl(h2,o	h1,o)∩̃int(cl(h2,o	NOUN
ejpam-4497	159	4	)	)	PUNCT
ejpam-4497	159	5	)	)	PUNCT
ejpam-4497	159	6	]	]	PUNCT
ejpam-4497	159	7	∪̃[(h1,o)∩̃	∪̃[(h1,o)∩̃	PROPN
ejpam-4497	159	8	cl(int(h2,o	cl(int(h2,o	NOUN
ejpam-4497	159	9	)	)	PUNCT
ejpam-4497	159	10	)	)	PUNCT
ejpam-4497	159	11	]	]	PUNCT
ejpam-4497	159	12	.	.	PUNCT
ejpam-4497	160	1	it	it	PRON
ejpam-4497	160	2	follows	follow	VERB
ejpam-4497	160	3	from	from	ADP
ejpam-4497	160	4	proposition	proposition	NOUN
ejpam-4497	160	5	2	2	NUM
ejpam-4497	160	6	that	that	SCONJ
ejpam-4497	160	7	(	(	PUNCT
ejpam-4497	160	8	h1,o)∩̃	h1,o)∩̃	PROPN
ejpam-4497	160	9	int(cl(h2,o))⊆̃int(cl[(h1,o)∩̃(h2,o	int(cl(h2,o))⊆̃int(cl[(h1,o)∩̃(h2,o	PROPN
ejpam-4497	160	10	)	)	PUNCT
ejpam-4497	160	11	]	]	PUNCT
ejpam-4497	160	12	and	and	CCONJ
ejpam-4497	160	13	(	(	PUNCT
ejpam-4497	160	14	h1,o)∩̃	h1,o)∩̃	PROPN
ejpam-4497	160	15	cl(int(h2,o))⊆̃cl(int[(h1,o)∩̃(h2,o	cl(int(h2,o))⊆̃cl(int[(h1,o)∩̃(h2,o	NOUN
ejpam-4497	160	16	)	)	PUNCT
ejpam-4497	160	17	]	]	PUNCT
ejpam-4497	160	18	hence	hence	ADV
ejpam-4497	160	19	,	,	PUNCT
ejpam-4497	160	20	(	(	PUNCT
ejpam-4497	160	21	h1,o)∩̃(h2,o	h1,o)∩̃(h2,o	NOUN
ejpam-4497	160	22	)	)	PUNCT
ejpam-4497	160	23	is	be	AUX
ejpam-4497	160	24	an	an	DET
ejpam-4497	160	25	is	is	NOUN
ejpam-4497	160	26	-	-	PUNCT
ejpam-4497	160	27	b	b	NOUN
ejpam-4497	160	28	-	-	PUNCT
ejpam-4497	160	29	open	open	ADJ
ejpam-4497	160	30	set	set	NOUN
ejpam-4497	160	31	.	.	PUNCT
ejpam-4497	161	1	corollary	corollary	ADJ
ejpam-4497	161	2	2	2	NUM
ejpam-4497	161	3	.	.	PUNCT
ejpam-4497	162	1	if	if	SCONJ
ejpam-4497	162	2	(	(	PUNCT
ejpam-4497	162	3	h1,o	h1,o	NOUN
ejpam-4497	162	4	)	)	PUNCT
ejpam-4497	162	5	is	be	AUX
ejpam-4497	162	6	is	be	AUX
ejpam-4497	162	7	-	-	PUNCT
ejpam-4497	162	8	closed	closed	ADJ
ejpam-4497	162	9	and	and	CCONJ
ejpam-4497	162	10	(	(	PUNCT
ejpam-4497	162	11	h2,o	h2,o	PROPN
ejpam-4497	162	12	)	)	PUNCT
ejpam-4497	162	13	is	be	AUX
ejpam-4497	162	14	is	be	AUX
ejpam-4497	162	15	-	-	PUNCT
ejpam-4497	162	16	b	b	NOUN
ejpam-4497	162	17	-	-	PUNCT
ejpam-4497	162	18	closed	closed	ADJ
ejpam-4497	162	19	,	,	PUNCT
ejpam-4497	162	20	then	then	ADV
ejpam-4497	162	21	(	(	PUNCT
ejpam-4497	162	22	h1,o)∩̃(h2,o	h1,o)∩̃(h2,o	NOUN
ejpam-4497	162	23	)	)	PUNCT
ejpam-4497	162	24	is	be	AUX
ejpam-4497	162	25	is	be	AUX
ejpam-4497	162	26	-	-	PUNCT
ejpam-4497	162	27	b	b	NOUN
ejpam-4497	162	28	-	-	PUNCT
ejpam-4497	162	29	closed	closed	ADJ
ejpam-4497	162	30	.	.	PUNCT
ejpam-4497	163	1	proposition	proposition	NOUN
ejpam-4497	163	2	7	7	NUM
ejpam-4497	163	3	.	.	PUNCT
ejpam-4497	164	1	the	the	DET
ejpam-4497	164	2	image	image	NOUN
ejpam-4497	164	3	of	of	ADP
ejpam-4497	164	4	an	an	DET
ejpam-4497	164	5	is	is	AUX
ejpam-4497	164	6	-	-	PUNCT
ejpam-4497	164	7	b	b	NOUN
ejpam-4497	164	8	-	-	PUNCT
ejpam-4497	164	9	open	open	ADJ
ejpam-4497	164	10	set	set	NOUN
ejpam-4497	164	11	under	under	ADP
ejpam-4497	164	12	an	an	DET
ejpam-4497	164	13	is	is	NOUN
ejpam-4497	164	14	-	-	PUNCT
ejpam-4497	164	15	homeomorphism	homeomorphism	PROPN
ejpam-4497	164	16	is	be	AUX
ejpam-4497	164	17	is	be	AUX
ejpam-4497	164	18	-	-	PUNCT
ejpam-4497	164	19	b	b	NOUN
ejpam-4497	164	20	-	-	PUNCT
ejpam-4497	164	21	open	open	ADJ
ejpam-4497	164	22	.	.	PUNCT
ejpam-4497	165	1	proof	proof	NOUN
ejpam-4497	165	2	.	.	PUNCT
ejpam-4497	166	1	consider	consider	VERB
ejpam-4497	166	2	fψ	fψ	ADJ
ejpam-4497	166	3	:	:	PUNCT
ejpam-4497	166	4	(	(	PUNCT
ejpam-4497	166	5	x1	x1	PROPN
ejpam-4497	166	6	,	,	PUNCT
ejpam-4497	166	7	µ1,o1	µ1,o1	PROPN
ejpam-4497	166	8	)	)	PUNCT
ejpam-4497	166	9	→	→	SYM
ejpam-4497	166	10	(	(	PUNCT
ejpam-4497	166	11	x2	x2	PROPN
ejpam-4497	166	12	,	,	PUNCT
ejpam-4497	166	13	µ2,o2	µ2,o2	PROPN
ejpam-4497	166	14	)	)	PUNCT
ejpam-4497	166	15	as	as	ADP
ejpam-4497	166	16	an	an	DET
ejpam-4497	166	17	is	be	AUX
ejpam-4497	166	18	-	-	PUNCT
ejpam-4497	166	19	continuous	continuous	ADJ
ejpam-4497	166	20	map	map	NOUN
ejpam-4497	166	21	and	and	CCONJ
ejpam-4497	166	22	let	let	VERB
ejpam-4497	166	23	(	(	PUNCT
ejpam-4497	166	24	h	h	NOUN
ejpam-4497	166	25	,	,	PUNCT
ejpam-4497	166	26	o1	o1	NOUN
ejpam-4497	166	27	)	)	PUNCT
ejpam-4497	166	28	be	be	VERB
ejpam-4497	166	29	an	an	DET
ejpam-4497	166	30	is	is	NOUN
ejpam-4497	166	31	-	-	PUNCT
ejpam-4497	166	32	b	b	NOUN
ejpam-4497	166	33	-	-	PUNCT
ejpam-4497	166	34	open	open	ADJ
ejpam-4497	166	35	subset	subset	NOUN
ejpam-4497	166	36	of	of	ADP
ejpam-4497	166	37	(	(	PUNCT
ejpam-4497	166	38	x1	x1	PROPN
ejpam-4497	166	39	,	,	PUNCT
ejpam-4497	166	40	µ1,o1	µ1,o1	PROPN
ejpam-4497	166	41	)	)	PUNCT
ejpam-4497	166	42	.	.	PUNCT
ejpam-4497	167	1	then	then	ADV
ejpam-4497	167	2	fψ(h	fψ(h	NUM
ejpam-4497	167	3	,	,	PUNCT
ejpam-4497	167	4	o1)⊆̃fψ[cl(int(h	o1)⊆̃fψ[cl(int(h	NOUN
ejpam-4497	167	5	,	,	PUNCT
ejpam-4497	167	6	o1))∪̃int(cl(h	o1))∪̃int(cl(h	NOUN
ejpam-4497	167	7	,	,	PUNCT
ejpam-4497	167	8	o1	o1	NOUN
ejpam-4497	167	9	)	)	PUNCT
ejpam-4497	167	10	)	)	PUNCT
ejpam-4497	167	11	]	]	PUNCT
ejpam-4497	167	12	.	.	PUNCT
ejpam-4497	168	1	it	it	PRON
ejpam-4497	168	2	follows	follow	VERB
ejpam-4497	168	3	from	from	ADP
ejpam-4497	168	4	lemma	lemma	PROPN
ejpam-4497	168	5	1	1	NUM
ejpam-4497	168	6	that	that	SCONJ
ejpam-4497	168	7	fψ(h	fψ(h	NUM
ejpam-4497	168	8	,	,	PUNCT
ejpam-4497	168	9	o1)⊆̃cl(int(fψ(h	o1)⊆̃cl(int(fψ(h	NUM
ejpam-4497	168	10	,	,	PUNCT
ejpam-4497	168	11	o1)))∪̃int(cl(fψ(h	o1)))∪̃int(cl(fψ(h	NOUN
ejpam-4497	168	12	,	,	PUNCT
ejpam-4497	168	13	o1	o1	NOUN
ejpam-4497	168	14	)	)	PUNCT
ejpam-4497	168	15	)	)	PUNCT
ejpam-4497	168	16	)	)	PUNCT
ejpam-4497	168	17	.	.	PUNCT
ejpam-4497	169	1	hence	hence	ADV
ejpam-4497	169	2	,	,	PUNCT
ejpam-4497	169	3	fψ(h	fψ(h	NUM
ejpam-4497	169	4	,	,	PUNCT
ejpam-4497	169	5	o1	o1	NOUN
ejpam-4497	169	6	)	)	PUNCT
ejpam-4497	169	7	is	be	AUX
ejpam-4497	169	8	an	an	DET
ejpam-4497	169	9	is	is	NOUN
ejpam-4497	169	10	-	-	PUNCT
ejpam-4497	169	11	b	b	NOUN
ejpam-4497	169	12	-	-	PUNCT
ejpam-4497	169	13	open	open	ADJ
ejpam-4497	169	14	subset	subset	NOUN
ejpam-4497	169	15	of	of	ADP
ejpam-4497	169	16	(	(	PUNCT
ejpam-4497	169	17	x2	x2	PROPN
ejpam-4497	169	18	,	,	PUNCT
ejpam-4497	169	19	µ2,o2	µ2,o2	PROPN
ejpam-4497	169	20	)	)	PUNCT
ejpam-4497	169	21	,	,	PUNCT
ejpam-4497	169	22	as	as	SCONJ
ejpam-4497	169	23	required	require	VERB
ejpam-4497	169	24	.	.	PUNCT
ejpam-4497	170	1	4	4	X
ejpam-4497	170	2	.	.	X
ejpam-4497	170	3	infra	infra	NOUN
ejpam-4497	170	4	b	b	NOUN
ejpam-4497	170	5	-	-	ADJ
ejpam-4497	170	6	interior	interior	ADJ
ejpam-4497	170	7	,	,	PUNCT
ejpam-4497	170	8	infra	infra	NOUN
ejpam-4497	170	9	b	b	NOUN
ejpam-4497	170	10	-	-	PUNCT
ejpam-4497	170	11	closure	closure	NOUN
ejpam-4497	170	12	,	,	PUNCT
ejpam-4497	170	13	infra	infra	NOUN
ejpam-4497	170	14	b	b	NOUN
ejpam-4497	170	15	-	-	PUNCT
ejpam-4497	170	16	limit	limit	NOUN
ejpam-4497	170	17	and	and	CCONJ
ejpam-4497	170	18	infra	infra	NOUN
ejpam-4497	170	19	b	b	NOUN
ejpam-4497	170	20	-	-	PUNCT
ejpam-4497	170	21	boundary	boundary	ADJ
ejpam-4497	170	22	soft	soft	ADJ
ejpam-4497	170	23	points	point	NOUN
ejpam-4497	170	24	of	of	ADP
ejpam-4497	170	25	a	a	DET
ejpam-4497	170	26	soft	soft	ADJ
ejpam-4497	170	27	set	set	NOUN
ejpam-4497	170	28	definition	definition	NOUN
ejpam-4497	170	29	15	15	NUM
ejpam-4497	170	30	.	.	PUNCT
ejpam-4497	171	1	let	let	AUX
ejpam-4497	171	2	(	(	PUNCT
ejpam-4497	171	3	h	h	NOUN
ejpam-4497	171	4	,	,	PUNCT
ejpam-4497	171	5	o	o	NOUN
ejpam-4497	171	6	)	)	PUNCT
ejpam-4497	171	7	be	be	VERB
ejpam-4497	171	8	an	an	DET
ejpam-4497	171	9	s	s	NOUN
ejpam-4497	171	10	-	-	PUNCT
ejpam-4497	171	11	set	set	VERB
ejpam-4497	171	12	in	in	ADP
ejpam-4497	171	13	(	(	PUNCT
ejpam-4497	171	14	x,µ,o	x,µ,o	PROPN
ejpam-4497	171	15	)	)	PUNCT
ejpam-4497	171	16	.	.	PUNCT
ejpam-4497	172	1	then	then	ADV
ejpam-4497	172	2	:	:	PUNCT
ejpam-4497	172	3	(	(	PUNCT
ejpam-4497	172	4	i	i	NOUN
ejpam-4497	172	5	)	)	PUNCT
ejpam-4497	172	6	the	the	PRON
ejpam-4497	172	7	is	be	AUX
ejpam-4497	172	8	-	-	PUNCT
ejpam-4497	172	9	b	b	NOUN
ejpam-4497	172	10	-	-	NOUN
ejpam-4497	172	11	interior	interior	ADJ
ejpam-4497	172	12	of	of	ADP
ejpam-4497	172	13	(	(	PUNCT
ejpam-4497	172	14	h	h	NOUN
ejpam-4497	172	15	,	,	PUNCT
ejpam-4497	172	16	o	o	NOUN
ejpam-4497	172	17	)	)	PUNCT
ejpam-4497	172	18	,	,	PUNCT
ejpam-4497	172	19	denoted	denote	VERB
ejpam-4497	172	20	by	by	ADP
ejpam-4497	172	21	bint(h	bint(h	NOUN
ejpam-4497	172	22	,	,	PUNCT
ejpam-4497	172	23	o	o	NOUN
ejpam-4497	172	24	)	)	PUNCT
ejpam-4497	172	25	,	,	PUNCT
ejpam-4497	172	26	is	be	AUX
ejpam-4497	172	27	the	the	DET
ejpam-4497	172	28	union	union	NOUN
ejpam-4497	172	29	of	of	ADP
ejpam-4497	172	30	all	all	PRON
ejpam-4497	172	31	is	be	AUX
ejpam-4497	172	32	-	-	PUNCT
ejpam-4497	172	33	b	b	NOUN
ejpam-4497	172	34	-	-	PUNCT
ejpam-4497	172	35	open	open	ADJ
ejpam-4497	172	36	sets	set	NOUN
ejpam-4497	172	37	that	that	PRON
ejpam-4497	172	38	are	be	AUX
ejpam-4497	172	39	contained	contain	VERB
ejpam-4497	172	40	in	in	ADP
ejpam-4497	172	41	(	(	PUNCT
ejpam-4497	172	42	h	h	NOUN
ejpam-4497	172	43	,	,	PUNCT
ejpam-4497	172	44	o	o	NOUN
ejpam-4497	172	45	)	)	PUNCT
ejpam-4497	172	46	.	.	PUNCT
ejpam-4497	173	1	t.m	t.m	PROPN
ejpam-4497	173	2	.	.	PUNCT
ejpam-4497	173	3	al	al	PROPN
ejpam-4497	173	4	-	-	PUNCT
ejpam-4497	173	5	shami	shami	PROPN
ejpam-4497	173	6	et	et	PROPN
ejpam-4497	173	7	al	al	PROPN
ejpam-4497	173	8	.	.	PUNCT
ejpam-4497	173	9	/	/	SYM
ejpam-4497	173	10	eur	eur	PROPN
ejpam-4497	173	11	.	.	PUNCT
ejpam-4497	174	1	j.	j.	PROPN
ejpam-4497	174	2	pure	pure	PROPN
ejpam-4497	174	3	appl	appl	PROPN
ejpam-4497	174	4	.	.	PROPN
ejpam-4497	174	5	math	math	PROPN
ejpam-4497	174	6	,	,	PUNCT
ejpam-4497	174	7	15	15	NUM
ejpam-4497	174	8	(	(	PUNCT
ejpam-4497	174	9	4	4	NUM
ejpam-4497	174	10	)	)	PUNCT
ejpam-4497	174	11	(	(	PUNCT
ejpam-4497	174	12	2022	2022	NUM
ejpam-4497	174	13	)	)	PUNCT
ejpam-4497	174	14	,	,	PUNCT
ejpam-4497	174	15	1455	1455	NUM
ejpam-4497	174	16	-	-	SYM
ejpam-4497	174	17	1471	1471	NUM
ejpam-4497	174	18	1460	1460	NUM
ejpam-4497	174	19	(	(	PUNCT
ejpam-4497	174	20	ii	ii	NOUN
ejpam-4497	174	21	)	)	PUNCT
ejpam-4497	174	22	the	the	PRON
ejpam-4497	174	23	is	be	AUX
ejpam-4497	174	24	-	-	PUNCT
ejpam-4497	174	25	b	b	NOUN
ejpam-4497	174	26	-	-	PUNCT
ejpam-4497	174	27	closure	closure	NOUN
ejpam-4497	174	28	of	of	ADP
ejpam-4497	174	29	(	(	PUNCT
ejpam-4497	174	30	h	h	NOUN
ejpam-4497	174	31	,	,	PUNCT
ejpam-4497	174	32	o	o	NOUN
ejpam-4497	174	33	)	)	PUNCT
ejpam-4497	174	34	,	,	PUNCT
ejpam-4497	174	35	denoted	denote	VERB
ejpam-4497	174	36	by	by	ADP
ejpam-4497	174	37	bcl(h	bcl(h	PROPN
ejpam-4497	174	38	,	,	PUNCT
ejpam-4497	174	39	o	o	NOUN
ejpam-4497	174	40	)	)	PUNCT
ejpam-4497	174	41	,	,	PUNCT
ejpam-4497	174	42	is	be	AUX
ejpam-4497	174	43	the	the	DET
ejpam-4497	174	44	intersection	intersection	NOUN
ejpam-4497	174	45	of	of	ADP
ejpam-4497	174	46	all	all	PRON
ejpam-4497	174	47	is	be	AUX
ejpam-4497	174	48	-	-	PUNCT
ejpam-4497	174	49	b	b	NOUN
ejpam-4497	174	50	-	-	PUNCT
ejpam-4497	174	51	closed	closed	ADJ
ejpam-4497	174	52	sets	set	NOUN
ejpam-4497	174	53	containing	contain	VERB
ejpam-4497	174	54	(	(	PUNCT
ejpam-4497	174	55	h	h	NOUN
ejpam-4497	174	56	,	,	PUNCT
ejpam-4497	174	57	o	o	NOUN
ejpam-4497	174	58	)	)	PUNCT
ejpam-4497	174	59	.	.	PUNCT
ejpam-4497	175	1	proposition	proposition	NOUN
ejpam-4497	175	2	8	8	NUM
ejpam-4497	175	3	.	.	PUNCT
ejpam-4497	176	1	we	we	PRON
ejpam-4497	176	2	have	have	VERB
ejpam-4497	176	3	the	the	DET
ejpam-4497	176	4	following	follow	VERB
ejpam-4497	176	5	properties	property	NOUN
ejpam-4497	176	6	.	.	PUNCT
ejpam-4497	177	1	(	(	PUNCT
ejpam-4497	177	2	i	i	NOUN
ejpam-4497	177	3	)	)	PUNCT
ejpam-4497	177	4	(	(	PUNCT
ejpam-4497	177	5	h	h	NOUN
ejpam-4497	177	6	,	,	PUNCT
ejpam-4497	177	7	o	o	NOUN
ejpam-4497	177	8	)	)	PUNCT
ejpam-4497	177	9	is	be	AUX
ejpam-4497	177	10	an	an	DET
ejpam-4497	177	11	is	is	NOUN
ejpam-4497	177	12	-	-	PUNCT
ejpam-4497	177	13	b	b	NOUN
ejpam-4497	177	14	-	-	PUNCT
ejpam-4497	177	15	open	open	ADJ
ejpam-4497	177	16	subset	subset	NOUN
ejpam-4497	177	17	of	of	ADP
ejpam-4497	177	18	(	(	PUNCT
ejpam-4497	177	19	x,µ,o	x,µ,o	PROPN
ejpam-4497	177	20	)	)	PUNCT
ejpam-4497	177	21	iff	iff	PROPN
ejpam-4497	177	22	bint(h	bint(h	NOUN
ejpam-4497	177	23	,	,	PUNCT
ejpam-4497	177	24	o	o	NOUN
ejpam-4497	177	25	)	)	PUNCT
ejpam-4497	178	1	=	=	SYM
ejpam-4497	178	2	(	(	PUNCT
ejpam-4497	178	3	h	h	NOUN
ejpam-4497	178	4	,	,	PUNCT
ejpam-4497	178	5	o	o	NOUN
ejpam-4497	178	6	)	)	PUNCT
ejpam-4497	178	7	.	.	PUNCT
ejpam-4497	179	1	(	(	PUNCT
ejpam-4497	179	2	ii	ii	NOUN
ejpam-4497	179	3	)	)	PUNCT
ejpam-4497	179	4	(	(	PUNCT
ejpam-4497	179	5	h	h	NOUN
ejpam-4497	179	6	,	,	PUNCT
ejpam-4497	179	7	o	o	NOUN
ejpam-4497	179	8	)	)	PUNCT
ejpam-4497	179	9	is	be	AUX
ejpam-4497	179	10	an	an	DET
ejpam-4497	179	11	is	is	NOUN
ejpam-4497	179	12	-	-	PUNCT
ejpam-4497	179	13	b	b	NOUN
ejpam-4497	179	14	-	-	PUNCT
ejpam-4497	179	15	closed	closed	ADJ
ejpam-4497	179	16	subset	subset	NOUN
ejpam-4497	179	17	of	of	ADP
ejpam-4497	179	18	(	(	PUNCT
ejpam-4497	179	19	x,µ,o	x,µ,o	PROPN
ejpam-4497	179	20	)	)	PUNCT
ejpam-4497	179	21	iff	iff	PROPN
ejpam-4497	179	22	bcl(h	bcl(h	PROPN
ejpam-4497	179	23	,	,	PUNCT
ejpam-4497	179	24	o	o	NOUN
ejpam-4497	179	25	)	)	PUNCT
ejpam-4497	180	1	=	=	SYM
ejpam-4497	180	2	(	(	PUNCT
ejpam-4497	180	3	h	h	NOUN
ejpam-4497	180	4	,	,	PUNCT
ejpam-4497	180	5	o	o	NOUN
ejpam-4497	180	6	)	)	PUNCT
ejpam-4497	180	7	.	.	PUNCT
ejpam-4497	181	1	proof	proof	NOUN
ejpam-4497	181	2	.	.	PUNCT
ejpam-4497	182	1	it	it	PRON
ejpam-4497	182	2	comes	come	VERB
ejpam-4497	182	3	from	from	ADP
ejpam-4497	182	4	proposition	proposition	NOUN
ejpam-4497	182	5	5	5	NUM
ejpam-4497	182	6	and	and	CCONJ
ejpam-4497	182	7	corollary	corollary	ADJ
ejpam-4497	182	8	1	1	NUM
ejpam-4497	182	9	.	.	PUNCT
ejpam-4497	183	1	the	the	DET
ejpam-4497	183	2	two	two	NUM
ejpam-4497	183	3	characterizations	characterization	NOUN
ejpam-4497	183	4	given	give	VERB
ejpam-4497	183	5	in	in	ADP
ejpam-4497	183	6	the	the	DET
ejpam-4497	183	7	the	the	DET
ejpam-4497	183	8	above	above	ADJ
ejpam-4497	183	9	proposition	proposition	NOUN
ejpam-4497	183	10	are	be	AUX
ejpam-4497	183	11	generally	generally	ADV
ejpam-4497	183	12	false	false	ADJ
ejpam-4497	183	13	for	for	SCONJ
ejpam-4497	183	14	is	be	AUX
ejpam-4497	183	15	-	-	PUNCT
ejpam-4497	183	16	open	open	ADJ
ejpam-4497	183	17	and	and	CCONJ
ejpam-4497	183	18	is	be	AUX
ejpam-4497	183	19	-	-	PUNCT
ejpam-4497	183	20	closed	closed	ADJ
ejpam-4497	183	21	sets	set	NOUN
ejpam-4497	183	22	.	.	PUNCT
ejpam-4497	184	1	proposition	proposition	NOUN
ejpam-4497	184	2	9	9	NUM
ejpam-4497	184	3	.	.	PUNCT
ejpam-4497	185	1	let	let	AUX
ejpam-4497	185	2	(	(	PUNCT
ejpam-4497	185	3	h	h	NOUN
ejpam-4497	185	4	,	,	PUNCT
ejpam-4497	185	5	o	o	NOUN
ejpam-4497	185	6	)	)	PUNCT
ejpam-4497	185	7	be	be	AUX
ejpam-4497	185	8	a	a	DET
ejpam-4497	185	9	subset	subset	NOUN
ejpam-4497	185	10	of	of	ADP
ejpam-4497	185	11	(	(	PUNCT
ejpam-4497	185	12	x,µ,o	x,µ,o	PROPN
ejpam-4497	185	13	)	)	PUNCT
ejpam-4497	185	14	.	.	PUNCT
ejpam-4497	186	1	(	(	PUNCT
ejpam-4497	186	2	i	i	NOUN
ejpam-4497	186	3	)	)	PUNCT
ejpam-4497	186	4	δxo	δxo	VERB
ejpam-4497	186	5	∈	∈	PROPN
ejpam-4497	186	6	bint(h	bint(h	NOUN
ejpam-4497	186	7	,	,	PUNCT
ejpam-4497	186	8	o	o	NOUN
ejpam-4497	186	9	)	)	PUNCT
ejpam-4497	186	10	iff	iff	PROPN
ejpam-4497	186	11	there	there	PRON
ejpam-4497	186	12	exists	exist	VERB
ejpam-4497	186	13	an	an	DET
ejpam-4497	186	14	is	is	NOUN
ejpam-4497	186	15	-	-	PUNCT
ejpam-4497	186	16	b	b	NOUN
ejpam-4497	186	17	-	-	PUNCT
ejpam-4497	186	18	open	open	ADJ
ejpam-4497	186	19	set	set	NOUN
ejpam-4497	186	20	(	(	PUNCT
ejpam-4497	186	21	f	f	PROPN
ejpam-4497	186	22	,	,	PUNCT
ejpam-4497	186	23	o	o	NOUN
ejpam-4497	186	24	)	)	PUNCT
ejpam-4497	186	25	such	such	ADJ
ejpam-4497	186	26	that	that	SCONJ
ejpam-4497	186	27	δxo	δxo	VERB
ejpam-4497	186	28	∈	∈	PROPN
ejpam-4497	186	29	(	(	PUNCT
ejpam-4497	186	30	f	f	NOUN
ejpam-4497	186	31	,	,	PUNCT
ejpam-4497	186	32	o)⊆̃(h	o)⊆̃(h	ADV
ejpam-4497	186	33	,	,	PUNCT
ejpam-4497	186	34	o	o	NOUN
ejpam-4497	186	35	)	)	PUNCT
ejpam-4497	186	36	.	.	PUNCT
ejpam-4497	187	1	(	(	PUNCT
ejpam-4497	187	2	ii	ii	NOUN
ejpam-4497	187	3	)	)	PUNCT
ejpam-4497	187	4	δxo	δxo	NOUN
ejpam-4497	187	5	∈	∈	PROPN
ejpam-4497	187	6	bcl(h	bcl(h	PROPN
ejpam-4497	187	7	,	,	PUNCT
ejpam-4497	187	8	o	o	NOUN
ejpam-4497	187	9	)	)	PUNCT
ejpam-4497	187	10	iff	iff	VERB
ejpam-4497	187	11	the	the	DET
ejpam-4497	187	12	intersection	intersection	NOUN
ejpam-4497	187	13	of	of	ADP
ejpam-4497	187	14	any	any	PRON
ejpam-4497	187	15	is	be	AUX
ejpam-4497	187	16	-	-	PUNCT
ejpam-4497	187	17	b	b	NOUN
ejpam-4497	187	18	-	-	PUNCT
ejpam-4497	187	19	open	open	ADJ
ejpam-4497	187	20	set	set	NOUN
ejpam-4497	187	21	(	(	PUNCT
ejpam-4497	187	22	f	f	X
ejpam-4497	187	23	,	,	PUNCT
ejpam-4497	187	24	o	o	NOUN
ejpam-4497	187	25	)	)	PUNCT
ejpam-4497	187	26	containing	contain	VERB
ejpam-4497	187	27	δxo	δxo	NOUN
ejpam-4497	187	28	and	and	CCONJ
ejpam-4497	187	29	(	(	PUNCT
ejpam-4497	187	30	h	h	NOUN
ejpam-4497	187	31	,	,	PUNCT
ejpam-4497	187	32	o	o	NOUN
ejpam-4497	187	33	)	)	PUNCT
ejpam-4497	187	34	is	be	AUX
ejpam-4497	187	35	non	non	ADJ
ejpam-4497	187	36	-	-	ADJ
ejpam-4497	187	37	null	null	ADJ
ejpam-4497	187	38	.	.	PUNCT
ejpam-4497	188	1	proof	proof	NOUN
ejpam-4497	188	2	.	.	PUNCT
ejpam-4497	189	1	the	the	DET
ejpam-4497	189	2	proof	proof	NOUN
ejpam-4497	189	3	of	of	ADP
ejpam-4497	189	4	(	(	PUNCT
ejpam-4497	189	5	i	i	NOUN
ejpam-4497	189	6	)	)	PUNCT
ejpam-4497	189	7	is	be	AUX
ejpam-4497	189	8	obvious	obvious	ADJ
ejpam-4497	189	9	,	,	PUNCT
ejpam-4497	189	10	so	so	ADV
ejpam-4497	189	11	we	we	PRON
ejpam-4497	189	12	prove	prove	VERB
ejpam-4497	189	13	(	(	PUNCT
ejpam-4497	189	14	ii	ii	NOUN
ejpam-4497	189	15	)	)	PUNCT
ejpam-4497	189	16	.	.	PUNCT
ejpam-4497	190	1	let	let	VERB
ejpam-4497	190	2	δxo	δxo	VERB
ejpam-4497	190	3	∈	∈	PROPN
ejpam-4497	190	4	bcl(h	bcl(h	PROPN
ejpam-4497	190	5	,	,	PUNCT
ejpam-4497	190	6	o	o	NOUN
ejpam-4497	190	7	)	)	PUNCT
ejpam-4497	190	8	.	.	PUNCT
ejpam-4497	191	1	then	then	ADV
ejpam-4497	191	2	every	every	PRON
ejpam-4497	191	3	is	be	AUX
ejpam-4497	191	4	-	-	PUNCT
ejpam-4497	191	5	b	b	NOUN
ejpam-4497	191	6	-	-	PUNCT
ejpam-4497	191	7	closed	closed	ADJ
ejpam-4497	191	8	set	set	NOUN
ejpam-4497	191	9	contains	contain	VERB
ejpam-4497	191	10	(	(	PUNCT
ejpam-4497	191	11	h	h	NOUN
ejpam-4497	191	12	,	,	PUNCT
ejpam-4497	191	13	o	o	NOUN
ejpam-4497	191	14	)	)	PUNCT
ejpam-4497	191	15	contains	contain	VERB
ejpam-4497	191	16	δxo	δxo	NOUN
ejpam-4497	191	17	as	as	ADV
ejpam-4497	191	18	well	well	ADV
ejpam-4497	191	19	.	.	PUNCT
ejpam-4497	192	1	suppose	suppose	VERB
ejpam-4497	192	2	that	that	SCONJ
ejpam-4497	192	3	there	there	PRON
ejpam-4497	192	4	exists	exist	VERB
ejpam-4497	192	5	an	an	DET
ejpam-4497	192	6	is	is	NOUN
ejpam-4497	192	7	-	-	PUNCT
ejpam-4497	192	8	b	b	NOUN
ejpam-4497	192	9	-	-	PUNCT
ejpam-4497	192	10	open	open	ADJ
ejpam-4497	192	11	set	set	NOUN
ejpam-4497	192	12	(	(	PUNCT
ejpam-4497	192	13	f	f	X
ejpam-4497	192	14	,	,	PUNCT
ejpam-4497	192	15	o	o	NOUN
ejpam-4497	192	16	)	)	PUNCT
ejpam-4497	192	17	containing	contain	VERB
ejpam-4497	192	18	δxo	δxo	NOUN
ejpam-4497	192	19	such	such	ADJ
ejpam-4497	192	20	that	that	PRON
ejpam-4497	192	21	(	(	PUNCT
ejpam-4497	192	22	h	h	NOUN
ejpam-4497	192	23	,	,	PUNCT
ejpam-4497	192	24	o)∩̃(f	o)∩̃(f	ADV
ejpam-4497	192	25	,	,	PUNCT
ejpam-4497	192	26	o	o	NOUN
ejpam-4497	192	27	)	)	PUNCT
ejpam-4497	193	1	=	=	SYM
ejpam-4497	194	1	φ	φ	PROPN
ejpam-4497	194	2	.	.	PUNCT
ejpam-4497	195	1	therefore	therefore	ADV
ejpam-4497	195	2	,	,	PUNCT
ejpam-4497	195	3	(	(	PUNCT
ejpam-4497	195	4	h	h	NOUN
ejpam-4497	195	5	,	,	PUNCT
ejpam-4497	195	6	o)⊆̃(fc	o)⊆̃(fc	PROPN
ejpam-4497	195	7	,	,	PUNCT
ejpam-4497	195	8	o	o	NOUN
ejpam-4497	195	9	)	)	PUNCT
ejpam-4497	195	10	which	which	PRON
ejpam-4497	195	11	means	mean	VERB
ejpam-4497	195	12	that	that	SCONJ
ejpam-4497	195	13	δxo	δxo	VERB
ejpam-4497	195	14	̸∈	̸∈	PROPN
ejpam-4497	195	15	bcl(h	bcl(h	PROPN
ejpam-4497	195	16	,	,	PUNCT
ejpam-4497	195	17	o	o	NOUN
ejpam-4497	195	18	)	)	PUNCT
ejpam-4497	195	19	.	.	PUNCT
ejpam-4497	196	1	this	this	PRON
ejpam-4497	196	2	is	be	AUX
ejpam-4497	196	3	a	a	DET
ejpam-4497	196	4	contradiction	contradiction	NOUN
ejpam-4497	196	5	.	.	PUNCT
ejpam-4497	197	1	conversely	conversely	ADV
ejpam-4497	197	2	,	,	PUNCT
ejpam-4497	197	3	suppose	suppose	VERB
ejpam-4497	197	4	that	that	SCONJ
ejpam-4497	197	5	there	there	PRON
ejpam-4497	197	6	exists	exist	VERB
ejpam-4497	197	7	an	an	DET
ejpam-4497	197	8	is	is	NOUN
ejpam-4497	197	9	-	-	PUNCT
ejpam-4497	197	10	b	b	NOUN
ejpam-4497	197	11	-	-	PUNCT
ejpam-4497	197	12	open	open	ADJ
ejpam-4497	197	13	set	set	NOUN
ejpam-4497	197	14	(	(	PUNCT
ejpam-4497	197	15	f	f	X
ejpam-4497	197	16	,	,	PUNCT
ejpam-4497	197	17	o	o	NOUN
ejpam-4497	197	18	)	)	PUNCT
ejpam-4497	197	19	containing	contain	VERB
ejpam-4497	197	20	δxo	δxo	NOUN
ejpam-4497	197	21	such	such	ADJ
ejpam-4497	197	22	that	that	PRON
ejpam-4497	197	23	(	(	PUNCT
ejpam-4497	197	24	h	h	NOUN
ejpam-4497	197	25	,	,	PUNCT
ejpam-4497	197	26	o)∩̃(f	o)∩̃(f	ADV
ejpam-4497	197	27	,	,	PUNCT
ejpam-4497	197	28	o	o	NOUN
ejpam-4497	197	29	)	)	PUNCT
ejpam-4497	197	30	=	=	SYM
ejpam-4497	198	1	φ	φ	PROPN
ejpam-4497	198	2	.	.	PUNCT
ejpam-4497	199	1	therefore	therefore	ADV
ejpam-4497	199	2	,	,	PUNCT
ejpam-4497	199	3	bcl(h	bcl(h	PROPN
ejpam-4497	199	4	,	,	PUNCT
ejpam-4497	199	5	o)⊆̃(fc	o)⊆̃(fc	PROPN
ejpam-4497	199	6	,	,	PUNCT
ejpam-4497	199	7	o	o	NOUN
ejpam-4497	199	8	)	)	PUNCT
ejpam-4497	199	9	which	which	PRON
ejpam-4497	199	10	means	mean	VERB
ejpam-4497	199	11	that	that	SCONJ
ejpam-4497	199	12	δxo	δxo	VERB
ejpam-4497	199	13	̸∈	̸∈	PROPN
ejpam-4497	199	14	bcl(h	bcl(h	PROPN
ejpam-4497	199	15	,	,	PUNCT
ejpam-4497	199	16	o	o	NOUN
ejpam-4497	199	17	)	)	PUNCT
ejpam-4497	199	18	.	.	PUNCT
ejpam-4497	200	1	hence	hence	ADV
ejpam-4497	200	2	,	,	PUNCT
ejpam-4497	200	3	the	the	DET
ejpam-4497	200	4	result	result	NOUN
ejpam-4497	200	5	holds	hold	VERB
ejpam-4497	200	6	.	.	PUNCT
ejpam-4497	201	1	proposition	proposition	NOUN
ejpam-4497	201	2	10	10	NUM
ejpam-4497	201	3	.	.	PUNCT
ejpam-4497	202	1	let	let	AUX
ejpam-4497	202	2	(	(	PUNCT
ejpam-4497	202	3	h	h	NOUN
ejpam-4497	202	4	,	,	PUNCT
ejpam-4497	202	5	o	o	NOUN
ejpam-4497	202	6	)	)	PUNCT
ejpam-4497	202	7	be	be	AUX
ejpam-4497	202	8	a	a	DET
ejpam-4497	202	9	subset	subset	NOUN
ejpam-4497	202	10	of	of	ADP
ejpam-4497	202	11	(	(	PUNCT
ejpam-4497	202	12	x,µ,o	x,µ,o	PROPN
ejpam-4497	202	13	)	)	PUNCT
ejpam-4497	202	14	.	.	PUNCT
ejpam-4497	203	1	then	then	ADV
ejpam-4497	203	2	:	:	PUNCT
ejpam-4497	203	3	(	(	PUNCT
ejpam-4497	203	4	i	i	NOUN
ejpam-4497	203	5	)	)	PUNCT
ejpam-4497	203	6	(	(	PUNCT
ejpam-4497	203	7	bint(h	bint(h	NOUN
ejpam-4497	203	8	,	,	PUNCT
ejpam-4497	203	9	o))c	o))c	NOUN
ejpam-4497	203	10	=	=	SYM
ejpam-4497	203	11	bcl(hc	bcl(hc	NOUN
ejpam-4497	203	12	,	,	PUNCT
ejpam-4497	203	13	o	o	NOUN
ejpam-4497	203	14	)	)	PUNCT
ejpam-4497	203	15	.	.	PUNCT
ejpam-4497	204	1	(	(	PUNCT
ejpam-4497	204	2	ii	ii	NOUN
ejpam-4497	204	3	)	)	PUNCT
ejpam-4497	204	4	(	(	PUNCT
ejpam-4497	204	5	bcl(h	bcl(h	PROPN
ejpam-4497	204	6	,	,	PUNCT
ejpam-4497	204	7	o))c	o))c	NOUN
ejpam-4497	204	8	=	=	NOUN
ejpam-4497	204	9	bint(hc	bint(hc	PROPN
ejpam-4497	204	10	,	,	PUNCT
ejpam-4497	204	11	o	o	NOUN
ejpam-4497	204	12	)	)	PUNCT
ejpam-4497	204	13	.	.	PUNCT
ejpam-4497	205	1	proof	proof	NOUN
ejpam-4497	205	2	.	.	PUNCT
ejpam-4497	206	1	(	(	PUNCT
ejpam-4497	206	2	i	i	NOUN
ejpam-4497	206	3	):	):	PUNCT
ejpam-4497	206	4	(	(	PUNCT
ejpam-4497	206	5	bint(h	bint(h	NOUN
ejpam-4497	206	6	,	,	PUNCT
ejpam-4497	206	7	o))c	o))c	NOUN
ejpam-4497	206	8	=	=	SYM
ejpam-4497	206	9	{	{	PUNCT
ejpam-4497	206	10	∪̃	∪̃	PROPN
ejpam-4497	206	11	j∈j	j∈j	NOUN
ejpam-4497	206	12	(	(	PUNCT
ejpam-4497	206	13	fj	fj	INTJ
ejpam-4497	206	14	,	,	PUNCT
ejpam-4497	206	15	o	o	NOUN
ejpam-4497	206	16	)	)	PUNCT
ejpam-4497	206	17	:	:	PUNCT
ejpam-4497	206	18	(	(	PUNCT
ejpam-4497	206	19	fj	fj	INTJ
ejpam-4497	206	20	,	,	PUNCT
ejpam-4497	206	21	o	o	NOUN
ejpam-4497	206	22	)	)	PUNCT
ejpam-4497	206	23	is	be	AUX
ejpam-4497	206	24	an	an	DET
ejpam-4497	206	25	is	is	NOUN
ejpam-4497	206	26	-	-	PUNCT
ejpam-4497	206	27	b	b	NOUN
ejpam-4497	206	28	-	-	PUNCT
ejpam-4497	206	29	open	open	ADJ
ejpam-4497	206	30	set	set	NOUN
ejpam-4497	206	31	contained	contain	VERB
ejpam-4497	206	32	in	in	ADP
ejpam-4497	206	33	(	(	PUNCT
ejpam-4497	206	34	h	h	NOUN
ejpam-4497	206	35	,	,	PUNCT
ejpam-4497	206	36	o)}c	o)}c	X
ejpam-4497	206	37	=	=	SYM
ejpam-4497	206	38	∩̃	∩̃	PUNCT
ejpam-4497	206	39	j∈j	j∈j	NOUN
ejpam-4497	206	40	{	{	PUNCT
ejpam-4497	206	41	(	(	PUNCT
ejpam-4497	206	42	fc	fc	PROPN
ejpam-4497	206	43	j	j	PROPN
ejpam-4497	206	44	,	,	PUNCT
ejpam-4497	206	45	o	o	NOUN
ejpam-4497	206	46	)	)	PUNCT
ejpam-4497	206	47	:	:	PUNCT
ejpam-4497	206	48	(	(	PUNCT
ejpam-4497	206	49	fc	fc	PROPN
ejpam-4497	206	50	j	j	PROPN
ejpam-4497	206	51	,	,	PUNCT
ejpam-4497	206	52	o	o	NOUN
ejpam-4497	206	53	)	)	PUNCT
ejpam-4497	206	54	is	be	AUX
ejpam-4497	206	55	an	an	DET
ejpam-4497	206	56	is	is	NOUN
ejpam-4497	206	57	-	-	PUNCT
ejpam-4497	206	58	b	b	NOUN
ejpam-4497	206	59	-	-	PUNCT
ejpam-4497	206	60	closed	closed	ADJ
ejpam-4497	206	61	set	set	NOUN
ejpam-4497	206	62	containing	contain	VERB
ejpam-4497	206	63	(	(	PUNCT
ejpam-4497	206	64	hc	hc	PROPN
ejpam-4497	206	65	,	,	PUNCT
ejpam-4497	206	66	o	o	NOUN
ejpam-4497	206	67	)	)	PUNCT
ejpam-4497	206	68	}	}	PUNCT
ejpam-4497	206	69	=	=	SYM
ejpam-4497	206	70	bcl(hc	bcl(hc	NOUN
ejpam-4497	206	71	,	,	PUNCT
ejpam-4497	206	72	o	o	NOUN
ejpam-4497	206	73	)	)	PUNCT
ejpam-4497	206	74	.	.	PUNCT
ejpam-4497	207	1	the	the	DET
ejpam-4497	207	2	proof	proof	NOUN
ejpam-4497	207	3	of	of	ADP
ejpam-4497	207	4	(	(	PUNCT
ejpam-4497	207	5	ii	ii	NOUN
ejpam-4497	207	6	)	)	PUNCT
ejpam-4497	207	7	is	be	AUX
ejpam-4497	207	8	similar	similar	ADJ
ejpam-4497	207	9	to	to	ADP
ejpam-4497	207	10	(	(	PUNCT
ejpam-4497	207	11	i	i	NOUN
ejpam-4497	207	12	)	)	PUNCT
ejpam-4497	207	13	.	.	PUNCT
ejpam-4497	208	1	proposition	proposition	NOUN
ejpam-4497	208	2	11	11	NUM
ejpam-4497	208	3	.	.	PUNCT
ejpam-4497	209	1	let	let	VERB
ejpam-4497	209	2	(	(	PUNCT
ejpam-4497	209	3	f	f	X
ejpam-4497	209	4	,	,	PUNCT
ejpam-4497	209	5	o	o	NOUN
ejpam-4497	209	6	)	)	PUNCT
ejpam-4497	209	7	be	be	VERB
ejpam-4497	209	8	an	an	DET
ejpam-4497	209	9	is	is	NOUN
ejpam-4497	209	10	-	-	PUNCT
ejpam-4497	209	11	open	open	ADJ
ejpam-4497	209	12	set	set	NOUN
ejpam-4497	209	13	and	and	CCONJ
ejpam-4497	209	14	(	(	PUNCT
ejpam-4497	209	15	λ	λ	PROPN
ejpam-4497	209	16	,	,	PUNCT
ejpam-4497	209	17	o	o	NOUN
ejpam-4497	209	18	)	)	PUNCT
ejpam-4497	209	19	be	be	AUX
ejpam-4497	209	20	an	an	DET
ejpam-4497	209	21	is	is	NOUN
ejpam-4497	209	22	-	-	PUNCT
ejpam-4497	209	23	closed	closed	ADJ
ejpam-4497	209	24	set	set	NOUN
ejpam-4497	209	25	in	in	ADP
ejpam-4497	209	26	(	(	PUNCT
ejpam-4497	209	27	x,µ,o	x,µ,o	PROPN
ejpam-4497	209	28	)	)	PUNCT
ejpam-4497	209	29	.	.	PUNCT
ejpam-4497	210	1	then	then	ADV
ejpam-4497	210	2	:	:	PUNCT
ejpam-4497	210	3	(	(	PUNCT
ejpam-4497	210	4	i	i	NOUN
ejpam-4497	210	5	)	)	PUNCT
ejpam-4497	210	6	(	(	PUNCT
ejpam-4497	210	7	f	f	PROPN
ejpam-4497	210	8	,	,	PUNCT
ejpam-4497	210	9	o)∩̃bcl(h	o)∩̃bcl(h	PROPN
ejpam-4497	210	10	,	,	PUNCT
ejpam-4497	210	11	o)⊆̃bcl((f	o)⊆̃bcl((f	NUM
ejpam-4497	210	12	,	,	PUNCT
ejpam-4497	210	13	o)∩̃(h	o)∩̃(h	PROPN
ejpam-4497	210	14	,	,	PUNCT
ejpam-4497	210	15	o	o	NOUN
ejpam-4497	210	16	)	)	PUNCT
ejpam-4497	210	17	)	)	PUNCT
ejpam-4497	210	18	.	.	PUNCT
ejpam-4497	211	1	(	(	PUNCT
ejpam-4497	211	2	ii	ii	NOUN
ejpam-4497	211	3	)	)	PUNCT
ejpam-4497	211	4	bint((λ	bint((λ	NOUN
ejpam-4497	211	5	,	,	PUNCT
ejpam-4497	211	6	o)∪̃(h	o)∪̃(h	ADV
ejpam-4497	211	7	,	,	PUNCT
ejpam-4497	211	8	o))⊆̃(λ	o))⊆̃(λ	ADV
ejpam-4497	211	9	,	,	PUNCT
ejpam-4497	211	10	o)∪̃bint(h	o)∪̃bint(h	ADJ
ejpam-4497	211	11	,	,	PUNCT
ejpam-4497	211	12	o	o	NOUN
ejpam-4497	211	13	)	)	PUNCT
ejpam-4497	211	14	.	.	PUNCT
ejpam-4497	212	1	t.m	t.m	PROPN
ejpam-4497	212	2	.	.	PUNCT
ejpam-4497	212	3	al	al	PROPN
ejpam-4497	212	4	-	-	PUNCT
ejpam-4497	212	5	shami	shami	PROPN
ejpam-4497	212	6	et	et	PROPN
ejpam-4497	212	7	al	al	PROPN
ejpam-4497	212	8	.	.	PUNCT
ejpam-4497	212	9	/	/	SYM
ejpam-4497	212	10	eur	eur	PROPN
ejpam-4497	212	11	.	.	PUNCT
ejpam-4497	213	1	j.	j.	PROPN
ejpam-4497	213	2	pure	pure	PROPN
ejpam-4497	213	3	appl	appl	PROPN
ejpam-4497	213	4	.	.	PROPN
ejpam-4497	213	5	math	math	PROPN
ejpam-4497	213	6	,	,	PUNCT
ejpam-4497	213	7	15	15	NUM
ejpam-4497	213	8	(	(	PUNCT
ejpam-4497	213	9	4	4	NUM
ejpam-4497	213	10	)	)	PUNCT
ejpam-4497	213	11	(	(	PUNCT
ejpam-4497	213	12	2022	2022	NUM
ejpam-4497	213	13	)	)	PUNCT
ejpam-4497	213	14	,	,	PUNCT
ejpam-4497	213	15	1455	1455	NUM
ejpam-4497	213	16	-	-	SYM
ejpam-4497	213	17	1471	1471	NUM
ejpam-4497	213	18	1461	1461	NUM
ejpam-4497	213	19	proof	proof	NOUN
ejpam-4497	213	20	.	.	PUNCT
ejpam-4497	214	1	(	(	PUNCT
ejpam-4497	214	2	i	i	NOUN
ejpam-4497	214	3	):	):	PUNCT
ejpam-4497	214	4	let	let	VERB
ejpam-4497	214	5	δxo	δxo	VERB
ejpam-4497	214	6	∈	∈	PROPN
ejpam-4497	214	7	(	(	PUNCT
ejpam-4497	214	8	f	f	PROPN
ejpam-4497	214	9	,	,	PUNCT
ejpam-4497	214	10	o)∩̃bcl(h	o)∩̃bcl(h	PROPN
ejpam-4497	214	11	,	,	PUNCT
ejpam-4497	214	12	o	o	NOUN
ejpam-4497	214	13	)	)	PUNCT
ejpam-4497	214	14	.	.	PUNCT
ejpam-4497	215	1	then	then	ADV
ejpam-4497	215	2	δxo	δxo	VERB
ejpam-4497	215	3	∈	∈	PROPN
ejpam-4497	215	4	(	(	PUNCT
ejpam-4497	215	5	f	f	PROPN
ejpam-4497	215	6	,	,	PUNCT
ejpam-4497	215	7	o	o	NOUN
ejpam-4497	215	8	)	)	PUNCT
ejpam-4497	215	9	and	and	CCONJ
ejpam-4497	215	10	δxo	δxo	VERB
ejpam-4497	215	11	∈	∈	PROPN
ejpam-4497	215	12	bcl(h	bcl(h	PROPN
ejpam-4497	215	13	,	,	PUNCT
ejpam-4497	215	14	o	o	NOUN
ejpam-4497	215	15	)	)	PUNCT
ejpam-4497	215	16	.	.	PUNCT
ejpam-4497	216	1	this	this	PRON
ejpam-4497	216	2	implies	imply	VERB
ejpam-4497	216	3	(	(	PUNCT
ejpam-4497	216	4	u	u	NOUN
ejpam-4497	216	5	,	,	PUNCT
ejpam-4497	216	6	o)∩̃(h	o)∩̃(h	PROPN
ejpam-4497	216	7	,	,	PUNCT
ejpam-4497	216	8	o	o	NOUN
ejpam-4497	216	9	)	)	PUNCT
ejpam-4497	216	10	̸=	̸=	PROPN
ejpam-4497	216	11	φ	φ	NUM
ejpam-4497	216	12	for	for	ADP
ejpam-4497	216	13	every	every	PRON
ejpam-4497	216	14	is	be	AUX
ejpam-4497	216	15	-	-	PUNCT
ejpam-4497	216	16	b	b	NOUN
ejpam-4497	216	17	-	-	PUNCT
ejpam-4497	216	18	open	open	ADJ
ejpam-4497	216	19	set	set	NOUN
ejpam-4497	216	20	(	(	PUNCT
ejpam-4497	216	21	u	u	NOUN
ejpam-4497	216	22	,	,	PUNCT
ejpam-4497	216	23	o	o	NOUN
ejpam-4497	216	24	)	)	PUNCT
ejpam-4497	216	25	containing	contain	VERB
ejpam-4497	216	26	δxo	δxo	NOUN
ejpam-4497	216	27	.	.	PUNCT
ejpam-4497	217	1	it	it	PRON
ejpam-4497	217	2	follows	follow	VERB
ejpam-4497	217	3	from	from	ADP
ejpam-4497	217	4	proposition	proposition	NOUN
ejpam-4497	217	5	6	6	NUM
ejpam-4497	217	6	that	that	PRON
ejpam-4497	217	7	(	(	PUNCT
ejpam-4497	217	8	f	f	X
ejpam-4497	217	9	,	,	PUNCT
ejpam-4497	217	10	o)∩̃(u	o)∩̃(u	PROPN
ejpam-4497	217	11	,	,	PUNCT
ejpam-4497	217	12	o	o	NOUN
ejpam-4497	217	13	)	)	PUNCT
ejpam-4497	217	14	is	be	AUX
ejpam-4497	217	15	an	an	DET
ejpam-4497	217	16	is	is	NOUN
ejpam-4497	217	17	-	-	PUNCT
ejpam-4497	217	18	b	b	NOUN
ejpam-4497	217	19	-	-	PUNCT
ejpam-4497	217	20	open	open	ADJ
ejpam-4497	217	21	set	set	NOUN
ejpam-4497	217	22	containing	contain	VERB
ejpam-4497	217	23	δxo	δxo	NOUN
ejpam-4497	217	24	.	.	PUNCT
ejpam-4497	218	1	therefore	therefore	ADV
ejpam-4497	218	2	,	,	PUNCT
ejpam-4497	218	3	[	[	X
ejpam-4497	218	4	(	(	PUNCT
ejpam-4497	218	5	f	f	X
ejpam-4497	218	6	,	,	PUNCT
ejpam-4497	218	7	o)∩̃(u	o)∩̃(u	PROPN
ejpam-4497	218	8	,	,	PUNCT
ejpam-4497	218	9	o)]∩̃(h	o)]∩̃(h	NUM
ejpam-4497	218	10	,	,	PUNCT
ejpam-4497	218	11	o	o	NOUN
ejpam-4497	218	12	)	)	PUNCT
ejpam-4497	218	13	̸=	̸=	PROPN
ejpam-4497	218	14	φ	φ	NUM
ejpam-4497	218	15	.	.	PUNCT
ejpam-4497	219	1	now	now	ADV
ejpam-4497	219	2	,	,	PUNCT
ejpam-4497	219	3	(	(	PUNCT
ejpam-4497	219	4	u	u	NOUN
ejpam-4497	219	5	,	,	PUNCT
ejpam-4497	219	6	o)∩̃[(f	o)∩̃[(f	ADP
ejpam-4497	219	7	,	,	PUNCT
ejpam-4497	219	8	o)∩̃(h	o)∩̃(h	PROPN
ejpam-4497	219	9	,	,	PUNCT
ejpam-4497	219	10	o	o	NOUN
ejpam-4497	219	11	)	)	PUNCT
ejpam-4497	219	12	]	]	PUNCT
ejpam-4497	219	13	̸=	̸=	PROPN
ejpam-4497	219	14	φ	φ	NUM
ejpam-4497	219	15	which	which	PRON
ejpam-4497	219	16	means	mean	VERB
ejpam-4497	219	17	that	that	SCONJ
ejpam-4497	219	18	δxo	δxo	NOUN
ejpam-4497	219	19	∈	∈	PRON
ejpam-4497	219	20	bcl((f	bcl((f	VERB
ejpam-4497	219	21	,	,	PUNCT
ejpam-4497	219	22	o)∩̃(h	o)∩̃(h	PROPN
ejpam-4497	219	23	,	,	PUNCT
ejpam-4497	219	24	o	o	NOUN
ejpam-4497	219	25	)	)	PUNCT
ejpam-4497	219	26	)	)	PUNCT
ejpam-4497	219	27	.	.	PUNCT
ejpam-4497	220	1	hence	hence	ADV
ejpam-4497	220	2	,	,	PUNCT
ejpam-4497	220	3	(	(	PUNCT
ejpam-4497	220	4	f	f	PROPN
ejpam-4497	220	5	,	,	PUNCT
ejpam-4497	220	6	o)∩̃bcl(h	o)∩̃bcl(h	PROPN
ejpam-4497	220	7	,	,	PUNCT
ejpam-4497	220	8	o)⊆̃bcl((f	o)⊆̃bcl((f	NUM
ejpam-4497	220	9	,	,	PUNCT
ejpam-4497	220	10	o)∩̃(h	o)∩̃(h	PROPN
ejpam-4497	220	11	,	,	PUNCT
ejpam-4497	220	12	o	o	NOUN
ejpam-4497	220	13	)	)	PUNCT
ejpam-4497	220	14	)	)	PUNCT
ejpam-4497	220	15	.	.	PUNCT
ejpam-4497	221	1	one	one	PRON
ejpam-4497	221	2	can	can	AUX
ejpam-4497	221	3	prove	prove	VERB
ejpam-4497	221	4	(	(	PUNCT
ejpam-4497	221	5	ii	ii	NOUN
ejpam-4497	221	6	)	)	PUNCT
ejpam-4497	221	7	following	follow	VERB
ejpam-4497	221	8	similar	similar	ADJ
ejpam-4497	221	9	arguments	argument	NOUN
ejpam-4497	221	10	.	.	PUNCT
ejpam-4497	222	1	theorem	theorem	NOUN
ejpam-4497	222	2	1	1	NUM
ejpam-4497	222	3	.	.	PUNCT
ejpam-4497	223	1	let	let	VERB
ejpam-4497	223	2	(	(	PUNCT
ejpam-4497	223	3	h	h	NOUN
ejpam-4497	223	4	,	,	PUNCT
ejpam-4497	223	5	o	o	NOUN
ejpam-4497	223	6	)	)	PUNCT
ejpam-4497	223	7	and	and	CCONJ
ejpam-4497	223	8	(	(	PUNCT
ejpam-4497	223	9	f	f	X
ejpam-4497	223	10	,	,	PUNCT
ejpam-4497	223	11	o	o	NOUN
ejpam-4497	223	12	)	)	PUNCT
ejpam-4497	223	13	are	be	AUX
ejpam-4497	223	14	in	in	ADP
ejpam-4497	223	15	(	(	PUNCT
ejpam-4497	223	16	x,µ,o	x,µ,o	PROPN
ejpam-4497	223	17	)	)	PUNCT
ejpam-4497	223	18	.	.	PUNCT
ejpam-4497	224	1	then	then	ADV
ejpam-4497	224	2	we	we	PRON
ejpam-4497	224	3	have	have	VERB
ejpam-4497	224	4	:	:	PUNCT
ejpam-4497	224	5	(	(	PUNCT
ejpam-4497	224	6	i	i	NOUN
ejpam-4497	224	7	)	)	PUNCT
ejpam-4497	224	8	bint(x̃	bint(x̃	NOUN
ejpam-4497	224	9	)	)	PUNCT
ejpam-4497	224	10	=	=	SYM
ejpam-4497	225	1	x̃.	x̃.	ADJ
ejpam-4497	225	2	(	(	PUNCT
ejpam-4497	225	3	ii	ii	NOUN
ejpam-4497	225	4	)	)	PUNCT
ejpam-4497	225	5	bint(h	bint(h	NOUN
ejpam-4497	225	6	,	,	PUNCT
ejpam-4497	225	7	o)⊆̃(h	o)⊆̃(h	ADV
ejpam-4497	225	8	,	,	PUNCT
ejpam-4497	225	9	o	o	NOUN
ejpam-4497	225	10	)	)	PUNCT
ejpam-4497	225	11	.	.	PUNCT
ejpam-4497	226	1	(	(	PUNCT
ejpam-4497	226	2	iii	iii	X
ejpam-4497	226	3	)	)	PUNCT
ejpam-4497	226	4	if	if	SCONJ
ejpam-4497	226	5	(	(	PUNCT
ejpam-4497	226	6	f	f	X
ejpam-4497	226	7	,	,	PUNCT
ejpam-4497	226	8	o)⊆̃(h	o)⊆̃(h	ADV
ejpam-4497	226	9	,	,	PUNCT
ejpam-4497	226	10	o	o	NOUN
ejpam-4497	226	11	)	)	PUNCT
ejpam-4497	226	12	,	,	PUNCT
ejpam-4497	226	13	then	then	ADV
ejpam-4497	226	14	bint(f	bint(f	NOUN
ejpam-4497	226	15	,	,	PUNCT
ejpam-4497	226	16	o)⊆̃bint(h	o)⊆̃bint(h	ADJ
ejpam-4497	226	17	,	,	PUNCT
ejpam-4497	226	18	o	o	NOUN
ejpam-4497	226	19	)	)	PUNCT
ejpam-4497	226	20	.	.	PUNCT
ejpam-4497	227	1	(	(	PUNCT
ejpam-4497	227	2	iv	iv	X
ejpam-4497	227	3	)	)	PUNCT
ejpam-4497	227	4	bint(bint(h	bint(bint(h	PROPN
ejpam-4497	227	5	,	,	PUNCT
ejpam-4497	227	6	o	o	NOUN
ejpam-4497	227	7	)	)	PUNCT
ejpam-4497	227	8	)	)	PUNCT
ejpam-4497	228	1	=	=	SYM
ejpam-4497	228	2	bint(h	bint(h	NOUN
ejpam-4497	228	3	,	,	PUNCT
ejpam-4497	228	4	o	o	NOUN
ejpam-4497	228	5	)	)	PUNCT
ejpam-4497	228	6	.	.	PUNCT
ejpam-4497	229	1	(	(	PUNCT
ejpam-4497	229	2	v	v	NOUN
ejpam-4497	229	3	)	)	PUNCT
ejpam-4497	229	4	bint(f	bint(f	NOUN
ejpam-4497	229	5	,	,	PUNCT
ejpam-4497	229	6	o)∩̃bint(h	o)∩̃bint(h	ADJ
ejpam-4497	229	7	,	,	PUNCT
ejpam-4497	229	8	o)⊆̃bint((f	o)⊆̃bint((f	PROPN
ejpam-4497	229	9	,	,	PUNCT
ejpam-4497	229	10	o)∩̃(h	o)∩̃(h	PROPN
ejpam-4497	229	11	,	,	PUNCT
ejpam-4497	229	12	o	o	NOUN
ejpam-4497	229	13	)	)	PUNCT
ejpam-4497	229	14	)	)	PUNCT
ejpam-4497	229	15	.	.	PUNCT
ejpam-4497	230	1	proof	proof	NOUN
ejpam-4497	230	2	.	.	PUNCT
ejpam-4497	231	1	(	(	PUNCT
ejpam-4497	231	2	i	i	NOUN
ejpam-4497	231	3	):	):	PUNCT
ejpam-4497	231	4	since	since	SCONJ
ejpam-4497	231	5	x̃	x̃	PROPN
ejpam-4497	231	6	is	be	AUX
ejpam-4497	231	7	is	be	AUX
ejpam-4497	231	8	-	-	PUNCT
ejpam-4497	231	9	b	b	NOUN
ejpam-4497	231	10	-	-	PUNCT
ejpam-4497	231	11	open	open	ADJ
ejpam-4497	231	12	,	,	PUNCT
ejpam-4497	231	13	bint(x̃	bint(x̃	NOUN
ejpam-4497	231	14	)	)	PUNCT
ejpam-4497	231	15	=	=	PUNCT
ejpam-4497	232	1	x̃.	x̃.	ADJ
ejpam-4497	232	2	(	(	PUNCT
ejpam-4497	232	3	ii	ii	NOUN
ejpam-4497	232	4	)	)	PUNCT
ejpam-4497	232	5	and	and	CCONJ
ejpam-4497	232	6	(	(	PUNCT
ejpam-4497	232	7	iii	iii	X
ejpam-4497	232	8	)	)	PUNCT
ejpam-4497	232	9	are	be	AUX
ejpam-4497	232	10	obvious	obvious	ADJ
ejpam-4497	232	11	.	.	PUNCT
ejpam-4497	233	1	(	(	PUNCT
ejpam-4497	233	2	iv	iv	X
ejpam-4497	233	3	):	):	PUNCT
ejpam-4497	233	4	clearly	clearly	ADV
ejpam-4497	233	5	bint(bint(h	bint(bint(h	ADJ
ejpam-4497	233	6	,	,	PUNCT
ejpam-4497	233	7	o	o	NOUN
ejpam-4497	233	8	)	)	PUNCT
ejpam-4497	233	9	)	)	PUNCT
ejpam-4497	233	10	is	be	AUX
ejpam-4497	233	11	the	the	DET
ejpam-4497	233	12	largest	large	ADJ
ejpam-4497	233	13	is	be	AUX
ejpam-4497	233	14	-	-	PUNCT
ejpam-4497	233	15	b	b	NOUN
ejpam-4497	233	16	-	-	PUNCT
ejpam-4497	233	17	open	open	ADJ
ejpam-4497	233	18	set	set	NOUN
ejpam-4497	233	19	contained	contain	VERB
ejpam-4497	233	20	in	in	ADP
ejpam-4497	233	21	bint(h	bint(h	NOUN
ejpam-4497	233	22	,	,	PUNCT
ejpam-4497	233	23	o	o	NOUN
ejpam-4497	233	24	)	)	PUNCT
ejpam-4497	233	25	;	;	PUNCT
ejpam-4497	233	26	however	however	ADV
ejpam-4497	233	27	,	,	PUNCT
ejpam-4497	233	28	bint(h	bint(h	NOUN
ejpam-4497	233	29	,	,	PUNCT
ejpam-4497	233	30	o	o	NOUN
ejpam-4497	233	31	)	)	PUNCT
ejpam-4497	233	32	is	be	AUX
ejpam-4497	233	33	an	an	DET
ejpam-4497	233	34	is	is	NOUN
ejpam-4497	233	35	-	-	PUNCT
ejpam-4497	233	36	b	b	NOUN
ejpam-4497	233	37	-	-	PUNCT
ejpam-4497	233	38	open	open	ADJ
ejpam-4497	233	39	set	set	NOUN
ejpam-4497	233	40	;	;	PUNCT
ejpam-4497	233	41	hence	hence	ADV
ejpam-4497	233	42	,	,	PUNCT
ejpam-4497	233	43	bint(bint(h	bint(bint(h	PROPN
ejpam-4497	233	44	,	,	PUNCT
ejpam-4497	233	45	o	o	NOUN
ejpam-4497	233	46	)	)	PUNCT
ejpam-4497	233	47	)	)	PUNCT
ejpam-4497	234	1	=	=	SYM
ejpam-4497	234	2	bint(h	bint(h	NOUN
ejpam-4497	234	3	,	,	PUNCT
ejpam-4497	234	4	o	o	NOUN
ejpam-4497	234	5	)	)	PUNCT
ejpam-4497	234	6	.	.	PUNCT
ejpam-4497	235	1	(	(	PUNCT
ejpam-4497	235	2	v	v	NOUN
ejpam-4497	235	3	):	):	PUNCT
ejpam-4497	235	4	it	it	PRON
ejpam-4497	235	5	comes	come	VERB
ejpam-4497	235	6	from	from	ADP
ejpam-4497	235	7	(	(	PUNCT
ejpam-4497	235	8	iii	iii	NOUN
ejpam-4497	235	9	)	)	PUNCT
ejpam-4497	235	10	.	.	PUNCT
ejpam-4497	236	1	theorem	theorem	NOUN
ejpam-4497	236	2	2	2	NUM
ejpam-4497	236	3	.	.	PUNCT
ejpam-4497	237	1	let	let	VERB
ejpam-4497	237	2	(	(	PUNCT
ejpam-4497	237	3	h	h	NOUN
ejpam-4497	237	4	,	,	PUNCT
ejpam-4497	237	5	o	o	NOUN
ejpam-4497	237	6	)	)	PUNCT
ejpam-4497	237	7	and	and	CCONJ
ejpam-4497	237	8	(	(	PUNCT
ejpam-4497	237	9	f	f	X
ejpam-4497	237	10	,	,	PUNCT
ejpam-4497	237	11	o	o	NOUN
ejpam-4497	237	12	)	)	PUNCT
ejpam-4497	237	13	be	be	VERB
ejpam-4497	237	14	subsets	subset	NOUN
ejpam-4497	237	15	of	of	ADP
ejpam-4497	237	16	(	(	PUNCT
ejpam-4497	237	17	x,µ,o	x,µ,o	PROPN
ejpam-4497	237	18	)	)	PUNCT
ejpam-4497	237	19	.	.	PUNCT
ejpam-4497	238	1	then	then	ADV
ejpam-4497	238	2	we	we	PRON
ejpam-4497	238	3	have	have	VERB
ejpam-4497	238	4	:	:	PUNCT
ejpam-4497	238	5	(	(	PUNCT
ejpam-4497	238	6	i	i	NOUN
ejpam-4497	238	7	)	)	PUNCT
ejpam-4497	238	8	bcl(φ	bcl(φ	NOUN
ejpam-4497	238	9	)	)	PUNCT
ejpam-4497	238	10	=	=	SYM
ejpam-4497	239	1	φ	φ	PROPN
ejpam-4497	239	2	.	.	PUNCT
ejpam-4497	239	3	(	(	PUNCT
ejpam-4497	239	4	ii	ii	NOUN
ejpam-4497	239	5	)	)	PUNCT
ejpam-4497	239	6	(	(	PUNCT
ejpam-4497	239	7	h	h	NOUN
ejpam-4497	239	8	,	,	PUNCT
ejpam-4497	239	9	o)⊆̃bcl(h	o)⊆̃bcl(h	PROPN
ejpam-4497	239	10	,	,	PUNCT
ejpam-4497	239	11	o	o	NOUN
ejpam-4497	239	12	)	)	PUNCT
ejpam-4497	239	13	.	.	PUNCT
ejpam-4497	240	1	(	(	PUNCT
ejpam-4497	240	2	iii	iii	X
ejpam-4497	240	3	)	)	PUNCT
ejpam-4497	240	4	if	if	SCONJ
ejpam-4497	240	5	(	(	PUNCT
ejpam-4497	240	6	f	f	X
ejpam-4497	240	7	,	,	PUNCT
ejpam-4497	240	8	o)⊆̃(h	o)⊆̃(h	ADV
ejpam-4497	240	9	,	,	PUNCT
ejpam-4497	240	10	o	o	NOUN
ejpam-4497	240	11	)	)	PUNCT
ejpam-4497	240	12	,	,	PUNCT
ejpam-4497	240	13	then	then	ADV
ejpam-4497	240	14	bcl(f	bcl(f	NOUN
ejpam-4497	240	15	,	,	PUNCT
ejpam-4497	240	16	o)⊆̃bcl(h	o)⊆̃bcl(h	PROPN
ejpam-4497	240	17	,	,	PUNCT
ejpam-4497	240	18	o	o	NOUN
ejpam-4497	240	19	)	)	PUNCT
ejpam-4497	240	20	.	.	PUNCT
ejpam-4497	241	1	(	(	PUNCT
ejpam-4497	241	2	iv	iv	X
ejpam-4497	241	3	)	)	PUNCT
ejpam-4497	241	4	bcl(bcl(h	bcl(bcl(h	PROPN
ejpam-4497	241	5	,	,	PUNCT
ejpam-4497	241	6	o))⊆̃bcl(h	o))⊆̃bcl(h	PROPN
ejpam-4497	241	7	,	,	PUNCT
ejpam-4497	241	8	o	o	NOUN
ejpam-4497	241	9	)	)	PUNCT
ejpam-4497	241	10	.	.	PUNCT
ejpam-4497	242	1	(	(	PUNCT
ejpam-4497	242	2	v	v	NOUN
ejpam-4497	242	3	)	)	PUNCT
ejpam-4497	242	4	bcl((f	bcl((f	VERB
ejpam-4497	242	5	,	,	PUNCT
ejpam-4497	242	6	o)∪̃(h	o)∪̃(h	ADV
ejpam-4497	242	7	,	,	PUNCT
ejpam-4497	242	8	o	o	NOUN
ejpam-4497	242	9	)	)	PUNCT
ejpam-4497	242	10	)	)	PUNCT
ejpam-4497	243	1	=	=	SYM
ejpam-4497	243	2	bcl(f	bcl(f	NOUN
ejpam-4497	243	3	,	,	PUNCT
ejpam-4497	243	4	o)∪̃bcl(h	o)∪̃bcl(h	PROPN
ejpam-4497	243	5	,	,	PUNCT
ejpam-4497	243	6	o	o	NOUN
ejpam-4497	243	7	)	)	PUNCT
ejpam-4497	243	8	.	.	PUNCT
ejpam-4497	244	1	proof	proof	NOUN
ejpam-4497	244	2	.	.	PUNCT
ejpam-4497	245	1	it	it	PRON
ejpam-4497	245	2	can	can	AUX
ejpam-4497	245	3	be	be	AUX
ejpam-4497	245	4	proved	prove	VERB
ejpam-4497	245	5	following	follow	VERB
ejpam-4497	245	6	similar	similar	ADJ
ejpam-4497	245	7	arguments	argument	NOUN
ejpam-4497	245	8	given	give	VERB
ejpam-4497	245	9	in	in	ADP
ejpam-4497	245	10	the	the	DET
ejpam-4497	245	11	proof	proof	NOUN
ejpam-4497	245	12	of	of	ADP
ejpam-4497	245	13	theorem	theorem	NOUN
ejpam-4497	245	14	1	1	NUM
ejpam-4497	245	15	.	.	PUNCT
ejpam-4497	245	16	definition	definition	NOUN
ejpam-4497	245	17	16	16	NUM
ejpam-4497	245	18	.	.	PUNCT
ejpam-4497	246	1	a	a	DET
ejpam-4497	246	2	s	s	NOUN
ejpam-4497	246	3	-	-	PUNCT
ejpam-4497	246	4	point	point	NOUN
ejpam-4497	246	5	δxo	δxo	NOUN
ejpam-4497	246	6	is	be	AUX
ejpam-4497	246	7	called	call	VERB
ejpam-4497	246	8	an	an	DET
ejpam-4497	246	9	is	be	AUX
ejpam-4497	246	10	-	-	PUNCT
ejpam-4497	246	11	b	b	NOUN
ejpam-4497	246	12	-	-	PUNCT
ejpam-4497	246	13	limit	limit	NOUN
ejpam-4497	246	14	point	point	NOUN
ejpam-4497	246	15	of	of	ADP
ejpam-4497	246	16	a	a	DET
ejpam-4497	246	17	subset	subset	NOUN
ejpam-4497	246	18	(	(	PUNCT
ejpam-4497	246	19	h	h	NOUN
ejpam-4497	246	20	,	,	PUNCT
ejpam-4497	246	21	o	o	NOUN
ejpam-4497	246	22	)	)	PUNCT
ejpam-4497	246	23	of	of	ADP
ejpam-4497	246	24	(	(	PUNCT
ejpam-4497	246	25	x,µ,o	x,µ,o	PROPN
ejpam-4497	246	26	)	)	PUNCT
ejpam-4497	246	27	provided	provide	VERB
ejpam-4497	246	28	that	that	SCONJ
ejpam-4497	246	29	[	[	X
ejpam-4497	246	30	(	(	PUNCT
ejpam-4497	246	31	f	f	X
ejpam-4497	246	32	,	,	PUNCT
ejpam-4497	246	33	o)\δxo	o)\δxo	PROPN
ejpam-4497	246	34	]	]	SYM
ejpam-4497	246	35	∩̃(h	∩̃(h	X
ejpam-4497	246	36	,	,	PUNCT
ejpam-4497	246	37	o	o	NOUN
ejpam-4497	246	38	)	)	PUNCT
ejpam-4497	246	39	̸=	̸=	PROPN
ejpam-4497	246	40	φ	φ	NUM
ejpam-4497	246	41	for	for	ADP
ejpam-4497	246	42	any	any	PRON
ejpam-4497	246	43	is	be	AUX
ejpam-4497	246	44	-	-	PUNCT
ejpam-4497	246	45	b	b	NOUN
ejpam-4497	246	46	-	-	PUNCT
ejpam-4497	246	47	open	open	ADJ
ejpam-4497	246	48	set	set	NOUN
ejpam-4497	246	49	(	(	PUNCT
ejpam-4497	246	50	f	f	X
ejpam-4497	246	51	,	,	PUNCT
ejpam-4497	246	52	o	o	NOUN
ejpam-4497	246	53	)	)	PUNCT
ejpam-4497	246	54	containing	contain	VERB
ejpam-4497	246	55	δxo	δxo	NOUN
ejpam-4497	246	56	.	.	PUNCT
ejpam-4497	247	1	the	the	DET
ejpam-4497	247	2	s	s	NOUN
ejpam-4497	247	3	-	-	PUNCT
ejpam-4497	247	4	set	set	NOUN
ejpam-4497	247	5	of	of	ADP
ejpam-4497	247	6	all	all	PRON
ejpam-4497	247	7	is	be	AUX
ejpam-4497	247	8	-	-	PUNCT
ejpam-4497	247	9	b	b	NOUN
ejpam-4497	247	10	-	-	PUNCT
ejpam-4497	247	11	limit	limit	NOUN
ejpam-4497	247	12	points	point	NOUN
ejpam-4497	247	13	of	of	ADP
ejpam-4497	247	14	(	(	PUNCT
ejpam-4497	247	15	h	h	NOUN
ejpam-4497	247	16	,	,	PUNCT
ejpam-4497	247	17	o	o	NOUN
ejpam-4497	247	18	)	)	PUNCT
ejpam-4497	247	19	is	be	AUX
ejpam-4497	247	20	called	call	VERB
ejpam-4497	247	21	an	an	DET
ejpam-4497	247	22	infra	infra	NOUN
ejpam-4497	247	23	b	b	NOUN
ejpam-4497	247	24	-	-	PUNCT
ejpam-4497	247	25	derived	derive	VERB
ejpam-4497	247	26	s	s	NOUN
ejpam-4497	247	27	-	-	PUNCT
ejpam-4497	247	28	set	set	NOUN
ejpam-4497	247	29	.	.	PUNCT
ejpam-4497	248	1	it	it	PRON
ejpam-4497	248	2	is	be	AUX
ejpam-4497	248	3	denoted	denote	VERB
ejpam-4497	248	4	by	by	ADP
ejpam-4497	248	5	(	(	PUNCT
ejpam-4497	248	6	h	h	NOUN
ejpam-4497	248	7	,	,	PUNCT
ejpam-4497	248	8	o)bs′.	o)bs′.	NUM
ejpam-4497	248	9	proposition	proposition	NOUN
ejpam-4497	248	10	12	12	NUM
ejpam-4497	248	11	.	.	PUNCT
ejpam-4497	249	1	consider	consider	VERB
ejpam-4497	249	2	(	(	PUNCT
ejpam-4497	249	3	f	f	NOUN
ejpam-4497	249	4	,	,	PUNCT
ejpam-4497	249	5	o	o	NOUN
ejpam-4497	249	6	)	)	PUNCT
ejpam-4497	249	7	and	and	CCONJ
ejpam-4497	249	8	(	(	PUNCT
ejpam-4497	249	9	h	h	NOUN
ejpam-4497	249	10	,	,	PUNCT
ejpam-4497	249	11	o	o	NOUN
ejpam-4497	249	12	)	)	PUNCT
ejpam-4497	249	13	as	as	ADP
ejpam-4497	249	14	s	s	NOUN
ejpam-4497	249	15	-	-	NOUN
ejpam-4497	249	16	sets	set	NOUN
ejpam-4497	249	17	in	in	ADP
ejpam-4497	249	18	(	(	PUNCT
ejpam-4497	249	19	x,µ,o	x,µ,o	PROPN
ejpam-4497	249	20	)	)	PUNCT
ejpam-4497	249	21	.	.	PUNCT
ejpam-4497	250	1	then	then	ADV
ejpam-4497	250	2	(	(	PUNCT
ejpam-4497	250	3	i	i	NOUN
ejpam-4497	250	4	)	)	PUNCT
ejpam-4497	250	5	φbs′	φbs′	PROPN
ejpam-4497	250	6	=	=	SYM
ejpam-4497	250	7	φ	φ	PROPN
ejpam-4497	250	8	and	and	CCONJ
ejpam-4497	250	9	x̃bs′⊆̃x̃.	x̃bs′⊆̃x̃.	PROPN
ejpam-4497	250	10	t.m	t.m	PROPN
ejpam-4497	250	11	.	.	PROPN
ejpam-4497	250	12	al	al	PROPN
ejpam-4497	250	13	-	-	PUNCT
ejpam-4497	250	14	shami	shami	PROPN
ejpam-4497	250	15	et	et	PROPN
ejpam-4497	250	16	al	al	PROPN
ejpam-4497	250	17	.	.	PUNCT
ejpam-4497	250	18	/	/	SYM
ejpam-4497	250	19	eur	eur	PROPN
ejpam-4497	250	20	.	.	PUNCT
ejpam-4497	251	1	j.	j.	PROPN
ejpam-4497	251	2	pure	pure	PROPN
ejpam-4497	251	3	appl	appl	PROPN
ejpam-4497	251	4	.	.	PROPN
ejpam-4497	251	5	math	math	PROPN
ejpam-4497	251	6	,	,	PUNCT
ejpam-4497	251	7	15	15	NUM
ejpam-4497	251	8	(	(	PUNCT
ejpam-4497	251	9	4	4	NUM
ejpam-4497	251	10	)	)	PUNCT
ejpam-4497	251	11	(	(	PUNCT
ejpam-4497	251	12	2022	2022	NUM
ejpam-4497	251	13	)	)	PUNCT
ejpam-4497	251	14	,	,	PUNCT
ejpam-4497	251	15	1455	1455	NUM
ejpam-4497	251	16	-	-	SYM
ejpam-4497	251	17	1471	1471	NUM
ejpam-4497	251	18	1462	1462	NUM
ejpam-4497	251	19	(	(	PUNCT
ejpam-4497	251	20	ii	ii	NOUN
ejpam-4497	251	21	)	)	PUNCT
ejpam-4497	251	22	if	if	SCONJ
ejpam-4497	251	23	(	(	PUNCT
ejpam-4497	251	24	f	f	X
ejpam-4497	251	25	,	,	PUNCT
ejpam-4497	251	26	o)⊆̃(h	o)⊆̃(h	ADV
ejpam-4497	251	27	,	,	PUNCT
ejpam-4497	251	28	o	o	NOUN
ejpam-4497	251	29	)	)	PUNCT
ejpam-4497	251	30	,	,	PUNCT
ejpam-4497	251	31	then	then	ADV
ejpam-4497	251	32	(	(	PUNCT
ejpam-4497	251	33	f	f	X
ejpam-4497	251	34	,	,	PUNCT
ejpam-4497	251	35	o)bs′⊆̃(h	o)bs′⊆̃(h	PROPN
ejpam-4497	251	36	,	,	PUNCT
ejpam-4497	251	37	o)bs′.	o)bs′.	PROPN
ejpam-4497	251	38	(	(	PUNCT
ejpam-4497	251	39	iii	iii	NOUN
ejpam-4497	251	40	)	)	PUNCT
ejpam-4497	251	41	if	if	SCONJ
ejpam-4497	251	42	δxo	δxo	VERB
ejpam-4497	251	43	∈	∈	PROPN
ejpam-4497	251	44	(	(	PUNCT
ejpam-4497	251	45	h	h	NOUN
ejpam-4497	251	46	,	,	PUNCT
ejpam-4497	251	47	o)bs′	o)bs′	PROPN
ejpam-4497	251	48	,	,	PUNCT
ejpam-4497	251	49	then	then	ADV
ejpam-4497	251	50	δxo	δxo	VERB
ejpam-4497	251	51	∈	∈	PROPN
ejpam-4497	251	52	(	(	PUNCT
ejpam-4497	251	53	(	(	PUNCT
ejpam-4497	251	54	h	h	NOUN
ejpam-4497	251	55	,	,	PUNCT
ejpam-4497	251	56	o	o	NOUN
ejpam-4497	251	57	)	)	PUNCT
ejpam-4497	251	58	\	\	PROPN
ejpam-4497	251	59	δxo	δxo	NOUN
ejpam-4497	251	60	)	)	PUNCT
ejpam-4497	251	61	bs′.	bs′.	NOUN
ejpam-4497	251	62	(	(	PUNCT
ejpam-4497	251	63	iv	iv	NOUN
ejpam-4497	251	64	)	)	PUNCT
ejpam-4497	251	65	(	(	PUNCT
ejpam-4497	251	66	f	f	X
ejpam-4497	251	67	,	,	PUNCT
ejpam-4497	251	68	o)bs′∪̃(h	o)bs′∪̃(h	PROPN
ejpam-4497	251	69	,	,	PUNCT
ejpam-4497	251	70	o)bs′⊆̃((f	o)bs′⊆̃((f	X
ejpam-4497	251	71	,	,	PUNCT
ejpam-4497	251	72	o)∪̃(h	o)∪̃(h	ADV
ejpam-4497	251	73	,	,	PUNCT
ejpam-4497	251	74	o))bs′.	o))bs′.	PROPN
ejpam-4497	251	75	proof	proof	NOUN
ejpam-4497	251	76	.	.	PUNCT
ejpam-4497	252	1	straightforward	straightforward	ADJ
ejpam-4497	252	2	.	.	PUNCT
ejpam-4497	253	1	theorem	theorem	NOUN
ejpam-4497	253	2	3	3	X
ejpam-4497	253	3	.	.	PUNCT
ejpam-4497	254	1	let	let	AUX
ejpam-4497	254	2	(	(	PUNCT
ejpam-4497	254	3	h	h	NOUN
ejpam-4497	254	4	,	,	PUNCT
ejpam-4497	254	5	o	o	NOUN
ejpam-4497	254	6	)	)	PUNCT
ejpam-4497	254	7	be	be	VERB
ejpam-4497	254	8	an	an	DET
ejpam-4497	254	9	s	s	NOUN
ejpam-4497	254	10	-	-	PUNCT
ejpam-4497	254	11	set	set	VERB
ejpam-4497	254	12	in	in	ADP
ejpam-4497	254	13	(	(	PUNCT
ejpam-4497	254	14	x,µ,o	x,µ,o	PROPN
ejpam-4497	254	15	)	)	PUNCT
ejpam-4497	254	16	.	.	PUNCT
ejpam-4497	255	1	then	then	ADV
ejpam-4497	255	2	(	(	PUNCT
ejpam-4497	255	3	i	i	NOUN
ejpam-4497	255	4	)	)	PUNCT
ejpam-4497	255	5	if	if	SCONJ
ejpam-4497	255	6	(	(	PUNCT
ejpam-4497	255	7	h	h	NOUN
ejpam-4497	255	8	,	,	PUNCT
ejpam-4497	255	9	o	o	NOUN
ejpam-4497	255	10	)	)	PUNCT
ejpam-4497	255	11	is	be	AUX
ejpam-4497	255	12	an	an	DET
ejpam-4497	255	13	is	is	NOUN
ejpam-4497	255	14	-	-	PUNCT
ejpam-4497	255	15	b	b	NOUN
ejpam-4497	255	16	-	-	PUNCT
ejpam-4497	255	17	closed	closed	ADJ
ejpam-4497	255	18	set	set	NOUN
ejpam-4497	255	19	,	,	PUNCT
ejpam-4497	255	20	then	then	ADV
ejpam-4497	255	21	(	(	PUNCT
ejpam-4497	255	22	h	h	NOUN
ejpam-4497	255	23	,	,	PUNCT
ejpam-4497	255	24	o)bs′	o)bs′	VERB
ejpam-4497	255	25	⊆	⊆	NUM
ejpam-4497	255	26	(	(	PUNCT
ejpam-4497	255	27	h	h	NOUN
ejpam-4497	255	28	,	,	PUNCT
ejpam-4497	255	29	o	o	NOUN
ejpam-4497	255	30	)	)	PUNCT
ejpam-4497	255	31	.	.	PUNCT
ejpam-4497	256	1	(	(	PUNCT
ejpam-4497	256	2	ii	ii	NOUN
ejpam-4497	256	3	)	)	PUNCT
ejpam-4497	256	4	(	(	PUNCT
ejpam-4497	256	5	(	(	PUNCT
ejpam-4497	256	6	h	h	NOUN
ejpam-4497	256	7	,	,	PUNCT
ejpam-4497	256	8	o)∪̃(h	o)∪̃(h	ADV
ejpam-4497	256	9	,	,	PUNCT
ejpam-4497	256	10	o)bs′)bs′⊆̃(h	o)bs′)bs′⊆̃(h	ADV
ejpam-4497	256	11	,	,	PUNCT
ejpam-4497	256	12	o)∪̃(h	o)∪̃(h	ADV
ejpam-4497	256	13	,	,	PUNCT
ejpam-4497	256	14	o)bs′.	o)bs′.	PROPN
ejpam-4497	256	15	(	(	PUNCT
ejpam-4497	256	16	iii	iii	NOUN
ejpam-4497	256	17	)	)	PUNCT
ejpam-4497	256	18	bcl(h	bcl(h	PROPN
ejpam-4497	256	19	,	,	PUNCT
ejpam-4497	256	20	o	o	NOUN
ejpam-4497	256	21	)	)	PUNCT
ejpam-4497	256	22	=	=	SYM
ejpam-4497	256	23	(	(	PUNCT
ejpam-4497	256	24	h	h	NOUN
ejpam-4497	256	25	,	,	PUNCT
ejpam-4497	256	26	o)∪̃(h	o)∪̃(h	ADV
ejpam-4497	256	27	,	,	PUNCT
ejpam-4497	256	28	o)bs′.	o)bs′.	NUM
ejpam-4497	256	29	proof	proof	NOUN
ejpam-4497	256	30	.	.	PUNCT
ejpam-4497	257	1	(	(	PUNCT
ejpam-4497	257	2	i	i	NOUN
ejpam-4497	257	3	)	)	PUNCT
ejpam-4497	257	4	consider	consider	VERB
ejpam-4497	257	5	(	(	PUNCT
ejpam-4497	257	6	h	h	NOUN
ejpam-4497	257	7	,	,	PUNCT
ejpam-4497	257	8	o	o	NOUN
ejpam-4497	257	9	)	)	PUNCT
ejpam-4497	257	10	as	as	ADP
ejpam-4497	257	11	an	an	DET
ejpam-4497	257	12	is	is	NOUN
ejpam-4497	257	13	-	-	PUNCT
ejpam-4497	257	14	b	b	NOUN
ejpam-4497	257	15	-	-	PUNCT
ejpam-4497	257	16	closed	closed	ADJ
ejpam-4497	257	17	set	set	NOUN
ejpam-4497	257	18	such	such	ADJ
ejpam-4497	257	19	that	that	SCONJ
ejpam-4497	257	20	δxo	δxo	NOUN
ejpam-4497	257	21	̸∈	̸∈	PROPN
ejpam-4497	257	22	(	(	PUNCT
ejpam-4497	257	23	h	h	PROPN
ejpam-4497	257	24	,	,	PUNCT
ejpam-4497	257	25	o	o	NOUN
ejpam-4497	257	26	)	)	PUNCT
ejpam-4497	257	27	.	.	PUNCT
ejpam-4497	258	1	then	then	ADV
ejpam-4497	258	2	δxo	δxo	VERB
ejpam-4497	258	3	∈	∈	PROPN
ejpam-4497	258	4	(	(	PUNCT
ejpam-4497	258	5	hc	hc	PROPN
ejpam-4497	258	6	,	,	PUNCT
ejpam-4497	258	7	o	o	NOUN
ejpam-4497	258	8	)	)	PUNCT
ejpam-4497	258	9	.	.	PUNCT
ejpam-4497	259	1	now	now	ADV
ejpam-4497	259	2	,	,	PUNCT
ejpam-4497	259	3	(	(	PUNCT
ejpam-4497	259	4	hc	hc	PROPN
ejpam-4497	259	5	,	,	PUNCT
ejpam-4497	259	6	o	o	NOUN
ejpam-4497	259	7	)	)	PUNCT
ejpam-4497	259	8	is	be	AUX
ejpam-4497	259	9	an	an	DET
ejpam-4497	259	10	is	is	NOUN
ejpam-4497	259	11	-	-	PUNCT
ejpam-4497	259	12	b	b	NOUN
ejpam-4497	259	13	-	-	PUNCT
ejpam-4497	259	14	open	open	ADJ
ejpam-4497	259	15	set	set	NOUN
ejpam-4497	259	16	such	such	ADJ
ejpam-4497	259	17	that	that	SCONJ
ejpam-4497	259	18	(	(	PUNCT
ejpam-4497	259	19	hc	hc	PROPN
ejpam-4497	259	20	,	,	PUNCT
ejpam-4497	259	21	o)∩̃(h	o)∩̃(h	PROPN
ejpam-4497	259	22	,	,	PUNCT
ejpam-4497	259	23	o	o	NOUN
ejpam-4497	259	24	)	)	PUNCT
ejpam-4497	259	25	=	=	SYM
ejpam-4497	260	1	φ	φ	PROPN
ejpam-4497	260	2	which	which	PRON
ejpam-4497	260	3	means	mean	VERB
ejpam-4497	260	4	that	that	SCONJ
ejpam-4497	260	5	δxo	δxo	VERB
ejpam-4497	260	6	̸∈	̸∈	PROPN
ejpam-4497	260	7	(	(	PUNCT
ejpam-4497	260	8	h	h	PROPN
ejpam-4497	260	9	,	,	PUNCT
ejpam-4497	260	10	o)bs′.	o)bs′.	PROPN
ejpam-4497	260	11	thus	thus	ADV
ejpam-4497	260	12	,	,	PUNCT
ejpam-4497	260	13	(	(	PUNCT
ejpam-4497	260	14	h	h	NOUN
ejpam-4497	260	15	,	,	PUNCT
ejpam-4497	260	16	o)bs′⊆̃(h	o)bs′⊆̃(h	PROPN
ejpam-4497	260	17	,	,	PUNCT
ejpam-4497	260	18	o	o	NOUN
ejpam-4497	260	19	)	)	PUNCT
ejpam-4497	260	20	.	.	PUNCT
ejpam-4497	261	1	(	(	PUNCT
ejpam-4497	261	2	ii	ii	NOUN
ejpam-4497	261	3	)	)	PUNCT
ejpam-4497	261	4	consider	consider	VERB
ejpam-4497	261	5	δxo	δxo	NOUN
ejpam-4497	261	6	̸∈	̸∈	PROPN
ejpam-4497	261	7	(	(	PUNCT
ejpam-4497	261	8	h	h	NOUN
ejpam-4497	261	9	,	,	PUNCT
ejpam-4497	261	10	o)∪̃(h	o)∪̃(h	ADV
ejpam-4497	261	11	,	,	PUNCT
ejpam-4497	261	12	o)bs′.	o)bs′.	PROPN
ejpam-4497	261	13	then	then	ADV
ejpam-4497	261	14	δxo	δxo	VERB
ejpam-4497	261	15	̸∈	̸∈	PROPN
ejpam-4497	261	16	(	(	PUNCT
ejpam-4497	261	17	h	h	PROPN
ejpam-4497	261	18	,	,	PUNCT
ejpam-4497	261	19	o	o	NOUN
ejpam-4497	261	20	)	)	PUNCT
ejpam-4497	261	21	and	and	CCONJ
ejpam-4497	261	22	δxo	δxo	VERB
ejpam-4497	261	23	̸∈	̸∈	PROPN
ejpam-4497	261	24	(	(	PUNCT
ejpam-4497	261	25	h	h	PROPN
ejpam-4497	261	26	,	,	PUNCT
ejpam-4497	261	27	o)bs′.	o)bs′.	PROPN
ejpam-4497	261	28	therefore	therefore	ADV
ejpam-4497	261	29	,	,	PUNCT
ejpam-4497	261	30	there	there	PRON
ejpam-4497	261	31	exists	exist	VERB
ejpam-4497	261	32	an	an	DET
ejpam-4497	261	33	is	is	NOUN
ejpam-4497	261	34	-	-	PUNCT
ejpam-4497	261	35	b	b	NOUN
ejpam-4497	261	36	-	-	PUNCT
ejpam-4497	261	37	open	open	ADJ
ejpam-4497	261	38	set	set	NOUN
ejpam-4497	261	39	(	(	PUNCT
ejpam-4497	261	40	f	f	PROPN
ejpam-4497	261	41	,	,	PUNCT
ejpam-4497	261	42	o	o	NOUN
ejpam-4497	261	43	)	)	PUNCT
ejpam-4497	261	44	such	such	ADJ
ejpam-4497	261	45	that	that	SCONJ
ejpam-4497	261	46	(	(	PUNCT
ejpam-4497	261	47	f	f	X
ejpam-4497	261	48	,	,	PUNCT
ejpam-4497	261	49	o)∩̃(h	o)∩̃(h	PROPN
ejpam-4497	261	50	,	,	PUNCT
ejpam-4497	261	51	o	o	NOUN
ejpam-4497	261	52	)	)	PUNCT
ejpam-4497	261	53	=	=	SYM
ejpam-4497	261	54	φ	φ	PROPN
ejpam-4497	261	55	(	(	PUNCT
ejpam-4497	261	56	1	1	NUM
ejpam-4497	261	57	)	)	PUNCT
ejpam-4497	261	58	this	this	PRON
ejpam-4497	261	59	implies	imply	VERB
ejpam-4497	261	60	that	that	SCONJ
ejpam-4497	261	61	(	(	PUNCT
ejpam-4497	261	62	f	f	X
ejpam-4497	261	63	,	,	PUNCT
ejpam-4497	261	64	o)∩̃(h	o)∩̃(h	PROPN
ejpam-4497	261	65	,	,	PUNCT
ejpam-4497	261	66	o)bs′	o)bs′	PROPN
ejpam-4497	261	67	=	=	SYM
ejpam-4497	261	68	φ	φ	X
ejpam-4497	261	69	(	(	PUNCT
ejpam-4497	261	70	2	2	NUM
ejpam-4497	261	71	)	)	PUNCT
ejpam-4497	261	72	it	it	PRON
ejpam-4497	261	73	follows	follow	VERB
ejpam-4497	261	74	from	from	ADP
ejpam-4497	261	75	(	(	PUNCT
ejpam-4497	261	76	1	1	NUM
ejpam-4497	261	77	)	)	PUNCT
ejpam-4497	261	78	and	and	CCONJ
ejpam-4497	261	79	(	(	PUNCT
ejpam-4497	261	80	2	2	X
ejpam-4497	261	81	)	)	PUNCT
ejpam-4497	261	82	that	that	SCONJ
ejpam-4497	261	83	(	(	PUNCT
ejpam-4497	261	84	f	f	X
ejpam-4497	261	85	,	,	PUNCT
ejpam-4497	261	86	o)∩̃((h	o)∩̃((h	PROPN
ejpam-4497	261	87	,	,	PUNCT
ejpam-4497	261	88	o)∪̃(h	o)∪̃(h	ADV
ejpam-4497	261	89	,	,	PUNCT
ejpam-4497	261	90	o)bs′	o)bs′	PROPN
ejpam-4497	261	91	)	)	PUNCT
ejpam-4497	261	92	=	=	PUNCT
ejpam-4497	261	93	φ	φ	PROPN
ejpam-4497	261	94	.	.	PUNCT
ejpam-4497	262	1	thus	thus	ADV
ejpam-4497	262	2	,	,	PUNCT
ejpam-4497	262	3	δxo	δxo	VERB
ejpam-4497	262	4	̸∈	̸∈	PROPN
ejpam-4497	262	5	(	(	PUNCT
ejpam-4497	262	6	(	(	PUNCT
ejpam-4497	262	7	h	h	NOUN
ejpam-4497	262	8	,	,	PUNCT
ejpam-4497	262	9	o)∪̃	o)∪̃	PROPN
ejpam-4497	262	10	(	(	PUNCT
ejpam-4497	262	11	h	h	NOUN
ejpam-4497	262	12	,	,	PUNCT
ejpam-4497	262	13	o)bs′)bs′.	o)bs′)bs′.	NOUN
ejpam-4497	262	14	hence	hence	ADV
ejpam-4497	262	15	,	,	PUNCT
ejpam-4497	262	16	(	(	PUNCT
ejpam-4497	262	17	(	(	PUNCT
ejpam-4497	262	18	h	h	NOUN
ejpam-4497	262	19	,	,	PUNCT
ejpam-4497	262	20	o)∪̃(h	o)∪̃(h	ADV
ejpam-4497	262	21	,	,	PUNCT
ejpam-4497	262	22	o)bs′)bs′⊆̃((h	o)bs′)bs′⊆̃((h	INTJ
ejpam-4497	262	23	,	,	PUNCT
ejpam-4497	262	24	o)∪̃(h	o)∪̃(h	ADV
ejpam-4497	262	25	,	,	PUNCT
ejpam-4497	262	26	o)bs′	o)bs′	PROPN
ejpam-4497	262	27	)	)	PUNCT
ejpam-4497	262	28	,	,	PUNCT
ejpam-4497	262	29	as	as	SCONJ
ejpam-4497	262	30	required	require	VERB
ejpam-4497	262	31	.	.	PUNCT
ejpam-4497	263	1	(	(	PUNCT
ejpam-4497	263	2	iii	iii	X
ejpam-4497	263	3	)	)	PUNCT
ejpam-4497	263	4	it	it	PRON
ejpam-4497	263	5	is	be	AUX
ejpam-4497	263	6	clear	clear	ADJ
ejpam-4497	263	7	that	that	SCONJ
ejpam-4497	263	8	(	(	PUNCT
ejpam-4497	263	9	h	h	NOUN
ejpam-4497	263	10	,	,	PUNCT
ejpam-4497	263	11	o)∪̃(h	o)∪̃(h	ADV
ejpam-4497	263	12	,	,	PUNCT
ejpam-4497	263	13	o)bs′⊆̃bcl(h	o)bs′⊆̃bcl(h	NOUN
ejpam-4497	263	14	,	,	PUNCT
ejpam-4497	263	15	o	o	NOUN
ejpam-4497	263	16	)	)	PUNCT
ejpam-4497	263	17	.	.	PUNCT
ejpam-4497	264	1	conversely	conversely	ADV
ejpam-4497	264	2	,	,	PUNCT
ejpam-4497	264	3	let	let	VERB
ejpam-4497	264	4	δxo	δxo	VERB
ejpam-4497	264	5	∈	∈	PROPN
ejpam-4497	264	6	bcl(h	bcl(h	PROPN
ejpam-4497	264	7	,	,	PUNCT
ejpam-4497	264	8	o	o	NOUN
ejpam-4497	264	9	)	)	PUNCT
ejpam-4497	264	10	.	.	PUNCT
ejpam-4497	265	1	then	then	ADV
ejpam-4497	265	2	for	for	ADP
ejpam-4497	265	3	every	every	PRON
ejpam-4497	265	4	is	be	AUX
ejpam-4497	265	5	-	-	PUNCT
ejpam-4497	265	6	b	b	NOUN
ejpam-4497	265	7	-	-	PUNCT
ejpam-4497	265	8	open	open	ADJ
ejpam-4497	265	9	set	set	NOUN
ejpam-4497	265	10	containing	contain	VERB
ejpam-4497	265	11	δxo	δxo	NOUN
ejpam-4497	265	12	we	we	PRON
ejpam-4497	265	13	have	have	VERB
ejpam-4497	265	14	(	(	PUNCT
ejpam-4497	265	15	h	h	NOUN
ejpam-4497	265	16	,	,	PUNCT
ejpam-4497	265	17	o)∩̃(f	o)∩̃(f	ADV
ejpam-4497	265	18	,	,	PUNCT
ejpam-4497	265	19	o	o	NOUN
ejpam-4497	265	20	)	)	PUNCT
ejpam-4497	265	21	̸=	̸=	PROPN
ejpam-4497	265	22	φ	φ	NUM
ejpam-4497	265	23	.	.	PUNCT
ejpam-4497	266	1	without	without	ADP
ejpam-4497	266	2	loss	loss	NOUN
ejpam-4497	266	3	of	of	ADP
ejpam-4497	266	4	generality	generality	NOUN
ejpam-4497	266	5	,	,	PUNCT
ejpam-4497	266	6	let	let	VERB
ejpam-4497	266	7	δxo	δxo	VERB
ejpam-4497	266	8	̸∈	̸∈	PROPN
ejpam-4497	266	9	(	(	PUNCT
ejpam-4497	266	10	h	h	PROPN
ejpam-4497	266	11	,	,	PUNCT
ejpam-4497	266	12	o	o	NOUN
ejpam-4497	266	13	)	)	PUNCT
ejpam-4497	266	14	.	.	PUNCT
ejpam-4497	267	1	then	then	ADV
ejpam-4497	268	1	[	[	X
ejpam-4497	268	2	(	(	PUNCT
ejpam-4497	268	3	h	h	NOUN
ejpam-4497	268	4	,	,	PUNCT
ejpam-4497	268	5	o)\δxo	o)\δxo	PROPN
ejpam-4497	268	6	]	]	PUNCT
ejpam-4497	268	7	∩̃(f	∩̃(f	X
ejpam-4497	268	8	,	,	PUNCT
ejpam-4497	268	9	o	o	X
ejpam-4497	268	10	)	)	PUNCT
ejpam-4497	268	11	̸=	̸=	PROPN
ejpam-4497	268	12	φ	φ	NUM
ejpam-4497	268	13	.	.	PUNCT
ejpam-4497	269	1	consequentially	consequentially	ADV
ejpam-4497	269	2	,	,	PUNCT
ejpam-4497	269	3	δxo	δxo	VERB
ejpam-4497	269	4	∈	∈	PROPN
ejpam-4497	269	5	(	(	PUNCT
ejpam-4497	269	6	h	h	NOUN
ejpam-4497	269	7	,	,	PUNCT
ejpam-4497	269	8	o)bs′.	o)bs′.	PROPN
ejpam-4497	269	9	hence	hence	ADV
ejpam-4497	269	10	,	,	PUNCT
ejpam-4497	269	11	the	the	DET
ejpam-4497	269	12	proof	proof	NOUN
ejpam-4497	269	13	is	be	AUX
ejpam-4497	269	14	complete	complete	ADJ
ejpam-4497	269	15	.	.	PUNCT
ejpam-4497	270	1	definition	definition	NOUN
ejpam-4497	270	2	17	17	NUM
ejpam-4497	270	3	.	.	PUNCT
ejpam-4497	271	1	the	the	DET
ejpam-4497	271	2	is	be	AUX
ejpam-4497	271	3	-	-	PUNCT
ejpam-4497	271	4	b	b	NOUN
ejpam-4497	271	5	-	-	PUNCT
ejpam-4497	271	6	boundary	boundary	ADJ
ejpam-4497	271	7	points	point	NOUN
ejpam-4497	271	8	of	of	ADP
ejpam-4497	271	9	a	a	DET
ejpam-4497	271	10	subset	subset	NOUN
ejpam-4497	271	11	(	(	PUNCT
ejpam-4497	271	12	h	h	NOUN
ejpam-4497	271	13	,	,	PUNCT
ejpam-4497	271	14	o	o	NOUN
ejpam-4497	271	15	)	)	PUNCT
ejpam-4497	271	16	of	of	ADP
ejpam-4497	271	17	(	(	PUNCT
ejpam-4497	271	18	x,µ,o	x,µ,o	PROPN
ejpam-4497	271	19	)	)	PUNCT
ejpam-4497	271	20	,	,	PUNCT
ejpam-4497	271	21	denoted	denote	VERB
ejpam-4497	271	22	by	by	ADP
ejpam-4497	271	23	bb(h	bb(h	NOUN
ejpam-4497	271	24	,	,	PUNCT
ejpam-4497	271	25	o	o	NOUN
ejpam-4497	271	26	)	)	PUNCT
ejpam-4497	271	27	,	,	PUNCT
ejpam-4497	271	28	are	be	AUX
ejpam-4497	271	29	all	all	DET
ejpam-4497	271	30	the	the	DET
ejpam-4497	271	31	s	s	NOUN
ejpam-4497	271	32	-	-	PUNCT
ejpam-4497	271	33	points	point	NOUN
ejpam-4497	271	34	which	which	PRON
ejpam-4497	271	35	belong	belong	VERB
ejpam-4497	271	36	to	to	ADP
ejpam-4497	271	37	the	the	DET
ejpam-4497	271	38	complement	complement	NOUN
ejpam-4497	271	39	of	of	ADP
ejpam-4497	271	40	bint(h	bint(h	NOUN
ejpam-4497	271	41	,	,	PUNCT
ejpam-4497	271	42	o)∪̃bint(hc	o)∪̃bint(hc	NUM
ejpam-4497	271	43	,	,	PUNCT
ejpam-4497	271	44	o	o	NOUN
ejpam-4497	271	45	)	)	PUNCT
ejpam-4497	271	46	.	.	PUNCT
ejpam-4497	272	1	proposition	proposition	NOUN
ejpam-4497	272	2	13	13	NUM
ejpam-4497	272	3	.	.	PUNCT
ejpam-4497	273	1	let	let	AUX
ejpam-4497	273	2	(	(	PUNCT
ejpam-4497	273	3	h	h	NOUN
ejpam-4497	273	4	,	,	PUNCT
ejpam-4497	273	5	o	o	NOUN
ejpam-4497	273	6	)	)	PUNCT
ejpam-4497	273	7	be	be	VERB
ejpam-4497	273	8	an	an	DET
ejpam-4497	273	9	s	s	NOUN
ejpam-4497	273	10	-	-	PUNCT
ejpam-4497	273	11	set	set	VERB
ejpam-4497	273	12	in	in	ADP
ejpam-4497	273	13	(	(	PUNCT
ejpam-4497	273	14	x,µ,o	x,µ,o	PROPN
ejpam-4497	273	15	)	)	PUNCT
ejpam-4497	273	16	.	.	PUNCT
ejpam-4497	274	1	then	then	ADV
ejpam-4497	274	2	:	:	PUNCT
ejpam-4497	274	3	(	(	PUNCT
ejpam-4497	274	4	i	i	NOUN
ejpam-4497	274	5	)	)	PUNCT
ejpam-4497	274	6	bb(h	bb(h	ADV
ejpam-4497	274	7	,	,	PUNCT
ejpam-4497	274	8	o	o	NOUN
ejpam-4497	274	9	)	)	PUNCT
ejpam-4497	274	10	=	=	SYM
ejpam-4497	274	11	bcl(h	bcl(h	PROPN
ejpam-4497	274	12	,	,	PUNCT
ejpam-4497	274	13	o)∩̃bcl((hc	o)∩̃bcl((hc	PROPN
ejpam-4497	274	14	,	,	PUNCT
ejpam-4497	274	15	o	o	NOUN
ejpam-4497	274	16	)	)	PUNCT
ejpam-4497	274	17	)	)	PUNCT
ejpam-4497	274	18	.	.	PUNCT
ejpam-4497	275	1	(	(	PUNCT
ejpam-4497	275	2	ii	ii	NOUN
ejpam-4497	275	3	)	)	PUNCT
ejpam-4497	275	4	bb(h	bb(h	NOUN
ejpam-4497	275	5	,	,	PUNCT
ejpam-4497	275	6	o	o	NOUN
ejpam-4497	275	7	)	)	PUNCT
ejpam-4497	275	8	=	=	SYM
ejpam-4497	275	9	bcl(h	bcl(h	PROPN
ejpam-4497	275	10	,	,	PUNCT
ejpam-4497	275	11	o	o	NOUN
ejpam-4497	275	12	)	)	PUNCT
ejpam-4497	275	13	\	\	PROPN
ejpam-4497	275	14	bint(h	bint(h	NOUN
ejpam-4497	275	15	,	,	PUNCT
ejpam-4497	275	16	o	o	NOUN
ejpam-4497	275	17	)	)	PUNCT
ejpam-4497	275	18	.	.	PUNCT
ejpam-4497	276	1	proof	proof	NOUN
ejpam-4497	276	2	.	.	PUNCT
ejpam-4497	277	1	t.m	t.m	PROPN
ejpam-4497	277	2	.	.	PUNCT
ejpam-4497	277	3	al	al	PROPN
ejpam-4497	277	4	-	-	PUNCT
ejpam-4497	277	5	shami	shami	PROPN
ejpam-4497	277	6	et	et	PROPN
ejpam-4497	277	7	al	al	PROPN
ejpam-4497	277	8	.	.	PUNCT
ejpam-4497	277	9	/	/	SYM
ejpam-4497	277	10	eur	eur	PROPN
ejpam-4497	277	11	.	.	PUNCT
ejpam-4497	278	1	j.	j.	PROPN
ejpam-4497	278	2	pure	pure	PROPN
ejpam-4497	278	3	appl	appl	PROPN
ejpam-4497	278	4	.	.	PROPN
ejpam-4497	278	5	math	math	PROPN
ejpam-4497	278	6	,	,	PUNCT
ejpam-4497	278	7	15	15	NUM
ejpam-4497	278	8	(	(	PUNCT
ejpam-4497	278	9	4	4	NUM
ejpam-4497	278	10	)	)	PUNCT
ejpam-4497	278	11	(	(	PUNCT
ejpam-4497	278	12	2022	2022	NUM
ejpam-4497	278	13	)	)	PUNCT
ejpam-4497	278	14	,	,	PUNCT
ejpam-4497	278	15	1455	1455	NUM
ejpam-4497	278	16	-	-	SYM
ejpam-4497	278	17	1471	1471	NUM
ejpam-4497	278	18	1463	1463	NUM
ejpam-4497	278	19	(	(	PUNCT
ejpam-4497	278	20	i	i	NOUN
ejpam-4497	278	21	)	)	PUNCT
ejpam-4497	278	22	bb(h	bb(h	ADV
ejpam-4497	278	23	,	,	PUNCT
ejpam-4497	278	24	o	o	NOUN
ejpam-4497	278	25	)	)	PUNCT
ejpam-4497	278	26	=	=	PRON
ejpam-4497	278	27	{	{	PUNCT
ejpam-4497	278	28	δxo	δxo	NOUN
ejpam-4497	278	29	∈	∈	NOUN
ejpam-4497	278	30	x̃	x̃	PROPN
ejpam-4497	278	31	:	:	PUNCT
ejpam-4497	278	32	δxo	δxo	VERB
ejpam-4497	278	33	̸∈	̸∈	PROPN
ejpam-4497	278	34	bint(h	bint(h	PROPN
ejpam-4497	278	35	,	,	PUNCT
ejpam-4497	278	36	o	o	NOUN
ejpam-4497	278	37	)	)	PUNCT
ejpam-4497	278	38	and	and	CCONJ
ejpam-4497	278	39	δxo	δxo	VERB
ejpam-4497	278	40	̸∈	̸∈	PROPN
ejpam-4497	278	41	bint((hc	bint((hc	PROPN
ejpam-4497	278	42	,	,	PUNCT
ejpam-4497	278	43	o	o	NOUN
ejpam-4497	278	44	)	)	PUNCT
ejpam-4497	278	45	)	)	PUNCT
ejpam-4497	278	46	}	}	PUNCT
ejpam-4497	279	1	=	=	PRON
ejpam-4497	279	2	{	{	PUNCT
ejpam-4497	279	3	δxo	δxo	NOUN
ejpam-4497	279	4	∈	∈	NOUN
ejpam-4497	279	5	x̃	x̃	PROPN
ejpam-4497	279	6	:	:	PUNCT
ejpam-4497	279	7	δxo	δxo	VERB
ejpam-4497	279	8	̸∈	̸∈	PROPN
ejpam-4497	279	9	(	(	PUNCT
ejpam-4497	279	10	bcl(hc	bcl(hc	NOUN
ejpam-4497	279	11	,	,	PUNCT
ejpam-4497	279	12	o))c	o))c	NOUN
ejpam-4497	279	13	and	and	CCONJ
ejpam-4497	279	14	δxo	δxo	VERB
ejpam-4497	279	15	̸∈	̸∈	PROPN
ejpam-4497	279	16	(	(	PUNCT
ejpam-4497	279	17	bcl(h	bcl(h	PROPN
ejpam-4497	279	18	,	,	PUNCT
ejpam-4497	279	19	o))c	o))c	NOUN
ejpam-4497	279	20	}	}	PUNCT
ejpam-4497	279	21	=	=	SYM
ejpam-4497	279	22	{	{	PUNCT
ejpam-4497	279	23	δxo	δxo	NOUN
ejpam-4497	279	24	∈	∈	NOUN
ejpam-4497	279	25	x̃	x̃	PROPN
ejpam-4497	279	26	:	:	PUNCT
ejpam-4497	279	27	δxo	δxo	VERB
ejpam-4497	279	28	∈	∈	PROPN
ejpam-4497	279	29	bcl(hc	bcl(hc	NOUN
ejpam-4497	279	30	,	,	PUNCT
ejpam-4497	279	31	o	o	NOUN
ejpam-4497	279	32	)	)	PUNCT
ejpam-4497	279	33	and	and	CCONJ
ejpam-4497	279	34	δxo	δxo	VERB
ejpam-4497	279	35	∈	∈	PROPN
ejpam-4497	279	36	bcl(h	bcl(h	PROPN
ejpam-4497	279	37	,	,	PUNCT
ejpam-4497	279	38	o	o	NOUN
ejpam-4497	279	39	)	)	PUNCT
ejpam-4497	279	40	}	}	PUNCT
ejpam-4497	279	41	=	=	SYM
ejpam-4497	279	42	bcl(h	bcl(h	PROPN
ejpam-4497	279	43	,	,	PUNCT
ejpam-4497	279	44	o)∩̃bcl(hc	o)∩̃bcl(hc	PROPN
ejpam-4497	279	45	,	,	PUNCT
ejpam-4497	279	46	o	o	NOUN
ejpam-4497	279	47	)	)	PUNCT
ejpam-4497	279	48	(	(	PUNCT
ejpam-4497	279	49	ii	ii	NOUN
ejpam-4497	279	50	)	)	PUNCT
ejpam-4497	279	51	bb(h	bb(h	NOUN
ejpam-4497	279	52	,	,	PUNCT
ejpam-4497	279	53	o	o	NOUN
ejpam-4497	279	54	)	)	PUNCT
ejpam-4497	279	55	=	=	SYM
ejpam-4497	279	56	bcl(h	bcl(h	PROPN
ejpam-4497	279	57	,	,	PUNCT
ejpam-4497	279	58	o)∩̃bcl(hc	o)∩̃bcl(hc	PROPN
ejpam-4497	279	59	,	,	PUNCT
ejpam-4497	279	60	o	o	NOUN
ejpam-4497	279	61	)	)	PUNCT
ejpam-4497	279	62	=	=	SYM
ejpam-4497	279	63	bcl(h	bcl(h	PROPN
ejpam-4497	279	64	,	,	PUNCT
ejpam-4497	279	65	o)∩̃(bint(h	o)∩̃(bint(h	NOUN
ejpam-4497	279	66	,	,	PUNCT
ejpam-4497	279	67	o))c	o))c	NOUN
ejpam-4497	279	68	=	=	SYM
ejpam-4497	279	69	bcl(h	bcl(h	PROPN
ejpam-4497	279	70	,	,	PUNCT
ejpam-4497	279	71	o	o	NOUN
ejpam-4497	279	72	)	)	PUNCT
ejpam-4497	279	73	\	\	PROPN
ejpam-4497	279	74	bint(h	bint(h	NOUN
ejpam-4497	279	75	,	,	PUNCT
ejpam-4497	279	76	o	o	NOUN
ejpam-4497	279	77	)	)	PUNCT
ejpam-4497	279	78	corollary	corollary	ADJ
ejpam-4497	279	79	3	3	X
ejpam-4497	279	80	.	.	PUNCT
ejpam-4497	280	1	let	let	AUX
ejpam-4497	280	2	(	(	PUNCT
ejpam-4497	280	3	h	h	NOUN
ejpam-4497	280	4	,	,	PUNCT
ejpam-4497	280	5	o	o	NOUN
ejpam-4497	280	6	)	)	PUNCT
ejpam-4497	280	7	be	be	AUX
ejpam-4497	280	8	a	a	DET
ejpam-4497	280	9	subset	subset	NOUN
ejpam-4497	280	10	of	of	ADP
ejpam-4497	280	11	(	(	PUNCT
ejpam-4497	280	12	x,µ,o	x,µ,o	PROPN
ejpam-4497	280	13	)	)	PUNCT
ejpam-4497	280	14	.	.	PUNCT
ejpam-4497	281	1	then	then	ADV
ejpam-4497	281	2	(	(	PUNCT
ejpam-4497	281	3	i	i	NOUN
ejpam-4497	281	4	)	)	PUNCT
ejpam-4497	281	5	bb(h	bb(h	ADV
ejpam-4497	281	6	,	,	PUNCT
ejpam-4497	281	7	o	o	NOUN
ejpam-4497	281	8	)	)	PUNCT
ejpam-4497	281	9	=	=	SYM
ejpam-4497	281	10	bb(hc	bb(hc	PROPN
ejpam-4497	281	11	,	,	PUNCT
ejpam-4497	281	12	o	o	NOUN
ejpam-4497	281	13	)	)	PUNCT
ejpam-4497	281	14	(	(	PUNCT
ejpam-4497	281	15	ii	ii	NOUN
ejpam-4497	281	16	)	)	PUNCT
ejpam-4497	281	17	bcl(h	bcl(h	PROPN
ejpam-4497	281	18	,	,	PUNCT
ejpam-4497	281	19	o	o	NOUN
ejpam-4497	281	20	)	)	PUNCT
ejpam-4497	281	21	=	=	SYM
ejpam-4497	281	22	bint(h	bint(h	NOUN
ejpam-4497	281	23	,	,	PUNCT
ejpam-4497	281	24	o)∪̃bb(h	o)∪̃bb(h	PROPN
ejpam-4497	281	25	,	,	PUNCT
ejpam-4497	281	26	o	o	NOUN
ejpam-4497	281	27	)	)	PUNCT
ejpam-4497	281	28	proposition	proposition	NOUN
ejpam-4497	281	29	14	14	NUM
ejpam-4497	281	30	.	.	PUNCT
ejpam-4497	282	1	let	let	AUX
ejpam-4497	282	2	(	(	PUNCT
ejpam-4497	282	3	h	h	NOUN
ejpam-4497	282	4	,	,	PUNCT
ejpam-4497	282	5	o	o	NOUN
ejpam-4497	282	6	)	)	PUNCT
ejpam-4497	282	7	be	be	AUX
ejpam-4497	282	8	a	a	DET
ejpam-4497	282	9	subset	subset	NOUN
ejpam-4497	282	10	of	of	ADP
ejpam-4497	282	11	(	(	PUNCT
ejpam-4497	282	12	x,µ,o	x,µ,o	PROPN
ejpam-4497	282	13	)	)	PUNCT
ejpam-4497	282	14	.	.	PUNCT
ejpam-4497	283	1	then	then	ADV
ejpam-4497	283	2	(	(	PUNCT
ejpam-4497	283	3	i	i	NOUN
ejpam-4497	283	4	)	)	PUNCT
ejpam-4497	283	5	(	(	PUNCT
ejpam-4497	283	6	h	h	NOUN
ejpam-4497	283	7	,	,	PUNCT
ejpam-4497	283	8	o	o	NOUN
ejpam-4497	283	9	)	)	PUNCT
ejpam-4497	283	10	is	be	AUX
ejpam-4497	283	11	is	be	AUX
ejpam-4497	283	12	-	-	PUNCT
ejpam-4497	283	13	b	b	NOUN
ejpam-4497	283	14	-	-	PUNCT
ejpam-4497	283	15	open	open	ADJ
ejpam-4497	283	16	iff	iff	PROPN
ejpam-4497	283	17	bb(h	bb(h	NOUN
ejpam-4497	283	18	,	,	PUNCT
ejpam-4497	283	19	o)∩̃(h	o)∩̃(h	PROPN
ejpam-4497	283	20	,	,	PUNCT
ejpam-4497	283	21	o	o	NOUN
ejpam-4497	283	22	)	)	PUNCT
ejpam-4497	283	23	=	=	SYM
ejpam-4497	284	1	φ	φ	PROPN
ejpam-4497	284	2	.	.	PUNCT
ejpam-4497	284	3	(	(	PUNCT
ejpam-4497	284	4	ii	ii	NOUN
ejpam-4497	284	5	)	)	PUNCT
ejpam-4497	284	6	(	(	PUNCT
ejpam-4497	284	7	h	h	NOUN
ejpam-4497	284	8	,	,	PUNCT
ejpam-4497	284	9	o	o	NOUN
ejpam-4497	284	10	)	)	PUNCT
ejpam-4497	284	11	is	be	AUX
ejpam-4497	284	12	is	be	AUX
ejpam-4497	284	13	-	-	PUNCT
ejpam-4497	284	14	b	b	NOUN
ejpam-4497	284	15	-	-	PUNCT
ejpam-4497	284	16	closed	closed	ADJ
ejpam-4497	284	17	iff	iff	PROPN
ejpam-4497	284	18	bb(h	bb(h	NOUN
ejpam-4497	284	19	,	,	PUNCT
ejpam-4497	284	20	o)⊆̃(h	o)⊆̃(h	ADV
ejpam-4497	284	21	,	,	PUNCT
ejpam-4497	284	22	o	o	NOUN
ejpam-4497	284	23	)	)	PUNCT
ejpam-4497	284	24	.	.	PUNCT
ejpam-4497	285	1	proof	proof	NOUN
ejpam-4497	285	2	.	.	PUNCT
ejpam-4497	286	1	(	(	PUNCT
ejpam-4497	286	2	i	i	NOUN
ejpam-4497	286	3	)	)	PUNCT
ejpam-4497	286	4	bb(h	bb(h	ADV
ejpam-4497	286	5	,	,	PUNCT
ejpam-4497	286	6	o	o	NOUN
ejpam-4497	286	7	)	)	PUNCT
ejpam-4497	286	8	∩	∩	NOUN
ejpam-4497	286	9	(	(	PUNCT
ejpam-4497	286	10	h	h	NOUN
ejpam-4497	286	11	,	,	PUNCT
ejpam-4497	286	12	o	o	NOUN
ejpam-4497	286	13	)	)	PUNCT
ejpam-4497	286	14	=	=	SYM
ejpam-4497	286	15	bb(h	bb(h	NOUN
ejpam-4497	286	16	,	,	PUNCT
ejpam-4497	286	17	o	o	NOUN
ejpam-4497	286	18	)	)	PUNCT
ejpam-4497	286	19	∩	∩	ADJ
ejpam-4497	286	20	bint(h	bint(h	NOUN
ejpam-4497	286	21	,	,	PUNCT
ejpam-4497	286	22	o	o	NOUN
ejpam-4497	286	23	)	)	PUNCT
ejpam-4497	287	1	=	=	SYM
ejpam-4497	287	2	φ	φ	X
ejpam-4497	287	3	.	.	PUNCT
ejpam-4497	288	1	conversely	conversely	ADV
ejpam-4497	288	2	,	,	PUNCT
ejpam-4497	288	3	let	let	VERB
ejpam-4497	288	4	δxo	δxo	VERB
ejpam-4497	288	5	∈	∈	PROPN
ejpam-4497	288	6	(	(	PUNCT
ejpam-4497	288	7	h	h	NOUN
ejpam-4497	288	8	,	,	PUNCT
ejpam-4497	288	9	o	o	NOUN
ejpam-4497	288	10	)	)	PUNCT
ejpam-4497	288	11	.	.	PUNCT
ejpam-4497	289	1	then	then	ADV
ejpam-4497	289	2	δxo	δxo	VERB
ejpam-4497	289	3	∈	∈	PROPN
ejpam-4497	289	4	bint(h	bint(h	NOUN
ejpam-4497	289	5	,	,	PUNCT
ejpam-4497	289	6	o	o	NOUN
ejpam-4497	289	7	)	)	PUNCT
ejpam-4497	289	8	or	or	CCONJ
ejpam-4497	289	9	δxo	δxo	VERB
ejpam-4497	289	10	∈	∈	PROPN
ejpam-4497	289	11	bb(h	bb(h	NOUN
ejpam-4497	289	12	,	,	PUNCT
ejpam-4497	289	13	o	o	NOUN
ejpam-4497	289	14	)	)	PUNCT
ejpam-4497	289	15	.	.	PUNCT
ejpam-4497	290	1	since	since	SCONJ
ejpam-4497	290	2	bb(h	bb(h	NOUN
ejpam-4497	290	3	,	,	PUNCT
ejpam-4497	290	4	o	o	NOUN
ejpam-4497	290	5	)	)	PUNCT
ejpam-4497	290	6	∩	∩	NOUN
ejpam-4497	290	7	(	(	PUNCT
ejpam-4497	290	8	h	h	NOUN
ejpam-4497	290	9	,	,	PUNCT
ejpam-4497	290	10	o	o	NOUN
ejpam-4497	290	11	)	)	PUNCT
ejpam-4497	290	12	=	=	SYM
ejpam-4497	290	13	φ	φ	PROPN
ejpam-4497	290	14	,	,	PUNCT
ejpam-4497	290	15	δxo	δxo	NOUN
ejpam-4497	290	16	∈	∈	PROPN
ejpam-4497	290	17	bint(h	bint(h	NOUN
ejpam-4497	290	18	,	,	PUNCT
ejpam-4497	290	19	o	o	NOUN
ejpam-4497	290	20	)	)	PUNCT
ejpam-4497	290	21	.	.	PUNCT
ejpam-4497	291	1	thus	thus	ADV
ejpam-4497	291	2	,	,	PUNCT
ejpam-4497	291	3	(	(	PUNCT
ejpam-4497	291	4	h	h	NOUN
ejpam-4497	291	5	,	,	PUNCT
ejpam-4497	291	6	o	o	NOUN
ejpam-4497	291	7	)	)	PUNCT
ejpam-4497	291	8	⊆	⊆	NUM
ejpam-4497	291	9	bint(h	bint(h	NOUN
ejpam-4497	291	10	,	,	PUNCT
ejpam-4497	291	11	o	o	NOUN
ejpam-4497	291	12	)	)	PUNCT
ejpam-4497	291	13	which	which	PRON
ejpam-4497	291	14	means	mean	VERB
ejpam-4497	291	15	that	that	SCONJ
ejpam-4497	291	16	(	(	PUNCT
ejpam-4497	291	17	h	h	NOUN
ejpam-4497	291	18	,	,	PUNCT
ejpam-4497	291	19	o	o	NOUN
ejpam-4497	291	20	)	)	PUNCT
ejpam-4497	291	21	=	=	SYM
ejpam-4497	291	22	bint(h	bint(h	NOUN
ejpam-4497	291	23	,	,	PUNCT
ejpam-4497	291	24	o	o	NOUN
ejpam-4497	291	25	)	)	PUNCT
ejpam-4497	291	26	.	.	PUNCT
ejpam-4497	292	1	hence	hence	ADV
ejpam-4497	292	2	,	,	PUNCT
ejpam-4497	292	3	(	(	PUNCT
ejpam-4497	292	4	h	h	NOUN
ejpam-4497	292	5	,	,	PUNCT
ejpam-4497	292	6	o	o	NOUN
ejpam-4497	292	7	)	)	PUNCT
ejpam-4497	292	8	is	be	AUX
ejpam-4497	292	9	is	be	AUX
ejpam-4497	292	10	-	-	PUNCT
ejpam-4497	292	11	b	b	NOUN
ejpam-4497	292	12	-	-	PUNCT
ejpam-4497	292	13	open	open	ADJ
ejpam-4497	292	14	.	.	PUNCT
ejpam-4497	293	1	(	(	PUNCT
ejpam-4497	293	2	ii	ii	NOUN
ejpam-4497	293	3	)	)	PUNCT
ejpam-4497	293	4	(	(	PUNCT
ejpam-4497	293	5	h	h	NOUN
ejpam-4497	293	6	,	,	PUNCT
ejpam-4497	293	7	o	o	NOUN
ejpam-4497	293	8	)	)	PUNCT
ejpam-4497	293	9	is	be	AUX
ejpam-4497	293	10	is	be	AUX
ejpam-4497	293	11	-	-	PUNCT
ejpam-4497	293	12	b	b	NOUN
ejpam-4497	293	13	-	-	PUNCT
ejpam-4497	293	14	closed⇔	closed⇔	ADJ
ejpam-4497	293	15	(	(	PUNCT
ejpam-4497	293	16	hc	hc	PROPN
ejpam-4497	293	17	,	,	PUNCT
ejpam-4497	293	18	o	o	NOUN
ejpam-4497	293	19	)	)	PUNCT
ejpam-4497	293	20	is	be	AUX
ejpam-4497	293	21	is	be	AUX
ejpam-4497	293	22	-	-	PUNCT
ejpam-4497	293	23	b	b	NOUN
ejpam-4497	293	24	-	-	PUNCT
ejpam-4497	293	25	open⇔	open⇔	ADJ
ejpam-4497	293	26	bb(hc	bb(hc	PROPN
ejpam-4497	293	27	,	,	PUNCT
ejpam-4497	293	28	o)∩(hc	o)∩(hc	PROPN
ejpam-4497	293	29	,	,	PUNCT
ejpam-4497	293	30	o	o	NOUN
ejpam-4497	293	31	)	)	PUNCT
ejpam-4497	294	1	=	=	SYM
ejpam-4497	294	2	φ⇔	φ⇔	PROPN
ejpam-4497	294	3	bb(h	bb(h	NOUN
ejpam-4497	294	4	,	,	PUNCT
ejpam-4497	294	5	o)∩	o)∩	PROPN
ejpam-4497	294	6	(	(	PUNCT
ejpam-4497	294	7	hc	hc	PROPN
ejpam-4497	294	8	,	,	PUNCT
ejpam-4497	294	9	o	o	NOUN
ejpam-4497	294	10	)	)	PUNCT
ejpam-4497	294	11	=	=	SYM
ejpam-4497	294	12	φ	φ	PROPN
ejpam-4497	294	13	⇔	⇔	PROPN
ejpam-4497	294	14	bb(h	bb(h	PROPN
ejpam-4497	294	15	,	,	PUNCT
ejpam-4497	294	16	o	o	NOUN
ejpam-4497	294	17	)	)	PUNCT
ejpam-4497	294	18	⊆	⊆	NUM
ejpam-4497	294	19	(	(	PUNCT
ejpam-4497	294	20	h	h	NOUN
ejpam-4497	294	21	,	,	PUNCT
ejpam-4497	294	22	o	o	NOUN
ejpam-4497	294	23	)	)	PUNCT
ejpam-4497	294	24	.	.	PUNCT
ejpam-4497	295	1	corollary	corollary	ADJ
ejpam-4497	295	2	4	4	NUM
ejpam-4497	295	3	.	.	PUNCT
ejpam-4497	295	4	a	a	DET
ejpam-4497	295	5	subset	subset	NOUN
ejpam-4497	295	6	(	(	PUNCT
ejpam-4497	295	7	h	h	NOUN
ejpam-4497	295	8	,	,	PUNCT
ejpam-4497	295	9	o	o	NOUN
ejpam-4497	295	10	)	)	PUNCT
ejpam-4497	295	11	of	of	ADP
ejpam-4497	295	12	(	(	PUNCT
ejpam-4497	295	13	x,µ,o	x,µ,o	PROPN
ejpam-4497	295	14	)	)	PUNCT
ejpam-4497	295	15	is	be	AUX
ejpam-4497	295	16	is	be	AUX
ejpam-4497	295	17	-	-	PUNCT
ejpam-4497	295	18	b	b	NOUN
ejpam-4497	295	19	-	-	PUNCT
ejpam-4497	295	20	open	open	ADJ
ejpam-4497	295	21	and	and	CCONJ
ejpam-4497	295	22	is	be	AUX
ejpam-4497	295	23	-	-	PUNCT
ejpam-4497	295	24	b	b	NOUN
ejpam-4497	295	25	-	-	PUNCT
ejpam-4497	295	26	closed	closed	ADJ
ejpam-4497	295	27	iff	iff	PROPN
ejpam-4497	295	28	bb(h	bb(h	NOUN
ejpam-4497	295	29	,	,	PUNCT
ejpam-4497	295	30	o	o	NOUN
ejpam-4497	295	31	)	)	PUNCT
ejpam-4497	295	32	=	=	SYM
ejpam-4497	296	1	φ	φ	X
ejpam-4497	296	2	.	.	PROPN
ejpam-4497	296	3	5	5	NUM
ejpam-4497	296	4	.	.	X
ejpam-4497	296	5	infra	infra	NOUN
ejpam-4497	296	6	soft	soft	ADJ
ejpam-4497	296	7	b	b	NOUN
ejpam-4497	296	8	-	-	PUNCT
ejpam-4497	296	9	homeomorphism	homeomorphism	PROPN
ejpam-4497	296	10	maps	map	NOUN
ejpam-4497	296	11	definition	definition	NOUN
ejpam-4497	296	12	18	18	NUM
ejpam-4497	296	13	.	.	PUNCT
ejpam-4497	297	1	fψ	fψ	PROPN
ejpam-4497	297	2	:	:	PUNCT
ejpam-4497	297	3	(	(	PUNCT
ejpam-4497	297	4	x,µ,o	x,µ,o	NOUN
ejpam-4497	297	5	)	)	PUNCT
ejpam-4497	297	6	→	→	PUNCT
ejpam-4497	297	7	(	(	PUNCT
ejpam-4497	297	8	s	s	PROPN
ejpam-4497	297	9	,	,	PUNCT
ejpam-4497	297	10	ν,∆	ν,∆	NUM
ejpam-4497	297	11	)	)	PUNCT
ejpam-4497	297	12	is	be	AUX
ejpam-4497	297	13	said	say	VERB
ejpam-4497	297	14	to	to	PART
ejpam-4497	297	15	be	be	AUX
ejpam-4497	297	16	is	be	AUX
ejpam-4497	297	17	-	-	PUNCT
ejpam-4497	297	18	b	b	NOUN
ejpam-4497	297	19	-	-	PUNCT
ejpam-4497	297	20	continuous	continuous	ADJ
ejpam-4497	297	21	at	at	ADP
ejpam-4497	297	22	δxo	δxo	NOUN
ejpam-4497	297	23	∈	∈	PROPN
ejpam-4497	297	24	x̃	x̃	PROPN
ejpam-4497	298	1	if	if	SCONJ
ejpam-4497	298	2	for	for	ADP
ejpam-4497	298	3	any	any	PRON
ejpam-4497	298	4	is	be	AUX
ejpam-4497	298	5	-	-	PUNCT
ejpam-4497	298	6	b	b	NOUN
ejpam-4497	298	7	-	-	PUNCT
ejpam-4497	298	8	open	open	ADJ
ejpam-4497	298	9	set	set	NOUN
ejpam-4497	298	10	(	(	PUNCT
ejpam-4497	298	11	f	f	X
ejpam-4497	298	12	,	,	PUNCT
ejpam-4497	298	13	∆	∆	PROPN
ejpam-4497	298	14	)	)	PUNCT
ejpam-4497	298	15	containing	contain	VERB
ejpam-4497	298	16	fψ(δ	fψ(δ	NOUN
ejpam-4497	298	17	x	x	X
ejpam-4497	298	18	o	o	NOUN
ejpam-4497	298	19	)	)	PUNCT
ejpam-4497	298	20	,	,	PUNCT
ejpam-4497	298	21	there	there	PRON
ejpam-4497	298	22	is	be	VERB
ejpam-4497	298	23	an	an	DET
ejpam-4497	298	24	is	is	NOUN
ejpam-4497	298	25	-	-	PUNCT
ejpam-4497	298	26	b	b	NOUN
ejpam-4497	298	27	-	-	PUNCT
ejpam-4497	298	28	open	open	ADJ
ejpam-4497	298	29	set	set	NOUN
ejpam-4497	298	30	(	(	PUNCT
ejpam-4497	298	31	h	h	NOUN
ejpam-4497	298	32	,	,	PUNCT
ejpam-4497	298	33	o	o	NOUN
ejpam-4497	298	34	)	)	PUNCT
ejpam-4497	298	35	containing	contain	VERB
ejpam-4497	298	36	δxo	δxo	NOUN
ejpam-4497	298	37	such	such	ADJ
ejpam-4497	298	38	that	that	DET
ejpam-4497	298	39	fψ(h	fψ(h	NOUN
ejpam-4497	298	40	,	,	PUNCT
ejpam-4497	298	41	o)⊆̃(f	o)⊆̃(f	PROPN
ejpam-4497	298	42	,	,	PUNCT
ejpam-4497	298	43	∆	∆	PROPN
ejpam-4497	298	44	)	)	PUNCT
ejpam-4497	298	45	.	.	PUNCT
ejpam-4497	299	1	fψ	fψ	PROPN
ejpam-4497	299	2	is	be	AUX
ejpam-4497	299	3	called	call	VERB
ejpam-4497	299	4	is	be	AUX
ejpam-4497	299	5	-	-	PUNCT
ejpam-4497	299	6	b	b	NOUN
ejpam-4497	299	7	-	-	PUNCT
ejpam-4497	299	8	continuous	continuous	ADJ
ejpam-4497	299	9	if	if	SCONJ
ejpam-4497	299	10	it	it	PRON
ejpam-4497	299	11	is	be	AUX
ejpam-4497	299	12	is	be	AUX
ejpam-4497	299	13	-	-	PUNCT
ejpam-4497	299	14	b	b	NOUN
ejpam-4497	299	15	-	-	PUNCT
ejpam-4497	299	16	continuous	continuous	ADJ
ejpam-4497	299	17	at	at	ADP
ejpam-4497	299	18	all	all	DET
ejpam-4497	299	19	δxo	δxo	NOUN
ejpam-4497	299	20	∈	∈	NOUN
ejpam-4497	299	21	x̃.	x̃.	ADJ
ejpam-4497	299	22	theorem	theorem	NOUN
ejpam-4497	299	23	4	4	NUM
ejpam-4497	299	24	.	.	PUNCT
ejpam-4497	300	1	if	if	SCONJ
ejpam-4497	300	2	fψ	fψ	NOUN
ejpam-4497	300	3	:	:	PUNCT
ejpam-4497	300	4	(	(	PUNCT
ejpam-4497	300	5	x,µ,o	x,µ,o	NOUN
ejpam-4497	300	6	)	)	PUNCT
ejpam-4497	300	7	→	→	PUNCT
ejpam-4497	300	8	(	(	PUNCT
ejpam-4497	300	9	s	s	PROPN
ejpam-4497	300	10	,	,	PUNCT
ejpam-4497	300	11	ν,∆	ν,∆	NUM
ejpam-4497	300	12	)	)	PUNCT
ejpam-4497	300	13	is	be	AUX
ejpam-4497	300	14	is	be	AUX
ejpam-4497	300	15	-	-	PUNCT
ejpam-4497	300	16	b	b	NOUN
ejpam-4497	300	17	-	-	PUNCT
ejpam-4497	300	18	continuous	continuous	ADJ
ejpam-4497	300	19	,	,	PUNCT
ejpam-4497	300	20	then	then	ADV
ejpam-4497	300	21	the	the	DET
ejpam-4497	300	22	next	next	ADJ
ejpam-4497	300	23	properties	property	NOUN
ejpam-4497	300	24	are	be	AUX
ejpam-4497	300	25	equivalent	equivalent	ADJ
ejpam-4497	300	26	.	.	PUNCT
ejpam-4497	301	1	(	(	PUNCT
ejpam-4497	301	2	i	i	NOUN
ejpam-4497	301	3	)	)	PUNCT
ejpam-4497	301	4	fψ	fψ	VERB
ejpam-4497	301	5	is	be	AUX
ejpam-4497	301	6	an	an	DET
ejpam-4497	301	7	is	is	NOUN
ejpam-4497	301	8	-	-	PUNCT
ejpam-4497	301	9	b	b	NOUN
ejpam-4497	301	10	-	-	PUNCT
ejpam-4497	301	11	continuous	continuous	ADJ
ejpam-4497	301	12	map	map	NOUN
ejpam-4497	301	13	;	;	PUNCT
ejpam-4497	301	14	t.m	t.m	PROPN
ejpam-4497	301	15	.	.	PROPN
ejpam-4497	301	16	al	al	PROPN
ejpam-4497	301	17	-	-	PUNCT
ejpam-4497	301	18	shami	shami	PROPN
ejpam-4497	301	19	et	et	PROPN
ejpam-4497	301	20	al	al	PROPN
ejpam-4497	301	21	.	.	PUNCT
ejpam-4497	301	22	/	/	SYM
ejpam-4497	301	23	eur	eur	PROPN
ejpam-4497	301	24	.	.	PUNCT
ejpam-4497	302	1	j.	j.	PROPN
ejpam-4497	302	2	pure	pure	PROPN
ejpam-4497	302	3	appl	appl	PROPN
ejpam-4497	302	4	.	.	PROPN
ejpam-4497	302	5	math	math	PROPN
ejpam-4497	302	6	,	,	PUNCT
ejpam-4497	302	7	15	15	NUM
ejpam-4497	302	8	(	(	PUNCT
ejpam-4497	302	9	4	4	NUM
ejpam-4497	302	10	)	)	PUNCT
ejpam-4497	302	11	(	(	PUNCT
ejpam-4497	302	12	2022	2022	NUM
ejpam-4497	302	13	)	)	PUNCT
ejpam-4497	302	14	,	,	PUNCT
ejpam-4497	302	15	1455	1455	NUM
ejpam-4497	302	16	-	-	SYM
ejpam-4497	302	17	1471	1471	NUM
ejpam-4497	302	18	1464	1464	NUM
ejpam-4497	302	19	(	(	PUNCT
ejpam-4497	302	20	ii	ii	NOUN
ejpam-4497	302	21	)	)	PUNCT
ejpam-4497	302	22	the	the	DET
ejpam-4497	302	23	inverse	inverse	ADJ
ejpam-4497	302	24	image	image	NOUN
ejpam-4497	302	25	of	of	ADP
ejpam-4497	302	26	each	each	PRON
ejpam-4497	302	27	is	be	AUX
ejpam-4497	302	28	-	-	PUNCT
ejpam-4497	302	29	b	b	NOUN
ejpam-4497	302	30	-	-	PUNCT
ejpam-4497	302	31	closed	closed	ADJ
ejpam-4497	302	32	set	set	NOUN
ejpam-4497	302	33	is	be	AUX
ejpam-4497	302	34	is	be	AUX
ejpam-4497	302	35	-	-	PUNCT
ejpam-4497	302	36	b	b	NOUN
ejpam-4497	302	37	-	-	PUNCT
ejpam-4497	302	38	closed	closed	ADJ
ejpam-4497	302	39	;	;	PUNCT
ejpam-4497	302	40	(	(	PUNCT
ejpam-4497	302	41	iii	iii	NOUN
ejpam-4497	302	42	)	)	PUNCT
ejpam-4497	302	43	bcl(f−1	bcl(f−1	NOUN
ejpam-4497	302	44	ψ	ψ	X
ejpam-4497	302	45	(	(	PUNCT
ejpam-4497	302	46	h,∆))⊆̃f−1	h,∆))⊆̃f−1	NUM
ejpam-4497	302	47	ψ	ψ	X
ejpam-4497	302	48	(	(	PUNCT
ejpam-4497	302	49	bcl(h,∆	bcl(h,∆	NOUN
ejpam-4497	302	50	)	)	PUNCT
ejpam-4497	302	51	)	)	PUNCT
ejpam-4497	302	52	for	for	ADP
ejpam-4497	302	53	each	each	DET
ejpam-4497	302	54	(	(	PUNCT
ejpam-4497	302	55	h,∆)⊆̃s̃	h,∆)⊆̃s̃	PROPN
ejpam-4497	302	56	;	;	PUNCT
ejpam-4497	302	57	(	(	PUNCT
ejpam-4497	302	58	iv	iv	X
ejpam-4497	302	59	)	)	PUNCT
ejpam-4497	302	60	fψ(bcl(f	fψ(bcl(f	NOUN
ejpam-4497	302	61	,	,	PUNCT
ejpam-4497	302	62	o))⊆̃bcl(fψ(f	o))⊆̃bcl(fψ(f	NOUN
ejpam-4497	302	63	,	,	PUNCT
ejpam-4497	302	64	o	o	NOUN
ejpam-4497	302	65	)	)	PUNCT
ejpam-4497	302	66	)	)	PUNCT
ejpam-4497	302	67	for	for	ADP
ejpam-4497	302	68	each	each	DET
ejpam-4497	302	69	(	(	PUNCT
ejpam-4497	302	70	f	f	PROPN
ejpam-4497	302	71	,	,	PUNCT
ejpam-4497	302	72	o)⊆̃x̃	o)⊆̃x̃	PROPN
ejpam-4497	302	73	;	;	PUNCT
ejpam-4497	302	74	(	(	PUNCT
ejpam-4497	302	75	v	v	NOUN
ejpam-4497	302	76	)	)	PUNCT
ejpam-4497	302	77	f−1	f−1	PROPN
ejpam-4497	302	78	ψ	ψ	NOUN
ejpam-4497	302	79	(	(	PUNCT
ejpam-4497	302	80	bint(h,∆))⊆̃bint(f−1	bint(h,∆))⊆̃bint(f−1	PRON
ejpam-4497	302	81	ψ	ψ	X
ejpam-4497	302	82	(	(	PUNCT
ejpam-4497	302	83	h,∆	h,∆	NUM
ejpam-4497	302	84	)	)	PUNCT
ejpam-4497	302	85	)	)	PUNCT
ejpam-4497	302	86	for	for	ADP
ejpam-4497	302	87	each	each	DET
ejpam-4497	302	88	(	(	PUNCT
ejpam-4497	302	89	h,∆)⊆̃s̃.	h,∆)⊆̃s̃.	NOUN
ejpam-4497	302	90	proof	proof	NOUN
ejpam-4497	302	91	.	.	PUNCT
ejpam-4497	303	1	(	(	PUNCT
ejpam-4497	303	2	i	i	NOUN
ejpam-4497	303	3	)	)	PUNCT
ejpam-4497	303	4	⇒	⇒	PROPN
ejpam-4497	303	5	(	(	PUNCT
ejpam-4497	303	6	ii	ii	PROPN
ejpam-4497	303	7	):	):	PUNCT
ejpam-4497	303	8	let	let	VERB
ejpam-4497	303	9	(	(	PUNCT
ejpam-4497	303	10	h,∆	h,∆	X
ejpam-4497	303	11	)	)	PUNCT
ejpam-4497	303	12	be	be	AUX
ejpam-4497	303	13	an	an	DET
ejpam-4497	303	14	is	is	NOUN
ejpam-4497	303	15	-	-	PUNCT
ejpam-4497	303	16	b	b	NOUN
ejpam-4497	303	17	-	-	PUNCT
ejpam-4497	303	18	closed	closed	ADJ
ejpam-4497	303	19	set	set	NOUN
ejpam-4497	303	20	in	in	ADP
ejpam-4497	303	21	(	(	PUNCT
ejpam-4497	303	22	s	s	PROPN
ejpam-4497	303	23	,	,	PUNCT
ejpam-4497	303	24	ν,∆	ν,∆	NOUN
ejpam-4497	303	25	)	)	PUNCT
ejpam-4497	303	26	.	.	PUNCT
ejpam-4497	304	1	then	then	ADV
ejpam-4497	304	2	f−1	f−1	PROPN
ejpam-4497	304	3	ψ	ψ	X
ejpam-4497	304	4	(	(	PUNCT
ejpam-4497	304	5	hc,∆	hc,∆	PROPN
ejpam-4497	304	6	)	)	PUNCT
ejpam-4497	304	7	is	be	AUX
ejpam-4497	304	8	an	an	DET
ejpam-4497	304	9	is	is	NOUN
ejpam-4497	304	10	-	-	PUNCT
ejpam-4497	304	11	b	b	NOUN
ejpam-4497	304	12	-	-	PUNCT
ejpam-4497	304	13	open	open	ADJ
ejpam-4497	304	14	subset	subset	NOUN
ejpam-4497	304	15	of	of	ADP
ejpam-4497	304	16	x̃.	x̃.	ADJ
ejpam-4497	304	17	obviously	obviously	ADV
ejpam-4497	304	18	,	,	PUNCT
ejpam-4497	304	19	f−1	f−1	PROPN
ejpam-4497	304	20	ψ	ψ	X
ejpam-4497	304	21	(	(	PUNCT
ejpam-4497	304	22	hc,∆	hc,∆	PROPN
ejpam-4497	304	23	)	)	PUNCT
ejpam-4497	304	24	=	=	PUNCT
ejpam-4497	305	1	x̃	x̃	PROPN
ejpam-4497	305	2	−	−	PROPN
ejpam-4497	305	3	f−1	f−1	PROPN
ejpam-4497	305	4	ψ	ψ	X
ejpam-4497	305	5	(	(	PUNCT
ejpam-4497	305	6	h,∆	h,∆	NUM
ejpam-4497	305	7	)	)	PUNCT
ejpam-4497	305	8	;	;	PUNCT
ejpam-4497	305	9	hence	hence	ADV
ejpam-4497	305	10	,	,	PUNCT
ejpam-4497	305	11	f−1	f−1	PROPN
ejpam-4497	305	12	ψ	ψ	X
ejpam-4497	305	13	(	(	PUNCT
ejpam-4497	305	14	h,∆	h,∆	NOUN
ejpam-4497	305	15	)	)	PUNCT
ejpam-4497	305	16	is	be	AUX
ejpam-4497	305	17	an	an	DET
ejpam-4497	305	18	is	is	NOUN
ejpam-4497	305	19	-	-	PUNCT
ejpam-4497	305	20	b	b	NOUN
ejpam-4497	305	21	-	-	PUNCT
ejpam-4497	305	22	closed	closed	ADJ
ejpam-4497	305	23	subset	subset	NOUN
ejpam-4497	305	24	of	of	ADP
ejpam-4497	305	25	x̃.	x̃.	PROPN
ejpam-4497	305	26	(	(	PUNCT
ejpam-4497	305	27	ii	ii	NOUN
ejpam-4497	305	28	)	)	PUNCT
ejpam-4497	305	29	⇒	⇒	NOUN
ejpam-4497	305	30	(	(	PUNCT
ejpam-4497	305	31	iii	iii	NOUN
ejpam-4497	305	32	):	):	PUNCT
ejpam-4497	305	33	according	accord	VERB
ejpam-4497	305	34	to	to	ADP
ejpam-4497	305	35	(	(	PUNCT
ejpam-4497	305	36	ii	ii	NOUN
ejpam-4497	305	37	)	)	PUNCT
ejpam-4497	305	38	,	,	PUNCT
ejpam-4497	305	39	f−1	f−1	PROPN
ejpam-4497	305	40	ψ	ψ	X
ejpam-4497	305	41	(	(	PUNCT
ejpam-4497	305	42	bcl(h,∆	bcl(h,∆	NOUN
ejpam-4497	305	43	)	)	PUNCT
ejpam-4497	305	44	)	)	PUNCT
ejpam-4497	305	45	is	be	AUX
ejpam-4497	305	46	an	an	DET
ejpam-4497	305	47	is	is	NOUN
ejpam-4497	305	48	-	-	PUNCT
ejpam-4497	305	49	b	b	NOUN
ejpam-4497	305	50	-	-	PUNCT
ejpam-4497	305	51	closed	closed	ADJ
ejpam-4497	305	52	subset	subset	NOUN
ejpam-4497	305	53	of	of	ADP
ejpam-4497	305	54	x̃.	x̃.	ADJ
ejpam-4497	305	55	then	then	ADV
ejpam-4497	305	56	bcl(f−1	bcl(f−1	VERB
ejpam-4497	305	57	ψ	ψ	X
ejpam-4497	305	58	(	(	PUNCT
ejpam-4497	305	59	h,∆))⊆̃bcl(f−1	h,∆))⊆̃bcl(f−1	PUNCT
ejpam-4497	305	60	ψ	ψ	X
ejpam-4497	305	61	(	(	PUNCT
ejpam-4497	305	62	bcl(h,∆	bcl(h,∆	NOUN
ejpam-4497	305	63	)	)	PUNCT
ejpam-4497	305	64	)	)	PUNCT
ejpam-4497	305	65	)	)	PUNCT
ejpam-4497	306	1	=	=	PUNCT
ejpam-4497	306	2	f−1	f−1	PROPN
ejpam-4497	306	3	ψ	ψ	X
ejpam-4497	306	4	(	(	PUNCT
ejpam-4497	306	5	bcl(h,∆	bcl(h,∆	NOUN
ejpam-4497	306	6	)	)	PUNCT
ejpam-4497	306	7	)	)	PUNCT
ejpam-4497	306	8	.	.	PUNCT
ejpam-4497	307	1	(	(	PUNCT
ejpam-4497	307	2	iii	iii	X
ejpam-4497	307	3	)	)	PUNCT
ejpam-4497	307	4	⇒	⇒	NOUN
ejpam-4497	307	5	(	(	PUNCT
ejpam-4497	307	6	vi	vi	ADJ
ejpam-4497	307	7	):	):	PUNCT
ejpam-4497	307	8	according	accord	VERB
ejpam-4497	307	9	to	to	ADP
ejpam-4497	307	10	(	(	PUNCT
ejpam-4497	307	11	iii	iii	NOUN
ejpam-4497	307	12	)	)	PUNCT
ejpam-4497	307	13	,	,	PUNCT
ejpam-4497	307	14	bcl(f−1	bcl(f−1	NOUN
ejpam-4497	307	15	ψ	ψ	X
ejpam-4497	307	16	(	(	PUNCT
ejpam-4497	307	17	fψ(f	fψ(f	X
ejpam-4497	307	18	,	,	PUNCT
ejpam-4497	307	19	o)))⊆̃f−1	o)))⊆̃f−1	NOUN
ejpam-4497	307	20	ψ	ψ	X
ejpam-4497	307	21	(	(	PUNCT
ejpam-4497	307	22	bcl(fψ(f	bcl(fψ(f	PROPN
ejpam-4497	307	23	,	,	PUNCT
ejpam-4497	307	24	o	o	NOUN
ejpam-4497	307	25	)	)	PUNCT
ejpam-4497	307	26	)	)	PUNCT
ejpam-4497	307	27	)	)	PUNCT
ejpam-4497	307	28	.	.	PUNCT
ejpam-4497	308	1	then	then	ADV
ejpam-4497	308	2	fψ(bcl(f	fψ(bcl(f	NOUN
ejpam-4497	308	3	,	,	PUNCT
ejpam-4497	308	4	o))⊆̃fψ(f−1	o))⊆̃fψ(f−1	PROPN
ejpam-4497	308	5	ψ	ψ	X
ejpam-4497	308	6	(	(	PUNCT
ejpam-4497	308	7	bcl(fψ(f	bcl(fψ(f	PROPN
ejpam-4497	308	8	,	,	PUNCT
ejpam-4497	308	9	o))))⊆̃bcl(fψ(f	o))))⊆̃bcl(fψ(f	PRON
ejpam-4497	308	10	,	,	PUNCT
ejpam-4497	308	11	o	o	NOUN
ejpam-4497	308	12	)	)	PUNCT
ejpam-4497	308	13	)	)	PUNCT
ejpam-4497	308	14	.	.	PUNCT
ejpam-4497	309	1	(	(	PUNCT
ejpam-4497	309	2	iv	iv	X
ejpam-4497	309	3	)	)	PUNCT
ejpam-4497	309	4	⇒	⇒	NOUN
ejpam-4497	309	5	(	(	PUNCT
ejpam-4497	309	6	v	v	NOUN
ejpam-4497	309	7	):	):	PUNCT
ejpam-4497	309	8	according	accord	VERB
ejpam-4497	309	9	to	to	ADP
ejpam-4497	309	10	(	(	PUNCT
ejpam-4497	309	11	iv	iv	NUM
ejpam-4497	309	12	)	)	PUNCT
ejpam-4497	309	13	,	,	PUNCT
ejpam-4497	309	14	fψ(bcl(x̃	fψ(bcl(x̃	PUNCT
ejpam-4497	309	15	−	−	PROPN
ejpam-4497	309	16	f−1	f−1	PROPN
ejpam-4497	309	17	ψ	ψ	X
ejpam-4497	309	18	(	(	PUNCT
ejpam-4497	309	19	h,∆)))⊆̃bcl(fψ(x̃	h,∆)))⊆̃bcl(fψ(x̃	PROPN
ejpam-4497	309	20	−	−	PROPN
ejpam-4497	309	21	f−1	f−1	PROPN
ejpam-4497	309	22	ψ	ψ	X
ejpam-4497	309	23	(	(	PUNCT
ejpam-4497	309	24	h,∆	h,∆	NOUN
ejpam-4497	309	25	)	)	PUNCT
ejpam-4497	309	26	)	)	PUNCT
ejpam-4497	309	27	)	)	PUNCT
ejpam-4497	309	28	.	.	PUNCT
ejpam-4497	310	1	therefore	therefore	ADV
ejpam-4497	310	2	,	,	PUNCT
ejpam-4497	310	3	fψ(x̃	fψ(x̃	PROPN
ejpam-4497	310	4	−	−	NOUN
ejpam-4497	310	5	bint(f−1	bint(f−1	PROPN
ejpam-4497	310	6	ψ	ψ	X
ejpam-4497	310	7	(	(	PUNCT
ejpam-4497	310	8	h,∆	h,∆	NOUN
ejpam-4497	310	9	)	)	PUNCT
ejpam-4497	310	10	)	)	PUNCT
ejpam-4497	310	11	)	)	PUNCT
ejpam-4497	311	1	=	=	NOUN
ejpam-4497	311	2	fψ(bcl(x̃	fψ(bcl(x̃	X
ejpam-4497	312	1	−	−	NUM
ejpam-4497	312	2	f−1	f−1	PROPN
ejpam-4497	312	3	ψ	ψ	X
ejpam-4497	312	4	(	(	PUNCT
ejpam-4497	312	5	h,∆	h,∆	NOUN
ejpam-4497	312	6	)	)	PUNCT
ejpam-4497	312	7	)	)	PUNCT
ejpam-4497	312	8	)	)	PUNCT
ejpam-4497	313	1	⊆	⊆	NUM
ejpam-4497	313	2	bcl(s̃	bcl(s̃	NUM
ejpam-4497	313	3	−	−	PROPN
ejpam-4497	313	4	(	(	PUNCT
ejpam-4497	313	5	h,∆	h,∆	NUM
ejpam-4497	313	6	)	)	PUNCT
ejpam-4497	313	7	)	)	PUNCT
ejpam-4497	314	1	=	=	SYM
ejpam-4497	314	2	s̃	s̃	PROPN
ejpam-4497	314	3	−	−	PROPN
ejpam-4497	314	4	bint(h,∆	bint(h,∆	NOUN
ejpam-4497	314	5	)	)	PUNCT
ejpam-4497	314	6	.	.	PUNCT
ejpam-4497	315	1	thus	thus	ADV
ejpam-4497	315	2	x̃−bint(f−1	x̃−bint(f−1	PROPN
ejpam-4497	315	3	ψ	ψ	X
ejpam-4497	315	4	(	(	PUNCT
ejpam-4497	315	5	h,∆))⊆̃f−1	h,∆))⊆̃f−1	NUM
ejpam-4497	315	6	ψ	ψ	X
ejpam-4497	315	7	(	(	PUNCT
ejpam-4497	315	8	s̃	s̃	PROPN
ejpam-4497	315	9	−bint(h,∆	−bint(h,∆	PROPN
ejpam-4497	315	10	)	)	PUNCT
ejpam-4497	315	11	)	)	PUNCT
ejpam-4497	316	1	=	=	SYM
ejpam-4497	316	2	f−1	f−1	PROPN
ejpam-4497	316	3	ψ	ψ	X
ejpam-4497	316	4	(	(	PUNCT
ejpam-4497	316	5	s̃)−f−1	s̃)−f−1	NOUN
ejpam-4497	316	6	ψ	ψ	X
ejpam-4497	316	7	(	(	PUNCT
ejpam-4497	316	8	bint(h,∆	bint(h,∆	NOUN
ejpam-4497	316	9	)	)	PUNCT
ejpam-4497	316	10	)	)	PUNCT
ejpam-4497	316	11	.	.	PUNCT
ejpam-4497	317	1	hence	hence	ADV
ejpam-4497	317	2	f−1	f−1	PROPN
ejpam-4497	317	3	ψ	ψ	X
ejpam-4497	317	4	(	(	PUNCT
ejpam-4497	317	5	bint(h,∆))⊆̃bint(f−1	bint(h,∆))⊆̃bint(f−1	PRON
ejpam-4497	317	6	ψ	ψ	X
ejpam-4497	317	7	(	(	PUNCT
ejpam-4497	317	8	h,∆	h,∆	NUM
ejpam-4497	317	9	)	)	PUNCT
ejpam-4497	317	10	)	)	PUNCT
ejpam-4497	317	11	.	.	PUNCT
ejpam-4497	318	1	(	(	PUNCT
ejpam-4497	318	2	v	v	NOUN
ejpam-4497	318	3	)	)	PUNCT
ejpam-4497	318	4	⇒	⇒	NOUN
ejpam-4497	318	5	(	(	PUNCT
ejpam-4497	318	6	i	i	NOUN
ejpam-4497	318	7	):	):	PUNCT
ejpam-4497	318	8	let	let	VERB
ejpam-4497	318	9	(	(	PUNCT
ejpam-4497	318	10	h,∆	h,∆	X
ejpam-4497	318	11	)	)	PUNCT
ejpam-4497	318	12	be	be	AUX
ejpam-4497	318	13	an	an	DET
ejpam-4497	318	14	is	is	NOUN
ejpam-4497	318	15	-	-	PUNCT
ejpam-4497	318	16	b	b	NOUN
ejpam-4497	318	17	-	-	PUNCT
ejpam-4497	318	18	open	open	ADJ
ejpam-4497	318	19	subset	subset	NOUN
ejpam-4497	318	20	of	of	ADP
ejpam-4497	318	21	s̃.	s̃.	PROPN
ejpam-4497	318	22	according	accord	VERB
ejpam-4497	318	23	to	to	ADP
ejpam-4497	318	24	(	(	PUNCT
ejpam-4497	318	25	v	v	NOUN
ejpam-4497	318	26	)	)	PUNCT
ejpam-4497	318	27	,	,	PUNCT
ejpam-4497	318	28	f−1	f−1	PROPN
ejpam-4497	318	29	ψ	ψ	X
ejpam-4497	318	30	(	(	PUNCT
ejpam-4497	318	31	h,∆)⊆̃bint(f−1	h,∆)⊆̃bint(f−1	NOUN
ejpam-4497	318	32	ψ	ψ	X
ejpam-4497	318	33	(	(	PUNCT
ejpam-4497	318	34	h,∆	h,∆	NUM
ejpam-4497	318	35	)	)	PUNCT
ejpam-4497	318	36	)	)	PUNCT
ejpam-4497	318	37	.	.	PUNCT
ejpam-4497	319	1	this	this	PRON
ejpam-4497	319	2	implies	imply	VERB
ejpam-4497	319	3	f−1	f−1	PROPN
ejpam-4497	319	4	ψ	ψ	X
ejpam-4497	319	5	(	(	PUNCT
ejpam-4497	319	6	h,∆	h,∆	NUM
ejpam-4497	319	7	)	)	PUNCT
ejpam-4497	319	8	=	=	SYM
ejpam-4497	319	9	bint(f−1	bint(f−1	PART
ejpam-4497	319	10	ψ	ψ	X
ejpam-4497	319	11	(	(	PUNCT
ejpam-4497	319	12	h,∆	h,∆	NUM
ejpam-4497	319	13	)	)	PUNCT
ejpam-4497	319	14	)	)	PUNCT
ejpam-4497	319	15	.	.	PUNCT
ejpam-4497	320	1	hence	hence	ADV
ejpam-4497	320	2	,	,	PUNCT
ejpam-4497	320	3	fψ	fψ	PROPN
ejpam-4497	320	4	is	be	AUX
ejpam-4497	320	5	is	be	AUX
ejpam-4497	320	6	-	-	PUNCT
ejpam-4497	320	7	b	b	NOUN
ejpam-4497	320	8	-	-	PUNCT
ejpam-4497	320	9	continuous	continuous	ADJ
ejpam-4497	320	10	.	.	PUNCT
ejpam-4497	321	1	theorem	theorem	NOUN
ejpam-4497	321	2	5	5	NUM
ejpam-4497	321	3	.	.	PUNCT
ejpam-4497	322	1	if	if	SCONJ
ejpam-4497	322	2	fψ	fψ	NOUN
ejpam-4497	322	3	:	:	PUNCT
ejpam-4497	322	4	(	(	PUNCT
ejpam-4497	322	5	x,µ,o	x,µ,o	NOUN
ejpam-4497	322	6	)	)	PUNCT
ejpam-4497	322	7	→	→	PUNCT
ejpam-4497	322	8	(	(	PUNCT
ejpam-4497	322	9	s	s	PROPN
ejpam-4497	322	10	,	,	PUNCT
ejpam-4497	322	11	ν,∆	ν,∆	NUM
ejpam-4497	322	12	)	)	PUNCT
ejpam-4497	322	13	is	be	AUX
ejpam-4497	322	14	is	be	AUX
ejpam-4497	322	15	-	-	PUNCT
ejpam-4497	322	16	b	b	NOUN
ejpam-4497	322	17	-	-	PUNCT
ejpam-4497	322	18	continuous	continuous	ADJ
ejpam-4497	322	19	,	,	PUNCT
ejpam-4497	322	20	then	then	ADV
ejpam-4497	322	21	the	the	DET
ejpam-4497	322	22	restriction	restriction	NOUN
ejpam-4497	322	23	s	s	NOUN
ejpam-4497	322	24	-	-	PUNCT
ejpam-4497	322	25	map	map	NOUN
ejpam-4497	322	26	fψ|m	fψ|m	NOUN
ejpam-4497	322	27	:	:	PUNCT
ejpam-4497	322	28	(	(	PUNCT
ejpam-4497	322	29	m	m	PROPN
ejpam-4497	322	30	,	,	PUNCT
ejpam-4497	322	31	µm	µm	NOUN
ejpam-4497	322	32	,	,	PUNCT
ejpam-4497	322	33	o	o	NOUN
ejpam-4497	322	34	)	)	PUNCT
ejpam-4497	322	35	→	→	SYM
ejpam-4497	322	36	(	(	PUNCT
ejpam-4497	322	37	s	s	PROPN
ejpam-4497	322	38	,	,	PUNCT
ejpam-4497	322	39	ν,∆	ν,∆	NUM
ejpam-4497	322	40	)	)	PUNCT
ejpam-4497	322	41	is	be	AUX
ejpam-4497	322	42	is	be	AUX
ejpam-4497	322	43	-	-	PUNCT
ejpam-4497	322	44	b	b	NOUN
ejpam-4497	322	45	-	-	PUNCT
ejpam-4497	322	46	continuous	continuous	ADJ
ejpam-4497	322	47	provided	provide	VERB
ejpam-4497	322	48	that	that	SCONJ
ejpam-4497	322	49	m̃	m̃	PROPN
ejpam-4497	322	50	is	be	AUX
ejpam-4497	322	51	an	an	DET
ejpam-4497	322	52	is	is	NOUN
ejpam-4497	322	53	-	-	PUNCT
ejpam-4497	322	54	open	open	ADJ
ejpam-4497	322	55	set	set	NOUN
ejpam-4497	322	56	.	.	PUNCT
ejpam-4497	323	1	proof	proof	NOUN
ejpam-4497	323	2	.	.	PUNCT
ejpam-4497	324	1	consider	consider	VERB
ejpam-4497	324	2	(	(	PUNCT
ejpam-4497	324	3	h,∆	h,∆	NUM
ejpam-4497	324	4	)	)	PUNCT
ejpam-4497	324	5	is	be	AUX
ejpam-4497	324	6	an	an	DET
ejpam-4497	324	7	is	is	NOUN
ejpam-4497	324	8	-	-	PUNCT
ejpam-4497	324	9	b	b	NOUN
ejpam-4497	324	10	-	-	PUNCT
ejpam-4497	324	11	open	open	ADJ
ejpam-4497	324	12	set	set	NOUN
ejpam-4497	324	13	in	in	ADP
ejpam-4497	324	14	(	(	PUNCT
ejpam-4497	324	15	s	s	PROPN
ejpam-4497	324	16	,	,	PUNCT
ejpam-4497	324	17	ν,∆	ν,∆	NOUN
ejpam-4497	324	18	)	)	PUNCT
ejpam-4497	324	19	.	.	PUNCT
ejpam-4497	325	1	by	by	ADP
ejpam-4497	325	2	hypothesis	hypothesis	NOUN
ejpam-4497	325	3	,	,	PUNCT
ejpam-4497	325	4	f−1	f−1	PROPN
ejpam-4497	325	5	ψ	ψ	X
ejpam-4497	325	6	(	(	PUNCT
ejpam-4497	325	7	h,∆	h,∆	NOUN
ejpam-4497	325	8	)	)	PUNCT
ejpam-4497	325	9	is	be	AUX
ejpam-4497	325	10	is	be	AUX
ejpam-4497	325	11	-	-	PUNCT
ejpam-4497	325	12	b	b	NOUN
ejpam-4497	325	13	-	-	PUNCT
ejpam-4497	325	14	open	open	ADJ
ejpam-4497	325	15	.	.	PUNCT
ejpam-4497	326	1	now	now	ADV
ejpam-4497	326	2	,	,	PUNCT
ejpam-4497	326	3	f−1	f−1	PROPN
ejpam-4497	326	4	ψ|m	ψ|m	X
ejpam-4497	326	5	(	(	PUNCT
ejpam-4497	326	6	h,∆	h,∆	NUM
ejpam-4497	326	7	)	)	PUNCT
ejpam-4497	326	8	=	=	SYM
ejpam-4497	326	9	f−1	f−1	PROPN
ejpam-4497	326	10	ψ	ψ	X
ejpam-4497	326	11	(	(	PUNCT
ejpam-4497	326	12	h,∆)∩̃m̃.	h,∆)∩̃m̃.	NOUN
ejpam-4497	326	13	since	since	SCONJ
ejpam-4497	326	14	m̃	m̃	PROPN
ejpam-4497	326	15	is	be	AUX
ejpam-4497	326	16	an	an	DET
ejpam-4497	326	17	is	is	NOUN
ejpam-4497	326	18	-	-	PUNCT
ejpam-4497	326	19	open	open	ADJ
ejpam-4497	326	20	set	set	NOUN
ejpam-4497	326	21	,	,	PUNCT
ejpam-4497	326	22	it	it	PRON
ejpam-4497	326	23	follows	follow	VERB
ejpam-4497	326	24	from	from	ADP
ejpam-4497	326	25	proposition	proposition	NOUN
ejpam-4497	326	26	6	6	NUM
ejpam-4497	326	27	that	that	PRON
ejpam-4497	326	28	f−1	f−1	PROPN
ejpam-4497	326	29	ψ|m	ψ|m	X
ejpam-4497	327	1	(	(	PUNCT
ejpam-4497	327	2	h,∆	h,∆	X
ejpam-4497	327	3	)	)	PUNCT
ejpam-4497	327	4	is	be	AUX
ejpam-4497	327	5	is	be	AUX
ejpam-4497	327	6	-	-	PUNCT
ejpam-4497	327	7	b	b	NOUN
ejpam-4497	327	8	-	-	PUNCT
ejpam-4497	327	9	open	open	ADJ
ejpam-4497	327	10	.	.	PUNCT
ejpam-4497	328	1	hence	hence	ADV
ejpam-4497	328	2	,	,	PUNCT
ejpam-4497	328	3	fψ|m	fψ|m	PROPN
ejpam-4497	328	4	is	be	AUX
ejpam-4497	328	5	an	an	DET
ejpam-4497	328	6	is	is	NOUN
ejpam-4497	328	7	-	-	PUNCT
ejpam-4497	328	8	b	b	NOUN
ejpam-4497	328	9	-	-	PUNCT
ejpam-4497	328	10	continuous	continuous	ADJ
ejpam-4497	328	11	map	map	NOUN
ejpam-4497	328	12	.	.	PUNCT
ejpam-4497	329	1	definition	definition	NOUN
ejpam-4497	329	2	19	19	NUM
ejpam-4497	329	3	.	.	PUNCT
ejpam-4497	330	1	if	if	SCONJ
ejpam-4497	330	2	the	the	DET
ejpam-4497	330	3	image	image	NOUN
ejpam-4497	330	4	of	of	ADP
ejpam-4497	330	5	each	each	PRON
ejpam-4497	330	6	is	be	AUX
ejpam-4497	330	7	-	-	PUNCT
ejpam-4497	330	8	b	b	NOUN
ejpam-4497	330	9	-	-	PUNCT
ejpam-4497	330	10	open	open	ADJ
ejpam-4497	330	11	(	(	PUNCT
ejpam-4497	330	12	resp	resp	NOUN
ejpam-4497	330	13	.	.	PUNCT
ejpam-4497	330	14	,	,	PUNCT
ejpam-4497	330	15	is	be	AUX
ejpam-4497	330	16	-	-	PUNCT
ejpam-4497	330	17	b	b	NOUN
ejpam-4497	330	18	-	-	PUNCT
ejpam-4497	330	19	closed	closed	ADJ
ejpam-4497	330	20	)	)	PUNCT
ejpam-4497	330	21	set	set	VERB
ejpam-4497	330	22	under	under	ADP
ejpam-4497	330	23	an	an	DET
ejpam-4497	330	24	s	s	NOUN
ejpam-4497	330	25	-	-	PUNCT
ejpam-4497	330	26	map	map	NOUN
ejpam-4497	330	27	fψ	fψ	NOUN
ejpam-4497	330	28	:	:	PUNCT
ejpam-4497	330	29	(	(	PUNCT
ejpam-4497	330	30	x,µ,o	x,µ,o	NOUN
ejpam-4497	330	31	)	)	PUNCT
ejpam-4497	330	32	→	→	PUNCT
ejpam-4497	330	33	(	(	PUNCT
ejpam-4497	330	34	s	s	PROPN
ejpam-4497	330	35	,	,	PUNCT
ejpam-4497	330	36	ν,∆	ν,∆	NUM
ejpam-4497	330	37	)	)	PUNCT
ejpam-4497	330	38	is	be	AUX
ejpam-4497	330	39	is	be	AUX
ejpam-4497	330	40	-	-	PUNCT
ejpam-4497	330	41	b	b	NOUN
ejpam-4497	330	42	-	-	PUNCT
ejpam-4497	330	43	open	open	ADJ
ejpam-4497	330	44	(	(	PUNCT
ejpam-4497	330	45	resp	resp	NOUN
ejpam-4497	330	46	.	.	PUNCT
ejpam-4497	330	47	,	,	PUNCT
ejpam-4497	330	48	is	be	AUX
ejpam-4497	330	49	-	-	PUNCT
ejpam-4497	330	50	b	b	NOUN
ejpam-4497	330	51	-	-	PUNCT
ejpam-4497	330	52	closed	closed	ADJ
ejpam-4497	330	53	)	)	PUNCT
ejpam-4497	330	54	,	,	PUNCT
ejpam-4497	330	55	then	then	ADV
ejpam-4497	330	56	fψ	fψ	PROPN
ejpam-4497	330	57	is	be	AUX
ejpam-4497	330	58	called	call	VERB
ejpam-4497	330	59	is	be	AUX
ejpam-4497	330	60	-	-	PUNCT
ejpam-4497	330	61	b	b	NOUN
ejpam-4497	330	62	-	-	PUNCT
ejpam-4497	330	63	open	open	ADJ
ejpam-4497	330	64	(	(	PUNCT
ejpam-4497	330	65	resp	resp	NOUN
ejpam-4497	330	66	.	.	PUNCT
ejpam-4497	330	67	,	,	PUNCT
ejpam-4497	330	68	is	be	AUX
ejpam-4497	330	69	-	-	PUNCT
ejpam-4497	330	70	b	b	NOUN
ejpam-4497	330	71	-	-	PUNCT
ejpam-4497	330	72	closed	closed	ADJ
ejpam-4497	330	73	)	)	PUNCT
ejpam-4497	330	74	.	.	PUNCT
ejpam-4497	331	1	proposition	proposition	NOUN
ejpam-4497	331	2	15	15	NUM
ejpam-4497	331	3	.	.	PUNCT
ejpam-4497	332	1	fψ	fψ	NOUN
ejpam-4497	332	2	:	:	PUNCT
ejpam-4497	332	3	(	(	PUNCT
ejpam-4497	332	4	x,µ,o	x,µ,o	NOUN
ejpam-4497	332	5	)	)	PUNCT
ejpam-4497	332	6	→	→	PUNCT
ejpam-4497	332	7	(	(	PUNCT
ejpam-4497	332	8	s	s	PROPN
ejpam-4497	332	9	,	,	PUNCT
ejpam-4497	332	10	ν,∆	ν,∆	NUM
ejpam-4497	332	11	)	)	PUNCT
ejpam-4497	332	12	is	be	AUX
ejpam-4497	332	13	an	an	DET
ejpam-4497	332	14	is	is	NOUN
ejpam-4497	332	15	-	-	PUNCT
ejpam-4497	332	16	b	b	NOUN
ejpam-4497	332	17	-	-	PUNCT
ejpam-4497	332	18	open	open	ADJ
ejpam-4497	332	19	map	map	NOUN
ejpam-4497	332	20	iff	iff	PROPN
ejpam-4497	332	21	fψ(bint(h	fψ(bint(h	PROPN
ejpam-4497	332	22	,	,	PUNCT
ejpam-4497	332	23	o	o	NOUN
ejpam-4497	332	24	)	)	PUNCT
ejpam-4497	332	25	)	)	PUNCT
ejpam-4497	333	1	⊆̃bint(fψ(h	⊆̃bint(fψ(h	NUM
ejpam-4497	333	2	,	,	PUNCT
ejpam-4497	333	3	o	o	NOUN
ejpam-4497	333	4	)	)	PUNCT
ejpam-4497	333	5	)	)	PUNCT
ejpam-4497	333	6	for	for	ADP
ejpam-4497	333	7	each	each	DET
ejpam-4497	333	8	subset	subset	NOUN
ejpam-4497	333	9	of	of	ADP
ejpam-4497	333	10	(	(	PUNCT
ejpam-4497	333	11	h	h	NOUN
ejpam-4497	333	12	,	,	PUNCT
ejpam-4497	333	13	o	o	NOUN
ejpam-4497	333	14	)	)	PUNCT
ejpam-4497	333	15	of	of	ADP
ejpam-4497	333	16	x̃.	x̃.	ADJ
ejpam-4497	333	17	proof	proof	NOUN
ejpam-4497	333	18	.	.	PUNCT
ejpam-4497	334	1	⇒	⇒	NOUN
ejpam-4497	334	2	:	:	PUNCT
ejpam-4497	334	3	let	let	VERB
ejpam-4497	334	4	(	(	PUNCT
ejpam-4497	334	5	h	h	NOUN
ejpam-4497	334	6	,	,	PUNCT
ejpam-4497	334	7	o	o	NOUN
ejpam-4497	334	8	)	)	PUNCT
ejpam-4497	334	9	be	be	AUX
ejpam-4497	334	10	a	a	DET
ejpam-4497	334	11	subset	subset	NOUN
ejpam-4497	334	12	of	of	ADP
ejpam-4497	334	13	x̃.	x̃.	ADJ
ejpam-4497	334	14	now	now	ADV
ejpam-4497	334	15	,	,	PUNCT
ejpam-4497	334	16	fψ(bint(h	fψ(bint(h	ADJ
ejpam-4497	334	17	,	,	PUNCT
ejpam-4497	334	18	o))⊆̃fψ(h	o))⊆̃fψ(h	NOUN
ejpam-4497	334	19	,	,	PUNCT
ejpam-4497	334	20	o	o	NOUN
ejpam-4497	334	21	)	)	PUNCT
ejpam-4497	334	22	and	and	CCONJ
ejpam-4497	334	23	bint(h	bint(h	NOUN
ejpam-4497	334	24	,	,	PUNCT
ejpam-4497	334	25	o	o	NOUN
ejpam-4497	334	26	)	)	PUNCT
ejpam-4497	334	27	is	be	AUX
ejpam-4497	334	28	an	an	DET
ejpam-4497	334	29	is	is	NOUN
ejpam-4497	334	30	-	-	PUNCT
ejpam-4497	334	31	b	b	NOUN
ejpam-4497	334	32	-	-	PUNCT
ejpam-4497	334	33	open	open	ADJ
ejpam-4497	334	34	set	set	NOUN
ejpam-4497	334	35	.	.	PUNCT
ejpam-4497	335	1	by	by	ADP
ejpam-4497	335	2	hypothesis	hypothesis	NOUN
ejpam-4497	335	3	,	,	PUNCT
ejpam-4497	335	4	fψ(bint(h	fψ(bint(h	ADJ
ejpam-4497	335	5	,	,	PUNCT
ejpam-4497	335	6	o	o	NOUN
ejpam-4497	335	7	)	)	PUNCT
ejpam-4497	335	8	)	)	PUNCT
ejpam-4497	335	9	is	be	AUX
ejpam-4497	335	10	is	be	AUX
ejpam-4497	335	11	-	-	PUNCT
ejpam-4497	335	12	b	b	NOUN
ejpam-4497	335	13	-	-	PUNCT
ejpam-4497	335	14	open	open	ADJ
ejpam-4497	335	15	.	.	PUNCT
ejpam-4497	336	1	therefore	therefore	ADV
ejpam-4497	336	2	,	,	PUNCT
ejpam-4497	336	3	fψ(bint(h	fψ(bint(h	PROPN
ejpam-4497	336	4	,	,	PUNCT
ejpam-4497	336	5	o))⊆̃	o))⊆̃	DET
ejpam-4497	336	6	bint(fψ(h	bint(fψ(h	NOUN
ejpam-4497	336	7	,	,	PUNCT
ejpam-4497	336	8	o	o	NOUN
ejpam-4497	336	9	)	)	PUNCT
ejpam-4497	336	10	)	)	PUNCT
ejpam-4497	336	11	.	.	PUNCT
ejpam-4497	337	1	⇐	⇐	ADJ
ejpam-4497	337	2	:	:	PUNCT
ejpam-4497	337	3	let	let	VERB
ejpam-4497	337	4	(	(	PUNCT
ejpam-4497	337	5	λ	λ	NOUN
ejpam-4497	337	6	,	,	PUNCT
ejpam-4497	337	7	o	o	NOUN
ejpam-4497	337	8	)	)	PUNCT
ejpam-4497	337	9	be	be	VERB
ejpam-4497	337	10	an	an	DET
ejpam-4497	337	11	is	is	NOUN
ejpam-4497	337	12	-	-	PUNCT
ejpam-4497	337	13	open	open	ADJ
ejpam-4497	337	14	subset	subset	NOUN
ejpam-4497	337	15	of	of	ADP
ejpam-4497	337	16	x̃.	x̃.	PROPN
ejpam-4497	337	17	then	then	ADV
ejpam-4497	337	18	fψ(h	fψ(h	NUM
ejpam-4497	337	19	,	,	PUNCT
ejpam-4497	337	20	o)⊆̃bint(fψ(h	o)⊆̃bint(fψ(h	PROPN
ejpam-4497	337	21	,	,	PUNCT
ejpam-4497	337	22	o	o	NOUN
ejpam-4497	337	23	)	)	PUNCT
ejpam-4497	337	24	)	)	PUNCT
ejpam-4497	337	25	.	.	PUNCT
ejpam-4497	338	1	therefore	therefore	ADV
ejpam-4497	338	2	,	,	PUNCT
ejpam-4497	338	3	fψ(h	fψ(h	PROPN
ejpam-4497	338	4	,	,	PUNCT
ejpam-4497	338	5	o	o	NOUN
ejpam-4497	338	6	)	)	PUNCT
ejpam-4497	338	7	=	=	PUNCT
ejpam-4497	338	8	bint(fψ(h	bint(fψ(h	X
ejpam-4497	338	9	,	,	PUNCT
ejpam-4497	338	10	o	o	NOUN
ejpam-4497	338	11	)	)	PUNCT
ejpam-4497	338	12	)	)	PUNCT
ejpam-4497	338	13	which	which	PRON
ejpam-4497	338	14	means	mean	VERB
ejpam-4497	338	15	that	that	SCONJ
ejpam-4497	338	16	fψ	fψ	NOUN
ejpam-4497	338	17	is	be	AUX
ejpam-4497	338	18	an	an	DET
ejpam-4497	338	19	is	is	NOUN
ejpam-4497	338	20	-	-	PUNCT
ejpam-4497	338	21	b	b	NOUN
ejpam-4497	338	22	-	-	PUNCT
ejpam-4497	338	23	open	open	ADJ
ejpam-4497	338	24	map	map	NOUN
ejpam-4497	338	25	.	.	PUNCT
ejpam-4497	339	1	t.m	t.m	PROPN
ejpam-4497	339	2	.	.	PUNCT
ejpam-4497	339	3	al	al	PROPN
ejpam-4497	339	4	-	-	PUNCT
ejpam-4497	339	5	shami	shami	PROPN
ejpam-4497	339	6	et	et	PROPN
ejpam-4497	339	7	al	al	PROPN
ejpam-4497	339	8	.	.	PUNCT
ejpam-4497	339	9	/	/	SYM
ejpam-4497	339	10	eur	eur	PROPN
ejpam-4497	339	11	.	.	PUNCT
ejpam-4497	340	1	j.	j.	PROPN
ejpam-4497	340	2	pure	pure	PROPN
ejpam-4497	340	3	appl	appl	PROPN
ejpam-4497	340	4	.	.	PROPN
ejpam-4497	340	5	math	math	PROPN
ejpam-4497	340	6	,	,	PUNCT
ejpam-4497	340	7	15	15	NUM
ejpam-4497	340	8	(	(	PUNCT
ejpam-4497	340	9	4	4	NUM
ejpam-4497	340	10	)	)	PUNCT
ejpam-4497	340	11	(	(	PUNCT
ejpam-4497	340	12	2022	2022	NUM
ejpam-4497	340	13	)	)	PUNCT
ejpam-4497	340	14	,	,	PUNCT
ejpam-4497	340	15	1455	1455	NUM
ejpam-4497	340	16	-	-	SYM
ejpam-4497	340	17	1471	1471	NUM
ejpam-4497	340	18	1465	1465	NUM
ejpam-4497	340	19	proposition	proposition	NOUN
ejpam-4497	340	20	16	16	NUM
ejpam-4497	340	21	.	.	PUNCT
ejpam-4497	341	1	fψ	fψ	ADP
ejpam-4497	341	2	:	:	PUNCT
ejpam-4497	341	3	(	(	PUNCT
ejpam-4497	341	4	x,µ,o	x,µ,o	NOUN
ejpam-4497	341	5	)	)	PUNCT
ejpam-4497	341	6	→	→	PUNCT
ejpam-4497	341	7	(	(	PUNCT
ejpam-4497	341	8	s	s	PROPN
ejpam-4497	341	9	,	,	PUNCT
ejpam-4497	341	10	ν,∆	ν,∆	NUM
ejpam-4497	341	11	)	)	PUNCT
ejpam-4497	341	12	is	be	AUX
ejpam-4497	341	13	an	an	DET
ejpam-4497	341	14	is	is	NOUN
ejpam-4497	341	15	-	-	PUNCT
ejpam-4497	341	16	b	b	NOUN
ejpam-4497	341	17	-	-	PUNCT
ejpam-4497	341	18	closed	closed	ADJ
ejpam-4497	341	19	map	map	NOUN
ejpam-4497	341	20	iff	iff	PROPN
ejpam-4497	341	21	bcl(fψ(h	bcl(fψ(h	PROPN
ejpam-4497	341	22	,	,	PUNCT
ejpam-4497	341	23	o	o	NOUN
ejpam-4497	341	24	)	)	PUNCT
ejpam-4497	341	25	)	)	PUNCT
ejpam-4497	341	26	⊆̃fψ(bcl(h	⊆̃fψ(bcl(h	PROPN
ejpam-4497	341	27	,	,	PUNCT
ejpam-4497	341	28	o	o	NOUN
ejpam-4497	341	29	)	)	PUNCT
ejpam-4497	341	30	)	)	PUNCT
ejpam-4497	341	31	for	for	ADP
ejpam-4497	341	32	each	each	DET
ejpam-4497	341	33	subset	subset	NOUN
ejpam-4497	341	34	(	(	PUNCT
ejpam-4497	341	35	h	h	NOUN
ejpam-4497	341	36	,	,	PUNCT
ejpam-4497	341	37	o	o	NOUN
ejpam-4497	341	38	)	)	PUNCT
ejpam-4497	341	39	of	of	ADP
ejpam-4497	341	40	x̃.	x̃.	ADJ
ejpam-4497	341	41	proof	proof	NOUN
ejpam-4497	341	42	.	.	PUNCT
ejpam-4497	342	1	⇒	⇒	NOUN
ejpam-4497	342	2	:	:	PUNCT
ejpam-4497	342	3	let	let	VERB
ejpam-4497	342	4	fψ	fψ	PART
ejpam-4497	342	5	be	be	AUX
ejpam-4497	342	6	an	an	DET
ejpam-4497	342	7	is	is	NOUN
ejpam-4497	342	8	-	-	PUNCT
ejpam-4497	342	9	b	b	NOUN
ejpam-4497	342	10	-	-	PUNCT
ejpam-4497	342	11	closed	closed	ADJ
ejpam-4497	342	12	map	map	NOUN
ejpam-4497	342	13	and	and	CCONJ
ejpam-4497	342	14	(	(	PUNCT
ejpam-4497	342	15	h	h	NOUN
ejpam-4497	342	16	,	,	PUNCT
ejpam-4497	342	17	o	o	NOUN
ejpam-4497	342	18	)	)	PUNCT
ejpam-4497	342	19	be	be	VERB
ejpam-4497	342	20	an	an	DET
ejpam-4497	342	21	s	s	NOUN
ejpam-4497	342	22	-	-	PUNCT
ejpam-4497	342	23	set	set	NOUN
ejpam-4497	342	24	of	of	ADP
ejpam-4497	342	25	x̃.	x̃.	ADJ
ejpam-4497	342	26	by	by	ADP
ejpam-4497	342	27	hypothesis	hypothesis	NOUN
ejpam-4497	342	28	,	,	PUNCT
ejpam-4497	342	29	fψ(bcl(h	fψ(bcl(h	PROPN
ejpam-4497	342	30	,	,	PUNCT
ejpam-4497	342	31	o	o	NOUN
ejpam-4497	342	32	)	)	PUNCT
ejpam-4497	342	33	)	)	PUNCT
ejpam-4497	342	34	is	be	AUX
ejpam-4497	342	35	is	be	AUX
ejpam-4497	342	36	-	-	PUNCT
ejpam-4497	342	37	b	b	NOUN
ejpam-4497	342	38	-	-	PUNCT
ejpam-4497	342	39	closed	closed	ADJ
ejpam-4497	342	40	.	.	PUNCT
ejpam-4497	343	1	since	since	SCONJ
ejpam-4497	343	2	fψ(h	fψ(h	NUM
ejpam-4497	343	3	,	,	PUNCT
ejpam-4497	343	4	o)⊆̃fψ(bcl(h	o)⊆̃fψ(bcl(h	NOUN
ejpam-4497	343	5	,	,	PUNCT
ejpam-4497	343	6	o	o	NOUN
ejpam-4497	343	7	)	)	PUNCT
ejpam-4497	343	8	)	)	PUNCT
ejpam-4497	343	9	,	,	PUNCT
ejpam-4497	343	10	bcl(fψ(h	bcl(fψ(h	PROPN
ejpam-4497	343	11	,	,	PUNCT
ejpam-4497	343	12	o	o	NOUN
ejpam-4497	343	13	)	)	PUNCT
ejpam-4497	343	14	)	)	PUNCT
ejpam-4497	343	15	⊆̃fψ(bcl(h	⊆̃fψ(bcl(h	PROPN
ejpam-4497	343	16	,	,	PUNCT
ejpam-4497	343	17	o	o	NOUN
ejpam-4497	343	18	)	)	PUNCT
ejpam-4497	343	19	)	)	PUNCT
ejpam-4497	343	20	.	.	PUNCT
ejpam-4497	344	1	⇐	⇐	ADJ
ejpam-4497	344	2	:	:	PUNCT
ejpam-4497	344	3	suppose	suppose	VERB
ejpam-4497	344	4	that	that	SCONJ
ejpam-4497	344	5	(	(	PUNCT
ejpam-4497	344	6	h	h	NOUN
ejpam-4497	344	7	,	,	PUNCT
ejpam-4497	344	8	o	o	NOUN
ejpam-4497	344	9	)	)	PUNCT
ejpam-4497	344	10	is	be	AUX
ejpam-4497	344	11	an	an	DET
ejpam-4497	344	12	is	is	NOUN
ejpam-4497	344	13	-	-	PUNCT
ejpam-4497	344	14	b	b	NOUN
ejpam-4497	344	15	-	-	PUNCT
ejpam-4497	344	16	closed	closed	ADJ
ejpam-4497	344	17	subset	subset	NOUN
ejpam-4497	344	18	of	of	ADP
ejpam-4497	344	19	x̃.	x̃.	ADJ
ejpam-4497	344	20	by	by	ADP
ejpam-4497	344	21	hypothesis	hypothesis	NOUN
ejpam-4497	344	22	,	,	PUNCT
ejpam-4497	344	23	fψ(h	fψ(h	NUM
ejpam-4497	344	24	,	,	PUNCT
ejpam-4497	344	25	o)⊆̃	o)⊆̃	PUNCT
ejpam-4497	344	26	bcl(fψ(h	bcl(fψ(h	PROPN
ejpam-4497	344	27	,	,	PUNCT
ejpam-4497	344	28	o	o	NOUN
ejpam-4497	344	29	)	)	PUNCT
ejpam-4497	344	30	)	)	PUNCT
ejpam-4497	345	1	⊆̃fψ(bcl(h	⊆̃fψ(bcl(h	PROPN
ejpam-4497	345	2	,	,	PUNCT
ejpam-4497	345	3	o	o	NOUN
ejpam-4497	345	4	)	)	PUNCT
ejpam-4497	345	5	)	)	PUNCT
ejpam-4497	346	1	=	=	SYM
ejpam-4497	346	2	fψ(h	fψ(h	NUM
ejpam-4497	346	3	,	,	PUNCT
ejpam-4497	346	4	o	o	NOUN
ejpam-4497	346	5	)	)	PUNCT
ejpam-4497	346	6	.	.	PUNCT
ejpam-4497	347	1	therefore	therefore	ADV
ejpam-4497	347	2	,	,	PUNCT
ejpam-4497	347	3	fψ(h	fψ(h	PROPN
ejpam-4497	347	4	,	,	PUNCT
ejpam-4497	347	5	o	o	NOUN
ejpam-4497	347	6	)	)	PUNCT
ejpam-4497	347	7	is	be	AUX
ejpam-4497	347	8	is	be	AUX
ejpam-4497	347	9	-	-	PUNCT
ejpam-4497	347	10	b	b	NOUN
ejpam-4497	347	11	-	-	PUNCT
ejpam-4497	347	12	closed	closed	ADJ
ejpam-4497	347	13	.	.	PUNCT
ejpam-4497	348	1	hence	hence	ADV
ejpam-4497	348	2	,	,	PUNCT
ejpam-4497	348	3	fψ	fψ	PROPN
ejpam-4497	348	4	is	be	AUX
ejpam-4497	348	5	an	an	DET
ejpam-4497	348	6	is	is	NOUN
ejpam-4497	348	7	-	-	PUNCT
ejpam-4497	348	8	bclosed	bclose	VERB
ejpam-4497	348	9	map	map	NOUN
ejpam-4497	348	10	.	.	PUNCT
ejpam-4497	349	1	proposition	proposition	NOUN
ejpam-4497	349	2	17	17	NUM
ejpam-4497	349	3	.	.	PUNCT
ejpam-4497	350	1	the	the	DET
ejpam-4497	350	2	concepts	concept	NOUN
ejpam-4497	350	3	of	of	ADP
ejpam-4497	350	4	is	be	AUX
ejpam-4497	350	5	-	-	PUNCT
ejpam-4497	350	6	b	b	NOUN
ejpam-4497	350	7	-	-	PUNCT
ejpam-4497	350	8	open	open	ADJ
ejpam-4497	350	9	and	and	CCONJ
ejpam-4497	350	10	is	be	AUX
ejpam-4497	350	11	-	-	PUNCT
ejpam-4497	350	12	b	b	NOUN
ejpam-4497	350	13	-	-	PUNCT
ejpam-4497	350	14	closed	close	VERB
ejpam-4497	350	15	maps	map	NOUN
ejpam-4497	350	16	are	be	AUX
ejpam-4497	350	17	equivalent	equivalent	ADJ
ejpam-4497	350	18	under	under	ADP
ejpam-4497	350	19	bijectiveness	bijectiveness	ADV
ejpam-4497	350	20	.	.	PUNCT
ejpam-4497	351	1	proof	proof	NOUN
ejpam-4497	351	2	.	.	PUNCT
ejpam-4497	352	1	it	it	PRON
ejpam-4497	352	2	comes	come	VERB
ejpam-4497	352	3	from	from	ADP
ejpam-4497	352	4	the	the	DET
ejpam-4497	352	5	fact	fact	NOUN
ejpam-4497	352	6	that	that	SCONJ
ejpam-4497	352	7	a	a	DET
ejpam-4497	352	8	bijective	bijective	ADJ
ejpam-4497	352	9	soft	soft	ADJ
ejpam-4497	352	10	map	map	NOUN
ejpam-4497	352	11	fψ	fψ	NOUN
ejpam-4497	352	12	:	:	PUNCT
ejpam-4497	352	13	(	(	PUNCT
ejpam-4497	352	14	x,µ,o	x,µ,o	NOUN
ejpam-4497	352	15	)	)	PUNCT
ejpam-4497	352	16	→	→	PUNCT
ejpam-4497	352	17	(	(	PUNCT
ejpam-4497	352	18	s	s	PROPN
ejpam-4497	352	19	,	,	PUNCT
ejpam-4497	352	20	ν,∆	ν,∆	NOUN
ejpam-4497	352	21	)	)	PUNCT
ejpam-4497	352	22	implies	imply	VERB
ejpam-4497	352	23	fψ(hc	fψ(hc	PROPN
ejpam-4497	352	24	,	,	PUNCT
ejpam-4497	352	25	o	o	NOUN
ejpam-4497	352	26	)	)	PUNCT
ejpam-4497	352	27	=	=	SYM
ejpam-4497	352	28	(	(	PUNCT
ejpam-4497	352	29	fψ(h	fψ(h	PROPN
ejpam-4497	352	30	,	,	PUNCT
ejpam-4497	352	31	o))c	o))c	NOUN
ejpam-4497	352	32	.	.	PUNCT
ejpam-4497	353	1	proposition	proposition	NOUN
ejpam-4497	353	2	18	18	NUM
ejpam-4497	353	3	.	.	PUNCT
ejpam-4497	354	1	let	let	VERB
ejpam-4497	354	2	fψ	fψ	VERB
ejpam-4497	354	3	:	:	PUNCT
ejpam-4497	354	4	(	(	PUNCT
ejpam-4497	354	5	x,µ,o	x,µ,o	NOUN
ejpam-4497	354	6	)	)	PUNCT
ejpam-4497	354	7	→	→	PUNCT
ejpam-4497	354	8	(	(	PUNCT
ejpam-4497	354	9	s	s	PROPN
ejpam-4497	354	10	,	,	PUNCT
ejpam-4497	354	11	ν,∆	ν,∆	NOUN
ejpam-4497	354	12	)	)	PUNCT
ejpam-4497	354	13	and	and	CCONJ
ejpam-4497	354	14	fν	fν	INTJ
ejpam-4497	354	15	:	:	PUNCT
ejpam-4497	354	16	(	(	PUNCT
ejpam-4497	354	17	s	s	X
ejpam-4497	354	18	,	,	PUNCT
ejpam-4497	354	19	ν,∆	ν,∆	NOUN
ejpam-4497	354	20	)	)	PUNCT
ejpam-4497	354	21	→	→	SYM
ejpam-4497	354	22	(	(	PUNCT
ejpam-4497	354	23	v	v	NOUN
ejpam-4497	354	24	,	,	PUNCT
ejpam-4497	354	25	σ	σ	PROPN
ejpam-4497	354	26	,	,	PUNCT
ejpam-4497	354	27	u	u	NOUN
ejpam-4497	354	28	)	)	PUNCT
ejpam-4497	354	29	be	be	VERB
ejpam-4497	354	30	two	two	NUM
ejpam-4497	354	31	s	s	NOUN
ejpam-4497	354	32	-	-	NOUN
ejpam-4497	354	33	maps	map	NOUN
ejpam-4497	354	34	.	.	PUNCT
ejpam-4497	355	1	then	then	ADV
ejpam-4497	355	2	:	:	PUNCT
ejpam-4497	355	3	(	(	PUNCT
ejpam-4497	355	4	i	i	NOUN
ejpam-4497	355	5	)	)	PUNCT
ejpam-4497	355	6	if	if	SCONJ
ejpam-4497	355	7	fψ	fψ	PROPN
ejpam-4497	355	8	and	and	CCONJ
ejpam-4497	355	9	fν	fν	NOUN
ejpam-4497	355	10	are	be	AUX
ejpam-4497	355	11	is	be	AUX
ejpam-4497	355	12	-	-	PUNCT
ejpam-4497	355	13	b	b	NOUN
ejpam-4497	355	14	-	-	PUNCT
ejpam-4497	355	15	open	open	ADJ
ejpam-4497	355	16	maps	map	NOUN
ejpam-4497	355	17	,	,	PUNCT
ejpam-4497	355	18	then	then	ADV
ejpam-4497	355	19	fν	fν	VERB
ejpam-4497	355	20	◦	◦	NOUN
ejpam-4497	355	21	fψ	fψ	NOUN
ejpam-4497	355	22	is	be	AUX
ejpam-4497	355	23	an	an	DET
ejpam-4497	355	24	is	is	NOUN
ejpam-4497	355	25	-	-	PUNCT
ejpam-4497	355	26	b	b	NOUN
ejpam-4497	355	27	-	-	PUNCT
ejpam-4497	355	28	open	open	ADJ
ejpam-4497	355	29	map	map	NOUN
ejpam-4497	355	30	.	.	PUNCT
ejpam-4497	356	1	(	(	PUNCT
ejpam-4497	356	2	ii	ii	NOUN
ejpam-4497	356	3	)	)	PUNCT
ejpam-4497	356	4	if	if	SCONJ
ejpam-4497	356	5	fν	fν	NOUN
ejpam-4497	356	6	◦	◦	NOUN
ejpam-4497	356	7	fψ	fψ	NOUN
ejpam-4497	356	8	is	be	AUX
ejpam-4497	356	9	an	an	DET
ejpam-4497	356	10	is	is	NOUN
ejpam-4497	356	11	-	-	PUNCT
ejpam-4497	356	12	b	b	NOUN
ejpam-4497	356	13	-	-	PUNCT
ejpam-4497	356	14	open	open	ADJ
ejpam-4497	356	15	map	map	NOUN
ejpam-4497	356	16	and	and	CCONJ
ejpam-4497	356	17	fψ	fψ	NOUN
ejpam-4497	356	18	is	be	AUX
ejpam-4497	356	19	a	a	DET
ejpam-4497	356	20	surjective	surjective	ADJ
ejpam-4497	356	21	is	be	AUX
ejpam-4497	356	22	-	-	PUNCT
ejpam-4497	356	23	b	b	NOUN
ejpam-4497	356	24	-	-	PUNCT
ejpam-4497	356	25	continuous	continuous	ADJ
ejpam-4497	356	26	map	map	NOUN
ejpam-4497	356	27	,	,	PUNCT
ejpam-4497	356	28	then	then	ADV
ejpam-4497	356	29	fν	fν	NOUN
ejpam-4497	356	30	is	be	AUX
ejpam-4497	356	31	an	an	DET
ejpam-4497	356	32	is	is	NOUN
ejpam-4497	356	33	-	-	PUNCT
ejpam-4497	356	34	b	b	NOUN
ejpam-4497	356	35	-	-	PUNCT
ejpam-4497	356	36	open	open	ADJ
ejpam-4497	356	37	map	map	NOUN
ejpam-4497	356	38	.	.	PUNCT
ejpam-4497	357	1	(	(	PUNCT
ejpam-4497	357	2	iii	iii	X
ejpam-4497	357	3	)	)	PUNCT
ejpam-4497	357	4	if	if	SCONJ
ejpam-4497	357	5	fν	fν	NOUN
ejpam-4497	357	6	◦	◦	NOUN
ejpam-4497	357	7	fψ	fψ	NOUN
ejpam-4497	357	8	is	be	AUX
ejpam-4497	357	9	an	an	DET
ejpam-4497	357	10	is	is	NOUN
ejpam-4497	357	11	-	-	PUNCT
ejpam-4497	357	12	b	b	NOUN
ejpam-4497	357	13	-	-	PUNCT
ejpam-4497	357	14	open	open	ADJ
ejpam-4497	357	15	map	map	NOUN
ejpam-4497	357	16	and	and	CCONJ
ejpam-4497	357	17	fν	fν	NOUN
ejpam-4497	357	18	is	be	AUX
ejpam-4497	357	19	an	an	DET
ejpam-4497	357	20	injective	injective	ADJ
ejpam-4497	357	21	is	be	AUX
ejpam-4497	357	22	-	-	PUNCT
ejpam-4497	357	23	b	b	NOUN
ejpam-4497	357	24	-	-	PUNCT
ejpam-4497	357	25	continuous	continuous	ADJ
ejpam-4497	357	26	map	map	NOUN
ejpam-4497	357	27	,	,	PUNCT
ejpam-4497	357	28	then	then	ADV
ejpam-4497	357	29	fψ	fψ	PROPN
ejpam-4497	357	30	is	be	AUX
ejpam-4497	357	31	an	an	DET
ejpam-4497	357	32	is	is	NOUN
ejpam-4497	357	33	-	-	PUNCT
ejpam-4497	357	34	b	b	NOUN
ejpam-4497	357	35	-	-	PUNCT
ejpam-4497	357	36	open	open	ADJ
ejpam-4497	357	37	map	map	NOUN
ejpam-4497	357	38	.	.	PUNCT
ejpam-4497	358	1	proof	proof	NOUN
ejpam-4497	358	2	.	.	PUNCT
ejpam-4497	359	1	(	(	PUNCT
ejpam-4497	359	2	i	i	NOUN
ejpam-4497	359	3	)	)	PUNCT
ejpam-4497	359	4	straightforward	straightforward	VERB
ejpam-4497	359	5	.	.	PUNCT
ejpam-4497	360	1	(	(	PUNCT
ejpam-4497	360	2	ii	ii	NOUN
ejpam-4497	360	3	)	)	PUNCT
ejpam-4497	360	4	consider	consider	VERB
ejpam-4497	360	5	(	(	PUNCT
ejpam-4497	360	6	h,∆	h,∆	NOUN
ejpam-4497	360	7	)	)	PUNCT
ejpam-4497	360	8	as	as	ADP
ejpam-4497	360	9	an	an	DET
ejpam-4497	360	10	is	is	NOUN
ejpam-4497	360	11	-	-	PUNCT
ejpam-4497	360	12	b	b	NOUN
ejpam-4497	360	13	-	-	PUNCT
ejpam-4497	360	14	open	open	ADJ
ejpam-4497	360	15	set	set	NOUN
ejpam-4497	360	16	in	in	ADP
ejpam-4497	360	17	(	(	PUNCT
ejpam-4497	360	18	s	s	PROPN
ejpam-4497	360	19	,	,	PUNCT
ejpam-4497	360	20	ν,∆	ν,∆	NOUN
ejpam-4497	360	21	)	)	PUNCT
ejpam-4497	360	22	.	.	PUNCT
ejpam-4497	361	1	by	by	ADP
ejpam-4497	361	2	hypothesis	hypothesis	NOUN
ejpam-4497	361	3	,	,	PUNCT
ejpam-4497	361	4	f−1	f−1	PROPN
ejpam-4497	361	5	ψ	ψ	X
ejpam-4497	361	6	(	(	PUNCT
ejpam-4497	361	7	h,∆	h,∆	NOUN
ejpam-4497	361	8	)	)	PUNCT
ejpam-4497	361	9	is	be	AUX
ejpam-4497	361	10	an	an	DET
ejpam-4497	361	11	is	is	NOUN
ejpam-4497	361	12	-	-	PUNCT
ejpam-4497	361	13	b	b	NOUN
ejpam-4497	361	14	-	-	PUNCT
ejpam-4497	361	15	open	open	ADJ
ejpam-4497	361	16	subset	subset	NOUN
ejpam-4497	361	17	of	of	ADP
ejpam-4497	361	18	(	(	PUNCT
ejpam-4497	361	19	x,µ,o	x,µ,o	PROPN
ejpam-4497	361	20	)	)	PUNCT
ejpam-4497	361	21	.	.	PUNCT
ejpam-4497	362	1	again	again	ADV
ejpam-4497	362	2	,	,	PUNCT
ejpam-4497	362	3	by	by	ADP
ejpam-4497	362	4	hypothesis	hypothesis	NOUN
ejpam-4497	362	5	,	,	PUNCT
ejpam-4497	362	6	(	(	PUNCT
ejpam-4497	362	7	fν	fν	NOUN
ejpam-4497	362	8	◦	◦	NOUN
ejpam-4497	362	9	fψ)(f−1	fψ)(f−1	NOUN
ejpam-4497	362	10	ψ	ψ	X
ejpam-4497	362	11	(	(	PUNCT
ejpam-4497	362	12	h,∆	h,∆	NUM
ejpam-4497	362	13	)	)	PUNCT
ejpam-4497	362	14	)	)	PUNCT
ejpam-4497	362	15	is	be	AUX
ejpam-4497	362	16	an	an	DET
ejpam-4497	362	17	is	is	NOUN
ejpam-4497	362	18	-	-	PUNCT
ejpam-4497	362	19	b	b	NOUN
ejpam-4497	362	20	-	-	PUNCT
ejpam-4497	362	21	open	open	ADJ
ejpam-4497	362	22	subset	subset	NOUN
ejpam-4497	362	23	of	of	ADP
ejpam-4497	362	24	(	(	PUNCT
ejpam-4497	362	25	v	v	PROPN
ejpam-4497	362	26	,	,	PUNCT
ejpam-4497	362	27	σ	σ	PROPN
ejpam-4497	362	28	,	,	PUNCT
ejpam-4497	362	29	u	u	NOUN
ejpam-4497	362	30	)	)	PUNCT
ejpam-4497	362	31	.	.	PUNCT
ejpam-4497	363	1	since	since	SCONJ
ejpam-4497	363	2	fψ	fψ	PROPN
ejpam-4497	363	3	is	be	AUX
ejpam-4497	363	4	surjective	surjective	ADJ
ejpam-4497	363	5	,	,	PUNCT
ejpam-4497	363	6	then	then	ADV
ejpam-4497	363	7	(	(	PUNCT
ejpam-4497	363	8	fν	fν	NOUN
ejpam-4497	363	9	◦	◦	NOUN
ejpam-4497	363	10	fψ)(f−1	fψ)(f−1	NOUN
ejpam-4497	363	11	ψ	ψ	X
ejpam-4497	363	12	(	(	PUNCT
ejpam-4497	363	13	h,∆	h,∆	NUM
ejpam-4497	363	14	)	)	PUNCT
ejpam-4497	363	15	)	)	PUNCT
ejpam-4497	364	1	=	=	SYM
ejpam-4497	364	2	fν(fψ(f	fν(fψ(f	NUM
ejpam-4497	364	3	−1	−1	NOUN
ejpam-4497	364	4	ψ	ψ	X
ejpam-4497	364	5	(	(	PUNCT
ejpam-4497	364	6	h,∆	h,∆	NOUN
ejpam-4497	364	7	)	)	PUNCT
ejpam-4497	364	8	)	)	PUNCT
ejpam-4497	364	9	)	)	PUNCT
ejpam-4497	365	1	=	=	SYM
ejpam-4497	365	2	fν(h,∆	fν(h,∆	NOUN
ejpam-4497	365	3	)	)	PUNCT
ejpam-4497	365	4	.	.	PUNCT
ejpam-4497	366	1	hence	hence	ADV
ejpam-4497	366	2	,	,	PUNCT
ejpam-4497	366	3	fν	fν	NOUN
ejpam-4497	366	4	is	be	AUX
ejpam-4497	366	5	an	an	DET
ejpam-4497	366	6	is	is	NOUN
ejpam-4497	366	7	-	-	PUNCT
ejpam-4497	366	8	b	b	NOUN
ejpam-4497	366	9	-	-	PUNCT
ejpam-4497	366	10	open	open	ADJ
ejpam-4497	366	11	map	map	NOUN
ejpam-4497	366	12	.	.	PUNCT
ejpam-4497	367	1	(	(	PUNCT
ejpam-4497	367	2	iii	iii	NOUN
ejpam-4497	367	3	)	)	PUNCT
ejpam-4497	367	4	consider	consider	VERB
ejpam-4497	367	5	(	(	PUNCT
ejpam-4497	367	6	h	h	NOUN
ejpam-4497	367	7	,	,	PUNCT
ejpam-4497	367	8	o	o	NOUN
ejpam-4497	367	9	)	)	PUNCT
ejpam-4497	367	10	as	as	ADP
ejpam-4497	367	11	an	an	DET
ejpam-4497	367	12	is	is	NOUN
ejpam-4497	367	13	-	-	PUNCT
ejpam-4497	367	14	b	b	NOUN
ejpam-4497	367	15	-	-	PUNCT
ejpam-4497	367	16	open	open	ADJ
ejpam-4497	367	17	subset	subset	NOUN
ejpam-4497	367	18	of	of	ADP
ejpam-4497	367	19	(	(	PUNCT
ejpam-4497	367	20	x,µ,o	x,µ,o	PROPN
ejpam-4497	367	21	)	)	PUNCT
ejpam-4497	367	22	.	.	PUNCT
ejpam-4497	368	1	by	by	ADP
ejpam-4497	368	2	hypothesis	hypothesis	NOUN
ejpam-4497	368	3	,	,	PUNCT
ejpam-4497	368	4	(	(	PUNCT
ejpam-4497	368	5	fν	fν	NOUN
ejpam-4497	368	6	◦	◦	NOUN
ejpam-4497	368	7	fψ)(h	fψ)(h	PROPN
ejpam-4497	368	8	,	,	PUNCT
ejpam-4497	368	9	o	o	NOUN
ejpam-4497	368	10	)	)	PUNCT
ejpam-4497	368	11	is	be	AUX
ejpam-4497	368	12	an	an	DET
ejpam-4497	368	13	is	is	NOUN
ejpam-4497	368	14	-	-	PUNCT
ejpam-4497	368	15	b	b	NOUN
ejpam-4497	368	16	-	-	PUNCT
ejpam-4497	368	17	open	open	ADJ
ejpam-4497	368	18	subset	subset	NOUN
ejpam-4497	368	19	of	of	ADP
ejpam-4497	368	20	(	(	PUNCT
ejpam-4497	368	21	v	v	PROPN
ejpam-4497	368	22	,	,	PUNCT
ejpam-4497	368	23	σ	σ	PROPN
ejpam-4497	368	24	,	,	PUNCT
ejpam-4497	368	25	u	u	NOUN
ejpam-4497	368	26	)	)	PUNCT
ejpam-4497	368	27	.	.	PUNCT
ejpam-4497	369	1	again	again	ADV
ejpam-4497	369	2	,	,	PUNCT
ejpam-4497	369	3	by	by	ADP
ejpam-4497	369	4	hypothesis	hypothesis	NOUN
ejpam-4497	369	5	,	,	PUNCT
ejpam-4497	369	6	f−1	f−1	PROPN
ejpam-4497	369	7	ν	ν	X
ejpam-4497	369	8	(	(	PUNCT
ejpam-4497	369	9	fν	fν	NOUN
ejpam-4497	369	10	◦	◦	NOUN
ejpam-4497	369	11	fψ(h	fψ(h	NUM
ejpam-4497	369	12	,	,	PUNCT
ejpam-4497	369	13	o	o	NOUN
ejpam-4497	369	14	)	)	PUNCT
ejpam-4497	369	15	)	)	PUNCT
ejpam-4497	369	16	is	be	AUX
ejpam-4497	369	17	an	an	DET
ejpam-4497	369	18	is	is	NOUN
ejpam-4497	369	19	-	-	PUNCT
ejpam-4497	369	20	b	b	NOUN
ejpam-4497	369	21	-	-	PUNCT
ejpam-4497	369	22	open	open	ADJ
ejpam-4497	369	23	subset	subset	NOUN
ejpam-4497	369	24	of	of	ADP
ejpam-4497	369	25	(	(	PUNCT
ejpam-4497	369	26	s	s	PROPN
ejpam-4497	369	27	,	,	PUNCT
ejpam-4497	369	28	ν,∆	ν,∆	NOUN
ejpam-4497	369	29	)	)	PUNCT
ejpam-4497	369	30	.	.	PUNCT
ejpam-4497	370	1	since	since	SCONJ
ejpam-4497	370	2	fν	fν	NOUN
ejpam-4497	370	3	is	be	AUX
ejpam-4497	370	4	injective	injective	ADJ
ejpam-4497	370	5	,	,	PUNCT
ejpam-4497	370	6	then	then	ADV
ejpam-4497	370	7	f−1	f−1	PROPN
ejpam-4497	370	8	ν	ν	X
ejpam-4497	370	9	(	(	PUNCT
ejpam-4497	370	10	fν	fν	NOUN
ejpam-4497	370	11	◦	◦	NOUN
ejpam-4497	370	12	fψ(h	fψ(h	NUM
ejpam-4497	370	13	,	,	PUNCT
ejpam-4497	370	14	o	o	NOUN
ejpam-4497	370	15	)	)	PUNCT
ejpam-4497	370	16	)	)	PUNCT
ejpam-4497	371	1	=	=	SYM
ejpam-4497	371	2	(	(	PUNCT
ejpam-4497	371	3	f−1	f−1	PROPN
ejpam-4497	371	4	ν	ν	PRON
ejpam-4497	371	5	fν)(fψ(h	fν)(fψ(h	NOUN
ejpam-4497	371	6	,	,	PUNCT
ejpam-4497	371	7	o	o	NOUN
ejpam-4497	371	8	)	)	PUNCT
ejpam-4497	371	9	)	)	PUNCT
ejpam-4497	372	1	=	=	SYM
ejpam-4497	372	2	fψ(h	fψ(h	NUM
ejpam-4497	372	3	,	,	PUNCT
ejpam-4497	372	4	o	o	NOUN
ejpam-4497	372	5	)	)	PUNCT
ejpam-4497	372	6	.	.	PUNCT
ejpam-4497	373	1	hence	hence	ADV
ejpam-4497	373	2	,	,	PUNCT
ejpam-4497	373	3	fψ	fψ	PROPN
ejpam-4497	373	4	is	be	AUX
ejpam-4497	373	5	an	an	DET
ejpam-4497	373	6	is	is	NOUN
ejpam-4497	373	7	-	-	PUNCT
ejpam-4497	373	8	b	b	NOUN
ejpam-4497	373	9	-	-	PUNCT
ejpam-4497	373	10	open	open	ADJ
ejpam-4497	373	11	map	map	NOUN
ejpam-4497	373	12	.	.	PUNCT
ejpam-4497	374	1	definition	definition	NOUN
ejpam-4497	374	2	20	20	NUM
ejpam-4497	374	3	.	.	PUNCT
ejpam-4497	375	1	a	a	DET
ejpam-4497	375	2	bijective	bijective	ADJ
ejpam-4497	375	3	s	s	NOUN
ejpam-4497	375	4	-	-	PUNCT
ejpam-4497	375	5	map	map	NOUN
ejpam-4497	375	6	fψ	fψ	NOUN
ejpam-4497	375	7	:	:	PUNCT
ejpam-4497	375	8	(	(	PUNCT
ejpam-4497	375	9	x,µ,o	x,µ,o	NOUN
ejpam-4497	375	10	)	)	PUNCT
ejpam-4497	375	11	→	→	PUNCT
ejpam-4497	375	12	(	(	PUNCT
ejpam-4497	375	13	s	s	PROPN
ejpam-4497	375	14	,	,	PUNCT
ejpam-4497	375	15	ν,∆	ν,∆	NUM
ejpam-4497	375	16	)	)	PUNCT
ejpam-4497	375	17	is	be	AUX
ejpam-4497	375	18	said	say	VERB
ejpam-4497	375	19	to	to	PART
ejpam-4497	375	20	be	be	AUX
ejpam-4497	375	21	an	an	DET
ejpam-4497	375	22	is	is	NOUN
ejpam-4497	375	23	-	-	PUNCT
ejpam-4497	375	24	bhomeomorphism	bhomeomorphism	NOUN
ejpam-4497	375	25	if	if	SCONJ
ejpam-4497	375	26	it	it	PRON
ejpam-4497	375	27	is	be	AUX
ejpam-4497	375	28	is	be	AUX
ejpam-4497	375	29	-	-	PUNCT
ejpam-4497	375	30	b	b	NOUN
ejpam-4497	375	31	-	-	PUNCT
ejpam-4497	375	32	continuous	continuous	ADJ
ejpam-4497	375	33	and	and	CCONJ
ejpam-4497	375	34	is	be	AUX
ejpam-4497	375	35	-	-	PUNCT
ejpam-4497	375	36	b	b	NOUN
ejpam-4497	375	37	-	-	PUNCT
ejpam-4497	375	38	open	open	ADJ
ejpam-4497	375	39	.	.	PUNCT
ejpam-4497	376	1	the	the	DET
ejpam-4497	376	2	proofs	proof	NOUN
ejpam-4497	376	3	of	of	ADP
ejpam-4497	376	4	the	the	DET
ejpam-4497	376	5	following	follow	VERB
ejpam-4497	376	6	two	two	NUM
ejpam-4497	376	7	results	result	NOUN
ejpam-4497	376	8	are	be	AUX
ejpam-4497	376	9	easy	easy	ADJ
ejpam-4497	376	10	and	and	CCONJ
ejpam-4497	376	11	so	so	ADV
ejpam-4497	376	12	is	be	AUX
ejpam-4497	376	13	omitted	omit	VERB
ejpam-4497	376	14	.	.	PUNCT
ejpam-4497	377	1	t.m	t.m	PROPN
ejpam-4497	377	2	.	.	PUNCT
ejpam-4497	377	3	al	al	PROPN
ejpam-4497	377	4	-	-	PUNCT
ejpam-4497	377	5	shami	shami	PROPN
ejpam-4497	377	6	et	et	PROPN
ejpam-4497	377	7	al	al	PROPN
ejpam-4497	377	8	.	.	PUNCT
ejpam-4497	377	9	/	/	SYM
ejpam-4497	377	10	eur	eur	PROPN
ejpam-4497	377	11	.	.	PUNCT
ejpam-4497	378	1	j.	j.	PROPN
ejpam-4497	378	2	pure	pure	PROPN
ejpam-4497	378	3	appl	appl	PROPN
ejpam-4497	378	4	.	.	PROPN
ejpam-4497	378	5	math	math	PROPN
ejpam-4497	378	6	,	,	PUNCT
ejpam-4497	378	7	15	15	NUM
ejpam-4497	378	8	(	(	PUNCT
ejpam-4497	378	9	4	4	NUM
ejpam-4497	378	10	)	)	PUNCT
ejpam-4497	378	11	(	(	PUNCT
ejpam-4497	378	12	2022	2022	NUM
ejpam-4497	378	13	)	)	PUNCT
ejpam-4497	378	14	,	,	PUNCT
ejpam-4497	378	15	1455	1455	NUM
ejpam-4497	378	16	-	-	SYM
ejpam-4497	378	17	1471	1471	NUM
ejpam-4497	378	18	1466	1466	NUM
ejpam-4497	378	19	proposition	proposition	NOUN
ejpam-4497	378	20	19	19	NUM
ejpam-4497	378	21	.	.	PUNCT
ejpam-4497	379	1	let	let	VERB
ejpam-4497	379	2	fψ	fψ	VERB
ejpam-4497	379	3	:	:	PUNCT
ejpam-4497	379	4	(	(	PUNCT
ejpam-4497	379	5	x,µ,o	x,µ,o	NOUN
ejpam-4497	379	6	)	)	PUNCT
ejpam-4497	379	7	→	→	PUNCT
ejpam-4497	379	8	(	(	PUNCT
ejpam-4497	379	9	s	s	PROPN
ejpam-4497	379	10	,	,	PUNCT
ejpam-4497	379	11	ν,∆	ν,∆	NOUN
ejpam-4497	379	12	)	)	PUNCT
ejpam-4497	379	13	and	and	CCONJ
ejpam-4497	379	14	fν	fν	INTJ
ejpam-4497	379	15	:	:	PUNCT
ejpam-4497	379	16	(	(	PUNCT
ejpam-4497	379	17	s	s	X
ejpam-4497	379	18	,	,	PUNCT
ejpam-4497	379	19	ν,∆	ν,∆	NOUN
ejpam-4497	379	20	)	)	PUNCT
ejpam-4497	379	21	→	→	SYM
ejpam-4497	379	22	(	(	PUNCT
ejpam-4497	379	23	v	v	NOUN
ejpam-4497	379	24	,	,	PUNCT
ejpam-4497	379	25	σ	σ	PROPN
ejpam-4497	379	26	,	,	PUNCT
ejpam-4497	379	27	u	u	NOUN
ejpam-4497	379	28	)	)	PUNCT
ejpam-4497	379	29	be	be	AUX
ejpam-4497	379	30	is	is	NOUN
ejpam-4497	379	31	-	-	PUNCT
ejpam-4497	379	32	bhomeomorphism	bhomeomorphism	NOUN
ejpam-4497	379	33	maps	map	NOUN
ejpam-4497	379	34	.	.	PUNCT
ejpam-4497	380	1	then	then	ADV
ejpam-4497	380	2	fν	fν	INTJ
ejpam-4497	380	3	◦	◦	NOUN
ejpam-4497	380	4	fψ	fψ	NOUN
ejpam-4497	380	5	is	be	AUX
ejpam-4497	380	6	an	an	DET
ejpam-4497	380	7	is	is	NOUN
ejpam-4497	380	8	-	-	PUNCT
ejpam-4497	380	9	b	b	NOUN
ejpam-4497	380	10	-	-	PUNCT
ejpam-4497	380	11	homeomorphism	homeomorphism	PROPN
ejpam-4497	380	12	map	map	NOUN
ejpam-4497	380	13	.	.	PUNCT
ejpam-4497	381	1	proposition	proposition	NOUN
ejpam-4497	381	2	20	20	NUM
ejpam-4497	381	3	.	.	PUNCT
ejpam-4497	382	1	if	if	SCONJ
ejpam-4497	382	2	fψ	fψ	NOUN
ejpam-4497	382	3	:	:	PUNCT
ejpam-4497	382	4	(	(	PUNCT
ejpam-4497	382	5	x,µ,o	x,µ,o	NOUN
ejpam-4497	382	6	)	)	PUNCT
ejpam-4497	382	7	→	→	PUNCT
ejpam-4497	382	8	(	(	PUNCT
ejpam-4497	382	9	s	s	PROPN
ejpam-4497	382	10	,	,	PUNCT
ejpam-4497	382	11	ν,∆	ν,∆	NUM
ejpam-4497	382	12	)	)	PUNCT
ejpam-4497	382	13	is	be	AUX
ejpam-4497	382	14	a	a	DET
ejpam-4497	382	15	bijective	bijective	ADJ
ejpam-4497	382	16	s	s	NOUN
ejpam-4497	382	17	-	-	NOUN
ejpam-4497	382	18	map	map	NOUN
ejpam-4497	382	19	,	,	PUNCT
ejpam-4497	382	20	then	then	ADV
ejpam-4497	382	21	the	the	DET
ejpam-4497	382	22	following	follow	VERB
ejpam-4497	382	23	items	item	NOUN
ejpam-4497	382	24	are	be	AUX
ejpam-4497	382	25	equivalent	equivalent	ADJ
ejpam-4497	382	26	.	.	PUNCT
ejpam-4497	383	1	(	(	PUNCT
ejpam-4497	383	2	i	i	NOUN
ejpam-4497	383	3	)	)	PUNCT
ejpam-4497	383	4	fψ	fψ	VERB
ejpam-4497	383	5	is	be	AUX
ejpam-4497	383	6	an	an	DET
ejpam-4497	383	7	is	is	NOUN
ejpam-4497	383	8	-	-	PUNCT
ejpam-4497	383	9	b	b	NOUN
ejpam-4497	383	10	-	-	PUNCT
ejpam-4497	383	11	homeomorphism	homeomorphism	NOUN
ejpam-4497	383	12	.	.	PUNCT
ejpam-4497	384	1	(	(	PUNCT
ejpam-4497	384	2	ii	ii	NOUN
ejpam-4497	384	3	)	)	PUNCT
ejpam-4497	384	4	fψ	fψ	NOUN
ejpam-4497	384	5	and	and	CCONJ
ejpam-4497	384	6	f−1	f−1	PROPN
ejpam-4497	384	7	ψ	ψ	NOUN
ejpam-4497	384	8	is	be	AUX
ejpam-4497	384	9	is	be	AUX
ejpam-4497	384	10	-	-	PUNCT
ejpam-4497	384	11	b	b	NOUN
ejpam-4497	384	12	-	-	PUNCT
ejpam-4497	384	13	continuous	continuous	ADJ
ejpam-4497	384	14	.	.	PUNCT
ejpam-4497	385	1	(	(	PUNCT
ejpam-4497	385	2	iii	iii	X
ejpam-4497	385	3	)	)	PUNCT
ejpam-4497	385	4	fψ	fψ	NOUN
ejpam-4497	385	5	is	be	AUX
ejpam-4497	385	6	is	be	AUX
ejpam-4497	385	7	-	-	PUNCT
ejpam-4497	385	8	b	b	NOUN
ejpam-4497	385	9	-	-	PUNCT
ejpam-4497	385	10	closed	closed	ADJ
ejpam-4497	385	11	and	and	CCONJ
ejpam-4497	385	12	is	be	AUX
ejpam-4497	385	13	-	-	PUNCT
ejpam-4497	385	14	b	b	NOUN
ejpam-4497	385	15	-	-	PUNCT
ejpam-4497	385	16	continuous	continuous	ADJ
ejpam-4497	385	17	.	.	PUNCT
ejpam-4497	386	1	proposition	proposition	NOUN
ejpam-4497	386	2	21	21	NUM
ejpam-4497	386	3	.	.	PUNCT
ejpam-4497	387	1	if	if	SCONJ
ejpam-4497	387	2	fψ	fψ	NOUN
ejpam-4497	387	3	:	:	PUNCT
ejpam-4497	387	4	(	(	PUNCT
ejpam-4497	387	5	x,µ,o	x,µ,o	NOUN
ejpam-4497	387	6	)	)	PUNCT
ejpam-4497	387	7	→	→	PUNCT
ejpam-4497	387	8	(	(	PUNCT
ejpam-4497	387	9	s	s	PROPN
ejpam-4497	387	10	,	,	PUNCT
ejpam-4497	387	11	ν,∆	ν,∆	NUM
ejpam-4497	387	12	)	)	PUNCT
ejpam-4497	387	13	is	be	AUX
ejpam-4497	387	14	an	an	DET
ejpam-4497	387	15	is	is	NOUN
ejpam-4497	387	16	-	-	PUNCT
ejpam-4497	387	17	b	b	NOUN
ejpam-4497	387	18	-	-	PUNCT
ejpam-4497	387	19	homeomorphism	homeomorphism	PROPN
ejpam-4497	387	20	map	map	NOUN
ejpam-4497	387	21	,	,	PUNCT
ejpam-4497	387	22	then	then	ADV
ejpam-4497	387	23	the	the	DET
ejpam-4497	387	24	following	follow	VERB
ejpam-4497	387	25	items	item	NOUN
ejpam-4497	387	26	hold	hold	VERB
ejpam-4497	387	27	for	for	ADP
ejpam-4497	387	28	each	each	DET
ejpam-4497	387	29	(	(	PUNCT
ejpam-4497	387	30	h	h	NOUN
ejpam-4497	387	31	,	,	PUNCT
ejpam-4497	387	32	o	o	NOUN
ejpam-4497	387	33	)	)	PUNCT
ejpam-4497	387	34	∈	∈	PROPN
ejpam-4497	387	35	s(x)a	s(x)a	PROPN
ejpam-4497	387	36	.	.	PUNCT
ejpam-4497	388	1	(	(	PUNCT
ejpam-4497	388	2	i	i	NOUN
ejpam-4497	388	3	)	)	PUNCT
ejpam-4497	388	4	fψ(bint(h	fψ(bint(h	PROPN
ejpam-4497	388	5	,	,	PUNCT
ejpam-4497	388	6	o	o	NOUN
ejpam-4497	388	7	)	)	PUNCT
ejpam-4497	388	8	)	)	PUNCT
ejpam-4497	389	1	=	=	PUNCT
ejpam-4497	389	2	bint(fψ(h	bint(fψ(h	X
ejpam-4497	389	3	,	,	PUNCT
ejpam-4497	389	4	o	o	NOUN
ejpam-4497	389	5	)	)	PUNCT
ejpam-4497	389	6	)	)	PUNCT
ejpam-4497	389	7	.	.	PUNCT
ejpam-4497	390	1	(	(	PUNCT
ejpam-4497	390	2	ii	ii	NOUN
ejpam-4497	390	3	)	)	PUNCT
ejpam-4497	390	4	fψ(bcl(h	fψ(bcl(h	PROPN
ejpam-4497	390	5	,	,	PUNCT
ejpam-4497	390	6	o	o	NOUN
ejpam-4497	390	7	)	)	PUNCT
ejpam-4497	390	8	)	)	PUNCT
ejpam-4497	391	1	=	=	SYM
ejpam-4497	391	2	bcl(fψ(h	bcl(fψ(h	PROPN
ejpam-4497	391	3	,	,	PUNCT
ejpam-4497	391	4	o	o	NOUN
ejpam-4497	391	5	)	)	PUNCT
ejpam-4497	391	6	)	)	PUNCT
ejpam-4497	391	7	.	.	PUNCT
ejpam-4497	392	1	proof	proof	NOUN
ejpam-4497	392	2	.	.	PUNCT
ejpam-4497	393	1	(	(	PUNCT
ejpam-4497	393	2	i	i	NOUN
ejpam-4497	393	3	):	):	PUNCT
ejpam-4497	393	4	according	accord	VERB
ejpam-4497	393	5	to	to	ADP
ejpam-4497	393	6	proposition	proposition	NOUN
ejpam-4497	393	7	15	15	NUM
ejpam-4497	393	8	(	(	PUNCT
ejpam-4497	393	9	i	i	NOUN
ejpam-4497	393	10	)	)	PUNCT
ejpam-4497	393	11	,	,	PUNCT
ejpam-4497	393	12	we	we	PRON
ejpam-4497	393	13	obtain	obtain	VERB
ejpam-4497	393	14	fψ(bint(h	fψ(bint(h	PROPN
ejpam-4497	393	15	,	,	PUNCT
ejpam-4497	393	16	o))⊆̃bint(fψ(h	o))⊆̃bint(fψ(h	PROPN
ejpam-4497	393	17	,	,	PUNCT
ejpam-4497	393	18	o	o	NOUN
ejpam-4497	393	19	)	)	PUNCT
ejpam-4497	393	20	)	)	PUNCT
ejpam-4497	393	21	.	.	PUNCT
ejpam-4497	394	1	conversely	conversely	ADV
ejpam-4497	394	2	,	,	PUNCT
ejpam-4497	394	3	let	let	VERB
ejpam-4497	394	4	δsκ	δsκ	PROPN
ejpam-4497	394	5	∈	∈	PROPN
ejpam-4497	394	6	bint(fψ(h	bint(fψ(h	VERB
ejpam-4497	394	7	,	,	PUNCT
ejpam-4497	394	8	o	o	NOUN
ejpam-4497	394	9	)	)	PUNCT
ejpam-4497	394	10	.	.	PUNCT
ejpam-4497	395	1	then	then	ADV
ejpam-4497	395	2	there	there	PRON
ejpam-4497	395	3	is	be	VERB
ejpam-4497	395	4	an	an	DET
ejpam-4497	395	5	is	is	NOUN
ejpam-4497	395	6	-	-	PUNCT
ejpam-4497	395	7	b	b	NOUN
ejpam-4497	395	8	-	-	PUNCT
ejpam-4497	395	9	open	open	ADJ
ejpam-4497	395	10	set	set	NOUN
ejpam-4497	395	11	(	(	PUNCT
ejpam-4497	395	12	f	f	X
ejpam-4497	395	13	,	,	PUNCT
ejpam-4497	395	14	∆	∆	PROPN
ejpam-4497	395	15	)	)	PUNCT
ejpam-4497	395	16	such	such	ADJ
ejpam-4497	395	17	that	that	SCONJ
ejpam-4497	395	18	δsκ	δsκ	PROPN
ejpam-4497	395	19	∈	∈	PROPN
ejpam-4497	395	20	(	(	PUNCT
ejpam-4497	395	21	f	f	PROPN
ejpam-4497	395	22	,	,	PUNCT
ejpam-4497	395	23	∆)⊆̃fψ(h	∆)⊆̃fψ(h	PROPN
ejpam-4497	395	24	,	,	PUNCT
ejpam-4497	395	25	o	o	NOUN
ejpam-4497	395	26	)	)	PUNCT
ejpam-4497	395	27	.	.	PUNCT
ejpam-4497	396	1	by	by	ADP
ejpam-4497	396	2	hypothesis	hypothesis	NOUN
ejpam-4497	396	3	,	,	PUNCT
ejpam-4497	396	4	δxo	δxo	VERB
ejpam-4497	396	5	=	=	SYM
ejpam-4497	396	6	f−1	f−1	PROPN
ejpam-4497	396	7	ψ	ψ	X
ejpam-4497	396	8	(	(	PUNCT
ejpam-4497	396	9	δsκ	δsκ	NOUN
ejpam-4497	396	10	)	)	PUNCT
ejpam-4497	396	11	∈	∈	PROPN
ejpam-4497	396	12	f−1	f−1	PROPN
ejpam-4497	396	13	ψ	ψ	X
ejpam-4497	396	14	(	(	PUNCT
ejpam-4497	396	15	f	f	PROPN
ejpam-4497	396	16	,	,	PUNCT
ejpam-4497	396	17	∆)⊆̃(h	∆)⊆̃(h	PROPN
ejpam-4497	396	18	,	,	PUNCT
ejpam-4497	396	19	o	o	NOUN
ejpam-4497	396	20	)	)	PUNCT
ejpam-4497	396	21	such	such	ADJ
ejpam-4497	396	22	that	that	SCONJ
ejpam-4497	396	23	f−1	f−1	PROPN
ejpam-4497	396	24	ψ	ψ	X
ejpam-4497	396	25	(	(	PUNCT
ejpam-4497	396	26	f	f	PROPN
ejpam-4497	396	27	,	,	PUNCT
ejpam-4497	396	28	∆	∆	PROPN
ejpam-4497	396	29	)	)	PUNCT
ejpam-4497	396	30	is	be	AUX
ejpam-4497	396	31	an	an	DET
ejpam-4497	396	32	infra	infra	NOUN
ejpam-4497	396	33	soft	soft	ADJ
ejpam-4497	396	34	b	b	NOUN
ejpam-4497	396	35	-	-	PUNCT
ejpam-4497	396	36	open	open	ADJ
ejpam-4497	396	37	set	set	NOUN
ejpam-4497	396	38	.	.	PUNCT
ejpam-4497	397	1	so	so	ADV
ejpam-4497	397	2	that	that	SCONJ
ejpam-4497	397	3	,	,	PUNCT
ejpam-4497	397	4	δxo	δxo	VERB
ejpam-4497	397	5	∈	∈	PROPN
ejpam-4497	397	6	bint(h	bint(h	NOUN
ejpam-4497	397	7	,	,	PUNCT
ejpam-4497	397	8	o	o	NOUN
ejpam-4497	397	9	)	)	PUNCT
ejpam-4497	397	10	which	which	PRON
ejpam-4497	397	11	means	mean	VERB
ejpam-4497	397	12	that	that	SCONJ
ejpam-4497	397	13	δsκ	δsκ	VERB
ejpam-4497	397	14	∈	∈	PROPN
ejpam-4497	397	15	fψ(bint(h	fψ(bint(h	PROPN
ejpam-4497	397	16	,	,	PUNCT
ejpam-4497	397	17	o	o	NOUN
ejpam-4497	397	18	)	)	PUNCT
ejpam-4497	397	19	)	)	PUNCT
ejpam-4497	397	20	.	.	PUNCT
ejpam-4497	398	1	one	one	PRON
ejpam-4497	398	2	can	can	AUX
ejpam-4497	398	3	achieve	achieve	VERB
ejpam-4497	398	4	item	item	NOUN
ejpam-4497	398	5	(	(	PUNCT
ejpam-4497	398	6	ii	ii	NOUN
ejpam-4497	398	7	)	)	PUNCT
ejpam-4497	398	8	following	follow	VERB
ejpam-4497	398	9	similar	similar	ADJ
ejpam-4497	398	10	arguments	argument	NOUN
ejpam-4497	398	11	.	.	PUNCT
ejpam-4497	399	1	theorem	theorem	NOUN
ejpam-4497	399	2	6	6	NUM
ejpam-4497	399	3	.	.	PUNCT
ejpam-4497	400	1	the	the	DET
ejpam-4497	400	2	property	property	NOUN
ejpam-4497	400	3	of	of	ADP
ejpam-4497	400	4	an	an	DET
ejpam-4497	400	5	is	is	NOUN
ejpam-4497	400	6	-	-	PUNCT
ejpam-4497	400	7	b	b	NOUN
ejpam-4497	400	8	-	-	PUNCT
ejpam-4497	400	9	dense	dense	ADJ
ejpam-4497	400	10	set	set	NOUN
ejpam-4497	400	11	is	be	AUX
ejpam-4497	400	12	an	an	DET
ejpam-4497	400	13	is	is	NOUN
ejpam-4497	400	14	-	-	PUNCT
ejpam-4497	400	15	topological	topological	ADJ
ejpam-4497	400	16	invariant	invariant	ADJ
ejpam-4497	400	17	.	.	PUNCT
ejpam-4497	401	1	proof	proof	NOUN
ejpam-4497	401	2	.	.	PUNCT
ejpam-4497	402	1	let	let	VERB
ejpam-4497	402	2	fψ	fψ	VERB
ejpam-4497	402	3	:	:	PUNCT
ejpam-4497	402	4	(	(	PUNCT
ejpam-4497	402	5	x,µ,o	x,µ,o	NOUN
ejpam-4497	402	6	)	)	PUNCT
ejpam-4497	402	7	→	→	PUNCT
ejpam-4497	402	8	(	(	PUNCT
ejpam-4497	402	9	s	s	PROPN
ejpam-4497	402	10	,	,	PUNCT
ejpam-4497	402	11	ν,∆	ν,∆	NUM
ejpam-4497	402	12	)	)	PUNCT
ejpam-4497	402	13	be	be	VERB
ejpam-4497	402	14	an	an	DET
ejpam-4497	402	15	is	is	NOUN
ejpam-4497	402	16	-	-	PUNCT
ejpam-4497	402	17	b	b	NOUN
ejpam-4497	402	18	-	-	PUNCT
ejpam-4497	402	19	homeomorphism	homeomorphism	NOUN
ejpam-4497	402	20	map	map	NOUN
ejpam-4497	402	21	and	and	CCONJ
ejpam-4497	402	22	consider	consider	VERB
ejpam-4497	402	23	(	(	PUNCT
ejpam-4497	402	24	h	h	NOUN
ejpam-4497	402	25	,	,	PUNCT
ejpam-4497	402	26	o	o	NOUN
ejpam-4497	402	27	)	)	PUNCT
ejpam-4497	402	28	as	as	ADP
ejpam-4497	402	29	an	an	DET
ejpam-4497	402	30	isb	isb	NOUN
ejpam-4497	402	31	-	-	PUNCT
ejpam-4497	402	32	dense	dense	ADJ
ejpam-4497	402	33	subset	subset	NOUN
ejpam-4497	402	34	of	of	ADP
ejpam-4497	402	35	(	(	PUNCT
ejpam-4497	402	36	x,µ,o	x,µ,o	PROPN
ejpam-4497	402	37	)	)	PUNCT
ejpam-4497	402	38	,	,	PUNCT
ejpam-4497	402	39	i.e.	i.e.	X
ejpam-4497	402	40	bcl(h	bcl(h	PROPN
ejpam-4497	402	41	,	,	PUNCT
ejpam-4497	402	42	o	o	NOUN
ejpam-4497	402	43	)	)	PUNCT
ejpam-4497	403	1	=	=	PUNCT
ejpam-4497	403	2	x̃.	x̃.	ADV
ejpam-4497	403	3	it	it	PRON
ejpam-4497	403	4	comes	come	VERB
ejpam-4497	403	5	from	from	ADP
ejpam-4497	403	6	proposition	proposition	NOUN
ejpam-4497	403	7	21	21	NUM
ejpam-4497	403	8	(	(	PUNCT
ejpam-4497	403	9	ii	ii	NOUN
ejpam-4497	403	10	)	)	PUNCT
ejpam-4497	403	11	that	that	PRON
ejpam-4497	403	12	bcl(fψ(h	bcl(fψ(h	PROPN
ejpam-4497	403	13	,	,	PUNCT
ejpam-4497	403	14	o	o	NOUN
ejpam-4497	403	15	)	)	PUNCT
ejpam-4497	403	16	)	)	PUNCT
ejpam-4497	403	17	=	=	SYM
ejpam-4497	403	18	fψ(bcl(h	fψ(bcl(h	PROPN
ejpam-4497	403	19	,	,	PUNCT
ejpam-4497	403	20	o	o	NOUN
ejpam-4497	403	21	)	)	PUNCT
ejpam-4497	403	22	)	)	PUNCT
ejpam-4497	404	1	=	=	SYM
ejpam-4497	404	2	fψ(x̃	fψ(x̃	NOUN
ejpam-4497	404	3	)	)	PUNCT
ejpam-4497	404	4	=	=	SYM
ejpam-4497	404	5	bcl(s̃	bcl(s̃	X
ejpam-4497	404	6	)	)	PUNCT
ejpam-4497	404	7	=	=	PUNCT
ejpam-4497	404	8	s̃.	s̃.	PROPN
ejpam-4497	404	9	thus	thus	ADV
ejpam-4497	404	10	,	,	PUNCT
ejpam-4497	404	11	fψ(h	fψ(h	NUM
ejpam-4497	404	12	,	,	PUNCT
ejpam-4497	404	13	o	o	NOUN
ejpam-4497	404	14	)	)	PUNCT
ejpam-4497	404	15	is	be	AUX
ejpam-4497	404	16	an	an	DET
ejpam-4497	404	17	is	is	NOUN
ejpam-4497	404	18	-	-	PUNCT
ejpam-4497	404	19	b	b	NOUN
ejpam-4497	404	20	-	-	PUNCT
ejpam-4497	404	21	dense	dense	ADJ
ejpam-4497	404	22	set	set	NOUN
ejpam-4497	404	23	in	in	ADP
ejpam-4497	404	24	(	(	PUNCT
ejpam-4497	404	25	s	s	PROPN
ejpam-4497	404	26	,	,	PUNCT
ejpam-4497	404	27	ν,∆	ν,∆	NOUN
ejpam-4497	404	28	)	)	PUNCT
ejpam-4497	404	29	,	,	PUNCT
ejpam-4497	404	30	as	as	SCONJ
ejpam-4497	404	31	required	require	VERB
ejpam-4497	404	32	.	.	PUNCT
ejpam-4497	405	1	we	we	PRON
ejpam-4497	405	2	complete	complete	VERB
ejpam-4497	405	3	this	this	DET
ejpam-4497	405	4	section	section	NOUN
ejpam-4497	405	5	by	by	ADP
ejpam-4497	405	6	studying	study	VERB
ejpam-4497	405	7	the	the	DET
ejpam-4497	405	8	concept	concept	NOUN
ejpam-4497	405	9	of	of	ADP
ejpam-4497	405	10	fixed	fix	VERB
ejpam-4497	405	11	soft	soft	ADJ
ejpam-4497	405	12	points	point	NOUN
ejpam-4497	405	13	with	with	ADP
ejpam-4497	405	14	respect	respect	NOUN
ejpam-4497	405	15	to	to	ADP
ejpam-4497	405	16	is	be	AUX
ejpam-4497	405	17	-	-	PUNCT
ejpam-4497	405	18	b	b	NOUN
ejpam-4497	405	19	-	-	PUNCT
ejpam-4497	405	20	open	open	ADJ
ejpam-4497	405	21	sets	set	NOUN
ejpam-4497	405	22	.	.	PUNCT
ejpam-4497	406	1	definition	definition	NOUN
ejpam-4497	406	2	21	21	NUM
ejpam-4497	406	3	.	.	PUNCT
ejpam-4497	407	1	we	we	PRON
ejpam-4497	407	2	say	say	VERB
ejpam-4497	407	3	that	that	SCONJ
ejpam-4497	407	4	(	(	PUNCT
ejpam-4497	407	5	x,µ,o	x,µ,o	PROPN
ejpam-4497	407	6	)	)	PUNCT
ejpam-4497	407	7	has	have	VERB
ejpam-4497	407	8	a	a	DET
ejpam-4497	407	9	b	b	NOUN
ejpam-4497	407	10	-	-	PUNCT
ejpam-4497	407	11	fixed	fix	VERB
ejpam-4497	407	12	s	s	NOUN
ejpam-4497	407	13	-	-	PUNCT
ejpam-4497	407	14	point	point	NOUN
ejpam-4497	407	15	property	property	NOUN
ejpam-4497	407	16	provided	provide	VERB
ejpam-4497	407	17	that	that	SCONJ
ejpam-4497	407	18	for	for	ADP
ejpam-4497	407	19	every	every	PRON
ejpam-4497	407	20	is	be	AUX
ejpam-4497	407	21	-	-	PUNCT
ejpam-4497	407	22	b	b	NOUN
ejpam-4497	407	23	-	-	PUNCT
ejpam-4497	407	24	continuous	continuous	ADJ
ejpam-4497	407	25	map	map	NOUN
ejpam-4497	407	26	fψ	fψ	ADP
ejpam-4497	407	27	:	:	PUNCT
ejpam-4497	407	28	(	(	PUNCT
ejpam-4497	407	29	x,µ,o	x,µ,o	NOUN
ejpam-4497	407	30	)	)	PUNCT
ejpam-4497	407	31	→	→	PUNCT
ejpam-4497	407	32	(	(	PUNCT
ejpam-4497	407	33	x,µ,o	x,µ,o	NUM
ejpam-4497	407	34	)	)	PUNCT
ejpam-4497	407	35	there	there	PRON
ejpam-4497	407	36	exists	exist	VERB
ejpam-4497	407	37	δso	δso	PROPN
ejpam-4497	407	38	∈	∈	PROPN
ejpam-4497	407	39	x	x	PUNCT
ejpam-4497	407	40	such	such	ADJ
ejpam-4497	407	41	that	that	SCONJ
ejpam-4497	407	42	fψ(δ	fψ(δ	NUM
ejpam-4497	407	43	s	s	NOUN
ejpam-4497	407	44	o	o	NOUN
ejpam-4497	407	45	)	)	PUNCT
ejpam-4497	407	46	=	=	SYM
ejpam-4497	407	47	δso	δso	PROPN
ejpam-4497	407	48	.	.	PUNCT
ejpam-4497	408	1	proposition	proposition	NOUN
ejpam-4497	408	2	22	22	NUM
ejpam-4497	408	3	.	.	PUNCT
ejpam-4497	409	1	the	the	DET
ejpam-4497	409	2	property	property	NOUN
ejpam-4497	409	3	of	of	ADP
ejpam-4497	409	4	being	be	AUX
ejpam-4497	409	5	a	a	DET
ejpam-4497	409	6	b	b	NOUN
ejpam-4497	409	7	-	-	PUNCT
ejpam-4497	409	8	fixed	fix	VERB
ejpam-4497	409	9	s	s	NOUN
ejpam-4497	409	10	-	-	PUNCT
ejpam-4497	409	11	point	point	NOUN
ejpam-4497	409	12	is	be	AUX
ejpam-4497	409	13	preserved	preserve	VERB
ejpam-4497	409	14	under	under	ADP
ejpam-4497	409	15	an	an	DET
ejpam-4497	409	16	is	is	NOUN
ejpam-4497	409	17	-	-	PUNCT
ejpam-4497	409	18	bhomeomorphism	bhomeomorphism	NOUN
ejpam-4497	409	19	.	.	PUNCT
ejpam-4497	410	1	proof	proof	NOUN
ejpam-4497	410	2	.	.	PUNCT
ejpam-4497	411	1	consider	consider	VERB
ejpam-4497	411	2	(	(	PUNCT
ejpam-4497	411	3	x1	x1	PROPN
ejpam-4497	411	4	,	,	PUNCT
ejpam-4497	411	5	µ1,o1	µ1,o1	PROPN
ejpam-4497	411	6	)	)	PUNCT
ejpam-4497	411	7	and	and	CCONJ
ejpam-4497	411	8	(	(	PUNCT
ejpam-4497	411	9	x2	x2	PROPN
ejpam-4497	411	10	,	,	PUNCT
ejpam-4497	411	11	µ2,o2	µ2,o2	PROPN
ejpam-4497	411	12	)	)	PUNCT
ejpam-4497	411	13	as	as	ADP
ejpam-4497	411	14	two	two	NUM
ejpam-4497	411	15	is	be	AUX
ejpam-4497	411	16	-	-	PUNCT
ejpam-4497	411	17	b	b	NOUN
ejpam-4497	411	18	-	-	PUNCT
ejpam-4497	411	19	homeomorphism	homeomorphism	NOUN
ejpam-4497	411	20	.	.	PUNCT
ejpam-4497	412	1	this	this	PRON
ejpam-4497	412	2	means	mean	VERB
ejpam-4497	412	3	that	that	SCONJ
ejpam-4497	412	4	there	there	PRON
ejpam-4497	412	5	exists	exist	VERB
ejpam-4497	412	6	a	a	DET
ejpam-4497	412	7	bijective	bijective	ADJ
ejpam-4497	412	8	s	s	NOUN
ejpam-4497	412	9	-	-	PUNCT
ejpam-4497	412	10	map	map	NOUN
ejpam-4497	412	11	fψ	fψ	NOUN
ejpam-4497	412	12	:	:	PUNCT
ejpam-4497	412	13	(	(	PUNCT
ejpam-4497	412	14	x1	x1	PROPN
ejpam-4497	412	15	,	,	PUNCT
ejpam-4497	412	16	µ1,o1	µ1,o1	PROPN
ejpam-4497	412	17	)	)	PUNCT
ejpam-4497	412	18	→	→	SYM
ejpam-4497	412	19	(	(	PUNCT
ejpam-4497	412	20	x2	x2	PROPN
ejpam-4497	412	21	,	,	PUNCT
ejpam-4497	412	22	µ2,o2	µ2,o2	PROPN
ejpam-4497	412	23	)	)	PUNCT
ejpam-4497	412	24	such	such	ADJ
ejpam-4497	412	25	that	that	DET
ejpam-4497	412	26	fψ	fψ	NOUN
ejpam-4497	412	27	and	and	CCONJ
ejpam-4497	412	28	f−1	f−1	PROPN
ejpam-4497	412	29	ψ	ψ	NOUN
ejpam-4497	412	30	are	be	AUX
ejpam-4497	412	31	is	be	AUX
ejpam-4497	412	32	-	-	PUNCT
ejpam-4497	412	33	b	b	NOUN
ejpam-4497	412	34	-	-	PUNCT
ejpam-4497	412	35	continuous	continuous	ADJ
ejpam-4497	412	36	.	.	PUNCT
ejpam-4497	412	37	suppose	suppose	VERB
ejpam-4497	412	38	that	that	SCONJ
ejpam-4497	412	39	(	(	PUNCT
ejpam-4497	412	40	x1	x1	PROPN
ejpam-4497	412	41	,	,	PUNCT
ejpam-4497	412	42	µ1,o1	µ1,o1	PROPN
ejpam-4497	412	43	)	)	PUNCT
ejpam-4497	412	44	has	have	VERB
ejpam-4497	412	45	the	the	DET
ejpam-4497	412	46	property	property	NOUN
ejpam-4497	412	47	of	of	ADP
ejpam-4497	412	48	b	b	NOUN
ejpam-4497	412	49	-	-	PUNCT
ejpam-4497	412	50	fixed	fix	VERB
ejpam-4497	412	51	soft	soft	ADJ
ejpam-4497	412	52	point	point	NOUN
ejpam-4497	412	53	.	.	PUNCT
ejpam-4497	413	1	that	that	PRON
ejpam-4497	413	2	is	be	AUX
ejpam-4497	413	3	any	any	DET
ejpam-4497	413	4	is	be	AUX
ejpam-4497	413	5	-	-	PUNCT
ejpam-4497	413	6	b	b	NOUN
ejpam-4497	413	7	-	-	PUNCT
ejpam-4497	413	8	continuous	continuous	ADJ
ejpam-4497	413	9	map	map	NOUN
ejpam-4497	413	10	fψ	fψ	ADP
ejpam-4497	413	11	:	:	PUNCT
ejpam-4497	413	12	(	(	PUNCT
ejpam-4497	413	13	x1	x1	PROPN
ejpam-4497	413	14	,	,	PUNCT
ejpam-4497	413	15	µ1,o1	µ1,o1	PROPN
ejpam-4497	413	16	)	)	PUNCT
ejpam-4497	413	17	→	→	SYM
ejpam-4497	413	18	(	(	PUNCT
ejpam-4497	413	19	x1	x1	PROPN
ejpam-4497	413	20	,	,	PUNCT
ejpam-4497	413	21	µ1,o1	µ1,o1	PROPN
ejpam-4497	413	22	)	)	PUNCT
ejpam-4497	413	23	has	have	VERB
ejpam-4497	413	24	a	a	DET
ejpam-4497	413	25	b	b	NOUN
ejpam-4497	413	26	-	-	PUNCT
ejpam-4497	413	27	fixed	fix	VERB
ejpam-4497	413	28	s	s	NOUN
ejpam-4497	413	29	-	-	NOUN
ejpam-4497	413	30	point	point	NOUN
ejpam-4497	413	31	.	.	PUNCT
ejpam-4497	414	1	now	now	ADV
ejpam-4497	414	2	,	,	PUNCT
ejpam-4497	414	3	consider	consider	VERB
ejpam-4497	414	4	cψ	cψ	NOUN
ejpam-4497	414	5	:	:	PUNCT
ejpam-4497	414	6	(	(	PUNCT
ejpam-4497	414	7	x2	x2	NOUN
ejpam-4497	414	8	,	,	PUNCT
ejpam-4497	414	9	µ2,o2	µ2,o2	PROPN
ejpam-4497	414	10	)	)	PUNCT
ejpam-4497	414	11	→	→	SYM
ejpam-4497	414	12	(	(	PUNCT
ejpam-4497	414	13	x2	x2	PROPN
ejpam-4497	414	14	,	,	PUNCT
ejpam-4497	414	15	µ2,o2	µ2,o2	PROPN
ejpam-4497	414	16	)	)	PUNCT
ejpam-4497	414	17	is	be	AUX
ejpam-4497	414	18	is	be	AUX
ejpam-4497	414	19	-	-	PUNCT
ejpam-4497	414	20	b	b	NOUN
ejpam-4497	414	21	-	-	PUNCT
ejpam-4497	414	22	continuous	continuous	ADJ
ejpam-4497	414	23	.	.	PUNCT
ejpam-4497	415	1	it	it	PRON
ejpam-4497	415	2	is	be	AUX
ejpam-4497	415	3	clear	clear	ADJ
ejpam-4497	415	4	that	that	SCONJ
ejpam-4497	415	5	cψ	cψ	NOUN
ejpam-4497	415	6	◦	◦	NOUN
ejpam-4497	415	7	fψ	fψ	ADP
ejpam-4497	415	8	:	:	PUNCT
ejpam-4497	415	9	(	(	PUNCT
ejpam-4497	415	10	x1	x1	PROPN
ejpam-4497	415	11	,	,	PUNCT
ejpam-4497	415	12	µ1,o1	µ1,o1	PROPN
ejpam-4497	415	13	)	)	PUNCT
ejpam-4497	415	14	→	→	SYM
ejpam-4497	415	15	(	(	PUNCT
ejpam-4497	415	16	x2	x2	PROPN
ejpam-4497	415	17	,	,	PUNCT
ejpam-4497	415	18	µ2,o2	µ2,o2	PROPN
ejpam-4497	415	19	)	)	PUNCT
ejpam-4497	415	20	is	be	AUX
ejpam-4497	415	21	is	be	AUX
ejpam-4497	415	22	-	-	PUNCT
ejpam-4497	415	23	b	b	NOUN
ejpam-4497	415	24	-	-	PUNCT
ejpam-4497	415	25	continuous	continuous	ADJ
ejpam-4497	415	26	.	.	PUNCT
ejpam-4497	416	1	therefore	therefore	ADV
ejpam-4497	416	2	,	,	PUNCT
ejpam-4497	416	3	f−1	f−1	PROPN
ejpam-4497	416	4	ψ	ψ	PART
ejpam-4497	416	5	◦	◦	VERB
ejpam-4497	416	6	cψ	cψ	NOUN
ejpam-4497	416	7	◦	◦	NOUN
ejpam-4497	416	8	fψ	fψ	NOUN
ejpam-4497	416	9	:	:	PUNCT
ejpam-4497	416	10	(	(	PUNCT
ejpam-4497	416	11	x1	x1	PROPN
ejpam-4497	416	12	,	,	PUNCT
ejpam-4497	416	13	µ1,o1	µ1,o1	PROPN
ejpam-4497	416	14	)	)	PUNCT
ejpam-4497	416	15	→	→	SYM
ejpam-4497	416	16	(	(	PUNCT
ejpam-4497	416	17	x1	x1	PROPN
ejpam-4497	416	18	,	,	PUNCT
ejpam-4497	416	19	µ1,o1	µ1,o1	PROPN
ejpam-4497	416	20	)	)	PUNCT
ejpam-4497	416	21	is	be	AUX
ejpam-4497	416	22	is	be	AUX
ejpam-4497	416	23	-	-	PUNCT
ejpam-4497	416	24	b	b	NOUN
ejpam-4497	416	25	-	-	PUNCT
ejpam-4497	416	26	continuous	continuous	ADJ
ejpam-4497	416	27	.	.	PUNCT
ejpam-4497	417	1	since	since	SCONJ
ejpam-4497	417	2	(	(	PUNCT
ejpam-4497	417	3	x1	x1	PROPN
ejpam-4497	417	4	,	,	PUNCT
ejpam-4497	417	5	µ1,o1	µ1,o1	PROPN
ejpam-4497	417	6	)	)	PUNCT
ejpam-4497	417	7	has	have	VERB
ejpam-4497	417	8	a	a	DET
ejpam-4497	417	9	b	b	NOUN
ejpam-4497	417	10	-	-	PUNCT
ejpam-4497	417	11	fixed	fix	VERB
ejpam-4497	417	12	s	s	NOUN
ejpam-4497	417	13	-	-	PUNCT
ejpam-4497	417	14	point	point	NOUN
ejpam-4497	417	15	property	property	NOUN
ejpam-4497	417	16	,	,	PUNCT
ejpam-4497	417	17	f−1	f−1	PROPN
ejpam-4497	417	18	ψ	ψ	X
ejpam-4497	417	19	(	(	PUNCT
ejpam-4497	417	20	hψ(fψ(δ	hψ(fψ(δ	PRON
ejpam-4497	417	21	s	s	X
ejpam-4497	417	22	o	o	NOUN
ejpam-4497	417	23	)	)	PUNCT
ejpam-4497	417	24	)	)	PUNCT
ejpam-4497	417	25	)	)	PUNCT
ejpam-4497	418	1	=	=	SYM
ejpam-4497	418	2	δso	δso	VERB
ejpam-4497	418	3	for	for	ADP
ejpam-4497	418	4	some	some	DET
ejpam-4497	418	5	δso	δso	NOUN
ejpam-4497	418	6	∈	∈	PROPN
ejpam-4497	418	7	x̃.	x̃.	ADV
ejpam-4497	418	8	thus	thus	ADV
ejpam-4497	418	9	,	,	PUNCT
ejpam-4497	418	10	fψ(f	fψ(f	PUNCT
ejpam-4497	418	11	−1	−1	NOUN
ejpam-4497	418	12	ψ	ψ	NOUN
ejpam-4497	418	13	(	(	PUNCT
ejpam-4497	418	14	hψ(fψ(δ	hψ(fψ(δ	NOUN
ejpam-4497	418	15	s	s	VERB
ejpam-4497	418	16	o	o	NOUN
ejpam-4497	418	17	)	)	PUNCT
ejpam-4497	418	18	)	)	PUNCT
ejpam-4497	418	19	)	)	PUNCT
ejpam-4497	418	20	)	)	PUNCT
ejpam-4497	419	1	=	=	PRON
ejpam-4497	419	2	fψ(δ	fψ(δ	NUM
ejpam-4497	419	3	s	s	PART
ejpam-4497	419	4	o	o	NOUN
ejpam-4497	419	5	)	)	PUNCT
ejpam-4497	419	6	.	.	PUNCT
ejpam-4497	420	1	this	this	PRON
ejpam-4497	420	2	implies	imply	VERB
ejpam-4497	420	3	that	that	SCONJ
ejpam-4497	420	4	hψ(fψ(δ	hψ(fψ(δ	NOUN
ejpam-4497	420	5	s	s	VERB
ejpam-4497	420	6	o	o	NOUN
ejpam-4497	420	7	)	)	PUNCT
ejpam-4497	420	8	)	)	PUNCT
ejpam-4497	421	1	=	=	PRON
ejpam-4497	421	2	fψ(δ	fψ(δ	NUM
ejpam-4497	421	3	s	s	PART
ejpam-4497	421	4	o	o	NOUN
ejpam-4497	421	5	)	)	PUNCT
ejpam-4497	421	6	.	.	PUNCT
ejpam-4497	422	1	hence	hence	ADV
ejpam-4497	422	2	,	,	PUNCT
ejpam-4497	422	3	fψ(δ	fψ(δ	PRON
ejpam-4497	422	4	s	s	PART
ejpam-4497	422	5	o	o	NOUN
ejpam-4497	422	6	)	)	PUNCT
ejpam-4497	422	7	is	be	AUX
ejpam-4497	422	8	a	a	DET
ejpam-4497	422	9	b	b	NOUN
ejpam-4497	422	10	-	-	PUNCT
ejpam-4497	422	11	fixed	fix	VERB
ejpam-4497	422	12	soft	soft	ADJ
ejpam-4497	422	13	point	point	NOUN
ejpam-4497	422	14	of	of	ADP
ejpam-4497	422	15	cψ	cψ	NOUN
ejpam-4497	422	16	which	which	PRON
ejpam-4497	422	17	means	mean	VERB
ejpam-4497	422	18	that	that	SCONJ
ejpam-4497	422	19	(	(	PUNCT
ejpam-4497	422	20	x2	x2	NOUN
ejpam-4497	422	21	,	,	PUNCT
ejpam-4497	422	22	µ2,o2	µ2,o2	PROPN
ejpam-4497	422	23	)	)	PUNCT
ejpam-4497	422	24	has	have	VERB
ejpam-4497	422	25	a	a	DET
ejpam-4497	422	26	b	b	NOUN
ejpam-4497	422	27	-	-	PUNCT
ejpam-4497	422	28	fixed	fix	VERB
ejpam-4497	422	29	s	s	NOUN
ejpam-4497	422	30	-	-	PUNCT
ejpam-4497	422	31	point	point	NOUN
ejpam-4497	422	32	property	property	NOUN
ejpam-4497	422	33	.	.	PUNCT
ejpam-4497	423	1	references	reference	NOUN
ejpam-4497	423	2	1467	1467	NUM
ejpam-4497	423	3	6	6	NUM
ejpam-4497	423	4	.	.	PUNCT
ejpam-4497	423	5	concluding	conclude	VERB
ejpam-4497	423	6	remark	remark	NOUN
ejpam-4497	423	7	and	and	CCONJ
ejpam-4497	423	8	further	further	ADJ
ejpam-4497	423	9	work	work	NOUN
ejpam-4497	423	10	in	in	ADP
ejpam-4497	423	11	this	this	DET
ejpam-4497	423	12	paper	paper	NOUN
ejpam-4497	423	13	,	,	PUNCT
ejpam-4497	423	14	we	we	PRON
ejpam-4497	423	15	have	have	AUX
ejpam-4497	423	16	formulated	formulate	VERB
ejpam-4497	423	17	the	the	DET
ejpam-4497	423	18	concept	concept	NOUN
ejpam-4497	423	19	of	of	ADP
ejpam-4497	423	20	is	be	AUX
ejpam-4497	423	21	-	-	PUNCT
ejpam-4497	423	22	b	b	NOUN
ejpam-4497	423	23	-	-	PUNCT
ejpam-4497	423	24	open	open	ADJ
ejpam-4497	423	25	sets	set	NOUN
ejpam-4497	423	26	and	and	CCONJ
ejpam-4497	423	27	discussed	discuss	VERB
ejpam-4497	423	28	its	its	PRON
ejpam-4497	423	29	main	main	ADJ
ejpam-4497	423	30	properties	property	NOUN
ejpam-4497	423	31	.	.	PUNCT
ejpam-4497	424	1	then	then	ADV
ejpam-4497	424	2	,	,	PUNCT
ejpam-4497	424	3	we	we	PRON
ejpam-4497	424	4	have	have	AUX
ejpam-4497	424	5	defined	define	VERB
ejpam-4497	424	6	novel	novel	ADJ
ejpam-4497	424	7	operators	operator	NOUN
ejpam-4497	424	8	and	and	CCONJ
ejpam-4497	424	9	mappings	mapping	NOUN
ejpam-4497	424	10	between	between	ADP
ejpam-4497	424	11	istss	istss	NOUN
ejpam-4497	424	12	depending	depend	VERB
ejpam-4497	424	13	on	on	ADP
ejpam-4497	424	14	the	the	DET
ejpam-4497	424	15	classes	class	NOUN
ejpam-4497	424	16	of	of	ADP
ejpam-4497	424	17	is	be	AUX
ejpam-4497	424	18	-	-	PUNCT
ejpam-4497	424	19	b	b	NOUN
ejpam-4497	424	20	-	-	PUNCT
ejpam-4497	424	21	open	open	ADJ
ejpam-4497	424	22	and	and	CCONJ
ejpam-4497	424	23	is	be	AUX
ejpam-4497	424	24	-	-	PUNCT
ejpam-4497	424	25	b	b	NOUN
ejpam-4497	424	26	-	-	PUNCT
ejpam-4497	424	27	closed	closed	ADJ
ejpam-4497	424	28	sets	set	NOUN
ejpam-4497	424	29	.	.	PUNCT
ejpam-4497	425	1	we	we	PRON
ejpam-4497	425	2	have	have	AUX
ejpam-4497	425	3	revealed	reveal	VERB
ejpam-4497	425	4	the	the	DET
ejpam-4497	425	5	relationships	relationship	NOUN
ejpam-4497	425	6	between	between	ADP
ejpam-4497	425	7	these	these	DET
ejpam-4497	425	8	operators	operator	NOUN
ejpam-4497	425	9	and	and	CCONJ
ejpam-4497	425	10	mappings	mapping	NOUN
ejpam-4497	425	11	and	and	CCONJ
ejpam-4497	425	12	investigated	investigate	VERB
ejpam-4497	425	13	their	their	PRON
ejpam-4497	425	14	basic	basic	ADJ
ejpam-4497	425	15	features	feature	NOUN
ejpam-4497	425	16	.	.	PUNCT
ejpam-4497	426	1	as	as	SCONJ
ejpam-4497	426	2	we	we	PRON
ejpam-4497	426	3	have	have	AUX
ejpam-4497	426	4	noted	note	VERB
ejpam-4497	426	5	that	that	SCONJ
ejpam-4497	426	6	several	several	ADJ
ejpam-4497	426	7	topological	topological	ADJ
ejpam-4497	426	8	characterizations	characterization	NOUN
ejpam-4497	426	9	still	still	ADV
ejpam-4497	426	10	have	have	AUX
ejpam-4497	426	11	been	be	AUX
ejpam-4497	426	12	valid	valid	ADJ
ejpam-4497	426	13	via	via	ADP
ejpam-4497	426	14	the	the	DET
ejpam-4497	426	15	structures	structure	NOUN
ejpam-4497	426	16	of	of	ADP
ejpam-4497	426	17	infra	infra	NOUN
ejpam-4497	426	18	topologies	topology	NOUN
ejpam-4497	426	19	,	,	PUNCT
ejpam-4497	426	20	which	which	PRON
ejpam-4497	426	21	confirms	confirm	VERB
ejpam-4497	426	22	the	the	DET
ejpam-4497	426	23	importance	importance	NOUN
ejpam-4497	426	24	of	of	ADP
ejpam-4497	426	25	infra	infra	NOUN
ejpam-4497	426	26	st	st	NOUN
ejpam-4497	426	27	-	-	PUNCT
ejpam-4497	426	28	structures	structure	NOUN
ejpam-4497	426	29	.	.	PUNCT
ejpam-4497	427	1	our	our	PRON
ejpam-4497	427	2	future	future	ADJ
ejpam-4497	427	3	works	work	NOUN
ejpam-4497	427	4	will	will	AUX
ejpam-4497	427	5	focus	focus	VERB
ejpam-4497	427	6	on	on	ADP
ejpam-4497	427	7	studying	study	VERB
ejpam-4497	427	8	further	further	ADJ
ejpam-4497	427	9	topological	topological	ADJ
ejpam-4497	427	10	concepts	concept	NOUN
ejpam-4497	427	11	and	and	CCONJ
ejpam-4497	427	12	notions	notion	NOUN
ejpam-4497	427	13	via	via	ADP
ejpam-4497	427	14	infra	infra	NOUN
ejpam-4497	427	15	st	st	NOUN
ejpam-4497	427	16	-	-	PUNCT
ejpam-4497	427	17	structures	structure	NOUN
ejpam-4497	427	18	.	.	PUNCT
ejpam-4497	428	1	also	also	ADV
ejpam-4497	428	2	,	,	PUNCT
ejpam-4497	428	3	we	we	PRON
ejpam-4497	428	4	will	will	AUX
ejpam-4497	428	5	research	research	VERB
ejpam-4497	428	6	the	the	DET
ejpam-4497	428	7	hybridizations	hybridization	NOUN
ejpam-4497	428	8	structures	structure	NOUN
ejpam-4497	428	9	obtained	obtain	VERB
ejpam-4497	428	10	from	from	ADP
ejpam-4497	428	11	ists	ist	NOUN
ejpam-4497	428	12	and	and	CCONJ
ejpam-4497	428	13	other	other	ADJ
ejpam-4497	428	14	structures	structure	NOUN
ejpam-4497	428	15	such	such	ADJ
ejpam-4497	428	16	as	as	ADP
ejpam-4497	428	17	rough	rough	ADJ
ejpam-4497	428	18	soft	soft	ADJ
ejpam-4497	428	19	and	and	CCONJ
ejpam-4497	428	20	fs	f	NOUN
ejpam-4497	428	21	-	-	PUNCT
ejpam-4497	428	22	structures	structure	NOUN
ejpam-4497	428	23	.	.	PUNCT
ejpam-4497	429	1	conflict	conflict	NOUN
ejpam-4497	429	2	of	of	ADP
ejpam-4497	429	3	interest	interest	NOUN
ejpam-4497	429	4	the	the	DET
ejpam-4497	429	5	authors	author	NOUN
ejpam-4497	429	6	declare	declare	VERB
ejpam-4497	429	7	that	that	SCONJ
ejpam-4497	429	8	there	there	PRON
ejpam-4497	429	9	is	be	VERB
ejpam-4497	429	10	no	no	DET
ejpam-4497	429	11	conflict	conflict	NOUN
ejpam-4497	429	12	of	of	ADP
ejpam-4497	429	13	interest	interest	NOUN
ejpam-4497	429	14	regarding	regard	VERB
ejpam-4497	429	15	the	the	DET
ejpam-4497	429	16	publication	publication	NOUN
ejpam-4497	429	17	of	of	ADP
ejpam-4497	429	18	this	this	DET
ejpam-4497	429	19	paper	paper	NOUN
ejpam-4497	429	20	.	.	PUNCT
ejpam-4497	430	1	references	reference	NOUN
ejpam-4497	430	2	[	[	X
ejpam-4497	430	3	1	1	NUM
ejpam-4497	430	4	]	]	X
ejpam-4497	430	5	r	r	NOUN
ejpam-4497	430	6	abu	abu	PROPN
ejpam-4497	430	7	-	-	PUNCT
ejpam-4497	430	8	gdairi	gdairi	PROPN
ejpam-4497	430	9	,	,	PUNCT
ejpam-4497	430	10	m	m	PROPN
ejpam-4497	430	11	el	el	PROPN
ejpam-4497	430	12	-	-	PUNCT
ejpam-4497	430	13	gayar	gayar	NOUN
ejpam-4497	430	14	,	,	PUNCT
ejpam-4497	430	15	tm	tm	PROPN
ejpam-4497	430	16	al	al	PROPN
ejpam-4497	430	17	-	-	PUNCT
ejpam-4497	430	18	shami	shami	PROPN
ejpam-4497	430	19	,	,	PUNCT
ejpam-4497	430	20	as	as	ADP
ejpam-4497	430	21	nawar	nawar	ADJ
ejpam-4497	430	22	,	,	PUNCT
ejpam-4497	430	23	and	and	CCONJ
ejpam-4497	430	24	mk	mk	PROPN
ejpam-4497	430	25	el	el	PROPN
ejpam-4497	430	26	-	-	PUNCT
ejpam-4497	430	27	bably	bably	ADV
ejpam-4497	430	28	.	.	PUNCT
ejpam-4497	431	1	some	some	DET
ejpam-4497	431	2	topological	topological	ADJ
ejpam-4497	431	3	approaches	approach	NOUN
ejpam-4497	431	4	for	for	ADP
ejpam-4497	431	5	generalized	generalized	ADJ
ejpam-4497	431	6	rough	rough	ADJ
ejpam-4497	431	7	sets	set	NOUN
ejpam-4497	431	8	and	and	CCONJ
ejpam-4497	431	9	their	their	PRON
ejpam-4497	431	10	decision	decision	NOUN
ejpam-4497	431	11	-	-	PUNCT
ejpam-4497	431	12	making	make	VERB
ejpam-4497	431	13	applications	application	NOUN
ejpam-4497	431	14	.	.	PUNCT
ejpam-4497	432	1	symmetry	symmetry	NOUN
ejpam-4497	432	2	,	,	PUNCT
ejpam-4497	432	3	14(1	14(1	NUM
ejpam-4497	432	4	)	)	PUNCT
ejpam-4497	432	5	,	,	PUNCT
ejpam-4497	432	6	2022	2022	NUM
ejpam-4497	432	7	.	.	PUNCT
ejpam-4497	433	1	[	[	X
ejpam-4497	433	2	2	2	X
ejpam-4497	433	3	]	]	X
ejpam-4497	433	4	hh	hh	PROPN
ejpam-4497	433	5	al	al	PROPN
ejpam-4497	433	6	-	-	PUNCT
ejpam-4497	433	7	jarrah	jarrah	PROPN
ejpam-4497	433	8	,	,	PUNCT
ejpam-4497	433	9	a	a	DET
ejpam-4497	433	10	rawshdeh	rawshdeh	NOUN
ejpam-4497	433	11	,	,	PUNCT
ejpam-4497	433	12	and	and	CCONJ
ejpam-4497	433	13	tm	tm	PROPN
ejpam-4497	433	14	al	al	PROPN
ejpam-4497	433	15	-	-	PUNCT
ejpam-4497	433	16	shami	shami	PROPN
ejpam-4497	433	17	.	.	PUNCT
ejpam-4497	434	1	on	on	ADP
ejpam-4497	434	2	soft	soft	ADJ
ejpam-4497	434	3	compact	compact	ADJ
ejpam-4497	434	4	and	and	CCONJ
ejpam-4497	434	5	soft	soft	ADJ
ejpam-4497	434	6	lindelöf	lindelöf	NOUN
ejpam-4497	434	7	spaces	space	NOUN
ejpam-4497	434	8	via	via	ADP
ejpam-4497	434	9	soft	soft	ADJ
ejpam-4497	434	10	regular	regular	ADJ
ejpam-4497	434	11	closed	closed	ADJ
ejpam-4497	434	12	sets	set	NOUN
ejpam-4497	434	13	.	.	PUNCT
ejpam-4497	435	1	afrika	afrika	ADJ
ejpam-4497	435	2	matematika	matematika	PROPN
ejpam-4497	435	3	,	,	PUNCT
ejpam-4497	435	4	33(23	33(23	NOUN
ejpam-4497	435	5	)	)	PUNCT
ejpam-4497	435	6	,	,	PUNCT
ejpam-4497	435	7	2022	2022	NUM
ejpam-4497	435	8	.	.	PUNCT
ejpam-4497	436	1	[	[	X
ejpam-4497	436	2	3	3	X
ejpam-4497	436	3	]	]	PUNCT
ejpam-4497	436	4	tm	tm	PROPN
ejpam-4497	436	5	al	al	PROPN
ejpam-4497	436	6	-	-	PUNCT
ejpam-4497	436	7	shami	shami	PROPN
ejpam-4497	436	8	.	.	PUNCT
ejpam-4497	437	1	soft	soft	ADJ
ejpam-4497	437	2	somewhere	somewhere	ADV
ejpam-4497	437	3	dense	dense	ADJ
ejpam-4497	437	4	sets	set	NOUN
ejpam-4497	437	5	on	on	ADP
ejpam-4497	437	6	soft	soft	ADJ
ejpam-4497	437	7	topological	topological	ADJ
ejpam-4497	437	8	spaces	space	NOUN
ejpam-4497	437	9	.	.	PUNCT
ejpam-4497	438	1	communications	communication	NOUN
ejpam-4497	438	2	of	of	ADP
ejpam-4497	438	3	the	the	DET
ejpam-4497	438	4	korean	korean	ADJ
ejpam-4497	438	5	mathematical	mathematical	ADJ
ejpam-4497	438	6	society	society	NOUN
ejpam-4497	438	7	,	,	PUNCT
ejpam-4497	438	8	33(4):1341–1356	33(4):1341–1356	NUM
ejpam-4497	438	9	,	,	PUNCT
ejpam-4497	438	10	2018	2018	NUM
ejpam-4497	438	11	.	.	PUNCT
ejpam-4497	439	1	[	[	X
ejpam-4497	439	2	4	4	X
ejpam-4497	439	3	]	]	PUNCT
ejpam-4497	439	4	tm	tm	PROPN
ejpam-4497	439	5	al	al	PROPN
ejpam-4497	439	6	-	-	PUNCT
ejpam-4497	439	7	shami	shami	PROPN
ejpam-4497	439	8	.	.	PUNCT
ejpam-4497	440	1	comment	comment	NOUN
ejpam-4497	440	2	on	on	ADP
ejpam-4497	440	3	soft	soft	ADJ
ejpam-4497	440	4	mappings	mapping	NOUN
ejpam-4497	440	5	space	space	NOUN
ejpam-4497	440	6	.	.	PUNCT
ejpam-4497	441	1	the	the	DET
ejpam-4497	441	2	scientific	scientific	ADJ
ejpam-4497	441	3	world	world	NOUN
ejpam-4497	441	4	journal	journal	NOUN
ejpam-4497	441	5	,	,	PUNCT
ejpam-4497	441	6	2019	2019	NUM
ejpam-4497	441	7	,	,	PUNCT
ejpam-4497	441	8	2019	2019	NUM
ejpam-4497	441	9	.	.	PUNCT
ejpam-4497	442	1	[	[	X
ejpam-4497	442	2	5	5	X
ejpam-4497	442	3	]	]	PUNCT
ejpam-4497	442	4	tm	tm	PROPN
ejpam-4497	442	5	al	al	PROPN
ejpam-4497	442	6	-	-	PUNCT
ejpam-4497	442	7	shami	shami	PROPN
ejpam-4497	442	8	.	.	PUNCT
ejpam-4497	443	1	investigation	investigation	NOUN
ejpam-4497	443	2	and	and	CCONJ
ejpam-4497	443	3	corrigendum	corrigendum	VERB
ejpam-4497	443	4	to	to	ADP
ejpam-4497	443	5	some	some	DET
ejpam-4497	443	6	results	result	NOUN
ejpam-4497	443	7	related	relate	VERB
ejpam-4497	443	8	to	to	ADP
ejpam-4497	443	9	g	g	NOUN
ejpam-4497	443	10	-	-	PUNCT
ejpam-4497	443	11	soft	soft	ADJ
ejpam-4497	443	12	equality	equality	NOUN
ejpam-4497	443	13	and	and	CCONJ
ejpam-4497	443	14	gf	gf	NOUN
ejpam-4497	443	15	-	-	PUNCT
ejpam-4497	443	16	soft	soft	ADJ
ejpam-4497	443	17	equality	equality	NOUN
ejpam-4497	443	18	relations	relation	NOUN
ejpam-4497	443	19	.	.	PUNCT
ejpam-4497	444	1	filomat	filomat	PROPN
ejpam-4497	444	2	,	,	PUNCT
ejpam-4497	444	3	33(11):3375–3383	33(11):3375–3383	NUM
ejpam-4497	444	4	,	,	PUNCT
ejpam-4497	444	5	2019	2019	NUM
ejpam-4497	444	6	.	.	PUNCT
ejpam-4497	445	1	[	[	X
ejpam-4497	445	2	6	6	NUM
ejpam-4497	445	3	]	]	PUNCT
ejpam-4497	445	4	tm	tm	PROPN
ejpam-4497	445	5	al	al	PROPN
ejpam-4497	445	6	-	-	PUNCT
ejpam-4497	445	7	shami	shami	PROPN
ejpam-4497	445	8	.	.	PUNCT
ejpam-4497	446	1	comments	comment	NOUN
ejpam-4497	446	2	on	on	ADP
ejpam-4497	446	3	some	some	DET
ejpam-4497	446	4	results	result	NOUN
ejpam-4497	446	5	related	relate	VERB
ejpam-4497	446	6	to	to	ADP
ejpam-4497	446	7	soft	soft	ADJ
ejpam-4497	446	8	separation	separation	NOUN
ejpam-4497	446	9	axioms	axiom	NOUN
ejpam-4497	446	10	.	.	PUNCT
ejpam-4497	447	1	afrika	afrika	ADJ
ejpam-4497	447	2	matematika	matematika	PROPN
ejpam-4497	447	3	,	,	PUNCT
ejpam-4497	447	4	31(7):1105–1119	31(7):1105–1119	NUM
ejpam-4497	447	5	,	,	PUNCT
ejpam-4497	447	6	2020	2020	NUM
ejpam-4497	447	7	.	.	PUNCT
ejpam-4497	448	1	[	[	X
ejpam-4497	448	2	7	7	X
ejpam-4497	448	3	]	]	PUNCT
ejpam-4497	448	4	tm	tm	PROPN
ejpam-4497	448	5	al	al	PROPN
ejpam-4497	448	6	-	-	PUNCT
ejpam-4497	448	7	shami	shami	PROPN
ejpam-4497	448	8	.	.	PUNCT
ejpam-4497	449	1	soft	soft	ADJ
ejpam-4497	449	2	separation	separation	NOUN
ejpam-4497	449	3	axioms	axiom	NOUN
ejpam-4497	449	4	and	and	CCONJ
ejpam-4497	449	5	fixed	fix	VERB
ejpam-4497	449	6	soft	soft	ADJ
ejpam-4497	449	7	points	point	NOUN
ejpam-4497	449	8	using	use	VERB
ejpam-4497	449	9	soft	soft	ADJ
ejpam-4497	449	10	semiopen	semiopen	ADJ
ejpam-4497	449	11	sets	set	NOUN
ejpam-4497	449	12	.	.	PUNCT
ejpam-4497	450	1	journal	journal	NOUN
ejpam-4497	450	2	of	of	ADP
ejpam-4497	450	3	applied	apply	VERB
ejpam-4497	450	4	mathematics	mathematic	NOUN
ejpam-4497	450	5	,	,	PUNCT
ejpam-4497	450	6	2020	2020	NUM
ejpam-4497	450	7	,	,	PUNCT
ejpam-4497	450	8	2020	2020	NUM
ejpam-4497	450	9	.	.	PUNCT
ejpam-4497	451	1	[	[	X
ejpam-4497	451	2	8	8	NUM
ejpam-4497	451	3	]	]	PUNCT
ejpam-4497	451	4	tm	tm	PROPN
ejpam-4497	451	5	al	al	PROPN
ejpam-4497	451	6	-	-	PUNCT
ejpam-4497	451	7	shami	shami	PROPN
ejpam-4497	451	8	.	.	PUNCT
ejpam-4497	452	1	bipolar	bipolar	ADJ
ejpam-4497	452	2	soft	soft	ADJ
ejpam-4497	452	3	sets	set	NOUN
ejpam-4497	452	4	:	:	PUNCT
ejpam-4497	452	5	relations	relation	NOUN
ejpam-4497	452	6	between	between	ADP
ejpam-4497	452	7	them	they	PRON
ejpam-4497	452	8	and	and	CCONJ
ejpam-4497	452	9	ordinary	ordinary	ADJ
ejpam-4497	452	10	points	point	NOUN
ejpam-4497	452	11	and	and	CCONJ
ejpam-4497	452	12	their	their	PRON
ejpam-4497	452	13	applications	application	NOUN
ejpam-4497	452	14	.	.	PUNCT
ejpam-4497	453	1	complexity	complexity	NOUN
ejpam-4497	453	2	,	,	PUNCT
ejpam-4497	453	3	2021	2021	NUM
ejpam-4497	453	4	,	,	PUNCT
ejpam-4497	453	5	2021	2021	NUM
ejpam-4497	453	6	.	.	PUNCT
ejpam-4497	454	1	references	reference	NOUN
ejpam-4497	454	2	1468	1468	NUM
ejpam-4497	454	3	[	[	X
ejpam-4497	454	4	9	9	NUM
ejpam-4497	454	5	]	]	PUNCT
ejpam-4497	454	6	tm	tm	PROPN
ejpam-4497	454	7	al	al	PROPN
ejpam-4497	454	8	-	-	PUNCT
ejpam-4497	454	9	shami	shami	PROPN
ejpam-4497	454	10	.	.	PUNCT
ejpam-4497	455	1	compactness	compactness	NOUN
ejpam-4497	455	2	on	on	ADP
ejpam-4497	455	3	soft	soft	ADJ
ejpam-4497	455	4	topological	topological	ADJ
ejpam-4497	455	5	ordered	order	VERB
ejpam-4497	455	6	spaces	space	NOUN
ejpam-4497	455	7	and	and	CCONJ
ejpam-4497	455	8	its	its	PRON
ejpam-4497	455	9	application	application	NOUN
ejpam-4497	455	10	on	on	ADP
ejpam-4497	455	11	the	the	DET
ejpam-4497	455	12	information	information	NOUN
ejpam-4497	455	13	system	system	NOUN
ejpam-4497	455	14	.	.	PUNCT
ejpam-4497	456	1	journal	journal	NOUN
ejpam-4497	456	2	of	of	ADP
ejpam-4497	456	3	mathematics	mathematic	NOUN
ejpam-4497	456	4	,	,	PUNCT
ejpam-4497	456	5	2021	2021	NUM
ejpam-4497	456	6	,	,	PUNCT
ejpam-4497	456	7	2021	2021	NUM
ejpam-4497	456	8	.	.	PUNCT
ejpam-4497	457	1	[	[	X
ejpam-4497	457	2	10	10	NUM
ejpam-4497	457	3	]	]	PUNCT
ejpam-4497	457	4	tm	tm	PROPN
ejpam-4497	457	5	al	al	PROPN
ejpam-4497	457	6	-	-	PUNCT
ejpam-4497	457	7	shami	shami	PROPN
ejpam-4497	457	8	.	.	PUNCT
ejpam-4497	458	1	homeomorphism	homeomorphism	PROPN
ejpam-4497	458	2	and	and	CCONJ
ejpam-4497	458	3	quotient	quotient	NOUN
ejpam-4497	458	4	mappings	mapping	NOUN
ejpam-4497	458	5	in	in	ADP
ejpam-4497	458	6	infrasoft	infrasoft	ADJ
ejpam-4497	458	7	topological	topological	ADJ
ejpam-4497	458	8	spaces	space	NOUN
ejpam-4497	458	9	.	.	PUNCT
ejpam-4497	459	1	journal	journal	NOUN
ejpam-4497	459	2	of	of	ADP
ejpam-4497	459	3	mathematics	mathematic	NOUN
ejpam-4497	459	4	,	,	PUNCT
ejpam-4497	459	5	2021	2021	NUM
ejpam-4497	459	6	,	,	PUNCT
ejpam-4497	459	7	2021	2021	NUM
ejpam-4497	459	8	.	.	PUNCT
ejpam-4497	460	1	[	[	X
ejpam-4497	460	2	11	11	NUM
ejpam-4497	460	3	]	]	PUNCT
ejpam-4497	460	4	tm	tm	PROPN
ejpam-4497	460	5	al	al	PROPN
ejpam-4497	460	6	-	-	PUNCT
ejpam-4497	460	7	shami	shami	PROPN
ejpam-4497	460	8	.	.	PUNCT
ejpam-4497	461	1	improvement	improvement	NOUN
ejpam-4497	461	2	of	of	ADP
ejpam-4497	461	3	the	the	DET
ejpam-4497	461	4	approximations	approximation	NOUN
ejpam-4497	461	5	and	and	CCONJ
ejpam-4497	461	6	accuracy	accuracy	NOUN
ejpam-4497	461	7	measure	measure	NOUN
ejpam-4497	461	8	of	of	ADP
ejpam-4497	461	9	a	a	DET
ejpam-4497	461	10	rough	rough	ADJ
ejpam-4497	461	11	set	set	NOUN
ejpam-4497	461	12	using	use	VERB
ejpam-4497	461	13	somewhere	somewhere	ADV
ejpam-4497	461	14	dense	dense	ADJ
ejpam-4497	461	15	sets	set	NOUN
ejpam-4497	461	16	.	.	PUNCT
ejpam-4497	462	1	soft	soft	ADJ
ejpam-4497	462	2	computing	computing	NOUN
ejpam-4497	462	3	,	,	PUNCT
ejpam-4497	462	4	25(23):14449–14460	25(23):14449–14460	NUM
ejpam-4497	462	5	,	,	PUNCT
ejpam-4497	462	6	2021	2021	NUM
ejpam-4497	462	7	.	.	PUNCT
ejpam-4497	463	1	[	[	X
ejpam-4497	463	2	12	12	NUM
ejpam-4497	463	3	]	]	PUNCT
ejpam-4497	463	4	tm	tm	PROPN
ejpam-4497	463	5	al	al	PROPN
ejpam-4497	463	6	-	-	PUNCT
ejpam-4497	463	7	shami	shami	PROPN
ejpam-4497	463	8	.	.	PUNCT
ejpam-4497	464	1	infra	infra	NOUN
ejpam-4497	464	2	soft	soft	ADJ
ejpam-4497	464	3	compact	compact	ADJ
ejpam-4497	464	4	spaces	space	NOUN
ejpam-4497	464	5	and	and	CCONJ
ejpam-4497	464	6	application	application	NOUN
ejpam-4497	464	7	to	to	ADP
ejpam-4497	464	8	fixed	fix	VERB
ejpam-4497	464	9	point	point	NOUN
ejpam-4497	464	10	theorem	theorem	VERB
ejpam-4497	464	11	.	.	PROPN
ejpam-4497	464	12	journal	journal	PROPN
ejpam-4497	464	13	of	of	ADP
ejpam-4497	464	14	function	function	NOUN
ejpam-4497	464	15	spaces	space	NOUN
ejpam-4497	464	16	,	,	PUNCT
ejpam-4497	464	17	2021	2021	NUM
ejpam-4497	464	18	,	,	PUNCT
ejpam-4497	464	19	2021	2021	NUM
ejpam-4497	464	20	.	.	PUNCT
ejpam-4497	465	1	[	[	X
ejpam-4497	465	2	13	13	NUM
ejpam-4497	465	3	]	]	PUNCT
ejpam-4497	465	4	tm	tm	PROPN
ejpam-4497	465	5	al	al	PROPN
ejpam-4497	465	6	-	-	PUNCT
ejpam-4497	465	7	shami	shami	PROPN
ejpam-4497	465	8	.	.	PUNCT
ejpam-4497	466	1	new	new	ADJ
ejpam-4497	466	2	soft	soft	ADJ
ejpam-4497	466	3	structure	structure	NOUN
ejpam-4497	466	4	:	:	PUNCT
ejpam-4497	466	5	infra	infra	NOUN
ejpam-4497	466	6	soft	soft	ADJ
ejpam-4497	466	7	topological	topological	ADJ
ejpam-4497	466	8	spaces	space	NOUN
ejpam-4497	466	9	.	.	PUNCT
ejpam-4497	467	1	mathematical	mathematical	ADJ
ejpam-4497	467	2	problems	problem	NOUN
ejpam-4497	467	3	in	in	ADP
ejpam-4497	467	4	engineering	engineering	NOUN
ejpam-4497	467	5	,	,	PUNCT
ejpam-4497	467	6	2021	2021	NUM
ejpam-4497	467	7	,	,	PUNCT
ejpam-4497	467	8	2021	2021	NUM
ejpam-4497	467	9	.	.	PUNCT
ejpam-4497	468	1	[	[	X
ejpam-4497	468	2	14	14	NUM
ejpam-4497	468	3	]	]	PUNCT
ejpam-4497	468	4	tm	tm	PROPN
ejpam-4497	468	5	al	al	PROPN
ejpam-4497	468	6	-	-	PUNCT
ejpam-4497	468	7	shami	shami	PROPN
ejpam-4497	468	8	.	.	PUNCT
ejpam-4497	469	1	on	on	ADP
ejpam-4497	469	2	soft	soft	ADJ
ejpam-4497	469	3	separation	separation	NOUN
ejpam-4497	469	4	axioms	axiom	NOUN
ejpam-4497	469	5	and	and	CCONJ
ejpam-4497	469	6	their	their	PRON
ejpam-4497	469	7	applications	application	NOUN
ejpam-4497	469	8	on	on	ADP
ejpam-4497	469	9	decision	decision	NOUN
ejpam-4497	469	10	-	-	PUNCT
ejpam-4497	469	11	making	make	VERB
ejpam-4497	469	12	problem	problem	NOUN
ejpam-4497	469	13	.	.	PUNCT
ejpam-4497	470	1	mathematical	mathematical	ADJ
ejpam-4497	470	2	problems	problem	NOUN
ejpam-4497	470	3	in	in	ADP
ejpam-4497	470	4	engineering	engineering	NOUN
ejpam-4497	470	5	,	,	PUNCT
ejpam-4497	470	6	2021	2021	NUM
ejpam-4497	470	7	,	,	PUNCT
ejpam-4497	470	8	2021	2021	NUM
ejpam-4497	470	9	.	.	PUNCT
ejpam-4497	471	1	[	[	X
ejpam-4497	471	2	15	15	NUM
ejpam-4497	471	3	]	]	X
ejpam-4497	471	4	tm	tm	PROPN
ejpam-4497	471	5	al	al	PROPN
ejpam-4497	471	6	-	-	PUNCT
ejpam-4497	471	7	shami	shami	PROPN
ejpam-4497	471	8	.	.	PUNCT
ejpam-4497	472	1	soft	soft	ADJ
ejpam-4497	472	2	somewhat	somewhat	ADV
ejpam-4497	472	3	open	open	ADJ
ejpam-4497	472	4	sets	set	NOUN
ejpam-4497	472	5	:	:	PUNCT
ejpam-4497	472	6	soft	soft	ADJ
ejpam-4497	472	7	separation	separation	NOUN
ejpam-4497	472	8	axioms	axiom	NOUN
ejpam-4497	472	9	and	and	CCONJ
ejpam-4497	472	10	medical	medical	ADJ
ejpam-4497	472	11	application	application	NOUN
ejpam-4497	472	12	to	to	ADP
ejpam-4497	472	13	nutrition	nutrition	NOUN
ejpam-4497	472	14	.	.	PUNCT
ejpam-4497	473	1	computational	computational	ADJ
ejpam-4497	473	2	and	and	CCONJ
ejpam-4497	473	3	applied	applied	ADJ
ejpam-4497	473	4	mathematics	mathematic	NOUN
ejpam-4497	473	5	,	,	PUNCT
ejpam-4497	473	6	41	41	NUM
ejpam-4497	473	7	,	,	PUNCT
ejpam-4497	473	8	2022	2022	NUM
ejpam-4497	473	9	.	.	PUNCT
ejpam-4497	474	1	[	[	X
ejpam-4497	474	2	16	16	NUM
ejpam-4497	474	3	]	]	PUNCT
ejpam-4497	474	4	tm	tm	PROPN
ejpam-4497	474	5	al	al	PROPN
ejpam-4497	474	6	-	-	PUNCT
ejpam-4497	474	7	shami	shami	PROPN
ejpam-4497	474	8	.	.	PUNCT
ejpam-4497	475	1	topological	topological	ADJ
ejpam-4497	475	2	approach	approach	NOUN
ejpam-4497	475	3	to	to	PART
ejpam-4497	475	4	generate	generate	VERB
ejpam-4497	475	5	new	new	ADJ
ejpam-4497	475	6	rough	rough	ADJ
ejpam-4497	475	7	set	set	NOUN
ejpam-4497	475	8	models	model	NOUN
ejpam-4497	475	9	.	.	PUNCT
ejpam-4497	476	1	complex	complex	ADJ
ejpam-4497	476	2	&	&	CCONJ
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ejpam-4497	476	4	systems	system	NOUN
ejpam-4497	476	5	,	,	PUNCT
ejpam-4497	476	6	2022	2022	NUM
ejpam-4497	476	7	.	.	PUNCT
ejpam-4497	477	1	[	[	X
ejpam-4497	477	2	17	17	NUM
ejpam-4497	477	3	]	]	PUNCT
ejpam-4497	477	4	tm	tm	PROPN
ejpam-4497	477	5	al	al	PROPN
ejpam-4497	477	6	-	-	PUNCT
ejpam-4497	477	7	shami	shami	PROPN
ejpam-4497	477	8	and	and	CCONJ
ejpam-4497	477	9	ea	ea	ADP
ejpam-4497	477	10	abo	abo	NOUN
ejpam-4497	477	11	-	-	PUNCT
ejpam-4497	477	12	tabl	tabl	NOUN
ejpam-4497	477	13	.	.	PUNCT
ejpam-4497	478	1	connectedness	connectedness	NOUN
ejpam-4497	478	2	and	and	CCONJ
ejpam-4497	478	3	local	local	ADJ
ejpam-4497	478	4	connectedness	connectedness	NOUN
ejpam-4497	478	5	on	on	ADP
ejpam-4497	478	6	infra	infra	NOUN
ejpam-4497	478	7	soft	soft	ADJ
ejpam-4497	478	8	topological	topological	ADJ
ejpam-4497	478	9	spaces	space	NOUN
ejpam-4497	478	10	.	.	PUNCT
ejpam-4497	479	1	mathematics	mathematic	NOUN
ejpam-4497	479	2	,	,	PUNCT
ejpam-4497	479	3	9(15	9(15	NUM
ejpam-4497	479	4	)	)	PUNCT
ejpam-4497	479	5	,	,	PUNCT
ejpam-4497	479	6	2021	2021	NUM
ejpam-4497	479	7	.	.	PUNCT
ejpam-4497	480	1	[	[	X
ejpam-4497	480	2	18	18	NUM
ejpam-4497	480	3	]	]	PUNCT
ejpam-4497	480	4	tm	tm	PROPN
ejpam-4497	480	5	al	al	PROPN
ejpam-4497	480	6	-	-	PUNCT
ejpam-4497	480	7	shami	shami	PROPN
ejpam-4497	480	8	and	and	CCONJ
ejpam-4497	480	9	ea	ea	ADP
ejpam-4497	480	10	abo	abo	NOUN
ejpam-4497	480	11	-	-	PUNCT
ejpam-4497	480	12	tabl	tabl	NOUN
ejpam-4497	480	13	.	.	PUNCT
ejpam-4497	481	1	soft	soft	ADJ
ejpam-4497	481	2	α	α	NOUN
ejpam-4497	481	3	-	-	PUNCT
ejpam-4497	481	4	separation	separation	NOUN
ejpam-4497	481	5	axioms	axiom	NOUN
ejpam-4497	481	6	and	and	CCONJ
ejpam-4497	481	7	α	α	X
ejpam-4497	481	8	-	-	PUNCT
ejpam-4497	481	9	fixed	fix	VERB
ejpam-4497	481	10	soft	soft	ADJ
ejpam-4497	481	11	points	point	NOUN
ejpam-4497	481	12	.	.	PUNCT
ejpam-4497	482	1	aims	aim	VERB
ejpam-4497	482	2	mathematics	mathematic	NOUN
ejpam-4497	482	3	,	,	PUNCT
ejpam-4497	482	4	6(6):5675–5694	6(6):5675–5694	NUM
ejpam-4497	482	5	,	,	PUNCT
ejpam-4497	482	6	2021	2021	NUM
ejpam-4497	482	7	.	.	PUNCT
ejpam-4497	483	1	[	[	X
ejpam-4497	483	2	19	19	NUM
ejpam-4497	483	3	]	]	X
ejpam-4497	483	4	tm	tm	PROPN
ejpam-4497	483	5	al	al	PROPN
ejpam-4497	483	6	-	-	PUNCT
ejpam-4497	483	7	shami	shami	PROPN
ejpam-4497	483	8	,	,	PUNCT
ejpam-4497	483	9	ea	ea	X
ejpam-4497	483	10	abo	abo	NOUN
ejpam-4497	483	11	-	-	PUNCT
ejpam-4497	483	12	tabl	tabl	NOUN
ejpam-4497	483	13	,	,	PUNCT
ejpam-4497	483	14	and	and	CCONJ
ejpam-4497	483	15	ba	ba	PROPN
ejpam-4497	483	16	asaad	asaad	NOUN
ejpam-4497	483	17	.	.	PUNCT
ejpam-4497	484	1	weak	weak	ADJ
ejpam-4497	484	2	forms	form	NOUN
ejpam-4497	484	3	of	of	ADP
ejpam-4497	484	4	soft	soft	ADJ
ejpam-4497	484	5	separation	separation	NOUN
ejpam-4497	484	6	axioms	axiom	NOUN
ejpam-4497	484	7	and	and	CCONJ
ejpam-4497	484	8	fixed	fix	VERB
ejpam-4497	484	9	soft	soft	ADJ
ejpam-4497	484	10	points	point	NOUN
ejpam-4497	484	11	.	.	PUNCT
ejpam-4497	485	1	fuzzy	fuzzy	ADJ
ejpam-4497	485	2	information	information	NOUN
ejpam-4497	485	3	and	and	CCONJ
ejpam-4497	485	4	engineering	engineering	NOUN
ejpam-4497	485	5	,	,	PUNCT
ejpam-4497	485	6	12(4):509–528	12(4):509–528	NUM
ejpam-4497	485	7	,	,	PUNCT
ejpam-4497	485	8	2020	2020	NUM
ejpam-4497	485	9	.	.	PUNCT
ejpam-4497	486	1	[	[	X
ejpam-4497	486	2	20	20	NUM
ejpam-4497	486	3	]	]	PUNCT
ejpam-4497	486	4	tm	tm	PROPN
ejpam-4497	486	5	al	al	PROPN
ejpam-4497	486	6	-	-	PUNCT
ejpam-4497	486	7	shami	shami	PROPN
ejpam-4497	486	8	,	,	PUNCT
ejpam-4497	486	9	i	i	PROPN
ejpam-4497	486	10	alshammari	alshammari	NOUN
ejpam-4497	486	11	,	,	PUNCT
ejpam-4497	486	12	and	and	CCONJ
ejpam-4497	486	13	ba	ba	PROPN
ejpam-4497	486	14	asaad	asaad	NOUN
ejpam-4497	486	15	.	.	PUNCT
ejpam-4497	487	1	soft	soft	ADJ
ejpam-4497	487	2	maps	map	NOUN
ejpam-4497	487	3	via	via	ADP
ejpam-4497	487	4	soft	soft	ADJ
ejpam-4497	487	5	somewhere	somewhere	ADV
ejpam-4497	487	6	dense	dense	ADJ
ejpam-4497	487	7	sets	set	NOUN
ejpam-4497	487	8	.	.	PUNCT
ejpam-4497	488	1	filomat	filomat	NOUN
ejpam-4497	488	2	,	,	PUNCT
ejpam-4497	488	3	34(10):3429–3440	34(10):3429–3440	NUM
ejpam-4497	488	4	,	,	PUNCT
ejpam-4497	488	5	2020	2020	NUM
ejpam-4497	488	6	.	.	PUNCT
ejpam-4497	489	1	[	[	X
ejpam-4497	489	2	21	21	NUM
ejpam-4497	489	3	]	]	PUNCT
ejpam-4497	489	4	tm	tm	PROPN
ejpam-4497	489	5	al	al	PROPN
ejpam-4497	489	6	-	-	PUNCT
ejpam-4497	489	7	shami	shami	PROPN
ejpam-4497	489	8	,	,	PUNCT
ejpam-4497	489	9	za	za	PROPN
ejpam-4497	489	10	ameen	ameen	PROPN
ejpam-4497	489	11	,	,	PUNCT
ejpam-4497	489	12	aa	aa	PROPN
ejpam-4497	489	13	azzam	azzam	PROPN
ejpam-4497	489	14	,	,	PUNCT
ejpam-4497	489	15	and	and	CCONJ
ejpam-4497	489	16	me	i	PRON
ejpam-4497	489	17	el	el	PROPN
ejpam-4497	489	18	-	-	PUNCT
ejpam-4497	489	19	shafei	shafei	PROPN
ejpam-4497	489	20	.	.	PUNCT
ejpam-4497	490	1	soft	soft	ADJ
ejpam-4497	490	2	separation	separation	NOUN
ejpam-4497	490	3	axioms	axiom	NOUN
ejpam-4497	490	4	via	via	ADP
ejpam-4497	490	5	soft	soft	ADJ
ejpam-4497	490	6	topological	topological	ADJ
ejpam-4497	490	7	operators	operator	NOUN
ejpam-4497	490	8	.	.	PUNCT
ejpam-4497	491	1	aims	aim	VERB
ejpam-4497	491	2	mathematics	mathematic	NOUN
ejpam-4497	491	3	,	,	PUNCT
ejpam-4497	491	4	7(8):15107–15119	7(8):15107–15119	NUM
ejpam-4497	491	5	,	,	PUNCT
ejpam-4497	491	6	2022	2022	NUM
ejpam-4497	491	7	.	.	PUNCT
ejpam-4497	492	1	[	[	X
ejpam-4497	492	2	22	22	NUM
ejpam-4497	492	3	]	]	PUNCT
ejpam-4497	492	4	tm	tm	PROPN
ejpam-4497	492	5	al	al	PROPN
ejpam-4497	492	6	-	-	PUNCT
ejpam-4497	492	7	shami	shami	PROPN
ejpam-4497	492	8	,	,	PUNCT
ejpam-4497	492	9	ba	ba	PROPN
ejpam-4497	492	10	asaad	asaad	NOUN
ejpam-4497	492	11	,	,	PUNCT
ejpam-4497	492	12	and	and	CCONJ
ejpam-4497	492	13	ea	ea	ADP
ejpam-4497	492	14	abo	abo	NOUN
ejpam-4497	492	15	-	-	PUNCT
ejpam-4497	492	16	tabl	tabl	NOUN
ejpam-4497	492	17	.	.	PUNCT
ejpam-4497	493	1	separation	separation	NOUN
ejpam-4497	493	2	axioms	axiom	NOUN
ejpam-4497	493	3	and	and	CCONJ
ejpam-4497	493	4	fixed	fix	VERB
ejpam-4497	493	5	points	point	NOUN
ejpam-4497	493	6	using	use	VERB
ejpam-4497	493	7	total	total	ADJ
ejpam-4497	493	8	belong	belong	NOUN
ejpam-4497	493	9	and	and	CCONJ
ejpam-4497	493	10	total	total	ADJ
ejpam-4497	493	11	non	non	ADJ
ejpam-4497	493	12	-	-	ADJ
ejpam-4497	493	13	belong	belong	ADJ
ejpam-4497	493	14	relations	relation	NOUN
ejpam-4497	493	15	with	with	ADP
ejpam-4497	493	16	respect	respect	NOUN
ejpam-4497	493	17	to	to	ADP
ejpam-4497	493	18	soft	soft	ADJ
ejpam-4497	493	19	β	β	ADJ
ejpam-4497	493	20	-	-	ADJ
ejpam-4497	493	21	open	open	ADJ
ejpam-4497	493	22	sets	set	NOUN
ejpam-4497	493	23	.	.	PUNCT
ejpam-4497	494	1	journal	journal	NOUN
ejpam-4497	494	2	of	of	ADP
ejpam-4497	494	3	interdisciplinary	interdisciplinary	ADJ
ejpam-4497	494	4	mathematics	mathematic	NOUN
ejpam-4497	494	5	,	,	PUNCT
ejpam-4497	494	6	24(4):1053–1077	24(4):1053–1077	PROPN
ejpam-4497	494	7	,	,	PUNCT
ejpam-4497	494	8	2021	2021	NUM
ejpam-4497	494	9	.	.	PUNCT
ejpam-4497	495	1	[	[	X
ejpam-4497	495	2	23	23	NUM
ejpam-4497	495	3	]	]	PUNCT
ejpam-4497	495	4	tm	tm	PROPN
ejpam-4497	495	5	al	al	PROPN
ejpam-4497	495	6	-	-	PUNCT
ejpam-4497	495	7	shami	shami	PROPN
ejpam-4497	495	8	and	and	CCONJ
ejpam-4497	495	9	aa	aa	PROPN
ejpam-4497	495	10	azzam	azzam	PROPN
ejpam-4497	495	11	.	.	PUNCT
ejpam-4497	496	1	infra	infra	NOUN
ejpam-4497	496	2	soft	soft	ADJ
ejpam-4497	496	3	semiopen	semiopen	ADJ
ejpam-4497	496	4	sets	set	NOUN
ejpam-4497	496	5	and	and	CCONJ
ejpam-4497	496	6	infra	infra	VERB
ejpam-4497	496	7	soft	soft	ADJ
ejpam-4497	496	8	semicontinuity	semicontinuity	NOUN
ejpam-4497	496	9	.	.	PUNCT
ejpam-4497	497	1	journal	journal	PROPN
ejpam-4497	497	2	of	of	ADP
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ejpam-4497	497	5	,	,	PUNCT
ejpam-4497	497	6	2021	2021	NUM
ejpam-4497	497	7	,	,	PUNCT
ejpam-4497	497	8	2021	2021	NUM
ejpam-4497	497	9	.	.	PUNCT
ejpam-4497	498	1	[	[	X
ejpam-4497	498	2	24	24	NUM
ejpam-4497	498	3	]	]	PUNCT
ejpam-4497	498	4	tm	tm	PROPN
ejpam-4497	498	5	al	al	PROPN
ejpam-4497	498	6	-	-	PUNCT
ejpam-4497	498	7	shami	shami	PROPN
ejpam-4497	498	8	and	and	CCONJ
ejpam-4497	498	9	me	i	PRON
ejpam-4497	498	10	el	el	PROPN
ejpam-4497	498	11	-	-	PUNCT
ejpam-4497	498	12	shafei	shafei	NOUN
ejpam-4497	498	13	.	.	PUNCT
ejpam-4497	499	1	on	on	ADP
ejpam-4497	499	2	supra	supra	PROPN
ejpam-4497	499	3	soft	soft	ADJ
ejpam-4497	499	4	topological	topological	ADJ
ejpam-4497	499	5	ordered	order	VERB
ejpam-4497	499	6	spaces	space	NOUN
ejpam-4497	499	7	.	.	PUNCT
ejpam-4497	500	1	arab	arab	PROPN
ejpam-4497	500	2	journal	journal	PROPN
ejpam-4497	500	3	of	of	ADP
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ejpam-4497	500	5	and	and	CCONJ
ejpam-4497	500	6	applied	applied	ADJ
ejpam-4497	500	7	sciences	science	NOUN
ejpam-4497	500	8	,	,	PUNCT
ejpam-4497	500	9	26(1):433–445	26(1):433–445	NOUN
ejpam-4497	500	10	,	,	PUNCT
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ejpam-4497	500	12	.	.	PUNCT
ejpam-4497	501	1	references	reference	NOUN
ejpam-4497	501	2	1469	1469	NUM
ejpam-4497	501	3	[	[	X
ejpam-4497	501	4	25	25	NUM
ejpam-4497	501	5	]	]	PUNCT
ejpam-4497	501	6	tm	tm	PROPN
ejpam-4497	501	7	al	al	PROPN
ejpam-4497	501	8	-	-	PUNCT
ejpam-4497	501	9	shami	shami	PROPN
ejpam-4497	501	10	and	and	CCONJ
ejpam-4497	501	11	me	i	PRON
ejpam-4497	501	12	el	el	PROPN
ejpam-4497	501	13	-	-	PUNCT
ejpam-4497	501	14	shafei	shafei	NOUN
ejpam-4497	501	15	.	.	PUNCT
ejpam-4497	502	1	some	some	DET
ejpam-4497	502	2	types	type	NOUN
ejpam-4497	502	3	of	of	ADP
ejpam-4497	502	4	soft	soft	ADJ
ejpam-4497	502	5	ordered	order	VERB
ejpam-4497	502	6	maps	map	NOUN
ejpam-4497	502	7	via	via	ADP
ejpam-4497	502	8	soft	soft	ADJ
ejpam-4497	502	9	pre	pre	ADJ
ejpam-4497	502	10	open	open	ADJ
ejpam-4497	502	11	sets	set	NOUN
ejpam-4497	502	12	.	.	PUNCT
ejpam-4497	503	1	applied	apply	VERB
ejpam-4497	503	2	mathematics	mathematics	PROPN
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ejpam-4497	503	4	information	information	NOUN
ejpam-4497	503	5	sciences	sciences	PROPN
ejpam-4497	503	6	,	,	PUNCT
ejpam-4497	503	7	13(5):707–715	13(5):707–715	NOUN
ejpam-4497	503	8	,	,	PUNCT
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ejpam-4497	503	10	.	.	PUNCT
ejpam-4497	504	1	[	[	X
ejpam-4497	504	2	26	26	NUM
ejpam-4497	504	3	]	]	PUNCT
ejpam-4497	504	4	tm	tm	PROPN
ejpam-4497	504	5	al	al	PROPN
ejpam-4497	504	6	-	-	PUNCT
ejpam-4497	504	7	shami	shami	PROPN
ejpam-4497	504	8	and	and	CCONJ
ejpam-4497	504	9	me	i	PRON
ejpam-4497	504	10	el	el	PROPN
ejpam-4497	504	11	-	-	PUNCT
ejpam-4497	504	12	shafei	shafei	NOUN
ejpam-4497	504	13	.	.	PUNCT
ejpam-4497	505	1	two	two	NUM
ejpam-4497	505	2	types	type	NOUN
ejpam-4497	505	3	of	of	ADP
ejpam-4497	505	4	separation	separation	NOUN
ejpam-4497	505	5	axioms	axiom	NOUN
ejpam-4497	505	6	on	on	ADP
ejpam-4497	505	7	supra	supra	PROPN
ejpam-4497	505	8	soft	soft	ADJ
ejpam-4497	505	9	topological	topological	ADJ
ejpam-4497	505	10	spaces	space	NOUN
ejpam-4497	505	11	.	.	PUNCT
ejpam-4497	506	1	demonstratio	demonstratio	PROPN
ejpam-4497	506	2	mathematica	mathematica	PROPN
ejpam-4497	506	3	,	,	PUNCT
ejpam-4497	506	4	52(1):147–165	52(1):147–165	PROPN
ejpam-4497	506	5	,	,	PUNCT
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ejpam-4497	506	7	.	.	PUNCT
ejpam-4497	507	1	[	[	X
ejpam-4497	507	2	27	27	NUM
ejpam-4497	507	3	]	]	PUNCT
ejpam-4497	507	4	tm	tm	PROPN
ejpam-4497	507	5	al	al	PROPN
ejpam-4497	507	6	-	-	PUNCT
ejpam-4497	507	7	shami	shami	PROPN
ejpam-4497	507	8	and	and	CCONJ
ejpam-4497	507	9	me	i	PRON
ejpam-4497	507	10	el	el	PROPN
ejpam-4497	507	11	-	-	PUNCT
ejpam-4497	507	12	shafei	shafei	PROPN
ejpam-4497	507	13	.	.	PUNCT
ejpam-4497	508	1	t	t	PROPN
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ejpam-4497	508	4	relation	relation	NOUN
ejpam-4497	508	5	.	.	PUNCT
ejpam-4497	509	1	turkish	turkish	ADJ
ejpam-4497	509	2	journal	journal	NOUN
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ejpam-4497	509	4	mathematics	mathematic	NOUN
ejpam-4497	509	5	,	,	PUNCT
ejpam-4497	509	6	44(4):1427–1441	44(4):1427–1441	NUM
ejpam-4497	509	7	,	,	PUNCT
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ejpam-4497	509	9	.	.	PUNCT
ejpam-4497	510	1	[	[	X
ejpam-4497	510	2	28	28	NUM
ejpam-4497	510	3	]	]	X
ejpam-4497	510	4	tm	tm	PROPN
ejpam-4497	510	5	al	al	PROPN
ejpam-4497	510	6	-	-	PUNCT
ejpam-4497	510	7	shami	shami	PROPN
ejpam-4497	510	8	,	,	PUNCT
ejpam-4497	510	9	me	me	PROPN
ejpam-4497	510	10	el	el	PROPN
ejpam-4497	510	11	-	-	PUNCT
ejpam-4497	510	12	shafei	shafei	PROPN
ejpam-4497	510	13	,	,	PUNCT
ejpam-4497	510	14	and	and	CCONJ
ejpam-4497	510	15	m	m	AUX
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ejpam-4497	510	17	-	-	PUNCT
ejpam-4497	510	18	elhamayel	elhamayel	NOUN
ejpam-4497	510	19	.	.	PUNCT
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ejpam-4497	511	2	soft	soft	ADJ
ejpam-4497	511	3	compact	compact	ADJ
ejpam-4497	511	4	and	and	CCONJ
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ejpam-4497	511	7	lindelöf	lindelöf	NOUN
ejpam-4497	511	8	spaces	space	NOUN
ejpam-4497	511	9	.	.	PUNCT
ejpam-4497	512	1	journal	journal	PROPN
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ejpam-4497	512	7	,	,	PUNCT
ejpam-4497	512	8	12(5):620	12(5):620	NUM
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ejpam-4497	512	10	630	630	NUM
ejpam-4497	512	11	,	,	PUNCT
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ejpam-4497	512	13	.	.	PUNCT
ejpam-4497	513	1	[	[	X
ejpam-4497	513	2	29	29	NUM
ejpam-4497	513	3	]	]	PUNCT
ejpam-4497	513	4	tm	tm	PROPN
ejpam-4497	513	5	al	al	PROPN
ejpam-4497	513	6	-	-	PUNCT
ejpam-4497	513	7	shami	shami	PROPN
ejpam-4497	513	8	,	,	PUNCT
ejpam-4497	513	9	me	me	PROPN
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ejpam-4497	513	11	-	-	PUNCT
ejpam-4497	513	12	shafei	shafei	PROPN
ejpam-4497	513	13	,	,	PUNCT
ejpam-4497	513	14	and	and	CCONJ
ejpam-4497	513	15	m	m	AUX
ejpam-4497	513	16	abo	abo	NOUN
ejpam-4497	513	17	-	-	PUNCT
ejpam-4497	513	18	elhamayel	elhamayel	NOUN
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ejpam-4497	514	7	-	-	ADJ
ejpam-4497	514	8	compact	compact	ADJ
ejpam-4497	514	9	spaces	space	NOUN
ejpam-4497	514	10	.	.	PUNCT
ejpam-4497	515	1	korean	korean	ADJ
ejpam-4497	515	2	journal	journal	PROPN
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ejpam-4497	515	4	mathematics	mathematic	NOUN
ejpam-4497	515	5	,	,	PUNCT
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ejpam-4497	515	7	,	,	PUNCT
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ejpam-4497	515	9	.	.	PUNCT
ejpam-4497	516	1	[	[	X
ejpam-4497	516	2	30	30	NUM
ejpam-4497	516	3	]	]	PUNCT
ejpam-4497	516	4	tm	tm	PROPN
ejpam-4497	516	5	al	al	PROPN
ejpam-4497	516	6	-	-	PUNCT
ejpam-4497	516	7	shami	shami	PROPN
ejpam-4497	516	8	,	,	PUNCT
ejpam-4497	516	9	me	me	PROPN
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ejpam-4497	516	11	-	-	PUNCT
ejpam-4497	516	12	shafei	shafei	PROPN
ejpam-4497	516	13	,	,	PUNCT
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ejpam-4497	516	15	ba	ba	PROPN
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ejpam-4497	517	7	via	via	ADP
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ejpam-4497	518	7	mathematics	mathematic	NOUN
ejpam-4497	518	8	,	,	PUNCT
ejpam-4497	518	9	12(1):176–193	12(1):176–193	NUM
ejpam-4497	518	10	,	,	PUNCT
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ejpam-4497	518	12	.	.	PUNCT
ejpam-4497	519	1	[	[	X
ejpam-4497	519	2	31	31	NUM
ejpam-4497	519	3	]	]	PUNCT
ejpam-4497	519	4	tm	tm	PROPN
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ejpam-4497	519	6	-	-	PUNCT
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ejpam-4497	519	8	,	,	PUNCT
ejpam-4497	519	9	me	me	PROPN
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ejpam-4497	519	11	-	-	PUNCT
ejpam-4497	519	12	shafei	shafei	PROPN
ejpam-4497	519	13	,	,	PUNCT
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ejpam-4497	519	15	ba	ba	PROPN
ejpam-4497	519	16	asaad	asaad	NOUN
ejpam-4497	519	17	.	.	PUNCT
ejpam-4497	520	1	sum	sum	NOUN
ejpam-4497	520	2	of	of	ADP
ejpam-4497	520	3	soft	soft	ADJ
ejpam-4497	520	4	topological	topological	ADJ
ejpam-4497	520	5	ordered	order	VERB
ejpam-4497	520	6	spaces	space	NOUN
ejpam-4497	520	7	.	.	PUNCT
ejpam-4497	521	1	advances	advance	NOUN
ejpam-4497	521	2	in	in	ADP
ejpam-4497	521	3	mathematics	mathematic	NOUN
ejpam-4497	521	4	:	:	PUNCT
ejpam-4497	521	5	scientific	scientific	ADJ
ejpam-4497	521	6	journal	journal	NOUN
ejpam-4497	521	7	,	,	PUNCT
ejpam-4497	521	8	9(7):4695–4710	9(7):4695–4710	NUM
ejpam-4497	521	9	,	,	PUNCT
ejpam-4497	521	10	2020	2020	NUM
ejpam-4497	521	11	.	.	PUNCT
ejpam-4497	522	1	[	[	X
ejpam-4497	522	2	32	32	NUM
ejpam-4497	522	3	]	]	PUNCT
ejpam-4497	522	4	tm	tm	PROPN
ejpam-4497	522	5	al	al	PROPN
ejpam-4497	522	6	-	-	PUNCT
ejpam-4497	522	7	shami	shami	PROPN
ejpam-4497	522	8	,	,	PUNCT
ejpam-4497	522	9	h	h	PROPN
ejpam-4497	522	10	işık	işık	PROPN
ejpam-4497	522	11	,	,	PUNCT
ejpam-4497	522	12	as	as	ADP
ejpam-4497	522	13	nawar	nawar	ADJ
ejpam-4497	522	14	,	,	PUNCT
ejpam-4497	522	15	and	and	CCONJ
ejpam-4497	522	16	ra	ra	PROPN
ejpam-4497	522	17	hosny	hosny	PROPN
ejpam-4497	522	18	.	.	PUNCT
ejpam-4497	523	1	some	some	DET
ejpam-4497	523	2	topological	topological	ADJ
ejpam-4497	523	3	approaches	approach	NOUN
ejpam-4497	523	4	for	for	ADP
ejpam-4497	523	5	generalized	generalized	ADJ
ejpam-4497	523	6	rough	rough	ADJ
ejpam-4497	523	7	sets	set	NOUN
ejpam-4497	523	8	via	via	ADP
ejpam-4497	523	9	ideals	ideal	NOUN
ejpam-4497	523	10	.	.	PUNCT
ejpam-4497	524	1	mathematical	mathematical	ADJ
ejpam-4497	524	2	problems	problem	NOUN
ejpam-4497	524	3	in	in	ADP
ejpam-4497	524	4	engineering	engineering	NOUN
ejpam-4497	524	5	,	,	PUNCT
ejpam-4497	524	6	2021	2021	NUM
ejpam-4497	524	7	,	,	PUNCT
ejpam-4497	524	8	2021	2021	NUM
ejpam-4497	524	9	.	.	PUNCT
ejpam-4497	525	1	[	[	X
ejpam-4497	525	2	33	33	NUM
ejpam-4497	525	3	]	]	PUNCT
ejpam-4497	525	4	tm	tm	PROPN
ejpam-4497	525	5	al	al	PROPN
ejpam-4497	525	6	-	-	PUNCT
ejpam-4497	525	7	shami	shami	PROPN
ejpam-4497	525	8	and	and	CCONJ
ejpam-4497	525	9	ldr	ldr	PROPN
ejpam-4497	525	10	kočinac	kočinac	PROPN
ejpam-4497	525	11	.	.	PUNCT
ejpam-4497	526	1	the	the	DET
ejpam-4497	526	2	equivalence	equivalence	NOUN
ejpam-4497	526	3	between	between	ADP
ejpam-4497	526	4	the	the	DET
ejpam-4497	526	5	enriched	enrich	VERB
ejpam-4497	526	6	and	and	CCONJ
ejpam-4497	526	7	extended	extended	ADJ
ejpam-4497	526	8	soft	soft	ADJ
ejpam-4497	526	9	topologies	topology	NOUN
ejpam-4497	526	10	.	.	PUNCT
ejpam-4497	526	11	applied	apply	VERB
ejpam-4497	526	12	and	and	CCONJ
ejpam-4497	526	13	computational	computational	ADJ
ejpam-4497	526	14	mathematics	mathematic	NOUN
ejpam-4497	526	15	,	,	PUNCT
ejpam-4497	526	16	18(2):149–162	18(2):149–162	NOUN
ejpam-4497	526	17	,	,	PUNCT
ejpam-4497	526	18	2019	2019	NUM
ejpam-4497	526	19	.	.	PUNCT
ejpam-4497	527	1	[	[	X
ejpam-4497	527	2	34	34	NUM
ejpam-4497	527	3	]	]	PUNCT
ejpam-4497	527	4	tm	tm	PROPN
ejpam-4497	527	5	al	al	PROPN
ejpam-4497	527	6	-	-	PUNCT
ejpam-4497	527	7	shami	shami	PROPN
ejpam-4497	527	8	and	and	CCONJ
ejpam-4497	527	9	ldr	ldr	PROPN
ejpam-4497	527	10	kočinac	kočinac	PROPN
ejpam-4497	527	11	.	.	PUNCT
ejpam-4497	528	1	nearly	nearly	ADV
ejpam-4497	528	2	soft	soft	ADJ
ejpam-4497	528	3	menger	menger	NOUN
ejpam-4497	528	4	spaces	space	NOUN
ejpam-4497	528	5	.	.	PUNCT
ejpam-4497	529	1	journal	journal	NOUN
ejpam-4497	529	2	of	of	ADP
ejpam-4497	529	3	mathematics	mathematic	NOUN
ejpam-4497	529	4	,	,	PUNCT
ejpam-4497	529	5	2020	2020	NUM
ejpam-4497	529	6	,	,	PUNCT
ejpam-4497	529	7	2020	2020	NUM
ejpam-4497	529	8	.	.	PUNCT
ejpam-4497	530	1	[	[	X
ejpam-4497	530	2	35	35	NUM
ejpam-4497	530	3	]	]	PUNCT
ejpam-4497	530	4	tm	tm	PROPN
ejpam-4497	530	5	al	al	PROPN
ejpam-4497	530	6	-	-	PUNCT
ejpam-4497	530	7	shami	shami	PROPN
ejpam-4497	530	8	and	and	CCONJ
ejpam-4497	530	9	ldr	ldr	PROPN
ejpam-4497	530	10	kočinac	kočinac	PROPN
ejpam-4497	530	11	.	.	PUNCT
ejpam-4497	531	1	almost	almost	ADV
ejpam-4497	531	2	soft	soft	ADJ
ejpam-4497	531	3	menger	menger	NOUN
ejpam-4497	531	4	and	and	CCONJ
ejpam-4497	531	5	weakly	weakly	ADJ
ejpam-4497	531	6	soft	soft	ADJ
ejpam-4497	531	7	menger	menger	NOUN
ejpam-4497	531	8	spaces	space	NOUN
ejpam-4497	531	9	.	.	PUNCT
ejpam-4497	532	1	applied	apply	VERB
ejpam-4497	532	2	and	and	CCONJ
ejpam-4497	532	3	computational	computational	ADJ
ejpam-4497	532	4	mathematics	mathematic	NOUN
ejpam-4497	532	5	,	,	PUNCT
ejpam-4497	532	6	21(1):35–51	21(1):35–51	NUM
ejpam-4497	532	7	,	,	PUNCT
ejpam-4497	532	8	2022	2022	NUM
ejpam-4497	532	9	.	.	PUNCT
ejpam-4497	533	1	[	[	X
ejpam-4497	533	2	36	36	NUM
ejpam-4497	533	3	]	]	PUNCT
ejpam-4497	533	4	tm	tm	PROPN
ejpam-4497	533	5	al	al	PROPN
ejpam-4497	533	6	-	-	PUNCT
ejpam-4497	533	7	shami	shami	PROPN
ejpam-4497	533	8	,	,	PUNCT
ejpam-4497	533	9	ldr	ldr	PROPN
ejpam-4497	533	10	kočinac	kočinac	PROPN
ejpam-4497	533	11	,	,	PUNCT
ejpam-4497	533	12	and	and	CCONJ
ejpam-4497	533	13	ba	ba	PROPN
ejpam-4497	533	14	asaad	asaad	NOUN
ejpam-4497	533	15	.	.	PUNCT
ejpam-4497	534	1	sum	sum	NOUN
ejpam-4497	534	2	of	of	ADP
ejpam-4497	534	3	soft	soft	ADJ
ejpam-4497	534	4	topological	topological	ADJ
ejpam-4497	534	5	spaces	space	NOUN
ejpam-4497	534	6	.	.	PUNCT
ejpam-4497	535	1	mathematics	mathematic	NOUN
ejpam-4497	535	2	,	,	PUNCT
ejpam-4497	535	3	8(6):990	8(6):990	NUM
ejpam-4497	535	4	,	,	PUNCT
ejpam-4497	535	5	2020	2020	NUM
ejpam-4497	535	6	.	.	PUNCT
ejpam-4497	536	1	[	[	X
ejpam-4497	536	2	37	37	NUM
ejpam-4497	536	3	]	]	PUNCT
ejpam-4497	536	4	tm	tm	PROPN
ejpam-4497	536	5	al	al	PROPN
ejpam-4497	536	6	-	-	PUNCT
ejpam-4497	536	7	shami	shami	PROPN
ejpam-4497	536	8	and	and	CCONJ
ejpam-4497	536	9	j	j	PROPN
ejpam-4497	536	10	-	-	PROPN
ejpam-4497	536	11	b	b	PROPN
ejpam-4497	536	12	liu	liu	PROPN
ejpam-4497	536	13	.	.	PUNCT
ejpam-4497	537	1	two	two	NUM
ejpam-4497	537	2	classes	class	NOUN
ejpam-4497	537	3	of	of	ADP
ejpam-4497	537	4	infrasoft	infrasoft	ADJ
ejpam-4497	537	5	separation	separation	NOUN
ejpam-4497	537	6	axioms	axiom	NOUN
ejpam-4497	537	7	.	.	PUNCT
ejpam-4497	538	1	journal	journal	NOUN
ejpam-4497	538	2	of	of	ADP
ejpam-4497	538	3	mathematics	mathematic	NOUN
ejpam-4497	538	4	,	,	PUNCT
ejpam-4497	538	5	2021	2021	NUM
ejpam-4497	538	6	,	,	PUNCT
ejpam-4497	538	7	2021	2021	NUM
ejpam-4497	538	8	.	.	PUNCT
ejpam-4497	539	1	[	[	X
ejpam-4497	539	2	38	38	NUM
ejpam-4497	539	3	]	]	PUNCT
ejpam-4497	539	4	tm	tm	PROPN
ejpam-4497	539	5	al	al	PROPN
ejpam-4497	539	6	-	-	PUNCT
ejpam-4497	539	7	shami	shami	PROPN
ejpam-4497	539	8	and	and	CCONJ
ejpam-4497	539	9	a	a	DET
ejpam-4497	539	10	mhemdi	mhemdi	NOUN
ejpam-4497	539	11	.	.	PUNCT
ejpam-4497	540	1	belong	belong	VERB
ejpam-4497	540	2	and	and	CCONJ
ejpam-4497	540	3	nonbelong	nonbelong	ADJ
ejpam-4497	540	4	relations	relation	NOUN
ejpam-4497	540	5	on	on	ADP
ejpam-4497	540	6	double	double	ADJ
ejpam-4497	540	7	-	-	PUNCT
ejpam-4497	540	8	framed	frame	VERB
ejpam-4497	540	9	soft	soft	ADJ
ejpam-4497	540	10	sets	set	NOUN
ejpam-4497	540	11	and	and	CCONJ
ejpam-4497	540	12	their	their	PRON
ejpam-4497	540	13	applications	application	NOUN
ejpam-4497	540	14	.	.	PUNCT
ejpam-4497	541	1	journal	journal	NOUN
ejpam-4497	541	2	of	of	ADP
ejpam-4497	541	3	mathematics	mathematic	NOUN
ejpam-4497	541	4	,	,	PUNCT
ejpam-4497	541	5	2021	2021	NUM
ejpam-4497	541	6	,	,	PUNCT
ejpam-4497	541	7	2021	2021	NUM
ejpam-4497	541	8	.	.	PUNCT
ejpam-4497	542	1	[	[	X
ejpam-4497	542	2	39	39	NUM
ejpam-4497	542	3	]	]	PUNCT
ejpam-4497	542	4	tm	tm	PROPN
ejpam-4497	542	5	al	al	PROPN
ejpam-4497	542	6	-	-	PUNCT
ejpam-4497	542	7	shami	shami	PROPN
ejpam-4497	542	8	and	and	CCONJ
ejpam-4497	542	9	a	a	DET
ejpam-4497	542	10	mhemdi	mhemdi	NOUN
ejpam-4497	542	11	.	.	PUNCT
ejpam-4497	543	1	two	two	NUM
ejpam-4497	543	2	families	family	NOUN
ejpam-4497	543	3	of	of	ADP
ejpam-4497	543	4	separation	separation	NOUN
ejpam-4497	543	5	axioms	axiom	NOUN
ejpam-4497	543	6	on	on	ADP
ejpam-4497	543	7	infra	infra	NOUN
ejpam-4497	543	8	soft	soft	ADJ
ejpam-4497	543	9	topological	topological	ADJ
ejpam-4497	543	10	spaces	space	NOUN
ejpam-4497	543	11	.	.	PUNCT
ejpam-4497	544	1	filomat	filomat	PROPN
ejpam-4497	544	2	,	,	PUNCT
ejpam-4497	544	3	36(4):1143–1157	36(4):1143–1157	NOUN
ejpam-4497	544	4	,	,	PUNCT
ejpam-4497	544	5	2022	2022	NUM
ejpam-4497	544	6	.	.	PUNCT
ejpam-4497	545	1	references	reference	NOUN
ejpam-4497	545	2	1470	1470	NUM
ejpam-4497	545	3	[	[	X
ejpam-4497	545	4	40	40	NUM
ejpam-4497	545	5	]	]	PUNCT
ejpam-4497	545	6	tm	tm	PROPN
ejpam-4497	545	7	al	al	PROPN
ejpam-4497	545	8	-	-	PUNCT
ejpam-4497	545	9	shami	shami	PROPN
ejpam-4497	545	10	,	,	PUNCT
ejpam-4497	545	11	a	a	DET
ejpam-4497	545	12	mhemdi	mhemdi	NOUN
ejpam-4497	545	13	,	,	PUNCT
ejpam-4497	545	14	a	a	DET
ejpam-4497	545	15	rawshdeh	rawshdeh	NOUN
ejpam-4497	545	16	,	,	PUNCT
ejpam-4497	545	17	and	and	CCONJ
ejpam-4497	545	18	hh	hh	PROPN
ejpam-4497	545	19	al	al	PROPN
ejpam-4497	545	20	-	-	PUNCT
ejpam-4497	545	21	jarrah	jarrah	PROPN
ejpam-4497	545	22	.	.	PUNCT
ejpam-4497	546	1	soft	soft	ADJ
ejpam-4497	546	2	version	version	NOUN
ejpam-4497	546	3	of	of	ADP
ejpam-4497	546	4	compact	compact	ADJ
ejpam-4497	546	5	and	and	CCONJ
ejpam-4497	546	6	lindelöf	lindelöf	NOUN
ejpam-4497	546	7	spaces	space	VERB
ejpam-4497	546	8	using	use	VERB
ejpam-4497	546	9	soft	soft	ADJ
ejpam-4497	546	10	somewhere	somewhere	ADV
ejpam-4497	546	11	dense	dense	ADJ
ejpam-4497	546	12	sets	set	NOUN
ejpam-4497	546	13	.	.	PUNCT
ejpam-4497	547	1	aims	aim	VERB
ejpam-4497	547	2	math	math	NOUN
ejpam-4497	547	3	,	,	PUNCT
ejpam-4497	547	4	6(8):8064–8077	6(8):8064–8077	NOUN
ejpam-4497	547	5	,	,	PUNCT
ejpam-4497	547	6	2021	2021	NUM
ejpam-4497	547	7	.	.	PUNCT
ejpam-4497	548	1	[	[	X
ejpam-4497	548	2	41	41	NUM
ejpam-4497	548	3	]	]	PUNCT
ejpam-4497	548	4	tm	tm	PROPN
ejpam-4497	548	5	al	al	PROPN
ejpam-4497	548	6	-	-	PUNCT
ejpam-4497	548	7	shami	shami	PROPN
ejpam-4497	548	8	and	and	CCONJ
ejpam-4497	548	9	ha	ha	INTJ
ejpam-4497	548	10	othman	othman	PROPN
ejpam-4497	548	11	.	.	PUNCT
ejpam-4497	549	1	infra	infra	NOUN
ejpam-4497	549	2	pre	pre	ADJ
ejpam-4497	549	3	-	-	ADJ
ejpam-4497	549	4	open	open	ADJ
ejpam-4497	549	5	sets	set	NOUN
ejpam-4497	549	6	and	and	CCONJ
ejpam-4497	549	7	their	their	PRON
ejpam-4497	549	8	applications	application	NOUN
ejpam-4497	549	9	to	to	PART
ejpam-4497	549	10	generate	generate	VERB
ejpam-4497	549	11	new	new	ADJ
ejpam-4497	549	12	types	type	NOUN
ejpam-4497	549	13	of	of	ADP
ejpam-4497	549	14	operators	operator	NOUN
ejpam-4497	549	15	and	and	CCONJ
ejpam-4497	549	16	maps	map	NOUN
ejpam-4497	549	17	.	.	PUNCT
ejpam-4497	550	1	european	european	ADJ
ejpam-4497	550	2	journal	journal	PROPN
ejpam-4497	550	3	of	of	ADP
ejpam-4497	550	4	pure	pure	ADJ
ejpam-4497	550	5	and	and	CCONJ
ejpam-4497	550	6	applied	applied	ADJ
ejpam-4497	550	7	mathematics	mathematic	NOUN
ejpam-4497	550	8	,	,	PUNCT
ejpam-4497	550	9	15(1):261–280	15(1):261–280	NUM
ejpam-4497	550	10	,	,	PUNCT
ejpam-4497	550	11	2022	2022	NUM
ejpam-4497	550	12	.	.	PUNCT
ejpam-4497	551	1	[	[	X
ejpam-4497	551	2	42	42	NUM
ejpam-4497	551	3	]	]	PUNCT
ejpam-4497	551	4	tm	tm	PROPN
ejpam-4497	551	5	al	al	PROPN
ejpam-4497	551	6	-	-	PUNCT
ejpam-4497	551	7	shami	shami	PROPN
ejpam-4497	551	8	,	,	PUNCT
ejpam-4497	551	9	a.	a.	NOUN
ejpam-4497	551	10	tercan	tercan	PROPN
ejpam-4497	551	11	,	,	PUNCT
ejpam-4497	551	12	and	and	CCONJ
ejpam-4497	551	13	a	a	DET
ejpam-4497	551	14	mhemdi	mhemdi	NOUN
ejpam-4497	551	15	.	.	PUNCT
ejpam-4497	552	1	new	new	ADJ
ejpam-4497	552	2	soft	soft	ADJ
ejpam-4497	552	3	separation	separation	NOUN
ejpam-4497	552	4	axioms	axiom	NOUN
ejpam-4497	552	5	and	and	CCONJ
ejpam-4497	552	6	fixed	fix	VERB
ejpam-4497	552	7	soft	soft	ADJ
ejpam-4497	552	8	points	point	NOUN
ejpam-4497	552	9	with	with	ADP
ejpam-4497	552	10	respect	respect	NOUN
ejpam-4497	552	11	to	to	ADP
ejpam-4497	552	12	total	total	ADJ
ejpam-4497	552	13	belong	belong	NOUN
ejpam-4497	552	14	and	and	CCONJ
ejpam-4497	552	15	total	total	ADJ
ejpam-4497	552	16	non	non	ADJ
ejpam-4497	552	17	-	-	ADJ
ejpam-4497	552	18	belong	belong	ADJ
ejpam-4497	552	19	relations	relation	NOUN
ejpam-4497	552	20	.	.	PUNCT
ejpam-4497	553	1	demonstratio	demonstratio	PROPN
ejpam-4497	553	2	mathematica	mathematica	PROPN
ejpam-4497	553	3	,	,	PUNCT
ejpam-4497	553	4	54(1):196–211	54(1):196–211	PROPN
ejpam-4497	553	5	,	,	PUNCT
ejpam-4497	553	6	2021	2021	NUM
ejpam-4497	553	7	.	.	PUNCT
ejpam-4497	554	1	[	[	X
ejpam-4497	554	2	43	43	NUM
ejpam-4497	554	3	]	]	X
ejpam-4497	554	4	jcr	jcr	PROPN
ejpam-4497	554	5	alcantud	alcantud	PROPN
ejpam-4497	554	6	,	,	PUNCT
ejpam-4497	554	7	tm	tm	PROPN
ejpam-4497	554	8	al	al	PROPN
ejpam-4497	554	9	-	-	PUNCT
ejpam-4497	554	10	shami	shami	PROPN
ejpam-4497	554	11	,	,	PUNCT
ejpam-4497	554	12	and	and	CCONJ
ejpam-4497	554	13	aa	aa	PROPN
ejpam-4497	554	14	azzam	azzam	PROPN
ejpam-4497	554	15	.	.	PROPN
ejpam-4497	555	1	caliber	caliber	PROPN
ejpam-4497	555	2	and	and	CCONJ
ejpam-4497	555	3	chain	chain	NOUN
ejpam-4497	555	4	conditions	condition	NOUN
ejpam-4497	555	5	in	in	ADP
ejpam-4497	555	6	soft	soft	ADJ
ejpam-4497	555	7	topologies	topology	NOUN
ejpam-4497	555	8	.	.	PUNCT
ejpam-4497	556	1	mathematics	mathematic	NOUN
ejpam-4497	556	2	,	,	PUNCT
ejpam-4497	556	3	9(19	9(19	NUM
ejpam-4497	556	4	)	)	PUNCT
ejpam-4497	556	5	,	,	PUNCT
ejpam-4497	556	6	2021	2021	NUM
ejpam-4497	556	7	.	.	PUNCT
ejpam-4497	557	1	[	[	X
ejpam-4497	557	2	44	44	NUM
ejpam-4497	557	3	]	]	SYM
ejpam-4497	557	4	mi	mi	PROPN
ejpam-4497	557	5	ali	ali	PROPN
ejpam-4497	557	6	,	,	PUNCT
ejpam-4497	557	7	f	f	PROPN
ejpam-4497	557	8	feng	feng	PROPN
ejpam-4497	557	9	,	,	PUNCT
ejpam-4497	557	10	x	x	PROPN
ejpam-4497	557	11	liu	liu	PROPN
ejpam-4497	557	12	,	,	PUNCT
ejpam-4497	557	13	wk	wk	X
ejpam-4497	557	14	min	min	NOUN
ejpam-4497	557	15	,	,	PUNCT
ejpam-4497	557	16	and	and	CCONJ
ejpam-4497	557	17	m	m	PROPN
ejpam-4497	557	18	shabir	shabir	PROPN
ejpam-4497	557	19	.	.	PUNCT
ejpam-4497	558	1	on	on	ADP
ejpam-4497	558	2	some	some	DET
ejpam-4497	558	3	new	new	ADJ
ejpam-4497	558	4	operations	operation	NOUN
ejpam-4497	558	5	in	in	ADP
ejpam-4497	558	6	soft	soft	ADJ
ejpam-4497	558	7	set	set	NOUN
ejpam-4497	558	8	theory	theory	NOUN
ejpam-4497	558	9	.	.	PUNCT
ejpam-4497	559	1	computers	computer	NOUN
ejpam-4497	559	2	&	&	CCONJ
ejpam-4497	559	3	mathematics	mathematics	PROPN
ejpam-4497	559	4	with	with	ADP
ejpam-4497	559	5	applications	application	NOUN
ejpam-4497	559	6	,	,	PUNCT
ejpam-4497	559	7	57(9):1547–1553	57(9):1547–1553	NUM
ejpam-4497	559	8	,	,	PUNCT
ejpam-4497	559	9	2009	2009	NUM
ejpam-4497	559	10	.	.	PUNCT
ejpam-4497	560	1	[	[	X
ejpam-4497	560	2	45	45	NUM
ejpam-4497	560	3	]	]	PUNCT
ejpam-4497	560	4	za	za	PROPN
ejpam-4497	560	5	ameen	ameen	PROPN
ejpam-4497	560	6	,	,	PUNCT
ejpam-4497	560	7	tm	tm	PROPN
ejpam-4497	560	8	al	al	PROPN
ejpam-4497	560	9	-	-	PUNCT
ejpam-4497	560	10	shami	shami	PROPN
ejpam-4497	560	11	,	,	PUNCT
ejpam-4497	560	12	m	m	VERB
ejpam-4497	560	13	abdelwaheb	abdelwaheb	NOUN
ejpam-4497	560	14	,	,	PUNCT
ejpam-4497	560	15	and	and	CCONJ
ejpam-4497	560	16	me	i	PRON
ejpam-4497	560	17	el	el	PROPN
ejpam-4497	560	18	-	-	PUNCT
ejpam-4497	560	19	shafei	shafei	NOUN
ejpam-4497	560	20	.	.	PUNCT
ejpam-4497	561	1	the	the	DET
ejpam-4497	561	2	role	role	NOUN
ejpam-4497	561	3	of	of	ADP
ejpam-4497	561	4	soft	soft	ADJ
ejpam-4497	561	5	θtopological	θtopological	ADJ
ejpam-4497	561	6	operators	operator	NOUN
ejpam-4497	561	7	in	in	ADP
ejpam-4497	561	8	characterizing	characterize	VERB
ejpam-4497	561	9	various	various	ADJ
ejpam-4497	561	10	soft	soft	ADJ
ejpam-4497	561	11	separation	separation	NOUN
ejpam-4497	561	12	axioms	axiom	NOUN
ejpam-4497	561	13	.	.	PUNCT
ejpam-4497	562	1	journal	journal	NOUN
ejpam-4497	562	2	of	of	ADP
ejpam-4497	562	3	mathematics	mathematic	NOUN
ejpam-4497	562	4	,	,	PUNCT
ejpam-4497	562	5	2022:7	2022:7	NUM
ejpam-4497	562	6	pages	page	NOUN
ejpam-4497	562	7	,	,	PUNCT
ejpam-4497	562	8	2022	2022	NUM
ejpam-4497	562	9	.	.	PUNCT
ejpam-4497	563	1	[	[	X
ejpam-4497	563	2	46	46	NUM
ejpam-4497	563	3	]	]	PUNCT
ejpam-4497	563	4	za	za	PROPN
ejpam-4497	563	5	ameen	ameen	PROPN
ejpam-4497	563	6	,	,	PUNCT
ejpam-4497	563	7	aa	aa	PROPN
ejpam-4497	563	8	azzam	azzam	PROPN
ejpam-4497	563	9	,	,	PUNCT
ejpam-4497	563	10	tm	tm	PROPN
ejpam-4497	563	11	al	al	PROPN
ejpam-4497	563	12	-	-	PUNCT
ejpam-4497	563	13	shami	shami	PROPN
ejpam-4497	563	14	,	,	PUNCT
ejpam-4497	563	15	and	and	CCONJ
ejpam-4497	563	16	me	i	PRON
ejpam-4497	563	17	el	el	PROPN
ejpam-4497	563	18	-	-	PUNCT
ejpam-4497	563	19	shafei	shafei	NOUN
ejpam-4497	563	20	.	.	PUNCT
ejpam-4497	564	1	generating	generate	VERB
ejpam-4497	564	2	soft	soft	ADJ
ejpam-4497	564	3	topologies	topology	NOUN
ejpam-4497	564	4	via	via	ADP
ejpam-4497	564	5	soft	soft	ADJ
ejpam-4497	564	6	set	set	ADJ
ejpam-4497	564	7	operators	operator	NOUN
ejpam-4497	564	8	.	.	PUNCT
ejpam-4497	565	1	symmetry	symmetry	PROPN
ejpam-4497	565	2	,	,	PUNCT
ejpam-4497	565	3	14(5	14(5	NUM
ejpam-4497	565	4	)	)	PUNCT
ejpam-4497	565	5	,	,	PUNCT
ejpam-4497	565	6	2022	2022	NUM
ejpam-4497	565	7	.	.	PUNCT
ejpam-4497	566	1	[	[	X
ejpam-4497	566	2	47	47	NUM
ejpam-4497	566	3	]	]	X
ejpam-4497	566	4	cg	cg	NOUN
ejpam-4497	566	5	.	.	PUNCT
ejpam-4497	566	6	aras	aras	PROPN
ejpam-4497	566	7	,	,	PUNCT
ejpam-4497	566	8	tm	tm	PROPN
ejpam-4497	566	9	al	al	PROPN
ejpam-4497	566	10	-	-	PUNCT
ejpam-4497	566	11	shami	shami	PROPN
ejpam-4497	566	12	,	,	PUNCT
ejpam-4497	566	13	a	a	DET
ejpam-4497	566	14	mhemdi	mhemdi	NOUN
ejpam-4497	566	15	,	,	PUNCT
ejpam-4497	566	16	and	and	CCONJ
ejpam-4497	566	17	s	s	VERB
ejpam-4497	566	18	bayramov	bayramov	ADJ
ejpam-4497	566	19	.	.	PUNCT
ejpam-4497	567	1	local	local	ADJ
ejpam-4497	567	2	compactness	compactness	NOUN
ejpam-4497	567	3	and	and	CCONJ
ejpam-4497	567	4	paracompactness	paracompactness	NOUN
ejpam-4497	567	5	on	on	ADP
ejpam-4497	567	6	bipolar	bipolar	ADJ
ejpam-4497	567	7	soft	soft	ADJ
ejpam-4497	567	8	topological	topological	ADJ
ejpam-4497	567	9	spaces	space	NOUN
ejpam-4497	567	10	.	.	PUNCT
ejpam-4497	568	1	journal	journal	NOUN
ejpam-4497	568	2	of	of	ADP
ejpam-4497	568	3	intelligent	intelligent	ADJ
ejpam-4497	568	4	and	and	CCONJ
ejpam-4497	568	5	fuzzy	fuzzy	ADJ
ejpam-4497	568	6	systems	system	NOUN
ejpam-4497	568	7	,	,	PUNCT
ejpam-4497	568	8	43(5):6755–6763	43(5):6755–6763	PROPN
ejpam-4497	568	9	.	.	PUNCT
ejpam-4497	569	1	[	[	X
ejpam-4497	569	2	48	48	NUM
ejpam-4497	569	3	]	]	PUNCT
ejpam-4497	569	4	ba	ba	PROPN
ejpam-4497	569	5	asaad	asaad	NOUN
ejpam-4497	569	6	,	,	PUNCT
ejpam-4497	569	7	tm	tm	PROPN
ejpam-4497	569	8	al	al	PROPN
ejpam-4497	569	9	-	-	PUNCT
ejpam-4497	569	10	shami	shami	PROPN
ejpam-4497	569	11	,	,	PUNCT
ejpam-4497	569	12	and	and	CCONJ
ejpam-4497	569	13	a	a	DET
ejpam-4497	569	14	mhemdi	mhemdi	NOUN
ejpam-4497	569	15	.	.	PUNCT
ejpam-4497	570	1	bioperators	bioperator	NOUN
ejpam-4497	570	2	on	on	ADP
ejpam-4497	570	3	soft	soft	ADJ
ejpam-4497	570	4	topological	topological	ADJ
ejpam-4497	570	5	spaces	space	NOUN
ejpam-4497	570	6	.	.	PUNCT
ejpam-4497	571	1	aims	aim	VERB
ejpam-4497	571	2	mathematics	mathematic	NOUN
ejpam-4497	571	3	,	,	PUNCT
ejpam-4497	571	4	6(11):12471–12490	6(11):12471–12490	NUM
ejpam-4497	571	5	,	,	PUNCT
ejpam-4497	571	6	2021	2021	NUM
ejpam-4497	571	7	.	.	PUNCT
ejpam-4497	572	1	[	[	X
ejpam-4497	572	2	49	49	NUM
ejpam-4497	572	3	]	]	PUNCT
ejpam-4497	572	4	a.	a.	NOUN
ejpam-4497	572	5	aygünoğlu	aygünoğlu	PROPN
ejpam-4497	572	6	and	and	CCONJ
ejpam-4497	572	7	h.	h.	PROPN
ejpam-4497	572	8	aygün	aygün	PROPN
ejpam-4497	572	9	.	.	PUNCT
ejpam-4497	573	1	some	some	DET
ejpam-4497	573	2	notes	note	NOUN
ejpam-4497	573	3	on	on	ADP
ejpam-4497	573	4	soft	soft	ADJ
ejpam-4497	573	5	topological	topological	ADJ
ejpam-4497	573	6	spaces	space	NOUN
ejpam-4497	573	7	.	.	PUNCT
ejpam-4497	574	1	neural	neural	ADJ
ejpam-4497	574	2	computing	computing	NOUN
ejpam-4497	574	3	and	and	CCONJ
ejpam-4497	574	4	applications	application	NOUN
ejpam-4497	574	5	,	,	PUNCT
ejpam-4497	574	6	21(1):113–119	21(1):113–119	NUM
ejpam-4497	574	7	,	,	PUNCT
ejpam-4497	574	8	2012	2012	NUM
ejpam-4497	574	9	.	.	PUNCT
ejpam-4497	575	1	[	[	X
ejpam-4497	575	2	50	50	NUM
ejpam-4497	575	3	]	]	X
ejpam-4497	575	4	n.	n.	PROPN
ejpam-4497	575	5	çağman	çağman	PROPN
ejpam-4497	575	6	and	and	CCONJ
ejpam-4497	575	7	s.	s.	PROPN
ejpam-4497	575	8	enginoğlu	enginoğlu	PROPN
ejpam-4497	575	9	.	.	PUNCT
ejpam-4497	575	10	soft	soft	ADJ
ejpam-4497	575	11	matrix	matrix	NOUN
ejpam-4497	575	12	theory	theory	NOUN
ejpam-4497	575	13	and	and	CCONJ
ejpam-4497	575	14	its	its	PRON
ejpam-4497	575	15	decision	decision	NOUN
ejpam-4497	575	16	making	making	NOUN
ejpam-4497	575	17	.	.	PUNCT
ejpam-4497	576	1	computers	computer	NOUN
ejpam-4497	576	2	&	&	CCONJ
ejpam-4497	576	3	mathematics	mathematics	PROPN
ejpam-4497	576	4	with	with	ADP
ejpam-4497	576	5	applications	application	NOUN
ejpam-4497	576	6	,	,	PUNCT
ejpam-4497	576	7	59(10):3308–3314	59(10):3308–3314	PROPN
ejpam-4497	576	8	,	,	PUNCT
ejpam-4497	576	9	2010	2010	NUM
ejpam-4497	576	10	.	.	PUNCT
ejpam-4497	577	1	[	[	X
ejpam-4497	577	2	51	51	NUM
ejpam-4497	577	3	]	]	PUNCT
ejpam-4497	577	4	n	n	PRON
ejpam-4497	577	5	çağman	çağman	NOUN
ejpam-4497	577	6	,	,	PUNCT
ejpam-4497	577	7	s	s	VERB
ejpam-4497	577	8	karataş	karataş	PROPN
ejpam-4497	577	9	,	,	PUNCT
ejpam-4497	577	10	and	and	CCONJ
ejpam-4497	577	11	s	s	VERB
ejpam-4497	577	12	enginoglu	enginoglu	NOUN
ejpam-4497	577	13	.	.	PUNCT
ejpam-4497	578	1	on	on	ADP
ejpam-4497	578	2	soft	soft	ADJ
ejpam-4497	578	3	topology	topology	NOUN
ejpam-4497	578	4	.	.	PUNCT
ejpam-4497	579	1	computers	computer	NOUN
ejpam-4497	579	2	&	&	CCONJ
ejpam-4497	579	3	mathematics	mathematics	PROPN
ejpam-4497	579	4	with	with	ADP
ejpam-4497	579	5	applications	application	NOUN
ejpam-4497	579	6	,	,	PUNCT
ejpam-4497	579	7	62:351–358	62:351–358	PROPN
ejpam-4497	579	8	,	,	PUNCT
ejpam-4497	579	9	2011	2011	NUM
ejpam-4497	579	10	.	.	PUNCT
ejpam-4497	580	1	[	[	X
ejpam-4497	580	2	52	52	NUM
ejpam-4497	580	3	]	]	PUNCT
ejpam-4497	580	4	me	i	PRON
ejpam-4497	580	5	el	el	PROPN
ejpam-4497	580	6	-	-	PUNCT
ejpam-4497	580	7	shafei	shafei	PROPN
ejpam-4497	580	8	,	,	PUNCT
ejpam-4497	580	9	m	m	NOUN
ejpam-4497	580	10	abo	abo	NOUN
ejpam-4497	580	11	-	-	PUNCT
ejpam-4497	580	12	elhamayel	elhamayel	NOUN
ejpam-4497	580	13	,	,	PUNCT
ejpam-4497	580	14	and	and	CCONJ
ejpam-4497	580	15	tm	tm	PROPN
ejpam-4497	580	16	al	al	PROPN
ejpam-4497	580	17	-	-	PUNCT
ejpam-4497	580	18	shami	shami	PROPN
ejpam-4497	580	19	.	.	PUNCT
ejpam-4497	581	1	partial	partial	ADJ
ejpam-4497	581	2	soft	soft	ADJ
ejpam-4497	581	3	separation	separation	NOUN
ejpam-4497	581	4	axioms	axiom	NOUN
ejpam-4497	581	5	and	and	CCONJ
ejpam-4497	581	6	soft	soft	ADJ
ejpam-4497	581	7	compact	compact	ADJ
ejpam-4497	581	8	spaces	space	NOUN
ejpam-4497	581	9	.	.	PUNCT
ejpam-4497	582	1	filomat	filomat	NOUN
ejpam-4497	582	2	,	,	PUNCT
ejpam-4497	582	3	32(13):4755–4771	32(13):4755–4771	NUM
ejpam-4497	582	4	,	,	PUNCT
ejpam-4497	582	5	2018	2018	NUM
ejpam-4497	582	6	.	.	PUNCT
ejpam-4497	583	1	[	[	X
ejpam-4497	583	2	53	53	NUM
ejpam-4497	583	3	]	]	PUNCT
ejpam-4497	583	4	me	i	PRON
ejpam-4497	583	5	el	el	PROPN
ejpam-4497	583	6	-	-	PROPN
ejpam-4497	583	7	shafei	shafei	PROPN
ejpam-4497	583	8	and	and	CCONJ
ejpam-4497	583	9	tm	tm	PROPN
ejpam-4497	583	10	al	al	PROPN
ejpam-4497	583	11	-	-	PUNCT
ejpam-4497	583	12	shami	shami	PROPN
ejpam-4497	583	13	.	.	PUNCT
ejpam-4497	584	1	applications	application	NOUN
ejpam-4497	584	2	of	of	ADP
ejpam-4497	584	3	partial	partial	ADJ
ejpam-4497	584	4	belong	belong	NOUN
ejpam-4497	584	5	and	and	CCONJ
ejpam-4497	584	6	total	total	ADJ
ejpam-4497	584	7	non	non	ADJ
ejpam-4497	584	8	-	-	ADJ
ejpam-4497	584	9	belong	belong	ADJ
ejpam-4497	584	10	relations	relation	NOUN
ejpam-4497	584	11	on	on	ADP
ejpam-4497	584	12	soft	soft	ADJ
ejpam-4497	584	13	separation	separation	NOUN
ejpam-4497	584	14	axioms	axiom	NOUN
ejpam-4497	584	15	and	and	CCONJ
ejpam-4497	584	16	decision	decision	NOUN
ejpam-4497	584	17	-	-	PUNCT
ejpam-4497	584	18	making	make	VERB
ejpam-4497	584	19	problem	problem	NOUN
ejpam-4497	584	20	.	.	PUNCT
ejpam-4497	585	1	computational	computational	ADJ
ejpam-4497	585	2	and	and	CCONJ
ejpam-4497	585	3	applied	applied	ADJ
ejpam-4497	585	4	mathematics	mathematic	NOUN
ejpam-4497	585	5	,	,	PUNCT
ejpam-4497	585	6	39(3):1–17	39(3):1–17	NUM
ejpam-4497	585	7	,	,	PUNCT
ejpam-4497	585	8	2020	2020	NUM
ejpam-4497	585	9	.	.	PUNCT
ejpam-4497	586	1	references	reference	NOUN
ejpam-4497	586	2	1471	1471	NUM
ejpam-4497	587	1	[	[	X
ejpam-4497	587	2	54	54	NUM
ejpam-4497	587	3	]	]	PUNCT
ejpam-4497	587	4	me	i	PRON
ejpam-4497	588	1	el	el	PROPN
ejpam-4497	588	2	-	-	PROPN
ejpam-4497	588	3	shafei	shafei	PROPN
ejpam-4497	588	4	and	and	CCONJ
ejpam-4497	588	5	tm	tm	PROPN
ejpam-4497	588	6	al	al	PROPN
ejpam-4497	588	7	-	-	PUNCT
ejpam-4497	588	8	shami	shami	PROPN
ejpam-4497	588	9	.	.	PUNCT
ejpam-4497	589	1	some	some	DET
ejpam-4497	589	2	operators	operator	NOUN
ejpam-4497	589	3	of	of	ADP
ejpam-4497	589	4	a	a	DET
ejpam-4497	589	5	soft	soft	ADJ
ejpam-4497	589	6	set	set	NOUN
ejpam-4497	589	7	and	and	CCONJ
ejpam-4497	589	8	soft	soft	ADJ
ejpam-4497	589	9	connected	connected	ADJ
ejpam-4497	589	10	spaces	space	NOUN
ejpam-4497	589	11	using	use	VERB
ejpam-4497	589	12	soft	soft	ADJ
ejpam-4497	589	13	somewhere	somewhere	ADV
ejpam-4497	589	14	dense	dense	ADJ
ejpam-4497	589	15	sets	set	NOUN
ejpam-4497	589	16	.	.	PUNCT
ejpam-4497	590	1	journal	journal	NOUN
ejpam-4497	590	2	of	of	ADP
ejpam-4497	590	3	interdisciplinary	interdisciplinary	ADJ
ejpam-4497	590	4	mathematics	mathematic	NOUN
ejpam-4497	590	5	,	,	PUNCT
ejpam-4497	590	6	24(6):1471–1495	24(6):1471–1495	NUM
ejpam-4497	590	7	,	,	PUNCT
ejpam-4497	590	8	2021	2021	NUM
ejpam-4497	590	9	.	.	PUNCT
ejpam-4497	591	1	[	[	X
ejpam-4497	591	2	55	55	NUM
ejpam-4497	591	3	]	]	X
ejpam-4497	591	4	f	f	PROPN
ejpam-4497	591	5	feng	feng	PROPN
ejpam-4497	591	6	,	,	PUNCT
ejpam-4497	591	7	c	c	PROPN
ejpam-4497	591	8	li	li	PROPN
ejpam-4497	591	9	,	,	PUNCT
ejpam-4497	591	10	b	b	PROPN
ejpam-4497	591	11	davvaz	davvaz	NOUN
ejpam-4497	591	12	,	,	PUNCT
ejpam-4497	591	13	and	and	CCONJ
ejpam-4497	591	14	mi	mi	PROPN
ejpam-4497	591	15	ali	ali	PROPN
ejpam-4497	591	16	.	.	PROPN
ejpam-4497	591	17	soft	soft	ADJ
ejpam-4497	591	18	sets	set	NOUN
ejpam-4497	591	19	combined	combine	VERB
ejpam-4497	591	20	with	with	ADP
ejpam-4497	591	21	fuzzy	fuzzy	ADJ
ejpam-4497	591	22	sets	set	NOUN
ejpam-4497	591	23	and	and	CCONJ
ejpam-4497	591	24	rough	rough	ADJ
ejpam-4497	591	25	sets	set	NOUN
ejpam-4497	591	26	:	:	PUNCT
ejpam-4497	591	27	a	a	DET
ejpam-4497	591	28	tentative	tentative	ADJ
ejpam-4497	591	29	approach	approach	NOUN
ejpam-4497	591	30	.	.	PUNCT
ejpam-4497	592	1	soft	soft	ADJ
ejpam-4497	592	2	computing	computing	NOUN
ejpam-4497	592	3	,	,	PUNCT
ejpam-4497	592	4	14(9):899–911	14(9):899–911	PROPN
ejpam-4497	592	5	,	,	PUNCT
ejpam-4497	592	6	2010	2010	NUM
ejpam-4497	592	7	.	.	PUNCT
ejpam-4497	593	1	[	[	X
ejpam-4497	593	2	56	56	NUM
ejpam-4497	593	3	]	]	X
ejpam-4497	593	4	ra	ra	PROPN
ejpam-4497	593	5	hosny	hosny	PROPN
ejpam-4497	593	6	,	,	PUNCT
ejpam-4497	593	7	ba	ba	PROPN
ejpam-4497	593	8	asaad	asaad	NOUN
ejpam-4497	593	9	,	,	PUNCT
ejpam-4497	593	10	aa	aa	PROPN
ejpam-4497	593	11	azzam	azzam	PROPN
ejpam-4497	593	12	,	,	PUNCT
ejpam-4497	593	13	and	and	CCONJ
ejpam-4497	593	14	tm	tm	PROPN
ejpam-4497	593	15	al	al	PROPN
ejpam-4497	593	16	-	-	PUNCT
ejpam-4497	593	17	shami	shami	PROPN
ejpam-4497	593	18	.	.	PUNCT
ejpam-4497	594	1	various	various	ADJ
ejpam-4497	594	2	topologies	topology	NOUN
ejpam-4497	594	3	generated	generate	VERB
ejpam-4497	594	4	from	from	ADP
ejpam-4497	594	5	-	-	PUNCT
ejpam-4497	594	6	neighbourhoods	neighbourhood	NOUN
ejpam-4497	594	7	via	via	ADP
ejpam-4497	594	8	ideals	ideal	NOUN
ejpam-4497	594	9	.	.	PUNCT
ejpam-4497	595	1	complexity	complexity	NOUN
ejpam-4497	595	2	,	,	PUNCT
ejpam-4497	595	3	2021	2021	NUM
ejpam-4497	595	4	,	,	PUNCT
ejpam-4497	595	5	2021	2021	NUM
ejpam-4497	595	6	.	.	PUNCT
ejpam-4497	596	1	[	[	X
ejpam-4497	596	2	57	57	NUM
ejpam-4497	596	3	]	]	X
ejpam-4497	596	4	s	s	AUX
ejpam-4497	596	5	hussain	hussain	NOUN
ejpam-4497	596	6	.	.	PUNCT
ejpam-4497	597	1	binary	binary	ADJ
ejpam-4497	597	2	soft	soft	ADJ
ejpam-4497	597	3	connected	connect	VERB
ejpam-4497	597	4	spaces	space	NOUN
ejpam-4497	597	5	and	and	CCONJ
ejpam-4497	597	6	an	an	DET
ejpam-4497	597	7	application	application	NOUN
ejpam-4497	597	8	of	of	ADP
ejpam-4497	597	9	binary	binary	ADJ
ejpam-4497	597	10	soft	soft	ADJ
ejpam-4497	597	11	sets	set	NOUN
ejpam-4497	597	12	in	in	ADP
ejpam-4497	597	13	decision	decision	NOUN
ejpam-4497	597	14	making	making	NOUN
ejpam-4497	597	15	problem	problem	NOUN
ejpam-4497	597	16	.	.	PUNCT
ejpam-4497	598	1	fuzzy	fuzzy	ADJ
ejpam-4497	598	2	information	information	NOUN
ejpam-4497	598	3	and	and	CCONJ
ejpam-4497	598	4	engineering	engineering	NOUN
ejpam-4497	598	5	,	,	PUNCT
ejpam-4497	598	6	11(4):506–521	11(4):506–521	NUM
ejpam-4497	598	7	,	,	PUNCT
ejpam-4497	598	8	2019	2019	NUM
ejpam-4497	598	9	.	.	PUNCT
ejpam-4497	599	1	[	[	X
ejpam-4497	599	2	58	58	NUM
ejpam-4497	599	3	]	]	PUNCT
ejpam-4497	599	4	a	a	DET
ejpam-4497	599	5	kharal	kharal	ADJ
ejpam-4497	599	6	and	and	CCONJ
ejpam-4497	599	7	b	b	PROPN
ejpam-4497	599	8	ahmad	ahmad	PROPN
ejpam-4497	599	9	.	.	PUNCT
ejpam-4497	599	10	mappings	mapping	NOUN
ejpam-4497	599	11	on	on	ADP
ejpam-4497	599	12	soft	soft	ADJ
ejpam-4497	599	13	classes	class	NOUN
ejpam-4497	599	14	.	.	PUNCT
ejpam-4497	600	1	new	new	ADJ
ejpam-4497	600	2	mathematics	mathematic	NOUN
ejpam-4497	600	3	and	and	CCONJ
ejpam-4497	600	4	natural	natural	ADJ
ejpam-4497	600	5	computation	computation	NOUN
ejpam-4497	600	6	,	,	PUNCT
ejpam-4497	600	7	7(03):471–481	7(03):471–481	NUM
ejpam-4497	600	8	,	,	PUNCT
ejpam-4497	600	9	2011	2011	NUM
ejpam-4497	600	10	.	.	PUNCT
ejpam-4497	601	1	[	[	X
ejpam-4497	601	2	59	59	NUM
ejpam-4497	601	3	]	]	PUNCT
ejpam-4497	601	4	ldr	ldr	PROPN
ejpam-4497	601	5	kočinac	kočinac	PROPN
ejpam-4497	601	6	,	,	PUNCT
ejpam-4497	601	7	tm	tm	PROPN
ejpam-4497	601	8	al	al	PROPN
ejpam-4497	601	9	-	-	PUNCT
ejpam-4497	601	10	shami	shami	PROPN
ejpam-4497	601	11	,	,	PUNCT
ejpam-4497	601	12	and	and	CCONJ
ejpam-4497	601	13	v	v	ADP
ejpam-4497	601	14	çetkin	çetkin	PROPN
ejpam-4497	601	15	.	.	PUNCT
ejpam-4497	602	1	selection	selection	NOUN
ejpam-4497	602	2	principles	principle	NOUN
ejpam-4497	602	3	in	in	ADP
ejpam-4497	602	4	the	the	DET
ejpam-4497	602	5	context	context	NOUN
ejpam-4497	602	6	of	of	ADP
ejpam-4497	602	7	soft	soft	ADJ
ejpam-4497	602	8	sets	set	NOUN
ejpam-4497	602	9	:	:	PUNCT
ejpam-4497	602	10	menger	menger	PROPN
ejpam-4497	602	11	spaces	space	VERB
ejpam-4497	602	12	.	.	PUNCT
ejpam-4497	603	1	soft	soft	ADJ
ejpam-4497	603	2	computing	computing	NOUN
ejpam-4497	603	3	,	,	PUNCT
ejpam-4497	603	4	25(20):12693–12702	25(20):12693–12702	NUM
ejpam-4497	603	5	,	,	PUNCT
ejpam-4497	603	6	2021	2021	NUM
ejpam-4497	603	7	.	.	PUNCT
ejpam-4497	604	1	[	[	X
ejpam-4497	604	2	60	60	NUM
ejpam-4497	604	3	]	]	X
ejpam-4497	604	4	f	f	PROPN
ejpam-4497	604	5	lin	lin	PROPN
ejpam-4497	604	6	.	.	PUNCT
ejpam-4497	605	1	soft	soft	ADJ
ejpam-4497	605	2	connected	connect	VERB
ejpam-4497	605	3	spaces	space	NOUN
ejpam-4497	605	4	and	and	CCONJ
ejpam-4497	605	5	soft	soft	ADJ
ejpam-4497	605	6	paracompact	paracompact	ADJ
ejpam-4497	605	7	spaces	space	NOUN
ejpam-4497	605	8	.	.	PUNCT
ejpam-4497	606	1	international	international	ADJ
ejpam-4497	606	2	journal	journal	PROPN
ejpam-4497	606	3	of	of	ADP
ejpam-4497	606	4	mathematical	mathematical	ADJ
ejpam-4497	606	5	and	and	CCONJ
ejpam-4497	606	6	computational	computational	ADJ
ejpam-4497	606	7	sciences	science	NOUN
ejpam-4497	606	8	,	,	PUNCT
ejpam-4497	606	9	7(2):277–283	7(2):277–283	NUM
ejpam-4497	606	10	,	,	PUNCT
ejpam-4497	606	11	2013	2013	NUM
ejpam-4497	606	12	.	.	PUNCT
ejpam-4497	607	1	[	[	X
ejpam-4497	607	2	61	61	NUM
ejpam-4497	607	3	]	]	SYM
ejpam-4497	607	4	pk	pk	NOUN
ejpam-4497	607	5	maji	maji	NOUN
ejpam-4497	607	6	,	,	PUNCT
ejpam-4497	607	7	r	r	NOUN
ejpam-4497	607	8	biswas	biswas	PROPN
ejpam-4497	607	9	,	,	PUNCT
ejpam-4497	607	10	and	and	CCONJ
ejpam-4497	607	11	ar	ar	PROPN
ejpam-4497	607	12	roy	roy	PROPN
ejpam-4497	607	13	.	.	PROPN
ejpam-4497	607	14	soft	soft	ADJ
ejpam-4497	607	15	set	set	NOUN
ejpam-4497	607	16	theory	theory	NOUN
ejpam-4497	607	17	.	.	PUNCT
ejpam-4497	608	1	computers	computer	NOUN
ejpam-4497	608	2	&	&	CCONJ
ejpam-4497	608	3	mathematics	mathematics	PROPN
ejpam-4497	608	4	with	with	ADP
ejpam-4497	608	5	applications	application	NOUN
ejpam-4497	608	6	,	,	PUNCT
ejpam-4497	608	7	45(4	45(4	NOUN
ejpam-4497	608	8	-	-	PUNCT
ejpam-4497	608	9	5):555–562	5):555–562	NUM
ejpam-4497	608	10	,	,	PUNCT
ejpam-4497	608	11	2003	2003	NUM
ejpam-4497	608	12	.	.	PUNCT
ejpam-4497	609	1	[	[	X
ejpam-4497	609	2	62	62	NUM
ejpam-4497	609	3	]	]	PUNCT
ejpam-4497	609	4	d	d	X
ejpam-4497	609	5	molodtsov	molodtsov	PROPN
ejpam-4497	609	6	.	.	PUNCT
ejpam-4497	610	1	soft	soft	ADJ
ejpam-4497	610	2	set	set	VERB
ejpam-4497	610	3	theoryfirst	theoryfirst	NOUN
ejpam-4497	610	4	results	result	NOUN
ejpam-4497	610	5	.	.	PUNCT
ejpam-4497	611	1	computers	computer	NOUN
ejpam-4497	611	2	&	&	CCONJ
ejpam-4497	611	3	mathematics	mathematics	PROPN
ejpam-4497	611	4	with	with	ADP
ejpam-4497	611	5	applications	application	NOUN
ejpam-4497	611	6	,	,	PUNCT
ejpam-4497	611	7	37(4	37(4	PROPN
ejpam-4497	611	8	-	-	PUNCT
ejpam-4497	611	9	5):19–31	5):19–31	NUM
ejpam-4497	611	10	,	,	PUNCT
ejpam-4497	611	11	1999	1999	NUM
ejpam-4497	611	12	.	.	PUNCT
ejpam-4497	612	1	[	[	X
ejpam-4497	612	2	63	63	NUM
ejpam-4497	612	3	]	]	PUNCT
ejpam-4497	612	4	sk	sk	X
ejpam-4497	612	5	nazmul	nazmul	PROPN
ejpam-4497	612	6	and	and	CCONJ
ejpam-4497	612	7	sk	sk	ADP
ejpam-4497	612	8	samanta	samanta	PROPN
ejpam-4497	612	9	.	.	PUNCT
ejpam-4497	613	1	neighbourhood	neighbourhood	NOUN
ejpam-4497	613	2	properties	property	NOUN
ejpam-4497	613	3	of	of	ADP
ejpam-4497	613	4	soft	soft	ADJ
ejpam-4497	613	5	topological	topological	ADJ
ejpam-4497	613	6	spaces	space	NOUN
ejpam-4497	613	7	.	.	PUNCT
ejpam-4497	614	1	annals	annal	NOUN
ejpam-4497	614	2	of	of	ADP
ejpam-4497	614	3	fuzzy	fuzzy	ADJ
ejpam-4497	614	4	mathematics	mathematic	NOUN
ejpam-4497	614	5	and	and	CCONJ
ejpam-4497	614	6	informatics	informatic	NOUN
ejpam-4497	614	7	,	,	PUNCT
ejpam-4497	614	8	6(1):1–15	6(1):1–15	NUM
ejpam-4497	614	9	,	,	PUNCT
ejpam-4497	614	10	2013	2013	NUM
ejpam-4497	614	11	.	.	PUNCT
ejpam-4497	615	1	[	[	X
ejpam-4497	615	2	64	64	NUM
ejpam-4497	615	3	]	]	PUNCT
ejpam-4497	615	4	as	as	ADP
ejpam-4497	615	5	salama	salama	NOUN
ejpam-4497	615	6	,	,	PUNCT
ejpam-4497	615	7	a	a	DET
ejpam-4497	615	8	mhemdi	mhemdi	NOUN
ejpam-4497	615	9	,	,	PUNCT
ejpam-4497	615	10	og	og	PROPN
ejpam-4497	615	11	elbarbary	elbarbary	NOUN
ejpam-4497	615	12	,	,	PUNCT
ejpam-4497	615	13	and	and	CCONJ
ejpam-4497	615	14	tm	tm	PROPN
ejpam-4497	615	15	al	al	PROPN
ejpam-4497	615	16	-	-	PUNCT
ejpam-4497	615	17	shami	shami	PROPN
ejpam-4497	615	18	.	.	PUNCT
ejpam-4497	616	1	topological	topological	ADJ
ejpam-4497	616	2	approaches	approach	NOUN
ejpam-4497	616	3	for	for	ADP
ejpam-4497	616	4	rough	rough	ADJ
ejpam-4497	616	5	continuous	continuous	ADJ
ejpam-4497	616	6	functions	function	NOUN
ejpam-4497	616	7	with	with	ADP
ejpam-4497	616	8	applications	application	NOUN
ejpam-4497	616	9	.	.	PUNCT
ejpam-4497	617	1	complexity	complexity	NOUN
ejpam-4497	617	2	,	,	PUNCT
ejpam-4497	617	3	2021	2021	NUM
ejpam-4497	617	4	,	,	PUNCT
ejpam-4497	617	5	2021	2021	NUM
ejpam-4497	617	6	.	.	PUNCT
ejpam-4497	618	1	[	[	X
ejpam-4497	618	2	65	65	NUM
ejpam-4497	618	3	]	]	X
ejpam-4497	618	4	m	m	VERB
ejpam-4497	618	5	shabir	shabir	NOUN
ejpam-4497	618	6	and	and	CCONJ
ejpam-4497	618	7	m	m	PROPN
ejpam-4497	618	8	naz	naz	PROPN
ejpam-4497	618	9	.	.	PUNCT
ejpam-4497	619	1	on	on	ADP
ejpam-4497	619	2	soft	soft	ADJ
ejpam-4497	619	3	topological	topological	ADJ
ejpam-4497	619	4	spaces	space	NOUN
ejpam-4497	619	5	.	.	PUNCT
ejpam-4497	620	1	computers	computer	NOUN
ejpam-4497	620	2	&	&	CCONJ
ejpam-4497	620	3	mathematics	mathematics	PROPN
ejpam-4497	620	4	with	with	ADP
ejpam-4497	620	5	applications	application	NOUN
ejpam-4497	620	6	,	,	PUNCT
ejpam-4497	620	7	61(7):1786–1799	61(7):1786–1799	NUM
ejpam-4497	620	8	,	,	PUNCT
ejpam-4497	620	9	2011	2011	NUM
ejpam-4497	620	10	.	.	PUNCT